LMFDB - Embedded newform 114.12.e.b.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,12,Mod(7,114)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("114.7");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	114.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$87.5911225838$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 294880699 x^{16} - 502930193282 x^{15} + \cdots + 10\!\cdots\!01 $ x^18 - 5x^17 + 294880699x^16 - 502930193282x^15 + 58010769323549578x^14 - 107962469874566484896x^13 + 6462950999566890012014308x^12 - 11896428734707375935312399680x^11 + 519285520583573846691128750232193x^10 - 692884029364083538053156632692698801x^9 + 24689309396155847956017564465034753902837x^8 - 8973166541658131218277079733218668822870496x^7 + 820043514499299080450708516880176278207316065440x^6 + 287778341167683358358263946237064064438256890402164x^5 + 13945925406732094645473488744875796514712230817314612762x^4 + 31434839715775176789744984590696756110658152748821063150434x^3 + 139902872770278728043786434425265070357181675994273961821746647x^2 + 124933492983128017052411326931038150648544220156661860270854588847*x + 105517350362802459566297751633435756408365362459904278213342175579601
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{13}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.4
Root			$3145.60 + 5448.34i$ of defining polynomial
Character	$\chi$	$=$	114.49
Dual form			114.12.e.b.7.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.0000 - 27.7128i) q^{2} +(121.500 - 210.444i) q^{3} +(-512.000 - 886.810i) q^{4} +(-2562.10 + 4437.69i) q^{5} +(-3888.00 - 6734.21i) q^{6} +62874.4 q^{7} -32768.0 q^{8} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})$	\(q+(16.0000 - 27.7128i) q^{2} +(121.500 - 210.444i) q^{3} +(-512.000 - 886.810i) q^{4} +(-2562.10 + 4437.69i) q^{5} +(-3888.00 - 6734.21i) q^{6} +62874.4 q^{7} -32768.0 q^{8} +(-29524.5 - 51137.9i) q^{9} +(81987.3 + 142006. i) q^{10} -240555. q^{11} -248832. q^{12} +(-21259.4 - 36822.4i) q^{13} +(1.00599e6 - 1.74243e6i) q^{14} +(622591. + 1.07836e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-1.19608e6 + 2.07167e6i) q^{17} -1.88957e6 q^{18} +(-3.89460e6 - 1.00659e7i) q^{19} +5.24719e6 q^{20} +(7.63924e6 - 1.32316e7i) q^{21} +(-3.84887e6 + 6.66644e6i) q^{22} +(1.92950e6 + 3.34198e6i) q^{23} +(-3.98131e6 + 6.89583e6i) q^{24} +(1.12853e7 + 1.95467e7i) q^{25} -1.36060e6 q^{26} -1.43489e7 q^{27} +(-3.21917e7 - 5.57577e7i) q^{28} +(7.50519e6 + 1.29994e7i) q^{29} +3.98458e7 q^{30} +2.96689e8 q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(-2.92274e7 + 5.06233e7i) q^{33} +(3.82746e7 + 6.62936e7i) q^{34} +(-1.61091e8 + 2.79017e8i) q^{35} +(-3.02331e7 + 5.23652e7i) q^{36} +1.72802e8 q^{37} +(-3.41268e8 - 5.31240e7i) q^{38} -1.03321e7 q^{39} +(8.39550e7 - 1.45414e8i) q^{40} +(5.96774e8 - 1.03364e9i) q^{41} +(-2.44456e8 - 4.23410e8i) q^{42} +(8.62547e8 - 1.49397e9i) q^{43} +(1.23164e8 + 2.13326e8i) q^{44} +3.02579e8 q^{45} +1.23488e8 q^{46} +(-8.27184e8 - 1.43272e9i) q^{47} +(1.27402e8 + 2.20667e8i) q^{48} +1.97587e9 q^{49} +7.22260e8 q^{50} +(2.90648e8 + 5.03417e8i) q^{51} +(-2.17696e7 + 3.77061e7i) q^{52} +(-2.89279e9 - 5.01045e9i) q^{53} +(-2.29583e8 + 3.97649e8i) q^{54} +(6.16326e8 - 1.06751e9i) q^{55} -2.06027e9 q^{56} +(-2.59150e9 - 4.03410e8i) q^{57} +4.80332e8 q^{58} +(-9.80800e8 + 1.69879e9i) q^{59} +(6.37533e8 - 1.10424e9i) q^{60} +(4.32514e9 + 7.49136e9i) q^{61} +(4.74703e9 - 8.22210e9i) q^{62} +(-1.85634e9 - 3.21527e9i) q^{63} +1.07374e9 q^{64} +2.17875e8 q^{65} +(9.35276e8 + 1.61995e9i) q^{66} +(-5.97827e9 - 1.03547e10i) q^{67} +2.44958e9 q^{68} +9.37735e8 q^{69} +(5.15491e9 + 8.92856e9i) q^{70} +(-6.16803e9 + 1.06833e10i) q^{71} +(9.67459e8 + 1.67569e9i) q^{72} +(1.72720e9 - 2.99160e9i) q^{73} +(2.76483e9 - 4.78883e9i) q^{74} +5.48466e9 q^{75} +(-6.93250e9 + 8.60751e9i) q^{76} -1.51247e10 q^{77} +(-1.65313e8 + 2.86331e8i) q^{78} +(-4.61795e9 + 7.99853e9i) q^{79} +(-2.68656e9 - 4.65326e9i) q^{80} +(-1.74339e9 + 3.01964e9i) q^{81} +(-1.90968e10 - 3.30766e10i) q^{82} +5.03791e10 q^{83} -1.56452e10 q^{84} +(-6.12897e9 - 1.06157e10i) q^{85} +(-2.76015e10 - 4.78072e10i) q^{86} +3.64752e9 q^{87} +7.88249e9 q^{88} +(-3.99477e10 - 6.91914e10i) q^{89} +(4.84127e9 - 8.38532e9i) q^{90} +(-1.33667e9 - 2.31519e9i) q^{91} +(1.97580e9 - 3.42219e9i) q^{92} +(3.60478e10 - 6.24366e10i) q^{93} -5.29398e10 q^{94} +(5.46477e10 + 8.50682e9i) q^{95} +8.15373e9 q^{96} +(-3.03663e10 + 5.25960e10i) q^{97} +(3.16139e10 - 5.47568e10i) q^{98} +(7.10225e9 + 1.23015e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 288 q^{2} + 2187 q^{3} - 9216 q^{4} + 10498 q^{5} - 69984 q^{6} + 33594 q^{7} - 589824 q^{8} - 531441 q^{9}+O(q^{10}) $ 18 * q + 288 * q^2 + 2187 * q^3 - 9216 * q^4 + 10498 * q^5 - 69984 * q^6 + 33594 * q^7 - 589824 * q^8 - 531441 * q^9	\( 18 q + 288 q^{2} + 2187 q^{3} - 9216 q^{4} + 10498 q^{5} - 69984 q^{6} + 33594 q^{7} - 589824 q^{8} - 531441 q^{9} - 335936 q^{10} - 1590640 q^{11} - 4478976 q^{12} - 1629109 q^{13} + 537504 q^{14} - 2551014 q^{15} - 9437184 q^{16} + 8652808 q^{17} - 34012224 q^{18} + 15090788 q^{19} - 21499904 q^{20} + 4081671 q^{21} - 25450240 q^{22} - 601786 q^{23} - 71663616 q^{24} - 162553579 q^{25} - 104262976 q^{26} - 258280326 q^{27} - 17200128 q^{28} - 43747792 q^{29} - 163264896 q^{30} + 526704522 q^{31} + 301989888 q^{32} - 193262760 q^{33} - 276889856 q^{34} + 325495254 q^{35} - 544195584 q^{36} + 1732073990 q^{37} + 550585952 q^{38} - 791746974 q^{39} - 343998464 q^{40} - 581264904 q^{41} - 130613472 q^{42} + 1231123053 q^{43} + 814407680 q^{44} - 1239792804 q^{45} - 38514304 q^{46} - 2452492126 q^{47} + 2293235712 q^{48} + 3293812732 q^{49} - 10403429056 q^{50} - 2102632344 q^{51} - 1668207616 q^{52} + 2454345210 q^{53} - 4132485216 q^{54} - 1870156300 q^{55} - 1100808192 q^{56} + 4181012073 q^{57} - 2799858688 q^{58} - 5356106228 q^{59} - 2612238336 q^{60} - 10202609247 q^{61} + 8427272352 q^{62} - 991846053 q^{63} + 19327352832 q^{64} + 25295139500 q^{65} + 6184408320 q^{66} + 2114873497 q^{67} - 17720950784 q^{68} - 292467996 q^{69} - 10415848128 q^{70} - 30585512466 q^{71} + 17414258688 q^{72} - 27334067553 q^{73} + 27713183840 q^{74} - 79001039394 q^{75} + 2165783552 q^{76} + 37560737032 q^{77} - 12667951584 q^{78} + 7599860935 q^{79} + 11007950848 q^{80} - 31381059609 q^{81} + 18600476928 q^{82} - 18534241528 q^{83} - 8359262208 q^{84} - 41278195680 q^{85} - 39395937696 q^{86} - 21261426912 q^{87} + 52122091520 q^{88} - 97795224572 q^{89} - 19836684864 q^{90} + 157694429951 q^{91} - 616228864 q^{92} + 63994599423 q^{93} - 156959496064 q^{94} + 213102831842 q^{95} + 146767085568 q^{96} - 149834378270 q^{97} + 52701003712 q^{98} + 46962850680 q^{99}+O(q^{100}) \) 18 * q + 288 * q^2 + 2187 * q^3 - 9216 * q^4 + 10498 * q^5 - 69984 * q^6 + 33594 * q^7 - 589824 * q^8 - 531441 * q^9 - 335936 * q^10 - 1590640 * q^11 - 4478976 * q^12 - 1629109 * q^13 + 537504 * q^14 - 2551014 * q^15 - 9437184 * q^16 + 8652808 * q^17 - 34012224 * q^18 + 15090788 * q^19 - 21499904 * q^20 + 4081671 * q^21 - 25450240 * q^22 - 601786 * q^23 - 71663616 * q^24 - 162553579 * q^25 - 104262976 * q^26 - 258280326 * q^27 - 17200128 * q^28 - 43747792 * q^29 - 163264896 * q^30 + 526704522 * q^31 + 301989888 * q^32 - 193262760 * q^33 - 276889856 * q^34 + 325495254 * q^35 - 544195584 * q^36 + 1732073990 * q^37 + 550585952 * q^38 - 791746974 * q^39 - 343998464 * q^40 - 581264904 * q^41 - 130613472 * q^42 + 1231123053 * q^43 + 814407680 * q^44 - 1239792804 * q^45 - 38514304 * q^46 - 2452492126 * q^47 + 2293235712 * q^48 + 3293812732 * q^49 - 10403429056 * q^50 - 2102632344 * q^51 - 1668207616 * q^52 + 2454345210 * q^53 - 4132485216 * q^54 - 1870156300 * q^55 - 1100808192 * q^56 + 4181012073 * q^57 - 2799858688 * q^58 - 5356106228 * q^59 - 2612238336 * q^60 - 10202609247 * q^61 + 8427272352 * q^62 - 991846053 * q^63 + 19327352832 * q^64 + 25295139500 * q^65 + 6184408320 * q^66 + 2114873497 * q^67 - 17720950784 * q^68 - 292467996 * q^69 - 10415848128 * q^70 - 30585512466 * q^71 + 17414258688 * q^72 - 27334067553 * q^73 + 27713183840 * q^74 - 79001039394 * q^75 + 2165783552 * q^76 + 37560737032 * q^77 - 12667951584 * q^78 + 7599860935 * q^79 + 11007950848 * q^80 - 31381059609 * q^81 + 18600476928 * q^82 - 18534241528 * q^83 - 8359262208 * q^84 - 41278195680 * q^85 - 39395937696 * q^86 - 21261426912 * q^87 + 52122091520 * q^88 - 97795224572 * q^89 - 19836684864 * q^90 + 157694429951 * q^91 - 616228864 * q^92 + 63994599423 * q^93 - 156959496064 * q^94 + 213102831842 * q^95 + 146767085568 * q^96 - 149834378270 * q^97 + 52701003712 * q^98 + 46962850680 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$3$	121.500	−	210.444i	0.288675	−	0.500000i
$3$	121.500	−	210.444i	0.288675	−	0.500000i
$4$	−512.000	−	886.810i	−0.250000	−	0.433013i
$5$	−2562.10	+	4437.69i	−0.366658	+	0.635071i	−0.989041	−	0.147642i	$-0.952832\pi$
$5$	−2562.10	+	4437.69i	−0.366658	+	0.635071i	0.622382	+	0.782713i	$0.286165\pi$
$6$	−3888.00	−	6734.21i	−0.204124	−	0.353553i
$7$	62874.4			1.41395			0.706976	−	0.707237i	$-0.250059\pi$
$7$	62874.4			1.41395			0.706976	+	0.707237i	$0.250059\pi$
$8$	−32768.0			−0.353553
$9$	−29524.5	−	51137.9i	−0.166667	−	0.288675i
$10$	81987.3	+	142006.i	0.259267	+	0.449063i
$11$	−240555.			−0.450354			−0.225177	−	0.974318i	$-0.572296\pi$
$11$	−240555.			−0.450354			−0.225177	+	0.974318i	$0.572296\pi$
$12$	−248832.			−0.288675
$13$	−21259.4	−	36822.4i	−0.0158804	−	0.0275057i	0.857976	−	0.513690i	$-0.171722\pi$
$13$	−21259.4	−	36822.4i	−0.0158804	−	0.0275057i	−0.873856	+	0.486184i	$0.838388\pi$
$14$	1.00599e6	−	1.74243e6i	0.499908	−	0.865866i
$15$	622591.	+	1.07836e6i	0.211690	+	0.366658i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−1.19608e6	+	2.07167e6i	−0.204311	+	0.353877i	−0.949913	−	0.312514i	$-0.898829\pi$
$17$	−1.19608e6	+	2.07167e6i	−0.204311	+	0.353877i	0.745602	+	0.666392i	$0.232162\pi$
$18$	−1.88957e6			−0.235702
$19$	−3.89460e6	−	1.00659e7i	−0.360843	−	0.932627i
$19$	−3.89460e6	−	1.00659e7i	−0.360843	−	0.932627i
$20$	5.24719e6			0.366658
$21$	7.63924e6	−	1.32316e7i	0.408173	−	0.706976i
$22$	−3.84887e6	+	6.66644e6i	−0.159224	+	0.275784i
$23$	1.92950e6	+	3.34198e6i	0.0625087	+	0.108268i	0.895586	−	0.444888i	$-0.146757\pi$
$23$	1.92950e6	+	3.34198e6i	0.0625087	+	0.108268i	−0.833077	+	0.553156i	$0.813423\pi$
$24$	−3.98131e6	+	6.89583e6i	−0.102062	+	0.176777i
$25$	1.12853e7	+	1.95467e7i	0.231123	+	0.400317i
$26$	−1.36060e6			−0.0224583
$27$	−1.43489e7			−0.192450
$28$	−3.21917e7	−	5.57577e7i	−0.353488	−	0.612259i
$29$	7.50519e6	+	1.29994e7i	0.0679474	+	0.117688i	0.897998	−	0.440000i	$-0.145022\pi$
$29$	7.50519e6	+	1.29994e7i	0.0679474	+	0.117688i	−0.830050	+	0.557689i	$0.811688\pi$
$30$	3.98458e7			0.299375
$31$	2.96689e8			1.86128			0.930642	−	0.365930i	$-0.119249\pi$
$31$	2.96689e8			1.86128			0.930642	+	0.365930i	$0.119249\pi$
$32$	1.67772e7	+	2.90590e7i	0.0883883	+	0.153093i
$33$	−2.92274e7	+	5.06233e7i	−0.130006	+	0.225177i
$34$	3.82746e7	+	6.62936e7i	0.144470	+	0.250229i
$35$	−1.61091e8	+	2.79017e8i	−0.518438	+	0.897960i
$36$	−3.02331e7	+	5.23652e7i	−0.0833333	+	0.144338i
$37$	1.72802e8			0.409675			0.204837	−	0.978796i	$-0.434333\pi$
$37$	1.72802e8			0.409675			0.204837	+	0.978796i	$0.434333\pi$
$38$	−3.41268e8	−	5.31240e7i	−0.698692	−	0.108763i
$39$	−1.03321e7			−0.0183372
$40$	8.39550e7	−	1.45414e8i	0.129633	−	0.224531i
$41$	5.96774e8	−	1.03364e9i	0.804449	−	1.39335i	−0.112213	−	0.993684i	$-0.535794\pi$
$41$	5.96774e8	−	1.03364e9i	0.804449	−	1.39335i	0.916662	−	0.399662i	$-0.130873\pi$
$42$	−2.44456e8	−	4.23410e8i	−0.288622	−	0.499908i
$43$	8.62547e8	−	1.49397e9i	0.894759	−	1.54977i	0.0606569	−	0.998159i	$-0.480680\pi$
$43$	8.62547e8	−	1.49397e9i	0.894759	−	1.54977i	0.834102	−	0.551610i	$-0.185986\pi$
$44$	1.23164e8	+	2.13326e8i	0.112588	+	0.195009i
$45$	3.02579e8			0.244439
$46$	1.23488e8			0.0884007
$47$	−8.27184e8	−	1.43272e9i	−0.526095	−	0.911223i	−0.999538	−	0.0303983i	$-0.990322\pi$
$47$	−8.27184e8	−	1.43272e9i	−0.526095	−	0.911223i	0.473443	−	0.880824i	$-0.343011\pi$
$48$	1.27402e8	+	2.20667e8i	0.0721688	+	0.125000i
$49$	1.97587e9			0.999262
$50$	7.22260e8			0.326858
$51$	2.90648e8	+	5.03417e8i	0.117959	+	0.204311i
$52$	−2.17696e7	+	3.77061e7i	−0.00794022	+	0.0137529i
$53$	−2.89279e9	−	5.01045e9i	−0.950165	−	1.64573i	−0.745063	−	0.666994i	$-0.767581\pi$
$53$	−2.89279e9	−	5.01045e9i	−0.950165	−	1.64573i	−0.205102	−	0.978741i	$-0.565753\pi$
$54$	−2.29583e8	+	3.97649e8i	−0.0680414	+	0.117851i
$55$	6.16326e8	−	1.06751e9i	0.165126	−	0.286007i
$56$	−2.06027e9			−0.499908
$57$	−2.59150e9	−	4.03410e8i	−0.570480	−	0.0888046i
$58$	4.80332e8			0.0960921
$59$	−9.80800e8	+	1.69879e9i	−0.178605	+	0.309353i	−0.941403	−	0.337284i	$-0.890492\pi$
$59$	−9.80800e8	+	1.69879e9i	−0.178605	+	0.309353i	0.762798	+	0.646637i	$0.223825\pi$
$60$	6.37533e8	−	1.10424e9i	0.105845	−	0.183329i
$61$	4.32514e9	+	7.49136e9i	0.655671	+	1.13566i	0.981725	+	0.190304i	$0.0609475\pi$
$61$	4.32514e9	+	7.49136e9i	0.655671	+	1.13566i	−0.326054	+	0.945351i	$0.605719\pi$
$62$	4.74703e9	−	8.22210e9i	0.658063	−	1.13980i
$63$	−1.85634e9	−	3.21527e9i	−0.235659	−	0.408173i
$64$	1.07374e9			0.125000
$65$	2.17875e8			0.0232908
$66$	9.35276e8	+	1.61995e9i	0.0919281	+	0.159224i
$67$	−5.97827e9	−	1.03547e10i	−0.540959	−	0.936969i	−0.998849	−	0.0479599i	$-0.984728\pi$
$67$	−5.97827e9	−	1.03547e10i	−0.540959	−	0.936969i	0.457890	−	0.889009i	$-0.348605\pi$
$68$	2.44958e9			0.204311
$69$	9.37735e8			0.0721789
$70$	5.15491e9	+	8.92856e9i	0.366591	+	0.634954i
$71$	−6.16803e9	+	1.06833e10i	−0.405719	+	0.702726i	−0.994405	−	0.105636i	$-0.966312\pi$
$71$	−6.16803e9	+	1.06833e10i	−0.405719	+	0.702726i	0.588686	+	0.808362i	$0.299645\pi$
$72$	9.67459e8	+	1.67569e9i	0.0589256	+	0.102062i
$73$	1.72720e9	−	2.99160e9i	0.0975142	−	0.168899i	−0.813141	−	0.582067i	$-0.802244\pi$
$73$	1.72720e9	−	2.99160e9i	0.0975142	−	0.168899i	0.910655	+	0.413167i	$0.135578\pi$
$74$	2.76483e9	−	4.78883e9i	0.144842	−	0.250873i
$75$	5.48466e9			0.266878
$76$	−6.93250e9	+	8.60751e9i	−0.313628	+	0.389406i
$77$	−1.51247e10			−0.636779
$78$	−1.65313e8	+	2.86331e8i	−0.00648316	+	0.0112292i
$79$	−4.61795e9	+	7.99853e9i	−0.168850	+	0.292456i	−0.938016	−	0.346593i	$-0.887339\pi$
$79$	−4.61795e9	+	7.99853e9i	−0.168850	+	0.292456i	0.769166	+	0.639049i	$0.220672\pi$
$80$	−2.68656e9	−	4.65326e9i	−0.0916646	−	0.158768i
$81$	−1.74339e9	+	3.01964e9i	−0.0555556	+	0.0962250i
$82$	−1.90968e10	−	3.30766e10i	−0.568831	−	0.985245i
$83$	5.03791e10			1.40385			0.701926	−	0.712250i	$-0.252324\pi$
$83$	5.03791e10			1.40385			0.701926	+	0.712250i	$0.252324\pi$
$84$	−1.56452e10			−0.408173
$85$	−6.12897e9	−	1.06157e10i	−0.149825	−	0.259504i
$86$	−2.76015e10	−	4.78072e10i	−0.632690	−	1.09585i
$87$	3.64752e9			0.0784589
$88$	7.88249e9			0.159224
$89$	−3.99477e10	−	6.91914e10i	−0.758309	−	1.31343i	−0.943712	−	0.330768i	$-0.892692\pi$
$89$	−3.99477e10	−	6.91914e10i	−0.758309	−	1.31343i	0.185403	−	0.982663i	$-0.440641\pi$
$90$	4.84127e9	−	8.38532e9i	0.0864222	−	0.149688i
$91$	−1.33667e9	−	2.31519e9i	−0.0224542	−	0.0388918i
$92$	1.97580e9	−	3.42219e9i	0.0312544	−	0.0541342i
$93$	3.60478e10	−	6.24366e10i	0.537307	−	0.930642i
$94$	−5.29398e10			−0.744010
$95$	5.46477e10	+	8.50682e9i	0.724590	+	0.112794i
$96$	8.15373e9			0.102062
$97$	−3.03663e10	+	5.25960e10i	−0.359044	+	0.621882i	−0.987801	−	0.155719i	$-0.950230\pi$
$97$	−3.03663e10	+	5.25960e10i	−0.359044	+	0.621882i	0.628758	+	0.777601i	$0.283564\pi$
$98$	3.16139e10	−	5.47568e10i	0.353292	−	0.611920i
$99$	7.10225e9	+	1.23015e10i	0.0750590	+	0.130006i
$100$	1.15562e10	−	2.00159e10i	0.115562	−	0.200159i
$101$	1.07441e10	+	1.86093e10i	0.101719	+	0.176182i	0.912393	−	0.409315i	$-0.134232\pi$
$101$	1.07441e10	+	1.86093e10i	0.101719	+	0.176182i	−0.810674	+	0.585498i	$0.800899\pi$
$102$	1.86015e10			0.166819
$103$	−1.64369e10			−0.139706			−0.0698529	−	0.997557i	$-0.522253\pi$
$103$	−1.64369e10			−0.139706			−0.0698529	+	0.997557i	$0.522253\pi$
$104$	6.96628e8	+	1.20660e9i	0.00561459	+	0.00972475i
$105$	3.91451e10	+	6.78012e10i	0.299320	+	0.518438i
$106$	−1.85138e11			−1.34374
$107$	−1.06887e11			−0.736740			−0.368370	−	0.929679i	$-0.620084\pi$
$107$	−1.06887e11			−0.736740			−0.368370	+	0.929679i	$0.620084\pi$
$108$	7.34664e9	+	1.27248e10i	0.0481125	+	0.0833333i
$109$	1.00012e11	−	1.73227e11i	0.622599	−	1.07837i	−0.366401	−	0.930457i	$-0.619410\pi$
$109$	1.00012e11	−	1.73227e11i	0.622599	−	1.07837i	0.989000	−	0.147916i	$-0.0472565\pi$
$110$	−1.97224e10	−	3.41602e10i	−0.116762	−	0.202237i
$111$	2.09954e10	−	3.63652e10i	0.118263	−	0.204837i
$112$	−3.29643e10	+	5.70959e10i	−0.176744	+	0.306130i
$113$	−5.28244e10			−0.269714			−0.134857	−	0.990865i	$-0.543057\pi$
$113$	−5.28244e10			−0.269714			−0.134857	+	0.990865i	$0.543057\pi$
$114$	−5.26437e10	+	6.53633e10i	−0.256077	+	0.317949i
$115$	−1.97743e10			−0.0916774
$116$	7.68531e9	−	1.33114e10i	0.0339737	−	0.0588441i
$117$	−1.25535e9	+	2.17432e9i	−0.00529348	+	0.00916858i
$118$	3.13856e10	+	5.43614e10i	0.126293	+	0.218746i
$119$	−7.52030e10	+	1.30255e11i	−0.288886	+	0.500365i
$120$	−2.04011e10	−	3.53357e10i	−0.0748438	−	0.129633i
$121$	−2.27445e11			−0.797181
$122$	2.76809e11			0.927259
$123$	−1.45016e11	−	2.51175e11i	−0.464449	−	0.804449i
$124$	−1.51905e11	−	2.63107e11i	−0.465321	−	0.805960i
$125$	−3.65862e11			−1.07229
$126$	−1.18806e11			−0.333272
$127$	−1.87277e11	−	3.24374e11i	−0.502996	−	0.871214i	−0.999994	−	0.00346279i	$-0.998898\pi$
$127$	−1.87277e11	−	3.24374e11i	−0.502996	−	0.871214i	0.496998	−	0.867752i	$-0.334436\pi$
$128$	1.71799e10	−	2.97564e10i	0.0441942	−	0.0765466i
$129$	−2.09599e11	−	3.63036e11i	−0.516589	−	0.894759i
$130$	3.48600e9	−	6.03793e9i	0.00823454	−	0.0142626i
$131$	−3.78967e10	+	6.56390e10i	−0.0858241	+	0.148652i	−0.905742	−	0.423829i	$-0.860686\pi$
$131$	−3.78967e10	+	6.56390e10i	−0.0858241	+	0.148652i	0.819918	+	0.572481i	$0.194019\pi$
$132$	5.98577e10			0.130006
$133$	−2.44871e11	−	6.32888e11i	−0.510215	−	1.31869i
$134$	−3.82610e11			−0.765032
$135$	3.67634e10	−	6.36760e10i	0.0705634	−	0.122219i
$136$	3.91932e10	−	6.78846e10i	0.0722348	−	0.125114i
$137$	−6.24914e9	−	1.08238e10i	−0.0110626	−	0.0191610i	0.860441	−	0.509550i	$-0.170188\pi$
$137$	−6.24914e9	−	1.08238e10i	−0.0110626	−	0.0191610i	−0.871504	+	0.490389i	$0.836855\pi$
$138$	1.50038e10	−	2.59873e10i	0.0255191	−	0.0442004i
$139$	1.34904e11	+	2.33661e11i	0.220518	+	0.381948i	0.954965	−	0.296717i	$-0.0958920\pi$
$139$	1.34904e11	+	2.33661e11i	0.220518	+	0.381948i	−0.734448	+	0.678665i	$0.762559\pi$
$140$	3.29914e11			0.518438
$141$	−4.02011e11			−0.607482
$142$	1.97377e11	+	3.41867e11i	0.286887	+	0.496902i
$143$	5.11405e9	+	8.85779e9i	0.00715182	+	0.0123873i
$144$	6.19174e10			0.0833333
$145$	−7.69163e10			−0.0996539
$146$	−5.52705e10	−	9.57313e10i	−0.0689529	−	0.119430i
$147$	2.40068e11	−	4.15810e11i	0.288462	−	0.499631i
$148$	−8.84746e10	−	1.53242e11i	−0.102419	−	0.177394i
$149$	8.03541e11	−	1.39177e12i	0.896362	−	1.55254i	0.0642515	−	0.997934i	$-0.479534\pi$
$149$	8.03541e11	−	1.39177e12i	0.896362	−	1.55254i	0.832110	−	0.554610i	$-0.187133\pi$
$150$	8.77546e10	−	1.51995e11i	0.0943557	−	0.163429i
$151$	1.16668e12			1.20943			0.604713	−	0.796444i	$-0.293288\pi$
$151$	1.16668e12			1.20943			0.604713	+	0.796444i	$0.293288\pi$
$152$	1.27618e11	+	3.29839e11i	0.127577	+	0.329733i
$153$	1.41255e11			0.136207
$154$	−2.41996e11	+	4.19149e11i	−0.225135	+	0.389946i
$155$	−7.60149e11	+	1.31662e12i	−0.682456	+	1.18205i
$156$	5.29002e9	+	9.16258e9i	0.00458429	+	0.00794022i
$157$	9.20276e11	−	1.59396e12i	0.769963	−	1.33362i	−0.167619	−	0.985852i	$-0.553608\pi$
$157$	9.20276e11	−	1.59396e12i	0.769963	−	1.33362i	0.937582	−	0.347764i	$-0.113059\pi$
$158$	1.47775e11	+	2.55953e11i	0.119395	+	0.206798i
$159$	−1.40589e12			−1.09716
$160$	−1.71940e11			−0.129633
$161$	1.21316e11	+	2.10125e11i	0.0883844	+	0.153086i
$162$	5.57886e10	+	9.66286e10i	0.0392837	+	0.0680414i
$163$	7.21115e11			0.490877			0.245438	−	0.969412i	$-0.421068\pi$
$163$	7.21115e11			0.490877			0.245438	+	0.969412i	$0.421068\pi$
$164$	−1.22219e12			−0.804449
$165$	−1.49767e11	−	2.59404e11i	−0.0953355	−	0.165126i
$166$	8.06066e11	−	1.39615e12i	0.496337	−	0.859680i
$167$	6.02689e11	+	1.04389e12i	0.359048	+	0.621890i	0.987802	−	0.155715i	$-0.0497681\pi$
$167$	6.02689e11	+	1.04389e12i	0.359048	+	0.621890i	−0.628754	+	0.777604i	$0.716435\pi$
$168$	−2.50323e11	+	4.33572e11i	−0.144311	+	0.249954i
$169$	8.95176e11	−	1.55049e12i	0.499496	−	0.865152i
$170$	−3.92254e11			−0.211884
$171$	−3.99763e11	+	4.96353e11i	−0.209086	+	0.259604i
$172$	−1.76650e12			−0.894759
$173$	9.90368e11	−	1.71537e12i	0.485896	−	0.841596i	−0.513973	−	0.857806i	$-0.671827\pi$
$173$	9.90368e11	−	1.71537e12i	0.485896	−	0.841596i	0.999869	+	0.0162106i	$0.00516021\pi$
$174$	5.83603e10	−	1.01083e11i	0.0277394	−	0.0480460i
$175$	7.09558e11	+	1.22899e12i	0.326797	+	0.566030i
$176$	1.26120e11	−	2.18446e11i	0.0562942	−	0.0975045i
$177$	2.38334e11	+	4.12807e11i	0.103118	+	0.178605i
$178$	−2.55665e12			−1.07241
$179$	−2.88171e12			−1.17208			−0.586041	−	0.810281i	$-0.699314\pi$
$179$	−2.88171e12			−1.17208			−0.586041	+	0.810281i	$0.699314\pi$
$180$	−1.54921e11	−	2.68330e11i	−0.0611097	−	0.105845i
$181$	−1.59428e12	−	2.76138e12i	−0.610004	−	1.05656i	−0.991239	−	0.132080i	$-0.957834\pi$
$181$	−1.59428e12	−	2.76138e12i	−0.610004	−	1.05656i	0.381235	−	0.924478i	$-0.375499\pi$
$182$	−8.55471e10			−0.0317550
$183$	2.10202e12			0.757104
$184$	−6.32257e10	−	1.09510e11i	−0.0221002	−	0.0382786i
$185$	−4.42736e11	+	7.66842e11i	−0.150211	+	0.260172i
$186$	−1.15353e12	−	1.99797e12i	−0.379933	−	0.658063i
$187$	2.87723e11	−	4.98351e11i	0.0920122	−	0.159370i
$188$	−8.47036e11	+	1.46711e12i	−0.263047	+	0.455611i
$189$	−9.02179e11			−0.272115
$190$	1.11011e12	−	1.37833e12i	0.325254	−	0.403840i
$191$	6.42191e12			1.82802			0.914010	−	0.405691i	$-0.132969\pi$
$191$	6.42191e12			1.82802			0.914010	+	0.405691i	$0.132969\pi$
$192$	1.30460e11	−	2.25963e11i	0.0360844	−	0.0625000i
$193$	−1.13480e12	+	1.96554e12i	−0.305039	+	0.528343i	−0.977270	−	0.211998i	$-0.932003\pi$
$193$	−1.13480e12	+	1.96554e12i	−0.305039	+	0.528343i	0.672231	+	0.740342i	$0.265336\pi$
$194$	9.71722e11	+	1.68307e12i	0.253882	+	0.439737i
$195$	2.64718e10	−	4.58506e10i	0.00672347	−	0.0116454i
$196$	−1.01164e12	−	1.75222e12i	−0.249815	−	0.432693i
$197$	4.32184e12			1.03778			0.518889	−	0.854842i	$-0.326346\pi$
$197$	4.32184e12			1.03778			0.518889	+	0.854842i	$0.326346\pi$
$198$	4.54544e11			0.106149
$199$	−8.01597e11	−	1.38841e12i	−0.182081	−	0.315373i	0.760508	−	0.649328i	$-0.224950\pi$
$199$	−8.01597e11	−	1.38841e12i	−0.182081	−	0.315373i	−0.942589	+	0.333955i	$0.891617\pi$
$200$	−3.69797e11	−	6.40508e11i	−0.0817144	−	0.141534i
$201$	−2.90544e12			−0.624646
$202$	6.87621e11			0.143852
$203$	4.71884e11	+	8.17328e11i	0.0960744	+	0.166406i
$204$	2.97623e11	−	5.15499e11i	0.0589795	−	0.102156i
$205$	3.05799e12	+	5.29660e12i	0.589916	+	1.02176i
$206$	−2.62990e11	+	4.55512e11i	−0.0493935	+	0.0855520i
$207$	1.13935e11	−	1.97341e11i	0.0208362	−	0.0360894i
$208$	4.45842e10			0.00794022
$209$	9.36864e11	+	2.42140e12i	0.162507	+	0.420012i
$210$	2.50528e12			0.423302
$211$	−1.19980e12	+	2.07812e12i	−0.197495	+	0.342072i	−0.947716	−	0.319116i	$-0.896614\pi$
$211$	−1.19980e12	+	2.07812e12i	−0.197495	+	0.342072i	0.750221	+	0.661188i	$0.229947\pi$
$212$	−2.96221e12	+	5.13071e12i	−0.475083	+	0.822867i
$213$	1.49883e12	+	2.59605e12i	0.234242	+	0.405719i
$214$	−1.71019e12	+	2.96214e12i	−0.260477	+	0.451159i
$215$	4.41987e12	+	7.65544e12i	0.656142	+	1.13647i
$216$	4.70185e11			0.0680414
$217$	1.86542e13			2.63177
$218$	−3.20040e12	−	5.54325e12i	−0.440244	−	0.762525i
$219$	−4.19710e11	−	7.26960e11i	−0.0562998	−	0.0975142i
$220$	−1.26224e12			−0.165126
$221$	1.01712e11			0.0129782
$222$	−6.71854e11	−	1.16368e12i	−0.0836245	−	0.144842i
$223$	−5.47194e12	+	9.47767e12i	−0.664453	+	1.15087i	0.314980	+	0.949098i	$0.398002\pi$
$223$	−5.47194e12	+	9.47767e12i	−0.664453	+	1.15087i	−0.979433	+	0.201768i	$0.935331\pi$
$224$	1.05486e12	+	1.82707e12i	0.124977	+	0.216466i
$225$	6.66387e11	−	1.15422e12i	0.0770411	−	0.133439i
$226$	−8.45191e11	+	1.46391e12i	−0.0953583	+	0.165165i
$227$	−4.66255e12			−0.513430			−0.256715	−	0.966487i	$-0.582640\pi$
$227$	−4.66255e12			−0.513430			−0.256715	+	0.966487i	$0.582640\pi$
$228$	9.69102e11	+	2.50472e12i	0.104166	+	0.269226i
$229$	−7.19764e12			−0.755257			−0.377629	−	0.925957i	$-0.623260\pi$
$229$	−7.19764e12			−0.755257			−0.377629	+	0.925957i	$0.623260\pi$
$230$	−3.16388e11	+	5.48001e11i	−0.0324129	+	0.0561407i
$231$	−1.83765e12	+	3.18291e12i	−0.183822	+	0.318389i
$232$	−2.45930e11	−	4.25963e11i	−0.0240230	−	0.0416091i
$233$	2.69387e12	−	4.66591e12i	0.256991	−	0.445122i	−0.708443	−	0.705768i	$-0.750602\pi$
$233$	2.69387e12	−	4.66591e12i	0.256991	−	0.445122i	0.965434	+	0.260646i	$0.0839355\pi$
$234$	4.01711e10	+	6.95784e10i	0.00374306	+	0.00648316i
$235$	8.47732e12			0.771588
$236$	2.00868e12			0.178605
$237$	1.12216e12	+	1.94364e12i	0.0974855	+	0.168850i
$238$	2.40649e12	+	4.16817e12i	0.204273	+	0.353812i
$239$	2.33748e12			0.193892			0.0969460	−	0.995290i	$-0.469093\pi$
$239$	2.33748e12			0.193892			0.0969460	+	0.995290i	$0.469093\pi$
$240$	−1.30567e12			−0.105845
$241$	7.68270e12	+	1.33068e13i	0.608723	+	1.05434i	0.991451	+	0.130479i	$0.0416514\pi$
$241$	7.68270e12	+	1.33068e13i	0.608723	+	1.05434i	−0.382728	+	0.923861i	$0.625015\pi$
$242$	−3.63912e12	+	6.30315e12i	−0.281846	+	0.488172i
$243$	4.23644e11	+	7.33773e11i	0.0320750	+	0.0555556i
$244$	4.42894e12	−	7.67115e12i	0.327835	−	0.567828i
$245$	−5.06238e12	+	8.76829e12i	−0.366388	+	0.634602i
$246$	−9.28103e12			−0.656830
$247$	−2.87853e11	+	3.57404e11i	−0.0199222	+	0.0247358i
$248$	−9.72192e12			−0.658063
$249$	6.12107e12	−	1.06020e13i	0.405257	−	0.701926i
$250$	−5.85379e12	+	1.01391e13i	−0.379112	+	0.656641i
$251$	6.65235e12	+	1.15222e13i	0.421473	+	0.730012i	0.996084	−	0.0884145i	$-0.0281800\pi$
$251$	6.65235e12	+	1.15222e13i	0.421473	+	0.730012i	−0.574611	+	0.818427i	$0.694847\pi$
$252$	−1.90089e12	+	3.29243e12i	−0.117829	+	0.204086i
$253$	−4.64149e11	−	8.03930e11i	−0.0281510	−	0.0487590i
$254$	−1.19857e13			−0.711344
$255$	−2.97868e12			−0.173003
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	1.17425e13	+	2.03385e13i	0.653322	+	1.13159i	0.982312	+	0.187253i	$0.0599584\pi$
$257$	1.17425e13	+	2.03385e13i	0.653322	+	1.13159i	−0.328990	+	0.944333i	$0.606708\pi$
$258$	−1.34143e13			−0.730568
$259$	1.08648e13			0.579260
$260$	−1.11552e11	−	1.93214e11i	−0.00582270	−	0.0100852i
$261$	4.43174e11	−	7.67600e11i	0.0226491	−	0.0392294i
$262$	1.21269e12	+	2.10045e12i	0.0606868	+	0.105113i
$263$	−5.69732e12	+	9.86804e12i	−0.279199	+	0.483587i	−0.971186	−	0.238323i	$-0.923402\pi$
$263$	−5.69732e12	+	9.86804e12i	−0.279199	+	0.483587i	0.691987	+	0.721910i	$0.256736\pi$
$264$	9.57723e11	−	1.65882e12i	0.0459640	−	0.0796121i
$265$	2.96465e13			1.39354
$266$	−2.14570e13	−	3.34014e12i	−0.987917	−	0.153786i
$267$	−1.94146e13			−0.875620
$268$	−6.12175e12	+	1.06032e13i	−0.270480	+	0.468484i
$269$	−8.13508e12	+	1.40904e13i	−0.352147	+	0.609937i	−0.986625	−	0.163004i	$-0.947882\pi$
$269$	−8.13508e12	+	1.40904e13i	−0.352147	+	0.609937i	0.634478	+	0.772941i	$0.281215\pi$
$270$	−1.17643e12	−	2.03763e12i	−0.0498959	−	0.0864222i
$271$	−5.13233e12	+	8.88945e12i	−0.213296	+	0.369440i	−0.952744	−	0.303774i	$-0.901753\pi$
$271$	−5.13233e12	+	8.88945e12i	−0.213296	+	0.369440i	0.739448	+	0.673214i	$0.235087\pi$
$272$	−1.25418e12	−	2.17231e12i	−0.0510778	−	0.0884693i
$273$	−6.49623e11			−0.0259279
$274$	−3.99945e11			−0.0156449
$275$	−2.71473e12	−	4.70206e12i	−0.104087	−	0.180284i
$276$	−4.80120e11	−	8.31593e11i	−0.0180447	−	0.0312544i
$277$	2.57905e13			0.950214			0.475107	−	0.879928i	$-0.342409\pi$
$277$	2.57905e13			0.950214			0.475107	+	0.879928i	$0.342409\pi$
$278$	8.63386e12			0.311859
$279$	−8.75961e12	−	1.51721e13i	−0.310214	−	0.537307i
$280$	5.27862e12	−	9.14284e12i	0.183295	−	0.317477i
$281$	9.32979e12	+	1.61597e13i	0.317678	+	0.550234i	0.980003	−	0.198982i	$-0.0637636\pi$
$281$	9.32979e12	+	1.61597e13i	0.317678	+	0.550234i	−0.662325	+	0.749217i	$0.730430\pi$
$282$	−6.43218e12	+	1.11409e13i	−0.214777	+	0.372005i
$283$	−2.44315e12	+	4.23165e12i	−0.0800063	+	0.138575i	−0.903252	−	0.429110i	$-0.858827\pi$
$283$	−2.44315e12	+	4.23165e12i	−0.0800063	+	0.138575i	0.823246	+	0.567685i	$0.192161\pi$
$284$	1.26321e13			0.405719
$285$	8.42991e12	−	1.04667e13i	0.265568	−	0.329734i
$286$	3.27299e11			0.0101142
$287$	3.75218e13	−	6.49897e13i	1.13745	−	1.97013i
$288$	9.90678e11	−	1.71590e12i	0.0294628	−	0.0510310i
$289$	1.42747e13	+	2.47245e13i	0.416514	+	0.721423i
$290$	−1.23066e12	+	2.13157e12i	−0.0352330	+	0.0610253i
$291$	7.37901e12	+	1.27808e13i	0.207294	+	0.359044i
$292$	−3.53731e12			−0.0975142
$293$	2.20885e13			0.597577			0.298789	−	0.954319i	$-0.403417\pi$
$293$	2.20885e13			0.597577			0.298789	+	0.954319i	$0.403417\pi$
$294$	−7.68217e12	−	1.33059e13i	−0.203973	−	0.353292i
$295$	−5.02582e12	−	8.70498e12i	−0.130974	−	0.226854i
$296$	−5.66237e12			−0.144842
$297$	3.45170e12			0.0866706
$298$	−2.57133e13	−	4.45367e13i	−0.633823	−	1.09781i
$299$	8.20399e10	−	1.42097e11i	0.00198533	−	0.00343870i
$300$	−2.80815e12	−	4.86385e12i	−0.0667195	−	0.115562i
$301$	5.42321e13	−	9.39328e13i	1.26515	−	2.19130i
$302$	1.86669e13	−	3.23320e13i	0.427597	−	0.740619i
$303$	5.22162e12			0.117455
$304$	1.11827e13	+	1.74077e12i	0.247025	+	0.0384535i
$305$	−4.43258e13			−0.961629
$306$	2.26008e12	−	3.91457e12i	0.0481566	−	0.0834096i
$307$	8.82703e12	−	1.52889e13i	0.184737	−	0.319974i	−0.758751	−	0.651381i	$-0.774190\pi$
$307$	8.82703e12	−	1.52889e13i	0.184737	−	0.319974i	0.943488	+	0.331407i	$0.107523\pi$
$308$	7.74386e12	+	1.34128e13i	0.159195	+	0.275733i
$309$	−1.99708e12	+	3.45904e12i	−0.0403296	+	0.0698529i
$310$	2.43248e13	+	4.21317e13i	0.482569	+	0.835834i
$311$	−3.50212e13			−0.682573			−0.341287	−	0.939959i	$-0.610863\pi$
$311$	−3.50212e13			−0.682573			−0.341287	+	0.939959i	$0.610863\pi$
$312$	3.38561e11			0.00648316
$313$	−3.26036e13	−	5.64711e13i	−0.613440	−	1.06251i	−0.990656	−	0.136383i	$-0.956452\pi$
$313$	−3.26036e13	−	5.64711e13i	−0.613440	−	1.06251i	0.377217	−	0.926125i	$-0.376881\pi$
$314$	−2.94488e13	−	5.10069e13i	−0.544446	−	0.943008i
$315$	1.90245e13			0.345625
$316$	9.45757e12			0.168850
$317$	−4.53309e13	−	7.85154e13i	−0.795368	−	1.37762i	−0.922605	−	0.385745i	$-0.873944\pi$
$317$	−4.53309e13	−	7.85154e13i	−0.795368	−	1.37762i	0.127237	−	0.991872i	$-0.459389\pi$
$318$	−2.24943e13	+	3.89613e13i	−0.387903	+	0.671868i
$319$	−1.80541e12	−	3.12706e12i	−0.0306004	−	0.0530014i
$320$	−2.75104e12	+	4.76494e12i	−0.0458323	+	0.0793839i
$321$	−1.29868e13	+	2.24938e13i	−0.212679	+	0.368370i
$322$	7.76422e12			0.124994
$323$	2.55115e13	+	3.97129e12i	0.403759	+	0.0628518i
$324$	3.57047e12			0.0555556
$325$	4.79838e11	−	8.31104e11i	0.00734068	−	0.0127144i
$326$	1.15378e13	−	1.99841e13i	0.173551	−	0.300599i
$327$	−2.43030e13	−	4.20941e13i	−0.359458	−	0.622599i
$328$	−1.95551e13	+	3.38704e13i	−0.284416	+	0.492622i
$329$	−5.20087e13	−	9.00817e13i	−0.743873	−	1.28843i
$330$	−9.58510e12			−0.134825
$331$	8.37918e13			1.15917			0.579586	−	0.814911i	$-0.303214\pi$
$331$	8.37918e13			1.15917			0.579586	+	0.814911i	$0.303214\pi$
$332$	−2.57941e13	−	4.46767e13i	−0.350963	−	0.607886i
$333$	−5.10189e12	−	8.83673e12i	−0.0682791	−	0.118263i
$334$	3.85721e13			0.507771
$335$	6.12678e13			0.793389
$336$	8.01033e12	+	1.38743e13i	0.102043	+	0.176744i
$337$	−3.96772e13	+	6.87229e13i	−0.497252	+	0.861266i	−0.999995	−	0.00317004i	$-0.998991\pi$
$337$	−3.96772e13	+	6.87229e13i	−0.497252	+	0.861266i	0.502743	+	0.864436i	$0.332324\pi$
$338$	−2.86456e13	−	4.96157e13i	−0.353197	−	0.611755i
$339$	−6.41817e12	+	1.11166e13i	−0.0778597	+	0.134857i
$340$	−6.27606e12	+	1.08705e13i	−0.0749123	+	0.129752i
$341$	−7.13700e13			−0.838237
$342$	7.35912e12	+	1.90202e13i	0.0850515	+	0.219822i
$343$	−9.17722e10			−0.00104374
$344$	−2.82639e13	+	4.89546e13i	−0.316345	+	0.547926i
$345$	−2.40257e12	+	4.16138e12i	−0.0264650	+	0.0458387i
$346$	−3.16918e13	−	5.48918e13i	−0.343580	−	0.595098i
$347$	−8.24414e13	+	1.42793e14i	−0.879697	+	1.52368i	−0.0280231	+	0.999607i	$0.508921\pi$
$347$	−8.24414e13	+	1.42793e14i	−0.879697	+	1.52368i	−0.851674	+	0.524072i	$0.824412\pi$
$348$	−1.86753e12	−	3.23466e12i	−0.0196147	−	0.0339737i
$349$	1.54341e14			1.59567			0.797835	−	0.602876i	$-0.205979\pi$
$349$	1.54341e14			1.59567			0.797835	+	0.602876i	$0.205979\pi$
$350$	4.54117e13			0.462161
$351$	3.05049e11	+	5.28361e11i	0.00305619	+	0.00529348i
$352$	−4.03584e12	−	6.99027e12i	−0.0398060	−	0.0689461i
$353$	−7.87129e13			−0.764338			−0.382169	−	0.924093i	$-0.624823\pi$
$353$	−7.87129e13			−0.764338			−0.382169	+	0.924093i	$0.624823\pi$
$354$	1.52534e13			0.145831
$355$	−3.16062e13	−	5.47436e13i	−0.297520	−	0.515321i
$356$	−4.09064e13	+	7.08520e13i	−0.379155	+	0.656715i
$357$	1.82743e13	+	3.16520e13i	0.166788	+	0.288886i
$358$	−4.61073e13	+	7.98602e13i	−0.414394	+	0.717751i
$359$	4.88714e13	−	8.46477e13i	0.432549	−	0.749197i	−0.564543	−	0.825404i	$-0.690948\pi$
$359$	4.88714e13	−	8.46477e13i	0.432549	−	0.749197i	0.997092	+	0.0762069i	$0.0242810\pi$
$360$	−9.91492e12			−0.0864222
$361$	−8.61544e13	+	7.84053e13i	−0.739585	+	0.673064i
$362$	−1.02034e14			−0.862676
$363$	−2.76346e13	+	4.78645e13i	−0.230126	+	0.398591i
$364$	−1.36875e12	+	2.37075e12i	−0.0112271	+	0.0194459i
$365$	8.85055e12	+	1.53296e13i	0.0715088	+	0.123857i
$366$	3.36323e13	−	5.82528e13i	0.267677	−	0.463629i
$367$	2.39501e13	+	4.14827e13i	0.187777	+	0.325240i	0.944509	−	0.328486i	$-0.106538\pi$
$367$	2.39501e13	+	4.14827e13i	0.187777	+	0.325240i	−0.756732	+	0.653726i	$0.773205\pi$
$368$	−4.04645e12			−0.0312544
$369$	−7.04778e13			−0.536299
$370$	1.41676e13	+	2.45389e13i	0.106215	+	0.183970i
$371$	−1.81882e14	−	3.15029e14i	−1.34349	−	2.32699i
$372$	−7.38258e13			−0.537307
$373$	2.47152e14			1.77242			0.886209	−	0.463286i	$-0.153330\pi$
$373$	2.47152e14			1.77242			0.886209	+	0.463286i	$0.153330\pi$
$374$	−9.20713e12	−	1.59472e13i	−0.0650625	−	0.112692i
$375$	−4.44522e13	+	7.69935e13i	−0.309543	+	0.536145i
$376$	2.71052e13	+	4.69475e13i	0.186003	+	0.322166i
$377$	3.19112e11	−	5.52718e11i	0.00215807	−	0.00373788i
$378$	−1.44349e13	+	2.50019e13i	−0.0962073	+	0.166636i
$379$	2.17131e14			1.42629			0.713143	−	0.701019i	$-0.247271\pi$
$379$	2.17131e14			1.42629			0.713143	+	0.701019i	$0.247271\pi$
$380$	−2.04357e13	−	5.28177e13i	−0.132306	−	0.341955i
$381$	−9.10167e13			−0.580810
$382$	1.02751e14	−	1.77969e14i	0.646303	−	1.11943i
$383$	−1.40367e14	+	2.43122e14i	−0.870304	+	1.50741i	−0.00862183	+	0.999963i	$0.502744\pi$
$383$	−1.40367e14	+	2.43122e14i	−0.870304	+	1.50741i	−0.861682	+	0.507448i	$0.830589\pi$
$384$	−4.17471e12	−	7.23081e12i	−0.0255155	−	0.0441942i
$385$	3.87511e13	−	6.71189e13i	0.233480	−	0.404400i
$386$	3.63137e13	+	6.28972e13i	0.215695	+	0.373595i
$387$	−1.01865e14			−0.596506
$388$	6.21902e13			0.359044
$389$	−1.55061e14	−	2.68573e14i	−0.882631	−	1.52876i	−0.848405	−	0.529348i	$-0.822437\pi$
$389$	−1.55061e14	−	2.68573e14i	−0.882631	−	1.52876i	−0.0342260	−	0.999414i	$-0.510897\pi$
$390$	−8.47099e11	−	1.46722e12i	−0.00475421	−	0.00823454i
$391$	−9.23134e12			−0.0510849
$392$	−6.47452e13			−0.353292
$393$	9.20890e12	+	1.59503e13i	0.0495506	+	0.0858241i
$394$	6.91494e13	−	1.19770e14i	0.366910	−	0.635506i
$395$	−2.36633e13	−	4.09861e13i	−0.123820	−	0.214463i
$396$	7.27271e12	−	1.25967e13i	0.0375295	−	0.0650030i
$397$	6.65631e13	−	1.15291e14i	0.338755	−	0.586741i	−0.645444	−	0.763808i	$-0.723328\pi$
$397$	6.65631e13	−	1.15291e14i	0.338755	−	0.586741i	0.984199	+	0.177067i	$0.0566609\pi$
$398$	−5.13022e13			−0.257501
$399$	−1.62939e14	−	2.53642e13i	−0.806631	−	0.125565i
$400$	−2.36670e13			−0.115562
$401$	−1.97612e13	+	3.42274e13i	−0.0951742	+	0.164847i	−0.909681	−	0.415307i	$-0.863674\pi$
$401$	−1.97612e13	+	3.42274e13i	−0.0951742	+	0.164847i	0.814507	+	0.580154i	$0.197007\pi$
$402$	−4.64871e13	+	8.05180e13i	−0.220846	+	0.382516i
$403$	−6.30744e12	−	1.09248e13i	−0.0295580	−	0.0511960i
$404$	1.10019e13	−	1.90559e13i	0.0508594	−	0.0880911i
$405$	−8.93350e12	−	1.54733e13i	−0.0407398	−	0.0705634i
$406$	3.02006e13			0.135870
$407$	−4.15683e13			−0.184499
$408$	−9.52395e12	−	1.64960e13i	−0.0417048	−	0.0722348i
$409$	2.24358e13	+	3.88599e13i	0.0969311	+	0.167890i	0.910413	−	0.413701i	$-0.135764\pi$
$409$	2.24358e13	+	3.88599e13i	0.0969311	+	0.167890i	−0.813482	+	0.581590i	$0.802431\pi$
$410$	1.95711e14			0.834267
$411$	−3.03708e12			−0.0127740
$412$	8.41568e12	+	1.45764e13i	0.0349265	+	0.0604944i
$413$	−6.16672e13	+	1.06811e14i	−0.252539	+	0.437411i
$414$	−3.64591e12	−	6.31491e12i	−0.0147335	−	0.0255191i
$415$	−1.29077e14	+	2.23567e14i	−0.514734	+	0.891545i
$416$	7.13347e11	−	1.23555e12i	0.00280729	−	0.00486237i
$417$	6.55634e13			0.254632
$418$	8.20936e13	+	1.27792e13i	0.314659	+	0.0489818i
$419$	1.45431e14			0.550149			0.275074	−	0.961423i	$-0.411298\pi$
$419$	1.45431e14			0.550149			0.275074	+	0.961423i	$0.411298\pi$
$420$	4.00845e13	−	6.94285e13i	0.149660	−	0.259219i
$421$	−1.02704e14	+	1.77888e14i	−0.378472	+	0.655533i	−0.990840	−	0.135040i	$-0.956884\pi$
$421$	−1.02704e14	+	1.77888e14i	−0.378472	+	0.655533i	0.612368	+	0.790573i	$0.290217\pi$
$422$	3.83937e13	+	6.64998e13i	0.139650	+	0.241881i
$423$	−4.88444e13	+	8.46010e13i	−0.175365	+	0.303741i
$424$	9.47908e13	+	1.64183e14i	0.335934	+	0.581855i
$425$	−5.39926e13			−0.188884
$426$	9.59251e13			0.331268
$427$	2.71941e14	+	4.71015e14i	0.927088	+	1.60576i
$428$	5.47262e13	+	9.47885e13i	0.184185	+	0.319018i
$429$	2.48543e12			0.00825821
$430$	2.82872e14			0.927925
$431$	1.13573e14	+	1.96714e14i	0.367832	+	0.637104i	0.989226	−	0.146394i	$-0.0467667\pi$
$431$	1.13573e14	+	1.96714e14i	0.367832	+	0.637104i	−0.621394	+	0.783498i	$0.713433\pi$
$432$	7.52296e12	−	1.30301e13i	0.0240563	−	0.0416667i
$433$	4.89472e13	+	8.47791e13i	0.154541	+	0.267673i	0.932892	−	0.360156i	$-0.117277\pi$
$433$	4.89472e13	+	8.47791e13i	0.154541	+	0.267673i	−0.778351	+	0.627830i	$0.783943\pi$
$434$	2.98467e14	−	5.16960e14i	0.930471	−	1.61162i
$435$	−9.34533e12	+	1.61866e13i	−0.0287676	+	0.0498269i
$436$	−2.04826e14			−0.622599
$437$	2.61255e13	−	3.24378e13i	0.0784181	−	0.0973652i
$438$	−2.68615e13			−0.0796200
$439$	2.52246e14	−	4.36903e14i	0.738362	−	1.27888i	−0.214871	−	0.976642i	$-0.568933\pi$
$439$	2.52246e14	−	4.36903e14i	0.738362	−	1.27888i	0.953233	−	0.302238i	$-0.0977336\pi$
$440$	−2.01958e13	+	3.49801e13i	−0.0583809	+	0.101119i
$441$	−5.83365e13	−	1.01042e14i	−0.166544	−	0.288462i
$442$	1.62739e12	−	2.81872e12i	0.00458849	−	0.00794749i
$443$	1.37046e14	+	2.37371e14i	0.381634	+	0.661009i	0.991296	−	0.131652i	$-0.0420283\pi$
$443$	1.37046e14	+	2.37371e14i	0.381634	+	0.661009i	−0.609662	+	0.792661i	$0.708695\pi$
$444$	−4.29986e13			−0.118263
$445$	4.09400e14			1.11216
$446$	1.75102e14	+	3.03285e14i	0.469839	+	0.813785i
$447$	−1.95260e14	−	3.38201e14i	−0.517515	−	0.896362i
$448$	6.75109e13			0.176744
$449$	−1.43691e13			−0.0371600			−0.0185800	−	0.999827i	$-0.505915\pi$
$449$	−1.43691e13			−0.0371600			−0.0185800	+	0.999827i	$0.505915\pi$
$450$	−2.13244e13	−	3.69349e13i	−0.0544763	−	0.0943557i
$451$	−1.43557e14	+	2.48647e14i	−0.362287	+	0.627499i
$452$	2.70461e13	+	4.68452e13i	0.0674285	+	0.116790i
$453$	1.41752e14	−	2.45521e14i	0.349131	−	0.604713i
$454$	−7.46007e13	+	1.29212e14i	−0.181525	+	0.314410i
$455$	1.36988e13			0.0329321
$456$	8.49184e13	+	1.32190e13i	0.201695	+	0.0313972i
$457$	2.18790e14			0.513438			0.256719	−	0.966486i	$-0.417358\pi$
$457$	2.18790e14			0.513438			0.256719	+	0.966486i	$0.417358\pi$
$458$	−1.15162e14	+	1.99467e14i	−0.267024	+	0.462499i
$459$	1.71625e13	−	2.97263e13i	0.0393197	−	0.0681037i
$460$	1.01244e13	+	1.75360e13i	0.0229194	+	0.0396975i
$461$	−3.26792e14	+	5.66021e14i	−0.730999	+	1.26613i	0.225458	+	0.974253i	$0.427612\pi$
$461$	−3.26792e14	+	5.66021e14i	−0.730999	+	1.26613i	−0.956457	+	0.291874i	$0.905721\pi$
$462$	5.88050e13	+	1.01853e14i	0.129982	+	0.225135i
$463$	−2.16683e14			−0.473292			−0.236646	−	0.971596i	$-0.576048\pi$
$463$	−2.16683e14			−0.473292			−0.236646	+	0.971596i	$0.576048\pi$
$464$	−1.57395e13			−0.0339737
$465$	1.84716e14	+	3.19938e14i	0.394016	+	0.682456i
$466$	−8.62037e13	−	1.49309e14i	−0.181720	−	0.314749i
$467$	7.94659e13			0.165553			0.0827767	−	0.996568i	$-0.473621\pi$
$467$	7.94659e13			0.165553			0.0827767	+	0.996568i	$0.473621\pi$
$468$	2.57095e12			0.00529348
$469$	−3.75881e14	−	6.51044e14i	−0.764891	−	1.32483i
$470$	1.35637e14	−	2.34930e14i	0.272798	−	0.472499i
$471$	−2.23627e14	−	3.87333e14i	−0.444538	−	0.769963i
$472$	3.21388e13	−	5.56661e13i	0.0631465	−	0.109373i
$473$	−2.07490e14	+	3.59383e14i	−0.402958	+	0.697944i
$474$	7.18184e13			0.137865
$475$	1.52804e14	−	1.89724e14i	0.289947	−	0.360003i
$476$	1.54016e14			0.288886
$477$	−1.70816e14	+	2.95862e14i	−0.316722	+	0.548578i
$478$	3.73997e13	−	6.47782e13i	0.0685512	−	0.118734i
$479$	−6.24234e13	−	1.08121e14i	−0.113110	−	0.195913i	0.803912	−	0.594748i	$-0.202748\pi$
$479$	−6.24234e13	−	1.08121e14i	−0.113110	−	0.195913i	−0.917023	+	0.398835i	$0.869415\pi$
$480$	−2.08907e13	+	3.61837e13i	−0.0374219	+	0.0648167i
$481$	−3.67367e12	−	6.36297e12i	−0.00650581	−	0.0112684i
$482$	4.91693e14			0.860865
$483$	5.89595e13			0.102057
$484$	1.16452e14	+	2.01701e14i	0.199295	+	0.345190i
$485$	−1.55603e14	−	2.69513e14i	−0.263293	−	0.456036i
$486$	2.71132e13			0.0453609
$487$	−1.81598e14			−0.300401			−0.150201	−	0.988656i	$-0.547992\pi$
$487$	−1.81598e14			−0.300401			−0.150201	+	0.988656i	$0.547992\pi$
$488$	−1.41726e14	−	2.45477e14i	−0.231815	−	0.401515i
$489$	8.76154e13	−	1.51754e14i	0.141704	−	0.245438i
$490$	1.61996e14	+	2.80585e14i	0.259075	+	0.448731i
$491$	2.79651e13	−	4.84370e13i	0.0442251	−	0.0766001i	−0.843066	−	0.537811i	$-0.819251\pi$
$491$	2.79651e13	−	4.84370e13i	0.0442251	−	0.0766001i	0.887291	+	0.461211i	$0.152585\pi$
$492$	−1.48496e14	+	2.57203e14i	−0.232224	+	0.402224i
$493$	−3.59073e13			−0.0555296
$494$	5.29900e12	+	1.36957e13i	0.00810394	+	0.0209452i
$495$	−7.27868e13			−0.110084
$496$	−1.55551e14	+	2.69422e14i	−0.232661	+	0.402980i
$497$	−3.87811e14	+	6.71708e14i	−0.573667	+	0.993621i
$498$	−1.95874e14	−	3.39264e14i	−0.286560	−	0.496337i
$499$	−2.35416e14	+	4.07752e14i	−0.340630	+	0.589988i	−0.984550	−	0.175105i	$-0.943974\pi$
$499$	−2.35416e14	+	4.07752e14i	−0.340630	+	0.589988i	0.643920	+	0.765093i	$0.277307\pi$
$500$	1.87321e14	+	3.24450e14i	0.268072	+	0.464315i
$501$	2.92907e14			0.414593
$502$	4.25750e14			0.596052
$503$	1.97098e14	+	3.41384e14i	0.272935	+	0.472737i	0.969612	−	0.244648i	$-0.0786724\pi$
$503$	1.97098e14	+	3.41384e14i	0.272935	+	0.472737i	−0.696677	+	0.717385i	$0.745339\pi$
$504$	6.08284e13	+	1.05358e14i	0.0833180	+	0.144311i
$505$	−1.10110e14			−0.149184
$506$	−2.97055e13			−0.0398116
$507$	−2.17528e14	−	3.76769e14i	−0.288384	−	0.499496i
$508$	−1.91772e14	+	3.32159e14i	−0.251498	+	0.435607i
$509$	5.34179e14	+	9.25225e14i	0.693009	+	1.20033i	0.970847	+	0.239699i	$0.0770488\pi$
$509$	5.34179e14	+	9.25225e14i	0.693009	+	1.20033i	−0.277838	+	0.960628i	$0.589618\pi$
$510$	−4.76589e13	+	8.25476e13i	−0.0611657	+	0.105942i
$511$	1.08597e14	−	1.88095e14i	0.137880	−	0.238816i
$512$	−3.51844e13			−0.0441942
$513$	5.58833e13	+	1.44435e14i	0.0694443	+	0.179484i
$514$	7.51518e14			0.923936
$515$	4.21130e13	−	7.29418e13i	0.0512243	−	0.0887231i
$516$	−2.14629e14	+	3.71749e14i	−0.258295	+	0.447380i
$517$	1.98983e14	+	3.44648e14i	0.236929	+	0.410373i
$518$	1.73837e14	−	3.01095e14i	0.204799	−	0.354723i
$519$	−2.40659e14	−	4.16834e14i	−0.280532	−	0.485896i
$520$	−7.13933e12			−0.00823454
$521$	−1.18253e15			−1.34960			−0.674800	−	0.738001i	$-0.735770\pi$
$521$	−1.18253e15			−1.34960			−0.674800	+	0.738001i	$0.735770\pi$
$522$	−1.41816e13	−	2.45632e13i	−0.0160153	−	0.0277394i
$523$	2.09409e13	+	3.62707e13i	0.0234011	+	0.0405319i	0.877489	−	0.479597i	$-0.159217\pi$
$523$	2.09409e13	+	3.62707e13i	0.0234011	+	0.0405319i	−0.854088	+	0.520129i	$0.825884\pi$
$524$	7.76124e13			0.0858241
$525$	3.44845e14			0.377353
$526$	1.82314e14	+	3.15777e14i	0.197423	+	0.341948i
$527$	−3.54865e14	+	6.14644e14i	−0.380281	+	0.658666i
$528$	−3.06471e13	−	5.30824e13i	−0.0325015	−	0.0562942i
$529$	4.68959e14	−	8.12261e14i	0.492185	−	0.852490i
$530$	4.74344e14	−	8.21587e14i	0.492692	−	0.853368i
$531$	1.15830e14			0.119070
$532$	−4.35877e14	+	5.41192e14i	−0.443456	+	0.550602i
$533$	−5.07482e13			−0.0511000
$534$	−3.10633e14	+	5.38032e14i	−0.309578	+	0.536206i
$535$	2.73856e14	−	4.74332e14i	0.270132	−	0.467882i
$536$	1.95896e14	+	3.39302e14i	0.191258	+	0.331268i
$537$	−3.50127e14	+	6.06438e14i	−0.338351	+	0.586041i
$538$	2.60323e14	+	4.50892e14i	0.249006	+	0.431291i
$539$	−4.75304e14			−0.450021
$540$	−7.52914e13			−0.0705634
$541$	2.79457e14	+	4.84034e14i	0.259257	+	0.449046i	0.966043	−	0.258381i	$-0.0831890\pi$
$541$	2.79457e14	+	4.84034e14i	0.259257	+	0.449046i	−0.706786	+	0.707427i	$0.749856\pi$
$542$	1.64234e14	+	2.84462e14i	0.150823	+	0.261234i
$543$	−7.74821e14			−0.704372
$544$	−8.02677e13			−0.0722348
$545$	5.12485e14	+	8.87649e14i	0.456562	+	0.790789i
$546$	−1.03940e13	+	1.80029e13i	−0.00916689	+	0.0158775i
$547$	−8.60187e14	−	1.48989e15i	−0.751040	−	1.30084i	−0.947319	−	0.320291i	$-0.896219\pi$
$547$	−8.60187e14	−	1.48989e15i	−0.751040	−	1.30084i	0.196280	−	0.980548i	$-0.437114\pi$
$548$	−6.39912e12	+	1.10836e13i	−0.00553130	+	0.00958049i
$549$	2.55395e14	−	4.42357e14i	0.218557	−	0.378552i
$550$	−1.73743e14			−0.147202
$551$	1.01621e14	−	1.26174e14i	0.0852409	−	0.105837i
$552$	−3.07277e13			−0.0255191
$553$	−2.90351e14	+	5.02903e14i	−0.238746	+	0.413520i
$554$	4.12648e14	−	7.14728e14i	0.335951	−	0.581885i
$555$	1.07585e14	+	1.86343e14i	0.0867241	+	0.150211i
$556$	1.38142e14	−	2.39269e14i	0.110259	−	0.190974i
$557$	−9.15338e14	−	1.58541e15i	−0.723399	−	1.25296i	−0.959630	−	0.281267i	$-0.909246\pi$
$557$	−9.15338e14	−	1.58541e15i	−0.723399	−	1.25296i	0.236231	−	0.971697i	$-0.424088\pi$
$558$	−5.60615e14			−0.438709
$559$	−7.33489e13			−0.0568367
$560$	−1.68916e14	−	2.92571e14i	−0.129609	−	0.224490i
$561$	−6.99167e13	−	1.21099e14i	−0.0531233	−	0.0920122i
$562$	5.97107e14			0.449265
$563$	−2.10969e15			−1.57189			−0.785947	−	0.618294i	$-0.787824\pi$
$563$	−2.10969e15			−1.57189			−0.785947	+	0.618294i	$0.787824\pi$
$564$	2.05830e14	+	3.56508e14i	0.151870	+	0.263047i
$565$	1.35342e14	−	2.34419e14i	0.0988929	−	0.171287i
$566$	7.81807e13	+	1.35413e14i	0.0565730	+	0.0979873i
$567$	−1.09615e14	+	1.89858e14i	−0.0785529	+	0.136058i
$568$	2.02114e14	−	3.50071e14i	0.143443	−	0.248451i
$569$	−1.57489e15			−1.10696			−0.553482	−	0.832861i	$-0.686701\pi$
$569$	−1.57489e15			−1.10696			−0.553482	+	0.832861i	$0.686701\pi$
$570$	−1.55184e14	−	4.01084e14i	−0.108027	−	0.279205i
$571$	−5.86479e13			−0.0404347			−0.0202173	−	0.999796i	$-0.506436\pi$
$571$	−5.86479e13			−0.0404347			−0.0202173	+	0.999796i	$0.506436\pi$
$572$	5.23678e12	−	9.07038e12i	0.00357591	−	0.00619366i
$573$	7.80263e14	−	1.35145e15i	0.527704	−	0.914010i
$574$	−1.20070e15	−	2.07967e15i	−0.804300	−	1.39309i
$575$	−4.35499e13	+	7.54307e13i	−0.0288944	+	0.0500466i
$576$	−3.17017e13	−	5.49089e13i	−0.0208333	−	0.0360844i
$577$	4.33322e14			0.282061			0.141031	−	0.990005i	$-0.454958\pi$
$577$	4.33322e14			0.282061			0.141031	+	0.990005i	$0.454958\pi$
$578$	9.13582e14			0.589040
$579$	2.75757e14	+	4.77626e14i	0.176114	+	0.305039i
$580$	3.93811e13	+	6.82101e13i	0.0249135	+	0.0431514i
$581$	3.16756e15			1.98498
$582$	4.72257e14			0.293158
$583$	6.95873e14	+	1.20529e15i	0.427911	+	0.741163i
$584$	−5.65970e13	+	9.80289e13i	−0.0344765	+	0.0597150i
$585$	−6.43266e12	−	1.11417e13i	−0.00388180	−	0.00672347i
$586$	3.53416e14	−	6.12134e14i	0.211275	−	0.365940i
$587$	1.03954e15	−	1.80053e15i	0.615645	−	1.06633i	−0.374626	−	0.927176i	$-0.622229\pi$
$587$	1.03954e15	−	1.80053e15i	0.615645	−	1.06633i	0.990271	−	0.139153i	$-0.0444379\pi$
$588$	−4.91659e14			−0.288462
$589$	−1.15549e15	−	2.98645e15i	−0.671632	−	1.73588i
$590$	−3.21653e14			−0.185226
$591$	5.25103e14	−	9.09506e14i	0.299581	−	0.518889i
$592$	−9.05980e13	+	1.56920e14i	−0.0512093	+	0.0886971i
$593$	1.38475e15	+	2.39845e15i	0.775478	+	1.34317i	0.934525	+	0.355896i	$0.115824\pi$
$593$	1.38475e15	+	2.39845e15i	0.775478	+	1.34317i	−0.159047	+	0.987271i	$0.550842\pi$
$594$	5.52271e13	−	9.56562e13i	0.0306427	−	0.0530747i
$595$	−3.85355e14	−	6.67455e14i	−0.211845	−	0.366926i
$596$	−1.64565e15			−0.896362
$597$	−3.89576e14			−0.210249
$598$	−2.62528e12	−	4.54711e12i	−0.00140384	−	0.00243153i
$599$	4.54993e14	+	7.88071e14i	0.241078	+	0.417559i	0.961022	−	0.276473i	$-0.0891658\pi$
$599$	4.54993e14	+	7.88071e14i	0.241078	+	0.417559i	−0.719944	+	0.694032i	$0.755832\pi$
$600$	−1.79721e14			−0.0943557
$601$	−2.57729e15			−1.34077			−0.670385	−	0.742014i	$-0.733871\pi$
$601$	−2.57729e15			−1.34077			−0.670385	+	0.742014i	$0.733871\pi$
$602$	−1.73543e15	−	3.00585e15i	−0.894594	−	1.54948i
$603$	−3.53011e14	+	6.11433e14i	−0.180320	+	0.312323i
$604$	−5.97341e14	−	1.03463e15i	−0.302356	−	0.523697i
$605$	5.82738e14	−	1.00933e15i	0.292293	−	0.506267i
$606$	8.35460e13	−	1.44706e14i	0.0415266	−	0.0719261i
$607$	−4.30727e14			−0.212160			−0.106080	−	0.994358i	$-0.533830\pi$
$607$	−4.30727e14			−0.212160			−0.106080	+	0.994358i	$0.533830\pi$
$608$	2.27164e14	−	2.82051e14i	0.110884	−	0.137676i
$609$	2.29336e14			0.110937
$610$	−7.09213e14	+	1.22839e15i	−0.339987	+	0.588875i
$611$	−3.51709e13	+	6.09177e13i	−0.0167092	+	0.0289412i
$612$	−7.23225e13	−	1.25266e14i	−0.0340518	−	0.0589795i
$613$	−1.15928e15	+	2.00794e15i	−0.540951	+	0.936954i	0.457899	+	0.889004i	$0.348602\pi$
$613$	−1.15928e15	+	2.00794e15i	−0.540951	+	0.936954i	−0.998850	+	0.0479498i	$0.984731\pi$
$614$	−2.82465e14	−	4.89244e14i	−0.130629	−	0.226256i
$615$	1.48618e15			0.681176
$616$	4.95607e14			0.225135
$617$	9.42754e14	+	1.63290e15i	0.424453	+	0.735175i	0.996369	−	0.0851374i	$-0.0271329\pi$
$617$	9.42754e14	+	1.63290e15i	0.424453	+	0.735175i	−0.571916	+	0.820312i	$0.693800\pi$
$618$	6.39066e13	+	1.10689e14i	0.0285173	+	0.0493935i
$619$	2.02583e15			0.895993			0.447996	−	0.894035i	$-0.352138\pi$
$619$	2.02583e15			0.895993			0.447996	+	0.894035i	$0.352138\pi$
$620$	1.55679e15			0.682456
$621$	−2.76862e13	−	4.79538e13i	−0.0120298	−	0.0208362i
$622$	−5.60340e14	+	9.70536e14i	−0.241326	+	0.417989i
$623$	−2.51169e15	−	4.35037e15i	−1.07221	−	1.85713i
$624$	5.41698e12	−	9.38249e12i	0.00229214	−	0.00397011i
$625$	3.86335e14	−	6.69153e14i	0.162041	−	0.280663i
$626$	−2.08663e15			−0.867535
$627$	6.23398e14	+	9.70422e13i	0.256918	+	0.0399935i
$628$	−1.88473e15			−0.769963
$629$	−2.06685e14	+	3.57989e14i	−0.0837010	+	0.144974i
$630$	3.04392e14	−	5.27222e14i	0.122197	−	0.211651i
$631$	−2.07550e15	−	3.59487e15i	−0.825964	−	1.43061i	−0.901180	−	0.433444i	$-0.857298\pi$
$631$	−2.07550e15	−	3.59487e15i	−0.825964	−	1.43061i	0.0752164	−	0.997167i	$-0.476035\pi$
$632$	1.51321e14	−	2.62096e14i	0.0596974	−	0.103399i
$633$	2.91552e14	+	5.04983e14i	0.114024	+	0.197495i
$634$	−2.90118e15			−1.12482
$635$	1.91929e15			0.737711
$636$	7.19818e14	+	1.24676e15i	0.274289	+	0.475083i
$637$	−4.20058e13	−	7.27561e13i	−0.0158687	−	0.0274854i
$638$	−1.15546e14			−0.0432754
$639$	7.28431e14			0.270479
$640$	8.80332e13	+	1.52478e14i	0.0324083	+	0.0561329i
$641$	−7.65279e14	+	1.32550e15i	−0.279319	+	0.483795i	−0.971216	−	0.238202i	$-0.923442\pi$
$641$	−7.65279e14	+	1.32550e15i	−0.279319	+	0.483795i	0.691897	+	0.721997i	$0.256775\pi$
$642$	4.15577e14	+	7.19800e14i	0.150386	+	0.260477i
$643$	−8.48046e14	+	1.46886e15i	−0.304270	+	0.527011i	−0.977098	−	0.212788i	$-0.931746\pi$
$643$	−8.48046e14	+	1.46886e15i	−0.304270	+	0.527011i	0.672829	+	0.739798i	$0.265079\pi$
$644$	1.24228e14	−	2.15168e14i	0.0441922	−	0.0765431i
$645$	2.14806e15			0.757647
$646$	5.18240e14	−	6.43456e14i	0.181239	−	0.225030i
$647$	2.55048e15			0.884400			0.442200	−	0.896916i	$-0.354198\pi$
$647$	2.55048e15			0.884400			0.442200	+	0.896916i	$0.354198\pi$
$648$	5.71275e13	−	9.89477e13i	0.0196419	−	0.0340207i
$649$	2.35936e14	−	4.08653e14i	0.0804356	−	0.139318i
$650$	−1.53548e13	−	2.65953e13i	−0.00519064	−	0.00899046i
$651$	2.26648e15	−	3.92566e15i	0.759726	−	1.31588i
$652$	−3.69211e14	−	6.39492e14i	−0.122719	−	0.212556i
$653$	−4.63824e14			−0.152873			−0.0764365	−	0.997074i	$-0.524354\pi$
$653$	−4.63824e14			−0.152873			−0.0764365	+	0.997074i	$0.524354\pi$
$654$	−1.55539e15			−0.508350
$655$	−1.94190e14	−	3.36348e14i	−0.0629362	−	0.109009i
$656$	6.25763e14	+	1.08385e15i	0.201112	+	0.348337i
$657$	−2.03979e14			−0.0650094
$658$	−3.32856e15			−1.05200
$659$	7.03053e14	+	1.21772e15i	0.220353	+	0.381662i	0.954915	−	0.296879i	$-0.0959458\pi$
$659$	7.03053e14	+	1.21772e15i	0.220353	+	0.381662i	−0.734562	+	0.678541i	$0.762613\pi$
$660$	−1.53362e14	+	2.65630e14i	−0.0476678	+	0.0825630i
$661$	−9.55735e14	−	1.65538e15i	−0.294598	−	0.510258i	0.680293	−	0.732940i	$-0.261852\pi$
$661$	−9.55735e14	−	1.65538e15i	−0.294598	−	0.510258i	−0.974891	+	0.222682i	$0.928519\pi$
$662$	1.34067e15	−	2.32211e15i	0.409829	−	0.709845i
$663$	1.23580e13	−	2.14047e13i	0.00374648	−	0.00648910i
$664$	−1.65082e15			−0.496337
$665$	3.43595e15	+	5.34862e14i	1.02454	+	0.159486i
$666$	−3.26521e14			−0.0965612
$667$	−2.89625e13	+	5.01645e13i	−0.00849461	+	0.0147131i
$668$	6.17153e14	−	1.06894e15i	0.179524	−	0.310945i
$669$	1.32968e15	+	2.30307e15i	0.383622	+	0.664453i
$670$	9.80285e14	−	1.69790e15i	0.280505	−	0.485849i
$671$	−1.04043e15	−	1.80208e15i	−0.295284	−	0.511447i
$672$	5.12661e14			0.144311
$673$	−9.32514e14			−0.260359			−0.130179	−	0.991490i	$-0.541555\pi$
$673$	−9.32514e14			−0.260359			−0.130179	+	0.991490i	$0.541555\pi$
$674$	1.26967e15	+	2.19913e15i	0.351610	+	0.609007i
$675$	−1.61932e14	−	2.80474e14i	−0.0444797	−	0.0770411i
$676$	−1.83332e15			−0.499496
$677$	−2.40544e15			−0.650066			−0.325033	−	0.945703i	$-0.605375\pi$
$677$	−2.40544e15			−0.650066			−0.325033	+	0.945703i	$0.605375\pi$
$678$	2.05381e14	+	3.55731e14i	0.0550551	+	0.0953583i
$679$	−1.90926e15	+	3.30694e15i	−0.507671	+	0.879312i
$680$	2.00834e14	+	3.47855e14i	0.0529710	+	0.0917485i
$681$	−5.66499e14	+	9.81206e14i	−0.148214	+	0.256715i
$682$	−1.14192e15	+	1.97786e15i	−0.296361	+	0.513313i
$683$	2.24672e15			0.578409			0.289205	−	0.957267i	$-0.406609\pi$
$683$	2.24672e15			0.578409			0.289205	+	0.957267i	$0.406609\pi$
$684$	6.44849e14	+	1.00381e14i	0.164683	+	0.0256357i
$685$	6.40438e13			0.0162248
$686$	−1.46835e12	+	2.54326e12i	−0.000369019	+	0.000639159i
$687$	−8.74513e14	+	1.51470e15i	−0.218024	+	0.377629i
$688$	9.04446e14	+	1.56655e15i	0.223690	+	0.387442i
$689$	−1.22998e14	+	2.13039e14i	−0.0301781	+	0.0522700i
$690$	7.68824e13	+	1.33164e14i	0.0187136	+	0.0324129i
$691$	3.83017e15			0.924887			0.462443	−	0.886649i	$-0.346973\pi$
$691$	3.83017e15			0.924887			0.462443	+	0.886649i	$0.346973\pi$
$692$	−2.02827e15			−0.485896
$693$	4.46550e14	+	7.73448e14i	0.106130	+	0.183822i
$694$	2.63812e15	+	4.56936e15i	0.622040	+	1.07740i
$695$	−1.38255e15			−0.323419
$696$	−1.19522e14			−0.0277394
$697$	1.42758e15	+	2.47264e15i	0.328716	+	0.569352i
$698$	2.46946e15	−	4.27724e15i	0.564154	−	0.977144i
$699$	−6.54610e14	−	1.13382e15i	−0.148374	−	0.256991i
$700$	7.26587e14	−	1.25849e15i	0.163399	−	0.283015i
$701$	6.99872e14	−	1.21221e15i	0.156160	−	0.270477i	−0.777321	−	0.629104i	$-0.783422\pi$
$701$	6.99872e14	−	1.21221e15i	0.156160	−	0.270477i	0.933481	+	0.358627i	$0.116755\pi$
$702$	1.95232e13			0.00432211
$703$	−6.72995e14	−	1.73941e15i	−0.147828	−	0.382073i
$704$	−2.58294e14			−0.0562942
$705$	1.02999e15	−	1.78400e15i	0.222738	−	0.385794i
$706$	−1.25941e15	+	2.18136e15i	−0.270234	+	0.468059i
$707$	6.75528e14	+	1.17005e15i	0.143826	+	0.249113i
$708$	2.44054e14	−	4.22715e14i	0.0515589	−	0.0893026i
$709$	−1.11064e15	−	1.92368e15i	−0.232818	−	0.403253i	0.725818	−	0.687887i	$-0.241461\pi$
$709$	−1.11064e15	−	1.92368e15i	−0.232818	−	0.403253i	−0.958636	+	0.284633i	$0.908128\pi$
$710$	−2.02280e15			−0.420757
$711$	5.45371e14			0.112567
$712$	1.30901e15	+	2.26726e15i	0.268103	+	0.464368i
$713$	5.72461e14	+	9.91532e14i	0.116347	+	0.201518i
$714$	1.16956e15			0.235874
$715$	−5.24109e13			−0.0104891
$716$	1.47543e15	+	2.55553e15i	0.293021	+	0.507527i
$717$	2.84004e14	−	4.91910e14i	0.0559718	−	0.0969460i
$718$	−1.56388e15	−	2.70873e15i	−0.305858	−	0.529762i
$719$	1.63759e15	−	2.83639e15i	0.317831	−	0.550500i	−0.662204	−	0.749323i	$-0.730379\pi$
$719$	1.63759e15	−	2.83639e15i	0.317831	−	0.550500i	0.980035	+	0.198824i	$0.0637122\pi$
$720$	−1.58639e14	+	2.74770e14i	−0.0305549	+	0.0529226i
$721$	−1.03346e15			−0.197537
$722$	7.94362e14	+	3.64207e15i	0.150683	+	0.690865i
$723$	3.73379e15			0.702893
$724$	−1.63254e15	+	2.82765e15i	−0.305002	+	0.528279i
$725$	−1.69397e14	+	2.93404e14i	−0.0314084	+	0.0544010i
$726$	8.84307e14	+	1.53166e15i	0.162724	+	0.281846i
$727$	−1.43858e15	+	2.49169e15i	−0.262720	+	0.455045i	−0.966964	−	0.254913i	$-0.917953\pi$
$727$	−1.43858e15	+	2.49169e15i	−0.262720	+	0.455045i	0.704243	+	0.709959i	$0.251286\pi$
$728$	4.38001e13	+	7.58640e13i	0.00793876	+	0.0137503i
$729$	2.05891e14			0.0370370
$730$	5.66435e14			0.101129
$731$	2.06335e15	+	3.57383e15i	0.365618	+	0.633269i
$732$	−1.07623e15	−	1.86409e15i	−0.189276	−	0.327835i
$733$	7.61733e15			1.32963			0.664815	−	0.747008i	$-0.268510\pi$
$733$	7.61733e15			1.32963			0.664815	+	0.747008i	$0.268510\pi$
$734$	1.53280e15			0.265557
$735$	1.23016e15	+	2.13069e15i	0.211534	+	0.366388i
$736$	−6.47431e13	+	1.12138e14i	−0.0110501	+	0.0191393i
$737$	1.43810e15	+	2.49086e15i	0.243623	+	0.421967i
$738$	−1.12764e15	+	1.95314e15i	−0.189610	+	0.328415i
$739$	−1.96528e15	+	3.40396e15i	−0.328004	+	0.568120i	−0.982116	−	0.188278i	$-0.939709\pi$
$739$	−1.96528e15	+	3.40396e15i	−0.328004	+	0.568120i	0.654111	+	0.756398i	$0.273043\pi$
$740$	9.06724e14			0.150211
$741$	4.02393e13	+	1.04002e14i	0.00661684	+	0.0171017i
$742$	−1.16405e16			−1.89998
$743$	−1.71833e15	+	2.97623e15i	−0.278398	+	0.482200i	−0.970987	−	0.239133i	$-0.923137\pi$
$743$	−1.71833e15	+	2.97623e15i	−0.278398	+	0.482200i	0.692588	+	0.721333i	$0.256470\pi$
$744$	−1.18121e15	+	2.04592e15i	−0.189967	+	0.329032i
$745$	4.11751e15	+	7.13173e15i	0.657317	+	1.13851i
$746$	3.95444e15	−	6.84929e15i	0.626644	−	1.08538i
$747$	−1.48742e15	−	2.57629e15i	−0.233975	−	0.405257i
$748$	−5.89257e14			−0.0920122
$749$	−6.72046e15			−1.04172
$750$	1.42247e15	+	2.46379e15i	0.218880	+	0.379112i
$751$	−3.21775e15	−	5.57331e15i	−0.491511	−	0.851321i	0.508442	−	0.861096i	$-0.330222\pi$
$751$	−3.21775e15	−	5.57331e15i	−0.491511	−	0.851321i	−0.999952	+	0.00977517i	$0.996888\pi$
$752$	1.73473e15			0.263047
$753$	3.23304e15			0.486675
$754$	−1.02116e13	−	1.76870e13i	−0.00152599	−	0.00264308i
$755$	−2.98916e15	+	5.17738e15i	−0.443446	+	0.768071i
$756$	4.61916e14	+	8.00062e14i	0.0680288	+	0.117829i
$757$	−6.24339e15	+	1.08139e16i	−0.912837	+	1.58108i	−0.102800	+	0.994702i	$0.532780\pi$
$757$	−6.24339e15	+	1.08139e16i	−0.912837	+	1.58108i	−0.810037	+	0.586378i	$0.800553\pi$
$758$	3.47410e15	−	6.01732e15i	0.504268	−	0.873418i
$759$	−2.25576e14			−0.0325060
$760$	−1.79070e15	−	2.78752e14i	−0.256181	−	0.0398789i
$761$	−2.55299e15			−0.362605			−0.181302	−	0.983427i	$-0.558031\pi$
$761$	−2.55299e15			−0.362605			−0.181302	+	0.983427i	$0.558031\pi$
$762$	−1.45627e15	+	2.52233e15i	−0.205347	+	0.355672i
$763$	6.28823e15	−	1.08915e16i	0.880325	−	1.52477i
$764$	−3.28802e15	−	5.69502e15i	−0.457005	−	0.791556i
$765$	−3.61910e14	+	6.26846e14i	−0.0499416	+	0.0865013i
$766$	4.49174e15	+	7.77992e15i	0.615398	+	1.06590i
$767$	8.34049e13			0.0113453
$768$	−2.67181e14			−0.0360844
$769$	9.31242e14	+	1.61296e15i	0.124873	+	0.216286i	0.921683	−	0.387943i	$-0.126814\pi$
$769$	9.31242e14	+	1.61296e15i	0.124873	+	0.216286i	−0.796810	+	0.604229i	$0.793481\pi$
$770$	−1.24004e15	−	2.14781e15i	−0.165096	−	0.285954i
$771$	5.70684e15			0.754391
$772$	2.32408e15			0.305039
$773$	5.48888e15	+	9.50702e15i	0.715314	+	1.23896i	0.962838	+	0.270078i	$0.0870495\pi$
$773$	5.48888e15	+	9.50702e15i	0.715314	+	1.23896i	−0.247525	+	0.968882i	$0.579617\pi$
$774$	−1.62984e15	+	2.82297e15i	−0.210897	+	0.365284i
$775$	3.34823e15	+	5.79931e15i	0.430186	+	0.745104i
$776$	9.95043e14	−	1.72346e15i	0.126941	−	0.219868i
$777$	1.32008e15	−	2.28644e15i	0.167218	−	0.289630i
$778$	−9.92389e15			−1.24823
$779$	−1.27287e16	−	1.98144e15i	−1.58975	−	0.247471i
$780$	−5.42143e13			−0.00672347
$781$	1.48375e15	−	2.56992e15i	0.182717	−	0.316475i
$782$	−1.47701e14	+	2.55826e14i	−0.0180612	+	0.0312830i
$783$	−1.07691e14	−	1.86527e14i	−0.0130765	−	0.0226491i
$784$	−1.03592e15	+	1.79427e15i	−0.124908	+	0.216347i
$785$	4.71568e15	+	8.16780e15i	0.564627	+	0.977963i
$786$	5.89369e14			0.0700751
$787$	9.84483e15			1.16238			0.581189	−	0.813769i	$-0.302588\pi$
$787$	9.84483e15			1.16238			0.581189	+	0.813769i	$0.302588\pi$
$788$	−2.21278e15	−	3.83265e15i	−0.259444	−	0.449371i
$789$	1.38445e15	+	2.39793e15i	0.161196	+	0.279199i
$790$	−1.51445e15			−0.175108
$791$	−3.32131e15			−0.381363
$792$	−2.32727e14	−	4.03094e14i	−0.0265374	−	0.0459640i
$793$	1.83900e14	−	3.18524e14i	0.0208247	−	0.0360694i
$794$	−2.13002e15	−	3.68930e15i	−0.239536	−	0.414888i
$795$	3.60205e15	−	6.23893e15i	0.402282	−	0.696772i
$796$	−8.20835e14	+	1.42173e15i	−0.0910404	+	0.157687i
$797$	9.95947e15			1.09702			0.548511	−	0.836143i	$-0.315195\pi$
$797$	9.95947e15			1.09702			0.548511	+	0.836143i	$0.315195\pi$
$798$	−3.30994e15	+	4.10968e15i	−0.362080	+	0.449565i
$799$	3.95752e15			0.429948
$800$	−3.78672e14	+	6.55880e14i	−0.0408572	+	0.0707668i
$801$	−2.35887e15	+	4.08568e15i	−0.252770	+	0.437810i
$802$	6.32359e14	+	1.09528e15i	0.0672984	+	0.116564i
$803$	−4.15487e14	+	7.19644e14i	−0.0439159	+	0.0760645i
$804$	1.48759e15	+	2.57657e15i	0.156161	+	0.270480i
$805$	−1.24330e15			−0.129628
$806$	−4.03676e14			−0.0418014
$807$	1.97682e15	+	3.42396e15i	0.203312	+	0.352147i
$808$	−3.52062e14	−	6.09789e14i	−0.0359631	−	0.0622898i
$809$	1.45275e15			0.147392			0.0736961	−	0.997281i	$-0.476521\pi$
$809$	1.45275e15			0.147392			0.0736961	+	0.997281i	$0.476521\pi$
$810$	−5.71744e14			−0.0576148
$811$	−5.45035e15	−	9.44028e15i	−0.545519	−	0.944866i	−0.998574	−	0.0533835i	$-0.982999\pi$
$811$	−5.45035e15	−	9.44028e15i	−0.545519	−	0.944866i	0.453056	−	0.891482i	$-0.350334\pi$
$812$	4.83210e14	−	8.36944e14i	0.0480372	−	0.0832028i
$813$	1.24716e15	+	2.16014e15i	0.123147	+	0.213296i
$814$	−6.65093e14	+	1.15197e15i	−0.0652301	+	0.112982i
$815$	−1.84757e15	+	3.20009e15i	−0.179984	+	0.311742i
$816$	−6.09533e14			−0.0589795
$817$	−1.83975e16	−	2.86387e15i	−1.76822	−	0.275253i
$818$	1.43589e15			0.137081
$819$	−7.89292e13	+	1.36709e14i	−0.00748473	+	0.0129639i
$820$	3.13138e15	−	5.42372e15i	0.294958	−	0.510882i
$821$	1.04194e16	+	1.80470e16i	0.974893	+	1.68856i	0.680288	+	0.732945i	$0.261855\pi$
$821$	1.04194e16	+	1.80470e16i	0.974893	+	1.68856i	0.294605	+	0.955619i	$0.404812\pi$
$822$	−4.85933e13	+	8.41661e13i	−0.00451629	+	0.00782244i
$823$	5.44538e14	+	9.43167e14i	0.0502723	+	0.0870742i	0.890067	−	0.455831i	$-0.150658\pi$
$823$	5.44538e14	+	9.43167e14i	0.0502723	+	0.0870742i	−0.839794	+	0.542905i	$0.817324\pi$
$824$	5.38603e14			0.0493935
$825$	−1.31936e15			−0.120190
$826$	1.97335e15	+	3.41794e15i	0.178572	+	0.309296i
$827$	−4.32729e15	−	7.49509e15i	−0.388988	−	0.673746i	0.603326	−	0.797495i	$-0.293842\pi$
$827$	−4.32729e15	−	7.49509e15i	−0.388988	−	0.673746i	−0.992314	+	0.123748i	$0.960508\pi$
$828$	−2.33338e14			−0.0208362
$829$	−6.88422e15			−0.610668			−0.305334	−	0.952245i	$-0.598768\pi$
$829$	−6.88422e15			−0.610668			−0.305334	+	0.952245i	$0.598768\pi$
$830$	4.13045e15	+	7.15415e15i	0.363972	+	0.630418i
$831$	3.13355e15	−	5.42747e15i	0.274303	−	0.475107i
$832$	−2.28271e13	−	3.95377e13i	−0.00198506	−	0.00343822i
$833$	−2.36330e15	+	4.09335e15i	−0.204160	+	0.353616i
$834$	1.04901e15	−	1.81695e15i	0.0900260	−	0.155930i
$835$	−6.17661e15			−0.526592
$836$	1.66765e15	−	2.07058e15i	0.141244	−	0.175371i
$837$	−4.25717e15			−0.358204
$838$	2.32690e15	−	4.03030e15i	0.194507	−	0.336896i
$839$	1.39874e15	−	2.42268e15i	0.116157	−	0.201190i	−0.802085	−	0.597210i	$-0.796276\pi$
$839$	1.39874e15	−	2.42268e15i	0.116157	−	0.201190i	0.918242	+	0.396021i	$0.129609\pi$
$840$	−1.28271e15	−	2.22171e15i	−0.105826	−	0.183295i
$841$	5.98760e15	−	1.03708e16i	0.490766	−	0.850032i
$842$	3.28652e15	+	5.69241e15i	0.267620	+	0.463532i
$843$	4.53428e15			0.366823
$844$	2.45720e15			0.197495
$845$	4.58707e15	+	7.94504e15i	0.366289	+	0.634430i
$846$	1.56302e15	+	2.70723e15i	0.124002	+	0.214777i
$847$	−1.43005e16			−1.12718
$848$	6.06661e15			0.475083
$849$	5.93685e14	+	1.02829e15i	0.0461917	+	0.0800063i
$850$	−8.63882e14	+	1.49629e15i	−0.0667806	+	0.115667i
$851$	3.33421e14	+	5.77501e14i	0.0256082	+	0.0443548i
$852$	1.53480e15	−	2.65836e15i	0.117121	−	0.202859i
$853$	5.98954e15	−	1.03742e16i	0.454123	−	0.786565i	−0.544514	−	0.838752i	$-0.683286\pi$
$853$	5.98954e15	−	1.03742e16i	0.454123	−	0.786565i	0.998637	+	0.0521869i	$0.0166192\pi$
$854$	1.74042e16			1.31110
$855$	−1.17843e15	−	3.04573e15i	−0.0882041	−	0.227970i
$856$	3.50248e15			0.260477
$857$	6.03040e15	−	1.04450e16i	0.445607	−	0.771813i	−0.552488	−	0.833521i	$-0.686321\pi$
$857$	6.03040e15	−	1.04450e16i	0.445607	−	0.771813i	0.998094	+	0.0617079i	$0.0196547\pi$
$858$	3.97668e13	−	6.88782e13i	0.00291972	−	0.00505710i
$859$	4.13729e15	+	7.16600e15i	0.301824	+	0.522775i	0.976549	−	0.215294i	$-0.0690711\pi$
$859$	4.13729e15	+	7.16600e15i	0.301824	+	0.522775i	−0.674725	+	0.738069i	$0.735738\pi$
$860$	4.52595e15	−	7.83917e15i	0.328071	−	0.568236i
$861$	−9.11780e15	−	1.57925e16i	−0.656709	−	1.13745i
$862$	7.26867e15			0.520194
$863$	−1.34722e16			−0.958028			−0.479014	−	0.877807i	$-0.659006\pi$
$863$	−1.34722e16			−0.958028			−0.479014	+	0.877807i	$0.659006\pi$
$864$	−2.40735e14	−	4.16965e14i	−0.0170103	−	0.0294628i
$865$	5.07485e15	+	8.78990e15i	0.356315	+	0.617156i
$866$	3.13262e15			0.218554
$867$	6.93752e15			0.480949
$868$	−9.55094e15	−	1.65427e16i	−0.657942	−	1.13959i
$869$	1.11087e15	−	1.92408e15i	0.0760422	−	0.131709i
$870$	2.99050e14	+	5.17971e14i	0.0203418	+	0.0352330i
$871$	−2.54189e14	+	4.40268e14i	−0.0171813	+	0.0297590i
$872$	−3.27721e15	+	5.67629e15i	−0.220122	+	0.381262i
$873$	3.58620e15			0.239362
$874$	−4.80936e14	−	1.24302e15i	−0.0318988	−	0.0824448i
$875$	−2.30034e16			−1.51617
$876$	−4.29783e14	+	7.44407e14i	−0.0281499	+	0.0487571i
$877$	−9.97946e14	+	1.72849e15i	−0.0649545	+	0.112504i	−0.896674	−	0.442692i	$-0.854024\pi$
$877$	−9.97946e14	+	1.72849e15i	−0.0649545	+	0.112504i	0.831719	+	0.555196i	$0.187357\pi$
$878$	−8.07187e15	−	1.39809e16i	−0.522101	−	0.904305i
$879$	2.68375e15	−	4.64839e15i	0.172506	−	0.298789i
$880$	6.46264e14	+	1.11936e15i	0.0412815	+	0.0715017i
$881$	7.24326e15			0.459797			0.229899	−	0.973215i	$-0.426161\pi$
$881$	7.24326e15			0.459797			0.229899	+	0.973215i	$0.426161\pi$
$882$	−3.73354e15			−0.235528
$883$	−1.42034e16	−	2.46009e16i	−0.890445	−	1.54230i	−0.839343	−	0.543602i	$-0.817060\pi$
$883$	−1.42034e16	−	2.46009e16i	−0.890445	−	1.54230i	−0.0511017	−	0.998693i	$-0.516273\pi$
$884$	−5.20765e13	−	9.01992e13i	−0.00324455	−	0.00561972i
$885$	−2.44255e15			−0.151236
$886$	8.77096e15			0.539711
$887$	−1.26816e16	−	2.19651e16i	−0.775520	−	1.34324i	−0.934502	−	0.355959i	$-0.884154\pi$
$887$	−1.26816e16	−	2.19651e16i	−0.775520	−	1.34324i	0.158982	−	0.987282i	$-0.449179\pi$
$888$	−6.87978e14	+	1.19161e15i	−0.0418122	+	0.0724209i
$889$	−1.17749e16	−	2.03948e16i	−0.711212	−	1.23186i
$890$	6.55040e15	−	1.13456e16i	0.393209	−	0.681057i
$891$	4.19381e14	−	7.26389e14i	0.0250197	−	0.0433353i
$892$	1.12065e16			0.664453
$893$	−1.12001e16	+	1.39062e16i	−0.659993	+	0.819458i
$894$	−1.24967e16			−0.731876
$895$	7.38323e15	−	1.27881e16i	0.429754	−	0.744355i
$896$	1.08017e15	−	1.87092e15i	0.0624885	−	0.108233i
$897$	−1.99357e13	−	3.45296e13i	−0.00114623	−	0.00198533i
$898$	−2.29906e14	+	3.98209e14i	−0.0131381	+	0.0227558i
$899$	2.22671e15	+	3.85678e15i	0.126469	+	0.219051i
$900$	−1.36476e15			−0.0770411
$901$	1.38400e16			0.776517
$902$	4.59381e15	+	7.95672e15i	0.256175	+	0.443709i
$903$	−1.31784e16	−	2.28257e16i	−0.730433	−	1.26515i
$904$	1.73095e15			0.0953583
$905$	1.63389e16			0.894653
$906$	−4.53606e15	−	7.85668e15i	−0.246873	−	0.427597i
$907$	1.14686e16	−	1.98642e16i	0.620400	−	1.07456i	−0.369012	−	0.929425i	$-0.620304\pi$
$907$	1.14686e16	−	1.98642e16i	0.620400	−	1.07456i	0.989411	−	0.145139i	$-0.0463629\pi$
$908$	2.38722e15	+	4.13479e15i	0.128357	+	0.222322i
$909$	6.34427e14	−	1.09886e15i	0.0339063	−	0.0587274i
$910$	2.19180e14	−	3.79632e14i	0.0116432	−	0.0201667i
$911$	−7.02620e15			−0.370996			−0.185498	−	0.982645i	$-0.559390\pi$
$911$	−7.02620e15			−0.370996			−0.185498	+	0.982645i	$0.559390\pi$
$912$	1.72503e15	−	2.14182e15i	0.0905367	−	0.112412i
$913$	−1.21189e16			−0.632230
$914$	3.50064e15	−	6.06329e15i	0.181528	−	0.314416i
$915$	−5.38559e15	+	9.32811e15i	−0.277598	+	0.480814i
$916$	3.68519e15	+	6.38294e15i	0.188814	+	0.327036i
$917$	−2.38273e15	+	4.12701e15i	−0.121351	+	0.210186i
$918$	−5.49199e14	−	9.51240e14i	−0.0278032	−	0.0481566i
$919$	−2.95496e16			−1.48702			−0.743510	−	0.668725i	$-0.766840\pi$
$919$	−2.95496e16			−1.48702			−0.743510	+	0.668725i	$0.766840\pi$
$920$	6.47963e14			0.0324129
$921$	−2.14497e15	−	3.71520e15i	−0.106658	−	0.184737i
$922$	1.04574e16	+	1.81127e16i	0.516894	+	0.895287i
$923$	5.24514e14			0.0257720
$924$	3.76352e15			0.183822
$925$	1.95012e15	+	3.37771e15i	0.0946853	+	0.164000i
$926$	−3.46692e15	+	6.00489e15i	−0.167334	+	0.289831i
$927$	4.85290e14	+	8.40548e14i	0.0232843	+	0.0403296i
$928$	−2.51832e14	+	4.36186e14i	−0.0120115	+	0.0208045i
$929$	−8.21783e15	+	1.42337e16i	−0.389646	+	0.674887i	−0.992402	−	0.123039i	$-0.960736\pi$
$929$	−8.21783e15	+	1.42337e16i	−0.389646	+	0.674887i	0.602756	+	0.797926i	$0.294069\pi$
$930$	1.18218e16			0.557223
$931$	−7.69522e15	−	1.98889e16i	−0.360577	−	0.931938i
$932$	−5.51704e15			−0.256991
$933$	−4.25508e15	+	7.37001e15i	−0.197042	+	0.341287i
$934$	1.27145e15	−	2.20222e15i	0.0585319	−	0.101380i
$935$	1.47435e15	+	2.55365e15i	0.0674741	+	0.116869i
$936$	4.11352e13	−	7.12483e13i	0.00187153	−	0.00324158i
$937$	1.71158e16	+	2.96454e16i	0.774156	+	1.34088i	0.935268	+	0.353941i	$0.115159\pi$
$937$	1.71158e16	+	2.96454e16i	0.774156	+	1.34088i	−0.161112	+	0.986936i	$0.551508\pi$
$938$	−2.40564e16			−1.08172
$939$	−1.58454e16			−0.708339
$940$	−4.34039e15	−	7.51778e15i	−0.192897	−	0.334107i
$941$	−8.96185e15	−	1.55224e16i	−0.395963	−	0.685828i	0.597260	−	0.802047i	$-0.296256\pi$
$941$	−8.96185e15	−	1.55224e16i	−0.395963	−	0.685828i	−0.993224	+	0.116219i	$0.962923\pi$
$942$	−1.43121e16			−0.628672
$943$	4.60589e15			0.201140
$944$	−1.02844e15	−	1.78132e15i	−0.0446513	−	0.0773383i
$945$	2.31148e15	−	4.00360e15i	0.0997734	−	0.172813i
$946$	6.63967e15	+	1.15002e16i	0.284934	+	0.493521i
$947$	2.67128e14	−	4.62679e14i	0.0113971	−	0.0197404i	−0.860271	−	0.509838i	$-0.829705\pi$
$947$	2.67128e14	−	4.62679e14i	0.0113971	−	0.0197404i	0.871668	+	0.490097i	$0.163039\pi$
$948$	1.14909e15	−	1.99029e15i	0.0487427	−	0.0844249i
$949$	−1.46877e14			−0.00619427
$950$	−2.81292e15	−	7.27020e15i	−0.117944	−	0.304836i
$951$	−2.20308e16			−0.918412
$952$	2.46425e15	−	4.26821e15i	0.102137	−	0.176906i
$953$	−2.69005e15	+	4.65930e15i	−0.110854	+	0.192004i	−0.916115	−	0.400916i	$-0.868692\pi$
$953$	−2.69005e15	+	4.65930e15i	−0.110854	+	0.192004i	0.805261	+	0.592920i	$0.202025\pi$
$954$	5.46612e15	+	9.46759e15i	0.223956	+	0.387903i
$955$	−1.64536e16	+	2.84985e16i	−0.670259	+	1.16092i
$956$	−1.19679e15	−	2.07290e15i	−0.0484730	−	0.0839577i
$957$	−8.77428e14			−0.0353342
$958$	−3.99510e15			−0.159962
$959$	−3.92911e14	−	6.80542e14i	−0.0156420	−	0.0270927i
$960$	6.68502e14	+	1.15788e15i	0.0264613	+	0.0458323i
$961$	6.26161e16			2.46438
$962$	−2.35115e14			−0.00920061
$963$	3.15579e15	+	5.46598e15i	0.122790	+	0.212679i
$964$	7.86708e15	−	1.36262e16i	0.304362	−	0.527170i
$965$	−5.81497e15	−	1.00718e16i	−0.223690	−	0.387443i
$966$	9.43353e14	−	1.63393e15i	0.0360828	−	0.0624972i
$967$	−6.54532e15	+	1.13368e16i	−0.248934	+	0.431167i	−0.963230	−	0.268677i	$-0.913414\pi$
$967$	−6.54532e15	+	1.13368e16i	−0.248934	+	0.431167i	0.714296	+	0.699844i	$0.246747\pi$
$968$	7.45292e15			0.281846
$969$	3.93539e15	−	4.88624e15i	0.147981	−	0.183736i
$970$	−9.95860e15			−0.372352
$971$	2.65453e15	−	4.59779e15i	0.0986921	−	0.170940i	−0.812451	−	0.583029i	$-0.801867\pi$
$971$	2.65453e15	−	4.59779e15i	0.0986921	−	0.170940i	0.911144	+	0.412089i	$0.135201\pi$
$972$	4.33812e14	−	7.51384e14i	0.0160375	−	0.0277778i
$973$	8.48202e15	+	1.46913e16i	0.311802	+	0.540056i
$974$	−2.90557e15	+	5.03259e15i	−0.106208	+	0.183957i
$975$	−1.16601e14	−	2.01958e14i	−0.00423814	−	0.00734068i
$976$	−9.07047e15			−0.327835
$977$	−3.88781e16			−1.39729			−0.698643	−	0.715470i	$-0.746212\pi$
$977$	−3.88781e16			−1.39729			−0.698643	+	0.715470i	$0.746212\pi$
$978$	−2.80369e15	−	4.85614e15i	−0.100200	−	0.173551i
$979$	9.60959e15	+	1.66443e16i	0.341507	+	0.591508i
$980$	1.03677e16			0.366388
$981$	−1.18113e16			−0.415066
$982$	−8.94884e14	−	1.54998e15i	−0.0312718	−	0.0541644i
$983$	−8.31961e14	+	1.44100e15i	−0.0289107	+	0.0500748i	−0.880119	−	0.474754i	$-0.842537\pi$
$983$	−8.31961e14	+	1.44100e15i	−0.0289107	+	0.0500748i	0.851208	+	0.524828i	$0.175871\pi$
$984$	4.75188e15	+	8.23051e15i	0.164207	+	0.284416i
$985$	−1.10730e16	+	1.91790e16i	−0.380510	+	0.659062i
$986$	−5.74516e14	+	9.95092e14i	−0.0196327	+	0.0340048i
$987$	−2.52762e16			−0.858950
$988$	4.64330e14	+	7.22806e13i	0.0156915	+	0.00244264i
$989$	6.65712e15			0.223721
$990$	−1.16459e15	+	2.01713e15i	−0.0389206	+	0.0674124i
$991$	2.71188e16	−	4.69711e16i	0.901290	−	1.56108i	0.0754697	−	0.997148i	$-0.475954\pi$
$991$	2.71188e16	−	4.69711e16i	0.901290	−	1.56108i	0.825821	−	0.563933i	$-0.190712\pi$
$992$	4.97762e15	+	8.62150e15i	0.164516	+	0.284950i
$993$	1.01807e16	−	1.76335e16i	0.334624	−	0.579586i
$994$	1.24100e16	+	2.14947e16i	0.405644	+	0.702596i
$995$	8.21510e15			0.267046
$996$	−1.25359e16			−0.405257
$997$	−2.07157e16	−	3.58806e16i	−0.666002	−	1.15355i	−0.979013	−	0.203800i	$-0.934671\pi$
$997$	−2.07157e16	−	3.58806e16i	−0.666002	−	1.15355i	0.313010	−	0.949750i	$-0.398663\pi$
$998$	7.53331e15	+	1.30481e16i	0.240862	+	0.417185i
$999$	−2.47952e15			−0.0788419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.12.e.b.49.4	yes	18
19.7	even	3	inner	114.12.e.b.7.4	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.12.e.b.7.4	✓	18	19.7	even	3	inner
114.12.e.b.49.4	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	114.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(16.0000 - 27.7128i) q^{2} +(121.500 - 210.444i) q^{3} +(-512.000 - 886.810i) q^{4} +(-2562.10 + 4437.69i) q^{5} +(-3888.00 - 6734.21i) q^{6} +62874.4 q^{7} -32768.0 q^{8} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})\)	\(q+(16.0000 - 27.7128i) q^{2} +(121.500 - 210.444i) q^{3} +(-512.000 - 886.810i) q^{4} +(-2562.10 + 4437.69i) q^{5} +(-3888.00 - 6734.21i) q^{6} +62874.4 q^{7} -32768.0 q^{8} +(-29524.5 - 51137.9i) q^{9} +(81987.3 + 142006. i) q^{10} -240555. q^{11} -248832. q^{12} +(-21259.4 - 36822.4i) q^{13} +(1.00599e6 - 1.74243e6i) q^{14} +(622591. + 1.07836e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-1.19608e6 + 2.07167e6i) q^{17} -1.88957e6 q^{18} +(-3.89460e6 - 1.00659e7i) q^{19} +5.24719e6 q^{20} +(7.63924e6 - 1.32316e7i) q^{21} +(-3.84887e6 + 6.66644e6i) q^{22} +(1.92950e6 + 3.34198e6i) q^{23} +(-3.98131e6 + 6.89583e6i) q^{24} +(1.12853e7 + 1.95467e7i) q^{25} -1.36060e6 q^{26} -1.43489e7 q^{27} +(-3.21917e7 - 5.57577e7i) q^{28} +(7.50519e6 + 1.29994e7i) q^{29} +3.98458e7 q^{30} +2.96689e8 q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(-2.92274e7 + 5.06233e7i) q^{33} +(3.82746e7 + 6.62936e7i) q^{34} +(-1.61091e8 + 2.79017e8i) q^{35} +(-3.02331e7 + 5.23652e7i) q^{36} +1.72802e8 q^{37} +(-3.41268e8 - 5.31240e7i) q^{38} -1.03321e7 q^{39} +(8.39550e7 - 1.45414e8i) q^{40} +(5.96774e8 - 1.03364e9i) q^{41} +(-2.44456e8 - 4.23410e8i) q^{42} +(8.62547e8 - 1.49397e9i) q^{43} +(1.23164e8 + 2.13326e8i) q^{44} +3.02579e8 q^{45} +1.23488e8 q^{46} +(-8.27184e8 - 1.43272e9i) q^{47} +(1.27402e8 + 2.20667e8i) q^{48} +1.97587e9 q^{49} +7.22260e8 q^{50} +(2.90648e8 + 5.03417e8i) q^{51} +(-2.17696e7 + 3.77061e7i) q^{52} +(-2.89279e9 - 5.01045e9i) q^{53} +(-2.29583e8 + 3.97649e8i) q^{54} +(6.16326e8 - 1.06751e9i) q^{55} -2.06027e9 q^{56} +(-2.59150e9 - 4.03410e8i) q^{57} +4.80332e8 q^{58} +(-9.80800e8 + 1.69879e9i) q^{59} +(6.37533e8 - 1.10424e9i) q^{60} +(4.32514e9 + 7.49136e9i) q^{61} +(4.74703e9 - 8.22210e9i) q^{62} +(-1.85634e9 - 3.21527e9i) q^{63} +1.07374e9 q^{64} +2.17875e8 q^{65} +(9.35276e8 + 1.61995e9i) q^{66} +(-5.97827e9 - 1.03547e10i) q^{67} +2.44958e9 q^{68} +9.37735e8 q^{69} +(5.15491e9 + 8.92856e9i) q^{70} +(-6.16803e9 + 1.06833e10i) q^{71} +(9.67459e8 + 1.67569e9i) q^{72} +(1.72720e9 - 2.99160e9i) q^{73} +(2.76483e9 - 4.78883e9i) q^{74} +5.48466e9 q^{75} +(-6.93250e9 + 8.60751e9i) q^{76} -1.51247e10 q^{77} +(-1.65313e8 + 2.86331e8i) q^{78} +(-4.61795e9 + 7.99853e9i) q^{79} +(-2.68656e9 - 4.65326e9i) q^{80} +(-1.74339e9 + 3.01964e9i) q^{81} +(-1.90968e10 - 3.30766e10i) q^{82} +5.03791e10 q^{83} -1.56452e10 q^{84} +(-6.12897e9 - 1.06157e10i) q^{85} +(-2.76015e10 - 4.78072e10i) q^{86} +3.64752e9 q^{87} +7.88249e9 q^{88} +(-3.99477e10 - 6.91914e10i) q^{89} +(4.84127e9 - 8.38532e9i) q^{90} +(-1.33667e9 - 2.31519e9i) q^{91} +(1.97580e9 - 3.42219e9i) q^{92} +(3.60478e10 - 6.24366e10i) q^{93} -5.29398e10 q^{94} +(5.46477e10 + 8.50682e9i) q^{95} +8.15373e9 q^{96} +(-3.03663e10 + 5.25960e10i) q^{97} +(3.16139e10 - 5.47568e10i) q^{98} +(7.10225e9 + 1.23015e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 288 q^{2} + 2187 q^{3} - 9216 q^{4} + 10498 q^{5} - 69984 q^{6} + 33594 q^{7} - 589824 q^{8} - 531441 q^{9}+O(q^{10}) \) 18 * q + 288 * q^2 + 2187 * q^3 - 9216 * q^4 + 10498 * q^5 - 69984 * q^6 + 33594 * q^7 - 589824 * q^8 - 531441 * q^9	\( 18 q + 288 q^{2} + 2187 q^{3} - 9216 q^{4} + 10498 q^{5} - 69984 q^{6} + 33594 q^{7} - 589824 q^{8} - 531441 q^{9} - 335936 q^{10} - 1590640 q^{11} - 4478976 q^{12} - 1629109 q^{13} + 537504 q^{14} - 2551014 q^{15} - 9437184 q^{16} + 8652808 q^{17} - 34012224 q^{18} + 15090788 q^{19} - 21499904 q^{20} + 4081671 q^{21} - 25450240 q^{22} - 601786 q^{23} - 71663616 q^{24} - 162553579 q^{25} - 104262976 q^{26} - 258280326 q^{27} - 17200128 q^{28} - 43747792 q^{29} - 163264896 q^{30} + 526704522 q^{31} + 301989888 q^{32} - 193262760 q^{33} - 276889856 q^{34} + 325495254 q^{35} - 544195584 q^{36} + 1732073990 q^{37} + 550585952 q^{38} - 791746974 q^{39} - 343998464 q^{40} - 581264904 q^{41} - 130613472 q^{42} + 1231123053 q^{43} + 814407680 q^{44} - 1239792804 q^{45} - 38514304 q^{46} - 2452492126 q^{47} + 2293235712 q^{48} + 3293812732 q^{49} - 10403429056 q^{50} - 2102632344 q^{51} - 1668207616 q^{52} + 2454345210 q^{53} - 4132485216 q^{54} - 1870156300 q^{55} - 1100808192 q^{56} + 4181012073 q^{57} - 2799858688 q^{58} - 5356106228 q^{59} - 2612238336 q^{60} - 10202609247 q^{61} + 8427272352 q^{62} - 991846053 q^{63} + 19327352832 q^{64} + 25295139500 q^{65} + 6184408320 q^{66} + 2114873497 q^{67} - 17720950784 q^{68} - 292467996 q^{69} - 10415848128 q^{70} - 30585512466 q^{71} + 17414258688 q^{72} - 27334067553 q^{73} + 27713183840 q^{74} - 79001039394 q^{75} + 2165783552 q^{76} + 37560737032 q^{77} - 12667951584 q^{78} + 7599860935 q^{79} + 11007950848 q^{80} - 31381059609 q^{81} + 18600476928 q^{82} - 18534241528 q^{83} - 8359262208 q^{84} - 41278195680 q^{85} - 39395937696 q^{86} - 21261426912 q^{87} + 52122091520 q^{88} - 97795224572 q^{89} - 19836684864 q^{90} + 157694429951 q^{91} - 616228864 q^{92} + 63994599423 q^{93} - 156959496064 q^{94} + 213102831842 q^{95} + 146767085568 q^{96} - 149834378270 q^{97} + 52701003712 q^{98} + 46962850680 q^{99}+O(q^{100}) \) 18 * q + 288 * q^2 + 2187 * q^3 - 9216 * q^4 + 10498 * q^5 - 69984 * q^6 + 33594 * q^7 - 589824 * q^8 - 531441 * q^9 - 335936 * q^10 - 1590640 * q^11 - 4478976 * q^12 - 1629109 * q^13 + 537504 * q^14 - 2551014 * q^15 - 9437184 * q^16 + 8652808 * q^17 - 34012224 * q^18 + 15090788 * q^19 - 21499904 * q^20 + 4081671 * q^21 - 25450240 * q^22 - 601786 * q^23 - 71663616 * q^24 - 162553579 * q^25 - 104262976 * q^26 - 258280326 * q^27 - 17200128 * q^28 - 43747792 * q^29 - 163264896 * q^30 + 526704522 * q^31 + 301989888 * q^32 - 193262760 * q^33 - 276889856 * q^34 + 325495254 * q^35 - 544195584 * q^36 + 1732073990 * q^37 + 550585952 * q^38 - 791746974 * q^39 - 343998464 * q^40 - 581264904 * q^41 - 130613472 * q^42 + 1231123053 * q^43 + 814407680 * q^44 - 1239792804 * q^45 - 38514304 * q^46 - 2452492126 * q^47 + 2293235712 * q^48 + 3293812732 * q^49 - 10403429056 * q^50 - 2102632344 * q^51 - 1668207616 * q^52 + 2454345210 * q^53 - 4132485216 * q^54 - 1870156300 * q^55 - 1100808192 * q^56 + 4181012073 * q^57 - 2799858688 * q^58 - 5356106228 * q^59 - 2612238336 * q^60 - 10202609247 * q^61 + 8427272352 * q^62 - 991846053 * q^63 + 19327352832 * q^64 + 25295139500 * q^65 + 6184408320 * q^66 + 2114873497 * q^67 - 17720950784 * q^68 - 292467996 * q^69 - 10415848128 * q^70 - 30585512466 * q^71 + 17414258688 * q^72 - 27334067553 * q^73 + 27713183840 * q^74 - 79001039394 * q^75 + 2165783552 * q^76 + 37560737032 * q^77 - 12667951584 * q^78 + 7599860935 * q^79 + 11007950848 * q^80 - 31381059609 * q^81 + 18600476928 * q^82 - 18534241528 * q^83 - 8359262208 * q^84 - 41278195680 * q^85 - 39395937696 * q^86 - 21261426912 * q^87 + 52122091520 * q^88 - 97795224572 * q^89 - 19836684864 * q^90 + 157694429951 * q^91 - 616228864 * q^92 + 63994599423 * q^93 - 156959496064 * q^94 + 213102831842 * q^95 + 146767085568 * q^96 - 149834378270 * q^97 + 52701003712 * q^98 + 46962850680 * q^99

Introduction

L-functions

Modular forms

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