LMFDB - Embedded newform 114.12.e.b.49.1

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			49.1
Root			$4884.76 + 8460.66i$ of defining polynomial
Character	$\chi$	$=$	114.49
Dual form			114.12.e.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.0000 - 27.7128i) q^{2} +(121.500 - 210.444i) q^{3} +(-512.000 - 886.810i) q^{4} +(-4301.26 + 7450.01i) q^{5} +(-3888.00 - 6734.21i) q^{6} -61427.8 q^{7} -32768.0 q^{8} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})$	\(q+(16.0000 - 27.7128i) q^{2} +(121.500 - 210.444i) q^{3} +(-512.000 - 886.810i) q^{4} +(-4301.26 + 7450.01i) q^{5} +(-3888.00 - 6734.21i) q^{6} -61427.8 q^{7} -32768.0 q^{8} +(-29524.5 - 51137.9i) q^{9} +(137640. + 238400. i) q^{10} -379161. q^{11} -248832. q^{12} +(-181193. - 313836. i) q^{13} +(-982845. + 1.70234e6i) q^{14} +(1.04521e6 + 1.81035e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-1.29160e6 + 2.23713e6i) q^{17} -1.88957e6 q^{18} +(-1.07765e7 - 597529. i) q^{19} +8.80899e6 q^{20} +(-7.46348e6 + 1.29271e7i) q^{21} +(-6.06658e6 + 1.05076e7i) q^{22} +(748308. + 1.29611e6i) q^{23} +(-3.98131e6 + 6.89583e6i) q^{24} +(-1.25877e7 - 2.18025e7i) q^{25} -1.15964e7 q^{26} -1.43489e7 q^{27} +(3.14510e7 + 5.44748e7i) q^{28} +(-3.32853e7 - 5.76518e7i) q^{29} +6.68932e7 q^{30} +2.30143e7 q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(-4.60681e7 + 7.97922e7i) q^{33} +(4.13314e7 + 7.15880e7i) q^{34} +(2.64217e8 - 4.57637e8i) q^{35} +(-3.02331e7 + 5.23652e7i) q^{36} +5.15865e8 q^{37} +(-1.88983e8 + 2.89087e8i) q^{38} -8.80600e7 q^{39} +(1.40944e8 - 2.44122e8i) q^{40} +(4.12955e8 - 7.15260e8i) q^{41} +(2.38831e8 + 4.13668e8i) q^{42} +(-7.05905e7 + 1.22266e8i) q^{43} +(1.94130e8 + 3.36244e8i) q^{44} +5.07971e8 q^{45} +4.78917e7 q^{46} +(1.25786e9 + 2.17867e9i) q^{47} +(1.27402e8 + 2.20667e8i) q^{48} +1.79605e9 q^{49} -8.05610e8 q^{50} +(3.13860e8 + 5.43621e8i) q^{51} +(-1.85542e8 + 3.21368e8i) q^{52} +(1.39897e9 + 2.42309e9i) q^{53} +(-2.29583e8 + 3.97649e8i) q^{54} +(1.63087e9 - 2.82475e9i) q^{55} +2.01287e9 q^{56} +(-1.43509e9 + 2.19525e9i) q^{57} -2.13026e9 q^{58} +(4.96561e9 - 8.60068e9i) q^{59} +(1.07029e9 - 1.85380e9i) q^{60} +(-6.05932e9 - 1.04950e10i) q^{61} +(3.68228e8 - 6.37790e8i) q^{62} +(1.81363e9 + 3.14129e9i) q^{63} +1.07374e9 q^{64} +3.11744e9 q^{65} +(1.47418e9 + 2.55335e9i) q^{66} +(3.21049e9 + 5.56074e9i) q^{67} +2.64521e9 q^{68} +3.63678e8 q^{69} +(-8.45495e9 - 1.46444e10i) q^{70} +(3.92758e9 - 6.80278e9i) q^{71} +(9.67459e8 + 1.67569e9i) q^{72} +(-1.13902e10 + 1.97285e10i) q^{73} +(8.25383e9 - 1.42961e10i) q^{74} -6.11760e9 q^{75} +(4.98768e9 + 9.86265e9i) q^{76} +2.32910e10 q^{77} +(-1.40896e9 + 2.44039e9i) q^{78} +(-8.86289e9 + 1.53510e10i) q^{79} +(-4.51020e9 - 7.81190e9i) q^{80} +(-1.74339e9 + 3.01964e9i) q^{81} +(-1.32146e10 - 2.28883e10i) q^{82} -1.54701e9 q^{83} +1.52852e10 q^{84} +(-1.11111e10 - 1.92449e10i) q^{85} +(2.25889e9 + 3.91252e9i) q^{86} -1.61766e10 q^{87} +1.24244e10 q^{88} +(1.58363e10 + 2.74293e10i) q^{89} +(8.12753e9 - 1.40773e10i) q^{90} +(1.11303e10 + 1.92783e10i) q^{91} +(7.66267e8 - 1.32721e9i) q^{92} +(2.79623e9 - 4.84322e9i) q^{93} +8.05028e10 q^{94} +(5.08042e10 - 7.77149e10i) q^{95} +8.15373e9 q^{96} +(-1.60086e10 + 2.77277e10i) q^{97} +(2.87368e10 - 4.97735e10i) q^{98} +(1.11945e10 + 1.93895e10i) 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
$5$	−4301.26	+	7450.01i	−0.615547	+	1.06616i	0.374742	+	0.927129i	$0.377731\pi$
$5$	−4301.26	+	7450.01i	−0.615547	+	1.06616i	−0.990288	+	0.139029i	$0.955602\pi$
$6$	−3888.00	−	6734.21i	−0.204124	−	0.353553i
$7$	−61427.8			−1.38142			−0.690710	−	0.723132i	$-0.742702\pi$
$7$	−61427.8			−1.38142			−0.690710	+	0.723132i	$0.742702\pi$
$8$	−32768.0			−0.353553
$9$	−29524.5	−	51137.9i	−0.166667	−	0.288675i
$10$	137640.	+	238400.i	0.435257	+	0.753888i
$11$	−379161.			−0.709846			−0.354923	−	0.934896i	$-0.615493\pi$
$11$	−379161.			−0.709846			−0.354923	+	0.934896i	$0.615493\pi$
$12$	−248832.			−0.288675
$13$	−181193.	−	313836.i	−0.135349	−	0.234431i	0.790382	−	0.612614i	$-0.209882\pi$
$13$	−181193.	−	313836.i	−0.135349	−	0.234431i	−0.925731	+	0.378184i	$0.876549\pi$
$14$	−982845.	+	1.70234e6i	−0.488406	+	0.845944i
$15$	1.04521e6	+	1.81035e6i	0.355386	+	0.615547i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−1.29160e6	+	2.23713e6i	−0.220628	+	0.382139i	−0.954999	−	0.296610i	$-0.904144\pi$
$17$	−1.29160e6	+	2.23713e6i	−0.220628	+	0.382139i	0.734371	+	0.678748i	$0.237477\pi$
$18$	−1.88957e6			−0.235702
$19$	−1.07765e7	−	597529.i	−0.998466	−	0.0553623i
$19$	−1.07765e7	−	597529.i	−0.998466	−	0.0553623i
$20$	8.80899e6			0.615547
$21$	−7.46348e6	+	1.29271e7i	−0.398782	+	0.690710i
$22$	−6.06658e6	+	1.05076e7i	−0.250968	+	0.434690i
$23$	748308.	+	1.29611e6i	0.0242425	+	0.0419892i	0.877892	−	0.478858i	$-0.158949\pi$
$23$	748308.	+	1.29611e6i	0.0242425	+	0.0419892i	−0.853650	+	0.520848i	$0.825616\pi$
$24$	−3.98131e6	+	6.89583e6i	−0.102062	+	0.176777i
$25$	−1.25877e7	−	2.18025e7i	−0.257795	−	0.446514i
$26$	−1.15964e7			−0.191412
$27$	−1.43489e7			−0.192450
$28$	3.14510e7	+	5.44748e7i	0.345355	+	0.598172i
$29$	−3.32853e7	−	5.76518e7i	−0.301344	−	0.521944i	0.675096	−	0.737730i	$-0.264102\pi$
$29$	−3.32853e7	−	5.76518e7i	−0.301344	−	0.521944i	−0.976441	+	0.215786i	$0.930769\pi$
$30$	6.68932e7			0.502592
$31$	2.30143e7			0.144380			0.0721902	−	0.997391i	$-0.477001\pi$
$31$	2.30143e7			0.144380			0.0721902	+	0.997391i	$0.477001\pi$
$32$	1.67772e7	+	2.90590e7i	0.0883883	+	0.153093i
$33$	−4.60681e7	+	7.97922e7i	−0.204915	+	0.354923i
$34$	4.13314e7	+	7.15880e7i	0.156008	+	0.270213i
$35$	2.64217e8	−	4.57637e8i	0.850328	−	1.47281i
$36$	−3.02331e7	+	5.23652e7i	−0.0833333	+	0.144338i
$37$	5.15865e8			1.22300			0.611500	−	0.791245i	$-0.290567\pi$
$37$	5.15865e8			1.22300			0.611500	+	0.791245i	$0.290567\pi$
$38$	−1.88983e8	+	2.89087e8i	−0.386914	+	0.591860i
$39$	−8.80600e7			−0.156287
$40$	1.40944e8	−	2.44122e8i	0.217629	−	0.376944i
$41$	4.12955e8	−	7.15260e8i	0.556663	−	0.964168i	−0.441110	−	0.897453i	$-0.645415\pi$
$41$	4.12955e8	−	7.15260e8i	0.556663	−	0.964168i	0.997772	−	0.0667146i	$-0.0212517\pi$
$42$	2.38831e8	+	4.13668e8i	0.281981	+	0.488406i
$43$	−7.05905e7	+	1.22266e8i	−0.0732267	+	0.126832i	−0.900314	−	0.435241i	$-0.856663\pi$
$43$	−7.05905e7	+	1.22266e8i	−0.0732267	+	0.126832i	0.827087	+	0.562074i	$0.189996\pi$
$44$	1.94130e8	+	3.36244e8i	0.177461	+	0.307372i
$45$	5.07971e8			0.410364
$46$	4.78917e7			0.0342840
$47$	1.25786e9	+	2.17867e9i	0.800005	+	1.38565i	0.919612	+	0.392829i	$0.128503\pi$
$47$	1.25786e9	+	2.17867e9i	0.800005	+	1.38565i	−0.119606	+	0.992821i	$0.538163\pi$
$48$	1.27402e8	+	2.20667e8i	0.0721688	+	0.125000i
$49$	1.79605e9			0.908321
$50$	−8.05610e8			−0.364578
$51$	3.13860e8	+	5.43621e8i	0.127380	+	0.220628i
$52$	−1.85542e8	+	3.21368e8i	−0.0676743	+	0.117215i
$53$	1.39897e9	+	2.42309e9i	0.459507	+	0.795889i	0.998935	−	0.0461425i	$-0.0146928\pi$
$53$	1.39897e9	+	2.42309e9i	0.459507	+	0.795889i	−0.539428	+	0.842032i	$0.681359\pi$
$54$	−2.29583e8	+	3.97649e8i	−0.0680414	+	0.117851i
$55$	1.63087e9	−	2.82475e9i	0.436943	−	0.756808i
$56$	2.01287e9			0.488406
$57$	−1.43509e9	+	2.19525e9i	−0.315914	+	0.483251i
$58$	−2.13026e9			−0.426165
$59$	4.96561e9	−	8.60068e9i	0.904245	−	1.56620i	0.0823186	−	0.996606i	$-0.473767\pi$
$59$	4.96561e9	−	8.60068e9i	0.904245	−	1.56620i	0.821927	−	0.569593i	$-0.192899\pi$
$60$	1.07029e9	−	1.85380e9i	0.177693	−	0.307773i
$61$	−6.05932e9	−	1.04950e10i	−0.918565	−	1.59100i	−0.801597	−	0.597865i	$-0.796016\pi$
$61$	−6.05932e9	−	1.04950e10i	−0.918565	−	1.59100i	−0.116968	−	0.993136i	$-0.537317\pi$
$62$	3.68228e8	−	6.37790e8i	0.0510461	−	0.0884145i
$63$	1.81363e9	+	3.14129e9i	0.230237	+	0.398782i
$64$	1.07374e9			0.125000
$65$	3.11744e9			0.333254
$66$	1.47418e9	+	2.55335e9i	0.144897	+	0.250968i
$67$	3.21049e9	+	5.56074e9i	0.290510	+	0.503177i	0.973930	−	0.226847i	$-0.0728419\pi$
$67$	3.21049e9	+	5.56074e9i	0.290510	+	0.503177i	−0.683421	+	0.730025i	$0.739509\pi$
$68$	2.64521e9			0.220628
$69$	3.63678e8			0.0279928
$70$	−8.45495e9	−	1.46444e10i	−0.601273	−	1.04144i
$71$	3.92758e9	−	6.80278e9i	0.258348	−	0.447471i	−0.707452	−	0.706762i	$-0.750155\pi$
$71$	3.92758e9	−	6.80278e9i	0.258348	−	0.447471i	0.965799	+	0.259290i	$0.0834886\pi$
$72$	9.67459e8	+	1.67569e9i	0.0589256	+	0.102062i
$73$	−1.13902e10	+	1.97285e10i	−0.643068	+	1.11383i	0.341676	+	0.939818i	$0.389006\pi$
$73$	−1.13902e10	+	1.97285e10i	−0.643068	+	1.11383i	−0.984744	+	0.174009i	$0.944328\pi$
$74$	8.25383e9	−	1.42961e10i	0.432396	−	0.748931i
$75$	−6.11760e9			−0.297676
$76$	4.98768e9	+	9.86265e9i	0.225644	+	0.446189i
$77$	2.32910e10			0.980595
$78$	−1.40896e9	+	2.44039e9i	−0.0552559	+	0.0957060i
$79$	−8.86289e9	+	1.53510e10i	−0.324061	+	0.561289i	−0.981322	−	0.192374i	$-0.938381\pi$
$79$	−8.86289e9	+	1.53510e10i	−0.324061	+	0.561289i	0.657261	+	0.753663i	$0.271715\pi$
$80$	−4.51020e9	−	7.81190e9i	−0.153887	−	0.266539i
$81$	−1.74339e9	+	3.01964e9i	−0.0555556	+	0.0962250i
$82$	−1.32146e10	−	2.28883e10i	−0.393620	−	0.681770i
$83$	−1.54701e9			−0.0431087			−0.0215543	−	0.999768i	$-0.506861\pi$
$83$	−1.54701e9			−0.0431087			−0.0215543	+	0.999768i	$0.506861\pi$
$84$	1.52852e10			0.398782
$85$	−1.11111e10	−	1.92449e10i	−0.271614	−	0.470449i
$86$	2.25889e9	+	3.91252e9i	0.0517791	+	0.0896840i
$87$	−1.61766e10			−0.347962
$88$	1.24244e10			0.250968
$89$	1.58363e10	+	2.74293e10i	0.300614	+	0.520679i	0.976275	−	0.216533i	$-0.0694750\pi$
$89$	1.58363e10	+	2.74293e10i	0.300614	+	0.520679i	−0.675661	+	0.737212i	$0.736142\pi$
$90$	8.12753e9	−	1.40773e10i	0.145086	−	0.251296i
$91$	1.11303e10	+	1.92783e10i	0.186973	+	0.323847i
$92$	7.66267e8	−	1.32721e9i	0.0121212	−	0.0209946i
$93$	2.79623e9	−	4.84322e9i	0.0416790	−	0.0721902i
$94$	8.05028e10			1.13138
$95$	5.08042e10	−	7.77149e10i	0.673628	−	1.03044i
$96$	8.15373e9			0.102062
$97$	−1.60086e10	+	2.77277e10i	−0.189282	+	0.327846i	−0.945011	−	0.327038i	$-0.893949\pi$
$97$	−1.60086e10	+	2.77277e10i	−0.189282	+	0.327846i	0.755729	+	0.654884i	$0.227283\pi$
$98$	2.87368e10	−	4.97735e10i	0.321140	−	0.556231i
$99$	1.11945e10	+	1.93895e10i	0.118308	+	0.204915i
$100$	−1.28898e10	+	2.23257e10i	−0.128898	+	0.223257i
$101$	−4.10937e10	−	7.11764e10i	−0.389052	−	0.673858i	0.603270	−	0.797537i	$-0.293864\pi$
$101$	−4.10937e10	−	7.11764e10i	−0.389052	−	0.673858i	−0.992322	+	0.123679i	$0.960531\pi$
$102$	2.00870e10			0.180142
$103$	9.29632e10			0.790145			0.395072	−	0.918650i	$-0.370720\pi$
$103$	9.29632e10			0.790145			0.395072	+	0.918650i	$0.370720\pi$
$104$	5.93735e9	+	1.02838e10i	0.0478530	+	0.0828838i
$105$	−6.42048e10	−	1.11206e11i	−0.490937	−	0.850328i
$106$	8.95343e10			0.649841
$107$	6.76793e10			0.466493			0.233246	−	0.972418i	$-0.425065\pi$
$107$	6.76793e10			0.466493			0.233246	+	0.972418i	$0.425065\pi$
$108$	7.34664e9	+	1.27248e10i	0.0481125	+	0.0833333i
$109$	2.87757e10	−	4.98409e10i	0.179135	−	0.310270i	−0.762450	−	0.647047i	$-0.776004\pi$
$109$	2.87757e10	−	4.98409e10i	0.179135	−	0.310270i	0.941584	+	0.336777i	$0.109337\pi$
$110$	−5.21879e10	−	9.03921e10i	−0.308965	−	0.535144i
$111$	6.26776e10	−	1.08561e11i	0.353050	−	0.611500i
$112$	3.22059e10	−	5.57822e10i	0.172678	−	0.299086i
$113$	3.37530e10			0.172338			0.0861689	−	0.996281i	$-0.472538\pi$
$113$	3.37530e10			0.172338			0.0861689	+	0.996281i	$0.472538\pi$
$114$	3.78752e10	+	7.48945e10i	0.184238	+	0.364312i
$115$	−1.28747e10			−0.0596895
$116$	−3.40841e10	+	5.90354e10i	−0.150672	+	0.260972i
$117$	−1.06993e10	+	1.85317e10i	−0.0451162	+	0.0781436i
$118$	−1.58899e11	−	2.75222e11i	−0.639398	−	1.10747i
$119$	7.93405e10	−	1.37422e11i	0.304780	−	0.527894i
$120$	−3.42493e10	−	5.93216e10i	−0.125648	−	0.217629i
$121$	−1.41549e11			−0.496119
$122$	−3.87796e11			−1.29905
$123$	−1.00348e11	−	1.73808e11i	−0.321389	−	0.556663i
$124$	−1.17833e10	−	2.04093e10i	−0.0360951	−	0.0625185i
$125$	−2.03474e11			−0.596353
$126$	1.16072e11			0.325604
$127$	−1.81963e11	−	3.15170e11i	−0.488723	−	0.846494i	0.511192	−	0.859466i	$-0.329204\pi$
$127$	−1.81963e11	−	3.15170e11i	−0.488723	−	0.846494i	−0.999916	+	0.0129725i	$0.995871\pi$
$128$	1.71799e10	−	2.97564e10i	0.0441942	−	0.0765466i
$129$	1.71535e10	+	2.97107e10i	0.0422775	+	0.0732267i
$130$	4.98791e10	−	8.63931e10i	0.117823	−	0.204075i
$131$	1.68074e11	−	2.91113e11i	0.380635	−	0.659280i	−0.610518	−	0.792003i	$-0.709039\pi$
$131$	1.68074e11	−	2.91113e11i	0.380635	−	0.659280i	0.991153	+	0.132723i	$0.0423720\pi$
$132$	9.43474e10			0.204915
$133$	6.61977e11	+	3.67049e10i	1.37930	+	0.0764786i
$134$	2.05472e11			0.410843
$135$	6.17184e10	−	1.06899e11i	0.118462	−	0.205182i
$136$	4.23233e10	−	7.33061e10i	0.0780038	−	0.135107i
$137$	4.38166e11	+	7.58927e11i	0.775668	+	1.34350i	0.934418	+	0.356178i	$0.115920\pi$
$137$	4.38166e11	+	7.58927e11i	0.775668	+	1.34350i	−0.158750	+	0.987319i	$0.550746\pi$
$138$	5.81884e9	−	1.00785e10i	0.00989695	−	0.0171420i
$139$	−3.91597e11	−	6.78266e11i	−0.640115	−	1.10871i	−0.985407	−	0.170216i	$-0.945553\pi$
$139$	−3.91597e11	−	6.78266e11i	−0.640115	−	1.10871i	0.345292	−	0.938495i	$-0.387780\pi$
$140$	−5.41117e11			−0.850328
$141$	6.11318e11			0.923767
$142$	−1.25683e11	−	2.17689e11i	−0.182679	−	0.316410i
$143$	6.87015e10	+	1.18995e11i	0.0960767	+	0.166410i
$144$	6.19174e10			0.0833333
$145$	5.72675e11			0.741966
$146$	3.64488e11	+	6.31311e11i	0.454718	+	0.787595i
$147$	2.18220e11	−	3.77968e11i	0.262210	−	0.454161i
$148$	−2.64123e11	−	4.57474e11i	−0.305750	−	0.529574i
$149$	−6.51051e10	+	1.12765e11i	−0.0726258	+	0.125792i	−0.900051	−	0.435784i	$-0.856471\pi$
$149$	−6.51051e10	+	1.12765e11i	−0.0726258	+	0.125792i	0.827426	+	0.561575i	$0.189805\pi$
$150$	−9.78816e10	+	1.69536e11i	−0.105244	+	0.182289i
$151$	9.77059e11			1.01286			0.506428	−	0.862282i	$-0.330966\pi$
$151$	9.77059e11			1.01286			0.506428	+	0.862282i	$0.330966\pi$
$152$	3.53125e11	+	1.95798e10i	0.353011	+	0.0195735i
$153$	1.52536e11			0.147085
$154$	3.72657e11	−	6.45460e11i	0.346693	−	0.600490i
$155$	−9.89904e10	+	1.71456e11i	−0.0888728	+	0.153932i
$156$	4.50867e10	+	7.80925e10i	0.0390718	+	0.0676743i
$157$	1.07259e11	−	1.85778e11i	0.0897401	−	0.155434i	−0.817661	−	0.575700i	$-0.804730\pi$
$157$	1.07259e11	−	1.85778e11i	0.0897401	−	0.155434i	0.907401	+	0.420265i	$0.138063\pi$
$158$	2.83612e11	+	4.91231e11i	0.229145	+	0.396891i
$159$	6.79901e11			0.530593
$160$	−2.88653e11			−0.217629
$161$	−4.59669e10	−	7.96170e10i	−0.0334891	−	0.0580047i
$162$	5.57886e10	+	9.66286e10i	0.0392837	+	0.0680414i
$163$	1.17582e12			0.800402			0.400201	−	0.916427i	$-0.368940\pi$
$163$	1.17582e12			0.800402			0.400201	+	0.916427i	$0.368940\pi$
$164$	−8.45733e11			−0.556663
$165$	−3.96302e11	−	6.86415e11i	−0.252269	−	0.436943i
$166$	−2.47522e10	+	4.28721e10i	−0.0152412	+	0.0263986i
$167$	−6.00702e11	−	1.04045e12i	−0.357864	−	0.619839i	0.629740	−	0.776806i	$-0.283162\pi$
$167$	−6.00702e11	−	1.04045e12i	−0.357864	−	0.619839i	−0.987604	+	0.156967i	$0.949828\pi$
$168$	2.44563e11	−	4.23596e11i	0.140991	−	0.244203i
$169$	8.30418e11	−	1.43833e12i	0.463361	−	0.802566i
$170$	−7.11108e11			−0.384120
$171$	2.87615e11	+	5.68730e11i	0.150429	+	0.297459i
$172$	1.44569e11			0.0732267
$173$	5.56630e11	−	9.64111e11i	0.273094	−	0.473013i	−0.696558	−	0.717500i	$-0.745286\pi$
$173$	5.56630e11	−	9.64111e11i	0.273094	−	0.473013i	0.969653	+	0.244487i	$0.0786195\pi$
$174$	−2.58826e11	+	4.48300e11i	−0.123023	+	0.213083i
$175$	7.73232e11	+	1.33928e12i	0.356124	+	0.616824i
$176$	1.98790e11	−	3.44314e11i	0.0887307	−	0.153686i
$177$	−1.20664e12	−	2.08997e12i	−0.522066	−	0.904245i
$178$	1.01352e12			0.425133
$179$	−1.48048e12			−0.602157			−0.301079	−	0.953599i	$-0.597347\pi$
$179$	−1.48048e12			−0.602157			−0.301079	+	0.953599i	$0.597347\pi$
$180$	−2.60081e11	−	4.50473e11i	−0.102591	−	0.177693i
$181$	2.30328e12	+	3.98941e12i	0.881283	+	1.52643i	0.849915	+	0.526919i	$0.176653\pi$
$181$	2.30328e12	+	3.98941e12i	0.881283	+	1.52643i	0.0313679	+	0.999508i	$0.490014\pi$
$182$	7.12340e11			0.264420
$183$	−2.94483e12			−1.06067
$184$	−2.45205e10	−	4.24708e10i	−0.00857101	−	0.0148454i
$185$	−2.21887e12	+	3.84319e12i	−0.752813	+	1.30391i
$186$	−8.94795e10	−	1.54983e11i	−0.0294715	−	0.0510461i
$187$	4.89726e11	−	8.48231e11i	0.156612	−	0.271260i
$188$	1.28805e12	−	2.23096e12i	0.400003	−	0.692825i
$189$	8.81422e11			0.265854
$190$	−1.34083e12	−	2.65137e12i	−0.392853	−	0.776828i
$191$	−5.81510e12			−1.65529			−0.827644	−	0.561254i	$-0.810319\pi$
$191$	−5.81510e12			−1.65529			−0.827644	+	0.561254i	$0.810319\pi$
$192$	1.30460e11	−	2.25963e11i	0.0360844	−	0.0625000i
$193$	−1.38790e12	+	2.40391e12i	−0.373072	+	0.646180i	−0.990036	−	0.140811i	$-0.955029\pi$
$193$	−1.38790e12	+	2.40391e12i	−0.373072	+	0.646180i	0.616964	+	0.786991i	$0.288362\pi$
$194$	5.12276e11	+	8.87288e11i	0.133843	+	0.231822i
$195$	3.78769e11	−	6.56048e11i	0.0962021	−	0.166627i
$196$	−9.19577e11	−	1.59275e12i	−0.227080	−	0.393315i
$197$	2.26340e12			0.543496			0.271748	−	0.962368i	$-0.412398\pi$
$197$	2.26340e12			0.543496			0.271748	+	0.962368i	$0.412398\pi$
$198$	7.16451e11			0.167312
$199$	1.74340e12	+	3.01966e12i	0.396010	+	0.685910i	0.993230	−	0.116168i	$-0.0370612\pi$
$199$	1.74340e12	+	3.01966e12i	0.396010	+	0.685910i	−0.597220	+	0.802078i	$0.703728\pi$
$200$	4.12472e11	+	7.14423e11i	0.0911444	+	0.157867i
$201$	1.56030e12			0.335452
$202$	−2.63000e12			−0.550203
$203$	2.04464e12	+	3.54142e12i	0.416283	+	0.721024i
$204$	3.21393e11	−	5.56668e11i	0.0636898	−	0.110314i
$205$	3.55246e12	+	6.15304e12i	0.685304	+	1.18698i
$206$	1.48741e12	−	2.57627e12i	0.279358	−	0.483863i
$207$	4.41868e10	−	7.65338e10i	0.00808083	−	0.0139964i
$208$	3.79990e11			0.0676743
$209$	4.08603e12	+	2.26560e11i	0.708757	+	0.0392987i
$210$	−4.10910e12			−0.694290
$211$	−3.65014e12	+	6.32223e12i	−0.600837	+	1.04068i	0.391858	+	0.920026i	$0.371832\pi$
$211$	−3.65014e12	+	6.32223e12i	−0.600837	+	1.04068i	−0.992695	+	0.120654i	$0.961501\pi$
$212$	1.43255e12	−	2.48125e12i	0.229753	−	0.397945i
$213$	−9.54403e11	−	1.65307e12i	−0.149157	−	0.258348i
$214$	1.08287e12	−	1.87558e12i	0.164930	−	0.285667i
$215$	−6.07256e11	−	1.05180e12i	−0.0901489	−	0.156142i
$216$	4.70185e11			0.0680414
$217$	−1.41372e12			−0.199450
$218$	−9.20821e11	−	1.59491e12i	−0.126667	−	0.219394i
$219$	2.76783e12	+	4.79402e12i	0.371276	+	0.643068i
$220$	−3.34002e12			−0.436943
$221$	9.36122e11			0.119447
$222$	−2.00568e12	−	3.47394e12i	−0.249644	−	0.432396i
$223$	−4.33626e12	+	7.51062e12i	−0.526548	+	0.912009i	0.472973	+	0.881077i	$0.343181\pi$
$223$	−4.33626e12	+	7.51062e12i	−0.526548	+	0.912009i	−0.999522	+	0.0309317i	$0.990153\pi$
$224$	−1.03059e12	−	1.78503e12i	−0.122101	−	0.211486i
$225$	−7.43289e11	+	1.28741e12i	−0.0859317	+	0.148838i
$226$	5.40048e11	−	9.35390e11i	0.0609306	−	0.105535i
$227$	−3.94527e12			−0.434445			−0.217223	−	0.976122i	$-0.569700\pi$
$227$	−3.94527e12			−0.434445			−0.217223	+	0.976122i	$0.569700\pi$
$228$	2.68154e12	+	1.48684e11i	0.288232	+	0.0159817i
$229$	1.58358e13			1.66167			0.830833	−	0.556521i	$-0.187864\pi$
$229$	1.58358e13			1.66167			0.830833	+	0.556521i	$0.187864\pi$
$230$	−2.05995e11	+	3.56793e11i	−0.0211034	+	0.0365522i
$231$	2.82986e12	−	4.90146e12i	0.283073	−	0.490298i
$232$	1.09069e12	+	1.88913e12i	0.106541	+	0.184535i
$233$	−8.34332e12	+	1.44511e13i	−0.795942	+	1.37861i	0.126297	+	0.991992i	$0.459691\pi$
$233$	−8.34332e12	+	1.44511e13i	−0.795942	+	1.37861i	−0.922239	+	0.386620i	$0.873643\pi$
$234$	3.42377e11	+	5.93015e11i	0.0319020	+	0.0552559i
$235$	−2.16415e13			−1.96976
$236$	−1.01696e13			−0.904245
$237$	2.15368e12	+	3.73029e12i	0.187096	+	0.324061i
$238$	−2.53889e12	−	4.39749e12i	−0.215512	−	0.373278i
$239$	−1.98928e13			−1.65009			−0.825045	−	0.565067i	$-0.808850\pi$
$239$	−1.98928e13			−1.65009			−0.825045	+	0.565067i	$0.808850\pi$
$240$	−2.19196e12			−0.177693
$241$	1.40969e12	+	2.44166e12i	0.111694	+	0.193460i	0.916453	−	0.400141i	$-0.131039\pi$
$241$	1.40969e12	+	2.44166e12i	0.111694	+	0.193460i	−0.804759	+	0.593601i	$0.797706\pi$
$242$	−2.26478e12	+	3.92271e12i	−0.175405	+	0.303810i
$243$	4.23644e11	+	7.33773e11i	0.0320750	+	0.0555556i
$244$	−6.20474e12	+	1.07469e13i	−0.459282	+	0.795500i
$245$	−7.72528e12	+	1.33806e13i	−0.559114	+	0.968414i
$246$	−6.42228e12			−0.454513
$247$	1.76511e12	+	3.49033e12i	0.122162	+	0.241565i
$248$	−7.54132e11			−0.0510461
$249$	−1.87962e11	+	3.25560e11i	−0.0124444	+	0.0215543i
$250$	−3.25558e12	+	5.63883e12i	−0.210843	+	0.365190i
$251$	9.66907e12	+	1.67473e13i	0.612603	+	1.06106i	0.990800	+	0.135335i	$0.0432109\pi$
$251$	9.66907e12	+	1.67473e13i	0.612603	+	1.06106i	−0.378197	+	0.925725i	$0.623456\pi$
$252$	1.85715e12	−	3.21668e12i	0.115118	−	0.199391i
$253$	−2.83729e11	−	4.91433e11i	−0.0172084	−	0.0298059i
$254$	−1.16456e13			−0.691159
$255$	−5.39998e12			−0.313632
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−3.20717e12	−	5.55498e12i	−0.178439	−	0.309065i	0.762907	−	0.646508i	$-0.223771\pi$
$257$	−3.20717e12	−	5.55498e12i	−0.178439	−	0.309065i	−0.941346	+	0.337443i	$0.890438\pi$
$258$	1.09782e12			0.0597894
$259$	−3.16884e13			−1.68948
$260$	−1.59613e12	−	2.76458e12i	−0.0833134	−	0.144303i
$261$	−1.96546e12	+	3.40428e12i	−0.100448	+	0.173981i
$262$	−5.37838e12	−	9.31562e12i	−0.269150	−	0.466181i
$263$	6.95770e12	−	1.20511e13i	0.340964	−	0.590568i	−0.643648	−	0.765322i	$-0.722580\pi$
$263$	6.95770e12	−	1.20511e13i	0.340964	−	0.590568i	0.984612	+	0.174754i	$0.0559131\pi$
$264$	1.50956e12	−	2.61463e12i	0.0724483	−	0.125484i
$265$	−2.40694e13			−1.13139
$266$	1.16088e13	−	1.77580e13i	0.534490	−	0.817607i
$267$	7.69645e12			0.347119
$268$	3.28755e12	−	5.69420e12i	0.145255	−	0.251589i
$269$	8.69278e11	−	1.50563e12i	0.0376289	−	0.0651751i	−0.846598	−	0.532233i	$-0.821353\pi$
$269$	8.69278e11	−	1.50563e12i	0.0376289	−	0.0651751i	0.884227	+	0.467058i	$0.154686\pi$
$270$	−1.97499e12	−	3.42078e12i	−0.0837653	−	0.145086i
$271$	1.01947e13	−	1.76578e13i	0.423687	−	0.733847i	−0.572610	−	0.819828i	$-0.694069\pi$
$271$	1.01947e13	−	1.76578e13i	0.423687	−	0.733847i	0.996297	+	0.0859811i	$0.0274025\pi$
$272$	−1.35435e12	−	2.34580e12i	−0.0551570	−	0.0955347i
$273$	5.40933e12			0.215898
$274$	2.80427e13			1.09696
$275$	4.77275e12	+	8.26665e12i	0.182995	+	0.316956i
$276$	−1.86203e11	−	3.22513e11i	−0.00699820	−	0.0121212i
$277$	2.98921e13			1.10133			0.550665	−	0.834726i	$-0.314374\pi$
$277$	2.98921e13			1.10133			0.550665	+	0.834726i	$0.314374\pi$
$278$	−2.50622e13			−0.905259
$279$	−6.79485e11	−	1.17690e12i	−0.0240634	−	0.0416790i
$280$	−8.65787e12	+	1.49959e13i	−0.300636	+	0.520718i
$281$	2.95189e12	+	5.11283e12i	0.100511	+	0.174091i	0.911895	−	0.410422i	$-0.134619\pi$
$281$	2.95189e12	+	5.11283e12i	0.100511	+	0.174091i	−0.811384	+	0.584513i	$0.801285\pi$
$282$	9.78109e12	−	1.69413e13i	0.326601	−	0.565689i
$283$	1.33068e13	−	2.30480e13i	0.435759	−	0.754757i	−0.561598	−	0.827410i	$-0.689813\pi$
$283$	1.33068e13	−	2.30480e13i	0.435759	−	0.754757i	0.997357	+	0.0726530i	$0.0231466\pi$
$284$	−8.04369e12			−0.258348
$285$	−1.01819e13	−	2.01338e13i	−0.320763	−	0.634278i
$286$	4.39690e12			0.135873
$287$	−2.53669e13	+	4.39368e13i	−0.768985	+	1.33192i
$288$	9.90678e11	−	1.71590e12i	0.0294628	−	0.0510310i
$289$	1.37995e13	+	2.39014e13i	0.402647	+	0.697404i
$290$	9.16280e12	−	1.58704e13i	0.262325	−	0.454360i
$291$	3.89009e12	+	6.73784e12i	0.109282	+	0.189282i
$292$	2.33272e13			0.643068
$293$	5.45347e13			1.47537			0.737685	−	0.675145i	$-0.235919\pi$
$293$	5.45347e13			1.47537			0.737685	+	0.675145i	$0.235919\pi$
$294$	−6.98304e12	−	1.20950e13i	−0.185410	−	0.321140i
$295$	4.27168e13	+	7.39876e13i	1.11321	+	1.92814i
$296$	−1.69039e13			−0.432396
$297$	5.44055e12			0.136610
$298$	2.08336e12	+	3.60849e12i	0.0513542	+	0.0889480i
$299$	2.71177e11	−	4.69692e11i	0.00656238	−	0.0113664i
$300$	3.13221e12	+	5.42515e12i	0.0744191	+	0.128898i
$301$	4.33622e12	−	7.51055e12i	0.101157	−	0.175209i
$302$	1.56329e13	−	2.70770e13i	0.358098	−	0.620245i
$303$	−1.99715e13			−0.449239
$304$	6.19261e12	−	9.47280e12i	0.136795	−	0.209254i
$305$	1.04251e14			2.26168
$306$	2.44058e12	−	4.22720e12i	0.0520025	−	0.0900710i
$307$	−1.41834e13	+	2.45664e13i	−0.296839	+	0.514139i	−0.975411	−	0.220394i	$-0.929266\pi$
$307$	−1.41834e13	+	2.45664e13i	−0.296839	+	0.514139i	0.678572	+	0.734534i	$0.262599\pi$
$308$	−1.19250e13	−	2.06547e13i	−0.245149	−	0.424610i
$309$	1.12950e13	−	1.95636e13i	0.228095	−	0.395072i
$310$	3.16769e12	+	5.48661e12i	0.0628426	+	0.108847i
$311$	3.72812e13			0.726620			0.363310	−	0.931668i	$-0.381647\pi$
$311$	3.72812e13			0.726620			0.363310	+	0.931668i	$0.381647\pi$
$312$	2.88555e12			0.0552559
$313$	4.10696e13	+	7.11347e13i	0.772729	+	1.33841i	0.936062	+	0.351834i	$0.114442\pi$
$313$	4.10696e13	+	7.11347e13i	0.772729	+	1.33841i	−0.163334	+	0.986571i	$0.552225\pi$
$314$	−3.43230e12	−	5.94491e12i	−0.0634558	−	0.109909i
$315$	−3.12035e13			−0.566886
$316$	1.81512e13			0.324061
$317$	−1.14169e13	−	1.97747e13i	−0.200319	−	0.346964i	0.748312	−	0.663347i	$-0.230865\pi$
$317$	−1.14169e13	−	1.97747e13i	−0.200319	−	0.346964i	−0.948631	+	0.316384i	$0.897531\pi$
$318$	1.08784e13	−	1.88420e13i	0.187593	−	0.324920i
$319$	1.26205e13	+	2.18593e13i	0.213908	+	0.370500i
$320$	−4.61845e12	+	7.99938e12i	−0.0769433	+	0.133270i
$321$	8.22303e12	−	1.42427e13i	0.134665	−	0.233246i
$322$	−2.94188e12			−0.0473607
$323$	1.52557e13	−	2.33366e13i	0.241446	−	0.369338i
$324$	3.57047e12			0.0555556
$325$	−4.56160e12	+	7.90093e12i	−0.0697845	+	0.120870i
$326$	1.88131e13	−	3.25852e13i	0.282985	−	0.490144i
$327$	−6.99249e12	−	1.21113e13i	−0.103423	−	0.179135i
$328$	−1.35317e13	+	2.34376e13i	−0.196810	+	0.340885i
$329$	−7.72674e13	−	1.33831e14i	−1.10514	−	1.91416i
$330$	−2.53633e13			−0.356763
$331$	7.41704e13			1.02607			0.513034	−	0.858368i	$-0.328521\pi$
$331$	7.41704e13			1.02607			0.513034	+	0.858368i	$0.328521\pi$
$332$	7.92071e11	+	1.37191e12i	0.0107772	+	0.0186666i
$333$	−1.52306e13	−	2.63803e13i	−0.203833	−	0.353050i
$334$	−3.84449e13			−0.506096
$335$	−5.52367e13			−0.715289
$336$	−7.82602e12	−	1.35551e13i	−0.0996954	−	0.172678i
$337$	−7.68961e12	+	1.33188e13i	−0.0963696	+	0.166917i	−0.910179	−	0.414214i	$-0.864056\pi$
$337$	−7.68961e12	+	1.33188e13i	−0.0963696	+	0.166917i	0.813810	+	0.581131i	$0.197390\pi$
$338$	−2.65734e13	−	4.60264e13i	−0.327646	−	0.567500i
$339$	4.10099e12	−	7.10312e12i	0.0497496	−	0.0861689i
$340$	−1.13777e13	+	1.97068e13i	−0.135807	+	0.235224i
$341$	−8.72612e12			−0.102488
$342$	2.03630e13	+	1.12907e12i	0.235341	+	0.0130490i
$343$	1.11355e13			0.126647
$344$	2.31311e12	−	4.00642e12i	0.0258896	−	0.0448420i
$345$	−1.56427e12	+	2.70940e12i	−0.0172309	+	0.0298448i
$346$	−1.78122e13	−	3.08516e13i	−0.193107	−	0.334471i
$347$	8.80978e13	−	1.52590e14i	0.940055	−	1.62822i	0.174692	−	0.984623i	$-0.444107\pi$
$347$	8.80978e13	−	1.52590e14i	0.940055	−	1.62822i	0.765362	−	0.643600i	$-0.222560\pi$
$348$	8.28244e12	+	1.43456e13i	0.0869906	+	0.150672i
$349$	−5.07401e13			−0.524579			−0.262290	−	0.964989i	$-0.584478\pi$
$349$	−5.07401e13			−0.524579			−0.262290	+	0.964989i	$0.584478\pi$
$350$	4.94869e13			0.503635
$351$	2.59993e12	+	4.50321e12i	0.0260479	+	0.0451162i
$352$	−6.36127e12	−	1.10180e13i	−0.0627421	−	0.108673i
$353$	−4.61284e13			−0.447927			−0.223964	−	0.974598i	$-0.571900\pi$
$353$	−4.61284e13			−0.447927			−0.223964	+	0.974598i	$0.571900\pi$
$354$	−7.72251e13			−0.738313
$355$	3.37871e13	+	5.85211e13i	0.318050	+	0.550879i
$356$	1.62164e13	−	2.80876e13i	0.150307	−	0.260339i
$357$	−1.92797e13	−	3.33935e13i	−0.175965	−	0.304780i
$358$	−2.36876e13	+	4.10282e13i	−0.212895	+	0.368744i
$359$	7.29099e13	−	1.26284e14i	0.645308	−	1.11771i	−0.338922	−	0.940814i	$-0.610062\pi$
$359$	7.29099e13	−	1.26284e14i	0.645308	−	1.11771i	0.984230	−	0.176892i	$-0.0566044\pi$
$360$	−1.66452e13			−0.145086
$361$	1.15776e14	+	1.28786e13i	0.993870	+	0.110555i
$362$	1.47410e14			1.24632
$363$	−1.71981e13	+	2.97881e13i	−0.143217	+	0.248059i
$364$	1.13974e13	−	1.97410e13i	0.0934867	−	0.161924i
$365$	−9.79848e13	−	1.69715e14i	−0.791677	−	1.37123i
$366$	−4.71173e13	+	8.16095e13i	−0.375002	+	0.649523i
$367$	3.26105e13	+	5.64831e13i	0.255679	+	0.442849i	0.965080	−	0.261957i	$-0.0843677\pi$
$367$	3.26105e13	+	5.64831e13i	0.255679	+	0.442849i	−0.709401	+	0.704805i	$0.751034\pi$
$368$	−1.56931e12			−0.0121212
$369$	−4.87692e13			−0.371108
$370$	7.10038e13	+	1.22982e14i	0.532319	+	0.922004i
$371$	−8.59358e13	−	1.48845e14i	−0.634772	−	1.09946i
$372$	−5.72669e12			−0.0416790
$373$	9.13132e13			0.654839			0.327420	−	0.944879i	$-0.393821\pi$
$373$	9.13132e13			0.654839			0.327420	+	0.944879i	$0.393821\pi$
$374$	−1.56712e13	−	2.71434e13i	−0.110741	−	0.191810i
$375$	−2.47221e13	+	4.28199e13i	−0.172152	+	0.298177i
$376$	−4.12174e13	−	7.13907e13i	−0.282845	−	0.489901i
$377$	−1.20621e13	+	2.08922e13i	−0.0815731	+	0.141289i
$378$	1.41027e13	−	2.44267e13i	0.0939937	−	0.162802i
$379$	−1.13596e14			−0.746183			−0.373092	−	0.927794i	$-0.621702\pi$
$379$	−1.13596e14			−0.746183			−0.373092	+	0.927794i	$0.621702\pi$
$380$	−9.49301e13	−	5.26363e12i	−0.614603	−	0.0340781i
$381$	−8.84341e13			−0.564329
$382$	−9.30416e13	+	1.61153e14i	−0.585233	+	1.01365i
$383$	1.20447e14	−	2.08620e14i	0.746797	−	1.29349i	−0.202553	−	0.979271i	$-0.564924\pi$
$383$	1.20447e14	−	2.08620e14i	0.746797	−	1.29349i	0.949350	−	0.314220i	$-0.101743\pi$
$384$	−4.17471e12	−	7.23081e12i	−0.0255155	−	0.0441942i
$385$	−1.00181e14	+	1.73518e14i	−0.603602	+	1.04547i
$386$	4.44128e13	+	7.69252e13i	0.263802	+	0.456918i
$387$	8.33659e12			0.0488178
$388$	3.27856e13			0.189282
$389$	1.36476e14	+	2.36384e14i	0.776844	+	1.34553i	0.933752	+	0.357920i	$0.116514\pi$
$389$	1.36476e14	+	2.36384e14i	0.776844	+	1.34553i	−0.156908	+	0.987613i	$0.550153\pi$
$390$	−1.21206e13	−	2.09935e13i	−0.0680251	−	0.117823i
$391$	−3.86607e12			−0.0213943
$392$	−5.88529e13			−0.321140
$393$	−4.08421e13	−	7.07405e13i	−0.219760	−	0.380635i
$394$	3.62143e13	−	6.27250e13i	0.192155	−	0.332822i
$395$	−7.62432e13	−	1.32057e14i	−0.398949	−	0.690999i
$396$	1.14632e13	−	1.98549e13i	0.0591538	−	0.102457i
$397$	3.04427e13	−	5.27283e13i	0.154930	−	0.268346i	−0.778104	−	0.628136i	$-0.783818\pi$
$397$	3.04427e13	−	5.27283e13i	0.154930	−	0.268346i	0.933033	+	0.359790i	$0.117152\pi$
$398$	1.11578e14			0.560043
$399$	8.81546e13	−	1.34850e14i	0.436409	−	0.667573i
$400$	2.63982e13			0.128898
$401$	2.70677e13	−	4.68826e13i	0.130364	−	0.225797i	−0.793453	−	0.608631i	$-0.791719\pi$
$401$	2.70677e13	−	4.68826e13i	0.130364	−	0.225797i	0.923817	+	0.382835i	$0.125052\pi$
$402$	2.49648e13	−	4.32403e13i	0.118600	−	0.205421i
$403$	−4.17004e12	−	7.22271e12i	−0.0195417	−	0.0338472i
$404$	−4.20799e13	+	7.28846e13i	−0.194526	+	0.336929i
$405$	−1.49976e13	−	2.59766e13i	−0.0683941	−	0.118462i
$406$	1.30857e14			0.588713
$407$	−1.95596e14			−0.868141
$408$	−1.02846e13	−	1.78134e13i	−0.0450355	−	0.0780038i
$409$	−8.23217e13	−	1.42585e14i	−0.355661	−	0.616023i	0.631570	−	0.775319i	$-0.282411\pi$
$409$	−8.23217e13	−	1.42585e14i	−0.355661	−	0.616023i	−0.987231	+	0.159296i	$0.949078\pi$
$410$	2.27357e14			0.969166
$411$	2.12949e14			0.895664
$412$	−4.75972e13	−	8.24407e13i	−0.197536	−	0.342143i
$413$	−3.05026e14	+	5.28321e14i	−1.24914	+	2.16358i
$414$	−1.41398e12	−	2.44908e12i	−0.00571401	−	0.00989695i
$415$	6.65411e12	−	1.15253e13i	0.0265354	−	0.0459607i
$416$	6.07984e12	−	1.05306e13i	0.0239265	−	0.0414419i
$417$	−1.90316e14			−0.739141
$418$	7.16552e13	−	1.09611e14i	0.274649	−	0.420129i
$419$	−2.48732e13			−0.0940924			−0.0470462	−	0.998893i	$-0.514981\pi$
$419$	−2.48732e13			−0.0940924			−0.0470462	+	0.998893i	$0.514981\pi$
$420$	−6.57457e13	+	1.13875e14i	−0.245469	+	0.425164i
$421$	−4.65906e13	+	8.06972e13i	−0.171691	+	0.297377i	−0.939011	−	0.343887i	$-0.888256\pi$
$421$	−4.65906e13	+	8.06972e13i	−0.171691	+	0.297377i	0.767320	+	0.641264i	$0.221590\pi$
$422$	1.16805e14	+	2.02312e14i	0.424856	+	0.735872i
$423$	7.42752e13	−	1.28648e14i	0.266668	−	0.461883i
$424$	−4.58415e13	−	7.93999e13i	−0.162460	−	0.281389i
$425$	6.50331e13			0.227507
$426$	−6.10818e13			−0.210940
$427$	3.72211e14	+	6.44688e14i	1.26892	+	2.19784i
$428$	−3.46518e13	−	6.00186e13i	−0.116623	−	0.201997i
$429$	3.33889e13			0.110940
$430$	−3.88644e13			−0.127490
$431$	−1.47888e14	−	2.56149e14i	−0.478969	−	0.829598i	0.520740	−	0.853715i	$-0.325656\pi$
$431$	−1.47888e14	−	2.56149e14i	−0.478969	−	0.829598i	−0.999709	+	0.0241168i	$0.992323\pi$
$432$	7.52296e12	−	1.30301e13i	0.0240563	−	0.0416667i
$433$	1.52685e14	+	2.64459e14i	0.482075	+	0.834978i	0.999788	−	0.0205763i	$-0.00655009\pi$
$433$	1.52685e14	+	2.64459e14i	0.482075	+	0.834978i	−0.517714	+	0.855554i	$0.673217\pi$
$434$	−2.26195e13	+	3.91781e13i	−0.0705162	+	0.122138i
$435$	6.95800e13	−	1.20516e14i	0.214187	−	0.370983i
$436$	−5.89326e13			−0.179135
$437$	−7.28969e12	−	1.44146e13i	−0.0218807	−	0.0432669i
$438$	1.77141e14			0.525063
$439$	−1.74821e14	+	3.02798e14i	−0.511727	+	0.886337i	0.488181	+	0.872742i	$0.337661\pi$
$439$	−1.74821e14	+	3.02798e14i	−0.511727	+	0.886337i	−0.999908	+	0.0135941i	$0.995673\pi$
$440$	−5.34404e13	+	9.25615e13i	−0.154483	+	0.267572i
$441$	−5.30274e13	−	9.18462e13i	−0.151387	−	0.262210i
$442$	1.49779e13	−	2.59426e13i	0.0422308	−	0.0731460i
$443$	−5.05878e13	−	8.76206e13i	−0.140872	−	0.243998i	0.786953	−	0.617013i	$-0.211657\pi$
$443$	−5.05878e13	−	8.76206e13i	−0.140872	−	0.243998i	−0.927825	+	0.373015i	$0.878324\pi$
$444$	−1.28364e14			−0.353050
$445$	−2.72465e14			−0.740168
$446$	1.38760e14	+	2.40340e14i	0.372326	+	0.644887i
$447$	1.58205e13	+	2.74020e13i	0.0419305	+	0.0726258i
$448$	−6.59576e13			−0.172678
$449$	1.06067e13			0.0274299			0.0137149	−	0.999906i	$-0.495634\pi$
$449$	1.06067e13			0.0274299			0.0137149	+	0.999906i	$0.495634\pi$
$450$	2.37852e13	+	4.11972e13i	0.0607629	+	0.105244i
$451$	−1.56577e14	+	2.71199e14i	−0.395145	+	0.684411i
$452$	−1.72815e13	−	2.99325e13i	−0.0430845	−	0.0746245i
$453$	1.18713e14	−	2.05616e14i	0.292386	−	0.506428i
$454$	−6.31244e13	+	1.09335e14i	−0.153600	+	0.266042i
$455$	−1.91498e14			−0.460363
$456$	4.70251e13	−	7.19341e13i	0.111692	−	0.170855i
$457$	4.14615e14			0.972986			0.486493	−	0.873685i	$-0.338276\pi$
$457$	4.14615e14			0.972986			0.486493	+	0.873685i	$0.338276\pi$
$458$	2.53372e14	−	4.38854e14i	0.587488	−	1.01756i
$459$	1.85331e13	−	3.21003e13i	0.0424599	−	0.0735427i
$460$	6.59183e12	+	1.14174e13i	0.0149224	+	0.0258463i
$461$	−3.20679e14	+	5.55432e14i	−0.717323	+	1.24244i	0.244733	+	0.969590i	$0.421300\pi$
$461$	−3.20679e14	+	5.55432e14i	−0.717323	+	1.24244i	−0.962057	+	0.272850i	$0.912034\pi$
$462$	−9.05555e13	−	1.56847e14i	−0.200163	−	0.346693i
$463$	4.30931e14			0.941266			0.470633	−	0.882329i	$-0.344026\pi$
$463$	4.30931e14			0.941266			0.470633	+	0.882329i	$0.344026\pi$
$464$	6.98043e13			0.150672
$465$	2.40547e13	+	4.16639e13i	0.0513107	+	0.0888728i
$466$	2.66986e14	+	4.62434e14i	0.562816	+	0.974826i
$467$	−3.95022e14			−0.822959			−0.411480	−	0.911419i	$-0.634988\pi$
$467$	−3.95022e14			−0.822959			−0.411480	+	0.911419i	$0.634988\pi$
$468$	2.19122e13			0.0451162
$469$	−1.97214e14	−	3.41584e14i	−0.401316	−	0.695099i
$470$	−3.46264e14	+	5.99746e14i	−0.696416	+	1.20623i
$471$	−2.60640e13	−	4.51442e13i	−0.0518115	−	0.0897401i
$472$	−1.62713e14	+	2.81827e14i	−0.319699	+	0.553735i
$473$	2.67652e13	−	4.63586e13i	0.0519797	−	0.0900314i
$474$	1.37836e14			0.264594
$475$	1.22623e14	+	2.42476e14i	0.232680	+	0.460102i
$476$	−1.62489e14			−0.304780
$477$	8.26079e13	−	1.43081e14i	0.153169	−	0.265296i
$478$	−3.18285e14	+	5.51285e14i	−0.583395	+	1.01047i
$479$	−4.59063e14	−	7.95121e14i	−0.831816	−	1.44075i	−0.896597	−	0.442848i	$-0.853968\pi$
$479$	−4.59063e14	−	7.95121e14i	−0.831816	−	1.44075i	0.0647804	−	0.997900i	$-0.479365\pi$
$480$	−3.50713e13	+	6.07453e13i	−0.0628240	+	0.108814i
$481$	−9.34713e13	−	1.61897e14i	−0.165531	−	0.286709i
$482$	9.02202e13			0.157959
$483$	−2.23399e13			−0.0386698
$484$	7.24728e13	+	1.25527e14i	0.124030	+	0.214826i
$485$	−1.37715e14	−	2.38529e14i	−0.233024	−	0.403609i
$486$	2.71132e13			0.0453609
$487$	−5.44519e14			−0.900749			−0.450374	−	0.892840i	$-0.648709\pi$
$487$	−5.44519e14			−0.900749			−0.450374	+	0.892840i	$0.648709\pi$
$488$	1.98552e14	+	3.43902e14i	0.324762	+	0.562504i
$489$	1.42862e14	−	2.47444e14i	0.231056	−	0.400201i
$490$	2.47209e14	+	4.28178e14i	0.395353	+	0.684772i
$491$	2.38922e14	−	4.13826e14i	0.377841	−	0.654439i	−0.612907	−	0.790155i	$-0.710000\pi$
$491$	2.38922e14	−	4.13826e14i	0.377841	−	0.654439i	0.990748	+	0.135716i	$0.0433333\pi$
$492$	−1.02757e14	+	1.77980e14i	−0.160695	+	0.278331i
$493$	1.71966e14			0.265940
$494$	1.24969e14	+	6.92918e12i	0.191118	+	0.0105970i
$495$	−1.92603e14			−0.291295
$496$	−1.20661e13	+	2.08991e13i	−0.0180475	+	0.0312593i
$497$	−2.41263e14	+	4.17880e14i	−0.356887	+	0.618146i
$498$	6.01479e12	+	1.04179e13i	0.00879952	+	0.0152412i
$499$	−5.28060e14	+	9.14627e14i	−0.764065	+	1.32340i	0.176675	+	0.984269i	$0.443466\pi$
$499$	−5.28060e14	+	9.14627e14i	−0.764065	+	1.32340i	−0.940740	+	0.339130i	$0.889867\pi$
$500$	1.04179e14	+	1.80443e14i	0.149088	+	0.258229i
$501$	−2.91941e14			−0.413226
$502$	6.18820e14			0.866352
$503$	4.15338e12	+	7.19387e12i	0.00575146	+	0.00996182i	0.868887	−	0.495011i	$-0.164836\pi$
$503$	4.15338e12	+	7.19387e12i	0.00575146	+	0.00996182i	−0.863135	+	0.504973i	$0.831503\pi$
$504$	−5.94289e13	−	1.02934e14i	−0.0814010	−	0.140991i
$505$	7.07019e14			0.957919
$506$	−1.81587e13			−0.0243364
$507$	−2.01792e14	−	3.49513e14i	−0.267522	−	0.463361i
$508$	−1.86330e14	+	3.22734e14i	−0.244362	+	0.423247i
$509$	−3.15561e14	−	5.46567e14i	−0.409388	−	0.709081i	0.585433	−	0.810721i	$-0.300924\pi$
$509$	−3.15561e14	−	5.46567e14i	−0.409388	−	0.709081i	−0.994821	+	0.101640i	$0.967591\pi$
$510$	−8.63996e13	+	1.49649e14i	−0.110886	+	0.192060i
$511$	6.99677e14	−	1.21188e15i	0.888348	−	1.53866i
$512$	−3.51844e13			−0.0441942
$513$	1.54631e14	+	8.57389e12i	0.192155	+	0.0106545i
$514$	−2.05259e14			−0.252351
$515$	−3.99859e14	+	6.92577e14i	−0.486371	+	0.842419i
$516$	1.75652e13	−	3.04238e13i	0.0211387	−	0.0366134i
$517$	−4.76930e14	−	8.26068e14i	−0.567880	−	0.983598i
$518$	−5.07015e14	+	8.78176e14i	−0.597320	+	1.03459i
$519$	−1.35261e14	−	2.34279e14i	−0.157671	−	0.273094i
$520$	−1.02152e14			−0.117823
$521$	1.11007e15			1.26691			0.633453	−	0.773781i	$-0.281637\pi$
$521$	1.11007e15			1.26691			0.633453	+	0.773781i	$0.281637\pi$
$522$	6.28948e13	+	1.08937e14i	0.0710275	+	0.123023i
$523$	−8.14550e13	−	1.41084e14i	−0.0910245	−	0.157659i	0.816918	−	0.576754i	$-0.195681\pi$
$523$	−8.14550e13	−	1.41084e14i	−0.0910245	−	0.157659i	−0.907942	+	0.419095i	$0.862347\pi$
$524$	−3.44216e14			−0.380635
$525$	3.75791e14			0.411216
$526$	−2.22646e14	−	3.85635e14i	−0.241098	−	0.417594i
$527$	−2.97254e13	+	5.14858e13i	−0.0318543	+	0.0551733i
$528$	−4.83059e13	−	8.36682e13i	−0.0512287	−	0.0887307i
$529$	4.75285e14	−	8.23218e14i	0.498825	−	0.863990i
$530$	−3.85110e14	+	6.67031e14i	−0.400007	+	0.692833i
$531$	−5.86428e14			−0.602830
$532$	−3.06382e14	−	6.05841e14i	−0.311709	−	0.616375i
$533$	−2.99299e14			−0.301374
$534$	1.23143e14	−	2.13290e14i	0.122725	−	0.212566i
$535$	−2.91106e14	+	5.04211e14i	−0.287148	+	0.497355i
$536$	−1.05201e14	−	1.82214e14i	−0.102711	−	0.177900i
$537$	−1.79878e14	+	3.11558e14i	−0.173828	+	0.301079i
$538$	−2.78169e13	−	4.81803e13i	−0.0266076	−	0.0460858i
$539$	−6.80992e14			−0.644768
$540$	−1.26399e14			−0.118462
$541$	−3.64620e14	−	6.31541e14i	−0.338264	−	0.585891i	0.645842	−	0.763471i	$-0.276506\pi$
$541$	−3.64620e14	−	6.31541e14i	−0.338264	−	0.585891i	−0.984106	+	0.177580i	$0.943173\pi$
$542$	−3.26231e14	−	5.65049e14i	−0.299592	−	0.518908i
$543$	1.11940e15			1.01762
$544$	−8.66781e13			−0.0780038
$545$	2.47543e14	+	4.28758e14i	0.220531	+	0.381972i
$546$	8.65493e13	−	1.49908e14i	0.0763316	−	0.132210i
$547$	−1.01055e14	−	1.75033e14i	−0.0882324	−	0.152823i	0.818532	−	0.574461i	$-0.194788\pi$
$547$	−1.01055e14	−	1.75033e14i	−0.0882324	−	0.152823i	−0.906764	+	0.421638i	$0.861455\pi$
$548$	4.48682e14	−	7.77141e14i	0.387834	−	0.671748i
$549$	−3.57797e14	+	6.19722e14i	−0.306188	+	0.530334i
$550$	3.05456e14			0.258794
$551$	3.24250e14	+	6.41174e14i	0.271986	+	0.537826i
$552$	−1.19170e13			−0.00989695
$553$	5.44428e14	−	9.42976e14i	0.447664	−	0.775376i
$554$	4.78274e14	−	8.28394e14i	0.389379	−	0.674425i
$555$	5.39185e14	+	9.33896e14i	0.434637	+	0.752813i
$556$	−4.00995e14	+	6.94544e14i	−0.320057	+	0.554356i
$557$	1.07163e14	+	1.85613e14i	0.0846922	+	0.146691i	0.905260	−	0.424858i	$-0.139676\pi$
$557$	1.07163e14	+	1.85613e14i	0.0846922	+	0.146691i	−0.820568	+	0.571549i	$0.806343\pi$
$558$	−4.34870e13			−0.0340308
$559$	5.11621e13			0.0396446
$560$	2.77052e14	+	4.79868e14i	0.212582	+	0.368203i
$561$	−1.19004e14	−	2.06120e14i	−0.0904199	−	0.156612i
$562$	1.88921e14			0.142145
$563$	1.13765e15			0.847641			0.423820	−	0.905746i	$-0.360689\pi$
$563$	1.13765e15			0.847641			0.423820	+	0.905746i	$0.360689\pi$
$564$	−3.12995e14	−	5.42123e14i	−0.230942	−	0.400003i
$565$	−1.45180e14	+	2.51460e14i	−0.106082	+	0.183739i
$566$	−4.25816e14	−	7.37535e14i	−0.308128	−	0.533694i
$567$	1.07093e14	−	1.85490e14i	0.0767456	−	0.132927i
$568$	−1.28699e14	+	2.22913e14i	−0.0913397	+	0.158205i
$569$	−1.71143e15			−1.20293			−0.601466	−	0.798899i	$-0.705416\pi$
$569$	−1.71143e15			−1.20293			−0.601466	+	0.798899i	$0.705416\pi$
$570$	−7.20876e14	−	3.99707e13i	−0.501821	−	0.0278246i
$571$	−1.65023e15			−1.13775			−0.568874	−	0.822425i	$-0.692621\pi$
$571$	−1.65023e15			−1.13775			−0.568874	+	0.822425i	$0.692621\pi$
$572$	7.03504e13	−	1.21850e14i	0.0480384	−	0.0832049i
$573$	−7.06534e14	+	1.22375e15i	−0.477840	+	0.827644i
$574$	8.11742e14	+	1.40598e15i	0.543754	+	0.941810i
$575$	1.88389e13	−	3.26299e13i	0.0124992	−	0.0216492i
$576$	−3.17017e13	−	5.49089e13i	−0.0208333	−	0.0360844i
$577$	3.50248e14			0.227986			0.113993	−	0.993482i	$-0.463636\pi$
$577$	3.50248e14			0.227986			0.113993	+	0.993482i	$0.463636\pi$
$578$	8.83166e14			0.569428
$579$	3.37260e14	+	5.84151e14i	0.215393	+	0.373072i
$580$	−2.93209e14	−	5.07854e14i	−0.185491	−	0.321281i
$581$	9.50297e13			0.0595512
$582$	2.48966e14			0.154548
$583$	−5.30436e14	−	9.18742e14i	−0.326179	−	0.564959i
$584$	3.73235e14	−	6.46463e14i	0.227359	−	0.393797i
$585$	−9.20409e13	−	1.59420e14i	−0.0555423	−	0.0962021i
$586$	8.72555e14	−	1.51131e15i	0.521622	−	0.903476i
$587$	3.73048e14	−	6.46139e14i	0.220930	−	0.382663i	−0.734160	−	0.678976i	$-0.762424\pi$
$587$	3.73048e14	−	6.46139e14i	0.220930	−	0.382663i	0.955091	+	0.296313i	$0.0957573\pi$
$588$	−4.46914e14			−0.262210
$589$	−2.48014e14	−	1.37517e13i	−0.144159	−	0.00799323i
$590$	2.73387e15			1.57432
$591$	2.75002e14	−	4.76318e14i	0.156894	−	0.271748i
$592$	−2.70462e14	+	4.68453e14i	−0.152875	+	0.264787i
$593$	1.12336e15	+	1.94572e15i	0.629100	+	1.08963i	0.987733	+	0.156154i	$0.0499098\pi$
$593$	1.12336e15	+	1.94572e15i	0.629100	+	1.08963i	−0.358633	+	0.933479i	$0.616757\pi$
$594$	8.70488e13	−	1.50773e14i	0.0482989	−	0.0836561i
$595$	6.82528e14	+	1.18217e15i	0.375213	+	0.649887i
$596$	1.33335e14			0.0726258
$597$	8.47294e14			0.457273
$598$	−8.67766e12	−	1.50302e13i	−0.00464030	−	0.00803724i
$599$	−7.39062e14	−	1.28009e15i	−0.391592	−	0.678256i	0.601068	−	0.799198i	$-0.294742\pi$
$599$	−7.39062e14	−	1.28009e15i	−0.391592	−	0.678256i	−0.992660	+	0.120941i	$0.961409\pi$
$600$	2.00462e14			0.105244
$601$	2.36509e15			1.23037			0.615187	−	0.788381i	$-0.289080\pi$
$601$	2.36509e15			1.23037			0.615187	+	0.788381i	$0.289080\pi$
$602$	−1.38759e14	−	2.40338e14i	−0.0715287	−	0.123891i
$603$	1.89576e14	−	3.28356e14i	0.0968365	−	0.167726i
$604$	−5.00254e14	−	8.66465e14i	−0.253214	−	0.438579i
$605$	6.08837e14	−	1.05454e15i	0.305384	−	0.528941i
$606$	−3.19545e14	+	5.53468e14i	−0.158830	+	0.275101i
$607$	−4.93837e14			−0.243246			−0.121623	−	0.992576i	$-0.538810\pi$
$607$	−4.93837e14			−0.243246			−0.121623	+	0.992576i	$0.538810\pi$
$608$	−1.63436e14	−	3.23179e14i	−0.0797772	−	0.157752i
$609$	9.93695e14			0.480682
$610$	1.66801e15	−	2.88909e15i	0.799624	−	1.38499i
$611$	4.55831e14	−	7.89522e14i	0.216559	−	0.375092i
$612$	−7.80984e13	−	1.35270e14i	−0.0367713	−	0.0636898i
$613$	7.76554e14	−	1.34503e15i	0.362359	−	0.627624i	−0.625989	−	0.779832i	$-0.715305\pi$
$613$	7.76554e14	−	1.34503e15i	0.362359	−	0.627624i	0.988349	+	0.152207i	$0.0486380\pi$
$614$	4.53870e14	+	7.86126e14i	0.209897	+	0.363551i
$615$	1.72650e15			0.791320
$616$	−7.63201e14			−0.346693
$617$	−1.02252e15	−	1.77106e15i	−0.460368	−	0.797381i	0.538611	−	0.842554i	$-0.318949\pi$
$617$	−1.02252e15	−	1.77106e15i	−0.460368	−	0.797381i	−0.998979	+	0.0451737i	$0.985616\pi$
$618$	−3.61441e14	−	6.26034e14i	−0.161288	−	0.279358i
$619$	2.14868e15			0.950326			0.475163	−	0.879898i	$-0.342389\pi$
$619$	2.14868e15			0.950326			0.475163	+	0.879898i	$0.342389\pi$
$620$	2.02732e14			0.0888728
$621$	−1.07374e13	−	1.85977e13i	−0.00466547	−	0.00808083i
$622$	5.96499e14	−	1.03317e15i	0.256899	−	0.444962i
$623$	−9.72791e14	−	1.68492e15i	−0.415274	−	0.719276i
$624$	4.61688e13	−	7.99667e13i	0.0195359	−	0.0338372i
$625$	1.48983e15	−	2.58045e15i	0.624878	−	1.08232i
$626$	2.62846e15			1.09280
$627$	5.44131e14	−	8.32355e14i	0.224250	−	0.343034i
$628$	−2.19667e14			−0.0897401
$629$	−6.66293e14	+	1.15405e15i	−0.269828	+	0.467356i
$630$	−4.99256e14	+	8.64737e14i	−0.200424	+	0.347145i
$631$	−7.16378e14	−	1.24080e15i	−0.285089	−	0.493789i	0.687542	−	0.726145i	$-0.258690\pi$
$631$	−7.16378e14	−	1.24080e15i	−0.285089	−	0.493789i	−0.972631	+	0.232356i	$0.925357\pi$
$632$	2.90419e14	−	5.03021e14i	0.114573	−	0.198446i
$633$	8.86985e14	+	1.53630e15i	0.346893	+	0.600837i
$634$	−7.30683e14			−0.283295
$635$	3.13069e15			1.20333
$636$	−3.48109e14	−	6.02943e14i	−0.132648	−	0.229753i
$637$	−3.25432e14	−	5.63665e14i	−0.122940	−	0.212939i
$638$	8.07711e14			0.302512
$639$	−4.63840e14			−0.172232
$640$	1.47790e14	+	2.55980e14i	0.0544071	+	0.0942359i
$641$	−1.59412e15	+	2.76109e15i	−0.581837	+	1.00777i	0.413425	+	0.910538i	$0.364332\pi$
$641$	−1.59412e15	+	2.76109e15i	−0.581837	+	1.00777i	−0.995262	+	0.0972324i	$0.969001\pi$
$642$	−2.63137e14	−	4.55767e14i	−0.0952224	−	0.164930i
$643$	1.10676e15	−	1.91696e15i	0.397093	−	0.687785i	−0.596273	−	0.802782i	$-0.703352\pi$
$643$	1.10676e15	−	1.91696e15i	0.397093	−	0.687785i	0.993366	+	0.114997i	$0.0366858\pi$
$644$	−4.70701e13	+	8.15278e13i	−0.0167445	+	0.0290024i
$645$	−2.95127e14			−0.104095
$646$	−4.02632e14	−	7.96166e14i	−0.140809	−	0.278436i
$647$	−2.61097e15			−0.905374			−0.452687	−	0.891669i	$-0.649535\pi$
$647$	−2.61097e15			−0.905374			−0.452687	+	0.891669i	$0.649535\pi$
$648$	5.71275e13	−	9.89477e13i	0.0196419	−	0.0340207i
$649$	−1.88277e15	+	3.26105e15i	−0.641875	+	1.11176i
$650$	1.45971e14	+	2.52830e14i	0.0493451	+	0.0854682i
$651$	−1.71767e14	+	2.97508e14i	−0.0575762	+	0.0997249i
$652$	−6.02019e14	−	1.04273e15i	−0.200100	−	0.346584i
$653$	−4.93312e15			−1.62592			−0.812961	−	0.582318i	$-0.802146\pi$
$653$	−4.93312e15			−1.62592			−0.812961	+	0.582318i	$0.802146\pi$
$654$	−4.47519e14			−0.146263
$655$	1.44586e15	+	2.50431e15i	0.468598	+	0.811635i
$656$	4.33015e14	+	7.50004e14i	0.139166	+	0.241042i
$657$	1.34516e15			0.428712
$658$	−4.94511e15			−1.56291
$659$	−7.26516e14	−	1.25836e15i	−0.227707	−	0.394399i	0.729421	−	0.684065i	$-0.239789\pi$
$659$	−7.26516e14	−	1.25836e15i	−0.227707	−	0.394399i	−0.957128	+	0.289665i	$0.906456\pi$
$660$	−4.05813e14	+	7.02889e14i	−0.126135	+	0.218472i
$661$	3.86446e14	+	6.69344e14i	0.119119	+	0.206320i	0.919419	−	0.393280i	$-0.128660\pi$
$661$	3.86446e14	+	6.69344e14i	0.119119	+	0.206320i	−0.800300	+	0.599600i	$0.795326\pi$
$662$	1.18673e15	−	2.05547e15i	0.362770	−	0.628336i
$663$	1.13739e14	−	1.97001e14i	0.0344813	−	0.0597234i
$664$	5.06925e13			0.0152412
$665$	−3.12079e15	+	4.77386e15i	−0.930563	+	1.42348i
$666$	−9.74761e14			−0.288264
$667$	4.98152e13	−	8.62825e13i	0.0146107	−	0.0253064i
$668$	−6.15118e14	+	1.06542e15i	−0.178932	+	0.309919i
$669$	1.05371e15	+	1.82508e15i	0.304003	+	0.526548i
$670$	−8.83787e14	+	1.53076e15i	−0.252893	+	0.438023i
$671$	2.29746e15	+	3.97931e15i	0.652039	+	1.12937i
$672$	−5.00866e14			−0.140991
$673$	4.22884e15			1.18070			0.590348	−	0.807149i	$-0.298990\pi$
$673$	4.22884e15			1.18070			0.590348	+	0.807149i	$0.298990\pi$
$674$	2.46068e14	+	4.26202e14i	0.0681436	+	0.118028i
$675$	1.80619e14	+	3.12842e14i	0.0496127	+	0.0859317i
$676$	−1.70070e15			−0.463361
$677$	−9.65317e14			−0.260875			−0.130437	−	0.991457i	$-0.541638\pi$
$677$	−9.65317e14			−0.260875			−0.130437	+	0.991457i	$0.541638\pi$
$678$	−1.31232e14	−	2.27300e14i	−0.0351783	−	0.0609306i
$679$	9.83374e14	−	1.70325e15i	0.261478	−	0.452893i
$680$	3.64087e14	+	6.30618e14i	0.0960299	+	0.166329i
$681$	−4.79351e14	+	8.30260e14i	−0.125414	+	0.217223i
$682$	−1.39618e14	+	2.41825e14i	−0.0362349	+	0.0627607i
$683$	1.52959e15			0.393787			0.196894	−	0.980425i	$-0.436915\pi$
$683$	1.52959e15			0.393787			0.196894	+	0.980425i	$0.436915\pi$
$684$	3.57097e14	−	5.46250e14i	0.0911964	−	0.139503i
$685$	−7.53868e15			−1.90984
$686$	1.78169e14	−	3.08597e14i	0.0447763	−	0.0775549i
$687$	1.92405e15	−	3.33255e15i	0.479682	−	0.830833i
$688$	−7.40195e13	−	1.28205e14i	−0.0183067	−	0.0317081i
$689$	5.06969e14	−	8.78097e14i	0.124387	−	0.215445i
$690$	5.00567e13	+	8.67008e13i	0.0121841	+	0.0211034i
$691$	5.26668e15			1.27177			0.635884	−	0.771785i	$-0.280636\pi$
$691$	5.26668e15			1.27177			0.635884	+	0.771785i	$0.280636\pi$
$692$	−1.13998e15			−0.273094
$693$	−6.87656e14	−	1.19106e15i	−0.163433	−	0.283073i
$694$	−2.81913e15	−	4.88288e15i	−0.664719	−	1.15133i
$695$	6.73745e15			1.57608
$696$	5.30076e14			0.123023
$697$	1.06675e15	+	1.84767e15i	0.245631	+	0.425445i
$698$	−8.11841e14	+	1.40615e15i	−0.185467	+	0.321238i
$699$	2.02743e15	+	3.51161e15i	0.459537	+	0.795942i
$700$	7.91790e14	−	1.37142e15i	0.178062	−	0.308412i
$701$	−2.80778e14	+	4.86322e14i	−0.0626491	+	0.108511i	−0.895649	−	0.444762i	$-0.853288\pi$
$701$	−2.80778e14	+	4.86322e14i	−0.0626491	+	0.108511i	0.833000	+	0.553273i	$0.186622\pi$
$702$	1.66395e14			0.0368373
$703$	−5.55922e15	−	3.08244e14i	−1.22112	−	0.0677081i
$704$	−4.07121e14			−0.0887307
$705$	−2.62944e15	+	4.55432e15i	−0.568621	+	0.984881i
$706$	−7.38054e14	+	1.27835e15i	−0.158366	+	0.274298i
$707$	2.52430e15	+	4.37221e15i	0.537444	+	0.930881i
$708$	−1.23560e15	+	2.14013e15i	−0.261033	+	0.452123i
$709$	1.07782e15	+	1.86684e15i	0.225939	+	0.391338i	0.956601	−	0.291402i	$-0.0941217\pi$
$709$	1.07782e15	+	1.86684e15i	0.225939	+	0.391338i	−0.730662	+	0.682740i	$0.760788\pi$
$710$	2.16238e15			0.449791
$711$	1.04669e15			0.216040
$712$	−5.18925e14	−	8.98804e14i	−0.106283	−	0.184088i
$713$	1.72218e13	+	2.98290e13i	0.00350014	+	0.00606242i
$714$	−1.23390e15			−0.248852
$715$	−1.18201e15			−0.236559
$716$	7.58004e14	+	1.31290e15i	0.150539	+	0.260742i
$717$	−2.41698e15	+	4.18632e15i	−0.476340	+	0.825045i
$718$	−2.33312e15	−	4.04108e15i	−0.456302	−	0.790338i
$719$	2.38736e15	−	4.13502e15i	0.463349	−	0.802544i	−0.535776	−	0.844360i	$-0.679981\pi$
$719$	2.38736e15	−	4.13502e15i	0.463349	−	0.802544i	0.999125	+	0.0418160i	$0.0133143\pi$
$720$	−2.66323e14	+	4.61285e14i	−0.0512955	+	0.0888465i
$721$	−5.71053e15			−1.09152
$722$	2.20932e15	−	3.00243e15i	0.419087	−	0.569532i
$723$	6.85110e14			0.128973
$724$	2.35856e15	−	4.08515e15i	0.440642	−	0.763214i
$725$	−8.37967e14	+	1.45140e15i	−0.155370	+	0.269109i
$726$	5.50341e14	+	9.53218e14i	0.101270	+	0.175405i
$727$	2.30928e15	−	3.99979e15i	0.421733	−	0.730463i	−0.574376	−	0.818591i	$-0.694755\pi$
$727$	2.30928e15	−	3.99979e15i	0.421733	−	0.730463i	0.996109	+	0.0881286i	$0.0280887\pi$
$728$	−3.64718e14	−	6.31710e14i	−0.0661051	−	0.114497i
$729$	2.05891e14			0.0370370
$730$	−6.27103e15			−1.11960
$731$	−1.82350e14	−	3.15839e14i	−0.0323117	−	0.0559656i
$732$	1.50775e15	+	2.61150e15i	0.265167	+	0.459282i
$733$	−4.19020e15			−0.731414			−0.365707	−	0.930730i	$-0.619173\pi$
$733$	−4.19020e15			−0.731414			−0.365707	+	0.930730i	$0.619173\pi$
$734$	2.08707e15			0.361584
$735$	1.87724e15	+	3.25148e15i	0.322805	+	0.559114i
$736$	−2.51090e13	+	4.34901e13i	−0.00428551	+	0.00742271i
$737$	−1.21729e15	−	2.10842e15i	−0.206217	−	0.357178i
$738$	−7.80307e14	+	1.35153e15i	−0.131207	+	0.227257i
$739$	4.54313e15	−	7.86894e15i	0.758248	−	1.31332i	−0.185496	−	0.982645i	$-0.559389\pi$
$739$	4.54313e15	−	7.86894e15i	0.758248	−	1.31332i	0.943743	−	0.330678i	$-0.107278\pi$
$740$	4.54424e15			0.752813
$741$	9.48980e14	+	5.26184e13i	0.156048	+	0.00865242i
$742$	−5.49989e15			−0.897703
$743$	2.01821e15	−	3.49563e15i	0.326984	−	0.566353i	−0.654928	−	0.755692i	$-0.727301\pi$
$743$	2.01821e15	−	3.49563e15i	0.326984	−	0.566353i	0.981912	+	0.189338i	$0.0606342\pi$
$744$	−9.16270e13	+	1.58703e14i	−0.0147358	+	0.0255231i
$745$	−5.60069e14	−	9.70067e14i	−0.0894091	−	0.154861i
$746$	1.46101e15	−	2.53054e15i	0.231521	−	0.401006i
$747$	4.56748e13	+	7.91111e13i	0.00718478	+	0.0124444i
$748$	−1.00296e15			−0.156612
$749$	−4.15739e15			−0.644422
$750$	7.91106e14	+	1.37024e15i	0.121730	+	0.210843i
$751$	7.93122e14	+	1.37373e15i	0.121149	+	0.209836i	0.920221	−	0.391399i	$-0.128009\pi$
$751$	7.93122e14	+	1.37373e15i	0.121149	+	0.209836i	−0.799072	+	0.601235i	$0.794675\pi$
$752$	−2.63792e15			−0.400003
$753$	4.69917e15			0.707373
$754$	3.85989e14	+	6.68552e14i	0.0576809	+	0.0999063i
$755$	−4.20259e15	+	7.27909e15i	−0.623460	+	1.07986i
$756$	−4.51288e14	−	7.81654e14i	−0.0664636	−	0.115118i
$757$	−5.05601e15	+	8.75726e15i	−0.739231	+	1.28039i	0.213611	+	0.976919i	$0.431478\pi$
$757$	−5.05601e15	+	8.75726e15i	−0.739231	+	1.28039i	−0.952842	+	0.303467i	$0.901856\pi$
$758$	−1.81753e15	+	3.14805e15i	−0.263816	+	0.456942i
$759$	−1.37892e14			−0.0198706
$760$	−1.66475e15	+	2.54656e15i	−0.238163	+	0.364317i
$761$	−2.29114e15			−0.325413			−0.162707	−	0.986674i	$-0.552022\pi$
$761$	−2.29114e15			−0.325413			−0.162707	+	0.986674i	$0.552022\pi$
$762$	−1.41495e15	+	2.45076e15i	−0.199521	+	0.345580i
$763$	−1.76763e15	+	3.06162e15i	−0.247460	+	0.428614i
$764$	2.97733e15	+	5.15689e15i	0.413822	+	0.716761i
$765$	−6.56097e14	+	1.13639e15i	−0.0905379	+	0.156816i
$766$	−3.85430e15	−	6.67585e15i	−0.528066	−	0.914636i
$767$	−3.59894e15			−0.489554
$768$	−2.67181e14			−0.0360844
$769$	−1.66879e13	−	2.89044e13i	−0.00223773	−	0.00387586i	0.864904	−	0.501937i	$-0.167379\pi$
$769$	−1.66879e13	−	2.89044e13i	−0.00223773	−	0.00387586i	−0.867142	+	0.498061i	$0.834046\pi$
$770$	3.20579e15	+	5.55259e15i	0.426811	+	0.739259i
$771$	−1.55868e15			−0.206043
$772$	2.84242e15			0.373072
$773$	−1.02453e15	−	1.77454e15i	−0.133517	−	0.231259i	0.791513	−	0.611153i	$-0.209294\pi$
$773$	−1.02453e15	−	1.77454e15i	−0.133517	−	0.231259i	−0.925030	+	0.379894i	$0.875961\pi$
$774$	1.33385e14	−	2.31030e14i	0.0172597	−	0.0298947i
$775$	−2.89696e14	−	5.01768e14i	−0.0372206	−	0.0644679i
$776$	5.24570e14	−	9.08583e14i	0.0669213	−	0.115911i
$777$	−3.85014e15	+	6.66865e15i	−0.487710	+	0.844738i
$778$	8.73447e15			1.09862
$779$	−4.87761e15	+	7.46125e15i	−0.609187	+	0.931871i
$780$	−7.75719e14			−0.0962021
$781$	−1.48919e15	+	2.57935e15i	−0.183387	+	0.317636i
$782$	−6.18571e13	+	1.07140e14i	−0.00756402	+	0.0131013i
$783$	4.77607e14	+	8.27240e14i	0.0579937	+	0.100448i
$784$	−9.41647e14	+	1.63098e15i	−0.113540	+	0.196657i
$785$	9.22700e14	+	1.59816e15i	0.110478	+	0.191354i
$786$	−2.61389e15			−0.310787
$787$	−9.58600e15			−1.13182			−0.565908	−	0.824468i	$-0.691474\pi$
$787$	−9.58600e15			−1.13182			−0.565908	+	0.824468i	$0.691474\pi$
$788$	−1.15886e15	−	2.00720e15i	−0.135874	−	0.235341i
$789$	−1.69072e15	−	2.92841e15i	−0.196856	−	0.340964i
$790$	−4.87956e15			−0.564199
$791$	−2.07337e15			−0.238071
$792$	−3.66823e14	−	6.35356e14i	−0.0418281	−	0.0724483i
$793$	−2.19582e15	+	3.80327e15i	−0.248653	+	0.430680i
$794$	−9.74166e14	−	1.68730e15i	−0.109552	−	0.189750i
$795$	−2.92443e15	+	5.06526e15i	−0.326605	+	0.565696i
$796$	1.78525e15	−	3.09214e15i	0.198005	−	0.342955i
$797$	−1.65665e16			−1.82478			−0.912388	−	0.409325i	$-0.865764\pi$
$797$	−1.65665e16			−1.82478			−0.912388	+	0.409325i	$0.865764\pi$
$798$	−2.32659e15	−	4.60061e15i	−0.254509	−	0.503268i
$799$	−6.49862e15			−0.706014
$800$	4.22372e14	−	7.31569e14i	0.0455722	−	0.0789333i
$801$	9.35119e14	−	1.61967e15i	0.100205	−	0.173560i
$802$	−8.66165e14	−	1.50024e15i	−0.0921811	−	0.159662i
$803$	4.31874e15	−	7.48027e15i	0.456479	−	0.790646i
$804$	−7.98874e14	−	1.38369e15i	−0.0838629	−	0.145255i
$805$	7.90863e14			0.0824563
$806$	−2.66882e14			−0.0276361
$807$	−2.11235e14	−	3.65869e14i	−0.0217250	−	0.0376289i
$808$	1.34656e15	+	2.33231e15i	0.137551	+	0.238245i
$809$	1.46004e16			1.48132			0.740659	−	0.671881i	$-0.234513\pi$
$809$	1.46004e16			1.48132			0.740659	+	0.671881i	$0.234513\pi$
$810$	−9.59845e14			−0.0967238
$811$	8.87885e15	+	1.53786e16i	0.888673	+	1.53923i	0.841445	+	0.540343i	$0.181705\pi$
$811$	8.87885e15	+	1.53786e16i	0.888673	+	1.53923i	0.0472278	+	0.998884i	$0.484961\pi$
$812$	2.09371e15	−	3.62642e15i	0.208142	−	0.360512i
$813$	−2.47732e15	−	4.29084e15i	−0.244616	−	0.423687i
$814$	−3.12953e15	+	5.42051e15i	−0.306934	+	0.531626i
$815$	−5.05750e15	+	8.75985e15i	−0.492685	+	0.853355i
$816$	−6.58212e14			−0.0636898
$817$	8.33777e14	−	1.27542e15i	0.0801361	−	0.122584i
$818$	−5.26859e15			−0.502980
$819$	6.57234e14	−	1.13836e15i	0.0623245	−	0.107949i
$820$	3.63772e15	−	6.30071e15i	0.342652	−	0.593490i
$821$	−6.41241e15	−	1.11066e16i	−0.599976	−	1.03919i	−0.992824	−	0.119586i	$-0.961843\pi$
$821$	−6.41241e15	−	1.11066e16i	−0.599976	−	1.03919i	0.392847	−	0.919604i	$-0.371490\pi$
$822$	3.40718e15	−	5.90141e15i	0.316665	−	0.548480i
$823$	−8.37214e15	−	1.45010e16i	−0.772925	−	1.33875i	−0.935953	−	0.352125i	$-0.885459\pi$
$823$	−8.37214e15	−	1.45010e16i	−0.772925	−	1.33875i	0.163028	−	0.986621i	$-0.447874\pi$
$824$	−3.04622e15			−0.279358
$825$	2.31956e15			0.211304
$826$	9.76084e15	+	1.69063e16i	0.883277	+	1.52988i
$827$	−4.81148e14	−	8.33372e14i	−0.0432512	−	0.0749133i	0.843589	−	0.536989i	$-0.180438\pi$
$827$	−4.81148e14	−	8.33372e14i	−0.0432512	−	0.0749133i	−0.886841	+	0.462075i	$0.847105\pi$
$828$	−9.04946e13			−0.00808083
$829$	1.44222e16			1.27933			0.639665	−	0.768654i	$-0.279073\pi$
$829$	1.44222e16			1.27933			0.639665	+	0.768654i	$0.279073\pi$
$830$	−2.12932e14	−	3.68808e14i	−0.0187634	−	0.0324991i
$831$	3.63189e15	−	6.29062e15i	0.317927	−	0.550665i
$832$	−1.94555e14	−	3.36979e14i	−0.0169186	−	0.0293039i
$833$	−2.31978e15	+	4.01799e15i	−0.200401	+	0.347105i
$834$	−3.04506e15	+	5.27420e15i	−0.261326	+	0.452630i
$835$	1.03351e16			0.881128
$836$	−1.89113e15	−	3.73953e15i	−0.160172	−	0.316726i
$837$	−3.30230e14			−0.0277860
$838$	−3.97971e14	+	6.89306e14i	−0.0332667	+	0.0576196i
$839$	1.11979e16	−	1.93953e16i	0.929919	−	1.61067i	0.146465	−	0.989216i	$-0.453210\pi$
$839$	1.11979e16	−	1.93953e16i	0.929919	−	1.61067i	0.783453	−	0.621450i	$-0.213456\pi$
$840$	2.10386e15	+	3.64400e15i	0.173573	+	0.300636i
$841$	3.88444e15	−	6.72804e15i	0.318383	−	0.551456i
$842$	1.49090e15	+	2.58231e15i	0.121404	+	0.210277i
$843$	1.43462e15			0.116061
$844$	7.47549e15			0.600837
$845$	7.14369e15	+	1.23732e16i	0.570441	+	0.988033i
$846$	−2.37681e15	−	4.11675e15i	−0.188563	−	0.326601i
$847$	8.69501e15			0.685349
$848$	−2.93386e15			−0.229753
$849$	−3.23354e15	−	5.60066e15i	−0.251586	−	0.435759i
$850$	1.04053e15	−	1.80225e15i	0.0804360	−	0.139319i
$851$	3.86025e14	+	6.68616e14i	0.0296485	+	0.0513528i
$852$	−9.77309e14	+	1.69275e15i	−0.0745786	+	0.129174i
$853$	8.64212e15	−	1.49686e16i	0.655240	−	1.13491i	−0.326593	−	0.945165i	$-0.605901\pi$
$853$	8.64212e15	−	1.49686e16i	0.655240	−	1.13491i	0.981833	−	0.189745i	$-0.0607660\pi$
$854$	2.38215e16			1.79453
$855$	−5.47415e15	−	3.03527e14i	−0.409735	−	0.0227187i
$856$	−2.21771e15			−0.164930
$857$	−9.87464e15	+	1.71034e16i	−0.729671	+	1.26383i	0.227352	+	0.973813i	$0.426993\pi$
$857$	−9.87464e15	+	1.71034e16i	−0.729671	+	1.26383i	−0.957022	+	0.290014i	$0.906340\pi$
$858$	5.34223e14	−	9.25301e14i	0.0392232	−	0.0679365i
$859$	1.47105e15	+	2.54794e15i	0.107317	+	0.185878i	0.914682	−	0.404174i	$-0.132441\pi$
$859$	1.47105e15	+	2.54794e15i	0.107317	+	0.185878i	−0.807366	+	0.590051i	$0.799108\pi$
$860$	−6.21830e14	+	1.07704e15i	−0.0450745	+	0.0780712i
$861$	6.16417e15	+	1.06767e16i	0.443974	+	0.768985i
$862$	−9.46482e15			−0.677364
$863$	−1.94368e16			−1.38218			−0.691092	−	0.722767i	$-0.742870\pi$
$863$	−1.94368e16			−1.38218			−0.691092	+	0.722767i	$0.742870\pi$
$864$	−2.40735e14	−	4.16965e14i	−0.0170103	−	0.0294628i
$865$	4.78842e15	+	8.29379e15i	0.336205	+	0.582324i
$866$	9.77187e15			0.681756
$867$	6.70654e15			0.464936
$868$	7.23823e14	+	1.25370e15i	0.0498625	+	0.0863643i
$869$	3.36046e15	−	5.82049e15i	0.230033	−	0.398429i
$870$	−2.22656e15	−	3.85651e15i	−0.151453	−	0.262325i
$871$	1.16344e15	−	2.01514e15i	0.0786402	−	0.136209i
$872$	−9.42921e14	+	1.63319e15i	−0.0633337	+	0.109697i
$873$	1.89059e15			0.126188
$874$	−5.16105e14	−	2.86167e13i	−0.0342315	−	0.00189804i
$875$	1.24990e16			0.823814
$876$	2.83426e15	−	4.90908e15i	0.185638	−	0.321534i
$877$	1.27071e16	−	2.20094e16i	0.827085	−	1.43255i	−0.0732295	−	0.997315i	$-0.523331\pi$
$877$	1.27071e16	−	2.20094e16i	0.827085	−	1.43255i	0.900315	−	0.435239i	$-0.143336\pi$
$878$	5.59426e15	+	9.68955e15i	0.361845	+	0.626735i
$879$	6.62597e15	−	1.14765e16i	0.425903	−	0.737685i
$880$	1.71009e15	+	2.96197e15i	0.109236	+	0.189202i
$881$	1.02812e16			0.652646			0.326323	−	0.945258i	$-0.394190\pi$
$881$	1.02812e16			0.652646			0.326323	+	0.945258i	$0.394190\pi$
$882$	−3.39376e15			−0.214093
$883$	−2.62683e15	−	4.54981e15i	−0.164683	−	0.285239i	0.771860	−	0.635793i	$-0.219327\pi$
$883$	−2.62683e15	−	4.54981e15i	−0.164683	−	0.285239i	−0.936543	+	0.350554i	$0.885993\pi$
$884$	−4.79294e14	−	8.30162e14i	−0.0298617	−	0.0517220i
$885$	2.07603e16			1.28542
$886$	−3.23762e15			−0.199223
$887$	4.23853e15	+	7.34135e15i	0.259200	+	0.448948i	0.966028	−	0.258438i	$-0.0832078\pi$
$887$	4.23853e15	+	7.34135e15i	0.259200	+	0.448948i	−0.706828	+	0.707386i	$0.749874\pi$
$888$	−2.05382e15	+	3.55732e15i	−0.124822	+	0.216198i
$889$	1.11776e16	+	1.93602e16i	0.675132	+	1.16936i
$890$	−4.35944e15	+	7.55077e15i	−0.261689	+	0.453258i
$891$	6.61027e14	−	1.14493e15i	0.0394359	−	0.0683049i
$892$	8.88065e15			0.526548
$893$	−1.22535e16	−	2.42301e16i	−0.722066	−	1.42781i
$894$	1.01252e15			0.0592987
$895$	6.36792e15	−	1.10296e16i	0.370656	−	0.641995i
$896$	−1.05532e15	+	1.82787e15i	−0.0610507	+	0.105743i
$897$	−6.58960e13	−	1.14135e14i	−0.00378879	−	0.00656238i
$898$	1.69707e14	−	2.93941e14i	0.00969793	−	0.0167973i
$899$	−7.66036e14	−	1.32681e15i	−0.0435082	−	0.0753584i
$900$	1.52226e15			0.0859317
$901$	−7.22768e15			−0.405520
$902$	5.01045e15	+	8.67836e15i	0.279409	+	0.483951i
$903$	−1.05370e15	−	1.82506e15i	−0.0584029	−	0.101157i
$904$	−1.10602e15			−0.0609306
$905$	−3.96281e16			−2.16988
$906$	−3.79880e15	−	6.57972e15i	−0.206748	−	0.358098i
$907$	1.01331e16	−	1.75510e16i	0.548151	−	0.949425i	−0.450250	−	0.892902i	$-0.648665\pi$
$907$	1.01331e16	−	1.75510e16i	0.548151	−	0.949425i	0.998401	−	0.0565229i	$-0.0180014\pi$
$908$	2.01998e15	+	3.49871e15i	0.108611	+	0.188120i
$909$	−2.42654e15	+	4.20289e15i	−0.129684	+	0.224619i
$910$	−3.06396e15	+	5.30694e15i	−0.162763	+	0.281914i
$911$	−1.88125e16			−0.993333			−0.496667	−	0.867941i	$-0.665443\pi$
$911$	−1.88125e16			−0.993333			−0.496667	+	0.867941i	$0.665443\pi$
$912$	−1.24109e15	−	2.45414e15i	−0.0651378	−	0.128804i
$913$	5.86567e14			0.0306005
$914$	6.63385e15	−	1.14902e16i	0.344002	−	0.595830i
$915$	1.26665e16	−	2.19390e16i	0.652890	−	1.13084i
$916$	−8.10791e15	−	1.40433e16i	−0.415417	−	0.719523i
$917$	−1.03244e16	+	1.78824e16i	−0.525817	+	0.910742i
$918$	−5.93060e14	−	1.02721e15i	−0.0300237	−	0.0520025i
$919$	−8.06050e15			−0.405627			−0.202813	−	0.979217i	$-0.565009\pi$
$919$	−8.06050e15			−0.405627			−0.202813	+	0.979217i	$0.565009\pi$
$920$	4.21877e14			0.0211034
$921$	3.44657e15	+	5.96964e15i	0.171380	+	0.296839i
$922$	1.02617e16	+	1.77738e16i	0.507224	+	0.878538i
$923$	−2.84661e15			−0.139868
$924$	−5.79555e15			−0.283073
$925$	−6.49353e15	−	1.12471e16i	−0.315283	−	0.546087i
$926$	6.89490e15	−	1.19423e16i	0.332788	−	0.576405i
$927$	−2.74469e15	−	4.75395e15i	−0.131691	−	0.228095i
$928$	1.11687e15	−	1.93447e15i	0.0532707	−	0.0922675i
$929$	1.18992e16	−	2.06099e16i	0.564196	−	0.977215i	−0.432928	−	0.901428i	$-0.642520\pi$
$929$	1.18992e16	−	2.06099e16i	0.564196	−	0.977215i	0.997124	−	0.0757871i	$-0.0241469\pi$
$930$	1.53950e15			0.0725643
$931$	−1.93551e16	−	1.07319e15i	−0.906928	−	0.0502868i
$932$	1.70871e16			0.795942
$933$	4.52966e15	−	7.84561e15i	0.209757	−	0.363310i
$934$	−6.32035e15	+	1.09472e16i	−0.290960	+	0.503958i
$935$	4.21288e15	+	7.29693e15i	0.192804	+	0.333946i
$936$	3.50594e14	−	6.07247e14i	0.0159510	−	0.0276279i
$937$	−1.20456e16	−	2.08637e16i	−0.544832	−	0.943676i	−0.998617	−	0.0525655i	$-0.983260\pi$
$937$	−1.20456e16	−	2.08637e16i	−0.544832	−	0.943676i	0.453786	−	0.891111i	$-0.350073\pi$
$938$	−1.26217e16			−0.567546
$939$	1.99598e16			0.892270
$940$	1.10804e16	+	1.91919e16i	0.492441	+	0.852932i
$941$	1.44323e16	+	2.49974e16i	0.637663	+	1.10446i	0.985944	+	0.167075i	$0.0534320\pi$
$941$	1.44323e16	+	2.49974e16i	0.637663	+	1.10446i	−0.348281	+	0.937390i	$0.613235\pi$
$942$	−1.66810e15			−0.0732725
$943$	1.23607e15			0.0539795
$944$	5.20682e15	+	9.01847e15i	0.226061	+	0.391550i
$945$	−3.79123e15	+	6.56660e15i	−0.163646	+	0.283443i
$946$	−8.56485e14	−	1.48348e15i	−0.0367552	−	0.0636618i
$947$	−5.63607e15	+	9.76197e15i	−0.240465	+	0.416498i	−0.960847	−	0.277080i	$-0.910633\pi$
$947$	−5.63607e15	+	9.76197e15i	−0.240465	+	0.416498i	0.720382	+	0.693578i	$0.243967\pi$
$948$	2.20537e15	−	3.81981e15i	0.0935482	−	0.162030i
$949$	8.25535e15			0.348154
$950$	8.68167e15	+	4.81375e14i	0.364018	+	0.0201839i
$951$	−5.54863e15			−0.231309
$952$	−2.59983e15	+	4.50303e15i	−0.107756	+	0.186639i
$953$	1.08570e16	−	1.88049e16i	0.447403	−	0.774924i	−0.550813	−	0.834628i	$-0.685682\pi$
$953$	1.08570e16	−	1.88049e16i	0.447403	−	0.774924i	0.998216	+	0.0597043i	$0.0190158\pi$
$954$	−2.64345e15	−	4.57860e15i	−0.108307	−	0.187593i
$955$	2.50123e16	−	4.33225e16i	1.01891	−	1.76480i
$956$	1.01851e16	+	1.76411e16i	0.412522	+	0.714510i
$957$	6.13355e15			0.247000
$958$	−2.93801e16			−1.17637
$959$	−2.69156e16	−	4.66192e16i	−1.07152	−	1.85593i
$960$	1.12228e15	+	1.94385e15i	0.0444232	+	0.0769433i
$961$	−2.48788e16			−0.979154
$962$	−5.98216e15			−0.234097
$963$	−1.99820e15	−	3.46098e15i	−0.0777488	−	0.134665i
$964$	1.44352e15	−	2.50026e15i	0.0558470	−	0.0967299i
$965$	−1.19394e16	−	2.06797e16i	−0.459287	−	0.795508i
$966$	−3.57439e14	+	6.19102e14i	−0.0136718	+	0.0236803i
$967$	2.54226e16	−	4.40332e16i	0.966884	−	1.67469i	0.262418	−	0.964954i	$-0.415480\pi$
$967$	2.54226e16	−	4.40332e16i	0.966884	−	1.67469i	0.704466	−	0.709738i	$-0.251187\pi$
$968$	4.63826e15			0.175405
$969$	−3.05749e15	−	6.04588e15i	−0.114970	−	0.227342i
$970$	−8.81373e15			−0.329545
$971$	−6.98141e15	+	1.20922e16i	−0.259560	+	0.449571i	−0.966124	−	0.258078i	$-0.916911\pi$
$971$	−6.98141e15	+	1.20922e16i	−0.259560	+	0.449571i	0.706564	+	0.707649i	$0.250244\pi$
$972$	4.33812e14	−	7.51384e14i	0.0160375	−	0.0277778i
$973$	2.40549e16	+	4.16644e16i	0.884268	+	1.53160i
$974$	−8.71230e15	+	1.50902e16i	−0.318463	+	0.551594i
$975$	1.10847e15	+	1.91993e15i	0.0402901	+	0.0697845i
$976$	1.27073e16			0.459282
$977$	−2.91436e16			−1.04742			−0.523712	−	0.851895i	$-0.675453\pi$
$977$	−2.91436e16			−1.04742			−0.523712	+	0.851895i	$0.675453\pi$
$978$	−4.57158e15	−	7.91821e15i	−0.163381	−	0.282985i
$979$	−6.00452e15	−	1.04001e16i	−0.213390	−	0.369602i
$980$	1.58214e16			0.559114
$981$	−3.39835e15			−0.119423
$982$	−7.64552e15	−	1.32424e16i	−0.267174	−	0.462759i
$983$	2.32114e16	−	4.02033e16i	0.806598	−	1.39707i	−0.108610	−	0.994084i	$-0.534640\pi$
$983$	2.32114e16	−	4.02033e16i	0.806598	−	1.39707i	0.915207	−	0.402983i	$-0.132027\pi$
$984$	3.28821e15	+	5.69535e15i	0.113628	+	0.196810i
$985$	−9.73546e15	+	1.68623e16i	−0.334547	+	0.579452i
$986$	2.75145e15	−	4.76565e15i	0.0940240	−	0.162854i
$987$	−3.75519e16			−1.27611
$988$	2.19152e15	−	3.35236e15i	0.0740599	−	0.113289i
$989$	−2.11294e14			−0.00710079
$990$	−3.08164e15	+	5.33756e15i	−0.102988	+	0.178381i
$991$	−4.75686e15	+	8.23912e15i	−0.158094	+	0.273827i	−0.934181	−	0.356799i	$-0.883868\pi$
$991$	−4.75686e15	+	8.23912e15i	−0.158094	+	0.273827i	0.776087	+	0.630625i	$0.217202\pi$
$992$	3.86115e14	+	6.68772e14i	0.0127615	+	0.0221036i
$993$	9.01170e15	−	1.56087e16i	0.296201	−	0.513034i
$994$	7.72041e15	+	1.33721e16i	0.252357	+	0.437095i
$995$	−2.99954e16			−0.975051
$996$	3.84947e14			0.0124444
$997$	2.98243e16	+	5.16571e16i	0.958840	+	1.66076i	0.725325	+	0.688407i	$0.241689\pi$
$997$	2.98243e16	+	5.16571e16i	0.958840	+	1.66076i	0.233515	+	0.972353i	$0.424977\pi$
$998$	1.68979e16	+	2.92681e16i	0.540275	+	0.935785i
$999$	−7.40209e15			−0.235366

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.12.e.b.49.1	yes	18
19.7	even	3	inner	114.12.e.b.7.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.12.e.b.7.1	✓	18	19.7	even	3	inner
114.12.e.b.49.1	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)

\(f(q)\)	\(=\)	\(q+(16.0000 - 27.7128i) q^{2} +(121.500 - 210.444i) q^{3} +(-512.000 - 886.810i) q^{4} +(-4301.26 + 7450.01i) q^{5} +(-3888.00 - 6734.21i) q^{6} -61427.8 q^{7} -32768.0 q^{8} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})\)	\(q+(16.0000 - 27.7128i) q^{2} +(121.500 - 210.444i) q^{3} +(-512.000 - 886.810i) q^{4} +(-4301.26 + 7450.01i) q^{5} +(-3888.00 - 6734.21i) q^{6} -61427.8 q^{7} -32768.0 q^{8} +(-29524.5 - 51137.9i) q^{9} +(137640. + 238400. i) q^{10} -379161. q^{11} -248832. q^{12} +(-181193. - 313836. i) q^{13} +(-982845. + 1.70234e6i) q^{14} +(1.04521e6 + 1.81035e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-1.29160e6 + 2.23713e6i) q^{17} -1.88957e6 q^{18} +(-1.07765e7 - 597529. i) q^{19} +8.80899e6 q^{20} +(-7.46348e6 + 1.29271e7i) q^{21} +(-6.06658e6 + 1.05076e7i) q^{22} +(748308. + 1.29611e6i) q^{23} +(-3.98131e6 + 6.89583e6i) q^{24} +(-1.25877e7 - 2.18025e7i) q^{25} -1.15964e7 q^{26} -1.43489e7 q^{27} +(3.14510e7 + 5.44748e7i) q^{28} +(-3.32853e7 - 5.76518e7i) q^{29} +6.68932e7 q^{30} +2.30143e7 q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(-4.60681e7 + 7.97922e7i) q^{33} +(4.13314e7 + 7.15880e7i) q^{34} +(2.64217e8 - 4.57637e8i) q^{35} +(-3.02331e7 + 5.23652e7i) q^{36} +5.15865e8 q^{37} +(-1.88983e8 + 2.89087e8i) q^{38} -8.80600e7 q^{39} +(1.40944e8 - 2.44122e8i) q^{40} +(4.12955e8 - 7.15260e8i) q^{41} +(2.38831e8 + 4.13668e8i) q^{42} +(-7.05905e7 + 1.22266e8i) q^{43} +(1.94130e8 + 3.36244e8i) q^{44} +5.07971e8 q^{45} +4.78917e7 q^{46} +(1.25786e9 + 2.17867e9i) q^{47} +(1.27402e8 + 2.20667e8i) q^{48} +1.79605e9 q^{49} -8.05610e8 q^{50} +(3.13860e8 + 5.43621e8i) q^{51} +(-1.85542e8 + 3.21368e8i) q^{52} +(1.39897e9 + 2.42309e9i) q^{53} +(-2.29583e8 + 3.97649e8i) q^{54} +(1.63087e9 - 2.82475e9i) q^{55} +2.01287e9 q^{56} +(-1.43509e9 + 2.19525e9i) q^{57} -2.13026e9 q^{58} +(4.96561e9 - 8.60068e9i) q^{59} +(1.07029e9 - 1.85380e9i) q^{60} +(-6.05932e9 - 1.04950e10i) q^{61} +(3.68228e8 - 6.37790e8i) q^{62} +(1.81363e9 + 3.14129e9i) q^{63} +1.07374e9 q^{64} +3.11744e9 q^{65} +(1.47418e9 + 2.55335e9i) q^{66} +(3.21049e9 + 5.56074e9i) q^{67} +2.64521e9 q^{68} +3.63678e8 q^{69} +(-8.45495e9 - 1.46444e10i) q^{70} +(3.92758e9 - 6.80278e9i) q^{71} +(9.67459e8 + 1.67569e9i) q^{72} +(-1.13902e10 + 1.97285e10i) q^{73} +(8.25383e9 - 1.42961e10i) q^{74} -6.11760e9 q^{75} +(4.98768e9 + 9.86265e9i) q^{76} +2.32910e10 q^{77} +(-1.40896e9 + 2.44039e9i) q^{78} +(-8.86289e9 + 1.53510e10i) q^{79} +(-4.51020e9 - 7.81190e9i) q^{80} +(-1.74339e9 + 3.01964e9i) q^{81} +(-1.32146e10 - 2.28883e10i) q^{82} -1.54701e9 q^{83} +1.52852e10 q^{84} +(-1.11111e10 - 1.92449e10i) q^{85} +(2.25889e9 + 3.91252e9i) q^{86} -1.61766e10 q^{87} +1.24244e10 q^{88} +(1.58363e10 + 2.74293e10i) q^{89} +(8.12753e9 - 1.40773e10i) q^{90} +(1.11303e10 + 1.92783e10i) q^{91} +(7.66267e8 - 1.32721e9i) q^{92} +(2.79623e9 - 4.84322e9i) q^{93} +8.05028e10 q^{94} +(5.08042e10 - 7.77149e10i) q^{95} +8.15373e9 q^{96} +(-1.60086e10 + 2.77277e10i) q^{97} +(2.87368e10 - 4.97735e10i) q^{98} +(1.11945e10 + 1.93895e10i) 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

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