LMFDB - Embedded newform 114.12.e.b.7.9

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			7.9
Root			$-6207.82 + 10752.3i$ of defining polynomial
Character	$\chi$	$=$	114.7
Dual form			114.12.e.b.49.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.0000 + 27.7128i) q^{2} +(121.500 + 210.444i) q^{3} +(-512.000 + 886.810i) q^{4} +(6791.32 + 11762.9i) q^{5} +(-3888.00 + 6734.21i) q^{6} +53208.1 q^{7} -32768.0 q^{8} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})$	\(q+(16.0000 + 27.7128i) q^{2} +(121.500 + 210.444i) q^{3} +(-512.000 + 886.810i) q^{4} +(6791.32 + 11762.9i) q^{5} +(-3888.00 + 6734.21i) q^{6} +53208.1 q^{7} -32768.0 q^{8} +(-29524.5 + 51137.9i) q^{9} +(-217322. + 376413. i) q^{10} +179766. q^{11} -248832. q^{12} +(1.00457e6 - 1.73996e6i) q^{13} +(851330. + 1.47455e6i) q^{14} +(-1.65029e6 + 2.85839e6i) q^{15} +(-524288. - 908093. i) q^{16} +(4.64881e6 + 8.05197e6i) q^{17} -1.88957e6 q^{18} +(3.04790e6 + 1.03538e7i) q^{19} -1.39086e7 q^{20} +(6.46479e6 + 1.11973e7i) q^{21} +(2.87625e6 + 4.98181e6i) q^{22} +(-785388. + 1.36033e6i) q^{23} +(-3.98131e6 - 6.89583e6i) q^{24} +(-6.78300e7 + 1.17485e8i) q^{25} +6.42922e7 q^{26} -1.43489e7 q^{27} +(-2.72426e7 + 4.71855e7i) q^{28} +(3.02426e7 - 5.23818e7i) q^{29} -1.05619e8 q^{30} +2.06145e8 q^{31} +(1.67772e7 - 2.90590e7i) q^{32} +(2.18415e7 + 3.78306e7i) q^{33} +(-1.48762e8 + 2.57663e8i) q^{34} +(3.61353e8 + 6.25883e8i) q^{35} +(-3.02331e7 - 5.23652e7i) q^{36} +6.78424e8 q^{37} +(-2.38166e8 + 2.50126e8i) q^{38} +4.88219e8 q^{39} +(-2.22538e8 - 3.85447e8i) q^{40} +(-2.39263e8 - 4.14415e8i) q^{41} +(-2.06873e8 + 3.58315e8i) q^{42} +(-7.51769e8 - 1.30210e9i) q^{43} +(-9.20400e7 + 1.59418e8i) q^{44} -8.02041e8 q^{45} -5.02648e7 q^{46} +(1.08968e8 - 1.88738e8i) q^{47} +(1.27402e8 - 2.20667e8i) q^{48} +8.53777e8 q^{49} -4.34112e9 q^{50} +(-1.12966e9 + 1.95663e9i) q^{51} +(1.02868e9 + 1.78172e9i) q^{52} +(1.87620e9 - 3.24967e9i) q^{53} +(-2.29583e8 - 3.97649e8i) q^{54} +(1.22085e9 + 2.11457e9i) q^{55} -1.74352e9 q^{56} +(-1.80857e9 + 1.89940e9i) q^{57} +1.93553e9 q^{58} +(1.78549e9 + 3.09257e9i) q^{59} +(-1.68990e9 - 2.92699e9i) q^{60} +(-5.39925e9 + 9.35178e9i) q^{61} +(3.29832e9 + 5.71286e9i) q^{62} +(-1.57094e9 + 2.72095e9i) q^{63} +1.07374e9 q^{64} +2.72893e10 q^{65} +(-6.98929e8 + 1.21058e9i) q^{66} +(-3.36192e9 + 5.82301e9i) q^{67} -9.52076e9 q^{68} -3.81699e8 q^{69} +(-1.15633e10 + 2.00282e10i) q^{70} +(-1.34417e10 - 2.32816e10i) q^{71} +(9.67459e8 - 1.67569e9i) q^{72} +(-3.10210e9 - 5.37299e9i) q^{73} +(1.08548e10 + 1.88011e10i) q^{74} -3.29654e10 q^{75} +(-1.07424e10 - 2.59822e9i) q^{76} +9.56499e9 q^{77} +(7.81151e9 + 1.35299e10i) q^{78} +(-6.65774e9 - 1.15315e10i) q^{79} +(7.12122e9 - 1.23343e10i) q^{80} +(-1.74339e9 - 3.01964e9i) q^{81} +(7.65640e9 - 1.32613e10i) q^{82} +1.43601e10 q^{83} -1.32399e10 q^{84} +(-6.31431e10 + 1.09367e11i) q^{85} +(2.40566e10 - 4.16673e10i) q^{86} +1.46979e10 q^{87} -5.89056e9 q^{88} +(-4.66529e9 + 8.08051e9i) q^{89} +(-1.28327e10 - 2.22268e10i) q^{90} +(5.34511e10 - 9.25800e10i) q^{91} +(-8.04237e8 - 1.39298e9i) q^{92} +(2.50466e10 + 4.33820e10i) q^{93} +6.97393e9 q^{94} +(-1.01091e11 + 1.06168e11i) q^{95} +8.15373e9 q^{96} +(-5.17359e10 - 8.96093e10i) q^{97} +(1.36604e10 + 2.36606e10i) q^{98} +(-5.30749e9 + 9.19284e9i) 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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

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

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
$5$	6791.32	+	11762.9i	0.971895	+	1.68337i	0.689823	+	0.723978i	$0.257688\pi$
$5$	6791.32	+	11762.9i	0.971895	+	1.68337i	0.282071	+	0.959393i	$0.408978\pi$
$6$	−3888.00	+	6734.21i	−0.204124	+	0.353553i
$7$	53208.1			1.19657			0.598286	−	0.801283i	$-0.295849\pi$
$7$	53208.1			1.19657			0.598286	+	0.801283i	$0.295849\pi$
$8$	−32768.0			−0.353553
$9$	−29524.5	+	51137.9i	−0.166667	+	0.288675i
$10$	−217322.	+	376413.i	−0.687233	+	1.19032i
$11$	179766.			0.336548			0.168274	−	0.985740i	$-0.446181\pi$
$11$	179766.			0.336548			0.168274	+	0.985740i	$0.446181\pi$
$12$	−248832.			−0.288675
$13$	1.00457e6	−	1.73996e6i	0.750395	−	1.29972i	−0.197236	−	0.980356i	$-0.563197\pi$
$13$	1.00457e6	−	1.73996e6i	0.750395	−	1.29972i	0.947631	−	0.319367i	$-0.103470\pi$
$14$	851330.	+	1.47455e6i	0.423052	+	0.732747i
$15$	−1.65029e6	+	2.85839e6i	−0.561124	+	0.971895i
$16$	−524288.	−	908093.i	−0.125000	−	0.216506i
$17$	4.64881e6	+	8.05197e6i	0.794095	+	1.37541i	0.923412	+	0.383809i	$0.125388\pi$
$17$	4.64881e6	+	8.05197e6i	0.794095	+	1.37541i	−0.129317	+	0.991603i	$0.541279\pi$
$18$	−1.88957e6			−0.235702
$19$	3.04790e6	+	1.03538e7i	0.282394	+	0.959298i
$19$	3.04790e6	+	1.03538e7i	0.282394	+	0.959298i
$20$	−1.39086e7			−0.971895
$21$	6.46479e6	+	1.11973e7i	0.345420	+	0.598286i
$22$	2.87625e6	+	4.98181e6i	0.118988	+	0.206093i
$23$	−785388.	+	1.36033e6i	−0.0254437	+	0.0440699i	−0.878467	−	0.477803i	$-0.841433\pi$
$23$	−785388.	+	1.36033e6i	−0.0254437	+	0.0440699i	0.853023	+	0.521873i	$0.174767\pi$
$24$	−3.98131e6	−	6.89583e6i	−0.102062	−	0.176777i
$25$	−6.78300e7	+	1.17485e8i	−1.38916	+	2.40609i
$26$	6.42922e7			1.06122
$27$	−1.43489e7			−0.192450
$28$	−2.72426e7	+	4.71855e7i	−0.299143	+	0.518131i
$29$	3.02426e7	−	5.23818e7i	0.273798	−	0.474232i	−0.696033	−	0.718010i	$-0.745053\pi$
$29$	3.02426e7	−	5.23818e7i	0.273798	−	0.474232i	0.969831	+	0.243777i	$0.0783867\pi$
$30$	−1.05619e8			−0.793549
$31$	2.06145e8			1.29325			0.646626	−	0.762807i	$-0.276179\pi$
$31$	2.06145e8			1.29325			0.646626	+	0.762807i	$0.276179\pi$
$32$	1.67772e7	−	2.90590e7i	0.0883883	−	0.153093i
$33$	2.18415e7	+	3.78306e7i	0.0971530	+	0.168274i
$34$	−1.48762e8	+	2.57663e8i	−0.561510	+	0.972564i
$35$	3.61353e8	+	6.25883e8i	1.16294	+	2.01427i
$36$	−3.02331e7	−	5.23652e7i	−0.0833333	−	0.144338i
$37$	6.78424e8			1.60839			0.804196	−	0.594364i	$-0.202596\pi$
$37$	6.78424e8			1.60839			0.804196	+	0.594364i	$0.202596\pi$
$38$	−2.38166e8	+	2.50126e8i	−0.487607	+	0.512094i
$39$	4.88219e8			0.866482
$40$	−2.22538e8	−	3.85447e8i	−0.343617	−	0.595162i
$41$	−2.39263e8	−	4.14415e8i	−0.322525	−	0.558630i	0.658483	−	0.752595i	$-0.271198\pi$
$41$	−2.39263e8	−	4.14415e8i	−0.322525	−	0.558630i	−0.981008	+	0.193966i	$0.937865\pi$
$42$	−2.06873e8	+	3.58315e8i	−0.244249	+	0.423052i
$43$	−7.51769e8	−	1.30210e9i	−0.779844	−	1.35073i	−0.932031	−	0.362378i	$-0.881965\pi$
$43$	−7.51769e8	−	1.30210e9i	−0.779844	−	1.35073i	0.152187	−	0.988352i	$-0.451368\pi$
$44$	−9.20400e7	+	1.59418e8i	−0.0841370	+	0.145730i
$45$	−8.02041e8			−0.647930
$46$	−5.02648e7			−0.0359829
$47$	1.08968e8	−	1.88738e8i	0.0693042	−	0.120038i	−0.829291	−	0.558817i	$-0.811255\pi$
$47$	1.08968e8	−	1.88738e8i	0.0693042	−	0.120038i	0.898595	+	0.438779i	$0.144589\pi$
$48$	1.27402e8	−	2.20667e8i	0.0721688	−	0.125000i
$49$	8.53777e8			0.431784
$50$	−4.34112e9			−1.96457
$51$	−1.12966e9	+	1.95663e9i	−0.458471	+	0.794095i
$52$	1.02868e9	+	1.78172e9i	0.375198	+	0.649861i
$53$	1.87620e9	−	3.24967e9i	0.616257	−	1.06739i	−0.373906	−	0.927467i	$-0.621982\pi$
$53$	1.87620e9	−	3.24967e9i	0.616257	−	1.06739i	0.990163	−	0.139921i	$-0.0446849\pi$
$54$	−2.29583e8	−	3.97649e8i	−0.0680414	−	0.117851i
$55$	1.22085e9	+	2.11457e9i	0.327089	+	0.566535i
$56$	−1.74352e9			−0.423052
$57$	−1.80857e9	+	1.89940e9i	−0.398129	+	0.418123i
$58$	1.93553e9			0.387209
$59$	1.78549e9	+	3.09257e9i	0.325142	+	0.563162i	0.981541	−	0.191252i	$-0.0612547\pi$
$59$	1.78549e9	+	3.09257e9i	0.325142	+	0.563162i	−0.656399	+	0.754414i	$0.727921\pi$
$60$	−1.68990e9	−	2.92699e9i	−0.280562	−	0.485947i
$61$	−5.39925e9	+	9.35178e9i	−0.818501	+	1.41769i	0.0882850	+	0.996095i	$0.471861\pi$
$61$	−5.39925e9	+	9.35178e9i	−0.818501	+	1.41769i	−0.906786	+	0.421591i	$0.861472\pi$
$62$	3.29832e9	+	5.71286e9i	0.457234	+	0.791952i
$63$	−1.57094e9	+	2.72095e9i	−0.199429	+	0.345420i
$64$	1.07374e9			0.125000
$65$	2.72893e10			2.91722
$66$	−6.98929e8	+	1.21058e9i	−0.0686976	+	0.118988i
$67$	−3.36192e9	+	5.82301e9i	−0.304211	+	0.526910i	−0.977085	−	0.212847i	$-0.931726\pi$
$67$	−3.36192e9	+	5.82301e9i	−0.304211	+	0.526910i	0.672874	+	0.739757i	$0.265060\pi$
$68$	−9.52076e9			−0.794095
$69$	−3.81699e8			−0.0293799
$70$	−1.15633e10	+	2.00282e10i	−0.822324	+	1.42431i
$71$	−1.34417e10	−	2.32816e10i	−0.884162	−	1.53141i	−0.846671	−	0.532116i	$-0.821397\pi$
$71$	−1.34417e10	−	2.32816e10i	−0.884162	−	1.53141i	−0.0374903	−	0.999297i	$-0.511936\pi$
$72$	9.67459e8	−	1.67569e9i	0.0589256	−	0.102062i
$73$	−3.10210e9	−	5.37299e9i	−0.175138	−	0.303347i	0.765071	−	0.643946i	$-0.222704\pi$
$73$	−3.10210e9	−	5.37299e9i	−0.175138	−	0.303347i	−0.940209	+	0.340598i	$0.889370\pi$
$74$	1.08548e10	+	1.88011e10i	0.568653	+	0.984935i
$75$	−3.29654e10			−1.60406
$76$	−1.07424e10	−	2.59822e9i	−0.485987	−	0.117544i
$77$	9.56499e9			0.402704
$78$	7.81151e9	+	1.35299e10i	0.306348	+	0.530610i
$79$	−6.65774e9	−	1.15315e10i	−0.243432	−	0.421637i	0.718257	−	0.695777i	$-0.244940\pi$
$79$	−6.65774e9	−	1.15315e10i	−0.243432	−	0.421637i	−0.961690	+	0.274141i	$0.911607\pi$
$80$	7.12122e9	−	1.23343e10i	0.242974	−	0.420843i
$81$	−1.74339e9	−	3.01964e9i	−0.0555556	−	0.0962250i
$82$	7.65640e9	−	1.32613e10i	0.228060	−	0.395011i
$83$	1.43601e10			0.400154			0.200077	−	0.979780i	$-0.435881\pi$
$83$	1.43601e10			0.400154			0.200077	+	0.979780i	$0.435881\pi$
$84$	−1.32399e10			−0.345420
$85$	−6.31431e10	+	1.09367e11i	−1.54355	+	2.67351i
$86$	2.40566e10	−	4.16673e10i	0.551433	−	0.955110i
$87$	1.46979e10			0.316155
$88$	−5.89056e9			−0.118988
$89$	−4.66529e9	+	8.08051e9i	−0.0885591	+	0.153389i	−0.906902	−	0.421341i	$-0.861560\pi$
$89$	−4.66529e9	+	8.08051e9i	−0.0885591	+	0.153389i	0.818343	+	0.574730i	$0.194893\pi$
$90$	−1.28327e10	−	2.22268e10i	−0.229078	−	0.396774i
$91$	5.34511e10	−	9.25800e10i	0.897902	−	1.55521i
$92$	−8.04237e8	−	1.39298e9i	−0.0127219	−	0.0220349i
$93$	2.50466e10	+	4.33820e10i	0.373330	+	0.646626i
$94$	6.97393e9			0.0980109
$95$	−1.01091e11	+	1.06168e11i	−1.34040	+	1.40771i
$96$	8.15373e9			0.102062
$97$	−5.17359e10	−	8.96093e10i	−0.611713	−	1.05952i	−0.990952	−	0.134219i	$-0.957147\pi$
$97$	−5.17359e10	−	8.96093e10i	−0.611713	−	1.05952i	0.379238	−	0.925299i	$-0.376186\pi$
$98$	1.36604e10	+	2.36606e10i	0.152659	+	0.264412i
$99$	−5.30749e9	+	9.19284e9i	−0.0560913	+	0.0971530i
$100$	−6.94579e10	−	1.20305e11i	−0.694579	−	1.20305i
$101$	6.77099e10	−	1.17277e11i	0.641039	−	1.11031i	−0.344162	−	0.938910i	$-0.611837\pi$
$101$	6.77099e10	−	1.17277e11i	0.641039	−	1.11031i	0.985201	−	0.171402i	$-0.0548298\pi$
$102$	−7.22982e10			−0.648376
$103$	−1.63666e11			−1.39108			−0.695542	−	0.718485i	$-0.744836\pi$
$103$	−1.63666e11			−1.39108			−0.695542	+	0.718485i	$0.744836\pi$
$104$	−3.29176e10	+	5.70150e10i	−0.265305	+	0.459521i
$105$	−8.78089e10	+	1.52089e11i	−0.671425	+	1.16294i
$106$	1.20077e11			0.871518
$107$	2.82693e11			1.94851			0.974257	−	0.225440i	$-0.0723819\pi$
$107$	2.82693e11			1.94851			0.974257	+	0.225440i	$0.0723819\pi$
$108$	7.34664e9	−	1.27248e10i	0.0481125	−	0.0833333i
$109$	−1.21165e11	−	2.09864e11i	−0.754276	−	1.30645i	−0.945733	−	0.324944i	$-0.894654\pi$
$109$	−1.21165e11	−	2.09864e11i	−0.754276	−	1.30645i	0.191457	−	0.981501i	$-0.438679\pi$
$110$	−3.90671e10	+	6.76662e10i	−0.231287	+	0.400601i
$111$	8.24286e10	+	1.42770e11i	0.464303	+	0.804196i
$112$	−2.78964e10	−	4.83179e10i	−0.149571	−	0.259065i
$113$	−1.58405e11			−0.808793			−0.404396	−	0.914584i	$-0.632518\pi$
$113$	−1.58405e11			−0.808793			−0.404396	+	0.914584i	$0.632518\pi$
$114$	−8.15747e10	−	1.97303e10i	−0.396807	−	0.0959746i
$115$	−2.13353e10			−0.0989146
$116$	3.09684e10	+	5.36389e10i	0.136899	+	0.237116i
$117$	5.93186e10	+	1.02743e11i	0.250132	+	0.433241i
$118$	−5.71358e10	+	9.89621e10i	−0.229910	+	0.398215i
$119$	2.47354e11	+	4.28430e11i	0.950191	+	1.64578i
$120$	5.40767e10	−	9.36637e10i	0.198387	−	0.343617i
$121$	−2.52996e11			−0.886735
$122$	−3.45552e11			−1.15754
$123$	5.81408e10	−	1.00703e11i	0.186210	−	0.322525i
$124$	−1.05546e11	+	1.82811e11i	−0.323313	+	0.559995i
$125$	−1.17941e12			−3.45668
$126$	−1.00540e11			−0.282035
$127$	−2.41964e11	+	4.19094e11i	−0.649876	+	1.12562i	0.333276	+	0.942829i	$0.391846\pi$
$127$	−2.41964e11	+	4.19094e11i	−0.649876	+	1.12562i	−0.983152	+	0.182790i	$0.941487\pi$
$128$	1.71799e10	+	2.97564e10i	0.0441942	+	0.0765466i
$129$	1.82680e11	−	3.16411e11i	0.450243	−	0.779844i
$130$	4.36629e11	+	7.56264e11i	1.03139	+	1.78643i
$131$	−2.79193e11	−	4.83577e11i	−0.632285	−	1.09515i	−0.987084	−	0.160207i	$-0.948784\pi$
$131$	−2.79193e11	−	4.83577e11i	−0.632285	−	1.09515i	0.354799	−	0.934943i	$-0.384549\pi$
$132$	−4.47314e10			−0.0971530
$133$	1.62173e11	+	5.50905e11i	0.337905	+	1.14787i
$134$	−2.15163e11			−0.430220
$135$	−9.74480e10	−	1.68785e11i	−0.187041	−	0.323965i
$136$	−1.52332e11	−	2.63847e11i	−0.280755	−	0.486282i
$137$	6.49881e10	−	1.12563e11i	0.115046	−	0.199265i	−0.802752	−	0.596313i	$-0.796632\pi$
$137$	6.49881e10	−	1.12563e11i	0.115046	−	0.199265i	0.917798	+	0.397048i	$0.129965\pi$
$138$	−6.10718e9	−	1.05779e10i	−0.0103874	−	0.0179914i
$139$	1.29824e11	−	2.24861e11i	0.212213	−	0.367564i	−0.740194	−	0.672394i	$-0.765266\pi$
$139$	1.29824e11	−	2.24861e11i	0.212213	−	0.367564i	0.952407	+	0.304830i	$0.0985995\pi$
$140$	−7.40052e11			−1.16294
$141$	5.29583e10			0.0800256
$142$	4.30133e11	−	7.45012e11i	0.625197	−	1.08287i
$143$	1.80586e11	−	3.12785e11i	0.252544	−	0.437419i
$144$	6.19174e10			0.0833333
$145$	8.21549e11			1.06441
$146$	9.92671e10	−	1.71936e11i	0.123841	−	0.214499i
$147$	1.03734e11	+	1.79672e11i	0.124645	+	0.215892i
$148$	−3.47353e11	+	6.01634e11i	−0.402098	+	0.696454i
$149$	−2.92973e11	−	5.07444e11i	−0.326816	−	0.566061i	0.655062	−	0.755575i	$-0.272642\pi$
$149$	−2.92973e11	−	5.07444e11i	−0.326816	−	0.566061i	−0.981878	+	0.189513i	$0.939309\pi$
$150$	−5.27446e11	−	9.13564e11i	−0.567122	−	0.982284i
$151$	−1.34685e12			−1.39619			−0.698096	−	0.716004i	$-0.745969\pi$
$151$	−1.34685e12			−1.39619			−0.698096	+	0.716004i	$0.745969\pi$
$152$	−9.98735e10	−	3.39272e11i	−0.0998414	−	0.339163i
$153$	−5.49015e11			−0.529397
$154$	1.53040e11	+	2.65073e11i	0.142377	+	0.246605i
$155$	1.40000e12	+	2.42486e12i	1.25691	+	2.17702i
$156$	−2.49968e11	+	4.32958e11i	−0.216620	+	0.375198i
$157$	−3.01633e11	−	5.22443e11i	−0.252366	−	0.437110i	0.711811	−	0.702371i	$-0.247875\pi$
$157$	−3.01633e11	−	5.22443e11i	−0.252366	−	0.437110i	−0.964177	+	0.265261i	$0.914542\pi$
$158$	2.13048e11	−	3.69010e11i	0.172133	−	0.298142i
$159$	9.11833e11			0.711592
$160$	4.55758e11			0.343617
$161$	−4.17890e10	+	7.23807e10i	−0.0304453	+	0.0527327i
$162$	5.57886e10	−	9.66286e10i	0.0392837	−	0.0680414i
$163$	1.10517e12			0.752311			0.376155	−	0.926557i	$-0.377246\pi$
$163$	1.10517e12			0.752311			0.376155	+	0.926557i	$0.377246\pi$
$164$	4.90010e11			0.322525
$165$	−2.96666e11	+	5.13840e11i	−0.188845	+	0.327089i
$166$	2.29761e11	+	3.97958e11i	0.141476	+	0.245043i
$167$	2.33898e11	−	4.05123e11i	0.139343	−	0.241349i	−0.787905	−	0.615797i	$-0.788834\pi$
$167$	2.33898e11	−	4.05123e11i	0.139343	−	0.241349i	0.927248	+	0.374447i	$0.122168\pi$
$168$	−2.11838e11	−	3.66914e11i	−0.122125	−	0.211526i
$169$	−1.12223e12	−	1.94375e12i	−0.626186	−	1.08459i
$170$	−4.04116e12			−2.18291
$171$	−6.19458e11	−	1.49827e11i	−0.323991	−	0.0783629i
$172$	1.53962e12			0.779844
$173$	−7.87387e11	−	1.36379e12i	−0.386309	−	0.669106i	0.605641	−	0.795738i	$-0.292917\pi$
$173$	−7.87387e11	−	1.36379e12i	−0.386309	−	0.669106i	−0.991950	+	0.126632i	$0.959583\pi$
$174$	2.35167e11	+	4.07321e11i	0.111778	+	0.193605i
$175$	−3.60911e12	+	6.25116e12i	−1.66223	+	2.87906i
$176$	−9.42490e10	−	1.63244e11i	−0.0420685	−	0.0728648i
$177$	−4.33875e11	+	7.51494e11i	−0.187721	+	0.325142i
$178$	−2.98578e11			−0.125241
$179$	3.45430e12			1.40497			0.702486	−	0.711697i	$-0.252073\pi$
$179$	3.45430e12			1.40497			0.702486	+	0.711697i	$0.252073\pi$
$180$	4.10645e11	−	7.11258e11i	0.161982	−	0.280562i
$181$	−3.15898e11	+	5.47151e11i	−0.120869	+	0.209351i	−0.920111	−	0.391659i	$-0.871901\pi$
$181$	−3.15898e11	+	5.47151e11i	−0.120869	+	0.209351i	0.799242	+	0.601010i	$0.205235\pi$
$182$	3.42087e12			1.26982
$183$	−2.62404e12			−0.945124
$184$	2.57356e10	−	4.45753e10i	0.00899572	−	0.0155811i
$185$	4.60740e12	+	7.98025e12i	1.56319	+	2.70752i
$186$	−8.01491e11	+	1.38822e12i	−0.263984	+	0.457234i
$187$	8.35696e11	+	1.44747e12i	0.267251	+	0.462892i
$188$	1.11583e11	+	1.93267e11i	0.0346521	+	0.0600192i
$189$	−7.63478e11			−0.230280
$190$	−4.55967e12	−	1.10284e12i	−1.33595	−	0.323122i
$191$	−4.57791e12			−1.30312			−0.651559	−	0.758598i	$-0.725885\pi$
$191$	−4.57791e12			−1.30312			−0.651559	+	0.758598i	$0.725885\pi$
$192$	1.30460e11	+	2.25963e11i	0.0360844	+	0.0625000i
$193$	−2.31236e12	−	4.00513e12i	−0.621571	−	1.07659i	−0.989193	−	0.146617i	$-0.953162\pi$
$193$	−2.31236e12	−	4.00513e12i	−0.621571	−	1.07659i	0.367623	−	0.929975i	$-0.380172\pi$
$194$	1.65555e12	−	2.86750e12i	0.432547	−	0.749193i
$195$	3.31565e12	+	5.74288e12i	0.842129	+	1.45861i
$196$	−4.37134e11	+	7.57138e11i	−0.107946	+	0.186968i
$197$	1.72275e12			0.413674			0.206837	−	0.978375i	$-0.433683\pi$
$197$	1.72275e12			0.413674			0.206837	+	0.978375i	$0.433683\pi$
$198$	−3.39679e11			−0.0793251
$199$	−2.48395e12	+	4.30233e12i	−0.564223	+	0.977264i	0.432898	+	0.901443i	$0.357491\pi$
$199$	−2.48395e12	+	4.30233e12i	−0.564223	+	0.977264i	−0.997121	+	0.0758207i	$0.975842\pi$
$200$	2.22265e12	−	3.84975e12i	0.491142	−	0.850683i
$201$	−1.63389e12			−0.351273
$202$	4.33343e12			0.906567
$203$	1.60915e12	−	2.78713e12i	0.327619	−	0.567453i
$204$	−1.15677e12	−	2.00359e12i	−0.229235	−	0.397047i
$205$	3.24982e12	−	5.62885e12i	0.626921	−	1.08586i
$206$	−2.61865e12	−	4.53564e12i	−0.491823	−	0.851862i
$207$	−4.63764e10	−	8.03262e10i	−0.00848125	−	0.0146900i
$208$	−2.10673e12			−0.375198
$209$	5.47907e11	+	1.86125e12i	0.0950392	+	0.322850i
$210$	−5.61977e12			−0.949538
$211$	−1.93517e12	−	3.35182e12i	−0.318542	−	0.551730i	0.661642	−	0.749820i	$-0.269860\pi$
$211$	−1.93517e12	−	3.35182e12i	−0.318542	−	0.551730i	−0.980184	+	0.198089i	$0.936526\pi$
$212$	1.92123e12	+	3.32766e12i	0.308128	+	0.533694i
$213$	3.26632e12	−	5.65743e12i	0.510471	−	0.884162i
$214$	4.52308e12	+	7.83421e12i	0.688904	+	1.19322i
$215$	1.02110e13	−	1.76860e13i	1.51585	−	2.62553i
$216$	4.70185e11			0.0680414
$217$	1.09686e13			1.54747
$218$	3.87727e12	−	6.71563e12i	0.533354	−	0.923796i
$219$	7.53809e11	−	1.30564e12i	0.101116	−	0.175138i
$220$	−2.50029e12			−0.327089
$221$	1.86801e13			2.38354
$222$	−2.63771e12	+	4.56866e12i	−0.328312	+	0.568653i
$223$	2.49611e12	+	4.32339e12i	0.303101	+	0.524986i	0.976837	−	0.213986i	$-0.0686448\pi$
$223$	2.49611e12	+	4.32339e12i	0.303101	+	0.524986i	−0.673736	+	0.738972i	$0.735311\pi$
$224$	8.92684e11	−	1.54617e12i	0.105763	−	0.183187i
$225$	−4.00530e12	−	6.93738e12i	−0.463053	−	0.802031i
$226$	−2.53448e12	−	4.38985e12i	−0.285951	−	0.495282i
$227$	9.48152e12			1.04408			0.522042	−	0.852920i	$-0.325170\pi$
$227$	9.48152e12			1.04408			0.522042	+	0.852920i	$0.325170\pi$
$228$	−7.58415e11	−	2.57635e12i	−0.0815202	−	0.276926i
$229$	7.58136e12			0.795521			0.397761	−	0.917489i	$-0.369787\pi$
$229$	7.58136e12			0.795521			0.397761	+	0.917489i	$0.369787\pi$
$230$	−3.41365e11	−	5.91261e11i	−0.0349716	−	0.0605726i
$231$	1.16215e12	+	2.01290e12i	0.116251	+	0.201352i
$232$	−9.90990e11	+	1.71645e12i	−0.0968023	+	0.167666i
$233$	−7.34494e12	−	1.27218e13i	−0.700697	−	1.21364i	−0.968222	−	0.250092i	$-0.919539\pi$
$233$	−7.34494e12	−	1.27218e13i	−0.700697	−	1.21364i	0.267525	−	0.963551i	$-0.413794\pi$
$234$	−1.89820e12	+	3.28777e12i	−0.176870	+	0.306348i
$235$	2.96014e12			0.269426
$236$	−3.65669e12			−0.325142
$237$	1.61783e12	−	2.80217e12i	0.140546	−	0.243432i
$238$	−7.91534e12	+	1.37098e13i	−0.671887	+	1.16374i
$239$	−6.31747e11			−0.0524028			−0.0262014	−	0.999657i	$-0.508341\pi$
$239$	−6.31747e11			−0.0524028			−0.0262014	+	0.999657i	$0.508341\pi$
$240$	3.46091e12			0.280562
$241$	−3.52513e11	+	6.10570e11i	−0.0279307	+	0.0483773i	−0.879653	−	0.475616i	$-0.842225\pi$
$241$	−3.52513e11	+	6.10570e11i	−0.0279307	+	0.0483773i	0.851722	+	0.523994i	$0.175558\pi$
$242$	−4.04794e12	−	7.01123e12i	−0.313508	−	0.543012i
$243$	4.23644e11	−	7.33773e11i	0.0320750	−	0.0555556i
$244$	−5.52883e12	−	9.57622e12i	−0.409251	−	0.708843i
$245$	5.79828e12	+	1.00429e13i	0.419648	+	0.726852i
$246$	3.72101e12			0.263341
$247$	2.10770e13	+	5.09783e12i	1.45873	+	0.352819i
$248$	−6.75496e12			−0.457234
$249$	1.74475e12	+	3.02199e12i	0.115514	+	0.200077i
$250$	−1.88705e13	−	3.26847e13i	−1.22212	−	2.11677i
$251$	−4.00122e12	+	6.93032e12i	−0.253506	+	0.439084i	−0.964489	−	0.264125i	$-0.914917\pi$
$251$	−4.00122e12	+	6.93032e12i	−0.253506	+	0.439084i	0.710983	+	0.703209i	$0.248250\pi$
$252$	−1.60865e12	−	2.78626e12i	−0.0997143	−	0.172710i
$253$	−1.41186e11	+	2.44541e11i	−0.00856304	+	0.0148316i
$254$	−1.54857e13			−0.919064
$255$	−3.06875e13			−1.78234
$256$	−5.49756e11	+	9.52205e11i	−0.0312500	+	0.0541266i
$257$	1.51750e12	−	2.62838e12i	0.0844297	−	0.146237i	−0.820718	−	0.571333i	$-0.806426\pi$
$257$	1.51750e12	−	2.62838e12i	0.0844297	−	0.146237i	0.905148	+	0.425096i	$0.139760\pi$
$258$	1.16915e13			0.636740
$259$	3.60977e13			1.92456
$260$	−1.39721e13	+	2.42004e13i	−0.729305	+	1.26319i
$261$	1.78580e12	+	3.09309e12i	0.0912660	+	0.158077i
$262$	8.93418e12	−	1.54745e13i	0.447093	−	0.774388i
$263$	1.50589e12	+	2.60829e12i	0.0737969	+	0.127820i	0.900562	−	0.434727i	$-0.143155\pi$
$263$	1.50589e12	+	2.60829e12i	0.0737969	+	0.127820i	−0.826766	+	0.562547i	$0.809822\pi$
$264$	−7.15703e11	−	1.23963e12i	−0.0343488	−	0.0594938i
$265$	5.09675e13			2.39575
$266$	−1.26724e13	+	1.33087e13i	−0.583456	+	0.612757i
$267$	−2.26733e12			−0.102259
$268$	−3.44260e12	−	5.96276e12i	−0.152106	−	0.263455i
$269$	−1.33221e13	−	2.30745e13i	−0.576679	−	0.998838i	−0.995857	−	0.0909338i	$-0.971015\pi$
$269$	−1.33221e13	−	2.30745e13i	−0.576679	−	0.998838i	0.419178	−	0.907904i	$-0.362318\pi$
$270$	3.11834e12	−	5.40112e12i	0.132258	−	0.229078i
$271$	7.04551e12	+	1.22032e13i	0.292807	+	0.507157i	0.974472	−	0.224507i	$-0.0720773\pi$
$271$	7.04551e12	+	1.22032e13i	0.292807	+	0.507157i	−0.681665	+	0.731664i	$0.738744\pi$
$272$	4.87463e12	−	8.44310e12i	0.198524	−	0.343853i
$273$	2.59772e13			1.03681
$274$	4.15924e12			0.162699
$275$	−1.21935e13	+	2.11198e13i	−0.467519	+	0.809766i
$276$	1.95430e11	−	3.38494e11i	0.00734498	−	0.0127219i
$277$	3.12119e13			1.14996			0.574979	−	0.818168i	$-0.305010\pi$
$277$	3.12119e13			1.14996			0.574979	+	0.818168i	$0.305010\pi$
$278$	8.30872e12			0.300115
$279$	−6.08633e12	+	1.05418e13i	−0.215542	+	0.373330i
$280$	−1.18408e13	−	2.05089e13i	−0.411162	−	0.712153i
$281$	−6.48819e12	+	1.12379e13i	−0.220922	+	0.382648i	−0.955088	−	0.296322i	$-0.904240\pi$
$281$	−6.48819e12	+	1.12379e13i	−0.220922	+	0.382648i	0.734166	+	0.678970i	$0.237573\pi$
$282$	8.47333e11	+	1.46762e12i	0.0282933	+	0.0490055i
$283$	1.35463e13	+	2.34628e13i	0.443603	+	0.768343i	0.997954	−	0.0639402i	$-0.0203667\pi$
$283$	1.35463e13	+	2.34628e13i	0.443603	+	0.768343i	−0.554351	+	0.832283i	$0.687033\pi$
$284$	2.75285e13			0.884162
$285$	−3.46250e13	−	8.37466e12i	−1.09080	−	0.263828i
$286$	1.15575e13			0.357151
$287$	−1.27307e13	−	2.20502e13i	−0.385924	−	0.668441i
$288$	9.90678e11	+	1.71590e12i	0.0294628	+	0.0510310i
$289$	−2.60869e13	+	4.51838e13i	−0.761173	+	1.31839i
$290$	1.31448e13	+	2.27674e13i	0.376326	+	0.651816i
$291$	1.25718e13	−	2.17751e13i	0.353173	−	0.611713i
$292$	6.35309e12			0.175138
$293$	1.12081e13			0.303222			0.151611	−	0.988440i	$-0.451554\pi$
$293$	1.12081e13			0.303222			0.151611	+	0.988440i	$0.451554\pi$
$294$	−3.31949e12	+	5.74952e12i	−0.0881375	+	0.152659i
$295$	−2.42517e13	+	4.20052e13i	−0.632007	+	1.09467i
$296$	−2.22306e13			−0.568653
$297$	−2.57944e12			−0.0647687
$298$	9.37513e12	−	1.62382e13i	0.231094	−	0.400266i
$299$	1.57795e12	+	2.73309e12i	0.0381857	+	0.0661396i
$300$	1.68783e13	−	2.92340e13i	0.401016	−	0.694579i
$301$	−4.00002e13	−	6.92824e13i	−0.933140	−	1.61625i
$302$	−2.15496e13	−	3.73249e13i	−0.493629	−	0.854990i
$303$	3.29070e13			0.740209
$304$	7.80422e12	−	8.19613e12i	0.172395	−	0.181052i
$305$	−1.46672e14			−3.18199
$306$	−8.78424e12	−	1.52147e13i	−0.187170	−	0.324188i
$307$	7.10395e12	+	1.23044e13i	0.148675	+	0.257513i	0.930738	−	0.365686i	$-0.119166\pi$
$307$	7.10395e12	+	1.23044e13i	0.148675	+	0.257513i	−0.782063	+	0.623200i	$0.785832\pi$
$308$	−4.89728e12	+	8.48233e12i	−0.100676	+	0.174376i
$309$	−1.98854e13	−	3.44425e13i	−0.401572	−	0.695542i
$310$	−4.47999e13	+	7.75957e13i	−0.888766	+	1.53939i
$311$	3.22066e13			0.627714			0.313857	−	0.949470i	$-0.398379\pi$
$311$	3.22066e13			0.627714			0.313857	+	0.949470i	$0.398379\pi$
$312$	−1.59980e13			−0.306348
$313$	−7.22571e12	+	1.25153e13i	−0.135952	+	0.235476i	−0.925961	−	0.377620i	$-0.876743\pi$
$313$	−7.22571e12	+	1.25153e13i	−0.135952	+	0.235476i	0.790009	+	0.613096i	$0.210076\pi$
$314$	9.65224e12	−	1.67182e13i	0.178449	−	0.309083i
$315$	−4.26751e13			−0.775294
$316$	1.36351e13			0.243432
$317$	−1.72323e13	+	2.98473e13i	−0.302356	+	0.523695i	−0.976669	−	0.214750i	$-0.931106\pi$
$317$	−1.72323e13	+	2.98473e13i	−0.302356	+	0.523695i	0.674313	+	0.738445i	$0.264440\pi$
$318$	1.45893e13	+	2.52694e13i	0.251586	+	0.435759i
$319$	5.43658e12	−	9.41644e12i	0.0921462	−	0.159602i
$320$	7.29213e12	+	1.26303e13i	0.121487	+	0.210421i
$321$	3.43471e13	+	5.94910e13i	0.562488	+	0.974257i
$322$	−2.67450e12			−0.0430561
$323$	−6.91992e13	+	7.26743e13i	−1.09518	+	1.15018i
$324$	3.57047e12			0.0555556
$325$	1.36279e14	+	2.36043e14i	2.08484	+	3.61104i
$326$	1.76827e13	+	3.06274e13i	0.265982	+	0.460694i
$327$	2.94430e13	−	5.09968e13i	0.435482	−	0.754276i
$328$	7.84016e12	+	1.35795e13i	0.114030	+	0.197505i
$329$	5.79797e12	−	1.00424e13i	0.0829274	−	0.143635i
$330$	−1.89866e13			−0.267067
$331$	−4.43649e13			−0.613741			−0.306870	−	0.951751i	$-0.599282\pi$
$331$	−4.43649e13			−0.613741			−0.306870	+	0.951751i	$0.599282\pi$
$332$	−7.35235e12	+	1.27347e13i	−0.100038	+	0.173272i
$333$	−2.00301e13	+	3.46932e13i	−0.268065	+	0.464303i
$334$	1.49695e13			0.197061
$335$	−9.13274e13			−1.18265
$336$	6.77882e12	−	1.17413e13i	0.0863551	−	0.149571i
$337$	5.37541e13	+	9.31048e13i	0.673670	+	1.16683i	0.976856	+	0.213899i	$0.0686162\pi$
$337$	5.37541e13	+	9.31048e13i	0.673670	+	1.16683i	−0.303186	+	0.952931i	$0.598050\pi$
$338$	3.59112e13	−	6.22001e13i	0.442780	−	0.766918i
$339$	−1.92462e13	−	3.33354e13i	−0.233478	−	0.404396i
$340$	−6.46585e13	−	1.11992e14i	−0.771777	−	1.33676i
$341$	3.70578e13			0.435241
$342$	−5.75921e12	−	1.95642e13i	−0.0665609	−	0.226109i
$343$	−5.97820e13			−0.679912
$344$	2.46340e13	+	4.26673e13i	0.275717	+	0.477555i
$345$	−2.59224e12	−	4.48989e12i	−0.0285542	−	0.0494573i
$346$	2.51964e13	−	4.36414e13i	0.273161	−	0.473130i
$347$	5.16583e12	+	8.94747e12i	0.0551223	+	0.0954747i	0.892270	−	0.451502i	$-0.149112\pi$
$347$	5.16583e12	+	8.94747e12i	0.0551223	+	0.0954747i	−0.837148	+	0.546977i	$0.815778\pi$
$348$	−7.52533e12	+	1.30343e13i	−0.0790387	+	0.136899i
$349$	−8.35262e13			−0.863541			−0.431771	−	0.901983i	$-0.642111\pi$
$349$	−8.35262e13			−0.863541			−0.431771	+	0.901983i	$0.642111\pi$
$350$	−2.30983e14			−2.35075
$351$	−1.44144e13	+	2.49665e13i	−0.144414	+	0.250132i
$352$	3.01597e12	−	5.22381e12i	0.0297469	−	0.0515232i
$353$	1.01008e14			0.980833			0.490416	−	0.871488i	$-0.336845\pi$
$353$	1.01008e14			0.980833			0.490416	+	0.871488i	$0.336845\pi$
$354$	−2.77680e13			−0.265477
$355$	1.82573e14	−	3.16226e14i	1.71862	−	2.97674i
$356$	−4.77725e12	−	8.27444e12i	−0.0442796	−	0.0766944i
$357$	−6.01071e13	+	1.04109e14i	−0.548593	+	0.950191i
$358$	5.52687e13	+	9.57282e13i	0.496733	+	0.860366i
$359$	−2.68367e13	−	4.64826e13i	−0.237526	−	0.411406i	0.722478	−	0.691394i	$-0.243003\pi$
$359$	−2.68367e13	−	4.64826e13i	−0.237526	−	0.411406i	−0.960004	+	0.279987i	$0.909670\pi$
$360$	2.62813e13			0.229078
$361$	−9.79109e13	+	6.31145e13i	−0.840507	+	0.541801i
$362$	−2.02175e13			−0.170934
$363$	−3.07390e13	−	5.32415e13i	−0.255978	−	0.443368i
$364$	5.47339e13	+	9.48019e13i	0.448951	+	0.777606i
$365$	4.21347e13	−	7.29794e13i	0.340431	−	0.589643i
$366$	−4.19846e13	−	7.27194e13i	−0.334152	−	0.578768i
$367$	−4.46835e13	+	7.73940e13i	−0.350335	+	0.606798i	−0.986308	−	0.164913i	$-0.947266\pi$
$367$	−4.46835e13	+	7.73940e13i	−0.350335	+	0.606798i	0.635973	+	0.771711i	$0.280599\pi$
$368$	1.64708e12			0.0127219
$369$	2.82564e13			0.215017
$370$	−1.47437e14	+	2.55368e14i	−1.10534	+	1.91451i
$371$	9.98290e13	−	1.72909e14i	0.737395	−	1.27721i
$372$	−5.12955e13			−0.373330
$373$	1.20954e14			0.867403			0.433702	−	0.901057i	$-0.357207\pi$
$373$	1.20954e14			0.867403			0.433702	+	0.901057i	$0.357207\pi$
$374$	−2.67423e13	+	4.63190e13i	−0.188975	+	0.327314i
$375$	−1.43298e14	−	2.48199e14i	−0.997856	−	1.72834i
$376$	−3.57065e12	+	6.18455e12i	−0.0245027	+	0.0424400i
$377$	−6.07614e13	−	1.05242e14i	−0.410914	−	0.711723i
$378$	−1.22157e13	−	2.11581e13i	−0.0814164	−	0.141017i
$379$	6.23301e13			0.409432			0.204716	−	0.978821i	$-0.434373\pi$
$379$	6.23301e13			0.409432			0.204716	+	0.978821i	$0.434373\pi$
$380$	−4.23921e13	−	1.44007e14i	−0.274457	−	0.932337i
$381$	−1.17595e14			−0.750413
$382$	−7.32466e13	−	1.26867e14i	−0.460722	−	0.797994i
$383$	−8.90821e13	−	1.54295e14i	−0.552328	−	0.956660i	−0.998106	−	0.0615168i	$-0.980406\pi$
$383$	−8.90821e13	−	1.54295e14i	−0.552328	−	0.956660i	0.445778	−	0.895144i	$-0.352927\pi$
$384$	−4.17471e12	+	7.23081e12i	−0.0255155	+	0.0441942i
$385$	6.49589e13	+	1.12512e14i	0.391386	+	0.677900i
$386$	7.39956e13	−	1.28164e14i	0.439517	−	0.761266i
$387$	8.87824e13			0.519896
$388$	1.05955e14			0.611713
$389$	−1.66388e14	+	2.88192e14i	−0.947107	+	1.64044i	−0.195629	+	0.980678i	$0.562675\pi$
$389$	−1.66388e14	+	2.88192e14i	−0.947107	+	1.64044i	−0.751478	+	0.659759i	$0.770658\pi$
$390$	−1.06101e14	+	1.83772e14i	−0.595475	+	1.03139i
$391$	−1.46045e13			−0.0808190
$392$	−2.79766e13			−0.152659
$393$	6.78439e13	−	1.17509e14i	0.365050	−	0.632285i
$394$	2.75640e13	+	4.77422e13i	0.146256	+	0.253322i
$395$	9.04297e13	−	1.56629e14i	0.473181	−	0.819573i
$396$	−5.43487e12	−	9.41347e12i	−0.0280457	−	0.0485765i
$397$	−4.91370e13	−	8.51078e13i	−0.250070	−	0.433133i	0.713475	−	0.700681i	$-0.247120\pi$
$397$	−4.91370e13	−	8.51078e13i	−0.250070	−	0.433133i	−0.963545	+	0.267547i	$0.913787\pi$
$398$	−1.58973e14			−0.797932
$399$	−9.62307e13	+	1.01063e14i	−0.476390	+	0.500314i
$400$	1.42250e14			0.694579
$401$	−1.99933e13	−	3.46295e13i	−0.0962922	−	0.166783i	0.813855	−	0.581068i	$-0.197365\pi$
$401$	−1.99933e13	−	3.46295e13i	−0.0962922	−	0.166783i	−0.910147	+	0.414285i	$0.864032\pi$
$402$	−2.61423e13	−	4.52797e13i	−0.124194	−	0.215110i
$403$	2.07086e14	−	3.58684e14i	0.970451	−	1.68087i
$404$	6.93350e13	+	1.20092e14i	0.320520	+	0.555156i
$405$	2.36799e13	−	4.10147e13i	0.107988	−	0.187041i
$406$	1.02986e14			0.463323
$407$	1.21957e14			0.541301
$408$	3.70167e13	−	6.41148e13i	0.162094	−	0.280755i
$409$	−3.96079e13	+	6.86028e13i	−0.171121	+	0.296390i	−0.938812	−	0.344430i	$-0.888072\pi$
$409$	−3.96079e13	+	6.86028e13i	−0.171121	+	0.296390i	0.767691	+	0.640820i	$0.221406\pi$
$410$	2.07988e14			0.886600
$411$	3.15842e13			0.132843
$412$	8.37970e13	−	1.45141e14i	0.347771	−	0.602357i
$413$	9.50028e13	+	1.64550e14i	0.389055	+	0.673863i
$414$	1.48404e12	−	2.57044e12i	0.00599715	−	0.0103874i
$415$	9.75238e13	+	1.68916e14i	0.388907	+	0.673607i
$416$	−3.37076e13	−	5.83834e13i	−0.132652	−	0.229761i
$417$	6.30943e13			0.245043
$418$	−4.28140e13	+	4.49641e13i	−0.164103	+	0.172344i
$419$	−6.06154e13			−0.229301			−0.114650	−	0.993406i	$-0.536575\pi$
$419$	−6.06154e13			−0.229301			−0.114650	+	0.993406i	$0.536575\pi$
$420$	−8.99163e13	−	1.55740e14i	−0.335712	−	0.581471i
$421$	1.63583e14	+	2.83334e14i	0.602819	+	1.04411i	0.992392	+	0.123117i	$0.0392891\pi$
$421$	1.63583e14	+	2.83334e14i	0.602819	+	1.04411i	−0.389573	+	0.920995i	$0.627378\pi$
$422$	6.19255e13	−	1.07258e14i	0.225243	−	0.390132i
$423$	6.43443e12	+	1.11448e13i	0.0231014	+	0.0400128i
$424$	−6.14793e13	+	1.06485e14i	−0.217880	+	0.377379i
$425$	−1.26131e15			−4.41250
$426$	2.09045e14			0.721915
$427$	−2.87284e14	+	4.97590e14i	−0.979395	+	1.69636i
$428$	−1.44739e14	+	2.50695e14i	−0.487129	+	0.843731i
$429$	8.77650e13			0.291613
$430$	6.53505e14			2.14374
$431$	−9.42695e13	+	1.63280e14i	−0.305314	+	0.528819i	−0.977331	−	0.211717i	$-0.932095\pi$
$431$	−9.42695e13	+	1.63280e14i	−0.305314	+	0.528819i	0.672017	+	0.740535i	$0.265428\pi$
$432$	7.52296e12	+	1.30301e13i	0.0240563	+	0.0416667i
$433$	2.71915e14	−	4.70970e14i	0.858518	−	1.48700i	−0.0148236	−	0.999890i	$-0.504719\pi$
$433$	2.71915e14	−	4.70970e14i	0.858518	−	1.48700i	0.873342	−	0.487107i	$-0.161948\pi$
$434$	1.75497e14	+	3.03970e14i	0.547113	+	0.947628i
$435$	9.98183e13	+	1.72890e14i	0.307269	+	0.532206i
$436$	2.48145e14			0.754276
$437$	−1.64783e13	−	3.98557e12i	−0.0494613	−	0.0119631i
$438$	4.82438e13			0.142999
$439$	6.91997e12	+	1.19857e13i	0.0202558	+	0.0350841i	0.875976	−	0.482355i	$-0.160219\pi$
$439$	6.91997e12	+	1.19857e13i	0.0202558	+	0.0350841i	−0.855720	+	0.517439i	$0.826885\pi$
$440$	−4.00047e13	−	6.92902e13i	−0.115643	−	0.200300i
$441$	−2.52073e13	+	4.36604e13i	−0.0719639	+	0.124645i
$442$	2.98882e14	+	5.17679e14i	0.842709	+	1.45961i
$443$	7.76605e12	−	1.34512e13i	0.0216262	−	0.0374577i	−0.855010	−	0.518612i	$-0.826449\pi$
$443$	7.76605e12	−	1.34512e13i	0.0216262	−	0.0374577i	0.876636	+	0.481154i	$0.159782\pi$
$444$	−1.68814e14			−0.464303
$445$	−1.26734e14			−0.344281
$446$	−7.98755e13	+	1.38348e14i	−0.214325	+	0.371221i
$447$	7.11924e13	−	1.23309e14i	0.188687	−	0.326816i
$448$	5.71318e13			0.149571
$449$	−8.84283e13			−0.228684			−0.114342	−	0.993441i	$-0.536476\pi$
$449$	−8.84283e13			−0.228684			−0.114342	+	0.993441i	$0.536476\pi$
$450$	1.28169e14	−	2.21996e14i	0.327428	−	0.567122i
$451$	−4.30112e13	−	7.44976e13i	−0.108545	−	0.188006i
$452$	8.11033e13	−	1.40475e14i	0.202198	−	0.350218i
$453$	−1.63642e14	−	2.83436e14i	−0.403046	−	0.698096i
$454$	1.51704e14	+	2.62760e14i	0.369140	+	0.639369i
$455$	1.45201e15			3.49066
$456$	5.92633e13	−	6.22394e13i	0.140760	−	0.147829i
$457$	6.68339e14			1.56840			0.784202	−	0.620505i	$-0.213073\pi$
$457$	6.68339e14			1.56840			0.784202	+	0.620505i	$0.213073\pi$
$458$	1.21302e14	+	2.10101e14i	0.281259	+	0.487155i
$459$	−6.67053e13	−	1.15537e14i	−0.152824	−	0.264698i
$460$	1.09237e13	−	1.89203e13i	0.0247286	−	0.0428313i
$461$	1.75234e14	+	3.03514e14i	0.391979	+	0.678927i	0.992710	−	0.120523i	$-0.0384573\pi$
$461$	1.75234e14	+	3.03514e14i	0.391979	+	0.678927i	−0.600732	+	0.799451i	$0.705124\pi$
$462$	−3.71887e13	+	6.44127e13i	−0.0822015	+	0.142377i
$463$	−2.40265e14			−0.524801			−0.262401	−	0.964959i	$-0.584514\pi$
$463$	−2.40265e14			−0.524801			−0.262401	+	0.964959i	$0.584514\pi$
$464$	−6.34234e13			−0.136899
$465$	−3.40199e14	+	5.89242e14i	−0.725675	+	1.25691i
$466$	2.35038e14	−	4.07098e14i	0.495468	−	0.858175i
$467$	1.78280e13			0.0371415			0.0185707	−	0.999828i	$-0.494088\pi$
$467$	1.78280e13			0.0371415			0.0185707	+	0.999828i	$0.494088\pi$
$468$	−1.21485e14			−0.250132
$469$	−1.78881e14	+	3.09831e14i	−0.364011	+	0.630485i
$470$	4.73622e13	+	8.20338e13i	0.0952563	+	0.164989i
$471$	7.32967e13	−	1.26954e14i	0.145703	−	0.252366i
$472$	−5.85071e13	−	1.01337e14i	−0.114955	−	0.199108i
$473$	−1.35142e14	−	2.34073e14i	−0.262455	−	0.454585i
$474$	1.03541e14			0.198762
$475$	−1.42315e15	−	3.44214e14i	−2.70045	−	0.653151i
$476$	−5.06582e14			−0.950191
$477$	1.10788e14	+	1.91890e14i	0.205419	+	0.355796i
$478$	−1.01079e13	−	1.75075e13i	−0.0185272	−	0.0320900i
$479$	−3.05503e14	+	5.29147e14i	−0.553568	+	0.958807i	0.444446	+	0.895806i	$0.353401\pi$
$479$	−3.05503e14	+	5.29147e14i	−0.553568	+	0.958807i	−0.998013	+	0.0630015i	$0.979933\pi$
$480$	5.53746e13	+	9.59116e13i	0.0991936	+	0.171808i
$481$	6.81522e14	−	1.18043e15i	1.20693	−	2.09046i
$482$	−2.25608e13			−0.0394999
$483$	−2.03095e13			−0.0351552
$484$	1.29534e14	−	2.24359e14i	0.221684	−	0.383968i
$485$	7.02711e14	−	1.21713e15i	1.18904	−	2.05948i
$486$	2.71132e13			0.0453609
$487$	−7.66738e14			−1.26835			−0.634173	−	0.773192i	$-0.718659\pi$
$487$	−7.66738e14			−1.26835			−0.634173	+	0.773192i	$0.718659\pi$
$488$	1.76923e14	−	3.06439e14i	0.289384	−	0.501228i
$489$	1.34278e14	+	2.32577e14i	0.217173	+	0.376155i
$490$	−1.85545e14	+	3.21373e14i	−0.296736	+	0.513962i
$491$	−1.33557e14	−	2.31328e14i	−0.211212	−	0.365831i	0.740882	−	0.671635i	$-0.234408\pi$
$491$	−1.33557e14	−	2.31328e14i	−0.211212	−	0.365831i	−0.952094	+	0.305805i	$0.901074\pi$
$492$	5.95362e13	+	1.03120e14i	0.0931050	+	0.161263i
$493$	5.62368e14			0.869687
$494$	1.95956e14	+	6.65667e14i	0.299682	+	1.01803i
$495$	−1.44179e14			−0.218059
$496$	−1.08079e14	−	1.87199e14i	−0.161657	−	0.279997i
$497$	−7.15205e14	−	1.23877e15i	−1.05796	−	1.83245i
$498$	−5.58319e13	+	9.67038e13i	−0.0816811	+	0.141476i
$499$	2.75807e14	+	4.77712e14i	0.399073	+	0.691215i	0.993612	−	0.112852i	$-0.0359986\pi$
$499$	2.75807e14	+	4.77712e14i	0.399073	+	0.691215i	−0.594539	+	0.804067i	$0.702665\pi$
$500$	6.03856e14	−	1.04591e15i	0.864169	−	1.49678i
$501$	1.13674e14			0.160900
$502$	−2.56078e14			−0.358511
$503$	1.99658e14	−	3.45817e14i	0.276479	−	0.478876i	−0.694028	−	0.719948i	$-0.744166\pi$
$503$	1.99658e14	−	3.45817e14i	0.276479	−	0.478876i	0.970507	+	0.241072i	$0.0774991\pi$
$504$	5.14767e13	−	8.91602e13i	0.0705087	−	0.122125i
$505$	1.83936e15			2.49209
$506$	−9.03589e12			−0.0121100
$507$	2.72701e14	−	4.72332e14i	0.361529	−	0.626186i
$508$	−2.47771e14	−	4.29153e14i	−0.324938	−	0.562810i
$509$	7.86936e13	−	1.36301e14i	0.102092	−	0.176828i	−0.810454	−	0.585802i	$-0.800780\pi$
$509$	7.86936e13	−	1.36301e14i	0.102092	−	0.176828i	0.912546	+	0.408973i	$0.134113\pi$
$510$	−4.91001e14	−	8.50438e14i	−0.630153	−	1.09146i
$511$	−1.65057e14	−	2.85887e14i	−0.209565	−	0.362977i
$512$	−3.51844e13			−0.0441942
$513$	−4.37340e13	−	1.48565e14i	−0.0543468	−	0.184617i
$514$	9.71197e13			0.119402
$515$	−1.11151e15	−	1.92519e15i	−1.35199	−	2.34171i
$516$	1.87064e14	+	3.24005e14i	0.225122	+	0.389922i
$517$	1.95886e13	−	3.39285e13i	0.0233242	−	0.0403987i
$518$	5.77563e14	+	1.00037e15i	0.680434	+	1.17855i
$519$	1.91335e14	−	3.31402e14i	0.223035	−	0.386309i
$520$	−8.94217e14			−1.03139
$521$	−4.10469e13			−0.0468460			−0.0234230	−	0.999726i	$-0.507456\pi$
$521$	−4.10469e13			−0.0468460			−0.0234230	+	0.999726i	$0.507456\pi$
$522$	−5.71455e13	+	9.89789e13i	−0.0645348	+	0.111778i
$523$	−3.00641e13	+	5.20725e13i	−0.0335961	+	0.0581901i	−0.882335	−	0.470623i	$-0.844029\pi$
$523$	−3.00641e13	+	5.20725e13i	−0.0335961	+	0.0581901i	0.848738	+	0.528813i	$0.177363\pi$
$524$	5.71788e14			0.632285
$525$	−1.75403e15			−1.91938
$526$	−4.81886e13	+	8.34652e13i	−0.0521823	+	0.0903824i
$527$	9.58328e14	+	1.65987e15i	1.02697	+	1.77876i
$528$	2.29025e13	−	3.96683e13i	0.0242883	−	0.0420685i
$529$	4.75171e14	+	8.23021e14i	0.498705	+	0.863783i
$530$	8.15480e14	+	1.41245e15i	0.847024	+	1.46709i
$531$	−2.10863e14			−0.216761
$532$	−5.71580e14	−	1.38247e14i	−0.581518	−	0.140650i
$533$	−9.61420e14			−0.968085
$534$	−3.62773e13	−	6.28341e13i	−0.0361541	−	0.0626207i
$535$	1.91986e15	+	3.32529e15i	1.89375	+	3.28007i
$536$	1.10163e14	−	1.90808e14i	0.107555	−	0.186291i
$537$	4.19697e14	+	7.26936e14i	0.405581	+	0.702486i
$538$	4.26307e14	−	7.38385e14i	0.407774	−	0.706285i
$539$	1.53480e14			0.145316
$540$	1.99574e14			0.187041
$541$	−1.78585e14	+	3.09318e14i	−0.165676	+	0.286960i	−0.936895	−	0.349610i	$-0.886314\pi$
$541$	−1.78585e14	+	3.09318e14i	−0.165676	+	0.286960i	0.771219	+	0.636570i	$0.219647\pi$
$542$	−2.25456e14	+	3.90502e14i	−0.207046	+	0.358614i
$543$	−1.53526e14			−0.139567
$544$	3.11976e14			0.280755
$545$	1.64574e15	−	2.85050e15i	1.46615	−	2.53945i
$546$	4.15636e14	+	7.19902e14i	0.366567	+	0.634912i
$547$	−1.83476e13	+	3.17790e13i	−0.0160195	+	0.0277467i	−0.873924	−	0.486063i	$-0.838433\pi$
$547$	−1.83476e13	+	3.17790e13i	−0.0160195	+	0.0277467i	0.857905	+	0.513809i	$0.171766\pi$
$548$	6.65478e13	+	1.15264e14i	0.0575229	+	0.0996325i
$549$	−3.18820e14	−	5.52213e14i	−0.272834	−	0.472562i
$550$	−7.80385e14			−0.661171
$551$	6.34525e14	+	1.53471e14i	0.532249	+	0.128734i
$552$	1.25075e13			0.0103874
$553$	−3.54246e14	−	6.13572e14i	−0.291284	−	0.504519i
$554$	4.99391e14	+	8.64971e14i	0.406572	+	0.704203i
$555$	−1.11960e15	+	1.93920e15i	−0.902507	+	1.56319i
$556$	1.32939e14	+	2.30258e14i	0.106107	+	0.183782i
$557$	−5.38471e14	+	9.32658e14i	−0.425558	+	0.737087i	−0.996472	−	0.0839220i	$-0.973255\pi$
$557$	−5.38471e14	+	9.32658e14i	−0.425558	+	0.737087i	0.570915	+	0.821009i	$0.306589\pi$
$558$	−3.89525e14			−0.304823
$559$	−3.02081e15			−2.34077
$560$	3.78907e14	−	6.56285e14i	0.290735	−	0.503569i
$561$	−2.03074e14	+	3.51735e14i	−0.154297	+	0.267251i
$562$	−4.15244e14			−0.312431
$563$	−2.01039e14			−0.149790			−0.0748952	−	0.997191i	$-0.523862\pi$
$563$	−2.01039e14			−0.149790			−0.0748952	+	0.997191i	$0.523862\pi$
$564$	−2.71146e13	+	4.69639e13i	−0.0200064	+	0.0346521i
$565$	−1.07578e15	−	1.86330e15i	−0.786062	−	1.36150i
$566$	−4.33481e14	+	7.50811e14i	−0.313675	+	0.543301i
$567$	−9.27626e13	−	1.60670e14i	−0.0664762	−	0.115140i
$568$	4.40456e14	+	7.62892e14i	0.312598	+	0.541436i
$569$	−2.28848e14			−0.160853			−0.0804264	−	0.996761i	$-0.525628\pi$
$569$	−2.28848e14			−0.160853			−0.0804264	+	0.996761i	$0.525628\pi$
$570$	−3.21915e14	−	1.09355e15i	−0.224094	−	0.761250i
$571$	−2.53595e15			−1.74841			−0.874204	−	0.485560i	$-0.838616\pi$
$571$	−2.53595e15			−1.74841			−0.874204	+	0.485560i	$0.838616\pi$
$572$	1.84921e14	+	3.20292e14i	0.126272	+	0.218709i
$573$	−5.56216e14	−	9.63395e14i	−0.376178	−	0.651559i
$574$	4.07383e14	−	7.05608e14i	0.272890	−	0.472659i
$575$	−1.06546e14	−	1.84543e14i	−0.0706908	−	0.122440i
$576$	−3.17017e13	+	5.49089e13i	−0.0208333	+	0.0360844i
$577$	6.58799e14			0.428831			0.214415	−	0.976743i	$-0.431215\pi$
$577$	6.58799e14			0.428831			0.214415	+	0.976743i	$0.431215\pi$
$578$	−1.66956e15			−1.07646
$579$	5.61904e14	−	9.73246e14i	0.358864	−	0.621571i
$580$	−4.20633e14	+	7.28558e14i	−0.266103	+	0.460904i
$581$	7.64072e14			0.478813
$582$	8.04597e14			0.499462
$583$	3.37276e14	−	5.84179e14i	0.207400	−	0.359227i
$584$	1.01649e14	+	1.76062e14i	0.0619205	+	0.107249i
$585$	−8.05704e14	+	1.39552e15i	−0.486203	+	0.842129i
$586$	1.79330e14	+	3.10608e14i	0.107205	+	0.185685i
$587$	6.79827e14	+	1.17749e15i	0.402614	+	0.697348i	0.994041	−	0.109011i	$-0.0347684\pi$
$587$	6.79827e14	+	1.17749e15i	0.402614	+	0.697348i	−0.591427	+	0.806359i	$0.701435\pi$
$588$	−2.12447e14			−0.124645
$589$	6.28309e14	+	2.13438e15i	0.365207	+	1.24062i
$590$	−1.55211e15			−0.893792
$591$	2.09314e14	+	3.62542e14i	0.119417	+	0.206837i
$592$	−3.55690e14	−	6.16073e14i	−0.201049	−	0.348227i
$593$	1.27341e15	−	2.20562e15i	0.713130	−	1.23518i	−0.250546	−	0.968105i	$-0.580610\pi$
$593$	1.27341e15	−	2.20562e15i	0.713130	−	1.23518i	0.963676	−	0.267073i	$-0.0860566\pi$
$594$	−4.12710e13	−	7.14836e13i	−0.0228992	−	0.0396626i
$595$	−3.35972e15	+	5.81921e15i	−1.84697	+	3.19905i
$596$	6.00008e14			0.326816
$597$	−1.20720e15			−0.651509
$598$	−5.04943e13	+	8.74588e13i	−0.0270014	+	0.0467678i
$599$	−1.19799e14	+	2.07499e14i	−0.0634757	+	0.109943i	−0.896017	−	0.444020i	$-0.853552\pi$
$599$	−1.19799e14	+	2.07499e14i	−0.0634757	+	0.109943i	0.832541	+	0.553963i	$0.186885\pi$
$600$	1.08021e15			0.567122
$601$	1.36473e15			0.709967			0.354983	−	0.934873i	$-0.384486\pi$
$601$	1.36473e15			0.709967			0.354983	+	0.934873i	$0.384486\pi$
$602$	1.28001e15	−	2.21704e15i	0.659829	−	1.14286i
$603$	−1.98518e14	−	3.43843e14i	−0.101404	−	0.175637i
$604$	6.89586e14	−	1.19440e15i	0.349048	−	0.604569i
$605$	−1.71818e15	−	2.97597e15i	−0.861814	−	1.49270i
$606$	5.26512e14	+	9.11946e14i	0.261703	+	0.453283i
$607$	2.82846e14			0.139320			0.0696598	−	0.997571i	$-0.477809\pi$
$607$	2.82846e14			0.139320			0.0696598	+	0.997571i	$0.477809\pi$
$608$	3.52005e14	+	8.51386e13i	0.171822	+	0.0415582i
$609$	7.82048e14			0.378302
$610$	−2.34675e15	−	4.06470e15i	−1.12500	−	1.94856i
$611$	−2.18930e14	−	3.79199e14i	−0.104011	−	0.180152i
$612$	2.81096e14	−	4.86872e14i	0.132349	−	0.229235i
$613$	1.14197e15	+	1.97796e15i	0.532873	+	0.922963i	0.999263	+	0.0383841i	$0.0122210\pi$
$613$	1.14197e15	+	1.97796e15i	0.532873	+	0.922963i	−0.466390	+	0.884579i	$0.654446\pi$
$614$	−2.27327e14	+	3.93741e14i	−0.105129	+	0.182089i
$615$	1.57941e15			0.723906
$616$	−3.13426e14			−0.142377
$617$	3.04894e14	−	5.28092e14i	0.137272	−	0.237761i	−0.789191	−	0.614147i	$-0.789500\pi$
$617$	3.04894e14	−	5.28092e14i	0.137272	−	0.237761i	0.926463	+	0.376386i	$0.122833\pi$
$618$	6.36333e14	−	1.10216e15i	0.283954	−	0.491823i
$619$	−1.54293e15			−0.682415			−0.341207	−	0.939988i	$-0.610836\pi$
$619$	−1.54293e15			−0.682415			−0.341207	+	0.939988i	$0.610836\pi$
$620$	−2.86719e15			−1.25691
$621$	1.12695e13	−	1.95193e13i	0.00489665	−	0.00848125i
$622$	5.15305e14	+	8.92534e14i	0.221931	+	0.384395i
$623$	−2.48231e14	+	4.29949e14i	−0.105967	+	0.183541i
$624$	−2.55967e14	−	4.43349e14i	−0.108310	−	0.187599i
$625$	−4.69772e15	−	8.13669e15i	−1.97037	−	3.41277i
$626$	−4.62445e14			−0.192266
$627$	−3.25119e14	+	3.41446e14i	−0.133990	+	0.140718i
$628$	6.17743e14			0.252366
$629$	3.15386e15	+	5.46265e15i	1.27722	+	2.21220i
$630$	−6.82802e14	−	1.18265e15i	−0.274108	−	0.474769i
$631$	5.57434e14	−	9.65503e14i	0.221836	−	0.384231i	−0.733530	−	0.679657i	$-0.762128\pi$
$631$	5.57434e14	−	9.65503e14i	0.221836	−	0.384231i	0.955365	+	0.295427i	$0.0954618\pi$
$632$	2.18161e14	+	3.77866e14i	0.0860663	+	0.149071i
$633$	4.70247e14	−	8.14492e14i	0.183910	−	0.318542i
$634$	−1.10287e15			−0.427595
$635$	−6.57303e15			−2.52645
$636$	−4.66858e14	+	8.08622e14i	−0.177898	+	0.308128i
$637$	8.57676e14	−	1.48554e15i	0.324008	−	0.561199i
$638$	3.47941e14			0.130314
$639$	1.58743e15			0.589441
$640$	−2.33348e14	+	4.04171e14i	−0.0859042	+	0.148790i
$641$	2.60946e15	+	4.51973e15i	0.952428	+	1.64965i	0.740147	+	0.672445i	$0.234756\pi$
$641$	2.60946e15	+	4.51973e15i	0.952428	+	1.64965i	0.212282	+	0.977209i	$0.431911\pi$
$642$	−1.09911e15	+	1.90371e15i	−0.397739	+	0.688904i
$643$	2.24433e15	+	3.88729e15i	0.805241	+	1.39472i	0.916128	+	0.400885i	$0.131297\pi$
$643$	2.24433e15	+	3.88729e15i	0.805241	+	1.39472i	−0.110888	+	0.993833i	$0.535369\pi$
$644$	−4.27919e13	−	7.41178e13i	−0.0152226	−	0.0263664i
$645$	4.96255e15			1.75036
$646$	−3.12119e15	−	7.54915e14i	−1.09155	−	0.264009i
$647$	1.97516e15			0.684904			0.342452	−	0.939535i	$-0.388743\pi$
$647$	1.97516e15			0.684904			0.342452	+	0.939535i	$0.388743\pi$
$648$	5.71275e13	+	9.89477e13i	0.0196419	+	0.0340207i
$649$	3.20971e14	+	5.55937e14i	0.109426	+	0.189531i
$650$	−4.36094e15	+	7.55338e15i	−1.47420	+	2.55339i
$651$	1.33268e15	+	2.30827e15i	0.446716	+	0.773735i
$652$	−5.65847e14	+	9.80076e14i	−0.188078	+	0.325760i
$653$	−4.68645e15			−1.54462			−0.772310	−	0.635246i	$-0.780899\pi$
$653$	−4.68645e15			−1.54462			−0.772310	+	0.635246i	$0.780899\pi$
$654$	1.88435e15			0.615864
$655$	3.79218e15	−	6.56825e15i	1.22903	−	2.12874i
$656$	−2.50885e14	+	4.34546e14i	−0.0806313	+	0.139657i
$657$	3.66351e14			0.116758
$658$	3.71070e14			0.117277
$659$	−1.89113e15	+	3.27554e15i	−0.592724	+	1.02663i	0.401140	+	0.916017i	$0.368614\pi$
$659$	−1.89113e15	+	3.27554e15i	−0.592724	+	1.02663i	−0.993864	+	0.110611i	$0.964719\pi$
$660$	−3.03786e14	−	5.26172e14i	−0.0944225	−	0.163545i
$661$	−1.11524e15	+	1.93165e15i	−0.343763	+	0.595414i	−0.985128	−	0.171821i	$-0.945035\pi$
$661$	−1.11524e15	+	1.93165e15i	−0.343763	+	0.595414i	0.641366	+	0.767235i	$0.278368\pi$
$662$	−7.09838e14	−	1.22947e15i	−0.216990	−	0.375838i
$663$	2.26964e15	+	3.93113e15i	0.688069	+	1.19177i
$664$	−4.70551e14			−0.141476
$665$	−5.37888e15	+	5.64900e15i	−1.60388	+	1.68443i
$666$	−1.28193e15			−0.379102
$667$	4.75044e13	+	8.22800e13i	0.0139329	+	0.0241325i
$668$	2.39511e14	+	4.14846e14i	0.0696716	+	0.120675i
$669$	−6.06555e14	+	1.05058e15i	−0.174995	+	0.303101i
$670$	−1.46124e15	−	2.53094e15i	−0.418129	−	0.724220i
$671$	−9.70600e14	+	1.68113e15i	−0.275465	+	0.477119i
$672$	4.33844e14			0.122125
$673$	2.59377e15			0.724184			0.362092	−	0.932142i	$-0.382063\pi$
$673$	2.59377e15			0.724184			0.362092	+	0.932142i	$0.382063\pi$
$674$	−1.72013e15	+	2.97935e15i	−0.476356	+	0.825073i
$675$	9.73287e14	−	1.68578e15i	0.267344	−	0.463053i
$676$	2.29832e15			0.626186
$677$	2.07658e15			0.561191			0.280595	−	0.959826i	$-0.409468\pi$
$677$	2.07658e15			0.561191			0.280595	+	0.959826i	$0.409468\pi$
$678$	6.15879e14	−	1.06673e15i	0.165094	−	0.285951i
$679$	−2.75277e15	−	4.76794e15i	−0.731959	−	1.26779i
$680$	2.06907e15	−	3.58374e15i	0.545729	−	0.945230i
$681$	1.15200e15	+	1.99533e15i	0.301401	+	0.522042i
$682$	5.92924e14	+	1.02698e15i	0.153881	+	0.266530i
$683$	7.46335e15			1.92141			0.960704	−	0.277574i	$-0.0895303\pi$
$683$	7.46335e15			1.92141			0.960704	+	0.277574i	$0.0895303\pi$
$684$	4.50030e14	−	4.72630e14i	0.114930	−	0.120702i
$685$	1.76542e15			0.447249
$686$	−9.56511e14	−	1.65673e15i	−0.240385	−	0.416359i
$687$	9.21135e14	+	1.59545e15i	0.229647	+	0.397761i
$688$	−7.88287e14	+	1.36535e15i	−0.194961	+	0.337682i
$689$	−3.76953e15	−	6.52902e15i	−0.924872	−	1.60193i
$690$	8.29516e13	−	1.43676e14i	0.0201909	−	0.0349716i
$691$	−6.49304e15			−1.56790			−0.783950	−	0.620824i	$-0.786798\pi$
$691$	−6.49304e15			−1.56790			−0.783950	+	0.620824i	$0.786798\pi$
$692$	1.61257e15			0.386309
$693$	−2.82402e14	+	4.89134e14i	−0.0671173	+	0.116251i
$694$	−1.65306e14	+	2.86319e14i	−0.0389774	+	0.0675108i
$695$	3.52670e15			0.824996
$696$	−4.81621e14			−0.111778
$697$	2.22457e15	−	3.85307e15i	0.512231	−	0.887210i
$698$	−1.33642e15	−	2.31475e15i	−0.305308	−	0.528809i
$699$	1.78482e15	−	3.09140e15i	0.404548	−	0.700697i
$700$	−3.69573e15	−	6.40119e15i	−0.831114	−	1.43953i
$701$	1.71877e15	+	2.97700e15i	0.383503	+	0.664247i	0.991560	−	0.129647i	$-0.0413843\pi$
$701$	1.71877e15	+	2.97700e15i	0.383503	+	0.664247i	−0.608057	+	0.793893i	$0.708051\pi$
$702$	−9.22523e14			−0.204232
$703$	2.06777e15	+	7.02425e15i	0.454201	+	1.54293i
$704$	1.93022e14			0.0420685
$705$	3.59657e14	+	6.22944e14i	0.0777765	+	0.134713i
$706$	1.61613e15	+	2.79922e15i	0.346777	+	0.600635i
$707$	3.60272e15	−	6.24009e15i	0.767050	−	1.32857i
$708$	−4.44288e14	−	7.69530e14i	−0.0938603	−	0.162571i
$709$	8.83814e14	−	1.53081e15i	0.185271	−	0.320898i	−0.758397	−	0.651793i	$-0.774017\pi$
$709$	8.83814e14	−	1.53081e15i	0.185271	−	0.320898i	0.943668	+	0.330895i	$0.107350\pi$
$710$	1.16847e16			2.43050
$711$	7.86266e14			0.162288
$712$	1.52872e14	−	2.64782e14i	0.0313104	−	0.0542312i
$713$	−1.61904e14	+	2.80425e14i	−0.0329052	+	0.0569935i
$714$	−3.84685e15			−0.775828
$715$	4.90568e15			0.981785
$716$	−1.76860e15	+	3.06330e15i	−0.351243	+	0.608371i
$717$	−7.67572e13	−	1.32947e14i	−0.0151274	−	0.0262014i
$718$	8.58776e14	−	1.48744e15i	0.167956	−	0.290908i
$719$	−2.34717e15	−	4.06542e15i	−0.455549	−	0.789035i	0.543170	−	0.839623i	$-0.317224\pi$
$719$	−2.34717e15	−	4.06542e15i	−0.455549	−	0.789035i	−0.998720	+	0.0505878i	$0.983891\pi$
$720$	4.20501e14	+	7.28329e14i	0.0809912	+	0.140281i
$721$	−8.70836e15			−1.66453
$722$	−3.31565e15	−	1.70355e15i	−0.628948	−	0.323148i
$723$	−1.71321e14			−0.0322516
$724$	−3.23480e14	−	5.60283e14i	−0.0604345	−	0.104676i
$725$	4.10272e15	+	7.10611e15i	0.760698	+	1.31757i
$726$	9.83648e14	−	1.70373e15i	0.181004	−	0.313508i
$727$	−1.28424e15	−	2.22437e15i	−0.234534	−	0.406225i	0.724603	−	0.689167i	$-0.242023\pi$
$727$	−1.28424e15	−	2.22437e15i	−0.234534	−	0.406225i	−0.959137	+	0.282941i	$0.908690\pi$
$728$	−1.75148e15	+	3.03366e15i	−0.317456	+	0.549850i
$729$	2.05891e14			0.0370370
$730$	2.69662e15			0.481442
$731$	6.98966e15	−	1.21064e16i	1.23854	−	2.14522i
$732$	1.34351e15	−	2.32702e15i	0.236281	−	0.409251i
$733$	6.24658e15			1.09036			0.545181	−	0.838319i	$-0.316461\pi$
$733$	6.24658e15			1.09036			0.545181	+	0.838319i	$0.316461\pi$
$734$	−2.85974e15			−0.495448
$735$	−1.40898e15	+	2.44043e15i	−0.242284	+	0.419648i
$736$	2.63532e13	+	4.56452e13i	0.00449786	+	0.00779053i
$737$	−6.04357e14	+	1.04678e15i	−0.102382	+	0.177330i
$738$	4.52103e14	+	7.83065e14i	0.0760199	+	0.131670i
$739$	−3.82597e15	−	6.62678e15i	−0.638554	−	1.10601i	−0.985750	−	0.168215i	$-0.946200\pi$
$739$	−3.82597e15	−	6.62678e15i	−0.638554	−	1.10601i	0.347197	−	0.937792i	$-0.387134\pi$
$740$	−9.43595e15			−1.56319
$741$	1.48804e15	+	5.05491e15i	0.244689	+	0.831215i
$742$	6.38906e15			1.04283
$743$	1.53411e15	+	2.65716e15i	0.248552	+	0.430505i	0.963124	−	0.269057i	$-0.0867118\pi$
$743$	1.53411e15	+	2.65716e15i	0.248552	+	0.430505i	−0.714572	+	0.699562i	$0.753379\pi$
$744$	−8.20727e14	−	1.42154e15i	−0.131992	−	0.228617i
$745$	3.97935e15	−	6.89243e15i	0.635261	−	1.10030i
$746$	1.93526e15	+	3.35197e15i	0.306673	+	0.531174i
$747$	−4.23974e14	+	7.34344e14i	−0.0666923	+	0.115514i
$748$	−1.71150e15			−0.267251
$749$	1.50415e16			2.33154
$750$	4.58553e15	−	7.94238e15i	0.705591	−	1.22212i
$751$	−2.57707e15	+	4.46362e15i	−0.393647	+	0.681816i	−0.992927	−	0.118723i	$-0.962120\pi$
$751$	−2.57707e15	+	4.46362e15i	−0.393647	+	0.681816i	0.599281	+	0.800539i	$0.295453\pi$
$752$	−2.28522e14			−0.0346521
$753$	−1.94459e15			−0.292723
$754$	1.94437e15	−	3.36774e15i	0.290560	−	0.503264i
$755$	−9.14687e15	−	1.58429e16i	−1.35695	−	2.35031i
$756$	3.90901e14	−	6.77060e14i	0.0575701	−	0.0997143i
$757$	1.07255e15	+	1.85771e15i	0.156816	+	0.271613i	0.933719	−	0.358007i	$-0.116544\pi$
$757$	1.07255e15	+	1.85771e15i	0.156816	+	0.271613i	−0.776903	+	0.629621i	$0.783210\pi$
$758$	9.97282e14	+	1.72734e15i	0.144756	+	0.250725i
$759$	−6.86163e13			−0.00988775
$760$	3.31256e15	−	3.47891e15i	0.473902	−	0.497701i
$761$	6.27880e15			0.891787			0.445893	−	0.895086i	$-0.352886\pi$
$761$	6.27880e15			0.891787			0.445893	+	0.895086i	$0.352886\pi$
$762$	−1.88151e15	−	3.25888e15i	−0.265311	−	0.459532i
$763$	−6.44695e15	−	1.11664e16i	−0.902546	−	1.56326i
$764$	2.34389e15	−	4.05974e15i	0.325780	−	0.564267i
$765$	−3.72854e15	−	6.45801e15i	−0.514518	−	0.891171i
$766$	2.85063e15	−	4.93743e15i	0.390555	−	0.676461i
$767$	7.17459e15			0.975939
$768$	−2.67181e14			−0.0360844
$769$	−2.28372e15	+	3.95552e15i	−0.306230	+	0.530406i	−0.977534	−	0.210776i	$-0.932401\pi$
$769$	−2.28372e15	+	3.95552e15i	−0.306230	+	0.530406i	0.671304	+	0.741182i	$0.265734\pi$
$770$	−2.07869e15	+	3.60039e15i	−0.276751	+	0.479348i
$771$	7.37503e14			0.0974910
$772$	4.73572e15			0.621571
$773$	−2.22406e15	+	3.85218e15i	−0.289841	+	0.502019i	−0.973772	−	0.227528i	$-0.926936\pi$
$773$	−2.22406e15	+	3.85218e15i	−0.289841	+	0.502019i	0.683931	+	0.729547i	$0.260269\pi$
$774$	1.42052e15	+	2.46041e15i	0.183811	+	0.318370i
$775$	−1.39828e16	+	2.42189e16i	−1.79653	+	3.11169i
$776$	1.69528e15	+	2.93632e15i	0.216273	+	0.374596i
$777$	4.38587e15	+	7.59655e15i	0.555572	+	0.962278i
$778$	−1.06488e16			−1.33941
$779$	3.56151e15	−	3.74036e15i	0.444814	−	0.467152i
$780$	−6.79046e15			−0.842129
$781$	−2.41635e15	−	4.18524e15i	−0.297563	−	0.515394i
$782$	−2.33671e14	−	4.04731e14i	−0.0285738	−	0.0494913i
$783$	−4.33949e14	+	7.51621e14i	−0.0526925	+	0.0912660i
$784$	−4.47625e14	−	7.75310e14i	−0.0539730	−	0.0934839i
$785$	4.09697e15	−	7.09616e15i	0.490546	−	0.849650i
$786$	4.34201e15			0.516258
$787$	−1.35953e16			−1.60520			−0.802600	−	0.596517i	$-0.796551\pi$
$787$	−1.35953e16			−1.60520			−0.802600	+	0.596517i	$0.796551\pi$
$788$	−8.82047e14	+	1.52775e15i	−0.103418	+	0.179126i
$789$	−3.65932e14	+	6.33814e14i	−0.0426067	+	0.0737969i
$790$	5.78750e15			0.669179
$791$	−8.42843e15			−0.967779
$792$	1.73916e14	−	3.01231e14i	0.0198313	−	0.0343488i
$793$	1.08478e16	+	1.87890e16i	1.22840	+	2.12765i
$794$	1.57238e15	−	2.72345e15i	0.176826	−	0.306271i
$795$	6.19255e15	+	1.07258e16i	0.691592	+	1.19787i
$796$	−2.54357e15	−	4.40558e15i	−0.282112	−	0.488632i
$797$	−5.02612e15			−0.553620			−0.276810	−	0.960925i	$-0.589277\pi$
$797$	−5.02612e15			−0.553620			−0.276810	+	0.960925i	$0.589277\pi$
$798$	−4.34044e15	−	1.04981e15i	−0.474808	−	0.114840i
$799$	2.02628e15			0.220136
$800$	2.27600e15	+	3.94214e15i	0.245571	+	0.425341i
$801$	−2.75480e14	−	4.77146e14i	−0.0295197	−	0.0511296i
$802$	6.39787e14	−	1.10814e15i	0.0680889	−	0.117933i
$803$	−5.57650e14	−	9.65879e14i	−0.0589422	−	0.102091i
$804$	8.36553e14	−	1.44895e15i	0.0878183	−	0.152106i
$805$	−1.13521e15			−0.118358
$806$	1.32535e16			1.37242
$807$	3.23727e15	−	5.60711e15i	0.332946	−	0.576679i
$808$	−2.21872e15	+	3.84293e15i	−0.226642	+	0.392555i
$809$	6.02117e15			0.610892			0.305446	−	0.952209i	$-0.401194\pi$
$809$	6.02117e15			0.610892			0.305446	+	0.952209i	$0.401194\pi$
$810$	1.51551e15			0.152719
$811$	−8.50952e14	+	1.47389e15i	−0.0851707	+	0.147520i	−0.905464	−	0.424423i	$-0.860477\pi$
$811$	−8.50952e14	+	1.47389e15i	−0.0851707	+	0.147520i	0.820293	+	0.571943i	$0.193810\pi$
$812$	1.64777e15	+	2.85403e15i	0.163810	+	0.283726i
$813$	−1.71206e15	+	2.96537e15i	−0.169052	+	0.292807i
$814$	1.95132e15	+	3.37978e15i	0.191379	+	0.331478i
$815$	7.50556e15	+	1.30000e16i	0.731167	+	1.26642i
$816$	2.36907e15			0.229235
$817$	1.11904e16	−	1.17523e16i	1.07553	−	1.12954i
$818$	−2.53490e15			−0.242002
$819$	3.15623e15	+	5.46675e15i	0.299301	+	0.518404i
$820$	3.32781e15	+	5.76394e15i	0.313460	+	0.542929i
$821$	6.67609e15	−	1.15633e16i	0.624647	−	1.08192i	−0.363962	−	0.931414i	$-0.618576\pi$
$821$	6.67609e15	−	1.15633e16i	0.624647	−	1.08192i	0.988609	−	0.150507i	$-0.0480905\pi$
$822$	5.05347e14	+	8.75287e14i	0.0469672	+	0.0813496i
$823$	5.12666e15	−	8.87964e15i	0.473299	−	0.819778i	−0.526234	−	0.850340i	$-0.676396\pi$
$823$	5.12666e15	−	8.87964e15i	0.473299	−	0.819778i	0.999533	+	0.0305620i	$0.00972971\pi$
$824$	5.36300e15			0.491823
$825$	−5.92605e15			−0.539844
$826$	−3.04009e15	+	5.26559e15i	−0.275104	+	0.476493i
$827$	−6.84683e15	+	1.18591e16i	−0.615473	+	1.06603i	0.374828	+	0.927094i	$0.377702\pi$
$827$	−6.84683e15	+	1.18591e16i	−0.615473	+	1.06603i	−0.990301	+	0.138937i	$0.955632\pi$
$828$	9.49788e13			0.00848125
$829$	−7.78162e15			−0.690271			−0.345136	−	0.938553i	$-0.612167\pi$
$829$	−7.78162e15			−0.690271			−0.345136	+	0.938553i	$0.612167\pi$
$830$	−3.12076e15	+	5.40532e15i	−0.274999	+	0.476312i
$831$	3.79225e15	+	6.56837e15i	0.331964	+	0.574979i
$832$	1.07864e15	−	1.86827e15i	0.0937994	−	0.162465i
$833$	3.96905e15	+	6.87459e15i	0.342877	+	0.593881i
$834$	1.00951e15	+	1.74852e15i	0.0866357	+	0.150057i
$835$	6.35390e15			0.541708
$836$	−1.93111e15	−	4.67071e14i	−0.163558	−	0.0395593i
$837$	−2.95795e15			−0.248887
$838$	−9.69846e14	−	1.67982e15i	−0.0810701	−	0.140417i
$839$	−5.90505e15	−	1.02278e16i	−0.490380	−	0.849363i	0.509559	−	0.860436i	$-0.329809\pi$
$839$	−5.90505e15	−	1.02278e16i	−0.490380	−	0.849363i	−0.999939	+	0.0110727i	$0.996475\pi$
$840$	2.87732e15	−	4.98367e15i	0.237384	−	0.411162i
$841$	4.27102e15	+	7.39763e15i	0.350069	+	0.606338i
$842$	−5.23466e15	+	9.06669e15i	−0.426257	+	0.738299i
$843$	−3.15326e15			−0.255099
$844$	3.96323e15			0.318542
$845$	1.52428e16	−	2.64013e16i	1.21717	−	2.10821i
$846$	−2.05902e14	+	3.56632e14i	−0.0163352	+	0.0282933i
$847$	−1.34614e16			−1.06104
$848$	−3.93467e15			−0.308128
$849$	−3.29175e15	+	5.70147e15i	−0.256114	+	0.443603i
$850$	−2.01810e16	−	3.49546e16i	−1.56005	−	2.70209i
$851$	−5.32826e14	+	9.22882e14i	−0.0409235	+	0.0708816i
$852$	3.34471e15	+	5.79321e15i	0.255236	+	0.442081i
$853$	−1.16559e16	−	2.01886e16i	−0.883742	−	1.53069i	−0.847149	−	0.531355i	$-0.821683\pi$
$853$	−1.16559e16	−	2.01886e16i	−0.883742	−	1.53069i	−0.0365925	−	0.999330i	$-0.511650\pi$
$854$	−1.83862e16			−1.38507
$855$	−2.44454e15	−	8.30415e15i	−0.182972	−	0.621558i
$856$	−9.26327e15			−0.688904
$857$	−7.01157e15	−	1.21444e16i	−0.518109	−	0.897390i	−0.999779	−	0.0210377i	$-0.993303\pi$
$857$	−7.01157e15	−	1.21444e16i	−0.518109	−	0.897390i	0.481670	−	0.876353i	$-0.340030\pi$
$858$	1.40424e15	+	2.43222e15i	0.103101	+	0.178576i
$859$	3.59818e15	−	6.23223e15i	0.262495	−	0.454654i	−0.704410	−	0.709794i	$-0.748788\pi$
$859$	3.59818e15	−	6.23223e15i	0.262495	−	0.454654i	0.966904	+	0.255140i	$0.0821214\pi$
$860$	1.04561e16	+	1.81105e16i	0.757927	+	1.31277i
$861$	3.09356e15	−	5.35821e15i	0.222814	−	0.385924i
$862$	−6.03325e15			−0.431779
$863$	1.34587e16			0.957067			0.478533	−	0.878069i	$-0.341169\pi$
$863$	1.34587e16			0.957067			0.478533	+	0.878069i	$0.341169\pi$
$864$	−2.40735e14	+	4.16965e14i	−0.0170103	+	0.0294628i
$865$	1.06948e16	−	1.85239e16i	0.750903	−	1.30060i
$866$	1.74026e16			1.21413
$867$	−1.26782e16			−0.878927
$868$	−5.61591e15	+	9.72705e15i	−0.386867	+	0.670074i
$869$	−1.19683e15	−	2.07298e15i	−0.0819266	−	0.141901i
$870$	−3.19418e15	+	5.53249e15i	−0.217272	+	0.376326i
$871$	6.75454e15	+	1.16992e16i	0.456558	+	0.790781i
$872$	3.97033e15	+	6.87681e15i	0.266677	+	0.461898i
$873$	6.10991e15			0.407809
$874$	−1.53202e14	−	5.20430e14i	−0.0101614	−	0.0345183i
$875$	−6.27540e16			−4.13616
$876$	7.71901e14	+	1.33697e15i	0.0505579	+	0.0875688i
$877$	1.72269e15	+	2.98379e15i	0.112127	+	0.194210i	0.916628	−	0.399742i	$-0.130900\pi$
$877$	1.72269e15	+	2.98379e15i	0.112127	+	0.194210i	−0.804501	+	0.593952i	$0.797567\pi$
$878$	−2.21439e14	+	3.83544e14i	−0.0143230	+	0.0248082i
$879$	1.36178e15	+	2.35868e15i	0.0875325	+	0.151611i
$880$	1.28015e15	−	2.21728e15i	0.0817723	−	0.141634i
$881$	−1.41561e15			−0.0898619			−0.0449310	−	0.998990i	$-0.514307\pi$
$881$	−1.41561e15			−0.0898619			−0.0449310	+	0.998990i	$0.514307\pi$
$882$	−1.61327e15			−0.101772
$883$	−8.57119e15	+	1.48457e16i	−0.537350	+	0.930718i	0.461695	+	0.887039i	$0.347241\pi$
$883$	−8.57119e15	+	1.48457e16i	−0.537350	+	0.930718i	−0.999046	+	0.0436793i	$0.986092\pi$
$884$	−9.56423e15	+	1.65657e16i	−0.595885	+	1.03210i
$885$	−1.17863e16			−0.729778
$886$	4.97027e14			0.0305840
$887$	−4.94436e15	+	8.56389e15i	−0.302364	+	0.523710i	−0.976671	−	0.214741i	$-0.931109\pi$
$887$	−4.94436e15	+	8.56389e15i	−0.302364	+	0.523710i	0.674307	+	0.738451i	$0.264443\pi$
$888$	−2.70102e15	−	4.67830e15i	−0.164156	−	0.284326i
$889$	−1.28745e16	+	2.22992e16i	−0.777624	+	1.34688i
$890$	−2.02774e15	−	3.51215e15i	−0.121722	−	0.210828i
$891$	−3.13402e14	−	5.42828e14i	−0.0186971	−	0.0323843i
$892$	−5.11203e15			−0.303101
$893$	2.28627e15	+	5.52974e14i	0.134724	+	0.0325853i
$894$	4.55631e15			0.266844
$895$	2.34592e16	+	4.06326e16i	1.36549	+	2.36509i
$896$	9.14109e14	+	1.58328e15i	0.0528815	+	0.0915934i
$897$	−3.83441e14	+	6.64140e14i	−0.0220465	+	0.0381857i
$898$	−1.41485e15	−	2.45060e15i	−0.0808521	−	0.140040i
$899$	6.23436e15	−	1.07982e16i	0.354090	−	0.613302i
$900$	8.20284e15			0.463053
$901$	3.48883e16			1.95746
$902$	1.37636e15	−	2.38392e15i	0.0767530	−	0.132940i
$903$	9.72005e15	−	1.68356e16i	0.538748	−	0.933140i
$904$	5.19061e15			0.285951
$905$	−8.58146e15			−0.469888
$906$	5.23654e15	−	9.06996e15i	0.284997	−	0.493629i
$907$	−9.10639e15	−	1.57727e16i	−0.492613	−	0.853231i	0.507351	−	0.861740i	$-0.330625\pi$
$907$	−9.10639e15	−	1.57727e16i	−0.492613	−	0.853231i	−0.999964	+	0.00850862i	$0.997292\pi$
$908$	−4.85454e15	+	8.40831e15i	−0.261021	+	0.452102i
$909$	3.99820e15	+	6.92509e15i	0.213680	+	0.370104i
$910$	2.32322e16	+	4.02394e16i	1.23414	+	2.13759i
$911$	−2.43479e15			−0.128561			−0.0642807	−	0.997932i	$-0.520475\pi$
$911$	−2.43479e15			−0.128561			−0.0642807	+	0.997932i	$0.520475\pi$
$912$	2.67304e15	+	6.46521e14i	0.140292	+	0.0339321i
$913$	2.58145e15			0.134671
$914$	1.06934e16	+	1.85216e16i	0.554515	+	0.960448i
$915$	−1.78207e16	−	3.08663e16i	−0.918561	−	1.59099i
$916$	−3.88165e15	+	6.72322e15i	−0.198880	+	0.344471i
$917$	−1.48553e16	−	2.57302e16i	−0.756574	−	1.31042i
$918$	2.13457e15	−	3.69718e15i	0.108063	−	0.187170i
$919$	7.71842e15			0.388412			0.194206	−	0.980961i	$-0.437787\pi$
$919$	7.71842e15			0.388412			0.194206	+	0.980961i	$0.437787\pi$
$920$	6.99115e14			0.0349716
$921$	−1.72626e15	+	2.98997e15i	−0.0858378	+	0.148675i
$922$	−5.60748e15	+	9.71244e15i	−0.277171	+	0.480074i
$923$	−5.40121e16			−2.65388
$924$	−2.38008e15			−0.116251
$925$	−4.60176e16	+	7.97047e16i	−2.23431	+	3.86994i
$926$	−3.84424e15	−	6.65842e15i	−0.185545	−	0.321374i
$927$	4.83215e15	−	8.36954e15i	0.231847	−	0.401572i
$928$	−1.01477e15	−	1.75764e15i	−0.0484011	−	0.0838332i
$929$	8.69320e15	+	1.50571e16i	0.412186	+	0.713928i	0.995129	−	0.0985860i	$-0.0314320\pi$
$929$	8.69320e15	+	1.50571e16i	0.412186	+	0.713928i	−0.582942	+	0.812514i	$0.698099\pi$
$930$	−2.17727e16			−1.02626
$931$	2.60223e15	+	8.83981e15i	0.121933	+	0.414209i
$932$	1.50424e16			0.700697
$933$	3.91310e15	+	6.77768e15i	0.181206	+	0.313857i
$934$	2.85248e14	+	4.94063e14i	0.0131315	+	0.0227444i
$935$	−1.13510e16	+	1.96604e16i	−0.519480	+	0.899765i
$936$	−1.94375e15	−	3.36668e15i	−0.0884349	−	0.153174i
$937$	1.85061e16	−	3.20535e16i	0.837041	−	1.44980i	−0.0553171	−	0.998469i	$-0.517617\pi$
$937$	1.85061e16	−	3.20535e16i	0.837041	−	1.44980i	0.892358	−	0.451328i	$-0.149050\pi$
$938$	−1.14484e16			−0.514789
$939$	−3.51170e15			−0.156984
$940$	−1.51559e15	+	2.62508e15i	−0.0673564	+	0.116665i
$941$	−4.90286e15	+	8.49200e15i	−0.216624	+	0.375203i	−0.953774	−	0.300526i	$-0.902838\pi$
$941$	−4.90286e15	+	8.49200e15i	−0.216624	+	0.375203i	0.737150	+	0.675729i	$0.236171\pi$
$942$	4.69099e15			0.206056
$943$	7.51656e14			0.0328250
$944$	1.87223e15	−	3.24279e15i	0.0812854	−	0.140790i
$945$	−5.18503e15	−	8.98073e15i	−0.223808	−	0.387647i
$946$	4.32455e15	−	7.49034e15i	0.185584	−	0.321440i
$947$	2.15356e16	+	3.73007e16i	0.918823	+	1.59145i	0.801206	+	0.598389i	$0.204192\pi$
$947$	2.15356e16	+	3.73007e16i	0.918823	+	1.59145i	0.117617	+	0.993059i	$0.462474\pi$
$948$	1.65666e15	+	2.86942e15i	0.0702728	+	0.121716i
$949$	−1.24650e16			−0.525690
$950$	−1.32313e16	−	4.49470e16i	−0.554782	−	1.88461i
$951$	−8.37491e15			−0.349130
$952$	−8.10530e15	−	1.40388e16i	−0.335943	−	0.581871i
$953$	5.58028e15	+	9.66533e15i	0.229956	+	0.398296i	0.957795	−	0.287453i	$-0.0928084\pi$
$953$	5.58028e15	+	9.66533e15i	0.229956	+	0.398296i	−0.727839	+	0.685748i	$0.759475\pi$
$954$	−3.54521e15	+	6.14048e15i	−0.145253	+	0.251586i
$955$	−3.10901e16	−	5.38496e16i	−1.26649	−	2.19363i
$956$	3.23454e14	−	5.60239e14i	0.0131007	−	0.0226911i
$957$	2.64218e15			0.106401
$958$	−1.95522e16			−0.782863
$959$	3.45789e15	−	5.98925e15i	0.137660	−	0.238435i
$960$	−1.77199e15	+	3.06917e15i	−0.0701405	+	0.121487i
$961$	1.70873e16			0.672502
$962$	4.36174e16			1.70686
$963$	−8.34636e15	+	1.44563e16i	−0.324752	+	0.562488i
$964$	−3.60973e14	−	6.25224e14i	−0.0139653	−	0.0241887i
$965$	3.14080e16	−	5.44002e16i	1.20820	−	2.09267i
$966$	−3.24951e14	−	5.62832e14i	−0.0124292	−	0.0215281i
$967$	1.00766e16	+	1.74532e16i	0.383238	+	0.663788i	0.991523	−	0.129931i	$-0.0414754\pi$
$967$	1.00766e16	+	1.74532e16i	0.383238	+	0.663788i	−0.608285	+	0.793719i	$0.708142\pi$
$968$	8.29017e15			0.313508
$969$	−2.37016e16	−	5.73264e15i	−0.891244	−	0.215563i
$970$	4.49735e16			1.68156
$971$	−4.57748e13	−	7.92842e13i	−0.00170185	−	0.00294768i	0.865173	−	0.501473i	$-0.167208\pi$
$971$	−4.57748e13	−	7.92842e13i	−0.00170185	−	0.00294768i	−0.866875	+	0.498525i	$0.833875\pi$
$972$	4.33812e14	+	7.51384e14i	0.0160375	+	0.0277778i
$973$	6.90768e15	−	1.19644e16i	0.253928	−	0.439817i
$974$	−1.22678e16	−	2.12485e16i	−0.448428	−	0.776700i
$975$	−3.31159e16	+	5.73584e16i	−1.20368	+	2.08484i
$976$	1.13230e16			0.409251
$977$	−3.32337e16			−1.19443			−0.597213	−	0.802083i	$-0.703725\pi$
$977$	−3.32337e16			−1.19443			−0.597213	+	0.802083i	$0.703725\pi$
$978$	−4.29690e15	+	7.44245e15i	−0.153565	+	0.265982i
$979$	−8.38658e14	+	1.45260e15i	−0.0298044	+	0.0516227i
$980$	−1.18749e16			−0.419648
$981$	1.43093e16			0.502851
$982$	4.27383e15	−	7.40250e15i	0.149350	−	0.258681i
$983$	−1.50337e16	−	2.60391e16i	−0.522421	−	0.904859i	−0.999660	−	0.0260856i	$-0.991696\pi$
$983$	−1.50337e16	−	2.60391e16i	−0.522421	−	0.904859i	0.477239	−	0.878773i	$-0.341638\pi$
$984$	−1.90516e15	+	3.29983e15i	−0.0658352	+	0.114030i
$985$	1.16997e16	+	2.02645e16i	0.402047	+	0.696366i
$986$	8.99789e15	+	1.55848e16i	0.307481	+	0.532572i
$987$	2.81781e15			0.0957563
$988$	−1.53122e16	+	1.60812e16i	−0.517457	+	0.543444i
$989$	2.36172e15			0.0793686
$990$	−2.30687e15	−	3.99562e15i	−0.0770957	−	0.133534i
$991$	−2.01523e16	−	3.49048e16i	−0.669760	−	1.16006i	−0.977971	−	0.208740i	$-0.933064\pi$
$991$	−2.01523e16	−	3.49048e16i	−0.669760	−	1.16006i	0.308212	−	0.951318i	$-0.400270\pi$
$992$	3.45854e15	−	5.99036e15i	0.114308	−	0.197988i
$993$	−5.39033e15	−	9.33633e15i	−0.177172	−	0.306870i
$994$	2.28866e16	−	3.96407e16i	0.748093	−	1.29573i
$995$	−6.74772e16			−2.19346
$996$	−3.57324e15			−0.115514
$997$	2.96204e16	−	5.13040e16i	0.952285	−	1.64941i	0.211823	−	0.977308i	$-0.432060\pi$
$997$	2.96204e16	−	5.13040e16i	0.952285	−	1.64941i	0.740462	−	0.672098i	$-0.234607\pi$
$998$	−8.82583e15	+	1.52868e16i	−0.282187	+	0.488763i
$999$	−9.73465e15			−0.309535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.12.e.b.7.9	✓	18
19.11	even	3	inner	114.12.e.b.49.9	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.12.e.b.7.9	✓	18	1.1	even	1	trivial
114.12.e.b.49.9	yes	18	19.11	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(16.0000 + 27.7128i) q^{2} +(121.500 + 210.444i) q^{3} +(-512.000 + 886.810i) q^{4} +(6791.32 + 11762.9i) q^{5} +(-3888.00 + 6734.21i) q^{6} +53208.1 q^{7} -32768.0 q^{8} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})\)	\(q+(16.0000 + 27.7128i) q^{2} +(121.500 + 210.444i) q^{3} +(-512.000 + 886.810i) q^{4} +(6791.32 + 11762.9i) q^{5} +(-3888.00 + 6734.21i) q^{6} +53208.1 q^{7} -32768.0 q^{8} +(-29524.5 + 51137.9i) q^{9} +(-217322. + 376413. i) q^{10} +179766. q^{11} -248832. q^{12} +(1.00457e6 - 1.73996e6i) q^{13} +(851330. + 1.47455e6i) q^{14} +(-1.65029e6 + 2.85839e6i) q^{15} +(-524288. - 908093. i) q^{16} +(4.64881e6 + 8.05197e6i) q^{17} -1.88957e6 q^{18} +(3.04790e6 + 1.03538e7i) q^{19} -1.39086e7 q^{20} +(6.46479e6 + 1.11973e7i) q^{21} +(2.87625e6 + 4.98181e6i) q^{22} +(-785388. + 1.36033e6i) q^{23} +(-3.98131e6 - 6.89583e6i) q^{24} +(-6.78300e7 + 1.17485e8i) q^{25} +6.42922e7 q^{26} -1.43489e7 q^{27} +(-2.72426e7 + 4.71855e7i) q^{28} +(3.02426e7 - 5.23818e7i) q^{29} -1.05619e8 q^{30} +2.06145e8 q^{31} +(1.67772e7 - 2.90590e7i) q^{32} +(2.18415e7 + 3.78306e7i) q^{33} +(-1.48762e8 + 2.57663e8i) q^{34} +(3.61353e8 + 6.25883e8i) q^{35} +(-3.02331e7 - 5.23652e7i) q^{36} +6.78424e8 q^{37} +(-2.38166e8 + 2.50126e8i) q^{38} +4.88219e8 q^{39} +(-2.22538e8 - 3.85447e8i) q^{40} +(-2.39263e8 - 4.14415e8i) q^{41} +(-2.06873e8 + 3.58315e8i) q^{42} +(-7.51769e8 - 1.30210e9i) q^{43} +(-9.20400e7 + 1.59418e8i) q^{44} -8.02041e8 q^{45} -5.02648e7 q^{46} +(1.08968e8 - 1.88738e8i) q^{47} +(1.27402e8 - 2.20667e8i) q^{48} +8.53777e8 q^{49} -4.34112e9 q^{50} +(-1.12966e9 + 1.95663e9i) q^{51} +(1.02868e9 + 1.78172e9i) q^{52} +(1.87620e9 - 3.24967e9i) q^{53} +(-2.29583e8 - 3.97649e8i) q^{54} +(1.22085e9 + 2.11457e9i) q^{55} -1.74352e9 q^{56} +(-1.80857e9 + 1.89940e9i) q^{57} +1.93553e9 q^{58} +(1.78549e9 + 3.09257e9i) q^{59} +(-1.68990e9 - 2.92699e9i) q^{60} +(-5.39925e9 + 9.35178e9i) q^{61} +(3.29832e9 + 5.71286e9i) q^{62} +(-1.57094e9 + 2.72095e9i) q^{63} +1.07374e9 q^{64} +2.72893e10 q^{65} +(-6.98929e8 + 1.21058e9i) q^{66} +(-3.36192e9 + 5.82301e9i) q^{67} -9.52076e9 q^{68} -3.81699e8 q^{69} +(-1.15633e10 + 2.00282e10i) q^{70} +(-1.34417e10 - 2.32816e10i) q^{71} +(9.67459e8 - 1.67569e9i) q^{72} +(-3.10210e9 - 5.37299e9i) q^{73} +(1.08548e10 + 1.88011e10i) q^{74} -3.29654e10 q^{75} +(-1.07424e10 - 2.59822e9i) q^{76} +9.56499e9 q^{77} +(7.81151e9 + 1.35299e10i) q^{78} +(-6.65774e9 - 1.15315e10i) q^{79} +(7.12122e9 - 1.23343e10i) q^{80} +(-1.74339e9 - 3.01964e9i) q^{81} +(7.65640e9 - 1.32613e10i) q^{82} +1.43601e10 q^{83} -1.32399e10 q^{84} +(-6.31431e10 + 1.09367e11i) q^{85} +(2.40566e10 - 4.16673e10i) q^{86} +1.46979e10 q^{87} -5.89056e9 q^{88} +(-4.66529e9 + 8.08051e9i) q^{89} +(-1.28327e10 - 2.22268e10i) q^{90} +(5.34511e10 - 9.25800e10i) q^{91} +(-8.04237e8 - 1.39298e9i) q^{92} +(2.50466e10 + 4.33820e10i) q^{93} +6.97393e9 q^{94} +(-1.01091e11 + 1.06168e11i) q^{95} +8.15373e9 q^{96} +(-5.17359e10 - 8.96093e10i) q^{97} +(1.36604e10 + 2.36606e10i) q^{98} +(-5.30749e9 + 9.19284e9i) 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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