LMFDB - Embedded newform 690.2.m.d.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + \cdots + 7921 $ x^20 - 5x^19 + 8x^18 - 32x^17 + 277x^16 - 1138x^15 + 2950x^14 - 6404x^13 + 24088x^12 - 93423x^11 + 318055x^10 - 798006x^9 + 1869818x^8 - 3381161x^7 + 6172602x^6 - 7296658x^5 + 10759748x^4 - 4308967x^3 + 7994447x^2 + 486652*x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Root			$2.31649 + 1.48872i$ of defining polynomial
Character	$\chi$	$=$	690.121
Dual form			690.2.m.d.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.455355 - 3.16706i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.455355 - 3.16706i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.142315 + 0.989821i) q^{10} +(-1.70813 - 3.74028i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.401459 + 2.79221i) q^{13} +(-2.69170 - 1.72985i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(5.33199 - 6.15345i) q^{17} +(0.841254 - 0.540641i) q^{18} +(-1.54536 - 1.78344i) q^{19} +(0.959493 + 0.281733i) q^{20} +(1.32917 - 2.91048i) q^{21} -4.11187 q^{22} +(-4.79382 + 0.138877i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(2.70666 + 0.794746i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-2.69170 + 1.72985i) q^{28} +(2.60460 - 3.00587i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-1.90249 + 0.558621i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.585180 - 4.07001i) q^{33} +(-3.38238 - 7.40639i) q^{34} +(1.32917 + 2.91048i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(1.51072 + 0.970881i) q^{37} +(-2.26424 + 0.664842i) q^{38} +(-0.401459 + 2.79221i) q^{39} +(0.654861 - 0.755750i) q^{40} +(2.69525 - 1.73213i) q^{41} +(-2.09531 - 2.41812i) q^{42} +(5.02388 + 1.47514i) q^{43} +(-1.70813 + 3.74028i) q^{44} -1.00000 q^{45} +(-1.86510 + 4.41830i) q^{46} -6.43522 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-3.10648 - 0.912145i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(6.84964 - 4.40199i) q^{51} +(1.84731 - 2.13191i) q^{52} +(0.655305 - 4.55775i) q^{53} +(0.959493 - 0.281733i) q^{54} +(3.45912 + 2.22304i) q^{55} +(0.455355 + 3.16706i) q^{56} +(-0.980311 - 2.14658i) q^{57} +(-1.65224 - 3.61791i) q^{58} +(-0.277471 - 1.92985i) q^{59} +(0.841254 + 0.540641i) q^{60} +(10.9636 - 3.21921i) q^{61} +(-0.282183 + 1.96262i) q^{62} +(2.09531 - 2.41812i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-1.84731 - 2.13191i) q^{65} +(-3.94531 - 1.15845i) q^{66} +(-2.01007 + 4.40145i) q^{67} -8.14218 q^{68} +(-4.63876 - 1.21732i) q^{69} +3.19963 q^{70} +(-4.33220 + 9.48619i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(8.35076 + 9.63729i) q^{73} +(1.51072 - 0.970881i) q^{74} +(0.654861 - 0.755750i) q^{75} +(-0.335839 + 2.33581i) q^{76} +(-12.6235 + 3.70660i) q^{77} +(2.37311 + 1.52511i) q^{78} +(1.92218 + 13.3690i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.455955 - 3.17124i) q^{82} +(-3.43056 - 2.20469i) q^{83} +(-3.07002 + 0.901440i) q^{84} +(-1.15875 + 8.05930i) q^{85} +(3.42883 - 3.95708i) q^{86} +(3.34595 - 2.15031i) q^{87} +(2.69270 + 3.10754i) q^{88} +(-10.2506 - 3.00986i) q^{89} +(-0.415415 + 0.909632i) q^{90} +9.02591 q^{91} +(3.24424 + 3.53198i) q^{92} -1.98280 q^{93} +(-2.67329 + 5.85368i) q^{94} +(2.26424 + 0.664842i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-10.0792 + 6.47750i) q^{97} +(-2.12019 + 2.44683i) q^{98} +(0.585180 - 4.07001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	0.455355	−	3.16706i	0.172108	−	1.19704i	−0.702313	−	0.711868i	$-0.747849\pi$
$7$	0.455355	−	3.16706i	0.172108	−	1.19704i	0.874421	−	0.485168i	$-0.161242\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	0.142315	+	0.989821i	0.0450039	+	0.313009i
$11$	−1.70813	−	3.74028i	−0.515021	−	1.12774i	−0.971290	−	0.237897i	$-0.923542\pi$
$11$	−1.70813	−	3.74028i	−0.515021	−	1.12774i	0.456270	−	0.889842i	$-0.349185\pi$
$12$	−0.415415	−	0.909632i	−0.119920	−	0.262588i
$13$	0.401459	+	2.79221i	0.111345	+	0.774420i	0.966614	+	0.256236i	$0.0824825\pi$
$13$	0.401459	+	2.79221i	0.111345	+	0.774420i	−0.855269	+	0.518183i	$0.826608\pi$
$14$	−2.69170	−	1.72985i	−0.719387	−	0.462322i
$15$	−0.959493	+	0.281733i	−0.247740	+	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	5.33199	−	6.15345i	1.29320	−	1.49243i	0.526932	−	0.849908i	$-0.323342\pi$
$17$	5.33199	−	6.15345i	1.29320	−	1.49243i	0.766266	−	0.642523i	$-0.222112\pi$
$18$	0.841254	−	0.540641i	0.198285	−	0.127430i
$19$	−1.54536	−	1.78344i	−0.354531	−	0.409150i	0.550269	−	0.834987i	$-0.314525\pi$
$19$	−1.54536	−	1.78344i	−0.354531	−	0.409150i	−0.904800	+	0.425837i	$0.859980\pi$
$20$	0.959493	+	0.281733i	0.214549	+	0.0629973i
$21$	1.32917	−	2.91048i	0.290050	−	0.635120i
$22$	−4.11187			−0.876653
$23$	−4.79382	+	0.138877i	−0.999581	+	0.0289579i
$23$	−4.79382	+	0.138877i	−0.999581	+	0.0289579i
$24$	−1.00000			−0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	2.70666	+	0.794746i	0.530819	+	0.155862i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	−2.69170	+	1.72985i	−0.508683	+	0.326911i
$29$	2.60460	−	3.00587i	0.483662	−	0.558176i	−0.460499	−	0.887660i	$-0.652329\pi$
$29$	2.60460	−	3.00587i	0.483662	−	0.558176i	0.944161	+	0.329484i	$0.106875\pi$
$30$	−0.142315	+	0.989821i	−0.0259830	+	0.180716i
$31$	−1.90249	+	0.558621i	−0.341697	+	0.100331i	−0.448079	−	0.893994i	$-0.647892\pi$
$31$	−1.90249	+	0.558621i	−0.341697	+	0.100331i	0.106382	+	0.994325i	$0.466073\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	−0.585180	−	4.07001i	−0.101867	−	0.708498i
$34$	−3.38238	−	7.40639i	−0.580074	−	1.27018i
$35$	1.32917	+	2.91048i	0.224671	+	0.491962i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	1.51072	+	0.970881i	0.248361	+	0.159612i	0.658899	−	0.752232i	$-0.271023\pi$
$37$	1.51072	+	0.970881i	0.248361	+	0.159612i	−0.410538	+	0.911844i	$0.634659\pi$
$38$	−2.26424	+	0.664842i	−0.367309	+	0.107852i
$39$	−0.401459	+	2.79221i	−0.0642849	+	0.447111i
$40$	0.654861	−	0.755750i	0.103543	−	0.119494i
$41$	2.69525	−	1.73213i	0.420927	−	0.270514i	−0.312985	−	0.949758i	$-0.601329\pi$
$41$	2.69525	−	1.73213i	0.420927	−	0.270514i	0.733912	+	0.679245i	$0.237692\pi$
$42$	−2.09531	−	2.41812i	−0.323314	−	0.373124i
$43$	5.02388	+	1.47514i	0.766134	+	0.224957i	0.641373	−	0.767230i	$-0.278365\pi$
$43$	5.02388	+	1.47514i	0.766134	+	0.224957i	0.124761	+	0.992187i	$0.460183\pi$
$44$	−1.70813	+	3.74028i	−0.257510	+	0.563869i
$45$	−1.00000			−0.149071
$46$	−1.86510	+	4.41830i	−0.274994	+	0.651443i
$47$	−6.43522			−0.938673			−0.469337	−	0.883019i	$-0.655507\pi$
$47$	−6.43522			−0.938673			−0.469337	+	0.883019i	$0.655507\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−3.10648	−	0.912145i	−0.443783	−	0.130306i
$50$	−0.654861	−	0.755750i	−0.0926113	−	0.106879i
$51$	6.84964	−	4.40199i	0.959141	−	0.616403i
$52$	1.84731	−	2.13191i	0.256176	−	0.295643i
$53$	0.655305	−	4.55775i	0.0900131	−	0.626055i	−0.894014	−	0.448038i	$-0.852123\pi$
$53$	0.655305	−	4.55775i	0.0900131	−	0.626055i	0.984027	−	0.178017i	$-0.0569681\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	3.45912	+	2.22304i	0.466428	+	0.299755i
$56$	0.455355	+	3.16706i	0.0608493	+	0.423216i
$57$	−0.980311	−	2.14658i	−0.129845	−	0.284322i
$58$	−1.65224	−	3.61791i	−0.216950	−	0.475055i
$59$	−0.277471	−	1.92985i	−0.0361236	−	0.251245i	0.963756	−	0.266787i	$-0.0859619\pi$
$59$	−0.277471	−	1.92985i	−0.0361236	−	0.251245i	−0.999879	+	0.0155415i	$0.995053\pi$
$60$	0.841254	+	0.540641i	0.108605	+	0.0697964i
$61$	10.9636	−	3.21921i	1.40375	−	0.412177i	0.509778	−	0.860306i	$-0.329727\pi$
$61$	10.9636	−	3.21921i	1.40375	−	0.412177i	0.893969	+	0.448128i	$0.147909\pi$
$62$	−0.282183	+	1.96262i	−0.0358372	+	0.249253i
$63$	2.09531	−	2.41812i	0.263984	−	0.304654i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−1.84731	−	2.13191i	−0.229131	−	0.264431i
$66$	−3.94531	−	1.15845i	−0.485634	−	0.142595i
$67$	−2.01007	+	4.40145i	−0.245570	+	0.537723i	−0.991775	−	0.127993i	$-0.959146\pi$
$67$	−2.01007	+	4.40145i	−0.245570	+	0.537723i	0.746205	+	0.665716i	$0.231874\pi$
$68$	−8.14218			−0.987384
$69$	−4.63876	−	1.21732i	−0.558441	−	0.146549i
$70$	3.19963			0.382429
$71$	−4.33220	+	9.48619i	−0.514137	+	1.12580i	0.457474	+	0.889223i	$0.348754\pi$
$71$	−4.33220	+	9.48619i	−0.514137	+	1.12580i	−0.971612	+	0.236581i	$0.923973\pi$
$72$	−0.959493	−	0.281733i	−0.113077	−	0.0332025i
$73$	8.35076	+	9.63729i	0.977383	+	1.12796i	0.991766	+	0.128063i	$0.0408760\pi$
$73$	8.35076	+	9.63729i	0.977383	+	1.12796i	−0.0143835	+	0.999897i	$0.504579\pi$
$74$	1.51072	−	0.970881i	0.175618	−	0.112863i
$75$	0.654861	−	0.755750i	0.0756168	−	0.0872664i
$76$	−0.335839	+	2.33581i	−0.0385234	+	0.267936i
$77$	−12.6235	+	3.70660i	−1.43858	+	0.422406i
$78$	2.37311	+	1.52511i	0.268702	+	0.172684i
$79$	1.92218	+	13.3690i	0.216262	+	1.50413i	0.751669	+	0.659540i	$0.229249\pi$
$79$	1.92218	+	13.3690i	0.216262	+	1.50413i	−0.535407	+	0.844594i	$0.679842\pi$
$80$	−0.415415	−	0.909632i	−0.0464448	−	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.455955	−	3.17124i	−0.0503518	−	0.350205i
$83$	−3.43056	−	2.20469i	−0.376553	−	0.241996i	0.338650	−	0.940912i	$-0.390030\pi$
$83$	−3.43056	−	2.20469i	−0.376553	−	0.241996i	−0.715203	+	0.698916i	$0.753666\pi$
$84$	−3.07002	+	0.901440i	−0.334967	+	0.0983551i
$85$	−1.15875	+	8.05930i	−0.125684	+	0.874154i
$86$	3.42883	−	3.95708i	0.369740	−	0.426703i
$87$	3.34595	−	2.15031i	0.358723	−	0.230537i
$88$	2.69270	+	3.10754i	0.287043	+	0.331265i
$89$	−10.2506	−	3.00986i	−1.08656	−	0.319044i	−0.311063	−	0.950389i	$-0.600685\pi$
$89$	−10.2506	−	3.00986i	−1.08656	−	0.319044i	−0.775502	+	0.631345i	$0.782503\pi$
$90$	−0.415415	+	0.909632i	−0.0437886	+	0.0958836i
$91$	9.02591			0.946172
$92$	3.24424	+	3.53198i	0.338235	+	0.368235i
$93$	−1.98280			−0.205607
$94$	−2.67329	+	5.85368i	−0.275728	+	0.603761i
$95$	2.26424	+	0.664842i	0.232307	+	0.0682114i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	−10.0792	+	6.47750i	−1.02339	+	0.657691i	−0.940824	−	0.338895i	$-0.889947\pi$
$97$	−10.0792	+	6.47750i	−1.02339	+	0.657691i	−0.0825627	+	0.996586i	$0.526310\pi$
$98$	−2.12019	+	2.44683i	−0.214172	+	0.247168i
$99$	0.585180	−	4.07001i	0.0588128	−	0.409052i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	14.1621	+	9.10144i	1.40918	+	0.905627i	0.999977	−	0.00681414i	$-0.00216902\pi$
$101$	14.1621	+	9.10144i	1.40918	+	0.905627i	0.409207	+	0.912442i	$0.365805\pi$
$102$	−1.15875	−	8.05930i	−0.114734	−	0.797990i
$103$	2.32765	+	5.09685i	0.229350	+	0.502207i	0.988962	−	0.148170i	$-0.0473382\pi$
$103$	2.32765	+	5.09685i	0.229350	+	0.502207i	−0.759612	+	0.650377i	$0.774611\pi$
$104$	−1.17185	−	2.56600i	−0.114910	−	0.251617i
$105$	0.455355	+	3.16706i	0.0444381	+	0.309074i
$106$	−3.87365	−	2.48944i	−0.376242	−	0.241796i
$107$	4.93810	−	1.44996i	0.477384	−	0.140172i	−0.0341839	−	0.999416i	$-0.510883\pi$
$107$	4.93810	−	1.44996i	0.477384	−	0.140172i	0.511568	+	0.859243i	$0.329065\pi$
$108$	0.142315	−	0.989821i	0.0136943	−	0.0952456i
$109$	5.64856	−	6.51878i	0.541034	−	0.624386i	−0.417737	−	0.908568i	$-0.637177\pi$
$109$	5.64856	−	6.51878i	0.541034	−	0.624386i	0.958770	+	0.284182i	$0.0917220\pi$
$110$	3.45912	−	2.22304i	0.329814	−	0.211959i
$111$	1.17600	+	1.35717i	0.111621	+	0.128817i
$112$	3.07002	+	0.901440i	0.290090	+	0.0851780i
$113$	−4.57456	+	10.0169i	−0.430338	+	0.942310i	0.562933	+	0.826502i	$0.309673\pi$
$113$	−4.57456	+	10.0169i	−0.430338	+	0.942310i	−0.993272	+	0.115807i	$0.963054\pi$
$114$	−2.35983			−0.221019
$115$	3.95774	−	2.70857i	0.369061	−	0.252575i
$116$	−3.97733			−0.369286
$117$	−1.17185	+	2.56600i	−0.108338	+	0.237227i
$118$	−1.87072	−	0.549293i	−0.172214	−	0.0505665i
$119$	−17.0604	−	19.6888i	−1.56392	−	1.80486i
$120$	0.841254	−	0.540641i	0.0767956	−	0.0493535i
$121$	−3.86855	+	4.46455i	−0.351687	+	0.405868i
$122$	1.62616	−	11.3102i	0.147225	−	1.02397i
$123$	3.07407	−	0.902629i	0.277180	−	0.0813873i
$124$	1.66804	+	1.07199i	0.149795	+	0.0962671i
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$	−1.32917	−	2.91048i	−0.118412	−	0.259287i
$127$	0.396371	+	0.867931i	0.0351722	+	0.0770164i	0.926403	−	0.376534i	$-0.122884\pi$
$127$	0.396371	+	0.867931i	0.0351722	+	0.0770164i	−0.891230	+	0.453551i	$0.850157\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	4.40478	+	2.83078i	0.387819	+	0.249236i
$130$	−2.70666	+	0.794746i	−0.237389	+	0.0697038i
$131$	1.31838	−	9.16955i	0.115188	−	0.801147i	−0.847551	−	0.530714i	$-0.821924\pi$
$131$	1.31838	−	9.16955i	0.115188	−	0.801147i	0.962739	−	0.270433i	$-0.0871670\pi$
$132$	−2.69270	+	3.10754i	−0.234369	+	0.270477i
$133$	−6.35196	+	4.08216i	−0.550785	+	0.353968i
$134$	3.16868	+	3.65686i	0.273733	+	0.315904i
$135$	−0.959493	−	0.281733i	−0.0825800	−	0.0242477i
$136$	−3.38238	+	7.40639i	−0.290037	+	0.635092i
$137$	11.2285			0.959314			0.479657	−	0.877456i	$-0.340761\pi$
$137$	11.2285			0.959314			0.479657	+	0.877456i	$0.340761\pi$
$138$	−3.03433	+	3.71387i	−0.258299	+	0.316146i
$139$	−2.83950			−0.240843			−0.120421	−	0.992723i	$-0.538425\pi$
$139$	−2.83950			−0.240843			−0.120421	+	0.992723i	$0.538425\pi$
$140$	1.32917	−	2.91048i	0.112336	−	0.245981i
$141$	−6.17455	−	1.81301i	−0.519991	−	0.152683i
$142$	6.82928	+	7.88141i	0.573101	+	0.661393i
$143$	9.75792	−	6.27103i	0.815998	−	0.524410i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−0.566034	+	3.93685i	−0.0470065	+	0.326938i
$146$	12.2354	−	3.59264i	1.01261	−	0.297329i
$147$	−2.72366	−	1.75039i	−0.224644	−	0.144370i
$148$	−0.255568	−	1.77752i	−0.0210076	−	0.146111i
$149$	9.53666	+	20.8824i	0.781273	+	1.71075i	0.700094	+	0.714051i	$0.253141\pi$
$149$	9.53666	+	20.8824i	0.781273	+	1.71075i	0.0811797	+	0.996699i	$0.474131\pi$
$150$	−0.415415	−	0.909632i	−0.0339185	−	0.0742711i
$151$	0.388348	+	2.70102i	0.0316033	+	0.219806i	0.999503	−	0.0315319i	$-0.0100386\pi$
$151$	0.388348	+	2.70102i	0.0316033	+	0.219806i	−0.967899	+	0.251338i	$0.919129\pi$
$152$	1.98522	+	1.27582i	0.161023	+	0.103483i
$153$	7.81236	−	2.29392i	0.631592	−	0.185452i
$154$	−1.87236	+	13.0225i	−0.150879	+	1.04939i
$155$	1.29846	−	1.49850i	0.104295	−	0.120363i
$156$	2.37311	−	1.52511i	0.190001	−	0.122106i
$157$	−8.04856	−	9.28853i	−0.642345	−	0.741306i	0.337443	−	0.941346i	$-0.390438\pi$
$157$	−8.04856	−	9.28853i	−0.642345	−	0.741306i	−0.979788	+	0.200040i	$0.935893\pi$
$158$	12.9594	+	3.80523i	1.03100	+	0.302727i
$159$	1.91283	−	4.18851i	0.151697	−	0.332170i
$160$	−1.00000			−0.0790569
$161$	−1.74306	+	15.2456i	−0.137372	+	1.20152i
$162$	1.00000			0.0785674
$163$	0.724220	−	1.58582i	0.0567253	−	0.124211i	−0.879147	−	0.476551i	$-0.841887\pi$
$163$	0.724220	−	1.58582i	0.0567253	−	0.124211i	0.935872	+	0.352340i	$0.114614\pi$
$164$	−3.07407	−	0.902629i	−0.240045	−	0.0704835i
$165$	2.69270	+	3.10754i	0.209626	+	0.241922i
$166$	−3.43056	+	2.20469i	−0.266263	+	0.171117i
$167$	−5.85651	+	6.75878i	−0.453191	+	0.523010i	−0.935660	−	0.352903i	$-0.885195\pi$
$167$	−5.85651	+	6.75878i	−0.453191	+	0.523010i	0.482469	+	0.875913i	$0.339740\pi$
$168$	−0.455355	+	3.16706i	−0.0351314	+	0.244344i
$169$	4.83814	−	1.42061i	0.372165	−	0.109277i
$170$	6.84964	+	4.40199i	0.525343	+	0.337618i
$171$	−0.335839	−	2.33581i	−0.0256823	−	0.178624i
$172$	−2.17510	−	4.76281i	−0.165850	−	0.363161i
$173$	−10.7049	−	23.4405i	−0.813878	−	1.78214i	−0.589752	−	0.807584i	$-0.700774\pi$
$173$	−10.7049	−	23.4405i	−0.813878	−	1.78214i	−0.224126	−	0.974560i	$-0.571953\pi$
$174$	−0.566034	−	3.93685i	−0.0429109	−	0.298452i
$175$	−2.69170	−	1.72985i	−0.203473	−	0.130764i
$176$	3.94531	−	1.15845i	0.297389	−	0.0873212i
$177$	0.277471	−	1.92985i	0.0208560	−	0.145056i
$178$	−6.99613	+	8.07396i	−0.524382	+	0.605169i
$179$	21.8632	−	14.0506i	1.63413	−	1.05019i	0.688353	−	0.725376i	$-0.258334\pi$
$179$	21.8632	−	14.0506i	1.63413	−	1.05019i	0.945777	−	0.324815i	$-0.105302\pi$
$180$	0.654861	+	0.755750i	0.0488104	+	0.0563302i
$181$	15.8678	+	4.65920i	1.17944	+	0.346315i	0.811959	−	0.583715i	$-0.198401\pi$
$181$	15.8678	+	4.65920i	1.17944	+	0.346315i	0.367483	+	0.930030i	$0.380220\pi$
$182$	3.74950	−	8.21025i	0.277931	−	0.608584i
$183$	11.4265			0.844669
$184$	4.56051	−	1.48383i	0.336205	−	0.109389i
$185$	−1.79580			−0.132030
$186$	−0.823687	+	1.80362i	−0.0603957	+	0.132248i
$187$	−32.1234	−	9.43228i	−2.34910	−	0.689757i
$188$	4.21417	+	4.86341i	0.307350	+	0.354701i
$189$	2.69170	−	1.72985i	0.195792	−	0.125828i
$190$	1.54536	−	1.78344i	0.112112	−	0.129385i
$191$	−2.00701	+	13.9591i	−0.145222	+	1.01004i	0.778681	+	0.627420i	$0.215889\pi$
$191$	−2.00701	+	13.9591i	−0.145222	+	1.01004i	−0.923904	+	0.382625i	$0.875020\pi$
$192$	0.959493	−	0.281733i	0.0692454	−	0.0203323i
$193$	−2.11465	−	1.35900i	−0.152216	−	0.0978231i	0.462316	−	0.886715i	$-0.347019\pi$
$193$	−2.11465	−	1.35900i	−0.152216	−	0.0978231i	−0.614532	+	0.788892i	$0.710655\pi$
$194$	1.70510	+	11.8592i	0.122419	+	0.851442i
$195$	−1.17185	−	2.56600i	−0.0839182	−	0.183755i
$196$	1.34496	+	2.94505i	0.0960685	+	0.210361i
$197$	0.401792	+	2.79453i	0.0286265	+	0.199102i	0.999116	−	0.0420424i	$-0.0133864\pi$
$197$	0.401792	+	2.79453i	0.0286265	+	0.199102i	−0.970489	+	0.241144i	$0.922477\pi$
$198$	−3.45912	−	2.22304i	−0.245829	−	0.157985i
$199$	13.1206	−	3.85256i	0.930095	−	0.273100i	0.218618	−	0.975810i	$-0.429845\pi$
$199$	13.1206	−	3.85256i	0.930095	−	0.273100i	0.711476	+	0.702710i	$0.248027\pi$
$200$	−0.142315	+	0.989821i	−0.0100632	+	0.0699909i
$201$	−3.16868	+	3.65686i	−0.223502	+	0.257935i
$202$	14.1621	−	9.10144i	0.996443	−	0.640375i
$203$	−8.33375	−	9.61766i	−0.584915	−	0.675028i
$204$	−7.81236	−	2.29392i	−0.546975	−	0.160606i
$205$	−1.33093	+	2.91432i	−0.0929560	+	0.203545i
$206$	5.60320			0.390393
$207$	−4.10790	−	2.47490i	−0.285519	−	0.172018i
$208$	−2.82092			−0.195596
$209$	−4.03091	+	8.82645i	−0.278824	+	0.610539i
$210$	3.07002	+	0.901440i	0.211852	+	0.0622052i
$211$	−0.0865472	−	0.0998808i	−0.00595815	−	0.00687608i	0.752763	−	0.658292i	$-0.228721\pi$
$211$	−0.0865472	−	0.0998808i	−0.00595815	−	0.00687608i	−0.758721	+	0.651416i	$0.774175\pi$
$212$	−3.87365	+	2.48944i	−0.266043	+	0.170976i
$213$	−6.82928	+	7.88141i	−0.467935	+	0.540026i
$214$	0.732433	−	5.09418i	0.0500681	−	0.348231i
$215$	−5.02388	+	1.47514i	−0.342626	+	0.100604i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	0.902879	+	6.27966i	0.0612915	+	0.426291i
$218$	−3.58320	−	7.84611i	−0.242685	−	0.531406i
$219$	5.29736	+	11.5996i	0.357962	+	0.783828i
$220$	−0.585180	−	4.07001i	−0.0394528	−	0.274400i
$221$	19.3223	+	12.4177i	1.29976	+	0.835304i
$222$	1.72305	−	0.505934i	0.115644	−	0.0339561i
$223$	−3.33635	+	23.2048i	−0.223418	+	1.55391i	0.501551	+	0.865128i	$0.332763\pi$
$223$	−3.33635	+	23.2048i	−0.223418	+	1.55391i	−0.724970	+	0.688781i	$0.758146\pi$
$224$	2.09531	−	2.41812i	0.139999	−	0.161567i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	7.21134	+	8.32233i	0.479691	+	0.553593i
$227$	−8.61833	−	2.53057i	−0.572019	−	0.167960i	−0.0170845	−	0.999854i	$-0.505438\pi$
$227$	−8.61833	−	2.53057i	−0.572019	−	0.167960i	−0.554934	+	0.831894i	$0.687257\pi$
$228$	−0.980311	+	2.14658i	−0.0649227	+	0.142161i
$229$	19.2838			1.27431			0.637156	−	0.770735i	$-0.280111\pi$
$229$	19.2838			1.27431			0.637156	+	0.770735i	$0.280111\pi$
$230$	−0.819695	−	4.72526i	−0.0540491	−	0.311575i
$231$	−13.1564			−0.865631
$232$	−1.65224	+	3.61791i	−0.108475	+	0.237527i
$233$	−5.68801	−	1.67015i	−0.372634	−	0.109415i	0.0900530	−	0.995937i	$-0.471296\pi$
$233$	−5.68801	−	1.67015i	−0.372634	−	0.109415i	−0.462687	+	0.886522i	$0.653115\pi$
$234$	1.84731	+	2.13191i	0.120763	+	0.139367i
$235$	5.41365	−	3.47914i	0.353148	−	0.226954i
$236$	−1.27678	+	1.47348i	−0.0831112	+	0.0959155i
$237$	−1.92218	+	13.3690i	−0.124859	+	0.868412i
$238$	−24.9967	+	7.33968i	−1.62029	+	0.475761i
$239$	−5.90305	−	3.79366i	−0.381836	−	0.245391i	0.335616	−	0.941999i	$-0.391056\pi$
$239$	−5.90305	−	3.79366i	−0.381836	−	0.245391i	−0.717452	+	0.696608i	$0.754692\pi$
$240$	−0.142315	−	0.989821i	−0.00918638	−	0.0638927i
$241$	2.43494	+	5.33177i	0.156848	+	0.343450i	0.971700	−	0.236220i	$-0.0759087\pi$
$241$	2.43494	+	5.33177i	0.156848	+	0.343450i	−0.814851	+	0.579670i	$0.803181\pi$
$242$	2.45404	+	5.37360i	0.157752	+	0.345428i
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$	−9.61256	−	6.17762i	−0.615381	−	0.395481i
$245$	3.10648	−	0.912145i	0.198466	−	0.0582748i
$246$	0.455955	−	3.17124i	0.0290706	−	0.202191i
$247$	4.35935	−	5.03096i	0.277379	−	0.320112i
$248$	1.66804	−	1.07199i	0.105921	−	0.0680711i
$249$	−2.67047	−	3.08188i	−0.169234	−	0.195306i
$250$	0.959493	+	0.281733i	0.0606837	+	0.0178183i
$251$	0.427016	−	0.935035i	0.0269530	−	0.0590189i	−0.895677	−	0.444706i	$-0.853308\pi$
$251$	0.427016	−	0.935035i	0.0269530	−	0.0590189i	0.922630	+	0.385687i	$0.126036\pi$
$252$	−3.19963			−0.201558
$253$	8.70791	+	17.6930i	0.547462	+	1.11235i
$254$	0.954156			0.0598691
$255$	−3.38238	+	7.40639i	−0.211813	+	0.463806i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−14.7093	−	16.9754i	−0.917541	−	1.05890i	−0.998067	−	0.0621463i	$-0.980205\pi$
$257$	−14.7093	−	16.9754i	−0.917541	−	1.05890i	0.0805260	−	0.996753i	$-0.474340\pi$
$258$	4.40478	−	2.83078i	0.274230	−	0.176237i
$259$	3.76275	−	4.34245i	0.233806	−	0.269827i
$260$	−0.401459	+	2.79221i	−0.0248974	+	0.173165i
$261$	3.81622	−	1.12054i	0.236218	−	0.0693600i
$262$	−7.79324	−	5.00841i	−0.481468	−	0.309421i
$263$	−4.07994	−	28.3766i	−0.251580	−	1.74978i	−0.588733	−	0.808327i	$-0.700373\pi$
$263$	−4.07994	−	28.3766i	−0.251580	−	1.74978i	0.337153	−	0.941450i	$-0.390536\pi$
$264$	1.70813	+	3.74028i	0.105128	+	0.230199i
$265$	1.91283	+	4.18851i	0.117504	+	0.257298i
$266$	1.07456	+	7.47374i	0.0658856	+	0.458244i
$267$	−8.98743	−	5.77587i	−0.550022	−	0.353478i
$268$	4.64271	−	1.36322i	0.283599	−	0.0832721i
$269$	−4.45827	+	31.0080i	−0.271826	+	1.89059i	0.157626	+	0.987499i	$0.449616\pi$
$269$	−4.45827	+	31.0080i	−0.271826	+	1.89059i	−0.429452	+	0.903090i	$0.641293\pi$
$270$	−0.654861	+	0.755750i	−0.0398536	+	0.0459935i
$271$	−2.04287	+	1.31287i	−0.124096	+	0.0797515i	−0.601216	−	0.799086i	$-0.705317\pi$
$271$	−2.04287	+	1.31287i	−0.124096	+	0.0797515i	0.477120	+	0.878838i	$0.341681\pi$
$272$	5.33199	+	6.15345i	0.323300	+	0.373108i
$273$	8.66029	+	2.54289i	0.524145	+	0.153903i
$274$	4.66448	−	10.2138i	0.281792	−	0.617038i
$275$	−4.11187			−0.247955
$276$	2.11775	+	4.30292i	0.127474	+	0.259005i
$277$	−12.9422			−0.777622			−0.388811	−	0.921318i	$-0.627114\pi$
$277$	−12.9422			−0.777622			−0.388811	+	0.921318i	$0.627114\pi$
$278$	−1.17957	+	2.58290i	−0.0707459	+	0.154912i
$279$	−1.90249	−	0.558621i	−0.113899	−	0.0334437i
$280$	−2.09531	−	2.41812i	−0.125219	−	0.144510i
$281$	26.0134	−	16.7178i	1.55183	−	0.997299i	0.567009	−	0.823711i	$-0.308100\pi$
$281$	26.0134	−	16.7178i	1.55183	−	0.997299i	0.984818	−	0.173588i	$-0.0555361\pi$
$282$	−4.21417	+	4.86341i	−0.250950	+	0.289612i
$283$	−1.78356	+	12.4049i	−0.106022	+	0.737398i	0.865579	+	0.500772i	$0.166951\pi$
$283$	−1.78356	+	12.4049i	−0.106022	+	0.737398i	−0.971601	+	0.236625i	$0.923959\pi$
$284$	10.0062	−	2.93808i	0.593757	−	0.174343i
$285$	1.98522	+	1.27582i	0.117594	+	0.0755732i
$286$	−1.65075	−	11.4812i	−0.0976107	−	0.678897i
$287$	−4.25847	−	9.32475i	−0.251370	−	0.550423i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	−7.01542	−	48.7933i	−0.412672	−	2.87020i
$290$	3.34595	+	2.15031i	0.196481	+	0.126271i
$291$	−11.4958	+	3.37548i	−0.673898	+	0.197874i
$292$	1.81479	−	12.6222i	0.106203	−	0.738656i
$293$	20.8314	−	24.0407i	1.21698	−	1.40447i	0.329170	−	0.944271i	$-0.393231\pi$
$293$	20.8314	−	24.0407i	1.21698	−	1.40447i	0.887814	−	0.460203i	$-0.152223\pi$
$294$	−2.72366	+	1.75039i	−0.158847	+	0.102085i
$295$	1.27678	+	1.47348i	0.0743369	+	0.0857894i
$296$	−1.72305	−	0.505934i	−0.100150	−	0.0294068i
$297$	1.70813	−	3.74028i	0.0991158	−	0.217033i
$298$	22.9569			1.32986
$299$	−2.31230	−	13.3296i	−0.133724	−	0.770871i
$300$	−1.00000			−0.0577350
$301$	6.95952	−	15.2392i	0.401140	−	0.878374i
$302$	2.61826	+	0.768791i	0.150664	+	0.0442389i
$303$	11.0243	+	12.7227i	0.633329	+	0.730900i
$304$	1.98522	−	1.27582i	0.113860	−	0.0731735i
$305$	−7.48275	+	8.63555i	−0.428461	+	0.494470i
$306$	1.15875	−	8.05930i	0.0662415	−	0.460720i
$307$	−0.111159	+	0.0326392i	−0.00634418	+	0.00186282i	−0.284903	−	0.958556i	$-0.591961\pi$
$307$	−0.111159	+	0.0326392i	−0.00634418	+	0.00186282i	0.278559	+	0.960419i	$0.410143\pi$
$308$	11.0679	+	7.11291i	0.630653	+	0.405296i
$309$	0.797418	+	5.54617i	0.0453635	+	0.315510i
$310$	−0.823687	−	1.80362i	−0.0467823	−	0.102439i
$311$	−3.13187	−	6.85784i	−0.177592	−	0.388872i	0.799812	−	0.600250i	$-0.204932\pi$
$311$	−3.13187	−	6.85784i	−0.177592	−	0.388872i	−0.977404	+	0.211378i	$0.932205\pi$
$312$	−0.401459	−	2.79221i	−0.0227281	−	0.158078i
$313$	−17.1927	−	11.0491i	−0.971788	−	0.624530i	−0.0445519	−	0.999007i	$-0.514186\pi$
$313$	−17.1927	−	11.0491i	−0.971788	−	0.624530i	−0.927236	+	0.374477i	$0.877822\pi$
$314$	−11.7926	+	3.46263i	−0.665497	+	0.195408i
$315$	−0.455355	+	3.16706i	−0.0256563	+	0.178444i
$316$	8.84489	−	10.2075i	0.497564	−	0.574219i
$317$	−7.54738	+	4.85040i	−0.423903	+	0.272426i	−0.735152	−	0.677903i	$-0.762889\pi$
$317$	−7.54738	+	4.85040i	−0.423903	+	0.272426i	0.311249	+	0.950328i	$0.399253\pi$
$318$	−3.01538	−	3.47994i	−0.169094	−	0.195145i
$319$	−15.6918	−	4.60753i	−0.878572	−	0.257972i
$320$	−0.415415	+	0.909632i	−0.0232224	+	0.0508500i
$321$	5.14657			0.287253
$322$	13.1438	+	7.91878i	0.732473	+	0.441296i
$323$	−19.2142			−1.06911
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	2.70666	+	0.794746i	0.150138	+	0.0440846i
$326$	−1.14166	−	1.31755i	−0.0632308	−	0.0729722i
$327$	7.25631	−	4.66334i	0.401275	−	0.257884i
$328$	−2.09807	+	2.42131i	−0.115847	+	0.133694i
$329$	−2.93031	+	20.3807i	−0.161553	+	1.12363i
$330$	3.94531	−	1.15845i	0.217182	−	0.0637704i
$331$	−15.3408	−	9.85892i	−0.843205	−	0.541895i	0.0462434	−	0.998930i	$-0.485275\pi$
$331$	−15.3408	−	9.85892i	−0.843205	−	0.541895i	−0.889449	+	0.457035i	$0.848911\pi$
$332$	0.580348	+	4.03641i	0.0318507	+	0.221527i
$333$	0.746001	+	1.63351i	0.0408806	+	0.0895160i
$334$	3.71512	+	8.13497i	0.203282	+	0.445126i
$335$	−0.688621	−	4.78946i	−0.0376234	−	0.261676i
$336$	2.69170	+	1.72985i	0.146844	+	0.0943711i
$337$	−17.9314	+	5.26514i	−0.976787	+	0.286810i	−0.730897	−	0.682487i	$-0.760898\pi$
$337$	−17.9314	+	5.26514i	−0.976787	+	0.286810i	−0.245889	+	0.969298i	$0.579080\pi$
$338$	0.717608	−	4.99107i	0.0390327	−	0.271478i
$339$	−7.21134	+	8.32233i	−0.391666	+	0.452007i
$340$	6.84964	−	4.40199i	0.371474	−	0.238732i
$341$	5.33910	+	6.16165i	0.289128	+	0.333672i
$342$	−2.26424	−	0.664842i	−0.122436	−	0.0359505i
$343$	5.00085	−	10.9503i	0.270020	−	0.591262i
$344$	−5.23597			−0.282305
$345$	4.56051	−	1.48383i	0.245530	−	0.0798865i
$346$	−25.7692			−1.38536
$347$	−8.97260	+	19.6473i	−0.481675	+	1.05472i	0.500325	+	0.865838i	$0.333214\pi$
$347$	−8.97260	+	19.6473i	−0.481675	+	1.05472i	−0.982000	+	0.188883i	$0.939513\pi$
$348$	−3.81622	−	1.12054i	−0.204571	−	0.0600675i
$349$	−0.111386	−	0.128546i	−0.00596233	−	0.00688090i	0.752761	−	0.658294i	$-0.228722\pi$
$349$	−0.111386	−	0.128546i	−0.00596233	−	0.00688090i	−0.758723	+	0.651413i	$0.774176\pi$
$350$	−2.69170	+	1.72985i	−0.143877	+	0.0924644i
$351$	−1.84731	+	2.13191i	−0.0986022	+	0.113793i
$352$	0.585180	−	4.07001i	0.0311902	−	0.216932i
$353$	−8.90210	+	2.61389i	−0.473811	+	0.139123i	−0.509915	−	0.860225i	$-0.670323\pi$
$353$	−8.90210	+	2.61389i	−0.473811	+	0.139123i	0.0361044	+	0.999348i	$0.488505\pi$
$354$	−1.64019	−	1.05408i	−0.0871750	−	0.0560240i
$355$	−1.48415	−	10.3225i	−0.0787702	−	0.547859i
$356$	4.43804	+	9.71795i	0.235216	+	0.515050i
$357$	−10.8224	−	23.6977i	−0.572781	−	1.25421i
$358$	−3.69859	−	25.7243i	−0.195477	−	1.35957i
$359$	−12.8365	−	8.24955i	−0.677487	−	0.435395i	0.156131	−	0.987736i	$-0.450098\pi$
$359$	−12.8365	−	8.24955i	−0.677487	−	0.435395i	−0.833618	+	0.552342i	$0.813734\pi$
$360$	0.959493	−	0.281733i	0.0505697	−	0.0148486i
$361$	1.91146	−	13.2945i	0.100603	−	0.699709i
$362$	10.8299	−	12.4983i	0.569205	−	0.656897i
$363$	−4.96966	+	3.19380i	−0.260839	+	0.167631i
$364$	−5.91071	−	6.82132i	−0.309805	−	0.357535i
$365$	−12.2354	−	3.59264i	−0.640431	−	0.188048i
$366$	4.74673	−	10.3939i	0.248115	−	0.543297i
$367$	−13.0792			−0.682729			−0.341364	−	0.939931i	$-0.610889\pi$
$367$	−13.0792			−0.682729			−0.341364	+	0.939931i	$0.610889\pi$
$368$	0.544768	−	4.76479i	0.0283980	−	0.248382i
$369$	3.20385			0.166786
$370$	−0.746001	+	1.63351i	−0.0387827	+	0.0849223i
$371$	−14.1363	−	4.15078i	−0.733919	−	0.215498i
$372$	1.29846	+	1.49850i	0.0673221	+	0.0776938i
$373$	2.12386	−	1.36492i	0.109969	−	0.0706729i	−0.484500	−	0.874791i	$-0.660999\pi$
$373$	2.12386	−	1.36492i	0.109969	−	0.0706729i	0.594469	+	0.804118i	$0.297362\pi$
$374$	−21.9244	+	25.3022i	−1.13369	+	1.30834i
$375$	−0.142315	+	0.989821i	−0.00734911	+	0.0511142i
$376$	6.17455	−	1.81301i	0.318428	−	0.0934989i
$377$	9.43866	+	6.06586i	0.486116	+	0.312407i
$378$	−0.455355	−	3.16706i	−0.0234209	−	0.162896i
$379$	−11.8283	−	25.9003i	−0.607577	−	1.33041i	−0.924219	−	0.381863i	$-0.875283\pi$
$379$	−11.8283	−	25.9003i	−0.607577	−	1.33041i	0.316642	−	0.948545i	$-0.397445\pi$
$380$	−0.980311	−	2.14658i	−0.0502889	−	0.110117i
$381$	0.135791	+	0.944444i	0.00695676	+	0.0483853i
$382$	11.8639	+	7.62446i	0.607009	+	0.390101i
$383$	−9.47628	+	2.78249i	−0.484216	+	0.142179i	−0.514724	−	0.857356i	$-0.672106\pi$
$383$	−9.47628	+	2.78249i	−0.484216	+	0.142179i	0.0305084	+	0.999535i	$0.490287\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	8.61564	−	9.94298i	0.439094	−	0.506741i
$386$	−2.11465	+	1.35900i	−0.107633	+	0.0691714i
$387$	3.42883	+	3.95708i	0.174297	+	0.201150i
$388$	11.4958	+	3.37548i	0.583613	+	0.171364i
$389$	−9.11705	+	19.9636i	−0.462253	+	1.01219i	0.524715	+	0.851278i	$0.324172\pi$
$389$	−9.11705	+	19.9636i	−0.462253	+	1.01219i	−0.986968	+	0.160915i	$0.948556\pi$
$390$	−2.82092			−0.142843
$391$	−24.7060	+	30.2390i	−1.24944	+	1.52925i
$392$	3.23763			0.163525
$393$	3.84834	−	8.42668i	0.194123	−	0.425070i
$394$	2.70890	+	0.795405i	0.136472	+	0.0400719i
$395$	−8.84489	−	10.2075i	−0.445035	−	0.513597i
$396$	−3.45912	+	2.22304i	−0.173827	+	0.111712i
$397$	−15.7062	+	18.1259i	−0.788272	+	0.909715i	−0.997678	−	0.0681144i	$-0.978302\pi$
$397$	−15.7062	+	18.1259i	−0.788272	+	0.909715i	0.209405	+	0.977829i	$0.432847\pi$
$398$	1.94609	−	13.5353i	0.0975485	−	0.678465i
$399$	−7.24474	+	2.12725i	−0.362691	+	0.106496i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	3.45334	+	24.0185i	0.172452	+	1.19943i	0.873684	+	0.486494i	$0.161725\pi$
$401$	3.45334	+	24.0185i	0.172452	+	1.19943i	−0.701232	+	0.712933i	$0.747366\pi$
$402$	2.01007	+	4.40145i	0.100253	+	0.219524i
$403$	−2.32356	−	5.08788i	−0.115745	−	0.253445i
$404$	−2.39581	−	16.6632i	−0.119196	−	0.829025i
$405$	−0.841254	−	0.540641i	−0.0418022	−	0.0268647i
$406$	−12.2105	+	3.58533i	−0.605997	+	0.177937i
$407$	1.05086	−	7.30891i	0.0520894	−	0.362289i
$408$	−5.33199	+	6.15345i	−0.263973	+	0.304641i
$409$	−19.2878	+	12.3955i	−0.953722	+	0.612920i	−0.922254	−	0.386585i	$-0.873655\pi$
$409$	−19.2878	+	12.3955i	−0.953722	+	0.612920i	−0.0314684	+	0.999505i	$0.510018\pi$
$410$	2.09807	+	2.42131i	0.103617	+	0.119580i
$411$	10.7737	+	3.16343i	0.531425	+	0.156041i
$412$	2.32765	−	5.09685i	0.114675	−	0.251104i
$413$	−6.23830			−0.306967
$414$	−3.95774	+	2.70857i	−0.194512	+	0.133119i
$415$	4.07791			0.200177
$416$	−1.17185	+	2.56600i	−0.0574549	+	0.125809i
$417$	−2.72448	−	0.799979i	−0.133418	−	0.0391751i
$418$	6.35433	+	7.33328i	0.310800	+	0.358683i
$419$	29.8191	−	19.1636i	1.45676	−	0.936201i	0.457871	−	0.889018i	$-0.348612\pi$
$419$	29.8191	−	19.1636i	1.45676	−	0.936201i	0.998886	−	0.0471828i	$-0.0150243\pi$
$420$	2.09531	−	2.41812i	0.102241	−	0.117992i
$421$	−0.0585764	+	0.407408i	−0.00285484	+	0.0198558i	−0.991199	−	0.132380i	$-0.957738\pi$
$421$	−0.0585764	+	0.407408i	−0.00285484	+	0.0198558i	0.988344	+	0.152236i	$0.0486473\pi$
$422$	−0.126808	+	0.0372341i	−0.00617291	+	0.00181253i
$423$	−5.41365	−	3.47914i	−0.263221	−	0.169162i
$424$	0.655305	+	4.55775i	0.0318244	+	0.221344i
$425$	−3.38238	−	7.40639i	−0.164070	−	0.359263i
$426$	4.33220	+	9.48619i	0.209896	+	0.459607i
$427$	−5.20310	−	36.1883i	−0.251796	−	1.75128i
$428$	−4.32957	−	2.78244i	−0.209278	−	0.134495i
$429$	11.1294	−	3.26789i	0.537333	−	0.157775i
$430$	−0.745156	+	5.18268i	−0.0359346	+	0.249931i
$431$	−13.5727	+	15.6637i	−0.653772	+	0.754493i	−0.981747	−	0.190193i	$-0.939089\pi$
$431$	−13.5727	+	15.6637i	−0.653772	+	0.754493i	0.327975	+	0.944687i	$0.393634\pi$
$432$	−0.841254	+	0.540641i	−0.0404748	+	0.0260116i
$433$	−15.9087	−	18.3596i	−0.764521	−	0.882305i	0.231369	−	0.972866i	$-0.425679\pi$
$433$	−15.9087	−	18.3596i	−0.764521	−	0.882305i	−0.995891	+	0.0905612i	$0.971134\pi$
$434$	6.08725	+	1.78738i	0.292198	+	0.0857969i
$435$	−1.65224	+	3.61791i	−0.0792191	+	0.173466i
$436$	−8.62559			−0.413091
$437$	7.65587	+	8.33489i	0.366230	+	0.398712i
$438$	12.7520			0.609312
$439$	8.57980	−	18.7871i	0.409491	−	0.896661i	−0.586728	−	0.809784i	$-0.699584\pi$
$439$	8.57980	−	18.7871i	0.409491	−	0.896661i	0.996219	−	0.0868769i	$-0.0276887\pi$
$440$	−3.94531	−	1.15845i	−0.188085	−	0.0552268i
$441$	−2.12019	−	2.44683i	−0.100962	−	0.116516i
$442$	19.3223	−	12.4177i	0.919068	−	0.590649i
$443$	24.6602	−	28.4594i	1.17164	−	1.35215i	0.248062	−	0.968744i	$-0.420206\pi$
$443$	24.6602	−	28.4594i	1.17164	−	1.35215i	0.923581	−	0.383404i	$-0.125248\pi$
$444$	0.255568	−	1.77752i	0.0121287	−	0.0843573i
$445$	10.2506	−	3.00986i	0.485926	−	0.142681i
$446$	19.7219	+	12.6745i	0.933857	+	0.600154i
$447$	3.26711	+	22.7233i	0.154529	+	1.07477i
$448$	−1.32917	−	2.91048i	−0.0627976	−	0.137507i
$449$	1.95537	+	4.28165i	0.0922794	+	0.202064i	0.950144	−	0.311813i	$-0.100936\pi$
$449$	1.95537	+	4.28165i	0.0922794	+	0.202064i	−0.857864	+	0.513877i	$0.828209\pi$
$450$	−0.142315	−	0.989821i	−0.00670879	−	0.0466606i
$451$	−11.0825	−	7.12229i	−0.521855	−	0.335376i
$452$	10.5660	−	3.10245i	0.496981	−	0.145927i
$453$	−0.388348	+	2.70102i	−0.0182462	+	0.126905i
$454$	−5.88207	+	6.78827i	−0.276059	+	0.318589i
$455$	−7.59308	+	4.87977i	−0.355969	+	0.228767i
$456$	1.54536	+	1.78344i	0.0723682	+	0.0835174i
$457$	25.3843	+	7.45349i	1.18743	+	0.348660i	0.815033	−	0.579415i	$-0.196719\pi$
$457$	25.3843	+	7.45349i	1.18743	+	0.348660i	0.372394	+	0.928075i	$0.378537\pi$
$458$	8.01080	−	17.5412i	0.374320	−	0.819647i
$459$	8.14218			0.380044
$460$	−4.63876	−	1.21732i	−0.216283	−	0.0567580i
$461$	5.64741			0.263026			0.131513	−	0.991314i	$-0.458017\pi$
$461$	5.64741			0.263026			0.131513	+	0.991314i	$0.458017\pi$
$462$	−5.46539	+	11.9675i	−0.254273	+	0.556780i
$463$	36.6034	+	10.7477i	1.70111	+	0.499490i	0.980940	−	0.194313i	$-0.0622476\pi$
$463$	36.6034	+	10.7477i	1.70111	+	0.499490i	0.720166	+	0.693802i	$0.244066\pi$
$464$	2.60460	+	3.00587i	0.120916	+	0.139544i
$465$	1.66804	−	1.07199i	0.0773536	−	0.0497121i
$466$	−3.88211	+	4.48019i	−0.179835	+	0.207541i
$467$	−0.284853	+	1.98119i	−0.0131814	+	0.0916787i	−0.995350	−	0.0963228i	$-0.969292\pi$
$467$	−0.284853	+	1.98119i	−0.0131814	+	0.0916787i	0.982169	+	0.188002i	$0.0602010\pi$
$468$	2.70666	−	0.794746i	0.125115	−	0.0367371i
$469$	13.0244	+	8.37025i	0.601409	+	0.386502i
$470$	−0.915827	−	6.36972i	−0.0422440	−	0.293813i
$471$	−5.10566	−	11.1798i	−0.235256	−	0.515139i
$472$	0.809933	+	1.77351i	0.0372802	+	0.0816322i
$473$	−3.06398	−	21.3105i	−0.140882	−	0.979856i
$474$	11.3624	+	7.30217i	0.521893	+	0.335400i
$475$	−2.26424	+	0.664842i	−0.103891	+	0.0305051i
$476$	−3.70758	+	25.7868i	−0.169937	+	1.18194i
$477$	3.01538	−	3.47994i	0.138065	−	0.159335i
$478$	−5.90305	+	3.79366i	−0.269999	+	0.173518i
$479$	6.87359	+	7.93254i	0.314062	+	0.362447i	0.890731	−	0.454531i	$-0.150193\pi$
$479$	6.87359	+	7.93254i	0.314062	+	0.362447i	−0.576669	+	0.816978i	$0.695648\pi$
$480$	−0.959493	−	0.281733i	−0.0437947	−	0.0128593i
$481$	−2.10441	+	4.60802i	−0.0959529	+	0.210107i
$482$	5.86146			0.266982
$483$	−5.96762	+	14.1369i	−0.271536	+	0.643253i
$484$	5.90744			0.268520
$485$	4.97715	−	10.8984i	0.226001	−	0.494873i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	12.6544	+	14.6040i	0.573426	+	0.661768i	0.966178	−	0.257876i	$-0.0830225\pi$
$487$	12.6544	+	14.6040i	0.573426	+	0.661768i	−0.392752	+	0.919644i	$0.628477\pi$
$488$	−9.61256	+	6.17762i	−0.435140	+	0.279648i
$489$	1.14166	−	1.31755i	0.0516277	−	0.0595815i
$490$	0.460762	−	3.20467i	0.0208151	−	0.144772i
$491$	−1.77644	+	0.521610i	−0.0801696	+	0.0235399i	−0.321571	−	0.946885i	$-0.604211\pi$
$491$	−1.77644	+	0.521610i	−0.0801696	+	0.0235399i	0.241402	+	0.970425i	$0.422393\pi$
$492$	−2.69525	−	1.73213i	−0.121511	−	0.0780905i
$493$	−4.60875	−	32.0545i	−0.207568	−	1.44366i
$494$	−2.76538	−	6.05534i	−0.124420	−	0.272443i
$495$	1.70813	+	3.74028i	0.0767748	+	0.168113i
$496$	−0.282183	−	1.96262i	−0.0126704	−	0.0881244i
$497$	28.0707	+	18.0399i	1.25914	+	0.809201i
$498$	−3.91273	+	1.14888i	−0.175334	+	0.0514826i
$499$	−0.252343	+	1.75508i	−0.0112964	+	0.0785683i	−0.994690	−	0.102919i	$-0.967182\pi$
$499$	−0.252343	+	1.75508i	−0.0112964	+	0.0785683i	0.983393	+	0.181487i	$0.0580910\pi$
$500$	0.654861	−	0.755750i	0.0292863	−	0.0337981i
$501$	−7.52345	+	4.83503i	−0.336123	+	0.216013i
$502$	−0.673149	−	0.776855i	−0.0300441	−	0.0346728i
$503$	5.82045	+	1.70904i	0.259521	+	0.0762023i	0.408905	−	0.912577i	$-0.365911\pi$
$503$	5.82045	+	1.70904i	0.259521	+	0.0762023i	−0.149384	+	0.988779i	$0.547729\pi$
$504$	−1.32917	+	2.91048i	−0.0592061	+	0.129643i
$505$	−16.8345			−0.749127
$506$	19.7115	−	0.571044i	0.876285	−	0.0253860i
$507$	5.04240			0.223941
$508$	0.396371	−	0.867931i	0.0175861	−	0.0385082i
$509$	−2.73230	−	0.802277i	−0.121107	−	0.0355603i	0.220617	−	0.975360i	$-0.429193\pi$
$509$	−2.73230	−	0.802277i	−0.121107	−	0.0355603i	−0.341725	+	0.939800i	$0.611011\pi$
$510$	5.33199	+	6.15345i	0.236105	+	0.272479i
$511$	34.3245	−	22.0590i	1.51842	−	0.975832i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	0.335839	−	2.33581i	0.0148277	−	0.103129i
$514$	−21.5519	+	6.32820i	−0.950612	+	0.279125i
$515$	−4.71371	−	3.02932i	−0.207711	−	0.133488i
$516$	−0.745156	−	5.18268i	−0.0328037	−	0.228155i
$517$	10.9922	+	24.0696i	0.483436	+	1.05858i
$518$	−2.38693	−	5.22664i	−0.104875	−	0.229645i
$519$	−3.66733	−	25.5069i	−0.160978	−	1.11963i
$520$	2.37311	+	1.52511i	0.104068	+	0.0668803i
$521$	−40.0515	+	11.7602i	−1.75469	+	0.515223i	−0.991403	−	0.130840i	$-0.958232\pi$
$521$	−40.0515	+	11.7602i	−1.75469	+	0.515223i	−0.763284	+	0.646063i	$0.776414\pi$
$522$	0.566034	−	3.93685i	0.0247746	−	0.172311i
$523$	20.6978	−	23.8865i	0.905051	−	1.04449i	−0.0937527	−	0.995596i	$-0.529886\pi$
$523$	20.6978	−	23.8865i	0.905051	−	1.04449i	0.998804	−	0.0488896i	$-0.0155682\pi$
$524$	−7.79324	+	5.00841i	−0.340449	+	0.218793i
$525$	−2.09531	−	2.41812i	−0.0914469	−	0.105535i
$526$	−27.5071	−	8.07683i	−1.19937	−	0.352166i
$527$	−6.70661	+	14.6854i	−0.292144	+	0.639707i
$528$	4.11187			0.178946
$529$	22.9614	−	1.33150i	0.998323	−	0.0578914i
$530$	4.60462			0.200012
$531$	0.809933	−	1.77351i	0.0351481	−	0.0769636i
$532$	7.24474	+	2.12725i	0.314099	+	0.0922279i
$533$	5.91851	+	6.83032i	0.256359	+	0.295854i
$534$	−8.98743	+	5.77587i	−0.388924	+	0.249946i
$535$	−3.37028	+	3.88952i	−0.145710	+	0.168158i
$536$	0.688621	−	4.78946i	0.0297439	−	0.206873i
$537$	24.9361	−	7.32189i	1.07607	−	0.315963i
$538$	26.3538	+	16.9366i	1.13619	+	0.730187i
$539$	1.89459	+	13.1772i	0.0816059	+	0.567581i
$540$	0.415415	+	0.909632i	0.0178766	+	0.0391443i
$541$	−2.59265	−	5.67711i	−0.111467	−	0.244078i	0.845675	−	0.533698i	$-0.179198\pi$
$541$	−2.59265	−	5.67711i	−0.111467	−	0.244078i	−0.957142	+	0.289620i	$0.906471\pi$
$542$	0.345593	+	2.40365i	0.0148445	+	0.103246i
$543$	13.9124	+	8.94093i	0.597037	+	0.383692i
$544$	7.81236	−	2.29392i	0.334952	−	0.0983509i
$545$	−1.22755	+	8.53779i	−0.0525824	+	0.365719i
$546$	5.91071	−	6.82132i	0.252955	−	0.291926i
$547$	10.2045	−	6.55804i	0.436313	−	0.280401i	−0.303989	−	0.952675i	$-0.598319\pi$
$547$	10.2045	−	6.55804i	0.436313	−	0.280401i	0.740302	+	0.672274i	$0.234682\pi$
$548$	−7.35310	−	8.48592i	−0.314109	−	0.362501i
$549$	10.9636	+	3.21921i	0.467916	+	0.137392i
$550$	−1.70813	+	3.74028i	−0.0728349	+	0.159486i
$551$	−9.38585			−0.399851
$552$	4.79382	−	0.138877i	0.204039	−	0.00591100i
$553$	43.2158			1.83772
$554$	−5.37638	+	11.7726i	−0.228421	+	0.500172i
$555$	−1.72305	−	0.505934i	−0.0731396	−	0.0214757i
$556$	1.85947	+	2.14595i	0.0788593	+	0.0910085i
$557$	−28.0026	+	17.9961i	−1.18651	+	0.762521i	−0.976571	−	0.215194i	$-0.930962\pi$
$557$	−28.0026	+	17.9961i	−1.18651	+	0.762521i	−0.209935	+	0.977715i	$0.567325\pi$
$558$	−1.29846	+	1.49850i	−0.0549682	+	0.0634367i
$559$	−2.10203	+	14.6199i	−0.0889063	+	0.618357i
$560$	−3.07002	+	0.901440i	−0.129732	+	0.0380928i
$561$	−28.1648	−	18.1004i	−1.18912	−	0.764200i
$562$	−4.40068	−	30.6074i	−0.185632	−	1.29110i
$563$	9.54624	+	20.9034i	0.402326	+	0.880971i	0.997029	+	0.0770257i	$0.0245424\pi$
$563$	9.54624	+	20.9034i	0.402326	+	0.880971i	−0.594703	+	0.803945i	$0.702730\pi$
$564$	2.67329	+	5.85368i	0.112566	+	0.246484i
$565$	−1.56717	−	10.8999i	−0.0659315	−	0.458564i
$566$	10.5430	+	6.77559i	0.443156	+	0.284799i
$567$	3.07002	−	0.901440i	0.128929	−	0.0378569i
$568$	1.48415	−	10.3225i	0.0622733	−	0.433121i
$569$	28.7516	−	33.1811i	1.20533	−	1.39102i	0.306994	−	0.951712i	$-0.400677\pi$
$569$	28.7516	−	33.1811i	1.20533	−	1.39102i	0.898335	−	0.439312i	$-0.144778\pi$
$570$	1.98522	−	1.27582i	0.0831517	−	0.0534383i
$571$	−26.7252	−	30.8426i	−1.11842	−	1.29072i	−0.952486	−	0.304584i	$-0.901483\pi$
$571$	−26.7252	−	30.8426i	−1.11842	−	1.29072i	−0.165931	−	0.986137i	$-0.553063\pi$
$572$	−11.1294	−	3.26789i	−0.465344	−	0.136637i
$573$	−5.85845	+	12.8282i	−0.244740	+	0.535906i
$574$	−10.2511			−0.427874
$575$	−1.86510	+	4.41830i	−0.0777800	+	0.184256i
$576$	1.00000			0.0416667
$577$	−3.46613	+	7.58976i	−0.144297	+	0.315966i	−0.967956	−	0.251119i	$-0.919202\pi$
$577$	−3.46613	+	7.58976i	−0.144297	+	0.315966i	0.823659	+	0.567085i	$0.191929\pi$
$578$	−47.2983	−	13.8880i	−1.96735	−	0.577666i
$579$	−1.64612	−	1.89972i	−0.0684102	−	0.0789496i
$580$	3.34595	−	2.15031i	0.138933	−	0.0892867i
$581$	−8.54450	+	9.86088i	−0.354486	+	0.409098i
$582$	−1.70510	+	11.8592i	−0.0706785	+	0.491580i
$583$	−18.1666	+	5.33420i	−0.752385	+	0.220920i
$584$	−10.7276	−	6.89423i	−0.443913	−	0.285285i
$585$	−0.401459	−	2.79221i	−0.0165983	−	0.115444i
$586$	−13.2145	−	28.9358i	−0.545887	−	1.19533i
$587$	17.1977	+	37.6577i	0.709825	+	1.55430i	0.827637	+	0.561264i	$0.189685\pi$
$587$	17.1977	+	37.6577i	0.709825	+	1.55430i	−0.117812	+	0.993036i	$0.537588\pi$
$588$	0.460762	+	3.20467i	0.0190015	+	0.132158i
$589$	3.93630	+	2.52971i	0.162192	+	0.104235i
$590$	1.87072	−	0.549293i	0.0770163	−	0.0226140i
$591$	−0.401792	+	2.79453i	−0.0165275	+	0.114951i
$592$	−1.17600	+	1.35717i	−0.0483332	+	0.0557794i
$593$	−37.1918	+	23.9017i	−1.52728	+	0.981526i	−0.536830	+	0.843690i	$0.680378\pi$
$593$	−37.1918	+	23.9017i	−1.52728	+	0.981526i	−0.990455	+	0.137836i	$0.955985\pi$
$594$	−2.69270	−	3.10754i	−0.110483	−	0.127504i
$595$	24.9967	+	7.33968i	1.02476	+	0.300898i
$596$	9.53666	−	20.8824i	0.390637	−	0.855375i
$597$	13.6745			0.559661
$598$	−13.0856	−	3.43398i	−0.535110	−	0.140426i
$599$	22.3444			0.912967			0.456483	−	0.889732i	$-0.349109\pi$
$599$	22.3444			0.912967			0.456483	+	0.889732i	$0.349109\pi$
$600$	−0.415415	+	0.909632i	−0.0169592	+	0.0371356i
$601$	15.3460	+	4.50600i	0.625977	+	0.183803i	0.579310	−	0.815107i	$-0.303322\pi$
$601$	15.3460	+	4.50600i	0.625977	+	0.183803i	0.0466667	+	0.998911i	$0.485140\pi$
$602$	−10.9710	−	12.6612i	−0.447144	−	0.516032i
$603$	−4.07059	+	2.61601i	−0.165767	+	0.106532i
$604$	1.78698	−	2.06229i	0.0727112	−	0.0839132i
$605$	0.840717	−	5.84731i	0.0341800	−	0.237727i
$606$	16.1526	−	4.74284i	0.656156	−	0.192665i
$607$	29.8447	+	19.1800i	1.21136	+	0.778494i	0.980886	−	0.194585i	$-0.0623359\pi$
$607$	29.8447	+	19.1800i	1.21136	+	0.778494i	0.230474	+	0.973078i	$0.425972\pi$
$608$	−0.335839	−	2.33581i	−0.0136201	−	0.0947298i
$609$	−5.28657	−	11.5760i	−0.214223	−	0.469082i
$610$	4.74673	+	10.3939i	0.192189	+	0.420836i
$611$	−2.58348	−	17.9685i	−0.104516	−	0.726927i
$612$	−6.84964	−	4.40199i	−0.276880	−	0.177940i
$613$	−30.2429	+	8.88012i	−1.22150	+	0.358665i	−0.828036	−	0.560675i	$-0.810542\pi$
$613$	−30.2429	+	8.88012i	−1.22150	+	0.358665i	−0.393464	+	0.919340i	$0.628724\pi$
$614$	−0.0164874	+	0.114673i	−0.000665379	+	0.00462781i
$615$	−2.09807	+	2.42131i	−0.0846025	+	0.0976365i
$616$	11.0679	−	7.11291i	0.445939	−	0.286587i
$617$	17.5572	+	20.2621i	0.706827	+	0.815722i	0.989658	−	0.143448i	$-0.0458189\pi$
$617$	17.5572	+	20.2621i	0.706827	+	0.815722i	−0.282831	+	0.959170i	$0.591273\pi$
$618$	5.37623	+	1.57860i	0.216264	+	0.0635007i
$619$	−18.3538	+	40.1892i	−0.737702	+	1.61534i	0.0495963	+	0.998769i	$0.484207\pi$
$619$	−18.3538	+	40.1892i	−0.737702	+	1.61534i	−0.787298	+	0.616572i	$0.788521\pi$
$620$	−1.98280			−0.0796314
$621$	−3.24424	−	3.53198i	−0.130187	−	0.141734i
$622$	−7.53914			−0.302292
$623$	−14.2001	+	31.0938i	−0.568914	+	1.24575i
$624$	−2.70666	−	0.794746i	−0.108353	−	0.0318153i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−17.1927	+	11.0491i	−0.687158	+	0.441610i
$627$	−6.35433	+	7.33328i	−0.253767	+	0.292863i
$628$	−1.74912	+	12.1654i	−0.0697975	+	0.485452i
$629$	14.0294	−	4.11941i	0.559389	−	0.164252i
$630$	2.69170	+	1.72985i	0.107240	+	0.0689189i
$631$	−2.28048	−	15.8611i	−0.0907846	−	0.631421i	−0.983515	−	0.180829i	$-0.942122\pi$
$631$	−2.28048	−	15.8611i	−0.0907846	−	0.631421i	0.892730	−	0.450592i	$-0.148787\pi$
$632$	−5.61081	−	12.2860i	−0.223186	−	0.488709i
$633$	−0.0549018	−	0.120218i	−0.00218215	−	0.00477824i
$634$	1.27679	+	8.88027i	0.0507078	+	0.352680i
$635$	−0.802687	−	0.515856i	−0.0318537	−	0.0204711i
$636$	−4.41810	+	1.29727i	−0.175189	+	0.0514401i
$637$	1.29977	−	9.04013i	0.0514989	−	0.358183i
$638$	−10.7098	+	12.3597i	−0.424004	+	0.489326i
$639$	−8.77310	+	5.63813i	−0.347058	+	0.223041i
$640$	0.654861	+	0.755750i	0.0258856	+	0.0298736i
$641$	29.6467	+	8.70505i	1.17097	+	0.343829i	0.808688	−	0.588238i	$-0.200178\pi$
$641$	29.6467	+	8.70505i	1.17097	+	0.343829i	0.362286	+	0.932067i	$0.381996\pi$
$642$	2.13796	−	4.68148i	0.0843786	−	0.184763i
$643$	14.9464			0.589430			0.294715	−	0.955585i	$-0.404775\pi$
$643$	14.9464			0.589430			0.294715	+	0.955585i	$0.404775\pi$
$644$	12.6633	−	8.66641i	0.499003	−	0.341504i
$645$	−5.23597			−0.206166
$646$	−7.98186	+	17.4778i	−0.314042	+	0.687657i
$647$	−9.72221	−	2.85470i	−0.382220	−	0.112230i	0.0849778	−	0.996383i	$-0.472918\pi$
$647$	−9.72221	−	2.85470i	−0.382220	−	0.112230i	−0.467197	+	0.884153i	$0.654736\pi$
$648$	−0.654861	−	0.755750i	−0.0257254	−	0.0296886i
$649$	−6.74423	+	4.33426i	−0.264734	+	0.170134i
$650$	1.84731	−	2.13191i	0.0724575	−	0.0836204i
$651$	−0.902879	+	6.27966i	−0.0353866	+	0.246119i
$652$	−1.67275	+	0.491163i	−0.0655098	+	0.0192354i
$653$	40.8580	+	26.2578i	1.59890	+	1.02755i	0.967760	+	0.251875i	$0.0810471\pi$
$653$	40.8580	+	26.2578i	1.59890	+	1.02755i	0.631135	+	0.775673i	$0.282589\pi$
$654$	−1.22755	−	8.53779i	−0.0480010	−	0.333854i
$655$	3.84834	+	8.42668i	0.150367	+	0.329258i
$656$	1.33093	+	2.91432i	0.0519640	+	0.113785i
$657$	1.81479	+	12.6222i	0.0708018	+	0.492438i
$658$	17.3217	+	11.1320i	0.675269	+	0.433969i
$659$	5.15105	−	1.51248i	0.200656	−	0.0589180i	−0.179860	−	0.983692i	$-0.557564\pi$
$659$	5.15105	−	1.51248i	0.200656	−	0.0589180i	0.380516	+	0.924774i	$0.375746\pi$
$660$	0.585180	−	4.07001i	0.0227781	−	0.158425i
$661$	9.08154	−	10.4807i	0.353231	−	0.407650i	−0.551130	−	0.834420i	$-0.685803\pi$
$661$	9.08154	−	10.4807i	0.353231	−	0.407650i	0.904360	+	0.426769i	$0.140348\pi$
$662$	−15.3408	+	9.85892i	−0.596236	+	0.383178i
$663$	15.0411	+	17.3584i	0.584150	+	0.674144i
$664$	3.91273	+	1.14888i	0.151843	+	0.0445852i
$665$	3.13663	−	6.86826i	0.121633	−	0.266340i
$666$	1.79580			0.0695857
$667$	−12.0685	+	14.7713i	−0.467296	+	0.571948i
$668$	8.94314			0.346021
$669$	−9.73875	+	21.3249i	−0.376522	+	0.824468i
$670$	−4.64271	−	1.36322i	−0.179364	−	0.0526659i
$671$	−30.7681	−	35.5082i	−1.18779	−	1.37078i
$672$	2.69170	−	1.72985i	0.103835	−	0.0667304i
$673$	3.90473	−	4.50630i	0.150516	−	0.173705i	−0.675484	−	0.737375i	$-0.736065\pi$
$673$	3.90473	−	4.50630i	0.150516	−	0.173705i	0.826001	+	0.563669i	$0.190611\pi$
$674$	−2.65964	+	18.4982i	−0.102446	+	0.712525i
$675$	0.959493	−	0.281733i	0.0369309	−	0.0108439i
$676$	−4.24193	−	2.72612i	−0.163151	−	0.104851i
$677$	5.22337	+	36.3293i	0.200750	+	1.39625i	0.802065	+	0.597237i	$0.203735\pi$
$677$	5.22337	+	36.3293i	0.200750	+	1.39625i	−0.601314	+	0.799013i	$0.705356\pi$
$678$	4.57456	+	10.0169i	0.175685	+	0.384696i
$679$	15.9250	+	34.8710i	0.611147	+	1.33823i
$680$	−1.15875	−	8.05930i	−0.0444361	−	0.309060i
$681$	−7.55629	−	4.85613i	−0.289557	−	0.186087i
$682$	7.82277	−	2.29697i	0.299549	−	0.0879557i
$683$	−5.81210	+	40.4240i	−0.222394	+	1.54678i	0.506551	+	0.862210i	$0.330920\pi$
$683$	−5.81210	+	40.4240i	−0.222394	+	1.54678i	−0.728944	+	0.684573i	$0.759989\pi$
$684$	−1.54536	+	1.78344i	−0.0590884	+	0.0681917i
$685$	−9.44600	+	6.07058i	−0.360913	+	0.231945i
$686$	−7.88335	−	9.09787i	−0.300988	−	0.347358i
$687$	18.5027	+	5.43289i	0.705923	+	0.207278i
$688$	−2.17510	+	4.76281i	−0.0829249	+	0.181580i
$689$	12.9893			0.494852
$690$	0.544768	−	4.76479i	0.0207390	−	0.181392i
$691$	26.8578			1.02172			0.510860	−	0.859664i	$-0.329327\pi$
$691$	26.8578			1.02172			0.510860	+	0.859664i	$0.329327\pi$
$692$	−10.7049	+	23.4405i	−0.406939	+	0.891072i
$693$	−12.6235	−	3.70660i	−0.479528	−	0.140802i
$694$	14.1444	+	16.3235i	0.536915	+	0.619633i
$695$	2.38874	−	1.53515i	0.0906099	−	0.0582315i
$696$	−2.60460	+	3.00587i	−0.0987271	+	0.113937i
$697$	3.71247	−	25.8208i	0.140620	−	0.978032i
$698$	−0.163201	+	0.0479200i	−0.00617723	+	0.00181380i
$699$	−4.98707	−	3.20499i	−0.188628	−	0.121224i
$700$	0.455355	+	3.16706i	0.0172108	+	0.119704i
$701$	−5.35247	−	11.7203i	−0.202160	−	0.442669i	0.781213	−	0.624264i	$-0.214601\pi$
$701$	−5.35247	−	11.7203i	−0.202160	−	0.442669i	−0.983373	+	0.181595i	$0.941874\pi$
$702$	1.17185	+	2.56600i	0.0442288	+	0.0968475i
$703$	−0.603099	−	4.19465i	−0.0227463	−	0.158204i
$704$	−3.45912	−	2.22304i	−0.130371	−	0.0837841i
$705$	6.17455	−	1.81301i	0.232547	−	0.0682819i
$706$	−1.32039	+	9.18348i	−0.0496934	+	0.345625i
$707$	35.2736	−	40.7079i	1.32660	−	1.53098i
$708$	−1.64019	+	1.05408i	−0.0616420	+	0.0396149i
$709$	−29.1516	−	33.6428i	−1.09481	−	1.26348i	−0.962209	−	0.272312i	$-0.912212\pi$
$709$	−29.1516	−	33.6428i	−1.09481	−	1.26348i	−0.132604	−	0.991169i	$-0.542334\pi$
$710$	−10.0062	−	2.93808i	−0.375525	−	0.110264i
$711$	−5.61081	+	12.2860i	−0.210422	+	0.460759i
$712$	10.6834			0.400377
$713$	9.04260	−	2.94214i	0.338648	−	0.110184i
$714$	−26.0520			−0.974970
$715$	−4.81851	+	10.5511i	−0.180202	+	0.394587i
$716$	−24.9361	−	7.32189i	−0.931905	−	0.273632i
$717$	−4.59513	−	5.30307i	−0.171608	−	0.198047i
$718$	−12.8365	+	8.24955i	−0.479056	+	0.307870i
$719$	−6.32312	+	7.29726i	−0.235812	+	0.272142i	−0.861305	−	0.508088i	$-0.830353\pi$
$719$	−6.32312	+	7.29726i	−0.235812	+	0.272142i	0.625493	+	0.780230i	$0.284898\pi$
$720$	0.142315	−	0.989821i	0.00530376	−	0.0368885i
$721$	17.2019	−	5.05095i	0.640634	−	0.188107i
$722$	−11.2990	−	7.26145i	−0.420506	−	0.270243i
$723$	0.834173	+	5.80180i	0.0310232	+	0.215771i
$724$	−6.86999	−	15.0432i	−0.255321	−	0.559075i
$725$	−1.65224	−	3.61791i	−0.0613628	−	0.134366i
$726$	0.840717	+	5.84731i	0.0312019	+	0.217014i
$727$	−37.6870	−	24.2200i	−1.39773	−	0.898269i	−0.397918	−	0.917421i	$-0.630267\pi$
$727$	−37.6870	−	24.2200i	−1.39773	−	0.898269i	−0.999817	+	0.0191519i	$0.993903\pi$
$728$	−8.66029	+	2.54289i	−0.320972	+	0.0942458i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−8.35076	+	9.63729i	−0.309076	+	0.356692i
$731$	35.8645	−	23.0487i	1.32650	−	0.852487i
$732$	−7.48275	−	8.63555i	−0.276570	−	0.319179i
$733$	−15.1713	−	4.45470i	−0.560365	−	0.164538i	−0.0107291	−	0.999942i	$-0.503415\pi$
$733$	−15.1713	−	4.45470i	−0.560365	−	0.164538i	−0.549636	+	0.835404i	$0.685233\pi$
$734$	−5.43330	+	11.8973i	−0.200547	+	0.439136i
$735$	3.23763			0.119422
$736$	−4.10790	−	2.47490i	−0.151419	−	0.0912262i
$737$	19.8961			0.732884
$738$	1.33093	−	2.91432i	0.0489921	−	0.107278i
$739$	31.6880	+	9.30443i	1.16566	+	0.342269i	0.806630	−	0.591057i	$-0.201289\pi$
$739$	31.6880	+	9.30443i	1.16566	+	0.342269i	0.359031	+	0.933326i	$0.383107\pi$
$740$	1.17600	+	1.35717i	0.0432305	+	0.0498906i
$741$	5.60015	−	3.59900i	0.205727	−	0.132212i
$742$	−9.64811	+	11.1345i	−0.354193	+	0.408761i
$743$	3.82112	−	26.5765i	0.140183	−	0.974997i	−0.791356	−	0.611356i	$-0.790624\pi$
$743$	3.82112	−	26.5765i	0.140183	−	0.974997i	0.931539	−	0.363641i	$-0.118467\pi$
$744$	1.90249	−	0.558621i	0.0697486	−	0.0204800i
$745$	−19.3126	−	12.4115i	−0.707559	−	0.454721i
$746$	−0.359293	−	2.49894i	−0.0131546	−	0.0914926i
$747$	−1.69403	−	3.70940i	−0.0619812	−	0.135720i
$748$	13.9079	+	30.4541i	0.508523	+	1.11351i
$749$	−2.34351	−	16.2995i	−0.0856301	−	0.595571i
$750$	0.841254	+	0.540641i	0.0307182	+	0.0197414i
$751$	−40.1925	+	11.8016i	−1.46664	+	0.430645i	−0.915007	−	0.403439i	$-0.867815\pi$
$751$	−40.1925	+	11.8016i	−1.46664	+	0.430645i	−0.551637	+	0.834084i	$0.685997\pi$
$752$	0.915827	−	6.36972i	0.0333968	−	0.232280i
$753$	0.673149	−	0.776855i	0.0245309	−	0.0283102i
$754$	9.43866	−	6.06586i	0.343736	−	0.220905i
$755$	−1.78698	−	2.06229i	−0.0650349	−	0.0750543i
$756$	−3.07002	−	0.901440i	−0.111656	−	0.0327850i
$757$	−11.8120	+	25.8646i	−0.429314	+	0.940065i	0.564124	+	0.825690i	$0.309214\pi$
$757$	−11.8120	+	25.8646i	−0.429314	+	0.940065i	−0.993438	+	0.114375i	$0.963513\pi$
$758$	−28.4734			−1.03420
$759$	3.37048	+	19.4296i	0.122341	+	0.705251i
$760$	−2.35983			−0.0856002
$761$	−15.6027	+	34.1652i	−0.565598	+	1.23849i	0.383511	+	0.923536i	$0.374715\pi$
$761$	−15.6027	+	34.1652i	−0.565598	+	1.23849i	−0.949108	+	0.314949i	$0.898012\pi$
$762$	0.915506	+	0.268817i	0.0331653	+	0.00973821i
$763$	−18.0733	−	20.8577i	−0.654297	−	0.755099i
$764$	11.8639	−	7.62446i	0.429220	−	0.275843i
$765$	−5.33199	+	6.15345i	−0.192779	+	0.222478i
$766$	−1.40555	+	9.77582i	−0.0507846	+	0.353215i
$767$	5.27715	−	1.54951i	0.190547	−	0.0559496i
$768$	−0.841254	−	0.540641i	−0.0303561	−	0.0195087i
$769$	−5.02043	−	34.9178i	−0.181041	−	1.25917i	−0.854307	−	0.519769i	$-0.826018\pi$
$769$	−5.02043	−	34.9178i	−0.181041	−	1.25917i	0.673266	−	0.739401i	$-0.264891\pi$
$770$	−5.46539	−	11.9675i	−0.196959	−	0.431280i
$771$	−9.33094	−	20.4319i	−0.336046	−	0.735837i
$772$	0.357735	+	2.48810i	0.0128752	+	0.0895488i
$773$	−42.7789	−	27.4924i	−1.53865	−	0.988831i	−0.988062	−	0.154055i	$-0.950767\pi$
$773$	−42.7789	−	27.4924i	−1.53865	−	0.988831i	−0.550590	−	0.834776i	$-0.685597\pi$
$774$	5.02388	−	1.47514i	0.180580	−	0.0530229i
$775$	−0.282183	+	1.96262i	−0.0101363	+	0.0704995i
$776$	7.84599	−	9.05476i	0.281655	−	0.325047i
$777$	4.83374	−	3.10646i	0.173410	−	0.111444i
$778$	14.3721	+	16.5863i	0.515266	+	0.594648i
$779$	−7.25430	−	2.13005i	−0.259912	−	0.0763171i
$780$	−1.17185	+	2.56600i	−0.0419591	+	0.0918776i
$781$	42.8810			1.53440
$782$	17.2431	+	35.0352i	0.616613	+	1.25285i
$783$	3.97733			0.142138
$784$	1.34496	−	2.94505i	0.0480342	−	0.105180i
$785$	11.7926	+	3.46263i	0.420897	+	0.123587i
$786$	−6.06652	−	7.00114i	−0.216386	−	0.249722i
$787$	20.9836	−	13.4853i	0.747984	−	0.480700i	−0.110285	−	0.993900i	$-0.535176\pi$
$787$	20.9836	−	13.4853i	0.747984	−	0.480700i	0.858269	+	0.513200i	$0.171540\pi$
$788$	1.84884	−	2.13368i	0.0658623	−	0.0760092i
$789$	4.07994	−	28.3766i	0.145250	−	1.01023i
$790$	−12.9594	+	3.80523i	−0.461075	+	0.135384i
$791$	29.6411	+	19.0491i	1.05391	+	0.677310i
$792$	0.585180	+	4.07001i	0.0207934	+	0.144622i
$793$	13.3902	+	29.3203i	0.475498	+	1.04120i
$794$	9.96333	+	21.8167i	0.353585	+	0.774244i
$795$	0.655305	+	4.55775i	0.0232413	+	0.161647i
$796$	−11.5037	−	7.39300i	−0.407739	−	0.262038i
$797$	15.5637	−	4.56992i	0.551295	−	0.161875i	0.00579136	−	0.999983i	$-0.498157\pi$
$797$	15.5637	−	4.56992i	0.551295	−	0.161875i	0.545504	+	0.838108i	$0.316338\pi$
$798$	−1.07456	+	7.47374i	−0.0380391	+	0.264568i
$799$	−34.3125	+	39.5988i	−1.21389	+	1.40090i
$800$	0.841254	−	0.540641i	0.0297428	−	0.0191145i
$801$	−6.99613	−	8.07396i	−0.247196	−	0.285279i
$802$	23.2826	+	6.83638i	0.822136	+	0.241401i
$803$	21.7820	−	47.6960i	0.768671	−	1.68315i
$804$	4.83871			0.170648
$805$	−6.77602	−	13.7678i	−0.238823	−	0.485249i
$806$	−5.59334			−0.197017
$807$	−13.0136	+	28.4959i	−0.458102	+	1.00310i
$808$	−16.1526	−	4.74284i	−0.568248	−	0.166853i
$809$	19.3820	+	22.3680i	0.681434	+	0.786416i	0.986120	−	0.166037i	$-0.0530970\pi$
$809$	19.3820	+	22.3680i	0.681434	+	0.786416i	−0.304686	+	0.952453i	$0.598552\pi$
$810$	−0.841254	+	0.540641i	−0.0295586	+	0.0189962i
$811$	−11.9321	+	13.7704i	−0.418992	+	0.483543i	−0.925530	−	0.378675i	$-0.876380\pi$
$811$	−11.9321	+	13.7704i	−0.418992	+	0.483543i	0.506538	+	0.862218i	$0.330925\pi$
$812$	−1.81110	+	12.5965i	−0.0635571	+	0.442049i
$813$	−2.33000	+	0.684150i	−0.0817167	+	0.0239942i
$814$	−6.21188	−	3.99213i	−0.217726	−	0.139924i
$815$	0.248107	+	1.72562i	0.00869080	+	0.0604458i
$816$	3.38238	+	7.40639i	0.118407	+	0.259275i
$817$	−5.13288	−	11.2394i	−0.179577	−	0.393218i
$818$	3.26292	+	22.6941i	0.114085	+	0.793482i
$819$	7.59308	+	4.87977i	0.265324	+	0.170513i
$820$	3.07407	−	0.902629i	0.107351	−	0.0315212i
$821$	1.96639	−	13.6765i	0.0686274	−	0.477314i	−0.926306	−	0.376773i	$-0.877034\pi$
$821$	1.96639	−	13.6765i	0.0686274	−	0.477314i	0.994933	−	0.100541i	$-0.0320573\pi$
$822$	7.35310	−	8.48592i	0.256469	−	0.295981i
$823$	−29.0881	+	18.6938i	−1.01395	+	0.651624i	−0.938412	−	0.345519i	$-0.887703\pi$
$823$	−29.0881	+	18.6938i	−1.01395	+	0.651624i	−0.0755352	+	0.997143i	$0.524067\pi$
$824$	−3.66931	−	4.23461i	−0.127827	−	0.147520i
$825$	−3.94531	−	1.15845i	−0.137358	−	0.0403319i
$826$	−2.59148	+	5.67456i	−0.0901693	+	0.197443i
$827$	42.8019			1.48837			0.744183	−	0.667975i	$-0.232839\pi$
$827$	42.8019			1.48837			0.744183	+	0.667975i	$0.232839\pi$
$828$	0.819695	+	4.72526i	0.0284864	+	0.164214i
$829$	−32.2803			−1.12114			−0.560570	−	0.828107i	$-0.689418\pi$
$829$	−32.2803			−1.12114			−0.560570	+	0.828107i	$0.689418\pi$
$830$	1.69403	−	3.70940i	0.0588005	−	0.128755i
$831$	−12.4180	−	3.64624i	−0.430774	−	0.126487i
$832$	1.84731	+	2.13191i	0.0640440	+	0.0739107i
$833$	−22.1766	+	14.2520i	−0.768372	+	0.493803i
$834$	−1.85947	+	2.14595i	−0.0643883	+	0.0743081i
$835$	1.27274	−	8.85211i	0.0440451	−	0.306340i
$836$	9.31027	−	2.73374i	0.322002	−	0.0945484i
$837$	−1.66804	−	1.07199i	−0.0576559	−	0.0370532i
$838$	−5.04449	−	35.0852i	−0.174259	−	1.21200i
$839$	16.2568	+	35.5974i	0.561246	+	1.22896i	0.951329	+	0.308178i	$0.0997191\pi$
$839$	16.2568	+	35.5974i	0.561246	+	1.22896i	−0.390083	+	0.920780i	$0.627554\pi$
$840$	−1.32917	−	2.91048i	−0.0458609	−	0.100421i
$841$	1.87583	+	13.0467i	0.0646836	+	0.449884i
$842$	0.346258	+	0.222526i	0.0119328	+	0.00766876i
$843$	29.6696	−	8.71178i	1.02188	−	0.300050i
$844$	−0.0188085	+	0.130816i	−0.000647415	+	0.00450287i
$845$	−3.30207	+	3.81079i	−0.113595	+	0.131095i
$846$	−5.41365	+	3.47914i	−0.186125	+	0.119615i
$847$	12.3779	+	14.2849i	0.425311	+	0.490835i
$848$	4.41810	+	1.29727i	0.151718	+	0.0445484i
$849$	−5.20619	+	11.4000i	−0.178676	+	0.391246i
$850$	−8.14218			−0.279274
$851$	−7.37695	−	4.44442i	−0.252879	−	0.152353i
$852$	10.4286			0.357278
$853$	−19.1923	+	42.0252i	−0.657131	+	1.43892i	0.228040	+	0.973652i	$0.426768\pi$
$853$	−19.1923	+	42.0252i	−0.657131	+	1.43892i	−0.885172	+	0.465265i	$0.845959\pi$
$854$	−35.0795	−	10.3003i	−1.20040	−	0.352468i
$855$	1.54536	+	1.78344i	0.0528503	+	0.0609925i
$856$	−4.32957	+	2.78244i	−0.147982	+	0.0951020i
$857$	23.0057	−	26.5500i	0.785860	−	0.906931i	−0.211658	−	0.977344i	$-0.567886\pi$
$857$	23.0057	−	26.5500i	0.785860	−	0.906931i	0.997518	+	0.0704129i	$0.0224317\pi$
$858$	1.65075	−	11.4812i	0.0563555	−	0.391961i
$859$	32.1441	−	9.43835i	1.09674	−	0.322032i	0.317184	−	0.948364i	$-0.397263\pi$
$859$	32.1441	−	9.43835i	1.09674	−	0.322032i	0.779557	+	0.626332i	$0.215444\pi$
$860$	4.40478	+	2.83078i	0.150202	+	0.0965288i
$861$	−1.45889	−	10.1468i	−0.0497188	−	0.345802i
$862$	8.60990	+	18.8531i	0.293254	+	0.642138i
$863$	10.1665	+	22.2616i	0.346073	+	0.757795i	0.999999	+	0.00123615i	$0.000393478\pi$
$863$	10.1665	+	22.2616i	0.346073	+	0.757795i	−0.653926	+	0.756559i	$0.726879\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	21.6784	+	13.9319i	0.737088	+	0.473697i
$866$	−23.3092	+	6.84418i	−0.792077	+	0.232575i
$867$	7.01542	−	48.7933i	0.238256	−	1.65711i
$868$	4.15459	−	4.79466i	0.141016	−	0.162741i
$869$	46.7207	−	30.0256i	1.58489	−	1.01855i
$870$	2.60460	+	3.00587i	0.0883042	+	0.101908i
$871$	−13.0967	−	3.84555i	−0.443766	−	0.130301i
$872$	−3.58320	+	7.84611i	−0.121342	+	0.265703i
$873$	−11.9812			−0.405501
$874$	10.7621	−	3.50159i	0.364032	−	0.118443i
$875$	3.19963			0.108167
$876$	5.29736	−	11.5996i	0.178981	−	0.391914i
$877$	−3.01386	−	0.884950i	−0.101771	−	0.0298826i	0.230451	−	0.973084i	$-0.425980\pi$
$877$	−3.01386	−	0.884950i	−0.101771	−	0.0298826i	−0.332222	+	0.943201i	$0.607798\pi$
$878$	−13.5252	−	15.6089i	−0.456454	−	0.526776i
$879$	26.7606	−	17.1980i	0.902614	−	0.580075i
$880$	−2.69270	+	3.10754i	−0.0907709	+	0.104755i
$881$	−0.617686	+	4.29610i	−0.0208104	+	0.144739i	−0.997577	−	0.0695643i	$-0.977839\pi$
$881$	−0.617686	+	4.29610i	−0.0208104	+	0.144739i	0.976767	+	0.214304i	$0.0687482\pi$
$882$	−3.10648	+	0.912145i	−0.104601	+	0.0307135i
$883$	31.1874	+	20.0429i	1.04954	+	0.674498i	0.947328	−	0.320264i	$-0.103772\pi$
$883$	31.1874	+	20.0429i	1.04954	+	0.674498i	0.102212	+	0.994763i	$0.467408\pi$
$884$	−3.26875	−	22.7347i	−0.109940	−	0.764650i
$885$	0.809933	+	1.77351i	0.0272256	+	0.0596157i
$886$	−15.6434	−	34.2542i	−0.525549	−	1.15079i
$887$	−2.86920	−	19.9558i	−0.0963385	−	0.670049i	−0.979569	−	0.201109i	$-0.935545\pi$
$887$	−2.86920	−	19.9558i	−0.0963385	−	0.670049i	0.883230	−	0.468939i	$-0.155364\pi$
$888$	−1.51072	−	0.970881i	−0.0506964	−	0.0325806i
$889$	2.92928	−	0.860114i	0.0982449	−	0.0288473i
$890$	1.52040	−	10.5746i	0.0509641	−	0.354463i
$891$	2.69270	−	3.10754i	0.0902088	−	0.104107i
$892$	19.7219	−	12.6745i	0.660337	−	0.424373i
$893$	9.94475	+	11.4769i	0.332788	+	0.384058i
$894$	22.0270	+	6.46772i	0.736694	+	0.216313i
$895$	−10.7961	+	23.6402i	−0.360875	+	0.790206i
$896$	−3.19963			−0.106892
$897$	1.53675	−	13.4411i	0.0513106	−	0.448785i
$898$	4.70702			0.157075
$899$	−3.27608	+	7.17361i	−0.109263	+	0.239253i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	−24.5518	−	28.3343i	−0.817939	−	0.943951i
$902$	−11.0825	+	7.12229i	−0.369007	+	0.237146i
$903$	10.9710	−	12.6612i	0.365092	−	0.421338i
$904$	1.56717	−	10.8999i	0.0521234	−	0.362527i
$905$	−15.8678	+	4.65920i	−0.527462	+	0.154877i
$906$	2.29561	+	1.47530i	0.0762665	+	0.0490135i
$907$	0.732087	+	5.09178i	0.0243086	+	0.169070i	0.998359	−	0.0572600i	$-0.0182364\pi$
$907$	0.732087	+	5.09178i	0.0243086	+	0.169070i	−0.974051	+	0.226330i	$0.927327\pi$
$908$	3.73133	+	8.17047i	0.123829	+	0.271147i
$909$	6.99332	+	15.3132i	0.231954	+	0.507908i
$910$	1.28452	+	8.93404i	0.0425814	+	0.296160i
$911$	−1.74063	−	1.11864i	−0.0576697	−	0.0370620i	0.511488	−	0.859290i	$-0.329094\pi$
$911$	−1.74063	−	1.11864i	−0.0576697	−	0.0370620i	−0.569158	+	0.822228i	$0.692731\pi$
$912$	2.26424	−	0.664842i	0.0749766	−	0.0220151i
$913$	−2.38631	+	16.5972i	−0.0789754	+	0.549286i
$914$	17.3249	−	19.9941i	0.573058	−	0.661344i
$915$	−9.61256	+	6.17762i	−0.317781	+	0.204226i
$916$	−12.6282	−	14.5738i	−0.417249	−	0.481531i
$917$	−28.4402	−	8.35079i	−0.939178	−	0.275767i
$918$	3.38238	−	7.40639i	0.111635	−	0.244447i
$919$	13.9384			0.459785			0.229892	−	0.973216i	$-0.426163\pi$
$919$	13.9384			0.459785			0.229892	+	0.973216i	$0.426163\pi$
$920$	−3.03433	+	3.71387i	−0.100039	+	0.122443i
$921$	−0.115852			−0.00381745
$922$	2.34602	−	5.13706i	0.0772620	−	0.169180i
$923$	−28.2266	−	8.28809i	−0.929091	−	0.272806i
$924$	8.61564	+	9.94298i	0.283434	+	0.327100i
$925$	1.51072	−	0.970881i	0.0496722	−	0.0319224i
$926$	24.9821	−	28.8309i	0.820963	−	0.947441i
$927$	−0.797418	+	5.54617i	−0.0261907	+	0.182160i
$928$	3.81622	−	1.12054i	0.125274	−	0.0367837i
$929$	−21.5409	−	13.8435i	−0.706733	−	0.454190i	0.137266	−	0.990534i	$-0.456168\pi$
$929$	−21.5409	−	13.8435i	−0.706733	−	0.454190i	−0.843999	+	0.536344i	$0.819805\pi$
$930$	−0.282183	−	1.96262i	−0.00925313	−	0.0643569i
$931$	3.17388	+	6.94983i	0.104020	+	0.227771i
$932$	2.46264	+	5.39242i	0.0806664	+	0.176635i
$933$	−1.07293	−	7.46240i	−0.0351262	−	0.244308i
$934$	1.68383	+	1.08213i	0.0550964	+	0.0354083i
$935$	32.1234	−	9.43228i	1.05055	−	0.308469i
$936$	0.401459	−	2.79221i	0.0131221	−	0.0912662i
$937$	17.5798	−	20.2882i	0.574307	−	0.662786i	−0.392064	−	0.919938i	$-0.628239\pi$
$937$	17.5798	−	20.2882i	0.574307	−	0.662786i	0.966371	+	0.257152i	$0.0827841\pi$
$938$	13.0244	−	8.37025i	0.425261	−	0.273298i
$939$	−13.3834	−	15.4452i	−0.436750	−	0.504037i
$940$	−6.17455	−	1.81301i	−0.201392	−	0.0591339i
$941$	−8.83165	+	19.3386i	−0.287903	+	0.630421i	−0.997224	−	0.0744659i	$-0.976275\pi$
$941$	−8.83165	+	19.3386i	−0.287903	+	0.630421i	0.709320	+	0.704886i	$0.249002\pi$
$942$	−12.2905			−0.400446
$943$	−12.6800	+	8.67784i	−0.412917	+	0.282589i
$944$	1.94970			0.0634572
$945$	−1.32917	+	2.91048i	−0.0432380	+	0.0946781i
$946$	−20.6575	−	6.06559i	−0.671634	−	0.197209i
$947$	−33.4019	−	38.5479i	−1.08542	−	1.25264i	−0.965653	−	0.259836i	$-0.916332\pi$
$947$	−33.4019	−	38.5479i	−1.08542	−	1.25264i	−0.119764	−	0.992802i	$-0.538214\pi$
$948$	11.3624	−	7.30217i	0.369034	−	0.237164i
$949$	−23.5568	+	27.1861i	−0.764688	+	0.882497i
$950$	−0.335839	+	2.33581i	−0.0108961	+	0.0757838i
$951$	−8.60817	+	2.52759i	−0.279139	+	0.0819626i
$952$	21.9163	+	14.0847i	0.710311	+	0.456489i
$953$	4.03020	+	28.0307i	0.130551	+	0.908003i	0.944837	+	0.327540i	$0.106220\pi$
$953$	4.03020	+	28.0307i	0.130551	+	0.908003i	−0.814286	+	0.580463i	$0.802871\pi$
$954$	−1.91283	−	4.18851i	−0.0619301	−	0.135608i
$955$	−5.85845	−	12.8282i	−0.189575	−	0.415111i
$956$	0.998618	+	6.94554i	0.0322976	+	0.224635i
$957$	−13.7581	−	8.84178i	−0.444736	−	0.285814i
$958$	10.0711	−	2.95714i	0.325382	−	0.0955408i
$959$	5.11294	−	35.5613i	0.165106	−	1.14833i
$960$	−0.654861	+	0.755750i	−0.0211355	+	0.0243917i
$961$	−22.7715	+	14.6343i	−0.734563	+	0.472075i
$962$	3.31740	+	3.82848i	0.106957	+	0.123435i
$963$	4.93810	+	1.44996i	0.159128	+	0.0467242i
$964$	2.43494	−	5.33177i	0.0784241	−	0.171725i
$965$	2.51369			0.0809185
$966$	10.3804	+	11.3010i	0.333983	+	0.363605i
$967$	−2.58820			−0.0832309			−0.0416154	−	0.999134i	$-0.513250\pi$
$967$	−2.58820			−0.0832309			−0.0416154	+	0.999134i	$0.513250\pi$
$968$	2.45404	−	5.37360i	0.0788758	−	0.172714i
$969$	−18.4359	−	5.41326i	−0.592246	−	0.173899i
$970$	−7.84599	−	9.05476i	−0.251920	−	0.290731i
$971$	−23.8020	+	15.2966i	−0.763841	+	0.490891i	−0.863635	−	0.504117i	$-0.831818\pi$
$971$	−23.8020	+	15.2966i	−0.763841	+	0.490891i	0.0997942	+	0.995008i	$0.468182\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−1.29298	+	8.99286i	−0.0414510	+	0.288298i
$974$	18.5411	−	5.44415i	0.594094	−	0.174442i
$975$	2.37311	+	1.52511i	0.0760004	+	0.0488425i
$976$	1.62616	+	11.3102i	0.0520520	+	0.362030i
$977$	10.3429	+	22.6478i	0.330899	+	0.724568i	0.999824	−	0.0187619i	$-0.00597245\pi$
$977$	10.3429	+	22.6478i	0.330899	+	0.724568i	−0.668925	+	0.743330i	$0.733245\pi$
$978$	−0.724220	−	1.58582i	−0.0231580	−	0.0507089i
$979$	6.25170	+	43.4815i	0.199805	+	1.38967i
$980$	−2.72366	−	1.75039i	−0.0870043	−	0.0559142i
$981$	8.27619	−	2.43011i	0.264238	−	0.0775874i
$982$	−0.263487	+	1.83259i	−0.00840821	+	0.0584804i
$983$	2.30554	−	2.66073i	0.0735353	−	0.0848643i	−0.717790	−	0.696260i	$-0.754846\pi$
$983$	2.30554	−	2.66073i	0.0735353	−	0.0848643i	0.791325	+	0.611396i	$0.209392\pi$
$984$	−2.69525	+	1.73213i	−0.0859214	+	0.0552183i
$985$	−1.84884	−	2.13368i	−0.0589091	−	0.0679847i
$986$	−31.0724	−	9.12367i	−0.989546	−	0.290557i
$987$	−8.55353	+	18.7296i	−0.272262	+	0.596170i
$988$	−6.65691			−0.211785
$989$	−24.2884	−	6.37387i	−0.772327	−	0.202677i
$990$	4.11187			0.130684
$991$	18.9791	−	41.5585i	0.602892	−	1.32015i	−0.324438	−	0.945907i	$-0.605175\pi$
$991$	18.9791	−	41.5585i	0.602892	−	1.32015i	0.927331	−	0.374243i	$-0.122098\pi$
$992$	−1.90249	−	0.558621i	−0.0604040	−	0.0177362i
$993$	−11.9418	−	13.7816i	−0.378961	−	0.437345i
$994$	28.0707	−	18.0399i	0.890347	−	0.572192i
$995$	−8.95490	+	10.3345i	−0.283890	+	0.327626i
$996$	−0.580348	+	4.03641i	−0.0183890	+	0.127898i
$997$	−32.2494	+	9.46927i	−1.02135	+	0.299895i	−0.749188	−	0.662357i	$-0.769556\pi$
$997$	−32.2494	+	9.46927i	−1.02135	+	0.299895i	−0.272160	+	0.962252i	$0.587738\pi$
$998$	1.49165	+	0.958627i	0.0472175	+	0.0303448i
$999$	0.255568	+	1.77752i	0.00808583	+	0.0562382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.d.121.2	✓	20
23.4	even	11	inner	690.2.m.d.211.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.d.121.2	✓	20	1.1	even	1	trivial
690.2.m.d.211.2	yes	20	23.4	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.455355 - 3.16706i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.455355 - 3.16706i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.142315 + 0.989821i) q^{10} +(-1.70813 - 3.74028i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.401459 + 2.79221i) q^{13} +(-2.69170 - 1.72985i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(5.33199 - 6.15345i) q^{17} +(0.841254 - 0.540641i) q^{18} +(-1.54536 - 1.78344i) q^{19} +(0.959493 + 0.281733i) q^{20} +(1.32917 - 2.91048i) q^{21} -4.11187 q^{22} +(-4.79382 + 0.138877i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(2.70666 + 0.794746i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-2.69170 + 1.72985i) q^{28} +(2.60460 - 3.00587i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-1.90249 + 0.558621i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.585180 - 4.07001i) q^{33} +(-3.38238 - 7.40639i) q^{34} +(1.32917 + 2.91048i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(1.51072 + 0.970881i) q^{37} +(-2.26424 + 0.664842i) q^{38} +(-0.401459 + 2.79221i) q^{39} +(0.654861 - 0.755750i) q^{40} +(2.69525 - 1.73213i) q^{41} +(-2.09531 - 2.41812i) q^{42} +(5.02388 + 1.47514i) q^{43} +(-1.70813 + 3.74028i) q^{44} -1.00000 q^{45} +(-1.86510 + 4.41830i) q^{46} -6.43522 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-3.10648 - 0.912145i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(6.84964 - 4.40199i) q^{51} +(1.84731 - 2.13191i) q^{52} +(0.655305 - 4.55775i) q^{53} +(0.959493 - 0.281733i) q^{54} +(3.45912 + 2.22304i) q^{55} +(0.455355 + 3.16706i) q^{56} +(-0.980311 - 2.14658i) q^{57} +(-1.65224 - 3.61791i) q^{58} +(-0.277471 - 1.92985i) q^{59} +(0.841254 + 0.540641i) q^{60} +(10.9636 - 3.21921i) q^{61} +(-0.282183 + 1.96262i) q^{62} +(2.09531 - 2.41812i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-1.84731 - 2.13191i) q^{65} +(-3.94531 - 1.15845i) q^{66} +(-2.01007 + 4.40145i) q^{67} -8.14218 q^{68} +(-4.63876 - 1.21732i) q^{69} +3.19963 q^{70} +(-4.33220 + 9.48619i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(8.35076 + 9.63729i) q^{73} +(1.51072 - 0.970881i) q^{74} +(0.654861 - 0.755750i) q^{75} +(-0.335839 + 2.33581i) q^{76} +(-12.6235 + 3.70660i) q^{77} +(2.37311 + 1.52511i) q^{78} +(1.92218 + 13.3690i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.455955 - 3.17124i) q^{82} +(-3.43056 - 2.20469i) q^{83} +(-3.07002 + 0.901440i) q^{84} +(-1.15875 + 8.05930i) q^{85} +(3.42883 - 3.95708i) q^{86} +(3.34595 - 2.15031i) q^{87} +(2.69270 + 3.10754i) q^{88} +(-10.2506 - 3.00986i) q^{89} +(-0.415415 + 0.909632i) q^{90} +9.02591 q^{91} +(3.24424 + 3.53198i) q^{92} -1.98280 q^{93} +(-2.67329 + 5.85368i) q^{94} +(2.26424 + 0.664842i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-10.0792 + 6.47750i) q^{97} +(-2.12019 + 2.44683i) q^{98} +(0.585180 - 4.07001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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