LMFDB - Embedded newform 690.2.w.b.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	690.7
Dual form			690.2.w.b.493.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 - 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.18918 + 0.455502i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.172948 - 0.316731i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 - 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.18918 + 0.455502i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.172948 - 0.316731i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-2.15111 + 0.610516i) q^{10} +(4.35576 - 3.77429i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(0.701781 - 0.383202i) q^{13} +(0.149912 - 0.328262i) q^{14} +(-0.0202515 + 2.23598i) q^{15} +(0.959493 - 0.281733i) q^{16} +(0.276383 + 0.369204i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(-0.891653 - 6.20158i) q^{19} +(-2.10207 + 0.762419i) q^{20} +(-0.272730 - 0.236322i) q^{21} +(4.07541 - 4.07541i) q^{22} +(2.21044 - 4.25605i) q^{23} -1.00000i q^{24} +(4.58504 - 1.99435i) q^{25} +(0.672656 - 0.432290i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(0.126112 - 0.338120i) q^{28} +(-9.47323 - 1.36204i) q^{29} +(0.139313 + 2.23172i) q^{30} +(1.31556 + 0.845457i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-2.76215 - 5.05850i) q^{33} +(0.302017 + 0.348547i) q^{34} +(-0.234343 + 0.772159i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(3.10334 + 8.32037i) q^{37} +(-1.33180 - 6.12217i) q^{38} +(-0.225270 - 0.767199i) q^{39} +(-2.04233 + 0.910437i) q^{40} +(-1.67365 - 3.66478i) q^{41} +(-0.288894 - 0.216263i) q^{42} +(7.03749 + 1.53091i) q^{43} +(3.77429 - 4.35576i) q^{44} +(2.18057 + 0.495080i) q^{45} +(1.90118 - 4.40290i) q^{46} +(-1.40356 - 1.40356i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(3.71408 + 5.77922i) q^{49} +(4.43108 - 2.31637i) q^{50} +(0.419516 - 0.191587i) q^{51} +(0.640103 - 0.479175i) q^{52} +(-1.55615 - 0.849720i) q^{53} +(-0.540641 + 0.841254i) q^{54} +(-7.81636 + 10.2467i) q^{55} +(0.101670 - 0.346255i) q^{56} +(-6.24939 - 0.446965i) q^{57} +(-9.54626 - 0.682762i) q^{58} +(-4.03973 + 13.7580i) q^{59} +(0.298167 + 2.21610i) q^{60} +(-4.25012 + 6.61332i) q^{61} +(1.37252 + 0.749453i) q^{62} +(-0.288894 + 0.216263i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-1.36178 + 1.15856i) q^{65} +(-3.11598 - 4.84857i) q^{66} +(-0.842709 - 11.7826i) q^{67} +(0.326113 + 0.326113i) q^{68} +(-3.68892 - 3.06461i) q^{69} +(-0.178661 + 0.786910i) q^{70} +(-2.46650 + 2.84649i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(12.9380 + 9.68526i) q^{73} +(3.68900 + 8.07778i) q^{74} +(-0.974158 - 4.90418i) q^{75} +(-1.76515 - 6.01156i) q^{76} +(-0.442113 - 2.03236i) q^{77} +(-0.279427 - 0.749173i) q^{78} +(3.46495 + 1.01740i) q^{79} +(-1.97217 + 1.05382i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-1.93083 - 3.53605i) q^{82} +(-0.718827 + 0.268108i) q^{83} +(-0.303586 - 0.195103i) q^{84} +(-0.773226 - 0.682362i) q^{85} +(7.12878 + 1.02496i) q^{86} +(-3.34460 + 8.96721i) q^{87} +(3.45394 - 4.61392i) q^{88} +(-3.65712 + 2.35029i) q^{89} +(2.21034 + 0.338258i) q^{90} -0.288550i q^{91} +(1.58224 - 4.52731i) q^{92} +(1.10578 - 1.10578i) q^{93} +(-1.50012 - 1.29986i) q^{94} +(4.77682 + 13.1702i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-0.902631 - 0.336664i) q^{97} +(4.11690 + 5.49953i) q^{98} +(-5.53004 + 1.62377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−2.18918	+	0.455502i	−0.979032	+	0.203707i
$5$	−2.18918	+	0.455502i	−0.979032	+	0.203707i
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	0.172948	−	0.316731i	0.0653682	−	0.119713i	−0.842951	−	0.537990i	$-0.819184\pi$
$7$	0.172948	−	0.316731i	0.0653682	−	0.119713i	0.908320	+	0.418277i	$0.137366\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	−2.15111	+	0.610516i	−0.680240	+	0.193062i
$11$	4.35576	−	3.77429i	1.31331	−	1.13799i	0.332485	−	0.943108i	$-0.392113\pi$
$11$	4.35576	−	3.77429i	1.31331	−	1.13799i	0.980827	−	0.194883i	$-0.0624327\pi$
$12$	0.0713392	−	0.997452i	0.0205938	−	0.287940i
$13$	0.701781	−	0.383202i	0.194639	−	0.106281i	−0.378974	−	0.925407i	$-0.623723\pi$
$13$	0.701781	−	0.383202i	0.194639	−	0.106281i	0.573613	+	0.819126i	$0.305541\pi$
$14$	0.149912	−	0.328262i	0.0400657	−	0.0877316i
$15$	−0.0202515	+	2.23598i	−0.00522893	+	0.577327i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	0.276383	+	0.369204i	0.0670327	+	0.0895452i	0.832805	−	0.553567i	$-0.186734\pi$
$17$	0.276383	+	0.369204i	0.0670327	+	0.0895452i	−0.765772	+	0.643112i	$0.777643\pi$
$18$	−0.936950	−	0.349464i	−0.220841	−	0.0823695i
$19$	−0.891653	−	6.20158i	−0.204559	−	1.42274i	−0.790538	−	0.612414i	$-0.790199\pi$
$19$	−0.891653	−	6.20158i	−0.204559	−	1.42274i	0.585978	−	0.810327i	$-0.300710\pi$
$20$	−2.10207	+	0.762419i	−0.470038	+	0.170482i
$21$	−0.272730	−	0.236322i	−0.0595145	−	0.0515696i
$22$	4.07541	−	4.07541i	0.868880	−	0.868880i
$23$	2.21044	−	4.25605i	0.460909	−	0.887448i
$23$	2.21044	−	4.25605i	0.460909	−	0.887448i
$24$		−	1.00000i		−	0.204124i
$25$	4.58504	−	1.99435i	0.917007	−	0.398871i
$26$	0.672656	−	0.432290i	0.131919	−	0.0847790i
$27$	−0.599278	+	0.800541i	−0.115331	+	0.154064i
$28$	0.126112	−	0.338120i	0.0238330	−	0.0638986i
$29$	−9.47323	−	1.36204i	−1.75913	−	0.252925i	−0.814293	−	0.580454i	$-0.802875\pi$
$29$	−9.47323	−	1.36204i	−1.75913	−	0.252925i	−0.944841	+	0.327529i	$0.893784\pi$
$30$	0.139313	+	2.23172i	0.0254349	+	0.407455i
$31$	1.31556	+	0.845457i	0.236281	+	0.151849i	0.653424	−	0.756992i	$-0.273332\pi$
$31$	1.31556	+	0.845457i	0.236281	+	0.151849i	−0.417143	+	0.908841i	$0.636968\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	−2.76215	−	5.05850i	−0.480829	−	0.880572i
$34$	0.302017	+	0.348547i	0.0517956	+	0.0597753i
$35$	−0.234343	+	0.772159i	−0.0396112	+	0.130519i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	3.10334	+	8.32037i	0.510186	+	1.36786i	0.895494	+	0.445073i	$0.146822\pi$
$37$	3.10334	+	8.32037i	0.510186	+	1.36786i	−0.385309	+	0.922788i	$0.625905\pi$
$38$	−1.33180	−	6.12217i	−0.216046	−	0.993147i
$39$	−0.225270	−	0.767199i	−0.0360721	−	0.122850i
$40$	−2.04233	+	0.910437i	−0.322920	+	0.143953i
$41$	−1.67365	−	3.66478i	−0.261380	−	0.572343i	0.732754	−	0.680493i	$-0.238234\pi$
$41$	−1.67365	−	3.66478i	−0.261380	−	0.572343i	−0.994135	+	0.108150i	$0.965507\pi$
$42$	−0.288894	−	0.216263i	−0.0445773	−	0.0333701i
$43$	7.03749	+	1.53091i	1.07321	+	0.233462i	0.714249	−	0.699892i	$-0.246768\pi$
$43$	7.03749	+	1.53091i	1.07321	+	0.233462i	0.358958	+	0.933354i	$0.383132\pi$
$44$	3.77429	−	4.35576i	0.568996	−	0.656656i
$45$	2.18057	+	0.495080i	0.325061	+	0.0738021i
$46$	1.90118	−	4.40290i	0.280314	−	0.649172i
$47$	−1.40356	−	1.40356i	−0.204731	−	0.204731i	0.597293	−	0.802023i	$-0.296243\pi$
$47$	−1.40356	−	1.40356i	−0.204731	−	0.204731i	−0.802023	+	0.597293i	$0.796243\pi$
$48$	−0.0713392	−	0.997452i	−0.0102969	−	0.143970i
$49$	3.71408	+	5.77922i	0.530583	+	0.825603i
$50$	4.43108	−	2.31637i	0.626649	−	0.327584i
$51$	0.419516	−	0.191587i	0.0587440	−	0.0268275i
$52$	0.640103	−	0.479175i	0.0887663	−	0.0664496i
$53$	−1.55615	−	0.849720i	−0.213753	−	0.116718i	0.368806	−	0.929506i	$-0.379767\pi$
$53$	−1.55615	−	0.849720i	−0.213753	−	0.116718i	−0.582559	+	0.812788i	$0.697949\pi$
$54$	−0.540641	+	0.841254i	−0.0735719	+	0.114480i
$55$	−7.81636	+	10.2467i	−1.05396	+	1.38166i
$56$	0.101670	−	0.346255i	0.0135862	−	0.0462703i
$57$	−6.24939	−	0.446965i	−0.827752	−	0.0592020i
$58$	−9.54626	−	0.682762i	−1.25349	−	0.0896510i
$59$	−4.03973	+	13.7580i	−0.525928	+	1.79115i	0.0813852	+	0.996683i	$0.474066\pi$
$59$	−4.03973	+	13.7580i	−0.525928	+	1.79115i	−0.607313	+	0.794463i	$0.707753\pi$
$60$	0.298167	+	2.21610i	0.0384932	+	0.286097i
$61$	−4.25012	+	6.61332i	−0.544172	+	0.846748i	−0.999040	−	0.0438106i	$-0.986050\pi$
$61$	−4.25012	+	6.61332i	−0.544172	+	0.846748i	0.454868	+	0.890559i	$0.349687\pi$
$62$	1.37252	+	0.749453i	0.174310	+	0.0951806i
$63$	−0.288894	+	0.216263i	−0.0363972	+	0.0272466i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−1.36178	+	1.15856i	−0.168908	+	0.143702i
$66$	−3.11598	−	4.84857i	−0.383551	−	0.596817i
$67$	−0.842709	−	11.7826i	−0.102953	−	1.43947i	−0.742048	−	0.670347i	$-0.766145\pi$
$67$	−0.842709	−	11.7826i	−0.102953	−	1.43947i	0.639095	−	0.769128i	$-0.279309\pi$
$68$	0.326113	+	0.326113i	0.0395470	+	0.0395470i
$69$	−3.68892	−	3.06461i	−0.444094	−	0.368936i
$70$	−0.178661	+	0.786910i	−0.0213541	+	0.0940537i
$71$	−2.46650	+	2.84649i	−0.292719	+	0.337816i	−0.882992	−	0.469388i	$-0.844475\pi$
$71$	−2.46650	+	2.84649i	−0.292719	+	0.337816i	0.590273	+	0.807204i	$0.299020\pi$
$72$	−0.977147	−	0.212565i	−0.115158	−	0.0250511i
$73$	12.9380	+	9.68526i	1.51428	+	1.13357i	0.951782	+	0.306774i	$0.0992497\pi$
$73$	12.9380	+	9.68526i	1.51428	+	1.13357i	0.562496	+	0.826800i	$0.309841\pi$
$74$	3.68900	+	8.07778i	0.428837	+	0.939023i
$75$	−0.974158	−	4.90418i	−0.112486	−	0.566286i
$76$	−1.76515	−	6.01156i	−0.202477	−	0.689573i
$77$	−0.442113	−	2.03236i	−0.0503834	−	0.231609i
$78$	−0.279427	−	0.749173i	−0.0316389	−	0.0848272i
$79$	3.46495	+	1.01740i	0.389837	+	0.114466i	0.470776	−	0.882253i	$-0.343974\pi$
$79$	3.46495	+	1.01740i	0.389837	+	0.114466i	−0.0809395	+	0.996719i	$0.525792\pi$
$80$	−1.97217	+	1.05382i	−0.220496	+	0.117820i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	−1.93083	−	3.53605i	−0.213224	−	0.390491i
$83$	−0.718827	+	0.268108i	−0.0789015	+	0.0294287i	−0.388605	−	0.921404i	$-0.627043\pi$
$83$	−0.718827	+	0.268108i	−0.0789015	+	0.0294287i	0.309704	+	0.950833i	$0.399770\pi$
$84$	−0.303586	−	0.195103i	−0.0331239	−	0.0212874i
$85$	−0.773226	−	0.682362i	−0.0838681	−	0.0740126i
$86$	7.12878	+	1.02496i	0.768716	+	0.110525i
$87$	−3.34460	+	8.96721i	−0.358578	+	0.961386i
$88$	3.45394	−	4.61392i	0.368191	−	0.491846i
$89$	−3.65712	+	2.35029i	−0.387654	+	0.249130i	−0.719922	−	0.694055i	$-0.755822\pi$
$89$	−3.65712	+	2.35029i	−0.387654	+	0.249130i	0.332268	+	0.943185i	$0.392186\pi$
$90$	2.21034	+	0.338258i	0.232990	+	0.0356555i
$91$		−	0.288550i		−	0.0302482i
$92$	1.58224	−	4.52731i	0.164960	−	0.472004i
$93$	1.10578	−	1.10578i	0.114664	−	0.114664i
$94$	−1.50012	−	1.29986i	−0.154725	−	0.134070i
$95$	4.77682	+	13.1702i	0.490092	+	1.35124i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	−0.902631	−	0.336664i	−0.0916483	−	0.0341831i	0.303222	−	0.952920i	$-0.401938\pi$
$97$	−0.902631	−	0.336664i	−0.0916483	−	0.0341831i	−0.394870	+	0.918737i	$0.629210\pi$
$98$	4.11690	+	5.49953i	0.415870	+	0.555537i
$99$	−5.53004	+	1.62377i	−0.555790	+	0.163195i
$100$	4.25454	−	2.62657i	0.425454	−	0.262657i
$101$	−0.117026	+	0.256251i	−0.0116445	+	0.0254980i	−0.915365	−	0.402625i	$-0.868098\pi$
$101$	−0.117026	+	0.256251i	−0.0116445	+	0.0254980i	0.903720	+	0.428123i	$0.140825\pi$
$102$	0.404780	−	0.221026i	0.0400792	−	0.0218849i
$103$	0.0737520	−	1.03119i	0.00726700	−	0.101606i	−0.992524	−	0.122050i	$-0.961053\pi$
$103$	0.0737520	−	1.03119i	0.00726700	−	0.101606i	0.999791	+	0.0204436i	$0.00650786\pi$
$104$	0.604288	−	0.523619i	0.0592553	−	0.0513450i
$105$	0.704700	+	0.393122i	0.0687717	+	0.0383648i
$106$	−1.61280	−	0.736541i	−0.156649	−	0.0715392i
$107$	16.8834	−	3.67277i	1.63218	−	0.355060i	0.699186	−	0.714940i	$-0.253546\pi$
$107$	16.8834	−	3.67277i	1.63218	−	0.355060i	0.932999	+	0.359880i	$0.117182\pi$
$108$	−0.479249	+	0.877679i	−0.0461158	+	0.0844547i
$109$	−0.277224	+	1.92813i	−0.0265532	+	0.184682i	−0.998781	−	0.0493534i	$-0.984284\pi$
$109$	−0.277224	+	1.92813i	−0.0265532	+	0.184682i	0.972228	+	0.234035i	$0.0751930\pi$
$110$	−7.06546	+	10.7782i	−0.673665	+	1.02766i
$111$	8.78989	−	1.26379i	0.834299	−	0.119954i
$112$	0.0767091	−	0.352626i	0.00724833	−	0.0333200i
$113$	3.97474	−	0.284279i	0.373912	−	0.0267427i	0.116881	−	0.993146i	$-0.462710\pi$
$113$	3.97474	−	0.284279i	0.373912	−	0.0267427i	0.257031	+	0.966403i	$0.417256\pi$
$114$	−6.26535			−0.586804
$115$	−2.90041	+	10.3241i	−0.270465	+	0.962730i
$116$	−9.57064			−0.888612
$117$	−0.797550	+	0.0570419i	−0.0737336	+	0.00527353i
$118$	−3.04795	+	14.0112i	−0.280586	+	1.28983i
$119$	0.164738	−	0.0236858i	0.0151015	−	0.00217127i
$120$	0.455502	+	2.18918i	0.0415815	+	0.199844i
$121$	3.16194	−	21.9918i	0.287449	−	1.99925i
$122$	−3.76750	+	6.89967i	−0.341094	+	0.624666i
$123$	−3.93679	+	0.856396i	−0.354968	+	0.0772187i
$124$	1.42249	+	0.649629i	0.127743	+	0.0583384i
$125$	−9.12904	+	6.45450i	−0.816527	+	0.577308i
$126$	−0.272730	+	0.236322i	−0.0242967	+	0.0210532i
$127$	−0.929590	+	12.9974i	−0.0824878	+	1.15333i	0.772616	+	0.634873i	$0.218948\pi$
$127$	−0.929590	+	12.9974i	−0.0824878	+	1.15333i	−0.855104	+	0.518456i	$0.826507\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	2.99185	−	6.55125i	0.263418	−	0.576805i
$130$	−1.27566	+	1.25276i	−0.111883	+	0.109874i
$131$	−11.2792	+	3.31187i	−0.985468	+	0.289359i	−0.734480	−	0.678631i	$-0.762574\pi$
$131$	−11.2792	+	3.31187i	−0.985468	+	0.289359i	−0.250988	+	0.967990i	$0.580756\pi$
$132$	−3.45394	−	4.61392i	−0.300627	−	0.401590i
$133$	−2.11844	−	0.790137i	−0.183692	−	0.0685136i
$134$	−1.68112	−	11.6925i	−0.145227	−	1.01008i
$135$	0.947280	−	2.02550i	0.0815288	−	0.174328i
$136$	0.348547	+	0.302017i	0.0298876	+	0.0258978i
$137$	7.32599	−	7.32599i	0.625902	−	0.625902i	−0.321133	−	0.947034i	$-0.604064\pi$
$137$	7.32599	−	7.32599i	0.625902	−	0.625902i	0.947034	+	0.321133i	$0.104064\pi$
$138$	−3.89815	−	2.79364i	−0.331833	−	0.237810i
$139$			0.971160i			0.0823727i	0.999151	+	0.0411864i	$0.0131137\pi$
$139$			0.971160i			0.0823727i	−0.999151	+	0.0411864i	$0.986886\pi$
$140$	−0.122068	+	0.797650i	−0.0103166	+	0.0674138i
$141$	−1.66984	+	1.07314i	−0.140625	+	0.0903745i
$142$	−2.25714	+	3.01519i	−0.189415	+	0.253029i
$143$	1.61048	−	4.31786i	0.134675	−	0.361078i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	21.3590	−	1.33331i	1.77377	−	0.110726i
$146$	13.5960	+	8.73760i	1.12521	+	0.723129i
$147$	6.43663	−	2.40074i	0.530884	−	0.198010i
$148$	4.25586	+	7.79403i	0.349830	+	0.640665i
$149$	−9.21404	−	10.6336i	−0.754844	−	0.871136i	0.240185	−	0.970727i	$-0.422792\pi$
$149$	−9.21404	−	10.6336i	−0.754844	−	0.871136i	−0.995028	+	0.0995909i	$0.968247\pi$
$150$	−1.32154	−	4.82219i	−0.107903	−	0.393730i
$151$	13.6711	+	4.01420i	1.11254	+	0.326671i	0.785823	−	0.618451i	$-0.212240\pi$
$151$	13.6711	+	4.01420i	1.11254	+	0.326671i	0.326717	+	0.945122i	$0.394058\pi$
$152$	−2.18952	−	5.87032i	−0.177593	−	0.476146i
$153$	−0.0980337	−	0.450654i	−0.00792555	−	0.0364332i
$154$	−0.585973	−	1.99564i	−0.0472191	−	0.160813i
$155$	−3.26510	−	1.25162i	−0.262259	−	0.100533i
$156$	−0.332161	−	0.727331i	−0.0265941	−	0.0582331i
$157$	−15.8500	−	11.8652i	−1.26497	−	0.946946i	−0.265120	−	0.964215i	$-0.585412\pi$
$157$	−15.8500	−	11.8652i	−1.26497	−	0.946946i	−0.999851	+	0.0172697i	$0.994503\pi$
$158$	3.52870	+	0.767621i	0.280728	+	0.0610687i
$159$	−1.16108	+	1.33996i	−0.0920799	+	0.106266i
$160$	−1.89197	+	1.19182i	−0.149573	+	0.0942219i
$161$	−0.965730	−	1.43619i	−0.0761102	−	0.113188i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	1.36794	+	19.1263i	0.107145	+	1.49808i	0.712243	+	0.701933i	$0.247680\pi$
$163$	1.36794	+	19.1263i	0.107145	+	1.49808i	−0.605097	+	0.796151i	$0.706866\pi$
$164$	−2.17817	−	3.38930i	−0.170086	−	0.264659i
$165$	8.35101	+	9.81582i	0.650125	+	0.764160i
$166$	−0.697868	+	0.318706i	−0.0541651	+	0.0247364i
$167$	2.59250	−	1.94072i	0.200614	−	0.150177i	−0.494248	−	0.869321i	$-0.664557\pi$
$167$	2.59250	−	1.94072i	0.200614	−	0.150177i	0.694862	+	0.719144i	$0.255466\pi$
$168$	−0.316731	−	0.172948i	−0.0244363	−	0.0133432i
$169$	−6.68268	+	10.3984i	−0.514052	+	0.799881i
$170$	−0.819935	−	0.625462i	−0.0628861	−	0.0479708i
$171$	−1.76515	+	6.01156i	−0.134985	+	0.459716i
$172$	7.18373	+	0.513791i	0.547755	+	0.0391762i
$173$	5.01029	+	0.358343i	0.380925	+	0.0272443i	0.260489	−	0.965477i	$-0.416116\pi$
$173$	5.01029	+	0.358343i	0.380925	+	0.0272443i	0.120436	+	0.992721i	$0.461571\pi$
$174$	−2.69636	+	9.18296i	−0.204411	+	0.696159i
$175$	0.161300	−	1.79714i	0.0121931	−	0.135851i
$176$	3.11598	−	4.84857i	0.234876	−	0.365474i
$177$	12.5849	+	6.87189i	0.945941	+	0.516523i
$178$	−3.48013	+	2.60520i	−0.260847	+	0.195268i
$179$	−21.3868	+	9.76701i	−1.59852	+	0.730020i	−0.997597	−	0.0692850i	$-0.977928\pi$
$179$	−21.3868	+	9.76701i	−1.59852	+	0.730020i	−0.600925	+	0.799305i	$0.705201\pi$
$180$	2.22883	+	0.179713i	0.166128	+	0.0133950i
$181$	2.81747	+	4.38407i	0.209421	+	0.325865i	0.930035	−	0.367471i	$-0.119776\pi$
$181$	2.81747	+	4.38407i	0.209421	+	0.325865i	−0.720614	+	0.693336i	$0.756140\pi$
$182$	−0.0205849	−	0.287814i	−0.00152585	−	0.0213342i
$183$	5.55875	+	5.55875i	0.410915	+	0.410915i
$184$	1.25524	−	4.62865i	0.0925372	−	0.341228i
$185$	−10.5837	−	16.8012i	−0.778130	−	1.23525i
$186$	1.02408	−	1.18185i	0.0750888	−	0.0866571i
$187$	2.59734	+	0.565017i	0.189936	+	0.0413181i
$188$	−1.58902	−	1.18953i	−0.115891	−	0.0867553i
$189$	0.149912	+	0.328262i	0.0109045	+	0.0238775i
$190$	5.70421	+	12.7959i	0.413827	+	0.928313i
$191$	5.16909	+	17.6043i	0.374022	+	1.27380i	0.904635	+	0.426188i	$0.140144\pi$
$191$	5.16909	+	17.6043i	0.374022	+	1.27380i	−0.530613	+	0.847614i	$0.678038\pi$
$192$	−0.212565	−	0.977147i	−0.0153406	−	0.0705195i
$193$	−1.53559	−	4.11709i	−0.110535	−	0.296354i	0.869891	−	0.493244i	$-0.164189\pi$
$193$	−1.53559	−	4.11709i	−0.110535	−	0.296354i	−0.980426	+	0.196889i	$0.936916\pi$
$194$	−0.924349	−	0.271413i	−0.0663644	−	0.0194863i
$195$	0.842618	+	1.57693i	0.0603411	+	0.112926i
$196$	4.49874	+	5.19183i	0.321339	+	0.370845i
$197$	−5.31109	−	9.72653i	−0.378399	−	0.692986i	0.617189	−	0.786815i	$-0.288271\pi$
$197$	−5.31109	−	9.72653i	−0.378399	−	0.692986i	−0.995588	+	0.0938284i	$0.970090\pi$
$198$	−5.40011	+	2.01414i	−0.383769	+	0.143138i
$199$	−4.15496	−	2.67023i	−0.294537	−	0.189287i	0.385024	−	0.922907i	$-0.374193\pi$
$199$	−4.15496	−	2.67023i	−0.294537	−	0.189287i	−0.679561	+	0.733619i	$0.737830\pi$
$200$	4.05632	−	2.92340i	0.286825	−	0.206715i
$201$	−11.6925	−	1.68112i	−0.824723	−	0.118577i
$202$	−0.0984471	+	0.263947i	−0.00692671	+	0.0185712i
$203$	−2.06978	+	2.76490i	−0.145270	+	0.194058i
$204$	0.387980	−	0.249340i	0.0271641	−	0.0174573i
$205$	5.33324	+	7.26052i	0.372490	+	0.507097i
$206$		−	1.03382i		−	0.0720298i
$207$	−3.77871	+	2.95319i	−0.262639	+	0.205261i
$208$	0.565394	−	0.565394i	0.0392030	−	0.0392030i
$209$	−27.2904	−	23.6473i	−1.88772	−	1.63572i
$210$	0.730949	+	0.341848i	0.0504403	+	0.0235897i
$211$	−2.57004	−	17.8750i	−0.176929	−	1.23057i	−0.863818	−	0.503804i	$-0.831933\pi$
$211$	−2.57004	−	17.8750i	−0.176929	−	1.23057i	0.686889	−	0.726762i	$-0.258976\pi$
$212$	−1.66123	−	0.619608i	−0.114094	−	0.0425549i
$213$	2.25714	+	3.01519i	0.154657	+	0.206598i
$214$	16.5784	−	4.86786i	1.13328	−	0.332760i
$215$	−16.1037	−	0.145853i	−1.09826	−	0.00994711i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	0.495305	−	0.270457i	0.0336235	−	0.0183598i
$218$	−0.138966	+	1.94300i	−0.00941196	+	0.131596i
$219$	12.2141	−	10.5836i	0.825352	−	0.715172i
$220$	−6.27855	+	11.2548i	−0.423300	+	0.758795i
$221$	0.335440	+	0.153190i	0.0225641	+	0.0103047i
$222$	8.67733	−	1.88764i	0.582384	−	0.126690i
$223$	−13.6499	+	24.9980i	−0.914067	+	1.67399i	−0.192910	+	0.981216i	$0.561793\pi$
$223$	−13.6499	+	24.9980i	−0.914067	+	1.67399i	−0.721157	+	0.692772i	$0.756389\pi$
$224$	0.0513576	−	0.357200i	0.00343147	−	0.0238664i
$225$	−4.99918	−	0.0905640i	−0.333279	−	0.00603760i
$226$	3.94433	−	0.567110i	0.262373	−	0.0377236i
$227$	2.27802	−	10.4719i	0.151197	−	0.695043i	−0.837662	−	0.546189i	$-0.816078\pi$
$227$	2.27802	−	10.4719i	0.151197	−	0.695043i	0.988859	−	0.148854i	$-0.0475584\pi$
$228$	−6.24939	+	0.446965i	−0.413876	+	0.0296010i
$229$	15.3433			1.01391			0.506956	−	0.861972i	$-0.330771\pi$
$229$	15.3433			1.01391			0.506956	+	0.861972i	$0.330771\pi$
$230$	−2.15651	+	10.5047i	−0.142196	+	0.692662i
$231$	−2.07989			−0.136847
$232$	−9.54626	+	0.682762i	−0.626743	+	0.0448255i
$233$	−2.61533	+	12.0225i	−0.171336	+	0.787618i	0.808609	+	0.588347i	$0.200221\pi$
$233$	−2.61533	+	12.0225i	−0.171336	+	0.787618i	−0.979944	+	0.199271i	$0.936143\pi$
$234$	−0.791449	+	0.113793i	−0.0517386	+	0.00743889i
$235$	3.71198	+	2.43333i	0.242143	+	0.158733i
$236$	−2.04063	+	14.1929i	−0.132834	+	0.923881i
$237$	1.73068	−	3.16950i	0.112419	−	0.205881i
$238$	0.162629	−	0.0353777i	0.0105417	−	0.00229320i
$239$	−0.814929	−	0.372166i	−0.0527134	−	0.0240734i	0.388884	−	0.921287i	$-0.372861\pi$
$239$	−0.814929	−	0.372166i	−0.0527134	−	0.0240734i	−0.441597	+	0.897213i	$0.645588\pi$
$240$	0.610516	+	2.15111i	0.0394086	+	0.138853i
$241$	9.47083	−	8.20652i	0.610070	−	0.528629i	−0.294115	−	0.955770i	$-0.595025\pi$
$241$	9.47083	−	8.20652i	0.610070	−	0.528629i	0.904185	+	0.427141i	$0.140479\pi$
$242$	1.58501	−	22.1613i	0.101888	−	1.42458i
$243$	0.877679	−	0.479249i	0.0563031	−	0.0307438i
$244$	−3.26569	+	7.15086i	−0.209064	+	0.457787i
$245$	−10.7632	−	10.9600i	−0.687638	−	0.700208i
$246$	−3.86567	+	1.13506i	−0.246466	+	0.0723689i
$247$	−3.00220	−	4.01047i	−0.191025	−	0.255180i
$248$	1.46521	+	0.546494i	0.0930408	+	0.0347024i
$249$	0.109184	+	0.759390i	0.00691924	+	0.0481244i
$250$	−8.64533	+	7.08931i	−0.546778	+	0.448367i
$251$	−14.1724	−	12.2804i	−0.894553	−	0.775135i	0.0805816	−	0.996748i	$-0.474322\pi$
$251$	−14.1724	−	12.2804i	−0.894553	−	0.775135i	−0.975135	+	0.221613i	$0.928868\pi$
$252$	−0.255176	+	0.255176i	−0.0160746	+	0.0160746i
$253$	−6.43541	−	26.8812i	−0.404591	−	1.69001i
$254$			13.0306i			0.817610i
$255$	−0.831129	+	0.610508i	−0.0520473	+	0.0382315i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−7.99838	+	10.6846i	−0.498925	+	0.666486i	−0.977347	−	0.211644i	$-0.932118\pi$
$257$	−7.99838	+	10.6846i	−0.498925	+	0.666486i	0.478421	+	0.878130i	$0.341209\pi$
$258$	2.51687	−	6.74799i	0.156693	−	0.420112i
$259$	3.17203	+	0.456069i	0.197100	+	0.0283388i
$260$	−1.18304	+	1.34057i	−0.0733688	+	0.0831386i
$261$	8.05134	+	5.17428i	0.498365	+	0.320280i
$262$	−11.0142	+	4.10808i	−0.680459	+	0.253798i
$263$	11.8502	+	21.7021i	0.730716	+	1.33821i	0.933355	+	0.358954i	$0.116866\pi$
$263$	11.8502	+	21.7021i	0.730716	+	1.33821i	−0.202639	+	0.979253i	$0.564952\pi$
$264$	−3.77429	−	4.35576i	−0.232292	−	0.268079i
$265$	3.79374	+	1.15136i	0.233047	+	0.0707277i
$266$	−2.16941	−	0.636996i	−0.133015	−	0.0390568i
$267$	1.51920	+	4.07313i	0.0929735	+	0.249272i
$268$	−2.51097	−	11.5427i	−0.153382	−	0.705086i
$269$	6.17359	+	21.0253i	0.376410	+	1.28194i	0.902199	+	0.431320i	$0.141952\pi$
$269$	6.17359	+	21.0253i	0.376410	+	1.28194i	−0.525789	+	0.850615i	$0.676230\pi$
$270$	0.800368	−	2.08792i	0.0487089	−	0.127067i
$271$	−10.1843	−	22.3005i	−0.618652	−	1.35466i	−0.916496	−	0.400045i	$-0.868995\pi$
$271$	−10.1843	−	22.3005i	−0.618652	−	1.35466i	0.297843	−	0.954615i	$-0.403733\pi$
$272$	0.369204	+	0.276383i	0.0223863	+	0.0167582i
$273$	−0.281955	−	0.0613356i	−0.0170647	−	0.00371220i
$274$	6.78470	−	7.82996i	0.409878	−	0.473025i
$275$	12.4441	−	25.9922i	0.750405	−	1.56739i
$276$	−4.08751	−	2.50843i	−0.246039	−	0.150990i
$277$	8.22454	+	8.22454i	0.494165	+	0.494165i	0.909616	−	0.415451i	$-0.136376\pi$
$277$	8.22454	+	8.22454i	0.494165	+	0.494165i	−0.415451	+	0.909616i	$0.636376\pi$
$278$	0.0692817	+	0.968685i	0.00415524	+	0.0580979i
$279$	−0.845457	−	1.31556i	−0.0506162	−	0.0787604i
$280$	−0.0648534	+	0.804326i	−0.00387573	+	0.0480677i
$281$	13.1859	−	6.02180i	0.786605	−	0.359230i	0.0187252	−	0.999825i	$-0.494039\pi$
$281$	13.1859	−	6.02180i	0.786605	−	0.359230i	0.767879	+	0.640594i	$0.221312\pi$
$282$	−1.58902	+	1.18953i	−0.0946250	+	0.0708354i
$283$	6.02193	+	3.28822i	0.357966	+	0.195464i	0.648161	−	0.761503i	$-0.275538\pi$
$283$	6.02193	+	3.28822i	0.357966	+	0.195464i	−0.290195	+	0.956968i	$0.593720\pi$
$284$	−2.03629	+	3.16853i	−0.120832	+	0.188018i
$285$	13.8846	−	1.86812i	0.822455	−	0.110658i
$286$	1.29834	−	4.42175i	0.0767726	−	0.261464i
$287$	−1.45020	−	0.103721i	−0.0856028	−	0.00612243i
$288$	−0.997452	−	0.0713392i	−0.0587754	−	0.00420370i
$289$	4.72953	−	16.1073i	0.278208	−	0.947488i
$290$	21.2095	−	2.85365i	1.24546	−	0.167572i
$291$	−0.520838	+	0.810440i	−0.0305321	+	0.0475088i
$292$	14.1847	+	7.74541i	0.830095	+	0.453266i
$293$	14.7363	−	11.0314i	0.860903	−	0.644464i	−0.0748210	−	0.997197i	$-0.523839\pi$
$293$	14.7363	−	11.0314i	0.860903	−	0.644464i	0.935724	+	0.352733i	$0.114748\pi$
$294$	6.24896	−	2.85381i	0.364447	−	0.166437i
$295$	2.57688	−	31.9590i	0.150032	−	1.86072i
$296$	4.80104	+	7.47056i	0.279055	+	0.434218i
$297$	0.411163	+	5.74882i	0.0238581	+	0.333580i
$298$	−9.94916	−	9.94916i	−0.576339	−	0.576339i
$299$	−0.0796797	−	3.83386i	−0.00460799	−	0.221718i
$300$	−1.66218	−	4.71563i	−0.0959660	−	0.272257i
$301$	1.70201	−	1.96422i	0.0981021	−	0.113216i
$302$	13.9227	+	3.02869i	0.801159	+	0.174281i
$303$	0.225519	+	0.168822i	0.0129558	+	0.00969856i
$304$	−2.60272	−	5.69917i	−0.149276	−	0.326870i
$305$	6.29191	−	16.4137i	0.360274	−	0.939845i
$306$	−0.129933	−	0.442512i	−0.00742778	−	0.0252967i
$307$	4.79327	+	22.0343i	0.273567	+	1.25757i	0.884746	+	0.466073i	$0.154332\pi$
$307$	4.79327	+	22.0343i	0.273567	+	1.25757i	−0.611180	+	0.791492i	$0.709305\pi$
$308$	−0.726848	−	1.94875i	−0.0414160	−	0.111041i
$309$	−0.991945	−	0.291261i	−0.0564298	−	0.0165693i
$310$	−3.34607	−	1.01550i	−0.190044	−	0.0576766i
$311$	−7.29352	−	8.41717i	−0.413578	−	0.477294i	0.510292	−	0.860001i	$-0.329537\pi$
$311$	−7.29352	−	8.41717i	−0.413578	−	0.477294i	−0.923870	+	0.382707i	$0.874992\pi$
$312$	−0.383202	−	0.701781i	−0.0216945	−	0.0397305i
$313$	18.8268	−	7.02202i	1.06415	−	0.396908i	0.244428	−	0.969668i	$-0.421400\pi$
$313$	18.8268	−	7.02202i	1.06415	−	0.396908i	0.819723	+	0.572760i	$0.194127\pi$
$314$	−16.6561	−	10.7042i	−0.939959	−	0.604075i
$315$	0.533933	−	0.605031i	0.0300837	−	0.0340896i
$316$	3.57447	+	0.513931i	0.201080	+	0.0289109i
$317$	4.13014	−	11.0733i	0.231972	−	0.621941i	−0.767853	−	0.640626i	$-0.778675\pi$
$317$	4.13014	−	11.0733i	0.231972	−	0.621941i	0.999825	+	0.0186846i	$0.00594785\pi$
$318$	−1.06253	+	1.41938i	−0.0595839	+	0.0795948i
$319$	−46.4039	+	29.8220i	−2.59812	+	1.66971i
$320$	−1.80213	+	1.32376i	−0.100742	+	0.0740003i
$321$		−	17.2783i		−	0.964381i
$322$	−1.06573	−	1.36364i	−0.0593906	−	0.0759924i
$323$	2.04321	−	2.04321i	0.113687	−	0.113687i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	2.45345	−	3.15659i	0.136093	−	0.175096i
$326$	2.72890	+	18.9799i	0.151140	+	1.05120i
$327$	1.82514	+	0.680742i	0.100931	+	0.0376451i
$328$	−2.41441	−	3.22527i	−0.133313	−	0.178086i
$329$	−0.687294	+	0.201808i	−0.0378918	+	0.0111260i
$330$	9.02999	+	9.19505i	0.497084	+	0.506171i
$331$	3.11744	−	6.82625i	0.171350	−	0.375204i	−0.804401	−	0.594086i	$-0.797514\pi$
$331$	3.11744	−	6.82625i	0.171350	−	0.375204i	0.975751	+	0.218882i	$0.0702410\pi$
$332$	−0.673354	+	0.367679i	−0.0369551	+	0.0201790i
$333$	0.633511	−	8.85765i	0.0347162	−	0.485396i
$334$	2.44744	−	2.12072i	0.133918	−	0.116041i
$335$	7.21185	+	25.4104i	0.394025	+	1.38832i
$336$	−0.328262	−	0.149912i	−0.0179081	−	0.00817837i
$337$	−20.7329	+	4.51016i	−1.12939	+	0.245684i	−0.738171	−	0.674613i	$-0.764310\pi$
$337$	−20.7329	+	4.51016i	−1.12939	+	0.245684i	−0.391220	+	0.920297i	$0.627947\pi$
$338$	−5.92383	+	10.8487i	−0.322214	+	0.590091i
$339$	0.567110	−	3.94433i	0.0308012	−	0.214227i
$340$	−0.862466	−	0.565375i	−0.0467738	−	0.0306618i
$341$	8.92126	−	1.28268i	0.483113	−	0.0694612i
$342$	−1.33180	+	6.12217i	−0.0720153	+	0.331049i
$343$	4.99247	−	0.357069i	0.269568	−	0.0192799i
$344$	7.20208			0.388310
$345$	9.47166	+	5.02868i	0.509937	+	0.270735i
$346$	5.02309			0.270043
$347$	34.0635	−	2.43627i	1.82863	−	0.130786i	0.885799	−	0.464069i	$-0.153611\pi$
$347$	34.0635	−	2.43627i	1.82863	−	0.130786i	0.942827	+	0.333283i	$0.108156\pi$
$348$	−2.03439	+	9.35192i	−0.109055	+	0.501316i
$349$	−18.9904	+	2.73040i	−1.01653	+	0.146155i	−0.630385	−	0.776282i	$-0.717103\pi$
$349$	−18.9904	+	2.73040i	−1.01653	+	0.146155i	−0.386146	+	0.922437i	$0.626194\pi$
$350$	0.0326821	−	1.80407i	0.00174693	−	0.0964315i
$351$	−0.113793	+	0.791449i	−0.00607383	+	0.0422444i
$352$	2.76215	−	5.05850i	0.147223	−	0.269619i
$353$	−11.9237	+	2.59384i	−0.634635	+	0.138056i	−0.518362	−	0.855161i	$-0.673458\pi$
$353$	−11.9237	+	2.59384i	−0.634635	+	0.138056i	−0.116272	+	0.993217i	$0.537095\pi$
$354$	13.0431	+	5.95658i	0.693233	+	0.316589i
$355$	4.10303	−	7.35497i	0.217766	−	0.390361i
$356$	−3.28542	+	2.84683i	−0.174127	+	0.150882i
$357$	0.0118731	−	0.166008i	0.000628393	−	0.00878608i
$358$	−20.6355	+	11.2678i	−1.09062	+	0.595524i
$359$	9.74579	−	21.3403i	0.514363	−	1.12630i	−0.457167	−	0.889381i	$-0.651136\pi$
$359$	9.74579	−	21.3403i	0.514363	−	1.12630i	0.971530	−	0.236917i	$-0.0761370\pi$
$360$	2.23598	+	0.0202515i	0.117846	+	0.00106735i
$361$	−19.4342	+	5.70639i	−1.02285	+	0.300337i
$362$	3.12305	+	4.17190i	0.164144	+	0.219270i
$363$	−20.8171	−	7.76437i	−1.09261	−	0.407524i
$364$	−0.0410649	−	0.285613i	−0.00215239	−	0.0149702i
$365$	−32.7353	−	15.3095i	−1.71344	−	0.801337i
$366$	5.94115	+	5.14803i	0.310549	+	0.269092i
$367$	0.783118	−	0.783118i	0.0408784	−	0.0408784i	−0.686372	−	0.727251i	$-0.740798\pi$
$367$	0.783118	−	0.783118i	0.0408784	−	0.0408784i	0.727251	+	0.686372i	$0.240798\pi$
$368$	0.921834	−	4.70640i	0.0480539	−	0.245338i
$369$			4.02886i			0.209734i
$370$	−11.7553	−	16.0034i	−0.611131	−	0.831976i
$371$	−0.538265	+	0.345922i	−0.0279453	+	0.0179594i
$372$	0.937154	−	1.25189i	0.0485892	−	0.0649075i
$373$	2.78539	−	7.46791i	0.144222	−	0.386674i	−0.844675	−	0.535280i	$-0.820206\pi$
$373$	2.78539	−	7.46791i	0.144222	−	0.386674i	0.988896	+	0.148606i	$0.0474788\pi$
$374$	2.63103	+	0.378285i	0.136047	+	0.0195607i
$375$	4.36648	+	10.2924i	0.225484	+	0.531498i
$376$	−1.66984	−	1.07314i	−0.0861152	−	0.0553429i
$377$	−7.17007	+	2.67430i	−0.369277	+	0.137733i
$378$	0.172948	+	0.316731i	0.00889549	+	0.0162909i
$379$	5.98350	+	6.90533i	0.307352	+	0.354703i	0.888321	−	0.459223i	$-0.151872\pi$
$379$	5.98350	+	6.90533i	0.307352	+	0.354703i	−0.580970	+	0.813925i	$0.697326\pi$
$380$	6.60252	+	12.3564i	0.338702	+	0.633869i
$381$	12.5027	+	3.67113i	0.640535	+	0.188078i
$382$	6.41179	+	17.1907i	0.328056	+	0.879552i
$383$	6.19095	+	28.4593i	0.316343	+	1.45420i	0.810964	+	0.585096i	$0.198943\pi$
$383$	6.19095	+	28.4593i	0.316343	+	1.45420i	−0.494621	+	0.869109i	$0.664693\pi$
$384$	−0.281733	−	0.959493i	−0.0143771	−	0.0489639i
$385$	1.89361	+	4.24782i	0.0965073	+	0.216489i
$386$	−1.82539	−	3.99705i	−0.0929100	−	0.203444i
$387$	−5.76556	−	4.31605i	−0.293080	−	0.219397i
$388$	−0.941356	−	0.204779i	−0.0477901	−	0.0103961i
$389$	8.80964	−	10.1669i	0.446666	−	0.515480i	−0.487109	−	0.873341i	$-0.661948\pi$
$389$	8.80964	−	10.1669i	0.446666	−	0.515480i	0.933775	+	0.357861i	$0.116494\pi$
$390$	0.952967	+	1.51280i	0.0482554	+	0.0766035i
$391$	2.18228	−	0.360195i	0.110363	−	0.0182159i
$392$	4.85766	+	4.85766i	0.245349	+	0.245349i
$393$	0.838619	+	11.7254i	0.0423027	+	0.591469i
$394$	−5.99144	−	9.32286i	−0.301844	−	0.469679i
$395$	−8.04882	−	0.648983i	−0.404980	−	0.0326539i
$396$	−5.24266	+	2.39424i	−0.263454	+	0.120315i
$397$	24.7711	−	18.5434i	1.24322	−	0.930666i	0.243990	−	0.969778i	$-0.421544\pi$
$397$	24.7711	−	18.5434i	1.24322	−	0.930666i	0.999235	+	0.0391115i	$0.0124528\pi$
$398$	−4.33486	−	2.36701i	−0.217287	−	0.118648i
$399$	−1.22239	+	1.90207i	−0.0611959	+	0.0952227i
$400$	3.83743	−	3.20532i	0.191872	−	0.160266i
$401$	−4.94425	+	16.8386i	−0.246904	+	0.840877i	0.739020	+	0.673683i	$0.235289\pi$
$401$	−4.94425	+	16.8386i	−0.246904	+	0.840877i	−0.985924	+	0.167194i	$0.946529\pi$
$402$	−11.7826	−	0.842709i	−0.587663	−	0.0420305i
$403$	1.24721	+	0.0892025i	0.0621282	+	0.00444349i
$404$	−0.0793665	+	0.270298i	−0.00394863	+	0.0134478i
$405$	−1.77785	−	1.35618i	−0.0883423	−	0.0673893i
$406$	−1.86726	+	2.90551i	−0.0926705	+	0.144198i
$407$	44.9209	+	24.5287i	2.22665	+	1.21584i
$408$	0.369204	−	0.276383i	0.0182783	−	0.0136830i
$409$	−12.0424	+	5.49957i	−0.595457	+	0.271936i	−0.690262	−	0.723560i	$-0.742505\pi$
$409$	−12.0424	+	5.49957i	−0.595457	+	0.271936i	0.0948045	+	0.995496i	$0.469777\pi$
$410$	5.83761	+	6.86156i	0.288299	+	0.338868i
$411$	−5.60132	−	8.71582i	−0.276293	−	0.429920i
$412$	−0.0737520	−	1.03119i	−0.00363350	−	0.0508030i
$413$	3.65893	+	3.65893i	0.180044	+	0.180044i
$414$	−3.55841	+	3.21523i	−0.174886	+	0.158020i
$415$	1.45152	−	0.914365i	0.0712522	−	0.0448844i
$416$	0.523619	−	0.604288i	0.0256725	−	0.0296277i
$417$	0.948966	+	0.206435i	0.0464711	+	0.0101092i
$418$	−28.9078	−	21.6401i	−1.41393	−	1.05845i
$419$	−6.49538	−	14.2229i	−0.317320	−	0.694834i	0.682013	−	0.731340i	$-0.261105\pi$
$419$	−6.49538	−	14.2229i	−0.317320	−	0.694834i	−0.999333	+	0.0365056i	$0.988377\pi$
$420$	0.753474	+	0.288831i	0.0367658	+	0.0140935i
$421$	−9.21735	−	31.3914i	−0.449226	−	1.52992i	−0.803803	−	0.594896i	$-0.797193\pi$
$421$	−9.21735	−	31.3914i	−0.449226	−	1.52992i	0.354577	−	0.935027i	$-0.384625\pi$
$422$	−3.83868	−	17.6461i	−0.186864	−	0.859000i
$423$	0.693664	+	1.85979i	0.0337271	+	0.0904259i
$424$	−1.70120	−	0.499519i	−0.0826178	−	0.0242588i
$425$	2.00355	+	1.14161i	0.0971864	+	0.0553762i
$426$	2.46650	+	2.84649i	0.119502	+	0.137913i
$427$	1.35959	+	2.48990i	0.0657952	+	0.120495i
$428$	16.1889	−	6.03815i	0.782520	−	0.291865i
$429$	−3.87685	−	2.49150i	−0.187176	−	0.120291i
$430$	−16.0731	+	1.00334i	−0.775112	+	0.0483855i
$431$	7.02890	+	1.01060i	0.338570	+	0.0486790i	0.309503	−	0.950898i	$-0.399837\pi$
$431$	7.02890	+	1.01060i	0.338570	+	0.0486790i	0.0290670	+	0.999577i	$0.490746\pi$
$432$	−0.349464	+	0.936950i	−0.0168136	+	0.0450790i
$433$	12.9175	−	17.2557i	0.620775	−	0.829258i	−0.374411	−	0.927263i	$-0.622155\pi$
$433$	12.9175	−	17.2557i	0.620775	−	0.829258i	0.995186	+	0.0980046i	$0.0312460\pi$
$434$	0.474749	−	0.305103i	0.0227887	−	0.0146454i
$435$	3.23735	−	21.1543i	0.155219	−	1.01427i
$436$			1.94796i			0.0932904i
$437$	−28.3652	−	9.91330i	−1.35689	−	0.474218i
$438$	11.4280	−	11.4280i	0.546049	−	0.546049i
$439$	16.3594	+	14.1755i	0.780794	+	0.676561i	0.951118	−	0.308827i	$-0.0999363\pi$
$439$	16.3594	+	14.1755i	0.780794	+	0.676561i	−0.170325	+	0.985388i	$0.554482\pi$
$440$	−5.45965	+	11.6740i	−0.260278	+	0.556535i
$441$	−0.977670	−	6.79985i	−0.0465557	−	0.323802i
$442$	0.345514	+	0.128870i	0.0164344	+	0.00612972i
$443$	−11.8413	−	15.8181i	−0.562597	−	0.751541i	0.425570	−	0.904926i	$-0.360074\pi$
$443$	−11.8413	−	15.8181i	−0.562597	−	0.751541i	−0.988167	+	0.153384i	$0.950983\pi$
$444$	8.52056	−	2.50186i	0.404368	−	0.118733i
$445$	6.93554	−	6.81104i	0.328776	−	0.322874i
$446$	−11.8318	+	25.9081i	−0.560253	+	1.22678i
$447$	−12.3492	+	6.74315i	−0.584095	+	0.318940i
$448$	0.0257444	−	0.359954i	0.00121631	−	0.0170062i
$449$	18.6316	−	16.1444i	0.879279	−	0.761899i	−0.0930142	−	0.995665i	$-0.529650\pi$
$449$	18.6316	−	16.1444i	0.879279	−	0.761899i	0.972293	+	0.233765i	$0.0751047\pi$
$450$	−4.99290	+	0.266304i	−0.235368	+	0.0125537i
$451$	−21.1220	−	9.64608i	−0.994595	−	0.454216i
$452$	3.89383	−	0.847050i	0.183150	−	0.0398419i
$453$	6.82847	−	12.5054i	0.320830	−	0.587555i
$454$	1.52516	−	10.6077i	0.0715793	−	0.497845i
$455$	0.131435	+	0.631688i	0.00616177	+	0.0296140i
$456$	−6.20158	+	0.891653i	−0.290416	+	0.0417555i
$457$	−3.93623	+	18.0946i	−0.184129	+	0.846428i	0.788677	+	0.614808i	$0.210766\pi$
$457$	−3.93623	+	18.0946i	−0.184129	+	0.846428i	−0.972806	+	0.231620i	$0.925597\pi$
$458$	15.3042	−	1.09458i	0.715118	−	0.0511462i
$459$	−0.461193			−0.0215267
$460$	−1.40162	+	10.6318i	−0.0653507	+	0.495711i
$461$	15.8460			0.738023			0.369011	−	0.929425i	$-0.379696\pi$
$461$	15.8460			0.738023			0.369011	+	0.929425i	$0.379696\pi$
$462$	−2.07459	+	0.148378i	−0.0965188	+	0.00690316i
$463$	−2.71946	+	12.5011i	−0.126384	+	0.580978i	0.869778	+	0.493444i	$0.164262\pi$
$463$	−2.71946	+	12.5011i	−0.126384	+	0.580978i	−0.996162	+	0.0875337i	$0.972101\pi$
$464$	−9.47323	+	1.36204i	−0.439784	+	0.0632313i
$465$	−1.91706	+	2.92443i	−0.0889018	+	0.135617i
$466$	−1.75099	+	12.1784i	−0.0811131	+	0.564154i
$467$	8.83148	−	16.1736i	0.408672	−	0.748427i	−0.589569	−	0.807718i	$-0.700702\pi$
$467$	8.83148	−	16.1736i	0.408672	−	0.748427i	0.998241	+	0.0592913i	$0.0188841\pi$
$468$	−0.781315	+	0.169965i	−0.0361163	+	0.00785662i
$469$	−3.87766	−	1.77087i	−0.179054	−	0.0817710i
$470$	3.87611	+	2.16232i	0.178792	+	0.0997403i
$471$	−14.9632	+	12.9657i	−0.689468	+	0.597428i
$472$	−1.02292	+	14.3023i	−0.0470839	+	0.658319i
$473$	36.4318	−	19.8932i	1.67513	−	0.914693i
$474$	1.50016	−	3.28489i	0.0689045	−	0.150880i
$475$	−16.4564	−	26.6562i	−0.755072	−	1.22307i
$476$	0.159691	−	0.0468894i	0.00731940	−	0.00214917i
$477$	1.06253	+	1.41938i	0.0486501	+	0.0649889i
$478$	−0.839403	−	0.313081i	−0.0383934	−	0.0143200i
$479$	1.14116	+	7.93694i	0.0521409	+	0.362648i	0.999142	+	0.0414174i	$0.0131873\pi$
$479$	1.14116	+	7.93694i	0.0521409	+	0.362648i	−0.947001	+	0.321230i	$0.895904\pi$
$480$	0.762419	+	2.10207i	0.0347995	+	0.0959461i
$481$	5.36624	+	4.64988i	0.244680	+	0.212016i
$482$	8.86126	−	8.86126i	0.403619	−	0.403619i
$483$	−1.60865	+	0.638376i	−0.0731960	+	0.0290471i
$484$		−	22.2179i		−	1.00991i
$485$	2.12937	+	0.325868i	0.0966899	+	0.0147969i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	1.82747	−	2.44121i	0.0828104	−	0.110622i	−0.757223	−	0.653156i	$-0.773444\pi$
$487$	1.82747	−	2.44121i	0.0828104	−	0.110622i	0.840033	+	0.542535i	$0.182535\pi$
$488$	−2.74723	+	7.36561i	−0.124361	+	0.333425i
$489$	18.9799	+	2.72890i	0.858303	+	0.123405i
$490$	−11.5177	−	10.1642i	−0.520316	−	0.459173i
$491$	−9.02477	−	5.79986i	−0.407282	−	0.261744i	0.320921	−	0.947106i	$-0.396008\pi$
$491$	−9.02477	−	5.79986i	−0.407282	−	0.261744i	−0.728203	+	0.685362i	$0.759644\pi$
$492$	−3.77484	+	1.40794i	−0.170183	+	0.0634750i
$493$	−2.11536	−	3.87400i	−0.0952712	−	0.174476i
$494$	−3.28066	−	3.78608i	−0.147604	−	0.170344i
$495$	11.3666	−	6.07366i	0.510892	−	0.272991i
$496$	1.50046	+	0.440575i	0.0673727	+	0.0197824i
$497$	0.474994	+	1.27351i	0.0213064	+	0.0571247i
$498$	0.163080	+	0.749666i	0.00730778	+	0.0335933i
$499$	−9.61783	−	32.7553i	−0.430553	−	1.46633i	−0.834224	−	0.551425i	$-0.814084\pi$
$499$	−9.61783	−	32.7553i	−0.430553	−	1.46633i	0.403671	−	0.914904i	$-0.367734\pi$
$500$	−8.11755	+	7.68800i	−0.363028	+	0.343818i
$501$	−1.34529	−	2.94578i	−0.0601033	−	0.131608i
$502$	−15.0124	−	11.2381i	−0.670034	−	0.501581i
$503$	−25.9822	−	5.65207i	−1.15849	−	0.252013i	−0.408053	−	0.912958i	$-0.633792\pi$
$503$	−25.9822	−	5.65207i	−1.15849	−	0.252013i	−0.750434	+	0.660945i	$0.770156\pi$
$504$	−0.236322	+	0.272730i	−0.0105266	+	0.0121483i
$505$	0.139468	−	0.614286i	0.00620626	−	0.0273354i
$506$	−8.33670	−	26.3536i	−0.370611	−	1.17156i
$507$	8.74031	+	8.74031i	0.388171	+	0.388171i
$508$	0.929590	+	12.9974i	0.0412439	+	0.576665i
$509$	23.7233	+	36.9141i	1.05152	+	1.63619i	0.721789	+	0.692114i	$0.243320\pi$
$509$	23.7233	+	36.9141i	1.05152	+	1.63619i	0.329727	+	0.944076i	$0.393043\pi$
$510$	−0.785458	+	0.668245i	−0.0347807	+	0.0295904i
$511$	5.30522	−	2.42281i	0.234689	−	0.107179i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	5.49897	+	3.00266i	0.242785	+	0.132571i
$514$	−7.21577	+	11.2280i	−0.318274	+	0.495244i
$515$	0.308252	+	2.29105i	0.0135832	+	0.100956i
$516$	2.02906	−	6.91035i	0.0893244	−	0.304211i
$517$	−11.4110	−	0.816133i	−0.501857	−	0.0358935i
$518$	3.19649	+	0.228617i	0.140446	+	0.0100449i
$519$	1.41517	−	4.81962i	0.0621190	−	0.211558i
$520$	−1.08439	+	1.42155i	−0.0475535	+	0.0623391i
$521$	−0.837441	+	1.30308i	−0.0366889	+	0.0570891i	−0.859114	−	0.511785i	$-0.828984\pi$
$521$	−0.837441	+	1.30308i	−0.0366889	+	0.0570891i	0.822425	+	0.568874i	$0.192621\pi$
$522$	8.39995	+	4.58672i	0.367656	+	0.200755i
$523$	3.63611	−	2.72196i	0.158996	−	0.119023i	−0.516817	−	0.856096i	$-0.672883\pi$
$523$	3.63611	−	2.72196i	0.158996	−	0.119023i	0.675813	+	0.737073i	$0.263792\pi$
$524$	−10.6931	+	4.88336i	−0.467129	+	0.213330i
$525$	−1.72178	−	0.539623i	−0.0751448	−	0.0235511i
$526$	13.3682	+	20.8014i	0.582883	+	0.906984i
$527$	0.0514510	+	0.719379i	0.00224124	+	0.0313367i
$528$	−4.07541	−	4.07541i	−0.177359	−	0.177359i
$529$	−13.2279	−	18.8155i	−0.575127	−	0.818064i
$530$	3.86621	+	0.877788i	0.167937	+	0.0381287i
$531$	9.38997	−	10.8366i	0.407490	−	0.470268i
$532$	−2.20933	−	0.480609i	−0.0957864	−	0.0208371i
$533$	−2.57889	−	1.93053i	−0.111704	−	0.0836206i
$534$	1.80590	+	3.95438i	0.0781491	+	0.171123i
$535$	−35.2880	+	15.7308i	−1.52563	+	0.680102i
$536$	−3.32802	−	11.3342i	−0.143749	−	0.489563i
$537$	4.99772	+	22.9741i	0.215667	+	0.991407i
$538$	7.65779	+	20.5313i	0.330151	+	0.885168i
$539$	37.9901	+	11.1549i	1.63635	+	0.480475i
$540$	0.649379	−	2.13970i	0.0279448	−	0.0920779i
$541$	0.942307	+	1.08748i	0.0405130	+	0.0467544i	0.775644	−	0.631170i	$-0.217425\pi$
$541$	0.942307	+	1.08748i	0.0405130	+	0.0467544i	−0.735131	+	0.677925i	$0.762880\pi$
$542$	−11.7493	−	21.5172i	−0.504674	−	0.924241i
$543$	4.88278	−	1.82118i	0.209540	−	0.0781544i
$544$	0.387980	+	0.249340i	0.0166345	+	0.0106904i
$545$	−0.271376	−	4.34731i	−0.0116245	−	0.186218i
$546$	−0.285613	−	0.0410649i	−0.0122231	−	0.00175742i
$547$	2.87929	−	7.71968i	0.123110	−	0.330070i	−0.860746	−	0.509035i	$-0.830002\pi$
$547$	2.87929	−	7.71968i	0.123110	−	0.330070i	0.983855	+	0.178965i	$0.0572750\pi$
$548$	6.20883	−	8.29402i	0.265228	−	0.354303i
$549$	6.61332	−	4.25012i	0.282249	−	0.181391i
$550$	10.5581	−	26.8137i	0.450198	−	1.14334i
$551$			59.9635i			2.55453i
$552$	−4.25605	−	2.21044i	−0.181149	−	0.0940826i
$553$	0.921497	−	0.921497i	0.0391860	−	0.0391860i
$554$	8.79032	+	7.61685i	0.373465	+	0.323609i
$555$	−18.6670	+	6.77049i	−0.792370	+	0.287391i
$556$	0.138210	+	0.961275i	0.00586143	+	0.0407671i
$557$	−29.8178	−	11.1215i	−1.26342	−	0.471232i	−0.373621	−	0.927581i	$-0.621884\pi$
$557$	−29.8178	−	11.1215i	−1.26342	−	0.471232i	−0.889801	+	0.456350i	$0.849157\pi$
$558$	−0.937154	−	1.25189i	−0.0396729	−	0.0529968i
$559$	5.52543	−	1.62241i	0.233701	−	0.0686207i
$560$	−0.00730824	+	0.806903i	−0.000308829	+	0.0340979i
$561$	1.10421	−	2.41788i	0.0466198	−	0.102083i
$562$	12.7227	−	6.94713i	0.536675	−	0.293047i
$563$	−2.41285	+	33.7361i	−0.101690	+	1.42181i	0.648817	+	0.760944i	$0.275264\pi$
$563$	−2.41285	+	33.7361i	−0.101690	+	1.42181i	−0.750507	+	0.660863i	$0.770191\pi$
$564$	−1.50012	+	1.29986i	−0.0631662	+	0.0547339i
$565$	−8.57194	+	2.43284i	−0.360624	+	0.102350i
$566$	6.24116	+	2.85024i	0.262336	+	0.119805i
$567$	0.352626	−	0.0767091i	0.0148089	−	0.00322148i
$568$	−1.80506	+	3.30573i	−0.0757388	+	0.138705i
$569$	−6.00761	+	41.7839i	−0.251852	+	1.75167i	0.335224	+	0.942139i	$0.391188\pi$
$569$	−6.00761	+	41.7839i	−0.251852	+	1.75167i	−0.587076	+	0.809532i	$0.699721\pi$
$570$	13.7160	−	2.85388i	0.574500	−	0.119536i
$571$	−18.6273	+	2.67820i	−0.779527	+	0.112079i	−0.520581	−	0.853813i	$-0.674284\pi$
$571$	−18.6273	+	2.67820i	−0.779527	+	0.112079i	−0.258947	+	0.965892i	$0.583375\pi$
$572$	0.979591	−	4.50311i	0.0409588	−	0.188284i
$573$	18.3008	−	1.30890i	0.764525	−	0.0546799i
$574$	−1.45391			−0.0606849
$575$	1.64687	−	23.9225i	0.0686794	−	0.997639i
$576$	−1.00000			−0.0416667
$577$	−42.6704	+	3.05185i	−1.77639	+	0.127050i	−0.920660	−	0.390366i	$-0.872348\pi$
$577$	−42.6704	+	3.05185i	−1.77639	+	0.127050i	−0.855734	+	0.517416i	$0.826894\pi$
$578$	3.56840	−	16.4037i	0.148426	−	0.682302i
$579$	−4.34941	+	0.625351i	−0.180755	+	0.0259887i
$580$	20.9519	−	4.35945i	0.869979	−	0.181016i
$581$	−0.0394015	+	0.274043i	−0.00163465	+	0.0113692i
$582$	−0.461695	+	0.845531i	−0.0191379	+	0.0350484i
$583$	−9.98529	+	2.17217i	−0.413549	+	0.0899620i
$584$	14.7011	+	6.71376i	0.608335	+	0.277817i
$585$	1.72000	−	0.488161i	0.0711133	−	0.0201830i
$586$	13.9118	−	12.0546i	0.574690	−	0.497971i
$587$	−1.26534	+	17.6918i	−0.0522263	+	0.730219i	0.902114	+	0.431498i	$0.142015\pi$
$587$	−1.26534	+	17.6918i	−0.0522263	+	0.730219i	−0.954340	+	0.298721i	$0.903440\pi$
$588$	6.02945	−	3.29233i	0.248650	−	0.135773i
$589$	4.07015	−	8.91239i	0.167708	−	0.367229i
$590$	0.290384	−	32.0614i	0.0119549	−	1.31995i
$591$	−10.6332	+	3.12219i	−0.437391	+	0.128430i
$592$	5.32175	+	7.10903i	0.218723	+	0.292179i
$593$	10.0924	+	3.76427i	0.414445	+	0.154580i	0.548032	−	0.836457i	$-0.315377\pi$
$593$	10.0924	+	3.76427i	0.414445	+	0.154580i	−0.133588	+	0.991037i	$0.542650\pi$
$594$	0.820232	+	5.70484i	0.0336545	+	0.234072i
$595$	−0.349853	+	0.126891i	−0.0143426	+	0.00520203i
$596$	−10.6336	−	9.21404i	−0.435568	−	0.377422i
$597$	−3.49240	+	3.49240i	−0.142935	+	0.142935i
$598$	−0.352981	−	3.81841i	−0.0144345	−	0.156146i
$599$		−	43.0835i		−	1.76034i	−0.474655	−	0.880172i	$-0.657427\pi$
$599$		−	43.0835i		−	1.76034i	0.474655	−	0.880172i	$-0.342573\pi$
$600$	−1.99435	−	4.58504i	−0.0814192	−	0.187183i
$601$	−25.5337	+	16.4095i	−1.04154	+	0.669357i	−0.945367	−	0.326007i	$-0.894297\pi$
$601$	−25.5337	+	16.4095i	−1.04154	+	0.669357i	−0.0961730	+	0.995365i	$0.530660\pi$
$602$	1.55755	−	2.08064i	0.0634808	−	0.0848004i
$603$	−4.12812	+	11.0679i	−0.168110	+	0.450720i
$604$	14.1032	+	2.02774i	0.573853	+	0.0825076i
$605$	3.09524	+	49.5843i	0.125840	+	2.01589i
$606$	0.236988	+	0.152303i	0.00962700	+	0.00618690i
$607$	−1.05627	+	0.393969i	−0.0428727	+	0.0159907i	−0.370809	−	0.928709i	$-0.620920\pi$
$607$	−1.05627	+	0.393969i	−0.0428727	+	0.0159907i	0.327936	+	0.944700i	$0.393647\pi$
$608$	−3.00266	−	5.49897i	−0.121774	−	0.223013i
$609$	2.26175	+	2.61020i	0.0916507	+	0.105771i
$610$	5.10494	−	16.8207i	0.206693	−	0.681052i
$611$	−1.52284	−	0.447146i	−0.0616076	−	0.0180896i
$612$	−0.161171	−	0.432115i	−0.00651493	−	0.0174672i
$613$	0.422743	+	1.94332i	0.0170744	+	0.0784900i	0.984896	−	0.173149i	$-0.0553942\pi$
$613$	0.422743	+	1.94332i	0.0170744	+	0.0784900i	−0.967821	+	0.251639i	$0.919031\pi$
$614$	6.35297	+	21.6362i	0.256385	+	0.873167i
$615$	8.22826	−	3.66802i	0.331796	−	0.147909i
$616$	−0.864018	−	1.89194i	−0.0348123	−	0.0762283i
$617$	12.1336	+	9.08309i	0.488480	+	0.365671i	0.814945	−	0.579538i	$-0.196767\pi$
$617$	12.1336	+	9.08309i	0.488480	+	0.365671i	−0.326466	+	0.945209i	$0.605858\pi$
$618$	−1.01020	−	0.219755i	−0.0406360	−	0.00883983i
$619$	5.12462	−	5.91413i	0.205976	−	0.237709i	−0.643357	−	0.765566i	$-0.722459\pi$
$619$	5.12462	−	5.91413i	0.205976	−	0.237709i	0.849333	+	0.527857i	$0.177004\pi$
$620$	−3.40999	−	0.774209i	−0.136949	−	0.0310930i
$621$	2.08248	+	4.32010i	0.0835669	+	0.173360i
$622$	−7.87541	−	7.87541i	−0.315775	−	0.315775i
$623$	0.111917	+	1.56480i	0.00448385	+	0.0626924i
$624$	−0.432290	−	0.672656i	−0.0173054	−	0.0269278i
$625$	17.0451	−	18.2884i	0.681804	−	0.731535i
$626$	18.2778	−	8.34721i	0.730529	−	0.333622i
$627$	−28.9078	+	21.6401i	−1.15447	+	0.864224i
$628$	−17.3773	−	9.48873i	−0.693430	−	0.378641i
$629$	−2.21421	+	3.44537i	−0.0882862	+	0.137376i
$630$	0.489410	−	0.641580i	0.0194986	−	0.0255612i
$631$	−9.91996	+	33.7843i	−0.394907	+	1.34493i	0.486956	+	0.873426i	$0.338107\pi$
$631$	−9.91996	+	33.7843i	−0.394907	+	1.34493i	−0.881864	+	0.471504i	$0.843711\pi$
$632$	3.60202	+	0.257622i	0.143281	+	0.0102476i
$633$	−18.0128	−	1.28830i	−0.715945	−	0.0512054i
$634$	3.32966	−	11.3398i	0.132238	−	0.450360i
$635$	−3.88529	−	28.8770i	−0.154183	−	1.14595i
$636$	−0.958569	+	1.49156i	−0.0380097	+	0.0591443i
$637$	4.82108	+	2.63251i	0.191018	+	0.104304i
$638$	−44.1582	+	33.0564i	−1.74824	+	1.30872i
$639$	3.42608	−	1.56464i	0.135533	−	0.0618961i
$640$	−1.70310	+	1.44895i	−0.0673209	+	0.0572747i
$641$	15.3426	+	23.8735i	0.605995	+	0.942947i	0.999719	+	0.0237183i	$0.00755046\pi$
$641$	15.3426	+	23.8735i	0.605995	+	0.942947i	−0.393723	+	0.919229i	$0.628813\pi$
$642$	−1.23262	−	17.2343i	−0.0486477	−	0.680183i
$643$	−10.7529	−	10.7529i	−0.424052	−	0.424052i	0.462544	−	0.886596i	$-0.346937\pi$
$643$	−10.7529	−	10.7529i	−0.424052	−	0.424052i	−0.886596	+	0.462544i	$0.846937\pi$
$644$	−1.16029	−	1.28413i	−0.0457219	−	0.0506019i
$645$	−3.56561	+	15.7047i	−0.140396	+	0.618371i
$646$	1.89225	−	2.18377i	0.0744494	−	0.0859192i
$647$	20.3844	+	4.43435i	0.801393	+	0.174332i	0.594568	−	0.804045i	$-0.297323\pi$
$647$	20.3844	+	4.43435i	0.801393	+	0.174332i	0.206826	+	0.978378i	$0.433687\pi$
$648$	0.800541	+	0.599278i	0.0314482	+	0.0235419i
$649$	34.3308	+	75.1739i	1.34760	+	2.95083i
$650$	2.22201	−	3.32358i	0.0871545	−	0.130361i
$651$	−0.158992	−	0.541476i	−0.00623137	−	0.0212221i
$652$	4.07597	+	18.7369i	0.159627	+	0.733794i
$653$	0.796548	+	2.13563i	0.0311713	+	0.0835736i	0.951603	−	0.307330i	$-0.0994354\pi$
$653$	0.796548	+	2.13563i	0.0311713	+	0.0835736i	−0.920432	+	0.390903i	$0.872163\pi$
$654$	1.86905	+	0.548804i	0.0730858	+	0.0214599i
$655$	23.1836	−	12.3880i	0.905860	−	0.484039i
$656$	−2.63834	−	3.04481i	−0.103010	−	0.118880i
$657$	−7.74541	−	14.1847i	−0.302177	−	0.553396i
$658$	−0.671147	+	0.250325i	−0.0261640	+	0.00975867i
$659$	12.3112	+	7.91193i	0.479577	+	0.308205i	0.758001	−	0.652253i	$-0.226176\pi$
$659$	12.3112	+	7.91193i	0.479577	+	0.308205i	−0.278425	+	0.960458i	$0.589812\pi$
$660$	9.66295	+	8.52743i	0.376130	+	0.331930i
$661$	−10.8384	−	1.55832i	−0.421564	−	0.0606118i	−0.0717316	−	0.997424i	$-0.522853\pi$
$661$	−10.8384	−	1.55832i	−0.421564	−	0.0606118i	−0.349833	+	0.936812i	$0.613762\pi$
$662$	2.62252	−	7.03125i	0.101927	−	0.273277i
$663$	0.220992	−	0.295211i	0.00858263	−	0.0114651i
$664$	−0.645409	+	0.414779i	−0.0250467	+	0.0160965i
$665$	4.99756	+	0.764800i	0.193797	+	0.0296577i
$666$		−	8.88027i		−	0.344104i
$667$	−26.7369	+	37.3078i	−1.03526	+	1.44456i
$668$	2.28992	−	2.28992i	0.0885996	−	0.0885996i
$669$	21.5252	+	18.6517i	0.832212	+	0.721116i
$670$	9.00623	+	24.8312i	0.347941	+	0.959312i
$671$	6.44806	+	44.8472i	0.248925	+	1.73131i
$672$	−0.338120	−	0.126112i	−0.0130433	−	0.00486488i
$673$	−11.2698	−	15.0547i	−0.434420	−	0.580317i	0.528896	−	0.848687i	$-0.322606\pi$
$673$	−11.2698	−	15.0547i	−0.434420	−	0.580317i	−0.963316	+	0.268369i	$0.913515\pi$
$674$	−20.3583	+	5.97773i	−0.784172	+	0.230254i
$675$	−1.15115	+	4.86568i	−0.0443076	+	0.187280i
$676$	−5.13480	+	11.2437i	−0.197492	+	0.432448i
$677$	−16.6538	+	9.09369i	−0.640059	+	0.349499i	−0.766283	−	0.642503i	$-0.777896\pi$
$677$	−16.6538	+	9.09369i	−0.640059	+	0.349499i	0.126224	+	0.992002i	$0.459714\pi$
$678$	0.284279	−	3.97474i	0.0109177	−	0.152649i
$679$	−0.262740	+	0.227666i	−0.0100830	+	0.00873700i
$680$	−0.900602	−	0.502407i	−0.0345365	−	0.0192664i
$681$	−9.74834	−	4.45192i	−0.373557	−	0.170598i
$682$	8.80702	−	1.91585i	0.337238	−	0.0733617i
$683$	0.195824	−	0.358624i	0.00749299	−	0.0137224i	−0.873906	−	0.486096i	$-0.838421\pi$
$683$	0.195824	−	0.358624i	0.00749299	−	0.0137224i	0.881399	+	0.472373i	$0.156603\pi$
$684$	−0.891653	+	6.20158i	−0.0340932	+	0.237123i
$685$	−12.7009	+	19.3749i	−0.485277	+	0.740278i
$686$	4.95428	−	0.712318i	0.189155	−	0.0271964i
$687$	3.26145	−	14.9926i	0.124432	−	0.572005i
$688$	7.18373	−	0.513791i	0.273877	−	0.0195881i
$689$	−1.41769			−0.0540096
$690$	9.80627	+	4.34017i	0.373318	+	0.165227i
$691$	−14.7818			−0.562327			−0.281163	−	0.959660i	$-0.590720\pi$
$691$	−14.7818			−0.562327			−0.281163	+	0.959660i	$0.590720\pi$
$692$	5.01029	−	0.358343i	0.190463	−	0.0136222i
$693$	−0.442113	+	2.03236i	−0.0167945	+	0.0772030i
$694$	33.8029	−	4.86013i	1.28314	−	0.184488i
$695$	−0.442365	−	2.12605i	−0.0167799	−	0.0806455i
$696$	−1.36204	+	9.47323i	−0.0516282	+	0.359082i
$697$	0.890485	−	1.63080i	0.0337295	−	0.0617710i
$698$	−18.7472	+	4.07821i	−0.709592	+	0.154362i
$699$	11.1918	+	5.11112i	0.423312	+	0.193320i
$700$	−0.0961020	−	1.80180i	−0.00363231	−	0.0681018i
$701$	−3.98777	+	3.45542i	−0.150616	+	0.130509i	−0.726909	−	0.686733i	$-0.759044\pi$
$701$	−3.98777	+	3.45542i	−0.150616	+	0.130509i	0.576293	+	0.817243i	$0.304499\pi$
$702$	−0.0570419	+	0.797550i	−0.00215291	+	0.0301016i
$703$	48.8323	−	26.6645i	1.84175	−	1.00567i
$704$	2.39424	−	5.24266i	0.0902365	−	0.197590i
$705$	3.16676	−	3.10991i	0.119267	−	0.117126i
$706$	−11.7083	+	3.43786i	−0.440647	+	0.129386i
$707$	0.0609232	+	0.0813839i	0.00229125	+	0.00306076i
$708$	13.4348	+	5.01092i	0.504911	+	0.188322i
$709$	6.69562	+	46.5691i	0.251459	+	1.74894i	0.589465	+	0.807794i	$0.299339\pi$
$709$	6.69562	+	46.5691i	0.251459	+	1.74894i	−0.338006	+	0.941144i	$0.609752\pi$
$710$	3.56787	−	7.62894i	0.133900	−	0.286309i
$711$	−2.72918	−	2.36485i	−0.102352	−	0.0886888i
$712$	−3.07395	+	3.07395i	−0.115201	+	0.115201i
$713$	6.50627	−	3.73025i	0.243662	−	0.139699i
$714$		−	0.166432i		−	0.00622857i
$715$	−1.55884	+	10.1862i	−0.0582972	+	0.380941i
$716$	−19.7791	+	12.7112i	−0.739179	+	0.475042i
$717$	−0.536886	+	0.717196i	−0.0200504	+	0.0267842i
$718$	8.19856	−	21.9812i	0.305968	−	0.820331i
$719$	4.83162	+	0.694681i	0.180189	+	0.0259072i	0.231819	−	0.972759i	$-0.425532\pi$
$719$	4.83162	+	0.694681i	0.180189	+	0.0259072i	−0.0516297	+	0.998666i	$0.516442\pi$
$720$	2.23172	−	0.139313i	0.0831714	−	0.00519188i
$721$	−0.313853	−	0.201701i	−0.0116885	−	0.00751175i
$722$	−18.9776	+	7.07827i	−0.706273	+	0.263426i
$723$	−6.00581	−	10.9988i	−0.223358	−	0.409050i
$724$	3.41271	+	3.93848i	0.126832	+	0.146372i
$725$	−46.1515	+	12.6480i	−1.71402	+	0.469733i
$726$	−21.3180	−	6.25952i	−0.791184	−	0.232312i
$727$	−0.680832	−	1.82538i	−0.0252507	−	0.0676996i	0.923713	−	0.383086i	$-0.125139\pi$
$727$	−0.680832	−	1.82538i	−0.0252507	−	0.0676996i	−0.948963	+	0.315386i	$0.897866\pi$
$728$	−0.0613356	−	0.281955i	−0.00227325	−	0.0104500i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	−33.7441	−	12.9352i	−1.24892	−	0.478753i
$731$	1.37982	+	3.02139i	0.0510346	+	0.111750i
$732$	6.29327	+	4.71108i	0.232606	+	0.174127i
$733$	−48.5191	−	10.5547i	−1.79210	−	0.389846i	−0.811260	−	0.584686i	$-0.801218\pi$
$733$	−48.5191	−	10.5547i	−1.79210	−	0.389846i	−0.980835	+	0.194839i	$0.937581\pi$
$734$	0.725255	−	0.836989i	0.0267697	−	0.0308938i
$735$	−12.9974	+	8.18755i	−0.479417	+	0.302002i
$736$	0.583734	−	4.76017i	0.0215167	−	0.175462i
$737$	−48.1416	−	48.1416i	−1.77332	−	1.77332i
$738$	0.287416	+	4.01860i	0.0105799	+	0.147927i
$739$	17.4551	+	27.1607i	0.642098	+	0.999123i	0.997913	+	0.0645672i	$0.0205667\pi$
$739$	17.4551	+	27.1607i	0.642098	+	0.999123i	−0.355816	+	0.934556i	$0.615797\pi$
$740$	−12.8671	−	15.1240i	−0.473002	−	0.555969i
$741$	−4.55698	+	2.08110i	−0.167405	+	0.0764513i
$742$	−0.512215	+	0.383440i	−0.0188040	+	0.0140765i
$743$	0.866378	+	0.473078i	0.0317843	+	0.0173556i	0.495063	−	0.868857i	$-0.335145\pi$
$743$	0.866378	+	0.473078i	0.0317843	+	0.0173556i	−0.463278	+	0.886213i	$0.653327\pi$
$744$	0.845457	−	1.31556i	0.0309960	−	0.0482307i
$745$	25.0148	+	19.0818i	0.916473	+	0.699104i
$746$	2.24554	−	7.64759i	0.0822149	−	0.279998i
$747$	0.765244	+	0.0547313i	0.0279988	+	0.00200251i
$748$	2.65132	+	0.189626i	0.0969417	+	0.00693341i
$749$	1.75668	−	5.98270i	0.0641877	−	0.218603i
$750$	5.08960	+	9.95469i	0.185846	+	0.363494i
$751$	−8.09436	+	12.5951i	−0.295367	+	0.459600i	−0.956942	−	0.290279i	$-0.906252\pi$
$751$	−8.09436	+	12.5951i	−0.295367	+	0.459600i	0.661575	+	0.749879i	$0.269888\pi$
$752$	−1.74214	−	0.951279i	−0.0635292	−	0.0346896i
$753$	−15.0124	+	11.2381i	−0.547080	+	0.409539i
$754$	−6.96102	+	3.17899i	−0.253505	+	0.115772i
$755$	−31.7570	−	2.56060i	−1.15576	−	0.0931896i
$756$	0.195103	+	0.303586i	0.00709582	+	0.0110413i
$757$	2.26887	+	31.7229i	0.0824634	+	1.15299i	0.855213	+	0.518277i	$0.173427\pi$
$757$	2.26887	+	31.7229i	0.0824634	+	1.15299i	−0.772749	+	0.634712i	$0.781119\pi$
$758$	6.46087	+	6.46087i	0.234669	+	0.234669i
$759$	−27.6348	+	0.574338i	−1.00308	+	0.0208472i
$760$	7.46719	+	11.8539i	0.270864	+	0.429985i
$761$	2.49445	−	2.87875i	0.0904238	−	0.104355i	−0.708734	−	0.705475i	$-0.750734\pi$
$761$	2.49445	−	2.87875i	0.0904238	−	0.104355i	0.799158	+	0.601121i	$0.205279\pi$
$762$	12.7328	+	2.76985i	0.461260	+	0.100341i
$763$	0.562753	+	0.421272i	0.0203730	+	0.0152511i
$764$	7.62183	+	16.6895i	0.275748	+	0.603804i
$765$	0.419887	+	0.941908i	0.0151811	+	0.0340548i
$766$	8.20544	+	27.9452i	0.296475	+	1.00970i
$767$	2.43710	+	11.2032i	0.0879986	+	0.404523i
$768$	−0.349464	−	0.936950i	−0.0126102	−	0.0338093i
$769$	10.7400	+	3.15355i	0.387294	+	0.113720i	0.469582	−	0.882889i	$-0.344405\pi$
$769$	10.7400	+	3.15355i	0.387294	+	0.113720i	−0.0822881	+	0.996609i	$0.526223\pi$
$770$	2.19182	+	4.10191i	0.0789877	+	0.147823i
$771$	8.74023	+	10.0868i	0.314772	+	0.363266i
$772$	−2.10589	−	3.85664i	−0.0757925	−	0.138804i
$773$	−27.1070	+	10.1104i	−0.974971	+	0.363645i	−0.785924	−	0.618323i	$-0.787812\pi$
$773$	−27.1070	+	10.1104i	−0.974971	+	0.363645i	−0.189047	+	0.981968i	$0.560540\pi$
$774$	−6.05878	−	3.89374i	−0.217778	−	0.139958i
$775$	7.71802	+	1.25276i	0.277239	+	0.0450006i
$776$	−0.953566	−	0.137102i	−0.0342310	−	0.00492168i
$777$	1.11991	−	3.00260i	0.0401766	−	0.107718i
$778$	8.06189	−	10.7694i	0.289033	−	0.386103i
$779$	−21.2351	+	13.6470i	−0.760828	+	0.488954i
$780$	1.05846	+	1.44096i	0.0378990	+	0.0515946i
$781$			21.7079i			0.776769i
$782$	2.15102	−	0.514960i	0.0769204	−	0.0184149i
$783$	6.76747	−	6.76747i	0.241850	−	0.241850i
$784$	5.19183	+	4.49874i	0.185422	+	0.160669i
$785$	40.1033	+	18.7553i	1.43135	+	0.669407i
$786$	1.67296	+	11.6357i	0.0596726	+	0.415032i
$787$	0.229077	+	0.0854413i	0.00816571	+	0.00304565i	0.353544	−	0.935418i	$-0.384977\pi$
$787$	0.229077	+	0.0854413i	0.00816571	+	0.00304565i	−0.345378	+	0.938464i	$0.612249\pi$
$788$	−6.64126	−	8.87168i	−0.236585	−	0.316041i
$789$	23.7251	−	6.96631i	0.844634	−	0.248007i
$790$	−8.07461	−	0.0731329i	−0.287282	−	0.00260195i
$791$	0.597384	−	1.30809i	0.0212405	−	0.0465103i
$792$	−5.05850	+	2.76215i	−0.179746	+	0.0981488i
$793$	−0.448422	+	6.26976i	−0.0159239	+	0.222646i
$794$	23.3851	−	20.2633i	0.829906	−	0.719117i
$795$	1.93147	−	3.46230i	0.0685021	−	0.122795i
$796$	−4.49268	−	2.05174i	−0.159239	−	0.0727219i
$797$	−27.8650	+	6.06165i	−0.987027	+	0.214715i	−0.676976	−	0.736005i	$-0.736710\pi$
$797$	−27.8650	+	6.06165i	−0.987027	+	0.214715i	−0.310051	+	0.950720i	$0.600346\pi$
$798$	−1.08358	+	1.98443i	−0.0383583	+	0.0702480i
$799$	0.130281	−	0.906122i	0.00460900	−	0.0320563i
$800$	3.59899	−	3.47092i	0.127244	−	0.122715i
$801$	4.30298	−	0.618675i	0.152038	−	0.0218598i
$802$	−3.73040	+	17.1484i	−0.131725	+	0.605530i
$803$	92.9099	−	6.64504i	3.27872	−	0.234499i
$804$	−11.8127			−0.416602
$805$	2.76835	+	2.70419i	0.0975714	+	0.0953101i
$806$	1.25040			0.0440435
$807$	21.8571	−	1.56325i	0.769407	−	0.0550290i
$808$	−0.0598815	+	0.275271i	−0.00210662	+	0.00968399i
$809$	−36.6470	+	5.26905i	−1.28844	+	0.185250i	−0.752267	−	0.658858i	$-0.771040\pi$
$809$	−36.6470	+	5.26905i	−1.28844	+	0.185250i	−0.536173	+	0.844108i	$0.680131\pi$
$810$	−1.87007	−	1.22590i	−0.0657077	−	0.0430736i
$811$	−0.256736	+	1.78564i	−0.00901521	+	0.0627022i	−0.993832	−	0.110892i	$-0.964629\pi$
$811$	−0.256736	+	1.78564i	−0.00901521	+	0.0627022i	0.984817	+	0.173595i	$0.0555382\pi$
$812$	−1.65522	+	3.03132i	−0.0580870	+	0.106378i
$813$	−23.9557	+	5.21124i	−0.840163	+	0.182766i
$814$	46.5563	+	21.2615i	1.63180	+	0.745217i
$815$	−11.7067	−	41.2478i	−0.410069	−	1.44485i
$816$	0.348547	−	0.302017i	0.0122016	−	0.0105727i
$817$	3.21908	−	45.0086i	0.112621	−	1.57465i
$818$	−11.6194	+	6.34465i	−0.406262	+	0.221836i
$819$	−0.119868	+	0.262474i	−0.00418852	+	0.00917158i
$820$	6.31224	+	6.42762i	0.220433	+	0.224462i
$821$	29.0566	−	8.53179i	1.01408	−	0.297762i	0.267860	−	0.963458i	$-0.413684\pi$
$821$	29.0566	−	8.53179i	1.01408	−	0.297762i	0.746223	+	0.665696i	$0.231865\pi$
$822$	−6.20883	−	8.29402i	−0.216558	−	0.289287i
$823$	−21.5659	−	8.04368i	−0.751741	−	0.280385i	−0.0557593	−	0.998444i	$-0.517758\pi$
$823$	−21.5659	−	8.04368i	−0.751741	−	0.280385i	−0.695982	+	0.718059i	$0.745031\pi$
$824$	−0.147128	−	1.02330i	−0.00512545	−	0.0356483i
$825$	−22.7530	−	17.6847i	−0.792158	−	0.615702i
$826$	3.91064	+	3.38858i	0.136068	+	0.117904i
$827$	25.8212	−	25.8212i	0.897893	−	0.897893i	−0.0973569	−	0.995250i	$-0.531039\pi$
$827$	25.8212	−	25.8212i	0.897893	−	0.897893i	0.995250	+	0.0973569i	$0.0310388\pi$
$828$	−3.31997	+	3.46090i	−0.115377	+	0.120274i
$829$		−	30.3005i		−	1.05238i	−0.850367	−	0.526190i	$-0.823620\pi$
$829$		−	30.3005i		−	1.05238i	0.850367	−	0.526190i	$-0.176380\pi$
$830$	1.38259	−	1.01559i	0.0479904	−	0.0352515i
$831$	9.78484	−	6.28833i	0.339432	−	0.218140i
$832$	0.479175	−	0.640103i	0.0166124	−	0.0221916i
$833$	−1.10720	+	2.96853i	−0.0383624	+	0.102853i
$834$	0.961275	+	0.138210i	0.0332862	+	0.00478584i
$835$	−4.79145	+	5.42948i	−0.165815	+	0.187895i
$836$	−30.3780	−	19.5227i	−1.05064	−	0.675208i
$837$	−1.46521	+	0.546494i	−0.0506450	+	0.0188896i
$838$	−7.49348	−	13.7233i	−0.258858	−	0.474063i
$839$	5.47449	+	6.31790i	0.189000	+	0.218118i	0.842339	−	0.538947i	$-0.181178\pi$
$839$	5.47449	+	6.31790i	0.189000	+	0.218118i	−0.653339	+	0.757065i	$0.726632\pi$
$840$	0.772159	+	0.234343i	0.0266420	+	0.00808561i
$841$	60.0616	+	17.6357i	2.07109	+	0.608127i
$842$	−11.4333	−	30.6539i	−0.394017	−	1.05640i
$843$	−3.08132	−	14.1646i	−0.106126	−	0.487854i
$844$	−5.08776	−	17.3273i	−0.175128	−	0.596431i
$845$	9.89308	−	25.8081i	0.340332	−	0.887825i
$846$	0.824573	+	1.80556i	0.0283494	+	0.0620765i
$847$	−6.41862	−	4.80492i	−0.220546	−	0.165099i
$848$	−1.73250	−	0.376883i	−0.0594945	−	0.0129422i
$849$	4.49313	−	5.18534i	0.154204	−	0.177961i
$850$	2.07989	+	0.995769i	0.0713395	+	0.0341546i
$851$	42.2716	+	5.18372i	1.44905	+	0.177696i
$852$	2.66328	+	2.66328i	0.0912424	+	0.0912424i
$853$	1.33623	+	18.6830i	0.0457518	+	0.639693i	0.967656	+	0.252275i	$0.0811786\pi$
$853$	1.33623	+	18.6830i	0.0457518	+	0.639693i	−0.921904	+	0.387419i	$0.873367\pi$
$854$	1.53375	+	2.38657i	0.0524840	+	0.0816667i
$855$	1.12596	−	13.9644i	0.0385071	−	0.477574i
$856$	15.7169	−	7.17767i	0.537193	−	0.245328i
$857$	−16.7623	+	12.5481i	−0.572590	+	0.428636i	−0.845939	−	0.533279i	$-0.820960\pi$
$857$	−16.7623	+	12.5481i	−0.572590	+	0.428636i	0.273349	+	0.961915i	$0.411869\pi$
$858$	−4.04472	−	2.20858i	−0.138084	−	0.0753998i
$859$	24.7389	−	38.4944i	0.844080	−	1.31341i	−0.103739	−	0.994605i	$-0.533081\pi$
$859$	24.7389	−	38.4944i	0.844080	−	1.31341i	0.947819	−	0.318809i	$-0.103283\pi$
$860$	−15.9605	+	2.14742i	−0.544250	+	0.0732266i
$861$	−0.409613	+	1.39501i	−0.0139596	+	0.0475420i
$862$	7.08308	+	0.506592i	0.241251	+	0.0172546i
$863$	9.78140	+	0.699579i	0.332963	+	0.0238140i	0.236820	−	0.971554i	$-0.423895\pi$
$863$	9.78140	+	0.699579i	0.332963	+	0.0238140i	0.0961428	+	0.995368i	$0.469349\pi$
$864$	−0.281733	+	0.959493i	−0.00958474	+	0.0326426i
$865$	−11.1317	+	1.49772i	−0.378488	+	0.0509240i
$866$	11.6536	−	18.1333i	0.396004	−	0.616195i
$867$	−14.7339	−	8.04530i	−0.500388	−	0.273233i
$868$	0.451774	−	0.338194i	0.0153342	−	0.0114790i
$869$	18.9324	−	8.64616i	0.642239	−	0.293301i
$870$	1.71997	−	21.3314i	0.0583123	−	0.723201i
$871$	−5.10651	−	7.94589i	−0.173028	−	0.269236i
$872$	0.138966	+	1.94300i	0.00470598	+	0.0657982i
$873$	0.681207	+	0.681207i	0.0230554	+	0.0230554i
$874$	−29.0001	−	7.86450i	−0.980944	−	0.266021i
$875$	0.465487	+	4.00774i	0.0157363	+	0.135486i
$876$	10.5836	−	12.2141i	0.357586	−	0.412676i
$877$	−35.4903	−	7.72043i	−1.19842	−	0.260700i	−0.431303	−	0.902207i	$-0.641946\pi$
$877$	−35.4903	−	7.72043i	−1.19842	−	0.260700i	−0.767118	+	0.641507i	$0.778310\pi$
$878$	17.3290	+	12.9723i	0.584826	+	0.437796i
$879$	−7.64692	−	16.7444i	−0.257924	−	0.564775i
$880$	−4.61292	+	12.0337i	−0.155502	+	0.405657i
$881$	−0.987804	−	3.36415i	−0.0332800	−	0.113341i	0.941178	−	0.337911i	$-0.109720\pi$
$881$	−0.987804	−	3.36415i	−0.0332800	−	0.113341i	−0.974458	+	0.224570i	$0.927902\pi$
$882$	−1.46027	−	6.71277i	−0.0491700	−	0.226031i
$883$	−4.99366	−	13.3885i	−0.168050	−	0.450560i	0.825438	−	0.564492i	$-0.190928\pi$
$883$	−4.99366	−	13.3885i	−0.168050	−	0.450560i	−0.993488	+	0.113932i	$0.963655\pi$
$884$	0.353827	+	0.103893i	0.0119005	+	0.00349430i
$885$	−30.6809	−	9.31136i	−1.03133	−	0.312998i
$886$	−12.9396	−	14.9331i	−0.434713	−	0.501686i
$887$	9.85754	+	18.0527i	0.330984	+	0.606152i	0.989182	−	0.146693i	$-0.0468629\pi$
$887$	9.85754	+	18.0527i	0.330984	+	0.606152i	−0.658198	+	0.752845i	$0.728681\pi$
$888$	8.32037	−	3.10334i	0.279213	−	0.104141i
$889$	3.95589	+	2.54230i	0.132676	+	0.0852659i
$890$	6.43198	−	7.28846i	0.215600	−	0.244310i
$891$	5.70484	+	0.820232i	0.191119	+	0.0274788i
$892$	−9.95341	+	26.6861i	−0.333265	+	0.893517i
$893$	−7.45281	+	9.95579i	−0.249399	+	0.333158i
$894$	−11.8366	+	7.60694i	−0.395876	+	0.254414i
$895$	42.3706	−	31.1235i	1.41629	−	1.04034i
$896$		−	0.360873i		−	0.0120559i
$897$	−3.76318	−	0.737087i	−0.125649	−	0.0246106i
$898$	17.4324	−	17.4324i	0.581726	−	0.581726i
$899$	−11.3110	−	9.80106i	−0.377244	−	0.326884i
$900$	−4.96118	+	0.621815i	−0.165373	+	0.0207272i
$901$	−0.116372	−	0.809384i	−0.00387691	−	0.0269645i
$902$	−21.7563	−	8.11468i	−0.724406	−	0.270189i
$903$	−1.55755	−	2.08064i	−0.0518319	−	0.0692393i
$904$	3.82348	−	1.12267i	0.127167	−	0.0373396i
$905$	−8.16491	−	8.31416i	−0.271411	−	0.276372i
$906$	5.91895	−	12.9607i	0.196644	−	0.430590i
$907$	1.83126	−	0.999946i	0.0608061	−	0.0332027i	−0.448558	−	0.893754i	$-0.648062\pi$
$907$	1.83126	−	0.999946i	0.0608061	−	0.0332027i	0.509364	+	0.860551i	$0.329881\pi$
$908$	0.764527	−	10.6895i	0.0253717	−	0.354743i
$909$	0.212901	−	0.184480i	0.00706149	−	0.00611882i
$910$	0.176164	+	0.620702i	0.00583979	+	0.0205761i
$911$	10.5643	+	4.82453i	0.350009	+	0.159844i	0.582659	−	0.812717i	$-0.302012\pi$
$911$	10.5643	+	4.82453i	0.350009	+	0.159844i	−0.232650	+	0.972561i	$0.574740\pi$
$912$	−6.12217	+	1.33180i	−0.202725	+	0.0441002i
$913$	−2.11912	+	3.88088i	−0.0701326	+	0.128438i
$914$	−2.63535	+	18.3293i	−0.0871697	+	0.606278i
$915$	−14.7011	−	9.63710i	−0.486005	−	0.318593i
$916$	15.1871	−	2.18358i	0.501796	−	0.0721474i
$917$	−0.901744	+	4.14525i	−0.0297782	+	0.136888i
$918$	−0.460018	+	0.0329012i	−0.0151829	+	0.00108590i
$919$	−22.1615			−0.731042			−0.365521	−	0.930803i	$-0.619109\pi$
$919$	−22.1615			−0.731042			−0.365521	+	0.930803i	$0.619109\pi$
$920$	−0.639580	+	10.7047i	−0.0210863	+	0.352924i
$921$	22.5497			0.743036
$922$	15.8056	−	1.13044i	0.520531	−	0.0372291i
$923$	−0.640162	+	2.94278i	−0.0210712	+	0.0968627i
$924$	−2.05872	+	0.295999i	−0.0677270	+	0.00973767i
$925$	30.8227	+	31.9600i	1.01344	+	1.05084i
$926$	−1.82071	+	12.6633i	−0.0598322	+	0.416142i
$927$	−0.495458	+	0.907363i	−0.0162730	+	0.0298017i
$928$	−9.35192	+	2.03439i	−0.306992	+	0.0667820i
$929$	−16.3631	−	7.47279i	−0.536856	−	0.245174i	0.128487	−	0.991711i	$-0.458988\pi$
$929$	−16.3631	−	7.47279i	−0.536856	−	0.245174i	−0.665344	+	0.746537i	$0.731715\pi$
$930$	−1.70355	+	3.05374i	−0.0558617	+	0.100136i
$931$	32.5286	−	28.1862i	1.06608	−	0.923766i
$932$	−0.877732	+	12.2723i	−0.0287511	+	0.401992i
$933$	−9.77516	+	5.33764i	−0.320025	+	0.174747i
$934$	7.65516	−	16.7625i	0.250485	−	0.548485i
$935$	−5.94342	−	0.0538304i	−0.194371	−	0.00176044i
$936$	−0.767199	+	0.225270i	−0.0250767	+	0.00736318i
$937$	6.90744	+	9.22726i	0.225656	+	0.301442i	0.899053	−	0.437840i	$-0.144256\pi$
$937$	6.90744	+	9.22726i	0.225656	+	0.301442i	−0.673397	+	0.739281i	$0.735165\pi$
$938$	−3.99411	−	1.48973i	−0.130412	−	0.0486413i
$939$	−2.85963	−	19.8891i	−0.0933204	−	0.649058i
$940$	4.02049	+	1.88029i	0.131134	+	0.0613283i
$941$	−28.4956	−	24.6916i	−0.928931	−	0.804923i	0.0521264	−	0.998640i	$-0.483400\pi$
$941$	−28.4956	−	24.6916i	−0.928931	−	0.804923i	−0.981057	+	0.193717i	$0.937946\pi$
$942$	−14.0001	+	14.0001i	−0.456149	+	0.456149i
$943$	−19.2970	−	0.977643i	−0.628397	−	0.0318364i
$944$			14.3389i			0.466691i
$945$	−0.477709	−	0.650339i	−0.0155399	−	0.0211555i
$946$	34.9198	−	22.4416i	1.13534	−	0.729639i
$947$	1.64668	−	2.19970i	0.0535099	−	0.0714808i	−0.772988	−	0.634421i	$-0.781239\pi$
$947$	1.64668	−	2.19970i	0.0535099	−	0.0714808i	0.826498	+	0.562940i	$0.190330\pi$
$948$	1.26199	−	3.38354i	0.0409877	−	0.109892i
$949$	12.7911	+	1.83908i	0.415215	+	0.0596989i
$950$	−18.3161	−	25.4143i	−0.594253	−	0.824549i
$951$	−9.94236	−	6.38956i	−0.322403	−	0.207196i
$952$	0.155939	−	0.0581621i	0.00505400	−	0.00188504i
$953$	18.3201	+	33.5507i	0.593446	+	1.08682i	0.985946	+	0.167063i	$0.0534284\pi$
$953$	18.3201	+	33.5507i	0.593446	+	1.08682i	−0.392500	+	0.919752i	$0.628390\pi$
$954$	1.16108	+	1.33996i	0.0375915	+	0.0433829i
$955$	−19.3349	−	36.1845i	−0.625662	−	1.17090i
$956$	−0.859599	−	0.252401i	−0.0278014	−	0.00816323i
$957$	19.2766	+	51.6825i	0.623124	+	1.67066i
$958$	1.70447	+	7.83530i	0.0550688	+	0.253147i
$959$	−1.05335	−	3.58738i	−0.0340145	−	0.115843i
$960$	0.910437	+	2.04233i	0.0293842	+	0.0659159i
$961$	−11.8620	−	25.9741i	−0.382644	−	0.837874i
$962$	5.68429	+	4.25521i	0.183269	+	0.137193i
$963$	−16.8834	−	3.67277i	−0.544061	−	0.118353i
$964$	8.20652	−	9.47083i	0.264314	−	0.305035i
$965$	5.23704	+	8.31359i	0.168586	+	0.267624i
$966$	−1.55901	+	0.751509i	−0.0501603	+	0.0241794i
$967$	−14.2422	−	14.2422i	−0.457998	−	0.457998i	0.440000	−	0.897998i	$-0.354979\pi$
$967$	−14.2422	−	14.2422i	−0.457998	−	0.457998i	−0.897998	+	0.440000i	$0.854979\pi$
$968$	−1.58501	−	22.1613i	−0.0509441	−	0.712292i
$969$	−1.56220	−	2.43083i	−0.0501852	−	0.0780897i
$970$	2.14720	+	0.173130i	0.0689423	+	0.00555887i
$971$	−31.4755	+	14.3744i	−1.01010	+	0.461296i	−0.850550	−	0.525895i	$-0.823731\pi$
$971$	−31.4755	+	14.3744i	−1.01010	+	0.461296i	−0.159547	+	0.987190i	$0.551003\pi$
$972$	0.800541	−	0.599278i	0.0256774	−	0.0192218i
$973$	0.307596	+	0.167960i	0.00986108	+	0.00538456i
$974$	1.64866	−	2.56536i	0.0528263	−	0.0821994i
$975$	−2.56294	−	3.06837i	−0.0820797	−	0.0982663i
$976$	−2.21477	+	7.54283i	−0.0708932	+	0.241440i
$977$	1.75054	+	0.125201i	0.0560046	+	0.00400553i	0.0993134	−	0.995056i	$-0.468335\pi$
$977$	1.75054	+	0.125201i	0.0560046	+	0.00400553i	−0.0433088	+	0.999062i	$0.513790\pi$
$978$	19.1263	+	1.36794i	0.611591	+	0.0437418i
$979$	−7.05888	+	24.0403i	−0.225603	+	0.768332i
$980$	−12.2135	−	9.31667i	−0.390145	−	0.297610i
$981$	1.05315	−	1.63873i	0.0336244	−	0.0523206i
$982$	−9.41553	−	5.14127i	−0.300462	−	0.164064i
$983$	−31.0274	+	23.2268i	−0.989619	+	0.740820i	−0.965904	−	0.258899i	$-0.916640\pi$
$983$	−31.0274	+	23.2268i	−0.989619	+	0.740820i	−0.0237150	+	0.999719i	$0.507549\pi$
$984$	−3.66478	+	1.67365i	−0.116829	+	0.0533540i
$985$	16.0574	+	18.8739i	0.511631	+	0.601373i
$986$	−2.38634	−	3.71322i	−0.0759967	−	0.118253i
$987$	0.0511010	+	0.714485i	0.00162656	+	0.0227423i
$988$	−3.54239	−	3.54239i	−0.112699	−	0.112699i
$989$	22.0716	−	26.5679i	0.701836	−	0.844811i
$990$	10.9044	−	6.86907i	0.346564	−	0.218314i
$991$	1.08344	−	1.25036i	0.0344167	−	0.0397190i	−0.738280	−	0.674494i	$-0.764362\pi$
$991$	1.08344	−	1.25036i	0.0344167	−	0.0397190i	0.772697	+	0.634775i	$0.218907\pi$
$992$	1.52807	+	0.332411i	0.0485162	+	0.0105541i
$993$	−6.00759	−	4.49722i	−0.190645	−	0.142715i
$994$	0.564635	+	1.23638i	0.0179091	+	0.0392155i
$995$	10.3122	+	3.95302i	0.326920	+	0.125319i
$996$	0.216145	+	0.736122i	0.00684881	+	0.0233249i
$997$	0.545801	+	2.50901i	0.0172857	+	0.0794610i	0.984982	−	0.172659i	$-0.0552359\pi$
$997$	0.545801	+	2.50901i	0.0172857	+	0.0794610i	−0.967696	+	0.252120i	$0.918872\pi$
$998$	−11.9301	−	31.9857i	−0.377640	−	1.01249i
$999$	−8.52056	−	2.50186i	−0.269579	−	0.0791554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.7.7	✓	240
5.3	odd	4	inner	690.2.w.b.283.1	yes	240
23.10	odd	22	inner	690.2.w.b.217.1	yes	240
115.33	even	44	inner	690.2.w.b.493.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.7	✓	240	1.1	even	1	trivial
690.2.w.b.217.1	yes	240	23.10	odd	22	inner
690.2.w.b.283.1	yes	240	5.3	odd	4	inner
690.2.w.b.493.7	yes	240	115.33	even	44	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.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.18918 + 0.455502i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.172948 - 0.316731i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 - 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.18918 + 0.455502i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.172948 - 0.316731i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-2.15111 + 0.610516i) q^{10} +(4.35576 - 3.77429i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(0.701781 - 0.383202i) q^{13} +(0.149912 - 0.328262i) q^{14} +(-0.0202515 + 2.23598i) q^{15} +(0.959493 - 0.281733i) q^{16} +(0.276383 + 0.369204i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(-0.891653 - 6.20158i) q^{19} +(-2.10207 + 0.762419i) q^{20} +(-0.272730 - 0.236322i) q^{21} +(4.07541 - 4.07541i) q^{22} +(2.21044 - 4.25605i) q^{23} -1.00000i q^{24} +(4.58504 - 1.99435i) q^{25} +(0.672656 - 0.432290i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(0.126112 - 0.338120i) q^{28} +(-9.47323 - 1.36204i) q^{29} +(0.139313 + 2.23172i) q^{30} +(1.31556 + 0.845457i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-2.76215 - 5.05850i) q^{33} +(0.302017 + 0.348547i) q^{34} +(-0.234343 + 0.772159i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(3.10334 + 8.32037i) q^{37} +(-1.33180 - 6.12217i) q^{38} +(-0.225270 - 0.767199i) q^{39} +(-2.04233 + 0.910437i) q^{40} +(-1.67365 - 3.66478i) q^{41} +(-0.288894 - 0.216263i) q^{42} +(7.03749 + 1.53091i) q^{43} +(3.77429 - 4.35576i) q^{44} +(2.18057 + 0.495080i) q^{45} +(1.90118 - 4.40290i) q^{46} +(-1.40356 - 1.40356i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(3.71408 + 5.77922i) q^{49} +(4.43108 - 2.31637i) q^{50} +(0.419516 - 0.191587i) q^{51} +(0.640103 - 0.479175i) q^{52} +(-1.55615 - 0.849720i) q^{53} +(-0.540641 + 0.841254i) q^{54} +(-7.81636 + 10.2467i) q^{55} +(0.101670 - 0.346255i) q^{56} +(-6.24939 - 0.446965i) q^{57} +(-9.54626 - 0.682762i) q^{58} +(-4.03973 + 13.7580i) q^{59} +(0.298167 + 2.21610i) q^{60} +(-4.25012 + 6.61332i) q^{61} +(1.37252 + 0.749453i) q^{62} +(-0.288894 + 0.216263i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-1.36178 + 1.15856i) q^{65} +(-3.11598 - 4.84857i) q^{66} +(-0.842709 - 11.7826i) q^{67} +(0.326113 + 0.326113i) q^{68} +(-3.68892 - 3.06461i) q^{69} +(-0.178661 + 0.786910i) q^{70} +(-2.46650 + 2.84649i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(12.9380 + 9.68526i) q^{73} +(3.68900 + 8.07778i) q^{74} +(-0.974158 - 4.90418i) q^{75} +(-1.76515 - 6.01156i) q^{76} +(-0.442113 - 2.03236i) q^{77} +(-0.279427 - 0.749173i) q^{78} +(3.46495 + 1.01740i) q^{79} +(-1.97217 + 1.05382i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-1.93083 - 3.53605i) q^{82} +(-0.718827 + 0.268108i) q^{83} +(-0.303586 - 0.195103i) q^{84} +(-0.773226 - 0.682362i) q^{85} +(7.12878 + 1.02496i) q^{86} +(-3.34460 + 8.96721i) q^{87} +(3.45394 - 4.61392i) q^{88} +(-3.65712 + 2.35029i) q^{89} +(2.21034 + 0.338258i) q^{90} -0.288550i q^{91} +(1.58224 - 4.52731i) q^{92} +(1.10578 - 1.10578i) q^{93} +(-1.50012 - 1.29986i) q^{94} +(4.77682 + 13.1702i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-0.902631 - 0.336664i) q^{97} +(4.11690 + 5.49953i) q^{98} +(-5.53004 + 1.62377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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