LMFDB - Embedded newform 690.2.n.b.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.4
Character	$\chi$	$=$	690.89
Dual form			690.2.n.b.659.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-1.56929 - 0.733032i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.76486 - 1.37305i) q^{5} +(0.502238 - 1.65764i) q^{6} +(-3.04110 + 1.95439i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.92533 + 2.30068i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-1.56929 - 0.733032i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.76486 - 1.37305i) q^{5} +(0.502238 - 1.65764i) q^{6} +(-3.04110 + 1.95439i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.92533 + 2.30068i) q^{9} +(1.61024 + 1.55149i) q^{10} +(0.00228746 - 0.0159096i) q^{11} +(1.71224 + 0.261220i) q^{12} +(1.50635 - 2.34393i) q^{13} +(-2.36729 - 2.73200i) q^{14} +(-3.77606 + 0.861020i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.07536 + 3.66235i) q^{17} +(-2.00326 + 2.23315i) q^{18} +(0.620061 + 2.11173i) q^{19} +(-1.30653 + 1.81465i) q^{20} +(6.20499 - 0.837784i) q^{21} +0.0160733 q^{22} +(3.58112 + 3.18992i) q^{23} +(-0.0148842 + 1.73199i) q^{24} +(1.22944 - 4.84649i) q^{25} +(2.53445 + 1.15744i) q^{26} +(-1.33492 - 5.02175i) q^{27} +(2.36729 - 2.73200i) q^{28} +(-1.90978 + 6.50410i) q^{29} +(-1.38965 - 3.61509i) q^{30} +(2.30438 + 5.04590i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.0152520 + 0.0232900i) q^{33} +(-3.77811 - 0.543210i) q^{34} +(-2.68361 + 7.62482i) q^{35} +(-2.49551 - 1.66506i) q^{36} +(7.30706 + 8.43280i) q^{37} +(-2.00199 + 0.914280i) q^{38} +(-4.08208 + 2.57410i) q^{39} +(-1.98212 - 1.03498i) q^{40} +(3.69098 + 3.19825i) q^{41} +(1.71232 + 6.02260i) q^{42} +(-0.521005 + 1.14084i) q^{43} +(0.00228746 + 0.0159096i) q^{44} +(6.55688 + 1.41679i) q^{45} +(-2.64781 + 3.99864i) q^{46} -8.02646 q^{47} +(-1.71648 + 0.231755i) q^{48} +(2.52071 - 5.51958i) q^{49} +(4.97213 + 0.527200i) q^{50} +(4.37217 - 4.95900i) q^{51} +(-0.784973 + 2.67337i) q^{52} +(2.54431 + 3.95903i) q^{53} +(4.78066 - 2.03600i) q^{54} +(-0.0178078 - 0.0312191i) q^{55} +(3.04110 + 1.95439i) q^{56} +(0.574915 - 3.76844i) q^{57} +(-6.70969 - 0.964707i) q^{58} +(-1.07153 + 1.66733i) q^{59} +(3.38053 - 1.88998i) q^{60} +(5.98839 - 2.73481i) q^{61} +(-4.66659 + 2.99903i) q^{62} +(-10.3515 - 3.23374i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-0.559847 - 6.20501i) q^{65} +(-0.0252236 - 0.0117822i) q^{66} +(1.47316 + 10.2460i) q^{67} -3.81696i q^{68} +(-3.28148 - 7.63098i) q^{69} +(-7.92913 - 1.57117i) q^{70} +(-12.0067 + 1.72631i) q^{71} +(1.29296 - 2.70707i) q^{72} +(-4.01957 - 13.6894i) q^{73} +(-7.30706 + 8.43280i) q^{74} +(-5.48198 + 6.70432i) q^{75} +(-1.18989 - 1.85150i) q^{76} +(0.0241373 + 0.0528534i) q^{77} +(-3.12884 - 3.67420i) q^{78} +(4.69308 - 7.30257i) q^{79} +(0.742363 - 2.10924i) q^{80} +(-1.58623 + 8.85911i) q^{81} +(-2.64042 + 4.10857i) q^{82} +(-0.587523 + 0.509092i) q^{83} +(-5.71761 + 2.55200i) q^{84} +(3.13074 + 7.94005i) q^{85} +(-1.20338 - 0.353343i) q^{86} +(7.76470 - 8.80687i) q^{87} +(-0.0154222 + 0.00452836i) q^{88} +(-4.77366 + 10.4529i) q^{89} +(-0.469226 + 6.69177i) q^{90} +10.0721i q^{91} +(-4.33476 - 2.05179i) q^{92} +(0.0825653 - 9.60765i) q^{93} +(-1.14228 - 7.94476i) q^{94} +(3.99384 + 2.87553i) q^{95} +(-0.473676 - 1.66602i) q^{96} +(5.55341 - 6.40897i) q^{97} +(5.82214 + 1.70953i) q^{98} +(0.0410071 - 0.0253686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9	$ 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) $ 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9 + 9 * q^12 + 11 * q^15 - 24 * q^16 + 6 * q^18 + 4 * q^23 + 2 * q^24 - 12 * q^25 - 2 * q^27 + 22 * q^30 + 28 * q^31 + 24 * q^32 + 36 * q^35 - 6 * q^36 - 4 * q^46 - 104 * q^47 + 9 * q^48 + 70 * q^49 - 54 * q^50 - 9 * q^54 - 26 * q^55 + 44 * q^57 - 11 * q^60 + 44 * q^61 - 28 * q^62 + 121 * q^63 - 24 * q^64 - 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 - 16 * q^72 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	−1.56929	−	0.733032i	−0.906029	−	0.423216i
$3$	−1.56929	−	0.733032i	−0.906029	−	0.423216i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	1.76486	−	1.37305i	0.789268	−	0.614049i
$5$	1.76486	−	1.37305i	0.789268	−	0.614049i
$6$	0.502238	−	1.65764i	0.205038	−	0.676727i
$7$	−3.04110	+	1.95439i	−1.14943	+	0.738692i	−0.969525	−	0.244993i	$-0.921214\pi$
$7$	−3.04110	+	1.95439i	−1.14943	+	0.738692i	−0.179902	+	0.983685i	$0.557578\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	1.92533	+	2.30068i	0.641776	+	0.766892i
$10$	1.61024	+	1.55149i	0.509204	+	0.490623i
$11$	0.00228746	−	0.0159096i	0.000689696	−	0.00479694i	−0.989474	−	0.144713i	$-0.953774\pi$
$11$	0.00228746	−	0.0159096i	0.000689696	−	0.00479694i	0.990163	+	0.139916i	$0.0446832\pi$
$12$	1.71224	+	0.261220i	0.494281	+	0.0754078i
$13$	1.50635	−	2.34393i	0.417787	−	0.650090i	−0.567027	−	0.823699i	$-0.691907\pi$
$13$	1.50635	−	2.34393i	0.417787	−	0.650090i	0.984815	+	0.173609i	$0.0555430\pi$
$14$	−2.36729	−	2.73200i	−0.632686	−	0.730159i
$15$	−3.77606	+	0.861020i	−0.974975	+	0.222314i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−1.07536	+	3.66235i	−0.260814	+	0.888250i	0.720111	+	0.693859i	$0.244091\pi$
$17$	−1.07536	+	3.66235i	−0.260814	+	0.888250i	−0.980924	+	0.194390i	$0.937727\pi$
$18$	−2.00326	+	2.23315i	−0.472172	+	0.526359i
$19$	0.620061	+	2.11173i	0.142252	+	0.484465i	0.999539	−	0.0303742i	$-0.00966990\pi$
$19$	0.620061	+	2.11173i	0.142252	+	0.484465i	−0.857287	+	0.514839i	$0.827852\pi$
$20$	−1.30653	+	1.81465i	−0.292150	+	0.405769i
$21$	6.20499	−	0.837784i	1.35404	−	0.182819i
$22$	0.0160733			0.00342683
$23$	3.58112	+	3.18992i	0.746714	+	0.665145i
$23$	3.58112	+	3.18992i	0.746714	+	0.665145i
$24$	−0.0148842	+	1.73199i	−0.00303822	+	0.353540i
$25$	1.22944	−	4.84649i	0.245888	−	0.969298i
$26$	2.53445	+	1.15744i	0.497046	+	0.226994i
$27$	−1.33492	−	5.02175i	−0.256905	−	0.966437i
$28$	2.36729	−	2.73200i	0.447377	−	0.516300i
$29$	−1.90978	+	6.50410i	−0.354636	+	1.20778i	0.568298	+	0.822823i	$0.307602\pi$
$29$	−1.90978	+	6.50410i	−0.354636	+	1.20778i	−0.922934	+	0.384958i	$0.874216\pi$
$30$	−1.38965	−	3.61509i	−0.253713	−	0.660022i
$31$	2.30438	+	5.04590i	0.413879	+	0.906270i	0.995672	+	0.0929327i	$0.0296241\pi$
$31$	2.30438	+	5.04590i	0.413879	+	0.906270i	−0.581793	+	0.813337i	$0.697649\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	−0.0152520	+	0.0232900i	−0.00265503	+	0.00405427i
$34$	−3.77811	−	0.543210i	−0.647940	−	0.0931598i
$35$	−2.68361	+	7.62482i	−0.453613	+	1.28883i
$36$	−2.49551	−	1.66506i	−0.415919	−	0.277509i
$37$	7.30706	+	8.43280i	1.20127	+	1.38634i	0.901752	+	0.432255i	$0.142282\pi$
$37$	7.30706	+	8.43280i	1.20127	+	1.38634i	0.299522	+	0.954089i	$0.403173\pi$
$38$	−2.00199	+	0.914280i	−0.324766	+	0.148316i
$39$	−4.08208	+	2.57410i	−0.653656	+	0.412185i
$40$	−1.98212	−	1.03498i	−0.313401	−	0.163645i
$41$	3.69098	+	3.19825i	0.576435	+	0.499483i	0.893586	−	0.448891i	$-0.148181\pi$
$41$	3.69098	+	3.19825i	0.576435	+	0.499483i	−0.317152	+	0.948375i	$0.602726\pi$
$42$	1.71232	+	6.02260i	0.264217	+	0.929308i
$43$	−0.521005	+	1.14084i	−0.0794525	+	0.173977i	−0.945189	−	0.326523i	$-0.894123\pi$
$43$	−0.521005	+	1.14084i	−0.0794525	+	0.173977i	0.865737	+	0.500499i	$0.166850\pi$
$44$	0.00228746	+	0.0159096i	0.000344848	+	0.00239847i
$45$	6.55688	+	1.41679i	0.977442	+	0.211202i
$46$	−2.64781	+	3.99864i	−0.390398	+	0.589567i
$47$	−8.02646			−1.17078			−0.585390	−	0.810752i	$-0.699059\pi$
$47$	−8.02646			−1.17078			−0.585390	+	0.810752i	$0.699059\pi$
$48$	−1.71648	+	0.231755i	−0.247752	+	0.0334509i
$49$	2.52071	−	5.51958i	0.360101	−	0.788512i
$50$	4.97213	+	0.527200i	0.703165	+	0.0745574i
$51$	4.37217	−	4.95900i	0.612226	−	0.694399i
$52$	−0.784973	+	2.67337i	−0.108856	+	0.370730i
$53$	2.54431	+	3.95903i	0.349488	+	0.543814i	0.970843	−	0.239715i	$-0.0770539\pi$
$53$	2.54431	+	3.95903i	0.349488	+	0.543814i	−0.621355	+	0.783529i	$0.713418\pi$
$54$	4.78066	−	2.03600i	0.650565	−	0.277065i
$55$	−0.0178078	−	0.0312191i	−0.00240120	−	0.00420958i
$56$	3.04110	+	1.95439i	0.406384	+	0.261167i
$57$	0.574915	−	3.76844i	0.0761494	−	0.499142i
$58$	−6.70969	−	0.964707i	−0.881025	−	0.126672i
$59$	−1.07153	+	1.66733i	−0.139501	+	0.217068i	−0.903973	−	0.427589i	$-0.859363\pi$
$59$	−1.07153	+	1.66733i	−0.139501	+	0.217068i	0.764472	+	0.644656i	$0.223000\pi$
$60$	3.38053	−	1.88998i	0.436424	−	0.243996i
$61$	5.98839	−	2.73481i	0.766735	−	0.350156i	0.00664818	−	0.999978i	$-0.497884\pi$
$61$	5.98839	−	2.73481i	0.766735	−	0.350156i	0.760087	+	0.649822i	$0.225157\pi$
$62$	−4.66659	+	2.99903i	−0.592657	+	0.380878i
$63$	−10.3515	−	3.23374i	−1.30417	−	0.407412i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−0.559847	−	6.20501i	−0.0694405	−	0.769637i
$66$	−0.0252236	−	0.0117822i	−0.00310480	−	0.00145029i
$67$	1.47316	+	10.2460i	0.179975	+	1.25175i	0.856816	+	0.515623i	$0.172439\pi$
$67$	1.47316	+	10.2460i	0.179975	+	1.25175i	−0.676841	+	0.736129i	$0.736651\pi$
$68$		−	3.81696i		−	0.462874i
$69$	−3.28148	−	7.63098i	−0.395044	−	0.918662i
$70$	−7.92913	−	1.57117i	−0.947712	−	0.187791i
$71$	−12.0067	+	1.72631i	−1.42494	+	0.204875i	−0.811262	−	0.584683i	$-0.801219\pi$
$71$	−12.0067	+	1.72631i	−1.42494	+	0.204875i	−0.613676	+	0.789558i	$0.710310\pi$
$72$	1.29296	−	2.70707i	0.152377	−	0.319032i
$73$	−4.01957	−	13.6894i	−0.470455	−	1.60222i	−0.763288	−	0.646058i	$-0.776416\pi$
$73$	−4.01957	−	13.6894i	−0.470455	−	1.60222i	0.292834	−	0.956163i	$-0.405402\pi$
$74$	−7.30706	+	8.43280i	−0.849429	+	0.980293i
$75$	−5.48198	+	6.70432i	−0.633005	+	0.774148i
$76$	−1.18989	−	1.85150i	−0.136489	−	0.212382i
$77$	0.0241373	+	0.0528534i	0.00275070	+	0.00602320i
$78$	−3.12884	−	3.67420i	−0.354271	−	0.416021i
$79$	4.69308	−	7.30257i	0.528012	−	0.821603i	−0.470126	−	0.882599i	$-0.655791\pi$
$79$	4.69308	−	7.30257i	0.528012	−	0.821603i	0.998138	+	0.0609964i	$0.0194278\pi$
$80$	0.742363	−	2.10924i	0.0829987	−	0.235820i
$81$	−1.58623	+	8.85911i	−0.176248	+	0.984346i
$82$	−2.64042	+	4.10857i	−0.291586	+	0.453716i
$83$	−0.587523	+	0.509092i	−0.0644890	+	0.0558801i	−0.686509	−	0.727121i	$-0.740858\pi$
$83$	−0.587523	+	0.509092i	−0.0644890	+	0.0558801i	0.622020	+	0.783001i	$0.286312\pi$
$84$	−5.71761	+	2.55200i	−0.623843	+	0.278446i
$85$	3.13074	+	7.94005i	0.339577	+	0.861219i
$86$	−1.20338	−	0.353343i	−0.129763	−	0.0381020i
$87$	7.76470	−	8.80687i	0.832464	−	0.944196i
$88$	−0.0154222	+	0.00452836i	−0.00164401	+	0.000482725i
$89$	−4.77366	+	10.4529i	−0.506007	+	1.10800i	0.468463	+	0.883483i	$0.344808\pi$
$89$	−4.77366	+	10.4529i	−0.506007	+	1.10800i	−0.974470	+	0.224518i	$0.927919\pi$
$90$	−0.469226	+	6.69177i	−0.0494607	+	0.705375i
$91$			10.0721i			1.05585i
$92$	−4.33476	−	2.05179i	−0.451930	−	0.213914i
$93$	0.0825653	−	9.60765i	0.00856162	−	0.996267i
$94$	−1.14228	−	7.94476i	−0.117818	−	0.819440i
$95$	3.99384	+	2.87553i	0.409760	+	0.295023i
$96$	−0.473676	−	1.66602i	−0.0483443	−	0.170038i
$97$	5.55341	−	6.40897i	0.563863	−	0.650733i	−0.400193	−	0.916431i	$-0.631057\pi$
$97$	5.55341	−	6.40897i	0.563863	−	0.650733i	0.964056	+	0.265698i	$0.0856024\pi$
$98$	5.82214	+	1.70953i	0.588125	+	0.172689i
$99$	0.0410071	−	0.0253686i	0.00412137	−	0.00254964i
$100$	0.185773	+	4.99655i	0.0185773	+	0.499655i
$101$	−4.24867	+	3.68149i	−0.422758	+	0.366322i	−0.840104	−	0.542426i	$-0.817506\pi$
$101$	−4.24867	+	3.68149i	−0.422758	+	0.366322i	0.417345	+	0.908748i	$0.362961\pi$
$102$	5.53075	+	3.62193i	0.547626	+	0.358624i
$103$	0.518220	−	3.60430i	0.0510618	−	0.355142i	−0.948232	−	0.317577i	$-0.897131\pi$
$103$	0.518220	−	3.60430i	0.0510618	−	0.355142i	0.999294	−	0.0375651i	$-0.0119602\pi$
$104$	−2.75788	−	0.396523i	−0.270432	−	0.0388823i
$105$	9.80060	−	9.99836i	0.956441	−	0.975740i
$106$	−3.55664	+	3.08184i	−0.345451	+	0.299335i
$107$	14.9799	−	6.84111i	1.44817	−	0.661355i	0.472643	−	0.881254i	$-0.343300\pi$
$107$	14.9799	−	6.84111i	1.44817	−	0.661355i	0.975523	+	0.219899i	$0.0705727\pi$
$108$	2.69564	+	4.44224i	0.259388	+	0.427455i
$109$	1.94794	−	6.63408i	0.186579	−	0.635430i	−0.812074	−	0.583554i	$-0.801662\pi$
$109$	1.94794	−	6.63408i	0.186579	−	0.635430i	0.998654	−	0.0518762i	$-0.0165201\pi$
$110$	0.0283670	−	0.0220695i	0.00270469	−	0.00210424i
$111$	−5.28537	−	18.5898i	−0.501665	−	1.76447i
$112$	−1.50171	+	3.28828i	−0.141898	+	0.310713i
$113$	−5.18962	+	0.746154i	−0.488198	+	0.0701923i	−0.382018	−	0.924155i	$-0.624771\pi$
$113$	−5.18962	+	0.746154i	−0.488198	+	0.0701923i	−0.106180	+	0.994347i	$0.533862\pi$
$114$	3.81190	+	0.0327584i	0.357017	+	0.00306810i
$115$	10.7001	+	0.712690i	0.997789	+	0.0664587i
$116$		−	6.77868i		−	0.629385i
$117$	8.29285	−	1.04720i	0.766674	−	0.0968138i
$118$	−1.80285	−	0.823335i	−0.165966	−	0.0757941i
$119$	−3.88739	−	13.2392i	−0.356356	−	1.21364i
$120$	2.35184	+	3.07715i	0.214693	+	0.280904i
$121$	10.5542	+	3.09899i	0.959470	+	0.281726i
$122$	3.55921	+	5.53823i	0.322235	+	0.501408i
$123$	−3.44779	−	7.72459i	−0.310877	−	0.696503i
$124$	−3.63263	−	4.19228i	−0.326220	−	0.376478i
$125$	−4.48471	−	10.2415i	−0.401124	−	0.916024i
$126$	1.72764	−	10.7064i	0.153911	−	0.953800i
$127$	4.01607	+	0.577424i	0.356368	+	0.0512381i	0.318174	−	0.948032i	$-0.396930\pi$
$127$	4.01607	+	0.577424i	0.356368	+	0.0512381i	0.0381943	+	0.999270i	$0.487839\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	1.65388	−	1.40839i	0.145616	−	0.124002i
$130$	6.06218	−	1.43721i	0.531688	−	0.126052i
$131$	1.49380	+	2.32440i	0.130514	+	0.203084i	0.900360	−	0.435146i	$-0.143303\pi$
$131$	1.49380	+	2.32440i	0.130514	+	0.203084i	−0.769846	+	0.638230i	$0.779667\pi$
$132$	0.00807260	−	0.0266436i	0.000702630	−	0.00231903i
$133$	−6.01282	−	5.21014i	−0.521378	−	0.451777i
$134$	−9.93209	+	2.91633i	−0.858002	+	0.251932i
$135$	−9.25108	−	7.02976i	−0.796206	−	0.605025i
$136$	3.77811	−	0.543210i	0.323970	−	0.0465799i
$137$		−	19.6648i		−	1.68007i	−0.542530	−	0.840037i	$-0.682533\pi$
$137$		−	19.6648i		−	1.68007i	0.542530	−	0.840037i	$-0.317467\pi$
$138$	7.08630	−	4.33408i	0.603226	−	0.368942i
$139$	−16.8875			−1.43238			−0.716189	−	0.697906i	$-0.754115\pi$
$139$	−16.8875			−1.43238			−0.716189	+	0.697906i	$0.754115\pi$
$140$	0.426747	−	8.07202i	0.0360667	−	0.682210i
$141$	12.5958	+	5.88366i	1.06076	+	0.495493i
$142$	−3.41748	−	11.6389i	−0.286788	−	0.976711i
$143$	−0.0338454	−	0.0293272i	−0.00283029	−	0.00245246i
$144$	2.86353	+	0.894543i	0.238627	+	0.0745452i
$145$	5.56000	+	14.1010i	0.461733	+	1.17103i
$146$	12.9780	−	5.92686i	1.07407	−	0.490510i
$147$	−8.00175	+	6.81405i	−0.659973	+	0.562014i
$148$	−9.38687	−	6.03258i	−0.771596	−	0.495875i
$149$	0.824068	−	5.73152i	0.0675103	−	0.469544i	−0.927821	−	0.373026i	$-0.878320\pi$
$149$	0.824068	−	5.73152i	0.0675103	−	0.469544i	0.995331	−	0.0965183i	$-0.0307706\pi$
$150$	−7.41624	−	4.47206i	−0.605534	−	0.365142i
$151$	−0.217280	−	0.139637i	−0.0176820	−	0.0113635i	0.531770	−	0.846889i	$-0.321527\pi$
$151$	−0.217280	−	0.139637i	−0.0176820	−	0.0113635i	−0.549452	+	0.835525i	$0.685163\pi$
$152$	1.66332	−	1.44127i	0.134913	−	0.116903i
$153$	−10.4963	+	4.57715i	−0.848576	+	0.370041i
$154$	−0.0488803	+	0.0314135i	−0.00393889	+	0.00253137i
$155$	10.9952	+	5.74124i	0.883156	+	0.461148i
$156$	3.19152	−	3.61988i	0.255526	−	0.289822i
$157$	−3.33608	+	0.979562i	−0.266248	+	0.0781776i	−0.412132	−	0.911124i	$-0.635216\pi$
$157$	−3.33608	+	0.979562i	−0.266248	+	0.0781776i	0.145884	+	0.989302i	$0.453398\pi$
$158$	7.89613	+	3.60604i	0.628183	+	0.286881i
$159$	−1.09066	−	8.07792i	−0.0864951	−	0.640620i
$160$	2.19342	+	0.434631i	0.173405	+	0.0343606i
$161$	−17.1249	−	2.70195i	−1.34963	−	0.212944i
$162$	−8.99468	−	0.309305i	−0.706689	−	0.0243013i
$163$	12.3545	−	1.77630i	0.967677	−	0.139131i	0.359685	−	0.933074i	$-0.382884\pi$
$163$	12.3545	−	1.77630i	0.967677	−	0.139131i	0.607992	+	0.793943i	$0.291975\pi$
$164$	−4.44252	−	2.02883i	−0.346903	−	0.158425i
$165$	0.00506093	+	0.0620454i	0.000393993	+	0.00483023i
$166$	−0.587523	−	0.509092i	−0.0456006	−	0.0395132i
$167$	11.3269	+	3.32589i	0.876505	+	0.257365i	0.688880	−	0.724876i	$-0.258103\pi$
$167$	11.3269	+	3.32589i	0.876505	+	0.257365i	0.187625	+	0.982241i	$0.439921\pi$
$168$	−3.33972	−	5.29623i	−0.257665	−	0.408613i
$169$	2.17548	+	4.76364i	0.167345	+	0.366434i
$170$	−7.41368	+	4.22886i	−0.568603	+	0.324339i
$171$	−3.66460	+	5.49234i	−0.280239	+	0.420009i
$172$	0.178488	−	1.24141i	0.0136096	−	0.0946569i
$173$	1.51063	−	10.5067i	0.114851	−	0.798807i	−0.848236	−	0.529618i	$-0.822335\pi$
$173$	1.51063	−	10.5067i	0.114851	−	0.798807i	0.963087	−	0.269189i	$-0.0867557\pi$
$174$	9.82227	+	6.43232i	0.744624	+	0.487633i
$175$	5.73310	+	17.1415i	0.433382	+	1.29577i
$176$	−0.00667707	−	0.0146207i	−0.000503303	−	0.00110208i
$177$	2.90374	−	1.83105i	0.218258	−	0.137630i
$178$	−11.0258	−	3.23748i	−0.826421	−	0.242659i
$179$	15.5519	+	13.4758i	1.16241	+	1.00723i	0.999789	+	0.0205409i	$0.00653884\pi$
$179$	15.5519	+	13.4758i	1.16241	+	1.00723i	0.162617	+	0.986689i	$0.448007\pi$
$180$	−6.69044	+	0.487889i	−0.498676	+	0.0363651i
$181$	−3.55252	−	1.62238i	−0.264057	−	0.120591i	0.278988	−	0.960295i	$-0.410001\pi$
$181$	−3.55252	−	1.62238i	−0.264057	−	0.120591i	−0.543044	+	0.839704i	$0.682728\pi$
$182$	−9.96961	+	1.43341i	−0.738997	+	0.106252i
$183$	−11.4022	−	0.0979872i	−0.842875	−	0.00724342i
$184$	1.41401	−	4.58264i	0.104242	−	0.337837i
$185$	24.4746	+	4.84969i	1.79941	+	0.356556i
$186$	9.52161	−	1.28559i	0.698158	−	0.0942638i
$187$	0.0558068	+	0.0254861i	0.00408100	+	0.00186373i
$188$	7.70133	−	2.26132i	0.561677	−	0.164923i
$189$	13.8741	+	12.6627i	1.00919	+	0.921074i
$190$	−2.27788	+	4.36242i	−0.165255	+	0.316483i
$191$	−22.1760	+	14.2517i	−1.60460	+	1.03122i	−0.639694	+	0.768630i	$0.720939\pi$
$191$	−22.1760	+	14.2517i	−1.60460	+	1.03122i	−0.964909	+	0.262586i	$0.915425\pi$
$192$	1.58165	−	0.705954i	0.114146	−	0.0509479i
$193$	−10.4138	+	9.02362i	−0.749603	+	0.649535i	−0.943457	−	0.331496i	$-0.892447\pi$
$193$	−10.4138	+	9.02362i	−0.749603	+	0.649535i	0.193854	+	0.981030i	$0.437901\pi$
$194$	7.13407	+	4.58479i	0.512197	+	0.329169i
$195$	−3.66991	+	10.1478i	−0.262808	+	0.726701i
$196$	−0.863556	+	6.00617i	−0.0616826	+	0.429012i
$197$	−13.4061	−	8.61558i	−0.955145	−	0.613835i	−0.0324948	−	0.999472i	$-0.510345\pi$
$197$	−13.4061	−	8.61558i	−0.955145	−	0.613835i	−0.922650	+	0.385637i	$0.873982\pi$
$198$	0.0309463	+	0.0369794i	0.00219926	+	0.00262801i
$199$	20.7984	−	9.49831i	1.47436	−	0.673318i	0.493807	−	0.869572i	$-0.335605\pi$
$199$	20.7984	−	9.49831i	1.47436	−	0.673318i	0.980553	+	0.196254i	$0.0628778\pi$
$200$	−4.91925	+	0.894965i	−0.347844	+	0.0632836i
$201$	5.19887	−	17.1588i	0.366700	−	1.21029i
$202$	−4.24867	−	3.68149i	−0.298935	−	0.259029i
$203$	−6.90376	−	23.5121i	−0.484549	−	1.65022i
$204$	−2.79796	+	5.98991i	−0.195896	+	0.419377i
$205$	10.9054	+	0.576542i	0.761669	+	0.0402674i
$206$	3.64136			0.253706
$207$	−0.444165	+	14.3806i	−0.0308716	+	0.999523i
$208$		−	2.78624i		−	0.193191i
$209$	0.0350153	−	0.00503444i	0.00242206	−	0.000348239i
$210$	11.2914	+	8.27793i	0.779178	+	0.571231i
$211$	−13.6151	+	3.99775i	−0.937301	+	0.275217i	−0.714490	−	0.699645i	$-0.753341\pi$
$211$	−13.6151	+	3.99775i	−0.937301	+	0.275217i	−0.222811	+	0.974862i	$0.571523\pi$
$212$	−3.55664	−	3.08184i	−0.244271	−	0.211662i
$213$	20.1075	+	6.09226i	1.37774	+	0.417435i
$214$	8.90335	+	13.8539i	0.608620	+	0.947032i
$215$	0.646939	+	2.72879i	0.0441208	+	0.186102i
$216$	−4.01340	+	3.30040i	−0.273077	+	0.224564i
$217$	−16.8695	−	10.8414i	−1.14518	−	0.735961i
$218$	6.84378	+	0.983987i	0.463519	+	0.0666440i
$219$	−3.72691	+	24.4291i	−0.251841	+	1.65076i
$220$	0.0258819	+	0.0249374i	0.00174495	+	0.00168128i
$221$	6.96441	+	8.03736i	0.468477	+	0.540651i
$222$	17.6484	−	7.87718i	1.18448	−	0.528681i
$223$	−5.77608	−	8.98776i	−0.386795	−	0.601865i	0.592190	−	0.805799i	$-0.298264\pi$
$223$	−5.77608	−	8.98776i	−0.386795	−	0.601865i	−0.978985	+	0.203934i	$0.934627\pi$
$224$	−3.46853	−	1.01845i	−0.231751	−	0.0680482i
$225$	13.5173	−	6.50253i	0.901153	−	0.433502i
$226$	−1.47712	−	5.03060i	−0.0982565	−	0.334631i
$227$	0.439253	+	0.200600i	0.0291542	+	0.0133143i	0.429939	−	0.902858i	$-0.358535\pi$
$227$	0.439253	+	0.200600i	0.0291542	+	0.0133143i	−0.400785	+	0.916172i	$0.631262\pi$
$228$	0.510065	+	3.77776i	0.0337799	+	0.250189i
$229$		−	1.68361i		−	0.111256i	−0.998452	−	0.0556280i	$-0.982284\pi$
$229$		−	1.68361i		−	0.111256i	0.998452	−	0.0556280i	$-0.0177161\pi$
$230$	0.817346	+	10.6926i	0.0538942	+	0.705050i
$231$	0.000864833	−	0.100636i	5.69018e−5	−	0.00662134i
$232$	6.70969	−	0.964707i	0.440512	−	0.0633361i
$233$	−10.9547	+	23.9874i	−0.717666	+	1.57147i	0.0994813	+	0.995039i	$0.468282\pi$
$233$	−10.9547	+	23.9874i	−0.717666	+	1.57147i	−0.817147	+	0.576429i	$0.804446\pi$
$234$	2.21674	+	8.05941i	0.144913	+	0.526860i
$235$	−14.1656	+	11.0208i	−0.924059	+	0.718916i
$236$	0.558382	−	1.90167i	0.0363476	−	0.123788i
$237$	−12.7178	+	8.01965i	−0.826110	+	0.520932i
$238$	12.5512	−	5.73196i	0.813576	−	0.371548i
$239$	5.17383	−	4.48315i	0.334667	−	0.289991i	−0.471273	−	0.881987i	$-0.656205\pi$
$239$	5.17383	−	4.48315i	0.334667	−	0.289991i	0.805941	+	0.591996i	$0.201660\pi$
$240$	−2.71112	+	2.76583i	−0.175002	+	0.178534i
$241$	−28.1687	−	4.05004i	−1.81450	−	0.260886i	−0.850347	−	0.526223i	$-0.823608\pi$
$241$	−28.1687	−	4.05004i	−1.81450	−	0.260886i	−0.964156	+	0.265337i	$0.914517\pi$
$242$	−1.56543	+	10.8878i	−0.100629	+	0.699893i
$243$	8.98327	−	12.7397i	0.576277	−	0.817254i
$244$	−4.97533	+	4.31115i	−0.318513	+	0.275993i
$245$	−3.13000	−	13.2023i	−0.199968	−	0.843467i
$246$	7.15529	−	4.51202i	0.456205	−	0.287676i
$247$	5.88379	+	1.72764i	0.374376	+	0.109927i
$248$	3.63263	−	4.19228i	0.230672	−	0.266210i
$249$	1.29517	−	0.368238i	0.0820783	−	0.0233361i
$250$	9.49897	−	5.89657i	0.600768	−	0.372932i
$251$	−0.225045	−	1.56523i	−0.0142047	−	0.0987962i	0.981486	−	0.191536i	$-0.0613467\pi$
$251$	−0.225045	−	1.56523i	−0.0142047	−	0.0987962i	−0.995690	+	0.0927394i	$0.970438\pi$
$252$	10.8433	+	0.186382i	0.683062	+	0.0117409i
$253$	0.0589422	−	0.0496775i	0.00370567	−	0.00312320i
$254$			4.05737i			0.254582i
$255$	0.907280	−	14.7552i	0.0568161	−	0.924004i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−12.9401	+	3.79956i	−0.807182	+	0.237010i	−0.659188	−	0.751978i	$-0.729100\pi$
$257$	−12.9401	+	3.79956i	−0.807182	+	0.237010i	−0.147994	+	0.988988i	$0.547282\pi$
$258$	1.62943	+	1.43661i	0.101444	+	0.0894395i
$259$	−38.7025	−	11.3641i	−2.40486	−	0.706130i
$260$	2.28532	+	5.79594i	0.141730	+	0.359449i
$261$	−18.6408	+	8.12874i	−1.15384	+	0.503156i
$262$	−2.08815	+	1.80939i	−0.129006	+	0.111785i
$263$	−1.52338	+	2.37042i	−0.0939355	+	0.146167i	−0.885041	−	0.465514i	$-0.845870\pi$
$263$	−1.52338	+	2.37042i	−0.0939355	+	0.146167i	0.791105	+	0.611680i	$0.209506\pi$
$264$	0.0275213	+	0.00419866i	0.00169382	+	0.000258409i
$265$	9.92631	+	3.49364i	0.609768	+	0.214612i
$266$	4.30140	−	6.69310i	0.263736	−	0.410380i
$267$	15.1535	−	12.9043i	0.927382	−	0.789730i
$268$	−4.30013	−	9.41596i	−0.262672	−	0.575171i
$269$	−5.92847	−	9.22487i	−0.361465	−	0.562451i	0.612123	−	0.790763i	$-0.290316\pi$
$269$	−5.92847	−	9.22487i	−0.361465	−	0.562451i	−0.973588	+	0.228312i	$0.926679\pi$
$270$	5.64164	−	10.1574i	0.343339	−	0.618157i
$271$	2.53311	−	2.92337i	0.153876	−	0.177582i	−0.673578	−	0.739116i	$-0.735243\pi$
$271$	2.53311	−	2.92337i	0.153876	−	0.177582i	0.827453	+	0.561534i	$0.189789\pi$
$272$	1.07536	+	3.66235i	0.0652034	+	0.222062i
$273$	7.38320	−	15.8061i	0.446852	−	0.956627i
$274$	19.4646	−	2.79859i	1.17590	−	0.169069i
$275$	−0.0742937	−	0.0306462i	−0.00448008	−	0.00184803i
$276$	5.29846	+	6.39737i	0.318930	+	0.385077i
$277$			11.1602i			0.670553i	0.942120	+	0.335277i	$0.108830\pi$
$277$			11.1602i			0.670553i	−0.942120	+	0.335277i	$0.891170\pi$
$278$	−2.40334	−	16.7156i	−0.144143	−	1.00254i
$279$	−7.17229	+	15.0166i	−0.429394	+	0.899023i
$280$	8.05059	−	0.726365i	0.481115	−	0.0434086i
$281$	6.05373	−	6.98637i	0.361135	−	0.416772i	−0.545885	−	0.837860i	$-0.683806\pi$
$281$	6.05373	−	6.98637i	0.361135	−	0.416772i	0.907020	+	0.421088i	$0.138352\pi$
$282$	−4.03120	+	13.3049i	−0.240054	+	0.792298i
$283$	−14.8659	+	9.55371i	−0.883683	+	0.567909i	−0.901910	−	0.431925i	$-0.857835\pi$
$283$	−14.8659	+	9.55371i	−0.883683	+	0.567909i	0.0182261	+	0.999834i	$0.494198\pi$
$284$	11.0340	−	5.03907i	0.654749	−	0.299014i
$285$	−4.15963	−	7.44015i	−0.246395	−	0.440716i
$286$	0.0242120	−	0.0376746i	0.00143169	−	0.00222775i
$287$	−17.4753	−	2.51257i	−1.03153	−	0.148312i
$288$	−0.477915	+	2.96169i	−0.0281614	+	0.174519i
$289$	2.04493	+	1.31420i	0.120290	+	0.0773057i
$290$	−13.1662	+	7.51020i	−0.773148	+	0.441014i
$291$	−13.4129	+	5.98670i	−0.786277	+	0.350946i
$292$	7.71349	+	12.0024i	0.451398	+	0.702389i
$293$	−1.98572	+	6.76273i	−0.116007	+	0.395083i	−0.996941	−	0.0781555i	$-0.975097\pi$
$293$	−1.98572	+	6.76273i	−0.116007	+	0.395083i	0.880934	+	0.473239i	$0.156915\pi$
$294$	−7.88346	−	6.95056i	−0.459773	−	0.405365i
$295$	0.398241	+	4.41386i	0.0231865	+	0.256985i
$296$	4.63528	−	10.1499i	0.269420	−	0.589948i
$297$	−0.0829479	+	0.00975104i	−0.00481312	+	0.000565813i
$298$	5.79046			0.335432
$299$	12.8714	−	3.58874i	0.744371	−	0.207542i
$300$	3.37110	−	7.97720i	0.194631	−	0.460564i
$301$	−0.645228	−	4.48766i	−0.0371903	−	0.258664i
$302$	0.107294	−	0.234940i	0.00617406	−	0.0135193i
$303$	9.36603	−	2.66291i	0.538065	−	0.152980i
$304$	1.66332	+	1.44127i	0.0953978	+	0.0826627i
$305$	6.81361	−	13.0489i	0.390146	−	0.747179i
$306$	−6.02434	−	9.73807i	−0.344389	−	0.556688i
$307$	28.7532	−	13.1311i	1.64103	−	0.749434i	0.641193	−	0.767380i	$-0.278440\pi$
$307$	28.7532	−	13.1311i	1.64103	−	0.749434i	0.999839	+	0.0179459i	$0.00571265\pi$
$308$	−0.0380501	−	0.0439122i	−0.00216811	−	0.00250213i
$309$	−3.45531	+	5.27631i	−0.196565	+	0.300159i
$310$	−4.11802	+	11.7003i	−0.233888	+	0.664535i
$311$	29.6592	+	4.26435i	1.68182	+	0.241809i	0.915981	−	0.401222i	$-0.131414\pi$
$311$	29.6592	+	4.26435i	1.68182	+	0.241809i	0.765840	+	0.643031i	$0.222323\pi$
$312$	4.03724	+	2.64387i	0.228564	+	0.149680i
$313$	−5.73952	−	6.62375i	−0.324417	−	0.374397i	0.569990	−	0.821652i	$-0.306947\pi$
$313$	−5.73952	−	6.62375i	−0.324417	−	0.374397i	−0.894406	+	0.447255i	$0.852402\pi$
$314$	−1.44437	−	3.16272i	−0.0815103	−	0.178483i
$315$	−22.7091	+	8.50614i	−1.27951	+	0.479267i
$316$	−2.44560	+	8.32895i	−0.137576	+	0.468540i
$317$	−12.5847	+	14.5235i	−0.706825	+	0.815719i	−0.989658	−	0.143450i	$-0.954180\pi$
$317$	−12.5847	+	14.5235i	−0.706825	+	0.815719i	0.282833	+	0.959169i	$0.408726\pi$
$318$	7.84048	−	2.22917i	0.439672	−	0.125006i
$319$	0.0991094	+	0.0452617i	0.00554906	+	0.00253417i
$320$	−0.118050	+	2.23295i	−0.00659921	+	0.124826i
$321$	−28.5226	−	0.245115i	−1.59198	−	0.0136810i
$322$	0.237324	−	17.3351i	0.0132256	−	0.966048i
$323$	−8.40069			−0.467427
$324$	−0.973920	−	8.94715i	−0.0541067	−	0.497064i
$325$	−9.50787	−	10.1823i	−0.527402	−	0.564810i
$326$	3.51645	+	11.9759i	0.194758	+	0.663285i
$327$	−7.91988	+	8.98288i	−0.437970	+	0.496754i
$328$	1.37595	−	4.68604i	0.0759739	−	0.258743i
$329$	24.4092	−	15.6869i	1.34573	−	0.864845i
$330$	−0.0606936	+	0.0138394i	−0.00334107	+	0.000761833i
$331$	−19.5193	−	22.5265i	−1.07288	−	1.23817i	−0.969905	−	0.243485i	$-0.921709\pi$
$331$	−19.5193	−	22.5265i	−1.07288	−	1.23817i	−0.102974	−	0.994684i	$-0.532836\pi$
$332$	0.420296	−	0.653994i	0.0230668	−	0.0358926i
$333$	−5.33267	+	33.0471i	−0.292229	+	1.81097i
$334$	−1.68005	+	11.6850i	−0.0919280	+	0.639373i
$335$	16.6683	+	16.0601i	0.910685	+	0.877455i
$336$	4.76703	−	4.05946i	0.260063	−	0.221462i
$337$	−4.36763	−	9.56379i	−0.237920	−	0.520973i	0.752577	−	0.658504i	$-0.228810\pi$
$337$	−4.36763	−	9.56379i	−0.237920	−	0.520973i	−0.990497	+	0.137531i	$0.956083\pi$
$338$	−4.40555	+	2.83128i	−0.239630	+	0.154001i
$339$	8.69096	+	2.63323i	0.472028	+	0.143017i
$340$	−5.24089	−	6.73639i	−0.284227	−	0.365332i
$341$	0.0855496	−	0.0251196i	0.00463277	−	0.00136030i
$342$	−5.95796	−	2.84566i	−0.322169	−	0.153875i
$343$	−0.479515	−	3.33510i	−0.0258914	−	0.180078i
$344$	1.25418			0.0676208
$345$	−16.2691	−	8.96193i	−0.875899	−	0.482494i
$346$	10.6147			0.570651
$347$	4.88147	+	33.9514i	0.262051	+	1.82260i	0.517386	+	0.855752i	$0.326905\pi$
$347$	4.88147	+	33.9514i	0.262051	+	1.82260i	−0.255335	+	0.966853i	$0.582186\pi$
$348$	−4.96900	+	10.6377i	−0.266366	+	0.570241i
$349$	19.2265	−	5.64541i	1.02917	−	0.302192i	0.276797	−	0.960928i	$-0.410727\pi$
$349$	19.2265	−	5.64541i	1.02917	−	0.302192i	0.752374	+	0.658736i	$0.228909\pi$
$350$	−16.1511	+	8.11423i	−0.863312	+	0.433724i
$351$	−13.7815	−	4.43557i	−0.735602	−	0.236753i
$352$	0.0135217	−	0.00868986i	0.000720708	−	0.000463171i
$353$	6.90622	+	15.1225i	0.367581	+	0.804890i	0.999553	+	0.0298988i	$0.00951852\pi$
$353$	6.90622	+	15.1225i	0.367581	+	0.804890i	−0.631972	+	0.774991i	$0.717754\pi$
$354$	2.22566	+	2.61360i	0.118293	+	0.138911i
$355$	−18.8199	+	19.5326i	−0.998855	+	1.03668i
$356$	1.63538	−	11.3743i	0.0866752	−	0.602839i
$357$	−3.60436	+	23.6257i	−0.190763	+	1.25041i
$358$	−11.1254	+	17.3114i	−0.587995	+	0.914938i
$359$	−11.6131	−	13.4022i	−0.612915	−	0.707342i	0.361430	−	0.932399i	$-0.382289\pi$
$359$	−11.6131	−	13.4022i	−0.612915	−	0.707342i	−0.974346	+	0.225057i	$0.927743\pi$
$360$	−1.43507	−	6.55291i	−0.0756349	−	0.345368i
$361$	11.9089	−	7.65337i	0.626783	−	0.402809i
$362$	1.10029	−	3.74725i	0.0578300	−	0.196951i
$363$	−14.2909	−	12.5998i	−0.750077	−	0.661315i
$364$	−2.83765	−	9.66414i	−0.148733	−	0.506538i
$365$	−25.8902	−	18.6407i	−1.35516	−	0.975700i
$366$	−1.52571	−	11.3001i	−0.0797503	−	0.590665i
$367$	24.8309			1.29616			0.648080	−	0.761572i	$-0.275572\pi$
$367$	24.8309			1.29616			0.648080	+	0.761572i	$0.275572\pi$
$368$	4.73723	+	0.747436i	0.246945	+	0.0389628i
$369$	−0.251805	+	14.6494i	−0.0131084	+	0.762620i
$370$	−1.31723	+	24.9157i	−0.0684794	+	1.29531i
$371$	−15.4750	−	7.06720i	−0.803422	−	0.366911i
$372$	2.62757	+	9.24173i	0.136233	+	0.479162i
$373$	−5.17827	+	5.97604i	−0.268120	+	0.309428i	−0.873804	−	0.486278i	$-0.838354\pi$
$373$	−5.17827	+	5.97604i	−0.268120	+	0.309428i	0.605684	+	0.795706i	$0.292900\pi$
$374$	−0.0172846	+	0.0588658i	−0.000893763	+	0.00304388i
$375$	−0.469524	+	19.3592i	−0.0242461	+	0.999706i
$376$	3.33431	+	7.30113i	0.171954	+	0.376527i
$377$	12.3684	+	14.2739i	0.637003	+	0.735141i
$378$	−10.5593	+	15.5350i	−0.543112	+	0.799033i
$379$	−21.8053	−	3.13512i	−1.12006	−	0.161040i	−0.442685	−	0.896677i	$-0.645974\pi$
$379$	−21.8053	−	3.13512i	−1.12006	−	0.161040i	−0.677376	+	0.735637i	$0.736883\pi$
$380$	−4.64220	−	1.63385i	−0.238140	−	0.0838150i
$381$	−5.87910	−	3.85005i	−0.301195	−	0.197244i
$382$	−17.2626	−	19.9221i	−0.883232	−	1.01930i
$383$	−2.76493	+	1.26270i	−0.141281	+	0.0645210i	−0.484801	−	0.874624i	$-0.661108\pi$
$383$	−2.76493	+	1.26270i	−0.141281	+	0.0645210i	0.343520	+	0.939145i	$0.388381\pi$
$384$	0.923861	+	1.46509i	0.0471456	+	0.0747649i
$385$	0.115170	+	0.0601368i	0.00586958	+	0.00306486i
$386$	−10.4138	−	9.02362i	−0.530049	−	0.459290i
$387$	−3.62781	+	0.997829i	−0.184412	+	0.0507225i
$388$	−3.52284	+	7.71394i	−0.178845	+	0.391616i
$389$	2.88102	+	20.0379i	0.146074	+	1.01596i	0.922566	+	0.385838i	$0.126088\pi$
$389$	2.88102	+	20.0379i	0.146074	+	1.01596i	−0.776493	+	0.630126i	$0.783003\pi$
$390$	−10.5668	−	2.18837i	−0.535072	−	0.110812i
$391$	−15.5336	+	9.68497i	−0.785568	+	0.489790i
$392$	−6.06793			−0.306477
$393$	−0.640343	−	4.74266i	−0.0323010	−	0.239235i
$394$	6.62000	−	14.4958i	0.333511	−	0.730286i
$395$	−1.74422	−	19.3318i	−0.0877611	−	0.972690i
$396$	−0.0321989	+	0.0358940i	−0.00161805	+	0.00180374i
$397$	−4.02772	+	13.7172i	−0.202146	+	0.688444i	0.794549	+	0.607200i	$0.207707\pi$
$397$	−4.02772	+	13.7172i	−0.202146	+	0.688444i	−0.996694	+	0.0812440i	$0.974111\pi$
$398$	12.3616	+	19.2350i	0.619629	+	0.964161i
$399$	5.61665	+	12.5838i	0.281184	+	0.629978i
$400$	−1.58594	−	4.74181i	−0.0792969	−	0.237091i
$401$	14.6717	+	9.42894i	0.732670	+	0.470859i	0.853024	−	0.521872i	$-0.174766\pi$
$401$	14.6717	+	9.42894i	0.732670	+	0.470859i	−0.120353	+	0.992731i	$0.538403\pi$
$402$	17.7241	+	2.70399i	0.883996	+	0.134863i
$403$	15.2984	+	2.19958i	0.762070	+	0.109569i
$404$	3.03937	−	4.72935i	0.151214	−	0.235294i
$405$	9.36457	+	17.8131i	0.465329	+	0.885138i
$406$	22.2902	−	10.1796i	1.10625	−	0.505205i
$407$	0.150878	−	0.0969631i	0.00747872	−	0.00480628i
$408$	−6.32713	−	1.91702i	−0.313240	−	0.0949068i
$409$	12.3065	−	14.2024i	0.608516	−	0.702265i	−0.364968	−	0.931020i	$-0.618920\pi$
$409$	12.3065	−	14.2024i	0.608516	−	0.702265i	0.973484	+	0.228755i	$0.0734655\pi$
$410$	0.981332	+	10.8765i	0.0484645	+	0.537151i
$411$	−14.4149	+	30.8597i	−0.711035	+	1.52219i
$412$	0.518220	+	3.60430i	0.0255309	+	0.177571i
$413$		−	7.16470i		−	0.352552i
$414$	−14.2975	+	1.60693i	−0.702683	+	0.0789765i
$415$	−0.337884	+	1.70517i	−0.0165861	+	0.0837037i
$416$	2.75788	−	0.396523i	0.135216	−	0.0194411i
$417$	26.5013	+	12.3791i	1.29778	+	0.606206i
$418$	0.00996639	+	0.0339424i	0.000487472	+	0.00166018i
$419$	9.60315	−	11.0826i	0.469145	−	0.541422i	−0.471029	−	0.882118i	$-0.656117\pi$
$419$	9.60315	−	11.0826i	0.469145	−	0.541422i	0.940174	+	0.340696i	$0.110663\pi$
$420$	−6.58674	+	12.3545i	−0.321400	+	0.602838i
$421$	17.9645	+	27.9533i	0.875536	+	1.36236i	0.931429	+	0.363924i	$0.118563\pi$
$421$	17.9645	+	27.9533i	0.875536	+	1.36236i	−0.0558922	+	0.998437i	$0.517800\pi$
$422$	−5.89469	−	12.9076i	−0.286949	−	0.628331i
$423$	−15.4536	−	18.4663i	−0.751378	−	0.897862i
$424$	2.54431	−	3.95903i	0.123563	−	0.192267i
$425$	16.4274	+	9.71437i	0.796848	+	0.471216i
$426$	−3.16865	+	20.7698i	−0.153522	+	1.00630i
$427$	−12.8664	+	20.0205i	−0.622648	+	0.968859i
$428$	−12.4458	+	10.7843i	−0.601590	+	0.521281i
$429$	0.0316154	+	0.0708326i	0.00152640	+	0.00341983i
$430$	−2.60895	+	1.02870i	−0.125815	+	0.0496084i
$431$	−21.8220	−	6.40751i	−1.05113	−	0.308639i	−0.289855	−	0.957071i	$-0.593607\pi$
$431$	−21.8220	−	6.40751i	−1.05113	−	0.308639i	−0.761273	+	0.648432i	$0.775425\pi$
$432$	−3.83797	−	3.50285i	−0.184654	−	0.168531i
$433$	25.8186	−	7.58104i	1.24076	−	0.364321i	0.405462	−	0.914112i	$-0.367111\pi$
$433$	25.8186	−	7.58104i	1.24076	−	0.364321i	0.835303	+	0.549790i	$0.185292\pi$
$434$	8.33025	−	18.2407i	0.399865	−	0.875582i
$435$	1.61127	−	26.2042i	0.0772546	−	1.25640i
$436$			6.91416i			0.331128i
$437$	−4.51576	+	9.54031i	−0.216018	+	0.456375i
$438$	−24.7108	−	0.212357i	−1.18073	−	0.0101468i
$439$	−4.61673	−	32.1101i	−0.220345	−	1.53253i	−0.736737	−	0.676179i	$-0.763635\pi$
$439$	−4.61673	−	32.1101i	−0.220345	−	1.53253i	0.516393	−	0.856352i	$-0.327274\pi$
$440$	−0.0210002	+	0.0291674i	−0.00100115	+	0.00139050i
$441$	17.5520	−	4.82766i	0.835808	−	0.229889i
$442$	−6.96441	+	8.03736i	−0.331263	+	0.382298i
$443$	5.05622	+	1.48464i	0.240228	+	0.0705374i	0.399630	−	0.916676i	$-0.369138\pi$
$443$	5.05622	+	1.48464i	0.240228	+	0.0705374i	−0.159402	+	0.987214i	$0.550957\pi$
$444$	10.3086	+	16.3477i	0.489226	+	0.775829i
$445$	5.92752	+	25.0023i	0.280991	+	1.18522i
$446$	8.07426	−	6.99638i	0.382327	−	0.331288i
$447$	−5.49459	+	8.39033i	−0.259885	+	0.396849i
$448$	0.514462	−	3.57816i	0.0243061	−	0.169052i
$449$	−7.37839	−	1.06085i	−0.348208	−	0.0500647i	−0.0340078	−	0.999422i	$-0.510827\pi$
$449$	−7.37839	−	1.06085i	−0.348208	−	0.0500647i	−0.314200	+	0.949357i	$0.601736\pi$
$450$	8.36005	+	12.4543i	0.394097	+	0.587101i
$451$	0.0593261	−	0.0514064i	0.00279356	−	0.00242063i
$452$	4.76918	−	2.17801i	0.224324	−	0.102445i
$453$	0.238616	+	0.378404i	0.0112111	+	0.0177790i
$454$	−0.136046	+	0.463330i	−0.00638496	+	0.0217452i
$455$	13.8296	+	17.7759i	0.648341	+	0.833346i
$456$	−3.66672	+	1.04251i	−0.171710	+	0.0488198i
$457$	3.17031	−	6.94201i	0.148301	−	0.324733i	−0.820873	−	0.571110i	$-0.806513\pi$
$457$	3.17031	−	6.94201i	0.148301	−	0.324733i	0.969174	+	0.246377i	$0.0792401\pi$
$458$	1.66647	−	0.239602i	0.0778691	−	0.0111959i
$459$	19.8269	+	0.511261i	0.925441	+	0.0238636i
$460$	−10.4675	+	2.33074i	−0.488048	+	0.108672i
$461$		−	3.00904i		−	0.140145i	−0.997542	−	0.0700724i	$-0.977677\pi$
$461$		−	3.00904i		−	0.140145i	0.997542	−	0.0700724i	$-0.0223230\pi$
$462$	0.0997344	−	0.0134659i	0.00464006	−	0.000626491i
$463$	28.0981	+	12.8320i	1.30583	+	0.596351i	0.942156	−	0.335176i	$-0.108796\pi$
$463$	28.0981	+	12.8320i	1.30583	+	0.596351i	0.363672	+	0.931527i	$0.381523\pi$
$464$	1.90978	+	6.50410i	0.0886591	+	0.301945i
$465$	−13.0461	−	17.0695i	−0.604999	−	0.791579i
$466$	−25.3023	−	7.42942i	−1.17211	−	0.344161i
$467$	−17.5028	−	27.2349i	−0.809934	−	1.26028i	−0.962309	−	0.271960i	$-0.912328\pi$
$467$	−17.5028	−	27.2349i	−0.809934	−	1.26028i	0.152374	−	0.988323i	$-0.451308\pi$
$468$	−7.66190	+	3.34115i	−0.354172	+	0.154445i
$469$	−24.5048	−	28.2801i	−1.13153	−	1.30585i
$470$	−12.9246	−	12.4530i	−0.596166	−	0.574412i
$471$	5.95332	+	0.908242i	0.274315	+	0.0418496i
$472$	1.96178	+	0.282062i	0.0902984	+	0.0129830i
$473$	0.0169586	+	0.0108986i	0.000779758	+	0.000501120i
$474$	−9.74796	−	11.4470i	−0.447738	−	0.525780i
$475$	10.9968	−	0.408866i	0.504569	−	0.0187600i
$476$	7.45985	+	11.6077i	0.341921	+	0.532040i
$477$	−4.20981	+	13.4761i	−0.192754	+	0.617027i
$478$	5.17383	+	4.48315i	0.236645	+	0.205054i
$479$	31.8283	−	9.34562i	1.45427	−	0.427012i	0.543319	−	0.839526i	$-0.317167\pi$
$479$	31.8283	−	9.34562i	1.45427	−	0.427012i	0.910951	+	0.412514i	$0.135349\pi$
$480$	−3.12351	−	2.28991i	−0.142568	−	0.104520i
$481$	30.7729	−	4.42448i	1.40312	−	0.201739i
$482$		−	28.4583i		−	1.29624i
$483$	24.8933	+	16.7932i	1.13268	+	0.764119i
$484$	−10.9997			−0.499988
$485$	1.00110	−	18.9361i	0.0454576	−	0.859842i
$486$	13.8885	+	7.07878i	0.629996	+	0.321100i
$487$	−2.20953	−	7.52496i	−0.100123	−	0.340989i	0.894162	−	0.447743i	$-0.147772\pi$
$487$	−2.20953	−	7.52496i	−0.100123	−	0.340989i	−0.994285	+	0.106755i	$0.965954\pi$
$488$	−4.97533	−	4.31115i	−0.225223	−	0.195157i
$489$	−20.6898	−	6.26870i	−0.935625	−	0.283480i
$490$	12.6225	−	4.97703i	0.570227	−	0.224839i
$491$	−6.78378	+	3.09805i	−0.306148	+	0.139813i	−0.562565	−	0.826753i	$-0.690185\pi$
$491$	−6.78378	+	3.09805i	−0.306148	+	0.139813i	0.256417	+	0.966566i	$0.417458\pi$
$492$	5.48440	+	6.44034i	0.247256	+	0.290353i
$493$	−21.7666	−	13.9885i	−0.980317	−	0.630011i
$494$	−0.872701	+	6.06977i	−0.0392647	+	0.273092i
$495$	0.0375392	−	0.101077i	0.00168726	−	0.00454307i
$496$	4.66659	+	2.99903i	0.209536	+	0.134661i
$497$	33.1398	−	28.7158i	1.48652	−	1.28808i
$498$	0.548812	+	1.22958i	0.0245928	+	0.0550990i
$499$	20.2977	−	13.0445i	0.908649	−	0.583953i	−0.000694210	−	1.00000i	$-0.500221\pi$
$499$	20.2977	−	13.0445i	0.908649	−	0.583953i	0.909343	+	0.416046i	$0.136585\pi$
$500$	7.18840	+	8.56312i	0.321475	+	0.382954i
$501$	−15.3372	−	13.5223i	−0.685217	−	0.604131i
$502$	1.51727	−	0.445510i	0.0677189	−	0.0198841i
$503$	14.1359	+	6.45564i	0.630288	+	0.287843i	0.704831	−	0.709375i	$-0.251023\pi$
$503$	14.1359	+	6.45564i	0.630288	+	0.287843i	−0.0745434	+	0.997218i	$0.523750\pi$
$504$	1.35867	+	10.7594i	0.0605202	+	0.479263i
$505$	−2.44340	+	12.3310i	−0.108730	+	0.548721i
$506$	0.0575602	+	0.0512724i	0.00255886	+	0.00227934i
$507$	0.0779468	−	9.07022i	0.00346174	−	0.402823i
$508$	−4.01607	+	0.577424i	−0.178184	+	0.0256190i
$509$	24.3197	+	11.1064i	1.07795	+	0.492284i	0.873616	−	0.486617i	$-0.161769\pi$
$509$	24.3197	+	11.1064i	1.07795	+	0.492284i	0.204336	+	0.978901i	$0.434496\pi$
$510$	14.7341	−	1.20183i	0.652436	−	0.0532180i
$511$	38.9783	+	33.7749i	1.72430	+	1.49411i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	9.77687	−	5.93279i	0.431659	−	0.261939i
$514$	−5.60246	−	12.2677i	−0.247114	−	0.541104i
$515$	−4.03432	−	7.07262i	−0.177773	−	0.311657i
$516$	−1.19010	+	1.81730i	−0.0523910	+	0.0800020i
$517$	−0.0183602	+	0.127698i	−0.000807482	+	0.00561616i
$518$	5.74047	−	39.9259i	0.252222	−	1.75424i
$519$	−10.0723	+	15.3806i	−0.442127	+	0.675135i
$520$	−5.41171	+	3.08691i	−0.237319	+	0.135370i
$521$	11.6764	+	25.5678i	0.511553	+	1.12015i	0.972539	+	0.232738i	$0.0747686\pi$
$521$	11.6764	+	25.5678i	0.511553	+	1.12015i	−0.460986	+	0.887407i	$0.652504\pi$
$522$	−10.6989	−	17.2942i	−0.468276	−	0.756947i
$523$	13.0356	+	3.82761i	0.570008	+	0.167370i	0.554021	−	0.832503i	$-0.313093\pi$
$523$	13.0356	+	3.82761i	0.570008	+	0.167370i	0.0159873	+	0.999872i	$0.494911\pi$
$524$	−2.08815	−	1.80939i	−0.0912213	−	0.0790437i
$525$	3.56836	−	31.1024i	0.155736	−	1.35742i
$526$	−2.56310	−	1.17053i	−0.111756	−	0.0510374i
$527$	−20.9579	+	3.01329i	−0.912939	+	0.131261i
$528$	−0.000239237		0.0278387i	−1.04115e−5		0.00121152i
$529$	2.64878	+	22.8470i	0.115165	+	0.993346i
$530$	−2.04542	+	10.3225i	−0.0888472	+	0.448379i
$531$	−5.89903	+	0.744914i	−0.255996	+	0.0323265i
$532$	7.23713	+	3.30509i	0.313769	+	0.143294i
$533$	13.0564	−	3.83371i	0.565536	−	0.166056i
$534$	14.9295	+	13.1628i	0.646064	+	0.569611i
$535$	17.0442	−	32.6419i	0.736887	−	1.41123i
$536$	8.70815	−	5.59639i	0.376135	−	0.241727i
$537$	−14.5272	−	32.5475i	−0.626896	−	1.40453i
$538$	8.28727	−	7.18096i	0.357290	−	0.309593i
$539$	−0.0820486	−	0.0527294i	−0.00353408	−	0.00227122i
$540$	10.8569	+	4.13867i	0.467205	+	0.178100i
$541$	−4.24105	+	29.4971i	−0.182337	+	1.26818i	0.668881	+	0.743369i	$0.266773\pi$
$541$	−4.24105	+	29.4971i	−0.182337	+	1.26818i	−0.851218	+	0.524812i	$0.824136\pi$
$542$	3.25411	+	2.09129i	0.139776	+	0.0898286i
$543$	4.38567	+	5.15009i	0.188207	+	0.221012i
$544$	−3.47203	+	1.58562i	−0.148862	+	0.0679830i
$545$	−5.67112	−	14.3828i	−0.242924	−	0.616093i
$546$	16.6959	+	5.05861i	0.714520	+	0.216489i
$547$	−4.42071	−	3.83056i	−0.189016	−	0.163783i	0.555212	−	0.831709i	$-0.312637\pi$
$547$	−4.42071	−	3.83056i	−0.189016	−	0.163783i	−0.744228	+	0.667926i	$0.767182\pi$
$548$	5.54020	+	18.8682i	0.236666	+	0.806009i
$549$	17.8215	+	8.51196i	0.760604	+	0.363281i
$550$	0.0197611	−	0.0778989i	0.000842617	−	0.00332162i
$551$	−14.9191			−0.635575
$552$	−5.57821	+	6.15497i	−0.237424	+	0.261973i
$553$			31.3799i			1.33441i
$554$	−11.0466	+	1.58827i	−0.469326	+	0.0674790i
$555$	−34.8527	−	25.5513i	−1.47942	−	1.08459i
$556$	16.2034	−	4.75776i	0.687178	−	0.201774i
$557$	24.2919	+	21.0490i	1.02928	+	0.891877i	0.994204	−	0.107508i	$-0.0342871\pi$
$557$	24.2919	+	21.0490i	1.02928	+	0.891877i	0.0350762	+	0.999385i	$0.488833\pi$
$558$	−15.8845	−	4.96219i	−0.672445	−	0.210066i
$559$	1.88924	+	2.93971i	0.0799062	+	0.124336i
$560$	1.86469	+	7.86528i	0.0787976	+	0.332369i
$561$	−0.0688948	−	0.0809032i	−0.00290874	−	0.00341574i
$562$	7.77680	+	4.99784i	0.328044	+	0.210821i
$563$	−18.3984	−	2.64529i	−0.775399	−	0.111486i	−0.256756	−	0.966476i	$-0.582654\pi$
$563$	−18.3984	−	2.64529i	−0.775399	−	0.111486i	−0.518643	+	0.854991i	$0.673563\pi$
$564$	−13.7432	−	2.09667i	−0.578694	−	0.0882859i
$565$	−8.13442	+	8.44248i	−0.342218	+	0.355178i
$566$	−11.5721	−	13.3549i	−0.486411	−	0.561349i
$567$	−12.4903	−	30.0415i	−0.524544	−	1.26163i
$568$	6.55809	+	10.2046i	0.275171	+	0.428175i
$569$	−31.1601	−	9.14944i	−1.30630	−	0.383564i	−0.446770	−	0.894649i	$-0.647426\pi$
$569$	−31.1601	−	9.14944i	−1.30630	−	0.383564i	−0.859530	+	0.511085i	$0.829244\pi$
$570$	6.77244	−	5.17614i	0.283666	−	0.216805i
$571$	−2.82959	−	9.63669i	−0.118415	−	0.403283i	0.878859	−	0.477083i	$-0.158306\pi$
$571$	−2.82959	−	9.63669i	−0.118415	−	0.403283i	−0.997273	+	0.0737994i	$0.976488\pi$
$572$	0.0407368	+	0.0186039i	0.00170329	+	0.000777868i
$573$	45.2475	−	6.10922i	1.89024	−	0.255216i
$574$		−	17.6550i		−	0.736905i
$575$	19.8627	−	13.4340i	0.828332	−	0.560237i
$576$	−2.99956	−	0.0515584i	−0.124982	−	0.00214827i
$577$	−16.8378	+	2.42092i	−0.700968	+	0.100784i	−0.483579	−	0.875301i	$-0.660663\pi$
$577$	−16.8378	+	2.42092i	−0.700968	+	0.100784i	−0.217390	+	0.976085i	$0.569754\pi$
$578$	−1.00980	+	2.21115i	−0.0420020	+	0.0919716i
$579$	22.9569	−	6.52699i	0.954055	−	0.271253i
$580$	−9.30750	−	11.9634i	−0.386473	−	0.496753i
$581$	0.791749	−	2.69645i	0.0328473	−	0.111868i
$582$	−7.83461	−	12.4244i	−0.324755	−	0.515006i
$583$	0.0688068	−	0.0314230i	0.00284968	−	0.00130141i
$584$	−10.7825	+	9.34310i	−0.446184	+	0.386620i
$585$	13.1978	−	13.2347i	0.545663	−	0.547187i
$586$	−6.97649	−	1.00307i	−0.288196	−	0.0414364i
$587$	−5.39106	+	37.4956i	−0.222513	+	1.54761i	0.505973	+	0.862549i	$0.331134\pi$
$587$	−5.39106	+	37.4956i	−0.222513	+	1.54761i	−0.728486	+	0.685061i	$0.759775\pi$
$588$	5.75788	−	8.79239i	0.237451	−	0.362592i
$589$	−9.22673	+	7.99500i	−0.380181	+	0.329428i
$590$	−4.31226	+	1.02235i	−0.177533	+	0.0420893i
$591$	14.7225	+	23.3474i	0.605604	+	0.960385i
$592$	10.7062	+	3.14363i	0.440023	+	0.129202i
$593$	−26.2792	+	30.3278i	−1.07916	+	1.24542i	−0.111335	+	0.993783i	$0.535513\pi$
$593$	−26.2792	+	30.3278i	−1.07916	+	1.24542i	−0.967823	+	0.251632i	$0.919033\pi$
$594$	−0.0214565	−	0.0807159i	−0.000880371	−	0.00331181i
$595$	−25.0389	−	18.0278i	−1.02649	−	0.739066i
$596$	0.824068	+	5.73152i	0.0337551	+	0.234772i
$597$	−39.6012	−	0.340321i	−1.62077	−	0.0139284i
$598$	5.38400	+	12.2296i	0.220168	+	0.500107i
$599$		−	33.6039i		−	1.37302i	−0.727121	−	0.686510i	$-0.759142\pi$
$599$		−	33.6039i		−	1.37302i	0.727121	−	0.686510i	$-0.240858\pi$
$600$	8.37576	+	2.20151i	0.341939	+	0.0898764i
$601$	−15.1375	+	33.1465i	−0.617471	+	1.35207i	0.299873	+	0.953979i	$0.403056\pi$
$601$	−15.1375	+	33.1465i	−0.617471	+	1.35207i	−0.917344	+	0.398094i	$0.869672\pi$
$602$	4.35016	−	1.27732i	0.177299	−	0.0520597i
$603$	−20.7365	+	23.1162i	−0.844456	+	0.941365i
$604$	0.247819	+	0.0727661i	0.0100836	+	0.00296081i
$605$	22.8817	−	9.02219i	0.930273	−	0.366804i
$606$	3.96873	+	8.89173i	0.161219	+	0.361202i
$607$	4.88592	−	4.23367i	0.198313	−	0.171839i	−0.550043	−	0.835136i	$-0.685389\pi$
$607$	4.88592	−	4.23367i	0.198313	−	0.171839i	0.748356	+	0.663297i	$0.230843\pi$
$608$	−1.18989	+	1.85150i	−0.0482563	+	0.0750883i
$609$	−6.40111	+	41.9579i	−0.259386	+	1.70022i
$610$	13.8858	+	4.88721i	0.562219	+	0.197877i
$611$	−12.0907	+	18.8135i	−0.489137	+	0.761112i
$612$	8.78159	−	7.34890i	0.354975	−	0.297062i
$613$	10.0682	+	22.0463i	0.406651	+	0.890441i	0.996552	+	0.0829661i	$0.0264393\pi$
$613$	10.0682	+	22.0463i	0.406651	+	0.890441i	−0.589901	+	0.807475i	$0.700833\pi$
$614$	17.0895	+	26.5918i	0.689676	+	1.07316i
$615$	−16.6911	−	8.89880i	−0.673052	−	0.358834i
$616$	0.0380501	−	0.0439122i	0.00153308	−	0.00176927i
$617$	−10.9103	−	37.1570i	−0.439232	−	1.49589i	−0.820622	−	0.571472i	$-0.806373\pi$
$617$	−10.9103	−	37.1570i	−0.439232	−	1.49589i	0.381390	−	0.924414i	$-0.375446\pi$
$618$	−5.71435	−	2.66924i	−0.229865	−	0.107373i
$619$	16.1584	−	2.32323i	0.649463	−	0.0933786i	0.190293	−	0.981727i	$-0.439056\pi$
$619$	16.1584	−	2.32323i	0.649463	−	0.0933786i	0.459170	+	0.888349i	$0.348147\pi$
$620$	−12.1673	−	2.41098i	−0.488651	−	0.0968271i
$621$	11.2385	−	22.2418i	0.450985	−	0.892531i
$622$			29.9642i			1.20146i
$623$	−5.91185	−	41.1178i	−0.236853	−	1.64735i
$624$	−2.04240	+	4.37241i	−0.0817615	+	0.175036i
$625$	−21.9769	−	11.9170i	−0.879078	−	0.476678i
$626$	5.73952	−	6.62375i	0.229397	−	0.264738i
$627$	−0.0586395	−	0.0177669i	−0.00234183	−	0.000709540i
$628$	2.92497	−	1.87977i	0.116719	−	0.0750108i
$629$	−38.7416	+	17.6927i	−1.54473	+	0.705454i
$630$	−11.6514	−	21.2674i	−0.464203	−	0.847313i
$631$	16.5140	−	25.6963i	0.657412	−	1.02295i	−0.339200	−	0.940714i	$-0.610156\pi$
$631$	16.5140	−	25.6963i	0.657412	−	1.02295i	0.996613	−	0.0822392i	$-0.0262071\pi$
$632$	−8.59222	−	1.23538i	−0.341780	−	0.0491406i
$633$	24.2965	+	3.70668i	0.965698	+	0.147327i
$634$	−16.1666	−	10.3897i	−0.642058	−	0.412626i
$635$	7.88062	−	4.49521i	0.312733	−	0.178387i
$636$	3.32229	+	7.44343i	0.131738	+	0.295151i
$637$	−9.14044	−	14.2228i	−0.362158	−	0.563528i
$638$	−0.0306963	+	0.104542i	−0.00121528	+	0.00413886i
$639$	−27.0886	−	24.2999i	−1.07161	−	0.961290i
$640$	−2.22702	+	0.200933i	−0.0880308	+	0.00794258i
$641$	19.5789	−	42.8718i	0.773321	−	1.69334i	0.0541189	−	0.998534i	$-0.482765\pi$
$641$	19.5789	−	42.8718i	0.773321	−	1.69334i	0.719202	−	0.694801i	$-0.244508\pi$
$642$	−3.81657	−	28.2672i	−0.150628	−	1.11562i
$643$	13.0632			0.515163			0.257581	−	0.966257i	$-0.417074\pi$
$643$	13.0632			0.515163			0.257581	+	0.966257i	$0.417074\pi$
$644$	17.1924	−	2.23214i	0.677477	−	0.0879584i
$645$	0.985059	−	4.75648i	0.0387867	−	0.187286i
$646$	−1.19554	−	8.31518i	−0.0470380	−	0.327156i
$647$	−4.60331	+	10.0798i	−0.180975	+	0.396280i	−0.978277	−	0.207300i	$-0.933532\pi$
$647$	−4.60331	+	10.0798i	−0.180975	+	0.396280i	0.797303	+	0.603580i	$0.206260\pi$
$648$	8.71748	−	2.23732i	0.342455	−	0.0878902i
$649$	0.0240755	+	0.0208616i	0.000945048	+	0.000818888i
$650$	8.72550	−	10.8602i	0.342242	−	0.425971i
$651$	18.5260	+	29.3792i	0.726093	+	1.15146i
$652$	−11.3536	+	5.18501i	−0.444641	+	0.203061i
$653$	−21.8727	−	25.2425i	−0.855947	−	0.987815i	0.144052	−	0.989570i	$-0.453987\pi$
$653$	−21.8727	−	25.2425i	−0.855947	−	0.987815i	−0.999998	+	0.00175515i	$0.999441\pi$
$654$	−10.0186	−	6.56087i	−0.391757	−	0.256550i
$655$	5.82788	+	2.05116i	0.227714	+	0.0801456i
$656$	4.83416	+	0.695047i	0.188742	+	0.0271370i
$657$	23.7559	−	35.6043i	0.926805	−	1.38905i
$658$	19.0010	+	21.9283i	0.740736	+	0.854855i
$659$	−16.2245	−	35.5266i	−0.632015	−	1.38392i	−0.906450	−	0.422314i	$-0.861218\pi$
$659$	−16.2245	−	35.5266i	−0.632015	−	1.38392i	0.274434	−	0.961606i	$-0.411509\pi$
$660$	−0.0223361	−	0.0581063i	−0.000869432	−	0.00226178i
$661$	13.3998	−	45.6355i	0.521191	−	1.77502i	−0.104037	−	0.994573i	$-0.533176\pi$
$661$	13.3998	−	45.6355i	0.521191	−	1.77502i	0.625228	−	0.780442i	$-0.285006\pi$
$662$	19.5193	−	22.5265i	0.758640	−	0.875517i
$663$	−5.03752	−	17.7181i	−0.195641	−	0.688113i
$664$	0.707152	+	0.322945i	0.0274428	+	0.0125327i
$665$	−17.7656	−	0.939220i	−0.688920	−	0.0364214i
$666$	−33.4696	−	0.575299i	−1.29692	−	0.0222924i
$667$	−27.5867	+	17.1999i	−1.06816	+	0.665983i
$668$	−11.8051			−0.456754
$669$	2.47602	+	18.3384i	0.0957283	+	0.709005i
$670$	−13.5245	+	18.7842i	−0.522495	+	0.725697i
$671$	−0.0298116	−	0.101529i	−0.00115086	−	0.00391948i
$672$	4.69656	+	4.14079i	0.181174	+	0.159734i
$673$	0.189305	−	0.644715i	0.00729718	−	0.0248519i	−0.955764	−	0.294135i	$-0.904969\pi$
$673$	0.189305	−	0.644715i	0.00729718	−	0.0248519i	0.963061	+	0.269283i	$0.0867867\pi$
$674$	8.84486	−	5.68425i	0.340691	−	0.218949i
$675$	−25.9791	+	0.295726i	−0.999935	+	0.0113825i
$676$	−3.42943	−	3.95778i	−0.131901	−	0.152222i
$677$	11.9288	−	18.5615i	0.458459	−	0.713377i	−0.532663	−	0.846327i	$-0.678809\pi$
$677$	11.9288	−	18.5615i	0.458459	−	0.713377i	0.991123	+	0.132951i	$0.0424452\pi$
$678$	−1.36957	+	8.97724i	−0.0525981	+	0.344769i
$679$	−4.36279	+	30.3439i	−0.167428	+	1.16449i
$680$	5.92197	−	6.14624i	0.227097	−	0.235697i
$681$	−0.542268	−	0.636786i	−0.0207797	−	0.0244017i
$682$	0.0370389	+	0.0811040i	0.00141829	+	0.00310563i
$683$	28.4000	−	18.2516i	1.08670	−	0.698378i	0.130603	−	0.991435i	$-0.458309\pi$
$683$	28.4000	−	18.2516i	1.08670	−	0.698378i	0.956095	+	0.293057i	$0.0946724\pi$
$684$	1.96879	−	6.30229i	0.0752784	−	0.240974i
$685$	−27.0008	−	34.7055i	−1.03165	−	1.32603i
$686$	3.23291	−	0.949268i	0.123433	−	0.0362432i
$687$	−1.23414	+	2.64207i	−0.0470854	+	0.100801i
$688$	0.178488	+	1.24141i	0.00680480	+	0.0473284i
$689$	13.1123			0.499540
$690$	6.55538	−	17.3789i	0.249559	−	0.661604i
$691$	−20.6708			−0.786355			−0.393178	−	0.919463i	$-0.628624\pi$
$691$	−20.6708			−0.786355			−0.393178	+	0.919463i	$0.628624\pi$
$692$	1.51063	+	10.5067i	0.0574256	+	0.399404i
$693$	−0.0751263	+	0.157292i	−0.00285381	+	0.00597504i
$694$	−32.9111	+	9.66357i	−1.24929	+	0.366824i
$695$	−29.8040	+	23.1874i	−1.13053	+	0.879550i
$696$	−11.2366	−	3.40451i	−0.425922	−	0.129048i
$697$	−15.6823	+	10.0784i	−0.594008	+	0.381746i
$698$	8.32416	+	18.2274i	0.315074	+	0.689916i
$699$	34.7746	−	29.6130i	1.31530	−	1.12007i
$700$	−10.3302	−	14.8319i	−0.390444	−	0.560594i
$701$	1.55650	−	10.8257i	0.0587881	−	0.408880i	−0.939085	−	0.343686i	$-0.888324\pi$
$701$	1.55650	−	10.8257i	0.0587881	−	0.408880i	0.997873	−	0.0651939i	$-0.0207666\pi$
$702$	2.42911	−	14.2725i	0.0916809	−	0.538680i
$703$	−13.2770	+	20.6594i	−0.500752	+	0.779185i
$704$	0.0105257	+	0.0121474i	0.000396704	+	0.000457821i
$705$	30.3084	−	6.91094i	1.14148	−	0.260281i
$706$	−13.9857	+	8.98808i	−0.526360	+	0.338271i
$707$	5.72553	−	19.4993i	0.215331	−	0.733348i
$708$	−2.27025	+	2.57496i	−0.0853213	+	0.0967730i
$709$	1.68526	+	5.73945i	0.0632911	+	0.215550i	0.985066	−	0.172175i	$-0.0550794\pi$
$709$	1.68526	+	5.73945i	0.0632911	+	0.215550i	−0.921775	+	0.387724i	$0.873261\pi$
$710$	−22.0121	−	15.8485i	−0.826101	−	0.594785i
$711$	25.8366	−	3.26258i	0.968947	−	0.122356i
$712$	11.4913			0.430655
$713$	−7.84375	+	25.4207i	−0.293751	+	0.952014i
$714$	−23.8982	−	0.205374i	−0.894369	−	0.00768594i
$715$	−0.100000	−	0.00528675i	−0.00373979	−	0.000197713i
$716$	−18.7185	−	8.54847i	−0.699545	−	0.319471i
$717$	−11.4055	+	3.24276i	−0.425947	+	0.121103i
$718$	11.6131	−	13.4022i	0.433396	−	0.500166i
$719$	6.35966	−	21.6590i	0.237175	−	0.807745i	−0.751765	−	0.659431i	$-0.770797\pi$
$719$	6.35966	−	21.6590i	0.237175	−	0.807745i	0.988940	−	0.148314i	$-0.0473845\pi$
$720$	6.28197	−	2.35304i	0.234115	−	0.0876926i
$721$	5.46827	+	11.9738i	0.203649	+	0.445929i
$722$	9.27028	+	10.6985i	0.345004	+	0.398156i
$723$	41.2359	+	27.0042i	1.53358	+	1.00430i
$724$	3.86569	+	0.555803i	0.143667	+	0.0206563i
$725$	29.1741	+	17.2521i	1.08350	+	0.640728i
$726$	10.4377	−	15.9385i	0.387379	−	0.591535i
$727$	−2.68972	−	3.10410i	−0.0997561	−	0.115125i	0.703676	−	0.710521i	$-0.251541\pi$
$727$	−2.68972	−	3.10410i	−0.0997561	−	0.115125i	−0.803432	+	0.595396i	$0.796995\pi$
$728$	9.16193	−	4.18411i	0.339564	−	0.155074i
$729$	−23.4360	+	13.4073i	−0.867999	+	0.496566i
$730$	14.7664	−	28.2796i	0.546530	−	1.04667i
$731$	−3.61789	−	3.13492i	−0.133812	−	0.115949i
$732$	10.9679	−	3.11835i	0.405387	−	0.115258i
$733$	−7.94247	+	17.3916i	−0.293362	+	0.642373i	−0.997721	−	0.0674706i	$-0.978507\pi$
$733$	−7.94247	+	17.3916i	−0.293362	+	0.642373i	0.704359	+	0.709844i	$0.251234\pi$
$734$	3.53380	+	24.5781i	0.130435	+	0.907195i
$735$	−4.76588	+	23.0127i	−0.175792	+	0.848835i
$736$	−0.0656506	+	4.79538i	−0.00241991	+	0.176760i
$737$	0.166381			0.00612871
$738$	−14.5362	+	1.83559i	−0.535084	+	0.0675691i
$739$	−10.4802	+	22.9484i	−0.385519	+	0.844170i	0.613016	+	0.790070i	$0.289956\pi$
$739$	−10.4802	+	22.9484i	−0.385519	+	0.844170i	−0.998536	+	0.0540992i	$0.982771\pi$
$740$	−24.8495	+	2.24205i	−0.913487	+	0.0824195i
$741$	−7.96694	−	7.02416i	−0.292673	−	0.258039i
$742$	4.79294	−	16.3233i	0.175954	−	0.599246i
$743$	−20.3889	−	31.7257i	−0.747996	−	1.16390i	−0.981484	−	0.191544i	$-0.938650\pi$
$743$	−20.3889	−	31.7257i	−0.747996	−	1.16390i	0.233488	−	0.972360i	$-0.424986\pi$
$744$	−8.77372	+	3.91606i	−0.321660	+	0.143570i
$745$	−6.41532	−	11.2468i	−0.235039	−	0.412051i
$746$	−6.65215	−	4.27508i	−0.243553	−	0.156522i
$747$	−2.30243	−	0.371533i	−0.0842415	−	0.0135937i
$748$	−0.0607265	−	0.00873115i	−0.00222038	−	0.000319243i
$749$	−32.1852	+	50.0812i	−1.17602	+	1.82993i
$750$	−19.2290	+	2.29036i	−0.702144	+	0.0836321i
$751$	28.6005	−	13.0614i	1.04365	−	0.476618i	0.181561	−	0.983380i	$-0.441885\pi$
$751$	28.6005	−	13.0614i	1.04365	−	0.476618i	0.862086	+	0.506762i	$0.169158\pi$
$752$	−6.75229	+	4.33943i	−0.246231	+	0.158243i
$753$	−0.794200	+	2.62125i	−0.0289423	+	0.0955238i
$754$	−12.3684	+	14.2739i	−0.450429	+	0.519823i
$755$	−0.575197	+	0.0518972i	−0.0209336	+	0.00188873i
$756$	−16.8796	−	8.24096i	−0.613905	−	0.299721i
$757$	−4.42407	−	30.7701i	−0.160796	−	1.11836i	−0.897138	−	0.441750i	$-0.854358\pi$
$757$	−4.42407	−	30.7701i	−0.160796	−	1.11836i	0.736343	−	0.676609i	$-0.236551\pi$
$758$		−	22.0295i		−	0.800147i
$759$	−0.128912	+	0.0347517i	−0.00467923	+	0.00126141i
$760$	0.956571	−	4.82747i	0.0346985	−	0.175111i
$761$	30.3626	−	4.36548i	1.10064	−	0.158249i	0.432030	−	0.901859i	$-0.357797\pi$
$761$	30.3626	−	4.36548i	1.10064	−	0.158249i	0.668613	+	0.743610i	$0.266888\pi$
$762$	2.97418	−	6.36718i	0.107743	−	0.230658i
$763$	7.04173	+	23.9819i	0.254928	+	0.868205i
$764$	17.2626	−	19.9221i	0.624539	−	0.720756i
$765$	−12.2398	+	22.4900i	−0.442531	+	0.813128i
$766$	−1.64334	−	2.55708i	−0.0593762	−	0.0923912i
$767$	2.29401	+	5.02317i	0.0828317	+	0.181376i
$768$	−1.31870	+	1.12296i	−0.0475843	+	0.0405214i
$769$	20.8430	−	32.4324i	0.751619	−	1.16954i	−0.228964	−	0.973435i	$-0.573534\pi$
$769$	20.8430	−	32.4324i	0.751619	−	1.16954i	0.980583	−	0.196107i	$-0.0628299\pi$
$770$	−0.0431344	+	0.122556i	−0.00155445	+	0.00441660i
$771$	23.0920	+	3.52292i	0.831637	+	0.126875i
$772$	7.44973	−	11.5920i	0.268122	−	0.417206i
$773$	1.20110	−	1.04076i	0.0432005	−	0.0374334i	−0.632993	−	0.774158i	$-0.718174\pi$
$773$	1.20110	−	1.04076i	0.0432005	−	0.0374334i	0.676193	+	0.736724i	$0.263628\pi$
$774$	−1.50396	−	3.44888i	−0.0540589	−	0.123967i
$775$	27.2880	−	4.96454i	0.980214	−	0.178331i
$776$	−8.13678	−	2.38917i	−0.292093	−	0.0857663i
$777$	52.4051	+	46.2037i	1.88002	+	1.65755i
$778$	−19.4240	+	5.70339i	−0.696383	+	0.204477i
$779$	−4.46523	+	9.77748i	−0.159983	+	0.350315i
$780$	0.662280	−	10.7707i	0.0237134	−	0.385653i
$781$			0.194972i			0.00697664i
$782$	−11.7970	−	13.9972i	−0.421862	−	0.500538i
$783$	35.2114	+	0.907967i	1.25835	+	0.0324481i
$784$	−0.863556	−	6.00617i	−0.0308413	−	0.214506i
$785$	−4.54272	+	6.30941i	−0.162137	+	0.225193i
$786$	4.60326	−	1.30878i	0.164193	−	0.0466825i
$787$	30.1260	−	34.7673i	1.07388	−	1.23932i	0.104297	−	0.994546i	$-0.466741\pi$
$787$	30.1260	−	34.7673i	1.07388	−	1.23932i	0.969580	−	0.244774i	$-0.0787139\pi$
$788$	15.2904	+	4.48965i	0.544696	+	0.159937i
$789$	4.12822	−	2.60319i	0.146968	−	0.0926760i
$790$	18.8868	−	4.47767i	0.671964	−	0.159308i
$791$	14.3238	−	12.4117i	0.509297	−	0.441309i
$792$	−0.0401110	−	0.0267629i	−0.00142528	−	0.000950977i
$793$	2.61043	−	18.1560i	0.0926992	−	0.644737i
$794$	−14.1507	−	2.03457i	−0.502191	−	0.0722042i
$795$	−13.0163	−	12.7588i	−0.461640	−	0.452509i
$796$	−17.2799	+	14.9732i	−0.612471	+	0.530709i
$797$	42.0861	−	19.2201i	1.49077	−	0.680811i	0.507279	−	0.861782i	$-0.330651\pi$
$797$	42.0861	−	19.2201i	1.49077	−	0.680811i	0.983488	+	0.180971i	$0.0579240\pi$
$798$	−11.6564	+	7.35034i	−0.412632	+	0.260199i
$799$	8.63135	−	29.3957i	0.305355	−	1.03994i
$800$	4.46785	−	2.24463i	0.157962	−	0.0793595i
$801$	−33.2395	+	9.14252i	−1.17446	+	0.323035i
$802$	−7.24496	+	15.8643i	−0.255829	+	0.560186i
$803$	−0.226988	+	0.0326359i	−0.00801023	+	0.00115170i
$804$	−0.154072	+	17.9285i	−0.00543370	+	0.632289i
$805$	−33.9329	+	18.7448i	−1.19598	+	0.660669i
$806$			15.4558i			0.544406i
$807$	2.54134	+	18.8222i	0.0894593	+	0.662574i
$808$	5.11376	+	2.33538i	0.179902	+	0.0821583i
$809$	5.13295	+	17.4812i	0.180465	+	0.614607i	0.999183	+	0.0404113i	$0.0128668\pi$
$809$	5.13295	+	17.4812i	0.180465	+	0.614607i	−0.818718	+	0.574195i	$0.805315\pi$
$810$	−16.2990	+	11.8043i	−0.572689	+	0.414761i
$811$	−22.9708	−	6.74482i	−0.806613	−	0.236843i	−0.147671	−	0.989037i	$-0.547178\pi$
$811$	−22.9708	−	6.74482i	−0.806613	−	0.236843i	−0.658942	+	0.752194i	$0.728996\pi$
$812$	13.2482	+	20.6146i	0.464921	+	0.723432i
$813$	−6.11811	+	2.73075i	−0.214571	+	0.0957716i
$814$	0.117448	+	0.135543i	0.00411656	+	0.00475076i
$815$	19.3649	−	20.0983i	0.678323	−	0.704012i
$816$	0.997067	−	6.53555i	0.0349043	−	0.228790i
$817$	−2.73221	−	0.392832i	−0.0955878	−	0.0137435i
$818$	15.8093	+	10.1600i	0.552758	+	0.355236i
$819$	−23.1727	+	19.3921i	−0.809720	+	0.677616i
$820$	−10.6261	+	2.51923i	−0.371080	+	0.0879753i
$821$	−25.9193	−	40.3312i	−0.904589	−	1.40757i	−0.913158	−	0.407605i	$-0.866364\pi$
$821$	−25.9193	−	40.3312i	−0.904589	−	1.40757i	0.00856920	−	0.999963i	$-0.497272\pi$
$822$	−32.5970	−	9.87639i	−1.13695	−	0.344479i
$823$	−10.4849	−	9.08523i	−0.365481	−	0.316691i	0.452688	−	0.891669i	$-0.350465\pi$
$823$	−10.4849	−	9.08523i	−0.365481	−	0.316691i	−0.818169	+	0.574978i	$0.805011\pi$
$824$	−3.49386	+	1.02589i	−0.121715	+	0.0357386i
$825$	0.0941235	+	0.102552i	0.00327696	+	0.00357041i
$826$	7.09177	−	1.01964i	0.246754	−	0.0354779i
$827$			9.07547i			0.315585i	0.987472	+	0.157793i	$0.0504377\pi$
$827$			9.07547i			0.315585i	−0.987472	+	0.157793i	$0.949562\pi$
$828$	−3.62532	−	13.9233i	−0.125989	−	0.483867i
$829$	12.1498			0.421979			0.210990	−	0.977488i	$-0.432331\pi$
$829$	12.1498			0.421979			0.210990	+	0.977488i	$0.432331\pi$
$830$	−1.73590	−	0.0917727i	−0.0602541	−	0.00318548i
$831$	8.18081	−	17.5136i	0.283789	−	0.607540i
$832$	0.784973	+	2.67337i	0.0272141	+	0.0926826i
$833$	17.5040	+	15.1673i	0.606476	+	0.525514i
$834$	−8.48155	+	27.9933i	−0.293692	+	0.969329i
$835$	24.5571	−	9.68279i	0.849832	−	0.335087i
$836$	−0.0321786	+	0.0146955i	−0.00111292	+	0.000508253i
$837$	22.2631	−	18.3079i	0.769524	−	0.632814i
$838$	12.3365	+	7.92818i	0.426157	+	0.273875i
$839$	0.623552	−	4.33690i	0.0215274	−	0.149726i	−0.976223	−	0.216770i	$-0.930448\pi$
$839$	0.623552	−	4.33690i	0.0215274	−	0.149726i	0.997750	+	0.0670440i	$0.0213568\pi$
$840$	−13.1661	−	4.76147i	−0.454275	−	0.164286i
$841$	−14.2597	−	9.16416i	−0.491714	−	0.316005i
$842$	−25.1122	+	21.7598i	−0.865423	+	0.749893i
$843$	−14.6213	+	6.52605i	−0.503583	+	0.224769i
$844$	11.9373	−	7.67163i	0.410898	−	0.264068i
$845$	10.3802	+	5.42009i	0.357088	+	0.186457i
$846$	16.0791	−	17.9243i	0.552810	−	0.616250i
$847$	−38.1529	+	11.2027i	−1.31095	+	0.384930i
$848$	4.28082	+	1.95499i	0.147004	+	0.0671345i
$849$	30.3320	−	4.09536i	1.04099	−	0.140552i
$850$	−7.27763	+	17.6427i	−0.249621	+	0.605140i
$851$	−0.732542	+	53.5078i	−0.0251112	+	1.83422i
$852$	−21.0094	−	0.180548i	−0.719769	−	0.00618548i
$853$	−35.0473	+	5.03904i	−1.20000	+	0.172533i	−0.713186	−	0.700975i	$-0.752749\pi$
$853$	−35.0473	+	5.03904i	−1.20000	+	0.172533i	−0.486810	+	0.873508i	$0.661840\pi$
$854$	−21.6478	−	9.88621i	−0.740772	−	0.338299i
$855$	1.07379	+	14.7249i	0.0367227	+	0.503580i
$856$	−12.4458	−	10.7843i	−0.425388	−	0.368601i
$857$	−4.11174	−	1.20731i	−0.140454	−	0.0412411i	0.210750	−	0.977540i	$-0.432409\pi$
$857$	−4.11174	−	1.20731i	−0.140454	−	0.0412411i	−0.351204	+	0.936299i	$0.614228\pi$
$858$	−0.0656123	+	0.0413741i	−0.00223997	+	0.00141249i
$859$	4.74643	+	10.3932i	0.161946	+	0.354613i	0.973157	−	0.230140i	$-0.0739186\pi$
$859$	4.74643	+	10.3932i	0.161946	+	0.354613i	−0.811211	+	0.584753i	$0.801191\pi$
$860$	−1.38952	−	2.43599i	−0.0473823	−	0.0830666i
$861$	25.5820	+	16.7529i	0.871831	+	0.570937i
$862$	3.23670	−	22.5117i	0.110242	−	0.766753i
$863$	1.20229	−	8.36211i	0.0409264	−	0.284650i	−0.959072	−	0.283161i	$-0.908617\pi$
$863$	1.20229	−	8.36211i	0.0409264	−	0.284650i	0.999999	−	0.00148879i	$-0.000473898\pi$
$864$	2.92100	−	4.29741i	0.0993744	−	0.146201i
$865$	−11.7602	−	20.6170i	−0.399858	−	0.700997i
$866$	11.1782	+	24.4770i	0.379852	+	0.831761i
$867$	−2.24574	−	3.56135i	−0.0762692	−	0.120950i
$868$	19.2406	+	5.64954i	0.653067	+	0.191758i
$869$	−0.105446	−	0.0913695i	−0.00357701	−	0.00309950i
$870$	26.1668	−	2.13438i	0.887138	−	0.0723622i
$871$	26.2351	+	11.9812i	0.888942	+	0.405966i
$872$	−6.84378	+	0.983987i	−0.231760	+	0.0333220i
$873$	25.4371	+	0.437230i	0.860916	+	0.0147980i
$874$	−10.0859	−	3.11206i	−0.341159	−	0.105267i
$875$	33.6543	+	22.3804i	1.13772	+	0.756595i
$876$	−3.30652	−	24.4895i	−0.111717	−	0.827423i
$877$	−13.1145	−	5.98918i	−0.442845	−	0.202240i	0.181497	−	0.983391i	$-0.441906\pi$
$877$	−13.1145	−	5.98918i	−0.442845	−	0.202240i	−0.624342	+	0.781151i	$0.714633\pi$
$878$	31.1262	−	9.13948i	1.05046	−	0.308443i
$879$	8.07346	−	9.15708i	0.272311	−	0.308861i
$880$	−0.0318592	−	0.0166355i	−0.00107397	−	0.000560784i
$881$	−12.8256	+	8.24252i	−0.432106	+	0.277698i	−0.738560	−	0.674188i	$-0.764494\pi$
$881$	−12.8256	+	8.24252i	−0.432106	+	0.277698i	0.306454	+	0.951885i	$0.400857\pi$
$882$	7.27643	+	16.6863i	0.245010	+	0.561856i
$883$	5.57730	−	4.83275i	0.187691	−	0.162635i	−0.555947	−	0.831218i	$-0.687644\pi$
$883$	5.57730	−	4.83275i	0.187691	−	0.162635i	0.743638	+	0.668583i	$0.233099\pi$
$884$	−8.94669	−	5.74969i	−0.300910	−	0.193383i
$885$	2.61055	−	7.21854i	0.0877527	−	0.242649i
$886$	−0.749954	+	5.21604i	−0.0251952	+	0.175236i
$887$	−1.32146	−	0.849249i	−0.0443702	−	0.0285150i	0.518268	−	0.855218i	$-0.326577\pi$
$887$	−1.32146	−	0.849249i	−0.0443702	−	0.0285150i	−0.562638	+	0.826703i	$0.690213\pi$
$888$	−14.7143	+	12.5302i	−0.493778	+	0.420487i
$889$	−13.3418	+	6.09298i	−0.447469	+	0.204352i
$890$	−23.9043	+	9.42539i	−0.801272	+	0.315940i
$891$	0.137317	+	0.0455013i	0.00460029	+	0.00152435i
$892$	8.07426	+	6.99638i	0.270346	+	0.234256i
$893$	−4.97689	−	16.9497i	−0.166545	−	0.567201i
$894$	−9.08689	−	4.24459i	−0.303911	−	0.141960i
$895$	45.9500	+	2.42926i	1.53594	+	0.0812010i
$896$	3.61496			0.120767
$897$	−22.8296	−	3.80338i	−0.762257	−	0.126991i
$898$		−	7.45426i		−	0.248752i
$899$	−37.2199	+	5.35141i	−1.24135	+	0.178479i
$900$	−11.1378	+	10.0474i	−0.371259	+	0.334913i
$901$	−17.2354	+	5.06077i	−0.574194	+	0.168599i
$902$	0.0593261	+	0.0514064i	0.00197534	+	0.00171164i
$903$	−2.27705	+	7.51540i	−0.0757755	+	0.250097i
$904$	2.83457	+	4.41068i	0.0942764	+	0.146697i
$905$	−8.49731	+	2.01453i	−0.282460	+	0.0669653i
$906$	−0.340594	+	0.290039i	−0.0113155	+	0.00963591i
$907$	13.9120	+	8.94073i	0.461942	+	0.296872i	0.750836	−	0.660489i	$-0.229651\pi$
$907$	13.9120	+	8.94073i	0.461942	+	0.296872i	−0.288894	+	0.957361i	$0.593287\pi$
$908$	−0.477976	−	0.0687225i	−0.0158622	−	0.00228064i
$909$	−16.6500	−	2.68674i	−0.552246	−	0.0891135i
$910$	−15.6268	+	16.2186i	−0.518023	+	0.537641i
$911$	15.5775	+	17.9774i	0.516107	+	0.595619i	0.952652	−	0.304064i	$-0.0983435\pi$
$911$	15.5775	+	17.9774i	0.516107	+	0.595619i	−0.436545	+	0.899682i	$0.643798\pi$
$912$	−1.55372	−	3.48104i	−0.0514489	−	0.115269i
$913$	0.00675553	+	0.0105118i	0.000223575	+	0.000347890i
$914$	7.32253	+	2.15009i	0.242208	+	0.0711186i
$915$	−20.2578	+	15.4829i	−0.669702	+	0.511850i
$916$	0.474327	+	1.61541i	0.0156722	+	0.0533747i
$917$	−9.08559	−	4.14925i	−0.300033	−	0.137020i
$918$	2.31561	+	19.6979i	0.0764264	+	0.650126i
$919$		−	1.44536i		−	0.0476780i	−0.999716	−	0.0238390i	$-0.992411\pi$
$919$		−	1.44536i		−	0.0476780i	0.999716	−	0.0238390i	$-0.00758892\pi$
$920$	−3.79669	−	10.0292i	−0.125173	−	0.330653i
$921$	−54.7476	−	0.470485i	−1.80399	−	0.0155030i
$922$	2.97841	−	0.428230i	0.0980886	−	0.0141030i
$923$	−14.0400	+	30.7434i	−0.462134	+	1.01193i
$924$	0.0275225	+	0.0968028i	0.000905425	+	0.00318458i
$925$	49.8531	−	25.0460i	1.63916	−	0.823507i
$926$	−8.70257	+	29.6382i	−0.285984	+	0.973973i
$927$	9.29008	−	5.74720i	0.305126	−	0.188763i
$928$	−6.16611	+	2.81597i	−0.202412	+	0.0924386i
$929$	−39.0519	+	33.8387i	−1.28125	+	1.11021i	−0.293207	+	0.956049i	$0.594722\pi$
$929$	−39.0519	+	33.8387i	−1.28125	+	1.11021i	−0.988045	+	0.154163i	$0.950732\pi$
$930$	15.0391	−	15.3426i	0.493151	−	0.503102i
$931$	13.2189	+	1.90059i	0.433231	+	0.0622892i
$932$	3.75291	−	26.1021i	0.122931	−	0.855002i
$933$	−43.4180	−	28.4332i	−1.42144	−	0.930861i
$934$	24.4668	−	21.2006i	0.800578	−	0.693705i
$935$	0.133485	−	0.0316464i	0.00436542	−	0.00103495i
$936$	−4.39754	−	7.10842i	−0.143738	−	0.232346i
$937$	−24.0459	−	7.06053i	−0.785547	−	0.230657i	−0.135728	−	0.990746i	$-0.543337\pi$
$937$	−24.0459	−	7.06053i	−0.785547	−	0.230657i	−0.649819	+	0.760089i	$0.725155\pi$
$938$	24.5048	−	28.2801i	0.800110	−	0.923377i
$939$	4.15152	+	14.6018i	0.135480	+	0.476513i
$940$	10.4868	−	14.5652i	0.342043	−	0.475066i
$941$	−1.48545	−	10.3316i	−0.0484244	−	0.336799i	−0.999603	−	0.0281596i	$-0.991035\pi$
$941$	−1.48545	−	10.3316i	−0.0484244	−	0.336799i	0.951179	−	0.308640i	$-0.0998738\pi$
$942$	−0.0517511	+	6.02198i	−0.00168614	+	0.196207i
$943$	3.01565	+	23.2273i	0.0982031	+	0.756384i
$944$			1.98196i			0.0645072i
$945$	41.8724	+	3.29791i	1.36211	+	0.107281i
$946$	−0.00837424	+	0.0183370i	−0.000272270	+	0.000596188i
$947$	−15.6108	+	4.58376i	−0.507284	+	0.148952i	−0.525353	−	0.850885i	$-0.676067\pi$
$947$	−15.6108	+	4.58376i	−0.507284	+	0.148952i	0.0180682	+	0.999837i	$0.494248\pi$
$948$	9.94325	−	11.2778i	0.322942	−	0.366287i
$949$	−38.1419	−	11.1995i	−1.23814	−	0.363550i
$950$	1.96972	+	10.8267i	0.0639060	+	0.351265i
$951$	30.3951	−	13.5665i	0.985629	−	0.439925i
$952$	−10.4280	+	9.03587i	−0.337972	+	0.292854i
$953$	−18.2060	+	28.3291i	−0.589750	+	0.917669i	0.410234	+	0.911980i	$0.365447\pi$
$953$	−18.2060	+	28.3291i	−0.589750	+	0.917669i	−0.999984	+	0.00568871i	$0.998189\pi$
$954$	−13.9380	−	2.24912i	−0.451260	−	0.0728179i
$955$	−19.5692	+	55.6011i	−0.633245	+	1.79921i
$956$	−3.70120	+	5.75919i	−0.119705	+	0.186265i
$957$	−0.122353	−	0.143679i	−0.00395510	−	0.00464449i
$958$	13.7801	+	30.1743i	0.445216	+	0.974887i
$959$	38.4327	+	59.8024i	1.24106	+	1.93112i
$960$	1.82208	−	3.41761i	0.0588074	−	0.110303i
$961$	0.149800	−	0.172878i	0.00483226	−	0.00557672i
$962$	8.75889	+	29.8300i	0.282398	+	0.961759i
$963$	44.5805	+	21.2926i	1.43659	+	0.686146i
$964$	28.1687	−	4.05004i	0.907251	−	0.130443i
$965$	−5.98897	+	30.2241i	−0.192792	+	0.972950i
$966$	−13.0796	+	27.0298i	−0.420830	+	0.869670i
$967$		−	1.94193i		−	0.0624483i	−0.999512	−	0.0312242i	$-0.990059\pi$
$967$		−	1.94193i		−	0.0624483i	0.999512	−	0.0312242i	$-0.00994057\pi$
$968$	−1.56543	−	10.8878i	−0.0503147	−	0.349947i
$969$	13.1831	+	6.15798i	0.423502	+	0.197823i
$970$	18.8858	−	1.70397i	0.606386	−	0.0547112i
$971$	−20.5482	+	23.7139i	−0.659424	+	0.761015i	−0.982683	−	0.185295i	$-0.940676\pi$
$971$	−20.5482	+	23.7139i	−0.659424	+	0.761015i	0.323259	+	0.946310i	$0.395221\pi$
$972$	−5.03019	+	14.7546i	−0.161343	+	0.473253i
$973$	51.3565	−	33.0048i	1.64641	−	1.05809i
$974$	7.13392	−	3.25795i	0.228586	−	0.104392i
$975$	7.45665	+	22.9485i	0.238804	+	0.734939i
$976$	3.55921	−	5.53823i	0.113927	−	0.177275i
$977$	49.6019	+	7.13167i	1.58690	+	0.228162i	0.878535	−	0.477679i	$-0.158522\pi$
$977$	49.6019	+	7.13167i	1.58690	+	0.228162i	0.708370	+	0.705841i	$0.249431\pi$
$978$	3.26042	−	21.3713i	0.104257	−	0.683380i
$979$	0.155382	+	0.0998578i	0.00496602	+	0.00319147i
$980$	6.72274	+	11.7857i	0.214750	+	0.376482i
$981$	19.0133	−	8.29119i	0.607048	−	0.264717i
$982$	−4.03195	−	6.27384i	−0.128665	−	0.200206i
$983$	−12.5082	+	42.5992i	−0.398951	+	1.35870i	0.478100	+	0.878305i	$0.341326\pi$
$983$	−12.5082	+	42.5992i	−0.398951	+	1.35870i	−0.877051	+	0.480397i	$0.840493\pi$
$984$	−5.59427	+	6.34513i	−0.178339	+	0.202275i
$985$	−35.4895	+	3.20204i	−1.13079	+	0.102026i
$986$	10.7484	−	23.5358i	0.342300	−	0.749532i
$987$	−49.8041	+	6.72444i	−1.58528	+	0.214041i
$988$	−6.13218			−0.195091
$989$	−5.50498	+	2.42352i	−0.175048	+	0.0770635i
$990$	0.105390	+	0.0227724i	0.00334953	+	0.000723754i
$991$	1.12295	+	7.81030i	0.0356717	+	0.248102i	0.999853	−	0.0171416i	$-0.00545661\pi$
$991$	1.12295	+	7.81030i	0.0356717	+	0.248102i	−0.964181	+	0.265244i	$0.914548\pi$
$992$	−2.30438	+	5.04590i	−0.0731642	+	0.160207i
$993$	14.1188	+	49.6589i	0.448046	+	1.57588i
$994$	33.1398	+	28.7158i	1.05113	+	0.910809i
$995$	23.6645	−	45.3205i	0.750215	−	1.43676i
$996$	−1.13896	+	0.718214i	−0.0360895	+	0.0227575i
$997$	20.7979	−	9.49806i	0.658675	−	0.300807i	−0.0578944	−	0.998323i	$-0.518439\pi$
$997$	20.7979	−	9.49806i	0.658675	−	0.300807i	0.716569	+	0.697516i	$0.245711\pi$
$998$	15.8004	+	18.2347i	0.500153	+	0.577208i
$999$	32.5931	−	47.9514i	1.03120	−	1.51711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.b.89.4	yes	240
3.2	odd	2		690.2.n.a.89.4	✓	240
5.4	even	2		690.2.n.a.89.21	yes	240
15.14	odd	2	inner	690.2.n.b.89.21	yes	240
23.15	odd	22	inner	690.2.n.b.659.21	yes	240
69.38	even	22		690.2.n.a.659.21	yes	240
115.84	odd	22		690.2.n.a.659.4	yes	240
345.314	even	22	inner	690.2.n.b.659.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.4	✓	240	3.2	odd	2
690.2.n.a.89.21	yes	240	5.4	even	2
690.2.n.a.659.4	yes	240	115.84	odd	22
690.2.n.a.659.21	yes	240	69.38	even	22
690.2.n.b.89.4	yes	240	1.1	even	1	trivial
690.2.n.b.89.21	yes	240	15.14	odd	2	inner
690.2.n.b.659.4	yes	240	345.314	even	22	inner
690.2.n.b.659.21	yes	240	23.15	odd	22	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.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-1.56929 - 0.733032i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.76486 - 1.37305i) q^{5} +(0.502238 - 1.65764i) q^{6} +(-3.04110 + 1.95439i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.92533 + 2.30068i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-1.56929 - 0.733032i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.76486 - 1.37305i) q^{5} +(0.502238 - 1.65764i) q^{6} +(-3.04110 + 1.95439i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.92533 + 2.30068i) q^{9} +(1.61024 + 1.55149i) q^{10} +(0.00228746 - 0.0159096i) q^{11} +(1.71224 + 0.261220i) q^{12} +(1.50635 - 2.34393i) q^{13} +(-2.36729 - 2.73200i) q^{14} +(-3.77606 + 0.861020i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.07536 + 3.66235i) q^{17} +(-2.00326 + 2.23315i) q^{18} +(0.620061 + 2.11173i) q^{19} +(-1.30653 + 1.81465i) q^{20} +(6.20499 - 0.837784i) q^{21} +0.0160733 q^{22} +(3.58112 + 3.18992i) q^{23} +(-0.0148842 + 1.73199i) q^{24} +(1.22944 - 4.84649i) q^{25} +(2.53445 + 1.15744i) q^{26} +(-1.33492 - 5.02175i) q^{27} +(2.36729 - 2.73200i) q^{28} +(-1.90978 + 6.50410i) q^{29} +(-1.38965 - 3.61509i) q^{30} +(2.30438 + 5.04590i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.0152520 + 0.0232900i) q^{33} +(-3.77811 - 0.543210i) q^{34} +(-2.68361 + 7.62482i) q^{35} +(-2.49551 - 1.66506i) q^{36} +(7.30706 + 8.43280i) q^{37} +(-2.00199 + 0.914280i) q^{38} +(-4.08208 + 2.57410i) q^{39} +(-1.98212 - 1.03498i) q^{40} +(3.69098 + 3.19825i) q^{41} +(1.71232 + 6.02260i) q^{42} +(-0.521005 + 1.14084i) q^{43} +(0.00228746 + 0.0159096i) q^{44} +(6.55688 + 1.41679i) q^{45} +(-2.64781 + 3.99864i) q^{46} -8.02646 q^{47} +(-1.71648 + 0.231755i) q^{48} +(2.52071 - 5.51958i) q^{49} +(4.97213 + 0.527200i) q^{50} +(4.37217 - 4.95900i) q^{51} +(-0.784973 + 2.67337i) q^{52} +(2.54431 + 3.95903i) q^{53} +(4.78066 - 2.03600i) q^{54} +(-0.0178078 - 0.0312191i) q^{55} +(3.04110 + 1.95439i) q^{56} +(0.574915 - 3.76844i) q^{57} +(-6.70969 - 0.964707i) q^{58} +(-1.07153 + 1.66733i) q^{59} +(3.38053 - 1.88998i) q^{60} +(5.98839 - 2.73481i) q^{61} +(-4.66659 + 2.99903i) q^{62} +(-10.3515 - 3.23374i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-0.559847 - 6.20501i) q^{65} +(-0.0252236 - 0.0117822i) q^{66} +(1.47316 + 10.2460i) q^{67} -3.81696i q^{68} +(-3.28148 - 7.63098i) q^{69} +(-7.92913 - 1.57117i) q^{70} +(-12.0067 + 1.72631i) q^{71} +(1.29296 - 2.70707i) q^{72} +(-4.01957 - 13.6894i) q^{73} +(-7.30706 + 8.43280i) q^{74} +(-5.48198 + 6.70432i) q^{75} +(-1.18989 - 1.85150i) q^{76} +(0.0241373 + 0.0528534i) q^{77} +(-3.12884 - 3.67420i) q^{78} +(4.69308 - 7.30257i) q^{79} +(0.742363 - 2.10924i) q^{80} +(-1.58623 + 8.85911i) q^{81} +(-2.64042 + 4.10857i) q^{82} +(-0.587523 + 0.509092i) q^{83} +(-5.71761 + 2.55200i) q^{84} +(3.13074 + 7.94005i) q^{85} +(-1.20338 - 0.353343i) q^{86} +(7.76470 - 8.80687i) q^{87} +(-0.0154222 + 0.00452836i) q^{88} +(-4.77366 + 10.4529i) q^{89} +(-0.469226 + 6.69177i) q^{90} +10.0721i q^{91} +(-4.33476 - 2.05179i) q^{92} +(0.0825653 - 9.60765i) q^{93} +(-1.14228 - 7.94476i) q^{94} +(3.99384 + 2.87553i) q^{95} +(-0.473676 - 1.66602i) q^{96} +(5.55341 - 6.40897i) q^{97} +(5.82214 + 1.70953i) q^{98} +(0.0410071 - 0.0253686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) \) 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9 + 9 * q^12 + 11 * q^15 - 24 * q^16 + 6 * q^18 + 4 * q^23 + 2 * q^24 - 12 * q^25 - 2 * q^27 + 22 * q^30 + 28 * q^31 + 24 * q^32 + 36 * q^35 - 6 * q^36 - 4 * q^46 - 104 * q^47 + 9 * q^48 + 70 * q^49 - 54 * q^50 - 9 * q^54 - 26 * q^55 + 44 * q^57 - 11 * q^60 + 44 * q^61 - 28 * q^62 + 121 * q^63 - 24 * q^64 - 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 - 16 * q^72 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Introduction

L-functions

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