LMFDB - Embedded newform 690.2.x.a.647.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (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:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			647.37
Character	$\chi$	$=$	690.647
Dual form			690.2.x.a.353.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.800541 + 0.599278i) q^{2} +(0.133838 + 1.72687i) q^{3} +(0.281733 + 0.959493i) q^{4} +(-2.19445 - 0.429407i) q^{5} +(-0.927733 + 1.46264i) q^{6} +(1.96645 + 0.427775i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-2.96417 + 0.462244i) q^{9} +O(q^{10})$	\(q+(0.800541 + 0.599278i) q^{2} +(0.133838 + 1.72687i) q^{3} +(0.281733 + 0.959493i) q^{4} +(-2.19445 - 0.429407i) q^{5} +(-0.927733 + 1.46264i) q^{6} +(1.96645 + 0.427775i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-2.96417 + 0.462244i) q^{9} +(-1.49941 - 1.65884i) q^{10} +(-2.75644 - 0.396317i) q^{11} +(-1.61921 + 0.614933i) q^{12} +(-3.25703 + 0.708524i) q^{13} +(1.31787 + 1.52090i) q^{14} +(0.447828 - 3.84701i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(-6.75203 + 3.68689i) q^{17} +(-2.64996 - 1.40632i) q^{18} +(0.595863 + 2.02932i) q^{19} +(-0.206235 - 2.22654i) q^{20} +(-0.475526 + 3.45306i) q^{21} +(-1.96914 - 1.96914i) q^{22} +(4.23982 + 2.24140i) q^{23} +(-1.66476 - 0.478080i) q^{24} +(4.63122 + 1.88462i) q^{25} +(-3.03199 - 1.38466i) q^{26} +(-1.19496 - 5.05688i) q^{27} +(0.143566 + 2.00731i) q^{28} +(8.71801 + 2.55984i) q^{29} +(2.66393 - 2.81131i) q^{30} +(-3.74038 - 8.19029i) q^{31} +(-0.997452 - 0.0713392i) q^{32} +(0.315470 - 4.81307i) q^{33} +(-7.61474 - 1.09483i) q^{34} +(-4.13159 - 1.78314i) q^{35} +(-1.27862 - 2.71388i) q^{36} +(-0.439743 + 6.14840i) q^{37} +(-0.739115 + 1.98164i) q^{38} +(-1.65945 - 5.52965i) q^{39} +(1.16921 - 1.90603i) q^{40} +(-4.27571 - 3.70492i) q^{41} +(-2.45002 + 2.47935i) q^{42} +(2.70820 + 7.26097i) q^{43} +(-0.396317 - 2.75644i) q^{44} +(6.70322 + 0.258465i) q^{45} +(2.05093 + 4.33517i) q^{46} +(-3.06623 + 3.06623i) q^{47} +(-1.04621 - 1.38038i) q^{48} +(-2.68349 - 1.22551i) q^{49} +(2.57807 + 4.28410i) q^{50} +(-7.27046 - 11.1664i) q^{51} +(-1.59744 - 2.92548i) q^{52} +(0.996029 + 0.216673i) q^{53} +(2.07387 - 4.76436i) q^{54} +(5.87869 + 2.05333i) q^{55} +(-1.08801 + 1.69297i) q^{56} +(-3.42463 + 1.30058i) q^{57} +(5.44507 + 7.27377i) q^{58} +(2.17379 + 1.39701i) q^{59} +(3.81734 - 0.654138i) q^{60} +(3.11627 + 6.82367i) q^{61} +(1.91393 - 8.79819i) q^{62} +(-6.02664 - 0.359020i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(7.45164 - 0.156229i) q^{65} +(3.13691 - 3.66400i) q^{66} +(4.93864 - 6.59725i) q^{67} +(-5.43981 - 5.43981i) q^{68} +(-3.30317 + 7.62162i) q^{69} +(-2.23891 - 3.90344i) q^{70} +(3.37763 - 0.485631i) q^{71} +(0.602774 - 2.93882i) q^{72} +(4.58501 - 8.39682i) q^{73} +(-4.03663 + 4.65852i) q^{74} +(-2.63467 + 8.24976i) q^{75} +(-1.77925 + 1.14345i) q^{76} +(-5.25087 - 1.95847i) q^{77} +(1.98534 - 5.42118i) q^{78} +(-6.84595 + 10.6525i) q^{79} +(2.07824 - 0.825169i) q^{80} +(8.57266 - 2.74034i) q^{81} +(-1.20260 - 5.52828i) q^{82} +(-0.354338 + 4.95429i) q^{83} +(-3.44716 + 0.516576i) q^{84} +(16.4002 - 5.19132i) q^{85} +(-2.18331 + 7.43567i) q^{86} +(-3.25371 + 15.3975i) q^{87} +(1.33461 - 2.44415i) q^{88} +(-0.267827 + 0.586459i) q^{89} +(5.21131 + 4.22400i) q^{90} -6.70788 q^{91} +(-0.956114 + 4.69956i) q^{92} +(13.6430 - 7.55534i) q^{93} +(-4.29217 + 0.617121i) q^{94} +(-0.436187 - 4.70911i) q^{95} +(-0.0103038 - 1.73202i) q^{96} +(15.7739 - 1.12817i) q^{97} +(-1.41382 - 2.58922i) q^{98} +(8.35377 - 0.0993971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{8}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.800541	+	0.599278i	0.566068	+	0.423753i
$2$	0.800541	+	0.599278i	0.566068	+	0.423753i
$3$	0.133838	+	1.72687i	0.0772717	+	0.997010i
$3$	0.133838	+	1.72687i	0.0772717	+	0.997010i
$4$	0.281733	+	0.959493i	0.140866	+	0.479746i
$5$	−2.19445	−	0.429407i	−0.981388	−	0.192036i
$5$	−2.19445	−	0.429407i	−0.981388	−	0.192036i
$6$	−0.927733	+	1.46264i	−0.378745	+	0.597120i
$7$	1.96645	+	0.427775i	0.743248	+	0.161684i	0.568217	−	0.822879i	$-0.307634\pi$
$7$	1.96645	+	0.427775i	0.743248	+	0.161684i	0.175032	+	0.984563i	$0.443997\pi$
$8$	−0.349464	+	0.936950i	−0.123554	+	0.331262i
$9$	−2.96417	+	0.462244i	−0.988058	+	0.154081i
$10$	−1.49941	−	1.65884i	−0.474156	−	0.524572i
$11$	−2.75644	−	0.396317i	−0.831099	−	0.119494i	−0.286384	−	0.958115i	$-0.592453\pi$
$11$	−2.75644	−	0.396317i	−0.831099	−	0.119494i	−0.544715	+	0.838621i	$0.683362\pi$
$12$	−1.61921	+	0.614933i	−0.467427	+	0.177516i
$13$	−3.25703	+	0.708524i	−0.903338	+	0.196509i	−0.640163	−	0.768239i	$-0.721133\pi$
$13$	−3.25703	+	0.708524i	−0.903338	+	0.196509i	−0.263175	+	0.964748i	$0.584770\pi$
$14$	1.31787	+	1.52090i	0.352215	+	0.406478i
$15$	0.447828	−	3.84701i	0.115629	−	0.993292i
$16$	−0.841254	+	0.540641i	−0.210313	+	0.135160i
$17$	−6.75203	+	3.68689i	−1.63761	+	0.894201i	−0.646232	+	0.763141i	$0.723656\pi$
$17$	−6.75203	+	3.68689i	−1.63761	+	0.894201i	−0.991374	+	0.131060i	$0.958162\pi$
$18$	−2.64996	−	1.40632i	−0.624601	−	0.331472i
$19$	0.595863	+	2.02932i	0.136700	+	0.465558i	0.999178	−	0.0405366i	$-0.0129067\pi$
$19$	0.595863	+	2.02932i	0.136700	+	0.465558i	−0.862478	+	0.506095i	$0.831089\pi$
$20$	−0.206235	−	2.22654i	−0.0461156	−	0.497869i
$21$	−0.475526	+	3.45306i	−0.103768	+	0.753520i
$22$	−1.96914	−	1.96914i	−0.419823	−	0.419823i
$23$	4.23982	+	2.24140i	0.884065	+	0.467365i
$23$	4.23982	+	2.24140i	0.884065	+	0.467365i
$24$	−1.66476	−	0.478080i	−0.339819	−	0.0975877i
$25$	4.63122	+	1.88462i	0.926244	+	0.376924i
$26$	−3.03199	−	1.38466i	−0.594622	−	0.271555i
$27$	−1.19496	−	5.05688i	−0.229970	−	0.973198i
$28$	0.143566	+	2.00731i	0.0271314	+	0.379347i
$29$	8.71801	+	2.55984i	1.61889	+	0.475350i	0.960721	−	0.277516i	$-0.0895113\pi$
$29$	8.71801	+	2.55984i	1.61889	+	0.475350i	0.658173	+	0.752867i	$0.271329\pi$
$30$	2.66393	−	2.81131i	0.486365	−	0.513273i
$31$	−3.74038	−	8.19029i	−0.671792	−	1.47102i	−0.871112	−	0.491085i	$-0.836600\pi$
$31$	−3.74038	−	8.19029i	−0.671792	−	1.47102i	0.199319	−	0.979935i	$-0.436127\pi$
$32$	−0.997452	−	0.0713392i	−0.176326	−	0.0126111i
$33$	0.315470	−	4.81307i	0.0549163	−	0.837847i
$34$	−7.61474	−	1.09483i	−1.30592	−	0.187763i
$35$	−4.13159	−	1.78314i	−0.698366	−	0.301405i
$36$	−1.27862	−	2.71388i	−0.213104	−	0.452313i
$37$	−0.439743	+	6.14840i	−0.0722932	+	1.01079i	0.823787	+	0.566899i	$0.191857\pi$
$37$	−0.439743	+	6.14840i	−0.0722932	+	1.01079i	−0.896080	+	0.443892i	$0.853597\pi$
$38$	−0.739115	+	1.98164i	−0.119900	+	0.321465i
$39$	−1.65945	−	5.52965i	−0.265724	−	0.885452i
$40$	1.16921	−	1.90603i	0.184869	−	0.301369i
$41$	−4.27571	−	3.70492i	−0.667753	−	0.578611i	0.253614	−	0.967306i	$-0.418381\pi$
$41$	−4.27571	−	3.70492i	−0.667753	−	0.578611i	−0.921367	+	0.388694i	$0.872926\pi$
$42$	−2.45002	+	2.47935i	−0.378046	+	0.382571i
$43$	2.70820	+	7.26097i	0.412997	+	1.10729i	0.962378	+	0.271715i	$0.0875909\pi$
$43$	2.70820	+	7.26097i	0.412997	+	1.10729i	−0.549381	+	0.835572i	$0.685136\pi$
$44$	−0.396317	−	2.75644i	−0.0597470	−	0.415549i
$45$	6.70322	+	0.258465i	0.999257	+	0.0385297i
$46$	2.05093	+	4.33517i	0.302393	+	0.639186i
$47$	−3.06623	+	3.06623i	−0.447256	+	0.447256i	−0.894441	−	0.447185i	$-0.852426\pi$
$47$	−3.06623	+	3.06623i	−0.447256	+	0.447256i	0.447185	+	0.894441i	$0.352426\pi$
$48$	−1.04621	−	1.38038i	−0.151007	−	0.199241i
$49$	−2.68349	−	1.22551i	−0.383355	−	0.175073i
$50$	2.57807	+	4.28410i	0.364594	+	0.605864i
$51$	−7.27046	−	11.1664i	−1.01807	−	1.56361i
$52$	−1.59744	−	2.92548i	−0.221524	−	0.405692i
$53$	0.996029	+	0.216673i	0.136815	+	0.0297623i	0.280451	−	0.959868i	$-0.409516\pi$
$53$	0.996029	+	0.216673i	0.136815	+	0.0297623i	−0.143636	+	0.989631i	$0.545880\pi$
$54$	2.07387	−	4.76436i	0.282217	−	0.648347i
$55$	5.87869	+	2.05333i	0.792683	+	0.276871i
$56$	−1.08801	+	1.69297i	−0.145391	+	0.226233i
$57$	−3.42463	+	1.30058i	−0.453603	+	0.172266i
$58$	5.44507	+	7.27377i	0.714973	+	0.955092i
$59$	2.17379	+	1.39701i	0.283003	+	0.181875i	0.674439	−	0.738330i	$-0.264385\pi$
$59$	2.17379	+	1.39701i	0.283003	+	0.181875i	−0.391437	+	0.920205i	$0.628022\pi$
$60$	3.81734	−	0.654138i	0.492817	−	0.0844489i
$61$	3.11627	+	6.82367i	0.398997	+	0.873681i	0.997371	+	0.0724645i	$0.0230864\pi$
$61$	3.11627	+	6.82367i	0.398997	+	0.873681i	−0.598374	+	0.801217i	$0.704186\pi$
$62$	1.91393	−	8.79819i	0.243069	−	1.11737i
$63$	−6.02664	−	0.359020i	−0.759285	−	0.0452323i
$64$	−0.755750	−	0.654861i	−0.0944687	−	0.0818576i
$65$	7.45164	−	0.156229i	0.924262	−	0.0193779i
$66$	3.13691	−	3.66400i	0.386127	−	0.451008i
$67$	4.93864	−	6.59725i	0.603351	−	0.805982i	−0.390036	−	0.920800i	$-0.627537\pi$
$67$	4.93864	−	6.59725i	0.603351	−	0.805982i	0.993387	+	0.114818i	$0.0366284\pi$
$68$	−5.43981	−	5.43981i	−0.659673	−	0.659673i
$69$	−3.30317	+	7.62162i	−0.397654	+	0.917535i
$70$	−2.23891	−	3.90344i	−0.267601	−	0.466551i
$71$	3.37763	−	0.485631i	0.400851	−	0.0576337i	0.0610589	−	0.998134i	$-0.480552\pi$
$71$	3.37763	−	0.485631i	0.400851	−	0.0576337i	0.339793	+	0.940500i	$0.389643\pi$
$72$	0.602774	−	2.93882i	0.0710375	−	0.346343i
$73$	4.58501	−	8.39682i	0.536635	−	0.982774i	−0.458910	−	0.888483i	$-0.651760\pi$
$73$	4.58501	−	8.39682i	0.536635	−	0.982774i	0.995545	−	0.0942907i	$-0.0300583\pi$
$74$	−4.03663	+	4.65852i	−0.469249	+	0.541542i
$75$	−2.63467	+	8.24976i	−0.304225	+	0.952600i
$76$	−1.77925	+	1.14345i	−0.204094	+	0.131163i
$77$	−5.25087	−	1.95847i	−0.598393	−	0.223189i
$78$	1.98534	−	5.42118i	0.224795	−	0.613828i
$79$	−6.84595	+	10.6525i	−0.770230	+	1.19850i	0.205314	+	0.978696i	$0.434178\pi$
$79$	−6.84595	+	10.6525i	−0.770230	+	1.19850i	−0.975544	+	0.219805i	$0.929458\pi$
$80$	2.07824	−	0.825169i	0.232355	−	0.0922567i
$81$	8.57266	−	2.74034i	0.952518	−	0.304483i
$82$	−1.20260	−	5.52828i	−0.132805	−	0.610496i
$83$	−0.354338	+	4.95429i	−0.0388937	+	0.543804i	0.940230	+	0.340540i	$0.110610\pi$
$83$	−0.354338	+	4.95429i	−0.0388937	+	0.543804i	−0.979124	+	0.203265i	$0.934845\pi$
$84$	−3.44716	+	0.516576i	−0.376116	+	0.0563630i
$85$	16.4002	−	5.19132i	1.77885	−	0.563078i
$86$	−2.18331	+	7.43567i	−0.235432	+	0.801809i
$87$	−3.25371	+	15.3975i	−0.348834	+	1.65078i
$88$	1.33461	−	2.44415i	0.142270	−	0.260547i
$89$	−0.267827	+	0.586459i	−0.0283896	+	0.0621645i	−0.923296	−	0.384090i	$-0.874515\pi$
$89$	−0.267827	+	0.586459i	−0.0283896	+	0.0621645i	0.894906	+	0.446255i	$0.147242\pi$
$90$	5.21131	+	4.22400i	0.549321	+	0.445249i
$91$	−6.70788			−0.703177
$92$	−0.956114	+	4.69956i	−0.0996818	+	0.489963i
$93$	13.6430	−	7.55534i	1.41471	−	0.783452i
$94$	−4.29217	+	0.617121i	−0.442704	+	0.0636512i
$95$	−0.436187	−	4.70911i	−0.0447518	−	0.483145i
$96$	−0.0103038	−	1.73202i	−0.00105163	−	0.176774i
$97$	15.7739	−	1.12817i	1.60159	−	0.114548i	0.758265	−	0.651946i	$-0.226047\pi$
$97$	15.7739	−	1.12817i	1.60159	−	0.114548i	0.843329	+	0.537398i	$0.180593\pi$
$98$	−1.41382	−	2.58922i	−0.142818	−	0.261551i
$99$	8.35377	−	0.0993971i	0.839586	−	0.00998979i
$100$	−0.503516	+	4.97458i	−0.0503516	+	0.497458i
$101$	3.34035	−	2.89443i	0.332377	−	0.288006i	−0.472643	−	0.881254i	$-0.656700\pi$
$101$	3.34035	−	2.89443i	0.332377	−	0.288006i	0.805020	+	0.593248i	$0.202155\pi$
$102$	0.871494	−	13.2962i	0.0862908	−	1.31652i
$103$	5.34836	+	7.14457i	0.526990	+	0.703976i	0.982502	−	0.186254i	$-0.0596347\pi$
$103$	5.34836	+	7.14457i	0.526990	+	0.703976i	−0.455512	+	0.890230i	$0.650544\pi$
$104$	0.474365	−	3.29928i	0.0465153	−	0.323521i
$105$	2.52629	−	7.37338i	0.246540	−	0.719568i
$106$	0.667515	+	0.770353i	0.0648348	+	0.0748233i
$107$	14.4575	+	5.39238i	1.39766	+	0.521301i	0.931611	−	0.363457i	$-0.118404\pi$
$107$	14.4575	+	5.39238i	1.39766	+	0.521301i	0.466051	+	0.884758i	$0.345676\pi$
$108$	4.51539	−	2.57124i	0.434493	−	0.247418i
$109$	−2.58060	+	8.78872i	−0.247177	+	0.841807i	0.738657	+	0.674082i	$0.235460\pi$
$109$	−2.58060	+	8.78872i	−0.247177	+	0.841807i	−0.985834	+	0.167725i	$0.946358\pi$
$110$	3.47562	+	5.16675i	0.331388	+	0.492630i
$111$	−10.6764	+	0.0635140i	−1.01336	+	0.00602848i
$112$	−1.88556	+	0.703276i	−0.178168	+	0.0664533i
$113$	−9.63349	+	12.8688i	−0.906242	+	1.21060i	0.0707869	+	0.997491i	$0.477449\pi$
$113$	−9.63349	+	12.8688i	−0.906242	+	1.21060i	−0.977029	+	0.213106i	$0.931642\pi$
$114$	−3.52097	−	1.01114i	−0.329769	−	0.0947016i
$115$	−8.34161	−	6.73926i	−0.777859	−	0.628439i
$116$			9.08606i			0.843620i
$117$	9.32690	−	3.60573i	0.862272	−	0.333350i
$118$	0.903010	+	2.42106i	0.0831288	+	0.222877i
$119$	−14.8547	+	4.36173i	−1.36173	+	0.399839i
$120$	3.44795	+	1.76398i	0.314753	+	0.161029i
$121$	−3.11351	−	0.914210i	−0.283047	−	0.0831100i
$122$	−1.59457	+	7.33014i	−0.144366	+	0.663639i
$123$	5.82567	−	7.87946i	0.525283	−	0.710467i
$124$	6.80474	−	5.89634i	0.611084	−	0.529507i
$125$	−9.35371	−	6.12439i	−0.836621	−	0.547782i
$126$	−4.60942	−	3.89904i	−0.410640	−	0.347354i
$127$	−1.67827	+	1.25633i	−0.148922	+	0.111482i	−0.671141	−	0.741330i	$-0.734195\pi$
$127$	−1.67827	+	1.25633i	−0.148922	+	0.111482i	0.522219	+	0.852812i	$0.325104\pi$
$128$	−0.212565	−	0.977147i	−0.0187883	−	0.0863684i
$129$	−12.1763	+	5.64852i	−1.07206	+	0.497324i
$130$	6.05897	+	4.34053i	0.531407	+	0.380690i
$131$	7.50989	+	11.6856i	0.656142	+	1.02098i	0.996733	+	0.0807654i	$0.0257365\pi$
$131$	7.50989	+	11.6856i	0.656142	+	1.02098i	−0.340591	+	0.940212i	$0.610627\pi$
$132$	4.70698	−	1.05331i	0.409690	−	0.0916785i
$133$	0.303641	+	4.24546i	0.0263290	+	0.368128i
$134$	7.90716	−	2.32175i	0.683075	−	0.200569i
$135$	0.450813	+	11.6102i	0.0387998	+	0.999247i
$136$	−1.09483	−	7.61474i	−0.0938813	−	0.652959i
$137$	−1.46084	+	1.46084i	−0.124808	+	0.124808i	−0.766752	−	0.641944i	$-0.778128\pi$
$137$	−1.46084	+	1.46084i	−0.124808	+	0.124808i	0.641944	+	0.766752i	$0.278128\pi$
$138$	−7.21179	+	4.12191i	−0.613908	+	0.350880i
$139$			6.55363i			0.555872i	0.960600	+	0.277936i	$0.0896503\pi$
$139$			6.55363i			0.555872i	−0.960600	+	0.277936i	$0.910350\pi$
$140$	0.546905	−	4.46660i	0.0462219	−	0.377496i
$141$	−5.70537	−	4.88461i	−0.480479	−	0.411359i
$142$	2.99496	+	1.63537i	0.251332	+	0.137238i
$143$	9.25862	−	0.662190i	0.774245	−	0.0553751i
$144$	2.24371	−	1.99142i	0.186976	−	0.165952i
$145$	−18.0320	−	9.36101i	−1.49748	−	0.777390i
$146$	8.70252	−	3.97431i	0.720226	−	0.328916i
$147$	1.75714	−	4.79806i	0.144927	−	0.395737i
$148$	−6.02324	+	1.31028i	−0.495107	+	0.107704i
$149$	−3.01405	+	20.9631i	−0.246920	+	1.71737i	0.368890	+	0.929473i	$0.379738\pi$
$149$	−3.01405	+	20.9631i	−0.246920	+	1.71737i	−0.615810	+	0.787895i	$0.711171\pi$
$150$	−7.05306	+	5.02538i	−0.575880	+	0.410320i
$151$	−13.0659	−	8.39694i	−1.06329	−	0.683333i	−0.112649	−	0.993635i	$-0.535934\pi$
$151$	−13.0659	−	8.39694i	−1.06329	−	0.683333i	−0.950638	+	0.310302i	$0.899570\pi$
$152$	−2.10960	−	0.150882i	−0.171112	−	0.0122381i
$153$	18.3099	−	14.0497i	1.48027	−	1.13585i
$154$	−3.02987	−	4.71457i	−0.244154	−	0.379911i
$155$	4.69111	+	19.5793i	0.376799	+	1.57265i
$156$	4.83814	−	3.15011i	0.387361	−	0.252211i
$157$	−3.64341	−	1.98945i	−0.290776	−	0.158776i	0.327240	−	0.944941i	$-0.393881\pi$
$157$	−3.64341	−	1.98945i	−0.290776	−	0.158776i	−0.618016	+	0.786166i	$0.712063\pi$
$158$	−11.8643	+	4.42515i	−0.943871	+	0.352046i
$159$	−0.240859	+	1.74901i	−0.0191014	+	0.138706i
$160$	2.15823	+	0.584863i	0.170623	+	0.0462375i
$161$	7.37859	+	6.22130i	0.581514	+	0.490307i
$162$	8.50500	+	2.94365i	0.668216	+	0.231275i
$163$	−14.0109	−	10.4884i	−1.09742	−	0.821516i	−0.112347	−	0.993669i	$-0.535837\pi$
$163$	−14.0109	−	10.4884i	−1.09742	−	0.821516i	−0.985070	+	0.172153i	$0.944928\pi$
$164$	2.35024	−	5.14631i	0.183523	−	0.401859i
$165$	−2.75905	+	10.4266i	−0.214791	+	0.811707i
$166$	−3.25266	+	3.75377i	−0.252455	+	0.291349i
$167$	−4.24947	+	2.32039i	−0.328834	+	0.179557i	−0.635182	−	0.772363i	$-0.719075\pi$
$167$	−4.24947	+	2.32039i	−0.328834	+	0.179557i	0.306348	+	0.951920i	$0.400893\pi$
$168$	−3.06917	−	1.65227i	−0.236791	−	0.127475i
$169$	−1.71897	+	0.785028i	−0.132229	+	0.0603867i
$170$	16.2400	+	5.67238i	1.24555	+	0.435052i
$171$	−2.70428	−	5.73983i	−0.206802	−	0.438936i
$172$	−6.20386	+	4.64415i	−0.473040	+	0.354113i
$173$	10.2396	−	7.66531i	0.778506	−	0.582782i	−0.134412	−	0.990926i	$-0.542914\pi$
$173$	10.2396	−	7.66531i	0.778506	−	0.582782i	0.912918	+	0.408143i	$0.133824\pi$
$174$	−11.8321	+	10.3765i	−0.896990	+	0.786637i
$175$	8.30087	+	5.68714i	0.627487	+	0.429907i
$176$	2.53313	−	1.15684i	0.190942	−	0.0872003i
$177$	−2.12152	+	3.94082i	−0.159463	+	0.296210i
$178$	−0.565858	+	0.308982i	−0.0424128	+	0.0231592i
$179$	12.4657	−	14.3862i	0.931734	−	1.07528i	−0.0652658	−	0.997868i	$-0.520790\pi$
$179$	12.4657	−	14.3862i	0.931734	−	1.07528i	0.996999	−	0.0774100i	$-0.0246650\pi$
$180$	1.64052	+	6.50451i	0.122277	+	0.484818i
$181$	8.95286	−	19.6040i	0.665461	−	1.45716i	−0.211884	−	0.977295i	$-0.567960\pi$
$181$	8.95286	−	19.6040i	0.665461	−	1.45716i	0.877345	−	0.479861i	$-0.159313\pi$
$182$	−5.36993	−	4.01988i	−0.398046	−	0.297974i
$183$	−11.3665	+	6.29466i	−0.840238	+	0.465315i
$184$	−3.58175	+	3.18921i	−0.264050	+	0.235112i
$185$	3.60516	−	13.3035i	0.265056	−	0.978095i
$186$	15.4495	+	2.12758i	1.13281	+	0.156001i
$187$	20.0727	−	7.48675i	1.46786	−	0.547485i
$188$	−3.80589	−	2.07817i	−0.277573	−	0.151566i
$189$	−0.186614	−	10.4553i	−0.0135742	−	0.760510i
$190$	2.47288	−	4.03123i	0.179402	−	0.292457i
$191$	−7.75031	−	12.0597i	−0.560793	−	0.872611i	0.438871	−	0.898550i	$-0.355379\pi$
$191$	−7.75031	−	12.0597i	−0.560793	−	0.872611i	−0.999664	+	0.0259395i	$0.991742\pi$
$192$	1.02971	−	1.39273i	0.0743131	−	0.100512i
$193$	15.4491	+	1.10494i	1.11205	+	0.0795355i	0.615252	−	0.788330i	$-0.289054\pi$
$193$	15.4491	+	1.10494i	1.11205	+	0.0795355i	0.496799	+	0.867866i	$0.334509\pi$
$194$	13.3037	+	8.54978i	0.955152	+	0.613839i
$195$	1.26710	+	12.8471i	0.0907392	+	0.920001i
$196$	0.419840	−	2.92005i	0.0299886	−	0.208575i
$197$	0.956894	−	0.208160i	0.0681759	−	0.0148308i	−0.178348	−	0.983967i	$-0.557075\pi$
$197$	0.956894	−	0.208160i	0.0681759	−	0.0148308i	0.246524	+	0.969137i	$0.420712\pi$
$198$	6.74711	+	4.92666i	0.479496	+	0.350122i
$199$	−3.08656	+	1.40958i	−0.218800	+	0.0999228i	−0.521800	−	0.853068i	$-0.674739\pi$
$199$	−3.08656	+	1.40958i	−0.218800	+	0.0999228i	0.302999	+	0.952991i	$0.402012\pi$
$200$	−3.38424	+	3.68061i	−0.239302	+	0.260259i
$201$	12.0536	+	7.64543i	0.850194	+	0.539267i
$202$	4.40865	−	0.315313i	0.310191	−	0.0221853i
$203$	16.0485	+	8.76315i	1.12638	+	0.615052i
$204$	8.66579	−	10.1219i	0.606727	−	0.708675i
$205$	7.79190	+	9.96628i	0.544210	+	0.696075i
$206$			8.92468i			0.621812i
$207$	−13.6037	−	4.68408i	−0.945519	−	0.325566i
$208$	2.35693	−	2.35693i	0.163424	−	0.163424i
$209$	−0.838207	−	5.82986i	−0.0579800	−	0.403260i
$210$	6.44110	−	4.38875i	0.444478	−	0.302852i
$211$	−24.9532	+	7.32692i	−1.71785	+	0.504406i	−0.984491	−	0.175437i	$-0.943866\pi$
$211$	−24.9532	+	7.32692i	−1.71785	+	0.504406i	−0.733358	+	0.679843i	$0.762048\pi$
$212$	0.0727177	+	1.01673i	0.00499427	+	0.0698290i
$213$	1.29068	+	5.76775i	0.0884359	+	0.395199i
$214$	8.34232	+	12.9809i	0.570269	+	0.887356i
$215$	−2.82510	−	17.0968i	−0.192671	−	1.16599i
$216$	5.15564	+	0.647586i	0.350797	+	0.0440626i
$217$	−3.85167	−	17.7058i	−0.261468	−	1.20195i
$218$	−7.33276	+	5.48924i	−0.496637	+	0.371778i
$219$	15.1139	+	6.79391i	1.02130	+	0.459090i
$220$	−0.313938	+	6.21906i	−0.0211657	+	0.419289i
$221$	19.3793	−	16.7923i	1.30359	−	1.12957i
$222$	−8.58493	−	6.34726i	−0.576183	−	0.426000i
$223$	3.89901	−	17.9235i	0.261097	−	1.20024i	−0.640600	−	0.767875i	$-0.721314\pi$
$223$	3.89901	−	17.9235i	0.261097	−	1.20024i	0.901697	−	0.432369i	$-0.142322\pi$
$224$	−1.93092	−	0.566970i	−0.129015	−	0.0378823i
$225$	−14.5989	−	3.44560i	−0.973260	−	0.229706i
$226$	−15.4240	+	4.52890i	−1.02599	+	0.301258i
$227$	1.70744	+	4.57783i	0.113327	+	0.303841i	0.981215	−	0.192919i	$-0.0617955\pi$
$227$	1.70744	+	4.57783i	0.113327	+	0.303841i	−0.867888	+	0.496760i	$0.834523\pi$
$228$	−2.21273	−	2.91949i	−0.146541	−	0.193348i
$229$		−	12.2131i		−	0.807067i	−0.914965	−	0.403533i	$-0.867782\pi$
$229$		−	12.2131i		−	0.807067i	0.914965	−	0.403533i	$-0.132218\pi$
$230$	−2.63912	−	10.3940i	−0.174018	−	0.685360i
$231$	2.67927	−	9.32971i	0.176283	−	0.613850i
$232$	−5.44507	+	7.27377i	−0.357487	+	0.477546i
$233$	−10.3093	+	3.84517i	−0.675384	+	0.251905i	−0.663669	−	0.748026i	$-0.731002\pi$
$233$	−10.3093	+	3.84517i	−0.675384	+	0.251905i	−0.0117147	+	0.999931i	$0.503729\pi$
$234$	9.62740	+	2.70287i	0.629363	+	0.176692i
$235$	8.04536	−	5.41204i	0.524821	−	0.353042i
$236$	−0.727992	+	2.47931i	−0.0473883	+	0.161390i
$237$	−19.3118	−	10.3964i	−1.25443	−	0.675317i
$238$	−14.5057	−	5.41034i	−0.940263	−	0.350700i
$239$	11.1926	+	12.9170i	0.723990	+	0.835529i	0.991781	−	0.127948i	$-0.0408391\pi$
$239$	11.1926	+	12.9170i	0.723990	+	0.835529i	−0.267791	+	0.963477i	$0.586294\pi$
$240$	1.70311	+	3.47842i	0.109935	+	0.224531i
$241$	3.06772	−	21.3365i	0.197609	−	1.37440i	−0.613586	−	0.789628i	$-0.710273\pi$
$241$	3.06772	−	21.3365i	0.197609	−	1.37440i	0.811195	−	0.584776i	$-0.198817\pi$
$242$	−1.94463	−	2.59772i	−0.125006	−	0.166988i
$243$	5.87957	+	14.4371i	0.377175	+	0.926142i
$244$	−5.66931	+	4.91248i	−0.362940	+	0.314490i
$245$	5.36254	+	3.84162i	0.342600	+	0.245432i
$246$	9.38567	−	2.81664i	0.598409	−	0.179582i
$247$	−3.37857	−	6.18738i	−0.214973	−	0.393694i
$248$	8.98102	−	0.642335i	0.570295	−	0.0407883i
$249$	−8.60286	+	0.0511786i	−0.545184	+	0.00324331i
$250$	−3.81782	−	10.5083i	−0.241460	−	0.664603i
$251$	−17.6095	+	2.53187i	−1.11150	+	0.159810i	−0.673517	−	0.739172i	$-0.735217\pi$
$251$	−17.6095	+	2.53187i	−1.11150	+	0.159810i	−0.437986	+	0.898982i	$0.644308\pi$
$252$	−1.35342	−	5.88367i	−0.0852576	−	0.370636i
$253$	−10.7985	−	7.85861i	−0.678898	−	0.494067i
$254$	−2.09642			−0.131541
$255$	11.1597	+	27.6262i	0.698849	+	1.73002i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	1.82597	−	3.34401i	0.113901	−	0.208593i	−0.814510	−	0.580150i	$-0.802994\pi$
$257$	1.82597	−	3.34401i	0.113901	−	0.208593i	0.928410	+	0.371557i	$0.121176\pi$
$258$	−13.1327	−	2.77512i	−0.817604	−	0.172771i
$259$	−3.49487	+	11.9024i	−0.217160	+	0.739580i
$260$	2.24927	+	7.10578i	0.139494	+	0.440682i
$261$	−27.0250	−	3.55796i	−1.67280	−	0.220232i
$262$	−0.990952	+	13.8553i	−0.0612212	+	0.855985i
$263$	2.00236	+	9.20469i	0.123471	+	0.567586i	0.996763	+	0.0803898i	$0.0256165\pi$
$263$	2.00236	+	9.20469i	0.123471	+	0.567586i	−0.873293	+	0.487196i	$0.838020\pi$
$264$	4.39936	+	1.97757i	0.270762	+	0.121711i
$265$	−2.09269	−	0.903179i	−0.128553	−	0.0554818i
$266$	−2.30113	+	3.58063i	−0.141091	+	0.219542i
$267$	−1.04858	−	0.384012i	−0.0641723	−	0.0235011i
$268$	7.72139	+	2.87993i	0.471659	+	0.175920i
$269$	−3.25027	+	2.08882i	−0.198172	+	0.127358i	−0.635964	−	0.771719i	$-0.719397\pi$
$269$	−3.25027	+	2.08882i	−0.198172	+	0.127358i	0.437791	+	0.899077i	$0.355761\pi$
$270$	−6.59684	+	9.56461i	−0.401471	+	0.582083i
$271$	−13.0266	+	15.0335i	−0.791311	+	0.913221i	−0.997871	−	0.0652126i	$-0.979227\pi$
$271$	−13.0266	+	15.0335i	−0.791311	+	0.913221i	0.206561	+	0.978434i	$0.433773\pi$
$272$	3.68689	−	6.75203i	0.223550	−	0.409402i
$273$	−0.897772	−	11.5836i	−0.0543357	−	0.701074i
$274$	−2.04492	+	0.294015i	−0.123538	+	0.0177621i
$275$	−12.0188	−	7.03028i	−0.724760	−	0.423942i
$276$	−8.24350	−	1.02211i	−0.496200	−	0.0615235i
$277$	10.8416	+	10.8416i	0.651407	+	0.651407i	0.953332	−	0.301924i	$-0.0976290\pi$
$277$	10.8416	+	10.8416i	0.651407	+	0.651407i	−0.301924	+	0.953332i	$0.597629\pi$
$278$	−3.92744	+	5.24645i	−0.235552	+	0.314661i
$279$	14.8731	+	22.5485i	0.890426	+	1.34994i
$280$	3.11455	−	3.24795i	0.186130	−	0.194102i
$281$	−5.66743	−	4.91086i	−0.338091	−	0.292957i	0.469223	−	0.883080i	$-0.344534\pi$
$281$	−5.66743	−	4.91086i	−0.338091	−	0.292957i	−0.807314	+	0.590122i	$0.799079\pi$
$282$	−1.64015	−	7.32944i	−0.0976694	−	0.436462i
$283$	1.33651	−	6.14385i	0.0794475	−	0.365214i	−0.920209	−	0.391428i	$-0.871981\pi$
$283$	1.33651	−	6.14385i	0.0794475	−	0.365214i	0.999656	+	0.0262135i	$0.00834497\pi$
$284$	1.41755	+	3.10400i	0.0841160	+	0.184188i
$285$	8.07365	−	1.38350i	0.478242	−	0.0819514i
$286$	7.80874	+	5.01837i	0.461741	+	0.296743i
$287$	−6.82309	−	9.11458i	−0.402754	−	0.538017i
$288$	2.98960	−	0.249604i	0.176164	−	0.0147081i
$289$	22.8058	−	35.4866i	1.34152	−	2.08745i
$290$	−8.82554	−	18.3001i	−0.518253	−	1.07462i
$291$	4.05936	+	27.0885i	0.237964	+	1.58795i
$292$	9.34844	+	2.03363i	0.547076	+	0.119009i
$293$	−5.80401	−	10.6293i	−0.339074	−	0.620968i	0.651389	−	0.758744i	$-0.274187\pi$
$293$	−5.80401	−	10.6293i	−0.339074	−	0.620968i	−0.990463	+	0.137776i	$0.956005\pi$
$294$	4.28203	−	2.78803i	0.249733	−	0.162601i
$295$	−4.17038	−	3.99910i	−0.242809	−	0.232837i
$296$	−5.60707	−	2.56066i	−0.325904	−	0.148836i
$297$	1.28970	+	14.4126i	0.0748361	+	0.836304i
$298$	−14.9756	+	14.9756i	−0.867514	+	0.867514i
$299$	−15.3973	−	4.29630i	−0.890450	−	0.248462i
$300$	−8.65786	−	0.203718i	−0.499862	−	0.0117617i
$301$	2.21948	+	15.4368i	0.127929	+	0.889765i
$302$	−5.42769	−	14.5522i	−0.312328	−	0.837384i
$303$	5.44537	+	5.38096i	0.312828	+	0.309128i
$304$	−1.59841	−	1.38503i	−0.0916748	−	0.0794367i
$305$	−3.90836	−	16.3123i	−0.223792	−	0.934042i
$306$	23.0775	−	0.274587i	1.31925	−	0.0156971i
$307$	−0.676268	+	1.81315i	−0.0385967	+	0.103482i	−0.954818	−	0.297190i	$-0.903951\pi$
$307$	−0.676268	+	1.81315i	−0.0385967	+	0.103482i	0.916222	+	0.400672i	$0.131223\pi$
$308$	0.399801	−	5.58994i	0.0227808	−	0.318517i
$309$	−11.6219	+	10.1922i	−0.661150	+	0.579811i
$310$	−7.97802	+	18.4853i	−0.453121	+	1.04990i
$311$	−4.48545	−	0.644910i	−0.254346	−	0.0365695i	0.0139621	−	0.999903i	$-0.495556\pi$
$311$	−4.48545	−	0.644910i	−0.254346	−	0.0365695i	−0.268309	+	0.963333i	$0.586465\pi$
$312$	5.76092	+	0.377597i	0.326148	+	0.0213772i
$313$	23.4163	+	1.67477i	1.32357	+	0.0946634i	0.715159	−	0.698962i	$-0.246354\pi$
$313$	23.4163	+	1.67477i	1.32357	+	0.0946634i	0.608407	+	0.793625i	$0.291809\pi$
$314$	−1.72447	−	3.77606i	−0.0973173	−	0.213095i
$315$	13.0710	+	3.37573i	0.736467	+	0.190201i
$316$	−12.1497	−	3.56748i	−0.683476	−	0.200687i
$317$	−1.11492	−	15.5887i	−0.0626203	−	0.875546i	−0.927561	−	0.373672i	$-0.878099\pi$
$317$	−1.11492	−	15.5887i	−0.0626203	−	0.875546i	0.864941	−	0.501874i	$-0.167356\pi$
$318$	−1.24096	+	1.25582i	−0.0695897	+	0.0704226i
$319$	−23.0162	−	10.5111i	−1.28866	−	0.588511i
$320$	1.37725	+	1.76158i	0.0769908	+	0.0984755i
$321$	−7.37698	+	25.6880i	−0.411743	+	1.43377i
$322$	2.17858	+	9.40223i	0.121407	+	0.523966i
$323$	−11.5052	−	11.5052i	−0.640164	−	0.640164i
$324$	5.04454	+	7.45336i	0.280252	+	0.414076i
$325$	−16.4193	−	2.85694i	−0.910780	−	0.158475i
$326$	−4.93081	−	16.7928i	−0.273093	−	0.930068i
$327$	−15.5224	−	3.28010i	−0.858390	−	0.181390i
$328$	4.96553	−	2.71138i	0.274176	−	0.149711i
$329$	−7.34126	+	4.71794i	−0.404737	+	0.260108i
$330$	−8.45714	+	6.69346i	−0.465550	+	0.368463i
$331$	15.9573	+	18.4157i	0.877091	+	1.01222i	0.999804	+	0.0197746i	$0.00629486\pi$
$331$	15.9573	+	18.4157i	0.877091	+	1.01222i	−0.122714	+	0.992442i	$0.539160\pi$
$332$	−4.85344	+	1.05580i	−0.266367	+	0.0579446i
$333$	−1.53859	−	18.4282i	−0.0843141	−	1.00986i
$334$	−4.79243	−	0.689048i	−0.262230	−	0.0377030i
$335$	−13.6705	+	12.3566i	−0.746899	+	0.675116i
$336$	−1.46683	−	3.16199i	−0.0800220	−	0.172501i
$337$	4.13548	−	11.0876i	0.225274	−	0.603982i	−0.774311	−	0.632806i	$-0.781903\pi$
$337$	4.13548	−	11.0876i	0.225274	−	0.603982i	0.999585	+	0.0288231i	$0.00917595\pi$
$338$	−1.84656	−	0.401694i	−0.100439	−	0.0218493i
$339$	−23.5122	−	14.9135i	−1.27700	−	0.809988i
$340$	9.60149	+	14.2733i	0.520714	+	0.774077i
$341$	7.06420	+	24.0584i	0.382548	+	1.30284i
$342$	1.27486	−	6.21559i	0.0689367	−	0.336100i
$343$	−16.0300	−	11.9999i	−0.865539	−	0.647934i
$344$	−7.74958			−0.417830
$345$	10.5214	−	15.3069i	0.566453	−	0.824094i
$346$	12.7909			0.687643
$347$	17.0303	+	12.7487i	0.914234	+	0.684387i	0.949090	−	0.315005i	$-0.102006\pi$
$347$	17.0303	+	12.7487i	0.914234	+	0.684387i	−0.0348559	+	0.999392i	$0.511097\pi$
$348$	−15.6905	+	1.21606i	−0.841097	+	0.0651879i
$349$	0.576243	+	1.96250i	0.0308456	+	0.105050i	0.973477	−	0.228785i	$-0.0734752\pi$
$349$	0.576243	+	1.96250i	0.0308456	+	0.105050i	−0.942631	+	0.333835i	$0.891657\pi$
$350$	3.23701	+	9.52731i	0.173026	+	0.509256i
$351$	7.47493	+	15.6238i	0.398982	+	0.833935i
$352$	2.72115	+	0.591949i	0.145038	+	0.0315510i
$353$	2.67124	−	7.16188i	0.142176	−	0.381188i	−0.846272	−	0.532752i	$-0.821158\pi$
$353$	2.67124	−	7.16188i	0.142176	−	0.381188i	0.988448	+	0.151563i	$0.0484307\pi$
$354$	−4.06001	+	1.88341i	−0.215787	+	0.100102i
$355$	−7.62058	−	0.384687i	−0.404459	−	0.0204170i
$356$	−0.638159	−	0.0917533i	−0.0338223	−	0.00486292i
$357$	−9.52028	−	25.0684i	−0.503866	−	1.32676i
$358$	18.6007	−	4.04633i	0.983077	−	0.213855i
$359$	−6.82390	−	7.87520i	−0.360151	−	0.415637i	0.546539	−	0.837434i	$-0.315945\pi$
$359$	−6.82390	−	7.87520i	−0.360151	−	0.415637i	−0.906690	+	0.421797i	$0.861400\pi$
$360$	−2.58470	+	6.19026i	−0.136226	+	0.326255i
$361$	12.2207	−	7.85378i	0.643196	−	0.413357i
$362$	18.9154	−	10.3286i	0.994171	−	0.542858i
$363$	1.16202	−	5.49899i	0.0609900	−	0.288622i
$364$	−1.88983	−	6.43616i	−0.0990539	−	0.337347i
$365$	−13.6672	+	16.4576i	−0.715375	+	0.861429i
$366$	−12.8716	−	1.77257i	−0.672811	−	0.0926537i
$367$	7.12141	+	7.12141i	0.371734	+	0.371734i	0.868109	−	0.496374i	$-0.165336\pi$
$367$	7.12141	+	7.12141i	0.371734	+	0.371734i	−0.496374	+	0.868109i	$0.665336\pi$
$368$	−4.77856	+	0.406634i	−0.249100	+	0.0211973i
$369$	14.3865	+	9.00561i	0.748932	+	0.468813i
$370$	10.8586	−	8.48954i	0.564511	−	0.441350i
$371$	1.86595	+	0.852152i	0.0968755	+	0.0442416i
$372$	11.0930	+	10.9618i	0.575143	+	0.568341i
$373$	0.0245644	+	0.343455i	0.00127190	+	0.0177834i	0.998048	−	0.0624446i	$-0.0198897\pi$
$373$	0.0245644	+	0.343455i	0.00127190	+	0.0177834i	−0.996777	+	0.0802281i	$0.974435\pi$
$374$	20.5557	+	6.03570i	1.06291	+	0.312099i
$375$	9.32414	−	16.9723i	0.481497	−	0.876448i
$376$	−1.80137	−	3.94445i	−0.0928985	−	0.203419i
$377$	−30.2085	−	2.16056i	−1.55582	−	0.111274i
$378$	6.11623	−	8.48172i	0.314585	−	0.436253i
$379$	12.2399	+	1.75983i	0.628722	+	0.0903965i	0.449308	−	0.893377i	$-0.351671\pi$
$379$	12.2399	+	1.75983i	0.628722	+	0.0903965i	0.179414	+	0.983774i	$0.442580\pi$
$380$	4.39547	−	1.74523i	0.225483	−	0.0895283i
$381$	−2.39415	−	2.73001i	−0.122656	−	0.139862i
$382$	1.02268	−	14.2989i	0.0523247	−	0.731595i
$383$	6.58260	−	17.6486i	0.336355	−	0.901803i	−0.653140	−	0.757237i	$-0.726549\pi$
$383$	6.58260	−	17.6486i	0.336355	−	0.901803i	0.989495	−	0.144566i	$-0.0461786\pi$
$384$	1.65896	−	0.497853i	0.0846584	−	0.0254060i
$385$	10.6818	+	6.55253i	0.544395	+	0.333948i
$386$	11.7055	+	10.1429i	0.595793	+	0.516258i
$387$	−11.3839	−	20.2709i	−0.578677	−	1.03043i
$388$	5.52648	+	14.8171i	0.280565	+	0.752223i
$389$	−0.720974	−	5.01449i	−0.0365549	−	0.254245i	0.963347	−	0.268259i	$-0.0864482\pi$
$389$	−0.720974	−	5.01449i	−0.0365549	−	0.254245i	−0.999902	+	0.0140140i	$0.995539\pi$
$390$	−6.68462	+	11.0440i	−0.338489	+	0.559234i
$391$	−36.8912	+	0.497733i	−1.86567	+	0.0251714i
$392$	2.08602	−	2.08602i	0.105360	−	0.105360i
$393$	−19.1745	+	14.5326i	−0.967223	+	0.733073i
$394$	0.890779	+	0.406805i	0.0448768	+	0.0204945i
$395$	19.5974	−	20.4367i	0.986050	−	1.02828i
$396$	2.44890	+	7.98738i	0.123062	+	0.401381i
$397$	11.3628	+	20.8094i	0.570283	+	1.04439i	0.990571	+	0.137004i	$0.0437472\pi$
$397$	11.3628	+	20.8094i	0.570283	+	1.04439i	−0.420288	+	0.907391i	$0.638071\pi$
$398$	−3.31565	−	0.721276i	−0.166199	−	0.0361543i
$399$	−7.29072	+	1.09255i	−0.364993	+	0.0546961i
$400$	−4.91493	+	0.918381i	−0.245747	+	0.0459191i
$401$	−1.79656	+	2.79551i	−0.0897161	+	0.139601i	−0.883211	−	0.468976i	$-0.844623\pi$
$401$	−1.79656	+	2.79551i	−0.0897161	+	0.139601i	0.793495	+	0.608577i	$0.208259\pi$
$402$	5.06765	+	13.3439i	0.252752	+	0.665534i
$403$	17.9856	+	24.0259i	0.895924	+	1.19681i
$404$	3.71827	+	2.38958i	0.184991	+	0.118886i
$405$	−19.9890	+	2.33239i	−0.993261	+	0.115897i
$406$	7.59593	+	16.6328i	0.376980	+	0.825471i
$407$	3.64884	−	16.7734i	0.180866	−	0.831429i
$408$	13.0032	−	2.90979i	0.643752	−	0.144056i
$409$	7.80851	+	6.76611i	0.386106	+	0.334563i	0.826188	−	0.563395i	$-0.190505\pi$
$409$	7.80851	+	6.76611i	0.386106	+	0.334563i	−0.440082	+	0.897958i	$0.645051\pi$
$410$	0.265174	+	12.6479i	0.0130960	+	0.624637i
$411$	−2.71821	−	2.32717i	−0.134079	−	0.114791i
$412$	−5.34836	+	7.14457i	−0.263495	+	0.351988i
$413$	3.67704	+	3.67704i	0.180935	+	0.180935i
$414$	−8.08322	−	11.9022i	−0.397269	−	0.584959i
$415$	2.90498	−	10.7198i	0.142600	−	0.526214i
$416$	3.29928	−	0.474365i	0.161760	−	0.0232576i
$417$	−11.3173	+	0.877128i	−0.554210	+	0.0429531i
$418$	2.82268	−	5.16936i	0.138062	−	0.252842i
$419$	−9.14937	+	10.5589i	−0.446976	+	0.515838i	−0.933865	−	0.357626i	$-0.883586\pi$
$419$	−9.14937	+	10.5589i	−0.446976	+	0.515838i	0.486889	+	0.873464i	$0.338132\pi$
$420$	7.78644	+	0.346633i	0.379939	+	0.0169140i
$421$	0.534769	−	0.343675i	0.0260631	−	0.0167497i	−0.527544	−	0.849527i	$-0.676887\pi$
$421$	0.534769	−	0.343675i	0.0260631	−	0.0167497i	0.553607	+	0.832778i	$0.313251\pi$
$422$	−24.3669	−	9.08839i	−1.18616	−	0.442416i
$423$	7.67151	−	10.5062i	0.373001	−	0.510829i
$424$	−0.551088	+	0.857509i	−0.0267632	+	0.0416443i
$425$	−38.2185	+	4.34976i	−1.85387	+	0.210994i
$426$	−2.42324	+	5.39079i	−0.117406	+	0.261185i
$427$	3.20899	+	14.7515i	0.155294	+	0.713874i
$428$	−1.10079	+	15.3911i	−0.0532089	+	0.743957i
$429$	2.38268	+	15.8998i	0.115037	+	0.767651i
$430$	7.98409	−	15.3797i	0.385027	−	0.741674i
$431$	7.10617	−	24.2014i	0.342292	−	1.16574i	−0.591015	−	0.806661i	$-0.701272\pi$
$431$	7.10617	−	24.2014i	0.342292	−	1.16574i	0.933307	−	0.359080i	$-0.116909\pi$
$432$	3.73922	+	3.60808i	0.179903	+	0.173594i
$433$	−12.3217	+	22.5656i	−0.592145	+	1.08443i	0.394088	+	0.919073i	$0.371060\pi$
$433$	−12.3217	+	22.5656i	−0.592145	+	1.08443i	−0.986233	+	0.165360i	$0.947121\pi$
$434$	7.52730	−	16.4825i	0.361322	−	0.791184i
$435$	13.7519	−	32.3919i	0.659353	−	1.55307i
$436$	−9.15976			−0.438673
$437$	−2.02218	+	9.93954i	−0.0967338	+	0.475472i
$438$	8.02785	+	14.4962i	0.383586	+	0.692656i
$439$	−21.6025	+	3.10597i	−1.03103	+	0.148240i	−0.637005	−	0.770860i	$-0.719827\pi$
$439$	−21.6025	+	3.10597i	−1.03103	+	0.148240i	−0.394025	+	0.919100i	$0.628918\pi$
$440$	−3.97826	+	4.79048i	−0.189656	+	0.228377i
$441$	8.52081	+	2.39219i	0.405753	+	0.113914i
$442$	25.5772	−	1.82932i	1.21658	−	0.0870117i
$443$	5.72048	+	10.4763i	0.271788	+	0.497743i	0.977549	−	0.210707i	$-0.0675766\pi$
$443$	5.72048	+	10.4763i	0.271788	+	0.497743i	−0.705761	+	0.708450i	$0.749395\pi$
$444$	−3.06882	−	10.2260i	−0.145640	−	0.485304i
$445$	0.839562	−	1.17195i	0.0397990	−	0.0555556i
$446$	13.8624	−	12.0119i	0.656406	−	0.568779i
$447$	−36.6041	−	2.39919i	−1.73131	−	0.113478i
$448$	−1.20601	−	1.61104i	−0.0569787	−	0.0761146i
$449$	2.94442	−	20.4789i	0.138956	−	0.966458i	−0.794372	−	0.607432i	$-0.792200\pi$
$449$	2.94442	−	20.4789i	0.138956	−	0.966458i	0.933327	−	0.359026i	$-0.116891\pi$
$450$	−9.62215	−	11.5071i	−0.453593	−	0.542452i
$451$	10.3174	+	11.9069i	0.485828	+	0.560676i
$452$	−15.0616	−	5.61769i	−0.708439	−	0.264234i
$453$	12.7517	−	23.6870i	0.599128	−	1.11291i
$454$	−1.37651	+	4.68797i	−0.0646030	+	0.220017i
$455$	14.7201	+	2.88041i	0.690089	+	0.135036i
$456$	−0.0217925	−	3.66321i	−0.00102053	−	0.171546i
$457$	1.49048	−	0.555920i	0.0697217	−	0.0260048i	−0.314361	−	0.949303i	$-0.601790\pi$
$457$	1.49048	−	0.555920i	0.0697217	−	0.0260048i	0.384083	+	0.923299i	$0.374518\pi$
$458$	7.31906	−	9.77712i	0.341997	−	0.456855i
$459$	26.7125	+	29.7385i	1.24683	+	1.38808i
$460$	4.11617	−	9.90238i	0.191917	−	0.461701i
$461$			1.91124i			0.0890152i	0.999009	+	0.0445076i	$0.0141719\pi$
$461$			1.91124i			0.0890152i	−0.999009	+	0.0445076i	$0.985828\pi$
$462$	7.73595	−	5.86319i	0.359909	−	0.272780i
$463$	2.66133	+	7.13529i	0.123682	+	0.331605i	0.984004	−	0.178146i	$-0.0570101\pi$
$463$	2.66133	+	7.13529i	0.123682	+	0.331605i	−0.860322	+	0.509752i	$0.829737\pi$
$464$	−8.71801	+	2.55984i	−0.404724	+	0.118838i
$465$	−33.1831	+	10.7214i	−1.53883	+	0.497194i
$466$	−10.5573	−	3.09991i	−0.489059	−	0.143601i
$467$	3.10498	−	14.2734i	0.143681	−	0.660493i	−0.847808	−	0.530304i	$-0.822078\pi$
$467$	3.10498	−	14.2734i	0.143681	−	0.660493i	0.991489	−	0.130189i	$-0.0415584\pi$
$468$	6.08736	+	7.93324i	0.281389	+	0.366714i
$469$	12.5337	−	10.8605i	0.578754	−	0.501493i
$470$	9.68395	+	0.488845i	0.446687	+	0.0225488i
$471$	2.94791	−	6.55798i	0.135832	−	0.302176i
$472$	−2.06859	+	1.54852i	−0.0952144	+	0.0712766i
$473$	−4.58736	−	21.0878i	−0.210927	−	0.969616i
$474$	−9.22956	−	19.8958i	−0.423928	−	0.913846i
$475$	−1.06493	+	10.5212i	−0.0488625	+	0.482746i
$476$	−8.37010	−	13.0241i	−0.383643	−	0.596960i
$477$	−3.05256	−	0.181848i	−0.139767	−	0.00832624i
$478$	1.21930	+	17.0480i	0.0557695	+	0.779759i
$479$	−20.4870	+	6.01552i	−0.936074	+	0.274856i	−0.713978	−	0.700169i	$-0.753108\pi$
$479$	−20.4870	+	6.01552i	−0.936074	+	0.274856i	−0.222097	+	0.975025i	$0.571290\pi$
$480$	−0.721130	+	3.80526i	−0.0329149	+	0.173685i
$481$	−2.92404	−	20.3371i	−0.133325	−	0.927292i
$482$	15.2423	−	15.2423i	0.694269	−	0.694269i
$483$	−9.75585	+	13.5745i	−0.443907	+	0.617662i
$484$		−	3.24496i		−	0.147498i
$485$	−35.0994	−	4.29769i	−1.59378	−	0.195148i
$486$	−3.94501	+	15.0810i	−0.178949	+	0.684089i
$487$	−20.5004	−	11.1941i	−0.928963	−	0.507252i	−0.0578448	−	0.998326i	$-0.518423\pi$
$487$	−20.5004	−	11.1941i	−0.928963	−	0.507252i	−0.871118	+	0.491073i	$0.836605\pi$
$488$	−7.48246	+	0.535156i	−0.338715	+	0.0242254i
$489$	16.2370	−	25.5987i	0.734260	−	1.15762i
$490$	1.99073	+	6.28903i	0.0899322	+	0.284109i
$491$	14.3408	−	6.54924i	0.647193	−	0.295563i	−0.0646437	−	0.997908i	$-0.520591\pi$
$491$	14.3408	−	6.54924i	0.647193	−	0.295563i	0.711836	+	0.702345i	$0.247864\pi$
$492$	9.20157	+	3.36979i	0.414839	+	0.151922i
$493$	−68.3021	+	14.8582i	−3.07617	+	0.669180i
$494$	1.00328	−	6.97795i	0.0451396	−	0.313953i
$495$	−18.3746	−	3.36904i	−0.825878	−	0.151427i
$496$	7.57461	+	4.86791i	0.340110	+	0.218576i
$497$	6.84969	+	0.489900i	0.307251	+	0.0219750i
$498$	−6.91761	−	5.11453i	−0.309986	−	0.229188i
$499$	−11.0997	−	17.2714i	−0.496890	−	0.773176i	0.498721	−	0.866762i	$-0.333803\pi$
$499$	−11.0997	−	17.2714i	−0.496890	−	0.773176i	−0.995611	+	0.0935866i	$0.970167\pi$
$500$	3.24106	−	10.7003i	0.144945	−	0.478530i
$501$	−4.57575	−	7.02774i	−0.204430	−	0.313976i
$502$	−15.6144	−	8.52612i	−0.696906	−	0.380539i
$503$	−16.2461	+	6.05949i	−0.724379	+	0.270179i	−0.684487	−	0.729025i	$-0.739974\pi$
$503$	−16.2461	+	6.05949i	−0.724379	+	0.270179i	−0.0398914	+	0.999204i	$0.512701\pi$
$504$	2.44248	−	5.52119i	0.108797	−	0.245933i
$505$	−8.57311	+	4.91731i	−0.381498	+	0.218817i
$506$	−3.93518	−	12.7625i	−0.174940	−	0.567361i
$507$	−1.58571	−	2.86338i	−0.0704237	−	0.127167i
$508$	−1.67827	−	1.25633i	−0.0744611	−	0.0557408i
$509$	−9.34613	+	20.4652i	−0.414260	+	0.907103i	0.581363	+	0.813644i	$0.302520\pi$
$509$	−9.34613	+	20.4652i	−0.414260	+	0.907103i	−0.995623	+	0.0934586i	$0.970208\pi$
$510$	−7.62193	+	28.8037i	−0.337505	+	1.27545i
$511$	12.6081	−	14.5506i	0.557752	−	0.643680i
$512$	0.877679	−	0.479249i	0.0387883	−	0.0211800i
$513$	9.55001	−	5.43816i	0.421643	−	0.240101i
$514$	3.46575	−	1.58275i	0.152868	−	0.0698123i
$515$	−8.66878	−	17.9750i	−0.381992	−	0.792074i
$516$	−8.85017	−	10.0917i	−0.389607	−	0.444263i
$517$	9.66710	−	7.23670i	0.425159	−	0.318270i
$518$	−9.93064	+	7.43398i	−0.436327	+	0.326631i
$519$	14.6075	+	16.6567i	0.641196	+	0.731146i
$520$	−2.45770	+	7.03640i	−0.107777	+	0.308567i
$521$	19.8812	−	9.07945i	0.871012	−	0.397778i	0.0707970	−	0.997491i	$-0.477446\pi$
$521$	19.8812	−	9.07945i	0.871012	−	0.397778i	0.800215	+	0.599713i	$0.204718\pi$
$522$	−19.5024	−	19.0438i	−0.853597	−	0.833523i
$523$	−8.52268	+	4.65373i	−0.372671	+	0.203494i	−0.654659	−	0.755924i	$-0.727188\pi$
$523$	−8.52268	+	4.65373i	−0.372671	+	0.203494i	0.281988	+	0.959418i	$0.409006\pi$
$524$	−9.09649	+	10.4979i	−0.397382	+	0.458603i
$525$	−8.70998	+	15.0957i	−0.380135	+	0.658830i
$526$	−3.91320	+	8.56870i	−0.170623	+	0.373613i
$527$	55.4518	+	41.5107i	2.41552	+	1.80823i
$528$	2.33675	+	4.21957i	0.101694	+	0.183633i
$529$	12.9522	+	19.0063i	0.563140	+	0.826361i
$530$	−1.13403	−	1.97714i	−0.0492592	−	0.0858813i
$531$	−7.08924	−	3.13615i	−0.307647	−	0.136097i
$532$	−3.98794	+	1.48742i	−0.172899	+	0.0644880i
$533$	16.5511	+	9.03760i	0.716909	+	0.391462i
$534$	−0.609306	−	0.935811i	−0.0263672	−	0.0404965i
$535$	−29.4108	−	18.0415i	−1.27154	−	0.780001i
$536$	4.45541	+	6.93276i	0.192444	+	0.299449i
$537$	26.5116	+	19.6013i	1.14406	+	0.845859i
$538$	−3.85376	−	0.275626i	−0.166147	−	0.0118831i
$539$	6.91119	+	4.44155i	0.297686	+	0.191311i
$540$	−11.0129	+	3.70352i	−0.473920	+	0.159374i
$541$	−5.91612	+	41.1475i	−0.254354	+	1.76907i	0.317057	+	0.948406i	$0.397305\pi$
$541$	−5.91612	+	41.1475i	−0.254354	+	1.76907i	−0.571411	+	0.820664i	$0.693604\pi$
$542$	−19.4376	+	4.22839i	−0.834916	+	0.181625i
$543$	35.0519	+	12.8367i	1.50422	+	0.550874i
$544$	6.99784	−	3.19581i	0.300030	−	0.137019i
$545$	9.43694	−	18.1783i	0.404234	−	0.778672i
$546$	6.22312	−	9.81120i	0.266325	−	0.419881i
$547$	−4.09974	+	0.293219i	−0.175292	+	0.0125372i	−0.158709	−	0.987325i	$-0.550733\pi$
$547$	−4.09974	+	0.293219i	−0.175292	+	0.0125372i	−0.0165830	+	0.999862i	$0.505279\pi$
$548$	−1.81324	−	0.990102i	−0.0774577	−	0.0422951i
$549$	−12.3914	−	18.7861i	−0.528850	−	0.801770i
$550$	−5.40844	−	12.8306i	−0.230617	−	0.547100i
$551$			19.2170i			0.818670i
$552$	−5.98674	−	5.75838i	−0.254812	−	0.245093i
$553$	−18.0191	+	18.0191i	−0.766250	+	0.766250i
$554$	2.18202	+	15.1763i	0.0927050	+	0.644777i
$555$	23.4560	+	4.44512i	0.995652	+	0.188685i
$556$	−6.28816	+	1.84637i	−0.266677	+	0.0783036i
$557$	−0.308550	−	4.31409i	−0.0130737	−	0.182794i	−0.999793	−	0.0203578i	$-0.993519\pi$
$557$	−0.308550	−	4.31409i	−0.0130737	−	0.182794i	0.986719	−	0.162436i	$-0.0519351\pi$
$558$	−1.60631	+	26.9641i	−0.0680006	+	1.14148i
$559$	−13.9653	−	21.7304i	−0.590668	−	0.919097i
$560$	4.43975	−	0.733634i	0.187614	−	0.0310017i
$561$	15.6152	+	33.6611i	0.659273	+	1.42117i
$562$	−1.59405	−	7.32771i	−0.0672408	−	0.309101i
$563$	30.2895	−	22.6745i	1.27655	−	0.955614i	0.276566	−	0.960995i	$-0.410804\pi$
$563$	30.2895	−	22.6745i	1.27655	−	0.955614i	0.999986	+	0.00538075i	$0.00171275\pi$
$564$	3.07936	−	6.85042i	0.129665	−	0.288455i
$565$	26.6662	−	24.1033i	1.12185	−	1.01403i
$566$	4.75181	−	4.11747i	0.199733	−	0.173070i
$567$	18.0300	−	1.72158i	0.757187	−	0.0722995i
$568$	−0.725351	+	3.33438i	−0.0304350	+	0.139908i
$569$	1.38723	+	0.407328i	0.0581558	+	0.0170761i	0.310681	−	0.950514i	$-0.399443\pi$
$569$	1.38723	+	0.407328i	0.0581558	+	0.0170761i	−0.252525	+	0.967590i	$0.581261\pi$
$570$	7.29239	+	3.73081i	0.305445	+	0.156267i
$571$	27.0165	−	7.93276i	1.13061	−	0.331976i	0.337660	−	0.941268i	$-0.390365\pi$
$571$	27.0165	−	7.93276i	1.13061	−	0.331976i	0.792946	+	0.609293i	$0.208546\pi$
$572$	3.24382	+	8.69702i	0.135631	+	0.363641i
$573$	19.7883	−	14.9979i	0.826668	−	0.626544i
$574$		−	11.3855i		−	0.475223i
$575$	15.4114	+	18.3709i	0.642698	+	0.766119i
$576$	2.54288	+	1.59178i	0.105953	+	0.0663242i
$577$	−5.22054	+	6.97383i	−0.217334	+	0.290324i	−0.895937	−	0.444181i	$-0.853495\pi$
$577$	−5.22054	+	6.97383i	−0.217334	+	0.290324i	0.678603	+	0.734505i	$0.262586\pi$
$578$	39.5233	−	14.7414i	1.64395	−	0.613163i
$579$	0.159592	+	26.8265i	0.00663240	+	1.11487i
$580$	3.90161	−	19.9389i	0.162006	−	0.827918i
$581$	−2.81611	+	9.59080i	−0.116832	+	0.397893i
$582$	−12.9838	+	24.1181i	−0.538197	+	0.999728i
$583$	−2.65962	−	0.991989i	−0.110150	−	0.0410840i
$584$	6.26510	+	7.23031i	0.259252	+	0.299193i
$585$	−22.0157	+	3.90756i	−0.910239	+	0.161558i
$586$	1.72352	−	11.9874i	0.0711981	−	0.495194i
$587$	9.09869	+	12.1544i	0.375543	+	0.501667i	0.948001	−	0.318267i	$-0.103101\pi$
$587$	9.09869	+	12.1544i	0.375543	+	0.501667i	−0.572458	+	0.819934i	$0.694010\pi$
$588$	5.09875	+	0.334195i	0.210269	+	0.0137820i
$589$	14.3920	−	12.4707i	0.593011	−	0.513847i
$590$	−0.941989	−	5.70066i	−0.0387811	−	0.234692i
$591$	0.487534	+	1.62457i	0.0200545	+	0.0668261i
$592$	−2.95414	−	5.41011i	−0.121415	−	0.222354i
$593$	26.4076	−	1.88871i	1.08443	−	0.0775601i	0.482338	−	0.875985i	$-0.339788\pi$
$593$	26.4076	−	1.88871i	1.08443	−	0.0775601i	0.602094	+	0.798425i	$0.294333\pi$
$594$	−7.60469	+	12.3108i	−0.312024	+	0.505117i
$595$	34.4708	−	3.19290i	1.41317	−	0.130896i
$596$	−20.9631	+	3.01405i	−0.858684	+	0.123460i
$597$	−2.84727	−	5.14144i	−0.116531	−	0.210425i
$598$	−9.75152	−	12.6666i	−0.398769	−	0.517978i
$599$	−27.1223			−1.10819			−0.554093	−	0.832455i	$-0.686935\pi$
$599$	−27.1223			−1.10819			−0.554093	+	0.832455i	$0.686935\pi$
$600$	−6.80889	−	5.35155i	−0.277972	−	0.218476i
$601$	0.106158	−	0.232454i	0.00433029	−	0.00948201i	−0.907454	−	0.420150i	$-0.861977\pi$
$601$	0.106158	−	0.232454i	0.00433029	−	0.00948201i	0.911785	+	0.410668i	$0.134705\pi$
$602$	−7.47417	+	13.6879i	−0.304624	+	0.557878i
$603$	−11.5894	+	21.8382i	−0.471959	+	0.889322i
$604$	4.37572	−	14.9023i	0.178045	−	0.606367i
$605$	6.43988	+	3.34315i	0.261818	+	0.135918i
$606$	1.13455	+	7.57097i	0.0460880	+	0.307550i
$607$	−1.37382	+	19.2085i	−0.0557616	+	0.779648i	0.890241	+	0.455490i	$0.150536\pi$
$607$	−1.37382	+	19.2085i	−0.0557616	+	0.779648i	−0.946003	+	0.324159i	$0.894919\pi$
$608$	−0.449574	−	2.06666i	−0.0182326	−	0.0838141i
$609$	−12.9849	+	28.8866i	−0.526176	+	1.17054i
$610$	6.64682	−	15.4009i	0.269122	−	0.623564i
$611$	7.81432	−	12.1593i	0.316134	−	0.491913i
$612$	18.6391	+	13.6100i	0.753439	+	0.550152i
$613$	31.6511	+	11.8053i	1.27838	+	0.476810i	0.894704	−	0.446659i	$-0.147386\pi$
$613$	31.6511	+	11.8053i	1.27838	+	0.476810i	0.383673	+	0.923469i	$0.374659\pi$
$614$	−1.62796	+	1.04623i	−0.0656991	+	0.0422222i
$615$	−16.1676	+	14.7895i	−0.651942	+	0.596370i
$616$	3.66998	−	4.23539i	0.147868	−	0.170649i
$617$	8.52482	−	15.6120i	0.343196	−	0.628517i	−0.647891	−	0.761733i	$-0.724349\pi$
$617$	8.52482	−	15.6120i	0.343196	−	0.628517i	0.991087	+	0.133216i	$0.0425305\pi$
$618$	−15.4118	+	1.19447i	−0.619953	+	0.0480484i
$619$	−15.6295	+	2.24718i	−0.628201	+	0.0903217i	−0.449060	−	0.893502i	$-0.648241\pi$
$619$	−15.6295	+	2.24718i	−0.628201	+	0.0903217i	−0.179141	+	0.983823i	$0.557332\pi$
$620$	−17.4646	+	10.0172i	−0.701395	+	0.402301i
$621$	6.26811	−	24.1187i	0.251531	−	0.967849i
$622$	−3.20431	−	3.20431i	−0.128481	−	0.128481i
$623$	−0.777540	+	1.03867i	−0.0311515	+	0.0416135i
$624$	4.38557	+	3.75467i	0.175563	+	0.150307i
$625$	17.8964	+	17.4562i	0.715856	+	0.698248i
$626$	17.7421	+	15.3736i	0.709115	+	0.614452i
$627$	9.95524	−	2.22774i	0.397574	−	0.0889672i
$628$	0.882399	−	4.05632i	0.0352116	−	0.161865i
$629$	−19.6993	−	43.1355i	−0.785463	−	1.71992i
$630$	8.44087	+	10.5356i	0.336292	+	0.419747i
$631$	13.3709	+	8.59297i	0.532288	+	0.342081i	0.779016	−	0.627004i	$-0.215719\pi$
$631$	13.3709	+	8.59297i	0.532288	+	0.342081i	−0.246728	+	0.969085i	$0.579355\pi$
$632$	−7.58845	−	10.1370i	−0.301852	−	0.403227i
$633$	−15.9923	−	42.1103i	−0.635639	−	1.67374i
$634$	8.44939	−	13.1475i	0.335568	−	0.522154i
$635$	4.22235	−	2.03631i	0.167559	−	0.0808083i
$636$	−1.74602	+	0.261651i	−0.0692343	+	0.0103751i
$637$	9.60850	+	2.09020i	0.380703	+	0.0828168i
$638$	−12.1263	−	22.2077i	−0.480086	−	0.879211i
$639$	−9.78742	+	3.00078i	−0.387184	+	0.118709i
$640$	0.0468706	+	2.23558i	0.00185272	+	0.0883689i
$641$	33.9249	+	15.4930i	1.33995	+	0.611935i	0.950962	−	0.309307i	$-0.100097\pi$
$641$	33.9249	+	15.4930i	1.33995	+	0.611935i	0.388989	+	0.921242i	$0.372824\pi$
$642$	−21.2998	+	16.1435i	−0.840637	+	0.637131i
$643$	−21.3268	+	21.3268i	−0.841048	+	0.841048i	−0.988995	−	0.147947i	$-0.952733\pi$
$643$	−21.3268	+	21.3268i	−0.841048	+	0.841048i	0.147947	+	0.988995i	$0.452733\pi$
$644$	−3.89051	+	8.83245i	−0.153307	+	0.348047i
$645$	29.1458	−	7.16680i	1.14761	−	0.282192i
$646$	−2.31557	−	16.1051i	−0.0911048	−	0.633648i
$647$	9.78586	+	26.2369i	0.384722	+	1.03148i	0.974593	+	0.223982i	$0.0719056\pi$
$647$	9.78586	+	26.2369i	0.384722	+	1.03148i	−0.589872	+	0.807497i	$0.700822\pi$
$648$	−0.428274	+	8.98980i	−0.0168242	+	0.353153i
$649$	−5.43826	−	4.71228i	−0.213470	−	0.184973i
$650$	−11.4322	−	12.1268i	−0.448410	−	0.475654i
$651$	30.0602	−	9.02107i	1.17815	−	0.353563i
$652$	6.11624	−	16.3983i	0.239530	−	0.642206i
$653$	−3.36620	+	47.0657i	−0.131730	+	1.84182i	0.317325	+	0.948317i	$0.397215\pi$
$653$	−3.36620	+	47.0657i	−0.131730	+	1.84182i	−0.449054	+	0.893504i	$0.648239\pi$
$654$	−10.4606	−	11.9281i	−0.409043	−	0.466425i
$655$	−11.4622	−	28.8683i	−0.447865	−	1.12798i
$656$	5.59998	+	0.805156i	0.218643	+	0.0314361i
$657$	−9.70939	+	27.0090i	−0.378800	+	1.05372i
$658$	−8.70433	−	0.622546i	−0.339330	−	0.0242694i
$659$	−12.4938	−	27.3576i	−0.486688	−	1.06570i	−0.980570	−	0.196170i	$-0.937150\pi$
$659$	−12.4938	−	27.3576i	−0.486688	−	1.06570i	0.493882	−	0.869529i	$-0.335578\pi$
$660$	−10.7815	+	0.290219i	−0.419671	+	0.0112968i
$661$	−36.9318	−	10.8442i	−1.43648	−	0.421789i	−0.531434	−	0.847099i	$-0.678347\pi$
$661$	−36.9318	−	10.8442i	−1.43648	−	0.421789i	−0.905048	+	0.425310i	$0.860165\pi$
$662$	1.73835	+	24.3053i	0.0675630	+	0.944654i
$663$	31.5918	+	31.2181i	1.22692	+	1.21241i
$664$	−4.51810	−	2.06335i	−0.175336	−	0.0800733i
$665$	1.15670	−	9.44683i	0.0448550	−	0.366332i
$666$	9.81191	−	15.6746i	0.380204	−	0.607378i
$667$	31.2252	+	30.3938i	1.20904	+	1.17685i
$668$	−3.42361	−	3.42361i	−0.132463	−	0.132463i
$669$	31.4734	+	4.33424i	1.21683	+	0.167572i
$670$	−18.3489	+	1.69958i	−0.708878	+	0.0656606i
$671$	−5.88547	−	20.0441i	−0.227206	−	0.773793i
$672$	0.720653	−	3.41034i	0.0277998	−	0.131557i
$673$	31.4101	−	17.1512i	1.21077	−	0.661131i	0.258390	−	0.966041i	$-0.416808\pi$
$673$	31.4101	−	17.1512i	1.21077	−	0.661131i	0.952381	+	0.304909i	$0.0986261\pi$
$674$	9.95520	−	6.39782i	0.383460	−	0.246435i
$675$	3.99621	−	25.6716i	0.153814	−	0.988100i
$676$	−1.23752	−	1.42817i	−0.0475969	−	0.0549297i
$677$	−11.3271	+	2.46405i	−0.435335	+	0.0947013i	−0.424892	−	0.905244i	$-0.639688\pi$
$677$	−11.3271	+	2.46405i	−0.435335	+	0.0947013i	−0.0104431	+	0.999945i	$0.503324\pi$
$678$	−9.88515	−	26.0291i	−0.379637	−	0.999643i
$679$	31.5011	+	4.52918i	1.20890	+	0.173814i
$680$	−0.867261	+	17.1803i	−0.0332579	+	0.658834i
$681$	−7.67680	+	3.56122i	−0.294176	+	0.136466i
$682$	−8.76251	+	23.4932i	−0.335534	+	0.899601i
$683$	−45.7079	−	9.94315i	−1.74896	−	0.380464i	−0.779636	−	0.626232i	$-0.784596\pi$
$683$	−45.7079	−	9.94315i	−1.74896	−	0.380464i	−0.969329	+	0.245768i	$0.920960\pi$
$684$	4.74544	−	4.21184i	0.181446	−	0.161044i
$685$	3.83305	−	2.57845i	0.146453	−	0.0985176i
$686$	−5.64140	−	19.2128i	−0.215390	−	0.733550i
$687$	21.0905	−	1.63459i	0.804654	−	0.0623634i
$688$	−6.20386	−	4.64415i	−0.236520	−	0.177057i
$689$	−3.39761			−0.129439
$690$	17.5959	−	5.94853i	0.669864	−	0.226457i
$691$	12.2988			0.467868			0.233934	−	0.972252i	$-0.424840\pi$
$691$	12.2988			0.467868			0.233934	+	0.972252i	$0.424840\pi$
$692$	10.2396	+	7.66531i	0.389253	+	0.291391i
$693$	16.4698	+	3.37808i	0.625636	+	0.128323i
$694$	5.99343	+	20.4117i	0.227507	+	0.774819i
$695$	2.81417	−	14.3816i	0.106748	−	0.545526i
$696$	−13.2896	−	8.42944i	−0.503742	−	0.319517i
$697$	42.5293	+	9.25168i	1.61091	+	0.350432i
$698$	−0.714779	+	1.91640i	−0.0270548	+	0.0725366i
$699$	−8.01989	−	17.2882i	−0.303340	−	0.653899i
$700$	−3.11814	+	9.56688i	−0.117855	+	0.361594i
$701$	19.6404	+	2.82386i	0.741808	+	0.106656i	0.502849	−	0.864374i	$-0.332285\pi$
$701$	19.6404	+	2.82386i	0.741808	+	0.106656i	0.238958	+	0.971030i	$0.423194\pi$
$702$	−3.37899	+	16.9870i	−0.127532	+	0.641134i
$703$	−12.7391	+	2.77122i	−0.480465	+	0.104519i
$704$	1.82365	+	2.10460i	0.0687313	+	0.0793202i
$705$	10.4227	+	13.1690i	0.392541	+	0.495972i
$706$	6.43039	−	4.13256i	0.242011	−	0.155531i
$707$	7.80679	−	4.26283i	0.293604	−	0.160320i
$708$	−4.37889	−	0.925322i	−0.164569	−	0.0347757i
$709$	6.94926	+	23.6670i	0.260985	+	0.888832i	0.980858	+	0.194726i	$0.0623819\pi$
$709$	6.94926	+	23.6670i	0.260985	+	0.888832i	−0.719873	+	0.694106i	$0.755800\pi$
$710$	−5.87006	−	4.87480i	−0.220299	−	0.182948i
$711$	15.3685	−	34.7404i	0.576365	−	1.30287i
$712$	−0.455886	−	0.455886i	−0.0170851	−	0.0170851i
$713$	2.49919	−	43.1091i	0.0935953	−	1.61445i
$714$	7.40154	−	25.7736i	0.276996	−	0.964551i
$715$	−20.6019	−	2.52257i	−0.770468	−	0.0943388i
$716$	17.3155	+	7.90772i	0.647111	+	0.295526i
$717$	−20.8079	+	21.0570i	−0.777087	+	0.786388i
$718$	−0.743381	−	10.3938i	−0.0277427	−	0.387894i
$719$	2.55655	+	0.750671i	0.0953432	+	0.0279953i	0.329056	−	0.944310i	$-0.393269\pi$
$719$	2.55655	+	0.750671i	0.0953432	+	0.0279953i	−0.233713	+	0.972306i	$0.575088\pi$
$720$	−5.77885	+	3.40660i	−0.215365	+	0.126957i
$721$	7.46102	+	16.3373i	0.277863	+	0.608435i
$722$	14.4898	+	1.03633i	0.539254	+	0.0385682i
$723$	37.2560	+	2.44192i	1.38556	+	0.0908161i
$724$	21.3322	+	3.06711i	0.792806	+	0.113988i
$725$	35.5507	+	28.2853i	1.32032	+	1.05049i
$726$	4.22567	−	3.70580i	0.156829	−	0.137535i
$727$	−2.26026	+	31.6026i	−0.0838285	+	1.17208i	0.765223	+	0.643766i	$0.222629\pi$
$727$	−2.26026	+	31.6026i	−0.0838285	+	1.17208i	−0.849051	+	0.528310i	$0.822826\pi$
$728$	2.34416	−	6.28495i	0.0868805	−	0.232936i
$729$	−24.1442	+	12.0855i	−0.894228	+	0.447612i
$730$	−20.8038	+	4.98450i	−0.769984	+	0.184485i
$731$	−45.0562	−	39.0414i	−1.66646	−	1.44400i
$732$	−9.24200	−	9.13269i	−0.341594	−	0.337554i
$733$	7.91005	+	21.2077i	0.292164	+	0.783323i	0.997244	+	0.0741948i	$0.0236387\pi$
$733$	7.91005	+	21.2077i	0.292164	+	0.783323i	−0.705079	+	0.709128i	$0.749089\pi$
$734$	1.43328	+	9.96868i	0.0529033	+	0.367951i
$735$	−5.91628	+	9.77457i	−0.218225	+	0.360541i
$736$	−4.06912	−	2.53816i	−0.149990	−	0.0935577i
$737$	−16.2277	+	16.2277i	−0.597754	+	0.597754i
$738$	6.12014	+	15.8309i	0.225285	+	0.582743i
$739$	30.3153	+	13.8445i	1.11517	+	0.509280i	0.885803	−	0.464061i	$-0.153608\pi$
$739$	30.3153	+	13.8445i	1.11517	+	0.509280i	0.229364	+	0.973341i	$0.426335\pi$
$740$	13.7803	−	0.288915i	0.506575	−	0.0106207i
$741$	10.2326	−	6.66246i	0.375905	−	0.244752i
$742$	0.983097	+	1.80041i	0.0360906	+	0.0660950i
$743$	−32.2458	−	7.01464i	−1.18298	−	0.257342i	−0.422294	−	0.906459i	$-0.638775\pi$
$743$	−32.2458	−	7.01464i	−1.18298	−	0.257342i	−0.760689	+	0.649117i	$0.775139\pi$
$744$	2.31124	+	15.4231i	0.0847341	+	0.565438i
$745$	15.6159	−	44.7083i	0.572122	−	1.63799i
$746$	−0.186160	+	0.289671i	−0.00681581	+	0.0106056i
$747$	−1.23977	−	14.8492i	−0.0453609	−	0.543303i
$748$	12.8386	+	17.1504i	0.469427	+	0.627081i
$749$	26.1233	+	16.7884i	0.954524	+	0.613436i
$750$	17.6355	−	7.99931i	0.643958	−	0.292093i
$751$	9.72507	+	21.2949i	0.354873	+	0.777063i	0.999917	+	0.0129176i	$0.00411192\pi$
$751$	9.72507	+	21.2949i	0.354873	+	0.777063i	−0.645044	+	0.764146i	$0.723161\pi$
$752$	0.921749	−	4.23721i	0.0336127	−	0.154515i
$753$	−6.72904	−	30.0705i	−0.245220	−	1.09583i
$754$	−22.8884	−	19.8329i	−0.833547	−	0.722272i
$755$	25.0667	+	24.0372i	0.912272	+	0.874805i
$756$	9.97920	−	3.12465i	0.362940	−	0.113642i
$757$	−5.22271	+	6.97672i	−0.189823	+	0.253573i	−0.885349	−	0.464927i	$-0.846080\pi$
$757$	−5.22271	+	6.97672i	−0.189823	+	0.253573i	0.695526	+	0.718501i	$0.255171\pi$
$758$	8.74392	+	8.74392i	0.317593	+	0.317593i
$759$	12.1256	−	19.6995i	0.440130	−	0.715045i
$760$	4.56463	+	1.23698i	0.165577	+	0.0448700i
$761$	13.8902	−	1.99711i	0.503520	−	0.0723952i	0.114125	−	0.993466i	$-0.463593\pi$
$761$	13.8902	−	1.99711i	0.503520	−	0.0723952i	0.389394	+	0.921071i	$0.372684\pi$
$762$	−0.280581	−	3.62024i	−0.0101644	−	0.131148i
$763$	−8.83422	+	16.1787i	−0.319820	+	0.585707i
$764$	9.38770	−	10.8340i	0.339635	−	0.391960i
$765$	−46.2133	+	22.9688i	−1.67084	+	0.830441i
$766$	15.8461	−	10.1837i	0.572542	−	0.367950i
$767$	−8.06990	−	3.00992i	−0.291387	−	0.108682i
$768$	1.62642	+	0.595625i	0.0586883	+	0.0214928i
$769$	−2.52332	+	3.92636i	−0.0909931	+	0.141588i	−0.883766	−	0.467929i	$-0.845000\pi$
$769$	−2.52332	+	3.92636i	−0.0909931	+	0.141588i	0.792773	+	0.609517i	$0.208637\pi$
$770$	4.62443	+	11.6469i	0.166653	+	0.419726i
$771$	6.01905	+	2.70565i	0.216771	+	0.0974417i
$772$	3.29233	+	15.1346i	0.118494	+	0.544706i
$773$	−1.88437	+	26.3469i	−0.0677761	+	0.947634i	0.843841	+	0.536593i	$0.180289\pi$
$773$	−1.88437	+	26.3469i	−0.0677761	+	0.947634i	−0.911617	+	0.411041i	$0.865165\pi$
$774$	3.03462	−	23.0498i	0.109077	−	0.828510i
$775$	−1.88692	−	44.9802i	−0.0677802	−	1.61574i
$776$	−4.45537	+	15.1736i	−0.159938	+	0.544700i
$777$	−21.0217	−	4.44219i	−0.754150	−	0.159363i
$778$	2.42790	−	4.44637i	0.0870444	−	0.159410i
$779$	4.97074	−	10.8844i	0.178095	−	0.389974i
$780$	−11.9697	+	4.83523i	−0.428585	+	0.173129i
$781$	−9.50272			−0.340034
$782$	−29.8312	−	21.7096i	−1.06676	−	0.776334i
$783$	2.52716	−	47.1449i	0.0903135	−	1.68482i
$784$	2.92005	−	0.419840i	0.104288	−	0.0149943i
$785$	7.14101	+	5.93026i	0.254873	+	0.211660i
$786$	−24.0590	+	0.143128i	−0.858156	+	0.00510519i
$787$	−36.5838	+	2.61653i	−1.30407	+	0.0932691i	−0.706023	−	0.708189i	$-0.749512\pi$
$787$	−36.5838	+	2.61653i	−1.30407	+	0.0932691i	−0.598050	+	0.801458i	$0.704058\pi$
$788$	0.469316	+	0.859488i	0.0167187	+	0.0306180i
$789$	−15.6273	+	4.68976i	−0.556348	+	0.166960i
$790$	27.9357	−	4.61616i	0.993909	−	0.164236i
$791$	−24.4487	+	21.1850i	−0.869297	+	0.753250i
$792$	−2.82621	+	7.86180i	−0.100425	+	0.279357i
$793$	−14.9845	−	20.0170i	−0.532115	−	0.710823i
$794$	−3.37423	+	23.4683i	−0.119747	+	0.832858i
$795$	1.27959	−	3.73469i	0.0453824	−	0.132456i
$796$	−2.22207	−	2.56441i	−0.0787592	−	0.0908930i
$797$	46.3098	+	17.2727i	1.64038	+	0.611830i	0.989131	−	0.147036i	$-0.0469733\pi$
$797$	46.3098	+	17.2727i	1.64038	+	0.611830i	0.651247	+	0.758865i	$0.274246\pi$
$798$	−6.49127	−	3.49453i	−0.229788	−	0.123705i
$799$	9.39844	−	32.0081i	0.332493	−	1.13237i
$800$	−4.48497	−	2.21021i	−0.158568	−	0.0781427i
$801$	0.522798	−	1.86217i	0.0184722	−	0.0657964i
$802$	−3.11351	+	1.16128i	−0.109942	+	0.0410062i
$803$	−15.9661	+	21.3282i	−0.563432	+	0.752657i
$804$	−3.93985	+	13.7193i	−0.138948	+	0.483842i
$805$	−13.5205	−	16.8207i	−0.476534	−	0.592853i
$806$			30.0121i			1.05713i
$807$	−4.04214	−	5.33323i	−0.142290	−	0.187739i
$808$	1.54460	+	4.14123i	0.0543389	+	0.145688i
$809$	27.8276	−	8.17091i	0.978365	−	0.287274i	0.246816	−	0.969062i	$-0.420616\pi$
$809$	27.8276	−	8.17091i	0.978365	−	0.287274i	0.731549	+	0.681789i	$0.238798\pi$
$810$	−17.3998	−	10.1118i	−0.611365	−	0.355292i
$811$	−25.4909	−	7.48482i	−0.895108	−	0.262827i	−0.198348	−	0.980132i	$-0.563558\pi$
$811$	−25.4909	−	7.48482i	−0.895108	−	0.262827i	−0.696760	+	0.717304i	$0.745376\pi$
$812$	−3.88679	+	17.8673i	−0.136400	+	0.627019i
$813$	−27.7044	−	20.4832i	−0.971637	−	0.718379i
$814$	12.9730	−	11.2412i	0.454703	−	0.394003i
$815$	26.2424	+	29.0327i	0.919230	+	1.01697i
$816$	12.1533	+	5.46310i	0.425452	+	0.191247i
$817$	−13.1211	+	9.82235i	−0.459050	+	0.343641i
$818$	2.19625	+	10.0960i	0.0767902	+	0.352999i
$819$	19.8833	−	3.10068i	0.694780	−	0.108346i
$820$	−7.36734	+	10.2841i	−0.257279	+	0.359136i
$821$	−16.4739	−	25.6339i	−0.574942	−	0.894628i	0.425002	−	0.905192i	$-0.360273\pi$
$821$	−16.4739	−	25.6339i	−0.574942	−	0.894628i	−0.999944	+	0.0105648i	$0.996637\pi$
$822$	−0.781415	−	3.49196i	−0.0272550	−	0.121796i
$823$	−1.24440	−	17.3990i	−0.0433772	−	0.606492i	−0.971927	−	0.235284i	$-0.924398\pi$
$823$	−1.24440	−	17.3990i	−0.0433772	−	0.606492i	0.928550	−	0.371208i	$-0.121056\pi$
$824$	−8.56317	+	2.51437i	−0.298312	+	0.0875923i
$825$	10.5318	−	21.6958i	0.366671	−	0.755352i
$826$	0.740054	+	5.14719i	0.0257498	+	0.179093i
$827$	−6.26893	+	6.26893i	−0.217992	+	0.217992i	−0.807652	−	0.589660i	$-0.799262\pi$
$827$	−6.26893	+	6.26893i	−0.217992	+	0.217992i	0.589660	+	0.807652i	$0.299262\pi$
$828$	0.661747	−	14.3723i	0.0229973	−	0.499471i
$829$		−	41.7090i		−	1.44862i	−0.689477	−	0.724308i	$-0.742160\pi$
$829$		−	41.7090i		−	1.44862i	0.689477	−	0.724308i	$-0.257840\pi$
$830$	8.74969	−	6.84075i	0.303706	−	0.237446i
$831$	−17.2710	+	20.1730i	−0.599124	+	0.699795i
$832$	2.92548	+	1.59744i	0.101423	+	0.0553811i
$833$	22.6373	−	1.61905i	0.784335	−	0.0560968i
$834$	−9.58559	−	6.08002i	−0.331922	−	0.210534i
$835$	10.3216	−	3.26722i	0.357195	−	0.113067i
$836$	5.35756	−	2.44672i	0.185295	−	0.0846214i
$837$	−36.9478	+	28.7017i	−1.27710	+	0.992076i
$838$	−13.6522	+	2.96985i	−0.471607	+	0.102592i
$839$	0.999183	−	6.94947i	0.0344956	−	0.239922i	−0.965277	−	0.261227i	$-0.915873\pi$
$839$	0.999183	−	6.94947i	0.0344956	−	0.239922i	0.999773	+	0.0213046i	$0.00678199\pi$
$840$	6.02564	+	4.94373i	0.207904	+	0.170575i
$841$	45.0546	+	28.9548i	1.55361	+	0.998443i
$842$	0.634062	+	0.0453490i	0.0218512	+	0.00156283i
$843$	7.72190	−	10.4442i	0.265957	−	0.359717i
$844$	−14.0603	−	21.8782i	−0.483974	−	0.753078i
$845$	4.10929	−	0.984566i	0.141364	−	0.0338701i
$846$	12.4375	−	3.81329i	0.427610	−	0.131103i
$847$	−5.73149	−	3.12963i	−0.196936	−	0.107535i
$848$	−0.955055	+	0.356217i	−0.0327967	+	0.0122325i
$849$	10.7885	+	1.48570i	0.370261	+	0.0509892i
$850$	−33.2022	−	19.4213i	−1.13883	−	0.666146i
$851$	−15.6455	+	25.0825i	−0.536320	+	0.859817i
$852$	−5.17049	+	2.86336i	−0.177138	+	0.0980971i
$853$	19.9402	+	14.9271i	0.682741	+	0.511094i	0.883431	−	0.468561i	$-0.155227\pi$
$853$	19.9402	+	14.9271i	0.682741	+	0.511094i	−0.200690	+	0.979655i	$0.564318\pi$
$854$	−6.27130	+	13.7322i	−0.214600	+	0.469907i
$855$	3.46969	+	13.7570i	0.118661	+	0.470480i
$856$	−10.1048	+	11.6615i	−0.345374	+	0.398583i
$857$	39.6491	−	21.6500i	1.35439	−	0.739551i	0.372323	−	0.928103i	$-0.378561\pi$
$857$	39.6491	−	21.6500i	1.35439	−	0.739551i	0.982063	+	0.188552i	$0.0603795\pi$
$858$	−7.62098	+	14.1564i	−0.260176	+	0.483290i
$859$	2.39169	−	1.09225i	0.0816033	−	0.0372670i	−0.374195	−	0.927350i	$-0.622081\pi$
$859$	2.39169	−	1.09225i	0.0816033	−	0.0372670i	0.455799	+	0.890083i	$0.349354\pi$
$860$	15.6083	−	7.52738i	0.532238	−	0.256682i
$861$	14.8265	−	13.0025i	0.505287	−	0.443124i
$862$	20.1921	−	15.1156i	0.687747	−	0.514841i
$863$	4.52093	−	3.38433i	0.153894	−	0.115204i	−0.519556	−	0.854437i	$-0.673903\pi$
$863$	4.52093	−	3.38433i	0.153894	−	0.115204i	0.673450	+	0.739233i	$0.264812\pi$
$864$	0.831158	+	5.12925i	0.0282766	+	0.174501i
$865$	−25.7619	+	12.4242i	−0.875932	+	0.422434i
$866$	−23.3871	+	10.6805i	−0.794727	+	0.362939i
$867$	64.3331	+	34.6333i	2.18487	+	1.17621i
$868$	15.9035	−	8.68396i	0.539800	−	0.294753i
$869$	23.0922	−	26.6499i	0.783350	−	0.904035i
$870$	30.4207	−	17.6898i	1.03136	−	0.599741i
$871$	−11.4110	+	24.9866i	−0.386647	+	0.846638i
$872$	−7.33276	−	5.48924i	−0.248319	−	0.185889i
$873$	−46.2350	+	10.6355i	−1.56482	+	0.359956i
$874$	−7.57538	+	6.74516i	−0.256241	+	0.228159i
$875$	−15.7738	−	16.0446i	−0.533250	−	0.542406i
$876$	−2.26064	+	16.4157i	−0.0763798	+	0.554636i
$877$	−30.0372	+	11.2033i	−1.01428	+	0.378308i	−0.800988	−	0.598680i	$-0.795692\pi$
$877$	−30.0372	+	11.2033i	−1.01428	+	0.378308i	−0.213295	+	0.976988i	$0.568419\pi$
$878$	−19.1550	−	10.4594i	−0.646450	−	0.352988i
$879$	17.5786	−	11.4454i	0.592911	−	0.386044i
$880$	−6.05559	+	1.45089i	−0.204134	+	0.0489095i
$881$	−9.21949	−	14.3458i	−0.310613	−	0.483323i	0.650490	−	0.759515i	$-0.274564\pi$
$881$	−9.21949	−	14.3458i	−0.310613	−	0.483323i	−0.961102	+	0.276192i	$0.910927\pi$
$882$	5.38767	+	7.02138i	0.181412	+	0.236422i
$883$	−10.3242	−	0.738398i	−0.347435	−	0.0248491i	−0.103469	−	0.994633i	$-0.532994\pi$
$883$	−10.3242	−	0.738398i	−0.347435	−	0.0248491i	−0.243967	+	0.969784i	$0.578449\pi$
$884$	21.5718	+	13.8634i	0.725540	+	0.466276i
$885$	6.34778	−	7.73694i	0.213378	−	0.260075i
$886$	−1.69872	+	11.8149i	−0.0570696	+	0.396928i
$887$	5.25968	−	1.14417i	0.176603	−	0.0384175i	−0.123394	−	0.992358i	$-0.539378\pi$
$887$	5.25968	−	1.14417i	0.176603	−	0.0384175i	0.299997	+	0.953940i	$0.403014\pi$
$888$	3.67150	−	10.0254i	0.123207	−	0.336431i
$889$	−3.83766	+	1.75260i	−0.128711	+	0.0587803i
$890$	1.37443	−	0.435062i	0.0460709	−	0.0145833i
$891$	−24.7161	+	4.15611i	−0.828020	+	0.139235i
$892$	18.2959	−	1.30855i	0.612592	−	0.0438135i
$893$	−8.04943	−	4.39532i	−0.269364	−	0.147084i
$894$	−27.8653	−	23.8567i	−0.931954	−	0.797886i
$895$	−33.5330	+	26.2170i	−1.12088	+	0.876338i
$896$		−	2.01244i		−	0.0672309i
$897$	5.35841	−	27.1642i	0.178912	−	0.906987i
$898$	14.6297	−	14.6297i	0.488198	−	0.488198i
$899$	−11.6429	−	80.9778i	−0.388311	−	2.70076i
$900$	−0.806960	−	14.9783i	−0.0268987	−	0.499276i
$901$	−7.52406	+	2.20926i	−0.250663	+	0.0736012i
$902$	1.12396	+	15.7150i	0.0374237	+	0.523252i
$903$	−26.3604	+	5.89881i	−0.877219	+	0.196300i
$904$	−8.69089	−	13.5233i	−0.289055	−	0.449778i
$905$	−28.0647	+	39.1756i	−0.932902	+	1.30224i
$906$	24.4033	−	11.3206i	0.810747	−	0.376100i
$907$	3.92725	+	18.0533i	0.130402	+	0.599448i	0.995245	+	0.0974056i	$0.0310544\pi$
$907$	3.92725	+	18.0533i	0.130402	+	0.599448i	−0.864843	+	0.502043i	$0.832582\pi$
$908$	−3.91135	+	2.92800i	−0.129803	+	0.0971692i
$909$	−8.56344	+	10.1236i	−0.284031	+	0.335780i
$910$	10.0579	+	11.1273i	0.333416	+	0.368867i
$911$	−15.4834	+	13.4164i	−0.512987	+	0.444506i	−0.872486	−	0.488640i	$-0.837493\pi$
$911$	−15.4834	+	13.4164i	−0.512987	+	0.444506i	0.359498	+	0.933146i	$0.382948\pi$
$912$	2.17784	−	2.94561i	0.0721153	−	0.0975390i
$913$	2.94018	−	13.5158i	0.0973058	−	0.447308i
$914$	1.52634	+	0.448174i	0.0504868	+	0.0148243i
$915$	27.6462	−	8.93246i	0.913957	−	0.295298i
$916$	11.7184	−	3.44084i	0.387187	−	0.113688i
$917$	9.76901	+	26.1917i	0.322601	+	0.864927i
$918$	3.56284	+	39.8152i	0.117591	+	1.31410i
$919$		−	20.7301i		−	0.683822i	−0.939732	−	0.341911i	$-0.888926\pi$
$919$		−	20.7301i		−	0.683822i	0.939732	−	0.341911i	$-0.111074\pi$
$920$	9.22944	−	5.46054i	0.304286	−	0.180029i
$921$	−3.22158	−	0.925160i	−0.106155	−	0.0304851i
$922$	−1.14536	+	1.53002i	−0.0377205	+	0.0503887i
$923$	−10.6570	+	3.97485i	−0.350779	+	0.130834i
$924$	9.70663	−	0.0577450i	0.319325	−	0.00189967i
$925$	−13.6240	+	27.6459i	−0.447953	+	0.908990i
$926$	−2.14552	+	7.30697i	−0.0705061	+	0.240122i
$927$	−19.1560	−	18.7055i	−0.629166	−	0.614370i
$928$	−8.51318	−	3.17525i	−0.279459	−	0.104233i
$929$	21.8499	+	25.2162i	0.716873	+	0.827315i	0.990927	−	0.134399i	$-0.0429103\pi$
$929$	21.8499	+	25.2162i	0.716873	+	0.827315i	−0.274054	+	0.961714i	$0.588365\pi$
$930$	−32.9896	−	11.3030i	−1.08177	−	0.370639i
$931$	0.887959	−	6.17589i	0.0291017	−	0.202407i
$932$	−6.59387	−	8.80838i	−0.215989	−	0.288528i
$933$	0.513352	−	7.83211i	0.0168064	−	0.256412i
$934$	11.0394	−	9.56567i	0.361219	−	0.312998i
$935$	−47.2635	+	7.80992i	−1.54568	+	0.255412i
$936$	0.118972	+	9.99891i	0.00388871	+	0.326825i
$937$	7.14317	+	13.0817i	0.233357	+	0.427362i	0.967949	−	0.251148i	$-0.0808080\pi$
$937$	7.14317	+	13.0817i	0.233357	+	0.427362i	−0.734592	+	0.678510i	$0.762626\pi$
$938$	16.5422	−	1.18312i	0.540123	−	0.0386304i
$939$	0.241894	+	40.6611i	0.00789391	+	1.32692i
$940$	7.45945	+	6.19472i	0.243300	+	0.202049i
$941$	−14.8985	+	2.14207i	−0.485676	+	0.0698296i	−0.380803	−	0.924656i	$-0.624352\pi$
$941$	−14.8985	+	2.14207i	−0.485676	+	0.0698296i	−0.104872	+	0.994486i	$0.533443\pi$
$942$	6.28997	−	3.48332i	0.204938	−	0.113493i
$943$	−9.82402	−	25.2918i	−0.319914	−	0.823614i
$944$	−2.58398			−0.0841015
$945$	−4.08005	+	23.0237i	−0.132724	+	0.748962i
$946$	8.96505	−	19.6307i	0.291479	−	0.638250i
$947$	−7.71722	+	14.1330i	−0.250776	+	0.459262i	−0.972495	−	0.232925i	$-0.925170\pi$
$947$	−7.71722	+	14.1330i	−0.250776	+	0.459262i	0.721719	+	0.692186i	$0.243352\pi$
$948$	4.53449	−	21.4585i	0.147273	−	0.696940i
$949$	−8.98418	+	30.5973i	−0.291639	+	0.993230i
$950$	−7.15765	+	7.78447i	−0.232225	+	0.252562i
$951$	26.7704	−	4.01169i	0.868090	−	0.130088i
$952$	1.10446	−	15.4424i	0.0357957	−	0.500490i
$953$	2.82768	+	12.9986i	0.0915975	+	0.421067i	0.999996	+	0.00296065i	$0.000942405\pi$
$953$	2.82768	+	12.9986i	0.0915975	+	0.421067i	−0.908398	+	0.418106i	$0.862694\pi$
$954$	−2.33472	−	1.97491i	−0.0755894	−	0.0639400i
$955$	11.8291	+	29.7925i	0.382782	+	0.964062i
$956$	−9.24041	+	14.3784i	−0.298856	+	0.465029i
$957$	15.0709	−	41.1528i	0.487175	−	1.33028i
$958$	−20.0056	−	7.46172i	−0.646353	−	0.241077i
$959$	−3.49759	+	2.24777i	−0.112943	+	0.0725841i
$960$	−2.85770	+	2.61411i	−0.0922318	+	0.0843700i
$961$	−32.7897	+	37.8414i	−1.05773	+	1.22069i
$962$	9.84677	−	18.0330i	0.317472	−	0.581407i
$963$	−45.3472	−	9.30105i	−1.46129	−	0.299722i
$964$	21.3365	−	3.06772i	0.687202	−	0.0988047i
$965$	−33.4278	−	9.05869i	−1.07608	−	0.291609i
$966$	−15.9449	+	5.02051i	−0.513018	+	0.161532i
$967$	−12.8893	−	12.8893i	−0.414492	−	0.414492i	0.468808	−	0.883300i	$-0.344684\pi$
$967$	−12.8893	−	12.8893i	−0.414492	−	0.414492i	−0.883300	+	0.468808i	$0.844684\pi$
$968$	1.94463	−	2.59772i	0.0625028	−	0.0834939i
$969$	18.3281	−	21.4078i	0.588783	−	0.687716i
$970$	−25.5230	−	24.4748i	−0.819495	−	0.785838i
$971$	−6.62457	−	5.74023i	−0.212593	−	0.184213i	0.542055	−	0.840343i	$-0.317647\pi$
$971$	−6.62457	−	5.74023i	−0.212593	−	0.184213i	−0.754647	+	0.656131i	$0.772192\pi$
$972$	−12.1959	+	9.70882i	−0.391182	+	0.311410i
$973$	−2.80348	+	12.8874i	−0.0898755	+	0.413151i
$974$	−9.70308	−	21.2468i	−0.310907	−	0.680790i
$975$	2.73604	−	28.7364i	0.0876234	−	0.920303i
$976$	−6.31072	−	4.05566i	−0.202001	−	0.129818i
$977$	−3.73312	−	4.98686i	−0.119433	−	0.159544i	0.736840	−	0.676067i	$-0.236317\pi$
$977$	−3.73312	−	4.98686i	−0.119433	−	0.159544i	−0.856273	+	0.516523i	$0.827226\pi$
$978$	28.3391	−	10.7624i	0.906185	−	0.344144i
$979$	0.970672	−	1.51040i	0.0310228	−	0.0482725i
$980$	−2.17521	+	6.22763i	−0.0694845	+	0.198934i
$981$	3.58682	−	27.2442i	0.114518	−	0.869840i
$982$	15.4052	+	3.35120i	0.491601	+	0.106941i
$983$	15.3924	+	28.1891i	0.490941	+	0.899092i	0.999280	+	0.0379348i	$0.0120779\pi$
$983$	15.3924	+	28.1891i	0.490941	+	0.899092i	−0.508339	+	0.861157i	$0.669740\pi$
$984$	5.34679	+	8.21195i	0.170450	+	0.261787i
$985$	−2.18924	+	0.0458991i	−0.0697550	+	0.00146247i
$986$	−63.5828	−	29.0373i	−2.02489	−	0.924736i
$987$	−9.12982	−	12.0460i	−0.290605	−	0.383427i
$988$	4.98490	−	4.98490i	0.158591	−	0.158591i
$989$	−4.79246	+	36.8554i	−0.152391	+	1.17193i
$990$	−12.6906	−	13.7086i	−0.403335	−	0.435686i
$991$	−6.27023	−	43.6104i	−0.199180	−	1.38533i	−0.806670	−	0.591002i	$-0.798733\pi$
$991$	−6.27023	−	43.6104i	−0.199180	−	1.38533i	0.607490	−	0.794327i	$-0.292177\pi$
$992$	3.14656	+	8.43626i	0.0999034	+	0.267852i
$993$	−29.6658	+	30.0209i	−0.941416	+	0.952684i
$994$	5.18988	+	4.49705i	0.164613	+	0.142638i
$995$	7.37858	−	1.76787i	0.233917	−	0.0560453i
$996$	−2.47281	−	8.23996i	−0.0783540	−	0.261093i
$997$	−12.4935	+	33.4963i	−0.395672	+	1.06084i	0.574517	+	0.818492i	$0.305190\pi$
$997$	−12.4935	+	33.4963i	−0.395672	+	1.06084i	−0.970190	+	0.242346i	$0.922083\pi$
$998$	1.46464	−	20.4783i	0.0463622	−	0.648229i
$999$	31.6172	−	5.12335i	1.00033	−	0.162096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.647.37	yes	960
3.2	odd	2	inner	690.2.x.a.647.16	yes	960
5.3	odd	4	inner	690.2.x.a.233.26	yes	960
15.8	even	4	inner	690.2.x.a.233.5	yes	960
23.8	even	11	inner	690.2.x.a.77.5	✓	960
69.8	odd	22	inner	690.2.x.a.77.26	yes	960
115.8	odd	44	inner	690.2.x.a.353.16	yes	960
345.8	even	44	inner	690.2.x.a.353.37	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.5	✓	960	23.8	even	11	inner
690.2.x.a.77.26	yes	960	69.8	odd	22	inner
690.2.x.a.233.5	yes	960	15.8	even	4	inner
690.2.x.a.233.26	yes	960	5.3	odd	4	inner
690.2.x.a.353.16	yes	960	115.8	odd	44	inner
690.2.x.a.353.37	yes	960	345.8	even	44	inner
690.2.x.a.647.16	yes	960	3.2	odd	2	inner
690.2.x.a.647.37	yes	960	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.800541 + 0.599278i) q^{2} +(0.133838 + 1.72687i) q^{3} +(0.281733 + 0.959493i) q^{4} +(-2.19445 - 0.429407i) q^{5} +(-0.927733 + 1.46264i) q^{6} +(1.96645 + 0.427775i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-2.96417 + 0.462244i) q^{9} +O(q^{10})\)	\(q+(0.800541 + 0.599278i) q^{2} +(0.133838 + 1.72687i) q^{3} +(0.281733 + 0.959493i) q^{4} +(-2.19445 - 0.429407i) q^{5} +(-0.927733 + 1.46264i) q^{6} +(1.96645 + 0.427775i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-2.96417 + 0.462244i) q^{9} +(-1.49941 - 1.65884i) q^{10} +(-2.75644 - 0.396317i) q^{11} +(-1.61921 + 0.614933i) q^{12} +(-3.25703 + 0.708524i) q^{13} +(1.31787 + 1.52090i) q^{14} +(0.447828 - 3.84701i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(-6.75203 + 3.68689i) q^{17} +(-2.64996 - 1.40632i) q^{18} +(0.595863 + 2.02932i) q^{19} +(-0.206235 - 2.22654i) q^{20} +(-0.475526 + 3.45306i) q^{21} +(-1.96914 - 1.96914i) q^{22} +(4.23982 + 2.24140i) q^{23} +(-1.66476 - 0.478080i) q^{24} +(4.63122 + 1.88462i) q^{25} +(-3.03199 - 1.38466i) q^{26} +(-1.19496 - 5.05688i) q^{27} +(0.143566 + 2.00731i) q^{28} +(8.71801 + 2.55984i) q^{29} +(2.66393 - 2.81131i) q^{30} +(-3.74038 - 8.19029i) q^{31} +(-0.997452 - 0.0713392i) q^{32} +(0.315470 - 4.81307i) q^{33} +(-7.61474 - 1.09483i) q^{34} +(-4.13159 - 1.78314i) q^{35} +(-1.27862 - 2.71388i) q^{36} +(-0.439743 + 6.14840i) q^{37} +(-0.739115 + 1.98164i) q^{38} +(-1.65945 - 5.52965i) q^{39} +(1.16921 - 1.90603i) q^{40} +(-4.27571 - 3.70492i) q^{41} +(-2.45002 + 2.47935i) q^{42} +(2.70820 + 7.26097i) q^{43} +(-0.396317 - 2.75644i) q^{44} +(6.70322 + 0.258465i) q^{45} +(2.05093 + 4.33517i) q^{46} +(-3.06623 + 3.06623i) q^{47} +(-1.04621 - 1.38038i) q^{48} +(-2.68349 - 1.22551i) q^{49} +(2.57807 + 4.28410i) q^{50} +(-7.27046 - 11.1664i) q^{51} +(-1.59744 - 2.92548i) q^{52} +(0.996029 + 0.216673i) q^{53} +(2.07387 - 4.76436i) q^{54} +(5.87869 + 2.05333i) q^{55} +(-1.08801 + 1.69297i) q^{56} +(-3.42463 + 1.30058i) q^{57} +(5.44507 + 7.27377i) q^{58} +(2.17379 + 1.39701i) q^{59} +(3.81734 - 0.654138i) q^{60} +(3.11627 + 6.82367i) q^{61} +(1.91393 - 8.79819i) q^{62} +(-6.02664 - 0.359020i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(7.45164 - 0.156229i) q^{65} +(3.13691 - 3.66400i) q^{66} +(4.93864 - 6.59725i) q^{67} +(-5.43981 - 5.43981i) q^{68} +(-3.30317 + 7.62162i) q^{69} +(-2.23891 - 3.90344i) q^{70} +(3.37763 - 0.485631i) q^{71} +(0.602774 - 2.93882i) q^{72} +(4.58501 - 8.39682i) q^{73} +(-4.03663 + 4.65852i) q^{74} +(-2.63467 + 8.24976i) q^{75} +(-1.77925 + 1.14345i) q^{76} +(-5.25087 - 1.95847i) q^{77} +(1.98534 - 5.42118i) q^{78} +(-6.84595 + 10.6525i) q^{79} +(2.07824 - 0.825169i) q^{80} +(8.57266 - 2.74034i) q^{81} +(-1.20260 - 5.52828i) q^{82} +(-0.354338 + 4.95429i) q^{83} +(-3.44716 + 0.516576i) q^{84} +(16.4002 - 5.19132i) q^{85} +(-2.18331 + 7.43567i) q^{86} +(-3.25371 + 15.3975i) q^{87} +(1.33461 - 2.44415i) q^{88} +(-0.267827 + 0.586459i) q^{89} +(5.21131 + 4.22400i) q^{90} -6.70788 q^{91} +(-0.956114 + 4.69956i) q^{92} +(13.6430 - 7.55534i) q^{93} +(-4.29217 + 0.617121i) q^{94} +(-0.436187 - 4.70911i) q^{95} +(-0.0103038 - 1.73202i) q^{96} +(15.7739 - 1.12817i) q^{97} +(-1.41382 - 2.58922i) q^{98} +(8.35377 - 0.0993971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

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