LMFDB - Embedded newform 74.2.h.a.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(3,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("74.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.h (of order $18$, degree $6$, 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:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.1
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	74.65
Dual form			74.2.h.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(-0.266044 + 1.50881i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.97937 + 2.35892i) q^{5} -1.53209i q^{6} +(0.153180 + 0.128533i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.613341 + 0.223238i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.266044 + 1.50881i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.97937 + 2.35892i) q^{5} -1.53209i q^{6} +(0.153180 + 0.128533i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.613341 + 0.223238i) q^{9} +(1.53967 - 2.66679i) q^{10} +(2.17174 + 3.76157i) q^{11} +(0.266044 + 1.50881i) q^{12} +(-1.59735 - 4.38867i) q^{13} +(-0.173172 - 0.0999810i) q^{14} +(-3.03256 - 3.61407i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.32445 - 6.38637i) q^{17} +(-0.642788 - 0.113341i) q^{18} +(4.07964 + 0.719350i) q^{19} +(-1.05320 + 2.89364i) q^{20} +(-0.234685 + 0.196924i) q^{21} +(-2.79194 - 3.32730i) q^{22} +(-0.896915 - 0.517834i) q^{23} +(-0.524005 - 1.43969i) q^{24} +(-0.778357 - 4.41428i) q^{25} +(2.33516 + 4.04462i) q^{26} +(-2.79813 + 4.84651i) q^{27} +(0.187903 + 0.0683910i) q^{28} +(1.25937 - 0.727100i) q^{29} +(3.61407 + 3.03256i) q^{30} +5.10852i q^{31} +(-0.642788 + 0.766044i) q^{32} +(-6.25329 + 2.27601i) q^{33} +(-1.18015 + 6.69298i) q^{34} +(-0.606398 + 0.106924i) q^{35} +0.652704 q^{36} +(5.64160 + 2.27429i) q^{37} -4.14257 q^{38} +(7.04665 - 1.24252i) q^{39} +(0.534723 - 3.03256i) q^{40} +(-4.46505 + 1.62515i) q^{41} +(0.196924 - 0.234685i) q^{42} -0.399970i q^{43} +(3.32730 + 2.79194i) q^{44} +(-1.74063 + 1.00495i) q^{45} +(0.973210 + 0.354220i) q^{46} +(4.10475 - 7.10963i) q^{47} +(0.766044 + 1.32683i) q^{48} +(-1.20859 - 6.85428i) q^{49} +(1.53306 + 4.21206i) q^{50} +(9.01743 + 5.20621i) q^{51} +(-3.00203 - 3.57768i) q^{52} +(-8.65606 + 7.26330i) q^{53} +(1.91404 - 5.25877i) q^{54} +(-13.1719 - 2.32256i) q^{55} +(-0.196924 - 0.0347230i) q^{56} +(-2.17073 + 5.96403i) q^{57} +(-1.11398 + 0.934742i) q^{58} +(-2.69714 - 3.21433i) q^{59} +(-4.08576 - 2.35892i) q^{60} +(-3.60153 - 9.89514i) q^{61} +(-0.887086 - 5.03091i) q^{62} +(0.0652579 + 0.113030i) q^{63} +(0.500000 - 0.866025i) q^{64} +(13.5143 + 4.91879i) q^{65} +(5.76306 - 3.32730i) q^{66} +(6.67299 + 5.59930i) q^{67} -6.79623i q^{68} +(1.01993 - 1.21551i) q^{69} +(0.578618 - 0.210600i) q^{70} +(2.45953 - 13.9487i) q^{71} +(-0.642788 + 0.113341i) q^{72} +7.27588 q^{73} +(-5.95081 - 1.26008i) q^{74} +6.86740 q^{75} +(4.07964 - 0.719350i) q^{76} +(-0.150819 + 0.855337i) q^{77} +(-6.72384 + 2.44728i) q^{78} +(-4.04665 + 4.82261i) q^{79} +3.07935i q^{80} +(-5.06805 - 4.25260i) q^{81} +(4.11502 - 2.37581i) q^{82} +(-14.4861 - 5.27251i) q^{83} +(-0.153180 + 0.265315i) q^{84} +(10.4640 + 18.1241i) q^{85} +(0.0694540 + 0.393893i) q^{86} +(0.762009 + 2.09360i) q^{87} +(-3.76157 - 2.17174i) q^{88} +(2.06611 + 2.46229i) q^{89} +(1.53967 - 1.29194i) q^{90} +(0.319409 - 0.877568i) q^{91} +(-1.01993 - 0.179842i) q^{92} +(-7.70781 - 1.35909i) q^{93} +(-2.80781 + 7.71440i) q^{94} +(-9.77198 + 8.19967i) q^{95} +(-0.984808 - 1.17365i) q^{96} +(2.07350 + 1.19713i) q^{97} +(2.38047 + 6.54027i) q^{98} +(0.492294 + 2.79194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	−0.266044	+	1.50881i	−0.153601	+	0.871114i	0.806453	+	0.591298i	$0.201384\pi$
$3$	−0.266044	+	1.50881i	−0.153601	+	0.871114i	−0.960054	+	0.279815i	$0.909727\pi$
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−1.97937	+	2.35892i	−0.885199	+	1.05494i	0.112918	+	0.993604i	$0.463980\pi$
$5$	−1.97937	+	2.35892i	−0.885199	+	1.05494i	−0.998117	+	0.0613353i	$0.980464\pi$
$6$		−	1.53209i		−	0.625473i
$7$	0.153180	+	0.128533i	0.0578965	+	0.0485809i	0.671277	−	0.741207i	$-0.265746\pi$
$7$	0.153180	+	0.128533i	0.0578965	+	0.0485809i	−0.613380	+	0.789788i	$0.710191\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	0.613341	+	0.223238i	0.204447	+	0.0744126i
$10$	1.53967	−	2.66679i	0.486888	−	0.843314i
$11$	2.17174	+	3.76157i	0.654805	+	1.13416i	0.981943	+	0.189179i	$0.0605827\pi$
$11$	2.17174	+	3.76157i	0.654805	+	1.13416i	−0.327137	+	0.944977i	$0.606084\pi$
$12$	0.266044	+	1.50881i	0.0768004	+	0.435557i
$13$	−1.59735	−	4.38867i	−0.443024	−	1.21720i	−0.937493	−	0.348004i	$-0.886860\pi$
$13$	−1.59735	−	4.38867i	−0.443024	−	1.21720i	0.494469	−	0.869195i	$-0.335363\pi$
$14$	−0.173172	−	0.0999810i	−0.0462822	−	0.0267210i
$15$	−3.03256	−	3.61407i	−0.783005	−	0.933149i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.32445	−	6.38637i	0.563761	−	1.54892i	−0.250316	−	0.968164i	$-0.580534\pi$
$17$	2.32445	−	6.38637i	0.563761	−	1.54892i	0.814077	−	0.580757i	$-0.197243\pi$
$18$	−0.642788	−	0.113341i	−0.151506	−	0.0267147i
$19$	4.07964	+	0.719350i	0.935933	+	0.165030i	0.620757	−	0.784003i	$-0.286825\pi$
$19$	4.07964	+	0.719350i	0.935933	+	0.165030i	0.315176	+	0.949033i	$0.397936\pi$
$20$	−1.05320	+	2.89364i	−0.235502	+	0.647038i
$21$	−0.234685	+	0.196924i	−0.0512125	+	0.0429724i
$22$	−2.79194	−	3.32730i	−0.595244	−	0.709384i
$23$	−0.896915	−	0.517834i	−0.187020	−	0.107976i	0.403567	−	0.914950i	$-0.367770\pi$
$23$	−0.896915	−	0.517834i	−0.187020	−	0.107976i	−0.590587	+	0.806974i	$0.701104\pi$
$24$	−0.524005	−	1.43969i	−0.106962	−	0.293876i
$25$	−0.778357	−	4.41428i	−0.155671	−	0.882856i
$26$	2.33516	+	4.04462i	0.457964	+	0.793216i
$27$	−2.79813	+	4.84651i	−0.538501	+	0.932711i
$28$	0.187903	+	0.0683910i	0.0355103	+	0.0129247i
$29$	1.25937	−	0.727100i	0.233860	−	0.135019i	−0.378492	−	0.925605i	$-0.623557\pi$
$29$	1.25937	−	0.727100i	0.233860	−	0.135019i	0.612351	+	0.790586i	$0.290224\pi$
$30$	3.61407	+	3.03256i	0.659836	+	0.553668i
$31$			5.10852i			0.917518i	0.888561	+	0.458759i	$0.151706\pi$
$31$			5.10852i			0.917518i	−0.888561	+	0.458759i	$0.848294\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−6.25329	+	2.27601i	−1.08856	+	0.396202i
$34$	−1.18015	+	6.69298i	−0.202395	+	1.14784i
$35$	−0.606398	+	0.106924i	−0.102500	+	0.0180735i
$36$	0.652704			0.108784
$37$	5.64160	+	2.27429i	0.927473	+	0.373891i
$37$	5.64160	+	2.27429i	0.927473	+	0.373891i
$38$	−4.14257			−0.672014
$39$	7.04665	−	1.24252i	1.12837	−	0.198962i
$40$	0.534723	−	3.03256i	0.0845471	−	0.479491i
$41$	−4.46505	+	1.62515i	−0.697324	+	0.253805i	−0.666268	−	0.745712i	$-0.732109\pi$
$41$	−4.46505	+	1.62515i	−0.697324	+	0.253805i	−0.0310562	+	0.999518i	$0.509887\pi$
$42$	0.196924	−	0.234685i	0.0303860	−	0.0362127i
$43$		−	0.399970i		−	0.0609948i	−0.999535	−	0.0304974i	$-0.990291\pi$
$43$		−	0.399970i		−	0.0609948i	0.999535	−	0.0304974i	$-0.00970913\pi$
$44$	3.32730	+	2.79194i	0.501610	+	0.420901i
$45$	−1.74063	+	1.00495i	−0.259477	+	0.149809i
$46$	0.973210	+	0.354220i	0.143492	+	0.0522268i
$47$	4.10475	−	7.10963i	0.598739	−	1.03705i	−0.394269	−	0.918995i	$-0.629002\pi$
$47$	4.10475	−	7.10963i	0.598739	−	1.03705i	0.993008	−	0.118051i	$-0.0376646\pi$
$48$	0.766044	+	1.32683i	0.110569	+	0.191511i
$49$	−1.20859	−	6.85428i	−0.172656	−	0.979182i
$50$	1.53306	+	4.21206i	0.216808	+	0.595675i
$51$	9.01743	+	5.20621i	1.26269	+	0.729016i
$52$	−3.00203	−	3.57768i	−0.416307	−	0.496135i
$53$	−8.65606	+	7.26330i	−1.18900	+	0.997690i	−0.189125	+	0.981953i	$0.560565\pi$
$53$	−8.65606	+	7.26330i	−1.18900	+	0.997690i	−0.999876	+	0.0157372i	$0.994990\pi$
$54$	1.91404	−	5.25877i	0.260467	−	0.715628i
$55$	−13.1719	−	2.32256i	−1.77610	−	0.313174i
$56$	−0.196924	−	0.0347230i	−0.0263151	−	0.00464006i
$57$	−2.17073	+	5.96403i	−0.287520	+	0.789955i
$58$	−1.11398	+	0.934742i	−0.146273	+	0.122738i
$59$	−2.69714	−	3.21433i	−0.351138	−	0.418470i	0.561347	−	0.827581i	$-0.310283\pi$
$59$	−2.69714	−	3.21433i	−0.351138	−	0.418470i	−0.912485	+	0.409111i	$0.865839\pi$
$60$	−4.08576	−	2.35892i	−0.527470	−	0.304535i
$61$	−3.60153	−	9.89514i	−0.461129	−	1.26694i	−0.924637	−	0.380849i	$-0.875632\pi$
$61$	−3.60153	−	9.89514i	−0.461129	−	1.26694i	0.463508	−	0.886093i	$-0.346591\pi$
$62$	−0.887086	−	5.03091i	−0.112660	−	0.638927i
$63$	0.0652579	+	0.113030i	0.00822173	+	0.0142404i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	13.5143	+	4.91879i	1.67624	+	0.610100i
$66$	5.76306	−	3.32730i	0.709384	−	0.409563i
$67$	6.67299	+	5.59930i	0.815235	+	0.684063i	0.951851	−	0.306561i	$-0.0991782\pi$
$67$	6.67299	+	5.59930i	0.815235	+	0.684063i	−0.136616	+	0.990624i	$0.543623\pi$
$68$		−	6.79623i		−	0.824164i
$69$	1.01993	−	1.21551i	0.122786	−	0.146330i
$70$	0.578618	−	0.210600i	0.0691581	−	0.0251715i
$71$	2.45953	−	13.9487i	0.291893	−	1.65541i	−0.387675	−	0.921796i	$-0.626722\pi$
$71$	2.45953	−	13.9487i	0.291893	−	1.65541i	0.679569	−	0.733612i	$-0.262167\pi$
$72$	−0.642788	+	0.113341i	−0.0757532	+	0.0133573i
$73$	7.27588			0.851577			0.425789	−	0.904823i	$-0.359997\pi$
$73$	7.27588			0.851577			0.425789	+	0.904823i	$0.359997\pi$
$74$	−5.95081	−	1.26008i	−0.691768	−	0.146482i
$75$	6.86740			0.792979
$76$	4.07964	−	0.719350i	0.467967	−	0.0825151i
$77$	−0.150819	+	0.855337i	−0.0171874	+	0.0974747i
$78$	−6.72384	+	2.44728i	−0.761325	+	0.277100i
$79$	−4.04665	+	4.82261i	−0.455284	+	0.542587i	−0.944039	−	0.329835i	$-0.893007\pi$
$79$	−4.04665	+	4.82261i	−0.455284	+	0.542587i	0.488754	+	0.872421i	$0.337451\pi$
$80$			3.07935i			0.344281i
$81$	−5.06805	−	4.25260i	−0.563116	−	0.472511i
$82$	4.11502	−	2.37581i	0.454427	−	0.262364i
$83$	−14.4861	−	5.27251i	−1.59006	−	0.578733i	−0.612696	−	0.790318i	$-0.709915\pi$
$83$	−14.4861	−	5.27251i	−1.59006	−	0.578733i	−0.977360	+	0.211585i	$0.932137\pi$
$84$	−0.153180	+	0.265315i	−0.0167133	+	0.0289482i
$85$	10.4640	+	18.1241i	1.13498	+	1.96584i
$86$	0.0694540	+	0.393893i	0.00748942	+	0.0424746i
$87$	0.762009	+	2.09360i	0.0816959	+	0.224458i
$88$	−3.76157	−	2.17174i	−0.400985	−	0.231509i
$89$	2.06611	+	2.46229i	0.219007	+	0.261002i	0.864350	−	0.502890i	$-0.167730\pi$
$89$	2.06611	+	2.46229i	0.219007	+	0.261002i	−0.645343	+	0.763893i	$0.723286\pi$
$90$	1.53967	−	1.29194i	0.162296	−	0.136182i
$91$	0.319409	−	0.877568i	0.0334831	−	0.0919941i
$92$	−1.01993	−	0.179842i	−0.106336	−	0.0187498i
$93$	−7.70781	−	1.35909i	−0.799262	−	0.140932i
$94$	−2.80781	+	7.71440i	−0.289604	+	0.795680i
$95$	−9.77198	+	8.19967i	−1.00258	+	0.841268i
$96$	−0.984808	−	1.17365i	−0.100512	−	0.119785i
$97$	2.07350	+	1.19713i	0.210532	+	0.121551i	0.601559	−	0.798829i	$-0.294547\pi$
$97$	2.07350	+	1.19713i	0.210532	+	0.121551i	−0.391027	+	0.920379i	$0.627880\pi$
$98$	2.38047	+	6.54027i	0.240463	+	0.660668i
$99$	0.492294	+	2.79194i	0.0494774	+	0.280600i
$100$	−2.24119	−	3.88185i	−0.224119	−	0.388185i
$101$	5.48150	−	9.49423i	0.545429	−	0.944711i	−0.453150	−	0.891434i	$-0.649700\pi$
$101$	5.48150	−	9.49423i	0.545429	−	0.944711i	0.998580	−	0.0532773i	$-0.0169667\pi$
$102$	−9.78448	−	3.56126i	−0.968808	−	0.352617i
$103$	−13.6274	+	7.86780i	−1.34275	+	0.775238i	−0.987210	−	0.159423i	$-0.949037\pi$
$103$	−13.6274	+	7.86780i	−1.34275	+	0.775238i	−0.355541	+	0.934661i	$0.615703\pi$
$104$	3.57768	+	3.00203i	0.350820	+	0.294373i
$105$		−	0.943387i		−	0.0920652i
$106$	7.26330	−	8.65606i	0.705474	−	0.840751i
$107$	17.4933	−	6.36704i	1.69114	−	0.615525i	0.696373	−	0.717680i	$-0.254796\pi$
$107$	17.4933	−	6.36704i	1.69114	−	0.615525i	0.994769	+	0.102154i	$0.0325736\pi$
$108$	−0.971782	+	5.51125i	−0.0935097	+	0.530320i
$109$	0.00691666	−	0.00121959i	0.000662495	−	0.000116816i	−0.173317	−	0.984866i	$-0.555448\pi$
$109$	0.00691666	−	0.00121959i	0.000662495	−	0.000116816i	0.173979	+	0.984749i	$0.444337\pi$
$110$	13.3751			1.27527
$111$	−4.93239	+	7.90705i	−0.468162	+	0.750504i
$112$	0.199962			0.0188946
$113$	2.52369	−	0.444994i	0.237408	−	0.0418615i	−0.0536779	−	0.998558i	$-0.517094\pi$
$113$	2.52369	−	0.444994i	0.237408	−	0.0418615i	0.291086	+	0.956697i	$0.405983\pi$
$114$	1.10211	−	6.25037i	0.103222	−	0.585401i
$115$	2.99685	−	1.09076i	0.279458	−	0.101714i
$116$	0.934742	−	1.11398i	0.0867886	−	0.103431i
$117$		−	3.04834i		−	0.281819i
$118$	3.21433	+	2.69714i	0.295903	+	0.248292i
$119$	1.17692	−	0.679493i	0.107888	−	0.0622891i
$120$	4.43331	+	1.61359i	0.404704	+	0.147300i
$121$	−3.93294	+	6.81205i	−0.357540	+	0.619277i
$122$	5.26509	+	9.11941i	0.476679	+	0.825632i
$123$	−1.26414	−	7.16929i	−0.113984	−	0.646433i
$124$	1.74722	+	4.80044i	0.156905	+	0.431092i
$125$	−1.38039	−	0.796967i	−0.123466	−	0.0712829i
$126$	−0.0838940	−	0.0999810i	−0.00747387	−	0.00890701i
$127$	−4.44843	+	3.73268i	−0.394735	+	0.331222i	−0.818454	−	0.574572i	$-0.805169\pi$
$127$	−4.44843	+	3.73268i	−0.394735	+	0.331222i	0.423720	+	0.905793i	$0.360724\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	0.603479	+	0.106410i	0.0531334	+	0.00936885i
$130$	−14.1631	−	2.49733i	−1.24218	−	0.219031i
$131$	−2.86257	+	7.86484i	−0.250104	+	0.687154i	0.749578	+	0.661916i	$0.230257\pi$
$131$	−2.86257	+	7.86484i	−0.250104	+	0.687154i	−0.999681	+	0.0252378i	$0.991966\pi$
$132$	−5.09773	+	4.27750i	−0.443700	+	0.372309i
$133$	0.532457	+	0.634558i	0.0461699	+	0.0550232i
$134$	−7.54392	−	4.35548i	−0.651695	−	0.376256i
$135$	−5.89398	−	16.1936i	−0.507273	−	1.39372i
$136$	1.18015	+	6.69298i	0.101197	+	0.573918i
$137$	0.788995	+	1.36658i	0.0674084	+	0.116755i	0.897760	−	0.440485i	$-0.145194\pi$
$137$	0.788995	+	1.36658i	0.0674084	+	0.116755i	−0.830351	+	0.557240i	$0.811860\pi$
$138$	−0.793368	+	1.37415i	−0.0675360	+	0.116976i
$139$	−9.32521	−	3.39410i	−0.790954	−	0.287884i	−0.0852214	−	0.996362i	$-0.527160\pi$
$139$	−9.32521	−	3.39410i	−0.790954	−	0.287884i	−0.705733	+	0.708478i	$0.749382\pi$
$140$	−0.533257	+	0.307876i	−0.0450684	+	0.0260203i
$141$	9.63506	+	8.08477i	0.811418	+	0.680861i
$142$			14.1639i			1.18861i
$143$	13.0393	−	15.5396i	1.09040	−	1.29949i
$144$	0.613341	−	0.223238i	0.0511117	−	0.0186031i
$145$	−0.777594	+	4.40996i	−0.0645757	+	0.366227i
$146$	−7.16534	+	1.26344i	−0.593008	+	0.104563i
$147$	10.6634			0.879499
$148$	6.07922	+	0.207592i	0.499709	+	0.0170640i
$149$	12.8504			1.05274			0.526372	−	0.850254i	$-0.323552\pi$
$149$	12.8504			1.05274			0.526372	+	0.850254i	$0.323552\pi$
$150$	−6.76307	+	1.19251i	−0.552202	+	0.0973682i
$151$	0.900597	−	5.10754i	0.0732895	−	0.415646i	−0.925985	−	0.377560i	$-0.876763\pi$
$151$	0.900597	−	5.10754i	0.0732895	−	0.415646i	0.999274	−	0.0380852i	$-0.0121258\pi$
$152$	−3.89275	+	1.41684i	−0.315743	+	0.114921i
$153$	2.85136	−	3.39811i	0.230519	−	0.274721i
$154$		−	0.868532i		−	0.0699883i
$155$	−12.0506	−	10.1116i	−0.967926	−	0.812186i
$156$	6.19672	−	3.57768i	0.496135	−	0.286444i
$157$	−11.2421	−	4.09177i	−0.897214	−	0.326559i	−0.148078	−	0.988976i	$-0.547309\pi$
$157$	−11.2421	−	4.09177i	−0.897214	−	0.326559i	−0.749136	+	0.662416i	$0.769531\pi$
$158$	3.14774	−	5.45204i	0.250421	−	0.433741i
$159$	−8.65606	−	14.9927i	−0.686470	−	1.18900i
$160$	−0.534723	−	3.03256i	−0.0422736	−	0.239745i
$161$	−0.0708304	−	0.194605i	−0.00558222	−	0.0153370i
$162$	5.72951	+	3.30793i	0.450153	+	0.259896i
$163$	−0.454390	−	0.541521i	−0.0355906	−	0.0424152i	0.747956	−	0.663749i	$-0.231036\pi$
$163$	−0.454390	−	0.541521i	−0.0355906	−	0.0424152i	−0.783546	+	0.621334i	$0.786591\pi$
$164$	−3.63995	+	3.05428i	−0.284232	+	0.238499i
$165$	7.00862	−	19.2560i	0.545621	−	1.49908i
$166$	15.1816	+	2.67692i	1.17832	+	0.207770i
$167$	−6.50943	−	1.14779i	−0.503715	−	0.0888185i	−0.0839840	−	0.996467i	$-0.526764\pi$
$167$	−6.50943	−	1.14779i	−0.503715	−	0.0888185i	−0.419731	+	0.907649i	$0.637876\pi$
$168$	0.104781	−	0.287884i	0.00808404	−	0.0222107i
$169$	−6.75037	+	5.66423i	−0.519259	+	0.435710i
$170$	−13.4522	−	16.0317i	−1.03174	−	1.22958i
$171$	2.34162	+	1.35194i	0.179068	+	0.103385i
$172$	−0.136798	−	0.375848i	−0.0104307	−	0.0286582i
$173$	2.67447	+	15.1676i	0.203336	+	1.15317i	0.900037	+	0.435813i	$0.143539\pi$
$173$	2.67447	+	15.1676i	0.203336	+	1.15317i	−0.696701	+	0.717361i	$0.745350\pi$
$174$	−1.11398	−	1.92947i	−0.0844508	−	0.146273i
$175$	0.448153	−	0.776223i	0.0338771	−	0.0586769i
$176$	4.08154	+	1.48556i	0.307658	+	0.111978i
$177$	5.56739	−	3.21433i	0.418470	−	0.241604i
$178$	−2.46229	−	2.06611i	−0.184557	−	0.154861i
$179$			2.55438i			0.190923i	0.995433	+	0.0954617i	$0.0304328\pi$
$179$			2.55438i			0.190923i	−0.995433	+	0.0954617i	$0.969567\pi$
$180$	−1.29194	+	1.53967i	−0.0962955	+	0.114760i
$181$	−7.88211	+	2.86885i	−0.585873	+	0.213240i	−0.617913	−	0.786246i	$-0.712022\pi$
$181$	−7.88211	+	2.86885i	−0.585873	+	0.213240i	0.0320404	+	0.999487i	$0.489799\pi$
$182$	−0.162168	+	0.919700i	−0.0120207	+	0.0681727i
$183$	15.8881	−	2.80150i	1.17448	−	0.207093i
$184$	1.03567			0.0763505
$185$	−16.5316	+	8.80641i	−1.21543	+	0.647460i
$186$	7.82671			0.573882
$187$	29.0709	−	5.12598i	2.12587	−	0.374849i
$188$	1.42556	−	8.08477i	0.103970	−	0.589643i
$189$	−1.05155	+	0.382734i	−0.0764893	+	0.0278398i
$190$	8.19967	−	9.77198i	0.594866	−	0.708934i
$191$		−	6.48182i		−	0.469008i	−0.972115	−	0.234504i	$-0.924653\pi$
$191$		−	6.48182i		−	0.469008i	0.972115	−	0.234504i	$-0.0753466\pi$
$192$	1.17365	+	0.984808i	0.0847008	+	0.0710724i
$193$	−18.1716	+	10.4914i	−1.30802	+	0.755186i	−0.981766	−	0.190096i	$-0.939120\pi$
$193$	−18.1716	+	10.4914i	−1.30802	+	0.755186i	−0.326255	+	0.945282i	$0.605787\pi$
$194$	−2.24988	−	0.818888i	−0.161532	−	0.0587927i
$195$	−11.0169	+	19.0819i	−0.788938	+	1.36648i
$196$	−3.48001	−	6.02755i	−0.248572	−	0.430539i
$197$	−0.287925	−	1.63290i	−0.0205138	−	0.116340i	0.972831	−	0.231515i	$-0.0743682\pi$
$197$	−0.287925	−	1.63290i	−0.0205138	−	0.116340i	−0.993345	+	0.115175i	$0.963257\pi$
$198$	−0.969630	−	2.66404i	−0.0689086	−	0.189325i
$199$	6.25254	+	3.60991i	0.443231	+	0.255900i	0.704967	−	0.709240i	$-0.250962\pi$
$199$	6.25254	+	3.60991i	0.443231	+	0.255900i	−0.261736	+	0.965139i	$0.584295\pi$
$200$	2.88122	+	3.43370i	0.203733	+	0.242799i
$201$	−10.2236	+	8.57863i	−0.721118	+	0.605090i
$202$	−3.74956	+	10.3018i	−0.263818	+	0.724835i
$203$	0.286367	+	0.0504942i	0.0200990	+	0.00354400i
$204$	10.2542	+	1.80810i	0.717940	+	0.126592i
$205$	5.00439	−	13.7495i	0.349522	−	0.960303i
$206$	12.0542	−	10.1147i	0.839854	−	0.704721i
$207$	−0.434515	−	0.517834i	−0.0302009	−	0.0359920i
$208$	−4.04462	−	2.33516i	−0.280444	−	0.161915i
$209$	6.15404	+	16.9081i	0.425684	+	1.16956i
$210$	0.163817	+	0.929055i	0.0113045	+	0.0641109i
$211$	−2.25434	−	3.90463i	−0.155195	−	0.268806i	0.777935	−	0.628345i	$-0.216267\pi$
$211$	−2.25434	−	3.90463i	−0.155195	−	0.268806i	−0.933130	+	0.359539i	$0.882934\pi$
$212$	−5.64984	+	9.78581i	−0.388033	+	0.672092i
$213$	20.3917	+	7.42196i	1.39721	+	0.508544i
$214$	−16.1219	+	9.30799i	−1.10207	+	0.636281i
$215$	0.943495	+	0.791686i	0.0643458	+	0.0539926i
$216$		−	5.59627i		−	0.380778i
$217$	−0.656614	+	0.782522i	−0.0445739	+	0.0531211i
$218$	−0.00659980	+	0.00240213i	−0.000446995	+	0.000162693i
$219$	−1.93571	+	10.9779i	−0.130803	+	0.741821i
$220$	−13.1719	+	2.32256i	−0.888050	+	0.156587i
$221$	−31.7406			−2.13511
$222$	3.48441	−	8.64343i	0.233858	−	0.580109i
$223$	13.6418			0.913526			0.456763	−	0.889588i	$-0.349009\pi$
$223$	13.6418			0.913526			0.456763	+	0.889588i	$0.349009\pi$
$224$	−0.196924	+	0.0347230i	−0.0131575	+	0.00232003i
$225$	0.508036	−	2.88122i	0.0338691	−	0.192081i
$226$	−2.40807	+	0.876467i	−0.160183	+	0.0583017i
$227$	−17.5084	+	20.8657i	−1.16207	+	1.38490i	−0.253414	+	0.967358i	$0.581554\pi$
$227$	−17.5084	+	20.8657i	−1.16207	+	1.38490i	−0.908657	+	0.417544i	$0.862891\pi$
$228$			6.34679i			0.420326i
$229$	1.56117	+	1.30998i	0.103165	+	0.0865658i	0.692911	−	0.721023i	$-0.256328\pi$
$229$	1.56117	+	1.30998i	0.103165	+	0.0865658i	−0.589746	+	0.807589i	$0.700772\pi$
$230$	−2.76191	+	1.59459i	−0.182115	+	0.105144i
$231$	−1.25042	−	0.455115i	−0.0822715	−	0.0299444i
$232$	−0.727100	+	1.25937i	−0.0477365	+	0.0826820i
$233$	1.94247	+	3.36446i	0.127256	+	0.220413i	0.922612	−	0.385728i	$-0.126050\pi$
$233$	1.94247	+	3.36446i	0.127256	+	0.220413i	−0.795357	+	0.606142i	$0.792716\pi$
$234$	0.529339	+	3.00203i	0.0346040	+	0.196249i
$235$	8.64623	+	23.7553i	0.564018	+	1.54963i
$236$	−3.63385	−	2.09801i	−0.236544	−	0.136569i
$237$	−6.19983	−	7.38867i	−0.402722	−	0.479946i
$238$	−1.04104	+	0.873540i	−0.0674809	+	0.0566232i
$239$	−6.35148	+	17.4506i	−0.410843	+	1.12878i	0.545900	+	0.837850i	$0.316188\pi$
$239$	−6.35148	+	17.4506i	−0.410843	+	1.12878i	−0.956744	+	0.290933i	$0.906034\pi$
$240$	−4.64616	−	0.819243i	−0.299908	−	0.0528819i
$241$	24.9528	+	4.39985i	1.60735	+	0.283420i	0.904036	−	0.427457i	$-0.140591\pi$
$241$	24.9528	+	4.39985i	1.60735	+	0.283420i	0.703317	+	0.710877i	$0.251702\pi$
$242$	2.69029	−	7.39151i	0.172938	−	0.475144i
$243$	−5.09627	+	4.27628i	−0.326926	+	0.274323i
$244$	−6.76867	−	8.06659i	−0.433320	−	0.516410i
$245$	18.5609	+	10.7162i	1.18581	+	0.684630i
$246$	2.48987	+	6.84086i	0.158748	+	0.436157i
$247$	−3.35960	−	19.0533i	−0.213766	−	1.21233i
$248$	−2.55426	−	4.42411i	−0.162196	−	0.280931i
$249$	11.8092	−	20.4541i	0.748376	−	1.29623i
$250$	1.49781	+	0.545158i	0.0947298	+	0.0344788i
$251$	11.0092	−	6.35615i	0.694893	−	0.401197i	−0.110549	−	0.993871i	$-0.535261\pi$
$251$	11.0092	−	6.35615i	0.694893	−	0.401197i	0.805443	+	0.592674i	$0.201928\pi$
$252$	0.0999810	+	0.0838940i	0.00629821	+	0.00528482i
$253$		−	4.49841i		−	0.282813i
$254$	3.73268	−	4.44843i	0.234209	−	0.279119i
$255$	−30.1298	+	10.9664i	−1.88680	+	0.686740i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	4.28106	−	0.754866i	0.267045	−	0.0470873i	−0.0385222	−	0.999258i	$-0.512265\pi$
$257$	4.28106	−	0.754866i	0.267045	−	0.0470873i	0.305567	+	0.952170i	$0.401154\pi$
$258$	−0.612789			−0.0381506
$259$	0.571857	+	1.07351i	0.0355335	+	0.0667044i
$260$	14.3816			0.891907
$261$	0.934742	−	0.164820i	0.0578591	−	0.0102021i
$262$	1.45336	−	8.24243i	0.0897891	−	0.509219i
$263$	6.11870	−	2.22703i	0.377295	−	0.137324i	−0.146409	−	0.989224i	$-0.546772\pi$
$263$	6.11870	−	2.22703i	0.377295	−	0.137324i	0.523705	+	0.851900i	$0.324549\pi$
$264$	4.27750	−	5.09773i	0.263262	−	0.313743i
$265$		−	34.7956i		−	2.13748i
$266$	−0.634558	−	0.532457i	−0.0389073	−	0.0326471i
$267$	−4.26481	+	2.46229i	−0.261002	+	0.150690i
$268$	8.18563	+	2.97933i	0.500017	+	0.181991i
$269$	4.95106	−	8.57549i	0.301872	−	0.522857i	−0.674688	−	0.738103i	$-0.735722\pi$
$269$	4.95106	−	8.57549i	0.301872	−	0.522857i	0.976560	+	0.215246i	$0.0690552\pi$
$270$	8.61642	+	14.9241i	0.524379	+	0.908251i
$271$	1.56719	+	8.88797i	0.0951999	+	0.539906i	0.994686	+	0.102956i	$0.0328301\pi$
$271$	1.56719	+	8.88797i	0.0951999	+	0.539906i	−0.899486	+	0.436950i	$0.856059\pi$
$272$	−2.32445	−	6.38637i	−0.140940	−	0.387230i
$273$	1.23911	+	0.715400i	0.0749943	+	0.0432980i
$274$	−1.01431	−	1.20881i	−0.0612768	−	0.0730269i
$275$	14.9142	−	12.5145i	0.899362	−	0.754655i
$276$	0.542696	−	1.49104i	0.0326664	−	0.0897503i
$277$	−0.204926	−	0.0361340i	−0.0123128	−	0.00217108i	0.167488	−	0.985874i	$-0.446434\pi$
$277$	−0.204926	−	0.0361340i	−0.0123128	−	0.00217108i	−0.179801	+	0.983703i	$0.557545\pi$
$278$	9.77292	+	1.72323i	0.586141	+	0.103352i
$279$	−1.14042	+	3.13327i	−0.0682749	+	0.187584i
$280$	0.471694	−	0.395798i	0.0281891	−	0.0236534i
$281$	−17.3934	−	20.7286i	−1.03760	−	1.23657i	−0.971073	−	0.238781i	$-0.923252\pi$
$281$	−17.3934	−	20.7286i	−1.03760	−	1.23657i	−0.0665281	−	0.997785i	$-0.521192\pi$
$282$	−10.8926	−	6.28884i	−0.648644	−	0.374495i
$283$	0.278026	+	0.763870i	0.0165269	+	0.0454074i	0.947682	−	0.319217i	$-0.103420\pi$
$283$	0.278026	+	0.763870i	0.0165269	+	0.0454074i	−0.931155	+	0.364624i	$0.881198\pi$
$284$	−2.45953	−	13.9487i	−0.145947	−	0.827704i
$285$	−9.77198	−	16.9256i	−0.578842	−	1.00258i
$286$	−10.1428	+	17.5678i	−0.599754	+	1.03880i
$287$	−0.892841	−	0.324967i	−0.0527027	−	0.0191822i
$288$	−0.565258	+	0.326352i	−0.0333081	+	0.0192305i
$289$	−22.3599	−	18.7621i	−1.31529	−	1.10366i
$290$		−	4.47799i		−	0.262957i
$291$	−2.35789	+	2.81003i	−0.138222	+	0.164727i
$292$	6.83709	−	2.48850i	0.400110	−	0.145628i
$293$	−1.52803	+	8.66589i	−0.0892684	+	0.506266i	0.907085	+	0.420947i	$0.138302\pi$
$293$	−1.52803	+	8.66589i	−0.0892684	+	0.506266i	−0.996354	+	0.0853194i	$0.972809\pi$
$294$	−10.5014	+	1.85167i	−0.612452	+	0.107992i
$295$	12.9210			0.752288
$296$	−6.02291	+	0.851207i	−0.350075	+	0.0494754i
$297$	−24.3073			−1.41045
$298$	−12.6552	+	2.23145i	−0.733094	+	0.129264i
$299$	−0.839921	+	4.76343i	−0.0485739	+	0.275476i
$300$	6.45325	−	2.34879i	0.372578	−	0.135607i
$301$	0.0514093	−	0.0612672i	0.00296318	−	0.00353138i
$302$			5.18633i			0.298440i
$303$	12.8667	+	10.7964i	0.739173	+	0.620239i
$304$	3.58757	−	2.07129i	0.205761	−	0.118796i
$305$	30.4706	+	11.0904i	1.74474	+	0.635033i
$306$	−2.21796	+	3.84162i	−0.126792	+	0.219611i
$307$	−12.2271	−	21.1779i	−0.697836	−	1.20869i	−0.969215	−	0.246215i	$-0.920813\pi$
$307$	−12.2271	−	21.1779i	−0.697836	−	1.20869i	0.271379	−	0.962472i	$-0.412520\pi$
$308$	0.150819	+	0.855337i	0.00859371	+	0.0487374i
$309$	−8.24554	−	22.6544i	−0.469072	−	1.28877i
$310$	13.6234	+	7.86546i	0.773756	+	0.446728i
$311$	0.00816038	+	0.00972517i	0.000462733	+	0.000551464i	0.766276	−	0.642512i	$-0.222108\pi$
$311$	0.00816038	+	0.00972517i	0.000462733	+	0.000551464i	−0.765813	+	0.643063i	$0.777663\pi$
$312$	−5.48132	+	4.59938i	−0.310319	+	0.260388i
$313$	5.97456	−	16.4150i	0.337702	−	0.927829i	−0.648343	−	0.761349i	$-0.724538\pi$
$313$	5.97456	−	16.4150i	0.337702	−	0.927829i	0.986045	−	0.166480i	$-0.0532402\pi$
$314$	11.7818	+	2.07745i	0.664885	+	0.117237i
$315$	−0.395798	−	0.0697898i	−0.0223007	−	0.00393221i
$316$	−2.15318	+	5.91581i	−0.121126	+	0.332790i
$317$	2.09046	−	1.75410i	0.117412	−	0.0985203i	−0.582191	−	0.813052i	$-0.697805\pi$
$317$	2.09046	−	1.75410i	0.117412	−	0.0985203i	0.699603	+	0.714531i	$0.253360\pi$
$318$	11.1280	+	13.2619i	0.624028	+	0.743688i
$319$	5.47008	+	3.15815i	0.306266	+	0.176822i
$320$	1.05320	+	2.89364i	0.0588756	+	0.161759i
$321$	4.95268	+	28.0880i	0.276432	+	1.56772i
$322$	0.103547	+	0.179349i	0.00577046	+	0.00999472i
$323$	14.0769	−	24.3820i	0.783262	−	1.35665i
$324$	−6.21688	−	2.26276i	−0.345382	−	0.125709i
$325$	−18.1295	+	10.4671i	−1.00565	+	0.580610i
$326$	0.541521	+	0.454390i	0.0299921	+	0.0251663i
$327$			0.0107604i			0.000595052i
$328$	3.05428	−	3.63995i	0.168644	−	0.200982i
$329$	1.54259	−	0.561455i	0.0850455	−	0.0309540i
$330$	−3.55837	+	20.1805i	−0.195882	+	1.11090i
$331$	−23.2573	+	4.10088i	−1.27834	+	0.225405i	−0.771273	−	0.636504i	$-0.780380\pi$
$331$	−23.2573	+	4.10088i	−1.27834	+	0.225405i	−0.507062	+	0.861909i	$0.669269\pi$
$332$	−15.4158			−0.846051
$333$	2.95251	+	2.65433i	0.161797	+	0.145456i
$334$	6.60985			0.361675
$335$	−26.4166	+	4.65795i	−1.44329	+	0.254491i
$336$	−0.0531988	+	0.301705i	−0.00290223	+	0.0164594i
$337$	21.0920	−	7.67685i	1.14895	−	0.418185i	0.303814	−	0.952731i	$-0.401740\pi$
$337$	21.0920	−	7.67685i	1.14895	−	0.418185i	0.845139	+	0.534546i	$0.179517\pi$
$338$	5.66423	−	6.75037i	0.308094	−	0.367172i
$339$			3.92616i			0.213240i
$340$	16.0317	+	13.4522i	0.869443	+	0.729549i
$341$	−19.2161	+	11.0944i	−1.04061	+	0.600796i
$342$	−2.54081	−	0.924779i	−0.137391	−	0.0500063i
$343$	1.39574	−	2.41749i	0.0753626	−	0.130532i
$344$	0.199985	+	0.346384i	0.0107825	+	0.0186758i
$345$	0.848464	+	4.81188i	0.0456798	+	0.259063i
$346$	−5.26767	−	14.4728i	−0.283192	−	0.778063i
$347$	−1.05232	−	0.607556i	−0.0564914	−	0.0326153i	0.471488	−	0.881872i	$-0.343717\pi$
$347$	−1.05232	−	0.607556i	−0.0564914	−	0.0326153i	−0.527980	+	0.849257i	$0.677050\pi$
$348$	1.43211	+	1.70672i	0.0767690	+	0.0914898i
$349$	13.5892	−	11.4027i	0.727415	−	0.610374i	−0.202011	−	0.979383i	$-0.564748\pi$
$349$	13.5892	−	11.4027i	0.727415	−	0.610374i	0.929426	+	0.369010i	$0.120303\pi$
$350$	−0.306554	+	0.842251i	−0.0163860	+	0.0450202i
$351$	25.7393	+	4.53854i	1.37386	+	0.242249i
$352$	−4.27750	−	0.754239i	−0.227991	−	0.0402011i
$353$	0.549304	−	1.50920i	0.0292365	−	0.0803266i	−0.924216	−	0.381871i	$-0.875280\pi$
$353$	0.549304	−	1.50920i	0.0292365	−	0.0803266i	0.953452	+	0.301544i	$0.0975021\pi$
$354$	−4.92464	+	4.13227i	−0.261742	+	0.219627i
$355$	28.0355	+	33.4115i	1.48797	+	1.77330i
$356$	2.78366	+	1.60715i	0.147534	+	0.0851786i
$357$	0.712116	+	1.95652i	0.0376892	+	0.103550i
$358$	−0.443564	−	2.51558i	−0.0234431	−	0.132952i
$359$	16.0062	+	27.7236i	0.844775	+	1.46319i	0.885816	+	0.464037i	$0.153599\pi$
$359$	16.0062	+	27.7236i	0.844775	+	1.46319i	−0.0410405	+	0.999157i	$0.513067\pi$
$360$	1.00495	−	1.74063i	0.0529655	−	0.0917390i
$361$	−1.72818	−	0.629006i	−0.0909568	−	0.0331056i
$362$	7.26419	−	4.19398i	0.381798	−	0.220431i
$363$	−9.23177	−	7.74638i	−0.484542	−	0.406579i
$364$		−	0.933888i		−	0.0489490i
$365$	−14.4016	+	17.1632i	−0.753816	+	0.898363i
$366$	−15.1602	+	5.51787i	−0.792438	+	0.288424i
$367$	2.78467	−	15.7927i	0.145359	−	0.824371i	−0.821720	−	0.569892i	$-0.806985\pi$
$367$	2.78467	−	15.7927i	0.145359	−	0.824371i	0.967078	−	0.254479i	$-0.0819038\pi$
$368$	−1.01993	+	0.179842i	−0.0531678	+	0.00937491i
$369$	−3.10139			−0.161452
$370$	14.7513	−	11.5433i	0.766882	−	0.600108i
$371$	−2.25951			−0.117308
$372$	−7.70781	+	1.35909i	−0.399631	+	0.0704658i
$373$	−0.193859	+	1.09943i	−0.0100376	+	0.0569262i	−0.989415	−	0.145113i	$-0.953646\pi$
$373$	−0.193859	+	1.09943i	−0.0100376	+	0.0569262i	0.979378	+	0.202039i	$0.0647567\pi$
$374$	−27.7391	+	10.0962i	−1.43435	+	0.522062i
$375$	1.56972	−	1.87072i	0.0810600	−	0.0966035i
$376$			8.20949i			0.423372i
$377$	−5.20266	−	4.36555i	−0.267951	−	0.224837i
$378$	0.969117	−	0.559520i	0.0498460	−	0.0287786i
$379$	−34.2433	−	12.4636i	−1.75896	−	0.640210i	−0.759021	−	0.651066i	$-0.774322\pi$
$379$	−34.2433	−	12.4636i	−1.75896	−	0.640210i	−0.999941	+	0.0108561i	$0.996544\pi$
$380$	−6.37821	+	11.0474i	−0.327195	+	0.566719i
$381$	−4.44843	−	7.70491i	−0.227900	−	0.394735i
$382$	1.12556	+	6.38335i	0.0575885	+	0.326601i
$383$	2.06267	+	5.66715i	0.105398	+	0.289578i	0.981170	−	0.193147i	$-0.0618694\pi$
$383$	2.06267	+	5.66715i	0.105398	+	0.289578i	−0.875772	+	0.482725i	$0.839647\pi$
$384$	−1.32683	−	0.766044i	−0.0677094	−	0.0390920i
$385$	−1.71914	−	2.04879i	−0.0876156	−	0.104416i
$386$	16.0737	−	13.4875i	0.818131	−	0.686494i
$387$	0.0892883	−	0.245318i	0.00453878	−	0.0124702i
$388$	2.35789	+	0.415760i	0.119704	+	0.0211070i
$389$	18.5468	+	3.27030i	0.940361	+	0.165811i	0.622759	−	0.782413i	$-0.286012\pi$
$389$	18.5468	+	3.27030i	0.940361	+	0.165811i	0.317601	+	0.948224i	$0.397123\pi$
$390$	7.53602	−	20.7050i	0.381601	−	1.04844i
$391$	−5.39191	+	4.52435i	−0.272681	+	0.228806i
$392$	4.47381	+	5.33168i	0.225962	+	0.269291i
$393$	−11.1050	−	6.41147i	−0.560173	−	0.323416i
$394$	0.567102	+	1.55810i	0.0285702	+	0.0784959i
$395$	−3.36634	−	19.0914i	−0.169379	−	0.960595i
$396$	1.41750	+	2.45519i	0.0712323	+	0.123378i
$397$	−13.7557	+	23.8255i	−0.690378	+	1.19577i	0.281336	+	0.959609i	$0.409222\pi$
$397$	−13.7557	+	23.8255i	−0.690378	+	1.19577i	−0.971714	+	0.236160i	$0.924111\pi$
$398$	−6.78441	−	2.46932i	−0.340072	−	0.123776i
$399$	−1.09909	+	0.634558i	−0.0550232	+	0.0317676i
$400$	−3.43370	−	2.88122i	−0.171685	−	0.144061i
$401$			22.0721i			1.10223i	0.834430	+	0.551114i	$0.185797\pi$
$401$			22.0721i			1.10223i	−0.834430	+	0.551114i	$0.814203\pi$
$402$	8.57863	−	10.2236i	0.427863	−	0.509907i
$403$	22.4196	−	8.16008i	1.11680	−	0.406483i
$404$	1.90370	−	10.7964i	0.0947128	−	0.537143i
$405$	20.0630	−	3.53766i	0.996941	−	0.175788i
$406$	−0.290785			−0.0144314
$407$	3.69721	+	26.1604i	0.183264	+	1.29672i
$408$	−10.4124			−0.515492
$409$	−1.39932	+	0.246737i	−0.0691917	+	0.0122004i	−0.208137	−	0.978100i	$-0.566740\pi$
$409$	−1.39932	+	0.246737i	−0.0691917	+	0.0122004i	0.138945	+	0.990300i	$0.455629\pi$
$410$	−2.54080	+	14.4096i	−0.125481	+	0.711638i
$411$	−2.27182	+	0.826875i	−0.112061	+	0.0407867i
$412$	−10.1147	+	12.0542i	−0.498313	+	0.593866i
$413$		−	0.839043i		−	0.0412866i
$414$	0.517834	+	0.434515i	0.0254502	+	0.0213552i
$415$	41.1107	−	23.7353i	2.01805	−	1.16512i
$416$	4.38867	+	1.59735i	0.215172	+	0.0783164i
$417$	7.60198	−	13.1670i	0.372271	−	0.644792i
$418$	−8.99661	−	15.5826i	−0.440038	−	0.762169i
$419$	−2.36856	−	13.4328i	−0.115712	−	0.656235i	−0.986395	−	0.164391i	$-0.947434\pi$
$419$	−2.36856	−	13.4328i	−0.115712	−	0.656235i	0.870683	−	0.491844i	$-0.163677\pi$
$420$	−0.322657	−	0.886494i	−0.0157441	−	0.0432565i
$421$	−24.2468	−	13.9989i	−1.18172	−	0.682264i	−0.225306	−	0.974288i	$-0.572338\pi$
$421$	−24.2468	−	13.9989i	−1.18172	−	0.682264i	−0.956411	+	0.292024i	$0.905671\pi$
$422$	2.89812	+	3.45385i	0.141078	+	0.168131i
$423$	4.10475	−	3.44429i	0.199580	−	0.167467i
$424$	3.86472	−	10.6182i	0.187687	−	0.515667i
$425$	−30.0005	−	5.28989i	−1.45524	−	0.256597i
$426$	−21.3707	−	3.76823i	−1.03541	−	0.182571i
$427$	0.720170	−	1.97865i	0.0348515	−	0.0957536i
$428$	14.2607	−	11.9661i	0.689316	−	0.578405i
$429$	19.9773	+	23.8081i	0.964515	+	1.14946i
$430$	−1.06664	−	0.615823i	−0.0514378	−	0.0296976i
$431$	−0.974582	−	2.67764i	−0.0469440	−	0.128977i	0.914005	−	0.405703i	$-0.132973\pi$
$431$	−0.974582	−	2.67764i	−0.0469440	−	0.128977i	−0.960949	+	0.276725i	$0.910751\pi$
$432$	0.971782	+	5.51125i	0.0467549	+	0.265160i
$433$	15.5676	+	26.9638i	0.748130	+	1.29580i	0.948718	+	0.316123i	$0.102381\pi$
$433$	15.5676	+	26.9638i	0.748130	+	1.29580i	−0.200588	+	0.979676i	$0.564285\pi$
$434$	0.510755	−	0.884654i	0.0245170	−	0.0424647i
$435$	−6.44693	−	2.34649i	−0.309106	−	0.112506i
$436$	0.00608240	−	0.00351168i	0.000291294	−	0.000168179i
$437$	−3.28659	−	2.75777i	−0.157219	−	0.131922i
$438$		−	11.1473i		−	0.532638i
$439$	−18.4994	+	22.0467i	−0.882929	+	1.05223i	0.115335	+	0.993327i	$0.463206\pi$
$439$	−18.4994	+	22.0467i	−0.882929	+	1.05223i	−0.998263	+	0.0589066i	$0.981239\pi$
$440$	12.5685	−	4.57455i	0.599179	−	0.218083i
$441$	0.788854	−	4.47381i	0.0375645	−	0.213039i
$442$	31.2584	−	5.51170i	1.48681	−	0.262165i
$443$	−19.3903			−0.921259			−0.460630	−	0.887592i	$-0.652376\pi$
$443$	−19.3903			−0.921259			−0.460630	+	0.887592i	$0.652376\pi$
$444$	−1.93056	+	9.11718i	−0.0916203	+	0.432682i
$445$	−9.89793			−0.469207
$446$	−13.4346	+	2.36888i	−0.636147	+	0.112170i
$447$	−3.41877	+	19.3888i	−0.161702	+	0.917060i
$448$	0.187903	−	0.0683910i	0.00887757	−	0.00323117i
$449$	10.9788	−	13.0840i	0.518120	−	0.617472i	−0.442015	−	0.897008i	$-0.645736\pi$
$449$	10.9788	−	13.0840i	0.518120	−	0.617472i	0.960135	+	0.279536i	$0.0901806\pi$
$450$			2.92567i			0.137917i
$451$	−15.8101	−	13.2662i	−0.744466	−	0.624681i
$452$	2.21929	−	1.28131i	0.104387	−	0.0602677i
$453$	7.46672	+	2.71766i	0.350817	+	0.127687i
$454$	13.6191	−	23.5890i	0.639175	−	1.10708i
$455$	1.43788	+	2.49049i	0.0674090	+	0.116756i
$456$	−1.10211	−	6.25037i	−0.0516110	−	0.292700i
$457$	−0.826507	−	2.27081i	−0.0386623	−	0.106224i	0.918859	−	0.394585i	$-0.129112\pi$
$457$	−0.826507	−	2.27081i	−0.0386623	−	0.106224i	−0.957522	+	0.288361i	$0.906890\pi$
$458$	−1.76493	−	1.01898i	−0.0824697	−	0.0476139i
$459$	24.4475	+	29.1354i	1.14111	+	1.35992i
$460$	2.44306	−	2.04997i	0.113908	−	0.0955802i
$461$	−6.40945	+	17.6098i	−0.298518	+	0.820171i	0.696230	+	0.717819i	$0.254859\pi$
$461$	−6.40945	+	17.6098i	−0.298518	+	0.820171i	−0.994748	+	0.102353i	$0.967363\pi$
$462$	1.31045	+	0.231068i	0.0609678	+	0.0107503i
$463$	5.08108	+	0.895932i	0.236138	+	0.0416375i	0.290465	−	0.956886i	$-0.406190\pi$
$463$	5.08108	+	0.895932i	0.236138	+	0.0416375i	−0.0543267	+	0.998523i	$0.517301\pi$
$464$	0.497366	−	1.36650i	0.0230896	−	0.0634382i
$465$	18.4626	−	15.4919i	0.856181	−	0.718421i
$466$	−2.49720	−	2.97604i	−0.115680	−	0.137863i
$467$	−26.7874	−	15.4657i	−1.23957	−	0.715668i	−0.270566	−	0.962701i	$-0.587211\pi$
$467$	−26.7874	−	15.4657i	−1.23957	−	0.715668i	−0.969007	+	0.247034i	$0.920544\pi$
$468$	−1.04259	−	2.86450i	−0.0481939	−	0.132412i
$469$	0.302471	+	1.71540i	0.0139668	+	0.0792097i
$470$	−12.6399	−	21.8930i	−0.583037	−	1.00985i
$471$	9.16461	−	15.8736i	0.422283	−	0.731416i
$472$	3.94296	+	1.43512i	0.181490	+	0.0660568i
$473$	1.50451	−	0.868631i	0.0691776	−	0.0399397i
$474$	7.38867	+	6.19983i	0.339373	+	0.284768i
$475$		−	18.5686i		−	0.851985i
$476$	0.873540	−	1.04104i	0.0400386	−	0.0477162i
$477$	−6.93056	+	2.52252i	−0.317328	+	0.115498i
$478$	3.22473	−	18.2884i	0.147496	−	0.836491i
$479$	12.6827	−	2.23629i	0.579485	−	0.102179i	0.123780	−	0.992310i	$-0.460498\pi$
$479$	12.6827	−	2.23629i	0.579485	−	0.102179i	0.455705	+	0.890131i	$0.349387\pi$
$480$	4.71783			0.215339
$481$	0.969525	−	28.3920i	0.0442065	−	1.29456i
$482$	−25.3378			−1.15410
$483$	0.312467	−	0.0550963i	0.0142177	−	0.00250697i
$484$	−1.36590	+	7.74638i	−0.0620862	+	0.352108i
$485$	−6.92815	+	2.52164i	−0.314591	+	0.114502i
$486$	4.27628	−	5.09627i	0.193976	−	0.231171i
$487$			17.2601i			0.782130i	0.920363	+	0.391065i	$0.127893\pi$
$487$			17.2601i			0.782130i	−0.920363	+	0.391065i	$0.872107\pi$
$488$	8.06659	+	6.76867i	0.365157	+	0.306403i
$489$	0.937942	−	0.541521i	0.0424152	−	0.0244884i
$490$	−20.1398	−	7.33028i	−0.909822	−	0.331148i
$491$	−8.55331	+	14.8148i	−0.386005	+	0.668581i	−0.991908	−	0.126958i	$-0.959479\pi$
$491$	−8.55331	+	14.8148i	−0.386005	+	0.668581i	0.605903	+	0.795539i	$0.292812\pi$
$492$	−3.63995	−	6.30457i	−0.164101	−	0.284232i
$493$	−1.71618	−	9.73293i	−0.0772928	−	0.438349i
$494$	6.61713	+	18.1804i	0.297719	+	0.817975i
$495$	−7.56038	−	4.36499i	−0.339814	−	0.196192i
$496$	3.28370	+	3.91336i	0.147442	+	0.175715i
$497$	2.16962	−	1.82053i	0.0973208	−	0.0816619i
$498$	−8.07795	+	22.1940i	−0.361982	+	0.994537i
$499$	−18.2596	−	3.21965i	−0.817410	−	0.144131i	−0.250717	−	0.968060i	$-0.580666\pi$
$499$	−18.2596	−	3.21965i	−0.817410	−	0.144131i	−0.566693	+	0.823929i	$0.691777\pi$
$500$	−1.56972	−	0.276784i	−0.0702000	−	0.0123782i
$501$	3.46360	−	9.51615i	0.154742	−	0.425150i
$502$	−9.73819	+	8.17131i	−0.434637	+	0.364703i
$503$	2.15713	+	2.57077i	0.0961818	+	0.114625i	0.811988	−	0.583674i	$-0.198385\pi$
$503$	2.15713	+	2.57077i	0.0961818	+	0.114625i	−0.715807	+	0.698299i	$0.753941\pi$
$504$	−0.113030	−	0.0652579i	−0.00503476	−	0.00290682i
$505$	11.5462	+	31.7230i	0.513800	+	1.41165i
$506$	0.781141	+	4.43007i	0.0347260	+	0.196941i
$507$	−6.75037	−	11.6920i	−0.299794	−	0.519259i
$508$	−2.90351	+	5.02902i	−0.128822	+	0.223127i
$509$	10.3552	+	3.76897i	0.458984	+	0.167057i	0.561156	−	0.827710i	$-0.310357\pi$
$509$	10.3552	+	3.76897i	0.458984	+	0.167057i	−0.102171	+	0.994767i	$0.532579\pi$
$510$	27.7678	−	16.0317i	1.22958	−	0.709897i
$511$	1.11452	+	0.935191i	0.0493033	+	0.0413704i
$512$			1.00000i			0.0441942i
$513$	−14.9017	+	17.7592i	−0.657926	+	0.784086i
$514$	−4.08494	+	1.48680i	−0.180179	+	0.0655798i
$515$	8.41419	−	47.7192i	0.370774	−	2.10276i
$516$	0.603479	−	0.106410i	0.0265667	−	0.00468442i
$517$	35.6578			1.56823
$518$	−0.749582	−	0.957896i	−0.0329347	−	0.0420875i
$519$	−23.5967			−1.03578
$520$	−14.1631	+	2.49733i	−0.621092	+	0.109515i
$521$	−1.36004	+	7.71318i	−0.0595845	+	0.337921i	−0.999998	−	0.00211306i	$-0.999327\pi$
$521$	−1.36004	+	7.71318i	−0.0595845	+	0.337921i	0.940413	+	0.340034i	$0.110439\pi$
$522$	−0.891920	+	0.324633i	−0.0390383	+	0.0142088i
$523$	1.16527	−	1.38872i	0.0509538	−	0.0607244i	−0.739966	−	0.672645i	$-0.765158\pi$
$523$	1.16527	−	1.38872i	0.0509538	−	0.0607244i	0.790919	+	0.611920i	$0.209603\pi$
$524$			8.36959i			0.365627i
$525$	1.05195	+	0.882688i	0.0459107	+	0.0385237i
$526$	−5.63903	+	3.25569i	−0.245873	+	0.141955i
$527$	32.6249	+	11.8745i	1.42116	+	0.517261i
$528$	−3.32730	+	5.76306i	−0.144802	+	0.250805i
$529$	−10.9637	−	18.9897i	−0.476682	−	0.825638i
$530$	6.04220	+	34.2670i	0.262456	+	1.48846i
$531$	−0.936708	−	2.57359i	−0.0406497	−	0.111684i
$532$	0.717378	+	0.414178i	0.0311023	+	0.0179569i
$533$	14.2645	+	16.9997i	0.617863	+	0.736341i
$534$	3.77245	−	3.16546i	0.163250	−	0.136983i
$535$	−19.6063	+	53.8680i	−0.847656	+	2.32892i
$536$	−8.57863	−	1.51264i	−0.370540	−	0.0653362i
$537$	−3.85408	−	0.679579i	−0.166316	−	0.0293260i
$538$	−3.38673	+	9.30496i	−0.146012	+	0.401165i
$539$	23.1581	−	19.4319i	0.997489	−	0.836993i
$540$	−11.0771	−	13.2011i	−0.476681	−	0.568086i
$541$	−6.02197	−	3.47679i	−0.258905	−	0.149479i	0.364930	−	0.931035i	$-0.381093\pi$
$541$	−6.02197	−	3.47679i	−0.258905	−	0.149479i	−0.623835	+	0.781556i	$0.714426\pi$
$542$	−3.08676	−	8.48080i	−0.132588	−	0.364282i
$543$	−2.23157	−	12.6559i	−0.0957659	−	0.543116i
$544$	3.39811	+	5.88571i	0.145693	+	0.252348i
$545$	−0.0108137	+	0.0187298i	−0.000463207	+	0.000802298i
$546$	−1.34451	−	0.489362i	−0.0575398	−	0.0209428i
$547$	4.21435	−	2.43316i	0.180193	−	0.104034i	−0.407191	−	0.913343i	$-0.633492\pi$
$547$	4.21435	−	2.43316i	0.180193	−	0.104034i	0.587383	+	0.809309i	$0.300158\pi$
$548$	1.20881	+	1.01431i	0.0516378	+	0.0433293i
$549$		−	6.87309i		−	0.293336i
$550$	−12.5145	+	14.9142i	−0.533621	+	0.635945i
$551$	5.66083	−	2.06037i	0.241160	−	0.0877749i
$552$	−0.275534	+	1.56263i	−0.0117275	+	0.0665100i
$553$	−1.23973	+	0.218598i	−0.0527187	+	0.00929573i
$554$	0.208088			0.00884079
$555$	−8.88907	−	27.2861i	−0.377320	−	1.15823i
$556$	−9.92368			−0.420858
$557$	−7.17172	+	1.26457i	−0.303876	+	0.0535815i	−0.323507	−	0.946226i	$-0.604862\pi$
$557$	−7.17172	+	1.26457i	−0.303876	+	0.0535815i	0.0196313	+	0.999807i	$0.493751\pi$
$558$	0.579004	−	3.28370i	0.0245112	−	0.139010i
$559$	−1.75534	+	0.638890i	−0.0742428	+	0.0270222i
$560$	−0.395798	+	0.471694i	−0.0167255	+	0.0199327i
$561$			45.2262i			1.90945i
$562$	20.7286	+	17.3934i	0.874384	+	0.733695i
$563$	23.9124	−	13.8058i	1.00779	−	0.581845i	0.0972430	−	0.995261i	$-0.468998\pi$
$563$	23.9124	−	13.8058i	1.00779	−	0.581845i	0.910543	+	0.413415i	$0.135664\pi$
$564$	11.8191	+	4.30182i	0.497676	+	0.181139i
$565$	−3.94560	+	6.83397i	−0.165992	+	0.287507i
$566$	−0.406447	−	0.703987i	−0.0170842	−	0.0295908i
$567$	−0.229723	−	1.30282i	−0.00964746	−	0.0547134i
$568$	4.84434	+	13.3097i	0.203264	+	0.558463i
$569$	−4.89110	−	2.82388i	−0.205046	−	0.118383i	0.393961	−	0.919127i	$-0.371104\pi$
$569$	−4.89110	−	2.82388i	−0.205046	−	0.118383i	−0.599007	+	0.800744i	$0.704438\pi$
$570$	12.5626	+	14.9715i	0.526190	+	0.627089i
$571$	10.3379	−	8.67450i	0.432626	−	0.363016i	−0.400315	−	0.916377i	$-0.631099\pi$
$571$	10.3379	−	8.67450i	0.432626	−	0.363016i	0.832942	+	0.553361i	$0.186655\pi$
$572$	6.93805	−	19.0621i	0.290095	−	0.797029i
$573$	9.77986	+	1.72445i	0.408560	+	0.0720401i
$574$	0.935706	+	0.164990i	0.0390556	+	0.00688656i
$575$	−1.58775	+	4.36230i	−0.0662136	+	0.181920i
$576$	0.500000	−	0.419550i	0.0208333	−	0.0174812i
$577$	27.0708	+	32.2617i	1.12697	+	1.34307i	0.932083	+	0.362246i	$0.117990\pi$
$577$	27.0708	+	32.2617i	1.12697	+	1.34307i	0.194888	+	0.980825i	$0.437566\pi$
$578$	25.2782	+	14.5944i	1.05143	+	0.607045i
$579$	−10.9951	−	30.2087i	−0.456940	−	1.25543i
$580$	0.777594	+	4.40996i	0.0322879	+	0.183114i
$581$	−1.54128	−	2.66958i	−0.0639433	−	0.110753i
$582$	1.83412	−	3.17678i	0.0760266	−	0.131682i
$583$	−46.1201	−	16.7864i	−1.91010	−	0.695220i
$584$	−6.30110	+	3.63794i	−0.260741	+	0.150539i
$585$	7.19078	+	6.03378i	0.297302	+	0.249466i
$586$		−	8.79957i		−	0.363507i
$587$	−26.6651	+	31.7782i	−1.10059	+	1.31163i	−0.154398	+	0.988009i	$0.549344\pi$
$587$	−26.6651	+	31.7782i	−1.10059	+	1.31163i	−0.946188	+	0.323618i	$0.895101\pi$
$588$	10.0203	−	3.64708i	0.413229	−	0.150403i
$589$	−3.67482	+	20.8409i	−0.151418	+	0.858735i
$590$	−12.7247	+	2.24370i	−0.523867	+	0.0923718i
$591$	2.54035			0.104496
$592$	5.78360	−	1.88414i	0.237704	−	0.0774378i
$593$	−29.6746			−1.21859			−0.609295	−	0.792944i	$-0.708548\pi$
$593$	−29.6746			−1.21859			−0.609295	+	0.792944i	$0.708548\pi$
$594$	23.9380	−	4.22092i	0.982189	−	0.173186i
$595$	−0.726682	+	4.12122i	−0.0297910	+	0.168953i
$596$	12.0754	−	4.39509i	0.494628	−	0.180030i
$597$	−7.11013	+	8.47352i	−0.290998	+	0.346798i
$598$		−	4.83691i		−	0.197796i
$599$	−3.43909	−	2.88574i	−0.140517	−	0.117908i	0.569820	−	0.821770i	$-0.307013\pi$
$599$	−3.43909	−	2.88574i	−0.140517	−	0.117908i	−0.710337	+	0.703862i	$0.751457\pi$
$600$	−5.94735	+	3.43370i	−0.242799	+	0.140180i
$601$	13.3480	+	4.85827i	0.544476	+	0.198173i	0.599590	−	0.800307i	$-0.295330\pi$
$601$	13.3480	+	4.85827i	0.544476	+	0.198173i	−0.0551145	+	0.998480i	$0.517552\pi$
$602$	−0.0399893	+	0.0692636i	−0.00162984	+	0.00282297i
$603$	2.84284	+	4.92394i	0.115769	+	0.200518i
$604$	−0.900597	−	5.10754i	−0.0366448	−	0.207823i
$605$	−8.28433	−	22.7610i	−0.336806	−	0.925367i
$606$	−14.5460	−	8.39814i	−0.590891	−	0.341151i
$607$	−16.2460	−	19.3612i	−0.659405	−	0.785848i	0.327895	−	0.944714i	$-0.393661\pi$
$607$	−16.2460	−	19.3612i	−0.659405	−	0.785848i	−0.987300	+	0.158866i	$0.949216\pi$
$608$	−3.17339	+	2.66279i	−0.128698	+	0.107991i
$609$	−0.152373	+	0.418641i	−0.00617445	+	0.0169642i
$610$	−31.9335	−	5.63073i	−1.29295	−	0.227982i
$611$	−37.7585	−	6.65785i	−1.52755	−	0.269348i
$612$	1.51718	−	4.16840i	0.0613282	−	0.168498i
$613$	1.12722	−	0.945851i	0.0455280	−	0.0382025i	−0.619740	−	0.784807i	$-0.712762\pi$
$613$	1.12722	−	0.945851i	0.0455280	−	0.0382025i	0.665268	+	0.746605i	$0.268317\pi$
$614$	15.7188	+	18.7330i	0.634360	+	0.756001i
$615$	19.4140	+	11.2087i	0.782846	+	0.451977i
$616$	−0.297055	−	0.816153i	−0.0119687	−	0.0328837i
$617$	−2.72180	−	15.4361i	−0.109575	−	0.621433i	−0.989294	−	0.145938i	$-0.953380\pi$
$617$	−2.72180	−	15.4361i	−0.109575	−	0.621433i	0.879718	−	0.475495i	$-0.157731\pi$
$618$	12.0542	+	20.8784i	0.484890	+	0.839854i
$619$	−20.1519	+	34.9042i	−0.809974	+	1.40292i	0.102907	+	0.994691i	$0.467186\pi$
$619$	−20.1519	+	34.9042i	−0.809974	+	1.40292i	−0.912881	+	0.408226i	$0.866148\pi$
$620$	−14.7822	−	5.38029i	−0.593669	−	0.216078i
$621$	5.01938	−	2.89794i	0.201421	−	0.116290i
$622$	−0.00972517	−	0.00816038i	−0.000389944	−	0.000327202i
$623$			0.642736i			0.0257507i
$624$	4.59938	−	5.48132i	0.184122	−	0.219429i
$625$	25.6726	−	9.34405i	1.02690	−	0.373762i
$626$	−3.03336	+	17.2031i	−0.121238	+	0.687572i
$627$	−27.1484	+	4.78699i	−1.08420	+	0.191174i
$628$	−11.9635			−0.477398
$629$	27.6380	−	30.7428i	1.10200	−	1.22580i
$630$	0.401904			0.0160122
$631$	29.0845	−	5.12838i	1.15783	−	0.204158i	0.438441	−	0.898760i	$-0.355531\pi$
$631$	29.0845	−	5.12838i	1.15783	−	0.204158i	0.719394	+	0.694602i	$0.244420\pi$
$632$	1.09320	−	6.19983i	0.0434851	−	0.246616i
$633$	6.49111	−	2.36257i	0.257999	−	0.0939038i
$634$	−1.75410	+	2.09046i	−0.0696644	+	0.0830228i
$635$		−	17.8818i		−	0.709618i
$636$	−13.2619	−	11.1280i	−0.525867	−	0.441254i
$637$	−28.1506	+	16.2528i	−1.11537	+	0.643959i
$638$	−5.93538	−	2.16030i	−0.234984	−	0.0855272i
$639$	4.62241	−	8.00626i	0.182860	−	0.316723i
$640$	−1.53967	−	2.66679i	−0.0608609	−	0.105414i
$641$	−4.14227	−	23.4920i	−0.163610	−	0.927877i	−0.950486	−	0.310767i	$-0.899414\pi$
$641$	−4.14227	−	23.4920i	−0.163610	−	0.927877i	0.786876	−	0.617111i	$-0.211697\pi$
$642$	−9.75488	−	26.8013i	−0.384994	−	1.05776i
$643$	17.4120	+	10.0528i	0.686663	+	0.396445i	0.802361	−	0.596839i	$-0.203577\pi$
$643$	17.4120	+	10.0528i	0.686663	+	0.396445i	−0.115698	+	0.993284i	$0.536910\pi$
$644$	−0.133118	−	0.158643i	−0.00524557	−	0.00625143i
$645$	−1.44552	+	1.21293i	−0.0569172	+	0.0477592i
$646$	−9.62919	+	26.4560i	−0.378855	+	1.04090i
$647$	15.3079	+	2.69919i	0.601815	+	0.106116i	0.466251	−	0.884652i	$-0.345604\pi$
$647$	15.3079	+	2.69919i	0.601815	+	0.106116i	0.135564	+	0.990769i	$0.456715\pi$
$648$	6.51536	+	1.14883i	0.255947	+	0.0451304i
$649$	6.23343	−	17.1262i	0.244683	−	0.672262i
$650$	16.0365	−	13.4562i	0.629004	−	0.527797i
$651$	−1.00599	−	1.19889i	−0.0394279	−	0.0469883i
$652$	−0.612198	−	0.353453i	−0.0239755	−	0.0138423i
$653$	1.10893	+	3.04676i	0.0433958	+	0.119229i	0.959498	−	0.281717i	$-0.0909038\pi$
$653$	1.10893	+	3.04676i	0.0433958	+	0.119229i	−0.916102	+	0.400946i	$0.868682\pi$
$654$	−0.00186852	−	0.0105969i	−7.30651e−5	−	0.000414373i
$655$	−12.8864	−	22.3199i	−0.503514	−	0.872113i
$656$	−2.37581	+	4.11502i	−0.0927596	+	0.160664i
$657$	4.46259	+	1.62425i	0.174102	+	0.0633681i
$658$	−1.42166	+	0.820793i	−0.0554219	+	0.0319978i
$659$	−10.8426	−	9.09798i	−0.422366	−	0.354407i	0.406696	−	0.913563i	$-0.366681\pi$
$659$	−10.8426	−	9.09798i	−0.422366	−	0.354407i	−0.829062	+	0.559156i	$0.811125\pi$
$660$		−	20.4918i		−	0.797644i
$661$	30.2776	−	36.0835i	1.17766	−	1.40348i	0.281614	−	0.959528i	$-0.409130\pi$
$661$	30.2776	−	36.0835i	1.17766	−	1.40348i	0.896049	−	0.443956i	$-0.146425\pi$
$662$	22.1918	−	8.07717i	0.862510	−	0.313928i
$663$	8.44442	−	47.8907i	0.327954	−	1.85992i
$664$	15.1816	−	2.67692i	0.589160	−	0.103885i
$665$	−2.55080			−0.0989157
$666$	−3.36858	−	2.10131i	−0.130530	−	0.0814240i
$667$	−1.50607			−0.0583153
$668$	−6.50943	+	1.14779i	−0.251857	+	0.0444093i
$669$	−3.62934	+	20.5830i	−0.140318	+	0.795785i
$670$	25.2064	−	9.17438i	0.973808	−	0.354437i
$671$	29.3996	−	35.0371i	1.13496	−	1.35259i
$672$		−	0.306359i		−	0.0118181i
$673$	−3.74538	−	3.14274i	−0.144374	−	0.121144i	0.567740	−	0.823208i	$-0.307818\pi$
$673$	−3.74538	−	3.14274i	−0.144374	−	0.121144i	−0.712114	+	0.702064i	$0.752262\pi$
$674$	−19.4385	+	11.2228i	−0.748742	+	0.432287i
$675$	23.5718	+	8.57943i	0.907279	+	0.330223i
$676$	−4.40599	+	7.63140i	−0.169461	+	0.293515i
$677$	−2.95124	−	5.11171i	−0.113426	−	0.196459i	0.803724	−	0.595003i	$-0.202849\pi$
$677$	−2.95124	−	5.11171i	−0.113426	−	0.196459i	−0.917149	+	0.398544i	$0.869516\pi$
$678$	−0.681770	−	3.86651i	−0.0261832	−	0.148492i
$679$	0.163746	+	0.449890i	0.00628401	+	0.0172652i
$680$	−18.1241	−	10.4640i	−0.695029	−	0.401275i
$681$	−26.8244	−	31.9680i	−1.02791	−	1.22502i
$682$	16.9976	−	14.2627i	0.650872	−	0.546147i
$683$	7.74555	−	21.2807i	0.296375	−	0.814285i	−0.698723	−	0.715392i	$-0.746248\pi$
$683$	7.74555	−	21.2807i	0.296375	−	0.814285i	0.995098	−	0.0988921i	$-0.0315299\pi$
$684$	2.66279	+	0.469523i	0.101814	+	0.0179526i
$685$	−4.78536	−	0.843787i	−0.182839	−	0.0322395i
$686$	−0.954739	+	2.62313i	−0.0364521	+	0.100151i
$687$	−2.39185	+	2.00700i	−0.0912549	+	0.0765720i
$688$	−0.257095	−	0.306394i	−0.00980167	−	0.0116812i
$689$	45.7030	+	26.3866i	1.74114	+	1.00525i
$690$	−1.67115	−	4.59144i	−0.0636195	−	0.174793i
$691$	7.27318	+	41.2483i	0.276685	+	1.56916i	0.733559	+	0.679626i	$0.237858\pi$
$691$	7.27318	+	41.2483i	0.276685	+	1.56916i	−0.456874	+	0.889531i	$0.651031\pi$
$692$	7.70082	+	13.3382i	0.292741	+	0.507042i
$693$	−0.283447	+	0.490945i	−0.0107673	+	0.0186494i
$694$	1.14183	+	0.415593i	0.0433433	+	0.0157757i
$695$	26.4644	−	15.2792i	1.00385	−	0.579574i
$696$	−1.70672	−	1.43211i	−0.0646930	−	0.0542839i
$697$			32.2930i			1.22319i
$698$	−11.4027	+	13.5892i	−0.431599	+	0.514360i
$699$	−5.59313	+	2.03573i	−0.211552	+	0.0769985i
$700$	0.155642	−	0.882688i	0.00588271	−	0.0333625i
$701$	8.72989	−	1.53931i	0.329723	−	0.0581391i	−0.00633605	−	0.999980i	$-0.502017\pi$
$701$	8.72989	−	1.53931i	0.329723	−	0.0581391i	0.336059	+	0.941841i	$0.390906\pi$
$702$	−26.1364			−0.986455
$703$	21.3797	+	13.3366i	0.806349	+	0.502998i
$704$	4.34349			0.163701
$705$	−38.1426	+	6.72557i	−1.43653	+	0.253300i
$706$	−0.278889	+	1.58166i	−0.0104961	+	0.0595265i
$707$	2.05998	−	0.749770i	0.0774734	−	0.0281980i
$708$	4.13227	−	4.92464i	0.155300	−	0.185079i
$709$			45.8415i			1.72161i	0.508931	+	0.860807i	$0.330041\pi$
$709$			45.8415i			1.72161i	−0.508931	+	0.860807i	$0.669959\pi$
$710$	−33.4115	−	28.0355i	−1.25391	−	1.05216i
$711$	−3.55857	+	2.05454i	−0.133457	+	0.0770513i
$712$	−3.02045	−	1.09935i	−0.113196	−	0.0412000i
$713$	2.64537	−	4.58191i	0.0990698	−	0.171594i
$714$	−1.04104	−	1.80314i	−0.0389601	−	0.0674809i
$715$	10.8471	+	61.5171i	0.405660	+	2.30061i
$716$	0.873650	+	2.40033i	0.0326498	+	0.0897047i
$717$	−24.6399	−	14.2258i	−0.920192	−	0.531273i
$718$	−20.5772	−	24.5229i	−0.767934	−	0.915188i
$719$	−4.97255	+	4.17246i	−0.185445	+	0.155607i	−0.730784	−	0.682609i	$-0.760845\pi$
$719$	−4.97255	+	4.17246i	−0.185445	+	0.155607i	0.545339	+	0.838215i	$0.316401\pi$
$720$	−0.687427	+	1.88869i	−0.0256189	+	0.0703873i
$721$	−3.09872	−	0.546388i	−0.115402	−	0.0203485i
$722$	1.81115	+	0.319355i	0.0674041	+	0.0118852i
$723$	−13.2771	+	36.4786i	−0.493781	+	1.35665i
$724$	−6.42556	+	5.39168i	−0.238804	+	0.200380i
$725$	−4.18987	−	4.99329i	−0.155608	−	0.185446i
$726$	10.4367	+	6.02561i	0.387341	+	0.223631i
$727$	9.11998	+	25.0569i	0.338241	+	0.929310i	0.985893	+	0.167374i	$0.0535287\pi$
$727$	9.11998	+	25.0569i	0.338241	+	0.929310i	−0.647652	+	0.761936i	$0.724249\pi$
$728$	0.162168	+	0.919700i	0.00601034	+	0.0340864i
$729$	−15.0201	−	26.0155i	−0.556299	−	0.963538i
$730$	11.2025	−	19.4033i	0.414622	−	0.718147i
$731$	−2.55435	−	0.929708i	−0.0944761	−	0.0343865i
$732$	13.9717	−	8.06659i	0.516410	−	0.298150i
$733$	−37.4593	−	31.4321i	−1.38359	−	1.16097i	−0.967862	−	0.251482i	$-0.919082\pi$
$733$	−37.4593	−	31.4321i	−1.38359	−	1.16097i	−0.415729	−	0.909489i	$-0.636473\pi$
$734$			16.0363i			0.591910i
$735$	−21.1067	+	25.1540i	−0.778532	+	0.927819i
$736$	0.973210	−	0.354220i	0.0358730	−	0.0130567i
$737$	−6.57015	+	37.2611i	−0.242014	+	1.37253i
$738$	3.05428	−	0.538551i	0.112429	−	0.0198244i
$739$	−53.7875			−1.97861			−0.989303	−	0.145878i	$-0.953399\pi$
$739$	−53.7875			−1.97861			−0.989303	+	0.145878i	$0.953399\pi$
$740$	−12.5227	+	13.9295i	−0.460343	+	0.512058i
$741$	29.6416			1.08891
$742$	2.22518	−	0.392359i	0.0816889	−	0.0144040i
$743$	−3.90547	+	22.1490i	−0.143278	+	0.812569i	0.825456	+	0.564467i	$0.190918\pi$
$743$	−3.90547	+	22.1490i	−0.143278	+	0.812569i	−0.968734	+	0.248103i	$0.920193\pi$
$744$	7.35470	−	2.67689i	0.269637	−	0.0981397i
$745$	−25.4356	+	30.3130i	−0.931889	+	1.11058i
$746$		−	1.11639i		−	0.0408738i
$747$	−7.70789	−	6.46769i	−0.282017	−	0.236640i
$748$	25.5645	−	14.7597i	0.934730	−	0.539667i
$749$	3.49800	+	1.27317i	0.127814	+	0.0465205i
$750$	−1.22102	+	2.11488i	−0.0445855	+	0.0772244i
$751$	−3.56277	−	6.17090i	−0.130007	−	0.225179i	0.793672	−	0.608346i	$-0.208167\pi$
$751$	−3.56277	−	6.17090i	−0.130007	−	0.225179i	−0.923679	+	0.383167i	$0.874833\pi$
$752$	−1.42556	−	8.08477i	−0.0519849	−	0.294821i
$753$	6.66131	+	18.3018i	0.242752	+	0.666955i
$754$	5.88169	+	3.39580i	0.214199	+	0.123668i
$755$	10.2656	+	12.2341i	0.373605	+	0.445245i
$756$	−0.857235	+	0.719305i	−0.0311773	+	0.0261609i
$757$	−1.85286	+	5.09070i	−0.0673434	+	0.185024i	−0.968799	−	0.247846i	$-0.920277\pi$
$757$	−1.85286	+	5.09070i	−0.0673434	+	0.185024i	0.901456	+	0.432871i	$0.142499\pi$
$758$	35.8874	+	6.32791i	1.30349	+	0.229840i
$759$	6.78726	+	1.19678i	0.246362	+	0.0434403i
$760$	4.36295	−	11.9871i	0.158261	−	0.434818i
$761$	19.7639	−	16.5839i	0.716440	−	0.601165i	−0.209958	−	0.977710i	$-0.567333\pi$
$761$	19.7639	−	16.5839i	0.716440	−	0.601165i	0.926398	+	0.376546i	$0.122888\pi$
$762$	5.71879	+	6.81539i	0.207170	+	0.246896i
$763$	0.00121625		0.000702202i	4.40312e−5		2.54214e-5i
$764$	−2.21691	−	6.09092i	−0.0802051	−	0.220362i
$765$	2.37199	+	13.4522i	0.0857595	+	0.486366i
$766$	−3.01543	−	5.22288i	−0.108952	−	0.188710i
$767$	−9.79838	+	16.9713i	−0.353799	+	0.612798i
$768$	1.43969	+	0.524005i	0.0519504	+	0.0189084i
$769$	−1.66740	+	0.962671i	−0.0601278	+	0.0347148i	−0.529763	−	0.848146i	$-0.677719\pi$
$769$	−1.66740	+	0.962671i	−0.0601278	+	0.0347148i	0.469635	+	0.882861i	$0.344386\pi$
$770$	2.04879	+	1.71914i	0.0738334	+	0.0619536i
$771$			6.66015i			0.239859i
$772$	−13.4875	+	16.0737i	−0.485424	+	0.578506i
$773$	−25.7461	+	9.37083i	−0.926025	+	0.337045i	−0.760633	−	0.649183i	$-0.775111\pi$
$773$	−25.7461	+	9.37083i	−0.926025	+	0.337045i	−0.165392	+	0.986228i	$0.552889\pi$
$774$	−0.0453329	+	0.257095i	−0.00162946	+	0.00924111i
$775$	22.5505	−	3.97625i	0.810036	−	0.142831i
$776$	−2.39427			−0.0859492
$777$	−1.77186	+	0.577225i	−0.0635651	+	0.0207078i
$778$	−18.8329			−0.675193
$779$	−19.3849	+	3.41807i	−0.694534	+	0.122465i
$780$	−3.82614	+	21.6991i	−0.136998	+	0.776952i
$781$	57.8105	−	21.0413i	2.06862	−	0.752918i
$782$	4.52435	−	5.39191i	0.161790	−	0.192814i
$783$			8.13809i			0.290832i
$784$	−5.33168	−	4.47381i	−0.190417	−	0.159779i
$785$	31.9043	−	18.4200i	1.13871	−	0.657437i
$786$	12.0496	+	4.38571i	0.429796	+	0.156433i
$787$	17.7666	−	30.7726i	0.633309	−	1.09692i	−0.353562	−	0.935411i	$-0.615030\pi$
$787$	17.7666	−	30.7726i	0.633309	−	1.09692i	0.986871	−	0.161512i	$-0.0516372\pi$
$788$	−0.829047	−	1.43595i	−0.0295336	−	0.0511537i
$789$	1.73232	+	9.82446i	0.0616722	+	0.349760i
$790$	6.63039	+	18.2168i	0.235899	+	0.648126i
$791$	0.443774	+	0.256213i	0.0157788	+	0.00910989i
$792$	−1.82231	−	2.17174i	−0.0647529	−	0.0771695i
$793$	−37.6736	+	31.6119i	−1.33783	+	1.12257i
$794$	9.40944	−	25.8522i	0.333928	−	0.917461i
$795$	52.5001	+	9.25719i	1.86199	+	0.328319i
$796$	7.11013	+	1.25371i	0.252012	+	0.0444365i
$797$	17.5674	−	48.2661i	0.622271	−	1.70967i	−0.0790896	−	0.996868i	$-0.525201\pi$
$797$	17.5674	−	48.2661i	0.622271	−	1.70967i	0.701360	−	0.712807i	$-0.252576\pi$
$798$	0.972199	−	0.815772i	0.0344155	−	0.0288780i
$799$	−35.8634	−	42.7404i	−1.26876	−	1.51205i
$800$	3.88185	+	2.24119i	0.137244	+	0.0792380i
$801$	0.717552	+	1.97146i	0.0253534	+	0.0696580i
$802$	−3.83278	−	21.7368i	−0.135340	−	0.767551i
$803$	15.8013	+	27.3687i	0.557617	+	0.965821i
$804$	−6.67299	+	11.5580i	−0.235338	+	0.407618i
$805$	0.599256	+	0.218111i	0.0211210	+	0.00768742i
$806$	−20.6621	+	11.9292i	−0.727790	+	0.420190i
$807$	11.6216	+	9.75169i	0.409100	+	0.343276i
$808$			10.9630i			0.385677i
$809$	10.7079	−	12.7612i	0.376470	−	0.448660i	−0.544227	−	0.838938i	$-0.683177\pi$
$809$	10.7079	−	12.7612i	0.376470	−	0.448660i	0.920697	+	0.390278i	$0.127621\pi$
$810$	−19.1439	+	6.96782i	−0.672649	+	0.244824i
$811$	−5.92190	+	33.5848i	−0.207946	+	1.17932i	0.684790	+	0.728741i	$0.259894\pi$
$811$	−5.92190	+	33.5848i	−0.207946	+	1.17932i	−0.892736	+	0.450581i	$0.851217\pi$
$812$	0.286367	−	0.0504942i	0.0100495	−	0.00177200i
$813$	−13.8272			−0.484942
$814$	−8.18375	−	25.1210i	−0.286840	−	0.880490i
$815$	2.17681			0.0762503
$816$	10.2542	−	1.80810i	0.358970	−	0.0632961i
$817$	0.287718	−	1.63173i	0.0100660	−	0.0570870i
$818$	1.33521	−	0.485977i	0.0466846	−	0.0169918i
$819$	0.391813	−	0.466944i	0.0136910	−	0.0163163i
$820$		−	14.6319i		−	0.510967i
$821$	16.5679	+	13.9021i	0.578222	+	0.485186i	0.884363	−	0.466800i	$-0.154593\pi$
$821$	16.5679	+	13.9021i	0.578222	+	0.485186i	−0.306140	+	0.951986i	$0.599038\pi$
$822$	2.09372	−	1.20881i	0.0730269	−	0.0421621i
$823$	−21.1059	−	7.68190i	−0.735704	−	0.267774i	−0.0531267	−	0.998588i	$-0.516919\pi$
$823$	−21.1059	−	7.68190i	−0.735704	−	0.267774i	−0.682577	+	0.730813i	$0.739141\pi$
$824$	7.86780	−	13.6274i	0.274088	−	0.474734i
$825$	14.9142	+	25.8322i	0.519247	+	0.899362i
$826$	0.145698	+	0.826296i	0.00506949	+	0.0287505i
$827$	−11.2613	−	30.9402i	−0.391594	−	1.07590i	−0.966274	−	0.257517i	$-0.917096\pi$
$827$	−11.2613	−	30.9402i	−0.391594	−	1.07590i	0.574680	−	0.818378i	$-0.305127\pi$
$828$	−0.585420	−	0.337992i	−0.0203447	−	0.0117460i
$829$	−11.8170	−	14.0829i	−0.410421	−	0.489121i	0.520747	−	0.853711i	$-0.325653\pi$
$829$	−11.8170	−	14.0829i	−0.410421	−	0.489121i	−0.931168	+	0.364590i	$0.881209\pi$
$830$	−36.3646	+	30.5135i	−1.26223	+	1.05914i
$831$	0.109039	−	0.299582i	0.00378252	−	0.0103924i
$832$	−4.59938	−	0.810994i	−0.159455	−	0.0281162i
$833$	−46.5832	−	8.21388i	−1.61401	−	0.284594i
$834$	−5.20006	+	14.2870i	−0.180063	+	0.494720i
$835$	15.5921	−	13.0833i	0.539586	−	0.452767i
$836$	11.5658	+	13.7836i	0.400012	+	0.476716i
$837$	−24.7585	−	14.2943i	−0.855779	−	0.494084i
$838$	4.66516	+	12.8174i	0.161155	+	0.442770i
$839$	1.94855	+	11.0508i	0.0672715	+	0.381516i	0.999792	+	0.0203984i	$0.00649345\pi$
$839$	1.94855	+	11.0508i	0.0672715	+	0.381516i	−0.932520	+	0.361117i	$0.882395\pi$
$840$	0.471694	+	0.816997i	0.0162750	+	0.0281891i
$841$	−13.4427	+	23.2834i	−0.463540	+	0.802874i
$842$	26.3093	+	9.57581i	0.906679	+	0.330004i
$843$	35.9030	−	20.7286i	1.23657	−	0.713931i
$844$	−3.45385	−	2.89812i	−0.118886	−	0.0997575i
$845$		−	27.1351i		−	0.933477i
$846$	−3.44429	+	4.10475i	−0.118417	+	0.141124i
$847$	−1.47802	+	0.537955i	−0.0507854	+	0.0184844i
$848$	−1.96217	+	11.1280i	−0.0673812	+	0.382138i
$849$	−1.22650	+	0.216266i	−0.0420935	+	0.00742223i
$850$	30.4633			1.04488
$851$	−3.88233	−	4.96126i	−0.133085	−	0.170070i
$852$	21.7003			0.743442
$853$	−0.0959745	+	0.0169229i	−0.00328610	+	0.000579429i	−0.175291	−	0.984517i	$-0.556087\pi$
$853$	−0.0959745	+	0.0169229i	−0.00328610	+	0.000579429i	0.172005	+	0.985096i	$0.444976\pi$
$854$	−0.365640	+	2.07365i	−0.0125119	+	0.0709587i
$855$	−7.82403	+	2.84772i	−0.267576	+	0.0973898i
$856$	−11.9661	+	14.2607i	−0.408994	+	0.487420i
$857$		−	27.1799i		−	0.928447i	−0.885718	−	0.464223i	$-0.846333\pi$
$857$		−	27.1799i		−	0.928447i	0.885718	−	0.464223i	$-0.153667\pi$
$858$	−23.8081	−	19.9773i	−0.812794	−	0.682015i
$859$	13.9714	−	8.06637i	0.476697	−	0.275221i	−0.242342	−	0.970191i	$-0.577916\pi$
$859$	13.9714	−	8.06637i	0.476697	−	0.275221i	0.719039	+	0.694970i	$0.244582\pi$
$860$	1.15737	+	0.421247i	0.0394659	+	0.0143644i
$861$	0.727850	−	1.26067i	0.0248051	−	0.0429637i
$862$	1.42474	+	2.46773i	0.0485270	+	0.0840512i
$863$	7.25123	+	41.1238i	0.246835	+	1.39987i	0.816193	+	0.577780i	$0.196081\pi$
$863$	7.25123	+	41.1238i	0.246835	+	1.39987i	−0.569358	+	0.822090i	$0.692808\pi$
$864$	−1.91404	−	5.25877i	−0.0651168	−	0.178907i
$865$	−41.0730	−	23.7135i	−1.39652	−	0.806283i
$866$	−20.0133	−	23.8509i	−0.680079	−	0.810487i
$867$	34.2573	−	28.7453i	1.16344	−	0.976241i
$868$	−0.349377	+	0.959906i	−0.0118586	+	0.0325813i
$869$	−26.9289	−	4.74829i	−0.913500	−	0.161075i
$870$	6.75645	+	1.19134i	0.229065	+	0.0403903i
$871$	13.9144	−	38.2296i	0.471473	−	1.29536i
$872$	−0.00538020	+	0.00451453i	−0.000182197	+	0.000152881i
$873$	1.00452	+	1.19713i	0.0339977	+	0.0405169i
$874$	3.71554	+	2.14517i	0.125680	+	0.0725613i
$875$	−0.109011	−	0.299505i	−0.00368524	−	0.0101251i
$876$	1.93571	+	10.9779i	0.0654015	+	0.370910i
$877$	−6.52496	−	11.3016i	−0.220332	−	0.381627i	0.734577	−	0.678526i	$-0.237381\pi$
$877$	−6.52496	−	11.3016i	−0.220332	−	0.381627i	−0.954909	+	0.296899i	$0.904048\pi$
$878$	14.3900	−	24.9242i	0.485638	−	0.841150i
$879$	−12.6687	−	4.61102i	−0.427304	−	0.155526i
$880$	−11.5832	+	6.68755i	−0.390469	+	0.225437i
$881$	−8.00075	−	6.71343i	−0.269552	−	0.226181i	0.497985	−	0.867186i	$-0.334073\pi$
$881$	−8.00075	−	6.71343i	−0.269552	−	0.226181i	−0.767537	+	0.641005i	$0.778518\pi$
$882$			4.54283i			0.152965i
$883$	20.7632	−	24.7446i	0.698736	−	0.832721i	−0.293647	−	0.955914i	$-0.594869\pi$
$883$	20.7632	−	24.7446i	0.698736	−	0.832721i	0.992383	+	0.123193i	$0.0393133\pi$
$884$	−29.8264	+	10.8559i	−1.00317	+	0.365125i
$885$	−3.43755	+	19.4953i	−0.115552	+	0.655329i
$886$	19.0957	−	3.36708i	0.641532	−	0.113119i
$887$	−9.33190			−0.313334			−0.156667	−	0.987651i	$-0.550075\pi$
$887$	−9.33190			−0.313334			−0.156667	+	0.987651i	$0.550075\pi$
$888$	0.318050	−	9.31390i	0.0106731	−	0.312554i
$889$	−1.16118			−0.0389448
$890$	9.74756	−	1.71876i	0.326739	−	0.0576129i
$891$	4.98994	−	28.2994i	0.167169	−	0.948065i
$892$	12.8191	−	4.66579i	0.429217	−	0.156222i
$893$	21.8602	−	26.0520i	0.731523	−	0.871796i
$894$		−	19.6879i		−	0.658463i
$895$	−6.02557	−	5.05606i	−0.201413	−	0.169005i
$896$	−0.173172	+	0.0999810i	−0.00578527	+	0.00334013i
$897$	−6.96367	−	2.53457i	−0.232510	−	0.0846268i
$898$	−8.53997	+	14.7917i	−0.284983	+	0.493604i
$899$	3.71441	+	6.43354i	0.123882	+	0.214571i
$900$	−0.508036	−	2.88122i	−0.0169345	−	0.0960406i
$901$	26.2655	+	72.1639i	0.875031	+	2.40413i
$902$	17.8735	+	10.3193i	0.595123	+	0.343594i
$903$	0.0787636	+	0.0938668i	0.00262109	+	0.00312369i
$904$	−1.96308	+	1.64722i	−0.0652910	+	0.0547857i
$905$	8.83420	−	24.2718i	0.293659	−	0.806821i
$906$	−7.82520	−	1.37979i	−0.259975	−	0.0458406i
$907$	31.2512	+	5.51042i	1.03768	+	0.182971i	0.666433	−	0.745565i	$-0.267820\pi$
$907$	31.2512	+	5.51042i	1.03768	+	0.182971i	0.371244	+	0.928535i	$0.378931\pi$
$908$	−9.31600	+	25.5955i	−0.309162	+	0.849417i
$909$	5.48150	−	4.59952i	0.181810	−	0.152557i
$910$	−1.84851	−	2.20296i	−0.0612774	−	0.0730276i
$911$	40.7663	+	23.5364i	1.35065	+	0.779797i	0.988340	−	0.152262i	$-0.0486558\pi$
$911$	40.7663	+	23.5364i	1.35065	+	0.779797i	0.362307	+	0.932059i	$0.381989\pi$
$912$	2.17073	+	5.96403i	0.0718801	+	0.197489i
$913$	−11.6272	−	65.9410i	−0.384803	−	2.18233i
$914$	1.20827	+	2.09279i	0.0399661	+	0.0692233i
$915$	−24.8398	+	43.0238i	−0.821179	+	1.42232i
$916$	1.91506	+	0.697025i	0.0632754	+	0.0230304i
$917$	−1.44938	+	0.836799i	−0.0478627	+	0.0276335i
$918$	−29.1354	−	24.4475i	−0.961610	−	0.806887i
$919$		−	36.4389i		−	1.20201i	−0.799246	−	0.601004i	$-0.794767\pi$
$919$		−	36.4389i		−	1.20201i	0.799246	−	0.601004i	$-0.205233\pi$
$920$	−2.04997	+	2.44306i	−0.0675854	+	0.0805452i
$921$	35.2065	−	12.8141i	1.16009	−	0.422239i
$922$	3.25416	−	18.4553i	0.107170	−	0.607792i
$923$	−65.1451	+	11.4868i	−2.14428	+	0.378094i
$924$	−1.33067			−0.0437758
$925$	5.64817	−	26.6738i	0.185711	−	0.877029i
$926$	−5.15947			−0.169551
$927$	−10.1147	+	1.78349i	−0.332209	+	0.0585774i
$928$	−0.252519	+	1.43211i	−0.00828935	+	0.0470112i
$929$	−32.2285	+	11.7302i	−1.05738	+	0.384856i	−0.811444	−	0.584430i	$-0.801318\pi$
$929$	−32.2285	+	11.7302i	−1.05738	+	0.384856i	−0.245938	+	0.969285i	$0.579096\pi$
$930$	−15.4919	+	18.4626i	−0.508000	+	0.605411i
$931$		−	28.8324i		−	0.944943i
$932$	2.97604	+	2.49720i	0.0974835	+	0.0817984i
$933$	−0.0168445	+	0.00972517i	−0.000551464	+	0.000318388i
$934$	29.0660	+	10.5792i	0.951070	+	0.346161i
$935$	−45.4501	+	78.7219i	−1.48638	+	2.57448i
$936$	1.52417	+	2.63994i	0.0498191	+	0.0862892i
$937$	−0.945344	−	5.36131i	−0.0308830	−	0.175146i	0.965465	−	0.260533i	$-0.0838984\pi$
$937$	−0.945344	−	5.36131i	−0.0308830	−	0.175146i	−0.996348	+	0.0853870i	$0.972787\pi$
$938$	−0.595752	−	1.63681i	−0.0194520	−	0.0534439i
$939$	23.1776	+	13.3816i	0.756373	+	0.436692i
$940$	16.2496	+	19.3655i	0.530003	+	0.631633i
$941$	−30.6634	+	25.7296i	−0.999598	+	0.838762i	−0.986929	−	0.161157i	$-0.948477\pi$
$941$	−30.6634	+	25.7296i	−0.999598	+	0.838762i	−0.0126693	+	0.999920i	$0.504033\pi$
$942$	−6.26896	+	17.2238i	−0.204254	+	0.561183i
$943$	4.84633	+	0.854539i	0.157818	+	0.0278276i
$944$	−4.13227	−	0.728630i	−0.134494	−	0.0237149i
$945$	1.17857	−	3.23810i	0.0383389	−	0.105335i
$946$	−1.33082	+	1.11669i	−0.0432687	+	0.0363068i
$947$	−22.5711	−	26.8992i	−0.733462	−	0.874106i	0.262402	−	0.964959i	$-0.415485\pi$
$947$	−22.5711	−	26.8992i	−0.733462	−	0.874106i	−0.995864	+	0.0908522i	$0.971041\pi$
$948$	−8.35301	−	4.82261i	−0.271293	−	0.156631i
$949$	−11.6221	−	31.9315i	−0.377269	−	1.03654i
$950$	3.22440	+	18.2865i	0.104613	+	0.593292i
$951$	2.09046	+	3.62078i	0.0677878	+	0.117412i
$952$	−0.679493	+	1.17692i	−0.0220225	+	0.0381441i
$953$	8.48235	+	3.08732i	0.274770	+	0.100008i	0.475730	−	0.879591i	$-0.342184\pi$
$953$	8.48235	+	3.08732i	0.274770	+	0.100008i	−0.200960	+	0.979599i	$0.564406\pi$
$954$	6.38723	−	3.68767i	0.206794	−	0.119393i
$955$	15.2901	+	12.8299i	0.494775	+	0.415166i
$956$			18.5705i			0.600613i
$957$	−6.22034	+	7.41311i	−0.201075	+	0.239632i
$958$	−12.1017	+	4.40464i	−0.390987	+	0.142307i
$959$	−0.0547926	+	0.310744i	−0.00176934	+	0.0100344i
$960$	−4.64616	+	0.819243i	−0.149954	+	0.0264410i
$961$	4.90299			0.158161
$962$	3.97542	+	28.1290i	0.128173	+	0.906915i
$963$	12.1507			0.391552
$964$	24.9528	−	4.39985i	0.803676	−	0.141710i
$965$	11.2200	−	63.6316i	0.361183	−	2.04837i
$966$	−0.298152	+	0.108518i	−0.00959289	+	0.00349153i
$967$	24.9706	−	29.7588i	0.802999	−	0.956977i	−0.196725	−	0.980459i	$-0.563031\pi$
$967$	24.9706	−	29.7588i	0.802999	−	0.956977i	0.999724	+	0.0234813i	$0.00747501\pi$
$968$		−	7.86588i		−	0.252819i
$969$	33.0427	+	27.7262i	1.06149	+	0.890692i
$970$	6.38502	−	3.68639i	0.205011	−	0.118363i
$971$	24.8643	+	9.04986i	0.797933	+	0.290424i	0.708630	−	0.705581i	$-0.249314\pi$
$971$	24.8643	+	9.04986i	0.797933	+	0.290424i	0.0893032	+	0.996004i	$0.471536\pi$
$972$	−3.32635	+	5.76141i	−0.106693	+	0.184797i
$973$	−0.992179	−	1.71850i	−0.0318078	−	0.0550927i
$974$	−2.99719	−	16.9979i	−0.0960361	−	0.544648i
$975$	−10.9696	−	30.1388i	−0.351309	−	0.965214i
$976$	−9.11941	−	5.26509i	−0.291905	−	0.168531i
$977$	35.4829	+	42.2869i	1.13520	+	1.35288i	0.927120	+	0.374765i	$0.122277\pi$
$977$	35.4829	+	42.2869i	1.13520	+	1.35288i	0.208079	+	0.978112i	$0.433279\pi$
$978$	−0.829659	+	0.696166i	−0.0265296	+	0.0222609i
$979$	−4.77503	+	13.1193i	−0.152611	+	0.419294i
$980$	21.1067	+	3.72168i	0.674229	+	0.118885i
$981$	0.00451453		0.000796033i	0.000144138		2.54154e-5i
$982$	5.85081	−	16.0750i	0.186707	−	0.512973i
$983$	−22.7515	+	19.0908i	−0.725661	+	0.608902i	−0.928945	−	0.370218i	$-0.879283\pi$
$983$	−22.7515	+	19.0908i	−0.725661	+	0.608902i	0.203284	+	0.979120i	$0.434838\pi$
$984$	4.67942	+	5.57672i	0.149175	+	0.177779i
$985$	4.42179	+	2.55292i	0.140890	+	0.0813429i
$986$	3.38021	+	9.28706i	0.107648	+	0.295760i
$987$	0.436735	+	2.47685i	0.0139014	+	0.0788389i
$988$	−9.67359	−	16.7551i	−0.307758	−	0.533052i
$989$	−0.207118	+	0.358739i	−0.00658597	+	0.0114072i
$990$	8.20350	+	2.98583i	0.260724	+	0.0948959i
$991$	−17.4731	+	10.0881i	−0.555050	+	0.320458i	−0.751156	−	0.660124i	$-0.770504\pi$
$991$	−17.4731	+	10.0881i	−0.555050	+	0.320458i	0.196106	+	0.980583i	$0.437170\pi$
$992$	−3.91336	−	3.28370i	−0.124249	−	0.104257i
$993$		−	36.1819i		−	1.14820i
$994$	−1.82053	+	2.16962i	−0.0577437	+	0.0688162i
$995$	−20.8915	+	7.60390i	−0.662306	+	0.241060i
$996$	4.10128	−	23.2595i	0.129954	−	0.737007i
$997$	36.4291	−	6.42343i	1.15372	−	0.203432i	0.436121	−	0.899888i	$-0.356352\pi$
$997$	36.4291	−	6.42343i	1.15372	−	0.203432i	0.717599	+	0.696456i	$0.245241\pi$
$998$	18.5412			0.586913
$999$	−26.8083	+	20.9783i	−0.848177	+	0.663724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.h.a.65.1	yes	12
3.2	odd	2		666.2.bj.c.361.2		12
4.3	odd	2		592.2.bq.b.65.1		12
37.2	odd	36		2738.2.a.r.1.6		6
37.4	even	18	inner	74.2.h.a.41.1	✓	12
37.35	odd	36		2738.2.a.s.1.5		6
111.41	odd	18		666.2.bj.c.559.2		12
148.115	odd	18		592.2.bq.b.337.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.41.1	✓	12	37.4	even	18	inner
74.2.h.a.65.1	yes	12	1.1	even	1	trivial
592.2.bq.b.65.1		12	4.3	odd	2
592.2.bq.b.337.1		12	148.115	odd	18
666.2.bj.c.361.2		12	3.2	odd	2
666.2.bj.c.559.2		12	111.41	odd	18
2738.2.a.r.1.6		6	37.2	odd	36
2738.2.a.s.1.5		6	37.35	odd	36

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.266044 + 1.50881i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.97937 + 2.35892i) q^{5} -1.53209i q^{6} +(0.153180 + 0.128533i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.613341 + 0.223238i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.266044 + 1.50881i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.97937 + 2.35892i) q^{5} -1.53209i q^{6} +(0.153180 + 0.128533i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.613341 + 0.223238i) q^{9} +(1.53967 - 2.66679i) q^{10} +(2.17174 + 3.76157i) q^{11} +(0.266044 + 1.50881i) q^{12} +(-1.59735 - 4.38867i) q^{13} +(-0.173172 - 0.0999810i) q^{14} +(-3.03256 - 3.61407i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.32445 - 6.38637i) q^{17} +(-0.642788 - 0.113341i) q^{18} +(4.07964 + 0.719350i) q^{19} +(-1.05320 + 2.89364i) q^{20} +(-0.234685 + 0.196924i) q^{21} +(-2.79194 - 3.32730i) q^{22} +(-0.896915 - 0.517834i) q^{23} +(-0.524005 - 1.43969i) q^{24} +(-0.778357 - 4.41428i) q^{25} +(2.33516 + 4.04462i) q^{26} +(-2.79813 + 4.84651i) q^{27} +(0.187903 + 0.0683910i) q^{28} +(1.25937 - 0.727100i) q^{29} +(3.61407 + 3.03256i) q^{30} +5.10852i q^{31} +(-0.642788 + 0.766044i) q^{32} +(-6.25329 + 2.27601i) q^{33} +(-1.18015 + 6.69298i) q^{34} +(-0.606398 + 0.106924i) q^{35} +0.652704 q^{36} +(5.64160 + 2.27429i) q^{37} -4.14257 q^{38} +(7.04665 - 1.24252i) q^{39} +(0.534723 - 3.03256i) q^{40} +(-4.46505 + 1.62515i) q^{41} +(0.196924 - 0.234685i) q^{42} -0.399970i q^{43} +(3.32730 + 2.79194i) q^{44} +(-1.74063 + 1.00495i) q^{45} +(0.973210 + 0.354220i) q^{46} +(4.10475 - 7.10963i) q^{47} +(0.766044 + 1.32683i) q^{48} +(-1.20859 - 6.85428i) q^{49} +(1.53306 + 4.21206i) q^{50} +(9.01743 + 5.20621i) q^{51} +(-3.00203 - 3.57768i) q^{52} +(-8.65606 + 7.26330i) q^{53} +(1.91404 - 5.25877i) q^{54} +(-13.1719 - 2.32256i) q^{55} +(-0.196924 - 0.0347230i) q^{56} +(-2.17073 + 5.96403i) q^{57} +(-1.11398 + 0.934742i) q^{58} +(-2.69714 - 3.21433i) q^{59} +(-4.08576 - 2.35892i) q^{60} +(-3.60153 - 9.89514i) q^{61} +(-0.887086 - 5.03091i) q^{62} +(0.0652579 + 0.113030i) q^{63} +(0.500000 - 0.866025i) q^{64} +(13.5143 + 4.91879i) q^{65} +(5.76306 - 3.32730i) q^{66} +(6.67299 + 5.59930i) q^{67} -6.79623i q^{68} +(1.01993 - 1.21551i) q^{69} +(0.578618 - 0.210600i) q^{70} +(2.45953 - 13.9487i) q^{71} +(-0.642788 + 0.113341i) q^{72} +7.27588 q^{73} +(-5.95081 - 1.26008i) q^{74} +6.86740 q^{75} +(4.07964 - 0.719350i) q^{76} +(-0.150819 + 0.855337i) q^{77} +(-6.72384 + 2.44728i) q^{78} +(-4.04665 + 4.82261i) q^{79} +3.07935i q^{80} +(-5.06805 - 4.25260i) q^{81} +(4.11502 - 2.37581i) q^{82} +(-14.4861 - 5.27251i) q^{83} +(-0.153180 + 0.265315i) q^{84} +(10.4640 + 18.1241i) q^{85} +(0.0694540 + 0.393893i) q^{86} +(0.762009 + 2.09360i) q^{87} +(-3.76157 - 2.17174i) q^{88} +(2.06611 + 2.46229i) q^{89} +(1.53967 - 1.29194i) q^{90} +(0.319409 - 0.877568i) q^{91} +(-1.01993 - 0.179842i) q^{92} +(-7.70781 - 1.35909i) q^{93} +(-2.80781 + 7.71440i) q^{94} +(-9.77198 + 8.19967i) q^{95} +(-0.984808 - 1.17365i) q^{96} +(2.07350 + 1.19713i) q^{97} +(2.38047 + 6.54027i) q^{98} +(0.492294 + 2.79194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Introduction

L-functions

Modular forms

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