LMFDB - Embedded newform 380.2.bb.a.59.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.20
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.594291 - 1.28328i) q^{2} +(0.300395 - 0.357997i) q^{3} +(-1.29364 + 1.52529i) q^{4} +(0.218254 + 2.22539i) q^{5} +(-0.637934 - 0.172738i) q^{6} +(-1.68031 - 2.91038i) q^{7} +(2.72617 + 0.753640i) q^{8} +(0.483020 + 2.73934i) q^{9} +O(q^{10})$	\(q+(-0.594291 - 1.28328i) q^{2} +(0.300395 - 0.357997i) q^{3} +(-1.29364 + 1.52529i) q^{4} +(0.218254 + 2.22539i) q^{5} +(-0.637934 - 0.172738i) q^{6} +(-1.68031 - 2.91038i) q^{7} +(2.72617 + 0.753640i) q^{8} +(0.483020 + 2.73934i) q^{9} +(2.72610 - 1.60261i) q^{10} +(0.107274 + 0.0619346i) q^{11} +(0.157446 + 0.921308i) q^{12} +(4.63813 - 3.89185i) q^{13} +(-2.73626 + 3.88593i) q^{14} +(0.862246 + 0.590363i) q^{15} +(-0.653006 - 3.94634i) q^{16} +(5.27335 + 0.929834i) q^{17} +(3.22830 - 2.24782i) q^{18} +(4.35738 - 0.115147i) q^{19} +(-3.67670 - 2.54595i) q^{20} +(-1.54667 - 0.272719i) q^{21} +(0.0157278 - 0.174470i) q^{22} +(2.96562 + 1.07940i) q^{23} +(1.08873 - 0.749573i) q^{24} +(-4.90473 + 0.971402i) q^{25} +(-7.75075 - 3.63914i) q^{26} +(2.33994 + 1.35096i) q^{27} +(6.61288 + 1.20202i) q^{28} +(3.07901 - 0.542912i) q^{29} +(0.245178 - 1.45735i) q^{30} +(3.24345 + 5.61782i) q^{31} +(-4.67620 + 3.18326i) q^{32} +(0.0543970 - 0.0197989i) q^{33} +(-1.94066 - 7.31980i) q^{34} +(6.11001 - 4.37455i) q^{35} +(-4.80314 - 2.80697i) q^{36} -4.80607 q^{37} +(-2.73732 - 5.52332i) q^{38} -2.82953i q^{39} +(-1.08214 + 6.23129i) q^{40} +(1.73589 - 2.06876i) q^{41} +(0.569194 + 2.14689i) q^{42} +(-11.3069 + 4.11538i) q^{43} +(-0.233242 + 0.0835027i) q^{44} +(-5.99069 + 1.67278i) q^{45} +(-0.377267 - 4.44721i) q^{46} +(-1.96698 - 11.1553i) q^{47} +(-1.60894 - 0.951687i) q^{48} +(-2.14689 + 3.71852i) q^{49} +(4.16142 + 5.71687i) q^{50} +(1.91697 - 1.60853i) q^{51} +(-0.0638607 + 12.1091i) q^{52} +(-0.110513 - 0.0402236i) q^{53} +(0.343067 - 3.80567i) q^{54} +(-0.114416 + 0.252244i) q^{55} +(-2.38744 - 9.20056i) q^{56} +(1.26771 - 1.59452i) q^{57} +(-2.52653 - 3.62859i) q^{58} +(-0.756119 + 4.28817i) q^{59} +(-2.01591 + 0.551459i) q^{60} +(-6.90121 - 2.51183i) q^{61} +(5.28171 - 7.50089i) q^{62} +(7.16091 - 6.00872i) q^{63} +(6.86405 + 4.10911i) q^{64} +(9.67318 + 9.47223i) q^{65} +(-0.0577353 - 0.0580405i) q^{66} +(1.55757 - 0.274642i) q^{67} +(-8.24007 + 6.84051i) q^{68} +(1.27728 - 0.737438i) q^{69} +(-9.24491 - 5.24112i) q^{70} +(2.80683 - 1.02160i) q^{71} +(-0.747681 + 7.83195i) q^{72} +(-4.12772 + 4.91923i) q^{73} +(2.85620 + 6.16755i) q^{74} +(-1.12560 + 2.04768i) q^{75} +(-5.46123 + 6.79521i) q^{76} -0.416278i q^{77} +(-3.63109 + 1.68156i) q^{78} +(8.67515 + 7.27931i) q^{79} +(8.63962 - 2.31450i) q^{80} +(-6.65500 + 2.42222i) q^{81} +(-3.68643 - 0.998202i) q^{82} +(3.57061 + 6.18447i) q^{83} +(2.41680 - 2.00631i) q^{84} +(-0.918314 + 11.9382i) q^{85} +(12.0008 + 12.0642i) q^{86} +(0.730558 - 1.26536i) q^{87} +(0.245771 + 0.249691i) q^{88} +(-2.78066 - 3.31386i) q^{89} +(5.70686 + 6.69363i) q^{90} +(-19.1203 - 6.95921i) q^{91} +(-5.48283 + 3.12708i) q^{92} +(2.98548 + 0.526421i) q^{93} +(-13.1465 + 9.15370i) q^{94} +(1.20726 + 9.67174i) q^{95} +(-0.265108 + 2.63030i) q^{96} +(1.90434 - 10.8000i) q^{97} +(6.04779 + 0.545186i) q^{98} +(-0.117845 + 0.323776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$

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 $

$2$	−0.594291	−	1.28328i	−0.420227	−	0.907419i
$2$	−0.594291	−	1.28328i	−0.420227	−	0.907419i
$3$	0.300395	−	0.357997i	0.173433	−	0.206690i	−0.672325	−	0.740256i	$-0.734704\pi$
$3$	0.300395	−	0.357997i	0.173433	−	0.206690i	0.845758	+	0.533566i	$0.179149\pi$
$4$	−1.29364	+	1.52529i	−0.646819	+	0.762644i
$5$	0.218254	+	2.22539i	0.0976062	+	0.995225i
$5$	0.218254	+	2.22539i	0.0976062	+	0.995225i
$6$	−0.637934	−	0.172738i	−0.260436	−	0.0705201i
$7$	−1.68031	−	2.91038i	−0.635098	−	1.10002i	−0.986494	−	0.163795i	$-0.947627\pi$
$7$	−1.68031	−	2.91038i	−0.635098	−	1.10002i	0.351397	−	0.936227i	$-0.385707\pi$
$8$	2.72617	+	0.753640i	0.963848	+	0.266452i
$9$	0.483020	+	2.73934i	0.161007	+	0.913114i
$10$	2.72610	−	1.60261i	0.862069	−	0.506790i
$11$	0.107274	+	0.0619346i	0.0323443	+	0.0186740i	0.516085	−	0.856537i	$-0.327389\pi$
$11$	0.107274	+	0.0619346i	0.0323443	+	0.0186740i	−0.483741	+	0.875211i	$0.660722\pi$
$12$	0.157446	+	0.921308i	0.0454508	+	0.265959i
$13$	4.63813	−	3.89185i	1.28638	−	1.07941i	0.294055	−	0.955789i	$-0.404995\pi$
$13$	4.63813	−	3.89185i	1.28638	−	1.07941i	0.992330	−	0.123616i	$-0.0394492\pi$
$14$	−2.73626	+	3.88593i	−0.731295	+	1.03856i
$15$	0.862246	+	0.590363i	0.222631	+	0.152431i
$16$	−0.653006	−	3.94634i	−0.163252	−	0.986584i
$17$	5.27335	+	0.929834i	1.27898	+	0.225518i	0.771545	−	0.636175i	$-0.219484\pi$
$17$	5.27335	+	0.929834i	1.27898	+	0.225518i	0.507431	+	0.861693i	$0.330595\pi$
$18$	3.22830	−	2.24782i	0.760918	−	0.529816i
$19$	4.35738	−	0.115147i	0.999651	−	0.0264166i
$19$	4.35738	−	0.115147i	0.999651	−	0.0264166i
$20$	−3.67670	−	2.54595i	−0.822136	−	0.569291i
$21$	−1.54667	−	0.272719i	−0.337510	−	0.0595122i
$22$	0.0157278	−	0.174470i	0.00335319	−	0.0371972i
$23$	2.96562	+	1.07940i	0.618374	+	0.225070i	0.632163	−	0.774835i	$-0.282167\pi$
$23$	2.96562	+	1.07940i	0.618374	+	0.225070i	−0.0137891	+	0.999905i	$0.504389\pi$
$24$	1.08873	−	0.749573i	0.222236	−	0.153006i
$25$	−4.90473	+	0.971402i	−0.980946	+	0.194280i
$26$	−7.75075	−	3.63914i	−1.52005	−	0.713695i
$27$	2.33994	+	1.35096i	0.450321	+	0.259993i
$28$	6.61288	+	1.20202i	1.24972	+	0.227161i
$29$	3.07901	−	0.542912i	0.571757	−	0.100816i	0.119708	−	0.992809i	$-0.461804\pi$
$29$	3.07901	−	0.542912i	0.571757	−	0.100816i	0.452049	+	0.891993i	$0.350693\pi$
$30$	0.245178	−	1.45735i	0.0447632	−	0.266075i
$31$	3.24345	+	5.61782i	0.582541	+	1.00899i	0.995177	+	0.0980944i	$0.0312747\pi$
$31$	3.24345	+	5.61782i	0.582541	+	1.00899i	−0.412636	+	0.910896i	$0.635392\pi$
$32$	−4.67620	+	3.18326i	−0.826643	+	0.562727i
$33$	0.0543970	−	0.0197989i	0.00946931	−	0.00344655i
$34$	−1.94066	−	7.31980i	−0.332821	−	1.25534i
$35$	6.11001	−	4.37455i	1.03278	−	0.739434i
$36$	−4.80314	−	2.80697i	−0.800523	−	0.467828i
$37$	−4.80607			−0.790113			−0.395057	−	0.918657i	$-0.629275\pi$
$37$	−4.80607			−0.790113			−0.395057	+	0.918657i	$0.629275\pi$
$38$	−2.73732	−	5.52332i	−0.444051	−	0.896001i
$39$		−	2.82953i		−	0.453087i
$40$	−1.08214	+	6.23129i	−0.171102	+	0.985253i
$41$	1.73589	−	2.06876i	0.271101	−	0.323086i	−0.613267	−	0.789876i	$-0.710145\pi$
$41$	1.73589	−	2.06876i	0.271101	−	0.323086i	0.884368	+	0.466790i	$0.154590\pi$
$42$	0.569194	+	2.14689i	0.0878285	+	0.331272i
$43$	−11.3069	+	4.11538i	−1.72429	+	0.627589i	−0.998198	−	0.0600104i	$-0.980887\pi$
$43$	−11.3069	+	4.11538i	−1.72429	+	0.627589i	−0.726090	+	0.687600i	$0.758664\pi$
$44$	−0.233242	+	0.0835027i	−0.0351625	+	0.0125885i
$45$	−5.99069	+	1.67278i	−0.893039	+	0.249363i
$46$	−0.377267	−	4.44721i	−0.0556249	−	0.655705i
$47$	−1.96698	−	11.1553i	−0.286914	−	1.62717i	−0.698367	−	0.715739i	$-0.746090\pi$
$47$	−1.96698	−	11.1553i	−0.286914	−	1.62717i	0.411453	−	0.911431i	$-0.365021\pi$
$48$	−1.60894	−	0.951687i	−0.232230	−	0.137364i
$49$	−2.14689	+	3.71852i	−0.306698	+	0.531217i
$50$	4.16142	+	5.71687i	0.588514	+	0.808487i
$51$	1.91697	−	1.60853i	0.268429	−	0.225239i
$52$	−0.0638607	+	12.1091i	−0.00885589	+	1.67923i
$53$	−0.110513	−	0.0402236i	−0.0151802	−	0.00552513i	0.334419	−	0.942425i	$-0.391460\pi$
$53$	−0.110513	−	0.0402236i	−0.0151802	−	0.00552513i	−0.349599	+	0.936899i	$0.613682\pi$
$54$	0.343067	−	3.80567i	0.0466855	−	0.517886i
$55$	−0.114416	+	0.252244i	−0.0154278	+	0.0340126i
$56$	−2.38744	−	9.20056i	−0.319035	−	1.22948i
$57$	1.26771	−	1.59452i	0.167913	−	0.211199i
$58$	−2.52653	−	3.62859i	−0.331750	−	0.476457i
$59$	−0.756119	+	4.28817i	−0.0984383	+	0.558272i	0.895201	+	0.445663i	$0.147032\pi$
$59$	−0.756119	+	4.28817i	−0.0984383	+	0.558272i	−0.993639	+	0.112609i	$0.964079\pi$
$60$	−2.01591	+	0.551459i	−0.260252	+	0.0711930i
$61$	−6.90121	−	2.51183i	−0.883609	−	0.321607i	−0.139944	−	0.990159i	$-0.544692\pi$
$61$	−6.90121	−	2.51183i	−0.883609	−	0.321607i	−0.743665	+	0.668552i	$0.766914\pi$
$62$	5.28171	−	7.50089i	0.670778	−	0.952613i
$63$	7.16091	−	6.00872i	0.902190	−	0.757027i
$64$	6.86405	+	4.10911i	0.858007	+	0.513638i
$65$	9.67318	+	9.47223i	1.19981	+	1.17489i
$66$	−0.0577353	−	0.0580405i	−0.00710672	−	0.00714430i
$67$	1.55757	−	0.274642i	0.190288	−	0.0335529i	−0.0776919	−	0.996977i	$-0.524755\pi$
$67$	1.55757	−	0.274642i	0.190288	−	0.0335529i	0.267980	+	0.963425i	$0.413644\pi$
$68$	−8.24007	+	6.84051i	−0.999255	+	0.829534i
$69$	1.27728	−	0.737438i	0.153766	−	0.0887771i
$70$	−9.24491	−	5.24112i	−1.10498	−	0.626434i
$71$	2.80683	−	1.02160i	0.333110	−	0.121242i	−0.170050	−	0.985435i	$-0.554393\pi$
$71$	2.80683	−	1.02160i	0.333110	−	0.121242i	0.503160	+	0.864193i	$0.332171\pi$
$72$	−0.747681	+	7.83195i	−0.0881150	+	0.923004i
$73$	−4.12772	+	4.91923i	−0.483114	+	0.575752i	−0.951452	−	0.307797i	$-0.900408\pi$
$73$	−4.12772	+	4.91923i	−0.483114	+	0.575752i	0.468339	+	0.883549i	$0.344853\pi$
$74$	2.85620	+	6.16755i	0.332027	+	0.716964i
$75$	−1.12560	+	2.04768i	−0.129973	+	0.236446i
$76$	−5.46123	+	6.79521i	−0.626446	+	0.779464i
$77$		−	0.416278i		−	0.0474392i
$78$	−3.63109	+	1.68156i	−0.411140	+	0.190400i
$79$	8.67515	+	7.27931i	0.976031	+	0.818987i	0.983486	−	0.180985i	$-0.0579287\pi$
$79$	8.67515	+	7.27931i	0.976031	+	0.818987i	−0.00745528	+	0.999972i	$0.502373\pi$
$80$	8.63962	−	2.31450i	0.965939	−	0.258769i
$81$	−6.65500	+	2.42222i	−0.739445	+	0.269136i
$82$	−3.68643	−	0.998202i	−0.407098	−	0.110233i
$83$	3.57061	+	6.18447i	0.391925	+	0.678834i	0.992703	−	0.120582i	$-0.0384760\pi$
$83$	3.57061	+	6.18447i	0.391925	+	0.678834i	−0.600778	+	0.799416i	$0.705143\pi$
$84$	2.41680	−	2.00631i	0.263695	−	0.218907i
$85$	−0.918314	+	11.9382i	−0.0996051	+	1.29488i
$86$	12.0008	+	12.0642i	1.29408	+	1.30092i
$87$	0.730558	−	1.26536i	0.0783240	−	0.135661i
$88$	0.245771	+	0.249691i	0.0261993	+	0.0266171i
$89$	−2.78066	−	3.31386i	−0.294749	−	0.351268i	0.598264	−	0.801299i	$-0.295857\pi$
$89$	−2.78066	−	3.31386i	−0.294749	−	0.351268i	−0.893013	+	0.450031i	$0.851413\pi$
$90$	5.70686	+	6.69363i	0.601556	+	0.705571i
$91$	−19.1203	−	6.95921i	−2.00435	−	0.729523i
$92$	−5.48283	+	3.12708i	−0.571624	+	0.326020i
$93$	2.98548	+	0.526421i	0.309580	+	0.0545873i
$94$	−13.1465	+	9.15370i	−1.35596	+	0.944132i
$95$	1.20726	+	9.67174i	0.123863	+	0.992299i
$96$	−0.265108	+	2.63030i	−0.0270575	+	0.268454i
$97$	1.90434	−	10.8000i	0.193356	−	1.09658i	−0.721384	−	0.692536i	$-0.756494\pi$
$97$	1.90434	−	10.8000i	0.193356	−	1.09658i	0.914740	−	0.404043i	$-0.132395\pi$
$98$	6.04779	+	0.545186i	0.610919	+	0.0550721i
$99$	−0.117845	+	0.323776i	−0.0118438	+	0.0325407i
$100$	4.86327	−	8.73777i	0.486327	−	0.873777i
$101$	8.07286	−	6.77394i	0.803280	−	0.674032i	−0.145714	−	0.989327i	$-0.546548\pi$
$101$	8.07286	−	6.77394i	0.803280	−	0.674032i	0.948994	+	0.315295i	$0.102103\pi$
$102$	−3.20344	−	1.50408i	−0.317187	−	0.148926i
$103$	11.2211	+	6.47850i	1.10565	+	0.638346i	0.937698	−	0.347450i	$-0.112952\pi$
$103$	11.2211	+	6.47850i	1.10565	+	0.638346i	0.167949	+	0.985796i	$0.446286\pi$
$104$	15.5774	−	7.11439i	1.52749	−	0.697623i
$105$	0.269340	−	3.50146i	0.0262849	−	0.341708i
$106$	0.0140588	+	0.165724i	0.00136551	+	0.0160966i
$107$	−10.3559	+	5.97895i	−1.00114	+	0.578007i	−0.908585	−	0.417700i	$-0.862836\pi$
$107$	−10.3559	+	5.97895i	−1.00114	+	0.578007i	−0.0925532	+	0.995708i	$0.529503\pi$
$108$	−5.08764	+	1.82142i	−0.489558	+	0.175266i
$109$	0.337802	+	0.928104i	0.0323556	+	0.0888963i	0.954819	−	0.297189i	$-0.0960492\pi$
$109$	0.337802	+	0.928104i	0.0323556	+	0.0888963i	−0.922463	+	0.386085i	$0.873827\pi$
$110$	0.391697	−	0.00307823i	0.0373468	−	0.000293497i
$111$	−1.44372	+	1.72056i	−0.137032	+	0.163308i
$112$	−10.3881	+	8.53157i	−0.981583	+	0.806158i
$113$	−8.40598			−0.790768			−0.395384	−	0.918516i	$-0.629388\pi$
$113$	−8.40598			−0.790768			−0.395384	+	0.918516i	$0.629388\pi$
$114$	−2.79961	−	0.679229i	−0.262208	−	0.0636157i
$115$	−1.75482	+	6.83525i	−0.163638	+	0.637390i
$116$	−3.15502	+	5.39870i	−0.292936	+	0.501257i
$117$	12.9014	+	10.8256i	1.19274	+	1.00082i
$118$	5.95229	−	1.57810i	0.547953	−	0.145276i
$119$	−6.15470	−	16.9099i	−0.564200	−	1.55013i
$120$	1.90571	+	2.25926i	0.173967	+	0.206241i
$121$	−5.49233	−	9.51299i	−0.499303	−	0.864817i
$122$	0.877926	+	10.3490i	0.0794837	+	0.936952i
$123$	−0.219155	−	1.24289i	−0.0197606	−	0.112068i
$124$	−12.7646	−	2.32023i	−1.14630	−	0.208362i
$125$	−3.23223	−	10.7029i	−0.289099	−	0.957299i
$126$	−11.9666	−	5.61856i	−1.06607	−	0.500541i
$127$	−12.2881	−	14.6443i	−1.09039	−	1.29947i	−0.950984	−	0.309239i	$-0.899926\pi$
$127$	−12.2881	−	14.6443i	−1.09039	−	1.29947i	−0.139405	−	0.990235i	$-0.544519\pi$
$128$	1.19391	−	11.2505i	0.105528	−	0.994416i
$129$	−1.92325	+	5.28408i	−0.169333	+	0.465238i
$130$	6.40689	−	18.0427i	0.561921	−	1.58245i
$131$	6.09336	+	1.07442i	0.532380	+	0.0938729i	0.433374	−	0.901214i	$-0.357323\pi$
$131$	6.09336	+	1.07442i	0.532380	+	0.0938729i	0.0990053	+	0.995087i	$0.468434\pi$
$132$	−0.0401710	+	0.108584i	−0.00349644	+	0.00945100i
$133$	−7.65687	−	12.4882i	−0.663935	−	1.08286i
$134$	−1.27810	−	1.83559i	−0.110411	−	0.158571i
$135$	−2.49572	+	5.50213i	−0.214798	+	0.473548i
$136$	13.6753	+	6.50910i	1.17265	+	0.558151i
$137$	−1.29187	+	3.54938i	−0.110372	+	0.303244i	−0.982566	−	0.185917i	$-0.940475\pi$
$137$	−1.29187	+	3.54938i	−0.110372	+	0.303244i	0.872194	+	0.489161i	$0.162697\pi$
$138$	−1.70542	−	1.20086i	−0.145175	−	0.102224i
$139$	−4.33196	−	5.16262i	−0.367432	−	0.437888i	0.550374	−	0.834918i	$-0.314485\pi$
$139$	−4.33196	−	5.16262i	−0.367432	−	0.437888i	−0.917805	+	0.397030i	$0.870041\pi$
$140$	−1.23168	+	14.9786i	−0.104096	+	1.26592i
$141$	−4.58445	−	2.64683i	−0.386080	−	0.222903i
$142$	−2.97908	−	2.99483i	−0.249999	−	0.251321i
$143$	0.738590	−	0.130233i	0.0617640	−	0.0108907i
$144$	10.4950	−	3.69497i	0.874579	−	0.307914i
$145$	1.88020	+	6.73350i	0.156142	+	0.559187i
$146$	8.76584	+	2.37359i	0.725466	+	0.196440i
$147$	0.686304	+	1.88560i	0.0566054	+	0.155522i
$148$	6.21731	−	7.33064i	0.511060	−	0.602575i
$149$	12.5667	+	10.5448i	1.02951	+	0.863860i	0.990792	−	0.135391i	$-0.0432289\pi$
$149$	12.5667	+	10.5448i	1.02951	+	0.863860i	0.0387155	+	0.999250i	$0.487673\pi$
$150$	3.29669	+	0.227544i	0.269174	+	0.0185789i
$151$	−12.5228			−1.01909			−0.509544	−	0.860445i	$-0.670186\pi$
$151$	−12.5228			−1.01909			−0.509544	+	0.860445i	$0.670186\pi$
$152$	11.9658	+	2.96998i	0.970551	+	0.240897i
$153$			14.8946i			1.20416i
$154$	−0.534203	+	0.247390i	−0.0430473	+	0.0199353i
$155$	−11.7939	+	8.44406i	−0.947313	+	0.678243i
$156$	4.31585	+	3.66039i	0.345544	+	0.293065i
$157$	−1.45751	−	4.00446i	−0.116322	−	0.319591i	0.867845	−	0.496834i	$-0.165504\pi$
$157$	−1.45751	−	4.00446i	−0.116322	−	0.319591i	−0.984167	+	0.177243i	$0.943282\pi$
$158$	4.18587	−	15.4587i	0.333010	−	1.22983i
$159$	−0.0475976	+	0.0274805i	−0.00377474	+	0.00217934i
$160$	−8.10461	−	9.71161i	−0.640725	−	0.767770i
$161$	−1.84170	−	10.4448i	−0.145146	−	0.823166i
$162$	7.06340	+	7.10075i	0.554953	+	0.557888i
$163$	−5.11904	+	8.86644i	−0.400954	+	0.694474i	−0.993841	−	0.110812i	$-0.964655\pi$
$163$	−5.11904	+	8.86644i	−0.400954	+	0.694474i	0.592887	+	0.805286i	$0.297988\pi$
$164$	0.909835	+	5.32396i	0.0710461	+	0.415732i
$165$	0.0559327	+	0.116733i	0.00435435	+	0.00908769i
$166$	5.81446	−	8.25748i	0.451289	−	0.640904i
$167$	5.66187	−	15.5558i	0.438128	−	1.20375i	−0.502580	−	0.864531i	$-0.667616\pi$
$167$	5.66187	−	15.5558i	0.438128	−	1.20375i	0.940708	−	0.339217i	$-0.110162\pi$
$168$	−4.01095	−	1.90911i	−0.309452	−	0.147291i
$169$	4.10829	−	23.2993i	0.316022	−	1.79225i
$170$	15.8659	−	5.91631i	1.21686	−	0.453760i
$171$	2.42013	+	11.8807i	0.185072	+	0.908542i
$172$	8.34990	−	22.5701i	0.636674	−	1.72095i
$173$	−1.69136	+	9.59221i	−0.128592	+	0.729282i	0.850517	+	0.525947i	$0.176289\pi$
$173$	−1.69136	+	9.59221i	−0.128592	+	0.729282i	−0.979109	+	0.203335i	$0.934822\pi$
$174$	−2.05798	−	0.185520i	−0.156015	−	0.0140642i
$175$	11.0686	+	12.6424i	0.836709	+	0.955675i
$176$	0.174364	−	0.463783i	0.0131432	−	0.0349590i
$177$	1.30802	+	1.55883i	0.0983166	+	0.117169i
$178$	−2.60010	+	5.53777i	−0.194886	+	0.415073i
$179$	−7.26304	+	12.5800i	−0.542865	+	0.940270i	0.455873	+	0.890045i	$0.349327\pi$
$179$	−7.26304	+	12.5800i	−0.542865	+	0.940270i	−0.998738	+	0.0502250i	$0.984006\pi$
$180$	5.19830	−	11.3015i	0.387458	−	0.842363i
$181$	−21.1417	+	3.72785i	−1.57145	+	0.277089i	−0.890410	−	0.455159i	$-0.849583\pi$
$181$	−21.1417	+	3.72785i	−1.57145	+	0.277089i	−0.681039	+	0.732247i	$0.738471\pi$
$182$	2.43235	+	28.6725i	0.180298	+	2.12535i
$183$	−2.97232	+	1.71607i	−0.219720	+	0.126856i
$184$	7.27132	+	5.17763i	0.536049	+	0.381700i
$185$	−1.04894	−	10.6954i	−0.0771199	−	0.786340i
$186$	−1.09870	−	4.14407i	−0.0805603	−	0.303858i
$187$	0.508104	+	0.426350i	0.0371563	+	0.0311778i
$188$	19.5596	+	11.4307i	1.42653	+	0.833671i
$189$		−	9.08016i		−	0.660484i
$190$	11.6941	−	7.29709i	0.848381	−	0.529386i
$191$		−	14.5924i		−	1.05587i	−0.849285	−	0.527935i	$-0.822967\pi$
$191$		−	14.5924i		−	1.05587i	0.849285	−	0.527935i	$-0.177033\pi$
$192$	3.53298	−	1.22296i	0.254971	−	0.0882592i
$193$	−1.87190	−	1.57071i	−0.134743	−	0.113062i	0.572926	−	0.819607i	$-0.305808\pi$
$193$	−1.87190	−	1.57071i	−0.134743	−	0.113062i	−0.707668	+	0.706545i	$0.750253\pi$
$194$	−14.9913	+	3.97456i	−1.07631	+	0.285357i
$195$	6.29681	−	0.617557i	0.450924	−	0.0442241i
$196$	−2.89452	−	8.08503i	−0.206751	−	0.577502i
$197$	20.7890	−	12.0025i	1.48116	−	0.855146i	0.481384	−	0.876510i	$-0.340134\pi$
$197$	20.7890	−	12.0025i	1.48116	−	0.855146i	0.999772	+	0.0213642i	$0.00680097\pi$
$198$	0.485530	−	0.0411886i	0.0345051	−	0.00292715i
$199$	0.465640	−	0.0821049i	0.0330083	−	0.00582026i	−0.157120	−	0.987580i	$-0.550221\pi$
$199$	0.465640	−	0.0821049i	0.0330083	−	0.00582026i	0.190128	+	0.981759i	$0.439110\pi$
$200$	−14.1032	−	1.04819i	−0.997249	−	0.0741182i
$201$	0.369567	−	0.640109i	0.0260672	−	0.0451498i
$202$	−13.4905	−	6.33409i	−0.949189	−	0.445665i
$203$	−6.75377	−	8.04882i	−0.474021	−	0.564917i
$204$	−0.0263941	+	5.00478i	−0.00184795	+	0.350405i
$205$	4.98266	+	3.41153i	0.348004	+	0.238271i
$206$	1.64517	−	18.2500i	0.114624	−	1.27154i
$207$	−1.52438	+	8.64522i	−0.105952	+	0.600884i
$208$	−18.3873	−	15.7622i	−1.27493	−	1.09291i
$209$	0.474565	+	0.257520i	0.0328263	+	0.0178131i
$210$	−4.65344	+	1.73525i	−0.321118	+	0.119743i
$211$	−1.27499	+	7.23082i	−0.0877739	+	0.497791i	0.908950	+	0.416906i	$0.136886\pi$
$211$	−1.27499	+	7.23082i	−0.0877739	+	0.497791i	−0.996723	+	0.0808845i	$0.974226\pi$
$212$	0.204317	−	0.116530i	0.0140325	−	0.00800331i
$213$	0.477428	−	1.31172i	0.0327128	−	0.0898778i
$214$	13.8271	+	9.73627i	0.945200	+	0.665557i
$215$	−11.6261	−	24.2641i	−0.792894	−	1.65480i
$216$	5.36094	+	5.44643i	0.364766	+	0.370583i
$217$	10.9000	−	18.8794i	0.739941	−	1.28161i
$218$	0.990269	−	0.985060i	0.0670695	−	0.0667167i
$219$	0.521122	+	2.95543i	0.0352141	+	0.199709i
$220$	−0.236732	−	0.500829i	−0.0159605	−	0.0337659i
$221$	28.0773	−	16.2104i	1.88868	−	1.09043i
$222$	3.06596	+	0.830192i	0.205774	+	0.0557188i
$223$	−3.52244	−	9.67782i	−0.235880	−	0.648075i	−0.999996	−	0.00299548i	$-0.999047\pi$
$223$	−3.52244	−	9.67782i	−0.235880	−	0.648075i	0.764116	−	0.645079i	$-0.223176\pi$
$224$	17.1220	+	8.26066i	1.14401	+	0.551938i
$225$	−5.03008	−	12.9665i	−0.335339	−	0.864435i
$226$	4.99559	+	10.7873i	0.332302	+	0.717558i
$227$		−	9.41783i		−	0.625083i	−0.949904	−	0.312542i	$-0.898820\pi$
$227$		−	9.41783i		−	0.625083i	0.949904	−	0.312542i	$-0.101180\pi$
$228$	0.792139	+	3.99636i	0.0524607	+	0.264665i
$229$	−11.7727			−0.777959			−0.388979	−	0.921246i	$-0.627172\pi$
$229$	−11.7727			−0.777959			−0.388979	+	0.921246i	$0.627172\pi$
$230$	9.81444	−	1.81019i	0.647145	−	0.119360i
$231$	−0.149026	−	0.125048i	−0.00980521	−	0.00822755i
$232$	8.80307	+	0.840389i	0.577950	+	0.0551742i
$233$	0.145204	+	0.398944i	0.00951262	+	0.0261357i	0.944358	−	0.328919i	$-0.106684\pi$
$233$	0.145204	+	0.398944i	0.00951262	+	0.0261357i	−0.934845	+	0.355055i	$0.884462\pi$
$234$	6.22510	−	22.9897i	0.406947	−	1.50289i
$235$	24.3956	−	6.81200i	1.59140	−	0.444366i
$236$	−5.56254	−	6.70063i	−0.362091	−	0.436174i
$237$	5.21195	−	0.919007i	0.338552	−	0.0596959i
$238$	−18.0425	+	17.9476i	−1.16952	+	1.16337i
$239$	−26.0654	−	15.0489i	−1.68603	−	0.973432i	−0.957505	−	0.288416i	$-0.906872\pi$
$239$	−26.0654	−	15.0489i	−1.68603	−	0.973432i	−0.728528	−	0.685016i	$-0.759795\pi$
$240$	1.76672	−	3.78823i	0.114041	−	0.244529i
$241$	5.17036	+	6.16180i	0.333052	+	0.396916i	0.906417	−	0.422384i	$-0.138807\pi$
$241$	5.17036	+	6.16180i	0.333052	+	0.396916i	−0.573365	+	0.819300i	$0.694362\pi$
$242$	−8.94383	+	12.7017i	−0.574931	+	0.816496i
$243$	−3.90432	+	10.7270i	−0.250463	+	0.688140i
$244$	12.7589	−	7.27693i	0.816807	−	0.465858i
$245$	−8.74372	−	3.96608i	−0.558616	−	0.253384i
$246$	−1.46474	+	1.01988i	−0.0933884	+	0.0650250i
$247$	19.7619	−	17.4923i	1.25742	−	1.11301i
$248$	4.60840	+	17.7595i	0.292634	+	1.12773i
$249$	3.28662	+	0.579519i	0.208281	+	0.0367255i
$250$	−11.8140	+	10.5085i	−0.747184	+	0.664617i
$251$	1.40827	−	3.86919i	0.0888892	−	0.244221i	−0.887280	−	0.461231i	$-0.847408\pi$
$251$	1.40827	−	3.86919i	0.0888892	−	0.244221i	0.976169	+	0.217010i	$0.0696303\pi$
$252$	−0.0985961	+	18.6956i	−0.00621097	+	1.17771i
$253$	0.251282	+	0.299466i	0.0157979	+	0.0188273i
$254$	−11.4902	+	24.4721i	−0.720957	+	1.53551i
$255$	3.99799	+	3.91494i	0.250364	+	0.245163i
$256$	−15.1472	+	5.15396i	−0.946698	+	0.322123i
$257$	1.39435	+	7.90776i	0.0869773	+	0.493273i	0.996912	+	0.0785220i	$0.0250201\pi$
$257$	1.39435	+	7.90776i	0.0869773	+	0.493273i	−0.909935	+	0.414751i	$0.863869\pi$
$258$	7.92395	−	0.672206i	0.493324	−	0.0418497i
$259$	8.07569	+	13.9875i	0.501799	+	0.869141i
$260$	−26.9615	+	2.50075i	−1.67208	+	0.155090i
$261$	2.97444	+	8.17221i	0.184113	+	0.505847i
$262$	−2.24244	−	8.45804i	−0.138538	−	0.522539i
$263$	−4.76930	−	4.00192i	−0.294088	−	0.246769i	0.483791	−	0.875184i	$-0.339260\pi$
$263$	−4.76930	−	4.00192i	−0.294088	−	0.246769i	−0.777878	+	0.628415i	$0.783704\pi$
$264$	0.163217	−	0.0129795i	0.0100453	−	0.000798832i
$265$	0.0653932	−	0.254714i	0.00401707	−	0.0156470i
$266$	−11.4754	+	17.2475i	−0.703605	+	1.05751i
$267$	−2.02165			−0.123723
$268$	−1.59603	+	2.73104i	−0.0974929	+	0.166825i
$269$	−15.8691	+	18.9121i	−0.967558	+	1.15309i	0.0206212	+	0.999787i	$0.493436\pi$
$269$	−15.8691	+	18.9121i	−0.967558	+	1.15309i	−0.988179	+	0.153303i	$0.951009\pi$
$270$	8.54398	−	0.0671446i	0.519970	−	0.00408629i
$271$	6.22615	+	17.1062i	0.378212	+	1.03913i	0.972097	+	0.234578i	$0.0753709\pi$
$271$	6.22615	+	17.1062i	0.378212	+	1.03913i	−0.593886	+	0.804549i	$0.702407\pi$
$272$	0.225910	−	21.4176i	0.0136978	−	1.29863i
$273$	−8.23502	+	4.75449i	−0.498406	+	0.287755i
$274$	5.32261	−	0.451529i	0.321551	−	0.0272778i
$275$	−0.586313	−	0.199567i	−0.0353560	−	0.0120343i
$276$	−0.527531	+	2.90220i	−0.0317537	+	0.174692i
$277$	4.03598	+	2.33018i	0.242499	+	0.140007i	0.616325	−	0.787492i	$-0.288621\pi$
$277$	4.03598	+	2.33018i	0.242499	+	0.140007i	−0.373826	+	0.927499i	$0.621954\pi$
$278$	−4.05067	+	8.62723i	−0.242943	+	0.517427i
$279$	−13.8225	+	11.5984i	−0.827530	+	0.694380i
$280$	19.9538	−	7.32105i	1.19247	−	0.437516i
$281$	−6.97083	+	19.1522i	−0.415845	+	1.14252i	0.538189	+	0.842824i	$0.319109\pi$
$281$	−6.97083	+	19.1522i	−0.415845	+	1.14252i	−0.954034	+	0.299700i	$0.903114\pi$
$282$	−0.672143	+	7.45613i	−0.0400255	+	0.444006i
$283$	−2.17388	+	12.3287i	−0.129224	+	0.732864i	0.849486	+	0.527612i	$0.176912\pi$
$283$	−2.17388	+	12.3287i	−0.129224	+	0.732864i	−0.978709	+	0.205252i	$0.934199\pi$
$284$	−2.07278	+	5.60281i	−0.122997	+	0.332466i
$285$	3.82511	+	2.47315i	0.226580	+	0.146497i
$286$	−0.606064	−	0.870425i	−0.0358373	−	0.0514693i
$287$	−8.93772	−	1.57596i	−0.527577	−	0.0930261i
$288$	−10.9787	−	11.2721i	−0.646929	−	0.664216i
$289$	10.9689	+	3.99235i	0.645228	+	0.234844i
$290$	7.52361	−	6.41448i	0.441802	−	0.376671i
$291$	−3.29433	−	3.92603i	−0.193117	−	0.230148i
$292$	−2.16346	−	12.6597i	−0.126607	−	0.740851i
$293$	1.10918	−	1.92115i	0.0647987	−	0.112235i	−0.831806	−	0.555067i	$-0.812693\pi$
$293$	1.10918	−	1.92115i	0.0647987	−	0.112235i	0.896605	+	0.442832i	$0.146026\pi$
$294$	2.01190	−	2.00132i	0.117337	−	0.116719i
$295$	−9.70787	−	0.746751i	−0.565214	−	0.0434775i
$296$	−13.1022	−	3.62205i	−0.761549	−	0.210527i
$297$	0.167343	+	0.289846i	0.00971022	+	0.0168186i
$298$	6.06361	−	22.3934i	0.351256	−	1.29721i
$299$	17.9558	−	6.53537i	1.03841	−	0.377950i
$300$	−1.66719	−	4.36582i	−0.0962553	−	0.252061i
$301$	30.9764	+	25.9923i	1.78545	+	1.49817i
$302$	7.44216	+	16.0703i	0.428248	+	0.924739i
$303$		−	4.92492i		−	0.282929i
$304$	−3.29980	−	17.1205i	−0.189257	−	0.981928i
$305$	4.08360	−	15.9061i	0.233826	−	0.910781i
$306$	19.1141	−	8.85175i	1.09268	−	0.506021i
$307$	−6.48351	+	7.72675i	−0.370033	+	0.440989i	−0.918642	−	0.395091i	$-0.870713\pi$
$307$	−6.48351	+	7.72675i	−0.370033	+	0.440989i	0.548609	+	0.836079i	$0.315158\pi$
$308$	0.634943	+	0.538512i	0.0361793	+	0.0306846i
$309$	5.69005	−	2.07101i	0.323696	−	0.117816i
$310$	17.8452	+	10.1168i	1.01354	+	0.574594i
$311$	0.331975	−	0.191666i	0.0188246	−	0.0108684i	−0.490558	−	0.871408i	$-0.663207\pi$
$311$	0.331975	−	0.191666i	0.0188246	−	0.0108684i	0.509383	+	0.860540i	$0.329874\pi$
$312$	2.13245	−	7.71379i	0.120726	−	0.436708i
$313$	−22.5307	+	3.97277i	−1.27351	+	0.224554i	−0.769222	−	0.638982i	$-0.779356\pi$
$313$	−22.5307	+	3.97277i	−1.27351	+	0.224554i	−0.504287	+	0.863536i	$0.668245\pi$
$314$	−4.27268	+	4.25021i	−0.241122	+	0.239853i
$315$	14.9346	+	14.6244i	0.841472	+	0.823992i
$316$	−22.3255	+	3.81531i	−1.25591	+	0.214628i
$317$	−21.8398	+	18.3258i	−1.22665	+	1.02928i	−0.228198	+	0.973615i	$0.573283\pi$
$317$	−21.8398	+	18.3258i	−1.22665	+	1.02928i	−0.998450	+	0.0556648i	$0.982272\pi$
$318$	0.0635521	+	0.0447499i	0.00356383	+	0.00250945i
$319$	0.363922	+	0.132457i	0.0203757	+	0.00741616i
$320$	−7.64626	+	16.1720i	−0.427439	+	0.904044i
$321$	−0.970401	+	5.50342i	−0.0541625	+	0.307171i
$322$	−12.3092	+	8.57068i	−0.685962	+	0.477625i
$323$	23.0851	+	3.44443i	1.28449	+	0.191653i
$324$	4.91457	−	13.2843i	0.273032	−	0.738015i
$325$	−18.9682	+	23.5940i	−1.05217	+	1.30876i
$326$	14.4204	+	1.29994i	0.798670	+	0.0719972i
$327$	0.433733	+	0.157866i	0.0239855	+	0.00873001i
$328$	6.29145	−	4.33156i	0.347387	−	0.239170i
$329$	−29.1611	+	24.4691i	−1.60770	+	1.34902i
$330$	0.116562	−	0.141151i	0.00641652	−	0.00777011i
$331$	9.80984	−	16.9911i	0.539198	−	0.933918i	−0.459750	−	0.888048i	$-0.652061\pi$
$331$	9.80984	−	16.9911i	0.539198	−	0.933918i	0.998947	−	0.0458692i	$-0.0146057\pi$
$332$	−14.0522	−	2.55426i	−0.771213	−	0.140183i
$333$	−2.32143	−	13.1655i	−0.127213	−	0.721463i
$334$	−23.3274	+	1.97891i	−1.27642	+	0.108281i
$335$	0.951134	+	3.40627i	0.0519660	+	0.186104i
$336$	−0.0662589	+	6.28176i	−0.00361472	+	0.342698i
$337$	−8.99330	+	3.27329i	−0.489896	+	0.178308i	−0.575144	−	0.818052i	$-0.695054\pi$
$337$	−8.99330	+	3.27329i	−0.489896	+	0.178308i	0.0852479	+	0.996360i	$0.472832\pi$
$338$	−32.3411	+	8.57444i	−1.75913	+	0.466388i
$339$	−2.52512	+	3.00932i	−0.137145	+	0.163444i
$340$	−17.0212	−	16.8444i	−0.923107	−	0.913516i
$341$			0.803528i			0.0435135i
$342$	13.8081	−	10.1663i	0.746656	−	0.549732i
$343$	−9.09460			−0.491062
$344$	−33.9261	+	2.69790i	−1.82917	+	0.145461i
$345$	1.91986	+	2.68150i	0.103362	+	0.144367i
$346$	13.3147	−	3.53006i	0.715802	−	0.189777i
$347$	−8.64421	+	3.14623i	−0.464045	+	0.168899i	−0.563453	−	0.826148i	$-0.690527\pi$
$347$	−8.64421	+	3.14623i	−0.464045	+	0.168899i	0.0994077	+	0.995047i	$0.468305\pi$
$348$	0.984967	+	2.75123i	0.0527998	+	0.147482i
$349$	−14.5699	−	25.2358i	−0.779908	−	1.35084i	−0.931994	−	0.362473i	$-0.881933\pi$
$349$	−14.5699	−	25.2358i	−0.779908	−	1.35084i	0.152086	−	0.988367i	$-0.451401\pi$
$350$	9.64580	−	21.7174i	0.515590	−	1.16085i
$351$	16.1107	−	2.84075i	0.859924	−	0.151628i
$352$	−0.698789	+	0.0518627i	−0.0372456	+	0.00276429i
$353$	11.6342	+	6.71703i	0.619228	+	0.357512i	0.776568	−	0.630033i	$-0.216959\pi$
$353$	11.6342	+	6.71703i	0.619228	+	0.357512i	−0.157340	+	0.987544i	$0.550292\pi$
$354$	1.22308	−	2.60496i	0.0650062	−	0.138452i
$355$	2.88607	+	6.02333i	0.153177	+	0.319685i
$356$	8.65175	+	0.0456274i	0.458542	+	0.00241824i
$357$	−7.90253	−	2.87629i	−0.418246	−	0.152229i
$358$	20.4600	+	1.84440i	1.08135	+	0.0974793i
$359$	31.1619	+	5.49469i	1.64466	+	0.289998i	0.917877	−	0.396866i	$-0.129902\pi$
$359$	31.1619	+	5.49469i	1.64466	+	0.289998i	0.726786	+	0.686864i	$0.241013\pi$
$360$	−17.5923	+	0.0454730i	−0.927197	+	0.00239664i
$361$	18.9735	−	1.00348i	0.998604	−	0.0528147i
$362$	17.3482	+	24.9154i	0.911801	+	1.30952i
$363$	−5.05549	−	0.891420i	−0.265345	−	0.0467874i
$364$	35.3495	−	20.1612i	1.85282	−	1.05674i
$365$	−11.8481	−	8.11216i	−0.620158	−	0.424610i
$366$	3.96863	+	2.79449i	0.207444	+	0.146070i
$367$	3.00569	−	2.52207i	0.156896	−	0.131651i	−0.560960	−	0.827843i	$-0.689568\pi$
$367$	3.00569	−	2.52207i	0.156896	−	0.131651i	0.717856	+	0.696192i	$0.245124\pi$
$368$	2.32310	−	12.4082i	0.121100	−	0.646822i
$369$	6.50551	+	3.75596i	0.338663	+	0.195527i
$370$	−13.1018	+	7.70226i	−0.681132	+	0.400422i
$371$	0.0686307	+	0.389224i	0.00356313	+	0.0202075i
$372$	−4.66507	+	3.87272i	−0.241873	+	0.200791i
$373$	0.240112	+	0.415886i	0.0124325	+	0.0215337i	0.872175	−	0.489194i	$-0.162709\pi$
$373$	0.240112	+	0.415886i	0.0124325	+	0.0215337i	−0.859742	+	0.510728i	$0.829376\pi$
$374$	0.245167	−	0.905418i	0.0126773	−	0.0468181i
$375$	−4.80257	−	2.05798i	−0.248003	−	0.106274i
$376$	3.04475	−	31.8937i	0.157021	−	1.64479i
$377$	12.1679	−	14.5011i	0.626678	−	0.746846i
$378$	−11.6524	+	5.39625i	−0.599336	+	0.277553i
$379$	12.0512			0.619030			0.309515	−	0.950895i	$-0.399833\pi$
$379$	12.0512			0.619030			0.309515	+	0.950895i	$0.399833\pi$
$380$	−16.3139	−	10.6703i	−0.836888	−	0.547375i
$381$	−8.93391			−0.457698
$382$	−18.7262	+	8.67213i	−0.958116	+	0.443705i
$383$	−5.15486	+	6.14332i	−0.263401	+	0.313909i	−0.881493	−	0.472196i	$-0.843461\pi$
$383$	−5.15486	+	6.14332i	−0.263401	+	0.313909i	0.618092	+	0.786105i	$0.287906\pi$
$384$	−3.66902	−	3.80703i	−0.187234	−	0.194276i
$385$	0.926381	−	0.0908543i	0.0472127	−	0.00463037i
$386$	−0.903217	+	3.33564i	−0.0459725	+	0.169780i
$387$	−16.7349	−	28.9857i	−0.850682	−	1.47343i
$388$	14.0097	+	16.8760i	0.711233	+	0.856749i
$389$	0.0952729	+	0.540320i	0.00483053	+	0.0273953i	0.987128	−	0.159934i	$-0.0511281\pi$
$389$	0.0952729	+	0.540320i	0.00483053	+	0.0273953i	−0.982297	+	0.187329i	$0.940017\pi$
$390$	−4.53464	−	7.71359i	−0.229620	−	0.390593i
$391$	14.6351	+	8.44958i	0.740129	+	0.427313i
$392$	−8.65521	+	8.51935i	−0.437154	+	0.430292i
$393$	2.21506	−	1.85866i	0.111735	−	0.0937568i
$394$	−27.7574	−	19.5452i	−1.39840	−	0.984674i
$395$	−14.3059	+	20.8943i	−0.719810	+	1.05131i
$396$	−0.341403	−	0.598595i	−0.0171561	−	0.0300805i
$397$	−12.2046	−	2.15200i	−0.612532	−	0.108006i	−0.141228	−	0.989977i	$-0.545105\pi$
$397$	−12.2046	−	2.15200i	−0.612532	−	0.108006i	−0.471303	+	0.881971i	$0.656216\pi$
$398$	−0.382089	−	0.548754i	−0.0191524	−	0.0275066i
$399$	−6.77081	−	1.01025i	−0.338965	−	0.0505756i
$400$	7.03630	+	18.7214i	0.351815	+	0.936070i
$401$	25.1953	+	4.44261i	1.25819	+	0.221853i	0.762696	−	0.646757i	$-0.223875\pi$
$401$	25.1953	+	4.44261i	1.25819	+	0.221853i	0.495496	+	0.868610i	$0.334986\pi$
$402$	−1.04107	−	0.0938488i	−0.0519239	−	0.00468075i
$403$	36.9072	+	13.4331i	1.83848	+	0.669152i
$404$	−0.111152	+	21.0765i	−0.00553004	+	1.04859i
$405$	−6.84287	−	14.2813i	−0.340025	−	0.709644i
$406$	−6.31523	+	13.4503i	−0.313420	+	0.667529i
$407$	−0.515566	−	0.297662i	−0.0255557	−	0.0147546i
$408$	6.43824	−	2.94042i	0.318740	−	0.145573i
$409$	24.2784	−	4.28093i	1.20049	−	0.211679i	0.462579	−	0.886578i	$-0.346924\pi$
$409$	24.2784	−	4.28093i	1.20049	−	0.211679i	0.737910	+	0.674899i	$0.235813\pi$
$410$	1.41681	−	8.42161i	0.0699713	−	0.415914i
$411$	0.882597	+	1.52870i	0.0435353	+	0.0754053i
$412$	−24.3976	+	8.73457i	−1.20198	+	0.430321i
$413$	13.7507	−	5.00485i	0.676629	−	0.246273i
$414$	12.0002	−	3.18155i	0.589778	−	0.156365i
$415$	−12.9836	+	9.29578i	−0.637338	+	0.456312i
$416$	−9.30001	+	32.9634i	−0.455970	+	1.61617i
$417$	−3.14950			−0.154232
$418$	0.0484424	−	0.762043i	0.00236940	−	0.0372728i
$419$		−	7.31772i		−	0.357494i	−0.983895	−	0.178747i	$-0.942796\pi$
$419$		−	7.31772i		−	0.357494i	0.983895	−	0.178747i	$-0.0572044\pi$
$420$	4.99231	+	4.94044i	0.243600	+	0.241069i
$421$	−12.4412	+	14.8269i	−0.606348	+	0.722618i	−0.978659	−	0.205490i	$-0.934121\pi$
$421$	−12.4412	+	14.8269i	−0.606348	+	0.722618i	0.372311	+	0.928108i	$0.378566\pi$
$422$	10.0369	−	2.66104i	0.488590	−	0.129537i
$423$	29.6081	−	10.7765i	1.43960	−	0.523970i
$424$	−0.270965	−	0.192944i	−0.0131592	−	0.00937017i
$425$	−26.7676	+	0.561956i	−1.29842	+	0.0272589i
$426$	−1.96705	+	0.166869i	−0.0953036	+	0.00808482i
$427$	4.28577	+	24.3058i	0.207403	+	1.17624i
$428$	4.27709	−	23.5303i	0.206741	−	1.13738i
$429$	0.175246	−	0.303535i	0.00846095	−	0.0146548i
$430$	−24.2284	+	29.3395i	−1.16840	+	1.41488i
$431$	17.1074	−	14.3548i	0.824032	−	0.691445i	−0.129880	−	0.991530i	$-0.541459\pi$
$431$	17.1074	−	14.3548i	0.824032	−	0.691445i	0.953913	+	0.300085i	$0.0970149\pi$
$432$	3.80337	−	10.1164i	0.182990	−	0.486724i
$433$	19.6537	+	7.15338i	0.944499	+	0.343769i	0.767941	−	0.640521i	$-0.221282\pi$
$433$	19.6537	+	7.15338i	0.944499	+	0.343769i	0.176558	+	0.984290i	$0.443504\pi$
$434$	−30.7054	−	2.76798i	−1.47390	−	0.132867i
$435$	2.97538	+	1.34961i	0.142658	+	0.0647087i
$436$	−1.85262	−	0.685384i	−0.0887244	−	0.0328240i
$437$	13.0466	+	4.36186i	0.624104	+	0.208656i
$438$	3.48296	−	2.42513i	0.166422	−	0.115877i
$439$	3.98417	−	22.5954i	0.190154	−	1.07842i	−0.728998	−	0.684516i	$-0.760014\pi$
$439$	3.98417	−	22.5954i	0.190154	−	1.07842i	0.919152	−	0.393903i	$-0.128875\pi$
$440$	−0.502019	+	0.601433i	−0.0239328	+	0.0286722i
$441$	−11.2233	−	4.08494i	−0.534442	−	0.194521i
$442$	−37.4886	−	26.3974i	−1.78315	−	1.25560i
$443$	−1.68095	+	1.41048i	−0.0798641	+	0.0670139i	−0.681846	−	0.731496i	$-0.738822\pi$
$443$	−1.68095	+	1.41048i	−0.0798641	+	0.0670139i	0.601982	+	0.798510i	$0.294378\pi$
$444$	−0.756698	−	4.42787i	−0.0359113	−	0.210137i
$445$	6.76774	−	6.91131i	0.320822	−	0.327628i
$446$	−10.3260	+	10.2717i	−0.488952	+	0.486381i
$447$	7.54998	−	1.33127i	0.357102	−	0.0629667i
$448$	0.425334	−	26.8816i	0.0200951	−	1.27004i
$449$	7.27665	−	4.20118i	0.343406	−	0.198266i	−0.318371	−	0.947966i	$-0.603136\pi$
$449$	7.27665	−	4.20118i	0.343406	−	0.198266i	0.661777	+	0.749700i	$0.269802\pi$
$450$	−13.6504	+	14.1609i	−0.643486	+	0.667552i
$451$	0.314344	−	0.114412i	0.0148019	−	0.00538744i
$452$	10.8743	−	12.8215i	0.511483	−	0.603074i
$453$	−3.76178	+	4.48311i	−0.176744	+	0.210635i
$454$	−12.0858	+	5.59693i	−0.567213	+	0.262677i
$455$	11.3139	−	44.0689i	0.530403	−	2.06598i
$456$	4.65770	−	3.39154i	0.218117	−	0.158823i
$457$			5.17318i			0.241991i	0.992653	+	0.120996i	$0.0386087\pi$
$457$			5.17318i			0.241991i	−0.992653	+	0.120996i	$0.961391\pi$
$458$	6.99638	+	15.1077i	0.326919	+	0.705935i
$459$	11.0831	+	9.29986i	0.517317	+	0.434081i
$460$	−8.15561	−	11.5189i	−0.380257	−	0.537073i
$461$	−33.6010	+	12.2297i	−1.56495	+	0.569596i	−0.971864	−	0.235541i	$-0.924314\pi$
$461$	−33.6010	+	12.2297i	−1.56495	+	0.569596i	−0.593088	+	0.805137i	$0.702091\pi$
$462$	−0.0719071	+	0.265558i	−0.00334542	+	0.0123549i
$463$	−12.9520	−	22.4334i	−0.601928	−	1.04257i	−0.992529	−	0.122010i	$-0.961066\pi$
$463$	−12.9520	−	22.4334i	−0.601928	−	1.04257i	0.390601	−	0.920560i	$-0.372267\pi$
$464$	−4.15312	−	11.7963i	−0.192804	−	0.547628i
$465$	−0.519899	+	6.75876i	−0.0241097	+	0.313430i
$466$	0.425666	−	0.423427i	0.0197186	−	0.0196149i
$467$	−6.29519	+	10.9036i	−0.291306	+	0.504558i	−0.974119	−	0.226036i	$-0.927423\pi$
$467$	−6.29519	+	10.9036i	−0.291306	+	0.504558i	0.682812	+	0.730594i	$0.260757\pi$
$468$	−33.2019	+	5.67401i	−1.53476	+	0.262281i
$469$	−3.41652	−	4.07165i	−0.157760	−	0.188012i
$470$	−23.2398	−	27.2582i	−1.07197	−	1.25733i
$471$	−1.87142	−	0.681140i	−0.0862303	−	0.0313853i
$472$	−5.29304	+	11.1204i	−0.243632	+	0.511860i
$473$	−1.46782	−	0.258817i	−0.0674905	−	0.0119004i
$474$	−4.27676	−	6.14225i	−0.196438	−	0.282123i
$475$	−21.2599	+	4.79753i	−0.975472	+	0.220126i
$476$	33.7544	+	12.4876i	1.54713	+	0.572367i
$477$	0.0568059	−	0.322163i	0.00260097	−	0.0147508i
$478$	−3.82155	+	42.3928i	−0.174794	+	1.93900i
$479$	9.04170	−	24.8419i	0.413126	−	1.13505i	−0.542393	−	0.840125i	$-0.682482\pi$
$479$	9.04170	−	24.8419i	0.413126	−	1.13505i	0.955519	−	0.294929i	$-0.0952961\pi$
$480$	−5.91132	−	0.0158950i	−0.269813	−	0.000725506i
$481$	−22.2912	+	18.7045i	−1.01639	+	0.852852i
$482$	4.83464	−	10.2969i	0.220212	−	0.469013i
$483$	−4.29245	−	2.47825i	−0.195313	−	0.112764i
$484$	21.6151	+	3.92898i	0.982506	+	0.178590i
$485$	24.4500	+	1.88075i	1.11022	+	0.0854003i
$486$	16.0861	−	1.36462i	0.729682	−	0.0619006i
$487$	12.9509	−	7.47722i	0.586862	−	0.338825i	−0.176994	−	0.984212i	$-0.556637\pi$
$487$	12.9509	−	7.47722i	0.586862	−	0.338825i	0.763856	+	0.645387i	$0.223304\pi$
$488$	−16.9209	−	12.0487i	−0.765972	−	0.545420i
$489$	1.63643	+	4.49604i	0.0740017	+	0.203318i
$490$	0.106703	+	13.5777i	0.00482035	+	0.613377i
$491$	−14.1447	+	16.8570i	−0.638341	+	0.760745i	−0.984107	−	0.177576i	$-0.943174\pi$
$491$	−14.1447	+	16.8570i	−0.638341	+	0.760745i	0.345767	+	0.938321i	$0.387619\pi$
$492$	2.17927	+	1.27357i	0.0982492	+	0.0574172i
$493$	16.7415			0.753999
$494$	−34.1920	−	14.9647i	−1.53837	−	0.673291i
$495$	−0.746248	−	0.191585i	−0.0335413	−	0.00861111i
$496$	20.0518	−	16.4682i	0.900353	−	0.739445i
$497$	−7.68961	−	6.45235i	−0.344926	−	0.289427i
$498$	−1.20952	−	4.56207i	−0.0541998	−	0.204431i
$499$	−10.3844	−	28.5310i	−0.464870	−	1.27722i	−0.921782	−	0.387709i	$-0.873267\pi$
$499$	−10.3844	−	28.5310i	−0.464870	−	1.27722i	0.456912	−	0.889512i	$-0.348956\pi$
$500$	20.5064	+	8.91563i	0.917073	+	0.398719i
$501$	−3.86815	−	6.69984i	−0.172816	−	0.299327i
$502$	−5.80219	+	0.492213i	−0.258964	+	0.0219685i
$503$	−2.58938	−	14.6851i	−0.115455	−	0.654778i	−0.986524	−	0.163617i	$-0.947684\pi$
$503$	−2.58938	−	14.6851i	−0.115455	−	0.654778i	0.871069	−	0.491161i	$-0.163427\pi$
$504$	24.0503	−	10.9841i	1.07129	−	0.489269i
$505$	16.8366	+	16.4868i	0.749218	+	0.733654i
$506$	0.234965	−	0.500435i	0.0104455	−	0.0222471i
$507$	−7.10697	−	8.46975i	−0.315632	−	0.376155i
$508$	38.2331	+	0.201633i	1.69632	+	0.00894601i
$509$	1.62332	−	4.46003i	0.0719524	−	0.197688i	−0.898503	−	0.438967i	$-0.855345\pi$
$509$	1.62332	−	4.46003i	0.0719524	−	0.197688i	0.970456	+	0.241279i	$0.0775669\pi$
$510$	2.64801	−	7.45717i	0.117256	−	0.330209i
$511$	21.2527	+	3.74742i	0.940164	+	0.165776i
$512$	15.6158	+	16.3752i	0.690128	+	0.723687i
$513$	10.3516	+	5.61722i	0.457032	+	0.248006i
$514$	9.31926	−	6.48886i	0.411055	−	0.286211i
$515$	−11.9681	+	26.3853i	−0.527380	+	1.16267i
$516$	−5.57176	−	9.76919i	−0.245283	−	0.430065i
$517$	0.479894	−	1.31850i	0.0211057	−	0.0579875i
$518$	13.1506	−	18.6761i	0.577806	−	0.820579i
$519$	2.92591	+	3.48696i	0.128433	+	0.153060i
$520$	19.2321	+	33.1130i	0.843384	+	1.45210i
$521$	30.2443	+	17.4615i	1.32502	+	0.765004i	0.984526	−	0.175241i	$-0.0560705\pi$
$521$	30.2443	+	17.4615i	1.32502	+	0.765004i	0.340499	+	0.940245i	$0.389404\pi$
$522$	8.71959	−	8.67372i	0.381646	−	0.379639i
$523$	−38.8181	+	6.84468i	−1.69740	+	0.299297i	−0.936784	−	0.349908i	$-0.886213\pi$
$523$	−38.8181	+	6.84468i	−1.69740	+	0.299297i	−0.760613	+	0.649205i	$0.775102\pi$
$524$	−9.52141	+	7.90422i	−0.415945	+	0.345297i
$525$	7.85090	−	0.164821i	0.342641	−	0.00719337i
$526$	−2.30125	+	8.49867i	−0.100339	+	0.370560i
$527$	11.8802	+	32.6406i	0.517510	+	1.42185i
$528$	−0.113655	−	0.201740i	−0.00494619	−	0.00877962i
$529$	−9.98922	−	8.38195i	−0.434314	−	0.364433i
$530$	−0.365733	+	0.0674563i	−0.0158864	+	0.00293012i
$531$	−12.1120			−0.525615
$532$	28.9532	+	4.47621i	1.25528	+	0.194068i
$533$		−	16.3510i		−	0.708241i
$534$	1.20145	+	2.59435i	0.0519917	+	0.112268i
$535$	−15.5657	−	21.7409i	−0.672965	−	0.939941i
$536$	4.45320	+	0.425127i	0.192349	+	0.0183627i
$537$	2.32181	+	6.37911i	0.100193	+	0.275279i
$538$	33.7005	+	9.12532i	1.45293	+	0.393421i
$539$	−0.460610	+	0.265933i	−0.0198399	+	0.0114546i
$540$	−5.16378	−	10.9245i	−0.222214	−	0.470114i
$541$	1.29084	+	7.32072i	0.0554976	+	0.314742i	0.999901	−	0.0140456i	$-0.00447099\pi$
$541$	1.29084	+	7.32072i	0.0554976	+	0.314742i	−0.944404	+	0.328788i	$0.893360\pi$
$542$	18.2520	−	18.1560i	0.783990	−	0.779866i
$543$	−5.01630	+	8.68849i	−0.215270	+	0.372859i
$544$	−27.6191	+	12.4384i	−1.18416	+	0.533291i
$545$	−1.99167	+	0.954305i	−0.0853137	+	0.0408779i
$546$	10.9954	+	7.74232i	0.470558	+	0.331341i
$547$	11.5905	−	31.8446i	0.495573	−	1.36158i	−0.399941	−	0.916541i	$-0.630969\pi$
$547$	11.5905	−	31.8446i	0.495573	−	1.36158i	0.895513	−	0.445034i	$-0.146809\pi$
$548$	−3.74262	−	6.56208i	−0.159877	−	0.280318i
$549$	3.54735	−	20.1180i	0.151397	−	0.858617i
$550$	0.0923397	+	0.871007i	0.00393738	+	0.0371399i
$551$	13.3539	−	2.72021i	0.568894	−	0.115885i
$552$	4.03785	−	1.04778i	0.171862	−	0.0445963i
$553$	6.60865	−	37.4795i	0.281028	−	1.59379i
$554$	0.591731	−	6.56412i	0.0251402	−	0.278883i
$555$	−4.14402	−	2.83732i	−0.175904	−	0.120438i
$556$	13.4785	+	0.0710824i	0.571614	+	0.00301456i
$557$	7.87765	+	9.38822i	0.333787	+	0.397792i	0.906667	−	0.421848i	$-0.138618\pi$
$557$	7.87765	+	9.38822i	0.333787	+	0.397792i	−0.572880	+	0.819639i	$0.694174\pi$
$558$	23.0987	+	10.8453i	0.977844	+	0.459119i
$559$	−36.4264	+	63.0924i	−1.54067	+	2.66853i
$560$	−21.2533	−	21.2555i	−0.898117	−	0.898210i
$561$	0.305264	−	0.0538263i	0.0128883	−	0.00227255i
$562$	28.7204	−	2.43642i	1.21150	−	0.102774i
$563$	3.27238	−	1.88931i	0.137915	−	0.0796250i	−0.429455	−	0.903088i	$-0.641294\pi$
$563$	3.27238	−	1.88931i	0.137915	−	0.0796250i	0.567370	+	0.823463i	$0.307961\pi$
$564$	9.96779	−	3.56856i	0.419720	−	0.150263i
$565$	−1.83464	−	18.7066i	−0.0771838	−	0.786992i
$566$	17.1131	−	4.53711i	0.719318	−	0.190709i
$567$	18.2321	+	15.2985i	0.765675	+	0.642477i
$568$	8.42184	−	0.669729i	0.353372	−	0.0281012i
$569$		−	5.11343i		−	0.214366i	−0.994239	−	0.107183i	$-0.965817\pi$
$569$		−	5.11343i		−	0.214366i	0.994239	−	0.107183i	$-0.0341831\pi$
$570$	0.900524	−	6.37847i	0.0377188	−	0.267165i
$571$			15.0942i			0.631673i	0.948814	+	0.315836i	$0.102285\pi$
$571$			15.0942i			0.631673i	−0.948814	+	0.315836i	$0.897715\pi$
$572$	−0.756825	+	1.29504i	−0.0316444	+	0.0541483i
$573$	−5.22404	−	4.38349i	−0.218237	−	0.183123i
$574$	3.28920	+	12.4062i	0.137288	+	0.517825i
$575$	−15.5941	−	2.41334i	−0.650319	−	0.100643i
$576$	−7.94077	+	20.7878i	−0.330866	+	0.866157i
$577$	−31.4897	+	18.1806i	−1.31093	+	0.756867i	−0.982250	−	0.187574i	$-0.939938\pi$
$577$	−31.4897	+	18.1806i	−1.31093	+	0.756867i	−0.328681	+	0.944441i	$0.606604\pi$
$578$	−1.39539	−	16.4488i	−0.0580405	−	0.684180i
$579$	−1.12462	+	0.198301i	−0.0467377	+	0.00824112i
$580$	−12.7028	−	5.84286i	−0.527456	−	0.242612i
$581$	11.9995	−	20.7837i	0.497821	−	0.862252i
$582$	−3.08042	+	6.56077i	−0.127688	+	0.271953i
$583$	−0.00936397	−	0.0111595i	−0.000387816	−	0.000462181i
$584$	−14.9602	+	10.2999i	−0.619058	+	0.426211i
$585$	−21.2753	+	31.0734i	−0.879627	+	1.28473i
$586$	−3.12455	−	0.281667i	−0.129074	−	0.0116355i
$587$	−8.00064	+	45.3739i	−0.330222	+	1.87278i	0.139878	+	0.990169i	$0.455329\pi$
$587$	−8.00064	+	45.3739i	−0.330222	+	1.87278i	−0.470100	+	0.882613i	$0.655782\pi$
$588$	−3.76392	−	1.39248i	−0.155221	−	0.0574248i
$589$	14.7798	+	24.1055i	0.608992	+	0.993249i
$590$	4.81100	+	12.9017i	0.198066	+	0.531156i
$591$	1.94805	−	11.0479i	0.0801319	−	0.454451i
$592$	3.13839	+	18.9664i	0.128987	+	0.779513i
$593$	12.5909	−	34.5933i	0.517047	−	1.42058i	−0.356711	−	0.934215i	$-0.616102\pi$
$593$	12.5909	−	34.5933i	0.517047	−	1.42058i	0.873758	−	0.486361i	$-0.161676\pi$
$594$	0.272505	−	0.387002i	0.0111810	−	0.0158789i
$595$	36.2878	−	17.3873i	1.48766	−	0.712808i
$596$	−32.3406	+	5.52682i	−1.32472	+	0.226387i
$597$	0.110483	−	0.191362i	0.00452176	−	0.00783192i
$598$	−19.0577	−	19.1585i	−0.779326	−	0.783447i
$599$	0.850222	+	4.82185i	0.0347391	+	0.197015i	0.997238	−	0.0742695i	$-0.0236625\pi$
$599$	0.850222	+	4.82185i	0.0347391	+	0.197015i	−0.962499	+	0.271285i	$0.912551\pi$
$600$	−4.61180	+	4.73405i	−0.188276	+	0.193267i
$601$	1.65208	−	0.953830i	0.0673899	−	0.0389076i	−0.465926	−	0.884823i	$-0.654279\pi$
$601$	1.65208	−	0.953830i	0.0673899	−	0.0389076i	0.533316	+	0.845916i	$0.320946\pi$
$602$	14.9465	−	55.1986i	0.609175	−	2.24973i
$603$	1.50468	+	4.13407i	0.0612753	+	0.168352i
$604$	16.1999	−	19.1008i	0.659165	−	0.777201i
$605$	19.9714	−	14.2988i	0.811953	−	0.581330i
$606$	−6.32007	+	2.92683i	−0.256735	+	0.118895i
$607$			16.1506i			0.655533i	0.944759	+	0.327767i	$0.106296\pi$
$607$			16.1506i			0.655533i	−0.944759	+	0.327767i	$0.893704\pi$
$608$	−20.0094	+	14.4091i	−0.811489	+	0.584368i
$609$	−4.91026			−0.198974
$610$	−22.8389	+	4.21244i	−0.924720	+	0.170557i
$611$	−52.5379	−	44.0846i	−2.12546	−	1.78347i
$612$	−22.7186	−	19.2683i	−0.918346	−	0.778873i
$613$	9.84341	+	27.0446i	0.397572	+	1.09232i	0.963463	+	0.267840i	$0.0863098\pi$
$613$	9.84341	+	27.0446i	0.397572	+	1.09232i	−0.565892	+	0.824480i	$0.691468\pi$
$614$	13.7687	+	3.72825i	0.555660	+	0.150460i
$615$	2.71809	−	0.758972i	0.109604	−	0.0306047i
$616$	0.313723	−	1.13485i	0.0126403	−	0.0457242i
$617$	7.05674	−	1.24429i	0.284094	−	0.0500934i	−0.0297856	−	0.999556i	$-0.509482\pi$
$617$	7.05674	−	1.24429i	0.284094	−	0.0500934i	0.313879	+	0.949463i	$0.398371\pi$
$618$	−6.03924	−	6.07117i	−0.242934	−	0.244218i
$619$	18.0822	+	10.4398i	0.726787	+	0.419610i	0.817245	−	0.576290i	$-0.195500\pi$
$619$	18.0822	+	10.4398i	0.726787	+	0.419610i	−0.0904588	+	0.995900i	$0.528833\pi$
$620$	2.37747	−	28.9127i	0.0954817	−	1.16116i
$621$	5.48114	+	6.53217i	0.219951	+	0.262127i
$622$	−0.443251	−	0.312113i	−0.0177728	−	0.0125146i
$623$	−4.97223	+	13.6611i	−0.199208	+	0.547320i
$624$	−11.1663	+	1.84770i	−0.447009	+	0.0739672i
$625$	23.1128	−	9.52892i	0.924510	−	0.381157i
$626$	18.4880	+	26.5523i	0.738927	+	1.06124i
$627$	0.234749	−	0.0925349i	0.00937496	−	0.00369549i
$628$	7.99345	+	2.95721i	0.318973	+	0.118005i
$629$	−25.3441	−	4.46885i	−1.01054	−	0.178185i
$630$	9.89174	−	27.8565i	0.394096	−	1.10983i
$631$	7.09703	−	19.4989i	0.282528	−	0.776240i	−0.714531	−	0.699604i	$-0.753360\pi$
$631$	7.09703	−	19.4989i	0.282528	−	0.776240i	0.997059	−	0.0766361i	$-0.0244180\pi$
$632$	18.1640	+	26.3826i	0.722525	+	1.04944i
$633$	2.20561	+	2.62855i	0.0876653	+	0.104475i
$634$	36.4964	+	17.1359i	1.44946	+	0.680552i
$635$	29.9075	−	30.5419i	1.18684	−	1.21202i
$636$	0.0196584	−	0.108150i	0.000779505	−	0.00428842i
$637$	4.51438	+	25.6023i	0.178866	+	1.01440i
$638$	−0.0462958	−	0.545733i	−0.00183287	−	0.0216058i
$639$	4.15428	+	7.19542i	0.164341	+	0.284646i
$640$	25.2974	+	0.201438i	0.999968	+	0.00796255i
$641$	−7.23199	−	19.8697i	−0.285647	−	0.784808i	−0.996663	−	0.0816317i	$-0.973987\pi$
$641$	−7.23199	−	19.8697i	−0.285647	−	0.784808i	0.711016	−	0.703176i	$-0.248235\pi$
$642$	7.63915	−	2.02533i	0.301493	−	0.0799334i
$643$	−10.6935	−	8.97290i	−0.421710	−	0.353856i	0.407103	−	0.913382i	$-0.366539\pi$
$643$	−10.6935	−	8.97290i	−0.421710	−	0.353856i	−0.828813	+	0.559526i	$0.810983\pi$
$644$	18.3138	+	10.7027i	0.721666	+	0.421744i
$645$	−12.1789	−	3.12671i	−0.479544	−	0.123114i
$646$	−9.29905	−	31.6717i	−0.365866	−	1.24611i
$647$	13.2331			0.520246			0.260123	−	0.965576i	$-0.416237\pi$
$647$	13.2331			0.520246			0.260123	+	0.965576i	$0.416237\pi$
$648$	−19.9682	+	1.58793i	−0.784424	+	0.0623797i
$649$	−0.346698	+	0.413178i	−0.0136091	+	0.0162187i
$650$	41.5504	+	10.3199i	1.62974	+	0.404781i
$651$	−3.48445	−	9.57344i	−0.136566	−	0.375213i
$652$	−6.90169	−	19.2780i	−0.270291	−	0.754984i
$653$	−10.2474	+	5.91634i	−0.401012	+	0.231524i	−0.686921	−	0.726732i	$-0.741038\pi$
$653$	−10.2474	+	5.91634i	−0.401012	+	0.231524i	0.285908	+	0.958257i	$0.407705\pi$
$654$	−0.0551767	−	0.650421i	−0.00215758	−	0.0254335i
$655$	−1.06111	+	13.7946i	−0.0414611	+	0.539000i
$656$	−9.29757	−	5.49951i	−0.363009	−	0.214720i
$657$	−15.4692	−	8.93116i	−0.603512	−	0.348438i
$658$	48.7309	+	22.8802i	1.89973	+	0.891965i
$659$	−7.77585	+	6.52471i	−0.302904	+	0.254167i	−0.781552	−	0.623840i	$-0.785572\pi$
$659$	−7.77585	+	6.52471i	−0.302904	+	0.254167i	0.478648	+	0.878007i	$0.341127\pi$
$660$	−0.250409	−	0.0656973i	−0.00974715	−	0.00255726i
$661$	1.60132	−	4.39958i	0.0622840	−	0.171124i	−0.904647	−	0.426161i	$-0.859866\pi$
$661$	1.60132	−	4.39958i	0.0622840	−	0.171124i	0.966931	+	0.255038i	$0.0820878\pi$
$662$	−27.6344	−	2.49114i	−1.07404	−	0.0968208i
$663$	2.63099	−	14.9211i	0.102179	−	0.579488i
$664$	5.07323	+	19.5509i	0.196880	+	0.758722i
$665$	26.1199	−	19.7651i	1.01289	−	0.766459i
$666$	−15.5154	+	10.8032i	−0.601211	+	0.418614i
$667$	9.71718	+	1.71340i	0.376251	+	0.0663431i
$668$	16.4027	+	28.7596i	0.634641	+	1.11274i
$669$	−4.52276	−	1.64615i	−0.174860	−	0.0636438i
$670$	3.80596	−	3.24489i	0.147037	−	0.125361i
$671$	−0.584750	−	0.696878i	−0.0225740	−	0.0269027i
$672$	8.10066	−	3.64816i	0.312490	−	0.140731i
$673$	9.59635	−	16.6214i	0.369912	−	0.640706i	−0.619639	−	0.784887i	$-0.712721\pi$
$673$	9.59635	−	16.6214i	0.369912	−	0.640706i	0.989551	+	0.144180i	$0.0460545\pi$
$674$	9.54520	+	9.59567i	0.367667	+	0.369611i
$675$	−12.7891	−	4.35309i	−0.492253	−	0.167551i
$676$	30.2235	+	36.4071i	1.16244	+	1.40027i
$677$	−14.3635	−	24.8783i	−0.552034	−	0.956150i	−0.998128	−	0.0611642i	$-0.980519\pi$
$677$	−14.3635	−	24.8783i	−0.552034	−	0.956150i	0.446094	−	0.894986i	$-0.352815\pi$
$678$	5.36246	+	1.45203i	0.205944	+	0.0557650i
$679$	−34.6322	+	12.6051i	−1.32906	+	0.483738i
$680$	−11.5006	+	31.8536i	−0.441028	+	1.22153i
$681$	−3.37156	−	2.82907i	−0.129198	−	0.108410i
$682$	1.03115	−	0.477529i	0.0394849	−	0.0182855i
$683$		−	19.2351i		−	0.736010i	−0.929824	−	0.368005i	$-0.880041\pi$
$683$		−	19.2351i		−	0.736010i	0.929824	−	0.368005i	$-0.119959\pi$
$684$	−21.2523	−	11.6780i	−0.812602	−	0.446518i
$685$	−8.18071	−	2.10025i	−0.312569	−	0.0802463i
$686$	5.40484	+	11.6710i	0.206358	+	0.445599i
$687$	−3.53645	+	4.21458i	−0.134924	+	0.160796i
$688$	23.6242	+	41.9335i	0.900663	+	1.59870i
$689$	−0.669119	+	0.243539i	−0.0254914	+	0.00927811i
$690$	2.30017	−	4.05731i	0.0875660	−	0.154459i
$691$	28.8741	−	16.6705i	1.09842	−	0.634175i	0.162617	−	0.986689i	$-0.448006\pi$
$691$	28.8741	−	16.6705i	1.09842	−	0.634175i	0.935807	+	0.352514i	$0.114673\pi$
$692$	−12.4429	−	14.9887i	−0.473007	−	0.569783i
$693$	1.14033	−	0.201070i	0.0433174	−	0.00763803i
$694$	9.17468	+	9.22320i	0.348266	+	0.350108i
$695$	10.5434	−	10.7671i	0.399934	−	0.408418i
$696$	2.94526	−	2.89902i	0.111640	−	0.109887i
$697$	11.0776	−	9.29520i	0.419593	−	0.352081i
$698$	−23.7259	+	33.6947i	−0.898040	+	1.27536i
$699$	0.186440	+	0.0678585i	0.00705179	+	0.00256664i
$700$	−33.6021	+	0.528169i	−1.27004	+	0.0199629i
$701$	2.17829	−	12.3537i	0.0822728	−	0.466592i	−0.915639	−	0.402001i	$-0.868315\pi$
$701$	2.17829	−	12.3537i	0.0822728	−	0.466592i	0.997912	−	0.0645908i	$-0.0205742\pi$
$702$	−13.2199	−	18.9864i	−0.498954	−	0.716594i
$703$	−20.9419	+	0.553405i	−0.789837	+	0.0208721i
$704$	0.481838	+	0.865923i	0.0181600	+	0.0326357i
$705$	4.88966	−	10.7799i	0.184155	−	0.405993i
$706$	1.70574	−	18.9219i	0.0641964	−	0.712136i
$707$	−33.2797	−	12.1128i	−1.25161	−	0.455549i
$708$	−4.06977	−	0.0214630i	−0.152951	−	0.000806630i
$709$	1.97546	−	1.65761i	0.0741900	−	0.0622528i	−0.604939	−	0.796272i	$-0.706802\pi$
$709$	1.97546	−	1.65761i	0.0741900	−	0.0622528i	0.679129	+	0.734019i	$0.262358\pi$
$710$	6.01448	−	7.28326i	0.225719	−	0.273336i
$711$	−15.7503	+	27.2803i	−0.590681	+	1.02309i
$712$	−5.08310	−	11.1298i	−0.190497	−	0.417106i
$713$	3.55498	+	20.1613i	0.133135	+	0.755046i
$714$	1.00531	+	11.8505i	0.0376227	+	0.443496i
$715$	0.451021	+	1.61523i	0.0168672	+	0.0604061i
$716$	−9.79231	−	27.3521i	−0.365956	−	1.02220i
$717$	−13.2174	+	4.81074i	−0.493613	+	0.179660i
$718$	−11.4680	−	43.2550i	−0.427982	−	1.61426i
$719$	−25.1654	+	29.9910i	−0.938512	+	1.11848i	0.0542677	+	0.998526i	$0.482718\pi$
$719$	−25.1654	+	29.9910i	−0.938512	+	1.11848i	−0.992780	+	0.119949i	$0.961727\pi$
$720$	10.5133	+	22.5489i	0.391808	+	0.840349i
$721$		−	43.5436i		−	1.62165i
$722$	−12.5635	−	23.7520i	−0.467566	−	0.883958i
$723$	3.75906			0.139801
$724$	21.6636	−	37.0696i	0.805122	−	1.37768i
$725$	−14.5743	+	5.65379i	−0.541276	+	0.209976i
$726$	1.86049	+	7.01740i	0.0690492	+	0.260440i
$727$	−11.4446	+	4.16549i	−0.424456	+	0.154489i	−0.545411	−	0.838169i	$-0.683626\pi$
$727$	−11.4446	+	4.16549i	−0.424456	+	0.154489i	0.120955	+	0.992658i	$0.461404\pi$
$728$	−46.8804	−	33.3818i	−1.73751	−	1.23721i
$729$	−7.95574	−	13.7798i	−0.294657	−	0.510361i
$730$	−3.36899	+	20.0255i	−0.124692	+	0.741176i
$731$	−63.4519	+	11.1883i	−2.34685	+	0.413814i
$732$	1.22760	−	6.75362i	0.0453735	−	0.249621i
$733$	3.59670	+	2.07656i	0.132847	+	0.0766993i	0.564951	−	0.825125i	$-0.308895\pi$
$733$	3.59670	+	2.07656i	0.132847	+	0.0766993i	−0.432104	+	0.901824i	$0.642229\pi$
$734$	−5.02279	−	2.35831i	−0.185395	−	0.0870468i
$735$	−4.04642	+	1.93884i	−0.149254	+	0.0715150i
$736$	−17.3038	+	4.39288i	−0.637828	+	0.161924i
$737$	0.184097	+	0.0670058i	0.00678130	+	0.00246819i
$738$	0.953797	−	10.5805i	0.0351098	−	0.389475i
$739$	−11.4880	−	2.02564i	−0.422593	−	0.0745145i	−0.0416921	−	0.999131i	$-0.513275\pi$
$739$	−11.4880	−	2.02564i	−0.422593	−	0.0745145i	−0.380900	+	0.924616i	$0.624386\pi$
$740$	17.6705	+	12.2360i	0.649580	+	0.449804i
$741$	−0.325812	−	12.3293i	−0.0119690	−	0.452929i
$742$	0.458699	−	0.319385i	0.0168394	−	0.0117250i
$743$	30.8221	+	5.43476i	1.13075	+	0.199382i	0.707557	−	0.706656i	$-0.249797\pi$
$743$	30.8221	+	5.43476i	1.13075	+	0.199382i	0.423195	+	0.906039i	$0.360908\pi$
$744$	7.74221	+	3.68509i	0.283843	+	0.135102i
$745$	−20.7234	+	30.2674i	−0.759248	+	1.10891i
$746$	0.391003	−	0.555289i	0.0143157	−	0.0203306i
$747$	−15.2167	+	12.7683i	−0.556750	+	0.467169i
$748$	−1.30761	+	0.223463i	−0.0478109	+	0.00817062i
$749$	34.8021	+	20.0930i	1.27164	+	0.734182i
$750$	0.213143	+	7.38610i	0.00778288	+	0.269702i
$751$	4.62967	+	26.2561i	0.168939	+	0.958100i	0.944910	+	0.327331i	$0.106149\pi$
$751$	4.62967	+	26.2561i	0.168939	+	0.958100i	−0.775971	+	0.630769i	$0.782740\pi$
$752$	−42.7382	+	15.0469i	−1.55850	+	0.548703i
$753$	−0.962121	−	1.66644i	−0.0350616	−	0.0607286i
$754$	−25.8403	−	6.99697i	−0.941049	−	0.254815i
$755$	−2.73314	−	27.8680i	−0.0994693	−	1.01422i
$756$	13.8499	+	11.7464i	0.503714	+	0.427213i
$757$	3.58939	−	4.27767i	0.130459	−	0.155474i	−0.696861	−	0.717207i	$-0.745420\pi$
$757$	3.58939	−	4.27767i	0.130459	−	0.155474i	0.827319	+	0.561732i	$0.189865\pi$
$758$	−7.16193	−	15.4652i	−0.260133	−	0.561720i
$759$	0.182692			0.00663129
$760$	−3.99780	+	27.2767i	−0.145015	+	0.989429i
$761$	−13.6711			−0.495578			−0.247789	−	0.968814i	$-0.579704\pi$
$761$	−13.6711			−0.495578			−0.247789	+	0.968814i	$0.579704\pi$
$762$	5.30934	+	11.4647i	0.192337	+	0.415324i
$763$	2.13353	−	2.54264i	0.0772388	−	0.0920497i
$764$	22.2576	+	18.8773i	0.805252	+	0.682956i
$765$	−33.1464	+	3.25082i	−1.19841	+	0.117534i
$766$	10.9471	+	2.96423i	0.395535	+	0.107102i
$767$	13.1819	+	22.8318i	0.475972	+	0.824407i
$768$	−2.70503	+	6.97087i	−0.0976095	+	0.251540i
$769$	−7.87761	−	44.6761i	−0.284074	−	1.61106i	−0.708575	−	0.705636i	$-0.750662\pi$
$769$	−7.87761	−	44.6761i	−0.284074	−	1.61106i	0.424501	−	0.905427i	$-0.360450\pi$
$770$	−0.667131	−	1.13482i	−0.0240417	−	0.0408959i
$771$	3.24981	+	1.87628i	0.117039	+	0.0675726i
$772$	4.81735	−	0.823258i	0.173380	−	0.0296297i
$773$	−41.3702	+	34.7137i	−1.48798	+	1.24857i	−0.590870	+	0.806767i	$0.701216\pi$
$773$	−41.3702	+	34.7137i	−1.48798	+	1.24857i	−0.897114	+	0.441800i	$0.854340\pi$
$774$	−27.2515	+	38.7015i	−0.979534	+	1.39110i
$775$	−21.3654	−	24.4032i	−0.767468	−	0.876589i
$776$	13.3309	−	28.0076i	0.478552	−	1.00542i
$777$	7.43339	+	1.31071i	0.266671	+	0.0470213i
$778$	0.636764	−	0.443369i	0.0228291	−	0.0158956i
$779$	7.32574	−	9.21424i	0.262472	−	0.330135i
$780$	−7.20384	+	10.4033i	−0.257939	+	0.372499i
$781$	0.364373	+	0.0642487i	0.0130383	+	0.00229900i
$782$	2.14571	−	23.8025i	0.0767303	−	0.851175i
$783$	7.93814	+	2.88925i	0.283686	+	0.103253i
$784$	16.0765	+	6.04413i	0.574159	+	0.215862i
$785$	8.59339	−	4.11751i	0.306711	−	0.146960i
$786$	−3.70157	−	1.73797i	−0.132031	−	0.0619913i
$787$	29.7726	+	17.1892i	1.06128	+	0.612730i	0.925786	−	0.378048i	$-0.123405\pi$
$787$	29.7726	+	17.1892i	1.06128	+	0.612730i	0.135494	+	0.990778i	$0.456738\pi$
$788$	−8.58611	+	47.2362i	−0.305867	+	1.68272i
$789$	−2.86535	+	0.505239i	−0.102009	+	0.0179870i
$790$	35.3153	+	5.94127i	1.25646	+	0.211381i
$791$	14.1246	+	24.4646i	0.502215	+	0.869861i
$792$	−0.565275	+	0.793856i	−0.0200862	+	0.0282085i
$793$	−41.7844	+	15.2083i	−1.48381	+	0.540061i
$794$	4.49146	+	16.9409i	0.159396	+	0.601210i
$795$	−0.0715432	−	0.0999256i	−0.00253738	−	0.00354399i
$796$	−0.477136	+	0.816449i	−0.0169116	+	0.0289383i
$797$	−28.0059			−0.992019			−0.496009	−	0.868317i	$-0.665202\pi$
$797$	−28.0059			−0.992019			−0.496009	+	0.868317i	$0.665202\pi$
$798$	2.72740	+	9.28926i	0.0965489	+	0.328836i
$799$		−	60.6549i		−	2.14582i
$800$	19.8433	−	20.1555i	0.701565	−	0.712605i
$801$	7.73468	−	9.21783i	0.273291	−	0.325696i
$802$	−9.27219	−	34.9729i	−0.327413	−	1.23494i
$803$	−0.747468	+	0.272056i	−0.0263776	+	0.00960065i
$804$	0.498264	+	1.39176i	0.0175724	+	0.0490837i
$805$	22.8418	−	6.37813i	0.805069	−	0.224800i
$806$	−4.69510	−	55.3457i	−0.165378	−	1.94947i
$807$	2.00346	+	11.3622i	0.0705253	+	0.399969i
$808$	27.1131	−	12.3829i	0.953837	−	0.435629i
$809$	1.69614	−	2.93780i	0.0596331	−	0.103288i	−0.834668	−	0.550754i	$-0.814340\pi$
$809$	1.69614	−	2.93780i	0.0596331	−	0.103288i	0.894301	+	0.447466i	$0.147674\pi$
$810$	−14.2603	+	17.2686i	−0.501057	+	0.606757i
$811$	−30.5042	+	25.5961i	−1.07115	+	0.898799i	−0.995156	−	0.0983093i	$-0.968657\pi$
$811$	−30.5042	+	25.5961i	−1.07115	+	0.898799i	−0.0759913	+	0.997108i	$0.524212\pi$
$812$	21.0137	+	0.110821i	0.737436	+	0.00388907i
$813$	7.99428	+	2.90968i	0.280372	+	0.102047i
$814$	−0.0755891	+	0.838516i	−0.00264940	+	0.0293900i
$815$	−20.8486	−	9.45674i	−0.730293	−	0.331255i
$816$	−7.59959	−	6.51463i	−0.266039	−	0.228058i
$817$	−48.7946	+	19.2342i	−1.70711	+	0.672920i
$818$	−19.9221	−	28.6120i	−0.696559	−	1.00039i
$819$	9.82818	−	55.7384i	0.343424	−	1.94766i
$820$	−11.6493	+	3.18671i	−0.406812	+	0.111285i
$821$	19.7179	+	7.17672i	0.688159	+	0.250469i	0.662347	−	0.749197i	$-0.269561\pi$
$821$	19.7179	+	7.17672i	0.688159	+	0.250469i	0.0258123	+	0.999667i	$0.491783\pi$
$822$	1.43724	−	2.04112i	0.0501295	−	0.0711921i
$823$	−17.9835	+	15.0900i	−0.626866	+	0.526003i	−0.899953	−	0.435987i	$-0.856400\pi$
$823$	−17.9835	+	15.0900i	−0.626866	+	0.526003i	0.273088	+	0.961989i	$0.411955\pi$
$824$	25.7082	+	26.1182i	0.895587	+	0.909870i
$825$	−0.247570	+	0.149950i	−0.00861928	+	0.00522058i
$826$	−14.5946	−	14.6717i	−0.507810	−	0.510495i
$827$	32.3805	−	5.70955i	1.12598	−	0.198541i	0.420515	−	0.907286i	$-0.361849\pi$
$827$	32.3805	−	5.70955i	1.12598	−	0.198541i	0.705465	+	0.708745i	$0.250738\pi$
$828$	−11.2144	−	13.5089i	−0.389729	−	0.469467i
$829$	42.2181	−	24.3746i	1.46629	−	0.846566i	0.467005	−	0.884254i	$-0.345333\pi$
$829$	42.2181	−	24.3746i	1.46629	−	0.846566i	0.999290	+	0.0376887i	$0.0119995\pi$
$830$	19.6451	+	11.1372i	0.681893	+	0.386578i
$831$	2.04659	−	0.744897i	0.0709954	−	0.0258402i
$832$	47.8284	−	7.65531i	1.65815	−	0.265400i
$833$	−14.7789	+	17.6128i	−0.512058	+	0.610247i
$834$	1.87172	+	4.04171i	0.0648124	+	0.139953i
$835$	35.8536	+	9.20474i	1.24076	+	0.318543i
$836$	−1.00671	+	0.390710i	−0.0348177	+	0.0135130i
$837$			17.5271i			0.605826i
$838$	−9.39072	+	4.34885i	−0.324397	+	0.150229i
$839$	19.1682	+	16.0840i	0.661758	+	0.555281i	0.910613	−	0.413260i	$-0.135610\pi$
$839$	19.1682	+	16.0840i	0.661758	+	0.555281i	−0.248855	+	0.968541i	$0.580054\pi$
$840$	3.37311	−	9.34261i	0.116383	−	0.322351i
$841$	−18.0656	+	6.57533i	−0.622951	+	0.226735i
$842$	26.4208	+	7.15416i	0.910521	+	0.246548i
$843$	4.76243	+	8.24877i	0.164027	+	0.284103i
$844$	−9.37972	−	11.2988i	−0.322863	−	0.388920i
$845$	52.7467	+	4.05739i	1.81454	+	0.139579i
$846$	−31.4251	−	31.5913i	−1.08042	−	1.08613i
$847$	−18.4576	+	31.9696i	−0.634212	+	1.09849i
$848$	−0.0865699	+	0.462389i	−0.00297282	+	0.0158785i
$849$	3.76061	+	4.48172i	0.129064	+	0.153812i
$850$	16.6289	+	34.0165i	0.570366	+	1.16676i
$851$	−14.2530	−	5.18766i	−0.488586	−	0.177831i
$852$	1.38314	+	2.42511i	0.0473855	+	0.0830829i
$853$	−15.1375	−	2.66915i	−0.518298	−	0.0913899i	−0.0916210	−	0.995794i	$-0.529205\pi$
$853$	−15.1375	−	2.66915i	−0.518298	−	0.0913899i	−0.426677	+	0.904404i	$0.640316\pi$
$854$	28.6443	−	19.9446i	0.980187	−	0.682490i
$855$	−25.9111	+	7.97875i	−0.886140	+	0.272867i
$856$	−32.7378	+	8.49509i	−1.11896	+	0.290356i
$857$	−3.98933	+	22.6246i	−0.136273	+	0.772841i	0.837692	+	0.546143i	$0.183904\pi$
$857$	−3.98933	+	22.6246i	−0.136273	+	0.772841i	−0.973965	+	0.226699i	$0.927207\pi$
$858$	−0.493669	−	0.0445024i	−0.0168536	−	0.00151929i
$859$	7.89087	−	21.6800i	0.269233	−	0.739711i	−0.729229	−	0.684270i	$-0.760121\pi$
$859$	7.89087	−	21.6800i	0.269233	−	0.739711i	0.998462	−	0.0554416i	$-0.0176567\pi$
$860$	52.0497	+	13.6558i	1.77488	+	0.465658i
$861$	−3.24904	+	2.72627i	−0.110727	+	0.0929110i
$862$	−28.5880	−	13.4227i	−0.973711	−	0.457179i
$863$	−2.31528	−	1.33673i	−0.0788132	−	0.0455028i	0.460076	−	0.887880i	$-0.347822\pi$
$863$	−2.31528	−	1.33673i	−0.0788132	−	0.0455028i	−0.538889	+	0.842377i	$0.681156\pi$
$864$	−15.2425	+	1.13127i	−0.518560	+	0.0384865i
$865$	−21.7156	−	1.67041i	−0.738351	−	0.0567956i
$866$	−2.50022	−	29.4725i	−0.0849609	−	1.00152i
$867$	4.72425	−	2.72755i	0.160444	−	0.0926323i
$868$	14.6958	+	41.0487i	0.498808	+	1.39328i
$869$	0.479776	+	1.31817i	0.0162753	+	0.0447160i
$870$	−0.0363096	−	4.62031i	−0.00123101	−	0.156643i
$871$	6.15536	−	7.33567i	0.208566	−	0.248560i
$872$	0.221452	+	2.78476i	0.00749930	+	0.0943037i
$873$	30.5049			1.03243
$874$	−2.15598	−	19.3347i	−0.0729270	−	0.654007i
$875$	−25.7185	+	27.3913i	−0.869443	+	0.925994i
$876$	−5.18202	−	3.02839i	−0.175084	−	0.102320i
$877$	0.198222	+	0.166328i	0.00669349	+	0.00561650i	0.646128	−	0.763229i	$-0.276387\pi$
$877$	0.198222	+	0.166328i	0.00669349	+	0.00561650i	−0.639435	+	0.768845i	$0.720832\pi$
$878$	−31.3641	+	8.31539i	−1.05849	+	0.280631i
$879$	−0.354575	−	0.974185i	−0.0119595	−	0.0328585i
$880$	1.07015	+	0.286807i	0.0360749	+	0.00966825i
$881$	−2.36861	−	4.10255i	−0.0798004	−	0.138218i	0.823363	−	0.567515i	$-0.192095\pi$
$881$	−2.36861	−	4.10255i	−0.0798004	−	0.138218i	−0.903164	+	0.429296i	$0.858762\pi$
$882$	1.42775	+	16.8303i	0.0480749	+	0.566706i
$883$	−2.30439	−	13.0688i	−0.0775489	−	0.439801i	−0.998717	−	0.0506369i	$-0.983875\pi$
$883$	−2.30439	−	13.0688i	−0.0775489	−	0.439801i	0.921168	−	0.389165i	$-0.127236\pi$
$884$	−11.5962	+	63.7963i	−0.390024	+	2.14570i
$885$	−3.18353	+	3.25107i	−0.107013	+	0.109284i
$886$	2.80902	+	1.31889i	0.0943708	+	0.0443091i
$887$	−5.32020	−	6.34036i	−0.178635	−	0.212889i	0.669296	−	0.742996i	$-0.266596\pi$
$887$	−5.32020	−	6.34036i	−0.178635	−	0.212889i	−0.847930	+	0.530108i	$0.822152\pi$
$888$	−5.23252	+	3.60250i	−0.175592	+	0.120892i
$889$	−21.9729	+	60.3700i	−0.736947	+	2.02474i
$890$	−12.8912	−	4.57761i	−0.432113	−	0.153442i
$891$	−0.863928	−	0.152334i	−0.0289427	−	0.00510337i
$892$	19.3182	+	7.14686i	0.646822	+	0.239294i
$893$	−9.85539	−	48.3814i	−0.329798	−	1.61902i
$894$	−6.19528	−	8.89762i	−0.207201	−	0.297581i
$895$	−29.5805	−	13.4175i	−0.988767	−	0.448497i
$896$	−34.7495	+	15.4297i	−1.16090	+	0.515469i
$897$	3.05419	−	8.39131i	0.101976	−	0.280178i
$898$	−9.71575	−	6.84129i	−0.324219	−	0.228297i
$899$	13.0366	+	15.5364i	0.434794	+	0.518168i
$900$	26.2848	+	9.10166i	0.876160	+	0.303389i
$901$	−0.545374	−	0.314872i	−0.0181691	−	0.0104899i
$902$	−0.333635	−	0.335399i	−0.0111088	−	0.0111676i
$903$	18.6104	−	3.28151i	0.619314	−	0.109202i
$904$	−22.9162	−	6.33508i	−0.762180	−	0.210702i
$905$	−12.9102	−	46.2349i	−0.429149	−	1.53690i
$906$	7.98870	+	2.16316i	0.265407	+	0.0718661i
$907$	5.86772	+	16.1214i	0.194834	+	0.535303i	0.998186	−	0.0602014i	$-0.0191743\pi$
$907$	5.86772	+	16.1214i	0.194834	+	0.535303i	−0.803352	+	0.595505i	$0.796952\pi$
$908$	14.3649	+	12.1833i	0.476716	+	0.404316i
$909$	22.4555	+	18.8424i	0.744801	+	0.624962i
$910$	−63.2767	+	11.6708i	−2.09760	+	0.386885i
$911$	55.5736			1.84123			0.920617	−	0.390467i	$-0.127686\pi$
$911$	55.5736			1.84123			0.920617	+	0.390467i	$0.127686\pi$
$912$	−7.12034	−	3.96160i	−0.235778	−	0.131182i
$913$			0.884577i			0.0292752i
$914$	6.63867	−	3.07438i	0.219588	−	0.101691i
$915$	−4.46765	−	6.24004i	−0.147696	−	0.206289i
$916$	15.2295	−	17.9567i	0.503198	−	0.593306i
$917$	−7.11176	−	19.5394i	−0.234851	−	0.645247i
$918$	5.34776	−	19.7497i	0.176502	−	0.651836i
$919$	−13.6433	+	7.87694i	−0.450050	+	0.259836i	−0.707851	−	0.706362i	$-0.750335\pi$
$919$	−13.6433	+	7.87694i	−0.450050	+	0.259836i	0.257801	+	0.966198i	$0.417002\pi$
$920$	−9.93526	+	17.3116i	−0.327556	+	0.570746i
$921$	0.818537	+	4.64216i	0.0269717	+	0.152964i
$922$	35.6630	+	35.8516i	1.17450	+	1.18071i
$923$	9.04252	−	15.6621i	0.297638	−	0.515524i
$924$	0.383520	−	0.0655414i	0.0126169	−	0.00215615i
$925$	23.5725	−	4.66862i	0.775058	−	0.153503i
$926$	−21.0913	+	29.9530i	−0.693102	+	0.984317i
$927$	−12.3268	+	33.8676i	−0.404866	+	1.11236i
$928$	−12.6698	+	12.3400i	−0.415907	+	0.405082i
$929$	−1.03954	+	5.89550i	−0.0341061	+	0.193425i	−0.997100	−	0.0760962i	$-0.975754\pi$
$929$	−1.03954	+	5.89550i	−0.0341061	+	0.193425i	0.962994	+	0.269521i	$0.0868655\pi$
$930$	8.98238	−	3.34949i	0.294544	−	0.109834i
$931$	−8.92662	+	16.4502i	−0.292558	+	0.539133i
$932$	−0.796346	−	0.294612i	−0.0260852	−	0.00965032i
$933$	0.0311079	−	0.176422i	0.00101843	−	0.00577578i
$934$	17.7336	+	1.59862i	0.580260	+	0.0523083i
$935$	−0.837900	+	1.22378i	−0.0274023	+	0.0400220i
$936$	27.0129	+	39.2354i	0.882945	+	1.28245i
$937$	−16.3408	−	19.4742i	−0.533830	−	0.636193i	0.429963	−	0.902847i	$-0.358527\pi$
$937$	−16.3408	−	19.4742i	−0.533830	−	0.636193i	−0.963793	+	0.266653i	$0.914082\pi$
$938$	−3.19468	+	6.80412i	−0.104310	+	0.222162i
$939$	−5.34587	+	9.25932i	−0.174456	+	0.302166i
$940$	−21.1688	+	46.0226i	−0.690452	+	1.50109i
$941$	−4.08175	+	0.719722i	−0.133061	+	0.0234623i	−0.239782	−	0.970827i	$-0.577076\pi$
$941$	−4.08175	+	0.719722i	−0.133061	+	0.0234623i	0.106721	+	0.994289i	$0.465965\pi$
$942$	0.238069	+	2.80635i	0.00775671	+	0.0914359i
$943$	7.38101	−	4.26143i	0.240359	−	0.138771i
$944$	17.4163	+	0.183704i	0.566852	+	0.00597907i
$945$	20.2069	−	1.98178i	0.657330	−	0.0644674i
$946$	0.540177	+	2.03744i	0.0175627	+	0.0662430i
$947$	21.6263	+	18.1466i	0.702760	+	0.589686i	0.922557	−	0.385860i	$-0.126095\pi$
$947$	21.6263	+	18.1466i	0.702760	+	0.589686i	−0.219797	+	0.975546i	$0.570540\pi$
$948$	−5.34062	+	9.13858i	−0.173455	+	0.296807i
$949$			38.8805i			1.26211i
$950$	18.7912	+	24.4314i	0.609666	+	0.792659i
$951$			13.3236i			0.432047i
$952$	−4.03481	−	50.7377i	−0.130769	−	1.64442i
$953$	6.44930	+	5.41160i	0.208913	+	0.175299i	0.741240	−	0.671240i	$-0.234238\pi$
$953$	6.44930	+	5.41160i	0.208913	+	0.175299i	−0.532327	+	0.846539i	$0.678682\pi$
$954$	−0.447185	+	0.118560i	−0.0144782	+	0.00383852i
$955$	32.4738	−	3.18485i	1.05083	−	0.103059i
$956$	56.6731	−	20.2895i	1.83294	−	0.656209i
$957$	0.156740	−	0.0904937i	0.00506667	−	0.00292525i
$958$	−37.2526	+	3.16022i	−1.20358	+	0.102102i
$959$	12.5008	−	2.20423i	0.403672	−	0.0711782i
$960$	3.49264	+	7.59534i	0.112725	+	0.245139i
$961$	−5.53993	+	9.59544i	−0.178708	+	0.309530i
$962$	37.2506	+	17.4900i	1.20101	+	0.563900i
$963$	−21.3805	−	25.4803i	−0.688976	−	0.821090i
$964$	−16.0871	−	0.0848396i	−0.518130	−	0.00273250i
$965$	3.08690	−	4.50853i	0.0993709	−	0.145135i
$966$	−0.629333	+	6.98124i	−0.0202485	+	0.224618i
$967$	6.12116	−	34.7148i	0.196843	−	1.11635i	−0.712926	−	0.701239i	$-0.752631\pi$
$967$	6.12116	−	34.7148i	0.196843	−	1.11635i	0.909769	−	0.415114i	$-0.136258\pi$
$968$	−7.80368	−	30.0733i	−0.250820	−	0.966593i
$969$	8.16774	−	7.22970i	0.262386	−	0.232251i
$970$	−12.1169	−	32.4940i	−0.389049	−	1.04332i
$971$	−3.69950	+	20.9809i	−0.118723	+	0.673309i	0.866117	+	0.499841i	$0.166608\pi$
$971$	−3.69950	+	20.9809i	−0.118723	+	0.673309i	−0.984840	+	0.173468i	$0.944503\pi$
$972$	−11.3110	−	19.8321i	−0.362802	−	0.636115i
$973$	−7.74618	+	21.2825i	−0.248331	+	0.682284i
$974$	−17.2920	−	12.1761i	−0.554072	−	0.390147i
$975$	2.74861	+	13.8781i	0.0880260	+	0.444454i
$976$	−5.40602	+	28.8747i	−0.173042	+	0.924258i
$977$	−9.36678	+	16.2237i	−0.299670	+	0.519043i	−0.976060	−	0.217500i	$-0.930210\pi$
$977$	−9.36678	+	16.2237i	−0.299670	+	0.519043i	0.676391	+	0.736543i	$0.263543\pi$
$978$	4.79719	−	4.77196i	0.153397	−	0.152590i
$979$	−0.0930494	−	0.527710i	−0.00297387	−	0.0168657i
$980$	17.3606	−	8.20602i	0.554565	−	0.262132i
$981$	−2.37923	+	1.37365i	−0.0759630	+	0.0438572i
$982$	30.0383	+	8.13370i	0.958562	+	0.259557i
$983$	−6.32466	−	17.3769i	−0.201725	−	0.554235i	0.797039	−	0.603927i	$-0.206398\pi$
$983$	−6.32466	−	17.3769i	−0.201725	−	0.554235i	−0.998765	+	0.0496919i	$0.984176\pi$
$984$	0.339237	−	3.55350i	0.0108145	−	0.113281i
$985$	31.2476	+	43.6441i	0.995632	+	1.39062i
$986$	−9.94932	−	21.4841i	−0.316851	−	0.684193i
$987$			17.7900i			0.566262i
$988$	1.11606	+	52.7714i	0.0355067	+	1.67888i
$989$	−37.9741			−1.20751
$990$	0.197630	+	1.07151i	0.00628109	+	0.0340547i
$991$	−10.5218	−	8.82881i	−0.334235	−	0.280456i	0.460188	−	0.887822i	$-0.347782\pi$
$991$	−10.5218	−	8.82881i	−0.334235	−	0.280456i	−0.794423	+	0.607365i	$0.792226\pi$
$992$	−33.0500	−	15.9453i	−1.04934	−	0.506263i
$993$	−3.13595	−	8.61596i	−0.0995164	−	0.273419i
$994$	−3.71033	+	13.7025i	−0.117685	+	0.434618i
$995$	0.284343	+	1.01831i	0.00901429	+	0.0322826i
$996$	−5.13562	+	4.26335i	−0.162728	+	0.135089i
$997$	32.9344	−	5.80722i	1.04304	−	0.183916i	0.374221	−	0.927340i	$-0.377910\pi$
$997$	32.9344	−	5.80722i	1.04304	−	0.183916i	0.668821	+	0.743423i	$0.266799\pi$
$998$	−30.4420	+	30.2818i	−0.963623	+	0.958555i
$999$	−11.2459	−	6.49283i	−0.355805	−	0.205424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.59.20	yes	336
4.3	odd	2	inner	380.2.bb.a.59.43	yes	336
5.4	even	2	inner	380.2.bb.a.59.37	yes	336
19.10	odd	18	inner	380.2.bb.a.219.14	yes	336
20.19	odd	2	inner	380.2.bb.a.59.14	✓	336
76.67	even	18	inner	380.2.bb.a.219.37	yes	336
95.29	odd	18	inner	380.2.bb.a.219.43	yes	336
380.219	even	18	inner	380.2.bb.a.219.20	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.14	✓	336	20.19	odd	2	inner
380.2.bb.a.59.20	yes	336	1.1	even	1	trivial
380.2.bb.a.59.37	yes	336	5.4	even	2	inner
380.2.bb.a.59.43	yes	336	4.3	odd	2	inner
380.2.bb.a.219.14	yes	336	19.10	odd	18	inner
380.2.bb.a.219.20	yes	336	380.219	even	18	inner
380.2.bb.a.219.37	yes	336	76.67	even	18	inner
380.2.bb.a.219.43	yes	336	95.29	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.594291 - 1.28328i) q^{2} +(0.300395 - 0.357997i) q^{3} +(-1.29364 + 1.52529i) q^{4} +(0.218254 + 2.22539i) q^{5} +(-0.637934 - 0.172738i) q^{6} +(-1.68031 - 2.91038i) q^{7} +(2.72617 + 0.753640i) q^{8} +(0.483020 + 2.73934i) q^{9} +O(q^{10})\)	\(q+(-0.594291 - 1.28328i) q^{2} +(0.300395 - 0.357997i) q^{3} +(-1.29364 + 1.52529i) q^{4} +(0.218254 + 2.22539i) q^{5} +(-0.637934 - 0.172738i) q^{6} +(-1.68031 - 2.91038i) q^{7} +(2.72617 + 0.753640i) q^{8} +(0.483020 + 2.73934i) q^{9} +(2.72610 - 1.60261i) q^{10} +(0.107274 + 0.0619346i) q^{11} +(0.157446 + 0.921308i) q^{12} +(4.63813 - 3.89185i) q^{13} +(-2.73626 + 3.88593i) q^{14} +(0.862246 + 0.590363i) q^{15} +(-0.653006 - 3.94634i) q^{16} +(5.27335 + 0.929834i) q^{17} +(3.22830 - 2.24782i) q^{18} +(4.35738 - 0.115147i) q^{19} +(-3.67670 - 2.54595i) q^{20} +(-1.54667 - 0.272719i) q^{21} +(0.0157278 - 0.174470i) q^{22} +(2.96562 + 1.07940i) q^{23} +(1.08873 - 0.749573i) q^{24} +(-4.90473 + 0.971402i) q^{25} +(-7.75075 - 3.63914i) q^{26} +(2.33994 + 1.35096i) q^{27} +(6.61288 + 1.20202i) q^{28} +(3.07901 - 0.542912i) q^{29} +(0.245178 - 1.45735i) q^{30} +(3.24345 + 5.61782i) q^{31} +(-4.67620 + 3.18326i) q^{32} +(0.0543970 - 0.0197989i) q^{33} +(-1.94066 - 7.31980i) q^{34} +(6.11001 - 4.37455i) q^{35} +(-4.80314 - 2.80697i) q^{36} -4.80607 q^{37} +(-2.73732 - 5.52332i) q^{38} -2.82953i q^{39} +(-1.08214 + 6.23129i) q^{40} +(1.73589 - 2.06876i) q^{41} +(0.569194 + 2.14689i) q^{42} +(-11.3069 + 4.11538i) q^{43} +(-0.233242 + 0.0835027i) q^{44} +(-5.99069 + 1.67278i) q^{45} +(-0.377267 - 4.44721i) q^{46} +(-1.96698 - 11.1553i) q^{47} +(-1.60894 - 0.951687i) q^{48} +(-2.14689 + 3.71852i) q^{49} +(4.16142 + 5.71687i) q^{50} +(1.91697 - 1.60853i) q^{51} +(-0.0638607 + 12.1091i) q^{52} +(-0.110513 - 0.0402236i) q^{53} +(0.343067 - 3.80567i) q^{54} +(-0.114416 + 0.252244i) q^{55} +(-2.38744 - 9.20056i) q^{56} +(1.26771 - 1.59452i) q^{57} +(-2.52653 - 3.62859i) q^{58} +(-0.756119 + 4.28817i) q^{59} +(-2.01591 + 0.551459i) q^{60} +(-6.90121 - 2.51183i) q^{61} +(5.28171 - 7.50089i) q^{62} +(7.16091 - 6.00872i) q^{63} +(6.86405 + 4.10911i) q^{64} +(9.67318 + 9.47223i) q^{65} +(-0.0577353 - 0.0580405i) q^{66} +(1.55757 - 0.274642i) q^{67} +(-8.24007 + 6.84051i) q^{68} +(1.27728 - 0.737438i) q^{69} +(-9.24491 - 5.24112i) q^{70} +(2.80683 - 1.02160i) q^{71} +(-0.747681 + 7.83195i) q^{72} +(-4.12772 + 4.91923i) q^{73} +(2.85620 + 6.16755i) q^{74} +(-1.12560 + 2.04768i) q^{75} +(-5.46123 + 6.79521i) q^{76} -0.416278i q^{77} +(-3.63109 + 1.68156i) q^{78} +(8.67515 + 7.27931i) q^{79} +(8.63962 - 2.31450i) q^{80} +(-6.65500 + 2.42222i) q^{81} +(-3.68643 - 0.998202i) q^{82} +(3.57061 + 6.18447i) q^{83} +(2.41680 - 2.00631i) q^{84} +(-0.918314 + 11.9382i) q^{85} +(12.0008 + 12.0642i) q^{86} +(0.730558 - 1.26536i) q^{87} +(0.245771 + 0.249691i) q^{88} +(-2.78066 - 3.31386i) q^{89} +(5.70686 + 6.69363i) q^{90} +(-19.1203 - 6.95921i) q^{91} +(-5.48283 + 3.12708i) q^{92} +(2.98548 + 0.526421i) q^{93} +(-13.1465 + 9.15370i) q^{94} +(1.20726 + 9.67174i) q^{95} +(-0.265108 + 2.63030i) q^{96} +(1.90434 - 10.8000i) q^{97} +(6.04779 + 0.545186i) q^{98} +(-0.117845 + 0.323776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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