LMFDB - Embedded newform 230.2.l.a.63.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

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

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			63.8
Character	$\chi$	$=$	230.63
Dual form			230.2.l.a.157.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.349464 + 0.936950i) q^{2} +(-0.926949 - 1.69758i) q^{3} +(-0.755750 + 0.654861i) q^{4} +(2.12979 - 0.681161i) q^{5} +(1.26661 - 1.46175i) q^{6} +(-0.983009 + 0.735871i) q^{7} +(-0.877679 - 0.479249i) q^{8} +(-0.400622 + 0.623380i) q^{9} +O(q^{10})$	\(q+(0.349464 + 0.936950i) q^{2} +(-0.926949 - 1.69758i) q^{3} +(-0.755750 + 0.654861i) q^{4} +(2.12979 - 0.681161i) q^{5} +(1.26661 - 1.46175i) q^{6} +(-0.983009 + 0.735871i) q^{7} +(-0.877679 - 0.479249i) q^{8} +(-0.400622 + 0.623380i) q^{9} +(1.38250 + 1.75747i) q^{10} +(3.08362 - 1.40824i) q^{11} +(1.81222 + 0.675923i) q^{12} +(4.09692 - 5.47285i) q^{13} +(-1.03300 - 0.663869i) q^{14} +(-3.13054 - 2.98409i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-3.00282 + 0.214766i) q^{17} +(-0.724078 - 0.157514i) q^{18} +(1.88225 + 2.17223i) q^{19} +(-1.16352 + 1.90951i) q^{20} +(2.16040 + 0.986621i) q^{21} +(2.39707 + 2.39707i) q^{22} +(-2.74231 + 3.93443i) q^{23} +1.93417i q^{24} +(4.07204 - 2.90146i) q^{25} +(6.55951 + 1.92605i) q^{26} +(-4.35813 - 0.311700i) q^{27} +(0.261015 - 1.19987i) q^{28} +(3.99884 + 3.46501i) q^{29} +(1.70194 - 3.97599i) q^{30} +(-5.92845 + 1.74075i) q^{31} +(0.977147 - 0.212565i) q^{32} +(-5.24896 - 3.92933i) q^{33} +(-1.25060 - 2.73844i) q^{34} +(-1.59236 + 2.23684i) q^{35} +(-0.105457 - 0.733470i) q^{36} +(1.42375 + 6.54487i) q^{37} +(-1.37749 + 2.52269i) q^{38} +(-13.0882 - 1.88180i) q^{39} +(-2.19572 - 0.422860i) q^{40} +(-2.34072 + 1.50429i) q^{41} +(-0.169432 + 2.36897i) q^{42} +(-7.40121 + 4.04137i) q^{43} +(-1.40824 + 3.08362i) q^{44} +(-0.428620 + 1.60056i) q^{45} +(-4.64470 - 1.19446i) q^{46} +(5.79351 - 5.79351i) q^{47} +(-1.81222 + 0.675923i) q^{48} +(-1.54733 + 5.26972i) q^{49} +(4.14156 + 2.80134i) q^{50} +(3.14805 + 4.89846i) q^{51} +(0.487706 + 6.81902i) q^{52} +(-6.30233 - 8.41893i) q^{53} +(-1.23096 - 4.19228i) q^{54} +(5.60824 - 5.09971i) q^{55} +(1.21543 - 0.174753i) q^{56} +(1.94279 - 5.20882i) q^{57} +(-1.84909 + 4.95761i) q^{58} +(7.66795 - 1.10249i) q^{59} +(4.32007 + 0.205163i) q^{60} +(0.704279 + 2.39855i) q^{61} +(-3.70278 - 4.94633i) q^{62} +(-0.0649124 - 0.907593i) q^{63} +(0.540641 + 0.841254i) q^{64} +(4.99771 - 14.4467i) q^{65} +(1.84726 - 6.29117i) q^{66} +(-8.58840 + 3.20331i) q^{67} +(2.12874 - 2.12874i) q^{68} +(9.22099 + 1.00827i) q^{69} +(-2.65228 - 0.710264i) q^{70} +(-1.74986 + 3.83166i) q^{71} +(0.650371 - 0.355130i) q^{72} +(-0.0550313 + 0.769439i) q^{73} +(-5.63467 + 3.62118i) q^{74} +(-8.70004 - 4.22310i) q^{75} +(-2.84502 - 0.409052i) q^{76} +(-1.99494 + 3.65346i) q^{77} +(-2.81071 - 12.9206i) q^{78} +(0.551491 + 3.83570i) q^{79} +(-0.371127 - 2.20505i) q^{80} +(4.43411 + 9.70936i) q^{81} +(-2.22744 - 1.66744i) q^{82} +(11.8197 - 2.57122i) q^{83} +(-2.27882 + 0.669122i) q^{84} +(-6.24911 + 2.50282i) q^{85} +(-6.37301 - 5.52225i) q^{86} +(2.17542 - 10.0002i) q^{87} +(-3.38133 - 0.241837i) q^{88} +(10.7709 + 3.16262i) q^{89} +(-1.64943 + 0.157743i) q^{90} +8.39466i q^{91} +(-0.504008 - 4.76927i) q^{92} +(8.45044 + 8.45044i) q^{93} +(7.45285 + 3.40360i) q^{94} +(5.48844 + 3.34429i) q^{95} +(-1.26661 - 1.46175i) q^{96} +(-6.29292 - 1.36894i) q^{97} +(-5.47819 + 0.391808i) q^{98} +(-0.357496 + 2.48644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 240 * q - 8 * q^3 - 8 * q^6	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

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

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

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

$2$	0.349464	+	0.936950i	0.247108	+	0.662524i
$2$	0.349464	+	0.936950i	0.247108	+	0.662524i
$3$	−0.926949	−	1.69758i	−0.535174	−	0.980098i	−0.995716	−	0.0924605i	$-0.970527\pi$
$3$	−0.926949	−	1.69758i	−0.535174	−	0.980098i	0.460542	−	0.887638i	$-0.347655\pi$
$4$	−0.755750	+	0.654861i	−0.377875	+	0.327430i
$5$	2.12979	−	0.681161i	0.952473	−	0.304625i
$5$	2.12979	−	0.681161i	0.952473	−	0.304625i
$6$	1.26661	−	1.46175i	0.517092	−	0.596756i
$7$	−0.983009	+	0.735871i	−0.371542	+	0.278133i	−0.768690	−	0.639622i	$-0.779091\pi$
$7$	−0.983009	+	0.735871i	−0.371542	+	0.278133i	0.397148	+	0.917755i	$0.370000\pi$
$8$	−0.877679	−	0.479249i	−0.310306	−	0.169440i
$9$	−0.400622	+	0.623380i	−0.133541	+	0.207793i
$10$	1.38250	+	1.75747i	0.437185	+	0.555760i
$11$	3.08362	−	1.40824i	0.929747	−	0.424601i	0.107805	−	0.994172i	$-0.465618\pi$
$11$	3.08362	−	1.40824i	0.929747	−	0.424601i	0.821942	+	0.569571i	$0.192891\pi$
$12$	1.81222	+	0.675923i	0.523143	+	0.195122i
$13$	4.09692	−	5.47285i	1.13628	−	1.51790i	0.313455	−	0.949603i	$-0.398513\pi$
$13$	4.09692	−	5.47285i	1.13628	−	1.51790i	0.822827	−	0.568292i	$-0.192396\pi$
$14$	−1.03300	−	0.663869i	−0.276081	−	0.177426i
$15$	−3.13054	−	2.98409i	−0.808301	−	0.770490i
$16$	0.142315	−	0.989821i	0.0355787	−	0.247455i
$17$	−3.00282	+	0.214766i	−0.728292	+	0.0520885i	−0.430561	−	0.902561i	$-0.641684\pi$
$17$	−3.00282	+	0.214766i	−0.728292	+	0.0520885i	−0.297731	+	0.954650i	$0.596230\pi$
$18$	−0.724078	−	0.157514i	−0.170667	−	0.0371263i
$19$	1.88225	+	2.17223i	0.431818	+	0.498344i	0.929401	−	0.369072i	$-0.120325\pi$
$19$	1.88225	+	2.17223i	0.431818	+	0.498344i	−0.497583	+	0.867416i	$0.665779\pi$
$20$	−1.16352	+	1.90951i	−0.260172	+	0.426978i
$21$	2.16040	+	0.986621i	0.471438	+	0.215298i
$22$	2.39707	+	2.39707i	0.511057	+	0.511057i
$23$	−2.74231	+	3.93443i	−0.571810	+	0.820386i
$23$	−2.74231	+	3.93443i	−0.571810	+	0.820386i
$24$			1.93417i			0.394811i
$25$	4.07204	−	2.90146i	0.814408	−	0.580293i
$26$	6.55951	+	1.92605i	1.28643	+	0.377729i
$27$	−4.35813	−	0.311700i	−0.838723	−	0.0599867i
$28$	0.261015	−	1.19987i	0.0493273	−	0.226754i
$29$	3.99884	+	3.46501i	0.742565	+	0.643436i	0.941668	−	0.336542i	$-0.109257\pi$
$29$	3.99884	+	3.46501i	0.742565	+	0.643436i	−0.199103	+	0.979979i	$0.563803\pi$
$30$	1.70194	−	3.97599i	0.310729	−	0.725913i
$31$	−5.92845	+	1.74075i	−1.06478	+	0.312648i	−0.766775	−	0.641916i	$-0.778140\pi$
$31$	−5.92845	+	1.74075i	−1.06478	+	0.312648i	−0.298007	+	0.954564i	$0.596322\pi$
$32$	0.977147	−	0.212565i	0.172737	−	0.0375766i
$33$	−5.24896	−	3.92933i	−0.913727	−	0.684008i
$34$	−1.25060	−	2.73844i	−0.214477	−	0.469639i
$35$	−1.59236	+	2.23684i	−0.269158	+	0.378095i
$36$	−0.105457	−	0.733470i	−0.0175762	−	0.122245i
$37$	1.42375	+	6.54487i	0.234063	+	1.07597i	0.932745	+	0.360538i	$0.117407\pi$
$37$	1.42375	+	6.54487i	0.234063	+	1.07597i	−0.698682	+	0.715433i	$0.746230\pi$
$38$	−1.37749	+	2.52269i	−0.223459	+	0.409234i
$39$	−13.0882	−	1.88180i	−2.09580	−	0.301330i
$40$	−2.19572	−	0.422860i	−0.347174	−	0.0668601i
$41$	−2.34072	+	1.50429i	−0.365559	+	0.234930i	−0.710505	−	0.703692i	$-0.751533\pi$
$41$	−2.34072	+	1.50429i	−0.365559	+	0.234930i	0.344946	+	0.938622i	$0.387897\pi$
$42$	−0.169432	+	2.36897i	−0.0261440	+	0.365541i
$43$	−7.40121	+	4.04137i	−1.12867	+	0.616302i	−0.931382	−	0.364042i	$-0.881396\pi$
$43$	−7.40121	+	4.04137i	−1.12867	+	0.616302i	−0.197291	+	0.980345i	$0.563215\pi$
$44$	−1.40824	+	3.08362i	−0.212301	+	0.464873i
$45$	−0.428620	+	1.60056i	−0.0638948	+	0.238597i
$46$	−4.64470	−	1.19446i	−0.684824	−	0.176114i
$47$	5.79351	−	5.79351i	0.845070	−	0.845070i	−0.144443	−	0.989513i	$-0.546139\pi$
$47$	5.79351	−	5.79351i	0.845070	−	0.845070i	0.989513	+	0.144443i	$0.0461389\pi$
$48$	−1.81222	+	0.675923i	−0.261571	+	0.0975611i
$49$	−1.54733	+	5.26972i	−0.221047	+	0.752817i
$50$	4.14156	+	2.80134i	0.585705	+	0.396169i
$51$	3.14805	+	4.89846i	0.440815	+	0.685921i
$52$	0.487706	+	6.81902i	0.0676326	+	0.945628i
$53$	−6.30233	−	8.41893i	−0.865692	−	1.15643i	−0.986501	−	0.163754i	$-0.947640\pi$
$53$	−6.30233	−	8.41893i	−0.865692	−	1.15643i	0.120809	−	0.992676i	$-0.461451\pi$
$54$	−1.23096	−	4.19228i	−0.167513	−	0.570497i
$55$	5.60824	−	5.09971i	0.756214	−	0.687645i
$56$	1.21543	−	0.174753i	0.162419	−	0.0233523i
$57$	1.94279	−	5.20882i	0.257329	−	0.689925i
$58$	−1.84909	+	4.95761i	−0.242798	+	0.650966i
$59$	7.66795	−	1.10249i	0.998282	−	0.143531i	0.376246	−	0.926520i	$-0.377215\pi$
$59$	7.66795	−	1.10249i	0.998282	−	0.143531i	0.622036	+	0.782988i	$0.286306\pi$
$60$	4.32007	+	0.205163i	0.557718	+	0.0264864i
$61$	0.704279	+	2.39855i	0.0901737	+	0.307103i	0.992213	−	0.124550i	$-0.0397486\pi$
$61$	0.704279	+	2.39855i	0.0901737	+	0.307103i	−0.902040	+	0.431653i	$0.857930\pi$
$62$	−3.70278	−	4.94633i	−0.470253	−	0.628185i
$63$	−0.0649124	−	0.907593i	−0.00817819	−	0.114346i
$64$	0.540641	+	0.841254i	0.0675801	+	0.105157i
$65$	4.99771	−	14.4467i	0.619889	−	1.79189i
$66$	1.84726	−	6.29117i	0.227381	−	0.774390i
$67$	−8.58840	+	3.20331i	−1.04924	+	0.391346i	−0.814167	−	0.580631i	$-0.802806\pi$
$67$	−8.58840	+	3.20331i	−1.04924	+	0.391346i	−0.235073	+	0.971978i	$0.575533\pi$
$68$	2.12874	−	2.12874i	0.258148	−	0.258148i
$69$	9.22099	+	1.00827i	1.11008	+	0.121381i
$70$	−2.65228	−	0.710264i	−0.317008	−	0.0848928i
$71$	−1.74986	+	3.83166i	−0.207670	+	0.454734i	−0.984593	−	0.174862i	$-0.944052\pi$
$71$	−1.74986	+	3.83166i	−0.207670	+	0.454734i	0.776923	+	0.629596i	$0.216779\pi$
$72$	0.650371	−	0.355130i	0.0766470	−	0.0418524i
$73$	−0.0550313	+	0.769439i	−0.00644093	+	0.0900560i	−0.999656	−	0.0262385i	$-0.991647\pi$
$73$	−0.0550313	+	0.769439i	−0.00644093	+	0.0900560i	0.993215	+	0.116294i	$0.0371016\pi$
$74$	−5.63467	+	3.62118i	−0.655017	+	0.420954i
$75$	−8.70004	−	4.22310i	−1.00459	−	0.487642i
$76$	−2.84502	−	0.409052i	−0.326346	−	0.0469215i
$77$	−1.99494	+	3.65346i	−0.227345	+	0.416351i
$78$	−2.81071	−	12.9206i	−0.318251	−	1.46297i
$79$	0.551491	+	3.83570i	0.0620476	+	0.431550i	0.997040	+	0.0768830i	$0.0244968\pi$
$79$	0.551491	+	3.83570i	0.0620476	+	0.431550i	−0.934993	+	0.354667i	$0.884594\pi$
$80$	−0.371127	−	2.20505i	−0.0414932	−	0.246533i
$81$	4.43411	+	9.70936i	0.492679	+	1.07882i
$82$	−2.22744	−	1.66744i	−0.245979	−	0.184138i
$83$	11.8197	−	2.57122i	1.29738	−	0.282228i	0.489722	−	0.871879i	$-0.337098\pi$
$83$	11.8197	−	2.57122i	1.29738	−	0.282228i	0.807658	+	0.589651i	$0.200735\pi$
$84$	−2.27882	+	0.669122i	−0.248640	+	0.0730072i
$85$	−6.24911	+	2.50282i	−0.677811	+	0.271468i
$86$	−6.37301	−	5.52225i	−0.687220	−	0.595479i
$87$	2.17542	−	10.0002i	0.233229	−	1.07214i
$88$	−3.38133	−	0.241837i	−0.360451	−	0.0257800i
$89$	10.7709	+	3.16262i	1.14171	+	0.335237i	0.797302	−	0.603581i	$-0.206260\pi$
$89$	10.7709	+	3.16262i	1.14171	+	0.335237i	0.344412	+	0.938819i	$0.388078\pi$
$90$	−1.64943	+	0.157743i	−0.173865	+	0.0166275i
$91$			8.39466i			0.880000i
$92$	−0.504008	−	4.76927i	−0.0525465	−	0.497231i
$93$	8.45044	+	8.45044i	0.876270	+	0.876270i
$94$	7.45285	+	3.40360i	0.768703	+	0.351055i
$95$	5.48844	+	3.34429i	0.563102	+	0.343117i
$96$	−1.26661	−	1.46175i	−0.129273	−	0.149189i
$97$	−6.29292	−	1.36894i	−0.638949	−	0.138995i	−0.118591	−	0.992943i	$-0.537838\pi$
$97$	−6.29292	−	1.36894i	−0.638949	−	0.138995i	−0.520358	+	0.853948i	$0.674201\pi$
$98$	−5.47819	+	0.391808i	−0.553381	+	0.0395786i
$99$	−0.357496	+	2.48644i	−0.0359297	+	0.249897i
$100$	−1.17739	+	4.85940i	−0.117739	+	0.485940i
$101$	−7.95674	−	5.11349i	−0.791725	−	0.508811i	0.0811808	−	0.996699i	$-0.474131\pi$
$101$	−7.95674	−	5.11349i	−0.791725	−	0.508811i	−0.872906	+	0.487889i	$0.837767\pi$
$102$	−3.48948	+	4.66140i	−0.345510	+	0.461547i
$103$	2.16597	+	0.807867i	0.213420	+	0.0796015i	0.453900	−	0.891053i	$-0.350032\pi$
$103$	2.16597	+	0.807867i	0.213420	+	0.0796015i	−0.240480	+	0.970654i	$0.577305\pi$
$104$	−6.21864	+	2.83996i	−0.609788	+	0.278481i
$105$	5.27325	+	0.629719i	0.514617	+	0.0614543i
$106$	5.68568	−	8.84709i	0.552242	−	0.859305i
$107$	0.840901	+	0.459167i	0.0812930	+	0.0443893i	0.519381	−	0.854543i	$-0.326162\pi$
$107$	0.840901	+	0.459167i	0.0812930	+	0.0443893i	−0.438088	+	0.898932i	$0.644344\pi$
$108$	3.49778	−	2.61840i	0.336574	−	0.251956i
$109$	−2.27494	+	2.62542i	−0.217900	+	0.251470i	−0.854167	−	0.519999i	$-0.825932\pi$
$109$	−2.27494	+	2.62542i	−0.217900	+	0.251470i	0.636267	+	0.771469i	$0.280478\pi$
$110$	6.73805	+	3.47247i	0.642448	+	0.331087i
$111$	9.79070	−	8.48369i	0.929293	−	0.805237i
$112$	0.588484	+	1.07773i	0.0556065	+	0.101836i
$113$	2.72859	+	7.31563i	0.256684	+	0.688197i	0.999818	+	0.0190545i	$0.00606559\pi$
$113$	2.72859	+	7.31563i	0.256684	+	0.688197i	−0.743134	+	0.669142i	$0.766662\pi$
$114$	5.55933			0.520679
$115$	−3.16056	+	10.2475i	−0.294724	+	0.955582i
$116$	−5.29122			−0.491277
$117$	1.77035	+	4.74648i	0.163669	+	0.438812i
$118$	3.71265	+	6.79921i	0.341777	+	0.625918i
$119$	2.79376	−	2.42081i	0.256104	−	0.221915i
$120$	1.31748	+	4.11938i	0.120269	+	0.376046i
$121$	0.322105	−	0.371729i	0.0292823	−	0.0337936i
$122$	−2.00120	+	1.49808i	−0.181181	+	0.135630i
$123$	4.72337	+	2.57916i	0.425892	+	0.232555i
$124$	3.34048	−	5.19788i	0.299984	−	0.466784i
$125$	6.69624	−	8.95324i	0.598930	−	0.800802i
$126$	0.827685	−	0.377991i	0.0737360	−	0.0336741i
$127$	−5.69516	−	2.12418i	−0.505363	−	0.188491i	0.0838343	−	0.996480i	$-0.473283\pi$
$127$	−5.69516	−	2.12418i	−0.505363	−	0.188491i	−0.589198	+	0.807989i	$0.700556\pi$
$128$	−0.599278	+	0.800541i	−0.0529692	+	0.0707585i
$129$	13.7211	+	8.81801i	1.20807	+	0.776382i
$130$	15.2824	−	0.366004i	1.34035	−	0.0321006i
$131$	−0.343618	+	2.38992i	−0.0300220	+	0.208808i	−0.999311	−	0.0371170i	$-0.988183\pi$
$131$	−0.343618	+	2.38992i	−0.0300220	+	0.208808i	0.969289	+	0.245925i	$0.0790917\pi$
$132$	6.54006	−	0.467755i	0.569239	−	0.0407128i
$133$	−3.44875	−	0.750229i	−0.299044	−	0.0650531i
$134$	−6.00268	−	6.92746i	−0.518552	−	0.598441i
$135$	−9.49424	+	2.30473i	−0.817134	+	0.198360i
$136$	2.73844	+	1.25060i	0.234820	+	0.107238i
$137$	11.5177	+	11.5177i	0.984027	+	0.984027i	0.999874	−	0.0158474i	$-0.00504459\pi$
$137$	11.5177	+	11.5177i	0.984027	+	0.984027i	−0.0158474	+	0.999874i	$0.505045\pi$
$138$	2.27771	+	8.99196i	0.193892	+	0.765446i
$139$		−	2.36411i		−	0.200522i	−0.994961	−	0.100261i	$-0.968032\pi$
$139$		−	2.36411i		−	0.200522i	0.994961	−	0.100261i	$-0.0319677\pi$
$140$	−0.261395	−	2.73326i	−0.0220919	−	0.231003i
$141$	−15.2052	−	4.46466i	−1.28051	−	0.375992i
$142$	−4.20158	−	0.300503i	−0.352589	−	0.0252177i
$143$	4.92626	−	22.6457i	0.411955	−	1.89372i
$144$	0.560020	+	0.485260i	0.0466683	+	0.0404383i
$145$	10.8769	+	4.65591i	0.903280	+	0.386652i
$146$	−0.740157	+	0.217330i	−0.0612558	+	0.0179863i
$147$	10.3801	−	2.25804i	0.856133	−	0.186240i
$148$	−5.36198	−	4.01393i	−0.440752	−	0.329943i
$149$	−7.08181	−	15.5070i	−0.580164	−	1.27038i	−0.941206	−	0.337833i	$-0.890306\pi$
$149$	−7.08181	−	15.5070i	−0.580164	−	1.27038i	0.361042	−	0.932550i	$-0.382421\pi$
$150$	0.916482	−	9.62732i	0.0748305	−	0.786068i
$151$	−1.51690	−	10.5503i	−0.123443	−	0.858568i	−0.953608	−	0.301050i	$-0.902663\pi$
$151$	−1.51690	−	10.5503i	−0.123443	−	0.858568i	0.830165	−	0.557518i	$-0.188246\pi$
$152$	−0.610971	−	2.80859i	−0.0495563	−	0.227807i
$153$	1.06912	−	1.95794i	0.0864329	−	0.158290i
$154$	−4.12027	−	0.592406i	−0.332021	−	0.0477374i
$155$	−11.4406	+	7.74567i	−0.918935	+	0.622147i
$156$	11.1237	−	7.14880i	0.890613	−	0.572362i
$157$	−1.41059	+	19.7227i	−0.112578	+	1.57404i	0.556500	+	0.830848i	$0.312144\pi$
$157$	−1.41059	+	19.7227i	−0.112578	+	1.57404i	−0.669077	+	0.743193i	$0.733311\pi$
$158$	−3.40114	+	1.85716i	−0.270580	+	0.147748i
$159$	−8.44987	+	18.5026i	−0.670118	+	1.46735i
$160$	1.93633	−	1.11831i	0.153080	−	0.0884105i
$161$	−0.199523	−	5.88556i	−0.0157247	−	0.463847i
$162$	−7.54761	+	7.54761i	−0.592997	+	0.592997i
$163$	11.5169	−	4.29560i	0.902077	−	0.336457i	0.144731	−	0.989471i	$-0.453768\pi$
$163$	11.5169	−	4.29560i	0.902077	−	0.336457i	0.757346	+	0.653014i	$0.226496\pi$
$164$	0.783897	−	2.66971i	0.0612121	−	0.208469i
$165$	−13.8557	−	4.79326i	−1.07867	−	0.373155i
$166$	6.53966	+	10.1759i	0.507576	+	0.789804i
$167$	−1.80228	−	25.1992i	−0.139465	−	1.94997i	−0.280233	−	0.959932i	$-0.590412\pi$
$167$	−1.80228	−	25.1992i	−0.139465	−	1.94997i	0.140768	−	0.990043i	$-0.455043\pi$
$168$	−1.42330	−	1.90131i	−0.109810	−	0.146689i
$169$	−9.50477	−	32.3703i	−0.731136	−	2.49002i
$170$	−4.52885	−	4.98045i	−0.347347	−	0.381983i
$171$	−2.10819	+	0.303113i	−0.161218	+	0.0231796i
$172$	2.94693	−	7.90102i	0.224701	−	0.602447i
$173$	−5.32333	+	14.2724i	−0.404725	+	1.08511i	0.561515	+	0.827467i	$0.310219\pi$
$173$	−5.32333	+	14.2724i	−0.404725	+	1.08511i	−0.966240	+	0.257644i	$0.917054\pi$
$174$	10.1299	−	1.45647i	0.767949	−	0.110414i
$175$	−1.86775	+	5.84866i	−0.141188	+	0.442117i
$176$	−0.955064	−	3.25265i	−0.0719906	−	0.245178i
$177$	−8.97936	−	11.9950i	−0.674930	−	0.901601i
$178$	0.800827	+	11.1970i	0.0600245	+	0.839252i
$179$	−8.47074	−	13.1807i	−0.633133	−	0.985174i	−0.998524	−	0.0543197i	$-0.982701\pi$
$179$	−8.47074	−	13.1807i	−0.633133	−	0.985174i	0.365391	−	0.930854i	$-0.380935\pi$
$180$	−0.724213	−	1.49031i	−0.0539797	−	0.111081i
$181$	0.978450	−	3.33229i	0.0727276	−	0.247687i	−0.915103	−	0.403220i	$-0.867891\pi$
$181$	0.978450	−	3.33229i	0.0727276	−	0.247687i	0.987831	+	0.155532i	$0.0497092\pi$
$182$	−7.86538	+	2.93363i	−0.583021	+	0.217455i
$183$	3.41891	−	3.41891i	0.252733	−	0.252733i
$184$	4.29244	−	2.13892i	0.316443	−	0.157683i
$185$	7.49041	+	12.9694i	0.550706	+	0.953531i
$186$	−4.96451	+	10.8708i	−0.364016	+	0.797083i
$187$	−8.95713	+	4.89096i	−0.655010	+	0.357663i
$188$	−0.584501	+	8.17239i	−0.0426291	+	0.596033i
$189$	4.51345	−	2.90062i	0.328305	−	0.210989i
$190$	−1.21542	+	6.31110i	−0.0881756	+	0.457855i
$191$	5.15843	+	0.741671i	0.373251	+	0.0536654i	0.326388	−	0.945236i	$-0.394168\pi$
$191$	5.15843	+	0.741671i	0.373251	+	0.0536654i	0.0468632	+	0.998901i	$0.485078\pi$
$192$	0.926949	−	1.69758i	0.0668968	−	0.122512i
$193$	2.17118	+	9.98077i	0.156285	+	0.718431i	0.986867	+	0.161535i	$0.0516444\pi$
$193$	2.17118	+	9.98077i	0.156285	+	0.718431i	−0.830582	+	0.556897i	$0.811992\pi$
$194$	−0.916521	−	6.37454i	−0.0658023	−	0.457665i
$195$	−29.1571	+	4.90734i	−2.08798	+	0.351422i
$196$	−2.28154	−	4.99587i	−0.162967	−	0.356848i
$197$	10.2259	+	7.65502i	0.728566	+	0.545398i	0.897921	−	0.440158i	$-0.145077\pi$
$197$	10.2259	+	7.65502i	0.728566	+	0.545398i	−0.169355	+	0.985555i	$0.554168\pi$
$198$	−2.45460	+	0.533966i	−0.174441	+	0.0379473i
$199$	12.5975	−	3.69896i	0.893013	−	0.262212i	0.197138	−	0.980376i	$-0.436835\pi$
$199$	12.5975	−	3.69896i	0.893013	−	0.262212i	0.695874	+	0.718164i	$0.255017\pi$
$200$	−4.96447	+	0.595034i	−0.351041	+	0.0420753i
$201$	13.3989	+	11.6102i	0.945084	+	0.818920i
$202$	2.01048	−	9.24205i	0.141457	−	0.650268i
$203$	−6.48069	−	0.463508i	−0.454855	−	0.0325319i
$204$	−5.58694	−	1.64047i	−0.391164	−	0.114856i
$205$	−3.96058	+	4.79823i	−0.276619	+	0.335123i
$206$			2.31173i			0.161066i
$207$	−1.35402	−	3.28572i	−0.0941107	−	0.228373i
$208$	−4.83409	−	4.83409i	−0.335184	−	0.335184i
$209$	8.86317	+	4.04768i	0.613078	+	0.279984i
$210$	1.25280	+	5.16084i	0.0864512	+	0.356131i
$211$	−7.81515	−	9.01916i	−0.538017	−	0.620905i	0.420032	−	0.907509i	$-0.362019\pi$
$211$	−7.81515	−	9.01916i	−0.538017	−	0.620905i	−0.958049	+	0.286605i	$0.907473\pi$
$212$	10.2762	+	2.23545i	0.705773	+	0.153532i
$213$	8.12658	−	0.581224i	0.556824	−	0.0398248i
$214$	−0.136351	+	0.948344i	−0.00932078	+	0.0648275i
$215$	−13.0102	+	13.6487i	−0.887290	+	0.930833i
$216$	3.67566	+	2.36220i	0.250097	+	0.160728i
$217$	4.54675	−	6.07375i	0.308654	−	0.412313i
$218$	−3.25490	−	1.21402i	−0.220450	−	0.0822235i
$219$	1.35720	−	0.619810i	0.0917108	−	0.0418829i
$220$	−0.898823	+	7.52672i	−0.0605986	+	0.507451i
$221$	−11.1270	+	17.3139i	−0.748480	+	1.16466i
$222$	11.3703	+	6.20865i	0.763124	+	0.416697i
$223$	−20.6740	+	15.4764i	−1.38443	+	1.03637i	−0.391191	+	0.920309i	$0.627937\pi$
$223$	−20.6740	+	15.4764i	−1.38443	+	1.03637i	−0.993242	+	0.116064i	$0.962972\pi$
$224$	−0.804123	+	0.928008i	−0.0537277	+	0.0620051i
$225$	0.177367	+	3.70082i	0.0118244	+	0.246721i
$226$	−5.90083	+	5.11310i	−0.392518	+	0.340119i
$227$	9.05939	+	16.5910i	0.601293	+	1.10119i	0.984143	+	0.177375i	$0.0567606\pi$
$227$	9.05939	+	16.5910i	0.601293	+	1.10119i	−0.382851	+	0.923810i	$0.625058\pi$
$228$	1.94279	+	5.20882i	0.128664	+	0.344962i
$229$	−16.1141			−1.06485			−0.532425	−	0.846477i	$-0.678719\pi$
$229$	−16.1141			−1.06485			−0.532425	+	0.846477i	$0.678719\pi$
$230$	−10.7059	+	0.619837i	−0.705925	+	0.0408709i
$231$	8.05125			0.529734
$232$	−1.84909	−	4.95761i	−0.121399	−	0.325483i
$233$	−10.1254	−	18.5433i	−0.663338	−	1.21481i	−0.965213	−	0.261466i	$-0.915794\pi$
$233$	−10.1254	−	18.5433i	−0.663338	−	1.21481i	0.301875	−	0.953348i	$-0.402388\pi$
$234$	−3.82854	+	3.31745i	−0.250280	+	0.216868i
$235$	8.39267	−	16.2853i	0.547477	−	1.06234i
$236$	−5.07308	+	5.85464i	−0.330229	+	0.381105i
$237$	6.00021	−	4.49170i	0.389756	−	0.291767i
$238$	3.24450	+	1.77163i	0.210309	+	0.114838i
$239$	−6.52812	+	10.1580i	−0.422269	+	0.657064i	−0.985586	−	0.169178i	$-0.945889\pi$
$239$	−6.52812	+	10.1580i	−0.422269	+	0.657064i	0.563316	+	0.826241i	$0.309525\pi$
$240$	−3.39924	+	2.67399i	−0.219420	+	0.172605i
$241$	10.8647	−	4.96172i	0.699854	−	0.319613i	−0.0335197	−	0.999438i	$-0.510672\pi$
$241$	10.8647	−	4.96172i	0.699854	−	0.319613i	0.733374	+	0.679825i	$0.237944\pi$
$242$	0.460856	+	0.171890i	0.0296249	+	0.0110495i
$243$	4.51700	−	6.03401i	0.289766	−	0.387082i
$244$	−2.10298	−	1.35150i	−0.134629	−	0.0865210i
$245$	0.294036	+	12.2774i	0.0187853	+	0.784373i
$246$	−0.765891	+	5.32689i	−0.0488314	+	0.339630i
$247$	19.5997	−	1.40180i	1.24710	−	0.0891944i
$248$	6.03753	+	1.31338i	0.383384	+	0.0834000i
$249$	−15.3211	−	17.6815i	−0.970935	−	1.12052i
$250$	10.7288	+	3.14520i	0.678551	+	0.198920i
$251$	−0.919601	−	0.419968i	−0.0580447	−	0.0265081i	0.386181	−	0.922423i	$-0.373794\pi$
$251$	−0.919601	−	0.419968i	−0.0580447	−	0.0265081i	−0.444226	+	0.895915i	$0.646521\pi$
$252$	0.643405	+	0.643405i	0.0405307	+	0.0405307i
$253$	−2.91560	+	15.9941i	−0.183302	+	1.00554i
$254$		−	6.07840i		−	0.381393i
$255$	10.0413	+	8.28838i	0.628813	+	0.519038i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−9.16410	−	0.655430i	−0.571641	−	0.0408846i	−0.217473	−	0.976066i	$-0.569781\pi$
$257$	−9.16410	−	0.655430i	−0.571641	−	0.0408846i	−0.354168	+	0.935182i	$0.615236\pi$
$258$	−3.46700	+	15.9375i	−0.215846	+	0.992228i
$259$	−6.21574	−	5.38597i	−0.386227	−	0.334668i
$260$	5.68356	+	14.1909i	0.352480	+	0.880082i
$261$	−3.76204	+	1.10463i	−0.232864	+	0.0683751i
$262$	−2.35931	+	0.513237i	−0.145759	+	0.0317079i
$263$	5.75031	+	4.30463i	0.354579	+	0.265435i	0.761687	−	0.647946i	$-0.224372\pi$
$263$	5.75031	+	4.30463i	0.354579	+	0.265435i	−0.407107	+	0.913380i	$0.633463\pi$
$264$	2.72378	+	5.96425i	0.167637	+	0.367074i
$265$	−19.1573	−	13.6377i	−1.17682	−	0.837756i
$266$	−0.502287	−	3.49348i	−0.0307972	−	0.214199i
$267$	−4.61527	−	21.2161i	−0.282450	−	1.29840i
$268$	4.39296	−	8.04510i	0.268343	−	0.491433i
$269$	−7.47323	−	1.07449i	−0.455651	−	0.0655127i	−0.0893315	−	0.996002i	$-0.528473\pi$
$269$	−7.47323	−	1.07449i	−0.455651	−	0.0655127i	−0.366319	+	0.930489i	$0.619382\pi$
$270$	−5.47732	−	8.09020i	−0.333339	−	0.492354i
$271$	−17.8817	+	11.4919i	−1.08624	+	0.698083i	−0.955990	−	0.293399i	$-0.905214\pi$
$271$	−17.8817	+	11.4919i	−1.08624	+	0.698083i	−0.130248	+	0.991481i	$0.541577\pi$
$272$	−0.214766	+	3.00282i	−0.0130221	+	0.182073i
$273$	14.2506	−	7.78142i	0.862487	−	0.470953i
$274$	−6.76651	+	14.8166i	−0.408780	+	0.895102i
$275$	8.47066	−	14.6814i	0.510800	−	0.885324i
$276$	−7.62904	+	5.27647i	−0.459214	+	0.317606i
$277$	−18.4280	+	18.4280i	−1.10723	+	1.10723i	−0.113720	+	0.993513i	$0.536277\pi$
$277$	−18.4280	+	18.4280i	−1.10723	+	1.10723i	−0.993513	+	0.113720i	$0.963723\pi$
$278$	2.21506	−	0.826173i	0.132850	−	0.0495506i
$279$	1.28992	−	4.39306i	0.0772254	−	0.263006i
$280$	2.46958	−	1.20009i	0.147586	−	0.0717192i
$281$	−14.0624	−	21.8815i	−0.838890	−	1.30534i	−0.950228	−	0.311556i	$-0.899150\pi$
$281$	−14.0624	−	21.8815i	−0.838890	−	1.30534i	0.111338	−	0.993783i	$-0.464486\pi$
$282$	−1.13052	−	15.8068i	−0.0673217	−	0.941280i
$283$	16.6140	+	22.1937i	0.987601	+	1.31928i	0.947388	+	0.320089i	$0.103713\pi$
$283$	16.6140	+	22.1937i	0.987601	+	1.31928i	0.0402131	+	0.999191i	$0.487196\pi$
$284$	−1.18675	−	4.04169i	−0.0704205	−	0.239830i
$285$	0.589694	−	12.4171i	0.0349304	−	0.735523i
$286$	22.9394	−	3.29819i	1.35643	−	0.195026i
$287$	1.19398	−	3.20119i	0.0704786	−	0.188961i
$288$	−0.258957	+	0.694292i	−0.0152592	+	0.0409115i
$289$	−7.85613	+	1.12954i	−0.462125	+	0.0664436i
$290$	−0.561254	+	11.8182i	−0.0329580	+	0.693989i
$291$	3.50933	+	11.9517i	0.205720	+	0.700619i
$292$	−0.462285	−	0.617541i	−0.0270532	−	0.0361388i
$293$	−2.01578	−	28.1843i	−0.117763	−	1.64654i	−0.622029	−	0.782995i	$-0.713691\pi$
$293$	−2.01578	−	28.1843i	−0.117763	−	1.64654i	0.504266	−	0.863549i	$-0.331763\pi$
$294$	5.74313	+	8.93649i	0.334946	+	0.521187i
$295$	15.5802	−	7.57118i	0.907113	−	0.440811i
$296$	1.88703	−	6.42663i	0.109681	−	0.373540i
$297$	−13.8778	+	5.17614i	−0.805270	+	0.300350i
$298$	12.0544	−	12.0544i	0.698295	−	0.698295i
$299$	10.2975	+	31.1273i	0.595522	+	1.80014i
$300$	9.34060	−	2.50571i	0.539280	−	0.144667i
$301$	4.30153	−	9.41903i	0.247936	−	0.542904i
$302$	9.35496	−	5.10820i	0.538318	−	0.293944i
$303$	−1.30506	+	18.2471i	−0.0749738	+	1.04827i
$304$	2.41799	−	1.55395i	0.138681	−	0.0891251i
$305$	3.13377	+	4.62870i	0.179439	+	0.265038i
$306$	2.20811	+	0.317478i	0.126229	+	0.0181490i
$307$	9.81051	−	17.9666i	0.559916	−	1.02541i	−0.432401	−	0.901682i	$-0.642333\pi$
$307$	9.81051	−	17.9666i	0.559916	−	1.02541i	0.992316	−	0.123727i	$-0.0394848\pi$
$308$	−0.884833	−	4.06751i	−0.0504180	−	0.231768i
$309$	−0.636329	−	4.42577i	−0.0361995	−	0.251773i
$310$	−11.2554	−	8.01248i	−0.639264	−	0.455078i
$311$	−5.98405	−	13.1032i	−0.339324	−	0.743017i	0.660646	−	0.750698i	$-0.270282\pi$
$311$	−5.98405	−	13.1032i	−0.339324	−	0.743017i	−0.999971	+	0.00768068i	$0.997555\pi$
$312$	10.5854	+	7.92414i	0.599281	+	0.448616i
$313$	24.1463	−	5.25270i	1.36483	−	0.296900i	0.530274	−	0.847826i	$-0.322089\pi$
$313$	24.1463	−	5.25270i	1.36483	−	0.296900i	0.834554	+	0.550926i	$0.185725\pi$
$314$	−18.9721	+	5.57071i	−1.07066	+	0.314373i
$315$	−0.756467	−	1.88877i	−0.0426221	−	0.106420i
$316$	−2.92864	−	2.53768i	−0.164749	−	0.142756i
$317$	3.16918	−	14.5685i	0.177999	−	0.818248i	−0.798375	−	0.602161i	$-0.794307\pi$
$317$	3.16918	−	14.5685i	0.177999	−	0.818248i	0.976374	−	0.216088i	$-0.0693297\pi$
$318$	−20.2890	−	1.45110i	−1.13775	−	0.0813734i
$319$	17.2105	+	5.05345i	0.963602	+	0.282939i
$320$	1.72448	+	1.42343i	0.0964015	+	0.0795723i
$321$		−	1.85312i		−	0.103431i
$322$	5.44475	−	2.24374i	0.303424	−	0.125039i
$323$	−6.11859	−	6.11859i	−0.340447	−	0.340447i
$324$	−9.70936	−	4.43411i	−0.539409	−	0.246340i
$325$	0.803553	−	34.1727i	0.0445731	−	1.89556i
$326$	8.04952	+	9.28964i	0.445822	+	0.514506i
$327$	6.56562	+	1.42826i	0.363080	+	0.0789832i
$328$	2.77533	−	0.198495i	0.153242	−	0.0109601i
$329$	−1.43179	+	9.95835i	−0.0789374	+	0.549022i
$330$	−0.351031	−	14.6572i	−0.0193236	−	0.806851i
$331$	17.3472	+	11.1484i	0.953487	+	0.612769i	0.922188	−	0.386741i	$-0.126399\pi$
$331$	17.3472	+	11.1484i	0.953487	+	0.612769i	0.0312988	+	0.999510i	$0.490036\pi$
$332$	−7.24894	+	9.68345i	−0.397837	+	0.531448i
$333$	−4.65033	−	1.73448i	−0.254836	−	0.0950490i
$334$	22.9806	−	10.4949i	1.25744	−	0.574254i
$335$	−16.1095	+	12.6725i	−0.880159	+	0.692371i
$336$	1.28404	−	1.99800i	0.0700499	−	0.109000i
$337$	−5.82375	−	3.18001i	−0.317240	−	0.173226i	0.312738	−	0.949840i	$-0.398754\pi$
$337$	−5.82375	−	3.18001i	−0.317240	−	0.173226i	−0.629977	+	0.776614i	$0.716936\pi$
$338$	27.0077	−	20.2177i	1.46903	−	1.09970i
$339$	9.88961	−	11.4132i	0.537130	−	0.619881i
$340$	3.08376	−	5.98380i	0.167241	−	0.324517i
$341$	−15.8297	+	13.7165i	−0.857227	+	0.742791i
$342$	−1.02074	−	1.86935i	−0.0551953	−	0.101083i
$343$	−5.36062	−	14.3724i	−0.289446	−	0.776035i
$344$	8.43271			0.454661
$345$	20.3256	−	4.13358i	1.09429	−	0.222544i
$346$	−15.2328			−0.818922
$347$	−3.47467	−	9.31595i	−0.186530	−	0.500106i	0.809701	−	0.586842i	$-0.199629\pi$
$347$	−3.47467	−	9.31595i	−0.186530	−	0.500106i	−0.996231	+	0.0867358i	$0.972356\pi$
$348$	4.90469	+	8.98227i	0.262919	+	0.481500i
$349$	5.68455	−	4.92569i	0.304287	−	0.263666i	−0.489310	−	0.872110i	$-0.662751\pi$
$349$	5.68455	−	4.92569i	0.304287	−	0.263666i	0.793597	+	0.608444i	$0.208206\pi$
$350$	−6.13261	+	0.293914i	−0.327802	+	0.0157103i
$351$	−19.5608	+	22.5744i	−1.04408	+	1.20493i
$352$	2.71381	−	2.03153i	0.144646	−	0.108281i
$353$	21.3708	+	11.6693i	1.13745	+	0.621097i	0.933746	−	0.357935i	$-0.116519\pi$
$353$	21.3708	+	11.6693i	1.13745	+	0.621097i	0.203707	+	0.979032i	$0.434701\pi$
$354$	8.10076	−	12.6050i	0.430551	−	0.669950i
$355$	−1.11686	+	9.35258i	−0.0592769	+	0.496383i
$356$	−10.2112	+	4.66329i	−0.541192	+	0.247154i
$357$	−6.69919	−	2.49867i	−0.354559	−	0.132244i
$358$	9.38946	−	12.5429i	0.496248	−	0.662910i
$359$	13.4835	+	8.66533i	0.711633	+	0.457339i	0.845717	−	0.533631i	$-0.179173\pi$
$359$	13.4835	+	8.66533i	0.711633	+	0.457339i	−0.134084	+	0.990970i	$0.542809\pi$
$360$	1.14326	−	1.19936i	0.0602549	−	0.0632118i
$361$	1.52826	−	10.6292i	0.0804345	−	0.559434i
$362$	3.46413	−	0.247759i	0.182070	−	0.0130219i
$363$	−0.929615	−	0.202225i	−0.0487921	−	0.0106141i
$364$	−5.49734	−	6.34426i	−0.288139	−	0.332530i
$365$	0.406906	+	1.67623i	0.0212985	+	0.0877379i
$366$	4.39813	+	2.00856i	0.229894	+	0.104989i
$367$	13.8234	+	13.8234i	0.721574	+	0.721574i	0.968926	−	0.247352i	$-0.0795604\pi$
$367$	13.8234	+	13.8234i	0.721574	+	0.721574i	−0.247352	+	0.968926i	$0.579560\pi$
$368$	3.50411	+	3.27432i	0.182665	+	0.170686i
$369$		−	2.06181i		−	0.107333i
$370$	−9.53407	+	11.5505i	−0.495653	+	0.600481i
$371$	12.3905	+	3.63818i	0.643283	+	0.188885i
$372$	−11.9203	−	0.852555i	−0.618038	−	0.0442029i
$373$	−6.23412	+	28.6578i	−0.322791	+	1.48384i	0.474504	+	0.880254i	$0.342628\pi$
$373$	−6.23412	+	28.6578i	−0.322791	+	1.48384i	−0.797294	+	0.603591i	$0.793736\pi$
$374$	−7.71278	−	6.68317i	−0.398819	−	0.345578i
$375$	−21.4059	−	3.06821i	−1.10540	−	0.158442i
$376$	−7.86138	+	2.30831i	−0.405420	+	0.119042i
$377$	35.3464	−	7.68914i	1.82043	−	0.396011i
$378$	4.29503	+	3.21522i	0.220912	+	0.165373i
$379$	1.51456	+	3.31643i	0.0777979	+	0.170354i	0.944534	−	0.328413i	$-0.106514\pi$
$379$	1.51456	+	3.31643i	0.0777979	+	0.170354i	−0.866736	+	0.498767i	$0.833786\pi$
$380$	−6.33793	+	1.06672i	−0.325129	+	0.0547216i
$381$	1.67315	+	11.6370i	0.0857179	+	0.596181i
$382$	1.10778	+	5.09238i	0.0566789	+	0.260549i
$383$	12.2644	−	22.4606i	0.626682	−	1.14768i	−0.350758	−	0.936466i	$-0.614076\pi$
$383$	12.2644	−	22.4606i	0.626682	−	1.14768i	0.977440	−	0.211216i	$-0.0677422\pi$
$384$	1.91448	+	0.275261i	0.0976980	+	0.0140469i
$385$	−1.76022	+	9.14000i	−0.0897089	+	0.465817i
$386$	−8.59273	+	5.52221i	−0.437358	+	0.281073i
$387$	0.445780	−	6.23282i	0.0226603	−	0.316832i
$388$	5.65233	−	3.08641i	0.286954	−	0.156689i
$389$	−8.13773	+	17.8191i	−0.412599	+	0.903466i	0.583237	+	0.812302i	$0.301786\pi$
$389$	−8.13773	+	17.8191i	−0.412599	+	0.903466i	−0.995836	+	0.0911640i	$0.970941\pi$
$390$	−14.7873	−	25.6038i	−0.748783	−	1.29650i
$391$	7.38968	−	12.4034i	0.373712	−	0.627265i
$392$	3.88356	−	3.88356i	0.196150	−	0.196150i
$393$	4.37559	−	1.63201i	0.220719	−	0.0823241i
$394$	−3.59878	+	12.2563i	−0.181304	+	0.617464i
$395$	3.78729	+	7.79360i	0.190559	+	0.392139i
$396$	−1.35809	−	2.11324i	−0.0682468	−	0.106194i
$397$	0.726566	+	10.1587i	0.0364653	+	0.509851i	0.982558	+	0.185956i	$0.0595381\pi$
$397$	0.726566	+	10.1587i	0.0364653	+	0.509851i	−0.946093	+	0.323896i	$0.895007\pi$
$398$	7.86811	+	10.5106i	0.394393	+	0.526847i
$399$	1.92324	+	6.54995i	0.0962824	+	0.327908i
$400$	−2.29242	−	4.44351i	−0.114621	−	0.222176i
$401$	4.96565	−	0.713952i	0.247973	−	0.0356531i	−0.0172077	−	0.999852i	$-0.505478\pi$
$401$	4.96565	−	0.713952i	0.247973	−	0.0356531i	0.265180	+	0.964199i	$0.414569\pi$
$402$	−6.19574	+	16.6114i	−0.309015	+	0.828502i
$403$	−14.7616	+	39.5773i	−0.735325	+	1.97148i
$404$	9.36192	−	1.34604i	0.465773	−	0.0669681i
$405$	16.0574	+	17.6586i	0.797898	+	0.877462i
$406$	−1.83049	−	6.23406i	−0.0908455	−	0.309391i
$407$	13.6071	+	18.1769i	0.674478	+	0.900997i
$408$	−0.415394	−	5.80797i	−0.0205651	−	0.287538i
$409$	−15.0034	−	23.3458i	−0.741872	−	1.15437i	−0.982951	−	0.183869i	$-0.941138\pi$
$409$	−15.0034	−	23.3458i	−0.741872	−	1.15437i	0.241079	−	0.970505i	$-0.422499\pi$
$410$	−5.87978	−	2.03406i	−0.290382	−	0.100455i
$411$	8.87593	−	30.2286i	0.437817	−	1.49107i
$412$	−2.16597	+	0.807867i	−0.106710	+	0.0398007i
$413$	−6.72638	+	6.72638i	−0.330983	+	0.330983i
$414$	2.60537	−	2.41689i	0.128047	−	0.118783i
$415$	23.4221	−	13.5273i	1.14975	−	0.664028i
$416$	2.83996	−	6.21864i	0.139240	−	0.304894i
$417$	−4.01327	+	2.19141i	−0.196531	+	0.107314i
$418$	−0.695107	+	9.71886i	−0.0339988	+	0.475365i
$419$	9.79338	−	6.29382i	0.478438	−	0.307473i	−0.279103	−	0.960261i	$-0.590037\pi$
$419$	9.79338	−	6.29382i	0.478438	−	0.307473i	0.757541	+	0.652788i	$0.226401\pi$
$420$	−4.39764	+	2.97733i	−0.214583	+	0.145279i
$421$	−15.7117	−	2.25899i	−0.765739	−	0.110097i	−0.251632	−	0.967823i	$-0.580967\pi$
$421$	−15.7117	−	2.25899i	−0.765739	−	0.110097i	−0.514107	+	0.857726i	$0.671876\pi$
$422$	5.71938	−	10.4743i	0.278415	−	0.509880i
$423$	1.29055	+	5.93256i	0.0627487	+	0.288451i
$424$	1.49666	+	10.4095i	0.0726843	+	0.505530i
$425$	−11.6045	+	9.58713i	−0.562900	+	0.465044i
$426$	3.38453	+	7.41108i	0.163981	+	0.359068i
$427$	−2.45734	−	1.83954i	−0.118919	−	0.0890216i
$428$	−0.936201	+	0.203658i	−0.0452530	+	0.00984418i
$429$	−43.0092	+	12.6286i	−2.07650	+	0.609717i
$430$	−17.3347	−	7.42020i	−0.835956	−	0.357834i
$431$	−11.3614	−	9.84467i	−0.547257	−	0.474201i	0.336802	−	0.941575i	$-0.390655\pi$
$431$	−11.3614	−	9.84467i	−0.547257	−	0.474201i	−0.884060	+	0.467374i	$0.845200\pi$
$432$	−0.928754	+	4.26941i	−0.0446847	+	0.205412i
$433$	1.95499	+	0.139823i	0.0939507	+	0.00671949i	0.118235	−	0.992986i	$-0.462276\pi$
$433$	1.95499	+	0.139823i	0.0939507	+	0.00671949i	−0.0242847	+	0.999705i	$0.507731\pi$
$434$	7.27973	+	2.13752i	0.349438	+	0.102604i
$435$	−2.17858	−	22.7802i	−0.104455	−	1.09223i
$436$		−	3.47393i		−	0.166371i
$437$	−13.7082	+	1.44866i	−0.655752	+	0.0692987i
$438$	1.05502	+	1.05502i	0.0504109	+	0.0504109i
$439$	−20.0871	−	9.17346i	−0.958704	−	0.437825i	−0.126298	−	0.991992i	$-0.540310\pi$
$439$	−20.0871	−	9.17346i	−0.958704	−	0.437825i	−0.832406	+	0.554167i	$0.813037\pi$
$440$	−7.36626	+	1.78817i	−0.351173	+	0.0852475i
$441$	−2.66514	−	3.07574i	−0.126911	−	0.146464i
$442$	−20.1107	−	4.37482i	−0.956569	−	0.208089i
$443$	−12.2046	+	0.872890i	−0.579858	+	0.0414722i	−0.358188	−	0.933650i	$-0.616605\pi$
$443$	−12.2046	+	0.872890i	−0.579858	+	0.0414722i	−0.221670	+	0.975122i	$0.571151\pi$
$444$	−1.84368	+	12.8231i	−0.0874973	+	0.608557i
$445$	25.0941	−	0.600989i	1.18957	−	0.0284896i
$446$	−21.7254	−	13.9621i	−1.02873	−	0.661123i
$447$	−19.7599	+	26.3961i	−0.934611	+	1.24849i
$448$	−1.15051	−	0.429118i	−0.0543564	−	0.0202739i
$449$	29.4535	−	13.4510i	1.39000	−	0.634790i	0.426987	−	0.904258i	$-0.359575\pi$
$449$	29.4535	−	13.4510i	1.39000	−	0.634790i	0.963009	+	0.269468i	$0.0868479\pi$
$450$	−3.40549	+	1.45949i	−0.160537	+	0.0688008i
$451$	−5.09948	+	7.93495i	−0.240125	+	0.373642i
$452$	−6.85285	−	3.74194i	−0.322331	−	0.176006i
$453$	−16.5038	+	12.3546i	−0.775417	+	0.580470i
$454$	−12.3790	+	14.2862i	−0.580977	+	0.670483i
$455$	5.71812	+	17.8789i	0.268070	+	0.838176i
$456$	−4.20146	+	3.64059i	−0.196752	+	0.170486i
$457$	−9.18193	−	16.8155i	−0.429513	−	0.786594i	0.569870	−	0.821735i	$-0.306994\pi$
$457$	−9.18193	−	16.8155i	−0.429513	−	0.786594i	−0.999382	+	0.0351413i	$0.988812\pi$
$458$	−5.63130	−	15.0981i	−0.263133	−	0.705488i
$459$	13.1537			0.613960
$460$	−4.32208	−	9.81426i	−0.201518	−	0.457592i
$461$	3.60200			0.167762			0.0838809	−	0.996476i	$-0.473268\pi$
$461$	3.60200			0.167762			0.0838809	+	0.996476i	$0.473268\pi$
$462$	2.81362	+	7.54362i	0.130902	+	0.350961i
$463$	−17.7726	−	32.5481i	−0.825963	−	1.51264i	−0.858293	−	0.513160i	$-0.828475\pi$
$463$	−17.7726	−	32.5481i	−0.825963	−	1.51264i	0.0323300	−	0.999477i	$-0.489707\pi$
$464$	3.99884	−	3.46501i	0.185641	−	0.160859i
$465$	23.7538	+	12.2416i	1.10156	+	0.567690i
$466$	13.8357	−	15.9672i	0.640926	−	0.739668i
$467$	13.0073	−	9.73712i	0.601905	−	0.450580i	−0.254366	−	0.967108i	$-0.581867\pi$
$467$	13.0073	−	9.73712i	0.601905	−	0.450580i	0.856270	+	0.516528i	$0.172776\pi$
$468$	−4.44622	−	2.42782i	−0.205527	−	0.112226i
$469$	6.08525	−	9.46883i	0.280991	−	0.437230i
$470$	18.1914	+	2.17238i	0.839109	+	0.100204i
$471$	34.7884	−	15.8873i	1.60296	−	0.732049i
$472$	−7.25837	−	2.70723i	−0.334093	−	0.124610i
$473$	−17.1313	+	22.8847i	−0.787698	+	1.05224i
$474$	6.30536	+	4.05221i	0.289615	+	0.186124i
$475$	13.9672	+	3.38413i	0.640861	+	0.155275i
$476$	−0.526092	+	3.65905i	−0.0241134	+	0.167712i
$477$	7.77304	−	0.555939i	0.355903	−	0.0254547i
$478$	−11.7988	−	2.56668i	−0.539667	−	0.117397i
$479$	7.69236	+	8.87745i	0.351473	+	0.405621i	0.903765	−	0.428030i	$-0.140792\pi$
$479$	7.69236	+	8.87745i	0.351473	+	0.405621i	−0.552292	+	0.833651i	$0.686247\pi$
$480$	−3.69331	−	2.25045i	−0.168576	−	0.102719i
$481$	41.6521	+	19.0219i	1.89917	+	0.867323i
$482$	8.44570	+	8.44570i	0.384691	+	0.384691i
$483$	−9.80627	+	5.79432i	−0.446201	+	0.263651i
$484$			0.491868i			0.0223576i
$485$	−14.3351	+	1.37093i	−0.650922	+	0.0622507i
$486$	7.23210	+	2.12353i	0.328055	+	0.0963255i
$487$	16.2893	+	1.16504i	0.738141	+	0.0527929i	0.435346	−	0.900263i	$-0.356626\pi$
$487$	16.2893	+	1.16504i	0.738141	+	0.0527929i	0.302794	+	0.953056i	$0.402080\pi$
$488$	0.531374	−	2.44269i	0.0240542	−	0.110575i
$489$	−17.9677	−	15.5691i	−0.812530	−	0.704061i
$490$	−11.4005	+	4.56600i	−0.515024	+	0.206271i
$491$	37.4107	−	10.9848i	1.68832	−	0.495736i	0.710241	−	0.703959i	$-0.248586\pi$
$491$	37.4107	−	10.9848i	1.68832	−	0.495736i	0.978081	+	0.208223i	$0.0667679\pi$
$492$	−5.25868	+	1.14396i	−0.237079	+	0.0515735i
$493$	−12.7520	−	9.54601i	−0.574320	−	0.429931i
$494$	8.16282	+	17.8741i	0.367262	+	0.804193i
$495$	0.932273	+	5.53911i	0.0419026	+	0.248965i
$496$	0.879326	+	6.11585i	0.0394829	+	0.274610i
$497$	−1.09948	−	5.05422i	−0.0493184	−	0.226713i
$498$	11.2125	−	20.5342i	0.502444	−	0.920157i
$499$	−17.6253	−	2.53413i	−0.789016	−	0.113443i	−0.263985	−	0.964527i	$-0.585037\pi$
$499$	−17.6253	−	2.53413i	−0.789016	−	0.113443i	−0.525031	+	0.851083i	$0.675946\pi$
$500$	0.802444	+	11.1515i	0.0358864	+	0.498711i
$501$	−41.1071	+	26.4179i	−1.83653	+	1.18027i
$502$	0.0721210	−	1.00838i	0.00321892	−	0.0450063i
$503$	−6.23170	+	3.40276i	−0.277858	+	0.151722i	−0.612136	−	0.790753i	$-0.709689\pi$
$503$	−6.23170	+	3.40276i	−0.277858	+	0.151722i	0.334278	+	0.942475i	$0.391508\pi$
$504$	−0.377991	+	0.827685i	−0.0168371	+	0.0368680i
$505$	−20.4293	−	5.47085i	−0.909093	−	0.243449i
$506$	−16.0046	+	2.85761i	−0.711491	+	0.127036i
$507$	−46.1407	+	46.1407i	−2.04918	+	2.04918i
$508$	5.69516	−	2.12418i	0.252682	−	0.0942454i
$509$	−3.19265	+	10.8732i	−0.141512	+	0.481944i	−0.999496	−	0.0317306i	$-0.989898\pi$
$509$	−3.19265	+	10.8732i	−0.141512	+	0.481944i	0.857985	+	0.513675i	$0.171716\pi$
$510$	−4.25671	+	12.3047i	−0.188490	+	0.544862i
$511$	−0.512111	−	0.796861i	−0.0226545	−	0.0352511i
$512$	−0.0713392	−	0.997452i	−0.00315278	−	0.0440816i
$513$	−7.52601	−	10.0536i	−0.332281	−	0.443876i
$514$	−2.58842	−	8.81535i	−0.114170	−	0.388829i
$515$	5.16337	+	0.245212i	0.227525	+	0.0108053i
$516$	−16.1443	+	2.32120i	−0.710712	+	0.102185i
$517$	9.70632	−	26.0237i	0.426884	−	1.14452i
$518$	2.87420	−	7.70604i	0.126285	−	0.338584i
$519$	29.1630	−	4.19301i	1.28011	−	0.184053i
$520$	−11.3100	+	10.2844i	−0.495974	+	0.451002i
$521$	2.48744	+	8.47144i	0.108977	+	0.371141i	0.995865	−	0.0908429i	$-0.0289561\pi$
$521$	2.48744	+	8.47144i	0.108977	+	0.371141i	−0.886889	+	0.461984i	$0.847138\pi$
$522$	−2.34968	−	3.13881i	−0.102843	−	0.137382i
$523$	−1.69841	−	23.7469i	−0.0742664	−	1.03838i	−0.888809	−	0.458277i	$-0.848467\pi$
$523$	−1.69841	−	23.7469i	−0.0742664	−	1.03838i	0.814543	−	0.580103i	$-0.196988\pi$
$524$	−1.30537	−	2.03120i	−0.0570255	−	0.0887334i
$525$	11.6599	−	2.25076i	0.508879	−	0.0982313i
$526$	−2.02369	+	6.89206i	−0.0882372	+	0.300508i
$527$	17.4283	−	6.50040i	0.759187	−	0.283162i
$528$	−4.63634	+	4.63634i	−0.201771	+	0.201771i
$529$	−7.95951	−	21.5788i	−0.346066	−	0.938210i
$530$	6.08303	−	22.7153i	0.264230	−	0.986691i
$531$	−2.38468	+	5.22172i	−0.103486	+	0.226604i
$532$	3.09769	−	1.69146i	0.134302	−	0.0733343i
$533$	−1.35700	+	18.9733i	−0.0587782	+	0.821827i
$534$	18.2655	−	11.7385i	0.790426	−	0.507976i
$535$	2.10371	+	0.405141i	0.0909514	+	0.0175158i
$536$	9.07304	+	1.30451i	0.391896	+	0.0563461i
$537$	−14.5234	+	26.5976i	−0.626731	+	1.14777i
$538$	−1.60488	−	7.37753i	−0.0691915	−	0.318068i
$539$	2.64966	+	18.4288i	0.114129	+	0.793786i
$540$	5.66599	−	7.95921i	0.243825	−	0.342510i
$541$	−10.9010	−	23.8698i	−0.468669	−	1.02624i	−0.985425	−	0.170109i	$-0.945588\pi$
$541$	−10.9010	−	23.8698i	−0.468669	−	1.02624i	0.516756	−	0.856133i	$-0.327139\pi$
$542$	−17.0164	−	12.7383i	−0.730915	−	0.547156i
$543$	−6.56381	+	1.42787i	−0.281680	+	0.0612757i
$544$	−2.88855	+	0.848154i	−0.123846	+	0.0363643i
$545$	−3.05682	+	7.14121i	−0.130940	+	0.305896i
$546$	12.2709	+	10.6328i	0.525145	+	0.455041i
$547$	−2.50695	+	11.5243i	−0.107190	+	0.492743i	0.891983	+	0.452069i	$0.149314\pi$
$547$	−2.50695	+	11.5243i	−0.107190	+	0.492743i	−0.999172	+	0.0406736i	$0.987050\pi$
$548$	−16.2470	−	1.16201i	−0.694039	−	0.0496387i
$549$	−1.77736	−	0.521880i	−0.0758558	−	0.0222733i
$550$	16.7160	+	2.80595i	0.712771	+	0.119646i
$551$			15.2084i			0.647900i
$552$	−7.60986	−	5.30409i	−0.323897	−	0.225757i
$553$	−3.36470	−	3.36470i	−0.143082	−	0.143082i
$554$	−23.7061	−	10.8262i	−1.00717	−	0.459961i
$555$	15.0734	−	24.7376i	0.639831	−	1.05005i
$556$	1.54817	+	1.78668i	0.0656569	+	0.0757721i
$557$	−30.4859	−	6.63181i	−1.29173	−	0.280999i	−0.486353	−	0.873762i	$-0.661673\pi$
$557$	−30.4859	−	6.63181i	−1.29173	−	0.280999i	−0.805376	+	0.592764i	$0.798037\pi$
$558$	4.56686	−	0.326628i	0.193330	−	0.0138273i
$559$	−8.20440	+	57.0629i	−0.347009	+	2.41350i
$560$	1.98746	+	1.89449i	0.0839854	+	0.0800566i
$561$	16.6056	+	10.6718i	0.701089	+	0.450563i
$562$	15.5875	−	20.8225i	0.657520	−	0.878344i
$563$	−15.2676	−	5.69451i	−0.643451	−	0.239995i	0.00649040	−	0.999979i	$-0.497934\pi$
$563$	−15.2676	−	5.69451i	−0.643451	−	0.239995i	−0.649942	+	0.759984i	$0.725207\pi$
$564$	14.4151	−	6.58315i	0.606985	−	0.277201i
$565$	10.7945	+	13.7222i	0.454126	+	0.577296i
$566$	−14.9884	+	23.3224i	−0.630010	+	0.980314i
$567$	−11.5036	−	6.28144i	−0.483106	−	0.263796i
$568$	3.37213	−	2.52435i	0.141492	−	0.105919i
$569$	−11.4435	+	13.2065i	−0.479736	+	0.553645i	−0.943094	−	0.332526i	$-0.892099\pi$
$569$	−11.4435	+	13.2065i	−0.479736	+	0.553645i	0.463358	+	0.886171i	$0.346644\pi$
$570$	11.8402	−	3.78680i	0.495933	−	0.158612i
$571$	17.9309	−	15.5372i	0.750384	−	0.650211i	−0.193270	−	0.981146i	$-0.561909\pi$
$571$	17.9309	−	15.5372i	0.750384	−	0.650211i	0.943654	+	0.330935i	$0.107364\pi$
$572$	11.1067	+	20.3405i	0.464396	+	0.850477i
$573$	−3.52256	−	9.44435i	−0.147157	−	0.394543i
$574$	3.41661			0.142607
$575$	0.248836	+	23.9779i	0.0103772	+	0.999946i
$576$	−0.741013			−0.0308755
$577$	4.34235	+	11.6423i	0.180774	+	0.484674i	0.995455	−	0.0952356i	$-0.0303604\pi$
$577$	4.34235	+	11.6423i	0.180774	+	0.484674i	−0.814681	+	0.579910i	$0.803088\pi$
$578$	−3.80376	−	6.96607i	−0.158216	−	0.289750i
$579$	14.9306	−	12.9374i	0.620494	−	0.537661i
$580$	−11.2692	+	3.60417i	−0.467928	+	0.149655i
$581$	−9.72678	+	11.2253i	−0.403535	+	0.465704i
$582$	−9.97173	+	7.46474i	−0.413341	+	0.309423i
$583$	−31.2899	−	17.0856i	−1.29590	−	0.707613i
$584$	0.417053	−	0.648947i	0.0172578	−	0.0268536i
$585$	7.00359	+	8.90313i	0.289563	+	0.368099i
$586$	25.7028	−	11.7381i	1.06177	−	0.484896i
$587$	5.19098	+	1.93614i	0.214255	+	0.0799129i	0.454300	−	0.890849i	$-0.349890\pi$
$587$	5.19098	+	1.93614i	0.214255	+	0.0799129i	−0.240045	+	0.970762i	$0.577162\pi$
$588$	−6.36602	+	8.50401i	−0.262530	+	0.350699i
$589$	−14.9401	−	9.60145i	−0.615598	−	0.395621i
$590$	12.5385	+	11.9520i	0.516203	+	0.492056i
$591$	3.51611	−	24.4551i	0.144634	−	1.00595i
$592$	6.68088	−	0.477826i	0.274582	−	0.0196385i
$593$	−29.8849	−	6.50107i	−1.22723	−	0.266967i	−0.448186	−	0.893940i	$-0.647930\pi$
$593$	−29.8849	−	6.50107i	−1.22723	−	0.266967i	−0.779041	+	0.626973i	$0.784294\pi$
$594$	−9.69957	−	11.1939i	−0.397978	−	0.459291i
$595$	4.30118	−	7.05882i	0.176331	−	0.289384i
$596$	15.5070	+	7.08181i	0.635191	+	0.290082i
$597$	−17.9565	−	17.9565i	−0.734911	−	0.734911i
$598$	−25.5661	+	20.5261i	−1.04548	+	0.839376i
$599$		−	7.13312i		−	0.291451i	−0.989325	−	0.145726i	$-0.953448\pi$
$599$		−	7.13312i		−	0.291451i	0.989325	−	0.145726i	$-0.0465517\pi$
$600$	5.61193	+	7.87601i	0.229106	+	0.321537i
$601$	17.7450	+	5.21042i	0.723836	+	0.212537i	0.622840	−	0.782350i	$-0.285979\pi$
$601$	17.7450	+	5.21042i	0.723836	+	0.212537i	0.100996	+	0.994887i	$0.467797\pi$
$602$	10.3284	+	0.738701i	0.420954	+	0.0301072i
$603$	1.44382	−	6.63715i	0.0587970	−	0.270286i
$604$	8.05535	+	6.98000i	0.327767	+	0.284012i
$605$	0.432810	−	1.01111i	0.0175962	−	0.0411075i
$606$	−17.5527	+	5.15395i	−0.713031	+	0.209365i
$607$	−37.7509	+	8.21220i	−1.53226	+	0.333323i	−0.898069	−	0.439854i	$-0.855030\pi$
$607$	−37.7509	+	8.21220i	−1.53226	+	0.333323i	−0.634191	+	0.773177i	$0.718667\pi$
$608$	2.30097	+	1.72249i	0.0933168	+	0.0698561i
$609$	5.22043	+	11.4311i	0.211542	+	0.463213i
$610$	−3.24172	+	4.55375i	−0.131253	+	0.184376i
$611$	−7.97144	−	55.4426i	−0.322490	−	2.24297i
$612$	0.474194	+	2.17983i	0.0191682	+	0.0881146i
$613$	16.6308	−	30.4571i	0.671713	−	1.23015i	−0.290245	−	0.956953i	$-0.593737\pi$
$613$	16.6308	−	30.4571i	0.671713	−	1.23015i	0.961958	−	0.273198i	$-0.0880815\pi$
$614$	20.2622	+	2.91327i	0.817717	+	0.117570i
$615$	11.8166	+	2.27569i	0.476493	+	0.0917648i
$616$	3.50184	−	2.25049i	0.141093	−	0.0906750i
$617$	−2.48141	+	34.6946i	−0.0998978	+	1.39675i	0.662217	+	0.749312i	$0.269616\pi$
$617$	−2.48141	+	34.6946i	−0.0998978	+	1.39675i	−0.762115	+	0.647442i	$0.775839\pi$
$618$	3.92435	−	2.14286i	0.157860	−	0.0861983i
$619$	7.95624	−	17.4217i	0.319788	−	0.700238i	−0.679658	−	0.733530i	$-0.737872\pi$
$619$	7.95624	−	17.4217i	0.319788	−	0.700238i	0.999446	+	0.0332912i	$0.0105989\pi$
$620$	3.57393	−	13.3458i	0.143532	−	0.535981i
$621$	13.1777	−	16.2920i	0.528803	−	0.653775i
$622$	10.1859	−	10.1859i	0.408416	−	0.408416i
$623$	−12.9152	+	4.81711i	−0.517436	+	0.192994i
$624$	−3.72530	+	12.6872i	−0.149131	+	0.507895i
$625$	8.16300	−	23.6298i	0.326520	−	0.945190i
$626$	13.3598	+	20.7882i	0.533964	+	0.830864i
$627$	−1.34445	−	18.7979i	−0.0536923	−	0.750717i
$628$	−11.8495	−	15.8291i	−0.472848	−	0.631652i
$629$	−5.68089	−	19.3473i	−0.226512	−	0.771429i
$630$	1.50532	−	1.36883i	0.0599736	−	0.0545355i
$631$	−28.4882	+	4.09599i	−1.13410	+	0.163059i	−0.683696	−	0.729767i	$-0.739629\pi$
$631$	−28.4882	+	4.09599i	−1.13410	+	0.163059i	−0.450403	+	0.892825i	$0.648720\pi$
$632$	1.35423	−	3.63082i	0.0538682	−	0.144426i
$633$	−8.06650	+	21.6271i	−0.320615	+	0.859601i
$634$	14.7575	−	2.12180i	0.586094	−	0.0842676i
$635$	−13.5764	−	0.644753i	−0.538764	−	0.0255862i
$636$	−5.73066	−	19.5169i	−0.227236	−	0.773893i
$637$	22.5011	+	30.0579i	0.891525	+	1.19094i
$638$	1.27961	+	17.8913i	0.0506604	+	0.708325i
$639$	−1.68755	−	2.62587i	−0.0667583	−	0.103878i
$640$	−0.731040	+	2.11319i	−0.0288969	+	0.0835312i
$641$	7.58857	−	25.8443i	0.299731	−	1.02079i	−0.662615	−	0.748960i	$-0.730554\pi$
$641$	7.58857	−	25.8443i	0.299731	−	1.02079i	0.962346	−	0.271828i	$-0.0876283\pi$
$642$	1.73628	−	0.647599i	0.0685255	−	0.0255587i
$643$	8.89632	−	8.89632i	0.350837	−	0.350837i	−0.509584	−	0.860421i	$-0.670201\pi$
$643$	8.89632	−	8.89632i	0.350837	−	0.350837i	0.860421	+	0.509584i	$0.170201\pi$
$644$	4.00501	+	4.31735i	0.157820	+	0.170128i
$645$	35.2296	+	9.43426i	1.38716	+	0.371474i
$646$	3.59458	−	7.87103i	0.141427	−	0.309682i
$647$	18.8933	−	10.3165i	0.742774	−	0.405585i	−0.0628418	−	0.998024i	$-0.520016\pi$
$647$	18.8933	−	10.3165i	0.742774	−	0.405585i	0.805616	+	0.592438i	$0.201835\pi$
$648$	0.761470	−	10.6467i	0.0299134	−	0.418244i
$649$	22.0925	−	14.1980i	0.867206	−	0.557320i
$650$	32.2989	−	11.1893i	1.26687	−	0.438879i
$651$	−14.5253	−	2.08842i	−0.569291	−	0.0818517i
$652$	−5.89091	+	10.7884i	−0.230706	+	0.422506i
$653$	1.37409	+	6.31659i	0.0537723	+	0.247187i	0.996185	−	0.0872645i	$-0.0278125\pi$
$653$	1.37409	+	6.31659i	0.0537723	+	0.247187i	−0.942413	+	0.334452i	$0.891449\pi$
$654$	0.956239	+	6.65079i	0.0373919	+	0.260066i
$655$	0.896082	+	5.32409i	0.0350128	+	0.208029i
$656$	1.15586	+	2.53097i	0.0451287	+	0.0988180i
$657$	−0.457606	−	0.342559i	−0.0178529	−	0.0133645i
$658$	−9.83083	+	2.13857i	−0.383246	+	0.0833700i
$659$	−11.2516	+	3.30376i	−0.438298	+	0.128696i	−0.493435	−	0.869783i	$-0.664259\pi$
$659$	−11.2516	+	3.30376i	−0.438298	+	0.128696i	0.0551364	+	0.998479i	$0.482441\pi$
$660$	13.6104	−	5.45106i	0.529783	−	0.212182i
$661$	−18.8706	−	16.3515i	−0.733982	−	0.635999i	0.205476	−	0.978662i	$-0.434126\pi$
$661$	−18.8706	−	16.3515i	−0.733982	−	0.635999i	−0.939458	+	0.342663i	$0.888671\pi$
$662$	−4.38323	+	20.1494i	−0.170359	+	0.783128i
$663$	39.7058	+	2.83982i	1.54205	+	0.110289i
$664$	−11.6062	−	3.40787i	−0.450406	−	0.132251i
$665$	−7.85615	+	0.751320i	−0.304648	+	0.0291349i
$666$		−	4.96326i		−	0.192322i
$667$	−24.5989	+	6.23103i	−0.952473	+	0.241266i
$668$	17.8641	+	17.8641i	0.691181	+	0.691181i
$669$	45.4361	+	20.7500i	1.75666	+	0.802240i
$670$	−17.5032	−	10.6653i	−0.676207	−	0.412035i
$671$	5.54948	+	6.40444i	0.214235	+	0.247241i
$672$	2.32075	+	0.504848i	0.0895248	+	0.0194749i
$673$	47.8409	−	3.42165i	1.84413	−	0.131895i	0.894859	−	0.446350i	$-0.147276\pi$
$673$	47.8409	−	3.42165i	1.84413	−	0.131895i	0.949272	+	0.314455i	$0.101822\pi$
$674$	0.944315	−	6.56786i	0.0363737	−	0.252984i
$675$	−18.6509	+	11.3757i	−0.717872	+	0.437851i
$676$	28.3812	+	18.2395i	1.09159	+	0.701520i
$677$	15.1819	−	20.2806i	0.583487	−	0.779448i	−0.407528	−	0.913193i	$-0.633609\pi$
$677$	15.1819	−	20.2806i	0.583487	−	0.779448i	0.991016	+	0.133745i	$0.0427002\pi$
$678$	14.1497	+	5.27756i	0.543415	+	0.202683i
$679$	7.19335	−	3.28509i	0.276056	−	0.126070i
$680$	6.68418	+	0.798209i	0.256327	+	0.0306099i
$681$	19.7670	−	30.7581i	0.757474	−	1.17865i
$682$	−18.3836	−	10.0382i	−0.703945	−	0.384383i
$683$	23.4042	−	17.5202i	0.895538	−	0.670392i	−0.0489979	−	0.998799i	$-0.515603\pi$
$683$	23.4042	−	17.5202i	0.895538	−	0.670392i	0.944536	+	0.328407i	$0.106512\pi$
$684$	1.39477	−	1.60965i	0.0533304	−	0.0615465i
$685$	32.3758	+	16.6850i	1.23702	+	0.637500i
$686$	11.5928	−	10.0453i	0.442617	−	0.383530i
$687$	14.9369	+	27.3550i	0.569880	+	1.04366i
$688$	2.94693	+	7.90102i	0.112351	+	0.301224i
$689$	−71.8957			−2.73901
$690$	10.9760	+	17.5995i	0.417850	+	0.670003i
$691$	24.3592			0.926668			0.463334	−	0.886184i	$-0.346653\pi$
$691$	24.3592			0.926668			0.463334	+	0.886184i	$0.346653\pi$
$692$	−5.32333	−	14.2724i	−0.202363	−	0.542555i
$693$	−1.47828	−	2.70726i	−0.0561551	−	0.102840i
$694$	7.51430	−	6.51118i	0.285239	−	0.247161i
$695$	−1.61034	−	5.03508i	−0.0610838	−	0.190991i
$696$	−6.70192	+	7.73443i	−0.254036	+	0.293173i
$697$	6.70569	−	5.01982i	0.253996	−	0.190139i
$698$	6.60167	+	3.60479i	0.249877	+	0.136443i
$699$	−22.0930	+	34.3774i	−0.835635	+	1.30027i
$700$	−2.41851	−	5.64324i	−0.0914111	−	0.213294i
$701$	−25.1061	+	11.4656i	−0.948244	+	0.433049i	−0.828646	−	0.559774i	$-0.810888\pi$
$701$	−25.1061	+	11.4656i	−0.948244	+	0.433049i	−0.119599	+	0.992822i	$0.538161\pi$
$702$	−27.9869	−	10.4386i	−1.05630	−	0.393978i
$703$	−11.5371	+	15.4118i	−0.435131	+	0.581267i
$704$	2.85182	+	1.83275i	0.107482	+	0.0690745i
$705$	−35.4252	+	0.848413i	−1.33419	+	0.0319531i
$706$	−3.46526	+	24.1014i	−0.130417	+	0.907068i
$707$	11.5844	−	0.828533i	0.435677	−	0.0311602i
$708$	14.6412	+	3.18500i	0.550250	+	0.119700i
$709$	25.9265	+	29.9208i	0.973691	+	1.12370i	0.992298	+	0.123872i	$0.0395313\pi$
$709$	25.9265	+	29.9208i	0.973691	+	1.12370i	−0.0186073	+	0.999827i	$0.505923\pi$
$710$	−9.15320	+	2.22195i	−0.343513	+	0.0833882i
$711$	−2.61204	−	1.19288i	−0.0979591	−	0.0447364i
$712$	−7.93771	−	7.93771i	−0.297478	−	0.297478i
$713$	9.40877	−	28.0988i	0.352361	−	1.05231i
$714$		−	7.15000i		−	0.267582i
$715$	−4.93342	−	51.5861i	−0.184500	−	1.92921i
$716$	15.0333	+	4.41418i	0.561821	+	0.164965i
$717$	23.2952	+	1.66610i	0.869975	+	0.0622218i
$718$	−3.40697	+	15.6616i	−0.127147	+	0.584486i
$719$	3.42425	+	2.96713i	0.127703	+	0.110655i	0.716371	−	0.697720i	$-0.245802\pi$
$719$	3.42425	+	2.96713i	0.127703	+	0.110655i	−0.588668	+	0.808375i	$0.700347\pi$
$720$	1.52327	+	0.652040i	0.0567688	+	0.0243001i
$721$	−2.72366	+	0.799738i	−0.101434	+	0.0297838i
$722$	10.4931	−	2.28264i	0.390514	−	0.0849512i
$723$	−18.4939	−	13.8444i	−0.687796	−	0.514878i
$724$	1.44273	+	3.15913i	0.0536185	+	0.117408i
$725$	26.3370	+	2.50718i	0.978133	+	0.0931143i
$726$	−0.135392	−	0.941673i	−0.00502487	−	0.0349488i
$727$	−5.72571	−	26.3207i	−0.212355	−	0.976180i	−0.952690	−	0.303942i	$-0.901697\pi$
$727$	−5.72571	−	26.3207i	−0.212355	−	0.976180i	0.740336	−	0.672238i	$-0.234667\pi$
$728$	4.02313	−	7.36782i	0.149107	−	0.273070i
$729$	17.2656	+	2.48242i	0.639468	+	0.0919416i
$730$	−1.42834	+	0.967033i	−0.0528654	+	0.0357915i
$731$	21.3566	−	13.7250i	0.789902	−	0.507639i
$732$	−0.344930	+	4.82275i	−0.0127490	+	0.178254i
$733$	−30.8456	+	16.8430i	−1.13931	+	0.622110i	−0.934243	−	0.356638i	$-0.883923\pi$
$733$	−30.8456	+	16.8430i	−1.13931	+	0.622110i	−0.205067	+	0.978748i	$0.565741\pi$
$734$	−8.12103	+	17.7826i	−0.299753	+	0.656367i
$735$	20.5693	−	11.8797i	0.758710	−	0.438188i
$736$	−1.84331	+	4.42744i	−0.0679454	+	0.163197i
$737$	−21.9723	+	21.9723i	−0.809361	+	0.809361i
$738$	1.93181	−	0.720527i	0.0711108	−	0.0265230i
$739$	−8.09710	+	27.5762i	−0.297857	+	1.01441i	0.665548	+	0.746355i	$0.268198\pi$
$739$	−8.09710	+	27.5762i	−0.297857	+	1.01441i	−0.963405	+	0.268052i	$0.913620\pi$
$740$	−14.1540	−	4.89646i	−0.520313	−	0.179998i
$741$	−20.5476	−	31.9727i	−0.754835	−	1.17455i
$742$	0.921245	+	12.8807i	0.0338200	+	0.472865i
$743$	−21.8121	−	29.1376i	−0.800210	−	1.06895i	−0.996091	−	0.0883274i	$-0.971848\pi$
$743$	−21.8121	−	29.1376i	−0.800210	−	1.06895i	0.195882	−	0.980627i	$-0.437243\pi$
$744$	−3.36691	−	11.4666i	−0.123437	−	0.420387i
$745$	−25.6455	−	28.2028i	−0.939580	−	1.03327i
$746$	−29.0295	+	4.17381i	−1.06285	+	0.152814i
$747$	−3.13238	+	8.39824i	−0.114608	+	0.307276i
$748$	3.56645	−	9.56202i	0.130402	−	0.349622i
$749$	−1.16450	+	0.167430i	−0.0425499	+	0.00611775i
$750$	−4.60584	−	21.1285i	−0.168182	−	0.771503i
$751$	2.27644	+	7.75284i	0.0830685	+	0.282905i	0.990543	−	0.137202i	$-0.0438108\pi$
$751$	2.27644	+	7.75284i	0.0830685	+	0.282905i	−0.907475	+	0.420107i	$0.861993\pi$
$752$	−4.91004	−	6.55904i	−0.179051	−	0.239184i
$753$	0.139494	+	1.95038i	0.00508345	+	0.0710759i
$754$	19.5566	+	30.4307i	0.712211	+	1.10822i
$755$	−10.4171	−	21.4366i	−0.379117	−	0.780159i
$756$	−1.51154	+	5.14783i	−0.0549741	+	0.187225i
$757$	−22.3510	+	8.33650i	−0.812362	+	0.302995i	−0.721099	−	0.692832i	$-0.756363\pi$
$757$	−22.3510	+	8.33650i	−0.812362	+	0.302995i	−0.0912623	+	0.995827i	$0.529090\pi$
$758$	−2.57805	+	2.57805i	−0.0936388	+	0.0936388i
$759$	29.8539	−	9.87628i	1.08363	−	0.358486i
$760$	−3.21434	−	5.56554i	−0.116596	−	0.201883i
$761$	−16.4549	+	36.0311i	−0.596489	+	1.30613i	0.334952	+	0.942235i	$0.391280\pi$
$761$	−16.4549	+	36.0311i	−0.596489	+	1.30613i	−0.931441	+	0.363893i	$0.881447\pi$
$762$	−10.3186	+	5.63437i	−0.373802	+	0.204112i
$763$	0.304315	−	4.25488i	0.0110169	−	0.154037i
$764$	−4.38418	+	2.81754i	−0.158614	+	0.101935i
$765$	0.943324	−	4.89825i	0.0341059	−	0.177096i
$766$	25.3304	+	3.64196i	0.915225	+	0.131589i
$767$	25.3813	−	46.4823i	0.916465	−	1.67838i
$768$	0.411137	+	1.88997i	0.0148356	+	0.0681983i
$769$	−2.52310	−	17.5486i	−0.0909855	−	0.632818i	−0.983380	−	0.181561i	$-0.941885\pi$
$769$	−2.52310	−	17.5486i	−0.0909855	−	0.632818i	0.892394	−	0.451257i	$-0.149024\pi$
$770$	−9.17885	+	1.54487i	−0.330783	+	0.0556731i
$771$	7.38201	+	16.1643i	0.265857	+	0.582145i
$772$	−8.17688	−	6.12114i	−0.294292	−	0.220305i
$773$	12.8857	−	2.80311i	0.463466	−	0.100821i	0.0252315	−	0.999682i	$-0.491968\pi$
$773$	12.8857	−	2.80311i	0.463466	−	0.100821i	0.438234	+	0.898861i	$0.355604\pi$
$774$	5.99562	−	1.76047i	0.215508	−	0.0632789i
$775$	−19.0902	+	24.2896i	−0.685739	+	0.872508i
$776$	4.86710	+	4.21736i	0.174719	+	0.151395i
$777$	−3.38144	+	15.5442i	−0.121309	+	0.557646i
$778$	−19.5395	−	1.39749i	−0.700524	−	0.0501025i
$779$	−7.67347	−	2.25314i	−0.274931	−	0.0807269i
$780$	18.8218	−	22.8025i	0.673929	−	0.816462i
$781$			14.2796i			0.510965i
$782$	14.2038	+	2.58923i	0.507925	+	0.0925907i
$783$	−16.3474	−	16.3474i	−0.584209	−	0.584209i
$784$	4.99587	+	2.28154i	0.178424	+	0.0814835i
$785$	10.4300	+	42.9661i	0.372264	+	1.53352i
$786$	3.05822	+	3.52938i	0.109083	+	0.125889i
$787$	14.2514	+	3.10021i	0.508009	+	0.110511i	0.459263	−	0.888301i	$-0.348114\pi$
$787$	14.2514	+	3.10021i	0.508009	+	0.110511i	0.0487465	+	0.998811i	$0.484477\pi$
$788$	−12.7412	+	0.911268i	−0.453886	+	0.0324626i
$789$	1.97721	−	13.7518i	0.0703905	−	0.489576i
$790$	−5.97869	+	6.27209i	−0.212712	+	0.223151i
$791$	−8.06559	−	5.18344i	−0.286779	−	0.184302i
$792$	1.50539	−	2.01097i	0.0534917	−	0.0714566i
$793$	16.0123	+	5.97228i	0.568614	+	0.212082i
$794$	−9.26430	+	4.23086i	−0.328778	+	0.150148i
$795$	−5.39320	+	45.1625i	−0.191277	+	1.60175i
$796$	−7.09825	+	11.0451i	−0.251591	+	0.391483i
$797$	48.7136	+	26.5996i	1.72552	+	0.942207i	0.950746	+	0.309972i	$0.100320\pi$
$797$	48.7136	+	26.5996i	1.72552	+	0.942207i	0.774777	+	0.632234i	$0.217862\pi$
$798$	−5.46487	+	4.09095i	−0.193454	+	0.144818i
$799$	−16.1526	+	18.6411i	−0.571440	+	0.659476i
$800$	3.36223	−	3.70073i	0.118873	−	0.130841i
$801$	−6.28657	+	5.44735i	−0.222125	+	0.192473i
$802$	2.40425	+	4.40306i	0.0848971	+	0.155477i
$803$	0.913861	+	2.45016i	0.0322494	+	0.0864641i
$804$	−17.7293			−0.625263
$805$	−4.43396	−	12.3991i	−0.156277	−	0.437012i
$806$	−42.2405			−1.48786
$807$	5.10327	+	13.6824i	0.179644	+	0.481643i
$808$	4.53283	+	8.30126i	0.159464	+	0.292037i
$809$	−6.31919	+	5.47561i	−0.222171	+	0.192512i	−0.758833	−	0.651285i	$-0.774230\pi$
$809$	−6.31919	+	5.47561i	−0.222171	+	0.192512i	0.536662	+	0.843797i	$0.319685\pi$
$810$	−10.9337	+	21.2160i	−0.384172	+	0.745454i
$811$	−14.6408	+	16.8963i	−0.514107	+	0.593311i	−0.952145	−	0.305645i	$-0.901128\pi$
$811$	−14.6408	+	16.8963i	−0.514107	+	0.593311i	0.438039	+	0.898956i	$0.355673\pi$
$812$	5.20131	−	3.89365i	0.182530	−	0.136640i
$813$	36.0839	+	19.7033i	1.26552	+	0.691024i
$814$	−12.2757	+	19.1013i	−0.430262	+	0.669501i
$815$	21.6027	−	16.9936i	0.756710	−	0.595261i
$816$	5.29661	−	2.41888i	0.185419	−	0.0846778i
$817$	−22.7097	−	8.47028i	−0.794512	−	0.296338i
$818$	16.6307	−	22.2160i	0.581478	−	0.776763i
$819$	−5.23306	−	3.36308i	−0.182858	−	0.117516i
$820$	−0.148963	−	6.21989i	−0.00520201	−	0.217208i
$821$	1.51923	−	10.5665i	0.0530215	−	0.368773i	−0.945985	−	0.324210i	$-0.894901\pi$
$821$	1.51923	−	10.5665i	0.0530215	−	0.368773i	0.999007	−	0.0445626i	$-0.0141894\pi$
$822$	31.4245	−	2.24753i	1.09606	−	0.0783915i
$823$	13.4041	+	2.91588i	0.467236	+	0.101641i	0.440019	−	0.897988i	$-0.354972\pi$
$823$	13.4041	+	2.91588i	0.467236	+	0.101641i	0.0272174	+	0.999630i	$0.491335\pi$
$824$	−1.51386	−	1.74709i	−0.0527379	−	0.0608627i
$825$	−32.7748	−	0.770681i	−1.14107	−	0.0268317i
$826$	−8.65290	−	3.95165i	−0.301073	−	0.137495i
$827$	4.87874	+	4.87874i	0.169650	+	0.169650i	0.786826	−	0.617175i	$-0.211723\pi$
$827$	4.87874	+	4.87874i	0.169650	+	0.169650i	−0.617175	+	0.786826i	$0.711723\pi$
$828$	3.17498	+	1.59649i	0.110338	+	0.0554817i
$829$		−	38.5688i		−	1.33955i	−0.742565	−	0.669774i	$-0.766391\pi$
$829$		−	38.5688i		−	1.33955i	0.742565	−	0.669774i	$-0.233609\pi$
$830$	20.8596	+	17.2180i	0.724046	+	0.597646i
$831$	48.3649	+	14.2012i	1.67776	+	0.492635i
$832$	6.81902	+	0.487706i	0.236407	+	0.0169082i
$833$	3.51460	−	16.1563i	0.121774	−	0.559784i
$834$	−3.45574	−	2.99442i	−0.119662	−	0.103688i
$835$	−21.0032	−	52.4415i	−0.726847	−	1.81481i
$836$	−9.34900	+	2.74511i	−0.323342	+	0.0949418i
$837$	26.3796	−	5.73853i	0.911812	−	0.198352i
$838$	9.31943	+	6.97644i	0.321934	+	0.240997i
$839$	7.93709	+	17.3798i	0.274019	+	0.600018i	0.995744	−	0.0921621i	$-0.0293778\pi$
$839$	7.93709	+	17.3798i	0.274019	+	0.600018i	−0.721725	+	0.692180i	$0.756651\pi$
$840$	−4.32643	−	3.07989i	−0.149276	−	0.106266i
$841$	−0.142743	−	0.992796i	−0.00492216	−	0.0342343i
$842$	−3.37410	−	15.5105i	−0.116279	−	0.534526i
$843$	−24.1104	+	44.1550i	−0.830408	+	1.52078i
$844$	11.8126	+	1.69839i	0.406606	+	0.0584611i
$845$	−42.2926	−	62.4677i	−1.45491	−	2.14895i
$846$	−5.10751	+	3.28240i	−0.175600	+	0.112851i
$847$	−0.0430874	+	0.602441i	−0.00148050	+	0.0207001i
$848$	−9.23016	+	5.04005i	−0.316965	+	0.173076i
$849$	22.2753	−	48.7761i	0.764486	−	1.67399i
$850$	−13.0380	−	7.52246i	−0.447200	−	0.258018i
$851$	−29.6547	−	12.3464i	−1.01655	−	0.423229i
$852$	−5.76104	+	5.76104i	−0.197370	+	0.197370i
$853$	23.8878	−	8.90970i	0.817904	−	0.305062i	0.0945326	−	0.995522i	$-0.469864\pi$
$853$	23.8878	−	8.90970i	0.817904	−	0.305062i	0.723371	+	0.690459i	$0.242592\pi$
$854$	0.864805	−	2.94526i	0.0295930	−	0.100785i
$855$	−4.28355	+	2.08159i	−0.146494	+	0.0711888i
$856$	−0.517986	−	0.806002i	−0.0177044	−	0.0275486i
$857$	−0.584396	−	8.17093i	−0.0199626	−	0.279114i	−0.997622	−	0.0689193i	$-0.978045\pi$
$857$	−0.584396	−	8.17093i	−0.0199626	−	0.279114i	0.977660	−	0.210194i	$-0.0674096\pi$
$858$	−26.8626	−	35.8842i	−0.917073	−	1.22507i
$859$	6.68434	+	22.7648i	0.228067	+	0.776724i	0.991417	+	0.130739i	$0.0417350\pi$
$859$	6.68434	+	22.7648i	0.228067	+	0.776724i	−0.763350	+	0.645985i	$0.776447\pi$
$860$	0.894480	−	18.8349i	0.0305015	−	0.642264i
$861$	−6.54105	+	0.940460i	−0.222918	+	0.0320508i
$862$	5.25358	−	14.0854i	0.178937	−	0.479750i
$863$	−15.0438	+	40.3341i	−0.512098	+	1.37299i	0.381604	+	0.924326i	$0.375372\pi$
$863$	−15.0438	+	40.3341i	−0.512098	+	1.37299i	−0.893702	+	0.448662i	$0.851901\pi$
$864$	−4.32479	+	0.621811i	−0.147132	+	0.0211544i
$865$	−1.61579	+	34.0233i	−0.0549385	+	1.15683i
$866$	0.552191	+	1.88059i	0.0187642	+	0.0639050i
$867$	9.19972	+	12.2894i	0.312439	+	0.417369i
$868$	0.541254	+	7.56772i	0.0183714	+	0.256865i
$869$	7.10219	+	11.0512i	0.240925	+	0.374887i
$870$	20.5826	−	10.0021i	0.697816	−	0.339103i
$871$	−17.6548	+	60.1267i	−0.598210	+	2.03732i
$872$	3.25490	−	1.21402i	0.110225	−	0.0411118i
$873$	3.37445	−	3.37445i	0.114208	−	0.114208i
$874$	−6.14784	−	12.3376i	−0.207954	−	0.417327i
$875$	0.00596829	+	13.7287i	0.000201765	+	0.464114i
$876$	−0.619810	+	1.35720i	−0.0209415	+	0.0458554i
$877$	−24.9403	+	13.6185i	−0.842175	+	0.459862i	−0.841577	−	0.540137i	$-0.818372\pi$
$877$	−24.9403	+	13.6185i	−0.842175	+	0.459862i	−0.000598267		1.00000i	$0.500190\pi$
$878$	1.57536	−	22.0264i	0.0531657	−	0.743354i
$879$	−45.9765	+	29.5473i	−1.55075	+	0.996607i
$880$	−4.24967	−	6.27692i	−0.143256	−	0.211595i
$881$	−3.07893	−	0.442684i	−0.103732	−	0.0149144i	0.0902534	−	0.995919i	$-0.471232\pi$
$881$	−3.07893	−	0.442684i	−0.103732	−	0.0149144i	−0.193985	+	0.981004i	$0.562141\pi$
$882$	1.95044	−	3.57196i	0.0656747	−	0.120274i
$883$	3.04732	+	14.0083i	0.102551	+	0.471418i	0.999567	+	0.0294206i	$0.00936620\pi$
$883$	3.04732	+	14.0083i	0.102551	+	0.471418i	−0.897016	+	0.441997i	$0.854270\pi$
$884$	−2.92899	−	20.3716i	−0.0985126	−	0.685170i
$885$	−27.2947	−	19.4305i	−0.917502	−	0.653150i
$886$	−5.08292	−	11.1300i	−0.170764	−	0.373921i
$887$	−37.9458	−	28.4059i	−1.27410	−	0.953777i	−0.274128	−	0.961693i	$-0.588389\pi$
$887$	−37.9458	−	28.4059i	−1.27410	−	0.953777i	−0.999969	+	0.00791616i	$0.997480\pi$
$888$	−12.6589	+	2.75377i	−0.424805	+	0.0924106i
$889$	7.16151	−	2.10281i	0.240189	−	0.0705260i
$890$	9.33257	+	23.3019i	0.312829	+	0.781080i
$891$	27.3463	+	23.6957i	0.916134	+	0.793835i
$892$	5.48950	−	25.2348i	0.183802	−	0.844925i
$893$	23.4897	+	1.68001i	0.786052	+	0.0562196i
$894$	−31.6372	−	9.28953i	−1.05811	−	0.310688i
$895$	−27.0191	−	22.3023i	−0.903150	−	0.745483i
$896$		−	1.22793i		−	0.0410223i
$897$	43.2958	−	46.3343i	1.44560	−	1.54706i
$898$	22.8958	+	22.8958i	0.764043	+	0.764043i
$899$	−29.7386	−	13.5812i	−0.991839	−	0.452958i
$900$	−2.55756	−	2.68074i	−0.0852521	−	0.0893580i
$901$	20.7329	+	23.9271i	0.690713	+	0.797126i
$902$	−9.21674	−	2.00498i	−0.306884	−	0.0667585i
$903$	−19.9769	+	1.42877i	−0.664788	+	0.0475466i
$904$	1.11118	−	7.72845i	0.0369574	−	0.257044i
$905$	−0.185933	−	7.76358i	−0.00618063	−	0.258070i
$906$	−17.3431	−	11.1458i	−0.576187	−	0.370293i
$907$	−14.0109	+	18.7164i	−0.465224	+	0.621467i	−0.970386	−	0.241558i	$-0.922342\pi$
$907$	−14.0109	+	18.7164i	−0.465224	+	0.621467i	0.505162	+	0.863024i	$0.331433\pi$
$908$	−17.7114	−	6.60603i	−0.587775	−	0.219229i
$909$	6.37529	−	2.91150i	0.211455	−	0.0965682i
$910$	−14.7534	+	11.6056i	−0.489069	+	0.384723i
$911$	25.2316	−	39.2611i	0.835959	−	1.30078i	−0.115595	−	0.993296i	$-0.536877\pi$
$911$	25.2316	−	39.2611i	0.835959	−	1.30078i	0.951554	−	0.307481i	$-0.0994862\pi$
$912$	−4.87931	−	2.66430i	−0.161570	−	0.0882240i
$913$	32.8266	−	24.5737i	1.08640	−	0.813270i
$914$	12.5465	−	14.4794i	0.415001	−	0.478936i
$915$	4.95274	−	9.61039i	0.163733	−	0.317710i
$916$	12.1782	−	10.5525i	0.402380	−	0.348664i
$917$	−1.42089	−	2.60217i	−0.0469219	−	0.0859311i
$918$	4.59673	+	12.3243i	0.151715	+	0.406763i
$919$	−24.2999			−0.801580			−0.400790	−	0.916170i	$-0.631264\pi$
$919$	−24.2999			−0.801580			−0.400790	+	0.916170i	$0.631264\pi$
$920$	7.68505	−	7.47930i	0.253369	−	0.246585i
$921$	−39.5936			−1.30465
$922$	1.25877	+	3.37489i	0.0414554	+	0.111146i
$923$	13.8010	+	25.2747i	0.454267	+	0.831928i
$924$	−6.08473	+	5.27245i	−0.200173	+	0.173451i
$925$	24.7873	+	22.5200i	0.815001	+	0.740454i
$926$	24.2850	−	28.0264i	0.798056	−	0.921005i
$927$	−1.37134	+	1.02658i	−0.0450409	+	0.0337172i
$928$	4.64399	+	2.53581i	0.152446	+	0.0832421i
$929$	−20.0501	+	31.1986i	−0.657824	+	1.02359i	0.338749	+	0.940877i	$0.389996\pi$
$929$	−20.0501	+	31.1986i	−0.657824	+	1.02359i	−0.996573	+	0.0827170i	$0.973640\pi$
$930$	−3.16864	+	26.5341i	−0.103904	+	0.870088i
$931$	−14.3595	+	6.55776i	−0.470614	+	0.214922i
$932$	19.7956	+	7.38337i	0.648426	+	0.241850i
$933$	−16.6969	+	22.3044i	−0.546632	+	0.730215i
$934$	13.6688	+	8.78438i	0.447256	+	0.287434i
$935$	−15.7453	+	16.5180i	−0.514927	+	0.540196i
$936$	0.720951	−	5.01432i	0.0235650	−	0.163898i
$937$	16.3507	−	1.16943i	0.534155	−	0.0382035i	0.198343	−	0.980133i	$-0.436444\pi$
$937$	16.3507	−	1.16943i	0.534155	−	0.0382035i	0.335812	+	0.941929i	$0.390989\pi$
$938$	10.9984	+	2.39255i	0.359110	+	0.0781197i
$939$	−31.2993	−	36.1213i	−1.02141	−	1.17877i
$940$	4.32185	+	17.8036i	0.140963	+	0.580690i
$941$	−32.4604	−	14.8242i	−1.05818	−	0.483254i	−0.191176	−	0.981556i	$-0.561230\pi$
$941$	−32.4604	−	14.8242i	−1.05818	−	0.483254i	−0.867004	+	0.498302i	$0.833957\pi$
$942$	27.0429	+	27.0429i	0.881105	+	0.881105i
$943$	0.500447	−	13.3346i	0.0162968	−	0.434235i
$944$		−	7.74680i		−	0.252137i
$945$	7.63693	−	9.25211i	0.248429	−	0.300971i
$946$	−27.4286	−	8.05377i	−0.891782	−	0.261851i
$947$	−14.3762	−	1.02820i	−0.467163	−	0.0334122i	−0.164226	−	0.986423i	$-0.552513\pi$
$947$	−14.3762	−	1.02820i	−0.467163	−	0.0334122i	−0.302937	+	0.953011i	$0.597967\pi$
$948$	−1.59322	+	7.32390i	−0.0517453	+	0.237869i
$949$	3.98556	+	3.45351i	0.129377	+	0.112106i
$950$	1.71029	+	14.2692i	0.0554892	+	0.462955i
$951$	−27.6689	+	8.12431i	−0.897224	+	0.263449i
$952$	−3.61220	+	0.785785i	−0.117072	+	0.0254674i
$953$	−18.4791	−	13.8333i	−0.598598	−	0.448105i	0.256519	−	0.966539i	$-0.417424\pi$
$953$	−18.4791	−	13.8333i	−0.598598	−	0.448105i	−0.855118	+	0.518434i	$0.826515\pi$
$954$	3.23729	+	7.08867i	0.104811	+	0.229504i
$955$	11.4916	−	1.93412i	0.371859	−	0.0625866i
$956$	−1.71842	−	11.9519i	−0.0555777	−	0.386552i
$957$	−7.37459	−	33.9004i	−0.238387	−	1.09585i
$958$	−5.62952	+	10.3097i	−0.181882	+	0.333091i
$959$	−19.7976	−	2.84647i	−0.639298	−	0.0919172i
$960$	0.817884	−	4.24690i	0.0263971	−	0.137068i
$961$	6.03749	−	3.88006i	0.194758	−	0.125163i
$962$	−3.26662	+	45.6734i	−0.105320	+	1.47257i
$963$	−0.623118	+	0.340248i	−0.0200797	+	0.0109643i
$964$	−4.96172	+	10.8647i	−0.159806	+	0.349927i
$965$	11.4227	+	19.7780i	0.367709	+	0.636678i
$966$	−8.85593	−	7.16307i	−0.284935	−	0.230468i
$967$	29.8120	−	29.8120i	0.958690	−	0.958690i	−0.0404896	−	0.999180i	$-0.512892\pi$
$967$	29.8120	−	29.8120i	0.958690	−	0.958690i	0.999180	+	0.0404896i	$0.0128918\pi$
$968$	−0.460856	+	0.171890i	−0.0148125	+	0.00552476i
$969$	−4.71517	+	16.0584i	−0.151473	+	0.515870i
$970$	−6.29409	−	12.9522i	−0.202091	−	0.415869i
$971$	5.82284	+	9.06052i	0.186864	+	0.290766i	0.922028	−	0.387123i	$-0.126531\pi$
$971$	5.82284	+	9.06052i	0.186864	+	0.290766i	−0.735164	+	0.677889i	$0.762895\pi$
$972$	0.537713	+	7.51821i	0.0172472	+	0.241147i
$973$	1.73968	+	2.32395i	0.0557717	+	0.0745023i
$974$	4.60096	+	15.6694i	0.147424	+	0.502081i
$975$	−58.7558	+	30.3123i	−1.88169	+	0.970770i
$976$	2.47437	−	0.355761i	0.0792026	−	0.0113876i
$977$	−11.7742	+	31.5678i	−0.376690	+	1.00994i	0.600881	+	0.799338i	$0.294817\pi$
$977$	−11.7742	+	31.5678i	−0.376690	+	1.00994i	−0.977571	+	0.210606i	$0.932456\pi$
$978$	8.30842	−	22.2757i	0.265674	−	0.712299i
$979$	37.6671	−	5.41572i	1.20385	−	0.173087i
$980$	−8.26220	−	9.08608i	−0.263926	−	0.290244i
$981$	−0.725244	−	2.46996i	−0.0231553	−	0.0788596i
$982$	23.3659	+	31.2132i	0.745636	+	0.996053i
$983$	−0.447970	−	6.26344i	−0.0142880	−	0.199773i	−0.999582	−	0.0289058i	$-0.990798\pi$
$983$	−0.447970	−	6.26344i	−0.0142880	−	0.199773i	0.985294	−	0.170867i	$-0.0546568\pi$
$984$	−2.90955	−	4.52734i	−0.0927530	−	0.144326i
$985$	26.9934	+	9.33812i	0.860080	+	0.297537i
$986$	4.48777	−	15.2839i	0.142920	−	0.486740i
$987$	18.2323	−	6.80029i	0.580340	−	0.216456i
$988$	−13.8945	+	13.8945i	−0.442043	+	0.442043i
$989$	4.39591	−	40.2022i	0.139782	−	1.27836i
$990$	−4.86407	+	2.80921i	−0.154590	+	0.0892827i
$991$	4.08645	−	8.94808i	0.129810	−	0.284245i	−0.833555	−	0.552436i	$-0.813698\pi$
$991$	4.08645	−	8.94808i	0.129810	−	0.284245i	0.963366	+	0.268191i	$0.0864257\pi$
$992$	−5.42295	+	2.96115i	−0.172179	+	0.0940167i
$993$	2.84528	−	39.7822i	0.0902922	−	1.26245i
$994$	4.35133	−	2.79643i	0.138016	−	0.0886973i
$995$	24.3105	−	16.4589i	0.770694	−	0.521783i
$996$	23.1578	+	3.32959i	0.733784	+	0.105502i
$997$	−16.1611	+	29.5968i	−0.511826	+	0.937340i	0.486157	+	0.873871i	$0.338398\pi$
$997$	−16.1611	+	29.5968i	−0.511826	+	0.937340i	−0.997984	+	0.0634688i	$0.979784\pi$
$998$	−3.78505	−	17.3996i	−0.119814	−	0.550774i
$999$	−4.16486	−	28.9672i	−0.131770	−	0.916482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.63.8	yes	240
5.2	odd	4	inner	230.2.l.a.17.2	✓	240
23.19	odd	22	inner	230.2.l.a.203.2	yes	240
115.42	even	44	inner	230.2.l.a.157.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.2	✓	240	5.2	odd	4	inner
230.2.l.a.63.8	yes	240	1.1	even	1	trivial
230.2.l.a.157.8	yes	240	115.42	even	44	inner
230.2.l.a.203.2	yes	240	23.19	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.349464 + 0.936950i) q^{2} +(-0.926949 - 1.69758i) q^{3} +(-0.755750 + 0.654861i) q^{4} +(2.12979 - 0.681161i) q^{5} +(1.26661 - 1.46175i) q^{6} +(-0.983009 + 0.735871i) q^{7} +(-0.877679 - 0.479249i) q^{8} +(-0.400622 + 0.623380i) q^{9} +O(q^{10})\)	\(q+(0.349464 + 0.936950i) q^{2} +(-0.926949 - 1.69758i) q^{3} +(-0.755750 + 0.654861i) q^{4} +(2.12979 - 0.681161i) q^{5} +(1.26661 - 1.46175i) q^{6} +(-0.983009 + 0.735871i) q^{7} +(-0.877679 - 0.479249i) q^{8} +(-0.400622 + 0.623380i) q^{9} +(1.38250 + 1.75747i) q^{10} +(3.08362 - 1.40824i) q^{11} +(1.81222 + 0.675923i) q^{12} +(4.09692 - 5.47285i) q^{13} +(-1.03300 - 0.663869i) q^{14} +(-3.13054 - 2.98409i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-3.00282 + 0.214766i) q^{17} +(-0.724078 - 0.157514i) q^{18} +(1.88225 + 2.17223i) q^{19} +(-1.16352 + 1.90951i) q^{20} +(2.16040 + 0.986621i) q^{21} +(2.39707 + 2.39707i) q^{22} +(-2.74231 + 3.93443i) q^{23} +1.93417i q^{24} +(4.07204 - 2.90146i) q^{25} +(6.55951 + 1.92605i) q^{26} +(-4.35813 - 0.311700i) q^{27} +(0.261015 - 1.19987i) q^{28} +(3.99884 + 3.46501i) q^{29} +(1.70194 - 3.97599i) q^{30} +(-5.92845 + 1.74075i) q^{31} +(0.977147 - 0.212565i) q^{32} +(-5.24896 - 3.92933i) q^{33} +(-1.25060 - 2.73844i) q^{34} +(-1.59236 + 2.23684i) q^{35} +(-0.105457 - 0.733470i) q^{36} +(1.42375 + 6.54487i) q^{37} +(-1.37749 + 2.52269i) q^{38} +(-13.0882 - 1.88180i) q^{39} +(-2.19572 - 0.422860i) q^{40} +(-2.34072 + 1.50429i) q^{41} +(-0.169432 + 2.36897i) q^{42} +(-7.40121 + 4.04137i) q^{43} +(-1.40824 + 3.08362i) q^{44} +(-0.428620 + 1.60056i) q^{45} +(-4.64470 - 1.19446i) q^{46} +(5.79351 - 5.79351i) q^{47} +(-1.81222 + 0.675923i) q^{48} +(-1.54733 + 5.26972i) q^{49} +(4.14156 + 2.80134i) q^{50} +(3.14805 + 4.89846i) q^{51} +(0.487706 + 6.81902i) q^{52} +(-6.30233 - 8.41893i) q^{53} +(-1.23096 - 4.19228i) q^{54} +(5.60824 - 5.09971i) q^{55} +(1.21543 - 0.174753i) q^{56} +(1.94279 - 5.20882i) q^{57} +(-1.84909 + 4.95761i) q^{58} +(7.66795 - 1.10249i) q^{59} +(4.32007 + 0.205163i) q^{60} +(0.704279 + 2.39855i) q^{61} +(-3.70278 - 4.94633i) q^{62} +(-0.0649124 - 0.907593i) q^{63} +(0.540641 + 0.841254i) q^{64} +(4.99771 - 14.4467i) q^{65} +(1.84726 - 6.29117i) q^{66} +(-8.58840 + 3.20331i) q^{67} +(2.12874 - 2.12874i) q^{68} +(9.22099 + 1.00827i) q^{69} +(-2.65228 - 0.710264i) q^{70} +(-1.74986 + 3.83166i) q^{71} +(0.650371 - 0.355130i) q^{72} +(-0.0550313 + 0.769439i) q^{73} +(-5.63467 + 3.62118i) q^{74} +(-8.70004 - 4.22310i) q^{75} +(-2.84502 - 0.409052i) q^{76} +(-1.99494 + 3.65346i) q^{77} +(-2.81071 - 12.9206i) q^{78} +(0.551491 + 3.83570i) q^{79} +(-0.371127 - 2.20505i) q^{80} +(4.43411 + 9.70936i) q^{81} +(-2.22744 - 1.66744i) q^{82} +(11.8197 - 2.57122i) q^{83} +(-2.27882 + 0.669122i) q^{84} +(-6.24911 + 2.50282i) q^{85} +(-6.37301 - 5.52225i) q^{86} +(2.17542 - 10.0002i) q^{87} +(-3.38133 - 0.241837i) q^{88} +(10.7709 + 3.16262i) q^{89} +(-1.64943 + 0.157743i) q^{90} +8.39466i q^{91} +(-0.504008 - 4.76927i) q^{92} +(8.45044 + 8.45044i) q^{93} +(7.45285 + 3.40360i) q^{94} +(5.48844 + 3.34429i) q^{95} +(-1.26661 - 1.46175i) q^{96} +(-6.29292 - 1.36894i) q^{97} +(-5.47819 + 0.391808i) q^{98} +(-0.357496 + 2.48644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 240 * q - 8 * q^3 - 8 * q^6	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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