LMFDB - Embedded newform 230.2.l.a.157.8

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			157.8
Character	$\chi$	$=$	230.157
Dual form			230.2.l.a.63.8

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{15}{22}\right)$

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	0.460542	+	0.887638i	$0.347655\pi$
$3$	−0.926949	+	1.69758i	−0.535174	+	0.980098i	−0.995716	+	0.0924605i	$0.970527\pi$
$4$	−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	0.397148	−	0.917755i	$-0.370000\pi$
$7$	−0.983009	−	0.735871i	−0.371542	−	0.278133i	−0.768690	+	0.639622i	$0.779091\pi$
$8$	−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	0.821942	−	0.569571i	$-0.192891\pi$
$11$	3.08362	+	1.40824i	0.929747	+	0.424601i	0.107805	+	0.994172i	$0.465618\pi$
$12$	1.81222	−	0.675923i	0.523143	−	0.195122i
$13$	4.09692	+	5.47285i	1.13628	+	1.51790i	0.822827	+	0.568292i	$0.192396\pi$
$13$	4.09692	+	5.47285i	1.13628	+	1.51790i	0.313455	+	0.949603i	$0.398513\pi$
$14$	−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	−0.297731	−	0.954650i	$-0.596230\pi$
$17$	−3.00282	−	0.214766i	−0.728292	−	0.0520885i	−0.430561	+	0.902561i	$0.641684\pi$
$18$	−0.724078	+	0.157514i	−0.170667	+	0.0371263i
$19$	1.88225	−	2.17223i	0.431818	−	0.498344i	−0.497583	−	0.867416i	$-0.665779\pi$
$19$	1.88225	−	2.17223i	0.431818	−	0.498344i	0.929401	+	0.369072i	$0.120325\pi$
$20$	−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	−0.199103	−	0.979979i	$-0.563803\pi$
$29$	3.99884	−	3.46501i	0.742565	−	0.643436i	0.941668	+	0.336542i	$0.109257\pi$
$30$	1.70194	+	3.97599i	0.310729	+	0.725913i
$31$	−5.92845	−	1.74075i	−1.06478	−	0.312648i	−0.298007	−	0.954564i	$-0.596322\pi$
$31$	−5.92845	−	1.74075i	−1.06478	−	0.312648i	−0.766775	+	0.641916i	$0.778140\pi$
$32$	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	−0.698682	−	0.715433i	$-0.746230\pi$
$37$	1.42375	−	6.54487i	0.234063	−	1.07597i	0.932745	−	0.360538i	$-0.117407\pi$
$38$	−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	0.344946	−	0.938622i	$-0.387897\pi$
$41$	−2.34072	−	1.50429i	−0.365559	−	0.234930i	−0.710505	+	0.703692i	$0.751533\pi$
$42$	−0.169432	−	2.36897i	−0.0261440	−	0.365541i
$43$	−7.40121	−	4.04137i	−1.12867	−	0.616302i	−0.197291	−	0.980345i	$-0.563215\pi$
$43$	−7.40121	−	4.04137i	−1.12867	−	0.616302i	−0.931382	+	0.364042i	$0.881396\pi$
$44$	−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	0.989513	−	0.144443i	$-0.0461389\pi$
$47$	5.79351	+	5.79351i	0.845070	+	0.845070i	−0.144443	+	0.989513i	$0.546139\pi$
$48$	−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	0.120809	+	0.992676i	$0.461451\pi$
$53$	−6.30233	+	8.41893i	−0.865692	+	1.15643i	−0.986501	+	0.163754i	$0.947640\pi$
$54$	−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	0.622036	−	0.782988i	$-0.286306\pi$
$59$	7.66795	+	1.10249i	0.998282	+	0.143531i	0.376246	+	0.926520i	$0.377215\pi$
$60$	4.32007	−	0.205163i	0.557718	−	0.0264864i
$61$	0.704279	−	2.39855i	0.0901737	−	0.307103i	−0.902040	−	0.431653i	$-0.857930\pi$
$61$	0.704279	−	2.39855i	0.0901737	−	0.307103i	0.992213	+	0.124550i	$0.0397486\pi$
$62$	−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	−0.235073	−	0.971978i	$-0.575533\pi$
$67$	−8.58840	−	3.20331i	−1.04924	−	0.391346i	−0.814167	+	0.580631i	$0.802806\pi$
$68$	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	0.776923	−	0.629596i	$-0.216779\pi$
$71$	−1.74986	−	3.83166i	−0.207670	−	0.454734i	−0.984593	+	0.174862i	$0.944052\pi$
$72$	0.650371	+	0.355130i	0.0766470	+	0.0418524i
$73$	−0.0550313	−	0.769439i	−0.00644093	−	0.0900560i	0.993215	−	0.116294i	$-0.0371016\pi$
$73$	−0.0550313	−	0.769439i	−0.00644093	−	0.0900560i	−0.999656	+	0.0262385i	$0.991647\pi$
$74$	−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	−0.934993	−	0.354667i	$-0.884594\pi$
$79$	0.551491	−	3.83570i	0.0620476	−	0.431550i	0.997040	−	0.0768830i	$-0.0244968\pi$
$80$	−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	0.807658	−	0.589651i	$-0.200735\pi$
$83$	11.8197	+	2.57122i	1.29738	+	0.282228i	0.489722	+	0.871879i	$0.337098\pi$
$84$	−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	0.344412	−	0.938819i	$-0.388078\pi$
$89$	10.7709	−	3.16262i	1.14171	−	0.335237i	0.797302	+	0.603581i	$0.206260\pi$
$90$	−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	−0.520358	−	0.853948i	$-0.674201\pi$
$97$	−6.29292	+	1.36894i	−0.638949	+	0.138995i	−0.118591	+	0.992943i	$0.537838\pi$
$98$	−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	−0.872906	−	0.487889i	$-0.837767\pi$
$101$	−7.95674	+	5.11349i	−0.791725	+	0.508811i	0.0811808	+	0.996699i	$0.474131\pi$
$102$	−3.48948	−	4.66140i	−0.345510	−	0.461547i
$103$	2.16597	−	0.807867i	0.213420	−	0.0796015i	−0.240480	−	0.970654i	$-0.577305\pi$
$103$	2.16597	−	0.807867i	0.213420	−	0.0796015i	0.453900	+	0.891053i	$0.350032\pi$
$104$	−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	−0.438088	−	0.898932i	$-0.644344\pi$
$107$	0.840901	−	0.459167i	0.0812930	−	0.0443893i	0.519381	+	0.854543i	$0.326162\pi$
$108$	3.49778	+	2.61840i	0.336574	+	0.251956i
$109$	−2.27494	−	2.62542i	−0.217900	−	0.251470i	0.636267	−	0.771469i	$-0.280478\pi$
$109$	−2.27494	−	2.62542i	−0.217900	−	0.251470i	−0.854167	+	0.519999i	$0.825932\pi$
$110$	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	−0.743134	−	0.669142i	$-0.766662\pi$
$113$	2.72859	−	7.31563i	0.256684	−	0.688197i	0.999818	−	0.0190545i	$-0.00606559\pi$
$114$	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	−0.589198	−	0.807989i	$-0.700556\pi$
$127$	−5.69516	+	2.12418i	−0.505363	+	0.188491i	0.0838343	+	0.996480i	$0.473283\pi$
$128$	−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	0.969289	−	0.245925i	$-0.0790917\pi$
$131$	−0.343618	−	2.38992i	−0.0300220	−	0.208808i	−0.999311	+	0.0371170i	$0.988183\pi$
$132$	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	−0.0158474	−	0.999874i	$-0.505045\pi$
$137$	11.5177	−	11.5177i	0.984027	−	0.984027i	0.999874	+	0.0158474i	$0.00504459\pi$
$138$	2.27771	−	8.99196i	0.193892	−	0.765446i
$139$			2.36411i			0.200522i	0.994961	+	0.100261i	$0.0319677\pi$
$139$			2.36411i			0.200522i	−0.994961	+	0.100261i	$0.968032\pi$
$140$	−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	0.361042	+	0.932550i	$0.382421\pi$
$149$	−7.08181	+	15.5070i	−0.580164	+	1.27038i	−0.941206	+	0.337833i	$0.890306\pi$
$150$	0.916482	+	9.62732i	0.0748305	+	0.786068i
$151$	−1.51690	+	10.5503i	−0.123443	+	0.858568i	0.830165	+	0.557518i	$0.188246\pi$
$151$	−1.51690	+	10.5503i	−0.123443	+	0.858568i	−0.953608	+	0.301050i	$0.902663\pi$
$152$	−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	−0.669077	−	0.743193i	$-0.733311\pi$
$157$	−1.41059	−	19.7227i	−0.112578	−	1.57404i	0.556500	−	0.830848i	$-0.312144\pi$
$158$	−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	0.757346	−	0.653014i	$-0.226496\pi$
$163$	11.5169	+	4.29560i	0.902077	+	0.336457i	0.144731	+	0.989471i	$0.453768\pi$
$164$	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	0.140768	+	0.990043i	$0.455043\pi$
$167$	−1.80228	+	25.1992i	−0.139465	+	1.94997i	−0.280233	+	0.959932i	$0.590412\pi$
$168$	−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	−0.966240	−	0.257644i	$-0.917054\pi$
$173$	−5.32333	−	14.2724i	−0.404725	−	1.08511i	0.561515	−	0.827467i	$-0.310219\pi$
$174$	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	0.365391	+	0.930854i	$0.380935\pi$
$179$	−8.47074	+	13.1807i	−0.633133	+	0.985174i	−0.998524	+	0.0543197i	$0.982701\pi$
$180$	−0.724213	+	1.49031i	−0.0539797	+	0.111081i
$181$	0.978450	+	3.33229i	0.0727276	+	0.247687i	0.987831	−	0.155532i	$-0.0497092\pi$
$181$	0.978450	+	3.33229i	0.0727276	+	0.247687i	−0.915103	+	0.403220i	$0.867891\pi$
$182$	−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	0.0468632	−	0.998901i	$-0.485078\pi$
$191$	5.15843	−	0.741671i	0.373251	−	0.0536654i	0.326388	+	0.945236i	$0.394168\pi$
$192$	0.926949	+	1.69758i	0.0668968	+	0.122512i
$193$	2.17118	−	9.98077i	0.156285	−	0.718431i	−0.830582	−	0.556897i	$-0.811992\pi$
$193$	2.17118	−	9.98077i	0.156285	−	0.718431i	0.986867	−	0.161535i	$-0.0516444\pi$
$194$	−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	−0.169355	−	0.985555i	$-0.554168\pi$
$197$	10.2259	−	7.65502i	0.728566	−	0.545398i	0.897921	+	0.440158i	$0.145077\pi$
$198$	−2.45460	−	0.533966i	−0.174441	−	0.0379473i
$199$	12.5975	+	3.69896i	0.893013	+	0.262212i	0.695874	−	0.718164i	$-0.255017\pi$
$199$	12.5975	+	3.69896i	0.893013	+	0.262212i	0.197138	+	0.980376i	$0.436835\pi$
$200$	−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	−0.958049	−	0.286605i	$-0.907473\pi$
$211$	−7.81515	+	9.01916i	−0.538017	+	0.620905i	0.420032	+	0.907509i	$0.362019\pi$
$212$	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	−0.993242	−	0.116064i	$-0.962972\pi$
$223$	−20.6740	−	15.4764i	−1.38443	−	1.03637i	−0.391191	−	0.920309i	$-0.627937\pi$
$224$	−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	−0.382851	−	0.923810i	$-0.625058\pi$
$227$	9.05939	−	16.5910i	0.601293	−	1.10119i	0.984143	−	0.177375i	$-0.0567606\pi$
$228$	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	0.301875	+	0.953348i	$0.402388\pi$
$233$	−10.1254	+	18.5433i	−0.663338	+	1.21481i	−0.965213	+	0.261466i	$0.915794\pi$
$234$	−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	0.563316	−	0.826241i	$-0.309525\pi$
$239$	−6.52812	−	10.1580i	−0.422269	−	0.657064i	−0.985586	+	0.169178i	$0.945889\pi$
$240$	−3.39924	−	2.67399i	−0.219420	−	0.172605i
$241$	10.8647	+	4.96172i	0.699854	+	0.319613i	0.733374	−	0.679825i	$-0.237944\pi$
$241$	10.8647	+	4.96172i	0.699854	+	0.319613i	−0.0335197	+	0.999438i	$0.510672\pi$
$242$	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	−0.444226	−	0.895915i	$-0.646521\pi$
$251$	−0.919601	+	0.419968i	−0.0580447	+	0.0265081i	0.386181	+	0.922423i	$0.373794\pi$
$252$	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	−0.354168	−	0.935182i	$-0.615236\pi$
$257$	−9.16410	+	0.655430i	−0.571641	+	0.0408846i	−0.217473	+	0.976066i	$0.569781\pi$
$258$	−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	−0.407107	−	0.913380i	$-0.633463\pi$
$263$	5.75031	−	4.30463i	0.354579	−	0.265435i	0.761687	+	0.647946i	$0.224372\pi$
$264$	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	−0.366319	−	0.930489i	$-0.619382\pi$
$269$	−7.47323	+	1.07449i	−0.455651	+	0.0655127i	−0.0893315	+	0.996002i	$0.528473\pi$
$270$	−5.47732	+	8.09020i	−0.333339	+	0.492354i
$271$	−17.8817	−	11.4919i	−1.08624	−	0.698083i	−0.130248	−	0.991481i	$-0.541577\pi$
$271$	−17.8817	−	11.4919i	−1.08624	−	0.698083i	−0.955990	+	0.293399i	$0.905214\pi$
$272$	−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	−0.993513	−	0.113720i	$-0.963723\pi$
$277$	−18.4280	−	18.4280i	−1.10723	−	1.10723i	−0.113720	−	0.993513i	$-0.536277\pi$
$278$	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	0.111338	+	0.993783i	$0.464486\pi$
$281$	−14.0624	+	21.8815i	−0.838890	+	1.30534i	−0.950228	+	0.311556i	$0.899150\pi$
$282$	−1.13052	+	15.8068i	−0.0673217	+	0.941280i
$283$	16.6140	−	22.1937i	0.987601	−	1.31928i	0.0402131	−	0.999191i	$-0.487196\pi$
$283$	16.6140	−	22.1937i	0.987601	−	1.31928i	0.947388	−	0.320089i	$-0.103713\pi$
$284$	−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	0.504266	+	0.863549i	$0.331763\pi$
$293$	−2.01578	+	28.1843i	−0.117763	+	1.64654i	−0.622029	+	0.782995i	$0.713691\pi$
$294$	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	0.992316	+	0.123727i	$0.0394848\pi$
$307$	9.81051	+	17.9666i	0.559916	+	1.02541i	−0.432401	+	0.901682i	$0.642333\pi$
$308$	−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	−0.999971	−	0.00768068i	$-0.997555\pi$
$311$	−5.98405	+	13.1032i	−0.339324	+	0.743017i	0.660646	+	0.750698i	$0.270282\pi$
$312$	10.5854	−	7.92414i	0.599281	−	0.448616i
$313$	24.1463	+	5.25270i	1.36483	+	0.296900i	0.834554	−	0.550926i	$-0.185725\pi$
$313$	24.1463	+	5.25270i	1.36483	+	0.296900i	0.530274	+	0.847826i	$0.322089\pi$
$314$	−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	0.976374	+	0.216088i	$0.0693297\pi$
$317$	3.16918	+	14.5685i	0.177999	+	0.818248i	−0.798375	+	0.602161i	$0.794307\pi$
$318$	−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	0.0312988	−	0.999510i	$-0.490036\pi$
$331$	17.3472	−	11.1484i	0.953487	−	0.612769i	0.922188	+	0.386741i	$0.126399\pi$
$332$	−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	−0.629977	−	0.776614i	$-0.716936\pi$
$337$	−5.82375	+	3.18001i	−0.317240	+	0.173226i	0.312738	+	0.949840i	$0.398754\pi$
$338$	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	−0.996231	−	0.0867358i	$-0.972356\pi$
$347$	−3.47467	+	9.31595i	−0.186530	+	0.500106i	0.809701	+	0.586842i	$0.199629\pi$
$348$	4.90469	−	8.98227i	0.262919	−	0.481500i
$349$	5.68455	+	4.92569i	0.304287	+	0.263666i	0.793597	−	0.608444i	$-0.208206\pi$
$349$	5.68455	+	4.92569i	0.304287	+	0.263666i	−0.489310	+	0.872110i	$0.662751\pi$
$350$	−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	0.203707	−	0.979032i	$-0.434701\pi$
$353$	21.3708	−	11.6693i	1.13745	−	0.621097i	0.933746	+	0.357935i	$0.116519\pi$
$354$	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	−0.134084	−	0.990970i	$-0.542809\pi$
$359$	13.4835	−	8.66533i	0.711633	−	0.457339i	0.845717	+	0.533631i	$0.179173\pi$
$360$	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	−0.247352	−	0.968926i	$-0.579560\pi$
$367$	13.8234	−	13.8234i	0.721574	−	0.721574i	0.968926	+	0.247352i	$0.0795604\pi$
$368$	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	−0.797294	−	0.603591i	$-0.793736\pi$
$373$	−6.23412	−	28.6578i	−0.322791	−	1.48384i	0.474504	−	0.880254i	$-0.342628\pi$
$374$	−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	−0.866736	−	0.498767i	$-0.833786\pi$
$379$	1.51456	−	3.31643i	0.0777979	−	0.170354i	0.944534	+	0.328413i	$0.106514\pi$
$380$	−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	0.977440	+	0.211216i	$0.0677422\pi$
$383$	12.2644	+	22.4606i	0.626682	+	1.14768i	−0.350758	+	0.936466i	$0.614076\pi$
$384$	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	−0.995836	−	0.0911640i	$-0.970941\pi$
$389$	−8.13773	−	17.8191i	−0.412599	−	0.903466i	0.583237	−	0.812302i	$-0.301786\pi$
$390$	−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	−0.946093	−	0.323896i	$-0.895007\pi$
$397$	0.726566	−	10.1587i	0.0364653	−	0.509851i	0.982558	−	0.185956i	$-0.0595381\pi$
$398$	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	0.265180	−	0.964199i	$-0.414569\pi$
$401$	4.96565	+	0.713952i	0.247973	+	0.0356531i	−0.0172077	+	0.999852i	$0.505478\pi$
$402$	−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	0.241079	+	0.970505i	$0.422499\pi$
$409$	−15.0034	+	23.3458i	−0.741872	+	1.15437i	−0.982951	+	0.183869i	$0.941138\pi$
$410$	−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	0.757541	−	0.652788i	$-0.226401\pi$
$419$	9.79338	+	6.29382i	0.478438	+	0.307473i	−0.279103	+	0.960261i	$0.590037\pi$
$420$	−4.39764	−	2.97733i	−0.214583	−	0.145279i
$421$	−15.7117	+	2.25899i	−0.765739	+	0.110097i	−0.514107	−	0.857726i	$-0.671876\pi$
$421$	−15.7117	+	2.25899i	−0.765739	+	0.110097i	−0.251632	+	0.967823i	$0.580967\pi$
$422$	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	−0.884060	−	0.467374i	$-0.845200\pi$
$431$	−11.3614	+	9.84467i	−0.547257	+	0.474201i	0.336802	+	0.941575i	$0.390655\pi$
$432$	−0.928754	−	4.26941i	−0.0446847	−	0.205412i
$433$	1.95499	−	0.139823i	0.0939507	−	0.00671949i	−0.0242847	−	0.999705i	$-0.507731\pi$
$433$	1.95499	−	0.139823i	0.0939507	−	0.00671949i	0.118235	+	0.992986i	$0.462276\pi$
$434$	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	−0.832406	−	0.554167i	$-0.813037\pi$
$439$	−20.0871	+	9.17346i	−0.958704	+	0.437825i	−0.126298	+	0.991992i	$0.540310\pi$
$440$	−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	−0.221670	−	0.975122i	$-0.571151\pi$
$443$	−12.2046	−	0.872890i	−0.579858	−	0.0414722i	−0.358188	+	0.933650i	$0.616605\pi$
$444$	−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	0.963009	−	0.269468i	$-0.0868479\pi$
$449$	29.4535	+	13.4510i	1.39000	+	0.634790i	0.426987	+	0.904258i	$0.359575\pi$
$450$	−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	−0.999382	−	0.0351413i	$-0.988812\pi$
$457$	−9.18193	+	16.8155i	−0.429513	+	0.786594i	0.569870	+	0.821735i	$0.306994\pi$
$458$	−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	0.0323300	+	0.999477i	$0.489707\pi$
$463$	−17.7726	+	32.5481i	−0.825963	+	1.51264i	−0.858293	+	0.513160i	$0.828475\pi$
$464$	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	0.856270	−	0.516528i	$-0.172776\pi$
$467$	13.0073	+	9.73712i	0.601905	+	0.450580i	−0.254366	+	0.967108i	$0.581867\pi$
$468$	−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	−0.552292	−	0.833651i	$-0.686247\pi$
$479$	7.69236	−	8.87745i	0.351473	−	0.405621i	0.903765	+	0.428030i	$0.140792\pi$
$480$	−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	0.302794	−	0.953056i	$-0.402080\pi$
$487$	16.2893	−	1.16504i	0.738141	−	0.0527929i	0.435346	+	0.900263i	$0.356626\pi$
$488$	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	0.978081	−	0.208223i	$-0.0667679\pi$
$491$	37.4107	+	10.9848i	1.68832	+	0.495736i	0.710241	+	0.703959i	$0.248586\pi$
$492$	−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	−0.525031	−	0.851083i	$-0.675946\pi$
$499$	−17.6253	+	2.53413i	−0.789016	+	0.113443i	−0.263985	+	0.964527i	$0.585037\pi$
$500$	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	0.334278	−	0.942475i	$-0.391508\pi$
$503$	−6.23170	−	3.40276i	−0.277858	−	0.151722i	−0.612136	+	0.790753i	$0.709689\pi$
$504$	−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	0.857985	−	0.513675i	$-0.171716\pi$
$509$	−3.19265	−	10.8732i	−0.141512	−	0.481944i	−0.999496	+	0.0317306i	$0.989898\pi$
$510$	−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	−0.886889	−	0.461984i	$-0.847138\pi$
$521$	2.48744	−	8.47144i	0.108977	−	0.371141i	0.995865	+	0.0908429i	$0.0289561\pi$
$522$	−2.34968	+	3.13881i	−0.102843	+	0.137382i
$523$	−1.69841	+	23.7469i	−0.0742664	+	1.03838i	0.814543	+	0.580103i	$0.196988\pi$
$523$	−1.69841	+	23.7469i	−0.0742664	+	1.03838i	−0.888809	+	0.458277i	$0.848467\pi$
$524$	−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	0.516756	+	0.856133i	$0.327139\pi$
$541$	−10.9010	+	23.8698i	−0.468669	+	1.02624i	−0.985425	+	0.170109i	$0.945588\pi$
$542$	−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	−0.999172	−	0.0406736i	$-0.987050\pi$
$547$	−2.50695	−	11.5243i	−0.107190	−	0.492743i	0.891983	−	0.452069i	$-0.149314\pi$
$548$	−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	−0.805376	−	0.592764i	$-0.798037\pi$
$557$	−30.4859	+	6.63181i	−1.29173	+	0.280999i	−0.486353	+	0.873762i	$0.661673\pi$
$558$	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	−0.649942	−	0.759984i	$-0.725207\pi$
$563$	−15.2676	+	5.69451i	−0.643451	+	0.239995i	0.00649040	+	0.999979i	$0.497934\pi$
$564$	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	0.463358	−	0.886171i	$-0.346644\pi$
$569$	−11.4435	−	13.2065i	−0.479736	−	0.553645i	−0.943094	+	0.332526i	$0.892099\pi$
$570$	11.8402	+	3.78680i	0.495933	+	0.158612i
$571$	17.9309	+	15.5372i	0.750384	+	0.650211i	0.943654	−	0.330935i	$-0.107364\pi$
$571$	17.9309	+	15.5372i	0.750384	+	0.650211i	−0.193270	+	0.981146i	$0.561909\pi$
$572$	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	−0.814681	−	0.579910i	$-0.803088\pi$
$577$	4.34235	−	11.6423i	0.180774	−	0.484674i	0.995455	+	0.0952356i	$0.0303604\pi$
$578$	−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	−0.240045	−	0.970762i	$-0.577162\pi$
$587$	5.19098	−	1.93614i	0.214255	−	0.0799129i	0.454300	+	0.890849i	$0.349890\pi$
$588$	−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	−0.779041	−	0.626973i	$-0.784294\pi$
$593$	−29.8849	+	6.50107i	−1.22723	+	0.266967i	−0.448186	+	0.893940i	$0.647930\pi$
$594$	−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	$0.0465517\pi$
$599$			7.13312i			0.291451i	−0.989325	+	0.145726i	$0.953448\pi$
$600$	5.61193	−	7.87601i	0.229106	−	0.321537i
$601$	17.7450	−	5.21042i	0.723836	−	0.212537i	0.100996	−	0.994887i	$-0.467797\pi$
$601$	17.7450	−	5.21042i	0.723836	−	0.212537i	0.622840	+	0.782350i	$0.285979\pi$
$602$	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	−0.634191	−	0.773177i	$-0.718667\pi$
$607$	−37.7509	−	8.21220i	−1.53226	−	0.333323i	−0.898069	+	0.439854i	$0.855030\pi$
$608$	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	0.961958	+	0.273198i	$0.0880815\pi$
$613$	16.6308	+	30.4571i	0.671713	+	1.23015i	−0.290245	+	0.956953i	$0.593737\pi$
$614$	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	−0.762115	−	0.647442i	$-0.775839\pi$
$617$	−2.48141	−	34.6946i	−0.0998978	−	1.39675i	0.662217	−	0.749312i	$-0.269616\pi$
$618$	3.92435	+	2.14286i	0.157860	+	0.0861983i
$619$	7.95624	+	17.4217i	0.319788	+	0.700238i	0.999446	−	0.0332912i	$-0.0105989\pi$
$619$	7.95624	+	17.4217i	0.319788	+	0.700238i	−0.679658	+	0.733530i	$0.737872\pi$
$620$	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	−0.450403	−	0.892825i	$-0.648720\pi$
$631$	−28.4882	−	4.09599i	−1.13410	−	0.163059i	−0.683696	+	0.729767i	$0.739629\pi$
$632$	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	0.962346	+	0.271828i	$0.0876283\pi$
$641$	7.58857	+	25.8443i	0.299731	+	1.02079i	−0.662615	+	0.748960i	$0.730554\pi$
$642$	1.73628	+	0.647599i	0.0685255	+	0.0255587i
$643$	8.89632	+	8.89632i	0.350837	+	0.350837i	0.860421	−	0.509584i	$-0.170201\pi$
$643$	8.89632	+	8.89632i	0.350837	+	0.350837i	−0.509584	+	0.860421i	$0.670201\pi$
$644$	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	0.805616	−	0.592438i	$-0.201835\pi$
$647$	18.8933	+	10.3165i	0.742774	+	0.405585i	−0.0628418	+	0.998024i	$0.520016\pi$
$648$	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	−0.942413	−	0.334452i	$-0.891449\pi$
$653$	1.37409	−	6.31659i	0.0537723	−	0.247187i	0.996185	+	0.0872645i	$0.0278125\pi$
$654$	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	0.0551364	−	0.998479i	$-0.482441\pi$
$659$	−11.2516	−	3.30376i	−0.438298	−	0.128696i	−0.493435	+	0.869783i	$0.664259\pi$
$660$	13.6104	+	5.45106i	0.529783	+	0.212182i
$661$	−18.8706	+	16.3515i	−0.733982	+	0.635999i	−0.939458	−	0.342663i	$-0.888671\pi$
$661$	−18.8706	+	16.3515i	−0.733982	+	0.635999i	0.205476	+	0.978662i	$0.434126\pi$
$662$	−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	0.949272	−	0.314455i	$-0.101822\pi$
$673$	47.8409	+	3.42165i	1.84413	+	0.131895i	0.894859	+	0.446350i	$0.147276\pi$
$674$	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	0.991016	−	0.133745i	$-0.0427002\pi$
$677$	15.1819	+	20.2806i	0.583487	+	0.779448i	−0.407528	+	0.913193i	$0.633609\pi$
$678$	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	0.944536	−	0.328407i	$-0.106512\pi$
$683$	23.4042	+	17.5202i	0.895538	+	0.670392i	−0.0489979	+	0.998799i	$0.515603\pi$
$684$	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	−0.119599	−	0.992822i	$-0.538161\pi$
$701$	−25.1061	−	11.4656i	−0.948244	−	0.433049i	−0.828646	+	0.559774i	$0.810888\pi$
$702$	−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	−0.0186073	−	0.999827i	$-0.505923\pi$
$709$	25.9265	−	29.9208i	0.973691	−	1.12370i	0.992298	−	0.123872i	$-0.0395313\pi$
$710$	−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	−0.588668	−	0.808375i	$-0.700347\pi$
$719$	3.42425	−	2.96713i	0.127703	−	0.110655i	0.716371	+	0.697720i	$0.245802\pi$
$720$	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	0.740336	+	0.672238i	$0.234667\pi$
$727$	−5.72571	+	26.3207i	−0.212355	+	0.976180i	−0.952690	+	0.303942i	$0.901697\pi$
$728$	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	−0.205067	−	0.978748i	$-0.565741\pi$
$733$	−30.8456	−	16.8430i	−1.13931	−	0.622110i	−0.934243	+	0.356638i	$0.883923\pi$
$734$	−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	−0.963405	−	0.268052i	$-0.913620\pi$
$739$	−8.09710	−	27.5762i	−0.297857	−	1.01441i	0.665548	−	0.746355i	$-0.268198\pi$
$740$	−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	0.195882	+	0.980627i	$0.437243\pi$
$743$	−21.8121	+	29.1376i	−0.800210	+	1.06895i	−0.996091	+	0.0883274i	$0.971848\pi$
$744$	−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	−0.907475	−	0.420107i	$-0.861993\pi$
$751$	2.27644	−	7.75284i	0.0830685	−	0.282905i	0.990543	+	0.137202i	$0.0438108\pi$
$752$	−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	−0.0912623	−	0.995827i	$-0.529090\pi$
$757$	−22.3510	−	8.33650i	−0.812362	−	0.302995i	−0.721099	+	0.692832i	$0.756363\pi$
$758$	−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	−0.931441	−	0.363893i	$-0.881447\pi$
$761$	−16.4549	−	36.0311i	−0.596489	−	1.30613i	0.334952	−	0.942235i	$-0.391280\pi$
$762$	−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	0.892394	+	0.451257i	$0.149024\pi$
$769$	−2.52310	+	17.5486i	−0.0909855	+	0.632818i	−0.983380	+	0.181561i	$0.941885\pi$
$770$	−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	0.438234	−	0.898861i	$-0.355604\pi$
$773$	12.8857	+	2.80311i	0.463466	+	0.100821i	0.0252315	+	0.999682i	$0.491968\pi$
$774$	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	0.0487465	−	0.998811i	$-0.484477\pi$
$787$	14.2514	−	3.10021i	0.508009	−	0.110511i	0.459263	+	0.888301i	$0.348114\pi$
$788$	−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	0.774777	−	0.632234i	$-0.217862\pi$
$797$	48.7136	−	26.5996i	1.72552	−	0.942207i	0.950746	−	0.309972i	$-0.100320\pi$
$798$	−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	0.536662	−	0.843797i	$-0.319685\pi$
$809$	−6.31919	−	5.47561i	−0.222171	−	0.192512i	−0.758833	+	0.651285i	$0.774230\pi$
$810$	−10.9337	−	21.2160i	−0.384172	−	0.745454i
$811$	−14.6408	−	16.8963i	−0.514107	−	0.593311i	0.438039	−	0.898956i	$-0.355673\pi$
$811$	−14.6408	−	16.8963i	−0.514107	−	0.593311i	−0.952145	+	0.305645i	$0.901128\pi$
$812$	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	0.999007	+	0.0445626i	$0.0141894\pi$
$821$	1.51923	+	10.5665i	0.0530215	+	0.368773i	−0.945985	+	0.324210i	$0.894901\pi$
$822$	31.4245	+	2.24753i	1.09606	+	0.0783915i
$823$	13.4041	−	2.91588i	0.467236	−	0.101641i	0.0272174	−	0.999630i	$-0.491335\pi$
$823$	13.4041	−	2.91588i	0.467236	−	0.101641i	0.440019	+	0.897988i	$0.354972\pi$
$824$	−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	−0.617175	−	0.786826i	$-0.711723\pi$
$827$	4.87874	−	4.87874i	0.169650	−	0.169650i	0.786826	+	0.617175i	$0.211723\pi$
$828$	3.17498	−	1.59649i	0.110338	−	0.0554817i
$829$			38.5688i			1.33955i	0.742565	+	0.669774i	$0.233609\pi$
$829$			38.5688i			1.33955i	−0.742565	+	0.669774i	$0.766391\pi$
$830$	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	−0.721725	−	0.692180i	$-0.756651\pi$
$839$	7.93709	−	17.3798i	0.274019	−	0.600018i	0.995744	+	0.0921621i	$0.0293778\pi$
$840$	−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	0.723371	−	0.690459i	$-0.242592\pi$
$853$	23.8878	+	8.90970i	0.817904	+	0.305062i	0.0945326	+	0.995522i	$0.469864\pi$
$854$	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	0.977660	+	0.210194i	$0.0674096\pi$
$857$	−0.584396	+	8.17093i	−0.0199626	+	0.279114i	−0.997622	+	0.0689193i	$0.978045\pi$
$858$	−26.8626	+	35.8842i	−0.917073	+	1.22507i
$859$	6.68434	−	22.7648i	0.228067	−	0.776724i	−0.763350	−	0.645985i	$-0.776447\pi$
$859$	6.68434	−	22.7648i	0.228067	−	0.776724i	0.991417	−	0.130739i	$-0.0417350\pi$
$860$	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	−0.893702	−	0.448662i	$-0.851901\pi$
$863$	−15.0438	−	40.3341i	−0.512098	−	1.37299i	0.381604	−	0.924326i	$-0.375372\pi$
$864$	−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	−0.000598267	−	1.00000i	$-0.500190\pi$
$877$	−24.9403	−	13.6185i	−0.842175	−	0.459862i	−0.841577	+	0.540137i	$0.818372\pi$
$878$	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	−0.193985	−	0.981004i	$-0.562141\pi$
$881$	−3.07893	+	0.442684i	−0.103732	+	0.0149144i	0.0902534	+	0.995919i	$0.471232\pi$
$882$	1.95044	+	3.57196i	0.0656747	+	0.120274i
$883$	3.04732	−	14.0083i	0.102551	−	0.471418i	−0.897016	−	0.441997i	$-0.854270\pi$
$883$	3.04732	−	14.0083i	0.102551	−	0.471418i	0.999567	−	0.0294206i	$-0.00936620\pi$
$884$	−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	−0.999969	−	0.00791616i	$-0.997480\pi$
$887$	−37.9458	+	28.4059i	−1.27410	+	0.953777i	−0.274128	+	0.961693i	$0.588389\pi$
$888$	−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	0.505162	−	0.863024i	$-0.331433\pi$
$907$	−14.0109	−	18.7164i	−0.465224	−	0.621467i	−0.970386	+	0.241558i	$0.922342\pi$
$908$	−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	0.951554	+	0.307481i	$0.0994862\pi$
$911$	25.2316	+	39.2611i	0.835959	+	1.30078i	−0.115595	+	0.993296i	$0.536877\pi$
$912$	−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	−0.996573	−	0.0827170i	$-0.973640\pi$
$929$	−20.0501	−	31.1986i	−0.657824	−	1.02359i	0.338749	−	0.940877i	$-0.389996\pi$
$930$	−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	0.335812	−	0.941929i	$-0.390989\pi$
$937$	16.3507	+	1.16943i	0.534155	+	0.0382035i	0.198343	+	0.980133i	$0.436444\pi$
$938$	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	−0.867004	−	0.498302i	$-0.833957\pi$
$941$	−32.4604	+	14.8242i	−1.05818	+	0.483254i	−0.191176	+	0.981556i	$0.561230\pi$
$942$	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	−0.302937	−	0.953011i	$-0.597967\pi$
$947$	−14.3762	+	1.02820i	−0.467163	+	0.0334122i	−0.164226	+	0.986423i	$0.552513\pi$
$948$	−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	−0.855118	−	0.518434i	$-0.826515\pi$
$953$	−18.4791	+	13.8333i	−0.598598	+	0.448105i	0.256519	+	0.966539i	$0.417424\pi$
$954$	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	0.999180	−	0.0404896i	$-0.0128918\pi$
$967$	29.8120	+	29.8120i	0.958690	+	0.958690i	−0.0404896	+	0.999180i	$0.512892\pi$
$968$	−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	−0.735164	−	0.677889i	$-0.762895\pi$
$971$	5.82284	−	9.06052i	0.186864	−	0.290766i	0.922028	+	0.387123i	$0.126531\pi$
$972$	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	−0.977571	−	0.210606i	$-0.932456\pi$
$977$	−11.7742	−	31.5678i	−0.376690	−	1.00994i	0.600881	−	0.799338i	$-0.294817\pi$
$978$	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	0.985294	+	0.170867i	$0.0546568\pi$
$983$	−0.447970	+	6.26344i	−0.0142880	+	0.199773i	−0.999582	+	0.0289058i	$0.990798\pi$
$984$	−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	0.963366	−	0.268191i	$-0.0864257\pi$
$991$	4.08645	+	8.94808i	0.129810	+	0.284245i	−0.833555	+	0.552436i	$0.813698\pi$
$992$	−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	−0.997984	−	0.0634688i	$-0.979784\pi$
$997$	−16.1611	−	29.5968i	−0.511826	−	0.937340i	0.486157	−	0.873871i	$-0.338398\pi$
$998$	−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.157.8	yes	240
5.3	odd	4	inner	230.2.l.a.203.2	yes	240
23.17	odd	22	inner	230.2.l.a.17.2	✓	240
115.63	even	44	inner	230.2.l.a.63.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.2	✓	240	23.17	odd	22	inner
230.2.l.a.63.8	yes	240	115.63	even	44	inner
230.2.l.a.157.8	yes	240	1.1	even	1	trivial
230.2.l.a.203.2	yes	240	5.3	odd	4	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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