LMFDB - Embedded newform 552.2.x.a.35.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(35,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 11, 20]))

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

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

chi := DirichletCharacter("552.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.x (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.20
Character	$\chi$	$=$	552.35
Dual form			552.2.x.a.347.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06473 + 0.930785i) q^{2} +(-0.424251 - 1.67929i) q^{3} +(0.267280 - 1.98206i) q^{4} +(-0.611012 + 0.179409i) q^{5} +(2.01477 + 1.39309i) q^{6} +(1.41902 - 1.22959i) q^{7} +(1.56029 + 2.35913i) q^{8} +(-2.64002 + 1.42488i) q^{9} +O(q^{10})$	\(q+(-1.06473 + 0.930785i) q^{2} +(-0.424251 - 1.67929i) q^{3} +(0.267280 - 1.98206i) q^{4} +(-0.611012 + 0.179409i) q^{5} +(2.01477 + 1.39309i) q^{6} +(1.41902 - 1.22959i) q^{7} +(1.56029 + 2.35913i) q^{8} +(-2.64002 + 1.42488i) q^{9} +(0.483568 - 0.759742i) q^{10} +(1.89865 - 2.95436i) q^{11} +(-3.44184 + 0.392051i) q^{12} +(3.75279 + 3.25181i) q^{13} +(-0.366385 + 2.62998i) q^{14} +(0.560502 + 0.949950i) q^{15} +(-3.85712 - 1.05953i) q^{16} +(2.10313 - 0.960465i) q^{17} +(1.48464 - 3.97440i) q^{18} +(1.65907 - 3.63286i) q^{19} +(0.192288 + 1.25901i) q^{20} +(-2.66686 - 1.86129i) q^{21} +(0.728330 + 4.91282i) q^{22} +(-3.57878 - 3.19254i) q^{23} +(3.29970 - 3.62104i) q^{24} +(-3.86512 + 2.48396i) q^{25} +(-7.02242 + 0.0307533i) q^{26} +(3.51282 + 3.82885i) q^{27} +(-2.05784 - 3.14123i) q^{28} +(-2.03808 - 4.46277i) q^{29} +(-1.48098 - 0.489729i) q^{30} +(-2.96087 + 0.425709i) q^{31} +(5.09297 - 2.46204i) q^{32} +(-5.76673 - 1.93500i) q^{33} +(-1.34526 + 2.98019i) q^{34} +(-0.646439 + 1.00588i) q^{35} +(2.11857 + 5.61352i) q^{36} +(2.90162 - 9.88202i) q^{37} +(1.61496 + 5.41224i) q^{38} +(3.86860 - 7.68159i) q^{39} +(-1.37661 - 1.16153i) q^{40} +(-2.02393 - 6.89286i) q^{41} +(4.57193 - 0.500504i) q^{42} +(0.756804 - 5.26369i) q^{43} +(-5.34825 - 4.55289i) q^{44} +(1.35745 - 1.34426i) q^{45} +(6.78199 + 0.0681011i) q^{46} -6.53022 q^{47} +(-0.142869 + 6.92673i) q^{48} +(-0.494472 + 3.43913i) q^{49} +(1.80326 - 6.24233i) q^{50} +(-2.50515 - 3.12428i) q^{51} +(7.44832 - 6.56910i) q^{52} +(-1.89278 - 2.18439i) q^{53} +(-7.30402 - 0.806997i) q^{54} +(-0.630059 + 2.14579i) q^{55} +(5.11484 + 1.42914i) q^{56} +(-6.80449 - 1.24482i) q^{57} +(6.32387 + 2.85461i) q^{58} +(10.4244 + 9.03283i) q^{59} +(2.03267 - 0.857046i) q^{60} +(-8.15953 + 1.17316i) q^{61} +(2.75627 - 3.20920i) q^{62} +(-1.99423 + 5.26808i) q^{63} +(-3.13099 + 7.36186i) q^{64} +(-2.87640 - 1.31361i) q^{65} +(7.94105 - 3.30735i) q^{66} +(12.6939 - 8.15785i) q^{67} +(-1.34158 - 4.42523i) q^{68} +(-3.84289 + 7.36425i) q^{69} +(-0.247976 - 1.67268i) q^{70} +(4.04999 - 2.60277i) q^{71} +(-7.48068 - 4.00492i) q^{72} +(-1.44386 + 3.16162i) q^{73} +(6.10860 + 13.2224i) q^{74} +(5.81107 + 5.43683i) q^{75} +(-6.75711 - 4.25937i) q^{76} +(-0.938422 - 6.52687i) q^{77} +(3.03091 + 11.7796i) q^{78} +(7.27743 + 6.30593i) q^{79} +(2.54684 - 0.0446178i) q^{80} +(4.93943 - 7.52343i) q^{81} +(8.57070 + 5.45517i) q^{82} +(1.16258 - 3.95938i) q^{83} +(-4.40199 + 4.78838i) q^{84} +(-1.11272 + 0.964175i) q^{85} +(4.09357 + 6.30881i) q^{86} +(-6.62962 + 5.31586i) q^{87} +(9.93218 - 0.130495i) q^{88} +(2.29892 + 0.330535i) q^{89} +(-0.194089 + 2.69476i) q^{90} +9.32367 q^{91} +(-7.28434 + 6.24006i) q^{92} +(1.97104 + 4.79155i) q^{93} +(6.95289 - 6.07823i) q^{94} +(-0.361944 + 2.51737i) q^{95} +(-6.29518 - 7.50804i) q^{96} +(-5.22565 + 1.53439i) q^{97} +(-2.67461 - 4.12197i) q^{98} +(-0.802871 + 10.5049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.06473	+	0.930785i	−0.752875	+	0.658164i
$2$	−1.06473	+	0.930785i	−0.752875	+	0.658164i
$3$	−0.424251	−	1.67929i	−0.244942	−	0.969538i
$3$	−0.424251	−	1.67929i	−0.244942	−	0.969538i
$4$	0.267280	−	1.98206i	0.133640	−	0.991030i
$5$	−0.611012	+	0.179409i	−0.273253	+	0.0802342i	−0.415488	−	0.909599i	$-0.636389\pi$
$5$	−0.611012	+	0.179409i	−0.273253	+	0.0802342i	0.142235	+	0.989833i	$0.454571\pi$
$6$	2.01477	+	1.39309i	0.822525	+	0.568729i
$7$	1.41902	−	1.22959i	0.536340	−	0.464741i	−0.344077	−	0.938941i	$-0.611808\pi$
$7$	1.41902	−	1.22959i	0.536340	−	0.464741i	0.880417	+	0.474200i	$0.157263\pi$
$8$	1.56029	+	2.35913i	0.551646	+	0.834078i
$9$	−2.64002	+	1.42488i	−0.880007	+	0.474960i
$10$	0.483568	−	0.759742i	0.152918	−	0.240251i
$11$	1.89865	−	2.95436i	0.572466	−	0.890774i	−0.427446	−	0.904041i	$-0.640587\pi$
$11$	1.89865	−	2.95436i	0.572466	−	0.890774i	0.999912	+	0.0132669i	$0.00422311\pi$
$12$	−3.44184	+	0.392051i	−0.993575	+	0.113175i
$13$	3.75279	+	3.25181i	1.04084	+	0.901889i	0.995277	−	0.0970726i	$-0.0309479\pi$
$13$	3.75279	+	3.25181i	1.04084	+	0.901889i	0.0455582	+	0.998962i	$0.485493\pi$
$14$	−0.366385	+	2.62998i	−0.0979206	+	0.702891i
$15$	0.560502	+	0.949950i	0.144721	+	0.245276i
$16$	−3.85712	−	1.05953i	−0.964281	−	0.264883i
$17$	2.10313	−	0.960465i	0.510083	−	0.232947i	−0.143711	−	0.989620i	$-0.545904\pi$
$17$	2.10313	−	0.960465i	0.510083	−	0.232947i	0.653794	+	0.756673i	$0.273176\pi$
$18$	1.48464	−	3.97440i	0.349933	−	0.936775i
$19$	1.65907	−	3.63286i	0.380617	−	0.833436i	−0.618256	−	0.785977i	$-0.712160\pi$
$19$	1.65907	−	3.63286i	0.380617	−	0.833436i	0.998873	−	0.0474589i	$-0.0151123\pi$
$20$	0.192288	+	1.25901i	0.0429970	+	0.281524i
$21$	−2.66686	−	1.86129i	−0.581956	−	0.406167i
$22$	0.728330	+	4.91282i	0.155281	+	1.04742i
$23$	−3.57878	−	3.19254i	−0.746228	−	0.665690i
$23$	−3.57878	−	3.19254i	−0.746228	−	0.665690i
$24$	3.29970	−	3.62104i	0.673549	−	0.739142i
$25$	−3.86512	+	2.48396i	−0.773024	+	0.496792i
$26$	−7.02242	+	0.0307533i	−1.37721	+	0.00603122i
$27$	3.51282	+	3.82885i	0.676042	+	0.736863i
$28$	−2.05784	−	3.14123i	−0.388896	−	0.593637i
$29$	−2.03808	−	4.46277i	−0.378462	−	0.828715i	−0.999007	−	0.0445451i	$-0.985816\pi$
$29$	−2.03808	−	4.46277i	−0.378462	−	0.828715i	0.620546	−	0.784170i	$-0.286911\pi$
$30$	−1.48098	−	0.489729i	−0.270389	−	0.0894119i
$31$	−2.96087	+	0.425709i	−0.531788	+	0.0764596i	−0.402978	−	0.915210i	$-0.632025\pi$
$31$	−2.96087	+	0.425709i	−0.531788	+	0.0764596i	−0.128810	+	0.991669i	$0.541116\pi$
$32$	5.09297	−	2.46204i	0.900319	−	0.435231i
$33$	−5.76673	−	1.93500i	−1.00386	−	0.336839i
$34$	−1.34526	+	2.98019i	−0.230711	+	0.511098i
$35$	−0.646439	+	1.00588i	−0.109268	+	0.170024i
$36$	2.11857	+	5.61352i	0.353096	+	0.935587i
$37$	2.90162	−	9.88202i	0.477024	−	1.62459i	−0.272174	−	0.962248i	$-0.587743\pi$
$37$	2.90162	−	9.88202i	0.477024	−	1.62459i	0.749198	−	0.662346i	$-0.230439\pi$
$38$	1.61496	+	5.41224i	0.261980	+	0.877981i
$39$	3.86860	−	7.68159i	0.619472	−	1.23004i
$40$	−1.37661	−	1.16153i	−0.217660	−	0.183653i
$41$	−2.02393	−	6.89286i	−0.316084	−	1.07648i	−0.952348	−	0.305013i	$-0.901339\pi$
$41$	−2.02393	−	6.89286i	−0.316084	−	1.07648i	0.636264	−	0.771471i	$-0.280479\pi$
$42$	4.57193	−	0.500504i	0.705464	−	0.0772295i
$43$	0.756804	−	5.26369i	0.115412	−	0.802705i	−0.847094	−	0.531443i	$-0.821650\pi$
$43$	0.756804	−	5.26369i	0.115412	−	0.802705i	0.962506	−	0.271262i	$-0.0874410\pi$
$44$	−5.34825	−	4.55289i	−0.806279	−	0.686374i
$45$	1.35745	−	1.34426i	0.202356	−	0.200391i
$46$	6.78199	+	0.0681011i	0.999950	+	0.0100410i
$47$	−6.53022			−0.952530			−0.476265	−	0.879302i	$-0.658010\pi$
$47$	−6.53022			−0.952530			−0.476265	+	0.879302i	$0.658010\pi$
$48$	−0.142869	+	6.92673i	−0.0206213	+	0.999787i
$49$	−0.494472	+	3.43913i	−0.0706388	+	0.491304i
$50$	1.80326	−	6.24233i	0.255019	−	0.882799i
$51$	−2.50515	−	3.12428i	−0.350791	−	0.437486i
$52$	7.44832	−	6.56910i	1.03290	−	0.910971i
$53$	−1.89278	−	2.18439i	−0.259994	−	0.300049i	0.610712	−	0.791853i	$-0.290883\pi$
$53$	−1.89278	−	2.18439i	−0.259994	−	0.300049i	−0.870706	+	0.491804i	$0.836338\pi$
$54$	−7.30402	−	0.806997i	−0.993952	−	0.109818i
$55$	−0.630059	+	2.14579i	−0.0849572	+	0.289338i
$56$	5.11484	+	1.42914i	0.683500	+	0.190977i
$57$	−6.80449	−	1.24482i	−0.901277	−	0.164880i
$58$	6.32387	+	2.85461i	0.830365	+	0.374829i
$59$	10.4244	+	9.03283i	1.35715	+	1.17597i	0.966868	+	0.255277i	$0.0821667\pi$
$59$	10.4244	+	9.03283i	1.35715	+	1.17597i	0.390278	+	0.920697i	$0.372379\pi$
$60$	2.03267	−	0.857046i	0.262417	−	0.110644i
$61$	−8.15953	+	1.17316i	−1.04472	+	0.150208i	−0.643244	−	0.765661i	$-0.722412\pi$
$61$	−8.15953	+	1.17316i	−1.04472	+	0.150208i	−0.401476	+	0.915869i	$0.631503\pi$
$62$	2.75627	−	3.20920i	0.350047	−	0.407568i
$63$	−1.99423	+	5.26808i	−0.251249	+	0.663715i
$64$	−3.13099	+	7.36186i	−0.391373	+	0.920232i
$65$	−2.87640	−	1.31361i	−0.356773	−	0.162933i
$66$	7.94105	−	3.30735i	0.977476	−	0.407106i
$67$	12.6939	−	8.15785i	1.55080	−	0.996641i	0.565713	−	0.824602i	$-0.308601\pi$
$67$	12.6939	−	8.15785i	1.55080	−	0.996641i	0.985090	−	0.172038i	$-0.0550353\pi$
$68$	−1.34158	−	4.42523i	−0.162690	−	0.536638i
$69$	−3.84289	+	7.36425i	−0.462630	+	0.886552i
$70$	−0.247976	−	1.67268i	−0.0296388	−	0.199923i
$71$	4.04999	−	2.60277i	0.480645	−	0.308892i	−0.277789	−	0.960642i	$-0.589601\pi$
$71$	4.04999	−	2.60277i	0.480645	−	0.308892i	0.758433	+	0.651751i	$0.225965\pi$
$72$	−7.48068	−	4.00492i	−0.881607	−	0.471985i
$73$	−1.44386	+	3.16162i	−0.168992	+	0.370040i	−0.975112	−	0.221711i	$-0.928836\pi$
$73$	−1.44386	+	3.16162i	−0.168992	+	0.370040i	0.806121	+	0.591751i	$0.201563\pi$
$74$	6.10860	+	13.2224i	0.710110	+	1.53708i
$75$	5.81107	+	5.43683i	0.671005	+	0.627791i
$76$	−6.75711	−	4.25937i	−0.775094	−	0.488584i
$77$	−0.938422	−	6.52687i	−0.106943	−	0.743805i
$78$	3.03091	+	11.7796i	0.343183	+	1.33378i
$79$	7.27743	+	6.30593i	0.818775	+	0.709472i	0.959846	−	0.280527i	$-0.0905092\pi$
$79$	7.27743	+	6.30593i	0.818775	+	0.709472i	−0.141071	+	0.989999i	$0.545055\pi$
$80$	2.54684	−	0.0446178i	0.284745	−	0.00498842i
$81$	4.93943	−	7.52343i	0.548825	−	0.835937i
$82$	8.57070	+	5.45517i	0.946475	+	0.602422i
$83$	1.16258	−	3.95938i	0.127610	−	0.434598i	−0.870758	−	0.491712i	$-0.836371\pi$
$83$	1.16258	−	3.95938i	0.127610	−	0.434598i	0.998368	+	0.0571133i	$0.0181896\pi$
$84$	−4.40199	+	4.78838i	−0.480296	+	0.522455i
$85$	−1.11272	+	0.964175i	−0.120691	+	0.104580i
$86$	4.09357	+	6.30881i	0.441421	+	0.680296i
$87$	−6.62962	+	5.31586i	−0.710770	+	0.569920i
$88$	9.93218	−	0.130495i	1.05877	−	0.0139108i
$89$	2.29892	+	0.330535i	0.243685	+	0.0350367i	0.263075	−	0.964775i	$-0.415263\pi$
$89$	2.29892	+	0.330535i	0.243685	+	0.0350367i	−0.0193898	+	0.999812i	$0.506172\pi$
$90$	−0.194089	+	2.69476i	−0.0204588	+	0.284053i
$91$	9.32367			0.977386
$92$	−7.28434	+	6.24006i	−0.759445	+	0.650571i
$93$	1.97104	+	4.79155i	0.204388	+	0.496861i
$94$	6.95289	−	6.07823i	0.717136	−	0.626921i
$95$	−0.361944	+	2.51737i	−0.0371346	+	0.258277i
$96$	−6.29518	−	7.50804i	−0.642499	−	0.766287i
$97$	−5.22565	+	1.53439i	−0.530584	+	0.155794i	−0.536042	−	0.844192i	$-0.680081\pi$
$97$	−5.22565	+	1.53439i	−0.530584	+	0.155794i	0.00545759	+	0.999985i	$0.498263\pi$
$98$	−2.67461	−	4.12197i	−0.270176	−	0.416382i
$99$	−0.802871	+	10.5049i	−0.0806916	+	1.05579i
$100$	3.89029	+	8.32481i	0.389029	+	0.832481i
$101$	−4.26166	−	1.25134i	−0.424051	−	0.124513i	0.0627425	−	0.998030i	$-0.480015\pi$
$101$	−4.26166	−	1.25134i	−0.424051	−	0.124513i	−0.486793	+	0.873517i	$0.661833\pi$
$102$	5.57533	+	0.994739i	0.552040	+	0.0984939i
$103$	6.47732	−	10.0789i	0.638229	−	0.993104i	−0.359961	−	0.932967i	$-0.617210\pi$
$103$	6.47732	−	10.0789i	0.638229	−	0.993104i	0.998190	−	0.0601365i	$-0.0191536\pi$
$104$	−1.81600	+	13.9271i	−0.178073	+	1.36566i
$105$	1.96341	+	0.658812i	0.191609	+	0.0642935i
$106$	4.04849	+	0.564001i	0.393224	+	0.0547806i
$107$	−19.4694	+	2.79928i	−1.88218	+	0.270617i	−0.985195	−	0.171440i	$-0.945158\pi$
$107$	−19.4694	+	2.79928i	−1.88218	+	0.270617i	−0.896987	+	0.442057i	$0.854249\pi$
$108$	8.52792	−	5.93924i	0.820599	−	0.571504i
$109$	−4.49147	+	2.05118i	−0.430205	+	0.196468i	−0.618735	−	0.785599i	$-0.712355\pi$
$109$	−4.49147	+	2.05118i	−0.430205	+	0.196468i	0.188531	+	0.982067i	$0.439627\pi$
$110$	−1.32642	−	2.87112i	−0.126470	−	0.273751i
$111$	−17.8258	−	0.680203i	−1.69195	−	0.0645620i
$112$	−6.77613	+	3.23918i	−0.640284	+	0.306074i
$113$	5.49021	+	8.54293i	0.516475	+	0.803651i	0.997321	−	0.0731540i	$-0.0233065\pi$
$113$	5.49021	+	8.54293i	0.516475	+	0.803651i	−0.480845	+	0.876806i	$0.659670\pi$
$114$	8.40357	−	5.00813i	0.787066	−	0.469054i
$115$	2.75945	+	1.30861i	0.257320	+	0.122029i
$116$	−9.39021	+	2.84678i	−0.871859	+	0.264317i
$117$	−14.5409	−	3.23757i	−1.34430	−	0.299313i
$118$	−19.5068	+	0.0854261i	−1.79574	+	0.00786411i
$119$	1.80340	−	3.94890i	0.165318	−	0.361995i
$120$	−1.36651	+	2.80450i	−0.124745	+	0.256014i
$121$	−0.553807	−	1.21267i	−0.0503461	−	0.110243i
$122$	7.59569	−	8.84386i	0.687682	−	0.800685i
$123$	−10.7165	+	6.32306i	−0.966270	+	0.570132i
$124$	0.0523986	+	5.98241i	0.00470553	+	0.537236i
$125$	4.00109	−	4.61750i	0.357868	−	0.413002i
$126$	−2.78014	−	7.46525i	−0.247674	−	0.665058i
$127$	−6.91534	+	10.7605i	−0.613637	+	0.954838i	0.385842	+	0.922565i	$0.373911\pi$
$127$	−6.91534	+	10.7605i	−0.613637	+	0.954838i	−0.999479	+	0.0322733i	$0.989725\pi$
$128$	−3.51866	−	10.7526i	−0.311009	−	0.950407i
$129$	−9.16033	+	0.962234i	−0.806522	+	0.0847200i
$130$	4.28526	−	1.27868i	0.375842	−	0.112147i
$131$	1.86721	−	1.61794i	0.163138	−	0.141360i	−0.569466	−	0.822015i	$-0.692850\pi$
$131$	1.86721	−	1.61794i	0.163138	−	0.141360i	0.732604	+	0.680655i	$0.238305\pi$
$132$	−5.37661	+	10.9128i	−0.467974	+	0.949840i
$133$	−2.11267	−	7.19509i	−0.183192	−	0.623893i
$134$	−5.92228	+	20.5011i	−0.511607	+	1.77103i
$135$	−2.83330	−	1.70924i	−0.243852	−	0.147108i
$136$	5.54735	+	3.46294i	0.475681	+	0.296945i
$137$		−	3.96510i		−	0.338761i	−0.985551	−	0.169381i	$-0.945823\pi$
$137$		−	3.96510i		−	0.338761i	0.985551	−	0.169381i	$-0.0541767\pi$
$138$	−2.76291	−	11.4178i	−0.235194	−	0.971948i
$139$	12.2638			1.04021			0.520103	−	0.854104i	$-0.325894\pi$
$139$	12.2638			1.04021			0.520103	+	0.854104i	$0.325894\pi$
$140$	1.82093	+	1.55013i	0.153897	+	0.131010i
$141$	2.77045	+	10.9661i	0.233314	+	0.923514i
$142$	−1.88951	+	6.54090i	−0.158564	+	0.548900i
$143$	16.7323	−	4.91303i	1.39922	−	0.410849i
$144$	11.6926	−	2.69876i	0.974383	−	0.224896i
$145$	2.04595	+	2.36115i	0.169907	+	0.196083i
$146$	−1.40547	−	4.71019i	−0.116318	−	0.389818i
$147$	5.98506	−	0.628693i	0.493640	−	0.0518537i
$148$	−18.8112	−	8.39246i	−1.54627	−	0.689856i
$149$	14.2287	+	9.14424i	1.16566	+	0.749125i	0.972697	−	0.232081i	$-0.0745533\pi$
$149$	14.2287	+	9.14424i	1.16566	+	0.749125i	0.192965	+	0.981206i	$0.438190\pi$
$150$	−11.2477	−	0.379874i	−0.918372	−	0.0310166i
$151$	−0.626011	−	0.542441i	−0.0509440	−	0.0441432i	0.629017	−	0.777392i	$-0.283458\pi$
$151$	−0.626011	−	0.542441i	−0.0509440	−	0.0441432i	−0.679961	+	0.733249i	$0.738003\pi$
$152$	11.1590	−	1.75435i	0.905117	−	0.142297i
$153$	−4.18375	+	5.53235i	−0.338236	+	0.447264i
$154$	7.07427	+	6.07585i	0.570061	+	0.489606i
$155$	1.73275	−	0.791321i	0.139178	−	0.0635604i
$156$	−14.1914	−	9.72093i	−1.13622	−	0.778298i
$157$	10.9199	+	4.98695i	0.871502	+	0.398002i	0.800399	−	0.599467i	$-0.204621\pi$
$157$	10.9199	+	4.98695i	0.871502	+	0.398002i	0.0711028	+	0.997469i	$0.477348\pi$
$158$	−13.6179	+	0.0596370i	−1.08338	+	0.00474447i
$159$	−2.86521	+	4.10526i	−0.227226	+	0.325568i
$160$	−2.67015	+	2.41806i	−0.211094	+	0.191165i
$161$	−9.00388	−	0.129849i	−0.709605	−	0.0102335i
$162$	1.74356	+	12.6079i	0.136987	+	0.990573i
$163$	−14.3579	+	9.22726i	−1.12460	+	0.722735i	−0.964426	−	0.264354i	$-0.914841\pi$
$163$	−14.3579	+	9.22726i	−1.12460	+	0.722735i	−0.160172	+	0.987089i	$0.551205\pi$
$164$	−14.2030	+	2.16922i	−1.10907	+	0.169388i
$165$	3.87070	+	0.147699i	0.301333	+	0.0114984i
$166$	2.44750	+	5.29776i	0.189963	+	0.411186i
$167$	−5.77994	−	12.6563i	−0.447265	−	0.979374i	−0.990207	−	0.139604i	$-0.955417\pi$
$167$	−5.77994	−	12.6563i	−0.447265	−	0.979374i	0.542942	−	0.839770i	$-0.317310\pi$
$168$	0.229957	−	9.19562i	0.0177416	−	0.709457i
$169$	1.65906	+	11.5390i	0.127620	+	0.887615i
$170$	0.287299	−	2.06228i	0.0220348	−	0.158170i
$171$	0.796409	+	11.9548i	0.0609029	+	0.914208i
$172$	−10.2307	−	2.90691i	−0.780081	−	0.221650i
$173$	5.07788	+	3.26335i	0.386064	+	0.248108i	0.719248	−	0.694754i	$-0.244487\pi$
$173$	5.07788	+	3.26335i	0.386064	+	0.248108i	−0.333184	+	0.942862i	$0.608123\pi$
$174$	2.11081	−	11.8307i	0.160020	−	0.896881i
$175$	−2.43044	+	8.27730i	−0.183724	+	0.625705i
$176$	−10.4536	+	9.38366i	−0.787968	+	0.707320i
$177$	10.7461	−	21.3378i	0.807730	−	1.60385i
$178$	−2.75538	+	1.78787i	−0.206524	+	0.134007i
$179$	5.25516	+	17.8974i	0.392789	+	1.33772i	0.884330	+	0.466862i	$0.154615\pi$
$179$	5.25516	+	17.8974i	0.392789	+	1.33772i	−0.491542	+	0.870854i	$0.663566\pi$
$180$	−2.30159	−	3.04984i	−0.171550	−	0.227321i
$181$	1.63490	+	0.235064i	0.121521	+	0.0174722i	0.202807	−	0.979219i	$-0.434994\pi$
$181$	1.63490	+	0.235064i	0.121521	+	0.0174722i	−0.0812857	+	0.996691i	$0.525903\pi$
$182$	−9.92715	+	8.67833i	−0.735849	+	0.643280i
$183$	5.43177	+	13.2045i	0.401528	+	0.976104i
$184$	1.94767	−	13.4241i	0.143584	−	0.989638i
$185$			6.55861i			0.482198i
$186$	−6.55852	−	3.26707i	−0.480894	−	0.239553i
$187$	1.15554	−	8.03699i	0.0845017	−	0.587723i
$188$	−1.74540	+	12.9433i	−0.127296	+	0.943986i
$189$	9.69268	+	1.11390i	0.705039	+	0.0810241i
$190$	−1.95776	−	3.01720i	−0.142031	−	0.218891i
$191$	3.59572	+	4.14968i	0.260177	+	0.300260i	0.870776	−	0.491680i	$-0.163617\pi$
$191$	3.59572	+	4.14968i	0.260177	+	0.300260i	−0.610599	+	0.791940i	$0.709071\pi$
$192$	13.6910	+	2.13455i	0.988063	+	0.154048i
$193$	−10.1514	−	2.98073i	−0.730716	−	0.214558i	−0.104850	−	0.994488i	$-0.533436\pi$
$193$	−10.1514	−	2.98073i	−0.730716	−	0.214558i	−0.625866	+	0.779930i	$0.715254\pi$
$194$	4.13569	−	6.49765i	0.296925	−	0.466504i
$195$	−0.985610	+	5.38761i	−0.0705810	+	0.385814i
$196$	6.68439	+	1.89928i	0.477456	+	0.135663i
$197$	10.3049	−	11.8925i	0.734192	−	0.847302i	−0.258745	−	0.965946i	$-0.583309\pi$
$197$	10.3049	−	11.8925i	0.734192	−	0.847302i	0.992937	+	0.118643i	$0.0378545\pi$
$198$	−8.92299	−	11.9322i	−0.634130	−	0.847983i
$199$	−9.71856	+	1.39732i	−0.688930	+	0.0990532i	−0.477884	−	0.878423i	$-0.658596\pi$
$199$	−9.71856	+	1.39732i	−0.688930	+	0.0990532i	−0.211046	+	0.977476i	$0.567687\pi$
$200$	−11.8907	−	5.24262i	−0.840799	−	0.370709i
$201$	−19.0848	−	17.8557i	−1.34614	−	1.25944i
$202$	5.70222	−	2.63436i	0.401207	−	0.185353i
$203$	−8.37945	−	3.82676i	−0.588122	−	0.268586i
$204$	−6.86208	+	4.13030i	−0.480442	+	0.289179i
$205$	2.47329	+	3.84851i	0.172742	+	0.268791i
$206$	2.48472	+	16.7602i	0.173119	+	1.16774i
$207$	13.9971	+	3.32903i	0.972863	+	0.231384i
$208$	−11.0296	−	16.5188i	−0.764763	−	1.14537i
$209$	−7.58279	−	11.7991i	−0.524513	−	0.816157i
$210$	−2.70371	+	1.12606i	−0.186574	+	0.0777055i
$211$	2.76183	−	6.04757i	0.190132	−	0.416332i	−0.790427	−	0.612557i	$-0.790141\pi$
$211$	2.76183	−	6.04757i	0.190132	−	0.416332i	0.980559	+	0.196225i	$0.0628683\pi$
$212$	−4.83550	+	3.16777i	−0.332103	+	0.217563i
$213$	−6.08901	−	5.69687i	−0.417212	−	0.390343i
$214$	18.1241	−	21.1023i	1.23894	−	1.44252i
$215$	0.481938	+	3.35195i	0.0328679	+	0.228601i
$216$	−3.55174	+	14.2613i	−0.241665	+	0.970360i
$217$	−3.67809	+	4.24475i	−0.249685	+	0.288152i
$218$	2.87297	−	6.36454i	0.194582	−	0.431061i
$219$	5.92184	+	1.08334i	0.400161	+	0.0732055i
$220$	4.08467	+	1.82234i	0.275389	+	0.122862i
$221$	11.0158	+	3.23454i	0.741005	+	0.217579i
$222$	19.6127	−	15.8677i	1.31632	−	1.06497i
$223$	11.5484	−	10.0067i	0.773337	−	0.670100i	−0.175989	−	0.984392i	$-0.556312\pi$
$223$	11.5484	−	10.0067i	0.773337	−	0.670100i	0.949326	+	0.314292i	$0.101767\pi$
$224$	4.19974	−	9.75595i	0.280607	−	0.651847i
$225$	6.66465	−	12.0650i	0.444310	−	0.804337i
$226$	−13.7972	−	3.98567i	−0.917776	−	0.265123i
$227$	16.3412	+	2.34951i	1.08461	+	0.155943i	0.661357	−	0.750071i	$-0.269981\pi$
$227$	16.3412	+	2.34951i	1.08461	+	0.155943i	0.423248	+	0.906014i	$0.360890\pi$
$228$	−4.28600	+	13.1542i	−0.283848	+	0.871158i
$229$			27.7269i			1.83225i	0.400895	+	0.916124i	$0.368699\pi$
$229$			27.7269i			1.83225i	−0.400895	+	0.916124i	$0.631301\pi$
$230$	−4.15609	+	1.17514i	−0.274045	+	0.0774865i
$231$	−10.5624	+	4.34491i	−0.694953	+	0.285874i
$232$	7.34826	−	11.7713i	0.482437	−	0.772824i
$233$	19.5167	+	2.80607i	1.27858	+	0.183832i	0.747941	−	0.663766i	$-0.231043\pi$
$233$	19.5167	+	2.80607i	1.27858	+	0.183832i	0.530639	+	0.847598i	$0.321952\pi$
$234$	18.4955	−	10.0873i	1.20909	−	0.659427i
$235$	3.99004	−	1.17158i	0.260282	−	0.0764255i
$236$	20.6899	−	18.2476i	1.34679	−	1.18782i
$237$	7.50202	−	14.8962i	0.487308	−	0.967613i
$238$	1.75545	+	5.88307i	0.113789	+	0.381343i
$239$	22.0021	+	6.46041i	1.42320	+	0.417889i	0.900585	−	0.434680i	$-0.143138\pi$
$239$	22.0021	+	6.46041i	1.42320	+	0.417889i	0.522615	+	0.852569i	$0.324957\pi$
$240$	−1.15542	−	4.25794i	−0.0745823	−	0.274849i
$241$	2.42068	+	1.55568i	0.155930	+	0.100210i	0.616279	−	0.787528i	$-0.288639\pi$
$241$	2.42068	+	1.55568i	0.155930	+	0.100210i	−0.460349	+	0.887738i	$0.652276\pi$
$242$	1.71839	+	0.775684i	0.110462	+	0.0498628i
$243$	−14.7296	−	5.10290i	−0.944903	−	0.327351i
$244$	0.144399	+	16.4862i	0.00924421	+	1.05542i
$245$	−0.314883	−	2.19006i	−0.0201171	−	0.139918i
$246$	5.52467	−	16.7070i	0.352240	−	1.06520i
$247$	18.0395	−	8.23837i	1.14783	−	0.524195i
$248$	−5.62412	−	6.32085i	−0.357132	−	0.401374i
$249$	−7.14217	−	0.272533i	−0.452616	−	0.0172711i
$250$	0.0378395	+	8.64052i	0.00239318	+	0.546474i
$251$	4.28087	+	6.66116i	0.270206	+	0.420449i	0.949666	−	0.313264i	$-0.101422\pi$
$251$	4.28087	+	6.66116i	0.270206	+	0.420449i	−0.679460	+	0.733712i	$0.737786\pi$
$252$	9.90863	+	5.36073i	0.624185	+	0.337694i
$253$	−16.2268	+	4.51150i	−1.02017	+	0.283635i
$254$	−2.65275	−	17.8936i	−0.166448	−	1.12275i
$255$	2.09120	+	1.45952i	0.130956	+	0.0913988i
$256$	13.7548	+	8.17348i	0.859674	+	0.510842i
$257$	14.4360	+	6.59270i	0.900493	+	0.411241i	0.811203	−	0.584764i	$-0.198813\pi$
$257$	14.4360	+	6.59270i	0.900493	+	0.411241i	0.0892897	+	0.996006i	$0.471540\pi$
$258$	8.85760	−	9.55081i	0.551450	−	0.594607i
$259$	−8.03336	−	17.5906i	−0.499169	−	1.09303i
$260$	−3.37245	+	5.35010i	−0.209151	+	0.331799i
$261$	11.7395	+	8.87779i	0.726656	+	0.549521i
$262$	−0.482105	+	3.46063i	−0.0297845	+	0.213798i
$263$	7.29126	−	8.41456i	0.449598	−	0.518864i	−0.485027	−	0.874499i	$-0.661190\pi$
$263$	7.29126	−	8.41456i	0.449598	−	0.518864i	0.934625	+	0.355635i	$0.115736\pi$
$264$	−4.43288	−	16.6236i	−0.272825	−	1.02311i
$265$	1.54841	+	0.995105i	0.0951183	+	0.0611288i
$266$	8.94649	+	5.69435i	0.548544	+	0.349143i
$267$	−0.420257	−	4.00079i	−0.0257193	−	0.244844i
$268$	−12.7765	−	27.3404i	−0.780451	−	1.67008i
$269$	0.200731	+	0.231656i	0.0122388	+	0.0141243i	0.761836	−	0.647770i	$-0.224298\pi$
$269$	0.200731	+	0.231656i	0.0122388	+	0.0141243i	−0.749597	+	0.661894i	$0.769753\pi$
$270$	4.60763	−	0.817324i	0.280411	−	0.0497408i
$271$	−2.02316	−	6.89026i	−0.122898	−	0.418554i	0.874943	−	0.484226i	$-0.160899\pi$
$271$	−2.02316	−	6.89026i	−0.122898	−	0.418554i	−0.997841	+	0.0656726i	$0.979081\pi$
$272$	−9.12965	+	1.47631i	−0.553567	+	0.0895142i
$273$	−3.95558	−	15.6571i	−0.239403	−	0.947613i
$274$	3.69065	+	4.22174i	0.222961	+	0.255045i
$275$			16.1351i			0.972986i
$276$	13.5693	+	9.58516i	0.816773	+	0.576959i
$277$		−	17.4231i		−	1.04685i	−0.852071	−	0.523426i	$-0.824654\pi$
$277$		−	17.4231i		−	1.04685i	0.852071	−	0.523426i	$-0.175346\pi$
$278$	−13.0576	+	11.4150i	−0.783144	+	0.684626i
$279$	7.21018	−	5.34277i	0.431662	−	0.319863i
$280$	−3.38163	+	0.0444298i	−0.202091	+	0.00265519i
$281$	2.51087	+	8.55124i	0.149786	+	0.510124i	0.999863	−	0.0165337i	$-0.00526308\pi$
$281$	2.51087	+	8.55124i	0.149786	+	0.510124i	−0.850077	+	0.526658i	$0.823445\pi$
$282$	−13.1569	−	9.09722i	−0.783480	−	0.541731i
$283$	−8.11873	−	9.36951i	−0.482608	−	0.556959i	0.461267	−	0.887261i	$-0.347395\pi$
$283$	−8.11873	−	9.36951i	−0.482608	−	0.556959i	−0.943875	+	0.330302i	$0.892849\pi$
$284$	−4.07636	−	8.72298i	−0.241887	−	0.517614i
$285$	4.38095	−	0.460191i	0.259505	−	0.0272594i
$286$	−13.2423	+	20.8052i	−0.783033	+	1.23023i
$287$	−11.3474	−	7.29252i	−0.669815	−	0.430464i
$288$	−9.93744	+	13.7567i	−0.585569	+	0.810622i
$289$	−7.63199	+	8.80779i	−0.448941	+	0.518105i
$290$	−4.37610	−	0.609640i	−0.256973	−	0.0357993i
$291$	4.79367	+	8.12440i	0.281010	+	0.476261i
$292$	5.88061	+	3.70686i	0.344136	+	0.216928i
$293$	−0.452927	−	0.991772i	−0.0264603	−	0.0579399i	0.895940	−	0.444174i	$-0.146503\pi$
$293$	−0.452927	−	0.991772i	−0.0264603	−	0.0579399i	−0.922401	+	0.386234i	$0.873776\pi$
$294$	−5.78727	+	6.24019i	−0.337521	+	0.363935i
$295$	−7.99003	−	3.64892i	−0.465197	−	0.212448i
$296$	27.8403	−	8.57352i	1.61819	−	0.498326i
$297$	17.9814	−	3.10848i	1.04339	−	0.180372i
$298$	−23.6610	+	3.50776i	−1.37064	+	0.203199i
$299$	−3.04889	−	23.6184i	−0.176322	−	1.36589i
$300$	12.3293	−	10.0647i	0.711833	−	0.581088i
$301$	−5.39825	−	8.39985i	−0.311150	−	0.484159i
$302$	1.17143	−	0.00513003i	0.0674080	−	0.000295200i
$303$	−0.293340	+	7.68743i	−0.0168519	+	0.441631i
$304$	−10.2484	+	12.2546i	−0.587785	+	0.702847i
$305$	4.77509	−	2.18071i	0.273421	−	0.124867i
$306$	−0.694885	−	9.78460i	−0.0397240	−	0.559349i
$307$	−0.399967	−	2.78183i	−0.0228273	−	0.158767i	0.975219	−	0.221240i	$-0.0710104\pi$
$307$	−0.399967	−	2.78183i	−0.0228273	−	0.158767i	−0.998047	+	0.0624727i	$0.980101\pi$
$308$	−13.1875	+	0.115506i	−0.751425	+	0.00658157i
$309$	−19.6734	−	6.60130i	−1.11918	−	0.375535i
$310$	−1.10835	+	2.45536i	−0.0629503	+	0.139455i
$311$	9.14613	+	5.87786i	0.518629	+	0.333303i	0.773630	−	0.633638i	$-0.218439\pi$
$311$	9.14613	+	5.87786i	0.518629	+	0.333303i	−0.255000	+	0.966941i	$0.582076\pi$
$312$	24.1580	−	2.85899i	1.36768	−	0.161859i
$313$	−6.37032	−	1.87049i	−0.360072	−	0.105727i	0.0966927	−	0.995314i	$-0.469174\pi$
$313$	−6.37032	−	1.87049i	−0.360072	−	0.105727i	−0.456764	+	0.889588i	$0.650992\pi$
$314$	−16.2685	+	4.85434i	−0.918082	+	0.273946i
$315$	0.273355	−	3.57664i	0.0154018	−	0.201521i
$316$	14.4438	−	12.7389i	0.812530	−	0.716616i
$317$	4.16515	−	1.22300i	0.233938	−	0.0686904i	−0.162662	−	0.986682i	$-0.552008\pi$
$317$	4.16515	−	1.22300i	0.233938	−	0.0686904i	0.396600	+	0.917991i	$0.370190\pi$
$318$	−0.770458	−	7.03787i	−0.0432052	−	0.394664i
$319$	−17.0542	−	2.45203i	−0.954854	−	0.137287i
$320$	0.592284	−	5.05991i	0.0331097	−	0.282857i
$321$	12.9607	+	31.5072i	0.723398	+	1.75856i
$322$	9.70752	−	8.24242i	0.540979	−	0.459332i
$323$		−	9.23385i		−	0.513785i
$324$	−13.5917	−	11.8011i	−0.755094	−	0.655617i
$325$	−22.5823	−	3.24685i	−1.25264	−	0.180103i
$326$	6.69863	−	23.1886i	0.371003	−	1.28430i
$327$	5.35004	+	6.67225i	0.295858	+	0.368976i
$328$	13.1032	−	15.5296i	0.723506	−	0.857477i
$329$	−9.26652	+	8.02949i	−0.510880	+	0.442680i
$330$	−4.25871	+	3.44553i	−0.234434	+	0.189670i
$331$	−31.7963	−	9.33623i	−1.74768	−	0.513166i	−0.757486	−	0.652852i	$-0.773572\pi$
$331$	−31.7963	−	9.33623i	−1.74768	−	0.513166i	−0.990196	+	0.139686i	$0.955391\pi$
$332$	−7.53699	−	3.36256i	−0.413646	−	0.184545i
$333$	6.42036	+	30.2232i	0.351833	+	1.65622i
$334$	17.9343	+	8.09561i	0.981324	+	0.442972i
$335$	−6.29251	+	7.26194i	−0.343796	+	0.396762i
$336$	8.31430	+	10.0048i	0.453582	+	0.545809i
$337$	3.72269	+	25.8919i	0.202788	+	1.41042i	0.795961	+	0.605347i	$0.206966\pi$
$337$	3.72269	+	25.8919i	0.202788	+	1.41042i	−0.593173	+	0.805075i	$0.702125\pi$
$338$	−12.5068	−	10.7416i	−0.680278	−	0.584268i
$339$	12.0168	−	12.8440i	0.652664	−	0.697590i
$340$	1.61365	+	2.46318i	0.0875122	+	0.133585i
$341$	−4.36397	+	9.55576i	−0.236322	+	0.517474i
$342$	−11.9753	−	11.9873i	−0.647551	−	0.648200i
$343$	10.6329	+	16.5452i	0.574124	+	0.893354i
$344$	13.5986	−	6.42749i	0.733185	−	0.346547i
$345$	1.02684	−	5.18909i	0.0552831	−	0.279371i
$346$	−8.44403	+	1.25184i	−0.453954	+	0.0672991i
$347$	−5.37378	−	8.36176i	−0.288479	−	0.448883i	0.666521	−	0.745486i	$-0.267783\pi$
$347$	−5.37378	−	8.36176i	−0.288479	−	0.448883i	−0.955001	+	0.296603i	$0.904146\pi$
$348$	8.76438	+	14.5611i	0.469820	+	0.780558i
$349$	20.7026	+	9.45458i	1.10819	+	0.506092i	0.883543	−	0.468349i	$-0.155151\pi$
$349$	20.7026	+	9.45458i	1.10819	+	0.506092i	0.224643	+	0.974441i	$0.427878\pi$
$350$	−5.11664	−	11.0753i	−0.273496	−	0.591998i
$351$	0.732172	+	25.7919i	0.0390805	+	1.37667i
$352$	2.39603	−	19.7210i	0.127709	−	1.05114i
$353$	−15.8256	+	2.27537i	−0.842309	+	0.121106i	−0.549945	−	0.835201i	$-0.685351\pi$
$353$	−15.8256	+	2.27537i	−0.842309	+	0.121106i	−0.292365	+	0.956307i	$0.594442\pi$
$354$	8.41923	+	32.7213i	0.447477	+	1.73912i
$355$	−2.00763	+	2.31693i	−0.106554	+	0.122970i
$356$	1.26960	−	4.46826i	0.0672885	−	0.236817i
$357$	−7.39644	−	1.35311i	−0.391461	−	0.0716140i
$358$	−22.2539	−	14.1644i	−1.17616	−	0.748613i
$359$	5.99607	+	1.76060i	0.316460	+	0.0929212i	0.436105	−	0.899896i	$-0.356357\pi$
$359$	5.99607	+	1.76060i	0.316460	+	0.0929212i	−0.119645	+	0.992817i	$0.538176\pi$
$360$	5.28930	+	1.10495i	0.278771	+	0.0582361i
$361$	1.99718	+	2.30487i	0.105115	+	0.121309i
$362$	−1.95952	+	1.27147i	−0.102990	+	0.0668267i
$363$	−1.80147	+	1.44448i	−0.0945525	+	0.0758155i
$364$	2.49203	−	18.4801i	0.130618	−	0.968619i
$365$	0.314994	−	2.19083i	0.0164875	−	0.114673i
$366$	−18.0739	−	9.00334i	−0.944736	−	0.470612i
$367$		−	6.91622i		−	0.361024i	−0.983573	−	0.180512i	$-0.942225\pi$
$367$		−	6.91622i		−	0.361024i	0.983573	−	0.180512i	$-0.0577754\pi$
$368$	10.4212	+	16.1058i	0.543243	+	0.839575i
$369$	15.1647	+	15.3135i	0.789444	+	0.797187i
$370$	−6.10465	−	6.98312i	−0.317366	−	0.363035i
$371$	−5.37180	−	0.772349i	−0.278890	−	0.0400983i
$372$	10.0240	−	2.62604i	0.519718	−	0.136154i
$373$	−3.44300	−	11.7258i	−0.178272	−	0.607137i	−0.999341	−	0.0363083i	$-0.988440\pi$
$373$	−3.44300	−	11.7258i	−0.178272	−	0.607137i	0.821069	−	0.570829i	$-0.193378\pi$
$374$	6.25036	+	9.63274i	0.323199	+	0.498097i
$375$	−9.45158	−	4.76000i	−0.488078	−	0.245805i
$376$	−10.1890	−	15.4056i	−0.525460	−	0.794485i
$377$	6.86359	−	23.3753i	0.353493	−	1.20389i
$378$	−11.3568	+	7.83580i	−0.584133	+	0.403030i
$379$	−15.4472	−	9.92733i	−0.793471	−	0.509933i	0.0800083	−	0.996794i	$-0.474505\pi$
$379$	−15.4472	−	9.92733i	−0.793471	−	0.509933i	−0.873479	+	0.486861i	$0.838142\pi$
$380$	4.89285	+	1.39024i	0.250998	+	0.0713177i
$381$	21.0038	+	7.04771i	1.07606	+	0.361065i
$382$	−7.69091	−	1.07143i	−0.393501	−	0.0548191i
$383$	5.06768	+	35.2465i	0.258946	+	1.80101i	0.540370	+	0.841427i	$0.318284\pi$
$383$	5.06768	+	35.2465i	0.258946	+	1.80101i	−0.281424	+	0.959584i	$0.590807\pi$
$384$	−16.5640	+	10.4707i	−0.845277	+	0.534329i
$385$	1.74437	+	3.81963i	0.0889011	+	0.194666i
$386$	13.5829	−	6.27514i	0.691352	−	0.319396i
$387$	5.50215	+	14.9746i	0.279690	+	0.761202i
$388$	1.64454	+	10.7677i	0.0834887	+	0.546645i
$389$	−27.7131	+	17.8102i	−1.40511	+	0.903011i	−0.999937	−	0.0112286i	$-0.996426\pi$
$389$	−27.7131	+	17.8102i	−1.40511	+	0.903011i	−0.405175	+	0.914239i	$0.632789\pi$
$390$	−3.96530	−	6.65371i	−0.200791	−	0.336924i
$391$	−10.5930	−	3.27701i	−0.535709	−	0.165726i
$392$	−8.88486	+	4.19951i	−0.448753	+	0.212107i
$393$	−3.50916	−	2.44916i	−0.177014	−	0.123544i
$394$	0.0974562	+	22.2538i	0.00490977	+	1.12113i
$395$	−5.57794	−	2.54736i	−0.280656	−	0.128171i
$396$	20.6068	+	4.39910i	1.03553	+	0.221063i
$397$	31.2507	−	14.2717i	1.56843	−	0.716276i	0.573721	−	0.819050i	$-0.305499\pi$
$397$	31.2507	−	14.2717i	1.56843	−	0.716276i	0.994705	+	0.102774i	$0.0327719\pi$
$398$	9.04699	−	10.5336i	0.453485	−	0.528004i
$399$	−11.1863	+	6.60031i	−0.560017	+	0.330429i
$400$	17.5401	−	5.48573i	0.877004	−	0.274287i
$401$	−6.77443	−	5.87008i	−0.338299	−	0.293138i	0.469098	−	0.883146i	$-0.344579\pi$
$401$	−6.77443	−	5.87008i	−0.338299	−	0.293138i	−0.807397	+	0.590008i	$0.799124\pi$
$402$	36.9399	+	1.24759i	1.84239	+	0.0622239i
$403$	−12.4958	−	8.03059i	−0.622462	−	0.400032i
$404$	−3.61928	+	8.11240i	−0.180066	+	0.403607i
$405$	−1.66828	+	5.48308i	−0.0828973	+	0.272457i
$406$	12.4837	−	3.72501i	0.619556	−	0.184869i
$407$	−23.6859	−	27.3350i	−1.17407	−	1.35494i
$408$	3.46181	−	10.7848i	0.171385	−	0.533925i
$409$	32.6522	−	9.58755i	1.61455	−	0.474074i	0.655002	−	0.755627i	$-0.272668\pi$
$409$	32.6522	−	9.58755i	1.61455	−	0.474074i	0.959546	+	0.281553i	$0.0908497\pi$
$410$	−6.21550	−	1.79551i	−0.306962	−	0.0886738i
$411$	−6.65855	+	1.68220i	−0.328442	+	0.0829768i
$412$	−18.2457	−	15.5323i	−0.898903	−	0.765223i
$413$	25.8992			1.27441
$414$	−18.0016	+	9.48374i	−0.884732	+	0.466100i
$415$			2.62780i			0.128994i
$416$	27.1189	+	7.32185i	1.32961	+	0.358983i
$417$	−5.20295	−	20.5945i	−0.254790	−	1.00852i
$418$	19.0560	+	5.50481i	0.932058	+	0.269249i
$419$	−4.03038	−	13.7262i	−0.196897	−	0.670570i	−0.997454	−	0.0713133i	$-0.977281\pi$
$419$	−4.03038	−	13.7262i	−0.196897	−	0.670570i	0.800557	−	0.599257i	$-0.204537\pi$
$420$	1.83059	−	3.71551i	0.0893235	−	0.181299i
$421$	−17.8416	+	15.4599i	−0.869549	+	0.753468i	−0.970418	−	0.241431i	$-0.922383\pi$
$421$	−17.8416	+	15.4599i	−0.869549	+	0.753468i	0.100869	+	0.994900i	$0.467838\pi$
$422$	2.68839	+	9.00967i	0.130869	+	0.438584i
$423$	17.2399	−	9.30479i	0.838234	−	0.452414i
$424$	2.19996	−	7.87361i	0.106840	−	0.382376i
$425$	−5.74307	+	8.93640i	−0.278580	+	0.433479i
$426$	11.7857	+	0.398043i	0.571018	+	0.0192852i
$427$	−10.1360	+	11.6976i	−0.490517	+	0.566087i
$428$	0.344551	+	39.3378i	0.0166545	+	1.90146i
$429$	−15.3491	−	26.0139i	−0.741061	−	1.25596i
$430$	−3.63308	−	3.12033i	−0.175203	−	0.150476i
$431$	−8.00903	−	17.5373i	−0.385781	−	0.844743i	−0.998516	−	0.0544548i	$-0.982658\pi$
$431$	−8.00903	−	17.5373i	−0.385781	−	0.844743i	0.612735	−	0.790289i	$-0.290069\pi$
$432$	−9.49259	−	18.4903i	−0.456712	−	0.889614i
$433$	−3.05116	+	6.68110i	−0.146629	+	0.321073i	−0.968668	−	0.248358i	$-0.920109\pi$
$433$	−3.05116	+	6.68110i	−0.146629	+	0.321073i	0.822039	+	0.569431i	$0.192836\pi$
$434$	−0.0347848	−	7.94300i	−0.00166972	−	0.381276i
$435$	3.09706	−	4.43746i	0.148493	−	0.212760i
$436$	2.86509	+	9.45060i	0.137213	+	0.452602i
$437$	−17.5355	+	7.70457i	−0.838838	+	0.368560i
$438$	−7.31349	+	4.35849i	−0.349452	+	0.208257i
$439$	−1.44365	−	2.24636i	−0.0689015	−	0.107213i	0.805093	−	0.593148i	$-0.202115\pi$
$439$	−1.44365	−	2.24636i	−0.0689015	−	0.107213i	−0.873995	+	0.485936i	$0.838479\pi$
$440$	−6.04526	+	1.86166i	−0.288197	+	0.0887510i
$441$	−3.59493	−	9.78393i	−0.171187	−	0.465901i
$442$	−14.7395	+	6.80947i	−0.701086	+	0.323893i
$443$	0.365530	−	0.166932i	0.0173668	−	0.00793117i	−0.406713	−	0.913556i	$-0.633325\pi$
$443$	0.365530	−	0.166932i	0.0173668	−	0.00793117i	0.424080	+	0.905625i	$0.360598\pi$
$444$	−6.11268	+	35.1500i	−0.290095	+	1.66814i
$445$	−1.46397	+	0.210487i	−0.0693988	+	0.00997804i
$446$	−2.98175	+	21.4035i	−0.141190	+	1.01348i
$447$	9.31927	−	27.7736i	0.440786	−	1.31364i
$448$	4.60912	+	14.2965i	0.217761	+	0.675444i
$449$	−18.8016	+	29.2559i	−0.887304	+	1.38067i	0.0371225	+	0.999311i	$0.488181\pi$
$449$	−18.8016	+	29.2559i	−0.887304	+	1.38067i	−0.924426	+	0.381361i	$0.875456\pi$
$450$	4.13394	+	19.0493i	0.194876	+	0.897993i
$451$	−24.2068	−	7.10774i	−1.13985	−	0.334691i
$452$	18.4000	−	8.59857i	0.865465	−	0.404443i
$453$	−0.645330	+	1.28138i	−0.0303202	+	0.0602047i
$454$	−19.5858	+	12.7086i	−0.919207	+	0.596443i
$455$	−5.69687	+	1.67275i	−0.267073	+	0.0784198i
$456$	−7.68030	−	17.9949i	−0.359663	−	0.842691i
$457$	−4.09863	+	28.5066i	−0.191726	+	1.33348i	0.635713	+	0.771926i	$0.280706\pi$
$457$	−4.09863	+	28.5066i	−0.191726	+	1.33348i	−0.827438	+	0.561556i	$0.810203\pi$
$458$	−25.8078	−	29.5216i	−1.20592	−	1.37945i
$459$	11.0654	+	4.67861i	0.516488	+	0.218379i
$460$	3.33129	−	5.11963i	0.155322	−	0.238704i
$461$	−42.1089			−1.96121			−0.980603	−	0.196004i	$-0.937203\pi$
$461$	−42.1089			−1.96121			−0.980603	+	0.196004i	$0.937203\pi$
$462$	7.20184	−	14.4574i	0.335060	−	0.672620i
$463$	17.9303	+	2.57799i	0.833292	+	0.119809i	0.545739	−	0.837955i	$-0.316249\pi$
$463$	17.9303	+	2.57799i	0.833292	+	0.119809i	0.287553	+	0.957765i	$0.407158\pi$
$464$	3.13268	+	19.3729i	0.145431	+	0.899362i
$465$	−2.06398	−	2.57407i	−0.0957147	−	0.119370i
$466$	−23.3918	+	15.1781i	−1.08360	+	0.703113i
$467$	11.3991	−	9.87735i	0.527486	−	0.457069i	−0.349946	−	0.936770i	$-0.613800\pi$
$467$	11.3991	−	9.87735i	0.527486	−	0.457069i	0.877432	+	0.479700i	$0.159255\pi$
$468$	−10.3035	+	27.9555i	−0.476281	+	1.29225i
$469$	7.98206	−	27.1844i	0.368577	−	1.25526i
$470$	−3.15781	+	4.96128i	−0.145659	+	0.228847i
$471$	3.74175	−	20.4534i	0.172411	−	0.942441i
$472$	−5.04446	+	38.6864i	−0.232190	+	1.78069i
$473$	−14.1139	−	12.2298i	−0.648960	−	0.562327i
$474$	5.87757	+	22.8431i	0.269966	+	1.04922i
$475$	2.61138	+	18.1625i	0.119818	+	0.833354i
$476$	−7.34494	−	4.62991i	−0.336655	−	0.212212i
$477$	8.10949	+	3.06984i	0.371308	+	0.140559i
$478$	−29.4395	+	13.6007i	−1.34653	+	0.622081i
$479$	−16.2387	+	35.5578i	−0.741966	+	1.62468i	0.0383275	+	0.999265i	$0.487797\pi$
$479$	−16.2387	+	35.5578i	−0.741966	+	1.62468i	−0.780293	+	0.625414i	$0.784930\pi$
$480$	5.19344	+	3.45809i	0.237047	+	0.157839i
$481$	43.0236	−	27.6496i	1.96171	−	1.26071i
$482$	−4.02537	+	0.596764i	−0.183350	+	0.0271819i
$483$	3.60185	+	15.1752i	0.163890	+	0.690496i
$484$	−2.55160	+	0.773557i	−0.115982	+	0.0351617i
$485$	2.91765	−	1.87506i	0.132484	−	0.0851420i
$486$	20.4327	−	8.27687i	0.926844	−	0.375447i
$487$	−16.8988	−	7.71744i	−0.765760	−	0.349711i	−0.00605739	−	0.999982i	$-0.501928\pi$
$487$	−16.8988	−	7.71744i	−0.765760	−	0.349711i	−0.759702	+	0.650271i	$0.774655\pi$
$488$	−15.4989	−	17.4189i	−0.701601	−	0.788517i
$489$	21.5866	+	20.1964i	0.976179	+	0.913312i
$490$	2.37374	+	2.03872i	0.107234	+	0.0921001i
$491$	8.03988	−	1.15596i	0.362834	−	0.0521677i	0.0415132	−	0.999138i	$-0.486782\pi$
$491$	8.03988	−	1.15596i	0.362834	−	0.0521677i	0.321321	+	0.946970i	$0.395873\pi$
$492$	9.66840	+	22.9307i	0.435885	+	1.03380i
$493$	−8.57267	−	7.42826i	−0.386094	−	0.334552i
$494$	−11.5390	+	25.5625i	−0.519163	+	1.15011i
$495$	−1.39412	−	6.56268i	−0.0626610	−	0.294971i
$496$	11.8715	+	1.49512i	0.533046	+	0.0671330i
$497$	2.54668	−	8.67320i	0.114234	−	0.389046i
$498$	7.85811	−	6.35764i	0.352131	−	0.284893i
$499$	9.03594	+	10.4280i	0.404504	+	0.466823i	0.921054	−	0.389434i	$-0.127329\pi$
$499$	9.03594	+	10.4280i	0.404504	+	0.466823i	−0.516550	+	0.856257i	$0.672784\pi$
$500$	−8.08275	−	9.16456i	−0.361472	−	0.409852i
$501$	−18.8014	+	15.0756i	−0.839987	+	0.673530i
$502$	−10.7581	−	3.10774i	−0.480155	−	0.138705i
$503$	5.00727	−	34.8264i	0.223263	−	1.55283i	−0.502311	−	0.864687i	$-0.667517\pi$
$503$	5.00727	−	34.8264i	0.223263	−	1.55283i	0.725574	−	0.688144i	$-0.241574\pi$
$504$	−15.5397	+	3.51509i	−0.692191	+	0.156574i
$505$	2.82842			0.125863
$506$	13.0778	−	19.9072i	0.581381	−	0.884981i
$507$	18.6734	−	7.68147i	0.829317	−	0.341146i
$508$	19.4796	+	16.5827i	0.864267	+	0.735738i
$509$	−0.457104	+	3.17923i	−0.0202608	+	0.140917i	−0.997441	−	0.0714954i	$-0.977223\pi$
$509$	−0.457104	+	3.17923i	−0.0202608	+	0.140917i	0.977180	+	0.212412i	$0.0681320\pi$
$510$	−3.58505	+	0.392468i	−0.158749	+	0.0173788i
$511$	1.83862	+	6.26177i	0.0813358	+	0.277004i
$512$	−22.2528	+	4.10024i	−0.983445	+	0.181207i
$513$	19.7377	−	6.40925i	0.871441	−	0.282975i
$514$	−21.5068	+	6.41739i	−0.948622	+	0.283059i
$515$	−2.14947	+	7.32042i	−0.0947169	+	0.322576i
$516$	−0.541169	+	18.4135i	−0.0238236	+	0.810610i
$517$	−12.3986	+	19.2926i	−0.545291	+	0.848489i
$518$	24.9264	+	11.2518i	1.09520	+	0.494377i
$519$	3.32582	−	9.91171i	0.145987	−	0.435076i
$520$	−1.38905	−	8.83541i	−0.0609138	−	0.387458i
$521$	9.03485	−	1.29902i	0.395824	−	0.0569109i	0.0584710	−	0.998289i	$-0.481377\pi$
$521$	9.03485	−	1.29902i	0.395824	−	0.0569109i	0.337353	+	0.941378i	$0.390468\pi$
$522$	−20.7626	+	1.47453i	−0.908756	+	0.0645382i
$523$	−3.24437	−	7.10418i	−0.141866	−	0.310644i	0.825340	−	0.564636i	$-0.190984\pi$
$523$	−3.24437	−	7.10418i	−0.141866	−	0.310644i	−0.967206	+	0.253992i	$0.918256\pi$
$524$	−2.70779	−	4.13336i	−0.118290	−	0.180567i
$525$	14.9311	+	0.569746i	0.651647	+	0.0248658i
$526$	0.0689556	+	15.7458i	0.00300661	+	0.686549i
$527$	−5.81821	+	3.73913i	−0.253445	+	0.162879i
$528$	20.1928	+	13.5735i	0.878779	+	0.590713i
$529$	2.61538	+	22.8508i	0.113712	+	0.993514i
$530$	−2.57486	+	0.381726i	−0.111845	+	0.0165811i
$531$	−40.3914	−	8.99328i	−1.75284	−	0.390275i
$532$	−14.8258	+	2.26433i	−0.642779	+	0.0981712i
$533$	14.8189	−	32.4489i	0.641878	−	1.40552i
$534$	4.17133	+	3.86857i	0.180511	+	0.167409i
$535$	11.3938	−	5.20339i	0.492598	−	0.224962i
$536$	39.0516	+	17.2179i	1.68677	+	0.743698i
$537$	27.8254	−	16.4179i	1.20076	−	0.708486i
$538$	−0.429345	−	0.0598126i	−0.0185104	−	0.00257870i
$539$	9.22159	+	7.99055i	0.397202	+	0.344178i
$540$	−4.14510	+	5.15893i	−0.178377	+	0.222005i
$541$	−2.33565	+	3.63434i	−0.100417	+	0.156253i	−0.887827	−	0.460178i	$-0.847786\pi$
$541$	−2.33565	+	3.63434i	−0.100417	+	0.156253i	0.787409	+	0.616431i	$0.211422\pi$
$542$	8.56747	+	5.45311i	0.368004	+	0.234231i
$543$	−0.298870	−	2.84520i	−0.0128258	−	0.122099i
$544$	8.34645	−	10.0696i	0.357851	−	0.431731i
$545$	2.37634	−	2.05911i	0.101791	−	0.0882025i
$546$	18.7850	+	12.9888i	0.803925	+	0.555867i
$547$	11.6348	−	3.41629i	0.497469	−	0.146070i	−0.0233668	−	0.999727i	$-0.507439\pi$
$547$	11.6348	−	3.41629i	0.497469	−	0.146070i	0.520836	+	0.853657i	$0.325620\pi$
$548$	−7.85907	−	1.05979i	−0.335723	−	0.0452721i
$549$	19.8697	−	14.7235i	0.848018	−	0.628385i
$550$	−15.0183	−	17.1795i	−0.640384	−	0.732536i
$551$	−19.5939			−0.834730
$552$	−23.3692	+	2.42449i	−0.994661	+	0.103193i
$553$	18.0805			0.768862
$554$	16.2171	+	18.5508i	0.689000	+	0.788148i
$555$	11.0138	−	2.78250i	0.467510	−	0.118110i
$556$	3.27788	−	24.3077i	0.139013	−	1.03087i
$557$	−17.2092	+	5.05309i	−0.729179	+	0.214106i	−0.625190	−	0.780472i	$-0.714979\pi$
$557$	−17.2092	+	5.05309i	−0.729179	+	0.214106i	−0.103989	+	0.994578i	$0.533161\pi$
$558$	−2.70389	+	12.3997i	−0.114465	+	0.524922i
$559$	19.9566	−	17.2925i	0.844076	−	0.731396i
$560$	3.55915	−	3.19487i	0.150402	−	0.135008i
$561$	−13.9867	+	1.46921i	−0.590517	+	0.0620301i
$562$	−10.6327	−	6.76764i	−0.448515	−	0.285476i
$563$	9.83583	−	15.3049i	0.414531	−	0.645023i	−0.569712	−	0.821844i	$-0.692945\pi$
$563$	9.83583	−	15.3049i	0.414531	−	0.645023i	0.984243	+	0.176822i	$0.0565816\pi$
$564$	22.4760	−	2.56018i	0.946410	−	0.107803i
$565$	−4.88726	−	4.23484i	−0.205609	−	0.178161i
$566$	17.3652	+	2.41917i	0.729914	+	0.101685i
$567$	−2.24158	−	16.7494i	−0.0941373	−	0.703408i
$568$	12.4594	+	5.49337i	0.522786	+	0.230497i
$569$	−3.67292	+	1.67737i	−0.153977	+	0.0703188i	−0.490913	−	0.871209i	$-0.663337\pi$
$569$	−3.67292	+	1.67737i	−0.153977	+	0.0703188i	0.336936	+	0.941528i	$0.390609\pi$
$570$	−4.23617	+	4.56770i	−0.177434	+	0.191320i
$571$	−7.29458	+	15.9729i	−0.305269	+	0.668445i	−0.998640	−	0.0521352i	$-0.983397\pi$
$571$	−7.29458	+	15.9729i	−0.305269	+	0.668445i	0.693371	+	0.720580i	$0.256125\pi$
$572$	−5.26573	−	34.4775i	−0.220171	−	1.44158i
$573$	5.44302	−	7.79875i	0.227385	−	0.325797i
$574$	18.8696	−	2.79744i	0.787602	−	0.116763i
$575$	21.7626	+	3.44999i	0.907562	+	0.143874i
$576$	−2.22390	−	23.8967i	−0.0926625	−	0.995698i
$577$	−28.2040	+	18.1256i	−1.17415	+	0.754579i	−0.974301	−	0.225248i	$-0.927681\pi$
$577$	−28.2040	+	18.1256i	−1.17415	+	0.754579i	−0.199846	+	0.979827i	$0.564044\pi$
$578$	−0.0721780	−	16.4816i	−0.00300221	−	0.685545i
$579$	−0.698747	+	18.3118i	−0.0290389	+	0.761011i
$580$	5.22679	−	3.42411i	0.217031	−	0.142178i
$581$	−3.21868	−	7.04794i	−0.133534	−	0.292398i
$582$	−12.6660	−	4.18839i	−0.525023	−	0.173614i
$583$	−10.0472	+	1.44457i	−0.416113	+	0.0598281i
$584$	−9.71152	+	1.52679i	−0.401866	+	0.0631789i
$585$	9.46549	−	0.630574i	0.391350	−	0.0260710i
$586$	1.40537	+	0.634387i	0.0580552	+	0.0262063i
$587$	−10.3221	+	16.0616i	−0.426040	+	0.662931i	−0.986220	−	0.165440i	$-0.947096\pi$
$587$	−10.3221	+	16.0616i	−0.426040	+	0.662931i	0.560180	+	0.828371i	$0.310732\pi$
$588$	0.353582	−	12.0308i	0.0145815	−	0.496142i
$589$	−3.36576	+	11.4627i	−0.138684	+	0.472313i
$590$	11.9035	−	3.55189i	0.490061	−	0.146229i
$591$	−24.3427	−	12.2595i	−1.00133	−	0.504287i
$592$	−21.6622	+	35.0418i	−0.890312	+	1.44021i
$593$	12.1992	+	41.5466i	0.500960	+	1.70611i	0.689708	+	0.724088i	$0.257739\pi$
$593$	12.1992	+	41.5466i	0.500960	+	1.70611i	−0.188748	+	0.982026i	$0.560443\pi$
$594$	−16.2520	+	20.0465i	−0.666826	+	0.822519i
$595$	−0.393431	+	2.73637i	−0.0161291	+	0.112180i
$596$	21.9275	−	25.7581i	0.898184	−	1.05509i
$597$	6.46961	+	15.7275i	0.264784	+	0.643682i
$598$	25.2299	+	22.3093i	1.03173	+	0.912295i
$599$	−33.0059			−1.34858			−0.674292	−	0.738465i	$-0.735551\pi$
$599$	−33.0059			−1.34858			−0.674292	+	0.738465i	$0.735551\pi$
$600$	−3.75922	+	22.1921i	−0.153470	+	0.905989i
$601$	−1.11422	+	7.74960i	−0.0454502	+	0.316113i	0.954396	+	0.298545i	$0.0965013\pi$
$601$	−1.11422	+	7.74960i	−0.0454502	+	0.316113i	−0.999846	+	0.0175677i	$0.994408\pi$
$602$	13.5661	+	3.91892i	0.552913	+	0.159723i
$603$	−21.8881	+	39.6242i	−0.891353	+	1.61362i
$604$	−1.24247	+	1.09581i	−0.0505554	+	0.0445877i
$605$	0.555947	+	0.641597i	0.0226024	+	0.0260846i
$606$	−6.84302	−	8.45804i	−0.277979	−	0.343584i
$607$	−8.36205	+	28.4785i	−0.339405	+	1.15591i	0.596193	+	0.802841i	$0.296679\pi$
$607$	−8.36205	+	28.4785i	−0.339405	+	1.15591i	−0.935598	+	0.353067i	$0.885139\pi$
$608$	−0.494648	−	22.5868i	−0.0200606	−	0.916015i
$609$	−2.87125	+	15.6950i	−0.116349	+	0.635994i
$610$	−3.05439	+	6.76644i	−0.123669	+	0.273965i
$611$	−24.5065	−	21.2350i	−0.991428	−	0.859077i
$612$	9.84722	+	9.77113i	0.398050	+	0.394974i
$613$	46.6007	−	6.70017i	1.88218	−	0.270617i	0.896989	−	0.442052i	$-0.145749\pi$
$613$	46.6007	−	6.70017i	1.88218	−	0.270617i	0.985195	+	0.171435i	$0.0548403\pi$
$614$	3.01514	+	2.58960i	0.121681	+	0.104508i
$615$	5.41346	−	5.78610i	0.218292	−	0.233318i
$616$	13.9335	−	12.3977i	0.561397	−	0.499516i
$617$	−10.6638	−	4.87000i	−0.429309	−	0.196059i	0.189028	−	0.981972i	$-0.439466\pi$
$617$	−10.6638	−	4.87000i	−0.429309	−	0.196059i	−0.618338	+	0.785913i	$0.712194\pi$
$618$	27.0912	−	11.2831i	1.08977	−	0.453874i
$619$	28.8260	−	18.5253i	1.15861	−	0.744596i	0.187278	−	0.982307i	$-0.440034\pi$
$619$	28.8260	−	18.5253i	1.15861	−	0.744596i	0.971336	+	0.237711i	$0.0763972\pi$
$620$	−1.10532	−	3.64592i	−0.0443905	−	0.146424i
$621$	−0.347862	−	24.9174i	−0.0139592	−	0.999903i
$622$	−15.2091	+	2.25477i	−0.609831	+	0.0904080i
$623$	3.66864	−	2.35769i	0.146981	−	0.0944590i
$624$	−23.0605	+	25.5300i	−0.923161	+	1.02202i
$625$	7.92679	−	17.3572i	0.317071	−	0.694290i
$626$	8.52367	−	3.93783i	0.340674	−	0.157387i
$627$	−16.5970	+	17.7395i	−0.662821	+	0.708446i
$628$	12.8031	−	20.3110i	0.510899	−	0.810496i
$629$	−3.38886	−	23.5700i	−0.135123	−	0.939799i
$630$	3.03803	+	4.06257i	0.121038	+	0.161857i
$631$	21.5519	+	18.6749i	0.857969	+	0.743435i	0.968122	−	0.250480i	$-0.0805885\pi$
$631$	21.5519	+	18.6749i	0.857969	+	0.743435i	−0.110153	+	0.993915i	$0.535134\pi$
$632$	−3.52160	+	27.0075i	−0.140082	+	1.07430i
$633$	−11.3273	−	2.07222i	−0.450221	−	0.0823635i
$634$	−3.29639	+	5.17902i	−0.130917	+	0.205685i
$635$	2.29482	−	7.81545i	0.0910673	−	0.310147i
$636$	7.37106	+	6.77626i	0.292282	+	0.268696i
$637$	−13.0390	+	11.2984i	−0.516625	+	0.447658i
$638$	20.4404	−	13.2631i	0.809243	−	0.525091i
$639$	−6.98341	+	12.6421i	−0.276260	+	0.500114i
$640$	4.07906	+	5.93870i	0.161239	+	0.234748i
$641$	42.3102	+	6.08329i	1.67115	+	0.240276i	0.911868	−	0.410483i	$-0.134640\pi$
$641$	42.3102	+	6.08329i	1.67115	+	0.240276i	0.759285	+	0.650759i	$0.225549\pi$
$642$	−43.1261	−	21.4829i	−1.70205	−	0.847861i
$643$	−0.0267278			−0.00105404			−0.000527021	−	1.00000i	$-0.500168\pi$
$643$	−0.0267278			−0.00105404			−0.000527021		1.00000i	$0.500168\pi$
$644$	−2.66393	+	17.8115i	−0.104973	+	0.701872i
$645$	5.42443	−	2.23138i	0.213587	−	0.0878607i
$646$	8.59472	+	9.83151i	0.338155	+	0.386816i
$647$	2.48968	−	17.3161i	0.0978794	−	0.680766i	−0.880515	−	0.474019i	$-0.842803\pi$
$647$	2.48968	−	17.3161i	0.0978794	−	0.680766i	0.978394	−	0.206748i	$-0.0662880\pi$
$648$	25.4557	−	0.0859910i	0.999994	−	0.00337805i
$649$	46.4786	−	13.6474i	1.82445	−	0.535706i
$650$	27.0661	−	17.5623i	1.06162	−	0.688850i
$651$	8.68859	+	4.37574i	0.340533	+	0.171499i
$652$	14.4514	+	30.9245i	0.565961	+	1.21110i
$653$	−43.3013	−	12.7144i	−1.69451	−	0.497553i	−0.715029	−	0.699095i	$-0.753587\pi$
$653$	−43.3013	−	12.7144i	−1.69451	−	0.497553i	−0.979480	+	0.201542i	$0.935405\pi$
$654$	−11.9068	−	2.12438i	−0.465591	−	0.0830698i
$655$	−0.850610	+	1.32358i	−0.0332361	+	0.0517164i
$656$	0.503336	+	28.7310i	0.0196520	+	1.12176i
$657$	−0.693102	−	10.4041i	−0.0270405	−	0.405902i
$658$	2.39258	−	17.1743i	0.0932724	−	0.669525i
$659$	−9.90004	+	1.42341i	−0.385651	+	0.0554482i	−0.332414	−	0.943134i	$-0.607863\pi$
$659$	−9.90004	+	1.42341i	−0.385651	+	0.0554482i	−0.0532370	+	0.998582i	$0.516954\pi$
$660$	1.32731	−	7.63248i	0.0516655	−	0.297094i
$661$	18.1473	−	8.28760i	0.705848	−	0.322350i	−0.0299495	−	0.999551i	$-0.509535\pi$
$661$	18.1473	−	8.28760i	0.705848	−	0.322350i	0.735798	+	0.677201i	$0.236807\pi$
$662$	42.5443	−	19.6550i	1.65353	−	0.763912i
$663$	0.758245	−	19.8710i	0.0294478	−	0.771726i
$664$	11.1546	−	3.43511i	0.432884	−	0.133308i
$665$	2.58173	+	4.01725i	0.100115	+	0.155782i
$666$	−34.9672	−	26.2035i	−1.35495	−	1.01536i
$667$	−6.95372	+	22.4779i	−0.269249	+	0.870349i
$668$	−26.6304	+	8.07341i	−1.03036	+	0.312370i
$669$	−21.7036	−	15.1477i	−0.839110	−	0.585644i
$670$	−0.0595101	−	13.5889i	−0.00229908	−	0.524987i
$671$	−12.0262	+	26.3336i	−0.464265	+	1.01660i
$672$	−18.1648	−	2.91359i	−0.700722	−	0.112394i
$673$	−1.47097	−	3.22098i	−0.0567017	−	0.124159i	0.879160	−	0.476526i	$-0.158104\pi$
$673$	−1.47097	−	3.22098i	−0.0567017	−	0.124159i	−0.935862	+	0.352367i	$0.885377\pi$
$674$	−28.0634	−	24.1027i	−1.08096	−	0.928403i
$675$	−23.0882	−	6.07326i	−0.888665	−	0.233760i
$676$	23.3144	−	0.204206i	0.896708	−	0.00785407i
$677$	−23.5037	+	27.1247i	−0.903321	+	1.04249i	0.0955713	+	0.995423i	$0.469532\pi$
$677$	−23.5037	+	27.1247i	−0.903321	+	1.04249i	−0.998892	+	0.0470649i	$0.985013\pi$
$678$	−0.839621	+	24.8604i	−0.0322454	+	0.954758i
$679$	−5.52864	+	8.60272i	−0.212170	+	0.330142i
$680$	−4.01078	−	1.12065i	−0.153806	−	0.0429750i
$681$	−2.98727	−	28.4384i	−0.114473	−	1.08976i
$682$	−4.24793	−	14.2362i	−0.162662	−	0.545132i
$683$	18.7583	−	16.2542i	0.717768	−	0.621949i	−0.217430	−	0.976076i	$-0.569767\pi$
$683$	18.7583	−	16.2542i	0.717768	−	0.621949i	0.935197	+	0.354127i	$0.115222\pi$
$684$	23.9080	+	1.61676i	0.914146	+	0.0618182i
$685$	0.711375	+	2.42272i	0.0271803	+	0.0925675i
$686$	−26.7211	−	7.71908i	−1.02022	−	0.294716i
$687$	46.5615	−	11.7632i	1.77643	−	0.448794i
$688$	−8.49613	+	19.5008i	−0.323912	+	0.743463i
$689$		−	14.3525i		−	0.546787i
$690$	3.73663	+	6.48072i	0.142251	+	0.246717i
$691$	−0.788857			−0.0300095			−0.0150048	−	0.999887i	$-0.504776\pi$
$691$	−0.788857			−0.0300095			−0.0150048	+	0.999887i	$0.504776\pi$
$692$	7.82538	−	9.19243i	0.297476	−	0.349444i
$693$	11.7775	+	15.8939i	0.447389	+	0.603760i
$694$	13.5046	+	3.90115i	0.512627	+	0.148086i
$695$	−7.49335	+	2.20025i	−0.284239	+	0.0834601i
$696$	−22.8849	−	7.34585i	−0.867451	−	0.278444i
$697$	−10.8769	−	12.5526i	−0.411993	−	0.475465i
$698$	−30.8428	+	9.20316i	−1.16742	+	0.348345i
$699$	−3.56777	−	33.9646i	−0.134945	−	1.28466i
$700$	15.7565	+	7.02963i	0.595540	+	0.265695i
$701$	32.2814	+	20.7460i	1.21925	+	0.783566i	0.982183	−	0.187926i	$-0.0601766\pi$
$701$	32.2814	+	20.7460i	1.21925	+	0.783566i	0.237070	+	0.971493i	$0.423813\pi$
$702$	−24.7862	−	26.7798i	−0.935496	−	1.01074i
$703$	−31.0860	−	26.9362i	−1.17243	−	1.01592i
$704$	15.8049	+	23.2277i	0.595671	+	0.875426i
$705$	−3.66020	−	6.20338i	−0.137851	−	0.233633i
$706$	14.7320	−	17.1528i	0.554446	−	0.645555i
$707$	−7.58601	+	3.46441i	−0.285301	+	0.130293i
$708$	−39.4206	−	27.0027i	−1.48152	−	1.01482i
$709$	−28.1651	−	12.8626i	−1.05776	−	0.483064i	−0.190899	−	0.981610i	$-0.561140\pi$
$709$	−28.1651	−	12.8626i	−1.05776	−	0.483064i	−0.866863	+	0.498546i	$0.833867\pi$
$710$	−0.0189867	−	4.33556i	−0.000712559	−	0.162711i
$711$	−28.1978	−	6.27832i	−1.05750	−	0.235455i
$712$	2.80721	+	5.93919i	0.105205	+	0.222581i
$713$	11.9554	+	7.92918i	0.447734	+	0.296950i
$714$	9.13463	−	5.44380i	0.341855	−	0.203729i
$715$	−9.34216	+	6.00384i	−0.349377	+	0.224531i
$716$	36.8784	−	5.63241i	1.37821	−	0.210493i
$717$	1.51446	−	39.6888i	0.0565585	−	1.48220i
$718$	−8.02291	+	3.70649i	−0.299412	+	0.138325i
$719$	0.991703	+	2.17153i	0.0369843	+	0.0809843i	0.927222	−	0.374511i	$-0.122189\pi$
$719$	0.991703	+	2.17153i	0.0369843	+	0.0809843i	−0.890238	+	0.455495i	$0.849462\pi$
$720$	−6.66013	+	3.74673i	−0.248208	+	0.139632i
$721$	−3.20146	−	22.2666i	−0.119228	−	0.829252i
$722$	−4.27179	−	0.595109i	−0.158980	−	0.0221477i
$723$	1.58546	−	4.72503i	0.0589638	−	0.175726i
$724$	0.902888	−	3.17765i	0.0335556	−	0.118096i
$725$	18.9628	+	12.1866i	0.704259	+	0.452600i
$726$	0.573570	−	3.21475i	0.0212872	−	0.119311i
$727$	11.9770	−	40.7899i	0.444202	−	1.51281i	−0.368218	−	0.929739i	$-0.620032\pi$
$727$	11.9770	−	40.7899i	0.444202	−	1.51281i	0.812420	−	0.583073i	$-0.198150\pi$
$728$	14.5476	+	21.9957i	0.539171	+	0.815216i
$729$	−2.32020	+	26.9001i	−0.0859334	+	0.996301i
$730$	1.70381	+	2.62582i	0.0630608	+	0.0971861i
$731$	−3.46394	−	11.7971i	−0.128118	−	0.436331i
$732$	27.6239	−	7.23679i	1.02101	−	0.267480i
$733$	−2.61749	−	0.376339i	−0.0966793	−	0.0139004i	0.0938054	−	0.995591i	$-0.470097\pi$
$733$	−2.61749	−	0.376339i	−0.0966793	−	0.0139004i	−0.190485	+	0.981690i	$0.561006\pi$
$734$	6.43751	+	7.36388i	0.237613	+	0.271806i
$735$	−3.54415	+	1.45791i	−0.130728	+	0.0537760i
$736$	−26.0868	−	7.44840i	−0.961572	−	0.274552i
$737$		−	52.9912i		−	1.95196i
$738$	−30.3998	−	2.18953i	−1.11903	−	0.0805978i
$739$	−0.970009	+	6.74656i	−0.0356824	+	0.248176i	−0.999854	−	0.0171039i	$-0.994555\pi$
$739$	−0.970009	+	6.74656i	−0.0356824	+	0.248176i	0.964171	+	0.265280i	$0.0854645\pi$
$740$	12.9996	+	1.75299i	0.477873	+	0.0644410i
$741$	−21.4879	−	26.7984i	−0.789377	−	0.984465i
$742$	6.43839	−	4.17765i	0.236361	−	0.153366i
$743$	0.418868	+	0.483399i	0.0153668	+	0.0177342i	0.763381	−	0.645949i	$-0.223538\pi$
$743$	0.418868	+	0.483399i	0.0153668	+	0.0177342i	−0.748014	+	0.663683i	$0.768993\pi$
$744$	−8.22849	+	12.1262i	−0.301671	+	0.444567i
$745$	−10.3345	−	3.03447i	−0.378626	−	0.111175i
$746$	14.5800	+	9.28003i	0.533812	+	0.339766i
$747$	2.57241	+	12.1094i	0.0941196	+	0.443059i
$748$	−15.6209	−	4.43848i	−0.571158	−	0.162287i
$749$	−24.1856	+	27.9116i	−0.883722	+	1.01987i
$750$	14.4939	−	3.72929i	0.529241	−	0.136175i
$751$	−35.8001	+	5.14727i	−1.30636	+	0.187827i	−0.760110	−	0.649794i	$-0.774855\pi$
$751$	−35.8001	+	5.14727i	−1.30636	+	0.187827i	−0.546252	+	0.837621i	$0.683946\pi$
$752$	25.1879	+	6.91897i	0.918507	+	0.252309i
$753$	9.36985	−	10.0148i	0.341456	−	0.364960i
$754$	14.4495	+	31.2768i	0.526219	+	1.13903i
$755$	0.479819	+	0.219126i	0.0174624	+	0.00797481i
$756$	4.79847	−	18.9137i	0.174519	−	0.687886i
$757$	12.3834	+	19.2689i	0.450081	+	0.700340i	0.989951	−	0.141408i	$-0.0451630\pi$
$757$	12.3834	+	19.2689i	0.450081	+	0.700340i	−0.539870	+	0.841748i	$0.681527\pi$
$758$	25.6873	−	3.80816i	0.933004	−	0.138319i
$759$	14.4603	+	25.3355i	0.524877	+	0.919619i
$760$	−6.50355	+	3.07396i	−0.235909	+	0.111504i
$761$	−1.73199	−	2.69502i	−0.0627844	−	0.0976945i	0.808442	−	0.588576i	$-0.200311\pi$
$761$	−1.73199	−	2.69502i	−0.0627844	−	0.0976945i	−0.871226	+	0.490881i	$0.836675\pi$
$762$	−28.9232	+	12.0461i	−1.04778	+	0.436386i
$763$	−3.85137	+	8.43333i	−0.139429	+	0.305307i
$764$	9.18597	−	6.01780i	0.332337	−	0.217716i
$765$	1.56376	−	4.13093i	0.0565380	−	0.149354i
$766$	−38.2026	−	32.8109i	−1.38031	−	1.18551i
$767$	9.74767	+	67.7965i	0.351968	+	2.44799i
$768$	7.89014	−	26.5659i	0.284711	−	0.958613i
$769$	16.7566	−	19.3381i	0.604257	−	0.697350i	−0.368381	−	0.929675i	$-0.620088\pi$
$769$	16.7566	−	19.3381i	0.604257	−	0.697350i	0.972638	+	0.232325i	$0.0746333\pi$
$770$	−5.41252	−	2.44323i	−0.195054	−	0.0880478i
$771$	4.94656	−	27.0392i	0.178146	−	0.973792i
$772$	−8.62126	+	19.3241i	−0.310286	+	0.695488i
$773$	45.4189	+	13.3362i	1.63360	+	0.479670i	0.964628	−	0.263614i	$-0.0849144\pi$
$773$	45.4189	+	13.3362i	1.63360	+	0.479670i	0.668977	+	0.743283i	$0.266733\pi$
$774$	−19.7964	−	10.8225i	−0.711568	−	0.389008i
$775$	10.3867	−	9.00011i	0.373101	−	0.323294i
$776$	−11.7733	−	9.93388i	−0.422639	−	0.356606i
$777$	−26.1315	+	20.9532i	−0.937464	+	0.751691i
$778$	12.9295	−	44.7579i	0.463544	−	1.60465i
$779$	−28.3987	−	4.08311i	−1.01749	−	0.146293i
$780$	10.4151	+	3.39354i	0.372921	+	0.121508i
$781$		−	16.9069i		−	0.604976i
$782$	14.3288	−	6.37064i	0.512396	−	0.227814i
$783$	9.92788	−	23.4804i	0.354793	−	0.839121i
$784$	5.55110	−	12.7412i	0.198253	−	0.455044i
$785$	−7.56688	−	1.08795i	−0.270074	−	0.0388307i
$786$	6.01593	−	0.658584i	0.214581	−	0.0234909i
$787$	40.7250	−	11.9579i	1.45169	−	0.426255i	0.541590	−	0.840643i	$-0.317823\pi$
$787$	40.7250	−	11.9579i	1.45169	−	0.426255i	0.910100	+	0.414388i	$0.136004\pi$
$788$	−20.8173	−	23.6035i	−0.741584	−	0.840839i
$789$	−17.2238	−	8.67424i	−0.613184	−	0.308811i
$790$	8.31001	−	2.47962i	0.295657	−	0.0882209i
$791$	18.2950	+	5.37190i	0.650496	+	0.191003i
$792$	−26.0352	+	14.4967i	−0.925121	+	0.515117i
$793$	−34.4359	−	22.1306i	−1.22285	−	0.785880i
$794$	−19.9895	+	44.2831i	−0.709401	+	1.57155i
$795$	1.01415	−	3.02241i	0.0359683	−	0.107194i
$796$	0.171989	+	19.6362i	0.00609600	+	0.695988i
$797$	−2.21507	−	15.4061i	−0.0784618	−	0.545714i	−0.990701	−	0.136056i	$-0.956557\pi$
$797$	−2.21507	−	15.4061i	−0.0784618	−	0.545714i	0.912239	−	0.409658i	$-0.134352\pi$
$798$	5.76690	−	17.4396i	0.204146	−	0.617354i
$799$	−13.7339	+	6.27205i	−0.485869	+	0.221889i
$800$	−13.5693	+	22.1668i	−0.479748	+	0.783716i
$801$	−6.54018	+	2.40307i	−0.231086	+	0.0849084i
$802$	12.6767	−	0.0555151i	0.447629	−	0.00196030i
$803$	6.59918	+	10.2685i	0.232880	+	0.362368i
$804$	−40.4920	+	33.0547i	−1.42804	+	1.16575i
$805$	5.52477	−	1.53604i	0.194723	−	0.0541383i
$806$	20.7794	−	3.08056i	0.731923	−	0.108508i
$807$	0.303857	−	0.435365i	0.0106963	−	0.0153256i
$808$	−3.69736	−	12.0062i	−0.130073	−	0.422378i
$809$	−20.1071	−	9.18262i	−0.706929	−	0.322844i	0.0293051	−	0.999571i	$-0.490671\pi$
$809$	−20.1071	−	9.18262i	−0.706929	−	0.322844i	−0.736234	+	0.676727i	$0.763398\pi$
$810$	−3.32732	−	7.39078i	−0.116910	−	0.259686i
$811$	−3.04653	−	6.67097i	−0.106978	−	0.234250i	0.848571	−	0.529082i	$-0.177464\pi$
$811$	−3.04653	−	6.67097i	−0.106978	−	0.234250i	−0.955549	+	0.294832i	$0.904736\pi$
$812$	−9.82454	+	15.5857i	−0.344774	+	0.546952i
$813$	−10.7124	+	6.32068i	−0.375701	+	0.221676i
$814$	50.6620	+	7.05778i	1.77570	+	0.247375i
$815$	7.11739	−	8.21390i	0.249311	−	0.287720i
$816$	6.35241	+	14.7050i	0.222379	+	0.514778i
$817$	−17.8667	−	11.4822i	−0.625076	−	0.401712i
$818$	−25.8417	+	40.6003i	−0.903533	+	1.41956i
$819$	−24.6147	+	13.2851i	−0.860107	+	0.464220i
$820$	8.28903	−	3.87357i	0.289466	−	0.135271i
$821$	25.3502	+	29.2557i	0.884728	+	1.02103i	0.999618	+	0.0276523i	$0.00880314\pi$
$821$	25.3502	+	29.2557i	0.884728	+	1.02103i	−0.114890	+	0.993378i	$0.536651\pi$
$822$	5.52376	−	7.98875i	0.192663	−	0.278640i
$823$	6.54787	+	22.3000i	0.228244	+	0.777329i	0.991372	+	0.131081i	$0.0418447\pi$
$823$	6.54787	+	22.3000i	0.228244	+	0.777329i	−0.763127	+	0.646248i	$0.776337\pi$
$824$	33.8839	−	0.445187i	1.18040	−	0.0155088i
$825$	27.0956	−	6.84536i	0.943347	−	0.238325i
$826$	−27.5755	+	24.1065i	−0.959474	+	0.838774i
$827$			37.7187i			1.31161i	0.754931	+	0.655805i	$0.227671\pi$
$827$			37.7187i			1.31161i	−0.754931	+	0.655805i	$0.772329\pi$
$828$	10.3395	−	26.8532i	0.359322	−	0.933214i
$829$			30.6131i			1.06324i	0.846984	+	0.531618i	$0.178416\pi$
$829$			30.6131i			1.06324i	−0.846984	+	0.531618i	$0.821584\pi$
$830$	−2.44592	−	2.79789i	−0.0848991	−	0.0971161i
$831$	−29.2584	+	7.39176i	−1.01496	+	0.256417i
$832$	−35.6893	+	17.4461i	−1.23730	+	0.604835i
$833$	2.26322	+	7.70783i	0.0784161	+	0.267061i
$834$	24.7088	+	17.0847i	0.855595	+	0.591595i
$835$	5.80227	+	6.69618i	0.200796	+	0.231731i
$836$	−25.4132	+	11.8759i	−0.878932	+	0.410736i
$837$	−12.0310	−	9.84130i	−0.415852	−	0.340165i
$838$	17.0674	+	10.8632i	0.589584	+	0.375265i
$839$	−37.1838	−	23.8965i	−1.28373	−	0.825000i	−0.292383	−	0.956301i	$-0.594448\pi$
$839$	−37.1838	−	23.8965i	−1.28373	−	0.825000i	−0.991343	+	0.131301i	$0.958085\pi$
$840$	1.50927	+	5.65988i	0.0520748	+	0.195285i
$841$	3.22842	−	3.72580i	0.111325	−	0.128476i
$842$	4.60664	−	33.0673i	0.158755	−	1.13957i
$843$	13.2948	−	7.84435i	0.457896	−	0.270174i
$844$	−11.2485	−	7.09051i	−0.387188	−	0.244065i
$845$	−3.08391	−	6.75281i	−0.106090	−	0.232304i
$846$	−9.69503	+	25.9537i	−0.333322	+	0.892306i
$847$	−2.27695	−	1.03985i	−0.0782369	−	0.0357296i
$848$	4.98627	+	10.4309i	0.171229	+	0.358199i
$849$	−12.2897	+	17.6087i	−0.421782	+	0.604329i
$850$	−2.20306	−	14.8604i	−0.0755645	−	0.509707i
$851$	−41.9330	+	26.1021i	−1.43745	+	0.894767i
$852$	−12.9190	+	10.5461i	−0.442598	+	0.361304i
$853$	3.73389	+	5.81004i	0.127846	+	0.198932i	0.899276	−	0.437383i	$-0.144094\pi$
$853$	3.73389	+	5.81004i	0.127846	+	0.198932i	−0.771430	+	0.636315i	$0.780458\pi$
$854$	−0.0958595	−	21.8892i	−0.00328024	−	0.749033i
$855$	−2.63142	−	7.16165i	−0.0899926	−	0.244923i
$856$	−36.9819	−	41.5632i	−1.26401	−	1.42060i
$857$	−5.92312	+	2.70500i	−0.202330	+	0.0924010i	−0.514003	−	0.857788i	$-0.671838\pi$
$857$	−5.92312	+	2.70500i	−0.202330	+	0.0924010i	0.311673	+	0.950189i	$0.399111\pi$
$858$	40.5559	+	13.4110i	1.38456	+	0.457844i
$859$	−3.13615	−	21.8124i	−0.107004	−	0.744230i	−0.970714	−	0.240240i	$-0.922774\pi$
$859$	−3.13615	−	21.8124i	−0.107004	−	0.744230i	0.863709	−	0.503990i	$-0.168135\pi$
$860$	6.77258	−	0.0593196i	0.230943	−	0.00202278i
$861$	−7.43211	+	22.1494i	−0.253285	+	0.754849i
$862$	24.8509	+	11.2178i	0.846425	+	0.382078i
$863$	45.8322	+	29.4546i	1.56015	+	1.00265i	0.982479	+	0.186374i	$0.0596737\pi$
$863$	45.8322	+	29.4546i	1.56015	+	1.00265i	0.577668	+	0.816272i	$0.303963\pi$
$864$	27.3175	+	10.8515i	0.929359	+	0.369176i
$865$	−3.68812	−	1.08293i	−0.125400	−	0.0368207i
$866$	−2.97002	−	9.95351i	−0.100925	−	0.338234i
$867$	18.0287	+	9.07960i	0.612287	+	0.308359i
$868$	7.43026	+	8.42474i	0.252199	+	0.285954i
$869$	32.4473	−	9.52739i	1.10070	−	0.323195i
$870$	0.832805	+	7.60738i	0.0282347	+	0.257914i
$871$	74.1652	+	10.6633i	2.51299	+	0.361313i
$872$	−11.8470	−	7.39551i	−0.401190	−	0.250444i
$873$	11.6095	−	11.4967i	0.392922	−	0.389106i
$874$	11.4992	−	24.5250i	0.388967	−	0.829572i
$875$		−	11.4720i		−	0.387825i
$876$	3.73004	−	11.4479i	0.126026	−	0.386788i
$877$	−24.2771	−	3.49052i	−0.819780	−	0.117867i	−0.280351	−	0.959898i	$-0.590451\pi$
$877$	−24.2771	−	3.49052i	−0.819780	−	0.117867i	−0.539429	+	0.842031i	$0.681360\pi$
$878$	3.62796	+	1.04803i	0.122438	+	0.0353693i
$879$	−1.47332	+	1.18136i	−0.0496937	+	0.0398461i
$880$	4.70374	−	7.60899i	0.158563	−	0.256499i
$881$	−20.7432	+	17.9741i	−0.698855	+	0.605561i	−0.930088	−	0.367337i	$-0.880269\pi$
$881$	−20.7432	+	17.9741i	−0.698855	+	0.605561i	0.231233	+	0.972898i	$0.425724\pi$
$882$	12.9343	+	7.07109i	0.435522	+	0.238096i
$883$	−27.3216	−	8.02234i	−0.919445	−	0.269973i	−0.212434	−	0.977176i	$-0.568139\pi$
$883$	−27.3216	−	8.02234i	−0.919445	−	0.269973i	−0.707011	+	0.707202i	$0.749957\pi$
$884$	9.35536	−	20.9695i	0.314655	−	0.705281i
$885$	−2.73782	+	14.9656i	−0.0920307	+	0.503064i
$886$	−0.233811	+	0.517966i	−0.00785504	+	0.0174014i
$887$	−8.34777	+	9.63384i	−0.280291	+	0.323473i	−0.878386	−	0.477952i	$-0.841379\pi$
$887$	−8.34777	+	9.63384i	−0.280291	+	0.323473i	0.598095	+	0.801425i	$0.295925\pi$
$888$	−26.2087	−	43.1147i	−0.879507	−	1.44683i
$889$	3.41795	+	23.7724i	0.114634	+	0.797300i
$890$	1.36281	−	1.58675i	0.0456814	−	0.0531880i
$891$	−12.8487	−	28.8773i	−0.430447	−	0.967424i
$892$	−16.7473	−	25.5642i	−0.560741	−	0.855952i
$893$	−10.8341	+	23.7234i	−0.362550	+	0.793873i
$894$	15.9288	+	38.2455i	0.532737	+	1.27912i
$895$	−6.42192	−	9.99271i	−0.214661	−	0.334019i
$896$	−18.2144	−	10.9317i	−0.608499	−	0.365202i
$897$	−38.3687	+	15.1401i	−1.28109	+	0.505514i
$898$	−7.21237	−	48.6498i	−0.240680	−	1.62346i
$899$	7.93433	+	12.3461i	0.264625	+	0.411764i
$900$	−22.1323	−	16.4345i	−0.737744	−	0.547816i
$901$	−6.07879	−	2.77609i	−0.202514	−	0.0924850i
$902$	32.3893	−	14.9635i	1.07845	−	0.498229i
$903$	−11.8156	+	12.6289i	−0.393197	+	0.420263i
$904$	−11.5876	+	26.2816i	−0.385397	+	0.874112i
$905$	−1.04112	+	0.149690i	−0.0346079	+	0.00497587i
$906$	−0.505594	−	1.96499i	−0.0167972	−	0.0652823i
$907$	37.5054	−	43.2835i	1.24535	−	1.43721i	0.388647	−	0.921387i	$-0.372942\pi$
$907$	37.5054	−	43.2835i	1.24535	−	1.43721i	0.856698	−	0.515818i	$-0.172512\pi$
$908$	9.02456	−	31.7613i	0.299491	−	1.05404i
$909$	13.0339	−	2.76880i	0.432306	−	0.0918353i
$910$	4.50863	−	7.08358i	0.149460	−	0.234818i
$911$	21.1694	+	6.21591i	0.701375	+	0.205942i	0.612928	−	0.790139i	$-0.289992\pi$
$911$	21.1694	+	6.21591i	0.701375	+	0.205942i	0.0884467	+	0.996081i	$0.471810\pi$
$912$	24.9268	+	12.0110i	0.825410	+	0.397723i
$913$	−9.49011	−	10.9522i	−0.314077	−	0.362464i
$914$	−22.1696	−	34.1666i	−0.733305	−	1.13013i
$915$	−5.68788	−	7.09358i	−0.188035	−	0.234507i
$916$	54.9565	+	7.41086i	1.81581	+	0.244862i
$917$	0.660200	−	4.59179i	0.0218017	−	0.151634i
$918$	−16.1364	+	5.31804i	−0.532580	+	0.175522i
$919$		−	40.3168i		−	1.32993i	−0.746875	−	0.664964i	$-0.768447\pi$
$919$		−	40.3168i		−	1.32993i	0.746875	−	0.664964i	$-0.231553\pi$
$920$	1.21836	+	8.55171i	0.0401681	+	0.281942i
$921$	−4.50181	+	1.85185i	−0.148340	+	0.0610207i
$922$	44.8344	−	39.1943i	1.47654	−	1.29080i
$923$	23.6624	+	3.40214i	0.778858	+	0.111983i
$924$	5.78877	+	22.0965i	0.190436	+	0.726923i
$925$	13.3314	+	45.4027i	0.438335	+	1.49283i
$926$	−21.4904	+	13.9444i	−0.706218	+	0.458241i
$927$	−2.73902	+	35.8379i	−0.0899613	+	1.17707i
$928$	−21.3674	−	17.7109i	−0.701419	−	0.581389i
$929$	14.3735	−	48.9515i	0.471578	−	1.60605i	−0.289358	−	0.957221i	$-0.593442\pi$
$929$	14.3735	−	48.9515i	0.471578	−	1.60605i	0.760936	−	0.648827i	$-0.224740\pi$
$930$	4.59348	+	0.819559i	0.150626	+	0.0268744i
$931$	11.6735	+	7.50211i	0.382584	+	0.245872i
$932$	10.7782	−	37.9332i	0.353053	−	1.24254i
$933$	5.99037	−	17.8527i	0.196116	−	0.584470i
$934$	−2.94319	+	21.1267i	−0.0963043	+	0.691288i
$935$	0.735858	+	5.11801i	0.0240651	+	0.167377i
$936$	−15.0501	−	39.3554i	−0.491929	−	1.28637i
$937$	−14.0341	−	30.7303i	−0.458473	−	1.00392i	−0.987833	−	0.155519i	$-0.950295\pi$
$937$	−14.0341	−	30.7303i	−0.458473	−	1.00392i	0.529360	−	0.848397i	$-0.322432\pi$
$938$	16.8041	+	36.3735i	0.548674	+	1.18764i
$939$	−0.438484	+	11.4912i	−0.0143094	+	0.375000i
$940$	−1.25569	−	8.22164i	−0.0409560	−	0.268160i
$941$	−30.9989	+	19.9218i	−1.01054	+	0.649432i	−0.937532	−	0.347899i	$-0.886895\pi$
$941$	−30.9989	+	19.9218i	−1.01054	+	0.649432i	−0.0730046	+	0.997332i	$0.523259\pi$
$942$	15.0537	+	25.2600i	0.490478	+	0.823014i
$943$	−14.7625	+	31.1295i	−0.480734	+	1.01372i
$944$	−30.6378	−	45.8857i	−0.997175	−	1.49345i
$945$	−6.12218	+	1.05835i	−0.199155	+	0.0344282i
$946$	26.4108	−	0.115661i	0.858688	−	0.00376046i
$947$	14.9411	+	6.82339i	0.485522	+	0.221730i	0.643109	−	0.765775i	$-0.277644\pi$
$947$	14.9411	+	6.82339i	0.485522	+	0.221730i	−0.157587	+	0.987505i	$0.550371\pi$
$948$	−27.5200	−	18.8509i	−0.893809	−	0.612249i
$949$	−15.6995	+	7.16972i	−0.509627	+	0.232739i
$950$	−19.6858	−	16.9075i	−0.638692	−	0.548551i
$951$	−3.82084	−	6.47563i	−0.123899	−	0.209987i
$952$	12.1298	−	1.90697i	0.393129	−	0.0618053i
$953$	14.6296	+	12.6766i	0.473898	+	0.410635i	0.858791	−	0.512326i	$-0.171216\pi$
$953$	14.6296	+	12.6766i	0.473898	+	0.410635i	−0.384893	+	0.922961i	$0.625762\pi$
$954$	−11.4917	+	4.27965i	−0.372059	+	0.138559i
$955$	−2.94151	−	1.89040i	−0.0951852	−	0.0611718i
$956$	18.6857	−	41.8828i	0.604337	−	1.35459i
$957$	3.11762	+	29.6793i	0.100778	+	0.959395i
$958$	−15.8069	−	52.9741i	−0.510698	−	1.71151i
$959$	−4.87544	−	5.62656i	−0.157436	−	0.181691i
$960$	−8.74832	+	1.15206i	−0.282351	+	0.0371825i
$961$	−21.1587	+	6.21277i	−0.682540	+	0.200412i
$962$	−20.0725	+	69.4849i	−0.647164	+	2.24028i
$963$	47.4111	−	35.1318i	1.52780	−	1.13211i
$964$	3.73045	−	4.38214i	0.120150	−	0.141139i
$965$	6.73741			0.216885
$966$	−17.9598	−	12.8049i	−0.577848	−	0.411990i
$967$		−	2.33875i		−	0.0752091i	−0.999293	−	0.0376045i	$-0.988027\pi$
$967$		−	2.33875i		−	0.0752091i	0.999293	−	0.0376045i	$-0.0119727\pi$
$968$	1.99674	−	3.19862i	0.0641777	−	0.102807i
$969$	−15.5063	+	3.91747i	−0.498134	+	0.125847i
$970$	−1.36122	+	4.71212i	−0.0437061	+	0.151297i
$971$	2.12050	+	7.22174i	0.0680499	+	0.231757i	0.986495	−	0.163792i	$-0.0523726\pi$
$971$	2.12050	+	7.22174i	0.0680499	+	0.231757i	−0.918445	+	0.395549i	$0.870554\pi$
$972$	−14.0512	+	27.8310i	−0.450692	+	0.892680i
$973$	17.4027	−	15.0795i	0.557903	−	0.483426i
$974$	25.1759	−	7.51223i	0.806688	−	0.240707i
$975$	4.12819	+	39.2997i	0.132208	+	1.25860i
$976$	32.7153	+	4.12024i	1.04719	+	0.131886i
$977$	−8.87146	+	13.8043i	−0.283823	+	0.441637i	−0.953667	−	0.300865i	$-0.902725\pi$
$977$	−8.87146	+	13.8043i	−0.283823	+	0.441637i	0.669844	+	0.742502i	$0.266361\pi$
$978$	−41.7823	−	1.41113i	−1.33605	−	0.0451230i
$979$	5.34138	−	6.16428i	0.170711	−	0.197011i
$980$	−4.42499	+	0.0387575i	−0.141351	+	0.00123806i
$981$	8.93488	−	11.8150i	0.285269	−	0.377223i
$982$	−7.48431	+	8.71417i	−0.238834	+	0.278080i
$983$	−11.3352	−	24.8207i	−0.361538	−	0.791657i	−0.999762	−	0.0218069i	$-0.993058\pi$
$983$	−11.3352	−	24.8207i	−0.361538	−	0.791657i	0.638224	−	0.769850i	$-0.279669\pi$
$984$	−31.6377	−	15.4157i	−1.00857	−	0.491434i
$985$	−4.16278	+	9.11521i	−0.132637	+	0.290435i
$986$	16.0416	−	0.0702512i	0.510870	−	0.00223726i
$987$	17.4152	+	12.1546i	0.554331	+	0.386887i
$988$	−11.5073	−	37.9574i	−0.366097	−	1.20758i
$989$	−19.5130	+	16.4215i	−0.620477	+	0.522173i
$990$	7.59279	+	5.68983i	0.241315	+	0.180835i
$991$	−17.2203	−	26.7953i	−0.547020	−	0.851180i	0.452149	−	0.891942i	$-0.350658\pi$
$991$	−17.2203	−	26.7953i	−0.547020	−	0.851180i	−0.999169	+	0.0407628i	$0.987021\pi$
$992$	−14.0315	+	9.45791i	−0.445501	+	0.300289i
$993$	−2.18861	+	57.3560i	−0.0694535	+	1.82014i
$994$	5.36136	+	11.6050i	0.170052	+	0.368088i
$995$	5.68746	−	2.59738i	0.180305	−	0.0823424i
$996$	−2.44914	+	14.0834i	−0.0776039	+	0.446248i
$997$	24.3768	−	3.50485i	0.772021	−	0.111000i	0.254963	−	0.966951i	$-0.417937\pi$
$997$	24.3768	−	3.50485i	0.772021	−	0.111000i	0.517057	+	0.855951i	$0.327027\pi$
$998$	−19.3270	−	2.69247i	−0.611787	−	0.0852288i
$999$	48.0297	−	23.6039i	1.51959	−	0.746793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.x.a.35.20	yes	920
3.2	odd	2	inner	552.2.x.a.35.73	yes	920
8.3	odd	2	inner	552.2.x.a.35.80	yes	920
23.2	even	11	inner	552.2.x.a.347.13	yes	920
24.11	even	2	inner	552.2.x.a.35.13	✓	920
69.2	odd	22	inner	552.2.x.a.347.80	yes	920
184.163	odd	22	inner	552.2.x.a.347.73	yes	920
552.347	even	22	inner	552.2.x.a.347.20	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.x.a.35.13	✓	920	24.11	even	2	inner
552.2.x.a.35.20	yes	920	1.1	even	1	trivial
552.2.x.a.35.73	yes	920	3.2	odd	2	inner
552.2.x.a.35.80	yes	920	8.3	odd	2	inner
552.2.x.a.347.13	yes	920	23.2	even	11	inner
552.2.x.a.347.20	yes	920	552.347	even	22	inner
552.2.x.a.347.73	yes	920	184.163	odd	22	inner
552.2.x.a.347.80	yes	920	69.2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.x (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06473 + 0.930785i) q^{2} +(-0.424251 - 1.67929i) q^{3} +(0.267280 - 1.98206i) q^{4} +(-0.611012 + 0.179409i) q^{5} +(2.01477 + 1.39309i) q^{6} +(1.41902 - 1.22959i) q^{7} +(1.56029 + 2.35913i) q^{8} +(-2.64002 + 1.42488i) q^{9} +O(q^{10})\)	\(q+(-1.06473 + 0.930785i) q^{2} +(-0.424251 - 1.67929i) q^{3} +(0.267280 - 1.98206i) q^{4} +(-0.611012 + 0.179409i) q^{5} +(2.01477 + 1.39309i) q^{6} +(1.41902 - 1.22959i) q^{7} +(1.56029 + 2.35913i) q^{8} +(-2.64002 + 1.42488i) q^{9} +(0.483568 - 0.759742i) q^{10} +(1.89865 - 2.95436i) q^{11} +(-3.44184 + 0.392051i) q^{12} +(3.75279 + 3.25181i) q^{13} +(-0.366385 + 2.62998i) q^{14} +(0.560502 + 0.949950i) q^{15} +(-3.85712 - 1.05953i) q^{16} +(2.10313 - 0.960465i) q^{17} +(1.48464 - 3.97440i) q^{18} +(1.65907 - 3.63286i) q^{19} +(0.192288 + 1.25901i) q^{20} +(-2.66686 - 1.86129i) q^{21} +(0.728330 + 4.91282i) q^{22} +(-3.57878 - 3.19254i) q^{23} +(3.29970 - 3.62104i) q^{24} +(-3.86512 + 2.48396i) q^{25} +(-7.02242 + 0.0307533i) q^{26} +(3.51282 + 3.82885i) q^{27} +(-2.05784 - 3.14123i) q^{28} +(-2.03808 - 4.46277i) q^{29} +(-1.48098 - 0.489729i) q^{30} +(-2.96087 + 0.425709i) q^{31} +(5.09297 - 2.46204i) q^{32} +(-5.76673 - 1.93500i) q^{33} +(-1.34526 + 2.98019i) q^{34} +(-0.646439 + 1.00588i) q^{35} +(2.11857 + 5.61352i) q^{36} +(2.90162 - 9.88202i) q^{37} +(1.61496 + 5.41224i) q^{38} +(3.86860 - 7.68159i) q^{39} +(-1.37661 - 1.16153i) q^{40} +(-2.02393 - 6.89286i) q^{41} +(4.57193 - 0.500504i) q^{42} +(0.756804 - 5.26369i) q^{43} +(-5.34825 - 4.55289i) q^{44} +(1.35745 - 1.34426i) q^{45} +(6.78199 + 0.0681011i) q^{46} -6.53022 q^{47} +(-0.142869 + 6.92673i) q^{48} +(-0.494472 + 3.43913i) q^{49} +(1.80326 - 6.24233i) q^{50} +(-2.50515 - 3.12428i) q^{51} +(7.44832 - 6.56910i) q^{52} +(-1.89278 - 2.18439i) q^{53} +(-7.30402 - 0.806997i) q^{54} +(-0.630059 + 2.14579i) q^{55} +(5.11484 + 1.42914i) q^{56} +(-6.80449 - 1.24482i) q^{57} +(6.32387 + 2.85461i) q^{58} +(10.4244 + 9.03283i) q^{59} +(2.03267 - 0.857046i) q^{60} +(-8.15953 + 1.17316i) q^{61} +(2.75627 - 3.20920i) q^{62} +(-1.99423 + 5.26808i) q^{63} +(-3.13099 + 7.36186i) q^{64} +(-2.87640 - 1.31361i) q^{65} +(7.94105 - 3.30735i) q^{66} +(12.6939 - 8.15785i) q^{67} +(-1.34158 - 4.42523i) q^{68} +(-3.84289 + 7.36425i) q^{69} +(-0.247976 - 1.67268i) q^{70} +(4.04999 - 2.60277i) q^{71} +(-7.48068 - 4.00492i) q^{72} +(-1.44386 + 3.16162i) q^{73} +(6.10860 + 13.2224i) q^{74} +(5.81107 + 5.43683i) q^{75} +(-6.75711 - 4.25937i) q^{76} +(-0.938422 - 6.52687i) q^{77} +(3.03091 + 11.7796i) q^{78} +(7.27743 + 6.30593i) q^{79} +(2.54684 - 0.0446178i) q^{80} +(4.93943 - 7.52343i) q^{81} +(8.57070 + 5.45517i) q^{82} +(1.16258 - 3.95938i) q^{83} +(-4.40199 + 4.78838i) q^{84} +(-1.11272 + 0.964175i) q^{85} +(4.09357 + 6.30881i) q^{86} +(-6.62962 + 5.31586i) q^{87} +(9.93218 - 0.130495i) q^{88} +(2.29892 + 0.330535i) q^{89} +(-0.194089 + 2.69476i) q^{90} +9.32367 q^{91} +(-7.28434 + 6.24006i) q^{92} +(1.97104 + 4.79155i) q^{93} +(6.95289 - 6.07823i) q^{94} +(-0.361944 + 2.51737i) q^{95} +(-6.29518 - 7.50804i) q^{96} +(-5.22565 + 1.53439i) q^{97} +(-2.67461 - 4.12197i) q^{98} +(-0.802871 + 10.5049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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