LMFDB - Embedded newform 300.2.w.a.103.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.13
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.344199 + 1.37169i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.76305 - 0.944266i) q^{4} +(1.92573 + 1.13647i) q^{5} +(-0.125382 + 1.40864i) q^{6} +(0.176718 + 0.176718i) q^{7} +(1.90208 - 2.09335i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.344199 + 1.37169i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.76305 - 0.944266i) q^{4} +(1.92573 + 1.13647i) q^{5} +(-0.125382 + 1.40864i) q^{6} +(0.176718 + 0.176718i) q^{7} +(1.90208 - 2.09335i) q^{8} +(0.951057 - 0.309017i) q^{9} +(-2.22172 + 2.25032i) q^{10} +(2.50557 + 0.814109i) q^{11} +(-1.88906 - 0.656838i) q^{12} +(-0.0867616 + 0.170279i) q^{13} +(-0.303228 + 0.181576i) q^{14} +(2.07980 + 0.821232i) q^{15} +(2.21672 + 3.32959i) q^{16} +(-0.150917 + 0.952856i) q^{17} +(0.0965224 + 1.41092i) q^{18} +(-3.11382 + 2.26232i) q^{19} +(-2.32203 - 3.82207i) q^{20} +(0.202187 + 0.146898i) q^{21} +(-1.97912 + 3.15664i) q^{22} +(-1.11018 - 2.17885i) q^{23} +(1.55119 - 2.36512i) q^{24} +(2.41685 + 4.37708i) q^{25} +(-0.203707 - 0.177620i) q^{26} +(0.891007 - 0.453990i) q^{27} +(-0.144695 - 0.478433i) q^{28} +(2.72431 - 3.74969i) q^{29} +(-1.84234 + 2.57017i) q^{30} +(4.34632 + 5.98219i) q^{31} +(-5.33014 + 1.89461i) q^{32} +(2.60208 + 0.412129i) q^{33} +(-1.25507 - 0.534983i) q^{34} +(0.139475 + 0.541147i) q^{35} +(-1.96856 - 0.353237i) q^{36} +(-10.3242 - 5.26047i) q^{37} +(-2.03143 - 5.04988i) q^{38} +(-0.0590559 + 0.181755i) q^{39} +(6.04192 - 1.86955i) q^{40} +(-1.65043 - 5.07949i) q^{41} +(-0.271090 + 0.226776i) q^{42} +(-6.04379 + 6.04379i) q^{43} +(-3.64872 - 3.80124i) q^{44} +(2.18267 + 0.485769i) q^{45} +(3.37082 - 0.772862i) q^{46} +(-0.924721 - 5.83846i) q^{47} +(2.71029 + 2.94182i) q^{48} -6.93754i q^{49} +(-6.83586 + 1.80858i) q^{50} +0.964733i q^{51} +(0.313755 - 0.218286i) q^{52} +(0.172149 + 1.08691i) q^{53} +(0.316050 + 1.37845i) q^{54} +(3.89983 + 4.41527i) q^{55} +(0.706064 - 0.0338001i) q^{56} +(-2.72158 + 2.72158i) q^{57} +(4.20570 + 5.02753i) q^{58} +(0.0901046 + 0.277314i) q^{59} +(-2.89134 - 3.41176i) q^{60} +(3.76061 - 11.5740i) q^{61} +(-9.70169 + 3.90273i) q^{62} +(0.222678 + 0.113460i) q^{63} +(-0.764188 - 7.96342i) q^{64} +(-0.360597 + 0.229309i) q^{65} +(-1.46094 + 3.42738i) q^{66} +(10.2944 + 1.63047i) q^{67} +(1.16583 - 1.53743i) q^{68} +(-1.43736 - 1.97835i) q^{69} +(-0.790291 + 0.00505473i) q^{70} +(5.12235 - 7.05030i) q^{71} +(1.16211 - 2.57866i) q^{72} +(-4.09140 + 2.08467i) q^{73} +(10.7693 - 12.3510i) q^{74} +(3.07182 + 3.94511i) q^{75} +(7.62607 - 1.04832i) q^{76} +(0.298912 + 0.586648i) q^{77} +(-0.228985 - 0.143566i) q^{78} +(-9.57962 - 6.96000i) q^{79} +(0.484816 + 8.93112i) q^{80} +(0.809017 - 0.587785i) q^{81} +(7.53555 - 0.515516i) q^{82} +(1.04899 - 6.62308i) q^{83} +(-0.217757 - 0.449907i) q^{84} +(-1.37352 + 1.66343i) q^{85} +(-6.20993 - 10.3705i) q^{86} +(2.10419 - 4.12970i) q^{87} +(6.47000 - 3.69652i) q^{88} +(13.6637 + 4.43960i) q^{89} +(-1.41759 + 2.82673i) q^{90} +(-0.0454238 + 0.0147591i) q^{91} +(-0.100107 + 4.88974i) q^{92} +(5.22863 + 5.22863i) q^{93} +(8.32683 + 0.741161i) q^{94} +(-8.56744 + 0.817841i) q^{95} +(-4.96814 + 2.70510i) q^{96} +(-4.05542 + 0.642315i) q^{97} +(9.51614 + 2.38789i) q^{98} +2.63451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.344199	+	1.37169i	−0.243385	+	0.969930i
$2$	−0.344199	+	1.37169i	−0.243385	+	0.969930i
$3$	0.987688	−	0.156434i	0.570242	−	0.0903175i
$3$	0.987688	−	0.156434i	0.570242	−	0.0903175i
$4$	−1.76305	−	0.944266i	−0.881527	−	0.472133i
$5$	1.92573	+	1.13647i	0.861212	+	0.508247i
$5$	1.92573	+	1.13647i	0.861212	+	0.508247i
$6$	−0.125382	+	1.40864i	−0.0511869	+	0.575077i
$7$	0.176718	+	0.176718i	0.0667932	+	0.0667932i	0.739714	−	0.672921i	$-0.234961\pi$
$7$	0.176718	+	0.176718i	0.0667932	+	0.0667932i	−0.672921	+	0.739714i	$0.734961\pi$
$8$	1.90208	−	2.09335i	0.672487	−	0.740109i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	−2.22172	+	2.25032i	−0.702570	+	0.711615i
$11$	2.50557	+	0.814109i	0.755458	+	0.245463i	0.661328	−	0.750097i	$-0.269993\pi$
$11$	2.50557	+	0.814109i	0.755458	+	0.245463i	0.0941298	+	0.995560i	$0.469993\pi$
$12$	−1.88906	−	0.656838i	−0.545326	−	0.189613i
$13$	−0.0867616	+	0.170279i	−0.0240634	+	0.0472270i	−0.902725	−	0.430218i	$-0.858437\pi$
$13$	−0.0867616	+	0.170279i	−0.0240634	+	0.0472270i	0.878662	+	0.477445i	$0.158437\pi$
$14$	−0.303228	+	0.181576i	−0.0810412	+	0.0485282i
$15$	2.07980	+	0.821232i	0.537003	+	0.212041i
$16$	2.21672	+	3.32959i	0.554181	+	0.832396i
$17$	−0.150917	+	0.952856i	−0.0366029	+	0.231101i	−0.999207	−	0.0398095i	$-0.987325\pi$
$17$	−0.150917	+	0.952856i	−0.0366029	+	0.231101i	0.962604	+	0.270911i	$0.0873249\pi$
$18$	0.0965224	+	1.41092i	0.0227506	+	0.332556i
$19$	−3.11382	+	2.26232i	−0.714359	+	0.519012i	−0.884577	−	0.466394i	$-0.845553\pi$
$19$	−3.11382	+	2.26232i	−0.714359	+	0.519012i	0.170218	+	0.985406i	$0.445553\pi$
$20$	−2.32203	−	3.82207i	−0.519221	−	0.854640i
$21$	0.202187	+	0.146898i	0.0441209	+	0.0320557i
$22$	−1.97912	+	3.15664i	−0.421949	+	0.672999i
$23$	−1.11018	−	2.17885i	−0.231488	−	0.454322i	0.745819	−	0.666149i	$-0.232059\pi$
$23$	−1.11018	−	2.17885i	−0.231488	−	0.454322i	−0.977307	+	0.211827i	$0.932059\pi$
$24$	1.55119	−	2.36512i	0.316635	−	0.482779i
$25$	2.41685	+	4.37708i	0.483371	+	0.875416i
$26$	−0.203707	−	0.177620i	−0.0399502	−	0.0348341i
$27$	0.891007	−	0.453990i	0.171474	−	0.0873705i
$28$	−0.144695	−	0.478433i	−0.0273447	−	0.0904153i
$29$	2.72431	−	3.74969i	0.505891	−	0.696299i	−0.477329	−	0.878725i	$-0.658395\pi$
$29$	2.72431	−	3.74969i	0.505891	−	0.696299i	0.983220	+	0.182426i	$0.0583949\pi$
$30$	−1.84234	+	2.57017i	−0.336364	+	0.469247i
$31$	4.34632	+	5.98219i	0.780621	+	1.07443i	0.995213	+	0.0977292i	$0.0311579\pi$
$31$	4.34632	+	5.98219i	0.780621	+	1.07443i	−0.214592	+	0.976704i	$0.568842\pi$
$32$	−5.33014	+	1.89461i	−0.942245	+	0.334923i
$33$	2.60208	+	0.412129i	0.452964	+	0.0717424i
$34$	−1.25507	−	0.534983i	−0.215244	−	0.0917489i
$35$	0.139475	+	0.541147i	0.0235756	+	0.0914705i
$36$	−1.96856	−	0.353237i	−0.328093	−	0.0588728i
$37$	−10.3242	−	5.26047i	−1.69730	−	0.864815i	−0.986963	−	0.160950i	$-0.948544\pi$
$37$	−10.3242	−	5.26047i	−1.69730	−	0.864815i	−0.710333	−	0.703865i	$-0.751456\pi$
$38$	−2.03143	−	5.04988i	−0.329541	−	0.819198i
$39$	−0.0590559	+	0.181755i	−0.00945651	+	0.0291042i
$40$	6.04192	−	1.86955i	0.955311	−	0.295602i
$41$	−1.65043	−	5.07949i	−0.257753	−	0.793283i	−0.993275	−	0.115782i	$-0.963063\pi$
$41$	−1.65043	−	5.07949i	−0.257753	−	0.793283i	0.735521	−	0.677502i	$-0.236937\pi$
$42$	−0.271090	+	0.226776i	−0.0418301	+	0.0349923i
$43$	−6.04379	+	6.04379i	−0.921670	+	0.921670i	−0.997147	−	0.0754777i	$-0.975952\pi$
$43$	−6.04379	+	6.04379i	−0.921670	+	0.921670i	0.0754777	+	0.997147i	$0.475952\pi$
$44$	−3.64872	−	3.80124i	−0.550065	−	0.573059i
$45$	2.18267	+	0.485769i	0.325373	+	0.0724141i
$46$	3.37082	−	0.772862i	0.497001	−	0.113952i
$47$	−0.924721	−	5.83846i	−0.134884	−	0.851626i	−0.958628	−	0.284663i	$-0.908118\pi$
$47$	−0.924721	−	5.83846i	−0.134884	−	0.851626i	0.823743	−	0.566963i	$-0.191882\pi$
$48$	2.71029	+	2.94182i	0.391197	+	0.424615i
$49$		−	6.93754i		−	0.991077i
$50$	−6.83586	+	1.80858i	−0.966737	+	0.255772i
$51$			0.964733i			0.135090i
$52$	0.313755	−	0.218286i	0.0435099	−	0.0302708i
$53$	0.172149	+	1.08691i	0.0236465	+	0.149298i	0.996687	−	0.0813380i	$-0.0259193\pi$
$53$	0.172149	+	1.08691i	0.0236465	+	0.149298i	−0.973040	+	0.230636i	$0.925919\pi$
$54$	0.316050	+	1.37845i	0.0430089	+	0.187583i
$55$	3.89983	+	4.41527i	0.525853	+	0.595355i
$56$	0.706064	−	0.0338001i	0.0943518	−	0.00451673i
$57$	−2.72158	+	2.72158i	−0.360482	+	0.360482i
$58$	4.20570	+	5.02753i	0.552235	+	0.660148i
$59$	0.0901046	+	0.277314i	0.0117306	+	0.0361031i	0.956750	−	0.290910i	$-0.0939579\pi$
$59$	0.0901046	+	0.277314i	0.0117306	+	0.0361031i	−0.945020	+	0.327013i	$0.893958\pi$
$60$	−2.89134	−	3.41176i	−0.373271	−	0.440457i
$61$	3.76061	−	11.5740i	0.481496	−	1.48189i	−0.355496	−	0.934678i	$-0.615688\pi$
$61$	3.76061	−	11.5740i	0.481496	−	1.48189i	0.836992	−	0.547215i	$-0.184312\pi$
$62$	−9.70169	+	3.90273i	−1.23212	+	0.495647i
$63$	0.222678	+	0.113460i	0.0280548	+	0.0142946i
$64$	−0.764188	−	7.96342i	−0.0955234	−	0.995427i
$65$	−0.360597	+	0.229309i	−0.0447266	+	0.0284423i
$66$	−1.46094	+	3.42738i	−0.179830	+	0.421882i
$67$	10.2944	+	1.63047i	1.25766	+	0.199193i	0.749461	−	0.662048i	$-0.230313\pi$
$67$	10.2944	+	1.63047i	1.25766	+	0.199193i	0.508196	+	0.861242i	$0.330313\pi$
$68$	1.16583	−	1.53743i	0.141377	−	0.186441i
$69$	−1.43736	−	1.97835i	−0.173038	−	0.238166i
$70$	−0.790291	+	0.00505473i	−0.0944579	+	0.000604155i
$71$	5.12235	−	7.05030i	0.607911	−	0.836717i	−0.388493	−	0.921452i	$-0.627004\pi$
$71$	5.12235	−	7.05030i	0.607911	−	0.836717i	0.996404	+	0.0847346i	$0.0270042\pi$
$72$	1.16211	−	2.57866i	0.136955	−	0.303899i
$73$	−4.09140	+	2.08467i	−0.478862	+	0.243993i	−0.676723	−	0.736238i	$-0.736601\pi$
$73$	−4.09140	+	2.08467i	−0.478862	+	0.243993i	0.197861	+	0.980230i	$0.436601\pi$
$74$	10.7693	−	12.3510i	1.25191	−	1.43577i
$75$	3.07182	+	3.94511i	0.354704	+	0.455542i
$76$	7.62607	−	1.04832i	0.874770	−	0.120251i
$77$	0.298912	+	0.586648i	0.0340642	+	0.0668547i
$78$	−0.228985	−	0.143566i	−0.0259274	−	0.0162557i
$79$	−9.57962	−	6.96000i	−1.07779	−	0.783061i	−0.100495	−	0.994938i	$-0.532043\pi$
$79$	−9.57962	−	6.96000i	−1.07779	−	0.783061i	−0.977297	+	0.211876i	$0.932043\pi$
$80$	0.484816	+	8.93112i	0.0542040	+	0.998530i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	7.53555	−	0.515516i	0.832162	−	0.0569292i
$83$	1.04899	−	6.62308i	0.115142	−	0.726978i	−0.860799	−	0.508944i	$-0.830036\pi$
$83$	1.04899	−	6.62308i	0.115142	−	0.726978i	0.975941	−	0.218033i	$-0.0699641\pi$
$84$	−0.217757	−	0.449907i	−0.0237592	−	0.0490889i
$85$	−1.37352	+	1.66343i	−0.148979	+	0.180424i
$86$	−6.20993	−	10.3705i	−0.669634	−	1.11828i
$87$	2.10419	−	4.12970i	0.225592	−	0.442750i
$88$	6.47000	−	3.69652i	0.689705	−	0.394051i
$89$	13.6637	+	4.43960i	1.44835	+	0.470596i	0.924489	−	0.381209i	$-0.124492\pi$
$89$	13.6637	+	4.43960i	1.44835	+	0.470596i	0.523858	+	0.851806i	$0.324492\pi$
$90$	−1.41759	+	2.82673i	−0.149427	+	0.297964i
$91$	−0.0454238	+	0.0147591i	−0.00476171	+	0.00154717i
$92$	−0.100107	+	4.88974i	−0.0104369	+	0.509790i
$93$	5.22863	+	5.22863i	0.542183	+	0.542183i
$94$	8.32683	+	0.741161i	0.858847	+	0.0764449i
$95$	−8.56744	+	0.817841i	−0.879001	+	0.0839087i
$96$	−4.96814	+	2.70510i	−0.507059	+	0.276089i
$97$	−4.05542	+	0.642315i	−0.411765	+	0.0652172i	−0.358881	−	0.933383i	$-0.616842\pi$
$97$	−4.05542	+	0.642315i	−0.411765	+	0.0652172i	−0.0528846	+	0.998601i	$0.516842\pi$
$98$	9.51614	+	2.38789i	0.961275	+	0.241214i
$99$	2.63451			0.264778
$100$	−0.127915	−	9.99918i	−0.0127915	−	0.999918i
$101$	6.83240			0.679849			0.339925	−	0.940453i	$-0.389598\pi$
$101$	6.83240			0.679849			0.339925	+	0.940453i	$0.389598\pi$
$102$	−1.32331	−	0.332060i	−0.131027	−	0.0328788i
$103$	−8.36102	+	1.32426i	−0.823836	+	0.130483i	−0.554099	−	0.832451i	$-0.686937\pi$
$103$	−8.36102	+	1.32426i	−0.823836	+	0.130483i	−0.269738	+	0.962934i	$0.586937\pi$
$104$	0.191426	+	0.505507i	0.0187708	+	0.0495690i
$105$	0.222412	+	0.512665i	0.0217052	+	0.0500310i
$106$	−1.55015	−	0.137977i	−0.150564	−	0.0134015i
$107$	−9.24105	−	9.24105i	−0.893366	−	0.893366i	0.101472	−	0.994838i	$-0.467645\pi$
$107$	−9.24105	−	9.24105i	−0.893366	−	0.893366i	−0.994838	+	0.101472i	$0.967645\pi$
$108$	−1.99958	−	0.0409374i	−0.192410	−	0.00393920i
$109$	−16.9198	+	5.49758i	−1.62062	+	0.526573i	−0.972089	−	0.234612i	$-0.924618\pi$
$109$	−16.9198	+	5.49758i	−1.62062	+	0.526573i	−0.648535	+	0.761185i	$0.724618\pi$
$110$	−7.39869	+	3.82962i	−0.705437	+	0.365140i
$111$	−11.0201	−	3.58063i	−1.04598	−	0.339859i
$112$	−0.196663	+	0.980133i	−0.0185829	+	0.0926139i
$113$	−6.56615	+	12.8868i	−0.617691	+	1.21229i	0.344211	+	0.938892i	$0.388147\pi$
$113$	−6.56615	+	12.8868i	−0.617691	+	1.21229i	−0.961902	+	0.273395i	$0.911853\pi$
$114$	−2.79639	−	4.66992i	−0.261906	−	0.437378i
$115$	0.338304	−	5.45756i	0.0315470	−	0.508920i
$116$	−8.34380	+	4.03843i	−0.774703	+	0.374959i
$117$	−0.0298960	+	0.188756i	−0.00276389	+	0.0174505i
$118$	−0.411401	+	0.0281445i	−0.0378726	+	0.00259091i
$119$	−0.195057	+	0.141717i	−0.0178808	+	0.0129912i
$120$	5.67507	−	2.79170i	0.518061	−	0.254846i
$121$	−3.28408	−	2.38602i	−0.298553	−	0.216911i
$122$	14.5815	+	9.14212i	1.32014	+	0.827688i
$123$	−2.42471	−	4.75877i	−0.218629	−	0.429084i
$124$	−2.01401	−	14.6510i	−0.180864	−	1.31570i
$125$	−0.320238	+	11.1758i	−0.0286429	+	0.999590i
$126$	−0.232277	+	0.266392i	−0.0206929	+	0.0237321i
$127$	−0.529736	+	0.269914i	−0.0470064	+	0.0239510i	−0.477336	−	0.878721i	$-0.658397\pi$
$127$	−0.529736	+	0.269914i	−0.0470064	+	0.0239510i	0.430329	+	0.902672i	$0.358397\pi$
$128$	11.1864	+	1.69277i	0.988743	+	0.149621i
$129$	−5.02393	+	6.91484i	−0.442332	+	0.608818i
$130$	−0.190423	−	0.573555i	−0.0167012	−	0.0503041i
$131$	7.32463	+	10.0815i	0.639956	+	0.880824i	0.998613	−	0.0526455i	$-0.0167653\pi$
$131$	7.32463	+	10.0815i	0.639956	+	0.880824i	−0.358657	+	0.933469i	$0.616765\pi$
$132$	−4.19844	−	3.18366i	−0.365428	−	0.277102i
$133$	−0.950062	−	0.150475i	−0.0823808	−	0.0130478i
$134$	−5.77980	+	13.5594i	−0.499298	+	1.17136i
$135$	2.23178	+	0.138344i	0.192081	+	0.0119067i
$136$	1.70760	+	2.12833i	0.146425	+	0.182503i
$137$	−9.74532	−	4.96549i	−0.832599	−	0.424230i	−0.0149087	−	0.999889i	$-0.504746\pi$
$137$	−9.74532	−	4.96549i	−0.832599	−	0.424230i	−0.817690	+	0.575659i	$0.804746\pi$
$138$	3.20842	−	1.29066i	0.273119	−	0.109868i
$139$	−4.43695	+	13.6555i	−0.376337	+	1.15825i	0.566235	+	0.824244i	$0.308400\pi$
$139$	−4.43695	+	13.6555i	−0.376337	+	1.15825i	−0.942572	+	0.334003i	$0.891600\pi$
$140$	0.265084	−	1.08577i	0.0224037	−	0.0917646i
$141$	−1.82667	−	5.62192i	−0.153834	−	0.473451i
$142$	7.90771	+	9.45296i	0.663600	+	0.793275i
$143$	−0.356013	+	0.356013i	−0.0297713	+	0.0297713i
$144$	3.13713	+	2.48162i	0.261427	+	0.206802i
$145$	9.50769	−	4.12477i	0.789571	−	0.342543i
$146$	−1.45127	−	6.32967i	−0.120108	−	0.523847i
$147$	−1.08527	−	6.85213i	−0.0895116	−	0.565154i
$148$	13.2349	+	19.0233i	1.08790	+	1.56371i
$149$			10.2756i			0.841808i	0.907105	+	0.420904i	$0.138287\pi$
$149$			10.2756i			0.841808i	−0.907105	+	0.420904i	$0.861713\pi$
$150$	−6.46878	+	2.85568i	−0.528174	+	0.233165i
$151$		−	18.7598i		−	1.52665i	−0.646016	−	0.763324i	$-0.723566\pi$
$151$		−	18.7598i		−	1.52665i	0.646016	−	0.763324i	$-0.276434\pi$
$152$	−1.18691	+	10.8214i	−0.0962712	+	0.877733i
$153$	0.150917	+	0.952856i	0.0122010	+	0.0770338i
$154$	−0.907582	+	0.208090i	−0.0731351	+	0.0167684i
$155$	1.57121	+	16.4595i	0.126203	+	1.32206i
$156$	0.275744	−	0.264680i	0.0220772	−	0.0211914i
$157$	−5.56867	+	5.56867i	−0.444428	+	0.444428i	−0.893497	−	0.449069i	$-0.851756\pi$
$157$	−5.56867	+	5.56867i	−0.444428	+	0.444428i	0.449069	+	0.893497i	$0.351756\pi$
$158$	12.8442	−	10.7446i	1.02183	−	0.854797i
$159$	0.340059	+	1.04659i	0.0269684	+	0.0830003i
$160$	−12.4176	−	2.40907i	−0.981696	−	0.190453i
$161$	0.188853	−	0.581231i	0.0148837	−	0.0458074i
$162$	0.527795	+	1.31203i	0.0414675	+	0.103083i
$163$	0.388509	+	0.197955i	0.0304304	+	0.0155050i	0.469139	−	0.883124i	$-0.344564\pi$
$163$	0.388509	+	0.197955i	0.0304304	+	0.0155050i	−0.438709	+	0.898629i	$0.644564\pi$
$164$	−1.88660	+	10.5139i	−0.147319	+	0.820995i
$165$	4.54252	+	3.75084i	0.353635	+	0.292003i
$166$	8.72374	+	3.71855i	0.677093	+	0.288615i
$167$	−10.3937	−	1.64620i	−0.804291	−	0.127387i	−0.259265	−	0.965806i	$-0.583480\pi$
$167$	−10.3937	−	1.64620i	−0.804291	−	0.127387i	−0.545026	+	0.838419i	$0.683480\pi$
$168$	0.692084	−	0.143837i	0.0533954	−	0.0110972i
$169$	7.61974	+	10.4877i	0.586134	+	0.806744i
$170$	−1.80894	−	2.45659i	−0.138739	−	0.188412i
$171$	−2.26232	+	3.11382i	−0.173004	+	0.238120i
$172$	16.3625	−	4.94859i	1.24763	−	0.377326i
$173$	−8.22786	+	4.19230i	−0.625553	+	0.318735i	−0.737876	−	0.674937i	$-0.764171\pi$
$173$	−8.22786	+	4.19230i	−0.625553	+	0.318735i	0.112323	+	0.993672i	$0.464171\pi$
$174$	4.94040	+	4.30772i	0.374530	+	0.326568i
$175$	−0.346408	+	1.20061i	−0.0261860	+	0.0907577i
$176$	2.84351	+	10.1472i	0.214337	+	0.764871i
$177$	0.132377	+	0.259804i	0.00995004	+	0.0195281i
$178$	−10.7928	+	17.2142i	−0.808952	+	1.29026i
$179$	16.6746	+	12.1148i	1.24632	+	0.905503i	0.998002	−	0.0631765i	$-0.0201231\pi$
$179$	16.6746	+	12.1148i	1.24632	+	0.905503i	0.248315	+	0.968679i	$0.420123\pi$
$180$	−3.38946	−	2.91745i	−0.252636	−	0.217454i
$181$	−4.10735	+	2.98416i	−0.305297	+	0.221811i	−0.729876	−	0.683580i	$-0.760422\pi$
$181$	−4.10735	+	2.98416i	−0.305297	+	0.221811i	0.424579	+	0.905391i	$0.360422\pi$
$182$	−0.00461005	−	0.0673873i	−0.000341719	−	0.00499508i
$183$	1.90374	−	12.0197i	0.140729	−	0.888525i
$184$	−6.67273	−	1.82036i	−0.491921	−	0.134198i
$185$	−13.9033	−	21.8635i	−1.02219	−	1.60743i
$186$	−8.97173	+	5.37236i	−0.657839	+	0.393920i
$187$	−1.15386	+	2.26458i	−0.0843788	+	0.165603i
$188$	−3.88272	+	11.1667i	−0.283177	+	0.814415i
$189$	0.237685	+	0.0772287i	0.0172891	+	0.00561756i
$190$	1.82708	−	12.0334i	0.132550	−	0.872991i
$191$	9.33935	−	3.03454i	0.675772	−	0.219571i	0.0490284	−	0.998797i	$-0.484388\pi$
$191$	9.33935	−	3.03454i	0.675772	−	0.219571i	0.626743	+	0.779226i	$0.284388\pi$
$192$	−2.00053	−	7.74583i	−0.144376	−	0.559007i
$193$	13.1195	+	13.1195i	0.944361	+	0.944361i	0.998532	−	0.0541709i	$-0.0172516\pi$
$193$	13.1195	+	13.1195i	0.944361	+	0.944361i	−0.0541709	+	0.998532i	$0.517252\pi$
$194$	0.514814	−	5.78385i	0.0369615	−	0.415256i
$195$	−0.320286	+	0.282896i	−0.0229362	+	0.0202586i
$196$	−6.55089	+	12.2313i	−0.467920	+	0.873662i
$197$	15.4704	−	2.45027i	1.10222	−	0.174574i	0.421292	−	0.906925i	$-0.361577\pi$
$197$	15.4704	−	2.45027i	1.10222	−	0.174574i	0.680928	+	0.732351i	$0.261577\pi$
$198$	−0.906796	+	3.61373i	−0.0644432	+	0.256816i
$199$	−22.0119			−1.56038			−0.780191	−	0.625542i	$-0.784878\pi$
$199$	−22.0119			−1.56038			−0.780191	+	0.625542i	$0.784878\pi$
$200$	13.7598	+	3.26625i	0.972964	+	0.230958i
$201$	10.4227			0.735159
$202$	−2.35170	+	9.37192i	−0.165465	+	0.659406i
$203$	1.14407	−	0.181203i	0.0802981	−	0.0127180i
$204$	0.910965	−	1.70088i	0.0637803	−	0.119085i
$205$	2.59444	−	11.6574i	0.181203	−	0.814187i
$206$	1.06139	−	11.9245i	0.0739504	−	0.830821i
$207$	−1.72915	−	1.72915i	−0.120184	−	0.120184i
$208$	−0.759286	+	0.0885817i	−0.0526470	+	0.00614203i
$209$	−9.64367	+	3.13342i	−0.667067	+	0.216743i
$210$	−0.779771	+	0.128621i	−0.0538093	+	0.00887571i
$211$	15.8836	+	5.16089i	1.09347	+	0.355291i	0.799587	−	0.600550i	$-0.205052\pi$
$211$	15.8836	+	5.16089i	1.09347	+	0.355291i	0.293885	+	0.955841i	$0.405052\pi$
$212$	0.722820	−	2.07883i	0.0496435	−	0.142775i
$213$	3.95637	−	7.76481i	0.271086	−	0.532036i
$214$	15.8566	−	9.49508i	1.08393	−	0.649070i
$215$	−18.5073	+	4.77008i	−1.26219	+	0.325317i
$216$	0.744406	−	2.72871i	0.0506504	−	0.185665i
$217$	−0.289089	+	1.82523i	−0.0196246	+	0.123905i
$218$	−1.71719	−	25.1010i	−0.116303	−	1.70005i
$219$	−3.71492	+	2.69904i	−0.251031	+	0.182385i
$220$	−2.70643	−	11.4668i	−0.182467	−	0.773094i
$221$	−0.149158	−	0.108369i	−0.0100334	−	0.00728972i
$222$	8.70460	−	13.8836i	0.584215	−	0.931808i
$223$	−9.86230	−	19.3559i	−0.660429	−	1.29616i	−0.941673	−	0.336528i	$-0.890747\pi$
$223$	−9.86230	−	19.3559i	−0.660429	−	1.29616i	0.281245	−	0.959636i	$-0.409253\pi$
$224$	−1.27675	−	0.607121i	−0.0853062	−	0.0405650i
$225$	3.65116	+	3.41600i	0.243410	+	0.227733i
$226$	−15.4166	−	13.4423i	−1.02550	−	0.894170i
$227$	14.8153	−	7.54875i	0.983323	−	0.501028i	0.113045	−	0.993590i	$-0.463939\pi$
$227$	14.8153	−	7.54875i	0.983323	−	0.501028i	0.870277	+	0.492562i	$0.163939\pi$
$228$	7.36819	−	2.22840i	0.487970	−	0.147579i
$229$	5.47711	−	7.53859i	0.361937	−	0.498164i	−0.588750	−	0.808315i	$-0.700380\pi$
$229$	5.47711	−	7.53859i	0.361937	−	0.498164i	0.950687	+	0.310151i	$0.100380\pi$
$230$	7.36963	+	2.34253i	0.485939	+	0.154462i
$231$	0.387004	+	0.532665i	0.0254630	+	0.0350468i
$232$	−2.66754	−	12.8351i	−0.175133	−	0.842667i
$233$	−13.6715	−	2.16536i	−0.895652	−	0.141857i	−0.308396	−	0.951258i	$-0.599792\pi$
$233$	−13.6715	−	2.16536i	−0.895652	−	0.141857i	−0.587257	+	0.809401i	$0.699792\pi$
$234$	−0.248624	−	0.105978i	−0.0162531	−	0.00692797i
$235$	4.85450	−	12.2942i	0.316672	−	0.801985i
$236$	0.102998	−	0.574002i	0.00670463	−	0.0373643i
$237$	−10.5505	−	5.37573i	−0.685326	−	0.349191i
$238$	−0.127253	−	0.316336i	−0.00824860	−	0.0205050i
$239$	0.321628	−	0.989869i	0.0208044	−	0.0640293i	−0.940115	−	0.340857i	$-0.889283\pi$
$239$	0.321628	−	0.989869i	0.0208044	−	0.0640293i	0.960920	+	0.276827i	$0.0892830\pi$
$240$	1.87598	+	8.74532i	0.121094	+	0.564508i
$241$	−0.429404	−	1.32157i	−0.0276603	−	0.0851298i	0.936273	−	0.351272i	$-0.114251\pi$
$241$	−0.429404	−	1.32157i	−0.0276603	−	0.0851298i	−0.963934	+	0.266142i	$0.914251\pi$
$242$	4.40325	−	3.68346i	0.283052	−	0.236782i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−17.5590	+	16.8545i	−1.12410	+	1.07900i
$245$	7.88434	−	13.3598i	0.503712	−	0.853527i
$246$	7.36213	−	1.68799i	0.469392	−	0.107622i
$247$	−0.115067	−	0.726502i	−0.00732151	−	0.0462262i
$248$	20.7898	+	2.28026i	1.32016	+	0.144797i
$249$		−	6.70564i		−	0.424953i
$250$	−15.2194	−	4.28595i	−0.962560	−	0.271067i
$251$			12.8188i			0.809114i	0.914513	+	0.404557i	$0.132574\pi$
$251$			12.8188i			0.809114i	−0.914513	+	0.404557i	$0.867426\pi$
$252$	−0.285457	−	0.410303i	−0.0179821	−	0.0258467i
$253$	−1.00781	−	6.36307i	−0.0633605	−	0.400043i
$254$	−0.187903	−	0.819536i	−0.0117901	−	0.0514223i
$255$	−1.09639	+	1.85781i	−0.0686589	+	0.116341i
$256$	−6.17228	+	14.7615i	−0.385768	+	0.922596i
$257$	10.9996	−	10.9996i	0.686135	−	0.686135i	−0.275241	−	0.961375i	$-0.588758\pi$
$257$	10.9996	−	10.9996i	0.686135	−	0.686135i	0.961375	+	0.275241i	$0.0887576\pi$
$258$	−7.75577	−	9.27134i	−0.482853	−	0.577208i
$259$	−0.894862	−	2.75410i	−0.0556040	−	0.171132i
$260$	0.852282	−	0.0637847i	0.0528563	−	0.00395576i
$261$	1.43225	−	4.40802i	0.0886542	−	0.272850i
$262$	−16.3498	+	6.57707i	−1.01009	+	0.406333i
$263$	6.19986	+	3.15899i	0.382300	+	0.194792i	0.634570	−	0.772865i	$-0.281177\pi$
$263$	6.19986	+	3.15899i	0.382300	+	0.194792i	−0.252270	+	0.967657i	$0.581177\pi$
$264$	5.81208	−	4.66314i	0.357709	−	0.286997i
$265$	−0.903728	+	2.28873i	−0.0555156	+	0.140595i
$266$	0.533415	−	1.25140i	0.0327058	−	0.0767280i
$267$	14.1900	+	2.24747i	0.868411	+	0.137543i
$268$	−16.6099	−	12.5952i	−1.01461	−	0.769376i
$269$	10.5934	+	14.5805i	0.645889	+	0.888990i	0.998912	−	0.0466246i	$-0.0148464\pi$
$269$	10.5934	+	14.5805i	0.645889	+	0.888990i	−0.353024	+	0.935614i	$0.614846\pi$
$270$	−0.957942	+	3.01369i	−0.0582985	+	0.183408i
$271$	1.80316	−	2.48183i	0.109534	−	0.150761i	−0.750731	−	0.660609i	$-0.770298\pi$
$271$	1.80316	−	2.48183i	0.109534	−	0.150761i	0.860265	+	0.509848i	$0.170298\pi$
$272$	−3.50716	+	1.60972i	−0.212653	+	0.0976038i
$273$	−0.0425557	+	0.0216832i	−0.00257559	+	0.00131233i
$274$	10.1654	−	11.6584i	0.614116	−	0.704311i
$275$	2.49217	+	12.9347i	0.150284	+	0.779989i
$276$	0.666048	+	4.84520i	0.0400914	+	0.291647i
$277$	6.03868	+	11.8516i	0.362829	+	0.712092i	0.998191	−	0.0601222i	$-0.0191490\pi$
$277$	6.03868	+	11.8516i	0.362829	+	0.712092i	−0.635362	+	0.772215i	$0.719149\pi$
$278$	−17.2039	−	10.7863i	−1.03182	−	0.646921i
$279$	5.98219	+	4.34632i	0.358144	+	0.260207i
$280$	1.39810	+	0.737334i	0.0835524	+	0.0440641i
$281$	−17.4485	+	12.6771i	−1.04089	+	0.756251i	−0.970459	−	0.241266i	$-0.922437\pi$
$281$	−17.4485	+	12.6771i	−1.04089	+	0.756251i	−0.0704309	+	0.997517i	$0.522437\pi$
$282$	8.34025	−	0.570567i	0.496655	−	0.0339767i
$283$	−2.15332	+	13.5956i	−0.128002	+	0.808172i	0.837244	+	0.546829i	$0.184165\pi$
$283$	−2.15332	+	13.5956i	−0.128002	+	0.808172i	−0.965246	+	0.261343i	$0.915835\pi$
$284$	−15.6883	+	7.59321i	−0.930932	+	0.450574i
$285$	−8.33402	+	2.14801i	−0.493665	+	0.127237i
$286$	−0.365800	−	0.610878i	−0.0216302	−	0.0361220i
$287$	0.605978	−	1.18930i	0.0357697	−	0.0702021i
$288$	−4.48380	+	3.44899i	−0.264211	+	0.203234i
$289$	15.2828	+	4.96568i	0.898988	+	0.292099i
$290$	2.38536	+	14.4613i	0.140073	+	0.849198i
$291$	−3.90501	+	1.26881i	−0.228916	+	0.0743792i
$292$	9.18185	+	0.187980i	0.537327	+	0.0110007i
$293$	−6.36868	−	6.36868i	−0.372062	−	0.372062i	0.496166	−	0.868228i	$-0.334741\pi$
$293$	−6.36868	−	6.36868i	−0.372062	−	0.372062i	−0.868228	+	0.496166i	$0.834741\pi$
$294$	9.77253	+	0.869841i	0.569946	+	0.0507302i
$295$	−0.141643	+	0.636432i	−0.00824676	+	0.0370545i
$296$	−30.6495	+	11.6064i	−1.78147	+	0.674608i
$297$	2.60208	−	0.412129i	0.150988	−	0.0239141i
$298$	−14.0949	−	3.53684i	−0.816495	−	0.204884i
$299$	0.467334			0.0270266
$300$	−1.69056	−	9.85606i	−0.0976044	−	0.569040i
$301$	−2.13610			−0.123123
$302$	25.7325	+	6.45709i	1.48074	+	0.371564i
$303$	6.74828	−	1.06882i	0.387679	−	0.0614023i
$304$	−14.4351	−	5.35279i	−0.827908	−	0.307004i
$305$	20.3954	−	18.0145i	1.16784	−	1.03150i
$306$	−1.35897	−	0.120960i	−0.0776869	−	0.00691482i
$307$	19.8224	+	19.8224i	1.13132	+	1.13132i	0.989957	+	0.141365i	$0.0451492\pi$
$307$	19.8224	+	19.8224i	1.13132	+	1.13132i	0.141365	+	0.989957i	$0.454851\pi$
$308$	0.0269536	−	1.31654i	0.00153582	−	0.0750171i
$309$	−8.05093	+	2.61590i	−0.458001	+	0.148814i
$310$	−23.1182	−	3.51014i	−1.31302	−	0.199362i
$311$	5.86739	+	1.90643i	0.332709	+	0.108104i	0.470608	−	0.882343i	$-0.344035\pi$
$311$	5.86739	+	1.90643i	0.332709	+	0.108104i	−0.137898	+	0.990446i	$0.544035\pi$
$312$	0.268148	+	0.469338i	0.0151809	+	0.0265710i
$313$	11.1734	−	21.9291i	0.631560	−	1.23951i	−0.324375	−	0.945929i	$-0.605154\pi$
$313$	11.1734	−	21.9291i	0.631560	−	1.23951i	0.955935	−	0.293578i	$-0.0948460\pi$
$314$	−5.72175	−	9.55520i	−0.322897	−	0.539231i
$315$	0.299872	+	0.471561i	0.0168959	+	0.0265694i
$316$	10.3173	+	21.3166i	0.580393	+	1.19915i
$317$	2.63873	−	16.6603i	0.148206	−	0.935735i	−0.795741	−	0.605637i	$-0.792918\pi$
$317$	2.63873	−	16.6603i	0.148206	−	0.935735i	0.943947	−	0.330098i	$-0.107082\pi$
$318$	−1.55265	+	0.106218i	−0.0870682	+	0.00595644i
$319$	9.87859	−	7.17722i	0.553095	−	0.401847i
$320$	7.57860	−	16.2039i	0.423657	−	0.905823i
$321$	−10.5729	−	7.68166i	−0.590122	−	0.428748i
$322$	0.732265	+	0.459107i	0.0408075	+	0.0255850i
$323$	−1.68574	−	3.30844i	−0.0937969	−	0.184087i
$324$	−1.98137	+	0.272370i	−0.110076	+	0.0151317i
$325$	−0.955016	+	0.0317775i	−0.0529748	+	0.00176270i
$326$	−0.405257	+	0.464777i	−0.0224451	+	0.0257416i
$327$	−15.8515	+	8.07674i	−0.876589	+	0.446645i
$328$	−13.7724	−	6.20668i	−0.760452	−	0.342707i
$329$	0.868346	−	1.19518i	0.0478735	−	0.0658922i
$330$	−6.70851	+	4.93988i	−0.369291	+	0.271932i
$331$	0.146758	+	0.201995i	0.00806656	+	0.0111027i	0.813031	−	0.582220i	$-0.197816\pi$
$331$	0.146758	+	0.201995i	0.00806656	+	0.0111027i	−0.804965	+	0.593323i	$0.797816\pi$
$332$	−8.10338	+	10.6863i	−0.444731	+	0.586488i
$333$	−11.4445	−	1.81263i	−0.627156	−	0.0993317i
$334$	5.83559	−	13.6903i	0.319309	−	0.749101i
$335$	17.9712	+	14.8391i	0.981869	+	0.810747i
$336$	−0.0409152	+	0.998831i	−0.00223211	+	0.0544907i
$337$	−5.73749	−	2.92340i	−0.312541	−	0.159248i	0.290683	−	0.956819i	$-0.406117\pi$
$337$	−5.73749	−	2.92340i	−0.312541	−	0.159248i	−0.603224	+	0.797572i	$0.706117\pi$
$338$	−17.0085	+	6.84206i	−0.925141	+	0.372159i
$339$	−4.46937	+	13.7553i	−0.242743	+	0.747086i
$340$	3.99231	−	1.63574i	0.216513	−	0.0887105i
$341$	6.01984	+	18.5272i	0.325993	+	1.00330i
$342$	−3.49250	−	4.17497i	−0.188853	−	0.225757i
$343$	2.46302	−	2.46302i	0.132990	−	0.132990i
$344$	1.15597	+	24.1475i	0.0623257	+	1.30195i
$345$	−0.519612	−	5.44329i	−0.0279750	−	0.293057i
$346$	−2.91851	−	12.7290i	−0.156900	−	0.684317i
$347$	1.70261	+	10.7499i	0.0914009	+	0.577083i	0.990302	+	0.138931i	$0.0443666\pi$
$347$	1.70261	+	10.7499i	0.0914009	+	0.577083i	−0.898901	+	0.438151i	$0.855633\pi$
$348$	−7.60933	+	5.29397i	−0.407903	+	0.283787i
$349$		−	9.51909i		−	0.509545i	−0.967001	−	0.254773i	$-0.917999\pi$
$349$		−	9.51909i		−	0.509545i	0.967001	−	0.254773i	$-0.0820006\pi$
$350$	−1.52763	−	0.888412i	−0.0816553	−	0.0474876i
$351$			0.191109i			0.0102006i
$352$	−14.8975	+	0.407764i	−0.794038	+	0.0217339i
$353$	−4.37237	−	27.6061i	−0.232718	−	1.46932i	−0.776511	−	0.630103i	$-0.783013\pi$
$353$	−4.37237	−	27.6061i	−0.232718	−	1.46932i	0.543794	−	0.839219i	$-0.316987\pi$
$354$	−0.401934	+	0.0921553i	−0.0213625	+	0.00489800i
$355$	17.8767	−	7.75555i	0.948798	−	0.411622i
$356$	−19.8976	−	20.7294i	−1.05457	−	1.09866i
$357$	−0.170486	+	0.170486i	−0.00902307	+	0.00902307i
$358$	−22.3571	+	18.7024i	−1.18161	+	0.988454i
$359$	−11.0850	−	34.1161i	−0.585043	−	1.80058i	−0.599097	−	0.800676i	$-0.704474\pi$
$359$	−11.0850	−	34.1161i	−0.585043	−	1.80058i	0.0140544	−	0.999901i	$-0.495526\pi$
$360$	5.16848	−	3.64510i	0.272403	−	0.192114i
$361$	−1.29355	+	3.98114i	−0.0680816	+	0.209534i
$362$	−2.67960	−	6.66114i	−0.140836	−	0.350102i
$363$	−3.61690	−	1.84290i	−0.189838	−	0.0967274i
$364$	0.0940211	+	0.0168711i	0.00492805	+	0.000884285i
$365$	−10.2481	−	0.635260i	−0.536410	−	0.0332510i
$366$	15.8321	+	6.74852i	0.827556	+	0.352751i
$367$	8.15534	+	1.29168i	0.425705	+	0.0674251i	0.365611	−	0.930768i	$-0.380860\pi$
$367$	8.15534	+	1.29168i	0.425705	+	0.0674251i	0.0600940	+	0.998193i	$0.480860\pi$
$368$	4.79371	−	8.52634i	0.249889	−	0.444466i
$369$	−3.13930	−	4.32087i	−0.163425	−	0.224936i
$370$	34.7753	−	11.5456i	1.80788	−	0.600228i
$371$	−0.161654	+	0.222498i	−0.00839266	+	0.0115515i
$372$	−4.28114	−	14.1556i	−0.221967	−	0.733932i
$373$	−16.8009	+	8.56049i	−0.869918	+	0.443245i	−0.831180	−	0.556004i	$-0.812334\pi$
$373$	−16.8009	+	8.56049i	−0.869918	+	0.443245i	−0.0387386	+	0.999249i	$0.512334\pi$
$374$	−2.70914	−	2.36221i	−0.140086	−	0.122147i
$375$	1.43198	+	11.0883i	0.0739470	+	0.572595i
$376$	−13.9808	−	9.16945i	−0.721005	−	0.472878i
$377$	0.402129	+	0.789222i	0.0207107	+	0.0406470i
$378$	−0.187745	+	0.299448i	−0.00965654	+	0.0154019i
$379$	5.75200	+	4.17907i	0.295460	+	0.214664i	0.725633	−	0.688082i	$-0.241547\pi$
$379$	5.75200	+	4.17907i	0.295460	+	0.214664i	−0.430172	+	0.902747i	$0.641547\pi$
$380$	15.8771	+	6.64805i	0.814479	+	0.341038i
$381$	−0.480990	+	0.349460i	−0.0246419	+	0.0179034i
$382$	0.947847	+	13.8552i	0.0484961	+	0.708891i
$383$	−4.72618	+	29.8399i	−0.241497	+	1.52475i	0.507195	+	0.861831i	$0.330682\pi$
$383$	−4.72618	+	29.8399i	−0.241497	+	1.52475i	−0.748692	+	0.662918i	$0.769318\pi$
$384$	11.3134	−	0.0780011i	0.577337	−	0.00398048i
$385$	−0.0910870	+	1.46943i	−0.00464222	+	0.0748890i
$386$	−22.5115	+	13.4801i	−1.14581	+	0.686120i
$387$	−3.88035	+	7.61562i	−0.197249	+	0.387124i
$388$	7.75644	+	2.69696i	0.393774	+	0.136917i
$389$	34.5907	+	11.2392i	1.75382	+	0.569851i	0.996531	−	0.0832281i	$-0.0265230\pi$
$389$	34.5907	+	11.2392i	1.75382	+	0.569851i	0.757290	+	0.653079i	$0.226523\pi$
$390$	−0.277803	−	0.536705i	−0.0140671	−	0.0271771i
$391$	2.24367	−	0.729014i	0.113468	−	0.0368678i
$392$	−14.5227	−	13.1958i	−0.733506	−	0.666486i
$393$	8.81154	+	8.81154i	0.444484	+	0.444484i
$394$	−1.96388	+	22.0639i	−0.0989390	+	1.11156i
$395$	−10.5379	−	24.2901i	−0.530218	−	1.22217i
$396$	−4.64479	−	2.48768i	−0.233409	−	0.125011i
$397$	35.1495	−	5.56713i	1.76410	−	0.279406i	0.811660	−	0.584130i	$-0.198564\pi$
$397$	35.1495	−	5.56713i	1.76410	−	0.279406i	0.952441	+	0.304724i	$0.0985641\pi$
$398$	7.57646	−	30.1934i	0.379774	−	1.51346i
$399$	−0.961905			−0.0481555
$400$	−9.21637	+	17.7499i	−0.460818	+	0.887494i
$401$	−8.79529			−0.439216			−0.219608	−	0.975588i	$-0.570478\pi$
$401$	−8.79529			−0.439216			−0.219608	+	0.975588i	$0.570478\pi$
$402$	−3.58747	+	14.2967i	−0.178927	+	0.713053i
$403$	−1.39574	+	0.221063i	−0.0695266	+	0.0110119i
$404$	−12.0459	−	6.45161i	−0.599306	−	0.320979i
$405$	2.22595	−	0.212487i	0.110608	−	0.0105586i
$406$	−0.145234	+	1.63168i	−0.00720783	+	0.0809789i
$407$	−21.5855	−	21.5855i	−1.06996	−	1.06996i
$408$	2.01952	+	1.83500i	0.0999811	+	0.0908460i
$409$	−9.78051	+	3.17788i	−0.483615	+	0.157136i	−0.540670	−	0.841235i	$-0.681829\pi$
$409$	−9.78051	+	3.17788i	−0.483615	+	0.157136i	0.0570545	+	0.998371i	$0.481829\pi$
$410$	15.0973	+	7.57122i	0.745602	+	0.373916i
$411$	−10.4021	−	3.37985i	−0.513098	−	0.166716i
$412$	15.9914	+	5.56030i	0.787839	+	0.273936i
$413$	−0.0330832	+	0.0649295i	−0.00162792	+	0.00319497i
$414$	2.96702	−	1.77668i	0.145821	−	0.0873189i
$415$	9.54703	−	11.5621i	0.468645	−	0.567561i
$416$	0.139839	−	1.07199i	0.00685616	−	0.0525588i
$417$	−2.24613	+	14.1815i	−0.109993	+	0.694471i
$418$	−0.978733	−	14.3066i	−0.0478714	−	0.699760i
$419$	13.2984	−	9.66189i	0.649672	−	0.472014i	−0.213488	−	0.976946i	$-0.568482\pi$
$419$	13.2984	−	9.66189i	0.649672	−	0.472014i	0.863159	+	0.504932i	$0.168482\pi$
$420$	0.0919678	−	1.11387i	0.00448757	−	0.0543515i
$421$	15.0738	+	10.9517i	0.734650	+	0.533755i	0.891031	−	0.453942i	$-0.149983\pi$
$421$	15.0738	+	10.9517i	0.734650	+	0.533755i	−0.156381	+	0.987697i	$0.549983\pi$
$422$	−12.5462	+	20.0110i	−0.610742	+	0.974118i
$423$	−2.68364	−	5.26695i	−0.130483	−	0.256088i
$424$	2.60271	+	1.70701i	0.126399	+	0.0828999i
$425$	−4.53547	+	1.64233i	−0.220003	+	0.0796649i
$426$	9.28912	+	8.09954i	0.450059	+	0.392424i
$427$	2.70990	−	1.38076i	0.131141	−	0.0668197i
$428$	7.56647	+	25.0185i	0.365739	+	1.20931i
$429$	−0.295937	+	0.407323i	−0.0142880	+	0.0196657i
$430$	−0.172873	−	27.0281i	−0.00833666	−	1.30341i
$431$	−14.7504	−	20.3021i	−0.710500	−	0.977920i	−0.999786	−	0.0206770i	$-0.993418\pi$
$431$	−14.7504	−	20.3021i	−0.710500	−	0.977920i	0.289286	−	0.957243i	$-0.406582\pi$
$432$	3.48671	+	1.96031i	0.167755	+	0.0943155i
$433$	6.23259	+	0.987146i	0.299519	+	0.0474392i	0.304385	−	0.952549i	$-0.401549\pi$
$433$	6.23259	+	0.987146i	0.299519	+	0.0474392i	−0.00486610	+	0.999988i	$0.501549\pi$
$434$	−2.40415	−	1.02478i	−0.115403	−	0.0491911i
$435$	8.74538	−	5.56132i	0.419309	−	0.266645i
$436$	35.0217	+	6.28427i	1.67724	+	0.300962i
$437$	8.38616	+	4.27296i	0.401164	+	0.204404i
$438$	−2.42358	−	6.02471i	−0.115803	−	0.287872i
$439$	−2.09652	+	6.45241i	−0.100061	+	0.307957i	−0.988540	−	0.150962i	$-0.951763\pi$
$439$	−2.09652	+	6.45241i	−0.100061	+	0.307957i	0.888478	+	0.458919i	$0.151763\pi$
$440$	16.6605	+	0.234498i	0.794257	+	0.0111792i
$441$	−2.14382	−	6.59799i	−0.102087	−	0.314190i
$442$	0.199989	−	0.167297i	0.00951250	−	0.00795752i
$443$	−26.2759	+	26.2759i	−1.24840	+	1.24840i	−0.291981	+	0.956424i	$0.594314\pi$
$443$	−26.2759	+	26.2759i	−1.24840	+	1.24840i	−0.956424	+	0.291981i	$0.905686\pi$
$444$	16.0479	+	16.7187i	0.761599	+	0.793435i
$445$	21.2670	+	24.0779i	1.00815	+	1.14140i
$446$	29.9448	−	6.86574i	1.41793	−	0.325102i
$447$	1.60745	+	10.1491i	0.0760300	+	0.480035i
$448$	1.27223	−	1.54233i	0.0601074	−	0.0728681i
$449$		−	12.3345i		−	0.582103i	−0.956707	−	0.291052i	$-0.905995\pi$
$449$		−	12.3345i		−	0.582103i	0.956707	−	0.291052i	$-0.0940051\pi$
$450$	−5.94241	+	3.83246i	−0.280128	+	0.180664i
$451$		−	14.0707i		−	0.662561i
$452$	23.7450	−	16.5199i	1.11687	−	0.777032i
$453$	−2.93467	−	18.5288i	−0.137883	−	0.870559i
$454$	5.25513	+	22.9202i	0.246636	+	1.07570i
$455$	−0.104247	−	0.0232010i	−0.00488718	−	0.00108768i
$456$	0.520545	+	10.8739i	0.0243767	+	0.509215i
$457$	−21.1144	+	21.1144i	−0.987689	+	0.987689i	−0.999925	−	0.0122358i	$-0.996105\pi$
$457$	−21.1144	+	21.1144i	−0.987689	+	0.987689i	0.0122358	+	0.999925i	$0.496105\pi$
$458$	8.45538	+	10.1077i	0.395094	+	0.472299i
$459$	0.298119	+	0.917516i	0.0139150	+	0.0428260i
$460$	−5.74984	+	9.30253i	−0.268088	+	0.433733i
$461$	−12.6107	+	38.8117i	−0.587339	+	1.80764i	0.00233064	+	0.999997i	$0.499258\pi$
$461$	−12.6107	+	38.8117i	−0.587339	+	1.80764i	−0.589669	+	0.807645i	$0.700742\pi$
$462$	−0.863856	+	0.347506i	−0.0401902	+	0.0161674i
$463$	35.5965	+	18.1373i	1.65431	+	0.842913i	0.995920	+	0.0902367i	$0.0287623\pi$
$463$	35.5965	+	18.1373i	1.65431	+	0.842913i	0.658390	+	0.752677i	$0.271238\pi$
$464$	18.5239	+	0.758798i	0.859952	+	0.0352263i
$465$	4.12671	+	16.0111i	0.191372	+	0.742497i
$466$	7.67592	−	18.0078i	0.355580	−	0.834194i
$467$	−20.1169	−	3.18620i	−0.930899	−	0.147440i	−0.327474	−	0.944860i	$-0.606198\pi$
$467$	−20.1169	−	3.18620i	−0.930899	−	0.147440i	−0.603424	+	0.797420i	$0.706198\pi$
$468$	0.230944	−	0.304557i	0.0106754	−	0.0140782i
$469$	1.53107	+	2.10733i	0.0706981	+	0.0973076i
$470$	15.1929	+	10.8905i	0.700796	+	0.502341i
$471$	−4.62898	+	6.37124i	−0.213292	+	0.293571i
$472$	0.751899	+	0.338852i	0.0346090	+	0.0155969i
$473$	−20.0635	+	10.2228i	−0.922519	+	0.470047i
$474$	11.0053	−	12.6216i	0.505489	−	0.579730i
$475$	−17.4280	−	8.16174i	−0.799652	−	0.374486i
$476$	0.477714	−	0.0656693i	0.0218960	−	0.00300995i
$477$	0.499596	+	0.980512i	0.0228749	+	0.0448945i
$478$	1.24709	+	0.781885i	0.0570404	+	0.0357626i
$479$	−5.74735	−	4.17569i	−0.262603	−	0.190792i	0.448691	−	0.893687i	$-0.351890\pi$
$479$	−5.74735	−	4.17569i	−0.262603	−	0.190792i	−0.711294	+	0.702895i	$0.751890\pi$
$480$	−12.6416	−	0.436867i	−0.577006	−	0.0199402i
$481$	1.79150	−	1.30160i	0.0816853	−	0.0593478i
$482$	1.96058	−	0.134126i	0.0893020	−	0.00610926i
$483$	0.0956038	−	0.603618i	0.00435012	−	0.0274656i
$484$	3.53697	+	7.30773i	0.160771	+	0.332170i
$485$	−8.53961	−	3.37195i	−0.387764	−	0.153113i
$486$	0.726544	+	1.21331i	0.0329567	+	0.0550371i
$487$	−12.3757	+	24.2887i	−0.560798	+	1.10063i	0.420349	+	0.907363i	$0.361908\pi$
$487$	−12.3757	+	24.2887i	−0.560798	+	1.10063i	−0.981147	+	0.193265i	$0.938092\pi$
$488$	−17.0753	−	29.8868i	−0.772963	−	1.35291i
$489$	0.414693	+	0.134742i	0.0187531	+	0.00609324i
$490$	15.6117	+	15.4133i	0.705265	+	0.696301i
$491$	−26.7341	+	8.68645i	−1.20650	+	0.392014i	−0.842147	−	0.539249i	$-0.818708\pi$
$491$	−26.7341	+	8.68645i	−1.20650	+	0.392014i	−0.364349	+	0.931263i	$0.618708\pi$
$492$	−0.218642	+	10.6795i	−0.00985714	+	0.481471i
$493$	3.16176	+	3.16176i	0.142399	+	0.142399i
$494$	1.03614	+	0.0922256i	0.0466181	+	0.00414942i
$495$	5.07335	+	2.99406i	0.228030	+	0.134573i
$496$	−10.2836	+	27.7323i	−0.461749	+	1.24522i
$497$	2.15113	−	0.340705i	0.0964913	−	0.0152827i
$498$	9.19804	+	2.30807i	0.412174	+	0.103427i
$499$	13.3239			0.596461			0.298231	−	0.954494i	$-0.403604\pi$
$499$	13.3239			0.596461			0.298231	+	0.954494i	$0.403604\pi$
$500$	11.1175	−	19.4011i	0.497189	−	0.867642i
$501$	−10.5233			−0.470146
$502$	−17.5834	−	4.41221i	−0.784784	−	0.196926i
$503$	40.2547	−	6.37572i	1.79487	−	0.284279i	0.832105	−	0.554619i	$-0.187136\pi$
$503$	40.2547	−	6.37572i	1.79487	−	0.284279i	0.962765	+	0.270339i	$0.0871358\pi$
$504$	0.661062	−	0.250332i	0.0294460	−	0.0111507i
$505$	13.1573	+	7.76485i	0.585494	+	0.345531i
$506$	9.07503	+	0.807758i	0.403434	+	0.0359092i
$507$	9.16656	+	9.16656i	0.407101	+	0.407101i
$508$	1.18882	+	0.0243387i	0.0527455	+	0.00107986i
$509$	−24.0302	+	7.80790i	−1.06512	+	0.346079i	−0.788586	−	0.614925i	$-0.789186\pi$
$509$	−24.0302	+	7.80790i	−1.06512	+	0.346079i	−0.276536	+	0.961004i	$0.589186\pi$
$510$	−2.17096	−	2.14337i	−0.0961318	−	0.0949099i
$511$	−1.09142	−	0.354625i	−0.0482818	−	0.0156877i
$512$	−18.1237	−	13.5473i	−0.800963	−	0.598714i
$513$	−1.74736	+	3.42939i	−0.0771479	+	0.151411i
$514$	11.3019	+	18.8740i	0.498507	+	0.832497i
$515$	−17.6060	−	6.95193i	−0.775815	−	0.306339i
$516$	15.3869	−	7.44732i	0.677371	−	0.327850i
$517$	2.43619	−	15.3815i	0.107143	−	0.676477i
$518$	4.08578	−	0.279513i	0.179519	−	0.0122811i
$519$	−7.47074	+	5.42781i	−0.327929	+	0.238254i
$520$	−0.205861	+	1.19102i	−0.00902762	+	0.0522296i
$521$	4.81010	+	3.49474i	0.210734	+	0.153108i	0.688146	−	0.725572i	$-0.258425\pi$
$521$	4.81010	+	3.49474i	0.210734	+	0.153108i	−0.477412	+	0.878680i	$0.658425\pi$
$522$	5.55345	+	3.48184i	0.243068	+	0.152396i
$523$	−20.2406	−	39.7244i	−0.885059	−	1.73703i	−0.641472	−	0.767147i	$-0.721676\pi$
$523$	−20.2406	−	39.7244i	−0.885059	−	1.73703i	−0.243587	−	0.969879i	$-0.578324\pi$
$524$	−3.39411	−	24.6906i	−0.148273	−	1.07861i
$525$	−0.154326	+	1.24002i	−0.00673533	+	0.0541189i
$526$	−6.46713	+	7.41696i	−0.281980	+	0.323395i
$527$	−6.35610	+	3.23859i	−0.276876	+	0.141075i
$528$	4.39587	+	9.57741i	0.191306	+	0.416803i
$529$	10.0042	−	13.7696i	0.434964	−	0.598677i
$530$	−2.82836	−	2.02741i	−0.122856	−	0.0880651i
$531$	0.171389	+	0.235897i	0.00743766	+	0.0102371i
$532$	1.53292	+	1.16241i	0.0664606	+	0.0503967i
$533$	1.00813	+	0.159671i	0.0436668	+	0.00691614i
$534$	−7.96699	+	18.6906i	−0.344765	+	0.808822i
$535$	−7.29353	−	28.2980i	−0.315327	−	1.22343i
$536$	22.9938	−	18.4484i	0.993182	−	0.796849i
$537$	18.3645	+	9.35717i	0.792486	+	0.403792i
$538$	−23.6461	+	9.51220i	−1.01946	+	0.410100i
$539$	5.64792	−	17.3825i	0.243273	−	0.748717i
$540$	−3.80412	−	2.35131i	−0.163703	−	0.101184i
$541$	−0.192846	−	0.593520i	−0.00829111	−	0.0255174i	0.946825	−	0.321748i	$-0.104270\pi$
$541$	−0.192846	−	0.593520i	−0.00829111	−	0.0255174i	−0.955116	+	0.296230i	$0.904270\pi$
$542$	2.78365	+	3.32761i	0.119568	+	0.142933i
$543$	−3.58995	+	3.58995i	−0.154060	+	0.154060i
$544$	−1.00088	−	5.36479i	−0.0429124	−	0.230013i
$545$	−38.8308	−	8.64209i	−1.66333	−	0.370186i
$546$	−0.0150950	−	0.0658365i	−0.000646006	−	0.00281754i
$547$	−2.59743	−	16.3996i	−0.111058	−	0.701194i	−0.978898	−	0.204350i	$-0.934492\pi$
$547$	−2.59743	−	16.3996i	−0.111058	−	0.701194i	0.867840	−	0.496844i	$-0.165508\pi$
$548$	12.4928	+	17.9566i	0.533665	+	0.767068i
$549$		−	12.1696i		−	0.519385i
$550$	−18.6001	−	1.03361i	−0.793112	−	0.0440732i
$551$			17.8391i			0.759972i
$552$	−6.87535	−	0.754100i	−0.292634	−	0.0320966i
$553$	−0.462934	−	2.92285i	−0.0196860	−	0.124292i
$554$	−18.3352	+	4.20389i	−0.778987	+	0.178606i
$555$	−17.1523	−	19.4193i	−0.728076	−	0.824305i
$556$	20.7170	−	19.8858i	0.878598	−	0.843345i
$557$	4.95983	−	4.95983i	0.210155	−	0.210155i	−0.594178	−	0.804333i	$-0.702523\pi$
$557$	4.95983	−	4.95983i	0.210155	−	0.210155i	0.804333	+	0.594178i	$0.202523\pi$
$558$	−8.02085	+	6.70970i	−0.339550	+	0.284044i
$559$	−0.504764	−	1.55350i	−0.0213492	−	0.0657062i
$560$	−1.49262	+	1.66397i	−0.0630745	+	0.0703154i
$561$	−0.785398	+	2.41721i	−0.0331595	+	0.102055i
$562$	−11.3832	−	28.2973i	−0.480173	−	1.19365i
$563$	13.2206	+	6.73624i	0.557183	+	0.283899i	0.709819	−	0.704384i	$-0.248777\pi$
$563$	13.2206	+	6.73624i	0.557183	+	0.283899i	−0.152637	+	0.988282i	$0.548777\pi$
$564$	−2.08806	+	11.6366i	−0.0879234	+	0.489990i
$565$	−27.2901	+	17.3542i	−1.14810	+	0.730096i
$566$	−17.9077	−	7.63326i	−0.752716	−	0.320850i
$567$	0.246840	+	0.0390957i	0.0103663	+	0.00164186i
$568$	−5.01561	−	24.1331i	−0.210450	−	1.01260i
$569$	−15.6861	−	21.5900i	−0.657595	−	0.905102i	0.341804	−	0.939771i	$-0.388962\pi$
$569$	−15.6861	−	21.5900i	−0.657595	−	0.905102i	−0.999399	+	0.0346696i	$0.988962\pi$
$570$	−0.0778462	−	12.1710i	−0.00326062	−	0.509788i
$571$	−27.7669	+	38.2179i	−1.16201	+	1.59937i	−0.458475	+	0.888707i	$0.651604\pi$
$571$	−27.7669	+	38.2179i	−1.16201	+	1.59937i	−0.703534	+	0.710661i	$0.748396\pi$
$572$	0.963842	−	0.291500i	0.0403003	−	0.0121882i
$573$	8.74966	−	4.45817i	0.365522	−	0.186243i
$574$	1.42277	+	1.24057i	0.0593853	+	0.0517803i
$575$	6.85386	−	10.1253i	0.285826	−	0.422254i
$576$	−3.18762	−	7.33751i	−0.132817	−	0.305730i
$577$	9.35098	+	18.3523i	0.389286	+	0.764018i	0.999604	−	0.0281393i	$-0.00895819\pi$
$577$	9.35098	+	18.3523i	0.389286	+	0.764018i	−0.610318	+	0.792157i	$0.708958\pi$
$578$	−12.0717	+	19.2541i	−0.502116	+	0.800863i
$579$	15.0103	+	10.9056i	0.623807	+	0.453222i
$580$	−20.6575	−	1.70560i	−0.857754	−	0.0708212i
$581$	1.35579	−	0.985042i	0.0562478	−	0.0408664i
$582$	−0.396318	−	5.79318i	−0.0164279	−	0.240135i
$583$	−0.453529	+	2.86347i	−0.0187832	+	0.118593i
$584$	−3.41823	+	12.5299i	−0.141447	+	0.518492i
$585$	−0.272088	+	0.329517i	−0.0112495	+	0.0136238i
$586$	10.9279	−	6.54374i	0.451428	−	0.270320i
$587$	15.5526	−	30.5238i	0.641926	−	1.25985i	−0.309185	−	0.951002i	$-0.600056\pi$
$587$	15.5526	−	30.5238i	0.641926	−	1.25985i	0.951111	−	0.308849i	$-0.0999437\pi$
$588$	−4.55684	+	13.1055i	−0.187921	+	0.540460i
$589$	−27.0673	−	8.79470i	−1.11529	−	0.362379i
$590$	−0.824233	−	0.413349i	−0.0339331	−	0.0170173i
$591$	14.8966	−	4.84020i	0.612765	−	0.199099i
$592$	−5.37082	−	46.0365i	−0.220739	−	1.89209i
$593$	22.8164	+	22.8164i	0.936957	+	0.936957i	0.998127	−	0.0611702i	$-0.0194832\pi$
$593$	22.8164	+	22.8164i	0.936957	+	0.936957i	−0.0611702	+	0.998127i	$0.519483\pi$
$594$	−0.330320	+	3.71109i	−0.0135532	+	0.152268i
$595$	−0.536684	+	0.0512314i	−0.0220019	+	0.00210028i
$596$	9.70288	−	18.1164i	0.397446	−	0.742077i
$597$	−21.7409	+	3.44342i	−0.889795	+	0.140930i
$598$	−0.160856	+	0.641036i	−0.00657788	+	0.0262139i
$599$	−17.5409			−0.716703			−0.358352	−	0.933587i	$-0.616661\pi$
$599$	−17.5409			−0.716703			−0.358352	+	0.933587i	$0.616661\pi$
$600$	14.1013	+	1.07353i	0.575684	+	0.0438266i
$601$	−9.13668			−0.372693			−0.186347	−	0.982484i	$-0.559665\pi$
$601$	−9.13668			−0.372693			−0.186347	+	0.982484i	$0.559665\pi$
$602$	0.735241	−	2.93006i	0.0299662	−	0.119420i
$603$	10.2944	−	1.63047i	0.419219	−	0.0663977i
$604$	−17.7142	+	33.0745i	−0.720781	+	1.34578i
$605$	−3.61259	−	8.32710i	−0.146873	−	0.338545i
$606$	−0.856659	+	9.62442i	−0.0347994	+	0.390966i
$607$	−5.75589	−	5.75589i	−0.233624	−	0.233624i	0.580579	−	0.814204i	$-0.302826\pi$
$607$	−5.75589	−	5.75589i	−0.233624	−	0.233624i	−0.814204	+	0.580579i	$0.802826\pi$
$608$	12.3109	−	17.9580i	0.499272	−	0.728293i
$609$	1.10164	−	0.357945i	0.0446407	−	0.0145046i
$610$	17.6901	+	34.1767i	0.716253	+	1.38377i
$611$	1.07440	+	0.349093i	0.0434655	+	0.0141228i
$612$	0.633674	−	1.82244i	0.0256147	−	0.0736679i
$613$	5.36315	−	10.5258i	0.216616	−	0.425132i	−0.756971	−	0.653448i	$-0.773322\pi$
$613$	5.36315	−	10.5258i	0.216616	−	0.425132i	0.973587	+	0.228316i	$0.0733218\pi$
$614$	−34.0129	+	20.3673i	−1.37265	+	0.821956i
$615$	0.738880	−	11.9197i	0.0297945	−	0.480650i
$616$	1.79661	+	0.490125i	0.0723875	+	0.0197477i
$617$	2.22140	−	14.0254i	0.0894303	−	0.564641i	−0.901764	−	0.432228i	$-0.857728\pi$
$617$	2.22140	−	14.0254i	0.0894303	−	0.564641i	0.991195	−	0.132413i	$-0.0422724\pi$
$618$	−0.817086	−	11.9437i	−0.0328680	−	0.480448i
$619$	21.4280	−	15.5683i	0.861263	−	0.625744i	−0.0669654	−	0.997755i	$-0.521332\pi$
$619$	21.4280	−	15.5683i	0.861263	−	0.625744i	0.928228	+	0.372011i	$0.121332\pi$
$620$	12.7721	−	30.5027i	0.512938	−	1.22502i
$621$	−1.97835	−	1.43736i	−0.0793886	−	0.0576792i
$622$	−4.63457	+	7.39203i	−0.185830	+	0.296394i
$623$	1.63006	+	3.19918i	0.0653071	+	0.128172i
$624$	−0.736081	+	0.206270i	−0.0294668	+	0.00825739i
$625$	−13.3176	+	21.1575i	−0.532706	+	0.846301i
$626$	26.2340	+	22.8744i	1.04852	+	0.914246i
$627$	−9.03477	+	4.60344i	−0.360814	+	0.183844i
$628$	15.0762	−	4.55956i	0.601605	−	0.181946i
$629$	6.57057	−	9.04362i	0.261986	−	0.360593i
$630$	−0.750050	+	0.249021i	−0.0298827	+	0.00992123i
$631$	−14.7217	−	20.2627i	−0.586062	−	0.806645i	0.408282	−	0.912856i	$-0.366128\pi$
$631$	−14.7217	−	20.2627i	−0.586062	−	0.806645i	−0.994344	+	0.106211i	$0.966128\pi$
$632$	−32.7909	+	6.81498i	−1.30435	+	0.271085i
$633$	16.4954	+	2.61261i	0.655633	+	0.103842i
$634$	21.9445	+	9.35397i	0.871526	+	0.371493i
$635$	−1.32688	−	0.0822505i	−0.0526555	−	0.00326401i
$636$	0.388721	−	2.16631i	0.0154138	−	0.0858997i
$637$	1.18132	+	0.601912i	0.0468056	+	0.0238486i
$638$	6.44470	+	16.0207i	0.255148	+	0.634267i
$639$	2.69298	−	8.28813i	0.106532	−	0.327873i
$640$	19.6181	+	15.9728i	0.775473	+	0.631381i
$641$	−0.0363080	−	0.111745i	−0.00143408	−	0.00441365i	0.950337	−	0.311223i	$-0.100739\pi$
$641$	−0.0363080	−	0.111745i	−0.00143408	−	0.00441365i	−0.951771	+	0.306809i	$0.900739\pi$
$642$	14.1760	−	11.8587i	0.559483	−	0.468025i
$643$	1.07400	−	1.07400i	0.0423544	−	0.0423544i	−0.685612	−	0.727967i	$-0.740465\pi$
$643$	1.07400	−	1.07400i	0.0423544	−	0.0423544i	0.727967	+	0.685612i	$0.240465\pi$
$644$	−0.881796	+	0.846414i	−0.0347476	+	0.0333534i
$645$	−17.5333	+	7.60654i	−0.690371	+	0.299507i
$646$	5.11838	−	1.17354i	0.201380	−	0.0461724i
$647$	6.72327	+	42.4490i	0.264319	+	1.66884i	0.660618	+	0.750722i	$0.270294\pi$
$647$	6.72327	+	42.4490i	0.264319	+	1.66884i	−0.396299	+	0.918122i	$0.629706\pi$
$648$	0.308377	−	2.81157i	0.0121142	−	0.110449i
$649$			0.768184i			0.0301538i
$650$	0.285127	−	1.32092i	0.0111836	−	0.0518108i
$651$			1.84799i			0.0724283i
$652$	−0.498040	−	0.715862i	−0.0195048	−	0.0280353i
$653$	1.20930	+	7.63522i	0.0473236	+	0.298789i	0.999986	−	0.00524001i	$-0.00166795\pi$
$653$	1.20930	+	7.63522i	0.0473236	+	0.298789i	−0.952663	+	0.304029i	$0.901668\pi$
$654$	−5.62270	−	24.5233i	−0.219865	−	0.958937i
$655$	2.64789	+	27.7385i	0.103462	+	1.08383i
$656$	13.2541	−	16.7551i	0.517484	−	0.654175i
$657$	−3.24696	+	3.24696i	−0.126676	+	0.126676i
$658$	1.34052	+	1.60248i	0.0522591	+	0.0624711i
$659$	−2.77377	−	8.53679i	−0.108051	−	0.332546i	0.882384	−	0.470531i	$-0.155938\pi$
$659$	−2.77377	−	8.53679i	−0.108051	−	0.332546i	−0.990434	+	0.137985i	$0.955938\pi$
$660$	−4.46692	−	10.9023i	−0.173874	−	0.424371i
$661$	9.41319	−	28.9708i	0.366130	−	1.12683i	−0.583140	−	0.812372i	$-0.698176\pi$
$661$	9.41319	−	28.9708i	0.366130	−	1.12683i	0.949270	−	0.314462i	$-0.101824\pi$
$662$	−0.327588	+	0.131780i	−0.0127321	+	0.00512177i
$663$	−0.164274	−	0.0837018i	−0.00637988	−	0.00325071i
$664$	−11.8691	−	14.7935i	−0.460611	−	0.574100i
$665$	−1.65855	−	1.36949i	−0.0643158	−	0.0531067i
$666$	6.42555	−	15.0744i	0.248985	−	0.584121i
$667$	−11.1945	−	1.77303i	−0.433452	−	0.0686520i
$668$	16.7703	+	12.7168i	0.648861	+	0.492028i
$669$	−12.7688	−	17.5748i	−0.493671	−	0.679479i
$670$	−26.5403	+	19.5432i	−1.02534	+	0.755020i
$671$	18.8449	−	25.9378i	0.727500	−	1.00132i
$672$	−1.35600	−	0.399919i	−0.0523089	−	0.0154272i
$673$	0.846696	−	0.431413i	0.0326377	−	0.0166298i	−0.437595	−	0.899172i	$-0.644170\pi$
$673$	0.846696	−	0.431413i	0.0326377	−	0.0166298i	0.470233	+	0.882542i	$0.344170\pi$
$674$	5.98482	−	6.86381i	0.230527	−	0.264384i
$675$	4.14058	+	2.80278i	0.159371	+	0.107879i
$676$	−3.53086	−	25.6854i	−0.135802	−	0.987900i
$677$	2.75206	+	5.40123i	0.105770	+	0.207586i	0.937826	−	0.347107i	$-0.112836\pi$
$677$	2.75206	+	5.40123i	0.105770	+	0.207586i	−0.832055	+	0.554693i	$0.812836\pi$
$678$	−17.3296	−	10.8651i	−0.665540	−	0.417273i
$679$	−0.830175	−	0.603157i	−0.0318592	−	0.0231471i
$680$	0.869578	+	6.03922i	0.0333468	+	0.231594i
$681$	13.4520	−	9.77343i	0.515481	−	0.374519i
$682$	−27.4855	+	1.88032i	−1.05247	+	0.0720011i
$683$	−2.07314	+	13.0893i	−0.0793264	+	0.500847i	0.915751	+	0.401746i	$0.131597\pi$
$683$	−2.07314	+	13.0893i	−0.0793264	+	0.500847i	−0.995077	+	0.0991009i	$0.968403\pi$
$684$	6.92887	−	3.35360i	0.264932	−	0.128228i
$685$	−13.1237	−	20.6375i	−0.501430	−	0.788518i
$686$	2.53072	+	4.22626i	0.0966234	+	0.161359i
$687$	4.23038	−	8.30258i	0.161399	−	0.316763i
$688$	−33.5207	−	6.72591i	−1.27797	−	0.256423i
$689$	−0.200013	−	0.0649883i	−0.00761991	−	0.00247586i
$690$	7.64535	+	1.16083i	0.291053	+	0.0441920i
$691$	−20.1481	+	6.54650i	−0.766468	+	0.249041i	−0.666053	−	0.745905i	$-0.732017\pi$
$691$	−20.1481	+	6.54650i	−0.766468	+	0.249041i	−0.100416	+	0.994946i	$0.532017\pi$
$692$	18.4648	+	0.378030i	0.701927	+	0.0143705i
$693$	0.465566	+	0.465566i	0.0176854	+	0.0176854i
$694$	−15.3315	−	1.36464i	−0.581975	−	0.0518009i
$695$	−24.0635	+	21.2543i	−0.912781	+	0.806223i
$696$	−4.64255	−	12.2598i	−0.175975	−	0.464706i
$697$	5.08910	−	0.806034i	0.192763	−	0.0305307i
$698$	13.0572	+	3.27646i	0.494223	+	0.124016i
$699$	−13.8420			−0.523551
$700$	1.74443	−	1.78964i	0.0659333	−	0.0676421i
$701$	5.50684			0.207991			0.103995	−	0.994578i	$-0.466837\pi$
$701$	5.50684			0.207991			0.103995	+	0.994578i	$0.466837\pi$
$702$	−0.262142	−	0.0657794i	−0.00989390	−	0.00248269i
$703$	44.0487	−	6.97663i	1.66133	−	0.263129i
$704$	4.56837	−	20.5750i	0.172177	−	0.775451i
$705$	2.87149	−	12.9022i	0.108147	−	0.485927i
$706$	39.3719	+	3.50444i	1.48178	+	0.131891i
$707$	1.20741	+	1.20741i	0.0454093	+	0.0454093i
$708$	0.0119367	−	0.583047i	0.000448609	−	0.0219123i
$709$	−44.2003	+	14.3615i	−1.65998	+	0.539359i	−0.980867	−	0.194679i	$-0.937633\pi$
$709$	−44.2003	+	14.3615i	−1.65998	+	0.539359i	−0.679108	+	0.734038i	$0.737633\pi$
$710$	4.48505	+	27.1907i	0.168321	+	1.02045i
$711$	−11.2615	−	3.65909i	−0.422340	−	0.137227i
$712$	35.2830	−	20.1583i	1.32229	−	0.755465i
$713$	8.20910	−	16.1113i	0.307433	−	0.603372i
$714$	−0.175172	−	0.292534i	−0.00655566	−	0.0109478i
$715$	−1.09018	+	0.280985i	−0.0407706	+	0.0105082i
$716$	−17.9586	−	37.1043i	−0.671145	−	1.38665i
$717$	0.162819	−	1.02800i	0.00608057	−	0.0383912i
$718$	50.6120	−	3.46243i	1.88882	−	0.129217i
$719$	34.8703	−	25.3348i	1.30044	−	0.944828i	0.300484	−	0.953787i	$-0.402852\pi$
$719$	34.8703	−	25.3348i	1.30044	−	0.944828i	0.999960	+	0.00895909i	$0.00285181\pi$
$720$	3.22096	+	8.34419i	0.120038	+	0.310969i
$721$	−1.71156	−	1.24352i	−0.0637420	−	0.0463113i
$722$	−5.01564	−	3.14465i	−0.186663	−	0.117032i
$723$	−0.630856	−	1.23812i	−0.0234618	−	0.0460464i
$724$	10.0593	−	1.38281i	0.373852	−	0.0513918i
$725$	22.9969	+	2.86207i	0.854084	+	0.106294i
$726$	3.77282	−	4.32694i	0.140023	−	0.160588i
$727$	−23.0801	+	11.7599i	−0.855994	+	0.436151i	−0.826181	−	0.563405i	$-0.809491\pi$
$727$	−23.0801	+	11.7599i	−0.855994	+	0.436151i	−0.0298130	+	0.999555i	$0.509491\pi$
$728$	−0.0555038	+	0.123161i	−0.00205711	+	0.00456464i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	4.39876	−	13.8385i	0.162805	−	0.512187i
$731$	−4.84675	−	6.67098i	−0.179263	−	0.246735i
$732$	−14.7062	+	19.3938i	−0.543558	+	0.716817i
$733$	21.7312	+	3.44188i	0.802659	+	0.127129i	0.544268	−	0.838912i	$-0.316808\pi$
$733$	21.7312	+	3.44188i	0.802659	+	0.127129i	0.258391	+	0.966040i	$0.416808\pi$
$734$	−4.57884	+	10.7420i	−0.169008	+	0.396494i
$735$	5.69733	−	14.4287i	0.210149	−	0.532211i
$736$	10.0455	+	9.51023i	0.370282	+	0.350552i
$737$	24.4659	+	12.4660i	0.901212	+	0.459190i
$738$	7.00743	−	2.81890i	0.257947	−	0.103765i
$739$	−12.1629	+	37.4335i	−0.447419	+	1.37701i	0.432390	+	0.901686i	$0.357670\pi$
$739$	−12.1629	+	37.4335i	−0.447419	+	1.37701i	−0.879809	+	0.475327i	$0.842330\pi$
$740$	3.86735	+	51.6749i	0.142167	+	1.89961i
$741$	−0.227300	−	0.699557i	−0.00835007	−	0.0256989i
$742$	−0.249556	−	0.298322i	−0.00916150	−	0.0109518i
$743$	−22.1429	+	22.1429i	−0.812343	+	0.812343i	−0.984985	−	0.172642i	$-0.944770\pi$
$743$	−22.1429	+	22.1429i	−0.812343	+	0.812343i	0.172642	+	0.984985i	$0.444770\pi$
$744$	20.8906	−	1.00006i	0.765886	−	0.0366639i
$745$	−11.6779	+	19.7880i	−0.427846	+	0.724975i
$746$	−5.95947	−	25.9921i	−0.218192	−	0.951639i
$747$	−1.04899	−	6.62308i	−0.0383806	−	0.242326i
$748$	4.17269	−	2.90303i	0.152569	−	0.106145i
$749$		−	3.26612i		−	0.119342i
$750$	−15.7025	−	1.85234i	−0.573375	−	0.0676378i
$751$		−	2.21081i		−	0.0806736i	−0.999186	−	0.0403368i	$-0.987157\pi$
$751$		−	2.21081i		−	0.0806736i	0.999186	−	0.0403368i	$-0.0128431\pi$
$752$	17.3898	−	16.0212i	0.634140	−	0.584232i
$753$	2.00530	+	12.6610i	0.0730771	+	0.461391i
$754$	−1.22098	+	0.279946i	−0.0444654	+	0.0101950i
$755$	21.3200	−	36.1262i	0.775914	−	1.31477i
$756$	−0.346128	−	0.360597i	−0.0125885	−	0.0131148i
$757$	−8.95051	+	8.95051i	−0.325312	+	0.325312i	−0.850801	−	0.525489i	$-0.823882\pi$
$757$	−8.95051	+	8.95051i	−0.325312	+	0.325312i	0.525489	+	0.850801i	$0.323882\pi$
$758$	−7.71221	+	6.45151i	−0.280120	+	0.234329i
$759$	−1.99081	−	6.12707i	−0.0722617	−	0.222399i
$760$	−14.5839	+	19.4902i	−0.529015	+	0.706984i
$761$	−0.436642	+	1.34385i	−0.0158283	+	0.0487143i	−0.958659	−	0.284558i	$-0.908153\pi$
$761$	−0.436642	+	1.34385i	−0.0158283	+	0.0487143i	0.942830	+	0.333273i	$0.108153\pi$
$762$	−0.313793	−	0.780052i	−0.0113675	−	0.0282583i
$763$	−3.96156	−	2.01852i	−0.143418	−	0.0730752i
$764$	−19.3312	−	3.46877i	−0.699378	−	0.125496i
$765$	−0.792270	+	2.00645i	−0.0286446	+	0.0725435i
$766$	−39.3043	−	16.7537i	−1.42012	−	0.605336i
$767$	−0.0550384	−	0.00871722i	−0.00198732	−	0.000314761i
$768$	−3.78708	+	15.5454i	−0.136654	+	0.560945i
$769$	−12.3460	−	16.9928i	−0.445207	−	0.612774i	0.526153	−	0.850390i	$-0.323634\pi$
$769$	−12.3460	−	16.9928i	−0.445207	−	0.612774i	−0.971359	+	0.237616i	$0.923634\pi$
$770$	−1.98425	−	0.630718i	−0.0715073	−	0.0227295i
$771$	9.14344	−	12.5849i	0.329293	−	0.453233i
$772$	−10.7421	−	35.5186i	−0.386616	−	1.27834i
$773$	15.8497	−	8.07581i	0.570073	−	0.290467i	−0.145097	−	0.989417i	$-0.546349\pi$
$773$	15.8497	−	8.07581i	0.570073	−	0.290467i	0.715170	+	0.698951i	$0.246349\pi$
$774$	−9.11064	−	7.94392i	−0.327475	−	0.285538i
$775$	−15.6801	+	33.4822i	−0.563246	+	1.20272i
$776$	−6.36914	+	9.71113i	−0.228639	+	0.348609i
$777$	−1.31468	−	2.58021i	−0.0471639	−	0.0925644i
$778$	−27.3228	+	43.5792i	−0.979569	+	1.56239i
$779$	16.6306	+	12.0828i	0.595852	+	0.432912i
$780$	0.831811	−	0.196326i	0.0297836	−	0.00702959i
$781$	18.5741	−	13.4949i	0.664634	−	0.482885i
$782$	0.227710	+	3.32855i	0.00814289	+	0.119029i
$783$	0.725053	−	4.57780i	0.0259113	−	0.163597i
$784$	23.0991	−	15.3786i	0.824969	−	0.549236i
$785$	−17.0524	+	4.39509i	−0.608626	+	0.156868i
$786$	−15.1196	+	9.05377i	−0.539299	+	0.322937i
$787$	6.97641	−	13.6920i	0.248682	−	0.488066i	−0.732596	−	0.680664i	$-0.761691\pi$
$787$	6.97641	−	13.6920i	0.248682	−	0.488066i	0.981278	+	0.192598i	$0.0616913\pi$
$788$	−29.5888	−	10.2882i	−1.05406	−	0.366502i
$789$	6.61771	+	2.15022i	0.235597	+	0.0765500i
$790$	36.9455	−	6.09407i	1.31446	−	0.216817i
$791$	−3.43769	+	1.11697i	−0.122230	+	0.0397150i
$792$	5.01105	−	5.51494i	0.178060	−	0.195965i
$793$	1.64453	+	1.64453i	0.0583989	+	0.0583989i
$794$	−4.46204	+	50.1303i	−0.158352	+	1.77906i
$795$	−0.534566	+	2.40192i	−0.0189591	+	0.0851874i
$796$	38.8082	+	20.7851i	1.37552	+	0.736708i
$797$	−14.9916	+	2.37443i	−0.531028	+	0.0841066i	−0.416190	−	0.909278i	$-0.636635\pi$
$797$	−14.9916	+	2.37443i	−0.531028	+	0.0841066i	−0.114838	+	0.993384i	$0.536635\pi$
$798$	0.331086	−	1.31943i	0.0117203	−	0.0467074i
$799$	5.70276			0.201749
$800$	−21.1750	−	18.7515i	−0.748651	−	0.662964i
$801$	14.3668			0.507627
$802$	3.02733	−	12.0644i	0.106899	−	0.426008i
$803$	−11.9484	+	1.89245i	−0.421652	+	0.0667830i
$804$	−18.3758	−	9.84179i	−0.648063	−	0.347093i
$805$	1.02423	−	0.904666i	0.0360995	−	0.0318853i
$806$	0.177181	−	1.99060i	0.00624095	−	0.0701161i
$807$	12.7438	+	12.7438i	0.448604	+	0.448604i
$808$	12.9958	−	14.3026i	0.457190	−	0.503163i
$809$	12.5987	−	4.09358i	0.442948	−	0.143923i	−0.0790472	−	0.996871i	$-0.525188\pi$
$809$	12.5987	−	4.09358i	0.442948	−	0.143923i	0.521995	+	0.852948i	$0.325188\pi$
$810$	−0.474703	+	3.12644i	−0.0166793	+	0.109852i
$811$	−42.5104	−	13.8125i	−1.49274	−	0.485021i	−0.554850	−	0.831950i	$-0.687225\pi$
$811$	−42.5104	−	13.8125i	−1.49274	−	0.485021i	−0.937891	+	0.346929i	$0.887225\pi$
$812$	−2.18817	−	0.760837i	−0.0767895	−	0.0267002i
$813$	1.39271	−	2.73335i	0.0488446	−	0.0958629i
$814$	37.0383	−	22.1789i	1.29819	−	0.777370i
$815$	0.523191	+	0.822738i	0.0183266	+	0.0288193i
$816$	−3.21216	+	2.13855i	−0.112448	+	0.0748641i
$817$	5.14627	−	32.4923i	0.180045	−	1.13676i
$818$	−0.992621	−	14.5096i	−0.0347062	−	0.507317i
$819$	−0.0386398	+	0.0280735i	−0.00135018	+	0.000980966i
$820$	−15.5818	+	18.1028i	−0.544140	+	0.632176i
$821$	14.5355	+	10.5607i	0.507293	+	0.368570i	0.811796	−	0.583942i	$-0.198490\pi$
$821$	14.5355	+	10.5607i	0.507293	+	0.368570i	−0.304503	+	0.952511i	$0.598490\pi$
$822$	8.21649	−	13.1051i	0.286583	−	0.457093i
$823$	8.43710	+	16.5587i	0.294099	+	0.577202i	0.990022	−	0.140915i	$-0.0450044\pi$
$823$	8.43710	+	16.5587i	0.294099	+	0.577202i	−0.695923	+	0.718117i	$0.745004\pi$
$824$	−13.1312	+	20.0213i	−0.457447	+	0.697477i
$825$	4.48492	+	12.3856i	0.156145	+	0.431210i
$826$	−0.0776757	−	0.0677285i	−0.00270268	−	0.00235657i
$827$	29.9200	−	15.2450i	1.04042	−	0.530120i	0.151630	−	0.988437i	$-0.451548\pi$
$827$	29.9200	−	15.2450i	1.04042	−	0.530120i	0.888789	+	0.458317i	$0.151548\pi$
$828$	1.41580	+	4.68135i	0.0492026	+	0.162688i
$829$	16.7470	−	23.0502i	0.581646	−	0.800567i	−0.412229	−	0.911080i	$-0.635250\pi$
$829$	16.7470	−	23.0502i	0.581646	−	0.800567i	0.993875	+	0.110513i	$0.0352495\pi$
$830$	12.5735	+	17.0752i	0.436433	+	0.592689i
$831$	7.81833	+	10.7610i	0.271215	+	0.373295i
$832$	1.42231	+	0.560794i	0.0493096	+	0.0194420i
$833$	6.61047	+	1.04700i	0.229039	+	0.0362763i
$834$	−18.6795	−	7.96224i	−0.646817	−	0.275710i
$835$	−18.1446	−	14.9823i	−0.627920	−	0.518485i
$836$	19.9611	+	3.58181i	0.690369	+	0.123879i
$837$	6.58845	+	3.35698i	0.227730	+	0.116034i
$838$	8.67578	+	21.5669i	0.299700	+	0.745017i
$839$	−6.56174	+	20.1950i	−0.226537	+	0.697208i	0.771595	+	0.636114i	$0.219459\pi$
$839$	−6.56174	+	20.1950i	−0.226537	+	0.697208i	−0.998132	+	0.0610942i	$0.980541\pi$
$840$	1.49623	+	0.509545i	0.0516249	+	0.0175810i
$841$	2.32319	+	7.15005i	0.0801101	+	0.246554i
$842$	−20.2107	+	16.9069i	−0.696507	+	0.582651i
$843$	−15.2505	+	15.2505i	−0.525257	+	0.525257i
$844$	−23.1304	−	24.0973i	−0.796181	−	0.829463i
$845$	2.75457	+	28.8560i	0.0947602	+	0.992678i
$846$	8.14831	−	1.86825i	0.280145	−	0.0642316i
$847$	−0.158703	−	1.00201i	−0.00545309	−	0.0344295i
$848$	−3.23734	+	2.98255i	−0.111171	+	0.102421i
$849$			13.7650i			0.472414i
$850$	−0.691667	−	6.78654i	−0.0237240	−	0.232776i
$851$			28.3350i			0.971313i
$852$	−14.3073	+	9.95392i	−0.490162	+	0.341016i
$853$	0.269113	+	1.69911i	0.00921426	+	0.0581766i	0.991867	−	0.127278i	$-0.0406241\pi$
$853$	0.269113	+	1.69911i	0.00921426	+	0.0581766i	−0.982653	+	0.185455i	$0.940624\pi$
$854$	0.961230	+	4.19239i	0.0328926	+	0.143461i
$855$	−7.89539	+	3.42530i	−0.270017	+	0.117143i
$856$	−36.9219	+	1.76750i	−1.26197	+	0.0604118i
$857$	−9.07518	+	9.07518i	−0.310002	+	0.310002i	−0.844910	−	0.534908i	$-0.820346\pi$
$857$	−9.07518	+	9.07518i	−0.310002	+	0.310002i	0.534908	+	0.844910i	$0.320346\pi$
$858$	−0.456859	−	0.546134i	−0.0155969	−	0.0186447i
$859$	−1.35894	−	4.18239i	−0.0463665	−	0.142701i	0.925193	−	0.379497i	$-0.123903\pi$
$859$	−1.35894	−	4.18239i	−0.0463665	−	0.142701i	−0.971560	+	0.236795i	$0.923903\pi$
$860$	37.1336	+	9.06591i	1.26625	+	0.309145i
$861$	0.412470	−	1.26945i	0.0140569	−	0.0432628i
$862$	32.9253	−	13.2449i	1.12144	−	0.451124i
$863$	31.8073	+	16.2066i	1.08273	+	0.551679i	0.901948	−	0.431844i	$-0.142137\pi$
$863$	31.8073	+	16.2066i	1.08273	+	0.551679i	0.180783	+	0.983523i	$0.442137\pi$
$864$	−3.88906	+	4.10795i	−0.132308	+	0.139755i
$865$	−20.6091	−	1.27752i	−0.700729	−	0.0434368i
$866$	−3.49931	+	8.20940i	−0.118911	+	0.278967i
$867$	15.8715	+	2.51379i	0.539023	+	0.0853728i
$868$	2.23319	−	2.94501i	0.0757993	−	0.0999602i
$869$	−18.3362	−	25.2376i	−0.622013	−	0.856128i
$870$	4.61824	+	13.9101i	0.156573	+	0.471598i
$871$	−1.17079	+	1.61146i	−0.0396707	+	0.0546021i
$872$	−20.6745	+	45.8758i	−0.700127	+	1.55355i
$873$	−3.65845	+	1.86407i	−0.123820	+	0.0630893i
$874$	−8.74768	+	10.0324i	−0.295895	+	0.339353i
$875$	−2.03155	+	1.91837i	−0.0686789	+	0.0648526i
$876$	9.09822	−	1.25069i	0.307400	−	0.0422570i
$877$	6.92550	+	13.5921i	0.233857	+	0.458971i	0.977875	−	0.209189i	$-0.0670823\pi$
$877$	6.92550	+	13.5921i	0.233857	+	0.458971i	−0.744018	+	0.668160i	$0.767082\pi$
$878$	−8.12908	−	5.09668i	−0.274343	−	0.172005i
$879$	−7.28655	−	5.29399i	−0.245769	−	0.178562i
$880$	−6.05617	+	22.7722i	−0.204153	+	0.767652i
$881$	27.0196	−	19.6309i	0.910313	−	0.661381i	−0.0307807	−	0.999526i	$-0.509799\pi$
$881$	27.0196	−	19.6309i	0.910313	−	0.661381i	0.941094	+	0.338145i	$0.109799\pi$
$882$	9.78829	−	0.669628i	0.329589	−	0.0225476i
$883$	3.46901	−	21.9024i	0.116741	−	0.737076i	−0.857985	−	0.513674i	$-0.828284\pi$
$883$	3.46901	−	21.9024i	0.116741	−	0.737076i	0.974727	−	0.223401i	$-0.0717160\pi$
$884$	0.160644	+	0.331906i	0.00540303	+	0.0111632i
$885$	−0.0403390	+	0.650754i	−0.00135598	+	0.0218749i
$886$	−26.9982	−	45.0864i	−0.907022	−	1.51471i
$887$	−10.7076	+	21.0148i	−0.359526	+	0.705609i	−0.997945	−	0.0640801i	$-0.979589\pi$
$887$	−10.7076	+	21.0148i	−0.359526	+	0.705609i	0.638419	+	0.769689i	$0.279589\pi$
$888$	−28.4565	+	16.2581i	−0.954939	+	0.545587i
$889$	−0.141313	−	0.0459152i	−0.00473947	−	0.00153995i
$890$	−40.3474	+	20.8842i	−1.35245	+	0.700038i
$891$	2.50557	−	0.814109i	0.0839398	−	0.0272737i
$892$	−0.889306	+	43.4381i	−0.0297762	+	1.45441i
$893$	16.0879	+	16.0879i	0.538361	+	0.538361i
$894$	−14.4746	−	1.28837i	−0.484104	−	0.0430896i
$895$	18.3426	+	42.2801i	0.613124	+	1.41327i
$896$	1.67769	+	2.27598i	0.0560476	+	0.0760350i
$897$	0.461580	−	0.0731072i	0.0154117	−	0.00244098i
$898$	16.9191	+	4.24553i	0.564599	+	0.141675i
$899$	34.2720			1.14304
$900$	−3.21157	−	9.47026i	−0.107052	−	0.315675i
$901$	−1.06164			−0.0353685
$902$	19.3005	+	4.84310i	0.642638	+	0.161258i
$903$	−2.10980	+	0.334159i	−0.0702096	+	0.0111201i
$904$	14.4872	+	38.2569i	0.481836	+	1.27241i
$905$	−11.3011	+	1.07879i	−0.375660	+	0.0358602i
$906$	26.4258	+	2.35213i	0.877940	+	0.0781444i
$907$	26.5114	+	26.5114i	0.880297	+	0.880297i	0.993564	−	0.113268i	$-0.0361319\pi$
$907$	26.5114	+	26.5114i	0.880297	+	0.880297i	−0.113268	+	0.993564i	$0.536132\pi$
$908$	−33.2481	−	0.680688i	−1.10338	−	0.0225894i
$909$	6.49800	−	2.11133i	0.215525	−	0.0700283i
$910$	0.0677063	−	0.135009i	0.00224444	−	0.00447550i
$911$	40.0136	+	13.0012i	1.32571	+	0.430749i	0.884452	−	0.466631i	$-0.154533\pi$
$911$	40.0136	+	13.0012i	1.32571	+	0.430749i	0.441258	+	0.897381i	$0.354533\pi$
$912$	−15.0947	−	3.02874i	−0.499836	−	0.100292i
$913$	8.02024	−	15.7406i	0.265431	−	0.520938i
$914$	−21.6948	−	36.2299i	−0.717600	−	1.19838i
$915$	17.3262	−	20.9832i	0.572787	−	0.693684i
$916$	−16.7749	+	8.11910i	−0.554257	+	0.268263i
$917$	−0.487187	+	3.07598i	−0.0160883	+	0.101578i
$918$	−1.36116	+	0.0931184i	−0.0449249	+	0.00307336i
$919$	34.7296	−	25.2325i	1.14562	−	0.832345i	0.157731	−	0.987482i	$-0.449582\pi$
$919$	34.7296	−	25.2325i	1.14562	−	0.832345i	0.987893	+	0.155138i	$0.0495821\pi$
$920$	−10.7811	−	11.0889i	−0.355442	−	0.365590i
$921$	22.6792	+	16.4774i	0.747306	+	0.542950i
$922$	−48.8970	−	30.6569i	−1.61034	−	1.00963i
$923$	0.756098	+	1.48393i	0.0248873	+	0.0488440i
$924$	−0.179331	−	1.30455i	−0.00589956	−	0.0429166i
$925$	−1.92671	−	57.9038i	−0.0633497	−	1.90387i
$926$	−37.1310	+	42.5845i	−1.22020	+	1.39941i
$927$	−7.54259	+	3.84314i	−0.247731	+	0.126225i
$928$	−7.41675	+	25.1479i	−0.243467	+	0.825519i
$929$	−17.0062	+	23.4070i	−0.557956	+	0.767960i	−0.991065	−	0.133381i	$-0.957416\pi$
$929$	−17.0062	+	23.4070i	−0.557956	+	0.767960i	0.433109	+	0.901341i	$0.357416\pi$
$930$	−23.3826	+	0.149556i	−0.766747	+	0.00490414i
$931$	15.6950	+	21.6023i	0.514381	+	0.707985i
$932$	22.0590	+	16.7272i	0.722566	+	0.547918i
$933$	6.09338	+	0.965097i	0.199488	+	0.0315959i
$934$	11.2947	−	26.4974i	0.369573	−	0.867022i
$935$	−4.79567	+	3.04963i	−0.156835	+	0.0997337i
$936$	0.338267	+	0.421612i	0.0110566	+	0.0137808i
$937$	−20.3509	−	10.3693i	−0.664836	−	0.338751i	0.0887940	−	0.996050i	$-0.471699\pi$
$937$	−20.3509	−	10.3693i	−0.664836	−	0.338751i	−0.753630	+	0.657299i	$0.771699\pi$
$938$	−3.41760	+	1.37481i	−0.111588	+	0.0448890i
$939$	7.60541	−	23.4070i	0.248193	−	0.763860i
$940$	−20.1677	+	17.0914i	−0.657799	+	0.557460i
$941$	−3.11642	−	9.59135i	−0.101592	−	0.312669i	0.887323	−	0.461148i	$-0.152562\pi$
$941$	−3.11642	−	9.59135i	−0.101592	−	0.312669i	−0.988916	+	0.148479i	$0.952562\pi$
$942$	−7.14607	−	8.54248i	−0.232831	−	0.278329i
$943$	−9.23518	+	9.23518i	−0.300739	+	0.300739i
$944$	−0.723602	+	0.914738i	−0.0235512	+	0.0297722i
$945$	0.369949	+	0.418845i	0.0120344	+	0.0136250i
$946$	−7.11673	−	31.0395i	−0.231385	−	1.00918i
$947$	6.29820	+	39.7653i	0.204664	+	1.29220i	0.849382	+	0.527778i	$0.176975\pi$
$947$	6.29820	+	39.7653i	0.204664	+	1.29220i	−0.644718	+	0.764420i	$0.723025\pi$
$948$	13.5249	+	19.4402i	0.439269	+	0.631387i
$949$		−	0.877551i		−	0.0284865i
$950$	17.1941	−	21.0965i	0.557849	−	0.684462i
$951$		−	16.8680i		−	0.546981i
$952$	−0.0743508	+	0.677878i	−0.00240972	+	0.0219702i
$953$	−2.29969	−	14.5197i	−0.0744943	−	0.470338i	−0.996530	−	0.0832336i	$-0.973475\pi$
$953$	−2.29969	−	14.5197i	−0.0744943	−	0.470338i	0.922036	−	0.387105i	$-0.126525\pi$
$954$	−1.51692	+	0.347798i	−0.0491120	+	0.0112604i
$955$	21.4337	+	4.77023i	0.693579	+	0.154361i
$956$	−1.50175	+	1.44149i	−0.0485700	+	0.0466211i
$957$	8.63421	−	8.63421i	0.279104	−	0.279104i
$958$	7.70598	−	6.44630i	0.248969	−	0.208271i
$959$	−0.844683	−	2.59967i	−0.0272762	−	0.0839476i
$960$	4.95046	−	17.1899i	0.159775	−	0.554802i
$961$	−7.31661	+	22.5182i	−0.236020	+	0.726394i
$962$	1.16876	+	2.90538i	0.0376822	+	0.0936733i
$963$	−11.6444	−	5.93312i	−0.375236	−	0.191192i
$964$	−0.490851	+	2.73547i	−0.0158092	+	0.0881036i
$965$	10.3546	+	40.1745i	0.333326	+	1.29326i
$966$	0.795069	+	0.338903i	0.0255809	+	0.0109040i
$967$	−46.6505	−	7.38871i	−1.50018	−	0.237605i	−0.648316	−	0.761371i	$-0.724527\pi$
$967$	−46.6505	−	7.38871i	−1.50018	−	0.237605i	−0.851862	+	0.523766i	$0.824527\pi$
$968$	−11.2413	+	2.33630i	−0.361311	+	0.0750917i
$969$	−2.18254	−	3.00401i	−0.0701132	−	0.0965025i
$970$	7.56459	−	10.5531i	0.242884	−	0.338838i
$971$	9.67925	−	13.3223i	0.310622	−	0.427534i	−0.624953	−	0.780662i	$-0.714882\pi$
$971$	9.67925	−	13.3223i	0.310622	−	0.427534i	0.935575	+	0.353128i	$0.114882\pi$
$972$	−1.91436	+	0.578971i	−0.0614033	+	0.0185705i
$973$	−3.19727	+	1.62909i	−0.102500	+	0.0522262i
$974$	−29.0568	−	25.3358i	−0.931041	−	0.811811i
$975$	−0.938287	+	0.180784i	−0.0300492	+	0.00578971i
$976$	46.8727	−	13.1350i	1.50036	−	0.420441i
$977$	−3.65591	−	7.17512i	−0.116963	−	0.229552i	0.825102	−	0.564984i	$-0.191118\pi$
$977$	−3.65591	−	7.17512i	−0.116963	−	0.229552i	−0.942064	+	0.335432i	$0.891118\pi$
$978$	−0.327560	+	0.522451i	−0.0104742	+	0.0167061i
$979$	30.6210	+	22.2474i	0.978651	+	0.711031i
$980$	−26.5157	+	16.1092i	−0.847014	+	0.514589i
$981$	−14.3928	+	10.4570i	−0.459528	+	0.333867i
$982$	−2.71324	−	39.6608i	−0.0865830	−	1.26563i
$983$	5.96372	−	37.6535i	0.190213	−	1.20096i	−0.689082	−	0.724683i	$-0.741986\pi$
$983$	5.96372	−	37.6535i	0.190213	−	1.20096i	0.879296	−	0.476276i	$-0.158014\pi$
$984$	−14.5738	−	3.97580i	−0.464594	−	0.126744i
$985$	32.5764	+	12.8631i	1.03797	+	0.409854i
$986$	−5.42523	+	3.24868i	−0.172774	+	0.103459i
$987$	0.670689	−	1.31630i	0.0213483	−	0.0418983i
$988$	−0.483143	+	1.38952i	−0.0153708	+	0.0442064i
$989$	19.8782	+	6.45882i	0.632090	+	0.205379i
$990$	−5.85315	+	5.92851i	−0.186025	+	0.188420i
$991$	−20.3267	+	6.60455i	−0.645699	+	0.209800i	−0.613517	−	0.789682i	$-0.710246\pi$
$991$	−20.3267	+	6.60455i	−0.645699	+	0.209800i	−0.0321823	+	0.999482i	$0.510246\pi$
$992$	−34.5004	−	23.6514i	−1.09539	−	0.750931i
$993$	0.176550	+	0.176550i	0.00560266	+	0.00560266i
$994$	−0.273074	+	3.06795i	−0.00866139	+	0.0973093i
$995$	−42.3889	−	25.0159i	−1.34382	−	0.793059i
$996$	−6.33191	+	11.8224i	−0.200634	+	0.374607i
$997$	−40.7447	+	6.45333i	−1.29040	+	0.204379i	−0.763643	−	0.645639i	$-0.776591\pi$
$997$	−40.7447	+	6.45333i	−1.29040	+	0.204379i	−0.526755	+	0.850017i	$0.676591\pi$
$998$	−4.58608	+	18.2763i	−0.145170	+	0.578525i
$999$	−11.5872			−0.366602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.103.13	yes	240
3.2	odd	2		900.2.bj.f.703.18		240
4.3	odd	2	inner	300.2.w.a.103.27	yes	240
12.11	even	2		900.2.bj.f.703.4		240
25.17	odd	20	inner	300.2.w.a.67.27	yes	240
75.17	even	20		900.2.bj.f.667.4		240
100.67	even	20	inner	300.2.w.a.67.13	✓	240
300.167	odd	20		900.2.bj.f.667.18		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.13	✓	240	100.67	even	20	inner
300.2.w.a.67.27	yes	240	25.17	odd	20	inner
300.2.w.a.103.13	yes	240	1.1	even	1	trivial
300.2.w.a.103.27	yes	240	4.3	odd	2	inner
900.2.bj.f.667.4		240	75.17	even	20
900.2.bj.f.667.18		240	300.167	odd	20
900.2.bj.f.703.4		240	12.11	even	2
900.2.bj.f.703.18		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.344199 + 1.37169i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.76305 - 0.944266i) q^{4} +(1.92573 + 1.13647i) q^{5} +(-0.125382 + 1.40864i) q^{6} +(0.176718 + 0.176718i) q^{7} +(1.90208 - 2.09335i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.344199 + 1.37169i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.76305 - 0.944266i) q^{4} +(1.92573 + 1.13647i) q^{5} +(-0.125382 + 1.40864i) q^{6} +(0.176718 + 0.176718i) q^{7} +(1.90208 - 2.09335i) q^{8} +(0.951057 - 0.309017i) q^{9} +(-2.22172 + 2.25032i) q^{10} +(2.50557 + 0.814109i) q^{11} +(-1.88906 - 0.656838i) q^{12} +(-0.0867616 + 0.170279i) q^{13} +(-0.303228 + 0.181576i) q^{14} +(2.07980 + 0.821232i) q^{15} +(2.21672 + 3.32959i) q^{16} +(-0.150917 + 0.952856i) q^{17} +(0.0965224 + 1.41092i) q^{18} +(-3.11382 + 2.26232i) q^{19} +(-2.32203 - 3.82207i) q^{20} +(0.202187 + 0.146898i) q^{21} +(-1.97912 + 3.15664i) q^{22} +(-1.11018 - 2.17885i) q^{23} +(1.55119 - 2.36512i) q^{24} +(2.41685 + 4.37708i) q^{25} +(-0.203707 - 0.177620i) q^{26} +(0.891007 - 0.453990i) q^{27} +(-0.144695 - 0.478433i) q^{28} +(2.72431 - 3.74969i) q^{29} +(-1.84234 + 2.57017i) q^{30} +(4.34632 + 5.98219i) q^{31} +(-5.33014 + 1.89461i) q^{32} +(2.60208 + 0.412129i) q^{33} +(-1.25507 - 0.534983i) q^{34} +(0.139475 + 0.541147i) q^{35} +(-1.96856 - 0.353237i) q^{36} +(-10.3242 - 5.26047i) q^{37} +(-2.03143 - 5.04988i) q^{38} +(-0.0590559 + 0.181755i) q^{39} +(6.04192 - 1.86955i) q^{40} +(-1.65043 - 5.07949i) q^{41} +(-0.271090 + 0.226776i) q^{42} +(-6.04379 + 6.04379i) q^{43} +(-3.64872 - 3.80124i) q^{44} +(2.18267 + 0.485769i) q^{45} +(3.37082 - 0.772862i) q^{46} +(-0.924721 - 5.83846i) q^{47} +(2.71029 + 2.94182i) q^{48} -6.93754i q^{49} +(-6.83586 + 1.80858i) q^{50} +0.964733i q^{51} +(0.313755 - 0.218286i) q^{52} +(0.172149 + 1.08691i) q^{53} +(0.316050 + 1.37845i) q^{54} +(3.89983 + 4.41527i) q^{55} +(0.706064 - 0.0338001i) q^{56} +(-2.72158 + 2.72158i) q^{57} +(4.20570 + 5.02753i) q^{58} +(0.0901046 + 0.277314i) q^{59} +(-2.89134 - 3.41176i) q^{60} +(3.76061 - 11.5740i) q^{61} +(-9.70169 + 3.90273i) q^{62} +(0.222678 + 0.113460i) q^{63} +(-0.764188 - 7.96342i) q^{64} +(-0.360597 + 0.229309i) q^{65} +(-1.46094 + 3.42738i) q^{66} +(10.2944 + 1.63047i) q^{67} +(1.16583 - 1.53743i) q^{68} +(-1.43736 - 1.97835i) q^{69} +(-0.790291 + 0.00505473i) q^{70} +(5.12235 - 7.05030i) q^{71} +(1.16211 - 2.57866i) q^{72} +(-4.09140 + 2.08467i) q^{73} +(10.7693 - 12.3510i) q^{74} +(3.07182 + 3.94511i) q^{75} +(7.62607 - 1.04832i) q^{76} +(0.298912 + 0.586648i) q^{77} +(-0.228985 - 0.143566i) q^{78} +(-9.57962 - 6.96000i) q^{79} +(0.484816 + 8.93112i) q^{80} +(0.809017 - 0.587785i) q^{81} +(7.53555 - 0.515516i) q^{82} +(1.04899 - 6.62308i) q^{83} +(-0.217757 - 0.449907i) q^{84} +(-1.37352 + 1.66343i) q^{85} +(-6.20993 - 10.3705i) q^{86} +(2.10419 - 4.12970i) q^{87} +(6.47000 - 3.69652i) q^{88} +(13.6637 + 4.43960i) q^{89} +(-1.41759 + 2.82673i) q^{90} +(-0.0454238 + 0.0147591i) q^{91} +(-0.100107 + 4.88974i) q^{92} +(5.22863 + 5.22863i) q^{93} +(8.32683 + 0.741161i) q^{94} +(-8.56744 + 0.817841i) q^{95} +(-4.96814 + 2.70510i) q^{96} +(-4.05542 + 0.642315i) q^{97} +(9.51614 + 2.38789i) q^{98} +2.63451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more