LMFDB - Embedded newform 234.2.z.a.41.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.6
Character	$\chi$	$=$	234.41
Dual form			234.2.z.a.137.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.60665 - 0.647043i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.84756 - 0.763001i) q^{5} +(-1.38444 + 1.04083i) q^{6} +(-1.37958 - 1.37958i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.16267 - 2.07915i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.60665 - 0.647043i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.84756 - 0.763001i) q^{5} +(-1.38444 + 1.04083i) q^{6} +(-1.37958 - 1.37958i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.16267 - 2.07915i) q^{9} +(-2.55305 + 1.47400i) q^{10} +(0.207457 + 0.774238i) q^{11} +(1.06788 - 1.36368i) q^{12} +(-3.58657 - 0.369493i) q^{13} +(1.68964 + 0.975511i) q^{14} +(4.08135 - 3.06837i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.02058 + 6.96385i) q^{17} +(-1.55086 + 2.56804i) q^{18} +(-1.18319 - 4.41574i) q^{19} +(2.08456 - 2.08456i) q^{20} +(-3.10916 - 1.32386i) q^{21} +(-0.400775 - 0.694163i) q^{22} +6.99376 q^{23} +(-0.678548 + 1.59360i) q^{24} +(3.19629 - 1.84538i) q^{25} +(3.55999 - 0.571370i) q^{26} +(2.12937 - 4.73981i) q^{27} +(-1.88454 - 0.504962i) q^{28} +(6.82146 + 3.93837i) q^{29} +(-3.14812 + 4.02015i) q^{30} +(0.619046 + 2.31031i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.834276 + 1.10970i) q^{33} +(2.08121 - 7.76717i) q^{34} +(-4.98106 - 2.87582i) q^{35} +(0.833356 - 2.88193i) q^{36} +(-2.09658 + 7.82455i) q^{37} +(2.28576 + 3.95904i) q^{38} +(-6.00145 + 1.72702i) q^{39} +(-1.47400 + 2.55305i) q^{40} +(-3.66359 - 3.66359i) q^{41} +(3.34586 + 0.474043i) q^{42} +2.33382i q^{43} +(0.566782 + 0.566782i) q^{44} +(4.57194 - 7.57061i) q^{45} +(-6.75546 + 1.81012i) q^{46} +(-5.14869 - 1.37959i) q^{47} +(0.242972 - 1.71492i) q^{48} -3.19351i q^{49} +(-2.60976 + 2.60976i) q^{50} +(-1.95377 + 13.7900i) q^{51} +(-3.29081 + 1.47329i) q^{52} +8.27924i q^{53} +(-0.830059 + 5.12943i) q^{54} +(1.18149 + 2.04640i) q^{55} +1.95102 q^{56} +(-4.75815 - 6.32899i) q^{57} +(-7.60835 - 2.03865i) q^{58} +(-8.52709 - 2.28483i) q^{59} +(2.00036 - 4.69796i) q^{60} -4.93917 q^{61} +(-1.19590 - 2.07137i) q^{62} +(-5.85193 - 0.115230i) q^{63} -1.00000i q^{64} +(-10.4949 + 1.68440i) q^{65} +(-1.09306 - 0.855961i) q^{66} +(0.549015 - 0.549015i) q^{67} +8.04117i q^{68} +(11.2366 - 4.52526i) q^{69} +(5.55565 + 1.48863i) q^{70} +(-2.57304 + 0.689443i) q^{71} +(-0.0590613 + 2.99942i) q^{72} +(5.68293 + 5.68293i) q^{73} -8.10057i q^{74} +(3.94129 - 5.03302i) q^{75} +(-3.23255 - 3.23255i) q^{76} +(0.781921 - 1.35433i) q^{77} +(5.34997 - 3.22146i) q^{78} +(0.554497 + 0.960416i) q^{79} +(0.763001 - 2.84756i) q^{80} +(0.354299 - 8.99302i) q^{81} +(4.48696 + 2.59055i) q^{82} +(0.614312 - 2.29264i) q^{83} +(-3.35454 + 0.408081i) q^{84} +(-6.13542 + 22.8977i) q^{85} +(-0.604036 - 2.25429i) q^{86} +(13.5080 + 1.91382i) q^{87} +(-0.694163 - 0.400775i) q^{88} +(-2.84070 - 0.761164i) q^{89} +(-2.45674 + 8.49595i) q^{90} +(4.43822 + 5.45771i) q^{91} +(6.05678 - 3.49688i) q^{92} +(2.48946 + 3.31132i) q^{93} +5.33031 q^{94} +(-6.73843 - 11.6713i) q^{95} +(0.209163 + 1.71938i) q^{96} +(2.59780 - 2.59780i) q^{97} +(0.826542 + 3.08469i) q^{98} +(2.05842 + 1.24309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	1.60665	−	0.647043i	0.927602	−	0.373570i
$3$	1.60665	−	0.647043i	0.927602	−	0.373570i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.84756	−	0.763001i	1.27347	−	0.341224i	0.442109	−	0.896962i	$-0.354231\pi$
$5$	2.84756	−	0.763001i	1.27347	−	0.341224i	0.831358	+	0.555737i	$0.187564\pi$
$6$	−1.38444	+	1.04083i	−0.565196	+	0.424916i
$7$	−1.37958	−	1.37958i	−0.521433	−	0.521433i	0.396571	−	0.918004i	$-0.370200\pi$
$7$	−1.37958	−	1.37958i	−0.521433	−	0.521433i	−0.918004	+	0.396571i	$0.870200\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.16267	−	2.07915i	0.720891	−	0.693049i
$10$	−2.55305	+	1.47400i	−0.807345	+	0.466121i
$11$	0.207457	+	0.774238i	0.0625505	+	0.233442i	0.990123	−	0.140202i	$-0.0447751\pi$
$11$	0.207457	+	0.774238i	0.0625505	+	0.233442i	−0.927572	+	0.373643i	$0.878108\pi$
$12$	1.06788	−	1.36368i	0.308271	−	0.393661i
$13$	−3.58657	−	0.369493i	−0.994735	−	0.102479i
$13$	−3.58657	−	0.369493i	−0.994735	−	0.102479i
$14$	1.68964	+	0.975511i	0.451574	+	0.260716i
$15$	4.08135	−	3.06837i	1.05380	−	0.792250i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.02058	+	6.96385i	−0.975135	+	1.68898i	−0.295645	+	0.955298i	$0.595535\pi$
$17$	−4.02058	+	6.96385i	−0.975135	+	1.68898i	−0.679490	+	0.733685i	$0.737799\pi$
$18$	−1.55086	+	2.56804i	−0.365541	+	0.605293i
$19$	−1.18319	−	4.41574i	−0.271443	−	1.01304i	−0.958188	−	0.286141i	$-0.907627\pi$
$19$	−1.18319	−	4.41574i	−0.271443	−	1.01304i	0.686744	−	0.726899i	$-0.259039\pi$
$20$	2.08456	−	2.08456i	0.466121	−	0.466121i
$21$	−3.10916	−	1.32386i	−0.678474	−	0.288890i
$22$	−0.400775	−	0.694163i	−0.0854456	−	0.147996i
$23$	6.99376			1.45830			0.729150	−	0.684354i	$-0.239916\pi$
$23$	6.99376			1.45830			0.729150	+	0.684354i	$0.239916\pi$
$24$	−0.678548	+	1.59360i	−0.138508	+	0.325293i
$25$	3.19629	−	1.84538i	0.639258	−	0.369076i
$26$	3.55999	−	0.571370i	0.698172	−	0.112055i
$27$	2.12937	−	4.73981i	0.409797	−	0.912177i
$28$	−1.88454	−	0.504962i	−0.356145	−	0.0954288i
$29$	6.82146	+	3.93837i	1.26671	+	0.731337i	0.974365	−	0.224975i	$-0.0722300\pi$
$29$	6.82146	+	3.93837i	1.26671	+	0.731337i	0.292348	+	0.956312i	$0.405563\pi$
$30$	−3.14812	+	4.02015i	−0.574766	+	0.733975i
$31$	0.619046	+	2.31031i	0.111184	+	0.414944i	0.998973	−	0.0453062i	$-0.0144263\pi$
$31$	0.619046	+	2.31031i	0.111184	+	0.414944i	−0.887789	+	0.460250i	$0.847760\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.834276	+	1.10970i	0.145229	+	0.193174i
$34$	2.08121	−	7.76717i	0.356924	−	1.33206i
$35$	−4.98106	−	2.87582i	−0.841953	−	0.486102i
$36$	0.833356	−	2.88193i	0.138893	−	0.480322i
$37$	−2.09658	+	7.82455i	−0.344676	+	1.28635i	0.548314	+	0.836272i	$0.315270\pi$
$37$	−2.09658	+	7.82455i	−0.344676	+	1.28635i	−0.892990	+	0.450076i	$0.851397\pi$
$38$	2.28576	+	3.95904i	0.370798	+	0.642242i
$39$	−6.00145	+	1.72702i	−0.961001	+	0.276544i
$40$	−1.47400	+	2.55305i	−0.233061	+	0.403673i
$41$	−3.66359	−	3.66359i	−0.572156	−	0.572156i	0.360574	−	0.932730i	$-0.382581\pi$
$41$	−3.66359	−	3.66359i	−0.572156	−	0.572156i	−0.932730	+	0.360574i	$0.882581\pi$
$42$	3.34586	+	0.474043i	0.516277	+	0.0731464i
$43$			2.33382i			0.355904i	0.984039	+	0.177952i	$0.0569471\pi$
$43$			2.33382i			0.355904i	−0.984039	+	0.177952i	$0.943053\pi$
$44$	0.566782	+	0.566782i	0.0854456	+	0.0854456i
$45$	4.57194	−	7.57061i	0.681545	−	1.12856i
$46$	−6.75546	+	1.81012i	−0.996038	+	0.266887i
$47$	−5.14869	−	1.37959i	−0.751013	−	0.201233i	−0.137046	−	0.990565i	$-0.543761\pi$
$47$	−5.14869	−	1.37959i	−0.751013	−	0.201233i	−0.613968	+	0.789331i	$0.710427\pi$
$48$	0.242972	−	1.71492i	0.0350699	−	0.247528i
$49$		−	3.19351i		−	0.456216i
$50$	−2.60976	+	2.60976i	−0.369076	+	0.369076i
$51$	−1.95377	+	13.7900i	−0.273583	+	1.93099i
$52$	−3.29081	+	1.47329i	−0.456353	+	0.204309i
$53$			8.27924i			1.13724i	0.822600	+	0.568620i	$0.192523\pi$
$53$			8.27924i			1.13724i	−0.822600	+	0.568620i	$0.807477\pi$
$54$	−0.830059	+	5.12943i	−0.112957	+	0.698026i
$55$	1.18149	+	2.04640i	0.159312	+	0.275936i
$56$	1.95102			0.260716
$57$	−4.75815	−	6.32899i	−0.630233	−	0.838295i
$58$	−7.60835	−	2.03865i	−0.999025	−	0.267688i
$59$	−8.52709	−	2.28483i	−1.11013	−	0.297459i	−0.343248	−	0.939245i	$-0.611527\pi$
$59$	−8.52709	−	2.28483i	−1.11013	−	0.297459i	−0.766884	+	0.641786i	$0.778194\pi$
$60$	2.00036	−	4.69796i	0.258246	−	0.606504i
$61$	−4.93917			−0.632396			−0.316198	−	0.948693i	$-0.602406\pi$
$61$	−4.93917			−0.632396			−0.316198	+	0.948693i	$0.602406\pi$
$62$	−1.19590	−	2.07137i	−0.151880	−	0.263064i
$63$	−5.85193	−	0.115230i	−0.737274	−	0.0145176i
$64$		−	1.00000i		−	0.125000i
$65$	−10.4949	+	1.68440i	−1.30173	+	0.208924i
$66$	−1.09306	−	0.855961i	−0.134546	−	0.105362i
$67$	0.549015	−	0.549015i	0.0670729	−	0.0670729i	−0.672775	−	0.739847i	$-0.734898\pi$
$67$	0.549015	−	0.549015i	0.0670729	−	0.0670729i	0.739847	+	0.672775i	$0.234898\pi$
$68$			8.04117i			0.975135i
$69$	11.2366	−	4.52526i	1.35272	−	0.544777i
$70$	5.55565	+	1.48863i	0.664027	+	0.177926i
$71$	−2.57304	+	0.689443i	−0.305363	+	0.0818218i	−0.408247	−	0.912872i	$-0.633860\pi$
$71$	−2.57304	+	0.689443i	−0.305363	+	0.0818218i	0.102884	+	0.994693i	$0.467193\pi$
$72$	−0.0590613	+	2.99942i	−0.00696045	+	0.353485i
$73$	5.68293	+	5.68293i	0.665137	+	0.665137i	0.956586	−	0.291449i	$-0.0941375\pi$
$73$	5.68293	+	5.68293i	0.665137	+	0.665137i	−0.291449	+	0.956586i	$0.594137\pi$
$74$		−	8.10057i		−	0.941672i
$75$	3.94129	−	5.03302i	0.455101	−	0.581163i
$76$	−3.23255	−	3.23255i	−0.370798	−	0.370798i
$77$	0.781921	−	1.35433i	0.0891082	−	0.154340i
$78$	5.34997	−	3.22146i	0.605765	−	0.364758i
$79$	0.554497	+	0.960416i	0.0623857	+	0.108055i	0.895531	−	0.444998i	$-0.146796\pi$
$79$	0.554497	+	0.960416i	0.0623857	+	0.108055i	−0.833146	+	0.553054i	$0.813462\pi$
$80$	0.763001	−	2.84756i	0.0853061	−	0.318367i
$81$	0.354299	−	8.99302i	0.0393666	−	0.999225i
$82$	4.48696	+	2.59055i	0.495502	+	0.286078i
$83$	0.614312	−	2.29264i	0.0674295	−	0.251650i	−0.923981	−	0.382439i	$-0.875084\pi$
$83$	0.614312	−	2.29264i	0.0674295	−	0.251650i	0.991410	+	0.130789i	$0.0417509\pi$
$84$	−3.35454	+	0.408081i	−0.366010	+	0.0445253i
$85$	−6.13542	+	22.8977i	−0.665479	+	2.48360i
$86$	−0.604036	−	2.25429i	−0.0651349	−	0.243087i
$87$	13.5080	+	1.91382i	1.44821	+	0.205183i
$88$	−0.694163	−	0.400775i	−0.0739980	−	0.0427228i
$89$	−2.84070	−	0.761164i	−0.301114	−	0.0806832i	0.105099	−	0.994462i	$-0.466484\pi$
$89$	−2.84070	−	0.761164i	−0.301114	−	0.0806832i	−0.406213	+	0.913779i	$0.633151\pi$
$90$	−2.45674	+	8.49595i	−0.258963	+	0.895552i
$91$	4.43822	+	5.45771i	0.465252	+	0.572123i
$92$	6.05678	−	3.49688i	0.631463	−	0.364575i
$93$	2.48946	+	3.31132i	0.258145	+	0.343368i
$94$	5.33031			0.549780
$95$	−6.73843	−	11.6713i	−0.691348	−	1.19745i
$96$	0.209163	+	1.71938i	0.0213476	+	0.175483i
$97$	2.59780	−	2.59780i	0.263767	−	0.263767i	−0.562816	−	0.826582i	$-0.690282\pi$
$97$	2.59780	−	2.59780i	0.263767	−	0.263767i	0.826582	+	0.562816i	$0.190282\pi$
$98$	0.826542	+	3.08469i	0.0834933	+	0.311601i
$99$	2.05842	+	1.24309i	0.206878	+	0.124935i
$100$	1.84538	−	3.19629i	0.184538	−	0.319629i
$101$	−6.82190	+	11.8159i	−0.678804	+	1.17572i	0.296537	+	0.955021i	$0.404168\pi$
$101$	−6.82190	+	11.8159i	−0.678804	+	1.17572i	−0.975341	+	0.220702i	$0.929165\pi$
$102$	−1.68191	−	13.8258i	−0.166534	−	1.36896i
$103$	−11.6669	−	6.73592i	−1.14958	−	0.663710i	−0.200794	−	0.979633i	$-0.564352\pi$
$103$	−11.6669	−	6.73592i	−1.14958	−	0.663710i	−0.948785	+	0.315924i	$0.897686\pi$
$104$	2.79736	−	2.27482i	0.274304	−	0.223064i
$105$	−9.86361	−	1.39748i	−0.962590	−	0.136380i
$106$	−2.14282	−	7.99713i	−0.208129	−	0.776750i
$107$	16.0522	−	9.26775i	1.55183	−	0.895947i	0.553833	−	0.832628i	$-0.313165\pi$
$107$	16.0522	−	9.26775i	1.55183	−	0.895947i	0.997993	−	0.0633192i	$-0.0201686\pi$
$108$	−0.525817	−	5.16948i	−0.0505968	−	0.497433i
$109$	4.23071	−	4.23071i	0.405229	−	0.405229i	−0.474842	−	0.880071i	$-0.657495\pi$
$109$	4.23071	−	4.23071i	0.405229	−	0.405229i	0.880071	+	0.474842i	$0.157495\pi$
$110$	−1.67088	−	1.67088i	−0.159312	−	0.159312i
$111$	1.69434	+	13.9279i	0.160819	+	1.32198i
$112$	−1.88454	+	0.504962i	−0.178073	+	0.0477144i
$113$	−5.17811	+	2.98958i	−0.487116	+	0.281236i	−0.723377	−	0.690453i	$-0.757411\pi$
$113$	−5.17811	+	2.98958i	−0.487116	+	0.281236i	0.236261	+	0.971690i	$0.424078\pi$
$114$	6.23409	+	4.88183i	0.583876	+	0.457225i
$115$	19.9151	−	5.33625i	1.85710	−	0.497608i
$116$	7.87674			0.731337
$117$	−8.52480	+	6.65791i	−0.788118	+	0.615524i
$118$	8.82789			0.812673
$119$	15.1539	−	4.06048i	1.38916	−	0.372224i
$120$	−0.716282	+	5.05561i	−0.0653873	+	0.461512i
$121$	8.96987	−	5.17876i	0.815443	−	0.470796i
$122$	4.77087	−	1.27835i	0.431935	−	0.115737i
$123$	−8.25661	−	3.51562i	−0.744474	−	0.316993i
$124$	1.69127	+	1.69127i	0.151880	+	0.151880i
$125$	−2.72919	+	2.72919i	−0.244106	+	0.244106i
$126$	5.68236	−	1.40329i	0.506225	−	0.125015i
$127$	1.93815	−	1.11899i	0.171983	−	0.0992946i	−0.411537	−	0.911393i	$-0.635008\pi$
$127$	1.93815	−	1.11899i	0.171983	−	0.0992946i	0.583521	+	0.812098i	$0.301675\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	1.51008	+	3.74963i	0.132955	+	0.330137i
$130$	9.70133	−	4.34328i	0.850863	−	0.380931i
$131$	7.37842	+	4.25993i	0.644656	+	0.372192i	0.786406	−	0.617710i	$-0.211940\pi$
$131$	7.37842	+	4.25993i	0.644656	+	0.372192i	−0.141750	+	0.989903i	$0.545273\pi$
$132$	1.27735	+	0.543890i	0.111179	+	0.0473395i
$133$	−4.45956	+	7.72418i	−0.386693	+	0.669772i
$134$	−0.388212	+	0.672403i	−0.0335364	+	0.0580868i
$135$	2.44702	−	15.1216i	0.210606	−	1.30146i
$136$	−2.08121	−	7.76717i	−0.178462	−	0.666029i
$137$	8.21858	−	8.21858i	0.702161	−	0.702161i	−0.262713	−	0.964874i	$-0.584617\pi$
$137$	8.21858	−	8.21858i	0.702161	−	0.702161i	0.964874	+	0.262713i	$0.0846173\pi$
$138$	−9.68245	+	7.27930i	−0.824225	+	0.619655i
$139$	−11.4143	−	19.7701i	−0.968147	−	1.67688i	−0.700910	−	0.713250i	$-0.747222\pi$
$139$	−11.4143	−	19.7701i	−0.968147	−	1.67688i	−0.267238	−	0.963631i	$-0.586111\pi$
$140$	−5.75163			−0.486102
$141$	−9.16481	+	1.11490i	−0.771816	+	0.0938917i
$142$	2.30692	−	1.33190i	0.193593	−	0.111771i
$143$	−0.457981	−	2.85351i	−0.0382983	−	0.238623i
$144$	−0.719258	−	2.91250i	−0.0599381	−	0.242709i
$145$	22.4295	+	6.00996i	1.86267	+	0.499100i
$146$	−6.96014	−	4.01844i	−0.576026	−	0.332568i
$147$	−2.06634	−	5.13087i	−0.170429	−	0.423187i
$148$	2.09658	+	7.82455i	0.172338	+	0.643174i
$149$	2.01425	−	7.51729i	0.165014	−	0.615840i	−0.833025	−	0.553236i	$-0.813393\pi$
$149$	2.01425	−	7.51729i	0.165014	−	0.615840i	0.998038	−	0.0626041i	$-0.0199405\pi$
$150$	−2.50435	+	5.88160i	−0.204480	+	0.480231i
$151$	2.05706	−	7.67704i	0.167401	−	0.624748i	−0.830321	−	0.557285i	$-0.811843\pi$
$151$	2.05706	−	7.67704i	0.167401	−	0.624748i	0.997722	−	0.0674629i	$-0.0214904\pi$
$152$	3.95904	+	2.28576i	0.321121	+	0.185399i
$153$	5.78367	+	23.4199i	0.467582	+	1.89339i
$154$	−0.404752	+	1.51056i	−0.0326159	+	0.121724i
$155$	3.52554	+	6.10641i	0.283178	+	0.490479i
$156$	−4.33390	+	4.49636i	−0.346990	+	0.359997i
$157$	1.97021	−	3.41251i	0.157240	−	0.272348i	−0.776632	−	0.629954i	$-0.783074\pi$
$157$	1.97021	−	3.41251i	0.157240	−	0.272348i	0.933872	+	0.357606i	$0.116407\pi$
$158$	−0.784177	−	0.784177i	−0.0623857	−	0.0623857i
$159$	5.35702	+	13.3019i	0.424839	+	1.05491i
$160$			2.94801i			0.233061i
$161$	−9.64846	−	9.64846i	−0.760405	−	0.760405i
$162$	1.98534	+	8.77829i	0.155983	+	0.689688i
$163$	−19.9290	+	5.33996i	−1.56096	+	0.418258i	−0.932967	−	0.359962i	$-0.882790\pi$
$163$	−19.9290	+	5.33996i	−1.56096	+	0.418258i	−0.627992	+	0.778220i	$0.716123\pi$
$164$	−5.00455	−	1.34097i	−0.390790	−	0.104712i
$165$	3.22235	+	2.52338i	0.250860	+	0.196445i
$166$			2.37352i			0.184221i
$167$	−3.99041	+	3.99041i	−0.308787	+	0.308787i	−0.844439	−	0.535652i	$-0.820066\pi$
$167$	−3.99041	+	3.99041i	−0.308787	+	0.308787i	0.535652	+	0.844439i	$0.320066\pi$
$168$	3.13462	−	1.26239i	0.241841	−	0.0973959i
$169$	12.7269	+	2.65042i	0.978996	+	0.203879i
$170$		−	23.7054i		−	1.81812i
$171$	−11.7398	−	7.08976i	−0.897767	−	0.542168i
$172$	1.16691	+	2.02114i	0.0889759	+	0.154111i
$173$	−16.4329			−1.24937			−0.624687	−	0.780876i	$-0.714773\pi$
$173$	−16.4329			−1.24937			−0.624687	+	0.780876i	$0.714773\pi$
$174$	−13.5431	+	1.64752i	−1.02670	+	0.124898i
$175$	−6.95539	−	1.86369i	−0.525778	−	0.140882i
$176$	0.774238	+	0.207457i	0.0583604	+	0.0156376i
$177$	−15.1785	+	1.84646i	−1.14088	+	0.138789i
$178$	2.94091			0.220431
$179$	−3.02863	−	5.24575i	−0.226371	−	0.392085i	0.730359	−	0.683063i	$-0.239353\pi$
$179$	−3.02863	−	5.24575i	−0.226371	−	0.392085i	−0.956730	+	0.290978i	$0.906019\pi$
$180$	0.174113	−	8.84231i	0.0129776	−	0.659067i
$181$			12.2487i			0.910436i	0.890380	+	0.455218i	$0.150439\pi$
$181$			12.2487i			0.910436i	−0.890380	+	0.455218i	$0.849561\pi$
$182$	−5.69955	−	4.12305i	−0.422479	−	0.305621i
$183$	−7.93554	+	3.19585i	−0.586612	+	0.236244i
$184$	−4.94534	+	4.94534i	−0.364575	+	0.364575i
$185$			23.8806i			1.75573i
$186$	−3.26167	−	2.55417i	−0.239157	−	0.187281i
$187$	−6.22578	−	1.66819i	−0.455274	−	0.121990i
$188$	−5.14869	+	1.37959i	−0.375507	+	0.100617i
$189$	−9.47659	+	3.60132i	−0.689320	+	0.261957i
$190$	9.52957	+	9.52957i	0.691348	+	0.691348i
$191$			0.420709i			0.0304415i	0.999884	+	0.0152207i	$0.00484510\pi$
$191$			0.420709i			0.0304415i	−0.999884	+	0.0152207i	$0.995155\pi$
$192$	−0.647043	−	1.60665i	−0.0466963	−	0.115950i
$193$	−9.60907	−	9.60907i	−0.691676	−	0.691676i	0.270924	−	0.962601i	$-0.412671\pi$
$193$	−9.60907	−	9.60907i	−0.691676	−	0.691676i	−0.962601	+	0.270924i	$0.912671\pi$
$194$	−1.83692	+	3.18164i	−0.131883	+	0.228429i
$195$	−15.7718	+	9.49689i	−1.12944	+	0.680086i
$196$	−1.59676	−	2.76566i	−0.114054	−	0.197547i
$197$	0.239457	−	0.893667i	0.0170606	−	0.0636712i	−0.956871	−	0.290514i	$-0.906174\pi$
$197$	0.239457	−	0.893667i	0.0170606	−	0.0636712i	0.973931	+	0.226843i	$0.0728404\pi$
$198$	−2.31001	−	0.667976i	−0.164165	−	0.0474710i
$199$	11.1074	+	6.41286i	0.787382	+	0.454595i	0.839040	−	0.544070i	$-0.183117\pi$
$199$	11.1074	+	6.41286i	0.787382	+	0.454595i	−0.0516579	+	0.998665i	$0.516451\pi$
$200$	−0.955238	+	3.56500i	−0.0675455	+	0.252083i
$201$	0.526841	−	1.23731i	0.0371605	−	0.0872733i
$202$	3.53128	−	13.1789i	0.248460	−	0.927264i
$203$	−3.97745	−	14.8441i	−0.279162	−	1.04185i
$204$	5.20298	+	12.9194i	0.364281	+	0.904537i
$205$	−13.2276	−	7.63696i	−0.923855	−	0.533388i
$206$	13.0128	+	3.48677i	0.906644	+	0.242935i
$207$	15.1252	−	14.5411i	1.05127	−	1.01067i
$208$	−2.11327	+	2.92131i	−0.146529	+	0.202557i
$209$	3.17337	−	1.83215i	0.219507	−	0.126732i
$210$	9.88921	−	1.20303i	0.682421	−	0.0830167i
$211$	6.84606			0.471302			0.235651	−	0.971838i	$-0.424278\pi$
$211$	6.84606			0.471302			0.235651	+	0.971838i	$0.424278\pi$
$212$	4.13962	+	7.17003i	0.284310	+	0.492440i
$213$	−3.68788	+	2.77256i	−0.252689	+	0.189973i
$214$	−13.1066	+	13.1066i	−0.895947	+	0.895947i
$215$	1.78070	+	6.64568i	0.121443	+	0.453231i
$216$	1.84586	+	4.85724i	0.125595	+	0.330493i
$217$	2.33324	−	4.04129i	0.158390	−	0.274340i
$218$	−2.99156	+	5.18154i	−0.202614	+	0.350938i
$219$	12.8076	+	5.45341i	0.865458	+	0.368507i
$220$	2.04640	+	1.18149i	0.137968	+	0.0796560i
$221$	16.9932	−	23.4908i	1.14309	−	1.58016i
$222$	−5.24141	−	13.0148i	−0.351781	−	0.873497i
$223$	4.57899	+	17.0890i	0.306632	+	1.14436i	0.931532	+	0.363660i	$0.118473\pi$
$223$	4.57899	+	17.0890i	0.306632	+	1.14436i	−0.624900	+	0.780705i	$0.714860\pi$
$224$	1.68964	−	0.975511i	0.112893	−	0.0651791i
$225$	3.07571	−	10.6365i	0.205047	−	0.709100i
$226$	4.22791	−	4.22791i	0.281236	−	0.281236i
$227$	13.6942	+	13.6942i	0.908916	+	0.908916i	0.996185	−	0.0872689i	$-0.0278139\pi$
$227$	13.6942	+	13.6942i	0.908916	+	0.908916i	−0.0872689	+	0.996185i	$0.527814\pi$
$228$	−7.28518	−	3.10199i	−0.482473	−	0.205434i
$229$	25.0861	−	6.72179i	1.65773	−	0.444188i	0.695971	−	0.718070i	$-0.254974\pi$
$229$	25.0861	−	6.72179i	1.65773	−	0.444188i	0.961763	+	0.273882i	$0.0883077\pi$
$230$	−17.8554	+	10.3088i	−1.17735	+	0.679745i
$231$	0.379969	−	2.68187i	0.0250001	−	0.176454i
$232$	−7.60835	+	2.03865i	−0.499512	+	0.133844i
$233$	−11.9090			−0.780184			−0.390092	−	0.920776i	$-0.627557\pi$
$233$	−11.9090			−0.780184			−0.390092	+	0.920776i	$0.627557\pi$
$234$	6.51113	−	8.63743i	0.425646	−	0.564646i
$235$	−15.7138			−1.02506
$236$	−8.52709	+	2.28483i	−0.555066	+	0.148730i
$237$	1.51231	+	1.18427i	0.0982354	+	0.0769268i
$238$	−13.5866	+	7.84425i	−0.880691	+	0.508467i
$239$	8.96480	−	2.40211i	0.579885	−	0.155380i	0.0430587	−	0.999073i	$-0.486290\pi$
$239$	8.96480	−	2.40211i	0.579885	−	0.155380i	0.536826	+	0.843693i	$0.319623\pi$
$240$	−0.616613	−	5.06873i	−0.0398022	−	0.327185i
$241$	−6.92428	−	6.92428i	−0.446032	−	0.446032i	0.448001	−	0.894033i	$-0.352136\pi$
$241$	−6.92428	−	6.92428i	−0.446032	−	0.446032i	−0.894033	+	0.448001i	$0.852136\pi$
$242$	−7.32387	+	7.32387i	−0.470796	+	0.470796i
$243$	−5.24963	−	14.6779i	−0.336764	−	0.941589i
$244$	−4.27745	+	2.46959i	−0.273836	+	0.158099i
$245$	−2.43665	−	9.09371i	−0.155672	−	0.580976i
$246$	8.88518	+	1.25886i	0.566499	+	0.0802619i
$247$	2.61202	+	16.2745i	0.166199	+	1.03552i
$248$	−2.07137	−	1.19590i	−0.131532	−	0.0759400i
$249$	−0.496451	−	4.08097i	−0.0314613	−	0.258621i
$250$	1.92983	−	3.34257i	0.122053	−	0.211402i
$251$	7.05445	−	12.2187i	0.445273	−	0.771235i	−0.552798	−	0.833315i	$-0.686440\pi$
$251$	7.05445	−	12.2187i	0.445273	−	0.771235i	0.998071	+	0.0620799i	$0.0197734\pi$
$252$	−5.12554	+	2.82617i	−0.322879	+	0.178032i
$253$	1.45090	+	5.41484i	0.0912174	+	0.340428i
$254$	−1.58250	+	1.58250i	−0.0992946	+	0.0992946i
$255$	4.95829	+	40.7585i	0.310500	+	2.55240i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.11976			−0.319362			−0.159681	−	0.987169i	$-0.551047\pi$
$257$	−5.11976			−0.319362			−0.159681	+	0.987169i	$0.551047\pi$
$258$	−2.42910	−	3.23103i	−0.151229	−	0.201155i
$259$	13.6870	−	7.90220i	0.850469	−	0.491019i
$260$	−8.24664	+	6.70618i	−0.511435	+	0.415900i
$261$	22.9410	−	5.66541i	1.42001	−	0.350680i
$262$	−8.22956	−	2.20510i	−0.508424	−	0.136232i
$263$	12.4904	+	7.21136i	0.770194	+	0.444671i	0.832944	−	0.553358i	$-0.186654\pi$
$263$	12.4904	+	7.21136i	0.770194	+	0.444671i	−0.0627501	+	0.998029i	$0.519987\pi$
$264$	−1.37460	−	0.194754i	−0.0846007	−	0.0119863i
$265$	6.31706	+	23.5756i	0.388054	+	1.44824i
$266$	2.30844	−	8.61521i	0.141539	−	0.528232i
$267$	−5.05653	+	0.615128i	−0.309455	+	0.0376452i
$268$	0.200953	−	0.749969i	0.0122752	−	0.0458116i
$269$	−10.3656	−	5.98459i	−0.632002	−	0.364887i	0.149525	−	0.988758i	$-0.452226\pi$
$269$	−10.3656	−	5.98459i	−0.632002	−	0.364887i	−0.781527	+	0.623871i	$0.785559\pi$
$270$	1.55011	+	15.2397i	0.0943370	+	0.927457i
$271$	6.16812	−	23.0197i	0.374687	−	1.39835i	−0.479115	−	0.877752i	$-0.659042\pi$
$271$	6.16812	−	23.0197i	0.374687	−	1.39835i	0.853802	−	0.520598i	$-0.174291\pi$
$272$	4.02058	+	6.96385i	0.243784	+	0.422246i
$273$	10.6620	+	5.89693i	0.645296	+	0.356899i
$274$	−5.81141	+	10.0657i	−0.351080	+	0.608089i
$275$	2.09185	+	2.09185i	0.126143	+	0.126143i
$276$	7.46851	−	9.53727i	0.449551	−	0.574076i
$277$		−	9.44410i		−	0.567441i	−0.958907	−	0.283721i	$-0.908431\pi$
$277$		−	9.44410i		−	0.567441i	0.958907	−	0.283721i	$-0.0915688\pi$
$278$	16.1422	+	16.1422i	0.968147	+	0.968147i
$279$	6.14227	+	3.70936i	0.367728	+	0.222073i
$280$	5.55565	−	1.48863i	0.332014	−	0.0889628i
$281$	18.8382	+	5.04768i	1.12379	+	0.301119i	0.772417	−	0.635115i	$-0.219047\pi$
$281$	18.8382	+	5.04768i	1.12379	+	0.301119i	0.351376	+	0.936235i	$0.385714\pi$
$282$	8.56397	−	3.44894i	0.509977	−	0.205381i
$283$		−	20.7236i		−	1.23189i	−0.787789	−	0.615946i	$-0.788774\pi$
$283$		−	20.7236i		−	1.23189i	0.787789	−	0.615946i	$-0.211226\pi$
$284$	−1.88359	+	1.88359i	−0.111771	+	0.111771i
$285$	−18.3781	−	14.3917i	−1.08863	−	0.852490i
$286$	1.18092	+	2.63775i	0.0698292	+	0.155973i
$287$			10.1084i			0.596682i
$288$	1.44856	+	2.62710i	0.0853573	+	0.154804i
$289$	−23.8302	−	41.2751i	−1.40178	−	2.42795i
$290$	−23.2207			−1.36357
$291$	2.49288	−	5.85465i	0.146135	−	0.343206i
$292$	7.76303	+	2.08010i	0.454297	+	0.121729i
$293$	18.6486	+	4.99688i	1.08946	+	0.291921i	0.758467	−	0.651711i	$-0.225949\pi$
$293$	18.6486	+	4.99688i	1.08946	+	0.291921i	0.330996	+	0.943632i	$0.392615\pi$
$294$	3.32389	+	4.42123i	0.193853	+	0.257851i
$295$	−26.0247			−1.51522
$296$	−4.05028	−	7.01530i	−0.235418	−	0.407756i
$297$	4.11149	+	0.665334i	0.238573	+	0.0386066i
$298$			7.78247i			0.450826i
$299$	−25.0836	−	2.58415i	−1.45062	−	0.149445i
$300$	0.896749	−	6.32937i	0.0517738	−	0.365426i
$301$	3.21969	−	3.21969i	0.185580	−	0.185580i
$302$			7.94785i			0.457348i
$303$	−3.31506	+	23.3981i	−0.190445	+	1.34418i
$304$	−4.41574	−	1.18319i	−0.253260	−	0.0678608i
$305$	−14.0646	+	3.76859i	−0.805335	+	0.215789i
$306$	−11.6481	−	21.1250i	−0.665879	−	1.20763i
$307$	−15.5762	−	15.5762i	−0.888978	−	0.888978i	0.105447	−	0.994425i	$-0.466373\pi$
$307$	−15.5762	−	15.5762i	−0.888978	−	0.888978i	−0.994425	+	0.105447i	$0.966373\pi$
$308$		−	1.56384i		−	0.0891082i
$309$	−23.1032	−	3.27327i	−1.31429	−	0.186210i
$310$	−4.98586	−	4.98586i	−0.283178	−	0.283178i
$311$	−4.85889	+	8.41584i	−0.275522	+	0.477218i	−0.970267	−	0.242038i	$-0.922184\pi$
$311$	−4.85889	+	8.41584i	−0.275522	+	0.477218i	0.694745	+	0.719257i	$0.255517\pi$
$312$	3.02248	−	5.46485i	0.171114	−	0.309386i
$313$	2.74916	+	4.76168i	0.155392	+	0.269146i	0.933202	−	0.359353i	$-0.117003\pi$
$313$	2.74916	+	4.76168i	0.155392	+	0.269146i	−0.777810	+	0.628500i	$0.783669\pi$
$314$	−1.01986	+	3.80616i	−0.0575539	+	0.214794i
$315$	−16.7516	+	4.13691i	−0.943848	+	0.233088i
$316$	0.960416	+	0.554497i	0.0540276	+	0.0311929i
$317$	0.270848	−	1.01082i	0.0152123	−	0.0567731i	−0.957902	−	0.287094i	$-0.907311\pi$
$317$	0.270848	−	1.01082i	0.0152123	−	0.0567731i	0.973115	+	0.230321i	$0.0739775\pi$
$318$	−8.61726	−	11.4621i	−0.483232	−	0.642764i
$319$	−1.63408	+	6.09847i	−0.0914910	+	0.341449i
$320$	−0.763001	−	2.84756i	−0.0426530	−	0.159183i
$321$	19.7937	−	25.2765i	1.10478	−	1.41080i
$322$	11.8169	+	6.82249i	0.658530	+	0.380203i
$323$	35.5077	+	9.51426i	1.97570	+	0.529388i
$324$	−4.18968	−	7.96534i	−0.232760	−	0.442519i
$325$	−12.1456	+	5.43757i	−0.673715	+	0.301622i
$326$	17.8678	−	10.3160i	0.989609	−	0.571351i
$327$	4.05984	−	9.53474i	0.224509	−	0.527272i
$328$	5.18109			0.286078
$329$	5.19978	+	9.00629i	0.286673	+	0.496533i
$330$	−3.76565	−	1.60339i	−0.207292	−	0.0882639i
$331$	−8.72945	+	8.72945i	−0.479814	+	0.479814i	−0.905072	−	0.425258i	$-0.860183\pi$
$331$	−8.72945	+	8.72945i	−0.479814	+	0.479814i	0.425258	+	0.905072i	$0.360183\pi$
$332$	−0.614312	−	2.29264i	−0.0337147	−	0.125825i
$333$	11.7342	+	21.2810i	0.643028	+	1.16619i
$334$	2.82165	−	4.88724i	0.154394	−	0.267418i
$335$	1.14445	−	1.98225i	0.0625282	−	0.108302i
$336$	−2.70108	+	2.03068i	−0.147356	+	0.110783i
$337$	18.3428	+	10.5902i	0.999195	+	0.576886i	0.908010	−	0.418948i	$-0.137601\pi$
$337$	18.3428	+	10.5902i	0.999195	+	0.576886i	0.0911852	+	0.995834i	$0.470934\pi$
$338$	−12.9793	+	0.733864i	−0.705979	+	0.0399170i
$339$	−6.38504	+	8.15368i	−0.346788	+	0.442847i
$340$	6.13542	+	22.8977i	0.332740	+	1.24180i
$341$	−1.66031	+	0.958578i	−0.0899106	+	0.0519099i
$342$	13.1748	+	3.80969i	0.712410	+	0.206005i
$343$	−14.0628	+	14.0628i	−0.759319	+	0.759319i
$344$	−1.65026	−	1.65026i	−0.0889759	−	0.0889759i
$345$	28.5440	−	21.4594i	1.53676	−	1.15534i
$346$	15.8730	−	4.25316i	0.853338	−	0.228651i
$347$	−2.17991	+	1.25857i	−0.117024	+	0.0675636i	−0.557369	−	0.830265i	$-0.688189\pi$
$347$	−2.17991	+	1.25857i	−0.117024	+	0.0675636i	0.440346	+	0.897828i	$0.354856\pi$
$348$	12.6552	−	5.09659i	0.678390	−	0.273206i
$349$	17.1855	−	4.60485i	0.919921	−	0.246492i	0.232369	−	0.972628i	$-0.425352\pi$
$349$	17.1855	−	4.60485i	0.919921	−	0.246492i	0.687552	+	0.726136i	$0.258686\pi$
$350$	7.20075			0.384896
$351$	−9.38845	+	16.2129i	−0.501118	+	0.865379i
$352$	−0.801550			−0.0427228
$353$	−3.01498	+	0.807861i	−0.160471	+	0.0429981i	−0.338160	−	0.941089i	$-0.609805\pi$
$353$	−3.01498	+	0.807861i	−0.160471	+	0.0429981i	0.177689	+	0.984087i	$0.443138\pi$
$354$	14.1834	−	5.71202i	0.753837	−	0.303590i
$355$	−6.80082	+	3.92646i	−0.360950	+	0.208395i
$356$	−2.84070	+	0.761164i	−0.150557	+	0.0403416i
$357$	21.7198	−	16.3290i	1.14953	−	0.864224i
$358$	4.28313	+	4.28313i	0.226371	+	0.226371i
$359$	14.3618	−	14.3618i	0.757986	−	0.757986i	−0.217970	−	0.975956i	$-0.569943\pi$
$359$	14.3618	−	14.3618i	0.757986	−	0.757986i	0.975956	+	0.217970i	$0.0699434\pi$
$360$	2.12038	+	8.58608i	0.111754	+	0.452526i
$361$	−1.64433	+	0.949354i	−0.0865436	+	0.0499660i
$362$	−3.17019	−	11.8313i	−0.166621	−	0.621839i
$363$	11.0606	−	14.1244i	0.580531	−	0.741337i
$364$	6.57246	+	2.50741i	0.344491	+	0.131424i
$365$	20.5186	+	11.8464i	1.07399	+	0.620069i
$366$	6.83799	−	5.14083i	0.357428	−	0.268715i
$367$	−11.6102	+	20.1095i	−0.606049	+	1.04971i	0.385835	+	0.922568i	$0.373913\pi$
$367$	−11.6102	+	20.1095i	−0.606049	+	1.04971i	−0.991885	+	0.127141i	$0.959420\pi$
$368$	3.49688	−	6.05678i	0.182288	−	0.315731i
$369$	−15.5403	−	0.306002i	−0.808994	−	0.0159298i
$370$	−6.18074	−	23.0668i	−0.321321	−	1.19919i
$371$	11.4219	−	11.4219i	0.592994	−	0.592994i
$372$	3.81160	+	1.62296i	0.197622	+	0.0841464i
$373$	−12.6570	−	21.9226i	−0.655355	−	1.13511i	−0.981805	−	0.189893i	$-0.939186\pi$
$373$	−12.6570	−	21.9226i	−0.655355	−	1.13511i	0.326450	−	0.945214i	$-0.394148\pi$
$374$	6.44540			0.333284
$375$	−2.61896	+	6.15077i	−0.135243	+	0.317624i
$376$	4.61619	−	2.66516i	0.238062	−	0.137445i
$377$	−23.0104	−	16.6457i	−1.18510	−	0.857298i
$378$	8.22159	−	5.93132i	0.422873	−	0.305074i
$379$	−22.2862	−	5.97156i	−1.14476	−	0.306738i	−0.363898	−	0.931439i	$-0.618554\pi$
$379$	−22.2862	−	5.97156i	−1.14476	−	0.306738i	−0.780865	+	0.624700i	$0.785221\pi$
$380$	−11.6713	−	6.73843i	−0.598725	−	0.345674i
$381$	2.38991	−	3.05190i	0.122439	−	0.156354i
$382$	−0.108888	−	0.406374i	−0.00557117	−	0.0207919i
$383$	−6.17345	+	23.0396i	−0.315448	+	1.17727i	0.608123	+	0.793843i	$0.291923\pi$
$383$	−6.17345	+	23.0396i	−0.315448	+	1.17727i	−0.923571	+	0.383426i	$0.874744\pi$
$384$	1.04083	+	1.38444i	0.0531145	+	0.0706495i
$385$	1.19321	−	4.45313i	0.0608118	−	0.226953i
$386$	11.7687	+	6.79464i	0.599009	+	0.345838i
$387$	4.85235	+	5.04728i	0.246659	+	0.256568i
$388$	0.950861	−	3.54866i	0.0482726	−	0.180156i
$389$	−12.4984	−	21.6479i	−0.633694	−	1.09759i	−0.986790	−	0.162004i	$-0.948204\pi$
$389$	−12.4984	−	21.6479i	−0.633694	−	1.09759i	0.353096	−	0.935587i	$-0.385129\pi$
$390$	12.7764	−	13.2553i	0.646957	−	0.671209i
$391$	−28.1190	+	48.7035i	−1.42204	+	2.46304i
$392$	2.25815	+	2.25815i	0.114054	+	0.114054i
$393$	14.6109	+	2.07009i	0.737024	+	0.104422i
$394$			0.925192i			0.0466105i
$395$	2.31176	+	2.31176i	0.116317	+	0.116317i
$396$	2.40419	+	0.0473406i	0.120815	+	0.00237896i
$397$	20.3908	−	5.46370i	1.02338	−	0.274215i	0.292173	−	0.956366i	$-0.405622\pi$
$397$	20.3908	−	5.46370i	1.02338	−	0.274215i	0.731212	+	0.682150i	$0.238955\pi$
$398$	−12.3887	−	3.31954i	−0.620989	−	0.166393i
$399$	−2.16709	+	15.2956i	−0.108490	+	0.765738i
$400$		−	3.69076i		−	0.184538i
$401$	−12.5004	+	12.5004i	−0.624242	+	0.624242i	−0.946613	−	0.322371i	$-0.895520\pi$
$401$	−12.5004	+	12.5004i	−0.624242	+	0.624242i	0.322371	+	0.946613i	$0.395520\pi$
$402$	−0.188649	+	1.33151i	−0.00940896	+	0.0664096i
$403$	−1.36661	−	8.51482i	−0.0680756	−	0.424154i
$404$			13.6438i			0.678804i
$405$	−5.85280	−	25.8785i	−0.290828	−	1.28591i
$406$	7.68385	+	13.3088i	0.381343	+	0.660506i
$407$	−6.49301			−0.321847
$408$	−8.36947	−	11.1325i	−0.414350	−	0.551142i
$409$	20.2046	+	5.41382i	0.999055	+	0.267696i	0.721050	−	0.692884i	$-0.243660\pi$
$409$	20.2046	+	5.41382i	0.999055	+	0.267696i	0.278005	+	0.960580i	$0.410327\pi$
$410$	14.7535	+	3.95318i	0.728622	+	0.195234i
$411$	7.88664	−	18.5222i	0.389019	−	0.913632i
$412$	−13.4718			−0.663710
$413$	8.61171	+	14.9159i	0.423754	+	0.733964i
$414$	−10.8463	+	17.9603i	−0.533068	+	0.882699i
$415$		−	6.99715i		−	0.343477i
$416$	1.28518	−	3.36873i	0.0630109	−	0.165165i
$417$	−31.1309	−	24.3782i	−1.52449	−	1.19381i
$418$	−2.59105	+	2.59105i	−0.126732	+	0.126732i
$419$		−	17.8998i		−	0.874462i	−0.899349	−	0.437231i	$-0.855959\pi$
$419$		−	17.8998i		−	0.874462i	0.899349	−	0.437231i	$-0.144041\pi$
$420$	−9.24088	+	3.72155i	−0.450909	+	0.181593i
$421$	0.922884	+	0.247286i	0.0449786	+	0.0120520i	0.281238	−	0.959638i	$-0.409255\pi$
$421$	0.922884	+	0.247286i	0.0449786	+	0.0120520i	−0.236260	+	0.971690i	$0.575922\pi$
$422$	−6.61278	+	1.77189i	−0.321905	+	0.0862542i
$423$	−14.0033	+	7.72128i	−0.680863	+	0.375422i
$424$	−5.85430	−	5.85430i	−0.284310	−	0.284310i
$425$			29.6780i			1.43959i
$426$	2.84463	−	3.63258i	0.137823	−	0.175999i
$427$	6.81399	+	6.81399i	0.329752	+	0.329752i
$428$	9.26775	−	16.0522i	0.447974	−	0.775913i
$429$	−2.58216	−	4.28827i	−0.124668	−	0.207040i
$430$	−3.44006	−	5.95835i	−0.165894	−	0.287337i
$431$	−10.1624	+	37.9267i	−0.489507	+	1.82687i	0.0693375	+	0.997593i	$0.477911\pi$
$431$	−10.1624	+	37.9267i	−0.489507	+	1.82687i	−0.558845	+	0.829272i	$0.688755\pi$
$432$	−3.04011	−	4.21399i	−0.146267	−	0.202746i
$433$	9.53436	+	5.50467i	0.458192	+	0.264537i	0.711284	−	0.702905i	$-0.248114\pi$
$433$	9.53436	+	5.50467i	0.458192	+	0.264537i	−0.253092	+	0.967442i	$0.581447\pi$
$434$	−1.20777	+	4.50747i	−0.0579749	+	0.216365i
$435$	39.9251	−	4.85690i	1.91426	−	0.232871i
$436$	1.54855	−	5.77926i	0.0741620	−	0.276776i
$437$	−8.27498	−	30.8826i	−0.395846	−	1.47732i
$438$	−13.7826	−	1.95273i	−0.658560	−	0.0933052i
$439$	3.69190	+	2.13152i	0.176205	+	0.101732i	0.585508	−	0.810666i	$-0.300895\pi$
$439$	3.69190	+	2.13152i	0.176205	+	0.101732i	−0.409304	+	0.912398i	$0.634228\pi$
$440$	−2.28246	−	0.611584i	−0.108812	−	0.0291561i
$441$	−6.63978	−	6.90652i	−0.316180	−	0.328882i
$442$	−10.3343	+	27.0885i	−0.491553	+	1.28847i
$443$	24.9846	−	14.4249i	1.18705	−	0.685346i	0.229419	−	0.973328i	$-0.426317\pi$
$443$	24.9846	−	14.4249i	1.18705	−	0.685346i	0.957636	+	0.287981i	$0.0929841\pi$
$444$	8.43130	+	11.2148i	0.400132	+	0.532229i
$445$	−8.66983			−0.410989
$446$	−8.84592	−	15.3216i	−0.418866	−	0.725498i
$447$	−1.62780	−	13.3810i	−0.0769923	−	0.632899i
$448$	−1.37958	+	1.37958i	−0.0651791	+	0.0651791i
$449$	6.56424	+	24.4981i	0.309786	+	1.15614i	0.928747	+	0.370714i	$0.120887\pi$
$449$	6.56424	+	24.4981i	0.309786	+	1.15614i	−0.618961	+	0.785421i	$0.712446\pi$
$450$	−0.217981	+	11.0701i	−0.0102757	+	0.521851i
$451$	2.07645	−	3.59652i	0.0977764	−	0.169354i
$452$	−2.98958	+	5.17811i	−0.140618	+	0.243558i
$453$	−1.66239	−	13.6653i	−0.0781060	−	0.642054i
$454$	−16.7719	−	9.68326i	−0.787144	−	0.454458i
$455$	16.8023	+	12.1548i	0.787705	+	0.569825i
$456$	7.83979	+	1.11075i	0.367132	+	0.0520155i
$457$	−7.44528	−	27.7862i	−0.348275	−	1.29978i	−0.888739	−	0.458414i	$-0.848418\pi$
$457$	−7.44528	−	27.7862i	−0.348275	−	1.29978i	0.540463	−	0.841368i	$-0.318249\pi$
$458$	−22.4916	+	12.9855i	−1.05096	+	0.606773i
$459$	24.4460	+	33.8854i	1.14104	+	1.58164i
$460$	14.5789	−	14.5789i	0.679745	−	0.679745i
$461$	26.1642	+	26.1642i	1.21859	+	1.21859i	0.968126	+	0.250464i	$0.0805832\pi$
$461$	26.1642	+	26.1642i	1.21859	+	1.21859i	0.250464	+	0.968126i	$0.419417\pi$
$462$	0.327097	+	2.68883i	0.0152179	+	0.125096i
$463$	−2.40613	+	0.644720i	−0.111822	+	0.0299627i	−0.314296	−	0.949325i	$-0.601769\pi$
$463$	−2.40613	+	0.644720i	−0.111822	+	0.0299627i	0.202474	+	0.979288i	$0.435102\pi$
$464$	6.82146	−	3.93837i	0.316678	−	0.182834i
$465$	9.61543	+	7.52972i	0.445905	+	0.349182i
$466$	11.5032	−	3.08227i	0.532875	−	0.142784i
$467$	−31.2741			−1.44719			−0.723596	−	0.690223i	$-0.757512\pi$
$467$	−31.2741			−1.44719			−0.723596	+	0.690223i	$0.757512\pi$
$468$	−4.05374	+	10.0283i	−0.187384	+	0.463559i
$469$	−1.51482			−0.0699480
$470$	15.1784	−	4.06703i	0.700126	−	0.187598i
$471$	0.957412	−	6.75753i	0.0441152	−	0.311371i
$472$	7.64518	−	4.41394i	0.351898	−	0.203168i
$473$	−1.80693	+	0.484165i	−0.0830827	+	0.0222619i
$474$	−1.76730	−	0.752505i	−0.0811746	−	0.0345637i
$475$	−11.9305	−	11.9305i	−0.547411	−	0.547411i
$476$	11.0934	−	11.0934i	0.508467	−	0.508467i
$477$	17.2137	+	17.9053i	0.788163	+	0.819826i
$478$	−8.03762	+	4.64052i	−0.367632	+	0.212253i
$479$	1.43340	+	5.34951i	0.0654936	+	0.244426i	0.990910	−	0.134526i	$-0.0429513\pi$
$479$	1.43340	+	5.34951i	0.0654936	+	0.244426i	−0.925416	+	0.378952i	$0.876285\pi$
$480$	1.90749	+	4.73643i	0.0870645	+	0.216187i
$481$	10.4107	−	27.2886i	0.474685	−	1.24425i
$482$	8.48048	+	4.89621i	0.386275	+	0.223016i
$483$	−21.7447	−	9.25877i	−0.989418	−	0.421289i
$484$	5.17876	−	8.96987i	0.235398	−	0.407721i
$485$	5.41526	−	9.37951i	0.245894	−	0.425902i
$486$	8.86968	+	12.8191i	0.402337	+	0.581485i
$487$	−0.759319	−	2.83382i	−0.0344080	−	0.128412i	0.946586	−	0.322453i	$-0.104507\pi$
$487$	−0.759319	−	2.83382i	−0.0344080	−	0.128412i	−0.980994	+	0.194040i	$0.937841\pi$
$488$	3.49252	−	3.49252i	0.158099	−	0.158099i
$489$	−28.5638	+	21.4744i	−1.29170	+	0.971105i
$490$	4.70725	+	8.15320i	0.212652	+	0.368324i
$491$	−35.6988			−1.61106			−0.805531	−	0.592553i	$-0.798120\pi$
$491$	−35.6988			−1.61106			−0.805531	+	0.592553i	$0.798120\pi$
$492$	−8.90824	+	1.08369i	−0.401615	+	0.0488566i
$493$	−54.8525	+	31.6691i	−2.47043	+	1.42630i
$494$	−6.73518	−	15.0440i	−0.303030	−	0.676860i
$495$	6.80994	+	1.96920i	0.306084	+	0.0885090i
$496$	2.31031	+	0.619046i	0.103736	+	0.0277960i
$497$	4.50085	+	2.59857i	0.201891	+	0.116562i
$498$	1.53577	+	3.81342i	0.0688194	+	0.170883i
$499$	4.71922	+	17.6124i	0.211261	+	0.788438i	0.987449	+	0.157936i	$0.0504841\pi$
$499$	4.71922	+	17.6124i	0.211261	+	0.788438i	−0.776188	+	0.630502i	$0.782849\pi$
$500$	−0.998954	+	3.72815i	−0.0446746	+	0.166728i
$501$	−3.82924	+	8.99318i	−0.171078	+	0.401786i
$502$	−3.65165	+	13.6281i	−0.162981	+	0.608254i
$503$	20.2816	+	11.7096i	0.904310	+	0.522104i	0.878596	−	0.477565i	$-0.158481\pi$
$503$	20.2816	+	11.7096i	0.904310	+	0.522104i	0.0257142	+	0.999669i	$0.491814\pi$
$504$	4.21942	−	4.05646i	0.187948	−	0.180689i
$505$	−10.4102	+	38.8515i	−0.463249	+	1.72887i
$506$	−2.80293	−	4.85481i	−0.124605	−	0.215823i
$507$	22.1627	−	3.97657i	0.984282	−	0.176605i
$508$	1.11899	−	1.93815i	0.0496473	−	0.0859917i
$509$	2.33968	+	2.33968i	0.103705	+	0.103705i	0.757055	−	0.653351i	$-0.226637\pi$
$509$	2.33968	+	2.33968i	0.103705	+	0.103705i	−0.653351	+	0.757055i	$0.726637\pi$
$510$	−15.3384	−	38.0864i	−0.679197	−	1.68649i
$511$		−	15.6801i		−	0.693648i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−23.4492	−	3.79462i	−1.03531	−	0.167537i
$514$	4.94531	−	1.32509i	0.218128	−	0.0584473i
$515$	−38.3618	−	10.2790i	−1.69042	−	0.452948i
$516$	3.18258	+	2.49224i	0.140105	+	0.109715i
$517$		−	4.27252i		−	0.187905i
$518$	−11.1754	+	11.1754i	−0.491019	+	0.491019i
$519$	−26.4020	+	10.6328i	−1.15892	+	0.466729i
$520$	6.22995	−	8.61206i	0.273201	−	0.377664i
$521$		−	7.00178i		−	0.306754i	−0.988168	−	0.153377i	$-0.950985\pi$
$521$		−	7.00178i		−	0.306754i	0.988168	−	0.153377i	$-0.0490148\pi$
$522$	−20.6930	+	11.4099i	−0.905709	+	0.499399i
$523$	−21.4957	−	37.2316i	−0.939940	−	1.62802i	−0.765580	−	0.643341i	$-0.777548\pi$
$523$	−21.4957	−	37.2316i	−0.939940	−	1.62802i	−0.174360	−	0.984682i	$-0.555786\pi$
$524$	8.51987			0.372192
$525$	−12.3808	+	1.50613i	−0.540342	+	0.0657328i
$526$	−13.9313	−	3.73287i	−0.607433	−	0.162761i
$527$	−18.5776	−	4.97785i	−0.809253	−	0.216839i
$528$	1.37817	−	0.167654i	0.0599770	−	0.00729622i
$529$	25.9127			1.12664
$530$	−12.2036	−	21.1373i	−0.530092	−	0.918146i
$531$	−23.1918	+	12.7877i	−1.00644	+	0.554940i
$532$			8.91912i			0.386693i
$533$	11.7860	+	14.4934i	0.510510	+	0.627778i
$534$	4.72503	−	1.90289i	0.204472	−	0.0823463i
$535$	38.6383	−	38.6383i	1.67048	−	1.67048i
$536$			0.776425i			0.0335364i
$537$	−8.26018	−	6.46844i	−0.356453	−	0.279134i
$538$	11.5613	+	3.09785i	0.498445	+	0.133558i
$539$	2.47254	−	0.662515i	0.106500	−	0.0285365i
$540$	−5.44161	−	14.3192i	−0.234170	−	0.616200i
$541$	8.12664	+	8.12664i	0.349391	+	0.349391i	0.859883	−	0.510491i	$-0.170536\pi$
$541$	8.12664	+	8.12664i	0.349391	+	0.349391i	−0.510491	+	0.859883i	$0.670536\pi$
$542$			23.8318i			1.02366i
$543$	7.92540	+	19.6794i	0.340112	+	0.844522i
$544$	−5.68596	−	5.68596i	−0.243784	−	0.243784i
$545$	8.81916	−	15.2752i	0.377771	−	0.654319i
$546$	−11.8250	−	2.93646i	−0.506063	−	0.125669i
$547$	2.01972	+	3.49826i	0.0863570	+	0.149575i	0.905969	−	0.423345i	$-0.139144\pi$
$547$	2.01972	+	3.49826i	0.0863570	+	0.149575i	−0.819612	+	0.572919i	$0.805811\pi$
$548$	3.00821	−	11.2268i	0.128504	−	0.479585i
$549$	−10.6818	+	10.2693i	−0.455888	+	0.438281i
$550$	−2.56199	−	1.47916i	−0.109243	−	0.0630717i
$551$	9.31971	−	34.7816i	0.397033	−	1.48175i
$552$	−4.74560	+	11.1453i	−0.201986	+	0.474375i
$553$	0.559999	−	2.08995i	0.0238136	−	0.0888735i
$554$	2.44431	+	9.12230i	0.103849	+	0.387570i
$555$	15.4517	+	38.3678i	0.655890	+	1.62862i
$556$	−19.7701	−	11.4143i	−0.838440	−	0.484074i
$557$	−22.2275	−	5.95584i	−0.941810	−	0.252357i	−0.244926	−	0.969542i	$-0.578764\pi$
$557$	−22.2275	−	5.95584i	−0.941810	−	0.252357i	−0.696883	+	0.717185i	$0.745430\pi$
$558$	−6.89303	−	1.99323i	−0.291805	−	0.0843801i
$559$	0.862329	−	8.37039i	0.0364726	−	0.354030i
$560$	−4.98106	+	2.87582i	−0.210488	+	0.121525i
$561$	−11.0821	+	1.34814i	−0.467885	+	0.0569184i
$562$	−19.5027			−0.822674
$563$	2.44455	+	4.23408i	0.103025	+	0.178445i	0.912930	−	0.408117i	$-0.133814\pi$
$563$	2.44455	+	4.23408i	0.103025	+	0.178445i	−0.809904	+	0.586562i	$0.800481\pi$
$564$	−7.37951	+	5.54794i	−0.310733	+	0.233610i
$565$	−12.4639	+	12.4639i	−0.524361	+	0.524361i
$566$	5.36367	+	20.0175i	0.225452	+	0.841397i
$567$	−12.8954	+	11.9178i	−0.541556	+	0.500501i
$568$	1.33190	−	2.30692i	0.0558853	−	0.0967963i
$569$	−10.6832	+	18.5038i	−0.447863	+	0.775721i	−0.998247	−	0.0591908i	$-0.981148\pi$
$569$	−10.6832	+	18.5038i	−0.447863	+	0.775721i	0.550384	+	0.834912i	$0.314481\pi$
$570$	21.4768	+	9.14469i	0.899563	+	0.383029i
$571$	21.5820	+	12.4604i	0.903179	+	0.521451i	0.878230	−	0.478238i	$-0.158724\pi$
$571$	21.5820	+	12.4604i	0.903179	+	0.521451i	0.0249486	+	0.999689i	$0.492058\pi$
$572$	−1.82338	−	2.24222i	−0.0762393	−	0.0937521i
$573$	0.272217	+	0.675934i	0.0113720	+	0.0282376i
$574$	−2.61625	−	9.76399i	−0.109200	−	0.407541i
$575$	22.3541	−	12.9061i	0.932230	−	0.538223i
$576$	−2.07915	−	2.16267i	−0.0866311	−	0.0901113i
$577$	−4.11164	+	4.11164i	−0.171170	+	0.171170i	−0.787493	−	0.616323i	$-0.788621\pi$
$577$	−4.11164	+	4.11164i	−0.171170	+	0.171170i	0.616323	+	0.787493i	$0.288621\pi$
$578$	33.7010	+	33.7010i	1.40178	+	1.40178i
$579$	−21.6559	−	9.22097i	−0.899990	−	0.383211i
$580$	22.4295	−	6.00996i	0.931333	−	0.249550i
$581$	−4.01038	+	2.31539i	−0.166379	+	0.0960587i
$582$	−0.892639	+	6.30036i	−0.0370011	+	0.261158i
$583$	−6.41010	+	1.71758i	−0.265479	+	0.0711350i
$584$	−8.03688			−0.332568
$585$	−19.1949	+	25.4632i	−0.793610	+	1.05277i
$586$	−19.3065			−0.797542
$587$	−17.3963	+	4.66134i	−0.718024	+	0.192394i	−0.599290	−	0.800532i	$-0.704550\pi$
$587$	−17.3963	+	4.66134i	−0.718024	+	0.192394i	−0.118734	+	0.992926i	$0.537884\pi$
$588$	−4.35493	−	3.41029i	−0.179594	−	0.140638i
$589$	9.46928	−	5.46709i	0.390175	−	0.225268i
$590$	25.1379	−	6.73569i	1.03491	−	0.277304i
$591$	−0.193516	−	1.59075i	−0.00796017	−	0.0654348i
$592$	5.72797	+	5.72797i	0.235418	+	0.235418i
$593$	8.08152	−	8.08152i	0.331868	−	0.331868i	−0.521427	−	0.853296i	$-0.674600\pi$
$593$	8.08152	−	8.08152i	0.331868	−	0.331868i	0.853296	+	0.521427i	$0.174600\pi$
$594$	−4.14360	+	0.421469i	−0.170014	+	0.0172931i
$595$	40.0535	−	23.1249i	1.64203	−	0.948029i
$596$	−2.01425	−	7.51729i	−0.0825069	−	0.307920i
$597$	21.9951	+	3.11628i	0.900201	+	0.127541i
$598$	24.8977	−	3.99602i	1.01814	−	0.163410i
$599$	−0.103217	−	0.0595921i	−0.00421731	−	0.00243487i	0.497890	−	0.867240i	$-0.334108\pi$
$599$	−0.103217	−	0.0595921i	−0.00421731	−	0.00243487i	−0.502107	+	0.864805i	$0.667442\pi$
$600$	0.771968	+	6.34580i	0.0315155	+	0.259066i
$601$	−13.5435	+	23.4581i	−0.552452	+	0.956875i	0.445645	+	0.895210i	$0.352974\pi$
$601$	−13.5435	+	23.4581i	−0.552452	+	0.956875i	−0.998097	+	0.0616651i	$0.980359\pi$
$602$	−2.27666	+	3.94330i	−0.0927899	+	0.160717i
$603$	0.0458567	−	2.32882i	0.00186743	−	0.0948370i
$604$	−2.05706	−	7.67704i	−0.0837004	−	0.312374i
$605$	21.5908	−	21.5908i	0.877792	−	0.877792i
$606$	−2.85377	−	23.4588i	−0.115927	−	0.952949i
$607$	9.24915	+	16.0200i	0.375412	+	0.650232i	0.990389	−	0.138313i	$-0.0441680\pi$
$607$	9.24915	+	16.0200i	0.375412	+	0.650232i	−0.614977	+	0.788545i	$0.710835\pi$
$608$	4.57151			0.185399
$609$	−15.9951	−	21.2757i	−0.648155	−	0.862134i
$610$	12.6100	−	7.28036i	0.510562	−	0.294773i
$611$	17.9564	+	6.85039i	0.726437	+	0.277137i
$612$	16.7188	+	17.3904i	0.675816	+	0.702965i
$613$	−21.0392	−	5.63743i	−0.849764	−	0.227694i	−0.192447	−	0.981307i	$-0.561642\pi$
$613$	−21.0392	−	5.63743i	−0.849764	−	0.227694i	−0.657317	+	0.753614i	$0.728309\pi$
$614$	19.0768	+	11.0140i	0.769878	+	0.444489i
$615$	−26.1936	−	3.71113i	−1.05623	−	0.149647i
$616$	0.404752	+	1.51056i	0.0163079	+	0.0608620i
$617$	0.679941	−	2.53758i	0.0273734	−	0.102159i	−0.950888	−	0.309536i	$-0.899826\pi$
$617$	0.679941	−	2.53758i	0.0273734	−	0.102159i	0.978261	+	0.207377i	$0.0664928\pi$
$618$	23.1631	−	2.81780i	0.931758	−	0.113349i
$619$	−3.69004	+	13.7714i	−0.148315	+	0.553520i	0.851270	+	0.524728i	$0.175833\pi$
$619$	−3.69004	+	13.7714i	−0.148315	+	0.553520i	−0.999585	+	0.0287923i	$0.990834\pi$
$620$	6.10641	+	3.52554i	0.245239	+	0.141589i
$621$	14.8923	−	33.1491i	0.597607	−	1.33023i
$622$	2.51514	−	9.38665i	0.100848	−	0.376370i
$623$	2.86889	+	4.96907i	0.114940	+	0.199081i
$624$	−1.50509	+	6.06092i	−0.0602517	+	0.242631i
$625$	−14.9160	+	25.8354i	−0.596642	+	1.03341i
$626$	−3.88790	−	3.88790i	−0.155392	−	0.155392i
$627$	3.91303	−	4.99693i	0.156272	−	0.199558i
$628$		−	3.94043i		−	0.157240i
$629$	−46.0595	−	46.0595i	−1.83651	−	1.83651i
$630$	15.1101	−	8.33159i	0.602002	−	0.331938i
$631$	34.0030	−	9.11109i	1.35364	−	0.362707i	0.492163	−	0.870503i	$-0.336206\pi$
$631$	34.0030	−	9.11109i	1.35364	−	0.362707i	0.861477	+	0.507797i	$0.169540\pi$
$632$	−1.07121	−	0.287029i	−0.0426103	−	0.0114174i
$633$	10.9992	−	4.42969i	0.437181	−	0.176064i
$634$			1.04647i			0.0415608i
$635$	4.66521	−	4.66521i	0.185133	−	0.185133i
$636$	11.2902	+	8.84124i	0.447687	+	0.350578i
$637$	−1.17998	+	11.4537i	−0.0467525	+	0.453814i
$638$		−	6.31360i		−	0.249958i
$639$	−4.13118	+	6.84076i	−0.163427	+	0.270616i
$640$	1.47400	+	2.55305i	0.0582651	+	0.100918i
$641$	5.81916			0.229843			0.114922	−	0.993375i	$-0.463338\pi$
$641$	5.81916			0.229843			0.114922	+	0.993375i	$0.463338\pi$
$642$	−12.5772	+	29.5382i	−0.496383	+	1.16578i
$643$	5.74185	+	1.53852i	0.226436	+	0.0606735i	0.370253	−	0.928931i	$-0.379271\pi$
$643$	5.74185	+	1.53852i	0.226436	+	0.0606735i	−0.143817	+	0.989604i	$0.545938\pi$
$644$	−13.1800	−	3.53158i	−0.519367	−	0.139164i
$645$	7.16101	+	9.52511i	0.281964	+	0.375051i
$646$	−36.7603			−1.44631
$647$	−2.47586	−	4.28832i	−0.0973362	−	0.168591i	0.813245	−	0.581921i	$-0.197699\pi$
$647$	−2.47586	−	4.28832i	−0.0973362	−	0.168591i	−0.910581	+	0.413330i	$0.864366\pi$
$648$	6.10850	+	6.60956i	0.239965	+	0.259648i
$649$		−	7.07600i		−	0.277757i
$650$	10.3244	−	8.39579i	0.404955	−	0.329310i
$651$	1.13382	−	8.00265i	0.0444379	−	0.313649i
$652$	−14.5890	+	14.5890i	−0.571351	+	0.571351i
$653$		−	20.4897i		−	0.801824i	−0.916117	−	0.400912i	$-0.868693\pi$
$653$		−	20.4897i		−	0.801824i	0.916117	−	0.400912i	$-0.131307\pi$
$654$	−1.45373	+	10.2606i	−0.0568453	+	0.401222i
$655$	24.2608	+	6.50067i	0.947949	+	0.254002i
$656$	−5.00455	+	1.34097i	−0.195395	+	0.0523559i
$657$	24.1060	+	0.474669i	0.940463	+	0.0185186i
$658$	−7.35360	−	7.35360i	−0.286673	−	0.286673i
$659$			4.80810i			0.187297i	0.995605	+	0.0936484i	$0.0298530\pi$
$659$			4.80810i			0.187297i	−0.995605	+	0.0936484i	$0.970147\pi$
$660$	4.05233	+	0.574136i	0.157737	+	0.0223482i
$661$	−28.8974	−	28.8974i	−1.12398	−	1.12398i	−0.991138	−	0.132839i	$-0.957591\pi$
$661$	−28.8974	−	28.8974i	−1.12398	−	1.12398i	−0.132839	−	0.991138i	$-0.542409\pi$
$662$	6.17265	−	10.6913i	0.239907	−	0.415531i
$663$	12.1027	−	48.7368i	0.470028	−	1.89278i
$664$	1.18676	+	2.05553i	0.0460552	+	0.0797699i
$665$	−6.80530	+	25.3977i	−0.263898	+	0.984881i
$666$	−16.8423	−	17.5189i	−0.652625	−	0.678843i
$667$	47.7077	+	27.5440i	1.84725	+	1.06651i
$668$	−1.46059	+	5.45101i	−0.0565120	+	0.210906i
$669$	18.4142	+	24.4933i	0.711932	+	0.946966i
$670$	−0.592413	+	2.21091i	−0.0228869	+	0.0854151i
$671$	−1.02466	−	3.82410i	−0.0395567	−	0.147628i
$672$	2.08346	−	2.66057i	0.0803713	−	0.102634i
$673$	22.6393	+	13.0708i	0.872680	+	0.503842i	0.868238	−	0.496148i	$-0.165253\pi$
$673$	22.6393	+	13.0708i	0.872680	+	0.503842i	0.00444195	+	0.999990i	$0.498586\pi$
$674$	−20.4587	−	5.48190i	−0.788040	−	0.211155i
$675$	−1.94066	−	19.0793i	−0.0746962	−	0.734362i
$676$	12.3471	−	4.06814i	0.474887	−	0.156467i
$677$	−34.5645	+	19.9558i	−1.32842	+	0.766964i	−0.985055	−	0.172238i	$-0.944900\pi$
$677$	−34.5645	+	19.9558i	−1.32842	+	0.766964i	−0.343365	+	0.939202i	$0.611567\pi$
$678$	4.05715	−	9.52842i	0.155814	−	0.365937i
$679$	−7.16775			−0.275073
$680$	−11.8527	−	20.5295i	−0.454531	−	0.787271i
$681$	30.8626	+	13.1411i	1.18266	+	0.503568i
$682$	1.35563	−	1.35563i	0.0519099	−	0.0519099i
$683$	−9.69531	−	36.1834i	−0.370981	−	1.38452i	−0.859129	−	0.511759i	$-0.828994\pi$
$683$	−9.69531	−	36.1834i	−0.370981	−	1.38452i	0.488148	−	0.872761i	$-0.337673\pi$
$684$	−13.7119	−	0.270000i	−0.524287	−	0.0103237i
$685$	17.1321	−	29.6737i	0.654584	−	1.13377i
$686$	9.94388	−	17.2233i	0.379659	−	0.657589i
$687$	35.9553	−	27.0313i	1.37178	−	1.03131i
$688$	2.02114	+	1.16691i	0.0770554	+	0.0444880i
$689$	3.05912	−	29.6941i	0.116543	−	1.13125i
$690$	−22.0172	+	28.1160i	−0.838182	+	1.07036i
$691$	12.0361	+	44.9193i	0.457875	+	1.70881i	0.679496	+	0.733679i	$0.262199\pi$
$691$	12.0361	+	44.9193i	0.457875	+	1.70881i	−0.221621	+	0.975133i	$0.571135\pi$
$692$	−14.2313	+	8.21647i	−0.540994	+	0.312343i
$693$	−1.12481	−	4.55470i	−0.0427279	−	0.173019i
$694$	1.77989	−	1.77989i	0.0675636	−	0.0675636i
$695$	−47.5875	−	47.5875i	−1.80510	−	1.80510i
$696$	−10.9049	+	8.19833i	−0.413349	+	0.310757i
$697$	40.2424	−	10.7829i	1.52429	−	0.408433i
$698$	−15.4081	+	8.89589i	−0.583206	+	0.336714i
$699$	−19.1336	+	7.70562i	−0.723700	+	0.291453i
$700$	−6.95539	+	1.86369i	−0.262889	+	0.0704409i
$701$	27.1053			1.02375			0.511876	−	0.859059i	$-0.328951\pi$
$701$	27.1053			1.02375			0.511876	+	0.859059i	$0.328951\pi$
$702$	4.87235	−	18.0903i	0.183895	−	0.682776i
$703$	37.0318			1.39668
$704$	0.774238	−	0.207457i	0.0291802	−	0.00781881i
$705$	−25.2467	+	10.1675i	−0.950844	+	0.382930i
$706$	2.70316	−	1.56067i	0.101735	−	0.0587365i
$707$	25.7123	−	6.88960i	0.967012	−	0.259110i
$708$	−12.2217	+	9.18831i	−0.459319	+	0.345318i
$709$	32.1360	+	32.1360i	1.20689	+	1.20689i	0.972028	+	0.234865i	$0.0754647\pi$
$709$	32.1360	+	32.1360i	1.20689	+	1.20689i	0.234865	+	0.972028i	$0.424535\pi$
$710$	5.55285	−	5.55285i	0.208395	−	0.208395i
$711$	3.19604	+	0.924186i	0.119861	+	0.0346597i
$712$	2.54690	−	1.47046i	0.0954492	−	0.0551076i
$713$	4.32946	+	16.1578i	0.162140	+	0.605113i
$714$	−16.7535	+	21.3941i	−0.626982	+	0.800655i
$715$	−3.48136	−	7.77610i	−0.130196	−	0.290810i
$716$	−5.24575	−	3.02863i	−0.196043	−	0.113185i
$717$	12.8491	−	9.65997i	0.479857	−	0.360758i
$718$	−10.1553	+	17.5895i	−0.378993	+	0.656435i
$719$	−10.2199	+	17.7014i	−0.381138	+	0.660150i	−0.991225	−	0.132184i	$-0.957801\pi$
$719$	−10.2199	+	17.7014i	−0.381138	+	0.660150i	0.610087	+	0.792334i	$0.291134\pi$
$720$	−4.27037	−	7.74472i	−0.159147	−	0.288629i
$721$	6.80276	+	25.3882i	0.253348	+	0.945508i
$722$	1.34259	−	1.34259i	0.0499660	−	0.0499660i
$723$	−15.6052	−	6.64462i	−0.580365	−	0.247116i
$724$	6.12433	+	10.6077i	0.227609	+	0.394230i
$725$	29.0711			1.07967
$726$	−7.02807	+	16.5058i	−0.260836	+	0.612587i
$727$	25.7087	−	14.8430i	0.953485	−	0.550495i	0.0593229	−	0.998239i	$-0.481106\pi$
$727$	25.7087	−	14.8430i	0.953485	−	0.550495i	0.894162	+	0.447744i	$0.147773\pi$
$728$	−6.99748	−	0.720889i	−0.259344	−	0.0267179i
$729$	−17.9316	−	20.1856i	−0.664133	−	0.747615i
$730$	−22.8855	−	6.13215i	−0.847030	−	0.226961i
$731$	−16.2524	−	9.38330i	−0.601115	−	0.347054i
$732$	−5.27445	+	6.73546i	−0.194949	+	0.248950i
$733$	−0.441496	−	1.64769i	−0.0163070	−	0.0608587i	0.957293	−	0.289120i	$-0.0933626\pi$
$733$	−0.441496	−	1.64769i	−0.0163070	−	0.0608587i	−0.973600	+	0.228261i	$0.926696\pi$
$734$	6.00990	−	22.4293i	0.221829	−	0.827879i
$735$	−9.79887	−	13.0338i	−0.361437	−	0.480760i
$736$	−1.81012	+	6.75546i	−0.0667219	+	0.249009i
$737$	0.538965	+	0.311172i	0.0198530	+	0.0114622i
$738$	15.0899	−	3.72654i	0.555469	−	0.137176i
$739$	−12.2243	+	45.6218i	−0.449679	+	1.67822i	0.253600	+	0.967309i	$0.418385\pi$
$739$	−12.2243	+	45.6218i	−0.449679	+	1.67822i	−0.703279	+	0.710914i	$0.748281\pi$
$740$	11.9403	+	20.6812i	0.438933	+	0.760255i
$741$	14.7269	+	24.4575i	0.541007	+	0.898467i
$742$	−8.07649	+	13.9889i	−0.296497	+	0.513548i
$743$	−22.8373	−	22.8373i	−0.837819	−	0.837819i	0.150753	−	0.988571i	$-0.451830\pi$
$743$	−22.8373	−	22.8373i	−0.837819	−	0.837819i	−0.988571	+	0.150753i	$0.951830\pi$
$744$	−4.10177	−	0.581142i	−0.150378	−	0.0213057i
$745$		−	22.9428i		−	0.840558i
$746$	17.8997	+	17.8997i	0.655355	+	0.655355i
$747$	−3.43818	−	6.23548i	−0.125797	−	0.228144i
$748$	−6.22578	+	1.66819i	−0.227637	+	0.0609952i
$749$	−34.9309	−	9.35972i	−1.27635	−	0.341997i
$750$	0.937788	−	6.61903i	0.0342432	−	0.241693i
$751$		−	36.8858i		−	1.34598i	−0.739651	−	0.672991i	$-0.765009\pi$
$751$		−	36.8858i		−	1.34598i	0.739651	−	0.672991i	$-0.234991\pi$
$752$	−3.76910	+	3.76910i	−0.137445	+	0.137445i
$753$	3.42806	−	24.1957i	0.124925	−	0.881740i
$754$	26.5346	+	10.1230i	0.966333	+	0.368658i
$755$		−	23.4303i		−	0.852717i
$756$	−6.40631	+	7.85712i	−0.232995	+	0.285761i
$757$	−6.73813	−	11.6708i	−0.244902	−	0.424182i	0.717202	−	0.696865i	$-0.245422\pi$
$757$	−6.73813	−	11.6708i	−0.244902	−	0.424182i	−0.962104	+	0.272683i	$0.912089\pi$
$758$	23.0723			0.838025
$759$	5.83473	+	7.76097i	0.211787	+	0.281706i
$760$	13.0176	+	3.48807i	0.472199	+	0.126525i
$761$	−39.5762	−	10.6044i	−1.43463	−	0.384409i	−0.543983	−	0.839096i	$-0.683085\pi$
$761$	−39.5762	−	10.6044i	−1.43463	−	0.384409i	−0.890651	+	0.454687i	$0.849751\pi$
$762$	−1.51858	+	3.56647i	−0.0550124	+	0.129199i
$763$	−11.6732			−0.422599
$764$	0.210355	+	0.364345i	0.00761037	+	0.0131815i
$765$	34.3388	+	62.2766i	1.24152	+	2.25162i
$766$		−	23.8524i		−	0.861821i
$767$	29.7388	+	11.3454i	1.07380	+	0.409658i
$768$	−1.36368	−	1.06788i	−0.0492076	−	0.0385339i
$769$	−15.4846	+	15.4846i	−0.558390	+	0.558390i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.60665 - 0.647043i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.84756 - 0.763001i) q^{5} +(-1.38444 + 1.04083i) q^{6} +(-1.37958 - 1.37958i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.16267 - 2.07915i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.60665 - 0.647043i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.84756 - 0.763001i) q^{5} +(-1.38444 + 1.04083i) q^{6} +(-1.37958 - 1.37958i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.16267 - 2.07915i) q^{9} +(-2.55305 + 1.47400i) q^{10} +(0.207457 + 0.774238i) q^{11} +(1.06788 - 1.36368i) q^{12} +(-3.58657 - 0.369493i) q^{13} +(1.68964 + 0.975511i) q^{14} +(4.08135 - 3.06837i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.02058 + 6.96385i) q^{17} +(-1.55086 + 2.56804i) q^{18} +(-1.18319 - 4.41574i) q^{19} +(2.08456 - 2.08456i) q^{20} +(-3.10916 - 1.32386i) q^{21} +(-0.400775 - 0.694163i) q^{22} +6.99376 q^{23} +(-0.678548 + 1.59360i) q^{24} +(3.19629 - 1.84538i) q^{25} +(3.55999 - 0.571370i) q^{26} +(2.12937 - 4.73981i) q^{27} +(-1.88454 - 0.504962i) q^{28} +(6.82146 + 3.93837i) q^{29} +(-3.14812 + 4.02015i) q^{30} +(0.619046 + 2.31031i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.834276 + 1.10970i) q^{33} +(2.08121 - 7.76717i) q^{34} +(-4.98106 - 2.87582i) q^{35} +(0.833356 - 2.88193i) q^{36} +(-2.09658 + 7.82455i) q^{37} +(2.28576 + 3.95904i) q^{38} +(-6.00145 + 1.72702i) q^{39} +(-1.47400 + 2.55305i) q^{40} +(-3.66359 - 3.66359i) q^{41} +(3.34586 + 0.474043i) q^{42} +2.33382i q^{43} +(0.566782 + 0.566782i) q^{44} +(4.57194 - 7.57061i) q^{45} +(-6.75546 + 1.81012i) q^{46} +(-5.14869 - 1.37959i) q^{47} +(0.242972 - 1.71492i) q^{48} -3.19351i q^{49} +(-2.60976 + 2.60976i) q^{50} +(-1.95377 + 13.7900i) q^{51} +(-3.29081 + 1.47329i) q^{52} +8.27924i q^{53} +(-0.830059 + 5.12943i) q^{54} +(1.18149 + 2.04640i) q^{55} +1.95102 q^{56} +(-4.75815 - 6.32899i) q^{57} +(-7.60835 - 2.03865i) q^{58} +(-8.52709 - 2.28483i) q^{59} +(2.00036 - 4.69796i) q^{60} -4.93917 q^{61} +(-1.19590 - 2.07137i) q^{62} +(-5.85193 - 0.115230i) q^{63} -1.00000i q^{64} +(-10.4949 + 1.68440i) q^{65} +(-1.09306 - 0.855961i) q^{66} +(0.549015 - 0.549015i) q^{67} +8.04117i q^{68} +(11.2366 - 4.52526i) q^{69} +(5.55565 + 1.48863i) q^{70} +(-2.57304 + 0.689443i) q^{71} +(-0.0590613 + 2.99942i) q^{72} +(5.68293 + 5.68293i) q^{73} -8.10057i q^{74} +(3.94129 - 5.03302i) q^{75} +(-3.23255 - 3.23255i) q^{76} +(0.781921 - 1.35433i) q^{77} +(5.34997 - 3.22146i) q^{78} +(0.554497 + 0.960416i) q^{79} +(0.763001 - 2.84756i) q^{80} +(0.354299 - 8.99302i) q^{81} +(4.48696 + 2.59055i) q^{82} +(0.614312 - 2.29264i) q^{83} +(-3.35454 + 0.408081i) q^{84} +(-6.13542 + 22.8977i) q^{85} +(-0.604036 - 2.25429i) q^{86} +(13.5080 + 1.91382i) q^{87} +(-0.694163 - 0.400775i) q^{88} +(-2.84070 - 0.761164i) q^{89} +(-2.45674 + 8.49595i) q^{90} +(4.43822 + 5.45771i) q^{91} +(6.05678 - 3.49688i) q^{92} +(2.48946 + 3.31132i) q^{93} +5.33031 q^{94} +(-6.73843 - 11.6713i) q^{95} +(0.209163 + 1.71938i) q^{96} +(2.59780 - 2.59780i) q^{97} +(0.826542 + 3.08469i) q^{98} +(2.05842 + 1.24309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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