LMFDB - Embedded newform 234.2.z.a.227.9

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			227.9
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.53071 - 0.810507i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.970449 + 3.62177i) q^{5} +(-1.17907 + 1.26878i) q^{6} +(2.29680 + 2.29680i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.68616 + 2.48131i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.53071 - 0.810507i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.970449 + 3.62177i) q^{5} +(-1.17907 + 1.26878i) q^{6} +(2.29680 + 2.29680i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.68616 + 2.48131i) q^{9} +(3.24719 + 1.87476i) q^{10} +(-2.11332 - 0.566263i) q^{11} +(0.920381 + 1.46728i) q^{12} +(-3.26412 - 1.53151i) q^{13} +(2.81299 - 1.62408i) q^{14} +(4.42095 - 4.75732i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.50770 + 6.07551i) q^{17} +(2.83317 - 0.986492i) q^{18} +(4.70354 + 1.26031i) q^{19} +(2.65132 - 2.65132i) q^{20} +(-1.65416 - 5.37730i) q^{21} +(-1.09394 + 1.89475i) q^{22} +0.831757 q^{23} +(1.65549 - 0.509261i) q^{24} +(-7.84529 - 4.52948i) q^{25} +(-2.32414 + 2.75652i) q^{26} +(-0.569900 - 5.16481i) q^{27} +(-0.840685 - 3.13748i) q^{28} +(-8.02571 + 4.63365i) q^{29} +(-3.45100 - 5.50159i) q^{30} +(0.527973 + 0.141470i) q^{31} +(0.965926 - 0.258819i) q^{32} +(2.77593 + 2.57965i) q^{33} +(6.77635 - 1.81572i) q^{34} +(-10.5474 + 6.08953i) q^{35} +(-0.219600 - 2.99195i) q^{36} +(1.90093 - 0.509353i) q^{37} +(2.43473 - 4.21708i) q^{38} +(3.75513 + 4.98989i) q^{39} +(-1.87476 - 3.24719i) q^{40} +(-1.24565 - 1.24565i) q^{41} +(-5.62220 + 0.206049i) q^{42} -0.0581115i q^{43} +(1.54706 + 1.54706i) q^{44} +(-10.6230 + 3.69888i) q^{45} +(0.215275 - 0.803416i) q^{46} +(1.56367 + 5.83570i) q^{47} +(-0.0634356 - 1.73089i) q^{48} +3.55054i q^{49} +(-6.40565 + 6.40565i) q^{50} +(-0.445026 - 12.1429i) q^{51} +(2.06106 + 2.95839i) q^{52} -1.62324i q^{53} +(-5.13632 - 0.786269i) q^{54} +(4.10174 - 7.10443i) q^{55} -3.24816 q^{56} +(-6.17827 - 5.74143i) q^{57} +(2.39855 + 8.95152i) q^{58} +(-0.755077 - 2.81798i) q^{59} +(-6.20731 + 1.90949i) q^{60} +3.57998 q^{61} +(0.273299 - 0.473367i) q^{62} +(-1.82630 + 9.57181i) q^{63} -1.00000i q^{64} +(8.71443 - 10.3356i) q^{65} +(3.21021 - 2.01368i) q^{66} +(9.19065 - 9.19065i) q^{67} -7.01540i q^{68} +(-1.27318 - 0.674146i) q^{69} +(3.15217 + 11.7641i) q^{70} +(2.31786 - 8.65035i) q^{71} +(-2.94684 - 0.562257i) q^{72} +(3.38343 + 3.38343i) q^{73} -1.96799i q^{74} +(8.33770 + 13.2920i) q^{75} +(-3.44323 - 3.44323i) q^{76} +(-3.55328 - 6.15446i) q^{77} +(5.79176 - 2.33570i) q^{78} +(-5.86001 + 10.1498i) q^{79} +(-3.62177 + 0.970449i) q^{80} +(-3.31376 + 8.36773i) q^{81} +(-1.52561 + 0.880809i) q^{82} +(14.0250 - 3.75798i) q^{83} +(-1.25610 + 5.48396i) q^{84} +(-25.4081 + 6.80809i) q^{85} +(-0.0561314 - 0.0150404i) q^{86} +(16.0407 - 0.587877i) q^{87} +(1.89475 - 1.09394i) q^{88} +(-3.50606 - 13.0848i) q^{89} +(0.823397 + 11.2184i) q^{90} +(-3.97946 - 11.0146i) q^{91} +(-0.720323 - 0.415879i) q^{92} +(-0.693511 - 0.644475i) q^{93} +6.04156 q^{94} +(-9.12909 + 15.8121i) q^{95} +(-1.68833 - 0.386713i) q^{96} +(6.97910 - 6.97910i) q^{97} +(3.42956 + 0.918947i) q^{98} +(-2.15832 - 6.19861i) 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 $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−1.53071	−	0.810507i	−0.883757	−	0.467947i
$3$	−1.53071	−	0.810507i	−0.883757	−	0.467947i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.970449	+	3.62177i	−0.433998	+	1.61970i	0.309454	+	0.950914i	$0.399854\pi$
$5$	−0.970449	+	3.62177i	−0.433998	+	1.61970i	−0.743452	+	0.668789i	$0.766813\pi$
$6$	−1.17907	+	1.26878i	−0.481352	+	0.517977i
$7$	2.29680	+	2.29680i	0.868107	+	0.868107i	0.992263	−	0.124156i	$-0.0396222\pi$
$7$	2.29680	+	2.29680i	0.868107	+	0.868107i	−0.124156	+	0.992263i	$0.539622\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.68616	+	2.48131i	0.562052	+	0.827102i
$10$	3.24719	+	1.87476i	1.02685	+	0.592852i
$11$	−2.11332	−	0.566263i	−0.637190	−	0.170735i	−0.0742600	−	0.997239i	$-0.523659\pi$
$11$	−2.11332	−	0.566263i	−0.637190	−	0.170735i	−0.562930	+	0.826504i	$0.690326\pi$
$12$	0.920381	+	1.46728i	0.265691	+	0.423566i
$13$	−3.26412	−	1.53151i	−0.905304	−	0.424764i
$13$	−3.26412	−	1.53151i	−0.905304	−	0.424764i
$14$	2.81299	−	1.62408i	0.751803	−	0.434054i
$15$	4.42095	−	4.75732i	1.14148	−	1.22834i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.50770	+	6.07551i	0.850742	+	1.47353i	0.880540	+	0.473972i	$0.157180\pi$
$17$	3.50770	+	6.07551i	0.850742	+	1.47353i	−0.0297983	+	0.999556i	$0.509487\pi$
$18$	2.83317	−	0.986492i	0.667784	−	0.232518i
$19$	4.70354	+	1.26031i	1.07907	+	0.289135i	0.754213	−	0.656630i	$-0.228019\pi$
$19$	4.70354	+	1.26031i	1.07907	+	0.289135i	0.324853	+	0.945765i	$0.394685\pi$
$20$	2.65132	−	2.65132i	0.592852	−	0.592852i
$21$	−1.65416	−	5.37730i	−0.360968	−	1.17342i
$22$	−1.09394	+	1.89475i	−0.233228	+	0.403963i
$23$	0.831757			0.173433			0.0867167	−	0.996233i	$-0.472363\pi$
$23$	0.831757			0.173433			0.0867167	+	0.996233i	$0.472363\pi$
$24$	1.65549	−	0.509261i	0.337926	−	0.103952i
$25$	−7.84529	−	4.52948i	−1.56906	−	0.905896i
$26$	−2.32414	+	2.75652i	−0.455801	+	0.540597i
$27$	−0.569900	−	5.16481i	−0.109677	−	0.993967i
$28$	−0.840685	−	3.13748i	−0.158875	−	0.592928i
$29$	−8.02571	+	4.63365i	−1.49034	+	0.860447i	−0.999939	−	0.0110518i	$-0.996482\pi$
$29$	−8.02571	+	4.63365i	−1.49034	+	0.860447i	−0.490398	+	0.871498i	$0.663149\pi$
$30$	−3.45100	−	5.50159i	−0.630063	−	1.00445i
$31$	0.527973	+	0.141470i	0.0948267	+	0.0254087i	0.305920	−	0.952057i	$-0.401036\pi$
$31$	0.527973	+	0.141470i	0.0948267	+	0.0254087i	−0.211094	+	0.977466i	$0.567703\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	2.77593	+	2.57965i	0.483227	+	0.449059i
$34$	6.77635	−	1.81572i	1.16213	−	0.311393i
$35$	−10.5474	+	6.08953i	−1.78283	+	1.02932i
$36$	−0.219600	−	2.99195i	−0.0366000	−	0.498659i
$37$	1.90093	−	0.509353i	0.312511	−	0.0837372i	−0.0991544	−	0.995072i	$-0.531614\pi$
$37$	1.90093	−	0.509353i	0.312511	−	0.0837372i	0.411666	+	0.911335i	$0.364947\pi$
$38$	2.43473	−	4.21708i	0.394966	−	0.684100i
$39$	3.75513	+	4.98989i	0.601302	+	0.799022i
$40$	−1.87476	−	3.24719i	−0.296426	−	0.513425i
$41$	−1.24565	−	1.24565i	−0.194538	−	0.194538i	0.603116	−	0.797654i	$-0.293926\pi$
$41$	−1.24565	−	1.24565i	−0.194538	−	0.194538i	−0.797654	+	0.603116i	$0.793926\pi$
$42$	−5.62220	+	0.206049i	−0.867525	+	0.0317941i
$43$		−	0.0581115i		−	0.00886192i	−0.999990	−	0.00443096i	$-0.998590\pi$
$43$		−	0.0581115i		−	0.00886192i	0.999990	−	0.00443096i	$-0.00141042\pi$
$44$	1.54706	+	1.54706i	0.233228	+	0.233228i
$45$	−10.6230	+	3.69888i	−1.58359	+	0.551396i
$46$	0.215275	−	0.803416i	0.0317405	−	0.118457i
$47$	1.56367	+	5.83570i	0.228085	+	0.851224i	0.981145	+	0.193272i	$0.0619101\pi$
$47$	1.56367	+	5.83570i	0.228085	+	0.851224i	−0.753060	+	0.657951i	$0.771423\pi$
$48$	−0.0634356	−	1.73089i	−0.00915615	−	0.249832i
$49$			3.55054i			0.507220i
$50$	−6.40565	+	6.40565i	−0.905896	+	0.905896i
$51$	−0.445026	−	12.1429i	−0.0623161	−	1.70034i
$52$	2.06106	+	2.95839i	0.285817	+	0.410254i
$53$		−	1.62324i		−	0.222969i	−0.993766	−	0.111484i	$-0.964440\pi$
$53$		−	1.62324i		−	0.222969i	0.993766	−	0.111484i	$-0.0355605\pi$
$54$	−5.13632	−	0.786269i	−0.698965	−	0.106998i
$55$	4.10174	−	7.10443i	0.553079	−	0.957961i
$56$	−3.24816			−0.434054
$57$	−6.17827	−	5.74143i	−0.818332	−	0.760470i
$58$	2.39855	+	8.95152i	0.314945	+	1.17539i
$59$	−0.755077	−	2.81798i	−0.0983026	−	0.366870i	0.899197	−	0.437544i	$-0.144152\pi$
$59$	−0.755077	−	2.81798i	−0.0983026	−	0.366870i	−0.997499	+	0.0706740i	$0.977485\pi$
$60$	−6.20731	+	1.90949i	−0.801361	+	0.246514i
$61$	3.57998			0.458369			0.229185	−	0.973383i	$-0.426394\pi$
$61$	3.57998			0.458369			0.229185	+	0.973383i	$0.426394\pi$
$62$	0.273299	−	0.473367i	0.0347090	−	0.0601177i
$63$	−1.82630	+	9.57181i	−0.230092	+	1.20593i
$64$		−	1.00000i		−	0.125000i
$65$	8.71443	−	10.3356i	1.08089	−	1.28198i
$66$	3.21021	−	2.01368i	0.395150	−	0.247866i
$67$	9.19065	−	9.19065i	1.12282	−	1.12282i	0.131500	−	0.991316i	$-0.458021\pi$
$67$	9.19065	−	9.19065i	1.12282	−	1.12282i	0.991316	−	0.131500i	$-0.0419795\pi$
$68$		−	7.01540i		−	0.850742i
$69$	−1.27318	−	0.674146i	−0.153273	−	0.0811576i
$70$	3.15217	+	11.7641i	0.376757	+	1.40608i
$71$	2.31786	−	8.65035i	0.275079	−	1.02661i	−0.680710	−	0.732553i	$-0.738329\pi$
$71$	2.31786	−	8.65035i	0.275079	−	1.02661i	0.955789	−	0.294055i	$-0.0950048\pi$
$72$	−2.94684	−	0.562257i	−0.347288	−	0.0662626i
$73$	3.38343	+	3.38343i	0.396001	+	0.396001i	0.876820	−	0.480819i	$-0.159661\pi$
$73$	3.38343	+	3.38343i	0.396001	+	0.396001i	−0.480819	+	0.876820i	$0.659661\pi$
$74$		−	1.96799i		−	0.228774i
$75$	8.33770	+	13.2920i	0.962755	+	1.53483i
$76$	−3.44323	−	3.44323i	−0.394966	−	0.394966i
$77$	−3.55328	−	6.15446i	−0.404934	−	0.701366i
$78$	5.79176	−	2.33570i	0.655788	−	0.264466i
$79$	−5.86001	+	10.1498i	−0.659302	+	1.14194i	0.321494	+	0.946911i	$0.395815\pi$
$79$	−5.86001	+	10.1498i	−0.659302	+	1.14194i	−0.980797	+	0.195033i	$0.937518\pi$
$80$	−3.62177	+	0.970449i	−0.404926	+	0.108500i
$81$	−3.31376	+	8.36773i	−0.368196	+	0.929748i
$82$	−1.52561	+	0.880809i	−0.168475	+	0.0972691i
$83$	14.0250	−	3.75798i	1.53944	−	0.412492i	0.613356	−	0.789807i	$-0.289819\pi$
$83$	14.0250	−	3.75798i	1.53944	−	0.412492i	0.926085	+	0.377315i	$0.123152\pi$
$84$	−1.25610	+	5.48396i	−0.137052	+	0.598349i
$85$	−25.4081	+	6.80809i	−2.75590	+	0.738441i
$86$	−0.0561314	−	0.0150404i	−0.00605280	−	0.00162184i
$87$	16.0407	−	0.587877i	1.71974	−	0.0630270i
$88$	1.89475	−	1.09394i	0.201981	−	0.116614i
$89$	−3.50606	−	13.0848i	−0.371642	−	1.38699i	−0.858190	−	0.513332i	$-0.828411\pi$
$89$	−3.50606	−	13.0848i	−0.371642	−	1.38699i	0.486548	−	0.873654i	$-0.338256\pi$
$90$	0.823397	+	11.2184i	0.0867936	+	1.18252i
$91$	−3.97946	−	11.0146i	−0.417160	−	1.15464i
$92$	−0.720323	−	0.415879i	−0.0750989	−	0.0433583i
$93$	−0.693511	−	0.644475i	−0.0719138	−	0.0668290i
$94$	6.04156			0.623139
$95$	−9.12909	+	15.8121i	−0.936625	+	1.62228i
$96$	−1.68833	−	0.386713i	−0.172314	−	0.0394687i
$97$	6.97910	−	6.97910i	0.708620	−	0.708620i	−0.257625	−	0.966245i	$-0.582940\pi$
$97$	6.97910	−	6.97910i	0.708620	−	0.708620i	0.966245	+	0.257625i	$0.0829398\pi$
$98$	3.42956	+	0.918947i	0.346438	+	0.0928277i
$99$	−2.15832	−	6.19861i	−0.216919	−	0.622983i
$100$	4.52948	+	7.84529i	0.452948	+	0.784529i
$101$	2.19946	+	3.80958i	0.218855	+	0.379068i	0.954458	−	0.298345i	$-0.0964346\pi$
$101$	2.19946	+	3.80958i	0.218855	+	0.379068i	−0.735603	+	0.677413i	$0.763101\pi$
$102$	−11.8443	−	2.71294i	−1.17276	−	0.268621i
$103$	8.09876	−	4.67582i	0.797994	−	0.460722i	−0.0447750	−	0.998997i	$-0.514257\pi$
$103$	8.09876	−	4.67582i	0.797994	−	0.460722i	0.842769	+	0.538275i	$0.180924\pi$
$104$	3.39102	−	1.22514i	0.332517	−	0.120135i
$105$	21.0806	−	0.772587i	2.05726	−	0.0753968i
$106$	−1.56793	−	0.420125i	−0.152290	−	0.0408061i
$107$	−4.41803	−	2.55075i	−0.427107	−	0.246590i	0.271007	−	0.962577i	$-0.412643\pi$
$107$	−4.41803	−	2.55075i	−0.427107	−	0.246590i	−0.698113	+	0.715987i	$0.745977\pi$
$108$	−2.08885	+	4.75780i	−0.201000	+	0.457820i
$109$	−0.923072	+	0.923072i	−0.0884142	+	0.0884142i	−0.749931	−	0.661516i	$-0.769913\pi$
$109$	−0.923072	+	0.923072i	−0.0884142	+	0.0884142i	0.661516	+	0.749931i	$0.269913\pi$
$110$	−5.80074	−	5.80074i	−0.553079	−	0.553079i
$111$	−3.32261	−	0.761047i	−0.315369	−	0.0722354i
$112$	−0.840685	+	3.13748i	−0.0794373	+	0.296464i
$113$	10.0193	+	5.78467i	0.942541	+	0.544176i	0.890756	−	0.454482i	$-0.150176\pi$
$113$	10.0193	+	5.78467i	0.942541	+	0.544176i	0.0517852	+	0.998658i	$0.483509\pi$
$114$	−7.14485	+	4.48176i	−0.669176	+	0.419756i
$115$	−0.807178	+	3.01243i	−0.0752698	+	0.280911i
$116$	9.26729			0.860447
$117$	−1.70367	−	10.6816i	−0.157505	−	0.987518i
$118$	−2.91739			−0.268568
$119$	−5.89774	+	22.0107i	−0.540645	+	2.01771i
$120$	0.237854	+	6.49002i	0.0217130	+	0.592455i
$121$	−5.38080	−	3.10661i	−0.489164	−	0.282419i
$122$	0.926566	−	3.45799i	0.0838874	−	0.313072i
$123$	0.897124	+	2.91634i	0.0808909	+	0.262958i
$124$	−0.386503	−	0.386503i	−0.0347090	−	0.0347090i
$125$	10.7616	−	10.7616i	0.962547	−	0.962547i
$126$	8.77297	+	4.24144i	0.781559	+	0.377857i
$127$	2.86070	+	1.65163i	0.253846	+	0.146558i	0.621524	−	0.783395i	$-0.286514\pi$
$127$	2.86070	+	1.65163i	0.253846	+	0.146558i	−0.367678	+	0.929953i	$0.619847\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−0.0470998	+	0.0889519i	−0.00414691	+	0.00783178i
$130$	−7.72799	−	11.0925i	−0.677790	−	0.972881i
$131$	9.54763	−	5.51233i	0.834181	−	0.481614i	−0.0211014	−	0.999777i	$-0.506717\pi$
$131$	9.54763	−	5.51233i	0.834181	−	0.481614i	0.855282	+	0.518163i	$0.173384\pi$
$132$	−1.11420	−	3.62200i	−0.0969785	−	0.315255i
$133$	7.90840	+	13.6977i	0.685745	+	1.18774i
$134$	−6.49877	−	11.2562i	−0.561408	−	0.972388i
$135$	19.2588	+	2.94814i	1.65753	+	0.253735i
$136$	−6.77635	−	1.81572i	−0.581067	−	0.155697i
$137$	−8.04563	+	8.04563i	−0.687384	+	0.687384i	−0.961653	−	0.274269i	$-0.911564\pi$
$137$	−8.04563	+	8.04563i	−0.687384	+	0.687384i	0.274269	+	0.961653i	$0.411564\pi$
$138$	−0.980698	+	1.05532i	−0.0834825	+	0.0898345i
$139$	−1.83834	+	3.18410i	−0.155926	+	0.270072i	−0.933396	−	0.358849i	$-0.883169\pi$
$139$	−1.83834	+	3.18410i	−0.155926	+	0.270072i	0.777470	+	0.628920i	$0.216503\pi$
$140$	12.1791			1.02932
$141$	2.33635	−	10.2001i	0.196756	−	0.859006i
$142$	−7.75569	−	4.47775i	−0.650843	−	0.375765i
$143$	6.03090	+	5.08492i	0.504329	+	0.425222i
$144$	−1.30580	+	2.70091i	−0.108816	+	0.225076i
$145$	−8.99344	−	33.5640i	−0.746864	−	2.78734i
$146$	4.14384	−	2.39245i	0.342947	−	0.198000i
$147$	2.87774	−	5.43485i	0.237352	−	0.448259i
$148$	−1.90093	−	0.509353i	−0.156256	−	0.0418686i
$149$	8.76537	−	2.34867i	0.718087	−	0.192411i	0.118769	−	0.992922i	$-0.462105\pi$
$149$	8.76537	−	2.34867i	0.718087	−	0.192411i	0.599318	+	0.800511i	$0.295439\pi$
$150$	14.9970	−	4.61338i	1.22450	−	0.376681i
$151$	−18.2244	+	4.88320i	−1.48308	+	0.397389i	−0.907393	−	0.420283i	$-0.861931\pi$
$151$	−18.2244	+	4.88320i	−1.48308	+	0.397389i	−0.575684	+	0.817672i	$0.695264\pi$
$152$	−4.21708	+	2.43473i	−0.342050	+	0.197483i
$153$	−9.16068	+	18.9479i	−0.740597	+	1.53185i
$154$	−6.86441	+	1.83931i	−0.553150	+	0.148216i
$155$	−1.02474	+	1.77490i	−0.0823092	+	0.142564i
$156$	−0.757091	−	6.19894i	−0.0606158	−	0.496312i
$157$	11.0256	+	19.0969i	0.879939	+	1.52410i	0.851407	+	0.524506i	$0.175750\pi$
$157$	11.0256	+	19.0969i	0.879939	+	1.52410i	0.0285320	+	0.999593i	$0.490917\pi$
$158$	8.28730	+	8.28730i	0.659302	+	0.659302i
$159$	−1.31565	+	2.48471i	−0.104337	+	0.197050i
$160$			3.74953i			0.296426i
$161$	1.91038	+	1.91038i	0.150559	+	0.150559i
$162$	7.22495	+	5.36658i	0.567645	+	0.421638i
$163$	−1.64426	+	6.13647i	−0.128789	+	0.480646i	−0.999946	−	0.0103577i	$-0.996703\pi$
$163$	−1.64426	+	6.13647i	−0.128789	+	0.480646i	0.871158	+	0.491003i	$0.163370\pi$
$164$	0.455940	+	1.70159i	0.0356030	+	0.132872i
$165$	−12.0368	+	7.55034i	−0.937062	+	0.587793i
$166$		−	14.5197i		−	1.12695i
$167$	−6.22875	+	6.22875i	−0.481995	+	0.481995i	−0.905768	−	0.423773i	$-0.860705\pi$
$167$	−6.22875	+	6.22875i	−0.481995	+	0.481995i	0.423773	+	0.905768i	$0.360705\pi$
$168$	4.97199	+	2.63266i	0.383598	+	0.203114i
$169$	8.30897	+	9.99805i	0.639151	+	0.769081i
$170$			26.3044i			2.01746i
$171$	4.80368	+	13.7960i	0.367347	+	1.05501i
$172$	−0.0290558	+	0.0503260i	−0.00221548	+	0.00383732i
$173$	−0.0504820			−0.00383808			−0.00191904	−	0.999998i	$-0.500611\pi$
$173$	−0.0504820			−0.00383808			−0.00191904	+	0.999998i	$0.500611\pi$
$174$	3.58378	−	15.6462i	0.271686	−	1.18614i
$175$	−7.61574	−	28.4223i	−0.575696	−	2.14853i
$176$	−0.566263	−	2.11332i	−0.0426837	−	0.159298i
$177$	−1.12819	+	4.92552i	−0.0848002	+	0.370224i
$178$	−13.5464			−1.01534
$179$	3.55609	−	6.15933i	0.265795	−	0.460370i	−0.701977	−	0.712200i	$-0.747699\pi$
$179$	3.55609	−	6.15933i	0.265795	−	0.460370i	0.967772	+	0.251830i	$0.0810323\pi$
$180$	11.0493	+	2.10820i	0.823563	+	0.157136i
$181$			20.6330i			1.53364i	0.641863	+	0.766820i	$0.278162\pi$
$181$			20.6330i			1.53364i	−0.641863	+	0.766820i	$0.721838\pi$
$182$	−11.6692	+	0.993078i	−0.864980	+	0.0736118i
$183$	−5.47991	−	2.90160i	−0.405087	−	0.214492i
$184$	−0.588141	+	0.588141i	−0.0433583	+	0.0433583i
$185$			7.37904i			0.542518i
$186$	−0.802009	+	0.503078i	−0.0588062	+	0.0368875i
$187$	−3.97256	−	14.8258i	−0.290502	−	1.08417i
$188$	1.56367	−	5.83570i	0.114042	−	0.425612i
$189$	10.5536	−	13.1714i	0.767658	−	0.958082i
$190$	12.9105	+	12.9105i	0.936625	+	0.936625i
$191$		−	22.4922i		−	1.62748i	−0.581232	−	0.813738i	$-0.697429\pi$
$191$		−	22.4922i		−	1.62748i	0.581232	−	0.813738i	$-0.302571\pi$
$192$	−0.810507	+	1.53071i	−0.0584933	+	0.110470i
$193$	4.78081	+	4.78081i	0.344131	+	0.344131i	0.857918	−	0.513787i	$-0.171758\pi$
$193$	4.78081	+	4.78081i	0.344131	+	0.344131i	−0.513787	+	0.857918i	$0.671758\pi$
$194$	−4.93497	−	8.54762i	−0.354310	−	0.613683i
$195$	−21.7164	+	8.75776i	−1.55514	+	0.627156i
$196$	1.77527	−	3.07486i	0.126805	−	0.219633i
$197$	5.95380	−	1.59532i	0.424191	−	0.113662i	−0.0404072	−	0.999183i	$-0.512866\pi$
$197$	5.95380	−	1.59532i	0.424191	−	0.113662i	0.464598	+	0.885522i	$0.346199\pi$
$198$	−6.54601	+	0.480457i	−0.465204	+	0.0341446i
$199$	3.29772	−	1.90394i	0.233769	−	0.134967i	−0.378541	−	0.925585i	$-0.623574\pi$
$199$	3.29772	−	1.90394i	0.233769	−	0.134967i	0.612310	+	0.790618i	$0.290241\pi$
$200$	8.75029	−	2.34463i	0.618739	−	0.165791i
$201$	−21.5173	+	6.61914i	−1.51771	+	0.466878i
$202$	4.24904	−	1.13853i	0.298961	−	0.0801064i
$203$	−29.0760	−	7.79088i	−2.04073	−	0.546813i
$204$	−5.68603	+	10.7385i	−0.398102	+	0.751849i
$205$	5.72030	−	3.30262i	0.399523	−	0.230665i
$206$	−2.42038	−	9.03299i	−0.168636	−	0.629358i
$207$	1.40247	+	2.06384i	0.0974785	+	0.143447i
$208$	−0.305736	−	3.59257i	−0.0211989	−	0.249100i
$209$	−9.22643	−	5.32688i	−0.638205	−	0.368468i
$210$	4.70980	−	20.5623i	0.325007	−	1.41893i
$211$	−19.1877			−1.32094			−0.660469	−	0.750853i	$-0.729642\pi$
$211$	−19.1877			−1.32094			−0.660469	+	0.750853i	$0.729642\pi$
$212$	−0.811618	+	1.40576i	−0.0557422	+	0.0965483i
$213$	−10.5591	+	11.3626i	−0.723501	+	0.778549i
$214$	−3.60730	+	3.60730i	−0.246590	+	0.246590i
$215$	0.210466	+	0.0563943i	0.0143537	+	0.00384606i
$216$	4.05505	+	3.24909i	0.275911	+	0.221072i
$217$	0.887718	+	1.53757i	0.0602622	+	0.104377i
$218$	0.652710	+	1.13053i	0.0442071	+	0.0765690i
$219$	−2.43676	−	7.92136i	−0.164661	−	0.535276i
$220$	−7.10443	+	4.10174i	−0.478980	+	0.276539i
$221$	−2.14486	−	25.2033i	−0.144279	−	1.69536i
$222$	−1.59507	+	3.01243i	−0.107054	+	0.202181i
$223$	−0.270983	−	0.0726098i	−0.0181464	−	0.00486231i	0.249734	−	0.968314i	$-0.419657\pi$
$223$	−0.270983	−	0.0726098i	−0.0181464	−	0.00486231i	−0.267881	+	0.963452i	$0.586323\pi$
$224$	2.81299	+	1.62408i	0.187951	+	0.108513i
$225$	−1.98935	−	27.1040i	−0.132623	−	1.80693i
$226$	8.18076	−	8.18076i	0.544176	−	0.544176i
$227$	9.00891	+	9.00891i	0.597942	+	0.597942i	0.939765	−	0.341822i	$-0.111044\pi$
$227$	9.00891	+	9.00891i	0.597942	+	0.597942i	−0.341822	+	0.939765i	$0.611044\pi$
$228$	2.47983	+	8.06136i	0.164231	+	0.533876i
$229$	−1.11470	+	4.16011i	−0.0736613	+	0.274908i	−0.992926	−	0.118731i	$-0.962117\pi$
$229$	−1.11470	+	4.16011i	−0.0736613	+	0.274908i	0.919265	+	0.393639i	$0.128784\pi$
$230$	2.70087	+	1.55935i	0.178090	+	0.102820i
$231$	0.450809	+	12.3007i	0.0296611	+	0.809324i
$232$	2.39855	−	8.95152i	0.157473	−	0.587696i
$233$	21.0744			1.38063			0.690313	−	0.723511i	$-0.257473\pi$
$233$	21.0744			1.38063			0.690313	+	0.723511i	$0.257473\pi$
$234$	−10.7586	−	1.11899i	−0.703313	−	0.0731507i
$235$	−22.6530			−1.47772
$236$	−0.755077	+	2.81798i	−0.0491513	+	0.183435i
$237$	17.1965	−	10.7869i	1.11703	−	0.700683i
$238$	19.7342	+	11.3936i	1.27918	+	0.738535i
$239$	3.36892	−	12.5730i	0.217917	−	0.813278i	−0.767202	−	0.641406i	$-0.778352\pi$
$239$	3.36892	−	12.5730i	0.217917	−	0.813278i	0.985119	−	0.171873i	$-0.0549818\pi$
$240$	6.33044	+	1.44999i	0.408628	+	0.0935965i
$241$	0.881282	+	0.881282i	0.0567684	+	0.0567684i	0.734921	−	0.678153i	$-0.237219\pi$
$241$	0.881282	+	0.881282i	0.0567684	+	0.0567684i	−0.678153	+	0.734921i	$0.737219\pi$
$242$	−4.39341	+	4.39341i	−0.282419	+	0.282419i
$243$	11.8545	−	10.1228i	0.760468	−	0.649375i
$244$	−3.10035	−	1.78999i	−0.198480	−	0.114592i
$245$	−12.8592	−	3.44562i	−0.821545	−	0.220132i
$246$	3.04917	−	0.111749i	0.194408	−	0.00712488i
$247$	−13.4227	−	11.3173i	−0.854069	−	0.720103i
$248$	−0.473367	+	0.273299i	−0.0300588	+	0.0173545i
$249$	−24.5141	−	5.61496i	−1.55352	−	0.355834i
$250$	−7.60960	−	13.1802i	−0.481273	−	0.833590i
$251$	−5.64794	−	9.78252i	−0.356495	−	0.617467i	0.630878	−	0.775882i	$-0.282695\pi$
$251$	−5.64794	−	9.78252i	−0.356495	−	0.617467i	−0.987373	+	0.158415i	$0.949362\pi$
$252$	6.36752	−	7.37628i	0.401116	−	0.464662i
$253$	−1.75777	−	0.470993i	−0.110510	−	0.0296111i
$254$	2.33575	−	2.33575i	0.146558	−	0.146558i
$255$	44.4105	+	10.1723i	2.78109	+	0.637012i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.62623			−0.101442			−0.0507209	−	0.998713i	$-0.516152\pi$
$257$	−1.62623			−0.101442			−0.0507209	+	0.998713i	$0.516152\pi$
$258$	0.0737307	+	0.0685174i	0.00459027	+	0.00426571i
$259$	5.53593	+	3.19617i	0.343986	+	0.198601i
$260$	−12.7147	+	4.59371i	−0.788534	+	0.284890i
$261$	−25.0301	−	12.1012i	−1.54932	−	0.749046i
$262$	−2.85339	−	10.6490i	−0.176283	−	0.657897i
$263$	9.85242	−	5.68830i	0.607526	−	0.350755i	−0.164470	−	0.986382i	$-0.552591\pi$
$263$	9.85242	−	5.68830i	0.607526	−	0.350755i	0.771997	+	0.635627i	$0.219258\pi$
$264$	−3.78696	+	0.138789i	−0.233071	+	0.00854188i
$265$	5.87898	+	1.57527i	0.361143	+	0.0967680i
$266$	15.2778	−	4.09369i	0.936745	−	0.251000i
$267$	−5.23856	+	22.8707i	−0.320595	+	1.39967i
$268$	−12.5547	+	3.36401i	−0.766898	+	0.205490i
$269$	−10.3721	+	5.98835i	−0.632400	+	0.365116i	−0.781681	−	0.623678i	$-0.785637\pi$
$269$	−10.3721	+	5.98835i	−0.632400	+	0.365116i	0.149281	+	0.988795i	$0.452304\pi$
$270$	7.83222	−	17.8395i	0.476654	−	1.08568i
$271$	23.9876	−	6.42745i	1.45714	−	0.390440i	0.558640	−	0.829410i	$-0.311323\pi$
$271$	23.9876	−	6.42745i	1.45714	−	0.390440i	0.898502	+	0.438970i	$0.144657\pi$
$272$	−3.50770	+	6.07551i	−0.212685	+	0.368382i
$273$	−2.83600	+	20.0855i	−0.171642	+	1.21563i
$274$	5.68912	+	9.85384i	0.343692	+	0.595292i
$275$	14.0147	+	14.0147i	0.845121	+	0.845121i
$276$	0.765534	+	1.22042i	0.0460797	+	0.0734605i
$277$			15.6518i			0.940425i	0.882553	+	0.470212i	$0.155823\pi$
$277$			15.6518i			0.940425i	−0.882553	+	0.470212i	$0.844177\pi$
$278$	2.59981	+	2.59981i	0.155926	+	0.155926i
$279$	0.539214	+	1.54860i	0.0322819	+	0.0927124i
$280$	3.15217	−	11.7641i	0.188378	−	0.703038i
$281$	1.13987	+	4.25406i	0.0679991	+	0.253776i	0.991555	−	0.129688i	$-0.0413976\pi$
$281$	1.13987	+	4.25406i	0.0679991	+	0.253776i	−0.923556	+	0.383464i	$0.874731\pi$
$282$	−9.24788	−	4.89673i	−0.550703	−	0.291596i
$283$			18.2539i			1.08508i	0.840030	+	0.542540i	$0.182537\pi$
$283$			18.2539i			1.08508i	−0.840030	+	0.542540i	$0.817463\pi$
$284$	−6.33250	+	6.33250i	−0.375765	+	0.375765i
$285$	26.7898	−	16.8045i	1.58689	−	0.995412i
$286$	6.47257	−	4.50933i	0.382731	−	0.266642i
$287$		−	5.72202i		−	0.337760i
$288$	2.27091	+	1.96035i	0.133815	+	0.115515i
$289$	−16.1079	+	27.8997i	−0.947523	+	1.64116i
$290$	−34.7480			−2.04047
$291$	−16.3396	+	5.02638i	−0.957844	+	0.294651i
$292$	−1.23842	−	4.62186i	−0.0724732	−	0.270474i
$293$	−2.89268	−	10.7956i	−0.168992	−	0.630688i	−0.997497	−	0.0707062i	$-0.977475\pi$
$293$	−2.89268	−	10.7956i	−0.168992	−	0.630688i	0.828505	−	0.559982i	$-0.189192\pi$
$294$	−4.50485	−	4.18632i	−0.262728	−	0.244151i
$295$	10.9388			0.636884
$296$	−0.983995	+	1.70433i	−0.0571936	+	0.0990622i
$297$	−1.72026	+	11.2376i	−0.0998194	+	0.652072i
$298$		−	9.07458i		−	0.525676i
$299$	−2.71496	−	1.27384i	−0.157010	−	0.0736682i
$300$	−0.574661	−	15.6801i	−0.0331781	−	0.905289i
$301$	0.133470	−	0.133470i	0.00769310	−	0.00769310i
$302$			18.8672i			1.08569i
$303$	−0.279049	−	7.61405i	−0.0160309	−	0.437416i
$304$	1.26031	+	4.70354i	0.0722837	+	0.269767i
$305$	−3.47419	+	12.9658i	−0.198931	+	0.742422i
$306$	15.9313	+	13.7526i	0.910734	+	0.786185i
$307$	−14.9777	−	14.9777i	−0.854823	−	0.854823i	0.135900	−	0.990723i	$-0.456608\pi$
$307$	−14.9777	−	14.9777i	−0.854823	−	0.854823i	−0.990723	+	0.135900i	$0.956608\pi$
$308$			7.10656i			0.404934i
$309$	−16.1866	+	0.593227i	−0.920826	+	0.0337475i
$310$	1.44920	+	1.44920i	0.0823092	+	0.0823092i
$311$	−6.94304	−	12.0257i	−0.393704	−	0.681915i	0.599231	−	0.800576i	$-0.295473\pi$
$311$	−6.94304	−	12.0257i	−0.393704	−	0.681915i	−0.992935	+	0.118661i	$0.962140\pi$
$312$	−6.18366	−	0.873109i	−0.350081	−	0.0494301i
$313$	4.79094	−	8.29816i	0.270800	−	0.469040i	−0.698267	−	0.715838i	$-0.746045\pi$
$313$	4.79094	−	8.29816i	0.270800	−	0.469040i	0.969067	+	0.246798i	$0.0793784\pi$
$314$	21.2998	−	5.70727i	1.20202	−	0.322080i
$315$	−32.8945	−	15.9034i	−1.85340	−	0.896054i
$316$	10.1498	−	5.86001i	0.570972	−	0.329651i
$317$	15.5549	−	4.16793i	0.873653	−	0.234095i	0.205986	−	0.978555i	$-0.433960\pi$
$317$	15.5549	−	4.16793i	0.873653	−	0.234095i	0.667667	+	0.744460i	$0.267293\pi$
$318$	2.05953	+	1.91391i	0.115493	+	0.107326i
$319$	19.5848	−	5.24772i	1.09654	−	0.293816i
$320$	3.62177	+	0.970449i	0.202463	+	0.0542498i
$321$	4.69532	+	7.48530i	0.262067	+	0.417789i
$322$	2.33972	−	1.35084i	0.130388	−	0.0752794i
$323$	8.84157	+	32.9972i	0.491958	+	1.83601i
$324$	7.05367	−	5.58979i	0.391870	−	0.310544i
$325$	18.6710	+	26.7999i	1.03568	+	1.48659i
$326$	5.50181	+	3.17647i	0.304717	+	0.175928i
$327$	2.16111	−	0.664800i	0.119510	−	0.0367635i
$328$	1.76162			0.0972691
$329$	−9.81197	+	16.9948i	−0.540951	+	0.936955i
$330$	4.17772	+	13.5808i	0.229976	+	0.747599i
$331$	5.22945	−	5.22945i	0.287437	−	0.287437i	−0.548629	−	0.836066i	$-0.684850\pi$
$331$	5.22945	−	5.22945i	0.287437	−	0.287437i	0.836066	+	0.548629i	$0.184850\pi$
$332$	−14.0250	−	3.75798i	−0.769721	−	0.206246i
$333$	4.46913	+	3.85795i	0.244907	+	0.211414i
$334$	4.40439	+	7.62863i	0.240998	+	0.417420i
$335$	24.3673	+	42.2054i	1.33133	+	2.30593i
$336$	3.82980	−	4.12120i	0.208933	−	0.224830i
$337$	16.2869	−	9.40326i	0.887205	−	0.512228i	0.0141778	−	0.999899i	$-0.495487\pi$
$337$	16.2869	−	9.40326i	0.887205	−	0.512228i	0.873027	+	0.487671i	$0.162154\pi$
$338$	11.8079	−	5.43816i	0.642265	−	0.295797i
$339$	−10.6482	−	16.9754i	−0.578331	−	0.921979i
$340$	25.4081	+	6.80809i	1.37795	+	0.369220i
$341$	−1.03567	−	0.597942i	−0.0560845	−	0.0323804i
$342$	14.5692	−	1.06933i	0.787812	−	0.0578230i
$343$	7.92271	−	7.92271i	0.427786	−	0.427786i
$344$	0.0410910	+	0.0410910i	0.00221548	+	0.00221548i
$345$	3.67715	−	3.95694i	0.197971	−	0.213034i
$346$	−0.0130657	+	0.0487619i	−0.000702417	+	0.00262145i
$347$	−21.4424	−	12.3798i	−1.15109	−	0.664582i	−0.201937	−	0.979398i	$-0.564724\pi$
$347$	−21.4424	−	12.3798i	−1.15109	−	0.664582i	−0.949153	+	0.314817i	$0.898057\pi$
$348$	−14.1856	−	7.51121i	−0.760425	−	0.402643i
$349$	0.883920	−	3.29884i	0.0473152	−	0.176583i	−0.938225	−	0.346027i	$-0.887531\pi$
$349$	0.883920	−	3.29884i	0.0473152	−	0.176583i	0.985540	+	0.169444i	$0.0541973\pi$
$350$	−29.4250			−1.57283
$351$	−6.04972	+	17.7314i	−0.322910	+	0.946430i
$352$	−2.18787			−0.116614
$353$	−1.15015	+	4.29243i	−0.0612165	+	0.228463i	−0.989756	−	0.142771i	$-0.954399\pi$
$353$	−1.15015	+	4.29243i	−0.0612165	+	0.228463i	0.928539	+	0.371234i	$0.121065\pi$
$354$	4.46569	+	2.36457i	0.237349	+	0.125675i
$355$	29.0802	+	16.7895i	1.54342	+	0.891092i
$356$	−3.50606	+	13.0848i	−0.185821	+	0.693493i
$357$	26.8676	−	28.9118i	1.42198	−	1.53018i
$358$	−5.02907	−	5.02907i	−0.265795	−	0.265795i
$359$	1.76025	−	1.76025i	0.0929022	−	0.0929022i	−0.659128	−	0.752031i	$-0.729075\pi$
$359$	1.76025	−	1.76025i	0.0929022	−	0.0929022i	0.752031	+	0.659128i	$0.229075\pi$
$360$	4.89612	−	10.1271i	0.258048	−	0.533746i
$361$	4.08043	+	2.35584i	0.214759	+	0.123991i
$362$	19.9300	+	5.34021i	1.04750	+	0.280675i
$363$	5.71853	+	9.11650i	0.300145	+	0.478492i
$364$	−2.06098	+	11.5286i	−0.108025	+	0.604265i
$365$	−15.5375	+	8.97055i	−0.813268	+	0.469540i
$366$	−4.22103	+	4.54220i	−0.220637	+	0.237425i
$367$	−4.07549	−	7.05896i	−0.212739	−	0.368475i	0.739832	−	0.672792i	$-0.234905\pi$
$367$	−4.07549	−	7.05896i	−0.212739	−	0.368475i	−0.952571	+	0.304317i	$0.901572\pi$
$368$	0.415879	+	0.720323i	0.0216792	+	0.0375494i
$369$	0.990482	−	5.19121i	0.0515624	−	0.270243i
$370$	7.12760	+	1.90984i	0.370546	+	0.0992876i
$371$	3.72824	−	3.72824i	0.193561	−	0.193561i
$372$	0.278361	+	0.904888i	0.0144323	+	0.0469162i
$373$	−11.8381	+	20.5043i	−0.612956	+	1.06167i	0.377784	+	0.925894i	$0.376686\pi$
$373$	−11.8381	+	20.5043i	−0.612956	+	1.06167i	−0.990740	+	0.135776i	$0.956647\pi$
$374$	−15.3488			−0.793667
$375$	−25.1953	+	7.75055i	−1.30108	+	0.400236i
$376$	−5.23214	−	3.02078i	−0.269827	−	0.155785i
$377$	33.2934	−	2.83334i	1.71470	−	0.145925i
$378$	−9.99118	−	13.6030i	−0.513891	−	0.699662i
$379$	2.92796	+	10.9273i	0.150399	+	0.561297i	0.999456	+	0.0329946i	$0.0105044\pi$
$379$	2.92796	+	10.9273i	0.150399	+	0.561297i	−0.849057	+	0.528302i	$0.822829\pi$
$380$	15.8121	−	9.12909i	0.811141	−	0.468313i
$381$	−3.04025	−	4.84678i	−0.155757	−	0.248308i
$382$	−21.7258	−	5.82140i	−1.11159	−	0.297849i
$383$	−29.0188	+	7.77555i	−1.48279	+	0.397312i	−0.907296	−	0.420494i	$-0.861857\pi$
$383$	−29.0188	+	7.77555i	−1.48279	+	0.397312i	−0.575494	+	0.817806i	$0.695190\pi$
$384$	1.26878	+	1.17907i	0.0647471	+	0.0601690i
$385$	25.7383	−	6.89655i	1.31174	−	0.351481i
$386$	5.85528	−	3.38055i	0.298026	−	0.172065i
$387$	0.144192	−	0.0979850i	0.00732971	−	0.00498086i
$388$	−9.53363	+	2.55453i	−0.483997	+	0.129687i
$389$	−4.55590	+	7.89104i	−0.230993	+	0.400092i	−0.958101	−	0.286432i	$-0.907531\pi$
$389$	−4.55590	+	7.89104i	−0.230993	+	0.400092i	0.727108	+	0.686524i	$0.240864\pi$
$390$	2.83873	+	23.2431i	0.143745	+	1.17696i
$391$	2.91755	+	5.05335i	0.147547	+	0.255559i
$392$	−2.51061	−	2.51061i	−0.126805	−	0.126805i
$393$	−19.0825	+	0.699356i	−0.962582	+	0.0352779i
$394$		−	6.16383i		−	0.310529i
$395$	−31.0735	−	31.0735i	−1.56348	−	1.56348i
$396$	−1.23015	+	6.44731i	−0.0618171	+	0.323989i
$397$	−2.78992	+	10.4121i	−0.140022	+	0.522570i	0.859904	+	0.510455i	$0.170523\pi$
$397$	−2.78992	+	10.4121i	−0.140022	+	0.522570i	−0.999927	+	0.0121147i	$0.996144\pi$
$398$	−0.985551	−	3.67812i	−0.0494012	−	0.184368i
$399$	−1.00335	−	27.3771i	−0.0502302	−	1.37057i
$400$		−	9.05896i		−	0.452948i
$401$	8.39762	−	8.39762i	0.419357	−	0.419357i	−0.465625	−	0.884982i	$-0.654170\pi$
$401$	8.39762	−	8.39762i	0.419357	−	0.419357i	0.884982	+	0.465625i	$0.154170\pi$
$402$	0.824507	+	22.4973i	0.0411227	+	1.12206i
$403$	−1.50670	−	1.27037i	−0.0750543	−	0.0632816i
$404$		−	4.39893i		−	0.218855i
$405$	−27.0901	−	20.1221i	−1.34612	−	0.999877i
$406$	−15.0508	+	26.0688i	−0.746960	+	1.29377i
$407$	−4.30571			−0.213426
$408$	8.90099	+	8.27162i	0.440664	+	0.409506i
$409$	−5.55756	−	20.7411i	−0.274804	−	1.02558i	−0.955973	−	0.293455i	$-0.905195\pi$
$409$	−5.55756	−	20.7411i	−0.274804	−	1.02558i	0.681169	−	0.732126i	$-0.261472\pi$
$410$	−1.70956	−	6.38017i	−0.0844292	−	0.315094i
$411$	18.8366	−	5.79449i	0.929140	−	0.285821i
$412$	−9.35164			−0.460722
$413$	4.73808	−	8.20659i	0.233146	−	0.403820i
$414$	2.35651	−	0.820522i	0.115816	−	0.0403264i
$415$			54.4421i			2.67246i
$416$	−3.54928	−	0.634506i	−0.174018	−	0.0311092i
$417$	5.39470	−	3.38395i	0.264180	−	0.165713i
$418$	−7.53335	+	7.53335i	−0.368468	+	0.368468i
$419$			10.7983i			0.527530i	0.964587	+	0.263765i	$0.0849644\pi$
$419$			10.7983i			0.527530i	−0.964587	+	0.263765i	$0.915036\pi$
$420$	−18.6426	−	9.87122i	−0.909667	−	0.481666i
$421$	−1.69956	−	6.34283i	−0.0828313	−	0.309131i	0.912063	−	0.410049i	$-0.134488\pi$
$421$	−1.69956	−	6.34283i	−0.0828313	−	0.309131i	−0.994895	+	0.100919i	$0.967822\pi$
$422$	−4.96615	+	18.5339i	−0.241748	+	0.902217i
$423$	−11.8436	+	13.7198i	−0.575854	+	0.667081i
$424$	1.14780	+	1.14780i	0.0557422	+	0.0557422i
$425$		−	63.5522i		−	3.08273i
$426$	8.24248	+	13.1402i	0.399349	+	0.636645i
$427$	8.22248	+	8.22248i	0.397913	+	0.397913i
$428$	2.55075	+	4.41803i	0.123295	+	0.213553i
$429$	−5.11020	−	12.6716i	−0.246723	−	0.611792i
$430$	0.108945	−	0.188699i	0.00525381	−	0.00909987i
$431$	−5.36331	+	1.43709i	−0.258341	+	0.0692224i	−0.385665	−	0.922639i	$-0.626028\pi$
$431$	−5.36331	+	1.43709i	−0.258341	+	0.0692224i	0.127324	+	0.991861i	$0.459361\pi$
$432$	4.18790	−	3.07595i	0.201491	−	0.147992i
$433$	31.1666	−	17.9940i	1.49777	−	0.864737i	0.497773	−	0.867308i	$-0.334151\pi$
$433$	31.1666	−	17.9940i	1.49777	−	0.864737i	0.999997	+	0.00257012i	$0.000818096\pi$
$434$	1.71494	−	0.459516i	0.0823197	−	0.0220575i
$435$	−13.4375	+	58.6660i	−0.644278	+	2.81282i
$436$	1.26094	−	0.337868i	0.0603881	−	0.0161809i
$437$	3.91220	+	1.04827i	0.187146	+	0.0501456i
$438$	−8.28212	+	0.303533i	−0.395735	+	0.0145034i
$439$	17.5924	−	10.1570i	0.839640	−	0.484767i	−0.0175016	−	0.999847i	$-0.505571\pi$
$439$	17.5924	−	10.1570i	0.839640	−	0.484767i	0.857142	+	0.515080i	$0.172238\pi$
$440$	2.12322	+	7.92396i	0.101220	+	0.377760i
$441$	−8.80997	+	5.98676i	−0.419523	+	0.285084i
$442$	−24.8996	−	4.45131i	−1.18435	−	0.211727i
$443$	−16.2468	−	9.38011i	−0.771910	−	0.445662i	0.0616456	−	0.998098i	$-0.480365\pi$
$443$	−16.2468	−	9.38011i	−0.771910	−	0.445662i	−0.833556	+	0.552436i	$0.813698\pi$
$444$	2.49694	+	2.32039i	0.118500	+	0.110121i
$445$	50.7925			2.40780
$446$	−0.140271	+	0.242957i	−0.00664204	+	0.0115044i
$447$	−15.3209	−	3.50926i	−0.724652	−	0.165982i
$448$	2.29680	−	2.29680i	0.108513	−	0.108513i
$449$	−15.3460	−	4.11194i	−0.724221	−	0.194055i	−0.122167	−	0.992510i	$-0.538984\pi$
$449$	−15.3460	−	4.11194i	−0.724221	−	0.194055i	−0.602054	+	0.798455i	$0.705651\pi$
$450$	−26.6953	−	5.09346i	−1.25843	−	0.240108i
$451$	1.92710	+	3.33783i	0.0907435	+	0.157172i
$452$	−5.78467	−	10.0193i	−0.272088	−	0.471271i
$453$	31.8541	+	7.29621i	1.49664	+	0.342806i
$454$	11.0336	−	6.37026i	0.517833	−	0.298971i
$455$	43.7541	−	3.72357i	2.05122	−	0.174564i
$456$	8.42850	−	0.308898i	0.394701	−	0.0144655i
$457$	0.847454	+	0.227075i	0.0396422	+	0.0106221i	0.278586	−	0.960411i	$-0.410134\pi$
$457$	0.847454	+	0.227075i	0.0396422	+	0.0106221i	−0.238943	+	0.971033i	$0.576801\pi$
$458$	3.72985	+	2.15343i	0.174285	+	0.100623i
$459$	29.3798	−	21.5790i	1.37133	−	1.00722i
$460$	2.20525	−	2.20525i	0.102820	−	0.102820i
$461$	16.4709	+	16.4709i	0.767127	+	0.767127i	0.977600	−	0.210473i	$-0.0675003\pi$
$461$	16.4709	+	16.4709i	0.767127	+	0.767127i	−0.210473	+	0.977600i	$0.567500\pi$
$462$	11.9982	+	2.74820i	0.558207	+	0.127858i
$463$	4.66680	−	17.4167i	0.216885	−	0.809424i	−0.768610	−	0.639718i	$-0.779051\pi$
$463$	4.66680	−	17.4167i	0.216885	−	0.809424i	0.985495	−	0.169707i	$-0.0542820\pi$
$464$	−8.02571	−	4.63365i	−0.372584	−	0.215112i
$465$	3.00716	−	1.88631i	0.139454	−	0.0874753i
$466$	5.45444	−	20.3563i	0.252672	−	0.942986i
$467$	−24.8989			−1.15218			−0.576091	−	0.817386i	$-0.695423\pi$
$467$	−24.8989			−1.15218			−0.576091	+	0.817386i	$0.695423\pi$
$468$	−3.86540	+	10.1024i	−0.178678	+	0.466984i
$469$	42.2181			1.94945
$470$	−5.86303	+	21.8811i	−0.270441	+	1.00930i
$471$	−1.39883	−	38.1682i	−0.0644548	−	1.75870i
$472$	2.52654	+	1.45870i	0.116293	+	0.0671419i
$473$	−0.0329064	+	0.122808i	−0.00151304	+	0.00564673i
$474$	−5.96855	−	19.4024i	−0.274144	−	0.891181i
$475$	−31.1921	−	31.1921i	−1.43119	−	1.43119i
$476$	16.1129	−	16.1129i	0.738535	−	0.738535i
$477$	4.02775	−	2.73703i	0.184418	−	0.125320i
$478$	−11.2726	−	6.50825i	−0.515598	−	0.297681i
$479$	−7.34248	−	1.96741i	−0.335487	−	0.0898934i	0.0871431	−	0.996196i	$-0.472226\pi$
$479$	−7.34248	−	1.96741i	−0.335487	−	0.0898934i	−0.422630	+	0.906302i	$0.638893\pi$
$480$	3.03902	−	5.73945i	0.138712	−	0.261969i
$481$	−6.98495	−	1.24870i	−0.318486	−	0.0569359i
$482$	1.07935	−	0.623161i	0.0491629	−	0.0283842i
$483$	−1.37586	−	4.47261i	−0.0626038	−	0.203511i
$484$	3.10661	+	5.38080i	0.141209	+	0.244582i
$485$	18.5038	+	32.0495i	0.840215	+	1.45529i
$486$	−6.70966	−	14.0706i	−0.304356	−	0.638253i
$487$	−32.0391	−	8.58485i	−1.45183	−	0.389017i	−0.555171	−	0.831736i	$-0.687347\pi$
$487$	−32.0391	−	8.58485i	−1.45183	−	0.389017i	−0.896660	+	0.442720i	$0.854014\pi$
$488$	−2.53143	+	2.53143i	−0.114592	+	0.114592i
$489$	7.49055	−	8.06048i	0.338734	−	0.364508i
$490$	−6.65642	+	11.5293i	−0.300706	+	0.520839i
$491$	−25.8478			−1.16650			−0.583248	−	0.812294i	$-0.698218\pi$
$491$	−25.8478			−1.16650			−0.583248	+	0.812294i	$0.698218\pi$
$492$	0.681240	−	2.97419i	0.0307127	−	0.134087i
$493$	−56.3035	−	32.5069i	−2.53578	−	1.46404i
$494$	−14.4057	+	10.0362i	−0.648145	+	0.451552i
$495$	24.5444	−	1.80149i	1.10319	−	0.0809708i
$496$	0.141470	+	0.527973i	0.00635218	+	0.0237067i
$497$	25.1917	−	14.5445i	1.13000	−	0.652408i
$498$	−11.7683	+	22.2255i	−0.527352	+	0.995949i
$499$	15.7626	+	4.22357i	0.705629	+	0.189073i	0.593751	−	0.804649i	$-0.297647\pi$
$499$	15.7626	+	4.22357i	0.705629	+	0.189073i	0.111879	+	0.993722i	$0.464313\pi$
$500$	−14.7006	+	3.93902i	−0.657432	+	0.176158i
$501$	14.5829	−	4.48597i	0.651514	−	0.200418i
$502$	−10.9110	+	2.92359i	−0.486981	+	0.130486i
$503$	6.80210	−	3.92720i	0.303291	−	0.175105i	−0.340630	−	0.940198i	$-0.610640\pi$
$503$	6.80210	−	3.92720i	0.303291	−	0.175105i	0.643920	+	0.765093i	$0.277307\pi$
$504$	−5.47690	−	8.05968i	−0.243961	−	0.359007i
$505$	−15.9319	+	4.26894i	−0.708960	+	0.189965i
$506$	−0.909889	+	1.57597i	−0.0404495	+	0.0700606i
$507$	−4.61513	−	22.0386i	−0.204965	−	0.978769i
$508$	−1.65163	−	2.86070i	−0.0732790	−	0.126923i
$509$	18.3184	+	18.3184i	0.811947	+	0.811947i	0.984926	−	0.172979i	$-0.0553391\pi$
$509$	18.3184	+	18.3184i	0.811947	+	0.811947i	−0.172979	+	0.984926i	$0.555339\pi$
$510$	21.3199	−	40.2645i	0.944063	−	1.78294i
$511$			15.5421i			0.687542i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	3.82871	−	25.0111i	0.169042	−	1.10427i
$514$	−0.420900	+	1.57082i	−0.0185651	+	0.0692860i
$515$	9.07529	+	33.8695i	0.399905	+	1.49247i
$516$	0.0852656	−	0.0534847i	0.00375361	−	0.00235453i
$517$		−	13.2182i		−	0.581334i
$518$	4.52007	−	4.52007i	0.198601	−	0.198601i
$519$	0.0772734	+	0.0409160i	0.00339193	+	0.00179602i
$520$	1.14636	+	13.4704i	0.0502714	+	0.590717i
$521$			44.6910i			1.95795i	0.203981	+	0.978975i	$0.434612\pi$
$521$			44.6910i			1.95795i	−0.203981	+	0.978975i	$0.565388\pi$
$522$	−18.1671	+	21.0452i	−0.795154	+	0.921123i
$523$	2.38397	−	4.12916i	0.104244	−	0.180556i	−0.809185	−	0.587554i	$-0.800091\pi$
$523$	2.38397	−	4.12916i	0.104244	−	0.180556i	0.913429	+	0.406998i	$0.133424\pi$
$524$	−11.0247			−0.481614
$525$	−11.3790	+	49.6790i	−0.496621	+	2.16817i
$526$	−2.94448	−	10.9889i	−0.128385	−	0.479141i
$527$	0.992467	+	3.70394i	0.0432325	+	0.161346i
$528$	−0.846078	+	3.69385i	−0.0368208	+	0.160754i
$529$	−22.3082			−0.969921
$530$	3.04319	−	5.27095i	0.132188	−	0.228956i
$531$	5.71911	−	6.62514i	0.248188	−	0.287506i
$532$		−	15.8168i		−	0.685745i
$533$	2.15823	+	5.97369i	0.0934834	+	0.258749i
$534$	20.7356	+	10.9794i	0.897317	+	0.475127i
$535$	13.5257	−	13.5257i	0.584766	−	0.584766i
$536$			12.9975i			0.561408i
$537$	−10.4355	+	6.54592i	−0.450326	+	0.282477i
$538$	3.09980	+	11.5686i	0.133642	+	0.498758i
$539$	2.01054	−	7.50343i	0.0866000	−	0.323196i
$540$	−15.2045	−	12.1826i	−0.654298	−	0.524254i
$541$	−31.0921	−	31.0921i	−1.33675	−	1.33675i	−0.899187	−	0.437565i	$-0.855841\pi$
$541$	−31.0921	−	31.0921i	−1.33675	−	1.33675i	−0.437565	−	0.899187i	$-0.644159\pi$
$542$		−	24.8338i		−	1.06670i
$543$	16.7232	−	31.5832i	0.717661	−	1.35536i
$544$	4.96063	+	4.96063i	0.212685	+	0.212685i
$545$	−2.44736	−	4.23894i	−0.104833	−	0.181576i
$546$	18.6671	+	7.93788i	0.798879	+	0.339710i
$547$	7.14869	−	12.3819i	0.305656	−	0.529412i	−0.671751	−	0.740777i	$-0.734458\pi$
$547$	7.14869	−	12.3819i	0.305656	−	0.529412i	0.977407	+	0.211365i	$0.0677910\pi$
$548$	10.9905	−	2.94490i	0.469492	−	0.125800i
$549$	6.03640	+	8.88302i	0.257627	+	0.379118i
$550$	17.1645	−	9.90992i	0.731896	−	0.422561i
$551$	−43.5891	+	11.6797i	−1.85696	+	0.497570i
$552$	1.37697	−	0.423582i	0.0586076	−	0.0180288i
$553$	−36.7713	+	9.85284i	−1.56368	+	0.418986i
$554$	15.1185	+	4.05098i	0.642322	+	0.172110i
$555$	5.98076	−	11.2952i	0.253869	−	0.479453i
$556$	3.18410	−	1.83834i	0.135036	−	0.0779630i
$557$	−11.2642	−	42.0386i	−0.477280	−	1.78123i	−0.612557	−	0.790426i	$-0.709859\pi$
$557$	−11.2642	−	42.0386i	−0.477280	−	1.78123i	0.135277	−	0.990808i	$-0.456807\pi$
$558$	1.63539	−	0.120033i	0.0692317	−	0.00508140i
$559$	−0.0889982	+	0.189683i	−0.00376422	+	0.00802273i
$560$	−10.5474	−	6.08953i	−0.445708	−	0.257330i
$561$	−5.93557	+	25.9138i	−0.250600	+	1.09408i
$562$	4.40413			0.185777
$563$	3.73481	−	6.46888i	0.157403	−	0.272631i	−0.776528	−	0.630083i	$-0.783021\pi$
$563$	3.73481	−	6.46888i	0.157403	−	0.272631i	0.933932	+	0.357452i	$0.116354\pi$
$564$	−7.12340	+	7.66540i	−0.299949	+	0.322772i
$565$	−30.6740	+	30.6740i	−1.29047	+	1.29047i
$566$	17.6319	+	4.72445i	0.741124	+	0.198583i
$567$	−26.8300	+	11.6079i	−1.12675	+	0.487488i
$568$	4.47775	+	7.75569i	0.187882	+	0.325422i
$569$	−20.6528	−	35.7717i	−0.865810	−	1.49963i	−0.866241	−	0.499627i	$-0.833470\pi$
$569$	−20.6528	−	35.7717i	−0.865810	−	1.49963i	0.000430492	−	1.00000i	$-0.499863\pi$
$570$	−9.29819	−	30.2263i	−0.389458	−	1.26604i
$571$	−38.0908	+	21.9917i	−1.59405	+	0.920326i	−0.601449	+	0.798911i	$0.705410\pi$
$571$	−38.0908	+	21.9917i	−1.59405	+	0.920326i	−0.992602	+	0.121415i	$0.961257\pi$
$572$	−2.68045	−	7.41912i	−0.112075	−	0.310209i
$573$	−18.2301	+	34.4290i	−0.761572	+	1.43829i
$574$	−5.52704	−	1.48097i	−0.230694	−	0.0618144i
$575$	−6.52538	−	3.76743i	−0.272127	−	0.157113i
$576$	2.48131	−	1.68616i	0.103388	−	0.0702565i
$577$	−27.8109	+	27.8109i	−1.15778	+	1.15778i	−0.172831	+	0.984952i	$0.555291\pi$
$577$	−27.8109	+	27.8109i	−1.15778	+	1.15778i	−0.984952	+	0.172831i	$0.944709\pi$
$578$	22.7800	+	22.7800i	0.947523	+	0.947523i
$579$	−3.44316	−	11.1929i	−0.143093	−	0.465162i
$580$	−8.99344	+	33.5640i	−0.373432	+	1.39367i
$581$	40.8438	+	23.5812i	1.69449	+	0.978313i
$582$	0.626106	+	17.0838i	0.0259529	+	0.708145i
$583$	−0.919179	+	3.43042i	−0.0380685	+	0.142074i
$584$	−4.78490			−0.198000
$585$	40.3397	+	4.19568i	1.66784	+	0.173470i
$586$	−11.1765			−0.461696
$587$	−2.71700	+	10.1400i	−0.112143	+	0.418522i	−0.999057	−	0.0434112i	$-0.986177\pi$
$587$	−2.71700	+	10.1400i	−0.112143	+	0.418522i	0.886915	+	0.461933i	$0.152844\pi$
$588$	−5.20962	+	3.26785i	−0.214841	+	0.134764i
$589$	2.30504	+	1.33082i	0.0949777	+	0.0548354i
$590$	2.83118	−	10.5661i	0.116558	−	0.435000i
$591$	−10.4066	−	2.38363i	−0.428069	−	0.0980495i
$592$	1.39158	+	1.39158i	0.0571936	+	0.0571936i
$593$	−24.8672	+	24.8672i	−1.02117	+	1.02117i	−0.0214039	+	0.999771i	$0.506814\pi$
$593$	−24.8672	+	24.8672i	−1.02117	+	1.02117i	−0.999771	+	0.0214039i	$0.993186\pi$
$594$	10.4095	+	4.57015i	0.427105	+	0.187515i
$595$	−73.9940	−	42.7205i	−3.03346	−	1.75137i
$596$	−8.76537	−	2.34867i	−0.359044	−	0.0962054i
$597$	−6.59101	+	0.241555i	−0.269752	+	0.00988619i
$598$	−1.93312	+	2.29275i	−0.0790512	+	0.0937576i
$599$	5.46701	−	3.15638i	0.223376	−	0.128966i	−0.384137	−	0.923276i	$-0.625501\pi$
$599$	5.46701	−	3.15638i	0.223376	−	0.128966i	0.607512	+	0.794310i	$0.292167\pi$
$600$	−15.2945	−	3.50322i	−0.624396	−	0.143018i
$601$	−16.8743	−	29.2272i	−0.688318	−	1.19220i	−0.972382	−	0.233396i	$-0.925016\pi$
$601$	−16.8743	−	29.2272i	−0.688318	−	1.19220i	0.284064	−	0.958805i	$-0.408317\pi$
$602$	−0.0943777	−	0.163467i	−0.00384655	−	0.00666242i
$603$	38.3017	+	7.30795i	1.55976	+	0.297603i
$604$	18.2244	+	4.88320i	0.741539	+	0.198695i
$605$	16.4732	−	16.4732i	0.669731	−	0.669731i
$606$	−7.42683	−	1.70112i	−0.301695	−	0.0691033i
$607$	−12.9072	+	22.3560i	−0.523888	+	0.907401i	0.475725	+	0.879594i	$0.342186\pi$
$607$	−12.9072	+	22.3560i	−0.523888	+	0.907401i	−0.999613	+	0.0278069i	$0.991148\pi$
$608$	4.86946			0.197483
$609$	38.1923	+	35.4919i	1.54763	+	1.43820i
$610$	11.6249	+	6.71161i	0.470677	+	0.271745i
$611$	3.83341	−	21.4432i	0.155083	−	0.867499i
$612$	17.4073	−	11.8290i	0.703650	−	0.478161i
$613$	4.39253	+	16.3932i	0.177413	+	0.662113i	0.996128	+	0.0879138i	$0.0280200\pi$
$613$	4.39253	+	16.3932i	0.177413	+	0.662113i	−0.818715	+	0.574200i	$0.805313\pi$
$614$	−18.3439	+	10.5908i	−0.740299	+	0.427412i
$615$	−11.4329	+	0.419008i	−0.461020	+	0.0168960i
$616$	6.86441	+	1.83931i	0.276575	+	0.0741080i
$617$	44.7003	−	11.9774i	1.79957	−	0.482193i	0.805657	−	0.592383i	$-0.201813\pi$
$617$	44.7003	−	11.9774i	1.79957	−	0.482193i	0.993911	+	0.110190i	$0.0351460\pi$
$618$	−3.61640	+	15.7886i	−0.145473	+	0.635112i
$619$	33.1257	−	8.87599i	1.33143	−	0.356756i	0.478183	−	0.878260i	$-0.341295\pi$
$619$	33.1257	−	8.87599i	1.33143	−	0.356756i	0.853249	+	0.521504i	$0.174629\pi$
$620$	1.77490	−	1.02474i	0.0712819	−	0.0411546i
$621$	−0.474018	−	4.29586i	−0.0190217	−	0.172387i
$622$	−13.4129	+	3.59398i	−0.537809	+	0.144106i
$623$	22.0004	−	38.1058i	0.881428	−	1.52668i
$624$	−2.44381	+	5.74698i	−0.0978306	+	0.230063i
$625$	5.88500	+	10.1931i	0.235400	+	0.407725i
$626$	−6.77542	−	6.77542i	−0.270800	−	0.270800i
$627$	9.80552	+	15.6320i	0.391595	+	0.624282i
$628$		−	22.0512i		−	0.879939i
$629$	9.76248	+	9.76248i	0.389256	+	0.389256i
$630$	−23.8752	+	27.6576i	−0.951211	+	1.10190i
$631$	−2.50134	+	9.33512i	−0.0995767	+	0.371625i	−0.997674	−	0.0681724i	$-0.978283\pi$
$631$	−2.50134	+	9.33512i	−0.0995767	+	0.371625i	0.898097	+	0.439798i	$0.144950\pi$
$632$	−3.03336	−	11.3207i	−0.120661	−	0.450312i
$633$	29.3709	+	15.5518i	1.16739	+	0.618129i
$634$		−	16.1037i		−	0.639558i
$635$	−8.75797	+	8.75797i	−0.347549	+	0.347549i
$636$	2.38174	−	1.49400i	0.0944420	−	0.0592408i
$637$	5.43768	−	11.5894i	0.215449	−	0.459188i
$638$		−	20.2756i		−	0.802721i
$639$	25.3724	−	8.83453i	1.00372	−	0.349489i
$640$	1.87476	−	3.24719i	0.0741066	−	0.128356i
$641$	−22.3227			−0.881695			−0.440848	−	0.897582i	$-0.645322\pi$
$641$	−22.3227			−0.881695			−0.440848	+	0.897582i	$0.645322\pi$
$642$	8.44548	−	2.59799i	0.333317	−	0.102535i
$643$	−9.67643	−	36.1129i	−0.381601	−	1.42415i	−0.843456	−	0.537199i	$-0.819483\pi$
$643$	−9.67643	−	36.1129i	−0.381601	−	1.42415i	0.461855	−	0.886956i	$-0.347184\pi$
$644$	−0.699246	−	2.60962i	−0.0275542	−	0.102834i
$645$	−0.276455	−	0.256908i	−0.0108854	−	0.0101157i
$646$	34.1612			1.34405
$647$	1.97324	−	3.41775i	0.0775760	−	0.134366i	−0.824628	−	0.565676i	$-0.808615\pi$
$647$	1.97324	−	3.41775i	0.0775760	−	0.134366i	0.902204	+	0.431310i	$0.141949\pi$
$648$	−3.57370	−	8.26007i	−0.140388	−	0.324486i
$649$			6.38288i			0.250550i
$650$	30.7191	−	11.0985i	1.20490	−	0.435320i
$651$	−0.112626	−	3.07308i	−0.00441416	−	0.120444i
$652$	4.49221	−	4.49221i	0.175928	−	0.175928i
$653$		−	14.8536i		−	0.581266i	−0.956835	−	0.290633i	$-0.906134\pi$
$653$		−	14.8536i		−	0.581266i	0.956835	−	0.290633i	$-0.0938659\pi$
$654$	−0.0828102	−	2.25954i	−0.00323814	−	0.0883549i
$655$	10.6989	+	39.9287i	0.418039	+	1.56014i
$656$	0.455940	−	1.70159i	0.0178015	−	0.0664360i
$657$	−2.69034	+	14.1003i	−0.104960	+	0.550106i
$658$	13.8762	+	13.8762i	0.540951	+	0.540951i
$659$			40.0270i			1.55923i	0.626259	+	0.779615i	$0.284585\pi$
$659$			40.0270i			1.55923i	−0.626259	+	0.779615i	$0.715415\pi$
$660$	14.1993	−	0.520394i	0.552708	−	0.0202563i
$661$	3.62807	+	3.62807i	0.141116	+	0.141116i	0.774136	−	0.633020i	$-0.218185\pi$
$661$	3.62807	+	3.62807i	0.141116	+	0.141116i	−0.633020	+	0.774136i	$0.718185\pi$
$662$	−3.69778	−	6.40474i	−0.143718	−	0.248927i
$663$	−17.1443	+	40.3174i	−0.665829	+	1.56580i
$664$	−7.25986	+	12.5744i	−0.281737	+	0.487983i
$665$	−57.2847	+	15.3494i	−2.22141	+	0.595224i
$666$	4.88319	−	3.31834i	0.189220	−	0.128583i
$667$	−6.67544	+	3.85407i	−0.258474	+	0.149230i
$668$	8.50863	−	2.27988i	0.329209	−	0.0882112i
$669$	0.355947	+	0.330779i	0.0137617	+	0.0127886i
$670$	47.0741	−	12.6135i	1.81863	−	0.487300i
$671$	−7.56564	−	2.02721i	−0.292068	−	0.0782595i
$672$	−2.98954	−	4.76595i	−0.115324	−	0.183850i
$673$	35.1333	−	20.2842i	1.35429	−	0.781899i	0.365441	−	0.930834i	$-0.380918\pi$
$673$	35.1333	−	20.2842i	1.35429	−	0.781899i	0.988847	+	0.148936i	$0.0475847\pi$
$674$	−4.86748	−	18.1657i	−0.187489	−	0.699717i
$675$	−18.9229	+	43.1008i	−0.728341	+	1.65895i
$676$	−2.19675	−	12.8131i	−0.0844904	−	0.492810i
$677$	−11.0747	−	6.39397i	−0.425635	−	0.245740i	0.271851	−	0.962339i	$-0.412364\pi$
$677$	−11.0747	−	6.39397i	−0.425635	−	0.245740i	−0.697485	+	0.716599i	$0.745698\pi$
$678$	−19.1530	+	5.89182i	−0.735565	+	0.226274i
$679$	32.0591			1.23032
$680$	13.1522	−	22.7803i	0.504364	−	0.873585i
$681$	−6.48825	−	21.0918i	−0.248630	−	0.808241i
$682$	−0.845618	+	0.845618i	−0.0323804	+	0.0323804i
$683$	31.3371	+	8.39675i	1.19908	+	0.321293i	0.802469	−	0.596693i	$-0.203519\pi$
$683$	31.3371	+	8.39675i	1.19908	+	0.321293i	0.396612	+	0.917986i	$0.370186\pi$
$684$	2.73789	−	14.3495i	0.104686	−	0.548668i
$685$	−21.3315	−	36.9473i	−0.815035	−	1.41168i
$686$	−5.60220	−	9.70330i	−0.213893	−	0.370474i
$687$	5.07808	−	5.46446i	0.193741	−	0.208482i
$688$	0.0503260	−	0.0290558i	0.00191866	−	0.00110774i
$689$	−2.48600	+	5.29844i	−0.0947091	+	0.201855i
$690$	−2.87039	−	4.57599i	−0.109274	−	0.174205i
$691$	9.31482	+	2.49590i	0.354353	+	0.0949485i	0.431604	−	0.902063i	$-0.357948\pi$
$691$	9.31482	+	2.49590i	0.354353	+	0.0949485i	−0.0772515	+	0.997012i	$0.524614\pi$
$692$	0.0437187	+	0.0252410i	0.00166194	+	0.000959519i
$693$	9.27972	−	19.1941i	0.352507	−	0.729125i
$694$	−17.5077	+	17.5077i	−0.664582	+	0.664582i
$695$	−9.74804	−	9.74804i	−0.369764	−	0.369764i
$696$	−10.9268	+	11.7581i	−0.414178	+	0.445691i
$697$	3.19860	−	11.9373i	0.121156	−	0.452159i
$698$	−2.95766	−	1.70760i	−0.111949	−	0.0646337i
$699$	−32.2588	−	17.0809i	−1.22014	−	0.646060i
$700$	−7.61574	+	28.4223i	−0.287848	+	1.07426i
$701$	45.7174			1.72672			0.863360	−	0.504588i	$-0.168355\pi$
$701$	45.7174			1.72672			0.863360	+	0.504588i	$0.168355\pi$
$702$	15.5614	+	10.4328i	0.587327	+	0.393760i
$703$	9.58306			0.361432
$704$	−0.566263	+	2.11332i	−0.0213418	+	0.0796488i
$705$	34.6752	+	18.3604i	1.30594	+	0.691493i
$706$	3.84849	+	2.22193i	0.144840	+	0.0836233i
$707$	−3.69811	+	13.8016i	−0.139082	+	0.519061i
$708$	3.43980	−	3.70153i	0.129276	−	0.139112i
$709$	11.3342	+	11.3342i	0.425664	+	0.425664i	0.887148	−	0.461484i	$-0.152683\pi$
$709$	11.3342	+	11.3342i	0.425664	+	0.425664i	−0.461484	+	0.887148i	$0.652683\pi$
$710$	23.7439	−	23.7439i	0.891092	−	0.891092i
$711$	−35.0657	+	2.57372i	−1.31507	+	0.0965219i
$712$	11.7315	+	6.77319i	0.439657	+	0.253836i
$713$	0.439145	+	0.117669i	0.0164461	+	0.00440672i
$714$	−20.9728	−	33.4350i	−0.784889	−	1.25127i
$715$	−24.2691	+	16.9079i	−0.907612	+	0.632318i
$716$	−6.15933	+	3.55609i	−0.230185	+	0.132897i
$717$	−15.3473	+	16.5151i	−0.573157	+	0.616766i
$718$	−1.24468	−	2.15585i	−0.0464511	−	0.0804557i
$719$	10.0799	+	17.4589i	0.375917	+	0.651107i	0.990464	−	0.137773i	$-0.0439944\pi$
$719$	10.0799	+	17.4589i	0.375917	+	0.651107i	−0.614547	+	0.788880i	$0.710661\pi$
$720$	−8.51484	−	7.35038i	−0.317329	−	0.273933i
$721$	29.3406	+	7.86179i	1.09270	+	0.292788i
$722$	3.33165	−	3.33165i	0.123991	−	0.123991i
$723$	−0.634703	−	2.06327i	−0.0236049	−	0.0767340i
$724$	10.3165	−	17.8687i	0.383410	−	0.664085i
$725$	83.9521			3.11790
$726$	10.2859	−	3.16415i	0.381747	−	0.117433i
$727$	19.8457	+	11.4579i	0.736036	+	0.424950i	0.820626	−	0.571465i	$-0.193625\pi$
$727$	19.8457	+	11.4579i	0.736036	+	0.424950i	−0.0845905	+	0.996416i	$0.526958\pi$
$728$	10.6024	+	4.97458i	0.392950	+	0.184370i
$729$	−26.3504	+	5.88684i	−0.975942	+	0.218031i
$730$	4.64350	+	17.3298i	0.171864	+	0.641404i
$731$	0.353057	−	0.203838i	0.0130583	−	0.00753921i
$732$	3.29494	+	5.25281i	0.121785	+	0.194150i
$733$	−26.3034	−	7.04796i	−0.971536	−	0.260322i	−0.262060	−	0.965052i	$-0.584402\pi$
$733$	−26.3034	−	7.04796i	−0.971536	−	0.260322i	−0.709476	+	0.704729i	$0.751069\pi$
$734$	−7.87325	+	2.10963i	−0.290607	+	0.0778679i
$735$	16.8911	+	15.6967i	0.623036	+	0.578983i
$736$	0.803416	−	0.215275i	0.0296143	−	0.00793513i
$737$	−24.6271	+	14.2185i	−0.907152	+	0.523744i
$738$	−4.75797	−	2.30032i	−0.175143	−	0.0846758i
$739$	23.3006	−	6.24337i	0.857126	−	0.229666i	0.196613	−	0.980481i	$-0.437006\pi$
$739$	23.3006	−	6.24337i	0.857126	−	0.229666i	0.660513	+	0.750815i	$0.270339\pi$
$740$	3.68952	−	6.39043i	0.135629	−	0.234917i
$741$	11.3736	+	28.2028i	0.417819	+	1.03605i
$742$	−2.63627	−	4.56615i	−0.0967804	−	0.167628i
$743$	32.2692	+	32.2692i	1.18384	+	1.18384i	0.978741	+	0.205101i	$0.0657524\pi$
$743$	32.2692	+	32.2692i	1.18384	+	1.18384i	0.205101	+	0.978741i	$0.434248\pi$
$744$	0.946099	−	0.0346738i	0.0346857	−	0.00127120i
$745$			34.0254i			1.24659i
$746$	16.7417	+	16.7417i	0.612956	+	0.612956i
$747$	32.9730	+	28.4637i	1.20642	+	1.04143i
$748$	−3.97256	+	14.8258i	−0.145251	+	0.542084i
$749$	−4.28875	−	16.0058i	−0.156708	−	0.584841i
$750$	0.965440	+	26.3427i	0.0352529	+	0.961901i
$751$			31.2358i			1.13981i	0.821711	+	0.569905i	$0.193020\pi$
$751$			31.2358i			1.13981i	−0.821711	+	0.569905i	$0.806980\pi$
$752$	−4.27203	+	4.27203i	−0.155785	+	0.155785i
$753$	0.716562	+	19.5519i	0.0261130	+	0.712512i
$754$	5.88016	−	32.8922i	0.214143	−	1.19786i
$755$		−	70.7433i		−	2.57461i
$756$	−15.7254	+	6.13003i	−0.571926	+	0.222947i
$757$	11.2648	−	19.5112i	0.409426	−	0.709147i	−0.585399	−	0.810745i	$-0.699062\pi$
$757$	11.2648	−	19.5112i	0.409426	−	0.709147i	0.994826	+	0.101598i	$0.0323956\pi$
$758$	11.3128			0.410898
$759$	2.30890	+	2.14564i	0.0838076	+	0.0778818i
$760$	−4.72557	−	17.6361i	−0.171414	−	0.639727i
$761$	−8.52630	−	31.8206i	−0.309078	−	1.15350i	−0.929378	−	0.369130i	$-0.879656\pi$
$761$	−8.52630	−	31.8206i	−0.309078	−	1.15350i	0.620300	−	0.784365i	$-0.287011\pi$
$762$	−5.46851	+	1.68222i	−0.198103	+	0.0609403i
$763$	−4.24021			−0.153506
$764$	−11.2461	+	19.4788i	−0.406869	+	0.704718i
$765$	−59.7350	−	51.5658i	−2.15972	−	1.86437i
$766$			30.0424i			1.08548i
$767$	−1.85110	+	10.3546i	−0.0668395	+	0.373885i
$768$	1.46728	−	0.920381i	0.0529458	−	0.0332114i
$769$	36.9455	−	36.9455i	1.33229	&mi

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.53071 - 0.810507i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.970449 + 3.62177i) q^{5} +(-1.17907 + 1.26878i) q^{6} +(2.29680 + 2.29680i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.68616 + 2.48131i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.53071 - 0.810507i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.970449 + 3.62177i) q^{5} +(-1.17907 + 1.26878i) q^{6} +(2.29680 + 2.29680i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.68616 + 2.48131i) q^{9} +(3.24719 + 1.87476i) q^{10} +(-2.11332 - 0.566263i) q^{11} +(0.920381 + 1.46728i) q^{12} +(-3.26412 - 1.53151i) q^{13} +(2.81299 - 1.62408i) q^{14} +(4.42095 - 4.75732i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.50770 + 6.07551i) q^{17} +(2.83317 - 0.986492i) q^{18} +(4.70354 + 1.26031i) q^{19} +(2.65132 - 2.65132i) q^{20} +(-1.65416 - 5.37730i) q^{21} +(-1.09394 + 1.89475i) q^{22} +0.831757 q^{23} +(1.65549 - 0.509261i) q^{24} +(-7.84529 - 4.52948i) q^{25} +(-2.32414 + 2.75652i) q^{26} +(-0.569900 - 5.16481i) q^{27} +(-0.840685 - 3.13748i) q^{28} +(-8.02571 + 4.63365i) q^{29} +(-3.45100 - 5.50159i) q^{30} +(0.527973 + 0.141470i) q^{31} +(0.965926 - 0.258819i) q^{32} +(2.77593 + 2.57965i) q^{33} +(6.77635 - 1.81572i) q^{34} +(-10.5474 + 6.08953i) q^{35} +(-0.219600 - 2.99195i) q^{36} +(1.90093 - 0.509353i) q^{37} +(2.43473 - 4.21708i) q^{38} +(3.75513 + 4.98989i) q^{39} +(-1.87476 - 3.24719i) q^{40} +(-1.24565 - 1.24565i) q^{41} +(-5.62220 + 0.206049i) q^{42} -0.0581115i q^{43} +(1.54706 + 1.54706i) q^{44} +(-10.6230 + 3.69888i) q^{45} +(0.215275 - 0.803416i) q^{46} +(1.56367 + 5.83570i) q^{47} +(-0.0634356 - 1.73089i) q^{48} +3.55054i q^{49} +(-6.40565 + 6.40565i) q^{50} +(-0.445026 - 12.1429i) q^{51} +(2.06106 + 2.95839i) q^{52} -1.62324i q^{53} +(-5.13632 - 0.786269i) q^{54} +(4.10174 - 7.10443i) q^{55} -3.24816 q^{56} +(-6.17827 - 5.74143i) q^{57} +(2.39855 + 8.95152i) q^{58} +(-0.755077 - 2.81798i) q^{59} +(-6.20731 + 1.90949i) q^{60} +3.57998 q^{61} +(0.273299 - 0.473367i) q^{62} +(-1.82630 + 9.57181i) q^{63} -1.00000i q^{64} +(8.71443 - 10.3356i) q^{65} +(3.21021 - 2.01368i) q^{66} +(9.19065 - 9.19065i) q^{67} -7.01540i q^{68} +(-1.27318 - 0.674146i) q^{69} +(3.15217 + 11.7641i) q^{70} +(2.31786 - 8.65035i) q^{71} +(-2.94684 - 0.562257i) q^{72} +(3.38343 + 3.38343i) q^{73} -1.96799i q^{74} +(8.33770 + 13.2920i) q^{75} +(-3.44323 - 3.44323i) q^{76} +(-3.55328 - 6.15446i) q^{77} +(5.79176 - 2.33570i) q^{78} +(-5.86001 + 10.1498i) q^{79} +(-3.62177 + 0.970449i) q^{80} +(-3.31376 + 8.36773i) q^{81} +(-1.52561 + 0.880809i) q^{82} +(14.0250 - 3.75798i) q^{83} +(-1.25610 + 5.48396i) q^{84} +(-25.4081 + 6.80809i) q^{85} +(-0.0561314 - 0.0150404i) q^{86} +(16.0407 - 0.587877i) q^{87} +(1.89475 - 1.09394i) q^{88} +(-3.50606 - 13.0848i) q^{89} +(0.823397 + 11.2184i) q^{90} +(-3.97946 - 11.0146i) q^{91} +(-0.720323 - 0.415879i) q^{92} +(-0.693511 - 0.644475i) q^{93} +6.04156 q^{94} +(-9.12909 + 15.8121i) q^{95} +(-1.68833 - 0.386713i) q^{96} +(6.97910 - 6.97910i) q^{97} +(3.42956 + 0.918947i) q^{98} +(-2.15832 - 6.19861i) 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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