LMFDB - Embedded newform 153.2.s.a.113.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,2,Mod(5,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([40, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			113.12
Character	$\chi$	$=$	153.113
Dual form			153.2.s.a.65.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.989181 - 0.130228i) q^{2} +(0.257461 - 1.71281i) q^{3} +(-0.970333 + 0.260000i) q^{4} +(-1.66678 - 3.37989i) q^{5} +(0.0316194 - 1.72781i) q^{6} +(3.57710 + 1.76403i) q^{7} +(-2.76951 + 1.14717i) q^{8} +(-2.86743 - 0.881962i) q^{9} +(-2.08890 - 3.12626i) q^{10} +(3.74295 - 1.27056i) q^{11} +(0.195507 + 1.72893i) q^{12} +(-0.0401405 - 0.149806i) q^{13} +(3.76813 + 1.27911i) q^{14} +(-6.21823 + 1.98468i) q^{15} +(-0.850202 + 0.490865i) q^{16} +(1.50184 + 3.83985i) q^{17} +(-2.95126 - 0.499000i) q^{18} +(3.79324 + 1.57121i) q^{19} +(2.49610 + 2.84626i) q^{20} +(3.94241 - 5.67273i) q^{21} +(3.53699 - 1.74425i) q^{22} +(-0.645419 + 0.735959i) q^{23} +(1.25184 + 5.03900i) q^{24} +(-5.60170 + 7.30028i) q^{25} +(-0.0592152 - 0.142958i) q^{26} +(-2.24888 + 4.68429i) q^{27} +(-3.92963 - 0.781652i) q^{28} +(0.325703 - 4.96927i) q^{29} +(-5.89250 + 2.77300i) q^{30} +(-1.57861 + 4.65042i) q^{31} +(3.97939 - 3.05349i) q^{32} +(-1.21256 - 6.73807i) q^{33} +(1.98565 + 3.60273i) q^{34} -15.0305i q^{35} +(3.01167 + 0.110266i) q^{36} +(-0.326442 - 1.64113i) q^{37} +(3.95681 + 1.06022i) q^{38} +(-0.266924 + 0.0301837i) q^{39} +(8.49347 + 7.44857i) q^{40} +(-4.85207 + 0.318021i) q^{41} +(3.16101 - 6.12476i) q^{42} +(-3.14609 - 2.41408i) q^{43} +(-3.30156 + 2.20603i) q^{44} +(1.79843 + 11.1616i) q^{45} +(-0.542593 + 0.812048i) q^{46} +(-0.797097 + 2.97481i) q^{47} +(0.621863 + 1.58261i) q^{48} +(5.42253 + 7.06678i) q^{49} +(-4.59039 + 7.95079i) q^{50} +(6.96360 - 1.58376i) q^{51} +(0.0778993 + 0.134926i) q^{52} +(0.152152 - 0.367326i) q^{53} +(-1.61453 + 4.92647i) q^{54} +(-10.5330 - 10.5330i) q^{55} +(-11.9305 - 0.781965i) q^{56} +(3.66779 - 6.09256i) q^{57} +(-0.324959 - 4.95792i) q^{58} +(-0.226196 + 1.71813i) q^{59} +(5.51774 - 3.54254i) q^{60} +(-3.50005 + 7.09741i) q^{61} +(-0.955910 + 4.80569i) q^{62} +(-8.70128 - 8.21311i) q^{63} +(4.92706 - 4.92706i) q^{64} +(-0.439424 + 0.385364i) q^{65} +(-2.07693 - 6.50726i) q^{66} +(-9.67537 - 5.58608i) q^{67} +(-2.45565 - 3.33546i) q^{68} +(1.09439 + 1.29496i) q^{69} +(-1.95739 - 14.8678i) q^{70} +(3.55751 - 0.707633i) q^{71} +(8.95314 - 0.846821i) q^{72} +(12.4119 + 8.29338i) q^{73} +(-0.536631 - 1.58086i) q^{74} +(11.0618 + 11.4742i) q^{75} +(-4.08922 - 0.538355i) q^{76} +(15.6302 + 2.05776i) q^{77} +(-0.260106 + 0.0646182i) q^{78} +(-3.82731 - 11.2749i) q^{79} +(3.07617 + 2.05543i) q^{80} +(7.44429 + 5.05793i) q^{81} +(-4.75816 + 0.946456i) q^{82} +(0.0575142 + 0.436864i) q^{83} +(-2.35055 + 6.52946i) q^{84} +(10.4750 - 11.4762i) q^{85} +(-3.42643 - 1.97825i) q^{86} +(-8.42756 - 1.83726i) q^{87} +(-8.90860 + 7.81263i) q^{88} +(-3.79574 + 3.79574i) q^{89} +(3.23253 + 10.8067i) q^{90} +(0.120677 - 0.606682i) q^{91} +(0.434922 - 0.881934i) q^{92} +(7.55885 + 3.90115i) q^{93} +(-0.401070 + 3.04643i) q^{94} +(-1.01196 - 15.4396i) q^{95} +(-4.20552 - 7.60209i) q^{96} +(7.24200 + 0.474666i) q^{97} +(6.28416 + 6.28416i) q^{98} +(-11.8532 + 0.342099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22}+ \cdots + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.989181	−	0.130228i	0.699456	−	0.0920852i	0.227592	−	0.973757i	$-0.426915\pi$
$2$	0.989181	−	0.130228i	0.699456	−	0.0920852i	0.471864	+	0.881671i	$0.343581\pi$
$3$	0.257461	−	1.71281i	0.148645	−	0.988891i
$3$	0.257461	−	1.71281i	0.148645	−	0.988891i
$4$	−0.970333	+	0.260000i	−0.485166	+	0.130000i
$5$	−1.66678	−	3.37989i	−0.745405	−	1.51153i	−0.855608	−	0.517624i	$-0.826817\pi$
$5$	−1.66678	−	3.37989i	−0.745405	−	1.51153i	0.110203	−	0.993909i	$-0.464850\pi$
$6$	0.0316194	−	1.72781i	0.0129086	−	0.705374i
$7$	3.57710	+	1.76403i	1.35202	+	0.666742i	0.966669	−	0.256029i	$-0.0824144\pi$
$7$	3.57710	+	1.76403i	1.35202	+	0.666742i	0.385349	+	0.922771i	$0.374081\pi$
$8$	−2.76951	+	1.14717i	−0.979171	+	0.405586i
$9$	−2.86743	−	0.881962i	−0.955809	−	0.293987i
$10$	−2.08890	−	3.12626i	−0.660568	−	0.988610i
$11$	3.74295	−	1.27056i	1.12854	−	0.383088i	0.306134	−	0.951988i	$-0.400964\pi$
$11$	3.74295	−	1.27056i	1.12854	−	0.383088i	0.822407	+	0.568900i	$0.192631\pi$
$12$	0.195507	+	1.72893i	0.0564381	+	0.499100i
$13$	−0.0401405	−	0.149806i	−0.0111330	−	0.0415488i	0.960136	−	0.279534i	$-0.0901798\pi$
$13$	−0.0401405	−	0.149806i	−0.0111330	−	0.0415488i	−0.971269	+	0.237985i	$0.923513\pi$
$14$	3.76813	+	1.27911i	1.00707	+	0.341856i
$15$	−6.21823	+	1.98468i	−1.60554	+	0.512443i
$16$	−0.850202	+	0.490865i	−0.212551	+	0.122716i
$17$	1.50184	+	3.83985i	0.364250	+	0.931301i
$17$	1.50184	+	3.83985i	0.364250	+	0.931301i
$18$	−2.95126	−	0.499000i	−0.695619	−	0.117615i
$19$	3.79324	+	1.57121i	0.870228	+	0.360460i	0.772699	−	0.634773i	$-0.218906\pi$
$19$	3.79324	+	1.57121i	0.870228	+	0.360460i	0.0975288	+	0.995233i	$0.468906\pi$
$20$	2.49610	+	2.84626i	0.558145	+	0.636442i
$21$	3.94241	−	5.67273i	0.860305	−	1.23789i
$22$	3.53699	−	1.74425i	0.754088	−	0.371875i
$23$	−0.645419	+	0.735959i	−0.134579	+	0.153458i	−0.815204	−	0.579174i	$-0.803375\pi$
$23$	−0.645419	+	0.735959i	−0.134579	+	0.153458i	0.680625	+	0.732632i	$0.261708\pi$
$24$	1.25184	+	5.03900i	0.255531	+	1.02858i
$25$	−5.60170	+	7.30028i	−1.12034	+	1.46006i
$26$	−0.0592152	−	0.142958i	−0.0116131	−	0.0280364i
$27$	−2.24888	+	4.68429i	−0.432798	+	0.901491i
$28$	−3.92963	−	0.781652i	−0.742630	−	0.147718i
$29$	0.325703	−	4.96927i	0.0604816	−	0.922771i	−0.854545	−	0.519377i	$-0.826164\pi$
$29$	0.325703	−	4.96927i	0.0604816	−	0.922771i	0.915027	−	0.403393i	$-0.132169\pi$
$30$	−5.89250	+	2.77300i	−1.07582	+	0.506278i
$31$	−1.57861	+	4.65042i	−0.283526	+	0.835240i	0.708102	+	0.706110i	$0.249552\pi$
$31$	−1.57861	+	4.65042i	−0.283526	+	0.835240i	−0.991628	+	0.129130i	$0.958782\pi$
$32$	3.97939	−	3.05349i	0.703464	−	0.539787i
$33$	−1.21256	−	6.73807i	−0.211080	−	1.17295i
$34$	1.98565	+	3.60273i	0.340536	+	0.617862i
$35$		−	15.0305i		−	2.54061i
$36$	3.01167	+	0.110266i	0.501945	+	0.0183777i
$37$	−0.326442	−	1.64113i	−0.0536667	−	0.269801i	0.944630	−	0.328136i	$-0.106421\pi$
$37$	−0.326442	−	1.64113i	−0.0536667	−	0.269801i	−0.998297	+	0.0583359i	$0.981421\pi$
$38$	3.95681	+	1.06022i	0.641879	+	0.171991i
$39$	−0.266924	+	0.0301837i	−0.0427421	+	0.00483327i
$40$	8.49347	+	7.44857i	1.34294	+	1.17772i
$41$	−4.85207	+	0.318021i	−0.757766	+	0.0496666i	−0.439388	−	0.898297i	$-0.644805\pi$
$41$	−4.85207	+	0.318021i	−0.757766	+	0.0496666i	−0.318378	+	0.947964i	$0.603138\pi$
$42$	3.16101	−	6.12476i	0.487755	−	0.945071i
$43$	−3.14609	−	2.41408i	−0.479775	−	0.368144i	0.340378	−	0.940289i	$-0.389445\pi$
$43$	−3.14609	−	2.41408i	−0.479775	−	0.368144i	−0.820153	+	0.572145i	$0.806112\pi$
$44$	−3.30156	+	2.20603i	−0.497729	+	0.332572i
$45$	1.79843	+	11.1616i	0.268094	+	1.66388i
$46$	−0.542593	+	0.812048i	−0.0800010	+	0.119730i
$47$	−0.797097	+	2.97481i	−0.116269	+	0.433920i	−0.999379	−	0.0352455i	$-0.988779\pi$
$47$	−0.797097	+	2.97481i	−0.116269	+	0.433920i	0.883110	+	0.469166i	$0.155445\pi$
$48$	0.621863	+	1.58261i	0.0897582	+	0.228430i
$49$	5.42253	+	7.06678i	0.774647	+	1.00954i
$50$	−4.59039	+	7.95079i	−0.649179	+	1.12441i
$51$	6.96360	−	1.58376i	0.975099	−	0.221770i
$52$	0.0778993	+	0.134926i	0.0108027	+	0.0187108i
$53$	0.152152	−	0.367326i	0.0208996	−	0.0504562i	−0.913085	−	0.407769i	$-0.866307\pi$
$53$	0.152152	−	0.367326i	0.0208996	−	0.0504562i	0.933985	+	0.357313i	$0.116307\pi$
$54$	−1.61453	+	4.92647i	−0.219709	+	0.670408i
$55$	−10.5330	−	10.5330i	−1.42027	−	1.42027i
$56$	−11.9305	−	0.781965i	−1.59428	−	0.104495i
$57$	3.66779	−	6.09256i	0.485811	−	0.806980i
$58$	−0.324959	−	4.95792i	−0.0426693	−	0.651007i
$59$	−0.226196	+	1.71813i	−0.0294482	+	0.223681i	−0.999841	−	0.0178524i	$-0.994317\pi$
$59$	−0.226196	+	1.71813i	−0.0294482	+	0.223681i	0.970392	+	0.241534i	$0.0776504\pi$
$60$	5.51774	−	3.54254i	0.712337	−	0.457340i
$61$	−3.50005	+	7.09741i	−0.448136	+	0.908730i	0.549193	+	0.835695i	$0.314935\pi$
$61$	−3.50005	+	7.09741i	−0.448136	+	0.908730i	−0.997329	+	0.0730347i	$0.976732\pi$
$62$	−0.955910	+	4.80569i	−0.121401	+	0.610323i
$63$	−8.70128	−	8.21311i	−1.09626	−	1.03475i
$64$	4.92706	−	4.92706i	0.615883	−	0.615883i
$65$	−0.439424	+	0.385364i	−0.0545038	+	0.0477986i
$66$	−2.07693	−	6.50726i	−0.255652	−	0.800988i
$67$	−9.67537	−	5.58608i	−1.18204	−	0.682448i	−0.225551	−	0.974231i	$-0.572418\pi$
$67$	−9.67537	−	5.58608i	−1.18204	−	0.682448i	−0.956485	+	0.291783i	$0.905751\pi$
$68$	−2.45565	−	3.33546i	−0.297791	−	0.404484i
$69$	1.09439	+	1.29496i	0.131749	+	0.155895i
$70$	−1.95739	−	14.8678i	−0.233953	−	1.77705i
$71$	3.55751	−	0.707633i	0.422199	−	0.0839806i	0.0205816	−	0.999788i	$-0.493448\pi$
$71$	3.55751	−	0.707633i	0.422199	−	0.0839806i	0.401617	+	0.915808i	$0.368448\pi$
$72$	8.95314	−	0.846821i	1.05514	−	0.0997989i
$73$	12.4119	+	8.29338i	1.45270	+	0.970666i	0.996741	+	0.0806676i	$0.0257052\pi$
$73$	12.4119	+	8.29338i	1.45270	+	0.970666i	0.455963	+	0.889998i	$0.349295\pi$
$74$	−0.536631	−	1.58086i	−0.0623821	−	0.183772i
$75$	11.0618	+	11.4742i	1.27730	+	1.32492i
$76$	−4.08922	−	0.538355i	−0.469065	−	0.0617536i
$77$	15.6302	+	2.05776i	1.78123	+	0.234503i
$78$	−0.260106	+	0.0646182i	−0.0294512	+	0.00731657i
$79$	−3.82731	−	11.2749i	−0.430606	−	1.26853i	−0.918430	−	0.395584i	$-0.870542\pi$
$79$	−3.82731	−	11.2749i	−0.430606	−	1.26853i	0.487824	−	0.872942i	$-0.337791\pi$
$80$	3.07617	+	2.05543i	0.343926	+	0.229804i
$81$	7.44429	+	5.05793i	0.827143	+	0.561992i
$82$	−4.75816	+	0.946456i	−0.525451	+	0.104519i
$83$	0.0575142	+	0.436864i	0.00631301	+	0.0479520i	0.994311	−	0.106512i	$-0.0339683\pi$
$83$	0.0575142	+	0.436864i	0.00631301	+	0.0479520i	−0.987998	+	0.154464i	$0.950635\pi$
$84$	−2.35055	+	6.52946i	−0.256466	+	0.712422i
$85$	10.4750	−	11.4762i	1.13618	−	1.24477i
$86$	−3.42643	−	1.97825i	−0.369482	−	0.213321i
$87$	−8.42756	−	1.83726i	−0.903529	−	0.196975i
$88$	−8.90860	+	7.81263i	−0.949660	+	0.832829i
$89$	−3.79574	+	3.79574i	−0.402347	+	0.402347i	−0.879059	−	0.476712i	$-0.841828\pi$
$89$	−3.79574	+	3.79574i	−0.402347	+	0.402347i	0.476712	+	0.879059i	$0.341828\pi$
$90$	3.23253	+	10.8067i	0.340738	+	1.13912i
$91$	0.120677	−	0.606682i	0.0126503	−	0.0635976i
$92$	0.434922	−	0.881934i	0.0453437	−	0.0919480i
$93$	7.55885	+	3.90115i	0.783817	+	0.404530i
$94$	−0.401070	+	3.04643i	−0.0413672	+	0.314215i
$95$	−1.01196	−	15.4396i	−0.103825	−	1.58407i
$96$	−4.20552	−	7.60209i	−0.429224	−	0.775885i
$97$	7.24200	+	0.474666i	0.735314	+	0.0481950i	0.428459	−	0.903561i	$-0.359057\pi$
$97$	7.24200	+	0.474666i	0.735314	+	0.0481950i	0.306855	+	0.951756i	$0.400723\pi$
$98$	6.28416	+	6.28416i	0.634796	+	0.634796i
$99$	−11.8532	+	0.342099i	−1.19129	+	0.0343823i
$100$	3.53744	−	8.54014i	0.353744	−	0.854014i
$101$	0.626967	+	1.08594i	0.0623855	+	0.108055i	0.895531	−	0.444999i	$-0.146796\pi$
$101$	0.626967	+	1.08594i	0.0623855	+	0.108055i	−0.833146	+	0.553053i	$0.813463\pi$
$102$	6.68201	−	2.47348i	0.661617	−	0.244911i
$103$	5.00719	−	8.67271i	0.493373	−	0.854547i	−0.506598	−	0.862183i	$-0.669097\pi$
$103$	5.00719	−	8.67271i	0.493373	−	0.854547i	0.999971	+	0.00763522i	$0.00243039\pi$
$104$	0.283023	+	0.368843i	0.0277527	+	0.0361680i
$105$	−25.7443	−	3.86976i	−2.51239	−	0.377649i
$106$	0.102669	−	0.383167i	0.00997211	−	0.0372164i
$107$	−2.18751	+	3.27383i	−0.211474	+	0.316494i	−0.922009	−	0.387169i	$-0.873453\pi$
$107$	−2.18751	+	3.27383i	−0.211474	+	0.316494i	0.710535	+	0.703662i	$0.248453\pi$
$108$	0.964251	−	5.13003i	0.0927851	−	0.493637i
$109$	−6.15435	+	4.11221i	−0.589480	+	0.393878i	−0.814233	−	0.580538i	$-0.802842\pi$
$109$	−6.15435	+	4.11221i	−0.589480	+	0.393878i	0.224753	+	0.974416i	$0.427842\pi$
$110$	−11.7907	−	9.04735i	−1.12420	−	0.862631i
$111$	−2.89499	+	0.136605i	−0.274781	+	0.0129659i
$112$	−3.90716	+	0.256089i	−0.369192	+	0.0241981i
$113$	−3.39386	−	2.97634i	−0.319268	−	0.279990i	0.484678	−	0.874692i	$-0.338937\pi$
$113$	−3.39386	−	2.97634i	−0.319268	−	0.279990i	−0.803946	+	0.594702i	$0.797270\pi$
$114$	2.83468	−	6.50429i	0.265493	−	0.609183i
$115$	3.56323	+	0.954764i	0.332273	+	0.0890322i
$116$	0.975970	+	4.90653i	0.0906165	+	0.455560i
$117$	−0.0170236	+	0.464962i	−0.00157383	+	0.0429857i
$118$			1.72900i			0.159167i
$119$	−1.40138	+	16.3848i	−0.128465	+	1.50200i
$120$	14.9447	−	12.6300i	1.36426	−	1.15295i
$121$	3.66844	−	2.81490i	0.333495	−	0.255900i
$122$	−2.53790	+	7.47642i	−0.229771	+	0.676884i
$123$	−0.704508	+	8.39255i	−0.0635233	+	0.756730i
$124$	0.322664	−	4.92289i	0.0289760	−	0.442089i
$125$	15.5303	+	3.08918i	1.38908	+	0.276304i
$126$	−9.67671	−	6.99109i	−0.862070	−	0.622816i
$127$	−0.465203	−	1.12310i	−0.0412801	−	0.0996590i	0.901895	−	0.431956i	$-0.142176\pi$
$127$	−0.465203	−	1.12310i	−0.0412801	−	0.0996590i	−0.943175	+	0.332297i	$0.892176\pi$
$128$	−1.87488	+	2.44339i	−0.165717	+	0.215967i
$129$	−4.94486	+	4.76712i	−0.435370	+	0.419722i
$130$	−0.384484	+	0.438420i	−0.0337215	+	0.0384520i
$131$	−17.1684	+	8.46650i	−1.50001	+	0.739722i	−0.992537	−	0.121947i	$-0.961086\pi$
$131$	−17.1684	+	8.46650i	−1.50001	+	0.739722i	−0.507471	+	0.861669i	$0.669420\pi$
$132$	2.92849	+	6.22291i	0.254892	+	0.541634i
$133$	10.7971	+	12.3118i	0.936230	+	1.06757i
$134$	−10.2982	−	4.26564i	−0.889625	−	0.368495i
$135$	19.5808	−	0.206683i	1.68524	−	0.0177885i
$136$	−8.56434	−	8.91166i	−0.734386	−	0.764169i
$137$	−18.1157	+	10.4591i	−1.54773	+	0.893581i	−0.549412	+	0.835551i	$0.685148\pi$
$137$	−18.1157	+	10.4591i	−1.54773	+	0.893581i	−0.998315	+	0.0580294i	$0.981518\pi$
$138$	1.25119	+	1.13843i	0.106508	+	0.0969095i
$139$	11.3603	+	3.85631i	0.963571	+	0.327088i	0.758510	−	0.651661i	$-0.225927\pi$
$139$	11.3603	+	3.85631i	0.963571	+	0.327088i	0.205061	+	0.978749i	$0.434261\pi$
$140$	3.90792	+	14.5846i	0.330279	+	1.23262i
$141$	4.89006	+	2.13117i	0.411817	+	0.179477i
$142$	3.42687	−	1.16326i	0.287576	−	0.0976190i
$143$	−0.340582	−	0.509717i	−0.0284809	−	0.0426246i
$144$	2.87082	−	0.657672i	0.239235	−	0.0548060i
$145$	−17.3385	+	7.18183i	−1.43988	+	0.596418i
$146$	13.3577	+	6.58727i	1.10549	+	0.545166i
$147$	13.5001	−	7.46834i	1.11347	−	0.615978i
$148$	0.743451	+	1.50757i	0.0611113	+	0.123922i
$149$	4.84561	−	1.29838i	0.396968	−	0.106367i	−0.0548121	−	0.998497i	$-0.517456\pi$
$149$	4.84561	−	1.29838i	0.396968	−	0.106367i	0.451780	+	0.892130i	$0.350789\pi$
$150$	12.4363	+	9.90948i	1.01542	+	0.809106i
$151$	−18.4319	+	2.42661i	−1.49997	+	0.197475i	−0.835355	−	0.549711i	$-0.814738\pi$
$151$	−18.4319	+	2.42661i	−1.49997	+	0.197475i	−0.664615	+	0.747186i	$0.731404\pi$
$152$	−12.3079			−0.998300
$153$	−0.919816	−	12.3351i	−0.0743627	−	0.997231i
$154$	15.7291			1.26749
$155$	18.3491	−	2.41570i	1.47383	−	0.194034i
$156$	0.251158	−	0.0986886i	0.0201087	−	0.00790141i
$157$	10.4620	−	2.80330i	0.834962	−	0.223727i	0.184085	−	0.982910i	$-0.441068\pi$
$157$	10.4620	−	2.80330i	0.834962	−	0.223727i	0.650877	+	0.759183i	$0.274401\pi$
$158$	−5.25421	−	10.6545i	−0.418003	−	0.847626i
$159$	−0.589987	−	0.355179i	−0.0467890	−	0.0281675i
$160$	−16.9532	−	8.36041i	−1.34027	−	0.660948i
$161$	−3.60699	+	1.49406i	−0.284270	+	0.117749i
$162$	8.02243	+	4.03375i	0.630301	+	0.316921i
$163$	11.6705	+	17.4662i	0.914106	+	1.36806i	0.929755	+	0.368178i	$0.120018\pi$
$163$	11.6705	+	17.4662i	0.914106	+	1.36806i	−0.0156497	+	0.999878i	$0.504982\pi$
$164$	4.62544	−	1.57012i	0.361186	−	0.122606i
$165$	−20.7529	+	15.3292i	−1.61561	+	1.19338i
$166$	0.113784	+	0.424647i	0.00883134	+	0.0329590i
$167$	11.1531	+	3.78598i	0.863057	+	0.292968i	0.717650	−	0.696404i	$-0.245218\pi$
$167$	11.1531	+	3.78598i	0.863057	+	0.292968i	0.145406	+	0.989372i	$0.453551\pi$
$168$	−4.41099	+	20.2333i	−0.340315	+	1.56103i
$169$	11.2375	−	6.48797i	0.864423	−	0.499075i
$170$	8.86718	−	12.7162i	0.680082	−	0.975289i
$171$	−9.49108	−	7.85082i	−0.725801	−	0.600367i
$172$	3.68042	+	1.52448i	0.280629	+	0.116240i
$173$	−10.7701	−	12.2809i	−0.818836	−	0.933703i	0.179915	−	0.983682i	$-0.442418\pi$
$173$	−10.7701	−	12.2809i	−0.818836	−	0.933703i	−0.998750	+	0.0499792i	$0.984085\pi$
$174$	−8.57564	−	0.719877i	−0.650118	−	0.0545738i
$175$	−32.9158	+	16.2323i	−2.48820	+	1.22704i
$176$	−2.55859	+	2.91751i	−0.192861	+	0.219916i
$177$	2.88459	+	0.829781i	0.216819	+	0.0623702i
$178$	−3.26036	+	4.24898i	−0.244374	+	0.318474i
$179$	−0.829352	−	2.00223i	−0.0619887	−	0.149654i	0.889850	−	0.456253i	$-0.150809\pi$
$179$	−0.829352	−	2.00223i	−0.0619887	−	0.149654i	−0.951839	+	0.306599i	$0.900809\pi$
$180$	−4.64710	−	10.3629i	−0.346374	−	0.772405i
$181$	1.59527	+	0.317319i	0.118575	+	0.0235861i	0.254021	−	0.967199i	$-0.418247\pi$
$181$	1.59527	+	0.317319i	0.118575	+	0.0235861i	−0.135446	+	0.990785i	$0.543247\pi$
$182$	0.0403639	−	0.615834i	0.00299197	−	0.0456486i
$183$	11.2554	+	7.82223i	0.832021	+	0.578236i
$184$	0.943226	−	2.77865i	0.0695355	−	0.204845i
$185$	−5.00274	+	3.83874i	−0.367809	+	0.282230i
$186$	7.98511	+	2.87457i	0.585497	+	0.210773i
$187$	10.5001	+	12.4642i	0.767841	+	0.911472i
$188$		−	3.09380i		−	0.225639i
$189$	−16.3077	+	12.7891i	−1.18621	+	0.930268i
$190$	−3.01168	−	15.1407i	−0.218490	−	1.09842i
$191$	−8.10871	−	2.17272i	−0.586726	−	0.157213i	−0.0467694	−	0.998906i	$-0.514893\pi$
$191$	−8.10871	−	2.17272i	−0.586726	−	0.157213i	−0.539956	+	0.841693i	$0.681559\pi$
$192$	−7.17059	−	9.70764i	−0.517493	−	0.700588i
$193$	1.96316	+	1.72164i	0.141311	+	0.123927i	0.727083	−	0.686549i	$-0.240875\pi$
$193$	1.96316	+	1.72164i	0.141311	+	0.123927i	−0.585772	+	0.810476i	$0.699209\pi$
$194$	7.22546	−	0.473582i	0.518758	−	0.0340012i
$195$	0.546921	+	0.851865i	0.0391658	+	0.0610033i
$196$	−7.09902	−	5.44727i	−0.507073	−	0.389091i
$197$	2.93389	−	1.96036i	0.209031	−	0.139670i	−0.446648	−	0.894710i	$-0.647382\pi$
$197$	2.93389	−	1.96036i	0.209031	−	0.139670i	0.655679	+	0.755040i	$0.272382\pi$
$198$	−11.6804	+	1.88202i	−0.830091	+	0.133749i
$199$	7.13355	−	10.6761i	0.505684	−	0.756810i	−0.487531	−	0.873106i	$-0.662102\pi$
$199$	7.13355	−	10.6761i	0.505684	−	0.756810i	0.993215	+	0.116296i	$0.0371022\pi$
$200$	7.13933	−	26.6443i	0.504827	−	1.88404i
$201$	−12.0589	+	15.1339i	−0.850570	+	1.06746i
$202$	0.761603	+	0.992540i	0.0535862	+	0.0698349i
$203$	9.93103	−	17.2011i	0.697022	−	1.20728i
$204$	−6.34523	+	3.34730i	−0.444255	+	0.234358i
$205$	9.16220	+	15.8694i	0.639916	+	1.10837i
$206$	3.82359	−	9.23095i	0.266402	−	0.643151i
$207$	2.49978	−	1.54107i	0.173747	−	0.107112i
$208$	0.107662	+	0.107662i	0.00746503	+	0.00746503i
$209$	16.1942	+	1.06142i	1.12018	+	0.0734202i
$210$	−25.9697	−	0.475254i	−1.79208	−	0.0327956i
$211$	−0.980821	−	14.9644i	−0.0675225	−	1.03019i	−0.888394	−	0.459082i	$-0.848179\pi$
$211$	−0.980821	−	14.9644i	−0.0675225	−	1.03019i	0.820872	−	0.571113i	$-0.193488\pi$
$212$	−0.0521328	+	0.395988i	−0.00358050	+	0.0271966i
$213$	−0.296120	−	6.27552i	−0.0202898	−	0.429992i
$214$	−1.73749	+	3.52329i	−0.118773	+	0.240847i
$215$	−2.91549	+	14.6572i	−0.198835	+	0.999612i
$216$	0.854640	−	15.5530i	0.0581509	−	1.05825i
$217$	−13.8503	+	13.8503i	−0.940222	+	0.940222i
$218$	−5.55224	+	4.86918i	−0.376045	+	0.329783i
$219$	17.4005	−	19.1240i	1.17582	−	1.29228i
$220$	12.9591	+	7.48194i	0.873703	+	0.504432i
$221$	0.514950	−	0.379119i	0.0346393	−	0.0255023i
$222$	−2.84588	+	0.512136i	−0.191003	+	0.0343723i
$223$	−2.95243	−	22.4260i	−0.197710	−	1.50175i	−0.746271	−	0.665643i	$-0.768158\pi$
$223$	−2.95243	−	22.4260i	−0.197710	−	1.50175i	0.548561	−	0.836110i	$-0.315176\pi$
$224$	19.6212	−	3.90289i	1.31099	−	0.260773i
$225$	22.5010	−	15.9925i	1.50007	−	1.06617i
$226$	−3.74474	−	2.50216i	−0.249097	−	0.166441i
$227$	7.17030	+	21.1230i	0.475910	+	1.40198i	0.874576	+	0.484888i	$0.161140\pi$
$227$	7.17030	+	21.1230i	0.475910	+	1.40198i	−0.398666	+	0.917096i	$0.630527\pi$
$228$	−1.97491	+	6.86544i	−0.130792	+	0.454675i
$229$	−24.8770	−	3.27511i	−1.64392	−	0.216426i	−0.748971	−	0.662603i	$-0.769452\pi$
$229$	−24.8770	−	3.27511i	−1.64392	−	0.216426i	−0.894945	+	0.446177i	$0.852785\pi$
$230$	3.64901	+	0.480402i	0.240609	+	0.0316768i
$231$	7.54871	−	26.2418i	0.496669	−	1.72658i
$232$	4.79856	+	14.1361i	0.315041	+	0.928081i
$233$	−16.5841	−	11.0812i	−1.08646	−	0.725951i	−0.122628	−	0.992453i	$-0.539132\pi$
$233$	−16.5841	−	11.0812i	−1.08646	−	0.725951i	−0.963835	+	0.266501i	$0.914132\pi$
$234$	0.0437117	+	0.462148i	0.00285752	+	0.0302116i
$235$	11.3831	−	2.26424i	0.742552	−	0.147703i
$236$	−0.227228	−	1.72597i	−0.0147913	−	0.112351i
$237$	−20.2971	+	3.65261i	−1.31844	+	0.237263i
$238$	0.747546	+	16.3901i	0.0484562	+	1.06241i
$239$	4.69428	+	2.71024i	0.303647	+	0.175311i	0.644080	−	0.764958i	$-0.277240\pi$
$239$	4.69428	+	2.71024i	0.303647	+	0.175311i	−0.340433	+	0.940269i	$0.610574\pi$
$240$	4.31255	−	4.73969i	0.278374	−	0.305946i
$241$	17.8200	−	15.6277i	1.14788	−	1.00667i	0.148041	−	0.988981i	$-0.452703\pi$
$241$	17.8200	−	15.6277i	1.14788	−	1.00667i	0.999844	−	0.0176869i	$-0.00563019\pi$
$242$	3.26217	−	3.26217i	0.209701	−	0.209701i
$243$	10.5799	−	11.4484i	0.678699	−	0.734416i
$244$	1.55089	−	7.79686i	0.0992857	−	0.499143i
$245$	14.8468	−	30.1063i	0.948526	−	1.92342i
$246$	0.396060	+	8.39349i	0.0252519	+	0.535149i
$247$	0.0831149	−	0.631320i	0.00528847	−	0.0401699i
$248$	−0.962856	−	14.6903i	−0.0611414	−	0.932837i
$249$	0.763072	+	0.0139645i	0.0483577	+	0.000884961i
$250$	15.7646	+	1.03327i	0.997041	+	0.0653495i
$251$	−15.9830	−	15.9830i	−1.00884	−	1.00884i	−0.999961	−	0.00887458i	$-0.997175\pi$
$251$	−15.9830	−	15.9830i	−1.00884	−	1.00884i	−0.00887458	−	0.999961i	$-0.502825\pi$
$252$	10.5785	+	5.70712i	0.666386	+	0.359514i
$253$	−1.48069	+	3.57470i	−0.0930901	+	0.224739i
$254$	−0.606429	−	1.05037i	−0.0380508	−	0.0659058i
$255$	−16.9597	−	20.8964i	−1.06206	−	1.30859i
$256$	−8.50431	+	14.7299i	−0.531520	+	0.920619i
$257$	7.88224	+	10.2723i	0.491680	+	0.640771i	0.971625	−	0.236529i	$-0.0760097\pi$
$257$	7.88224	+	10.2723i	0.491680	+	0.640771i	−0.479944	+	0.877299i	$0.659343\pi$
$258$	−4.27054	+	5.35951i	−0.265872	+	0.333668i
$259$	1.72730	−	6.44636i	0.107329	−	0.400557i
$260$	0.326193	−	0.488182i	0.0202296	−	0.0302758i
$261$	−5.31664	+	13.9618i	−0.329092	+	0.864212i
$262$	−15.8800	+	10.6107i	−0.981072	+	0.655532i
$263$	−15.2125	−	11.6730i	−0.938043	−	0.719785i	0.0219651	−	0.999759i	$-0.493008\pi$
$263$	−15.2125	−	11.6730i	−0.938043	−	0.719785i	−0.960008	+	0.279973i	$0.909674\pi$
$264$	11.0879	+	17.2702i	0.682415	+	1.06291i
$265$	−1.49513	+	0.0979957i	−0.0918448	+	0.00601983i
$266$	12.2837	+	10.7725i	0.753159	+	0.660503i
$267$	5.52412	+	7.47862i	0.338070	+	0.457684i
$268$	10.8407	+	2.90476i	0.662202	+	0.177437i
$269$	−0.828131	−	4.16330i	−0.0504920	−	0.253841i	0.947292	−	0.320370i	$-0.103807\pi$
$269$	−0.828131	−	4.16330i	−0.0504920	−	0.253841i	−0.997784	+	0.0665296i	$0.978807\pi$
$270$	19.3420	−	2.75441i	1.17712	−	0.167628i
$271$		−	3.33726i		−	0.202724i	−0.994850	−	0.101362i	$-0.967680\pi$
$271$		−	3.33726i		−	0.202724i	0.994850	−	0.101362i	$-0.0323200\pi$
$272$	−3.16172	−	2.52745i	−0.191707	−	0.153249i
$273$	−1.00806	−	0.362893i	−0.0610106	−	0.0219633i
$274$	−16.5576	+	12.7051i	−1.00028	+	0.767543i
$275$	−11.6914	+	34.4418i	−0.705020	+	2.07692i
$276$	−1.39861	−	0.972001i	−0.0841864	−	0.0585076i
$277$	−0.204438	+	3.11912i	−0.0122835	+	0.187410i	0.987308	+	0.158819i	$0.0507686\pi$
$277$	−0.204438	+	3.11912i	−0.0122835	+	0.187410i	−0.999591	+	0.0285907i	$0.990898\pi$
$278$	11.7396	+	2.33516i	0.704096	+	0.140053i
$279$	8.62803	−	11.9425i	0.516547	−	0.714978i
$280$	17.2425	+	41.6271i	1.03044	+	2.48769i
$281$	8.56631	−	11.1638i	0.511023	−	0.665979i	−0.464577	−	0.885533i	$-0.653794\pi$
$281$	8.56631	−	11.1638i	0.511023	−	0.665979i	0.975600	+	0.219554i	$0.0704603\pi$
$282$	5.11469	+	1.47129i	0.304575	+	0.0876141i
$283$	−5.71974	+	6.52212i	−0.340004	+	0.387700i	−0.896421	−	0.443203i	$-0.853842\pi$
$283$	−5.71974	+	6.52212i	−0.340004	+	0.387700i	0.556418	+	0.830903i	$0.312175\pi$
$284$	−3.26799	+	1.61159i	−0.193919	+	0.0956304i
$285$	−26.7056	−	2.24179i	−1.58190	−	0.132792i
$286$	−0.403276	−	0.459848i	−0.0238462	−	0.0271914i
$287$	−17.9174	−	7.42161i	−1.05763	−	0.438084i
$288$	−14.1037	+	5.24600i	−0.831068	+	0.309124i
$289$	−12.4889	+	11.5337i	−0.734644	+	0.678453i
$290$	−16.2156	+	9.36208i	−0.952213	+	0.549760i
$291$	2.67754	−	12.2820i	0.156960	−	0.719981i
$292$	−14.2000	−	4.82024i	−0.830990	−	0.282083i
$293$	−7.51018	−	28.0284i	−0.438749	−	1.63743i	−0.731932	−	0.681378i	$-0.761381\pi$
$293$	−7.51018	−	28.0284i	−0.438749	−	1.63743i	0.293183	−	0.956056i	$-0.405286\pi$
$294$	12.3815	−	9.14563i	0.722103	−	0.533384i
$295$	6.18410	−	2.09922i	0.360052	−	0.122221i
$296$	2.78674	+	4.17066i	0.161976	+	0.242414i
$297$	−2.46579	+	20.3904i	−0.143079	+	1.18317i
$298$	4.62409	−	1.91536i	0.267867	−	0.110954i
$299$	0.136159	+	0.0671461i	0.00787427	+	0.00388316i
$300$	−13.7169	−	8.25771i	−0.791944	−	0.476759i
$301$	−6.99538	−	14.1852i	−0.403207	−	0.817623i
$302$	−17.9165	+	4.80071i	−1.03098	+	0.276250i
$303$	2.02142	−	0.794287i	0.116128	−	0.0456306i
$304$	−3.99627	+	0.526119i	−0.229202	+	0.0301750i
$305$	29.8223			1.70762
$306$	−2.51624	−	12.0818i	−0.143844	−	0.690672i
$307$	5.60179			0.319711			0.159855	−	0.987140i	$-0.448897\pi$
$307$	5.60179			0.319711			0.159855	+	0.987140i	$0.448897\pi$
$308$	−15.7015	+	2.06715i	−0.894678	+	0.117787i
$309$	−13.5655	−	10.8092i	−0.771716	−	0.614916i
$310$	17.8360	−	4.77914i	1.01302	−	0.271437i
$311$	8.82261	+	17.8905i	0.500284	+	1.01448i	0.989798	+	0.142480i	$0.0455077\pi$
$311$	8.82261	+	17.8905i	0.500284	+	1.01448i	−0.489513	+	0.871996i	$0.662826\pi$
$312$	0.704625	−	0.389802i	0.0398915	−	0.0220682i
$313$	18.9849	+	9.36233i	1.07309	+	0.529190i	0.890959	−	0.454084i	$-0.150033\pi$
$313$	18.9849	+	9.36233i	1.07309	+	0.529190i	0.182132	+	0.983274i	$0.441700\pi$
$314$	9.98378	−	4.13542i	0.563417	−	0.233375i
$315$	−13.2563	+	43.0988i	−0.746908	+	2.42834i
$316$	6.64524	+	9.94531i	0.373824	+	0.559467i
$317$	18.2057	−	6.18002i	1.02254	−	0.347104i	0.240708	−	0.970598i	$-0.422620\pi$
$317$	18.2057	−	6.18002i	1.02254	−	0.347104i	0.781829	+	0.623493i	$0.214287\pi$
$318$	−0.629858	−	0.274503i	−0.0353207	−	0.0153934i
$319$	−5.09466	−	19.0135i	−0.285246	−	1.06455i
$320$	−24.8652	−	8.44061i	−1.39001	−	0.471844i
$321$	5.04426	+	4.58966i	0.281543	+	0.256170i
$322$	−3.37339	+	1.94763i	−0.187992	+	0.108537i
$323$	−0.336377	+	16.9252i	−0.0187165	+	0.941742i
$324$	−8.53850	−	2.97236i	−0.474361	−	0.165131i
$325$	1.31848	+	0.546134i	0.0731363	+	0.0302941i
$326$	13.8188	+	15.7574i	0.765355	+	0.872720i
$327$	5.45892	+	11.6000i	0.301879	+	0.641479i
$328$	13.0731	−	6.44692i	0.721839	−	0.355971i
$329$	−8.09896	+	9.23509i	−0.446510	+	0.509147i
$330$	−18.5320	+	17.8659i	−1.02016	+	0.983488i
$331$	4.76462	−	6.20937i	0.261887	−	0.341298i	−0.643839	−	0.765161i	$-0.722659\pi$
$331$	4.76462	−	6.20937i	0.261887	−	0.341298i	0.905726	+	0.423863i	$0.139326\pi$
$332$	−0.169393	−	0.408950i	−0.00929662	−	0.0224440i
$333$	−0.511369	+	4.99374i	−0.0280229	+	0.273655i
$334$	11.5255	+	2.29257i	0.630648	+	0.125444i
$335$	−2.75364	+	42.0124i	−0.150448	+	2.29539i
$336$	−0.567310	+	6.75816i	−0.0309493	+	0.368688i
$337$	4.08393	−	12.0309i	0.222466	−	0.655363i	−0.777194	−	0.629262i	$-0.783357\pi$
$337$	4.08393	−	12.0309i	0.222466	−	0.655363i	0.999659	−	0.0261012i	$-0.00830922\pi$
$338$	10.2710	−	7.88122i	0.558669	−	0.428682i
$339$	−5.97168	+	5.04675i	−0.324337	+	0.274102i
$340$	−7.18046	+	13.8593i	−0.389415	+	0.751625i
$341$			19.4120i			1.05122i
$342$	−10.4108	−	6.52987i	−0.562951	−	0.353095i
$343$	1.48421	+	7.46165i	0.0801401	+	0.402891i
$344$	11.4825	+	3.07673i	0.619096	+	0.165886i
$345$	2.55272	−	5.85732i	0.137434	−	0.315347i
$346$	−12.2529	−	10.7455i	−0.658720	−	0.577682i
$347$	16.5212	−	1.08285i	0.886902	−	0.0581306i	0.384861	−	0.922975i	$-0.374249\pi$
$347$	16.5212	−	1.08285i	0.886902	−	0.0581306i	0.502041	+	0.864844i	$0.332583\pi$
$348$	8.65522	−	0.408410i	0.463969	−	0.0218931i
$349$	−17.6839	−	13.5693i	−0.946598	−	0.726350i	0.0152647	−	0.999883i	$-0.495141\pi$
$349$	−17.6839	−	13.5693i	−0.946598	−	0.726350i	−0.961862	+	0.273533i	$0.911808\pi$
$350$	−30.4458	+	20.3432i	−1.62739	+	1.08739i
$351$	0.792007	+	0.148868i	0.0422742	+	0.00794596i
$352$	11.0150	−	16.4851i	0.587102	−	0.878660i
$353$	−4.11642	+	15.3627i	−0.219095	+	0.817674i	0.765590	+	0.643329i	$0.222447\pi$
$353$	−4.11642	+	15.3627i	−0.219095	+	0.817674i	−0.984685	+	0.174344i	$0.944219\pi$
$354$	2.96144	+	0.445149i	0.157399	+	0.0236594i
$355$	−8.32130	−	10.8445i	−0.441649	−	0.575568i
$356$	2.69624	−	4.67002i	0.142900	−	0.247510i
$357$	27.7033	+	6.61876i	1.46621	+	0.350302i
$358$	−1.08113	−	1.87256i	−0.0571393	−	0.0989681i
$359$	1.61713	−	3.90411i	0.0853491	−	0.206051i	−0.875443	−	0.483322i	$-0.839430\pi$
$359$	1.61713	−	3.90411i	0.0853491	−	0.206051i	0.960792	+	0.277271i	$0.0894300\pi$
$360$	−17.7851	−	28.8492i	−0.937355	−	1.52048i
$361$	−1.51509	−	1.51509i	−0.0797417	−	0.0797417i
$362$	1.61933	+	0.106137i	0.0851102	+	0.00557842i
$363$	−3.87690	−	7.00807i	−0.203484	−	0.367828i
$364$	0.0406409	+	0.620060i	0.00213016	+	0.0325000i
$365$	7.34280	−	55.7741i	0.384340	−	2.91935i
$366$	12.1523	+	6.27183i	0.635210	+	0.327834i
$367$	1.90095	−	3.85474i	0.0992288	−	0.201216i	−0.841598	−	0.540105i	$-0.818384\pi$
$367$	1.90095	−	3.85474i	0.0992288	−	0.201216i	0.940826	+	0.338889i	$0.110051\pi$
$368$	0.187480	−	0.942527i	0.00977309	−	0.0491326i
$369$	14.1934	+	3.36744i	0.738881	+	0.175302i
$370$	−4.44870	+	4.44870i	−0.231277	+	0.231277i
$371$	1.19224	−	1.04556i	0.0618979	−	0.0542830i
$372$	−8.34890	−	1.82011i	−0.432870	−	0.0943685i
$373$	16.5321	+	9.54481i	0.855999	+	0.494211i	0.862670	−	0.505766i	$-0.168790\pi$
$373$	16.5321	+	9.54481i	0.855999	+	0.494211i	−0.00667136	+	0.999978i	$0.502124\pi$
$374$	12.0097	+	10.9619i	0.621004	+	0.566828i
$375$	9.28962	−	25.8052i	0.479714	−	1.33257i
$376$	−1.20504	−	9.15318i	−0.0621451	−	0.472039i
$377$	−0.757503	+	0.150677i	−0.0390134	+	0.00776024i
$378$	−14.4658	+	14.7744i	−0.744039	+	0.759914i
$379$	−3.35115	−	2.23916i	−0.172137	−	0.115018i	0.466517	−	0.884512i	$-0.345509\pi$
$379$	−3.35115	−	2.23916i	−0.172137	−	0.115018i	−0.638654	+	0.769494i	$0.720509\pi$
$380$	4.99623	+	14.7184i	0.256301	+	0.755039i
$381$	−2.04343	+	0.507650i	−0.104688	+	0.0260077i
$382$	−8.30393	−	1.09323i	−0.424866	−	0.0559347i
$383$	13.5445	+	1.78317i	0.692092	+	0.0911156i	0.468363	−	0.883536i	$-0.344844\pi$
$383$	13.5445	+	1.78317i	0.692092	+	0.0911156i	0.223728	+	0.974652i	$0.428177\pi$
$384$	3.70235	+	3.84039i	0.188935	+	0.195979i
$385$	−19.0971	−	56.2582i	−0.973278	−	2.86718i
$386$	2.16612	+	1.44736i	0.110253	+	0.0736686i
$387$	6.89207	+	9.69694i	0.350343	+	0.492923i
$388$	−7.15056	+	1.42234i	−0.363015	+	0.0722082i
$389$	0.217623	+	1.65301i	0.0110339	+	0.0838111i	0.996076	−	0.0885040i	$-0.0282086\pi$
$389$	0.217623	+	1.65301i	0.0110339	+	0.0838111i	−0.985042	+	0.172315i	$0.944875\pi$
$390$	0.651941	+	0.771424i	0.0330123	+	0.0390626i
$391$	−3.79529	−	1.37302i	−0.191936	−	0.0694366i
$392$	−23.1246	−	13.3510i	−1.16797	−	0.674326i
$393$	10.0813	+	31.5859i	0.508535	+	1.59330i
$394$	2.64685	−	2.32123i	0.133346	−	0.116942i
$395$	−31.7287	+	31.7287i	−1.59644	+	1.59644i
$396$	11.4126	−	3.41379i	0.573506	−	0.171549i
$397$	3.81082	−	19.1583i	0.191260	−	0.961527i	−0.759242	−	0.650808i	$-0.774430\pi$
$397$	3.81082	−	19.1583i	0.191260	−	0.961527i	0.950502	−	0.310719i	$-0.100570\pi$
$398$	5.66604	−	11.4896i	0.284013	−	0.575921i
$399$	23.8675	−	15.3236i	1.19487	−	0.767141i
$400$	1.17913	−	8.95639i	0.0589566	−	0.447820i
$401$	0.174661	+	2.66481i	0.00872216	+	0.133074i	0.999999	+	0.00127968i	$0.000407334\pi$
$401$	0.174661	+	2.66481i	0.00872216	+	0.133074i	−0.991277	+	0.131795i	$0.957926\pi$
$402$	−9.95759	+	16.5405i	−0.496639	+	0.824967i
$403$	0.760029	+	0.0498149i	0.0378597	+	0.00248146i
$404$	−0.890710	−	0.890710i	−0.0443145	−	0.0443145i
$405$	4.68727	−	33.5913i	0.232912	−	1.66917i
$406$	7.58352	−	18.3082i	0.376364	−	0.908623i
$407$	−3.30701	−	5.72791i	−0.163922	−	0.283922i
$408$	−17.4690	+	12.3747i	−0.864842	+	0.612637i
$409$	−6.94771	+	12.0338i	−0.343542	+	0.595033i	−0.985088	−	0.172052i	$-0.944960\pi$
$409$	−6.94771	+	12.0338i	−0.343542	+	0.595033i	0.641546	+	0.767085i	$0.278294\pi$
$410$	11.1297	+	14.5045i	0.549657	+	0.716327i
$411$	13.2504	+	33.7215i	0.653592	+	1.66336i
$412$	−2.60374	+	9.71728i	−0.128277	+	0.478736i
$413$	−3.83996	+	5.74691i	−0.188952	+	0.282787i
$414$	2.27204	−	1.84994i	0.111665	−	0.0909197i
$415$	1.38069	−	0.922546i	0.0677753	−	0.0452860i
$416$	−0.617168	−	0.473570i	−0.0302592	−	0.0232187i
$417$	9.52997	−	18.4652i	0.466685	−	0.904246i
$418$	16.1572	−	1.05900i	0.790275	−	0.0517974i
$419$	−16.8505	−	14.7775i	−0.823201	−	0.721928i	0.140162	−	0.990129i	$-0.455238\pi$
$419$	−16.8505	−	14.7775i	−0.823201	−	0.721928i	−0.963363	+	0.268201i	$0.913571\pi$
$420$	25.9867	−	2.93857i	1.26802	−	0.143387i
$421$	9.59465	+	2.57088i	0.467615	+	0.125297i	0.484930	−	0.874553i	$-0.338845\pi$
$421$	9.59465	+	2.57088i	0.467615	+	0.125297i	−0.0173150	+	0.999850i	$0.505512\pi$
$422$	−2.91900	−	14.6748i	−0.142095	−	0.714358i
$423$	4.90929	−	7.82704i	0.238698	−	0.380564i
$424$			1.19186i			0.0578818i
$425$	−36.4449	−	10.5459i	−1.76784	−	0.511549i
$426$	−1.11017	−	6.16906i	−0.0537877	−	0.298892i
$427$	−25.0401	+	19.2140i	−1.21178	+	0.929829i
$428$	1.27141	−	3.74546i	0.0614560	−	0.181044i
$429$	−0.960734	+	0.452119i	−0.0463847	+	0.0218285i
$430$	−0.975174	+	14.8783i	−0.0470271	+	0.717494i
$431$	−23.8944	−	4.75288i	−1.15095	−	0.228938i	−0.417497	−	0.908678i	$-0.637093\pi$
$431$	−23.8944	−	4.75288i	−1.15095	−	0.228938i	−0.733453	+	0.679740i	$0.762093\pi$
$432$	−0.387344	−	5.08649i	−0.0186361	−	0.244724i
$433$	15.1506	+	36.5767i	0.728090	+	1.75777i	0.648858	+	0.760909i	$0.275247\pi$
$433$	15.1506	+	36.5767i	0.728090	+	1.75777i	0.0792323	+	0.996856i	$0.474753\pi$
$434$	−11.8968	+	15.5042i	−0.571063	+	0.744224i
$435$	7.83712	+	31.5465i	0.375761	+	1.51254i
$436$	4.90260	−	5.59034i	0.234792	−	0.267729i
$437$	−3.60457	+	1.77758i	−0.172430	+	0.0850331i
$438$	14.7218	−	21.1831i	0.703435	−	1.01217i
$439$	−18.2682	−	20.8309i	−0.871895	−	0.994206i	−0.999997	−	0.00244453i	$-0.999222\pi$
$439$	−18.2682	−	20.8309i	−0.871895	−	0.994206i	0.128102	−	0.991761i	$-0.459111\pi$
$440$	41.2545	+	17.0882i	1.96673	+	0.814646i
$441$	−9.31608	−	25.0459i	−0.443623	−	1.19266i
$442$	0.460007	−	0.442078i	0.0218803	−	0.0210275i
$443$	17.2243	−	9.94445i	0.818351	−	0.472475i	−0.0314967	−	0.999504i	$-0.510027\pi$
$443$	17.2243	−	9.94445i	0.818351	−	0.472475i	0.849847	+	0.527029i	$0.176694\pi$
$444$	2.77359	−	0.885250i	0.131629	−	0.0420121i
$445$	19.1558	+	6.50252i	0.908072	+	0.308249i
$446$	−5.84098	−	21.7988i	−0.276578	−	1.03220i
$447$	−0.976317	−	8.63388i	−0.0461782	−	0.408368i
$448$	26.3161	−	8.93311i	1.24332	−	0.422050i
$449$	14.6741	+	21.9613i	0.692512	+	1.03642i	0.996488	+	0.0837374i	$0.0266857\pi$
$449$	14.6741	+	21.9613i	0.692512	+	1.03642i	−0.303976	+	0.952680i	$0.598314\pi$
$450$	20.1749	−	18.7498i	0.951055	−	0.883873i
$451$	−17.7570	+	7.35518i	−0.836143	+	0.346342i
$452$	4.06702	+	2.00563i	0.191297	+	0.0943371i
$453$	−0.589181	+	32.1951i	−0.0276821	+	1.51266i
$454$	9.84353	+	19.9607i	0.461980	+	0.936803i
$455$	−2.25166	+	0.603331i	−0.105559	+	0.0282846i
$456$	−3.16879	+	21.0810i	−0.148392	+	0.987209i
$457$	−5.78608	+	0.761752i	−0.270662	+	0.0356333i	−0.264635	−	0.964349i	$-0.585252\pi$
$457$	−5.78608	+	0.761752i	−0.270662	+	0.0356333i	−0.00602627	+	0.999982i	$0.501918\pi$
$458$	−25.0343			−1.16978
$459$	−21.3644	−	1.60033i	−0.997206	−	0.0746969i
$460$	−3.70576			−0.172782
$461$	−15.3601	+	2.02220i	−0.715392	+	0.0941832i	−0.479431	−	0.877579i	$-0.659157\pi$
$461$	−15.3601	+	2.02220i	−0.715392	+	0.0941832i	−0.235961	+	0.971763i	$0.575824\pi$
$462$	4.04962	−	26.9409i	0.188405	−	1.25340i
$463$	−0.720861	+	0.193154i	−0.0335013	+	0.00897664i	−0.275531	−	0.961292i	$-0.588854\pi$
$463$	−0.720861	+	0.193154i	−0.0335013	+	0.00897664i	0.242029	+	0.970269i	$0.422187\pi$
$464$	2.16233	+	4.38476i	0.100383	+	0.203558i
$465$	0.586533	−	32.0504i	0.0271998	−	1.48630i
$466$	−17.8478	−	8.80155i	−0.826783	−	0.407724i
$467$	3.39287	−	1.40537i	0.157003	−	0.0650329i	−0.302798	−	0.953055i	$-0.597921\pi$
$467$	3.39287	−	1.40537i	0.157003	−	0.0650329i	0.459801	+	0.888022i	$0.347921\pi$
$468$	−0.104371	−	0.455594i	−0.00482457	−	0.0210598i
$469$	−24.7558	−	37.0497i	−1.14312	−	1.71079i
$470$	10.9651	−	3.72214i	0.505781	−	0.171690i
$471$	−2.10794	−	18.6412i	−0.0971289	−	0.858942i
$472$	−1.34453	−	5.01787i	−0.0618872	−	0.230966i
$473$	−14.8429	−	5.03848i	−0.682477	−	0.231670i
$474$	−19.6019	+	6.25635i	−0.900343	+	0.287364i
$475$	−32.7188	+	18.8902i	−1.50124	+	0.866743i
$476$	−2.90025	−	16.2631i	−0.132933	−	0.745419i
$477$	−0.760252	+	0.919090i	−0.0348095	+	0.0420822i
$478$	4.99644	+	2.06959i	0.228532	+	0.0946609i
$479$	4.34878	+	4.95884i	0.198701	+	0.226575i	0.842606	−	0.538530i	$-0.181020\pi$
$479$	4.34878	+	4.95884i	0.198701	+	0.226575i	−0.643905	+	0.765105i	$0.722687\pi$
$480$	−18.6846	+	26.8852i	−0.852830	+	1.22713i
$481$	−0.232749	+	0.114779i	−0.0106124	+	0.00523347i
$482$	15.5920	−	17.7793i	0.710196	−	0.809823i
$483$	1.63039	+	6.56274i	0.0741851	+	0.298615i
$484$	−2.82774	+	3.68518i	−0.128534	+	0.167508i
$485$	−10.4665	−	25.2683i	−0.475259	−	1.14738i
$486$	8.97450	−	12.7024i	0.407091	−	0.576190i
$487$	−15.6152	−	3.10605i	−0.707591	−	0.140749i	−0.171840	−	0.985125i	$-0.554971\pi$
$487$	−15.6152	−	3.10605i	−0.707591	−	0.140749i	−0.535751	+	0.844376i	$0.679971\pi$
$488$	1.55151	−	23.6715i	0.0702337	−	1.07156i
$489$	32.9209	−	15.4925i	1.48873	−	0.700596i
$490$	10.7655	−	31.7140i	0.486334	−	1.43269i
$491$	−22.1908	+	17.0276i	−1.00145	+	0.768443i	−0.972918	−	0.231149i	$-0.925751\pi$
$491$	−22.1908	+	17.0276i	−1.00145	+	0.768443i	−0.0285365	+	0.999593i	$0.509085\pi$
$492$	−1.49845	−	8.32674i	−0.0675555	−	0.375398i
$493$	19.5704	−	6.21241i	0.881408	−	0.279793i
$494$		−	0.635314i		−	0.0285841i
$495$	20.9129	+	39.4924i	0.939966	+	1.77505i
$496$	−0.940593	−	4.72868i	−0.0422339	−	0.212324i
$497$	13.9739	+	3.74429i	0.626814	+	0.167954i
$498$	0.756635	−	0.0855600i	0.0339056	−	0.00383404i
$499$	4.48183	+	3.93046i	0.200634	+	0.175951i	0.753767	−	0.657141i	$-0.228235\pi$
$499$	4.48183	+	3.93046i	0.200634	+	0.175951i	−0.553133	+	0.833093i	$0.686568\pi$
$500$	−15.8728	+	1.04036i	−0.709853	+	0.0465262i
$501$	9.35617	−	18.1285i	0.418003	−	0.809920i
$502$	−17.8915	−	13.7286i	−0.798535	−	0.612737i
$503$	21.3853	−	14.2892i	0.953521	−	0.637123i	0.0215937	−	0.999767i	$-0.493126\pi$
$503$	21.3853	−	14.2892i	0.953521	−	0.637123i	0.931928	+	0.362644i	$0.118126\pi$
$504$	33.5201	+	12.7645i	1.49311	+	0.568574i
$505$	2.62534	−	3.92909i	0.116826	−	0.174842i
$506$	−0.999142	+	3.72885i	−0.0444173	+	0.165768i
$507$	−8.21944	−	20.9181i	−0.365038	−	0.929005i
$508$	0.743408	+	0.968828i	0.0329834	+	0.0429848i
$509$	−17.6806	+	30.6238i	−0.783681	+	1.35738i	0.146103	+	0.989269i	$0.453327\pi$
$509$	−17.6806	+	30.6238i	−0.783681	+	1.35738i	−0.929784	+	0.368106i	$0.880006\pi$
$510$	−19.4975	−	18.4617i	−0.863364	−	0.817499i
$511$	29.7689	+	51.5613i	1.31690	+	2.28094i
$512$	−4.13686	+	9.98726i	−0.182825	+	0.441379i
$513$	−15.8905	+	14.2351i	−0.701584	+	0.628496i
$514$	9.13470	+	9.13470i	0.402914	+	0.402914i
$515$	−37.6587	−	2.46828i	−1.65944	−	0.108765i
$516$	3.55870	−	5.91136i	0.156663	−	0.260233i
$517$	0.796177	+	12.1473i	0.0350158	+	0.534238i
$518$	0.869111	−	6.60155i	0.0381865	−	0.290056i
$519$	−23.8078	+	15.2853i	−1.04505	+	0.670949i
$520$	0.774912	−	1.57137i	0.0339821	−	0.0689090i
$521$	2.84917	−	14.3237i	0.124824	−	0.627534i	−0.866830	−	0.498605i	$-0.833846\pi$
$521$	2.84917	−	14.3237i	0.124824	−	0.627534i	0.991654	−	0.128929i	$-0.0411540\pi$
$522$	−3.44090	+	14.5031i	−0.150604	+	0.634783i
$523$	5.76220	−	5.76220i	0.251964	−	0.251964i	−0.569812	−	0.821775i	$-0.692984\pi$
$523$	5.76220	−	5.76220i	0.251964	−	0.251964i	0.821775	+	0.569812i	$0.192984\pi$
$524$	14.4577	−	12.6791i	0.631590	−	0.553889i
$525$	19.3283	+	60.5576i	0.843554	+	2.64295i
$526$	−16.5681	−	9.56557i	−0.722401	−	0.417079i
$527$	−20.2278	+	0.922582i	−0.881135	+	0.0401883i
$528$	4.33840	+	5.13352i	0.188805	+	0.223408i
$529$	2.87703	+	21.8532i	0.125088	+	0.950140i
$530$	−1.46619	+	0.291643i	−0.0636871	+	0.0126682i
$531$	2.16393	−	4.72711i	0.0939064	−	0.205139i
$532$	−13.6779	−	9.13926i	−0.593011	−	0.396237i
$533$	0.242406	+	0.714106i	0.0104998	+	0.0309314i
$534$	6.43827	+	6.67831i	0.278611	+	0.288999i
$535$	14.7113	+	1.93678i	0.636024	+	0.0837342i
$536$	33.2043	+	4.37143i	1.43421	+	0.188817i
$537$	−3.64297	+	0.905025i	−0.157206	+	0.0390547i
$538$	−1.36135	−	4.01040i	−0.0586919	−	0.172901i
$539$	29.2750	+	19.5609i	1.26096	+	0.842549i
$540$	−18.9461	+	5.29155i	−0.815311	+	0.227712i
$541$	−21.3599	+	4.24876i	−0.918336	+	0.182668i	−0.631558	−	0.775329i	$-0.717584\pi$
$541$	−21.3599	+	4.24876i	−0.918336	+	0.182668i	−0.286778	+	0.957997i	$0.592584\pi$
$542$	−0.434605	−	3.30115i	−0.0186679	−	0.141797i
$543$	0.954225	−	2.65069i	0.0409497	−	0.113752i
$544$	17.7014	+	10.6944i	0.758941	+	0.458519i
$545$	24.1567	+	13.9469i	1.03476	+	0.597420i
$546$	−1.04441	−	0.227689i	−0.0446968	−	0.00974418i
$547$	27.2258	−	23.8764i	1.16409	−	1.02088i	0.164687	−	0.986346i	$-0.447339\pi$
$547$	27.2258	−	23.8764i	1.16409	−	1.02088i	0.999404	−	0.0345337i	$-0.0109946\pi$
$548$	14.8589	−	14.8589i	0.634740	−	0.634740i
$549$	16.2958	−	17.2644i	0.695488	−	0.736826i
$550$	−7.07964	+	35.5918i	−0.301877	+	1.51764i
$551$	9.04324	−	18.3379i	0.385255	−	0.781220i
$552$	−4.51646	−	2.33096i	−0.192233	−	0.0992123i
$553$	6.19860	−	47.0830i	0.263591	−	2.00217i
$554$	0.203971	+	3.11200i	0.00866590	+	0.132216i
$555$	5.28702	+	9.55707i	0.224421	+	0.405675i
$556$	−12.0260	−	0.788222i	−0.510014	−	0.0334281i
$557$	20.6898	+	20.6898i	0.876655	+	0.876655i	0.993187	−	0.116532i	$-0.0371777\pi$
$557$	20.6898	+	20.6898i	0.876655	+	0.876655i	−0.116532	+	0.993187i	$0.537178\pi$
$558$	6.97944	−	12.9369i	0.295463	−	0.547662i
$559$	−0.235359	+	0.568207i	−0.00995463	+	0.0240326i
$560$	7.37792	+	12.7789i	0.311774	+	0.540009i
$561$	24.0521	−	14.7756i	1.01548	−	0.623825i
$562$	7.01978	−	12.1586i	0.296112	−	0.512881i
$563$	19.1462	+	24.9518i	0.806917	+	1.05159i	0.997552	+	0.0699334i	$0.0222787\pi$
$563$	19.1462	+	24.9518i	0.806917	+	1.05159i	−0.190635	+	0.981661i	$0.561055\pi$
$564$	−5.29909	−	0.796532i	−0.223132	−	0.0335400i
$565$	−4.40288	+	16.4318i	−0.185230	+	0.691290i
$566$	−4.80850	+	7.19642i	−0.202116	+	0.302488i
$567$	17.7066	+	31.2247i	0.743609	+	1.31131i
$568$	−9.04080	+	6.04087i	−0.379344	+	0.253469i
$569$	−12.2788	−	9.42184i	−0.514753	−	0.394984i	0.318459	−	0.947936i	$-0.396835\pi$
$569$	−12.2788	−	9.42184i	−0.514753	−	0.394984i	−0.833213	+	0.552952i	$0.813501\pi$
$570$	−26.7086	+	1.26029i	−1.11870	+	0.0527876i
$571$	−0.609409	+	0.0399427i	−0.0255030	+	0.00167155i	−0.0781493	−	0.996942i	$-0.524901\pi$
$571$	−0.609409	+	0.0399427i	−0.0255030	+	0.00167155i	0.0526463	+	0.998613i	$0.483234\pi$
$572$	0.463004	+	0.406044i	0.0193592	+	0.0169775i
$573$	−5.80913	+	13.3293i	−0.242680	+	0.556839i
$574$	−18.6900	−	5.00797i	−0.780106	−	0.209029i
$575$	−1.75726	−	8.83436i	−0.0732829	−	0.368418i
$576$	−18.4735	+	9.78251i	−0.769728	+	0.407605i
$577$		−	7.81171i		−	0.325206i	−0.986692	−	0.162603i	$-0.948011\pi$
$577$		−	7.81171i		−	0.325206i	0.986692	−	0.162603i	$-0.0519890\pi$
$578$	−10.8518	+	13.0353i	−0.451376	+	0.542198i
$579$	3.45428	−	2.91926i	0.143555	−	0.121320i
$580$	14.9568	−	11.4768i	0.621048	−	0.476547i
$581$	−0.564908	+	1.66416i	−0.0234363	+	0.0690412i
$582$	1.04912	−	12.4978i	0.0434873	−	0.518049i
$583$	0.102785	−	1.56820i	0.00425693	−	0.0649482i
$584$	−43.8889	−	8.73004i	−1.81613	−	0.361252i
$585$	1.59989	−	0.717449i	0.0661474	−	0.0296629i
$586$	−11.0790	−	26.7471i	−0.457669	−	1.10491i
$587$	1.42366	−	1.85536i	0.0587609	−	0.0765787i	−0.763048	−	0.646341i	$-0.776298\pi$
$587$	1.42366	−	1.85536i	0.0587609	−	0.0765787i	0.821809	+	0.569763i	$0.192965\pi$
$588$	−11.1579	+	10.7568i	−0.460142	+	0.443603i
$589$	−13.2948	+	15.1598i	−0.547803	+	0.624650i
$590$	5.84382	−	2.88185i	0.240586	−	0.118644i
$591$	−2.60236	−	5.52991i	−0.107047	−	0.227470i
$592$	1.08312	+	1.23506i	0.0445158	+	0.0507605i
$593$	16.7241	+	6.92737i	0.686778	+	0.284473i	0.698657	−	0.715456i	$-0.253781\pi$
$593$	16.7241	+	6.92737i	0.686778	+	0.284473i	−0.0118788	+	0.999929i	$0.503781\pi$
$594$	0.216290	+	20.4909i	0.00887449	+	0.840751i
$595$	57.7148	−	22.5734i	2.36608	−	0.925418i
$596$	−4.36427	+	2.51971i	−0.178768	+	0.103212i
$597$	−16.4495	−	14.9671i	−0.673234	−	0.612562i
$598$	0.143430	+	0.0486879i	0.00586529	+	0.00199100i
$599$	1.44193	+	5.38135i	0.0589156	+	0.219876i	0.989107	−	0.147199i	$-0.0470258\pi$
$599$	1.44193	+	5.38135i	0.0589156	+	0.219876i	−0.930191	+	0.367075i	$0.880359\pi$
$600$	−43.7985	−	19.0882i	−1.78807	−	0.779271i
$601$	−30.4290	+	10.3293i	−1.24123	+	0.421339i	−0.863392	−	0.504534i	$-0.831664\pi$
$601$	−30.4290	+	10.3293i	−1.24123	+	0.421339i	−0.377834	+	0.925873i	$0.623331\pi$
$602$	−8.76701	−	13.1208i	−0.357317	−	0.534762i
$603$	22.8167	+	24.5510i	0.929169	+	0.999794i
$604$	17.2542	−	7.14692i	0.702063	−	0.290804i
$605$	−15.6285	−	7.70713i	−0.635390	−	0.313339i
$606$	1.89611	−	1.04894i	0.0770244	−	0.0426103i
$607$	8.91110	+	18.0699i	0.361690	+	0.733436i	0.999319	−	0.0369085i	$-0.0117510\pi$
$607$	8.91110	+	18.0699i	0.361690	+	0.733436i	−0.637628	+	0.770344i	$0.720084\pi$
$608$	19.8925	−	5.33017i	0.806745	−	0.216167i
$609$	−26.9053	−	21.4386i	−1.09026	−	0.868734i
$610$	29.4996	−	3.88370i	1.19440	−	0.157246i
$611$	0.477641			0.0193233
$612$	4.09964	+	11.7300i	0.165718	+	0.474156i
$613$	−47.6793			−1.92575			−0.962874	−	0.269950i	$-0.912993\pi$
$613$	−47.6793			−1.92575			−0.962874	+	0.269950i	$0.912993\pi$
$614$	5.54118	−	0.729510i	0.223624	−	0.0294406i
$615$	29.5401	−	11.6073i	1.19117	−	0.468053i
$616$	−45.6487	+	12.2315i	−1.83924	+	0.492823i
$617$	−6.27871	−	12.7320i	−0.252771	−	0.512570i	0.733090	−	0.680131i	$-0.238077\pi$
$617$	−6.27871	−	12.7320i	−0.252771	−	0.512570i	−0.985862	+	0.167562i	$0.946411\pi$
$618$	−14.8264	−	8.92568i	−0.596407	−	0.359043i
$619$	−33.8025	−	16.6696i	−1.35864	−	0.670007i	−0.390543	−	0.920585i	$-0.627713\pi$
$619$	−33.8025	−	16.6696i	−1.35864	−	0.670007i	−0.968096	+	0.250578i	$0.919379\pi$
$620$	−17.1766	+	7.11480i	−0.689831	+	0.285737i
$621$	−1.99597	−	4.67841i	−0.0800955	−	0.187738i
$622$	11.0570	+	16.5480i	0.443345	+	0.663513i
$623$	−20.2735	+	6.88194i	−0.812242	+	0.275719i
$624$	0.212124	−	0.156686i	0.00849174	−	0.00627246i
$625$	−3.53654	−	13.1985i	−0.141461	−	0.527941i
$626$	19.9988	+	6.78866i	0.799311	+	0.271329i
$627$	5.98739	−	27.4643i	0.239113	−	1.09682i
$628$	−9.42281	+	5.44026i	−0.376011	+	0.217090i
$629$	5.81145	−	3.71821i	0.231718	−	0.148255i
$630$	−7.50020	+	44.3588i	−0.298815	+	1.76730i
$631$	−25.6573	−	10.6276i	−1.02140	−	0.423079i	−0.191800	−	0.981434i	$-0.561433\pi$
$631$	−25.6573	−	10.6276i	−1.02140	−	0.423079i	−0.829602	+	0.558355i	$0.811433\pi$
$632$	23.5340	+	26.8354i	0.936134	+	1.06746i
$633$	−25.8837	−	2.17280i	−1.02879	−	0.0863609i
$634$	17.2040	−	8.48405i	0.683256	−	0.336945i
$635$	−3.02056	+	3.44429i	−0.119867	+	0.136683i
$636$	0.664830	+	0.191245i	0.0263622	+	0.00758336i
$637$	0.840986	−	1.09599i	0.0333211	−	0.0434249i
$638$	−7.51564	−	18.1444i	−0.297547	−	0.718342i
$639$	−10.8250	−	1.10850i	−0.428231	−	0.0438517i
$640$	11.3834	+	2.26430i	0.449968	+	0.0895042i
$641$	−3.21794	+	49.0963i	−0.127101	+	1.93919i	0.172266	+	0.985051i	$0.444891\pi$
$641$	−3.21794	+	49.0963i	−0.127101	+	1.93919i	−0.299367	+	0.954138i	$0.596775\pi$
$642$	5.58738	+	3.88310i	0.220516	+	0.153254i
$643$	−13.5556	+	39.9336i	−0.534582	+	1.57483i	0.258691	+	0.965960i	$0.416709\pi$
$643$	−13.5556	+	39.9336i	−0.534582	+	1.57483i	−0.793273	+	0.608867i	$0.791624\pi$
$644$	3.11152	−	2.38755i	0.122611	−	0.0940828i
$645$	24.3543	+	8.76734i	0.958951	+	0.345213i
$646$	1.87140	+	16.7859i	0.0736291	+	0.660431i
$647$		−	16.4675i		−	0.647403i	−0.946159	−	0.323702i	$-0.895073\pi$
$647$		−	16.4675i		−	0.647403i	0.946159	−	0.323702i	$-0.104927\pi$
$648$	−26.4194	−	5.46813i	−1.03785	−	0.214809i
$649$	1.33634	+	6.71826i	0.0524561	+	0.263715i
$650$	1.37534	+	0.368521i	0.0539453	+	0.0144546i
$651$	20.1571	+	27.2889i	0.790017	+	1.06954i
$652$	−15.8655	−	13.9137i	−0.621341	−	0.544901i
$653$	−24.5572	+	1.60957i	−0.960999	+	0.0629872i	−0.537821	−	0.843059i	$-0.680752\pi$
$653$	−24.5572	+	1.60957i	−0.960999	+	0.0629872i	−0.423178	+	0.906046i	$0.639086\pi$
$654$	6.91050	+	10.7636i	0.270222	+	0.420888i
$655$	57.2317	+	43.9154i	2.23623	+	1.71592i
$656$	3.96914	−	2.65209i	0.154969	−	0.103547i
$657$	−28.2758	−	34.7275i	−1.10314	−	1.35485i
$658$	−6.80866	+	10.1899i	−0.265429	+	0.397243i
$659$	3.64026	−	13.5856i	0.141804	−	0.529221i	−0.858073	−	0.513529i	$-0.828338\pi$
$659$	3.64026	−	13.5856i	0.141804	−	0.529221i	0.999877	−	0.0156925i	$-0.00499529\pi$
$660$	16.1516	−	20.2702i	0.628700	−	0.789015i
$661$	24.6935	+	32.1812i	0.960467	+	1.25171i	0.967797	+	0.251732i	$0.0810002\pi$
$661$	24.6935	+	32.1812i	0.960467	+	1.25171i	−0.00732968	+	0.999973i	$0.502333\pi$
$662$	3.90444	−	6.76268i	0.151750	−	0.262839i
$663$	−0.516779	−	0.979619i	−0.0200700	−	0.0380453i
$664$	−0.660444	−	1.14392i	−0.0256302	−	0.0443928i
$665$	23.6160	−	57.0141i	0.915790	−	2.21091i
$666$	0.144489	+	5.00630i	0.00559882	+	0.193990i
$667$	3.44697	+	3.44697i	0.133467	+	0.133467i
$668$	−11.8066	−	0.773847i	−0.456812	−	0.0299410i
$669$	−39.1715	−	0.716851i	−1.51446	−	0.0277151i
$670$	2.74735	+	41.9165i	0.106139	+	1.61938i
$671$	−4.08284	+	31.0122i	−0.157616	+	1.19721i
$672$	−1.63323	−	34.6121i	−0.0630031	−	1.33519i
$673$	−9.51808	+	19.3007i	−0.366895	+	0.743989i	−0.999536	−	0.0304558i	$-0.990304\pi$
$673$	−9.51808	+	19.3007i	−0.366895	+	0.743989i	0.632641	+	0.774445i	$0.281971\pi$
$674$	2.47298	−	12.4325i	0.0952558	−	0.478883i
$675$	−21.5990	−	42.6574i	−0.831347	−	1.64189i
$676$	−9.21724	+	9.21724i	−0.354509	+	0.354509i
$677$	26.1344	−	22.9192i	1.00443	−	0.880857i	0.0115400	−	0.999933i	$-0.496327\pi$
$677$	26.1344	−	22.9192i	1.00443	−	0.880857i	0.992885	+	0.119076i	$0.0379933\pi$
$678$	−5.24984	+	5.76982i	−0.201619	+	0.221589i
$679$	25.0681	+	14.4731i	0.962024	+	0.555425i
$680$	−15.8456	+	43.8003i	−0.607651	+	1.67966i
$681$	38.0258	−	6.84300i	1.45715	−	0.262224i
$682$	2.52799	+	19.2020i	0.0968016	+	0.735281i
$683$	36.6473	−	7.28959i	1.40227	−	0.278929i	0.564716	−	0.825285i	$-0.308986\pi$
$683$	36.6473	−	7.28959i	1.40227	−	0.278929i	0.837553	+	0.546357i	$0.183986\pi$
$684$	11.2507	+	5.15023i	0.430182	+	0.196924i
$685$	65.5454	+	43.7960i	2.50436	+	1.67336i
$686$	2.43987	+	7.18763i	0.0931548	+	0.274425i
$687$	−12.0145	+	41.7663i	−0.458381	+	1.59348i
$688$	3.85980	+	0.508153i	0.147154	+	0.0193731i
$689$	−0.0611353	−	0.00804862i	−0.00232907	−	0.000306628i
$690$	1.76231	−	6.12638i	0.0670902	−	0.233227i
$691$	11.5329	+	33.9748i	0.438732	+	1.29246i	0.911508	+	0.411281i	$0.134919\pi$
$691$	11.5329	+	33.9748i	0.438732	+	1.29246i	−0.472776	+	0.881183i	$0.656748\pi$
$692$	13.6436	+	9.11638i	0.518653	+	0.346553i
$693$	−43.0037	−	19.6857i	−1.63357	−	0.747799i
$694$	16.2014	−	3.22266i	0.614996	−	0.122330i
$695$	−5.90123	−	44.8243i	−0.223846	−	1.70028i
$696$	25.4479	−	4.57953i	0.964600	−	0.173586i
$697$	−8.50819	−	18.1536i	−0.322271	−	0.687617i
$698$	−19.2597	−	11.1196i	−0.728990	−	0.420882i
$699$	−23.2497	+	25.5525i	−0.879384	+	0.966484i
$700$	27.7189	−	24.3088i	1.04768	−	0.918787i
$701$	−7.61094	+	7.61094i	−0.287461	+	0.287461i	−0.836076	−	0.548614i	$-0.815156\pi$
$701$	−7.61094	+	7.61094i	−0.287461	+	0.287461i	0.548614	+	0.836076i	$0.315156\pi$
$702$	0.802825	+	0.0441152i	0.0303007	+	0.00166502i
$703$	1.34029	−	6.73811i	0.0505501	−	0.254133i
$704$	12.1816	−	24.7019i	0.459112	−	0.930986i
$705$	−0.947508	−	20.0800i	−0.0356852	−	0.756258i
$706$	−2.07123	+	15.7325i	−0.0779517	+	0.592102i
$707$	0.327095	+	4.99050i	0.0123017	+	0.187687i
$708$	−3.01475	−	0.0551709i	−0.113301	−	0.00207345i
$709$	15.9948	+	1.04835i	0.600696	+	0.0393717i	0.362718	−	0.931899i	$-0.381849\pi$
$709$	15.9948	+	1.04835i	0.600696	+	0.0393717i	0.237978	+	0.971271i	$0.423516\pi$
$710$	−9.64353	−	9.64353i	−0.361915	−	0.361915i
$711$	1.03051	+	35.7055i	0.0386471	+	1.33906i
$712$	6.15799	−	14.8667i	0.230780	−	0.557153i
$713$	−2.40366	−	4.16326i	−0.0900177	−	0.155915i
$714$	28.2655	+	2.93940i	1.05781	+	0.110004i
$715$	−1.15511	+	2.00071i	−0.0431987	+	0.0748224i
$716$	1.32533	+	1.72720i	0.0495298	+	0.0645485i
$717$	5.85072	−	7.34261i	0.218499	−	0.274215i
$718$	1.09121	−	4.07246i	0.0407237	−	0.151983i
$719$	−1.80867	+	2.70687i	−0.0674521	+	0.100949i	−0.863662	−	0.504071i	$-0.831835\pi$
$719$	−1.80867	+	2.70687i	−0.0674521	+	0.100949i	0.796210	+	0.605020i	$0.206835\pi$
$720$	−7.00787	−	8.60685i	−0.261168	−	0.320759i
$721$	33.2102	−	22.1903i	1.23681	−	0.826411i
$722$	−1.69601	−	1.30139i	−0.0631189	−	0.0484328i
$723$	−22.1793	−	34.5457i	−0.824857	−	1.28477i
$724$	−1.63044	+	0.106865i	−0.0605950	+	0.00397160i
$725$	34.4526	+	30.2141i	1.27954	+	1.12212i
$726$	−4.74760	−	6.42736i	−0.176200	−	0.238542i
$727$	−29.7205	−	7.96359i	−1.10227	−	0.295353i	−0.338583	−	0.940937i	$-0.609948\pi$
$727$	−29.7205	−	7.96359i	−1.10227	−	0.295353i	−0.763690	+	0.645583i	$0.776614\pi$
$728$	0.361752	+	1.81865i	0.0134074	+	0.0674037i
$729$	−16.8851	−	21.0688i	−0.625372	−	0.780327i
$730$		−	56.1269i		−	2.07735i
$731$	4.54479	−	15.7061i	0.168095	−	0.580911i
$732$	−12.9552	−	4.66377i	−0.478839	−	0.172378i
$733$	31.2703	−	23.9945i	1.15499	−	0.886258i	0.160092	−	0.987102i	$-0.448821\pi$
$733$	31.2703	−	23.9945i	1.15499	−	0.886258i	0.994902	+	0.100844i	$0.0321543\pi$
$734$	1.37839	−	4.06059i	0.0508772	−	0.149879i
$735$	−47.7439	−	33.1809i	−1.76106	−	1.22390i
$736$	−0.321127	+	4.89945i	−0.0118369	+	0.180596i
$737$	−43.3119	−	8.61526i	−1.59541	−	0.317347i
$738$	14.4784	+	1.48262i	0.532958	+	0.0545760i
$739$	−18.2822	−	44.1371i	−0.672521	−	1.62361i	−0.777313	−	0.629114i	$-0.783418\pi$
$739$	−18.2822	−	44.1371i	−0.672521	−	1.62361i	0.104792	−	0.994494i	$-0.466582\pi$
$740$	3.85625	−	5.02557i	0.141759	−	0.184744i
$741$	−1.05993	−	0.304900i	−0.0389376	−	0.0112008i
$742$	1.04318	−	1.18951i	0.0382962	−	0.0436685i
$743$	34.5173	−	17.0220i	1.26632	−	0.624478i	0.319907	−	0.947449i	$-0.396348\pi$
$743$	34.5173	−	17.0220i	1.26632	−	0.624478i	0.946409	+	0.322971i	$0.104682\pi$
$744$	−25.4096	−	2.13300i	−0.931563	−	0.0781995i
$745$	−12.4649	−	14.2135i	−0.456679	−	0.520743i
$746$	17.5962	+	7.28859i	0.644243	+	0.266854i
$747$	0.220380	−	1.30340i	0.00806327	−	0.0476890i
$748$	−13.4293	−	9.36439i	−0.491022	−	0.342396i
$749$	−13.6001	+	7.85201i	−0.496936	+	0.286906i
$750$	5.82856	−	26.7357i	0.212829	−	0.976251i
$751$	−16.2086	−	5.50208i	−0.591460	−	0.200774i	0.00963183	−	0.999954i	$-0.496934\pi$
$751$	−16.2086	−	5.50208i	−0.591460	−	0.200774i	−0.601092	+	0.799180i	$0.705267\pi$
$752$	−0.782534	−	2.92046i	−0.0285361	−	0.106498i
$753$	−31.4907	+	23.2608i	−1.14759	+	0.847669i
$754$	−0.729685	+	0.247695i	−0.0265736	+	0.00902050i
$755$	38.9236	+	58.2533i	1.41657	+	2.12005i
$756$	12.4988	−	16.6497i	0.454575	−	0.605542i
$757$	−15.7999	+	6.54452i	−0.574256	+	0.237865i	−0.650861	−	0.759197i	$-0.725592\pi$
$757$	−15.7999	+	6.54452i	−0.574256	+	0.237865i	0.0766049	+	0.997062i	$0.475592\pi$
$758$	−3.60649	−	1.77852i	−0.130994	−	0.0645989i
$759$	5.74156	+	3.45648i	0.208405	+	0.125462i
$760$	20.5145	+	41.5992i	0.744138	+	1.50896i
$761$	14.3185	−	3.83664i	0.519046	−	0.139078i	0.0102209	−	0.999948i	$-0.496747\pi$
$761$	14.3185	−	3.83664i	0.519046	−	0.139078i	0.508825	+	0.860870i	$0.330080\pi$
$762$	−1.95521	+	0.768269i	−0.0708297	+	0.0278315i
$763$	−29.2688	+	3.85331i	−1.05960	+	0.139499i
$764$	8.43306			0.305097
$765$	−40.1580	+	23.6687i	−1.45192	+	0.855743i
$766$	13.6302			0.492478
$767$	0.266466	−	0.0350810i	0.00962154	−	0.00126670i
$768$	23.0400	+	18.3586i	0.831384	+	0.662460i
$769$	−18.5448	+	4.96907i	−0.668743	+	0.179189i	−0.577188	−	0.816611i	$-0.695850\pi$
$769$	−18.5448	+	4.96907i	−0.668743	+	0.179189i	−0.0915543	+	0.995800i	$0.529184\pi$
$770$	−26.2169	−	53.1626i	−0.944791	−	1.91585i
$771$	19.6239	−	10.8560i	0.706738	−	0.390971i
$772$	−2.35254	−	1.16015i	−0.0846699	−	0.0417546i
$773$	1.22123	−	0.505851i	0.0439247	−	0.0181942i	−0.360613	−	0.932716i	$-0.617432\pi$
$773$	1.22123	−	0.505851i	0.0439247	−	0.0181942i	0.404538	+	0.914521i	$0.367432\pi$
$774$	8.08031	+	8.69448i	0.290441	+	0.312517i
$775$	−25.1065	−	37.5745i	−0.901852	−	1.34972i
$776$	−20.6013	+	6.99322i	−0.739545	+	0.251042i
$777$	−10.5967	−	4.61821i	−0.380153	−	0.165677i
$778$	0.430537	+	1.60679i	0.0154355	+	0.0576061i
$779$	−18.9047	−	6.41729i	−0.677332	−	0.229923i
$780$	−0.752180	−	0.684393i	−0.0269324	−	0.0245052i
$781$	12.4165	−	7.16866i	0.444297	−	0.256515i
$782$	−3.93303	−	0.863911i	−0.140645	−	0.0308934i
$783$	22.5450	+	12.7010i	0.805693	+	0.453897i
$784$	−8.07908	−	3.34646i	−0.288539	−	0.119517i
$785$	−26.9127	−	30.6881i	−0.960556	−	1.09530i
$786$	14.0856	+	29.9313i	0.502417	+	1.06761i
$787$	14.5122	−	7.15662i	0.517304	−	0.255106i	−0.164845	−	0.986320i	$-0.552712\pi$
$787$	14.5122	−	7.15662i	0.517304	−	0.255106i	0.682149	+	0.731213i	$0.261046\pi$
$788$	−2.33715	+	2.66501i	−0.0832577	+	0.0949372i
$789$	−23.9102	+	23.0508i	−0.851225	+	0.820629i
$790$	−27.2534	+	35.5173i	−0.969633	+	1.26365i
$791$	−6.88984	−	16.6335i	−0.244975	−	0.591421i
$792$	32.4352	−	14.5451i	1.15253	−	0.516838i
$793$	1.20373	+	0.239437i	0.0427458	+	0.00850266i
$794$	1.27464	−	19.4473i	0.0452354	−	0.690158i
$795$	−0.217088	+	2.58609i	−0.00769933	+	0.0917193i
$796$	−4.14613	+	12.2141i	−0.146956	+	0.432918i
$797$	14.0084	−	10.7490i	0.496204	−	0.380751i	−0.330126	−	0.943937i	$-0.607091\pi$
$797$	14.0084	−	10.7490i	0.496204	−	0.380751i	0.826330	+	0.563186i	$0.190425\pi$
$798$	21.6137	−	18.2661i	0.765118	−	0.646611i
$799$	−12.6199	+	1.40695i	−0.446461	+	0.0497744i
$800$			46.1554i			1.63184i
$801$	14.2317	−	7.53630i	0.502852	−	0.266282i
$802$	0.519805	+	2.61324i	0.0183550	+	0.0922766i
$803$	56.9944	+	15.2716i	2.01129	+	0.538923i
$804$	7.76636	−	17.8202i	0.273898	−	0.628470i
$805$	11.0618	+	9.70094i	0.389877	+	0.341913i
$806$	0.758293	−	0.0497012i	0.0267097	−	0.00175065i
$807$	−7.34414	+	0.346545i	−0.258526	+	0.0121989i
$808$	−2.98215	−	2.28828i	−0.104912	−	0.0805015i
$809$	−15.3704	+	10.2701i	−0.540393	+	0.361079i	−0.795614	−	0.605804i	$-0.792852\pi$
$809$	−15.3704	+	10.2701i	−0.540393	+	0.361079i	0.255221	+	0.966883i	$0.417852\pi$
$810$	0.262023	−	33.8383i	0.00920653	−	1.18896i
$811$	6.43331	−	9.62813i	0.225904	−	0.338089i	−0.701152	−	0.713012i	$-0.747331\pi$
$811$	6.43331	−	9.62813i	0.225904	−	0.338089i	0.927056	+	0.374922i	$0.122331\pi$
$812$	−5.16413	+	19.2728i	−0.181226	+	0.676343i
$813$	−5.71608	−	0.859213i	−0.200472	−	0.0301339i
$814$	−4.01716	−	5.23527i	−0.140802	−	0.183496i
$815$	39.5816	−	68.5573i	1.38648	−	2.40146i
$816$	−5.14306	+	4.76470i	−0.180043	+	0.166798i
$817$	−8.14084	−	14.1004i	−0.284812	−	0.493309i
$818$	−5.30540	+	12.8084i	−0.185499	+	0.447834i
$819$	−0.881102	+	1.63319i	−0.0307882	+	0.0570681i
$820$	−13.0164	−	13.0164i	−0.454553	−	0.454553i
$821$	45.9917	+	3.01445i	1.60512	+	0.105205i	0.841426	−	0.540372i	$-0.181716\pi$
$821$	45.9917	+	3.01445i	1.60512	+	0.105205i	0.763695	+	0.645577i	$0.223383\pi$
$822$	17.4985	+	31.6311i	0.610329	+	1.10326i
$823$	−3.63112	−	55.4002i	−0.126573	−	1.93113i	−0.315097	−	0.949059i	$-0.602037\pi$
$823$	−3.63112	−	55.4002i	−0.126573	−	1.93113i	0.188524	−	0.982069i	$-0.439630\pi$
$824$	−3.91841	+	29.7633i	−0.136504	+	1.03685i
$825$	55.9822	+	28.8926i	1.94905	+	1.00591i
$826$	−3.05001	+	6.18480i	−0.106123	+	0.215197i
$827$	4.84525	−	24.3587i	0.168486	−	0.847036i	−0.800388	−	0.599482i	$-0.795373\pi$
$827$	4.84525	−	24.3587i	0.168486	−	0.847036i	0.968874	−	0.247554i	$-0.0796267\pi$
$828$	−2.02494	+	2.14530i	−0.0703715	+	0.0745543i
$829$	−16.1402	+	16.1402i	−0.560572	+	0.560572i	−0.929470	−	0.368898i	$-0.879735\pi$
$829$	−16.1402	+	16.1402i	−0.560572	+	0.560572i	0.368898	+	0.929470i	$0.379735\pi$
$830$	1.24561	−	1.09237i	0.0432357	−	0.0379167i
$831$	5.28982	+	1.15321i	0.183502	+	0.0400045i
$832$	−0.935880	−	0.540331i	−0.0324458	−	0.0187326i
$833$	−18.9916	+	31.4349i	−0.658021	+	1.08915i
$834$	7.02217	−	19.5065i	0.243158	−	0.675456i
$835$	−5.79361	−	44.0068i	−0.200496	−	1.52292i
$836$	−15.9897	+	3.18055i	−0.553016	+	0.110002i
$837$	−18.2338	−	17.8529i	−0.630252	−	0.617086i
$838$	−18.5926	−	12.4232i	−0.642272	−	0.429152i
$839$	−14.3783	−	42.3570i	−0.496393	−	1.46233i	−0.849924	−	0.526905i	$-0.823352\pi$
$839$	−14.3783	−	42.3570i	−0.496393	−	1.46233i	0.353531	−	0.935423i	$-0.384981\pi$
$840$	75.7385	−	18.8158i	2.61323	−	0.649206i
$841$	4.16431	+	0.548242i	0.143597	+	0.0189049i
$842$	9.82565	+	1.29357i	0.338614	+	0.0445794i
$843$	−16.9160	−	17.5467i	−0.582619	−	0.604341i
$844$	4.84248	+	14.2655i	0.166685	+	0.491038i
$845$	−40.6590	−	27.1675i	−1.39871	−	0.934591i
$846$	3.83687	−	8.38168i	0.131914	−	0.288168i
$847$	18.0880	−	3.59792i	0.621510	−	0.123626i
$848$	0.0509479	+	0.386988i	0.00174956	+	0.0132892i
$849$	9.69853	+	11.4760i	0.332853	+	0.393856i
$850$	−37.4239	−	5.68560i	−1.28363	−	0.195015i
$851$	1.41850	+	0.818970i	0.0486255	+	0.0280739i
$852$	1.91897	+	6.01236i	0.0657429	+	0.205980i
$853$	−9.83430	+	8.62445i	−0.336720	+	0.295296i	−0.810962	−	0.585099i	$-0.801056\pi$
$853$	−9.83430	+	8.62445i	−0.336720	+	0.295296i	0.474242	+	0.880395i	$0.342722\pi$
$854$	−22.2670	+	22.2670i	−0.761961	+	0.761961i
$855$	−10.7154	+	45.1644i	−0.366459	+	1.54459i
$856$	2.30268	−	11.5764i	0.0787041	−	0.395672i
$857$	−17.3923	+	35.2681i	−0.594109	+	1.20473i	0.367426	+	0.930053i	$0.380239\pi$
$857$	−17.3923	+	35.2681i	−0.594109	+	1.20473i	−0.961535	+	0.274681i	$0.911428\pi$
$858$	−0.891460	+	0.572342i	−0.0304340	+	0.0195394i
$859$	1.31179	−	9.96406i	0.0447578	−	0.339969i	−0.954385	−	0.298578i	$-0.903488\pi$
$859$	1.31179	−	9.96406i	0.0447578	−	0.339969i	0.999143	−	0.0413913i	$-0.0131790\pi$
$860$	−0.981866	−	14.9804i	−0.0334813	−	0.510827i
$861$	−17.3248	+	28.7782i	−0.590428	+	0.980760i
$862$	−24.2548	−	1.58974i	−0.826122	−	0.0541469i
$863$	−7.51462	−	7.51462i	−0.255801	−	0.255801i	0.567543	−	0.823344i	$-0.307894\pi$
$863$	−7.51462	−	7.51462i	−0.255801	−	0.255801i	−0.823344	+	0.567543i	$0.807894\pi$
$864$	5.35425	+	25.5076i	0.182155	+	0.867785i
$865$	−23.5569	+	56.8714i	−0.800958	+	1.93368i
$866$	19.7500	+	34.2080i	0.671132	+	1.16243i
$867$	16.5396	+	24.3607i	0.561715	+	0.827331i
$868$	9.83835	−	17.0405i	0.333935	−	0.578393i
$869$	−28.6509	−	37.3385i	−0.971914	−	1.26662i
$870$	11.8606	+	30.1846i	0.402111	+	1.02335i
$871$	−0.448456	+	1.67366i	−0.0151954	+	0.0567099i
$872$	12.3272	−	18.4489i	0.417450	−	0.624759i
$873$	−20.3473	−	7.74824i	−0.688651	−	0.262238i
$874$	−3.33408	+	2.22776i	−0.112777	+	0.0753552i
$875$	50.1042	+	38.4463i	1.69383	+	1.29972i
$876$	−11.9121	+	23.0808i	−0.402472	+	0.779828i
$877$	43.7486	−	2.86743i	1.47728	−	0.0968263i	0.694668	−	0.719330i	$-0.255551\pi$
$877$	43.7486	−	2.86743i	1.47728	−	0.0968263i	0.782617	+	0.622504i	$0.213885\pi$
$878$	−20.7833	−	18.2265i	−0.701404	−	0.615115i
$879$	−49.9408	+	5.64729i	−1.68446	+	0.190478i
$880$	14.1255	+	3.78491i	0.476169	+	0.127589i
$881$	9.86914	+	49.6155i	0.332500	+	1.67159i	0.679462	+	0.733711i	$0.262213\pi$
$881$	9.86914	+	49.6155i	0.332500	+	1.67159i	−0.346962	+	0.937879i	$0.612787\pi$
$882$	−12.4770	−	23.5618i	−0.420122	−	0.793365i
$883$			32.3402i			1.08834i	0.838977	+	0.544168i	$0.183154\pi$
$883$			32.3402i			1.08834i	−0.838977	+	0.544168i	$0.816846\pi$
$884$	−0.401102	+	0.501759i	−0.0134905	+	0.0168760i
$885$	−2.00340	−	11.1327i	−0.0673435	−	0.374220i
$886$	15.7429	−	12.0799i	0.528893	−	0.405834i
$887$	−9.24018	+	27.2207i	−0.310255	+	0.913981i	0.674232	+	0.738520i	$0.264475\pi$
$887$	−9.24018	+	27.2207i	−0.310255	+	0.913981i	−0.984486	+	0.175461i	$0.943858\pi$
$888$	7.86101	−	3.69938i	0.263798	−	0.124143i
$889$	0.317104	−	4.83808i	0.0106353	−	0.162264i
$890$	19.7954	+	3.93754i	0.663542	+	0.131987i
$891$	34.2900	+	9.47314i	1.14876	+	0.317362i
$892$	8.69559	+	20.9930i	0.291150	+	0.702898i
$893$	−7.69763	+	10.0317i	−0.257591	+	0.335699i
$894$	−2.09013	−	8.41332i	−0.0699043	−	0.281384i
$895$	−5.38498	+	6.14039i	−0.180000	+	0.205251i
$896$	−11.0169	+	5.43291i	−0.368047	+	0.181501i
$897$	0.150064	−	0.215927i	0.00501049	−	0.00720958i
$898$	17.3753	+	19.8127i	0.579820	+	0.661158i
$899$	22.5951	+	9.35918i	0.753587	+	0.312146i
$900$	−17.6754	+	21.3684i	−0.589181	+	0.712278i
$901$	1.63899	+	0.0325738i	0.0546026	+	0.00108519i
$902$	−16.6070	+	9.58806i	−0.552953	+	0.319247i
$903$	−26.0976	+	8.32961i	−0.868475	+	0.277192i
$904$	12.8137	+	4.34967i	0.426178	+	0.144668i
$905$	−1.58645	−	5.92073i	−0.0527355	−	0.196812i
$906$	3.60990	+	31.9235i	0.119931	+	1.06059i
$907$	−2.51368	+	0.853279i	−0.0834654	+	0.0283327i	−0.362860	−	0.931844i	$-0.618200\pi$
$907$	−2.51368	+	0.853279i	−0.0834654	+	0.0283327i	0.279394	+	0.960176i	$0.409866\pi$
$908$	−12.4496	−	18.6321i	−0.413153	−	0.618328i
$909$	−0.840025	−	3.66681i	−0.0278619	−	0.121620i
$910$	−2.14873	+	0.890032i	−0.0712296	+	0.0295043i
$911$	38.7826	+	19.1255i	1.28493	+	0.633655i	0.951072	−	0.308970i	$-0.0999843\pi$
$911$	38.7826	+	19.1255i	1.28493	+	0.633655i	0.333853	+	0.942625i	$0.391651\pi$
$912$	−0.127742	+	6.98030i	−0.00422995	+	0.231141i
$913$	0.770334	+	1.56208i	0.0254943	+	0.0516974i
$914$	−5.62428	+	1.50702i	−0.186035	+	0.0498478i
$915$	7.67806	−	51.0798i	0.253829	−	1.68865i
$916$	24.9905	−	3.29006i	0.825708	−	0.108707i
$917$	−76.3482			−2.52124
$918$	−21.3417	+	1.19924i	−0.704381	+	0.0395807i
$919$	30.6732			1.01182			0.505908	−	0.862588i	$-0.331158\pi$
$919$	30.6732			1.01182			0.505908	+	0.862588i	$0.331158\pi$
$920$	−10.9637	+	1.44340i	−0.361462	+	0.0475874i
$921$	1.44224	−	9.59479i	0.0475234	−	0.316159i
$922$	−14.9306	+	4.00064i	−0.491713	+	0.131754i
$923$	−0.248808	−	0.504533i	−0.00818962	−	0.0166069i
$924$	−0.501903	+	27.4259i	−0.0165114	+	0.902247i
$925$	13.8094	+	6.81002i	0.454049	+	0.223912i
$926$	−0.687908	+	0.284941i	−0.0226061	+	0.00936373i
$927$	−22.0068	+	20.4522i	−0.722797	+	0.671739i
$928$	−13.8775	−	20.7692i	−0.455553	−	0.681783i
$929$	27.3014	−	9.26757i	0.895729	−	0.304059i	0.164650	−	0.986352i	$-0.447350\pi$
$929$	27.3014	−	9.26757i	0.895729	−	0.304059i	0.731079	+	0.682293i	$0.239017\pi$
$930$	−3.59368	−	31.7801i	−0.117841	−	1.04211i
$931$	9.46554	+	35.3259i	0.310221	+	1.15776i
$932$	18.9732	+	6.44055i	0.621489	+	0.210967i
$933$	32.9144	−	10.5053i	1.07757	−	0.343929i
$934$	3.17314	−	1.83202i	0.103828	−	0.0599454i
$935$	24.6263	−	56.2641i	0.805366	−	1.84003i
$936$	−0.486243	−	1.30725i	−0.0158934	−	0.0427287i
$937$	5.84662	+	2.42175i	0.191001	+	0.0791151i	0.476134	−	0.879373i	$-0.342038\pi$
$937$	5.84662	+	2.42175i	0.191001	+	0.0791151i	−0.285133	+	0.958488i	$0.592038\pi$
$938$	−29.3129	−	33.4249i	−0.957099	−	1.09136i
$939$	20.9237	−	30.1071i	0.682821	−	0.982508i
$940$	−10.4567	+	5.15667i	−0.341060	+	0.168192i
$941$	2.83508	−	3.23279i	0.0924209	−	0.105386i	−0.703781	−	0.710417i	$-0.748506\pi$
$941$	2.83508	−	3.23279i	0.0924209	−	0.105386i	0.796201	+	0.605032i	$0.206840\pi$
$942$	−4.51275	−	18.1650i	−0.147033	−	0.591848i
$943$	2.89757	−	3.77618i	0.0943577	−	0.122969i
$944$	−0.651056	−	1.57179i	−0.0211901	−	0.0511574i
$945$	70.4070	+	33.8018i	2.29034	+	1.09957i
$946$	−15.3385	−	3.05101i	−0.498696	−	0.0991968i
$947$	0.526262	−	8.02920i	0.0171012	−	0.260914i	−0.980744	−	0.195299i	$-0.937432\pi$
$947$	0.526262	−	8.02920i	0.0171012	−	0.260914i	0.997845	−	0.0656153i	$-0.0209010\pi$
$948$	18.7453	−	8.82150i	0.608819	−	0.286509i
$949$	0.744180	−	2.19228i	0.0241571	−	0.0711646i
$950$	−29.9048	+	22.9468i	−0.970240	+	0.744491i
$951$	−5.89792	−	32.7741i	−0.191253	−	1.06277i
$952$	−14.9151	−	46.9857i	−0.483400	−	1.52282i
$953$			19.0532i			0.617193i	0.951193	+	0.308597i	$0.0998593\pi$
$953$			19.0532i			0.617193i	−0.951193	+	0.308597i	$0.900141\pi$
$954$	−0.632335	+	1.00815i	−0.0204726	+	0.0326401i
$955$	6.17185	+	31.0280i	0.199716	+	1.00404i
$956$	−5.25967	−	1.40932i	−0.170110	−	0.0455808i
$957$	−33.8782	+	3.83094i	−1.09513	+	0.123837i
$958$	4.94751	+	4.33885i	0.159847	+	0.140182i
$959$	−83.2519	+	5.45662i	−2.68834	+	0.176203i
$960$	−20.8590	+	40.4163i	−0.673220	+	1.30443i
$961$	5.45953	+	4.18924i	0.176114	+	0.135137i
$962$	−0.215283	+	0.143848i	−0.00694100	+	0.00463783i
$963$	9.15991	−	7.45819i	0.295174	−	0.240337i
$964$	−13.2281	+	19.7973i	−0.426048	+	0.637627i
$965$	2.54682	−	9.50486i	0.0819850	−	0.305972i
$966$	2.46740	+	6.27941i	0.0793873	+	0.202037i
$967$	12.1992	+	15.8983i	0.392300	+	0.511255i	0.947192	−	0.320667i	$-0.103907\pi$
$967$	12.1992	+	15.8983i	0.392300	+	0.511255i	−0.554892	+	0.831922i	$0.687240\pi$
$968$	−6.93064	+	12.0042i	−0.222759	+	0.385830i
$969$	28.9030	+	4.93372i	0.928498	+	0.158494i
$970$	−13.6439	−	23.6319i	−0.438079	−	0.758775i
$971$	−14.3246	+	34.5827i	−0.459699	+	1.10981i	0.508820	+	0.860873i	$0.330082\pi$
$971$	−14.3246	+	34.5827i	−0.459699	+	1.10981i	−0.968519	+	0.248939i	$0.919918\pi$
$972$	−7.28941	+	13.8595i	−0.233808	+	0.444545i
$973$	33.8344	+	33.8344i	1.08468	+	1.08468i
$974$	−15.8507	−	1.03891i	−0.507890	−	0.0332889i
$975$	1.27488	−	2.11770i	0.0408289	−	0.0678208i
$976$	−0.508112	−	7.75229i	−0.0162643	−	0.248145i
$977$	6.40289	−	48.6347i	0.204846	−	1.55596i	−0.512156	−	0.858893i	$-0.671153\pi$
$977$	6.40289	−	48.6347i	0.204846	−	1.55596i	0.717002	−	0.697071i	$-0.245514\pi$
$978$	30.5472	−	19.6121i	0.976790	−	0.627126i
$979$	−9.38453	+	19.0299i	−0.299931	+	0.608200i
$980$	−6.57869	+	33.0733i	−0.210148	+	1.05649i
$981$	21.2740	−	6.36355i	0.679226	−	0.203173i
$982$	−19.7332	+	19.7332i	−0.629712	+	0.629712i
$983$	−41.0339	+	35.9858i	−1.30878	+	1.14777i	−0.329745	+	0.944070i	$0.606963\pi$
$983$	−41.0339	+	35.9858i	−1.30878	+	1.14777i	−0.979034	+	0.203699i	$0.934704\pi$
$984$	−7.67654	−	24.0515i	−0.244719	−	0.766733i
$985$	−11.5159	−	6.64873i	−0.366928	−	0.211846i
$986$	18.5497	−	8.69381i	0.590742	−	0.276867i
$987$	13.7328	+	16.2496i	0.437119	+	0.517232i
$988$	0.0834941	+	0.634201i	0.00265630	+	0.0201766i
$989$	3.80721	−	0.757302i	0.121062	−	0.0240808i
$990$	25.8297	+	36.3416i	0.820921	+	1.15501i
$991$	−7.43161	−	4.96564i	−0.236073	−	0.157739i	0.431907	−	0.901918i	$-0.357841\pi$
$991$	−7.43161	−	4.96564i	−0.236073	−	0.157739i	−0.667980	+	0.744179i	$0.732841\pi$
$992$	7.91815	+	23.3261i	0.251401	+	0.740605i
$993$	−9.40877	−	9.75955i	−0.298578	−	0.309710i
$994$	14.3103	+	1.88399i	0.453895	+	0.0597564i
$995$	−47.9741	−	6.31591i	−1.52088	−	0.200228i
$996$	−0.744065	+	0.184848i	−0.0235766	+	0.00585715i
$997$	10.8705	+	32.0234i	0.344271	+	1.01419i	0.971843	+	0.235631i	$0.0757157\pi$
$997$	10.8705	+	32.0234i	0.344271	+	1.01419i	−0.627572	+	0.778559i	$0.715951\pi$
$998$	4.94519	+	3.30427i	0.156537	+	0.104595i
$999$	8.42166	+	2.16157i	0.266450	+	0.0683890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.113.12	yes	256
3.2	odd	2		459.2.y.a.368.5		256
9.2	odd	6	inner	153.2.s.a.11.12	✓	256
9.7	even	3		459.2.y.a.62.5		256
17.14	odd	16	inner	153.2.s.a.14.12	yes	256
51.14	even	16		459.2.y.a.422.5		256
153.65	even	48	inner	153.2.s.a.65.12	yes	256
153.133	odd	48		459.2.y.a.116.5		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.12	✓	256	9.2	odd	6	inner
153.2.s.a.14.12	yes	256	17.14	odd	16	inner
153.2.s.a.65.12	yes	256	153.65	even	48	inner
153.2.s.a.113.12	yes	256	1.1	even	1	trivial
459.2.y.a.62.5		256	9.7	even	3
459.2.y.a.116.5		256	153.133	odd	48
459.2.y.a.368.5		256	3.2	odd	2
459.2.y.a.422.5		256	51.14	even	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.989181 - 0.130228i) q^{2} +(0.257461 - 1.71281i) q^{3} +(-0.970333 + 0.260000i) q^{4} +(-1.66678 - 3.37989i) q^{5} +(0.0316194 - 1.72781i) q^{6} +(3.57710 + 1.76403i) q^{7} +(-2.76951 + 1.14717i) q^{8} +(-2.86743 - 0.881962i) q^{9} +(-2.08890 - 3.12626i) q^{10} +(3.74295 - 1.27056i) q^{11} +(0.195507 + 1.72893i) q^{12} +(-0.0401405 - 0.149806i) q^{13} +(3.76813 + 1.27911i) q^{14} +(-6.21823 + 1.98468i) q^{15} +(-0.850202 + 0.490865i) q^{16} +(1.50184 + 3.83985i) q^{17} +(-2.95126 - 0.499000i) q^{18} +(3.79324 + 1.57121i) q^{19} +(2.49610 + 2.84626i) q^{20} +(3.94241 - 5.67273i) q^{21} +(3.53699 - 1.74425i) q^{22} +(-0.645419 + 0.735959i) q^{23} +(1.25184 + 5.03900i) q^{24} +(-5.60170 + 7.30028i) q^{25} +(-0.0592152 - 0.142958i) q^{26} +(-2.24888 + 4.68429i) q^{27} +(-3.92963 - 0.781652i) q^{28} +(0.325703 - 4.96927i) q^{29} +(-5.89250 + 2.77300i) q^{30} +(-1.57861 + 4.65042i) q^{31} +(3.97939 - 3.05349i) q^{32} +(-1.21256 - 6.73807i) q^{33} +(1.98565 + 3.60273i) q^{34} -15.0305i q^{35} +(3.01167 + 0.110266i) q^{36} +(-0.326442 - 1.64113i) q^{37} +(3.95681 + 1.06022i) q^{38} +(-0.266924 + 0.0301837i) q^{39} +(8.49347 + 7.44857i) q^{40} +(-4.85207 + 0.318021i) q^{41} +(3.16101 - 6.12476i) q^{42} +(-3.14609 - 2.41408i) q^{43} +(-3.30156 + 2.20603i) q^{44} +(1.79843 + 11.1616i) q^{45} +(-0.542593 + 0.812048i) q^{46} +(-0.797097 + 2.97481i) q^{47} +(0.621863 + 1.58261i) q^{48} +(5.42253 + 7.06678i) q^{49} +(-4.59039 + 7.95079i) q^{50} +(6.96360 - 1.58376i) q^{51} +(0.0778993 + 0.134926i) q^{52} +(0.152152 - 0.367326i) q^{53} +(-1.61453 + 4.92647i) q^{54} +(-10.5330 - 10.5330i) q^{55} +(-11.9305 - 0.781965i) q^{56} +(3.66779 - 6.09256i) q^{57} +(-0.324959 - 4.95792i) q^{58} +(-0.226196 + 1.71813i) q^{59} +(5.51774 - 3.54254i) q^{60} +(-3.50005 + 7.09741i) q^{61} +(-0.955910 + 4.80569i) q^{62} +(-8.70128 - 8.21311i) q^{63} +(4.92706 - 4.92706i) q^{64} +(-0.439424 + 0.385364i) q^{65} +(-2.07693 - 6.50726i) q^{66} +(-9.67537 - 5.58608i) q^{67} +(-2.45565 - 3.33546i) q^{68} +(1.09439 + 1.29496i) q^{69} +(-1.95739 - 14.8678i) q^{70} +(3.55751 - 0.707633i) q^{71} +(8.95314 - 0.846821i) q^{72} +(12.4119 + 8.29338i) q^{73} +(-0.536631 - 1.58086i) q^{74} +(11.0618 + 11.4742i) q^{75} +(-4.08922 - 0.538355i) q^{76} +(15.6302 + 2.05776i) q^{77} +(-0.260106 + 0.0646182i) q^{78} +(-3.82731 - 11.2749i) q^{79} +(3.07617 + 2.05543i) q^{80} +(7.44429 + 5.05793i) q^{81} +(-4.75816 + 0.946456i) q^{82} +(0.0575142 + 0.436864i) q^{83} +(-2.35055 + 6.52946i) q^{84} +(10.4750 - 11.4762i) q^{85} +(-3.42643 - 1.97825i) q^{86} +(-8.42756 - 1.83726i) q^{87} +(-8.90860 + 7.81263i) q^{88} +(-3.79574 + 3.79574i) q^{89} +(3.23253 + 10.8067i) q^{90} +(0.120677 - 0.606682i) q^{91} +(0.434922 - 0.881934i) q^{92} +(7.55885 + 3.90115i) q^{93} +(-0.401070 + 3.04643i) q^{94} +(-1.01196 - 15.4396i) q^{95} +(-4.20552 - 7.60209i) q^{96} +(7.24200 + 0.474666i) q^{97} +(6.28416 + 6.28416i) q^{98} +(-11.8532 + 0.342099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22}+ \cdots + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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