LMFDB - Embedded newform 510.2.bd.a.73.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(7,510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(510, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 4, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("510.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.5
Character	$\chi$	$=$	510.73
Dual form			510.2.bd.a.7.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923880 + 0.382683i) q^{2} +(0.195090 - 0.980785i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.54906 - 1.61258i) q^{5} +(0.555570 - 0.831470i) q^{6} +(-2.38187 - 1.59151i) q^{7} +(0.382683 + 0.923880i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-0.814041 - 2.08263i) q^{10} +(-4.28649 - 2.86414i) q^{11} +(0.831470 - 0.555570i) q^{12} -2.91395i q^{13} +(-1.59151 - 2.38187i) q^{14} +(-1.88380 + 1.20470i) q^{15} +1.00000i q^{16} +(-1.25589 + 3.92718i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(1.97083 - 0.816345i) q^{19} +(0.0449109 - 2.23562i) q^{20} +(-2.02561 + 2.02561i) q^{21} +(-2.86414 - 4.28649i) q^{22} +(4.01334 - 0.798303i) q^{23} +(0.980785 - 0.195090i) q^{24} +(-0.200807 + 4.99597i) q^{25} +(1.11512 - 2.69214i) q^{26} +(-0.555570 + 0.831470i) q^{27} +(-0.558866 - 2.80961i) q^{28} +(0.854970 - 4.29822i) q^{29} +(-2.20142 + 0.392099i) q^{30} +(8.29948 - 5.54553i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(-3.64536 + 3.64536i) q^{33} +(-2.66316 + 3.14763i) q^{34} +(1.12323 + 6.30630i) q^{35} +(-0.382683 - 0.923880i) q^{36} +(-2.92662 - 0.582142i) q^{37} +2.13321 q^{38} +(-2.85796 - 0.568484i) q^{39} +(0.897026 - 2.04825i) q^{40} +(0.827029 + 4.15776i) q^{41} +(-2.64659 + 1.09625i) q^{42} +(2.99715 - 1.24146i) q^{43} +(-1.00575 - 5.05627i) q^{44} +(0.814041 + 2.08263i) q^{45} +(4.01334 + 0.798303i) q^{46} -9.53671 q^{47} +(0.980785 + 0.195090i) q^{48} +(0.461601 + 1.11440i) q^{49} +(-2.09740 + 4.53883i) q^{50} +(3.60671 + 1.99792i) q^{51} +(2.06048 - 2.06048i) q^{52} +(0.355737 - 0.858826i) q^{53} +(-0.831470 + 0.555570i) q^{54} +(2.02140 + 11.3490i) q^{55} +(0.558866 - 2.80961i) q^{56} +(-0.416169 - 2.09222i) q^{57} +(2.43475 - 3.64386i) q^{58} +(3.38281 - 8.16682i) q^{59} +(-2.18390 - 0.480195i) q^{60} +(13.0180 - 2.58943i) q^{61} +(9.78990 - 1.94733i) q^{62} +(1.59151 + 2.38187i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(-4.69897 + 4.51390i) q^{65} +(-4.76290 + 1.97286i) q^{66} +(0.511063 + 0.511063i) q^{67} +(-3.66499 + 1.88888i) q^{68} -4.09197i q^{69} +(-1.37559 + 6.25611i) q^{70} +(-0.561901 - 0.840944i) q^{71} -1.00000i q^{72} +(0.880112 - 0.588072i) q^{73} +(-2.48107 - 1.65780i) q^{74} +(4.86079 + 1.17161i) q^{75} +(1.97083 + 0.816345i) q^{76} +(5.65154 + 13.6440i) q^{77} +(-2.42286 - 1.61891i) q^{78} +(-2.06743 + 3.09413i) q^{79} +(1.61258 - 1.54906i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-0.827029 + 4.15776i) q^{82} +(-4.92020 - 2.03801i) q^{83} -2.86465 q^{84} +(8.27833 - 4.05822i) q^{85} +3.24409 q^{86} +(-4.04884 - 1.67708i) q^{87} +(1.00575 - 5.05627i) q^{88} +(-1.75569 - 1.75569i) q^{89} +(-0.0449109 + 2.23562i) q^{90} +(-4.63760 + 6.94065i) q^{91} +(3.40235 + 2.27338i) q^{92} +(-3.81983 - 9.22188i) q^{93} +(-8.81077 - 3.64954i) q^{94} +(-4.36936 - 1.91355i) q^{95} +(0.831470 + 0.555570i) q^{96} +(-3.62628 + 2.42300i) q^{97} +1.20622i q^{98} +(2.86414 + 4.28649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{15} + 16 q^{20} + 16 q^{25} - 16 q^{28} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 32 q^{35} - 16 q^{37} - 16 q^{40} + 48 q^{41} + 16 q^{44} + 32 q^{47} - 64 q^{49} - 16 q^{50} + 32 q^{51} + 16 q^{52}+ \cdots - 80 q^{97}+O(q^{100}) $ 64 * q - 16 * q^15 + 16 * q^20 + 16 * q^25 - 16 * q^28 + 32 * q^29 + 16 * q^31 + 16 * q^33 + 32 * q^35 - 16 * q^37 - 16 * q^40 + 48 * q^41 + 16 * q^44 + 32 * q^47 - 64 * q^49 - 16 * q^50 + 32 * q^51 + 16 * q^52 + 80 * q^53 - 16 * q^55 + 16 * q^56 - 32 * q^57 + 64 * q^59 - 48 * q^61 + 32 * q^65 + 16 * q^67 - 48 * q^68 - 64 * q^71 + 16 * q^73 + 48 * q^74 - 32 * q^75 - 80 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 48 * q^82 - 32 * q^83 - 16 * q^85 - 64 * q^86 - 32 * q^87 - 16 * q^88 - 32 * q^89 - 16 * q^90 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 112 * q^95 - 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.923880	+	0.382683i	0.653281	+	0.270598i
$2$	0.923880	+	0.382683i	0.653281	+	0.270598i
$3$	0.195090	−	0.980785i	0.112635	−	0.566257i
$3$	0.195090	−	0.980785i	0.112635	−	0.566257i
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$	−1.54906	−	1.61258i	−0.692762	−	0.721166i
$5$	−1.54906	−	1.61258i	−0.692762	−	0.721166i
$6$	0.555570	−	0.831470i	0.226811	−	0.339446i
$7$	−2.38187	−	1.59151i	−0.900262	−	0.601536i	0.0169845	−	0.999856i	$-0.494593\pi$
$7$	−2.38187	−	1.59151i	−0.900262	−	0.601536i	−0.917247	+	0.398320i	$0.869593\pi$
$8$	0.382683	+	0.923880i	0.135299	+	0.326641i
$9$	−0.923880	−	0.382683i	−0.307960	−	0.127561i
$10$	−0.814041	−	2.08263i	−0.257422	−	0.658585i
$11$	−4.28649	−	2.86414i	−1.29243	−	0.863572i	−0.296615	−	0.954997i	$-0.595858\pi$
$11$	−4.28649	−	2.86414i	−1.29243	−	0.863572i	−0.995812	+	0.0914252i	$0.970858\pi$
$12$	0.831470	−	0.555570i	0.240025	−	0.160379i
$13$		−	2.91395i		−	0.808185i	−0.914718	−	0.404092i	$-0.867587\pi$
$13$		−	2.91395i		−	0.808185i	0.914718	−	0.404092i	$-0.132413\pi$
$14$	−1.59151	−	2.38187i	−0.425350	−	0.636581i
$15$	−1.88380	+	1.20470i	−0.486395	+	0.311052i
$16$			1.00000i			0.250000i
$17$	−1.25589	+	3.92718i	−0.304599	+	0.952481i
$17$	−1.25589	+	3.92718i	−0.304599	+	0.952481i
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	1.97083	−	0.816345i	0.452140	−	0.187282i	−0.144980	−	0.989435i	$-0.546312\pi$
$19$	1.97083	−	0.816345i	0.452140	−	0.187282i	0.597120	+	0.802152i	$0.296312\pi$
$20$	0.0449109	−	2.23562i	0.0100424	−	0.499899i
$21$	−2.02561	+	2.02561i	−0.442025	+	0.442025i
$22$	−2.86414	−	4.28649i	−0.610638	−	0.913884i
$23$	4.01334	−	0.798303i	0.836840	−	0.166458i	0.241974	−	0.970283i	$-0.422205\pi$
$23$	4.01334	−	0.798303i	0.836840	−	0.166458i	0.594866	+	0.803825i	$0.297205\pi$
$24$	0.980785	−	0.195090i	0.200202	−	0.0398226i
$25$	−0.200807	+	4.99597i	−0.0401615	+	0.999193i
$26$	1.11512	−	2.69214i	0.218693	−	0.527972i
$27$	−0.555570	+	0.831470i	−0.106920	+	0.160016i
$28$	−0.558866	−	2.80961i	−0.105616	−	0.530966i
$29$	0.854970	−	4.29822i	0.158764	−	0.798160i	−0.816539	−	0.577290i	$-0.804110\pi$
$29$	0.854970	−	4.29822i	0.158764	−	0.798160i	0.975303	−	0.220870i	$-0.0708898\pi$
$30$	−2.20142	+	0.392099i	−0.401923	+	0.0715872i
$31$	8.29948	−	5.54553i	1.49063	−	0.996007i	0.499041	−	0.866578i	$-0.333686\pi$
$31$	8.29948	−	5.54553i	1.49063	−	0.996007i	0.991589	−	0.129429i	$-0.0413143\pi$
$32$	−0.382683	+	0.923880i	−0.0676495	+	0.163320i
$33$	−3.64536	+	3.64536i	−0.634576	+	0.634576i
$34$	−2.66316	+	3.14763i	−0.456728	+	0.539814i
$35$	1.12323	+	6.30630i	0.189860	+	1.06596i
$36$	−0.382683	−	0.923880i	−0.0637806	−	0.153980i
$37$	−2.92662	−	0.582142i	−0.481134	−	0.0957035i	−0.0514363	−	0.998676i	$-0.516380\pi$
$37$	−2.92662	−	0.582142i	−0.481134	−	0.0957035i	−0.429698	+	0.902973i	$0.641380\pi$
$38$	2.13321			0.346053
$39$	−2.85796	−	0.568484i	−0.457640	−	0.0910303i
$40$	0.897026	−	2.04825i	0.141832	−	0.323857i
$41$	0.827029	+	4.15776i	0.129160	+	0.649333i	0.990070	+	0.140575i	$0.0448951\pi$
$41$	0.827029	+	4.15776i	0.129160	+	0.649333i	−0.860910	+	0.508758i	$0.830105\pi$
$42$	−2.64659	+	1.09625i	−0.408378	+	0.169156i
$43$	2.99715	−	1.24146i	0.457061	−	0.189321i	−0.142260	−	0.989829i	$-0.545437\pi$
$43$	2.99715	−	1.24146i	0.457061	−	0.189321i	0.599322	+	0.800508i	$0.295437\pi$
$44$	−1.00575	−	5.05627i	−0.151623	−	0.762261i
$45$	0.814041	+	2.08263i	0.121350	+	0.310460i
$46$	4.01334	+	0.798303i	0.591735	+	0.117703i
$47$	−9.53671			−1.39107			−0.695536	−	0.718491i	$-0.744833\pi$
$47$	−9.53671			−1.39107			−0.695536	+	0.718491i	$0.744833\pi$
$48$	0.980785	+	0.195090i	0.141564	+	0.0281589i
$49$	0.461601	+	1.11440i	0.0659429	+	0.159200i
$50$	−2.09740	+	4.53883i	−0.296616	+	0.641887i
$51$	3.60671	+	1.99792i	0.505040	+	0.279764i
$52$	2.06048	−	2.06048i	0.285737	−	0.285737i
$53$	0.355737	−	0.858826i	0.0488643	−	0.117969i	−0.897563	−	0.440887i	$-0.854664\pi$
$53$	0.355737	−	0.858826i	0.0488643	−	0.117969i	0.946427	+	0.322918i	$0.104664\pi$
$54$	−0.831470	+	0.555570i	−0.113149	+	0.0756035i
$55$	2.02140	+	11.3490i	0.272565	+	1.53030i
$56$	0.558866	−	2.80961i	0.0746815	−	0.375449i
$57$	−0.416169	−	2.09222i	−0.0551229	−	0.277122i
$58$	2.43475	−	3.64386i	0.319698	−	0.478462i
$59$	3.38281	−	8.16682i	0.440404	−	1.06323i	−0.535403	−	0.844597i	$-0.679840\pi$
$59$	3.38281	−	8.16682i	0.440404	−	1.06323i	0.975807	−	0.218633i	$-0.0701598\pi$
$60$	−2.18390	−	0.480195i	−0.281940	−	0.0619929i
$61$	13.0180	−	2.58943i	1.66678	−	0.331543i	0.730531	−	0.682880i	$-0.239273\pi$
$61$	13.0180	−	2.58943i	1.66678	−	0.331543i	0.936249	+	0.351337i	$0.114273\pi$
$62$	9.78990	−	1.94733i	1.24332	−	0.247311i
$63$	1.59151	+	2.38187i	0.200512	+	0.300087i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$	−4.69897	+	4.51390i	−0.582836	+	0.559880i
$66$	−4.76290	+	1.97286i	−0.586272	+	0.242842i
$67$	0.511063	+	0.511063i	0.0624363	+	0.0624363i	0.737635	−	0.675199i	$-0.235942\pi$
$67$	0.511063	+	0.511063i	0.0624363	+	0.0624363i	−0.675199	+	0.737635i	$0.735942\pi$
$68$	−3.66499	+	1.88888i	−0.444445	+	0.229061i
$69$		−	4.09197i		−	0.492615i
$70$	−1.37559	+	6.25611i	−0.164415	+	0.747748i
$71$	−0.561901	−	0.840944i	−0.0666854	−	0.0998017i	0.796628	−	0.604470i	$-0.206615\pi$
$71$	−0.561901	−	0.840944i	−0.0666854	−	0.0998017i	−0.863314	+	0.504668i	$0.831615\pi$
$72$		−	1.00000i		−	0.117851i
$73$	0.880112	−	0.588072i	0.103009	−	0.0688286i	−0.502999	−	0.864287i	$-0.667770\pi$
$73$	0.880112	−	0.588072i	0.103009	−	0.0688286i	0.606008	+	0.795459i	$0.292770\pi$
$74$	−2.48107	−	1.65780i	−0.288419	−	0.192715i
$75$	4.86079	+	1.17161i	0.561276	+	0.135286i
$76$	1.97083	+	0.816345i	0.226070	+	0.0936412i
$77$	5.65154	+	13.6440i	0.644053	+	1.55488i
$78$	−2.42286	−	1.61891i	−0.274335	−	0.183305i
$79$	−2.06743	+	3.09413i	−0.232604	+	0.348117i	−0.929349	−	0.369202i	$-0.879631\pi$
$79$	−2.06743	+	3.09413i	−0.232604	+	0.348117i	0.696745	+	0.717319i	$0.254631\pi$
$80$	1.61258	−	1.54906i	0.180292	−	0.173191i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	−0.827029	+	4.15776i	−0.0913301	+	0.459147i
$83$	−4.92020	−	2.03801i	−0.540062	−	0.223701i	0.0959417	−	0.995387i	$-0.469414\pi$
$83$	−4.92020	−	2.03801i	−0.540062	−	0.223701i	−0.636004	+	0.771686i	$0.719414\pi$
$84$	−2.86465			−0.312559
$85$	8.27833	−	4.05822i	0.897911	−	0.440176i
$86$	3.24409			0.349820
$87$	−4.04884	−	1.67708i	−0.434081	−	0.179802i
$88$	1.00575	−	5.05627i	0.107214	−	0.539000i
$89$	−1.75569	−	1.75569i	−0.186103	−	0.186103i	0.607906	−	0.794009i	$-0.292010\pi$
$89$	−1.75569	−	1.75569i	−0.186103	−	0.186103i	−0.794009	+	0.607906i	$0.792010\pi$
$90$	−0.0449109	+	2.23562i	−0.00473403	+	0.235655i
$91$	−4.63760	+	6.94065i	−0.486152	+	0.727578i
$92$	3.40235	+	2.27338i	0.354719	+	0.237016i
$93$	−3.81983	−	9.22188i	−0.396098	−	0.956265i
$94$	−8.81077	−	3.64954i	−0.908761	−	0.376421i
$95$	−4.36936	−	1.91355i	−0.448287	−	0.196326i
$96$	0.831470	+	0.555570i	0.0848615	+	0.0567026i
$97$	−3.62628	+	2.42300i	−0.368193	+	0.246019i	−0.725878	−	0.687824i	$-0.758566\pi$
$97$	−3.62628	+	2.42300i	−0.368193	+	0.246019i	0.357685	+	0.933842i	$0.383566\pi$
$98$			1.20622i			0.121847i
$99$	2.86414	+	4.28649i	0.287857	+	0.430809i
$100$	−3.67467	+	3.39069i	−0.367467	+	0.339069i
$101$			15.5826i			1.55053i	0.631637	+	0.775264i	$0.282383\pi$
$101$			15.5826i			1.55053i	−0.631637	+	0.775264i	$0.717617\pi$
$102$	2.56759	+	3.22606i	0.254230	+	0.319428i
$103$	12.4071	+	12.4071i	1.22250	+	1.22250i	0.966739	+	0.255765i	$0.0823274\pi$
$103$	12.4071	+	12.4071i	1.22250	+	1.22250i	0.255765	+	0.966739i	$0.417673\pi$
$104$	2.69214	−	1.11512i	0.263986	−	0.109347i
$105$	6.40426	+	0.128654i	0.624992	+	0.0125554i
$106$	0.657317	−	0.657317i	0.0638443	−	0.0638443i
$107$	−9.01125	−	13.4863i	−0.871150	−	1.30377i	−0.951704	−	0.307018i	$-0.900669\pi$
$107$	−9.01125	−	13.4863i	−0.871150	−	1.30377i	0.0805537	−	0.996750i	$-0.474331\pi$
$108$	−0.980785	+	0.195090i	−0.0943761	+	0.0187726i
$109$	−10.0894	+	2.00691i	−0.966392	+	0.192227i	−0.652968	−	0.757386i	$-0.726476\pi$
$109$	−10.0894	+	2.00691i	−0.966392	+	0.192227i	−0.313425	+	0.949613i	$0.601476\pi$
$110$	−2.47556	+	11.2587i	−0.236036	+	1.07348i
$111$	−1.14191	+	2.75682i	−0.108386	+	0.261666i
$112$	1.59151	−	2.38187i	0.150384	−	0.225066i
$113$	−2.14775	−	10.7975i	−0.202044	−	1.01574i	−0.940073	−	0.340974i	$-0.889243\pi$
$113$	−2.14775	−	10.7975i	−0.202044	−	1.01574i	0.738029	−	0.674769i	$-0.235757\pi$
$114$	0.416169	−	2.09222i	0.0389778	−	0.195955i
$115$	−7.50424	−	5.23520i	−0.699774	−	0.488185i
$116$	3.64386	−	2.43475i	0.338324	−	0.226061i
$117$	−1.11512	+	2.69214i	−0.103093	+	0.248889i
$118$	6.25062	−	6.25062i	0.575416	−	0.575416i
$119$	9.24154	−	7.35526i	0.847170	−	0.674255i
$120$	−1.83390	−	1.27938i	−0.167411	−	0.116791i
$121$	5.96120	+	14.3916i	0.541927	+	1.30833i
$122$	13.0180	+	2.58943i	1.17859	+	0.234436i
$123$	4.23921			0.382237
$124$	9.78990	+	1.94733i	0.879159	+	0.174876i
$125$	8.36744	−	7.41525i	0.748407	−	0.663240i
$126$	0.558866	+	2.80961i	0.0497877	+	0.250300i
$127$	15.7747	−	6.53408i	1.39978	−	0.579806i	0.450082	−	0.892987i	$-0.351395\pi$
$127$	15.7747	−	6.53408i	1.39978	−	0.579806i	0.949693	+	0.313181i	$0.101395\pi$
$128$	−0.923880	+	0.382683i	−0.0816602	+	0.0338248i
$129$	−0.632891	−	3.18176i	−0.0557230	−	0.280138i
$130$	−6.06868	+	2.37208i	−0.532258	+	0.208045i
$131$	0.496923	+	0.0988441i	0.0434163	+	0.00863605i	0.216751	−	0.976227i	$-0.430454\pi$
$131$	0.496923	+	0.0988441i	0.0434163	+	0.00863605i	−0.173334	+	0.984863i	$0.555454\pi$
$132$	−5.15532			−0.448713
$133$	−5.99349	−	1.19218i	−0.519701	−	0.103375i
$134$	0.276585	+	0.667736i	0.0238933	+	0.0576836i
$135$	2.20142	−	0.392099i	0.189468	−	0.0337465i
$136$	−4.10885	+	0.342572i	−0.352331	+	0.0293753i
$137$	−9.48171	+	9.48171i	−0.810077	+	0.810077i	−0.984645	−	0.174568i	$-0.944147\pi$
$137$	−9.48171	+	9.48171i	−0.810077	+	0.810077i	0.174568	+	0.984645i	$0.444147\pi$
$138$	1.56593	−	3.78049i	0.133301	−	0.321816i
$139$	14.5306	−	9.70905i	1.23247	−	0.823511i	0.243254	−	0.969963i	$-0.421785\pi$
$139$	14.5306	−	9.70905i	1.23247	−	0.823511i	0.989218	+	0.146451i	$0.0467852\pi$
$140$	−3.66499	+	5.25347i	−0.309748	+	0.443999i
$141$	−1.86052	+	9.35346i	−0.156684	+	0.787704i
$142$	−0.197313	−	0.991961i	−0.0165582	−	0.0832435i
$143$	−8.34598	+	12.4906i	−0.697926	+	1.04452i
$144$	0.382683	−	0.923880i	0.0318903	−	0.0769900i
$145$	−8.25562	+	5.27952i	−0.685592	+	0.438440i
$146$	1.03816	−	0.206504i	0.0859190	−	0.0170904i
$147$	1.18304	−	0.235322i	0.0975758	−	0.0194090i
$148$	−1.65780	−	2.48107i	−0.136270	−	0.203943i
$149$	−6.61721	+	6.61721i	−0.542103	+	0.542103i	−0.924145	−	0.382042i	$-0.875221\pi$
$149$	−6.61721	+	6.61721i	−0.542103	+	0.542103i	0.382042	+	0.924145i	$0.375221\pi$
$150$	4.04243	+	2.94258i	0.330063	+	0.240260i
$151$	14.0769	−	5.83083i	1.14556	−	0.474506i	0.272517	−	0.962151i	$-0.412144\pi$
$151$	14.0769	−	5.83083i	1.14556	−	0.474506i	0.873042	+	0.487645i	$0.162144\pi$
$152$	1.50841	+	1.50841i	0.122348	+	0.122348i
$153$	2.66316	−	3.14763i	0.215304	−	0.254471i
$154$			14.7682i			1.19006i
$155$	−21.7990	−	4.79316i	−1.75094	−	0.384996i
$156$	−1.61891	−	2.42286i	−0.129616	−	0.193984i
$157$		−	1.79195i		−	0.143013i	−0.997440	−	0.0715067i	$-0.977219\pi$
$157$		−	1.79195i		−	0.143013i	0.997440	−	0.0715067i	$-0.0227807\pi$
$158$	−3.09413	+	2.06743i	−0.246156	+	0.164476i
$159$	−0.772923	−	0.516451i	−0.0612968	−	0.0409572i
$160$	2.08263	−	0.814041i	0.164646	−	0.0643556i
$161$	−10.8298	−	4.48584i	−0.853505	−	0.353533i
$162$	0.382683	+	0.923880i	0.0300665	+	0.0725868i
$163$	−15.5013	−	10.3576i	−1.21416	−	0.811273i	−0.227451	−	0.973790i	$-0.573039\pi$
$163$	−15.5013	−	10.3576i	−1.21416	−	0.811273i	−0.986706	+	0.162516i	$0.948039\pi$
$164$	−2.35518	+	3.52478i	−0.183909	+	0.275239i
$165$	11.5253	+	0.231530i	0.897246	+	0.0180246i
$166$	−3.76576	−	3.76576i	−0.292280	−	0.292280i
$167$	−3.21370	+	16.1564i	−0.248684	+	1.25022i	0.631421	+	0.775440i	$0.282472\pi$
$167$	−3.21370	+	16.1564i	−0.248684	+	1.25022i	−0.880105	+	0.474778i	$0.842528\pi$
$168$	−2.64659	−	1.09625i	−0.204189	−	0.0845778i
$169$	4.50888			0.346837
$170$	9.20120	−	0.581328i	0.705700	−	0.0445858i
$171$	−2.13321			−0.163131
$172$	2.99715	+	1.24146i	0.228531	+	0.0946605i
$173$	−4.65209	+	23.3876i	−0.353692	+	1.77813i	0.237285	+	0.971440i	$0.423742\pi$
$173$	−4.65209	+	23.3876i	−0.353692	+	1.77813i	−0.590977	+	0.806688i	$0.701258\pi$
$174$	−3.09885	−	3.09885i	−0.234923	−	0.234923i
$175$	8.42945	−	11.5802i	0.637206	−	0.875377i
$176$	2.86414	−	4.28649i	0.215893	−	0.323107i
$177$	−7.34995	−	4.91108i	−0.552456	−	0.369139i
$178$	−0.950173	−	2.29392i	−0.0712185	−	0.171937i
$179$	10.4028	+	4.30897i	0.777539	+	0.322067i	0.735922	−	0.677066i	$-0.236749\pi$
$179$	10.4028	+	4.30897i	0.777539	+	0.322067i	0.0416174	+	0.999134i	$0.486749\pi$
$180$	−0.897026	+	2.04825i	−0.0668604	+	0.152668i
$181$	−9.42755	−	6.29929i	−0.700744	−	0.468222i	0.153463	−	0.988154i	$-0.450957\pi$
$181$	−9.42755	−	6.29929i	−0.700744	−	0.468222i	−0.854208	+	0.519932i	$0.825957\pi$
$182$	−6.94065	+	4.63760i	−0.514476	+	0.343762i
$183$		−	13.2730i		−	0.981169i
$184$	2.27338	+	3.40235i	0.167595	+	0.250824i
$185$	3.59478	+	5.62118i	0.264293	+	0.413277i
$186$		−	9.98169i		−	0.731893i
$187$	16.6314	−	13.2368i	1.21621	−	0.967969i
$188$	−6.74347	−	6.74347i	−0.491818	−	0.491818i
$189$	2.64659	−	1.09625i	0.192511	−	0.0797408i
$190$	−3.30448	−	3.43997i	−0.239732	−	0.249561i
$191$	8.43143	−	8.43143i	0.610077	−	0.610077i	−0.332889	−	0.942966i	$-0.608023\pi$
$191$	8.43143	−	8.43143i	0.610077	−	0.610077i	0.942966	+	0.332889i	$0.108023\pi$
$192$	0.555570	+	0.831470i	0.0400948	+	0.0600062i
$193$	−22.7607	+	4.52739i	−1.63835	+	0.325889i	−0.926458	−	0.376398i	$-0.877163\pi$
$193$	−22.7607	+	4.52739i	−1.63835	+	0.325889i	−0.711894	+	0.702286i	$0.752163\pi$
$194$	−4.27749	+	0.850845i	−0.307106	+	0.0610871i
$195$	3.51044	+	5.48930i	0.251388	+	0.393097i
$196$	−0.461601	+	1.11440i	−0.0329715	+	0.0796002i
$197$	11.3685	−	17.0141i	0.809969	−	1.21220i	−0.164210	−	0.986425i	$-0.552508\pi$
$197$	11.3685	−	17.0141i	0.809969	−	1.21220i	0.974179	−	0.225778i	$-0.0724925\pi$
$198$	1.00575	+	5.05627i	0.0714758	+	0.359333i
$199$	−0.100975	+	0.507638i	−0.00715796	+	0.0359855i	−0.984199	−	0.177065i	$-0.943340\pi$
$199$	−0.100975	+	0.507638i	−0.00715796	+	0.0359855i	0.977041	+	0.213050i	$0.0683398\pi$
$200$	−4.69252	+	1.72635i	−0.331811	+	0.122071i
$201$	0.600946	−	0.401540i	0.0423875	−	0.0283224i
$202$	−5.96321	+	14.3965i	−0.419570	+	1.01293i
$203$	−8.87711	+	8.87711i	−0.623051	+	0.623051i
$204$	1.13759	+	3.96307i	0.0796470	+	0.277470i
$205$	5.42358	−	7.77428i	0.378799	−	0.542979i
$206$	6.71465	+	16.2106i	0.467832	+	1.12945i
$207$	−4.01334	−	0.798303i	−0.278947	−	0.0554859i
$208$	2.91395			0.202046
$209$	−10.7861	−	2.14549i	−0.746089	−	0.148406i
$210$	5.86753	+	2.56967i	0.404898	+	0.177324i
$211$	−0.0490468	−	0.246575i	−0.00337652	−	0.0169749i	0.979060	−	0.203570i	$-0.0652546\pi$
$211$	−0.0490468	−	0.246575i	−0.00337652	−	0.0169749i	−0.982437	+	0.186596i	$0.940255\pi$
$212$	0.858826	−	0.355737i	0.0589844	−	0.0244321i
$213$	−0.934407	+	0.387044i	−0.0640245	+	0.0265198i
$214$	−3.16433	−	15.9082i	−0.216309	−	1.08746i
$215$	−6.64473	−	2.91004i	−0.453167	−	0.198463i
$216$	−0.980785	−	0.195090i	−0.0667340	−	0.0132742i
$217$	−28.5941			−1.94109
$218$	−10.0894	−	2.00691i	−0.683343	−	0.135925i
$219$	−0.405071	−	0.977928i	−0.0273722	−	0.0660823i
$220$	−6.59564	+	9.45433i	−0.444678	+	0.637411i
$221$	11.4436	+	3.65961i	0.769781	+	0.246172i
$222$	−2.10998	+	2.10998i	−0.141612	+	0.141612i
$223$	1.90864	−	4.60786i	0.127812	−	0.308565i	−0.847000	−	0.531592i	$-0.821594\pi$
$223$	1.90864	−	4.60786i	0.127812	−	0.308565i	0.974812	+	0.223027i	$0.0715939\pi$
$224$	2.38187	−	1.59151i	0.159145	−	0.106338i
$225$	2.09740	−	4.53883i	0.139826	−	0.302588i
$226$	2.14775	−	10.7975i	0.142866	−	0.718238i
$227$	−3.70314	−	18.6169i	−0.245786	−	1.23565i	−0.884623	−	0.466307i	$-0.845584\pi$
$227$	−3.70314	−	18.6169i	−0.245786	−	1.23565i	0.638837	−	0.769342i	$-0.279416\pi$
$228$	1.18515	−	1.77370i	0.0784884	−	0.117466i
$229$	2.56210	−	6.18547i	0.169309	−	0.408747i	−0.816337	−	0.577576i	$-0.803999\pi$
$229$	2.56210	−	6.18547i	0.169309	−	0.408747i	0.985645	+	0.168829i	$0.0539986\pi$
$230$	−4.92959	−	7.70844i	−0.325048	−	0.508280i
$231$	14.4844	−	2.88113i	0.953006	−	0.189565i
$232$	4.29822	−	0.854970i	0.282192	−	0.0561315i
$233$	−0.987530	−	1.47794i	−0.0646952	−	0.0968232i	0.797711	−	0.603039i	$-0.206044\pi$
$233$	−0.987530	−	1.47794i	−0.0646952	−	0.0968232i	−0.862407	+	0.506216i	$0.831044\pi$
$234$	−2.06048	+	2.06048i	−0.134697	+	0.134697i
$235$	14.7730	+	15.3787i	0.963682	+	1.00319i
$236$	8.16682	−	3.38281i	0.531615	−	0.220202i
$237$	2.63134	+	2.63134i	0.170924	+	0.170924i
$238$	11.3528	−	3.25879i	0.735893	−	0.211236i
$239$		−	17.4887i		−	1.13125i	−0.824662	−	0.565626i	$-0.808635\pi$
$239$		−	17.4887i		−	1.13125i	0.824662	−	0.565626i	$-0.191365\pi$
$240$	−1.20470	−	1.88380i	−0.0777631	−	0.121599i
$241$	14.8614	+	22.2417i	0.957309	+	1.43271i	0.900761	+	0.434315i	$0.143009\pi$
$241$	14.8614	+	22.2417i	0.957309	+	1.43271i	0.0565479	+	0.998400i	$0.481991\pi$
$242$			15.5774i			1.00135i
$243$	0.831470	−	0.555570i	0.0533388	−	0.0356398i
$244$	11.0361	+	7.37408i	0.706514	+	0.472077i
$245$	1.08201	−	2.47065i	0.0691271	−	0.157844i
$246$	3.91652	+	1.62228i	0.249708	+	0.103433i
$247$	−2.37879	−	5.74291i	−0.151359	−	0.365412i
$248$	8.29948	+	5.54553i	0.527017	+	0.352142i
$249$	−2.95874	+	4.42806i	−0.187502	+	0.280617i
$250$	10.5682	−	3.64872i	0.668392	−	0.230765i
$251$	−1.67282	−	1.67282i	−0.105587	−	0.105587i	0.652340	−	0.757927i	$-0.273788\pi$
$251$	−1.67282	−	1.67282i	−0.105587	−	0.105587i	−0.757927	+	0.652340i	$0.773788\pi$
$252$	−0.558866	+	2.80961i	−0.0352052	+	0.176989i
$253$	−19.4896	−	8.07287i	−1.22530	−	0.507537i
$254$	17.0744			1.07134
$255$	−2.36522	−	8.91099i	−0.148116	−	0.558028i
$256$	−1.00000			−0.0625000
$257$	−7.40057	−	3.06542i	−0.461635	−	0.191215i	0.139730	−	0.990190i	$-0.455376\pi$
$257$	−7.40057	−	3.06542i	−0.461635	−	0.191215i	−0.601365	+	0.798974i	$0.705376\pi$
$258$	0.632891	−	3.18176i	0.0394021	−	0.198088i
$259$	6.04435	+	6.04435i	0.375578	+	0.375578i
$260$	−6.51448	−	0.130868i	−0.404011	−	0.00811611i
$261$	−2.43475	+	3.64386i	−0.150707	+	0.225549i
$262$	0.421271	+	0.281484i	0.0260262	+	0.0173901i
$263$	−5.37067	−	12.9659i	−0.331170	−	0.799515i	−0.998500	−	0.0547525i	$-0.982563\pi$
$263$	−5.37067	−	12.9659i	−0.331170	−	0.799515i	0.667330	−	0.744762i	$-0.267437\pi$
$264$	−4.76290	−	1.97286i	−0.293136	−	0.121421i
$265$	−1.93598	+	0.756722i	−0.118926	+	0.0464851i
$266$	−5.08103	−	3.39504i	−0.311538	−	0.208163i
$267$	−2.06447	+	1.37944i	−0.126344	+	0.0844202i
$268$			0.722752i			0.0441491i
$269$	13.9160	+	20.8268i	0.848475	+	1.26983i	0.961101	+	0.276196i	$0.0890738\pi$
$269$	13.9160	+	20.8268i	0.848475	+	1.26983i	−0.112626	+	0.993637i	$0.535926\pi$
$270$	2.18390	+	0.480195i	0.132908	+	0.0292237i
$271$		−	24.3091i		−	1.47667i	−0.674434	−	0.738335i	$-0.735612\pi$
$271$		−	24.3091i		−	1.47667i	0.674434	−	0.738335i	$-0.264388\pi$
$272$	−3.92718	−	1.25589i	−0.238120	−	0.0761497i
$273$	5.90254	+	5.90254i	0.357238	+	0.357238i
$274$	−12.3884	+	5.13146i	−0.748414	+	0.310003i
$275$	15.1699	−	20.8400i	0.914781	−	1.25670i
$276$	2.89346	−	2.89346i	0.174166	−	0.174166i
$277$	−5.47148	−	8.18864i	−0.328749	−	0.492008i	0.629870	−	0.776701i	$-0.283108\pi$
$277$	−5.47148	−	8.18864i	−0.328749	−	0.492008i	−0.958619	+	0.284693i	$0.908108\pi$
$278$	17.1400	−	3.40937i	1.02799	−	0.204480i
$279$	−9.78990	+	1.94733i	−0.586106	+	0.116584i
$280$	−5.39642	+	3.45104i	−0.322498	+	0.206239i
$281$	12.5805	−	30.3719i	0.750488	−	1.81184i	0.193958	−	0.981010i	$-0.437868\pi$
$281$	12.5805	−	30.3719i	0.750488	−	1.81184i	0.556530	−	0.830827i	$-0.312132\pi$
$282$	−5.29831	+	7.92948i	−0.315510	+	0.472194i
$283$	−0.622785	−	3.13095i	−0.0370207	−	0.186116i	0.957850	−	0.287268i	$-0.0927471\pi$
$283$	−0.622785	−	3.13095i	−0.0370207	−	0.186116i	−0.994871	+	0.101152i	$0.967747\pi$
$284$	0.197313	−	0.991961i	0.0117084	−	0.0588621i
$285$	−2.72920	+	3.91209i	−0.161664	+	0.231732i
$286$	−12.4906	+	8.34598i	−0.738587	+	0.493508i
$287$	4.64725	−	11.2195i	0.274319	−	0.662264i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	−13.8455	−	9.86423i	−0.814439	−	0.580249i
$290$	−9.64758	+	1.71835i	−0.566525	+	0.100905i
$291$	1.66899	+	4.02931i	0.0978381	+	0.236202i
$292$	1.03816	+	0.206504i	0.0607539	+	0.0120847i
$293$	29.6988			1.73502			0.867510	−	0.497420i	$-0.165719\pi$
$293$	29.6988			1.73502			0.867510	+	0.497420i	$0.165719\pi$
$294$	1.18304	+	0.235322i	0.0689965	+	0.0137243i
$295$	−18.4098	+	7.19589i	−1.07186	+	0.418961i
$296$	−0.582142	−	2.92662i	−0.0338363	−	0.170107i
$297$	4.76290	−	1.97286i	0.276371	−	0.114477i
$298$	−8.64580	+	3.58121i	−0.500838	+	0.207454i
$299$	−2.32622	−	11.6947i	−0.134529	−	0.676321i
$300$	2.60864	+	4.26556i	0.150610	+	0.246272i
$301$	−9.11463	−	1.81301i	−0.525358	−	0.104500i
$302$	15.2367			0.876773
$303$	15.2832	+	3.04002i	0.877997	+	0.174644i
$304$	0.816345	+	1.97083i	0.0468206	+	0.113035i
$305$	−24.3413	−	16.9813i	−1.39378	−	0.972345i
$306$	3.66499	−	1.88888i	0.209513	−	0.107980i
$307$	−18.2449	+	18.2449i	−1.04129	+	1.04129i	−0.0421801	+	0.999110i	$0.513430\pi$
$307$	−18.2449	+	18.2449i	−1.04129	+	1.04129i	−0.999110	+	0.0421801i	$0.986570\pi$
$308$	−5.65154	+	13.6440i	−0.322027	+	0.777441i
$309$	14.5892	−	9.74817i	0.829948	−	0.554554i
$310$	−18.3054	−	12.7704i	−1.03968	−	0.725311i
$311$	2.74379	−	13.7939i	0.155586	−	0.782183i	−0.821644	−	0.570001i	$-0.806943\pi$
$311$	2.74379	−	13.7939i	0.155586	−	0.782183i	0.977230	−	0.212182i	$-0.0680571\pi$
$312$	−0.568484	−	2.85796i	−0.0321841	−	0.161800i
$313$	1.03118	−	1.54328i	0.0582860	−	0.0872311i	−0.801182	−	0.598421i	$-0.795795\pi$
$313$	1.03118	−	1.54328i	0.0582860	−	0.0872311i	0.859468	+	0.511190i	$0.170795\pi$
$314$	0.685750	−	1.65555i	0.0386991	−	0.0934279i
$315$	1.37559	−	6.25611i	0.0775058	−	0.352492i
$316$	−3.64978	+	0.725986i	−0.205316	+	0.0408399i
$317$	23.6250	−	4.69930i	1.32691	−	0.263939i	0.519775	−	0.854303i	$-0.326016\pi$
$317$	23.6250	−	4.69930i	1.32691	−	0.263939i	0.807137	+	0.590364i	$0.201016\pi$
$318$	−0.516451	−	0.772923i	−0.0289611	−	0.0433434i
$319$	−15.9756	+	15.9756i	−0.894460	+	0.894460i
$320$	2.23562	+	0.0449109i	0.124975	+	0.00251060i
$321$	−14.9852	+	6.20705i	−0.836390	+	0.346444i
$322$	−8.28875	−	8.28875i	−0.461914	−	0.461914i
$323$	0.730779	+	8.76505i	0.0406616	+	0.487700i
$324$			1.00000i			0.0555556i
$325$	14.5580	+	0.585143i	0.807533	+	0.0324579i
$326$	−10.3576	−	15.5013i	−0.573657	−	0.858538i
$327$			10.2871i			0.568878i
$328$	−3.52478	+	2.35518i	−0.194623	+	0.130043i
$329$	22.7152	+	15.1778i	1.25233	+	0.836780i
$330$	10.5594	+	4.62446i	0.581276	+	0.254568i
$331$	13.0602	+	5.40973i	0.717856	+	0.297346i	0.711551	−	0.702635i	$-0.247993\pi$
$331$	13.0602	+	5.40973i	0.717856	+	0.297346i	0.00630484	+	0.999980i	$0.497993\pi$
$332$	−2.03801	−	4.92020i	−0.111851	−	0.270031i
$333$	2.48107	+	1.65780i	0.135962	+	0.0908468i
$334$	−9.15185	+	13.6967i	−0.500767	+	0.749451i
$335$	0.0324595	−	1.61580i	0.00177345	−	0.0882804i
$336$	−2.02561	−	2.02561i	−0.110506	−	0.110506i
$337$	−0.598475	+	3.00874i	−0.0326010	+	0.163896i	−0.993656	−	0.112460i	$-0.964127\pi$
$337$	−0.598475	+	3.00874i	−0.0326010	+	0.163896i	0.961055	+	0.276356i	$0.0891270\pi$
$338$	4.16566	+	1.72547i	0.226582	+	0.0938534i
$339$	−11.0090			−0.597928
$340$	8.72326	+	2.98407i	0.473085	+	0.161834i
$341$	−51.4589			−2.78665
$342$	−1.97083	−	0.816345i	−0.106570	−	0.0441429i
$343$	−3.23794	+	16.2782i	−0.174833	+	0.878942i
$344$	2.29392	+	2.29392i	0.123680	+	0.123680i
$345$	−6.59861	+	6.33872i	−0.355257	+	0.341265i
$346$	−13.2480	+	19.8271i	−0.712218	+	1.06591i
$347$	19.3972	+	12.9608i	1.04130	+	0.695772i	0.953815	−	0.300394i	$-0.0971183\pi$
$347$	19.3972	+	12.9608i	1.04130	+	0.695772i	0.0874810	+	0.996166i	$0.472118\pi$
$348$	−1.67708	−	4.04884i	−0.0899011	−	0.217041i
$349$	−18.9376	−	7.84419i	−1.01370	−	0.419890i	−0.186899	−	0.982379i	$-0.559844\pi$
$349$	−18.9376	−	7.84419i	−1.01370	−	0.419890i	−0.826805	+	0.562489i	$0.809844\pi$
$350$	12.2193	−	7.47285i	0.653150	−	0.399441i
$351$	2.42286	+	1.61891i	0.129323	+	0.0864108i
$352$	4.28649	−	2.86414i	0.228471	−	0.152659i
$353$			24.6861i			1.31391i	0.753930	+	0.656955i	$0.228156\pi$
$353$			24.6861i			1.31391i	−0.753930	+	0.656955i	$0.771844\pi$
$354$	−4.91108	−	7.34995i	−0.261021	−	0.390645i
$355$	−0.485667	+	2.20878i	−0.0257765	+	0.117230i
$356$		−	2.48292i		−	0.131595i
$357$	−5.41099	−	10.4989i	−0.286380	−	0.555661i
$358$	7.96194	+	7.96194i	0.420801	+	0.420801i
$359$	29.9737	−	12.4155i	1.58195	−	0.655266i	0.593230	−	0.805033i	$-0.297852\pi$
$359$	29.9737	−	12.4155i	1.58195	−	0.655266i	0.988721	+	0.149767i	$0.0478524\pi$
$360$	−1.61258	+	1.54906i	−0.0849903	+	0.0816428i
$361$	−10.2173	+	10.2173i	−0.537751	+	0.537751i
$362$	−6.29929	−	9.42755i	−0.331083	−	0.495501i
$363$	15.2780	−	3.03899i	0.801889	−	0.159506i
$364$	−8.18706	+	1.62851i	−0.429119	+	0.0853570i
$365$	−2.31166	−	0.508288i	−0.120998	−	0.0266050i
$366$	5.07936	−	12.2627i	0.265502	−	0.640979i
$367$	−10.3446	+	15.4818i	−0.539984	+	0.808143i	−0.996675	−	0.0814828i	$-0.974034\pi$
$367$	−10.3446	+	15.4818i	−0.539984	+	0.808143i	0.456691	+	0.889625i	$0.349034\pi$
$368$	0.798303	+	4.01334i	0.0416144	+	0.209210i
$369$	0.827029	−	4.15776i	0.0430534	−	0.216444i
$370$	1.17001	+	6.56896i	0.0608258	+	0.341504i
$371$	−2.21415	+	1.47945i	−0.114953	+	0.0768092i
$372$	3.81983	−	9.22188i	0.198049	−	0.478132i
$373$	19.6537	−	19.6537i	1.01763	−	1.01763i	0.0177869	−	0.999842i	$-0.494338\pi$
$373$	19.6537	−	19.6537i	1.01763	−	1.01763i	0.999842	−	0.0177869i	$-0.00566204\pi$
$374$	20.4309	−	5.86463i	1.05646	−	0.303253i
$375$	−5.64036	−	9.65331i	−0.291267	−	0.498495i
$376$	−3.64954	−	8.81077i	−0.188211	−	0.454381i
$377$	−12.5248	−	2.49134i	−0.645061	−	0.128311i
$378$	2.86465			0.147342
$379$	−14.9033	−	2.96445i	−0.765531	−	0.152274i	−0.203145	−	0.979149i	$-0.565116\pi$
$379$	−14.9033	−	2.96445i	−0.765531	−	0.152274i	−0.562386	+	0.826875i	$0.690116\pi$
$380$	−1.73652	−	4.44268i	−0.0890817	−	0.227905i
$381$	−3.33105	−	16.7463i	−0.170655	−	0.857939i
$382$	11.0162	−	4.56306i	0.563638	−	0.233466i
$383$	−24.6164	+	10.1964i	−1.25784	+	0.521014i	−0.909246	−	0.416260i	$-0.863341\pi$
$383$	−24.6164	+	10.1964i	−1.25784	+	0.521014i	−0.348593	+	0.937274i	$0.613341\pi$
$384$	0.195090	+	0.980785i	0.00995566	+	0.0500505i
$385$	13.2475	−	30.2490i	0.675153	−	1.54163i
$386$	−22.7607	−	4.52739i	−1.15849	−	0.230438i
$387$	−3.24409			−0.164907
$388$	−4.27749	−	0.850845i	−0.217157	−	0.0431951i
$389$	4.45042	+	10.7443i	0.225645	+	0.544756i	0.995638	−	0.0932963i	$-0.0297404\pi$
$389$	4.45042	+	10.7443i	0.225645	+	0.544756i	−0.769993	+	0.638052i	$0.779740\pi$
$390$	1.14256	+	6.41484i	0.0578557	+	0.324828i
$391$	−1.90525	+	16.7637i	−0.0963526	+	0.847776i
$392$	−0.852927	+	0.852927i	−0.0430793	+	0.0430793i
$393$	0.193890	−	0.468091i	0.00978044	−	0.0236121i
$394$	17.0141	−	11.3685i	0.857157	−	0.572734i
$395$	8.19211	−	1.45911i	0.412190	−	0.0734159i
$396$	−1.00575	+	5.05627i	−0.0505410	+	0.254087i
$397$	2.04393	+	10.2755i	0.102582	+	0.515714i	0.997573	+	0.0696300i	$0.0221819\pi$
$397$	2.04393	+	10.2755i	0.102582	+	0.515714i	−0.894991	+	0.446084i	$0.852818\pi$
$398$	−0.287554	+	0.430355i	−0.0144138	+	0.0215717i
$399$	−2.33854	+	5.64574i	−0.117074	+	0.282641i
$400$	−4.99597	−	0.200807i	−0.249798	−	0.0100404i
$401$	10.6786	−	2.12411i	0.533265	−	0.106073i	0.0788895	−	0.996883i	$-0.474863\pi$
$401$	10.6786	−	2.12411i	0.533265	−	0.106073i	0.454375	+	0.890810i	$0.349863\pi$
$402$	0.708865	−	0.141002i	0.0353550	−	0.00703254i
$403$	−16.1594	−	24.1843i	−0.804958	−	1.20470i
$404$	−11.0186	+	11.0186i	−0.548195	+	0.548195i
$405$	0.0449109	−	2.23562i	0.00223164	−	0.111089i
$406$	−11.5985	+	4.80426i	−0.575624	+	0.238431i
$407$	10.8776	+	10.8776i	0.539184	+	0.539184i
$408$	−0.465607	+	4.09673i	−0.0230510	+	0.202818i
$409$			16.6033i			0.820982i	0.911865	+	0.410491i	$0.134643\pi$
$409$			16.6033i			0.820982i	−0.911865	+	0.410491i	$0.865357\pi$
$410$	7.98582	−	5.10698i	0.394392	−	0.252216i
$411$	7.44973	+	11.1493i	0.367468	+	0.549955i
$412$			17.5462i			0.864441i
$413$	−21.0550	+	14.0685i	−1.03605	+	0.692267i
$414$	−3.40235	−	2.27338i	−0.167216	−	0.111730i
$415$	4.33525	+	11.0912i	0.212809	+	0.544446i
$416$	2.69214	+	1.11512i	0.131993	+	0.0546733i
$417$	−6.68771	−	16.1456i	−0.327499	−	0.790652i
$418$	−9.14400	−	6.10983i	−0.447248	−	0.298841i
$419$	7.50113	−	11.2262i	0.366454	−	0.548438i	−0.601722	−	0.798705i	$-0.705519\pi$
$419$	7.50113	−	11.2262i	0.366454	−	0.548438i	0.968177	+	0.250268i	$0.0805186\pi$
$420$	4.43752	+	4.61947i	0.216529	+	0.225407i
$421$	6.87122	+	6.87122i	0.334883	+	0.334883i	0.854437	−	0.519554i	$-0.173902\pi$
$421$	6.87122	+	6.87122i	0.334883	+	0.334883i	−0.519554	+	0.854437i	$0.673902\pi$
$422$	0.0490468	−	0.246575i	0.00238756	−	0.0120031i
$423$	8.81077	+	3.64954i	0.428394	+	0.177447i
$424$	0.929587			0.0451447
$425$	−19.3679	−	7.06301i	−0.939479	−	0.342606i
$426$	−1.01139			−0.0490022
$427$	−35.1282	−	14.5506i	−1.69997	−	0.704152i
$428$	3.16433	−	15.9082i	0.152954	−	0.768950i
$429$	10.6224	+	10.6224i	0.512855	+	0.512855i
$430$	−5.02531	−	5.23135i	−0.242342	−	0.252278i
$431$	−11.8559	+	17.7436i	−0.571079	+	0.854680i	−0.998787	−	0.0492370i	$-0.984321\pi$
$431$	−11.8559	+	17.7436i	−0.571079	+	0.854680i	0.427708	+	0.903917i	$0.359321\pi$
$432$	−0.831470	−	0.555570i	−0.0400041	−	0.0267299i
$433$	−4.94767	−	11.9447i	−0.237770	−	0.574027i	0.759282	−	0.650762i	$-0.225551\pi$
$433$	−4.94767	−	11.9447i	−0.237770	−	0.574027i	−0.997052	+	0.0767348i	$0.975551\pi$
$434$	−26.4175	−	10.9425i	−1.26808	−	0.525256i
$435$	3.56748	+	9.12697i	0.171048	+	0.437605i
$436$	−8.55341	−	5.71521i	−0.409634	−	0.273709i
$437$	7.25793	−	4.84959i	0.347194	−	0.231987i
$438$		−	1.05850i		−	0.0505772i
$439$	11.0906	+	16.5982i	0.529324	+	0.792189i	0.995723	−	0.0923849i	$-0.0294490\pi$
$439$	11.0906	+	16.5982i	0.529324	+	0.792189i	−0.466399	+	0.884574i	$0.654449\pi$
$440$	−9.71159	+	6.21062i	−0.462982	+	0.296080i
$441$		−	1.20622i		−	0.0574391i
$442$	9.17205	+	7.76032i	0.436270	+	0.369121i
$443$	19.9292	+	19.9292i	0.946865	+	0.946865i	0.998658	−	0.0517928i	$-0.0164935\pi$
$443$	19.9292	+	19.9292i	0.946865	+	0.946865i	−0.0517928	+	0.998658i	$0.516494\pi$
$444$	−2.75682	+	1.14191i	−0.130833	+	0.0541928i
$445$	−0.111510	+	5.55086i	−0.00528610	+	0.263136i
$446$	3.52670	−	3.52670i	0.166994	−	0.166994i
$447$	5.19911	+	7.78102i	0.245909	+	0.368029i
$448$	2.80961	−	0.558866i	0.132741	−	0.0264039i
$449$	−16.7481	+	3.33139i	−0.790389	+	0.157218i	−0.573747	−	0.819033i	$-0.694511\pi$
$449$	−16.7481	+	3.33139i	−0.790389	+	0.157218i	−0.216643	+	0.976251i	$0.569511\pi$
$450$	3.67467	−	3.39069i	0.173226	−	0.159839i
$451$	8.36336	−	20.1909i	0.393815	−	0.950754i
$452$	6.11629	−	9.15367i	0.287686	−	0.430552i
$453$	−2.97253	−	14.9439i	−0.139662	−	0.702127i
$454$	3.70314	−	18.6169i	0.173797	−	0.873736i
$455$	18.3763	−	3.27303i	0.861493	−	0.153442i
$456$	1.77370	−	1.18515i	0.0830611	−	0.0554997i
$457$	−4.54442	+	10.9712i	−0.212579	+	0.513212i	−0.993818	−	0.111021i	$-0.964588\pi$
$457$	−4.54442	+	10.9712i	−0.212579	+	0.513212i	0.781239	+	0.624232i	$0.214588\pi$
$458$	4.73415	−	4.73415i	0.221212	−	0.221212i
$459$	−2.56759	−	3.22606i	−0.119845	−	0.150580i
$460$	−1.60446	−	9.00815i	−0.0748082	−	0.420007i
$461$	9.22805	+	22.2785i	0.429793	+	1.03761i	0.979353	+	0.202158i	$0.0647955\pi$
$461$	9.22805	+	22.2785i	0.429793	+	1.03761i	−0.549560	+	0.835454i	$0.685205\pi$
$462$	14.4844	+	2.88113i	0.673877	+	0.134042i
$463$	−8.52514			−0.396197			−0.198098	−	0.980182i	$-0.563477\pi$
$463$	−8.52514			−0.396197			−0.198098	+	0.980182i	$0.563477\pi$
$464$	4.29822	+	0.854970i	0.199540	+	0.0396910i
$465$	−8.95384	+	20.4450i	−0.415224	+	0.948116i
$466$	−0.346774	−	1.74335i	−0.0160640	−	0.0807592i
$467$	8.53520	−	3.53540i	0.394962	−	0.163599i	−0.176358	−	0.984326i	$-0.556432\pi$
$467$	8.53520	−	3.53540i	0.394962	−	0.163599i	0.571320	+	0.820728i	$0.306432\pi$
$468$	−2.69214	+	1.11512i	−0.124444	+	0.0515465i
$469$	−0.403921	−	2.03065i	−0.0186513	−	0.0937667i
$470$	7.76327	+	19.8614i	0.358093	+	0.916138i
$471$	−1.75752	−	0.349592i	−0.0809822	−	0.0161084i
$472$	8.83971			0.406880
$473$	−16.4030	−	3.26276i	−0.754211	−	0.150022i
$474$	1.42407	+	3.43802i	0.0654098	+	0.157913i
$475$	3.68267	+	10.0101i	0.168973	+	0.459296i
$476$	11.7357	+	1.33380i	0.537905	+	0.0611347i
$477$	−0.657317	+	0.657317i	−0.0300965	+	0.0300965i
$478$	6.69265	−	16.1575i	0.306115	−	0.739026i
$479$	−23.3716	+	15.6164i	−1.06787	+	0.713531i	−0.959821	−	0.280614i	$-0.909462\pi$
$479$	−23.3716	+	15.6164i	−1.06787	+	0.713531i	−0.108054	+	0.994145i	$0.534462\pi$
$480$	−0.392099	−	2.20142i	−0.0178968	−	0.100481i
$481$	−1.69633	+	8.52804i	−0.0773461	+	0.388845i
$482$	5.21864	+	26.2359i	0.237703	+	1.19501i
$483$	−6.51243	+	9.74653i	−0.296326	+	0.443483i
$484$	−5.96120	+	14.3916i	−0.270964	+	0.654164i
$485$	9.52461	+	2.09427i	0.432490	+	0.0950959i
$486$	0.980785	−	0.195090i	0.0444893	−	0.00884948i
$487$	33.5162	−	6.66678i	1.51876	−	0.302101i	0.635915	−	0.771759i	$-0.280623\pi$
$487$	33.5162	−	6.66678i	1.51876	−	0.302101i	0.882848	+	0.469659i	$0.155623\pi$
$488$	7.37408	+	11.0361i	0.333809	+	0.499581i
$489$	−13.1828	+	13.1828i	−0.596146	+	0.596146i
$490$	1.94512	−	1.86851i	0.0878717	−	0.0844107i
$491$	−1.64980	+	0.683369i	−0.0744544	+	0.0308400i	−0.419600	−	0.907709i	$-0.637830\pi$
$491$	−1.64980	+	0.683369i	−0.0744544	+	0.0308400i	0.345145	+	0.938549i	$0.387830\pi$
$492$	2.99758	+	2.99758i	0.135141	+	0.135141i
$493$	15.8061	+	8.75573i	0.711873	+	0.394338i
$494$		−	6.21608i		−	0.279675i
$495$	2.47556	−	11.2587i	0.111268	−	0.506041i
$496$	5.54553	+	8.29948i	0.249002	+	0.372657i
$497$			2.89729i			0.129961i
$498$	−4.42806	+	2.95874i	−0.198426	+	0.132584i
$499$	12.2769	+	8.20318i	0.549591	+	0.367225i	0.799147	−	0.601135i	$-0.205285\pi$
$499$	12.2769	+	8.20318i	0.549591	+	0.367225i	−0.249556	+	0.968360i	$0.580285\pi$
$500$	11.1600	+	0.673302i	0.499093	+	0.0301110i
$501$	15.2190	+	6.30391i	0.679934	+	0.281638i
$502$	−0.905322	−	2.18564i	−0.0404065	−	0.0975499i
$503$	25.7576	+	17.2107i	1.14847	+	0.767386i	0.976031	−	0.217633i	$-0.0698337\pi$
$503$	25.7576	+	17.2107i	1.14847	+	0.767386i	0.172444	+	0.985019i	$0.444834\pi$
$504$	−1.59151	+	2.38187i	−0.0708917	+	0.106097i
$505$	25.1282	−	24.1385i	1.11819	−	1.07415i
$506$	−14.9167	−	14.9167i	−0.663129	−	0.663129i
$507$	0.879639	−	4.42224i	0.0390661	−	0.196399i
$508$	15.7747	+	6.53408i	0.699888	+	0.289903i
$509$	41.6177			1.84467			0.922336	−	0.386389i	$-0.126278\pi$
$509$	41.6177			1.84467			0.922336	+	0.386389i	$0.126278\pi$
$510$	1.22491	−	9.13781i	0.0542398	−	0.404629i
$511$	−3.03224			−0.134138
$512$	−0.923880	−	0.382683i	−0.0408301	−	0.0169124i
$513$	−0.416169	+	2.09222i	−0.0183743	+	0.0923739i
$514$	−5.66415	−	5.66415i	−0.249835	−	0.249835i
$515$	0.788018	−	39.2267i	0.0347242	−	1.72853i
$516$	1.80232	−	2.69737i	0.0793428	−	0.118745i
$517$	40.8790	+	27.3145i	1.79786	+	1.20129i
$518$	3.27118	+	7.89732i	0.143727	+	0.346988i
$519$	22.0307	+	9.12540i	0.967039	+	0.400561i
$520$	−5.96851	−	2.61389i	−0.261737	−	0.114627i
$521$	15.9242	+	10.6402i	0.697652	+	0.466156i	0.853140	−	0.521682i	$-0.174695\pi$
$521$	15.9242	+	10.6402i	0.697652	+	0.466156i	−0.155489	+	0.987838i	$0.549695\pi$
$522$	−3.64386	+	2.43475i	−0.159487	+	0.106566i
$523$			30.4063i			1.32957i	0.747033	+	0.664787i	$0.231478\pi$
$523$			30.4063i			1.32957i	−0.747033	+	0.664787i	$0.768522\pi$
$524$	0.281484	+	0.421271i	0.0122967	+	0.0184033i
$525$	−9.71314	−	10.5267i	−0.423916	−	0.459421i
$526$		−	14.0342i		−	0.611922i
$527$	11.3550	+	39.5581i	0.494633	+	1.72318i
$528$	−3.64536	−	3.64536i	−0.158644	−	0.158644i
$529$	−5.77961	+	2.39399i	−0.251287	+	0.104087i
$530$	−2.07820	−	0.0417486i	−0.0902712	−	0.00181344i
$531$	−6.25062	+	6.25062i	−0.271254	+	0.271254i
$532$	−3.39504	−	5.08103i	−0.147194	−	0.220291i
$533$	12.1155	−	2.40992i	0.524781	−	0.104385i
$534$	−2.43521	+	0.484394i	−0.105382	+	0.0209618i
$535$	−7.78868	+	35.4224i	−0.336734	+	1.53145i
$536$	−0.276585	+	0.667736i	−0.0119467	+	0.0288418i
$537$	6.25565	−	9.36225i	0.269951	−	0.404011i
$538$	4.88666	+	24.5669i	0.210679	+	1.05915i
$539$	1.21316	−	6.09897i	0.0522545	−	0.262701i
$540$	1.83390	+	1.27938i	0.0789183	+	0.0550559i
$541$	−17.9984	+	12.0262i	−0.773813	+	0.517045i	−0.878663	−	0.477443i	$-0.841564\pi$
$541$	−17.9984	+	12.0262i	−0.773813	+	0.517045i	0.104850	+	0.994488i	$0.466564\pi$
$542$	9.30268	−	22.4586i	0.399584	−	0.964682i
$543$	−8.01747	+	8.01747i	−0.344063	+	0.344063i
$544$	−3.14763	−	2.66316i	−0.134954	−	0.114182i
$545$	18.8655	+	13.1612i	0.808108	+	0.563762i
$546$	3.19443	+	7.71204i	0.136709	+	0.330045i
$547$	14.0128	+	2.78732i	0.599144	+	0.119177i	0.485339	−	0.874326i	$-0.338696\pi$
$547$	14.0128	+	2.78732i	0.599144	+	0.119177i	0.113805	+	0.993503i	$0.463696\pi$
$548$	−13.4092			−0.572811
$549$	−13.0180	−	2.58943i	−0.555593	−	0.110514i
$550$	21.9903	−	13.4484i	0.937671	−	0.573442i
$551$	−1.82383	−	9.16902i	−0.0776979	−	0.390613i
$552$	3.78049	−	1.56593i	0.160908	−	0.0666503i
$553$	9.84871	−	4.07947i	0.418810	−	0.173477i
$554$	−1.92133	−	9.65916i	−0.0816294	−	0.410379i
$555$	6.21448	−	2.42907i	0.263790	−	0.103108i
$556$	17.1400	+	3.40937i	0.726900	+	0.144589i
$557$	−23.6649			−1.00271			−0.501357	−	0.865241i	$-0.667166\pi$
$557$	−23.6649			−1.00271			−0.501357	+	0.865241i	$0.667166\pi$
$558$	−9.78990	−	1.94733i	−0.414439	−	0.0824371i
$559$	−3.61756	−	8.73356i	−0.153006	−	0.369390i
$560$	−6.30630	+	1.12323i	−0.266490	+	0.0474650i
$561$	−9.73781	−	18.8942i	−0.411131	−	0.797713i
$562$	23.2457	−	23.2457i	0.980559	−	0.980559i
$563$	−2.07225	+	5.00284i	−0.0873347	+	0.210845i	−0.961512	−	0.274761i	$-0.911401\pi$
$563$	−2.07225	+	5.00284i	−0.0873347	+	0.210845i	0.874178	+	0.485606i	$0.161401\pi$
$564$	−7.92948	+	5.29831i	−0.333891	+	0.223099i
$565$	−14.0848	+	20.1894i	−0.592551	+	0.849375i
$566$	0.622785	−	3.13095i	0.0261776	−	0.131604i
$567$	−0.558866	−	2.80961i	−0.0234701	−	0.117992i
$568$	0.561901	−	0.840944i	0.0235768	−	0.0352852i
$569$	−5.48001	+	13.2299i	−0.229734	+	0.554627i	−0.996145	−	0.0877239i	$-0.972041\pi$
$569$	−5.48001	+	13.2299i	−0.229734	+	0.554627i	0.766411	+	0.642351i	$0.222041\pi$
$570$	−4.01854	+	2.56988i	−0.168318	+	0.107640i
$571$	−45.0903	+	8.96903i	−1.88697	+	0.375342i	−0.996776	−	0.0802357i	$-0.974433\pi$
$571$	−45.0903	+	8.96903i	−1.88697	+	0.375342i	−0.890196	+	0.455578i	$0.849433\pi$
$572$	−14.7337	+	2.93072i	−0.616048	+	0.122539i
$573$	−6.62453	−	9.91431i	−0.276744	−	0.414176i
$574$	8.58701	−	8.58701i	0.358415	−	0.358415i
$575$	3.18239	+	20.2108i	0.132715	+	0.842850i
$576$	0.923880	−	0.382683i	0.0384950	−	0.0159451i
$577$	−5.05738	−	5.05738i	−0.210541	−	0.210541i	0.593956	−	0.804497i	$-0.297565\pi$
$577$	−5.05738	−	5.05738i	−0.210541	−	0.210541i	−0.804497	+	0.593956i	$0.797565\pi$
$578$	−9.01666	−	14.4118i	−0.375044	−	0.599452i
$579$			23.2066i			0.964435i
$580$	−9.57079	−	2.10442i	−0.397405	−	0.0873814i
$581$	8.47575	+	12.6849i	0.351633	+	0.526256i
$582$			4.36129i			0.180781i
$583$	−3.98467	+	2.66247i	−0.165028	+	0.110268i
$584$	0.880112	+	0.588072i	0.0364193	+	0.0243346i
$585$	6.06868	−	2.37208i	0.250909	−	0.0980733i
$586$	27.4381	+	11.3652i	1.13346	+	0.469493i
$587$	1.64902	+	3.98108i	0.0680622	+	0.164317i	0.954250	−	0.299009i	$-0.0966560\pi$
$587$	1.64902	+	3.98108i	0.0680622	+	0.164317i	−0.886188	+	0.463326i	$0.846656\pi$
$588$	1.00294	+	0.670140i	0.0413604	+	0.0276361i
$589$	11.8298	−	17.7045i	0.487438	−	0.729503i
$590$	−19.7622	−	0.396999i	−0.813597	−	0.0163442i
$591$	−14.4693	−	14.4693i	−0.595187	−	0.595187i
$592$	0.582142	−	2.92662i	0.0239259	−	0.120284i
$593$	23.6817	+	9.80928i	0.972491	+	0.402819i	0.811639	−	0.584160i	$-0.198576\pi$
$593$	23.6817	+	9.80928i	0.972491	+	0.402819i	0.160852	+	0.986979i	$0.448576\pi$
$594$	5.15532			0.211525
$595$	−26.1766	−	3.50893i	−1.07314	−	0.143852i
$596$	−9.35815			−0.383325
$597$	0.478185	+	0.198071i	0.0195708	+	0.00810649i
$598$	2.32622	−	11.6947i	0.0951261	−	0.478231i
$599$	−7.96906	−	7.96906i	−0.325607	−	0.325607i	0.525306	−	0.850913i	$-0.323951\pi$
$599$	−7.96906	−	7.96906i	−0.325607	−	0.325607i	−0.850913	+	0.525306i	$0.823951\pi$
$600$	0.777716	+	4.93915i	0.0317501	+	0.201640i
$601$	19.7014	−	29.4853i	0.803638	−	1.20273i	−0.172378	−	0.985031i	$-0.555145\pi$
$601$	19.7014	−	29.4853i	0.803638	−	1.20273i	0.976016	−	0.217699i	$-0.0698550\pi$
$602$	−7.72701	−	5.16302i	−0.314929	−	0.210429i
$603$	−0.276585	−	0.667736i	−0.0112634	−	0.0271923i
$604$	14.0769	+	5.83083i	0.572780	+	0.237253i
$605$	13.9733	−	31.9064i	0.568095	−	1.29718i
$606$	12.9565	+	8.65724i	0.526321	+	0.351676i
$607$	−3.04570	+	2.03507i	−0.123621	+	0.0826009i	−0.615843	−	0.787869i	$-0.711185\pi$
$607$	−3.04570	+	2.03507i	−0.123621	+	0.0826009i	0.492222	+	0.870469i	$0.336185\pi$
$608$			2.13321i			0.0865132i
$609$	6.97470	+	10.4384i	0.282629	+	0.422985i
$610$	−15.9900	−	25.0037i	−0.647416	−	1.01237i
$611$			27.7895i			1.12424i
$612$	4.10885	−	0.342572i	0.166090	−	0.0138477i
$613$	3.11578	+	3.11578i	0.125845	+	0.125845i	0.767224	−	0.641379i	$-0.221637\pi$
$613$	3.11578	+	3.11578i	0.125845	+	0.125845i	−0.641379	+	0.767224i	$0.721637\pi$
$614$	−23.8381	+	9.87406i	−0.962027	+	0.398484i
$615$	−6.56681	−	6.83605i	−0.264799	−	0.275656i
$616$	−10.4427	+	10.4427i	−0.420748	+	0.420748i
$617$	−0.998915	−	1.49498i	−0.0402148	−	0.0601857i	0.810817	−	0.585299i	$-0.199023\pi$
$617$	−0.998915	−	1.49498i	−0.0402148	−	0.0601857i	−0.851032	+	0.525113i	$0.824023\pi$
$618$	17.2091	−	3.42310i	0.692251	−	0.137697i
$619$	−36.8350	+	7.32693i	−1.48052	+	0.294494i	−0.868240	−	0.496145i	$-0.834748\pi$
$619$	−36.8350	+	7.32693i	−1.48052	+	0.294494i	−0.612282	+	0.790639i	$0.709748\pi$
$620$	−12.0249	−	18.8035i	−0.482934	−	0.755167i
$621$	−1.56593	+	3.78049i	−0.0628385	+	0.151706i
$622$	7.81364	−	11.6939i	0.313299	−	0.468884i
$623$	1.38762	+	6.97604i	0.0555938	+	0.279489i
$624$	0.568484	−	2.85796i	0.0227576	−	0.114410i
$625$	−24.9194	−	2.00645i	−0.996774	−	0.0802581i
$626$	1.54328	−	1.03118i	0.0616817	−	0.0412144i
$627$	−4.20852	+	10.1603i	−0.168072	+	0.405762i
$628$	1.26710	−	1.26710i	0.0505628	−	0.0505628i
$629$	5.96170	−	10.7623i	0.237709	−	0.429120i
$630$	3.66499	−	5.25347i	0.146017	−	0.209303i
$631$	−10.8550	−	26.2062i	−0.432130	−	1.04325i	−0.978599	−	0.205774i	$-0.934029\pi$
$631$	−10.8550	−	26.2062i	−0.432130	−	1.04325i	0.546470	−	0.837479i	$-0.315971\pi$
$632$	−3.64978	−	0.725986i	−0.145180	−	0.0288782i
$633$	−0.251406			−0.00999248
$634$	23.6250	+	4.69930i	0.938268	+	0.186633i
$635$	−34.9727	−	15.3162i	−1.38785	−	0.607803i
$636$	−0.181353	−	0.911725i	−0.00719113	−	0.0361522i
$637$	3.24732	−	1.34508i	0.128663	−	0.0532941i
$638$	−20.8731	+	8.64591i	−0.826373	+	0.342295i
$639$	0.197313	+	0.991961i	0.00780560	+	0.0392414i
$640$	2.04825	+	0.897026i	0.0809644	+	0.0354581i
$641$	−23.6445	−	4.70318i	−0.933901	−	0.185764i	−0.295390	−	0.955377i	$-0.595449\pi$
$641$	−23.6445	−	4.70318i	−0.933901	−	0.185764i	−0.638511	+	0.769612i	$0.720449\pi$
$642$	−16.2198			−0.640145
$643$	22.2003	+	4.41591i	0.875493	+	0.174146i	0.612327	−	0.790604i	$-0.290233\pi$
$643$	22.2003	+	4.41591i	0.875493	+	0.174146i	0.263166	+	0.964751i	$0.415233\pi$
$644$	−4.48584	−	10.8298i	−0.176767	−	0.426753i
$645$	−4.15044	+	5.94933i	−0.163423	+	0.234255i
$646$	−2.67909	+	8.37750i	−0.105407	+	0.329608i
$647$	16.3975	−	16.3975i	0.644651	−	0.644651i	−0.307044	−	0.951695i	$-0.599340\pi$
$647$	16.3975	−	16.3975i	0.644651	−	0.644651i	0.951695	+	0.307044i	$0.0993400\pi$
$648$	−0.382683	+	0.923880i	−0.0150332	+	0.0362934i
$649$	−37.8914	+	25.3182i	−1.48737	+	0.993826i
$650$	13.2259	+	6.11171i	0.518763	+	0.239721i
$651$	−5.57842	+	28.0446i	−0.218636	+	1.09916i
$652$	−3.63712	−	18.2850i	−0.142441	−	0.716098i
$653$	3.49890	−	5.23648i	0.136923	−	0.204919i	−0.756671	−	0.653796i	$-0.773176\pi$
$653$	3.49890	−	5.23648i	0.136923	−	0.204919i	0.893594	+	0.448876i	$0.148176\pi$
$654$	−3.93670	+	9.50404i	−0.153937	+	0.371637i
$655$	−0.610371	−	0.954442i	−0.0238492	−	0.0372931i
$656$	−4.15776	+	0.827029i	−0.162333	+	0.0322901i
$657$	−1.03816	+	0.206504i	−0.0405026	+	0.00805647i
$658$	15.1778	+	22.7152i	0.591693	+	0.885530i
$659$	13.4704	−	13.4704i	0.524734	−	0.524734i	−0.394263	−	0.918997i	$-0.629000\pi$
$659$	13.4704	−	13.4704i	0.524734	−	0.524734i	0.918997	+	0.394263i	$0.129000\pi$
$660$	7.98592	+	8.31335i	0.310852	+	0.323597i
$661$	15.0039	−	6.21483i	0.583585	−	0.241729i	−0.0713030	−	0.997455i	$-0.522716\pi$
$661$	15.0039	−	6.21483i	0.583585	−	0.241729i	0.654888	+	0.755726i	$0.272716\pi$
$662$	9.99588	+	9.99588i	0.388501	+	0.388501i
$663$	5.82183	−	10.5098i	0.226101	−	0.408166i
$664$		−	5.32559i		−	0.206673i
$665$	7.36181	+	11.5117i	0.285479	+	0.446405i
$666$	1.65780	+	2.48107i	0.0642384	+	0.0961396i
$667$		−	17.9328i		−	0.694360i
$668$	−13.6967	+	9.15185i	−0.529942	+	0.354096i
$669$	−4.14697	−	2.77091i	−0.160331	−	0.107130i
$670$	0.648327	−	1.48038i	0.0250471	−	0.0571921i
$671$	−63.2180	−	26.1857i	−2.44050	−	1.01089i
$672$	−1.09625	−	2.64659i	−0.0422889	−	0.102094i
$673$	26.2658	+	17.5502i	1.01247	+	0.676511i	0.946964	−	0.321341i	$-0.104134\pi$
$673$	26.2658	+	17.5502i	1.01247	+	0.676511i	0.0655070	+	0.997852i	$0.479134\pi$
$674$	−1.70431	+	2.55069i	−0.0656477	+	0.0982488i
$675$	−4.04243	−	2.94258i	−0.155593	−	0.113260i
$676$	3.18826	+	3.18826i	0.122625	+	0.122625i
$677$	2.70173	−	13.5825i	0.103836	−	0.522017i	−0.893500	−	0.449064i	$-0.851758\pi$
$677$	2.70173	−	13.5825i	0.103836	−	0.522017i	0.997335	−	0.0729535i	$-0.0232425\pi$
$678$	−10.1710	−	4.21297i	−0.390615	−	0.161798i
$679$	12.4936			0.479459
$680$	6.91729	+	6.09517i	0.265266	+	0.233739i
$681$	−18.9817			−0.727379
$682$	−47.5418	−	19.6925i	−1.82047	−	0.754063i
$683$	2.46337	−	12.3842i	0.0942583	−	0.473868i	−0.904607	−	0.426246i	$-0.859836\pi$
$683$	2.46337	−	12.3842i	0.0942583	−	0.473868i	0.998865	−	0.0476221i	$-0.0151643\pi$
$684$	−1.50841	−	1.50841i	−0.0576754	−	0.0576754i
$685$	29.9777	+	0.602218i	1.14539	+	0.0230096i
$686$	−9.22088	+	13.8000i	−0.352055	+	0.526887i
$687$	−5.56677	−	3.71960i	−0.212386	−	0.141912i
$688$	1.24146	+	2.99715i	0.0473302	+	0.114265i
$689$	−2.50258	−	1.03660i	−0.0953406	−	0.0394914i
$690$	−8.52204	+	3.33103i	−0.324429	+	0.126810i
$691$	−16.7704	−	11.2056i	−0.637976	−	0.426282i	0.194071	−	0.980988i	$-0.437831\pi$
$691$	−16.7704	−	11.2056i	−0.637976	−	0.426282i	−0.832047	+	0.554706i	$0.812831\pi$
$692$	−19.8271	+	13.2480i	−0.753712	+	0.503614i
$693$		−	14.7682i		−	0.560997i
$694$	12.9608	+	19.3972i	0.491985	+	0.736308i
$695$	−38.1655	−	8.39181i	−1.44770	−	0.318320i
$696$		−	4.38243i		−	0.166116i
$697$	−17.3669	−	1.97381i	−0.657819	−	0.0747633i
$698$	−14.4942	−	14.4942i	−0.548613	−	0.548613i
$699$	−1.64220	+	0.680222i	−0.0621138	+	0.0257284i
$700$	14.1489	−	2.22788i	0.534779	−	0.0842061i
$701$	−1.56960	+	1.56960i	−0.0592831	+	0.0592831i	−0.736127	−	0.676844i	$-0.763347\pi$
$701$	−1.56960	+	1.56960i	−0.0592831	+	0.0592831i	0.676844	+	0.736127i	$0.263347\pi$
$702$	1.61891	+	2.42286i	0.0611016	+	0.0914451i
$703$	−6.24311	+	1.24183i	−0.235463	+	0.0468366i
$704$	5.05627	−	1.00575i	0.190565	−	0.0379058i
$705$	17.9652	−	11.4889i	0.676610	−	0.432696i
$706$	−9.44697	+	22.8070i	−0.355541	+	0.858353i
$707$	24.8000	−	37.1158i	0.932698	−	1.39588i
$708$	−1.72454	−	8.66985i	−0.0648122	−	0.325833i
$709$	−5.01075	+	25.1907i	−0.188182	+	0.946057i	0.765085	+	0.643929i	$0.222697\pi$
$709$	−5.01075	+	25.1907i	−0.188182	+	0.946057i	−0.953267	+	0.302128i	$0.902303\pi$
$710$	−1.29396	+	1.85479i	−0.0485616	+	0.0696092i
$711$	3.09413	−	2.06743i	0.116039	−	0.0775348i
$712$	0.950173	−	2.29392i	0.0356093	−	0.0859683i
$713$	28.8816	−	28.8816i	1.08163	−	1.08163i
$714$	−0.981349	−	11.7704i	−0.0367261	−	0.440497i
$715$	33.0706	−	5.89026i	1.23677	−	0.220283i
$716$	4.30897	+	10.4028i	0.161034	+	0.388770i
$717$	−17.1527	−	3.41188i	−0.640579	−	0.127419i
$718$	32.4433			1.21077
$719$	−32.3970	−	6.44417i	−1.20821	−	0.240327i	−0.450412	−	0.892821i	$-0.648723\pi$
$719$	−32.3970	−	6.44417i	−1.20821	−	0.240327i	−0.757794	+	0.652494i	$0.773723\pi$
$720$	−2.08263	+	0.814041i	−0.0776149	+	0.0303375i
$721$	−9.80599	−	49.2980i	−0.365194	−	1.83595i
$722$	−13.3495	+	5.52955i	−0.496817	+	0.205789i
$723$	24.7137	−	10.2367i	0.919111	−	0.380708i
$724$	−2.21202	−	11.1206i	−0.0822089	−	0.413292i
$725$	21.3021	+	5.13452i	0.791140	+	0.190691i
$726$	15.2780	+	3.03899i	0.567021	+	0.112788i
$727$	−42.1614			−1.56368			−0.781841	−	0.623478i	$-0.785719\pi$
$727$	−42.1614			−1.56368			−0.781841	+	0.623478i	$0.785719\pi$
$728$	−8.18706	−	1.62851i	−0.303433	−	0.0603565i
$729$	−0.382683	−	0.923880i	−0.0141735	−	0.0342178i
$730$	−1.94118	−	1.35423i	−0.0718464	−	0.0501223i
$731$	1.11134	+	13.3295i	0.0411042	+	0.493009i
$732$	9.38543	−	9.38543i	0.346895	−	0.346895i
$733$	8.85117	−	21.3686i	0.326926	−	0.789268i	−0.671892	−	0.740649i	$-0.734518\pi$
$733$	8.85117	−	21.3686i	0.326926	−	0.789268i	0.998817	−	0.0486189i	$-0.0154820\pi$
$734$	−15.4818	+	10.3446i	−0.571443	+	0.381826i
$735$	−2.21208	−	1.54322i	−0.0815939	−	0.0569225i
$736$	−0.798303	+	4.01334i	−0.0294259	+	0.147934i
$737$	−0.726911	−	3.65443i	−0.0267761	−	0.134613i
$738$	2.35518	−	3.52478i	0.0866954	−	0.129749i
$739$	15.9741	−	38.5648i	0.587616	−	1.41863i	−0.298159	−	0.954516i	$-0.596373\pi$
$739$	15.9741	−	38.5648i	0.587616	−	1.41863i	0.885775	−	0.464114i	$-0.153627\pi$
$740$	−1.43288	+	6.51667i	−0.0526738	+	0.239557i
$741$	−6.09664	+	1.21270i	−0.223966	+	0.0445495i
$742$	−2.61177	+	0.519514i	−0.0958812	+	0.0190720i
$743$	11.2753	+	16.8747i	0.413651	+	0.619072i	0.978531	−	0.206101i	$-0.0660775\pi$
$743$	11.2753	+	16.8747i	0.413651	+	0.619072i	−0.564880	+	0.825173i	$0.691077\pi$
$744$	7.05812	−	7.05812i	0.258763	−	0.258763i
$745$	20.9212	+	0.420283i	0.766495	+	0.0153980i
$746$	25.6788	−	10.6365i	0.940166	−	0.389430i
$747$	3.76576	+	3.76576i	0.137782	+	0.137782i
$748$	21.1200	+	2.40036i	0.772223	+	0.0877657i
$749$			46.4641i			1.69776i
$750$	−1.51685	−	11.0770i	−0.0553876	−	0.404474i
$751$	−17.7241	−	26.5260i	−0.646763	−	0.967949i	−0.999481	−	0.0322193i	$-0.989743\pi$
$751$	−17.7241	−	26.5260i	−0.646763	−	0.967949i	0.352718	−	0.935730i	$-0.385257\pi$
$752$		−	9.53671i		−	0.347768i
$753$	−1.96702	+	1.31432i	−0.0716823	+	0.0478966i
$754$	−10.6180	−	7.09474i	−0.386686	−	0.258375i
$755$	−31.2086	−	13.6677i	−1.13580	−	0.497419i
$756$	2.64659	+	1.09625i	0.0962556	+	0.0398704i
$757$	−2.28255	−	5.51056i	−0.0829607	−	0.200285i	0.876956	−	0.480571i	$-0.159571\pi$
$757$	−2.28255	−	5.51056i	−0.0829607	−	0.200285i	−0.959916	+	0.280286i	$0.909571\pi$
$758$	−12.6344	−	8.44204i	−0.458902	−	0.306629i
$759$	−11.7200	+	17.5402i	−0.425409	+	0.636669i
$760$	0.0958045	−	4.76904i	0.00347520	−	0.172991i
$761$	18.5412	+	18.5412i	0.672117	+	0.672117i	0.958204	−	0.286087i	$-0.0923546\pi$
$761$	18.5412	+	18.5412i	0.672117	+	0.672117i	−0.286087	+	0.958204i	$0.592355\pi$
$762$	3.33105	−	16.7463i	0.120671	−	0.606654i
$763$	27.2257	+	11.2773i	0.985638	+	0.408265i
$764$	11.9238			0.431390
$765$	−9.20120	+	0.581328i	−0.332670	+	0.0210179i
$766$	−26.6446			−0.962708
$767$	−23.7977	−	9.85734i	−0.859286	−	0.355928i
$768$	−0.195090	+	0.980785i	−0.00703972	+	0.0353910i
$769$	2.65469	+	2.65469i	0.0957307	+	0.0957307i	0.753350	−	0.657620i	$-0.228437\pi$
$769$	2.65469	+	2.65469i	0.0957307	+	0.0957307i	−0.657620	+	0.753350i	$0.728437\pi$
$770$	23.8149	−	22.8769i	0.858228	−	0.824425i
$771$	−4.45030	+	6.66034i	−0.160274	+	0.239866i
$772$	−19.2956	−	12.8929i	−0.694464	−	0.464026i
$773$	−4.66751	−	11.2684i	−0.167879	−	0.405295i	0.817441	−	0.576012i	$-0.195392\pi$
$773$	−4.66751	−	11.2684i	−0.167879	−	0.405295i	−0.985320	+	0.170717i	$0.945392\pi$
$774$	−2.99715	−	1.24146i	−0.107730	−	0.0446234i
$775$	26.0387	+	42.5775i	0.935338	+	1.52943i
$776$	−3.62628	−	2.42300i	−0.130176	−	0.0869807i
$777$	7.10740	−	4.74902i	0.254977	−	0.170370i
$778$			11.6295i			0.416938i
$779$	5.02410	+	7.51909i	0.180007	+	0.269399i
$780$	−1.39927	+	6.36378i	−0.0501018	+	0.227860i
$781$			5.21407i			0.186574i
$782$	−8.17541	+	14.7585i	−0.292352	+	0.527764i
$783$	3.09885	+	3.09885i	0.110744	+	0.110744i
$784$	−1.11440	+	0.461601i	−0.0398001	+	0.0164857i
$785$	−2.88966	+	2.77585i	−0.103136	+	0.0990742i
$786$	0.358261	−	0.358261i	0.0127788	−	0.0127788i
$787$	8.04727	+	12.0436i	0.286854	+	0.429308i	0.946711	−	0.322084i	$-0.104383\pi$
$787$	8.04727	+	12.0436i	0.286854	+	0.429308i	−0.659857	+	0.751391i	$0.729383\pi$
$788$	20.0695	−	3.99207i	0.714946	−	0.142212i
$789$	−13.7646	+	2.73794i	−0.490032	+	0.0974734i
$790$	8.12690	+	1.78694i	0.289142	+	0.0635765i
$791$	−12.0687	+	29.1364i	−0.429113	+	1.03597i
$792$	−2.86414	+	4.28649i	−0.101773	+	0.152314i
$793$	−7.54549	−	37.9337i	−0.267948	−	1.34707i
$794$	−2.04393	+	10.2755i	−0.0725364	+	0.364665i
$795$	0.364490	+	2.04641i	0.0129271	+	0.0725788i
$796$	−0.430355	+	0.287554i	−0.0152535	+	0.0101921i
$797$	8.16699	−	19.7169i	0.289290	−	0.698407i	−0.710697	−	0.703498i	$-0.751621\pi$
$797$	8.16699	−	19.7169i	0.289290	−	0.698407i	0.999987	+	0.00509100i	$0.00162052\pi$
$798$	−4.32106	+	4.32106i	−0.152964	+	0.152964i
$799$	11.9771	−	37.4524i	0.423719	−	1.32497i
$800$	−4.53883	−	2.09740i	−0.160472	−	0.0741541i
$801$	0.950173	+	2.29392i	0.0335727	+	0.0810517i
$802$	10.6786	+	2.12411i	0.377075	+	0.0750049i
$803$	−5.45692			−0.192571
$804$	0.708865	+	0.141002i	0.0249997	+	0.00497275i
$805$	9.54224	+	24.4127i	0.336320	+	0.860434i
$806$	−5.67443	−	28.5273i	−0.199873	−	1.00483i
$807$	23.1415	−	9.58553i	0.814620	−	0.337427i
$808$	−14.3965	+	5.96321i	−0.506466	+	0.209785i
$809$	8.67977	+	43.6361i	0.305164	+	1.53416i	0.763749	+	0.645514i	$0.223357\pi$
$809$	8.67977	+	43.6361i	0.305164	+	1.53416i	−0.458584	+	0.888651i	$0.651643\pi$
$810$	0.897026	−	2.04825i	0.0315183	−	0.0719683i
$811$	36.9214	+	7.34412i	1.29648	+	0.257887i	0.794645	−	0.607074i	$-0.207657\pi$
$811$	36.9214	+	7.34412i	1.29648	+	0.257887i	0.501839	+	0.864961i	$0.332657\pi$
$812$	−12.5541			−0.440564
$813$	−23.8420	−	4.74246i	−0.836175	−	0.166325i
$814$	5.88693	+	14.2123i	0.206337	+	0.498141i
$815$	7.31001	+	41.0417i	0.256059	+	1.43763i
$816$	−1.99792	+	3.60671i	−0.0699411	+	0.126260i
$817$	4.89342	−	4.89342i	0.171199	−	0.171199i
$818$	−6.35382	+	15.3395i	−0.222156	+	0.536332i
$819$	6.94065	−	4.63760i	0.242526	−	0.162051i
$820$	9.33229	−	1.66219i	0.325898	−	0.0580463i
$821$	6.32641	−	31.8050i	0.220793	−	1.11000i	−0.698253	−	0.715851i	$-0.746039\pi$
$821$	6.32641	−	31.8050i	0.220793	−	1.11000i	0.919046	−	0.394151i	$-0.128961\pi$
$822$	2.61600	+	13.1515i	0.0912434	+	0.458712i
$823$	−14.8471	+	22.2202i	−0.517536	+	0.774547i	−0.994540	−	0.104354i	$-0.966723\pi$
$823$	−14.8471	+	22.2202i	−0.517536	+	0.774547i	0.477004	+	0.878901i	$0.341723\pi$
$824$	−6.71465	+	16.2106i	−0.233916	+	0.564723i
$825$	−17.4801	−	18.9441i	−0.608579	−	0.659550i
$826$	−24.8361	+	4.94021i	−0.864158	+	0.171892i
$827$	41.6428	−	8.28326i	1.44806	−	0.288037i	0.592429	−	0.805622i	$-0.298169\pi$
$827$	41.6428	−	8.28326i	1.44806	−	0.288037i	0.855632	+	0.517585i	$0.173169\pi$
$828$	−2.27338	−	3.40235i	−0.0790053	−	0.118240i
$829$	21.7736	−	21.7736i	0.756229	−	0.756229i	−0.219405	−	0.975634i	$-0.570411\pi$
$829$	21.7736	−	21.7736i	0.756229	−	0.756229i	0.975634	+	0.219405i	$0.0704115\pi$
$830$	−0.239177	+	11.9060i	−0.00830196	+	0.413262i
$831$	−9.09873	+	3.76882i	−0.315632	+	0.130739i
$832$	2.06048	+	2.06048i	0.0714341	+	0.0714341i
$833$	−4.95618	+	0.413217i	−0.171721	+	0.0143171i
$834$		−	17.4758i		−	0.605139i
$835$	31.0316	−	19.8449i	1.07389	−	0.686761i
$836$	−6.10983	−	9.14400i	−0.211313	−	0.316252i
$837$			9.98169i			0.345018i
$838$	11.2262	−	7.50113i	0.387804	−	0.259122i
$839$	−36.8971	−	24.6539i	−1.27383	−	0.851146i	−0.279780	−	0.960064i	$-0.590261\pi$
$839$	−36.8971	−	24.6539i	−1.27383	−	0.851146i	−0.994051	+	0.108918i	$0.965261\pi$
$840$	2.33194	+	5.96600i	0.0804597	+	0.205847i
$841$	9.04875	+	3.74811i	0.312026	+	0.129245i
$842$	3.71868	+	8.97768i	0.128154	+	0.309391i
$843$	−27.3340	−	18.2640i	−0.941433	−	0.629046i
$844$	0.139674	−	0.209036i	0.00480776	−	0.00719532i
$845$	−6.98454	−	7.27092i	−0.240276	−	0.250127i
$846$	6.74347	+	6.74347i	0.231845	+	0.231845i
$847$	8.70565	−	43.7663i	0.299130	−	1.50383i
$848$	0.858826	+	0.355737i	0.0294922	+	0.0122161i
$849$	−3.19229			−0.109559
$850$	−15.1907	−	13.9371i	−0.521036	−	0.478039i
$851$	−12.2103			−0.418563
$852$	−0.934407	−	0.387044i	−0.0320123	−	0.0132599i
$853$	6.20708	−	31.2051i	0.212526	−	1.06844i	−0.716262	−	0.697831i	$-0.754148\pi$
$853$	6.20708	−	31.2051i	0.212526	−	1.06844i	0.928788	−	0.370611i	$-0.120852\pi$
$854$	−26.8860	−	26.8860i	−0.920019	−	0.920019i
$855$	3.30448	+	3.43997i	0.113011	+	0.117644i
$856$	9.01125	−	13.4863i	0.307998	−	0.460952i
$857$	−29.5960	−	19.7754i	−1.01098	−	0.675515i	−0.0643792	−	0.997926i	$-0.520507\pi$
$857$	−29.5960	−	19.7754i	−1.01098	−	0.675515i	−0.946600	+	0.322411i	$0.895507\pi$
$858$	5.74881	+	13.8789i	0.196261	+	0.473816i
$859$	−6.40837	−	2.65443i	−0.218651	−	0.0905681i	0.270669	−	0.962672i	$-0.412755\pi$
$859$	−6.40837	−	2.65443i	−0.218651	−	0.0905681i	−0.489320	+	0.872104i	$0.662755\pi$
$860$	−2.64083	−	6.75624i	−0.0900514	−	0.230386i
$861$	−10.0973	−	6.74677i	−0.344113	−	0.229929i
$862$	−17.7436	+	11.8559i	−0.604350	+	0.403814i
$863$		−	9.43702i		−	0.321240i	−0.987016	−	0.160620i	$-0.948651\pi$
$863$		−	9.43702i		−	0.321240i	0.987016	−	0.160620i	$-0.0513494\pi$
$864$	−0.555570	−	0.831470i	−0.0189009	−	0.0282872i
$865$	44.9207	−	28.7271i	1.52735	−	0.976749i
$866$		−	12.9289i		−	0.439342i
$867$	−12.3758	+	11.6550i	−0.420305	+	0.395825i
$868$	−20.2191	−	20.2191i	−0.686279	−	0.686279i
$869$	17.7241	−	7.34156i	0.601248	−	0.249045i
$870$	−0.196819	+	9.79744i	−0.00667279	+	0.332164i
$871$	1.48921	−	1.48921i	0.0504601	−	0.0504601i
$872$	−5.71521	−	8.55341i	−0.193541	−	0.289655i
$873$	4.27749	−	0.850845i	0.144771	−	0.0287968i
$874$	8.56131	−	1.70295i	0.289591	−	0.0576031i
$875$	−31.7316	+	4.34525i	−1.07272	+	0.146896i
$876$	0.405071	−	0.977928i	0.0136861	−	0.0330411i
$877$	3.63288	−	5.43698i	0.122674	−	0.183594i	−0.765050	−	0.643971i	$-0.777286\pi$
$877$	3.63288	−	5.43698i	0.122674	−	0.183594i	0.887723	+	0.460377i	$0.152286\pi$
$878$	3.89449	+	19.5789i	0.131433	+	0.660757i
$879$	5.79394	−	29.1281i	0.195425	−	0.982467i
$880$	−11.3490	+	2.02140i	−0.382576	+	0.0681413i
$881$	18.0348	−	12.0505i	0.607607	−	0.405990i	−0.213353	−	0.976975i	$-0.568439\pi$
$881$	18.0348	−	12.0505i	0.607607	−	0.405990i	0.820961	+	0.570985i	$0.193439\pi$
$882$	0.461601	−	1.11440i	0.0155429	−	0.0375239i
$883$	1.01190	−	1.01190i	0.0340531	−	0.0340531i	−0.689875	−	0.723928i	$-0.742335\pi$
$883$	1.01190	−	1.01190i	0.0340531	−	0.0340531i	0.723928	+	0.689875i	$0.242335\pi$
$884$	5.50412	+	10.6796i	0.185124	+	0.359194i
$885$	3.46604	+	19.4599i	0.116510	+	0.654138i
$886$	10.7856	+	26.0388i	0.362350	+	0.874789i
$887$	29.9911	+	5.96561i	1.00700	+	0.200306i	0.670923	−	0.741527i	$-0.265898\pi$
$887$	29.9911	+	5.96561i	1.00700	+	0.200306i	0.336081	+	0.941833i	$0.390898\pi$
$888$	−2.98396			−0.100135
$889$	−47.9723	−	9.54228i	−1.60894	−	0.320038i
$890$	−2.22725	+	5.08566i	−0.0746574	+	0.170472i
$891$	−1.00575	−	5.05627i	−0.0336940	−	0.169391i
$892$	4.60786	−	1.90864i	0.154283	−	0.0639059i
$893$	−18.7952	+	7.78524i	−0.628959	+	0.260523i
$894$	1.82568	+	9.17833i	0.0610600	+	0.306969i
$895$	−9.16600	−	23.4501i	−0.306386	−	0.783851i
$896$	2.80961	+	0.558866i	0.0938624	+	0.0186704i
$897$	−11.9238			−0.398124
$898$	−16.7481	−	3.33139i	−0.558890	−	0.111170i
$899$	−16.7401	−	40.4143i	−0.558315	−	1.34789i
$900$	4.69252	−	1.72635i	0.156417	−	0.0575451i
$901$	2.92600	+	2.47564i	0.0974790	+	0.0824755i
$902$	15.4535	−	15.4535i	0.514544	−	0.514544i
$903$	−3.55635	+	8.58579i	−0.118348	+	0.285717i
$904$	9.15367	−	6.11629i	0.304447	−	0.203425i
$905$	4.44578	+	24.9606i	0.147783	+	0.829720i
$906$	2.97253	−	14.9439i	0.0987558	−	0.496479i
$907$	10.4259	+	52.4144i	0.346185	+	1.74039i	0.625529	+	0.780201i	$0.284883\pi$
$907$	10.4259	+	52.4144i	0.346185	+	1.74039i	−0.279344	+	0.960191i	$0.590117\pi$
$908$	10.5457	−	15.7827i	0.349970	−	0.523767i
$909$	5.96321	−	14.3965i	0.197787	−	0.477500i
$910$	18.2300	+	4.00841i	0.604318	+	0.132877i
$911$	−22.4609	+	4.46775i	−0.744162	+	0.148023i	−0.552587	−	0.833455i	$-0.686359\pi$
$911$	−22.4609	+	4.46775i	−0.744162	+	0.148023i	−0.191575	+	0.981478i	$0.561359\pi$
$912$	2.09222	−	0.416169i	0.0692804	−	0.0137807i
$913$	15.2532	+	22.8281i	0.504809	+	0.755500i
$914$	−8.39700	+	8.39700i	−0.277748	+	0.277748i
$915$	−21.4037	+	20.5607i	−0.707586	+	0.679716i
$916$	6.18547	−	2.56210i	0.204374	−	0.0846543i
$917$	−1.02629	−	1.02629i	−0.0338912	−	0.0338912i
$918$	−1.13759	−	3.96307i	−0.0375459	−	0.130801i
$919$		−	2.18321i		−	0.0720176i	−0.999351	−	0.0360088i	$-0.988536\pi$
$919$		−	2.18321i		−	0.0720176i	0.999351	−	0.0360088i	$-0.0114644\pi$
$920$	1.96494	−	8.93644i	0.0647823	−	0.294626i
$921$	14.3349	+	21.4537i	0.472351	+	0.706924i
$922$			24.1141i			0.794154i
$923$	−2.45047	+	1.63735i	−0.0806582	+	0.0538941i
$924$	12.2793	+	8.20477i	0.403960	+	0.269917i
$925$	3.49605	−	14.5044i	0.114949	−	0.476902i
$926$	−7.87620	−	3.26243i	−0.258828	−	0.107210i
$927$	−6.71465	−	16.2106i	−0.220538	−	0.532426i
$928$	3.64386	+	2.43475i	0.119616	+	0.0799245i
$929$	−22.8901	+	34.2575i	−0.751001	+	1.12395i	0.237299	+	0.971437i	$0.423738\pi$
$929$	−22.8901	+	34.2575i	−0.751001	+	1.12395i	−0.988301	+	0.152517i	$0.951262\pi$
$930$	−16.0962	+	15.4623i	−0.527817	+	0.507028i
$931$	1.81947	+	1.81947i	0.0596308	+	0.0596308i
$932$	0.346774	−	1.74335i	0.0113590	−	0.0571054i
$933$	−12.9936	−	5.38213i	−0.425392	−	0.176203i
$934$	9.23843			0.302291
$935$	−47.1084	−	6.31479i	−1.54061	−	0.206516i
$936$	−2.91395			−0.0952455
$937$	2.11719	+	0.876968i	0.0691655	+	0.0286493i	0.416998	−	0.908907i	$-0.363082\pi$
$937$	2.11719	+	0.876968i	0.0691655	+	0.0286493i	−0.347832	+	0.937557i	$0.613082\pi$
$938$	0.403921	−	2.03065i	0.0131885	−	0.0663030i
$939$	−1.31245	−	1.31245i	−0.0428301	−	0.0428301i
$940$	−0.428302	+	21.3204i	−0.0139697	+	0.695396i
$941$	6.98452	−	10.4531i	0.227689	−	0.340760i	−0.699981	−	0.714161i	$-0.746808\pi$
$941$	6.98452	−	10.4531i	0.227689	−	0.340760i	0.927670	+	0.373401i	$0.121808\pi$
$942$	−1.48995	−	0.995555i	−0.0485453	−	0.0324369i
$943$	6.63830	+	16.0263i	0.216173	+	0.521887i
$944$	8.16682	+	3.38281i	0.265807	+	0.110101i
$945$	−5.86753	−	2.56967i	−0.190871	−	0.0835912i
$946$	−13.9058	−	9.29155i	−0.452116	−	0.302094i
$947$	−13.7971	+	9.21890i	−0.448344	+	0.299574i	−0.759169	−	0.650893i	$-0.774395\pi$
$947$	−13.7971	+	9.21890i	−0.448344	+	0.299574i	0.310825	+	0.950467i	$0.399395\pi$
$948$			3.72128i			0.120862i
$949$	−1.71361	−	2.56461i	−0.0556263	−	0.0832506i
$950$	−0.428364	+	10.6575i	−0.0138980	+	0.345773i
$951$		−	24.0878i		−	0.781102i
$952$	10.3320	+	5.72333i	0.334860	+	0.185494i
$953$	−13.8223	−	13.8223i	−0.447748	−	0.447748i	0.446857	−	0.894605i	$-0.352543\pi$
$953$	−13.8223	−	13.8223i	−0.447748	−	0.447748i	−0.894605	+	0.446857i	$0.852543\pi$
$954$	−0.858826	+	0.355737i	−0.0278055	+	0.0115174i
$955$	−26.6571	−	0.535511i	−0.862605	−	0.0173287i
$956$	12.3664	−	12.3664i	0.399958	−	0.399958i
$957$	12.5519	+	18.7853i	0.405746	+	0.607242i
$958$	−27.5687	+	5.48375i	−0.890703	+	0.177172i
$959$	37.6745	−	7.49392i	1.21657	−	0.241991i
$960$	0.480195	−	2.18390i	0.0154982	−	0.0704850i
$961$	26.2652	−	63.4098i	0.847264	−	2.04548i
$962$	−4.83075	+	7.22973i	−0.155750	+	0.233096i
$963$	3.16433	+	15.9082i	0.101969	+	0.512633i
$964$	−5.21864	+	26.2359i	−0.168081	+	0.845001i
$965$	42.5586	+	29.6902i	1.37001	+	0.955761i
$966$	−9.74653	+	6.51243i	−0.313590	+	0.209534i
$967$	0.0499633	−	0.120622i	0.00160671	−	0.00387894i	−0.923074	−	0.384622i	$-0.874332\pi$
$967$	0.0499633	−	0.120622i	0.00160671	−	0.00387894i	0.924681	+	0.380743i	$0.124332\pi$
$968$	−11.0149	+	11.0149i	−0.354031	+	0.354031i
$969$	8.73920	+	0.993238i	0.280743	+	0.0319074i
$970$	7.99815	+	5.57977i	0.256805	+	0.179155i
$971$	8.35842	+	20.1790i	0.268234	+	0.647575i	0.999400	−	0.0346245i	$-0.0110235\pi$
$971$	8.35842	+	20.1790i	0.268234	+	0.647575i	−0.731166	+	0.682200i	$0.761024\pi$
$972$	0.980785	+	0.195090i	0.0314587	+	0.00625752i
$973$	−50.0622			−1.60492
$974$	33.5162	+	6.66678i	1.07393	+	0.213617i
$975$	3.41403	−	14.1641i	0.109336	−	0.453615i
$976$	2.58943	+	13.0180i	0.0828858	+	0.416695i
$977$	−7.62486	+	3.15832i	−0.243941	+	0.101044i	−0.501304	−	0.865271i	$-0.667146\pi$
$977$	−7.62486	+	3.15832i	−0.243941	+	0.101044i	0.257363	+	0.966315i	$0.417146\pi$
$978$	−17.2241	+	7.13447i	−0.550767	+	0.228135i
$979$	2.49721	+	12.5543i	0.0798111	+	0.401238i
$980$	2.51211	−	0.981913i	0.0802463	−	0.0313661i
$981$	10.0894	+	2.00691i	0.322131	+	0.0640758i
$982$	−1.78573			−0.0569849
$983$	−36.4397	−	7.24830i	−1.16224	−	0.231185i	−0.423964	−	0.905679i	$-0.639362\pi$
$983$	−36.4397	−	7.24830i	−1.16224	−	0.231185i	−0.738280	+	0.674494i	$0.764362\pi$
$984$	1.62228	+	3.91652i	0.0517163	+	0.124854i
$985$	−45.0470	+	8.02340i	−1.43532	+	0.255647i
$986$	11.2523	+	14.1380i	0.358346	+	0.450245i
$987$	19.3177	−	19.3177i	0.614889	−	0.614889i
$988$	2.37879	−	5.74291i	0.0756794	−	0.182706i
$989$	11.0375	−	7.37504i	0.350973	−	0.234513i
$990$	6.59564	−	9.45433i	0.209623	−	0.300478i
$991$	−7.84830	+	39.4561i	−0.249309	+	1.25336i	0.629805	+	0.776753i	$0.283135\pi$
$991$	−7.84830	+	39.4561i	−0.249309	+	1.25336i	−0.879115	+	0.476610i	$0.841865\pi$
$992$	1.94733	+	9.78990i	0.0618279	+	0.310830i
$993$	7.85371	−	11.7539i	0.249230	−	0.372999i
$994$	−1.10875	+	2.67675i	−0.0351673	+	0.0849013i
$995$	0.975023	−	0.623533i	0.0309103	−	0.0197673i
$996$	−5.22326	+	1.03897i	−0.165505	+	0.0329210i
$997$	−13.9918	+	2.78314i	−0.443125	+	0.0881430i	−0.411610	−	0.911360i	$-0.635033\pi$
$997$	−13.9918	+	2.78314i	−0.443125	+	0.0881430i	−0.0315152	+	0.999503i	$0.510033\pi$
$998$	8.20318	+	12.2769i	0.259667	+	0.388619i
$999$	2.10998	−	2.10998i	0.0667568	−	0.0667568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.bd.a.73.5	yes	64
5.2	odd	4		510.2.bi.a.277.4	yes	64
17.7	odd	16		510.2.bi.a.313.4	yes	64
85.7	even	16	inner	510.2.bd.a.7.5	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.a.7.5	✓	64	85.7	even	16	inner
510.2.bd.a.73.5	yes	64	1.1	even	1	trivial
510.2.bi.a.277.4	yes	64	5.2	odd	4
510.2.bi.a.313.4	yes	64	17.7	odd	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{2} +(0.195090 - 0.980785i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.54906 - 1.61258i) q^{5} +(0.555570 - 0.831470i) q^{6} +(-2.38187 - 1.59151i) q^{7} +(0.382683 + 0.923880i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-0.814041 - 2.08263i) q^{10} +(-4.28649 - 2.86414i) q^{11} +(0.831470 - 0.555570i) q^{12} -2.91395i q^{13} +(-1.59151 - 2.38187i) q^{14} +(-1.88380 + 1.20470i) q^{15} +1.00000i q^{16} +(-1.25589 + 3.92718i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(1.97083 - 0.816345i) q^{19} +(0.0449109 - 2.23562i) q^{20} +(-2.02561 + 2.02561i) q^{21} +(-2.86414 - 4.28649i) q^{22} +(4.01334 - 0.798303i) q^{23} +(0.980785 - 0.195090i) q^{24} +(-0.200807 + 4.99597i) q^{25} +(1.11512 - 2.69214i) q^{26} +(-0.555570 + 0.831470i) q^{27} +(-0.558866 - 2.80961i) q^{28} +(0.854970 - 4.29822i) q^{29} +(-2.20142 + 0.392099i) q^{30} +(8.29948 - 5.54553i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(-3.64536 + 3.64536i) q^{33} +(-2.66316 + 3.14763i) q^{34} +(1.12323 + 6.30630i) q^{35} +(-0.382683 - 0.923880i) q^{36} +(-2.92662 - 0.582142i) q^{37} +2.13321 q^{38} +(-2.85796 - 0.568484i) q^{39} +(0.897026 - 2.04825i) q^{40} +(0.827029 + 4.15776i) q^{41} +(-2.64659 + 1.09625i) q^{42} +(2.99715 - 1.24146i) q^{43} +(-1.00575 - 5.05627i) q^{44} +(0.814041 + 2.08263i) q^{45} +(4.01334 + 0.798303i) q^{46} -9.53671 q^{47} +(0.980785 + 0.195090i) q^{48} +(0.461601 + 1.11440i) q^{49} +(-2.09740 + 4.53883i) q^{50} +(3.60671 + 1.99792i) q^{51} +(2.06048 - 2.06048i) q^{52} +(0.355737 - 0.858826i) q^{53} +(-0.831470 + 0.555570i) q^{54} +(2.02140 + 11.3490i) q^{55} +(0.558866 - 2.80961i) q^{56} +(-0.416169 - 2.09222i) q^{57} +(2.43475 - 3.64386i) q^{58} +(3.38281 - 8.16682i) q^{59} +(-2.18390 - 0.480195i) q^{60} +(13.0180 - 2.58943i) q^{61} +(9.78990 - 1.94733i) q^{62} +(1.59151 + 2.38187i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(-4.69897 + 4.51390i) q^{65} +(-4.76290 + 1.97286i) q^{66} +(0.511063 + 0.511063i) q^{67} +(-3.66499 + 1.88888i) q^{68} -4.09197i q^{69} +(-1.37559 + 6.25611i) q^{70} +(-0.561901 - 0.840944i) q^{71} -1.00000i q^{72} +(0.880112 - 0.588072i) q^{73} +(-2.48107 - 1.65780i) q^{74} +(4.86079 + 1.17161i) q^{75} +(1.97083 + 0.816345i) q^{76} +(5.65154 + 13.6440i) q^{77} +(-2.42286 - 1.61891i) q^{78} +(-2.06743 + 3.09413i) q^{79} +(1.61258 - 1.54906i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-0.827029 + 4.15776i) q^{82} +(-4.92020 - 2.03801i) q^{83} -2.86465 q^{84} +(8.27833 - 4.05822i) q^{85} +3.24409 q^{86} +(-4.04884 - 1.67708i) q^{87} +(1.00575 - 5.05627i) q^{88} +(-1.75569 - 1.75569i) q^{89} +(-0.0449109 + 2.23562i) q^{90} +(-4.63760 + 6.94065i) q^{91} +(3.40235 + 2.27338i) q^{92} +(-3.81983 - 9.22188i) q^{93} +(-8.81077 - 3.64954i) q^{94} +(-4.36936 - 1.91355i) q^{95} +(0.831470 + 0.555570i) q^{96} +(-3.62628 + 2.42300i) q^{97} +1.20622i q^{98} +(2.86414 + 4.28649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{15} + 16 q^{20} + 16 q^{25} - 16 q^{28} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 32 q^{35} - 16 q^{37} - 16 q^{40} + 48 q^{41} + 16 q^{44} + 32 q^{47} - 64 q^{49} - 16 q^{50} + 32 q^{51} + 16 q^{52}+ \cdots - 80 q^{97}+O(q^{100}) \) 64 * q - 16 * q^15 + 16 * q^20 + 16 * q^25 - 16 * q^28 + 32 * q^29 + 16 * q^31 + 16 * q^33 + 32 * q^35 - 16 * q^37 - 16 * q^40 + 48 * q^41 + 16 * q^44 + 32 * q^47 - 64 * q^49 - 16 * q^50 + 32 * q^51 + 16 * q^52 + 80 * q^53 - 16 * q^55 + 16 * q^56 - 32 * q^57 + 64 * q^59 - 48 * q^61 + 32 * q^65 + 16 * q^67 - 48 * q^68 - 64 * q^71 + 16 * q^73 + 48 * q^74 - 32 * q^75 - 80 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 48 * q^82 - 32 * q^83 - 16 * q^85 - 64 * q^86 - 32 * q^87 - 16 * q^88 - 32 * q^89 - 16 * q^90 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 112 * q^95 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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