LMFDB - Embedded newform 756.2.cf.a.491.57

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			491.57
Character	$\chi$	$=$	756.491
Dual form			756.2.cf.a.659.57

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.152848 - 1.40593i) q^{2} +(0.0477819 - 1.73139i) q^{3} +(-1.95328 - 0.429787i) q^{4} +(-0.988005 - 2.71452i) q^{5} +(-2.42691 - 0.331818i) q^{6} +(0.984808 - 0.173648i) q^{7} +(-0.902804 + 2.68047i) q^{8} +(-2.99543 - 0.165458i) q^{9} +(-3.96744 + 0.974157i) q^{10} +(-3.71947 - 1.35378i) q^{11} +(-0.837461 + 3.36135i) q^{12} +(0.633183 + 0.531304i) q^{13} +(-0.0936112 - 1.41111i) q^{14} +(-4.74711 + 1.58092i) q^{15} +(3.63057 + 1.67898i) q^{16} +(-0.212149 - 0.122484i) q^{17} +(-0.690469 + 4.18608i) q^{18} +(6.07372 - 3.50666i) q^{19} +(0.763180 + 5.72684i) q^{20} +(-0.253597 - 1.71339i) q^{21} +(-2.47183 + 5.02239i) q^{22} +(-1.46788 + 8.32475i) q^{23} +(4.59781 + 1.69119i) q^{24} +(-2.56225 + 2.14999i) q^{25} +(0.843757 - 0.809002i) q^{26} +(-0.429601 + 5.17836i) q^{27} +(-1.99823 - 0.0840748i) q^{28} +(-6.46796 - 7.70821i) q^{29} +(1.49707 + 6.91574i) q^{30} +(-1.64886 - 0.290738i) q^{31} +(2.91546 - 4.84769i) q^{32} +(-2.52164 + 6.37517i) q^{33} +(-0.204630 + 0.279544i) q^{34} +(-1.44437 - 2.50172i) q^{35} +(5.77979 + 1.61058i) q^{36} +(4.90834 - 8.50150i) q^{37} +(-4.00176 - 9.07520i) q^{38} +(0.950150 - 1.07090i) q^{39} +(8.16818 - 0.197641i) q^{40} +(-0.575510 + 0.685866i) q^{41} +(-2.44766 + 0.0946521i) q^{42} +(0.711282 - 1.95423i) q^{43} +(6.68331 + 4.24287i) q^{44} +(2.51036 + 8.29465i) q^{45} +(11.4796 + 3.33615i) q^{46} +(1.44871 + 8.21605i) q^{47} +(3.08045 - 6.20571i) q^{48} +(0.939693 - 0.342020i) q^{49} +(2.63109 + 3.93097i) q^{50} +(-0.222205 + 0.361460i) q^{51} +(-1.00843 - 1.30992i) q^{52} -0.346076i q^{53} +(7.21475 + 1.39549i) q^{54} +11.4341i q^{55} +(-0.423629 + 2.79652i) q^{56} +(-5.78119 - 10.6835i) q^{57} +(-11.8258 + 7.91530i) q^{58} +(-7.21907 + 2.62753i) q^{59} +(9.95187 - 1.04772i) q^{60} +(-0.228940 - 1.29838i) q^{61} +(-0.660781 + 2.27374i) q^{62} +(-2.97866 + 0.357207i) q^{63} +(-6.36989 - 4.83989i) q^{64} +(0.816648 - 2.24372i) q^{65} +(8.57761 + 4.51968i) q^{66} +(-5.53344 + 6.59450i) q^{67} +(0.361742 + 0.330424i) q^{68} +(14.3433 + 2.93924i) q^{69} +(-3.73801 + 1.64830i) q^{70} +(5.35194 - 9.26982i) q^{71} +(3.14780 - 7.87981i) q^{72} +(-2.27260 - 3.93625i) q^{73} +(-11.2023 - 8.20022i) q^{74} +(3.60004 + 4.53900i) q^{75} +(-13.3708 + 4.23907i) q^{76} +(-3.89804 - 0.687330i) q^{77} +(-1.36038 - 1.49953i) q^{78} +(6.39122 + 7.61676i) q^{79} +(0.970620 - 11.5141i) q^{80} +(8.94525 + 0.991239i) q^{81} +(0.876314 + 0.913960i) q^{82} +(-5.88967 + 4.94202i) q^{83} +(-0.241046 + 3.45570i) q^{84} +(-0.122882 + 0.696897i) q^{85} +(-2.63879 - 1.29871i) q^{86} +(-13.6550 + 10.8303i) q^{87} +(6.98671 - 8.74774i) q^{88} +(9.44436 - 5.45270i) q^{89} +(12.0454 - 2.26157i) q^{90} +(0.715824 + 0.413281i) q^{91} +(6.44504 - 15.6297i) q^{92} +(-0.582167 + 2.84092i) q^{93} +(11.7726 - 0.780980i) q^{94} +(-15.5198 - 13.0226i) q^{95} +(-8.25395 - 5.27943i) q^{96} +(-8.36991 - 3.04640i) q^{97} +(-0.337226 - 1.37342i) q^{98} +(10.9174 + 4.67056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	0.152848	−	1.40593i	0.108080	−	0.994142i
$2$	0.152848	−	1.40593i	0.108080	−	0.994142i
$3$	0.0477819	−	1.73139i	0.0275869	−	0.999619i
$3$	0.0477819	−	1.73139i	0.0275869	−	0.999619i
$4$	−1.95328	−	0.429787i	−0.976638	−	0.214893i
$5$	−0.988005	−	2.71452i	−0.441849	−	1.21397i	−0.938274	−	0.345892i	$-0.887576\pi$
$5$	−0.988005	−	2.71452i	−0.441849	−	1.21397i	0.496425	−	0.868080i	$-0.334646\pi$
$6$	−2.42691	−	0.331818i	−0.990782	−	0.135464i
$7$	0.984808	−	0.173648i	0.372222	−	0.0656328i
$7$	0.984808	−	0.173648i	0.372222	−	0.0656328i
$8$	−0.902804	+	2.68047i	−0.319189	+	0.947691i
$9$	−2.99543	−	0.165458i	−0.998478	−	0.0551528i
$10$	−3.96744	+	0.974157i	−1.25462	+	0.308055i
$11$	−3.71947	−	1.35378i	−1.12146	−	0.408179i	−0.286276	−	0.958147i	$-0.592417\pi$
$11$	−3.71947	−	1.35378i	−1.12146	−	0.408179i	−0.835185	+	0.549969i	$0.814640\pi$
$12$	−0.837461	+	3.36135i	−0.241754	+	0.970338i
$13$	0.633183	+	0.531304i	0.175613	+	0.147357i	0.726358	−	0.687317i	$-0.241212\pi$
$13$	0.633183	+	0.531304i	0.175613	+	0.147357i	−0.550744	+	0.834674i	$0.685656\pi$
$14$	−0.0936112	−	1.41111i	−0.0250187	−	0.377136i
$15$	−4.74711	+	1.58092i	−1.22570	+	0.408192i
$16$	3.63057	+	1.67898i	0.907642	+	0.419746i
$17$	−0.212149	−	0.122484i	−0.0514536	−	0.0297067i	0.474053	−	0.880497i	$-0.342791\pi$
$17$	−0.212149	−	0.122484i	−0.0514536	−	0.0297067i	−0.525506	+	0.850790i	$0.676124\pi$
$18$	−0.690469	+	4.18608i	−0.162745	+	0.986668i
$19$	6.07372	−	3.50666i	1.39341	−	0.804484i	0.399716	−	0.916639i	$-0.369109\pi$
$19$	6.07372	−	3.50666i	1.39341	−	0.804484i	0.993691	+	0.112156i	$0.0357755\pi$
$20$	0.763180	+	5.72684i	0.170652	+	1.28056i
$21$	−0.253597	−	1.71339i	−0.0553394	−	0.373891i
$22$	−2.47183	+	5.02239i	−0.526995	+	1.07078i
$23$	−1.46788	+	8.32475i	−0.306074	+	1.73583i	0.312334	+	0.949972i	$0.398889\pi$
$23$	−1.46788	+	8.32475i	−0.306074	+	1.73583i	−0.618407	+	0.785858i	$0.712222\pi$
$24$	4.59781	+	1.69119i	0.938525	+	0.345212i
$25$	−2.56225	+	2.14999i	−0.512451	+	0.429997i
$26$	0.843757	−	0.809002i	0.165474	−	0.158658i
$27$	−0.429601	+	5.17836i	−0.0826767	+	0.996576i
$28$	−1.99823	−	0.0840748i	−0.377630	−	0.0158886i
$29$	−6.46796	−	7.70821i	−1.20107	−	1.43138i	−0.873688	−	0.486486i	$-0.838278\pi$
$29$	−6.46796	−	7.70821i	−1.20107	−	1.43138i	−0.327381	−	0.944892i	$-0.606166\pi$
$30$	1.49707	+	6.91574i	0.273327	+	1.26264i
$31$	−1.64886	−	0.290738i	−0.296143	−	0.0522181i	0.0236024	−	0.999721i	$-0.492486\pi$
$31$	−1.64886	−	0.290738i	−0.296143	−	0.0522181i	−0.319746	+	0.947503i	$0.603598\pi$
$32$	2.91546	−	4.84769i	0.515385	−	0.856959i
$33$	−2.52164	+	6.37517i	−0.438961	+	1.10977i
$34$	−0.204630	+	0.279544i	−0.0350938	+	0.0479415i
$35$	−1.44437	−	2.50172i	−0.244143	−	0.422867i
$36$	5.77979	+	1.61058i	0.963299	+	0.268431i
$37$	4.90834	−	8.50150i	0.806926	−	1.39764i	−0.108057	−	0.994145i	$-0.534463\pi$
$37$	4.90834	−	8.50150i	0.806926	−	1.39764i	0.914983	−	0.403493i	$-0.132204\pi$
$38$	−4.00176	−	9.07520i	−0.649172	−	1.47219i
$39$	0.950150	−	1.07090i	0.152146	−	0.171482i
$40$	8.16818	−	0.197641i	1.29150	−	0.0312499i
$41$	−0.575510	+	0.685866i	−0.0898796	+	0.107114i	−0.809110	−	0.587658i	$-0.800050\pi$
$41$	−0.575510	+	0.685866i	−0.0898796	+	0.107114i	0.719230	+	0.694772i	$0.244495\pi$
$42$	−2.44766	+	0.0946521i	−0.377682	+	0.0146051i
$43$	0.711282	−	1.95423i	0.108470	−	0.298018i	−0.873568	−	0.486702i	$-0.838200\pi$
$43$	0.711282	−	1.95423i	0.108470	−	0.298018i	0.982038	+	0.188684i	$0.0604222\pi$
$44$	6.68331	+	4.24287i	1.00755	+	0.639637i
$45$	2.51036	+	8.29465i	0.374223	+	1.23649i
$46$	11.4796	+	3.33615i	1.69258	+	0.491889i
$47$	1.44871	+	8.21605i	0.211316	+	1.19843i	0.887186	+	0.461413i	$0.152657\pi$
$47$	1.44871	+	8.21605i	0.211316	+	1.19843i	−0.675869	+	0.737022i	$0.736232\pi$
$48$	3.08045	−	6.20571i	0.444625	−	0.895717i
$49$	0.939693	−	0.342020i	0.134242	−	0.0488600i
$50$	2.63109	+	3.93097i	0.372093	+	0.555923i
$51$	−0.222205	+	0.361460i	−0.0311149	+	0.0506145i
$52$	−1.00843	−	1.30992i	−0.139845	−	0.181653i
$53$		−	0.346076i		−	0.0475372i	−0.999717	−	0.0237686i	$-0.992434\pi$
$53$		−	0.346076i		−	0.0475372i	0.999717	−	0.0237686i	$-0.00756650\pi$
$54$	7.21475	+	1.39549i	0.981803	+	0.189902i
$55$			11.4341i			1.54178i
$56$	−0.423629	+	2.79652i	−0.0566098	+	0.373701i
$57$	−5.78119	−	10.6835i	−0.765738	−	1.41507i
$58$	−11.8258	+	7.91530i	−1.55281	+	1.03933i
$59$	−7.21907	+	2.62753i	−0.939843	+	0.342075i	−0.766104	−	0.642717i	$-0.777807\pi$
$59$	−7.21907	+	2.62753i	−0.939843	+	0.342075i	−0.173739	+	0.984792i	$0.555585\pi$
$60$	9.95187	−	1.04772i	1.28478	−	0.135261i
$61$	−0.228940	−	1.29838i	−0.0293127	−	0.166241i	0.966637	−	0.256149i	$-0.0824537\pi$
$61$	−0.228940	−	1.29838i	−0.0293127	−	0.166241i	−0.995950	+	0.0899082i	$0.971343\pi$
$62$	−0.660781	+	2.27374i	−0.0839193	+	0.288765i
$63$	−2.97866	+	0.357207i	−0.375276	+	0.0450038i
$64$	−6.36989	−	4.83989i	−0.796236	−	0.604986i
$65$	0.816648	−	2.24372i	0.101293	−	0.278299i
$66$	8.57761	+	4.51968i	1.05583	+	0.556334i
$67$	−5.53344	+	6.59450i	−0.676017	+	0.805646i	−0.989590	−	0.143918i	$-0.954030\pi$
$67$	−5.53344	+	6.59450i	−0.676017	+	0.805646i	0.313572	+	0.949564i	$0.398474\pi$
$68$	0.361742	+	0.330424i	0.0438677	+	0.0400698i
$69$	14.3433	+	2.93924i	1.72673	+	0.353843i
$70$	−3.73801	+	1.64830i	−0.446777	+	0.197009i
$71$	5.35194	−	9.26982i	0.635158	−	1.10013i	−0.351324	−	0.936254i	$-0.614268\pi$
$71$	5.35194	−	9.26982i	0.635158	−	1.10013i	0.986482	−	0.163872i	$-0.0523983\pi$
$72$	3.14780	−	7.87981i	0.370971	−	0.928644i
$73$	−2.27260	−	3.93625i	−0.265987	−	0.460704i	0.701834	−	0.712340i	$-0.252365\pi$
$73$	−2.27260	−	3.93625i	−0.265987	−	0.460704i	−0.967822	+	0.251636i	$0.919031\pi$
$74$	−11.2023	−	8.20022i	−1.30224	−	0.953256i
$75$	3.60004	+	4.53900i	0.415697	+	0.524118i
$76$	−13.3708	+	4.23907i	−1.53373	+	0.486255i
$77$	−3.89804	−	0.687330i	−0.444223	−	0.0783285i
$78$	−1.36038	−	1.49953i	−0.154033	−	0.169788i
$79$	6.39122	+	7.61676i	0.719068	+	0.856952i	0.994540	−	0.104357i	$-0.0332785\pi$
$79$	6.39122	+	7.61676i	0.719068	+	0.856952i	−0.275472	+	0.961309i	$0.588834\pi$
$80$	0.970620	−	11.5141i	0.108519	−	1.28732i
$81$	8.94525	+	0.991239i	0.993916	+	0.110138i
$82$	0.876314	+	0.913960i	0.0967727	+	0.100930i
$83$	−5.88967	+	4.94202i	−0.646475	+	0.542457i	−0.905999	−	0.423280i	$-0.860879\pi$
$83$	−5.88967	+	4.94202i	−0.646475	+	0.542457i	0.259524	+	0.965737i	$0.416434\pi$
$84$	−0.241046	+	3.45570i	−0.0263002	+	0.377048i
$85$	−0.122882	+	0.696897i	−0.0133284	+	0.0755891i
$86$	−2.63879	−	1.29871i	−0.284549	−	0.140044i
$87$	−13.6550	+	10.8303i	−1.46397	+	1.16112i
$88$	6.98671	−	8.74774i	0.744786	−	0.932513i
$89$	9.44436	−	5.45270i	1.00110	−	0.577985i	0.0925263	−	0.995710i	$-0.470506\pi$
$89$	9.44436	−	5.45270i	1.00110	−	0.577985i	0.908574	+	0.417725i	$0.137172\pi$
$90$	12.0454	−	2.26157i	1.26970	−	0.238391i
$91$	0.715824	+	0.413281i	0.0750387	+	0.0433236i
$92$	6.44504	−	15.6297i	0.671942	−	1.62950i
$93$	−0.582167	+	2.84092i	−0.0603679	+	0.294590i
$94$	11.7726	−	0.780980i	1.21425	−	0.0805519i
$95$	−15.5198	−	13.0226i	−1.59230	−	1.33609i
$96$	−8.25395	−	5.27943i	−0.842415	−	0.538830i
$97$	−8.36991	−	3.04640i	−0.849835	−	0.309315i	−0.119862	−	0.992791i	$-0.538245\pi$
$97$	−8.36991	−	3.04640i	−0.849835	−	0.309315i	−0.729973	+	0.683476i	$0.760468\pi$
$98$	−0.337226	−	1.37342i	−0.0340650	−	0.138736i
$99$	10.9174	+	4.67056i	1.09724	+	0.469409i
$100$	5.92882	−	3.09829i	0.592882	−	0.309829i
$101$	−11.6107	+	2.04727i	−1.15531	+	0.203711i	−0.718291	−	0.695743i	$-0.755075\pi$
$101$	−11.6107	+	2.04727i	−1.15531	+	0.203711i	−0.437014	+	0.899455i	$0.643964\pi$
$102$	0.474223	+	0.367653i	0.0469551	+	0.0364030i
$103$	−3.51054	−	9.64512i	−0.345904	−	0.950362i	−0.983646	−	0.180113i	$-0.942354\pi$
$103$	−3.51054	−	9.64512i	−0.345904	−	0.950362i	0.637742	−	0.770250i	$-0.279868\pi$
$104$	−1.99579	+	1.21757i	−0.195703	+	0.119392i
$105$	−4.40047	+	2.38123i	−0.429442	+	0.232384i
$106$	−0.486559	−	0.0528971i	−0.0472588	−	0.00513782i
$107$	4.74321			0.458543			0.229272	−	0.973362i	$-0.426366\pi$
$107$	4.74321			0.458543			0.229272	+	0.973362i	$0.426366\pi$
$108$	3.06472	−	9.93013i	0.294903	−	0.955527i
$109$	−8.88293			−0.850830			−0.425415	−	0.904998i	$-0.639872\pi$
$109$	−8.88293			−0.850830			−0.425415	+	0.904998i	$0.639872\pi$
$110$	16.0756	+	1.74768i	1.53274	+	0.166635i
$111$	−14.4849	−	8.90448i	−1.37484	−	0.845176i
$112$	3.86696	+	1.02304i	0.365394	+	0.0966677i
$113$	−2.17165	−	5.96655i	−0.204291	−	0.561285i	0.794661	−	0.607054i	$-0.207649\pi$
$113$	−2.17165	−	5.96655i	−0.204291	−	0.561285i	−0.998952	+	0.0457682i	$0.985426\pi$
$114$	−15.9039	+	6.49499i	−1.48954	+	0.608312i
$115$	24.0480	−	4.24031i	2.24249	−	0.395411i
$116$	9.32081	+	17.8361i	0.865415	+	1.65604i
$117$	−1.80875	−	1.69625i	−0.167219	−	0.156818i
$118$	2.59070	+	10.5511i	0.238493	+	0.971309i
$119$	−0.230195	−	0.0837840i	−0.0211019	−	0.00768047i
$120$	0.0480967	−	14.1518i	0.00439061	−	1.29187i
$121$	3.57524	+	2.99998i	0.325022	+	0.272726i
$122$	−1.86043	+	0.123418i	−0.168435	+	0.0111737i
$123$	1.16000	+	1.02921i	0.104594	+	0.0928003i
$124$	3.09571	+	1.27655i	0.278003	+	0.114637i
$125$	−4.14088	−	2.39074i	−0.370371	−	0.213834i
$126$	0.0469259	+	4.24238i	0.00418049	+	0.377941i
$127$	−11.5724	+	6.68135i	−1.02689	+	0.592874i	−0.916092	−	0.400969i	$-0.868674\pi$
$127$	−11.5724	+	6.68135i	−1.02689	+	0.592874i	−0.110797	+	0.993843i	$0.535340\pi$
$128$	−7.77816	+	8.21585i	−0.687499	+	0.726185i
$129$	−3.34956	−	1.32489i	−0.294912	−	0.116650i
$130$	−3.02969	−	1.49110i	−0.265721	−	0.130778i
$131$	3.69259	−	20.9417i	0.322623	−	1.82968i	−0.203257	−	0.979125i	$-0.565153\pi$
$131$	3.69259	−	20.9417i	0.322623	−	1.82968i	0.525880	−	0.850559i	$-0.323736\pi$
$132$	7.66542	−	11.3687i	0.667189	−	0.989517i
$133$	5.37252	−	4.50808i	0.465856	−	0.390900i
$134$	8.42562	+	8.78758i	0.727863	+	0.759132i
$135$	14.4812	−	3.95009i	1.24635	−	0.339970i
$136$	0.519844	−	0.458080i	0.0445763	−	0.0392800i
$137$	−1.37353	−	1.63691i	−0.117349	−	0.139851i	0.704172	−	0.710029i	$-0.251318\pi$
$137$	−1.37353	−	1.63691i	−0.117349	−	0.139851i	−0.821521	+	0.570179i	$0.806874\pi$
$138$	6.32471	−	19.7164i	0.538395	−	1.67837i
$139$	−18.5750	−	3.27528i	−1.57551	−	0.277805i	−0.683546	−	0.729908i	$-0.739563\pi$
$139$	−18.5750	−	3.27528i	−1.57551	−	0.277805i	−0.891966	+	0.452102i	$0.850674\pi$
$140$	1.74604	+	5.50731i	0.147567	+	0.465453i
$141$	14.2944	−	2.11571i	1.20381	−	0.178175i
$142$	−12.2147	−	8.94132i	−1.02503	−	0.750339i
$143$	−1.63584	−	2.83336i	−0.136796	−	0.236937i
$144$	−10.5973	−	5.62999i	−0.883110	−	0.469166i
$145$	−14.5337	+	25.1732i	−1.20696	+	2.09052i
$146$	−5.88146	+	2.59346i	−0.486753	+	0.214637i
$147$	−0.547270	−	1.64332i	−0.0451381	−	0.135539i
$148$	−13.2412	+	14.4962i	−1.08842	+	1.19158i
$149$	−0.486040	+	0.579240i	−0.0398180	+	0.0474532i	−0.785586	−	0.618753i	$-0.787638\pi$
$149$	−0.486040	+	0.579240i	−0.0398180	+	0.0474532i	0.745768	+	0.666206i	$0.232083\pi$
$150$	6.93177	−	4.36763i	0.565976	−	0.356615i
$151$	−2.89899	+	7.96490i	−0.235916	+	0.648175i	0.764079	+	0.645123i	$0.223194\pi$
$151$	−2.89899	+	7.96490i	−0.235916	+	0.648175i	−0.999995	+	0.00305203i	$0.999029\pi$
$152$	3.91614	+	19.4463i	0.317641	+	1.57730i
$153$	0.615211	+	0.401995i	0.0497369	+	0.0324993i
$154$	−1.56214	+	5.37531i	−0.125881	+	0.433155i
$155$	0.839865	+	4.76311i	0.0674595	+	0.382582i
$156$	−2.31616	+	1.68340i	−0.185441	+	0.134780i
$157$	7.82779	−	2.84908i	0.624726	−	0.227382i	−0.0102084	−	0.999948i	$-0.503249\pi$
$157$	7.82779	−	2.84908i	0.624726	−	0.227382i	0.634934	+	0.772566i	$0.281027\pi$
$158$	11.6855	−	7.82140i	0.929649	−	0.622237i
$159$	−0.599194	−	0.0165362i	−0.0475191	−	0.00131141i
$160$	−16.0397	−	3.12453i	−1.26805	−	0.247016i
$161$			8.45317i			0.666203i
$162$	2.76088	−	12.4249i	0.216915	−	0.976191i
$163$		−	3.51426i		−	0.275258i	−0.990484	−	0.137629i	$-0.956052\pi$
$163$		−	3.51426i		−	0.275258i	0.990484	−	0.137629i	$-0.0439482\pi$
$164$	1.41891	−	1.09234i	0.110798	−	0.0852973i
$165$	19.7969	+	0.546344i	1.54119	+	0.0425328i
$166$	6.04791	+	9.03584i	0.469408	+	0.701317i
$167$	19.9432	−	7.25873i	1.54325	−	0.561697i	0.576428	−	0.817148i	$-0.304446\pi$
$167$	19.9432	−	7.25873i	1.54325	−	0.561697i	0.966822	+	0.255451i	$0.0822238\pi$
$168$	4.82163	+	0.867091i	0.371997	+	0.0668975i
$169$	−2.13879	−	12.1297i	−0.164522	−	0.933052i
$170$	0.961006	+	0.279282i	0.0737058	+	0.0214200i
$171$	−18.7736	+	9.49903i	−1.43565	+	0.726409i
$172$	−2.22923	+	3.51145i	−0.169977	+	0.267746i
$173$	0.354979	−	0.975296i	0.0269885	−	0.0741504i	−0.925467	−	0.378829i	$-0.876327\pi$
$173$	0.354979	−	0.975296i	0.0269885	−	0.0741504i	0.952455	+	0.304679i	$0.0985491\pi$
$174$	13.1394	+	20.8533i	0.996098	+	1.58089i
$175$	−2.14999	+	2.56225i	−0.162524	+	0.193688i
$176$	−11.2308	−	11.1599i	−0.846554	−	0.841209i
$177$	4.20434	+	12.6246i	0.316017	+	0.948922i
$178$	−6.22256	−	14.1115i	−0.466401	−	1.05770i
$179$	8.71482	−	15.0945i	0.651376	−	1.12822i	−0.331413	−	0.943486i	$-0.607525\pi$
$179$	8.71482	−	15.0945i	0.651376	−	1.12822i	0.982789	−	0.184731i	$-0.0591413\pi$
$180$	−1.33850	−	17.2806i	−0.0997660	−	1.28802i
$181$	12.7642	+	22.1082i	0.948752	+	1.64329i	0.748058	+	0.663633i	$0.230986\pi$
$181$	12.7642	+	22.1082i	0.948752	+	1.64329i	0.200694	+	0.979654i	$0.435680\pi$
$182$	0.690456	−	0.943229i	0.0511800	−	0.0699168i
$183$	−2.25895	+	0.334345i	−0.166986	+	0.0247155i
$184$	−20.9891	−	11.4502i	−1.54734	−	0.844122i
$185$	−27.9270	−	4.92428i	−2.05323	−	0.362040i
$186$	3.90516	+	1.25271i	0.286340	+	0.0918535i
$187$	0.623264	+	0.742777i	0.0455776	+	0.0543172i
$188$	0.701419	−	16.6708i	0.0511562	−	1.21585i
$189$	0.476139	+	5.17429i	0.0346340	+	0.376374i
$190$	−20.6811	+	19.8292i	−1.50036	+	1.43856i
$191$	1.97871	−	1.66034i	0.143175	−	0.120138i	−0.568387	−	0.822761i	$-0.692433\pi$
$191$	1.97871	−	1.66034i	0.143175	−	0.120138i	0.711562	+	0.702623i	$0.247988\pi$
$192$	−8.68411	+	10.7975i	−0.626721	+	0.779243i
$193$	3.16270	−	17.9365i	0.227656	−	1.29110i	−0.629887	−	0.776687i	$-0.716899\pi$
$193$	3.16270	−	17.9365i	0.227656	−	1.29110i	0.857542	−	0.514413i	$-0.171990\pi$
$194$	−5.56234	+	11.3019i	−0.399353	+	0.811427i
$195$	−3.84574	−	1.52115i	−0.275399	−	0.108932i
$196$	−1.98247	+	0.264192i	−0.141605	+	0.0188708i
$197$	19.1635	−	11.0640i	1.36534	−	0.788280i	0.375012	−	0.927020i	$-0.377638\pi$
$197$	19.1635	−	11.0640i	1.36534	−	0.788280i	0.990329	+	0.138740i	$0.0443052\pi$
$198$	8.23519	−	14.6352i	0.585249	−	1.04008i
$199$	−4.83073	−	2.78902i	−0.342441	−	0.197709i	0.318910	−	0.947785i	$-0.396683\pi$
$199$	−4.83073	−	2.78902i	−0.342441	−	0.197709i	−0.661351	+	0.750076i	$0.730017\pi$
$200$	−3.44977	−	8.80908i	−0.243936	−	0.622896i
$201$	11.1533	+	9.89565i	0.786690	+	0.697985i
$202$	1.10366	+	16.6367i	0.0776530	+	1.17055i
$203$	−7.70821	−	6.46796i	−0.541010	−	0.453961i
$204$	0.589378	−	0.610530i	0.0412647	−	0.0427456i
$205$	2.43041	+	0.884596i	0.169747	+	0.0617828i
$206$	−14.0969	+	3.46133i	−0.982180	+	0.241162i
$207$	5.77433	−	24.6934i	0.401344	−	1.71631i
$208$	1.40676	+	2.99204i	0.0975415	+	0.207461i
$209$	−27.3382	+	4.82047i	−1.89102	+	0.333439i
$210$	2.67524	+	6.55071i	0.184609	+	0.452042i
$211$	−1.91546	−	5.26267i	−0.131865	−	0.362297i	0.856134	−	0.516754i	$-0.172860\pi$
$211$	−1.91546	−	5.26267i	−0.131865	−	0.362297i	−0.988000	+	0.154456i	$0.950637\pi$
$212$	−0.148739	+	0.675982i	−0.0102154	+	0.0464266i
$213$	−15.7940	−	9.70923i	−1.08219	−	0.665265i
$214$	0.724990	−	6.66862i	0.0495593	−	0.455857i
$215$	−6.00756			−0.409712
$216$	−13.4926	−	5.82658i	−0.918057	−	0.396449i
$217$	−1.67429			−0.113658
$218$	−1.35774	+	12.4888i	−0.0919576	+	0.845846i
$219$	−6.92379	+	3.74668i	−0.467866	+	0.253177i
$220$	4.91423	−	22.3340i	0.331317	−	1.50576i
$221$	−0.0692527	−	0.190270i	−0.00465844	−	0.0127990i
$222$	−14.7331	+	19.0037i	−0.988818	+	1.27544i
$223$	15.2792	−	2.69414i	1.02317	−	0.180413i	0.363206	−	0.931709i	$-0.381682\pi$
$223$	15.2792	−	2.69414i	1.02317	−	0.180413i	0.659965	+	0.751296i	$0.270571\pi$
$224$	2.02937	−	5.28031i	0.135593	−	0.352805i
$225$	8.03080	−	6.01620i	0.535387	−	0.401080i
$226$	−8.72047	+	2.14121i	−0.580077	+	0.142431i
$227$	16.8221	+	6.12274i	1.11652	+	0.406380i	0.833381	−	0.552699i	$-0.186402\pi$
$227$	16.8221	+	6.12274i	1.11652	+	0.406380i	0.283139	+	0.959079i	$0.408624\pi$
$228$	6.70061	+	23.3526i	0.443759	+	1.54656i
$229$	−4.03805	−	3.38832i	−0.266842	−	0.223907i	0.499542	−	0.866289i	$-0.333502\pi$
$229$	−4.03805	−	3.38832i	−0.266842	−	0.223907i	−0.766384	+	0.642383i	$0.777946\pi$
$230$	−2.28589	−	34.4579i	−0.150727	−	2.27209i
$231$	−1.37629	+	6.71619i	−0.0905534	+	0.441893i
$232$	26.5010	−	10.3782i	1.73987	−	0.681361i
$233$	−7.31312	−	4.22223i	−0.479099	−	0.276608i	0.240942	−	0.970539i	$-0.422544\pi$
$233$	−7.31312	−	4.22223i	−0.479099	−	0.276608i	−0.720041	+	0.693932i	$0.755877\pi$
$234$	−2.66127	+	2.28371i	−0.173973	+	0.149291i
$235$	20.8713	−	12.0501i	1.36150	−	0.786060i
$236$	15.2301	−	2.02962i	0.991395	−	0.132117i
$237$	13.4930	−	10.7018i	0.876463	−	0.695154i
$238$	−0.152979	+	0.310831i	−0.00991617	+	0.0201482i
$239$	0.357013	−	2.02472i	0.0230933	−	0.130969i	−0.971082	−	0.238748i	$-0.923263\pi$
$239$	0.357013	−	2.02472i	0.0230933	−	0.130969i	0.994175	+	0.107780i	$0.0343741\pi$
$240$	−19.8890	−	2.23069i	−1.28383	−	0.143990i
$241$	−12.5331	+	10.5165i	−0.807326	+	0.677427i	−0.949968	−	0.312348i	$-0.898885\pi$
$241$	−12.5331	+	10.5165i	−0.807326	+	0.677427i	0.142642	+	0.989774i	$0.454440\pi$
$242$	4.76423	−	4.56799i	0.306256	−	0.293642i
$243$	2.14364	−	15.4404i	0.137515	−	0.990500i
$244$	−0.110845	+	2.63449i	−0.00709613	+	0.168656i
$245$	−1.85684	−	2.21290i	−0.118629	−	0.141377i
$246$	1.62429	−	1.47357i	0.103561	−	0.0939515i
$247$	5.70888	+	1.00663i	0.363247	+	0.0640503i
$248$	2.26791	−	4.15724i	0.144012	−	0.263985i
$249$	8.27515	+	10.4335i	0.524416	+	0.661194i
$250$	−3.99413	+	5.45636i	−0.252611	+	0.345091i
$251$	6.83069	+	11.8311i	0.431150	+	0.746773i	0.996973	−	0.0777538i	$-0.0247748\pi$
$251$	6.83069	+	11.8311i	0.431150	+	0.746773i	−0.565823	+	0.824527i	$0.691441\pi$
$252$	5.97166	+	0.582465i	0.376179	+	0.0366918i
$253$	16.7296	−	28.9765i	1.05178	−	1.82173i
$254$	7.62469	+	17.2913i	0.478415	+	1.08495i
$255$	1.20073	+	0.246055i	0.0751926	+	0.0154086i
$256$	10.3620	+	12.1913i	0.647627	+	0.761958i
$257$	−14.3511	+	17.1030i	−0.895197	+	1.06685i	0.102201	+	0.994764i	$0.467411\pi$
$257$	−14.3511	+	17.1030i	−0.895197	+	1.06685i	−0.997398	+	0.0720901i	$0.977033\pi$
$258$	−2.37467	+	4.50673i	−0.147840	+	0.280577i
$259$	3.35750	−	9.22466i	0.208625	−	0.573193i
$260$	−2.55946	+	4.03162i	−0.158731	+	0.250031i
$261$	18.0989	+	24.1596i	1.12030	+	1.49544i
$262$	−28.8781	−	8.39241i	−1.78410	−	0.518485i
$263$	−4.45260	−	25.2520i	−0.274559	−	1.55710i	−0.740358	−	0.672212i	$-0.765344\pi$
$263$	−4.45260	−	25.2520i	−0.274559	−	1.55710i	0.465799	−	0.884891i	$-0.345767\pi$
$264$	−14.8119	−	12.5147i	−0.911611	−	0.770228i
$265$	−0.939432	+	0.341925i	−0.0577088	+	0.0210043i
$266$	−5.51686	−	8.24243i	−0.338260	−	0.505376i
$267$	−8.98949	−	16.6124i	−0.550148	−	1.01666i
$268$	13.6426	−	10.5027i	0.833352	−	0.641553i
$269$			6.64010i			0.404854i	0.979297	+	0.202427i	$0.0648829\pi$
$269$			6.64010i			0.404854i	−0.979297	+	0.202427i	$0.935117\pi$
$270$	−3.34012	−	20.9633i	−0.203273	−	1.27579i
$271$			16.0559i			0.975325i	0.873032	+	0.487662i	$0.162150\pi$
$271$			16.0559i			0.975325i	−0.873032	+	0.487662i	$0.837850\pi$
$272$	−0.564571	−	0.800880i	−0.0342321	−	0.0485605i
$273$	0.749755	−	1.21962i	0.0453772	−	0.0738150i
$274$	−2.51132	+	1.68089i	−0.151714	+	0.101546i
$275$	12.4408	−	4.52809i	0.750210	−	0.273054i
$276$	−26.7531	−	11.9057i	−1.61035	−	0.716639i
$277$	3.44322	+	19.5274i	0.206883	+	1.17329i	0.894449	+	0.447169i	$0.147568\pi$
$277$	3.44322	+	19.5274i	0.206883	+	1.17329i	−0.687567	+	0.726121i	$0.741321\pi$
$278$	−7.44396	+	25.6145i	−0.446459	+	1.53626i
$279$	4.89094	+	1.14370i	0.292813	+	0.0684717i
$280$	8.00977	−	1.61303i	0.478675	−	0.0963969i
$281$	1.76928	−	4.86107i	0.105547	−	0.289987i	−0.875666	−	0.482918i	$-0.839577\pi$
$281$	1.76928	−	4.86107i	0.105547	−	0.289987i	0.981212	+	0.192931i	$0.0617993\pi$
$282$	−0.789663	−	20.4203i	−0.0470238	−	1.21601i
$283$	4.73462	−	5.64250i	0.281444	−	0.335412i	−0.606739	−	0.794901i	$-0.707523\pi$
$283$	4.73462	−	5.64250i	0.281444	−	0.335412i	0.888184	+	0.459489i	$0.151967\pi$
$284$	−14.4379	+	15.8063i	−0.856729	+	0.937933i
$285$	−23.2889	+	26.2486i	−1.37951	+	1.55483i
$286$	−4.23353	+	1.86680i	−0.250334	+	0.110386i
$287$	−0.447667	+	0.775383i	−0.0264250	+	0.0457694i
$288$	−9.53515	+	14.0386i	−0.561864	+	0.827230i
$289$	−8.47000	−	14.6705i	−0.498235	−	0.862968i
$290$	33.1702	+	24.2811i	1.94782	+	1.42583i
$291$	−5.67444	+	14.3460i	−0.332641	+	0.840979i
$292$	2.74726	+	8.66532i	0.160771	+	0.507100i
$293$	22.5728	+	3.98019i	1.31871	+	0.232525i	0.788341	−	0.615239i	$-0.210940\pi$
$293$	22.5728	+	3.98019i	1.31871	+	0.232525i	0.530374	+	0.847764i	$0.322052\pi$
$294$	−2.39404	+	0.518246i	−0.139623	+	0.0302247i
$295$	14.2650	+	17.0003i	0.830538	+	0.989796i
$296$	18.3568	+	20.8319i	1.06697	+	1.21083i
$297$	8.60823	−	18.6792i	0.499500	−	1.08388i
$298$	0.740081	+	0.771874i	0.0428717	+	0.0447135i
$299$	−5.35241	+	4.49120i	−0.309538	+	0.259733i
$300$	−5.08107	−	10.4132i	−0.293356	−	0.601204i
$301$	0.361128	−	2.04806i	0.0208150	−	0.118048i
$302$	10.7550	+	5.29319i	0.618880	+	0.304589i
$303$	2.98985	+	20.2004i	0.171763	+	1.16049i
$304$	27.9387	−	2.53350i	1.60239	−	0.145306i
$305$	−3.29829	+	1.90427i	−0.188860	+	0.109038i
$306$	0.659210	−	0.803499i	0.0376845	−	0.0459330i
$307$	0.545489	+	0.314938i	0.0311327	+	0.0179745i	0.515486	−	0.856898i	$-0.327612\pi$
$307$	0.545489	+	0.314938i	0.0311327	+	0.0179745i	−0.484353	+	0.874873i	$0.660945\pi$
$308$	7.31854	+	3.01787i	0.417013	+	0.171959i
$309$	−16.8672	+	5.61725i	−0.959543	+	0.319554i
$310$	6.82497	−	0.452759i	0.387632	−	0.0257150i
$311$	12.4281	+	10.4284i	0.704735	+	0.591343i	0.923116	−	0.384521i	$-0.125633\pi$
$311$	12.4281	+	10.4284i	0.704735	+	0.591343i	−0.218382	+	0.975863i	$0.570078\pi$
$312$	2.01273	+	3.51367i	0.113948	+	0.198922i
$313$	5.20486	+	1.89441i	0.294196	+	0.107079i	0.484902	−	0.874569i	$-0.338855\pi$
$313$	5.20486	+	1.89441i	0.294196	+	0.107079i	−0.190706	+	0.981647i	$0.561078\pi$
$314$	−2.80915	−	11.4408i	−0.158529	−	0.645641i
$315$	3.91258	+	7.73271i	0.220449	+	0.435689i
$316$	−9.21022	−	17.6245i	−0.518116	−	0.991455i
$317$	6.29023	−	1.10914i	0.353295	−	0.0622954i	0.00581547	−	0.999983i	$-0.498149\pi$
$317$	6.29023	−	1.10914i	0.353295	−	0.0622954i	0.347479	+	0.937688i	$0.387038\pi$
$318$	−0.114834	+	0.839896i	−0.00643958	+	0.0470991i
$319$	13.6222	+	37.4266i	0.762695	+	2.09549i
$320$	−6.84450	+	22.0730i	−0.382619	+	1.23392i
$321$	0.226640	−	8.21235i	0.0126498	−	0.458369i
$322$	11.8846	+	1.29205i	0.662301	+	0.0720031i
$323$	−1.71804			−0.0955943
$324$	−17.0465	−	5.78071i	−0.947028	−	0.321151i
$325$	−2.76467			−0.153357
$326$	−4.94081	−	0.537148i	−0.273646	−	0.0297499i
$327$	−0.424443	+	15.3798i	−0.0234718	+	0.850507i
$328$	−1.31887	−	2.16184i	−0.0728227	−	0.119368i
$329$	2.85341	+	7.83967i	0.157313	+	0.432215i
$330$	3.79404	−	27.7496i	0.208855	−	1.52756i
$331$	9.85911	−	1.73843i	0.541906	−	0.0955526i	0.104006	−	0.994577i	$-0.466834\pi$
$331$	9.85911	−	1.73843i	0.541906	−	0.0955526i	0.437899	+	0.899024i	$0.355723\pi$
$332$	13.6282	−	7.12182i	0.747942	−	0.390861i
$333$	−16.1093	+	24.6535i	−0.882782	+	1.35101i
$334$	−7.15698	−	29.1482i	−0.391613	−	1.59492i
$335$	23.3680	+	8.50525i	1.27673	+	0.464691i
$336$	1.95605	−	6.64634i	0.106711	−	0.362588i
$337$	−0.348513	−	0.292437i	−0.0189847	−	0.0159301i	0.633246	−	0.773951i	$-0.281722\pi$
$337$	−0.348513	−	0.292437i	−0.0189847	−	0.0159301i	−0.652231	+	0.758021i	$0.726167\pi$
$338$	−17.3804	+	1.15299i	−0.945368	+	0.0627144i
$339$	−10.4342	+	3.47488i	−0.566708	+	0.188729i
$340$	0.539539	−	1.30842i	0.0292606	−	0.0709590i
$341$	5.73927	+	3.31357i	0.310799	+	0.179440i
$342$	10.4855	+	27.8463i	0.566988	+	1.50576i
$343$	0.866025	−	0.500000i	0.0467610	−	0.0269975i
$344$	4.59612	+	3.67086i	0.247806	+	0.197920i
$345$	−6.19258	−	41.8391i	−0.333397	−	2.25254i
$346$	−1.31694	−	0.648147i	−0.0707991	−	0.0348446i
$347$	0.348598	−	1.97700i	0.0187137	−	0.106131i	−0.974020	−	0.226461i	$-0.927284\pi$
$347$	0.348598	−	1.97700i	0.0187137	−	0.106131i	0.992734	+	0.120331i	$0.0383954\pi$
$348$	31.3266	−	15.2857i	1.67928	−	0.819401i
$349$	−1.55760	+	1.30698i	−0.0833766	+	0.0699613i	−0.683523	−	0.729929i	$-0.739553\pi$
$349$	−1.55760	+	1.30698i	−0.0833766	+	0.0699613i	0.600147	+	0.799890i	$0.295109\pi$
$350$	3.27373	+	3.41437i	0.174988	+	0.182506i
$351$	−3.02330	+	3.05060i	−0.161372	+	0.162829i
$352$	−17.4066	+	14.0840i	−0.927777	+	0.750677i
$353$	−1.25734	−	1.49844i	−0.0669215	−	0.0797539i	0.731545	−	0.681793i	$-0.238800\pi$
$353$	−1.25734	−	1.49844i	−0.0669215	−	0.0797539i	−0.798467	+	0.602039i	$0.794355\pi$
$354$	18.3919	−	3.98136i	0.977518	−	0.211607i
$355$	−30.4509	−	5.36931i	−1.61617	−	0.284974i
$356$	−20.7909	+	6.59157i	−1.10192	+	0.349352i
$357$	−0.156062	+	0.394554i	−0.00825968	+	0.0208820i
$358$	−19.8898	−	14.5596i	−1.05121	−	0.769498i
$359$	4.37599	+	7.57943i	0.230956	+	0.400027i	0.958090	−	0.286468i	$-0.0924814\pi$
$359$	4.37599	+	7.57943i	0.230956	+	0.400027i	−0.727134	+	0.686496i	$0.759148\pi$
$360$	−24.5000	−	0.759473i	−1.29126	−	0.0400277i
$361$	15.0934	−	26.1425i	0.794387	−	1.37592i
$362$	33.0335	−	14.5663i	1.73620	−	0.765588i
$363$	5.36497	−	6.04679i	0.281588	−	0.317374i
$364$	−1.22058	−	1.11490i	−0.0639757	−	0.0584368i
$365$	−8.43971	+	10.0581i	−0.441755	+	0.526463i
$366$	0.124790	+	3.22702i	0.00652289	+	0.168679i
$367$	5.59511	−	15.3724i	0.292062	−	0.802434i	−0.703702	−	0.710495i	$-0.748471\pi$
$367$	5.59511	−	15.3724i	0.292062	−	0.802434i	0.995765	−	0.0919395i	$-0.0293066\pi$
$368$	−19.3063	+	27.7590i	−1.00641	+	1.44704i
$369$	1.83739	−	1.95924i	0.0956504	−	0.101994i
$370$	−11.1918	+	38.5107i	−0.581832	+	2.00207i
$371$	−0.0600955	−	0.340819i	−0.00312000	−	0.0176944i
$372$	2.35812	−	5.29890i	0.122263	−	0.274735i
$373$	11.7969	−	4.29373i	0.610821	−	0.222321i	−0.0180414	−	0.999837i	$-0.505743\pi$
$373$	11.7969	−	4.29373i	0.610821	−	0.222321i	0.628862	+	0.777517i	$0.283521\pi$
$374$	1.13956	−	0.762733i	0.0589251	−	0.0394400i
$375$	−4.33716	+	7.05525i	−0.223970	+	0.364331i
$376$	−23.3308	−	3.53425i	−1.20320	−	0.182265i
$377$		−	8.31716i		−	0.428356i
$378$	7.34747	+	0.121462i	0.377913	+	0.00624733i
$379$		−	23.3931i		−	1.20162i	−0.799390	−	0.600812i	$-0.794844\pi$
$379$		−	23.3931i		−	1.20162i	0.799390	−	0.600812i	$-0.205156\pi$
$380$	24.7174	+	32.1070i	1.26798	+	1.64705i
$381$	11.0151	+	20.3557i	0.564320	+	1.04285i
$382$	−2.03187	−	3.03571i	−0.103960	−	0.155320i
$383$	1.21216	−	0.441189i	0.0619383	−	0.0225437i	−0.310865	−	0.950454i	$-0.600619\pi$
$383$	1.21216	−	0.441189i	0.0619383	−	0.0225437i	0.372804	+	0.927910i	$0.378397\pi$
$384$	13.8532	+	13.8596i	0.706943	+	0.707271i
$385$	1.98551	+	11.2604i	0.101191	+	0.573883i
$386$	−24.7341	−	7.18809i	−1.25893	−	0.365864i
$387$	−2.45394	+	5.73609i	−0.124741	+	0.291582i
$388$	15.0394	+	9.54773i	0.763511	+	0.484712i
$389$	4.79152	−	13.1646i	0.242940	−	0.667471i	−0.756962	−	0.653459i	$-0.773317\pi$
$389$	4.79152	−	13.1646i	0.242940	−	0.667471i	0.999902	−	0.0140126i	$-0.00446050\pi$
$390$	−2.72644	+	5.17433i	−0.138059	+	0.262013i
$391$	1.33106	−	1.58629i	0.0673145	−	0.0802222i
$392$	0.0684180	+	2.82760i	0.00345563	+	0.142815i
$393$	−36.0818	−	7.39395i	−1.82009	−	0.372975i
$394$	−12.6262	−	28.6336i	−0.636097	−	1.44254i
$395$	14.3613	−	24.8745i	0.722595	−	1.25157i
$396$	−19.3174	−	13.8151i	−0.970735	−	0.694233i
$397$	4.87314	+	8.44052i	0.244576	+	0.423618i	0.962012	−	0.273006i	$-0.0880179\pi$
$397$	4.87314	+	8.44052i	0.244576	+	0.423618i	−0.717436	+	0.696624i	$0.754685\pi$
$398$	−4.65954	+	6.36537i	−0.233561	+	0.319067i
$399$	−7.54854	−	9.51734i	−0.377900	−	0.476463i
$400$	−12.9122	+	3.50369i	−0.645611	+	0.175184i
$401$	13.9535	+	2.46038i	0.696805	+	0.122866i	0.510821	−	0.859687i	$-0.329342\pi$
$401$	13.9535	+	2.46038i	0.696805	+	0.122866i	0.185984	+	0.982553i	$0.440453\pi$
$402$	15.6173	−	14.1682i	0.778922	−	0.706644i
$403$	−0.889558	−	1.06013i	−0.0443121	−	0.0528091i
$404$	23.5587	+	0.991224i	1.17209	+	0.0493152i
$405$	−6.14721	−	25.2614i	−0.305457	−	1.25525i
$406$	−10.2717	+	9.84858i	−0.509775	+	0.488777i
$407$	−29.7655	+	24.9762i	−1.47542	+	1.23803i
$408$	−0.768276	−	0.921941i	−0.0380353	−	0.0456429i
$409$	1.60138	−	9.08189i	0.0791833	−	0.449071i	−0.919278	−	0.393610i	$-0.871226\pi$
$409$	1.60138	−	9.08189i	0.0791833	−	0.449071i	0.998461	−	0.0554607i	$-0.0176628\pi$
$410$	1.61516	−	3.28177i	0.0797672	−	0.162075i
$411$	−2.89976	+	2.29990i	−0.143035	+	0.113446i
$412$	2.71170	+	20.3484i	0.133596	+	1.00249i
$413$	−6.65313	+	3.84119i	−0.327379	+	0.189012i
$414$	−33.8345	−	11.8926i	−1.66288	−	0.584491i
$415$	19.2342	+	11.1049i	0.944172	+	0.545118i
$416$	4.42162	−	1.52048i	0.216788	−	0.0745478i
$417$	−6.55833	+	32.0041i	−0.321163	+	1.56725i
$418$	2.59864	+	39.1724i	0.127104	+	1.91599i
$419$	−16.1602	−	13.5600i	−0.789479	−	0.662451i	0.156138	−	0.987735i	$-0.450096\pi$
$419$	−16.1602	−	13.5600i	−0.789479	−	0.662451i	−0.945616	+	0.325284i	$0.894540\pi$
$420$	9.61874	−	2.75993i	0.469347	−	0.134671i
$421$	18.9819	+	6.90883i	0.925119	+	0.336716i	0.760273	−	0.649603i	$-0.225065\pi$
$421$	18.9819	+	6.90883i	0.925119	+	0.336716i	0.164846	+	0.986319i	$0.447287\pi$
$422$	−7.69172	+	1.88861i	−0.374427	+	0.0919360i
$423$	−2.98011	−	24.8503i	−0.144898	−	1.20827i
$424$	0.927649	+	0.312439i	0.0450506	+	0.0151734i
$425$	0.806918	−	0.142281i	0.0391413	−	0.00690166i
$426$	−16.0646	+	20.7212i	−0.778331	+	1.00394i
$427$	−0.450923	−	1.23890i	−0.0218217	−	0.0599546i
$428$	−9.26479	−	2.03857i	−0.447831	−	0.0985379i
$429$	−4.98381	+	2.69689i	−0.240621	+	0.130207i
$430$	−0.918243	+	8.44620i	−0.0442816	+	0.407312i
$431$	−15.2753			−0.735787			−0.367894	−	0.929868i	$-0.619921\pi$
$431$	−15.2753			−0.735787			−0.367894	+	0.929868i	$0.619921\pi$
$432$	−10.2541	+	18.0791i	−0.493350	+	0.869831i
$433$	2.98946			0.143664			0.0718321	−	0.997417i	$-0.477115\pi$
$433$	2.98946			0.143664			0.0718321	+	0.997417i	$0.477115\pi$
$434$	−0.255912	+	2.35394i	−0.0122842	+	0.112993i
$435$	42.8902	+	26.3664i	2.05643	+	1.26417i
$436$	17.3508	+	3.81777i	0.830953	+	0.182838i
$437$	20.2766	+	55.7095i	0.969962	+	2.66495i
$438$	4.20927	+	10.3070i	0.201127	+	0.492489i
$439$	0.950483	−	0.167596i	0.0453641	−	0.00799891i	−0.150920	−	0.988546i	$-0.548224\pi$
$439$	0.950483	−	0.167596i	0.0453641	−	0.00799891i	0.196284	+	0.980547i	$0.437112\pi$
$440$	−30.6489	−	10.3228i	−1.46113	−	0.492118i
$441$	−2.87138	+	0.869019i	−0.136732	+	0.0413818i
$442$	−0.278092	+	0.0682820i	−0.0132275	+	0.00324784i
$443$	−21.9883	−	8.00307i	−1.04469	−	0.380237i	−0.238036	−	0.971256i	$-0.576504\pi$
$443$	−21.9883	−	8.00307i	−1.04469	−	0.380237i	−0.806658	+	0.591019i	$0.798726\pi$
$444$	24.4659	+	23.6183i	1.16110	+	1.12088i
$445$	−24.1326	−	20.2496i	−1.14399	−	0.959924i
$446$	−1.45237	−	21.8933i	−0.0687717	−	1.03668i
$447$	0.979668	+	0.869204i	0.0463367	+	0.0411119i
$448$	−7.11355	−	3.66024i	−0.336084	−	0.172930i
$449$	28.5702	+	16.4950i	1.34831	+	0.778448i	0.988010	−	0.154387i	$-0.0493404\pi$
$449$	28.5702	+	16.4950i	1.34831	+	0.778448i	0.360302	+	0.932836i	$0.382674\pi$
$450$	−7.23086	−	12.2103i	−0.340866	−	0.575599i
$451$	3.06910	−	1.77195i	0.144518	−	0.0834377i
$452$	1.67748	+	12.5876i	0.0789019	+	0.592073i
$453$	13.6518	+	5.39986i	0.641420	+	0.253708i
$454$	11.1794	−	22.7148i	0.524673	−	1.06606i
$455$	0.414623	−	2.35144i	0.0194378	−	0.110237i
$456$	33.8562	−	5.85120i	1.58546	−	0.274007i
$457$	25.6657	−	21.5361i	1.20059	−	1.00742i	0.200978	−	0.979596i	$-0.435588\pi$
$457$	25.6657	−	21.5361i	1.20059	−	1.00742i	0.999613	−	0.0278199i	$-0.00885649\pi$
$458$	−5.38095	+	5.15931i	−0.251435	+	0.241079i
$459$	0.725406	−	1.04596i	0.0338591	−	0.0488214i
$460$	−48.7948	−	2.05302i	−2.27507	−	0.0957225i
$461$	26.2641	+	31.3003i	1.22324	+	1.45780i	0.847264	+	0.531172i	$0.178248\pi$
$461$	26.2641	+	31.3003i	1.22324	+	1.45780i	0.375977	+	0.926629i	$0.377307\pi$
$462$	9.23213	+	2.96153i	0.429518	+	0.137783i
$463$	−17.6080	−	3.10477i	−0.818315	−	0.144291i	−0.251206	−	0.967934i	$-0.580827\pi$
$463$	−17.6080	−	3.10477i	−0.818315	−	0.144291i	−0.567109	+	0.823643i	$0.691938\pi$
$464$	−10.5404	−	38.8448i	−0.489325	−	1.80332i
$465$	8.28694	−	1.22654i	0.384297	−	0.0568796i
$466$	−7.05396	+	9.63638i	−0.326768	+	0.446397i
$467$	14.6901	+	25.4440i	0.679776	+	1.17741i	0.975048	+	0.221994i	$0.0712565\pi$
$467$	14.6901	+	25.4440i	0.679776	+	1.17741i	−0.295272	+	0.955413i	$0.595410\pi$
$468$	2.80396	+	4.09062i	0.129613	+	0.189089i
$469$	−4.30425	+	7.45518i	−0.198752	+	0.344248i
$470$	−13.7514	−	31.1854i	−0.634305	−	1.43848i
$471$	−4.55885	−	13.6891i	−0.210061	−	0.630761i
$472$	−0.525613	−	21.7227i	−0.0241933	−	0.999867i
$473$	−5.29118	+	6.30579i	−0.243289	+	0.289940i
$474$	−12.9835	−	20.6059i	−0.596354	−	0.946461i
$475$	−8.02313	+	22.0434i	−0.368127	+	1.01142i
$476$	0.413624	+	0.262588i	0.0189584	+	0.0120357i
$477$	−0.0572612	+	1.03665i	−0.00262181	+	0.0474649i
$478$	−2.79205	−	0.811411i	−0.127705	−	0.0371131i
$479$	4.95871	+	28.1223i	0.226569	+	1.28494i	0.859662	+	0.510863i	$0.170674\pi$
$479$	4.95871	+	28.1223i	0.226569	+	1.28494i	−0.633093	+	0.774076i	$0.718215\pi$
$480$	−6.17619	+	27.6216i	−0.281903	+	1.26075i
$481$	7.62476	−	2.77519i	0.347659	−	0.126538i
$482$	12.8698	+	19.2280i	0.586203	+	0.875813i
$483$	14.6358	+	0.403909i	0.665950	+	0.0183785i
$484$	−5.69407	−	7.39638i	−0.258821	−	0.336199i
$485$			25.7302i			1.16835i
$486$	−21.3804	−	5.37384i	−0.969835	−	0.243762i
$487$			35.6923i			1.61737i	0.588241	+	0.808686i	$0.299821\pi$
$487$			35.6923i			1.61737i	−0.588241	+	0.808686i	$0.700179\pi$
$488$	3.68697	+	0.558517i	0.166901	+	0.0252829i
$489$	−6.08457	−	0.167918i	−0.275154	−	0.00759353i
$490$	−3.39499	+	2.27235i	−0.153370	+	0.102654i
$491$	−4.34295	+	1.58070i	−0.195994	+	0.0713361i	−0.438152	−	0.898901i	$-0.644367\pi$
$491$	−4.34295	+	1.58070i	−0.195994	+	0.0713361i	0.242158	+	0.970237i	$0.422145\pi$
$492$	−1.82347	−	2.50888i	−0.0822083	−	0.113109i
$493$	0.428035	+	2.42751i	0.0192777	+	0.109329i
$494$	2.28784	−	7.87242i	0.102935	−	0.354197i
$495$	1.89187	−	34.2501i	0.0850332	−	1.53943i
$496$	−5.49814	−	3.82395i	−0.246874	−	0.171700i
$497$	3.66094	−	10.0583i	0.164216	−	0.451179i
$498$	15.9336	−	10.0395i	0.713999	−	0.449883i
$499$	−1.54851	+	1.84545i	−0.0693210	+	0.0826135i	−0.799590	−	0.600546i	$-0.794950\pi$
$499$	−1.54851	+	1.84545i	−0.0693210	+	0.0826135i	0.730269	+	0.683159i	$0.239395\pi$
$500$	7.06077	+	6.44946i	0.315767	+	0.288429i
$501$	−11.6148	−	34.8763i	−0.518910	−	1.55816i
$502$	17.6778	−	7.79511i	0.788997	−	0.347913i
$503$	13.2868	−	23.0135i	0.592431	−	1.02612i	−0.401473	−	0.915871i	$-0.631502\pi$
$503$	13.2868	−	23.0135i	0.592431	−	1.02612i	0.993904	−	0.110249i	$-0.0351649\pi$
$504$	1.73166	−	8.30671i	0.0771343	−	0.370010i
$505$	17.0288	+	29.4947i	0.757771	+	1.31250i
$506$	−38.1818	−	27.9496i	−1.69739	−	1.24251i
$507$	−21.1034	+	3.12350i	−0.937235	+	0.138720i
$508$	25.4757	−	8.07684i	1.13030	−	0.358352i
$509$	11.2306	+	1.98025i	0.497786	+	0.0877731i	0.416904	−	0.908951i	$-0.363115\pi$
$509$	11.2306	+	1.98025i	0.497786	+	0.0877731i	0.0808820	+	0.996724i	$0.474226\pi$
$510$	0.529466	−	1.65053i	0.0234451	−	0.0730868i
$511$	−2.92160	−	3.48182i	−0.129244	−	0.154027i
$512$	18.7240	−	12.7049i	0.827490	−	0.561481i
$513$	15.5495	+	32.9584i	0.686527	+	1.45515i
$514$	21.8520	+	22.7908i	0.963852	+	1.00526i
$515$	−22.7135	+	19.0589i	−1.00088	+	0.839834i
$516$	5.97318	+	4.02746i	0.262955	+	0.177299i
$517$	5.73425	−	32.5206i	0.252192	−	1.43025i
$518$	−12.4560	−	6.13038i	−0.547287	−	0.269354i
$519$	−1.67166	−	0.661209i	−0.0733776	−	0.0290238i
$520$	5.27697	+	4.21464i	0.231410	+	0.184824i
$521$	14.6183	−	8.43990i	0.640441	−	0.369759i	−0.144343	−	0.989528i	$-0.546107\pi$
$521$	14.6183	−	8.43990i	0.640441	−	0.369759i	0.784784	+	0.619769i	$0.212774\pi$
$522$	36.7331	−	21.7531i	1.60776	−	0.952107i
$523$	−10.8668	−	6.27396i	−0.475173	−	0.274341i	0.243230	−	0.969969i	$-0.421793\pi$
$523$	−10.8668	−	6.27396i	−0.475173	−	0.274341i	−0.718403	+	0.695628i	$0.755126\pi$
$524$	−16.2131	+	39.3179i	−0.708273	+	1.71761i
$525$	4.33354	+	3.84490i	0.189131	+	0.167805i
$526$	−36.1831	+	2.40033i	−1.57766	+	0.104660i
$527$	0.314192	+	0.263638i	0.0136864	+	0.0114843i
$528$	−19.8588	+	18.9117i	−0.864242	+	0.823025i
$529$	−45.5339	−	16.5730i	−1.97973	−	0.720564i
$530$	0.337133	+	1.37304i	0.0146441	+	0.0596409i
$531$	22.0590	−	6.67612i	0.957279	−	0.289719i
$532$	−12.4315	+	6.49648i	−0.538975	+	0.281658i
$533$	−0.728807	+	0.128508i	−0.0315681	+	0.00556631i
$534$	−24.7299	+	10.0994i	−1.07017	+	0.437045i
$535$	−4.68632	−	12.8755i	−0.202607	−	0.556658i
$536$	−12.6808	−	20.7858i	−0.547726	−	0.897809i
$537$	−25.7181	−	15.8100i	−1.10982	−	0.682252i
$538$	9.33551	+	1.01493i	0.402482	+	0.0437565i
$539$	−3.95817			−0.170491
$540$	−29.9835	+	1.49177i	−1.29029	+	0.0641955i
$541$	31.9387			1.37315			0.686576	−	0.727058i	$-0.259113\pi$
$541$	31.9387			1.37315			0.686576	+	0.727058i	$0.259113\pi$
$542$	22.5734	+	2.45411i	0.969612	+	0.105413i
$543$	38.8878	−	21.0434i	1.66883	−	0.903058i
$544$	−1.21227	+	0.671334i	−0.0519759	+	0.0287832i
$545$	8.77638	+	24.1129i	0.375939	+	1.03288i
$546$	−1.60011	−	1.24052i	−0.0684783	−	0.0530893i
$547$	16.5868	−	2.92469i	0.709199	−	0.125051i	0.192598	−	0.981278i	$-0.438309\pi$
$547$	16.5868	−	2.92469i	0.709199	−	0.125051i	0.516600	+	0.856227i	$0.327197\pi$
$548$	1.97936	+	3.78766i	0.0845540	+	0.161801i
$549$	0.470945	+	3.92709i	0.0200995	+	0.167604i
$550$	−4.46462	−	18.1830i	−0.190372	−	0.775327i
$551$	−66.3146	−	24.1365i	−2.82510	−	1.02825i
$552$	−20.8277	+	35.7932i	−0.886487	+	1.52346i
$553$	7.61676	+	6.39122i	0.323897	+	0.271782i
$554$	27.9805	−	1.85619i	1.18878	−	0.0788619i
$555$	−9.86026	+	48.1172i	−0.418545	+	2.04246i
$556$	34.8744	+	14.3808i	1.47901	+	0.609882i
$557$	−30.0023	−	17.3218i	−1.27124	−	0.733949i	−0.296016	−	0.955183i	$-0.595658\pi$
$557$	−30.0023	−	17.3218i	−1.27124	−	0.733949i	−0.975221	+	0.221234i	$0.928991\pi$
$558$	2.35554	−	6.70150i	0.0997178	−	0.283697i
$559$	1.48866	−	0.859480i	0.0629638	−	0.0363521i
$560$	−1.04353	−	11.5077i	−0.0440971	−	0.486290i
$561$	1.31582	−	1.04362i	0.0555539	−	0.0440618i
$562$	−6.56389	−	3.23049i	−0.276881	−	0.136270i
$563$	−2.00417	+	11.3662i	−0.0844657	+	0.479029i	0.913005	+	0.407949i	$0.133756\pi$
$563$	−2.00417	+	11.3662i	−0.0844657	+	0.479029i	−0.997471	+	0.0710802i	$0.977355\pi$
$564$	−28.8303	−	2.01100i	−1.21397	−	0.0846782i
$565$	−14.0507	+	11.7900i	−0.591118	+	0.496007i
$566$	−7.20929	−	7.51899i	−0.303029	−	0.316047i
$567$	8.98148	−	0.577146i	0.377187	−	0.0242378i
$568$	20.0158	+	22.7146i	0.839844	+	0.953082i
$569$	−18.4603	−	22.0001i	−0.773896	−	0.922293i	0.224745	−	0.974418i	$-0.427845\pi$
$569$	−18.4603	−	22.0001i	−0.773896	−	0.922293i	−0.998641	+	0.0521243i	$0.983401\pi$
$570$	33.3440	+	36.7545i	1.39663	+	1.53948i
$571$	−17.6466	−	3.11157i	−0.738487	−	0.130215i	−0.208263	−	0.978073i	$-0.566781\pi$
$571$	−17.6466	−	3.11157i	−0.738487	−	0.130215i	−0.530224	+	0.847858i	$0.677892\pi$
$572$	1.97750	+	6.23738i	0.0826836	+	0.260798i
$573$	−2.78015	−	3.50526i	−0.116142	−	0.146434i
$574$	1.02171	+	0.747905i	0.0426453	+	0.0312169i
$575$	−14.1370	−	24.4860i	−0.589555	−	1.02114i
$576$	18.2798	+	15.5515i	0.761658	+	0.647980i
$577$	7.74571	−	13.4160i	0.322458	−	0.558514i	−0.658536	−	0.752549i	$-0.728824\pi$
$577$	7.74571	−	13.4160i	0.322458	−	0.558514i	0.980995	+	0.194035i	$0.0621575\pi$
$578$	−21.9203	+	9.66587i	−0.911762	+	0.402047i
$579$	−30.9041	−	6.33291i	−1.28433	−	0.263187i
$580$	39.2075	−	42.9237i	1.62800	−	1.78231i
$581$	−4.94202	+	5.88967i	−0.205029	+	0.244345i
$582$	19.3022	+	10.1706i	0.800101	+	0.421586i
$583$	−0.468510	+	1.28722i	−0.0194037	+	0.0533112i
$584$	12.6027	−	2.53797i	0.521505	−	0.105022i
$585$	−2.81746	+	6.58580i	−0.116488	+	0.272289i
$586$	9.04606	−	31.1273i	0.373689	−	1.28586i
$587$	0.266188	+	1.50963i	0.0109868	+	0.0623091i	0.989808	−	0.142407i	$-0.0454841\pi$
$587$	0.266188	+	1.50963i	0.0109868	+	0.0623091i	−0.978821	+	0.204716i	$0.934373\pi$
$588$	0.362693	+	3.44506i	0.0149572	+	0.142072i
$589$	−11.0342	+	4.01612i	−0.454657	+	0.165481i
$590$	26.0816	−	17.4571i	1.07376	−	0.718696i
$591$	−18.2405	−	33.7081i	−0.750315	−	1.38657i
$592$	32.0939	−	22.6242i	1.31905	−	0.929850i
$593$		−	35.5387i		−	1.45940i	−0.683769	−	0.729699i	$-0.739660\pi$
$593$		−	35.5387i		−	1.45940i	0.683769	−	0.729699i	$-0.260340\pi$
$594$	−24.9458	−	14.9576i	−1.02354	−	0.613719i
$595$			0.707648i			0.0290107i
$596$	1.19832	−	0.922522i	0.0490851	−	0.0377880i
$597$	−5.05971	+	8.23062i	−0.207080	+	0.336857i
$598$	5.49621	+	8.21158i	0.224757	+	0.335796i
$599$	41.9968	−	15.2856i	1.71594	−	0.624552i	0.718466	−	0.695562i	$-0.244845\pi$
$599$	41.9968	−	15.2856i	1.71594	−	0.624552i	0.997476	+	0.0710105i	$0.0226224\pi$
$600$	−15.4168	+	5.55199i	−0.629388	+	0.226659i
$601$	−3.33958	−	18.9397i	−0.136224	−	0.772567i	−0.973999	−	0.226551i	$-0.927255\pi$
$601$	−3.33958	−	18.9397i	−0.136224	−	0.772567i	0.837775	−	0.546016i	$-0.183856\pi$
$602$	−2.82422	−	0.820761i	−0.115107	−	0.0334517i
$603$	17.6662	−	18.8378i	0.719422	−	0.767136i
$604$	9.08573	−	14.3117i	0.369693	−	0.582335i
$605$	4.61116	−	12.6691i	0.187470	−	0.515071i
$606$	28.8574	−	1.11593i	1.17225	−	0.0453315i
$607$	10.7007	−	12.7526i	0.434327	−	0.517610i	−0.503839	−	0.863798i	$-0.668079\pi$
$607$	10.7007	−	12.7526i	0.434327	−	0.517610i	0.938165	+	0.346187i	$0.112524\pi$
$608$	0.708450	−	39.6670i	0.0287314	−	1.60871i
$609$	−11.5669	+	13.0369i	−0.468713	+	0.528281i
$610$	2.17313	+	4.92823i	0.0879875	+	0.199538i
$611$	−3.44792	+	5.97197i	−0.139488	+	0.241600i
$612$	−1.02890	−	1.04962i	−0.0415910	−	0.0424282i
$613$	8.31281	+	14.3982i	0.335751	+	0.581538i	0.983629	−	0.180206i	$-0.0576765\pi$
$613$	8.31281	+	14.3982i	0.335751	+	0.581538i	−0.647878	+	0.761744i	$0.724343\pi$
$614$	0.526158	−	0.718781i	0.0212340	−	0.0290076i
$615$	1.64771	−	4.16572i	0.0664421	−	0.167978i
$616$	5.36154	−	9.82808i	0.216022	−	0.395984i
$617$	−36.8594	−	6.49931i	−1.48390	−	0.261652i	−0.627768	−	0.778401i	$-0.716031\pi$
$617$	−36.8594	−	6.49931i	−1.48390	−	0.261652i	−0.856137	+	0.516748i	$0.827142\pi$
$618$	5.31934	+	24.5727i	0.213975	+	0.988460i
$619$	−4.88758	−	5.82479i	−0.196448	−	0.234118i	0.658824	−	0.752298i	$-0.271054\pi$
$619$	−4.88758	−	5.82479i	−0.196448	−	0.234118i	−0.855272	+	0.518179i	$0.826610\pi$
$620$	0.406635	−	9.66462i	0.0163309	−	0.388141i
$621$	−42.4780	−	11.1775i	−1.70458	−	0.448539i
$622$	16.5613	−	15.8791i	0.664046	−	0.636694i
$623$	8.35402	−	7.00986i	0.334697	−	0.280844i
$624$	5.24761	−	2.29269i	0.210072	−	0.0917812i
$625$	−5.30258	+	30.0724i	−0.212103	+	1.20290i
$626$	3.45896	−	7.02810i	0.138248	−	0.280899i
$627$	7.03984	+	47.5635i	0.281144	+	1.89950i
$628$	−16.5143	+	2.20076i	−0.658993	+	0.0878199i
$629$	−2.08260	+	1.20239i	−0.0830385	+	0.0479423i
$630$	11.4697	−	4.31888i	0.456963	−	0.172068i
$631$	2.40296	+	1.38735i	0.0956603	+	0.0552295i	0.547067	−	0.837089i	$-0.315744\pi$
$631$	2.40296	+	1.38735i	0.0956603	+	0.0552295i	−0.451407	+	0.892318i	$0.649078\pi$
$632$	−26.1865	+	10.2551i	−1.04164	+	0.407924i
$633$	−9.20327	+	3.06494i	−0.365797	+	0.121821i
$634$	−0.597920	−	9.01315i	−0.0237464	−	0.357958i
$635$	29.5703	+	24.8124i	1.17346	+	0.984652i
$636$	1.16328	+	0.289825i	0.0461272	+	0.0114923i
$637$	0.776714	+	0.282701i	0.0307745	+	0.0112010i
$638$	54.7013	−	13.4312i	2.16564	−	0.531747i
$639$	−17.5651	+	26.8816i	−0.694866	+	1.06342i
$640$	29.9870	+	12.9967i	1.18534	+	0.513740i
$641$	−31.6223	+	5.57586i	−1.24901	+	0.220233i	−0.758771	−	0.651357i	$-0.774200\pi$
$641$	−31.6223	+	5.57586i	−1.24901	+	0.220233i	−0.490234	+	0.871591i	$0.663089\pi$
$642$	−11.5113	−	1.57388i	−0.454317	−	0.0621161i
$643$	7.01542	+	19.2747i	0.276661	+	0.760121i	0.997735	+	0.0672627i	$0.0214266\pi$
$643$	7.01542	+	19.2747i	0.276661	+	0.760121i	−0.721074	+	0.692858i	$0.756351\pi$
$644$	3.63306	−	16.5114i	0.143163	−	0.650639i
$645$	−0.287053	+	10.4014i	−0.0113027	+	0.409556i
$646$	−0.262599	+	2.41544i	−0.0103318	+	0.0950344i
$647$	6.98871			0.274755			0.137377	−	0.990519i	$-0.456133\pi$
$647$	6.98871			0.274755			0.137377	+	0.990519i	$0.456133\pi$
$648$	−10.7328	+	23.0826i	−0.421624	+	0.906771i
$649$	30.4082			1.19362
$650$	−0.422575	+	3.88694i	−0.0165747	+	0.152458i
$651$	−0.0800009	+	2.89886i	−0.00313548	+	0.113615i
$652$	−1.51038	+	6.86432i	−0.0591512	+	0.268828i
$653$	−11.2248	−	30.8399i	−0.439261	−	1.20686i	−0.939974	−	0.341246i	$-0.889151\pi$
$653$	−11.2248	−	30.8399i	−0.439261	−	1.20686i	0.500713	−	0.865613i	$-0.333071\pi$
$654$	21.5581	+	2.94751i	0.842988	+	0.115257i
$655$	−60.4950	+	10.6669i	−2.36373	+	0.416790i
$656$	−3.24099	+	1.52381i	−0.126539	+	0.0594948i
$657$	6.15613	+	12.1668i	0.240174	+	0.474673i
$658$	11.4582	−	2.81341i	0.446685	−	0.109678i
$659$	−9.78656	−	3.56202i	−0.381230	−	0.138756i	0.144295	−	0.989535i	$-0.453909\pi$
$659$	−9.78656	−	3.56202i	−0.381230	−	0.138756i	−0.525525	+	0.850778i	$0.676131\pi$
$660$	−38.4340	−	9.57562i	−1.49604	−	0.372730i
$661$	−14.1672	−	11.8877i	−0.551040	−	0.462377i	0.324253	−	0.945970i	$-0.394887\pi$
$661$	−14.1672	−	11.8877i	−0.551040	−	0.462377i	−0.875293	+	0.483593i	$0.839331\pi$
$662$	−0.937161	−	14.1269i	−0.0364238	−	0.549059i
$663$	−0.332741	+	0.110812i	−0.0129226	+	0.00430358i
$664$	−7.92974	−	20.2488i	−0.307734	−	0.785805i
$665$	−17.5454	−	10.1298i	−0.680380	−	0.392817i
$666$	32.1989	+	26.4167i	1.24768	+	1.02363i
$667$	73.6631	−	42.5294i	2.85225	−	1.64674i
$668$	−42.0742	+	5.60697i	−1.62790	+	0.216940i
$669$	−3.93454	−	26.5830i	−0.152118	−	1.02776i
$670$	15.5295	−	31.5537i	0.599958	−	1.21903i
$671$	−0.906183	+	5.13922i	−0.0349828	+	0.198397i
$672$	−9.04531	−	3.76594i	−0.348931	−	0.145274i
$673$	7.00366	−	5.87677i	0.269971	−	0.226533i	−0.497744	−	0.867324i	$-0.665838\pi$
$673$	7.00366	−	5.87677i	0.269971	−	0.226533i	0.767715	+	0.640791i	$0.221394\pi$
$674$	−0.464415	+	0.445286i	−0.0178886	+	0.0171518i
$675$	−10.0327	−	14.1919i	−0.386158	−	0.546247i
$676$	−1.03553	+	24.6118i	−0.0398282	+	0.946608i
$677$	26.5318	+	31.6193i	1.01970	+	1.21523i	0.976356	+	0.216169i	$0.0693561\pi$
$677$	26.5318	+	31.6193i	1.01970	+	1.21523i	0.0433420	+	0.999060i	$0.486199\pi$
$678$	3.29058	+	15.2009i	0.126374	+	0.583786i
$679$	−8.77175	−	1.54670i	−0.336629	−	0.0593568i
$680$	−1.75708	−	0.958543i	−0.0673808	−	0.0367584i
$681$	11.4046	−	28.8330i	0.437027	−	1.10488i
$682$	5.53588	−	7.56254i	0.211980	−	0.289585i
$683$	−22.3067	−	38.6364i	−0.853543	−	1.47838i	−0.877990	−	0.478679i	$-0.841116\pi$
$683$	−22.3067	−	38.6364i	−0.853543	−	1.47838i	0.0244473	−	0.999701i	$-0.492217\pi$
$684$	40.7526	−	10.4856i	1.55821	−	0.400925i
$685$	−3.08637	+	5.34575i	−0.117924	+	0.204251i
$686$	−0.570594	−	1.29399i	−0.0217854	−	0.0494049i
$687$	−6.05946	+	6.82954i	−0.231183	+	0.260563i
$688$	5.86348	−	5.90074i	0.223543	−	0.224964i
$689$	0.183872	−	0.219130i	0.00700495	−	0.00834818i
$690$	−59.7693	+	2.31131i	−2.27538	+	0.0879899i
$691$	1.73411	−	4.76443i	0.0659687	−	0.181248i	−0.902328	−	0.431050i	$-0.858143\pi$
$691$	1.73411	−	4.76443i	0.0659687	−	0.181248i	0.968297	+	0.249802i	$0.0803656\pi$
$692$	−1.11254	+	1.75246i	−0.0422924	+	0.0666184i
$693$	11.5626	+	2.70381i	0.439227	+	0.102709i
$694$	−2.72624	−	0.792284i	−0.103486	−	0.0300747i
$695$	9.46140	+	53.6583i	0.358891	+	2.03537i
$696$	−16.7024	−	46.3794i	−0.633104	−	1.75801i
$697$	0.206101	−	0.0750148i	0.00780665	−	0.00284139i
$698$	1.59945	+	2.38965i	0.0605401	+	0.0904496i
$699$	−7.65978	+	12.4601i	−0.289719	+	0.471286i
$700$	5.30074	−	4.08075i	0.200349	−	0.154238i
$701$		−	5.30395i		−	0.200327i	−0.994971	−	0.100164i	$-0.968063\pi$
$701$		−	5.30395i		−	0.200327i	0.994971	−	0.100164i	$-0.0319366\pi$
$702$	3.82683	+	4.71683i	0.144434	+	0.178025i
$703$		−	68.8476i		−	2.59664i
$704$	17.1405	+	26.6252i	0.646006	+	1.00347i
$705$	−19.8661	−	36.7122i	−0.748201	−	1.38266i
$706$	−2.29888	+	1.53870i	−0.0865196	+	0.0579097i
$707$	−11.0788	+	4.03234i	−0.416660	+	0.151652i
$708$	−2.78634	−	26.4663i	−0.104717	−	0.994663i
$709$	0.950240	+	5.38908i	0.0356870	+	0.202391i	0.997438	−	0.0715334i	$-0.0227893\pi$
$709$	0.950240	+	5.38908i	0.0356870	+	0.202391i	−0.961751	+	0.273925i	$0.911678\pi$
$710$	−12.2032	+	41.9911i	−0.457979	+	1.57590i
$711$	−17.8842	−	23.8730i	−0.670710	−	0.895306i
$712$	6.08943	+	30.2381i	0.228211	+	1.13322i
$713$	4.84064	−	13.2996i	0.181283	−	0.498072i
$714$	0.530861	+	0.279719i	0.0198670	+	0.0104682i
$715$	−6.07499	+	7.23989i	−0.227192	+	0.270757i
$716$	−23.5099	+	25.7382i	−0.878605	+	0.961882i
$717$	−3.48853	−	0.714875i	−0.130282	−	0.0266975i
$718$	11.3250	−	4.99383i	0.422646	−	0.186368i
$719$	−21.4749	+	37.1955i	−0.800877	+	1.38716i	0.118163	+	0.992994i	$0.462300\pi$
$719$	−21.4749	+	37.1955i	−0.800877	+	1.38716i	−0.919040	+	0.394165i	$0.871034\pi$
$720$	−4.81253	+	34.3291i	−0.179353	+	1.27937i
$721$	−5.13206	−	8.88899i	−0.191128	−	0.331043i
$722$	−34.4475	−	25.2160i	−1.28200	−	0.938443i
$723$	17.6093	+	22.2021i	0.654897	+	0.825706i
$724$	−15.4301	−	48.6692i	−0.573455	−	1.80878i
$725$	33.1451	+	5.84438i	1.23098	+	0.217055i
$726$	−7.68134	−	8.46702i	−0.285081	−	0.314240i
$727$	32.7377	+	39.0153i	1.21418	+	1.44700i	0.858828	+	0.512264i	$0.171193\pi$
$727$	32.7377	+	39.0153i	1.21418	+	1.44700i	0.355348	+	0.934734i	$0.384362\pi$
$728$	−1.75404	+	1.54564i	−0.0650090	+	0.0572851i
$729$	−26.6309	−	4.44926i	−0.986329	−	0.164787i
$730$	12.8509	+	13.4030i	0.475634	+	0.496067i
$731$	−0.390260	+	0.327467i	−0.0144343	+	0.0121118i
$732$	4.55604	+	0.317797i	0.168396	+	0.0117461i
$733$	−3.87976	+	22.0032i	−0.143302	+	0.812708i	0.825412	+	0.564530i	$0.190943\pi$
$733$	−3.87976	+	22.0032i	−0.143302	+	0.812708i	−0.968715	+	0.248178i	$0.920168\pi$
$734$	−20.7574	−	10.2160i	−0.766168	−	0.377078i
$735$	−3.92012	+	3.10919i	−0.144596	+	0.114684i
$736$	36.0763	+	31.3863i	1.32979	+	1.15691i
$737$	29.5089	−	17.0370i	1.08698	−	0.627565i
$738$	−2.47372	−	2.88270i	−0.0910588	−	0.106114i
$739$	−37.9816	−	21.9287i	−1.39717	−	0.806659i	−0.403079	−	0.915165i	$-0.632060\pi$
$739$	−37.9816	−	21.9287i	−1.39717	−	0.806659i	−0.994096	+	0.108506i	$0.965393\pi$
$740$	52.4327	+	21.6211i	1.92746	+	0.794808i
$741$	2.01565	−	9.83621i	0.0740468	−	0.361342i
$742$	−0.488352	+	0.0323966i	−0.0179280	+	0.00118932i
$743$	3.94759	+	3.31242i	0.144823	+	0.121521i	0.712321	−	0.701854i	$-0.247644\pi$
$743$	3.94759	+	3.31242i	0.144823	+	0.121521i	−0.567498	+	0.823375i	$0.692089\pi$
$744$	−7.08944	−	4.12528i	−0.259912	−	0.151240i
$745$	2.05257	+	0.747075i	0.0752004	+	0.0273707i
$746$	−4.23354	−	17.2419i	−0.155001	−	0.631271i
$747$	18.4598	−	13.8290i	0.675409	−	0.505976i
$748$	−0.898170	−	1.71872i	−0.0328403	−	0.0628426i
$749$	4.67115	−	0.823650i	0.170680	−	0.0300955i
$750$	9.25625	+	7.17612i	0.337991	+	0.262035i
$751$	−2.80348	−	7.70249i	−0.102300	−	0.281068i	0.877974	−	0.478708i	$-0.158895\pi$
$751$	−2.80348	−	7.70249i	−0.102300	−	0.281068i	−0.980275	+	0.197640i	$0.936672\pi$
$752$	−8.53498	+	32.2613i	−0.311239	+	1.17645i
$753$	20.8107	−	11.2613i	0.758383	−	0.410384i
$754$	−11.6933	−	1.27126i	−0.425846	−	0.0462966i
$755$	24.4851			0.891105
$756$	1.29381	−	10.3115i	0.0470555	−	0.375024i
$757$	18.9096			0.687280			0.343640	−	0.939102i	$-0.388340\pi$
$757$	18.9096			0.687280			0.343640	+	0.939102i	$0.388340\pi$
$758$	−32.8891	−	3.57559i	−1.19459	−	0.129871i
$759$	−49.3702	−	30.3500i	−1.79203	−	1.10163i
$760$	48.9182	−	29.8435i	1.77445	−	1.08254i
$761$	−4.94134	−	13.5762i	−0.179123	−	0.492137i	0.817341	−	0.576154i	$-0.195447\pi$
$761$	−4.94134	−	13.5762i	−0.179123	−	0.492137i	−0.996464	+	0.0840168i	$0.973225\pi$
$762$	30.3023	−	12.3751i	1.09774	−	0.448303i
$763$	−8.74798	+	1.54250i	−0.316698	+	0.0558424i
$764$	−4.57856	+	2.39267i	−0.165646	+	0.0865637i
$765$	0.483392	−	2.06718i	0.0174771	−	0.0747389i
$766$	−0.435005	−	1.77164i	−0.0157174	−	0.0640120i
$767$	−5.96701	−	2.17181i	−0.215456	−	0.0784196i
$768$	21.6031	−	17.3582i	0.779534	−	0.626360i
$769$	−21.8892	−	18.3672i	−0.789343	−	0.662338i	0.156239	−	0.987719i	$-0.450063\pi$
$769$	−21.8892	−	18.3672i	−0.789343	−	0.662338i	−0.945583	+	0.325381i	$0.894507\pi$
$770$	16.1348	−	1.07036i	0.581458	−	0.0385731i
$771$	28.9262	+	25.6646i	1.04175	+	0.924287i
$772$	−13.8865	+	33.6757i	−0.499786	+	1.21202i
$773$	−26.5860	−	15.3494i	−0.956230	−	0.552080i	−0.0612195	−	0.998124i	$-0.519499\pi$
$773$	−26.5860	−	15.3494i	−0.956230	−	0.552080i	−0.895011	+	0.446044i	$0.852832\pi$
$774$	7.68945	+	4.32682i	0.276392	+	0.155524i
$775$	4.84987	−	2.80008i	0.174213	−	0.100582i
$776$	15.7222	−	19.6850i	0.564393	−	0.706651i
$777$	−15.8111	−	6.25392i	−0.567219	−	0.224358i
$778$	−17.7761	−	8.74872i	−0.637305	−	0.313657i
$779$	−1.09038	+	6.18388i	−0.0390671	+	0.221560i
$780$	6.85802	+	4.62407i	0.245556	+	0.165568i
$781$	−32.4556	+	27.2335i	−1.16135	+	0.974491i
$782$	−2.02677	−	2.11383i	−0.0724770	−	0.0755905i
$783$	42.6945	−	30.1820i	1.52578	−	1.07862i
$784$	3.98586	+	0.336002i	0.142352	+	0.0120001i
$785$	−15.4678	−	18.4338i	−0.552069	−	0.657931i
$786$	−15.9104	+	49.5984i	−0.567505	+	1.76912i
$787$	−16.1873	−	2.85425i	−0.577013	−	0.101743i	−0.122477	−	0.992471i	$-0.539084\pi$
$787$	−16.1873	−	2.85425i	−0.577013	−	0.101743i	−0.454536	+	0.890728i	$0.650195\pi$
$788$	−42.1867	+	13.3749i	−1.50284	+	0.476461i
$789$	−43.9338	+	6.50261i	−1.56408	+	0.231499i
$790$	−32.7767	−	23.9930i	−1.16614	−	0.853632i
$791$	−3.17473	−	5.49880i	−0.112881	−	0.195515i
$792$	−22.3756	+	25.0473i	−0.795083	+	0.890016i
$793$	0.544874	−	0.943750i	0.0193491	−	0.0335135i
$794$	12.6116	−	5.56117i	0.447570	−	0.197359i
$795$	0.547119	+	1.64286i	0.0194043	+	0.0582663i
$796$	8.23706	+	7.52391i	0.291955	+	0.266678i
$797$	−10.3572	+	12.3432i	−0.366871	+	0.437220i	−0.917625	−	0.397448i	$-0.869896\pi$
$797$	−10.3572	+	12.3432i	−0.366871	+	0.437220i	0.550754	+	0.834668i	$0.314340\pi$
$798$	−14.5345	+	9.15801i	−0.514515	+	0.324190i
$799$	0.698993	−	1.92047i	0.0247286	−	0.0679413i
$800$	2.95233	+	18.6892i	0.104381	+	0.660764i
$801$	−29.1921	+	14.7706i	−1.03145	+	0.521892i
$802$	5.59189	−	19.2416i	0.197456	−	0.679444i
$803$	3.12405	+	17.7174i	0.110245	+	0.625232i
$804$	−17.5324	−	24.1225i	−0.618319	−	0.850733i
$805$	22.9463	−	8.35178i	0.808752	−	0.294362i
$806$	−1.62644	+	1.08862i	−0.0572890	+	0.0383449i
$807$	11.4966	+	0.317277i	0.404700	+	0.0111687i
$808$	4.99449	−	32.9704i	0.175706	−	1.15989i
$809$			36.1246i			1.27007i	0.772483	+	0.635036i	$0.219015\pi$
$809$			36.1246i			1.27007i	−0.772483	+	0.635036i	$0.780985\pi$
$810$	−36.4554	+	4.78139i	−1.28091	+	0.168001i
$811$			27.1352i			0.952845i	0.879216	+	0.476422i	$0.158067\pi$
$811$			27.1352i			0.952845i	−0.879216	+	0.476422i	$0.841933\pi$
$812$	12.2764	+	15.9466i	0.430818	+	0.559615i
$813$	27.7990	+	0.767180i	0.974954	+	0.0269062i
$814$	30.5652	+	45.6658i	1.07131	+	1.60059i
$815$	−9.53955	+	3.47211i	−0.334156	+	0.121623i
$816$	−1.41361	+	0.939226i	−0.0494864	+	0.0328795i
$817$	−2.53270	−	14.3637i	−0.0886081	−	0.502522i
$818$	−12.5237	−	3.63958i	−0.437882	−	0.127255i
$819$	−2.07582	−	1.35640i	−0.0725351	−	0.0473963i
$820$	−4.36707	−	2.77242i	−0.152505	−	0.0968170i
$821$	17.1448	−	47.1049i	0.598357	−	1.64397i	−0.156190	−	0.987727i	$-0.549921\pi$
$821$	17.1448	−	47.1049i	0.598357	−	1.64397i	0.754547	−	0.656246i	$-0.227857\pi$
$822$	2.79028	+	4.42839i	0.0973222	+	0.154458i
$823$	8.26687	−	9.85208i	0.288165	−	0.343422i	−0.602469	−	0.798142i	$-0.705816\pi$
$823$	8.26687	−	9.85208i	0.288165	−	0.343422i	0.890634	+	0.454720i	$0.150261\pi$
$824$	29.0228	−	0.702251i	1.01106	−	0.0244641i
$825$	−7.24545	−	21.7563i	−0.252254	−	0.757457i
$826$	4.38352	+	9.94095i	0.152522	+	0.345890i
$827$	13.0582	−	22.6175i	0.454080	−	0.786489i	−0.544555	−	0.838725i	$-0.683301\pi$
$827$	13.0582	−	22.6175i	0.454080	−	0.786489i	0.998635	+	0.0522359i	$0.0166348\pi$
$828$	−21.8917	+	45.7512i	−0.760791	+	1.58996i
$829$	6.61918	+	11.4648i	0.229894	+	0.398187i	0.957776	−	0.287514i	$-0.0928289\pi$
$829$	6.61918	+	11.4648i	0.229894	+	0.398187i	−0.727883	+	0.685702i	$0.759496\pi$
$830$	18.5526	−	25.3446i	0.643971	−	0.879725i
$831$	33.9742	−	5.02850i	1.17855	−	0.174437i
$832$	−1.46186	−	6.44888i	−0.0506808	−	0.223575i
$833$	−0.241246	−	0.0425383i	−0.00835869	−	0.00147386i
$834$	43.9931	+	14.1123i	1.52336	+	0.488670i
$835$	−39.4080	−	46.9646i	−1.36377	−	1.62528i
$836$	55.4708	+	2.33391i	1.91850	+	0.0807201i
$837$	2.21390	−	8.41348i	0.0765235	−	0.290812i
$838$	−21.5345	+	20.6475i	−0.743897	+	0.713256i
$839$	17.0596	−	14.3147i	0.588962	−	0.494198i	−0.298914	−	0.954280i	$-0.596624\pi$
$839$	17.0596	−	14.3147i	0.588962	−	0.494198i	0.887876	+	0.460082i	$0.152180\pi$
$840$	−2.41006	−	13.9451i	−0.0831551	−	0.481152i
$841$	−12.5462	+	71.1533i	−0.432629	+	2.45356i
$842$	12.6147	−	25.6312i	0.434730	−	0.883308i
$843$	−8.33187	−	3.29559i	−0.286965	−	0.113506i
$844$	1.47959	+	11.1027i	0.0509294	+	0.382170i
$845$	−30.8131	+	17.7900i	−1.06000	+	0.611994i
$846$	−35.3933	+	0.391493i	−1.21685	+	0.0134598i
$847$	4.04186	+	2.33357i	0.138880	+	0.0801825i
$848$	0.581057	−	1.25645i	0.0199536	−	0.0431468i
$849$	−9.54316	−	8.46710i	−0.327520	−	0.290590i
$850$	−0.0767018	−	1.15622i	−0.00263085	−	0.0396579i
$851$	63.5680	+	53.3399i	2.17908	+	1.82847i
$852$	26.6771	+	25.7528i	0.913941	+	0.882277i
$853$	−37.8668	−	13.7824i	−1.29654	−	0.471900i	−0.400669	−	0.916223i	$-0.631222\pi$
$853$	−37.8668	−	13.7824i	−1.29654	−	0.471900i	−0.895867	+	0.444323i	$0.853444\pi$
$854$	−1.81073	+	0.444602i	−0.0619619	+	0.0152140i
$855$	44.3338	+	41.5763i	1.51618	+	1.42188i
$856$	−4.28219	+	12.7141i	−0.146362	+	0.434557i
$857$	23.8999	−	4.21420i	0.816405	−	0.143954i	0.250174	−	0.968201i	$-0.419512\pi$
$857$	23.8999	−	4.21420i	0.816405	−	0.143954i	0.566231	+	0.824247i	$0.308401\pi$
$858$	3.02988	+	7.41910i	0.103438	+	0.253284i
$859$	−14.0073	−	38.4847i	−0.477923	−	1.31308i	−0.911253	−	0.411846i	$-0.864884\pi$
$859$	−14.0073	−	38.4847i	−0.477923	−	1.31308i	0.433331	−	0.901235i	$-0.357338\pi$
$860$	11.7344	+	2.58197i	0.400140	+	0.0880444i
$861$	1.32110	+	0.812137i	0.0450230	+	0.0276776i
$862$	−2.33480	+	21.4760i	−0.0795237	+	0.731477i
$863$	−31.3406			−1.06685			−0.533423	−	0.845849i	$-0.679095\pi$
$863$	−31.3406			−1.06685			−0.533423	+	0.845849i	$0.679095\pi$
$864$	23.8506	+	17.1799i	0.811415	+	0.584471i
$865$	−2.99818			−0.101941
$866$	0.456933	−	4.20297i	0.0155272	−	0.142823i
$867$	−25.8050	+	13.9639i	−0.876385	+	0.474239i
$868$	3.27035	+	0.719589i	0.111003	+	0.0244244i
$869$	−13.4605	−	36.9826i	−0.456618	−	1.25455i
$870$	43.6250	−	56.2705i	1.47903	−	1.90775i
$871$	−7.00737	+	1.23559i	−0.237436	+	0.0418663i
$872$	8.01955	−	23.8105i	0.271576	−	0.806324i
$873$	24.5675	+	10.5102i	0.831482	+	0.355715i
$874$	81.4229	−	19.9924i	2.75417	−	0.676253i
$875$	−4.49312	−	1.63536i	−0.151895	−	0.0552853i
$876$	15.1343	−	4.34253i	0.511342	−	0.146721i
$877$	−38.2545	−	32.0993i	−1.29176	−	1.08392i	−0.991506	−	0.130058i	$-0.958484\pi$
$877$	−38.2545	−	32.0993i	−1.29176	−	1.08392i	−0.300255	−	0.953859i	$-0.597072\pi$
$878$	−0.0903485	−	1.36193i	−0.00304911	−	0.0459629i
$879$	7.96983	−	38.8921i	0.268816	−	1.31180i
$880$	−19.1977	+	41.5123i	−0.647154	+	1.39938i
$881$	42.5662	+	24.5756i	1.43409	+	0.827973i	0.997430	−	0.0716529i	$-0.0228274\pi$
$881$	42.5662	+	24.5756i	1.43409	+	0.827973i	0.436662	+	0.899626i	$0.356161\pi$
$882$	0.782895	+	4.16978i	0.0263614	+	0.140404i
$883$	−49.6565	+	28.6692i	−1.67108	+	0.964796i	−0.704038	+	0.710162i	$0.748622\pi$
$883$	−49.6565	+	28.6692i	−1.67108	+	0.964796i	−0.967038	+	0.254634i	$0.918045\pi$
$884$	0.0534939	+	0.401414i	0.00179920	+	0.0135010i
$885$	30.1158	−	23.8859i	1.01233	−	0.802916i
$886$	−14.6126	+	29.6907i	−0.490920	+	0.997478i
$887$	6.08497	−	34.5096i	0.204313	−	1.15872i	−0.694203	−	0.719779i	$-0.744243\pi$
$887$	6.08497	−	34.5096i	0.204313	−	1.15872i	0.898517	−	0.438940i	$-0.144646\pi$
$888$	36.9452	−	30.7874i	1.23980	−	1.03316i
$889$	−10.2364	+	8.58938i	−0.343319	+	0.288079i
$890$	−32.1581	+	30.8336i	−1.07794	+	1.03354i
$891$	−31.9296	−	15.7967i	−1.06968	−	0.529211i
$892$	−31.0024	−	1.30441i	−1.03804	−	0.0436750i
$893$	37.6100	+	44.8218i	1.25857	+	1.49991i
$894$	1.37178	−	1.24449i	0.0458792	−	0.0416219i
$895$	−49.5847	−	8.74311i	−1.65743	−	0.292250i
$896$	−6.23333	+	9.44170i	−0.208241	+	0.315425i
$897$	7.52028	+	9.48171i	0.251095	+	0.316585i
$898$	27.5577	−	37.6465i	0.919614	−	1.25628i
$899$	8.42366	+	14.5902i	0.280945	+	0.486611i
$900$	−18.2720	+	8.29976i	−0.609068	+	0.276659i
$901$	−0.0423888	+	0.0734196i	−0.00141218	+	0.00244596i
$902$	−2.02213	−	4.58578i	−0.0673294	−	0.152690i
$903$	−3.52873	−	0.723113i	−0.117429	−	0.0240637i
$904$	17.9537	−	0.434418i	0.597133	−	0.0144485i
$905$	47.4021	−	56.4916i	1.57570	−	1.87784i
$906$	9.67848	−	18.3682i	0.321546	−	0.610242i
$907$	−1.57478	+	4.32666i	−0.0522896	+	0.143664i	−0.963088	−	0.269187i	$-0.913245\pi$
$907$	−1.57478	+	4.32666i	−0.0522896	+	0.143664i	0.910798	+	0.412852i	$0.135467\pi$
$908$	−30.2267	−	19.1893i	−1.00311	−	0.636819i
$909$	35.1177	−	4.21139i	1.16478	−	0.139683i
$910$	−3.24259	−	0.942344i	−0.107491	−	0.0312384i
$911$	−3.79302	−	21.5113i	−0.125668	−	0.712700i	−0.980909	−	0.194469i	$-0.937702\pi$
$911$	−3.79302	−	21.5113i	−0.125668	−	0.712700i	0.855241	−	0.518231i	$-0.173409\pi$
$912$	−3.05151	−	48.4938i	−0.101046	−	1.60579i
$913$	28.5968	−	10.4084i	0.946416	−	0.344467i
$914$	−26.3553	−	39.3759i	−0.871755	−	1.30244i
$915$	3.13944	+	5.80162i	0.103787	+	0.191796i
$916$	6.43116	+	8.35383i	0.212491	+	0.276018i
$917$		−	21.2648i		−	0.702224i
$918$	−1.35967	−	1.17974i	−0.0448759	−	0.0389373i
$919$			19.9077i			0.656694i	0.944557	+	0.328347i	$0.106492\pi$
$919$			19.9077i			0.656694i	−0.944557	+	0.328347i	$0.893508\pi$
$920$	−10.3446	+	68.2882i	−0.341051	+	2.25140i
$921$	0.571346	−	0.929406i	0.0188265	−	0.0306250i
$922$	48.0205	−	32.1413i	1.58147	−	1.05852i
$923$	8.31385	−	3.02599i	0.273654	−	0.0996018i
$924$	5.57481	−	12.5271i	0.183398	−	0.412110i
$925$	5.70169	+	32.3359i	0.187470	+	1.06320i
$926$	−7.05644	+	24.2811i	−0.231889	+	0.797926i
$927$	8.91972	+	29.4722i	0.292962	+	0.967993i
$928$	−56.2241	+	8.88169i	−1.84565	+	0.291556i
$929$	6.04729	−	16.6148i	0.198405	−	0.545114i	−0.800094	−	0.599874i	$-0.795217\pi$
$929$	6.04729	−	16.6148i	0.198405	−	0.545114i	0.998500	+	0.0547603i	$0.0174395\pi$
$930$	−0.457793	−	11.8383i	−0.0150116	−	0.388194i
$931$	4.50808	−	5.37252i	0.147746	−	0.176077i
$932$	12.4699	+	11.3903i	0.408465	+	0.373101i
$933$	18.6496	−	21.0197i	0.610559	−	0.688153i
$934$	38.0178	−	16.7642i	1.24398	−	0.548540i
$935$	1.40050	−	2.42573i	0.0458011	−	0.0793299i
$936$	6.17971	−	3.31693i	0.201990	−	0.108417i
$937$	−12.0207	−	20.8205i	−0.392700	−	0.680176i	0.600105	−	0.799921i	$-0.295125\pi$
$937$	−12.0207	−	20.8205i	−0.392700	−	0.680176i	−0.992805	+	0.119746i	$0.961792\pi$
$938$	9.82357	+	7.19099i	0.320751	+	0.234794i
$939$	3.52867	−	8.92113i	0.115154	−	0.291130i
$940$	−45.9464	+	14.5669i	−1.49861	+	0.475119i
$941$	0.766002	+	0.135067i	0.0249709	+	0.00440305i	0.186120	−	0.982527i	$-0.440409\pi$
$941$	0.766002	+	0.135067i	0.0249709	+	0.00440305i	−0.161149	+	0.986930i	$0.551520\pi$
$942$	−19.9427	+	4.31707i	−0.649769	+	0.140658i
$943$	−4.86489	−	5.79775i	−0.158423	−	0.188801i
$944$	−30.6209	−	2.58129i	−0.996625	−	0.0840139i
$945$	13.5753	−	6.40472i	0.441605	−	0.208345i
$946$	8.05674	+	8.40286i	0.261947	+	0.273200i
$947$	1.28711	−	1.08001i	0.0418253	−	0.0350956i	−0.621635	−	0.783307i	$-0.713531\pi$
$947$	1.28711	−	1.08001i	0.0418253	−	0.0350956i	0.663461	+	0.748211i	$0.269087\pi$
$948$	−30.9550	+	15.1044i	−1.00537	+	0.490567i
$949$	0.652377	−	3.69981i	0.0211770	−	0.120101i
$950$	29.7651	+	14.6492i	0.965708	+	0.475284i
$951$	−1.61979	−	10.9439i	−0.0525254	−	0.354879i
$952$	0.432402	−	0.541391i	0.0140142	−	0.0175466i
$953$	19.6229	−	11.3293i	0.635648	−	0.366991i	−0.147288	−	0.989094i	$-0.547055\pi$
$953$	19.6229	−	11.3293i	0.635648	−	0.366991i	0.782936	+	0.622102i	$0.213721\pi$
$954$	1.44870	+	0.238955i	0.0469035	+	0.00773645i
$955$	−6.46200	−	3.73084i	−0.209105	−	0.120727i
$956$	−1.56755	+	3.80140i	−0.0506980	+	0.122946i
$957$	65.4510	−	21.7970i	2.11573	−	0.704597i
$958$	40.2958	−	2.67317i	1.30190	−	0.0863662i
$959$	−1.63691	−	1.37353i	−0.0528585	−	0.0443536i
$960$	37.8900	+	12.9052i	1.22290	+	0.416513i
$961$	−26.4963	−	9.64385i	−0.854718	−	0.311092i
$962$	−2.73629	−	11.1441i	−0.0882214	−	0.359299i
$963$	−14.2080	−	0.784804i	−0.457845	−	0.0252899i
$964$	29.0004	−	15.1550i	0.934039	−	0.488111i
$965$	−51.8139	+	9.13619i	−1.66795	+	0.294104i
$966$	2.80491	−	20.5151i	0.0902466	−	0.660062i
$967$	16.9851	+	46.6661i	0.546203	+	1.50068i	0.838798	+	0.544443i	$0.183259\pi$
$967$	16.9851	+	46.6661i	0.546203	+	1.50068i	−0.292595	+	0.956237i	$0.594519\pi$
$968$	−11.2691	+	6.87494i	−0.362203	+	0.220969i
$969$	−0.0820913	+	2.97460i	−0.00263715	+	0.0955580i
$970$	36.1748	+	3.93280i	1.16150	+	0.126275i
$971$	13.0868			0.419976			0.209988	−	0.977704i	$-0.432657\pi$
$971$	13.0868			0.419976			0.209988	+	0.977704i	$0.432657\pi$
$972$	−10.8232	+	29.2380i	−0.347154	+	0.937808i
$973$	−18.8616			−0.604674
$974$	50.1808	+	5.45549i	1.60790	+	0.174805i
$975$	−0.132101	+	4.78673i	−0.00423063	+	0.153298i
$976$	1.34878	−	5.09824i	0.0431734	−	0.163191i
$977$	11.1883	+	30.7396i	0.357945	+	0.983446i	0.979741	+	0.200267i	$0.0641810\pi$
$977$	11.1883	+	30.7396i	0.357945	+	0.983446i	−0.621796	+	0.783179i	$0.713597\pi$
$978$	−1.16609	+	8.52881i	−0.0372876	+	0.272721i
$979$	−42.5097	+	7.49561i	−1.35862	+	0.239561i
$980$	2.67585	+	5.12045i	0.0854769	+	0.163567i
$981$	26.6082	+	1.46976i	0.849535	+	0.0469257i
$982$	1.55855	+	6.34748i	0.0497352	+	0.202556i
$983$	−5.17699	−	1.88427i	−0.165120	−	0.0600989i	0.258137	−	0.966108i	$-0.416891\pi$
$983$	−5.17699	−	1.88427i	−0.165120	−	0.0600989i	−0.423258	+	0.906009i	$0.639114\pi$
$984$	−3.80602	+	2.18019i	−0.121331	+	0.0695020i
$985$	−48.9672	−	41.0884i	−1.56022	−	1.30918i
$986$	3.47833	−	0.230747i	0.110773	−	0.00734850i
$987$	13.7099	−	4.56577i	0.436390	−	0.145330i
$988$	−10.7184	−	4.41983i	−0.340997	−	0.140613i
$989$	15.2244	+	8.78982i	0.484108	+	0.279500i
$990$	−47.8641	−	7.89490i	−1.52122	−	0.250916i
$991$	10.8934	−	6.28933i	0.346041	−	0.199787i	−0.316899	−	0.948459i	$-0.602642\pi$
$991$	10.8934	−	6.28933i	0.346041	−	0.199787i	0.662940	+	0.748672i	$0.269308\pi$
$992$	−6.21658	+	7.14551i	−0.197377	+	0.226870i
$993$	−2.53881	−	17.1530i	−0.0805667	−	0.544335i
$994$	−13.5818	−	6.68442i	−0.430787	−	0.212017i
$995$	−2.79808	+	15.8687i	−0.0887051	+	0.503071i
$996$	−11.6795	−	23.9360i	−0.370078	−	0.758440i
$997$	−31.4861	+	26.4200i	−0.997176	+	0.836730i	−0.986591	−	0.163214i	$-0.947814\pi$
$997$	−31.4861	+	26.4200i	−0.997176	+	0.836730i	−0.0105852	+	0.999944i	$0.503369\pi$
$998$	2.35788	+	2.45917i	0.0746374	+	0.0778438i
$999$	41.9152	+	29.0694i	1.32614	+	0.919716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.491.57	yes	648
4.3	odd	2	inner	756.2.cf.a.491.5	✓	648
27.11	odd	18	inner	756.2.cf.a.659.5	yes	648
108.11	even	18	inner	756.2.cf.a.659.57	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.5	✓	648	4.3	odd	2	inner
756.2.cf.a.491.57	yes	648	1.1	even	1	trivial
756.2.cf.a.659.5	yes	648	27.11	odd	18	inner
756.2.cf.a.659.57	yes	648	108.11	even	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.152848 - 1.40593i) q^{2} +(0.0477819 - 1.73139i) q^{3} +(-1.95328 - 0.429787i) q^{4} +(-0.988005 - 2.71452i) q^{5} +(-2.42691 - 0.331818i) q^{6} +(0.984808 - 0.173648i) q^{7} +(-0.902804 + 2.68047i) q^{8} +(-2.99543 - 0.165458i) q^{9} +(-3.96744 + 0.974157i) q^{10} +(-3.71947 - 1.35378i) q^{11} +(-0.837461 + 3.36135i) q^{12} +(0.633183 + 0.531304i) q^{13} +(-0.0936112 - 1.41111i) q^{14} +(-4.74711 + 1.58092i) q^{15} +(3.63057 + 1.67898i) q^{16} +(-0.212149 - 0.122484i) q^{17} +(-0.690469 + 4.18608i) q^{18} +(6.07372 - 3.50666i) q^{19} +(0.763180 + 5.72684i) q^{20} +(-0.253597 - 1.71339i) q^{21} +(-2.47183 + 5.02239i) q^{22} +(-1.46788 + 8.32475i) q^{23} +(4.59781 + 1.69119i) q^{24} +(-2.56225 + 2.14999i) q^{25} +(0.843757 - 0.809002i) q^{26} +(-0.429601 + 5.17836i) q^{27} +(-1.99823 - 0.0840748i) q^{28} +(-6.46796 - 7.70821i) q^{29} +(1.49707 + 6.91574i) q^{30} +(-1.64886 - 0.290738i) q^{31} +(2.91546 - 4.84769i) q^{32} +(-2.52164 + 6.37517i) q^{33} +(-0.204630 + 0.279544i) q^{34} +(-1.44437 - 2.50172i) q^{35} +(5.77979 + 1.61058i) q^{36} +(4.90834 - 8.50150i) q^{37} +(-4.00176 - 9.07520i) q^{38} +(0.950150 - 1.07090i) q^{39} +(8.16818 - 0.197641i) q^{40} +(-0.575510 + 0.685866i) q^{41} +(-2.44766 + 0.0946521i) q^{42} +(0.711282 - 1.95423i) q^{43} +(6.68331 + 4.24287i) q^{44} +(2.51036 + 8.29465i) q^{45} +(11.4796 + 3.33615i) q^{46} +(1.44871 + 8.21605i) q^{47} +(3.08045 - 6.20571i) q^{48} +(0.939693 - 0.342020i) q^{49} +(2.63109 + 3.93097i) q^{50} +(-0.222205 + 0.361460i) q^{51} +(-1.00843 - 1.30992i) q^{52} -0.346076i q^{53} +(7.21475 + 1.39549i) q^{54} +11.4341i q^{55} +(-0.423629 + 2.79652i) q^{56} +(-5.78119 - 10.6835i) q^{57} +(-11.8258 + 7.91530i) q^{58} +(-7.21907 + 2.62753i) q^{59} +(9.95187 - 1.04772i) q^{60} +(-0.228940 - 1.29838i) q^{61} +(-0.660781 + 2.27374i) q^{62} +(-2.97866 + 0.357207i) q^{63} +(-6.36989 - 4.83989i) q^{64} +(0.816648 - 2.24372i) q^{65} +(8.57761 + 4.51968i) q^{66} +(-5.53344 + 6.59450i) q^{67} +(0.361742 + 0.330424i) q^{68} +(14.3433 + 2.93924i) q^{69} +(-3.73801 + 1.64830i) q^{70} +(5.35194 - 9.26982i) q^{71} +(3.14780 - 7.87981i) q^{72} +(-2.27260 - 3.93625i) q^{73} +(-11.2023 - 8.20022i) q^{74} +(3.60004 + 4.53900i) q^{75} +(-13.3708 + 4.23907i) q^{76} +(-3.89804 - 0.687330i) q^{77} +(-1.36038 - 1.49953i) q^{78} +(6.39122 + 7.61676i) q^{79} +(0.970620 - 11.5141i) q^{80} +(8.94525 + 0.991239i) q^{81} +(0.876314 + 0.913960i) q^{82} +(-5.88967 + 4.94202i) q^{83} +(-0.241046 + 3.45570i) q^{84} +(-0.122882 + 0.696897i) q^{85} +(-2.63879 - 1.29871i) q^{86} +(-13.6550 + 10.8303i) q^{87} +(6.98671 - 8.74774i) q^{88} +(9.44436 - 5.45270i) q^{89} +(12.0454 - 2.26157i) q^{90} +(0.715824 + 0.413281i) q^{91} +(6.44504 - 15.6297i) q^{92} +(-0.582167 + 2.84092i) q^{93} +(11.7726 - 0.780980i) q^{94} +(-15.5198 - 13.0226i) q^{95} +(-8.25395 - 5.27943i) q^{96} +(-8.36991 - 3.04640i) q^{97} +(-0.337226 - 1.37342i) q^{98} +(10.9174 + 4.67056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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