LMFDB - Embedded newform 756.2.cf.a.659.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(155,756)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			659.5
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41111 + 0.0936112i) q^{2} +(-0.0477819 - 1.73139i) q^{3} +(1.98247 - 0.264192i) q^{4} +(-0.988005 + 2.71452i) q^{5} +(0.229503 + 2.43871i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(-2.77276 + 0.558386i) q^{8} +(-2.99543 + 0.165458i) q^{9} +O(q^{10})$	\(q+(-1.41111 + 0.0936112i) q^{2} +(-0.0477819 - 1.73139i) q^{3} +(1.98247 - 0.264192i) q^{4} +(-0.988005 + 2.71452i) q^{5} +(0.229503 + 2.43871i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(-2.77276 + 0.558386i) q^{8} +(-2.99543 + 0.165458i) q^{9} +(1.14008 - 3.92298i) q^{10} +(3.71947 - 1.35378i) q^{11} +(-0.552146 - 3.41982i) q^{12} +(0.633183 - 0.531304i) q^{13} +(1.40593 + 0.152848i) q^{14} +(4.74711 + 1.58092i) q^{15} +(3.86041 - 1.04751i) q^{16} +(-0.212149 + 0.122484i) q^{17} +(4.21140 - 0.513887i) q^{18} +(-6.07372 - 3.50666i) q^{19} +(-1.24154 + 5.64249i) q^{20} +(-0.253597 + 1.71339i) q^{21} +(-5.12186 + 2.25851i) q^{22} +(1.46788 + 8.32475i) q^{23} +(1.09927 + 4.77405i) 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} +(-6.84670 - 1.78647i) q^{30} +(1.64886 - 0.290738i) q^{31} +(-5.34941 + 1.83953i) q^{32} +(-2.52164 - 6.37517i) q^{33} +(0.287900 - 0.192698i) q^{34} +(1.44437 - 2.50172i) q^{35} +(-5.89466 + 1.11939i) q^{36} +(4.90834 + 8.50150i) q^{37} +(8.89896 + 4.37973i) q^{38} +(-0.950150 - 1.07090i) q^{39} +(1.22375 - 8.07841i) q^{40} +(-0.575510 - 0.685866i) q^{41} +(0.197462 - 2.44152i) q^{42} +(-0.711282 - 1.95423i) q^{43} +(7.01609 - 3.66648i) q^{44} +(2.51036 - 8.29465i) q^{45} +(-2.85063 - 11.6097i) q^{46} +(-1.44871 + 8.21605i) q^{47} +(-1.99810 - 6.63382i) q^{48} +(0.939693 + 0.342020i) q^{49} +(3.81689 + 2.79402i) q^{50} +(0.222205 + 0.361460i) q^{51} +(1.11490 - 1.22058i) q^{52} +0.346076i q^{53} +(-1.09097 - 7.26703i) q^{54} +11.4341i q^{55} +(2.82760 - 0.0684180i) q^{56} +(-5.78119 + 10.6835i) q^{57} +(8.40543 - 11.4826i) q^{58} +(7.21907 + 2.62753i) q^{59} +(9.82869 + 1.87998i) q^{60} +(-0.228940 + 1.29838i) q^{61} +(-2.29950 + 0.564615i) q^{62} +(2.97866 + 0.357207i) q^{63} +(7.37641 - 3.09654i) q^{64} +(0.816648 + 2.24372i) q^{65} +(4.15510 + 8.76002i) q^{66} +(5.53344 + 6.59450i) q^{67} +(-0.388220 + 0.298869i) q^{68} +(14.3433 - 2.93924i) q^{69} +(-1.80397 + 3.66541i) q^{70} +(-5.35194 - 9.26982i) q^{71} +(8.21323 - 2.13139i) q^{72} +(-2.27260 + 3.93625i) q^{73} +(-7.72205 - 11.5371i) q^{74} +(-3.60004 + 4.53900i) q^{75} +(-12.9674 - 5.34724i) q^{76} +(-3.89804 + 0.687330i) q^{77} +(1.44102 + 1.42222i) 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} +(-0.0500871 + 3.46374i) q^{84} +(-0.122882 - 0.696897i) q^{85} +(1.18664 + 2.69106i) q^{86} +(13.6550 + 10.8303i) q^{87} +(-9.55726 + 5.83059i) q^{88} +(9.44436 + 5.45270i) q^{89} +(-2.76593 + 11.9397i) q^{90} +(-0.715824 + 0.413281i) q^{91} +(5.10936 + 16.1158i) q^{92} +(-0.582167 - 2.84092i) q^{93} +(1.27518 - 11.7294i) q^{94} +(15.5198 - 13.0226i) q^{95} +(3.44055 + 9.17402i) q^{96} +(-8.36991 + 3.04640i) q^{97} +(-1.35803 - 0.394663i) q^{98} +(-10.9174 + 4.67056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q+O(q^{10}) $ 648 * 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} - 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

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 $

$2$	−1.41111	+	0.0936112i	−0.997807	+	0.0661931i
$2$	−1.41111	+	0.0936112i	−0.997807	+	0.0661931i
$3$	−0.0477819	−	1.73139i	−0.0275869	−	0.999619i
$3$	−0.0477819	−	1.73139i	−0.0275869	−	0.999619i
$4$	1.98247	−	0.264192i	0.991237	−	0.132096i
$5$	−0.988005	+	2.71452i	−0.441849	+	1.21397i	0.496425	+	0.868080i	$0.334646\pi$
$5$	−0.988005	+	2.71452i	−0.441849	+	1.21397i	−0.938274	+	0.345892i	$0.887576\pi$
$6$	0.229503	+	2.43871i	0.0936943	+	0.995601i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$8$	−2.77276	+	0.558386i	−0.980319	+	0.197419i
$9$	−2.99543	+	0.165458i	−0.998478	+	0.0551528i
$10$	1.14008	−	3.92298i	0.360524	−	1.24056i
$11$	3.71947	−	1.35378i	1.12146	−	0.408179i	0.286276	−	0.958147i	$-0.407583\pi$
$11$	3.71947	−	1.35378i	1.12146	−	0.408179i	0.835185	+	0.549969i	$0.185360\pi$
$12$	−0.552146	−	3.41982i	−0.159391	−	0.987216i
$13$	0.633183	−	0.531304i	0.175613	−	0.147357i	−0.550744	−	0.834674i	$-0.685656\pi$
$13$	0.633183	−	0.531304i	0.175613	−	0.147357i	0.726358	+	0.687317i	$0.241212\pi$
$14$	1.40593	+	0.152848i	0.375750	+	0.0408503i
$15$	4.74711	+	1.58092i	1.22570	+	0.408192i
$16$	3.86041	−	1.04751i	0.965101	−	0.261877i
$17$	−0.212149	+	0.122484i	−0.0514536	+	0.0297067i	−0.525506	−	0.850790i	$-0.676124\pi$
$17$	−0.212149	+	0.122484i	−0.0514536	+	0.0297067i	0.474053	+	0.880497i	$0.342791\pi$
$18$	4.21140	−	0.513887i	0.992637	−	0.121124i
$19$	−6.07372	−	3.50666i	−1.39341	−	0.804484i	−0.399716	−	0.916639i	$-0.630891\pi$
$19$	−6.07372	−	3.50666i	−1.39341	−	0.804484i	−0.993691	+	0.112156i	$0.964224\pi$
$20$	−1.24154	+	5.64249i	−0.277617	+	1.26170i
$21$	−0.253597	+	1.71339i	−0.0553394	+	0.373891i
$22$	−5.12186	+	2.25851i	−1.09198	+	0.481516i
$23$	1.46788	+	8.32475i	0.306074	+	1.73583i	0.618407	+	0.785858i	$0.287778\pi$
$23$	1.46788	+	8.32475i	0.306074	+	1.73583i	−0.312334	+	0.949972i	$0.601111\pi$
$24$	1.09927	+	4.77405i	0.224388	+	0.974500i
$25$	−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	−0.327381	+	0.944892i	$0.606166\pi$
$29$	−6.46796	+	7.70821i	−1.20107	+	1.43138i	−0.873688	+	0.486486i	$0.838278\pi$
$30$	−6.84670	−	1.78647i	−1.25003	−	0.326163i
$31$	1.64886	−	0.290738i	0.296143	−	0.0522181i	−0.0236024	−	0.999721i	$-0.507514\pi$
$31$	1.64886	−	0.290738i	0.296143	−	0.0522181i	0.319746	+	0.947503i	$0.396402\pi$
$32$	−5.34941	+	1.83953i	−0.945650	+	0.325185i
$33$	−2.52164	−	6.37517i	−0.438961	−	1.10977i
$34$	0.287900	−	0.192698i	0.0493744	−	0.0330475i
$35$	1.44437	−	2.50172i	0.244143	−	0.422867i
$36$	−5.89466	+	1.11939i	−0.982443	+	0.186564i
$37$	4.90834	+	8.50150i	0.806926	+	1.39764i	0.914983	+	0.403493i	$0.132204\pi$
$37$	4.90834	+	8.50150i	0.806926	+	1.39764i	−0.108057	+	0.994145i	$0.534463\pi$
$38$	8.89896	+	4.37973i	1.44360	+	0.710485i
$39$	−0.950150	−	1.07090i	−0.152146	−	0.171482i
$40$	1.22375	−	8.07841i	0.193492	−	1.27731i
$41$	−0.575510	−	0.685866i	−0.0898796	−	0.107114i	0.719230	−	0.694772i	$-0.244495\pi$
$41$	−0.575510	−	0.685866i	−0.0898796	−	0.107114i	−0.809110	+	0.587658i	$0.800050\pi$
$42$	0.197462	−	2.44152i	0.0304690	−	0.376734i
$43$	−0.711282	−	1.95423i	−0.108470	−	0.298018i	0.873568	−	0.486702i	$-0.161800\pi$
$43$	−0.711282	−	1.95423i	−0.108470	−	0.298018i	−0.982038	+	0.188684i	$0.939578\pi$
$44$	7.01609	−	3.66648i	1.05772	−	0.552742i
$45$	2.51036	−	8.29465i	0.374223	−	1.23649i
$46$	−2.85063	−	11.6097i	−0.420302	−	1.71176i
$47$	−1.44871	+	8.21605i	−0.211316	+	1.19843i	0.675869	+	0.737022i	$0.263768\pi$
$47$	−1.44871	+	8.21605i	−0.211316	+	1.19843i	−0.887186	+	0.461413i	$0.847343\pi$
$48$	−1.99810	−	6.63382i	−0.288401	−	0.957510i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	3.81689	+	2.79402i	0.539790	+	0.395134i
$51$	0.222205	+	0.361460i	0.0311149	+	0.0506145i
$52$	1.11490	−	1.22058i	0.154609	−	0.169264i
$53$			0.346076i			0.0475372i	0.999717	+	0.0237686i	$0.00756650\pi$
$53$			0.346076i			0.0475372i	−0.999717	+	0.0237686i	$0.992434\pi$
$54$	−1.09097	−	7.26703i	−0.148462	−	0.988918i
$55$			11.4341i			1.54178i
$56$	2.82760	−	0.0684180i	0.377854	−	0.00914274i
$57$	−5.78119	+	10.6835i	−0.765738	+	1.41507i
$58$	8.40543	−	11.4826i	1.10369	−	1.50774i
$59$	7.21907	+	2.62753i	0.939843	+	0.342075i	0.766104	−	0.642717i	$-0.222193\pi$
$59$	7.21907	+	2.62753i	0.939843	+	0.342075i	0.173739	+	0.984792i	$0.444415\pi$
$60$	9.82869	+	1.87998i	1.26888	+	0.242705i
$61$	−0.228940	+	1.29838i	−0.0293127	+	0.166241i	−0.995950	−	0.0899082i	$-0.971343\pi$
$61$	−0.228940	+	1.29838i	−0.0293127	+	0.166241i	0.966637	+	0.256149i	$0.0824537\pi$
$62$	−2.29950	+	0.564615i	−0.292037	+	0.0717062i
$63$	2.97866	+	0.357207i	0.375276	+	0.0450038i
$64$	7.37641	−	3.09654i	0.922051	−	0.387068i
$65$	0.816648	+	2.24372i	0.101293	+	0.278299i
$66$	4.15510	+	8.76002i	0.511458	+	1.07828i
$67$	5.53344	+	6.59450i	0.676017	+	0.805646i	0.989590	−	0.143918i	$-0.0459702\pi$
$67$	5.53344	+	6.59450i	0.676017	+	0.805646i	−0.313572	+	0.949564i	$0.601526\pi$
$68$	−0.388220	+	0.298869i	−0.0470786	+	0.0362432i
$69$	14.3433	−	2.93924i	1.72673	−	0.353843i
$70$	−1.80397	+	3.66541i	−0.215616	+	0.438101i
$71$	−5.35194	−	9.26982i	−0.635158	−	1.10013i	−0.986482	−	0.163872i	$-0.947602\pi$
$71$	−5.35194	−	9.26982i	−0.635158	−	1.10013i	0.351324	−	0.936254i	$-0.385732\pi$
$72$	8.21323	−	2.13139i	0.967939	−	0.251186i
$73$	−2.27260	+	3.93625i	−0.265987	+	0.460704i	−0.967822	−	0.251636i	$-0.919031\pi$
$73$	−2.27260	+	3.93625i	−0.265987	+	0.460704i	0.701834	+	0.712340i	$0.252365\pi$
$74$	−7.72205	−	11.5371i	−0.897671	−	1.34116i
$75$	−3.60004	+	4.53900i	−0.415697	+	0.524118i
$76$	−12.9674	−	5.34724i	−1.48746	−	0.613370i
$77$	−3.89804	+	0.687330i	−0.444223	+	0.0783285i
$78$	1.44102	+	1.42222i	0.163163	+	0.161034i
$79$	−6.39122	+	7.61676i	−0.719068	+	0.856952i	−0.994540	−	0.104357i	$-0.966722\pi$
$79$	−6.39122	+	7.61676i	−0.719068	+	0.856952i	0.275472	+	0.961309i	$0.411166\pi$
$80$	−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	$-0.139121\pi$
$83$	5.88967	+	4.94202i	0.646475	+	0.542457i	−0.259524	+	0.965737i	$0.583566\pi$
$84$	−0.0500871	+	3.46374i	−0.00546495	+	0.377925i
$85$	−0.122882	−	0.696897i	−0.0133284	−	0.0755891i
$86$	1.18664	+	2.69106i	0.127958	+	0.290184i
$87$	13.6550	+	10.8303i	1.46397	+	1.16112i
$88$	−9.55726	+	5.83059i	−1.01881	+	0.621543i
$89$	9.44436	+	5.45270i	1.00110	+	0.577985i	0.908574	−	0.417725i	$-0.137172\pi$
$89$	9.44436	+	5.45270i	1.00110	+	0.577985i	0.0925263	+	0.995710i	$0.470506\pi$
$90$	−2.76593	+	11.9397i	−0.291555	+	1.25855i
$91$	−0.715824	+	0.413281i	−0.0750387	+	0.0433236i
$92$	5.10936	+	16.1158i	0.532688	+	1.68019i
$93$	−0.582167	−	2.84092i	−0.0603679	−	0.294590i
$94$	1.27518	−	11.7294i	0.131525	−	1.20979i
$95$	15.5198	−	13.0226i	1.59230	−	1.33609i
$96$	3.44055	+	9.17402i	0.351149	+	0.936319i
$97$	−8.36991	+	3.04640i	−0.849835	+	0.309315i	−0.729973	−	0.683476i	$-0.760468\pi$
$97$	−8.36991	+	3.04640i	−0.849835	+	0.309315i	−0.119862	+	0.992791i	$0.538245\pi$
$98$	−1.35803	−	0.394663i	−0.137182	−	0.0398670i
$99$	−10.9174	+	4.67056i	−1.09724	+	0.469409i
$100$	−5.64761	−	3.58537i	−0.564761	−	0.358537i
$101$	−11.6107	−	2.04727i	−1.15531	−	0.203711i	−0.437014	−	0.899455i	$-0.643964\pi$
$101$	−11.6107	−	2.04727i	−1.15531	−	0.203711i	−0.718291	+	0.695743i	$0.755075\pi$
$102$	−0.347392	−	0.489259i	−0.0343970	−	0.0484439i
$103$	3.51054	−	9.64512i	0.345904	−	0.950362i	−0.637742	−	0.770250i	$-0.720132\pi$
$103$	3.51054	−	9.64512i	0.345904	−	0.950362i	0.983646	−	0.180113i	$-0.0576462\pi$
$104$	−1.45899	+	1.82674i	−0.143066	+	0.179127i
$105$	−4.40047	−	2.38123i	−0.429442	−	0.232384i
$106$	−0.0323966	−	0.488352i	−0.00314664	−	0.0474330i
$107$	−4.74321			−0.458543			−0.229272	−	0.973362i	$-0.573634\pi$
$107$	−4.74321			−0.458543			−0.229272	+	0.973362i	$0.573634\pi$
$108$	2.21975	+	10.1525i	0.213596	+	0.976922i
$109$	−8.88293			−0.850830			−0.425415	−	0.904998i	$-0.639872\pi$
$109$	−8.88293			−0.850830			−0.425415	+	0.904998i	$0.639872\pi$
$110$	−1.07036	−	16.1348i	−0.102055	−	1.53839i
$111$	14.4849	−	8.90448i	1.37484	−	0.845176i
$112$	−3.98365	+	0.361241i	−0.376420	+	0.0341340i
$113$	−2.17165	+	5.96655i	−0.204291	+	0.561285i	−0.998952	−	0.0457682i	$-0.985426\pi$
$113$	−2.17165	+	5.96655i	−0.204291	+	0.561285i	0.794661	+	0.607054i	$0.207649\pi$
$114$	7.15781	−	15.6169i	0.670390	−	1.46265i
$115$	−24.0480	−	4.24031i	−2.24249	−	0.395411i
$116$	−10.7861	+	16.9901i	−1.00146	+	1.57749i
$117$	−1.80875	+	1.69625i	−0.167219	+	0.156818i
$118$	−10.4329	−	3.03195i	−0.960424	−	0.279113i
$119$	0.230195	−	0.0837840i	0.0211019	−	0.00768047i
$120$	−14.0454	−	1.73279i	−1.28216	−	0.158181i
$121$	3.57524	−	2.99998i	0.325022	−	0.272726i
$122$	0.201516	−	1.85359i	0.0182444	−	0.167816i
$123$	−1.16000	+	1.02921i	−0.104594	+	0.0928003i
$124$	3.19200	−	1.01199i	0.286650	−	0.0908798i
$125$	−4.14088	+	2.39074i	−0.370371	+	0.213834i
$126$	−4.23666	−	0.225223i	−0.377432	−	0.0200645i
$127$	11.5724	+	6.68135i	1.02689	+	0.592874i	0.916092	−	0.400969i	$-0.131326\pi$
$127$	11.5724	+	6.68135i	1.02689	+	0.592874i	0.110797	+	0.993843i	$0.464660\pi$
$128$	−10.1191	+	5.06008i	−0.894408	+	0.447252i
$129$	−3.34956	+	1.32489i	−0.294912	+	0.116650i
$130$	−1.36242	−	3.08969i	−0.119492	−	0.270984i
$131$	−3.69259	−	20.9417i	−0.322623	−	1.82968i	−0.525880	−	0.850559i	$-0.676264\pi$
$131$	−3.69259	−	20.9417i	−0.322623	−	1.82968i	0.203257	−	0.979125i	$-0.434847\pi$
$132$	−6.68335	−	11.9724i	−0.581711	−	1.04206i
$133$	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	−0.821521	−	0.570179i	$-0.806874\pi$
$137$	−1.37353	+	1.63691i	−0.117349	+	0.139851i	0.704172	+	0.710029i	$0.251318\pi$
$138$	−19.9648	+	5.49029i	−1.69952	+	0.467365i
$139$	18.5750	−	3.27528i	1.57551	−	0.277805i	0.683546	−	0.729908i	$-0.260437\pi$
$139$	18.5750	−	3.27528i	1.57551	−	0.277805i	0.891966	+	0.452102i	$0.149326\pi$
$140$	2.20249	−	5.34118i	0.186144	−	0.451412i
$141$	14.2944	+	2.11571i	1.20381	+	0.178175i
$142$	8.41994	+	12.5798i	0.706586	+	1.05567i
$143$	1.63584	−	2.83336i	0.136796	−	0.236937i
$144$	−11.3903	+	3.77647i	−0.949189	+	0.314706i
$145$	−14.5337	−	25.1732i	−1.20696	−	2.09052i
$146$	2.83841	−	5.76724i	0.234909	−	0.477300i
$147$	0.547270	−	1.64332i	0.0451381	−	0.135539i
$148$	11.9767	+	15.5573i	0.984477	+	1.27880i
$149$	−0.486040	−	0.579240i	−0.0398180	−	0.0474532i	0.745768	−	0.666206i	$-0.232083\pi$
$149$	−0.486040	−	0.579240i	−0.0398180	−	0.0474532i	−0.785586	+	0.618753i	$0.787638\pi$
$150$	4.65516	−	6.74204i	0.380092	−	0.550485i
$151$	2.89899	+	7.96490i	0.235916	+	0.648175i	0.999995	+	0.00305203i	$0.000971493\pi$
$151$	2.89899	+	7.96490i	0.235916	+	0.648175i	−0.764079	+	0.645123i	$0.776806\pi$
$152$	18.7990	+	6.33166i	1.52480	+	0.513565i
$153$	0.615211	−	0.401995i	0.0497369	−	0.0324993i
$154$	5.43623	−	1.33480i	0.438064	−	0.107561i
$155$	−0.839865	+	4.76311i	−0.0674595	+	0.382582i
$156$	−2.16657	−	1.87201i	−0.173464	−	0.149881i
$157$	7.82779	+	2.84908i	0.624726	+	0.227382i	0.634934	−	0.772566i	$-0.281027\pi$
$157$	7.82779	+	2.84908i	0.624726	+	0.227382i	−0.0102084	+	0.999948i	$0.503249\pi$
$158$	8.30571	−	11.3464i	0.660767	−	0.902670i
$159$	0.599194	−	0.0165362i	0.0475191	−	0.00131141i
$160$	0.291805	−	16.3385i	0.0230692	−	1.29168i
$161$		−	8.45317i		−	0.666203i
$162$	−12.5300	+	2.23613i	−0.984446	+	0.175687i
$163$		−	3.51426i		−	0.275258i	−0.990484	−	0.137629i	$-0.956052\pi$
$163$		−	3.51426i		−	0.275258i	0.990484	−	0.137629i	$-0.0439482\pi$
$164$	−1.32213	−	1.20767i	−0.103241	−	0.0943030i
$165$	19.7969	−	0.546344i	1.54119	−	0.0425328i
$166$	−8.77361	−	6.42240i	−0.680964	−	0.498475i
$167$	−19.9432	−	7.25873i	−1.54325	−	0.561697i	−0.576428	−	0.817148i	$-0.695554\pi$
$167$	−19.9432	−	7.25873i	−1.54325	−	0.561697i	−0.966822	+	0.255451i	$0.917776\pi$
$168$	−0.253566	−	4.89241i	−0.0195631	−	0.377458i
$169$	−2.13879	+	12.1297i	−0.164522	+	0.933052i
$170$	0.238637	+	0.971896i	0.0183026	+	0.0745411i
$171$	18.7736	+	9.49903i	1.43565	+	0.726409i
$172$	−1.92639	−	3.68630i	−0.146886	−	0.281078i
$173$	0.354979	+	0.975296i	0.0269885	+	0.0741504i	0.952455	−	0.304679i	$-0.0985491\pi$
$173$	0.354979	+	0.975296i	0.0269885	+	0.0741504i	−0.925467	+	0.378829i	$0.876327\pi$
$174$	−20.2825	−	14.0044i	−1.53762	−	1.06167i
$175$	2.14999	+	2.56225i	0.162524	+	0.193688i
$176$	12.9406	−	9.12229i	0.975432	−	0.687618i
$177$	4.20434	−	12.6246i	0.316017	−	0.948922i
$178$	−13.8375	−	6.81027i	−1.03716	−	0.510452i
$179$	−8.71482	−	15.0945i	−0.651376	−	1.12822i	−0.982789	−	0.184731i	$-0.940859\pi$
$179$	−8.71482	−	15.0945i	−0.651376	−	1.12822i	0.331413	−	0.943486i	$-0.392475\pi$
$180$	2.78535	−	17.1071i	0.207608	−	1.27509i
$181$	12.7642	−	22.1082i	0.948752	−	1.64329i	0.200694	−	0.979654i	$-0.435680\pi$
$181$	12.7642	−	22.1082i	0.948752	−	1.64329i	0.748058	−	0.663633i	$-0.230986\pi$
$182$	0.971420	−	0.650195i	0.0720064	−	0.0481957i
$183$	2.25895	+	0.334345i	0.166986	+	0.0247155i
$184$	−8.71850	−	22.2629i	−0.642736	−	1.64124i
$185$	−27.9270	+	4.92428i	−2.05323	+	0.362040i
$186$	1.08744	+	3.95436i	0.0797353	+	0.289948i
$187$	−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	$-0.307567\pi$
$191$	−1.97871	−	1.66034i	−0.143175	−	0.120138i	−0.711562	+	0.702623i	$0.752012\pi$
$192$	−5.71379	−	12.6235i	−0.412357	−	0.911022i
$193$	3.16270	+	17.9365i	0.227656	+	1.29110i	0.857542	+	0.514413i	$0.171990\pi$
$193$	3.16270	+	17.9365i	0.227656	+	1.29110i	−0.629887	+	0.776687i	$0.716899\pi$
$194$	11.5257	−	5.08233i	0.827497	−	0.364890i
$195$	3.84574	−	1.52115i	0.275399	−	0.108932i
$196$	1.95328	+	0.429787i	0.139520	+	0.0306991i
$197$	19.1635	+	11.0640i	1.36534	+	0.788280i	0.990329	−	0.138740i	$-0.0443052\pi$
$197$	19.1635	+	11.0640i	1.36534	+	0.788280i	0.375012	+	0.927020i	$0.377638\pi$
$198$	14.9685	−	7.61268i	1.06376	−	0.541009i
$199$	4.83073	−	2.78902i	0.342441	−	0.197709i	−0.318910	−	0.947785i	$-0.603317\pi$
$199$	4.83073	−	2.78902i	0.342441	−	0.197709i	0.661351	+	0.750076i	$0.269983\pi$
$200$	8.30504	+	4.53067i	0.587255	+	0.320367i
$201$	11.1533	−	9.89565i	0.786690	−	0.697985i
$202$	16.5756	+	1.80204i	1.16626	+	0.126791i
$203$	7.70821	−	6.46796i	0.541010	−	0.453961i
$204$	0.536010	+	0.657880i	0.0375282	+	0.0460608i
$205$	2.43041	−	0.884596i	0.169747	−	0.0617828i
$206$	−4.05087	+	13.9390i	−0.282238	+	0.971174i
$207$	−5.77433	−	24.6934i	−0.401344	−	1.71631i
$208$	1.88780	−	2.71431i	0.130895	−	0.188204i
$209$	−27.3382	−	4.82047i	−1.89102	−	0.333439i
$210$	6.43246	+	2.94825i	0.443882	+	0.203448i
$211$	1.91546	−	5.26267i	0.131865	−	0.362297i	−0.856134	−	0.516754i	$-0.827140\pi$
$211$	1.91546	−	5.26267i	0.131865	−	0.362297i	0.988000	+	0.154456i	$0.0493626\pi$
$212$	0.0914305	+	0.686087i	0.00627948	+	0.0471207i
$213$	−15.7940	+	9.70923i	−1.08219	+	0.665265i
$214$	6.69320	−	0.444018i	0.457538	−	0.0303524i
$215$	6.00756			0.409712
$216$	−4.08271	−	14.1185i	−0.277793	−	0.960641i
$217$	−1.67429			−0.113658
$218$	12.5348	−	0.831542i	0.848964	−	0.0563191i
$219$	6.92379	+	3.74668i	0.467866	+	0.253177i
$220$	3.02080	+	22.6678i	0.203662	+	1.52826i
$221$	−0.0692527	+	0.190270i	−0.00465844	+	0.0127990i
$222$	−19.6062	+	13.9212i	−1.31588	+	0.934327i
$223$	−15.2792	−	2.69414i	−1.02317	−	0.180413i	−0.363206	−	0.931709i	$-0.618318\pi$
$223$	−15.2792	−	2.69414i	−1.02317	−	0.180413i	−0.659965	+	0.751296i	$0.729429\pi$
$224$	5.58757	−	0.882666i	0.373335	−	0.0589756i
$225$	8.03080	+	6.01620i	0.535387	+	0.401080i
$226$	2.50590	−	8.62275i	0.166690	−	0.573577i
$227$	−16.8221	+	6.12274i	−1.11652	+	0.406380i	−0.833381	−	0.552699i	$-0.813598\pi$
$227$	−16.8221	+	6.12274i	−1.11652	+	0.406380i	−0.283139	+	0.959079i	$0.591376\pi$
$228$	−8.63856	+	22.7072i	−0.572103	+	1.50382i
$229$	−4.03805	+	3.38832i	−0.266842	+	0.223907i	−0.766384	−	0.642383i	$-0.777946\pi$
$229$	−4.03805	+	3.38832i	−0.266842	+	0.223907i	0.499542	+	0.866289i	$0.333502\pi$
$230$	34.3313	+	3.73239i	2.26374	+	0.246106i
$231$	1.37629	+	6.71619i	0.0905534	+	0.441893i
$232$	13.6299	−	24.9846i	0.894849	−	1.64032i
$233$	−7.31312	+	4.22223i	−0.479099	+	0.276608i	−0.720041	−	0.693932i	$-0.755877\pi$
$233$	−7.31312	+	4.22223i	−0.479099	+	0.276608i	0.240942	+	0.970539i	$0.422544\pi$
$234$	2.39356	−	2.56292i	0.156472	−	0.167543i
$235$	−20.8713	−	12.0501i	−1.36150	−	0.786060i
$236$	15.0058	+	3.30178i	0.976793	+	0.214928i
$237$	13.4930	+	10.7018i	0.876463	+	0.695154i
$238$	−0.316987	+	0.139777i	−0.0205472	+	0.00906043i
$239$	−0.357013	−	2.02472i	−0.0230933	−	0.130969i	0.971082	−	0.238748i	$-0.0767370\pi$
$239$	−0.357013	−	2.02472i	−0.0230933	−	0.130969i	−0.994175	+	0.107780i	$0.965626\pi$
$240$	19.9818	+	1.13036i	1.28982	+	0.0729643i
$241$	−12.5331	−	10.5165i	−0.807326	−	0.677427i	0.142642	−	0.989774i	$-0.454440\pi$
$241$	−12.5331	−	10.5165i	−0.807326	−	0.677427i	−0.949968	+	0.312348i	$0.898885\pi$
$242$	−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
$246$	1.54055	−	1.56091i	0.0982219	−	0.0995202i
$247$	−5.70888	+	1.00663i	−0.363247	+	0.0640503i
$248$	−4.40954	+	1.72685i	−0.280006	+	0.109655i
$249$	8.27515	−	10.4335i	0.524416	−	0.661194i
$250$	5.61944	−	3.76123i	0.355405	−	0.237881i
$251$	−6.83069	+	11.8311i	−0.431150	+	0.746773i	−0.996973	−	0.0777538i	$-0.975225\pi$
$251$	−6.83069	+	11.8311i	−0.431150	+	0.746773i	0.565823	+	0.824527i	$0.308559\pi$
$252$	5.99948	−	0.0787838i	0.377932	−	0.00496291i
$253$	16.7296	+	28.9765i	1.05178	+	1.82173i
$254$	−16.9555	−	8.34483i	−1.06388	−	0.523601i
$255$	−1.20073	+	0.246055i	−0.0751926	+	0.0154086i
$256$	13.8055	−	8.08760i	0.862841	−	0.505475i
$257$	−14.3511	−	17.1030i	−0.895197	−	1.06685i	−0.997398	−	0.0720901i	$-0.977033\pi$
$257$	−14.3511	−	17.1030i	−0.895197	−	1.06685i	0.102201	−	0.994764i	$-0.467411\pi$
$258$	4.60257	−	2.18312i	0.286544	−	0.135915i
$259$	−3.35750	−	9.22466i	−0.208625	−	0.573193i
$260$	2.21176	+	4.23237i	0.137167	+	0.262480i
$261$	18.0989	−	24.1596i	1.12030	−	1.49544i
$262$	7.17103	+	29.2054i	0.443028	+	1.80432i
$263$	4.45260	−	25.2520i	0.274559	−	1.55710i	−0.465799	−	0.884891i	$-0.654233\pi$
$263$	4.45260	−	25.2520i	0.274559	−	1.55710i	0.740358	−	0.672212i	$-0.234656\pi$
$264$	10.5517	+	16.2688i	0.649413	+	1.00127i
$265$	−0.939432	−	0.341925i	−0.0577088	−	0.0210043i
$266$	−8.00323	−	5.85848i	−0.490710	−	0.359206i
$267$	8.98949	−	16.6124i	0.550148	−	1.01666i
$268$	12.7121	+	11.6115i	0.776516	+	0.709287i
$269$		−	6.64010i		−	0.404854i	−0.979297	−	0.202427i	$-0.935117\pi$
$269$		−	6.64010i		−	0.404854i	0.979297	−	0.202427i	$-0.0648829\pi$
$270$	20.8044	+	4.21841i	1.26612	+	0.256724i
$271$			16.0559i			0.975325i	0.873032	+	0.487662i	$0.162150\pi$
$271$			16.0559i			0.975325i	−0.873032	+	0.487662i	$0.837850\pi$
$272$	−0.690677	+	0.695065i	−0.0418784	+	0.0421445i
$273$	0.749755	+	1.21962i	0.0453772	+	0.0738150i
$274$	1.78497	−	2.43844i	0.107834	−	0.147312i
$275$	−12.4408	−	4.52809i	−0.750210	−	0.273054i
$276$	27.6586	−	9.61635i	1.66485	−	0.578836i
$277$	3.44322	−	19.5274i	0.206883	−	1.17329i	−0.687567	−	0.726121i	$-0.741321\pi$
$277$	3.44322	−	19.5274i	0.206883	−	1.17329i	0.894449	−	0.447169i	$-0.147568\pi$
$278$	−25.9048	+	6.36061i	−1.55367	+	0.381484i
$279$	−4.89094	+	1.14370i	−0.292813	+	0.0684717i
$280$	−2.60796	+	7.74318i	−0.155855	+	0.462743i
$281$	1.76928	+	4.86107i	0.105547	+	0.289987i	0.981212	−	0.192931i	$-0.0617993\pi$
$281$	1.76928	+	4.86107i	0.105547	+	0.289987i	−0.875666	+	0.482918i	$0.839577\pi$
$282$	−20.3691	−	1.64738i	−1.21296	−	0.0981002i
$283$	−4.73462	−	5.64250i	−0.281444	−	0.335412i	0.606739	−	0.794901i	$-0.292477\pi$
$283$	−4.73462	−	5.64250i	−0.281444	−	0.335412i	−0.888184	+	0.459489i	$0.848033\pi$
$284$	−13.0591	−	16.9632i	−0.774914	−	1.00658i
$285$	−23.2889	−	26.2486i	−1.37951	−	1.55483i
$286$	−2.04312	+	4.15131i	−0.120812	+	0.245472i
$287$	0.447667	+	0.775383i	0.0264250	+	0.0457694i
$288$	15.7194	−	6.39528i	0.926276	−	0.376846i
$289$	−8.47000	+	14.6705i	−0.498235	+	0.862968i
$290$	22.8652	+	34.1616i	1.34269	+	2.00604i
$291$	5.67444	+	14.3460i	0.332641	+	0.840979i
$292$	−3.46544	+	8.40392i	−0.202800	+	0.491802i
$293$	22.5728	−	3.98019i	1.31871	−	0.232525i	0.530374	−	0.847764i	$-0.322052\pi$
$293$	22.5728	−	3.98019i	1.31871	−	0.232525i	0.788341	+	0.615239i	$0.210940\pi$
$294$	−0.618427	+	2.37014i	−0.0360674	+	0.138229i
$295$	−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
$300$	−5.93782	+	9.94954i	−0.342820	+	0.574437i
$301$	0.361128	+	2.04806i	0.0208150	+	0.118048i
$302$	−4.83640	−	10.9680i	−0.278304	−	0.631137i
$303$	−2.98985	+	20.2004i	−0.171763	+	1.16049i
$304$	−27.1203	−	7.17488i	−1.55545	−	0.411507i
$305$	−3.29829	−	1.90427i	−0.188860	−	0.109038i
$306$	−0.830500	+	0.624850i	−0.0474765	+	0.0357203i
$307$	−0.545489	+	0.314938i	−0.0311327	+	0.0179745i	−0.515486	−	0.856898i	$-0.672388\pi$
$307$	−0.545489	+	0.314938i	−0.0311327	+	0.0179745i	0.484353	+	0.874873i	$0.339055\pi$
$308$	−7.54618	+	2.39244i	−0.429983	+	0.136322i
$309$	−16.8672	−	5.61725i	−0.959543	−	0.319554i
$310$	0.739262	−	6.79990i	0.0419873	−	0.386208i
$311$	−12.4281	+	10.4284i	−0.704735	+	0.591343i	−0.923116	−	0.384521i	$-0.874367\pi$
$311$	−12.4281	+	10.4284i	−0.704735	+	0.591343i	0.218382	+	0.975863i	$0.429922\pi$
$312$	3.23252	+	2.43880i	0.183005	+	0.138070i
$313$	5.20486	−	1.89441i	0.294196	−	0.107079i	−0.190706	−	0.981647i	$-0.561078\pi$
$313$	5.20486	−	1.89441i	0.294196	−	0.107079i	0.484902	+	0.874569i	$0.338855\pi$
$314$	−11.3126	−	3.28761i	−0.638407	−	0.185530i
$315$	−3.91258	+	7.73271i	−0.220449	+	0.435689i
$316$	−10.6581	+	16.7885i	−0.599567	+	0.944429i
$317$	6.29023	+	1.10914i	0.353295	+	0.0622954i	0.347479	−	0.937688i	$-0.387038\pi$
$317$	6.29023	+	1.10914i	0.353295	+	0.0622954i	0.00581547	+	0.999983i	$0.498149\pi$
$318$	−0.843981	+	0.0794257i	−0.0473281	+	0.00445397i
$319$	−13.6222	+	37.4266i	−0.762695	+	2.09549i
$320$	1.11770	+	23.0828i	0.0624814	+	1.29037i
$321$	0.226640	+	8.21235i	0.0126498	+	0.458369i
$322$	0.791312	+	11.9284i	0.0440981	+	0.664742i
$323$	1.71804			0.0955943
$324$	17.4718	−	4.32837i	0.970658	−	0.240465i
$325$	−2.76467			−0.153357
$326$	0.328975	+	4.95902i	0.0182202	+	0.274655i
$327$	0.424443	+	15.3798i	0.0234718	+	0.850507i
$328$	1.97873	+	1.58039i	0.109257	+	0.0872623i
$329$	2.85341	−	7.83967i	0.157313	−	0.432215i
$330$	−27.8845	+	2.62417i	−1.53499	+	0.144456i
$331$	−9.85911	−	1.73843i	−0.541906	−	0.0955526i	−0.104006	−	0.994577i	$-0.533166\pi$
$331$	−9.85911	−	1.73843i	−0.541906	−	0.0955526i	−0.437899	+	0.899024i	$0.644277\pi$
$332$	12.9818	+	8.24142i	0.712466	+	0.452307i
$333$	−16.1093	−	24.6535i	−0.882782	−	1.35101i
$334$	28.8216	+	8.37597i	1.57705	+	0.458313i
$335$	−23.3680	+	8.50525i	−1.27673	+	0.464691i
$336$	0.815795	+	6.88001i	0.0445053	+	0.375335i
$337$	−0.348513	+	0.292437i	−0.0189847	+	0.0159301i	−0.652231	−	0.758021i	$-0.726167\pi$
$337$	−0.348513	+	0.292437i	−0.0189847	+	0.0159301i	0.633246	+	0.773951i	$0.281722\pi$
$338$	1.88260	−	17.3165i	0.102400	−	0.941896i
$339$	10.4342	+	3.47488i	0.566708	+	0.188729i
$340$	−0.427724	−	1.34912i	−0.0231966	−	0.0731661i
$341$	5.73927	−	3.31357i	0.310799	−	0.179440i
$342$	−27.3809	−	11.6468i	−1.48059	−	0.629785i
$343$	−0.866025	−	0.500000i	−0.0467610	−	0.0269975i
$344$	3.06343	+	5.02145i	0.165169	+	0.270738i
$345$	−6.19258	+	41.8391i	−0.333397	+	2.25254i
$346$	−0.592213	−	1.34302i	−0.0318376	−	0.0722013i
$347$	−0.348598	−	1.97700i	−0.0187137	−	0.106131i	0.974020	−	0.226461i	$-0.0727157\pi$
$347$	−0.348598	−	1.97700i	−0.0187137	−	0.106131i	−0.992734	+	0.120331i	$0.961605\pi$
$348$	29.9319	+	17.8632i	1.60452	+	0.957566i
$349$	−1.55760	−	1.30698i	−0.0833766	−	0.0699613i	0.600147	−	0.799890i	$-0.295109\pi$
$349$	−1.55760	−	1.30698i	−0.0833766	−	0.0699613i	−0.683523	+	0.729929i	$0.739553\pi$
$350$	−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	−0.798467	−	0.602039i	$-0.794355\pi$
$353$	−1.25734	+	1.49844i	−0.0669215	+	0.0797539i	0.731545	+	0.681793i	$0.238800\pi$
$354$	−4.75099	+	18.2083i	−0.252512	+	0.967759i
$355$	30.4509	−	5.36931i	1.61617	−	0.284974i
$356$	20.1637	+	8.31472i	1.06868	+	0.440679i
$357$	−0.156062	−	0.394554i	−0.00825968	−	0.0208820i
$358$	13.7106	+	20.4842i	0.724628	+	1.08263i
$359$	−4.37599	+	7.57943i	−0.230956	+	0.400027i	−0.958090	−	0.286468i	$-0.907519\pi$
$359$	−4.37599	+	7.57943i	−0.230956	+	0.400027i	0.727134	+	0.686496i	$0.240852\pi$
$360$	−2.32903	+	24.4008i	−0.122750	+	1.28604i
$361$	15.0934	+	26.1425i	0.794387	+	1.37592i
$362$	−15.9421	+	32.3920i	−0.837897	+	1.70248i
$363$	−5.36497	−	6.04679i	−0.281588	−	0.317374i
$364$	−1.30992	+	1.00843i	−0.0686583	+	0.0528563i
$365$	−8.43971	−	10.0581i	−0.441755	−	0.526463i
$366$	−3.21892	−	0.260336i	−0.168256	−	0.0136080i
$367$	−5.59511	−	15.3724i	−0.292062	−	0.802434i	−0.995765	−	0.0919395i	$-0.970693\pi$
$367$	−5.59511	−	15.3724i	−0.292062	−	0.802434i	0.703702	−	0.710495i	$-0.251529\pi$
$368$	14.3868	+	30.5993i	0.749966	+	1.59510i
$369$	1.83739	+	1.95924i	0.0956504	+	0.101994i
$370$	38.9471	−	9.56299i	2.02476	−	0.497156i
$371$	0.0600955	−	0.340819i	0.00312000	−	0.0176944i
$372$	−1.90468	−	5.47825i	−0.0987530	−	0.284034i
$373$	11.7969	+	4.29373i	0.610821	+	0.222321i	0.628862	−	0.777517i	$-0.283521\pi$
$373$	11.7969	+	4.29373i	0.610821	+	0.222321i	−0.0180414	+	0.999837i	$0.505743\pi$
$374$	0.809963	−	1.10649i	0.0418822	−	0.0572150i
$375$	4.33716	+	7.05525i	0.223970	+	0.364331i
$376$	−0.570798	−	23.5901i	−0.0294366	−	1.21657i
$377$			8.31716i			0.428356i
$378$	−0.187514	+	7.34608i	−0.00964467	+	0.377841i
$379$		−	23.3931i		−	1.20162i	−0.799390	−	0.600812i	$-0.794844\pi$
$379$		−	23.3931i		−	1.20162i	0.799390	−	0.600812i	$-0.205156\pi$
$380$	27.3271	−	29.9172i	1.40185	−	1.53472i
$381$	11.0151	−	20.3557i	0.564320	−	1.04285i
$382$	2.94761	+	2.15769i	0.150813	+	0.110397i
$383$	−1.21216	−	0.441189i	−0.0619383	−	0.0225437i	0.310865	−	0.950454i	$-0.399381\pi$
$383$	−1.21216	−	0.441189i	−0.0619383	−	0.0225437i	−0.372804	+	0.927910i	$0.621603\pi$
$384$	9.24449	+	17.2783i	0.471756	+	0.881729i
$385$	1.98551	−	11.2604i	0.101191	−	0.573883i
$386$	−6.14198	−	25.0144i	−0.312619	−	1.27320i
$387$	2.45394	+	5.73609i	0.124741	+	0.291582i
$388$	−15.7883	+	8.25067i	−0.801529	+	0.418864i
$389$	4.79152	+	13.1646i	0.242940	+	0.667471i	0.999902	+	0.0140126i	$0.00446050\pi$
$389$	4.79152	+	13.1646i	0.242940	+	0.667471i	−0.756962	+	0.653459i	$0.773317\pi$
$390$	−5.28437	+	2.50651i	−0.267585	+	0.126922i
$391$	−1.33106	−	1.58629i	−0.0673145	−	0.0802222i
$392$	−2.79652	−	0.423629i	−0.141246	−	0.0213965i
$393$	−36.0818	+	7.39395i	−1.82009	+	0.372975i
$394$	−28.0775	−	13.8187i	−1.41453	−	0.696175i
$395$	−14.3613	−	24.8745i	−0.722595	−	1.25157i
$396$	−20.4096	+	12.1436i	−1.02562	+	0.610237i
$397$	4.87314	−	8.44052i	0.244576	−	0.423618i	−0.717436	−	0.696624i	$-0.754685\pi$
$397$	4.87314	−	8.44052i	0.244576	−	0.423618i	0.962012	+	0.273006i	$0.0880179\pi$
$398$	−6.55562	+	4.38783i	−0.328603	+	0.219942i
$399$	7.54854	−	9.51734i	0.377900	−	0.476463i
$400$	−12.1435	−	5.61584i	−0.607173	−	0.280792i
$401$	13.9535	−	2.46038i	0.696805	−	0.122866i	0.185984	−	0.982553i	$-0.440453\pi$
$401$	13.9535	−	2.46038i	0.696805	−	0.122866i	0.510821	+	0.859687i	$0.329342\pi$
$402$	−14.8122	+	15.0079i	−0.738763	+	0.748528i
$403$	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
$408$	−0.817955	−	0.878166i	−0.0404948	−	0.0434757i
$409$	1.60138	+	9.08189i	0.0791833	+	0.449071i	0.998461	+	0.0554607i	$0.0176628\pi$
$409$	1.60138	+	9.08189i	0.0791833	+	0.449071i	−0.919278	+	0.393610i	$0.871226\pi$
$410$	−3.34677	+	1.47578i	−0.165285	+	0.0728834i
$411$	2.89976	+	2.29990i	0.143035	+	0.113446i
$412$	4.41139	−	20.0487i	0.217333	−	0.987727i
$413$	−6.65313	−	3.84119i	−0.327379	−	0.189012i
$414$	10.4598	+	34.3046i	0.514071	+	1.68598i
$415$	−19.2342	+	11.1049i	−0.944172	+	0.545118i
$416$	−2.40981	+	4.00692i	−0.118151	+	0.196455i
$417$	−6.55833	−	32.0041i	−0.321163	−	1.56725i
$418$	39.0285	+	4.24305i	1.90895	+	0.207535i
$419$	16.1602	−	13.5600i	0.789479	−	0.662451i	−0.156138	−	0.987735i	$-0.549904\pi$
$419$	16.1602	−	13.5600i	0.789479	−	0.662451i	0.945616	+	0.325284i	$0.105460\pi$
$420$	−9.35291	−	3.55816i	−0.456375	−	0.173620i
$421$	18.9819	−	6.90883i	0.925119	−	0.336716i	0.164846	−	0.986319i	$-0.447287\pi$
$421$	18.9819	−	6.90883i	0.925119	−	0.336716i	0.760273	+	0.649603i	$0.225065\pi$
$422$	−2.21028	+	7.60553i	−0.107595	+	0.370231i
$423$	2.98011	−	24.8503i	0.144898	−	1.20827i
$424$	−0.193244	−	0.959587i	−0.00938477	−	0.0466017i
$425$	0.806918	+	0.142281i	0.0391413	+	0.00690166i
$426$	21.3782	−	15.1793i	1.03578	−	0.735439i
$427$	0.450923	−	1.23890i	0.0218217	−	0.0599546i
$428$	−9.40329	+	1.25312i	−0.454525	+	0.0605717i
$429$	−4.98381	−	2.69689i	−0.240621	−	0.130207i
$430$	−8.47734	+	0.562375i	−0.408814	+	0.0271201i
$431$	15.2753			0.735787			0.367894	−	0.929868i	$-0.380079\pi$
$431$	15.2753			0.735787			0.367894	+	0.929868i	$0.380079\pi$
$432$	7.08280	+	19.5406i	0.340772	+	0.940146i
$433$	2.98946			0.143664			0.0718321	−	0.997417i	$-0.477115\pi$
$433$	2.98946			0.143664			0.0718321	+	0.997417i	$0.477115\pi$
$434$	2.36261	−	0.156733i	0.113409	−	0.00752341i
$435$	−42.8902	+	26.3664i	−2.05643	+	1.26417i
$436$	−17.6102	+	2.34680i	−0.843375	+	0.112391i
$437$	20.2766	−	55.7095i	0.969962	−	2.66495i
$438$	−10.1210	−	4.63883i	−0.483599	−	0.221652i
$439$	−0.950483	−	0.167596i	−0.0453641	−	0.00799891i	0.150920	−	0.988546i	$-0.451776\pi$
$439$	−0.950483	−	0.167596i	−0.0453641	−	0.00799891i	−0.196284	+	0.980547i	$0.562888\pi$
$440$	−6.38465	−	31.7041i	−0.304376	−	1.51143i
$441$	−2.87138	−	0.869019i	−0.136732	−	0.0413818i
$442$	0.0799119	−	0.274975i	0.00380102	−	0.0130792i
$443$	21.9883	−	8.00307i	1.04469	−	0.380237i	0.238036	−	0.971256i	$-0.423496\pi$
$443$	21.9883	−	8.00307i	1.04469	−	0.380237i	0.806658	+	0.591019i	$0.201274\pi$
$444$	26.3634	−	21.4797i	1.25115	−	1.01938i
$445$	−24.1326	+	20.2496i	−1.14399	+	0.959924i
$446$	21.8129	+	2.37142i	1.03287	+	0.112290i
$447$	−0.979668	+	0.869204i	−0.0463367	+	0.0411119i
$448$	−7.80205	+	1.76860i	−0.368612	+	0.0835584i
$449$	28.5702	−	16.4950i	1.34831	−	0.778448i	0.360302	−	0.932836i	$-0.382674\pi$
$449$	28.5702	−	16.4950i	1.34831	−	0.778448i	0.988010	+	0.154387i	$0.0493404\pi$
$450$	−11.8955	−	7.73775i	−0.560761	−	0.364761i
$451$	−3.06910	−	1.77195i	−0.144518	−	0.0834377i
$452$	−2.72892	+	12.4023i	−0.128357	+	0.583353i
$453$	13.6518	−	5.39986i	0.641420	−	0.253708i
$454$	23.1647	−	10.2146i	1.08717	−	0.479395i
$455$	−0.414623	−	2.35144i	−0.0194378	−	0.110237i
$456$	10.0643	−	32.8510i	0.471305	−	1.53839i
$457$	25.6657	+	21.5361i	1.20059	+	1.00742i	0.999613	+	0.0278199i	$0.00885649\pi$
$457$	25.6657	+	21.5361i	1.20059	+	1.00742i	0.200978	+	0.979596i	$0.435588\pi$
$458$	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	0.375977	−	0.926629i	$-0.377307\pi$
$461$	26.2641	−	31.3003i	1.22324	−	1.45780i	0.847264	−	0.531172i	$-0.178248\pi$
$462$	−2.57081	−	9.34846i	−0.119605	−	0.434930i
$463$	17.6080	−	3.10477i	0.818315	−	0.144291i	0.251206	−	0.967934i	$-0.419173\pi$
$463$	17.6080	−	3.10477i	0.818315	−	0.144291i	0.567109	+	0.823643i	$0.308062\pi$
$464$	−16.8945	+	36.5320i	−0.784309	+	1.69596i
$465$	8.28694	+	1.22654i	0.384297	+	0.0568796i
$466$	9.92439	−	6.64264i	0.459738	−	0.307714i
$467$	−14.6901	+	25.4440i	−0.679776	+	1.17741i	0.295272	+	0.955413i	$0.404590\pi$
$467$	−14.6901	+	25.4440i	−0.679776	+	1.17741i	−0.975048	+	0.221994i	$0.928743\pi$
$468$	−3.13766	+	3.84063i	−0.145039	+	0.177533i
$469$	−4.30425	−	7.45518i	−0.198752	−	0.344248i
$470$	30.5798	+	15.0502i	1.41054	+	0.694214i
$471$	4.55885	−	13.6891i	0.210061	−	0.630761i
$472$	−21.4839	−	3.25448i	−0.988878	−	0.149799i
$473$	−5.29118	−	6.30579i	−0.243289	−	0.289940i
$474$	−20.0419	−	13.8383i	−0.920555	−	0.635613i
$475$	8.02313	+	22.0434i	0.368127	+	1.01142i
$476$	0.434220	−	0.226915i	0.0199024	−	0.0104006i
$477$	−0.0572612	−	1.03665i	−0.00262181	−	0.0474649i
$478$	0.693323	+	2.82369i	0.0317119	+	0.129153i
$479$	−4.95871	+	28.1223i	−0.226569	+	1.28494i	0.633093	+	0.774076i	$0.281785\pi$
$479$	−4.95871	+	28.1223i	−0.226569	+	1.28494i	−0.859662	+	0.510863i	$0.829326\pi$
$480$	−28.3024	+	0.275458i	−1.29182	+	0.0125729i
$481$	7.62476	+	2.77519i	0.347659	+	0.126538i
$482$	18.6700	+	13.6667i	0.850396	+	0.622501i
$483$	−14.6358	+	0.403909i	−0.665950	+	0.0183785i
$484$	6.29525	−	6.89193i	0.286148	−	0.313270i
$485$		−	25.7302i		−	1.16835i
$486$	4.47031	+	21.5874i	0.202778	+	0.979225i
$487$			35.6923i			1.61737i	0.588241	+	0.808686i	$0.299821\pi$
$487$			35.6923i			1.61737i	−0.588241	+	0.808686i	$0.700179\pi$
$488$	−0.0902030	−	3.72794i	−0.00408330	−	0.168756i
$489$	−6.08457	+	0.167918i	−0.275154	+	0.00759353i
$490$	2.41306	−	3.29647i	0.109011	−	0.148919i
$491$	4.34295	+	1.58070i	0.195994	+	0.0713361i	0.438152	−	0.898901i	$-0.355633\pi$
$491$	4.34295	+	1.58070i	0.195994	+	0.0713361i	−0.242158	+	0.970237i	$0.577855\pi$
$492$	−2.02777	+	2.34684i	−0.0914190	+	0.105804i
$493$	0.428035	−	2.42751i	0.0192777	−	0.109329i
$494$	7.96164	−	1.95488i	0.358211	−	0.0879543i
$495$	−1.89187	−	34.2501i	−0.0850332	−	1.53943i
$496$	6.06070	−	2.84955i	0.272134	−	0.127949i
$497$	3.66094	+	10.0583i	0.164216	+	0.451179i
$498$	−10.7005	+	15.4974i	−0.479500	+	0.694456i
$499$	1.54851	+	1.84545i	0.0693210	+	0.0826135i	0.799590	−	0.600546i	$-0.205050\pi$
$499$	1.54851	+	1.84545i	0.0693210	+	0.0826135i	−0.730269	+	0.683159i	$0.760605\pi$
$500$	−7.57757	+	5.83356i	−0.338879	+	0.260885i
$501$	−11.6148	+	34.8763i	−0.518910	+	1.55816i
$502$	8.53135	−	17.3344i	0.380773	−	0.773674i
$503$	−13.2868	−	23.0135i	−0.592431	−	1.02612i	−0.993904	−	0.110249i	$-0.964835\pi$
$503$	−13.2868	−	23.0135i	−0.592431	−	1.02612i	0.401473	−	0.915871i	$-0.368498\pi$
$504$	−8.45857	+	0.672792i	−0.376775	+	0.0299685i
$505$	17.0288	−	29.4947i	0.757771	−	1.31250i
$506$	−26.3198	−	39.3229i	−1.17006	−	1.74812i
$507$	21.1034	+	3.12350i	0.937235	+	0.138720i
$508$	24.7072	+	10.1883i	1.09621	+	0.452031i
$509$	11.2306	−	1.98025i	0.497786	−	0.0877731i	0.0808820	−	0.996724i	$-0.474226\pi$
$509$	11.2306	−	1.98025i	0.497786	−	0.0877731i	0.416904	+	0.908951i	$0.363115\pi$
$510$	1.67133	−	0.459614i	0.0740078	−	0.0203520i
$511$	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
$516$	−6.29038	+	3.51148i	−0.276919	+	0.154584i
$517$	5.73425	+	32.5206i	0.252192	+	1.43025i
$518$	5.60134	+	12.7027i	0.246109	+	0.558126i
$519$	1.67166	−	0.661209i	0.0733776	−	0.0290238i
$520$	−3.51723	−	5.76530i	−0.154241	−	0.252825i
$521$	14.6183	+	8.43990i	0.640441	+	0.369759i	0.784784	−	0.619769i	$-0.212774\pi$
$521$	14.6183	+	8.43990i	0.640441	+	0.369759i	−0.144343	+	0.989528i	$0.546107\pi$
$522$	−23.2780	+	35.7862i	−1.01885	+	1.56632i
$523$	10.8668	−	6.27396i	0.475173	−	0.274341i	−0.243230	−	0.969969i	$-0.578207\pi$
$523$	10.8668	−	6.27396i	0.475173	−	0.274341i	0.718403	+	0.695628i	$0.244874\pi$
$524$	−12.8531	−	40.5408i	−0.561489	−	1.77103i
$525$	4.33354	−	3.84490i	0.189131	−	0.167805i
$526$	−3.91925	+	36.0502i	−0.170888	+	1.57186i
$527$	−0.314192	+	0.263638i	−0.0136864	+	0.0114843i
$528$	−16.4126	−	21.9693i	−0.714266	−	0.956091i
$529$	−45.5339	+	16.5730i	−1.97973	+	0.720564i
$530$	1.35765	+	0.394553i	0.0589726	+	0.0171383i
$531$	−22.0590	−	6.67612i	−0.957279	−	0.289719i
$532$	11.8419	+	7.51777i	0.513410	+	0.325937i
$533$	−0.728807	−	0.128508i	−0.0315681	−	0.00556631i
$534$	−11.1301	+	24.2835i	−0.481645	+	1.05085i
$535$	4.68632	−	12.8755i	0.202607	−	0.556658i
$536$	−19.0252	−	15.1952i	−0.821763	−	0.656331i
$537$	−25.7181	+	15.8100i	−1.10982	+	0.682252i
$538$	0.621588	+	9.36992i	0.0267985	+	0.403966i
$539$	3.95817			0.170491
$540$	−29.7522	−	4.00513i	−1.28033	−	0.172353i
$541$	31.9387			1.37315			0.686576	−	0.727058i	$-0.259113\pi$
$541$	31.9387			1.37315			0.686576	+	0.727058i	$0.259113\pi$
$542$	−1.50301	−	22.6566i	−0.0645598	−	0.973186i
$543$	−38.8878	−	21.0434i	−1.66883	−	0.903058i
$544$	0.909556	−	1.04547i	0.0389969	−	0.0448241i
$545$	8.77638	−	24.1129i	0.375939	−	1.03288i
$546$	−1.17216	−	1.65084i	−0.0501638	−	0.0706495i
$547$	−16.5868	−	2.92469i	−0.709199	−	0.125051i	−0.192598	−	0.981278i	$-0.561691\pi$
$547$	−16.5868	−	2.92469i	−0.709199	−	0.125051i	−0.516600	+	0.856227i	$0.672803\pi$
$548$	−2.29053	+	3.60800i	−0.0978465	+	0.154126i
$549$	0.470945	−	3.92709i	0.0200995	−	0.167604i
$550$	17.9793	+	5.22504i	0.766639	+	0.222796i
$551$	66.3146	−	24.1365i	2.82510	−	1.02825i
$552$	−38.1292	+	16.1589i	−1.62289	+	0.687768i
$553$	7.61676	−	6.39122i	0.323897	−	0.271782i
$554$	−3.03077	+	27.8777i	−0.128765	+	1.18441i
$555$	9.86026	+	48.1172i	0.418545	+	2.04246i
$556$	35.9592	−	11.4005i	1.52501	−	0.483490i
$557$	−30.0023	+	17.3218i	−1.27124	+	0.733949i	−0.975221	−	0.221234i	$-0.928991\pi$
$557$	−30.0023	+	17.3218i	−1.27124	+	0.733949i	−0.296016	+	0.955183i	$0.595658\pi$
$558$	6.79459	−	2.07174i	0.287638	−	0.0877037i
$559$	−1.48866	−	0.859480i	−0.0629638	−	0.0363521i
$560$	2.95528	−	11.1706i	0.124883	−	0.472045i
$561$	1.31582	+	1.04362i	0.0555539	+	0.0440618i
$562$	−2.95171	−	6.69389i	−0.124510	−	0.282365i
$563$	2.00417	+	11.3662i	0.0844657	+	0.479029i	0.997471	+	0.0710802i	$0.0226446\pi$
$563$	2.00417	+	11.3662i	0.0844657	+	0.479029i	−0.913005	+	0.407949i	$0.866244\pi$
$564$	28.8973	+	0.417866i	1.21680	+	0.0175953i
$565$	−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	−0.998641	−	0.0521243i	$-0.983401\pi$
$569$	−18.4603	+	22.0001i	−0.773896	+	0.922293i	0.224745	+	0.974418i	$0.427845\pi$
$570$	35.3203	+	34.8596i	1.47941	+	1.46011i
$571$	17.6466	−	3.11157i	0.738487	−	0.130215i	0.208263	−	0.978073i	$-0.433219\pi$
$571$	17.6466	−	3.11157i	0.738487	−	0.130215i	0.530224	+	0.847858i	$0.322108\pi$
$572$	2.49446	−	6.04923i	0.104299	−	0.252931i
$573$	−2.78015	+	3.50526i	−0.116142	+	0.146434i
$574$	−0.704293	−	1.05225i	−0.0293966	−	0.0439199i
$575$	14.1370	−	24.4860i	0.589555	−	1.02114i
$576$	−21.5832	+	10.4960i	−0.899300	+	0.437332i
$577$	7.74571	+	13.4160i	0.322458	+	0.558514i	0.980995	−	0.194035i	$-0.0621575\pi$
$577$	7.74571	+	13.4160i	0.322458	+	0.558514i	−0.658536	+	0.752549i	$0.728824\pi$
$578$	10.5788	−	21.4946i	0.440020	−	0.894055i
$579$	30.9041	−	6.33291i	1.28433	−	0.263187i
$580$	−35.4633	−	46.0654i	−1.47253	−	1.91276i
$581$	−4.94202	−	5.88967i	−0.205029	−	0.244345i
$582$	−9.35022	−	19.7127i	−0.387579	−	0.817116i
$583$	0.468510	+	1.28722i	0.0194037	+	0.0533112i
$584$	4.10342	−	12.1833i	0.169801	−	0.504148i
$585$	−2.81746	−	6.58580i	−0.116488	−	0.272289i
$586$	−31.4801	+	7.72955i	−1.30043	+	0.319305i
$587$	−0.266188	+	1.50963i	−0.0109868	+	0.0623091i	−0.989808	−	0.142407i	$-0.954516\pi$
$587$	−0.266188	+	1.50963i	−0.0109868	+	0.0623091i	0.978821	+	0.204716i	$0.0656270\pi$
$588$	0.650798	−	3.40242i	0.0268385	−	0.140313i
$589$	−11.0342	−	4.01612i	−0.454657	−	0.165481i
$590$	18.5380	−	25.3247i	0.763199	−	1.04260i
$591$	18.2405	−	33.7081i	0.750315	−	1.38657i
$592$	27.8536	+	27.6777i	1.14477	+	1.13755i
$593$			35.5387i			1.45940i	0.683769	+	0.729699i	$0.260340\pi$
$593$			35.5387i			1.45940i	−0.683769	+	0.729699i	$0.739660\pi$
$594$	−13.8958	−	25.5526i	−0.570150	−	1.04843i
$595$			0.707648i			0.0290107i
$596$	−1.11659	−	1.01992i	−0.0457374	−	0.0417776i
$597$	−5.05971	−	8.23062i	−0.207080	−	0.336857i
$598$	−7.97327	−	5.83655i	−0.326051	−	0.238674i
$599$	−41.9968	−	15.2856i	−1.71594	−	0.624552i	−0.718466	−	0.695562i	$-0.755155\pi$
$599$	−41.9968	−	15.2856i	−1.71594	−	0.624552i	−0.997476	+	0.0710105i	$0.977378\pi$
$600$	7.44754	−	14.5958i	0.304045	−	0.595870i
$601$	−3.33958	+	18.9397i	−0.136224	+	0.772567i	0.837775	+	0.546016i	$0.183856\pi$
$601$	−3.33958	+	18.9397i	−0.136224	+	0.772567i	−0.973999	+	0.226551i	$0.927255\pi$
$602$	−0.701312	−	2.85623i	−0.0285834	−	0.116411i
$603$	−17.6662	−	18.8378i	−0.719422	−	0.767136i
$604$	7.85143	+	15.0243i	0.319470	+	0.611331i
$605$	4.61116	+	12.6691i	0.187470	+	0.515071i
$606$	2.32803	−	28.7850i	0.0945698	−	1.16931i
$607$	−10.7007	−	12.7526i	−0.434327	−	0.517610i	0.503839	−	0.863798i	$-0.331921\pi$
$607$	−10.7007	−	12.7526i	−0.434327	−	0.517610i	−0.938165	+	0.346187i	$0.887476\pi$
$608$	38.9414	+	7.58579i	1.57928	+	0.307645i
$609$	−11.5669	−	13.0369i	−0.468713	−	0.528281i
$610$	4.83252	+	2.37838i	0.195663	+	0.0962978i
$611$	3.44792	+	5.97197i	0.139488	+	0.241600i
$612$	1.11344	−	0.959478i	0.0450080	−	0.0387846i
$613$	8.31281	−	14.3982i	0.335751	−	0.581538i	−0.647878	−	0.761744i	$-0.724343\pi$
$613$	8.31281	−	14.3982i	0.335751	−	0.581538i	0.983629	+	0.180206i	$0.0576765\pi$
$614$	0.740264	−	0.495477i	0.0298746	−	0.0199958i
$615$	−1.64771	−	4.16572i	−0.0664421	−	0.167978i
$616$	10.4245	−	4.08241i	0.420017	−	0.164485i
$617$	−36.8594	+	6.49931i	−1.48390	+	0.261652i	−0.856137	−	0.516748i	$-0.827142\pi$
$617$	−36.8594	+	6.49931i	−1.48390	+	0.261652i	−0.627768	+	0.778401i	$0.716031\pi$
$618$	24.3274	+	6.34761i	0.978591	+	0.255338i
$619$	4.88758	−	5.82479i	0.196448	−	0.234118i	−0.658824	−	0.752298i	$-0.728946\pi$
$619$	4.88758	−	5.82479i	0.196448	−	0.234118i	0.855272	+	0.518179i	$0.173390\pi$
$620$	−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
$624$	−4.78974	−	3.13883i	−0.191743	−	0.125654i
$625$	−5.30258	−	30.0724i	−0.212103	−	1.20290i
$626$	−7.16730	+	3.16046i	−0.286463	+	0.126317i
$627$	−7.03984	+	47.5635i	−0.281144	+	1.89950i
$628$	16.2711	+	3.58019i	0.649287	+	0.142865i
$629$	−2.08260	−	1.20239i	−0.0830385	−	0.0479423i
$630$	4.79721	−	11.2780i	0.191126	−	0.449326i
$631$	−2.40296	+	1.38735i	−0.0956603	+	0.0552295i	−0.547067	−	0.837089i	$-0.684256\pi$
$631$	−2.40296	+	1.38735i	−0.0956603	+	0.0552295i	0.451407	+	0.892318i	$0.350922\pi$
$632$	13.4682	−	24.6882i	0.535737	−	0.982045i
$633$	−9.20327	−	3.06494i	−0.365797	−	0.121821i
$634$	−8.98005	−	0.976281i	−0.356643	−	0.0387731i
$635$	−29.5703	+	24.8124i	−1.17346	+	0.984652i
$636$	1.18352	−	0.191085i	0.0469295	−	0.00757700i
$637$	0.776714	−	0.282701i	0.0307745	−	0.0112010i
$638$	15.7188	−	54.0883i	0.622315	−	2.14138i
$639$	17.5651	+	26.8816i	0.694866	+	1.06342i
$640$	−3.73801	−	32.4678i	−0.147758	−	1.28340i
$641$	−31.6223	−	5.57586i	−1.24901	−	0.220233i	−0.490234	−	0.871591i	$-0.663089\pi$
$641$	−31.6223	−	5.57586i	−1.24901	−	0.220233i	−0.758771	+	0.651357i	$0.774200\pi$
$642$	−1.08858	−	11.5673i	−0.0429629	−	0.456526i
$643$	−7.01542	+	19.2747i	−0.276661	+	0.760121i	0.721074	+	0.692858i	$0.243649\pi$
$643$	−7.01542	+	19.2747i	−0.276661	+	0.760121i	−0.997735	+	0.0672627i	$0.978573\pi$
$644$	−2.23326	−	16.7582i	−0.0880027	−	0.660365i
$645$	−0.287053	−	10.4014i	−0.0113027	−	0.409556i
$646$	−2.42435	+	0.160828i	−0.0953847	+	0.00632769i
$647$	−6.98871			−0.274755			−0.137377	−	0.990519i	$-0.543867\pi$
$647$	−6.98871			−0.274755			−0.137377	+	0.990519i	$0.543867\pi$
$648$	−24.2495	+	7.74337i	−0.952612	+	0.304188i
$649$	30.4082			1.19362
$650$	3.90126	−	0.258805i	0.153020	−	0.0101511i
$651$	0.0800009	+	2.89886i	0.00313548	+	0.113615i
$652$	−0.928440	−	6.96694i	−0.0363605	−	0.272846i
$653$	−11.2248	+	30.8399i	−0.439261	+	1.20686i	0.500713	+	0.865613i	$0.333071\pi$
$653$	−11.2248	+	30.8399i	−0.439261	+	1.20686i	−0.939974	+	0.341246i	$0.889151\pi$
$654$	−2.03866	−	21.6629i	−0.0797180	−	0.847088i
$655$	60.4950	+	10.6669i	2.36373	+	0.416790i
$656$	−2.94015	−	2.04487i	−0.114794	−	0.0798388i
$657$	6.15613	−	12.1668i	0.240174	−	0.474673i
$658$	−3.29259	+	11.3298i	−0.128359	+	0.441680i
$659$	9.78656	−	3.56202i	0.381230	−	0.138756i	−0.144295	−	0.989535i	$-0.546091\pi$
$659$	9.78656	−	3.56202i	0.381230	−	0.138756i	0.525525	+	0.850778i	$0.323869\pi$
$660$	39.1026	−	6.31330i	1.52206	−	0.245745i
$661$	−14.1672	+	11.8877i	−0.551040	+	0.462377i	−0.875293	−	0.483593i	$-0.839331\pi$
$661$	−14.1672	+	11.8877i	−0.551040	+	0.462377i	0.324253	+	0.945970i	$0.394887\pi$
$662$	14.0750	+	1.53019i	0.547042	+	0.0594726i
$663$	0.332741	+	0.110812i	0.0129226	+	0.00430358i
$664$	−19.0902	−	10.4143i	−0.740843	−	0.404154i
$665$	−17.5454	+	10.1298i	−0.680380	+	0.392817i
$666$	25.0398	+	33.2809i	0.970273	+	1.28961i
$667$	−73.6631	−	42.5294i	−2.85225	−	1.64674i
$668$	−41.4545	−	9.12141i	−1.60392	−	0.352918i
$669$	−3.93454	+	26.5830i	−0.152118	+	1.02776i
$670$	32.1787	−	14.1894i	1.24317	−	0.548183i
$671$	0.906183	+	5.13922i	0.0349828	+	0.198397i
$672$	−1.79522	−	9.63209i	−0.0692523	−	0.371566i
$673$	7.00366	+	5.87677i	0.269971	+	0.226533i	0.767715	−	0.640791i	$-0.221394\pi$
$673$	7.00366	+	5.87677i	0.269971	+	0.226533i	−0.497744	+	0.867324i	$0.665838\pi$
$674$	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	0.0433420	−	0.999060i	$-0.486199\pi$
$677$	26.5318	−	31.6193i	1.01970	−	1.21523i	0.976356	−	0.216169i	$-0.0693561\pi$
$678$	−15.0491	−	3.92668i	−0.577957	−	0.150803i
$679$	8.77175	−	1.54670i	0.336629	−	0.0593568i
$680$	0.729859	+	1.86371i	0.0279888	+	0.0714701i
$681$	11.4046	+	28.8330i	0.437027	+	1.10488i
$682$	−7.78857	+	5.21308i	−0.298240	+	0.199619i
$683$	22.3067	−	38.6364i	0.853543	−	1.47838i	−0.0244473	−	0.999701i	$-0.507783\pi$
$683$	22.3067	−	38.6364i	0.853543	−	1.47838i	0.877990	−	0.478679i	$-0.158884\pi$
$684$	39.7278	+	13.8717i	1.51903	+	0.530399i
$685$	−3.08637	−	5.34575i	−0.117924	−	0.204251i
$686$	1.26886	+	0.624486i	0.0484455	+	0.0238430i
$687$	6.05946	+	6.82954i	0.231183	+	0.260563i
$688$	−4.79291	−	6.79906i	−0.182728	−	0.259212i
$689$	0.183872	+	0.219130i	0.00700495	+	0.00834818i
$690$	4.82181	−	59.6193i	0.183563	−	2.26967i
$691$	−1.73411	−	4.76443i	−0.0659687	−	0.181248i	0.902328	−	0.431050i	$-0.141857\pi$
$691$	−1.73411	−	4.76443i	−0.0659687	−	0.181248i	−0.968297	+	0.249802i	$0.919634\pi$
$692$	0.961401	+	1.83972i	0.0365470	+	0.0699355i
$693$	11.5626	−	2.70381i	0.439227	−	0.102709i
$694$	0.676980	+	2.75713i	0.0256978	+	0.104659i
$695$	−9.46140	+	53.6583i	−0.358891	+	2.03537i
$696$	−43.9095	−	22.4049i	−1.66438	−	0.849257i
$697$	0.206101	+	0.0750148i	0.00780665	+	0.00284139i
$698$	2.32030	+	1.69849i	0.0878247	+	0.0642889i
$699$	7.65978	+	12.4601i	0.289719	+	0.471286i
$700$	4.93922	+	4.51159i	0.186685	+	0.170522i
$701$			5.30395i			0.200327i	0.994971	+	0.100164i	$0.0319366\pi$
$701$			5.30395i			0.200327i	−0.994971	+	0.100164i	$0.968063\pi$
$702$	−4.55179	−	4.02173i	−0.171796	−	0.151790i
$703$		−	68.8476i		−	2.59664i
$704$	23.2443	−	21.5035i	0.876052	−	0.810443i
$705$	−19.8661	+	36.7122i	−0.748201	+	1.38266i
$706$	1.63398	−	2.23217i	0.0614955	−	0.0840087i
$707$	11.0788	+	4.03234i	0.416660	+	0.151652i
$708$	4.99967	−	26.1387i	0.187899	−	0.982351i
$709$	0.950240	−	5.38908i	0.0356870	−	0.202391i	−0.961751	−	0.273925i	$-0.911678\pi$
$709$	0.950240	−	5.38908i	0.0356870	−	0.202391i	0.997438	+	0.0715334i	$0.0227893\pi$
$710$	−42.4670	+	10.4272i	−1.59376	+	0.391328i
$711$	17.8842	−	23.8730i	0.670710	−	0.895306i
$712$	−29.2317	−	9.84544i	−1.09550	−	0.368974i
$713$	4.84064	+	13.2996i	0.181283	+	0.498072i
$714$	0.257156	+	0.542150i	0.00962381	+	0.0202895i
$715$	6.07499	+	7.23989i	0.227192	+	0.270757i
$716$	−21.2647	−	27.6221i	−0.794701	−	1.03229i
$717$	−3.48853	+	0.714875i	−0.130282	+	0.0266975i
$718$	5.46549	−	11.1051i	0.203970	−	0.414438i
$719$	21.4749	+	37.1955i	0.800877	+	1.38716i	0.919040	+	0.394165i	$0.128966\pi$
$719$	21.4749	+	37.1955i	0.800877	+	1.38716i	−0.118163	+	0.992994i	$0.537700\pi$
$720$	1.00232	−	34.6503i	0.0373544	−	1.29134i
$721$	−5.13206	+	8.88899i	−0.191128	+	0.331043i
$722$	−23.7457	−	35.4770i	−0.883722	−	1.32032i
$723$	−17.6093	+	22.2021i	−0.654897	+	0.825706i
$724$	19.4638	−	47.2010i	0.723367	−	1.75421i
$725$	33.1451	−	5.84438i	1.23098	−	0.217055i
$726$	8.13663	+	8.03048i	0.301979	+	0.298039i
$727$	−32.7377	+	39.0153i	−1.21418	+	1.44700i	−0.355348	+	0.934734i	$0.615638\pi$
$727$	−32.7377	+	39.0153i	−1.21418	+	1.44700i	−0.858828	+	0.512264i	$0.828807\pi$
$728$	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
$732$	4.56663	+	0.0660353i	0.168788	+	0.00244074i
$733$	−3.87976	−	22.0032i	−0.143302	−	0.812708i	−0.968715	−	0.248178i	$-0.920168\pi$
$733$	−3.87976	−	22.0032i	−0.143302	−	0.812708i	0.825412	−	0.564530i	$-0.190943\pi$
$734$	9.33436	+	21.1685i	0.344537	+	0.781342i
$735$	3.92012	+	3.10919i	0.144596	+	0.114684i
$736$	−23.1659	−	41.8323i	−0.853905	−	1.54196i
$737$	29.5089	+	17.0370i	1.08698	+	0.627565i
$738$	−2.77616	−	2.59271i	−0.102192	−	0.0954391i
$739$	37.9816	−	21.9287i	1.39717	−	0.806659i	0.403079	−	0.915165i	$-0.367940\pi$
$739$	37.9816	−	21.9287i	1.39717	−	0.806659i	0.994096	+	0.108506i	$0.0346066\pi$
$740$	−54.0635	+	17.1403i	−1.98741	+	0.630091i
$741$	2.01565	+	9.83621i	0.0740468	+	0.361342i
$742$	−0.0528971	+	0.486559i	−0.00194191	+	0.0178621i
$743$	−3.94759	+	3.31242i	−0.144823	+	0.121521i	−0.712321	−	0.701854i	$-0.752356\pi$
$743$	−3.94759	+	3.31242i	−0.144823	+	0.121521i	0.567498	+	0.823375i	$0.307911\pi$
$744$	3.20054	+	7.55213i	0.117338	+	0.276875i
$745$	2.05257	−	0.747075i	0.0752004	−	0.0273707i
$746$	−17.0487	−	4.95460i	−0.624197	−	0.181401i
$747$	−18.4598	−	13.8290i	−0.675409	−	0.505976i
$748$	−1.03937	+	1.63720i	−0.0380031	+	0.0598618i
$749$	4.67115	+	0.823650i	0.170680	+	0.0300955i
$750$	−6.78067	−	9.54974i	−0.247595	−	0.348707i
$751$	2.80348	−	7.70249i	0.102300	−	0.281068i	−0.877974	−	0.478708i	$-0.841105\pi$
$751$	2.80348	−	7.70249i	0.102300	−	0.281068i	0.980275	+	0.197640i	$0.0633276\pi$
$752$	3.01376	+	33.2348i	0.109900	+	1.21195i
$753$	20.8107	+	11.2613i	0.758383	+	0.410384i
$754$	−0.778580	−	11.7364i	−0.0283542	−	0.427416i
$755$	−24.4851			−0.891105
$756$	−0.423072	−	10.3837i	−0.0153870	−	0.377651i
$757$	18.9096			0.687280			0.343640	−	0.939102i	$-0.388340\pi$
$757$	18.9096			0.687280			0.343640	+	0.939102i	$0.388340\pi$
$758$	2.18986	+	33.0103i	0.0795393	+	1.19899i
$759$	49.3702	−	30.3500i	1.79203	−	1.10163i
$760$	−35.7610	+	44.7747i	−1.29719	+	1.62415i
$761$	−4.94134	+	13.5762i	−0.179123	+	0.492137i	−0.996464	−	0.0840168i	$-0.973225\pi$
$761$	−4.94134	+	13.5762i	−0.179123	+	0.492137i	0.817341	+	0.576154i	$0.195447\pi$
$762$	−13.6380	+	29.7553i	−0.494053	+	1.07792i
$763$	8.74798	+	1.54250i	0.316698	+	0.0558424i
$764$	−4.36139	−	2.76881i	−0.157790	−	0.100172i
$765$	0.483392	+	2.06718i	0.0174771	+	0.0747389i
$766$	1.75179	+	0.509096i	0.0632947	+	0.0183944i
$767$	5.96701	−	2.17181i	0.215456	−	0.0784196i
$768$	−14.6625	−	23.5162i	−0.529086	−	0.848568i
$769$	−21.8892	+	18.3672i	−0.789343	+	0.662338i	−0.945583	−	0.325381i	$-0.894507\pi$
$769$	−21.8892	+	18.3672i	−0.789343	+	0.662338i	0.156239	+	0.987719i	$0.450063\pi$
$770$	−1.74768	+	16.0756i	−0.0629820	+	0.579323i
$771$	−28.9262	+	25.6646i	−1.04175	+	0.924287i
$772$	11.0086	+	34.7232i	0.396210	+	1.24971i
$773$	−26.5860	+	15.3494i	−0.956230	+	0.552080i	−0.895011	−	0.446044i	$-0.852832\pi$
$773$	−26.5860	+	15.3494i	−0.956230	+	0.552080i	−0.0612195	+	0.998124i	$0.519499\pi$
$774$	−3.99975	−	7.86454i	−0.143768	−	0.282685i
$775$	−4.84987	−	2.80008i	−0.174213	−	0.100582i
$776$	21.5067	−	13.1206i	0.772045	−	0.471001i
$777$	−15.8111	+	6.25392i	−0.567219	+	0.224358i
$778$	−7.99373	−	18.1282i	−0.286589	−	0.649927i
$779$	1.09038	+	6.18388i	0.0390671	+	0.221560i
$780$	7.22220	−	4.03165i	0.258596	−	0.144356i
$781$	−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
$786$	50.2234	−	13.8114i	1.79141	−	0.492635i
$787$	16.1873	−	2.85425i	0.577013	−	0.101743i	0.122477	−	0.992471i	$-0.460916\pi$
$787$	16.1873	−	2.85425i	0.577013	−	0.101743i	0.454536	+	0.890728i	$0.349805\pi$
$788$	40.9141	+	16.8713i	1.45751	+	0.601016i
$789$	−43.9338	−	6.50261i	−1.56408	−	0.231499i
$790$	22.5939	+	33.7563i	0.803856	+	1.20100i
$791$	3.17473	−	5.49880i	0.112881	−	0.195515i
$792$	27.6634	−	19.0465i	0.982977	−	0.676788i
$793$	0.544874	+	0.943750i	0.0193491	+	0.0335135i
$794$	−6.08642	+	12.3667i	−0.215999	+	0.438878i
$795$	−0.547119	+	1.64286i	−0.0194043	+	0.0582663i
$796$	8.83996	−	6.80540i	0.313324	−	0.241211i
$797$	−10.3572	−	12.3432i	−0.366871	−	0.437220i	0.550754	−	0.834668i	$-0.314340\pi$
$797$	−10.3572	−	12.3432i	−0.366871	−	0.437220i	−0.917625	+	0.397448i	$0.869896\pi$
$798$	−9.76090	+	14.1367i	−0.345532	+	0.500432i
$799$	−0.698993	−	1.92047i	−0.0247286	−	0.0679413i
$800$	17.6615	+	6.78782i	0.624428	+	0.239986i
$801$	−29.1921	−	14.7706i	−1.03145	−	0.521892i
$802$	−19.4596	+	4.77808i	−0.687144	+	0.168720i
$803$	−3.12405	+	17.7174i	−0.110245	+	0.625232i
$804$	19.4967	−	22.5645i	0.687595	−	0.795787i
$805$	22.9463	+	8.35178i	0.808752	+	0.294362i
$806$	−1.15603	+	1.57924i	−0.0407193	+	0.0556264i
$807$	−11.4966	+	0.317277i	−0.404700	+	0.0111687i
$808$	33.3368	−	0.806634i	1.17278	−	0.0283773i
$809$		−	36.1246i		−	1.27007i	−0.772483	−	0.635036i	$-0.780985\pi$
$809$		−	36.1246i		−	1.27007i	0.772483	−	0.635036i	$-0.219015\pi$
$810$	6.30965	−	36.2221i	0.221698	−	1.27272i
$811$			27.1352i			0.952845i	0.879216	+	0.476422i	$0.158067\pi$
$811$			27.1352i			0.952845i	−0.879216	+	0.476422i	$0.841933\pi$
$812$	13.5725	−	14.8590i	0.476303	−	0.521449i
$813$	27.7990	−	0.767180i	0.974954	−	0.0269062i
$814$	−44.3406	−	32.4579i	−1.55414	−	1.13765i
$815$	9.53955	+	3.47211i	0.334156	+	0.121623i
$816$	1.23643	+	1.16262i	0.0432838	+	0.0406998i
$817$	−2.53270	+	14.3637i	−0.0886081	+	0.502522i
$818$	−3.10990	−	12.6657i	−0.108735	−	0.442844i
$819$	2.07582	−	1.35640i	0.0725351	−	0.0473963i
$820$	4.58451	−	2.39578i	0.160098	−	0.0836643i
$821$	17.1448	+	47.1049i	0.598357	+	1.64397i	0.754547	+	0.656246i	$0.227857\pi$
$821$	17.1448	+	47.1049i	0.598357	+	1.64397i	−0.156190	+	0.987727i	$0.549921\pi$
$822$	−4.30718	−	2.97397i	−0.150230	−	0.103729i
$823$	−8.26687	−	9.85208i	−0.288165	−	0.343422i	0.602469	−	0.798142i	$-0.294184\pi$
$823$	−8.26687	−	9.85208i	−0.288165	−	0.343422i	−0.890634	+	0.454720i	$0.849739\pi$
$824$	−4.34818	+	28.7039i	−0.151476	+	0.999946i
$825$	−7.24545	+	21.7563i	−0.252254	+	0.757457i
$826$	9.74789	+	4.79754i	0.339172	+	0.166928i
$827$	−13.0582	−	22.6175i	−0.454080	−	0.786489i	0.544555	−	0.838725i	$-0.316699\pi$
$827$	−13.0582	−	22.6175i	−0.454080	−	0.786489i	−0.998635	+	0.0522359i	$0.983365\pi$
$828$	−17.9712	−	47.4284i	−0.624544	−	1.64825i
$829$	6.61918	−	11.4648i	0.229894	−	0.398187i	−0.727883	−	0.685702i	$-0.759496\pi$
$829$	6.61918	−	11.4648i	0.229894	−	0.398187i	0.957776	+	0.287514i	$0.0928289\pi$
$830$	26.1021	−	17.4708i	0.906018	−	0.606420i
$831$	−33.9742	−	5.02850i	−1.17855	−	0.174437i
$832$	3.02541	−	5.87980i	0.104887	−	0.203845i
$833$	−0.241246	+	0.0425383i	−0.00835869	+	0.00147386i
$834$	12.2505	+	44.5475i	0.424200	+	1.54255i
$835$	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	$-0.403376\pi$
$839$	−17.0596	−	14.3147i	−0.588962	−	0.494198i	−0.887876	+	0.460082i	$0.847820\pi$
$840$	13.5311	+	4.14542i	0.466867	+	0.143031i
$841$	−12.5462	−	71.1533i	−0.432629	−	2.45356i
$842$	−26.1388	+	11.5261i	−0.900802	+	0.397214i
$843$	8.33187	−	3.29559i	0.286965	−	0.113506i
$844$	2.40699	−	10.9392i	0.0828519	−	0.376541i
$845$	−30.8131	−	17.7900i	−1.06000	−	0.611994i
$846$	−1.87899	+	35.3456i	−0.0646010	+	1.21521i
$847$	−4.04186	+	2.33357i	−0.138880	+	0.0801825i
$848$	0.362517	+	1.33599i	0.0124489	+	0.0458783i
$849$	−9.54316	+	8.46710i	−0.327520	+	0.290590i
$850$	−1.15197	−	0.125238i	−0.0395123	−	0.00429564i
$851$	−63.5680	+	53.3399i	−2.17908	+	1.82847i
$852$	−28.7460	+	23.4209i	−0.984823	+	0.802388i
$853$	−37.8668	+	13.7824i	−1.29654	+	0.471900i	−0.895867	−	0.444323i	$-0.853444\pi$
$853$	−37.8668	+	13.7824i	−1.29654	+	0.471900i	−0.400669	+	0.916223i	$0.631222\pi$
$854$	−0.520328	+	1.79044i	−0.0178053	+	0.0612676i
$855$	−44.3338	+	41.5763i	−1.51618	+	1.42188i
$856$	13.1518	−	2.64854i	0.449519	−	0.0905253i
$857$	23.8999	+	4.21420i	0.816405	+	0.143954i	0.566231	−	0.824247i	$-0.308401\pi$
$857$	23.8999	+	4.21420i	0.816405	+	0.143954i	0.250174	+	0.968201i	$0.419512\pi$
$858$	7.28518	+	3.33908i	0.248712	+	0.113994i
$859$	14.0073	−	38.4847i	0.477923	−	1.31308i	−0.433331	−	0.901235i	$-0.642662\pi$
$859$	14.0073	−	38.4847i	0.477923	−	1.31308i	0.911253	−	0.411846i	$-0.135116\pi$
$860$	11.9098	−	1.58715i	0.406122	−	0.0541213i
$861$	1.32110	−	0.812137i	0.0450230	−	0.0276776i
$862$	−21.5552	+	1.42994i	−0.734173	+	0.0487041i
$863$	31.3406			1.06685			0.533423	−	0.845849i	$-0.320905\pi$
$863$	31.3406			1.06685			0.533423	+	0.845849i	$0.320905\pi$
$864$	−11.8238	−	26.9109i	−0.402255	−	0.915527i
$865$	−2.99818			−0.101941
$866$	−4.21846	+	0.279847i	−0.143349	+	0.00950958i
$867$	25.8050	+	13.9639i	0.876385	+	0.474239i
$868$	−3.31924	+	0.442335i	−0.112662	+	0.0150138i
$869$	−13.4605	+	36.9826i	−0.456618	+	1.25455i
$870$	58.0546	−	41.2209i	1.96824	−	1.39752i
$871$	7.00737	+	1.23559i	0.237436	+	0.0418663i
$872$	24.6302	−	4.96010i	0.834085	−	0.167970i
$873$	24.5675	−	10.5102i	0.831482	−	0.355715i
$874$	−23.3975	+	80.5105i	−0.791433	+	2.72331i
$875$	4.49312	−	1.63536i	0.151895	−	0.0552853i
$876$	14.7161	+	5.59848i	0.497210	+	0.189155i
$877$	−38.2545	+	32.0993i	−1.29176	+	1.08392i	−0.300255	+	0.953859i	$0.597072\pi$
$877$	−38.2545	+	32.0993i	−1.29176	+	1.08392i	−0.991506	+	0.130058i	$0.958484\pi$
$878$	1.35693	+	0.147521i	0.0457941	+	0.00497858i
$879$	−7.96983	−	38.8921i	−0.268816	−	1.31180i
$880$	11.9773	+	44.1403i	0.403755	+	1.48797i
$881$	42.5662	−	24.5756i	1.43409	−	0.827973i	0.436662	−	0.899626i	$-0.356161\pi$
$881$	42.5662	−	24.5756i	1.43409	−	0.827973i	0.997430	+	0.0716529i	$0.0228274\pi$
$882$	4.13318	+	0.957489i	0.139172	+	0.0322403i
$883$	49.6565	+	28.6692i	1.67108	+	0.964796i	0.967038	+	0.254634i	$0.0819549\pi$
$883$	49.6565	+	28.6692i	1.67108	+	0.964796i	0.704038	+	0.710162i	$0.251378\pi$
$884$	−0.0870238	+	0.395502i	−0.00292693	+	0.0133022i
$885$	30.1158	+	23.8859i	1.01233	+	0.802916i
$886$	−30.2787	+	13.3516i	−1.01723	+	0.448555i
$887$	−6.08497	−	34.5096i	−0.204313	−	1.15872i	−0.898517	−	0.438940i	$-0.855354\pi$
$887$	−6.08497	−	34.5096i	−0.204313	−	1.15872i	0.694203	−	0.719779i	$-0.255757\pi$
$888$	−35.1910	+	32.7782i	−1.18093	+	1.09996i
$889$	−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
$894$	1.30105	−	1.31825i	0.0435138	−	0.0440889i
$895$	49.5847	−	8.74311i	1.65743	−	0.292250i
$896$	10.8440	−	3.22605i	0.362273	−	0.107775i
$897$	7.52028	−	9.48171i	0.251095	−	0.316585i
$898$	−38.7717	+	25.9508i	−1.29383	+	0.865990i
$899$	−8.42366	+	14.5902i	−0.280945	+	0.486611i
$900$	17.5103	+	9.80528i	0.583676	+	0.326843i
$901$	−0.0423888	−	0.0734196i	−0.00141218	−	0.00244596i
$902$	4.49672	+	2.21311i	0.149724	+	0.0736886i
$903$	3.52873	−	0.723113i	0.117429	−	0.0240637i
$904$	2.68982	−	17.7564i	0.0894620	−	0.590570i
$905$	47.4021	+	56.4916i	1.57570	+	1.87784i
$906$	−18.7588	+	8.89778i	−0.623219	+	0.295609i
$907$	1.57478	+	4.32666i	0.0522896	+	0.143664i	0.963088	−	0.269187i	$-0.0867550\pi$
$907$	1.57478	+	4.32666i	0.0522896	+	0.143664i	−0.910798	+	0.412852i	$0.864533\pi$
$908$	−31.7318	+	16.5824i	−1.05306	+	0.550307i
$909$	35.1177	+	4.21139i	1.16478	+	0.139683i
$910$	0.805201	+	3.27934i	0.0266922	+	0.108709i
$911$	3.79302	−	21.5113i	0.125668	−	0.712700i	−0.855241	−	0.518231i	$-0.826591\pi$
$911$	3.79302	−	21.5113i	0.125668	−	0.712700i	0.980909	−	0.194469i	$-0.0622982\pi$
$912$	−11.1267	+	47.2986i	−0.368441	+	1.56621i
$913$	28.5968	+	10.4084i	0.946416	+	0.344467i
$914$	−38.2332	−	27.9872i	−1.26464	−	0.925735i
$915$	−3.13944	+	5.80162i	−0.103787	+	0.191796i
$916$	−7.11015	+	7.78408i	−0.234926	+	0.257193i
$917$			21.2648i			0.702224i
$918$	1.12154	+	1.40806i	0.0370164	+	0.0464731i
$919$			19.9077i			0.656694i	0.944557	+	0.328347i	$0.106492\pi$
$919$			19.9077i			0.656694i	−0.944557	+	0.328347i	$0.893508\pi$
$920$	69.0471	−	1.67070i	2.27641	−	0.0550813i
$921$	0.571346	+	0.929406i	0.0188265	+	0.0306250i
$922$	−34.1315	+	46.6269i	−1.12406	+	1.53557i
$923$	−8.31385	−	3.02599i	−0.273654	−	0.0996018i
$924$	4.50283	+	12.9511i	0.148132	+	0.426059i
$925$	5.70169	−	32.3359i	0.187470	−	1.06320i
$926$	−24.5563	+	6.02949i	−0.806969	+	0.198141i
$927$	−8.91972	+	29.4722i	−0.292962	+	0.967993i
$928$	20.4203	−	53.1323i	0.670328	−	1.74415i
$929$	6.04729	+	16.6148i	0.198405	+	0.545114i	0.998500	−	0.0547603i	$-0.0174395\pi$
$929$	6.04729	+	16.6148i	0.198405	+	0.545114i	−0.800094	+	0.599874i	$0.795217\pi$
$930$	−11.8086	−	0.955041i	−0.387220	−	0.0313170i
$931$	−4.50808	−	5.37252i	−0.147746	−	0.176077i
$932$	−13.3826	+	10.3025i	−0.438362	+	0.337471i
$933$	18.6496	+	21.0197i	0.610559	+	0.688153i
$934$	18.3475	−	37.2795i	0.600349	−	1.21982i
$935$	−1.40050	−	2.42573i	−0.0458011	−	0.0793299i
$936$	4.06807	−	5.71328i	0.132969	−	0.186744i
$937$	−12.0207	+	20.8205i	−0.392700	+	0.680176i	−0.992805	−	0.119746i	$-0.961792\pi$
$937$	−12.0207	+	20.8205i	−0.392700	+	0.680176i	0.600105	+	0.799921i	$0.295125\pi$
$938$	6.77167	+	10.1172i	0.221103	+	0.330337i
$939$	−3.52867	−	8.92113i	−0.115154	−	0.291130i
$940$	−44.5604	−	18.3749i	−1.45340	−	0.599323i
$941$	0.766002	−	0.135067i	0.0249709	−	0.00440305i	−0.161149	−	0.986930i	$-0.551520\pi$
$941$	0.766002	−	0.135067i	0.0249709	−	0.00440305i	0.186120	+	0.982527i	$0.440409\pi$
$942$	−5.15159	+	19.7436i	−0.167848	+	0.643282i
$943$	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	$-0.286469\pi$
$947$	−1.28711	−	1.08001i	−0.0418253	−	0.0350956i	−0.663461	+	0.748211i	$0.730913\pi$
$948$	29.5768	+	17.6512i	0.960609	+	0.573285i
$949$	0.652377	+	3.69981i	0.0211770	+	0.120101i
$950$	−13.3850	−	30.3546i	−0.434268	−	0.984834i
$951$	1.61979	−	10.9439i	0.0525254	−	0.354879i
$952$	−0.591491	+	0.360851i	−0.0191703	+	0.0116952i
$953$	19.6229	+	11.3293i	0.635648	+	0.366991i	0.782936	−	0.622102i	$-0.213721\pi$
$953$	19.6229	+	11.3293i	0.635648	+	0.366991i	−0.147288	+	0.989094i	$0.547055\pi$
$954$	0.177844	+	1.45747i	0.00575791	+	0.0471872i
$955$	6.46200	−	3.73084i	0.209105	−	0.120727i
$956$	−1.24269	−	3.91964i	−0.0401913	−	0.126770i
$957$	65.4510	+	21.7970i	2.11573	+	0.704597i
$958$	4.36474	−	40.1478i	0.141018	−	1.29712i
$959$	1.63691	−	1.37353i	0.0528585	−	0.0443536i
$960$	39.9120	−	3.03812i	1.28815	−	0.0980549i
$961$	−26.4963	+	9.64385i	−0.854718	+	0.311092i
$962$	−11.0192	−	3.20233i	−0.355273	−	0.103247i
$963$	14.2080	−	0.784804i	0.457845	−	0.0252899i
$964$	−27.6248	−	17.5375i	−0.889736	−	0.564846i
$965$	−51.8139	−	9.13619i	−1.66795	−	0.294104i
$966$	20.6149	−	1.94003i	0.663273	−	0.0624195i
$967$	−16.9851	+	46.6661i	−0.546203	+	1.50068i	0.292595	+	0.956237i	$0.405481\pi$
$967$	−16.9851	+	46.6661i	−0.546203	+	1.50068i	−0.838798	+	0.544443i	$0.816741\pi$
$968$	−8.23814	+	10.3146i	−0.264784	+	0.331524i
$969$	−0.0820913	−	2.97460i	−0.00263715	−	0.0955580i
$970$	2.40863	+	36.3081i	0.0773365	+	1.16578i
$971$	−13.0868			−0.419976			−0.209988	−	0.977704i	$-0.567343\pi$
$971$	−13.0868			−0.419976			−0.209988	+	0.977704i	$0.567343\pi$
$972$	−8.32894	−	30.0438i	−0.267151	−	0.963655i
$973$	−18.8616			−0.604674
$974$	−3.34120	−	50.3658i	−0.107059	−	1.61382i
$975$	0.132101	+	4.78673i	0.00423063	+	0.153298i
$976$	0.476263	+	5.25209i	0.0152448	+	0.168115i
$977$	11.1883	−	30.7396i	0.357945	−	0.983446i	−0.621796	−	0.783179i	$-0.713597\pi$
$977$	11.1883	−	30.7396i	0.357945	−	0.983446i	0.979741	−	0.200267i	$-0.0641810\pi$
$978$	8.57029	−	0.806535i	0.274048	−	0.0257902i
$979$	42.5097	+	7.49561i	1.35862	+	0.239561i
$980$	−3.09651	+	4.87758i	−0.0989145	+	0.155808i
$981$	26.6082	−	1.46976i	0.849535	−	0.0469257i
$982$	−6.27636	−	1.82400i	−0.200287	−	0.0582062i
$983$	5.17699	−	1.88427i	0.165120	−	0.0600989i	−0.258137	−	0.966108i	$-0.583109\pi$
$983$	5.17699	−	1.88427i	0.165120	−	0.0600989i	0.423258	+	0.906009i	$0.360886\pi$
$984$	2.64172	−	3.50147i	0.0842150	−	0.111623i
$985$	−48.9672	+	41.0884i	−1.56022	+	1.30918i
$986$	−0.376763	+	3.46555i	−0.0119986	+	0.110366i
$987$	−13.7099	−	4.56577i	−0.436390	−	0.145330i
$988$	−11.0518	+	3.50386i	−0.351603	+	0.111473i
$989$	15.2244	−	8.78982i	0.484108	−	0.279500i
$990$	5.87584	+	48.1537i	0.186746	+	1.53042i
$991$	−10.8934	−	6.28933i	−0.346041	−	0.199787i	0.316899	−	0.948459i	$-0.397358\pi$
$991$	−10.8934	−	6.28933i	−0.346041	−	0.199787i	−0.662940	+	0.748672i	$0.730692\pi$
$992$	−8.28558	+	4.58839i	−0.263068	+	0.145682i
$993$	−2.53881	+	17.1530i	−0.0805667	+	0.544335i
$994$	−6.10757	−	13.8508i	−0.193720	−	0.439319i
$995$	2.79808	+	15.8687i	0.0887051	+	0.503071i
$996$	13.6488	−	22.8703i	0.432480	−	0.724673i
$997$	−31.4861	−	26.4200i	−0.997176	−	0.836730i	−0.0105852	−	0.999944i	$-0.503369\pi$
$997$	−31.4861	−	26.4200i	−0.997176	−	0.836730i	−0.986591	+	0.163214i	$0.947814\pi$
$998$	−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.659.5	yes	648
4.3	odd	2	inner	756.2.cf.a.659.57	yes	648
27.5	odd	18	inner	756.2.cf.a.491.57	yes	648
108.59	even	18	inner	756.2.cf.a.491.5	✓	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.5	✓	648	108.59	even	18	inner
756.2.cf.a.491.57	yes	648	27.5	odd	18	inner
756.2.cf.a.659.5	yes	648	1.1	even	1	trivial
756.2.cf.a.659.57	yes	648	4.3	odd	2	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.41111 + 0.0936112i) q^{2} +(-0.0477819 - 1.73139i) q^{3} +(1.98247 - 0.264192i) q^{4} +(-0.988005 + 2.71452i) q^{5} +(0.229503 + 2.43871i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(-2.77276 + 0.558386i) q^{8} +(-2.99543 + 0.165458i) q^{9} +O(q^{10})\)	\(q+(-1.41111 + 0.0936112i) q^{2} +(-0.0477819 - 1.73139i) q^{3} +(1.98247 - 0.264192i) q^{4} +(-0.988005 + 2.71452i) q^{5} +(0.229503 + 2.43871i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(-2.77276 + 0.558386i) q^{8} +(-2.99543 + 0.165458i) q^{9} +(1.14008 - 3.92298i) q^{10} +(3.71947 - 1.35378i) q^{11} +(-0.552146 - 3.41982i) q^{12} +(0.633183 - 0.531304i) q^{13} +(1.40593 + 0.152848i) q^{14} +(4.74711 + 1.58092i) q^{15} +(3.86041 - 1.04751i) q^{16} +(-0.212149 + 0.122484i) q^{17} +(4.21140 - 0.513887i) q^{18} +(-6.07372 - 3.50666i) q^{19} +(-1.24154 + 5.64249i) q^{20} +(-0.253597 + 1.71339i) q^{21} +(-5.12186 + 2.25851i) q^{22} +(1.46788 + 8.32475i) q^{23} +(1.09927 + 4.77405i) 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} +(-6.84670 - 1.78647i) q^{30} +(1.64886 - 0.290738i) q^{31} +(-5.34941 + 1.83953i) q^{32} +(-2.52164 - 6.37517i) q^{33} +(0.287900 - 0.192698i) q^{34} +(1.44437 - 2.50172i) q^{35} +(-5.89466 + 1.11939i) q^{36} +(4.90834 + 8.50150i) q^{37} +(8.89896 + 4.37973i) q^{38} +(-0.950150 - 1.07090i) q^{39} +(1.22375 - 8.07841i) q^{40} +(-0.575510 - 0.685866i) q^{41} +(0.197462 - 2.44152i) q^{42} +(-0.711282 - 1.95423i) q^{43} +(7.01609 - 3.66648i) q^{44} +(2.51036 - 8.29465i) q^{45} +(-2.85063 - 11.6097i) q^{46} +(-1.44871 + 8.21605i) q^{47} +(-1.99810 - 6.63382i) q^{48} +(0.939693 + 0.342020i) q^{49} +(3.81689 + 2.79402i) q^{50} +(0.222205 + 0.361460i) q^{51} +(1.11490 - 1.22058i) q^{52} +0.346076i q^{53} +(-1.09097 - 7.26703i) q^{54} +11.4341i q^{55} +(2.82760 - 0.0684180i) q^{56} +(-5.78119 + 10.6835i) q^{57} +(8.40543 - 11.4826i) q^{58} +(7.21907 + 2.62753i) q^{59} +(9.82869 + 1.87998i) q^{60} +(-0.228940 + 1.29838i) q^{61} +(-2.29950 + 0.564615i) q^{62} +(2.97866 + 0.357207i) q^{63} +(7.37641 - 3.09654i) q^{64} +(0.816648 + 2.24372i) q^{65} +(4.15510 + 8.76002i) q^{66} +(5.53344 + 6.59450i) q^{67} +(-0.388220 + 0.298869i) q^{68} +(14.3433 - 2.93924i) q^{69} +(-1.80397 + 3.66541i) q^{70} +(-5.35194 - 9.26982i) q^{71} +(8.21323 - 2.13139i) q^{72} +(-2.27260 + 3.93625i) q^{73} +(-7.72205 - 11.5371i) q^{74} +(-3.60004 + 4.53900i) q^{75} +(-12.9674 - 5.34724i) q^{76} +(-3.89804 + 0.687330i) q^{77} +(1.44102 + 1.42222i) 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} +(-0.0500871 + 3.46374i) q^{84} +(-0.122882 - 0.696897i) q^{85} +(1.18664 + 2.69106i) q^{86} +(13.6550 + 10.8303i) q^{87} +(-9.55726 + 5.83059i) q^{88} +(9.44436 + 5.45270i) q^{89} +(-2.76593 + 11.9397i) q^{90} +(-0.715824 + 0.413281i) q^{91} +(5.10936 + 16.1158i) q^{92} +(-0.582167 - 2.84092i) q^{93} +(1.27518 - 11.7294i) q^{94} +(15.5198 - 13.0226i) q^{95} +(3.44055 + 9.17402i) q^{96} +(-8.36991 + 3.04640i) q^{97} +(-1.35803 - 0.394663i) q^{98} +(-10.9174 + 4.67056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q+O(q^{10}) \) 648 * q	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66} - 78 q^{68} - 42 q^{72} - 24 q^{81} - 30 q^{86} - 36 q^{89} + 198 q^{90} + 114 q^{92} - 144 q^{93} - 54 q^{94} + 156 q^{96} + 36 q^{97}+O(q^{100}) \) 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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