LMFDB - Embedded newform 630.2.cd.a.23.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.17
Character	$\chi$	$=$	630.23
Dual form			630.2.cd.a.137.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.970368 + 1.43471i) q^{3} +1.00000i q^{4} +(-1.84064 - 1.26967i) q^{5} +(0.328338 - 1.70065i) q^{6} +(-1.20135 - 2.35728i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.11677 + 2.78439i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.970368 + 1.43471i) q^{3} +1.00000i q^{4} +(-1.84064 - 1.26967i) q^{5} +(0.328338 - 1.70065i) q^{6} +(-1.20135 - 2.35728i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.11677 + 2.78439i) q^{9} +(0.403736 + 2.19932i) q^{10} +(3.49512 + 2.01791i) q^{11} +(-1.43471 + 0.970368i) q^{12} +(-5.43898 + 1.45737i) q^{13} +(-0.817368 + 2.51633i) q^{14} +(0.0355071 - 3.87282i) q^{15} -1.00000 q^{16} +(-2.10979 + 7.87383i) q^{17} +(2.75854 - 1.17918i) q^{18} +(-1.94823 - 1.12481i) q^{19} +(1.26967 - 1.84064i) q^{20} +(2.21626 - 4.01101i) q^{21} +(-1.04455 - 3.89830i) q^{22} +(2.74000 + 0.734182i) q^{23} +(1.70065 + 0.328338i) q^{24} +(1.77589 + 4.67399i) q^{25} +(4.87645 + 2.81542i) q^{26} +(-5.07846 + 1.09964i) q^{27} +(2.35728 - 1.20135i) q^{28} +(3.85395 + 6.67524i) q^{29} +(-2.76361 + 2.71339i) q^{30} -5.44844 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.496444 + 6.97259i) q^{33} +(7.05948 - 4.07579i) q^{34} +(-0.781720 + 5.86421i) q^{35} +(-2.78439 - 1.11677i) q^{36} +(-1.45573 - 5.43287i) q^{37} +(0.582246 + 2.17297i) q^{38} +(-7.36871 - 6.38916i) q^{39} +(-2.19932 + 0.403736i) q^{40} +(-4.90767 - 2.83345i) q^{41} +(-4.40334 + 1.26908i) q^{42} +(-1.26568 + 4.72357i) q^{43} +(-2.01791 + 3.49512i) q^{44} +(5.59082 - 3.70712i) q^{45} +(-1.41833 - 2.45662i) q^{46} +(-0.691285 - 0.691285i) q^{47} +(-0.970368 - 1.43471i) q^{48} +(-4.11353 + 5.66382i) q^{49} +(2.04927 - 4.56076i) q^{50} +(-13.3439 + 4.61358i) q^{51} +(-1.45737 - 5.43898i) q^{52} +(-11.0557 - 2.96238i) q^{53} +(4.36858 + 2.81345i) q^{54} +(-3.87117 - 8.15188i) q^{55} +(-2.51633 - 0.817368i) q^{56} +(-0.276725 - 3.88663i) q^{57} +(1.99495 - 7.44526i) q^{58} +7.90943 q^{59} +(3.87282 + 0.0355071i) q^{60} +2.51163 q^{61} +(3.85263 + 3.85263i) q^{62} +(7.90521 - 0.712471i) q^{63} -1.00000i q^{64} +(11.8616 + 4.22321i) q^{65} +(4.57933 - 5.28140i) q^{66} +(-3.12653 + 3.12653i) q^{67} +(-7.87383 - 2.10979i) q^{68} +(1.60548 + 4.64353i) q^{69} +(4.69938 - 3.59386i) q^{70} +4.36829i q^{71} +(1.17918 + 2.75854i) q^{72} +(1.02927 - 3.84131i) q^{73} +(-2.81226 + 4.87098i) q^{74} +(-4.98255 + 7.08337i) q^{75} +(1.12481 - 1.94823i) q^{76} +(0.557925 - 10.6632i) q^{77} +(0.692647 + 9.72828i) q^{78} +6.34457i q^{79} +(1.84064 + 1.26967i) q^{80} +(-6.50564 - 6.21905i) q^{81} +(1.46670 + 5.47380i) q^{82} +(-5.09362 - 1.36483i) q^{83} +(4.01101 + 2.21626i) q^{84} +(13.8805 - 11.8141i) q^{85} +(4.23504 - 2.44510i) q^{86} +(-5.83726 + 12.0067i) q^{87} +(3.89830 - 1.04455i) q^{88} +(3.54958 - 6.14806i) q^{89} +(-6.57464 - 1.33198i) q^{90} +(9.96952 + 11.0704i) q^{91} +(-0.734182 + 2.74000i) q^{92} +(-5.28699 - 7.81692i) q^{93} +0.977624i q^{94} +(2.15785 + 4.54398i) q^{95} +(-0.328338 + 1.70065i) q^{96} +(8.57569 + 2.29785i) q^{97} +(6.91363 - 1.09622i) q^{98} +(-9.52189 + 7.47823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.970368	+	1.43471i	0.560242	+	0.828329i
$3$	0.970368	+	1.43471i	0.560242	+	0.828329i
$4$			1.00000i			0.500000i
$5$	−1.84064	−	1.26967i	−0.823158	−	0.567813i
$5$	−1.84064	−	1.26967i	−0.823158	−	0.567813i
$6$	0.328338	−	1.70065i	0.134043	−	0.694286i
$7$	−1.20135	−	2.35728i	−0.454066	−	0.890968i
$7$	−1.20135	−	2.35728i	−0.454066	−	0.890968i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.11677	+	2.78439i	−0.372257	+	0.928130i
$10$	0.403736	+	2.19932i	0.127673	+	0.695485i
$11$	3.49512	+	2.01791i	1.05382	+	0.608422i	0.923716	−	0.383078i	$-0.125136\pi$
$11$	3.49512	+	2.01791i	1.05382	+	0.608422i	0.130102	+	0.991501i	$0.458469\pi$
$12$	−1.43471	+	0.970368i	−0.414164	+	0.280121i
$13$	−5.43898	+	1.45737i	−1.50850	+	0.404202i	−0.915937	−	0.401322i	$-0.868551\pi$
$13$	−5.43898	+	1.45737i	−1.50850	+	0.404202i	−0.592564	+	0.805524i	$0.701884\pi$
$14$	−0.817368	+	2.51633i	−0.218451	+	0.672517i
$15$	0.0355071	−	3.87282i	0.00916790	−	0.999958i
$16$	−1.00000			−0.250000
$17$	−2.10979	+	7.87383i	−0.511698	+	1.90968i	−0.109940	+	0.993938i	$0.535066\pi$
$17$	−2.10979	+	7.87383i	−0.511698	+	1.90968i	−0.401758	+	0.915746i	$0.631601\pi$
$18$	2.75854	−	1.17918i	0.650193	−	0.277936i
$19$	−1.94823	−	1.12481i	−0.446956	−	0.258050i	0.259588	−	0.965719i	$-0.416413\pi$
$19$	−1.94823	−	1.12481i	−0.446956	−	0.258050i	−0.706544	+	0.707670i	$0.749747\pi$
$20$	1.26967	−	1.84064i	0.283906	−	0.411579i
$21$	2.21626	−	4.01101i	0.483627	−	0.875274i
$22$	−1.04455	−	3.89830i	−0.222698	−	0.831120i
$23$	2.74000	+	0.734182i	0.571330	+	0.153087i	0.532907	−	0.846174i	$-0.321100\pi$
$23$	2.74000	+	0.734182i	0.571330	+	0.153087i	0.0384236	+	0.999262i	$0.487766\pi$
$24$	1.70065	+	0.328338i	0.347143	+	0.0670217i
$25$	1.77589	+	4.67399i	0.355177	+	0.934799i
$26$	4.87645	+	2.81542i	0.956351	+	0.552150i
$27$	−5.07846	+	1.09964i	−0.977351	+	0.211626i
$28$	2.35728	−	1.20135i	0.445484	−	0.227033i
$29$	3.85395	+	6.67524i	0.715660	+	1.23956i	0.962704	+	0.270556i	$0.0872075\pi$
$29$	3.85395	+	6.67524i	0.715660	+	1.23956i	−0.247044	+	0.969004i	$0.579459\pi$
$30$	−2.76361	+	2.71339i	−0.504563	+	0.495395i
$31$	−5.44844			−0.978569			−0.489284	−	0.872124i	$-0.662742\pi$
$31$	−5.44844			−0.978569			−0.489284	+	0.872124i	$0.662742\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.496444	+	6.97259i	0.0864197	+	1.21377i
$34$	7.05948	−	4.07579i	1.21069	−	0.698993i
$35$	−0.781720	+	5.86421i	−0.132135	+	0.991232i
$36$	−2.78439	−	1.11677i	−0.464065	−	0.186129i
$37$	−1.45573	−	5.43287i	−0.239321	−	0.893159i	−0.976153	−	0.217083i	$-0.930346\pi$
$37$	−1.45573	−	5.43287i	−0.239321	−	0.893159i	0.736832	−	0.676076i	$-0.236321\pi$
$38$	0.582246	+	2.17297i	0.0944528	+	0.352503i
$39$	−7.36871	−	6.38916i	−1.17994	−	1.02308i
$40$	−2.19932	+	0.403736i	−0.347743	+	0.0638363i
$41$	−4.90767	−	2.83345i	−0.766450	−	0.442510i	0.0651570	−	0.997875i	$-0.479245\pi$
$41$	−4.90767	−	2.83345i	−0.766450	−	0.442510i	−0.831607	+	0.555365i	$0.812579\pi$
$42$	−4.40334	+	1.26908i	−0.679451	+	0.195823i
$43$	−1.26568	+	4.72357i	−0.193014	+	0.720337i	0.799758	+	0.600322i	$0.204961\pi$
$43$	−1.26568	+	4.72357i	−0.193014	+	0.720337i	−0.992772	+	0.120015i	$0.961706\pi$
$44$	−2.01791	+	3.49512i	−0.304211	+	0.526909i
$45$	5.59082	−	3.70712i	0.833430	−	0.552625i
$46$	−1.41833	−	2.45662i	−0.209121	−	0.362209i
$47$	−0.691285	−	0.691285i	−0.100834	−	0.100834i	0.654890	−	0.755724i	$-0.272715\pi$
$47$	−0.691285	−	0.691285i	−0.100834	−	0.100834i	−0.755724	+	0.654890i	$0.772715\pi$
$48$	−0.970368	−	1.43471i	−0.140061	−	0.207082i
$49$	−4.11353	+	5.66382i	−0.587648	+	0.809117i
$50$	2.04927	−	4.56076i	0.289811	−	0.644988i
$51$	−13.3439	+	4.61358i	−1.86852	+	0.646031i
$52$	−1.45737	−	5.43898i	−0.202101	−	0.754250i
$53$	−11.0557	−	2.96238i	−1.51862	−	0.406914i	−0.599335	−	0.800498i	$-0.704568\pi$
$53$	−11.0557	−	2.96238i	−1.51862	−	0.406914i	−0.919289	+	0.393584i	$0.871235\pi$
$54$	4.36858	+	2.81345i	0.594488	+	0.382862i
$55$	−3.87117	−	8.15188i	−0.521989	−	1.09920i
$56$	−2.51633	−	0.817368i	−0.336259	−	0.109225i
$57$	−0.276725	−	3.88663i	−0.0366532	−	0.514797i
$58$	1.99495	−	7.44526i	0.261950	−	0.977610i
$59$	7.90943			1.02972			0.514860	−	0.857274i	$-0.327844\pi$
$59$	7.90943			1.02972			0.514860	+	0.857274i	$0.327844\pi$
$60$	3.87282	+	0.0355071i	0.499979	+	0.00458395i
$61$	2.51163			0.321581			0.160790	−	0.986989i	$-0.448596\pi$
$61$	2.51163			0.321581			0.160790	+	0.986989i	$0.448596\pi$
$62$	3.85263	+	3.85263i	0.489284	+	0.489284i
$63$	7.90521	−	0.712471i	0.995963	−	0.0897629i
$64$		−	1.00000i		−	0.125000i
$65$	11.8616	+	4.22321i	1.47124	+	0.523824i
$66$	4.57933	−	5.28140i	0.563676	−	0.650096i
$67$	−3.12653	+	3.12653i	−0.381966	+	0.381966i	−0.871810	−	0.489844i	$-0.837054\pi$
$67$	−3.12653	+	3.12653i	−0.381966	+	0.381966i	0.489844	+	0.871810i	$0.337054\pi$
$68$	−7.87383	−	2.10979i	−0.954842	−	0.255849i
$69$	1.60548	+	4.64353i	0.193277	+	0.559015i
$70$	4.69938	−	3.59386i	0.561683	−	0.429548i
$71$			4.36829i			0.518421i	0.965821	+	0.259210i	$0.0834623\pi$
$71$			4.36829i			0.518421i	−0.965821	+	0.259210i	$0.916538\pi$
$72$	1.17918	+	2.75854i	0.138968	+	0.325097i
$73$	1.02927	−	3.84131i	0.120467	−	0.449591i	−0.879170	−	0.476508i	$-0.841902\pi$
$73$	1.02927	−	3.84131i	0.120467	−	0.449591i	0.999638	+	0.0269171i	$0.00856902\pi$
$74$	−2.81226	+	4.87098i	−0.326919	+	0.566240i
$75$	−4.98255	+	7.08337i	−0.575335	+	0.817918i
$76$	1.12481	−	1.94823i	0.129025	−	0.223478i
$77$	0.557925	−	10.6632i	0.0635815	−	1.21518i
$78$	0.692647	+	9.72828i	0.0784268	+	1.10151i
$79$			6.34457i			0.713820i	0.934139	+	0.356910i	$0.116170\pi$
$79$			6.34457i			0.713820i	−0.934139	+	0.356910i	$0.883830\pi$
$80$	1.84064	+	1.26967i	0.205789	+	0.141953i
$81$	−6.50564	−	6.21905i	−0.722849	−	0.691006i
$82$	1.46670	+	5.47380i	0.161970	+	0.604480i
$83$	−5.09362	−	1.36483i	−0.559098	−	0.149810i	−0.0318061	−	0.999494i	$-0.510126\pi$
$83$	−5.09362	−	1.36483i	−0.559098	−	0.149810i	−0.527292	+	0.849684i	$0.676793\pi$
$84$	4.01101	+	2.21626i	0.437637	+	0.241814i
$85$	13.8805	−	11.8141i	1.50555	−	1.28142i
$86$	4.23504	−	2.44510i	0.456676	−	0.263662i
$87$	−5.83726	+	12.0067i	−0.625820	+	1.28726i
$88$	3.89830	−	1.04455i	0.415560	−	0.111349i
$89$	3.54958	−	6.14806i	0.376255	−	0.651693i	−0.614259	−	0.789105i	$-0.710545\pi$
$89$	3.54958	−	6.14806i	0.376255	−	0.651693i	0.990514	+	0.137412i	$0.0438783\pi$
$90$	−6.57464	−	1.33198i	−0.693027	−	0.140403i
$91$	9.96952	+	11.0704i	1.04509	+	1.16049i
$92$	−0.734182	+	2.74000i	−0.0765437	+	0.285665i
$93$	−5.28699	−	7.81692i	−0.548235	−	0.810577i
$94$			0.977624i			0.100834i
$95$	2.15785	+	4.54398i	0.221391	+	0.466203i
$96$	−0.328338	+	1.70065i	−0.0335108	+	0.173571i
$97$	8.57569	+	2.29785i	0.870729	+	0.233311i	0.666403	−	0.745592i	$-0.267833\pi$
$97$	8.57569	+	2.29785i	0.870729	+	0.233311i	0.204326	+	0.978903i	$0.434500\pi$
$98$	6.91363	−	1.09622i	0.698382	−	0.110735i
$99$	−9.52189	+	7.47823i	−0.956986	+	0.751590i
$100$	−4.67399	+	1.77589i	−0.467399	+	0.177589i
$101$	9.24413	+	5.33710i	0.919826	+	0.531062i	0.883579	−	0.468281i	$-0.155127\pi$
$101$	9.24413	+	5.33710i	0.919826	+	0.531062i	0.0362462	+	0.999343i	$0.488460\pi$
$102$	12.6979	+	6.17327i	1.25728	+	0.611245i
$103$	−0.256134	+	0.955905i	−0.0252376	+	0.0941881i	−0.977396	−	0.211417i	$-0.932192\pi$
$103$	−0.256134	+	0.955905i	−0.0252376	+	0.0941881i	0.952158	+	0.305605i	$0.0988588\pi$
$104$	−2.81542	+	4.87645i	−0.276075	+	0.478176i
$105$	−9.17198	+	4.56890i	−0.895093	+	0.445879i
$106$	5.72288	+	9.91231i	0.555855	+	0.962769i
$107$	16.2947	−	4.36614i	1.57526	−	0.422091i	0.637808	−	0.770195i	$-0.279841\pi$
$107$	16.2947	−	4.36614i	1.57526	−	0.422091i	0.937456	+	0.348104i	$0.113175\pi$
$108$	−1.09964	−	5.07846i	−0.105813	−	0.488675i
$109$	4.11112	−	2.37356i	0.393774	−	0.227346i	−0.290020	−	0.957021i	$-0.593662\pi$
$109$	4.11112	−	2.37356i	0.393774	−	0.227346i	0.683794	+	0.729675i	$0.260329\pi$
$110$	−3.02691	+	8.50158i	−0.288605	+	0.810594i
$111$	6.38199	−	7.36044i	0.605751	−	0.698622i
$112$	1.20135	+	2.35728i	0.113517	+	0.222742i
$113$	−0.0731747	−	0.273092i	−0.00688370	−	0.0256903i	0.962399	−	0.271641i	$-0.0875664\pi$
$113$	−0.0731747	−	0.273092i	−0.00688370	−	0.0256903i	−0.969282	+	0.245951i	$0.920900\pi$
$114$	−2.55259	+	2.94394i	−0.239072	+	0.275725i
$115$	−4.11118	−	4.83026i	−0.383370	−	0.450424i
$116$	−6.67524	+	3.85395i	−0.619780	+	0.357830i
$117$	2.01621	−	16.7718i	0.186399	−	1.55055i
$118$	−5.59281	−	5.59281i	−0.514860	−	0.514860i
$119$	21.0954	−	4.48584i	1.93381	−	0.411216i
$120$	−2.71339	−	2.76361i	−0.247698	−	0.252281i
$121$	2.64391	+	4.57938i	0.240355	+	0.416307i
$122$	−1.77599	−	1.77599i	−0.160790	−	0.160790i
$123$	−0.697081	−	9.79056i	−0.0628537	−	0.882785i
$124$		−	5.44844i		−	0.489284i
$125$	2.66566	−	10.8579i	0.238424	−	0.971161i
$126$	−6.09362	−	5.08604i	−0.542863	−	0.453100i
$127$	0.939520	−	0.939520i	0.0833689	−	0.0833689i	−0.664193	−	0.747562i	$-0.731225\pi$
$127$	0.939520	−	0.939520i	0.0833689	−	0.0833689i	0.747562	+	0.664193i	$0.231225\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−8.00511	+	2.76772i	−0.704811	+	0.243685i
$130$	−5.40113	−	11.3736i	−0.473710	−	0.997534i
$131$	−0.434224	+	0.250699i	−0.0379383	+	0.0219037i	−0.518849	−	0.854866i	$-0.673639\pi$
$131$	−0.434224	+	0.250699i	−0.0379383	+	0.0219037i	0.480911	+	0.876769i	$0.340306\pi$
$132$	−6.97259	+	0.496444i	−0.606886	+	0.0432099i
$133$	−0.310996	+	5.94382i	−0.0269668	+	0.515395i
$134$	4.42158			0.381966
$135$	10.7438	+	4.42392i	0.924678	+	0.380751i
$136$	4.07579	+	7.05948i	0.349496	+	0.605346i
$137$	−16.2181	+	4.34563i	−1.38561	+	0.371272i	−0.873155	−	0.487443i	$-0.837930\pi$
$137$	−16.2181	+	4.34563i	−1.38561	+	0.371272i	−0.512453	+	0.858715i	$0.671263\pi$
$138$	2.14823	−	4.41871i	0.182869	−	0.376146i
$139$	−7.73280	−	4.46453i	−0.655887	−	0.378677i	0.134821	−	0.990870i	$-0.456954\pi$
$139$	−7.73280	−	4.46453i	−0.655887	−	0.378677i	−0.790708	+	0.612193i	$0.790287\pi$
$140$	−5.86421	−	0.781720i	−0.495616	−	0.0660674i
$141$	0.320991	−	1.66259i	0.0270323	−	0.140016i
$142$	3.08885	−	3.08885i	0.259210	−	0.259210i
$143$	−21.9507	−	5.88167i	−1.83561	−	0.491850i
$144$	1.11677	−	2.78439i	0.0930643	−	0.232032i
$145$	1.38161	−	17.1799i	0.114737	−	1.42671i
$146$	−3.44402	+	1.98841i	−0.285029	+	0.164562i
$147$	−12.1176	−	0.405732i	−0.999440	−	0.0334642i
$148$	5.43287	−	1.45573i	0.446579	−	0.119661i
$149$	3.39548	+	5.88115i	0.278169	+	0.481803i	0.970930	−	0.239365i	$-0.0769392\pi$
$149$	3.39548	+	5.88115i	0.278169	+	0.481803i	−0.692761	+	0.721167i	$0.743606\pi$
$150$	8.53190	−	1.48551i	0.696627	−	0.121291i
$151$	8.57983	−	14.8607i	0.698216	−	1.20935i	−0.270868	−	0.962616i	$-0.587311\pi$
$151$	8.57983	−	14.8607i	0.698216	−	1.20935i	0.969084	−	0.246730i	$-0.0793559\pi$
$152$	−2.17297	+	0.582246i	−0.176251	+	0.0472264i
$153$	−19.5676	−	14.6677i	−1.58195	−	1.18582i
$154$	−7.93452	+	7.14549i	−0.639382	+	0.575800i
$155$	10.0286	+	6.91771i	0.805516	+	0.555644i
$156$	6.38916	−	7.36871i	0.511542	−	0.589969i
$157$	4.00088	−	4.00088i	0.319305	−	0.319305i	−0.529195	−	0.848500i	$-0.677506\pi$
$157$	4.00088	−	4.00088i	0.319305	−	0.319305i	0.848500	+	0.529195i	$0.177506\pi$
$158$	4.48629	−	4.48629i	0.356910	−	0.356910i
$159$	−6.47800	−	18.7364i	−0.513738	−	1.48589i
$160$	−0.403736	−	2.19932i	−0.0319181	−	0.173871i
$161$	−1.56102	−	7.34096i	−0.123026	−	0.578549i
$162$	0.202646	+	8.99772i	0.0159214	+	0.706928i
$163$	−7.66135	+	2.05285i	−0.600083	+	0.160792i	−0.546057	−	0.837748i	$-0.683872\pi$
$163$	−7.66135	+	2.05285i	−0.600083	+	0.160792i	−0.0540258	+	0.998540i	$0.517205\pi$
$164$	2.83345	−	4.90767i	0.221255	−	0.383225i
$165$	7.93910	−	13.4643i	0.618058	−	1.04820i
$166$	2.63665	+	4.56682i	0.204644	+	0.354454i
$167$	−9.36811	+	2.51018i	−0.724926	+	0.194243i	−0.602369	−	0.798218i	$-0.705776\pi$
$167$	−9.36811	+	2.51018i	−0.724926	+	0.194243i	−0.122558	+	0.992461i	$0.539110\pi$
$168$	−1.26908	−	4.40334i	−0.0979116	−	0.339725i
$169$	16.2002	−	9.35319i	1.24617	−	0.719476i
$170$	−18.1688	−	1.46114i	−1.39349	−	0.112064i
$171$	5.30765	−	4.16848i	0.405886	−	0.318772i
$172$	−4.72357	−	1.26568i	−0.360169	−	0.0965069i
$173$	−10.1980	+	10.1980i	−0.775342	+	0.775342i	−0.979035	−	0.203693i	$-0.934706\pi$
$173$	−10.1980	+	10.1980i	−0.775342	+	0.775342i	0.203693	+	0.979035i	$0.434706\pi$
$174$	12.6176	−	4.36247i	0.956538	−	0.330718i
$175$	8.88446	−	9.80135i	0.671602	−	0.740912i
$176$	−3.49512	−	2.01791i	−0.263455	−	0.152106i
$177$	7.67506	+	11.3477i	0.576893	+	0.852947i
$178$	−6.85727	+	1.83740i	−0.513974	+	0.137719i
$179$	9.41000	+	16.2986i	0.703337	+	1.21821i	0.967288	+	0.253679i	$0.0816407\pi$
$179$	9.41000	+	16.2986i	0.703337	+	1.21821i	−0.263952	+	0.964536i	$0.585026\pi$
$180$	3.70712	+	5.59082i	0.276312	+	0.416715i
$181$	17.2161			1.27966			0.639830	−	0.768517i	$-0.279005\pi$
$181$	17.2161			1.27966			0.639830	+	0.768517i	$0.279005\pi$
$182$	0.778427	−	14.8775i	0.0577009	−	1.10279i
$183$	2.43720	+	3.60345i	0.180163	+	0.266375i
$184$	2.45662	−	1.41833i	0.181104	−	0.104561i
$185$	−4.21847	+	11.8482i	−0.310148	+	0.871100i
$186$	−1.78893	+	9.26586i	−0.131171	+	0.679406i
$187$	−23.2626	+	23.2626i	−1.70113	+	1.70113i
$188$	0.691285	−	0.691285i	0.0504171	−	0.0504171i
$189$	8.69315	+	10.6503i	0.632334	+	0.774696i
$190$	1.68725	−	4.73891i	0.122406	−	0.343797i
$191$		−	6.51496i		−	0.471406i	−0.971825	−	0.235703i	$-0.924261\pi$
$191$		−	6.51496i		−	0.471406i	0.971825	−	0.235703i	$-0.0757392\pi$
$192$	1.43471	−	0.970368i	0.103541	−	0.0700303i
$193$	−13.8329	−	13.8329i	−0.995716	−	0.995716i	0.00427524	−	0.999991i	$-0.498639\pi$
$193$	−13.8329	−	13.8329i	−0.995716	−	0.995716i	−0.999991	+	0.00427524i	$0.998639\pi$
$194$	−4.43910	−	7.68875i	−0.318709	−	0.552020i
$195$	5.45101	+	21.1159i	0.390355	+	1.51214i
$196$	−5.66382	−	4.11353i	−0.404558	−	0.293824i
$197$	4.97268	+	4.97268i	0.354289	+	0.354289i	0.861703	−	0.507414i	$-0.169398\pi$
$197$	4.97268	+	4.97268i	0.354289	+	0.354289i	−0.507414	+	0.861703i	$0.669398\pi$
$198$	12.0209	+	1.44509i	0.854288	+	0.102698i
$199$	0.468461	−	0.270466i	0.0332083	−	0.0191728i	−0.483304	−	0.875453i	$-0.660563\pi$
$199$	0.468461	−	0.270466i	0.0332083	−	0.0191728i	0.516512	+	0.856280i	$0.327230\pi$
$200$	4.56076	+	2.04927i	0.322494	+	0.144905i
$201$	−7.51953	−	1.45177i	−0.530387	−	0.102400i
$202$	−2.76269	−	10.3105i	−0.194382	−	0.725444i
$203$	11.1055	−	17.1041i	0.779451	−	1.20047i
$204$	−4.61358	−	13.3439i	−0.323016	−	0.934261i
$205$	5.43571	+	11.4465i	0.379646	+	0.799455i
$206$	0.857041	−	0.494813i	0.0597129	−	0.0344752i
$207$	−5.10421	+	6.80932i	−0.354767	+	0.473281i
$208$	5.43898	−	1.45737i	0.377125	−	0.101050i
$209$	−4.53954	−	7.86272i	−0.314007	−	0.543875i
$210$	9.71627	+	3.25487i	0.670486	+	0.224607i
$211$	0.185525	−	0.321338i	0.0127720	−	0.0221218i	−0.859569	−	0.511020i	$-0.829268\pi$
$211$	0.185525	−	0.321338i	0.0127720	−	0.0221218i	0.872341	+	0.488898i	$0.162601\pi$
$212$	2.96238	−	11.0557i	0.203457	−	0.759312i
$213$	−6.26722	+	4.23885i	−0.429423	+	0.290441i
$214$	−14.6094	−	8.43474i	−0.998677	−	0.576587i
$215$	8.32701	−	7.08739i	0.567898	−	0.483356i
$216$	−2.81345	+	4.36858i	−0.191431	+	0.297244i
$217$	6.54546	+	12.8435i	0.444335	+	0.871873i
$218$	−4.58536	−	1.22864i	−0.310560	−	0.0832143i
$219$	6.50993	−	2.25077i	0.439900	−	0.152093i
$220$	8.15188	−	3.87117i	0.549599	−	0.260994i
$221$		−	45.9003i		−	3.08759i
$222$	−9.71736	+	0.691870i	−0.652187	+	0.0464353i
$223$	3.72445	−	13.8998i	0.249407	−	0.930801i	−0.721709	−	0.692196i	$-0.756643\pi$
$223$	3.72445	−	13.8998i	0.249407	−	0.930801i	0.971117	−	0.238605i	$-0.0766901\pi$
$224$	0.817368	−	2.51633i	0.0546127	−	0.168129i
$225$	−14.9975	−	0.275026i	−0.999832	−	0.0183350i
$226$	−0.141363	+	0.244847i	−0.00940331	+	0.0162870i
$227$	13.1035	−	3.51107i	0.869710	−	0.233038i	0.203747	−	0.979023i	$-0.434688\pi$
$227$	13.1035	−	3.51107i	0.869710	−	0.233038i	0.665962	+	0.745985i	$0.268021\pi$
$228$	3.88663	−	0.276725i	0.257398	−	0.0183266i
$229$	−17.2866	+	9.98041i	−1.14233	+	0.659524i	−0.947006	−	0.321215i	$-0.895909\pi$
$229$	−17.2866	+	9.98041i	−1.14233	+	0.659524i	−0.195323	+	0.980739i	$0.562576\pi$
$230$	−0.508460	+	6.32255i	−0.0335269	+	0.416897i
$231$	15.8399	−	9.54675i	1.04219	−	0.628130i
$232$	7.44526	+	1.99495i	0.488805	+	0.130975i
$233$	3.37172	+	12.5834i	0.220889	+	0.824368i	0.984010	+	0.178113i	$0.0569992\pi$
$233$	3.37172	+	12.5834i	0.220889	+	0.824368i	−0.763121	+	0.646255i	$0.776334\pi$
$234$	−13.2851	+	10.4338i	−0.868475	+	0.682076i
$235$	0.394702	+	2.15011i	0.0257475	+	0.140257i
$236$			7.90943i			0.514860i
$237$	−9.10260	+	6.15656i	−0.591277	+	0.399912i
$238$	−18.0887	−	11.7447i	−1.17251	−	0.761298i
$239$	−13.0958	+	22.6826i	−0.847098	+	1.46722i	0.0366892	+	0.999327i	$0.488319\pi$
$239$	−13.0958	+	22.6826i	−0.847098	+	1.46722i	−0.883787	+	0.467890i	$0.845014\pi$
$240$	−0.0355071	+	3.87282i	−0.00229198	+	0.249989i
$241$	−3.76203	+	6.51603i	−0.242334	+	0.419734i	−0.961379	−	0.275229i	$-0.911246\pi$
$241$	−3.76203	+	6.51603i	−0.242334	+	0.419734i	0.719045	+	0.694964i	$0.244580\pi$
$242$	1.36859	−	5.10764i	0.0879761	−	0.328331i
$243$	2.60966	−	15.3685i	0.167410	−	0.985887i
$244$			2.51163i			0.160790i
$245$	14.7627	−	5.20221i	0.943154	−	0.332357i
$246$	−6.43006	+	7.41588i	−0.409966	+	0.472819i
$247$	12.2357	+	3.27854i	0.778537	+	0.208608i
$248$	−3.85263	+	3.85263i	−0.244642	+	0.244642i
$249$	−2.98455	−	8.63225i	−0.189138	−	0.547047i
$250$	−9.56261	+	5.79280i	−0.604792	+	0.366369i
$251$			16.6314i			1.04976i	0.851175	+	0.524882i	$0.175890\pi$
$251$			16.6314i			1.04976i	−0.851175	+	0.524882i	$0.824110\pi$
$252$	0.712471	+	7.90521i	0.0448814	+	0.497982i
$253$	8.09513	+	8.09513i	0.508936	+	0.508936i
$254$	−1.32868			−0.0833689
$255$	30.4190	+	8.45040i	1.90491	+	0.529185i
$256$	1.00000			0.0625000
$257$	5.21847	−	19.4756i	0.325520	−	1.21486i	−0.588269	−	0.808665i	$-0.700190\pi$
$257$	5.21847	−	19.4756i	0.325520	−	1.21486i	0.913789	−	0.406190i	$-0.133143\pi$
$258$	7.61755	+	3.70339i	0.474248	+	0.230563i
$259$	−11.0580	+	9.95833i	−0.687108	+	0.618781i
$260$	−4.22321	+	11.8616i	−0.261912	+	0.735622i
$261$	−22.8904	+	3.27618i	−1.41688	+	0.202790i
$262$	0.484314	+	0.129772i	0.0299210	+	0.00801731i
$263$	−2.36545	−	8.82799i	−0.145860	−	0.544357i	−0.999716	−	0.0238471i	$-0.992409\pi$
$263$	−2.36545	−	8.82799i	−0.145860	−	0.544357i	0.853856	−	0.520510i	$-0.174258\pi$
$264$	5.28140	+	4.57933i	0.325048	+	0.281838i
$265$	16.5884	+	19.4898i	1.01902	+	1.19725i
$266$	4.42283	−	3.98301i	0.271181	−	0.244214i
$267$	12.2651	−	0.873265i	0.750610	−	0.0534429i
$268$	−3.12653	−	3.12653i	−0.190983	−	0.190983i
$269$	4.60889	+	7.98283i	0.281009	+	0.486722i	0.971633	−	0.236492i	$-0.0759976\pi$
$269$	4.60889	+	7.98283i	0.281009	+	0.486722i	−0.690625	+	0.723213i	$0.742664\pi$
$270$	−4.46882	−	10.7252i	−0.271964	−	0.652714i
$271$	−13.7953	+	23.8942i	−0.838008	+	1.45147i	0.0535501	+	0.998565i	$0.482946\pi$
$271$	−13.7953	+	23.8942i	−0.838008	+	1.45147i	−0.891558	+	0.452907i	$0.850387\pi$
$272$	2.10979	−	7.87383i	0.127925	−	0.477421i
$273$	−6.20866	+	25.0457i	−0.375765	+	1.51583i
$274$	14.5408	+	8.39512i	0.878440	+	0.507168i
$275$	−3.22475	+	19.9197i	−0.194460	+	1.20121i
$276$	−4.64353	+	1.60548i	−0.279508	+	0.0966383i
$277$	−2.51198	−	9.37484i	−0.150930	−	0.563279i	−0.999420	−	0.0340669i	$-0.989154\pi$
$277$	−2.51198	−	9.37484i	−0.150930	−	0.563279i	0.848489	−	0.529213i	$-0.177513\pi$
$278$	2.31101	+	8.62482i	0.138605	+	0.517282i
$279$	6.08467	−	15.1706i	0.364279	−	0.908239i
$280$	3.59386	+	4.69938i	0.214774	+	0.280842i
$281$	20.5796	−	11.8816i	1.22768	−	0.708799i	0.261133	−	0.965303i	$-0.415904\pi$
$281$	20.5796	−	11.8816i	1.22768	−	0.708799i	0.966543	+	0.256503i	$0.0825705\pi$
$282$	−1.40261	+	0.948655i	−0.0835239	+	0.0564916i
$283$	13.7496	+	13.7496i	0.817326	+	0.817326i	0.985720	−	0.168393i	$-0.0538579\pi$
$283$	13.7496	+	13.7496i	0.817326	+	0.817326i	−0.168393	+	0.985720i	$0.553858\pi$
$284$	−4.36829			−0.259210
$285$	−4.42538	+	7.50522i	−0.262137	+	0.444571i
$286$	11.3625	+	19.6805i	0.671880	+	1.16373i
$287$	−0.783411	+	14.9727i	−0.0462433	+	0.883811i
$288$	−2.75854	+	1.17918i	−0.162548	+	0.0694840i
$289$	−42.8235	−	24.7242i	−2.51903	−	1.45436i
$290$	−13.1250	+	11.1711i	−0.770726	+	0.655989i
$291$	5.02483	+	14.5334i	0.294561	+	0.851961i
$292$	3.84131	+	1.02927i	0.224795	+	0.0602337i
$293$	−1.04014	−	3.88184i	−0.0607654	−	0.226779i	0.928865	−	0.370419i	$-0.120786\pi$
$293$	−1.04014	−	3.88184i	−0.0607654	−	0.226779i	−0.989630	+	0.143640i	$0.954119\pi$
$294$	8.28152	+	8.85531i	0.482988	+	0.516452i
$295$	−14.5584	−	10.0423i	−0.847622	−	0.584688i
$296$	−4.87098	−	2.81226i	−0.283120	−	0.163459i
$297$	−19.9688	−	6.40450i	−1.15871	−	0.371627i
$298$	1.75763	−	6.55957i	0.101817	−	0.379986i
$299$	−15.9728			−0.923730
$300$	−7.08337	−	4.98255i	−0.408959	−	0.287668i
$301$	12.6553	−	2.69109i	0.729439	−	0.155112i
$302$	−16.5749	+	4.44124i	−0.953781	+	0.255565i
$303$	1.31303	+	18.4416i	0.0754315	+	1.05944i
$304$	1.94823	+	1.12481i	0.111739	+	0.0645125i
$305$	−4.62299	−	3.18893i	−0.264712	−	0.182598i
$306$	3.46476	+	24.2081i	0.198067	+	1.38388i
$307$	−14.5848	+	14.5848i	−0.832397	+	0.832397i	−0.987844	−	0.155448i	$-0.950318\pi$
$307$	−14.5848	+	14.5848i	−0.832397	+	0.832397i	0.155448	+	0.987844i	$0.450318\pi$
$308$	10.6632	+	0.557925i	0.607591	+	0.0317907i
$309$	−1.61999	+	0.560102i	−0.0921579	+	0.0318631i
$310$	−2.19973	−	11.9828i	−0.124936	−	0.680580i
$311$		−	14.9374i		−	0.847020i	−0.905891	−	0.423510i	$-0.860798\pi$
$311$		−	14.9374i		−	0.847020i	0.905891	−	0.423510i	$-0.139202\pi$
$312$	−9.72828	+	0.692647i	−0.550755	+	0.0392134i
$313$	21.3799	+	21.3799i	1.20846	+	1.20846i	0.971525	+	0.236939i	$0.0761441\pi$
$313$	21.3799	+	21.3799i	1.20846	+	1.20846i	0.236939	+	0.971525i	$0.423856\pi$
$314$	−5.65809			−0.319305
$315$	−15.4552	−	8.72559i	−0.870803	−	0.491632i
$316$	−6.34457			−0.356910
$317$	−1.68087	−	1.68087i	−0.0944071	−	0.0944071i	0.658326	−	0.752733i	$-0.271265\pi$
$317$	−1.68087	−	1.68087i	−0.0944071	−	0.0944071i	−0.752733	+	0.658326i	$0.771265\pi$
$318$	−8.66797	+	17.8292i	−0.486076	+	0.999814i
$319$			31.1077i			1.74169i
$320$	−1.26967	+	1.84064i	−0.0709766	+	0.102895i
$321$	22.0759	+	19.1413i	1.23216	+	1.06836i
$322$	−4.08703	+	6.29465i	−0.227762	+	0.350787i
$323$	12.9669	−	12.9669i	0.721500	−	0.721500i
$324$	6.21905	−	6.50564i	0.345503	−	0.361424i
$325$	−16.4707	−	22.8336i	−0.913633	−	1.26658i
$326$	6.86898	+	3.96581i	0.380438	+	0.219646i
$327$	7.39467	+	3.59504i	0.408926	+	0.198806i
$328$	−5.47380	+	1.46670i	−0.302240	+	0.0809849i
$329$	−0.799079	+	2.46002i	−0.0440547	+	0.135626i
$330$	−15.1345	+	3.90692i	−0.833127	+	0.215069i
$331$	−2.16159			−0.118812			−0.0594060	−	0.998234i	$-0.518921\pi$
$331$	−2.16159			−0.118812			−0.0594060	+	0.998234i	$0.518921\pi$
$332$	1.36483	−	5.09362i	0.0749049	−	0.279549i
$333$	16.7530	+	2.01395i	0.918056	+	0.110364i
$334$	8.39922	+	4.84929i	0.459585	+	0.265341i
$335$	9.72445	−	1.78515i	0.531303	−	0.0975331i
$336$	−2.21626	+	4.01101i	−0.120907	+	0.218818i
$337$	1.36129	+	5.08039i	0.0741540	+	0.276747i	0.993040	−	0.117776i	$-0.0375766\pi$
$337$	1.36129	+	5.08039i	0.0741540	+	0.276747i	−0.918886	+	0.394523i	$0.870910\pi$
$338$	−18.0690	−	4.84157i	−0.982823	−	0.263347i
$339$	0.320801	−	0.369984i	0.0174235	−	0.0200948i
$340$	11.8141	+	13.8805i	0.640711	+	0.752776i
$341$	−19.0429	−	10.9945i	−1.03123	−	0.595383i
$342$	−6.70064	−	0.805515i	−0.362329	−	0.0435573i
$343$	18.2930	+	2.89254i	0.987728	+	0.156183i
$344$	2.44510	+	4.23504i	0.131831	+	0.228338i
$345$	2.94064	−	10.5855i	0.158319	−	0.569903i
$346$	14.4222			0.775342
$347$	23.1172	+	23.1172i	1.24100	+	1.24100i	0.959588	+	0.281408i	$0.0908016\pi$
$347$	23.1172	+	23.1172i	1.24100	+	1.24100i	0.281408	+	0.959588i	$0.409198\pi$
$348$	−12.0067	−	5.83726i	−0.643628	−	0.312910i
$349$	−4.81018	+	2.77716i	−0.257483	+	0.148658i	−0.623186	−	0.782074i	$-0.714162\pi$
$349$	−4.81018	+	2.77716i	−0.257483	+	0.148658i	0.365703	+	0.930732i	$0.380829\pi$
$350$	−13.2129	+	0.648341i	−0.706257	+	0.0346553i
$351$	26.0191	−	13.3821i	1.38879	−	0.714284i
$352$	1.04455	+	3.89830i	0.0556745	+	0.207780i
$353$	−7.02417	−	26.2146i	−0.373859	−	1.39526i	−0.855005	−	0.518620i	$-0.826446\pi$
$353$	−7.02417	−	26.2146i	−0.373859	−	1.39526i	0.481146	−	0.876641i	$-0.340221\pi$
$354$	2.59696	−	13.4511i	0.138027	−	0.714920i
$355$	5.54628	−	8.04044i	0.294366	−	0.426742i
$356$	6.14806	+	3.54958i	0.325846	+	0.188128i
$357$	26.9062	+	25.9128i	1.42403	+	1.37145i
$358$	4.87098	−	18.1787i	0.257439	−	0.960776i
$359$	−17.3762	+	30.0965i	−0.917083	+	1.58843i	−0.113260	+	0.993565i	$0.536129\pi$
$359$	−17.3762	+	30.0965i	−0.917083	+	1.58843i	−0.803823	+	0.594869i	$0.797204\pi$
$360$	1.33198	−	6.57464i	0.0702014	−	0.346514i
$361$	−6.96959	−	12.0717i	−0.366820	−	0.635352i
$362$	−12.1736	−	12.1736i	−0.639830	−	0.639830i
$363$	−4.00451	+	8.23692i	−0.210182	+	0.432326i
$364$	−11.0704	+	9.96952i	−0.580246	+	0.522545i
$365$	−6.77170	+	5.76361i	−0.354447	+	0.301681i
$366$	0.824662	−	4.27139i	0.0431058	−	0.223269i
$367$	−2.14276	−	7.99688i	−0.111851	−	0.417434i	0.887181	−	0.461422i	$-0.152660\pi$
$367$	−2.14276	−	7.99688i	−0.111851	−	0.417434i	−0.999032	+	0.0439877i	$0.985994\pi$
$368$	−2.74000	−	0.734182i	−0.142833	−	0.0382719i
$369$	13.3702	−	10.5006i	0.696023	−	0.546637i
$370$	11.3609	−	5.39507i	0.590624	−	0.280476i
$371$	6.29863	+	29.6203i	0.327008	+	1.53781i
$372$	7.81692	−	5.28699i	0.405288	−	0.274118i
$373$	0.313155	−	1.16871i	0.0162145	−	0.0605135i	−0.957345	−	0.288949i	$-0.906694\pi$
$373$	0.313155	−	1.16871i	0.0162145	−	0.0605135i	0.973559	+	0.228435i	$0.0733609\pi$
$374$	32.8983			1.70113
$375$	18.1646	−	6.71173i	0.938016	−	0.346592i
$376$	−0.977624			−0.0504171
$377$	−30.6898	−	30.6898i	−1.58061	−	1.58061i
$378$	1.38392	−	13.6779i	0.0711811	−	0.703515i
$379$		−	6.96937i		−	0.357993i	−0.983850	−	0.178996i	$-0.942715\pi$
$379$		−	6.96937i		−	0.357993i	0.983850	−	0.178996i	$-0.0572850\pi$
$380$	−4.54398	+	2.15785i	−0.233101	+	0.110695i
$381$	2.25962	+	0.436257i	0.115764	+	0.0223501i
$382$	−4.60677	+	4.60677i	−0.235703	+	0.235703i
$383$	−16.8356	−	4.51108i	−0.860259	−	0.230506i	−0.198388	−	0.980124i	$-0.563571\pi$
$383$	−16.8356	−	4.51108i	−0.860259	−	0.230506i	−0.661871	+	0.749618i	$0.730237\pi$
$384$	−1.70065	−	0.328338i	−0.0867857	−	0.0167554i
$385$	−14.5656	+	18.9187i	−0.742333	+	0.964184i
$386$			19.5627i			0.995716i
$387$	−11.7388	−	8.79928i	−0.596716	−	0.447293i
$388$	−2.29785	+	8.57569i	−0.116656	+	0.435365i
$389$	4.71672	−	8.16960i	0.239147	−	0.414215i	−0.721323	−	0.692599i	$-0.756465\pi$
$389$	4.71672	−	8.16960i	0.239147	−	0.414215i	0.960470	+	0.278384i	$0.0897988\pi$
$390$	11.0768	−	18.7857i	0.560894	−	0.951249i
$391$	−11.5616	+	20.0254i	−0.584697	+	1.01273i
$392$	1.09622	+	6.91363i	0.0553673	+	0.349191i
$393$	−0.781038	−	0.379714i	−0.0393981	−	0.0191540i
$394$		−	7.03243i		−	0.354289i
$395$	8.05549	−	11.6780i	0.405316	−	0.587586i
$396$	−7.47823	−	9.52189i	−0.375795	−	0.478493i
$397$	8.43451	+	31.4780i	0.423316	+	1.57984i	0.767573	+	0.640962i	$0.221464\pi$
$397$	8.43451	+	31.4780i	0.423316	+	1.57984i	−0.344257	+	0.938876i	$0.611869\pi$
$398$	−0.522500	−	0.140003i	−0.0261905	−	0.00701774i
$399$	−8.82943	+	5.32151i	−0.442024	+	0.266409i
$400$	−1.77589	−	4.67399i	−0.0887944	−	0.233700i
$401$	2.40497	−	1.38851i	0.120098	−	0.0693388i	−0.438747	−	0.898610i	$-0.644578\pi$
$401$	2.40497	−	1.38851i	0.120098	−	0.0693388i	0.558846	+	0.829272i	$0.311244\pi$
$402$	4.29055	+	6.34367i	0.213993	+	0.316393i
$403$	29.6339	−	7.94039i	1.47617	−	0.395539i
$404$	−5.33710	+	9.24413i	−0.265531	+	0.459913i
$405$	4.07839	+	19.7070i	0.202657	+	0.979250i
$406$	−19.9472	+	4.24168i	−0.989962	+	0.210511i
$407$	5.87508	−	21.9261i	0.291217	−	1.08684i
$408$	−6.17327	+	12.6979i	−0.305623	+	0.628638i
$409$			2.56372i			0.126768i	0.997989	+	0.0633840i	$0.0201893\pi$
$409$			2.56372i			0.126768i	−0.997989	+	0.0633840i	$0.979811\pi$
$410$	4.25024	−	11.9375i	0.209905	−	0.589551i
$411$	−21.9723	−	19.0514i	−1.08381	−	0.939736i
$412$	−0.955905	−	0.256134i	−0.0470941	−	0.0126188i
$413$	−9.50196	−	18.6447i	−0.467561	−	0.917447i
$414$	8.42414	−	1.20570i	0.414024	−	0.0592568i
$415$	7.64263	+	8.97937i	0.375162	+	0.440780i
$416$	−4.87645	−	2.81542i	−0.239088	−	0.138037i
$417$	−1.09836	−	15.4265i	−0.0537869	−	0.755441i
$418$	−2.34984	+	8.76972i	−0.114934	+	0.428941i
$419$	1.77594	−	3.07603i	0.0867606	−	0.150274i	−0.819380	−	0.573251i	$-0.805682\pi$
$419$	1.77594	−	3.07603i	0.0867606	−	0.150274i	0.906140	+	0.422978i	$0.139015\pi$
$420$	−4.56890	−	9.17198i	−0.222939	−	0.447547i
$421$	−11.2389	−	19.4664i	−0.547751	−	0.948733i	−0.998428	−	0.0560461i	$-0.982151\pi$
$421$	−11.2389	−	19.4664i	−0.547751	−	0.948733i	0.450677	−	0.892687i	$-0.351183\pi$
$422$	−0.358406	+	0.0960347i	−0.0174469	+	0.00467489i
$423$	2.69681	−	1.15280i	0.131124	−	0.0560510i
$424$	−9.91231	+	5.72288i	−0.481384	+	0.277927i
$425$	−40.5490	+	4.12191i	−1.96691	+	0.199942i
$426$	7.42891	+	1.43427i	0.359932	+	0.0694908i
$427$	−3.01733	−	5.92061i	−0.146019	−	0.286518i
$428$	4.36614	+	16.2947i	0.211045	+	0.787632i
$429$	−12.8618	−	37.2002i	−0.620973	−	1.79604i
$430$	−10.8996	−	0.876549i	−0.525627	−	0.0422710i
$431$	−14.6980	+	8.48587i	−0.707976	+	0.408750i	−0.810311	−	0.586000i	$-0.800702\pi$
$431$	−14.6980	+	8.48587i	−0.707976	+	0.408750i	0.102335	+	0.994750i	$0.467368\pi$
$432$	5.07846	−	1.09964i	0.244338	−	0.0529065i
$433$	11.4103	+	11.4103i	0.548343	+	0.548343i	0.925961	−	0.377618i	$-0.123257\pi$
$433$	11.4103	+	11.4103i	0.548343	+	0.548343i	−0.377618	+	0.925961i	$0.623257\pi$
$434$	4.45338	−	13.7101i	0.213769	−	0.658104i
$435$	25.9888	−	14.6886i	1.24607	−	0.704266i
$436$	2.37356	+	4.11112i	0.113673	+	0.196887i
$437$	−4.51235	−	4.51235i	−0.215855	−	0.215855i
$438$	−6.19475	−	3.01168i	−0.295997	−	0.143903i
$439$			30.3315i			1.44764i	0.689986	+	0.723822i	$0.257616\pi$
$439$			30.3315i			1.44764i	−0.689986	+	0.723822i	$0.742384\pi$
$440$	−8.50158	−	3.02691i	−0.405297	−	0.144303i
$441$	−11.1764	−	17.7789i	−0.532209	−	0.846613i
$442$	−32.4564	+	32.4564i	−1.54379	+	1.54379i
$443$	−7.07855	+	7.07855i	−0.336312	+	0.336312i	−0.854977	−	0.518665i	$-0.826429\pi$
$443$	−7.07855	+	7.07855i	−0.336312	+	0.336312i	0.518665	+	0.854977i	$0.326429\pi$
$444$	7.36044	+	6.38199i	0.349311	+	0.302876i
$445$	−14.3395	+	6.80955i	−0.679757	+	0.322804i
$446$	−12.4622	+	7.19508i	−0.590104	+	0.340697i
$447$	−5.14286	+	10.5784i	−0.243249	+	0.500341i
$448$	−2.35728	+	1.20135i	−0.111371	+	0.0567583i
$449$	−10.3595			−0.488896			−0.244448	−	0.969662i	$-0.578607\pi$
$449$	−10.3595			−0.488896			−0.244448	+	0.969662i	$0.578607\pi$
$450$	10.4103	+	10.7993i	0.490748	+	0.509083i
$451$	−11.4353	−	19.8065i	−0.538466	−	0.932650i
$452$	0.273092	−	0.0731747i	0.0128452	−	0.00344185i
$453$	29.6463	−	2.11080i	1.39291	−	0.0991740i
$454$	−11.7483	−	6.78287i	−0.551374	−	0.318336i
$455$	−4.29456	−	33.0345i	−0.201332	−	1.54868i
$456$	−2.94394	−	2.55259i	−0.137862	−	0.119536i
$457$	8.01020	−	8.01020i	0.374701	−	0.374701i	−0.494485	−	0.869186i	$-0.664643\pi$
$457$	8.01020	−	8.01020i	0.374701	−	0.374701i	0.869186	+	0.494485i	$0.164643\pi$
$458$	19.2807	+	5.16624i	0.900927	+	0.241403i
$459$	2.05609	−	42.3070i	0.0959702	−	1.97472i
$460$	4.83026	−	4.11118i	0.225212	−	0.191685i
$461$	18.5773	−	10.7256i	0.865233	−	0.499543i	−0.000528125	−	1.00000i	$-0.500168\pi$
$461$	18.5773	−	10.7256i	0.865233	−	0.499543i	0.865761	+	0.500457i	$0.166835\pi$
$462$	−17.9511	−	4.44996i	−0.835161	−	0.207031i
$463$	−20.3212	+	5.44506i	−0.944408	+	0.253053i	−0.697988	−	0.716110i	$-0.745921\pi$
$463$	−20.3212	+	5.44506i	−0.944408	+	0.253053i	−0.246420	+	0.969163i	$0.579254\pi$
$464$	−3.85395	−	6.67524i	−0.178915	−	0.309890i
$465$	−0.193459	+	21.1008i	−0.00897142	+	0.978528i
$466$	6.51366	−	11.2820i	0.301740	−	0.522628i
$467$	13.3869	−	3.58702i	0.619474	−	0.165988i	0.0645853	−	0.997912i	$-0.479428\pi$
$467$	13.3869	−	3.58702i	0.619474	−	0.165988i	0.554889	+	0.831925i	$0.312761\pi$
$468$	16.7718	+	2.01621i	0.775275	+	0.0931995i
$469$	11.1261	+	3.61406i	0.513757	+	0.166882i
$470$	1.24126	−	1.79945i	0.0572550	−	0.0830025i
$471$	9.62241	+	1.85777i	0.443377	+	0.0856013i
$472$	5.59281	−	5.59281i	0.257430	−	0.257430i
$473$	−13.9554	+	13.9554i	−0.641671	+	0.641671i
$474$	10.7899	+	2.08316i	0.495595	+	0.0956827i
$475$	1.79753	−	11.1036i	0.0824762	−	0.509467i
$476$	4.48584	+	21.0954i	0.205608	+	0.966906i
$477$	20.5952	−	27.4752i	0.942988	−	1.25800i
$478$	25.2992	−	6.77889i	1.15716	−	0.310059i
$479$	−10.7251	+	18.5765i	−0.490044	+	0.848780i	−0.999934	−	0.0114587i	$-0.996352\pi$
$479$	−10.7251	+	18.5765i	−0.490044	+	0.848780i	0.509891	+	0.860239i	$0.329686\pi$
$480$	2.76361	−	2.71339i	0.126141	−	0.123849i
$481$	15.8354	+	27.4277i	0.722032	+	1.25060i
$482$	7.26769	−	1.94737i	0.331034	−	0.0887003i
$483$	9.01737	−	9.36304i	0.410304	−	0.426033i
$484$	−4.57938	+	2.64391i	−0.208154	+	0.120178i
$485$	−12.8672	−	15.1178i	−0.584271	−	0.686463i
$486$	−12.7125	+	9.02184i	−0.576649	+	0.409239i
$487$	30.2939	+	8.11723i	1.37275	+	0.367827i	0.868482	−	0.495721i	$-0.165096\pi$
$487$	30.2939	+	8.11723i	1.37275	+	0.367827i	0.504267	+	0.863548i	$0.331763\pi$
$488$	1.77599	−	1.77599i	0.0803952	−	0.0803952i
$489$	−10.3796	−	8.99977i	−0.469380	−	0.406984i
$490$	−14.1173	−	6.76028i	−0.637755	−	0.305398i
$491$	7.40877	+	4.27746i	0.334353	+	0.193039i	0.657772	−	0.753217i	$-0.271499\pi$
$491$	7.40877	+	4.27746i	0.334353	+	0.193039i	−0.323419	+	0.946256i	$0.604832\pi$
$492$	9.79056	−	0.697081i	0.441393	−	0.0314269i
$493$	−60.6907	+	16.2620i	−2.73337	+	0.732404i
$494$	−6.33365	−	10.9702i	−0.284964	−	0.493573i
$495$	27.0212	−	1.67506i	1.21451	−	0.0752884i
$496$	5.44844			0.244642
$497$	10.2973	−	5.24783i	0.461896	−	0.235397i
$498$	−3.99353	+	8.21432i	−0.178954	+	0.368093i
$499$	33.9823	−	19.6197i	1.52126	−	0.878299i	0.521573	−	0.853207i	$-0.325345\pi$
$499$	33.9823	−	19.6197i	1.52126	−	0.878299i	0.999685	−	0.0250919i	$-0.00798785\pi$
$500$	10.8579	+	2.66566i	0.485581	+	0.119212i
$501$	−12.6919	−	11.0047i	−0.567032	−	0.491654i
$502$	11.7602	−	11.7602i	0.524882	−	0.524882i
$503$	−11.9284	+	11.9284i	−0.531859	+	0.531859i	−0.921125	−	0.389266i	$-0.872729\pi$
$503$	−11.9284	+	11.9284i	−0.531859	+	0.531859i	0.389266	+	0.921125i	$0.372729\pi$
$504$	5.08604	−	6.09362i	0.226550	−	0.271432i
$505$	−10.2387	−	21.5606i	−0.455618	−	0.959436i
$506$		−	11.4482i		−	0.508936i
$507$	29.1393	+	14.1665i	1.29412	+	0.629157i
$508$	0.939520	+	0.939520i	0.0416845	+	0.0416845i
$509$	9.19691	+	15.9295i	0.407646	+	0.706063i	0.994625	−	0.103538i	$-0.0330165\pi$
$509$	9.19691	+	15.9295i	0.407646	+	0.706063i	−0.586980	+	0.809602i	$0.699683\pi$
$510$	−15.5342	−	27.4848i	−0.687864	−	1.21705i
$511$	−10.2915	+	2.18845i	−0.455271	+	0.0968113i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	11.1309	+	3.56997i	0.491442	+	0.157618i
$514$	−17.4614	+	10.0813i	−0.770187	+	0.444668i
$515$	1.68513	−	1.43427i	0.0742558	−	0.0632014i
$516$	−2.76772	−	8.00511i	−0.121842	−	0.352405i
$517$	−1.02117	−	3.81107i	−0.0449112	−	0.167611i
$518$	14.8608	+	0.777554i	0.652945	+	0.0341637i
$519$	−24.5270	−	4.73535i	−1.07662	−	0.207859i
$520$	11.3736	−	5.40113i	0.498767	−	0.236855i
$521$	3.62099	−	2.09058i	0.158638	−	0.0915898i	−0.418579	−	0.908180i	$-0.637472\pi$
$521$	3.62099	−	2.09058i	0.158638	−	0.0915898i	0.577218	+	0.816590i	$0.304138\pi$
$522$	18.5026	+	13.8694i	0.809836	+	0.607046i
$523$	15.9197	−	4.26566i	0.696118	−	0.186524i	0.106627	−	0.994299i	$-0.465995\pi$
$523$	15.9197	−	4.26566i	0.696118	−	0.186524i	0.589491	+	0.807775i	$0.299328\pi$
$524$	−0.250699	−	0.434224i	−0.0109519	−	0.0189692i
$525$	22.6833	+	3.23568i	0.989979	+	0.141217i
$526$	−4.56970	+	7.91496i	−0.199249	+	0.345109i
$527$	11.4950	−	42.9001i	0.500732	−	1.86876i
$528$	−0.496444	−	6.97259i	−0.0216049	−	0.303443i
$529$	−12.9500	−	7.47668i	−0.563043	−	0.325073i
$530$	2.05161	−	25.5111i	0.0891161	−	1.10813i
$531$	−8.83303	+	22.0229i	−0.383321	+	0.955713i
$532$	−5.94382	−	0.310996i	−0.257697	−	0.0134834i
$533$	30.8221	+	8.25875i	1.33505	+	0.357726i
$534$	−9.29020	−	8.05522i	−0.402026	−	0.348584i
$535$	−35.5361	−	12.6523i	−1.53636	−	0.547008i
$536$			4.42158i			0.190983i
$537$	−14.2526	+	29.3162i	−0.615044	+	1.26509i
$538$	2.38574	−	8.90369i	0.102856	−	0.383865i
$539$	−25.8064	+	11.4950i	−1.11156	+	0.495124i
$540$	−4.42392	+	10.7438i	−0.190375	+	0.462339i
$541$	8.39930	−	14.5480i	0.361114	−	0.625468i	−0.627030	−	0.778995i	$-0.715730\pi$
$541$	8.39930	−	14.5480i	0.361114	−	0.625468i	0.988145	+	0.153527i	$0.0490631\pi$
$542$	26.6506	−	7.14100i	1.14474	−	0.306732i
$543$	16.7059	+	24.7000i	0.716919	+	1.05998i
$544$	−7.05948	+	4.07579i	−0.302673	+	0.174748i
$545$	−10.5807	−	0.850903i	−0.453228	−	0.0364487i
$546$	22.1002	−	13.3198i	0.945800	−	0.570035i
$547$	28.0521	+	7.51654i	1.19942	+	0.321384i	0.802603	−	0.596513i	$-0.203448\pi$
$547$	28.0521	+	7.51654i	1.19942	+	0.321384i	0.396818	+	0.917897i	$0.370114\pi$
$548$	−4.34563	−	16.2181i	−0.185636	−	0.692804i
$549$	−2.80491	+	6.99334i	−0.119711	+	0.298469i
$550$	16.3656	−	11.8051i	0.697833	−	0.503373i
$551$		−	17.3399i		−	0.738704i
$552$	4.41871	+	2.14823i	0.188073	+	0.0914347i
$553$	14.9559	−	7.62202i	0.635990	−	0.324121i
$554$	−4.85277	+	8.40525i	−0.206175	+	0.357105i
$555$	−21.0922	+	5.44489i	−0.895315	+	0.231123i
$556$	4.46453	−	7.73280i	0.189338	−	0.327944i
$557$	−3.36439	+	12.5561i	−0.142554	+	0.532018i	0.857298	+	0.514820i	$0.172141\pi$
$557$	−3.36439	+	12.5561i	−0.142554	+	0.532018i	−0.999852	+	0.0171981i	$0.994525\pi$
$558$	−15.0297	+	6.42471i	−0.636259	+	0.271980i
$559$		−	27.5359i		−	1.16465i
$560$	0.781720	−	5.86421i	0.0330337	−	0.247808i
$561$	−55.9484	−	10.8018i	−2.36214	−	0.456051i
$562$	−22.9536	−	6.15039i	−0.968238	−	0.259439i
$563$	−24.0428	+	24.0428i	−1.01328	+	1.01328i	−0.0133729	+	0.999911i	$0.504257\pi$
$563$	−24.0428	+	24.0428i	−1.01328	+	1.01328i	−0.999911	+	0.0133729i	$0.995743\pi$
$564$	1.66259	+	0.320991i	0.0700078	+	0.0135162i
$565$	−0.212048	+	0.595571i	−0.00892092	+	0.0250558i
$566$		−	19.4448i		−	0.817326i
$567$	−6.84453	+	22.8069i	−0.287443	+	0.957798i
$568$	3.08885	+	3.08885i	0.129605	+	0.129605i
$569$	42.7890			1.79381			0.896904	−	0.442224i	$-0.145811\pi$
$569$	42.7890			1.79381			0.896904	+	0.442224i	$0.145811\pi$
$570$	8.43621	−	2.17778i	0.353354	−	0.0912171i
$571$	−9.32156			−0.390095			−0.195048	−	0.980794i	$-0.562486\pi$
$571$	−9.32156			−0.390095			−0.195048	+	0.980794i	$0.562486\pi$
$572$	5.88167	−	21.9507i	0.245925	−	0.917805i
$573$	9.34706	−	6.32191i	0.390479	−	0.264101i
$574$	11.1413	−	10.0333i	0.465027	−	0.418784i
$575$	1.43438	+	14.1106i	0.0598176	+	0.588452i
$576$	2.78439	+	1.11677i	0.116016	+	0.0465322i
$577$	5.79174	+	1.55189i	0.241113	+	0.0646061i	0.377352	−	0.926070i	$-0.376835\pi$
$577$	5.79174	+	1.55189i	0.241113	+	0.0646061i	−0.136239	+	0.990676i	$0.543501\pi$
$578$	12.7982	+	47.7635i	0.532334	+	1.98670i
$579$	6.42318	−	33.2692i	0.266938	−	1.38262i
$580$	17.1799	+	1.38161i	0.713357	+	0.0573683i
$581$	2.90191	+	13.6467i	0.120392	+	0.566162i
$582$	6.72355	−	13.8297i	0.278700	−	0.573261i
$583$	−32.6633	−	32.6633i	−1.35278	−	1.35278i
$584$	−1.98841	−	3.44402i	−0.0822808	−	0.142515i
$585$	−25.0057	+	28.3108i	−1.03386	+	1.17051i
$586$	−2.00939	+	3.48036i	−0.0830070	+	0.143772i
$587$	−6.63946	+	24.7788i	−0.274040	+	1.02273i	0.682442	+	0.730939i	$0.260918\pi$
$587$	−6.63946	+	24.7788i	−0.274040	+	1.02273i	−0.956482	+	0.291791i	$0.905749\pi$
$588$	0.405732	−	12.1176i	0.0167321	−	0.499720i
$589$	10.6148	+	6.12848i	0.437377	+	0.252520i
$590$	3.19332	+	17.3953i	0.131467	+	0.716155i
$591$	−2.30901	+	11.9597i	−0.0949801	+	0.491955i
$592$	1.45573	+	5.43287i	0.0598303	+	0.223290i
$593$	8.87139	+	33.1085i	0.364304	+	1.35960i	0.868361	+	0.495932i	$0.165174\pi$
$593$	8.87139	+	33.1085i	0.364304	+	1.35960i	−0.504057	+	0.863670i	$0.668160\pi$
$594$	9.59142	+	18.6487i	0.393541	+	0.765167i
$595$	−44.5245	−	18.5273i	−1.82533	−	0.759547i
$596$	−5.88115	+	3.39548i	−0.240901	+	0.139084i
$597$	0.842618	+	0.409653i	0.0344861	+	0.0167660i
$598$	11.2945	+	11.2945i	0.461865	+	0.461865i
$599$	−27.1170			−1.10797			−0.553985	−	0.832527i	$-0.686894\pi$
$599$	−27.1170			−1.10797			−0.553985	+	0.832527i	$0.686894\pi$
$600$	1.48551	+	8.53190i	0.0606455	+	0.348313i
$601$	−10.4626	−	18.1217i	−0.426778	−	0.739201i	0.569807	−	0.821779i	$-0.307018\pi$
$601$	−10.4626	−	18.1217i	−0.426778	−	0.739201i	−0.996585	+	0.0825778i	$0.973685\pi$
$602$	−10.8515	−	7.04575i	−0.442275	−	0.287163i
$603$	−5.21385	−	12.1971i	−0.212324	−	0.496703i
$604$	14.8607	+	8.57983i	0.604673	+	0.349108i
$605$	0.947820	−	11.7859i	0.0385344	−	0.479163i
$606$	12.1117	−	13.9686i	0.492005	−	0.567436i
$607$	−5.72513	−	1.53404i	−0.232376	−	0.0622650i	0.140752	−	0.990045i	$-0.455048\pi$
$607$	−5.72513	−	1.53404i	−0.232376	−	0.0622650i	−0.373128	+	0.927780i	$0.621715\pi$
$608$	−0.582246	−	2.17297i	−0.0236132	−	0.0881257i
$609$	35.3158	−	0.664173i	1.43107	−	0.0269136i
$610$	1.01403	+	5.52386i	0.0410570	+	0.223655i
$611$	4.76734	+	2.75242i	0.192866	+	0.111351i
$612$	14.6677	−	19.5676i	0.592908	−	0.790975i
$613$	−7.08464	+	26.4402i	−0.286146	+	1.06791i	0.661852	+	0.749634i	$0.269771\pi$
$613$	−7.08464	+	26.4402i	−0.286146	+	1.06791i	−0.947998	+	0.318276i	$0.896896\pi$
$614$	20.6260			0.832397
$615$	−11.1477	+	18.9059i	−0.449518	+	0.762361i
$616$	−7.14549	−	7.93452i	−0.287900	−	0.319691i
$617$	−20.1645	+	5.40306i	−0.811791	+	0.217519i	−0.640754	−	0.767746i	$-0.721378\pi$
$617$	−20.1645	+	5.40306i	−0.811791	+	0.217519i	−0.171037	+	0.985265i	$0.554712\pi$
$618$	1.54156	+	0.749453i	0.0620105	+	0.0301474i
$619$	−31.3681	−	18.1104i	−1.26079	−	0.727917i	−0.287562	−	0.957762i	$-0.592845\pi$
$619$	−31.3681	−	18.1104i	−1.26079	−	0.727917i	−0.973227	+	0.229845i	$0.926178\pi$
$620$	−6.91771	+	10.0286i	−0.277822	+	0.402758i
$621$	−14.7223	−	0.715497i	−0.590787	−	0.0287119i
$622$	−10.5623	+	10.5623i	−0.423510	+	0.423510i
$623$	−18.7570	−	0.981413i	−0.751482	−	0.0393195i
$624$	7.36871	+	6.38916i	0.294984	+	0.255771i
$625$	−18.6924	+	16.6010i	−0.747698	+	0.664039i
$626$		−	30.2357i		−	1.20846i
$627$	6.87567	−	14.1426i	0.274588	−	0.564803i
$628$	4.00088	+	4.00088i	0.159652	+	0.159652i
$629$	45.8488			1.82811
$630$	4.75857	+	17.0984i	0.189586	+	0.681217i
$631$	−16.4625			−0.655360			−0.327680	−	0.944789i	$-0.606267\pi$
$631$	−16.4625			−0.655360			−0.327680	+	0.944789i	$0.606267\pi$
$632$	4.48629	+	4.48629i	0.178455	+	0.178455i
$633$	0.641054	−	0.0456426i	0.0254796	−	0.00181413i
$634$			2.37711i			0.0944071i
$635$	−2.92219	+	0.536437i	−0.115964	+	0.0212879i
$636$	18.7364	−	6.47800i	0.742945	−	0.256869i
$637$	14.1191	−	36.8003i	0.559421	−	1.45808i
$638$	21.9964	−	21.9964i	0.870847	−	0.870847i
$639$	−12.1630	−	4.87838i	−0.481162	−	0.192986i
$640$	2.19932	−	0.403736i	0.0869357	−	0.0159591i
$641$	8.11862	+	4.68729i	0.320666	+	0.185137i	0.651689	−	0.758486i	$-0.274061\pi$
$641$	8.11862	+	4.68729i	0.320666	+	0.185137i	−0.331023	+	0.943623i	$0.607394\pi$
$642$	−2.07510	−	29.1450i	−0.0818979	−	1.15026i
$643$	18.0419	−	4.83432i	0.711504	−	0.190647i	0.115126	−	0.993351i	$-0.463273\pi$
$643$	18.0419	−	4.83432i	0.711504	−	0.190647i	0.596378	+	0.802704i	$0.296606\pi$
$644$	7.34096	−	1.56102i	0.289274	−	0.0615129i
$645$	18.2486	+	5.06946i	0.718538	+	0.199610i
$646$	−18.3380			−0.721500
$647$	1.55168	−	5.79096i	0.0610030	−	0.227666i	−0.928693	−	0.370849i	$-0.879067\pi$
$647$	1.55168	−	5.79096i	0.0610030	−	0.227666i	0.989696	+	0.143182i	$0.0457336\pi$
$648$	−8.99772	+	0.202646i	−0.353464	+	0.00796070i
$649$	27.6444	+	15.9605i	1.08514	+	0.626504i
$650$	−4.49923	+	27.7924i	−0.176474	+	1.09011i
$651$	−12.0752	+	21.8537i	−0.473263	+	0.856516i
$652$	−2.05285	−	7.66135i	−0.0803959	−	0.300042i
$653$	−1.76821	−	0.473789i	−0.0691952	−	0.0185408i	0.224055	−	0.974576i	$-0.428070\pi$
$653$	−1.76821	−	0.473789i	−0.0691952	−	0.0185408i	−0.293251	+	0.956036i	$0.594737\pi$
$654$	−2.68674	−	7.77089i	−0.105060	−	0.303866i
$655$	1.11755	+	0.0898738i	0.0436664	+	0.00351166i
$656$	4.90767	+	2.83345i	0.191612	+	0.110627i
$657$	9.54622	+	7.15576i	0.372434	+	0.279173i
$658$	2.30453	−	1.17447i	0.0898401	−	0.0457854i
$659$	−10.0764	−	17.4528i	−0.392520	−	0.679864i	0.600261	−	0.799804i	$-0.295063\pi$
$659$	−10.0764	−	17.4528i	−0.392520	−	0.679864i	−0.992781	+	0.119940i	$0.961730\pi$
$660$	13.4643	+	7.93910i	0.524098	+	0.309029i
$661$	−7.38567			−0.287269			−0.143635	−	0.989631i	$-0.545879\pi$
$661$	−7.38567			−0.287269			−0.143635	+	0.989631i	$0.545879\pi$
$662$	1.52848	+	1.52848i	0.0594060	+	0.0594060i
$663$	65.8535	−	44.5402i	2.55754	−	1.72980i
$664$	−4.56682	+	2.63665i	−0.177227	+	0.102322i
$665$	8.11911	−	10.5456i	0.314846	−	0.408939i
$666$	−10.4220	−	13.2702i	−0.403846	−	0.514210i
$667$	5.65900	+	21.1197i	0.219117	+	0.817757i
$668$	−2.51018	−	9.36811i	−0.0971217	−	0.362463i
$669$	23.5563	−	8.14445i	0.910738	−	0.314883i
$670$	−8.13851	−	5.61393i	−0.314418	−	0.216885i
$671$	8.77843	+	5.06823i	0.338888	+	0.195657i
$672$	4.40334	−	1.26908i	0.169863	−	0.0489558i
$673$	−7.51502	+	28.0464i	−0.289683	+	1.08111i	0.655666	+	0.755051i	$0.272388\pi$
$673$	−7.51502	+	28.0464i	−0.289683	+	1.08111i	−0.945349	+	0.326060i	$0.894279\pi$
$674$	2.62980	−	4.55495i	0.101296	−	0.175450i
$675$	−14.1585	−	21.7839i	−0.544961	−	0.838462i
$676$	9.35319	+	16.2002i	0.359738	+	0.623085i
$677$	10.1033	+	10.1033i	0.388301	+	0.388301i	0.874081	−	0.485780i	$-0.161464\pi$
$677$	10.1033	+	10.1033i	0.388301	+	0.388301i	−0.485780	+	0.874081i	$0.661464\pi$
$678$	−0.488458	+	0.0347779i	−0.0187591	+	0.00133564i
$679$	−4.88570	−	22.9758i	−0.187496	−	0.881731i
$680$	1.46114	−	18.1688i	0.0560322	−	0.696743i
$681$	17.7526	+	15.3927i	0.680280	+	0.589848i
$682$	5.69115	+	21.2396i	0.217925	+	0.813308i
$683$	15.4841	+	4.14896i	0.592484	+	0.158755i	0.542588	−	0.839999i	$-0.317444\pi$
$683$	15.4841	+	4.14896i	0.592484	+	0.158755i	0.0498955	+	0.998754i	$0.484111\pi$
$684$	4.16848	+	5.30765i	0.159386	+	0.202943i
$685$	35.3692	+	12.5929i	1.35139	+	0.481150i
$686$	−10.8898	−	14.9804i	−0.415773	−	0.571955i
$687$	−31.0933	−	15.1165i	−1.18628	−	0.576731i
$688$	1.26568	−	4.72357i	0.0482535	−	0.180084i
$689$	64.4492			2.45532
$690$	−9.56441	+	5.40571i	−0.364111	+	0.205792i
$691$	−40.0887			−1.52504			−0.762522	−	0.646962i	$-0.776039\pi$
$691$	−40.0887			−1.52504			−0.762522	+	0.646962i	$0.776039\pi$
$692$	−10.1980	−	10.1980i	−0.387671	−	0.387671i
$693$	29.0674	+	13.4618i	1.10418	+	0.511372i
$694$		−	32.6927i		−	1.24100i
$695$	8.56480	+	18.0357i	0.324881	+	0.684132i
$696$	4.36247	+	12.6176i	0.165359	+	0.478269i
$697$	32.6642	−	32.6642i	1.23724	−	1.23724i
$698$	5.36506	+	1.43756i	0.203071	+	0.0544126i
$699$	−14.7817	+	17.0480i	−0.559097	+	0.644814i
$700$	9.80135	+	8.88446i	0.370456	+	0.335801i
$701$			6.47804i			0.244672i	0.992489	+	0.122336i	$0.0390386\pi$
$701$			6.47804i			0.244672i	−0.992489	+	0.122336i	$0.960961\pi$
$702$	−27.8608	−	8.93567i	−1.05154	−	0.337255i
$703$	−3.27486	+	12.2219i	−0.123514	+	0.460959i
$704$	2.01791	−	3.49512i	0.0760528	−	0.131727i
$705$	−2.70177	+	2.65268i	−0.101754	+	0.0999056i
$706$	−13.5697	+	23.5033i	−0.510701	+	0.884560i
$707$	1.47564	−	28.2027i	0.0554971	−	1.06067i
$708$	−11.3477	+	7.67506i	−0.426473	+	0.288446i
$709$			5.70443i			0.214234i	0.994246	+	0.107117i	$0.0341620\pi$
$709$			5.70443i			0.214234i	−0.994246	+	0.107117i	$0.965838\pi$
$710$	−9.60726	+	1.76364i	−0.360554	+	0.0661881i
$711$	−17.6657	−	7.08543i	−0.662517	−	0.265725i
$712$	−1.83740	−	6.85727i	−0.0688595	−	0.256987i
$713$	−14.9287	−	4.00015i	−0.559086	−	0.149807i
$714$	−0.702404	−	37.3487i	−0.0262868	−	1.39774i
$715$	32.9355	+	38.6961i	1.23172	+	1.44715i
$716$	−16.2986	+	9.41000i	−0.609107	+	0.351668i
$717$	−45.2507	+	3.22182i	−1.68992	+	0.120321i
$718$	33.5683	−	8.99460i	1.25276	−	0.335676i
$719$	20.0896	−	34.7962i	0.749216	−	1.29768i	−0.198983	−	0.980003i	$-0.563764\pi$
$719$	20.0896	−	34.7962i	0.749216	−	1.29768i	0.948199	−	0.317677i	$-0.102903\pi$
$720$	−5.59082	+	3.70712i	−0.208358	+	0.138156i
$721$	2.56104	−	0.544593i	0.0953781	−	0.0202817i
$722$	−3.60772	+	13.4642i	−0.134266	+	0.501086i
$723$	−12.9992	+	0.925531i	−0.483444	+	0.0344209i
$724$			17.2161i			0.639830i
$725$	−24.3558	+	29.8678i	−0.904553	+	1.10926i
$726$	8.65600	−	2.99276i	0.321254	−	0.111072i
$727$	3.75326	+	1.00568i	0.139201	+	0.0372987i	0.327747	−	0.944766i	$-0.393711\pi$
$727$	3.75326	+	1.00568i	0.139201	+	0.0372987i	−0.188546	+	0.982064i	$0.560377\pi$
$728$	14.8775	+	0.778427i	0.551395	+	0.0288504i
$729$	24.5816	−	11.1690i	0.910429	−	0.413665i
$730$	8.86381	+	0.712828i	0.328064	+	0.0263830i
$731$	−34.5223	−	19.9314i	−1.27685	−	0.737191i
$732$	−3.60345	+	2.43720i	−0.133187	+	0.0900816i
$733$	0.763643	−	2.84996i	0.0282058	−	0.105266i	−0.950388	−	0.311067i	$-0.899314\pi$
$733$	0.763643	−	2.84996i	0.0282058	−	0.105266i	0.978594	+	0.205802i	$0.0659802\pi$
$734$	−4.13949	+	7.16981i	−0.152791	+	0.264643i
$735$	21.7889	+	16.1321i	0.803695	+	0.595041i
$736$	1.41833	+	2.45662i	0.0522803	+	0.0905522i
$737$	−17.2366	+	4.61854i	−0.634919	+	0.170126i
$738$	−16.8791	−	2.02912i	−0.621330	−	0.0746930i
$739$	−22.9604	+	13.2562i	−0.844613	+	0.487638i	−0.858830	−	0.512261i	$-0.828808\pi$
$739$	−22.9604	+	13.2562i	−0.844613	+	0.487638i	0.0142163	+	0.999899i	$0.495475\pi$
$740$	−11.8482	−	4.21847i	−0.435550	−	0.155074i
$741$	7.16936	+	20.7360i	0.263373	+	0.761756i
$742$	16.4909	−	25.3985i	0.605401	−	0.932410i
$743$	12.9095	+	48.1787i	0.473602	+	1.76751i	0.626664	+	0.779290i	$0.284420\pi$
$743$	12.9095	+	48.1787i	0.473602	+	1.76751i	−0.153062	+	0.988217i	$0.548913\pi$
$744$	−9.26586	−	1.78893i	−0.339703	−	0.0655853i
$745$	1.21725	−	15.1362i	0.0445968	−	0.554547i
$746$	−1.04784	+	0.604968i	−0.0383640	+	0.0221495i
$747$	9.48864	−	12.6584i	0.347171	−	0.463148i
$748$	−23.2626	−	23.2626i	−0.850566	−	0.850566i
$749$	−29.8677	−	33.1658i	−1.09134	−	1.21185i
$750$	−17.5902	−	8.09840i	−0.642304	−	0.295712i
$751$	2.96868	+	5.14190i	0.108329	+	0.187631i	0.915093	−	0.403242i	$-0.132117\pi$
$751$	2.96868	+	5.14190i	0.108329	+	0.187631i	−0.806765	+	0.590873i	$0.798783\pi$
$752$	0.691285	+	0.691285i	0.0252086	+	0.0252086i
$753$	−23.8612	+	16.1386i	−0.869549	+	0.588122i
$754$			43.4020i			1.58061i
$755$	−34.6605	+	16.4596i	−1.26142	+	0.599027i
$756$	−10.6503	+	8.69315i	−0.387348	+	0.316167i
$757$	29.0797	−	29.0797i	1.05692	−	1.05692i	0.0586398	−	0.998279i	$-0.481324\pi$
$757$	29.0797	−	29.0797i	1.05692	−	1.05692i	0.998279	−	0.0586398i	$-0.0186763\pi$
$758$	−4.92809	+	4.92809i	−0.178996	+	0.178996i
$759$	−3.75889	+	19.4694i	−0.136439	+	0.706694i
$760$	4.73891	+	1.68725i	0.171898	+	0.0612030i
$761$	11.8714	−	6.85393i	0.430336	−	0.248455i	−0.269154	−	0.963097i	$-0.586744\pi$
$761$	11.8714	−	6.85393i	0.430336	−	0.248455i	0.699490	+	0.714642i	$0.253411\pi$
$762$	−1.28931	−	1.90627i	−0.0467068	−	0.0690569i
$763$	−10.5340	−	6.83960i	−0.381357	−	0.247610i
$764$	6.51496			0.235703
$765$	17.3938	+	51.8424i	0.628874	+	1.87437i
$766$	8.71475	+	15.0944i	0.314877	+	0.545382i
$767$	−43.0192	+	11.5270i	−1.55333	+	0.416214i
$768$	0.970368	+	1.43471i	0.0350151	+	0.0517706i
$769$	−2.93486	−	1.69444i	−0.105834	−	0.0611032i	0.446149	−	0.894959i	$-0.352795\pi$
$769$	−2.93486	−	1.69444i	−0.105834	−	0.0611032i	−0.551983	+	0.833856i	$0.686129\pi$
$770$	23.6770	−	3.07806i	0.853259	−	0.110925i
$771$	33.0057	−	11.4115i	1.18867	−	0.410976i
$772$	13.8329	−	13.8329i	0.497858	−	0.497858i
$773$	25.1483	+	6.73847i	0.904522	+	0.242366i	0.680957	−	0.732323i	$-0.261564\pi$
$773$	25.1483	+	6.73847i	0.904522	+	0.242366i	0.223565	+	0.974689i	$0.428231\pi$
$774$	2.07854	+	14.5226i	0.0747114	+	0.522004i
$775$	−9.67582	−	25.4660i	−0.347566	−	0.914765i
$776$	7.68875	−	4.43910i	0.276010	−	0.159355i
$777$	−25.0176	−	6.20169i	−0.897501	−	0.222485i
$778$	−9.11200	+	2.44155i	−0.326681	+	0.0875339i
$779$	6.37420	+	11.0404i	0.228379	+	0.395565i
$780$	−21.1159	+	5.45101i	−0.756071	+	0.195177i
$781$	−8.81481	+	15.2677i	−0.315419	+	0.546321i
$782$	22.3354	−	5.98475i	0.798711	−	0.214014i
$783$	−26.9125	−	29.6620i	−0.961774	−	1.06003i
$784$	4.11353	−	5.66382i	0.146912	−	0.202279i
$785$	−12.4439	+	2.28438i	−0.444143	+	0.0815329i
$786$	0.283779	+	0.820775i	0.0101220	+	0.0292761i
$787$	4.21145	−	4.21145i	0.150122	−	0.150122i	−0.628050	−	0.778173i	$-0.716147\pi$
$787$	4.21145	−	4.21145i	0.150122	−	0.150122i	0.778173	+	0.628050i	$0.216147\pi$
$788$	−4.97268	+	4.97268i	−0.177144	+	0.177144i
$789$	10.3702	−	11.9601i	0.369190	−	0.425792i
$790$	−13.9537	+	2.56153i	−0.496451	+	0.0911352i
$791$	−0.555846	+	0.500571i	−0.0197636	+	0.0177983i
$792$	−1.44509	+	12.0209i	−0.0513490	+	0.427144i
$793$	−13.6607	+	3.66037i	−0.485105	+	0.129983i
$794$	16.2942	−	28.2224i	0.578261	−	1.00158i
$795$	−11.8653	+	42.7117i	−0.420819	+	1.51483i
$796$	0.270466	+	0.468461i	0.00958641	+	0.0166041i
$797$	−10.4989	+	2.81316i	−0.371888	+	0.0996472i	−0.439922	−	0.898036i	$-0.644994\pi$
$797$	−10.4989	+	2.81316i	−0.371888	+	0.0996472i	0.0680339	+	0.997683i	$0.478327\pi$
$798$	10.0062	+	2.48048i	0.354216	+	0.0878079i
$799$	6.90152	−	3.98460i	0.244158	−	0.140965i
$800$	−2.04927	+	4.56076i	−0.0724527	+	0.161247i
$801$	13.1545	+	16.7494i	0.464792	+	0.591811i
$802$	−2.68239	−	0.718745i	−0.0947186	−	0.0253798i
$803$	11.3488	−	11.3488i	0.400492	−	0.400492i
$804$	1.45177	−	7.51953i	0.0512000	−	0.265193i
$805$	−6.44731	+	15.4940i	−0.227238	+	0.546092i
$806$	−26.5691	−	15.3397i	−0.935855	−	0.540316i
$807$	−6.98071	+	14.3587i	−0.245733	+	0.505450i
$808$	10.3105	−	2.76269i	0.362722	−	0.0971910i
$809$	2.88842	+	5.00289i	0.101551	+	0.175892i	0.912324	−	0.409469i	$-0.134286\pi$
$809$	2.88842	+	5.00289i	0.101551	+	0.175892i	−0.810773	+	0.585361i	$0.800953\pi$
$810$	11.0511	−	16.8188i	0.388297	−	0.590953i
$811$	34.4371			1.20925			0.604625	−	0.796511i	$-0.293323\pi$
$811$	34.4371			1.20925			0.604625	+	0.796511i	$0.293323\pi$
$812$	17.1041	+	11.1055i	0.600236	+	0.389726i
$813$	−47.6678	+	3.39392i	−1.67178	+	0.119030i
$814$	−19.6584	+	11.3498i	−0.689026	+	0.397809i
$815$	16.7082	+	5.94881i	0.585263	+	0.208378i
$816$	13.3439	−	4.61358i	0.467130	−	0.161508i
$817$	7.77897	−	7.77897i	0.272152	−	0.272152i
$818$	1.81283	−	1.81283i	0.0633840	−	0.0633840i
$819$	−41.9579	+	15.3959i	−1.46613	+	0.537977i
$820$	−11.4465	+	5.43571i	−0.399728	+	0.189823i
$821$		−	0.280025i		−	0.00977293i	−0.999988	−	0.00488646i	$-0.998445\pi$
$821$		−	0.280025i		−	0.00977293i	0.999988	−	0.00488646i	$-0.00155542\pi$
$822$	2.06536	+	29.0081i	0.0720376	+	1.01177i
$823$	14.6433	+	14.6433i	0.510432	+	0.510432i	0.914659	−	0.404227i	$-0.132459\pi$
$823$	14.6433	+	14.6433i	0.510432	+	0.510432i	−0.404227	+	0.914659i	$0.632459\pi$
$824$	0.494813	+	0.857041i	0.0172376	+	0.0298564i
$825$	−31.7082	+	14.7029i	−1.10394	+	0.511889i
$826$	−6.46492	+	19.9027i	−0.224943	+	0.692504i
$827$	22.0696	+	22.0696i	0.767435	+	0.767435i	0.977654	−	0.210219i	$-0.0674179\pi$
$827$	22.0696	+	22.0696i	0.767435	+	0.767435i	−0.210219	+	0.977654i	$0.567418\pi$
$828$	−6.80932	−	5.10421i	−0.236640	−	0.177383i
$829$	32.0597	−	18.5097i	1.11348	−	0.642867i	0.173750	−	0.984790i	$-0.444412\pi$
$829$	32.0597	−	18.5097i	1.11348	−	0.642867i	0.939728	+	0.341923i	$0.111078\pi$
$830$	0.945220	−	11.7535i	0.0328091	−	0.407971i
$831$	11.0126	−	12.7010i	0.382023	−	0.440593i
$832$	1.45737	+	5.43898i	0.0505252	+	0.188563i
$833$	−35.9173	−	44.3387i	−1.24446	−	1.53625i
$834$	−10.1316	+	11.6849i	−0.350827	+	0.404614i
$835$	20.4304	+	7.27406i	0.707022	+	0.251729i
$836$	7.86272	−	4.53954i	0.271938	−	0.157003i
$837$	27.6697	−	5.99132i	0.956405	−	0.207090i
$838$	−3.43086	+	0.919296i	−0.118517	+	0.0317566i
$839$	6.93864	+	12.0181i	0.239548	+	0.414910i	0.960585	−	0.277987i	$-0.0896673\pi$
$839$	6.93864	+	12.0181i	0.239548	+	0.414910i	−0.721036	+	0.692897i	$0.756334\pi$
$840$	−3.25487	+	9.71627i	−0.112304	+	0.335243i
$841$	−15.2058	+	26.3373i	−0.524339	+	0.908183i
$842$	−5.81769	+	21.7119i	−0.200491	+	0.748242i
$843$	37.0165	+	17.9962i	1.27492	+	0.619821i
$844$	0.321338	+	0.185525i	0.0110609	+	0.00638602i
$845$	−41.6941	−	3.35305i	−1.43432	−	0.115348i
$846$	−2.72209	−	1.09178i	−0.0935873	−	0.0375363i
$847$	7.61863	−	11.7338i	0.261779	−	0.403180i
$848$	11.0557	+	2.96238i	0.379656	+	0.101728i
$849$	−6.38447	+	33.0687i	−0.219114	+	1.13492i
$850$	31.5871	+	25.7578i	1.08343	+	0.883486i
$851$		−	15.9549i		−	0.546926i
$852$	−4.23885	−	6.26722i	−0.145221	−	0.214711i
$853$	12.8255	−	47.8654i	0.439137	−	1.63888i	−0.291832	−	0.956470i	$-0.594265\pi$
$853$	12.8255	−	47.8654i	0.439137	−	1.63888i	0.730969	−	0.682411i	$-0.239069\pi$
$854$	−2.05292	+	6.32008i	−0.0702496	+	0.216269i
$855$	−15.0620	+	0.933705i	−0.515111	+	0.0319320i
$856$	8.43474	−	14.6094i	0.288293	−	0.499339i
$857$	−38.3674	+	10.2805i	−1.31060	+	0.351175i	−0.845450	−	0.534054i	$-0.820668\pi$
$857$	−38.3674	+	10.2805i	−1.31060	+	0.351175i	−0.465154	+	0.885230i	$0.654001\pi$
$858$	−17.2099	+	35.3992i	−0.587536	+	1.20851i
$859$	−8.42446	+	4.86386i	−0.287439	+	0.165953i	−0.636786	−	0.771040i	$-0.719737\pi$
$859$	−8.42446	+	4.86386i	−0.287439	+	0.165953i	0.349347	+	0.936993i	$0.386403\pi$
$860$	7.08739	+	8.32701i	0.241678	+	0.283949i
$861$	−22.2417	+	13.4051i	−0.757993	+	0.456843i
$862$	16.3934	+	4.39261i	0.558363	+	0.149613i
$863$	−1.88755	−	7.04444i	−0.0642530	−	0.239796i	0.926329	−	0.376715i	$-0.122946\pi$
$863$	−1.88755	−	7.04444i	−0.0642530	−	0.239796i	−0.990582	+	0.136920i	$0.956280\pi$
$864$	−4.36858	−	2.81345i	−0.148622	−	0.0957156i
$865$	31.7190	−	5.82276i	1.07848	−	0.197980i
$866$		−	16.1366i		−	0.548343i
$867$	−6.08262	−	85.4308i	−0.206577	−	2.90138i
$868$	−12.8435	+	6.54546i	−0.435937	+	0.222167i
$869$	−12.8028	+	22.1750i	−0.434304	+	0.752236i
$870$	−28.7633	−	7.99045i	−0.975168	−	0.270901i
$871$	12.4486	−	21.5616i	0.421805	−	0.730587i
$872$	1.22864	−	4.58536i	0.0416072	−	0.155280i
$873$	−15.9752	+	21.3119i	−0.540678	+	0.721298i
$874$			6.38143i			0.215855i
$875$	−28.7975	+	6.76042i	−0.973534	+	0.228544i
$876$	2.25077	+	6.50993i	0.0760465	+	0.219950i
$877$	20.8901	+	5.59749i	0.705409	+	0.189014i	0.593652	−	0.804722i	$-0.297686\pi$
$877$	20.8901	+	5.59749i	0.705409	+	0.189014i	0.111757	+	0.993736i	$0.464352\pi$
$878$	21.4476	−	21.4476i	0.723822	−	0.723822i
$879$	4.55999	−	5.25910i	0.153805	−	0.177385i
$880$	3.87117	+	8.15188i	0.130497	+	0.274800i
$881$		−	12.9981i		−	0.437919i	−0.975734	−	0.218959i	$-0.929734\pi$
$881$		−	12.9981i		−	0.437919i	0.975734	−	0.218959i	$-0.0702662\pi$
$882$	−4.66866	+	20.4745i	−0.157202	+	0.689411i
$883$	−19.5519	−	19.5519i	−0.657974	−	0.657974i	0.296926	−	0.954900i	$-0.404038\pi$
$883$	−19.5519	−	19.5519i	−0.657974	−	0.657974i	−0.954900	+	0.296926i	$0.904038\pi$
$884$	45.9003			1.54379
$885$	0.280841	−	30.6318i	0.00944037	−	1.02968i
$886$	10.0106			0.336312
$887$	3.19084	−	11.9084i	0.107138	−	0.399844i	−0.891441	−	0.453136i	$-0.850305\pi$
$887$	3.19084	−	11.9084i	0.107138	−	0.399844i	0.998579	+	0.0532929i	$0.0169717\pi$
$888$	−0.691870	−	9.71736i	−0.0232176	−	0.326093i
$889$	−3.34340	−	1.08602i	−0.112134	−	0.0364240i
$890$	14.9546	+	5.32447i	0.501280	+	0.178477i
$891$	−10.1885	−	34.8641i	−0.341328	−	1.16799i
$892$	13.8998	+	3.72445i	0.465401	+	0.124704i
$893$	0.569218	+	2.12435i	0.0190482	+	0.0710887i
$894$	11.1166	−	3.84351i	0.371795	−	0.128546i
$895$	3.37341	−	41.9474i	0.112761	−	1.40215i
$896$	2.51633	+	0.817368i	0.0840646	+	0.0273064i
$897$	−15.4995	−	22.9163i	−0.517513	−	0.765152i
$898$	7.32529	+	7.32529i	0.244448	+	0.244448i
$899$	−20.9980	−	36.3696i	−0.700323	−	1.21299i
$900$	0.275026	−	14.9975i	0.00916752	−	0.499916i
$901$	46.6505	−	80.8011i	1.55415	−	2.69187i
$902$	−5.91933	+	22.0912i	−0.197092	+	0.735558i
$903$	16.1412	+	15.5453i	0.537146	+	0.517315i
$904$	−0.244847	−	0.141363i	−0.00814351	−	0.00470165i
$905$	−31.6885	−	21.8587i	−1.05336	−	0.726607i
$906$	−22.4557	−	19.4706i	−0.746040	−	0.646866i
$907$	6.27631	+	23.4235i	0.208401	+	0.777764i	0.988386	+	0.151966i	$0.0485603\pi$
$907$	6.27631	+	23.4235i	0.208401	+	0.777764i	−0.779984	+	0.625799i	$0.784773\pi$
$908$	3.51107	+	13.1035i	0.116519	+	0.434855i
$909$	−25.1842	+	19.7789i	−0.835306	+	0.656026i
$910$	−20.3222	+	26.3957i	−0.673675	+	0.875007i
$911$	−11.2697	+	6.50654i	−0.373380	+	0.215571i	−0.674934	−	0.737878i	$-0.735828\pi$
$911$	−11.2697	+	6.50654i	−0.373380	+	0.215571i	0.301554	+	0.953449i	$0.402495\pi$
$912$	0.276725	+	3.88663i	0.00916330	+	0.128699i
$913$	−15.0487	−	15.0487i	−0.498040	−	0.498040i
$914$	−11.3281			−0.374701
$915$	0.0891807	−	9.72708i	0.00294822	−	0.321567i
$916$	−9.98041	−	17.2866i	−0.329762	−	0.571165i
$917$	1.11262	+	0.722411i	0.0367420	+	0.0238561i
$918$	−31.3694	+	28.4617i	−1.03534	+	0.939375i
$919$	−31.3155	−	18.0800i	−1.03300	−	0.596404i	−0.115159	−	0.993347i	$-0.536738\pi$
$919$	−31.3155	−	18.0800i	−1.03300	−	0.596404i	−0.917843	+	0.396943i	$0.870071\pi$
$920$	−6.32255	−	0.508460i	−0.208448	−	0.0167634i
$921$	−35.0775	−	6.77229i	−1.15584	−	0.223154i
$922$	−20.7203	−	5.55200i	−0.682388	−	0.182845i
$923$	−6.36621	−	23.7590i	−0.209546	−	0.782038i
$924$	9.54675	+	15.8399i	0.314065	+	0.521096i
$925$	22.8080	−	16.4523i	0.749922	−	0.540947i
$926$	18.2195	+	10.5190i	0.598730	+	0.345677i
$927$	−2.37557	−	1.78070i	−0.0780239	−	0.0584860i
$928$	−1.99495	+	7.44526i	−0.0654875	+	0.244403i
$929$	−54.2995			−1.78151			−0.890755	−	0.454485i	$-0.849823\pi$
$929$	−54.2995			−1.78151			−0.890755	+	0.454485i	$0.849823\pi$
$930$	15.0573	−	14.7837i	0.493749	−	0.484778i
$931$	14.3849	−	6.40748i	0.471445	−	0.209997i
$932$	−12.5834	+	3.37172i	−0.412184	+	0.110444i
$933$	21.4307	−	14.4947i	0.701611	−	0.474536i
$934$	−12.0024	−	6.92959i	−0.392731	−	0.226743i
$935$	72.3538	−	13.2822i	2.36622	−	0.434375i
$936$	−10.4338	−	13.2851i	−0.341038	−	0.434238i
$937$	−7.89177	+	7.89177i	−0.257813	+	0.257813i	−0.824164	−	0.566351i	$-0.808355\pi$
$937$	−7.89177	+	7.89177i	−0.257813	+	0.257813i	0.566351	+	0.824164i	$0.308355\pi$
$938$	−5.31184	−	10.4229i	−0.173438	−	0.340319i
$939$	−9.92754	+	51.4203i	−0.323973	+	1.67804i
$940$	−2.15011	+	0.394702i	−0.0701287	+	0.0128738i
$941$			18.7226i			0.610340i	0.952298	+	0.305170i	$0.0987133\pi$
$941$			18.7226i			0.610340i	−0.952298	+	0.305170i	$0.901287\pi$
$942$	−5.49043	−	8.11771i	−0.178888	−	0.264489i
$943$	−11.3668	−	11.3668i	−0.370153	−	0.370153i
$944$	−7.90943			−0.257430
$945$	−2.47858	−	30.6408i	−0.0806282	−	0.996744i
$946$	19.7359			0.641671
$947$	−3.97187	−	3.97187i	−0.129068	−	0.129068i	0.639622	−	0.768690i	$-0.279091\pi$
$947$	−3.97187	−	3.97187i	−0.129068	−	0.129068i	−0.768690	+	0.639622i	$0.779091\pi$
$948$	−6.15656	−	9.10260i	−0.199956	−	0.295639i
$949$			22.3928i			0.726901i
$950$	−9.12246	+	6.58037i	−0.295972	+	0.213495i
$951$	0.780495	−	4.04262i	0.0253093	−	0.131091i
$952$	11.7447	−	18.0887i	0.380649	−	0.586257i
$953$	−5.52560	+	5.52560i	−0.178992	+	0.178992i	−0.790916	−	0.611925i	$-0.790396\pi$
$953$	−5.52560	+	5.52560i	−0.178992	+	0.178992i	0.611925	+	0.790916i	$0.290396\pi$
$954$	−33.9909	+	4.86492i	−1.10050	+	0.157508i
$955$	−8.27183	+	11.9917i	−0.267670	+	0.388041i
$956$	−22.6826	−	13.0958i	−0.733608	−	0.423549i
$957$	−44.6304	+	30.1859i	−1.44270	+	0.975771i
$958$	20.7194	−	5.55173i	0.669412	−	0.179368i
$959$	29.7275	+	33.0100i	0.959949	+	1.06595i
$960$	−3.87282	−	0.0355071i	−0.124995	−	0.00114599i
$961$	−1.31450			−0.0424033
$962$	8.19701	−	30.5917i	0.264282	−	0.986315i
$963$	−6.04039	+	50.2466i	−0.194649	+	1.61918i
$964$	−6.51603	−	3.76203i	−0.209867	−	0.121167i
$965$	7.89817	+	43.0246i	0.254251	+	1.38501i
$966$	−12.9969	+	0.244429i	−0.418169	+	0.00786437i
$967$	−15.2018	−	56.7340i	−0.488858	−	1.82444i	−0.562022	−	0.827123i	$-0.689976\pi$
$967$	−15.2018	−	56.7340i	−0.488858	−	1.82444i	0.0731638	−	0.997320i	$-0.476690\pi$
$968$	5.10764	+	1.36859i	0.164166	+	0.0439880i
$969$	31.1865	+	6.02107i	1.00185	+	0.193425i
$970$	−1.59138	+	19.7884i	−0.0510963	+	0.635367i
$971$	31.1210	+	17.9677i	0.998719	+	0.576611i	0.907869	−	0.419254i	$-0.137708\pi$
$971$	31.1210	+	17.9677i	0.998719	+	0.576611i	0.0908499	+	0.995865i	$0.471042\pi$
$972$	15.3685	+	2.60966i	0.492944	+	0.0837049i
$973$	−1.23439	+	23.5918i	−0.0395726	+	0.756319i
$974$	−15.6813	−	27.1608i	−0.502461	−	0.870288i
$975$	16.7769	−	45.7877i	0.537290	−	1.46638i
$976$	−2.51163			−0.0803952
$977$	19.5751	+	19.5751i	0.626262	+	0.626262i	0.947126	−	0.320863i	$-0.103973\pi$
$977$	19.5751	+	19.5751i	0.626262	+	0.626262i	−0.320863	+	0.947126i	$0.603973\pi$
$978$	0.975663	+	13.7033i	0.0311983	+	0.438182i
$979$	24.8124	−	14.3255i	0.793009	−	0.457844i
$980$	5.20221	+	14.7627i	0.166178	+	0.471577i
$981$	2.01772	+	14.0977i	0.0644209	+	0.450105i
$982$	−2.21417	−	8.26341i	−0.0706571	−	0.263696i
$983$	10.4860	+	39.1343i	0.334452	+	1.24819i	0.904462	+	0.426554i	$0.140273\pi$
$983$	10.4860	+	39.1343i	0.334452	+	1.24819i	−0.570010	+	0.821638i	$0.693061\pi$
$984$	−7.41588	−	6.43006i	−0.236410	−	0.204983i
$985$	−2.83925	−	15.4665i	−0.0904659	−	0.492805i
$986$	54.4138	+	31.4158i	1.73289	+	1.00048i
$987$	−4.30482	+	1.24068i	−0.137024	+	0.0394914i
$988$	−3.27854	+	12.2357i	−0.104304	+	0.389268i
$989$	−6.93592	+	12.0134i	−0.220549	+	0.382003i
$990$	−20.2913	−	17.9224i	−0.644901	−	0.569612i
$991$	20.2501	+	35.0742i	0.643266	+	1.11417i	0.984699	+	0.174263i	$0.0557542\pi$
$991$	20.2501	+	35.0742i	0.643266	+	1.11417i	−0.341434	+	0.939906i	$0.610912\pi$
$992$	−3.85263	−	3.85263i	−0.122321	−	0.122321i
$993$	−2.09754	−	3.10126i	−0.0665635	−	0.0984154i
$994$	−10.9921	−	3.57050i	−0.348647	−	0.113249i
$995$	−1.20567	−	0.0969599i	−0.0382222	−	0.00307384i
$996$	8.63225	−	2.98455i	0.273523	−	0.0945692i
$997$	11.4443	+	42.7108i	0.362445	+	1.35266i	0.870851	+	0.491547i	$0.163568\pi$
$997$	11.4443	+	42.7108i	0.362445	+	1.35266i	−0.508406	+	0.861118i	$0.669765\pi$
$998$	−37.9024	−	10.1559i	−1.19978	−	0.321480i
$999$	13.3671	+	25.9899i	0.422916	+	0.822283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.23.17	yes	192
5.2	odd	4	inner	630.2.cd.a.527.42	yes	192
7.4	even	3		630.2.bt.a.473.39	yes	192
9.2	odd	6		630.2.bt.a.443.28	yes	192
35.32	odd	12		630.2.bt.a.347.28	yes	192
45.2	even	12		630.2.bt.a.317.39	✓	192
63.11	odd	6	inner	630.2.cd.a.263.42	yes	192
315.137	even	12	inner	630.2.cd.a.137.17	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.39	✓	192	45.2	even	12
630.2.bt.a.347.28	yes	192	35.32	odd	12
630.2.bt.a.443.28	yes	192	9.2	odd	6
630.2.bt.a.473.39	yes	192	7.4	even	3
630.2.cd.a.23.17	yes	192	1.1	even	1	trivial
630.2.cd.a.137.17	yes	192	315.137	even	12	inner
630.2.cd.a.263.42	yes	192	63.11	odd	6	inner
630.2.cd.a.527.42	yes	192	5.2	odd	4	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.970368 + 1.43471i) q^{3} +1.00000i q^{4} +(-1.84064 - 1.26967i) q^{5} +(0.328338 - 1.70065i) q^{6} +(-1.20135 - 2.35728i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.11677 + 2.78439i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.970368 + 1.43471i) q^{3} +1.00000i q^{4} +(-1.84064 - 1.26967i) q^{5} +(0.328338 - 1.70065i) q^{6} +(-1.20135 - 2.35728i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.11677 + 2.78439i) q^{9} +(0.403736 + 2.19932i) q^{10} +(3.49512 + 2.01791i) q^{11} +(-1.43471 + 0.970368i) q^{12} +(-5.43898 + 1.45737i) q^{13} +(-0.817368 + 2.51633i) q^{14} +(0.0355071 - 3.87282i) q^{15} -1.00000 q^{16} +(-2.10979 + 7.87383i) q^{17} +(2.75854 - 1.17918i) q^{18} +(-1.94823 - 1.12481i) q^{19} +(1.26967 - 1.84064i) q^{20} +(2.21626 - 4.01101i) q^{21} +(-1.04455 - 3.89830i) q^{22} +(2.74000 + 0.734182i) q^{23} +(1.70065 + 0.328338i) q^{24} +(1.77589 + 4.67399i) q^{25} +(4.87645 + 2.81542i) q^{26} +(-5.07846 + 1.09964i) q^{27} +(2.35728 - 1.20135i) q^{28} +(3.85395 + 6.67524i) q^{29} +(-2.76361 + 2.71339i) q^{30} -5.44844 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.496444 + 6.97259i) q^{33} +(7.05948 - 4.07579i) q^{34} +(-0.781720 + 5.86421i) q^{35} +(-2.78439 - 1.11677i) q^{36} +(-1.45573 - 5.43287i) q^{37} +(0.582246 + 2.17297i) q^{38} +(-7.36871 - 6.38916i) q^{39} +(-2.19932 + 0.403736i) q^{40} +(-4.90767 - 2.83345i) q^{41} +(-4.40334 + 1.26908i) q^{42} +(-1.26568 + 4.72357i) q^{43} +(-2.01791 + 3.49512i) q^{44} +(5.59082 - 3.70712i) q^{45} +(-1.41833 - 2.45662i) q^{46} +(-0.691285 - 0.691285i) q^{47} +(-0.970368 - 1.43471i) q^{48} +(-4.11353 + 5.66382i) q^{49} +(2.04927 - 4.56076i) q^{50} +(-13.3439 + 4.61358i) q^{51} +(-1.45737 - 5.43898i) q^{52} +(-11.0557 - 2.96238i) q^{53} +(4.36858 + 2.81345i) q^{54} +(-3.87117 - 8.15188i) q^{55} +(-2.51633 - 0.817368i) q^{56} +(-0.276725 - 3.88663i) q^{57} +(1.99495 - 7.44526i) q^{58} +7.90943 q^{59} +(3.87282 + 0.0355071i) q^{60} +2.51163 q^{61} +(3.85263 + 3.85263i) q^{62} +(7.90521 - 0.712471i) q^{63} -1.00000i q^{64} +(11.8616 + 4.22321i) q^{65} +(4.57933 - 5.28140i) q^{66} +(-3.12653 + 3.12653i) q^{67} +(-7.87383 - 2.10979i) q^{68} +(1.60548 + 4.64353i) q^{69} +(4.69938 - 3.59386i) q^{70} +4.36829i q^{71} +(1.17918 + 2.75854i) q^{72} +(1.02927 - 3.84131i) q^{73} +(-2.81226 + 4.87098i) q^{74} +(-4.98255 + 7.08337i) q^{75} +(1.12481 - 1.94823i) q^{76} +(0.557925 - 10.6632i) q^{77} +(0.692647 + 9.72828i) q^{78} +6.34457i q^{79} +(1.84064 + 1.26967i) q^{80} +(-6.50564 - 6.21905i) q^{81} +(1.46670 + 5.47380i) q^{82} +(-5.09362 - 1.36483i) q^{83} +(4.01101 + 2.21626i) q^{84} +(13.8805 - 11.8141i) q^{85} +(4.23504 - 2.44510i) q^{86} +(-5.83726 + 12.0067i) q^{87} +(3.89830 - 1.04455i) q^{88} +(3.54958 - 6.14806i) q^{89} +(-6.57464 - 1.33198i) q^{90} +(9.96952 + 11.0704i) q^{91} +(-0.734182 + 2.74000i) q^{92} +(-5.28699 - 7.81692i) q^{93} +0.977624i q^{94} +(2.15785 + 4.54398i) q^{95} +(-0.328338 + 1.70065i) q^{96} +(8.57569 + 2.29785i) q^{97} +(6.91363 - 1.09622i) q^{98} +(-9.52189 + 7.47823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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