LMFDB - Embedded newform 630.2.bk.c.101.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("630.101");

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.bk (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.11
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.c.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.14223 - 1.30204i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30204 - 1.14223i) q^{6} +(2.06989 + 1.64790i) q^{7} -1.00000i q^{8} +(-0.390607 + 2.97446i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.14223 - 1.30204i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30204 - 1.14223i) q^{6} +(2.06989 + 1.64790i) q^{7} -1.00000i q^{8} +(-0.390607 + 2.97446i) q^{9} +(0.866025 + 0.500000i) q^{10} +(0.568614 - 0.328290i) q^{11} +(1.14223 + 1.30204i) q^{12} +(-2.39457 + 1.38250i) q^{13} +(-1.64790 + 2.06989i) q^{14} +(-1.69871 + 0.338184i) q^{15} +1.00000 q^{16} +(3.36928 - 5.83577i) q^{17} +(-2.97446 - 0.390607i) q^{18} +(-0.633612 + 0.365816i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.218666 - 4.57736i) q^{21} +(0.328290 + 0.568614i) q^{22} +(6.23613 + 3.60043i) q^{23} +(-1.30204 + 1.14223i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.38250 - 2.39457i) q^{26} +(4.31903 - 2.88894i) q^{27} +(-2.06989 - 1.64790i) q^{28} +(6.21225 + 3.58664i) q^{29} +(-0.338184 - 1.69871i) q^{30} -8.01306i q^{31} +1.00000i q^{32} +(-1.07694 - 0.365374i) q^{33} +(5.83577 + 3.36928i) q^{34} +(2.46207 - 0.968625i) q^{35} +(0.390607 - 2.97446i) q^{36} +(1.05061 + 1.81971i) q^{37} +(-0.365816 - 0.633612i) q^{38} +(4.53523 + 1.53868i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(3.35799 + 5.81621i) q^{41} +(4.57736 - 0.218666i) q^{42} +(6.29106 - 10.8964i) q^{43} +(-0.568614 + 0.328290i) q^{44} +(2.38066 + 1.82551i) q^{45} +(-3.60043 + 6.23613i) q^{46} +5.85866 q^{47} +(-1.14223 - 1.30204i) q^{48} +(1.56886 + 6.82193i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-11.4469 + 2.27887i) q^{51} +(2.39457 - 1.38250i) q^{52} +(5.77309 + 3.33309i) q^{53} +(2.88894 + 4.31903i) q^{54} -0.656579i q^{55} +(1.64790 - 2.06989i) q^{56} +(1.20004 + 0.407140i) q^{57} +(-3.58664 + 6.21225i) q^{58} -9.25800 q^{59} +(1.69871 - 0.338184i) q^{60} -1.56571i q^{61} +8.01306 q^{62} +(-5.71012 + 5.51312i) q^{63} -1.00000 q^{64} +2.76501i q^{65} +(0.365374 - 1.07694i) q^{66} -6.56740 q^{67} +(-3.36928 + 5.83577i) q^{68} +(-2.43521 - 12.2322i) q^{69} +(0.968625 + 2.46207i) q^{70} -1.54080i q^{71} +(2.97446 + 0.390607i) q^{72} +(5.95292 + 3.43692i) q^{73} +(-1.81971 + 1.05061i) q^{74} +(-0.556482 + 1.64022i) q^{75} +(0.633612 - 0.365816i) q^{76} +(1.71796 + 0.257496i) q^{77} +(-1.53868 + 4.53523i) q^{78} -15.0706 q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.69485 - 2.32369i) q^{81} +(-5.81621 + 3.35799i) q^{82} +(8.71114 - 15.0881i) q^{83} +(0.218666 + 4.57736i) q^{84} +(-3.36928 - 5.83577i) q^{85} +(10.8964 + 6.29106i) q^{86} +(-2.42589 - 12.1854i) q^{87} +(-0.328290 - 0.568614i) q^{88} +(1.32440 + 2.29393i) q^{89} +(-1.82551 + 2.38066i) q^{90} +(-7.23471 - 1.08438i) q^{91} +(-6.23613 - 3.60043i) q^{92} +(-10.4333 + 9.15279i) q^{93} +5.85866i q^{94} +0.731632i q^{95} +(1.30204 - 1.14223i) q^{96} +(-4.02448 - 2.32353i) q^{97} +(-6.82193 + 1.56886i) q^{98} +(0.754380 + 1.81955i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.14223	−	1.30204i	−0.659469	−	0.751732i
$3$	−1.14223	−	1.30204i	−0.659469	−	0.751732i
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.30204	−	1.14223i	0.531555	−	0.466315i
$7$	2.06989	+	1.64790i	0.782344	+	0.622847i
$7$	2.06989	+	1.64790i	0.782344	+	0.622847i
$8$		−	1.00000i		−	0.353553i
$9$	−0.390607	+	2.97446i	−0.130202	+	0.991487i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	0.568614	−	0.328290i	0.171444	−	0.0989831i	−0.411823	−	0.911264i	$-0.635108\pi$
$11$	0.568614	−	0.328290i	0.171444	−	0.0989831i	0.583266	+	0.812281i	$0.301774\pi$
$12$	1.14223	+	1.30204i	0.329734	+	0.375866i
$13$	−2.39457	+	1.38250i	−0.664133	+	0.383438i	−0.793850	−	0.608114i	$-0.791927\pi$
$13$	−2.39457	+	1.38250i	−0.664133	+	0.383438i	0.129717	+	0.991551i	$0.458593\pi$
$14$	−1.64790	+	2.06989i	−0.440419	+	0.553200i
$15$	−1.69871	+	0.338184i	−0.438606	+	0.0873187i
$16$	1.00000			0.250000
$17$	3.36928	−	5.83577i	0.817172	−	1.41538i	−0.0905864	−	0.995889i	$-0.528874\pi$
$17$	3.36928	−	5.83577i	0.817172	−	1.41538i	0.907758	−	0.419494i	$-0.137793\pi$
$18$	−2.97446	−	0.390607i	−0.701087	−	0.0920670i
$19$	−0.633612	+	0.365816i	−0.145361	+	0.0839240i	−0.570916	−	0.821008i	$-0.693412\pi$
$19$	−0.633612	+	0.365816i	−0.145361	+	0.0839240i	0.425556	+	0.904932i	$0.360079\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−0.218666	−	4.57736i	−0.0477169	−	0.998861i
$22$	0.328290	+	0.568614i	0.0699916	+	0.121229i
$23$	6.23613	+	3.60043i	1.30032	+	0.750741i	0.980459	−	0.196723i	$-0.0630298\pi$
$23$	6.23613	+	3.60043i	1.30032	+	0.750741i	0.319863	+	0.947464i	$0.396363\pi$
$24$	−1.30204	+	1.14223i	−0.265777	+	0.233157i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.38250	−	2.39457i	−0.271131	−	0.469613i
$27$	4.31903	−	2.88894i	0.831197	−	0.555977i
$28$	−2.06989	−	1.64790i	−0.391172	−	0.311424i
$29$	6.21225	+	3.58664i	1.15359	+	0.666023i	0.949758	−	0.312984i	$-0.101329\pi$
$29$	6.21225	+	3.58664i	1.15359	+	0.666023i	0.203827	+	0.979007i	$0.434662\pi$
$30$	−0.338184	−	1.69871i	−0.0617436	−	0.310141i
$31$		−	8.01306i		−	1.43919i	−0.694395	−	0.719594i	$-0.744328\pi$
$31$		−	8.01306i		−	1.43919i	0.694395	−	0.719594i	$-0.255672\pi$
$32$			1.00000i			0.176777i
$33$	−1.07694	−	0.365374i	−0.187471	−	0.0636035i
$34$	5.83577	+	3.36928i	1.00083	+	0.577828i
$35$	2.46207	−	0.968625i	0.416165	−	0.163728i
$36$	0.390607	−	2.97446i	0.0651012	−	0.495744i
$37$	1.05061	+	1.81971i	0.172719	+	0.299158i	0.939369	−	0.342907i	$-0.111411\pi$
$37$	1.05061	+	1.81971i	0.172719	+	0.299158i	−0.766651	+	0.642065i	$0.778078\pi$
$38$	−0.365816	−	0.633612i	−0.0593432	−	0.102785i
$39$	4.53523	+	1.53868i	0.726217	+	0.246385i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	3.35799	+	5.81621i	0.524430	+	0.908339i	0.999595	+	0.0284427i	$0.00905482\pi$
$41$	3.35799	+	5.81621i	0.524430	+	0.908339i	−0.475166	+	0.879896i	$0.657612\pi$
$42$	4.57736	−	0.218666i	0.706301	−	0.0337409i
$43$	6.29106	−	10.8964i	0.959378	−	1.66169i	0.235364	−	0.971907i	$-0.424372\pi$
$43$	6.29106	−	10.8964i	0.959378	−	1.66169i	0.724015	−	0.689785i	$-0.242295\pi$
$44$	−0.568614	+	0.328290i	−0.0857219	+	0.0494915i
$45$	2.38066	+	1.82551i	0.354887	+	0.272131i
$46$	−3.60043	+	6.23613i	−0.530854	+	0.919467i
$47$	5.85866			0.854573			0.427286	−	0.904116i	$-0.359470\pi$
$47$	5.85866			0.854573			0.427286	+	0.904116i	$0.359470\pi$
$48$	−1.14223	−	1.30204i	−0.164867	−	0.187933i
$49$	1.56886	+	6.82193i	0.224123	+	0.974561i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−11.4469	+	2.27887i	−1.60289	+	0.319106i
$52$	2.39457	−	1.38250i	0.332067	−	0.191719i
$53$	5.77309	+	3.33309i	0.792994	+	0.457835i	0.841016	−	0.541011i	$-0.181958\pi$
$53$	5.77309	+	3.33309i	0.792994	+	0.457835i	−0.0480213	+	0.998846i	$0.515292\pi$
$54$	2.88894	+	4.31903i	0.393135	+	0.587745i
$55$		−	0.656579i		−	0.0885332i
$56$	1.64790	−	2.06989i	0.220210	−	0.276600i
$57$	1.20004	+	0.407140i	0.158949	+	0.0539270i
$58$	−3.58664	+	6.21225i	−0.470949	+	0.815708i
$59$	−9.25800			−1.20529			−0.602645	−	0.798010i	$-0.705886\pi$
$59$	−9.25800			−1.20529			−0.602645	+	0.798010i	$0.705886\pi$
$60$	1.69871	−	0.338184i	0.219303	−	0.0436593i
$61$		−	1.56571i		−	0.200469i	−0.994964	−	0.100234i	$-0.968041\pi$
$61$		−	1.56571i		−	0.200469i	0.994964	−	0.100234i	$-0.0319593\pi$
$62$	8.01306			1.01766
$63$	−5.71012	+	5.51312i	−0.719408	+	0.694588i
$64$	−1.00000			−0.125000
$65$			2.76501i			0.342957i
$66$	0.365374	−	1.07694i	0.0449745	−	0.132562i
$67$	−6.56740			−0.802336			−0.401168	−	0.916005i	$-0.631396\pi$
$67$	−6.56740			−0.802336			−0.401168	+	0.916005i	$0.631396\pi$
$68$	−3.36928	+	5.83577i	−0.408586	+	0.707691i
$69$	−2.43521	−	12.2322i	−0.293165	−	1.47258i
$70$	0.968625	+	2.46207i	0.115773	+	0.294273i
$71$		−	1.54080i		−	0.182859i	−0.995812	−	0.0914294i	$-0.970856\pi$
$71$		−	1.54080i		−	0.182859i	0.995812	−	0.0914294i	$-0.0291436\pi$
$72$	2.97446	+	0.390607i	0.350544	+	0.0460335i
$73$	5.95292	+	3.43692i	0.696736	+	0.402261i	0.806131	−	0.591738i	$-0.201558\pi$
$73$	5.95292	+	3.43692i	0.696736	+	0.402261i	−0.109395	+	0.993998i	$0.534891\pi$
$74$	−1.81971	+	1.05061i	−0.211537	+	0.122131i
$75$	−0.556482	+	1.64022i	−0.0642570	+	0.189397i
$76$	0.633612	−	0.365816i	0.0726803	−	0.0419620i
$77$	1.71796	+	0.257496i	0.195779	+	0.0293444i
$78$	−1.53868	+	4.53523i	−0.174221	+	0.513513i
$79$	−15.0706			−1.69558			−0.847790	−	0.530332i	$-0.822067\pi$
$79$	−15.0706			−1.69558			−0.847790	+	0.530332i	$0.822067\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−8.69485	−	2.32369i	−0.966095	−	0.258188i
$82$	−5.81621	+	3.35799i	−0.642293	+	0.370828i
$83$	8.71114	−	15.0881i	0.956172	−	1.65614i	0.224508	−	0.974472i	$-0.427922\pi$
$83$	8.71114	−	15.0881i	0.956172	−	1.65614i	0.731664	−	0.681666i	$-0.238744\pi$
$84$	0.218666	+	4.57736i	0.0238584	+	0.499430i
$85$	−3.36928	−	5.83577i	−0.365450	−	0.632978i
$86$	10.8964	+	6.29106i	1.17499	+	0.678383i
$87$	−2.42589	−	12.1854i	−0.260082	−	1.30641i
$88$	−0.328290	−	0.568614i	−0.0349958	−	0.0606145i
$89$	1.32440	+	2.29393i	0.140386	+	0.243156i	0.927642	−	0.373470i	$-0.121832\pi$
$89$	1.32440	+	2.29393i	0.140386	+	0.243156i	−0.787256	+	0.616627i	$0.788499\pi$
$90$	−1.82551	+	2.38066i	−0.192425	+	0.250943i
$91$	−7.23471	−	1.08438i	−0.758403	−	0.113674i
$92$	−6.23613	−	3.60043i	−0.650161	−	0.375371i
$93$	−10.4333	+	9.15279i	−1.08188	+	0.949100i
$94$			5.85866i			0.604274i
$95$			0.731632i			0.0750639i
$96$	1.30204	−	1.14223i	0.132889	−	0.116579i
$97$	−4.02448	−	2.32353i	−0.408624	−	0.235919i	0.281575	−	0.959539i	$-0.409143\pi$
$97$	−4.02448	−	2.32353i	−0.408624	−	0.235919i	−0.690198	+	0.723620i	$0.742477\pi$
$98$	−6.82193	+	1.56886i	−0.689119	+	0.158479i
$99$	0.754380	+	1.81955i	0.0758181	+	0.182872i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	2.26853	+	3.92921i	0.225727	+	0.390971i	0.956537	−	0.291610i	$-0.0941910\pi$
$101$	2.26853	+	3.92921i	0.225727	+	0.390971i	−0.730810	+	0.682581i	$0.760858\pi$
$102$	−2.27887	−	11.4469i	−0.225642	−	1.13341i
$103$	3.28552	+	1.89690i	0.323732	+	0.186907i	0.653055	−	0.757311i	$-0.273487\pi$
$103$	3.28552	+	1.89690i	0.323732	+	0.186907i	−0.329323	+	0.944217i	$0.606820\pi$
$104$	1.38250	+	2.39457i	0.135566	+	0.234807i
$105$	−4.07344	−	2.09931i	−0.397527	−	0.204871i
$106$	−3.33309	+	5.77309i	−0.323739	+	0.560732i
$107$	−5.69580	+	3.28847i	−0.550634	+	0.317909i	−0.749378	−	0.662143i	$-0.769647\pi$
$107$	−5.69580	+	3.28847i	−0.550634	+	0.317909i	0.198744	+	0.980052i	$0.436314\pi$
$108$	−4.31903	+	2.88894i	−0.415599	+	0.277989i
$109$	−4.84359	+	8.38935i	−0.463932	+	0.803554i	−0.999153	−	0.0411586i	$-0.986895\pi$
$109$	−4.84359	+	8.38935i	−0.463932	+	0.803554i	0.535221	+	0.844712i	$0.320228\pi$
$110$	0.656579			0.0626024
$111$	1.16929	−	3.44646i	0.110984	−	0.327124i
$112$	2.06989	+	1.64790i	0.195586	+	0.155712i
$113$	−10.5658	+	6.10019i	−0.993950	+	0.573857i	−0.906453	−	0.422307i	$-0.861220\pi$
$113$	−10.5658	+	6.10019i	−0.993950	+	0.573857i	−0.0874975	+	0.996165i	$0.527887\pi$
$114$	−0.407140	+	1.20004i	−0.0381322	+	0.112394i
$115$	6.23613	−	3.60043i	0.581522	−	0.335742i
$116$	−6.21225	−	3.58664i	−0.576793	−	0.333011i
$117$	−3.17687	−	7.66256i	−0.293702	−	0.708404i
$118$		−	9.25800i		−	0.852268i
$119$	16.5908	−	6.52715i	1.52088	−	0.598343i
$120$	0.338184	+	1.69871i	0.0308718	+	0.155071i
$121$	−5.28445	+	9.15294i	−0.480405	+	0.832085i
$122$	1.56571			0.141753
$123$	3.73732	−	11.0157i	0.336983	−	0.993252i
$124$			8.01306i			0.719594i
$125$	−1.00000			−0.0894427
$126$	−5.51312	−	5.71012i	−0.491148	−	0.508698i
$127$	2.97414			0.263912			0.131956	−	0.991256i	$-0.457874\pi$
$127$	2.97414			0.263912			0.131956	+	0.991256i	$0.457874\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−21.3734	+	4.25507i	−1.88183	+	0.374638i
$130$	−2.76501			−0.242507
$131$	4.65849	−	8.06874i	0.407014	−	0.704969i	−0.587540	−	0.809195i	$-0.699903\pi$
$131$	4.65849	−	8.06874i	0.407014	−	0.704969i	0.994554	+	0.104226i	$0.0332367\pi$
$132$	1.07694	+	0.365374i	0.0937353	+	0.0318018i
$133$	−1.91433	−	0.286931i	−0.165994	−	0.0248800i
$134$		−	6.56740i		−	0.567337i
$135$	−0.342384	−	5.18486i	−0.0294678	−	0.446242i
$136$	−5.83577	−	3.36928i	−0.500413	−	0.288914i
$137$	14.8086	−	8.54973i	1.26518	−	0.730453i	0.291109	−	0.956690i	$-0.405976\pi$
$137$	14.8086	−	8.54973i	1.26518	−	0.730453i	0.974072	+	0.226237i	$0.0726424\pi$
$138$	12.2322	−	2.43521i	1.04127	−	0.207299i
$139$	−12.6560	+	7.30697i	−1.07347	+	0.619769i	−0.929128	−	0.369759i	$-0.879440\pi$
$139$	−12.6560	+	7.30697i	−1.07347	+	0.619769i	−0.144343	+	0.989528i	$0.546107\pi$
$140$	−2.46207	+	0.968625i	−0.208082	+	0.0818638i
$141$	−6.69195	−	7.62819i	−0.563564	−	0.642410i
$142$	1.54080			0.129301
$143$	−0.907724	+	1.57222i	−0.0759077	+	0.131476i
$144$	−0.390607	+	2.97446i	−0.0325506	+	0.247872i
$145$	6.21225	−	3.58664i	0.515899	−	0.297854i
$146$	−3.43692	+	5.95292i	−0.284441	+	0.492667i
$147$	7.09040	−	9.83495i	0.584807	−	0.811173i
$148$	−1.05061	−	1.81971i	−0.0863595	−	0.149579i
$149$	−7.54707	−	4.35730i	−0.618280	−	0.356964i	0.157919	−	0.987452i	$-0.449521\pi$
$149$	−7.54707	−	4.35730i	−0.618280	−	0.356964i	−0.776199	+	0.630488i	$0.782855\pi$
$150$	−1.64022	−	0.556482i	−0.133924	−	0.0454365i
$151$	4.31171	+	7.46809i	0.350882	+	0.607745i	0.986404	−	0.164337i	$-0.0525486\pi$
$151$	4.31171	+	7.46809i	0.350882	+	0.607745i	−0.635522	+	0.772082i	$0.719215\pi$
$152$	0.365816	+	0.633612i	0.0296716	+	0.0513927i
$153$	16.0422	+	12.3013i	1.29694	+	0.994502i
$154$	−0.257496	+	1.71796i	−0.0207496	+	0.138437i
$155$	−6.93952	−	4.00653i	−0.557395	−	0.321812i
$156$	−4.53523	−	1.53868i	−0.363109	−	0.123193i
$157$			16.1434i			1.28839i	0.764863	+	0.644193i	$0.222806\pi$
$157$			16.1434i			1.28839i	−0.764863	+	0.644193i	$0.777194\pi$
$158$		−	15.0706i		−	1.19896i
$159$	−2.25440	−	11.3239i	−0.178785	−	0.898047i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	6.97493	+	17.7290i	0.549702	+	1.39724i
$162$	2.32369	−	8.69485i	0.182567	−	0.683132i
$163$	−1.04426	−	1.80871i	−0.0817928	−	0.141669i	0.822227	−	0.569159i	$-0.192731\pi$
$163$	−1.04426	−	1.80871i	−0.0817928	−	0.141669i	−0.904020	+	0.427490i	$0.859398\pi$
$164$	−3.35799	−	5.81621i	−0.262215	−	0.454170i
$165$	−0.854892	+	0.749967i	−0.0665532	+	0.0583848i
$166$	15.0881	+	8.71114i	1.17107	+	0.676116i
$167$	3.73797	+	6.47435i	0.289253	+	0.501001i	0.973632	−	0.228126i	$-0.0732598\pi$
$167$	3.73797	+	6.47435i	0.289253	+	0.501001i	−0.684379	+	0.729127i	$0.739927\pi$
$168$	−4.57736	+	0.218666i	−0.353151	+	0.0168705i
$169$	−2.67737	+	4.63733i	−0.205951	+	0.356718i
$170$	5.83577	−	3.36928i	0.447583	−	0.258412i
$171$	−0.840613	−	2.02755i	−0.0642833	−	0.155050i
$172$	−6.29106	+	10.8964i	−0.479689	+	0.830846i
$173$	−17.9027			−1.36112			−0.680559	−	0.732693i	$-0.738263\pi$
$173$	−17.9027			−1.36112			−0.680559	+	0.732693i	$0.738263\pi$
$174$	12.1854	−	2.42589i	0.923770	−	0.183906i
$175$	0.392179	−	2.61652i	0.0296459	−	0.197791i
$176$	0.568614	−	0.328290i	0.0428609	−	0.0247458i
$177$	10.5748	+	12.0543i	0.794850	+	0.906055i
$178$	−2.29393	+	1.32440i	−0.171937	+	0.0992681i
$179$	−8.68355	−	5.01345i	−0.649039	−	0.374723i	0.139049	−	0.990286i	$-0.455595\pi$
$179$	−8.68355	−	5.01345i	−0.649039	−	0.374723i	−0.788088	+	0.615563i	$0.788929\pi$
$180$	−2.38066	−	1.82551i	−0.177444	−	0.136065i
$181$		−	8.57389i		−	0.637292i	−0.947874	−	0.318646i	$-0.896772\pi$
$181$		−	8.57389i		−	0.637292i	0.947874	−	0.318646i	$-0.103228\pi$
$182$	1.08438	−	7.23471i	0.0803793	−	0.536272i
$183$	−2.03862	+	1.78841i	−0.150699	+	0.132203i
$184$	3.60043	−	6.23613i	0.265427	−	0.459733i
$185$	2.10122			0.154484
$186$	−9.15279	−	10.4333i	−0.671115	−	0.765008i
$187$		−	4.42441i		−	0.323545i
$188$	−5.85866			−0.427286
$189$	13.7006	+	1.13753i	0.996571	+	0.0827434i
$190$	−0.731632			−0.0530782
$191$			10.7152i			0.775326i	0.921801	+	0.387663i	$0.126718\pi$
$191$			10.7152i			0.775326i	−0.921801	+	0.387663i	$0.873282\pi$
$192$	1.14223	+	1.30204i	0.0824336	+	0.0939665i
$193$	−1.23612			−0.0889782			−0.0444891	−	0.999010i	$-0.514166\pi$
$193$	−1.23612			−0.0889782			−0.0444891	+	0.999010i	$0.514166\pi$
$194$	2.32353	−	4.02448i	0.166820	−	0.288941i
$195$	3.60015	−	3.15828i	0.257812	−	0.226169i
$196$	−1.56886	−	6.82193i	−0.112062	−	0.487280i
$197$		−	15.5323i		−	1.10663i	−0.832972	−	0.553315i	$-0.813363\pi$
$197$		−	15.5323i		−	1.10663i	0.832972	−	0.553315i	$-0.186637\pi$
$198$	−1.81955	+	0.754380i	−0.129310	+	0.0536115i
$199$	14.8736	+	8.58726i	1.05436	+	0.608735i	0.923867	−	0.382715i	$-0.125011\pi$
$199$	14.8736	+	8.58726i	1.05436	+	0.608735i	0.130493	+	0.991449i	$0.458344\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	7.50150	+	8.55101i	0.529115	+	0.603142i
$202$	−3.92921	+	2.26853i	−0.276458	+	0.159613i
$203$	6.94822	+	17.6611i	0.487670	+	1.23957i
$204$	11.4469	−	2.27887i	0.801444	−	0.159553i
$205$	6.71598			0.469064
$206$	−1.89690	+	3.28552i	−0.132163	+	0.228913i
$207$	−13.1452	+	17.1428i	−0.913656	+	1.19150i
$208$	−2.39457	+	1.38250i	−0.166033	+	0.0958594i
$209$	−0.240187	+	0.416017i	−0.0166141	+	0.0287765i
$210$	2.09931	−	4.07344i	0.144866	−	0.281094i
$211$	−11.1982	−	19.3958i	−0.770913	−	1.33526i	−0.937063	−	0.349160i	$-0.886467\pi$
$211$	−11.1982	−	19.3958i	−0.770913	−	1.33526i	0.166150	−	0.986100i	$-0.446866\pi$
$212$	−5.77309	−	3.33309i	−0.396497	−	0.228918i
$213$	−2.00618	+	1.75995i	−0.137461	+	0.120590i
$214$	−3.28847	−	5.69580i	−0.224795	−	0.389357i
$215$	−6.29106	−	10.8964i	−0.429047	−	0.743131i
$216$	−2.88894	−	4.31903i	−0.196568	−	0.293873i
$217$	13.2047	−	16.5861i	0.896395	−	1.12594i
$218$	−8.38935	−	4.84359i	−0.568198	−	0.328049i
$219$	−2.32462	−	11.6767i	−0.157083	−	0.789037i
$220$			0.656579i			0.0442666i
$221$			18.6322i			1.25334i
$222$	3.44646	+	1.16929i	0.231311	+	0.0784775i
$223$	2.68635	+	1.55096i	0.179891	+	0.103860i	0.587241	−	0.809412i	$-0.300214\pi$
$223$	2.68635	+	1.55096i	0.179891	+	0.103860i	−0.407350	+	0.913272i	$0.633547\pi$
$224$	−1.64790	+	2.06989i	−0.110105	+	0.138300i
$225$	2.77126	−	1.14896i	0.184751	−	0.0765970i
$226$	−6.10019	−	10.5658i	−0.405778	−	0.702829i
$227$	−14.4824	−	25.0842i	−0.961229	−	1.66490i	−0.719422	−	0.694573i	$-0.755593\pi$
$227$	−14.4824	−	25.0842i	−0.961229	−	1.66490i	−0.241807	−	0.970324i	$-0.577740\pi$
$228$	−1.20004	−	0.407140i	−0.0794746	−	0.0269635i
$229$	−22.7549	−	13.1376i	−1.50369	−	0.868154i	−0.999991	−	0.00427312i	$-0.998640\pi$
$229$	−22.7549	−	13.1376i	−1.50369	−	0.868154i	−0.503696	−	0.863881i	$-0.668027\pi$
$230$	3.60043	+	6.23613i	0.237405	+	0.411198i
$231$	−1.62704	−	2.53096i	−0.107051	−	0.166525i
$232$	3.58664	−	6.21225i	0.235475	−	0.407854i
$233$	−4.26732	+	2.46374i	−0.279562	+	0.161405i	−0.633225	−	0.773968i	$-0.718269\pi$
$233$	−4.26732	+	2.46374i	−0.279562	+	0.161405i	0.353663	+	0.935373i	$0.384936\pi$
$234$	7.66256	−	3.17687i	0.500918	−	0.207679i
$235$	2.92933	−	5.07374i	0.191088	−	0.330975i
$236$	9.25800			0.602645
$237$	17.2142	+	19.6226i	1.11818	+	1.27462i
$238$	6.52715	+	16.5908i	0.423092	+	1.07542i
$239$	−13.4424	+	7.76099i	−0.869518	+	0.502016i	−0.867188	−	0.497981i	$-0.834075\pi$
$239$	−13.4424	+	7.76099i	−0.869518	+	0.502016i	−0.00232989	+	0.999997i	$0.500742\pi$
$240$	−1.69871	+	0.338184i	−0.109652	+	0.0218297i
$241$	9.15179	−	5.28379i	0.589519	−	0.340359i	−0.175389	−	0.984499i	$-0.556118\pi$
$241$	9.15179	−	5.28379i	0.589519	−	0.340359i	0.764907	+	0.644141i	$0.222785\pi$
$242$	−9.15294	−	5.28445i	−0.588373	−	0.339697i
$243$	6.90601	+	13.9752i	0.443021	+	0.896511i
$244$			1.56571i			0.100234i
$245$	6.69239	+	2.05229i	0.427561	+	0.131116i
$246$	11.0157	+	3.73732i	0.702335	+	0.238283i
$247$	1.01148	−	1.75194i	0.0643592	−	0.111473i
$248$	−8.01306			−0.508830
$249$	−29.5955	+	5.89193i	−1.87554	+	0.373386i
$250$		−	1.00000i		−	0.0632456i
$251$	−1.92533			−0.121526			−0.0607630	−	0.998152i	$-0.519353\pi$
$251$	−1.92533			−0.121526			−0.0607630	+	0.998152i	$0.519353\pi$
$252$	5.71012	−	5.51312i	0.359704	−	0.347294i
$253$	4.72793			0.297243
$254$			2.97414i			0.186614i
$255$	−3.74989	+	11.0528i	−0.234827	+	0.692150i
$256$	1.00000			0.0625000
$257$	−1.77121	+	3.06783i	−0.110485	+	0.191366i	−0.915966	−	0.401256i	$-0.868574\pi$
$257$	−1.77121	+	3.06783i	−0.110485	+	0.191366i	0.805481	+	0.592622i	$0.201907\pi$
$258$	−4.25507	−	21.3734i	−0.264909	−	1.33065i
$259$	−0.824052	+	5.49788i	−0.0512041	+	0.341622i
$260$		−	2.76501i		−	0.171478i
$261$	−13.0949	+	17.0771i	−0.810553	+	1.05705i
$262$	8.06874	+	4.65849i	0.498488	+	0.287802i
$263$	8.24353	−	4.75941i	0.508318	−	0.293477i	−0.223824	−	0.974630i	$-0.571854\pi$
$263$	8.24353	−	4.75941i	0.508318	−	0.293477i	0.732142	+	0.681152i	$0.238521\pi$
$264$	−0.365374	+	1.07694i	−0.0224872	+	0.0662808i
$265$	5.77309	−	3.33309i	0.354638	−	0.204750i
$266$	0.286931	−	1.91433i	0.0175928	−	0.117375i
$267$	1.47401	−	4.34463i	0.0902080	−	0.265887i
$268$	6.56740			0.401168
$269$	−1.90191	+	3.29420i	−0.115961	+	0.200851i	−0.918164	−	0.396201i	$-0.870328\pi$
$269$	−1.90191	+	3.29420i	−0.115961	+	0.200851i	0.802202	+	0.597052i	$0.203662\pi$
$270$	5.18486	−	0.342384i	0.315541	−	0.0208368i
$271$	−1.08398	+	0.625837i	−0.0658472	+	0.0380169i	−0.532562	−	0.846391i	$-0.678771\pi$
$271$	−1.08398	+	0.625837i	−0.0658472	+	0.0380169i	0.466715	+	0.884408i	$0.345437\pi$
$272$	3.36928	−	5.83577i	0.204293	−	0.353846i
$273$	6.85182	+	10.6585i	0.414691	+	0.645080i
$274$	8.54973	+	14.8086i	0.516508	+	0.894618i
$275$	−0.568614	−	0.328290i	−0.0342887	−	0.0197966i
$276$	2.43521	+	12.2322i	0.146583	+	0.736292i
$277$	7.52096	+	13.0267i	0.451891	+	0.782698i	0.998504	−	0.0546878i	$-0.0174164\pi$
$277$	7.52096	+	13.0267i	0.451891	+	0.782698i	−0.546613	+	0.837385i	$0.684083\pi$
$278$	−7.30697	−	12.6560i	−0.438243	−	0.759059i
$279$	23.8346	+	3.12996i	1.42694	+	0.187386i
$280$	−0.968625	−	2.46207i	−0.0578864	−	0.147137i
$281$	27.1483	+	15.6741i	1.61953	+	0.935038i	0.987041	+	0.160471i	$0.0513012\pi$
$281$	27.1483	+	15.6741i	1.61953	+	0.935038i	0.632492	+	0.774567i	$0.282032\pi$
$282$	7.62819	−	6.69195i	0.454252	−	0.398500i
$283$			21.1008i			1.25431i	0.778893	+	0.627157i	$0.215781\pi$
$283$			21.1008i			1.25431i	−0.778893	+	0.627157i	$0.784219\pi$
$284$			1.54080i			0.0914294i
$285$	0.952613	−	0.835695i	0.0564279	−	0.0495023i
$286$	−1.57222	−	0.907724i	−0.0929675	−	0.0536748i
$287$	−2.63386	+	17.5725i	−0.155472	+	1.03727i
$288$	−2.97446	−	0.390607i	−0.175272	−	0.0230168i
$289$	−14.2042	−	24.6023i	−0.835539	−	1.44720i
$290$	3.58664	+	6.21225i	0.210615	+	0.364796i
$291$	1.57156	+	7.89404i	0.0921266	+	0.462757i
$292$	−5.95292	−	3.43692i	−0.348368	−	0.201130i
$293$	6.76886	+	11.7240i	0.395441	+	0.684924i	0.993157	−	0.116784i	$-0.0372584\pi$
$293$	6.76886	+	11.7240i	0.395441	+	0.684924i	−0.597716	+	0.801708i	$0.703925\pi$
$294$	9.83495	+	7.09040i	0.573586	+	0.413521i
$295$	−4.62900	+	8.01766i	−0.269511	+	0.466806i
$296$	1.81971	−	1.05061i	0.105768	−	0.0610654i
$297$	1.50745	−	3.06059i	0.0874712	−	0.177593i
$298$	4.35730	−	7.54707i	0.252412	−	0.437190i
$299$	−19.9104			−1.15145
$300$	0.556482	−	1.64022i	0.0321285	−	0.0946983i
$301$	30.9780	−	12.1874i	1.78554	−	0.702468i
$302$	−7.46809	+	4.31171i	−0.429741	+	0.248111i
$303$	2.52479	−	7.44178i	0.145045	−	0.427519i
$304$	−0.633612	+	0.365816i	−0.0363402	+	0.0209810i
$305$	−1.35595	−	0.782856i	−0.0776412	−	0.0448262i
$306$	−12.3013	+	16.0422i	−0.703219	+	0.917073i
$307$			14.6424i			0.835688i	0.908519	+	0.417844i	$0.137214\pi$
$307$			14.6424i			0.835688i	−0.908519	+	0.417844i	$0.862786\pi$
$308$	−1.71796	−	0.257496i	−0.0978896	−	0.0146722i
$309$	−1.28300	−	6.44457i	−0.0729873	−	0.366619i
$310$	4.00653	−	6.93952i	0.227556	−	0.394138i
$311$	−4.81516			−0.273043			−0.136521	−	0.990637i	$-0.543592\pi$
$311$	−4.81516			−0.273043			−0.136521	+	0.990637i	$0.543592\pi$
$312$	1.53868	−	4.53523i	0.0871104	−	0.256757i
$313$			7.23831i			0.409134i	0.978853	+	0.204567i	$0.0655786\pi$
$313$			7.23831i			0.409134i	−0.978853	+	0.204567i	$0.934421\pi$
$314$	−16.1434			−0.911026
$315$	1.91944	+	7.70167i	0.108148	+	0.433940i
$316$	15.0706			0.847790
$317$			3.73823i			0.209960i	0.994474	+	0.104980i	$0.0334779\pi$
$317$			3.73823i			0.209960i	−0.994474	+	0.104980i	$0.966522\pi$
$318$	11.3239	−	2.25440i	0.635015	−	0.126420i
$319$	4.70983			0.263700
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	10.7877	+	3.65995i	0.602108	+	0.204279i
$322$	−17.7290	+	6.97493i	−0.987997	+	0.388698i
$323$			4.93016i			0.274321i
$324$	8.69485	+	2.32369i	0.483047	+	0.129094i
$325$	2.39457	+	1.38250i	0.132827	+	0.0766875i
$326$	1.80871	−	1.04426i	0.100175	−	0.0578363i
$327$	16.4558	−	3.27605i	0.910006	−	0.181166i
$328$	5.81621	−	3.35799i	0.321146	−	0.185414i
$329$	12.1268	+	9.65447i	0.668570	+	0.532268i
$330$	−0.749967	−	0.854892i	−0.0412843	−	0.0470602i
$331$	−4.80118			−0.263896			−0.131948	−	0.991257i	$-0.542123\pi$
$331$	−4.80118			−0.263896			−0.131948	+	0.991257i	$0.542123\pi$
$332$	−8.71114	+	15.0881i	−0.478086	+	0.828069i
$333$	−5.82302	+	2.41420i	−0.319100	+	0.132298i
$334$	−6.47435	+	3.73797i	−0.354261	+	0.204533i
$335$	−3.28370	+	5.68754i	−0.179408	+	0.310743i
$336$	−0.218666	−	4.57736i	−0.0119292	−	0.249715i
$337$	−12.0518	−	20.8744i	−0.656505	−	1.13710i	−0.981514	−	0.191389i	$-0.938701\pi$
$337$	−12.0518	−	20.8744i	−0.656505	−	1.13710i	0.325009	−	0.945711i	$-0.394633\pi$
$338$	−4.63733	−	2.67737i	−0.252238	−	0.145630i
$339$	20.0113	+	6.78929i	1.08687	+	0.368743i
$340$	3.36928	+	5.83577i	0.182725	+	0.316489i
$341$	−2.63061	−	4.55634i	−0.142455	−	0.246740i
$342$	2.02755	−	0.840613i	0.109637	−	0.0454551i
$343$	−7.99448	+	16.7059i	−0.431661	+	0.902036i
$344$	−10.8964	−	6.29106i	−0.587497	−	0.339191i
$345$	−11.8110	−	4.00715i	−0.635883	−	0.215737i
$346$		−	17.9027i		−	0.962455i
$347$		−	21.6900i		−	1.16438i	−0.813053	−	0.582190i	$-0.802196\pi$
$347$		−	21.6900i		−	1.16438i	0.813053	−	0.582190i	$-0.197804\pi$
$348$	2.42589	+	12.1854i	0.130041	+	0.653204i
$349$	−16.3083	−	9.41562i	−0.872965	−	0.504007i	−0.00463264	−	0.999989i	$-0.501475\pi$
$349$	−16.3083	−	9.41562i	−0.872965	−	0.504007i	−0.868332	+	0.495983i	$0.834808\pi$
$350$	2.61652	+	0.392179i	0.139859	+	0.0209628i
$351$	−6.34823	+	12.8888i	−0.338843	+	0.687955i
$352$	0.328290	+	0.568614i	0.0174979	+	0.0303073i
$353$	−4.77214	−	8.26558i	−0.253995	−	0.439933i	0.710627	−	0.703569i	$-0.248411\pi$
$353$	−4.77214	−	8.26558i	−0.253995	−	0.439933i	−0.964622	+	0.263636i	$0.915078\pi$
$354$	−12.0543	+	10.5748i	−0.640677	+	0.562044i
$355$	−1.33437	−	0.770398i	−0.0708209	−	0.0408885i
$356$	−1.32440	−	2.29393i	−0.0701932	−	0.121578i
$357$	−27.4492	−	14.1463i	−1.45276	−	0.748703i
$358$	5.01345	−	8.68355i	0.264969	−	0.458940i
$359$	8.21398	−	4.74234i	0.433517	−	0.250291i	−0.267327	−	0.963606i	$-0.586140\pi$
$359$	8.21398	−	4.74234i	0.433517	−	0.250291i	0.700844	+	0.713315i	$0.252807\pi$
$360$	1.82551	−	2.38066i	0.0962127	−	0.125472i
$361$	−9.23236	+	15.9909i	−0.485914	+	0.841627i
$362$	8.57389			0.450633
$363$	17.9536	−	3.57423i	0.942317	−	0.187598i
$364$	7.23471	+	1.08438i	0.379202	+	0.0568368i
$365$	5.95292	−	3.43692i	0.311590	−	0.179896i
$366$	−1.78841	−	2.03862i	−0.0934815	−	0.106560i
$367$	0.312821	−	0.180608i	0.0163291	−	0.00942764i	−0.491813	−	0.870701i	$-0.663666\pi$
$367$	0.312821	−	0.180608i	0.0163291	−	0.00942764i	0.508142	+	0.861273i	$0.330332\pi$
$368$	6.23613	+	3.60043i	0.325081	+	0.187685i
$369$	−18.6117	+	7.71636i	−0.968889	+	0.401698i
$370$			2.10122i			0.109237i
$371$	6.45704	+	16.4126i	0.335233	+	0.852099i
$372$	10.4333	−	9.15279i	0.540942	−	0.474550i
$373$	−4.74354	+	8.21606i	−0.245611	+	0.425411i	−0.962303	−	0.271978i	$-0.912322\pi$
$373$	−4.74354	+	8.21606i	−0.245611	+	0.425411i	0.716692	+	0.697390i	$0.245655\pi$
$374$	4.42441			0.228781
$375$	1.14223	+	1.30204i	0.0589847	+	0.0672370i
$376$		−	5.85866i		−	0.302137i
$377$	−19.8342			−1.02151
$378$	−1.13753	+	13.7006i	−0.0585084	+	0.704682i
$379$	30.4526			1.56424			0.782122	−	0.623125i	$-0.214137\pi$
$379$	30.4526			1.56424			0.782122	+	0.623125i	$0.214137\pi$
$380$		−	0.731632i		−	0.0375319i
$381$	−3.39716	−	3.87244i	−0.174042	−	0.198391i
$382$	−10.7152			−0.548238
$383$	10.5388	−	18.2537i	0.538505	−	0.932718i	−0.460480	−	0.887670i	$-0.652323\pi$
$383$	10.5388	−	18.2537i	0.538505	−	0.932718i	0.998985	−	0.0450480i	$-0.0143441\pi$
$384$	−1.30204	+	1.14223i	−0.0664444	+	0.0582893i
$385$	1.08198	−	1.35905i	0.0551426	−	0.0692633i
$386$		−	1.23612i		−	0.0629171i
$387$	29.9537	+	22.9688i	1.52263	+	1.16757i
$388$	4.02448	+	2.32353i	0.204312	+	0.117960i
$389$	26.6991	−	15.4147i	1.35370	−	0.781557i	0.364931	−	0.931035i	$-0.381093\pi$
$389$	26.6991	−	15.4147i	1.35370	−	0.781557i	0.988765	+	0.149478i	$0.0477592\pi$
$390$	3.15828	+	3.60015i	0.159926	+	0.182300i
$391$	42.0226	−	24.2617i	2.12517	−	1.22697i
$392$	6.82193	−	1.56886i	0.344559	−	0.0792395i
$393$	−15.8269	+	3.15085i	−0.798361	+	0.158939i
$394$	15.5323			0.782505
$395$	−7.53532	+	13.0516i	−0.379143	+	0.656696i
$396$	−0.754380	−	1.81955i	−0.0379090	−	0.0914361i
$397$	12.1734	−	7.02834i	0.610968	−	0.352742i	−0.162376	−	0.986729i	$-0.551916\pi$
$397$	12.1734	−	7.02834i	0.610968	−	0.352742i	0.773344	+	0.633987i	$0.218583\pi$
$398$	−8.58726	+	14.8736i	−0.430440	+	0.745545i
$399$	1.81302	+	2.82028i	0.0907645	+	0.141190i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	29.4253	+	16.9887i	1.46943	+	0.848374i	0.999412	−	0.0342842i	$-0.0109151\pi$
$401$	29.4253	+	16.9887i	1.46943	+	0.848374i	0.470015	+	0.882658i	$0.344248\pi$
$402$	−8.55101	+	7.50150i	−0.426486	+	0.374141i
$403$	11.0781	+	19.1878i	0.551839	+	0.955813i
$404$	−2.26853	−	3.92921i	−0.112863	−	0.195485i
$405$	−6.35980	+	6.36812i	−0.316021	+	0.316434i
$406$	−17.6611	+	6.94822i	−0.876505	+	0.344835i
$407$	1.19478	+	0.689808i	0.0592231	+	0.0341925i
$408$	2.27887	+	11.4469i	0.112821	+	0.566706i
$409$			11.4908i			0.568185i	0.958797	+	0.284093i	$0.0916924\pi$
$409$			11.4908i			0.568185i	−0.958797	+	0.284093i	$0.908308\pi$
$410$			6.71598i			0.331679i
$411$	−28.0469	−	9.51554i	−1.38345	−	0.469367i
$412$	−3.28552	−	1.89690i	−0.161866	−	0.0934534i
$413$	−19.1630	−	15.2562i	−0.942950	−	0.750711i
$414$	−17.1428	−	13.1452i	−0.842521	−	0.646052i
$415$	−8.71114	−	15.0881i	−0.427613	−	0.740647i
$416$	−1.38250	−	2.39457i	−0.0677828	−	0.117403i
$417$	23.9701	+	8.13239i	1.17382	+	0.398245i
$418$	−0.416017	−	0.240187i	−0.0203480	−	0.0117479i
$419$	−14.4601	−	25.0456i	−0.706421	−	1.22356i	−0.966176	−	0.257883i	$-0.916975\pi$
$419$	−14.4601	−	25.0456i	−0.706421	−	1.22356i	0.259755	−	0.965675i	$-0.416358\pi$
$420$	4.07344	+	2.09931i	0.198763	+	0.102436i
$421$	−0.473626	+	0.820343i	−0.0230831	+	0.0399811i	−0.877336	−	0.479876i	$-0.840682\pi$
$421$	−0.473626	+	0.820343i	−0.0230831	+	0.0399811i	0.854253	+	0.519857i	$0.174015\pi$
$422$	19.3958	−	11.1982i	0.944172	−	0.545118i
$423$	−2.28843	+	17.4264i	−0.111267	+	0.847298i
$424$	3.33309	−	5.77309i	0.161869	−	0.280366i
$425$	−6.73857			−0.326869
$426$	−1.75995	−	2.00618i	−0.0852698	−	0.0971995i
$427$	2.58013	−	3.24085i	0.124861	−	0.156835i
$428$	5.69580	−	3.28847i	0.275317	−	0.158954i
$429$	3.08393	−	0.613955i	0.148893	−	0.0296420i
$430$	10.8964	−	6.29106i	0.525473	−	0.303382i
$431$	10.1746	+	5.87431i	0.490094	+	0.282956i	0.724613	−	0.689156i	$-0.242018\pi$
$431$	10.1746	+	5.87431i	0.490094	+	0.282956i	−0.234520	+	0.972111i	$0.575352\pi$
$432$	4.31903	−	2.88894i	0.207799	−	0.138994i
$433$		−	31.4858i		−	1.51311i	−0.653930	−	0.756555i	$-0.726881\pi$
$433$		−	31.4858i		−	1.51311i	0.653930	−	0.756555i	$-0.273119\pi$
$434$	16.5861	+	13.2047i	0.796160	+	0.633847i
$435$	−11.7658	−	3.99180i	−0.564126	−	0.191392i
$436$	4.84359	−	8.38935i	0.231966	−	0.401777i
$437$	−5.26838			−0.252021
$438$	11.6767	−	2.32462i	0.557934	−	0.111075i
$439$		−	28.6453i		−	1.36717i	−0.729872	−	0.683583i	$-0.760421\pi$
$439$		−	28.6453i		−	1.36717i	0.729872	−	0.683583i	$-0.239579\pi$
$440$	−0.656579			−0.0313012
$441$	−20.9044	+	2.00183i	−0.995446	+	0.0953250i
$442$	−18.6322			−0.886243
$443$			12.6900i			0.602920i	0.953479	+	0.301460i	$0.0974740\pi$
$443$			12.6900i			0.602920i	−0.953479	+	0.301460i	$0.902526\pi$
$444$	−1.16929	+	3.44646i	−0.0554920	+	0.163562i
$445$	2.64880			0.125565
$446$	−1.55096	+	2.68635i	−0.0734402	+	0.127202i
$447$	2.94714	+	14.8036i	0.139395	+	0.700188i
$448$	−2.06989	−	1.64790i	−0.0977930	−	0.0778559i
$449$		−	3.80547i		−	0.179591i	−0.995960	−	0.0897956i	$-0.971379\pi$
$449$		−	3.80547i		−	0.179591i	0.995960	−	0.0897956i	$-0.0286214\pi$
$450$	1.14896	+	2.77126i	0.0541623	+	0.130639i
$451$	3.81880	+	2.20479i	0.179820	+	0.103819i
$452$	10.5658	−	6.10019i	0.496975	−	0.286929i
$453$	4.79877	−	14.1443i	0.225466	−	0.664558i
$454$	25.0842	−	14.4824i	1.17726	−	0.679692i
$455$	−4.55645	+	5.72325i	−0.213610	+	0.268310i
$456$	0.407140	−	1.20004i	0.0190661	−	0.0561970i
$457$	−40.3773			−1.88877			−0.944386	−	0.328840i	$-0.893342\pi$
$457$	−40.3773			−1.88877			−0.944386	+	0.328840i	$0.893342\pi$
$458$	13.1376	−	22.7549i	0.613878	−	1.06327i
$459$	−2.30718	−	34.9385i	−0.107690	−	1.63079i
$460$	−6.23613	+	3.60043i	−0.290761	+	0.167871i
$461$	−7.52397	+	13.0319i	−0.350426	+	0.606956i	−0.986324	−	0.164817i	$-0.947297\pi$
$461$	−7.52397	+	13.0319i	−0.350426	+	0.606956i	0.635898	+	0.771773i	$0.280630\pi$
$462$	2.53096	−	1.62704i	0.117751	−	0.0756965i
$463$	−12.4404	−	21.5474i	−0.578156	−	1.00139i	−0.995691	−	0.0927341i	$-0.970439\pi$
$463$	−12.4404	−	21.5474i	−0.578156	−	1.00139i	0.417535	−	0.908661i	$-0.362894\pi$
$464$	6.21225	+	3.58664i	0.288396	+	0.166506i
$465$	2.70989	+	13.6119i	0.125668	+	0.631237i
$466$	−2.46374	−	4.26732i	−0.114131	−	0.197680i
$467$	−17.4957	−	30.3035i	−0.809605	−	1.40228i	−0.913138	−	0.407651i	$-0.866348\pi$
$467$	−17.4957	−	30.3035i	−0.809605	−	1.40228i	0.103533	−	0.994626i	$-0.466985\pi$
$468$	3.17687	+	7.66256i	0.146851	+	0.354202i
$469$	−13.5938	−	10.8224i	−0.627702	−	0.499733i
$470$	5.07374	+	2.92933i	0.234034	+	0.135120i
$471$	21.0193	−	18.4395i	0.968520	−	0.849649i
$472$			9.25800i			0.426134i
$473$		−	8.26117i		−	0.379849i
$474$	−19.6226	+	17.2142i	−0.901294	+	0.790674i
$475$	0.633612	+	0.365816i	0.0290721	+	0.0167848i
$476$	−16.5908	+	6.52715i	−0.760438	+	0.299171i
$477$	−12.1692	+	15.8699i	−0.557188	+	0.726633i
$478$	−7.76099	−	13.4424i	−0.354979	−	0.614842i
$479$	6.06228	+	10.5002i	0.276993	+	0.479765i	0.970636	−	0.240553i	$-0.0773289\pi$
$479$	6.06228	+	10.5002i	0.276993	+	0.479765i	−0.693643	+	0.720319i	$0.743996\pi$
$480$	−0.338184	−	1.69871i	−0.0154359	−	0.0775354i
$481$	−5.03150	−	2.90494i	−0.229417	−	0.132454i
$482$	5.28379	+	9.15179i	0.240670	+	0.416853i
$483$	15.1168	−	29.3323i	0.687839	−	1.33466i
$484$	5.28445	−	9.15294i	0.240202	−	0.416043i
$485$	−4.02448	+	2.32353i	−0.182742	+	0.105506i
$486$	−13.9752	+	6.90601i	−0.633929	+	0.313263i
$487$	3.55858	−	6.16364i	0.161255	−	0.279301i	−0.774064	−	0.633107i	$-0.781779\pi$
$487$	3.55858	−	6.16364i	0.161255	−	0.279301i	0.935319	+	0.353806i	$0.115113\pi$
$488$	−1.56571			−0.0708764
$489$	−1.16222	+	3.42564i	−0.0525576	+	0.154913i
$490$	−2.05229	+	6.69239i	−0.0927130	+	0.302331i
$491$	16.3865	−	9.46076i	0.739513	−	0.426958i	−0.0823791	−	0.996601i	$-0.526252\pi$
$491$	16.3865	−	9.46076i	0.739513	−	0.426958i	0.821892	+	0.569643i	$0.192919\pi$
$492$	−3.73732	+	11.0157i	−0.168491	+	0.496626i
$493$	41.8617	−	24.1688i	1.88535	−	1.08851i
$494$	1.75194	+	1.01148i	0.0788236	+	0.0455088i
$495$	1.95297	+	0.256465i	0.0877795	+	0.0115272i
$496$		−	8.01306i		−	0.359797i
$497$	2.53908	−	3.18927i	0.113893	−	0.143058i
$498$	−5.89193	−	29.5955i	−0.264024	−	1.32621i
$499$	9.50411	−	16.4616i	0.425463	−	0.736923i	−0.571001	−	0.820949i	$-0.693445\pi$
$499$	9.50411	−	16.4616i	0.425463	−	0.736923i	0.996464	+	0.0840266i	$0.0267781\pi$
$500$	1.00000			0.0447214
$501$	4.16022	−	12.2622i	0.185865	−	0.547835i
$502$		−	1.92533i		−	0.0859318i
$503$	−26.9377			−1.20109			−0.600546	−	0.799590i	$-0.705050\pi$
$503$	−26.9377			−1.20109			−0.600546	+	0.799590i	$0.705050\pi$
$504$	5.51312	+	5.71012i	0.245574	+	0.254349i
$505$	4.53706			0.201896
$506$			4.72793i			0.210182i
$507$	9.09616	−	1.81088i	0.403975	−	0.0804242i
$508$	−2.97414			−0.131956
$509$	−9.65163	+	16.7171i	−0.427801	+	0.740973i	−0.996677	−	0.0814499i	$-0.974045\pi$
$509$	−9.65163	+	16.7171i	−0.427801	+	0.740973i	0.568876	+	0.822423i	$0.307378\pi$
$510$	−11.0528	−	3.74989i	−0.489424	−	0.166048i
$511$	6.65817	+	16.9238i	0.294540	+	0.748666i
$512$			1.00000i			0.0441942i
$513$	−1.67977	+	3.41044i	−0.0741635	+	0.150575i
$514$	−3.06783	−	1.77121i	−0.135316	−	0.0781248i
$515$	3.28552	−	1.89690i	0.144777	−	0.0835873i
$516$	21.3734	−	4.25507i	0.940914	−	0.187319i
$517$	3.33132	−	1.92334i	0.146511	−	0.0845882i
$518$	−5.49788	−	0.824052i	−0.241563	−	0.0362068i
$519$	20.4491	+	23.3100i	0.897614	+	1.02320i
$520$	2.76501			0.121254
$521$	2.29540	−	3.97574i	0.100563	−	0.174180i	−0.811354	−	0.584556i	$-0.801269\pi$
$521$	2.29540	−	3.97574i	0.100563	−	0.174180i	0.911917	+	0.410375i	$0.134602\pi$
$522$	−17.0771	−	13.0949i	−0.747445	−	0.573147i
$523$	−7.54094	+	4.35376i	−0.329742	+	0.190377i	−0.655727	−	0.754998i	$-0.727638\pi$
$523$	−7.54094	+	4.35376i	−0.329742	+	0.190377i	0.325985	+	0.945375i	$0.394304\pi$
$524$	−4.65849	+	8.06874i	−0.203507	+	0.352484i
$525$	−3.85477	+	2.47805i	−0.168236	+	0.108151i
$526$	4.75941	+	8.24353i	0.207520	+	0.359435i
$527$	−46.7624	−	26.9983i	−2.03700	−	1.17606i
$528$	−1.07694	−	0.365374i	−0.0468676	−	0.0159009i
$529$	14.4262	+	24.9869i	0.627225	+	1.08639i
$530$	3.33309	+	5.77309i	0.144780	+	0.250767i
$531$	3.61624	−	27.5376i	0.156932	−	1.19503i
$532$	1.91433	+	0.286931i	0.0829969	+	0.0124400i
$533$	−16.0819	−	9.28487i	−0.696583	−	0.402172i
$534$	4.34463	+	1.47401i	0.188010	+	0.0637867i
$535$			6.57695i			0.284346i
$536$			6.56740i			0.283669i
$537$	3.39093	+	17.0328i	0.146330	+	0.735021i
$538$	−3.29420	−	1.90191i	−0.142023	−	0.0819970i
$539$	3.13165	+	3.36400i	0.134890	+	0.144898i
$540$	0.342384	+	5.18486i	0.0147339	+	0.223121i
$541$	−5.63297	−	9.75660i	−0.242180	−	0.419469i	0.719155	−	0.694850i	$-0.244529\pi$
$541$	−5.63297	−	9.75660i	−0.242180	−	0.419469i	−0.961335	+	0.275381i	$0.911196\pi$
$542$	−0.625837	−	1.08398i	−0.0268820	−	0.0465610i
$543$	−11.1635	+	9.79338i	−0.479073	+	0.420274i
$544$	5.83577	+	3.36928i	0.250207	+	0.144457i
$545$	4.84359	+	8.38935i	0.207477	+	0.359360i
$546$	−10.6585	+	6.85182i	−0.456141	+	0.293231i
$547$	−18.9696	+	32.8563i	−0.811082	+	1.40484i	0.101025	+	0.994884i	$0.467788\pi$
$547$	−18.9696	+	32.8563i	−0.811082	+	1.40484i	−0.912107	+	0.409952i	$0.865546\pi$
$548$	−14.8086	+	8.54973i	−0.632591	+	0.365226i
$549$	4.65715	+	0.611578i	0.198762	+	0.0261015i
$550$	0.328290	−	0.568614i	0.0139983	−	0.0242458i
$551$	−5.24821			−0.223581
$552$	−12.2322	+	2.43521i	−0.520637	+	0.103650i
$553$	−31.1945	−	24.8349i	−1.32653	−	1.05609i
$554$	−13.0267	+	7.52096i	−0.553451	+	0.319535i
$555$	−2.40008	−	2.73586i	−0.101878	−	0.116131i
$556$	12.6560	−	7.30697i	0.536735	−	0.309884i
$557$	−18.9332	−	10.9311i	−0.802224	−	0.463164i	0.0420244	−	0.999117i	$-0.486619\pi$
$557$	−18.9332	−	10.9311i	−0.802224	−	0.463164i	−0.844248	+	0.535952i	$0.819953\pi$
$558$	−3.12996	+	23.8346i	−0.132502	+	1.00900i
$559$			34.7897i			1.47145i
$560$	2.46207	−	0.968625i	0.104041	−	0.0409319i
$561$	−5.76075	+	5.05370i	−0.243219	+	0.213368i
$562$	−15.6741	+	27.1483i	−0.661171	+	1.14518i
$563$	−23.0291			−0.970560			−0.485280	−	0.874359i	$-0.661282\pi$
$563$	−23.0291			−0.970560			−0.485280	+	0.874359i	$0.661282\pi$
$564$	6.69195	+	7.62819i	0.281782	+	0.321205i
$565$			12.2004i			0.513274i
$566$	−21.1008			−0.886934
$567$	−14.1681	−	19.1380i	−0.595006	−	0.803721i
$568$	−1.54080			−0.0646504
$569$		−	21.1650i		−	0.887283i	−0.896204	−	0.443641i	$-0.853686\pi$
$569$		−	21.1650i		−	0.887283i	0.896204	−	0.443641i	$-0.146314\pi$
$570$	0.835695	+	0.952613i	0.0350034	+	0.0399006i
$571$	10.7682			0.450633			0.225317	−	0.974286i	$-0.427658\pi$
$571$	10.7682			0.450633			0.225317	+	0.974286i	$0.427658\pi$
$572$	0.907724	−	1.57222i	0.0379538	−	0.0657380i
$573$	13.9516	−	12.2393i	0.582837	−	0.511303i
$574$	−17.5725	−	2.63386i	−0.733463	−	0.109935i
$575$		−	7.20086i		−	0.300297i
$576$	0.390607	−	2.97446i	0.0162753	−	0.123936i
$577$	10.1757	+	5.87494i	0.423620	+	0.244577i	0.696625	−	0.717436i	$-0.254684\pi$
$577$	10.1757	+	5.87494i	0.423620	+	0.244577i	−0.273005	+	0.962013i	$0.588018\pi$
$578$	24.6023	−	14.2042i	1.02332	−	0.590815i
$579$	1.41194	+	1.60948i	0.0586783	+	0.0668878i
$580$	−6.21225	+	3.58664i	−0.257949	+	0.148927i
$581$	42.8948	−	16.8757i	1.77958	−	0.700120i
$582$	−7.89404	+	1.57156i	−0.327218	+	0.0651433i
$583$	4.37688			0.181272
$584$	3.43692	−	5.95292i	0.142221	−	0.246333i
$585$	−8.22441	−	1.08003i	−0.340038	−	0.0446538i
$586$	−11.7240	+	6.76886i	−0.484315	+	0.279619i
$587$	−12.5348	+	21.7109i	−0.517366	+	0.896105i	0.482430	+	0.875934i	$0.339754\pi$
$587$	−12.5348	+	21.7109i	−0.517366	+	0.896105i	−0.999797	+	0.0201704i	$0.993579\pi$
$588$	−7.09040	+	9.83495i	−0.292403	+	0.405586i
$589$	2.93131	+	5.07718i	0.120782	+	0.209201i
$590$	−8.01766	−	4.62900i	−0.330082	−	0.190573i
$591$	−20.2236	+	17.7415i	−0.831889	+	0.729787i
$592$	1.05061	+	1.81971i	0.0431797	+	0.0747895i
$593$	16.2045	+	28.0670i	0.665438	+	1.15257i	0.979166	+	0.203060i	$0.0650886\pi$
$593$	16.2045	+	28.0670i	0.665438	+	1.15257i	−0.313728	+	0.949513i	$0.601578\pi$
$594$	3.06059	+	1.50745i	0.125577	+	0.0618515i
$595$	2.64272	−	17.6316i	0.108341	−	0.722826i
$596$	7.54707	+	4.35730i	0.309140	+	0.178482i
$597$	−5.80814	−	29.1746i	−0.237711	−	1.19404i
$598$		−	19.9104i		−	0.814198i
$599$			8.59069i			0.351006i	0.984479	+	0.175503i	$0.0561552\pi$
$599$			8.59069i			0.351006i	−0.984479	+	0.175503i	$0.943845\pi$
$600$	1.64022	+	0.556482i	0.0669618	+	0.0227183i
$601$	−28.6965	−	16.5680i	−1.17056	−	0.675821i	−0.216745	−	0.976228i	$-0.569544\pi$
$601$	−28.6965	−	16.5680i	−1.17056	−	0.675821i	−0.953811	+	0.300407i	$0.902877\pi$
$602$	12.1874	+	30.9780i	0.496720	+	1.26257i
$603$	2.56528	−	19.5345i	0.104466	−	0.795506i
$604$	−4.31171	−	7.46809i	−0.175441	−	0.303872i
$605$	5.28445	+	9.15294i	0.214844	+	0.372120i
$606$	7.44178	+	2.52479i	0.302302	+	0.102563i
$607$	20.7623	+	11.9871i	0.842714	+	0.486541i	0.858186	−	0.513339i	$-0.171592\pi$
$607$	20.7623	+	11.9871i	0.842714	+	0.486541i	−0.0154716	+	0.999880i	$0.504925\pi$
$608$	−0.365816	−	0.633612i	−0.0148358	−	0.0256964i
$609$	15.0589	−	29.2199i	0.610219	−	1.18405i
$610$	0.782856	−	1.35595i	0.0316969	−	0.0549006i
$611$	−14.0289	+	8.09961i	−0.567550	+	0.327675i
$612$	−16.0422	−	12.3013i	−0.648468	−	0.497251i
$613$	16.0872	−	27.8638i	0.649754	−	1.12541i	−0.333427	−	0.942776i	$-0.608205\pi$
$613$	16.0872	−	27.8638i	0.649754	−	1.12541i	0.983181	−	0.182631i	$-0.0584615\pi$
$614$	−14.6424			−0.590920
$615$	−7.67121	−	8.74446i	−0.309333	−	0.352611i
$616$	0.257496	−	1.71796i	0.0103748	−	0.0692184i
$617$	−32.2651	+	18.6283i	−1.29894	+	0.749946i	−0.980222	−	0.197902i	$-0.936587\pi$
$617$	−32.2651	+	18.6283i	−1.29894	+	0.749946i	−0.318723	+	0.947848i	$0.603254\pi$
$618$	6.44457	−	1.28300i	0.259239	−	0.0516098i
$619$	−19.6732	+	11.3583i	−0.790733	+	0.456530i	−0.840221	−	0.542245i	$-0.817575\pi$
$619$	−19.6732	+	11.3583i	−0.790733	+	0.456530i	0.0494873	+	0.998775i	$0.484241\pi$
$620$	6.93952	+	4.00653i	0.278698	+	0.160906i
$621$	37.3354	−	2.46546i	1.49822	−	0.0989355i
$622$		−	4.81516i		−	0.193070i
$623$	−1.03880	+	6.93066i	−0.0416188	+	0.277671i
$624$	4.53523	+	1.53868i	0.181554	+	0.0615963i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.23831			−0.289301
$627$	0.816020	−	0.162455i	0.0325887	−	0.00648782i
$628$		−	16.1434i		−	0.644193i
$629$	14.1592			0.564564
$630$	−7.70167	+	1.91944i	−0.306842	+	0.0764723i
$631$	−4.22820			−0.168322			−0.0841610	−	0.996452i	$-0.526821\pi$
$631$	−4.22820			−0.168322			−0.0841610	+	0.996452i	$0.526821\pi$
$632$			15.0706i			0.599478i
$633$	−12.4631	+	36.7349i	−0.495365	+	1.46008i
$634$	−3.73823			−0.148464
$635$	1.48707	−	2.57568i	0.0590125	−	0.102213i
$636$	2.25440	+	11.3239i	0.0893926	+	0.449024i
$637$	−13.1881	−	14.1666i	−0.522531	−	0.561301i
$638$			4.70983i			0.186464i
$639$	4.58304	+	0.601846i	0.181302	+	0.0238087i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	−27.9375	+	16.1297i	−1.10346	+	0.637085i	−0.937128	−	0.348985i	$-0.886527\pi$
$641$	−27.9375	+	16.1297i	−1.10346	+	0.637085i	−0.166335	+	0.986069i	$0.553193\pi$
$642$	−3.65995	+	10.7877i	−0.144447	+	0.425755i
$643$	−17.8975	+	10.3331i	−0.705810	+	0.407500i	−0.809508	−	0.587109i	$-0.800266\pi$
$643$	−17.8975	+	10.3331i	−0.705810	+	0.407500i	0.103698	+	0.994609i	$0.466933\pi$
$644$	−6.97493	−	17.7290i	−0.274851	−	0.698620i
$645$	−7.00172	+	20.6375i	−0.275693	+	0.812600i
$646$	−4.93016			−0.193974
$647$	−11.2156	+	19.4260i	−0.440930	+	0.763714i	−0.997759	−	0.0669137i	$-0.978685\pi$
$647$	−11.2156	+	19.4260i	−0.440930	+	0.763714i	0.556828	+	0.830628i	$0.312018\pi$
$648$	−2.32369	+	8.69485i	−0.0912833	+	0.341566i
$649$	−5.26423	+	3.03931i	−0.206639	+	0.119303i
$650$	−1.38250	+	2.39457i	−0.0542263	+	0.0939226i
$651$	−36.6786	+	1.75219i	−1.43755	+	0.0686736i
$652$	1.04426	+	1.80871i	0.0408964	+	0.0708347i
$653$	2.48621	+	1.43542i	0.0972931	+	0.0561722i	0.547857	−	0.836572i	$-0.315444\pi$
$653$	2.48621	+	1.43542i	0.0972931	+	0.0561722i	−0.450564	+	0.892744i	$0.648777\pi$
$654$	3.27605	+	16.4558i	0.128104	+	0.643471i
$655$	−4.65849	−	8.06874i	−0.182022	−	0.315272i
$656$	3.35799	+	5.81621i	0.131107	+	0.227085i
$657$	−12.5482	+	16.3642i	−0.489553	+	0.638430i
$658$	−9.65447	+	12.1268i	−0.376370	+	0.472750i
$659$	32.1692	+	18.5729i	1.25313	+	0.723497i	0.971731	−	0.236092i	$-0.0758667\pi$
$659$	32.1692	+	18.5729i	1.25313	+	0.723497i	0.281404	+	0.959589i	$0.409200\pi$
$660$	0.854892	−	0.749967i	0.0332766	−	0.0291924i
$661$		−	42.5477i		−	1.65491i	−0.561528	−	0.827457i	$-0.689786\pi$
$661$		−	42.5477i		−	1.65491i	0.561528	−	0.827457i	$-0.310214\pi$
$662$		−	4.80118i		−	0.186603i
$663$	24.2598	−	21.2823i	0.942174	−	0.826536i
$664$	−15.0881	−	8.71114i	−0.585533	−	0.338058i
$665$	−1.20566	+	1.51440i	−0.0467533	+	0.0587258i
$666$	−2.41420	−	5.82302i	−0.0935485	−	0.225638i
$667$	25.8269	+	44.7335i	1.00002	+	1.73209i
$668$	−3.73797	−	6.47435i	−0.144626	−	0.250500i
$669$	−1.04902	−	5.26929i	−0.0405575	−	0.203722i
$670$	−5.68754	−	3.28370i	−0.219729	−	0.126860i
$671$	−0.514007	−	0.890286i	−0.0198430	−	0.0343691i
$672$	4.57736	−	0.218666i	0.176575	−	0.00843523i
$673$	−21.7915	+	37.7439i	−0.839999	+	1.45492i	0.0498957	+	0.998754i	$0.484111\pi$
$673$	−21.7915	+	37.7439i	−0.839999	+	1.45492i	−0.889895	+	0.456166i	$0.849222\pi$
$674$	20.8744	−	12.0518i	0.804051	−	0.464219i
$675$	−4.66141	−	2.29592i	−0.179418	−	0.0883699i
$676$	2.67737	−	4.63733i	0.102976	−	0.178359i
$677$	−5.29631			−0.203554			−0.101777	−	0.994807i	$-0.532453\pi$
$677$	−5.29631			−0.203554			−0.101777	+	0.994807i	$0.532453\pi$
$678$	−6.78929	+	20.0113i	−0.260741	+	0.768530i
$679$	−4.50126	−	11.4414i	−0.172743	−	0.439080i
$680$	−5.83577	+	3.36928i	−0.223792	+	0.129206i
$681$	−16.1184	+	47.5086i	−0.617657	+	1.82053i
$682$	4.55634	−	2.63061i	0.174471	−	0.100731i
$683$	15.0590	+	8.69432i	0.576216	+	0.332679i	0.759628	−	0.650357i	$-0.225381\pi$
$683$	15.0590	+	8.69432i	0.576216	+	0.332679i	−0.183412	+	0.983036i	$0.558714\pi$
$684$	0.840613	+	2.02755i	0.0321416	+	0.0775252i
$685$		−	17.0995i		−	0.653337i
$686$	−16.7059	−	7.99448i	−0.637836	−	0.305230i
$687$	8.88581	+	44.6339i	0.339015	+	1.70289i
$688$	6.29106	−	10.8964i	0.239845	−	0.415423i
$689$	−18.4321			−0.702205
$690$	4.00715	−	11.8110i	0.152549	−	0.449637i
$691$		−	10.2475i		−	0.389833i	−0.980820	−	0.194917i	$-0.937556\pi$
$691$		−	10.2475i		−	0.389833i	0.980820	−	0.194917i	$-0.0624436\pi$
$692$	17.9027			0.680559
$693$	−1.43696	+	5.00941i	−0.0545856	+	0.190292i
$694$	21.6900			0.823341
$695$			14.6139i			0.554338i
$696$	−12.1854	+	2.42589i	−0.461885	+	0.0919530i
$697$	45.2561			1.71420
$698$	9.41562	−	16.3083i	0.356386	−	0.617280i
$699$	8.08216	+	2.74205i	0.305695	+	0.103714i
$700$	−0.392179	+	2.61652i	−0.0148230	+	0.0988953i
$701$		−	34.2446i		−	1.29340i	−0.762745	−	0.646699i	$-0.776149\pi$
$701$		−	34.2446i		−	1.29340i	0.762745	−	0.646699i	$-0.223851\pi$
$702$	−12.8888	−	6.34823i	−0.486458	−	0.239598i
$703$	−1.33136	−	0.768659i	−0.0502130	−	0.0289905i
$704$	−0.568614	+	0.328290i	−0.0214305	+	0.0123729i
$705$	−9.95219	+	1.98130i	−0.374821	+	0.0746202i
$706$	8.26558	−	4.77214i	0.311079	−	0.179602i
$707$	−1.77934	+	11.8713i	−0.0669188	+	0.446467i
$708$	−10.5748	−	12.0543i	−0.397425	−	0.453027i
$709$	6.48217			0.243443			0.121721	−	0.992564i	$-0.461159\pi$
$709$	6.48217			0.243443			0.121721	+	0.992564i	$0.461159\pi$
$710$	0.770398	−	1.33437i	0.0289125	−	0.0500780i
$711$	5.88671	−	44.8271i	0.220769	−	1.68115i
$712$	2.29393	−	1.32440i	0.0859687	−	0.0496341i
$713$	28.8505	−	49.9705i	1.08046	−	1.87141i
$714$	14.1463	−	27.4492i	0.529413	−	1.02726i
$715$	0.907724	+	1.57222i	0.0339469	+	0.0587978i
$716$	8.68355	+	5.01345i	0.324519	+	0.187361i
$717$	25.4595	+	8.63769i	0.950802	+	0.322581i
$718$	4.74234	+	8.21398i	0.176983	+	0.306543i
$719$	−13.4027	−	23.2142i	−0.499838	−	0.865745i	0.500162	−	0.865932i	$-0.333274\pi$
$719$	−13.4027	−	23.2142i	−0.499838	−	0.865745i	−1.00000		0.000186880i	$0.999941\pi$
$720$	2.38066	+	1.82551i	0.0887218	+	0.0680326i
$721$	3.67476	+	9.34057i	0.136855	+	0.347861i
$722$	−15.9909	−	9.23236i	−0.595120	−	0.343593i
$723$	−17.3332	−	5.88066i	−0.644628	−	0.218704i
$724$			8.57389i			0.318646i
$725$		−	7.17328i		−	0.266409i
$726$	3.57423	+	17.9536i	0.132652	+	0.666319i
$727$	−35.4292	−	20.4551i	−1.31400	−	0.758637i	−0.331242	−	0.943546i	$-0.607468\pi$
$727$	−35.4292	−	20.4551i	−1.31400	−	0.758637i	−0.982756	+	0.184909i	$0.940801\pi$
$728$	−1.08438	+	7.23471i	−0.0401897	+	0.268136i
$729$	10.3080	−	24.9549i	0.381778	−	0.924254i
$730$	3.43692	+	5.95292i	0.127206	+	0.220327i
$731$	−42.3928	−	73.4264i	−1.56795	−	2.71577i
$732$	2.03862	−	1.78841i	0.0753494	−	0.0661014i
$733$	18.6446	+	10.7645i	0.688655	+	0.397595i	0.803108	−	0.595834i	$-0.203178\pi$
$733$	18.6446	+	10.7645i	0.688655	+	0.397595i	−0.114453	+	0.993429i	$0.536512\pi$
$734$	0.180608	+	0.312821i	0.00666635	+	0.0115464i
$735$	−4.97211	−	11.0579i	−0.183399	−	0.407878i
$736$	−3.60043	+	6.23613i	−0.132714	+	0.229867i
$737$	−3.73432	+	2.15601i	−0.137555	+	0.0794177i
$738$	−7.71636	−	18.6117i	−0.284043	−	0.685108i
$739$	−17.3918	+	30.1235i	−0.639769	+	1.10811i	0.345714	+	0.938340i	$0.387637\pi$
$739$	−17.3918	+	30.1235i	−0.639769	+	1.10811i	−0.985483	+	0.169772i	$0.945697\pi$
$740$	−2.10122			−0.0772422
$741$	−3.43645	+	0.684135i	−0.126241	+	0.0251323i
$742$	−16.4126	+	6.45704i	−0.602525	+	0.237045i
$743$	24.8388	−	14.3407i	0.911248	−	0.526109i	0.0304153	−	0.999537i	$-0.490317\pi$
$743$	24.8388	−	14.3407i	0.911248	−	0.526109i	0.880832	+	0.473428i	$0.156984\pi$
$744$	9.15279	+	10.4333i	0.335557	+	0.382504i
$745$	−7.54707	+	4.35730i	−0.276503	+	0.159639i
$746$	−8.21606	−	4.74354i	−0.300811	−	0.173674i
$747$	41.4765	+	31.8045i	1.51754	+	1.16367i
$748$			4.42441i			0.161772i
$749$	−17.2087	−	2.57934i	−0.628794	−	0.0942470i
$750$	−1.30204	+	1.14223i	−0.0475437	+	0.0417085i
$751$	7.66167	−	13.2704i	0.279578	−	0.484244i	−0.691702	−	0.722183i	$-0.743139\pi$
$751$	7.66167	−	13.2704i	0.279578	−	0.484244i	0.971280	+	0.237940i	$0.0764720\pi$
$752$	5.85866			0.213643
$753$	2.19918	+	2.50686i	0.0801426	+	0.0913550i
$754$		−	19.8342i		−	0.722318i
$755$	8.62341			0.313838
$756$	−13.7006	−	1.13753i	−0.498285	−	0.0413717i
$757$	0.00588405			0.000213860			0.000106930	−	1.00000i	$-0.499966\pi$
$757$	0.00588405			0.000213860			0.000106930		1.00000i	$0.499966\pi$
$758$			30.4526i			1.10609i
$759$	−5.40040	−	6.15595i	−0.196022	−	0.223447i
$760$	0.731632			0.0265391
$761$	−2.82935	+	4.90058i	−0.102564	+	0.177646i	−0.912740	−	0.408540i	$-0.866038\pi$
$761$	−2.82935	+	4.90058i	−0.102564	+	0.177646i	0.810176	+	0.586186i	$0.199371\pi$
$762$	3.87244	−	3.39716i	0.140284	−	0.123066i
$763$	−23.8505	+	9.38325i	−0.863445	+	0.339696i
$764$		−	10.7152i		−	0.387663i
$765$	18.6744	−	7.74232i	0.675173	−	0.279924i
$766$	18.2537	+	10.5388i	0.659531	+	0.380781i
$767$	22.1689	−	12.7992i	0.800473	−	0.462153i
$768$	−1.14223	−	1.30204i	−0.0412168	−	0.0469833i
$769$	−13.4866	+	7.78647i	−0.486338	+	0.280787i	−0.723054	−	0.690791i	$-0.757262\pi$
$769$	−13.4866	+	7.78647i	−0.486338	+	0.280787i	0.236716	+	0.971579i	$0.423929\pi$
$770$	1.35905	+	1.08198i	0.0489766	+	0.0389917i
$771$	6.01756	−	1.19799i	0.216717	−	0.0431445i
$772$	1.23612			0.0444891
$773$	9.05480	−	15.6834i	0.325678	−	0.564092i	−0.655971	−	0.754786i	$-0.727741\pi$
$773$	9.05480	−	15.6834i	0.325678	−	0.564092i	0.981649	+	0.190695i	$0.0610740\pi$
$774$	−22.9688	+	29.9537i	−0.825595	+	1.07666i
$775$	−6.93952	+	4.00653i	−0.249275	+	0.143919i
$776$	−2.32353	+	4.02448i	−0.0834100	+	0.144470i
$777$	8.09971	−	5.20692i	0.290576	−	0.186797i
$778$	15.4147	+	26.6991i	0.552644	+	0.957208i
$779$	−4.25533	−	2.45681i	−0.152463	−	0.0880245i
$780$	−3.60015	+	3.15828i	−0.128906	+	0.113085i
$781$	−0.505828	−	0.876119i	−0.0180999	−	0.0313500i
$782$	24.2617	+	42.0226i	0.867598	+	1.50272i
$783$	37.1925	−	2.45602i	1.32915	−	0.0877710i
$784$	1.56886	+	6.82193i	0.0560308	+	0.243640i
$785$	13.9806	+	8.07171i	0.498989	+	0.288092i
$786$	−3.15085	−	15.8269i	−0.112387	−	0.564526i
$787$			43.8660i			1.56365i	0.623496	+	0.781826i	$0.285712\pi$
$787$			43.8660i			1.56365i	−0.623496	+	0.781826i	$0.714288\pi$
$788$			15.5323i			0.553315i
$789$	−15.6130	−	5.29704i	−0.555836	−	0.188580i
$790$	−13.0516	−	7.53532i	−0.464354	−	0.268095i
$791$	−31.9226	−	4.78473i	−1.13504	−	0.170125i
$792$	1.81955	−	0.754380i	0.0646551	−	0.0268057i
$793$	2.16460	+	3.74920i	0.0768673	+	0.133138i
$794$	7.02834	+	12.1734i	0.249426	+	0.432019i
$795$	−10.9340	−	3.70961i	−0.387790	−	0.131566i
$796$	−14.8736	−	8.58726i	−0.527180	−	0.304367i
$797$	−5.25439	−	9.10087i	−0.186120	−	0.322369i	0.757833	−	0.652448i	$-0.226258\pi$
$797$	−5.25439	−	9.10087i	−0.186120	−	0.322369i	−0.943953	+	0.330079i	$0.892925\pi$
$798$	−2.82028	+	1.81302i	−0.0998367	+	0.0641802i
$799$	19.7395	−	34.1898i	0.698333	−	1.20955i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−7.34053	+	3.04336i	−0.259365	+	0.107532i
$802$	−16.9887	+	29.4253i	−0.599891	+	1.03904i
$803$	4.51322			0.159268
$804$	−7.50150	−	8.55101i	−0.264558	−	0.301571i
$805$	18.8412	+	2.82402i	0.664066	+	0.0995337i
$806$	−19.1878	+	11.0781i	−0.675862	+	0.390209i
$807$	6.46160	−	1.28639i	0.227459	−	0.0452830i
$808$	3.92921	−	2.26853i	0.138229	−	0.0798065i
$809$	27.9421	+	16.1324i	0.982392	+	0.567184i	0.902992	−	0.429658i	$-0.141366\pi$
$809$	27.9421	+	16.1324i	0.982392	+	0.567184i	0.0794007	+	0.996843i	$0.474699\pi$
$810$	−6.36812	−	6.35980i	−0.223753	−	0.223461i
$811$			48.8854i			1.71660i	0.513151	+	0.858299i	$0.328478\pi$
$811$			48.8854i			1.71660i	−0.513151	+	0.858299i	$0.671522\pi$
$812$	−6.94822	−	17.6611i	−0.243835	−	0.619783i
$813$	2.05302	+	0.696534i	0.0720027	+	0.0244285i
$814$	−0.689808	+	1.19478i	−0.0241777	+	0.0418771i
$815$	−2.08852			−0.0731577
$816$	−11.4469	+	2.27887i	−0.400722	+	0.0797766i
$817$			9.20549i			0.322059i
$818$	−11.4908			−0.401768
$819$	6.05137	−	21.0958i	0.211452	−	0.737147i
$820$	−6.71598			−0.234532
$821$			34.8494i			1.21625i	0.793841	+	0.608126i	$0.208078\pi$
$821$			34.8494i			1.21625i	−0.793841	+	0.608126i	$0.791922\pi$
$822$	9.51554	−	28.0469i	0.331892	−	0.978248i
$823$	−42.3839			−1.47741			−0.738705	−	0.674029i	$-0.764562\pi$
$823$	−42.3839			−1.47741			−0.738705	+	0.674029i	$0.764562\pi$
$824$	1.89690	−	3.28552i	0.0660815	−	0.114457i
$825$	0.222044	+	1.11534i	0.00773060	+	0.0388312i
$826$	15.2562	−	19.1630i	0.530833	−	0.666767i
$827$		−	9.24262i		−	0.321397i	−0.987004	−	0.160699i	$-0.948625\pi$
$827$		−	9.24262i		−	0.321397i	0.987004	−	0.160699i	$-0.0513748\pi$
$828$	13.1452	−	17.1428i	0.456828	−	0.595752i
$829$	11.4514	+	6.61149i	0.397725	+	0.229626i	0.685502	−	0.728071i	$-0.259583\pi$
$829$	11.4514	+	6.61149i	0.397725	+	0.229626i	−0.287777	+	0.957697i	$0.592916\pi$
$830$	15.0881	−	8.71114i	0.523717	−	0.302368i
$831$	8.37055	−	24.6721i	0.290371	−	0.855865i
$832$	2.39457	−	1.38250i	0.0830167	−	0.0479297i
$833$	45.0972	+	13.8295i	1.56252	+	0.479164i
$834$	−8.13239	+	23.9701i	−0.281601	+	0.830016i
$835$	7.47594			0.258716
$836$	0.240187	−	0.416017i	0.00830705	−	0.0143882i
$837$	−23.1493	−	34.6087i	−0.800157	−	1.19625i
$838$	25.0456	−	14.4601i	0.865186	−	0.499515i
$839$	−9.52343	+	16.4951i	−0.328785	+	0.569473i	−0.982271	−	0.187466i	$-0.939973\pi$
$839$	−9.52343	+	16.4951i	−0.328785	+	0.569473i	0.653486	+	0.756939i	$0.273306\pi$
$840$	−2.09931	+	4.07344i	−0.0724330	+	0.140547i
$841$	11.2280	+	19.4475i	0.387172	+	0.670602i
$842$	−0.820343	−	0.473626i	−0.0282709	−	0.0163222i
$843$	−10.6014	−	53.2516i	−0.365133	−	1.83408i
$844$	11.1982	+	19.3958i	0.385456	+	0.667630i
$845$	2.67737	+	4.63733i	0.0921042	+	0.159529i
$846$	−17.4264	−	2.28843i	−0.599130	−	0.0786780i
$847$	−26.0213	+	10.2373i	−0.894103	+	0.351758i
$848$	5.77309	+	3.33309i	0.198249	+	0.114459i
$849$	27.4741	−	24.1021i	0.942908	−	0.827180i
$850$		−	6.73857i		−	0.231131i
$851$			15.1306i			0.518669i
$852$	2.00618	−	1.75995i	0.0687304	−	0.0602948i
$853$	15.0469	+	8.68732i	0.515195	+	0.297448i	0.734967	−	0.678103i	$-0.237198\pi$
$853$	15.0469	+	8.68732i	0.515195	+	0.297448i	−0.219771	+	0.975551i	$0.570531\pi$
$854$	3.24085	+	2.58013i	0.110899	+	0.0882903i
$855$	−2.17621	−	0.285781i	−0.0744249	−	0.00977350i
$856$	3.28847	+	5.69580i	0.112398	+	0.194679i
$857$	−7.94536	−	13.7618i	−0.271408	−	0.470093i	0.697814	−	0.716279i	$-0.254156\pi$
$857$	−7.94536	−	13.7618i	−0.271408	−	0.470093i	−0.969223	+	0.246186i	$0.920823\pi$
$858$	0.613955	+	3.08393i	0.0209601	+	0.105284i
$859$	1.71028	+	0.987428i	0.0583538	+	0.0336906i	0.528893	−	0.848688i	$-0.322607\pi$
$859$	1.71028	+	0.987428i	0.0583538	+	0.0336906i	−0.470539	+	0.882379i	$0.655941\pi$
$860$	6.29106	+	10.8964i	0.214524	+	0.371566i
$861$	25.8886	−	16.6425i	0.882280	−	0.567176i
$862$	−5.87431	+	10.1746i	−0.200080	+	0.346549i
$863$	23.5615	−	13.6032i	0.802043	−	0.463060i	−0.0421423	−	0.999112i	$-0.513418\pi$
$863$	23.5615	−	13.6032i	0.802043	−	0.463060i	0.844185	+	0.536052i	$0.180085\pi$
$864$	2.88894	+	4.31903i	0.0982839	+	0.146936i
$865$	−8.95135	+	15.5042i	−0.304355	+	0.527159i
$866$	31.4858			1.06993
$867$	−15.8087	+	46.5960i	−0.536892	+	1.58248i
$868$	−13.2047	+	16.5861i	−0.448197	+	0.562970i
$869$	−8.56939	+	4.94754i	−0.290697	+	0.167834i
$870$	3.99180	−	11.7658i	0.135335	−	0.398897i
$871$	15.7261	−	9.07946i	0.532858	−	0.307646i
$872$	8.38935	+	4.84359i	0.284099	+	0.164025i
$873$	8.48325	−	11.0631i	0.287115	−	0.374428i
$874$		−	5.26838i		−	0.178206i
$875$	−2.06989	−	1.64790i	−0.0699749	−	0.0557091i
$876$	2.32462	+	11.6767i	0.0785416	+	0.394519i
$877$	4.42988	−	7.67277i	0.149586	−	0.259091i	−0.781488	−	0.623920i	$-0.785539\pi$
$877$	4.42988	−	7.67277i	0.149586	−	0.259091i	0.931075	+	0.364829i	$0.118872\pi$
$878$	28.6453			0.966733
$879$	7.53350	−	22.2049i	0.254099	−	0.748952i
$880$		−	0.656579i		−	0.0221333i
$881$	13.6049			0.458361			0.229180	−	0.973384i	$-0.426395\pi$
$881$	13.6049			0.458361			0.229180	+	0.973384i	$0.426395\pi$
$882$	−2.00183	−	20.9044i	−0.0674050	−	0.703887i
$883$	35.3206			1.18863			0.594316	−	0.804232i	$-0.297423\pi$
$883$	35.3206			1.18863			0.594316	+	0.804232i	$0.297423\pi$
$884$		−	18.6322i		−	0.626669i
$885$	15.7267	−	3.13091i	0.528647	−	0.105244i
$886$	−12.6900			−0.426329
$887$	8.00631	−	13.8673i	0.268826	−	0.465619i	−0.699733	−	0.714404i	$-0.746698\pi$
$887$	8.00631	−	13.8673i	0.268826	−	0.465619i	0.968559	+	0.248785i	$0.0800312\pi$
$888$	−3.44646	−	1.16929i	−0.115656	−	0.0392387i
$889$	6.15613	+	4.90108i	0.206470	+	0.164377i
$890$			2.64880i			0.0887881i
$891$	−5.70686	+	1.53314i	−0.191187	+	0.0513623i
$892$	−2.68635	−	1.55096i	−0.0899455	−	0.0519301i
$893$	−3.71212	+	2.14319i	−0.124221	+	0.0717192i
$894$	−14.8036	+	2.94714i	−0.495107	+	0.0985670i
$895$	−8.68355	+	5.01345i	−0.290259	+	0.167581i
$896$	1.64790	−	2.06989i	0.0550524	−	0.0691501i
$897$	22.7423	+	25.9241i	0.759345	+	0.865582i
$898$	3.80547			0.126990
$899$	28.7400	−	49.7791i	0.958532	−	1.66023i
$900$	−2.77126	+	1.14896i	−0.0923755	+	0.0382985i
$901$	38.9023	−	22.4603i	1.29602	−	0.748260i
$902$	−2.20479	+	3.81880i	−0.0734114	+	0.127152i
$903$	−51.2525	−	26.4138i	−1.70558	−	0.878995i
$904$	6.10019	+	10.5658i	0.202889	+	0.351414i
$905$	−7.42520	−	4.28694i	−0.246822	−	0.142503i
$906$	14.1443	+	4.79877i	0.469913	+	0.159429i
$907$	11.7210	+	20.3013i	0.389189	+	0.674095i	0.992341	−	0.123532i	$-0.0394220\pi$
$907$	11.7210	+	20.3013i	0.389189	+	0.674095i	−0.603152	+	0.797626i	$0.706089\pi$
$908$	14.4824	+	25.0842i	0.480615	+	0.832449i
$909$	−12.5734	+	5.21287i	−0.417033	+	0.172900i
$910$	−5.72325	−	4.55645i	−0.189724	−	0.151045i
$911$	−32.0609	−	18.5104i	−1.06222	−	0.613275i	−0.136178	−	0.990684i	$-0.543482\pi$
$911$	−32.0609	−	18.5104i	−1.06222	−	0.613275i	−0.926047	+	0.377409i	$0.876815\pi$
$912$	1.20004	+	0.407140i	0.0397373	+	0.0134818i
$913$		−	11.4391i		−	0.378579i
$914$		−	40.3773i		−	1.33556i
$915$	0.529498	+	2.65970i	0.0175047	+	0.0879269i
$916$	22.7549	+	13.1376i	0.751843	+	0.434077i
$917$	22.9390	−	9.02466i	0.757513	−	0.298020i
$918$	34.9385	−	2.30718i	1.15314	−	0.0761483i
$919$	−1.61312	−	2.79400i	−0.0532118	−	0.0921656i	0.838193	−	0.545374i	$-0.183613\pi$
$919$	−1.61312	−	2.79400i	−0.0532118	−	0.0921656i	−0.891404	+	0.453209i	$0.850279\pi$
$920$	−3.60043	−	6.23613i	−0.118703	−	0.205599i
$921$	19.0650	−	16.7251i	0.628213	−	0.551110i
$922$	−13.0319	−	7.52397i	−0.429183	−	0.247789i
$923$	2.13016	+	3.68954i	0.0701150	+	0.121443i
$924$	1.62704	+	2.53096i	0.0535255	+	0.0832626i
$925$	1.05061	−	1.81971i	0.0345438	−	0.0598316i
$926$	21.5474	−	12.4404i	0.708093	−	0.408818i
$927$	−6.92560	+	9.03172i	−0.227466	+	0.296641i
$928$	−3.58664	+	6.21225i	−0.117737	+	0.203927i
$929$	−54.2140			−1.77871			−0.889353	−	0.457222i	$-0.848845\pi$
$929$	−54.2140			−1.77871			−0.889353	+	0.457222i	$0.848845\pi$
$930$	−13.6119	+	2.70989i	−0.446352	+	0.0888607i
$931$	−3.48962	−	3.74854i	−0.114368	−	0.122853i
$932$	4.26732	−	2.46374i	0.139781	−	0.0807025i
$933$	5.50003	+	6.26952i	0.180063	+	0.205255i
$934$	30.3035	−	17.4957i	0.991560	−	0.572477i
$935$	−3.83165	−	2.21220i	−0.125308	−	0.0723468i
$936$	−7.66256	+	3.17687i	−0.250459	+	0.103839i
$937$		−	44.7766i		−	1.46279i	−0.681956	−	0.731393i	$-0.738870\pi$
$937$		−	44.7766i		−	1.46279i	0.681956	−	0.731393i	$-0.261130\pi$
$938$	10.8224	−	13.5938i	0.353364	−	0.443853i
$939$	9.42456	−	8.26784i	0.307559	−	0.269811i
$940$	−2.92933	+	5.07374i	−0.0955441	+	0.165487i
$941$	14.8263			0.483324			0.241662	−	0.970360i	$-0.422307\pi$
$941$	14.8263			0.483324			0.241662	+	0.970360i	$0.422307\pi$
$942$	18.4395	+	21.0193i	0.600793	+	0.684847i
$943$			48.3608i			1.57484i
$944$	−9.25800			−0.301322
$945$	7.83543	−	11.2963i	0.254886	−	0.367468i
$946$	8.26117			0.268594
$947$		−	12.1763i		−	0.395676i	−0.980235	−	0.197838i	$-0.936608\pi$
$947$		−	12.1763i		−	0.395676i	0.980235	−	0.197838i	$-0.0633920\pi$
$948$	−17.2142	−	19.6226i	−0.559091	−	0.637311i
$949$	−19.0062			−0.616968
$950$	−0.365816	+	0.633612i	−0.0118686	+	0.0205571i
$951$	4.86732	−	4.26993i	0.157834	−	0.138462i
$952$	−6.52715	−	16.5908i	−0.211546	−	0.537711i
$953$			54.1766i			1.75495i	0.479619	+	0.877477i	$0.340775\pi$
$953$			54.1766i			1.75495i	−0.479619	+	0.877477i	$0.659225\pi$
$954$	−15.8699	−	12.1692i	−0.513807	−	0.393991i
$955$	9.27965	+	5.35761i	0.300282	+	0.173368i
$956$	13.4424	−	7.76099i	0.434759	−	0.251008i
$957$	−5.37972	−	6.13238i	−0.173902	−	0.198232i
$958$	−10.5002	+	6.06228i	−0.339245	+	0.195863i
$959$	44.7411	+	6.70604i	1.44477	+	0.216549i
$960$	1.69871	−	0.338184i	0.0548258	−	0.0109148i
$961$	−33.2092			−1.07126
$962$	2.90494	−	5.03150i	0.0936590	−	0.162222i
$963$	−7.55662	−	18.2265i	−0.243509	−	0.587339i
$964$	−9.15179	+	5.28379i	−0.294759	+	0.170179i
$965$	−0.618062	+	1.07052i	−0.0198961	+	0.0344611i
$966$	29.3323	+	15.1168i	0.943750	+	0.486375i
$967$	−6.01241	−	10.4138i	−0.193346	−	0.334885i	0.753011	−	0.658008i	$-0.228601\pi$
$967$	−6.01241	−	10.4138i	−0.193346	−	0.334885i	−0.946357	+	0.323123i	$0.895267\pi$
$968$	9.15294	+	5.28445i	0.294187	+	0.169849i
$969$	6.41925	−	5.63139i	0.206216	−	0.180906i
$970$	−2.32353	−	4.02448i	−0.0746041	−	0.129218i
$971$	29.0141	+	50.2539i	0.931107	+	1.61272i	0.781434	+	0.623988i	$0.214489\pi$
$971$	29.0141	+	50.2539i	0.931107	+	1.61272i	0.149673	+	0.988736i	$0.452178\pi$
$972$	−6.90601	−	13.9752i	−0.221510	−	0.448256i
$973$	−38.2377	−	5.73127i	−1.22584	−	0.183736i
$974$	6.16364	+	3.55858i	0.197496	+	0.114024i
$975$	−0.935081	−	4.69696i	−0.0299465	−	0.150423i
$976$		−	1.56571i		−	0.0501172i
$977$			7.62513i			0.243950i	0.992533	+	0.121975i	$0.0389227\pi$
$977$			7.62513i			0.243950i	−0.992533	+	0.121975i	$0.961077\pi$
$978$	−3.42564	−	1.16222i	−0.109540	−	0.0371638i
$979$	1.50615	+	0.869575i	0.0481367	+	0.0277917i
$980$	−6.69239	−	2.05229i	−0.213781	−	0.0655580i
$981$	−23.0619	−	17.6840i	−0.736308	−	0.564607i
$982$	9.46076	+	16.3865i	0.301905	+	0.522915i
$983$	−7.44861	−	12.9014i	−0.237574	−	0.411490i	0.722444	−	0.691430i	$-0.243019\pi$
$983$	−7.44861	−	12.9014i	−0.237574	−	0.411490i	−0.960018	+	0.279940i	$0.909686\pi$
$984$	−11.0157	−	3.73732i	−0.351168	−	0.119141i
$985$	−13.4514	−	7.76614i	−0.428596	−	0.247450i
$986$	24.1688	+	41.8617i	0.769693	+	1.33315i
$987$	−1.28109	−	26.8172i	−0.0407775	−	0.853599i
$988$	−1.01148	+	1.75194i	−0.0321796	+	0.0557367i
$989$	78.4637	−	45.3011i	2.49500	−	1.44049i
$990$	−0.256465	+	1.95297i	−0.00815098	+	0.0620695i
$991$	−23.9760	+	41.5276i	−0.761622	+	1.31917i	0.180393	+	0.983595i	$0.442263\pi$
$991$	−23.9760	+	41.5276i	−0.761622	+	1.31917i	−0.942014	+	0.335573i	$0.891070\pi$
$992$	8.01306			0.254415
$993$	5.48406	+	6.25131i	0.174031	+	0.198379i
$994$	3.18927	+	2.53908i	0.101158	+	0.0805346i
$995$	14.8736	−	8.58726i	0.471524	−	0.272234i
$996$	29.5955	−	5.89193i	0.937769	−	0.186693i
$997$	1.69163	−	0.976662i	0.0535744	−	0.0309312i	−0.472974	−	0.881077i	$-0.656819\pi$
$997$	1.69163	−	0.976662i	0.0535744	−	0.0309312i	0.526548	+	0.850145i	$0.323486\pi$
$998$	16.4616	+	9.50411i	0.521083	+	0.300847i
$999$	9.79464	+	4.82422i	0.309889	+	0.152631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.c.101.11	yes	32
3.2	odd	2		1890.2.bk.c.521.8		32
7.5	odd	6		630.2.t.c.551.9	yes	32
9.4	even	3		1890.2.t.c.1151.5		32
9.5	odd	6		630.2.t.c.311.9	✓	32
21.5	even	6		1890.2.t.c.1601.5		32
63.5	even	6	inner	630.2.bk.c.131.3	yes	32
63.40	odd	6		1890.2.bk.c.341.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.9	✓	32	9.5	odd	6
630.2.t.c.551.9	yes	32	7.5	odd	6
630.2.bk.c.101.11	yes	32	1.1	even	1	trivial
630.2.bk.c.131.3	yes	32	63.5	even	6	inner
1890.2.t.c.1151.5		32	9.4	even	3
1890.2.t.c.1601.5		32	21.5	even	6
1890.2.bk.c.341.8		32	63.40	odd	6
1890.2.bk.c.521.8		32	3.2	odd	2

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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.14223 - 1.30204i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30204 - 1.14223i) q^{6} +(2.06989 + 1.64790i) q^{7} -1.00000i q^{8} +(-0.390607 + 2.97446i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.14223 - 1.30204i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30204 - 1.14223i) q^{6} +(2.06989 + 1.64790i) q^{7} -1.00000i q^{8} +(-0.390607 + 2.97446i) q^{9} +(0.866025 + 0.500000i) q^{10} +(0.568614 - 0.328290i) q^{11} +(1.14223 + 1.30204i) q^{12} +(-2.39457 + 1.38250i) q^{13} +(-1.64790 + 2.06989i) q^{14} +(-1.69871 + 0.338184i) q^{15} +1.00000 q^{16} +(3.36928 - 5.83577i) q^{17} +(-2.97446 - 0.390607i) q^{18} +(-0.633612 + 0.365816i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.218666 - 4.57736i) q^{21} +(0.328290 + 0.568614i) q^{22} +(6.23613 + 3.60043i) q^{23} +(-1.30204 + 1.14223i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.38250 - 2.39457i) q^{26} +(4.31903 - 2.88894i) q^{27} +(-2.06989 - 1.64790i) q^{28} +(6.21225 + 3.58664i) q^{29} +(-0.338184 - 1.69871i) q^{30} -8.01306i q^{31} +1.00000i q^{32} +(-1.07694 - 0.365374i) q^{33} +(5.83577 + 3.36928i) q^{34} +(2.46207 - 0.968625i) q^{35} +(0.390607 - 2.97446i) q^{36} +(1.05061 + 1.81971i) q^{37} +(-0.365816 - 0.633612i) q^{38} +(4.53523 + 1.53868i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(3.35799 + 5.81621i) q^{41} +(4.57736 - 0.218666i) q^{42} +(6.29106 - 10.8964i) q^{43} +(-0.568614 + 0.328290i) q^{44} +(2.38066 + 1.82551i) q^{45} +(-3.60043 + 6.23613i) q^{46} +5.85866 q^{47} +(-1.14223 - 1.30204i) q^{48} +(1.56886 + 6.82193i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-11.4469 + 2.27887i) q^{51} +(2.39457 - 1.38250i) q^{52} +(5.77309 + 3.33309i) q^{53} +(2.88894 + 4.31903i) q^{54} -0.656579i q^{55} +(1.64790 - 2.06989i) q^{56} +(1.20004 + 0.407140i) q^{57} +(-3.58664 + 6.21225i) q^{58} -9.25800 q^{59} +(1.69871 - 0.338184i) q^{60} -1.56571i q^{61} +8.01306 q^{62} +(-5.71012 + 5.51312i) q^{63} -1.00000 q^{64} +2.76501i q^{65} +(0.365374 - 1.07694i) q^{66} -6.56740 q^{67} +(-3.36928 + 5.83577i) q^{68} +(-2.43521 - 12.2322i) q^{69} +(0.968625 + 2.46207i) q^{70} -1.54080i q^{71} +(2.97446 + 0.390607i) q^{72} +(5.95292 + 3.43692i) q^{73} +(-1.81971 + 1.05061i) q^{74} +(-0.556482 + 1.64022i) q^{75} +(0.633612 - 0.365816i) q^{76} +(1.71796 + 0.257496i) q^{77} +(-1.53868 + 4.53523i) q^{78} -15.0706 q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.69485 - 2.32369i) q^{81} +(-5.81621 + 3.35799i) q^{82} +(8.71114 - 15.0881i) q^{83} +(0.218666 + 4.57736i) q^{84} +(-3.36928 - 5.83577i) q^{85} +(10.8964 + 6.29106i) q^{86} +(-2.42589 - 12.1854i) q^{87} +(-0.328290 - 0.568614i) q^{88} +(1.32440 + 2.29393i) q^{89} +(-1.82551 + 2.38066i) q^{90} +(-7.23471 - 1.08438i) q^{91} +(-6.23613 - 3.60043i) q^{92} +(-10.4333 + 9.15279i) q^{93} +5.85866i q^{94} +0.731632i q^{95} +(1.30204 - 1.14223i) q^{96} +(-4.02448 - 2.32353i) q^{97} +(-6.82193 + 1.56886i) q^{98} +(0.754380 + 1.81955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more