LMFDB - Embedded newform 132.2.j.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [132,2,Mod(7,132)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(132, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("132.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.j (of order $10$, 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:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	132.7
Dual form			132.2.j.a.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.246398 + 1.39258i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.87858 - 0.686259i) q^{4} +(-3.06643 + 2.22789i) q^{5} +(0.664670 - 1.24828i) q^{6} +(-0.793217 - 2.44127i) q^{7} +(1.41855 - 2.44698i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.246398 + 1.39258i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.87858 - 0.686259i) q^{4} +(-3.06643 + 2.22789i) q^{5} +(0.664670 - 1.24828i) q^{6} +(-0.793217 - 2.44127i) q^{7} +(1.41855 - 2.44698i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.34696 - 4.81920i) q^{10} +(-3.19932 + 0.874260i) q^{11} +(1.57457 + 1.23318i) q^{12} +(-2.76004 + 3.79887i) q^{13} +(3.59512 - 0.503097i) q^{14} +(3.60480 - 1.17127i) q^{15} +(3.05810 + 2.57838i) q^{16} +(0.685574 + 0.943612i) q^{17} +(-1.01788 + 0.981795i) q^{18} +(0.147787 - 0.454840i) q^{19} +(7.28943 - 2.08090i) q^{20} +2.56690i q^{21} +(-0.429174 - 4.67074i) q^{22} +4.80592i q^{23} +(-2.10528 + 1.88886i) q^{24} +(2.89440 - 8.90806i) q^{25} +(-4.61018 - 4.77963i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.185225 + 5.13047i) q^{28} +(3.70237 - 1.20297i) q^{29} +(0.742878 + 5.30859i) q^{30} +(-3.70718 + 5.10249i) q^{31} +(-4.34412 + 3.62335i) q^{32} +(3.31290 + 0.157175i) q^{33} +(-1.48298 + 0.722215i) q^{34} +(7.87123 + 5.71878i) q^{35} +(-1.11643 - 1.65939i) q^{36} +(-0.163997 - 0.504731i) q^{37} +(0.596989 + 0.317877i) q^{38} +(3.79887 - 2.76004i) q^{39} +(1.10173 + 10.6639i) q^{40} +(0.197223 + 0.0640816i) q^{41} +(-3.57463 - 0.632480i) q^{42} -0.387725 q^{43} +(6.61014 + 0.553199i) q^{44} -3.79031 q^{45} +(-6.69264 - 1.18417i) q^{46} +(-11.6025 - 3.76989i) q^{47} +(-2.11166 - 3.39719i) q^{48} +(0.332506 - 0.241580i) q^{49} +(11.6920 + 6.22562i) q^{50} +(-0.360428 - 1.10928i) q^{51} +(7.79196 - 5.24237i) q^{52} +(-8.74531 - 6.35384i) q^{53} +(1.27145 - 0.619200i) q^{54} +(7.86274 - 9.80860i) q^{55} +(-7.09896 - 1.52208i) q^{56} +(-0.281107 + 0.386910i) q^{57} +(0.762984 + 5.45227i) q^{58} +(5.25007 - 1.70585i) q^{59} +(-7.57569 - 0.273505i) q^{60} +(6.33692 + 8.72202i) q^{61} +(-6.19220 - 6.41979i) q^{62} +(0.793217 - 2.44127i) q^{63} +(-3.97544 - 6.94233i) q^{64} -17.7981i q^{65} +(-1.03517 + 4.57476i) q^{66} -6.06244i q^{67} +(-0.640342 - 2.24313i) q^{68} +(1.48511 - 4.57070i) q^{69} +(-9.90334 + 9.55225i) q^{70} +(-0.999528 - 1.37573i) q^{71} +(2.58593 - 1.14585i) q^{72} +(-5.26623 + 1.71110i) q^{73} +(0.743288 - 0.104015i) q^{74} +(-5.50548 + 7.57765i) q^{75} +(-0.589767 + 0.753032i) q^{76} +(4.67206 + 7.11694i) q^{77} +(2.90756 + 5.97032i) q^{78} +(10.3403 + 7.51269i) q^{79} +(-15.1218 - 1.09331i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-0.137834 + 0.258860i) q^{82} +(-8.06986 + 5.86309i) q^{83} +(1.76156 - 4.82213i) q^{84} +(-4.20453 - 1.36613i) q^{85} +(0.0955346 - 0.539940i) q^{86} -3.89290 q^{87} +(-2.39910 + 9.06887i) q^{88} +0.485931 q^{89} +(0.933925 - 5.27833i) q^{90} +(11.4634 + 3.72468i) q^{91} +(3.29810 - 9.02829i) q^{92} +(5.10249 - 3.70718i) q^{93} +(8.10872 - 15.2286i) q^{94} +(0.560158 + 1.72399i) q^{95} +(5.25118 - 2.10360i) q^{96} +(2.60928 + 1.89576i) q^{97} +(0.254491 + 0.522567i) q^{98} +(-3.10218 - 1.17322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) $ 48 * q - 4 * q^4 + 12 * q^9	$ 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.246398	+	1.39258i	−0.174230	+	0.984705i
$2$	−0.246398	+	1.39258i	−0.174230	+	0.984705i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−1.87858	−	0.686259i	−0.939288	−	0.343129i
$5$	−3.06643	+	2.22789i	−1.37135	+	0.996343i	−0.373718	+	0.927542i	$0.621917\pi$
$5$	−3.06643	+	2.22789i	−1.37135	+	0.996343i	−0.997630	+	0.0688009i	$0.978083\pi$
$6$	0.664670	−	1.24828i	0.271350	−	0.509610i
$7$	−0.793217	−	2.44127i	−0.299808	−	0.922714i	−0.981564	−	0.191134i	$-0.938783\pi$
$7$	−0.793217	−	2.44127i	−0.299808	−	0.922714i	0.681756	−	0.731580i	$-0.261217\pi$
$8$	1.41855	−	2.44698i	0.501533	−	0.865139i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−2.34696	−	4.81920i	−0.742175	−	1.52397i
$11$	−3.19932	+	0.874260i	−0.964632	+	0.263599i
$11$	−3.19932	+	0.874260i	−0.964632	+	0.263599i
$12$	1.57457	+	1.23318i	0.454538	+	0.355989i
$13$	−2.76004	+	3.79887i	−0.765498	+	1.05362i	0.231238	+	0.972897i	$0.425722\pi$
$13$	−2.76004	+	3.79887i	−0.765498	+	1.05362i	−0.996737	+	0.0807211i	$0.974278\pi$
$14$	3.59512	−	0.503097i	0.960836	−	0.134458i
$15$	3.60480	−	1.17127i	0.930756	−	0.302421i
$16$	3.05810	+	2.57838i	0.764524	+	0.644595i
$17$	0.685574	+	0.943612i	0.166276	+	0.228860i	0.884022	−	0.467446i	$-0.154826\pi$
$17$	0.685574	+	0.943612i	0.166276	+	0.228860i	−0.717745	+	0.696306i	$0.754826\pi$
$18$	−1.01788	+	0.981795i	−0.239917	+	0.231411i
$19$	0.147787	−	0.454840i	0.0339046	−	0.104348i	−0.932672	−	0.360725i	$-0.882529\pi$
$19$	0.147787	−	0.454840i	0.0339046	−	0.104348i	0.966577	+	0.256378i	$0.0825292\pi$
$20$	7.28943	−	2.08090i	1.62997	−	0.465303i
$21$			2.56690i			0.560145i
$22$	−0.429174	−	4.67074i	−0.0915002	−	0.995805i
$23$			4.80592i			1.00210i	0.865417	+	0.501052i	$0.167053\pi$
$23$			4.80592i			1.00210i	−0.865417	+	0.501052i	$0.832947\pi$
$24$	−2.10528	+	1.88886i	−0.429738	+	0.385562i
$25$	2.89440	−	8.90806i	0.578881	−	1.78161i
$26$	−4.61018	−	4.77963i	−0.904131	−	0.937362i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−0.185225	+	5.13047i	−0.0350042	+	0.969567i
$29$	3.70237	−	1.20297i	0.687513	−	0.223386i	0.0556313	−	0.998451i	$-0.482283\pi$
$29$	3.70237	−	1.20297i	0.687513	−	0.223386i	0.631882	+	0.775065i	$0.282283\pi$
$30$	0.742878	+	5.30859i	0.135630	+	0.969211i
$31$	−3.70718	+	5.10249i	−0.665829	+	0.916434i	−0.999657	−	0.0261996i	$-0.991659\pi$
$31$	−3.70718	+	5.10249i	−0.665829	+	0.916434i	0.333828	+	0.942634i	$0.391659\pi$
$32$	−4.34412	+	3.62335i	−0.767938	+	0.640524i
$33$	3.31290	+	0.157175i	0.576702	+	0.0273606i
$34$	−1.48298	+	0.722215i	−0.254329	+	0.123859i
$35$	7.87123	+	5.71878i	1.33048	+	0.966651i
$36$	−1.11643	−	1.65939i	−0.186071	−	0.276566i
$37$	−0.163997	−	0.504731i	−0.0269609	−	0.0829773i	0.936671	−	0.350211i	$-0.113890\pi$
$37$	−0.163997	−	0.504731i	−0.0269609	−	0.0829773i	−0.963632	+	0.267234i	$0.913890\pi$
$38$	0.596989	+	0.317877i	0.0968444	+	0.0515664i
$39$	3.79887	−	2.76004i	0.608307	−	0.441961i
$40$	1.10173	+	10.6639i	0.174198	+	1.68611i
$41$	0.197223	+	0.0640816i	0.0308010	+	0.0100079i	0.324377	−	0.945928i	$-0.394845\pi$
$41$	0.197223	+	0.0640816i	0.0308010	+	0.0100079i	−0.293576	+	0.955936i	$0.594845\pi$
$42$	−3.57463	−	0.632480i	−0.551577	−	0.0975937i
$43$	−0.387725			−0.0591275			−0.0295638	−	0.999563i	$-0.509412\pi$
$43$	−0.387725			−0.0591275			−0.0295638	+	0.999563i	$0.509412\pi$
$44$	6.61014	+	0.553199i	0.996516	+	0.0833980i
$45$	−3.79031			−0.565027
$46$	−6.69264	−	1.18417i	−0.986776	−	0.174596i
$47$	−11.6025	−	3.76989i	−1.69240	−	0.549895i	−0.705150	−	0.709059i	$-0.749120\pi$
$47$	−11.6025	−	3.76989i	−1.69240	−	0.549895i	−0.987252	+	0.159164i	$0.949120\pi$
$48$	−2.11166	−	3.39719i	−0.304792	−	0.490342i
$49$	0.332506	−	0.241580i	0.0475009	−	0.0345114i
$50$	11.6920	+	6.22562i	1.65350	+	0.880436i
$51$	−0.360428	−	1.10928i	−0.0504700	−	0.155331i
$52$	7.79196	−	5.24237i	1.08055	−	0.726986i
$53$	−8.74531	−	6.35384i	−1.20126	−	0.872767i	−0.206853	−	0.978372i	$-0.566322\pi$
$53$	−8.74531	−	6.35384i	−1.20126	−	0.872767i	−0.994408	+	0.105605i	$0.966322\pi$
$54$	1.27145	−	0.619200i	0.173023	−	0.0842624i
$55$	7.86274	−	9.80860i	1.06021	−	1.32259i
$56$	−7.09896	−	1.52208i	−0.948639	−	0.203396i
$57$	−0.281107	+	0.386910i	−0.0372335	+	0.0512475i
$58$	0.762984	+	5.45227i	0.100185	+	0.715918i
$59$	5.25007	−	1.70585i	0.683501	−	0.222083i	0.0533735	−	0.998575i	$-0.483003\pi$
$59$	5.25007	−	1.70585i	0.683501	−	0.222083i	0.630128	+	0.776492i	$0.283003\pi$
$60$	−7.57569	−	0.273505i	−0.978018	−	0.0353093i
$61$	6.33692	+	8.72202i	0.811359	+	1.11674i	0.991112	+	0.133029i	$0.0424702\pi$
$61$	6.33692	+	8.72202i	0.811359	+	1.11674i	−0.179753	+	0.983712i	$0.557530\pi$
$62$	−6.19220	−	6.41979i	−0.786411	−	0.815315i
$63$	0.793217	−	2.44127i	0.0999360	−	0.307571i
$64$	−3.97544	−	6.94233i	−0.496929	−	0.867791i
$65$		−	17.7981i		−	2.20758i
$66$	−1.03517	+	4.57476i	−0.127421	+	0.563114i
$67$		−	6.06244i		−	0.740645i	−0.928903	−	0.370322i	$-0.879247\pi$
$67$		−	6.06244i		−	0.740645i	0.928903	−	0.370322i	$-0.120753\pi$
$68$	−0.640342	−	2.24313i	−0.0776528	−	0.272019i
$69$	1.48511	−	4.57070i	0.178786	−	0.550248i
$70$	−9.90334	+	9.55225i	−1.18368	+	1.14171i
$71$	−0.999528	−	1.37573i	−0.118622	−	0.163269i	0.745577	−	0.666420i	$-0.232174\pi$
$71$	−0.999528	−	1.37573i	−0.118622	−	0.163269i	−0.864199	+	0.503150i	$0.832174\pi$
$72$	2.58593	−	1.14585i	0.304755	−	0.135039i
$73$	−5.26623	+	1.71110i	−0.616366	+	0.200269i	−0.600526	−	0.799605i	$-0.705042\pi$
$73$	−5.26623	+	1.71110i	−0.616366	+	0.200269i	−0.0158396	+	0.999875i	$0.505042\pi$
$74$	0.743288	−	0.104015i	0.0864055	−	0.0120915i
$75$	−5.50548	+	7.57765i	−0.635718	+	0.874991i
$76$	−0.589767	+	0.753032i	−0.0676509	+	0.0863787i
$77$	4.67206	+	7.11694i	0.532431	+	0.811050i
$78$	2.90756	+	5.97032i	0.329216	+	0.676005i
$79$	10.3403	+	7.51269i	1.16338	+	0.845244i	0.990201	−	0.139647i	$-0.0445968\pi$
$79$	10.3403	+	7.51269i	1.16338	+	0.845244i	0.173177	+	0.984891i	$0.444597\pi$
$80$	−15.1218	−	1.09331i	−1.69067	−	0.122235i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−0.137834	+	0.258860i	−0.0152212	+	0.0285863i
$83$	−8.06986	+	5.86309i	−0.885782	+	0.643558i	−0.934775	−	0.355241i	$-0.884399\pi$
$83$	−8.06986	+	5.86309i	−0.885782	+	0.643558i	0.0489929	+	0.998799i	$0.484399\pi$
$84$	1.76156	−	4.82213i	0.192202	−	0.526137i
$85$	−4.20453	−	1.36613i	−0.456045	−	0.148178i
$86$	0.0955346	−	0.539940i	0.0103018	−	0.0582232i
$87$	−3.89290			−0.417363
$88$	−2.39910	+	9.06887i	−0.255745	+	0.966744i
$89$	0.485931			0.0515085			0.0257543	−	0.999668i	$-0.491801\pi$
$89$	0.485931			0.0515085			0.0257543	+	0.999668i	$0.491801\pi$
$90$	0.933925	−	5.27833i	0.0984443	−	0.556385i
$91$	11.4634	+	3.72468i	1.20169	+	0.390453i
$92$	3.29810	−	9.02829i	0.343851	−	0.941264i
$93$	5.10249	−	3.70718i	0.529104	−	0.384416i
$94$	8.10872	−	15.2286i	0.836350	−	1.57071i
$95$	0.560158	+	1.72399i	0.0574710	+	0.176877i
$96$	5.25118	−	2.10360i	0.535946	−	0.214698i
$97$	2.60928	+	1.89576i	0.264933	+	0.192485i	0.712319	−	0.701856i	$-0.247645\pi$
$97$	2.60928	+	1.89576i	0.264933	+	0.192485i	−0.447386	+	0.894341i	$0.647645\pi$
$98$	0.254491	+	0.522567i	0.0257075	+	0.0527873i
$99$	−3.10218	−	1.17322i	−0.311781	−	0.117913i
$100$	−11.5506	+	14.7482i	−1.15506	+	1.47482i
$101$	−3.78115	+	5.20430i	−0.376238	+	0.517848i	−0.954583	−	0.297945i	$-0.903699\pi$
$101$	−3.78115	+	5.20430i	−0.376238	+	0.517848i	0.578345	+	0.815792i	$0.303699\pi$
$102$	1.63358	−	0.228601i	0.161748	−	0.0226349i
$103$	−6.33768	+	2.05924i	−0.624470	+	0.202903i	−0.604124	−	0.796890i	$-0.706477\pi$
$103$	−6.33768	+	2.05924i	−0.624470	+	0.202903i	−0.0203461	+	0.999793i	$0.506477\pi$
$104$	5.38052	+	12.1427i	0.527603	+	1.19069i
$105$	−5.71878	−	7.87123i	−0.558096	−	0.768153i
$106$	11.0031	−	10.6130i	1.06871	−	1.03083i
$107$	−0.208774	+	0.642539i	−0.0201829	+	0.0621166i	−0.960641	−	0.277794i	$-0.910397\pi$
$107$	−0.208774	+	0.642539i	−0.0201829	+	0.0621166i	0.940458	+	0.339910i	$0.110397\pi$
$108$	0.549004	+	1.92317i	0.0528280	+	0.185057i
$109$			4.69333i			0.449539i	0.974412	+	0.224770i	$0.0721629\pi$
$109$			4.69333i			0.449539i	−0.974412	+	0.224770i	$0.927837\pi$
$110$	11.7219	+	13.3663i	1.11764	+	1.27443i
$111$			0.530706i			0.0503723i
$112$	3.86879	−	9.51086i	0.365566	−	0.898692i
$113$	−5.15316	+	15.8598i	−0.484768	+	1.49196i	0.347548	+	0.937662i	$0.387014\pi$
$113$	−5.15316	+	15.8598i	−0.484768	+	1.49196i	−0.832316	+	0.554301i	$0.812986\pi$
$114$	−0.469541	−	0.486798i	−0.0439765	−	0.0455928i
$115$	−10.7071	−	14.7370i	−0.998439	−	1.37423i
$116$	−7.78074	−	0.280907i	−0.722423	−	0.0260816i
$117$	−4.46585	+	1.45104i	−0.412868	+	0.134149i
$118$	1.08193	+	7.73148i	0.0996002	+	0.711740i
$119$	1.75980	−	2.42216i	0.161321	−	0.222039i
$120$	2.24751	−	10.4824i	0.205169	−	0.956907i
$121$	9.47134	−	5.59408i	0.861031	−	0.508553i
$122$	−13.7075	+	6.67560i	−1.24102	+	0.604381i
$123$	−0.167768	−	0.121890i	−0.0151271	−	0.0109905i
$124$	10.4658	−	7.04134i	0.939860	−	0.632331i
$125$	5.11434	+	15.7403i	0.457440	+	1.40786i
$126$	3.20423	+	1.70614i	0.285455	+	0.151995i
$127$	−11.5742	+	8.40916i	−1.02705	+	0.746192i	−0.967715	−	0.252046i	$-0.918896\pi$
$127$	−11.5742	+	8.40916i	−1.02705	+	0.746192i	−0.0593300	+	0.998238i	$0.518896\pi$
$128$	10.6473	−	3.82555i	0.941098	−	0.338134i
$129$	0.368749	+	0.119814i	0.0324665	+	0.0105490i
$130$	24.7853	+	4.38540i	2.17381	+	0.384625i
$131$	6.62698			0.579002			0.289501	−	0.957178i	$-0.406511\pi$
$131$	6.62698			0.579002			0.289501	+	0.957178i	$0.406511\pi$
$132$	−6.11567	−	2.56877i	−0.532301	−	0.223583i
$133$	−1.22762			−0.106448
$134$	8.44245	+	1.49377i	0.729317	+	0.129042i
$135$	3.60480	+	1.17127i	0.310252	+	0.100807i
$136$	3.28152	−	0.339027i	0.281388	−	0.0290713i
$137$	9.66254	−	7.02025i	0.825527	−	0.599780i	−0.0927635	−	0.995688i	$-0.529570\pi$
$137$	9.66254	−	7.02025i	0.825527	−	0.599780i	0.918290	+	0.395908i	$0.129570\pi$
$138$	5.99915	+	3.19435i	0.510682	+	0.271921i
$139$	3.47067	+	10.6816i	0.294379	+	0.906004i	0.983429	+	0.181291i	$0.0580276\pi$
$139$	3.47067	+	10.6816i	0.294379	+	0.906004i	−0.689051	+	0.724713i	$0.741972\pi$
$140$	−10.8621	−	16.1449i	−0.918019	−	1.36449i
$141$	9.86969	+	7.17075i	0.831178	+	0.603886i
$142$	2.16210	−	1.05295i	0.181440	−	0.0883615i
$143$	5.50907	−	14.5668i	0.460691	−	1.21814i
$144$	0.958520	+	3.88346i	0.0798767	+	0.323621i
$145$	−8.67296	+	11.9373i	−0.720250	+	0.991340i
$146$	−1.08526	−	7.75527i	−0.0898171	−	0.641831i
$147$	−0.390884	+	0.127006i	−0.0322396	+	0.0104753i
$148$	−0.0382951	+	1.06072i	−0.00314784	+	0.0871907i
$149$	−6.87722	−	9.46568i	−0.563404	−	0.775459i	0.428351	−	0.903613i	$-0.359095\pi$
$149$	−6.87722	−	9.46568i	−0.563404	−	0.775459i	−0.991754	+	0.128154i	$0.959095\pi$
$150$	−9.19596	−	9.53396i	−0.750847	−	0.778444i
$151$	−4.36497	+	13.4340i	−0.355216	+	1.09324i	0.600668	+	0.799499i	$0.294901\pi$
$151$	−4.36497	+	13.4340i	−0.355216	+	1.09324i	−0.955884	+	0.293744i	$0.905099\pi$
$152$	−0.903343	−	1.00684i	−0.0732708	−	0.0816659i
$153$			1.16637i			0.0942953i
$154$	−11.0621	+	4.75264i	−0.891411	+	0.382979i
$155$		−	23.9056i		−	1.92014i
$156$	−9.03058	+	2.57794i	−0.723025	+	0.206401i
$157$	0.936252	−	2.88149i	0.0747210	−	0.229968i	−0.906720	−	0.421734i	$-0.861422\pi$
$157$	0.936252	−	2.88149i	0.0747210	−	0.229968i	0.981441	+	0.191766i	$0.0614216\pi$
$158$	−13.0099	+	12.5487i	−1.03501	+	0.998318i
$159$	6.35384	+	8.74531i	0.503892	+	0.693548i
$160$	5.24849	−	20.7890i	0.414930	−	1.64351i
$161$	11.7326	−	3.81214i	0.924655	−	0.300439i
$162$	−1.40057	+	0.195994i	−0.110039	+	0.0153987i
$163$	4.36835	−	6.01251i	0.342155	−	0.470937i	−0.602914	−	0.797806i	$-0.705994\pi$
$163$	4.36835	−	6.01251i	0.342155	−	0.470937i	0.945069	+	0.326870i	$0.105994\pi$
$164$	−0.326522	−	0.255728i	−0.0254971	−	0.0199690i
$165$	−10.5089	+	6.89881i	−0.818120	+	0.537072i
$166$	−6.17645	−	12.6826i	−0.479386	−	0.984361i
$167$	15.0825	+	10.9581i	1.16712	+	0.847960i	0.990661	−	0.136349i	$-0.0435368\pi$
$167$	15.0825	+	10.9581i	1.16712	+	0.847960i	0.176456	+	0.984309i	$0.443537\pi$
$168$	6.28117	+	3.64128i	0.484603	+	0.280931i
$169$	−2.79638	−	8.60639i	−0.215107	−	0.662030i
$170$	2.93844	−	5.51854i	0.225368	−	0.423253i
$171$	0.386910	−	0.281107i	0.0295878	−	0.0214968i
$172$	0.728371	+	0.266080i	0.0555378	+	0.0202884i
$173$	2.20212	+	0.715513i	0.167424	+	0.0543995i	0.391530	−	0.920165i	$-0.371946\pi$
$173$	2.20212	+	0.715513i	0.167424	+	0.0543995i	−0.224105	+	0.974565i	$0.571946\pi$
$174$	0.959202	−	5.42119i	0.0727169	−	0.410979i
$175$	−24.0429			−1.81747
$176$	−12.0380	−	5.57549i	−0.907400	−	0.420269i
$177$	−5.52025			−0.414927
$178$	−0.119732	+	0.676699i	−0.00897431	+	0.0507207i
$179$	−11.3758	−	3.69621i	−0.850266	−	0.276268i	−0.148708	−	0.988881i	$-0.547512\pi$
$179$	−11.3758	−	3.69621i	−0.850266	−	0.276268i	−0.701557	+	0.712613i	$0.747512\pi$
$180$	7.12040	+	2.60114i	0.530723	+	0.193877i
$181$	−6.52224	+	4.73869i	−0.484794	+	0.352224i	−0.803179	−	0.595738i	$-0.796860\pi$
$181$	−6.52224	+	4.73869i	−0.484794	+	0.352224i	0.318385	+	0.947962i	$0.396860\pi$
$182$	−8.01149	+	15.0460i	−0.593851	+	1.11528i
$183$	−3.33152	−	10.2534i	−0.246273	−	0.757950i
$184$	11.7600	+	6.81743i	0.866958	+	0.502588i
$185$	1.62737	+	1.18235i	0.119647	+	0.0869284i
$186$	3.90531	+	8.01908i	0.286351	+	0.587988i
$187$	−3.01834	−	2.41955i	−0.220723	−	0.176935i
$188$	19.2091	+	15.0444i	1.40097	+	1.09722i
$189$	−1.50879	+	2.07667i	−0.109748	+	0.151055i
$190$	−2.53882	+	0.355279i	−0.184185	+	0.0257747i
$191$	5.58275	−	1.81395i	0.403954	−	0.131253i	−0.0999912	−	0.994988i	$-0.531881\pi$
$191$	5.58275	−	1.81395i	0.403954	−	0.131253i	0.503945	+	0.863736i	$0.331881\pi$
$192$	1.63557	+	7.83102i	0.118037	+	0.565155i
$193$	−10.9443	−	15.0636i	−0.787790	−	1.08430i	−0.994380	−	0.105872i	$-0.966237\pi$
$193$	−10.9443	−	15.0636i	−0.787790	−	1.08430i	0.206590	−	0.978428i	$-0.433763\pi$
$194$	−3.28292	+	3.16654i	−0.235700	+	0.227344i
$195$	−5.49990	+	16.9270i	−0.393856	+	1.21216i
$196$	−0.790425	+	0.225641i	−0.0564589	+	0.0161172i
$197$			14.0020i			0.997604i	0.866716	+	0.498802i	$0.166226\pi$
$197$			14.0020i			0.997604i	−0.866716	+	0.498802i	$0.833774\pi$
$198$	2.39818	−	4.03097i	0.170431	−	0.286469i
$199$			12.2877i			0.871049i	0.900177	+	0.435524i	$0.143437\pi$
$199$			12.2877i			0.871049i	−0.900177	+	0.435524i	$0.856563\pi$
$200$	−17.6920	−	19.7191i	−1.25101	−	1.39435i
$201$	−1.87340	+	5.76572i	−0.132139	+	0.406683i
$202$	−6.31576	−	6.54789i	−0.444375	−	0.460708i
$203$	−5.87357	−	8.08427i	−0.412244	−	0.567405i
$204$	−0.0841638	+	2.33122i	−0.00589264	+	0.163218i
$205$	−0.747537	+	0.242889i	−0.0522102	+	0.0169641i
$206$	−1.30607	−	9.33314i	−0.0909981	−	0.650270i
$207$	−2.82485	+	3.88807i	−0.196341	+	0.270240i
$208$	−18.2354	+	4.50089i	−1.26440	+	0.312081i
$209$	−0.0751683	+	1.58439i	−0.00519950	+	0.109594i
$210$	12.3704	−	6.02443i	0.853641	−	0.415725i
$211$	−7.18092	−	5.21724i	−0.494355	−	0.359170i	0.312502	−	0.949917i	$-0.398833\pi$
$211$	−7.18092	−	5.21724i	−0.494355	−	0.359170i	−0.806857	+	0.590747i	$0.798833\pi$
$212$	12.0684	+	17.9377i	0.828858	+	1.23197i
$213$	0.525483	+	1.61727i	0.0360055	+	0.110814i
$214$	−0.843348	−	0.449055i	−0.0576501	−	0.0306968i
$215$	1.18893	−	0.863809i	0.0810845	−	0.0589113i
$216$	−2.81345	+	0.290669i	−0.191431	+	0.0197775i
$217$	15.3972	+	5.00284i	1.04523	+	0.339615i
$218$	−6.53585	−	1.15642i	−0.442663	−	0.0783230i
$219$	5.53724			0.374172
$220$	−21.5020	+	13.0303i	−1.44966	+	0.878505i
$221$	−5.47688			−0.368415
$222$	−0.739052	−	0.130765i	−0.0496019	−	0.00877635i
$223$	−0.283602	−	0.0921479i	−0.0189914	−	0.00617068i	0.299506	−	0.954094i	$-0.403178\pi$
$223$	−0.283602	−	0.0921479i	−0.0189914	−	0.00617068i	−0.318497	+	0.947924i	$0.603178\pi$
$224$	12.2914	+	7.73106i	0.821254	+	0.516553i
$225$	7.57765	−	5.50548i	0.505176	−	0.367032i
$226$	−20.8164	−	11.0840i	−1.38468	−	0.737298i
$227$	3.44600	+	10.6057i	0.228719	+	0.703925i	0.997893	+	0.0648850i	$0.0206681\pi$
$227$	3.44600	+	10.6057i	0.228719	+	0.703925i	−0.769174	+	0.639040i	$0.779332\pi$
$228$	0.793601	−	0.533929i	0.0525575	−	0.0353603i
$229$	−23.6155	−	17.1577i	−1.56056	−	1.13381i	−0.935552	−	0.353188i	$-0.885098\pi$
$229$	−23.6155	−	17.1577i	−1.56056	−	1.13381i	−0.625004	−	0.780622i	$-0.714902\pi$
$230$	23.1607	−	11.2793i	1.52717	−	0.743736i
$231$	−2.24414	−	8.21236i	−0.147654	−	0.540333i
$232$	2.30834	−	10.7661i	0.151550	−	0.706830i
$233$	8.44411	−	11.6223i	0.553192	−	0.761404i	−0.437249	−	0.899341i	$-0.644047\pi$
$233$	8.44411	−	11.6223i	0.553192	−	0.761404i	0.990441	+	0.137937i	$0.0440471\pi$
$234$	−0.920321	−	6.57659i	−0.0601633	−	0.429925i
$235$	43.9772	−	14.2891i	2.86876	−	0.932116i
$236$	−11.0333	−	0.398335i	−0.718208	−	0.0259294i
$237$	−7.51269	−	10.3403i	−0.488002	−	0.671677i
$238$	2.93945	+	3.04749i	0.190536	+	0.197539i
$239$	7.80842	−	24.0318i	0.505084	−	1.55449i	−0.295544	−	0.955329i	$-0.595501\pi$
$239$	7.80842	−	24.0318i	0.505084	−	1.55449i	0.800629	−	0.599161i	$-0.204499\pi$
$240$	14.0438	+	5.71269i	0.906525	+	0.368752i
$241$			6.17197i			0.397572i	0.980043	+	0.198786i	$0.0636998\pi$
$241$			6.17197i			0.397572i	−0.980043	+	0.198786i	$0.936300\pi$
$242$	5.45651	+	14.5680i	0.350758	+	0.936466i
$243$		−	1.00000i		−	0.0641500i
$244$	−5.91882	−	20.7337i	−0.378914	−	1.32734i
$245$	−0.481393	+	1.48158i	−0.0307551	+	0.0946544i
$246$	0.211080	−	0.203597i	0.0134580	−	0.0129809i
$247$	1.31998	+	1.81680i	0.0839886	+	0.115600i
$248$	7.22689	+	16.3095i	0.458908	+	1.03566i
$249$	9.48669	−	3.08241i	0.601194	−	0.195340i
$250$	−23.1799	+	3.24377i	−1.46602	+	0.205154i
$251$	−11.1398	+	15.3326i	−0.703138	+	0.967787i	0.296779	+	0.954946i	$0.404087\pi$
$251$	−11.1398	+	15.3326i	−0.703138	+	0.967787i	−0.999918	+	0.0128407i	$0.995913\pi$
$252$	−3.16546	+	4.04176i	−0.199405	+	0.254607i
$253$	−4.20162	−	15.3757i	−0.264154	−	0.966661i
$254$	−8.85859	−	18.1900i	−0.555837	−	1.14135i
$255$	3.57659	+	2.59854i	0.223975	+	0.162727i
$256$	2.70393	+	15.7699i	0.168995	+	0.985617i
$257$	−2.68605	−	8.26683i	−0.167551	−	0.515670i	0.831664	−	0.555280i	$-0.187389\pi$
$257$	−2.68605	−	8.26683i	−0.167551	−	0.515670i	−0.999215	+	0.0396091i	$0.987389\pi$
$258$	−0.257709	+	0.483991i	−0.0160443	+	0.0301320i
$259$	−1.10210	+	0.800723i	−0.0684812	+	0.0497545i
$260$	−12.2141	+	33.4350i	−0.757485	+	2.07355i
$261$	3.70237	+	1.20297i	0.229171	+	0.0744622i
$262$	−1.63287	+	9.22863i	−0.100879	+	0.570146i
$263$	27.0815			1.66992			0.834959	−	0.550312i	$-0.185491\pi$
$263$	27.0815			1.66992			0.834959	+	0.550312i	$0.185491\pi$
$264$	5.08411	−	7.88364i	0.312906	−	0.485205i
$265$	40.9725			2.51692
$266$	0.302482	−	1.70956i	0.0185463	−	0.104820i
$267$	−0.462148	−	0.150161i	−0.0282830	−	0.00918969i
$268$	−4.16040	+	11.3888i	−0.254137	+	0.695679i
$269$	18.5490	−	13.4767i	1.13095	−	0.821686i	0.145121	−	0.989414i	$-0.453643\pi$
$269$	18.5490	−	13.4767i	1.13095	−	0.821686i	0.985833	+	0.167728i	$0.0536430\pi$
$270$	−2.51931	+	4.73139i	−0.153320	+	0.287943i
$271$	−4.94899	−	15.2314i	−0.300630	−	0.925243i	−0.981272	−	0.192627i	$-0.938299\pi$
$271$	−4.94899	−	15.2314i	−0.300630	−	0.925243i	0.680642	−	0.732616i	$-0.261701\pi$
$272$	−0.336436	+	4.65333i	−0.0203994	+	0.282149i
$273$	−9.75135	−	7.08477i	−0.590179	−	0.428790i
$274$	7.39545	+	15.1857i	0.446776	+	0.917400i
$275$	−1.47217	+	31.0302i	−0.0887754	+	1.87119i
$276$	−5.92658	+	7.56724i	−0.356738	+	0.455494i
$277$	9.25995	−	12.7452i	0.556376	−	0.765786i	−0.434484	−	0.900680i	$-0.643069\pi$
$277$	9.25995	−	12.7452i	0.556376	−	0.765786i	0.990860	+	0.134893i	$0.0430692\pi$
$278$	−15.7302	+	2.20127i	−0.943436	+	0.132023i
$279$	−5.99834	+	1.94898i	−0.359111	+	0.116682i
$280$	25.1595	−	11.1484i	1.50357	−	0.666243i
$281$	8.02055	+	11.0393i	0.478466	+	0.658552i	0.978209	−	0.207622i	$-0.0665723\pi$
$281$	8.02055	+	11.0393i	0.478466	+	0.658552i	−0.499743	+	0.866174i	$0.666572\pi$
$282$	−12.4177	+	11.9775i	−0.739466	+	0.713251i
$283$	−3.54428	+	10.9082i	−0.210685	+	0.648423i	0.788746	+	0.614719i	$0.210730\pi$
$283$	−3.54428	+	10.9082i	−0.210685	+	0.648423i	−0.999432	+	0.0337043i	$0.989270\pi$
$284$	0.933581	+	3.27035i	0.0553979	+	0.194060i
$285$		−	1.81271i		−	0.107376i
$286$	18.9281	+	11.2611i	1.11924	+	0.665881i
$287$		−	0.532305i		−	0.0314210i
$288$	−5.64421	+	0.377944i	−0.332589	+	0.0222706i
$289$	4.83290	−	14.8741i	0.284288	−	0.874949i
$290$	−14.4867	−	15.0191i	−0.850688	−	0.881955i
$291$	−1.89576	−	2.60928i	−0.111131	−	0.152959i
$292$	11.0673	+	0.399561i	0.647663	+	0.0233825i
$293$	−6.23593	+	2.02618i	−0.364307	+	0.118371i	−0.485450	−	0.874265i	$-0.661344\pi$
$293$	−6.23593	+	2.02618i	−0.364307	+	0.118371i	0.121143	+	0.992635i	$0.461344\pi$
$294$	−0.0805535	−	0.575633i	−0.00469797	−	0.0335716i
$295$	−12.2985	+	16.9275i	−0.716047	+	0.985555i
$296$	−1.46771	−	0.314688i	−0.0853086	−	0.0182909i
$297$	2.58781	+	2.07443i	0.150160	+	0.120371i
$298$	14.8763	−	7.24478i	0.861760	−	0.419679i
$299$	−18.2571	−	13.2646i	−1.05583	−	0.767109i
$300$	15.5427	−	10.4570i	0.897358	−	0.603735i
$301$	0.307550	+	0.946542i	0.0177269	+	0.0545578i
$302$	−17.6324	−	9.38869i	−1.01463	−	0.540258i
$303$	5.20430	−	3.78115i	0.298979	−	0.217221i
$304$	1.62470	−	1.00990i	0.0931827	−	0.0579215i
$305$	−38.8634	−	12.6275i	−2.22531	−	0.723048i
$306$	−1.62427	−	0.287391i	−0.0928531	−	0.0164290i
$307$	26.0796			1.48844			0.744219	−	0.667935i	$-0.232822\pi$
$307$	26.0796			1.48844			0.744219	+	0.667935i	$0.232822\pi$
$308$	−3.89277	−	16.5760i	−0.221811	−	0.944503i
$309$	6.66383			0.379092
$310$	33.2906	+	5.89029i	1.89078	+	0.334546i
$311$	−11.3364	−	3.68343i	−0.642830	−	0.208868i	−0.0305801	−	0.999532i	$-0.509735\pi$
$311$	−11.3364	−	3.68343i	−0.642830	−	0.208868i	−0.612250	+	0.790664i	$0.709735\pi$
$312$	−1.36488	−	13.2110i	−0.0772714	−	0.747928i
$313$	−26.0639	+	18.9366i	−1.47322	+	1.07036i	−0.493556	+	0.869714i	$0.664303\pi$
$313$	−26.0639	+	18.9366i	−1.47322	+	1.07036i	−0.979664	+	0.200643i	$0.935697\pi$
$314$	3.78202	+	2.01380i	0.213432	+	0.113645i
$315$	3.00654	+	9.25319i	0.169399	+	0.521358i
$316$	−14.2695	−	21.2093i	−0.802719	−	1.19312i
$317$	−0.477091	−	0.346627i	−0.0267961	−	0.0194685i	0.574307	−	0.818640i	$-0.305272\pi$
$317$	−0.477091	−	0.346627i	−0.0267961	−	0.0194685i	−0.601103	+	0.799172i	$0.705272\pi$
$318$	−13.7441	+	6.69343i	−0.770734	+	0.375349i
$319$	−10.7934	+	7.08553i	−0.604313	+	0.396714i
$320$	27.6571	+	12.4313i	1.54608	+	0.694932i
$321$	0.397111	−	0.546576i	0.0221646	−	0.0305069i
$322$	2.41784	+	17.2779i	0.134741	+	0.962858i
$323$	0.530511	−	0.172374i	0.0295184	−	0.00959112i
$324$	0.0721588	−	1.99870i	0.00400882	−	0.111039i
$325$	25.8519	+	35.5821i	1.43401	+	1.97374i
$326$	7.29658	+	7.56476i	0.404120	+	0.418973i
$327$	1.45032	−	4.46362i	0.0802027	−	0.246839i
$328$	0.436577	−	0.391698i	0.0241059	−	0.0216279i
$329$			31.3152i			1.72647i
$330$	−7.01779	−	16.3344i	−0.386317	−	0.899180i
$331$		−	2.11968i		−	0.116508i	−0.998302	−	0.0582540i	$-0.981447\pi$
$331$		−	2.11968i		−	0.116508i	0.998302	−	0.0582540i	$-0.0185533\pi$
$332$	19.1834	−	5.47626i	1.05283	−	0.300549i
$333$	0.163997	−	0.504731i	0.00898698	−	0.0276591i
$334$	−18.9763	+	18.3036i	−1.03834	+	1.00153i
$335$	13.5065	+	18.5900i	0.737937	+	1.01568i
$336$	−6.61845	+	7.84985i	−0.361066	+	0.428244i
$337$	−27.1558	+	8.82344i	−1.47927	+	0.480644i	−0.933894	−	0.357549i	$-0.883613\pi$
$337$	−27.1558	+	8.82344i	−1.47927	+	0.480644i	−0.545374	+	0.838193i	$0.683613\pi$
$338$	12.6741	−	1.77360i	0.689382	−	0.0964714i
$339$	9.80189	−	13.4911i	0.532366	−	0.732738i
$340$	6.96101	+	5.45178i	0.377514	+	0.295664i
$341$	7.39955	−	19.5656i	0.400708	−	1.05953i
$342$	0.296131	+	0.608069i	0.0160129	+	0.0328806i
$343$	−15.3902	−	11.1816i	−0.830993	−	0.603751i
$344$	−0.550007	+	0.948756i	−0.0296544	+	0.0511535i
$345$	5.62904	+	17.3244i	0.303057	+	0.932714i
$346$	−1.53901	+	2.89034i	−0.0827377	+	0.155386i
$347$	−2.46695	+	1.79235i	−0.132433	+	0.0962182i	−0.652030	−	0.758194i	$-0.726082\pi$
$347$	−2.46695	+	1.79235i	−0.132433	+	0.0962182i	0.519597	+	0.854412i	$0.326082\pi$
$348$	7.31311	+	2.67154i	0.392024	+	0.143209i
$349$	1.75032	+	0.568714i	0.0936926	+	0.0304426i	0.355488	−	0.934681i	$-0.384315\pi$
$349$	1.75032	+	0.568714i	0.0936926	+	0.0304426i	−0.261796	+	0.965123i	$0.584315\pi$
$350$	5.92411	−	33.4817i	0.316657	−	1.78967i
$351$	4.69567			0.250636
$352$	10.7305	−	15.3902i	0.571937	−	0.820298i
$353$	−23.3261			−1.24152			−0.620761	−	0.784000i	$-0.713176\pi$
$353$	−23.3261			−1.24152			−0.620761	+	0.784000i	$0.713176\pi$
$354$	1.36018	−	7.68741i	0.0722926	−	0.408581i
$355$	6.12996	+	1.99175i	0.325345	+	0.105711i
$356$	−0.912858	−	0.333474i	−0.0483814	−	0.0176741i
$357$	−2.42216	+	1.75980i	−0.128194	+	0.0931387i
$358$	7.95025	−	14.9310i	0.420184	−	0.789127i
$359$	−1.66383	−	5.12073i	−0.0878134	−	0.270262i	0.897501	−	0.441013i	$-0.145381\pi$
$359$	−1.66383	−	5.12073i	−0.0878134	−	0.270262i	−0.985314	+	0.170751i	$0.945381\pi$
$360$	−5.37675	+	9.27483i	−0.283380	+	0.488826i
$361$	15.1863	+	11.0335i	0.799278	+	0.580710i
$362$	−4.99195	−	10.2504i	−0.262371	−	0.538747i
$363$	−10.7364	+	2.39348i	−0.563517	+	0.125625i
$364$	−18.9788	−	14.8640i	−0.994758	−	0.779083i
$365$	12.3364	−	16.9796i	0.645715	−	0.888751i
$366$	15.0995	−	2.11301i	0.789265	−	0.110449i
$367$	−5.32010	+	1.72861i	−0.277707	+	0.0902325i	−0.444559	−	0.895749i	$-0.646640\pi$
$367$	−5.32010	+	1.72861i	−0.277707	+	0.0902325i	0.166852	+	0.985982i	$0.446640\pi$
$368$	−12.3915	+	14.6970i	−0.645951	+	0.766133i
$369$	0.121890	+	0.167768i	0.00634536	+	0.00873364i
$370$	−2.04751	+	1.97492i	−0.106445	+	0.102671i
$371$	−8.57452	+	26.3897i	−0.445167	+	1.37008i
$372$	−12.1295	+	3.46258i	−0.628885	+	0.179527i
$373$		−	10.9744i		−	0.568234i	−0.958790	−	0.284117i	$-0.908300\pi$
$373$		−	10.9744i		−	0.568234i	0.958790	−	0.284117i	$-0.0917004\pi$
$374$	4.11314	−	3.60711i	0.212685	−	0.186519i
$375$		−	16.5504i		−	0.854656i
$376$	−25.6836	+	23.0434i	−1.32453	+	1.18837i
$377$	−5.64876	+	17.3851i	−0.290926	+	0.895378i
$378$	−2.52017	−	2.61280i	−0.129624	−	0.134388i
$379$	2.08094	+	2.86416i	0.106891	+	0.147122i	0.859111	−	0.511789i	$-0.171017\pi$
$379$	2.08094	+	2.86416i	0.106891	+	0.147122i	−0.752220	+	0.658912i	$0.771017\pi$
$380$	0.130803	−	3.62306i	0.00671005	−	0.185859i
$381$	13.6063	−	4.42096i	0.697072	−	0.226492i
$382$	1.15049	+	8.22140i	0.0588644	+	0.420643i
$383$	4.62411	−	6.36454i	0.236281	−	0.325213i	−0.674367	−	0.738396i	$-0.735583\pi$
$383$	4.62411	−	6.36454i	0.236281	−	0.325213i	0.910648	+	0.413184i	$0.135583\pi$
$384$	−11.3084	+	0.348116i	−0.577077	+	0.0177647i
$385$	−30.1823	−	11.4147i	−1.53823	−	0.581749i
$386$	23.6739	−	11.5293i	1.20497	−	0.586824i
$387$	−0.313676	−	0.227899i	−0.0159451	−	0.0115848i
$388$	−3.60076	−	5.35197i	−0.182801	−	0.271705i
$389$	1.59577	+	4.91127i	0.0809087	+	0.249011i	0.983326	−	0.181852i	$-0.0582092\pi$
$389$	1.59577	+	4.91127i	0.0809087	+	0.249011i	−0.902417	+	0.430863i	$0.858209\pi$
$390$	−22.2170	−	11.8298i	−1.12500	−	0.599027i
$391$	−4.53492	+	3.29481i	−0.229341	+	0.166626i
$392$	−0.119465	−	1.15633i	−0.00603389	−	0.0584035i
$393$	−6.30264	−	2.04785i	−0.317926	−	0.103300i
$394$	−19.4990	−	3.45007i	−0.982345	−	0.173812i
$395$	−48.4453			−2.43755
$396$	5.02255	+	4.33289i	0.252393	+	0.217736i
$397$	29.6678			1.48898			0.744492	−	0.667632i	$-0.232692\pi$
$397$	29.6678			1.48898			0.744492	+	0.667632i	$0.232692\pi$
$398$	−17.1116	−	3.02765i	−0.857726	−	0.151762i
$399$	1.16753	+	0.379354i	0.0584497	+	0.0189915i
$400$	31.8197	−	19.7788i	1.59099	−	0.988942i
$401$	−11.8185	+	8.58666i	−0.590189	+	0.428797i	−0.842383	−	0.538879i	$-0.818848\pi$
$401$	−11.8185	+	8.58666i	−0.590189	+	0.428797i	0.252194	+	0.967677i	$0.418848\pi$
$402$	−7.56765	−	4.02952i	−0.377440	−	0.200974i
$403$	−9.15175	−	28.1662i	−0.455881	−	1.40306i
$404$	10.6747	−	7.18184i	0.531085	−	0.357310i
$405$	−3.06643	−	2.22789i	−0.152372	−	0.110705i
$406$	12.7053	−	6.18749i	0.630551	−	0.307080i
$407$	0.965946	+	1.47142i	0.0478801	+	0.0729357i
$408$	−3.22568	−	0.691612i	−0.159695	−	0.0342399i
$409$	−22.0197	+	30.3075i	−1.08880	+	1.49861i	−0.239360	+	0.970931i	$0.576938\pi$
$409$	−22.0197	+	30.3075i	−1.08880	+	1.49861i	−0.849444	+	0.527679i	$0.823062\pi$
$410$	−0.154052	−	1.10085i	−0.00760810	−	0.0543673i
$411$	−11.3590	+	3.69076i	−0.560298	+	0.182052i
$412$	13.3190	+	0.480854i	0.656179	+	0.0236900i
$413$	−8.32889	−	11.4637i	−0.409838	−	0.564094i
$414$	−4.71843	−	4.89185i	−0.231898	−	0.240421i
$415$	11.6833	−	35.9575i	0.573511	−	1.76509i
$416$	−1.77470	−	26.5034i	−0.0870118	−	1.29943i
$417$		−	11.2313i		−	0.550001i
$418$	−2.18787	−	0.495067i	−0.107012	−	0.0242145i
$419$		−	17.1505i		−	0.837855i	−0.908020	−	0.418927i	$-0.862406\pi$
$419$		−	17.1505i		−	0.837855i	0.908020	−	0.418927i	$-0.137594\pi$
$420$	5.34147	+	18.7113i	0.260637	+	0.913017i
$421$	−3.39183	+	10.4390i	−0.165308	+	0.508765i	−0.999059	−	0.0433757i	$-0.986189\pi$
$421$	−3.39183	+	10.4390i	−0.165308	+	0.508765i	0.833751	+	0.552140i	$0.186189\pi$
$422$	9.03481	−	8.71451i	0.439807	−	0.424216i
$423$	−7.17075	−	9.86969i	−0.348654	−	0.479881i
$424$	−27.9534	+	12.3864i	−1.35754	+	0.601536i
$425$	10.3901	−	3.37594i	0.503993	−	0.163757i
$426$	−2.38166	+	0.333287i	−0.115392	+	0.0161478i
$427$	16.2663	−	22.3886i	0.787180	−	1.08346i
$428$	0.833145	−	1.06379i	0.0402716	−	0.0514200i
$429$	−9.74083	+	12.1515i	−0.470292	+	0.586679i
$430$	0.909976	+	1.86853i	0.0438830	+	0.0901084i
$431$	−0.0199751	−	0.0145128i	−0.000962167	−	0.000699055i	0.587304	−	0.809366i	$-0.300189\pi$
$431$	−0.0199751	−	0.0145128i	−0.000962167	−	0.000699055i	−0.588266	+	0.808667i	$0.700189\pi$
$432$	0.288447	−	3.98959i	0.0138779	−	0.191949i
$433$	3.91386	+	12.0456i	0.188088	+	0.578876i	0.999988	−	0.00492123i	$-0.00156648\pi$
$433$	3.91386	+	12.0456i	0.188088	+	0.578876i	−0.811900	+	0.583797i	$0.801566\pi$
$434$	−10.7607	+	20.2091i	−0.516530	+	0.970070i
$435$	11.9373	−	8.67296i	0.572350	−	0.415837i
$436$	3.22084	−	8.81677i	0.154250	−	0.422247i
$437$	2.18593	+	0.710250i	0.104567	+	0.0339759i
$438$	−1.36436	+	7.71107i	−0.0651918	+	0.368449i
$439$	35.6300			1.70053			0.850263	−	0.526358i	$-0.176443\pi$
$439$	35.6300			1.70053			0.850263	+	0.526358i	$0.176443\pi$
$440$	−12.8478	−	33.1540i	−0.612494	−	1.58055i
$441$	0.411000			0.0195714
$442$	1.34949	−	7.62701i	0.0641887	−	0.362780i
$443$	18.5921	+	6.04094i	0.883338	+	0.287014i	0.715343	−	0.698774i	$-0.246271\pi$
$443$	18.5921	+	6.04094i	0.883338	+	0.287014i	0.167995	+	0.985788i	$0.446271\pi$
$444$	0.364201	−	0.996971i	0.0172842	−	0.0473141i
$445$	−1.49007	+	1.08260i	−0.0706362	+	0.0513202i
$446$	0.198202	−	0.372234i	0.00938516	−	0.0176258i
$447$	3.61557	+	11.1276i	0.171010	+	0.526316i
$448$	−13.7947	+	15.2119i	−0.651739	+	0.718694i
$449$	22.1455	+	16.0897i	1.04511	+	0.759319i	0.971277	−	0.237951i	$-0.0764759\pi$
$449$	22.1455	+	16.0897i	1.04511	+	0.759319i	0.0738358	+	0.997270i	$0.476476\pi$
$450$	5.79973	+	11.9090i	0.273402	+	0.561398i
$451$	−0.687004	−	0.0325937i	−0.0323497	−	0.00153478i
$452$	20.5645	−	26.2574i	0.967274	−	1.23505i
$453$	8.30267	−	11.4276i	0.390093	−	0.536917i
$454$	−15.6184	+	2.18562i	−0.733008	+	0.102576i
$455$	−43.4499	+	14.1177i	−2.03696	+	0.661849i
$456$	0.547998	+	1.23671i	0.0256624	+	0.0579145i
$457$	11.2322	+	15.4598i	0.525420	+	0.723178i	0.986424	−	0.164220i	$-0.0525106\pi$
$457$	11.2322	+	15.4598i	0.525420	+	0.723178i	−0.461004	+	0.887398i	$0.652511\pi$
$458$	29.7123	−	28.6589i	1.38836	−	1.33914i
$459$	0.360428	−	1.10928i	0.0168233	−	0.0517769i
$460$	10.0006	+	35.0324i	0.466282	+	1.63339i
$461$		−	13.1594i		−	0.612893i	−0.951888	−	0.306446i	$-0.900860\pi$
$461$		−	13.1594i		−	0.612893i	0.951888	−	0.306446i	$-0.0991400\pi$
$462$	11.9893	−	1.10165i	0.557795	−	0.0512533i
$463$			37.3352i			1.73512i	0.497336	+	0.867558i	$0.334312\pi$
$463$			37.3352i			1.73512i	−0.497336	+	0.867558i	$0.665688\pi$
$464$	14.4239	+	5.86730i	0.669614	+	0.272383i
$465$	−7.38724	+	22.7356i	−0.342575	+	1.05434i
$466$	14.1044	+	14.6228i	0.653376	+	0.677390i
$467$	6.21875	+	8.55937i	0.287769	+	0.396080i	0.928288	−	0.371862i	$-0.121281\pi$
$467$	6.21875	+	8.55937i	0.287769	+	0.396080i	−0.640519	+	0.767943i	$0.721281\pi$
$468$	9.38522	+	0.338834i	0.433832	+	0.0156626i
$469$	−14.8001	+	4.80883i	−0.683403	+	0.222051i
$470$	9.06282	+	64.7627i	0.418037	+	2.98728i
$471$	−1.78086	+	2.45114i	−0.0820575	+	0.112943i
$472$	3.27330	−	15.2667i	0.150666	−	0.702705i
$473$	1.24046	−	0.338973i	0.0570363	−	0.0155860i
$474$	16.2509	−	7.91421i	0.746428	−	0.363512i
$475$	−3.62399	−	2.63298i	−0.166280	−	0.120810i
$476$	−4.96816	+	3.34254i	−0.227715	+	0.153205i
$477$	−3.34041	−	10.2807i	−0.152947	−	0.470722i
$478$	31.5424	+	16.7953i	1.44271	+	0.768197i
$479$	−11.0748	+	8.04633i	−0.506021	+	0.367646i	−0.811312	−	0.584613i	$-0.801246\pi$
$479$	−11.0748	+	8.04633i	−0.506021	+	0.367646i	0.305291	+	0.952259i	$0.401246\pi$
$480$	−11.4158	+	18.1496i	−0.521056	+	0.828412i
$481$	2.37005	+	0.770076i	0.108065	+	0.0351124i
$482$	−8.59499	−	1.52076i	−0.391491	−	0.0692687i
$483$	−12.3363			−0.561323
$484$	−21.6316	+	4.00912i	−0.983255	+	0.182233i
$485$	−12.2247			−0.555096
$486$	1.39258	+	0.246398i	0.0631689	+	0.0111768i
$487$	4.85451	+	1.57733i	0.219979	+	0.0714754i	0.416933	−	0.908937i	$-0.363105\pi$
$487$	4.85451	+	1.57733i	0.219979	+	0.0714754i	−0.196954	+	0.980413i	$0.563105\pi$
$488$	30.3319	−	3.13371i	1.37306	−	0.141856i
$489$	−6.01251	+	4.36835i	−0.271895	+	0.197544i
$490$	−1.94460	−	1.03544i	−0.0878482	−	0.0467763i
$491$	10.0078	+	30.8010i	0.451648	+	1.39003i	0.875026	+	0.484075i	$0.160844\pi$
$491$	10.0078	+	30.8010i	0.451648	+	1.39003i	−0.423379	+	0.905953i	$0.639156\pi$
$492$	0.231516	+	0.344113i	0.0104376	+	0.0155138i
$493$	3.67339	+	2.66887i	0.165441	+	0.120200i
$494$	−2.85529	+	1.39053i	−0.128466	+	0.0625630i
$495$	12.1264	−	3.31372i	0.545043	−	0.148941i
$496$	−24.4931	+	6.04541i	−1.09977	+	0.271447i
$497$	−2.56569	+	3.53137i	−0.115087	+	0.158404i
$498$	1.95502	+	13.9705i	0.0876064	+	0.626033i
$499$	−25.1179	+	8.16130i	−1.12443	+	0.365350i	−0.811457	−	0.584412i	$-0.801325\pi$
$499$	−25.1179	+	8.16130i	−1.12443	+	0.365350i	−0.312974	+	0.949762i	$0.601325\pi$
$500$	1.19425	−	33.0792i	0.0534087	−	1.47934i
$501$	−10.9581	−	15.0825i	−0.489570	−	0.673835i
$502$	−18.6071	−	19.2910i	−0.830477	−	0.861001i
$503$	−0.273966	+	0.843180i	−0.0122155	+	0.0375955i	−0.956978	−	0.290159i	$-0.906292\pi$
$503$	−0.273966	+	0.843180i	−0.0122155	+	0.0375955i	0.944763	+	0.327754i	$0.106292\pi$
$504$	−4.84853	−	5.40405i	−0.215971	−	0.240716i
$505$		−	24.3826i		−	1.08501i
$506$	22.4472	−	2.06258i	0.997900	−	0.0916926i
$507$			9.04929i			0.401893i
$508$	27.5139	−	7.85434i	1.22073	−	0.348480i
$509$	12.7139	−	39.1293i	0.563532	−	1.73437i	−0.108740	−	0.994070i	$-0.534682\pi$
$509$	12.7139	−	39.1293i	0.563532	−	1.73437i	0.672272	−	0.740304i	$-0.265318\pi$
$510$	−4.49995	+	4.34042i	−0.199261	+	0.192197i
$511$	8.35453	+	11.4990i	0.369583	+	0.508687i
$512$	−22.6271	−	0.120219i	−0.999986	−	0.00531297i
$513$	−0.454840	+	0.147787i	−0.0200817	+	0.00652494i
$514$	12.1741	−	1.70363i	0.536976	−	0.0751438i
$515$	14.8463	−	20.4342i	0.654206	−	0.900437i
$516$	−0.610499	−	0.478136i	−0.0268757	−	0.0210488i
$517$	40.4161	+	1.91747i	1.77750	+	0.0843302i
$518$	−0.843518	−	1.73206i	−0.0370620	−	0.0761025i
$519$	−1.87324	−	1.36099i	−0.0822260	−	0.0597407i
$520$	−43.5515	−	25.2474i	−1.90986	−	1.10717i
$521$	−5.92861	−	18.2464i	−0.259737	−	0.799389i	−0.992859	−	0.119292i	$-0.961938\pi$
$521$	−5.92861	−	18.2464i	−0.259737	−	0.799389i	0.733122	−	0.680097i	$-0.238062\pi$
$522$	−2.58750	+	4.85945i	−0.113252	+	0.212692i
$523$	14.1087	−	10.2506i	0.616929	−	0.448225i	−0.234918	−	0.972015i	$-0.575482\pi$
$523$	14.1087	−	10.2506i	0.616929	−	0.448225i	0.851848	+	0.523790i	$0.175482\pi$
$524$	−12.4493	−	4.54783i	−0.543850	−	0.198673i
$525$	22.8661	+	7.42966i	0.997960	+	0.324257i
$526$	−6.67283	+	37.7133i	−0.290949	+	1.64438i
$527$	−7.35632			−0.320446
$528$	9.72591	+	9.02256i	0.423266	+	0.392657i
$529$	−0.0968663			−0.00421158
$530$	−10.0955	+	57.0577i	−0.438522	+	2.47843i
$531$	5.25007	+	1.70585i	0.227834	+	0.0740276i
$532$	2.30617	+	0.842462i	0.0999851	+	0.0365254i
$533$	−0.787782	+	0.572357i	−0.0341226	+	0.0247915i
$534$	0.322984	−	0.606580i	0.0139769	−	0.0262493i
$535$	−0.791318	−	2.43543i	−0.0342116	−	0.105293i
$536$	−14.8347	−	8.59987i	−0.640761	−	0.371458i
$537$	9.67681	+	7.03062i	0.417585	+	0.303394i
$538$	14.1969	+	29.1517i	0.612073	+	1.25682i
$539$	−0.852591	+	1.06359i	−0.0367237	+	0.0458120i
$540$	−5.96810	−	4.67415i	−0.256826	−	0.201143i
$541$	18.2983	−	25.1854i	0.786704	−	1.08281i	−0.207807	−	0.978170i	$-0.566632\pi$
$541$	18.2983	−	25.1854i	0.786704	−	1.08281i	0.994511	−	0.104635i	$-0.0333675\pi$
$542$	22.4304	−	3.13889i	0.963470	−	0.134827i
$543$	7.66735	−	2.49127i	0.329038	−	0.106911i
$544$	−6.39725	−	1.61508i	−0.274280	−	0.0692462i
$545$	−10.4562	−	14.3918i	−0.447895	−	0.616475i
$546$	12.2688	−	11.8339i	0.525058	−	0.506444i
$547$	−7.04890	+	21.6943i	−0.301389	+	0.927581i	0.679611	+	0.733573i	$0.262149\pi$
$547$	−7.04890	+	21.6943i	−0.301389	+	0.927581i	−0.981000	+	0.194008i	$0.937851\pi$
$548$	−22.9695	+	6.55707i	−0.981210	+	0.280104i
$549$			10.7810i			0.460122i
$550$	−42.8494	−	9.69590i	−1.82711	−	0.413435i
$551$		−	1.86177i		−	0.0793141i
$552$	−9.07772	−	10.1178i	−0.386373	−	0.430642i
$553$	10.1384	−	31.2027i	0.431128	−	1.32688i
$554$	15.4672	+	16.0356i	0.657136	+	0.681289i
$555$	−1.18235	−	1.62737i	−0.0501881	−	0.0690780i
$556$	0.810440	−	22.4480i	0.0343703	−	0.952009i
$557$	−31.1035	+	10.1061i	−1.31790	+	0.428211i	−0.881773	−	0.471675i	$-0.843650\pi$
$557$	−31.1035	+	10.1061i	−1.31790	+	0.428211i	−0.436125	+	0.899886i	$0.643650\pi$
$558$	−1.23614	−	8.83341i	−0.0523299	−	0.373948i
$559$	1.07014	−	1.47292i	0.0452620	−	0.0622978i
$560$	9.32580	+	37.7836i	0.394087	+	1.59665i
$561$	2.12293	+	3.23385i	0.0896300	+	0.136533i
$562$	−17.3495	+	8.44922i	−0.731842	+	0.356409i
$563$	15.9372	+	11.5790i	0.671672	+	0.487998i	0.870584	−	0.492019i	$-0.163741\pi$
$563$	15.9372	+	11.5790i	0.671672	+	0.487998i	−0.198912	+	0.980017i	$0.563741\pi$
$564$	−13.6200	−	20.2440i	−0.573505	−	0.852425i
$565$	−19.5321	−	60.1136i	−0.821721	−	2.52900i
$566$	−14.3172	−	7.62345i	−0.601798	−	0.320437i
$567$	2.07667	−	1.50879i	0.0872119	−	0.0633632i
$568$	−4.78427	+	0.494282i	−0.200744	+	0.0207396i
$569$	17.9385	+	5.82857i	0.752021	+	0.244347i	0.659851	−	0.751397i	$-0.270619\pi$
$569$	17.9385	+	5.82857i	0.752021	+	0.244347i	0.0921706	+	0.995743i	$0.470619\pi$
$570$	2.52435	+	0.446647i	0.105733	+	0.0187080i
$571$	−14.8404			−0.621051			−0.310526	−	0.950565i	$-0.600505\pi$
$571$	−14.8404			−0.621051			−0.310526	+	0.950565i	$0.600505\pi$
$572$	−20.3458	+	23.5842i	−0.850701	+	0.986107i
$573$	−5.87005			−0.245225
$574$	0.741279	+	0.131159i	0.0309404	+	0.00547446i
$575$	42.8114	+	13.9103i	1.78536	+	0.580098i
$576$	0.864403	−	7.95316i	0.0360168	−	0.331382i
$577$	1.16356	−	0.845376i	0.0484396	−	0.0351934i	−0.563302	−	0.826251i	$-0.690469\pi$
$577$	1.16356	−	0.845376i	0.0484396	−	0.0351934i	0.611742	+	0.791058i	$0.290469\pi$
$578$	19.5226	+	10.3952i	0.812035	+	0.432382i
$579$	5.75377	+	17.7083i	0.239119	+	0.735932i
$580$	24.4849	−	16.4732i	1.01668	−	0.684014i
$581$	20.7146	+	15.0500i	0.859384	+	0.624379i
$582$	4.10075	−	1.99708i	0.169982	−	0.0827815i
$583$	33.5340	+	12.6823i	1.38884	+	0.525248i
$584$	−3.28337	+	15.3136i	−0.135867	+	0.633683i
$585$	10.4614	−	14.3989i	0.432527	−	0.595322i
$586$	−1.28510	−	9.18330i	−0.0530871	−	0.379359i
$587$	5.90918	−	1.92001i	0.243898	−	0.0792473i	−0.184517	−	0.982829i	$-0.559072\pi$
$587$	5.90918	−	1.92001i	0.243898	−	0.0792473i	0.428415	+	0.903582i	$0.359072\pi$
$588$	0.821465	+	0.0296573i	0.0338767	+	0.00122305i
$589$	1.77295	+	2.44025i	0.0730530	+	0.100549i
$590$	−20.5426	−	21.2976i	−0.845724	−	0.876808i
$591$	4.32687	−	13.3167i	0.177984	−	0.547777i
$592$	0.799869	−	1.96636i	0.0328744	−	0.0808170i
$593$			12.3149i			0.505713i	0.967504	+	0.252857i	$0.0813701\pi$
$593$			12.3149i			0.505713i	−0.967504	+	0.252857i	$0.918630\pi$
$594$	−3.52645	+	3.09260i	−0.144692	+	0.126891i
$595$			11.3480i			0.465224i
$596$	6.42347	+	22.5015i	0.263116	+	0.921699i
$597$	3.79709	−	11.6863i	0.155405	−	0.478286i
$598$	22.9705	−	22.1562i	0.939333	−	0.906033i
$599$	−4.99434	−	6.87412i	−0.204063	−	0.280869i	0.694703	−	0.719296i	$-0.255536\pi$
$599$	−4.99434	−	6.87412i	−0.204063	−	0.280869i	−0.898767	+	0.438427i	$0.855536\pi$
$600$	10.7326	+	24.2211i	0.438155	+	0.988821i
$601$	−1.83690	+	0.596844i	−0.0749286	+	0.0243458i	−0.346241	−	0.938145i	$-0.612542\pi$
$601$	−1.83690	+	0.596844i	−0.0749286	+	0.0243458i	0.271313	+	0.962491i	$0.412542\pi$
$602$	−1.39392	+	0.195063i	−0.0568119	+	0.00795019i
$603$	3.56341	−	4.90462i	0.145113	−	0.199731i
$604$	17.4191	−	22.2413i	0.708774	−	0.904985i
$605$	−16.5802	+	38.2550i	−0.674080	+	1.55529i
$606$	3.98324	+	8.17909i	0.161808	+	0.332253i
$607$	−34.8462	−	25.3172i	−1.41436	−	1.02759i	−0.992670	−	0.120856i	$-0.961436\pi$
$607$	−34.8462	−	25.3172i	−1.41436	−	1.02759i	−0.421693	−	0.906739i	$-0.638564\pi$
$608$	1.00604	+	2.51136i	0.0408004	+	0.101849i
$609$	3.08792	+	9.50363i	0.125129	+	0.385107i
$610$	27.1607	−	51.0092i	1.09970	−	2.06530i
$611$	46.3448	−	33.6715i	1.87491	−	1.36220i
$612$	0.800431	−	2.19111i	0.0323555	−	0.0885705i
$613$	−36.1624	−	11.7499i	−1.46059	−	0.474573i	−0.532337	−	0.846532i	$-0.678686\pi$
$613$	−36.1624	−	11.7499i	−1.46059	−	0.474573i	−0.928249	+	0.371959i	$0.878686\pi$
$614$	−6.42594	+	36.3180i	−0.259330	+	1.46567i
$615$	0.786007			0.0316948
$616$	24.0426	−	1.33672i	0.968703	−	0.0538582i
$617$	−1.21793			−0.0490319			−0.0245159	−	0.999699i	$-0.507804\pi$
$617$	−1.21793			−0.0490319			−0.0245159	+	0.999699i	$0.507804\pi$
$618$	−1.64195	+	9.27994i	−0.0660490	+	0.373294i
$619$	−20.3457	−	6.61071i	−0.817762	−	0.265707i	−0.129880	−	0.991530i	$-0.541459\pi$
$619$	−20.3457	−	6.61071i	−0.817762	−	0.265707i	−0.687882	+	0.725823i	$0.741459\pi$
$620$	−16.4054	+	44.9085i	−0.658858	+	1.80357i
$621$	3.88807	−	2.82485i	0.156023	−	0.113357i
$622$	7.92276	−	14.8793i	0.317674	−	0.596607i
$623$	−0.385449	−	1.18629i	−0.0154427	−	0.0475277i
$624$	18.7338	+	1.35445i	0.749951	+	0.0542215i
$625$	−12.8622	−	9.34497i	−0.514490	−	0.373799i
$626$	−19.9486	−	40.9621i	−0.797308	−	1.63718i
$627$	0.561091	−	1.48361i	0.0224078	−	0.0592497i
$628$	−3.73627	+	4.77058i	−0.149093	+	0.190367i
$629$	0.363838	−	0.500780i	0.0145072	−	0.0199674i
$630$	−13.6266	+	1.90690i	−0.542898	+	0.0759726i
$631$	−31.6495	+	10.2835i	−1.25995	+	0.409381i	−0.861475	−	0.507800i	$-0.830459\pi$
$631$	−31.6495	+	10.2835i	−1.25995	+	0.409381i	−0.398471	+	0.917181i	$0.630459\pi$
$632$	33.0517	−	14.6455i	1.31473	−	0.582566i
$633$	5.21724	+	7.18092i	0.207367	+	0.285416i
$634$	0.600261	−	0.578981i	0.0238394	−	0.0229943i
$635$	16.7568	−	51.5722i	0.664974	−	2.04658i
$636$	−5.93463	−	20.7891i	−0.235323	−	0.824342i
$637$			1.92992i			0.0764662i
$638$	−7.20773	−	16.7765i	−0.285357	−	0.664189i
$639$		−	1.70050i		−	0.0672707i
$640$	−24.1263	+	35.4518i	−0.953676	+	1.40136i
$641$	−4.08520	+	12.5730i	−0.161356	+	0.496602i	−0.998749	−	0.0499983i	$-0.984078\pi$
$641$	−4.08520	+	12.5730i	−0.161356	+	0.496602i	0.837393	+	0.546601i	$0.184078\pi$
$642$	0.663306	+	0.687685i	0.0261786	+	0.0271408i
$643$	−26.4073	−	36.3466i	−1.04140	−	1.43337i	−0.896031	−	0.443992i	$-0.853562\pi$
$643$	−26.4073	−	36.3466i	−1.04140	−	1.43337i	−0.145373	−	0.989377i	$-0.546438\pi$
$644$	−24.6566	−	0.890176i	−0.971607	−	0.0350778i
$645$	−1.39767	+	0.454131i	−0.0550333	+	0.0178814i
$646$	0.109328	+	0.781254i	0.00430144	+	0.0307380i
$647$	6.96239	−	9.58290i	0.273720	−	0.376743i	−0.649921	−	0.760001i	$-0.725198\pi$
$647$	6.96239	−	9.58290i	0.273720	−	0.376743i	0.923641	+	0.383259i	$0.125198\pi$
$648$	2.76557	+	0.592962i	0.108642	+	0.0232937i
$649$	−15.3053	+	10.0475i	−0.600786	+	0.394399i
$650$	−55.9209	+	27.2336i	−2.19340	+	1.06819i
$651$	−13.0976	−	9.51597i	−0.513336	−	0.372960i
$652$	−12.3324	+	8.29715i	−0.482975	+	0.324942i
$653$	6.25913	+	19.2636i	0.244939	+	0.753844i	0.995647	+	0.0932097i	$0.0297127\pi$
$653$	6.25913	+	19.2636i	0.244939	+	0.753844i	−0.750708	+	0.660635i	$0.770287\pi$
$654$	5.85861	+	3.11951i	0.229090	+	0.121983i
$655$	−20.3212	+	14.7642i	−0.794014	+	0.576885i
$656$	0.437900	+	0.704483i	0.0170971	+	0.0275054i
$657$	−5.26623	−	1.71110i	−0.205455	−	0.0667564i
$658$	−43.6091	−	7.71601i	−1.70006	−	0.300801i
$659$	−20.0329			−0.780370			−0.390185	−	0.920736i	$-0.627589\pi$
$659$	−20.0329			−0.780370			−0.390185	+	0.920736i	$0.627589\pi$
$660$	24.4762	−	5.74810i	0.952735	−	0.223744i
$661$	−23.6029			−0.918044			−0.459022	−	0.888425i	$-0.651800\pi$
$661$	−23.6029			−0.918044			−0.459022	+	0.888425i	$0.651800\pi$
$662$	2.95183	+	0.522284i	0.114726	+	0.0202991i
$663$	5.20882	+	1.69245i	0.202294	+	0.0657293i
$664$	2.89939	+	28.0639i	0.112518	+	1.08909i
$665$	3.76440	−	2.73499i	0.145977	−	0.106059i
$666$	0.662471	+	0.352744i	0.0256702	+	0.0136686i
$667$	5.78139	+	17.7933i	0.223856	+	0.688959i
$668$	−20.8135	−	30.9360i	−0.805299	−	1.19695i
$669$	0.241246	+	0.175276i	0.00932712	+	0.00677655i
$670$	−29.2161	+	14.2283i	−1.12872	+	0.549688i
$671$	−27.8992	−	22.3645i	−1.07704	−	0.863370i
$672$	−9.30079	−	11.1509i	−0.358786	−	0.430156i
$673$	18.9021	−	26.0165i	0.728623	−	1.00286i	−0.270570	−	0.962700i	$-0.587212\pi$
$673$	18.9021	−	26.0165i	0.728623	−	1.00286i	0.999193	−	0.0401631i	$-0.0127877\pi$
$674$	−5.59626	−	39.9907i	−0.215560	−	1.54039i
$675$	−8.90806	+	2.89440i	−0.342871	+	0.111406i
$676$	−0.652986	+	18.0868i	−0.0251149	+	0.695646i
$677$	−9.41284	−	12.9557i	−0.361765	−	0.497926i	0.588875	−	0.808224i	$-0.299571\pi$
$677$	−9.41284	−	12.9557i	−0.361765	−	0.497926i	−0.950639	+	0.310298i	$0.899571\pi$
$678$	16.3724	+	16.9741i	0.628777	+	0.651888i
$679$	2.55833	−	7.87372i	0.0981795	−	0.302165i
$680$	−9.30724	+	8.35048i	−0.356916	+	0.320226i
$681$		−	11.1515i		−	0.427326i
$682$	25.4234	+	15.1254i	0.973513	+	0.579182i
$683$			47.1544i			1.80431i	0.431409	+	0.902157i	$0.358017\pi$
$683$			47.1544i			1.80431i	−0.431409	+	0.902157i	$0.641983\pi$
$684$	−0.919752	+	0.262560i	−0.0351676	+	0.0100392i
$685$	−13.9892	+	43.0542i	−0.534498	+	1.64502i
$686$	19.3635	−	18.6770i	0.739301	−	0.713091i
$687$	17.1577	+	23.6155i	0.654606	+	0.900987i
$688$	−1.18570	−	0.999702i	−0.0452044	−	0.0381133i
$689$	48.2749	−	15.6855i	1.83913	−	0.597569i
$690$	−25.5126	+	3.57021i	−0.971250	+	0.135916i
$691$	6.07413	−	8.36032i	0.231071	−	0.318042i	−0.677699	−	0.735339i	$-0.737023\pi$
$691$	6.07413	−	8.36032i	0.231071	−	0.318042i	0.908770	+	0.417298i	$0.137023\pi$
$692$	−3.64583	−	2.85537i	−0.138594	−	0.108545i
$693$	−0.403452	+	8.50389i	−0.0153259	+	0.323036i
$694$	−1.88814	−	3.87707i	−0.0716728	−	0.147171i
$695$	−34.4401	−	25.0222i	−1.30639	−	0.949145i
$696$	−5.52227	+	9.52586i	−0.209321	+	0.361077i
$697$	0.0747427	+	0.230035i	0.00283108	+	0.00871318i
$698$	−1.22326	+	2.29734i	−0.0463010	+	0.0869556i
$699$	−11.6223	+	8.44411i	−0.439597	+	0.319386i
$700$	45.1664	+	16.4996i	1.70713	+	0.623627i
$701$	33.3655	+	10.8411i	1.26020	+	0.409462i	0.861564	−	0.507649i	$-0.169485\pi$
$701$	33.3655	+	10.8411i	1.26020	+	0.409462i	0.398632	+	0.917111i	$0.369485\pi$
$702$	−1.15700	+	6.53911i	−0.0436682	+	0.246803i
$703$	−0.253809			−0.00957257
$704$	18.7881	+	18.7352i	0.708103	+	0.706109i
$705$	−46.2404			−1.74151
$706$	5.74749	−	32.4835i	0.216310	−	1.22253i
$707$	15.7044	+	5.10267i	0.590624	+	0.191906i
$708$	10.3702	+	3.78832i	0.389736	+	0.142374i
$709$	−16.0509	+	11.6617i	−0.602806	+	0.437964i	−0.846874	−	0.531794i	$-0.821518\pi$
$709$	−16.0509	+	11.6617i	−0.602806	+	0.437964i	0.244068	+	0.969758i	$0.421518\pi$
$710$	−4.28408	+	8.04572i	−0.160779	+	0.301951i
$711$	3.94965	+	12.1558i	0.148124	+	0.455878i
$712$	0.689317	−	1.18906i	0.0258332	−	0.0445620i
$713$	−24.5222	−	17.8164i	−0.918362	−	0.667229i
$714$	−1.85386	−	3.80667i	−0.0693789	−	0.142461i
$715$	15.5601	+	56.9417i	0.581916	+	2.12950i
$716$	18.8337	+	14.7503i	0.703849	+	0.551246i
$717$	−14.8525	+	20.4427i	−0.554676	+	0.763447i
$718$	7.54101	−	1.05528i	0.281428	−	0.0393827i
$719$	−3.69036	+	1.19907i	−0.137627	+	0.0447178i	−0.377021	−	0.926205i	$-0.623051\pi$
$719$	−3.69036	+	1.19907i	−0.137627	+	0.0447178i	0.239393	+	0.970923i	$0.423051\pi$
$720$	−11.5912	−	9.77287i	−0.431977	−	0.364213i
$721$	10.0543	+	13.8386i	0.374442	+	0.515375i
$722$	−19.1069	+	18.4295i	−0.711085	+	0.685876i
$723$	1.90724	−	5.86990i	0.0709312	−	0.218304i
$724$	15.5045	−	4.42604i	0.576220	−	0.164492i
$725$		−	36.4628i		−	1.35419i
$726$	−0.687688	−	15.5411i	−0.0255225	−	0.576786i
$727$		−	21.8617i		−	0.810805i	−0.914138	−	0.405402i	$-0.867131\pi$
$727$		−	21.8617i		−	0.810805i	0.914138	−	0.405402i	$-0.132869\pi$
$728$	25.3756	−	22.7671i	0.940483	−	0.843804i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	20.6058	+	21.3631i	0.762655	+	0.790686i
$731$	−0.265814	−	0.365862i	−0.00983150	−	0.0135319i
$732$	−0.777945	+	21.5480i	−0.0287537	+	0.796436i
$733$	47.2508	−	15.3527i	1.74525	−	0.567066i	0.749740	−	0.661733i	$-0.230179\pi$
$733$	47.2508	−	15.3527i	1.74525	−	0.567066i	0.995509	+	0.0946671i	$0.0301787\pi$
$734$	−1.09637	−	7.83461i	−0.0404676	−	0.289181i
$735$	0.915664	−	1.26030i	0.0337748	−	0.0464870i
$736$	−17.4135	−	20.8775i	−0.641871	−	0.769554i
$737$	5.30015	+	19.3957i	0.195233	+	0.714450i
$738$	−0.263664	+	0.128405i	−0.00970561	+	0.00472665i
$739$	25.8219	+	18.7607i	0.949875	+	0.690125i	0.950777	−	0.309875i	$-0.100287\pi$
$739$	25.8219	+	18.7607i	0.949875	+	0.690125i	−0.000902372		1.00000i	$0.500287\pi$
$740$	−2.24574	−	3.33794i	−0.0825550	−	0.122705i
$741$	−0.693957	−	2.13578i	−0.0254931	−	0.0784598i
$742$	−34.6371	−	18.4431i	−1.27157	−	0.677067i
$743$	1.29508	−	0.940928i	0.0475118	−	0.0345193i	−0.563776	−	0.825928i	$-0.690652\pi$
$743$	1.29508	−	0.940928i	0.0475118	−	0.0345193i	0.611288	+	0.791408i	$0.290652\pi$
$744$	−1.83326	−	17.7445i	−0.0672104	−	0.650545i
$745$	42.1770	+	13.7041i	1.54525	+	0.502081i
$746$	15.2828	+	2.70407i	0.559543	+	0.0990031i
$747$	−9.97489			−0.364962
$748$	4.00974	+	6.61667i	0.146610	+	0.241929i
$749$	1.73422			0.0633668
$750$	23.0477	+	4.07797i	0.841585	+	0.148906i
$751$	−5.31625	−	1.72735i	−0.193993	−	0.0630320i	0.210409	−	0.977613i	$-0.432520\pi$
$751$	−5.31625	−	1.72735i	−0.193993	−	0.0630320i	−0.404402	+	0.914581i	$0.632520\pi$
$752$	−25.7614	−	41.4444i	−0.939423	−	1.51132i
$753$	15.3326	−	11.1398i	0.558752	−	0.405957i
$754$	−22.8184	−	12.1500i	−0.830996	−	0.442478i
$755$	−16.5446	−	50.9191i	−0.602120	−	1.85313i
$756$	4.25951	−	2.86576i	0.154917	−	0.104227i
$757$	−2.80013	−	2.03441i	−0.101772	−	0.0739419i	0.535735	−	0.844386i	$-0.320035\pi$
$757$	−2.80013	−	2.03441i	−0.101772	−	0.0739419i	−0.637508	+	0.770444i	$0.720035\pi$
$758$	−4.50133	+	2.19216i	−0.163496	+	0.0796227i
$759$	−0.755369	+	15.9215i	−0.0274181	+	0.577915i
$760$	5.01318	+	1.07487i	0.181847	+	0.0389895i
$761$	−9.53580	+	13.1249i	−0.345673	+	0.475778i	−0.946088	−	0.323911i	$-0.895002\pi$
$761$	−9.53580	+	13.1249i	−0.345673	+	0.475778i	0.600415	+	0.799689i	$0.295002\pi$
$762$	2.80399	+	20.0372i	0.101578	+	0.725872i
$763$	11.4577	−	3.72283i	0.414796	−	0.134775i
$764$	−11.7325	−	0.423576i	−0.424466	−	0.0153244i
$765$	−2.59854	−	3.57659i	−0.0939505	−	0.129312i
$766$	7.72378	+	8.00766i	0.279071	+	0.289329i
$767$	−8.01011	+	24.6526i	−0.289228	+	0.890153i
$768$	2.30157	−	15.8336i	0.0830508	−	0.571346i
$769$			34.9287i			1.25956i	0.776773	+	0.629781i	$0.216855\pi$
$769$			34.9287i			1.25956i	−0.776773	+	0.629781i	$0.783145\pi$
$770$	23.3328	−	39.2188i	0.840857	−	1.41335i
$771$			8.69226i			0.313044i
$772$	10.2222	+	35.8087i	0.367907	+	1.28878i
$773$	−6.76522	+	20.8212i	−0.243328	+	0.748887i	0.752579	+	0.658502i	$0.228810\pi$
$773$	−6.76522	+	20.8212i	−0.243328	+	0.748887i	−0.995907	+	0.0903846i	$0.971190\pi$
$774$	0.394658	−	0.380666i	0.0141857	−	0.0136828i
$775$	34.7232	+	47.7924i	1.24729	+	1.71675i
$776$	8.34028	−	3.69565i	0.299398	−	0.132666i
$777$	1.29560	−	0.420965i	0.0464793	−	0.0151020i
$778$	−7.23255	+	1.01211i	−0.259299	+	0.0362861i
$779$	0.0582938	−	0.0802345i	0.00208859	−	0.00287470i
$780$	21.9483	−	28.0242i	0.785874	−	1.00343i
$781$	4.40056	+	3.52756i	0.157464	+	0.126226i
$782$	−3.47091	−	7.12709i	−0.124119	−	0.254864i
$783$	−3.14942	−	2.28819i	−0.112551	−	0.0817733i
$784$	1.63972	+	0.118552i	0.0585615	+	0.00423400i
$785$	3.54869	+	10.9217i	0.126658	+	0.389814i
$786$	4.40476	−	8.27236i	0.157113	−	0.295065i
$787$	37.1166	−	26.9668i	1.32306	−	0.961262i	0.323175	−	0.946339i	$-0.395250\pi$
$787$	37.1166	−	26.9668i	1.32306	−	0.961262i	0.999889	−	0.0149229i	$-0.00475029\pi$
$788$	9.60902	−	26.3039i	0.342307	−	0.937037i
$789$	−25.7561	−	8.36865i	−0.916940	−	0.297932i
$790$	11.9368	−	67.4642i	0.424693	−	2.40027i
$791$	42.8056			1.52199
$792$	−7.27146	+	5.92671i	−0.258380	+	0.210596i
$793$	−50.6240			−1.79771
$794$	−7.31008	+	41.3149i	−0.259425	+	1.46621i
$795$	−38.9672	−	12.6612i	−1.38202	−	0.449047i
$796$	8.43251	−	23.0833i	0.298882	−	0.818166i
$797$	11.1987	−	8.13633i	0.396678	−	0.288204i	−0.371508	−	0.928430i	$-0.621159\pi$
$797$	11.1987	−	8.13633i	0.396678	−	0.288204i	0.768187	+	0.640226i	$0.221159\pi$
$798$	−0.815959	+	1.53241i	−0.0288846	+	0.0542468i
$799$	−4.39708	−	13.5328i	−0.155557	−	0.478757i
$800$	19.7034	+	49.1851i	0.696620	+	1.73895i
$801$	0.393126	+	0.285623i	0.0138904	+	0.0100920i
$802$	−9.04558	−	18.5740i	−0.319410	−	0.655871i
$803$	15.3524	−	10.0784i	0.541775	−	0.355660i
$804$	7.47610	−	9.54572i	0.263662	−	0.336651i
$805$	−27.4840	+	37.8285i	−0.968684	+	1.33328i
$806$	41.4787	−	5.80449i	1.46103	−	0.204454i
$807$	−21.8057	+	7.08510i	−0.767596	+	0.249407i
$808$	7.37109	+	16.6350i	0.259314	+	0.585216i
$809$	8.66334	+	11.9241i	0.304587	+	0.419228i	0.933683	−	0.358099i	$-0.116575\pi$
$809$	8.66334	+	11.9241i	0.304587	+	0.419228i	−0.629097	+	0.777327i	$0.716575\pi$
$810$	3.85808	−	3.72131i	0.135559	−	0.130754i
$811$	7.06616	−	21.7474i	0.248126	−	0.763655i	−0.746980	−	0.664846i	$-0.768497\pi$
$811$	7.06616	−	21.7474i	0.248126	−	0.763655i	0.995106	−	0.0988082i	$-0.0315030\pi$
$812$	5.48604	+	19.2177i	0.192522	+	0.674409i
$813$			16.0153i			0.561680i
$814$	−2.28708	+	0.982605i	−0.0801622	+	0.0344403i
$815$			28.1692i			0.986722i
$816$	1.75793	−	4.32161i	0.0615398	−	0.151287i
$817$	−0.0573006	+	0.176353i	−0.00200469	+	0.00616981i
$818$	−36.7801	−	38.1320i	−1.28599	−	1.33325i
$819$	7.08477	+	9.75135i	0.247562	+	0.340740i
$820$	1.57099	+	0.0567173i	0.0548613	+	0.00198065i
$821$	−2.30909	+	0.750270i	−0.0805879	+	0.0261846i	−0.349033	−	0.937110i	$-0.613490\pi$
$821$	−2.30909	+	0.750270i	−0.0805879	+	0.0261846i	0.268446	+	0.963295i	$0.413490\pi$
$822$	−2.34086	−	16.7277i	−0.0816470	−	0.583447i
$823$	10.0535	−	13.8374i	0.350442	−	0.482342i	−0.597013	−	0.802232i	$-0.703646\pi$
$823$	10.0535	−	13.8374i	0.350442	−	0.482342i	0.947455	+	0.319890i	$0.103646\pi$
$824$	−3.95140	+	18.4293i	−0.137653	+	0.642016i
$825$	10.9890	−	29.0566i	0.382587	−	1.01162i
$826$	18.0164	−	8.77404i	0.626872	−	0.305288i
$827$	−21.5873	−	15.6841i	−0.750666	−	0.545391i	0.145367	−	0.989378i	$-0.453564\pi$
$827$	−21.5873	−	15.6841i	−0.750666	−	0.545391i	−0.896033	+	0.443987i	$0.853564\pi$
$828$	7.97492	−	5.36546i	0.277148	−	0.186463i
$829$	−1.45022	−	4.46331i	−0.0503681	−	0.155017i	0.922709	−	0.385498i	$-0.125970\pi$
$829$	−1.45022	−	4.46331i	−0.0503681	−	0.155017i	−0.973077	+	0.230480i	$0.925970\pi$
$830$	47.1951	+	25.1298i	1.63817	+	0.872269i
$831$	−12.7452	+	9.25995i	−0.442127	+	0.321224i
$832$	37.3454	+	4.05895i	1.29472	+	0.140719i
$833$	0.455915	+	0.148136i	0.0157965	+	0.00513260i
$834$	15.6406	+	2.76737i	0.541588	+	0.0958263i
$835$	−70.6627			−2.44538
$836$	1.22851	−	2.92480i	0.0424888	−	0.101156i
$837$	6.30702			0.218003
$838$	23.8834	+	4.22584i	0.825040	+	0.145979i
$839$	−52.6957	−	17.1219i	−1.81926	−	0.591113i	−0.999839	−	0.0179159i	$-0.994297\pi$
$839$	−52.6957	−	17.1219i	−1.81926	−	0.591113i	−0.819418	−	0.573197i	$-0.805703\pi$
$840$	−27.3731	+	2.82803i	−0.944463	+	0.0975762i
$841$	−11.2011	+	8.13807i	−0.386245	+	0.280623i
$842$	−13.7014	−	7.29555i	−0.472182	−	0.251421i
$843$	−4.21665	−	12.9775i	−0.145229	−	0.446970i
$844$	9.90952	+	14.7290i	0.341100	+	0.506992i
$845$	27.7490	+	20.1608i	0.954595	+	0.693554i
$846$	15.5112	−	7.55400i	0.533287	−	0.259712i
$847$	−21.1695	−	18.6848i	−0.727393	−	0.642017i
$848$	−10.3614	−	41.9794i	−0.355812	−	1.44158i
$849$	6.74162	−	9.27904i	0.231372	−	0.318456i
$850$	2.14119	+	15.3009i	0.0734421	+	0.524816i
$851$	2.42570	−	0.788157i	0.0831518	−	0.0270177i
$852$	0.122706	−	3.39878i	0.00420384	−	0.116440i
$853$	25.5025	+	35.1012i	0.873190	+	1.20184i	0.978261	+	0.207378i	$0.0664930\pi$
$853$	25.5025	+	35.1012i	0.873190	+	1.20184i	−0.105071	+	0.994465i	$0.533507\pi$
$854$	27.1700	+	28.1686i	0.929739	+	0.963911i
$855$	−0.560158	+	1.72399i	−0.0191570	+	0.0589591i
$856$	1.27613	+	1.42234i	0.0436171	+	0.0486145i
$857$		−	31.9961i		−	1.09297i	−0.837470	−	0.546483i	$-0.815966\pi$
$857$		−	31.9961i		−	1.09297i	0.837470	−	0.546483i	$-0.184034\pi$
$858$	−14.5218	−	16.5590i	−0.495767	−	0.565315i
$859$			56.1734i			1.91661i	0.285746	+	0.958305i	$0.407759\pi$
$859$			56.1734i			1.91661i	−0.285746	+	0.958305i	$0.592241\pi$
$860$	−2.82630	+	0.806817i	−0.0963759	+	0.0275122i
$861$	−0.164491	+	0.506252i	−0.00560585	+	0.0172530i
$862$	0.0251321	−	0.0242411i	0.000856001	−	0.000825655i
$863$	31.8967	+	43.9020i	1.08578	+	1.49444i	0.852999	+	0.521912i	$0.174781\pi$
$863$	31.8967	+	43.9020i	1.08578	+	1.49444i	0.232776	+	0.972530i	$0.425219\pi$
$864$	5.48476	+	1.38471i	0.186595	+	0.0471089i
$865$	−8.34674	+	2.71202i	−0.283798	+	0.0922115i
$866$	−17.7389	+	2.48236i	−0.602792	+	0.0843541i
$867$	−9.19272	+	12.6527i	−0.312201	+	0.429708i
$868$	−25.4915	−	19.9647i	−0.865238	−	0.677644i
$869$	−39.6501	−	14.9954i	−1.34504	−	0.508684i
$870$	9.13650	+	18.7607i	0.309756	+	0.636047i
$871$	23.0305	+	16.7326i	0.780357	+	0.566963i
$872$	11.4845	+	6.65772i	0.388914	+	0.225459i
$873$	0.996658	+	3.06740i	0.0337318	+	0.103816i
$874$	−1.52769	+	2.86908i	−0.0516749	+	0.0970481i
$875$	34.3696	−	24.9710i	1.16190	−	0.844173i
$876$	−10.4021	−	3.79998i	−0.351455	−	0.128389i
$877$	−19.7822	−	6.42762i	−0.667997	−	0.217045i	−0.0446644	−	0.999002i	$-0.514222\pi$
$877$	−19.7822	−	6.42762i	−0.667997	−	0.217045i	−0.623333	+	0.781957i	$0.714222\pi$
$878$	−8.77914	+	49.6177i	−0.296282	+	1.67452i
$879$	6.55685			0.221157
$880$	49.3353	−	9.72253i	1.66309	−	0.327747i
$881$	−5.96500			−0.200966			−0.100483	−	0.994939i	$-0.532039\pi$
$881$	−5.96500			−0.200966			−0.100483	+	0.994939i	$0.532039\pi$
$882$	−0.101270	+	0.572352i	−0.00340992	+	0.0192721i
$883$	−10.0046	−	3.25070i	−0.336683	−	0.109395i	0.135796	−	0.990737i	$-0.456641\pi$
$883$	−10.0046	−	3.25070i	−0.336683	−	0.109395i	−0.472479	+	0.881342i	$0.656641\pi$
$884$	10.2887	+	3.75856i	0.346048	+	0.126414i
$885$	16.9275	−	12.2985i	0.569010	−	0.413410i
$886$	−12.9936	+	24.4026i	−0.436527	+	0.819821i
$887$	−11.2068	−	34.4911i	−0.376288	−	1.15810i	−0.942605	−	0.333909i	$-0.891632\pi$
$887$	−11.2068	−	34.4911i	−0.376288	−	1.15810i	0.566317	−	0.824188i	$-0.308368\pi$
$888$	1.29863	+	0.752832i	0.0435791	+	0.0252634i
$889$	29.7099	+	21.5855i	0.996438	+	0.723955i
$890$	−1.14046	−	2.34180i	−0.0382283	−	0.0784973i
$891$	−1.82012	−	2.77258i	−0.0609762	−	0.0928848i
$892$	0.469531	+	0.367731i	0.0157210	+	0.0123125i
$893$	−3.42939	+	4.72016i	−0.114760	+	0.157954i
$894$	−16.3869	+	2.29317i	−0.548061	+	0.0766951i
$895$	43.1178	−	14.0098i	1.44127	−	0.468296i
$896$	−17.7848	−	22.9585i	−0.594150	−	0.766989i
$897$	13.2646	+	18.2571i	0.442890	+	0.609586i
$898$	−27.8628	+	26.8751i	−0.929795	+	0.896832i
$899$	−7.58718	+	23.3509i	−0.253047	+	0.778797i
$900$	−18.0134	+	5.14224i	−0.600446	+	0.171408i
$901$		−	12.6082i		−	0.420040i
$902$	0.214666	−	0.948679i	0.00714758	−	0.0315875i
$903$		−	0.995253i		−	0.0331200i
$904$	31.4986	+	35.1076i	1.04763	+	1.16766i
$905$	9.44271	−	29.0617i	0.313886	−	0.966043i
$906$	13.8682	+	14.3779i	0.460739	+	0.477674i
$907$	−19.5299	−	26.8805i	−0.648478	−	0.892553i	0.350554	−	0.936543i	$-0.385993\pi$
$907$	−19.5299	−	26.8805i	−0.648478	−	0.892553i	−0.999032	+	0.0439891i	$0.985993\pi$
$908$	0.804678	−	22.2885i	0.0267042	−	0.739668i
$909$	−6.11803	+	1.98787i	−0.202922	+	0.0659334i
$910$	−8.95415	−	63.9862i	−0.296827	−	2.12112i
$911$	9.52554	−	13.1108i	0.315595	−	0.434379i	−0.621521	−	0.783398i	$-0.713485\pi$
$911$	9.52554	−	13.1108i	0.315595	−	0.434379i	0.937116	+	0.349018i	$0.113485\pi$
$912$	−1.85725	+	0.458410i	−0.0614998	+	0.0151795i
$913$	20.6922	−	25.8131i	0.684812	−	0.854288i
$914$	−24.2966	+	11.8325i	−0.803661	+	0.391384i
$915$	33.0592	+	24.0189i	1.09290	+	0.794041i
$916$	32.5889	+	48.4383i	1.07677	+	1.60045i
$917$	−5.25664	−	16.1783i	−0.173589	−	0.534253i
$918$	1.45596	+	0.775250i	0.0480538	+	0.0255871i
$919$	−24.8194	+	18.0324i	−0.818718	+	0.594833i	−0.916345	−	0.400390i	$-0.868875\pi$
$919$	−24.8194	+	18.0324i	−0.818718	+	0.594833i	0.0976272	+	0.995223i	$0.468875\pi$
$920$	−51.2497	+	5.29481i	−1.68965	+	0.174565i
$921$	−24.8031	−	8.05903i	−0.817291	−	0.265554i
$922$	18.3255	+	3.24244i	0.603519	+	0.106784i
$923$	7.98498			0.262829
$924$	−1.42001	+	16.9676i	−0.0467149	+	0.558193i
$925$	−4.97085			−0.163440
$926$	−51.9924	−	9.19932i	−1.70858	−	0.302308i
$927$	−6.33768	−	2.05924i	−0.208157	−	0.0676342i
$928$	−11.7247	+	18.6408i	−0.384883	+	0.611915i
$929$	−17.5153	+	12.7256i	−0.574658	+	0.417513i	−0.836794	−	0.547517i	$-0.815573\pi$
$929$	−17.5153	+	12.7256i	−0.574658	+	0.417513i	0.262136	+	0.965031i	$0.415573\pi$
$930$	−29.8410	−	15.8893i	−0.978525	−	0.521032i
$931$	−0.0607403	−	0.186939i	−0.00199068	−	0.00612669i
$932$	−23.8388	+	16.0386i	−0.780867	+	0.525361i
$933$	9.64335	+	7.00630i	0.315709	+	0.229376i
$934$	−13.4519	+	6.55111i	−0.440160	+	0.214359i
$935$	14.6460	+	0.694854i	0.478976	+	0.0227241i
$936$	−2.78435	+	12.9862i	−0.0910094	+	0.424468i
$937$	−11.6048	+	15.9727i	−0.379113	+	0.521805i	−0.955349	−	0.295479i	$-0.904521\pi$
$937$	−11.6048	+	15.9727i	−0.379113	+	0.521805i	0.576236	+	0.817283i	$0.304521\pi$
$938$	−3.05000	−	21.7952i	−0.0995859	−	0.711639i
$939$	30.6400	−	9.95553i	0.999898	−	0.324887i
$940$	−92.4205	−	3.33665i	−3.01443	−	0.108830i
$941$	11.6683	+	16.0600i	0.380374	+	0.523540i	0.955684	−	0.294396i	$-0.0951183\pi$
$941$	11.6683	+	16.0600i	0.380374	+	0.523540i	−0.575309	+	0.817936i	$0.695118\pi$
$942$	−2.97462	−	3.08395i	−0.0969182	−	0.100480i
$943$	−0.307971	+	0.947837i	−0.0100289	+	0.0308658i
$944$	20.4536	+	8.32001i	0.665707	+	0.270793i
$945$		−	9.72938i		−	0.316497i
$946$	0.166401	+	1.81096i	0.00541018	+	0.0588795i
$947$			34.7819i			1.13026i	0.825002	+	0.565129i	$0.191174\pi$
$947$			34.7819i			1.13026i	−0.825002	+	0.565129i	$0.808826\pi$
$948$	7.01702	+	24.5807i	0.227902	+	0.798346i
$949$	8.03476	−	24.7285i	0.260819	−	0.802720i
$950$	4.55959	−	4.39795i	0.147933	−	0.142688i
$951$	0.346627	+	0.477091i	0.0112402	+	0.0154707i
$952$	−3.43062	−	7.74216i	−0.111187	−	0.250925i
$953$	3.49956	−	1.13708i	0.113362	−	0.0368335i	−0.251787	−	0.967783i	$-0.581018\pi$
$953$	3.49956	−	1.13708i	0.113362	−	0.0368335i	0.365149	+	0.930949i	$0.381018\pi$
$954$	15.1398	−	2.11865i	0.490171	−	0.0685939i
$955$	−13.0778	+	18.0001i	−0.423189	+	0.582470i
$956$	−31.1608	+	39.7870i	−1.00781	+	1.28680i
$957$	12.4547	−	3.40341i	0.402602	−	0.110017i
$958$	−8.47637	−	17.4052i	−0.273859	−	0.562337i
$959$	−24.8028	−	18.0203i	−0.800925	−	0.581906i
$960$	−22.4620	−	20.3694i	−0.724958	−	0.657420i
$961$	−2.71273	−	8.34891i	−0.0875073	−	0.269320i
$962$	−1.65637	+	3.11075i	−0.0534035	+	0.100294i
$963$	−0.546576	+	0.397111i	−0.0176132	+	0.0127967i
$964$	4.23557	−	11.5945i	0.136419	−	0.373434i
$965$	67.1200	+	21.8086i	2.16067	+	0.702044i
$966$	3.03965	−	17.1794i	0.0977990	−	0.552737i
$967$	32.8772			1.05726			0.528630	−	0.848852i	$-0.322706\pi$
$967$	32.8772			1.05726			0.528630	+	0.848852i	$0.322706\pi$
$968$	−0.253049	−	31.1117i	−0.00813331	−	0.999967i
$969$	−0.557813			−0.0179195
$970$	3.01214	−	17.0239i	0.0967141	−	0.546606i
$971$	−18.5168	−	6.01648i	−0.594233	−	0.193078i	−0.00356654	−	0.999994i	$-0.501135\pi$
$971$	−18.5168	−	6.01648i	−0.594233	−	0.193078i	−0.590667	+	0.806915i	$0.701135\pi$
$972$	−0.686259	+	1.87858i	−0.0220118	+	0.0602554i
$973$	23.3238	−	16.9457i	0.747725	−	0.543254i
$974$	−3.39270	+	6.37166i	−0.108709	+	0.204161i
$975$	−13.5912	−	41.8293i	−0.435265	−	1.33961i
$976$	−3.10975	+	43.0118i	−0.0995408	+	1.37677i
$977$	−32.2562	−	23.4355i	−1.03197	−	0.749769i	−0.0632667	−	0.997997i	$-0.520152\pi$
$977$	−32.2562	−	23.4355i	−1.03197	−	0.749769i	−0.968702	+	0.248228i	$0.920152\pi$
$978$	−4.60182	−	9.44928i	−0.147150	−	0.302155i
$979$	−1.55465	+	0.424830i	−0.0496868	+	0.0135776i
$980$	1.92108	−	2.45289i	0.0613666	−	0.0783548i
$981$	−2.75867	+	3.79698i	−0.0880775	+	0.121228i
$982$	−45.3588	+	6.34746i	−1.44746	+	0.202556i
$983$	0.741401	−	0.240896i	0.0236470	−	0.00768339i	−0.297170	−	0.954825i	$-0.596043\pi$
$983$	0.741401	−	0.240896i	0.0236470	−	0.00768339i	0.320817	+	0.947141i	$0.396043\pi$
$984$	−0.536250	+	0.237617i	−0.0170950	+	0.00757495i
$985$	−31.1950	−	42.9362i	−0.993956	−	1.36806i
$986$	−4.62174	+	4.45790i	−0.147186	+	0.141968i
$987$	9.67694	−	29.7826i	0.308020	−	0.947990i
$988$	−1.23289	−	4.31885i	−0.0392236	−	0.137401i
$989$		−	1.86338i		−	0.0592519i
$990$	1.62670	+	17.7036i	0.0517000	+	0.562656i
$991$		−	59.4034i		−	1.88701i	−0.331355	−	0.943506i	$-0.607506\pi$
$991$		−	59.4034i		−	1.88701i	0.331355	−	0.943506i	$-0.392494\pi$
$992$	−2.38370	−	35.5982i	−0.0756826	−	1.13024i
$993$	−0.655016	+	2.01593i	−0.0207863	+	0.0639737i
$994$	−4.28555	−	4.44306i	−0.135929	−	0.140925i
$995$	−27.3756	−	37.6792i	−0.867863	−	1.19451i
$996$	−19.9368	−	0.719777i	−0.631721	−	0.0228070i
$997$	−4.21701	+	1.37019i	−0.133554	+	0.0433943i	−0.375031	−	0.927012i	$-0.622368\pi$
$997$	−4.21701	+	1.37019i	−0.133554	+	0.0433943i	0.241477	+	0.970406i	$0.422368\pi$
$998$	−5.17629	−	36.9897i	−0.163853	−	1.17089i
$999$	−0.311941	+	0.429350i	−0.00986937	+	0.0135840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.j.a.7.7	yes	48
3.2	odd	2		396.2.r.b.271.6		48
4.3	odd	2	inner	132.2.j.a.7.2	✓	48
11.8	odd	10	inner	132.2.j.a.19.2	yes	48
12.11	even	2		396.2.r.b.271.11		48
33.8	even	10		396.2.r.b.19.11		48
44.19	even	10	inner	132.2.j.a.19.7	yes	48
132.107	odd	10		396.2.r.b.19.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.2	✓	48	4.3	odd	2	inner
132.2.j.a.7.7	yes	48	1.1	even	1	trivial
132.2.j.a.19.2	yes	48	11.8	odd	10	inner
132.2.j.a.19.7	yes	48	44.19	even	10	inner
396.2.r.b.19.6		48	132.107	odd	10
396.2.r.b.19.11		48	33.8	even	10
396.2.r.b.271.6		48	3.2	odd	2
396.2.r.b.271.11		48	12.11	even	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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.246398 + 1.39258i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.87858 - 0.686259i) q^{4} +(-3.06643 + 2.22789i) q^{5} +(0.664670 - 1.24828i) q^{6} +(-0.793217 - 2.44127i) q^{7} +(1.41855 - 2.44698i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.246398 + 1.39258i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.87858 - 0.686259i) q^{4} +(-3.06643 + 2.22789i) q^{5} +(0.664670 - 1.24828i) q^{6} +(-0.793217 - 2.44127i) q^{7} +(1.41855 - 2.44698i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.34696 - 4.81920i) q^{10} +(-3.19932 + 0.874260i) q^{11} +(1.57457 + 1.23318i) q^{12} +(-2.76004 + 3.79887i) q^{13} +(3.59512 - 0.503097i) q^{14} +(3.60480 - 1.17127i) q^{15} +(3.05810 + 2.57838i) q^{16} +(0.685574 + 0.943612i) q^{17} +(-1.01788 + 0.981795i) q^{18} +(0.147787 - 0.454840i) q^{19} +(7.28943 - 2.08090i) q^{20} +2.56690i q^{21} +(-0.429174 - 4.67074i) q^{22} +4.80592i q^{23} +(-2.10528 + 1.88886i) q^{24} +(2.89440 - 8.90806i) q^{25} +(-4.61018 - 4.77963i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.185225 + 5.13047i) q^{28} +(3.70237 - 1.20297i) q^{29} +(0.742878 + 5.30859i) q^{30} +(-3.70718 + 5.10249i) q^{31} +(-4.34412 + 3.62335i) q^{32} +(3.31290 + 0.157175i) q^{33} +(-1.48298 + 0.722215i) q^{34} +(7.87123 + 5.71878i) q^{35} +(-1.11643 - 1.65939i) q^{36} +(-0.163997 - 0.504731i) q^{37} +(0.596989 + 0.317877i) q^{38} +(3.79887 - 2.76004i) q^{39} +(1.10173 + 10.6639i) q^{40} +(0.197223 + 0.0640816i) q^{41} +(-3.57463 - 0.632480i) q^{42} -0.387725 q^{43} +(6.61014 + 0.553199i) q^{44} -3.79031 q^{45} +(-6.69264 - 1.18417i) q^{46} +(-11.6025 - 3.76989i) q^{47} +(-2.11166 - 3.39719i) q^{48} +(0.332506 - 0.241580i) q^{49} +(11.6920 + 6.22562i) q^{50} +(-0.360428 - 1.10928i) q^{51} +(7.79196 - 5.24237i) q^{52} +(-8.74531 - 6.35384i) q^{53} +(1.27145 - 0.619200i) q^{54} +(7.86274 - 9.80860i) q^{55} +(-7.09896 - 1.52208i) q^{56} +(-0.281107 + 0.386910i) q^{57} +(0.762984 + 5.45227i) q^{58} +(5.25007 - 1.70585i) q^{59} +(-7.57569 - 0.273505i) q^{60} +(6.33692 + 8.72202i) q^{61} +(-6.19220 - 6.41979i) q^{62} +(0.793217 - 2.44127i) q^{63} +(-3.97544 - 6.94233i) q^{64} -17.7981i q^{65} +(-1.03517 + 4.57476i) q^{66} -6.06244i q^{67} +(-0.640342 - 2.24313i) q^{68} +(1.48511 - 4.57070i) q^{69} +(-9.90334 + 9.55225i) q^{70} +(-0.999528 - 1.37573i) q^{71} +(2.58593 - 1.14585i) q^{72} +(-5.26623 + 1.71110i) q^{73} +(0.743288 - 0.104015i) q^{74} +(-5.50548 + 7.57765i) q^{75} +(-0.589767 + 0.753032i) q^{76} +(4.67206 + 7.11694i) q^{77} +(2.90756 + 5.97032i) q^{78} +(10.3403 + 7.51269i) q^{79} +(-15.1218 - 1.09331i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-0.137834 + 0.258860i) q^{82} +(-8.06986 + 5.86309i) q^{83} +(1.76156 - 4.82213i) q^{84} +(-4.20453 - 1.36613i) q^{85} +(0.0955346 - 0.539940i) q^{86} -3.89290 q^{87} +(-2.39910 + 9.06887i) q^{88} +0.485931 q^{89} +(0.933925 - 5.27833i) q^{90} +(11.4634 + 3.72468i) q^{91} +(3.29810 - 9.02829i) q^{92} +(5.10249 - 3.70718i) q^{93} +(8.10872 - 15.2286i) q^{94} +(0.560158 + 1.72399i) q^{95} +(5.25118 - 2.10360i) q^{96} +(2.60928 + 1.89576i) q^{97} +(0.254491 + 0.522567i) q^{98} +(-3.10218 - 1.17322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) \) 48 * q - 4 * q^4 + 12 * q^9	\( 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more