LMFDB - Embedded newform 605.2.g.q.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	605.81
Dual form			605.2.g.q.366.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.389057 - 0.282666i) q^{2} +(-0.494946 + 1.52329i) q^{3} +(-0.546569 - 1.68217i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.623145 - 0.452741i) q^{6} +(-0.148607 - 0.457364i) q^{7} +(-0.560059 + 1.72368i) q^{8} +(0.351618 + 0.255466i) q^{9} +O(q^{10})$	\(q+(-0.389057 - 0.282666i) q^{2} +(-0.494946 + 1.52329i) q^{3} +(-0.546569 - 1.68217i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.623145 - 0.452741i) q^{6} +(-0.148607 - 0.457364i) q^{7} +(-0.560059 + 1.72368i) q^{8} +(0.351618 + 0.255466i) q^{9} +0.480901 q^{10} +2.83294 q^{12} +(-3.87971 - 2.81878i) q^{13} +(-0.0714650 + 0.219947i) q^{14} +(-0.494946 - 1.52329i) q^{15} +(-2.15675 + 1.56697i) q^{16} +(2.02440 - 1.47081i) q^{17} +(-0.0645880 - 0.198781i) q^{18} +(1.77913 - 5.47560i) q^{19} +(1.43094 + 1.03964i) q^{20} +0.770249 q^{21} +4.43462 q^{23} +(-2.34847 - 1.70626i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.712656 + 2.19333i) q^{26} +(-4.45054 + 3.23350i) q^{27} +(-0.688138 + 0.499962i) q^{28} +(-2.78501 - 8.57138i) q^{29} +(-0.238020 + 0.732550i) q^{30} +(-6.44956 - 4.68588i) q^{31} +4.90680 q^{32} -1.20336 q^{34} +(0.389057 + 0.282666i) q^{35} +(0.237552 - 0.731110i) q^{36} +(1.60793 + 4.94869i) q^{37} +(-2.23995 + 1.62742i) q^{38} +(6.21405 - 4.51478i) q^{39} +(-0.560059 - 1.72368i) q^{40} +(2.61158 - 8.03761i) q^{41} +(-0.299671 - 0.217724i) q^{42} -8.53158 q^{43} -0.434624 q^{45} +(-1.72532 - 1.25352i) q^{46} +(2.96708 - 9.13174i) q^{47} +(-1.31947 - 4.06092i) q^{48} +(5.47602 - 3.97856i) q^{49} +(-0.389057 + 0.282666i) q^{50} +(1.23850 + 3.81172i) q^{51} +(-2.62112 + 8.06698i) q^{52} +(-4.93542 - 3.58579i) q^{53} +2.64552 q^{54} +0.871579 q^{56} +(7.46034 + 5.42026i) q^{57} +(-1.33931 + 4.12198i) q^{58} +(0.855586 + 2.63322i) q^{59} +(-2.29190 + 1.66516i) q^{60} +(3.25657 - 2.36604i) q^{61} +(1.18471 + 3.64615i) q^{62} +(0.0645880 - 0.198781i) q^{63} +(2.40447 + 1.74695i) q^{64} +4.79559 q^{65} +7.60168 q^{67} +(-3.58063 - 2.60148i) q^{68} +(-2.19490 + 6.75521i) q^{69} +(-0.0714650 - 0.219947i) q^{70} +(2.23995 - 1.62742i) q^{71} +(-0.637268 + 0.463003i) q^{72} +(1.54651 + 4.75966i) q^{73} +(0.773253 - 2.37983i) q^{74} +(1.29579 + 0.941443i) q^{75} -10.1833 q^{76} -3.69380 q^{78} +(-2.93251 - 2.13059i) q^{79} +(0.823805 - 2.53541i) q^{80} +(-2.31986 - 7.13980i) q^{81} +(-3.28802 + 2.38888i) q^{82} +(-1.38713 + 1.00781i) q^{83} +(-0.420994 - 1.29569i) q^{84} +(-0.773253 + 2.37983i) q^{85} +(3.31927 + 2.41159i) q^{86} +14.4351 q^{87} -15.7408 q^{89} +(0.169094 + 0.122854i) q^{90} +(-0.712656 + 2.19333i) q^{91} +(-2.42383 - 7.45977i) q^{92} +(10.3301 - 7.50527i) q^{93} +(-3.73560 + 2.71407i) q^{94} +(1.77913 + 5.47560i) q^{95} +(-2.42860 + 7.47447i) q^{96} +(2.94319 + 2.13835i) q^{97} -3.25509 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.389057	−	0.282666i	−0.275105	−	0.199875i	0.441675	−	0.897175i	$-0.354385\pi$
$2$	−0.389057	−	0.282666i	−0.275105	−	0.199875i	−0.716779	+	0.697300i	$0.754385\pi$
$3$	−0.494946	+	1.52329i	−0.285757	+	0.879470i	0.700413	+	0.713737i	$0.252999\pi$
$3$	−0.494946	+	1.52329i	−0.285757	+	0.879470i	−0.986171	+	0.165733i	$0.947001\pi$
$4$	−0.546569	−	1.68217i	−0.273284	−	0.841083i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$	0.623145	−	0.452741i	0.254398	−	0.184831i
$7$	−0.148607	−	0.457364i	−0.0561680	−	0.172867i	0.919037	−	0.394172i	$-0.128969\pi$
$7$	−0.148607	−	0.457364i	−0.0561680	−	0.172867i	−0.975205	+	0.221305i	$0.928969\pi$
$8$	−0.560059	+	1.72368i	−0.198011	+	0.609414i
$9$	0.351618	+	0.255466i	0.117206	+	0.0851552i
$10$	0.480901			0.152074
$11$		0			0
$11$		0			0
$12$	2.83294			0.817801
$13$	−3.87971	−	2.81878i	−1.07604	−	0.781788i	−0.0990507	−	0.995082i	$-0.531581\pi$
$13$	−3.87971	−	2.81878i	−1.07604	−	0.781788i	−0.976988	+	0.213295i	$0.931581\pi$
$14$	−0.0714650	+	0.219947i	−0.0190998	+	0.0587832i
$15$	−0.494946	−	1.52329i	−0.127795	−	0.393311i
$16$	−2.15675	+	1.56697i	−0.539188	+	0.391743i
$17$	2.02440	−	1.47081i	0.490990	−	0.356725i	−0.314575	−	0.949233i	$-0.601862\pi$
$17$	2.02440	−	1.47081i	0.490990	−	0.356725i	0.805565	+	0.592508i	$0.201862\pi$
$18$	−0.0645880	−	0.198781i	−0.0152235	−	0.0468532i
$19$	1.77913	−	5.47560i	0.408161	−	1.25619i	−0.510066	−	0.860135i	$-0.670379\pi$
$19$	1.77913	−	5.47560i	0.408161	−	1.25619i	0.918227	−	0.396055i	$-0.129621\pi$
$20$	1.43094	+	1.03964i	0.319967	+	0.232470i
$21$	0.770249			0.168082
$22$		0			0
$23$	4.43462			0.924683			0.462342	−	0.886702i	$-0.347009\pi$
$23$	4.43462			0.924683			0.462342	+	0.886702i	$0.347009\pi$
$24$	−2.34847	−	1.70626i	−0.479379	−	0.348289i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.712656	+	2.19333i	0.139763	+	0.430147i
$27$	−4.45054	+	3.23350i	−0.856506	+	0.622288i
$28$	−0.688138	+	0.499962i	−0.130046	+	0.0944839i
$29$	−2.78501	−	8.57138i	−0.517163	−	1.59167i	−0.779311	−	0.626637i	$-0.784431\pi$
$29$	−2.78501	−	8.57138i	−0.517163	−	1.59167i	0.262148	−	0.965028i	$-0.415569\pi$
$30$	−0.238020	+	0.732550i	−0.0434563	+	0.133745i
$31$	−6.44956	−	4.68588i	−1.15837	−	0.841609i	−0.168803	−	0.985650i	$-0.553990\pi$
$31$	−6.44956	−	4.68588i	−1.15837	−	0.841609i	−0.989572	+	0.144041i	$0.953990\pi$
$32$	4.90680			0.867409
$33$		0			0
$34$	−1.20336			−0.206374
$35$	0.389057	+	0.282666i	0.0657626	+	0.0477794i
$36$	0.237552	−	0.731110i	0.0395920	−	0.121852i
$37$	1.60793	+	4.94869i	0.264341	+	0.813559i	0.991844	+	0.127455i	$0.0406807\pi$
$37$	1.60793	+	4.94869i	0.264341	+	0.813559i	−0.727503	+	0.686105i	$0.759319\pi$
$38$	−2.23995	+	1.62742i	−0.363368	+	0.264003i
$39$	6.21405	−	4.51478i	0.995045	−	0.722943i
$40$	−0.560059	−	1.72368i	−0.0885530	−	0.272538i
$41$	2.61158	−	8.03761i	0.407860	−	1.25526i	−0.510624	−	0.859804i	$-0.670585\pi$
$41$	2.61158	−	8.03761i	0.407860	−	1.25526i	0.918483	−	0.395459i	$-0.129415\pi$
$42$	−0.299671	−	0.217724i	−0.0462402	−	0.0335955i
$43$	−8.53158			−1.30105			−0.650527	−	0.759483i	$-0.725452\pi$
$43$	−8.53158			−1.30105			−0.650527	+	0.759483i	$0.725452\pi$
$44$		0			0
$45$	−0.434624			−0.0647899
$46$	−1.72532	−	1.25352i	−0.254385	−	0.184821i
$47$	2.96708	−	9.13174i	0.432793	−	1.33200i	−0.462538	−	0.886600i	$-0.653061\pi$
$47$	2.96708	−	9.13174i	0.432793	−	1.33200i	0.895331	−	0.445401i	$-0.146939\pi$
$48$	−1.31947	−	4.06092i	−0.190449	−	0.586143i
$49$	5.47602	−	3.97856i	0.782289	−	0.568366i
$50$	−0.389057	+	0.282666i	−0.0550210	+	0.0399751i
$51$	1.23850	+	3.81172i	0.173425	+	0.533748i
$52$	−2.62112	+	8.06698i	−0.363484	+	1.11869i
$53$	−4.93542	−	3.58579i	−0.677932	−	0.492546i	0.194739	−	0.980855i	$-0.437614\pi$
$53$	−4.93542	−	3.58579i	−0.677932	−	0.492546i	−0.872671	+	0.488309i	$0.837614\pi$
$54$	2.64552			0.360009
$55$		0			0
$56$	0.871579			0.116470
$57$	7.46034	+	5.42026i	0.988147	+	0.717931i
$58$	−1.33931	+	4.12198i	−0.175861	+	0.541243i
$59$	0.855586	+	2.63322i	0.111388	+	0.342816i	0.991177	−	0.132549i	$-0.0423160\pi$
$59$	0.855586	+	2.63322i	0.111388	+	0.342816i	−0.879789	+	0.475365i	$0.842316\pi$
$60$	−2.29190	+	1.66516i	−0.295883	+	0.214972i
$61$	3.25657	−	2.36604i	0.416961	−	0.302940i	−0.359453	−	0.933163i	$-0.617037\pi$
$61$	3.25657	−	2.36604i	0.416961	−	0.302940i	0.776414	+	0.630223i	$0.217037\pi$
$62$	1.18471	+	3.64615i	0.150458	+	0.463061i
$63$	0.0645880	−	0.198781i	0.00813732	−	0.0250441i
$64$	2.40447	+	1.74695i	0.300559	+	0.218369i
$65$	4.79559			0.594820
$66$		0			0
$67$	7.60168			0.928693			0.464346	−	0.885654i	$-0.346289\pi$
$67$	7.60168			0.928693			0.464346	+	0.885654i	$0.346289\pi$
$68$	−3.58063	−	2.60148i	−0.434215	−	0.315476i
$69$	−2.19490	+	6.75521i	−0.264235	+	0.813231i
$70$	−0.0714650	−	0.219947i	−0.00854170	−	0.0262887i
$71$	2.23995	−	1.62742i	0.265834	−	0.193139i	−0.446881	−	0.894593i	$-0.647465\pi$
$71$	2.23995	−	1.62742i	0.265834	−	0.193139i	0.712715	+	0.701454i	$0.247465\pi$
$72$	−0.637268	+	0.463003i	−0.0751028	+	0.0545654i
$73$	1.54651	+	4.75966i	0.181005	+	0.557076i	0.999857	−	0.0169292i	$-0.00538900\pi$
$73$	1.54651	+	4.75966i	0.181005	+	0.557076i	−0.818852	+	0.574005i	$0.805389\pi$
$74$	0.773253	−	2.37983i	0.0898889	−	0.276649i
$75$	1.29579	+	0.941443i	0.149624	+	0.108709i
$76$	−10.1833			−1.16810
$77$		0			0
$78$	−3.69380			−0.418240
$79$	−2.93251	−	2.13059i	−0.329933	−	0.239710i	0.410469	−	0.911874i	$-0.365365\pi$
$79$	−2.93251	−	2.13059i	−0.329933	−	0.239710i	−0.740402	+	0.672164i	$0.765365\pi$
$80$	0.823805	−	2.53541i	0.0921042	−	0.283468i
$81$	−2.31986	−	7.13980i	−0.257762	−	0.793311i
$82$	−3.28802	+	2.38888i	−0.363101	+	0.263808i
$83$	−1.38713	+	1.00781i	−0.152258	+	0.110622i	−0.661306	−	0.750116i	$-0.729998\pi$
$83$	−1.38713	+	1.00781i	−0.152258	+	0.110622i	0.509048	+	0.860738i	$0.329998\pi$
$84$	−0.420994	−	1.29569i	−0.0459342	−	0.141371i
$85$	−0.773253	+	2.37983i	−0.0838711	+	0.258129i
$86$	3.31927	+	2.41159i	0.357926	+	0.260049i
$87$	14.4351			1.54761
$88$		0			0
$89$	−15.7408			−1.66852			−0.834262	−	0.551368i	$-0.814106\pi$
$89$	−15.7408			−1.66852			−0.834262	+	0.551368i	$0.814106\pi$
$90$	0.169094	+	0.122854i	0.0178240	+	0.0129499i
$91$	−0.712656	+	2.19333i	−0.0747066	+	0.229923i
$92$	−2.42383	−	7.45977i	−0.252702	−	0.777735i
$93$	10.3301	−	7.50527i	1.07118	−	0.778261i
$94$	−3.73560	+	2.71407i	−0.385298	+	0.279935i
$95$	1.77913	+	5.47560i	0.182535	+	0.561785i
$96$	−2.42860	+	7.47447i	−0.247868	+	0.762860i
$97$	2.94319	+	2.13835i	0.298836	+	0.217117i	0.727091	−	0.686541i	$-0.240872\pi$
$97$	2.94319	+	2.13835i	0.298836	+	0.217117i	−0.428256	+	0.903658i	$0.640872\pi$
$98$	−3.25509			−0.328814
$99$		0			0
$100$	−1.76873			−0.176873
$101$	6.22818	+	4.52504i	0.619727	+	0.450258i	0.852826	−	0.522195i	$-0.174887\pi$
$101$	6.22818	+	4.52504i	0.619727	+	0.450258i	−0.233099	+	0.972453i	$0.574887\pi$
$102$	0.595597	−	1.83306i	0.0589729	−	0.181500i
$103$	2.81293	+	8.65732i	0.277167	+	0.853031i	0.988638	+	0.150316i	$0.0480291\pi$
$103$	2.81293	+	8.65732i	0.277167	+	0.853031i	−0.711471	+	0.702715i	$0.751971\pi$
$104$	7.03154	−	5.10872i	0.689500	−	0.500951i
$105$	−0.623145	+	0.452741i	−0.0608127	+	0.0441830i
$106$	0.906576	+	2.79016i	0.0880545	+	0.271004i
$107$	−5.18879	+	15.9694i	−0.501619	+	1.54382i	0.304762	+	0.952429i	$0.401423\pi$
$107$	−5.18879	+	15.9694i	−0.501619	+	1.54382i	−0.806381	+	0.591396i	$0.798577\pi$
$108$	7.87182	+	5.71921i	0.757466	+	0.550331i
$109$	−17.8817			−1.71276			−0.856380	−	0.516346i	$-0.827292\pi$
$109$	−17.8817			−1.71276			−0.856380	+	0.516346i	$0.827292\pi$
$110$		0			0
$111$	−8.33411			−0.791039
$112$	1.03718	+	0.753558i	0.0980046	+	0.0712045i
$113$	−0.142930	+	0.439893i	−0.0134457	+	0.0413817i	−0.957554	−	0.288253i	$-0.906926\pi$
$113$	−0.142930	+	0.439893i	−0.0134457	+	0.0413817i	0.944109	+	0.329635i	$0.106926\pi$
$114$	−1.37037	−	4.21758i	−0.128347	−	0.395012i
$115$	−3.58769	+	2.60661i	−0.334553	+	0.243067i
$116$	−12.8963	+	9.36970i	−1.19739	+	0.869955i
$117$	−0.644077	−	1.98227i	−0.0595450	−	0.183261i
$118$	0.411452	−	1.26632i	0.0378772	−	0.116574i
$119$	−0.973537	−	0.707316i	−0.0892440	−	0.0648396i
$120$	2.90286			0.264994
$121$		0			0
$122$	−1.93579			−0.175258
$123$	10.9510	+	7.95637i	0.987418	+	0.717401i
$124$	−4.35730	+	13.4104i	−0.391297	+	1.20429i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	−0.0813172	+	0.0590804i	−0.00724431	+	0.00526330i
$127$	−12.8063	+	9.30433i	−1.13638	+	0.825626i	−0.986610	−	0.163096i	$-0.947852\pi$
$127$	−12.8063	+	9.30433i	−1.13638	+	0.825626i	−0.149766	+	0.988721i	$0.547852\pi$
$128$	−3.47424	−	10.6926i	−0.307083	−	0.945103i
$129$	4.22267	−	12.9960i	0.371786	−	1.14424i
$130$	−1.86576	−	1.35555i	−0.163638	−	0.118890i
$131$	9.60460			0.839158			0.419579	−	0.907719i	$-0.362178\pi$
$131$	9.60460			0.839158			0.419579	+	0.907719i	$0.362178\pi$
$132$		0			0
$133$	−2.76873			−0.240080
$134$	−2.95749	−	2.14874i	−0.255488	−	0.185623i
$135$	1.69995	−	5.23192i	0.146309	−	0.450292i
$136$	1.40143	+	4.31317i	0.120172	+	0.369851i
$137$	−3.21349	+	2.33474i	−0.274547	+	0.199470i	−0.716535	−	0.697551i	$-0.754273\pi$
$137$	−3.21349	+	2.33474i	−0.274547	+	0.199470i	0.441988	+	0.897021i	$0.354273\pi$
$138$	2.76341	−	2.00774i	0.235237	−	0.170910i
$139$	2.84960	+	8.77016i	0.241700	+	0.743875i	0.996162	+	0.0875316i	$0.0278979\pi$
$139$	2.84960	+	8.77016i	0.241700	+	0.743875i	−0.754462	+	0.656344i	$0.772102\pi$
$140$	0.262846	−	0.808955i	0.0222145	−	0.0683692i
$141$	12.4417	+	9.03944i	1.04778	+	0.761258i
$142$	−1.33149			−0.111736
$143$		0			0
$144$	−1.15866			−0.0965550
$145$	7.29125	+	5.29740i	0.605505	+	0.439925i
$146$	0.743716	−	2.28892i	0.0615504	−	0.189433i
$147$	3.35016	+	10.3107i	0.276316	+	0.850414i
$148$	7.44567	−	5.40960i	0.612031	−	0.444666i
$149$	−6.18907	+	4.49662i	−0.507029	+	0.368378i	−0.811695	−	0.584081i	$-0.801455\pi$
$149$	−6.18907	+	4.49662i	−0.507029	+	0.368378i	0.304667	+	0.952459i	$0.401455\pi$
$150$	−0.238020	−	0.732550i	−0.0194343	−	0.0598125i
$151$	−0.887492	+	2.73142i	−0.0722231	+	0.222280i	−0.980652	−	0.195760i	$-0.937283\pi$
$151$	−0.887492	+	2.73142i	−0.0722231	+	0.222280i	0.908429	+	0.418040i	$0.137283\pi$
$152$	8.44179	+	6.13332i	0.684719	+	0.497478i
$153$	1.08756			0.0879240
$154$		0			0
$155$	7.97209			0.640334
$156$	−10.9910	−	7.98544i	−0.879985	−	0.639347i
$157$	5.40213	−	16.6260i	0.431137	−	1.32690i	−0.465857	−	0.884860i	$-0.654254\pi$
$157$	5.40213	−	16.6260i	0.431137	−	1.32690i	0.896994	−	0.442043i	$-0.145746\pi$
$158$	0.538665	+	1.65784i	0.0428539	+	0.131891i
$159$	7.90496	−	5.74329i	0.626904	−	0.455472i
$160$	−3.96969	+	2.88415i	−0.313831	+	0.228012i
$161$	−0.659014	−	2.02824i	−0.0519376	−	0.159847i
$162$	−1.11562	+	3.43354i	−0.0876517	+	0.269764i
$163$	−10.6524	−	7.73940i	−0.834358	−	0.606197i	0.0864308	−	0.996258i	$-0.472454\pi$
$163$	−10.6524	−	7.73940i	−0.834358	−	0.606197i	−0.920789	+	0.390061i	$0.872454\pi$
$164$	−14.9480			−1.16724
$165$		0			0
$166$	0.824549			0.0639974
$167$	12.8454	+	9.33274i	0.994008	+	0.722189i	0.960795	−	0.277259i	$-0.0894261\pi$
$167$	12.8454	+	9.33274i	0.994008	+	0.722189i	0.0332128	+	0.999448i	$0.489426\pi$
$168$	−0.431385	+	1.32767i	−0.0332820	+	0.102432i
$169$	3.08945	+	9.50835i	0.237650	+	0.731411i
$170$	0.973537	−	0.707316i	0.0746669	−	0.0542487i
$171$	2.02440	−	1.47081i	0.154810	−	0.112476i
$172$	4.66310	+	14.3515i	0.355558	+	1.09429i
$173$	7.05194	−	21.7036i	0.536149	−	1.65010i	−0.205005	−	0.978761i	$-0.565721\pi$
$173$	7.05194	−	21.7036i	0.536149	−	1.65010i	0.741153	−	0.671336i	$-0.234279\pi$
$174$	−5.61608	−	4.08032i	−0.425754	−	0.309328i
$175$	−0.480901			−0.0363527
$176$		0			0
$177$	−4.43462			−0.333327
$178$	6.12408	+	4.44940i	0.459019	+	0.333497i
$179$	−0.142930	+	0.439893i	−0.0106831	+	0.0328792i	−0.956256	−	0.292531i	$-0.905502\pi$
$179$	−0.142930	+	0.439893i	−0.0106831	+	0.0328792i	0.945573	+	0.325410i	$0.105502\pi$
$180$	0.237552	+	0.731110i	0.0177061	+	0.0544937i
$181$	2.53095	−	1.83884i	0.188124	−	0.136680i	−0.489737	−	0.871870i	$-0.662907\pi$
$181$	2.53095	−	1.83884i	0.188124	−	0.136680i	0.677861	+	0.735190i	$0.262907\pi$
$182$	0.897244	−	0.651886i	0.0665082	−	0.0483210i
$183$	1.99233	+	6.13175i	0.147277	+	0.453272i
$184$	−2.48365	+	7.64389i	−0.183097	+	0.563515i
$185$	−4.20961	−	3.05846i	−0.309496	−	0.224862i
$186$	−6.14050			−0.450243
$187$		0			0
$188$	−16.9828			−1.23860
$189$	2.14027	+	1.55500i	0.155682	+	0.113109i
$190$	0.855586	−	2.63322i	0.0620707	−	0.191034i
$191$	−1.68011	−	5.17085i	−0.121569	−	0.374150i	0.871692	−	0.490055i	$-0.163023\pi$
$191$	−1.68011	−	5.17085i	−0.121569	−	0.374150i	−0.993260	+	0.115905i	$0.963023\pi$
$192$	−3.85119	+	2.79806i	−0.277936	+	0.201932i
$193$	2.59432	−	1.88488i	0.186743	−	0.135677i	−0.490486	−	0.871449i	$-0.663181\pi$
$193$	2.59432	−	1.88488i	0.186743	−	0.135677i	0.677229	+	0.735772i	$0.263181\pi$
$194$	−0.540628	−	1.66388i	−0.0388148	−	0.119460i
$195$	−2.37356	+	7.30506i	−0.169974	+	0.523126i
$196$	−9.68563	−	7.03702i	−0.691830	−	0.502644i
$197$	19.4048			1.38253			0.691267	−	0.722600i	$-0.257053\pi$
$197$	19.4048			1.38253			0.691267	+	0.722600i	$0.257053\pi$
$198$		0			0
$199$	20.3509			1.44264			0.721319	−	0.692603i	$-0.243536\pi$
$199$	20.3509			1.44264			0.721319	+	0.692603i	$0.243536\pi$
$200$	1.46625	+	1.06529i	0.103680	+	0.0753277i
$201$	−3.76242	+	11.5795i	−0.265381	+	0.816758i
$202$	−1.14404	−	3.52099i	−0.0804944	−	0.247736i
$203$	−3.50637	+	2.54753i	−0.246099	+	0.178801i
$204$	5.73502	−	4.16674i	0.401532	−	0.291730i
$205$	2.61158	+	8.03761i	0.182400	+	0.561371i
$206$	1.35274	−	4.16331i	0.0942500	−	0.290072i
$207$	1.55929	+	1.13289i	0.108378	+	0.0787416i
$208$	12.7845			0.886446
$209$		0			0
$210$	0.370413			0.0255610
$211$	5.56593	+	4.04388i	0.383174	+	0.278392i	0.762653	−	0.646808i	$-0.223897\pi$
$211$	5.56593	+	4.04388i	0.383174	+	0.278392i	−0.379478	+	0.925201i	$0.623897\pi$
$212$	−3.33435	+	10.2621i	−0.229004	+	0.704802i
$213$	1.37037	+	4.21758i	0.0938965	+	0.288984i
$214$	6.53276	−	4.74633i	0.446570	−	0.324452i
$215$	6.90219	−	5.01474i	0.470726	−	0.342002i
$216$	−3.08098	−	9.48227i	−0.209634	−	0.645187i
$217$	−1.18471	+	3.64615i	−0.0804230	+	0.247517i
$218$	6.95702	+	5.05457i	0.471189	+	0.342339i
$219$	−8.01576			−0.541655
$220$		0			0
$221$	−12.0000			−0.807207
$222$	3.24244	+	2.35577i	0.217619	+	0.158109i
$223$	−0.320956	+	0.987800i	−0.0214928	+	0.0661480i	−0.961228	−	0.275756i	$-0.911072\pi$
$223$	−0.320956	+	0.987800i	−0.0214928	+	0.0661480i	0.939735	+	0.341904i	$0.111072\pi$
$224$	−0.729183	−	2.24420i	−0.0487206	−	0.149947i
$225$	0.351618	−	0.255466i	0.0234412	−	0.0170310i
$226$	0.179951	−	0.130742i	0.0119702	−	0.00869684i
$227$	−0.148607	−	0.457364i	−0.00986336	−	0.0303563i	0.946004	−	0.324156i	$-0.105080\pi$
$227$	−0.148607	−	0.457364i	−0.00986336	−	0.0303563i	−0.955867	+	0.293799i	$0.905080\pi$
$228$	5.04018	−	15.5121i	0.333794	−	1.02731i
$229$	−10.9539	−	7.95849i	−0.723856	−	0.525912i	0.163758	−	0.986501i	$-0.447638\pi$
$229$	−10.9539	−	7.95849i	−0.723856	−	0.525912i	−0.887614	+	0.460588i	$0.847638\pi$
$230$	2.13261			0.140620
$231$		0			0
$232$	16.3341			1.07239
$233$	−17.1142	−	12.4342i	−1.12119	−	0.814590i	−0.136799	−	0.990599i	$-0.543681\pi$
$233$	−17.1142	−	12.4342i	−1.12119	−	0.814590i	−0.984389	+	0.176008i	$0.943681\pi$
$234$	−0.309737	+	0.953273i	−0.0202482	+	0.0623174i
$235$	2.96708	+	9.13174i	0.193551	+	0.595689i
$236$	3.96188	−	2.87848i	0.257897	−	0.187373i
$237$	4.69693	−	3.41252i	0.305099	−	0.221667i
$238$	0.178827	+	0.550373i	0.0115916	+	0.0356754i
$239$	−0.827051	+	2.54540i	−0.0534975	+	0.164648i	−0.974236	−	0.225533i	$-0.927588\pi$
$239$	−0.827051	+	2.54540i	−0.0534975	+	0.164648i	0.920738	+	0.390181i	$0.127588\pi$
$240$	3.45442	+	2.50978i	0.222982	+	0.162006i
$241$	4.56912			0.294323			0.147161	−	0.989112i	$-0.452986\pi$
$241$	4.56912			0.294323			0.147161	+	0.989112i	$0.452986\pi$
$242$		0			0
$243$	−4.47932			−0.287349
$244$	−5.76000	−	4.18489i	−0.368746	−	0.267910i
$245$	−2.09165	+	6.43745i	−0.133631	+	0.411274i
$246$	−2.01157	−	6.19096i	−0.128253	−	0.394721i
$247$	−22.3370	+	16.2288i	−1.42127	+	1.03261i
$248$	11.6891	−	8.49263i	0.742259	−	0.539282i
$249$	−0.848631	−	2.61182i	−0.0537798	−	0.165517i
$250$	0.148607	−	0.457364i	0.00939870	−	0.0289262i
$251$	9.25269	+	6.72247i	0.584025	+	0.424319i	0.840173	−	0.542319i	$-0.182453\pi$
$251$	9.25269	+	6.72247i	0.584025	+	0.424319i	−0.256148	+	0.966638i	$0.582453\pi$
$252$	−0.369685			−0.0232880
$253$		0			0
$254$	7.61241			0.477645
$255$	−3.24244	−	2.35577i	−0.203050	−	0.147524i
$256$	0.166087	−	0.511163i	0.0103804	−	0.0319477i
$257$	−6.19415	−	19.0636i	−0.386381	−	1.18916i	−0.935474	−	0.353396i	$-0.885027\pi$
$257$	−6.19415	−	19.0636i	−0.386381	−	1.18916i	0.549093	−	0.835761i	$-0.314973\pi$
$258$	−5.31641	+	3.86260i	−0.330985	+	0.240475i
$259$	2.02440	−	1.47081i	0.125790	−	0.0913920i
$260$	−2.62112	−	8.06698i	−0.162555	−	0.500293i
$261$	1.21043	−	3.72533i	0.0749239	−	0.230592i
$262$	−3.73674	−	2.71490i	−0.230856	−	0.167727i
$263$	6.55852			0.404416			0.202208	−	0.979343i	$-0.435188\pi$
$263$	6.55852			0.404416			0.202208	+	0.979343i	$0.435188\pi$
$264$		0			0
$265$	6.10051			0.374752
$266$	1.07720	+	0.782628i	0.0660471	+	0.0479860i
$267$	7.79086	−	23.9778i	0.476793	−	1.46742i
$268$	−4.15484	−	12.7873i	−0.253797	−	0.781108i
$269$	−1.53483	+	1.11512i	−0.0935803	+	0.0679901i	−0.633592	−	0.773668i	$-0.718420\pi$
$269$	−1.53483	+	1.11512i	−0.0935803	+	0.0679901i	0.540011	+	0.841658i	$0.318420\pi$
$270$	−2.14027	+	1.55500i	−0.130253	+	0.0946340i
$271$	−3.50861	−	10.7984i	−0.213133	−	0.655956i	−0.999281	−	0.0379175i	$-0.987928\pi$
$271$	−3.50861	−	10.7984i	−0.213133	−	0.655956i	0.786148	−	0.618038i	$-0.212072\pi$
$272$	−2.06141	+	6.34436i	−0.124991	+	0.384683i
$273$	−2.98834	−	2.17116i	−0.180863	−	0.131405i
$274$	1.91018			0.115398
$275$		0			0
$276$	12.5630			0.756206
$277$	−18.4731	−	13.4215i	−1.10994	−	0.806418i	−0.127285	−	0.991866i	$-0.540626\pi$
$277$	−18.4731	−	13.4215i	−1.10994	−	0.806418i	−0.982654	+	0.185448i	$0.940626\pi$
$278$	1.37037	−	4.21758i	0.0821896	−	0.252954i
$279$	−1.07070	−	3.29528i	−0.0641012	−	0.197283i
$280$	−0.705122	+	0.512301i	−0.0421391	+	0.0306159i
$281$	18.2931	−	13.2907i	1.09128	−	0.792858i	0.111662	−	0.993746i	$-0.464383\pi$
$281$	18.2931	−	13.2907i	1.09128	−	0.792858i	0.979614	+	0.200888i	$0.0643827\pi$
$282$	−2.28539	−	7.03371i	−0.136093	−	0.418852i
$283$	−8.51857	+	26.2175i	−0.506377	+	1.55847i	0.292067	+	0.956398i	$0.405657\pi$
$283$	−8.51857	+	26.2175i	−0.506377	+	1.55847i	−0.798444	+	0.602069i	$0.794343\pi$
$284$	−3.96188	−	2.87848i	−0.235094	−	0.170806i
$285$	−9.22149			−0.546234
$286$		0			0
$287$	−4.06421			−0.239903
$288$	1.72532	+	1.25352i	0.101666	+	0.0738643i
$289$	−3.31838	+	10.2129i	−0.195199	+	0.600760i
$290$	−1.33931	−	4.12198i	−0.0786472	−	0.242051i
$291$	−4.71405	+	3.42495i	−0.276342	+	0.200774i
$292$	7.16126	−	5.20296i	0.419081	−	0.304480i
$293$	−6.75472	−	20.7889i	−0.394615	−	1.21450i	−0.929261	−	0.369424i	$-0.879555\pi$
$293$	−6.75472	−	20.7889i	−0.394615	−	1.21450i	0.534646	−	0.845076i	$-0.320445\pi$
$294$	1.61109	−	4.95844i	0.0939609	−	0.289182i
$295$	−2.23995	−	1.62742i	−0.130415	−	0.0947521i
$296$	−9.43050			−0.548137
$297$		0			0
$298$	3.67895			0.213116
$299$	−17.2051	−	12.5002i	−0.994995	−	0.722906i
$300$	0.875428	−	2.69429i	0.0505429	−	0.155555i
$301$	1.26785	+	3.90204i	0.0730776	+	0.224910i
$302$	1.11737	−	0.811814i	0.0642972	−	0.0467146i
$303$	−9.97554	+	7.24766i	−0.573080	+	0.416367i
$304$	4.74297	+	14.5974i	0.272028	+	0.837216i
$305$	−1.24390	+	3.82833i	−0.0712254	+	0.219209i
$306$	−0.423123	−	0.307417i	−0.0241883	−	0.0175738i
$307$	−9.80019			−0.559326			−0.279663	−	0.960098i	$-0.590223\pi$
$307$	−9.80019			−0.559326			−0.279663	+	0.960098i	$0.590223\pi$
$308$		0			0
$309$	−14.5798			−0.829418
$310$	−3.10160	−	2.25344i	−0.176159	−	0.127987i
$311$	3.01943	−	9.29284i	0.171216	−	0.526948i	−0.828225	−	0.560396i	$-0.810649\pi$
$311$	3.01943	−	9.29284i	0.171216	−	0.526948i	0.999440	+	0.0334480i	$0.0106488\pi$
$312$	4.30181	+	13.2396i	0.243542	+	0.749545i
$313$	0.725814	−	0.527335i	0.0410254	−	0.0298067i	−0.567084	−	0.823660i	$-0.691928\pi$
$313$	0.725814	−	0.527335i	0.0410254	−	0.0298067i	0.608109	+	0.793854i	$0.291928\pi$
$314$	−6.80136	+	4.94148i	−0.383823	+	0.278864i
$315$	0.0645880	+	0.198781i	0.00363912	+	0.0112001i
$316$	−1.98119	+	6.09748i	−0.111451	+	0.343010i
$317$	2.15864	+	1.56834i	0.121241	+	0.0880868i	0.646753	−	0.762699i	$-0.276126\pi$
$317$	2.15864	+	1.56834i	0.121241	+	0.0880868i	−0.525512	+	0.850786i	$0.676126\pi$
$318$	−4.69891			−0.263502
$319$		0			0
$320$	−2.97209			−0.166145
$321$	−21.7579	−	15.8080i	−1.21441	−	0.882318i
$322$	−0.316921	+	0.975381i	−0.0176613	+	0.0543559i
$323$	−4.45192	−	13.7016i	−0.247711	−	0.762378i
$324$	−10.7424	+	7.80479i	−0.596798	+	0.433599i
$325$	−3.87971	+	2.81878i	−0.215208	+	0.156358i
$326$	1.95671	+	6.02214i	0.108372	+	0.333535i
$327$	8.85050	−	27.2390i	0.489434	−	1.50632i
$328$	12.3917	+	9.00307i	0.684215	+	0.497111i
$329$	−4.61746			−0.254569
$330$		0			0
$331$	18.9744			1.04293			0.521464	−	0.853273i	$-0.325386\pi$
$331$	18.9744			1.04293			0.521464	+	0.853273i	$0.325386\pi$
$332$	2.45347	+	1.78255i	0.134652	+	0.0978303i
$333$	−0.698843	+	2.15082i	−0.0382964	+	0.117864i
$334$	−2.35955	−	7.26194i	−0.129109	−	0.397355i
$335$	−6.14989	+	4.46815i	−0.336004	+	0.244121i
$336$	−1.66123	+	1.20696i	−0.0906278	+	0.0658449i
$337$	−1.48192	−	4.56088i	−0.0807252	−	0.248447i	0.902546	−	0.430593i	$-0.141696\pi$
$337$	−1.48192	−	4.56088i	−0.0807252	−	0.248447i	−0.983271	+	0.182146i	$0.941696\pi$
$338$	1.48572	−	4.57257i	0.0808125	−	0.248715i
$339$	−0.599342	−	0.435447i	−0.0325518	−	0.0236502i
$340$	4.42590			0.240028
$341$		0			0
$342$	−1.20336			−0.0650702
$343$	−5.35682	−	3.89196i	−0.289241	−	0.210146i
$344$	4.77818	−	14.7057i	0.257622	−	0.792880i
$345$	−2.19490	−	6.75521i	−0.118169	−	0.363688i
$346$	−8.87850	+	6.45060i	−0.477311	+	0.346787i
$347$	0.209106	−	0.151924i	0.0112254	−	0.00815573i	−0.582158	−	0.813075i	$-0.697792\pi$
$347$	0.209106	−	0.151924i	0.0112254	−	0.00815573i	0.593384	+	0.804920i	$0.297792\pi$
$348$	−7.88978	−	24.2822i	−0.422937	−	1.30166i
$349$	0.415599	−	1.27908i	0.0222465	−	0.0684677i	−0.939317	−	0.343051i	$-0.888540\pi$
$349$	0.415599	−	1.27908i	0.0222465	−	0.0684677i	0.961563	+	0.274583i	$0.0885398\pi$
$350$	0.187098	+	0.135935i	0.0100008	+	0.00726601i
$351$	26.3813			1.40813
$352$		0			0
$353$	35.4537			1.88701			0.943506	−	0.331355i	$-0.107506\pi$
$353$	35.4537			1.88701			0.943506	+	0.331355i	$0.107506\pi$
$354$	1.72532	+	1.25352i	0.0916998	+	0.0666238i
$355$	−0.855586	+	2.63322i	−0.0454098	+	0.139757i
$356$	8.60345	+	26.4787i	0.455982	+	1.40337i
$357$	1.55929	−	1.13289i	0.0825266	−	0.0599591i
$358$	0.179951	−	0.130742i	0.00951071	−	0.00690994i
$359$	−2.42321	−	7.45787i	−0.127892	−	0.393611i	0.866525	−	0.499134i	$-0.166348\pi$
$359$	−2.42321	−	7.45787i	−0.127892	−	0.393611i	−0.994417	+	0.105523i	$0.966348\pi$
$360$	0.243415	−	0.749154i	0.0128291	−	0.0394839i
$361$	−11.4456	−	8.31572i	−0.602400	−	0.437669i
$362$	−1.50446			−0.0790727
$363$		0			0
$364$	4.07906			0.213801
$365$	−4.04881	−	2.94163i	−0.211924	−	0.153972i
$366$	0.958111	−	2.94876i	0.0500813	−	0.154134i
$367$	0.329579	+	1.01434i	0.0172039	+	0.0529482i	0.959290	−	0.282423i	$-0.0911382\pi$
$367$	0.329579	+	1.01434i	0.0172039	+	0.0529482i	−0.942086	+	0.335371i	$0.891138\pi$
$368$	−9.56438	+	6.94893i	−0.498578	+	0.362238i
$369$	2.97161	−	2.15900i	0.154696	−	0.112393i
$370$	0.773253	+	2.37983i	0.0401995	+	0.123721i
$371$	−0.906576	+	2.79016i	−0.0470671	+	0.144858i
$372$	−18.2712	−	13.2748i	−0.947320	−	0.688268i
$373$	−37.6388			−1.94886			−0.974431	−	0.224689i	$-0.927863\pi$
$373$	−37.6388			−1.94886			−0.974431	+	0.224689i	$0.927863\pi$
$374$		0			0
$375$	−1.60168			−0.0827104
$376$	14.0785	+	10.2286i	0.726042	+	0.527501i
$377$	−13.3558	+	41.1048i	−0.687857	+	2.11701i
$378$	−0.393141	−	1.20996i	−0.0202210	−	0.0622338i
$379$	−28.4350	+	20.6592i	−1.46061	+	1.06119i	−0.477401	+	0.878685i	$0.658421\pi$
$379$	−28.4350	+	20.6592i	−1.46061	+	1.06119i	−0.983205	+	0.182507i	$0.941579\pi$
$380$	8.23846	−	5.98559i	0.422624	−	0.307054i
$381$	−7.83473	−	24.1128i	−0.401386	−	1.23534i
$382$	−0.807967	+	2.48667i	−0.0413392	+	0.127229i
$383$	−0.667074	−	0.484658i	−0.0340859	−	0.0247649i	0.570612	−	0.821220i	$-0.306706\pi$
$383$	−0.667074	−	0.484658i	−0.0340859	−	0.0247649i	−0.604698	+	0.796455i	$0.706706\pi$
$384$	18.0075			0.918942
$385$		0			0
$386$	−1.54213			−0.0784924
$387$	−2.99986	−	2.17952i	−0.152491	−	0.110791i
$388$	1.98841	−	6.11969i	0.100946	−	0.310680i
$389$	1.49678	+	4.60661i	0.0758896	+	0.233564i	0.981804	−	0.189896i	$-0.0608152\pi$
$389$	1.49678	+	4.60661i	0.0758896	+	0.233564i	−0.905915	+	0.423461i	$0.860815\pi$
$390$	2.98834	−	2.17116i	0.151321	−	0.109941i
$391$	8.97747	−	6.52251i	0.454010	−	0.329858i
$392$	3.79089	+	11.6672i	0.191469	+	0.589280i
$393$	−4.75376	+	14.6306i	−0.239795	+	0.738014i
$394$	−7.54957	−	5.48508i	−0.380342	−	0.276334i
$395$	3.62478			0.182382
$396$		0			0
$397$	−7.33178			−0.367971			−0.183986	−	0.982929i	$-0.558900\pi$
$397$	−7.33178			−0.367971			−0.183986	+	0.982929i	$0.558900\pi$
$398$	−7.91766	−	5.75252i	−0.396876	−	0.288348i
$399$	1.37037	−	4.21758i	0.0686045	−	0.211143i
$400$	0.823805	+	2.53541i	0.0411903	+	0.126771i
$401$	25.2008	−	18.3094i	1.25847	−	0.914330i	0.259785	−	0.965666i	$-0.416348\pi$
$401$	25.2008	−	18.3094i	1.25847	−	0.914330i	0.998681	+	0.0513367i	$0.0163482\pi$
$402$	4.73694	−	3.44159i	0.236257	−	0.171651i
$403$	11.8140	+	36.3597i	0.588497	+	1.81121i
$404$	4.20774	−	12.9501i	0.209343	−	0.644290i
$405$	6.07348	+	4.41264i	0.301793	+	0.219266i
$406$	2.08428			0.103441
$407$		0			0
$408$	−7.26384			−0.359613
$409$	5.85089	+	4.25092i	0.289308	+	0.210194i	0.722967	−	0.690883i	$-0.242778\pi$
$409$	5.85089	+	4.25092i	0.289308	+	0.210194i	−0.433659	+	0.901077i	$0.642778\pi$
$410$	1.25591	−	3.86529i	0.0620250	−	0.190893i
$411$	−1.96597	−	6.05064i	−0.0969742	−	0.298456i
$412$	13.0256	−	9.46364i	0.641725	−	0.466240i
$413$	1.07720	−	0.782628i	0.0530053	−	0.0385106i
$414$	−0.286423	−	0.881520i	−0.0140769	−	0.0433244i
$415$	0.529838	−	1.63067i	0.0260087	−	0.0800467i
$416$	−19.0370	−	13.8312i	−0.933365	−	0.678130i
$417$	−14.7699			−0.723284
$418$		0			0
$419$	−2.30620			−0.112665			−0.0563327	−	0.998412i	$-0.517941\pi$
$419$	−2.30620			−0.112665			−0.0563327	+	0.998412i	$0.517941\pi$
$420$	1.10218	+	0.800779i	0.0537807	+	0.0390740i
$421$	2.05125	−	6.31310i	0.0999718	−	0.307681i	−0.888546	−	0.458788i	$-0.848284\pi$
$421$	2.05125	−	6.31310i	0.0999718	−	0.307681i	0.988517	+	0.151107i	$0.0482837\pi$
$422$	−1.02239	−	3.14660i	−0.0497693	−	0.153174i
$423$	3.37612	−	2.45290i	0.164153	−	0.119264i
$424$	8.94489	−	6.49885i	0.434402	−	0.315612i
$425$	−0.773253	−	2.37983i	−0.0375083	−	0.115439i
$426$	0.659014	−	2.02824i	0.0319293	−	0.0982684i
$427$	−1.56609	−	1.13783i	−0.0757882	−	0.0550634i
$428$	29.6993			1.43557
$429$		0			0
$430$	−4.10284			−0.197857
$431$	26.5707	+	19.3047i	1.27986	+	0.929876i	0.999549	−	0.0300317i	$-0.00956081\pi$
$431$	26.5707	+	19.3047i	1.27986	+	0.929876i	0.280316	+	0.959908i	$0.409561\pi$
$432$	4.53189	−	13.9477i	0.218041	−	0.671060i
$433$	0.729904	+	2.24641i	0.0350769	+	0.107956i	0.967062	−	0.254541i	$-0.0819244\pi$
$433$	0.729904	+	2.24641i	0.0350769	+	0.107956i	−0.931985	+	0.362497i	$0.881924\pi$
$434$	1.49156	−	1.08368i	0.0715972	−	0.0520184i
$435$	−11.6782	+	8.48474i	−0.559929	+	0.406812i
$436$	9.77361	+	30.0801i	0.468071	+	1.44057i
$437$	7.88978	−	24.2822i	0.377419	−	1.16158i
$438$	3.11859	+	2.26579i	0.149012	+	0.108264i
$439$	30.8847			1.47404			0.737022	−	0.675869i	$-0.236231\pi$
$439$	30.8847			1.47404			0.737022	+	0.675869i	$0.236231\pi$
$440$		0			0
$441$	2.94185			0.140088
$442$	4.66868	+	3.39200i	0.222067	+	0.161341i
$443$	−4.25665	+	13.1006i	−0.202239	+	0.622429i	0.797576	+	0.603218i	$0.206115\pi$
$443$	−4.25665	+	13.1006i	−0.202239	+	0.622429i	−0.999815	+	0.0192105i	$0.993885\pi$
$444$	4.55517	+	14.0194i	0.216179	+	0.665329i
$445$	12.7346	−	9.25223i	0.603678	−	0.438598i
$446$	0.404088	−	0.293587i	0.0191341	−	0.0139017i
$447$	−3.78639	−	11.6533i	−0.179090	−	0.551183i
$448$	0.441672	−	1.35933i	0.0208671	−	0.0642222i
$449$	31.4839	+	22.8744i	1.48582	+	1.07951i	0.975623	+	0.219452i	$0.0704268\pi$
$449$	31.4839	+	22.8744i	1.48582	+	1.07951i	0.510195	+	0.860059i	$0.329573\pi$
$450$	−0.209011			−0.00985288
$451$		0			0
$452$	0.818095			0.0384800
$453$	−3.72148	−	2.70381i	−0.174850	−	0.127036i
$454$	−0.0714650	+	0.219947i	−0.00335402	+	0.0103226i
$455$	−0.712656	−	2.19333i	−0.0334098	−	0.102825i
$456$	−13.5210	+	9.82361i	−0.633181	+	0.460033i
$457$	1.07720	−	0.782628i	0.0503891	−	0.0366098i	−0.562306	−	0.826929i	$-0.690086\pi$
$457$	1.07720	−	0.782628i	0.0503891	−	0.0366098i	0.612695	+	0.790320i	$0.290086\pi$
$458$	2.01210	+	6.19262i	0.0940194	+	0.289362i
$459$	−4.25379	+	13.0918i	−0.198550	+	0.611074i
$460$	6.34566	+	4.61039i	0.295868	+	0.214961i
$461$	−5.73993			−0.267335			−0.133668	−	0.991026i	$-0.542675\pi$
$461$	−5.73993			−0.267335			−0.133668	+	0.991026i	$0.542675\pi$
$462$		0			0
$463$	−3.44535			−0.160119			−0.0800595	−	0.996790i	$-0.525511\pi$
$463$	−3.44535			−0.160119			−0.0800595	+	0.996790i	$0.525511\pi$
$464$	19.4377	+	14.1223i	0.902371	+	0.655611i
$465$	−3.94576	+	12.1438i	−0.182980	+	0.563155i
$466$	3.14367	+	9.67521i	0.145628	+	0.448196i
$467$	22.0185	−	15.9974i	1.01890	−	0.740272i	0.0528403	−	0.998603i	$-0.483173\pi$
$467$	22.0185	−	15.9974i	1.01890	−	0.740272i	0.966056	+	0.258331i	$0.0831726\pi$
$468$	−2.98247	+	2.16689i	−0.137865	+	0.100165i
$469$	−1.12966	−	3.47673i	−0.0521628	−	0.160541i
$470$	1.42687	−	4.39146i	0.0658167	−	0.202563i
$471$	22.6525	+	16.4580i	1.04377	+	0.758344i
$472$	−5.01802			−0.230973
$473$		0			0
$474$	−2.79198			−0.128240
$475$	−4.65783	−	3.38411i	−0.213716	−	0.155274i
$476$	−0.657718	+	2.02425i	−0.0301465	+	0.0927813i
$477$	−0.819337	−	2.52166i	−0.0375149	−	0.115459i
$478$	1.04127	−	0.756527i	0.0476266	−	0.0346027i
$479$	11.3118	−	8.21851i	0.516850	−	0.375513i	−0.298566	−	0.954389i	$-0.596508\pi$
$479$	11.3118	−	8.21851i	0.516850	−	0.375513i	0.815416	+	0.578876i	$0.196508\pi$
$480$	−2.42860	−	7.47447i	−0.110850	−	0.341161i
$481$	7.71095	−	23.7319i	0.351589	−	1.08208i
$482$	−1.77765	−	1.29154i	−0.0809696	−	0.0588279i
$483$	3.41576			0.155423
$484$		0			0
$485$	−3.63798			−0.165192
$486$	1.74271	+	1.26615i	0.0790510	+	0.0574339i
$487$	−2.30333	+	7.08893i	−0.104374	+	0.321230i	−0.989583	−	0.143963i	$-0.954015\pi$
$487$	−2.30333	+	7.08893i	−0.104374	+	0.321230i	0.885209	+	0.465194i	$0.154015\pi$
$488$	2.25443	+	6.93841i	0.102053	+	0.314087i
$489$	17.0617	−	12.3960i	0.771556	−	0.560568i
$490$	2.63342	−	1.91329i	0.118966	−	0.0864338i
$491$	4.93673	+	15.1937i	0.222792	+	0.685682i	0.998508	+	0.0546007i	$0.0173886\pi$
$491$	4.93673	+	15.1937i	0.222792	+	0.685682i	−0.775717	+	0.631081i	$0.782611\pi$
$492$	7.39846	−	22.7701i	0.333548	−	1.02656i
$493$	−18.2449	−	13.2557i	−0.821709	−	0.597006i
$494$	13.2777			0.597392
$495$		0			0
$496$	21.2527			0.954275
$497$	−1.07720	−	0.782628i	−0.0483188	−	0.0351057i
$498$	−0.408107	+	1.25603i	−0.0182877	+	0.0562838i
$499$	−7.52484	−	23.1591i	−0.336858	−	1.03674i	−0.965799	−	0.259290i	$-0.916511\pi$
$499$	−7.52484	−	23.1591i	−0.336858	−	1.03674i	0.628941	−	0.777453i	$-0.283489\pi$
$500$	1.43094	−	1.03964i	0.0639934	−	0.0464939i
$501$	−20.5742	+	14.9481i	−0.919189	+	0.667830i
$502$	−1.69961	−	5.23085i	−0.0758572	−	0.233464i
$503$	−8.51857	+	26.2175i	−0.379824	+	1.16898i	0.560341	+	0.828262i	$0.310670\pi$
$503$	−8.51857	+	26.2175i	−0.379824	+	1.16898i	−0.940166	+	0.340717i	$0.889330\pi$
$504$	0.306463	+	0.222658i	0.0136509	+	0.00991799i
$505$	−7.69845			−0.342577
$506$		0			0
$507$	−16.0131			−0.711165
$508$	22.6510	+	16.4569i	1.00497	+	0.730156i
$509$	5.46497	−	16.8194i	0.242231	−	0.745509i	−0.753849	−	0.657048i	$-0.771805\pi$
$509$	5.46497	−	16.8194i	0.242231	−	0.745509i	0.996080	−	0.0884613i	$-0.0281949\pi$
$510$	0.595597	+	1.83306i	0.0263735	+	0.0811693i
$511$	1.94707	−	1.41463i	0.0861335	−	0.0625797i
$512$	−18.4005	+	13.3687i	−0.813194	+	0.590820i
$513$	9.78730	+	30.1222i	0.432120	+	1.32993i
$514$	−2.97877	+	9.16772i	−0.131388	+	0.404371i
$515$	−7.36436	−	5.35052i	−0.324512	−	0.235772i
$516$	−24.1695			−1.06400
$517$		0			0
$518$	−1.20336			−0.0528725
$519$	29.5705	+	21.4843i	1.29800	+	0.943054i
$520$	−2.68581	+	8.26608i	−0.117781	+	0.362491i
$521$	−1.66558	−	5.12612i	−0.0729703	−	0.224580i	0.907919	−	0.419145i	$-0.137670\pi$
$521$	−1.66558	−	5.12612i	−0.0729703	−	0.224580i	−0.980889	+	0.194566i	$0.937670\pi$
$522$	−1.52395	+	1.10722i	−0.0667016	+	0.0484615i
$523$	−30.4786	+	22.1440i	−1.33274	+	0.968291i	−0.333060	+	0.942906i	$0.608081\pi$
$523$	−30.4786	+	22.1440i	−1.33274	+	0.968291i	−0.999678	+	0.0253853i	$0.991919\pi$
$524$	−5.24957	−	16.1565i	−0.229329	−	0.705801i
$525$	0.238020	−	0.732550i	0.0103880	−	0.0319711i
$526$	−2.55164	−	1.85387i	−0.111257	−	0.0808327i
$527$	−19.9486			−0.868973
$528$		0			0
$529$	−3.33411			−0.144961
$530$	−2.37345	−	1.72441i	−0.103096	−	0.0749036i
$531$	−0.371858	+	1.14446i	−0.0161373	+	0.0496654i
$532$	1.51330	+	4.65747i	0.0656101	+	0.201927i
$533$	−32.7884	+	23.8222i	−1.42022	+	1.03185i
$534$	−9.80881	+	7.12652i	−0.424469	+	0.308395i
$535$	−5.18879	−	15.9694i	−0.224331	−	0.690419i
$536$	−4.25739	+	13.1029i	−0.183891	+	0.565959i
$537$	−0.599342	−	0.435447i	−0.0258635	−	0.0187909i
$538$	0.912344			0.0393339
$539$		0			0
$540$	−9.73010			−0.418717
$541$	−23.4332	−	17.0252i	−1.00747	−	0.731973i	−0.0437962	−	0.999040i	$-0.513945\pi$
$541$	−23.4332	−	17.0252i	−1.00747	−	0.731973i	−0.963678	+	0.267068i	$0.913945\pi$
$542$	−1.68729	+	5.19296i	−0.0724755	+	0.223057i
$543$	1.54840	+	4.76548i	0.0664482	+	0.204507i
$544$	9.93335	−	7.21700i	0.425889	−	0.309426i
$545$	14.4666	−	10.5106i	0.619683	−	0.450226i
$546$	0.548922	+	1.68941i	0.0234917	+	0.0723001i
$547$	−6.09986	+	18.7734i	−0.260811	+	0.802694i	0.731818	+	0.681500i	$0.238672\pi$
$547$	−6.09986	+	18.7734i	−0.260811	+	0.802694i	−0.992629	+	0.121194i	$0.961328\pi$
$548$	5.68381	+	4.12953i	0.242800	+	0.176405i
$549$	1.74951			0.0746672
$550$		0			0
$551$	−51.8884			−2.21052
$552$	−10.4146	−	7.56662i	−0.443273	−	0.322057i
$553$	−0.538665	+	1.65784i	−0.0229064	+	0.0704986i
$554$	3.39328	+	10.4434i	0.144167	+	0.443699i
$555$	6.74244	−	4.89867i	0.286201	−	0.207937i
$556$	13.1954	−	9.58699i	0.559608	−	0.406579i
$557$	5.15442	+	15.8637i	0.218400	+	0.672165i	0.998895	+	0.0470033i	$0.0149671\pi$
$557$	5.15442	+	15.8637i	0.218400	+	0.672165i	−0.780495	+	0.625162i	$0.785033\pi$
$558$	−0.514901	+	1.58470i	−0.0217975	+	0.0670858i
$559$	33.1001	+	24.0486i	1.39998	+	1.01715i
$560$	−1.28203			−0.0541756
$561$		0			0
$562$	−10.8739			−0.458688
$563$	3.96969	+	2.88415i	0.167302	+	0.121552i	0.668286	−	0.743905i	$-0.267028\pi$
$563$	3.96969	+	2.88415i	0.167302	+	0.121552i	−0.500984	+	0.865457i	$0.667028\pi$
$564$	8.40558	−	25.8697i	0.353939	−	1.08931i
$565$	−0.142930	−	0.439893i	−0.00601311	−	0.0185065i
$566$	10.7250	−	7.79218i	0.450806	−	0.327530i
$567$	−2.92074	+	2.12204i	−0.122660	+	0.0891174i
$568$	1.55065	+	4.77242i	0.0650640	+	0.200246i
$569$	−6.93230	+	21.3354i	−0.290617	+	0.894428i	0.694041	+	0.719935i	$0.255829\pi$
$569$	−6.93230	+	21.3354i	−0.290617	+	0.894428i	−0.984658	+	0.174493i	$0.944171\pi$
$570$	3.58769	+	2.60661i	0.150272	+	0.109179i
$571$	0.195590			0.00818520			0.00409260	−	0.999992i	$-0.498697\pi$
$571$	0.195590			0.00818520			0.00409260	+	0.999992i	$0.498697\pi$
$572$		0			0
$573$	8.70826			0.363793
$574$	1.58121	+	1.14882i	0.0659984	+	0.0479507i
$575$	1.37037	−	4.21758i	0.0571486	−	0.175885i
$576$	0.399170	+	1.22852i	0.0166321	+	0.0511883i
$577$	33.3704	−	24.2450i	1.38923	−	1.00933i	0.393277	−	0.919420i	$-0.371341\pi$
$577$	33.3704	−	24.2450i	1.38923	−	1.00933i	0.995950	−	0.0899127i	$-0.0286588\pi$
$578$	4.17789	−	3.03541i	0.173777	−	0.126257i
$579$	1.58717	+	4.88481i	0.0659605	+	0.203006i
$580$	4.92594	−	15.1605i	0.204539	−	0.629505i
$581$	0.667074	+	0.484658i	0.0276749	+	0.0201070i
$582$	2.80215			0.116153
$583$		0			0
$584$	−9.07028			−0.375331
$585$	1.68622	+	1.22511i	0.0697165	+	0.0506520i
$586$	−3.24835	+	9.99740i	−0.134188	+	0.412989i
$587$	−0.548443	−	1.68793i	−0.0226367	−	0.0696685i	0.939100	−	0.343644i	$-0.111661\pi$
$587$	−0.548443	−	1.68793i	−0.0226367	−	0.0696685i	−0.961737	+	0.273975i	$0.911661\pi$
$588$	15.5133	−	11.2710i	0.639756	−	0.464810i
$589$	−37.1326	+	26.9784i	−1.53002	+	1.11163i
$590$	0.411452	+	1.26632i	0.0169392	+	0.0521335i
$591$	−9.60432	+	29.5591i	−0.395069	+	1.21590i
$592$	−11.2223	−	8.15351i	−0.461235	−	0.335107i
$593$	−29.0094			−1.19127			−0.595636	−	0.803254i	$-0.703100\pi$
$593$	−29.0094			−1.19127			−0.595636	+	0.803254i	$0.703100\pi$
$594$		0			0
$595$	1.20336			0.0493329
$596$	10.9468	+	7.95333i	0.448399	+	0.325781i
$597$	−10.0726	+	31.0003i	−0.412244	+	1.26876i
$598$	3.16036	+	9.72659i	0.129237	+	0.397750i
$599$	−32.5768	+	23.6685i	−1.33105	+	0.967067i	−0.331331	+	0.943515i	$0.607498\pi$
$599$	−32.5768	+	23.6685i	−1.33105	+	0.967067i	−0.999723	+	0.0235521i	$0.992502\pi$
$600$	−2.34847	+	1.70626i	−0.0958757	+	0.0696578i
$601$	−4.23221	−	13.0254i	−0.172636	−	0.531318i	0.826882	−	0.562375i	$-0.190112\pi$
$601$	−4.23221	−	13.0254i	−0.172636	−	0.531318i	−0.999518	+	0.0310577i	$0.990112\pi$
$602$	0.609710	−	1.87649i	0.0248499	−	0.0764802i
$603$	2.67289	+	1.94197i	0.108848	+	0.0790830i
$604$	5.07978			0.206693
$605$		0			0
$606$	5.92972			0.240879
$607$	−17.1142	−	12.4342i	−0.694643	−	0.504688i	0.183540	−	0.983012i	$-0.441244\pi$
$607$	−17.1142	−	12.4342i	−0.694643	−	0.504688i	−0.878183	+	0.478324i	$0.841244\pi$
$608$	8.72985	−	26.8677i	0.354042	−	1.08963i
$609$	−2.14515	−	6.60210i	−0.0869259	−	0.267530i
$610$	1.56609	−	1.13783i	0.0634090	−	0.0460693i
$611$	−37.2518	+	27.0650i	−1.50704	+	1.09493i
$612$	−0.594426	−	1.82946i	−0.0240283	−	0.0739514i
$613$	−7.18526	+	22.1140i	−0.290210	+	0.893174i	0.694579	+	0.719417i	$0.255591\pi$
$613$	−7.18526	+	22.1140i	−0.290210	+	0.893174i	−0.984788	+	0.173758i	$0.944409\pi$
$614$	3.81283	+	2.77018i	0.153873	+	0.111796i
$615$	−13.5362			−0.545831
$616$		0			0
$617$	−13.1028			−0.527501			−0.263750	−	0.964591i	$-0.584960\pi$
$617$	−13.1028			−0.527501			−0.263750	+	0.964591i	$0.584960\pi$
$618$	5.67239	+	4.12123i	0.228177	+	0.165780i
$619$	5.15076	−	15.8524i	0.207027	−	0.637163i	−0.792597	−	0.609745i	$-0.791272\pi$
$619$	5.15076	−	15.8524i	0.207027	−	0.637163i	0.999624	−	0.0274172i	$-0.00872827\pi$
$620$	−4.35730	−	13.4104i	−0.174993	−	0.538574i
$621$	−19.7365	+	14.3394i	−0.791997	+	0.575419i
$622$	−3.80150	+	2.76195i	−0.152426	+	0.110744i
$623$	2.33919	+	7.19929i	0.0937177	+	0.288433i
$624$	−6.32764	+	19.4745i	−0.253308	+	0.779603i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−0.431443			−0.0172439
$627$		0			0
$628$	−30.9204			−1.23386
$629$	10.5337	+	7.65318i	0.420006	+	0.305152i
$630$	0.0310604	−	0.0955941i	0.00123748	−	0.00380856i
$631$	−0.823085	−	2.53319i	−0.0327665	−	0.100845i	0.933336	−	0.359005i	$-0.116884\pi$
$631$	−0.823085	−	2.53319i	−0.0327665	−	0.100845i	−0.966102	+	0.258160i	$0.916884\pi$
$632$	5.31484	−	3.86145i	0.211413	−	0.153600i
$633$	−8.91483	+	6.47700i	−0.354333	+	0.257438i
$634$	−0.396515	−	1.22035i	−0.0157476	−	0.0484662i
$635$	4.89157	−	15.0547i	0.194116	−	0.597428i
$636$	−13.9818	−	10.1584i	−0.554413	−	0.402805i
$637$	−32.4601			−1.28611
$638$		0			0
$639$	1.20336			0.0476041
$640$	9.09569	+	6.60841i	0.359539	+	0.261220i
$641$	−0.142930	+	0.439893i	−0.00564540	+	0.0173747i	−0.953840	−	0.300317i	$-0.902908\pi$
$641$	−0.142930	+	0.439893i	−0.00564540	+	0.0173747i	0.948194	+	0.317691i	$0.102908\pi$
$642$	3.99666	+	12.3004i	0.157736	+	0.485460i
$643$	27.0714	−	19.6686i	1.06759	−	0.775652i	0.0921153	−	0.995748i	$-0.470637\pi$
$643$	27.0714	−	19.6686i	1.06759	−	0.775652i	0.975478	+	0.220096i	$0.0706372\pi$
$644$	−3.05164	+	2.21714i	−0.120251	+	0.0873677i
$645$	4.22267	+	12.9960i	0.166268	+	0.511719i
$646$	−2.14093	+	6.58911i	−0.0842339	+	0.259245i
$647$	32.5700	+	23.6635i	1.28046	+	0.930309i	0.999567	−	0.0294300i	$-0.00936921\pi$
$647$	32.5700	+	23.6635i	1.28046	+	0.930309i	0.280894	+	0.959739i	$0.409369\pi$
$648$	13.6060			0.534495
$649$		0			0
$650$	2.30620			0.0904567
$651$	−4.96777	−	3.60929i	−0.194702	−	0.141459i
$652$	−7.19670	+	22.1492i	−0.281845	+	0.867429i
$653$	4.74297	+	14.5974i	0.185607	+	0.571239i	0.999958	−	0.00913312i	$-0.00290720\pi$
$653$	4.74297	+	14.5974i	0.185607	+	0.571239i	−0.814352	+	0.580372i	$0.802907\pi$
$654$	−11.1429	+	8.09580i	−0.435722	+	0.316571i
$655$	−7.77028	+	5.64544i	−0.303610	+	0.220586i
$656$	6.96218	+	21.4274i	0.271827	+	0.836599i
$657$	−0.672149	+	2.06866i	−0.0262230	+	0.0807062i
$658$	1.79645	+	1.30520i	0.0700331	+	0.0508820i
$659$	36.6635			1.42821			0.714104	−	0.700039i	$-0.246834\pi$
$659$	36.6635			1.42821			0.714104	+	0.700039i	$0.246834\pi$
$660$		0			0
$661$	−8.03024			−0.312340			−0.156170	−	0.987730i	$-0.549915\pi$
$661$	−8.03024			−0.312340			−0.156170	+	0.987730i	$0.549915\pi$
$662$	−7.38213	−	5.36343i	−0.286915	−	0.208456i
$663$	5.93935	−	18.2794i	0.230665	−	0.709915i
$664$	−0.960272	−	2.95541i	−0.0372658	−	0.114692i
$665$	2.23995	−	1.62742i	0.0868617	−	0.0631087i
$666$	0.879854	−	0.639251i	0.0340937	−	0.0247705i
$667$	−12.3505	−	38.0108i	−0.478212	−	1.47179i
$668$	8.67832	−	26.7091i	0.335774	−	1.03341i
$669$	−1.34585	−	0.977815i	−0.0520335	−	0.0378045i
$670$	3.65565			0.141230
$671$		0			0
$672$	3.77946			0.145796
$673$	9.51299	+	6.91160i	0.366699	+	0.266422i	0.755841	−	0.654755i	$-0.227228\pi$
$673$	9.51299	+	6.91160i	0.366699	+	0.266422i	−0.389142	+	0.921178i	$0.627228\pi$
$674$	−0.712656	+	2.19333i	−0.0274505	+	0.0844839i
$675$	1.69995	+	5.23192i	0.0654312	+	0.201377i
$676$	14.3060	−	10.3939i	0.550232	−	0.399767i
$677$	22.0819	−	16.0435i	0.848678	−	0.616601i	−0.0761030	−	0.997100i	$-0.524248\pi$
$677$	22.0819	−	16.0435i	0.848678	−	0.616601i	0.924781	+	0.380499i	$0.124248\pi$
$678$	0.110092	+	0.338828i	0.00422805	+	0.0130126i
$679$	0.540628	−	1.66388i	0.0207474	−	0.0638539i
$680$	−3.66900	−	2.66569i	−0.140700	−	0.102224i
$681$	0.770249			0.0295160
$682$		0			0
$683$	49.5738			1.89689			0.948444	−	0.316945i	$-0.102657\pi$
$683$	49.5738			1.89689			0.948444	+	0.316945i	$0.102657\pi$
$684$	−3.58063	−	2.60148i	−0.136909	−	0.0994701i
$685$	1.22744	−	3.77768i	0.0468982	−	0.144338i
$686$	0.983983	+	3.02839i	0.0375686	+	0.115624i
$687$	17.5447	−	12.7470i	0.669371	−	0.486327i
$688$	18.4005	−	13.3687i	0.701512	−	0.509678i
$689$	9.04046	+	27.8237i	0.344414	+	1.06000i
$690$	−1.05553	+	3.24859i	−0.0401833	+	0.123672i
$691$	20.4886	+	14.8859i	0.779424	+	0.566285i	0.904806	−	0.425824i	$-0.140016\pi$
$691$	20.4886	+	14.8859i	0.779424	+	0.566285i	−0.125382	+	0.992109i	$0.540016\pi$
$692$	−40.3635			−1.53439
$693$		0			0
$694$	−0.124298			−0.00471829
$695$	−7.46034	−	5.42026i	−0.282987	−	0.205602i
$696$	−8.08450	+	24.8815i	−0.306442	+	0.943132i
$697$	−6.53495	−	20.1125i	−0.247529	−	0.761816i
$698$	−0.523246	+	0.380160i	−0.0198051	+	0.0143893i
$699$	27.4114	−	19.9156i	1.03680	−	0.753276i
$700$	0.262846	+	0.808955i	0.00993463	+	0.0305756i
$701$	−5.64125	+	17.3620i	−0.213067	+	0.655753i	0.786218	+	0.617949i	$0.212036\pi$
$701$	−5.64125	+	17.3620i	−0.213067	+	0.655753i	−0.999285	+	0.0378039i	$0.987964\pi$
$702$	−10.2638	−	7.45712i	−0.387384	−	0.281451i
$703$	29.9578			1.12988
$704$		0			0
$705$	−15.3788			−0.579199
$706$	−13.7935	−	10.0216i	−0.519126	−	0.377167i
$707$	1.14404	−	3.52099i	0.0430261	−	0.132421i
$708$	2.42383	+	7.45977i	0.0910930	+	0.280356i
$709$	−3.50448	+	2.54616i	−0.131614	+	0.0956229i	−0.651644	−	0.758525i	$-0.725921\pi$
$709$	−3.50448	+	2.54616i	−0.131614	+	0.0956229i	0.520031	+	0.854148i	$0.325921\pi$
$710$	1.07720	−	0.782628i	0.0404264	−	0.0293715i
$711$	−0.486830	−	1.49831i	−0.0182575	−	0.0561909i
$712$	8.81579	−	27.1322i	0.330386	−	1.01682i
$713$	−28.6014	−	20.7801i	−1.07113	−	0.778221i
$714$	−0.926885			−0.0346878
$715$		0			0
$716$	0.818095			0.0305737
$717$	−3.46803	−	2.51967i	−0.129516	−	0.0940989i
$718$	−1.16532	+	3.58650i	−0.0434895	+	0.133847i
$719$	−7.44747	−	22.9210i	−0.277744	−	0.854807i	−0.988480	−	0.151349i	$-0.951638\pi$
$719$	−7.44747	−	22.9210i	−0.277744	−	0.854807i	0.710737	−	0.703458i	$-0.248362\pi$
$720$	0.937375	−	0.681043i	0.0349339	−	0.0253810i
$721$	3.54153	−	2.57307i	0.131893	−	0.0958261i
$722$	2.10242	+	6.47058i	0.0782439	+	0.240810i
$723$	−2.26147	+	6.96008i	−0.0841049	+	0.258848i
$724$	−4.47657	−	3.25242i	−0.166370	−	0.120875i
$725$	−9.01248			−0.334715
$726$		0			0
$727$	−25.1066			−0.931151			−0.465576	−	0.885008i	$-0.654153\pi$
$727$	−25.1066			−0.931151			−0.465576	+	0.885008i	$0.654153\pi$
$728$	−3.38148	−	2.45679i	−0.125326	−	0.0910545i
$729$	9.17661	−	28.2427i	0.339874	−	1.04603i
$730$	0.743716	+	2.28892i	0.0275262	+	0.0847169i
$731$	−17.2714	+	12.5484i	−0.638804	+	0.464118i
$732$	9.22568	−	6.70285i	0.340991	−	0.247744i
$733$	−5.39119	−	16.5924i	−0.199128	−	0.612854i	−0.999904	−	0.0138888i	$-0.995579\pi$
$733$	−5.39119	−	16.5924i	−0.199128	−	0.612854i	0.800775	−	0.598965i	$-0.204421\pi$
$734$	0.158495	−	0.487798i	0.00585016	−	0.0180049i
$735$	−8.77083	−	6.37238i	−0.323517	−	0.235049i
$736$	21.7598			0.802078
$737$		0			0
$738$	−1.76640			−0.0650222
$739$	4.20704	+	3.05659i	0.154759	+	0.112439i	0.662470	−	0.749089i	$-0.269508\pi$
$739$	4.20704	+	3.05659i	0.154759	+	0.112439i	−0.507711	+	0.861527i	$0.669508\pi$
$740$	−2.84399	+	8.75291i	−0.104547	+	0.321764i
$741$	−13.6655	−	42.0581i	−0.502015	−	1.54504i
$742$	1.14139	−	0.829271i	0.0419019	−	0.0304435i
$743$	30.0896	−	21.8614i	1.10388	−	0.802016i	0.122191	−	0.992507i	$-0.461008\pi$
$743$	30.0896	−	21.8614i	1.10388	−	0.802016i	0.981689	+	0.190491i	$0.0610080\pi$
$744$	7.15124	+	22.0093i	0.262177	+	0.806898i
$745$	2.36402	−	7.27569i	0.0866108	−	0.266561i
$746$	14.6436	+	10.6392i	0.536141	+	0.389529i
$747$	−0.745203			−0.0272656
$748$		0			0
$749$	8.07494			0.295052
$750$	0.623145	+	0.452741i	0.0227540	+	0.0165318i
$751$	12.7998	−	39.3939i	0.467073	−	1.43750i	−0.389283	−	0.921118i	$-0.627277\pi$
$751$	12.7998	−	39.3939i	0.467073	−	1.43750i	0.856356	−	0.516385i	$-0.172723\pi$
$752$	7.90991	+	24.3442i	0.288445	+	0.887742i
$753$	−14.8198	+	10.7672i	−0.540065	+	0.392380i
$754$	16.8151	−	12.2169i	0.612370	−	0.444913i
$755$	−0.887492	−	2.73142i	−0.0322991	−	0.0994065i
$756$	1.44596	−	4.45020i	0.0525889	−	0.161852i
$757$	−3.16834	−	2.30193i	−0.115155	−	0.0836651i	0.528717	−	0.848798i	$-0.322673\pi$
$757$	−3.16834	−	2.30193i	−0.115155	−	0.0836651i	−0.643872	+	0.765133i	$0.722673\pi$
$758$	16.9025			0.613926
$759$		0			0
$760$	−10.4346			−0.378504
$761$	31.6576	+	23.0006i	1.14759	+	0.833770i	0.988158	−	0.153439i	$-0.0490349\pi$
$761$	31.6576	+	23.0006i	1.14759	+	0.833770i	0.159428	+	0.987210i	$0.449035\pi$
$762$	−3.76773	+	11.5959i	−0.136490	+	0.420074i
$763$	2.65734	+	8.17847i	0.0962023	+	0.296080i
$764$	−7.77994	+	5.65245i	−0.281468	+	0.204499i
$765$	−0.879854	+	0.639251i	−0.0318112	+	0.0231122i
$766$	0.122533	+	0.377119i	0.00442731	+	0.0136259i
$767$	4.10304	−	12.6279i	0.148152	−	0.455965i
$768$	0.696444	+	0.505996i	0.0251308	+	0.0182586i
$769$	11.6755			0.421028			0.210514	−	0.977591i	$-0.432486\pi$
$769$	11.6755			0.421028			0.210514	+	0.977591i	$0.432486\pi$
$770$		0			0
$771$	32.1052			1.15624
$772$	−4.58866	−	3.33386i	−0.165149	−	0.119988i
$773$	−2.39995	+	7.38629i	−0.0863202	+	0.265666i	−0.984895	−	0.173155i	$-0.944604\pi$
$773$	−2.39995	+	7.38629i	−0.0863202	+	0.265666i	0.898574	+	0.438821i	$0.144604\pi$
$774$	0.551037	+	1.69592i	0.0198066	+	0.0609585i
$775$	−6.44956	+	4.68588i	−0.231675	+	0.168322i
$776$	−5.33420	+	3.87552i	−0.191487	+	0.139123i
$777$	1.23850	+	3.81172i	0.0444311	+	0.136745i
$778$	0.719801	−	2.21532i	0.0258061	−	0.0794231i
$779$	−39.3644	−	28.5999i	−1.41038	−	1.02470i
$780$	13.5856			0.486444
$781$		0			0
$782$	−5.33644			−0.190831
$783$	40.1104	+	29.1419i	1.43343	+	1.04145i
$784$	−5.57612	+	17.1615i	−0.199147	+	0.612912i
$785$	5.40213	+	16.6260i	0.192810	+	0.593409i
$786$	5.98505	−	4.34840i	0.213480	−	0.155102i
$787$	1.15631	−	0.840111i	0.0412181	−	0.0299467i	−0.566985	−	0.823728i	$-0.691890\pi$
$787$	1.15631	−	0.840111i	0.0412181	−	0.0299467i	0.608204	+	0.793781i	$0.291890\pi$
$788$	−10.6061	−	32.6421i	−0.377825	−	1.16283i
$789$	−3.24611	+	9.99051i	−0.115565	+	0.355672i
$790$	−1.41024	−	1.02460i	−0.0501742	−	0.0364537i
$791$	0.222432			0.00790876
$792$		0			0
$793$	−19.3039			−0.685501
$794$	2.85248	+	2.07245i	0.101231	+	0.0735484i
$795$	−3.01943	+	9.29284i	−0.107088	+	0.329583i
$796$	−11.1232	−	34.2336i	−0.394250	−	1.21338i
$797$	29.4311	−	21.3829i	1.04250	−	0.757422i	0.0717298	−	0.997424i	$-0.477148\pi$
$797$	29.4311	−	21.3829i	1.04250	−	0.757422i	0.970772	+	0.240002i	$0.0771481\pi$
$798$	−1.72532	+	1.25352i	−0.0610757	+	0.0443741i
$799$	−7.42453	−	22.8503i	−0.262661	−	0.808387i
$800$	1.51629	−	4.66665i	0.0536088	−	0.164991i
$801$	−5.53476	−	4.02124i	−0.195561	−	0.142083i
$802$	−14.9800			−0.528962
$803$		0			0
$804$	21.5351			0.759486
$805$	1.72532	+	1.25352i	0.0608096	+	0.0441808i
$806$	5.68136	−	17.4854i	0.200117	−	0.615898i
$807$	−0.938990	−	2.88991i	−0.0330540	−	0.101730i
$808$	−11.2879	+	8.20112i	−0.397106	+	0.288514i
$809$	−22.5501	+	16.3836i	−0.792820	+	0.576018i	−0.908799	−	0.417234i	$-0.863000\pi$
$809$	−22.5501	+	16.3836i	−0.792820	+	0.576018i	0.115979	+	0.993252i	$0.463000\pi$
$810$	−1.11562	−	3.43354i	−0.0391990	−	0.120642i
$811$	12.1071	−	37.2617i	0.425136	−	1.30843i	−0.477728	−	0.878508i	$-0.658539\pi$
$811$	12.1071	−	37.2617i	0.425136	−	1.30843i	0.902864	−	0.429927i	$-0.141461\pi$
$812$	6.20184	+	4.50590i	0.217642	+	0.158126i
$813$	18.1856			0.637798
$814$		0			0
$815$	13.1671			0.461222
$816$	−8.64400	−	6.28023i	−0.302600	−	0.219852i
$817$	−15.1788	+	46.7155i	−0.531039	+	1.63437i
$818$	−1.07474	−	3.30770i	−0.0375773	−	0.115651i
$819$	−0.810903	+	0.589155i	−0.0283352	+	0.0205868i
$820$	12.0932	−	8.78622i	0.422312	−	0.306828i
$821$	−4.25739	−	13.1029i	−0.148584	−	0.457294i	0.848871	−	0.528601i	$-0.177283\pi$
$821$	−4.25739	−	13.1029i	−0.148584	−	0.457294i	−0.997454	+	0.0713067i	$0.977283\pi$
$822$	−0.945438	+	2.90976i	−0.0329759	+	0.101489i
$823$	16.0832	+	11.6852i	0.560626	+	0.407319i	0.831688	−	0.555243i	$-0.187375\pi$
$823$	16.0832	+	11.6852i	0.560626	+	0.407319i	−0.271062	+	0.962562i	$0.587375\pi$
$824$	−16.4979			−0.574731
$825$		0			0
$826$	−0.640313			−0.0222793
$827$	−10.7819	−	7.83351i	−0.374924	−	0.272398i	0.384326	−	0.923197i	$-0.374434\pi$
$827$	−10.7819	−	7.83351i	−0.374924	−	0.272398i	−0.759250	+	0.650799i	$0.774434\pi$
$828$	1.05345	−	3.24220i	0.0366100	−	0.112674i
$829$	15.8186	+	48.6845i	0.549401	+	1.69088i	0.710289	+	0.703910i	$0.248564\pi$
$829$	15.8186	+	48.6845i	0.549401	+	1.69088i	−0.160888	+	0.986973i	$0.551436\pi$
$830$	−0.667074	+	0.484658i	−0.0231545	+	0.0168227i
$831$	29.5879	−	21.4969i	1.02639	−	0.745719i
$832$	−4.40440	−	13.5553i	−0.152695	−	0.469947i
$833$	5.23395	−	16.1084i	0.181345	−	0.558124i
$834$	5.74632	+	4.17495i	0.198979	+	0.144567i
$835$	−15.8778			−0.549474
$836$		0			0
$837$	43.8558			1.51588
$838$	0.897244	+	0.651886i	0.0309948	+	0.0225190i
$839$	−5.21432	+	16.0480i	−0.180018	+	0.554040i	−0.999827	−	0.0185978i	$-0.994080\pi$
$839$	−5.21432	+	16.0480i	−0.180018	+	0.554040i	0.819809	+	0.572638i	$0.194080\pi$
$840$	−0.431385	−	1.32767i	−0.0148842	−	0.0458088i
$841$	−42.2508	+	30.6970i	−1.45692	+	1.05852i
$842$	−2.58255	+	1.87633i	−0.0890007	+	0.0646628i
$843$	11.1915	+	34.4439i	0.385455	+	1.18631i
$844$	3.76032	−	11.5731i	0.129436	−	0.398362i
$845$	−8.08828	−	5.87648i	−0.278245	−	0.202157i
$846$	−2.00686			−0.0689972
$847$		0			0
$848$	16.2633			0.558484
$849$	−35.7205	−	25.9525i	−1.22592	−	0.890686i
$850$	−0.371858	+	1.14446i	−0.0127546	+	0.0392547i
$851$	7.13055	+	21.9456i	0.244432	+	0.752284i
$852$	6.34566	−	4.61039i	0.217399	−	0.157950i
$853$	−4.38699	+	3.18734i	−0.150208	+	0.109132i	−0.660351	−	0.750957i	$-0.729592\pi$
$853$	−4.38699	+	3.18734i	−0.150208	+	0.109132i	0.510143	+	0.860090i	$0.329592\pi$
$854$	0.287671	+	0.885360i	0.00984390	+	0.0302964i
$855$	−0.773253	+	2.37983i	−0.0264447	+	0.0813884i
$856$	−24.6202	−	17.8877i	−0.841503	−	0.611387i
$857$	27.8386			0.950947			0.475474	−	0.879730i	$-0.342277\pi$
$857$	27.8386			0.950947			0.475474	+	0.879730i	$0.342277\pi$
$858$		0			0
$859$	48.1899			1.64422			0.822109	−	0.569330i	$-0.192797\pi$
$859$	48.1899			1.64422			0.822109	+	0.569330i	$0.192797\pi$
$860$	−12.2081	−	8.86974i	−0.416294	−	0.302456i
$861$	2.01157	−	6.19096i	0.0685540	−	0.210987i
$862$	−4.88071	−	15.0213i	−0.166238	−	0.511627i
$863$	−21.7309	+	15.7884i	−0.739728	+	0.537444i	−0.892626	−	0.450798i	$-0.851139\pi$
$863$	−21.7309	+	15.7884i	−0.739728	+	0.537444i	0.152898	+	0.988242i	$0.451139\pi$
$864$	−21.8379	+	15.8662i	−0.742941	+	0.539778i
$865$	7.05194	+	21.7036i	0.239773	+	0.737946i
$866$	0.351011	−	1.08030i	0.0119279	−	0.0367101i
$867$	−13.9148	−	10.1097i	−0.472571	−	0.343343i
$868$	6.78095			0.230160
$869$		0			0
$870$	6.94185			0.235351
$871$	−29.4923	−	21.4274i	−0.999309	−	0.726041i
$872$	10.0148	−	30.8225i	0.339145	−	1.04378i
$873$	0.488604	+	1.50377i	0.0165367	+	0.0508948i
$874$	−9.93335	+	7.21700i	−0.336001	+	0.244119i
$875$	0.389057	−	0.282666i	0.0131525	−	0.00955587i
$876$	4.38117	+	13.4838i	0.148026	+	0.455577i
$877$	12.3247	−	37.9317i	0.416177	−	1.28086i	−0.495017	−	0.868883i	$-0.664838\pi$
$877$	12.3247	−	37.9317i	0.416177	−	1.28086i	0.911194	−	0.411978i	$-0.135162\pi$
$878$	−12.0159	−	8.73005i	−0.405517	−	0.294625i
$879$	35.0107			1.18088
$880$		0			0
$881$	−2.82222			−0.0950829			−0.0475415	−	0.998869i	$-0.515139\pi$
$881$	−2.82222			−0.0950829			−0.0475415	+	0.998869i	$0.515139\pi$
$882$	−1.14455	−	0.831564i	−0.0385390	−	0.0280002i
$883$	15.6142	−	48.0556i	0.525460	−	1.61720i	−0.237943	−	0.971279i	$-0.576473\pi$
$883$	15.6142	−	48.0556i	0.525460	−	1.61720i	0.763404	−	0.645922i	$-0.223527\pi$
$884$	6.55883	+	20.1860i	0.220597	+	0.678928i
$885$	3.58769	−	2.60661i	0.120599	−	0.0876201i
$886$	5.35918	−	3.89367i	0.180045	−	0.130811i
$887$	−8.75120	−	26.9334i	−0.293836	−	0.904336i	−0.983610	−	0.180310i	$-0.942290\pi$
$887$	−8.75120	−	26.9334i	−0.293836	−	0.904336i	0.689773	−	0.724025i	$-0.257710\pi$
$888$	4.66759	−	14.3654i	0.156634	−	0.482070i
$889$	6.15857	+	4.47446i	0.206552	+	0.150069i
$890$	−7.56978			−0.253740
$891$		0			0
$892$	1.83707			0.0615096
$893$	−44.7230	−	32.4931i	−1.49660	−	1.08734i
$894$	−1.82088	+	5.60409i	−0.0608994	+	0.187429i
$895$	−0.142930	−	0.439893i	−0.00477762	−	0.0147040i
$896$	−4.37413	+	3.17799i	−0.146129	+	0.106169i
$897$	27.5570	−	20.0213i	0.920101	−	0.668493i
$898$	−5.78321	−	17.7989i	−0.192988	−	0.593957i
$899$	−22.2024	+	68.3318i	−0.740490	+	2.27899i
$900$	−0.621919	−	0.451851i	−0.0207306	−	0.0150617i
$901$	−15.2653			−0.508561
$902$		0			0
$903$	−6.57144			−0.218684
$904$	−0.678188	−	0.492732i	−0.0225562	−	0.0163880i
$905$	−0.966735	+	2.97531i	−0.0321354	+	0.0989025i
$906$	0.683590	+	2.10387i	0.0227108	+	0.0698965i
$907$	−41.3009	+	30.0069i	−1.37138	+	0.996362i	−0.373747	+	0.927531i	$0.621927\pi$
$907$	−41.3009	+	30.0069i	−1.37138	+	0.996362i	−0.997628	+	0.0688315i	$0.978073\pi$
$908$	−0.688138	+	0.499962i	−0.0228367	+	0.0165918i
$909$	1.03395	+	3.18217i	0.0342939	+	0.105546i
$910$	−0.342717	+	1.05477i	−0.0113610	+	0.0349654i
$911$	20.3410	+	14.7786i	0.673928	+	0.489637i	0.871338	−	0.490684i	$-0.163253\pi$
$911$	20.3410	+	14.7786i	0.673928	+	0.489637i	−0.197410	+	0.980321i	$0.563253\pi$
$912$	−24.5835			−0.814040
$913$		0			0
$914$	−0.640313			−0.0211797
$915$	−5.21598	−	3.78963i	−0.172435	−	0.125281i
$916$	−7.40043	+	22.7762i	−0.244517	+	0.752547i
$917$	−1.42731	−	4.39280i	−0.0471338	−	0.145063i
$918$	5.35559	−	3.89106i	0.176761	−	0.128424i
$919$	20.7231	−	15.0562i	0.683591	−	0.496658i	−0.190956	−	0.981599i	$-0.561159\pi$
$919$	20.7231	−	15.0562i	0.683591	−	0.496658i	0.874547	+	0.484941i	$0.161159\pi$
$920$	−2.48365	−	7.64389i	−0.0818835	−	0.252011i
$921$	4.85056	−	14.9285i	0.159832	−	0.491911i
$922$	2.23316	+	1.62249i	0.0735452	+	0.0534337i
$923$	−13.2777			−0.437041
$924$		0			0
$925$	5.20336			0.171085
$926$	1.34044	+	0.973885i	0.0440495	+	0.0320039i
$927$	−1.22257	+	3.76268i	−0.0401544	+	0.123583i
$928$	−13.6655	−	42.0581i	−0.448592	−	1.38062i
$929$	6.96381	−	5.05950i	0.228475	−	0.165997i	−0.467658	−	0.883909i	$-0.654902\pi$
$929$	6.96381	−	5.05950i	0.228475	−	0.165997i	0.696133	+	0.717912i	$0.254902\pi$
$930$	4.96777	−	3.60929i	0.162899	−	0.118353i
$931$	−12.0425	−	37.0629i	−0.394676	−	1.21469i
$932$	−11.5623	+	35.5850i	−0.378735	+	1.16563i
$933$	12.6612	+	9.19890i	0.414509	+	0.301159i
$934$	−13.0884			−0.428266
$935$		0			0
$936$	3.77752			0.123472
$937$	−4.82692	−	3.50696i	−0.157689	−	0.114567i	0.506143	−	0.862450i	$-0.331071\pi$
$937$	−4.82692	−	3.50696i	−0.157689	−	0.114567i	−0.663832	+	0.747882i	$0.731071\pi$
$938$	−0.543254	+	1.67196i	−0.0177379	+	0.0545916i
$939$	0.444044	+	1.36663i	0.0144908	+	0.0445981i
$940$	13.7394	−	9.98225i	0.448129	−	0.325585i
$941$	−18.4763	+	13.4238i	−0.602311	+	0.437605i	−0.846699	−	0.532073i	$-0.821413\pi$
$941$	−18.4763	+	13.4238i	−0.602311	+	0.437605i	0.244387	+	0.969678i	$0.421413\pi$
$942$	−4.16098	−	12.8062i	−0.135572	−	0.417248i
$943$	11.5814	−	35.6438i	0.377141	−	1.16072i
$944$	−5.97147	−	4.33853i	−0.194355	−	0.141207i
$945$	−2.64552			−0.0860586
$946$		0			0
$947$	−2.30620			−0.0749415			−0.0374708	−	0.999298i	$-0.511930\pi$
$947$	−2.30620			−0.0749415			−0.0374708	+	0.999298i	$0.511930\pi$
$948$	−8.30763	−	6.03584i	−0.269819	−	0.196035i
$949$	7.41641	−	22.8254i	0.240747	−	0.740942i
$950$	0.855586	+	2.63322i	0.0277589	+	0.0854330i
$951$	−3.45744	+	2.51198i	−0.112115	+	0.0814565i
$952$	1.76443	−	1.28193i	0.0571854	−	0.0415476i
$953$	−8.84186	−	27.2124i	−0.286416	−	0.881498i	−0.985971	−	0.166919i	$-0.946618\pi$
$953$	−8.84186	−	27.2124i	−0.286416	−	0.881498i	0.699555	−	0.714579i	$-0.253382\pi$
$954$	−0.394020	+	1.21267i	−0.0127569	+	0.0392616i
$955$	4.39859	+	3.19576i	0.142335	+	0.103412i
$956$	4.73383			0.153103
$957$		0			0
$958$	−6.72404			−0.217244
$959$	1.54537	+	1.12278i	0.0499026	+	0.0362564i
$960$	1.47103	−	4.52735i	0.0474771	−	0.146120i
$961$	10.0598	+	30.9609i	0.324510	+	0.998740i
$962$	−9.70820	+	7.05342i	−0.313005	+	0.227411i
$963$	−5.90412	+	4.28959i	−0.190257	+	0.138230i
$964$	−2.49734	−	7.68602i	−0.0804339	−	0.247550i
$965$	−0.990941	+	3.04980i	−0.0318995	+	0.0981767i
$966$	−1.32893	−	0.965522i	−0.0427575	−	0.0310652i
$967$	31.7422			1.02076			0.510380	−	0.859949i	$-0.329505\pi$
$967$	31.7422			1.02076			0.510380	+	0.859949i	$0.329505\pi$
$968$		0			0
$969$	23.0749			0.741274
$970$	1.41538	+	1.02834i	0.0454452	+	0.0330179i
$971$	−11.4343	+	35.1913i	−0.366946	+	1.12934i	0.581808	+	0.813326i	$0.302346\pi$
$971$	−11.4343	+	35.1913i	−0.366946	+	1.12934i	−0.948754	+	0.316017i	$0.897654\pi$
$972$	2.44826	+	7.53497i	0.0785279	+	0.241684i
$973$	3.58769	−	2.60661i	0.115016	−	0.0835640i
$974$	2.89993	−	2.10692i	0.0929198	−	0.0675102i
$975$	−2.37356	−	7.30506i	−0.0760147	−	0.233949i
$976$	−3.31610	+	10.2059i	−0.106146	+	0.326683i
$977$	−27.4027	−	19.9092i	−0.876689	−	0.636952i	0.0556841	−	0.998448i	$-0.482266\pi$
$977$	−27.4027	−	19.9092i	−0.876689	−	0.636952i	−0.932374	+	0.361496i	$0.882266\pi$
$978$	−10.1419			−0.324303
$979$		0			0
$980$	11.9721			0.382434
$981$	−6.28755	−	4.56817i	−0.200746	−	0.145850i
$982$	2.37408	−	7.30666i	0.0757599	−	0.233165i
$983$	−11.6659	−	35.9039i	−0.372084	−	1.14516i	−0.945425	−	0.325839i	$-0.894353\pi$
$983$	−11.6659	−	35.9039i	−0.372084	−	1.14516i	0.573342	−	0.819316i	$-0.305647\pi$
$984$	−19.8475	+	14.4200i	−0.632714	+	0.459694i
$985$	−15.6988	+	11.4058i	−0.500205	+	0.363421i
$986$	3.35136	+	10.3144i	0.106729	+	0.328479i
$987$	2.28539	−	7.03371i	0.0727448	−	0.223886i
$988$	39.5083	+	28.7044i	1.25692	+	0.913209i
$989$	−37.8343			−1.20306
$990$		0			0
$991$	−44.9354			−1.42742			−0.713710	−	0.700441i	$-0.752987\pi$
$991$	−44.9354			−1.42742			−0.713710	+	0.700441i	$0.752987\pi$
$992$	−31.6467	−	22.9927i	−1.00478	−	0.730019i
$993$	−9.39132	+	28.9035i	−0.298024	+	0.917225i
$994$	0.197868	+	0.608974i	0.00627598	+	0.0193155i
$995$	−16.4642	+	11.9620i	−0.521951	+	0.379220i
$996$	−3.92968	+	2.85508i	−0.124517	+	0.0904666i
$997$	0.122533	+	0.377119i	0.00388067	+	0.0119435i	0.952978	−	0.303039i	$-0.0980013\pi$
$997$	0.122533	+	0.377119i	0.00388067	+	0.0119435i	−0.949097	+	0.314983i	$0.898001\pi$
$998$	−3.61870	+	11.1372i	−0.114548	+	0.352543i
$999$	−23.1577	−	16.8251i	−0.732678	−	0.532322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.q.81.3		24
11.2	odd	10	inner	605.2.g.q.511.3		24
11.3	even	5	inner	605.2.g.q.366.3		24
11.4	even	5	inner	605.2.g.q.251.4		24
11.5	even	5		605.2.a.m.1.4	yes	6
11.6	odd	10		605.2.a.m.1.3	✓	6
11.7	odd	10	inner	605.2.g.q.251.3		24
11.8	odd	10	inner	605.2.g.q.366.4		24
11.9	even	5	inner	605.2.g.q.511.4		24
11.10	odd	2	inner	605.2.g.q.81.4		24
33.5	odd	10		5445.2.a.bx.1.3		6
33.17	even	10		5445.2.a.bx.1.4		6
44.27	odd	10		9680.2.a.cw.1.6		6
44.39	even	10		9680.2.a.cw.1.5		6
55.39	odd	10		3025.2.a.bg.1.4		6
55.49	even	10		3025.2.a.bg.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.3	✓	6	11.6	odd	10
605.2.a.m.1.4	yes	6	11.5	even	5
605.2.g.q.81.3		24	1.1	even	1	trivial
605.2.g.q.81.4		24	11.10	odd	2	inner
605.2.g.q.251.3		24	11.7	odd	10	inner
605.2.g.q.251.4		24	11.4	even	5	inner
605.2.g.q.366.3		24	11.3	even	5	inner
605.2.g.q.366.4		24	11.8	odd	10	inner
605.2.g.q.511.3		24	11.2	odd	10	inner
605.2.g.q.511.4		24	11.9	even	5	inner
3025.2.a.bg.1.3		6	55.49	even	10
3025.2.a.bg.1.4		6	55.39	odd	10
5445.2.a.bx.1.3		6	33.5	odd	10
5445.2.a.bx.1.4		6	33.17	even	10
9680.2.a.cw.1.5		6	44.39	even	10
9680.2.a.cw.1.6		6	44.27	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.389057 - 0.282666i) q^{2} +(-0.494946 + 1.52329i) q^{3} +(-0.546569 - 1.68217i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.623145 - 0.452741i) q^{6} +(-0.148607 - 0.457364i) q^{7} +(-0.560059 + 1.72368i) q^{8} +(0.351618 + 0.255466i) q^{9} +O(q^{10})\)	\(q+(-0.389057 - 0.282666i) q^{2} +(-0.494946 + 1.52329i) q^{3} +(-0.546569 - 1.68217i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.623145 - 0.452741i) q^{6} +(-0.148607 - 0.457364i) q^{7} +(-0.560059 + 1.72368i) q^{8} +(0.351618 + 0.255466i) q^{9} +0.480901 q^{10} +2.83294 q^{12} +(-3.87971 - 2.81878i) q^{13} +(-0.0714650 + 0.219947i) q^{14} +(-0.494946 - 1.52329i) q^{15} +(-2.15675 + 1.56697i) q^{16} +(2.02440 - 1.47081i) q^{17} +(-0.0645880 - 0.198781i) q^{18} +(1.77913 - 5.47560i) q^{19} +(1.43094 + 1.03964i) q^{20} +0.770249 q^{21} +4.43462 q^{23} +(-2.34847 - 1.70626i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.712656 + 2.19333i) q^{26} +(-4.45054 + 3.23350i) q^{27} +(-0.688138 + 0.499962i) q^{28} +(-2.78501 - 8.57138i) q^{29} +(-0.238020 + 0.732550i) q^{30} +(-6.44956 - 4.68588i) q^{31} +4.90680 q^{32} -1.20336 q^{34} +(0.389057 + 0.282666i) q^{35} +(0.237552 - 0.731110i) q^{36} +(1.60793 + 4.94869i) q^{37} +(-2.23995 + 1.62742i) q^{38} +(6.21405 - 4.51478i) q^{39} +(-0.560059 - 1.72368i) q^{40} +(2.61158 - 8.03761i) q^{41} +(-0.299671 - 0.217724i) q^{42} -8.53158 q^{43} -0.434624 q^{45} +(-1.72532 - 1.25352i) q^{46} +(2.96708 - 9.13174i) q^{47} +(-1.31947 - 4.06092i) q^{48} +(5.47602 - 3.97856i) q^{49} +(-0.389057 + 0.282666i) q^{50} +(1.23850 + 3.81172i) q^{51} +(-2.62112 + 8.06698i) q^{52} +(-4.93542 - 3.58579i) q^{53} +2.64552 q^{54} +0.871579 q^{56} +(7.46034 + 5.42026i) q^{57} +(-1.33931 + 4.12198i) q^{58} +(0.855586 + 2.63322i) q^{59} +(-2.29190 + 1.66516i) q^{60} +(3.25657 - 2.36604i) q^{61} +(1.18471 + 3.64615i) q^{62} +(0.0645880 - 0.198781i) q^{63} +(2.40447 + 1.74695i) q^{64} +4.79559 q^{65} +7.60168 q^{67} +(-3.58063 - 2.60148i) q^{68} +(-2.19490 + 6.75521i) q^{69} +(-0.0714650 - 0.219947i) q^{70} +(2.23995 - 1.62742i) q^{71} +(-0.637268 + 0.463003i) q^{72} +(1.54651 + 4.75966i) q^{73} +(0.773253 - 2.37983i) q^{74} +(1.29579 + 0.941443i) q^{75} -10.1833 q^{76} -3.69380 q^{78} +(-2.93251 - 2.13059i) q^{79} +(0.823805 - 2.53541i) q^{80} +(-2.31986 - 7.13980i) q^{81} +(-3.28802 + 2.38888i) q^{82} +(-1.38713 + 1.00781i) q^{83} +(-0.420994 - 1.29569i) q^{84} +(-0.773253 + 2.37983i) q^{85} +(3.31927 + 2.41159i) q^{86} +14.4351 q^{87} -15.7408 q^{89} +(0.169094 + 0.122854i) q^{90} +(-0.712656 + 2.19333i) q^{91} +(-2.42383 - 7.45977i) q^{92} +(10.3301 - 7.50527i) q^{93} +(-3.73560 + 2.71407i) q^{94} +(1.77913 + 5.47560i) q^{95} +(-2.42860 + 7.47447i) q^{96} +(2.94319 + 2.13835i) q^{97} -3.25509 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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