LMFDB - Embedded newform 135.2.q.a.122.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.9
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0928047 + 0.0649826i) q^{2} +(1.57132 - 0.728671i) q^{3} +(-0.679650 - 1.86732i) q^{4} +(0.584024 + 2.15845i) q^{5} +(0.193177 + 0.0344841i) q^{6} +(0.344848 + 0.739528i) q^{7} +(0.116914 - 0.436329i) q^{8} +(1.93808 - 2.28995i) q^{9} +O(q^{10})$	\(q+(0.0928047 + 0.0649826i) q^{2} +(1.57132 - 0.728671i) q^{3} +(-0.679650 - 1.86732i) q^{4} +(0.584024 + 2.15845i) q^{5} +(0.193177 + 0.0344841i) q^{6} +(0.344848 + 0.739528i) q^{7} +(0.116914 - 0.436329i) q^{8} +(1.93808 - 2.28995i) q^{9} +(-0.0860616 + 0.238266i) q^{10} +(-0.792138 - 0.944033i) q^{11} +(-2.42861 - 2.43892i) q^{12} +(-2.08344 - 2.97546i) q^{13} +(-0.0160530 + 0.0910408i) q^{14} +(2.49049 + 2.96605i) q^{15} +(-3.00531 + 2.52175i) q^{16} +(1.65815 + 6.18829i) q^{17} +(0.328669 - 0.0865769i) q^{18} +(-2.78289 + 1.60671i) q^{19} +(3.63360 - 2.55755i) q^{20} +(1.08074 + 0.910753i) q^{21} +(-0.0121684 - 0.139086i) q^{22} +(0.471164 + 0.219707i) q^{23} +(-0.134231 - 0.770802i) q^{24} +(-4.31783 + 2.52118i) q^{25} -0.411524i q^{26} +(1.37671 - 5.01046i) q^{27} +(1.14656 - 1.14656i) q^{28} +(0.754929 + 4.28141i) q^{29} +(0.0383876 + 0.437102i) q^{30} +(-6.93274 + 2.52331i) q^{31} +(-1.34278 + 0.117478i) q^{32} +(-1.93259 - 0.906167i) q^{33} +(-0.248247 + 0.682053i) q^{34} +(-1.39484 + 1.17624i) q^{35} +(-5.59329 - 2.06265i) q^{36} +(8.35299 - 2.23818i) q^{37} +(-0.362674 - 0.0317298i) q^{38} +(-5.44188 - 3.15725i) q^{39} +(1.01007 - 0.00247331i) q^{40} +(-8.94143 - 1.57662i) q^{41} +(0.0411146 + 0.154751i) q^{42} +(0.490289 - 5.60402i) q^{43} +(-1.22444 + 2.12079i) q^{44} +(6.07463 + 2.84586i) q^{45} +(0.0294491 + 0.0510073i) q^{46} +(2.14663 - 1.00099i) q^{47} +(-2.88476 + 6.15236i) q^{48} +(4.07153 - 4.85226i) q^{49} +(-0.564548 - 0.0466068i) q^{50} +(7.11471 + 8.51552i) q^{51} +(-4.14014 + 5.91273i) q^{52} +(4.55111 + 4.55111i) q^{53} +(0.453358 - 0.375532i) q^{54} +(1.57502 - 2.26113i) q^{55} +(0.362995 - 0.0640058i) q^{56} +(-3.20205 + 4.55246i) q^{57} +(-0.208156 + 0.446393i) q^{58} +(-10.5708 - 8.86992i) q^{59} +(3.84592 - 6.66643i) q^{60} +(3.01780 + 1.09839i) q^{61} +(-0.807362 - 0.216332i) q^{62} +(2.36182 + 0.643579i) q^{63} +(6.66285 + 3.84680i) q^{64} +(5.20561 - 6.23475i) q^{65} +(-0.120468 - 0.209681i) q^{66} +(9.77239 - 6.84270i) q^{67} +(10.4286 - 7.30217i) q^{68} +(0.900442 + 0.00190622i) q^{69} +(-0.205883 + 0.0185205i) q^{70} +(4.14187 + 2.39131i) q^{71} +(-0.772582 - 1.11336i) q^{72} +(-5.46389 - 1.46405i) q^{73} +(0.920640 + 0.335086i) q^{74} +(-4.94757 + 7.10785i) q^{75} +(4.89163 + 4.10457i) q^{76} +(0.424972 - 0.911356i) q^{77} +(-0.299866 - 0.646635i) q^{78} +(9.54938 - 1.68381i) q^{79} +(-7.19826 - 5.01405i) q^{80} +(-1.48773 - 8.87619i) q^{81} +(-0.727355 - 0.727355i) q^{82} +(4.76170 - 6.80042i) q^{83} +(0.966147 - 2.63708i) q^{84} +(-12.3887 + 7.19314i) q^{85} +(0.409665 - 0.488220i) q^{86} +(4.30598 + 6.17736i) q^{87} +(-0.504521 + 0.235262i) q^{88} +(-0.689073 - 1.19351i) q^{89} +(0.378823 + 0.658854i) q^{90} +(1.48197 - 2.56685i) q^{91} +(0.0900380 - 1.02914i) q^{92} +(-9.05487 + 9.01661i) q^{93} +(0.264265 + 0.0465970i) q^{94} +(-5.09327 - 5.06839i) q^{95} +(-2.02433 + 1.16304i) q^{96} +(-6.18004 - 0.540683i) q^{97} +(0.693170 - 0.185734i) q^{98} +(-3.69701 - 0.0156531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0928047	+	0.0649826i	0.0656229	+	0.0459496i	0.605928	−	0.795520i	$-0.292802\pi$
$2$	0.0928047	+	0.0649826i	0.0656229	+	0.0459496i	−0.540305	+	0.841469i	$0.681691\pi$
$3$	1.57132	−	0.728671i	0.907200	−	0.420699i
$3$	1.57132	−	0.728671i	0.907200	−	0.420699i
$4$	−0.679650	−	1.86732i	−0.339825	−	0.933662i
$5$	0.584024	+	2.15845i	0.261183	+	0.965289i
$5$	0.584024	+	2.15845i	0.261183	+	0.965289i
$6$	0.193177	+	0.0344841i	0.0788640	+	0.0140781i
$7$	0.344848	+	0.739528i	0.130340	+	0.279515i	0.960637	−	0.277805i	$-0.0896071\pi$
$7$	0.344848	+	0.739528i	0.130340	+	0.279515i	−0.830297	+	0.557321i	$0.811829\pi$
$8$	0.116914	−	0.436329i	0.0413353	−	0.154265i
$9$	1.93808	−	2.28995i	0.646025	−	0.763316i
$10$	−0.0860616	+	0.238266i	−0.0272151	+	0.0753463i
$11$	−0.792138	−	0.944033i	−0.238839	−	0.284637i	0.633289	−	0.773916i	$-0.281705\pi$
$11$	−0.792138	−	0.944033i	−0.238839	−	0.284637i	−0.872127	+	0.489279i	$0.837260\pi$
$12$	−2.42861	−	2.43892i	−0.701080	−	0.704055i
$13$	−2.08344	−	2.97546i	−0.577843	−	0.825245i	0.418718	−	0.908116i	$-0.362480\pi$
$13$	−2.08344	−	2.97546i	−0.577843	−	0.825245i	−0.996560	+	0.0828718i	$0.973591\pi$
$14$	−0.0160530	+	0.0910408i	−0.00429033	+	0.0243317i
$15$	2.49049	+	2.96605i	0.643042	+	0.765831i
$16$	−3.00531	+	2.52175i	−0.751327	+	0.630438i
$17$	1.65815	+	6.18829i	0.402160	+	1.50088i	0.809234	+	0.587486i	$0.199882\pi$
$17$	1.65815	+	6.18829i	0.402160	+	1.50088i	−0.407074	+	0.913395i	$0.633451\pi$
$18$	0.328669	−	0.0865769i	0.0774681	−	0.0204064i
$19$	−2.78289	+	1.60671i	−0.638440	+	0.368603i	−0.784013	−	0.620744i	$-0.786831\pi$
$19$	−2.78289	+	1.60671i	−0.638440	+	0.368603i	0.145573	+	0.989347i	$0.453497\pi$
$20$	3.63360	−	2.55755i	0.812497	−	0.571887i
$21$	1.08074	+	0.910753i	0.235836	+	0.198743i
$22$	−0.0121684	−	0.139086i	−0.00259432	−	0.0296532i
$23$	0.471164	+	0.219707i	0.0982444	+	0.0458121i	0.471119	−	0.882070i	$-0.343850\pi$
$23$	0.471164	+	0.219707i	0.0982444	+	0.0458121i	−0.372875	+	0.927882i	$0.621628\pi$
$24$	−0.134231	−	0.770802i	−0.0273999	−	0.157339i
$25$	−4.31783	+	2.52118i	−0.863566	+	0.504235i
$26$		−	0.411524i		−	0.0807066i
$27$	1.37671	−	5.01046i	0.264948	−	0.964263i
$28$	1.14656	−	1.14656i	0.216680	−	0.216680i
$29$	0.754929	+	4.28141i	0.140187	+	0.795038i	0.971107	+	0.238646i	$0.0767037\pi$
$29$	0.754929	+	4.28141i	0.140187	+	0.795038i	−0.830920	+	0.556392i	$0.812185\pi$
$30$	0.0383876	+	0.437102i	0.00700858	+	0.0798036i
$31$	−6.93274	+	2.52331i	−1.24516	+	0.453200i	−0.878762	−	0.477260i	$-0.841630\pi$
$31$	−6.93274	+	2.52331i	−1.24516	+	0.453200i	−0.366394	+	0.930460i	$0.619408\pi$
$32$	−1.34278	+	0.117478i	−0.237372	+	0.0207674i
$33$	−1.93259	−	0.906167i	−0.336421	−	0.157743i
$34$	−0.248247	+	0.682053i	−0.0425740	+	0.116971i
$35$	−1.39484	+	1.17624i	−0.235771	+	0.198821i
$36$	−5.59329	−	2.06265i	−0.932215	−	0.343775i
$37$	8.35299	−	2.23818i	1.37322	−	0.367954i	0.504569	−	0.863372i	$-0.331652\pi$
$37$	8.35299	−	2.23818i	1.37322	−	0.367954i	0.868655	+	0.495417i	$0.164985\pi$
$38$	−0.362674	−	0.0317298i	−0.0588334	−	0.00514726i
$39$	−5.44188	−	3.15725i	−0.871398	−	0.505565i
$40$	1.01007	−	0.00247331i	0.159707	−	0.000391065i
$41$	−8.94143	−	1.57662i	−1.39642	−	0.246226i	−0.575747	−	0.817628i	$-0.695289\pi$
$41$	−8.94143	−	1.57662i	−1.39642	−	0.246226i	−0.820670	+	0.571402i	$0.806400\pi$
$42$	0.0411146	+	0.154751i	0.00634412	+	0.0238787i
$43$	0.490289	−	5.60402i	0.0747683	−	0.854606i	−0.862514	−	0.506034i	$-0.831111\pi$
$43$	0.490289	−	5.60402i	0.0747683	−	0.854606i	0.937282	−	0.348572i	$-0.113333\pi$
$44$	−1.22444	+	2.12079i	−0.184591	+	0.319721i
$45$	6.07463	+	2.84586i	0.905552	+	0.424236i
$46$	0.0294491	+	0.0510073i	0.00434203	+	0.00752062i
$47$	2.14663	−	1.00099i	0.313118	−	0.146010i	−0.259706	−	0.965688i	$-0.583626\pi$
$47$	2.14663	−	1.00099i	0.313118	−	0.146010i	0.572824	+	0.819678i	$0.305848\pi$
$48$	−2.88476	+	6.15236i	−0.416380	+	0.888016i
$49$	4.07153	−	4.85226i	0.581647	−	0.693180i
$50$	−0.564548	−	0.0466068i	−0.0798391	−	0.00659120i
$51$	7.11471	+	8.51552i	0.996258	+	1.19241i
$52$	−4.14014	+	5.91273i	−0.574134	+	0.819949i
$53$	4.55111	+	4.55111i	0.625143	+	0.625143i	0.946842	−	0.321699i	$-0.104254\pi$
$53$	4.55111	+	4.55111i	0.625143	+	0.625143i	−0.321699	+	0.946842i	$0.604254\pi$
$54$	0.453358	−	0.375532i	0.0616942	−	0.0511034i
$55$	1.57502	−	2.26113i	0.212376	−	0.304891i
$56$	0.362995	−	0.0640058i	0.0485072	−	0.00855313i
$57$	−3.20205	+	4.55246i	−0.424122	+	0.602988i
$58$	−0.208156	+	0.446393i	−0.0273323	+	0.0586142i
$59$	−10.5708	−	8.86992i	−1.37620	−	1.15477i	−0.970596	−	0.240714i	$-0.922618\pi$
$59$	−10.5708	−	8.86992i	−1.37620	−	1.15477i	−0.405600	−	0.914051i	$-0.632937\pi$
$60$	3.84592	−	6.66643i	0.496506	−	0.860632i
$61$	3.01780	+	1.09839i	0.386390	+	0.140634i	0.527908	−	0.849301i	$-0.322976\pi$
$61$	3.01780	+	1.09839i	0.386390	+	0.140634i	−0.141519	+	0.989936i	$0.545199\pi$
$62$	−0.807362	−	0.216332i	−0.102535	−	0.0274742i
$63$	2.36182	+	0.643579i	0.297562	+	0.0810833i
$64$	6.66285	+	3.84680i	0.832856	+	0.480850i
$65$	5.20561	−	6.23475i	0.645677	−	0.773325i
$66$	−0.120468	−	0.209681i	−0.0148286	−	0.0258100i
$67$	9.77239	−	6.84270i	1.19389	−	0.835969i	0.204160	−	0.978938i	$-0.434554\pi$
$67$	9.77239	−	6.84270i	1.19389	−	0.835969i	0.989727	+	0.142969i	$0.0456649\pi$
$68$	10.4286	−	7.30217i	1.26465	−	0.885518i
$69$	0.900442	+	0.00190622i	0.108400	+	0.000229482i
$70$	−0.205883	+	0.0185205i	−0.0246077	+	0.00221362i
$71$	4.14187	+	2.39131i	0.491550	+	0.283796i	0.725217	−	0.688520i	$-0.241739\pi$
$71$	4.14187	+	2.39131i	0.491550	+	0.283796i	−0.233667	+	0.972317i	$0.575073\pi$
$72$	−0.772582	−	1.11336i	−0.0910496	−	0.131211i
$73$	−5.46389	−	1.46405i	−0.639500	−	0.171354i	−0.0755232	−	0.997144i	$-0.524063\pi$
$73$	−5.46389	−	1.46405i	−0.639500	−	0.171354i	−0.563977	+	0.825790i	$0.690729\pi$
$74$	0.920640	+	0.335086i	0.107022	+	0.0389529i
$75$	−4.94757	+	7.10785i	−0.571297	+	0.820744i
$76$	4.89163	+	4.10457i	0.561109	+	0.470826i
$77$	0.424972	−	0.911356i	0.0484301	−	0.103859i
$78$	−0.299866	−	0.646635i	−0.0339531	−	0.0732170i
$79$	9.54938	−	1.68381i	1.07439	−	0.189444i	0.391656	−	0.920112i	$-0.371902\pi$
$79$	9.54938	−	1.68381i	1.07439	−	0.189444i	0.682733	+	0.730668i	$0.260791\pi$
$80$	−7.19826	−	5.01405i	−0.804790	−	0.560588i
$81$	−1.48773	−	8.87619i	−0.165303	−	0.986243i
$82$	−0.727355	−	0.727355i	−0.0803229	−	0.0803229i
$83$	4.76170	−	6.80042i	0.522665	−	0.746443i	−0.467856	−	0.883805i	$-0.654973\pi$
$83$	4.76170	−	6.80042i	0.522665	−	0.746443i	0.990521	+	0.137362i	$0.0438624\pi$
$84$	0.966147	−	2.63708i	0.105415	−	0.287729i
$85$	−12.3887	+	7.19314i	−1.34375	+	0.780206i
$86$	0.409665	−	0.488220i	0.0441753	−	0.0526461i
$87$	4.30598	+	6.17736i	0.461649	+	0.662283i
$88$	−0.504521	+	0.235262i	−0.0537821	+	0.0250790i
$89$	−0.689073	−	1.19351i	−0.0730416	−	0.126512i	0.827191	−	0.561920i	$-0.189937\pi$
$89$	−0.689073	−	1.19351i	−0.0730416	−	0.126512i	−0.900233	+	0.435409i	$0.856604\pi$
$90$	0.378823	+	0.658854i	0.0399314	+	0.0694493i
$91$	1.48197	−	2.56685i	0.155353	−	0.269079i
$92$	0.0900380	−	1.02914i	0.00938711	−	0.107295i
$93$	−9.05487	+	9.01661i	−0.938946	+	0.934979i
$94$	0.264265	+	0.0465970i	0.0272568	+	0.00480611i
$95$	−5.09327	−	5.06839i	−0.522559	−	0.520006i
$96$	−2.02433	+	1.16304i	−0.206607	+	0.118702i
$97$	−6.18004	−	0.540683i	−0.627488	−	0.0548981i	−0.231023	−	0.972948i	$-0.574207\pi$
$97$	−6.18004	−	0.540683i	−0.627488	−	0.0548981i	−0.396464	+	0.918050i	$0.629763\pi$
$98$	0.693170	−	0.185734i	0.0700207	−	0.0187620i
$99$	−3.69701	−	0.0156531i	−0.371564	−	0.00157319i
$100$	7.64247	+	6.34927i	0.764247	+	0.634927i
$101$	−0.358110	+	0.983900i	−0.0356333	+	0.0979017i	−0.956233	−	0.292605i	$-0.905478\pi$
$101$	−0.358110	+	0.983900i	−0.0356333	+	0.0979017i	0.920600	+	0.390507i	$0.127700\pi$
$102$	0.106918	+	1.25261i	0.0105864	+	0.124027i
$103$	5.46070	−	0.477749i	0.538058	−	0.0470740i	0.185112	−	0.982717i	$-0.440735\pi$
$103$	5.46070	−	0.477749i	0.538058	−	0.0470740i	0.352947	+	0.935643i	$0.385180\pi$
$104$	−1.54186	+	0.561192i	−0.151192	+	0.0550294i
$105$	−1.33464	+	2.86462i	−0.130248	+	0.279559i
$106$	0.126622	+	0.718107i	0.0122986	+	0.0697487i
$107$	−7.41541	+	7.41541i	−0.716875	+	0.716875i	−0.967964	−	0.251089i	$-0.919211\pi$
$107$	−7.41541	+	7.41541i	−0.716875	+	0.716875i	0.251089	+	0.967964i	$0.419211\pi$
$108$	−10.2918	+	0.834591i	−0.990331	+	0.0803085i
$109$			13.2925i			1.27319i	0.771199	+	0.636595i	$0.219658\pi$
$109$			13.2925i			1.27319i	−0.771199	+	0.636595i	$0.780342\pi$
$110$	0.293104	−	0.107495i	0.0279463	−	0.0102492i
$111$	11.4943	−	9.60348i	1.09099	−	0.911522i
$112$	−2.90128	−	1.35289i	−0.274145	−	0.127836i
$113$	1.20301	+	13.7505i	0.113170	+	1.29353i	0.814276	+	0.580477i	$0.197134\pi$
$113$	1.20301	+	13.7505i	0.113170	+	1.29353i	−0.701107	+	0.713056i	$0.747310\pi$
$114$	−0.592996	+	0.214412i	−0.0555392	+	0.0200816i
$115$	−0.199057	+	1.14530i	−0.0185621	+	0.106800i
$116$	7.48170	−	4.31956i	0.694658	−	0.401061i
$117$	−10.8515	−	0.995699i	−1.00322	−	0.0920524i
$118$	−0.404626	−	1.51009i	−0.0372489	−	0.139015i
$119$	−4.00461	+	3.36027i	−0.367102	+	0.308035i
$120$	1.58535	−	0.739899i	0.144722	−	0.0675432i
$121$	1.64641	−	9.33728i	0.149674	−	0.848843i
$122$	0.208690	+	0.298040i	0.0188939	+	0.0269833i
$123$	−15.1987	+	4.03800i	−1.37042	+	0.364094i
$124$	9.42367	+	11.2307i	0.846271	+	1.00855i
$125$	−7.96355	−	7.84741i	−0.712282	−	0.701893i
$126$	0.177367	+	0.213205i	0.0158011	+	0.0189938i
$127$	3.01921	−	11.2678i	0.267911	−	0.999858i	−0.692533	−	0.721386i	$-0.743505\pi$
$127$	3.01921	−	11.2678i	0.267911	−	0.999858i	0.960444	−	0.278472i	$-0.0898280\pi$
$128$	1.50767	+	3.23321i	0.133261	+	0.285778i
$129$	−3.31309	−	9.16296i	−0.291702	−	0.806754i
$130$	0.888256	−	0.240340i	0.0779052	−	0.0210792i
$131$	−2.06228	−	5.66608i	−0.180182	−	0.495047i	0.816415	−	0.577465i	$-0.195958\pi$
$131$	−2.06228	−	5.66608i	−0.180182	−	0.495047i	−0.996598	+	0.0824178i	$0.973736\pi$
$132$	−0.378622	+	4.22465i	−0.0329549	+	0.367708i
$133$	−2.14788	−	1.50396i	−0.186245	−	0.130410i
$134$	1.35158			0.116759
$135$	11.6189	+	0.0453404i	0.999992	+	0.00390228i
$136$	2.89399			0.248157
$137$	−10.9750	−	7.68477i	−0.937657	−	0.656554i	0.00151614	−	0.999999i	$-0.499517\pi$
$137$	−10.9750	−	7.68477i	−0.937657	−	0.656554i	−0.939173	+	0.343444i	$0.888406\pi$
$138$	0.0834414	+	0.0586900i	0.00710301	+	0.00499602i
$139$	−2.32343	−	6.38357i	−0.197071	−	0.541447i	0.801315	−	0.598242i	$-0.204134\pi$
$139$	−2.32343	−	6.38357i	−0.197071	−	0.541447i	−0.998386	+	0.0567952i	$0.981912\pi$
$140$	3.14442	+	1.80518i	0.265752	+	0.152566i
$141$	2.64365	−	3.13706i	0.222635	−	0.264188i
$142$	0.228992	+	0.491074i	0.0192166	+	0.0412100i
$143$	−1.15856	+	4.32381i	−0.0968839	+	0.361575i
$144$	−0.0498312	+	11.7694i	−0.00415260	+	0.980779i
$145$	−8.80033	+	4.12993i	−0.730828	+	0.342972i
$146$	−0.411938	−	0.490928i	−0.0340922	−	0.0406295i
$147$	2.86196	−	10.5913i	0.236051	−	0.873552i
$148$	−9.85652	−	14.0766i	−0.810201	−	1.15709i
$149$	−2.75408	+	15.6192i	−0.225623	+	1.27957i	0.635868	+	0.771798i	$0.280642\pi$
$149$	−2.75408	+	15.6192i	−0.225623	+	1.27957i	−0.861491	+	0.507773i	$0.830469\pi$
$150$	−0.921045	+	0.338136i	−0.0752030	+	0.0276087i
$151$	−0.777628	+	0.652507i	−0.0632825	+	0.0531003i	−0.673880	−	0.738841i	$-0.735374\pi$
$151$	−0.777628	+	0.652507i	−0.0632825	+	0.0531003i	0.610598	+	0.791941i	$0.290929\pi$
$152$	0.375692	+	1.40210i	0.0304727	+	0.113726i
$153$	17.3845	+	8.19630i	1.40545	+	0.662632i
$154$	0.0986617	−	0.0569624i	0.00795039	−	0.00459016i
$155$	−9.49533	−	13.4903i	−0.762683	−	1.08357i
$156$	−2.19703	+	12.3076i	−0.175903	+	0.985395i
$157$	1.36005	+	15.5455i	0.108544	+	1.24066i	0.833754	+	0.552136i	$0.186187\pi$
$157$	1.36005	+	15.5455i	0.108544	+	1.24066i	−0.725210	+	0.688528i	$0.758257\pi$
$158$	0.995646	+	0.464278i	0.0792094	+	0.0369359i
$159$	10.4675	+	3.83497i	0.830127	+	0.304133i
$160$	−1.03779	−	2.82972i	−0.0820442	−	0.223709i
$161$			0.424205i			0.0334320i
$162$	0.438730	−	0.920428i	0.0344698	−	0.0723157i
$163$	1.25033	−	1.25033i	0.0979331	−	0.0979331i	−0.656443	−	0.754376i	$-0.727940\pi$
$163$	1.25033	−	1.25033i	0.0979331	−	0.0979331i	0.754376	+	0.656443i	$0.227940\pi$
$164$	3.13299	+	17.7681i	0.244646	+	1.38746i
$165$	0.827240	−	4.70063i	0.0644005	−	0.365943i
$166$	0.883817	−	0.321683i	0.0685975	−	0.0249675i
$167$	4.87345	−	0.426371i	0.377119	−	0.0329936i	0.102979	−	0.994684i	$-0.467163\pi$
$167$	4.87345	−	0.426371i	0.377119	−	0.0329936i	0.274140	+	0.961690i	$0.411607\pi$
$168$	0.523741	−	0.365077i	0.0404075	−	0.0281663i
$169$	−0.0663864	+	0.182395i	−0.00510665	+	0.0140304i
$170$	−1.61716	−	0.137494i	−0.124031	−	0.0105453i
$171$	−1.71419	+	9.48660i	−0.131087	+	0.725459i
$172$	−10.7978	+	2.89325i	−0.823321	+	0.220608i
$173$	2.34398	+	0.205071i	0.178209	+	0.0155913i	0.175911	−	0.984406i	$-0.443713\pi$
$173$	2.34398	+	0.205071i	0.178209	+	0.0155913i	0.00229816	+	0.999997i	$0.499268\pi$
$174$	−0.00180600	+	0.853102i	−0.000136912	+	0.0646735i
$175$	−3.35348	−	2.32374i	−0.253499	−	0.175658i
$176$	4.76124	+	0.839535i	0.358892	+	0.0632823i
$177$	−23.0733	−	6.23485i	−1.73429	−	0.468640i
$178$	0.0136081	−	0.155541i	0.00101997	−	0.0116583i
$179$	9.70081	−	16.8023i	0.725073	−	1.25586i	−0.233871	−	0.972268i	$-0.575139\pi$
$179$	9.70081	−	16.8023i	0.725073	−	1.25586i	0.958944	−	0.283595i	$-0.0915273\pi$
$180$	1.18552	−	13.2775i	0.0883634	−	0.989645i
$181$	−2.02017	−	3.49903i	−0.150158	−	0.260081i	0.781128	−	0.624371i	$-0.214645\pi$
$181$	−2.02017	−	3.49903i	−0.150158	−	0.260081i	−0.931285	+	0.364291i	$0.881312\pi$
$182$	0.304334	−	0.141913i	0.0225587	−	0.0105193i
$183$	5.54228	−	0.473066i	0.409697	−	0.0349701i
$184$	0.150950	−	0.179895i	0.0111282	−	0.0132621i
$185$	9.70935	+	16.7224i	0.713846	+	1.22945i
$186$	−1.42626	+	0.248376i	−0.104578	+	0.0182118i
$187$	4.52847	−	6.46733i	0.331155	−	0.472938i
$188$	−3.32813	−	3.32813i	−0.242729	−	0.242729i
$189$	4.18013	−	0.709727i	0.304060	−	0.0516250i
$190$	−0.143323	−	0.801345i	−0.0103977	−	0.0581357i
$191$	−0.548539	+	0.0967222i	−0.0396909	+	0.00699857i	−0.193458	−	0.981108i	$-0.561970\pi$
$191$	−0.548539	+	0.0967222i	−0.0396909	+	0.00699857i	0.153767	+	0.988107i	$0.450859\pi$
$192$	13.2725	+	1.18951i	0.957860	+	0.0858456i
$193$	−8.39357	+	18.0001i	−0.604183	+	1.29567i	0.331708	+	0.943382i	$0.392375\pi$
$193$	−8.39357	+	18.0001i	−0.604183	+	1.29567i	−0.935890	+	0.352292i	$0.885403\pi$
$194$	−0.538402	−	0.451773i	−0.0386550	−	0.0324354i
$195$	3.63659	−	13.5900i	0.260421	−	0.973197i
$196$	−11.8280	−	4.30503i	−0.844854	−	0.307502i
$197$	16.1238	+	4.32035i	1.14877	+	0.307812i	0.782473	−	0.622685i	$-0.213958\pi$
$197$	16.1238	+	4.32035i	1.14877	+	0.307812i	0.366299	+	0.930497i	$0.380625\pi$
$198$	−0.342083	−	0.241694i	−0.0243108	−	0.0171764i
$199$	−20.8934	−	12.0628i	−1.48110	−	0.855112i	−0.481327	−	0.876541i	$-0.659845\pi$
$199$	−20.8934	−	12.0628i	−1.48110	−	0.855112i	−0.999770	+	0.0214296i	$0.993178\pi$
$200$	0.595246	+	2.17875i	0.0420903	+	0.154061i
$201$	10.3694	−	17.8729i	0.731404	−	1.26066i
$202$	−0.0971707	+	0.0680397i	−0.00683691	+	0.00478725i
$203$	−2.90589	+	2.03473i	−0.203954	+	0.142810i
$204$	11.0657	−	19.0730i	0.774756	−	1.33538i
$205$	−1.81896	−	20.2204i	−0.127042	−	1.41226i
$206$	0.537824	+	0.310513i	0.0374720	+	0.0216344i
$207$	1.41627	−	0.653131i	0.0984375	−	0.0453958i
$208$	13.7648	+	3.68826i	0.954415	+	0.255735i
$209$	3.72122	+	1.35441i	0.257402	+	0.0936867i
$210$	−0.310012	+	0.179122i	−0.0213928	+	0.0123606i
$211$	21.4119	+	17.9667i	1.47406	+	1.23688i	0.912265	+	0.409601i	$0.134332\pi$
$211$	21.4119	+	17.9667i	1.47406	+	1.23688i	0.561792	+	0.827279i	$0.310112\pi$
$212$	5.40523	−	11.5916i	0.371233	−	0.796111i
$213$	8.25067	+	0.739444i	0.565327	+	0.0506658i
$214$	−1.17006	+	0.206313i	−0.0799835	+	0.0141032i
$215$	12.3824	−	2.21462i	0.844470	−	0.151036i
$216$	−2.02525	−	1.18649i	−0.137801	−	0.0807304i
$217$	−4.25680	−	4.25680i	−0.288970	−	0.288970i
$218$	−0.863780	+	1.23361i	−0.0585026	+	0.0835503i
$219$	−9.65232	+	1.68090i	−0.652243	+	0.113585i
$220$	−5.29273	−	1.40430i	−0.356836	−	0.0946779i
$221$	14.9584	−	17.8267i	1.00621	−	1.19915i
$222$	1.69078	−	0.144318i	0.113478	−	0.00968602i
$223$	3.93150	−	1.83329i	0.263273	−	0.122766i	−0.286500	−	0.958080i	$-0.592492\pi$
$223$	3.93150	−	1.83329i	0.263273	−	0.122766i	0.549773	+	0.835314i	$0.314714\pi$
$224$	−0.549933	−	0.952512i	−0.0367440	−	0.0636424i
$225$	−2.59492	+	14.7738i	−0.172995	+	0.984923i
$226$	−0.781895	+	1.35428i	−0.0520109	+	0.0900855i
$227$	−2.21851	+	25.3576i	−0.147247	+	1.68305i	0.459521	+	0.888167i	$0.348021\pi$
$227$	−2.21851	+	25.3576i	−0.147247	+	1.68305i	−0.606768	+	0.794879i	$0.707534\pi$
$228$	10.6772	+	2.88518i	0.707114	+	0.191076i
$229$	−5.08120	−	0.895953i	−0.335775	−	0.0592062i	0.00321862	−	0.999995i	$-0.498975\pi$
$229$	−5.08120	−	0.895953i	−0.335775	−	0.0592062i	−0.338994	+	0.940789i	$0.610087\pi$
$230$	−0.0928979	+	0.0933539i	−0.00612550	+	0.00615558i
$231$	0.00368713	−	1.74170i	0.000242596	−	0.114595i
$232$	1.95636	+	0.171160i	0.128442	+	0.0112372i
$233$	−7.55194	+	2.02354i	−0.494744	+	0.132566i	−0.497560	−	0.867430i	$-0.665770\pi$
$233$	−7.55194	+	2.02354i	−0.494744	+	0.132566i	0.00281565	+	0.999996i	$0.499104\pi$
$234$	−0.942369	−	0.797565i	−0.0616046	−	0.0521385i
$235$	3.41428	+	4.04880i	0.222723	+	0.264115i
$236$	−9.37859	+	25.7675i	−0.610494	+	1.67732i
$237$	13.7782	−	9.60417i	0.894988	−	0.623858i
$238$	−0.590005	+	0.0516188i	−0.0382444	+	0.00334595i
$239$	−10.8598	+	3.95265i	−0.702462	+	0.255675i	−0.668462	−	0.743746i	$-0.733047\pi$
$239$	−10.8598	+	3.95265i	−0.702462	+	0.255675i	−0.0340005	+	0.999422i	$0.510825\pi$
$240$	−14.9643	−	2.63350i	−0.965944	−	0.169992i
$241$	2.63129	+	14.9228i	0.169496	+	0.961259i	0.944307	+	0.329066i	$0.106734\pi$
$241$	2.63129	+	14.9228i	0.169496	+	0.961259i	−0.774811	+	0.632193i	$0.782155\pi$
$242$	0.759555	−	0.759555i	0.0488261	−	0.0488261i
$243$	−8.80551	−	12.8632i	−0.564874	−	0.825177i
$244$		−	6.38173i		−	0.408548i
$245$	12.8512	+	5.95437i	0.821036	+	0.380411i
$246$	−1.67291	−	0.612902i	−0.106661	−	0.0390772i
$247$	10.5787	+	4.93292i	0.673106	+	0.313874i
$248$	0.290459	+	3.31996i	0.0184442	+	0.210818i
$249$	2.52688	−	14.1553i	0.160134	−	0.897057i
$250$	−0.229111	−	1.24577i	−0.0144902	−	0.0787893i
$251$	−13.8298	+	7.98465i	−0.872930	+	0.503986i	−0.868321	−	0.496003i	$-0.834801\pi$
$251$	−13.8298	+	7.98465i	−0.872930	+	0.503986i	−0.00460934	+	0.999989i	$0.501467\pi$
$252$	−0.403444	−	4.84770i	−0.0254146	−	0.305376i
$253$	−0.165816	−	0.618833i	−0.0104247	−	0.0389057i
$254$	1.01241	−	0.849512i	0.0635242	−	0.0533031i
$255$	−14.2252	+	20.3300i	−0.890816	+	1.27312i
$256$	2.60177	−	14.7554i	0.162611	−	0.922212i
$257$	13.2591	+	18.9360i	0.827080	+	1.18119i	0.981172	+	0.193136i	$0.0618660\pi$
$257$	13.2591	+	18.9360i	0.827080	+	1.18119i	−0.154092	+	0.988057i	$0.549245\pi$
$258$	0.287962	−	1.06566i	0.0179277	−	0.0663451i
$259$	4.53571	+	5.40545i	0.281835	+	0.335878i
$260$	−15.1803	−	5.48312i	−0.941442	−	0.340048i
$261$	11.2673	+	6.56896i	0.697430	+	0.406608i
$262$	0.176807	−	0.659851i	0.0109231	−	0.0407657i
$263$	0.0491363	+	0.105373i	0.00302987	+	0.00649758i	0.907817	−	0.419367i	$-0.137748\pi$
$263$	0.0491363	+	0.105373i	0.00302987	+	0.00649758i	−0.904787	+	0.425864i	$0.859970\pi$
$264$	−0.621333	+	0.737301i	−0.0382404	+	0.0453777i
$265$	−7.16539	+	12.4813i	−0.440167	+	0.766721i
$266$	−0.101602	−	0.279149i	−0.00622962	−	0.0171158i
$267$	−1.95243	−	1.37327i	−0.119487	−	0.0840430i
$268$	−19.4193	−	13.5976i	−1.18622	−	0.830604i
$269$	16.5806			1.01094			0.505468	−	0.862845i	$-0.331320\pi$
$269$	16.5806			1.01094			0.505468	+	0.862845i	$0.331320\pi$
$270$	1.07534	+	0.759231i	0.0654431	+	0.0462054i
$271$	−31.4952			−1.91320			−0.956599	−	0.291408i	$-0.905876\pi$
$271$	−31.4952			−1.91320			−0.956599	+	0.291408i	$0.905876\pi$
$272$	−20.5886	−	14.4163i	−1.24837	−	0.874116i
$273$	0.458256	−	5.11320i	0.0277349	−	0.309465i
$274$	−0.519155	−	1.42637i	−0.0313633	−	0.0861700i
$275$	5.80039	+	2.07906i	0.349777	+	0.125372i
$276$	−0.608426	−	1.68271i	−0.0366230	−	0.101287i
$277$	−0.477906	−	1.02487i	−0.0287146	−	0.0615786i	0.891427	−	0.453164i	$-0.149705\pi$
$277$	−0.477906	−	1.02487i	−0.0287146	−	0.0615786i	−0.920142	+	0.391585i	$0.871927\pi$
$278$	0.199196	−	0.743408i	0.0119470	−	0.0445866i
$279$	−7.65792	+	20.7660i	−0.458468	+	1.24323i
$280$	0.350151	+	0.746126i	0.0209255	+	0.0445896i
$281$	−15.9976	−	19.0652i	−0.954338	−	1.13734i	−0.990434	−	0.137988i	$-0.955937\pi$
$281$	−15.9976	−	19.0652i	−0.954338	−	1.13734i	0.0360958	−	0.999348i	$-0.488508\pi$
$282$	0.449197	−	0.119343i	0.0267493	−	0.00710680i
$283$	13.1825	+	18.8266i	0.783618	+	1.11912i	0.990057	+	0.140664i	$0.0449236\pi$
$283$	13.1825	+	18.8266i	0.783618	+	1.11912i	−0.206439	+	0.978459i	$0.566187\pi$
$284$	1.65033	−	9.35947i	0.0979289	−	0.555382i
$285$	−11.6963	−	4.25273i	−0.692831	−	0.251910i
$286$	−0.388493	+	0.325984i	−0.0229721	+	0.0192758i
$287$	−1.91748	−	7.15614i	−0.113185	−	0.422413i
$288$	−2.33339	+	3.30258i	−0.137496	+	0.194606i
$289$	−20.8231	+	12.0222i	−1.22489	+	0.707188i
$290$	−1.08509	−	0.188591i	−0.0637184	−	0.0110745i
$291$	−10.1048	+	3.65363i	−0.592353	+	0.214180i
$292$	0.979689	+	11.1979i	0.0573320	+	0.655307i
$293$	−15.8638	−	7.39741i	−0.926773	−	0.432161i	−0.100185	−	0.994969i	$-0.531944\pi$
$293$	−15.8638	−	7.39741i	−0.926773	−	0.432161i	−0.826588	+	0.562807i	$0.809721\pi$
$294$	0.953850	−	0.796941i	0.0556297	−	0.0464785i
$295$	12.9717	−	27.9967i	0.755243	−	1.63003i
$296$		−	3.90632i		−	0.227050i
$297$	−5.82058	+	2.66931i	−0.337744	+	0.154889i
$298$	−1.27056	+	1.27056i	−0.0736018	+	0.0736018i
$299$	−0.327911	−	1.85968i	−0.0189636	−	0.107548i
$300$	16.6353	+	4.40787i	0.960438	+	0.254489i
$301$	4.31341	−	1.56995i	0.248621	−	0.0904906i
$302$	−0.114569	+	0.0100235i	−0.00659272	+	0.000576788i
$303$	0.154235	+	1.80696i	0.00886057	+	0.103807i
$304$	4.31174	−	11.8464i	0.247295	−	0.679439i
$305$	−0.608353	+	7.15526i	−0.0348342	+	0.409709i
$306$	1.08075	+	1.89034i	0.0617821	+	0.108064i
$307$	0.890598	−	0.238635i	0.0508291	−	0.0136196i	−0.233315	−	0.972401i	$-0.574957\pi$
$307$	0.890598	−	0.238635i	0.0508291	−	0.0136196i	0.284144	+	0.958782i	$0.408291\pi$
$308$	−1.99063	−	0.174158i	−0.113427	−	0.00992355i
$309$	8.23236	−	4.72975i	0.468323	−	0.269066i
$310$	−0.00457650	−	1.86900i	−0.000259928	−	0.106152i
$311$	8.25248	+	1.45513i	0.467955	+	0.0825131i	0.402653	−	0.915352i	$-0.368088\pi$
$311$	8.25248	+	1.45513i	0.467955	+	0.0825131i	0.0653015	+	0.997866i	$0.479199\pi$
$312$	−2.01383	+	2.00532i	−0.114011	+	0.113529i
$313$	0.138297	−	1.58074i	0.00781702	−	0.0893490i	−0.991284	−	0.131743i	$-0.957943\pi$
$313$	0.138297	−	1.58074i	0.00781702	−	0.0893490i	0.999101	+	0.0423936i	$0.0134983\pi$
$314$	−0.883965	+	1.53107i	−0.0498851	+	0.0864034i
$315$	−0.00977237	+	5.47375i	−0.000550611	+	0.308411i
$316$	−9.63446	−	16.6874i	−0.541981	−	0.938739i
$317$	−9.24972	+	4.31321i	−0.519516	+	0.242254i	−0.664646	−	0.747158i	$-0.731418\pi$
$317$	−9.24972	+	4.31321i	−0.519516	+	0.242254i	0.145130	+	0.989413i	$0.453640\pi$
$318$	0.722227	+	1.03611i	0.0405005	+	0.0581021i
$319$	3.44379	−	4.10415i	0.192815	−	0.229788i
$320$	−4.41186	+	16.6281i	−0.246631	+	0.929537i
$321$	−6.24856	+	17.0554i	−0.348761	+	0.951937i
$322$	−0.0275659	+	0.0393682i	−0.00153619	+	0.00219390i
$323$	−14.5572	−	14.5572i	−0.809985	−	0.809985i
$324$	−15.5636	+	8.81077i	−0.864643	+	0.489487i
$325$	16.4976	+	7.59482i	0.915123	+	0.421285i
$326$	0.197286	−	0.0347868i	0.0109266	−	0.00192666i
$327$	9.68586	+	20.8867i	0.535629	+	1.15504i
$328$	−1.73330	+	3.71707i	−0.0957055	+	0.205241i
$329$	1.48052	+	1.24231i	0.0816238	+	0.0684905i
$330$	0.382231	−	0.382484i	0.0210411	−	0.0210551i
$331$	7.45973	+	2.71512i	0.410024	+	0.149236i	0.538793	−	0.842438i	$-0.318880\pi$
$331$	7.45973	+	2.71512i	0.410024	+	0.149236i	−0.128769	+	0.991675i	$0.541103\pi$
$332$	−15.9349	−	4.26974i	−0.874540	−	0.234332i
$333$	11.0634	−	23.4657i	0.606272	−	1.28591i
$334$	0.479986	+	0.277120i	0.0262636	+	0.0151633i
$335$	20.4769	+	17.0969i	1.11878	+	0.934105i
$336$	−5.54465	−	0.0117379i	−0.302485	−	0.000640355i
$337$	1.96309	−	1.37457i	0.106937	−	0.0748778i	−0.518885	−	0.854844i	$-0.673653\pi$
$337$	1.96309	−	1.37457i	0.106937	−	0.0748778i	0.625822	+	0.779966i	$0.284764\pi$
$338$	−0.0180135	+	0.0126132i	−0.000979805	+	0.000686067i
$339$	11.9099	+	20.7297i	0.646855	+	1.12588i
$340$	21.8519	+	18.2450i	1.18509	+	0.989472i
$341$	7.87377	+	4.54592i	0.426389	+	0.246176i
$342$	−0.775549	+	0.769009i	−0.0419369	+	0.0415833i
$343$	10.5097	+	2.81606i	0.567469	+	0.152053i
$344$	−2.38787	−	0.869115i	−0.128746	−	0.0468595i
$345$	0.521765	+	1.94467i	0.0280909	+	0.104698i
$346$	0.204206	+	0.171349i	0.0109782	+	0.00921179i
$347$	10.1468	−	21.7598i	0.544708	−	1.16813i	−0.420656	−	0.907220i	$-0.638200\pi$
$347$	10.1468	−	21.7598i	0.544708	−	1.16813i	0.965363	−	0.260909i	$-0.0840222\pi$
$348$	8.60858	−	12.2391i	0.461468	−	0.656085i
$349$	18.2123	−	3.21131i	0.974880	−	0.171898i	0.336554	−	0.941664i	$-0.390738\pi$
$349$	18.2123	−	3.21131i	0.974880	−	0.171898i	0.638326	+	0.769767i	$0.279627\pi$
$350$	−0.160216	−	0.433571i	−0.00856391	−	0.0231754i
$351$	−17.7767	+	6.34263i	−0.948851	+	0.338545i
$352$	1.17457	+	1.17457i	0.0626048	+	0.0626048i
$353$	16.5605	−	23.6509i	0.881429	−	1.25881i	−0.0835552	−	0.996503i	$-0.526627\pi$
$353$	16.5605	−	23.6509i	0.881429	−	1.25881i	0.964984	−	0.262308i	$-0.0844836\pi$
$354$	−1.73615	−	2.07798i	−0.0922755	−	0.110444i
$355$	−2.74258	+	10.3366i	−0.145561	+	0.548610i
$356$	−1.76034	+	2.09789i	−0.0932978	+	0.111188i
$357$	−3.84398	+	8.19809i	−0.203445	+	0.433889i
$358$	1.99214	−	0.928949i	0.105288	−	0.0490965i
$359$	−14.8587	−	25.7360i	−0.784210	−	1.35829i	−0.929470	−	0.368899i	$-0.879735\pi$
$359$	−14.8587	−	25.7360i	−0.784210	−	1.35829i	0.145259	−	0.989394i	$-0.453598\pi$
$360$	1.95194	−	2.31781i	0.102876	−	0.122159i
$361$	−4.33700	+	7.51190i	−0.228263	+	0.395363i
$362$	0.0398950	−	0.456002i	0.00209684	−	0.0239670i
$363$	−4.21677	−	15.8715i	−0.221323	−	0.833039i
$364$	−5.80035	−	1.02276i	−0.304021	−	0.0536071i
$365$	−0.0309719	−	12.6486i	−0.00162114	−	0.662057i
$366$	0.545091	+	0.316249i	0.0284924	+	0.0165306i
$367$	−11.9998	−	1.04985i	−0.626385	−	0.0548016i	−0.230456	−	0.973083i	$-0.574022\pi$
$367$	−11.9998	−	1.04985i	−0.626385	−	0.0548016i	−0.395929	+	0.918281i	$0.629577\pi$
$368$	−1.97004	+	0.527871i	−0.102695	+	0.0275172i
$369$	−20.9395	+	17.4198i	−1.09007	+	0.906839i
$370$	−0.185590	+	2.18286i	−0.00964838	+	0.113481i
$371$	−1.79623	+	4.93511i	−0.0932558	+	0.256218i
$372$	22.9911	+	10.7802i	1.19203	+	0.558929i
$373$	10.0076	−	0.875548i	0.518172	−	0.0453341i	0.174929	−	0.984581i	$-0.444030\pi$
$373$	10.0076	−	0.875548i	0.518172	−	0.0453341i	0.343242	+	0.939247i	$0.388475\pi$
$374$	0.840527	−	0.305927i	0.0434626	−	0.0158191i
$375$	−18.2315	−	6.52795i	−0.941468	−	0.337102i
$376$	−0.185790	−	1.05367i	−0.00958138	−	0.0543387i
$377$	11.1663	−	11.1663i	0.575095	−	0.575095i
$378$	0.434056	+	0.205770i	0.0223254	+	0.0105836i
$379$		−	10.8604i		−	0.557863i	−0.960311	−	0.278932i	$-0.910020\pi$
$379$		−	10.8604i		−	0.557863i	0.960311	−	0.278932i	$-0.0899803\pi$
$380$	−6.00268	+	12.9555i	−0.307931	+	0.664604i
$381$	−3.46642	−	19.9053i	−0.177590	−	1.01978i
$382$	−0.0571923	−	0.0266692i	−0.00292621	−	0.00136451i
$383$	0.230605	+	2.63583i	0.0117834	+	0.134685i	0.999808	−	0.0196141i	$-0.00624376\pi$
$383$	0.230605	+	2.63583i	0.0117834	+	0.134685i	−0.988024	+	0.154299i	$0.950688\pi$
$384$	4.72498	+	3.98180i	0.241121	+	0.203196i
$385$	2.21531	+	0.385029i	0.112903	+	0.0196229i
$386$	−1.94865	+	1.12506i	−0.0991839	+	0.0572639i
$387$	−11.8827	−	11.9838i	−0.604032	−	0.609169i
$388$	3.19063	+	11.9076i	0.161980	+	0.604517i
$389$	21.4540	−	18.0020i	1.08776	−	0.912739i	0.0912181	−	0.995831i	$-0.470924\pi$
$389$	21.4540	−	18.0020i	1.08776	−	0.912739i	0.996542	+	0.0830919i	$0.0264795\pi$
$390$	1.22060	−	1.02490i	0.0618076	−	0.0518977i
$391$	−0.578353	+	3.28001i	−0.0292486	+	0.165877i
$392$	−1.64116	−	2.34382i	−0.0828912	−	0.118381i
$393$	−7.36921	−	7.40048i	−0.371727	−	0.373305i
$394$	1.21561	+	1.44871i	0.0612418	+	0.0729851i
$395$	9.21150	+	19.6285i	0.463481	+	0.987617i
$396$	2.48344	+	6.91415i	0.124798	+	0.347449i
$397$	1.22098	−	4.55674i	0.0612790	−	0.228696i	−0.928494	−	0.371347i	$-0.878896\pi$
$397$	1.22098	−	4.55674i	0.0612790	−	0.228696i	0.989773	+	0.142651i	$0.0455626\pi$
$398$	−1.15514	−	2.47720i	−0.0579018	−	0.124171i
$399$	−4.47089	−	0.798102i	−0.223825	−	0.0399551i
$400$	6.61863	−	18.4654i	0.330932	−	0.923271i
$401$	1.42496	+	3.91506i	0.0711593	+	0.195509i	0.970174	−	0.242410i	$-0.0779380\pi$
$401$	1.42496	+	3.91506i	0.0711593	+	0.195509i	−0.899015	+	0.437919i	$0.855716\pi$
$402$	2.12376	−	0.984858i	0.105924	−	0.0491202i
$403$	21.9520	+	15.3709i	1.09351	+	0.765681i
$404$	2.08065			0.103516
$405$	18.2900	−	8.39509i	0.908835	−	0.417155i
$406$	−0.401902			−0.0199461
$407$	−8.72964	−	6.11256i	−0.432712	−	0.302988i
$408$	4.54737	−	2.10877i	0.225129	−	0.104400i
$409$	−4.16426	−	11.4412i	−0.205910	−	0.565732i	0.793153	−	0.609023i	$-0.208438\pi$
$409$	−4.16426	−	11.4412i	−0.205910	−	0.565732i	−0.999063	+	0.0432906i	$0.986216\pi$
$410$	1.14517	−	1.99475i	0.0565558	−	0.0985138i
$411$	−22.8449	−	4.07805i	−1.12685	−	0.201155i
$412$	−4.60348	−	9.87218i	−0.226797	−	0.486368i
$413$	2.91426	−	10.8761i	0.143401	−	0.535180i
$414$	0.173879	+	0.0314192i	0.00854567	+	0.00154417i
$415$	17.4593	+	6.30630i	0.857044	+	0.309564i
$416$	3.14715	+	3.75063i	0.154302	+	0.183890i
$417$	−8.30237	−	8.33759i	−0.406569	−	0.408294i
$418$	0.257334	+	0.367510i	0.0125866	+	0.0179755i
$419$	−1.06706	+	6.05161i	−0.0521294	+	0.295641i	−0.999715	−	0.0238606i	$-0.992404\pi$
$419$	−1.06706	+	6.05161i	−0.0521294	+	0.295641i	0.947586	+	0.319501i	$0.103515\pi$
$420$	6.25627	+	0.545262i	0.305275	+	0.0266061i
$421$	−3.35083	+	2.81168i	−0.163309	+	0.137033i	−0.720780	−	0.693164i	$-0.756216\pi$
$421$	−3.35083	+	2.81168i	−0.163309	+	0.137033i	0.557471	+	0.830197i	$0.311772\pi$
$422$	0.819602	+	3.05880i	0.0398976	+	0.148900i
$423$	1.86812	−	6.85567i	0.0908310	−	0.333334i
$424$	2.51787	−	1.45369i	0.122278	−	0.0705975i
$425$	−22.7614	−	22.5395i	−1.10409	−	1.09333i
$426$	0.717651	+	0.604774i	0.0347703	+	0.0293014i
$427$	0.228391	+	2.61052i	0.0110526	+	0.126332i
$428$	18.8869	+	8.80709i	0.912931	+	0.425707i
$429$	1.33017	+	7.63829i	0.0642213	+	0.368780i
$430$	1.29305	+	0.599110i	0.0623566	+	0.0288917i
$431$			30.2828i			1.45867i	0.684157	+	0.729335i	$0.260170\pi$
$431$			30.2828i			1.45867i	−0.684157	+	0.729335i	$0.739830\pi$
$432$	8.49769	+	18.5297i	0.408845	+	0.891510i
$433$	10.8459	−	10.8459i	0.521222	−	0.521222i	−0.396718	−	0.917941i	$-0.629851\pi$
$433$	10.8459	−	10.8459i	0.521222	−	0.521222i	0.917941	+	0.396718i	$0.129851\pi$
$434$	−0.118433	−	0.671669i	−0.00568498	−	0.0322411i
$435$	−10.8188	+	12.9020i	−0.518719	+	0.618602i
$436$	24.8214	−	9.03424i	1.18873	−	0.432662i
$437$	−1.66420	+	0.145599i	−0.0796097	+	0.00696494i
$438$	−1.00501	−	0.471237i	−0.0480212	−	0.0225166i
$439$	−7.27898	+	19.9988i	−0.347407	+	0.954492i	0.635777	+	0.771873i	$0.280680\pi$
$439$	−7.27898	+	19.9988i	−0.347407	+	0.954492i	−0.983184	+	0.182619i	$0.941543\pi$
$440$	−0.802453	−	0.951585i	−0.0382555	−	0.0453650i
$441$	−3.22049	−	18.7276i	−0.153357	−	0.891793i
$442$	2.54663	−	0.682368i	0.121131	−	0.0324569i
$443$	−38.2232	−	3.34409i	−1.81604	−	0.158883i	−0.872169	−	0.489204i	$-0.837287\pi$
$443$	−38.2232	−	3.34409i	−1.81604	−	0.158883i	−0.943869	+	0.330321i	$0.892843\pi$
$444$	−25.7449	−	14.9366i	−1.22180	−	0.708859i
$445$	2.17370	−	2.18437i	0.103043	−	0.103549i
$446$	0.483993	+	0.0853411i	0.0229177	+	0.00404102i
$447$	7.05370	+	26.5495i	0.333629	+	1.25575i
$448$	−0.547148	+	6.25393i	−0.0258503	+	0.295470i
$449$	13.8474	−	23.9843i	0.653497	−	1.13189i	−0.328771	−	0.944410i	$-0.606634\pi$
$449$	13.8474	−	23.9843i	0.653497	−	1.13189i	0.982268	−	0.187481i	$-0.0600323\pi$
$450$	−1.20086	+	1.20246i	−0.0566092	+	0.0566844i
$451$	5.59447	+	9.68991i	0.263433	+	0.456280i
$452$	24.8589	−	11.5919i	1.16927	−	0.545237i
$453$	−0.746437	+	1.59193i	−0.0350707	+	0.0747955i
$454$	−1.85369	+	2.20915i	−0.0869981	+	0.103680i
$455$	6.40592	+	1.69966i	0.300314	+	0.0796813i
$456$	1.61200	+	1.92939i	0.0754890	+	0.0903520i
$457$	−9.23637	+	13.1909i	−0.432059	+	0.617044i	−0.974860	−	0.222817i	$-0.928475\pi$
$457$	−9.23637	+	13.1909i	−0.432059	+	0.617044i	0.542801	+	0.839861i	$0.317364\pi$
$458$	−0.413338	−	0.413338i	−0.0193140	−	0.0193140i
$459$	33.2889	+	0.211419i	1.55380	+	0.00986817i
$460$	2.27393	−	0.406699i	0.106023	−	0.0189625i
$461$	−4.66067	+	0.821802i	−0.217069	+	0.0382751i	−0.281125	−	0.959671i	$-0.590708\pi$
$461$	−4.66067	+	0.821802i	−0.217069	+	0.0382751i	0.0640559	+	0.997946i	$0.479596\pi$
$462$	0.113522	−	0.161398i	0.00528152	−	0.00750891i
$463$	−0.268361	+	0.575502i	−0.0124718	+	0.0267458i	−0.912445	−	0.409199i	$-0.865808\pi$
$463$	−0.268361	+	0.575502i	−0.0124718	+	0.0267458i	0.899973	+	0.435945i	$0.143586\pi$
$464$	−13.0655	−	10.9632i	−0.606549	−	0.508955i
$465$	−24.7502	−	14.2786i	−1.14776	−	0.662153i
$466$	−0.832350	−	0.302951i	−0.0385579	−	0.0140339i
$467$	10.3035	+	2.76083i	0.476791	+	0.127756i	0.489208	−	0.872167i	$-0.337286\pi$
$467$	10.3035	+	2.76083i	0.476791	+	0.127756i	−0.0124169	+	0.999923i	$0.503953\pi$
$468$	5.51595	+	20.9400i	0.254975	+	0.967953i
$469$	8.43036	+	4.86727i	0.389278	+	0.224750i
$470$	0.0537595	+	0.597616i	0.00247974	+	0.0275660i
$471$	13.4646	+	23.4358i	0.620417	+	1.07987i
$472$	−5.10607	+	3.57531i	−0.235026	+	0.164567i
$473$	−5.67876	+	3.97631i	−0.261110	+	0.182831i
$474$	1.90278	+	0.00402815i	0.0873977	+	0.000185019i
$475$	7.96529	−	13.9537i	0.365472	−	0.640237i
$476$	8.99644	+	5.19410i	0.412351	+	0.238071i
$477$	19.2422	−	1.60141i	0.881040	−	0.0733235i
$478$	−1.26469	−	0.338874i	−0.0578458	−	0.0154997i
$479$	6.25290	+	2.27587i	0.285702	+	0.103987i	0.480896	−	0.876777i	$-0.340311\pi$
$479$	6.25290	+	2.27587i	0.285702	+	0.103987i	−0.195194	+	0.980765i	$0.562534\pi$
$480$	−3.69263	−	3.69018i	−0.168545	−	0.168433i
$481$	−24.0626	−	20.1909i	−1.09716	−	0.920626i
$482$	−0.725524	+	1.55589i	−0.0330467	+	0.0708689i
$483$	0.309106	+	0.666560i	0.0140648	+	0.0303295i
$484$	−18.5547	+	3.27169i	−0.843396	+	0.148713i
$485$	−2.44225	−	13.6551i	−0.110897	−	0.620045i
$486$	0.0186933	−	1.76597i	0.000847947	−	0.0801062i
$487$	−9.82088	−	9.82088i	−0.445027	−	0.445027i	0.448671	−	0.893697i	$-0.351898\pi$
$487$	−9.82088	−	9.82088i	−0.445027	−	0.445027i	−0.893697	+	0.448671i	$0.851898\pi$
$488$	0.832081	−	1.18833i	0.0376665	−	0.0537934i
$489$	1.05358	−	2.87574i	0.0476446	−	0.130045i
$490$	0.805726	+	1.38770i	0.0363990	+	0.0626899i
$491$	−3.96956	+	4.73074i	−0.179144	+	0.213495i	−0.848142	−	0.529769i	$-0.822279\pi$
$491$	−3.96956	+	4.73074i	−0.179144	+	0.213495i	0.668999	+	0.743264i	$0.266723\pi$
$492$	17.8700	+	25.6364i	0.805643	+	1.15578i
$493$	−25.2428	+	11.7709i	−1.13688	+	0.530136i
$494$	0.661198	+	1.14523i	0.0297487	+	0.0515263i
$495$	−2.12536	−	7.98896i	−0.0955277	−	0.359077i
$496$	14.4719	−	25.0660i	0.649805	−	1.12550i
$497$	−0.340127	+	3.88767i	−0.0152568	+	0.174386i
$498$	1.15436	−	1.14948i	0.0517279	−	0.0515094i
$499$	−0.467311	−	0.0823996i	−0.0209197	−	0.00368871i	0.163179	−	0.986597i	$-0.447825\pi$
$499$	−0.467311	−	0.0823996i	−0.0209197	−	0.00368871i	−0.184098	+	0.982908i	$0.558936\pi$
$500$	−9.24122	+	20.2040i	−0.413280	+	0.903552i
$501$	7.34704	−	4.22111i	0.328242	−	0.188585i
$502$	−1.80234	−	0.157684i	−0.0804422	−	0.00703778i
$503$	−18.5422	+	4.96837i	−0.826756	+	0.221529i	−0.647298	−	0.762237i	$-0.724101\pi$
$503$	−18.5422	+	4.96837i	−0.826756	+	0.221529i	−0.179458	+	0.983766i	$0.557434\pi$
$504$	0.556942	−	0.955287i	0.0248081	−	0.0425519i
$505$	−2.33285	−	0.198343i	−0.103810	−	0.00882614i
$506$	0.0248249	−	0.0682057i	0.00110360	−	0.00303211i
$507$	0.0285921	+	0.334975i	0.00126982	+	0.0148768i
$508$	−23.0927	+	2.02035i	−1.02457	+	0.0896385i
$509$	−4.28872	+	1.56097i	−0.190094	+	0.0691886i	−0.435313	−	0.900279i	$-0.643362\pi$
$509$	−4.28872	+	1.56097i	−0.190094	+	0.0691886i	0.245219	+	0.969468i	$0.421140\pi$
$510$	−2.64126	+	0.962333i	−0.116957	+	0.0426128i
$511$	−0.801508	−	4.54558i	−0.0354566	−	0.201084i
$512$	6.24544	−	6.24544i	0.276012	−	0.276012i
$513$	4.21908	+	16.1555i	0.186277	+	0.713285i
$514$			2.61896i			0.115517i
$515$	4.22038	+	11.5076i	0.185972	+	0.507087i
$516$	−14.8585	+	12.4142i	−0.654108	+	0.546506i
$517$	−2.64540	−	1.23357i	−0.116344	−	0.0542523i
$518$	0.0696754	+	0.796393i	0.00306136	+	0.0349915i
$519$	3.83256	−	1.38576i	0.168231	−	0.0608279i
$520$	−2.11179	−	3.00029i	−0.0926081	−	0.131571i
$521$	12.7475	−	7.35977i	0.558478	−	0.322437i	−0.194057	−	0.980990i	$-0.562165\pi$
$521$	12.7475	−	7.35977i	0.558478	−	0.322437i	0.752534	+	0.658553i	$0.228831\pi$
$522$	0.618793	+	1.34181i	0.0270839	+	0.0587294i
$523$	3.33822	+	12.4584i	0.145970	+	0.544768i	0.999710	+	0.0240685i	$0.00766199\pi$
$523$	3.33822	+	12.4584i	0.145970	+	0.544768i	−0.853740	+	0.520699i	$0.825671\pi$
$524$	−9.17877	+	7.70190i	−0.400976	+	0.336459i
$525$	−6.96262	−	1.20775i	−0.303873	−	0.0527104i
$526$	−0.00228734	+	0.0129721i	−9.97326e−5	+	0.000565611i
$527$	−27.1105	−	38.7178i	−1.18095	−	1.68657i
$528$	8.09316	−	2.15020i	0.352210	−	0.0935756i
$529$	−14.6104	−	17.4120i	−0.635234	−	0.757043i
$530$	−1.47605	+	0.692699i	−0.0641155	+	0.0300889i
$531$	−40.7986	+	7.01591i	−1.77051	+	0.304465i
$532$	−1.34858	+	5.03295i	−0.0584682	+	0.218206i
$533$	13.9378	+	29.8897i	0.603712	+	1.29467i
$534$	−0.0919557	−	0.254320i	−0.00397931	−	0.0110055i
$535$	−20.3366	−	11.6750i	−0.879227	−	0.504756i
$536$	−1.84314	−	5.06398i	−0.0796114	−	0.218731i
$537$	2.99970	−	33.4705i	0.129446	−	1.44436i
$538$	1.53876	+	1.07745i	0.0663405	+	0.0464521i
$539$	−7.80591			−0.336224
$540$	−7.81210	−	21.7270i	−0.336179	−	0.934981i
$541$	26.5994			1.14360			0.571798	−	0.820394i	$-0.306246\pi$
$541$	26.5994			1.14360			0.571798	+	0.820394i	$0.306246\pi$
$542$	−2.92290	−	2.04664i	−0.125550	−	0.0879107i
$543$	−5.72397	−	4.02605i	−0.245639	−	0.172774i
$544$	−2.95352	−	8.11472i	−0.126631	−	0.347916i
$545$	−28.6912	+	7.76313i	−1.22900	+	0.332536i
$546$	0.374797	−	0.444750i	0.0160398	−	0.0190336i
$547$	2.39975	+	5.14628i	0.102606	+	0.220039i	0.950908	−	0.309473i	$-0.100153\pi$
$547$	2.39975	+	5.14628i	0.102606	+	0.220039i	−0.848302	+	0.529512i	$0.822375\pi$
$548$	−6.89080	+	25.7168i	−0.294360	+	1.09857i
$549$	8.36398	−	4.78184i	0.356966	−	0.204084i
$550$	0.403201	+	0.569871i	0.0171926	+	0.0242994i
$551$	−8.97986	−	10.7018i	−0.382555	−	0.455911i
$552$	0.106106	−	0.392666i	0.00451617	−	0.0167130i
$553$	4.53831	+	6.48138i	0.192989	+	0.275616i
$554$	0.0222469	−	0.126169i	0.000945181	−	0.00536039i
$555$	27.4416	+	19.2013i	1.16483	+	0.815048i
$556$	−10.3411	+	8.67719i	−0.438559	+	0.367995i
$557$	8.94116	+	33.3689i	0.378849	+	1.41388i	0.847638	+	0.530575i	$0.178024\pi$
$557$	8.94116	+	33.3689i	0.378849	+	1.41388i	−0.468789	+	0.883310i	$0.655310\pi$
$558$	−2.06012	+	1.42955i	−0.0872118	+	0.0605177i
$559$	−17.6960	+	10.2168i	−0.748463	+	0.432125i
$560$	1.22573	−	7.05240i	0.0517966	−	0.298018i
$561$	2.40311	−	13.4620i	0.101459	−	0.568366i
$562$	−0.245748	−	2.80891i	−0.0103662	−	0.118487i
$563$	−20.2108	−	9.42446i	−0.851785	−	0.397194i	−0.0528435	−	0.998603i	$-0.516828\pi$
$563$	−20.2108	−	9.42446i	−0.851785	−	0.397194i	−0.798941	+	0.601409i	$0.794606\pi$
$564$	−7.65467	−	2.80444i	−0.322320	−	0.118088i
$565$	−28.9771	+	10.6272i	−1.21908	+	0.447091i
$566$			2.60383i			0.109447i
$567$	6.05115	−	4.16115i	0.254125	−	0.174752i
$568$	1.52764	−	1.52764i	0.0640983	−	0.0640983i
$569$	7.59648	+	43.0818i	0.318461	+	1.80608i	0.552121	+	0.833764i	$0.313819\pi$
$569$	7.59648	+	43.0818i	0.318461	+	1.80608i	−0.233660	+	0.972318i	$0.575070\pi$
$570$	−0.809123	−	1.15473i	−0.0338904	−	0.0483664i
$571$	−6.30344	+	2.29426i	−0.263791	+	0.0960119i	−0.470530	−	0.882384i	$-0.655937\pi$
$571$	−6.30344	+	2.29426i	−0.263791	+	0.0960119i	0.206739	+	0.978396i	$0.433715\pi$
$572$	8.86138	−	0.775270i	0.370513	−	0.0324157i
$573$	−0.791450	+	0.551686i	−0.0330633	+	0.0230470i
$574$	0.287073	−	0.788726i	0.0119822	−	0.0329208i
$575$	−2.58833	+	0.239228i	−0.107941	+	0.00997648i
$576$	21.7221	−	7.80219i	0.905086	−	0.325091i
$577$	4.79931	−	1.28597i	0.199798	−	0.0535357i	−0.157532	−	0.987514i	$-0.550354\pi$
$577$	4.79931	−	1.28597i	0.199798	−	0.0535357i	0.357330	+	0.933978i	$0.383687\pi$
$578$	−2.71371	−	0.237419i	−0.112876	−	0.00987533i
$579$	−0.0728241	+	34.4000i	−0.00302646	+	1.42961i
$580$	13.6931	+	13.6262i	0.568573	+	0.565796i
$581$	6.67116	+	1.17631i	0.276767	+	0.0488014i
$582$	−1.17519	−	0.317560i	−0.0487133	−	0.0131633i
$583$	0.691292	−	7.90150i	0.0286304	−	0.327247i
$584$	−1.27761	+	2.21288i	−0.0528679	+	0.0915698i
$585$	−4.18838	−	24.0040i	−0.173168	−	0.992443i
$586$	−0.991533	−	1.71739i	−0.0409599	−	0.0709446i
$587$	38.3006	−	17.8599i	1.58084	−	0.737156i	0.583641	−	0.812012i	$-0.301628\pi$
$587$	38.3006	−	17.8599i	1.58084	−	0.737156i	0.997194	+	0.0748562i	$0.0238498\pi$
$588$	−21.7224	+	1.85414i	−0.895818	+	0.0764633i
$589$	15.2389	−	18.1610i	0.627906	−	0.748310i
$590$	3.02314	−	1.75529i	0.124461	−	0.0722643i
$591$	28.4837	−	4.96029i	1.17166	−	0.204039i
$592$	−19.4592	+	27.7906i	−0.799768	+	1.14219i
$593$	5.82461	+	5.82461i	0.239188	+	0.239188i	0.816514	−	0.577326i	$-0.195904\pi$
$593$	5.82461	+	5.82461i	0.239188	+	0.239188i	−0.577326	+	0.816514i	$0.695904\pi$
$594$	−0.713636	−	0.130512i	−0.0292809	−	0.00535496i
$595$	−9.59176	−	6.68128i	−0.393224	−	0.273906i
$596$	31.0378	−	5.47281i	1.27136	−	0.224175i
$597$	−41.6201	−	3.73008i	−1.70340	−	0.152662i
$598$	0.0904149	−	0.193895i	0.00369734	−	0.00792897i
$599$	4.98951	+	4.18670i	0.203866	+	0.171064i	0.739005	−	0.673700i	$-0.235296\pi$
$599$	4.98951	+	4.18670i	0.203866	+	0.171064i	−0.535139	+	0.844764i	$0.679741\pi$
$600$	2.52292	+	2.98977i	0.102998	+	0.122057i
$601$	22.5591	+	8.21084i	0.920205	+	0.334927i	0.758320	−	0.651882i	$-0.226020\pi$
$601$	22.5591	+	8.21084i	0.920205	+	0.334927i	0.161885	+	0.986810i	$0.448243\pi$
$602$	0.502325	+	0.134597i	0.0204732	+	0.00548578i
$603$	3.27020	−	35.6399i	0.133173	−	1.45137i
$604$	1.74696	+	1.00861i	0.0710827	+	0.0410396i
$605$	21.1156	−	1.89949i	0.858472	−	0.0772252i
$606$	−0.103107	+	0.177717i	−0.00418845	+	0.00721928i
$607$	−24.5836	+	17.2136i	−0.997817	+	0.698679i	−0.953828	−	0.300353i	$-0.902896\pi$
$607$	−24.5836	+	17.2136i	−0.997817	+	0.698679i	−0.0439890	+	0.999032i	$0.514007\pi$
$608$	3.54806	−	2.48438i	0.143893	−	0.100755i
$609$	−3.08343	+	5.31464i	−0.124947	+	0.215360i
$610$	−0.521425	+	0.624510i	−0.0211119	+	0.0252857i
$611$	−7.45079	−	4.30172i	−0.301427	−	0.174029i
$612$	3.48979	−	38.0331i	0.141066	−	1.53740i
$613$	−8.77093	−	2.35016i	−0.354255	−	0.0949223i	0.0773029	−	0.997008i	$-0.475369\pi$
$613$	−8.77093	−	2.35016i	−0.354255	−	0.0949223i	−0.431558	+	0.902085i	$0.642036\pi$
$614$	0.0981589	+	0.0357269i	0.00396137	+	0.00144182i
$615$	−17.5922	−	30.4473i	−0.709387	−	1.22775i
$616$	−0.347966	−	0.291978i	−0.0140199	−	0.0117641i
$617$	−5.96112	+	12.7837i	−0.239986	+	0.514651i	−0.989002	−	0.147900i	$-0.952748\pi$
$617$	−5.96112	+	12.7837i	−0.239986	+	0.514651i	0.749017	+	0.662551i	$0.230526\pi$
$618$	1.07135	+	0.0960171i	0.0430962	+	0.00386237i
$619$	3.14514	−	0.554573i	0.126414	−	0.0222902i	−0.110083	−	0.993922i	$-0.535112\pi$
$619$	3.14514	−	0.554573i	0.126414	−	0.0222902i	0.236497	+	0.971632i	$0.424001\pi$
$620$	−18.7373	+	26.8995i	−0.752507	+	1.08031i
$621$	1.74949	−	2.05827i	0.0702046	−	0.0825956i
$622$	0.671311	+	0.671311i	0.0269171	+	0.0269171i
$623$	0.645009	−	0.921168i	0.0258417	−	0.0369058i
$624$	24.3163	−	4.23457i	0.973433	−	0.169518i
$625$	12.2873	−	21.7720i	0.491494	−	0.870881i
$626$	0.115556	−	0.137714i	0.00461853	−	0.00550415i
$627$	6.83414	−	0.583334i	0.272929	−	0.0232961i
$628$	28.1041	−	13.1051i	1.12147	−	0.522952i
$629$	27.7010	+	47.9795i	1.10451	+	1.91307i
$630$	−0.356605	+	0.507355i	−0.0142075	+	0.0202135i
$631$	4.87996	−	8.45234i	0.194268	−	0.336482i	−0.752392	−	0.658715i	$-0.771100\pi$
$631$	4.87996	−	8.45234i	0.194268	−	0.336482i	0.946660	+	0.322233i	$0.104434\pi$
$632$	0.381759	−	4.36353i	0.0151856	−	0.173572i
$633$	46.7367	+	12.6292i	1.85762	+	0.501965i
$634$	−1.13870	−	0.200784i	−0.0452236	−	0.00797414i
$635$	26.0844	−	0.0638713i	1.03513	−	0.00253465i
$636$	0.0468967	−	22.1526i	0.00185957	−	0.878410i
$637$	−22.9205	−	2.00529i	−0.908144	−	0.0794523i
$638$	0.586298	−	0.157098i	0.0232118	−	0.00621957i
$639$	13.5032	−	4.85013i	0.534180	−	0.191868i
$640$	−6.09822	+	5.14251i	−0.241053	+	0.203276i
$641$	−3.49998	+	9.61611i	−0.138241	+	0.379813i	−0.989423	−	0.145056i	$-0.953664\pi$
$641$	−3.49998	+	9.61611i	−0.138241	+	0.379813i	0.851183	+	0.524870i	$0.175886\pi$
$642$	−1.68820	+	1.17677i	−0.0666278	+	0.0464434i
$643$	−13.9040	+	1.21644i	−0.548320	+	0.0479718i	−0.357950	−	0.933741i	$-0.616524\pi$
$643$	−13.9040	+	1.21644i	−0.548320	+	0.0479718i	−0.190370	+	0.981712i	$0.560969\pi$
$644$	0.792127	−	0.288311i	0.0312142	−	0.0113610i
$645$	17.8429	−	12.5025i	0.702563	−	0.492287i
$646$	−0.405013	−	2.29694i	−0.0159350	−	0.0903720i
$647$	−26.7302	+	26.7302i	−1.05087	+	1.05087i	−0.0522394	+	0.998635i	$0.516636\pi$
$647$	−26.7302	+	26.7302i	−1.05087	+	1.05087i	−0.998635	+	0.0522394i	$0.983364\pi$
$648$	−4.04687	−	0.388612i	−0.158976	−	0.0152661i
$649$			17.0053i			0.667518i
$650$	1.03753	+	1.77689i	0.0406951	+	0.0696955i
$651$	−9.79059	−	3.58697i	−0.383723	−	0.140585i
$652$	−3.18455	−	1.48498i	−0.124717	−	0.0581563i
$653$	0.358345	+	4.09590i	0.0140231	+	0.160285i	0.999977	−	0.00673072i	$-0.00214247\pi$
$653$	0.358345	+	4.09590i	0.0140231	+	0.160285i	−0.985954	+	0.167016i	$0.946587\pi$
$654$	−0.458379	+	2.56780i	−0.0179240	+	0.100409i
$655$	11.0255	−	7.76046i	0.430803	−	0.303226i
$656$	30.8476	−	17.8099i	1.20440	−	0.695359i
$657$	−13.9420	+	9.67460i	−0.543930	+	0.377442i
$658$	0.0566713	+	0.211500i	0.00220928	+	0.00824513i
$659$	23.3538	−	19.5962i	0.909736	−	0.763359i	−0.0623330	−	0.998055i	$-0.519854\pi$
$659$	23.3538	−	19.5962i	0.909736	−	0.763359i	0.972069	+	0.234697i	$0.0754096\pi$
$660$	−9.33983	+	1.65006i	−0.363552	+	0.0642284i
$661$	−2.49857	+	14.1701i	−0.0971833	+	0.551154i	0.896873	+	0.442288i	$0.145833\pi$
$661$	−2.49857	+	14.1701i	−0.0971833	+	0.551154i	−0.994056	+	0.108866i	$0.965278\pi$
$662$	0.515863	+	0.736728i	0.0200496	+	0.0286338i
$663$	10.5145	−	38.9111i	0.408351	−	1.51118i
$664$	−2.41051	−	2.87273i	−0.0935458	−	0.111484i
$665$	1.99182	−	5.51444i	0.0772393	−	0.213841i
$666$	2.55160	−	1.45880i	0.0988724	−	0.0565272i
$667$	−0.584963	+	2.18311i	−0.0226498	+	0.0845304i
$668$	−4.10841	−	8.81052i	−0.158959	−	0.340889i
$669$	4.84177	−	5.74545i	0.187193	−	0.222132i
$670$	0.789355	+	2.91732i	0.0304955	+	0.112706i
$671$	−1.35360	−	3.71898i	−0.0522550	−	0.143570i
$672$	−1.55819	−	1.09598i	−0.0601084	−	0.0422783i
$673$	3.89377	+	2.72645i	0.150094	+	0.105097i	0.646211	−	0.763159i	$-0.276353\pi$
$673$	3.89377	+	2.72645i	0.150094	+	0.105097i	−0.496117	+	0.868255i	$0.665241\pi$
$674$	0.271508			0.0104581
$675$	6.68783	+	25.1052i	0.257415	+	0.966301i
$676$	0.385711			0.0148350
$677$	−24.2852	−	17.0047i	−0.933356	−	0.653543i	0.00471373	−	0.999989i	$-0.498500\pi$
$677$	−24.2852	−	17.0047i	−0.933356	−	0.653543i	−0.938070	+	0.346446i	$0.887388\pi$
$678$	−0.241778	+	2.69775i	−0.00928545	+	0.103606i
$679$	−1.73132	−	4.75677i	−0.0664420	−	0.182548i
$680$	1.69016	+	6.24654i	0.0648146	+	0.239544i
$681$	14.9914	+	41.4615i	0.574472	+	1.58881i
$682$	0.435318	+	0.933541i	0.0166692	+	0.0357472i
$683$	2.52954	−	9.44037i	0.0967901	−	0.361226i	−0.900495	−	0.434867i	$-0.856795\pi$
$683$	2.52954	−	9.44037i	0.0967901	−	0.361226i	0.997285	+	0.0736414i	$0.0234620\pi$
$684$	18.8796	−	3.24662i	0.721880	−	0.124138i
$685$	10.1776	−	28.1771i	0.388864	−	1.07659i
$686$	0.792353	+	0.944289i	0.0302522	+	0.0360531i
$687$	−8.63703	+	2.29470i	−0.329523	+	0.0875483i
$688$	12.6585	+	18.0782i	0.482601	+	0.689225i
$689$	4.05968	−	23.0236i	0.154662	−	0.877130i
$690$	−0.0779477	+	0.214381i	−0.00296742	+	0.00816133i
$691$	5.93833	−	4.98285i	0.225905	−	0.189556i	−0.522809	−	0.852450i	$-0.675116\pi$
$691$	5.93833	−	4.98285i	0.225905	−	0.189556i	0.748714	+	0.662893i	$0.230672\pi$
$692$	−1.21015	−	4.51634i	−0.0460030	−	0.171685i
$693$	−1.26333	−	2.73944i	−0.0479899	−	0.104063i
$694$	2.35568	−	1.36005i	0.0894204	−	0.0516269i
$695$	12.4217	−	8.74317i	0.471181	−	0.331647i
$696$	3.19879	−	1.15660i	0.121250	−	0.0438408i
$697$	−5.06966	−	57.9464i	−0.192027	−	2.19488i
$698$	1.89886	+	0.885454i	0.0718730	+	0.0335149i
$699$	−10.3920	+	8.68250i	−0.393061	+	0.328402i
$700$	−2.05998	+	7.84135i	−0.0778599	+	0.296375i
$701$		−	11.8234i		−	0.446564i	−0.974754	−	0.223282i	$-0.928323\pi$
$701$		−	11.8234i		−	0.446564i	0.974754	−	0.223282i	$-0.0716771\pi$
$702$	−2.06192	−	0.566550i	−0.0778223	−	0.0213831i
$703$	−19.6494	+	19.6494i	−0.741092	+	0.741092i
$704$	−1.64639	−	9.33714i	−0.0620507	−	0.351907i
$705$	8.31515	+	3.87406i	0.313167	+	0.145906i
$706$	3.07379	−	1.11877i	0.115684	−	0.0421055i
$707$	−0.851116	+	0.0744630i	−0.0320095	+	0.00280047i
$708$	4.03928	+	47.3228i	0.151805	+	1.77850i
$709$	−9.00610	+	24.7441i	−0.338231	+	0.929283i	0.647665	+	0.761925i	$0.275746\pi$
$709$	−9.00610	+	24.7441i	−0.338231	+	0.929283i	−0.985896	+	0.167357i	$0.946477\pi$
$710$	−0.926224	+	0.781067i	−0.0347606	+	0.0293129i
$711$	14.6516	−	25.1309i	0.549477	−	0.942484i
$712$	−0.601324	+	0.161124i	−0.0225356	+	0.00603839i
$713$	−3.82084	−	0.334281i	−0.143092	−	0.0125189i
$714$	−0.889473	+	0.511030i	−0.0332877	+	0.0191248i
$715$	−10.0094	+	0.0245094i	−0.374329	+	0.000916599i
$716$	−37.9685	−	6.69487i	−1.41895	−	0.250199i
$717$	−14.1840	+	14.1241i	−0.529712	+	0.527474i
$718$	0.293435	−	3.35397i	0.0109509	−	0.125169i
$719$	−15.9538	+	27.6328i	−0.594977	+	1.03053i	0.398573	+	0.917136i	$0.369505\pi$
$719$	−15.9538	+	27.6328i	−0.594977	+	1.03053i	−0.993550	+	0.113393i	$0.963828\pi$
$720$	−25.4327	+	6.76602i	−0.947820	+	0.252155i
$721$	2.23642	+	3.87359i	0.0832885	+	0.144260i
$722$	−0.890637	+	0.415311i	−0.0331461	+	0.0154563i
$723$	15.0084	+	21.5310i	0.558167	+	0.800748i
$724$	−5.16082	+	6.15042i	−0.191800	+	0.228579i
$725$	−14.0539	−	16.5831i	−0.521947	−	0.615881i
$726$	0.640036	−	1.74697i	0.0237540	−	0.0648361i
$727$	12.2503	−	17.4952i	0.454338	−	0.648863i	−0.524997	−	0.851104i	$-0.675934\pi$
$727$	12.2503	−	17.4952i	0.454338	−	0.648863i	0.979336	+	0.202241i	$0.0648225\pi$
$728$	−0.946725	−	0.946725i	−0.0350880	−	0.0350880i
$729$	−23.2093	−	13.7959i	−0.859605	−	0.510960i
$730$	0.819064	−	1.17586i	0.0303149	−	0.0435206i
$731$	35.4923	−	6.25825i	1.31273	−	0.231470i
$732$	−4.65018	−	10.0277i	−0.171876	−	0.370635i
$733$	15.6653	−	33.5943i	0.578611	−	1.24083i	−0.371358	−	0.928490i	$-0.621108\pi$
$733$	15.6653	−	33.5943i	0.578611	−	1.24083i	0.949969	−	0.312345i	$-0.101114\pi$
$734$	−1.04542	−	0.877209i	−0.0385870	−	0.0323784i
$735$	24.5322	−	0.00813637i	0.904882	−	0.000300115i
$736$	−0.658480	−	0.239667i	−0.0242719	−	0.00883425i
$737$	−14.2008	−	3.80510i	−0.523094	−	0.140163i
$738$	−3.07527	+	0.255936i	−0.113202	+	0.00942114i
$739$	−0.0105302	−	0.00607959i	−0.000387358	−	0.000223641i	0.499806	−	0.866137i	$-0.333405\pi$
$739$	−0.0105302	−	0.00607959i	−0.000387358	−	0.000223641i	−0.500194	+	0.865914i	$0.666738\pi$
$740$	24.6272	−	29.4959i	0.905312	−	1.08429i
$741$	20.2170	+	0.0427989i	0.742688	+	0.00157226i
$742$	−0.487396	+	0.341278i	−0.0178929	+	0.0125287i
$743$	−16.1496	+	11.3081i	−0.592471	+	0.414852i	−0.830992	−	0.556285i	$-0.812226\pi$
$743$	−16.1496	+	11.3081i	−0.592471	+	0.414852i	0.238521	+	0.971137i	$0.423337\pi$
$744$	2.87556	+	5.00506i	0.105423	+	0.183495i
$745$	−35.3216	+	3.17741i	−1.29408	+	0.116411i
$746$	0.985644	+	0.569062i	0.0360870	+	0.0208348i
$747$	−6.34406	−	24.0838i	−0.232117	−	0.881179i
$748$	−15.1544	−	4.06060i	−0.554099	−	0.148470i
$749$	−8.04109	−	2.92672i	−0.293815	−	0.106940i
$750$	−1.26776	−	1.79055i	−0.0462921	−	0.0653817i
$751$	−25.5632	−	21.4501i	−0.932814	−	0.782724i	0.0435062	−	0.999053i	$-0.486147\pi$
$751$	−25.5632	−	21.4501i	−0.932814	−	0.782724i	−0.976321	+	0.216329i	$0.930592\pi$
$752$	−3.92704	+	8.42156i	−0.143204	+	0.307103i
$753$	−15.9128	+	22.6238i	−0.579896	+	0.824457i
$754$	1.76191	−	0.310672i	0.0641648	−	0.0113140i
$755$	−1.86256	−	1.29739i	−0.0677855	−	0.0472170i
$756$	−4.16632	−	7.32329i	−0.151527	−	0.266346i
$757$	28.4224	+	28.4224i	1.03303	+	1.03303i	0.999436	+	0.0335950i	$0.0106956\pi$
$757$	28.4224	+	28.4224i	1.03303	+	1.03303i	0.0335950	+	0.999436i	$0.489304\pi$
$758$	0.705739	−	1.00790i	0.0256336	−	0.0366086i
$759$	−0.711475	−	0.851557i	−0.0258249	−	0.0309096i
$760$	−2.80696	+	1.62978i	−0.101819	+	0.0591182i
$761$	−14.3996	+	17.1608i	−0.521985	+	0.622078i	−0.961049	−	0.276378i	$-0.910866\pi$
$761$	−14.3996	+	17.1608i	−0.521985	+	0.622078i	0.439064	+	0.898456i	$0.355310\pi$
$762$	0.971801	−	2.07257i	0.0352046	−	0.0750812i
$763$	−9.83017	+	4.58388i	−0.355876	+	0.165948i
$764$	0.553426	+	0.958563i	0.0200223	+	0.0346796i
$765$	−7.53838	+	42.3104i	−0.272551	+	1.52974i
$766$	−0.149882	+	0.259603i	−0.00541545	+	0.00937983i
$767$	−4.36856	+	49.9328i	−0.157739	+	1.80297i
$768$	−6.66362	−	25.0812i	−0.240453	−	0.905041i
$769$	3.68867	+	0.650412i	0.133017	+	0.0234545i	0.239760	−	0.970832i	$-0.422931\pi$
$769$	3.68867	+	0.650412i	0.133017	+	0.0234545i	−0.106743	+	0.994287i	$0.534042\pi$
$770$	0.180571	+	0.179689i	0.00650734	+	0.00647555i
$771$	34.6324	+	20.0929i	1.24725	+	0.723627i
$772$	39.3167	+	3.43976i	1.41504	+	0.123800i
$773$	10.7936	−	2.89214i	0.388220	−	0.104023i	−0.0594292	−	0.998233i	$-0.518928\pi$
$773$	10.7936	−	2.89214i	0.388220	−	0.104023i	0.447649	+	0.894209i	$0.352261\pi$
$774$	−0.324036	−	1.88432i	−0.0116472	−	0.0677304i
$775$	23.5727	−	28.3739i	0.846756	−	1.01922i
$776$	−0.958447	+	2.63331i	−0.0344063	+	0.0945304i
$777$	11.0658	+	5.18863i	0.396984	+	0.186141i
$778$	3.16085	−	0.276538i	0.113322	−	0.00991439i
$779$	27.4162	−	9.97869i	0.982288	−	0.357524i
$780$	−27.8484	+	2.44573i	−0.997134	+	0.0875712i
$781$	−1.02346	−	5.80431i	−0.0366222	−	0.207695i
$782$	−0.266817	+	0.266817i	−0.00954136	+	0.00954136i
$783$	22.4912	+	2.11174i	0.803768	+	0.0754673i
$784$			24.8499i			0.887498i
$785$	−32.7598	+	12.0145i	−1.16925	+	0.428817i
$786$	−0.202995	−	1.16567i	−0.00724061	−	0.0415781i
$787$	28.7051	+	13.3854i	1.02323	+	0.477138i	0.860456	−	0.509526i	$-0.170179\pi$
$787$	28.7051	+	13.3854i	1.02323	+	0.477138i	0.162771	+	0.986664i	$0.447957\pi$
$788$	−2.89103	−	33.0446i	−0.102989	−	1.17717i
$789$	0.153991	+	0.129770i	0.00548223	+	0.00461995i
$790$	−0.420640	+	2.42020i	−0.0149657	+	0.0861070i
$791$	−9.75400	+	5.63147i	−0.346812	+	0.200232i
$792$	−0.439062	+	1.61128i	−0.0156014	+	0.0572544i
$793$	−3.01919	−	11.2678i	−0.107215	−	0.400130i
$794$	0.409421	−	0.343545i	0.0145298	−	0.0121920i
$795$	−2.16433	+	24.8333i	−0.0767610	+	0.880747i
$796$	−8.32498	+	47.2133i	−0.295071	+	1.67343i
$797$	4.41609	+	6.30683i	0.156426	+	0.223400i	0.889714	−	0.456519i	$-0.150904\pi$
$797$	4.41609	+	6.30683i	0.156426	+	0.223400i	−0.733288	+	0.679919i	$0.762015\pi$
$798$	−0.363057	−	0.364598i	−0.0128521	−	0.0129066i
$799$	9.75385	+	11.6242i	0.345067	+	0.411234i
$800$	5.50172	−	3.89264i	0.194515	−	0.137625i
$801$	−4.06855	−	0.735170i	−0.143755	−	0.0259759i
$802$	−0.122167	+	0.455934i	−0.00431387	+	0.0160996i
$803$	2.94605	+	6.31782i	0.103964	+	0.222951i
$804$	−40.4221	−	7.21577i	−1.42558	−	0.254481i
$805$	−0.915625	+	0.247746i	−0.0322715	+	0.00873189i
$806$	1.03840	+	2.85299i	0.0365762	+	0.100492i
$807$	26.0534	−	12.0818i	0.917122	−	0.425299i
$808$	0.387436	+	0.271285i	0.0136299	+	0.00954378i
$809$	−39.1614			−1.37684			−0.688421	−	0.725311i	$-0.741696\pi$
$809$	−39.1614			−1.37684			−0.688421	+	0.725311i	$0.741696\pi$
$810$	2.24293	+	0.409424i	0.0788085	+	0.0143857i
$811$	17.1440			0.602008			0.301004	−	0.953623i	$-0.402678\pi$
$811$	17.1440			0.602008			0.301004	+	0.953623i	$0.402678\pi$
$812$	5.77448	+	4.04334i	0.202645	+	0.141893i
$813$	−49.4890	+	22.9497i	−1.73565	+	0.804880i
$814$	−0.412942	−	1.13455i	−0.0144736	−	0.0397659i
$815$	3.42899	+	1.96855i	0.120112	+	0.0689553i
$816$	−42.8559	−	7.65024i	−1.50026	−	0.267812i
$817$	7.63959	+	16.3832i	0.267276	+	0.573174i
$818$	0.357017	−	1.33240i	0.0124828	−	0.0465864i
$819$	−3.00578	−	8.36837i	−0.105030	−	0.292415i
$820$	−36.5218	+	17.1394i	−1.27540	+	0.598534i
$821$	−26.7100	−	31.8317i	−0.932184	−	1.11093i	−0.993615	−	0.112822i	$-0.964011\pi$
$821$	−26.7100	−	31.8317i	−0.932184	−	1.11093i	0.0614313	−	0.998111i	$-0.480433\pi$
$822$	−1.85511	−	1.86298i	−0.0647044	−	0.0649789i
$823$	−6.39643	−	9.13505i	−0.222966	−	0.318428i	0.692048	−	0.721852i	$-0.256709\pi$
$823$	−6.39643	−	9.13505i	−0.222966	−	0.318428i	−0.915013	+	0.403424i	$0.867820\pi$
$824$	0.429976	−	2.43851i	0.0149789	−	0.0849496i
$825$	10.6292	−	0.959721i	0.370061	−	0.0334132i
$826$	0.977217	−	0.819982i	0.0340017	−	0.0285308i
$827$	−6.87074	−	25.6420i	−0.238919	−	0.891658i	−0.976343	−	0.216228i	$-0.930625\pi$
$827$	−6.87074	−	25.6420i	−0.238919	−	0.891658i	0.737424	−	0.675430i	$-0.236042\pi$
$828$	−2.18218	−	2.20073i	−0.0758358	−	0.0764807i
$829$	36.2779	−	20.9451i	1.25998	−	0.727453i	0.286914	−	0.957956i	$-0.407371\pi$
$829$	36.2779	−	20.9451i	1.25998	−	0.727453i	0.973071	+	0.230504i	$0.0740374\pi$
$830$	1.21051	+	1.71981i	0.0420173	+	0.0596954i
$831$	−1.49774	−	1.26216i	−0.0519559	−	0.0437840i
$832$	−2.43565	−	27.8396i	−0.0844410	−	0.965165i
$833$	36.7784	+	17.1501i	1.27430	+	0.594214i
$834$	−0.228701	−	1.31328i	−0.00791926	−	0.0454751i
$835$	3.76651	+	10.2701i	0.130345	+	0.355411i
$836$		−	7.86925i		−	0.272164i
$837$	3.09855	+	38.2100i	0.107102	+	1.32073i
$838$	−0.492278	+	0.492278i	−0.0170055	+	0.0170055i
$839$	−1.94726	−	11.0435i	−0.0672268	−	0.381262i	−0.999795	−	0.0202674i	$-0.993548\pi$
$839$	−1.94726	−	11.0435i	−0.0672268	−	0.381262i	0.932568	−	0.360995i	$-0.117563\pi$
$840$	1.09388	+	0.917256i	0.0377424	+	0.0316483i
$841$	9.49050	−	3.45426i	0.327259	−	0.119112i
$842$	−0.493683	+	0.0431917i	−0.0170134	+	0.00148848i
$843$	−39.0296	−	18.3005i	−1.34425	−	0.630303i
$844$	18.9971	−	52.1940i	0.653906	−	1.79659i
$845$	−0.432463	−	0.0367688i	−0.0148772	−	0.00126488i
$846$	0.618869	−	0.514844i	0.0212772	−	0.0177007i
$847$	7.47294	−	2.00237i	0.256773	−	0.0688022i
$848$	−25.1543	−	2.20071i	−0.863801	−	0.0755728i
$849$	34.4323	+	19.9768i	1.18171	+	0.685602i
$850$	−0.647687	−	3.57087i	−0.0222155	−	0.122480i
$851$	4.42737	+	0.780665i	0.151768	+	0.0267609i
$852$	−4.22679	−	15.9092i	−0.144807	−	0.545042i
$853$	−3.28205	+	37.5140i	−0.112375	+	1.28446i	0.705355	+	0.708854i	$0.250787\pi$
$853$	−3.28205	+	37.5140i	−0.112375	+	1.28446i	−0.817731	+	0.575601i	$0.804768\pi$
$854$	−0.148443	+	0.257111i	−0.00507961	+	0.00879814i
$855$	−21.4775	+	1.84041i	−0.734515	+	0.0629406i
$856$	2.36859	+	4.10252i	0.0809568	+	0.140221i
$857$	27.5476	−	12.8457i	0.941009	−	0.438800i	0.109299	−	0.994009i	$-0.465140\pi$
$857$	27.5476	−	12.8457i	0.941009	−	0.438800i	0.831711	+	0.555209i	$0.187362\pi$
$858$	−0.372910	+	0.795308i	−0.0127309	+	0.0271514i
$859$	−19.6543	+	23.4231i	−0.670598	+	0.799187i	−0.988865	−	0.148814i	$-0.952455\pi$
$859$	−19.6543	+	23.4231i	−0.670598	+	0.799187i	0.318268	+	0.948001i	$0.396899\pi$
$860$	−12.5511	−	21.6167i	−0.427989	−	0.737124i
$861$	−8.22744	−	9.84735i	−0.280390	−	0.335597i
$862$	−1.96785	+	2.81039i	−0.0670253	+	0.0957221i
$863$	17.7157	+	17.7157i	0.603051	+	0.603051i	0.941121	−	0.338070i	$-0.109774\pi$
$863$	17.7157	+	17.7157i	0.603051	+	0.603051i	−0.338070	+	0.941121i	$0.609774\pi$
$864$	−1.26000	+	6.88967i	−0.0428662	+	0.234391i
$865$	0.926301	+	5.17912i	0.0314952	+	0.176096i
$866$	1.71135	−	0.301757i	0.0581541	−	0.0102541i
$867$	−23.9594	+	34.0639i	−0.813704	+	1.15687i
$868$	−5.05569	+	10.8420i	−0.171601	+	0.368000i
$869$	−9.15400	−	7.68112i	−0.310528	−	0.260564i
$870$	−1.84243	+	0.494334i	−0.0624644	+	0.0167595i
$871$	−40.7204	−	14.8210i	−1.37976	−	0.502191i
$872$	5.79989	+	1.55408i	0.196409	+	0.0526277i
$873$	−13.2155	+	13.1041i	−0.447277	+	0.443506i
$874$	−0.163907	−	0.0946320i	−0.00554425	−	0.00320097i
$875$	3.05717	−	8.59544i	0.103351	−	0.290579i
$876$	9.69899	+	16.8816i	0.327698	+	0.570376i
$877$	25.7226	−	18.0112i	0.868591	−	0.608194i	−0.0520323	−	0.998645i	$-0.516570\pi$
$877$	25.7226	−	18.0112i	0.868591	−	0.608194i	0.920624	+	0.390451i	$0.127681\pi$
$878$	−1.97510	+	1.38298i	−0.0666563	+	0.0466733i
$879$	−30.3174	−	0.0641812i	−1.02258	−	0.00216478i
$880$	0.968582	+	10.7672i	0.0326509	+	0.362963i
$881$	−20.4197	−	11.7893i	−0.687957	−	0.397192i	0.114889	−	0.993378i	$-0.463349\pi$
$881$	−20.4197	−	11.7893i	−0.687957	−	0.397192i	−0.802846	+	0.596186i	$0.796682\pi$
$882$	0.918094	−	1.94729i	0.0309138	−	0.0655687i
$883$	15.8726	+	4.25306i	0.534156	+	0.143127i	0.515807	−	0.856705i	$-0.327492\pi$
$883$	15.8726	+	4.25306i	0.534156	+	0.143127i	0.0183494	+	0.999832i	$0.494159\pi$
$884$	−43.4547	−	15.8162i	−1.46154	−	0.531957i
$885$	−0.0177253	−	53.4439i	−0.000595828	−	1.79650i
$886$	−3.32998	−	2.79419i	−0.111873	−	0.0938726i
$887$	−16.4901	+	35.3631i	−0.553683	+	1.18738i	0.407941	+	0.913008i	$0.366247\pi$
$887$	−16.4901	+	35.3631i	−0.553683	+	1.18738i	−0.961624	+	0.274369i	$0.911531\pi$
$888$	−2.84643	−	6.13807i	−0.0955198	−	0.205980i
$889$	9.37405	−	1.65290i	0.314395	−	0.0554364i
$890$	0.343675	−	0.0614673i	0.0115200	−	0.00206039i
$891$	−7.20093	+	8.43563i	−0.241240	+	0.282604i
$892$	−6.09538	−	6.09538i	−0.204089	−	0.204089i
$893$	−4.36555	+	6.23466i	−0.146088	+	0.208635i
$894$	−1.07064	+	2.92228i	−0.0358074	+	0.0977358i
$895$	41.9325	+	11.1258i	1.40165	+	0.371894i
$896$	−1.87113	+	2.22993i	−0.0625102	+	0.0744968i
$897$	−1.87035	−	2.68320i	−0.0624490	−	0.0895895i
$898$	2.84366	−	1.32602i	0.0948943	−	0.0442499i
$899$	−16.0371	−	27.7770i	−0.534866	−	0.926415i
$900$	29.3512	−	5.19548i	0.978373	−	0.173183i
$901$	−20.6172	+	35.7100i	−0.686858	+	1.18967i
$902$	−0.110482	+	1.26281i	−0.00367864	+	0.0420470i
$903$	5.63376	−	5.60995i	0.187480	−	0.186688i
$904$	6.14036	+	1.08271i	0.204225	+	0.0360105i
$905$	6.37267	−	6.40395i	0.211835	−	0.212875i
$906$	−0.172721	+	0.0992334i	−0.00573826	+	0.00329681i
$907$	7.11684	+	0.622643i	0.236311	+	0.0206745i	0.204696	−	0.978826i	$-0.434379\pi$
$907$	7.11684	+	0.622643i	0.236311	+	0.0206745i	0.0316149	+	0.999500i	$0.489935\pi$
$908$	48.8587	−	13.0917i	1.62143	−	0.434462i
$909$	1.55904	+	2.72693i	0.0517099	+	0.0904465i
$910$	0.484051	+	0.574010i	0.0160461	+	0.0190282i
$911$	−8.33512	+	22.9005i	−0.276155	+	0.758729i	0.721635	+	0.692274i	$0.243391\pi$
$911$	−8.33512	+	22.9005i	−0.276155	+	0.758729i	−0.997789	+	0.0664549i	$0.978831\pi$
$912$	−1.85703	−	21.7563i	−0.0614924	−	0.720424i
$913$	−10.1917	+	0.891662i	−0.337297	+	0.0295097i
$914$	−1.71436	+	0.623975i	−0.0567059	+	0.0206393i
$915$	4.25792	+	11.6865i	0.140762	+	0.386343i
$916$	1.78041	+	10.0972i	0.0588263	+	0.333620i
$917$	3.47905	−	3.47905i	0.114888	−	0.114888i
$918$	3.07563	+	2.18282i	0.101511	+	0.0720439i
$919$		−	22.6610i		−	0.747517i	−0.927526	−	0.373758i	$-0.878069\pi$
$919$		−	22.6610i		−	0.747517i	0.927526	−	0.373758i	$-0.121931\pi$
$920$	0.476454	+	0.220755i	0.0157082	+	0.00727809i
$921$	1.22553	−	1.02392i	0.0403824	−	0.0337395i
$922$	−0.485935	−	0.226595i	−0.0160034	−	0.00746251i
$923$	−1.51409	−	17.3061i	−0.0498369	−	0.569638i
$924$	−3.25481	+	1.17686i	−0.107076	+	0.0387158i
$925$	−30.4240	+	30.7234i	−1.00033	+	1.01018i
$926$	−0.0623027	+	0.0359705i	−0.00204740	+	0.00118206i
$927$	9.48922	−	13.4306i	0.311667	−	0.441120i
$928$	−1.51668	−	5.66031i	−0.0497873	−	0.185809i
$929$	−22.2920	+	18.7052i	−0.731377	+	0.613698i	−0.930507	−	0.366275i	$-0.880633\pi$
$929$	−22.2920	+	18.7052i	−0.731377	+	0.613698i	0.199130	+	0.979973i	$0.436189\pi$
$930$	−1.36907	−	2.93345i	−0.0448937	−	0.0961916i
$931$	−3.53449	+	20.0451i	−0.115838	+	0.656951i
$932$	8.91127	+	12.7266i	0.291898	+	0.416874i
$933$	14.0276	−	3.72687i	0.459242	−	0.122012i
$934$	0.776812	+	0.925769i	0.0254181	+	0.0302921i
$935$	16.6042	+	5.99741i	0.543014	+	0.196136i
$936$	−1.70315	+	4.61842i	−0.0556690	+	0.150958i
$937$	8.40546	−	31.3696i	0.274594	−	1.02480i	−0.681518	−	0.731801i	$-0.738680\pi$
$937$	8.40546	−	31.3696i	0.274594	−	1.02480i	0.956113	−	0.292999i	$-0.0946533\pi$
$938$	0.466089	+	0.999532i	0.0152184	+	0.0326359i
$939$	−0.934535	−	2.58462i	−0.0304974	−	0.0843460i
$940$	5.23991	−	9.12733i	0.170907	−	0.297701i
$941$	7.58961	+	20.8523i	0.247414	+	0.679765i	0.999779	+	0.0210183i	$0.00669081\pi$
$941$	7.58961	+	20.8523i	0.247414	+	0.679765i	−0.752365	+	0.658747i	$0.771087\pi$
$942$	−0.273341	+	3.04992i	−0.00890592	+	0.0993718i
$943$	−3.86648	−	2.70734i	−0.125910	−	0.0881632i
$944$	54.1361			1.76198
$945$	3.97321	+	8.60811i	0.129248	+	0.280022i
$946$	−0.785407			−0.0255358
$947$	−16.3365	−	11.4390i	−0.530866	−	0.371716i	0.277197	−	0.960813i	$-0.410595\pi$
$947$	−16.3365	−	11.4390i	−0.530866	−	0.371716i	−0.808062	+	0.589097i	$0.799484\pi$
$948$	−27.2984	−	19.2008i	−0.886611	−	0.623613i
$949$	7.02749	+	19.3079i	0.228122	+	0.626760i
$950$	1.64596	−	0.777360i	0.0534020	−	0.0252209i
$951$	−11.3913	+	13.5174i	−0.369389	+	0.438333i
$952$	0.997985	+	2.14019i	0.0323449	+	0.0693638i
$953$	6.93017	−	25.8637i	0.224490	−	0.837809i	−0.758118	−	0.652117i	$-0.773881\pi$
$953$	6.93017	−	25.8637i	0.224490	−	0.837809i	0.982608	−	0.185691i	$-0.0594525\pi$
$954$	1.88983	+	1.10179i	0.0611855	+	0.0356717i
$955$	−0.529130	−	1.12751i	−0.0171223	−	0.0364853i
$956$	14.7617	+	17.5924i	0.477429	+	0.568977i
$957$	2.42071	−	8.95831i	0.0782504	−	0.289581i
$958$	0.432407	+	0.617541i	0.0139704	+	0.0199519i
$959$	1.89841	−	10.7664i	0.0613027	−	0.347665i
$960$	5.18396	+	29.3428i	0.167311	+	0.947033i
$961$	17.9484	−	15.0605i	0.578980	−	0.485822i
$962$	−0.921065	−	3.43746i	−0.0296963	−	0.110828i
$963$	2.60928	+	31.3525i	0.0840828	+	1.01032i
$964$	26.0773	−	15.0557i	0.839892	−	0.484912i
$965$	−43.7544	−	7.60465i	−1.40850	−	0.244802i
$966$	−0.0146283	+	0.0819464i	−0.000470658	+	0.00263658i
$967$	4.84971	+	55.4324i	0.155956	+	1.78259i	0.522950	+	0.852363i	$0.324831\pi$
$967$	4.84971	+	55.4324i	0.155956	+	1.78259i	−0.366994	+	0.930223i	$0.619613\pi$
$968$	−3.88163	−	1.81003i	−0.124760	−	0.0581767i
$969$	−33.4814	−	12.2666i	−1.07558	−	0.394059i
$970$	0.660690	−	1.42596i	0.0212135	−	0.0457848i
$971$		−	31.2029i		−	1.00135i	−0.865635	−	0.500675i	$-0.833085\pi$
$971$		−	31.2029i		−	1.00135i	0.865635	−	0.500675i	$-0.166915\pi$
$972$	−18.0352	+	25.1852i	−0.578478	+	0.807817i
$973$	3.91960	−	3.91960i	0.125657	−	0.125657i
$974$	−0.273238	−	1.54961i	−0.00875512	−	0.0496527i
$975$	31.4571	−	0.0874604i	1.00743	−	0.00280097i
$976$	−11.8393	+	4.30915i	−0.378966	+	0.137932i
$977$	6.15704	−	0.538672i	0.196981	−	0.0172336i	0.0117619	−	0.999931i	$-0.496256\pi$
$977$	6.15704	−	0.538672i	0.196981	−	0.0172336i	0.185219	+	0.982697i	$0.440700\pi$
$978$	0.284650	−	0.198418i	0.00910211	−	0.00634469i
$979$	−0.580871	+	1.59593i	−0.0185647	+	0.0510062i
$980$	2.38438	−	28.0443i	0.0761662	−	0.895843i
$981$	30.4391	+	25.7618i	0.971846	+	0.822512i
$982$	−0.675810	+	0.181083i	−0.0215659	+	0.00577858i
$983$	29.9051	+	2.61636i	0.953824	+	0.0834488i	0.553431	−	0.832895i	$-0.313318\pi$
$983$	29.9051	+	2.61636i	0.953824	+	0.0834488i	0.400393	+	0.916344i	$0.368874\pi$
$984$	−0.0150384	+	7.10371i	−0.000479407	+	0.226458i
$985$	0.0913970	+	37.3256i	0.00291215	+	1.18929i
$986$	−3.10756	−	0.547947i	−0.0989649	−	0.0174502i
$987$	3.23160	+	0.873242i	0.102863	+	0.0277956i
$988$	2.02156	−	23.1065i	0.0643143	−	0.735116i
$989$	1.46225	−	2.53269i	0.0464969	−	0.0805349i
$990$	0.321900	−	0.879525i	0.0102307	−	0.0279531i
$991$	12.6389	+	21.8911i	0.401486	+	0.695395i	0.993906	−	0.110235i	$-0.0351604\pi$
$991$	12.6389	+	21.8911i	0.401486	+	0.695395i	−0.592419	+	0.805630i	$0.701827\pi$
$992$	9.01271	−	4.20270i	0.286154	−	0.133436i
$993$	13.7000	−	1.16938i	0.434757	−	0.0371091i
$994$	−0.284196	+	0.338692i	−0.00901416	+	0.0107427i
$995$	13.8348	−	52.1425i	0.438592	−	1.65303i
$996$	−28.1500	+	4.90218i	−0.891966	+	0.155331i
$997$	27.0029	−	38.5642i	0.855191	−	1.22134i	−0.118383	−	0.992968i	$-0.537771\pi$
$997$	27.0029	−	38.5642i	0.855191	−	1.22134i	0.973574	−	0.228371i	$-0.0733400\pi$
$998$	−0.0380142	−	0.0380142i	−0.00120332	−	0.00120332i
$999$	0.285374	−	44.9336i	0.00902884	−	1.42164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.9	yes	192
3.2	odd	2		405.2.r.a.152.8		192
5.2	odd	4		675.2.ba.b.68.8		192
5.3	odd	4	inner	135.2.q.a.68.9	yes	192
5.4	even	2		675.2.ba.b.257.8		192
15.8	even	4		405.2.r.a.233.8		192
27.2	odd	18	inner	135.2.q.a.2.9	✓	192
27.25	even	9		405.2.r.a.332.8		192
135.2	even	36		675.2.ba.b.218.8		192
135.29	odd	18		675.2.ba.b.407.8		192
135.83	even	36	inner	135.2.q.a.83.9	yes	192
135.133	odd	36		405.2.r.a.8.8		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.9	✓	192	27.2	odd	18	inner
135.2.q.a.68.9	yes	192	5.3	odd	4	inner
135.2.q.a.83.9	yes	192	135.83	even	36	inner
135.2.q.a.122.9	yes	192	1.1	even	1	trivial
405.2.r.a.8.8		192	135.133	odd	36
405.2.r.a.152.8		192	3.2	odd	2
405.2.r.a.233.8		192	15.8	even	4
405.2.r.a.332.8		192	27.25	even	9
675.2.ba.b.68.8		192	5.2	odd	4
675.2.ba.b.218.8		192	135.2	even	36
675.2.ba.b.257.8		192	5.4	even	2
675.2.ba.b.407.8		192	135.29	odd	18

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0928047 + 0.0649826i) q^{2} +(1.57132 - 0.728671i) q^{3} +(-0.679650 - 1.86732i) q^{4} +(0.584024 + 2.15845i) q^{5} +(0.193177 + 0.0344841i) q^{6} +(0.344848 + 0.739528i) q^{7} +(0.116914 - 0.436329i) q^{8} +(1.93808 - 2.28995i) q^{9} +O(q^{10})\)	\(q+(0.0928047 + 0.0649826i) q^{2} +(1.57132 - 0.728671i) q^{3} +(-0.679650 - 1.86732i) q^{4} +(0.584024 + 2.15845i) q^{5} +(0.193177 + 0.0344841i) q^{6} +(0.344848 + 0.739528i) q^{7} +(0.116914 - 0.436329i) q^{8} +(1.93808 - 2.28995i) q^{9} +(-0.0860616 + 0.238266i) q^{10} +(-0.792138 - 0.944033i) q^{11} +(-2.42861 - 2.43892i) q^{12} +(-2.08344 - 2.97546i) q^{13} +(-0.0160530 + 0.0910408i) q^{14} +(2.49049 + 2.96605i) q^{15} +(-3.00531 + 2.52175i) q^{16} +(1.65815 + 6.18829i) q^{17} +(0.328669 - 0.0865769i) q^{18} +(-2.78289 + 1.60671i) q^{19} +(3.63360 - 2.55755i) q^{20} +(1.08074 + 0.910753i) q^{21} +(-0.0121684 - 0.139086i) q^{22} +(0.471164 + 0.219707i) q^{23} +(-0.134231 - 0.770802i) q^{24} +(-4.31783 + 2.52118i) q^{25} -0.411524i q^{26} +(1.37671 - 5.01046i) q^{27} +(1.14656 - 1.14656i) q^{28} +(0.754929 + 4.28141i) q^{29} +(0.0383876 + 0.437102i) q^{30} +(-6.93274 + 2.52331i) q^{31} +(-1.34278 + 0.117478i) q^{32} +(-1.93259 - 0.906167i) q^{33} +(-0.248247 + 0.682053i) q^{34} +(-1.39484 + 1.17624i) q^{35} +(-5.59329 - 2.06265i) q^{36} +(8.35299 - 2.23818i) q^{37} +(-0.362674 - 0.0317298i) q^{38} +(-5.44188 - 3.15725i) q^{39} +(1.01007 - 0.00247331i) q^{40} +(-8.94143 - 1.57662i) q^{41} +(0.0411146 + 0.154751i) q^{42} +(0.490289 - 5.60402i) q^{43} +(-1.22444 + 2.12079i) q^{44} +(6.07463 + 2.84586i) q^{45} +(0.0294491 + 0.0510073i) q^{46} +(2.14663 - 1.00099i) q^{47} +(-2.88476 + 6.15236i) q^{48} +(4.07153 - 4.85226i) q^{49} +(-0.564548 - 0.0466068i) q^{50} +(7.11471 + 8.51552i) q^{51} +(-4.14014 + 5.91273i) q^{52} +(4.55111 + 4.55111i) q^{53} +(0.453358 - 0.375532i) q^{54} +(1.57502 - 2.26113i) q^{55} +(0.362995 - 0.0640058i) q^{56} +(-3.20205 + 4.55246i) q^{57} +(-0.208156 + 0.446393i) q^{58} +(-10.5708 - 8.86992i) q^{59} +(3.84592 - 6.66643i) q^{60} +(3.01780 + 1.09839i) q^{61} +(-0.807362 - 0.216332i) q^{62} +(2.36182 + 0.643579i) q^{63} +(6.66285 + 3.84680i) q^{64} +(5.20561 - 6.23475i) q^{65} +(-0.120468 - 0.209681i) q^{66} +(9.77239 - 6.84270i) q^{67} +(10.4286 - 7.30217i) q^{68} +(0.900442 + 0.00190622i) q^{69} +(-0.205883 + 0.0185205i) q^{70} +(4.14187 + 2.39131i) q^{71} +(-0.772582 - 1.11336i) q^{72} +(-5.46389 - 1.46405i) q^{73} +(0.920640 + 0.335086i) q^{74} +(-4.94757 + 7.10785i) q^{75} +(4.89163 + 4.10457i) q^{76} +(0.424972 - 0.911356i) q^{77} +(-0.299866 - 0.646635i) q^{78} +(9.54938 - 1.68381i) q^{79} +(-7.19826 - 5.01405i) q^{80} +(-1.48773 - 8.87619i) q^{81} +(-0.727355 - 0.727355i) q^{82} +(4.76170 - 6.80042i) q^{83} +(0.966147 - 2.63708i) q^{84} +(-12.3887 + 7.19314i) q^{85} +(0.409665 - 0.488220i) q^{86} +(4.30598 + 6.17736i) q^{87} +(-0.504521 + 0.235262i) q^{88} +(-0.689073 - 1.19351i) q^{89} +(0.378823 + 0.658854i) q^{90} +(1.48197 - 2.56685i) q^{91} +(0.0900380 - 1.02914i) q^{92} +(-9.05487 + 9.01661i) q^{93} +(0.264265 + 0.0465970i) q^{94} +(-5.09327 - 5.06839i) q^{95} +(-2.02433 + 1.16304i) q^{96} +(-6.18004 - 0.540683i) q^{97} +(0.693170 - 0.185734i) q^{98} +(-3.69701 - 0.0156531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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