LMFDB - Embedded newform 690.2.r.b.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.r (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	690.49
Dual form			690.2.r.b.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-0.0689747 - 2.23500i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.33127 - 2.07150i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-0.0689747 - 2.23500i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.33127 - 2.07150i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(0.386347 + 2.20244i) q^{10} +(0.195345 - 1.35866i) q^{11} +(0.989821 + 0.142315i) q^{12} +(-1.28134 + 1.99380i) q^{13} +(1.61253 + 1.86095i) q^{14} +(0.865713 - 2.06168i) q^{15} +(0.841254 - 0.540641i) q^{16} +(1.22064 - 4.15712i) q^{17} +(-0.755750 - 0.654861i) q^{18} +(-1.41790 + 0.416332i) q^{19} +(-0.695854 - 2.12504i) q^{20} +(-0.350435 - 2.43733i) q^{21} +1.37263i q^{22} +(-3.09115 - 3.66671i) q^{23} -1.00000 q^{24} +(-4.99048 + 0.308318i) q^{25} +(0.984548 - 2.15586i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-1.86095 - 1.61253i) q^{28} +(-4.32057 - 1.26863i) q^{29} +(-0.563493 + 2.16390i) q^{30} +(-0.724175 - 1.58572i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(0.742099 - 1.15473i) q^{33} +(-0.616596 + 4.28852i) q^{34} +(-4.53798 + 3.11828i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-4.86649 + 4.21684i) q^{37} +(1.34422 - 0.613883i) q^{38} +(-1.99380 + 1.28134i) q^{39} +(0.991196 + 2.00438i) q^{40} +(7.09843 - 8.19203i) q^{41} +(0.693737 + 2.36265i) q^{42} +(1.80187 + 0.822885i) q^{43} +(-0.195345 - 1.35866i) q^{44} +(1.64393 - 1.51574i) q^{45} +(3.58151 + 3.18948i) q^{46} -6.48708i q^{47} +(0.989821 - 0.142315i) q^{48} +(0.389082 - 0.851971i) q^{49} +(4.89581 - 1.01540i) q^{50} +(2.83726 - 3.27438i) q^{51} +(-0.667716 + 2.27403i) q^{52} +(4.17973 + 6.50379i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-3.05008 - 0.342885i) q^{55} +(2.07150 + 1.33127i) q^{56} +(-1.46272 - 0.210307i) q^{57} +(4.45714 + 0.640839i) q^{58} +(-10.6767 - 6.86149i) q^{59} +(0.249802 - 2.22207i) q^{60} +(3.05942 + 6.69919i) q^{61} +(0.942475 + 1.46652i) q^{62} +(0.693737 - 2.36265i) q^{63} +(0.654861 - 0.755750i) q^{64} +(4.54453 + 2.72627i) q^{65} +(-0.570210 + 1.24859i) q^{66} +(8.92842 - 1.28371i) q^{67} -4.33262i q^{68} +(-1.28860 - 4.61947i) q^{69} +(4.04802 - 3.73236i) q^{70} +(-0.0401170 - 0.279020i) q^{71} +(-0.909632 - 0.415415i) q^{72} +(-2.12963 - 7.25284i) q^{73} +(4.21684 - 4.86649i) q^{74} +(-4.66758 - 1.79267i) q^{75} +(-1.24317 + 0.798936i) q^{76} +(-3.07451 + 1.40408i) q^{77} +(1.79115 - 1.55204i) q^{78} +(3.05383 + 1.96258i) q^{79} +(-1.26636 - 1.84291i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-5.86033 + 9.11886i) q^{82} +(10.9029 - 9.44742i) q^{83} +(-1.02292 - 2.23987i) q^{84} +(-9.37537 - 2.44140i) q^{85} +(-1.90064 - 0.558077i) q^{86} +(-3.40312 - 2.94882i) q^{87} +(0.386714 + 1.31703i) q^{88} +(-4.93258 + 10.8009i) q^{89} +(-1.41149 + 1.73427i) q^{90} +5.83596 q^{91} +(-3.99897 - 2.64731i) q^{92} -1.74326i q^{93} +(0.923208 + 6.42105i) q^{94} +(1.02830 + 3.14029i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(-1.25165 - 1.08456i) q^{97} +(-0.263874 + 0.898671i) q^{98} +(1.15473 - 0.742099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.989821	+	0.142315i	−0.699909	+	0.100632i
$2$	−0.989821	+	0.142315i	−0.699909	+	0.100632i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$4$	0.959493	−	0.281733i	0.479746	−	0.140866i
$5$	−0.0689747	−	2.23500i	−0.0308464	−	0.999524i
$5$	−0.0689747	−	2.23500i	−0.0308464	−	0.999524i
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	−1.33127	−	2.07150i	−0.503173	−	0.782953i	0.493030	−	0.870012i	$-0.335889\pi$
$7$	−1.33127	−	2.07150i	−0.503173	−	0.782953i	−0.996203	+	0.0870595i	$0.972253\pi$
$8$	−0.909632	+	0.415415i	−0.321603	+	0.146871i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	0.386347	+	2.20244i	0.122174	+	0.696472i
$11$	0.195345	−	1.35866i	0.0588988	−	0.409650i	−0.938948	−	0.344060i	$-0.888198\pi$
$11$	0.195345	−	1.35866i	0.0588988	−	0.409650i	0.997847	−	0.0655907i	$-0.0208932\pi$
$12$	0.989821	+	0.142315i	0.285737	+	0.0410828i
$13$	−1.28134	+	1.99380i	−0.355379	+	0.552981i	−0.972209	−	0.234116i	$-0.924780\pi$
$13$	−1.28134	+	1.99380i	−0.355379	+	0.552981i	0.616829	+	0.787097i	$0.288417\pi$
$14$	1.61253	+	1.86095i	0.430966	+	0.497361i
$15$	0.865713	−	2.06168i	0.223526	−	0.532325i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	1.22064	−	4.15712i	0.296049	−	1.00825i	−0.668361	−	0.743837i	$-0.733004\pi$
$17$	1.22064	−	4.15712i	0.296049	−	1.00825i	0.964410	−	0.264413i	$-0.0851780\pi$
$18$	−0.755750	−	0.654861i	−0.178132	−	0.154352i
$19$	−1.41790	+	0.416332i	−0.325288	+	0.0955132i	−0.440299	−	0.897851i	$-0.645128\pi$
$19$	−1.41790	+	0.416332i	−0.325288	+	0.0955132i	0.115011	+	0.993364i	$0.463310\pi$
$20$	−0.695854	−	2.12504i	−0.155598	−	0.475173i
$21$	−0.350435	−	2.43733i	−0.0764713	−	0.531869i
$22$			1.37263i			0.292645i
$23$	−3.09115	−	3.66671i	−0.644549	−	0.764563i
$23$	−3.09115	−	3.66671i	−0.644549	−	0.764563i
$24$	−1.00000			−0.204124
$25$	−4.99048	+	0.308318i	−0.998097	+	0.0616635i
$26$	0.984548	−	2.15586i	0.193086	−	0.422799i
$27$	0.281733	+	0.959493i	0.0542195	+	0.184655i
$28$	−1.86095	−	1.61253i	−0.351687	−	0.304739i
$29$	−4.32057	−	1.26863i	−0.802309	−	0.235579i	−0.145227	−	0.989398i	$-0.546391\pi$
$29$	−4.32057	−	1.26863i	−0.802309	−	0.235579i	−0.657082	+	0.753819i	$0.728209\pi$
$30$	−0.563493	+	2.16390i	−0.102879	+	0.395073i
$31$	−0.724175	−	1.58572i	−0.130066	−	0.284804i	0.833384	−	0.552695i	$-0.186401\pi$
$31$	−0.724175	−	1.58572i	−0.130066	−	0.284804i	−0.963449	+	0.267891i	$0.913673\pi$
$32$	−0.755750	+	0.654861i	−0.133599	+	0.115764i
$33$	0.742099	−	1.15473i	0.129183	−	0.201012i
$34$	−0.616596	+	4.28852i	−0.105745	+	0.735475i
$35$	−4.53798	+	3.11828i	−0.767059	+	0.527085i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−4.86649	+	4.21684i	−0.800047	+	0.693245i	−0.955627	−	0.294579i	$-0.904821\pi$
$37$	−4.86649	+	4.21684i	−0.800047	+	0.693245i	0.155580	+	0.987823i	$0.450275\pi$
$38$	1.34422	−	0.613883i	0.218061	−	0.0995849i
$39$	−1.99380	+	1.28134i	−0.319264	+	0.205178i
$40$	0.991196	+	2.00438i	0.156722	+	0.316920i
$41$	7.09843	−	8.19203i	1.10859	−	1.27938i	0.151859	−	0.988402i	$-0.451474\pi$
$41$	7.09843	−	8.19203i	1.10859	−	1.27938i	0.956730	−	0.290978i	$-0.0939806\pi$
$42$	0.693737	+	2.36265i	0.107046	+	0.364565i
$43$	1.80187	+	0.822885i	0.274782	+	0.125489i	0.548040	−	0.836452i	$-0.315374\pi$
$43$	1.80187	+	0.822885i	0.274782	+	0.125489i	−0.273258	+	0.961941i	$0.588101\pi$
$44$	−0.195345	−	1.35866i	−0.0294494	−	0.204825i
$45$	1.64393	−	1.51574i	0.245063	−	0.225954i
$46$	3.58151	+	3.18948i	0.528065	+	0.470263i
$47$		−	6.48708i		−	0.946238i	−0.880998	−	0.473119i	$-0.843128\pi$
$47$		−	6.48708i		−	0.946238i	0.880998	−	0.473119i	$-0.156872\pi$
$48$	0.989821	−	0.142315i	0.142868	−	0.0205414i
$49$	0.389082	−	0.851971i	0.0555831	−	0.121710i
$50$	4.89581	−	1.01540i	0.692372	−	0.143599i
$51$	2.83726	−	3.27438i	0.397296	−	0.458504i
$52$	−0.667716	+	2.27403i	−0.0925956	+	0.315352i
$53$	4.17973	+	6.50379i	0.574130	+	0.893364i	0.999934	−	0.0114513i	$-0.00364515\pi$
$53$	4.17973	+	6.50379i	0.574130	+	0.893364i	−0.425804	+	0.904815i	$0.640009\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	−3.05008	−	0.342885i	−0.411272	−	0.0462346i
$56$	2.07150	+	1.33127i	0.276816	+	0.177899i
$57$	−1.46272	−	0.210307i	−0.193741	−	0.0278558i
$58$	4.45714	+	0.640839i	0.585251	+	0.0841463i
$59$	−10.6767	−	6.86149i	−1.38999	−	0.893290i	−0.390361	−	0.920662i	$-0.627650\pi$
$59$	−10.6767	−	6.86149i	−1.38999	−	0.893290i	−0.999625	+	0.0273722i	$0.991286\pi$
$60$	0.249802	−	2.22207i	0.0322492	−	0.286868i
$61$	3.05942	+	6.69919i	0.391718	+	0.857743i	0.998043	+	0.0625263i	$0.0199157\pi$
$61$	3.05942	+	6.69919i	0.391718	+	0.857743i	−0.606325	+	0.795217i	$0.707357\pi$
$62$	0.942475	+	1.46652i	0.119694	+	0.186248i
$63$	0.693737	−	2.36265i	0.0874026	−	0.297666i
$64$	0.654861	−	0.755750i	0.0818576	−	0.0944687i
$65$	4.54453	+	2.72627i	0.563680	+	0.338153i
$66$	−0.570210	+	1.24859i	−0.0701880	+	0.153690i
$67$	8.92842	−	1.28371i	1.09078	−	0.156831i	0.426628	−	0.904427i	$-0.359702\pi$
$67$	8.92842	−	1.28371i	1.09078	−	0.156831i	0.664153	+	0.747597i	$0.268792\pi$
$68$		−	4.33262i		−	0.525408i
$69$	−1.28860	−	4.61947i	−0.155129	−	0.556119i
$70$	4.04802	−	3.73236i	0.483830	−	0.446102i
$71$	−0.0401170	−	0.279020i	−0.00476102	−	0.0331136i	0.987302	−	0.158852i	$-0.0507792\pi$
$71$	−0.0401170	−	0.279020i	−0.00476102	−	0.0331136i	−0.992063	+	0.125738i	$0.959870\pi$
$72$	−0.909632	−	0.415415i	−0.107201	−	0.0489571i
$73$	−2.12963	−	7.25284i	−0.249254	−	0.848881i	−0.985137	−	0.171772i	$-0.945051\pi$
$73$	−2.12963	−	7.25284i	−0.249254	−	0.848881i	0.735883	−	0.677109i	$-0.236767\pi$
$74$	4.21684	−	4.86649i	0.490198	−	0.565719i
$75$	−4.66758	−	1.79267i	−0.538966	−	0.206999i
$76$	−1.24317	+	0.798936i	−0.142601	+	0.0916443i
$77$	−3.07451	+	1.40408i	−0.350373	+	0.160010i
$78$	1.79115	−	1.55204i	0.202808	−	0.175734i
$79$	3.05383	+	1.96258i	0.343583	+	0.220807i	0.701040	−	0.713122i	$-0.252720\pi$
$79$	3.05383	+	1.96258i	0.343583	+	0.220807i	−0.357457	+	0.933930i	$0.616356\pi$
$80$	−1.26636	−	1.84291i	−0.141583	−	0.206044i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−5.86033	+	9.11886i	−0.647166	+	1.00701i
$83$	10.9029	−	9.44742i	1.19675	−	1.03699i	0.198368	−	0.980128i	$-0.436436\pi$
$83$	10.9029	−	9.44742i	1.19675	−	1.03699i	0.998382	−	0.0568618i	$-0.0181095\pi$
$84$	−1.02292	−	2.23987i	−0.111609	−	0.244390i
$85$	−9.37537	−	2.44140i	−1.01690	−	0.264807i
$86$	−1.90064	−	0.558077i	−0.204951	−	0.0601790i
$87$	−3.40312	−	2.94882i	−0.364852	−	0.316146i
$88$	0.386714	+	1.31703i	0.0412239	+	0.140396i
$89$	−4.93258	+	10.8009i	−0.522853	+	1.14489i	0.445495	+	0.895284i	$0.353028\pi$
$89$	−4.93258	+	10.8009i	−0.522853	+	1.14489i	−0.968348	+	0.249604i	$0.919700\pi$
$90$	−1.41149	+	1.73427i	−0.148784	+	0.182808i
$91$	5.83596			0.611775
$92$	−3.99897	−	2.64731i	−0.416921	−	0.276001i
$93$		−	1.74326i		−	0.180767i
$94$	0.923208	+	6.42105i	0.0952217	+	0.662281i
$95$	1.02830	+	3.14029i	0.105502	+	0.322187i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	−1.25165	−	1.08456i	−0.127086	−	0.110121i	0.588999	−	0.808134i	$-0.299522\pi$
$97$	−1.25165	−	1.08456i	−0.127086	−	0.110121i	−0.716085	+	0.698013i	$0.754068\pi$
$98$	−0.263874	+	0.898671i	−0.0266553	+	0.0907795i
$99$	1.15473	−	0.742099i	0.116055	−	0.0745837i
$100$	−4.70147	+	1.70181i	−0.470147	+	0.170181i
$101$	−5.18852	−	5.98787i	−0.516277	−	0.595815i	0.436418	−	0.899744i	$-0.356247\pi$
$101$	−5.18852	−	5.98787i	−0.516277	−	0.595815i	−0.952695	+	0.303929i	$0.901701\pi$
$102$	−2.34239	+	3.64483i	−0.231931	+	0.360892i
$103$	−1.42372	−	0.204700i	−0.140284	−	0.0201697i	0.0718153	−	0.997418i	$-0.477121\pi$
$103$	−1.42372	−	0.204700i	−0.140284	−	0.0201697i	−0.212099	+	0.977248i	$0.568030\pi$
$104$	0.337291	−	2.34591i	0.0330741	−	0.230036i
$105$	−5.42327	+	0.951339i	−0.529257	+	0.0928411i
$106$	−5.06277	−	5.84275i	−0.491740	−	0.567498i
$107$	13.9152	−	6.35486i	1.34523	−	0.614347i	0.392949	−	0.919560i	$-0.371455\pi$
$107$	13.9152	−	6.35486i	1.34523	−	0.614347i	0.952284	+	0.305213i	$0.0987276\pi$
$108$	0.540641	+	0.841254i	0.0520232	+	0.0809497i
$109$	−6.43715	−	1.89012i	−0.616567	−	0.181040i	−0.0414890	−	0.999139i	$-0.513210\pi$
$109$	−6.43715	−	1.89012i	−0.616567	−	0.181040i	−0.575078	+	0.818099i	$0.695028\pi$
$110$	3.06783	−	0.0946767i	0.292506	−	0.00902707i
$111$	−6.17846	+	1.81416i	−0.586433	+	0.172192i
$112$	−2.23987	−	1.02292i	−0.211648	−	0.0966565i
$113$	15.8181	−	2.27429i	1.48804	−	0.213948i	0.650157	−	0.759800i	$-0.274703\pi$
$113$	15.8181	−	2.27429i	1.48804	−	0.213948i	0.837881	+	0.545852i	$0.183794\pi$
$114$	1.47776			0.138405
$115$	−7.98191	+	7.16164i	−0.744317	+	0.667827i
$116$	−4.50297			−0.418090
$117$	−2.34591	+	0.337291i	−0.216880	+	0.0311826i
$118$	11.5445	+	5.27220i	1.06276	+	0.485345i
$119$	−10.2365	+	3.00570i	−0.938376	+	0.275532i
$120$	0.0689747	+	2.23500i	0.00629650	+	0.204027i
$121$	8.74663	+	2.56824i	0.795149	+	0.233477i
$122$	−3.98167	−	6.19560i	−0.360483	−	0.560923i
$123$	9.86005	−	4.50294i	0.889051	−	0.406016i
$124$	−1.14159	−	1.31746i	−0.102518	−	0.118312i
$125$	1.03331	+	11.1325i	0.0924219	+	0.995720i
$126$	−0.350435	+	2.43733i	−0.0312193	+	0.217135i
$127$	−0.0259523	−	0.00373137i	−0.00230289	−	0.000331106i	0.141163	−	0.989986i	$-0.454916\pi$
$127$	−0.0259523	−	0.00373137i	−0.00230289	−	0.000331106i	−0.143466	+	0.989655i	$0.545825\pi$
$128$	−0.540641	+	0.841254i	−0.0477863	+	0.0743570i
$129$	1.29720	+	1.49705i	0.114212	+	0.131808i
$130$	−4.88627	−	2.05177i	−0.428554	−	0.179952i
$131$	−4.63326	+	2.97762i	−0.404810	+	0.260156i	−0.727164	−	0.686463i	$-0.759162\pi$
$131$	−4.63326	+	2.97762i	−0.404810	+	0.260156i	0.322354	+	0.946619i	$0.395526\pi$
$132$	0.386714	−	1.31703i	0.0336591	−	0.114632i
$133$	2.75004	+	2.38292i	0.238459	+	0.206626i
$134$	−8.65485	+	2.54129i	−0.747665	+	0.219534i
$135$	2.12504	−	0.695854i	0.182894	−	0.0598896i
$136$	0.616596	+	4.28852i	0.0528727	+	0.367738i
$137$			12.0848i			1.03247i	0.856446	+	0.516236i	$0.172667\pi$
$137$			12.0848i			1.03247i	−0.856446	+	0.516236i	$0.827333\pi$
$138$	1.93290	+	4.38906i	0.164540	+	0.373622i
$139$	0.402122			0.0341076			0.0170538	−	0.999855i	$-0.494571\pi$
$139$	0.402122			0.0341076			0.0170538	+	0.999855i	$0.494571\pi$
$140$	−3.47564	+	4.27046i	−0.293745	+	0.360920i
$141$	2.69483	−	5.90086i	0.226946	−	0.496942i
$142$	0.0794174	+	0.270471i	0.00666456	+	0.0226974i
$143$	2.45859	+	2.13038i	0.205597	+	0.178151i
$144$	0.959493	+	0.281733i	0.0799577	+	0.0234777i
$145$	−2.53739	+	9.74399i	−0.210719	+	0.809194i
$146$	3.14014	+	6.87594i	0.259880	+	0.569057i
$147$	0.707843	−	0.613349i	0.0583819	−	0.0505882i
$148$	−3.48135	+	5.41708i	−0.286165	+	0.445281i
$149$	−0.204500	+	1.42233i	−0.0167533	+	0.116522i	−0.996482	−	0.0838073i	$-0.973292\pi$
$149$	−0.204500	+	1.42233i	−0.0167533	+	0.116522i	0.979729	+	0.200329i	$0.0642011\pi$
$150$	4.87520	+	1.11015i	0.398058	+	0.0906437i
$151$	−2.54526	−	1.63574i	−0.207130	−	0.133115i	0.432963	−	0.901412i	$-0.357468\pi$
$151$	−2.54526	−	1.63574i	−0.207130	−	0.133115i	−0.640093	+	0.768297i	$0.721104\pi$
$152$	1.11681	−	0.967725i	0.0905856	−	0.0784929i
$153$	3.94109	−	1.79984i	0.318618	−	0.145508i
$154$	2.84340	−	1.82734i	0.229127	−	0.147251i
$155$	−3.49414	+	1.72791i	−0.280656	+	0.138789i
$156$	−1.55204	+	1.79115i	−0.124263	+	0.143407i
$157$	5.05034	+	17.1999i	0.403061	+	1.37270i	0.872016	+	0.489478i	$0.162813\pi$
$157$	5.05034	+	17.1999i	0.403061	+	1.37270i	−0.468955	+	0.883222i	$0.655369\pi$
$158$	−3.30205	−	1.50800i	−0.262697	−	0.119970i
$159$	1.10025	+	7.65238i	0.0872552	+	0.606873i
$160$	1.51574	+	1.64393i	0.119830	+	0.129964i
$161$	−3.48044	+	11.2847i	−0.274297	+	0.889359i
$162$		−	1.00000i		−	0.0785674i
$163$	6.10641	−	0.877969i	0.478291	−	0.0687679i	0.101047	−	0.994882i	$-0.467781\pi$
$163$	6.10641	−	0.877969i	0.478291	−	0.0687679i	0.377244	+	0.926114i	$0.376872\pi$
$164$	4.50294	−	9.86005i	0.351620	−	0.769941i
$165$	−2.63201	−	1.57895i	−0.204902	−	0.122921i
$166$	−9.44742	+	10.9029i	−0.733262	+	0.846230i
$167$	−1.14521	+	3.90022i	−0.0886189	+	0.301808i	−0.991861	−	0.127322i	$-0.959362\pi$
$167$	−1.14521	+	3.90022i	−0.0886189	+	0.301808i	0.903243	+	0.429130i	$0.141180\pi$
$168$	1.33127	+	2.07150i	0.102710	+	0.159820i
$169$	3.06698	+	6.71575i	0.235922	+	0.516596i
$170$	9.62739	+	1.08230i	0.738387	+	0.0830083i
$171$	−1.24317	−	0.798936i	−0.0950675	−	0.0610962i
$172$	1.96071	+	0.281908i	0.149503	+	0.0214953i
$173$	23.4795	+	3.37584i	1.78511	+	0.256660i	0.954077	−	0.299560i	$-0.0968400\pi$
$173$	23.4795	+	3.37584i	1.78511	+	0.256660i	0.831035	+	0.556221i	$0.187749\pi$
$174$	3.78814	+	2.43449i	0.287178	+	0.184558i
$175$	7.28237	+	9.92733i	0.550495	+	0.750435i
$176$	−0.570210	−	1.24859i	−0.0429812	−	0.0941158i
$177$	−6.86149	−	10.6767i	−0.515741	−	0.802509i
$178$	3.34526	−	11.3929i	0.250737	−	0.853933i
$179$	−5.54629	+	6.40076i	−0.414549	+	0.478416i	−0.924169	−	0.381984i	$-0.875241\pi$
$179$	−5.54629	+	6.40076i	−0.414549	+	0.478416i	0.509619	+	0.860400i	$0.329786\pi$
$180$	1.15031	−	1.91750i	0.0857390	−	0.142922i
$181$	1.43069	−	3.13277i	0.106342	−	0.232857i	−0.848979	−	0.528426i	$-0.822782\pi$
$181$	1.43069	−	3.13277i	0.106342	−	0.232857i	0.955321	+	0.295570i	$0.0955095\pi$
$182$	−5.77656	+	0.830544i	−0.428187	+	0.0615640i
$183$			7.36472i			0.544416i
$184$	4.33502	+	2.05125i	0.319582	+	0.151220i
$185$	9.76032	+	10.5858i	0.717593	+	0.778282i
$186$	0.248091	+	1.72551i	0.0181909	+	0.126521i
$187$	−5.40965	−	2.47051i	−0.395593	−	0.180661i
$188$	−1.82762	−	6.22431i	−0.133293	−	0.453955i
$189$	1.61253	−	1.86095i	0.117294	−	0.135364i
$190$	−1.46475	−	2.96198i	−0.106264	−	0.214885i
$191$	−4.06963	+	2.61539i	−0.294468	+	0.189243i	−0.679530	−	0.733647i	$-0.737816\pi$
$191$	−4.06963	+	2.61539i	−0.294468	+	0.189243i	0.385062	+	0.922891i	$0.374180\pi$
$192$	0.909632	−	0.415415i	0.0656470	−	0.0299800i
$193$	0.149856	−	0.129851i	0.0107868	−	0.00934686i	−0.649451	−	0.760404i	$-0.725001\pi$
$193$	0.149856	−	0.129851i	0.0107868	−	0.00934686i	0.660237	+	0.751057i	$0.270456\pi$
$194$	1.39326	+	0.895396i	0.100030	+	0.0642857i
$195$	3.00132	+	4.36777i	0.214929	+	0.312783i
$196$	0.133294	−	0.927077i	0.00952097	−	0.0662198i
$197$	−10.3567	+	16.1154i	−0.737887	+	1.14817i	0.245980	+	0.969275i	$0.420890\pi$
$197$	−10.3567	+	16.1154i	−0.737887	+	1.14817i	−0.983867	+	0.178900i	$0.942746\pi$
$198$	−1.03736	+	0.898880i	−0.0737222	+	0.0638806i
$199$	−0.0983199	−	0.215290i	−0.00696971	−	0.0152615i	0.906115	−	0.423031i	$-0.139034\pi$
$199$	−0.0983199	−	0.215290i	−0.00696971	−	0.0152615i	−0.913085	+	0.407770i	$0.866307\pi$
$200$	4.41143	−	2.35358i	0.311935	−	0.166423i
$201$	8.65485	+	2.54129i	0.610466	+	0.179249i
$202$	5.98787	+	5.18852i	0.421305	+	0.365063i
$203$	3.12388	+	10.6389i	0.219253	+	0.746707i
$204$	1.79984	−	3.94109i	0.126014	−	0.275932i
$205$	−18.7988	−	15.3000i	−1.31297	−	1.06860i
$206$	1.43836			0.100216
$207$	0.746846	−	4.73732i	0.0519094	−	0.329267i
$208$			2.37004i			0.164332i
$209$	0.288673	+	2.00777i	0.0199679	+	0.138880i
$210$	5.23268	−	1.71347i	0.361089	−	0.118241i
$211$	21.1066	−	6.19746i	1.45304	−	0.426651i	0.542493	−	0.840060i	$-0.317480\pi$
$211$	21.1066	−	6.19746i	1.45304	−	0.426651i	0.910545	+	0.413410i	$0.135662\pi$
$212$	5.84275	+	5.06277i	0.401282	+	0.347713i
$213$	0.0794174	−	0.270471i	0.00544159	−	0.0185324i
$214$	−12.8692	+	8.27052i	−0.879719	+	0.565361i
$215$	1.71487	−	4.08394i	0.116953	−	0.278522i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	−2.32075	+	3.61115i	−0.157543	+	0.245141i
$218$	6.64062	+	0.954777i	0.449760	+	0.0646657i
$219$	1.07576	−	7.48210i	0.0726933	−	0.505593i
$220$	−3.02313	+	0.530311i	−0.203819	+	0.0357535i
$221$	6.72442	+	7.76039i	0.452333	+	0.522020i
$222$	5.85739	−	2.67498i	0.393122	−	0.179533i
$223$	−4.22368	−	6.57217i	−0.282838	−	0.440105i	0.670544	−	0.741870i	$-0.266061\pi$
$223$	−4.22368	−	6.57217i	−0.282838	−	0.440105i	−0.953382	+	0.301765i	$0.902424\pi$
$224$	2.36265	+	0.693737i	0.157861	+	0.0463522i
$225$	−3.50108	−	3.56965i	−0.233406	−	0.237977i
$226$	−15.3334	+	4.50229i	−1.01996	+	0.299488i
$227$	−21.6716	−	9.89707i	−1.43839	−	0.656892i	−0.464848	−	0.885390i	$-0.653891\pi$
$227$	−21.6716	−	9.89707i	−1.43839	−	0.656892i	−0.973544	+	0.228499i	$0.926618\pi$
$228$	−1.46272	+	0.210307i	−0.0968707	+	0.0139279i
$229$	28.5773			1.88844			0.944220	−	0.329315i	$-0.106818\pi$
$229$	28.5773			1.88844			0.944220	+	0.329315i	$0.106818\pi$
$230$	6.88146	−	8.22469i	0.453750	−	0.542320i
$231$	−3.37995			−0.222385
$232$	4.45714	−	0.640839i	0.292625	−	0.0420732i
$233$	−11.1534	−	5.09360i	−0.730686	−	0.333693i	0.0150934	−	0.999886i	$-0.495195\pi$
$233$	−11.1534	−	5.09360i	−0.730686	−	0.333693i	−0.745779	+	0.666193i	$0.767923\pi$
$234$	2.27403	−	0.667716i	0.148658	−	0.0436500i
$235$	−14.4987	+	0.447445i	−0.945788	+	0.0291881i
$236$	−12.1773	−	3.57558i	−0.792675	−	0.232750i
$237$	1.96258	+	3.05383i	0.127483	+	0.198368i
$238$	9.70452	−	4.43191i	0.629051	−	0.287278i
$239$	−12.3494	−	14.2519i	−0.798815	−	0.921882i	0.199501	−	0.979898i	$-0.436068\pi$
$239$	−12.3494	−	14.2519i	−0.798815	−	0.921882i	−0.998316	+	0.0580159i	$0.981523\pi$
$240$	−0.386347	−	2.20244i	−0.0249386	−	0.142167i
$241$	−0.323648	+	2.25102i	−0.0208480	+	0.145001i	−0.997587	−	0.0694321i	$-0.977881\pi$
$241$	−0.323648	+	2.25102i	−0.0208480	+	0.145001i	0.976739	+	0.214433i	$0.0687904\pi$
$242$	−9.02311	−	1.29733i	−0.580027	−	0.0833953i
$243$	−0.540641	+	0.841254i	−0.0346821	+	0.0539664i
$244$	4.82287	+	5.56589i	0.308752	+	0.356319i
$245$	−1.93099	−	0.810835i	−0.123367	−	0.0518024i
$246$	−9.11886	+	5.86033i	−0.581397	+	0.373641i
$247$	0.986723	−	3.36047i	0.0627837	−	0.213822i
$248$	1.31746	+	1.14159i	0.0836591	+	0.0724910i
$249$	13.8422	−	4.06445i	0.877216	−	0.257574i
$250$	−2.60711	−	10.8721i	−0.164888	−	0.687613i
$251$	1.97882	+	13.7630i	0.124902	+	0.868713i	0.951878	+	0.306476i	$0.0991499\pi$
$251$	1.97882	+	13.7630i	0.124902	+	0.868713i	−0.826976	+	0.562237i	$0.809941\pi$
$252$		−	2.46240i		−	0.155116i
$253$	−5.58565	+	3.48354i	−0.351167	+	0.219008i
$254$	0.0262191			0.00164514
$255$	−7.51394	−	6.11545i	−0.470541	−	0.382964i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	3.48678	+	11.8749i	0.217500	+	0.740736i	0.993879	+	0.110470i	$0.0352357\pi$
$257$	3.48678	+	11.8749i	0.217500	+	0.740736i	−0.776380	+	0.630265i	$0.782946\pi$
$258$	−1.49705	−	1.29720i	−0.0932020	−	0.0807600i
$259$	15.2138	+	4.46718i	0.945340	+	0.277577i
$260$	5.12853	+	1.33550i	0.318058	+	0.0828240i
$261$	−1.87060	−	4.09604i	−0.115787	−	0.253539i
$262$	4.16235	−	3.60669i	0.257151	−	0.222822i
$263$	−6.51812	+	10.1424i	−0.401924	+	0.625406i	−0.981939	−	0.189200i	$-0.939411\pi$
$263$	−6.51812	+	10.1424i	−0.401924	+	0.625406i	0.580014	+	0.814606i	$0.303047\pi$
$264$	−0.195345	+	1.35866i	−0.0120227	+	0.0836195i
$265$	14.2477	−	9.79031i	0.875229	−	0.601414i
$266$	−3.06117	−	1.96730i	−0.187693	−	0.120623i
$267$	−8.97367	+	7.77573i	−0.549180	+	0.475867i
$268$	8.20509	−	3.74714i	0.501206	−	0.228893i
$269$	−26.0600	+	16.7477i	−1.58890	+	1.02113i	−0.616640	+	0.787245i	$0.711507\pi$
$269$	−26.0600	+	16.7477i	−1.58890	+	1.02113i	−0.972265	+	0.233882i	$0.924857\pi$
$270$	−2.00438	+	0.991196i	−0.121983	+	0.0603223i
$271$	−2.59684	+	2.99691i	−0.157747	+	0.182050i	−0.829121	−	0.559069i	$-0.811159\pi$
$271$	−2.59684	+	2.99691i	−0.157747	+	0.182050i	0.671374	+	0.741118i	$0.265704\pi$
$272$	−1.22064	−	4.15712i	−0.0740122	−	0.252062i
$273$	5.30858	+	2.42435i	0.321290	+	0.146728i
$274$	−1.71984	−	11.9618i	−0.103900	−	0.722638i
$275$	−0.555970	+	6.84059i	−0.0335263	+	0.412503i
$276$	−2.53786	−	4.06931i	−0.152761	−	0.244944i
$277$		−	13.7227i		−	0.824517i	−0.911067	−	0.412259i	$-0.864740\pi$
$277$		−	13.7227i		−	0.824517i	0.911067	−	0.412259i	$-0.135260\pi$
$278$	−0.398029	+	0.0572280i	−0.0238722	+	0.00343231i
$279$	0.724175	−	1.58572i	0.0433552	−	0.0949346i
$280$	2.83252	−	4.72163i	0.169275	−	0.282171i
$281$	16.7123	−	19.2871i	0.996974	−	1.15057i	0.00838045	−	0.999965i	$-0.497332\pi$
$281$	16.7123	−	19.2871i	0.996974	−	1.15057i	0.988594	−	0.150605i	$-0.0481222\pi$
$282$	−1.82762	+	6.22431i	−0.108833	+	0.370652i
$283$	−1.73005	−	2.69201i	−0.102841	−	0.160024i	0.786019	−	0.618202i	$-0.212139\pi$
$283$	−1.73005	−	2.69201i	−0.102841	−	0.160024i	−0.888860	+	0.458178i	$0.848502\pi$
$284$	−0.117101	−	0.256416i	−0.00694867	−	0.0152155i
$285$	−0.369146	+	3.28368i	−0.0218663	+	0.194509i
$286$	−2.73675	−	1.75880i	−0.161827	−	0.104000i
$287$	−26.4197	−	3.79858i	−1.55951	−	0.224223i
$288$	−0.989821	−	0.142315i	−0.0583258	−	0.00838598i
$289$	−1.49037	−	0.957805i	−0.0876690	−	0.0563415i
$290$	1.12485	−	10.0059i	0.0660534	−	0.587568i
$291$	−0.688000	−	1.50651i	−0.0403313	−	0.0883132i
$292$	−4.08672	−	6.35907i	−0.239157	−	0.372136i
$293$	7.80260	−	26.5732i	0.455833	−	1.55242i	−0.336106	−	0.941824i	$-0.609110\pi$
$293$	7.80260	−	26.5732i	0.455833	−	1.55242i	0.791939	−	0.610600i	$-0.209072\pi$
$294$	−0.613349	+	0.707843i	−0.0357713	+	0.0412822i
$295$	−14.5990	+	24.3357i	−0.849989	+	1.41688i
$296$	2.67498	−	5.85739i	0.155480	−	0.340454i
$297$	1.35866	−	0.195345i	0.0788373	−	0.0113351i
$298$		−	1.43695i		−	0.0832405i
$299$	11.2715	−	1.46484i	0.651848	−	0.0847136i
$300$	−4.98357	−	0.405041i	−0.287726	−	0.0233850i
$301$	−0.694169	−	4.82805i	−0.0400112	−	0.278284i
$302$	2.75214	+	1.25686i	0.158368	+	0.0723243i
$303$	−2.23219	−	7.60214i	−0.128236	−	0.436732i
$304$	−0.967725	+	1.11681i	−0.0555029	+	0.0640537i
$305$	14.7617	−	7.29988i	0.845252	−	0.417990i
$306$	−3.64483	+	2.34239i	−0.208361	+	0.133906i
$307$	14.7438	−	6.73329i	0.841476	−	0.384289i	0.0524309	−	0.998625i	$-0.483303\pi$
$307$	14.7438	−	6.73329i	0.841476	−	0.384289i	0.789045	+	0.614335i	$0.210576\pi$
$308$	−2.55440	+	2.21340i	−0.145550	+	0.126120i
$309$	−1.21003	−	0.777638i	−0.0688361	−	0.0442383i
$310$	3.21267	−	2.20759i	0.182467	−	0.125383i
$311$	1.02746	−	7.14611i	0.0582617	−	0.405219i	−0.939732	−	0.341911i	$-0.888926\pi$
$311$	1.02746	−	7.14611i	0.0582617	−	0.405219i	0.997994	−	0.0633079i	$-0.0201650\pi$
$312$	1.28134	−	1.99380i	0.0725415	−	0.112877i
$313$	5.09748	−	4.41699i	0.288127	−	0.249663i	−0.498789	−	0.866723i	$-0.666222\pi$
$313$	5.09748	−	4.41699i	0.288127	−	0.249663i	0.786916	+	0.617060i	$0.211676\pi$
$314$	−7.44673	−	16.3061i	−0.420243	−	0.920205i
$315$	−5.32838	−	1.38754i	−0.300220	−	0.0781791i
$316$	3.48305	+	1.02272i	0.195937	+	0.0575323i
$317$	21.2988	+	18.4555i	1.19626	+	1.03656i	0.998412	+	0.0563317i	$0.0179404\pi$
$317$	21.2988	+	18.4555i	1.19626	+	1.03656i	0.197847	+	0.980233i	$0.436605\pi$
$318$	−2.17809	−	7.41790i	−0.122141	−	0.415975i
$319$	−2.56764	+	5.62235i	−0.143760	+	0.314791i
$320$	−1.73427	−	1.41149i	−0.0969488	−	0.0789046i
$321$	15.2976			0.853830
$322$	1.83903	−	11.6652i	0.102485	−	0.650074i
$323$			6.40256i			0.356248i
$324$	0.142315	+	0.989821i	0.00790638	+	0.0549901i
$325$	5.77977	−	10.3451i	0.320604	−	0.573842i
$326$	−5.91931	+	1.73807i	−0.327840	+	0.0962626i
$327$	−5.07025	−	4.39340i	−0.280386	−	0.242956i
$328$	−3.05387	+	10.4005i	−0.168622	+	0.574273i
$329$	−13.4380	+	8.63607i	−0.740860	+	0.476122i
$330$	2.82993	+	1.18830i	0.155782	+	0.0654138i
$331$	−19.0498	−	21.9846i	−1.04707	−	1.20838i	−0.977528	−	0.210804i	$-0.932392\pi$
$331$	−19.0498	−	21.9846i	−1.04707	−	1.20838i	−0.0695416	−	0.997579i	$-0.522154\pi$
$332$	7.79962	−	12.1364i	0.428060	−	0.666074i
$333$	−6.37375	−	0.916407i	−0.349279	−	0.0502188i
$334$	0.578492	−	4.02350i	0.0316537	−	0.220156i
$335$	−3.48494	−	19.8665i	−0.190403	−	1.08542i
$336$	−1.61253	−	1.86095i	−0.0879705	−	0.101523i
$337$	10.1564	−	4.63829i	0.553257	−	0.252664i	−0.119111	−	0.992881i	$-0.538004\pi$
$337$	10.1564	−	4.63829i	0.553257	−	0.252664i	0.672368	+	0.740217i	$0.265277\pi$
$338$	−3.99151	−	6.21092i	−0.217110	−	0.337829i
$339$	15.3334	+	4.50229i	0.832796	+	0.244531i
$340$	−9.68343	+	0.298841i	−0.525158	+	0.0162070i
$341$	−2.29592	+	0.674142i	−0.124331	+	0.0365068i
$342$	1.34422	+	0.613883i	0.0726869	+	0.0331950i
$343$	−19.3442	+	2.78127i	−1.04449	+	0.150174i
$344$	−1.98088			−0.106802
$345$	−10.2357	+	3.19865i	−0.551069	+	0.172210i
$346$	−23.7209			−1.27524
$347$	−15.5275	+	2.23252i	−0.833562	+	0.119848i	−0.545865	−	0.837873i	$-0.683799\pi$
$347$	−15.5275	+	2.23252i	−0.833562	+	0.119848i	−0.287697	+	0.957721i	$0.592890\pi$
$348$	−4.09604	−	1.87060i	−0.219571	−	0.100275i
$349$	19.9634	−	5.86178i	1.06862	−	0.313774i	0.300300	−	0.953845i	$-0.402913\pi$
$349$	19.9634	−	5.86178i	1.06862	−	0.313774i	0.768316	+	0.640071i	$0.221095\pi$
$350$	−8.62105	−	8.78989i	−0.460815	−	0.469840i
$351$	−2.27403	−	0.667716i	−0.121379	−	0.0356401i
$352$	0.742099	+	1.15473i	0.0395540	+	0.0615472i
$353$	−1.33026	+	0.607509i	−0.0708026	+	0.0323344i	−0.450502	−	0.892776i	$-0.648755\pi$
$353$	−1.33026	+	0.607509i	−0.0708026	+	0.0323344i	0.379699	+	0.925110i	$0.376028\pi$
$354$	8.31110	+	9.59152i	0.441730	+	0.509784i
$355$	−0.620844	+	0.108907i	−0.0329510	+	0.00578019i
$356$	−1.68983	+	11.7530i	−0.0895607	+	0.622908i
$357$	−10.5600	−	1.51830i	−0.558896	−	0.0803572i
$358$	4.57892	−	7.12493i	0.242003	−	0.376564i
$359$	−5.40862	−	6.24188i	−0.285456	−	0.329434i	0.594853	−	0.803835i	$-0.297210\pi$
$359$	−5.40862	−	6.24188i	−0.285456	−	0.329434i	−0.880309	+	0.474401i	$0.842665\pi$
$360$	−0.865713	+	2.06168i	−0.0456271	+	0.108660i
$361$	−14.1467	+	9.09154i	−0.744564	+	0.478502i
$362$	−0.970285	+	3.30449i	−0.0509970	+	0.173680i
$363$	6.88933	+	5.96964i	0.361596	+	0.313325i
$364$	5.59957	−	1.64418i	0.293497	−	0.0861785i
$365$	−16.0632	+	5.25999i	−0.840788	+	0.275320i
$366$	−1.04811	−	7.28976i	−0.0547856	−	0.381042i
$367$		−	10.9373i		−	0.570920i	−0.958391	−	0.285460i	$-0.907854\pi$
$367$		−	10.9373i		−	0.570920i	0.958391	−	0.285460i	$-0.0921464\pi$
$368$	−4.58282	−	1.41344i	−0.238896	−	0.0736804i
$369$	10.8396			0.564287
$370$	−11.1675	−	9.08899i	−0.580570	−	0.472514i
$371$	7.90823	−	17.3166i	0.410575	−	0.899034i
$372$	−0.491132	−	1.67264i	−0.0254640	−	0.0867224i
$373$	−23.5485	−	20.4049i	−1.21929	−	1.05652i	−0.996663	−	0.0816214i	$-0.973990\pi$
$373$	−23.5485	−	20.4049i	−1.21929	−	1.05652i	−0.222631	−	0.974903i	$-0.571464\pi$
$374$	5.70618	+	1.67549i	0.295060	+	0.0866373i
$375$	−3.68467	+	10.5557i	−0.190276	+	0.545095i
$376$	2.69483	+	5.90086i	0.138975	+	0.304314i
$377$	8.06551	−	6.98880i	0.415395	−	0.359942i
$378$	−1.33127	+	2.07150i	−0.0684732	+	0.106546i
$379$	4.48952	−	31.2253i	0.230611	−	1.60394i	−0.464862	−	0.885383i	$-0.653896\pi$
$379$	4.48952	−	31.2253i	0.230611	−	1.60394i	0.695473	−	0.718552i	$-0.255195\pi$
$380$	1.87137	+	2.72338i	0.0959994	+	0.139706i
$381$	−0.0220569	−	0.0141751i	−0.00113001	−	0.000726214i
$382$	3.65600	−	3.16794i	0.187057	−	0.162086i
$383$	10.5776	−	4.83061i	0.540488	−	0.246833i	−0.126414	−	0.991978i	$-0.540347\pi$
$383$	10.5776	−	4.83061i	0.540488	−	0.246833i	0.666903	+	0.745145i	$0.267620\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	3.35020	+	6.77470i	0.170742	+	0.345271i
$386$	−0.129851	+	0.149856i	−0.00660922	+	0.00762745i
$387$	0.558077	+	1.90064i	0.0283686	+	0.0966147i
$388$	−1.50651	−	0.688000i	−0.0764815	−	0.0349279i
$389$	2.05492	+	14.2923i	0.104188	+	0.724646i	0.973218	+	0.229885i	$0.0738352\pi$
$389$	2.05492	+	14.2923i	0.104188	+	0.724646i	−0.869029	+	0.494761i	$0.835256\pi$
$390$	−3.59237	−	3.89618i	−0.181907	−	0.197291i
$391$	−19.0162	+	8.37454i	−0.961688	+	0.423519i
$392$			0.936610i			0.0473060i
$393$	−5.45151	+	0.783809i	−0.274992	+	0.0395379i
$394$	7.95786	−	17.4253i	0.400911	−	0.877873i
$395$	4.17574	−	6.96070i	0.210104	−	0.350231i
$396$	0.898880	−	1.03736i	0.0451704	−	0.0521295i
$397$	−3.69214	+	12.5743i	−0.185303	+	0.631086i	0.813472	+	0.581605i	$0.197575\pi$
$397$	−3.69214	+	12.5743i	−0.185303	+	0.631086i	−0.998775	+	0.0494810i	$0.984243\pi$
$398$	0.127958	+	0.199107i	0.00641396	+	0.00998032i
$399$	1.51162	+	3.30999i	0.0756757	+	0.165707i
$400$	−4.03157	+	2.95743i	−0.201579	+	0.147872i
$401$	19.4204	+	12.4808i	0.969810	+	0.623259i	0.926696	−	0.375811i	$-0.122636\pi$
$401$	19.4204	+	12.4808i	0.969810	+	0.623259i	0.0431139	+	0.999070i	$0.486272\pi$
$402$	−8.92842	−	1.28371i	−0.445309	−	0.0640258i
$403$	4.08953	+	0.587985i	0.203714	+	0.0292896i
$404$	−6.66532	−	4.28354i	−0.331612	−	0.213114i
$405$	2.22207	+	0.249802i	0.110416	+	0.0124127i
$406$	−4.60616	−	10.0861i	−0.228600	−	0.500564i
$407$	4.77859	+	7.43564i	0.236866	+	0.368571i
$408$	−1.22064	+	4.15712i	−0.0604307	+	0.205808i
$409$	−4.90589	+	5.66169i	−0.242580	+	0.279953i	−0.863964	−	0.503554i	$-0.832026\pi$
$409$	−4.90589	+	5.66169i	−0.242580	+	0.279953i	0.621383	+	0.783507i	$0.286571\pi$
$410$	20.7849	+	12.4689i	1.02649	+	0.615795i
$411$	−5.02020	+	10.9927i	−0.247628	+	0.542230i
$412$	−1.42372	+	0.204700i	−0.0701418	+	0.0100849i
$413$			31.2512i			1.53777i
$414$	−0.0650526	+	4.79539i	−0.00319716	+	0.235681i
$415$	−21.8671	−	23.7164i	−1.07341	−	1.16419i
$416$	−0.337291	−	2.34591i	−0.0165371	−	0.115018i
$417$	0.365783	+	0.167048i	0.0179125	+	0.00818036i
$418$	−0.571470	−	1.94625i	−0.0279515	−	0.0951940i
$419$	18.2376	−	21.0474i	0.890967	−	1.02823i	−0.108450	−	0.994102i	$-0.534589\pi$
$419$	18.2376	−	21.0474i	0.890967	−	1.02823i	0.999417	−	0.0341292i	$-0.0108658\pi$
$420$	−4.93557	+	2.44072i	−0.240831	+	0.119095i
$421$	26.7271	−	17.1765i	1.30260	−	0.837129i	0.309106	−	0.951028i	$-0.399970\pi$
$421$	26.7271	−	17.1765i	1.30260	−	0.837129i	0.993492	+	0.113899i	$0.0363339\pi$
$422$	−20.0098	+	9.13816i	−0.974061	+	0.444839i
$423$	4.90261	−	4.24814i	0.238373	−	0.206551i
$424$	−6.50379	−	4.17973i	−0.315852	−	0.202986i
$425$	−4.80988	+	21.1224i	−0.233313	+	1.02459i
$426$	−0.0401170	+	0.279020i	−0.00194368	+	0.0135186i
$427$	9.80444	−	15.2560i	0.474470	−	0.738290i
$428$	11.5612	−	10.0178i	0.558830	−	0.484229i
$429$	1.35142	+	2.95919i	0.0652471	+	0.142871i
$430$	−1.11621	+	4.28642i	−0.0538283	+	0.206710i
$431$	26.2934	+	7.72045i	1.26651	+	0.371881i	0.844914	−	0.534903i	$-0.179652\pi$
$431$	26.2934	+	7.72045i	1.26651	+	0.371881i	0.421596	+	0.906784i	$0.361470\pi$
$432$	0.755750	+	0.654861i	0.0363610	+	0.0315070i
$433$	−1.12139	−	3.81912i	−0.0538908	−	0.183535i	0.928149	−	0.372209i	$-0.121399\pi$
$433$	−1.12139	−	3.81912i	−0.0538908	−	0.183535i	−0.982040	+	0.188673i	$0.939581\pi$
$434$	1.78320	−	3.90467i	0.0855965	−	0.187430i
$435$	−6.35589	+	7.80937i	−0.304742	+	0.374431i
$436$	−6.70891			−0.321298
$437$	5.90951	+	3.91208i	0.282690	+	0.187140i
$438$			7.55904i			0.361185i
$439$	−3.36973	−	23.4370i	−0.160828	−	1.11858i	−0.897077	−	0.441874i	$-0.854314\pi$
$439$	−3.36973	−	23.4370i	−0.160828	−	1.11858i	0.736249	−	0.676711i	$-0.236595\pi$
$440$	2.91689	−	0.955149i	0.139057	−	0.0455349i
$441$	0.898671	−	0.263874i	0.0427939	−	0.0125654i
$442$	−7.76039	−	6.72442i	−0.369124	−	0.319848i
$443$	−1.33569	+	4.54893i	−0.0634603	+	0.216126i	−0.985118	−	0.171877i	$-0.945017\pi$
$443$	−1.33569	+	4.54893i	−0.0634603	+	0.216126i	0.921658	+	0.388003i	$0.126835\pi$
$444$	−5.41708	+	3.48135i	−0.257083	+	0.165217i
$445$	24.4802	+	10.2794i	1.16047	+	0.487288i
$446$	5.11600	+	5.90418i	0.242250	+	0.279571i
$447$	−0.776875	+	1.20884i	−0.0367449	+	0.0571763i
$448$	−2.43733	−	0.350435i	−0.115153	−	0.0165565i
$449$	3.45421	−	24.0246i	0.163014	−	1.13379i	−0.729897	−	0.683557i	$-0.760432\pi$
$449$	3.45421	−	24.0246i	0.163014	−	1.13379i	0.892911	−	0.450233i	$-0.148659\pi$
$450$	3.97346	+	3.03506i	0.187311	+	0.143074i
$451$	−9.74351	−	11.2446i	−0.458804	−	0.529488i
$452$	14.5366	−	6.63863i	0.683743	−	0.312255i
$453$	−1.63574	−	2.54526i	−0.0768538	−	0.119587i
$454$	22.8595	+	6.71215i	1.07285	+	0.315017i
$455$	−0.402534	−	13.0434i	−0.0188711	−	0.611484i
$456$	1.41790	−	0.416332i	0.0663992	−	0.0194966i
$457$	18.0715	+	8.25297i	0.845349	+	0.386058i	0.790519	−	0.612438i	$-0.209811\pi$
$457$	18.0715	+	8.25297i	0.845349	+	0.386058i	0.0548300	+	0.998496i	$0.482538\pi$
$458$	−28.2864	+	4.06697i	−1.32174	+	0.190037i
$459$	4.33262			0.202229
$460$	−5.64092	+	9.12031i	−0.263009	+	0.425237i
$461$	30.6721			1.42854			0.714271	−	0.699869i	$-0.246758\pi$
$461$	30.6721			1.42854			0.714271	+	0.699869i	$0.246758\pi$
$462$	3.34555	−	0.481017i	0.155649	−	0.0223790i
$463$	−8.79152	−	4.01495i	−0.408576	−	0.186591i	0.200515	−	0.979691i	$-0.435738\pi$
$463$	−8.79152	−	4.01495i	−0.408576	−	0.186591i	−0.609091	+	0.793100i	$0.708466\pi$
$464$	−4.32057	+	1.26863i	−0.200577	+	0.0588948i
$465$	−3.89618	+	0.120241i	−0.180681	+	0.00557602i
$466$	11.7648	+	3.45446i	0.544994	+	0.160025i
$467$	−14.2636	−	22.1946i	−0.660041	−	1.02704i	−0.996356	−	0.0852943i	$-0.972817\pi$
$467$	−14.2636	−	22.1946i	−0.660041	−	1.02704i	0.336315	−	0.941750i	$-0.390819\pi$
$468$	−2.15586	+	0.984548i	−0.0996547	+	0.0455108i
$469$	−14.5454	−	16.7862i	−0.671642	−	0.775117i
$470$	14.2874	−	2.50626i	0.659029	−	0.115605i
$471$	−2.55114	+	17.7435i	−0.117550	+	0.817580i
$472$	12.5622	+	1.80617i	0.578223	+	0.0831359i
$473$	1.47001	−	2.28737i	0.0675909	−	0.105174i
$474$	−2.37721	−	2.74345i	−0.109189	−	0.126011i
$475$	6.94764	−	2.51486i	0.318779	−	0.115390i
$476$	−8.97502	+	5.76789i	−0.411369	+	0.264371i
$477$	−2.17809	+	7.41790i	−0.0997280	+	0.339643i
$478$	14.2519	+	12.3494i	0.651869	+	0.564848i
$479$	14.1062	−	4.14196i	0.644529	−	0.189251i	0.0568983	−	0.998380i	$-0.481879\pi$
$479$	14.1062	−	4.14196i	0.644529	−	0.189251i	0.587631	+	0.809129i	$0.300061\pi$
$480$	0.695854	+	2.12504i	0.0317613	+	0.0969943i
$481$	−2.17192	−	15.1060i	−0.0990309	−	0.688775i
$482$		−	2.27417i		−	0.103585i
$483$	−7.85375	+	8.81910i	−0.357358	+	0.401283i
$484$	9.11589			0.414359
$485$	−2.33767	+	2.87226i	−0.106148	+	0.130423i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	7.98901	+	27.2081i	0.362017	+	1.23292i	0.916268	+	0.400566i	$0.131186\pi$
$487$	7.98901	+	27.2081i	0.362017	+	1.23292i	−0.554251	+	0.832349i	$0.686995\pi$
$488$	−5.56589	−	4.82287i	−0.251956	−	0.218321i
$489$	5.91931	+	1.73807i	0.267680	+	0.0785981i
$490$	2.02673	+	0.527773i	0.0915585	+	0.0238424i
$491$	2.49113	+	5.45482i	0.112423	+	0.246172i	0.957477	−	0.288508i	$-0.0931592\pi$
$491$	2.49113	+	5.45482i	0.112423	+	0.246172i	−0.845054	+	0.534681i	$0.820432\pi$
$492$	8.19203	−	7.09843i	0.369325	−	0.320022i
$493$	−10.5477	+	16.4126i	−0.475045	+	0.739185i
$494$	−0.498435	+	3.46669i	−0.0224256	+	0.155974i
$495$	−1.73824	−	2.52964i	−0.0781281	−	0.113699i
$496$	−1.46652	−	0.942475i	−0.0658487	−	0.0423184i
$497$	−0.524583	+	0.454554i	−0.0235308	+	0.0203895i
$498$	−13.1229	+	5.99303i	−0.588052	+	0.268554i
$499$	−5.63018	+	3.61830i	−0.252042	+	0.161977i	−0.660561	−	0.750772i	$-0.729682\pi$
$499$	−5.63018	+	3.61830i	−0.252042	+	0.161977i	0.408519	+	0.912750i	$0.366045\pi$
$500$	4.12784	+	10.3904i	0.184602	+	0.464674i
$501$	−2.66193	+	3.07203i	−0.118926	+	0.137248i
$502$	−3.91736	−	13.3413i	−0.174840	−	0.595451i
$503$	−3.63103	−	1.65824i	−0.161900	−	0.0739371i	0.332817	−	0.942991i	$-0.392001\pi$
$503$	−3.63103	−	1.65824i	−0.161900	−	0.0739371i	−0.494717	+	0.869054i	$0.664728\pi$
$504$	0.350435	+	2.43733i	0.0156096	+	0.108567i
$505$	−13.0250	+	12.0094i	−0.579606	+	0.534410i
$506$	5.03304	−	4.24300i	0.223746	−	0.188624i
$507$			7.38293i			0.327887i
$508$	−0.0259523	+	0.00373137i	−0.00115145	+	0.000165553i
$509$	−10.8577	+	23.7751i	−0.481260	+	1.05381i	0.500855	+	0.865531i	$0.333019\pi$
$509$	−10.8577	+	23.7751i	−0.481260	+	1.05381i	−0.982115	+	0.188281i	$0.939708\pi$
$510$	8.30778	+	4.98385i	0.367875	+	0.220689i
$511$	−12.1891	+	14.0670i	−0.539216	+	0.622288i
$512$	−0.281733	+	0.959493i	−0.0124509	+	0.0424040i
$513$	−0.798936	−	1.24317i	−0.0352739	−	0.0548872i
$514$	−5.14127	−	11.2578i	−0.226772	−	0.496561i
$515$	−0.359305	+	3.19615i	−0.0158329	+	0.140839i
$516$	1.66642	+	1.07094i	0.0733600	+	0.0471456i
$517$	−8.81372	−	1.26722i	−0.387627	−	0.0557324i
$518$	−15.6947	−	2.25656i	−0.689585	−	0.0991474i
$519$	19.9553	+	12.8245i	0.875941	+	0.562933i
$520$	−5.26639	−	0.592039i	−0.230946	−	0.0259626i
$521$	7.47555	+	16.3692i	0.327510	+	0.717146i	0.999731	−	0.0232042i	$-0.00738678\pi$
$521$	7.47555	+	16.3692i	0.327510	+	0.717146i	−0.672221	+	0.740351i	$0.734660\pi$
$522$	2.43449	+	3.78814i	0.106555	+	0.165802i
$523$	−8.62122	+	29.3612i	−0.376980	+	1.28387i	0.524632	+	0.851329i	$0.324203\pi$
$523$	−8.62122	+	29.3612i	−0.376980	+	1.28387i	−0.901612	+	0.432546i	$0.857615\pi$
$524$	−3.60669	+	4.16235i	−0.157559	+	0.181833i
$525$	2.50031	+	12.0554i	0.109123	+	0.526142i
$526$	5.00836	−	10.9668i	0.218375	−	0.478174i
$527$	−7.47599	+	1.07489i	−0.325659	+	0.0468227i
$528$		−	1.37263i		−	0.0597360i
$529$	−3.88959	+	22.6687i	−0.169113	+	0.985597i
$530$	−12.7094	+	11.7183i	−0.552060	+	0.509011i
$531$	−1.80617	−	12.5622i	−0.0783813	−	0.545154i
$532$	3.30999	+	1.51162i	0.143506	+	0.0655371i
$533$	7.23778	+	24.6496i	0.313503	+	1.06769i
$534$	7.77573	−	8.97367i	0.336489	−	0.388329i
$535$	−15.1629	−	30.6622i	−0.655551	−	1.32564i
$536$	−7.58830	+	4.87671i	−0.327765	+	0.210642i
$537$	−7.70406	+	3.51833i	−0.332455	+	0.151827i
$538$	23.4113	−	20.2860i	1.00933	−	0.874591i
$539$	−1.08153	−	0.695057i	−0.0465848	−	0.0299382i
$540$	1.84291	−	1.26636i	0.0793064	−	0.0544954i
$541$	1.71739	−	11.9447i	0.0738366	−	0.513545i	−0.919018	−	0.394215i	$-0.871016\pi$
$541$	1.71739	−	11.9447i	0.0738366	−	0.513545i	0.992855	−	0.119329i	$-0.0380745\pi$
$542$	2.14390	−	3.33598i	0.0920885	−	0.143293i
$543$	2.60280	−	2.25533i	0.111697	−	0.0967857i
$544$	1.79984	+	3.94109i	0.0771673	+	0.168973i
$545$	−3.78042	+	14.5174i	−0.161935	+	0.621858i
$546$	−5.59957	−	1.64418i	−0.239639	−	0.0703645i
$547$	24.5715	+	21.2913i	1.05060	+	0.910351i	0.996106	−	0.0881636i	$-0.0280998\pi$
$547$	24.5715	+	21.2913i	1.05060	+	0.910351i	0.0544945	+	0.998514i	$0.482645\pi$
$548$	3.40468	+	11.5953i	0.145441	+	0.495325i
$549$	−3.05942	+	6.69919i	−0.130573	+	0.285914i
$550$	−0.423205	−	6.85008i	−0.0180455	−	0.292088i
$551$	6.65430			0.283483
$552$	3.09115	+	3.66671i	0.131568	+	0.156066i
$553$		−	8.93874i		−	0.380114i
$554$	1.95294	+	13.5830i	0.0829727	+	0.577088i
$555$	4.48081	+	13.6837i	0.190200	+	0.580843i
$556$	0.385834	−	0.113291i	0.0163630	−	0.00480461i
$557$	−14.5164	−	12.5786i	−0.615082	−	0.532971i	0.290646	−	0.956831i	$-0.406130\pi$
$557$	−14.5164	−	12.5786i	−0.615082	−	0.532971i	−0.905728	+	0.423859i	$0.860675\pi$
$558$	−0.491132	+	1.67264i	−0.0207913	+	0.0708086i
$559$	−3.94947	+	2.53817i	−0.167045	+	0.107353i
$560$	−2.13173	+	5.07668i	−0.0900819	+	0.214529i
$561$	−3.89451	−	4.49450i	−0.164426	−	0.189758i
$562$	−13.7974	+	21.4692i	−0.582008	+	0.905622i
$563$	−31.5499	−	4.53619i	−1.32967	−	0.191177i	−0.559400	−	0.828898i	$-0.688968\pi$
$563$	−31.5499	−	4.53619i	−1.32967	−	0.191177i	−0.770268	+	0.637720i	$0.779878\pi$
$564$	0.923208	−	6.42105i	0.0388741	−	0.270375i
$565$	−6.17410	−	35.1966i	−0.259746	−	1.48073i
$566$	2.09556	+	2.41840i	0.0880828	+	0.101653i
$567$	2.23987	−	1.02292i	0.0940658	−	0.0429584i
$568$	0.152401	+	0.237140i	0.00639460	+	0.00995019i
$569$	−28.2936	−	8.30774i	−1.18613	−	0.348279i	−0.371595	−	0.928395i	$-0.621189\pi$
$569$	−28.2936	−	8.30774i	−1.18613	−	0.348279i	−0.814534	+	0.580116i	$0.803007\pi$
$570$	−0.101928	−	3.30279i	−0.00426929	−	0.138339i
$571$	27.6898	−	8.13046i	1.15878	−	0.340249i	0.354823	−	0.934934i	$-0.384541\pi$
$571$	27.6898	−	8.13046i	1.15878	−	0.340249i	0.803959	+	0.594685i	$0.202723\pi$
$572$	2.95919	+	1.35142i	0.123730	+	0.0565057i
$573$	−4.78834	+	0.688460i	−0.200036	+	0.0287608i
$574$	26.6914			1.11408
$575$	16.5568	+	17.3456i	0.690468	+	0.723363i
$576$	1.00000			0.0416667
$577$	3.69850	−	0.531763i	0.153970	−	0.0221376i	−0.0648985	−	0.997892i	$-0.520672\pi$
$577$	3.69850	−	0.531763i	0.153970	−	0.0221376i	0.218869	+	0.975754i	$0.429763\pi$
$578$	1.61151	+	0.735954i	0.0670301	+	0.0306116i
$579$	0.190255	−	0.0558640i	0.00790675	−	0.00232163i
$580$	0.310591	+	10.0642i	0.0128966	+	0.417891i
$581$	−34.0851	−	10.0083i	−1.41409	−	0.415213i
$582$	0.895396	+	1.39326i	0.0371154	+	0.0577526i
$583$	9.65291	−	4.40833i	0.399783	−	0.182575i
$584$	4.95012	+	5.71274i	0.204837	+	0.236395i
$585$	0.915656	+	5.21986i	0.0378577	+	0.215815i
$586$	−3.94142	+	27.4132i	−0.162818	+	1.13243i
$587$	22.2498	+	3.19904i	0.918349	+	0.132039i	0.585250	−	0.810853i	$-0.300997\pi$
$587$	22.2498	+	3.19904i	0.918349	+	0.132039i	0.333099	+	0.942892i	$0.391906\pi$
$588$	0.506370	−	0.787927i	0.0208823	−	0.0324936i
$589$	1.68699	+	1.94689i	0.0695113	+	0.0802204i
$590$	10.9871	−	26.1657i	0.452332	−	1.07722i
$591$	−16.1154	+	10.3567i	−0.662899	+	0.426019i
$592$	−1.81416	+	6.17846i	−0.0745615	+	0.253933i
$593$	−28.3667	−	24.5799i	−1.16488	−	1.00937i	−0.999733	−	0.0231061i	$-0.992644\pi$
$593$	−28.3667	−	24.5799i	−1.16488	−	1.00937i	−0.165148	−	0.986269i	$-0.552810\pi$
$594$	−1.31703	+	0.386714i	−0.0540383	+	0.0158671i
$595$	7.42381	+	22.6712i	0.304346	+	0.929430i
$596$	0.204500	+	1.42233i	0.00837664	+	0.0582608i
$597$		−	0.236679i		−	0.00968661i
$598$	−10.9483	+	3.05403i	−0.447710	+	0.124888i
$599$	−28.5587			−1.16688			−0.583438	−	0.812158i	$-0.698293\pi$
$599$	−28.5587			−1.16688			−0.583438	+	0.812158i	$0.698293\pi$
$600$	4.99048	−	0.308318i	0.203736	−	0.0125870i
$601$	−6.62299	+	14.5023i	−0.270157	+	0.591562i	−0.995279	−	0.0970590i	$-0.969056\pi$
$601$	−6.62299	+	14.5023i	−0.270157	+	0.591562i	0.725121	+	0.688621i	$0.241784\pi$
$602$	1.37421	+	4.68012i	0.0560085	+	0.190747i
$603$	6.81704	+	5.90700i	0.277611	+	0.240552i
$604$	−2.90300	−	0.852398i	−0.118121	−	0.0346836i
$605$	5.13674	−	19.7259i	0.208838	−	0.801972i
$606$	3.29137	+	7.20709i	0.133703	+	0.292768i
$607$	35.1373	−	30.4467i	1.42618	−	1.23579i	0.496188	−	0.868215i	$-0.334733\pi$
$607$	35.1373	−	30.4467i	1.42618	−	1.23579i	0.929993	−	0.367578i	$-0.119813\pi$
$608$	0.798936	−	1.24317i	0.0324011	−	0.0504172i
$609$	−1.57800	+	10.9752i	−0.0639438	+	0.444739i
$610$	−13.5726	+	9.32639i	−0.549537	+	0.377614i
$611$	12.9340	+	8.31215i	0.523252	+	0.336273i
$612$	3.27438	−	2.83726i	0.132359	−	0.114690i
$613$	15.5086	−	7.08256i	0.626388	−	0.286062i	−0.0768212	−	0.997045i	$-0.524477\pi$
$613$	15.5086	−	7.08256i	0.626388	−	0.286062i	0.703209	+	0.710983i	$0.251750\pi$
$614$	−13.6355	+	8.76302i	−0.550285	+	0.353647i
$615$	−10.7442	−	21.7267i	−0.433247	−	0.876104i
$616$	2.21340	−	2.55440i	0.0891804	−	0.102920i
$617$	1.34657	+	4.58599i	0.0542108	+	0.184625i	0.982147	−	0.188113i	$-0.0602371\pi$
$617$	1.34657	+	4.58599i	0.0542108	+	0.184625i	−0.927937	+	0.372738i	$0.878419\pi$
$618$	1.30838	+	0.597518i	0.0526308	+	0.0240357i
$619$	6.03690	+	41.9875i	0.242643	+	1.68762i	0.638747	+	0.769416i	$0.279453\pi$
$619$	6.03690	+	41.9875i	0.242643	+	1.68762i	−0.396104	+	0.918206i	$0.629638\pi$
$620$	−2.86580	+	2.64233i	−0.115093	+	0.106119i
$621$	2.64731	−	3.99897i	0.106233	−	0.160473i
$622$			7.21960i			0.289480i
$623$	28.9406	−	4.16102i	1.15948	−	0.166708i
$624$	−0.984548	+	2.15586i	−0.0394135	+	0.0863035i
$625$	24.8099	−	3.07731i	0.992395	−	0.123092i
$626$	−4.41699	+	5.09748i	−0.176539	+	0.203736i
$627$	−0.571470	+	1.94625i	−0.0228223	+	0.0777256i
$628$	9.69153	+	15.0803i	0.386734	+	0.601770i
$629$	11.5897	+	25.3779i	0.462111	+	1.01188i
$630$	5.47162	+	0.615110i	0.217994	+	0.0245066i
$631$	−4.92443	−	3.16474i	−0.196039	−	0.125986i	0.438939	−	0.898517i	$-0.355354\pi$
$631$	−4.92443	−	3.16474i	−0.196039	−	0.125986i	−0.634978	+	0.772530i	$0.718991\pi$
$632$	−3.59315	−	0.516617i	−0.142928	−	0.0205499i
$633$	21.7738	+	3.13059i	0.865429	+	0.124430i
$634$	−23.7085	−	15.2365i	−0.941585	−	0.605120i
$635$	−0.00654958	+	0.0582608i	−0.000259912	+	0.00231201i
$636$	3.21160	+	7.03243i	0.127348	+	0.278854i
$637$	1.20011	+	1.86741i	0.0475503	+	0.0739897i
$638$	1.74136	−	5.93053i	0.0689412	−	0.234792i
$639$	0.184598	−	0.213038i	0.00730260	−	0.00842765i
$640$	1.91750	+	1.15031i	0.0757957	+	0.0454700i
$641$	15.5861	−	34.1289i	0.615616	−	1.34801i	−0.303050	−	0.952975i	$-0.598005\pi$
$641$	15.5861	−	34.1289i	0.615616	−	1.34801i	0.918666	−	0.395036i	$-0.129268\pi$
$642$	−15.1419	+	2.17708i	−0.597603	+	0.0859224i
$643$		−	3.60991i		−	0.142361i	−0.997463	−	0.0711805i	$-0.977323\pi$
$643$		−	3.60991i		−	0.142361i	0.997463	−	0.0711805i	$-0.0226766\pi$
$644$	−0.160185	+	11.8081i	−0.00631218	+	0.465306i
$645$	3.25643	−	3.00250i	0.128222	−	0.118223i
$646$	−0.911180	−	6.33740i	−0.0358499	−	0.249342i
$647$	−28.4315	−	12.9842i	−1.11776	−	0.510463i	−0.231120	−	0.972925i	$-0.574239\pi$
$647$	−28.4315	−	12.9842i	−1.11776	−	0.510463i	−0.886639	+	0.462462i	$0.846966\pi$
$648$	−0.281733	−	0.959493i	−0.0110675	−	0.0376924i
$649$	−11.4081	+	13.1656i	−0.447805	+	0.516795i
$650$	−4.24868	+	11.0623i	−0.166647	+	0.433901i
$651$	−3.61115	+	2.32075i	−0.141532	+	0.0909572i
$652$	5.61171	−	2.56278i	0.219771	−	0.100366i
$653$	−23.3725	+	20.2523i	−0.914635	+	0.792536i	−0.978676	−	0.205412i	$-0.934147\pi$
$653$	−23.3725	+	20.2523i	−0.914635	+	0.792536i	0.0640408	+	0.997947i	$0.479601\pi$
$654$	5.64389	+	3.62711i	0.220694	+	0.141831i
$655$	6.97457	+	10.1500i	0.272519	+	0.396593i
$656$	1.54264	−	10.7293i	0.0602299	−	0.418908i
$657$	4.08672	−	6.35907i	0.159438	−	0.248091i
$658$	12.0722	−	10.4606i	0.470622	−	0.407796i
$659$	−13.3874	−	29.3143i	−0.521499	−	1.14192i	−0.968869	−	0.247575i	$-0.920366\pi$
$659$	−13.3874	−	29.3143i	−0.521499	−	1.14192i	0.447370	−	0.894349i	$-0.352361\pi$
$660$	−2.97023	−	0.773466i	−0.115616	−	0.0301071i
$661$	−4.53333	−	1.33111i	−0.176326	−	0.0517740i	0.192378	−	0.981321i	$-0.438380\pi$
$661$	−4.53333	−	1.33111i	−0.176326	−	0.0517740i	−0.368704	+	0.929547i	$0.620198\pi$
$662$	21.9846	+	19.0498i	0.854456	+	0.740390i
$663$	2.89296	+	9.85252i	0.112353	+	0.382640i
$664$	−5.99303	+	13.1229i	−0.232575	+	0.509268i
$665$	5.13616	−	6.31071i	0.199172	−	0.244719i
$666$	6.43930			0.249518
$667$	8.70380	+	19.7638i	0.337013	+	0.765258i
$668$			4.06488i			0.157275i
$669$	−1.11181	−	7.73284i	−0.0429852	−	0.298969i
$670$	6.27677	+	19.1683i	0.242493	+	0.740538i
$671$	9.69954	−	2.84804i	0.374447	−	0.109947i
$672$	1.86095	+	1.61253i	0.0717879	+	0.0622045i
$673$	−9.87698	+	33.6379i	−0.380729	+	1.29665i	0.516957	+	0.856011i	$0.327065\pi$
$673$	−9.87698	+	33.6379i	−0.380729	+	1.29665i	−0.897687	+	0.440634i	$0.854754\pi$
$674$	−9.39297	+	6.03650i	−0.361804	+	0.232517i
$675$	−1.70181	−	4.70147i	−0.0655027	−	0.180960i
$676$	4.83479	+	5.57965i	0.185954	+	0.214602i
$677$	17.8508	−	27.7764i	0.686061	−	1.06753i	−0.307201	−	0.951645i	$-0.599392\pi$
$677$	17.8508	−	27.7764i	0.686061	−	1.06753i	0.993262	−	0.115888i	$-0.0369713\pi$
$678$	−15.8181	−	2.27429i	−0.607489	−	0.0873438i
$679$	−0.580382	+	4.03665i	−0.0222730	+	0.154912i
$680$	9.54233	−	1.67389i	0.365932	−	0.0641909i
$681$	−15.6018	−	18.0054i	−0.597861	−	0.689968i
$682$	2.17661	−	0.994023i	0.0833465	−	0.0380631i
$683$	−6.05584	−	9.42307i	−0.231720	−	0.360564i	0.705849	−	0.708362i	$-0.250566\pi$
$683$	−6.05584	−	9.42307i	−0.231720	−	0.360564i	−0.937569	+	0.347799i	$0.886929\pi$
$684$	−1.41790	−	0.416332i	−0.0542147	−	0.0159189i
$685$	27.0095	−	0.833545i	1.03198	−	0.0318481i
$686$	18.7514	−	5.50592i	0.715933	−	0.210217i
$687$	25.9948	+	11.8714i	0.991764	+	0.452923i
$688$	1.96071	−	0.281908i	0.0747515	−	0.0107476i
$689$	−18.3229			−0.698047
$690$	9.67625	−	4.62278i	0.368369	−	0.175986i
$691$	−40.6308			−1.54567			−0.772834	−	0.634608i	$-0.781161\pi$
$691$	−40.6308			−1.54567			−0.772834	+	0.634608i	$0.781161\pi$
$692$	23.4795	−	3.37584i	0.892556	−	0.128330i
$693$	−3.07451	−	1.40408i	−0.116791	−	0.0533367i
$694$	15.0518	−	4.41960i	0.571358	−	0.167766i
$695$	−0.0277363	−	0.898745i	−0.00105210	−	0.0340913i
$696$	4.32057	+	1.26863i	0.163771	+	0.0480874i
$697$	−25.3906	−	39.5086i	−0.961738	−	1.49649i
$698$	−18.9260	+	8.64320i	−0.716359	+	0.327150i
$699$	−8.02956	−	9.26661i	−0.303706	−	0.350495i
$700$	9.78423	+	7.47352i	0.369809	+	0.282473i
$701$	−2.36552	+	16.4526i	−0.0893445	+	0.621405i	0.895121	+	0.445824i	$0.147089\pi$
$701$	−2.36552	+	16.4526i	−0.0893445	+	0.621405i	−0.984465	+	0.175581i	$0.943820\pi$
$702$	2.34591	+	0.337291i	0.0885407	+	0.0127302i
$703$	5.14459	−	8.00513i	0.194032	−	0.301919i
$704$	−0.898880	−	1.03736i	−0.0338778	−	0.0390971i
$705$	−13.3743	−	5.61595i	−0.503706	−	0.211509i
$706$	1.23026	−	0.790641i	0.0463015	−	0.0297562i
$707$	−5.49654	+	18.7195i	−0.206719	+	0.704019i
$708$	−9.59152	−	8.31110i	−0.360471	−	0.312350i
$709$	−14.2543	+	4.18545i	−0.535333	+	0.157188i	−0.538214	−	0.842808i	$-0.680901\pi$
$709$	−14.2543	+	4.18545i	−0.535333	+	0.157188i	0.00288153	+	0.999996i	$0.499083\pi$
$710$	0.599026	−	0.196154i	0.0224810	−	0.00736153i
$711$	0.516617	+	3.59315i	0.0193746	+	0.134754i
$712$		−	11.8739i		−	0.444992i
$713$	−3.57586	+	7.55704i	−0.133917	+	0.283013i
$714$	10.6686			0.399263
$715$	4.59182	−	5.64190i	0.171724	−	0.210995i
$716$	−3.51833	+	7.70406i	−0.131486	+	0.287914i
$717$	−5.31292	−	18.0941i	−0.198415	−	0.675738i
$718$	6.24188	+	5.40862i	0.232945	+	0.201848i
$719$	22.6693	+	6.65631i	0.845422	+	0.248238i	0.675629	−	0.737241i	$-0.263872\pi$
$719$	22.6693	+	6.65631i	0.845422	+	0.248238i	0.169793	+	0.985480i	$0.445690\pi$
$720$	0.563493	−	2.16390i	0.0210001	−	0.0806439i
$721$	1.47132	+	3.22175i	0.0547950	+	0.119984i
$722$	12.7089	−	11.0123i	0.472975	−	0.409835i
$723$	−1.22951	+	1.91315i	−0.0457259	+	0.0711509i
$724$	0.490131	−	3.40894i	0.0182156	−	0.126692i
$725$	21.9529	+	4.99899i	0.815309	+	0.185658i
$726$	−7.66878	−	4.92842i	−0.284615	−	0.182911i
$727$	−5.18426	+	4.49218i	−0.192273	+	0.166606i	−0.745677	−	0.666307i	$-0.767874\pi$
$727$	−5.18426	+	4.49218i	−0.192273	+	0.166606i	0.553404	+	0.832913i	$0.313329\pi$
$728$	−5.30858	+	2.42435i	−0.196749	+	0.0898523i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	15.1512	−	7.49248i	0.560770	−	0.277309i
$731$	5.62027	−	6.48613i	0.207873	−	0.239898i
$732$	2.07488	+	7.06640i	0.0766899	+	0.261182i
$733$	−12.4508	−	5.68609i	−0.459881	−	0.210020i	0.171983	−	0.985100i	$-0.444983\pi$
$733$	−12.4508	−	5.68609i	−0.459881	−	0.210020i	−0.631864	+	0.775079i	$0.717710\pi$
$734$	1.55653	+	10.8259i	0.0574527	+	0.399593i
$735$	−1.41966	−	1.53973i	−0.0523650	−	0.0567936i
$736$	4.73732	+	0.746846i	0.174620	+	0.0275291i
$737$		−	12.3814i		−	0.456076i
$738$	−10.7293	+	1.54264i	−0.394950	+	0.0567853i
$739$	0.375514	−	0.822260i	0.0138135	−	0.0302473i	−0.902600	−	0.430481i	$-0.858344\pi$
$739$	0.375514	−	0.822260i	0.0138135	−	0.0302473i	0.916413	+	0.400234i	$0.131071\pi$
$740$	12.3473	+	7.40718i	0.453897	+	0.272293i
$741$	2.29354	−	2.64689i	0.0842554	−	0.0972360i
$742$	−5.36333	+	18.2658i	−0.196894	+	0.670559i
$743$	−21.3637	−	33.2425i	−0.783757	−	1.21955i	−0.971432	−	0.237319i	$-0.923731\pi$
$743$	−21.3637	−	33.2425i	−0.783757	−	1.21955i	0.187674	−	0.982231i	$-0.439905\pi$
$744$	0.724175	+	1.58572i	0.0265495	+	0.0581354i
$745$	3.19301	+	0.358953i	0.116983	+	0.0131510i
$746$	26.2127	+	16.8459i	0.959715	+	0.616772i
$747$	14.2798	+	2.05312i	0.522470	+	0.0751198i
$748$	−5.88655	−	0.846358i	−0.215233	−	0.0309459i
$749$	−31.6890	−	20.3653i	−1.15789	−	0.744131i
$750$	2.14493	−	10.9727i	0.0783218	−	0.400665i
$751$	−8.29003	−	18.1526i	−0.302508	−	0.662399i	0.695940	−	0.718100i	$-0.254988\pi$
$751$	−8.29003	−	18.1526i	−0.302508	−	0.662399i	−0.998448	+	0.0557008i	$0.982261\pi$
$752$	−3.50718	−	5.45728i	−0.127894	−	0.199007i
$753$	−3.91736	+	13.3413i	−0.142756	+	0.486184i
$754$	−6.98880	+	8.06551i	−0.254517	+	0.293728i
$755$	−3.48033	+	5.80149i	−0.126662	+	0.211138i
$756$	1.02292	−	2.23987i	0.0372031	−	0.0814634i
$757$	−28.6003	+	4.11210i	−1.03950	+	0.149457i	−0.640864	−	0.767654i	$-0.721424\pi$
$757$	−28.6003	+	4.11210i	−1.03950	+	0.149457i	−0.398631	+	0.917111i	$0.630515\pi$
$758$			31.5464i			1.14582i
$759$	−6.52800	+	0.848373i	−0.236951	+	0.0307940i
$760$	−2.23990	−	2.42934i	−0.0812498	−	0.0881213i
$761$	−1.33674	−	9.29720i	−0.0484566	−	0.337023i	−0.999600	−	0.0282743i	$-0.990999\pi$
$761$	−1.33674	−	9.29720i	−0.0484566	−	0.337023i	0.951144	−	0.308749i	$-0.0999103\pi$
$762$	0.0238498	+	0.0108918i	0.000863986	+	0.000394569i
$763$	4.65422	+	15.8508i	0.168494	+	0.573838i
$764$	−3.16794	+	3.65600i	−0.114612	+	0.132269i
$765$	−4.29448	−	8.68421i	−0.155267	−	0.313978i
$766$	−9.78243	+	6.28679i	−0.353454	+	0.227151i
$767$	27.3609	−	12.4953i	0.987944	−	0.451179i
$768$	0.755750	−	0.654861i	0.0272708	−	0.0236303i
$769$	4.23787	+	2.72352i	0.152822	+	0.0982125i	0.614817	−	0.788670i	$-0.289230\pi$
$769$	4.23787	+	2.72352i	0.152822	+	0.0982125i	−0.461995	+	0.886882i	$0.652866\pi$
$770$	−4.28024	−	6.22896i	−0.154249	−	0.224476i
$771$	−1.76132	+	12.2503i	−0.0634324	+	0.441182i
$772$	0.107202	−	0.166810i	0.00385829	−	0.00600362i
$773$	19.7485	−	17.1122i	0.710303	−	0.615481i	−0.222895	−	0.974842i	$-0.571551\pi$
$773$	19.7485	−	17.1122i	0.710303	−	0.615481i	0.933199	+	0.359361i	$0.117005\pi$
$774$	−0.822885	−	1.80187i	−0.0295780	−	0.0647668i
$775$	4.10289	+	7.69024i	0.147380	+	0.276242i
$776$	1.58909	+	0.466598i	0.0570450	+	0.0167499i
$777$	11.9832	+	10.3835i	0.429896	+	0.372507i
$778$	−4.06800	−	13.8543i	−0.145845	−	0.496702i
$779$	−6.65425	+	14.5708i	−0.238413	+	0.522052i
$780$	4.11029	+	3.34528i	0.147172	+	0.119780i
$781$	−0.386929			−0.0138454
$782$	17.6308	−	10.9956i	0.630475	−	0.393201i
$783$		−	4.50297i		−	0.160923i
$784$	−0.133294	−	0.927077i	−0.00476048	−	0.0331099i
$785$	38.0935	−	12.4739i	1.35961	−	0.445212i
$786$	5.28448	−	1.55166i	0.188491	−	0.0553460i
$787$	18.9116	+	16.3870i	0.674125	+	0.584133i	0.923185	−	0.384355i	$-0.125576\pi$
$787$	18.9116	+	16.3870i	0.674125	+	0.584133i	−0.249060	+	0.968488i	$0.580122\pi$
$788$	−5.39699	+	18.3804i	−0.192260	+	0.654776i
$789$	−10.1424	+	6.51812i	−0.361079	+	0.232051i
$790$	−3.14262	+	7.48412i	−0.111809	+	0.266273i
$791$	−25.7693	−	29.7394i	−0.916252	−	1.05741i
$792$	−0.742099	+	1.15473i	−0.0263693	+	0.0410315i
$793$	−17.2770	−	2.48406i	−0.613524	−	0.0882114i
$794$	1.86506	−	12.9717i	0.0661884	−	0.460350i
$795$	17.0272	−	2.98687i	0.603893	−	0.105933i
$796$	−0.154992	−	0.178870i	−0.00549353	−	0.00633987i
$797$	32.6954	−	14.9315i	1.15813	−	0.528901i	0.258698	−	0.965958i	$-0.416707\pi$
$797$	32.6954	−	14.9315i	1.15813	−	0.528901i	0.899434	+	0.437057i	$0.143979\pi$
$798$	−1.96730	−	3.06117i	−0.0696415	−	0.108364i
$799$	−26.9676	−	7.91840i	−0.954045	−	0.280133i
$800$	3.56965	−	3.50108i	0.126206	−	0.123782i
$801$	−11.3929	+	3.34526i	−0.402548	+	0.118199i
$802$	−20.9990	−	9.58990i	−0.741499	−	0.338631i
$803$	−10.2701	+	1.47662i	−0.362425	+	0.0521089i
$804$	9.02023			0.318119
$805$	25.4614	+	7.00043i	0.897397	+	0.246733i
$806$	−4.13158			−0.145529
$807$	−30.6622	+	4.40857i	−1.07936	+	0.155189i
$808$	7.20709	+	3.29137i	0.253545	+	0.115790i
$809$	−50.4839	+	14.8234i	−1.77492	+	0.521163i	−0.994560	−	0.104170i	$-0.966781\pi$
$809$	−50.4839	+	14.8234i	−1.77492	+	0.521163i	−0.780358	+	0.625333i	$0.784963\pi$
$810$	−2.23500	+	0.0689747i	−0.0785300	+	0.00242352i
$811$	47.0871	+	13.8260i	1.65345	+	0.485498i	0.969717	−	0.244231i	$-0.0785356\pi$
$811$	47.0871	+	13.8260i	1.65345	+	0.485498i	0.683736	+	0.729729i	$0.260354\pi$
$812$	5.99467	+	9.32789i	0.210372	+	0.327345i
$813$	−3.60713	+	1.64732i	−0.126508	+	0.0577741i
$814$	−5.78816	−	6.67989i	−0.202875	−	0.234130i
$815$	−2.38345	−	13.5873i	−0.0834887	−	0.475942i
$816$	0.616596	−	4.28852i	0.0215852	−	0.150128i
$817$	−2.89746	−	0.416592i	−0.101369	−	0.0145747i
$818$	4.05021	−	6.30225i	0.141612	−	0.220353i
$819$	3.82174	+	4.41053i	0.133543	+	0.154116i
$820$	−22.3478	−	9.38399i	−0.780421	−	0.327703i
$821$	−28.6574	+	18.4170i	−1.00015	+	0.642758i	−0.934826	−	0.355106i	$-0.884445\pi$
$821$	−28.6574	+	18.4170i	−1.00015	+	0.642758i	−0.0653251	+	0.997864i	$0.520808\pi$
$822$	3.40468	−	11.5953i	0.118752	−	0.404431i
$823$	−22.4031	−	19.4124i	−0.780922	−	0.676673i	0.170227	−	0.985405i	$-0.445550\pi$
$823$	−22.4031	−	19.4124i	−0.780922	−	0.676673i	−0.951149	+	0.308732i	$0.900095\pi$
$824$	1.38010	−	0.405234i	0.0480780	−	0.0141170i
$825$	−3.34741	+	5.99146i	−0.116542	+	0.208596i
$826$	−4.44752	−	30.9332i	−0.154749	−	1.07630i
$827$			20.4925i			0.712594i	0.934373	+	0.356297i	$0.115961\pi$
$827$			20.4925i			0.712594i	−0.934373	+	0.356297i	$0.884039\pi$
$828$	−0.618065	−	4.75584i	−0.0214792	−	0.165277i
$829$	−5.54128			−0.192456			−0.0962282	−	0.995359i	$-0.530678\pi$
$829$	−5.54128			−0.192456			−0.0962282	+	0.995359i	$0.530678\pi$
$830$	25.0197	+	20.3630i	0.868446	+	0.706810i
$831$	5.70062	−	12.4826i	0.197752	−	0.433017i
$832$	0.667716	+	2.27403i	0.0231489	+	0.0788379i
$833$	−3.06682	−	2.65741i	−0.106259	−	0.0920738i
$834$	−0.385834	−	0.113291i	−0.0133603	−	0.00392295i
$835$	8.79600	+	2.29053i	0.304398	+	0.0792670i
$836$	0.842633	+	1.84511i	0.0291431	+	0.0638144i
$837$	1.31746	−	1.14159i	0.0455382	−	0.0394591i
$838$	−15.0567	+	23.4286i	−0.520124	+	0.809328i
$839$	4.17943	−	29.0685i	0.144290	−	1.00356i	−0.781063	−	0.624452i	$-0.785323\pi$
$839$	4.17943	−	29.0685i	0.144290	−	1.00356i	0.925353	−	0.379106i	$-0.123768\pi$
$840$	4.53798	−	3.11828i	0.156575	−	0.107591i
$841$	−7.33848	−	4.71616i	−0.253051	−	0.162626i
$842$	−24.0106	+	20.8053i	−0.827459	+	0.716997i
$843$	23.2142	−	10.6016i	0.799540	−	0.365138i
$844$	18.5056	−	11.8928i	0.636989	−	0.409368i
$845$	14.7982	−	7.31793i	0.509073	−	0.251744i
$846$	−4.24814	+	4.90261i	−0.146054	+	0.168555i
$847$	−6.32403	−	21.5377i	−0.217296	−	0.740043i
$848$	7.03243	+	3.21160i	0.241495	+	0.110287i
$849$	−0.455408	−	3.16743i	−0.0156296	−	0.108706i
$850$	1.75489	−	21.5919i	0.0601922	−	0.740596i
$851$	30.5050	+	4.80916i	1.04570	+	0.164856i
$852$		−	0.281889i		−	0.00965737i
$853$	23.0248	−	3.31047i	0.788355	−	0.113348i	0.263634	−	0.964623i	$-0.415079\pi$
$853$	23.0248	−	3.31047i	0.788355	−	0.113348i	0.524721	+	0.851274i	$0.324170\pi$
$854$	−7.53349	+	16.4960i	−0.257791	+	0.564483i
$855$	−1.69988	+	2.83359i	−0.0581346	+	0.0969069i
$856$	−10.0178	+	11.5612i	−0.342402	+	0.395153i
$857$	−2.47161	+	8.41753i	−0.0844285	+	0.287537i	−0.990875	−	0.134783i	$-0.956966\pi$
$857$	−2.47161	+	8.41753i	−0.0844285	+	0.287537i	0.906447	+	0.422321i	$0.138784\pi$
$858$	−1.75880	−	2.73675i	−0.0600445	−	0.0934310i
$859$	14.8316	+	32.4767i	0.506048	+	1.10809i	0.974456	+	0.224579i	$0.0721006\pi$
$859$	14.8316	+	32.4767i	0.506048	+	1.10809i	−0.468408	+	0.883513i	$0.655172\pi$
$860$	0.494826	−	4.40164i	0.0168734	−	0.150095i
$861$	−22.4542	−	14.4305i	−0.765238	−	0.491789i
$862$	−27.1245	−	3.89992i	−0.923865	−	0.132832i
$863$	−18.4051	−	2.64626i	−0.626517	−	0.0900796i	−0.178259	−	0.983984i	$-0.557046\pi$
$863$	−18.4051	−	2.64626i	−0.626517	−	0.0900796i	−0.448258	+	0.893904i	$0.647956\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	5.92552	−	52.7096i	0.201474	−	1.79218i
$866$	1.65350	+	3.62066i	0.0561882	+	0.123035i
$867$	−0.957805	−	1.49037i	−0.0325288	−	0.0506157i
$868$	−1.20936	+	4.11870i	−0.0410484	+	0.139798i
$869$	3.26302	−	3.76573i	0.110691	−	0.127744i
$870$	5.17981	−	8.63442i	0.175612	−	0.292734i
$871$	−8.88086	+	19.4464i	−0.300916	+	0.658915i
$872$	6.64062	−	0.954777i	0.224880	−	0.0323328i
$873$		−	1.65618i		−	0.0560530i
$874$	−6.40610	−	3.03125i	−0.216690	−	0.102534i
$875$	21.6853	−	16.9609i	0.733098	−	0.573382i
$876$	−1.07576	−	7.48210i	−0.0363467	−	0.252797i
$877$	−39.8205	−	18.1854i	−1.34464	−	0.614078i	−0.392506	−	0.919750i	$-0.628392\pi$
$877$	−39.8205	−	18.1854i	−1.34464	−	0.614078i	−0.952137	+	0.305672i	$0.901119\pi$
$878$	6.67085	+	22.7188i	0.225130	+	0.766724i
$879$	18.1364	−	20.9305i	0.611726	−	0.705969i
$880$	−2.75127	+	1.36054i	−0.0927451	+	0.0458639i
$881$	−12.1724	+	7.82272i	−0.410098	+	0.263554i	−0.729384	−	0.684104i	$-0.760193\pi$
$881$	−12.1724	+	7.82272i	−0.410098	+	0.263554i	0.319286	+	0.947658i	$0.396557\pi$
$882$	−0.851971	+	0.389082i	−0.0286873	+	0.0131011i
$883$	−43.8903	+	38.0312i	−1.47703	+	1.27985i	−0.599453	+	0.800410i	$0.704615\pi$
$883$	−43.8903	+	38.0312i	−1.47703	+	1.27985i	−0.877574	+	0.479441i	$0.840839\pi$
$884$	8.63839	+	5.55155i	0.290540	+	0.186719i
$885$	−23.3892	+	16.0719i	−0.786218	+	0.540250i
$886$	0.674710	−	4.69271i	0.0226673	−	0.157655i
$887$	19.0909	−	29.7060i	0.641010	−	0.997431i	−0.356983	−	0.934111i	$-0.616195\pi$
$887$	19.0909	−	29.7060i	0.641010	−	0.997431i	0.997993	−	0.0633204i	$-0.0201690\pi$
$888$	4.86649	−	4.21684i	0.163309	−	0.141508i
$889$	0.0268200	+	0.0587276i	0.000899513	+	0.00196966i
$890$	−25.6939	−	6.69084i	−0.861261	−	0.224277i
$891$	1.31703	+	0.386714i	0.0441221	+	0.0129554i
$892$	−5.90418	−	5.11600i	−0.197687	−	0.171296i
$893$	2.70078	+	9.19802i	0.0903783	+	0.307800i
$894$	0.596932	−	1.30710i	0.0199644	−	0.0437159i
$895$	14.6883	+	11.9545i	0.490975	+	0.399595i
$896$	2.46240			0.0822628
$897$	10.8614	+	3.34989i	0.362653	+	0.111850i
$898$			24.2716i			0.809955i
$899$	1.11715	+	7.76993i	0.0372589	+	0.259142i
$900$	−4.36495	−	2.43869i	−0.145498	−	0.0812896i
$901$	32.1390	−	9.43685i	1.07070	−	0.314387i
$902$	11.2446	+	9.74351i	0.374405	+	0.324423i
$903$	1.37421	−	4.68012i	0.0457307	−	0.155745i
$904$	−13.4438	+	8.63983i	−0.447136	+	0.287357i
$905$	−7.10042	−	2.98151i	−0.236026	−	0.0991086i
$906$	1.98132	+	2.28656i	0.0658249	+	0.0759660i
$907$	−15.3115	+	23.8252i	−0.508411	+	0.791103i	−0.996665	−	0.0815981i	$-0.973998\pi$
$907$	−15.3115	+	23.8252i	−0.508411	+	0.791103i	0.488254	+	0.872702i	$0.337634\pi$
$908$	−23.5820	−	3.39059i	−0.782598	−	0.112521i
$909$	1.12757	−	7.84244i	0.0373992	−	0.260117i
$910$	2.25471	+	12.8534i	0.0747428	+	0.426085i
$911$	−11.5872	−	13.3724i	−0.383901	−	0.443046i	0.530604	−	0.847620i	$-0.321965\pi$
$911$	−11.5872	−	13.3724i	−0.383901	−	0.443046i	−0.914505	+	0.404574i	$0.867420\pi$
$912$	−1.34422	+	0.613883i	−0.0445114	+	0.0203277i
$913$	−10.7060	−	16.6588i	−0.354316	−	0.551327i
$914$	−19.0621	−	5.59713i	−0.630517	−	0.185137i
$915$	16.4602	−	0.507980i	0.544157	−	0.0167933i
$916$	27.4197	−	8.05115i	0.905972	−	0.266018i
$917$	12.3363	+	5.63378i	0.407379	+	0.186044i
$918$	−4.28852	+	0.616596i	−0.141542	+	0.0203507i
$919$	34.7480			1.14623			0.573116	−	0.819475i	$-0.305735\pi$
$919$	34.7480			1.14623			0.573116	+	0.819475i	$0.305735\pi$
$920$	4.28555	−	9.83026i	0.141290	−	0.324094i
$921$	16.2086			0.534091
$922$	−30.3599	+	4.36509i	−0.999850	+	0.143757i
$923$	0.607714	+	0.277534i	0.0200032	+	0.00913514i
$924$	−3.24304	+	0.952243i	−0.106688	+	0.0313265i
$925$	22.9860	−	22.5445i	0.755776	−	0.741259i
$926$	9.27342	+	2.72292i	0.304743	+	0.0894807i
$927$	−0.777638	−	1.21003i	−0.0255410	−	0.0397425i
$928$	4.09604	−	1.87060i	0.134459	−	0.0614055i
$929$	−32.3398	−	37.3221i	−1.06103	−	1.22450i	−0.973584	−	0.228329i	$-0.926674\pi$
$929$	−32.3398	−	37.3221i	−1.06103	−	1.22450i	−0.0874495	−	0.996169i	$-0.527872\pi$
$930$	3.83941	−	0.673501i	0.125899	−	0.0220850i
$931$	−0.196976	+	1.37000i	−0.00645561	+	0.0448998i
$932$	−12.1367	−	1.74499i	−0.397550	−	0.0571591i
$933$	3.90321	−	6.07351i	0.127785	−	0.198838i
$934$	17.2770	+	19.9388i	0.565322	+	0.652417i
$935$	−5.14846	+	12.2610i	−0.168373	+	0.400978i
$936$	1.99380	−	1.28134i	0.0651694	−	0.0418818i
$937$	−8.60294	+	29.2989i	−0.281046	+	0.957154i	0.691097	+	0.722762i	$0.257128\pi$
$937$	−8.60294	+	29.2989i	−0.281046	+	0.957154i	−0.972142	+	0.234391i	$0.924690\pi$
$938$	16.7862	+	14.5454i	0.548090	+	0.474923i
$939$	6.47172	−	1.90027i	0.211197	−	0.0620129i
$940$	−13.7853	+	4.51406i	−0.449627	+	0.147233i
$941$	5.36039	+	37.2823i	0.174744	+	1.21537i	0.868695	+	0.495348i	$0.164959\pi$
$941$	5.36039	+	37.2823i	0.174744	+	1.21537i	−0.693951	+	0.720022i	$0.744132\pi$
$942$		−	17.9260i		−	0.584061i
$943$	−51.9802	−	0.705145i	−1.69271	−	0.0229627i
$944$	−12.6914			−0.413070
$945$	−4.27046	−	3.47564i	−0.138918	−	0.113063i
$946$	−1.12952	+	2.47329i	−0.0367237	+	0.0804137i
$947$	11.0913	+	37.7735i	0.360418	+	1.22747i	0.917742	+	0.397177i	$0.130010\pi$
$947$	11.0913	+	37.7735i	0.360418	+	1.22747i	−0.557323	+	0.830295i	$0.688172\pi$
$948$	2.74345	+	2.37721i	0.0891030	+	0.0772082i
$949$	17.1895	+	5.04729i	0.557995	+	0.163842i
$950$	−6.51902	+	3.47802i	−0.211505	+	0.112842i
$951$	11.7074	+	25.6356i	0.379637	+	0.831290i
$952$	8.06281	−	6.98646i	0.261317	−	0.226433i
$953$	−3.07781	+	4.78916i	−0.0997000	+	0.155136i	−0.887520	−	0.460770i	$-0.847573\pi$
$953$	−3.07781	+	4.78916i	−0.0997000	+	0.155136i	0.787820	+	0.615906i	$0.211210\pi$
$954$	1.10025	−	7.65238i	0.0356218	−	0.247755i
$955$	6.12612	+	8.91525i	0.198237	+	0.288491i
$956$	−15.8644	−	10.1954i	−0.513091	−	0.329743i
$957$	−4.67121	+	4.04763i	−0.150999	+	0.130841i
$958$	−13.3732	+	6.10732i	−0.432067	+	0.197319i
$959$	25.0336	−	16.0881i	0.808378	−	0.519513i
$960$	−0.991196	−	2.00438i	−0.0319907	−	0.0646910i
$961$	18.3106	−	21.1316i	0.590665	−	0.681663i
$962$	4.29962	+	14.6432i	0.138625	+	0.472115i
$963$	13.9152	+	6.35486i	0.448411	+	0.204782i
$964$	0.323648	+	2.25102i	0.0104240	+	0.0725005i
$965$	−0.300553	−	0.325972i	−0.00967514	−	0.0104934i
$966$	6.51872	−	9.84704i	0.209736	−	0.316823i
$967$		−	46.9609i		−	1.51016i	−0.655632	−	0.755081i	$-0.727598\pi$
$967$		−	46.9609i		−	1.51016i	0.655632	−	0.755081i	$-0.272402\pi$
$968$	−9.02311	+	1.29733i	−0.290014	+	0.0416977i
$969$	−2.65972	+	5.82398i	−0.0854426	+	0.187093i
$970$	1.90511	−	3.17571i	0.0611695	−	0.101966i
$971$	4.00582	−	4.62296i	0.128553	−	0.148358i	−0.687824	−	0.725878i	$-0.741434\pi$
$971$	4.00582	−	4.62296i	0.128553	−	0.148358i	0.816377	+	0.577520i	$0.195979\pi$
$972$	−0.281733	+	0.959493i	−0.00903658	+	0.0307758i
$973$	−0.535334	−	0.832996i	−0.0171620	−	0.0267046i
$974$	−11.7798	−	25.7942i	−0.377449	−	0.826499i
$975$	9.55497	−	7.00922i	0.306004	−	0.224475i
$976$	6.19560	+	3.98167i	0.198316	+	0.127450i
$977$	−23.3775	−	3.36118i	−0.747914	−	0.107534i	−0.242189	−	0.970229i	$-0.577866\pi$
$977$	−23.3775	−	3.36118i	−0.747914	−	0.107534i	−0.505724	+	0.862695i	$0.668775\pi$
$978$	−6.10641	−	0.877969i	−0.195262	−	0.0280744i
$979$	13.7111	+	8.81158i	0.438208	+	0.281619i
$980$	−2.08121	−	0.233967i	−0.0664820	−	0.00747379i
$981$	−2.78698	−	6.10264i	−0.0889814	−	0.194842i
$982$	−3.24208	−	5.04477i	−0.103459	−	0.160985i
$983$	5.17236	−	17.6155i	0.164973	−	0.561846i	−0.834961	−	0.550310i	$-0.814510\pi$
$983$	5.17236	−	17.6155i	0.164973	−	0.561846i	0.999933	−	0.0115361i	$-0.00367214\pi$
$984$	−7.09843	+	8.19203i	−0.226290	+	0.261152i
$985$	36.7323	+	22.0358i	1.17039	+	0.702119i
$986$	8.10461	−	17.7466i	0.258103	−	0.565167i
$987$	−15.8112	+	2.27330i	−0.503275	+	0.0723601i
$988$		−	3.50234i		−	0.111424i
$989$	−2.55256	−	9.15059i	−0.0811665	−	0.290972i
$990$	2.08055	+	2.25651i	0.0661243	+	0.0717166i
$991$	7.08164	+	49.2539i	0.224956	+	1.56460i	0.718903	+	0.695110i	$0.244644\pi$
$991$	7.08164	+	49.2539i	0.224956	+	1.56460i	−0.493947	+	0.869492i	$0.664446\pi$
$992$	1.58572	+	0.724175i	0.0503467	+	0.0229926i
$993$	−8.19554	−	27.9115i	−0.260078	−	0.885743i
$994$	0.454554	−	0.524583i	0.0144176	−	0.0166388i
$995$	−0.474393	+	0.234595i	−0.0150393	+	0.00743716i
$996$	12.1364	−	7.79962i	0.384558	−	0.247140i
$997$	−12.5957	+	5.75226i	−0.398910	+	0.182176i	−0.604760	−	0.796408i	$-0.706731\pi$
$997$	−12.5957	+	5.75226i	−0.398910	+	0.182176i	0.205851	+	0.978583i	$0.434004\pi$
$998$	5.05794	−	4.38273i	0.160106	−	0.138733i
$999$	−5.41708	−	3.48135i	−0.171389	−	0.110145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.b.49.3	✓	120
5.4	even	2	inner	690.2.r.b.49.12	yes	120
23.8	even	11	inner	690.2.r.b.169.12	yes	120
115.54	even	22	inner	690.2.r.b.169.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.b.49.3	✓	120	1.1	even	1	trivial
690.2.r.b.49.12	yes	120	5.4	even	2	inner
690.2.r.b.169.3	yes	120	115.54	even	22	inner
690.2.r.b.169.12	yes	120	23.8	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-0.0689747 - 2.23500i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.33127 - 2.07150i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-0.0689747 - 2.23500i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.33127 - 2.07150i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(0.386347 + 2.20244i) q^{10} +(0.195345 - 1.35866i) q^{11} +(0.989821 + 0.142315i) q^{12} +(-1.28134 + 1.99380i) q^{13} +(1.61253 + 1.86095i) q^{14} +(0.865713 - 2.06168i) q^{15} +(0.841254 - 0.540641i) q^{16} +(1.22064 - 4.15712i) q^{17} +(-0.755750 - 0.654861i) q^{18} +(-1.41790 + 0.416332i) q^{19} +(-0.695854 - 2.12504i) q^{20} +(-0.350435 - 2.43733i) q^{21} +1.37263i q^{22} +(-3.09115 - 3.66671i) q^{23} -1.00000 q^{24} +(-4.99048 + 0.308318i) q^{25} +(0.984548 - 2.15586i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-1.86095 - 1.61253i) q^{28} +(-4.32057 - 1.26863i) q^{29} +(-0.563493 + 2.16390i) q^{30} +(-0.724175 - 1.58572i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(0.742099 - 1.15473i) q^{33} +(-0.616596 + 4.28852i) q^{34} +(-4.53798 + 3.11828i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-4.86649 + 4.21684i) q^{37} +(1.34422 - 0.613883i) q^{38} +(-1.99380 + 1.28134i) q^{39} +(0.991196 + 2.00438i) q^{40} +(7.09843 - 8.19203i) q^{41} +(0.693737 + 2.36265i) q^{42} +(1.80187 + 0.822885i) q^{43} +(-0.195345 - 1.35866i) q^{44} +(1.64393 - 1.51574i) q^{45} +(3.58151 + 3.18948i) q^{46} -6.48708i q^{47} +(0.989821 - 0.142315i) q^{48} +(0.389082 - 0.851971i) q^{49} +(4.89581 - 1.01540i) q^{50} +(2.83726 - 3.27438i) q^{51} +(-0.667716 + 2.27403i) q^{52} +(4.17973 + 6.50379i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-3.05008 - 0.342885i) q^{55} +(2.07150 + 1.33127i) q^{56} +(-1.46272 - 0.210307i) q^{57} +(4.45714 + 0.640839i) q^{58} +(-10.6767 - 6.86149i) q^{59} +(0.249802 - 2.22207i) q^{60} +(3.05942 + 6.69919i) q^{61} +(0.942475 + 1.46652i) q^{62} +(0.693737 - 2.36265i) q^{63} +(0.654861 - 0.755750i) q^{64} +(4.54453 + 2.72627i) q^{65} +(-0.570210 + 1.24859i) q^{66} +(8.92842 - 1.28371i) q^{67} -4.33262i q^{68} +(-1.28860 - 4.61947i) q^{69} +(4.04802 - 3.73236i) q^{70} +(-0.0401170 - 0.279020i) q^{71} +(-0.909632 - 0.415415i) q^{72} +(-2.12963 - 7.25284i) q^{73} +(4.21684 - 4.86649i) q^{74} +(-4.66758 - 1.79267i) q^{75} +(-1.24317 + 0.798936i) q^{76} +(-3.07451 + 1.40408i) q^{77} +(1.79115 - 1.55204i) q^{78} +(3.05383 + 1.96258i) q^{79} +(-1.26636 - 1.84291i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-5.86033 + 9.11886i) q^{82} +(10.9029 - 9.44742i) q^{83} +(-1.02292 - 2.23987i) q^{84} +(-9.37537 - 2.44140i) q^{85} +(-1.90064 - 0.558077i) q^{86} +(-3.40312 - 2.94882i) q^{87} +(0.386714 + 1.31703i) q^{88} +(-4.93258 + 10.8009i) q^{89} +(-1.41149 + 1.73427i) q^{90} +5.83596 q^{91} +(-3.99897 - 2.64731i) q^{92} -1.74326i q^{93} +(0.923208 + 6.42105i) q^{94} +(1.02830 + 3.14029i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(-1.25165 - 1.08456i) q^{97} +(-0.263874 + 0.898671i) q^{98} +(1.15473 - 0.742099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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