LMFDB - Embedded newform 966.2.r.b.701.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(113,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("966.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			701.13
Character	$\chi$	$=$	966.701
Dual form			966.2.r.b.113.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 + 0.841254i) q^{2} +(-1.58317 + 0.702554i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.47166 - 0.432119i) q^{5} +(-1.44695 - 0.952016i) q^{6} +(-0.755750 + 0.654861i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.01284 - 2.22452i) q^{9} +O(q^{10})$	\(q+(0.540641 + 0.841254i) q^{2} +(-1.58317 + 0.702554i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.47166 - 0.432119i) q^{5} +(-1.44695 - 0.952016i) q^{6} +(-0.755750 + 0.654861i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.01284 - 2.22452i) q^{9} +(1.15916 + 1.00442i) q^{10} +(-4.02571 - 2.58716i) q^{11} +(0.0186059 - 1.73195i) q^{12} +(3.32052 - 3.83209i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-2.02630 + 1.71804i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.822964 - 1.80204i) q^{17} +(2.95961 + 0.490639i) q^{18} +(-5.65727 - 2.58359i) q^{19} +(-0.218281 + 1.51818i) q^{20} +(0.736403 - 1.56771i) q^{21} -4.78537i q^{22} +(1.11914 - 4.66342i) q^{23} +(1.46707 - 0.920711i) q^{24} +(-2.22721 + 1.43134i) q^{25} +(5.01897 + 0.721619i) q^{26} +(-1.62381 + 4.93591i) q^{27} +(-0.281733 - 0.959493i) q^{28} +(2.37958 - 1.08672i) q^{29} +(-2.54081 - 0.775790i) q^{30} +(0.789658 + 5.49220i) q^{31} +(0.281733 - 0.959493i) q^{32} +(8.19099 + 1.26764i) q^{33} +(1.07104 - 1.66658i) q^{34} +(-0.829230 + 1.29031i) q^{35} +(1.18733 + 2.75504i) q^{36} +(0.902936 - 3.07512i) q^{37} +(-0.885098 - 6.15599i) q^{38} +(-2.56469 + 8.39968i) q^{39} +(-1.39519 + 0.637160i) q^{40} +(-2.42026 - 8.24266i) q^{41} +(1.71697 - 0.228066i) q^{42} +(4.26663 + 0.613449i) q^{43} +(4.02571 - 2.58716i) q^{44} +(2.00096 - 4.14353i) q^{45} +(4.52818 - 1.57975i) q^{46} -7.86753i q^{47} +(1.56771 + 0.736403i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-2.40824 - 1.09980i) q^{50} +(2.56892 + 2.27475i) q^{51} +(2.10639 + 4.61236i) q^{52} +(-4.60242 - 5.31148i) q^{53} +(-5.03025 + 1.30252i) q^{54} +(-7.04244 - 2.06785i) q^{55} +(0.654861 - 0.755750i) q^{56} +(10.7715 + 0.115716i) q^{57} +(2.20070 + 1.41431i) q^{58} +(11.2971 + 9.78900i) q^{59} +(-0.721027 - 2.55689i) q^{60} +(11.2272 - 1.61423i) q^{61} +(-4.19341 + 3.63361i) q^{62} +(-0.0644489 + 2.99931i) q^{63} +(0.959493 - 0.281733i) q^{64} +(3.23077 - 7.07440i) q^{65} +(3.36198 + 7.57603i) q^{66} +(0.714523 + 1.11182i) q^{67} +1.98106 q^{68} +(1.50452 + 8.16924i) q^{69} -1.53379 q^{70} +(-6.86593 - 10.6836i) q^{71} +(-1.67577 + 2.48833i) q^{72} +(-5.50379 + 12.0516i) q^{73} +(3.07512 - 0.902936i) q^{74} +(2.52045 - 3.83078i) q^{75} +(4.70023 - 4.07277i) q^{76} +(4.73666 - 0.681029i) q^{77} +(-8.45284 + 2.38365i) q^{78} +(-9.23367 - 8.00102i) q^{79} +(-1.29031 - 0.829230i) q^{80} +(-0.896982 - 8.95519i) q^{81} +(5.62568 - 6.49238i) q^{82} +(2.43946 + 0.716290i) q^{83} +(1.12013 + 1.32111i) q^{84} +(-1.98982 - 2.29637i) q^{85} +(1.79065 + 3.92097i) q^{86} +(-3.00379 + 3.39224i) q^{87} +(4.35292 + 1.98791i) q^{88} +(-1.21799 + 8.47132i) q^{89} +(4.56755 - 0.556847i) q^{90} +5.07058i q^{91} +(3.77709 + 2.95526i) q^{92} +(-5.10872 - 8.14029i) q^{93} +(6.61858 - 4.25351i) q^{94} +(-9.44201 - 1.35756i) q^{95} +(0.228066 + 1.71697i) q^{96} +(0.679054 + 2.31265i) q^{97} +(0.909632 - 0.415415i) q^{98} +(-13.8583 + 3.74773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	−1.58317	+	0.702554i	−0.914042	+	0.405620i
$3$	−1.58317	+	0.702554i	−0.914042	+	0.405620i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	1.47166	−	0.432119i	0.658147	−	0.193249i	0.0644287	−	0.997922i	$-0.479477\pi$
$5$	1.47166	−	0.432119i	0.658147	−	0.193249i	0.593718	+	0.804673i	$0.297659\pi$
$6$	−1.44695	−	0.952016i	−0.590715	−	0.388659i
$7$	−0.755750	+	0.654861i	−0.285646	+	0.247514i
$7$	−0.755750	+	0.654861i	−0.285646	+	0.247514i
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	2.01284	−	2.22452i	0.670945	−	0.741507i
$10$	1.15916	+	1.00442i	0.366559	+	0.317625i
$11$	−4.02571	−	2.58716i	−1.21380	−	0.780059i	−0.232506	−	0.972595i	$-0.574693\pi$
$11$	−4.02571	−	2.58716i	−1.21380	−	0.780059i	−0.981290	+	0.192536i	$0.938329\pi$
$12$	0.0186059	−	1.73195i	0.00537106	−	0.499971i
$13$	3.32052	−	3.83209i	0.920947	−	1.06283i	−0.0768862	−	0.997040i	$-0.524498\pi$
$13$	3.32052	−	3.83209i	0.920947	−	1.06283i	0.997833	−	0.0657900i	$-0.0209567\pi$
$14$	−0.959493	−	0.281733i	−0.256435	−	0.0752962i
$15$	−2.02630	+	1.71804i	−0.523188	+	0.443596i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.822964	−	1.80204i	−0.199598	−	0.437059i	0.783193	−	0.621778i	$-0.213590\pi$
$17$	−0.822964	−	1.80204i	−0.199598	−	0.437059i	−0.982791	+	0.184720i	$0.940862\pi$
$18$	2.95961	+	0.490639i	0.697586	+	0.115645i
$19$	−5.65727	−	2.58359i	−1.29787	−	0.592716i	−0.357830	−	0.933787i	$-0.616483\pi$
$19$	−5.65727	−	2.58359i	−1.29787	−	0.592716i	−0.940038	+	0.341071i	$0.889210\pi$
$20$	−0.218281	+	1.51818i	−0.0488092	+	0.339475i
$21$	0.736403	−	1.56771i	0.160696	−	0.342102i
$22$		−	4.78537i		−	1.02024i
$23$	1.11914	−	4.66342i	0.233357	−	0.972391i
$23$	1.11914	−	4.66342i	0.233357	−	0.972391i
$24$	1.46707	−	0.920711i	0.299464	−	0.187939i
$25$	−2.22721	+	1.43134i	−0.445441	+	0.286268i
$26$	5.01897	+	0.721619i	0.984300	+	0.141521i
$27$	−1.62381	+	4.93591i	−0.312502	+	0.949917i
$28$	−0.281733	−	0.959493i	−0.0532424	−	0.181327i
$29$	2.37958	−	1.08672i	0.441877	−	0.201798i	−0.182037	−	0.983292i	$-0.558269\pi$
$29$	2.37958	−	1.08672i	0.441877	−	0.201798i	0.623913	+	0.781493i	$0.285542\pi$
$30$	−2.54081	−	0.775790i	−0.463886	−	0.141639i
$31$	0.789658	+	5.49220i	0.141827	+	0.986427i	0.929101	+	0.369825i	$0.120582\pi$
$31$	0.789658	+	5.49220i	0.141827	+	0.986427i	−0.787275	+	0.616603i	$0.788509\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	8.19099	+	1.26764i	1.42587	+	0.220667i
$34$	1.07104	−	1.66658i	0.183682	−	0.285816i
$35$	−0.829230	+	1.29031i	−0.140165	+	0.218102i
$36$	1.18733	+	2.75504i	0.197889	+	0.459173i
$37$	0.902936	−	3.07512i	0.148442	−	0.505546i	−0.851378	−	0.524553i	$-0.824232\pi$
$37$	0.902936	−	3.07512i	0.148442	−	0.505546i	0.999819	+	0.0190071i	$0.00605052\pi$
$38$	−0.885098	−	6.15599i	−0.143582	−	0.998634i
$39$	−2.56469	+	8.39968i	−0.410680	+	1.34503i
$40$	−1.39519	+	0.637160i	−0.220598	+	0.100744i
$41$	−2.42026	−	8.24266i	−0.377982	−	1.28729i	−0.900573	−	0.434705i	$-0.856853\pi$
$41$	−2.42026	−	8.24266i	−0.377982	−	1.28729i	0.522591	−	0.852583i	$-0.324965\pi$
$42$	1.71697	−	0.228066i	0.264934	−	0.0351913i
$43$	4.26663	+	0.613449i	0.650655	+	0.0935500i	0.459736	−	0.888056i	$-0.347944\pi$
$43$	4.26663	+	0.613449i	0.650655	+	0.0935500i	0.190919	+	0.981606i	$0.438853\pi$
$44$	4.02571	−	2.58716i	0.606898	−	0.390030i
$45$	2.00096	−	4.14353i	0.298285	−	0.617680i
$46$	4.52818	−	1.57975i	0.667643	−	0.232922i
$47$		−	7.86753i		−	1.14760i	−0.818997	−	0.573798i	$-0.805469\pi$
$47$		−	7.86753i		−	1.14760i	0.818997	−	0.573798i	$-0.194531\pi$
$48$	1.56771	+	0.736403i	0.226279	+	0.106291i
$49$	0.142315	−	0.989821i	0.0203307	−	0.141403i
$50$	−2.40824	−	1.09980i	−0.340576	−	0.155536i
$51$	2.56892	+	2.27475i	0.359720	+	0.318529i
$52$	2.10639	+	4.61236i	0.292104	+	0.639619i
$53$	−4.60242	−	5.31148i	−0.632191	−	0.729588i	0.345783	−	0.938315i	$-0.387613\pi$
$53$	−4.60242	−	5.31148i	−0.632191	−	0.729588i	−0.977974	+	0.208727i	$0.933068\pi$
$54$	−5.03025	+	1.30252i	−0.684531	+	0.177251i
$55$	−7.04244	−	2.06785i	−0.949602	−	0.278828i
$56$	0.654861	−	0.755750i	0.0875094	−	0.100991i
$57$	10.7715	+	0.115716i	1.42672	+	0.0153269i
$58$	2.20070	+	1.41431i	0.288966	+	0.185707i
$59$	11.2971	+	9.78900i	1.47076	+	1.27442i	0.886398	+	0.462925i	$0.153200\pi$
$59$	11.2971	+	9.78900i	1.47076	+	1.27442i	0.584360	+	0.811494i	$0.301345\pi$
$60$	−0.721027	−	2.55689i	−0.0930842	−	0.330093i
$61$	11.2272	−	1.61423i	1.43750	−	0.206681i	0.620903	−	0.783888i	$-0.286766\pi$
$61$	11.2272	−	1.61423i	1.43750	−	0.206681i	0.816599	+	0.577206i	$0.195857\pi$
$62$	−4.19341	+	3.63361i	−0.532563	+	0.461469i
$63$	−0.0644489	+	2.99931i	−0.00811980	+	0.377877i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	3.23077	−	7.07440i	0.400728	−	0.877471i
$66$	3.36198	+	7.57603i	0.413831	+	0.932545i
$67$	0.714523	+	1.11182i	0.0872929	+	0.135830i	0.882154	−	0.470961i	$-0.156093\pi$
$67$	0.714523	+	1.11182i	0.0872929	+	0.135830i	−0.794861	+	0.606791i	$0.792456\pi$
$68$	1.98106			0.240239
$69$	1.50452	+	8.16924i	0.181123	+	0.983461i
$70$	−1.53379			−0.183323
$71$	−6.86593	−	10.6836i	−0.814836	−	1.26791i	−0.960418	−	0.278563i	$-0.910142\pi$
$71$	−6.86593	−	10.6836i	−0.814836	−	1.26791i	0.145582	−	0.989346i	$-0.453495\pi$
$72$	−1.67577	+	2.48833i	−0.197491	+	0.293253i
$73$	−5.50379	+	12.0516i	−0.644170	+	1.41054i	0.252395	+	0.967624i	$0.418782\pi$
$73$	−5.50379	+	12.0516i	−0.644170	+	1.41054i	−0.896565	+	0.442912i	$0.853945\pi$
$74$	3.07512	−	0.902936i	0.357475	−	0.104964i
$75$	2.52045	−	3.83078i	0.291036	−	0.442340i
$76$	4.70023	−	4.07277i	0.539154	−	0.467179i
$77$	4.73666	−	0.681029i	0.539792	−	0.0776104i
$78$	−8.45284	+	2.38365i	−0.957096	+	0.269895i
$79$	−9.23367	−	8.00102i	−1.03887	−	0.900185i	−0.0437677	−	0.999042i	$-0.513936\pi$
$79$	−9.23367	−	8.00102i	−1.03887	−	0.900185i	−0.995102	+	0.0988563i	$0.968482\pi$
$80$	−1.29031	−	0.829230i	−0.144261	−	0.0927107i
$81$	−0.896982	−	8.95519i	−0.0996647	−	0.995021i
$82$	5.62568	−	6.49238i	0.621252	−	0.716963i
$83$	2.43946	+	0.716290i	0.267765	+	0.0786230i	0.412859	−	0.910795i	$-0.364530\pi$
$83$	2.43946	+	0.716290i	0.267765	+	0.0786230i	−0.145094	+	0.989418i	$0.546348\pi$
$84$	1.12013	+	1.32111i	0.122216	+	0.144144i
$85$	−1.98982	−	2.29637i	−0.215826	−	0.249077i
$86$	1.79065	+	3.92097i	0.193091	+	0.422809i
$87$	−3.00379	+	3.39224i	−0.322040	+	0.363686i
$88$	4.35292	+	1.98791i	0.464023	+	0.211912i
$89$	−1.21799	+	8.47132i	−0.129107	+	0.897958i	0.817583	+	0.575811i	$0.195314\pi$
$89$	−1.21799	+	8.47132i	−0.129107	+	0.897958i	−0.946690	+	0.322147i	$0.895595\pi$
$90$	4.56755	−	0.556847i	0.481463	−	0.0586969i
$91$			5.07058i			0.531541i
$92$	3.77709	+	2.95526i	0.393789	+	0.308108i
$93$	−5.10872	−	8.14029i	−0.529750	−	0.844108i
$94$	6.61858	−	4.25351i	0.682655	−	0.438716i
$95$	−9.44201	−	1.35756i	−0.968730	−	0.139282i
$96$	0.228066	+	1.71697i	0.0232769	+	0.175238i
$97$	0.679054	+	2.31265i	0.0689475	+	0.234814i	0.986756	−	0.162209i	$-0.0518618\pi$
$97$	0.679054	+	2.31265i	0.0689475	+	0.234814i	−0.917809	+	0.397022i	$0.870044\pi$
$98$	0.909632	−	0.415415i	0.0918867	−	0.0419633i
$99$	−13.8583	+	3.74773i	−1.39281	+	0.376661i
$100$	−0.376776	−	2.62054i	−0.0376776	−	0.262054i
$101$	−4.40886	+	15.0152i	−0.438698	+	1.49407i	0.382787	+	0.923837i	$0.374964\pi$
$101$	−4.40886	+	15.0152i	−0.438698	+	1.49407i	−0.821485	+	0.570231i	$0.806854\pi$
$102$	−0.524781	+	3.39094i	−0.0519611	+	0.335753i
$103$	4.85646	−	7.55681i	0.478522	−	0.744594i	−0.515128	−	0.857113i	$-0.672256\pi$
$103$	4.85646	−	7.55681i	0.478522	−	0.744594i	0.993650	+	0.112519i	$0.0358919\pi$
$104$	−2.74136	+	4.26564i	−0.268813	+	0.418281i
$105$	0.406299	−	2.62535i	0.0396508	−	0.256208i
$106$	1.98004	−	6.74341i	0.192319	−	0.654978i
$107$	0.411809	+	2.86420i	0.0398111	+	0.276892i	0.999997	−	0.00246968i	$-0.000786125\pi$
$107$	0.411809	+	2.86420i	0.0398111	+	0.276892i	−0.960186	+	0.279362i	$0.909877\pi$
$108$	−3.81531	−	3.52752i	−0.367128	−	0.339436i
$109$	12.6046	−	5.75631i	1.20730	−	0.551355i	0.292889	−	0.956146i	$-0.405383\pi$
$109$	12.6046	−	5.75631i	1.20730	−	0.551355i	0.914409	+	0.404792i	$0.132656\pi$
$110$	−2.06785	−	7.04244i	−0.197161	−	0.671470i
$111$	0.730937	+	5.50279i	0.0693775	+	0.522301i
$112$	0.989821	+	0.142315i	0.0935293	+	0.0134475i
$113$	8.74044	−	5.61714i	0.822231	−	0.528416i	−0.0605693	−	0.998164i	$-0.519292\pi$
$113$	8.74044	−	5.61714i	0.822231	−	0.528416i	0.882800	+	0.469748i	$0.155655\pi$
$114$	5.72618	+	9.12414i	0.536306	+	0.854554i
$115$	−0.368154	−	7.34658i	−0.0343306	−	0.685073i
$116$			2.61598i			0.242888i
$117$	−1.84089	−	15.0999i	−0.170190	−	1.39599i
$118$	−2.12735	+	14.7961i	−0.195839	+	1.36209i
$119$	1.80204	+	0.822964i	0.165193	+	0.0754409i
$120$	1.76117	−	1.98892i	0.160772	−	0.181563i
$121$	4.94333	+	10.8244i	0.449393	+	0.984034i
$122$	7.42789	+	8.57224i	0.672489	+	0.776094i
$123$	9.62260	+	11.3491i	0.867641	+	1.02332i
$124$	−5.32391	−	1.56324i	−0.478101	−	0.140383i
$125$	−7.68128	+	8.86467i	−0.687035	+	0.792881i
$126$	−2.55802	+	1.56733i	−0.227887	+	0.139629i
$127$	−16.1697	−	10.3916i	−1.43482	−	0.922106i	−0.999764	−	0.0217047i	$-0.993091\pi$
$127$	−16.1697	−	10.3916i	−1.43482	−	0.922106i	−0.435060	−	0.900401i	$-0.643273\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	−7.18577	+	2.02635i	−0.632672	+	0.178410i
$130$	7.69805	−	1.10681i	0.675163	−	0.0970738i
$131$	2.48338	−	2.15186i	0.216974	−	0.188009i	−0.539592	−	0.841927i	$-0.681421\pi$
$131$	2.48338	−	2.15186i	0.216974	−	0.188009i	0.756565	+	0.653918i	$0.226876\pi$
$132$	−4.55574	+	6.92419i	−0.396527	+	0.602673i
$133$	5.96737	−	1.75218i	0.517437	−	0.151933i
$134$	−0.549022	+	1.20219i	−0.0474283	+	0.103853i
$135$	−0.256798	+	7.96567i	−0.0221017	+	0.685576i
$136$	1.07104	+	1.66658i	0.0918412	+	0.142908i
$137$	−14.3856			−1.22904			−0.614521	−	0.788900i	$-0.710651\pi$
$137$	−14.3856			−1.22904			−0.614521	+	0.788900i	$0.710651\pi$
$138$	−6.05900	+	5.68230i	−0.515776	+	0.483710i
$139$	10.8930			0.923928			0.461964	−	0.886899i	$-0.347145\pi$
$139$	10.8930			0.923928			0.461964	+	0.886899i	$0.347145\pi$
$140$	−0.829230	−	1.29031i	−0.0700827	−	0.109051i
$141$	5.52736	+	12.4556i	0.465488	+	1.04895i
$142$	5.27561	−	11.5520i	0.442719	−	0.969420i
$143$	−23.2817	+	6.83612i	−1.94691	+	0.571665i
$144$	−2.99931	−	0.0644489i	−0.249942	−	0.00537075i
$145$	3.03234	−	2.62754i	0.251822	−	0.218205i
$146$	−13.1141	+	1.88552i	−1.08533	+	0.156046i
$147$	0.470095	+	1.66704i	0.0387728	+	0.137495i
$148$	2.42213	+	2.09879i	0.199098	+	0.172519i
$149$	−13.2727	−	8.52984i	−1.08734	−	0.698792i	−0.131100	−	0.991369i	$-0.541851\pi$
$149$	−13.2727	−	8.52984i	−1.08734	−	0.698792i	−0.956242	+	0.292577i	$0.905487\pi$
$150$	4.58531	+	0.0492588i	0.374389	+	0.00402196i
$151$	7.42593	−	8.56998i	0.604313	−	0.697415i	−0.368336	−	0.929693i	$-0.620072\pi$
$151$	7.42593	−	8.56998i	0.604313	−	0.697415i	0.972649	+	0.232278i	$0.0746179\pi$
$152$	5.96737	+	1.75218i	0.484018	+	0.142120i
$153$	−5.66516	−	1.79651i	−0.458001	−	0.145239i
$154$	3.13375	+	3.61654i	0.252525	+	0.291429i
$155$	3.53539	+	7.74143i	0.283969	+	0.621806i
$156$	−6.57521	−	5.82228i	−0.526438	−	0.466156i
$157$	−20.2363	−	9.24159i	−1.61503	−	0.737559i	−0.616279	−	0.787528i	$-0.711361\pi$
$157$	−20.2363	−	9.24159i	−1.61503	−	0.737559i	−0.998751	+	0.0499686i	$0.984088\pi$
$158$	1.73879	−	12.0935i	0.138331	−	0.962110i
$159$	11.0180	+	5.17551i	0.873785	+	0.410445i
$160$		−	1.53379i		−	0.121257i
$161$	2.20810	+	4.25726i	0.174023	+	0.335519i
$162$	7.04864	−	5.59613i	0.553793	−	0.439674i
$163$	−9.02579	+	5.80053i	−0.706955	+	0.454332i	−0.844077	−	0.536222i	$-0.819851\pi$
$163$	−9.02579	+	5.80053i	−0.706955	+	0.454332i	0.137122	+	0.990554i	$0.456215\pi$
$164$	8.50321	+	1.22258i	0.663989	+	0.0954672i
$165$	12.6021	−	1.67395i	0.981075	−	0.130317i
$166$	0.716290	+	2.43946i	0.0555949	+	0.189339i
$167$	−8.82938	+	4.03224i	−0.683238	+	0.312024i	−0.726625	−	0.687034i	$-0.758912\pi$
$167$	−8.82938	+	4.03224i	−0.683238	+	0.312024i	0.0433871	+	0.999058i	$0.486185\pi$
$168$	−0.505799	+	1.65655i	−0.0390233	+	0.127806i
$169$	−1.80893	−	12.5814i	−0.139149	−	0.967799i
$170$	0.856055	−	2.91546i	0.0656564	−	0.223605i
$171$	−17.1344	+	7.38437i	−1.31030	+	0.564697i
$172$	−2.33043	+	3.62623i	−0.177694	+	0.276497i
$173$	−10.7780	+	16.7709i	−0.819438	+	1.27507i	0.139149	+	0.990271i	$0.455563\pi$
$173$	−10.7780	+	16.7709i	−0.819438	+	1.27507i	−0.958587	+	0.284799i	$0.908073\pi$
$174$	−4.47770	−	0.692970i	−0.339454	−	0.0525339i
$175$	0.745883	−	2.54024i	0.0563834	−	0.192024i
$176$	0.681029	+	4.73666i	0.0513345	+	0.357039i
$177$	−24.7625	−	7.56079i	−1.86126	−	0.568304i
$178$	−7.78502	+	3.55530i	−0.583512	+	0.266481i
$179$	−5.01029	−	17.0635i	−0.374487	−	1.27538i	−0.904164	−	0.427185i	$-0.859505\pi$
$179$	−5.01029	−	17.0635i	−0.374487	−	1.27538i	0.529678	−	0.848199i	$-0.322313\pi$
$180$	2.93786	+	3.54142i	0.218975	+	0.263962i
$181$	−11.8710	−	1.70680i	−0.882367	−	0.126865i	−0.313787	−	0.949493i	$-0.601598\pi$
$181$	−11.8710	−	1.70680i	−0.882367	−	0.126865i	−0.568580	+	0.822628i	$0.692507\pi$
$182$	−4.26564	+	2.74136i	−0.316190	+	0.203203i
$183$	−16.6405	+	10.4433i	−1.23010	+	0.771994i
$184$	−0.444077	+	4.77523i	−0.0327378	+	0.352034i
$185$		−	4.91571i		−	0.361410i
$186$	4.08606	−	8.69870i	0.299604	−	0.637820i
$187$	−1.34916	+	9.38362i	−0.0986604	+	0.686198i
$188$	7.15655	+	3.26829i	0.521945	+	0.238364i
$189$	−2.00514	−	4.79368i	−0.145853	−	0.348689i
$190$	−3.96269	−	8.67707i	−0.287484	−	0.629501i
$191$	4.27621	+	4.93501i	0.309416	+	0.357085i	0.889065	−	0.457782i	$-0.151356\pi$
$191$	4.27621	+	4.93501i	0.309416	+	0.357085i	−0.579649	+	0.814866i	$0.696810\pi$
$192$	−1.32111	+	1.12013i	−0.0953426	+	0.0808381i
$193$	2.66400	+	0.782220i	0.191759	+	0.0563054i	0.376202	−	0.926538i	$-0.377230\pi$
$193$	2.66400	+	0.782220i	0.191759	+	0.0563054i	−0.184443	+	0.982843i	$0.559048\pi$
$194$	−1.57840	+	1.82157i	−0.113322	+	0.130781i
$195$	−0.144702	+	13.4697i	−0.0103623	+	0.964588i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	−0.398734	−	0.345505i	−0.0284086	−	0.0246162i	0.640541	−	0.767924i	$-0.278710\pi$
$197$	−0.398734	−	0.345505i	−0.0284086	−	0.0246162i	−0.668949	+	0.743308i	$0.733256\pi$
$198$	−10.6451	−	9.63216i	−0.756517	−	0.684528i
$199$	18.4522	−	2.65302i	1.30804	−	0.188068i	0.547197	−	0.837004i	$-0.315695\pi$
$199$	18.4522	−	2.65302i	1.30804	−	0.188068i	0.760843	+	0.648936i	$0.224786\pi$
$200$	2.00084	−	1.73373i	0.141480	−	0.122594i
$201$	−1.91232	−	1.25821i	−0.134885	−	0.0887470i
$202$	−15.0152	+	4.40886i	−1.05647	+	0.310206i
$203$	−1.08672	+	2.37958i	−0.0762726	+	0.167014i
$204$	−3.13635	+	1.39180i	−0.219589	+	0.0974458i
$205$	−7.12362	−	11.0846i	−0.497535	−	0.774180i
$206$	8.98279			0.625861
$207$	−8.12123	−	11.8763i	−0.564465	−	0.825457i
$208$	−5.07058			−0.351581
$209$	16.0903	+	25.0371i	1.11299	+	1.73185i
$210$	2.42825	−	1.07757i	0.167565	−	0.0743595i
$211$	−10.8734	+	23.8094i	−0.748554	+	1.63910i	0.0203936	+	0.999792i	$0.493508\pi$
$211$	−10.8734	+	23.8094i	−0.748554	+	1.63910i	−0.768947	+	0.639312i	$0.779219\pi$
$212$	6.74341	−	1.98004i	0.463139	−	0.135990i
$213$	18.3757	+	12.0902i	1.25908	+	0.828409i
$214$	−2.18687	+	1.89494i	−0.149492	+	0.129535i
$215$	6.54412	−	0.940902i	0.446305	−	0.0641690i
$216$	0.904829	−	5.11677i	0.0615658	−	0.348152i
$217$	−4.19341	−	3.63361i	−0.284667	−	0.246665i
$218$	11.6571	+	7.49154i	0.789515	+	0.507391i
$219$	0.246508	−	22.9465i	0.0166574	−	1.55058i
$220$	4.80652	−	5.54701i	0.324055	−	0.373980i
$221$	−9.63824	−	2.83004i	−0.648338	−	0.190369i
$222$	−4.23406	+	3.58993i	−0.284172	+	0.240941i
$223$	5.84353	+	6.74380i	0.391312	+	0.451598i	0.916886	−	0.399150i	$-0.130695\pi$
$223$	5.84353	+	6.74380i	0.391312	+	0.451598i	−0.525574	+	0.850748i	$0.676149\pi$
$224$	0.415415	+	0.909632i	0.0277561	+	0.0607773i
$225$	−1.29896	+	7.83551i	−0.0865973	+	0.522368i
$226$	9.45087	+	4.31607i	0.628663	+	0.287101i
$227$	0.197343	−	1.37255i	0.0130981	−	0.0910994i	−0.982224	−	0.187714i	$-0.939892\pi$
$227$	0.197343	−	1.37255i	0.0130981	−	0.0910994i	0.995322	+	0.0966144i	$0.0308014\pi$
$228$	−4.57991	+	9.75005i	−0.303312	+	0.645713i
$229$		−	10.1559i		−	0.671119i	−0.942019	−	0.335559i	$-0.891075\pi$
$229$		−	10.1559i		−	0.671119i	0.942019	−	0.335559i	$-0.108925\pi$
$230$	5.98130	−	4.28157i	0.394395	−	0.282319i
$231$	−7.02046	+	4.40594i	−0.461912	+	0.289890i
$232$	−2.20070	+	1.41431i	−0.144483	+	0.0928537i
$233$	5.52402	+	0.794235i	0.361891	+	0.0520320i	0.320862	−	0.947126i	$-0.396027\pi$
$233$	5.52402	+	0.794235i	0.361891	+	0.0520320i	0.0410287	+	0.999158i	$0.486936\pi$
$234$	11.7076	−	9.71230i	0.765351	−	0.634913i
$235$	−3.39971	−	11.5783i	−0.221772	−	0.755287i
$236$	−13.5974	+	6.20971i	−0.885114	+	0.404218i
$237$	20.2396	+	6.17980i	1.31470	+	0.401421i
$238$	0.281935	+	1.96090i	0.0182751	+	0.127106i
$239$	3.62979	−	12.3619i	0.234791	−	0.799626i	−0.754829	−	0.655921i	$-0.772280\pi$
$239$	3.62979	−	12.3619i	0.234791	−	0.799626i	0.989621	−	0.143705i	$-0.0459015\pi$
$240$	2.62535	+	0.406299i	0.169466	+	0.0262265i
$241$	6.35076	−	9.88198i	0.409089	−	0.636554i	−0.574177	−	0.818731i	$-0.694678\pi$
$241$	6.35076	−	9.88198i	0.409089	−	0.636554i	0.983266	+	0.182177i	$0.0583143\pi$
$242$	−6.43348	+	10.0107i	−0.413560	+	0.643512i
$243$	7.71158	+	13.5474i	0.494698	+	0.869065i
$244$	−3.19561	+	10.8832i	−0.204578	+	0.696728i
$245$	−0.218281	−	1.51818i	−0.0139455	−	0.0969929i
$246$	−4.34514	+	14.2309i	−0.277036	+	0.907326i
$247$	−28.6856	+	13.1003i	−1.82522	+	0.833552i
$248$	−1.56324	−	5.32391i	−0.0992660	−	0.338069i
$249$	−4.36530	+	0.579845i	−0.276640	+	0.0367462i
$250$	−11.6103	−	1.66930i	−0.734297	−	0.105576i
$251$	−9.44890	+	6.07244i	−0.596409	+	0.383289i	−0.803739	−	0.594982i	$-0.797159\pi$
$251$	−9.44890	+	6.07244i	−0.596409	+	0.383289i	0.207330	+	0.978271i	$0.433523\pi$
$252$	−2.70149	−	1.30458i	−0.170178	−	0.0821810i
$253$	−16.5704	+	15.8782i	−1.04177	+	0.998252i
$254$		−	19.2209i		−	1.20603i
$255$	4.76354	+	2.23759i	0.298305	+	0.140123i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	0.157766	+	0.0720492i	0.00984115	+	0.00449430i	0.420330	−	0.907372i	$-0.361914\pi$
$257$	0.157766	+	0.0720492i	0.00984115	+	0.00449430i	−0.410488	+	0.911866i	$0.634642\pi$
$258$	−5.58959	−	4.94953i	−0.347993	−	0.308144i
$259$	1.33138	+	2.91532i	0.0827279	+	0.181149i
$260$	5.09299	+	5.87762i	0.315854	+	0.364515i
$261$	2.37228	−	7.48080i	0.146840	−	0.463050i
$262$	3.15287	+	0.925767i	0.194785	+	0.0571941i
$263$	−5.68758	+	6.56382i	−0.350711	+	0.404742i	−0.903506	−	0.428575i	$-0.859016\pi$
$263$	−5.68758	+	6.56382i	−0.350711	+	0.404742i	0.552795	+	0.833317i	$0.313561\pi$
$264$	−8.28802	−	0.0890360i	−0.510092	−	0.00547978i
$265$	−9.06840	−	5.82791i	−0.557067	−	0.358005i
$266$	4.70023	+	4.07277i	0.288190	+	0.249718i
$267$	−4.02327	−	14.2672i	−0.246220	−	0.873140i
$268$	−1.30817	+	0.188087i	−0.0799092	+	0.0114892i
$269$	−0.802378	+	0.695264i	−0.0489218	+	0.0423910i	−0.678979	−	0.734158i	$-0.737577\pi$
$269$	−0.802378	+	0.695264i	−0.0489218	+	0.0423910i	0.630057	+	0.776549i	$0.283032\pi$
$270$	−6.83999	+	4.09054i	−0.416268	+	0.248942i
$271$	29.8375	−	8.76107i	1.81250	−	0.532197i	0.813703	−	0.581281i	$-0.197448\pi$
$271$	29.8375	−	8.76107i	1.81250	−	0.532197i	0.998795	+	0.0490833i	$0.0156300\pi$
$272$	−0.822964	+	1.80204i	−0.0498995	+	0.109265i
$273$	−3.56235	−	8.02757i	−0.215604	−	0.485851i
$274$	−7.77743	−	12.1019i	−0.469852	−	0.731103i
$275$	12.6692			0.763981
$276$	−8.05600	−	2.02507i	−0.484914	−	0.121895i
$277$	17.9074			1.07595			0.537975	−	0.842961i	$-0.319189\pi$
$277$	17.9074			1.07595			0.537975	+	0.842961i	$0.319189\pi$
$278$	5.88917	+	9.16373i	0.353209	+	0.549604i
$279$	13.8070	+	9.29828i	0.826601	+	0.556673i
$280$	0.637160	−	1.39519i	0.0380776	−	0.0833783i
$281$	3.97362	−	1.16676i	0.237047	−	0.0696031i	−0.161052	−	0.986946i	$-0.551489\pi$
$281$	3.97362	−	1.16676i	0.237047	−	0.0696031i	0.398098	+	0.917343i	$0.369670\pi$
$282$	−7.49001	+	11.3839i	−0.446023	+	0.677903i
$283$	1.41836	−	1.22902i	0.0843128	−	0.0730575i	−0.611685	−	0.791102i	$-0.709508\pi$
$283$	1.41836	−	1.22902i	0.0843128	−	0.0730575i	0.695998	+	0.718044i	$0.254962\pi$
$284$	12.5704	−	1.80734i	0.745913	−	0.107246i
$285$	15.9020	−	4.48428i	0.941955	−	0.265626i
$286$	−18.3379	−	15.8899i	−1.08435	−	0.939591i
$287$	7.22691	+	4.64445i	0.426591	+	0.274153i
$288$	−1.56733	−	2.55802i	−0.0923558	−	0.150733i
$289$	8.56256	−	9.88172i	0.503680	−	0.581278i
$290$	3.84984	+	1.13041i	0.226070	+	0.0663802i
$291$	−2.69981	−	3.18423i	−0.158266	−	0.186663i
$292$	−8.67619	−	10.0129i	−0.507736	−	0.585958i
$293$	2.59749	+	5.68771i	0.151747	+	0.332280i	0.970205	−	0.242287i	$-0.0778977\pi$
$293$	2.59749	+	5.68771i	0.151747	+	0.332280i	−0.818457	+	0.574567i	$0.805170\pi$
$294$	−1.14825	+	1.29674i	−0.0669672	+	0.0756272i
$295$	20.8555	+	9.52440i	1.21426	+	0.554532i
$296$	−0.456111	+	3.17232i	−0.0265109	+	0.184387i
$297$	19.3070	−	15.6695i	1.12031	−	0.909235i
$298$		−	15.7773i		−	0.913953i
$299$	−14.1545	−	19.7737i	−0.818576	−	1.14354i
$300$	2.43757	+	3.88404i	0.140733	+	0.224245i
$301$	−3.62623	+	2.33043i	−0.209012	+	0.134324i
$302$	11.2243	+	1.61381i	0.645885	+	0.0928642i
$303$	−3.56902	−	26.8690i	−0.205035	−	1.54358i
$304$	1.75218	+	5.96737i	0.100494	+	0.342252i
$305$	15.8252	−	7.22711i	0.906146	−	0.413823i
$306$	−1.55150	−	5.73710i	−0.0886932	−	0.327968i
$307$	−1.14747	−	7.98080i	−0.0654893	−	0.455488i	−0.996009	−	0.0892476i	$-0.971554\pi$
$307$	−1.14747	−	7.98080i	−0.0654893	−	0.455488i	0.930520	−	0.366241i	$-0.119355\pi$
$308$	−1.34819	+	4.59153i	−0.0768205	+	0.261626i
$309$	−2.37953	+	15.3756i	−0.135367	+	0.874688i
$310$	−4.60113	+	7.15949i	−0.261326	+	0.406632i
$311$	−1.94160	+	3.02118i	−0.110098	+	0.171316i	−0.891930	−	0.452173i	$-0.850649\pi$
$311$	−1.94160	+	3.02118i	−0.110098	+	0.171316i	0.781832	+	0.623489i	$0.214285\pi$
$312$	1.34319	−	8.67918i	0.0760432	−	0.491362i
$313$	8.18169	−	27.8643i	0.462456	−	1.57498i	−0.316937	−	0.948447i	$-0.602654\pi$
$313$	8.18169	−	27.8643i	0.462456	−	1.57498i	0.779393	−	0.626535i	$-0.215528\pi$
$314$	−3.16603	−	22.0202i	−0.178669	−	1.24267i
$315$	1.20121	+	4.44182i	0.0676805	+	0.250268i
$316$	11.1138	−	5.07550i	0.625200	−	0.285519i
$317$	3.98296	+	13.5647i	0.223705	+	0.761869i	0.992486	+	0.122357i	$0.0390454\pi$
$317$	3.98296	+	13.5647i	0.223705	+	0.761869i	−0.768781	+	0.639512i	$0.779136\pi$
$318$	1.60287	+	12.0670i	0.0898844	+	0.676685i
$319$	−12.3910	−	1.78156i	−0.693763	−	0.0997480i
$320$	1.29031	−	0.829230i	0.0721304	−	0.0463554i
$321$	−2.66422	−	4.24518i	−0.148702	−	0.236943i
$322$	−2.38765	+	4.15922i	−0.133058	+	0.231784i
$323$			12.3208i			0.685549i
$324$	8.51855	+	2.90420i	0.473253	+	0.161344i
$325$	−1.91047	+	13.2876i	−0.105974	+	0.737066i
$326$	−9.75943	−	4.45698i	−0.540525	−	0.246849i
$327$	−15.9110	+	17.9686i	−0.879881	+	0.993665i
$328$	3.56868	+	7.81433i	0.197048	+	0.431474i
$329$	5.15213	+	5.94588i	0.284046	+	0.327807i
$330$	8.22144	+	9.69659i	0.452575	+	0.533779i
$331$	19.1105	+	5.61136i	1.05041	+	0.308428i	0.760983	−	0.648772i	$-0.224717\pi$
$331$	19.1105	+	5.61136i	1.05041	+	0.308428i	0.289427	+	0.957200i	$0.406535\pi$
$332$	−1.66495	+	1.92145i	−0.0913759	+	0.105453i
$333$	−5.02320	−	8.19831i	−0.275270	−	0.449264i
$334$	−8.16567	−	5.24775i	−0.446805	−	0.287144i
$335$	1.53197	+	1.32746i	0.0837007	+	0.0725271i
$336$	−1.66704	+	0.470095i	−0.0909443	+	0.0256458i
$337$	14.4549	−	2.07830i	0.787409	−	0.113212i	0.263132	−	0.964760i	$-0.415245\pi$
$337$	14.4549	−	2.07830i	0.787409	−	0.113212i	0.524277	+	0.851548i	$0.324335\pi$
$338$	9.60616	−	8.32378i	0.522506	−	0.452754i
$339$	−9.89123	+	15.0335i	−0.537218	+	0.816507i
$340$	2.91546	−	0.856055i	0.158113	−	0.0464261i
$341$	11.0303	−	24.1529i	0.597323	−	1.30796i
$342$	−15.4757	−	10.4221i	−0.836830	−	0.563562i
$343$	0.540641	+	0.841254i	0.0291919	+	0.0454234i
$344$	−4.31050			−0.232407
$345$	5.74422	+	11.3722i	0.309258	+	0.612260i
$346$	−19.9357			−1.07175
$347$	5.72175	+	8.90322i	0.307160	+	0.477950i	0.960177	−	0.279394i	$-0.0901334\pi$
$347$	5.72175	+	8.90322i	0.307160	+	0.477950i	−0.653017	+	0.757343i	$0.726497\pi$
$348$	−1.83787	−	4.14153i	−0.0985200	−	0.222009i
$349$	10.3726	−	22.7128i	0.555232	−	1.21579i	−0.399063	−	0.916924i	$-0.630664\pi$
$349$	10.3726	−	22.7128i	0.555232	−	1.21579i	0.954295	−	0.298866i	$-0.0966083\pi$
$350$	2.54024	−	0.745883i	0.135782	−	0.0398691i
$351$	13.5230	+	22.6124i	0.721802	+	1.20696i
$352$	−3.61654	+	3.13375i	−0.192762	+	0.167029i
$353$	15.9709	−	2.29626i	0.850043	−	0.122218i	0.296494	−	0.955035i	$-0.404182\pi$
$353$	15.9709	−	2.29626i	0.850043	−	0.122218i	0.553549	+	0.832817i	$0.313273\pi$
$354$	−7.02708	−	24.9192i	−0.373485	−	1.32444i
$355$	−14.7209	−	12.7557i	−0.781305	−	0.677004i
$356$	−7.19981	−	4.62704i	−0.381589	−	0.245233i
$357$	−3.43110	−	0.0368594i	−0.181593	−	0.00195081i
$358$	11.6459	−	13.4401i	0.615507	−	0.710333i
$359$	7.39088	+	2.17016i	0.390076	+	0.114537i	0.470889	−	0.882193i	$-0.343933\pi$
$359$	7.39088	+	2.17016i	0.390076	+	0.114537i	−0.0808127	+	0.996729i	$0.525752\pi$
$360$	−1.39090	+	4.38612i	−0.0733071	+	0.231169i
$361$	12.8874	+	14.8729i	0.678286	+	0.782784i
$362$	−4.98212	−	10.9093i	−0.261854	−	0.573381i
$363$	−15.4308	−	13.6638i	−0.809908	−	0.717166i
$364$	−4.61236	−	2.10639i	−0.241753	−	0.110405i
$365$	−2.89199	+	20.1142i	−0.151374	+	1.05283i
$366$	−17.7820	−	8.35280i	−0.929482	−	0.436608i
$367$			4.35380i			0.227267i	0.993523	+	0.113633i	$0.0362489\pi$
$367$			4.35380i			0.227267i	−0.993523	+	0.113633i	$0.963751\pi$
$368$	−4.25726	+	2.20810i	−0.221925	+	0.115105i
$369$	−23.2076	−	11.2072i	−1.20814	−	0.583424i
$370$	4.13536	−	2.65763i	0.214987	−	0.138164i
$371$	6.95656	+	1.00020i	0.361166	+	0.0519279i
$372$	9.52691	−	1.26546i	0.493947	−	0.0656112i
$373$	−0.417580	−	1.42215i	−0.0216215	−	0.0736360i	0.947976	−	0.318343i	$-0.103126\pi$
$373$	−0.417580	−	1.42215i	−0.0216215	−	0.0736360i	−0.969597	+	0.244707i	$0.921308\pi$
$374$	−8.62342	+	3.93818i	−0.445906	+	0.203639i
$375$	5.93284	−	19.4308i	0.306371	−	1.00340i
$376$	1.11967	+	7.78745i	0.0577423	+	0.401607i
$377$	3.73705	−	12.7272i	0.192468	−	0.655485i
$378$	2.94864	−	4.27849i	0.151662	−	0.220062i
$379$	−8.34084	+	12.9786i	−0.428440	+	0.666666i	−0.986617	−	0.163056i	$-0.947865\pi$
$379$	−8.34084	+	12.9786i	−0.428440	+	0.666666i	0.558177	+	0.829722i	$0.311501\pi$
$380$	5.15723	−	8.02480i	0.264560	−	0.411664i
$381$	32.8999	+	5.09160i	1.68551	+	0.260850i
$382$	−1.83970	+	6.26544i	−0.0941272	+	0.320568i
$383$	3.04596	+	21.1851i	0.155641	+	1.08251i	0.906548	+	0.422102i	$0.138708\pi$
$383$	3.04596	+	21.1851i	0.155641	+	1.08251i	−0.750907	+	0.660408i	$0.770383\pi$
$384$	−1.65655	−	0.505799i	−0.0845356	−	0.0258115i
$385$	6.67647	−	3.04904i	0.340265	−	0.155394i
$386$	0.782220	+	2.66400i	0.0398140	+	0.135594i
$387$	9.95265	−	8.25643i	0.505922	−	0.419698i
$388$	−2.38575	−	0.343019i	−0.121118	−	0.0174141i
$389$	17.5139	−	11.2555i	0.887992	−	0.570678i	−0.0152147	−	0.999884i	$-0.504843\pi$
$389$	17.5139	−	11.2555i	0.887992	−	0.570678i	0.903206	+	0.429207i	$0.141207\pi$
$390$	−11.4097	+	7.16056i	−0.577753	+	0.362589i
$391$	−9.32468	+	1.82109i	−0.471570	+	0.0920964i
$392$			1.00000i			0.0505076i
$393$	−2.41980	+	5.15146i	−0.122063	+	0.259857i
$394$	0.0750854	−	0.522230i	0.00378275	−	0.0263096i
$395$	−17.0462	−	7.78476i	−0.857689	−	0.391694i
$396$	2.34789	−	14.1628i	0.117986	−	0.711708i
$397$	13.6861	+	29.9683i	0.686884	+	1.50407i	0.855181	+	0.518330i	$0.173446\pi$
$397$	13.6861	+	29.9683i	0.686884	+	1.50407i	−0.168297	+	0.985736i	$0.553827\pi$
$398$	12.2079	+	14.0886i	0.611925	+	0.706199i
$399$	−8.21635	+	6.96639i	−0.411332	+	0.348756i
$400$	2.54024	+	0.745883i	0.127012	+	0.0372941i
$401$	−21.3210	+	24.6058i	−1.06472	+	1.22875i	−0.0922474	+	0.995736i	$0.529405\pi$
$401$	−21.3210	+	24.6058i	−1.06472	+	1.22875i	−0.972473	+	0.233016i	$0.925140\pi$
$402$	0.0245900	−	2.28899i	0.00122644	−	0.114164i
$403$	23.6687	+	15.2109i	1.17902	+	0.757710i
$404$	−11.8268	−	10.2480i	−0.588405	−	0.509856i
$405$	−5.18976	−	12.7914i	−0.257881	−	0.635610i
$406$	−2.58935	+	0.372293i	−0.128507	+	0.0184766i
$407$	−11.5908	+	10.0435i	−0.574534	+	0.497837i
$408$	−2.86650	−	1.88600i	−0.141913	−	0.0933711i
$409$	−10.3177	+	3.02955i	−0.510178	+	0.149802i	−0.526683	−	0.850062i	$-0.676564\pi$
$409$	−10.3177	+	3.02955i	−0.510178	+	0.149802i	0.0165047	+	0.999864i	$0.494746\pi$
$410$	5.47361	−	11.9855i	0.270323	−	0.591924i
$411$	22.7748	−	10.1066i	1.12340	−	0.498524i
$412$	4.85646	+	7.55681i	0.239261	+	0.372297i
$413$	−14.9482			−0.735554
$414$	5.60028	−	13.2528i	0.275239	−	0.651340i
$415$	3.89958			0.191423
$416$	−2.74136	−	4.26564i	−0.134406	−	0.209140i
$417$	−17.2454	+	7.65289i	−0.844509	+	0.374763i
$418$	−12.3634	+	27.0721i	−0.604715	+	1.32414i
$419$	8.32917	−	2.44567i	0.406907	−	0.119479i	−0.0718728	−	0.997414i	$-0.522898\pi$
$419$	8.32917	−	2.44567i	0.406907	−	0.119479i	0.478779	+	0.877935i	$0.341079\pi$
$420$	2.21932	+	1.46019i	0.108292	+	0.0712501i
$421$	4.85399	−	4.20600i	0.236569	−	0.204988i	−0.528506	−	0.848930i	$-0.677247\pi$
$421$	4.85399	−	4.20600i	0.236569	−	0.204988i	0.765075	+	0.643942i	$0.222702\pi$
$422$	−25.9083	+	3.72505i	−1.26120	+	0.181333i
$423$	−17.5015	−	15.8360i	−0.850951	−	0.769975i
$424$	5.31148	+	4.60242i	0.257948	+	0.223513i
$425$	4.41224	+	2.83557i	0.214025	+	0.137545i
$426$	−0.236288	+	21.9951i	−0.0114482	+	1.06567i
$427$	−7.42789	+	8.57224i	−0.359461	+	0.414840i
$428$	−2.77644	−	0.815235i	−0.134204	−	0.0394059i
$429$	32.0561	−	27.1794i	1.54768	−	1.31223i
$430$	4.32955	+	4.99657i	0.208790	+	0.240956i
$431$	−13.0947	−	28.6734i	−0.630750	−	1.38115i	−0.907437	−	0.420189i	$-0.861964\pi$
$431$	−13.0947	−	28.6734i	−0.630750	−	1.38115i	0.276687	−	0.960960i	$-0.410764\pi$
$432$	4.79368	−	2.00514i	0.230636	−	0.0964724i
$433$	−28.9200	−	13.2073i	−1.38981	−	0.634704i	−0.426842	−	0.904326i	$-0.640374\pi$
$433$	−28.9200	−	13.2073i	−1.38981	−	0.634704i	−0.962966	+	0.269622i	$0.913101\pi$
$434$	0.789658	−	5.49220i	0.0379048	−	0.263634i
$435$	−2.95472	+	6.29022i	−0.141668	+	0.301593i
$436$			13.8568i			0.663619i
$437$	−18.3797	+	23.4909i	−0.879219	+	1.12372i
$438$	19.4371	−	12.1984i	0.928739	−	0.582863i
$439$	6.01565	−	3.86602i	0.287111	−	0.184515i	−0.389155	−	0.921172i	$-0.627233\pi$
$439$	6.01565	−	3.86602i	0.287111	−	0.184515i	0.676267	+	0.736657i	$0.263597\pi$
$440$	7.26504	+	1.04456i	0.346347	+	0.0497972i
$441$	−1.91542	−	2.30893i	−0.0912105	−	0.109949i
$442$	−2.83004	−	9.63824i	−0.134611	−	0.458444i
$443$	−29.3723	+	13.4139i	−1.39552	+	0.637314i	−0.964271	−	0.264918i	$-0.914655\pi$
$443$	−29.3723	+	13.4139i	−1.39552	+	0.637314i	−0.431251	+	0.902232i	$0.641928\pi$
$444$	−5.30915	−	1.62106i	−0.251961	−	0.0769319i
$445$	1.86815	+	12.9932i	0.0885586	+	0.615938i
$446$	−2.51399	+	8.56186i	−0.119041	+	0.405416i
$447$	27.0056	+	4.17938i	1.27732	+	0.197678i
$448$	−0.540641	+	0.841254i	−0.0255429	+	0.0397455i
$449$	11.7363	−	18.2621i	0.553872	−	0.861841i	−0.445570	−	0.895247i	$-0.646999\pi$
$449$	11.7363	−	18.2621i	0.553872	−	0.861841i	0.999442	+	0.0334058i	$0.0106354\pi$
$450$	−7.29392	+	3.14345i	−0.343839	+	0.148183i
$451$	−11.5819	+	39.4442i	−0.545368	+	1.85735i
$452$	1.47862	+	10.2840i	0.0695484	+	0.483720i
$453$	−5.73561	+	18.7848i	−0.269483	+	0.882588i
$454$	1.26136	−	0.576042i	0.0591983	−	0.0270350i
$455$	2.19109	+	7.46218i	0.102720	+	0.349832i
$456$	−10.6783	+	1.41841i	−0.500059	+	0.0664231i
$457$	−1.95357	−	0.280881i	−0.0913843	−	0.0131391i	0.0964710	−	0.995336i	$-0.469244\pi$
$457$	−1.95357	−	0.280881i	−0.0913843	−	0.0131391i	−0.187855	+	0.982197i	$0.560154\pi$
$458$	8.54366	−	5.49068i	0.399219	−	0.256562i
$459$	10.2310	−	1.13591i	0.477544	−	0.0530196i
$460$	6.83563	+	2.71700i	0.318713	+	0.126681i
$461$			26.4565i			1.23220i	0.787667	+	0.616101i	$0.211289\pi$
$461$			26.4565i			1.23220i	−0.787667	+	0.616101i	$0.788711\pi$
$462$	−7.50206	−	3.52396i	−0.349027	−	0.163949i
$463$	−1.23983	+	8.62319i	−0.0576197	+	0.400754i	0.940518	+	0.339745i	$0.110341\pi$
$463$	−1.23983	+	8.62319i	−0.0576197	+	0.400754i	−0.998137	+	0.0610086i	$0.980568\pi$
$464$	−2.37958	−	1.08672i	−0.110469	−	0.0504496i
$465$	−11.0359	−	9.77217i	−0.511777	−	0.453174i
$466$	2.31836	+	5.07650i	0.107396	+	0.235164i
$467$	1.14109	+	1.31688i	0.0528031	+	0.0609381i	0.781537	−	0.623859i	$-0.214436\pi$
$467$	1.14109	+	1.31688i	0.0528031	+	0.0609381i	−0.728734	+	0.684797i	$0.759891\pi$
$468$	14.5001	+	4.59821i	0.670268	+	0.212552i
$469$	−1.26809	−	0.372344i	−0.0585549	−	0.0171933i
$470$	7.90230	−	9.11974i	0.364506	−	0.420662i
$471$	38.5301	+	0.413919i	1.77537	+	0.0190724i
$472$	−12.5752	−	8.08161i	−0.578822	−	0.371986i
$473$	−15.5891	−	13.5080i	−0.716788	−	0.621100i
$474$	5.74357	+	20.3677i	0.263811	+	0.935519i
$475$	16.2979	−	2.34328i	0.747799	−	0.107517i
$476$	−1.49719	+	1.29732i	−0.0686235	+	0.0594626i
$477$	−21.0794	−	0.452953i	−0.965160	−	0.0207393i
$478$	12.3619	−	3.62979i	0.565421	−	0.166023i
$479$	12.7762	−	27.9761i	0.583762	−	1.27826i	−0.355378	−	0.934723i	$-0.615648\pi$
$479$	12.7762	−	27.9761i	0.583762	−	1.27826i	0.939139	−	0.343537i	$-0.111625\pi$
$480$	1.07757	+	2.42825i	0.0491842	+	0.110834i
$481$	−8.78590	−	13.6711i	−0.400603	−	0.623350i
$482$	11.7467			0.535049
$483$	−6.48675	−	5.18865i	−0.295157	−	0.236092i
$484$	−11.8997			−0.540897
$485$	1.99868	+	3.11000i	0.0907552	+	0.141218i
$486$	−7.22759	+	13.8117i	−0.327850	+	0.626510i
$487$	−2.20807	+	4.83501i	−0.100057	+	0.219095i	−0.953040	−	0.302844i	$-0.902064\pi$
$487$	−2.20807	+	4.83501i	−0.100057	+	0.219095i	0.852983	+	0.521939i	$0.174791\pi$
$488$	−10.8832	+	3.19561i	−0.492661	+	0.144658i
$489$	10.2142	−	15.5243i	0.461900	−	0.702034i
$490$	1.15916	−	1.00442i	0.0523656	−	0.0453750i
$491$	13.9438	−	2.00481i	0.629274	−	0.0904760i	0.179704	−	0.983721i	$-0.442486\pi$
$491$	13.9438	−	2.00481i	0.629274	−	0.0904760i	0.449571	+	0.893245i	$0.351577\pi$
$492$	−14.3209	+	4.03842i	−0.645637	+	0.182066i
$493$	−3.91661	−	3.39376i	−0.176395	−	0.152847i
$494$	−26.5293	−	17.0493i	−1.19361	−	0.767086i
$495$	−18.7752	+	11.5038i	−0.843885	+	0.517058i
$496$	3.63361	−	4.19341i	0.163154	−	0.188290i
$497$	12.1852	+	3.57789i	0.546580	+	0.160491i
$498$	−2.84786	−	3.35884i	−0.127616	−	0.150513i
$499$	26.1650	+	30.1960i	1.17130	+	1.35176i	0.923802	+	0.382870i	$0.125064\pi$
$499$	26.1650	+	30.1960i	1.17130	+	1.35176i	0.247502	+	0.968887i	$0.420390\pi$
$500$	−4.87267	−	10.6697i	−0.217912	−	0.477162i
$501$	11.1455	−	12.5868i	0.497945	−	0.562338i
$502$	−10.2169	−	4.66591i	−0.456003	−	0.208250i
$503$	3.98378	−	27.7078i	0.177628	−	1.23543i	−0.684604	−	0.728916i	$-0.740025\pi$
$503$	3.98378	−	27.7078i	0.177628	−	1.23543i	0.862232	−	0.506514i	$-0.169066\pi$
$504$	−0.363053	−	2.97795i	−0.0161717	−	0.132648i
$505$			24.0024i			1.06809i
$506$	−22.3162	−	5.35551i	−0.992076	−	0.238081i
$507$	11.7029	+	18.6476i	0.519746	+	0.828168i
$508$	16.1697	−	10.3916i	0.717412	−	0.461053i
$509$	10.7922	+	1.55168i	0.478354	+	0.0687769i	0.377275	−	0.926101i	$-0.376861\pi$
$509$	10.7922	+	1.55168i	0.478354	+	0.0687769i	0.101079	+	0.994878i	$0.467770\pi$
$510$	0.692987	+	5.21708i	0.0306860	+	0.231016i
$511$	−3.73265	−	12.7122i	−0.165123	−	0.562356i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	21.9387	−	23.7285i	0.968618	−	1.04764i
$514$	0.0246829	+	0.171674i	0.00108872	+	0.00757220i
$515$	3.88163	−	13.2196i	0.171045	−	0.582527i
$516$	1.14185	−	7.37818i	0.0502670	−	0.324806i
$517$	−20.3546	+	31.6723i	−0.895194	+	1.39295i
$518$	−1.73272	+	2.69617i	−0.0761314	+	0.118463i
$519$	5.28093	−	34.1233i	0.231807	−	1.49785i
$520$	−2.19109	+	7.46218i	−0.0960858	+	0.327238i
$521$	−0.415870	−	2.89244i	−0.0182196	−	0.126720i	0.978682	−	0.205383i	$-0.0658440\pi$
$521$	−0.415870	−	2.89244i	−0.0182196	−	0.126720i	−0.996901	+	0.0786629i	$0.974935\pi$
$522$	7.57580	−	2.04874i	0.331584	−	0.0896710i
$523$	10.0768	−	4.60192i	0.440628	−	0.201228i	−0.182732	−	0.983163i	$-0.558494\pi$
$523$	10.0768	−	4.60192i	0.440628	−	0.201228i	0.623361	+	0.781935i	$0.285767\pi$
$524$	0.925767	+	3.15287i	0.0404423	+	0.137734i
$525$	0.603801	+	4.54565i	0.0263520	+	0.198389i
$526$	−8.59677	−	1.23603i	−0.374837	−	0.0538934i
$527$	9.24729	−	5.94287i	0.402818	−	0.258876i
$528$	−4.40594	−	7.02046i	−0.191744	−	0.305526i
$529$	−20.4950	−	10.4381i	−0.891089	−	0.453829i
$530$		−	10.7796i		−	0.468237i
$531$	44.5150	−	5.42699i	1.93179	−	0.235511i
$532$	−0.885098	+	6.15599i	−0.0383739	+	0.266896i
$533$	−39.6232	−	18.0953i	−1.71627	−	0.783794i
$534$	9.82720	−	11.0980i	0.425265	−	0.480259i
$535$	1.84372	+	4.03718i	0.0797109	+	0.174542i
$536$	−0.865479	−	0.998816i	−0.0373830	−	0.0431423i
$537$	19.9201	+	23.4943i	0.859617	+	1.01386i
$538$	−1.01869	−	0.299115i	−0.0439189	−	0.0128958i
$539$	−3.13375	+	3.61654i	−0.134980	+	0.155775i
$540$	−7.13915	−	3.54265i	−0.307220	−	0.152451i
$541$	9.83502	+	6.32059i	0.422841	+	0.271743i	0.734709	−	0.678382i	$-0.237319\pi$
$541$	9.83502	+	6.32059i	0.422841	+	0.271743i	−0.311869	+	0.950125i	$0.600955\pi$
$542$	23.5016	+	20.3643i	1.00948	+	0.874721i
$543$	19.9930	−	5.63790i	0.857980	−	0.241945i
$544$	−1.96090	+	0.281935i	−0.0840729	+	0.0120879i
$545$	16.0622	−	13.9180i	0.688031	−	0.596182i
$546$	4.82727	−	7.33688i	0.206588	−	0.313989i
$547$	3.91253	−	1.14882i	0.167288	−	0.0491201i	−0.197016	−	0.980400i	$-0.563125\pi$
$547$	3.91253	−	1.14882i	0.167288	−	0.0491201i	0.364304	+	0.931280i	$0.381307\pi$
$548$	5.97598	−	13.0856i	0.255281	−	0.558988i
$549$	19.0077	−	28.2244i	0.811229	−	1.20459i
$550$	6.84948	+	10.6580i	0.292063	+	0.454459i
$551$	−16.2696			−0.693106
$552$	−2.65181	−	7.87197i	−0.112868	−	0.335053i
$553$	12.2179			0.519558
$554$	9.68146	+	15.0646i	0.411326	+	0.640035i
$555$	3.45355	+	7.78239i	0.146595	+	0.330344i
$556$	−4.52510	+	9.90858i	−0.191907	+	0.420217i
$557$	24.9415	−	7.32348i	1.05680	−	0.310306i	0.293241	−	0.956039i	$-0.405266\pi$
$557$	24.9415	−	7.32348i	1.05680	−	0.310306i	0.763563	+	0.645733i	$0.223448\pi$
$558$	−0.357606	+	16.6422i	−0.0151387	+	0.704520i
$559$	16.5182	−	14.3131i	0.698647	−	0.605381i
$560$	1.51818	−	0.218281i	0.0641548	−	0.00922407i
$561$	−4.45655	−	15.8037i	−0.188156	−	0.667233i
$562$	3.12985	+	2.71203i	0.132025	+	0.114400i
$563$	0.801344	+	0.514992i	0.0337726	+	0.0217043i	0.557418	−	0.830232i	$-0.311792\pi$
$563$	0.801344	+	0.514992i	0.0337726	+	0.0217043i	−0.523646	+	0.851936i	$0.675428\pi$
$564$	−13.6262	−	0.146382i	−0.573765	−	0.00616381i
$565$	10.4357	−	12.0434i	0.439033	−	0.506671i
$566$	1.80074	+	0.528745i	0.0756907	+	0.0222248i
$567$	6.54230	+	6.18048i	0.274751	+	0.259556i
$568$	8.31648	+	9.59773i	0.348952	+	0.402712i
$569$	13.9588	+	30.5655i	0.585182	+	1.28137i	0.938310	+	0.345795i	$0.112391\pi$
$569$	13.9588	+	30.5655i	0.585182	+	1.28137i	−0.353128	+	0.935575i	$0.614882\pi$
$570$	12.3697	+	10.9533i	0.518110	+	0.458781i
$571$	−11.0654	−	5.05342i	−0.463074	−	0.211479i	0.170195	−	0.985410i	$-0.445560\pi$
$571$	−11.0654	−	5.05342i	−0.463074	−	0.211479i	−0.633269	+	0.773932i	$0.718287\pi$
$572$	3.45321	−	24.0176i	0.144386	−	1.00423i
$573$	−10.2371	−	4.80867i	−0.427659	−	0.200885i
$574$			8.59065i			0.358567i
$575$	4.18238	+	11.9883i	0.174417	+	0.499946i
$576$	1.30458	−	2.70149i	0.0543576	−	0.112562i
$577$	−15.4065	+	9.90118i	−0.641382	+	0.412191i	−0.820508	−	0.571635i	$-0.806309\pi$
$577$	−15.4065	+	9.90118i	−0.641382	+	0.412191i	0.179126	+	0.983826i	$0.442673\pi$
$578$	12.9423	+	1.86082i	0.538329	+	0.0774000i
$579$	−4.76711	+	0.633216i	−0.198114	+	0.0263156i
$580$	1.13041	+	3.84984i	0.0469379	+	0.159856i
$581$	−2.31269	+	1.05617i	−0.0959465	+	0.0438173i
$582$	1.21912	−	3.99276i	0.0505340	−	0.165505i
$583$	4.78633	+	33.2897i	0.198230	+	1.37872i
$584$	3.73265	−	12.7122i	0.154458	−	0.526036i
$585$	−9.23413	−	21.4265i	−0.381784	−	0.885877i
$586$	−3.38050	+	5.26016i	−0.139647	+	0.217295i
$587$	−6.76581	+	10.5278i	−0.279255	+	0.434529i	−0.952341	−	0.305035i	$-0.901332\pi$
$587$	−6.76581	+	10.5278i	−0.279255	+	0.434529i	0.673086	+	0.739564i	$0.264968\pi$
$588$	−1.71167	−	0.264899i	−0.0705883	−	0.0109242i
$589$	9.72227	−	33.1110i	0.400599	−	1.36431i
$590$	3.26291	+	22.6941i	0.134332	+	0.934300i
$591$	0.873998	+	0.266860i	0.0359515	+	0.0109771i
$592$	−2.91532	+	1.33138i	−0.119819	+	0.0547194i
$593$	1.86059	+	6.33660i	0.0764054	+	0.260213i	0.988834	−	0.149024i	$-0.0476131\pi$
$593$	1.86059	+	6.33660i	0.0764054	+	0.260213i	−0.912428	+	0.409237i	$0.865795\pi$
$594$	23.6202	+	7.77053i	0.969147	+	0.318829i
$595$	3.00761	+	0.432429i	0.123300	+	0.0177279i
$596$	13.2727	−	8.52984i	0.543671	−	0.349396i
$597$	−27.3490	+	17.1638i	−1.11932	+	0.702469i
$598$	8.98215	−	22.5980i	0.367308	−	0.924100i
$599$		−	38.5168i		−	1.57375i	−0.617109	−	0.786877i	$-0.711696\pi$
$599$		−	38.5168i		−	1.57375i	0.617109	−	0.786877i	$-0.288304\pi$
$600$	−1.94962	+	4.15049i	−0.0795927	+	0.169443i
$601$	−1.75756	+	12.2241i	−0.0716923	+	0.498631i	0.922062	+	0.387042i	$0.126503\pi$
$601$	−1.75756	+	12.2241i	−0.0716923	+	0.498631i	−0.993754	+	0.111589i	$0.964406\pi$
$602$	−3.92097	−	1.79065i	−0.159807	−	0.0729814i
$603$	3.91148	+	0.648440i	0.159288	+	0.0264065i
$604$	4.71068	+	10.3150i	0.191675	+	0.419710i
$605$	11.9523	+	13.7937i	0.485931	+	0.560794i
$606$	20.6741	−	17.5289i	0.839828	−	0.712064i
$607$	11.4432	+	3.36003i	0.464466	+	0.136380i	0.505589	−	0.862775i	$-0.331275\pi$
$607$	11.4432	+	3.36003i	0.464466	+	0.136380i	−0.0411227	+	0.999154i	$0.513093\pi$
$608$	−4.07277	+	4.70023i	−0.165173	+	0.190620i
$609$	0.0486726	−	4.53075i	0.00197231	−	0.183595i
$610$	14.6356	+	9.40571i	0.592577	+	0.380826i
$611$	−30.1490	−	26.1243i	−1.21970	−	1.05688i
$612$	3.98756	−	4.40692i	0.161187	−	0.178139i
$613$	17.7229	−	2.54816i	0.715819	−	0.102919i	0.225224	−	0.974307i	$-0.427689\pi$
$613$	17.7229	−	2.54816i	0.715819	−	0.102919i	0.490595	+	0.871388i	$0.336779\pi$
$614$	6.09351	−	5.28006i	0.245914	−	0.213086i
$615$	19.0654	+	12.5440i	0.768791	+	0.505823i
$616$	−4.59153	+	1.34819i	−0.184998	+	0.0543203i
$617$	−4.25434	+	9.31571i	−0.171273	+	0.375036i	−0.975731	−	0.218974i	$-0.929729\pi$
$617$	−4.25434	+	9.31571i	−0.171273	+	0.375036i	0.804457	+	0.594011i	$0.202456\pi$
$618$	−14.2213	+	6.31090i	−0.572063	+	0.253861i
$619$	14.6887	+	22.8560i	0.590388	+	0.918662i	0.999980	+	0.00639281i	$0.00203491\pi$
$619$	14.6887	+	22.8560i	0.590388	+	0.918662i	−0.409591	+	0.912269i	$0.634329\pi$
$620$	−8.51051			−0.341790
$621$	21.2010	+	13.0965i	0.850766	+	0.525545i
$622$	−3.59129			−0.143998
$623$	−4.62704	−	7.19981i	−0.185378	−	0.288454i
$624$	8.02757	−	3.56235i	0.321360	−	0.142608i
$625$	−1.97463	+	4.32384i	−0.0789853	+	0.172954i
$626$	27.8643	−	8.18169i	1.11368	−	0.327006i
$627$	−43.0636	−	28.3335i	−1.71979	−	1.13153i
$628$	16.8129	−	14.5685i	0.670908	−	0.581345i
$629$	−6.28456	+	0.903584i	−0.250582	+	0.0360283i
$630$	−3.08727	+	3.41195i	−0.123000	+	0.135935i
$631$	−5.49123	−	4.75818i	−0.218602	−	0.189420i	0.538675	−	0.842514i	$-0.318925\pi$
$631$	−5.49123	−	4.75818i	−0.218602	−	0.189420i	−0.757277	+	0.653094i	$0.773471\pi$
$632$	10.2784	+	6.60550i	0.408851	+	0.262753i
$633$	0.487004	−	45.3333i	0.0193567	−	1.80184i
$634$	−9.25800	+	10.6843i	−0.367682	+	0.424328i
$635$	−28.2867	−	8.30572i	−1.12252	−	0.329602i
$636$	−9.28485	+	7.87234i	−0.368168	+	0.312159i
$637$	−3.32052	−	3.83209i	−0.131564	−	0.151833i
$638$	−5.20034	−	11.3872i	−0.205883	−	0.450822i
$639$	−37.5859	−	6.23093i	−1.48687	−	0.246492i
$640$	1.39519	+	0.637160i	0.0551495	+	0.0251860i
$641$	−6.63517	+	46.1486i	−0.262073	+	1.82276i	0.255140	+	0.966904i	$0.417878\pi$
$641$	−6.63517	+	46.1486i	−0.262073	+	1.82276i	−0.517213	+	0.855857i	$0.673031\pi$
$642$	2.13089	−	4.53640i	0.0840996	−	0.179037i
$643$		−	18.1484i		−	0.715704i	−0.933778	−	0.357852i	$-0.883509\pi$
$643$		−	18.1484i		−	0.715704i	0.933778	−	0.357852i	$-0.116491\pi$
$644$	−4.78982	+	0.240029i	−0.188745	+	0.00945846i
$645$	−9.69940	+	6.08720i	−0.381913	+	0.239683i
$646$	−10.3649	+	6.66114i	−0.407803	+	0.262079i
$647$	−4.95833	−	0.712900i	−0.194932	−	0.0280270i	0.0441572	−	0.999025i	$-0.485940\pi$
$647$	−4.95833	−	0.712900i	−0.194932	−	0.0280270i	−0.239089	+	0.970998i	$0.576849\pi$
$648$	2.16231	+	8.73638i	0.0849435	+	0.343198i
$649$	−20.1531	−	68.6351i	−0.791078	−	2.69416i
$650$	−12.2112	+	5.57665i	−0.478961	+	0.218734i
$651$	9.19167	+	2.80651i	0.360250	+	0.109996i
$652$	−1.52689	−	10.6198i	−0.0597978	−	0.415903i
$653$	8.73674	−	29.7546i	0.341895	−	1.16439i	−0.591730	−	0.806136i	$-0.701555\pi$
$653$	8.73674	−	29.7546i	0.341895	−	1.16439i	0.933625	−	0.358252i	$-0.116627\pi$
$654$	−23.7183	−	3.67064i	−0.927458	−	0.143533i
$655$	2.72483	−	4.23992i	0.106468	−	0.165667i
$656$	−4.64445	+	7.22691i	−0.181335	+	0.282163i
$657$	15.7309	+	36.5013i	0.613719	+	1.42405i
$658$	−2.21654	+	7.54884i	−0.0864097	+	0.294284i
$659$	−2.83145	−	19.6932i	−0.110298	−	0.767136i	−0.967630	−	0.252373i	$-0.918789\pi$
$659$	−2.83145	−	19.6932i	−0.110298	−	0.767136i	0.857332	−	0.514763i	$-0.172120\pi$
$660$	−3.71244	+	12.1587i	−0.144507	+	0.473276i
$661$	−1.40628	+	0.642225i	−0.0546979	+	0.0249797i	−0.442576	−	0.896731i	$-0.645935\pi$
$661$	−1.40628	+	0.642225i	−0.0546979	+	0.0249797i	0.387878	+	0.921711i	$0.373208\pi$
$662$	5.61136	+	19.1105i	0.218092	+	0.742752i
$663$	17.2472	−	2.29095i	0.669826	−	0.0889732i
$664$	−2.51657	−	0.361828i	−0.0976617	−	0.0140416i
$665$	8.02480	−	5.15723i	0.311189	−	0.199989i
$666$	4.18111	−	8.65812i	0.162015	−	0.335495i
$667$	−2.40473	−	12.3132i	−0.0931117	−	0.476768i
$668$		−	9.70655i		−	0.375558i
$669$	−13.9892	−	6.57116i	−0.540853	−	0.254056i
$670$	−0.288485	+	2.00646i	−0.0111452	+	0.0775163i
$671$	−49.3739	−	22.5483i	−1.90606	−	0.870467i
$672$	−1.29674	−	1.14825i	−0.0500227	−	0.0442946i
$673$	−11.8047	−	25.8488i	−0.455039	−	0.996397i	−0.988590	−	0.150629i	$-0.951870\pi$
$673$	−11.8047	−	25.8488i	−0.455039	−	0.996397i	0.533551	−	0.845768i	$-0.320857\pi$
$674$	9.56329	+	11.0366i	0.368364	+	0.425115i
$675$	−3.44840	−	13.3175i	−0.132729	−	0.512592i
$676$	12.1959	+	3.58104i	0.469073	+	0.137732i
$677$	−8.08507	+	9.33067i	−0.310735	+	0.358607i	−0.889539	−	0.456860i	$-0.848974\pi$
$677$	−8.08507	+	9.33067i	−0.310735	+	0.358607i	0.578804	+	0.815467i	$0.303520\pi$
$678$	−17.9946	−	0.193311i	−0.691078	−	0.00742406i
$679$	−2.02766	−	1.30310i	−0.0778143	−	0.0500082i
$680$	2.29637	+	1.98982i	0.0880619	+	0.0763061i
$681$	0.651864	+	2.31162i	0.0249795	+	0.0885815i
$682$	26.2822	−	3.77881i	1.00640	−	0.144698i
$683$	−24.8856	+	21.5635i	−0.952220	+	0.825104i	−0.984680	−	0.174369i	$-0.944211\pi$
$683$	−24.8856	+	21.5635i	−0.952220	+	0.825104i	0.0324600	+	0.999473i	$0.489666\pi$
$684$	0.400827	−	18.6536i	0.0153260	−	0.713238i
$685$	−21.1707	+	6.21628i	−0.808891	+	0.237512i
$686$	−0.415415	+	0.909632i	−0.0158606	+	0.0347299i
$687$	7.13504	+	16.0784i	0.272219	+	0.613431i
$688$	−2.33043	−	3.62623i	−0.0888470	−	0.138249i
$689$	−35.6365			−1.35764
$690$	−6.46136	+	10.9806i	−0.245980	+	0.418026i
$691$	−38.0899			−1.44901			−0.724504	−	0.689271i	$-0.757931\pi$
$691$	−38.0899			−1.44901			−0.724504	+	0.689271i	$0.757931\pi$
$692$	−10.7780	−	16.7709i	−0.409719	−	0.637535i
$693$	8.01915	−	11.9076i	0.304622	−	0.452332i
$694$	−4.39645	+	9.62688i	−0.166887	+	0.365431i
$695$	16.0307	−	4.70705i	0.608081	−	0.178549i
$696$	2.49045	−	3.78519i	0.0944004	−	0.143477i
$697$	−12.8618	+	11.1448i	−0.487176	+	0.422140i
$698$	24.7151	−	3.55349i	0.935480	−	0.134502i
$699$	−9.30344	+	2.62352i	−0.351889	+	0.0992306i
$700$	2.00084	+	1.73373i	0.0756245	+	0.0655290i
$701$	22.9891	+	14.7742i	0.868287	+	0.558014i	0.897228	−	0.441567i	$-0.145577\pi$
$701$	22.9891	+	14.7742i	0.868287	+	0.558014i	−0.0289410	+	0.999581i	$0.509213\pi$
$702$	−11.7117	+	23.6014i	−0.442030	+	0.890778i
$703$	−13.0530	+	15.0640i	−0.492303	+	0.568148i
$704$	−4.59153	−	1.34819i	−0.173050	−	0.0508120i
$705$	13.5167	+	15.9420i	0.509069	+	0.600409i
$706$	10.5662	+	12.1941i	0.397666	+	0.458930i
$707$	−6.50087	−	14.2349i	−0.244490	−	0.535359i
$708$	17.1643	−	19.3839i	0.645072	−	0.728492i
$709$	16.9011	+	7.71845i	0.634733	+	0.289873i	0.706677	−	0.707536i	$-0.250193\pi$
$709$	16.9011	+	7.71845i	0.634733	+	0.289873i	−0.0719448	+	0.997409i	$0.522921\pi$
$710$	2.77209	−	19.2803i	0.104035	−	0.723576i
$711$	−36.3843	+	4.43575i	−1.36452	+	0.166353i
$712$		−	8.55843i		−	0.320741i
$713$	26.4962	+	2.46404i	0.992290	+	0.0922789i
$714$	−1.82399	−	2.90636i	−0.0682610	−	0.108768i
$715$	−31.3088	+	20.1209i	−1.17088	+	0.752480i
$716$	17.6028	+	2.53091i	0.657849	+	0.0945844i
$717$	2.93835	+	22.1211i	0.109735	+	0.826128i
$718$	2.17016	+	7.39088i	0.0809896	+	0.275825i
$719$	21.8317	−	9.97019i	0.814184	−	0.371825i	0.0356002	−	0.999366i	$-0.488666\pi$
$719$	21.8317	−	9.97019i	0.814184	−	0.371825i	0.778584	+	0.627541i	$0.215938\pi$
$720$	−4.44182	+	1.20121i	−0.165537	+	0.0447665i
$721$	1.27838	+	8.89136i	0.0476095	+	0.331132i
$722$	−5.54440	+	18.8825i	−0.206341	+	0.702734i
$723$	−3.11170	+	20.1066i	−0.115725	+	0.747772i
$724$	6.48397	−	10.0892i	0.240975	−	0.374964i
$725$	−3.74435	+	5.82632i	−0.139062	+	0.216384i
$726$	3.15222	−	20.3685i	0.116990	−	0.755944i
$727$	8.67007	−	29.5275i	0.321555	−	1.09512i	−0.627136	−	0.778910i	$-0.715773\pi$
$727$	8.67007	−	29.5275i	0.321555	−	1.09512i	0.948691	−	0.316206i	$-0.102409\pi$
$728$	−0.721619	−	5.01897i	−0.0267450	−	0.186015i
$729$	−21.7265	−	16.0300i	−0.804684	−	0.593703i
$730$	−18.4847	+	8.44167i	−0.684149	+	0.312440i
$731$	−2.40582	−	8.19348i	−0.0889825	−	0.303047i
$732$	−2.58688	−	19.4751i	−0.0956139	−	0.719819i
$733$	−24.7541	−	3.55911i	−0.914315	−	0.131459i	−0.330931	−	0.943655i	$-0.607363\pi$
$733$	−24.7541	−	3.55911i	−0.914315	−	0.131459i	−0.583384	+	0.812196i	$0.698272\pi$
$734$	−3.66265	+	2.35384i	−0.135191	+	0.0868819i
$735$	1.41218	+	2.25018i	0.0520890	+	0.0829990i
$736$	−4.15922	−	2.38765i	−0.153311	−	0.0880099i
$737$		−	6.32445i		−	0.232964i
$738$	−3.11886	−	25.5825i	−0.114807	−	0.941706i
$739$	0.111204	−	0.773442i	0.00409071	−	0.0284515i	−0.987674	−	0.156526i	$-0.949971\pi$
$739$	0.111204	−	0.773442i	0.00409071	−	0.0284515i	0.991765	+	0.128074i	$0.0408796\pi$
$740$	4.47149	+	2.04206i	0.164375	+	0.0750676i
$741$	36.2105	−	40.8932i	1.33023	−	1.50225i
$742$	2.91958	+	6.39298i	0.107181	+	0.234694i
$743$	10.2876	+	11.8726i	0.377417	+	0.435562i	0.912399	−	0.409301i	$-0.134227\pi$
$743$	10.2876	+	11.8726i	0.377417	+	0.435562i	−0.534983	+	0.844863i	$0.679682\pi$
$744$	6.21521	+	7.33038i	0.227861	+	0.268745i
$745$	−23.2188	−	6.81766i	−0.850672	−	0.249780i
$746$	0.970626	−	1.12016i	0.0355371	−	0.0410120i
$747$	6.50363	−	3.98485i	0.237955	−	0.145798i
$748$	−7.97518	−	5.12534i	−0.291601	−	0.187401i
$749$	−2.18687	−	1.89494i	−0.0799067	−	0.0692395i
$750$	19.5537	−	5.51404i	0.714002	−	0.201344i
$751$	32.9729	−	4.74079i	1.20320	−	0.172994i	0.488587	−	0.872515i	$-0.337512\pi$
$751$	32.9729	−	4.74079i	1.20320	−	0.172994i	0.714612	+	0.699521i	$0.246603\pi$
$752$	−5.94588	+	5.15213i	−0.216824	+	0.187879i
$753$	10.6930	−	16.2520i	0.389673	−	0.592257i
$754$	12.7272	−	3.73705i	0.463498	−	0.136095i
$755$	7.22521	−	15.8210i	0.262952	−	0.575785i
$756$	5.19345	+	0.167427i	0.188884	+	0.00608927i
$757$	−15.6122	−	24.2931i	−0.567435	−	0.882946i	0.432389	−	0.901687i	$-0.357671\pi$
$757$	−15.6122	−	24.2931i	−0.567435	−	0.882946i	−0.999824	+	0.0187408i	$0.994034\pi$
$758$	−15.4277			−0.560359
$759$	15.0784	−	36.7794i	0.547312	−	1.33501i
$760$	9.53910			0.346020
$761$	5.54222	+	8.62387i	0.200905	+	0.312615i	0.927057	−	0.374919i	$-0.122330\pi$
$761$	5.54222	+	8.62387i	0.200905	+	0.312615i	−0.726152	+	0.687534i	$0.758693\pi$
$762$	13.5037	+	30.4299i	0.489188	+	1.10236i
$763$	−5.75631	+	12.6046i	−0.208392	+	0.456316i
$764$	−6.26544	+	1.83970i	−0.226676	+	0.0665580i
$765$	−9.11351	−	0.195831i	−0.329500	−	0.00708027i
$766$	−16.1753	+	14.0160i	−0.584437	+	0.506418i
$767$	75.0246	−	10.7869i	2.70898	−	0.389493i
$768$	−0.470095	−	1.66704i	−0.0169631	−	0.0601540i
$769$	31.0659	+	26.9188i	1.12027	+	0.970716i	0.999758	−	0.0219961i	$-0.00700215\pi$
$769$	31.0659	+	26.9188i	1.12027	+	0.970716i	0.120508	+	0.992712i	$0.461548\pi$
$770$	6.17459	+	3.96817i	0.222517	+	0.143003i
$771$	−0.300388	−	0.00322699i	−0.0108182	−	0.000116217i
$772$	−1.81820	+	2.09831i	−0.0654383	+	0.0755199i
$773$	23.0313	+	6.76259i	0.828377	+	0.243233i	0.668320	−	0.743874i	$-0.267014\pi$
$773$	23.0313	+	6.76259i	0.828377	+	0.243233i	0.160057	+	0.987108i	$0.448832\pi$
$774$	12.3266	+	3.90894i	0.443069	+	0.140504i
$775$	−9.61992	−	11.1020i	−0.345558	−	0.398795i
$776$	−1.00127	−	2.19247i	−0.0359434	−	0.0787050i
$777$	−4.15596	−	3.68007i	−0.149094	−	0.132022i
$778$	18.9375	+	8.64846i	0.678942	+	0.310062i
$779$	−7.60357	+	52.8840i	−0.272426	+	1.89476i
$780$	−12.1924	−	5.72716i	−0.436558	−	0.205065i
$781$			60.7723i			2.17460i
$782$	−6.57330	−	6.85987i	−0.235061	−	0.245308i
$783$	1.49996	+	13.5100i	0.0536041	+	0.482809i
$784$	−0.841254	+	0.540641i	−0.0300448	+	0.0193086i
$785$	−33.7744	−	4.85603i	−1.20546	−	0.173319i
$786$	−5.64192	+	0.749419i	−0.201241	+	0.0267309i
$787$	11.5984	+	39.5006i	0.413439	+	1.40804i	0.858625	+	0.512605i	$0.171319\pi$
$787$	11.5984	+	39.5006i	0.413439	+	1.40804i	−0.445186	+	0.895438i	$0.646862\pi$
$788$	0.479922	−	0.219173i	0.0170965	−	0.00780772i
$789$	4.39295	−	14.3875i	0.156393	−	0.512207i
$790$	−2.66694	−	18.5490i	−0.0948854	−	0.659943i
$791$	−2.92714	+	9.96892i	−0.104077	+	0.354454i
$792$	13.1839	−	5.68182i	0.468468	−	0.201895i
$793$	31.0944	−	48.3839i	1.10420	−	1.71816i
$794$	−17.8117	+	27.7155i	−0.632113	+	0.983588i
$795$	18.4512	+	2.85551i	0.654397	+	0.101275i
$796$	−5.25204	+	17.8868i	−0.186154	+	0.633981i
$797$	−3.95645	−	27.5177i	−0.140145	−	0.974727i	−0.931596	−	0.363495i	$-0.881583\pi$
$797$	−3.95645	−	27.5177i	−0.140145	−	0.974727i	0.791452	−	0.611232i	$-0.209326\pi$
$798$	−10.3026	−	3.14572i	−0.364708	−	0.111357i
$799$	−14.1776	+	6.47469i	−0.501567	+	0.229058i
$800$	0.745883	+	2.54024i	0.0263709	+	0.0898112i
$801$	16.3930	+	19.7608i	0.579218	+	0.698214i
$802$	−32.2267	−	4.63350i	−1.13796	−	0.163614i
$803$	53.3362	−	34.2771i	1.88219	−	1.20961i
$804$	1.93891	−	1.21683i	0.0683801	−	0.0429144i
$805$	5.08922	+	5.31109i	0.179372	+	0.187191i
$806$			28.1350i			0.991012i
$807$	0.781838	−	1.66443i	0.0275220	−	0.0585908i
$808$	2.22710	−	15.4898i	0.0783490	−	0.544929i
$809$	−27.6779	−	12.6401i	−0.973104	−	0.444402i	−0.135559	−	0.990769i	$-0.543283\pi$
$809$	−27.6779	−	12.6401i	−0.973104	−	0.444402i	−0.837546	+	0.546368i	$0.816010\pi$
$810$	7.95502	−	11.2815i	0.279511	−	0.396390i
$811$	7.67426	+	16.8043i	0.269480	+	0.590078i	0.995195	−	0.0979175i	$-0.0312181\pi$
$811$	7.67426	+	16.8043i	0.269480	+	0.590078i	−0.725715	+	0.687995i	$0.758491\pi$
$812$	−1.71310	−	1.97703i	−0.0601181	−	0.0693800i
$813$	−41.0826	+	34.8327i	−1.44083	+	1.22164i
$814$	−14.7156	−	4.32088i	−0.515780	−	0.151447i
$815$	−10.7764	+	12.4366i	−0.377481	+	0.435636i
$816$	0.0368594	−	3.43110i	0.00129034	−	0.120113i
$817$	−22.5526	−	14.4937i	−0.789015	−	0.507069i
$818$	−8.12680	−	7.04191i	−0.284147	−	0.246215i
$819$	11.2796	+	10.2062i	0.394141	+	0.356635i
$820$	13.0421	−	1.87518i	0.455451	−	0.0654840i
$821$	20.1876	−	17.4926i	0.704552	−	0.610498i	−0.227091	−	0.973874i	$-0.572921\pi$
$821$	20.1876	−	17.4926i	0.704552	−	0.610498i	0.931643	+	0.363376i	$0.118376\pi$
$822$	20.8152	+	13.6953i	0.726014	+	0.477678i
$823$	−29.0031	+	8.51607i	−1.01098	+	0.296851i	−0.744956	−	0.667114i	$-0.767529\pi$
$823$	−29.0031	+	8.51607i	−1.01098	+	0.296851i	−0.266027	+	0.963965i	$0.585711\pi$
$824$	−3.73159	+	8.17104i	−0.129996	+	0.284652i
$825$	−20.0574	+	8.90079i	−0.698310	+	0.309886i
$826$	−8.08161	−	12.5752i	−0.281195	−	0.437548i
$827$	12.7885			0.444700			0.222350	−	0.974967i	$-0.428627\pi$
$827$	12.7885			0.444700			0.222350	+	0.974967i	$0.428627\pi$
$828$	14.1767	−	2.45375i	0.492675	−	0.0852738i
$829$	33.8268			1.17485			0.587427	−	0.809277i	$-0.300141\pi$
$829$	33.8268			1.17485			0.587427	+	0.809277i	$0.300141\pi$
$830$	2.10827	+	3.28054i	0.0731792	+	0.113869i
$831$	−28.3504	+	12.5809i	−0.983464	+	0.436427i
$832$	2.10639	−	4.61236i	0.0730261	−	0.159905i
$833$	−1.90082	+	0.558130i	−0.0658594	+	0.0193381i
$834$	−15.7616	−	10.3703i	−0.545778	−	0.359093i
$835$	−11.2515	+	9.74944i	−0.389373	+	0.337393i
$836$	−29.4587	+	4.23552i	−1.01885	+	0.146489i
$837$	−28.3913	−	5.02060i	−0.981345	−	0.173537i
$838$	6.56051	+	5.68472i	0.226629	+	0.196375i
$839$	31.3162	+	20.1257i	1.08116	+	0.694816i	0.954824	−	0.297172i	$-0.0960434\pi$
$839$	31.3162	+	20.1257i	1.08116	+	0.694816i	0.126331	+	0.991988i	$0.459680\pi$
$840$	−0.0285375	+	2.65645i	−0.000984639	+	0.0916563i
$841$	−14.5095	+	16.7449i	−0.500328	+	0.577410i
$842$	6.16258	+	1.80950i	0.212377	+	0.0623594i
$843$	−5.47120	+	4.63886i	−0.188438	+	0.159771i
$844$	−17.1408	−	19.7815i	−0.590011	−	0.680908i
$845$	−8.09879	−	17.7339i	−0.278607	−	0.610064i
$846$	3.86011	−	23.2848i	0.132713	−	0.800547i
$847$	−10.8244	−	4.94333i	−0.371930	−	0.169855i
$848$	−1.00020	+	6.95656i	−0.0343471	+	0.238889i
$849$	−1.38205	+	2.94222i	−0.0474319	+	0.100977i
$850$			5.24484i			0.179896i
$851$	−13.3301	−	7.65227i	−0.456949	−	0.262316i
$852$	−18.6312	+	11.6927i	−0.638295	+	0.400584i
$853$	10.7151	−	6.88617i	0.366878	−	0.235778i	−0.344192	−	0.938899i	$-0.611847\pi$
$853$	10.7151	−	6.88617i	0.366878	−	0.235778i	0.711070	+	0.703121i	$0.248211\pi$
$854$	−11.2272	−	1.61423i	−0.384188	−	0.0552380i
$855$	−22.0251	+	18.2714i	−0.753243	+	0.624869i
$856$	−0.815235	−	2.77644i	−0.0278642	−	0.0948967i
$857$	−13.2793	+	6.06444i	−0.453612	+	0.207157i	−0.629101	−	0.777324i	$-0.716577\pi$
$857$	−13.2793	+	6.06444i	−0.453612	+	0.207157i	0.175489	+	0.984481i	$0.443849\pi$
$858$	40.1955	+	12.2730i	1.37225	+	0.418993i
$859$	−5.60409	−	38.9773i	−0.191209	−	1.32989i	−0.828814	−	0.559525i	$-0.810984\pi$
$859$	−5.60409	−	38.9773i	−0.191209	−	1.32989i	0.637605	−	0.770364i	$-0.279925\pi$
$860$	−1.86265	+	6.34360i	−0.0635158	+	0.216315i
$861$	−14.7044	−	2.27565i	−0.501124	−	0.0775540i
$862$	17.0421	−	26.5180i	0.580455	−	0.903206i
$863$	24.8544	−	38.6743i	0.846055	−	1.31649i	−0.100827	−	0.994904i	$-0.532149\pi$
$863$	24.8544	−	38.6743i	0.846055	−	1.31649i	0.946881	−	0.321583i	$-0.104215\pi$
$864$	4.27849	+	2.94864i	0.145557	+	0.100315i
$865$	−8.61457	+	29.3385i	−0.292904	+	0.997540i
$866$	−4.52463	−	31.4695i	−0.153753	−	1.06938i
$867$	−6.61352	+	21.6601i	−0.224607	+	0.735615i
$868$	5.04725	−	2.30500i	0.171315	−	0.0782369i
$869$	16.4721	+	56.0988i	0.558778	+	1.90302i
$870$	−6.88911	+	0.915083i	−0.233563	+	0.0310242i
$871$	6.63318	+	0.953708i	0.224757	+	0.0323151i
$872$	−11.6571	+	7.49154i	−0.394758	+	0.253695i
$873$	6.51135	+	3.14441i	0.220376	+	0.106422i
$874$	−29.6986	−	2.76185i	−1.00457	−	0.0934208i
$875$		−	11.7296i		−	0.396534i
$876$	20.7704	+	9.75653i	0.701768	+	0.329643i
$877$	−3.83006	+	26.6387i	−0.129332	+	0.899523i	0.817071	+	0.576536i	$0.195596\pi$
$877$	−3.83006	+	26.6387i	−0.129332	+	0.899523i	−0.946403	+	0.322987i	$0.895313\pi$
$878$	6.50461	+	2.97056i	0.219520	+	0.100251i
$879$	−8.10819	−	7.17972i	−0.273482	−	0.242166i
$880$	3.04904	+	6.67647i	0.102783	+	0.225064i
$881$	9.35424	+	10.7954i	0.315152	+	0.363705i	0.891120	−	0.453767i	$-0.149920\pi$
$881$	9.35424	+	10.7954i	0.315152	+	0.363705i	−0.575968	+	0.817472i	$0.695375\pi$
$882$	0.906841	−	2.85966i	0.0305349	−	0.0962897i
$883$	−31.1205	−	9.13779i	−1.04729	−	0.307511i	−0.287566	−	0.957761i	$-0.592846\pi$
$883$	−31.1205	−	9.13779i	−1.04729	−	0.307511i	−0.759721	+	0.650249i	$0.774664\pi$
$884$	6.57817	−	7.59161i	0.221248	−	0.255333i
$885$	−39.7092	−	0.426585i	−1.33481	−	0.0143395i
$886$	−27.1644	−	17.4575i	−0.912605	−	0.586496i
$887$	10.0596	+	8.71666i	0.337767	+	0.292677i	0.807184	−	0.590300i	$-0.200990\pi$
$887$	10.0596	+	8.71666i	0.337767	+	0.292677i	−0.469417	+	0.882977i	$0.655536\pi$
$888$	−1.50663	−	5.34275i	−0.0505590	−	0.179291i
$889$	19.0253	−	2.73542i	0.638087	−	0.0917430i
$890$	−9.92061	+	8.59626i	−0.332540	+	0.288147i
$891$	−19.5576	+	38.3716i	−0.655203	+	1.28550i
$892$	−8.56186	+	2.51399i	−0.286672	+	0.0841746i
$893$	−20.3265	+	44.5087i	−0.680199	+	1.48943i
$894$	11.0844	+	24.9781i	0.370717	+	0.835392i
$895$	−14.7469	−	22.9466i	−0.492935	−	0.767021i
$896$	−1.00000			−0.0334077
$897$	36.3010	+	21.3607i	1.21206	+	0.713213i
$898$	21.7082			0.724412
$899$	7.84752	+	12.2110i	0.261729	+	0.407259i
$900$	−6.58783	−	4.43657i	−0.219594	−	0.147886i
$901$	−5.78386	+	12.6649i	−0.192688	+	0.421929i
$902$	−39.4442	+	11.5819i	−1.31335	+	0.385633i
$903$	4.10367	−	6.23709i	0.136561	−	0.207557i
$904$	−7.85207	+	6.80386i	−0.261156	+	0.226293i
$905$	−18.2077	+	2.61787i	−0.605244	+	0.0870210i
$906$	−18.9037	+	5.33074i	−0.628034	+	0.177102i
$907$	11.1088	+	9.62584i	0.368862	+	0.319621i	0.819493	−	0.573090i	$-0.194255\pi$
$907$	11.1088	+	9.62584i	0.368862	+	0.319621i	−0.450631	+	0.892711i	$0.648801\pi$
$908$	1.16654	+	0.749688i	0.0387129	+	0.0248793i
$909$	24.5273	+	40.0307i	0.813519	+	1.32773i
$910$	−5.09299	+	5.87762i	−0.168831	+	0.194841i
$911$	−52.6801	−	15.4683i	−1.74537	−	0.512487i	−0.755585	−	0.655051i	$-0.772647\pi$
$911$	−52.6801	−	15.4683i	−1.74537	−	0.512487i	−0.989786	+	0.142564i	$0.954465\pi$
$912$	−6.96639	−	8.21635i	−0.230680	−	0.272070i
$913$	−7.96738	−	9.19485i	−0.263682	−	0.304305i
$914$	−0.819889	−	1.79531i	−0.0271195	−	0.0593834i
$915$	−19.9764	+	22.5598i	−0.660401	+	0.745803i
$916$	9.23810	+	4.21890i	0.305235	+	0.139396i
$917$	−0.467643	+	3.25253i	−0.0154429	+	0.107408i
$918$	6.48691	+	7.99278i	0.214100	+	0.263801i
$919$			6.66268i			0.219781i	0.993944	+	0.109891i	$0.0350501\pi$
$919$			6.66268i			0.219781i	−0.993944	+	0.109891i	$0.964950\pi$
$920$	1.40993	+	7.21941i	0.0464842	+	0.238017i
$921$	7.42357	+	11.8288i	0.244615	+	0.389772i
$922$	−22.2566	+	14.3035i	−0.732983	+	0.471059i
$923$	−63.7389	−	9.16428i	−2.09799	−	0.301646i
$924$	−1.09138	−	8.21633i	−0.0359037	−	0.270297i
$925$	2.39051	+	8.14133i	0.0785995	+	0.267685i
$926$	−7.92459	+	3.61904i	−0.260418	+	0.118929i
$927$	−7.03500	−	26.0139i	−0.231060	−	0.854409i
$928$	−0.372293	−	2.58935i	−0.0122211	−	0.0849996i
$929$	3.33867	−	11.3705i	0.109538	−	0.373053i	−0.886419	−	0.462884i	$-0.846815\pi$
$929$	3.33867	−	11.3705i	0.109538	−	0.373053i	0.995957	+	0.0898311i	$0.0286327\pi$
$930$	2.25442	−	14.5672i	0.0739254	−	0.477678i
$931$	−3.36241	+	5.23201i	−0.110198	+	0.171472i
$932$	−3.01722	+	4.69489i	−0.0988324	+	0.153786i
$933$	0.951328	−	6.14711i	0.0311451	−	0.201247i
$934$	−0.490915	+	1.67190i	−0.0160632	+	0.0547063i
$935$	2.06933	+	14.3925i	0.0676744	+	0.470686i
$936$	3.97110	+	14.6843i	0.129799	+	0.479970i
$937$	−41.0406	+	18.7426i	−1.34074	+	0.612294i	−0.951160	−	0.308700i	$-0.900106\pi$
$937$	−41.0406	+	18.7426i	−1.34074	+	0.612294i	−0.389577	+	0.920994i	$0.627379\pi$
$938$	−0.372344	−	1.26809i	−0.0121575	−	0.0414045i
$939$	6.62317	+	49.8619i	0.216139	+	1.62718i
$940$	11.9443	+	1.71733i	0.389581	+	0.0560132i
$941$	−2.36081	+	1.51720i	−0.0769602	+	0.0494593i	−0.578555	−	0.815643i	$-0.696383\pi$
$941$	−2.36081	+	1.51720i	−0.0769602	+	0.0494593i	0.501595	+	0.865103i	$0.332747\pi$
$942$	20.4827	+	32.6374i	0.667364	+	1.06338i
$943$	−41.1477	+	2.06200i	−1.33995	+	0.0671481i
$944$		−	14.9482i		−	0.486523i
$945$	−5.02233	−	6.18822i	−0.163376	−	0.201303i
$946$	2.93558	−	20.4174i	0.0954438	−	0.663826i
$947$	40.3558	+	18.4299i	1.31139	+	0.598890i	0.943621	−	0.331029i	$-0.107396\pi$
$947$	40.3558	+	18.4299i	1.31139	+	0.598890i	0.367765	+	0.929919i	$0.380123\pi$
$948$	−14.0292	+	15.8434i	−0.455647	+	0.514570i
$949$	27.9074	+	61.1087i	0.905913	+	1.98367i
$950$	10.7826	+	12.4438i	0.349834	+	0.403730i
$951$	−15.8356	−	18.6769i	−0.513505	−	0.605641i
$952$	−1.90082	−	0.558130i	−0.0616058	−	0.0180891i
$953$	−2.03097	+	2.34387i	−0.0657897	+	0.0759254i	−0.787690	−	0.616071i	$-0.788723\pi$
$953$	−2.03097	+	2.34387i	−0.0657897	+	0.0759254i	0.721901	+	0.691997i	$0.243269\pi$
$954$	−11.0153	−	17.9780i	−0.356635	−	0.582060i
$955$	8.42564	+	5.41483i	0.272647	+	0.175220i
$956$	9.73693	+	8.43710i	0.314915	+	0.272875i
$957$	20.8687	−	5.88484i	0.674588	−	0.190230i
$958$	30.4423	−	4.37695i	0.983547	−	0.141413i
$959$	10.8719	−	9.42055i	0.351072	−	0.304205i
$960$	−1.46019	+	2.21932i	−0.0471275	+	0.0716282i
$961$	0.203632	−	0.0597916i	0.00656876	−	0.00192876i
$962$	6.75087	−	14.7823i	0.217657	−	0.476602i
$963$	7.20037	+	4.84908i	0.232029	+	0.156259i
$964$	6.35076	+	9.88198i	0.204544	+	0.318277i
$965$	4.25852			0.137086
$966$	0.857967	−	8.26220i	0.0276046	−	0.265832i
$967$	−3.88990			−0.125091			−0.0625454	−	0.998042i	$-0.519922\pi$
$967$	−3.88990			−0.125091			−0.0625454	+	0.998042i	$0.519922\pi$
$968$	−6.43348	−	10.0107i	−0.206780	−	0.321756i
$969$	−8.65604	−	19.5059i	−0.278072	−	0.626621i
$970$	−1.53573	+	3.36279i	−0.0493094	+	0.107973i
$971$	27.1365	−	7.96799i	0.870851	−	0.255705i	0.184374	−	0.982856i	$-0.440974\pi$
$971$	27.1365	−	7.96799i	0.870851	−	0.255705i	0.686477	+	0.727151i	$0.259156\pi$
$972$	−15.5266	+	1.38691i	−0.498017	+	0.0444851i
$973$	−8.23234	+	7.13337i	−0.263917	+	0.228685i
$974$	−5.26124	+	0.756453i	−0.168581	+	0.0242383i
$975$	−6.31068	−	22.3788i	−0.202104	−	0.716694i
$976$	−8.57224	−	7.42789i	−0.274391	−	0.237761i
$977$	−20.9846	−	13.4860i	−0.671358	−	0.431455i	0.160057	−	0.987108i	$-0.448832\pi$
$977$	−20.9846	−	13.4860i	−0.671358	−	0.431455i	−0.831415	+	0.555652i	$0.812469\pi$
$978$	18.5821	+	0.199622i	0.594189	+	0.00638321i
$979$	26.8200	−	30.9519i	0.857170	−	0.989227i
$980$	1.47166	+	0.432119i	0.0470105	+	0.0138035i
$981$	12.5659	−	39.6256i	0.401198	−	1.26515i
$982$	9.22514	+	10.6464i	0.294386	+	0.339739i
$983$	−7.34481	−	16.0829i	−0.234263	−	0.512965i	0.755592	−	0.655042i	$-0.227349\pi$
$983$	−7.34481	−	16.0829i	−0.234263	−	0.512965i	−0.989856	+	0.142077i	$0.954622\pi$
$984$	−11.1398	−	9.86419i	−0.355124	−	0.314459i
$985$	−0.736100	−	0.336166i	−0.0234541	−	0.0107111i
$986$	0.737535	−	5.12967i	0.0234879	−	0.163362i
$987$	−12.3340	−	5.79367i	−0.392595	−	0.184415i
$988$		−	31.5354i		−	1.00328i
$989$	7.63574	−	19.2106i	0.242802	−	0.610860i
$990$	−19.8283	−	9.57531i	−0.630184	−	0.304323i
$991$	12.6710	−	8.14315i	0.402507	−	0.258676i	−0.323689	−	0.946164i	$-0.604923\pi$
$991$	12.6710	−	8.14315i	0.402507	−	0.258676i	0.726196	+	0.687488i	$0.241287\pi$
$992$	5.49220	+	0.789658i	0.174377	+	0.0250717i
$993$	−34.1974	+	4.54246i	−1.08522	+	0.144151i
$994$	3.57789	+	12.1852i	0.113484	+	0.386491i
$995$	26.0089	−	11.8779i	0.824539	−	0.376554i
$996$	1.28597	−	4.21169i	0.0407474	−	0.133453i
$997$	−6.88072	−	47.8565i	−0.217915	−	1.51563i	−0.745717	−	0.666262i	$-0.767893\pi$
$997$	−6.88072	−	47.8565i	−0.217915	−	1.51563i	0.527803	−	0.849367i	$-0.323016\pi$
$998$	−11.2566	+	38.3365i	−0.356322	+	1.21352i
$999$	13.7123	+	9.45022i	0.433839	+	0.298992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.r.b.701.13	yes	240
3.2	odd	2		966.2.r.a.701.11	yes	240
23.21	odd	22		966.2.r.a.113.11	✓	240
69.44	even	22	inner	966.2.r.b.113.13	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.r.a.113.11	✓	240	23.21	odd	22
966.2.r.a.701.11	yes	240	3.2	odd	2
966.2.r.b.113.13	yes	240	69.44	even	22	inner
966.2.r.b.701.13	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(-1.58317 + 0.702554i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.47166 - 0.432119i) q^{5} +(-1.44695 - 0.952016i) q^{6} +(-0.755750 + 0.654861i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.01284 - 2.22452i) q^{9} +O(q^{10})\)	\(q+(0.540641 + 0.841254i) q^{2} +(-1.58317 + 0.702554i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.47166 - 0.432119i) q^{5} +(-1.44695 - 0.952016i) q^{6} +(-0.755750 + 0.654861i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.01284 - 2.22452i) q^{9} +(1.15916 + 1.00442i) q^{10} +(-4.02571 - 2.58716i) q^{11} +(0.0186059 - 1.73195i) q^{12} +(3.32052 - 3.83209i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-2.02630 + 1.71804i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.822964 - 1.80204i) q^{17} +(2.95961 + 0.490639i) q^{18} +(-5.65727 - 2.58359i) q^{19} +(-0.218281 + 1.51818i) q^{20} +(0.736403 - 1.56771i) q^{21} -4.78537i q^{22} +(1.11914 - 4.66342i) q^{23} +(1.46707 - 0.920711i) q^{24} +(-2.22721 + 1.43134i) q^{25} +(5.01897 + 0.721619i) q^{26} +(-1.62381 + 4.93591i) q^{27} +(-0.281733 - 0.959493i) q^{28} +(2.37958 - 1.08672i) q^{29} +(-2.54081 - 0.775790i) q^{30} +(0.789658 + 5.49220i) q^{31} +(0.281733 - 0.959493i) q^{32} +(8.19099 + 1.26764i) q^{33} +(1.07104 - 1.66658i) q^{34} +(-0.829230 + 1.29031i) q^{35} +(1.18733 + 2.75504i) q^{36} +(0.902936 - 3.07512i) q^{37} +(-0.885098 - 6.15599i) q^{38} +(-2.56469 + 8.39968i) q^{39} +(-1.39519 + 0.637160i) q^{40} +(-2.42026 - 8.24266i) q^{41} +(1.71697 - 0.228066i) q^{42} +(4.26663 + 0.613449i) q^{43} +(4.02571 - 2.58716i) q^{44} +(2.00096 - 4.14353i) q^{45} +(4.52818 - 1.57975i) q^{46} -7.86753i q^{47} +(1.56771 + 0.736403i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-2.40824 - 1.09980i) q^{50} +(2.56892 + 2.27475i) q^{51} +(2.10639 + 4.61236i) q^{52} +(-4.60242 - 5.31148i) q^{53} +(-5.03025 + 1.30252i) q^{54} +(-7.04244 - 2.06785i) q^{55} +(0.654861 - 0.755750i) q^{56} +(10.7715 + 0.115716i) q^{57} +(2.20070 + 1.41431i) q^{58} +(11.2971 + 9.78900i) q^{59} +(-0.721027 - 2.55689i) q^{60} +(11.2272 - 1.61423i) q^{61} +(-4.19341 + 3.63361i) q^{62} +(-0.0644489 + 2.99931i) q^{63} +(0.959493 - 0.281733i) q^{64} +(3.23077 - 7.07440i) q^{65} +(3.36198 + 7.57603i) q^{66} +(0.714523 + 1.11182i) q^{67} +1.98106 q^{68} +(1.50452 + 8.16924i) q^{69} -1.53379 q^{70} +(-6.86593 - 10.6836i) q^{71} +(-1.67577 + 2.48833i) q^{72} +(-5.50379 + 12.0516i) q^{73} +(3.07512 - 0.902936i) q^{74} +(2.52045 - 3.83078i) q^{75} +(4.70023 - 4.07277i) q^{76} +(4.73666 - 0.681029i) q^{77} +(-8.45284 + 2.38365i) q^{78} +(-9.23367 - 8.00102i) q^{79} +(-1.29031 - 0.829230i) q^{80} +(-0.896982 - 8.95519i) q^{81} +(5.62568 - 6.49238i) q^{82} +(2.43946 + 0.716290i) q^{83} +(1.12013 + 1.32111i) q^{84} +(-1.98982 - 2.29637i) q^{85} +(1.79065 + 3.92097i) q^{86} +(-3.00379 + 3.39224i) q^{87} +(4.35292 + 1.98791i) q^{88} +(-1.21799 + 8.47132i) q^{89} +(4.56755 - 0.556847i) q^{90} +5.07058i q^{91} +(3.77709 + 2.95526i) q^{92} +(-5.10872 - 8.14029i) q^{93} +(6.61858 - 4.25351i) q^{94} +(-9.44201 - 1.35756i) q^{95} +(0.228066 + 1.71697i) q^{96} +(0.679054 + 2.31265i) q^{97} +(0.909632 - 0.415415i) q^{98} +(-13.8583 + 3.74773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more