LMFDB - Embedded newform 280.2.br.a.67.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(67,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))

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

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

chi := DirichletCharacter("280.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.br (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.19
Character	$\chi$	$=$	280.67
Dual form			280.2.br.a.163.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309645 + 1.37990i) q^{2} +(-0.220018 - 0.821117i) q^{3} +(-1.80824 - 0.854556i) q^{4} +(-2.20849 - 0.350108i) q^{5} +(1.20119 - 0.0493476i) q^{6} +(2.38534 + 1.14463i) q^{7} +(1.73911 - 2.23058i) q^{8} +(1.97225 - 1.13868i) q^{9} +O(q^{10})$	\(q+(-0.309645 + 1.37990i) q^{2} +(-0.220018 - 0.821117i) q^{3} +(-1.80824 - 0.854556i) q^{4} +(-2.20849 - 0.350108i) q^{5} +(1.20119 - 0.0493476i) q^{6} +(2.38534 + 1.14463i) q^{7} +(1.73911 - 2.23058i) q^{8} +(1.97225 - 1.13868i) q^{9} +(1.16696 - 2.93908i) q^{10} +(0.933320 - 1.61656i) q^{11} +(-0.303846 + 1.67279i) q^{12} +(1.16000 + 1.16000i) q^{13} +(-2.31808 + 2.93709i) q^{14} +(0.198427 + 1.89046i) q^{15} +(2.53947 + 3.09049i) q^{16} +(5.24683 - 1.40589i) q^{17} +(0.960566 + 3.07409i) q^{18} +(1.58626 - 0.915829i) q^{19} +(3.69429 + 2.52036i) q^{20} +(0.415057 - 2.21048i) q^{21} +(1.94169 + 1.78845i) q^{22} +(0.605573 - 2.26003i) q^{23} +(-2.21420 - 0.937248i) q^{24} +(4.75485 + 1.54642i) q^{25} +(-1.95987 + 1.24149i) q^{26} +(-3.17222 - 3.17222i) q^{27} +(-3.33511 - 4.10816i) q^{28} -3.08470 q^{29} +(-2.67008 - 0.311561i) q^{30} +(-5.06562 - 2.92464i) q^{31} +(-5.05089 + 2.54725i) q^{32} +(-1.53273 - 0.410694i) q^{33} +(0.315325 + 7.67542i) q^{34} +(-4.86725 - 3.36302i) q^{35} +(-4.53937 + 0.373607i) q^{36} +(9.54578 + 2.55778i) q^{37} +(0.772574 + 2.47246i) q^{38} +(0.697275 - 1.20772i) q^{39} +(-4.62176 + 4.31733i) q^{40} -4.49591 q^{41} +(2.92172 + 1.25720i) q^{42} +(-1.18585 + 1.18585i) q^{43} +(-3.06911 + 2.12555i) q^{44} +(-4.75436 + 1.82426i) q^{45} +(2.93110 + 1.53544i) q^{46} +(-4.50200 - 1.20631i) q^{47} +(1.97892 - 2.76516i) q^{48} +(4.37966 + 5.46064i) q^{49} +(-3.60622 + 6.08237i) q^{50} +(-2.30879 - 3.99894i) q^{51} +(-1.10627 - 3.08884i) q^{52} +(11.4262 - 3.06164i) q^{53} +(5.35960 - 3.39508i) q^{54} +(-2.62720 + 3.24339i) q^{55} +(6.70155 - 3.33005i) q^{56} +(-1.10101 - 1.10101i) q^{57} +(0.955162 - 4.25658i) q^{58} +(-7.77422 - 4.48845i) q^{59} +(1.25670 - 3.58797i) q^{60} +(-8.16355 + 4.71323i) q^{61} +(5.60425 - 6.08445i) q^{62} +(6.00785 - 0.458642i) q^{63} +(-1.95097 - 7.75846i) q^{64} +(-2.15572 - 2.96797i) q^{65} +(1.04132 - 1.98784i) q^{66} +(-3.25136 + 0.871200i) q^{67} +(-10.6889 - 1.94154i) q^{68} -1.98899 q^{69} +(6.14775 - 5.67496i) q^{70} -3.09202i q^{71} +(0.890052 - 6.37956i) q^{72} +(2.17707 + 8.12492i) q^{73} +(-6.48528 + 12.3802i) q^{74} +(0.223641 - 4.24453i) q^{75} +(-3.65097 + 0.300489i) q^{76} +(4.07664 - 2.78773i) q^{77} +(1.45062 + 1.33613i) q^{78} +(5.84357 + 10.1214i) q^{79} +(-4.52638 - 7.71439i) q^{80} +(1.50922 - 2.61405i) q^{81} +(1.39213 - 6.20389i) q^{82} +(4.95881 - 4.95881i) q^{83} +(-2.63950 + 3.64239i) q^{84} +(-12.0798 + 1.26792i) q^{85} +(-1.26916 - 2.00354i) q^{86} +(0.678689 + 2.53290i) q^{87} +(-1.98271 - 4.89322i) q^{88} +(-7.31128 + 4.22117i) q^{89} +(-1.04513 - 7.12540i) q^{90} +(1.43922 + 4.09476i) q^{91} +(-3.02634 + 3.56918i) q^{92} +(-1.28694 + 4.80294i) q^{93} +(3.05860 - 5.83877i) q^{94} +(-3.82388 + 1.46724i) q^{95} +(3.20288 + 3.58693i) q^{96} +(6.17682 + 6.17682i) q^{97} +(-8.89127 + 4.35263i) q^{98} -4.25101i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.309645	+	1.37990i	−0.218952	+	0.975736i
$2$	−0.309645	+	1.37990i	−0.218952	+	0.975736i
$3$	−0.220018	−	0.821117i	−0.127027	−	0.474072i	0.872877	−	0.487941i	$-0.162252\pi$
$3$	−0.220018	−	0.821117i	−0.127027	−	0.474072i	−0.999904	+	0.0138690i	$0.995585\pi$
$4$	−1.80824	−	0.854556i	−0.904120	−	0.427278i
$5$	−2.20849	−	0.350108i	−0.987666	−	0.156573i
$5$	−2.20849	−	0.350108i	−0.987666	−	0.156573i
$6$	1.20119	−	0.0493476i	0.490382	−	0.0201461i
$7$	2.38534	+	1.14463i	0.901572	+	0.432628i
$7$	2.38534	+	1.14463i	0.901572	+	0.432628i
$8$	1.73911	−	2.23058i	0.614869	−	0.788629i
$9$	1.97225	−	1.13868i	0.657417	−	0.379560i
$10$	1.16696	−	2.93908i	0.369025	−	0.929419i
$11$	0.933320	−	1.61656i	0.281407	−	0.487411i	−0.690325	−	0.723500i	$-0.742532\pi$
$11$	0.933320	−	1.61656i	0.281407	−	0.487411i	0.971731	+	0.236089i	$0.0758657\pi$
$12$	−0.303846	+	1.67279i	−0.0877128	+	0.482894i
$13$	1.16000	+	1.16000i	0.321726	+	0.321726i	0.849429	−	0.527703i	$-0.176947\pi$
$13$	1.16000	+	1.16000i	0.321726	+	0.321726i	−0.527703	+	0.849429i	$0.676947\pi$
$14$	−2.31808	+	2.93709i	−0.619532	+	0.784972i
$15$	0.198427	+	1.89046i	0.0512336	+	0.488114i
$16$	2.53947	+	3.09049i	0.634867	+	0.772622i
$17$	5.24683	−	1.40589i	1.27254	−	0.340977i	0.441539	−	0.897242i	$-0.354433\pi$
$17$	5.24683	−	1.40589i	1.27254	−	0.340977i	0.831005	+	0.556265i	$0.187766\pi$
$18$	0.960566	+	3.07409i	0.226407	+	0.724571i
$19$	1.58626	−	0.915829i	0.363914	−	0.210106i	−0.306882	−	0.951747i	$-0.599286\pi$
$19$	1.58626	−	0.915829i	0.363914	−	0.210106i	0.670796	+	0.741642i	$0.265953\pi$
$20$	3.69429	+	2.52036i	0.826069	+	0.563569i
$21$	0.415057	−	2.21048i	0.0905728	−	0.482366i
$22$	1.94169	+	1.78845i	0.413969	+	0.381298i
$23$	0.605573	−	2.26003i	0.126271	−	0.471249i	−0.873611	−	0.486625i	$-0.838228\pi$
$23$	0.605573	−	2.26003i	0.126271	−	0.471249i	0.999882	+	0.0153761i	$0.00489455\pi$
$24$	−2.21420	−	0.937248i	−0.451972	−	0.191315i
$25$	4.75485	+	1.54642i	0.950970	+	0.309284i
$26$	−1.95987	+	1.24149i	−0.384362	+	0.243477i
$27$	−3.17222	−	3.17222i	−0.610493	−	0.610493i
$28$	−3.33511	−	4.10816i	−0.630277	−	0.776370i
$29$	−3.08470			−0.572815			−0.286408	−	0.958108i	$-0.592461\pi$
$29$	−3.08470			−0.572815			−0.286408	+	0.958108i	$0.592461\pi$
$30$	−2.67008	−	0.311561i	−0.487488	−	0.0568830i
$31$	−5.06562	−	2.92464i	−0.909813	−	0.525281i	−0.0294420	−	0.999566i	$-0.509373\pi$
$31$	−5.06562	−	2.92464i	−0.909813	−	0.525281i	−0.880371	+	0.474286i	$0.842706\pi$
$32$	−5.05089	+	2.54725i	−0.892880	+	0.450295i
$33$	−1.53273	−	0.410694i	−0.266814	−	0.0714926i
$34$	0.315325	+	7.67542i	0.0540778	+	1.31632i
$35$	−4.86725	−	3.36302i	−0.822715	−	0.568454i
$36$	−4.53937	+	0.373607i	−0.756562	+	0.0622678i
$37$	9.54578	+	2.55778i	1.56932	+	0.420497i	0.935598	−	0.353067i	$-0.114861\pi$
$37$	9.54578	+	2.55778i	1.56932	+	0.420497i	0.633718	+	0.773564i	$0.281528\pi$
$38$	0.772574	+	2.47246i	0.125328	+	0.401087i
$39$	0.697275	−	1.20772i	0.111653	−	0.193389i
$40$	−4.62176	+	4.31733i	−0.730764	+	0.682630i
$41$	−4.49591			−0.702142			−0.351071	−	0.936349i	$-0.614182\pi$
$41$	−4.49591			−0.702142			−0.351071	+	0.936349i	$0.614182\pi$
$42$	2.92172	+	1.25720i	0.450830	+	0.193990i
$43$	−1.18585	+	1.18585i	−0.180840	+	0.180840i	−0.791722	−	0.610882i	$-0.790815\pi$
$43$	−1.18585	+	1.18585i	−0.180840	+	0.180840i	0.610882	+	0.791722i	$0.290815\pi$
$44$	−3.06911	+	2.12555i	−0.462685	+	0.320439i
$45$	−4.75436	+	1.82426i	−0.708738	+	0.271945i
$46$	2.93110	+	1.53544i	0.432167	+	0.226388i
$47$	−4.50200	−	1.20631i	−0.656684	−	0.175958i	−0.0849348	−	0.996387i	$-0.527068\pi$
$47$	−4.50200	−	1.20631i	−0.656684	−	0.175958i	−0.571749	+	0.820429i	$0.693735\pi$
$48$	1.97892	−	2.76516i	0.285633	−	0.399117i
$49$	4.37966	+	5.46064i	0.625665	+	0.780092i
$50$	−3.60622	+	6.08237i	−0.509996	+	0.860177i
$51$	−2.30879	−	3.99894i	−0.323296	−	0.559964i
$52$	−1.10627	−	3.08884i	−0.153412	−	0.428345i
$53$	11.4262	−	3.06164i	1.56951	−	0.420548i	0.633849	−	0.773457i	$-0.281474\pi$
$53$	11.4262	−	3.06164i	1.56951	−	0.420548i	0.935658	+	0.352908i	$0.114807\pi$
$54$	5.35960	−	3.39508i	0.729349	−	0.462012i
$55$	−2.62720	+	3.24339i	−0.354251	+	0.437338i
$56$	6.70155	−	3.33005i	0.895532	−	0.444996i
$57$	−1.10101	−	1.10101i	−0.145832	−	0.145832i
$58$	0.955162	−	4.25658i	0.125419	−	0.558916i
$59$	−7.77422	−	4.48845i	−1.01212	−	0.584346i	−0.100307	−	0.994957i	$-0.531982\pi$
$59$	−7.77422	−	4.48845i	−1.01212	−	0.584346i	−0.911811	+	0.410610i	$0.865316\pi$
$60$	1.25670	−	3.58797i	0.162239	−	0.463205i
$61$	−8.16355	+	4.71323i	−1.04524	+	0.603467i	−0.921312	−	0.388825i	$-0.872881\pi$
$61$	−8.16355	+	4.71323i	−1.04524	+	0.603467i	−0.123924	+	0.992292i	$0.539548\pi$
$62$	5.60425	−	6.08445i	0.711740	−	0.772726i
$63$	6.00785	−	0.458642i	0.756917	−	0.0577835i
$64$	−1.95097	−	7.75846i	−0.243872	−	0.969808i
$65$	−2.15572	−	2.96797i	−0.267384	−	0.368132i
$66$	1.04132	−	1.98784i	0.128177	−	0.244687i
$67$	−3.25136	+	0.871200i	−0.397217	+	0.106434i	−0.451898	−	0.892070i	$-0.649253\pi$
$67$	−3.25136	+	0.871200i	−0.397217	+	0.106434i	0.0546802	+	0.998504i	$0.482586\pi$
$68$	−10.6889	−	1.94154i	−1.29623	−	0.235446i
$69$	−1.98899			−0.239446
$70$	6.14775	−	5.67496i	0.734796	−	0.678288i
$71$		−	3.09202i		−	0.366955i	−0.983024	−	0.183477i	$-0.941265\pi$
$71$		−	3.09202i		−	0.366955i	0.983024	−	0.183477i	$-0.0587354\pi$
$72$	0.890052	−	6.37956i	0.104894	−	0.751838i
$73$	2.17707	+	8.12492i	0.254806	+	0.950950i	0.968198	+	0.250184i	$0.0804913\pi$
$73$	2.17707	+	8.12492i	0.254806	+	0.950950i	−0.713392	+	0.700765i	$0.752842\pi$
$74$	−6.48528	+	12.3802i	−0.753899	+	1.43917i
$75$	0.223641	−	4.24453i	0.0258238	−	0.490116i
$76$	−3.65097	+	0.300489i	−0.418795	+	0.0344684i
$77$	4.07664	−	2.78773i	0.464576	−	0.317691i
$78$	1.45062	+	1.33613i	0.164250	+	0.151287i
$79$	5.84357	+	10.1214i	0.657453	+	1.13874i	0.981273	+	0.192623i	$0.0616996\pi$
$79$	5.84357	+	10.1214i	0.657453	+	1.13874i	−0.323820	+	0.946119i	$0.604967\pi$
$80$	−4.52638	−	7.71439i	−0.506065	−	0.862495i
$81$	1.50922	−	2.61405i	0.167691	−	0.290450i
$82$	1.39213	−	6.20389i	0.153735	−	0.685105i
$83$	4.95881	−	4.95881i	0.544300	−	0.544300i	−0.380487	−	0.924786i	$-0.624243\pi$
$83$	4.95881	−	4.95881i	0.544300	−	0.544300i	0.924786	+	0.380487i	$0.124243\pi$
$84$	−2.63950	+	3.64239i	−0.287993	+	0.397417i
$85$	−12.0798	+	1.26792i	−1.31024	+	0.137526i
$86$	−1.26916	−	2.00354i	−0.136857	−	0.216047i
$87$	0.678689	+	2.53290i	0.0727631	+	0.271556i
$88$	−1.98271	−	4.89322i	−0.211358	−	0.521619i
$89$	−7.31128	+	4.22117i	−0.774994	+	0.447443i	−0.834653	−	0.550776i	$-0.814332\pi$
$89$	−7.31128	+	4.22117i	−0.774994	+	0.447443i	0.0596589	+	0.998219i	$0.480999\pi$
$90$	−1.04513	−	7.12540i	−0.110167	−	0.751083i
$91$	1.43922	+	4.09476i	0.150871	+	0.429247i
$92$	−3.02634	+	3.56918i	−0.315518	+	0.372113i
$93$	−1.28694	+	4.80294i	−0.133450	+	0.498042i
$94$	3.05860	−	5.83877i	0.315470	−	0.602223i
$95$	−3.82388	+	1.46724i	−0.392322	+	0.150535i
$96$	3.20288	+	3.58693i	0.326892	+	0.366090i
$97$	6.17682	+	6.17682i	0.627161	+	0.627161i	0.947353	−	0.320192i	$-0.103747\pi$
$97$	6.17682	+	6.17682i	0.627161	+	0.627161i	−0.320192	+	0.947353i	$0.603747\pi$
$98$	−8.89127	+	4.35263i	−0.898154	+	0.439682i
$99$		−	4.25101i		−	0.427243i
$100$	−7.27641	−	6.85958i	−0.727641	−	0.685958i
$101$	−6.45847	−	3.72880i	−0.642642	−	0.371030i	0.142990	−	0.989724i	$-0.454328\pi$
$101$	−6.45847	−	3.72880i	−0.642642	−	0.371030i	−0.785632	+	0.618695i	$0.787662\pi$
$102$	6.23304	−	1.94765i	0.617163	−	0.192846i
$103$	4.15849	−	15.5197i	0.409748	−	1.52920i	−0.385379	−	0.922758i	$-0.625929\pi$
$103$	4.15849	−	15.5197i	0.409748	−	1.52920i	0.795127	−	0.606443i	$-0.207404\pi$
$104$	4.60484	−	0.570101i	0.451542	−	0.0559030i
$105$	−1.69055	+	4.73650i	−0.164981	+	0.462235i
$106$	0.686692	+	16.7150i	0.0666975	+	1.62350i
$107$	−3.67887	+	13.7297i	−0.355649	+	1.32730i	0.524016	+	0.851708i	$0.324433\pi$
$107$	−3.67887	+	13.7297i	−0.355649	+	1.32730i	−0.879665	+	0.475593i	$0.842233\pi$
$108$	3.02529	+	8.44697i	0.291109	+	0.812810i
$109$	8.31157	−	14.3961i	0.796104	−	1.37889i	−0.126032	−	0.992026i	$-0.540224\pi$
$109$	8.31157	−	14.3961i	0.796104	−	1.37889i	0.922136	−	0.386866i	$-0.126442\pi$
$110$	−3.66205	−	4.62956i	−0.349163	−	0.441412i
$111$		−	8.40096i		−	0.797384i
$112$	2.52003	+	10.2786i	0.238120	+	0.971236i
$113$	−2.07682	+	2.07682i	−0.195371	+	0.195371i	−0.798012	−	0.602641i	$-0.794115\pi$
$113$	−2.07682	+	2.07682i	−0.195371	+	0.195371i	0.602641	+	0.798012i	$0.294115\pi$
$114$	1.86020	−	1.17836i	0.174224	−	0.110363i
$115$	−2.12866	+	4.77923i	−0.198498	+	0.445666i
$116$	5.57789	+	2.63605i	0.517894	+	0.244751i
$117$	3.60868	+	0.966942i	0.333622	+	0.0893939i
$118$	8.60085	−	9.33781i	0.791772	−	0.859615i
$119$	14.1247	+	2.65216i	1.29481	+	0.243123i
$120$	4.56190	+	2.84511i	0.416443	+	0.259722i
$121$	3.75783	+	6.50875i	0.341621	+	0.591704i
$122$	−3.97598	−	12.7243i	−0.359968	−	1.15200i
$123$	0.989178	+	3.69166i	0.0891912	+	0.332866i
$124$	6.66060	+	9.61731i	0.598139	+	0.863660i
$125$	−9.95962	−	5.07996i	−0.890815	−	0.454366i
$126$	−1.22742	+	8.43223i	−0.109347	+	0.751203i
$127$	−12.5701	+	12.5701i	−1.11541	+	1.11541i	−0.123009	+	0.992406i	$0.539254\pi$
$127$	−12.5701	+	12.5701i	−1.11541	+	1.11541i	−0.992406	+	0.123009i	$0.960746\pi$
$128$	11.3100	−	0.289779i	0.999672	−	0.0256130i
$129$	1.23462	+	0.712811i	0.108703	+	0.0627595i
$130$	4.76301	−	2.05566i	0.417743	−	0.180293i
$131$	6.36434	+	11.0234i	0.556055	+	0.963115i	0.997821	+	0.0659846i	$0.0210188\pi$
$131$	6.36434	+	11.0234i	0.556055	+	0.963115i	−0.441766	+	0.897130i	$0.645648\pi$
$132$	2.42058	+	2.05244i	0.210685	+	0.178642i
$133$	4.83205	−	0.368882i	0.418992	−	0.0319861i
$134$	−0.195401	−	4.75631i	−0.0168801	−	0.410883i
$135$	5.89519	+	8.11643i	0.507377	+	0.698551i
$136$	5.98890	−	14.1485i	0.513544	−	1.21322i
$137$	−14.6670	+	3.93000i	−1.25308	+	0.335763i	−0.823527	−	0.567277i	$-0.807997\pi$
$137$	−14.6670	+	3.93000i	−1.25308	+	0.335763i	−0.429557	+	0.903040i	$0.641330\pi$
$138$	0.615879	−	2.74460i	0.0524271	−	0.233636i
$139$			14.5355i			1.23288i	0.787401	+	0.616442i	$0.211426\pi$
$139$			14.5355i			1.23288i	−0.787401	+	0.616442i	$0.788574\pi$
$140$	5.92726	+	10.2405i	0.500945	+	0.865479i
$141$			3.96207i			0.333667i
$142$	4.26667	+	0.957427i	0.358051	+	0.0803455i
$143$	2.95786	−	0.792556i	0.247348	−	0.0662768i
$144$	8.52754	+	3.20358i	0.710628	+	0.266965i
$145$	6.81253	+	1.07998i	0.565750	+	0.0896874i
$146$	−11.8857	+	0.488292i	−0.983666	+	0.0404114i
$147$	3.52022	−	4.79765i	0.290343	−	0.395703i
$148$	−15.0753	−	12.7825i	−1.23918	−	1.05071i
$149$	4.65382	+	8.06065i	0.381256	+	0.660354i	0.991242	−	0.132058i	$-0.0421584\pi$
$149$	4.65382	+	8.06065i	0.381256	+	0.660354i	−0.609986	+	0.792412i	$0.708825\pi$
$150$	5.78777	+	1.62290i	0.472569	+	0.132509i
$151$	−19.1408	−	11.0509i	−1.55765	−	0.899312i	−0.997481	−	0.0709374i	$-0.977401\pi$
$151$	−19.1408	−	11.0509i	−1.55765	−	0.899312i	−0.560174	−	0.828375i	$-0.689266\pi$
$152$	0.715860	−	5.13102i	0.0580639	−	0.416180i
$153$	8.74722	−	8.74722i	0.707171	−	0.707171i
$154$	2.58448	+	6.48855i	0.208263	+	0.522863i
$155$	10.1634	+	8.23255i	0.816347	+	0.661254i
$156$	−2.29290	+	1.58798i	−0.183579	+	0.127140i
$157$	1.42303	+	5.31081i	0.113570	+	0.423849i	0.999176	−	0.0405886i	$-0.0129233\pi$
$157$	1.42303	+	5.31081i	0.113570	+	0.423849i	−0.885606	+	0.464437i	$0.846257\pi$
$158$	−15.7759	+	4.92951i	−1.25506	+	0.392171i
$159$	−5.02792	−	8.70862i	−0.398740	−	0.690638i
$160$	12.0467	−	3.85723i	0.952371	−	0.304941i
$161$	4.03139	−	4.69778i	0.317718	−	0.370237i
$162$	3.13980	+	2.89200i	0.246686	+	0.227217i
$163$	2.10716	+	0.564611i	0.165045	+	0.0442238i	0.340395	−	0.940282i	$-0.389439\pi$
$163$	2.10716	+	0.564611i	0.165045	+	0.0442238i	−0.175350	+	0.984506i	$0.556106\pi$
$164$	8.12968	+	3.84200i	0.634821	+	0.300010i
$165$	3.24123	+	1.44363i	0.252329	+	0.112387i
$166$	5.30718	+	8.37812i	0.411917	+	0.650268i
$167$	−16.9396	+	16.9396i	−1.31083	+	1.31083i	−0.390019	+	0.920807i	$0.627532\pi$
$167$	−16.9396	+	16.9396i	−1.31083	+	1.31083i	−0.920807	+	0.390019i	$0.872468\pi$
$168$	−4.20882	−	4.77009i	−0.324717	−	0.368020i
$169$		−	10.3088i		−	0.792985i
$170$	1.99084	−	17.0615i	0.152690	−	1.30856i
$171$	2.08567	−	3.61249i	0.159495	−	0.276254i
$172$	3.15766	−	1.13092i	0.240770	−	0.0862320i
$173$	−3.32567	+	12.4116i	−0.252846	+	0.943633i	0.716431	+	0.697658i	$0.245775\pi$
$173$	−3.32567	+	12.4116i	−0.252846	+	0.943633i	−0.969276	+	0.245974i	$0.920892\pi$
$174$	−3.70530	+	0.152223i	−0.280898	+	0.0115400i
$175$	9.57184	+	9.13126i	0.723563	+	0.690258i
$176$	7.36609	−	1.22078i	0.555240	−	0.0920199i
$177$	−1.97508	+	7.37108i	−0.148456	+	0.554044i
$178$	−3.56089	−	11.3959i	−0.266900	−	0.854158i
$179$	−2.18534	−	1.26171i	−0.163340	−	0.0943046i	0.416102	−	0.909318i	$-0.363396\pi$
$179$	−2.18534	−	1.26171i	−0.163340	−	0.0943046i	−0.579442	+	0.815014i	$0.696729\pi$
$180$	10.1560	+	0.764163i	0.756980	+	0.0569573i
$181$			0.231987i			0.0172435i	0.999963	+	0.00862174i	$0.00274442\pi$
$181$			0.231987i			0.0172435i	−0.999963	+	0.00862174i	$0.997256\pi$
$182$	−6.09600	+	0.718062i	−0.451865	+	0.0532263i
$183$	5.66624	+	5.66624i	0.418860	+	0.418860i
$184$	−3.98802	−	5.28123i	−0.294000	−	0.389337i
$185$	−20.1862	−	8.99089i	−1.48412	−	0.661023i
$186$	−6.22908	−	3.26306i	−0.456738	−	0.239259i
$187$	2.62428	−	9.79395i	0.191907	−	0.716205i
$188$	7.10984	+	6.02850i	0.518538	+	0.439674i
$189$	−3.93580	−	11.1978i	−0.286287	−	0.814521i
$190$	−0.840592	−	5.73089i	−0.0609829	−	0.415763i
$191$	7.94857	−	4.58911i	0.575139	−	0.332056i	−0.184060	−	0.982915i	$-0.558924\pi$
$191$	7.94857	−	4.58911i	0.575139	−	0.332056i	0.759199	+	0.650858i	$0.225591\pi$
$192$	−5.94135	+	3.30897i	−0.428780	+	0.238805i
$193$	−0.411453	−	1.53556i	−0.0296171	−	0.110532i	0.949535	−	0.313661i	$-0.101556\pi$
$193$	−0.411453	−	1.53556i	−0.0296171	−	0.110532i	−0.979152	+	0.203129i	$0.934889\pi$
$194$	−10.4360	+	6.61076i	−0.749261	+	0.474625i
$195$	−1.96275	+	2.42311i	−0.140556	+	0.173522i
$196$	−3.25305	−	13.6168i	−0.232361	−	0.972630i
$197$	1.63865	−	1.63865i	0.116749	−	0.116749i	−0.646319	−	0.763068i	$-0.723692\pi$
$197$	1.63865	−	1.63865i	0.116749	−	0.116749i	0.763068	+	0.646319i	$0.223692\pi$
$198$	5.86596	+	1.31630i	0.416876	+	0.0935456i
$199$	4.72619	−	8.18600i	0.335031	−	0.580290i	−0.648460	−	0.761249i	$-0.724587\pi$
$199$	4.72619	−	8.18600i	0.335031	−	0.580290i	0.983491	+	0.180959i	$0.0579200\pi$
$200$	11.7186	−	7.91667i	0.828632	−	0.559793i
$201$	1.43071	+	2.47807i	0.100915	+	0.174790i
$202$	7.14520	−	7.75743i	0.502734	−	0.545811i
$203$	−7.35806	−	3.53084i	−0.516434	−	0.247816i
$204$	0.757527	+	9.20405i	0.0530375	+	0.644412i
$205$	9.92916	+	1.57405i	0.693482	+	0.109937i
$206$	20.1280	+	10.5439i	1.40238	+	0.734627i
$207$	−1.37911	−	5.14690i	−0.0958546	−	0.357734i
$208$	−0.639182	+	6.53074i	−0.0443193	+	0.452826i
$209$		−	3.41905i		−	0.236501i
$210$	−6.01242	−	3.79943i	−0.414897	−	0.262185i
$211$	−20.4033			−1.40462			−0.702309	−	0.711872i	$-0.747848\pi$
$211$	−20.4033			−1.40462			−0.702309	+	0.711872i	$0.747848\pi$
$212$	−23.2776	−	4.22814i	−1.59871	−	0.290390i
$213$	−2.53891	+	0.680298i	−0.173963	+	0.0466133i
$214$	−17.8065	−	9.32779i	−1.21723	−	0.637635i
$215$	3.03410	−	2.20375i	0.206924	−	0.150295i
$216$	−12.5927	+	1.55904i	−0.856826	+	0.106079i
$217$	−8.73560	−	12.7745i	−0.593011	−	0.867189i
$218$	17.2915	+	15.9268i	1.17113	+	1.07870i
$219$	6.19251	−	3.57525i	0.418451	−	0.241593i
$220$	7.52226	−	3.61974i	0.507151	−	0.244043i
$221$	7.71715	+	4.45550i	0.519112	+	0.299709i
$222$	11.5925	+	2.60131i	0.778036	+	0.174589i
$223$	−14.6489	−	14.6489i	−0.980964	−	0.980964i	0.0188583	−	0.999822i	$-0.493997\pi$
$223$	−14.6489	−	14.6489i	−0.980964	−	0.980964i	−0.999822	+	0.0188583i	$0.993997\pi$
$224$	−14.9637	+	0.294673i	−0.999806	+	0.0196887i
$225$	11.1386	−	2.36432i	0.742575	−	0.157621i
$226$	−2.22273	−	3.50888i	−0.147854	−	0.233407i
$227$	20.4876	−	5.48964i	1.35981	−	0.364360i	0.496063	−	0.868286i	$-0.334778\pi$
$227$	20.4876	−	5.48964i	1.35981	−	0.364360i	0.863747	+	0.503926i	$0.168112\pi$
$228$	1.05001	+	2.93176i	0.0695389	+	0.194161i
$229$	−0.631523	−	1.09383i	−0.0417322	−	0.0722823i	0.844405	−	0.535706i	$-0.179954\pi$
$229$	−0.631523	−	1.09383i	−0.0417322	−	0.0722823i	−0.886137	+	0.463423i	$0.846621\pi$
$230$	−5.93573	−	4.41719i	−0.391391	−	0.291261i
$231$	−3.18599	−	2.73405i	−0.209622	−	0.179887i
$232$	−5.36465	+	6.88068i	−0.352206	+	0.451739i
$233$	−14.4826	−	3.88061i	−0.948789	−	0.254227i	−0.248941	−	0.968519i	$-0.580082\pi$
$233$	−14.4826	−	3.88061i	−0.948789	−	0.254227i	−0.699848	+	0.714291i	$0.746749\pi$
$234$	−2.45169	+	4.68020i	−0.160272	+	0.305954i
$235$	9.52027	+	4.24030i	0.621034	+	0.276607i
$236$	10.2220	+	14.7597i	0.665397	+	0.960775i
$237$	7.02513	−	7.02513i	0.456331	−	0.456331i
$238$	−8.03334	+	18.6694i	−0.520724	+	1.21016i
$239$	18.0162			1.16537			0.582687	−	0.812697i	$-0.302001\pi$
$239$	18.0162			1.16537			0.582687	+	0.812697i	$0.302001\pi$
$240$	−5.33854	+	5.41399i	−0.344601	+	0.349472i
$241$	6.15262	−	10.6567i	0.396325	−	0.686456i	−0.596944	−	0.802283i	$-0.703619\pi$
$241$	6.15262	−	10.6567i	0.396325	−	0.686456i	0.993269	+	0.115827i	$0.0369519\pi$
$242$	−10.1450	+	3.17002i	−0.652145	+	0.203777i
$243$	−15.4785	−	4.14745i	−0.992945	−	0.266059i
$244$	18.7894	−	1.54644i	1.20287	−	0.0990004i
$245$	−7.76061	−	13.5931i	−0.495807	−	0.868433i
$246$	−5.40042	+	0.221862i	−0.344318	+	0.0141454i
$247$	2.90243	+	0.777703i	0.184677	+	0.0494840i
$248$	−15.3333	+	6.21300i	−0.973668	+	0.394526i
$249$	−5.16279	−	2.98074i	−0.327178	−	0.188896i
$250$	10.0938	−	12.1703i	0.638386	−	0.769716i
$251$	6.34468			0.400473			0.200236	−	0.979748i	$-0.435829\pi$
$251$	6.34468			0.400473			0.200236	+	0.979748i	$0.435829\pi$
$252$	−11.2556	−	4.30471i	−0.709034	−	0.271171i
$253$	−3.08828	−	3.08828i	−0.194158	−	0.194158i
$254$	−13.4532	−	21.2377i	−0.844128	−	1.33257i
$255$	3.69888	+	9.63995i	0.231633	+	0.603677i
$256$	−3.10221	+	15.6964i	−0.193888	+	0.981024i
$257$	5.34003	−	19.9293i	0.333102	−	1.24315i	−0.572810	−	0.819688i	$-0.694147\pi$
$257$	5.34003	−	19.9293i	0.333102	−	1.24315i	0.905912	−	0.423466i	$-0.139187\pi$
$258$	−1.36590	+	1.48294i	−0.0850373	+	0.0923237i
$259$	19.8422	+	17.0275i	1.23293	+	1.05804i
$260$	1.36176	+	7.20899i	0.0844530	+	0.447083i
$261$	−6.08381	+	3.51249i	−0.376578	+	0.217418i
$262$	−17.1818	+	5.36882i	−1.06149	+	0.331687i
$263$	−23.0421	+	6.17410i	−1.42083	+	0.380712i	−0.885780	−	0.464106i	$-0.846376\pi$
$263$	−23.0421	+	6.17410i	−1.42083	+	0.380712i	−0.535055	+	0.844817i	$0.679709\pi$
$264$	−3.58168	+	2.70463i	−0.220437	+	0.166459i
$265$	−26.3065	+	2.76119i	−1.61600	+	0.169619i
$266$	−0.987200	+	6.78197i	−0.0605291	+	0.415829i
$267$	5.07469	+	5.07469i	0.310566	+	0.310566i
$268$	6.62374	+	1.20313i	0.404609	+	0.0734931i
$269$	−4.64531	+	8.04591i	−0.283229	+	0.490568i	−0.972178	−	0.234242i	$-0.924739\pi$
$269$	−4.64531	+	8.04591i	−0.283229	+	0.490568i	0.688949	+	0.724810i	$0.258072\pi$
$270$	−13.0253	+	5.62155i	−0.792692	+	0.342117i
$271$	19.8751	−	11.4749i	1.20733	−	0.697050i	0.245152	−	0.969485i	$-0.421162\pi$
$271$	19.8751	−	11.4749i	1.20733	−	0.697050i	0.962174	+	0.272435i	$0.0878290\pi$
$272$	17.6690	+	12.6451i	1.07134	+	0.766720i
$273$	3.04562	−	2.08269i	0.184329	−	0.126050i
$274$	−0.881458	−	21.4558i	−0.0532508	−	1.29619i
$275$	6.93767	−	6.24318i	0.418357	−	0.376478i
$276$	3.59656	+	1.69970i	0.216488	+	0.102310i
$277$	−4.35545	−	16.2548i	−0.261694	−	0.976655i	−0.964243	−	0.265020i	$-0.914622\pi$
$277$	−4.35545	−	16.2548i	−0.261694	−	0.976655i	0.702549	−	0.711635i	$-0.252045\pi$
$278$	−20.0575	−	4.50083i	−1.20297	−	0.269942i
$279$	−13.3209			−0.797502
$280$	−15.9662	+	5.00811i	−0.954162	+	0.299292i
$281$	−26.0899			−1.55640			−0.778198	−	0.628019i	$-0.783866\pi$
$281$	−26.0899			−1.55640			−0.778198	+	0.628019i	$0.783866\pi$
$282$	−5.46726	−	1.22683i	−0.325571	−	0.0730570i
$283$	8.19820	+	30.5961i	0.487332	+	1.81875i	0.569320	+	0.822116i	$0.307206\pi$
$283$	8.19820	+	30.5961i	0.487332	+	1.81875i	−0.0819879	+	0.996633i	$0.526127\pi$
$284$	−2.64230	+	5.59111i	−0.156792	+	0.331771i
$285$	2.04609	+	2.81704i	0.121200	+	0.166867i
$286$	0.177762	+	4.32695i	0.0105113	+	0.255858i
$287$	−10.7242	−	5.14613i	−0.633032	−	0.303767i
$288$	−7.06112	+	10.7752i	−0.416080	+	0.634933i
$289$	10.8303	−	6.25289i	0.637078	−	0.367817i
$290$	−3.59973	+	9.06620i	−0.211383	+	0.532385i
$291$	3.71288	−	6.43090i	0.217653	−	0.376986i
$292$	3.00654	−	16.5522i	0.175945	−	0.968646i
$293$	15.1299	+	15.1299i	0.883901	+	0.883901i	0.993929	−	0.110027i	$-0.0350939\pi$
$293$	15.1299	+	15.1299i	0.883901	+	0.883901i	−0.110027	+	0.993929i	$0.535094\pi$
$294$	5.53025	+	6.34312i	0.322531	+	0.369938i
$295$	15.5978	+	12.6345i	0.908141	+	0.735610i
$296$	22.3065	−	16.8443i	1.29654	−	0.979058i
$297$	−8.08877	+	2.16738i	−0.469358	+	0.125764i
$298$	−12.5639	+	3.92586i	−0.727808	+	0.227419i
$299$	3.32410	−	1.91917i	0.192238	−	0.110988i
$300$	−4.03158	+	7.48401i	−0.232764	+	0.432090i
$301$	−4.18599	+	1.47129i	−0.241276	+	0.0848037i
$302$	21.1760	−	22.9905i	1.21854	−	1.32295i
$303$	−1.64080	+	6.12356i	−0.0942617	+	0.351789i
$304$	6.85862	+	2.57661i	0.393369	+	0.147779i
$305$	19.6792	−	7.55099i	1.12683	−	0.432368i
$306$	9.36175	+	14.7788i	0.535176	+	0.844848i
$307$	−8.26698	−	8.26698i	−0.471821	−	0.471821i	0.430682	−	0.902504i	$-0.358273\pi$
$307$	−8.26698	−	8.26698i	−0.471821	−	0.471821i	−0.902504	+	0.430682i	$0.858273\pi$
$308$	−9.75382	+	1.55717i	−0.555775	+	0.0887280i
$309$	−13.6584			−0.777001
$310$	−14.5071	+	11.4753i	−0.823950	+	0.651756i
$311$	16.5870	+	9.57654i	0.940565	+	0.543036i	0.890137	−	0.455692i	$-0.150608\pi$
$311$	16.5870	+	9.57654i	0.940565	+	0.543036i	0.0504278	+	0.998728i	$0.483942\pi$
$312$	−1.48127	−	3.65568i	−0.0838602	−	0.206962i
$313$	−5.92477	−	1.58754i	−0.334888	−	0.0897330i	0.0874566	−	0.996168i	$-0.472126\pi$
$313$	−5.92477	−	1.58754i	−0.334888	−	0.0897330i	−0.422345	+	0.906435i	$0.638793\pi$
$314$	−7.76901	+	0.319170i	−0.438430	+	0.0180118i
$315$	−13.4288	−	1.09049i	−0.756629	−	0.0614421i
$316$	−1.91731	−	23.2955i	−0.107857	−	1.31048i
$317$	0.634542	+	0.170025i	0.0356394	+	0.00954956i	0.276595	−	0.960987i	$-0.410794\pi$
$317$	0.634542	+	0.170025i	0.0356394	+	0.00954956i	−0.240955	+	0.970536i	$0.577461\pi$
$318$	13.5739	−	4.24145i	0.761185	−	0.237849i
$319$	−2.87902	+	4.98660i	−0.161194	+	0.279196i
$320$	1.59240	+	17.8175i	0.0890180	+	0.996030i
$321$	12.0831			0.674414
$322$	5.23416	+	7.01755i	0.291688	+	0.391072i
$323$	7.03531	−	7.03531i	0.391455	−	0.391455i
$324$	−4.96289	+	3.43711i	−0.275716	+	0.190951i
$325$	3.72178	+	7.30947i	0.206447	+	0.405456i
$326$	−1.43158	+	2.73284i	−0.0792877	+	0.151358i
$327$	−13.6495	−	3.65738i	−0.754821	−	0.202254i
$328$	−7.81889	+	10.0285i	−0.431726	+	0.553730i
$329$	−9.35801	−	8.03055i	−0.515924	−	0.442739i
$330$	−2.99570	+	4.02556i	−0.164908	+	0.221600i
$331$	−13.2977	−	23.0322i	−0.730906	−	1.26597i	−0.956497	−	0.291744i	$-0.905765\pi$
$331$	−13.2977	−	23.0322i	−0.730906	−	1.26597i	0.225591	−	0.974222i	$-0.427569\pi$
$332$	−13.2043	+	4.72914i	−0.724680	+	0.259545i
$333$	21.7392	−	5.82499i	1.19130	−	0.319208i
$334$	−18.1297	−	28.6202i	−0.992012	−	1.56603i
$335$	7.48562	−	0.785708i	0.408983	−	0.0429278i
$336$	7.88547	−	4.33071i	0.430188	−	0.236260i
$337$	14.6913	+	14.6913i	0.800285	+	0.800285i	0.983140	−	0.182855i	$-0.0585340\pi$
$337$	14.6913	+	14.6913i	0.800285	+	0.800285i	−0.182855	+	0.983140i	$0.558534\pi$
$338$	14.2251	+	3.19206i	0.773744	+	0.173625i
$339$	2.16225	+	1.24838i	0.117437	+	0.0678025i
$340$	22.9267	+	8.03015i	1.24337	+	0.435496i
$341$	−9.45570	+	5.45925i	−0.512055	+	0.295635i
$342$	4.33905	+	3.99661i	0.234629	+	0.216112i
$343$	4.19656	+	18.0385i	0.226593	+	0.973990i
$344$	0.582803	+	4.70744i	0.0314227	+	0.253808i
$345$	4.39265	+	0.696360i	0.236492	+	0.0374907i
$346$	−16.0969	−	8.43225i	−0.865375	−	0.453321i
$347$	11.2039	−	3.00207i	0.601456	−	0.161160i	0.0547722	−	0.998499i	$-0.482557\pi$
$347$	11.2039	−	3.00207i	0.601456	−	0.161160i	0.546684	+	0.837339i	$0.315890\pi$
$348$	0.937275	−	5.16007i	0.0502432	−	0.276609i
$349$	−17.5410			−0.938950			−0.469475	−	0.882946i	$-0.655557\pi$
$349$	−17.5410			−0.938950			−0.469475	+	0.882946i	$0.655557\pi$
$350$	−15.5641	+	10.3807i	−0.831935	+	0.554873i
$351$		−	7.35954i		−	0.392823i
$352$	−0.596313	+	10.5425i	−0.0317836	+	0.561915i
$353$	1.63267	+	6.09321i	0.0868983	+	0.324309i	0.995667	−	0.0929915i	$-0.0296430\pi$
$353$	1.63267	+	6.09321i	0.0868983	+	0.324309i	−0.908769	+	0.417300i	$0.862976\pi$
$354$	−9.55978	−	5.00782i	−0.508096	−	0.266163i
$355$	−1.08254	+	6.82869i	−0.0574553	+	0.362429i
$356$	16.8278	−	1.38499i	0.891871	−	0.0734043i
$357$	−0.929945	−	12.1815i	−0.0492179	−	0.644715i
$358$	2.41771	−	2.62487i	0.127780	−	0.138729i
$359$	−5.97175	−	10.3434i	−0.315177	−	0.545903i	0.664298	−	0.747468i	$-0.268731\pi$
$359$	−5.97175	−	10.3434i	−0.315177	−	0.545903i	−0.979475	+	0.201565i	$0.935397\pi$
$360$	−4.19920	+	13.7776i	−0.221317	+	0.726141i
$361$	−7.82251	+	13.5490i	−0.411711	+	0.713105i
$362$	−0.320119	−	0.0718337i	−0.0168251	−	0.00377549i
$363$	4.51765	−	4.51765i	0.237115	−	0.237115i
$364$	0.896740	−	8.63420i	0.0470019	−	0.452555i
$365$	−1.96343	−	18.7060i	−0.102770	−	0.979117i
$366$	−9.57335	+	6.06431i	−0.500407	+	0.316987i
$367$	2.00028	+	7.46513i	0.104414	+	0.389677i	0.998278	−	0.0586606i	$-0.0186830\pi$
$367$	2.00028	+	7.46513i	0.104414	+	0.389677i	−0.893864	+	0.448337i	$0.852016\pi$
$368$	8.52242	−	3.86775i	0.444262	−	0.201621i
$369$	−8.86705	+	5.11940i	−0.461600	+	0.266505i
$370$	18.6571	−	25.0710i	0.969935	−	1.30338i
$371$	30.7597	+	5.77569i	1.59697	+	0.299859i
$372$	6.43149	−	7.58511i	0.333457	−	0.393269i
$373$	−7.90744	+	29.5110i	−0.409431	+	1.52802i	0.386302	+	0.922372i	$0.373752\pi$
$373$	−7.90744	+	29.5110i	−0.409431	+	1.52802i	−0.795734	+	0.605647i	$0.792914\pi$
$374$	12.7021	+	6.65389i	0.656808	+	0.344064i
$375$	−1.97995	+	9.29569i	−0.102244	+	0.480027i
$376$	−10.5202	+	7.94416i	−0.542540	+	0.409689i
$377$	−3.57826	−	3.57826i	−0.184290	−	0.184290i
$378$	16.6705	−	1.96366i	0.857440	−	0.101000i
$379$		−	9.07083i		−	0.465937i	−0.972484	−	0.232969i	$-0.925156\pi$
$379$		−	9.07083i		−	0.465937i	0.972484	−	0.232969i	$-0.0748439\pi$
$380$	8.16834	+	0.614609i	0.419027	+	0.0315288i
$381$	13.0871	+	7.55587i	0.670475	+	0.387099i
$382$	3.87128	+	12.3892i	0.198072	+	0.633888i
$383$	2.60323	−	9.71537i	0.133019	−	0.496432i	−0.866980	−	0.498344i	$-0.833942\pi$
$383$	2.60323	−	9.71537i	0.133019	−	0.496432i	0.999998	+	0.00191152i	$0.000608457\pi$
$384$	−2.72634	−	9.22307i	−0.139128	−	0.470663i
$385$	−9.97922	+	4.72941i	−0.508588	+	0.241033i
$386$	2.24633	−	0.0922846i	0.114335	−	0.00469716i
$387$	−0.988486	+	3.68908i	−0.0502476	+	0.187527i
$388$	−5.89073	−	16.4476i	−0.299057	−	0.835001i
$389$	3.80108	−	6.58367i	0.192723	−	0.333805i	−0.753429	−	0.657529i	$-0.771602\pi$
$389$	3.80108	−	6.58367i	0.192723	−	0.333805i	0.946152	+	0.323724i	$0.104935\pi$
$390$	−2.73588	−	3.45870i	−0.138537	−	0.175138i
$391$		−	12.7094i		−	0.642740i
$392$	19.7971	−	0.272506i	0.999905	−	0.0137636i
$393$	7.65120	−	7.65120i	0.385952	−	0.385952i
$394$	1.75377	+	2.76857i	0.0883537	+	0.139479i
$395$	−9.36189	−	24.3988i	−0.471048	−	1.22764i
$396$	−3.63273	+	7.68685i	−0.182551	+	0.386279i
$397$	17.1225	+	4.58796i	0.859353	+	0.230263i	0.661478	−	0.749964i	$-0.269929\pi$
$397$	17.1225	+	4.58796i	0.859353	+	0.230263i	0.197875	+	0.980227i	$0.436596\pi$
$398$	9.83241	+	9.05641i	0.492854	+	0.453957i
$399$	−1.36603	−	3.88652i	−0.0683871	−	0.194569i
$400$	7.29559	+	18.6219i	0.364780	+	0.931094i
$401$	−9.80442	−	16.9818i	−0.489610	−	0.848029i	0.510319	−	0.859985i	$-0.329527\pi$
$401$	−9.80442	−	16.9818i	−0.489610	−	0.848029i	−0.999929	+	0.0119566i	$0.996194\pi$
$402$	−3.86250	+	1.20692i	−0.192644	+	0.0601957i
$403$	−2.48354	−	9.26870i	−0.123714	−	0.461707i
$404$	8.49200	+	12.2617i	0.422493	+	0.610042i
$405$	−4.24830	+	5.24471i	−0.211100	+	0.260612i
$406$	7.15058	−	9.06007i	0.354877	−	0.449644i
$407$	13.0441	−	13.0441i	0.646571	−	0.646571i
$408$	−12.9352	−	1.80467i	−0.640389	−	0.0893446i
$409$	−5.09526	−	2.94175i	−0.251944	−	0.145460i	0.368710	−	0.929544i	$-0.379800\pi$
$409$	−5.09526	−	2.94175i	−0.251944	−	0.145460i	−0.620654	+	0.784084i	$0.713133\pi$
$410$	−5.24654	+	13.2138i	−0.259108	+	0.652585i
$411$	6.45399	+	11.1786i	0.318352	+	0.551401i
$412$	−20.7820	+	24.5097i	−1.02386	+	1.20751i
$413$	−13.4065	−	19.6050i	−0.659692	−	0.964701i
$414$	7.52923	−	0.309319i	0.370042	−	0.0152022i
$415$	−12.6876	+	9.21535i	−0.622809	+	0.452364i
$416$	−8.81384	−	2.90422i	−0.432134	−	0.142391i
$417$	11.9353	−	3.19806i	0.584475	−	0.156610i
$418$	4.71794	+	1.05869i	0.230762	+	0.0517822i
$419$		−	1.52381i		−	0.0744432i	−0.999307	−	0.0372216i	$-0.988149\pi$
$419$		−	1.52381i		−	0.0744432i	0.999307	−	0.0372216i	$-0.0118507\pi$
$420$	7.10454	−	7.12006i	0.346666	−	0.347423i
$421$		−	22.7719i		−	1.10984i	−0.831905	−	0.554918i	$-0.812750\pi$
$421$		−	22.7719i		−	1.10984i	0.831905	−	0.554918i	$-0.187250\pi$
$422$	6.31776	−	28.1544i	0.307544	−	1.37054i
$423$	−10.2527	+	2.74719i	−0.498502	+	0.133573i
$424$	13.0422	−	30.8116i	0.633385	−	1.49634i
$425$	27.1220	+	1.42904i	1.31561	+	0.0693184i
$426$	−0.152584	−	3.71409i	−0.00739270	−	0.179948i
$427$	−24.8677	+	1.89841i	−1.20343	+	0.0918707i
$428$	18.3851	−	21.6828i	0.888677	−	1.04808i
$429$	−1.30156	−	2.25437i	−0.0628400	−	0.108842i
$430$	2.10146	+	4.86913i	0.101341	+	0.234810i
$431$	10.4440	+	6.02987i	0.503072	+	0.290449i	0.729981	−	0.683467i	$-0.239529\pi$
$431$	10.4440	+	6.02987i	0.503072	+	0.290449i	−0.226909	+	0.973916i	$0.572862\pi$
$432$	1.74795	−	17.8594i	0.0840985	−	0.859262i
$433$	8.77873	−	8.77873i	0.421879	−	0.421879i	−0.463972	−	0.885850i	$-0.653576\pi$
$433$	8.77873	−	8.77873i	0.421879	−	0.421879i	0.885850	+	0.463972i	$0.153576\pi$
$434$	20.3324	−	8.09868i	0.975989	−	0.388749i
$435$	−0.612088	−	5.83150i	−0.0293474	−	0.279599i
$436$	−27.3316	+	18.9288i	−1.30894	+	0.906526i
$437$	−1.10920	−	4.13960i	−0.0530604	−	0.198024i
$438$	3.01600	+	9.65210i	0.144110	+	0.461195i
$439$	−7.34056	−	12.7142i	−0.350346	−	0.606817i	0.635964	−	0.771719i	$-0.280603\pi$
$439$	−7.34056	−	12.7142i	−0.350346	−	0.606817i	−0.986310	+	0.164902i	$0.947269\pi$
$440$	2.66564	+	11.5008i	0.127080	+	0.548279i
$441$	14.8557	+	5.78273i	0.707415	+	0.275368i
$442$	−8.53771	+	9.26927i	−0.406098	+	0.440894i
$443$	26.4240	+	7.08028i	1.25544	+	0.336394i	0.824436	−	0.565955i	$-0.191493\pi$
$443$	26.4240	+	7.08028i	1.25544	+	0.336394i	0.431005	+	0.902350i	$0.358159\pi$
$444$	−7.17909	+	15.1910i	−0.340705	+	0.720931i
$445$	17.6248	−	6.76267i	0.835494	−	0.320581i
$446$	24.7500	−	15.6781i	1.17195	−	0.742378i
$447$	5.59481	−	5.59481i	0.264626	−	0.264626i
$448$	4.22682	−	20.7397i	0.199698	−	0.979857i
$449$			24.0931i			1.13703i	0.822674	+	0.568513i	$0.192481\pi$
$449$			24.0931i			1.13703i	−0.822674	+	0.568513i	$0.807519\pi$
$450$	−0.186492	+	16.1023i	−0.00879133	+	0.759069i
$451$	−4.19612	+	7.26789i	−0.197588	+	0.342232i
$452$	5.53016	−	1.98063i	0.260117	−	0.0931612i
$453$	−4.86280	+	18.1482i	−0.228474	+	0.852678i
$454$	1.23127	+	29.9706i	0.0577862	+	1.40659i
$455$	−1.74490	−	9.54711i	−0.0818022	−	0.447575i
$456$	−4.37067	+	0.541109i	−0.204675	+	0.0253398i
$457$	−7.26497	+	27.1132i	−0.339841	+	1.26830i	0.558684	+	0.829381i	$0.311307\pi$
$457$	−7.26497	+	27.1132i	−0.339841	+	1.26830i	−0.898525	+	0.438923i	$0.855360\pi$
$458$	1.70492	−	0.532739i	0.0796657	−	0.0248933i
$459$	−21.1039	−	12.1843i	−0.985044	−	0.568716i
$460$	7.93325	−	6.82295i	0.369890	−	0.318122i
$461$			38.9010i			1.81180i	0.423489	+	0.905901i	$0.360805\pi$
$461$			38.9010i			1.81180i	−0.423489	+	0.905901i	$0.639195\pi$
$462$	4.75923	−	3.54975i	0.221419	−	0.165150i
$463$	−3.45161	−	3.45161i	−0.160410	−	0.160410i	0.622338	−	0.782748i	$-0.286183\pi$
$463$	−3.45161	−	3.45161i	−0.160410	−	0.160410i	−0.782748	+	0.622338i	$0.786183\pi$
$464$	−7.83350	−	9.53324i	−0.363661	−	0.442569i
$465$	4.52375	−	10.1567i	0.209784	−	0.471005i
$466$	9.83932	−	18.7830i	0.455798	−	0.870104i
$467$	−6.42790	+	23.9892i	−0.297448	+	1.11009i	0.641806	+	0.766867i	$0.278185\pi$
$467$	−6.42790	+	23.9892i	−0.297448	+	1.11009i	−0.939254	+	0.343223i	$0.888481\pi$
$468$	−5.69905	−	4.83228i	−0.263439	−	0.223372i
$469$	−8.75280	−	1.64349i	−0.404167	−	0.0758895i
$470$	−8.79908	+	11.8240i	−0.405872	+	0.545402i
$471$	4.04770	−	2.33694i	0.186508	−	0.107681i
$472$	−23.5321	+	9.53510i	−1.08315	+	0.438889i
$473$	0.810214	+	3.02376i	0.0372537	+	0.139033i
$474$	7.51868	+	11.8693i	0.345344	+	0.545173i
$475$	8.95870	−	1.90160i	0.411053	−	0.0872515i
$476$	−23.2744	−	16.8661i	−1.06678	−	0.773055i
$477$	19.0491	−	19.0491i	0.872198	−	0.872198i
$478$	−5.57863	+	24.8606i	−0.255161	+	1.13710i
$479$	−2.72511	+	4.72004i	−0.124514	+	0.215664i	−0.921543	−	0.388277i	$-0.873070\pi$
$479$	−2.72511	+	4.72004i	−0.124514	+	0.215664i	0.797029	+	0.603941i	$0.206404\pi$
$480$	−5.81771	−	9.04305i	−0.265541	−	0.412757i
$481$	8.10607	+	14.0401i	0.369605	+	0.640175i
$482$	12.8000	+	11.7898i	0.583023	+	0.537010i
$483$	−4.74440	−	2.27665i	−0.215878	−	0.103591i
$484$	−1.23296	−	14.9807i	−0.0560438	−	0.680939i
$485$	−11.4789	−	15.8040i	−0.521229	−	0.717622i
$486$	10.5159	−	20.0745i	0.477010	−	0.910598i
$487$	6.29631	+	23.4981i	0.285313	+	1.06480i	0.948610	+	0.316447i	$0.102490\pi$
$487$	6.29631	+	23.4981i	0.285313	+	1.06480i	−0.663297	+	0.748356i	$0.730844\pi$
$488$	−3.68410	+	26.4063i	−0.166772	+	1.19536i
$489$		−	1.85445i		−	0.0838610i
$490$	21.1602	−	6.49982i	0.955919	−	0.293632i
$491$	5.59720			0.252598			0.126299	−	0.991992i	$-0.459690\pi$
$491$	5.59720			0.252598			0.126299	+	0.991992i	$0.459690\pi$
$492$	1.36606	−	7.52072i	0.0615868	−	0.339060i
$493$	−16.1849	+	4.33674i	−0.728933	+	0.195317i
$494$	−1.97187	+	3.76424i	−0.0887187	+	0.169361i
$495$	−1.48831	+	9.38831i	−0.0668947	+	0.421973i
$496$	−3.82543	−	23.0823i	−0.171767	−	1.03642i
$497$	3.53921	−	7.37550i	0.158755	−	0.330836i
$498$	5.71174	−	6.20115i	0.255949	−	0.277880i
$499$	−17.4171	+	10.0558i	−0.779699	+	0.450159i	−0.836323	−	0.548236i	$-0.815299\pi$
$499$	−17.4171	+	10.0558i	−0.779699	+	0.450159i	0.0566248	+	0.998396i	$0.481966\pi$
$500$	13.6683	+	17.6968i	0.611264	+	0.791427i
$501$	17.6364	+	10.1824i	0.787936	+	0.454915i
$502$	−1.96460	+	8.75502i	−0.0876842	+	0.390755i
$503$	−1.01463	−	1.01463i	−0.0452400	−	0.0452400i	0.684125	−	0.729365i	$-0.260184\pi$
$503$	−1.01463	−	1.01463i	−0.0452400	−	0.0452400i	−0.729365	+	0.684125i	$0.760184\pi$
$504$	9.42528	−	14.1986i	0.419836	−	0.632456i
$505$	12.9580	+	10.4962i	0.576623	+	0.467074i
$506$	5.21777	−	3.30524i	0.231958	−	0.146936i
$507$	−8.46473	+	2.26812i	−0.375932	+	0.100731i
$508$	33.4716	−	11.9879i	1.48506	−	0.531876i
$509$	9.69183	+	16.7867i	0.429583	+	0.744060i	0.996836	−	0.0794839i	$-0.0253272\pi$
$509$	9.69183	+	16.7867i	0.429583	+	0.744060i	−0.567253	+	0.823543i	$0.691994\pi$
$510$	−14.4475	+	2.11912i	−0.639746	+	0.0938362i
$511$	−4.10697	+	21.8726i	−0.181682	+	0.967586i
$512$	−20.6988	−	9.14104i	−0.914768	−	0.403981i
$513$	−7.93718	−	2.12676i	−0.350435	−	0.0938988i
$514$	25.8469	+	13.5397i	1.14006	+	0.597210i
$515$	−14.6175	+	32.8192i	−0.644126	+	1.44618i
$516$	−1.62336	−	2.34399i	−0.0714645	−	0.103188i
$517$	−6.15187	+	6.15187i	−0.270559	+	0.270559i
$518$	−29.6403	+	22.1077i	−1.30232	+	0.971357i
$519$	10.9230			0.479468
$520$	−10.3693	−	0.353130i	−0.454726	−	0.0154858i
$521$	−12.4388	+	21.5447i	−0.544955	+	0.943889i	0.453655	+	0.891177i	$0.350120\pi$
$521$	−12.4388	+	21.5447i	−0.544955	+	0.943889i	−0.998610	+	0.0527120i	$0.983213\pi$
$522$	−2.96306	−	9.48266i	−0.129690	−	0.415045i
$523$	−33.2839	−	8.91840i	−1.45540	−	0.389974i	−0.557504	−	0.830174i	$-0.688241\pi$
$523$	−33.2839	−	8.91840i	−1.45540	−	0.389974i	−0.897900	+	0.440200i	$0.854908\pi$
$524$	−2.08817	−	25.3716i	−0.0912223	−	1.10836i
$525$	5.39186	−	9.86864i	0.235320	−	0.430703i
$526$	−1.38479	−	33.7075i	−0.0603795	−	1.46972i
$527$	−30.6902	−	8.22341i	−1.33689	−	0.358218i
$528$	−2.62307	−	5.77982i	−0.114155	−	0.251535i
$529$	15.1776	+	8.76277i	0.659894	+	0.380990i
$530$	4.33550	−	37.1553i	0.188322	−	1.61392i
$531$	−20.4436			−0.887178
$532$	−9.05275	−	3.46224i	−0.392486	−	0.150107i
$533$	−5.21525	−	5.21525i	−0.225897	−	0.225897i
$534$	−8.57390	+	5.43120i	−0.371029	+	0.235031i
$535$	12.9316	−	29.0339i	0.559083	−	1.25525i
$536$	−3.71121	+	8.76754i	−0.160300	+	0.378700i
$537$	−0.555196	+	2.07202i	−0.0239585	+	0.0894143i
$538$	−9.66414	−	8.90142i	−0.416651	−	0.383768i
$539$	12.9151	−	1.98345i	0.556291	−	0.0854330i
$540$	−3.72398	−	19.7142i	−0.160254	−	0.848365i
$541$	−11.5314	+	6.65767i	−0.495775	+	0.286236i	−0.726967	−	0.686672i	$-0.759071\pi$
$541$	−11.5314	+	6.65767i	−0.495775	+	0.286236i	0.231192	+	0.972908i	$0.425737\pi$
$542$	9.67997	+	30.9787i	0.415790	+	1.33065i
$543$	0.190489	−	0.0510413i	0.00817466	−	0.00219039i
$544$	−22.9200	+	20.4660i	−0.982689	+	0.877472i
$545$	−23.3962	+	28.8836i	−1.00218	+	1.23724i
$546$	1.93084	+	4.84754i	0.0826323	+	0.207455i
$547$	5.13218	+	5.13218i	0.219436	+	0.219436i	0.808261	−	0.588825i	$-0.200409\pi$
$547$	5.13218	+	5.13218i	0.219436	+	0.219436i	−0.588825	+	0.808261i	$0.700409\pi$
$548$	29.8798	+	5.42736i	1.27640	+	0.231845i
$549$	−10.7337	+	18.5913i	−0.458104	+	0.793459i
$550$	6.46675	+	11.5065i	0.275743	+	0.490637i
$551$	−4.89315	+	2.82506i	−0.208455	+	0.120352i
$552$	−3.45907	+	4.43659i	−0.147228	+	0.188834i
$553$	2.35370	+	30.8316i	0.100089	+	1.31109i
$554$	23.7786	−	0.976881i	1.01026	−	0.0415037i
$555$	−2.94124	+	18.5534i	−0.124849	+	0.787549i
$556$	12.4214	−	26.2836i	0.526784	−	1.11467i
$557$	1.00077	+	3.73492i	0.0424039	+	0.158253i	0.983881	−	0.178822i	$-0.0572288\pi$
$557$	1.00077	+	3.73492i	0.0424039	+	0.158253i	−0.941477	+	0.337076i	$0.890562\pi$
$558$	4.12475	−	18.3815i	0.174614	−	0.778151i
$559$	−2.75116			−0.116362
$560$	−1.96684	−	23.5824i	−0.0831141	−	0.996540i
$561$	−8.61937			−0.363910
$562$	8.07861	−	36.0015i	0.340776	−	1.51863i
$563$	0.439379	+	1.63979i	0.0185176	+	0.0691088i	0.974566	−	0.224099i	$-0.0719439\pi$
$563$	0.439379	+	1.63979i	0.0185176	+	0.0691088i	−0.956049	+	0.293208i	$0.905277\pi$
$564$	3.38582	−	7.16438i	0.142569	−	0.301675i
$565$	5.31375	−	3.85953i	0.223551	−	0.162372i
$566$	−44.7580	+	1.83877i	−1.88132	+	0.0772892i
$567$	6.59211	−	4.50789i	0.276843	−	0.189314i
$568$	−6.89699	−	5.37737i	−0.289391	−	0.225629i
$569$	21.1209	−	12.1941i	0.885433	−	0.511205i	0.0129872	−	0.999916i	$-0.495866\pi$
$569$	21.1209	−	12.1941i	0.885433	−	0.511205i	0.872446	+	0.488711i	$0.162533\pi$
$570$	−4.52079	+	1.95112i	−0.189355	+	0.0817235i
$571$	−3.15521	+	5.46498i	−0.132041	+	0.228702i	−0.924463	−	0.381271i	$-0.875487\pi$
$571$	−3.15521	+	5.46498i	−0.132041	+	0.228702i	0.792422	+	0.609973i	$0.208820\pi$
$572$	−6.02580	−	1.09452i	−0.251951	−	0.0457644i
$573$	−5.51702	−	5.51702i	−0.230477	−	0.230477i
$574$	10.4218	−	13.2049i	0.435000	−	0.551162i
$575$	6.37436	−	9.80963i	0.265829	−	0.409090i
$576$	−12.6822	−	13.0801i	−0.528425	−	0.545004i
$577$	31.3085	−	8.38908i	1.30339	−	0.349242i	0.460658	−	0.887578i	$-0.347613\pi$
$577$	31.3085	−	8.38908i	1.30339	−	0.349242i	0.842731	+	0.538336i	$0.180947\pi$
$578$	5.27480	+	16.8809i	0.219403	+	0.702154i
$579$	−1.17035	+	0.675703i	−0.0486381	+	0.0280812i
$580$	−11.3958	−	7.77456i	−0.473185	−	0.322821i
$581$	17.5044	−	6.15244i	0.726205	−	0.255246i
$582$	7.72431	+	7.11469i	0.320183	+	0.294913i
$583$	5.71498	−	21.3286i	0.236690	−	0.883340i
$584$	21.9094	+	9.27403i	0.906619	+	0.383762i
$585$	−7.63119	−	3.39891i	−0.315511	−	0.140528i
$586$	−25.5627	+	16.1929i	−1.05599	+	0.668922i
$587$	−17.6905	−	17.6905i	−0.730165	−	0.730165i	0.240487	−	0.970652i	$-0.422693\pi$
$587$	−17.6905	−	17.6905i	−0.730165	−	0.730165i	−0.970652	+	0.240487i	$0.922693\pi$
$588$	−10.4653	+	5.66707i	−0.431580	+	0.233706i
$589$	−10.7139			−0.441458
$590$	−22.2641	+	17.6112i	−0.916600	+	0.725043i
$591$	−1.70605	−	0.984991i	−0.0701777	−	0.0405171i
$592$	16.3364	+	35.9965i	0.671422	+	1.47945i
$593$	−17.2545	−	4.62333i	−0.708557	−	0.189857i	−0.113497	−	0.993538i	$-0.536205\pi$
$593$	−17.2545	−	4.62333i	−0.708557	−	0.189857i	−0.595060	+	0.803681i	$0.702872\pi$
$594$	−0.486120	−	11.8328i	−0.0199457	−	0.485505i
$595$	−30.2657	−	10.8024i	−1.24077	−	0.442856i
$596$	−1.52694	−	18.5525i	−0.0625460	−	0.759942i
$597$	−7.76151	−	2.07969i	−0.317657	−	0.0851160i
$598$	1.61897	+	5.18118i	0.0662046	+	0.211874i
$599$	−18.8104	+	32.5806i	−0.768574	+	1.33121i	0.169762	+	0.985485i	$0.445700\pi$
$599$	−18.8104	+	32.5806i	−0.768574	+	1.33121i	−0.938336	+	0.345724i	$0.887633\pi$
$600$	−9.07882	−	7.88056i	−0.370641	−	0.321722i
$601$	20.9825			0.855894			0.427947	−	0.903804i	$-0.359237\pi$
$601$	20.9825			0.855894			0.427947	+	0.903804i	$0.359237\pi$
$602$	−0.734061	−	6.23182i	−0.0299181	−	0.253990i
$603$	−5.42049	+	5.42049i	−0.220739	+	0.220739i
$604$	25.1675	+	36.3396i	1.02405	+	1.47864i
$605$	−6.02035	−	15.6901i	−0.244762	−	0.637895i
$606$	−7.94183	−	4.16027i	−0.322615	−	0.168999i
$607$	18.0832	+	4.84539i	0.733975	+	0.196668i	0.606399	−	0.795161i	$-0.292613\pi$
$607$	18.0832	+	4.84539i	0.733975	+	0.196668i	0.127577	+	0.991829i	$0.459280\pi$
$608$	−5.67919	+	8.66637i	−0.230322	+	0.351468i
$609$	−1.28033	+	6.81867i	−0.0518815	+	0.276306i
$610$	4.32602	+	29.4935i	0.175156	+	1.19416i
$611$	−3.82300	−	6.62163i	−0.154662	−	0.267882i
$612$	−23.2921	+	8.34209i	−0.941526	+	0.337209i
$613$	−16.7074	+	4.47673i	−0.674805	+	0.180813i	−0.579918	−	0.814675i	$-0.696916\pi$
$613$	−16.7074	+	4.47673i	−0.674805	+	0.180813i	−0.0948867	+	0.995488i	$0.530249\pi$
$614$	13.9674	−	8.84776i	0.563679	−	0.357067i
$615$	−0.892109	−	8.49932i	−0.0359733	−	0.342726i
$616$	0.871479	−	13.9414i	0.0351129	−	0.561717i
$617$	−13.7466	−	13.7466i	−0.553415	−	0.553415i	0.374009	−	0.927425i	$-0.377983\pi$
$617$	−13.7466	−	13.7466i	−0.553415	−	0.553415i	−0.927425	+	0.374009i	$0.877983\pi$
$618$	4.22926	−	18.8472i	0.170126	−	0.758147i
$619$	−25.1521	−	14.5216i	−1.01095	−	0.583671i	−0.0994786	−	0.995040i	$-0.531717\pi$
$619$	−25.1521	−	14.5216i	−1.01095	−	0.583671i	−0.911469	+	0.411369i	$0.865051\pi$
$620$	−11.3428	−	23.5717i	−0.455536	−	0.946661i
$621$	−9.09031	+	5.24829i	−0.364782	+	0.210607i
$622$	−18.3507	+	19.9231i	−0.735798	+	0.798844i
$623$	−22.2715	+	1.70022i	−0.892290	+	0.0681179i
$624$	5.50314	−	0.912035i	0.220302	−	0.0365106i
$625$	20.2172	+	14.7060i	0.808687	+	0.588239i
$626$	4.02522	−	7.68401i	0.160880	−	0.307115i
$627$	−2.80744	+	0.752251i	−0.112118	+	0.0300420i
$628$	1.96521	−	10.8193i	0.0784204	−	0.431736i
$629$	53.6811			2.14040
$630$	5.66293	−	18.1928i	0.225617	−	0.724817i
$631$			20.6648i			0.822651i	0.911489	+	0.411326i	$0.134934\pi$
$631$			20.6648i			0.822651i	−0.911489	+	0.411326i	$0.865066\pi$
$632$	32.7391	+	4.56764i	1.30229	+	0.181691i
$633$	4.48908	+	16.7535i	0.178425	+	0.665890i
$634$	−0.431100	+	0.822956i	−0.0171212	+	0.0326838i
$635$	32.1618	−	23.3600i	1.27630	−	0.927013i
$636$	1.64969	+	20.0439i	0.0654144	+	0.794793i
$637$	−1.25394	+	11.4147i	−0.0496829	+	0.452269i
$638$	−5.98953	−	5.51683i	−0.237128	−	0.218413i
$639$	−3.52082	−	6.09823i	−0.139281	−	0.241242i
$640$	−25.0795	−	3.31975i	−0.991353	−	0.131225i
$641$	−0.126349	+	0.218842i	−0.00499048	+	0.00864376i	−0.868510	−	0.495672i	$-0.834922\pi$
$641$	−0.126349	+	0.218842i	−0.00499048	+	0.00864376i	0.863519	+	0.504316i	$0.168255\pi$
$642$	−3.74147	+	16.6735i	−0.147664	+	0.658049i
$643$	6.48325	−	6.48325i	0.255675	−	0.255675i	−0.567618	−	0.823292i	$-0.692135\pi$
$643$	6.48325	−	6.48325i	0.255675	−	0.255675i	0.823292	+	0.567618i	$0.192135\pi$
$644$	−11.3042	+	5.04966i	−0.445449	+	0.198984i
$645$	−2.47709	−	2.00649i	−0.0975355	−	0.0790053i
$646$	7.52957	+	11.8865i	0.296247	+	0.467666i
$647$	0.353717	+	1.32009i	0.0139061	+	0.0518981i	0.972530	−	0.232777i	$-0.0747811\pi$
$647$	0.353717	+	1.32009i	0.0139061	+	0.0518981i	−0.958624	+	0.284675i	$0.908114\pi$
$648$	−3.20614	−	7.91257i	−0.125949	−	0.310835i
$649$	−14.5117	+	8.37832i	−0.569633	+	0.328878i
$650$	−11.2388	+	2.87234i	−0.440820	+	0.112662i
$651$	−8.56737	+	9.98356i	−0.335782	+	0.391287i
$652$	−3.32776	−	2.82164i	−0.130325	−	0.110504i
$653$	12.3076	−	45.9326i	0.481634	−	1.79748i	−0.113129	−	0.993580i	$-0.536087\pi$
$653$	12.3076	−	45.9326i	0.481634	−	1.79748i	0.594763	−	0.803901i	$-0.297246\pi$
$654$	9.27332	−	17.7025i	0.362616	−	0.692222i
$655$	−10.1962	−	26.5732i	−0.398399	−	1.03830i
$656$	−11.4172	−	13.8945i	−0.445767	−	0.542490i
$657$	13.5454	+	13.5454i	0.528456	+	0.528456i
$658$	13.9790	−	10.4265i	0.544958	−	0.406467i
$659$		−	19.0428i		−	0.741802i	−0.928672	−	0.370901i	$-0.879049\pi$
$659$		−	19.0428i		−	0.741802i	0.928672	−	0.370901i	$-0.120951\pi$
$660$	−4.62726	−	5.38025i	−0.180116	−	0.209426i
$661$	−2.33892	−	1.35038i	−0.0909736	−	0.0525236i	0.453823	−	0.891092i	$-0.350060\pi$
$661$	−2.33892	−	1.35038i	−0.0909736	−	0.0525236i	−0.544797	+	0.838568i	$0.683393\pi$
$662$	35.8997	−	11.2176i	1.39528	−	0.435985i
$663$	1.96058	−	7.31697i	0.0761425	−	0.284168i
$664$	−2.43709	−	19.6849i	−0.0945774	−	0.763924i
$665$	−10.8007	−	0.877070i	−0.418833	−	0.0340113i
$666$	1.30648	+	31.8015i	0.0506252	+	1.23228i
$667$	−1.86801	+	6.97152i	−0.0723298	+	0.269938i
$668$	45.1067	−	16.1550i	1.74523	−	0.625057i
$669$	−8.80545	+	15.2515i	−0.340438	+	0.589657i
$670$	−1.23368	+	10.5727i	−0.0476613	+	0.408458i
$671$			17.5958i			0.679278i
$672$	3.53424	+	12.2221i	0.136336	+	0.471479i
$673$	12.8751	−	12.8751i	0.496298	−	0.496298i	−0.413985	−	0.910284i	$-0.635864\pi$
$673$	12.8751	−	12.8751i	0.496298	−	0.496298i	0.910284	+	0.413985i	$0.135864\pi$
$674$	−24.8215	+	15.7234i	−0.956090	+	0.605643i
$675$	−10.1778	−	19.9890i	−0.391745	−	0.769377i
$676$	−8.80945	+	18.6408i	−0.338825	+	0.716954i
$677$	−16.1621	−	4.33061i	−0.621158	−	0.166439i	−0.0655041	−	0.997852i	$-0.520866\pi$
$677$	−16.1621	−	4.33061i	−0.621158	−	0.166439i	−0.555654	+	0.831413i	$0.687532\pi$
$678$	−2.39216	+	2.59714i	−0.0918705	+	0.0997424i
$679$	7.66363	+	21.8039i	0.294103	+	0.836758i
$680$	−18.1799	+	29.1500i	−0.697168	+	1.11785i
$681$	−9.01527	−	15.6149i	−0.345466	−	0.598364i
$682$	−4.60531	−	14.7383i	−0.176346	−	0.564360i
$683$	−7.21207	−	26.9158i	−0.275962	−	1.02991i	−0.955194	−	0.295981i	$-0.904353\pi$
$683$	−7.21207	−	26.9158i	−0.275962	−	1.02991i	0.679231	−	0.733924i	$-0.262313\pi$
$684$	−6.85847	+	4.74993i	−0.262240	+	0.181618i
$685$	33.7678	−	3.54435i	1.29020	−	0.135423i
$686$	−26.1908	+	0.205292i	−0.999969	+	0.00783808i
$687$	−0.759216	+	0.759216i	−0.0289659	+	0.0289659i
$688$	−6.67625	−	0.653424i	−0.254530	−	0.0249115i
$689$	16.8059	+	9.70287i	0.640253	+	0.369650i
$690$	−2.32107	+	5.84579i	−0.0883615	+	0.222545i
$691$	3.83064	+	6.63487i	0.145724	+	0.252402i	0.929643	−	0.368461i	$-0.120115\pi$
$691$	3.83064	+	6.63487i	0.145724	+	0.252402i	−0.783919	+	0.620864i	$0.786782\pi$
$692$	16.6200	−	19.6011i	0.631797	−	0.745122i
$693$	4.86582	−	10.1401i	0.184837	−	0.385190i
$694$	0.673332	+	16.3898i	0.0255593	+	0.622148i
$695$	5.08899	−	32.1014i	0.193036	−	1.21768i
$696$	6.83016	+	2.89113i	0.258896	+	0.109588i
$697$	−23.5893	+	6.32073i	−0.893507	+	0.239415i
$698$	5.43149	−	24.2049i	0.205585	−	0.916167i
$699$			12.7457i			0.482088i
$700$	−9.50501	−	24.6912i	−0.359256	−	0.933239i
$701$			28.8628i			1.09013i	0.838393	+	0.545067i	$0.183496\pi$
$701$			28.8628i			1.09013i	−0.838393	+	0.545067i	$0.816504\pi$
$702$	10.1554	+	2.27884i	0.383292	+	0.0860093i
$703$	17.4846	−	4.68499i	0.659445	−	0.176698i
$704$	−14.3629	−	4.08727i	−0.541322	−	0.154045i
$705$	1.38715	−	8.75020i	0.0522432	−	0.329552i
$706$	−8.91356	+	0.366191i	−0.335466	+	0.0137818i
$707$	−11.1375	−	16.2870i	−0.418870	−	0.612535i
$708$	9.87042	−	11.6409i	0.370953	−	0.437491i
$709$	−8.82622	−	15.2875i	−0.331476	−	0.574132i	0.651326	−	0.758798i	$-0.274213\pi$
$709$	−8.82622	−	15.2875i	−0.331476	−	0.574132i	−0.982801	+	0.184666i	$0.940880\pi$
$710$	−9.08769	−	3.60826i	−0.341055	−	0.135416i
$711$	23.0500	+	13.3079i	0.864442	+	0.499086i
$712$	−3.29949	+	23.6495i	−0.123654	+	0.886302i
$713$	−9.67738	+	9.67738i	−0.362421	+	0.362421i
$714$	17.0972	+	2.48872i	0.639848	+	0.0931379i
$715$	−6.80988	+	0.714781i	−0.254675	+	0.0267313i
$716$	2.87343	+	4.14897i	0.107385	+	0.155054i
$717$	−3.96389	−	14.7934i	−0.148034	−	0.552471i
$718$	16.1219	−	5.03764i	0.601665	−	0.188003i
$719$	20.1004	+	34.8150i	0.749620	+	1.29838i	0.948005	+	0.318255i	$0.103097\pi$
$719$	20.1004	+	34.8150i	0.749620	+	1.29838i	−0.198385	+	0.980124i	$0.563570\pi$
$720$	−17.7114	−	10.0606i	−0.660064	−	0.374937i
$721$	27.6837	−	32.2598i	1.03099	−	1.20142i
$722$	−16.2740	−	14.9896i	−0.605657	−	0.557857i
$723$	−10.1040	−	2.70737i	−0.375774	−	0.100688i
$724$	0.198246	−	0.419489i	0.00736777	−	0.0155902i
$725$	−14.6673	−	4.77025i	−0.544730	−	0.177162i
$726$	4.83504	+	7.63277i	0.179445	+	0.283279i
$727$	22.7088	−	22.7088i	0.842221	−	0.842221i	−0.146926	−	0.989147i	$-0.546938\pi$
$727$	22.7088	−	22.7088i	0.842221	−	0.842221i	0.989147	+	0.146926i	$0.0469380\pi$
$728$	11.6366	+	3.91094i	0.431283	+	0.144949i
$729$			4.56682i			0.169142i
$730$	26.4203	+	3.08288i	0.977861	+	0.114103i
$731$	−4.55477	+	7.88909i	−0.168464	+	0.291789i
$732$	−5.40380	−	15.0880i	−0.199730	−	0.557670i
$733$	2.85536	−	10.6563i	0.105465	−	0.393601i	−0.892932	−	0.450191i	$-0.851356\pi$
$733$	2.85536	−	10.6563i	0.105465	−	0.393601i	0.998398	+	0.0565898i	$0.0180227\pi$
$734$	−10.9205	+	0.448641i	−0.403083	+	0.0165596i
$735$	−9.45407	+	9.36310i	−0.348719	+	0.345363i
$736$	2.69819	+	12.9577i	0.0994565	+	0.477628i
$737$	−1.62622	+	6.06913i	−0.0599025	+	0.223559i
$738$	−4.31861	−	13.8208i	−0.158970	−	0.508752i
$739$	−13.1322	−	7.58185i	−0.483074	−	0.278903i	0.238623	−	0.971112i	$-0.423304\pi$
$739$	−13.1322	−	7.58185i	−0.483074	−	0.278903i	−0.721697	+	0.692209i	$0.756637\pi$
$740$	28.8184	+	33.5080i	1.05938	+	1.23178i
$741$		−	2.55434i		−	0.0938360i
$742$	−17.4944	+	40.6569i	−0.642241	+	1.49256i
$743$	2.53511	+	2.53511i	0.0930042	+	0.0930042i	0.752078	−	0.659074i	$-0.229052\pi$
$743$	2.53511	+	2.53511i	0.0930042	+	0.0930042i	−0.659074	+	0.752078i	$0.729052\pi$
$744$	8.47520	+	11.2235i	0.310716	+	0.411473i
$745$	−7.45581	−	19.4312i	−0.273160	−	0.711904i
$746$	−38.2736	−	20.0494i	−1.40130	−	0.734059i
$747$	4.13352	−	15.4265i	0.151238	−	0.564426i
$748$	−13.1148	+	15.4672i	−0.479525	+	0.565538i
$749$	−24.4907	+	28.5391i	−0.894872	+	1.04279i
$750$	−12.2140	−	5.61049i	−0.445993	−	0.204866i
$751$	6.56734	−	3.79166i	0.239646	−	0.138360i	−0.375368	−	0.926876i	$-0.622484\pi$
$751$	6.56734	−	3.79166i	0.239646	−	0.138360i	0.615014	+	0.788516i	$0.289150\pi$
$752$	−7.70460	−	16.9767i	−0.280958	−	0.619078i
$753$	−1.39594	−	5.20972i	−0.0508709	−	0.189853i
$754$	6.04562	−	3.82964i	0.220168	−	0.139467i
$755$	38.4032	+	31.1072i	1.39764	+	1.13211i
$756$	−2.45229	+	23.6117i	−0.0891888	+	0.858749i
$757$	−14.6616	+	14.6616i	−0.532886	+	0.532886i	−0.921430	−	0.388544i	$-0.872978\pi$
$757$	−14.6616	+	14.6616i	−0.532886	+	0.532886i	0.388544	+	0.921430i	$0.372978\pi$
$758$	12.5168	+	2.80873i	0.454631	+	0.102018i
$759$	−1.85636	+	3.21531i	−0.0673816	+	0.116708i
$760$	−3.37738	+	11.0812i	−0.122510	+	0.401956i
$761$	−14.1703	−	24.5437i	−0.513674	−	0.889709i	−0.999874	−	0.0158615i	$-0.994951\pi$
$761$	−14.1703	−	24.5437i	−0.513674	−	0.889709i	0.486201	−	0.873847i	$-0.338382\pi$
$762$	−14.4787	+	15.7193i	−0.524508	+	0.569450i
$763$	36.3040	−	24.8258i	1.31429	−	0.898754i
$764$	−18.2946	+	1.50571i	−0.661875	+	0.0544748i
$765$	−22.3806	+	16.2557i	−0.809173	+	0.587725i
$766$	12.6001	+	6.60050i	0.455262	+	0.238486i
$767$	−3.81149	−	14.2247i	−0.137625	−	0.513624i
$768$	13.5711	−	0.906199i	0.489705	−	0.0326996i
$769$		−	13.9851i		−	0.504317i	−0.967686	−	0.252159i	$-0.918860\pi$
$769$		−	13.9851i		−	0.504317i	0.967686	−	0.252159i	$-0.0811404\pi$
$770$	−3.43610	−	15.2347i	−0.123828	−	0.549022i
$771$	−17.5392			−0.631658
$772$	−0.568220	+	3.12828i	−0.0204507	+	0.112589i
$773$	1.04256	−	0.279354i	0.0374984	−	0.0100477i	−0.240021	−	0.970768i	$-0.577154\pi$
$773$	1.04256	−	0.279354i	0.0374984	−	0.0100477i	0.277519	+	0.960720i	$0.410488\pi$
$774$	−4.78448	−	2.50632i	−0.171975	−	0.0900876i
$775$	−19.5636	−	21.7398i	−0.702744	−	0.780917i
$776$	24.5201	−	3.03570i	0.880219	−	0.108975i
$777$	9.61596	−	20.0391i	0.344971	−	0.718899i
$778$	7.90781	+	7.28371i	0.283509	+	0.261134i
$779$	−7.13169	+	4.11748i	−0.255519	+	0.147524i
$780$	5.61981	−	2.70427i	0.201222	−	0.0968285i
$781$	−4.99843	−	2.88584i	−0.178858	−	0.103264i
$782$	17.5376	+	3.93539i	0.627145	+	0.140729i
$783$	9.78535	+	9.78535i	0.349700	+	0.349700i
$784$	−5.75404	+	27.4024i	−0.205501	+	0.978657i
$785$	−1.28338	−	12.2271i	−0.0458059	−	0.436403i
$786$	8.18872	+	12.9270i	0.292082	+	0.461092i
$787$	19.7191	−	5.28372i	0.702911	−	0.188344i	0.110377	−	0.993890i	$-0.464794\pi$
$787$	19.7191	−	5.28372i	0.702911	−	0.188344i	0.592534	+	0.805545i	$0.298128\pi$
$788$	−4.36339	+	1.56275i	−0.155439	+	0.0556708i
$789$	10.1393	+	17.5618i	0.360969	+	0.625217i
$790$	36.5667	−	5.36351i	1.30099	−	0.190825i
$791$	−7.33111	+	2.57673i	−0.260664	+	0.0916181i
$792$	−9.48222	−	7.39299i	−0.336936	−	0.262698i
$793$	−14.9371	−	4.00237i	−0.530430	−	0.142128i
$794$	−11.6328	+	22.2067i	−0.412833	+	0.788085i
$795$	8.05516	+	20.9932i	0.285687	+	0.744552i
$796$	−15.5415	+	10.7635i	−0.550853	+	0.381501i
$797$	15.6200	−	15.6200i	0.553290	−	0.553290i	−0.374099	−	0.927389i	$-0.622048\pi$
$797$	15.6200	−	15.6200i	0.553290	−	0.553290i	0.927389	+	0.374099i	$0.122048\pi$
$798$	5.78599	−	0.681545i	0.204822	−	0.0241264i
$799$	−25.3172			−0.895657
$800$	−27.9553	+	4.30102i	−0.988371	+	0.152064i
$801$	−9.61312	+	16.6504i	−0.339663	+	0.588314i
$802$	26.4690	−	8.27080i	0.934653	−	0.292052i
$803$	15.1663	+	4.06380i	0.535207	+	0.143408i
$804$	−0.469425	−	5.70357i	−0.0165554	−	0.201150i
$805$	−10.5480	+	8.96356i	−0.371768	+	0.315924i
$806$	13.5589	−	0.557032i	0.477591	−	0.0196206i
$807$	7.62868	+	2.04410i	0.268542	+	0.0719557i
$808$	−19.5494	+	7.92133i	−0.687745	+	0.278671i
$809$	16.8004	+	9.69972i	0.590671	+	0.341024i	0.765363	−	0.643599i	$-0.222560\pi$
$809$	16.8004	+	9.69972i	0.590671	+	0.341024i	−0.174692	+	0.984623i	$0.555893\pi$
$810$	−5.92170	−	7.48622i	−0.208067	−	0.263039i
$811$	11.5439			0.405360			0.202680	−	0.979245i	$-0.435035\pi$
$811$	11.5439			0.405360			0.202680	+	0.979245i	$0.435035\pi$
$812$	10.2878	+	12.6725i	0.361032	+	0.444717i
$813$	−13.7951	−	13.7951i	−0.483815	−	0.483815i
$814$	13.9605	+	22.0385i	0.489314	+	0.772450i
$815$	−4.45596	−	1.98467i	−0.156086	−	0.0695200i
$816$	6.49558	−	17.2905i	0.227391	−	0.605288i
$817$	−0.795030	+	2.96709i	−0.0278146	+	0.103805i
$818$	5.63703	−	6.12004i	0.197094	−	0.213982i
$819$	7.50112	+	6.43707i	0.262110	+	0.224930i
$820$	−16.6092	−	11.3313i	−0.580018	−	0.395706i
$821$	21.6919	−	12.5238i	0.757053	−	0.437085i	−0.0711837	−	0.997463i	$-0.522678\pi$
$821$	21.6919	−	12.5238i	0.757053	−	0.437085i	0.828237	+	0.560379i	$0.189344\pi$
$822$	−17.4238	+	5.44444i	−0.607725	+	0.189897i
$823$	−23.2094	+	6.21894i	−0.809029	+	0.216779i	−0.639544	−	0.768754i	$-0.720877\pi$
$823$	−23.2094	+	6.21894i	−0.809029	+	0.216779i	−0.169484	+	0.985533i	$0.554210\pi$
$824$	−27.3858	−	36.2663i	−0.954031	−	1.26340i
$825$	−6.65279	−	4.32303i	−0.231621	−	0.150509i
$826$	31.2042	−	12.4291i	1.08573	−	0.432462i
$827$	22.0216	+	22.0216i	0.765766	+	0.765766i	0.977358	−	0.211592i	$-0.0678649\pi$
$827$	22.0216	+	22.0216i	0.765766	+	0.765766i	−0.211592	+	0.977358i	$0.567865\pi$
$828$	−1.90456	+	10.4854i	−0.0661879	+	0.364391i
$829$	12.8190	−	22.2031i	0.445221	−	0.771145i	−0.552847	−	0.833283i	$-0.686458\pi$
$829$	12.8190	−	22.2031i	0.445221	−	0.771145i	0.998068	+	0.0621378i	$0.0197918\pi$
$830$	−8.78761	−	20.3611i	−0.305022	−	0.706743i
$831$	−12.3888	+	7.15267i	−0.429762	+	0.248123i
$832$	6.73668	−	11.2629i	0.233552	−	0.390472i
$833$	30.6564	+	22.4938i	1.06218	+	0.779363i
$834$	0.717291	+	17.4598i	0.0248377	+	0.604583i
$835$	43.3416	−	31.4802i	1.49990	−	1.08942i
$836$	−2.92177	+	6.18246i	−0.101052	+	0.213825i
$837$	6.79167	+	25.3468i	0.234754	+	0.876115i
$838$	2.10271	+	0.471841i	0.0726368	+	0.0162995i
$839$	20.3744			0.703403			0.351702	−	0.936112i	$-0.385603\pi$
$839$	20.3744			0.703403			0.351702	+	0.936112i	$0.385603\pi$
$840$	7.62508	+	12.0082i	0.263090	+	0.414323i
$841$	−19.4846			−0.671883
$842$	31.4229	+	7.05120i	1.08291	+	0.243000i
$843$	5.74025	+	21.4229i	0.197705	+	0.737844i
$844$	36.8940	+	17.4357i	1.26994	+	0.600163i
$845$	−3.60919	+	22.7669i	−0.124160	+	0.783204i
$846$	−0.616166	−	14.9983i	−0.0211842	−	0.515652i
$847$	1.51359	+	19.8269i	0.0520077	+	0.681259i
$848$	38.4784	+	27.5375i	1.32135	+	0.945643i
$849$	23.3192	−	13.4634i	0.800314	−	0.462061i
$850$	−10.3701	+	36.9831i	−0.355692	+	1.26851i
$851$	11.5613	−	20.0248i	0.396317	−	0.686442i
$852$	5.17231	+	0.939497i	0.177200	+	0.0321866i
$853$	3.84573	+	3.84573i	0.131675	+	0.131675i	0.769873	−	0.638197i	$-0.220320\pi$
$853$	3.84573	+	3.84573i	0.131675	+	0.131675i	−0.638197	+	0.769873i	$0.720320\pi$
$854$	5.08053	−	34.9027i	0.173852	−	1.19435i
$855$	−5.87095	+	7.24794i	−0.200782	+	0.247874i
$856$	24.2273	+	32.0835i	0.828071	+	1.09659i
$857$	27.0419	−	7.24585i	0.923734	−	0.247514i	0.234553	−	0.972103i	$-0.424637\pi$
$857$	27.0419	−	7.24585i	0.923734	−	0.247514i	0.689181	+	0.724590i	$0.257971\pi$
$858$	3.51382	−	1.09797i	0.119960	−	0.0374841i
$859$	31.0792	−	17.9436i	1.06041	−	0.612228i	0.134864	−	0.990864i	$-0.456940\pi$
$859$	31.0792	−	17.9436i	1.06041	−	0.612228i	0.925546	+	0.378636i	$0.123607\pi$
$860$	−7.36961	+	1.39210i	−0.251302	+	0.0474704i
$861$	−1.86606	+	9.93810i	−0.0635950	+	0.338690i
$862$	−11.5546	+	12.5446i	−0.393550	+	0.427271i
$863$	3.04071	−	11.3481i	0.103507	−	0.386293i	−0.894665	−	0.446738i	$-0.852585\pi$
$863$	3.04071	−	11.3481i	0.103507	−	0.386293i	0.998171	+	0.0604455i	$0.0192521\pi$
$864$	24.1030	+	7.94208i	0.819999	+	0.270195i
$865$	11.6901	−	26.2464i	0.397475	−	0.892406i
$866$	9.39547	+	14.8320i	0.319271	+	0.504013i
$867$	−7.51722	−	7.51722i	−0.255298	−	0.255298i
$868$	4.87953	+	30.5644i	0.165622	+	1.03742i
$869$	21.8157			0.740047
$870$	8.23641	+	0.961073i	0.279240	+	0.0325834i
$871$	−4.78217	−	2.76099i	−0.162038	−	0.0935525i
$872$	−17.6568	−	43.5760i	−0.597935	−	1.47567i
$873$	19.2156	+	5.14882i	0.650351	+	0.174261i
$874$	6.05569	−	0.248782i	0.204837	−	0.00841519i
$875$	−17.9424	−	23.5175i	−0.606563	−	0.795035i
$876$	−14.2528	+	1.17306i	−0.481558	+	0.0396340i
$877$	−21.9335	−	5.87707i	−0.740642	−	0.198455i	−0.131279	−	0.991345i	$-0.541908\pi$
$877$	−21.9335	−	5.87707i	−0.740642	−	0.198455i	−0.609364	+	0.792891i	$0.708575\pi$
$878$	19.8173	−	6.19234i	0.668802	−	0.208981i
$879$	9.09460	−	15.7523i	0.306753	−	0.531312i
$880$	−16.6953	+	0.117158i	−0.562799	+	0.00394941i
$881$	25.9213			0.873310			0.436655	−	0.899629i	$-0.356163\pi$
$881$	25.9213			0.873310			0.436655	+	0.899629i	$0.356163\pi$
$882$	−12.5796	+	18.7088i	−0.423576	+	0.629957i
$883$	−12.1232	+	12.1232i	−0.407977	+	0.407977i	−0.881032	−	0.473056i	$-0.843151\pi$
$883$	−12.1232	+	12.1232i	−0.407977	+	0.407977i	0.473056	+	0.881032i	$0.343151\pi$
$884$	−10.1470	−	14.6514i	−0.341280	−	0.492778i
$885$	6.94261	−	15.5875i	0.233373	−	0.523967i
$886$	−17.9521	+	34.2700i	−0.603113	+	1.15132i
$887$	5.13155	+	1.37499i	0.172301	+	0.0461678i	0.343938	−	0.938992i	$-0.388239\pi$
$887$	5.13155	+	1.37499i	0.172301	+	0.0461678i	−0.171637	+	0.985160i	$0.554906\pi$
$888$	−18.7390	−	14.6102i	−0.628840	−	0.490287i
$889$	−44.3719	+	15.5958i	−1.48819	+	0.523067i
$890$	3.87439	+	26.4144i	0.129870	+	0.885413i
$891$	−2.81717	−	4.87949i	−0.0943789	−	0.163469i
$892$	13.9704	+	39.0071i	0.467765	+	1.30605i
$893$	−8.24612	+	2.20954i	−0.275946	+	0.0739395i
$894$	5.98787	+	9.45268i	0.200264	+	0.316145i
$895$	4.38457	+	3.55158i	0.146560	+	0.118716i
$896$	27.3098	+	12.2545i	0.912358	+	0.409394i
$897$	−2.30722	−	2.30722i	−0.0770359	−	0.0770359i
$898$	−33.2461	−	7.46031i	−1.10944	−	0.248954i
$899$	15.6259	+	9.02165i	0.521155	+	0.300889i
$900$	−22.1618	−	5.24333i	−0.738726	−	0.174778i
$901$	55.6470	−	32.1278i	1.85387	−	1.07033i
$902$	−8.72965	−	8.04068i	−0.290666	−	0.267725i
$903$	2.12909	+	3.11348i	0.0708517	+	0.103610i
$904$	1.02069	+	8.24435i	0.0339476	+	0.274203i
$905$	0.0812207	−	0.512342i	0.00269987	−	0.0170308i
$906$	−23.5370	−	12.3297i	−0.781963	−	0.409626i
$907$	43.9219	−	11.7688i	1.45840	−	0.390778i	0.559465	−	0.828854i	$-0.311007\pi$
$907$	43.9219	−	11.7688i	1.45840	−	0.390778i	0.898938	+	0.438077i	$0.144340\pi$
$908$	−41.7377	−	7.58123i	−1.38511	−	0.251592i
$909$	−16.9836			−0.563312
$910$	13.7143	+	0.548425i	0.454626	+	0.0181801i
$911$			23.2828i			0.771395i	0.922625	+	0.385698i	$0.126039\pi$
$911$			23.2828i			0.771395i	−0.922625	+	0.385698i	$0.873961\pi$
$912$	0.606677	−	6.19863i	0.0200891	−	0.205257i
$913$	−3.38804	−	12.6444i	−0.112128	−	0.418467i
$914$	−35.1640	−	18.4204i	−1.16312	−	0.609293i
$915$	−10.5300	−	14.4976i	−0.348112	−	0.479276i
$916$	0.207206	+	2.51758i	0.00684628	+	0.0831831i
$917$	2.56345	+	33.5792i	0.0846527	+	1.10888i
$918$	23.3478	−	25.3484i	0.770593	−	0.836622i
$919$	−2.61109	−	4.52254i	−0.0861320	−	0.149185i	0.819741	−	0.572734i	$-0.194117\pi$
$919$	−2.61109	−	4.52254i	−0.0861320	−	0.149185i	−0.905873	+	0.423549i	$0.860784\pi$
$920$	6.95849	+	13.0598i	0.229415	+	0.430568i
$921$	−4.96927	+	8.60703i	−0.163743	+	0.283611i
$922$	−53.6795	−	12.0455i	−1.76784	−	0.396697i
$923$	3.58674	−	3.58674i	0.118059	−	0.118059i
$924$	3.42463	+	7.66642i	0.112662	+	0.252207i
$925$	41.4333	+	26.9237i	1.36232	+	0.885244i
$926$	5.83165	−	3.69410i	0.191640	−	0.121396i
$927$	−9.47038	−	35.3439i	−0.311048	−	1.16085i
$928$	15.5805	−	7.85753i	0.511455	−	0.257936i
$929$	−24.2578	+	14.0052i	−0.795872	+	0.459497i	−0.842026	−	0.539437i	$-0.818637\pi$
$929$	−24.2578	+	14.0052i	−0.795872	+	0.459497i	0.0461537	+	0.998934i	$0.485304\pi$
$930$	12.6144	+	9.38728i	0.413643	+	0.307821i
$931$	11.9483	+	4.65099i	0.391590	+	0.152430i
$932$	22.8719	+	19.3933i	0.749194	+	0.635249i
$933$	4.21401	−	15.7269i	0.137961	−	0.514876i
$934$	−31.1124	−	16.2980i	−1.01803	−	0.533286i
$935$	−9.22464	+	20.7111i	−0.301678	+	0.677324i
$936$	8.43274	−	6.36782i	0.275633	−	0.208139i
$937$	−7.32900	−	7.32900i	−0.239428	−	0.239428i	0.577185	−	0.816613i	$-0.304151\pi$
$937$	−7.32900	−	7.32900i	−0.239428	−	0.239428i	−0.816613	+	0.577185i	$0.804151\pi$
$938$	4.97811	−	11.5691i	0.162541	−	0.377744i
$939$			5.21422i			0.170160i
$940$	−13.5914	−	15.8031i	−0.443302	−	0.515440i
$941$	−11.1615	−	6.44408i	−0.363854	−	0.210071i	0.306916	−	0.951737i	$-0.400703\pi$
$941$	−11.1615	−	6.44408i	−0.363854	−	0.210071i	−0.670770	+	0.741666i	$0.734036\pi$
$942$	1.97139	+	6.30904i	0.0642315	+	0.205560i
$943$	−2.72260	+	10.1609i	−0.0886600	+	0.330884i
$944$	−5.87089	−	35.4244i	−0.191081	−	1.15297i
$945$	4.77173	+	26.1082i	0.155224	+	0.849300i
$946$	−4.42336	+	0.181722i	−0.143816	+	0.00590830i
$947$	−2.66298	+	9.93839i	−0.0865353	+	0.322954i	−0.995601	−	0.0936997i	$-0.970131\pi$
$947$	−2.66298	+	9.93839i	−0.0865353	+	0.322954i	0.909065	+	0.416654i	$0.136797\pi$
$948$	−18.7065	+	6.69976i	−0.607559	+	0.217598i
$949$	−6.89951	+	11.9503i	−0.223967	+	0.387923i
$950$	−0.149994	+	12.9509i	−0.00486645	+	0.420183i
$951$		−	0.558442i		−	0.0181087i
$952$	30.4803	−	26.8938i	0.987871	−	0.871634i
$953$	12.5051	−	12.5051i	0.405081	−	0.405081i	−0.474938	−	0.880019i	$-0.657530\pi$
$953$	12.5051	−	12.5051i	0.405081	−	0.405081i	0.880019	+	0.474938i	$0.157530\pi$
$954$	20.3874	+	32.1842i	0.660065	+	1.04200i
$955$	−19.1610	+	7.35214i	−0.620036	+	0.237910i
$956$	−32.5777	−	15.3959i	−1.05364	−	0.497939i
$957$	4.72802	+	1.26687i	0.152835	+	0.0409520i
$958$	−5.66936	−	5.22192i	−0.183169	−	0.168712i
$959$	−39.4841	−	7.41383i	−1.27501	−	0.239405i
$960$	14.2799	−	5.22772i	0.460882	−	0.168724i
$961$	1.60703	+	2.78346i	0.0518398	+	0.0897891i
$962$	−21.8840	+	6.83811i	−0.705567	+	0.220469i
$963$	8.37810	+	31.2675i	0.269980	+	1.00758i
$964$	−20.2321	+	14.0120i	−0.651633	+	0.451297i
$965$	0.371077	+	3.53533i	0.0119454	+	0.113806i
$966$	4.61062	−	5.84184i	0.148344	−	0.187958i
$967$	4.48487	−	4.48487i	0.144224	−	0.144224i	−0.631308	−	0.775532i	$-0.717482\pi$
$967$	4.48487	−	4.48487i	0.144224	−	0.144224i	0.775532	+	0.631308i	$0.217482\pi$
$968$	21.0536	+	2.93731i	0.676687	+	0.0944088i
$969$	−7.32470	−	4.22892i	−0.235303	−	0.135852i
$970$	25.3623	−	10.9461i	0.814333	−	0.351457i
$971$	−6.92198	−	11.9892i	−0.222137	−	0.384752i	0.733320	−	0.679884i	$-0.237970\pi$
$971$	−6.92198	−	11.9892i	−0.222137	−	0.384752i	−0.955457	+	0.295132i	$0.904637\pi$
$972$	24.4446	+	20.7268i	0.784061	+	0.664813i
$973$	−16.6377	+	34.6720i	−0.533380	+	1.11153i
$974$	−34.3747	+	1.41219i	−1.10144	+	0.0452496i
$975$	5.18307	−	4.66423i	0.165991	−	0.149375i
$976$	−35.2972	−	13.2603i	−1.12984	−	0.424450i
$977$	−46.0797	+	12.3470i	−1.47422	+	0.395016i	−0.904376	−	0.426736i	$-0.859663\pi$
$977$	−46.0797	+	12.3470i	−1.47422	+	0.395016i	−0.569845	+	0.821752i	$0.692997\pi$
$978$	2.55895	+	0.574220i	0.0818262	+	0.0183615i
$979$			15.7588i			0.503654i
$980$	2.41697	+	31.2115i	0.0772073	+	0.997015i
$981$		−	37.8568i		−	1.20868i
$982$	−1.73314	+	7.72356i	−0.0553068	+	0.246469i
$983$	11.1501	−	2.98766i	0.355633	−	0.0952916i	−0.0765792	−	0.997063i	$-0.524400\pi$
$983$	11.1501	−	2.98766i	0.355633	−	0.0952916i	0.432212	+	0.901772i	$0.357733\pi$
$984$	9.95484	+	4.21378i	0.317349	+	0.134330i
$985$	−4.19265	+	3.04524i	−0.133589	+	0.0970293i
$986$	−0.972684	−	23.6764i	−0.0309766	−	0.754010i
$987$	−4.53510	+	9.45088i	−0.144354	+	0.300825i
$988$	−4.58369	−	3.88656i	−0.145827	−	0.123648i
$989$	1.96193	+	3.39816i	0.0623857	+	0.108055i
$990$	−12.4941	−	4.96076i	−0.397088	−	0.157663i
$991$	−36.9708	−	21.3451i	−1.17442	−	0.678050i	−0.219701	−	0.975567i	$-0.570508\pi$
$991$	−36.9708	−	21.3451i	−1.17442	−	0.678050i	−0.954717	+	0.297517i	$0.903842\pi$
$992$	33.0357	+	1.86860i	1.04888	+	0.0593281i
$993$	−15.9864	+	15.9864i	−0.507314	+	0.507314i
$994$	9.08155	+	7.16753i	0.288049	+	0.227340i
$995$	−13.3037	+	16.4240i	−0.421756	+	0.520676i
$996$	6.78835	+	9.80178i	0.215097	+	0.310581i
$997$	3.85227	+	14.3769i	0.122003	+	0.455320i	0.999715	−	0.0238675i	$-0.00759799\pi$
$997$	3.85227	+	14.3769i	0.122003	+	0.455320i	−0.877712	+	0.479188i	$0.840931\pi$
$998$	−8.48285	−	27.1476i	−0.268520	−	0.859343i
$999$	−22.1674	−	38.3951i	−0.701347	−	1.21477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.67.19	yes	176
5.3	odd	4	inner	280.2.br.a.123.42	yes	176
7.2	even	3	inner	280.2.br.a.107.41	yes	176
8.3	odd	2	inner	280.2.br.a.67.18	✓	176
35.23	odd	12	inner	280.2.br.a.163.18	yes	176
40.3	even	4	inner	280.2.br.a.123.41	yes	176
56.51	odd	6	inner	280.2.br.a.107.42	yes	176
280.163	even	12	inner	280.2.br.a.163.19	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.18	✓	176	8.3	odd	2	inner
280.2.br.a.67.19	yes	176	1.1	even	1	trivial
280.2.br.a.107.41	yes	176	7.2	even	3	inner
280.2.br.a.107.42	yes	176	56.51	odd	6	inner
280.2.br.a.123.41	yes	176	40.3	even	4	inner
280.2.br.a.123.42	yes	176	5.3	odd	4	inner
280.2.br.a.163.18	yes	176	35.23	odd	12	inner
280.2.br.a.163.19	yes	176	280.163	even	12	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309645 + 1.37990i) q^{2} +(-0.220018 - 0.821117i) q^{3} +(-1.80824 - 0.854556i) q^{4} +(-2.20849 - 0.350108i) q^{5} +(1.20119 - 0.0493476i) q^{6} +(2.38534 + 1.14463i) q^{7} +(1.73911 - 2.23058i) q^{8} +(1.97225 - 1.13868i) q^{9} +O(q^{10})\)	\(q+(-0.309645 + 1.37990i) q^{2} +(-0.220018 - 0.821117i) q^{3} +(-1.80824 - 0.854556i) q^{4} +(-2.20849 - 0.350108i) q^{5} +(1.20119 - 0.0493476i) q^{6} +(2.38534 + 1.14463i) q^{7} +(1.73911 - 2.23058i) q^{8} +(1.97225 - 1.13868i) q^{9} +(1.16696 - 2.93908i) q^{10} +(0.933320 - 1.61656i) q^{11} +(-0.303846 + 1.67279i) q^{12} +(1.16000 + 1.16000i) q^{13} +(-2.31808 + 2.93709i) q^{14} +(0.198427 + 1.89046i) q^{15} +(2.53947 + 3.09049i) q^{16} +(5.24683 - 1.40589i) q^{17} +(0.960566 + 3.07409i) q^{18} +(1.58626 - 0.915829i) q^{19} +(3.69429 + 2.52036i) q^{20} +(0.415057 - 2.21048i) q^{21} +(1.94169 + 1.78845i) q^{22} +(0.605573 - 2.26003i) q^{23} +(-2.21420 - 0.937248i) q^{24} +(4.75485 + 1.54642i) q^{25} +(-1.95987 + 1.24149i) q^{26} +(-3.17222 - 3.17222i) q^{27} +(-3.33511 - 4.10816i) q^{28} -3.08470 q^{29} +(-2.67008 - 0.311561i) q^{30} +(-5.06562 - 2.92464i) q^{31} +(-5.05089 + 2.54725i) q^{32} +(-1.53273 - 0.410694i) q^{33} +(0.315325 + 7.67542i) q^{34} +(-4.86725 - 3.36302i) q^{35} +(-4.53937 + 0.373607i) q^{36} +(9.54578 + 2.55778i) q^{37} +(0.772574 + 2.47246i) q^{38} +(0.697275 - 1.20772i) q^{39} +(-4.62176 + 4.31733i) q^{40} -4.49591 q^{41} +(2.92172 + 1.25720i) q^{42} +(-1.18585 + 1.18585i) q^{43} +(-3.06911 + 2.12555i) q^{44} +(-4.75436 + 1.82426i) q^{45} +(2.93110 + 1.53544i) q^{46} +(-4.50200 - 1.20631i) q^{47} +(1.97892 - 2.76516i) q^{48} +(4.37966 + 5.46064i) q^{49} +(-3.60622 + 6.08237i) q^{50} +(-2.30879 - 3.99894i) q^{51} +(-1.10627 - 3.08884i) q^{52} +(11.4262 - 3.06164i) q^{53} +(5.35960 - 3.39508i) q^{54} +(-2.62720 + 3.24339i) q^{55} +(6.70155 - 3.33005i) q^{56} +(-1.10101 - 1.10101i) q^{57} +(0.955162 - 4.25658i) q^{58} +(-7.77422 - 4.48845i) q^{59} +(1.25670 - 3.58797i) q^{60} +(-8.16355 + 4.71323i) q^{61} +(5.60425 - 6.08445i) q^{62} +(6.00785 - 0.458642i) q^{63} +(-1.95097 - 7.75846i) q^{64} +(-2.15572 - 2.96797i) q^{65} +(1.04132 - 1.98784i) q^{66} +(-3.25136 + 0.871200i) q^{67} +(-10.6889 - 1.94154i) q^{68} -1.98899 q^{69} +(6.14775 - 5.67496i) q^{70} -3.09202i q^{71} +(0.890052 - 6.37956i) q^{72} +(2.17707 + 8.12492i) q^{73} +(-6.48528 + 12.3802i) q^{74} +(0.223641 - 4.24453i) q^{75} +(-3.65097 + 0.300489i) q^{76} +(4.07664 - 2.78773i) q^{77} +(1.45062 + 1.33613i) q^{78} +(5.84357 + 10.1214i) q^{79} +(-4.52638 - 7.71439i) q^{80} +(1.50922 - 2.61405i) q^{81} +(1.39213 - 6.20389i) q^{82} +(4.95881 - 4.95881i) q^{83} +(-2.63950 + 3.64239i) q^{84} +(-12.0798 + 1.26792i) q^{85} +(-1.26916 - 2.00354i) q^{86} +(0.678689 + 2.53290i) q^{87} +(-1.98271 - 4.89322i) q^{88} +(-7.31128 + 4.22117i) q^{89} +(-1.04513 - 7.12540i) q^{90} +(1.43922 + 4.09476i) q^{91} +(-3.02634 + 3.56918i) q^{92} +(-1.28694 + 4.80294i) q^{93} +(3.05860 - 5.83877i) q^{94} +(-3.82388 + 1.46724i) q^{95} +(3.20288 + 3.58693i) q^{96} +(6.17682 + 6.17682i) q^{97} +(-8.89127 + 4.35263i) q^{98} -4.25101i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more