LMFDB - Embedded newform 529.2.c.o.399.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,2,Mod(118,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("529.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	529.c (of order $11$, degree $10$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	20.0.54296067514572573056640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 2 x^{18} - 3 x^{17} + 5 x^{16} - 8 x^{15} + 13 x^{14} - 21 x^{13} + 34 x^{12} + \cdots + 1 $ x^20 - x^19 + 2x^18 - 3x^17 + 5x^16 - 8x^15 + 13x^14 - 21x^13 + 34x^12 - 55x^11 + 89x^10 + 55x^9 + 34x^8 + 21x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			399.2
Root			$-1.36118 + 0.874775i$ of defining polynomial
Character	$\chi$	$=$	529.399
Dual form			529.2.c.o.118.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.230270 - 1.60156i) q^{2} +(0.928896 + 2.03400i) q^{3} +(-0.592999 - 0.174120i) q^{4} +(2.11917 + 2.44566i) q^{5} +(3.47148 - 1.01932i) q^{6} +(-1.03985 - 0.668269i) q^{7} +(0.928896 - 2.03400i) q^{8} +(-1.30972 + 1.51150i) q^{9} +O(q^{10})$	\(q+(0.230270 - 1.60156i) q^{2} +(0.928896 + 2.03400i) q^{3} +(-0.592999 - 0.174120i) q^{4} +(2.11917 + 2.44566i) q^{5} +(3.47148 - 1.01932i) q^{6} +(-1.03985 - 0.668269i) q^{7} +(0.928896 - 2.03400i) q^{8} +(-1.30972 + 1.51150i) q^{9} +(4.40486 - 2.83083i) q^{10} +(0.108719 + 0.756156i) q^{11} +(-0.196674 - 1.36790i) q^{12} +(2.52376 - 1.62192i) q^{13} +(-1.30972 + 1.51150i) q^{14} +(-3.00597 + 6.58216i) q^{15} +(-4.08353 - 2.62433i) q^{16} +(-5.02397 + 1.47517i) q^{17} +(2.11917 + 2.44566i) q^{18} +(1.91899 + 0.563465i) q^{19} +(-0.830830 - 1.81926i) q^{20} +(0.393349 - 2.73580i) q^{21} +1.23607 q^{22} +5.00000 q^{24} +(-0.778766 + 5.41644i) q^{25} +(-2.01647 - 4.41545i) q^{26} +(2.14549 + 0.629973i) q^{27} +(0.500269 + 0.577341i) q^{28} +(2.87848 - 0.845198i) q^{29} +(9.84957 + 6.32993i) q^{30} +(-2.78669 + 6.10200i) q^{31} +(-2.21472 + 2.55592i) q^{32} +(-1.43703 + 0.923525i) q^{33} +(1.20571 + 8.38590i) q^{34} +(-0.569259 - 3.95929i) q^{35} +(1.03985 - 0.668269i) q^{36} +(-2.11917 + 2.44566i) q^{37} +(1.34431 - 2.94363i) q^{38} +(5.64330 + 3.62673i) q^{39} +(6.94296 - 2.03864i) q^{40} +(-3.58349 - 4.13556i) q^{41} +(-4.29098 - 1.25995i) q^{42} +(0.0671920 - 0.467330i) q^{44} -6.47214 q^{45} +2.23607 q^{47} +(1.54470 - 10.7436i) q^{48} +(-2.27321 - 4.97763i) q^{49} +(8.49545 + 2.49449i) q^{50} +(-7.66724 - 8.84847i) q^{51} +(-1.77900 + 0.522361i) q^{52} +(-7.12721 - 4.58038i) q^{53} +(1.50299 - 3.29108i) q^{54} +(-1.61890 + 1.86832i) q^{55} +(-2.32517 + 1.49429i) q^{56} +(0.636451 + 4.42662i) q^{57} +(-0.690811 - 4.80469i) q^{58} +(-2.07969 + 1.33654i) q^{59} +(2.92863 - 3.37981i) q^{60} +(4.54641 - 9.95526i) q^{61} +(9.13105 + 5.86817i) q^{62} +(2.37200 - 0.696481i) q^{63} +(-2.77403 - 3.20141i) q^{64} +(9.31495 + 2.73512i) q^{65} +(1.14818 + 2.51416i) q^{66} +(1.02980 - 7.16242i) q^{67} +3.23607 q^{68} -6.47214 q^{70} +(-1.10492 + 7.68491i) q^{71} +(1.85779 + 4.06800i) q^{72} +(-14.8454 - 4.35900i) q^{73} +(3.42890 + 3.95716i) q^{74} +(-11.7404 + 3.44730i) q^{75} +(-1.03985 - 0.668269i) q^{76} +(0.392265 - 0.858940i) q^{77} +(7.10793 - 8.20298i) q^{78} +(5.84189 - 3.75436i) q^{79} +(-2.23551 - 15.5483i) q^{80} +(1.56546 + 10.8880i) q^{81} +(-7.44854 + 4.78689i) q^{82} +(8.66778 - 10.0032i) q^{83} +(-0.709614 + 1.55384i) q^{84} +(-14.2544 - 9.16077i) q^{85} +(4.39294 + 5.06972i) q^{87} +(1.63901 + 0.481257i) q^{88} +(-0.634698 - 1.38979i) q^{89} +(-1.49034 + 10.3655i) q^{90} -3.70820 q^{91} -15.0000 q^{93} +(0.514900 - 3.58121i) q^{94} +(2.68862 + 5.88726i) q^{95} +(-7.25598 - 2.13055i) q^{96} +(-2.81053 - 3.24352i) q^{97} +(-8.49545 + 2.49449i) q^{98} +(-1.28532 - 0.826026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q + q^2 + q^4 + 2 * q^5 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{11} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 10 q^{15} + 3 q^{16} - 6 q^{17} + 2 q^{18} + 4 q^{19} + 4 q^{20} + 10 q^{21} - 20 q^{22} + 100 q^{24} - 2 q^{25} + 3 q^{26} + 6 q^{28} + 6 q^{29} - 10 q^{30} - 9 q^{32} - 10 q^{33} + 8 q^{34} - 8 q^{35} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 10 q^{40} - 2 q^{41} - 8 q^{44} - 40 q^{45} + 15 q^{48} + 2 q^{49} + 11 q^{50} - 10 q^{51} + 3 q^{52} + 8 q^{53} - 5 q^{54} + 4 q^{55} + 10 q^{56} - 3 q^{58} - 4 q^{59} - 4 q^{61} - 15 q^{62} - 4 q^{63} - 4 q^{64} + 6 q^{65} - 10 q^{66} + 10 q^{67} + 20 q^{68} - 40 q^{70} - 20 q^{71} - 22 q^{73} + 6 q^{74} - 20 q^{75} - 2 q^{76} + 16 q^{77} + 15 q^{78} + 4 q^{79} - 18 q^{80} + 22 q^{81} + 11 q^{82} + 22 q^{83} - 10 q^{84} + 16 q^{85} - 10 q^{88} + 12 q^{89} - 12 q^{90} + 60 q^{91} - 300 q^{93} + 5 q^{94} - 4 q^{95} + 5 q^{96} - 22 q^{97} - 11 q^{98} + 12 q^{99}+O(q^{100}) $ 20 * q + q^2 + q^4 + 2 * q^5 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^11 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 10 * q^15 + 3 * q^16 - 6 * q^17 + 2 * q^18 + 4 * q^19 + 4 * q^20 + 10 * q^21 - 20 * q^22 + 100 * q^24 - 2 * q^25 + 3 * q^26 + 6 * q^28 + 6 * q^29 - 10 * q^30 - 9 * q^32 - 10 * q^33 + 8 * q^34 - 8 * q^35 + 2 * q^36 - 2 * q^37 - 2 * q^38 + 10 * q^40 - 2 * q^41 - 8 * q^44 - 40 * q^45 + 15 * q^48 + 2 * q^49 + 11 * q^50 - 10 * q^51 + 3 * q^52 + 8 * q^53 - 5 * q^54 + 4 * q^55 + 10 * q^56 - 3 * q^58 - 4 * q^59 - 4 * q^61 - 15 * q^62 - 4 * q^63 - 4 * q^64 + 6 * q^65 - 10 * q^66 + 10 * q^67 + 20 * q^68 - 40 * q^70 - 20 * q^71 - 22 * q^73 + 6 * q^74 - 20 * q^75 - 2 * q^76 + 16 * q^77 + 15 * q^78 + 4 * q^79 - 18 * q^80 + 22 * q^81 + 11 * q^82 + 22 * q^83 - 10 * q^84 + 16 * q^85 - 10 * q^88 + 12 * q^89 - 12 * q^90 + 60 * q^91 - 300 * q^93 + 5 * q^94 - 4 * q^95 + 5 * q^96 - 22 * q^97 - 11 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	0.230270	−	1.60156i	0.162826	−	1.13248i	−0.730449	−	0.682967i	$-0.760689\pi$
$2$	0.230270	−	1.60156i	0.162826	−	1.13248i	0.893275	−	0.449510i	$-0.148402\pi$
$3$	0.928896	+	2.03400i	0.536298	+	1.17433i	0.962892	+	0.269886i	$0.0869862\pi$
$3$	0.928896	+	2.03400i	0.536298	+	1.17433i	−0.426594	+	0.904443i	$0.640287\pi$
$4$	−0.592999	−	0.174120i	−0.296500	−	0.0870601i
$5$	2.11917	+	2.44566i	0.947723	+	1.09373i	0.995489	+	0.0948725i	$0.0302443\pi$
$5$	2.11917	+	2.44566i	0.947723	+	1.09373i	−0.0477661	+	0.998859i	$0.515210\pi$
$6$	3.47148	−	1.01932i	1.41723	−	0.416135i
$7$	−1.03985	−	0.668269i	−0.393025	−	0.252582i	0.329171	−	0.944270i	$-0.393231\pi$
$7$	−1.03985	−	0.668269i	−0.393025	−	0.252582i	−0.722196	+	0.691688i	$0.756867\pi$
$8$	0.928896	−	2.03400i	0.328414	−	0.719127i
$9$	−1.30972	+	1.51150i	−0.436574	+	0.503833i
$10$	4.40486	−	2.83083i	1.39294	−	0.895188i
$11$	0.108719	+	0.756156i	0.0327800	+	0.227990i	0.999625	−	0.0273730i	$-0.00871420\pi$
$11$	0.108719	+	0.756156i	0.0327800	+	0.227990i	−0.966845	+	0.255363i	$0.917805\pi$
$12$	−0.196674	−	1.36790i	−0.0567750	−	0.394879i
$13$	2.52376	−	1.62192i	0.699965	−	0.449840i	−0.141651	−	0.989917i	$-0.545241\pi$
$13$	2.52376	−	1.62192i	0.699965	−	0.449840i	0.841616	+	0.540076i	$0.181605\pi$
$14$	−1.30972	+	1.51150i	−0.350038	+	0.403965i
$15$	−3.00597	+	6.58216i	−0.776138	+	1.69951i
$16$	−4.08353	−	2.62433i	−1.02088	−	0.656081i
$17$	−5.02397	+	1.47517i	−1.21849	+	0.357781i	−0.826895	−	0.562356i	$-0.809895\pi$
$17$	−5.02397	+	1.47517i	−1.21849	+	0.357781i	−0.391596	+	0.920137i	$0.628077\pi$
$18$	2.11917	+	2.44566i	0.499494	+	0.576447i
$19$	1.91899	+	0.563465i	0.440246	+	0.129268i	0.494341	−	0.869268i	$-0.335409\pi$
$19$	1.91899	+	0.563465i	0.440246	+	0.129268i	−0.0540955	+	0.998536i	$0.517228\pi$
$20$	−0.830830	−	1.81926i	−0.185779	−	0.406800i
$21$	0.393349	−	2.73580i	0.0858357	−	0.597000i
$22$	1.23607			0.263531
$23$		0			0
$23$		0			0
$24$	5.00000			1.02062
$25$	−0.778766	+	5.41644i	−0.155753	+	1.08329i
$26$	−2.01647	−	4.41545i	−0.395462	−	0.865940i
$27$	2.14549	+	0.629973i	0.412900	+	0.121238i
$28$	0.500269	+	0.577341i	0.0945420	+	0.109107i
$29$	2.87848	−	0.845198i	0.534520	−	0.156949i	−0.00332258	−	0.999994i	$-0.501058\pi$
$29$	2.87848	−	0.845198i	0.534520	−	0.156949i	0.537843	+	0.843045i	$0.319239\pi$
$30$	9.84957	+	6.32993i	1.79828	+	1.15568i
$31$	−2.78669	+	6.10200i	−0.500504	+	1.09595i	0.475801	+	0.879553i	$0.342158\pi$
$31$	−2.78669	+	6.10200i	−0.500504	+	1.09595i	−0.976305	+	0.216398i	$0.930569\pi$
$32$	−2.21472	+	2.55592i	−0.391510	+	0.451827i
$33$	−1.43703	+	0.923525i	−0.250155	+	0.160765i
$34$	1.20571	+	8.38590i	0.206778	+	1.43817i
$35$	−0.569259	−	3.95929i	−0.0962224	−	0.669241i
$36$	1.03985	−	0.668269i	0.173308	−	0.111378i
$37$	−2.11917	+	2.44566i	−0.348390	+	0.402064i	−0.902717	−	0.430236i	$-0.858430\pi$
$37$	−2.11917	+	2.44566i	−0.348390	+	0.402064i	0.554327	+	0.832299i	$0.312976\pi$
$38$	1.34431	−	2.94363i	0.218076	−	0.477520i
$39$	5.64330	+	3.62673i	0.903651	+	0.580741i
$40$	6.94296	−	2.03864i	1.09778	−	0.322337i
$41$	−3.58349	−	4.13556i	−0.559647	−	0.645867i	0.403457	−	0.914999i	$-0.367809\pi$
$41$	−3.58349	−	4.13556i	−0.559647	−	0.645867i	−0.963103	+	0.269132i	$0.913263\pi$
$42$	−4.29098	−	1.25995i	−0.662113	−	0.194414i
$43$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$43$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$44$	0.0671920	−	0.467330i	0.0101296	−	0.0704527i
$45$	−6.47214			−0.964809
$46$		0			0
$47$	2.23607			0.326164			0.163082	−	0.986613i	$-0.447856\pi$
$47$	2.23607			0.326164			0.163082	+	0.986613i	$0.447856\pi$
$48$	1.54470	−	10.7436i	0.222958	−	1.55071i
$49$	−2.27321	−	4.97763i	−0.324744	−	0.711090i
$50$	8.49545	+	2.49449i	1.20144	+	0.352774i
$51$	−7.66724	−	8.84847i	−1.07363	−	1.23903i
$52$	−1.77900	+	0.522361i	−0.246703	+	0.0724384i
$53$	−7.12721	−	4.58038i	−0.978998	−	0.629164i	−0.0498052	−	0.998759i	$-0.515860\pi$
$53$	−7.12721	−	4.58038i	−0.978998	−	0.629164i	−0.929193	+	0.369595i	$0.879496\pi$
$54$	1.50299	−	3.29108i	0.204530	−	0.447859i
$55$	−1.61890	+	1.86832i	−0.218293	+	0.251924i
$56$	−2.32517	+	1.49429i	−0.310714	+	0.199683i
$57$	0.636451	+	4.42662i	0.0843000	+	0.586320i
$58$	−0.690811	−	4.80469i	−0.0907079	−	0.630887i
$59$	−2.07969	+	1.33654i	−0.270753	+	0.174002i	−0.668971	−	0.743288i	$-0.733265\pi$
$59$	−2.07969	+	1.33654i	−0.270753	+	0.174002i	0.398218	+	0.917291i	$0.369629\pi$
$60$	2.92863	−	3.37981i	0.378084	−	0.436332i
$61$	4.54641	−	9.95526i	0.582109	−	1.27464i	−0.357986	−	0.933727i	$-0.616536\pi$
$61$	4.54641	−	9.95526i	0.582109	−	1.27464i	0.940095	−	0.340913i	$-0.110736\pi$
$62$	9.13105	+	5.86817i	1.15964	+	0.745258i
$63$	2.37200	−	0.696481i	0.298844	−	0.0877484i
$64$	−2.77403	−	3.20141i	−0.346754	−	0.400176i
$65$	9.31495	+	2.73512i	1.15538	+	0.339250i
$66$	1.14818	+	2.51416i	0.141331	+	0.309472i
$67$	1.02980	−	7.16242i	0.125810	−	0.875028i	−0.824973	−	0.565172i	$-0.808810\pi$
$67$	1.02980	−	7.16242i	0.125810	−	0.875028i	0.950783	−	0.309857i	$-0.100281\pi$
$68$	3.23607			0.392431
$69$		0			0
$70$	−6.47214			−0.773568
$71$	−1.10492	+	7.68491i	−0.131130	+	0.912031i	0.812954	+	0.582327i	$0.197858\pi$
$71$	−1.10492	+	7.68491i	−0.131130	+	0.912031i	−0.944085	+	0.329703i	$0.893051\pi$
$72$	1.85779	+	4.06800i	0.218943	+	0.479418i
$73$	−14.8454	−	4.35900i	−1.73752	−	0.510183i	−0.749172	−	0.662375i	$-0.769549\pi$
$73$	−14.8454	−	4.35900i	−1.73752	−	0.510183i	−0.988351	+	0.152192i	$0.951367\pi$
$74$	3.42890	+	3.95716i	0.398601	+	0.460010i
$75$	−11.7404	+	3.44730i	−1.35567	+	0.398060i
$76$	−1.03985	−	0.668269i	−0.119279	−	0.0766557i
$77$	0.392265	−	0.858940i	0.0447027	−	0.0978853i
$78$	7.10793	−	8.20298i	0.804814	−	0.928805i
$79$	5.84189	−	3.75436i	0.657264	−	0.422398i	−0.169050	−	0.985607i	$-0.554070\pi$
$79$	5.84189	−	3.75436i	0.657264	−	0.422398i	0.826314	+	0.563209i	$0.190434\pi$
$80$	−2.23551	−	15.5483i	−0.249938	−	1.73835i
$81$	1.56546	+	10.8880i	0.173940	+	1.20978i
$82$	−7.44854	+	4.78689i	−0.822554	+	0.528623i
$83$	8.66778	−	10.0032i	0.951413	−	1.09799i	−0.0436805	−	0.999046i	$-0.513908\pi$
$83$	8.66778	−	10.0032i	0.951413	−	1.09799i	0.995093	−	0.0989431i	$-0.0315462\pi$
$84$	−0.709614	+	1.55384i	−0.0774252	+	0.169538i
$85$	−14.2544	−	9.16077i	−1.54611	−	0.993624i
$86$		0			0
$87$	4.39294	+	5.06972i	0.470973	+	0.543531i
$88$	1.63901	+	0.481257i	0.174719	+	0.0513021i
$89$	−0.634698	−	1.38979i	−0.0672778	−	0.147318i	0.873006	−	0.487710i	$-0.162168\pi$
$89$	−0.634698	−	1.38979i	−0.0672778	−	0.147318i	−0.940284	+	0.340392i	$0.889440\pi$
$90$	−1.49034	+	10.3655i	−0.157096	+	1.09262i
$91$	−3.70820			−0.388725
$92$		0			0
$93$	−15.0000			−1.55543
$94$	0.514900	−	3.58121i	0.0531079	−	0.369373i
$95$	2.68862	+	5.88726i	0.275847	+	0.604020i
$96$	−7.25598	−	2.13055i	−0.740560	−	0.217448i
$97$	−2.81053	−	3.24352i	−0.285366	−	0.329330i	0.594910	−	0.803793i	$-0.297188\pi$
$97$	−2.81053	−	3.24352i	−0.285366	−	0.329330i	−0.880276	+	0.474463i	$0.842642\pi$
$98$	−8.49545	+	2.49449i	−0.858170	+	0.251981i
$99$	−1.28532	−	0.826026i	−0.129180	−	0.0830187i
$100$	1.40492	−	3.07634i	0.140492	−	0.307634i
$101$	2.92863	−	3.37981i	0.291409	−	0.336304i	−0.591101	−	0.806598i	$-0.701306\pi$
$101$	2.92863	−	3.37981i	0.291409	−	0.336304i	0.882510	+	0.470294i	$0.155852\pi$
$102$	−15.9369	+	10.2420i	−1.57799	+	1.01411i
$103$	−2.58733	−	17.9953i	−0.254937	−	1.77313i	−0.567639	−	0.823277i	$-0.692143\pi$
$103$	−2.58733	−	17.9953i	−0.254937	−	1.77313i	0.312702	−	0.949851i	$-0.398766\pi$
$104$	−0.954677	−	6.63992i	−0.0936138	−	0.651098i
$105$	7.52440	−	4.83564i	0.734306	−	0.471910i
$106$	−8.97696	+	10.3600i	−0.871920	+	1.00625i
$107$	−5.57338	+	12.2040i	−0.538799	+	1.17980i	0.423021	+	0.906120i	$0.360970\pi$
$107$	−5.57338	+	12.2040i	−0.538799	+	1.17980i	−0.961819	+	0.273685i	$0.911758\pi$
$108$	−1.16258	−	0.747147i	−0.111870	−	0.0718943i
$109$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$109$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$110$	2.61944	+	3.02300i	0.249754	+	0.288232i
$111$	−6.94296	−	2.03864i	−0.658996	−	0.193499i
$112$	2.49249	+	5.45779i	0.235518	+	0.515713i
$113$	−1.88369	+	13.1013i	−0.177203	+	1.23247i	0.685996	+	0.727606i	$0.259367\pi$
$113$	−1.88369	+	13.1013i	−0.177203	+	1.23247i	−0.863198	+	0.504865i	$0.831542\pi$
$114$	7.23607			0.677720
$115$		0			0
$116$	−1.85410			−0.172149
$117$	−0.853889	+	5.93893i	−0.0789421	+	0.549054i
$118$	1.66166	+	3.63853i	0.152968	+	0.334954i
$119$	6.20997	+	1.82341i	0.569267	+	0.167152i
$120$	10.5959	+	12.2283i	0.967266	+	1.11628i
$121$	9.99447	−	2.93464i	0.908588	−	0.266786i
$122$	−14.8971	−	9.57378i	−1.34872	−	0.866769i
$123$	5.08305	−	11.1303i	0.458323	−	1.00359i
$124$	2.71499	−	3.13326i	0.243813	−	0.281375i
$125$	−1.28532	+	0.826026i	−0.114963	+	0.0738820i
$126$	−0.569259	−	3.95929i	−0.0507137	−	0.352721i
$127$	2.94708	+	20.4974i	0.261511	+	1.81885i	0.521512	+	0.853244i	$0.325368\pi$
$127$	2.94708	+	20.4974i	0.261511	+	1.81885i	−0.260001	+	0.965608i	$0.583723\pi$
$128$	−11.4562	+	7.36247i	−1.01260	+	0.650756i
$129$		0			0
$130$	6.52542	−	14.2887i	0.572318	−	1.25320i
$131$	4.45174	+	2.86096i	0.388951	+	0.249963i	0.720472	−	0.693485i	$-0.243925\pi$
$131$	4.45174	+	2.86096i	0.388951	+	0.249963i	−0.331521	+	0.943448i	$0.607562\pi$
$132$	1.01296	−	0.297433i	0.0881672	−	0.0258882i
$133$	−1.61890	−	1.86832i	−0.140377	−	0.162004i
$134$	−11.2339	−	3.29858i	−0.970465	−	0.284954i
$135$	3.00597	+	6.58216i	0.258713	+	0.566502i
$136$	−1.66625	+	11.5890i	−0.142880	+	0.993751i
$137$	13.8885			1.18658			0.593289	−	0.804989i	$-0.297829\pi$
$137$	13.8885			1.18658			0.593289	+	0.804989i	$0.297829\pi$
$138$		0			0
$139$	2.70820			0.229707			0.114853	−	0.993382i	$-0.463360\pi$
$139$	2.70820			0.229707			0.114853	+	0.993382i	$0.463360\pi$
$140$	−0.351822	+	2.44697i	−0.0297344	+	0.206807i
$141$	2.07708	+	4.54816i	0.174921	+	0.383024i
$142$	12.0534	+	3.53921i	1.01150	+	0.297004i
$143$	1.50081	+	1.73202i	0.125504	+	0.144839i
$144$	9.31495	−	2.73512i	0.776246	−	0.227926i
$145$	8.16706	+	5.24865i	0.678237	+	0.435877i
$146$	−10.3997	+	22.7721i	−0.860684	+	1.88463i
$147$	8.01292	−	9.24740i	0.660895	−	0.762713i
$148$	1.68251	−	1.08128i	0.138301	−	0.0888808i
$149$	1.69192	+	11.7675i	0.138607	+	0.964034i	0.933830	+	0.357717i	$0.116445\pi$
$149$	1.69192	+	11.7675i	0.138607	+	0.964034i	−0.795223	+	0.606317i	$0.792646\pi$
$150$	2.81760	+	19.5969i	0.230056	+	1.60008i
$151$	−0.198593	+	0.127628i	−0.0161613	+	0.0103862i	−0.548697	−	0.836022i	$-0.684876\pi$
$151$	−0.198593	+	0.127628i	−0.0161613	+	0.0103862i	0.532535	+	0.846408i	$0.321239\pi$
$152$	2.92863	−	3.37981i	0.237543	−	0.274139i
$153$	4.35028	−	9.52579i	0.351699	−	0.770114i
$154$	−1.28532	−	0.826026i	−0.103574	−	0.0665630i
$155$	−20.8289	+	6.11591i	−1.67302	+	0.491242i
$156$	−2.71499	−	3.13326i	−0.217373	−	0.250862i
$157$	−14.7919	−	4.34330i	−1.18052	−	0.346633i	−0.368149	−	0.929767i	$-0.620008\pi$
$157$	−14.7919	−	4.34330i	−1.18052	−	0.346633i	−0.812376	+	0.583134i	$0.801826\pi$
$158$	−4.66763	−	10.2207i	−0.371337	−	0.813114i
$159$	2.69605	−	18.7514i	0.213811	−	1.48709i
$160$	−10.9443			−0.865221
$161$		0			0
$162$	17.7984			1.39837
$163$	1.45674	−	10.1319i	0.114101	−	0.793590i	−0.849757	−	0.527174i	$-0.823251\pi$
$163$	1.45674	−	10.1319i	0.114101	−	0.793590i	0.963858	−	0.266416i	$-0.0858394\pi$
$164$	1.40492	+	3.07634i	0.109706	+	0.240222i
$165$	−5.30395	−	1.55738i	−0.412912	−	0.121242i
$166$	−14.0248	−	16.1854i	−1.08853	−	1.25623i
$167$	−10.0479	+	2.95034i	−0.777533	+	0.228304i	−0.646337	−	0.763052i	$-0.723700\pi$
$167$	−10.0479	+	2.95034i	−0.777533	+	0.228304i	−0.131196	+	0.991356i	$0.541882\pi$
$168$	−5.19923	−	3.34134i	−0.401130	−	0.257790i
$169$	−1.66166	+	3.63853i	−0.127820	+	0.279887i
$170$	−17.9539	+	20.7199i	−1.37700	+	1.58915i
$171$	−3.36501	+	2.16256i	−0.257329	+	0.165375i
$172$		0			0
$173$	−0.719505	−	5.00427i	−0.0547030	−	0.380467i	−0.998720	−	0.0505720i	$-0.983896\pi$
$173$	−0.719505	−	5.00427i	−0.0547030	−	0.380467i	0.944017	−	0.329895i	$-0.107014\pi$
$174$	9.13105	−	5.86817i	0.692223	−	0.444865i
$175$	4.42943	−	5.11184i	0.334834	−	0.386419i
$176$	1.54044	−	3.37310i	0.116115	−	0.254257i
$177$	−4.65034	−	2.98859i	−0.349541	−	0.224636i
$178$	−2.37200	+	0.696481i	−0.177789	+	0.0522035i
$179$	8.32210	+	9.60422i	0.622023	+	0.717853i	0.976090	−	0.217367i	$-0.0697469\pi$
$179$	8.32210	+	9.60422i	0.622023	+	0.717853i	−0.354067	+	0.935220i	$0.615201\pi$
$180$	3.83797	+	1.12693i	0.286066	+	0.0839964i
$181$	−6.08686	−	13.3284i	−0.452433	−	0.990689i	−0.989148	−	0.146926i	$-0.953062\pi$
$181$	−6.08686	−	13.3284i	−0.452433	−	0.990689i	0.536715	−	0.843764i	$-0.319665\pi$
$182$	−0.853889	+	5.93893i	−0.0632945	+	0.440223i
$183$	24.4721			1.80903
$184$		0			0
$185$	−10.4721			−0.769927
$186$	−3.45405	+	24.0235i	−0.253264	+	1.76149i
$187$	−1.66166	−	3.63853i	−0.121513	−	0.266076i
$188$	−1.32599	−	0.389345i	−0.0967075	−	0.0283959i
$189$	−1.80999	−	2.08884i	−0.131657	−	0.151941i
$190$	10.0479	−	2.95034i	0.728954	−	0.214040i
$191$	−3.21330	−	2.06506i	−0.232506	−	0.149423i	0.419201	−	0.907894i	$-0.362310\pi$
$191$	−3.21330	−	2.06506i	−0.232506	−	0.149423i	−0.651707	+	0.758471i	$0.725947\pi$
$192$	3.93487	−	8.61616i	0.283975	−	0.621818i
$193$	5.20239	−	6.00388i	0.374476	−	0.432169i	−0.536961	−	0.843607i	$-0.680428\pi$
$193$	5.20239	−	6.00388i	0.374476	−	0.432169i	0.911438	+	0.411438i	$0.134973\pi$
$194$	−5.84189	+	3.75436i	−0.419423	+	0.269547i
$195$	3.08940	+	21.4872i	0.221236	+	1.53873i
$196$	0.481304	+	3.34754i	0.0343789	+	0.239110i
$197$	6.28596	−	4.03974i	0.447856	−	0.287820i	−0.297208	−	0.954813i	$-0.596055\pi$
$197$	6.28596	−	4.03974i	0.447856	−	0.287820i	0.745064	+	0.666993i	$0.232419\pi$
$198$	−1.61890	+	1.86832i	−0.115051	+	0.132775i
$199$	−10.6796	+	23.3850i	−0.757055	+	1.65772i	−0.00379787	+	0.999993i	$0.501209\pi$
$199$	−10.6796	+	23.3850i	−0.757055	+	1.65772i	−0.753257	+	0.657726i	$0.771518\pi$
$200$	10.2936	+	6.61532i	0.727870	+	0.467774i
$201$	15.5249	−	4.55853i	1.09504	−	0.321534i
$202$	−4.73862	−	5.46866i	−0.333408	−	0.384773i
$203$	−3.55800	−	1.04472i	−0.249722	−	0.0733251i
$204$	3.00597	+	6.58216i	0.210460	+	0.460843i
$205$	2.52014	−	17.5280i	0.176014	−	1.22421i
$206$	−29.4164			−2.04954
$207$		0			0
$208$	−14.5623			−1.00971
$209$	−0.217438	+	1.51231i	−0.0150405	+	0.104609i
$210$	−6.01194	−	13.1643i	−0.414863	−	0.908424i
$211$	−3.27802	−	0.962513i	−0.225668	−	0.0662621i	0.166944	−	0.985966i	$-0.446610\pi$
$211$	−3.27802	−	0.962513i	−0.225668	−	0.0662621i	−0.392612	+	0.919704i	$0.628428\pi$
$212$	3.42890	+	3.95716i	0.235497	+	0.271779i
$213$	−16.6575	+	4.89107i	−1.14135	+	0.335131i
$214$	18.2621	+	11.7363i	1.24837	+	0.802280i
$215$		0			0
$216$	3.27430	−	3.77875i	0.222788	−	0.257111i
$217$	6.97550	−	4.48288i	0.473528	−	0.304318i
$218$		0			0
$219$	−4.92363	−	34.2446i	−0.332708	−	2.31404i
$220$	1.28532	−	0.826026i	0.0866563	−	0.0556906i
$221$	−10.2867	+	11.8715i	−0.691957	+	0.798561i
$222$	−4.86376	+	10.6502i	−0.326434	+	0.714792i
$223$	3.36501	+	2.16256i	0.225338	+	0.144816i	0.648439	−	0.761267i	$-0.275422\pi$
$223$	3.36501	+	2.16256i	0.225338	+	0.144816i	−0.423101	+	0.906082i	$0.639058\pi$
$224$	4.01101	−	1.17774i	0.267997	−	0.0786909i
$225$	−7.16697	−	8.27113i	−0.477798	−	0.551409i
$226$	20.5489	+	6.03370i	1.36689	+	0.401356i
$227$	4.22907	+	9.26036i	0.280693	+	0.614632i	0.996493	−	0.0836732i	$-0.0266652\pi$
$227$	4.22907	+	9.26036i	0.280693	+	0.614632i	−0.715800	+	0.698305i	$0.753938\pi$
$228$	0.393349	−	2.73580i	0.0260501	−	0.181183i
$229$	−12.0000			−0.792982			−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000			−0.792982			−0.396491	+	0.918039i	$0.629772\pi$
$230$		0			0
$231$	2.11146			0.138924
$232$	0.954677	−	6.63992i	0.0626776	−	0.435932i
$233$	−6.42736	−	14.0739i	−0.421070	−	0.922015i	−0.994692	−	0.102895i	$-0.967189\pi$
$233$	−6.42736	−	14.0739i	−0.421070	−	0.922015i	0.573622	−	0.819120i	$-0.305538\pi$
$234$	9.31495	+	2.73512i	0.608938	+	0.178800i
$235$	4.73862	+	5.46866i	0.309113	+	0.356736i
$236$	1.46597	−	0.430449i	0.0954268	−	0.0280198i
$237$	13.0629	+	8.39500i	0.848525	+	0.545314i
$238$	4.35028	−	9.52579i	0.281987	−	0.617465i
$239$	−11.9421	+	13.7819i	−0.772469	+	0.891477i	−0.996542	−	0.0830955i	$-0.973519\pi$
$239$	−11.9421	+	13.7819i	−0.772469	+	0.891477i	0.224072	+	0.974573i	$0.428065\pi$
$240$	29.5487	−	18.9898i	1.90736	−	1.22579i
$241$	−2.43709	−	16.9503i	−0.156987	−	1.09187i	−0.904147	−	0.427222i	$-0.859492\pi$
$241$	−2.43709	−	16.9503i	−0.156987	−	1.09187i	0.747160	−	0.664644i	$-0.231417\pi$
$242$	−2.39859	−	16.6826i	−0.154187	−	1.07240i
$243$	−15.0488	+	9.67128i	−0.965381	+	0.620413i
$244$	−4.42943	+	5.11184i	−0.283565	+	0.327252i
$245$	7.35625	−	16.1079i	0.469974	−	1.02910i
$246$	−16.6555	−	10.7038i	−1.06191	−	0.682450i
$247$	5.75696	−	1.69040i	0.366306	−	0.107557i
$248$	9.82291	+	11.3362i	0.623755	+	0.719852i
$249$	28.3979	+	8.33837i	1.79964	+	0.528423i
$250$	1.02696	+	2.24873i	0.0649508	+	0.142222i
$251$	−2.23551	+	15.5483i	−0.141104	+	0.981401i	0.789075	+	0.614296i	$0.210560\pi$
$251$	−2.23551	+	15.5483i	−0.141104	+	0.981401i	−0.930180	+	0.367105i	$0.880349\pi$
$252$	−1.52786			−0.0962464
$253$		0			0
$254$	33.5066			2.10239
$255$	5.39210	−	37.5029i	0.337667	−	2.34852i
$256$	5.63399	+	12.3367i	0.352124	+	0.771044i
$257$	−1.41250	−	0.414749i	−0.0881096	−	0.0258713i	0.237381	−	0.971417i	$-0.423711\pi$
$257$	−1.41250	−	0.414749i	−0.0881096	−	0.0258713i	−0.325490	+	0.945545i	$0.605529\pi$
$258$		0			0
$259$	3.83797	−	1.12693i	0.238480	−	0.0700240i
$260$	−5.04752	−	3.24384i	−0.313034	−	0.201175i
$261$	−2.49249	+	5.45779i	−0.154281	+	0.337829i
$262$	5.60712	−	6.47096i	0.346409	−	0.399777i
$263$	−12.5719	+	8.07948i	−0.775218	+	0.498202i	−0.867443	−	0.497536i	$-0.834238\pi$
$263$	−12.5719	+	8.07948i	−0.775218	+	0.498202i	0.0922255	+	0.995738i	$0.470602\pi$
$264$	0.543594	+	3.78078i	0.0334559	+	0.232691i
$265$	−3.90176	−	27.1373i	−0.239683	−	1.66703i
$266$	−3.36501	+	2.16256i	−0.206322	+	0.132595i
$267$	2.23727	−	2.58195i	0.136919	−	0.158013i
$268$	−1.85779	+	4.06800i	−0.113483	+	0.248493i
$269$	8.36565	+	5.37628i	0.510063	+	0.327798i	0.770230	−	0.637766i	$-0.220141\pi$
$269$	8.36565	+	5.37628i	0.510063	+	0.327798i	−0.260167	+	0.965564i	$0.583778\pi$
$270$	11.2339	−	3.29858i	0.683676	−	0.200745i
$271$	−5.23889	−	6.04600i	−0.318240	−	0.367268i	0.573980	−	0.818869i	$-0.305399\pi$
$271$	−5.23889	−	6.04600i	−0.318240	−	0.367268i	−0.892220	+	0.451601i	$0.850853\pi$
$272$	24.3869	+	7.16063i	1.47867	+	0.434177i
$273$	−3.44454	−	7.54248i	−0.208473	−	0.456492i
$274$	3.19812	−	22.2434i	0.193205	−	1.34377i
$275$	−4.18034			−0.252084
$276$		0			0
$277$	6.52786			0.392221			0.196111	−	0.980582i	$-0.437169\pi$
$277$	6.52786			0.392221			0.196111	+	0.980582i	$0.437169\pi$
$278$	0.623619	−	4.33736i	0.0374022	−	0.260138i
$279$	−5.57338	−	12.2040i	−0.333669	−	0.730634i
$280$	−8.58197	−	2.51989i	−0.512871	−	0.150592i
$281$	8.66778	+	10.0032i	0.517076	+	0.596738i	0.952896	−	0.303296i	$-0.0980870\pi$
$281$	8.66778	+	10.0032i	0.517076	+	0.596738i	−0.435820	+	0.900034i	$0.643542\pi$
$282$	7.76246	−	2.27926i	0.462248	−	0.135728i
$283$	12.0230	+	7.72673i	0.714695	+	0.459306i	0.846788	−	0.531931i	$-0.178533\pi$
$283$	12.0230	+	7.72673i	0.714695	+	0.459306i	−0.132093	+	0.991237i	$0.542170\pi$
$284$	1.99332	−	4.36475i	0.118282	−	0.259001i
$285$	−9.47723	+	10.9373i	−0.561383	+	0.647870i
$286$	3.11954	−	2.00481i	0.184462	−	0.118547i
$287$	0.962608	+	6.69508i	0.0568209	+	0.395198i
$288$	−0.962608	−	6.69508i	−0.0567222	−	0.394512i
$289$	8.76284	−	5.63154i	0.515461	−	0.331267i
$290$	10.2867	−	11.8715i	0.604055	−	0.697117i
$291$	3.98663	−	8.72951i	0.233701	−	0.511733i
$292$	8.04432	+	5.16977i	0.470758	+	0.302538i
$293$	10.0479	−	2.95034i	0.587007	−	0.172361i	0.0252756	−	0.999681i	$-0.491954\pi$
$293$	10.0479	−	2.95034i	0.587007	−	0.172361i	0.561731	+	0.827320i	$0.310135\pi$
$294$	−12.9652	−	14.9626i	−0.756145	−	0.872637i
$295$	−7.67594	−	2.25386i	−0.446911	−	0.131225i
$296$	3.00597	+	6.58216i	0.174719	+	0.382580i
$297$	−0.243103	+	1.69082i	−0.0141063	+	0.0981111i
$298$	19.2361			1.11432
$299$		0			0
$300$	7.56231			0.436610
$301$		0			0
$302$	0.158674	+	0.347449i	0.00913069	+	0.0199934i
$303$	9.59493	+	2.81733i	0.551214	+	0.161851i
$304$	−6.35752	−	7.33697i	−0.364629	−	0.420804i
$305$	33.9818	−	9.97796i	1.94579	−	0.571336i
$306$	−14.2544	−	9.16077i	−0.814871	−	0.523686i
$307$	7.67360	−	16.8028i	0.437956	−	0.958989i	−0.554013	−	0.832508i	$-0.686904\pi$
$307$	7.67360	−	16.8028i	0.437956	−	0.958989i	0.991969	−	0.126481i	$-0.0403684\pi$
$308$	−0.382172	+	0.441050i	−0.0217762	+	0.0251311i
$309$	34.1990	−	21.9784i	1.94552	−	1.25031i
$310$	4.99875	+	34.7671i	0.283910	+	1.97464i
$311$	1.30650	+	9.08690i	0.0740847	+	0.515271i	0.992747	+	0.120226i	$0.0383619\pi$
$311$	1.30650	+	9.08690i	0.0740847	+	0.515271i	−0.918662	+	0.395045i	$0.870729\pi$
$312$	12.6188	−	8.10961i	0.714399	−	0.459116i
$313$	13.3334	−	15.3876i	0.753649	−	0.869757i	−0.241268	−	0.970459i	$-0.577563\pi$
$313$	13.3334	−	15.3876i	0.753649	−	0.869757i	0.994917	+	0.100701i	$0.0321087\pi$
$314$	−10.3622	+	22.6901i	−0.584774	+	1.28048i
$315$	6.73003	+	4.32513i	0.379194	+	0.243693i
$316$	−4.11795	+	1.20914i	−0.231653	+	0.0680194i
$317$	0.927550	+	1.07045i	0.0520964	+	0.0601224i	0.781200	−	0.624281i	$-0.214608\pi$
$317$	0.927550	+	1.07045i	0.0520964	+	0.0601224i	−0.729103	+	0.684404i	$0.760063\pi$
$318$	−29.4108	−	8.63580i	−1.64928	−	0.484272i
$319$	0.952046	+	2.08469i	0.0533044	+	0.116720i
$320$	1.95088	−	13.5687i	0.109058	−	0.758512i
$321$	−30.0000			−1.67444
$322$		0			0
$323$	−10.4721			−0.582685
$324$	0.967509	−	6.72918i	0.0537505	−	0.373843i
$325$	6.81962	+	14.9329i	0.378285	+	0.828328i
$326$	−15.8914	−	4.66614i	−0.880144	−	0.258434i
$327$		0			0
$328$	−11.7404	+	3.44730i	−0.648256	+	0.190345i
$329$	−2.32517	−	1.49429i	−0.128191	−	0.0823831i
$330$	−3.71558	+	8.13600i	−0.204536	+	0.447872i
$331$	−7.63075	+	8.80635i	−0.419424	+	0.484041i	−0.925661	−	0.378353i	$-0.876490\pi$
$331$	−7.63075	+	8.80635i	−0.419424	+	0.484041i	0.506237	+	0.862394i	$0.331036\pi$
$332$	−6.88174	+	4.42263i	−0.377685	+	0.242723i
$333$	−0.921081	−	6.40626i	−0.0504749	−	0.351061i
$334$	2.41142	+	16.7718i	0.131947	+	0.917712i
$335$	19.6991	−	12.6599i	1.07628	−	0.691682i
$336$	−8.78588	+	10.1394i	−0.479309	+	0.553152i
$337$	−1.41923	+	3.10767i	−0.0773102	+	0.169286i	−0.944340	−	0.328970i	$-0.893299\pi$
$337$	−1.41923	+	3.10767i	−0.0773102	+	0.169286i	0.867030	+	0.498256i	$0.166026\pi$
$338$	5.44471	+	3.49910i	0.296153	+	0.190326i
$339$	−28.3979	+	8.33837i	−1.54236	+	0.452878i
$340$	6.85779	+	7.91431i	0.371916	+	0.429214i
$341$	−4.91703	−	1.44377i	−0.266272	−	0.0781845i
$342$	2.68862	+	5.88726i	0.145384	+	0.318347i
$343$	−2.19398	+	15.2595i	−0.118464	+	0.823935i
$344$		0			0
$345$		0			0
$346$	−8.18034			−0.439778
$347$	−3.68432	+	25.6250i	−0.197785	+	1.37562i	0.612909	+	0.790154i	$0.289999\pi$
$347$	−3.68432	+	25.6250i	−0.197785	+	1.37562i	−0.810694	+	0.585470i	$0.800910\pi$
$348$	−1.72227	−	3.77124i	−0.0923233	−	0.202160i
$349$	2.31853	+	0.680781i	0.124108	+	0.0364414i	0.343197	−	0.939264i	$-0.388490\pi$
$349$	2.31853	+	0.680781i	0.124108	+	0.0364414i	−0.219089	+	0.975705i	$0.570308\pi$
$350$	−7.16697	−	8.27113i	−0.383091	−	0.442110i
$351$	6.43647	−	1.88992i	0.343554	−	0.100876i
$352$	−2.17346	−	1.39680i	−0.115846	−	0.0744494i
$353$	−14.6894	+	32.1652i	−0.781836	+	1.71198i	−0.0831671	+	0.996536i	$0.526504\pi$
$353$	−14.6894	+	32.1652i	−0.781836	+	1.71198i	−0.698669	+	0.715446i	$0.746224\pi$
$354$	−5.85725	+	6.75963i	−0.311309	+	0.359270i
$355$	−21.1362	+	13.5834i	−1.12179	+	0.720932i
$356$	0.134384	+	0.934661i	0.00712233	+	0.0495369i
$357$	2.05960	+	14.3248i	0.109006	+	0.758150i
$358$	17.2981	−	11.1168i	0.914234	−	0.587542i
$359$	−10.4048	+	12.0078i	−0.549143	+	0.633745i	−0.960683	−	0.277646i	$-0.910446\pi$
$359$	−10.4048	+	12.0078i	−0.549143	+	0.633745i	0.411540	+	0.911392i	$0.364991\pi$
$360$	−6.01194	+	13.1643i	−0.316857	+	0.693820i
$361$	−12.6188	−	8.10961i	−0.664148	−	0.426822i
$362$	−22.7479	+	6.67937i	−1.19560	+	0.351060i
$363$	15.2529	+	17.6028i	0.800569	+	0.923906i
$364$	2.19896	+	0.645674i	0.115257	+	0.0338425i
$365$	−20.7994	−	45.5443i	−1.08869	−	2.38390i
$366$	5.63520	−	39.1937i	0.294557	−	2.04869i
$367$	18.1803			0.949006			0.474503	−	0.880254i	$-0.342628\pi$
$367$	18.1803			0.949006			0.474503	+	0.880254i	$0.342628\pi$
$368$		0			0
$369$	10.9443			0.569736
$370$	−2.41142	+	16.7718i	−0.125364	+	0.871925i
$371$	4.35028	+	9.52579i	0.225855	+	0.494554i
$372$	8.89499	+	2.61180i	0.461184	+	0.135416i
$373$	3.73808	+	4.31397i	0.193550	+	0.223369i	0.844227	−	0.535986i	$-0.180060\pi$
$373$	3.73808	+	4.31397i	0.193550	+	0.223369i	−0.650676	+	0.759355i	$0.725515\pi$
$374$	−6.20997	+	1.82341i	−0.321110	+	0.0942864i
$375$	−2.87407	−	1.84705i	−0.148416	−	0.0953812i
$376$	2.07708	−	4.54816i	0.107117	−	0.234553i
$377$	5.89375	−	6.80175i	0.303543	−	0.350308i
$378$	−3.76220	+	2.41782i	−0.193507	+	0.124359i
$379$	2.89763	+	20.1534i	0.148841	+	1.03521i	0.918121	+	0.396300i	$0.129706\pi$
$379$	2.89763	+	20.1534i	0.148841	+	1.03521i	−0.769280	+	0.638912i	$0.779385\pi$
$380$	−0.569259	−	3.95929i	−0.0292024	−	0.203107i
$381$	−38.9542	+	25.0343i	−1.99568	+	1.28255i
$382$	−4.04726	+	4.67079i	−0.207076	+	0.238978i
$383$	10.3622	−	22.6901i	0.529485	−	1.15941i	−0.436237	−	0.899832i	$-0.643689\pi$
$383$	10.3622	−	22.6901i	0.529485	−	1.15941i	0.965722	−	0.259579i	$-0.0835836\pi$
$384$	−25.6169	−	16.4630i	−1.30726	−	0.840123i
$385$	2.93195	−	0.860898i	0.149426	−	0.0438754i
$386$	−8.41765	−	9.71448i	−0.428447	−	0.494454i
$387$		0			0
$388$	1.10188	+	2.41278i	0.0559394	+	0.122490i
$389$	−4.90590	+	34.1213i	−0.248739	+	1.73002i	0.356783	+	0.934187i	$0.383874\pi$
$389$	−4.90590	+	34.1213i	−0.248739	+	1.73002i	−0.605521	+	0.795829i	$0.707035\pi$
$390$	35.1246			1.77860
$391$		0			0
$392$	−12.2361			−0.618015
$393$	−1.68399	+	11.7124i	−0.0849458	+	0.590811i
$394$	−5.02244	−	10.9976i	−0.253027	−	0.554051i
$395$	21.5619	+	6.33113i	1.08489	+	0.318554i
$396$	0.618367	+	0.713633i	0.0310741	+	0.0358614i
$397$	−2.31853	+	0.680781i	−0.116364	+	0.0341674i	−0.339396	−	0.940644i	$-0.610223\pi$
$397$	−2.31853	+	0.680781i	−0.116364	+	0.0341674i	0.223032	+	0.974811i	$0.428404\pi$
$398$	34.9934	+	22.4889i	1.75406	+	1.12727i
$399$	2.29636	−	5.02832i	0.114962	−	0.251731i
$400$	17.3946	−	20.0745i	0.869731	−	1.00372i
$401$	6.88174	−	4.42263i	0.343658	−	0.220855i	−0.357414	−	0.933946i	$-0.616342\pi$
$401$	6.88174	−	4.42263i	0.343658	−	0.220855i	0.701072	+	0.713091i	$0.252705\pi$
$402$	−3.72585	−	25.9139i	−0.185829	−	1.29247i
$403$	2.86403	+	19.9198i	0.142668	+	0.992275i
$404$	−2.32517	+	1.49429i	−0.115681	+	0.0743439i
$405$	−23.3109	+	26.9022i	−1.15833	+	1.33678i
$406$	−2.49249	+	5.45779i	−0.123700	+	0.270866i
$407$	−2.07969	−	1.33654i	−0.103087	−	0.0662497i
$408$	−25.1199	+	7.37585i	−1.24362	+	0.365159i
$409$	15.2980	+	17.6548i	0.756437	+	0.872975i	0.995176	−	0.0981090i	$-0.0312794\pi$
$409$	15.2980	+	17.6548i	0.756437	+	0.872975i	−0.238739	+	0.971084i	$0.576734\pi$
$410$	−27.4918	−	8.07234i	−1.35773	−	0.398664i
$411$	12.9010	+	28.2493i	0.636360	+	1.39343i
$412$	−1.59906	+	11.1217i	−0.0787800	+	0.547927i
$413$	3.05573			0.150363
$414$		0			0
$415$	42.8328			2.10258
$416$	−1.44391	+	10.0426i	−0.0707936	+	0.492380i
$417$	2.51564	+	5.50848i	0.123191	+	0.269752i
$418$	2.37200	+	0.696481i	0.116018	+	0.0340660i
$419$	20.5734	+	23.7429i	1.00507	+	1.15992i	0.987104	+	0.160080i	$0.0511752\pi$
$419$	20.5734	+	23.7429i	1.00507	+	1.15992i	0.0179709	+	0.999839i	$0.494279\pi$
$420$	−5.30395	+	1.55738i	−0.258806	+	0.0759923i
$421$	−19.9446	−	12.8176i	−0.972041	−	0.624693i	−0.0447356	−	0.998999i	$-0.514245\pi$
$421$	−19.9446	−	12.8176i	−0.972041	−	0.624693i	−0.927305	+	0.374306i	$0.877881\pi$
$422$	−2.29636	+	5.02832i	−0.111785	+	0.244775i
$423$	−2.92863	+	3.37981i	−0.142395	+	0.164332i
$424$	−15.9369	+	10.2420i	−0.773966	+	0.497398i
$425$	−4.07767	−	28.3608i	−0.197796	−	1.37570i
$426$	3.99765	+	27.8043i	0.193687	+	1.34712i
$427$	−11.3804	+	7.31372i	−0.550734	+	0.353935i
$428$	5.42997	−	6.26652i	0.262468	−	0.302904i
$429$	−2.12884	+	4.66151i	−0.102781	+	0.225060i
$430$		0			0
$431$	25.3998	−	7.45806i	1.22347	−	0.359242i	0.394686	−	0.918816i	$-0.370853\pi$
$431$	25.3998	−	7.45806i	1.22347	−	0.359242i	0.828781	+	0.559574i	$0.189035\pi$
$432$	−7.10793	−	8.20298i	−0.341980	−	0.394666i
$433$	−38.5528	−	11.3201i	−1.85273	−	0.544010i	−0.999757	−	0.0220502i	$-0.992981\pi$
$433$	−38.5528	−	11.3201i	−1.85273	−	0.544010i	−0.852970	−	0.521960i	$-0.825201\pi$
$434$	−5.57338	−	12.2040i	−0.267531	−	0.585810i
$435$	−3.08940	+	21.4872i	−0.148125	+	1.03023i
$436$		0			0
$437$		0			0
$438$	−55.9787			−2.67477
$439$	0.753101	−	5.23793i	0.0359436	−	0.249993i	−0.963926	−	0.266172i	$-0.914241\pi$
$439$	0.753101	−	5.23793i	0.0359436	−	0.249993i	0.999869	+	0.0161791i	$0.00515018\pi$
$440$	2.29636	+	5.02832i	0.109475	+	0.239716i
$441$	10.5010	+	3.08336i	0.500045	+	0.146827i
$442$	16.6442	+	19.2084i	0.791684	+	0.913652i
$443$	2.03855	−	0.598572i	0.0968544	−	0.0284390i	−0.232946	−	0.972490i	$-0.574837\pi$
$443$	2.03855	−	0.598572i	0.0968544	−	0.0284390i	0.329801	+	0.944051i	$0.393018\pi$
$444$	3.76220	+	2.41782i	0.178546	+	0.114745i
$445$	2.05392	−	4.49747i	0.0973654	−	0.213200i
$446$	4.23835	−	4.89131i	0.200692	−	0.231610i
$447$	−22.3635	+	14.3722i	−1.05776	+	0.679781i
$448$	0.745170	+	5.18277i	0.0352060	+	0.244863i
$449$	−0.419014	−	2.91430i	−0.0197745	−	0.137534i	0.977543	−	0.210738i	$-0.0675868\pi$
$449$	−0.419014	−	2.91430i	−0.0197745	−	0.137534i	−0.997317	+	0.0732037i	$0.976678\pi$
$450$	−14.8971	+	9.57378i	−0.702256	+	0.451312i
$451$	2.73754	−	3.15929i	0.128906	−	0.148765i
$452$	3.39824	−	7.44110i	0.159840	−	0.350000i
$453$	−0.444067	−	0.285385i	−0.0208641	−	0.0134085i
$454$	15.8049	−	4.64074i	0.741761	−	0.217801i
$455$	−7.85833	−	9.06899i	−0.368404	−	0.425161i
$456$	9.59493	+	2.81733i	0.449324	+	0.131933i
$457$	14.5913	+	31.9505i	0.682552	+	1.49458i	0.859916	+	0.510435i	$0.170516\pi$
$457$	14.5913	+	31.9505i	0.682552	+	1.49458i	−0.177365	+	0.984145i	$0.556757\pi$
$458$	−2.76324	+	19.2188i	−0.129118	+	0.898034i
$459$	−11.7082			−0.546492
$460$		0			0
$461$	7.47214			0.348012			0.174006	−	0.984745i	$-0.444329\pi$
$461$	7.47214			0.348012			0.174006	+	0.984745i	$0.444329\pi$
$462$	0.486206	−	3.38163i	0.0226203	−	0.157328i
$463$	−8.30830	−	18.1926i	−0.386119	−	0.845484i	−0.998491	−	0.0549137i	$-0.982512\pi$
$463$	−8.30830	−	18.1926i	−0.386119	−	0.845484i	0.612372	−	0.790570i	$-0.290216\pi$
$464$	−13.9724	−	4.10268i	−0.648654	−	0.190462i
$465$	−31.7876	−	36.6849i	−1.47412	−	1.70122i
$466$	−24.0204	+	7.05302i	−1.11272	+	0.326725i
$467$	−26.0320	−	16.7297i	−1.20462	−	0.774160i	−0.224867	−	0.974389i	$-0.572195\pi$
$467$	−26.0320	−	16.7297i	−1.20462	−	0.774160i	−0.979749	+	0.200230i	$0.935831\pi$
$468$	1.54044	−	3.37310i	0.0712070	−	0.155922i
$469$	−5.85725	+	6.75963i	−0.270463	+	0.312131i
$470$	9.84957	−	6.32993i	0.454327	−	0.291978i
$471$	−4.90590	−	34.1213i	−0.226052	−	1.57222i
$472$	0.786697	+	5.47160i	0.0362107	+	0.251851i
$473$		0			0
$474$	16.4531	−	18.9879i	0.755717	−	0.872144i
$475$	−4.54641	+	9.95526i	−0.208604	+	0.456779i
$476$	−3.36501	−	2.16256i	−0.154235	−	0.0991209i
$477$	16.2579	−	4.77375i	0.744399	−	0.218575i
$478$	19.3227	+	22.2996i	0.883800	+	1.01996i
$479$	16.8840	+	4.95758i	0.771448	+	0.226517i	0.643688	−	0.765288i	$-0.277403\pi$
$479$	16.8840	+	4.95758i	0.771448	+	0.226517i	0.127759	+	0.991805i	$0.459222\pi$
$480$	−10.1661	−	22.2606i	−0.464017	−	1.01605i
$481$	−1.38162	+	9.60939i	−0.0629965	+	0.438150i
$482$	−27.7082			−1.26207
$483$		0			0
$484$	−6.43769			−0.292622
$485$	1.97655	−	13.7472i	0.0897503	−	0.624227i
$486$	12.0239	+	26.3286i	0.545415	+	1.19429i
$487$	1.23947	+	0.363941i	0.0561657	+	0.0164917i	0.309695	−	0.950836i	$-0.399773\pi$
$487$	1.23947	+	0.363941i	0.0561657	+	0.0164917i	−0.253529	+	0.967328i	$0.581591\pi$
$488$	−16.0258	−	18.4948i	−0.725456	−	0.837221i
$489$	21.9614	−	6.44845i	0.993129	−	0.291609i
$490$	−24.1040	−	15.4907i	−1.08891	−	0.699798i
$491$	16.4722	−	36.0692i	0.743382	−	1.62778i	−0.0345293	−	0.999404i	$-0.510993\pi$
$491$	16.4722	−	36.0692i	0.743382	−	1.62778i	0.777911	−	0.628375i	$-0.216280\pi$
$492$	−4.95226	+	5.71521i	−0.223265	+	0.257662i
$493$	−13.2146	+	8.49250i	−0.595155	+	0.382483i
$494$	−1.38162	−	9.60939i	−0.0621621	−	0.432347i
$495$	−0.703643	−	4.89395i	−0.0316264	−	0.219967i
$496$	27.3932	−	17.6045i	1.22999	−	0.790466i
$497$	6.28453	−	7.25274i	0.281900	−	0.325330i
$498$	19.8936	−	43.5610i	0.891454	−	1.95201i
$499$	27.5159	+	17.6834i	1.23178	+	0.791617i	0.984167	−	0.177242i	$-0.0567174\pi$
$499$	27.5159	+	17.6834i	1.23178	+	0.791617i	0.247613	+	0.968859i	$0.420354\pi$
$500$	0.906022	−	0.266032i	0.0405185	−	0.0118973i
$501$	−15.3345	−	17.6969i	−0.685094	−	0.790641i
$502$	24.3869	+	7.16063i	1.08844	+	0.319595i
$503$	−3.76189	−	8.23738i	−0.167734	−	0.367287i	0.807034	−	0.590504i	$-0.201071\pi$
$503$	−3.76189	−	8.23738i	−0.167734	−	0.367287i	−0.974769	+	0.223218i	$0.928344\pi$
$504$	0.786697	−	5.47160i	0.0350423	−	0.243724i
$505$	14.4721			0.644002
$506$		0			0
$507$	−8.94427			−0.397229
$508$	1.82140	−	12.6681i	0.0808115	−	0.562056i
$509$	14.2508	+	31.2049i	0.631655	+	1.38313i	0.906731	+	0.421710i	$0.138570\pi$
$509$	14.2508	+	31.2049i	0.631655	+	1.38313i	−0.275076	+	0.961423i	$0.588703\pi$
$510$	−58.8217	−	17.2716i	−2.60467	−	0.764799i
$511$	12.5240	+	14.4534i	0.554027	+	0.639382i
$512$	−5.07744	+	1.49087i	−0.224393	+	0.0658878i
$513$	3.76220	+	2.41782i	0.166105	+	0.106749i
$514$	−0.989504	+	2.16671i	−0.0436452	+	0.0955696i
$515$	38.5273	−	44.4629i	1.69772	−	1.95927i
$516$		0			0
$517$	0.243103	+	1.69082i	0.0106916	+	0.0743620i
$518$	−0.921081	−	6.40626i	−0.0404700	−	0.281475i
$519$	9.51033	−	6.11192i	0.417457	−	0.268283i
$520$	14.2159	−	16.4060i	0.623406	−	0.719449i
$521$	1.90409	−	4.16938i	0.0834198	−	0.182664i	−0.863325	−	0.504648i	$-0.831622\pi$
$521$	1.90409	−	4.16938i	0.0834198	−	0.182664i	0.946745	+	0.321984i	$0.104350\pi$
$522$	8.16706	+	5.24865i	0.357463	+	0.229727i
$523$	−0.839929	+	0.246625i	−0.0367275	+	0.0107842i	−0.300045	−	0.953925i	$-0.597002\pi$
$523$	−0.839929	+	0.246625i	−0.0367275	+	0.0107842i	0.263317	+	0.964709i	$0.415183\pi$
$524$	−2.14173	−	2.47169i	−0.0935618	−	0.107976i
$525$	14.5120	+	4.26110i	0.633354	+	0.185969i
$526$	10.0449	+	21.9952i	0.437977	+	0.959037i
$527$	4.99875	−	34.7671i	0.217749	−	1.51448i
$528$	8.29180			0.360854
$529$		0			0
$530$	−44.3607			−1.92690
$531$	0.703643	−	4.89395i	0.0305355	−	0.212379i
$532$	0.634698	+	1.38979i	0.0275176	+	0.0602552i
$533$	−15.7514	−	4.62504i	−0.682270	−	0.200333i
$534$	−3.61998	−	4.17768i	−0.156652	−	0.180786i
$535$	−41.6577	+	12.2318i	−1.80102	+	0.528828i
$536$	−13.6118	−	8.74775i	−0.587939	−	0.377845i
$537$	−11.8046	+	25.8485i	−0.509406	+	1.11544i
$538$	10.5368	−	12.1601i	0.454275	−	0.524261i
$539$	3.51673	−	2.26006i	0.151476	−	0.0973478i
$540$	−0.636451	−	4.42662i	−0.0273885	−	0.190491i
$541$	1.07926	+	7.50640i	0.0464009	+	0.322725i	0.999780	+	0.0209517i	$0.00666962\pi$
$541$	1.07926	+	7.50640i	0.0464009	+	0.322725i	−0.953380	+	0.301774i	$0.902421\pi$
$542$	−10.8894	+	6.99820i	−0.467740	+	0.300599i
$543$	21.4558	−	24.7613i	0.920757	−	1.06261i
$544$	7.35625	−	16.1079i	0.315397	−	0.690623i
$545$		0			0
$546$	−12.8729	+	3.77984i	−0.550911	+	0.161762i
$547$	−24.5841	−	28.3716i	−1.05114	−	1.21308i	−0.976420	−	0.215878i	$-0.930739\pi$
$547$	−24.5841	−	28.3716i	−1.05114	−	1.21308i	−0.0747216	−	0.997204i	$-0.523807\pi$
$548$	−8.23590	−	2.41828i	−0.351820	−	0.103304i
$549$	9.09283	+	19.9105i	0.388073	+	0.849760i
$550$	−0.962608	+	6.69508i	−0.0410457	+	0.285479i
$551$	6.00000			0.255609
$552$		0			0
$553$	−8.58359			−0.365011
$554$	1.50317	−	10.4548i	0.0638637	−	0.444182i
$555$	−9.72753	−	21.3003i	−0.412911	−	0.904148i
$556$	−1.60596	−	0.471553i	−0.0681080	−	0.0199983i
$557$	−12.7150	−	14.6739i	−0.538754	−	0.621755i	0.419472	−	0.907768i	$-0.362215\pi$
$557$	−12.7150	−	14.6739i	−0.538754	−	0.621755i	−0.958226	+	0.286013i	$0.907670\pi$
$558$	−20.8289	+	6.11591i	−0.881756	+	0.258907i
$559$		0			0
$560$	−8.06587	+	17.6618i	−0.340845	+	0.746347i
$561$	5.85725	−	6.75963i	0.247293	−	0.285392i
$562$	18.0166	−	11.5786i	0.759986	−	0.488413i
$563$	2.14265	+	14.9025i	0.0903021	+	0.628065i	0.983836	+	0.179070i	$0.0573088\pi$
$563$	2.14265	+	14.9025i	0.0903021	+	0.628065i	−0.893534	+	0.448995i	$0.851782\pi$
$564$	−0.439777	−	3.05872i	−0.0185180	−	0.128795i
$565$	−36.0333	+	23.1572i	−1.51593	+	0.974229i
$566$	15.1434	−	17.4764i	0.636525	−	0.734589i
$567$	5.64829	−	12.3680i	0.237206	−	0.519409i
$568$	14.6047	+	9.38589i	0.612801	+	0.393823i
$569$	−0.173035	+	0.0508076i	−0.00725400	+	0.00212997i	−0.285358	−	0.958421i	$-0.592112\pi$
$569$	−0.173035	+	0.0508076i	−0.00725400	+	0.00212997i	0.278104	+	0.960551i	$0.410294\pi$
$570$	15.3345	+	17.6969i	0.642291	+	0.741243i
$571$	26.5858	+	7.80630i	1.11258	+	0.326684i	0.785840	−	0.618430i	$-0.212231\pi$
$571$	26.5858	+	7.80630i	1.11258	+	0.326684i	0.326742	+	0.945113i	$0.394049\pi$
$572$	−0.588397	−	1.28841i	−0.0246021	−	0.0538711i
$573$	1.21551	−	8.45408i	0.0507788	−	0.353174i
$574$	10.9443			0.456805
$575$		0			0
$576$	8.47214			0.353006
$577$	1.83423	−	12.7574i	0.0763600	−	0.531096i	−0.915356	−	0.402646i	$-0.868091\pi$
$577$	1.83423	−	12.7574i	0.0763600	−	0.531096i	0.991716	−	0.128450i	$-0.0410002\pi$
$578$	−7.00145	−	15.3310i	−0.291222	−	0.637687i
$579$	17.0444	+	5.00468i	0.708340	+	0.207987i
$580$	−3.92916	−	4.53450i	−0.163150	−	0.188285i
$581$	−15.6980	+	4.60934i	−0.651261	+	0.191227i
$582$	−13.0629	−	8.39500i	−0.541473	−	0.347984i
$583$	2.68862	−	5.88726i	0.111351	−	0.243825i
$584$	−22.6561	+	26.1465i	−0.937514	+	1.08195i
$585$	−16.3341	+	10.4973i	−0.675333	+	0.434010i
$586$	−2.41142	−	16.7718i	−0.0996149	−	0.692837i
$587$	1.60699	+	11.1769i	0.0663276	+	0.461318i	0.995735	+	0.0922624i	$0.0294099\pi$
$587$	1.60699	+	11.1769i	0.0663276	+	0.461318i	−0.929407	+	0.369056i	$0.879681\pi$
$588$	−6.36182	+	4.08849i	−0.262357	+	0.168607i
$589$	−8.78588	+	10.1394i	−0.362016	+	0.417789i
$590$	−5.37724	+	11.7745i	−0.221378	+	0.484749i
$591$	14.0558	+	9.03314i	0.578180	+	0.371574i
$592$	15.0719	−	4.42551i	0.619452	−	0.181887i
$593$	−9.78642	−	11.2941i	−0.401880	−	0.463794i	0.518352	−	0.855167i	$-0.326546\pi$
$593$	−9.78642	−	11.2941i	−0.401880	−	0.463794i	−0.920232	+	0.391373i	$0.872000\pi$
$594$	2.65197	+	0.778690i	0.108812	+	0.0319500i
$595$	8.70056	+	19.0516i	0.356688	+	0.781039i
$596$	1.04566	−	7.27274i	0.0428320	−	0.297903i
$597$	−57.4853			−2.35272
$598$		0			0
$599$	−1.88854			−0.0771638			−0.0385819	−	0.999255i	$-0.512284\pi$
$599$	−1.88854			−0.0771638			−0.0385819	+	0.999255i	$0.512284\pi$
$600$	−3.89383	+	27.0822i	−0.158965	+	1.10563i
$601$	4.61587	+	10.1073i	0.188285	+	0.412287i	0.980108	−	0.198464i	$-0.0635952\pi$
$601$	4.61587	+	10.1073i	0.188285	+	0.412287i	−0.791823	+	0.610750i	$0.790868\pi$
$602$		0			0
$603$	9.47723	+	10.9373i	0.385943	+	0.445402i
$604$	0.139988	−	0.0411042i	0.00569604	−	0.00167251i
$605$	28.3571	+	18.2240i	1.15288	+	0.740912i
$606$	6.72156	−	14.7182i	0.273045	−	0.597884i
$607$	−11.4783	+	13.2467i	−0.465890	+	0.537666i	−0.939264	−	0.343196i	$-0.888491\pi$
$607$	−11.4783	+	13.2467i	−0.465890	+	0.537666i	0.473374	+	0.880862i	$0.343036\pi$
$608$	−5.69018	+	3.65686i	−0.230767	+	0.148305i
$609$	−1.18005	−	8.20740i	−0.0478179	−	0.332581i
$610$	−8.15534	−	56.7217i	−0.330200	−	2.29659i
$611$	5.64330	−	3.62673i	0.228303	−	0.146722i
$612$	−4.23835	+	4.89131i	−0.171325	+	0.197720i
$613$	−3.20210	+	7.01163i	−0.129332	+	0.283197i	−0.963209	−	0.268753i	$-0.913389\pi$
$613$	−3.20210	+	7.01163i	−0.129332	+	0.283197i	0.833878	+	0.551950i	$0.186116\pi$
$614$	−25.1438	−	16.1590i	−1.01472	−	0.652123i
$615$	37.9928	−	11.1557i	1.53202	−	0.449841i
$616$	−1.38271	−	1.59573i	−0.0557110	−	0.0642939i
$617$	15.8049	+	4.64074i	0.636281	+	0.186829i	0.583936	−	0.811800i	$-0.301512\pi$
$617$	15.8049	+	4.64074i	0.636281	+	0.186829i	0.0523457	+	0.998629i	$0.483330\pi$
$618$	−27.3248	−	59.8329i	−1.09916	−	2.40683i
$619$	1.05546	−	7.34092i	0.0424227	−	0.295056i	−0.957554	−	0.288253i	$-0.906925\pi$
$619$	1.05546	−	7.34092i	0.0424227	−	0.295056i	0.999977	−	0.00680300i	$-0.00216548\pi$
$620$	13.4164			0.538816
$621$		0			0
$622$	14.8541			0.595595
$623$	−0.268768	+	1.86932i	−0.0107680	+	0.0748928i
$624$	−13.5269	−	29.6197i	−0.541508	−	1.18574i
$625$	21.5084	+	6.31543i	0.860335	+	0.252617i
$626$	−21.5739	−	24.8976i	−0.862267	−	0.995109i
$627$	−3.27802	+	0.962513i	−0.130911	+	0.0384391i
$628$	8.01535	+	5.15115i	0.319847	+	0.205553i
$629$	7.03890	−	15.4131i	0.280660	−	0.614559i
$630$	8.47670	−	9.78263i	0.337720	−	0.389749i
$631$	−27.2235	+	17.4955i	−1.08375	+	0.696485i	−0.955421	−	0.295246i	$-0.904598\pi$
$631$	−27.2235	+	17.4955i	−1.08375	+	0.696485i	−0.128331	+	0.991731i	$0.540962\pi$
$632$	−2.20985	−	15.3698i	−0.0879029	−	0.611378i
$633$	−1.08719	−	7.56156i	−0.0432119	−	0.300545i
$634$	1.92798	−	1.23904i	0.0765699	−	0.0492085i
$635$	−43.8843	+	50.6452i	−1.74149	+	2.00979i
$636$	−4.86376	+	10.6502i	−0.192861	+	0.422306i
$637$	−13.8104	−	8.87538i	−0.547186	−	0.351655i
$638$	3.55800	−	1.04472i	0.140862	−	0.0413609i
$639$	−10.1686	−	11.7352i	−0.402263	−	0.464236i
$640$	−42.2838	−	12.4156i	−1.67141	−	0.490771i
$641$	18.8204	+	41.2108i	0.743359	+	1.62773i	0.777948	+	0.628328i	$0.216261\pi$
$641$	18.8204	+	41.2108i	0.743359	+	1.62773i	−0.0345888	+	0.999402i	$0.511012\pi$
$642$	−6.90811	+	48.0469i	−0.272641	+	1.89626i
$643$	19.5967			0.772820			0.386410	−	0.922327i	$-0.373715\pi$
$643$	19.5967			0.772820			0.386410	+	0.922327i	$0.373715\pi$
$644$		0			0
$645$		0			0
$646$	−2.41142	+	16.7718i	−0.0948761	+	0.659878i
$647$	−2.78669	−	6.10200i	−0.109556	−	0.239894i	0.846911	−	0.531735i	$-0.178460\pi$
$647$	−2.78669	−	6.10200i	−0.109556	−	0.239894i	−0.956467	+	0.291840i	$0.905732\pi$
$648$	23.6004	+	6.92970i	0.927112	+	0.272225i
$649$	−1.23673	−	1.42727i	−0.0485460	−	0.0560251i
$650$	25.4863	−	7.48347i	0.999657	−	0.293526i
$651$	15.5977	+	10.0240i	0.611322	+	0.392873i
$652$	−2.62801	+	5.75455i	−0.102921	+	0.225366i
$653$	−15.9164	+	18.3685i	−0.622855	+	0.718813i	−0.976247	−	0.216662i	$-0.930483\pi$
$653$	−15.9164	+	18.3685i	−0.622855	+	0.718813i	0.353391	+	0.935476i	$0.385028\pi$
$654$		0			0
$655$	2.43709	+	16.9503i	0.0952248	+	0.662303i
$656$	3.78021	+	26.2919i	0.147592	+	1.02653i
$657$	26.0320	−	16.7297i	1.01560	−	0.652689i
$658$	−2.92863	+	3.37981i	−0.114170	+	0.131759i
$659$	8.57935	−	18.7862i	0.334204	−	0.731805i	−0.665692	−	0.746227i	$-0.731864\pi$
$659$	8.57935	−	18.7862i	0.334204	−	0.731805i	0.999896	+	0.0144220i	$0.00459082\pi$
$660$	2.87407	+	1.84705i	0.111873	+	0.0718963i
$661$	4.85094	−	1.42436i	0.188680	−	0.0554013i	−0.186028	−	0.982545i	$-0.559561\pi$
$661$	4.85094	−	1.42436i	0.188680	−	0.0554013i	0.374707	+	0.927143i	$0.377743\pi$
$662$	12.3468	+	14.2490i	0.479872	+	0.553802i
$663$	−33.7018	−	9.89575i	−1.30887	−	0.384319i
$664$	−12.2949	−	26.9221i	−0.477136	−	1.04478i
$665$	1.13852	−	7.91857i	0.0441499	−	0.307069i
$666$	−10.4721			−0.405787
$667$		0			0
$668$	6.47214			0.250414
$669$	−1.27290	+	8.85323i	−0.0492133	+	0.342286i
$670$	−15.7395	−	34.4646i	−0.608069	−	1.33148i
$671$	8.02201	+	2.35548i	0.309686	+	0.0909321i
$672$	6.12133	+	7.06439i	0.236135	+	0.272515i
$673$	−2.87848	+	0.845198i	−0.110957	+	0.0325800i	−0.336740	−	0.941598i	$-0.609324\pi$
$673$	−2.87848	+	0.845198i	−0.110957	+	0.0325800i	0.225783	+	0.974178i	$0.427506\pi$
$674$	4.65034	+	2.98859i	0.179124	+	0.115116i
$675$	−5.08305	+	11.1303i	−0.195647	+	0.428406i
$676$	1.61890	−	1.86832i	0.0622656	−	0.0718583i
$677$	15.1426	−	9.73153i	0.581976	−	0.374013i	−0.216280	−	0.976331i	$-0.569392\pi$
$677$	15.1426	−	9.73153i	0.581976	−	0.374013i	0.798256	+	0.602318i	$0.205756\pi$
$678$	6.81525	+	47.4011i	0.261738	+	1.82043i
$679$	0.754973	+	5.25095i	0.0289732	+	0.201513i
$680$	−31.8739	+	20.4841i	−1.22231	+	0.785529i
$681$	−14.9072	+	17.2038i	−0.571245	+	0.659252i
$682$	−3.44454	+	7.54248i	−0.131898	+	0.288817i
$683$	−19.0096	−	12.2167i	−0.727382	−	0.467460i	0.123816	−	0.992305i	$-0.460487\pi$
$683$	−19.0096	−	12.2167i	−0.727382	−	0.467460i	−0.851198	+	0.524845i	$0.824123\pi$
$684$	2.37200	−	0.696481i	0.0906956	−	0.0266306i
$685$	29.4322	+	33.9666i	1.12455	+	1.29780i
$686$	23.9339	+	7.02761i	0.913799	+	0.268316i
$687$	−11.1468	−	24.4080i	−0.425275	−	0.931223i
$688$		0			0
$689$	−25.4164			−0.968288
$690$		0			0
$691$	24.9443			0.948925			0.474462	−	0.880276i	$-0.342642\pi$
$691$	24.9443			0.948925			0.474462	+	0.880276i	$0.342642\pi$
$692$	−0.444679	+	3.09281i	−0.0169041	+	0.117571i
$693$	0.784529	+	1.71788i	0.0298018	+	0.0652569i
$694$	40.1918	+	11.8014i	1.52566	+	0.447974i
$695$	5.73915	+	6.62334i	0.217699	+	0.251238i
$696$	14.3924	−	4.22599i	0.545542	−	0.160186i
$697$	24.1040	+	15.4907i	0.913004	+	0.586752i
$698$	1.62420	−	3.55651i	0.0614770	−	0.134616i
$699$	22.6561	−	26.1465i	0.856931	−	0.988951i
$700$	−3.51673	+	2.26006i	−0.132920	+	0.0854223i
$701$	3.72585	+	25.9139i	0.140723	+	0.978753i	0.930744	+	0.365672i	$0.119161\pi$
$701$	3.72585	+	25.9139i	0.140723	+	0.978753i	−0.790020	+	0.613081i	$0.789930\pi$
$702$	−1.54470	−	10.7436i	−0.0583009	−	0.405492i
$703$	−5.44471	+	3.49910i	−0.205351	+	0.131971i
$704$	2.11917	−	2.44566i	0.0798694	−	0.0921742i
$705$	−6.72156	+	14.7182i	−0.253148	+	0.554318i
$706$	48.1321	+	30.9326i	1.81148	+	1.16417i
$707$	−5.30395	+	1.55738i	−0.199475	+	0.0585713i
$708$	2.23727	+	2.58195i	0.0840818	+	0.0970356i
$709$	−15.4180	−	4.52713i	−0.579034	−	0.170020i	−0.0209161	−	0.999781i	$-0.506658\pi$
$709$	−15.4180	−	4.52713i	−0.579034	−	0.170020i	−0.558118	+	0.829761i	$0.688476\pi$
$710$	16.8876	+	36.9788i	0.633782	+	1.38779i
$711$	−1.97655	+	13.7472i	−0.0741263	+	0.515559i
$712$	−3.41641			−0.128035
$713$		0			0
$714$	23.4164			0.876337
$715$	−1.05546	+	7.34092i	−0.0394721	+	0.274535i
$716$	−3.26271	−	7.14434i	−0.121933	−	0.266997i
$717$	−39.1253	−	11.4882i	−1.46116	−	0.429036i
$718$	16.8353	+	19.4290i	0.628288	+	0.725083i
$719$	20.0959	−	5.90068i	0.749450	−	0.220058i	0.115366	−	0.993323i	$-0.463196\pi$
$719$	20.0959	−	5.90068i	0.749450	−	0.220058i	0.634083	+	0.773265i	$0.281378\pi$
$720$	26.4292	+	16.9850i	0.984957	+	0.632993i
$721$	−9.33526	+	20.4414i	−0.347663	+	0.761277i
$722$	−15.8938	+	18.3424i	−0.591506	+	0.682634i
$723$	32.2131	−	20.7021i	1.19802	−	0.769920i
$724$	1.28876	+	8.96355i	0.0478966	+	0.333128i
$725$	2.33630	+	16.2493i	0.0867679	+	0.603484i
$726$	31.7043	−	20.3751i	1.17666	−	0.756190i
$727$	9.35914	−	10.8010i	0.347111	−	0.400588i	−0.555169	−	0.831737i	$-0.687347\pi$
$727$	9.35914	−	10.8010i	0.347111	−	0.400588i	0.902280	+	0.431150i	$0.141892\pi$
$728$	−3.44454	+	7.54248i	−0.127663	+	0.279543i
$729$	−5.88877	−	3.78449i	−0.218103	−	0.140166i
$730$	−77.7316	+	22.8240i	−2.87697	+	0.844756i
$731$		0			0
$732$	−14.5120	−	4.26110i	−0.536377	−	0.157495i
$733$	−11.1181	−	24.3453i	−0.410658	−	0.899215i	−0.996078	−	0.0884848i	$-0.971798\pi$
$733$	−11.1181	−	24.3453i	−0.410658	−	0.899215i	0.585420	−	0.810730i	$-0.300930\pi$
$734$	4.18639	−	29.1170i	0.154523	−	1.07473i
$735$	39.5967			1.46055
$736$		0			0
$737$	5.52786			0.203621
$738$	2.52014	−	17.5280i	0.0927676	−	0.645213i
$739$	20.4303	+	44.7360i	0.751539	+	1.64564i	0.763580	+	0.645713i	$0.223440\pi$
$739$	20.4303	+	44.7360i	0.751539	+	1.64564i	−0.0120410	+	0.999928i	$0.503833\pi$
$740$	6.20997	+	1.82341i	0.228283	+	0.0670299i
$741$	8.78588	+	10.1394i	0.322757	+	0.372482i
$742$	16.2579	−	4.77375i	0.596847	−	0.175250i
$743$	0.736423	+	0.473271i	0.0270168	+	0.0173626i	0.554079	−	0.832464i	$-0.313070\pi$
$743$	0.736423	+	0.473271i	0.0270168	+	0.0173626i	−0.527063	+	0.849826i	$0.676707\pi$
$744$	−13.9334	+	30.5100i	−0.510825	+	1.11855i
$745$	−25.1939	+	29.0753i	−0.923033	+	1.06524i
$746$	7.76987	−	4.99340i	0.284475	−	0.182821i
$747$	3.76738	+	26.2027i	0.137841	+	0.958706i
$748$	0.351822	+	2.44697i	0.0128639	+	0.0894702i
$749$	13.9510	−	8.96577i	0.509759	−	0.327602i
$750$	−3.61998	+	4.17768i	−0.132183	+	0.152547i
$751$	−18.4281	+	40.3519i	−0.672451	+	1.47246i	0.197998	+	0.980202i	$0.436556\pi$
$751$	−18.4281	+	40.3519i	−0.672451	+	1.47246i	−0.870449	+	0.492259i	$0.836171\pi$
$752$	−9.13105	−	5.86817i	−0.332975	−	0.213990i
$753$	−33.7018	+	9.89575i	−1.22816	+	0.360621i
$754$	−9.53628	−	11.0055i	−0.347291	−	0.400795i
$755$	−0.732987	−	0.215225i	−0.0266761	−	0.00783282i
$756$	0.709614	+	1.55384i	0.0258084	+	0.0565125i
$757$	6.77372	−	47.1123i	0.246195	−	1.71232i	−0.373624	−	0.927580i	$-0.621885\pi$
$757$	6.77372	−	47.1123i	0.246195	−	1.71232i	0.619819	−	0.784745i	$-0.287206\pi$
$758$	32.9443			1.19659
$759$		0			0
$760$	14.4721			0.524960
$761$	2.32044	−	16.1390i	0.0841158	−	0.585038i	−0.903553	−	0.428477i	$-0.859050\pi$
$761$	2.32044	−	16.1390i	0.0841158	−	0.585038i	0.987668	−	0.156561i	$-0.0500407\pi$
$762$	31.1241	+	68.1523i	1.12751	+	2.46890i
$763$		0			0
$764$	1.54592	+	1.78408i	0.0559293	+	0.0645458i
$765$	32.5158	−	9.54751i	1.17561	−	0.345191i
$766$	−33.9536	−	21.8206i	−1.22679	−	0.788411i
$767$	−3.08089	+	6.74620i	−0.111244	+	0.243591i
$768$	−19.8595	+	22.9190i	−0.716617	+	0.827020i
$769$	14.4061	−	9.25826i	0.519499	−	0.333862i	−0.254475	−	0.967079i	$-0.581903\pi$
$769$	14.4061	−	9.25826i	0.519499	−	0.333862i	0.773974	+	0.633218i	$0.218266\pi$
$770$	−0.703643	−	4.89395i	−0.0253575	−	0.176366i
$771$	−0.468471	−	3.25829i	−0.0168716	−	0.117344i
$772$	−4.13041	+	2.65445i	−0.148657	+	0.0955359i
$773$	9.47723	−	10.9373i	0.340872	−	0.393388i	−0.559268	−	0.828987i	$-0.688918\pi$
$773$	9.47723	−	10.9373i	0.340872	−	0.393388i	0.900141	+	0.435599i	$0.143463\pi$
$774$		0			0
$775$	−30.8809	−	19.8460i	−1.10927	−	0.712888i
$776$	−9.20801	+	2.70372i	−0.330548	+	0.0970578i
$777$	5.85725	+	6.75963i	0.210128	+	0.242500i
$778$	53.5177	+	15.7142i	1.91870	+	0.563382i
$779$	−4.54641	−	9.95526i	−0.162892	−	0.356684i
$780$	1.90935	−	13.2798i	0.0683658	−	0.475495i
$781$	−5.93112			−0.212232
$782$		0			0
$783$	6.70820			0.239732
$784$	−3.78021	+	26.2919i	−0.135008	+	0.938998i
$785$	−20.7245	−	45.3802i	−0.739687	−	1.61969i
$786$	18.3704	+	5.39402i	0.655249	+	0.192398i
$787$	−33.6706	−	38.8579i	−1.20023	−	1.38514i	−0.902615	−	0.430449i	$-0.858355\pi$
$787$	−33.6706	−	38.8579i	−1.20023	−	1.38514i	−0.297612	−	0.954687i	$-0.596190\pi$
$788$	−4.43097	+	1.30105i	−0.157847	+	0.0463480i
$789$	−28.1117	−	18.0663i	−1.00080	−	0.643176i
$790$	15.1048	−	33.0748i	0.537404	−	1.17675i
$791$	10.7140	−	12.3646i	0.380945	−	0.439634i
$792$	−2.87407	+	1.84705i	−0.102125	+	0.0656320i
$793$	−4.67260	−	32.4986i	−0.165929	−	1.15406i
$794$	0.556427	+	3.87003i	0.0197468	+	0.137342i
$795$	51.5730	−	33.1440i	1.82911	−	1.17550i
$796$	10.4048	−	12.0078i	0.368788	−	0.425604i
$797$	4.30398	−	9.42441i	0.152455	−	0.333830i	−0.817959	−	0.575276i	$-0.804895\pi$
$797$	4.30398	−	9.42441i	0.152455	−	0.333830i	0.970414	+	0.241447i	$0.0776219\pi$
$798$	−7.52440	−	4.83564i	−0.266361	−	0.171180i
$799$	−11.2339	+	3.29858i	−0.397428	+	0.116695i
$800$	−12.1192	−	13.9863i	−0.428480	−	0.494492i
$801$	2.93195	+	0.860898i	0.103595	+	0.0304183i
$802$	−5.49846	−	12.0400i	−0.194157	−	0.425145i
$803$	1.68211	−	11.6994i	0.0593605	−	0.412861i
$804$	−10.0000			−0.352673
$805$		0			0
$806$	32.5623			1.14696
$807$	−3.16452	+	22.0097i	−0.111396	+	0.774779i
$808$	−4.15415	−	9.09632i	−0.146142	−	0.320007i
$809$	−45.9487	−	13.4918i	−1.61547	−	0.474345i	−0.655675	−	0.755043i	$-0.727616\pi$
$809$	−45.9487	−	13.4918i	−1.61547	−	0.474345i	−0.959796	+	0.280698i	$0.909434\pi$
$810$	37.7178	+	43.5287i	1.32527	+	1.52944i
$811$	53.3982	−	15.6791i	1.87506	−	0.550568i	0.877599	−	0.479395i	$-0.159144\pi$
$811$	53.3982	−	15.6791i	1.87506	−	0.550568i	0.997464	−	0.0711727i	$-0.0226741\pi$
$812$	1.92798	+	1.23904i	0.0676589	+	0.0434817i
$813$	7.43117	−	16.2720i	0.260622	−	0.570684i
$814$	−2.61944	+	3.02300i	−0.0918114	+	0.105956i
$815$	27.8662	−	17.9085i	0.976110	−	0.627308i
$816$	8.08815	+	56.2543i	0.283142	+	1.96930i
$817$		0			0
$818$	31.7980	−	20.4353i	1.11179	−	0.714505i
$819$	4.85671	−	5.60495i	0.169707	−	0.195853i
$820$	−4.54641	+	9.95526i	−0.158768	+	0.347653i
$821$	−17.7132	−	11.3836i	−0.618195	−	0.397290i	0.193727	−	0.981055i	$-0.437942\pi$
$821$	−17.7132	−	11.3836i	−0.618195	−	0.397290i	−0.811922	+	0.583766i	$0.801579\pi$
$822$	48.2138	−	14.1568i	1.68165	−	0.493777i
$823$	−18.0355	−	20.8141i	−0.628679	−	0.725534i	0.348652	−	0.937252i	$-0.386640\pi$
$823$	−18.0355	−	20.8141i	−0.628679	−	0.725534i	−0.977331	+	0.211718i	$0.932094\pi$
$824$	−39.0058	−	11.4531i	−1.35883	−	0.398989i
$825$	−3.88310	−	8.50281i	−0.135192	−	0.296030i
$826$	0.703643	−	4.89395i	0.0244829	−	0.170282i
$827$	10.4721			0.364152			0.182076	−	0.983284i	$-0.441718\pi$
$827$	10.4721			0.364152			0.182076	+	0.983284i	$0.441718\pi$
$828$		0			0
$829$	−40.2492			−1.39791			−0.698957	−	0.715164i	$-0.746352\pi$
$829$	−40.2492			−1.39791			−0.698957	+	0.715164i	$0.746352\pi$
$830$	9.86312	−	68.5995i	0.342354	−	2.38112i
$831$	6.06371	+	13.2777i	0.210348	+	0.460597i
$832$	−12.1934	−	3.58031i	−0.422731	−	0.124125i
$833$	18.7634	+	21.6541i	0.650113	+	0.750270i
$834$	9.40147	−	2.76052i	0.325546	−	0.0955890i
$835$	−28.5089	−	18.3215i	−0.986590	−	0.634043i
$836$	0.392265	−	0.858940i	0.0135668	−	0.0297071i
$837$	−9.82291	+	11.3362i	−0.339529	+	0.391838i
$838$	42.7633	−	27.4823i	1.47723	−	0.949360i
$839$	0.124581	+	0.866478i	0.00430100	+	0.0299141i	0.991859	−	0.127342i	$-0.0406444\pi$
$839$	0.124581	+	0.866478i	0.00430100	+	0.0299141i	−0.987558	+	0.157256i	$0.949735\pi$
$840$	−2.84630	−	19.7964i	−0.0982066	−	0.683042i
$841$	−16.8251	+	10.8128i	−0.580175	+	0.372856i
$842$	−25.1209	+	28.9911i	−0.865723	+	0.999098i
$843$	−12.2949	+	26.9221i	−0.423460	+	0.927248i
$844$	1.77627	+	1.14154i	0.0611417	+	0.0392934i
$845$	−12.4199	+	3.64682i	−0.427259	+	0.125455i
$846$	4.73862	+	5.46866i	0.162917	+	0.188016i
$847$	−12.3538	−	3.62742i	−0.424483	−	0.124639i
$848$	17.0838	+	37.4083i	0.586659	+	1.28461i
$849$	−4.54802	+	31.6321i	−0.156088	+	1.08561i
$850$	−46.3607			−1.59016
$851$		0			0
$852$	10.7295			0.367586
$853$	5.32491	−	37.0356i	0.182321	−	1.26807i	−0.668934	−	0.743322i	$-0.733249\pi$
$853$	5.32491	−	37.0356i	0.182321	−	1.26807i	0.851255	−	0.524752i	$-0.175842\pi$
$854$	9.09283	+	19.9105i	0.311150	+	0.681324i
$855$	−12.4199	−	3.64682i	−0.424753	−	0.124719i
$856$	19.6458	+	22.6725i	0.671480	+	0.774930i
$857$	7.16946	−	2.10514i	0.244904	−	0.0719103i	−0.156977	−	0.987602i	$-0.550175\pi$
$857$	7.16946	−	2.10514i	0.244904	−	0.0719103i	0.401881	+	0.915692i	$0.368357\pi$
$858$	6.97550	+	4.48288i	0.238140	+	0.153043i
$859$	−1.36746	+	2.99432i	−0.0466572	+	0.102165i	−0.931525	−	0.363677i	$-0.881521\pi$
$859$	−1.36746	+	2.99432i	−0.0466572	+	0.102165i	0.884868	+	0.465842i	$0.154248\pi$
$860$		0			0
$861$	−12.7236	+	8.17698i	−0.433620	+	0.278671i
$862$	−6.09575	−	42.3968i	−0.207622	−	1.44404i
$863$	−6.48116	−	45.0775i	−0.220621	−	1.53446i	−0.735697	−	0.677311i	$-0.763145\pi$
$863$	−6.48116	−	45.0775i	−0.220621	−	1.53446i	0.515076	−	0.857145i	$-0.327764\pi$
$864$	−6.36182	+	4.08849i	−0.216433	+	0.139093i
$865$	10.7140	−	12.3646i	0.364286	−	0.420408i
$866$	−27.0074	+	59.1380i	−0.917750	+	2.00959i
$867$	19.5943	+	12.5925i	0.665458	+	0.427664i
$868$	−4.91703	+	1.44377i	−0.166895	+	0.0490047i
$869$	3.47400	+	4.00921i	0.117848	+	0.136003i
$870$	33.7018	+	9.89575i	1.14260	+	0.335497i
$871$	−9.01791	−	19.7465i	−0.305560	−	0.669084i
$872$		0			0
$873$	8.58359			0.290511
$874$		0			0
$875$	1.88854			0.0638444
$876$	−3.04297	+	21.1643i	−0.102812	+	0.715076i
$877$	−11.4355	−	25.0402i	−0.386149	−	0.845548i	−0.998489	−	0.0549537i	$-0.982499\pi$
$877$	−11.4355	−	25.0402i	−0.386149	−	0.845548i	0.612340	−	0.790595i	$-0.290228\pi$
$878$	−8.21547	−	2.41228i	−0.277259	−	0.0814105i
$879$	15.3345	+	17.6969i	0.517219	+	0.596903i
$880$	11.5139	−	3.38079i	0.388134	−	0.113966i
$881$	18.3559	+	11.7966i	0.618425	+	0.397438i	0.812008	−	0.583646i	$-0.198375\pi$
$881$	18.3559	+	11.7966i	0.618425	+	0.397438i	−0.193583	+	0.981084i	$0.562011\pi$
$882$	7.35625	−	16.1079i	0.247698	−	0.542383i
$883$	−2.61944	+	3.02300i	−0.0881513	+	0.101732i	−0.798111	−	0.602510i	$-0.794167\pi$
$883$	−2.61944	+	3.02300i	−0.0881513	+	0.101732i	0.709960	+	0.704242i	$0.248713\pi$
$884$	8.16706	−	5.24865i	0.274688	−	0.176531i
$885$	−2.54581	−	17.7065i	−0.0855763	−	0.595196i
$886$	−0.489235	−	3.40270i	−0.0164362	−	0.114316i
$887$	−29.5018	+	18.9597i	−0.990574	+	0.636603i	−0.932296	−	0.361697i	$-0.882198\pi$
$887$	−29.5018	+	18.9597i	−0.990574	+	0.636603i	−0.0582785	+	0.998300i	$0.518561\pi$
$888$	−10.5959	+	12.2283i	−0.355574	+	0.410354i
$889$	10.6333	−	23.2836i	0.356629	−	0.780908i
$890$	−6.73003	−	4.32513i	−0.225591	−	0.144979i
$891$	−8.06286	+	2.36747i	−0.270116	+	0.0793132i
$892$	−1.61890	−	1.86832i	−0.0542049	−	0.0625558i
$893$	4.29098	+	1.25995i	0.143592	+	0.0421625i
$894$	17.8683	+	39.1261i	0.597606	+	1.30857i
$895$	−5.85264	+	40.7060i	−0.195632	+	1.36065i
$896$	16.8328			0.562345
$897$		0			0
$898$	−4.76393			−0.158974
$899$	−2.86403	+	19.9198i	−0.0955208	+	0.664362i
$900$	2.80984	+	6.15269i	0.0936613	+	0.205090i
$901$	42.5638	+	12.4978i	1.41800	+	0.416364i
$902$	−4.42943	−	5.11184i	−0.147484	−	0.170206i
$903$		0			0
$904$	24.8984	+	16.0012i	0.828107	+	0.532192i
$905$	19.6975	−	43.1315i	0.654767	−	1.43374i
$906$	−0.559318	+	0.645487i	−0.0185821	+	0.0214449i
$907$	33.8598	−	21.7604i	1.12430	−	0.722541i	0.159934	−	0.987128i	$-0.448872\pi$
$907$	33.8598	−	21.7604i	1.12430	−	0.722541i	0.964362	+	0.264586i	$0.0852354\pi$
$908$	−0.895416	−	6.22775i	−0.0297154	−	0.206675i
$909$	1.27290	+	8.85323i	0.0422195	+	0.293643i
$910$	−16.3341	+	10.4973i	−0.541471	+	0.347982i
$911$	20.5004	−	23.6587i	0.679208	−	0.783848i	−0.306579	−	0.951845i	$-0.599185\pi$
$911$	20.5004	−	23.6587i	0.679208	−	0.783848i	0.985787	+	0.167997i	$0.0537300\pi$
$912$	9.01791	−	19.7465i	0.298613	−	0.653871i
$913$	8.50630	+	5.46667i	0.281517	+	0.180920i
$914$	54.5307	−	16.0117i	1.80371	−	0.529618i
$915$	51.8607	+	59.8505i	1.71446	+	1.97859i
$916$	7.11599	+	2.08944i	0.235119	+	0.0690372i
$917$	−2.71724	−	5.94992i	−0.0897311	−	0.196484i
$918$	−2.69605	+	18.7514i	−0.0889829	+	0.618890i
$919$	0.875388			0.0288764			0.0144382	−	0.999896i	$-0.495404\pi$
$919$	0.875388			0.0288764			0.0144382	+	0.999896i	$0.495404\pi$
$920$		0			0
$921$	41.3050			1.36104
$922$	1.72061	−	11.9671i	0.0566653	−	0.394116i
$923$	9.67576	+	21.1870i	0.318482	+	0.697377i
$924$	−1.25209	−	0.367647i	−0.0411908	−	0.0120947i
$925$	−11.5964	−	13.3830i	−0.381288	−	0.440029i
$926$	−31.0498	+	9.11706i	−1.02036	+	0.299605i
$927$	30.5886	+	19.6581i	1.00466	+	0.645656i
$928$	−4.21476	+	9.22903i	−0.138356	+	0.302958i
$929$	27.4677	−	31.6994i	0.901185	−	1.04002i	−0.0978106	−	0.995205i	$-0.531184\pi$
$929$	27.4677	−	31.6994i	0.901185	−	1.04002i	0.998995	−	0.0448174i	$-0.0142706\pi$
$930$	−66.0729	+	42.4625i	−2.16662	+	1.39240i
$931$	−1.55753	−	10.8329i	−0.0510461	−	0.355033i
$932$	1.36086	+	9.46498i	0.0445764	+	0.310036i
$933$	−17.2691	+	11.0982i	−0.565366	+	0.363339i
$934$	−32.7881	+	37.8395i	−1.07286	+	1.23815i
$935$	5.37724	−	11.7745i	0.175855	−	0.385068i
$936$	11.2866	+	7.25346i	0.368914	+	0.237087i
$937$	−11.3409	+	3.32998i	−0.370490	+	0.108786i	−0.461677	−	0.887048i	$-0.652752\pi$
$937$	−11.3409	+	3.32998i	−0.370490	+	0.108786i	0.0911868	+	0.995834i	$0.470934\pi$
$938$	9.47723	+	10.9373i	0.309443	+	0.357116i
$939$	43.6837	+	12.8267i	1.42556	+	0.418583i
$940$	−1.85779	−	4.06800i	−0.0605945	−	0.132683i
$941$	3.50841	−	24.4015i	0.114371	−	0.795468i	−0.849211	−	0.528054i	$-0.822922\pi$
$941$	3.50841	−	24.4015i	0.114371	−	0.795468i	0.963582	−	0.267414i	$-0.0861690\pi$
$942$	−55.7771			−1.81732
$943$		0			0
$944$	12.0000			0.390567
$945$	1.27290	−	8.85323i	0.0414075	−	0.287996i
$946$		0			0
$947$	31.8363	+	9.34798i	1.03454	+	0.303769i	0.754556	−	0.656236i	$-0.227852\pi$
$947$	31.8363	+	9.34798i	1.03454	+	0.303769i	0.279985	+	0.960004i	$0.409671\pi$
$948$	−6.28453	−	7.25274i	−0.204112	−	0.235558i
$949$	−44.5362	+	13.0770i	−1.44571	+	0.424498i
$950$	14.8971	+	9.57378i	0.483325	+	0.310614i
$951$	−1.31570	+	2.88097i	−0.0426644	+	0.0934219i
$952$	9.47723	−	10.9373i	0.307159	−	0.354480i
$953$	9.69786	−	6.23243i	0.314144	−	0.201888i	−0.374061	−	0.927404i	$-0.622035\pi$
$953$	9.69786	−	6.23243i	0.314144	−	0.201888i	0.688206	+	0.725516i	$0.258399\pi$
$954$	−3.90176	−	27.1373i	−0.126324	−	0.878604i
$955$	−1.75911	−	12.2349i	−0.0569234	−	0.395911i
$956$	9.48136	−	6.09330i	0.306649	−	0.197071i
$957$	−3.35591	+	3.87292i	−0.108481	+	0.125194i
$958$	11.8278	−	25.8992i	0.382137	−	0.836764i
$959$	−14.4420	−	9.28128i	−0.466355	−	0.299708i
$960$	29.4108	−	8.63580i	0.949231	−	0.278719i
$961$	−9.16805	−	10.5805i	−0.295744	−	0.341306i
$962$	15.0719	+	4.42551i	0.485938	+	0.142684i
$963$	−11.1468	−	24.4080i	−0.359199	−	0.786536i
$964$	−1.50620	+	10.4759i	−0.0485115	+	0.337405i
$965$	25.7082			0.827576
$966$		0			0
$967$	−39.5410			−1.27155			−0.635777	−	0.771873i	$-0.719320\pi$
$967$	−39.5410			−1.27155			−0.635777	+	0.771873i	$0.719320\pi$
$968$	3.31477	−	23.0547i	0.106541	−	0.741007i
$969$	−9.72753	−	21.3003i	−0.312493	−	0.684265i
$970$	−21.5619	−	6.33113i	−0.692309	−	0.203280i
$971$	−4.92970	−	5.68918i	−0.158202	−	0.182574i	0.671115	−	0.741353i	$-0.265816\pi$
$971$	−4.92970	−	5.68918i	−0.158202	−	0.182574i	−0.829317	+	0.558779i	$0.811270\pi$
$972$	10.6079	−	3.11476i	0.340248	−	0.0999059i
$973$	−2.81612	−	1.80981i	−0.0902806	−	0.0580198i
$974$	0.868288	−	1.90129i	0.0278217	−	0.0609211i
$975$	−24.0388	+	27.7422i	−0.769856	+	0.888462i
$976$	−44.6913	+	28.7213i	−1.43053	+	0.919347i
$977$	7.77786	+	54.0962i	0.248836	+	1.73069i	0.604963	+	0.796253i	$0.293188\pi$
$977$	7.77786	+	54.0962i	0.248836	+	1.73069i	−0.356128	+	0.934437i	$0.615903\pi$
$978$	−5.27055	−	36.6575i	−0.168534	−	1.17218i
$979$	0.981898	−	0.631027i	0.0313816	−	0.0201677i
$980$	−7.16697	+	8.27113i	−0.228941	+	0.264212i
$981$		0			0
$982$	−53.9740	−	34.6870i	−1.72238	−	1.10691i
$983$	30.2508	−	8.88243i	0.964850	−	0.283305i	0.238893	−	0.971046i	$-0.423215\pi$
$983$	30.2508	−	8.88243i	0.964850	−	0.283305i	0.725957	+	0.687741i	$0.241397\pi$
$984$	−17.9174	−	20.6778i	−0.571187	−	0.659185i
$985$	23.2009	+	6.81239i	0.739241	+	0.217061i
$986$	10.5584	+	23.1196i	0.336247	+	0.736277i
$987$	0.879554	−	6.11743i	0.0279965	−	0.194720i
$988$	−3.70820			−0.117974
$989$		0			0
$990$	−8.00000			−0.254257
$991$	−3.41556	+	23.7557i	−0.108499	+	0.754625i	0.860836	+	0.508882i	$0.169941\pi$
$991$	−3.41556	+	23.7557i	−0.108499	+	0.754625i	−0.969335	+	0.245743i	$0.920968\pi$
$992$	−9.42449	−	20.6367i	−0.299228	−	0.655217i
$993$	−25.0003	−	7.34075i	−0.793360	−	0.232952i
$994$	−10.1686	−	11.7352i	−0.322528	−	0.372217i
$995$	−79.8236	+	23.4383i	−2.53058	+	0.743045i
$996$	−15.3880	−	9.88929i	−0.487589	−	0.313354i
$997$	−15.3009	+	33.5043i	−0.484585	+	1.06109i	0.496593	+	0.867984i	$0.334584\pi$
$997$	−15.3009	+	33.5043i	−0.484585	+	1.06109i	−0.981177	+	0.193108i	$0.938143\pi$
$998$	34.6572	−	39.9965i	1.09705	−	1.26607i
$999$	−6.08737	+	3.91211i	−0.192596	+	0.123774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.o.399.2		20
23.2	even	11	inner	529.2.c.o.170.2		20
23.3	even	11	inner	529.2.c.o.118.2		20
23.4	even	11	inner	529.2.c.o.266.2		20
23.5	odd	22		529.2.c.n.177.2		20
23.6	even	11	inner	529.2.c.o.334.1		20
23.7	odd	22		529.2.a.a.1.1		2
23.8	even	11	inner	529.2.c.o.466.1		20
23.9	even	11	inner	529.2.c.o.487.1		20
23.10	odd	22		529.2.c.n.501.2		20
23.11	odd	22		529.2.c.n.255.1		20
23.12	even	11	inner	529.2.c.o.255.1		20
23.13	even	11	inner	529.2.c.o.501.2		20
23.14	odd	22		529.2.c.n.487.1		20
23.15	odd	22		529.2.c.n.466.1		20
23.16	even	11		23.2.a.a.1.1	✓	2
23.17	odd	22		529.2.c.n.334.1		20
23.18	even	11	inner	529.2.c.o.177.2		20
23.19	odd	22		529.2.c.n.266.2		20
23.20	odd	22		529.2.c.n.118.2		20
23.21	odd	22		529.2.c.n.170.2		20
23.22	odd	2		529.2.c.n.399.2		20
69.53	even	22		4761.2.a.w.1.2		2
69.62	odd	22		207.2.a.d.1.2		2
92.7	even	22		8464.2.a.bb.1.1		2
92.39	odd	22		368.2.a.h.1.1		2
115.39	even	22		575.2.a.f.1.2		2
115.62	odd	44		575.2.b.d.24.1		4
115.108	odd	44		575.2.b.d.24.4		4
161.62	odd	22		1127.2.a.c.1.1		2
184.85	even	22		1472.2.a.t.1.1		2
184.131	odd	22		1472.2.a.s.1.2		2
253.131	odd	22		2783.2.a.c.1.2		2
276.131	even	22		3312.2.a.ba.1.2		2
299.246	even	22		3887.2.a.i.1.2		2
345.269	odd	22		5175.2.a.be.1.1		2
391.16	even	22		6647.2.a.b.1.1		2
437.246	odd	22		8303.2.a.e.1.2		2
460.39	odd	22		9200.2.a.bt.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.a.a.1.1	✓	2	23.16	even	11
207.2.a.d.1.2		2	69.62	odd	22
368.2.a.h.1.1		2	92.39	odd	22
529.2.a.a.1.1		2	23.7	odd	22
529.2.c.n.118.2		20	23.20	odd	22
529.2.c.n.170.2		20	23.21	odd	22
529.2.c.n.177.2		20	23.5	odd	22
529.2.c.n.255.1		20	23.11	odd	22
529.2.c.n.266.2		20	23.19	odd	22
529.2.c.n.334.1		20	23.17	odd	22
529.2.c.n.399.2		20	23.22	odd	2
529.2.c.n.466.1		20	23.15	odd	22
529.2.c.n.487.1		20	23.14	odd	22
529.2.c.n.501.2		20	23.10	odd	22
529.2.c.o.118.2		20	23.3	even	11	inner
529.2.c.o.170.2		20	23.2	even	11	inner
529.2.c.o.177.2		20	23.18	even	11	inner
529.2.c.o.255.1		20	23.12	even	11	inner
529.2.c.o.266.2		20	23.4	even	11	inner
529.2.c.o.334.1		20	23.6	even	11	inner
529.2.c.o.399.2		20	1.1	even	1	trivial
529.2.c.o.466.1		20	23.8	even	11	inner
529.2.c.o.487.1		20	23.9	even	11	inner
529.2.c.o.501.2		20	23.13	even	11	inner
575.2.a.f.1.2		2	115.39	even	22
575.2.b.d.24.1		4	115.62	odd	44
575.2.b.d.24.4		4	115.108	odd	44
1127.2.a.c.1.1		2	161.62	odd	22
1472.2.a.s.1.2		2	184.131	odd	22
1472.2.a.t.1.1		2	184.85	even	22
2783.2.a.c.1.2		2	253.131	odd	22
3312.2.a.ba.1.2		2	276.131	even	22
3887.2.a.i.1.2		2	299.246	even	22
4761.2.a.w.1.2		2	69.53	even	22
5175.2.a.be.1.1		2	345.269	odd	22
6647.2.a.b.1.1		2	391.16	even	22
8303.2.a.e.1.2		2	437.246	odd	22
8464.2.a.bb.1.1		2	92.7	even	22
9200.2.a.bt.1.2		2	460.39	odd	22

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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	529.c (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.230270 - 1.60156i) q^{2} +(0.928896 + 2.03400i) q^{3} +(-0.592999 - 0.174120i) q^{4} +(2.11917 + 2.44566i) q^{5} +(3.47148 - 1.01932i) q^{6} +(-1.03985 - 0.668269i) q^{7} +(0.928896 - 2.03400i) q^{8} +(-1.30972 + 1.51150i) q^{9} +O(q^{10})\)	\(q+(0.230270 - 1.60156i) q^{2} +(0.928896 + 2.03400i) q^{3} +(-0.592999 - 0.174120i) q^{4} +(2.11917 + 2.44566i) q^{5} +(3.47148 - 1.01932i) q^{6} +(-1.03985 - 0.668269i) q^{7} +(0.928896 - 2.03400i) q^{8} +(-1.30972 + 1.51150i) q^{9} +(4.40486 - 2.83083i) q^{10} +(0.108719 + 0.756156i) q^{11} +(-0.196674 - 1.36790i) q^{12} +(2.52376 - 1.62192i) q^{13} +(-1.30972 + 1.51150i) q^{14} +(-3.00597 + 6.58216i) q^{15} +(-4.08353 - 2.62433i) q^{16} +(-5.02397 + 1.47517i) q^{17} +(2.11917 + 2.44566i) q^{18} +(1.91899 + 0.563465i) q^{19} +(-0.830830 - 1.81926i) q^{20} +(0.393349 - 2.73580i) q^{21} +1.23607 q^{22} +5.00000 q^{24} +(-0.778766 + 5.41644i) q^{25} +(-2.01647 - 4.41545i) q^{26} +(2.14549 + 0.629973i) q^{27} +(0.500269 + 0.577341i) q^{28} +(2.87848 - 0.845198i) q^{29} +(9.84957 + 6.32993i) q^{30} +(-2.78669 + 6.10200i) q^{31} +(-2.21472 + 2.55592i) q^{32} +(-1.43703 + 0.923525i) q^{33} +(1.20571 + 8.38590i) q^{34} +(-0.569259 - 3.95929i) q^{35} +(1.03985 - 0.668269i) q^{36} +(-2.11917 + 2.44566i) q^{37} +(1.34431 - 2.94363i) q^{38} +(5.64330 + 3.62673i) q^{39} +(6.94296 - 2.03864i) q^{40} +(-3.58349 - 4.13556i) q^{41} +(-4.29098 - 1.25995i) q^{42} +(0.0671920 - 0.467330i) q^{44} -6.47214 q^{45} +2.23607 q^{47} +(1.54470 - 10.7436i) q^{48} +(-2.27321 - 4.97763i) q^{49} +(8.49545 + 2.49449i) q^{50} +(-7.66724 - 8.84847i) q^{51} +(-1.77900 + 0.522361i) q^{52} +(-7.12721 - 4.58038i) q^{53} +(1.50299 - 3.29108i) q^{54} +(-1.61890 + 1.86832i) q^{55} +(-2.32517 + 1.49429i) q^{56} +(0.636451 + 4.42662i) q^{57} +(-0.690811 - 4.80469i) q^{58} +(-2.07969 + 1.33654i) q^{59} +(2.92863 - 3.37981i) q^{60} +(4.54641 - 9.95526i) q^{61} +(9.13105 + 5.86817i) q^{62} +(2.37200 - 0.696481i) q^{63} +(-2.77403 - 3.20141i) q^{64} +(9.31495 + 2.73512i) q^{65} +(1.14818 + 2.51416i) q^{66} +(1.02980 - 7.16242i) q^{67} +3.23607 q^{68} -6.47214 q^{70} +(-1.10492 + 7.68491i) q^{71} +(1.85779 + 4.06800i) q^{72} +(-14.8454 - 4.35900i) q^{73} +(3.42890 + 3.95716i) q^{74} +(-11.7404 + 3.44730i) q^{75} +(-1.03985 - 0.668269i) q^{76} +(0.392265 - 0.858940i) q^{77} +(7.10793 - 8.20298i) q^{78} +(5.84189 - 3.75436i) q^{79} +(-2.23551 - 15.5483i) q^{80} +(1.56546 + 10.8880i) q^{81} +(-7.44854 + 4.78689i) q^{82} +(8.66778 - 10.0032i) q^{83} +(-0.709614 + 1.55384i) q^{84} +(-14.2544 - 9.16077i) q^{85} +(4.39294 + 5.06972i) q^{87} +(1.63901 + 0.481257i) q^{88} +(-0.634698 - 1.38979i) q^{89} +(-1.49034 + 10.3655i) q^{90} -3.70820 q^{91} -15.0000 q^{93} +(0.514900 - 3.58121i) q^{94} +(2.68862 + 5.88726i) q^{95} +(-7.25598 - 2.13055i) q^{96} +(-2.81053 - 3.24352i) q^{97} +(-8.49545 + 2.49449i) q^{98} +(-1.28532 - 0.826026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q + q^2 + q^4 + 2 * q^5 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{11} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 10 q^{15} + 3 q^{16} - 6 q^{17} + 2 q^{18} + 4 q^{19} + 4 q^{20} + 10 q^{21} - 20 q^{22} + 100 q^{24} - 2 q^{25} + 3 q^{26} + 6 q^{28} + 6 q^{29} - 10 q^{30} - 9 q^{32} - 10 q^{33} + 8 q^{34} - 8 q^{35} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 10 q^{40} - 2 q^{41} - 8 q^{44} - 40 q^{45} + 15 q^{48} + 2 q^{49} + 11 q^{50} - 10 q^{51} + 3 q^{52} + 8 q^{53} - 5 q^{54} + 4 q^{55} + 10 q^{56} - 3 q^{58} - 4 q^{59} - 4 q^{61} - 15 q^{62} - 4 q^{63} - 4 q^{64} + 6 q^{65} - 10 q^{66} + 10 q^{67} + 20 q^{68} - 40 q^{70} - 20 q^{71} - 22 q^{73} + 6 q^{74} - 20 q^{75} - 2 q^{76} + 16 q^{77} + 15 q^{78} + 4 q^{79} - 18 q^{80} + 22 q^{81} + 11 q^{82} + 22 q^{83} - 10 q^{84} + 16 q^{85} - 10 q^{88} + 12 q^{89} - 12 q^{90} + 60 q^{91} - 300 q^{93} + 5 q^{94} - 4 q^{95} + 5 q^{96} - 22 q^{97} - 11 q^{98} + 12 q^{99}+O(q^{100}) \) 20 * q + q^2 + q^4 + 2 * q^5 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^11 - 5 * q^12 - 6 * q^13 - 4 * q^14 + 10 * q^15 + 3 * q^16 - 6 * q^17 + 2 * q^18 + 4 * q^19 + 4 * q^20 + 10 * q^21 - 20 * q^22 + 100 * q^24 - 2 * q^25 + 3 * q^26 + 6 * q^28 + 6 * q^29 - 10 * q^30 - 9 * q^32 - 10 * q^33 + 8 * q^34 - 8 * q^35 + 2 * q^36 - 2 * q^37 - 2 * q^38 + 10 * q^40 - 2 * q^41 - 8 * q^44 - 40 * q^45 + 15 * q^48 + 2 * q^49 + 11 * q^50 - 10 * q^51 + 3 * q^52 + 8 * q^53 - 5 * q^54 + 4 * q^55 + 10 * q^56 - 3 * q^58 - 4 * q^59 - 4 * q^61 - 15 * q^62 - 4 * q^63 - 4 * q^64 + 6 * q^65 - 10 * q^66 + 10 * q^67 + 20 * q^68 - 40 * q^70 - 20 * q^71 - 22 * q^73 + 6 * q^74 - 20 * q^75 - 2 * q^76 + 16 * q^77 + 15 * q^78 + 4 * q^79 - 18 * q^80 + 22 * q^81 + 11 * q^82 + 22 * q^83 - 10 * q^84 + 16 * q^85 - 10 * q^88 + 12 * q^89 - 12 * q^90 + 60 * q^91 - 300 * q^93 + 5 * q^94 - 4 * q^95 + 5 * q^96 - 22 * q^97 - 11 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more