LMFDB - Embedded newform 507.2.p.b.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			64.3
Character	$\chi$	$=$	507.64
Dual form			507.2.p.b.103.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10986 - 0.256183i) q^{2} +(0.748511 - 0.663123i) q^{3} +(2.44400 + 0.602391i) q^{4} +(1.00545 + 1.91572i) q^{5} +(-1.74913 + 1.20734i) q^{6} +(-2.58799 - 0.981496i) q^{7} +(-1.02769 - 0.389750i) q^{8} +(0.120537 - 0.992709i) q^{9} +O(q^{10})$	\(q+(-2.10986 - 0.256183i) q^{2} +(0.748511 - 0.663123i) q^{3} +(2.44400 + 0.602391i) q^{4} +(1.00545 + 1.91572i) q^{5} +(-1.74913 + 1.20734i) q^{6} +(-2.58799 - 0.981496i) q^{7} +(-1.02769 - 0.389750i) q^{8} +(0.120537 - 0.992709i) q^{9} +(-1.63057 - 4.29947i) q^{10} +(-1.16415 + 0.141354i) q^{11} +(2.22882 - 1.16977i) q^{12} +(-3.10234 - 1.83725i) q^{13} +(5.20886 + 2.73382i) q^{14} +(2.02294 + 0.767200i) q^{15} +(-2.38921 - 1.25395i) q^{16} +(1.86667 - 4.92200i) q^{17} +(-0.508631 + 2.06360i) q^{18} -3.30417i q^{19} +(1.30330 + 5.28768i) q^{20} +(-2.58799 + 0.981496i) q^{21} +2.49241 q^{22} +8.27952 q^{23} +(-1.02769 + 0.389750i) q^{24} +(0.181276 - 0.262624i) q^{25} +(6.07483 + 4.67111i) q^{26} +(-0.568065 - 0.822984i) q^{27} +(-5.73380 - 3.95776i) q^{28} +(-0.268690 + 2.21286i) q^{29} +(-4.07158 - 2.13693i) q^{30} +(0.145578 - 0.100485i) q^{31} +(6.52876 + 4.50648i) q^{32} +(-0.777646 + 0.877781i) q^{33} +(-5.19934 + 9.90652i) q^{34} +(-0.721817 - 5.94470i) q^{35} +(0.892591 - 2.35357i) q^{36} +(6.25798 - 4.31957i) q^{37} +(-0.846475 + 6.97135i) q^{38} +(-3.54046 + 0.682033i) q^{39} +(-0.286632 - 2.36063i) q^{40} +(-7.94989 - 8.97357i) q^{41} +(5.71174 - 1.40782i) q^{42} +(1.65985 - 2.40470i) q^{43} +(-2.93034 - 0.355807i) q^{44} +(2.02294 - 0.767200i) q^{45} +(-17.4686 - 2.12107i) q^{46} +(2.15094 + 8.72672i) q^{47} +(-2.61987 + 0.645741i) q^{48} +(0.494790 + 0.438346i) q^{49} +(-0.449747 + 0.507660i) q^{50} +(-1.86667 - 4.92200i) q^{51} +(-6.47537 - 6.35905i) q^{52} +(3.45657 - 9.11423i) q^{53} +(0.987703 + 1.88191i) q^{54} +(-1.44129 - 2.08806i) q^{55} +(2.27710 + 2.01734i) q^{56} +(-2.19107 - 2.47321i) q^{57} +(1.13380 - 4.60000i) q^{58} +(-1.39645 - 2.66070i) q^{59} +(4.48191 + 3.09364i) q^{60} +(-3.99196 - 10.5259i) q^{61} +(-0.332892 + 0.174715i) q^{62} +(-1.28629 + 2.45082i) q^{63} +(-8.58090 - 7.60201i) q^{64} +(0.400411 - 7.79046i) q^{65} +(1.86560 - 1.65277i) q^{66} +(-0.292614 - 1.18718i) q^{67} +(7.52710 - 10.9049i) q^{68} +(6.19731 - 5.49033i) q^{69} +12.7274i q^{70} +(-0.171258 - 0.193310i) q^{71} +(-0.510782 + 0.973213i) q^{72} +(0.516559 - 0.0627216i) q^{73} +(-14.3101 + 7.51050i) q^{74} +(-0.0384647 - 0.316785i) q^{75} +(1.99041 - 8.07539i) q^{76} +(3.15155 + 0.776788i) q^{77} +(7.64459 - 0.531988i) q^{78} +(5.31272 - 1.30947i) q^{79} -5.83783i q^{80} +(-0.970942 - 0.239316i) q^{81} +(14.4743 + 20.9696i) q^{82} +(-6.40073 + 7.22493i) q^{83} +(-6.91629 + 0.839790i) q^{84} +(11.3060 - 1.37279i) q^{85} +(-4.11809 + 4.64837i) q^{86} +(1.26628 + 1.83453i) q^{87} +(1.25148 + 0.308461i) q^{88} +13.9011i q^{89} +(-4.46467 + 1.10044i) q^{90} +(6.22558 + 7.79972i) q^{91} +(20.2351 + 4.98751i) q^{92} +(0.0423326 - 0.171750i) q^{93} +(-2.30255 - 18.9632i) q^{94} +(6.32986 - 3.32217i) q^{95} +(7.87519 - 0.956221i) q^{96} +(1.45106 - 2.76477i) q^{97} +(-0.931641 - 1.05161i) q^{98} +1.17270i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{26}\right)$

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 $

$2$	−2.10986	−	0.256183i	−1.49190	−	0.181149i	−0.666416	−	0.745580i	$-0.732173\pi$
$2$	−2.10986	−	0.256183i	−1.49190	−	0.181149i	−0.825480	+	0.564431i	$0.809096\pi$
$3$	0.748511	−	0.663123i	0.432153	−	0.382854i
$3$	0.748511	−	0.663123i	0.432153	−	0.382854i
$4$	2.44400	+	0.602391i	1.22200	+	0.301196i
$5$	1.00545	+	1.91572i	0.449649	+	0.856734i	0.999766	+	0.0216466i	$0.00689086\pi$
$5$	1.00545	+	1.91572i	0.449649	+	0.856734i	−0.550117	+	0.835088i	$0.685417\pi$
$6$	−1.74913	+	1.20734i	−0.714081	+	0.492895i
$7$	−2.58799	−	0.981496i	−0.978169	−	0.370970i	−0.186860	−	0.982387i	$-0.559831\pi$
$7$	−2.58799	−	0.981496i	−0.978169	−	0.370970i	−0.791309	+	0.611416i	$0.790600\pi$
$8$	−1.02769	−	0.389750i	−0.363342	−	0.137797i
$9$	0.120537	−	0.992709i	0.0401789	−	0.330903i
$10$	−1.63057	−	4.29947i	−0.515633	−	1.35961i
$11$	−1.16415	+	0.141354i	−0.351005	+	0.0426197i	−0.294141	−	0.955762i	$-0.595033\pi$
$11$	−1.16415	+	0.141354i	−0.351005	+	0.0426197i	−0.0568646	+	0.998382i	$0.518110\pi$
$12$	2.22882	−	1.16977i	0.643404	−	0.337685i
$13$	−3.10234	−	1.83725i	−0.860435	−	0.509561i
$13$	−3.10234	−	1.83725i	−0.860435	−	0.509561i
$14$	5.20886	+	2.73382i	1.39213	+	0.730644i
$15$	2.02294	+	0.767200i	0.522321	+	0.198090i
$16$	−2.38921	−	1.25395i	−0.597303	−	0.313489i
$17$	1.86667	−	4.92200i	0.452733	−	1.19376i	−0.493349	−	0.869832i	$-0.664227\pi$
$17$	1.86667	−	4.92200i	0.452733	−	1.19376i	0.946082	−	0.323928i	$-0.105003\pi$
$18$	−0.508631	+	2.06360i	−0.119886	+	0.486395i
$19$		−	3.30417i		−	0.758030i	−0.925391	−	0.379015i	$-0.876263\pi$
$19$		−	3.30417i		−	0.758030i	0.925391	−	0.379015i	$-0.123737\pi$
$20$	1.30330	+	5.28768i	0.291426	+	1.18236i
$21$	−2.58799	+	0.981496i	−0.564746	+	0.214180i
$22$	2.49241			0.531384
$23$	8.27952			1.72640			0.863199	−	0.504863i	$-0.168457\pi$
$23$	8.27952			1.72640			0.863199	+	0.504863i	$0.168457\pi$
$24$	−1.02769	+	0.389750i	−0.209775	+	0.0795573i
$25$	0.181276	−	0.262624i	0.0362552	−	0.0525248i
$26$	6.07483	+	4.67111i	1.19137	+	0.916079i
$27$	−0.568065	−	0.822984i	−0.109324	−	0.158383i
$28$	−5.73380	−	3.95776i	−1.08359	−	0.747946i
$29$	−0.268690	+	2.21286i	−0.0498945	+	0.410918i	0.946267	+	0.323386i	$0.104821\pi$
$29$	−0.268690	+	2.21286i	−0.0498945	+	0.410918i	−0.996162	+	0.0875324i	$0.972102\pi$
$30$	−4.07158	−	2.13693i	−0.743365	−	0.390148i
$31$	0.145578	−	0.100485i	0.0261466	−	0.0180477i	−0.554920	−	0.831904i	$-0.687251\pi$
$31$	0.145578	−	0.100485i	0.0261466	−	0.0180477i	0.581066	+	0.813856i	$0.302636\pi$
$32$	6.52876	+	4.50648i	1.15413	+	0.796640i
$33$	−0.777646	+	0.877781i	−0.135371	+	0.152802i
$34$	−5.19934	+	9.90652i	−0.891680	+	1.69895i
$35$	−0.721817	−	5.94470i	−0.122009	−	1.00484i
$36$	0.892591	−	2.35357i	0.148765	−	0.392261i
$37$	6.25798	−	4.31957i	1.02881	−	0.710133i	0.0709784	−	0.997478i	$-0.477388\pi$
$37$	6.25798	−	4.31957i	1.02881	−	0.710133i	0.957827	+	0.287345i	$0.0927725\pi$
$38$	−0.846475	+	6.97135i	−0.137316	+	1.13090i
$39$	−3.54046	+	0.682033i	−0.566927	+	0.109213i
$40$	−0.286632	−	2.36063i	−0.0453205	−	0.373248i
$41$	−7.94989	−	8.97357i	−1.24156	−	1.40144i	−0.883960	−	0.467562i	$-0.845132\pi$
$41$	−7.94989	−	8.97357i	−1.24156	−	1.40144i	−0.357603	−	0.933874i	$-0.616406\pi$
$42$	5.71174	−	1.40782i	0.881341	−	0.217231i
$43$	1.65985	−	2.40470i	0.253124	−	0.366714i	−0.675736	−	0.737144i	$-0.736174\pi$
$43$	1.65985	−	2.40470i	0.253124	−	0.366714i	0.928861	+	0.370430i	$0.120790\pi$
$44$	−2.93034	−	0.355807i	−0.441765	−	0.0536400i
$45$	2.02294	−	0.767200i	0.301562	−	0.114367i
$46$	−17.4686	−	2.12107i	−2.57561	−	0.312735i
$47$	2.15094	+	8.72672i	0.313747	+	1.27292i	0.890116	+	0.455733i	$0.150623\pi$
$47$	2.15094	+	8.72672i	0.313747	+	1.27292i	−0.576369	+	0.817189i	$0.695531\pi$
$48$	−2.61987	+	0.645741i	−0.378146	+	0.0932047i
$49$	0.494790	+	0.438346i	0.0706843	+	0.0626208i
$50$	−0.449747	+	0.507660i	−0.0636039	+	0.0717939i
$51$	−1.86667	−	4.92200i	−0.261386	−	0.689217i
$52$	−6.47537	−	6.35905i	−0.897973	−	0.881842i
$53$	3.45657	−	9.11423i	0.474797	−	1.25194i	−0.457166	−	0.889382i	$-0.651135\pi$
$53$	3.45657	−	9.11423i	0.474797	−	1.25194i	0.931962	−	0.362555i	$-0.118095\pi$
$54$	0.987703	+	1.88191i	0.134409	+	0.256096i
$55$	−1.44129	−	2.08806i	−0.194343	−	0.281554i
$56$	2.27710	+	2.01734i	0.304291	+	0.269578i
$57$	−2.19107	−	2.47321i	−0.290215	−	0.327585i
$58$	1.13380	−	4.60000i	0.148875	−	0.604009i
$59$	−1.39645	−	2.66070i	−0.181802	−	0.346394i	0.777451	−	0.628943i	$-0.216512\pi$
$59$	−1.39645	−	2.66070i	−0.181802	−	0.346394i	−0.959253	+	0.282549i	$0.908820\pi$
$60$	4.48191	+	3.09364i	0.578612	+	0.399387i
$61$	−3.99196	−	10.5259i	−0.511117	−	1.34771i	−0.903770	−	0.428019i	$-0.859212\pi$
$61$	−3.99196	−	10.5259i	−0.511117	−	1.34771i	0.392652	−	0.919687i	$-0.371558\pi$
$62$	−0.332892	+	0.174715i	−0.0422773	+	0.0221888i
$63$	−1.28629	+	2.45082i	−0.162057	+	0.308774i
$64$	−8.58090	−	7.60201i	−1.07261	−	0.950251i
$65$	0.400411	−	7.79046i	0.0496649	−	0.966287i
$66$	1.86560	−	1.65277i	0.229639	−	0.203443i
$67$	−0.292614	−	1.18718i	−0.0357485	−	0.145037i	0.950356	−	0.311166i	$-0.100719\pi$
$67$	−0.292614	−	1.18718i	−0.0357485	−	0.145037i	−0.986104	+	0.166129i	$0.946873\pi$
$68$	7.52710	−	10.9049i	0.912795	−	1.32241i
$69$	6.19731	−	5.49033i	0.746068	−	0.660959i
$70$			12.7274i			1.52122i
$71$	−0.171258	−	0.193310i	−0.0203245	−	0.0229417i	0.738261	−	0.674516i	$-0.235647\pi$
$71$	−0.171258	−	0.193310i	−0.0203245	−	0.0229417i	−0.758585	+	0.651574i	$0.774109\pi$
$72$	−0.510782	+	0.973213i	−0.0601962	+	0.114694i
$73$	0.516559	−	0.0627216i	0.0604587	−	0.00734101i	−0.0902514	−	0.995919i	$-0.528767\pi$
$73$	0.516559	−	0.0627216i	0.0604587	−	0.00734101i	0.150710	+	0.988578i	$0.451844\pi$
$74$	−14.3101	+	7.51050i	−1.66351	+	0.873078i
$75$	−0.0384647	−	0.316785i	−0.00444152	−	0.0365792i
$76$	1.99041	−	8.07539i	0.228315	−	0.926311i
$77$	3.15155	+	0.776788i	0.359153	+	0.0885233i
$78$	7.64459	−	0.531988i	0.865580	−	0.0602357i
$79$	5.31272	−	1.30947i	0.597728	−	0.147327i	0.0711674	−	0.997464i	$-0.477328\pi$
$79$	5.31272	−	1.30947i	0.597728	−	0.147327i	0.526560	+	0.850138i	$0.323481\pi$
$80$		−	5.83783i		−	0.652689i
$81$	−0.970942	−	0.239316i	−0.107882	−	0.0265906i
$82$	14.4743	+	20.9696i	1.59842	+	2.31571i
$83$	−6.40073	+	7.22493i	−0.702571	+	0.793039i	−0.986140	−	0.165913i	$-0.946943\pi$
$83$	−6.40073	+	7.22493i	−0.702571	+	0.793039i	0.283569	+	0.958952i	$0.408481\pi$
$84$	−6.91629	+	0.839790i	−0.754629	+	0.0916286i
$85$	11.3060	−	1.37279i	1.22631	−	0.148900i
$86$	−4.11809	+	4.64837i	−0.444065	+	0.501246i
$87$	1.26628	+	1.83453i	0.135760	+	0.196682i
$88$	1.25148	+	0.308461i	0.133408	+	0.0328820i
$89$			13.9011i			1.47352i	0.676156	+	0.736759i	$0.263645\pi$
$89$			13.9011i			1.47352i	−0.676156	+	0.736759i	$0.736355\pi$
$90$	−4.46467	+	1.10044i	−0.470617	+	0.115997i
$91$	6.22558	+	7.79972i	0.652618	+	0.817632i
$92$	20.2351	+	4.98751i	2.10966	+	0.519984i
$93$	0.0423326	−	0.171750i	0.00438969	−	0.0178097i
$94$	−2.30255	−	18.9632i	−0.237490	−	1.95590i
$95$	6.32986	−	3.32217i	0.649430	−	0.340847i
$96$	7.87519	−	0.956221i	0.803758	−	0.0975939i
$97$	1.45106	−	2.76477i	0.147333	−	0.280720i	−0.800594	−	0.599207i	$-0.795483\pi$
$97$	1.45106	−	2.76477i	0.147333	−	0.280720i	0.947927	+	0.318487i	$0.103175\pi$
$98$	−0.931641	−	1.05161i	−0.0941100	−	0.106228i
$99$			1.17270i			0.117861i
$100$	0.601241	−	0.532653i	0.0601241	−	0.0532653i
$101$	−4.00010	+	5.79514i	−0.398025	+	0.576638i	−0.969839	−	0.243744i	$-0.921624\pi$
$101$	−4.00010	+	5.79514i	−0.398025	+	0.576638i	0.571815	+	0.820383i	$0.306240\pi$
$102$	2.67747	+	10.8629i	0.265109	+	1.07559i
$103$	−10.7760	+	9.54670i	−1.06179	+	0.940664i	−0.998356	−	0.0573221i	$-0.981744\pi$
$103$	−10.7760	+	9.54670i	−1.06179	+	0.940664i	−0.0634344	+	0.997986i	$0.520205\pi$
$104$	2.47216	+	3.09725i	0.242416	+	0.303710i
$105$	−4.48235	−	3.97102i	−0.437433	−	0.387532i
$106$	−9.62780	+	18.3442i	−0.935135	+	1.78175i
$107$	−2.75823	+	1.44763i	−0.266648	+	0.139948i	−0.592749	−	0.805387i	$-0.701957\pi$
$107$	−2.75823	+	1.44763i	−0.266648	+	0.139948i	0.326101	+	0.945335i	$0.394265\pi$
$108$	−0.892591	−	2.35357i	−0.0858896	−	0.226472i
$109$	−4.68110	−	3.23113i	−0.448368	−	0.309486i	0.322398	−	0.946604i	$-0.395511\pi$
$109$	−4.68110	−	3.23113i	−0.448368	−	0.309486i	−0.770766	+	0.637118i	$0.780126\pi$
$110$	2.50598	+	4.77475i	0.238936	+	0.455255i
$111$	1.81976	−	7.38306i	0.172724	−	0.700769i
$112$	4.95250	+	5.59022i	0.467968	+	0.528226i
$113$	−14.0481	−	12.4456i	−1.32154	−	1.17078i	−0.972297	−	0.233747i	$-0.924901\pi$
$113$	−14.0481	−	12.4456i	−1.32154	−	1.17078i	−0.349240	−	0.937033i	$-0.613560\pi$
$114$	3.98926	+	5.77944i	0.373629	+	0.541295i
$115$	8.32460	+	15.8612i	0.776273	+	1.47906i
$116$	−1.98969	+	5.24638i	−0.184738	+	0.487114i
$117$	−2.19780	+	2.85827i	−0.203187	+	0.264247i
$118$	2.26468	+	5.97146i	0.208480	+	0.549718i
$119$	−9.66184	+	10.9060i	−0.885699	+	0.999748i
$120$	−1.77993	−	1.57688i	−0.162485	−	0.143949i
$121$	−9.34509	+	2.30336i	−0.849554	+	0.209396i
$122$	5.72590	+	23.2309i	0.518399	+	2.10323i
$123$	−11.9012	−	1.44506i	−1.07309	−	0.130297i
$124$	0.416324	−	0.157891i	0.0373870	−	0.0141790i
$125$	11.4242	+	1.38715i	1.02181	+	0.124070i
$126$	3.34175	−	4.84135i	0.297706	−	0.431302i
$127$	13.4822	−	3.32306i	1.19635	−	0.294874i	0.409671	−	0.912234i	$-0.365644\pi$
$127$	13.4822	−	3.32306i	1.19635	−	0.294874i	0.786681	+	0.617359i	$0.211797\pi$
$128$	5.63584	+	6.36155i	0.498142	+	0.562287i
$129$	−0.352200	−	2.90063i	−0.0310095	−	0.255386i
$130$	−2.84060	+	16.3342i	−0.249137	+	1.43260i
$131$	−0.861320	+	7.09361i	−0.0752539	+	0.619771i	0.905475	+	0.424399i	$0.139515\pi$
$131$	−0.861320	+	7.09361i	−0.0752539	+	0.619771i	−0.980729	+	0.195372i	$0.937408\pi$
$132$	−2.42933	+	1.67685i	−0.211446	+	0.145951i
$133$	−3.24303	+	8.55117i	−0.281207	+	0.741481i
$134$	0.313239	+	2.57975i	0.0270597	+	0.222857i
$135$	1.00545	−	1.91572i	0.0865350	−	0.164879i
$136$	−3.83669	+	4.33073i	−0.328994	+	0.371357i
$137$	2.45617	+	1.69537i	0.209845	+	0.144845i	0.668352	−	0.743845i	$-0.267000\pi$
$137$	2.45617	+	1.69537i	0.209845	+	0.144845i	−0.458507	+	0.888691i	$0.651616\pi$
$138$	−14.4820	+	9.99619i	−1.23279	+	0.850932i
$139$	18.6506	+	9.78858i	1.58192	+	0.830257i	0.999853	+	0.0171172i	$0.00544884\pi$
$139$	18.6506	+	9.78858i	1.58192	+	0.830257i	0.582069	+	0.813140i	$0.302243\pi$
$140$	1.81692	−	14.9636i	0.153557	−	1.26466i
$141$	7.39689	+	5.10570i	0.622930	+	0.429978i
$142$	0.311807	+	0.451730i	0.0261663	+	0.0379084i
$143$	3.87130	+	1.70031i	0.323734	+	0.142187i
$144$	−1.53280	+	2.22064i	−0.127733	+	0.185054i
$145$	−4.50937	+	1.71018i	−0.374483	+	0.142023i
$146$	−1.10594			−0.0915279
$147$	0.661033			0.0545211
$148$	17.8966	−	6.78727i	1.47109	−	0.557910i
$149$	−3.70243	−	15.0213i	−0.303315	−	1.23060i	−0.902747	−	0.430171i	$-0.858453\pi$
$149$	−3.70243	−	15.0213i	−0.303315	−	1.23060i	0.599433	−	0.800425i	$-0.295393\pi$
$150$			0.678226i			0.0553769i
$151$	−3.43775	+	13.9475i	−0.279760	+	1.13503i	0.647936	+	0.761695i	$0.275632\pi$
$151$	−3.43775	+	13.9475i	−0.279760	+	1.13503i	−0.927696	+	0.373336i	$0.878214\pi$
$152$	−1.28780	+	3.39565i	−0.104454	+	0.275424i
$153$	−4.66111	−	2.44634i	−0.376828	−	0.197775i
$154$	−6.45034	−	2.44629i	−0.519783	−	0.197128i
$155$	0.338872	+	0.177854i	0.0272188	+	0.0142855i
$156$	−9.06372	−	0.465854i	−0.725678	−	0.0372982i
$157$	−0.667325	+	0.350239i	−0.0532583	+	0.0279521i	−0.491142	−	0.871079i	$-0.663420\pi$
$157$	−0.667325	+	0.350239i	−0.0532583	+	0.0279521i	0.437884	+	0.899032i	$0.355728\pi$
$158$	−11.5446	+	1.40176i	−0.918436	+	0.111518i
$159$	−3.45657	−	9.11423i	−0.274124	−	0.722806i
$160$	−2.06882	+	17.0383i	−0.163555	+	1.34699i
$161$	−21.4273	−	8.12631i	−1.68871	−	0.640443i
$162$	1.98724	+	0.753662i	0.156133	+	0.0592133i
$163$	16.0880	−	11.1047i	1.26011	−	0.869790i	0.264590	−	0.964361i	$-0.414763\pi$
$163$	16.0880	−	11.1047i	1.26011	−	0.869790i	0.995518	+	0.0945709i	$0.0301479\pi$
$164$	−14.0239	−	26.7203i	−1.09508	−	2.08651i
$165$	−2.46346	−	0.607188i	−0.191780	−	0.0472695i
$166$	15.3556	−	13.6038i	1.19182	−	1.05586i
$167$	13.5743	+	1.64821i	1.05041	+	0.127543i	0.627489	−	0.778625i	$-0.284083\pi$
$167$	13.5743	+	1.64821i	1.05041	+	0.127543i	0.422919	+	0.906168i	$0.361006\pi$
$168$	3.04218			0.234709
$169$	6.24904	+	11.3995i	0.480695	+	0.876888i
$170$	−24.2057			−1.85649
$171$	−3.28008	−	0.398274i	−0.250834	−	0.0304568i
$172$	5.50524	−	4.87721i	0.419770	−	0.371884i
$173$	19.3183	+	4.76152i	1.46874	+	0.362012i	0.890923	−	0.454155i	$-0.150059\pi$
$173$	19.3183	+	4.76152i	1.46874	+	0.362012i	0.577817	+	0.816166i	$0.303905\pi$
$174$	−2.20170	−	4.19499i	−0.166911	−	0.318022i
$175$	−0.726905	+	0.501746i	−0.0549489	+	0.0379285i
$176$	2.95866	+	1.12207i	0.223017	+	0.0845792i
$177$	−2.80963	−	1.06555i	−0.211185	−	0.0800917i
$178$	3.56124	−	29.3295i	0.266926	−	2.19834i
$179$	1.22717	+	3.23579i	0.0917234	+	0.241855i	0.973025	−	0.230699i	$-0.0741014\pi$
$179$	1.22717	+	3.23579i	0.0917234	+	0.241855i	−0.881302	+	0.472554i	$0.843332\pi$
$180$	5.40622	−	0.656434i	0.402956	−	0.0489277i
$181$	3.97698	−	2.08728i	0.295606	−	0.155146i	−0.310400	−	0.950606i	$-0.600463\pi$
$181$	3.97698	−	2.08728i	0.295606	−	0.155146i	0.606006	+	0.795460i	$0.292771\pi$
$182$	−11.1369	−	18.0512i	−0.825526	−	1.33804i
$183$	−9.96800	−	5.23161i	−0.736856	−	0.386732i
$184$	−8.50874	−	3.22694i	−0.627273	−	0.237893i
$185$	14.5671	+	7.64542i	1.07100	+	0.562103i
$186$	−0.133316	+	0.351524i	−0.00977517	+	0.0257750i
$187$	−1.47734	+	5.99381i	−0.108034	+	0.438311i
$188$			22.6238i			1.65001i
$189$	0.662392	+	2.68743i	0.0481819	+	0.195482i
$190$	−14.2062	+	5.38770i	−1.03063	+	0.390865i
$191$	−1.77063			−0.128118			−0.0640591	−	0.997946i	$-0.520405\pi$
$191$	−1.77063			−0.128118			−0.0640591	+	0.997946i	$0.520405\pi$
$192$	−11.4640			−0.827340
$193$	−12.8709	+	4.88130i	−0.926470	+	0.351364i	−0.771262	−	0.636518i	$-0.780374\pi$
$193$	−12.8709	+	4.88130i	−0.926470	+	0.351364i	−0.155208	+	0.987882i	$0.549605\pi$
$194$	−3.76983	+	5.46154i	−0.270658	+	0.392116i
$195$	−4.86632	−	6.09676i	−0.348484	−	0.436598i
$196$	0.945210	+	1.36937i	0.0675150	+	0.0978124i
$197$	−5.04816	−	3.48449i	−0.359666	−	0.248260i	0.374504	−	0.927225i	$-0.377813\pi$
$197$	−5.04816	−	3.48449i	−0.359666	−	0.248260i	−0.734170	+	0.678966i	$0.762428\pi$
$198$	0.300427	−	2.47424i	0.0213504	−	0.175837i
$199$	−13.7242	−	7.20304i	−0.972885	−	0.510610i	−0.0981296	−	0.995174i	$-0.531286\pi$
$199$	−13.7242	−	7.20304i	−0.972885	−	0.510610i	−0.874756	+	0.484564i	$0.838978\pi$
$200$	−0.288652	+	0.199242i	−0.0204108	+	0.0140886i
$201$	−1.00627	−	0.694580i	−0.0709770	−	0.0489919i
$202$	9.92427	−	11.2022i	0.698269	−	0.788183i
$203$	2.86728	−	5.46315i	0.201244	−	0.383438i
$204$	−1.59716	−	13.1538i	−0.111824	−	0.920951i
$205$	9.19763	−	24.2522i	0.642390	−	1.69384i
$206$	25.1815	−	17.3816i	1.75448	−	1.21103i
$207$	0.997985	−	8.21915i	0.0693648	−	0.571270i
$208$	5.10832	+	8.27977i	0.354198	+	0.574098i
$209$	0.467057	+	3.84656i	0.0323070	+	0.266072i
$210$	8.43983	+	9.52659i	0.582403	+	0.657397i
$211$	6.06356	−	1.49453i	0.417432	−	0.102888i	−0.0250048	−	0.999687i	$-0.507960\pi$
$211$	6.06356	−	1.49453i	0.417432	−	0.102888i	0.442437	+	0.896799i	$0.354114\pi$
$212$	13.9382	−	20.1930i	0.957279	−	1.38686i
$213$	−0.256376	−	0.0311297i	−0.0175666	−	0.00213297i
$214$	6.19033	−	2.34768i	0.423162	−	0.160484i
$215$	6.27562	+	0.761998i	0.427994	+	0.0519678i
$216$	0.263034	+	1.06717i	0.0178972	+	0.0726118i
$217$	−0.475380	+	0.117171i	−0.0322709	+	0.00795407i
$218$	9.04870	+	8.01645i	0.612855	+	0.542942i
$219$	0.345058	−	0.389490i	0.0233169	−	0.0263193i
$220$	−2.26467	−	5.97144i	−0.152684	−	0.402594i
$221$	−14.8340	+	11.8402i	−0.997840	+	0.796457i
$222$	−5.73086	+	15.1110i	−0.384630	+	1.01419i
$223$	−11.1236	−	21.1942i	−0.744891	−	1.41927i	−0.902021	−	0.431693i	$-0.857916\pi$
$223$	−11.1236	−	21.1942i	−0.744891	−	1.41927i	0.157130	−	0.987578i	$-0.449776\pi$
$224$	−12.4733	−	18.0707i	−0.833406	−	1.20740i
$225$	−0.238859	−	0.211610i	−0.0159239	−	0.0141073i
$226$	26.4513	+	29.8573i	1.75951	+	1.98608i
$227$	−5.73065	+	23.2502i	−0.380357	+	1.54317i	0.399216	+	0.916857i	$0.369282\pi$
$227$	−5.73065	+	23.2502i	−0.380357	+	1.54317i	−0.779573	+	0.626312i	$0.784564\pi$
$228$	−3.86514	−	7.36440i	−0.255975	−	0.487720i
$229$	−0.868662	−	0.599594i	−0.0574028	−	0.0396223i	0.539018	−	0.842294i	$-0.318796\pi$
$229$	−0.868662	−	0.599594i	−0.0574028	−	0.0396223i	−0.596421	+	0.802672i	$0.703411\pi$
$230$	−13.5004	−	35.5975i	−0.890188	−	2.34723i
$231$	2.87408	−	1.50843i	0.189100	−	0.0992476i
$232$	1.13859	−	2.16941i	0.0747522	−	0.142428i
$233$	14.9490	+	13.2437i	0.979344	+	0.867623i	0.991209	−	0.132306i	$-0.0422382\pi$
$233$	14.9490	+	13.2437i	0.979344	+	0.867623i	−0.0118646	+	0.999930i	$0.503777\pi$
$234$	5.36929	−	5.46750i	0.351001	−	0.357422i
$235$	−14.5553	+	12.8948i	−0.949480	+	0.841166i
$236$	−1.81012	−	7.34396i	−0.117829	−	0.478051i
$237$	3.10829	−	4.50314i	0.201905	−	0.292510i
$238$	23.1791	−	20.5348i	1.50247	−	1.33108i
$239$		−	22.0316i		−	1.42510i	−0.701619	−	0.712552i	$-0.747539\pi$
$239$		−	22.0316i		−	1.42510i	0.701619	−	0.712552i	$-0.252461\pi$
$240$	−3.87120	−	4.36968i	−0.249885	−	0.282062i
$241$	−5.91347	+	11.2672i	−0.380920	+	0.725783i	−0.998137	−	0.0610102i	$-0.980568\pi$
$241$	−5.91347	+	11.2672i	−0.380920	+	0.725783i	0.617217	+	0.786793i	$0.288260\pi$
$242$	20.3069	−	2.46571i	1.30538	−	0.158502i
$243$	−0.885456	+	0.464723i	−0.0568020	+	0.0298120i
$244$	−3.41561	−	28.1300i	−0.218662	−	1.80084i
$245$	−0.342262	+	1.38861i	−0.0218663	+	0.0887150i
$246$	24.7396	+	6.09776i	1.57734	+	0.388779i
$247$	−6.07059	+	10.2507i	−0.386262	+	0.652235i
$248$	−0.188772	+	0.0465282i	−0.0119871	+	0.00295455i
$249$			9.65240i			0.611696i
$250$	−23.7481	−	5.85337i	−1.50196	−	0.370200i
$251$	1.67548	+	2.42736i	0.105756	+	0.153213i	0.872288	−	0.488992i	$-0.162635\pi$
$251$	1.67548	+	2.42736i	0.105756	+	0.153213i	−0.766533	+	0.642205i	$0.778020\pi$
$252$	−4.62003	+	5.21494i	−0.291035	+	0.328510i
$253$	−9.63862	+	1.17034i	−0.605975	+	0.0735787i
$254$	−29.2969	+	3.55729i	−1.83825	+	0.223204i
$255$	7.55232	−	8.52480i	0.472944	−	0.533844i
$256$	2.76343	+	4.00352i	0.172714	+	0.250220i
$257$	11.9980	+	2.95723i	0.748412	+	0.184467i	0.595034	−	0.803701i	$-0.297139\pi$
$257$	11.9980	+	2.95723i	0.748412	+	0.184467i	0.153378	+	0.988168i	$0.450985\pi$
$258$			6.21015i			0.386627i
$259$	−20.4352	+	5.03683i	−1.26978	+	0.312974i
$260$	5.67151	−	18.7987i	0.351732	−	1.16584i
$261$	2.16434	+	0.533462i	0.133969	+	0.0330205i
$262$	3.63453	−	14.7459i	0.224542	−	0.911003i
$263$	−0.358258	−	2.95052i	−0.0220911	−	0.181937i	0.977487	−	0.210998i	$-0.0676713\pi$
$263$	−0.358258	−	2.95052i	−0.0220911	−	0.181937i	−0.999578	+	0.0290612i	$0.990748\pi$
$264$	1.14129	−	0.598995i	0.0702416	−	0.0368656i
$265$	20.9357	−	2.54205i	1.28607	−	0.156157i
$266$	9.03302	−	17.2110i	0.553850	−	1.05527i
$267$	9.21816	+	10.4051i	0.564142	+	0.636785i
$268$		−	3.07774i		−	0.188003i
$269$	−18.5683	+	16.4500i	−1.13213	+	1.00298i	−0.132195	+	0.991224i	$0.542203\pi$
$269$	−18.5683	+	16.4500i	−1.13213	+	1.00298i	−0.999931	+	0.0117527i	$0.996259\pi$
$270$	−2.61212	+	3.78432i	−0.158969	+	0.230306i
$271$	−1.75415	−	7.11688i	−0.106557	−	0.432320i	0.893296	−	0.449469i	$-0.148387\pi$
$271$	−1.75415	−	7.11688i	−0.106557	−	0.432320i	−0.999853	+	0.0171498i	$0.994541\pi$
$272$	−10.6318	+	9.41897i	−0.644649	+	0.571109i
$273$	9.83208	+	1.70985i	0.595065	+	0.103485i
$274$	−4.74785	−	4.20623i	−0.286828	−	0.254108i
$275$	−0.173910	+	0.331358i	−0.0104872	+	0.0199817i
$276$	18.4535	−	9.68516i	1.11077	−	0.582978i
$277$	1.67418	+	4.41444i	0.100591	+	0.265238i	0.975859	−	0.218401i	$-0.0700840\pi$
$277$	1.67418	+	4.41444i	0.100591	+	0.265238i	−0.875268	+	0.483639i	$0.839315\pi$
$278$	−36.8425	−	25.4305i	−2.20966	−	1.52522i
$279$	−0.0822051	−	0.156629i	−0.00492149	−	0.00937711i
$280$	−1.57514	+	6.39061i	−0.0941328	+	0.381912i
$281$	−14.1964	−	16.0245i	−0.846888	−	0.955939i	0.152588	−	0.988290i	$-0.451239\pi$
$281$	−14.1964	−	16.0245i	−0.846888	−	0.955939i	−0.999477	+	0.0323508i	$0.989701\pi$
$282$	−14.2984	−	12.6673i	−0.851458	−	0.754326i
$283$	−13.7257	−	19.8851i	−0.815906	−	1.18204i	−0.980662	−	0.195710i	$-0.937299\pi$
$283$	−13.7257	−	19.8851i	−0.815906	−	1.18204i	0.164755	−	0.986334i	$-0.447317\pi$
$284$	−0.302105	−	0.575613i	−0.0179266	−	0.0341564i
$285$	2.53496	−	6.68415i	0.150158	−	0.395935i
$286$	−7.73231	−	4.57918i	−0.457221	−	0.270773i
$287$	11.7667	+	31.0263i	0.694568	+	1.83142i
$288$	5.26057	−	5.93796i	0.309982	−	0.349898i
$289$	−8.01692	−	7.10237i	−0.471583	−	0.417786i
$290$	9.95226	−	2.45301i	0.584417	−	0.144046i
$291$	−0.747245	−	3.03169i	−0.0438043	−	0.177721i
$292$	1.30025	+	0.157879i	0.0760915	+	0.00923918i
$293$	17.7379	−	6.72712i	1.03626	−	0.393002i	0.222950	−	0.974830i	$-0.428431\pi$
$293$	17.7379	−	6.72712i	1.03626	−	0.393002i	0.813312	+	0.581828i	$0.197662\pi$
$294$	−1.39469	−	0.169346i	−0.0813398	−	0.00987644i
$295$	3.69311	−	5.35039i	0.215021	−	0.311512i
$296$	−8.11479	+	2.00012i	−0.471663	+	0.116254i
$297$	0.777646	+	0.877781i	0.0451236	+	0.0509340i
$298$	3.96339	+	32.6414i	0.229593	+	1.89087i
$299$	−25.6859	−	15.2115i	−1.48545	−	0.879705i
$300$	0.0968210	−	0.797393i	0.00558996	−	0.0460375i
$301$	−6.65588	+	4.59422i	−0.383638	+	0.264807i
$302$	10.8263	−	28.5466i	0.622983	−	1.64267i
$303$	0.848774	+	6.99028i	0.0487608	+	0.401581i
$304$	−4.14328	+	7.89437i	−0.237634	+	0.452773i
$305$	16.1510	−	18.2307i	0.924803	−	1.04389i
$306$	9.20758	+	6.35553i	0.526362	+	0.363321i
$307$	0.277789	−	0.191744i	0.0158543	−	0.0109434i	−0.560111	−	0.828417i	$-0.689242\pi$
$307$	0.277789	−	0.191744i	0.0158543	−	0.0109434i	0.575966	+	0.817474i	$0.304626\pi$
$308$	7.23446	+	3.79694i	0.412222	+	0.216351i
$309$	−1.73532	+	14.2916i	−0.0987187	+	0.813021i
$310$	−0.669409	−	0.462060i	−0.0380199	−	0.0262432i
$311$	8.11870	+	11.7620i	0.460369	+	0.666960i	0.982577	−	0.185859i	$-0.0595066\pi$
$311$	8.11870	+	11.7620i	0.460369	+	0.666960i	−0.522207	+	0.852819i	$0.674891\pi$
$312$	3.90430	+	0.678977i	0.221037	+	0.0384395i
$313$	−6.61769	+	9.58738i	−0.374054	+	0.541911i	−0.964128	−	0.265439i	$-0.914483\pi$
$313$	−6.61769	+	9.58738i	−0.374054	+	0.541911i	0.590074	+	0.807349i	$0.299099\pi$
$314$	1.49769	−	0.567998i	0.0845194	−	0.0320540i
$315$	−5.98836			−0.337406
$316$	13.7731			0.774797
$317$	23.2965	−	8.83520i	1.30846	−	0.496234i	0.400889	−	0.916127i	$-0.368701\pi$
$317$	23.2965	−	8.83520i	1.30846	−	0.496234i	0.907574	+	0.419892i	$0.137932\pi$
$318$	4.95797	+	20.1153i	0.278029	+	1.12801i
$319$		−	2.61409i		−	0.146361i
$320$	5.93567	−	24.0820i	0.331814	−	1.34622i
$321$	−1.10461	+	2.91261i	−0.0616531	+	0.162566i
$322$	43.1268	+	22.6347i	2.40336	+	1.26138i
$323$	−16.2631	−	6.16779i	−0.904905	−	0.343185i
$324$	−2.22882	−	1.16977i	−0.123823	−	0.0649874i
$325$	−1.04489	+	0.481699i	−0.0579598	+	0.0267199i
$326$	−36.7883	+	19.3080i	−2.03751	+	1.06937i
$327$	−5.64649	+	0.685607i	−0.312251	+	0.0379142i
$328$	4.67254	+	12.3205i	0.257998	+	0.680284i
$329$	2.99861	−	24.6958i	0.165319	−	1.36152i
$330$	5.04200	+	1.91218i	0.277553	+	0.105262i
$331$	−0.00653877	−	0.00247983i	−0.000359403	−	0.000136304i	0.354425	−	0.935084i	$-0.384677\pi$
$331$	−0.00653877	−	0.00247983i	−0.000359403	−	0.000136304i	−0.354785	+	0.934948i	$0.615446\pi$
$332$	−19.9956	+	13.8020i	−1.09740	+	0.757481i
$333$	−3.53376	−	6.73302i	−0.193649	−	0.368967i
$334$	−28.2176	−	6.95500i	−1.54400	−	0.380561i
$335$	1.98010	−	1.75421i	0.108184	−	0.0958429i
$336$	7.41401	+	0.900223i	0.404467	+	0.0491112i
$337$	4.73425			0.257891			0.128945	−	0.991652i	$-0.458841\pi$
$337$	4.73425			0.257891			0.128945	+	0.991652i	$0.458841\pi$
$338$	−10.2642	−	25.6523i	−0.558300	−	1.39530i
$339$	−18.7681			−1.01934
$340$	28.4587	+	3.45552i	1.54339	+	0.187402i
$341$	−0.155271	+	0.137558i	−0.00840840	+	0.00744919i
$342$	6.81849	+	1.68061i	0.368702	+	0.0908768i
$343$	8.15373	+	15.5356i	0.440260	+	0.838846i
$344$	−2.64303	+	1.82436i	−0.142503	+	0.0983626i
$345$	16.7490	+	6.35205i	0.901734	+	0.341983i
$346$	−39.5390	−	14.9952i	−2.12563	−	0.806145i
$347$	−3.53812	+	29.1390i	−0.189936	+	1.56427i	0.516374	+	0.856363i	$0.327281\pi$
$347$	−3.53812	+	29.1390i	−0.189936	+	1.56427i	−0.706310	+	0.707902i	$0.749642\pi$
$348$	1.98969	+	5.24638i	0.106658	+	0.281235i
$349$	−0.563669	+	0.0684418i	−0.0301725	+	0.00366361i	−0.135609	−	0.990762i	$-0.543299\pi$
$349$	−0.563669	+	0.0684418i	−0.0301725	+	0.00366361i	0.105436	+	0.994426i	$0.466376\pi$
$350$	1.66221	−	0.872394i	0.0888487	−	0.0466314i
$351$	0.250305	+	3.59685i	0.0133603	+	0.191986i
$352$	−8.23748	−	4.32336i	−0.439059	−	0.230436i
$353$	−7.14347	−	2.70916i	−0.380209	−	0.144194i	0.157094	−	0.987584i	$-0.449787\pi$
$353$	−7.14347	−	2.70916i	−0.380209	−	0.144194i	−0.537303	+	0.843390i	$0.680557\pi$
$354$	5.65495	+	2.96795i	0.300557	+	0.157745i
$355$	0.198137	−	0.522444i	0.0105160	−	0.0277284i
$356$	−8.37392	+	33.9743i	−0.443817	+	1.80064i
$357$			14.5702i			0.771137i
$358$	−1.76021	−	7.14146i	−0.0930300	−	0.377438i
$359$	−0.901580	+	0.341924i	−0.0475836	+	0.0180461i	−0.378282	−	0.925690i	$-0.623485\pi$
$359$	−0.901580	+	0.341924i	−0.0475836	+	0.0180461i	0.330698	+	0.943737i	$0.392716\pi$
$360$	−2.37796			−0.125330
$361$	8.08243			0.425391
$362$	−8.92559	+	3.38503i	−0.469119	+	0.177913i
$363$	−5.46749	+	7.92103i	−0.286969	+	0.415746i
$364$	10.5168	+	22.8127i	0.551231	+	1.19571i
$365$	0.639529	+	0.926517i	0.0334745	+	0.0484961i
$366$	19.6908	+	13.5916i	1.02926	+	0.710444i
$367$	1.12167	−	9.23782i	0.0585509	−	0.482210i	−0.933709	−	0.358033i	$-0.883448\pi$
$367$	1.12167	−	9.23782i	0.0585509	−	0.482210i	0.992260	−	0.124178i	$-0.0396292\pi$
$368$	−19.7815	−	10.3821i	−1.03118	−	0.541206i
$369$	−9.86639	+	6.81028i	−0.513624	+	0.354529i
$370$	−28.7760	−	19.8626i	−1.49599	−	1.03261i
$371$	−17.8912	+	20.1949i	−0.928863	+	1.04847i
$372$	0.206922	−	0.394257i	0.0107284	−	0.0204412i
$373$	1.28951	+	10.6200i	0.0667681	+	0.549885i	0.987259	+	0.159121i	$0.0508660\pi$
$373$	1.28951	+	10.6200i	0.0667681	+	0.549885i	−0.920491	+	0.390764i	$0.872211\pi$
$374$	4.65250	−	12.2676i	0.240575	−	0.634345i
$375$	9.47097	−	6.53734i	0.489079	−	0.337587i
$376$	1.19074	−	9.80665i	0.0614079	−	0.505739i
$377$	4.89915	−	6.37140i	0.252319	−	0.328144i
$378$	−0.709079	−	5.83979i	−0.0364711	−	0.300367i
$379$	9.15036	+	10.3286i	0.470023	+	0.530546i	0.934939	−	0.354809i	$-0.115454\pi$
$379$	9.15036	+	10.3286i	0.470023	+	0.530546i	−0.464916	+	0.885355i	$0.653916\pi$
$380$	17.4714	−	4.30632i	0.896264	−	0.220909i
$381$	7.88797	−	11.4277i	0.404113	−	0.585459i
$382$	3.73578	+	0.453606i	0.191139	+	0.0232085i
$383$	0.153570	−	0.0582415i	0.00784707	−	0.00297600i	−0.350678	−	0.936496i	$-0.614049\pi$
$383$	0.153570	−	0.0582415i	0.00784707	−	0.00297600i	0.358525	+	0.933520i	$0.383280\pi$
$384$	8.43697	+	1.02443i	0.430547	+	0.0522779i
$385$	1.68061	+	6.81850i	0.0856518	+	0.347503i
$386$	28.4064	−	7.00154i	1.44585	−	0.356369i
$387$	−2.18710	−	1.93760i	−0.111176	−	0.0984938i
$388$	5.21187	−	5.88299i	0.264593	−	0.298663i
$389$	7.17098	+	18.9083i	0.363583	+	0.958690i	0.984589	+	0.174884i	$0.0559550\pi$
$389$	7.17098	+	18.9083i	0.363583	+	0.958690i	−0.621006	+	0.783806i	$0.713276\pi$
$390$	8.70536	+	14.1100i	0.440813	+	0.714487i
$391$	15.4551	−	40.7517i	0.781598	−	2.06090i
$392$	−0.337643	−	0.643326i	−0.0170536	−	0.0324929i
$393$	4.05923	+	5.88080i	0.204761	+	0.296647i
$394$	9.75824	+	8.64505i	0.491613	+	0.435531i
$395$	7.85022	+	8.86107i	0.394987	+	0.445849i
$396$	−0.706426	+	2.86608i	−0.0354992	+	0.144026i
$397$	11.0601	+	21.0732i	0.555089	+	1.05763i	0.987745	+	0.156075i	$0.0498842\pi$
$397$	11.0601	+	21.0732i	0.555089	+	1.05763i	−0.432656	+	0.901559i	$0.642423\pi$
$398$	27.1109	+	18.7133i	1.35895	+	0.938014i
$399$	3.24303	+	8.55117i	0.162355	+	0.428094i
$400$	−0.762425	+	0.400152i	−0.0381212	+	0.0200076i
$401$	3.58928	−	6.83881i	0.179240	−	0.341514i	−0.779215	−	0.626757i	$-0.784382\pi$
$401$	3.58928	−	6.83881i	0.179240	−	0.341514i	0.958455	+	0.285243i	$0.0920743\pi$
$402$	1.94515	+	1.72326i	0.0970155	+	0.0859482i
$403$	−0.636249	+	0.0442766i	−0.0316938	+	0.00220557i
$404$	−13.2672	+	11.7537i	−0.660067	+	0.584768i
$405$	−0.517768	−	2.10067i	−0.0257281	−	0.104383i
$406$	−7.44914	+	10.7919i	−0.369694	+	0.535595i
$407$	−6.67466	+	5.91323i	−0.330850	+	0.293108i
$408$			5.78580i			0.286440i
$409$	3.75019	+	4.23309i	0.185435	+	0.209313i	0.833876	−	0.551952i	$-0.186117\pi$
$409$	3.75019	+	4.23309i	0.185435	+	0.209313i	−0.648441	+	0.761265i	$0.724579\pi$
$410$	−25.6187	+	48.8124i	−1.26522	+	2.41067i
$411$	2.96271	−	0.359738i	0.146140	−	0.0177446i
$412$	−32.0873	+	16.8407i	−1.58083	+	0.829684i
$413$	1.00252	+	8.25649i	0.0493307	+	0.406275i
$414$	−4.21122	+	17.0856i	−0.206970	+	0.839711i
$415$	−20.2765	−	4.99771i	−0.995334	−	0.245328i
$416$	−11.9749	−	25.9756i	−0.587119	−	1.27356i
$417$	20.4512	−	5.04077i	1.00150	−	0.246847i
$418$		−	8.23536i		−	0.402805i
$419$	27.1196	+	6.68437i	1.32488	+	0.326553i	0.837404	−	0.546585i	$-0.184072\pi$
$419$	27.1196	+	6.68437i	1.32488	+	0.326553i	0.487474	+	0.873138i	$0.337918\pi$
$420$	−8.56275	−	12.4053i	−0.417819	−	0.605316i
$421$	21.9273	−	24.7508i	1.06867	−	1.20628i	0.0910657	−	0.995845i	$-0.470973\pi$
$421$	21.9273	−	24.7508i	1.06867	−	1.20628i	0.977607	−	0.210438i	$-0.0674889\pi$
$422$	−13.1761	+	1.59987i	−0.641404	+	0.0778806i
$423$	8.92236	−	1.08337i	0.433820	−	0.0526753i
$424$	−7.10454	+	8.01937i	−0.345027	+	0.389455i
$425$	−0.954251	−	1.38247i	−0.0462880	−	0.0670597i
$426$	0.532944	+	0.131359i	0.0258212	+	0.00636435i
$427$			31.1591i			1.50789i
$428$	−7.61314	+	1.87647i	−0.367995	+	0.0907026i
$429$	4.02522	−	1.29445i	0.194340	−	0.0624965i
$430$	−13.0455	−	3.21542i	−0.629108	−	0.155061i
$431$	−8.90541	+	36.1306i	−0.428958	+	1.74035i	0.216243	+	0.976340i	$0.430620\pi$
$431$	−8.90541	+	36.1306i	−0.428958	+	1.74035i	−0.645201	+	0.764013i	$0.723227\pi$
$432$	0.325242	+	2.67861i	0.0156482	+	0.128875i
$433$	−33.4578	+	17.5600i	−1.60788	+	0.843879i	−0.609170	+	0.793040i	$0.708497\pi$
$433$	−33.4578	+	17.5600i	−1.60788	+	0.843879i	−0.998707	+	0.0508394i	$0.983810\pi$
$434$	1.03300	−	0.125429i	0.0495857	−	0.00602080i
$435$	−2.24125	+	4.27035i	−0.107460	+	0.204748i
$436$	−9.49419	−	10.7167i	−0.454689	−	0.513238i
$437$		−	27.3570i		−	1.30866i
$438$	−0.827805	+	0.733371i	−0.0395540	+	0.0350418i
$439$	9.02408	−	13.0736i	0.430696	−	0.623971i	−0.546208	−	0.837650i	$-0.683929\pi$
$439$	9.02408	−	13.0736i	0.430696	−	0.623971i	0.976904	+	0.213679i	$0.0685446\pi$
$440$	0.667366	+	2.70761i	0.0318154	+	0.129080i
$441$	0.494790	−	0.438346i	0.0235614	−	0.0208736i
$442$	34.3309	−	21.1809i	1.63295	−	1.00747i
$443$	−4.34262	−	3.84722i	−0.206324	−	0.182787i	0.553632	−	0.832761i	$-0.313241\pi$
$443$	−4.34262	−	3.84722i	−0.206324	−	0.182787i	−0.759956	+	0.649974i	$0.774780\pi$
$444$	8.89498	−	16.9480i	0.422137	−	0.804315i
$445$	−26.6306	+	13.9768i	−1.26241	+	0.662565i
$446$	18.0396	+	47.5666i	0.854200	+	2.25234i
$447$	−12.7323	−	8.78847i	−0.602217	−	0.415681i
$448$	14.7459	+	28.0961i	0.696680	+	1.32741i
$449$	5.76780	−	23.4009i	0.272199	−	1.10436i	−0.662541	−	0.749026i	$-0.730522\pi$
$449$	5.76780	−	23.4009i	0.272199	−	1.10436i	0.934741	−	0.355331i	$-0.115632\pi$
$450$	0.449747	+	0.507660i	0.0212013	+	0.0239313i
$451$	10.5233	+	9.32285i	0.495524	+	0.438996i
$452$	−26.8365	−	38.8794i	−1.26228	−	1.82873i
$453$	6.67571	+	12.7195i	0.313652	+	0.597614i
$454$	18.0472	−	47.5865i	0.846997	−	2.23335i
$455$	−8.68256	+	19.7686i	−0.407045	+	0.926768i
$456$	1.28780	+	3.39565i	0.0603068	+	0.159016i
$457$	17.9396	−	20.2496i	0.839178	−	0.947236i	−0.160027	−	0.987113i	$-0.551158\pi$
$457$	17.9396	−	20.2496i	0.839178	−	0.947236i	0.999205	+	0.0398766i	$0.0126965\pi$
$458$	1.67915	+	1.48760i	0.0784615	+	0.0695108i
$459$	−5.11111	+	1.25978i	−0.238566	+	0.0588013i
$460$	10.7907	+	43.7794i	0.503117	+	2.04123i
$461$	−20.4414	−	2.48203i	−0.952049	−	0.115600i	−0.370250	−	0.928932i	$-0.620728\pi$
$461$	−20.4414	−	2.48203i	−0.952049	−	0.115600i	−0.581799	+	0.813333i	$0.697651\pi$
$462$	−6.45034	+	2.44629i	−0.300097	+	0.113812i
$463$	2.71884	+	0.330127i	0.126355	+	0.0153423i	0.183470	−	0.983025i	$-0.441267\pi$
$463$	2.71884	+	0.330127i	0.126355	+	0.0153423i	−0.0571147	+	0.998368i	$0.518190\pi$
$464$	3.41679	−	4.95007i	0.158620	−	0.229801i
$465$	0.371588	−	0.0915882i	0.0172320	−	0.00424730i
$466$	−28.1476	−	31.7720i	−1.30391	−	1.47181i
$467$	0.327934	+	2.70078i	0.0151750	+	0.124977i	0.998328	−	0.0578091i	$-0.0184115\pi$
$467$	0.327934	+	2.70078i	0.0151750	+	0.124977i	−0.983153	+	0.182786i	$0.941488\pi$
$468$	−7.09321	+	5.66166i	−0.327884	+	0.261710i
$469$	−0.407931	+	3.35962i	−0.0188365	+	0.155133i
$470$	34.0130	−	23.4775i	1.56890	−	1.08294i
$471$	−0.267248	+	0.704676i	−0.0123142	+	0.0324697i
$472$	0.398098	+	3.27863i	0.0183239	+	0.150911i
$473$	−1.59240	+	3.03407i	−0.0732187	+	0.139507i
$474$	−7.71169	+	8.70470i	−0.354210	+	0.399820i
$475$	−0.867755	−	0.598968i	−0.0398153	−	0.0274825i
$476$	−30.1832	+	20.8339i	−1.38344	+	0.954922i
$477$	−8.63114	−	4.52997i	−0.395193	−	0.207413i
$478$	−5.64413	+	46.4836i	−0.258156	+	2.12611i
$479$	9.58219	+	6.61411i	0.437822	+	0.302206i	0.766510	−	0.642232i	$-0.221991\pi$
$479$	9.58219	+	6.61411i	0.437822	+	0.302206i	−0.328689	+	0.944438i	$0.606607\pi$
$480$	9.74992	+	14.1252i	0.445021	+	0.644724i
$481$	−27.3505	+	1.90332i	−1.24708	+	0.0867841i
$482$	15.3631	−	22.2572i	0.699768	−	1.01379i
$483$	−21.4273	+	8.12631i	−0.974977	+	0.369760i
$484$	−24.2269			−1.10122
$485$	6.75548			0.306751
$486$	1.98724	−	0.753662i	0.0901432	−	0.0341868i
$487$	2.13097	+	8.64569i	0.0965635	+	0.391774i	0.999258	−	0.0385079i	$-0.0122605\pi$
$487$	2.13097	+	8.64569i	0.0965635	+	0.391774i	−0.902695	+	0.430281i	$0.858414\pi$
$488$			12.3732i			0.560108i
$489$	4.67823	−	18.9803i	0.211557	−	0.858320i
$490$	1.07786	−	2.84209i	0.0486929	−	0.128393i
$491$	14.2123	+	7.45917i	0.641391	+	0.336628i	0.753867	−	0.657027i	$-0.228186\pi$
$491$	14.2123	+	7.45917i	0.641391	+	0.336628i	−0.112477	+	0.993654i	$0.535878\pi$
$492$	−28.2159	−	10.7009i	−1.27207	−	0.482433i
$493$	10.3901	+	5.45317i	0.467949	+	0.245598i
$494$	15.4341	−	20.0723i	0.694415	−	0.903096i
$495$	−2.24657	+	1.17909i	−0.100976	+	0.0529961i
$496$	−0.473820	+	0.0575322i	−0.0212752	+	0.00258327i
$497$	0.253481	+	0.668373i	0.0113702	+	0.0299806i
$498$	2.47279	−	20.3652i	0.110808	−	0.912588i
$499$	−3.94970	−	1.49792i	−0.176813	−	0.0670562i	0.264610	−	0.964356i	$-0.414757\pi$
$499$	−3.94970	−	1.49792i	−0.176813	−	0.0670562i	−0.441423	+	0.897299i	$0.645526\pi$
$500$	27.0851	+	10.2720i	1.21128	+	0.459378i
$501$	11.2534	−	7.76770i	0.502767	−	0.347035i
$502$	−2.91319	−	5.55061i	−0.130022	−	0.247736i
$503$	17.7964	+	4.38641i	0.793500	+	0.195580i	0.615174	−	0.788391i	$-0.289086\pi$
$503$	17.7964	+	4.38641i	0.793500	+	0.195580i	0.178326	+	0.983971i	$0.442932\pi$
$504$	2.27710	−	2.01734i	0.101430	−	0.0898594i
$505$	−15.1237	−	1.83635i	−0.672997	−	0.0817166i
$506$	20.6360			0.917380
$507$	12.2368	+	4.38880i	0.543454	+	0.194913i
$508$	34.9523			1.55076
$509$	−13.8188	−	1.67790i	−0.612506	−	0.0743717i	−0.191596	−	0.981474i	$-0.561366\pi$
$509$	−13.8188	−	1.67790i	−0.612506	−	0.0743717i	−0.420910	+	0.907102i	$0.638289\pi$
$510$	−18.1182	+	16.0514i	−0.802289	+	0.710766i
$511$	−1.39841	−	0.344677i	−0.0618621	−	0.0152476i
$512$	−12.7041	−	24.2057i	−0.561448	−	1.06975i
$513$	−2.71928	+	1.87698i	−0.120059	+	0.0828709i
$514$	−24.5564	−	9.31302i	−1.08314	−	0.410780i
$515$	−29.1234	−	11.0451i	−1.28333	−	0.486704i
$516$	0.886538	−	7.30130i	0.0390276	−	0.321422i
$517$	−3.73758	−	9.85519i	−0.164379	−	0.433431i
$518$	44.4059	−	5.39185i	1.95108	−	0.236904i
$519$	17.6174	−	9.24632i	0.773318	−	0.405869i
$520$	−3.44783	+	7.85008i	−0.151197	+	0.344249i
$521$	16.1609	+	8.48190i	0.708023	+	0.371599i	0.779976	−	0.625809i	$-0.215231\pi$
$521$	16.1609	+	8.48190i	0.708023	+	0.371599i	−0.0719537	+	0.997408i	$0.522923\pi$
$522$	−4.42979	−	1.68000i	−0.193887	−	0.0735316i
$523$	−25.0205	−	13.1318i	−1.09407	−	0.574212i	−0.181607	−	0.983371i	$-0.558130\pi$
$523$	−25.0205	−	13.1318i	−1.09407	−	0.574212i	−0.912463	+	0.409159i	$0.865822\pi$
$524$	−6.37819	+	16.8179i	−0.278633	+	0.734694i
$525$	−0.211377	+	0.857590i	−0.00922524	+	0.0374283i
$526$			6.31696i			0.275432i
$527$	−0.222842	−	0.904107i	−0.00970716	−	0.0393835i
$528$	2.95866	−	1.12207i	0.128759	−	0.0488318i
$529$	45.5504			1.98045
$530$	−44.8226			−1.94697
$531$	−2.80963	+	1.06555i	−0.121927	+	0.0462410i
$532$	−13.0771	+	18.9455i	−0.566965	+	0.821391i
$533$	8.17659	+	42.4450i	0.354167	+	1.83850i
$534$	−16.7834	−	24.3150i	−0.726289	−	1.05221i
$535$	−5.54649	−	3.82847i	−0.239796	−	0.165519i
$536$	−0.161989	+	1.33410i	−0.00699684	+	0.0576242i
$537$	3.06428	+	1.60826i	0.132234	+	0.0694015i
$538$	43.3906	−	29.9504i	1.87070	−	1.29125i
$539$	−0.637973	−	0.440361i	−0.0274794	−	0.0189677i
$540$	3.61132	−	4.07633i	0.155406	−	0.175417i
$541$	5.04855	−	9.61921i	0.217054	−	0.413562i	−0.752446	−	0.658654i	$-0.771126\pi$
$541$	5.04855	−	9.61921i	0.217054	−	0.413562i	0.969500	+	0.245092i	$0.0788182\pi$
$542$	1.87779	+	15.4650i	0.0806581	+	0.664279i
$543$	1.59269	−	4.19957i	0.0683488	−	0.180221i
$544$	34.3679	−	23.7224i	1.47351	−	1.01709i
$545$	1.48334	−	12.2164i	0.0635391	−	0.523292i
$546$	−20.3063	−	6.12636i	−0.869029	−	0.262184i
$547$	−4.01703	−	33.0832i	−0.171756	−	1.41454i	−0.782472	−	0.622686i	$-0.786041\pi$
$547$	−4.01703	−	33.0832i	−0.171756	−	1.41454i	0.610716	−	0.791850i	$-0.290882\pi$
$548$	4.98160	+	5.62306i	0.212803	+	0.240205i
$549$	−10.9304	+	2.69409i	−0.466496	+	0.114981i
$550$	0.451815	−	0.654567i	0.0192654	−	0.0279108i
$551$	7.31168	+	0.887799i	0.311488	+	0.0378215i
$552$	−8.50874	+	3.22694i	−0.362156	+	0.137348i
$553$	−15.0345	−	1.82552i	−0.639333	−	0.0776290i
$554$	−2.40137	−	9.74275i	−0.102025	−	0.413930i
$555$	15.9735	−	3.93712i	0.678038	−	0.167121i
$556$	39.6854	+	35.1582i	1.68304	+	1.49104i
$557$	7.21885	−	8.14840i	0.305873	−	0.345259i	−0.575396	−	0.817875i	$-0.695152\pi$
$557$	7.21885	−	8.14840i	0.305873	−	0.345259i	0.881268	+	0.472616i	$0.156690\pi$
$558$	0.133316	+	0.351524i	0.00564370	+	0.0148812i
$559$	−9.56745	+	4.41066i	−0.404660	+	0.186551i
$560$	−5.72981	+	15.1083i	−0.242128	+	0.638440i
$561$	2.86883	+	5.46609i	0.121122	+	0.230779i
$562$	25.8473	+	37.4463i	1.09030	+	1.57958i
$563$	−18.3100	−	16.2213i	−0.771676	−	0.683645i	0.182395	−	0.983225i	$-0.441615\pi$
$563$	−18.3100	−	16.2213i	−0.771676	−	0.683645i	−0.954071	+	0.299580i	$0.903153\pi$
$564$	15.0023	+	16.9341i	0.631713	+	0.713056i
$565$	9.71753	−	39.4256i	0.408820	−	1.65865i
$566$	23.8650	+	45.4710i	1.00312	+	1.91129i
$567$	2.27790	+	1.57232i	0.0956629	+	0.0660313i
$568$	0.100657	+	0.265410i	0.00422346	+	0.0111363i
$569$	−33.6156	+	17.6428i	−1.40924	+	0.739626i	−0.986055	−	0.166417i	$-0.946780\pi$
$569$	−33.6156	+	17.6428i	−1.40924	+	0.739626i	−0.423185	+	0.906043i	$0.639088\pi$
$570$	−7.06079	+	13.4532i	−0.295744	+	0.563493i
$571$	22.1679	+	19.6391i	0.927700	+	0.821870i	0.984296	−	0.176527i	$-0.0564863\pi$
$571$	22.1679	+	19.6391i	0.927700	+	0.821870i	−0.0565962	+	0.998397i	$0.518025\pi$
$572$	8.43720	+	6.48759i	0.352777	+	0.271260i
$573$	−1.32534	+	1.17414i	−0.0553667	+	0.0490506i
$574$	−16.8777	−	68.4756i	−0.704462	−	2.85812i
$575$	1.50088	−	2.17440i	0.0625910	−	0.0906787i
$576$	−8.58090	+	7.60201i	−0.357537	+	0.316750i
$577$		−	26.4199i		−	1.09987i	−0.835206	−	0.549937i	$-0.814652\pi$
$577$		−	26.4199i		−	1.09987i	0.835206	−	0.549937i	$-0.185348\pi$
$578$	15.0951	+	17.0388i	0.627872	+	0.708721i
$579$	−6.39713	+	12.1887i	−0.265856	+	0.506545i
$580$	−12.0511	+	1.46327i	−0.500394	+	0.0607589i
$581$	23.6563	−	12.4158i	0.981427	−	0.515093i
$582$	0.799914	+	6.58788i	0.0331575	+	0.273077i
$583$	−2.73565	+	11.0990i	−0.113299	+	0.459672i
$584$	−0.555306	−	0.136871i	−0.0229787	−	0.00566375i
$585$	−7.68539	−	1.33653i	−0.317752	−	0.0552586i
$586$	−39.1480	+	9.64911i	−1.61719	+	0.398601i
$587$			0.0995677i			0.00410960i	0.999998	+	0.00205480i	$0.000654064\pi$
$587$			0.0995677i			0.00410960i	−0.999998	+	0.00205480i	$0.999346\pi$
$588$	1.61556	+	0.398200i	0.0666247	+	0.0164215i
$589$	−0.332021	−	0.481015i	−0.0136807	−	0.0198199i
$590$	−9.16262	+	10.3425i	−0.377219	+	0.425792i
$591$	−6.08925	+	0.739368i	−0.250478	+	0.0304135i
$592$	−20.3682	+	2.47314i	−0.837127	+	0.101646i
$593$	9.89328	−	11.1672i	0.406268	−	0.458582i	−0.509392	−	0.860534i	$-0.670130\pi$
$593$	9.89328	−	11.1672i	0.406268	−	0.458582i	0.915661	+	0.401952i	$0.131668\pi$
$594$	−1.41585	−	2.05121i	−0.0580931	−	0.0841624i
$595$	−30.6072	−	7.54399i	−1.25477	−	0.309273i
$596$		−	38.9424i		−	1.59514i
$597$	−15.0492	+	3.70930i	−0.615924	+	0.151812i
$598$	50.2967	+	38.6745i	2.05678	+	1.58152i
$599$	−28.9896	−	7.14529i	−1.18448	−	0.291948i	−0.402600	−	0.915376i	$-0.631894\pi$
$599$	−28.9896	−	7.14529i	−1.18448	−	0.291948i	−0.781881	+	0.623427i	$0.785740\pi$
$600$	−0.0839373	+	0.340547i	−0.00342673	+	0.0139028i
$601$	−5.71250	−	47.0467i	−0.233018	−	1.91908i	−0.370986	−	0.928638i	$-0.620980\pi$
$601$	−5.71250	−	47.0467i	−0.233018	−	1.91908i	0.137968	−	0.990437i	$-0.455943\pi$
$602$	15.2199	−	7.98804i	0.620318	−	0.325568i
$603$	−1.21380	+	0.147382i	−0.0494296	+	0.00600185i
$604$	−16.8037	+	32.0168i	−0.683733	+	1.30274i
$605$	−13.8086	−	15.5866i	−0.561398	−	0.633687i
$606$		−	14.9660i		−	0.607951i
$607$	8.06147	−	7.14184i	0.327205	−	0.289878i	−0.483487	−	0.875352i	$-0.660630\pi$
$607$	8.06147	−	7.14184i	0.327205	−	0.289878i	0.810692	+	0.585473i	$0.199091\pi$
$608$	14.8902	−	21.5722i	0.603877	−	0.874866i
$609$	−1.47655	−	5.99059i	−0.0598327	−	0.242751i
$610$	−38.7467	+	34.3266i	−1.56881	+	1.38984i
$611$	9.36019	−	31.0251i	0.378673	−	1.25514i
$612$	−9.91808	−	8.78666i	−0.400915	−	0.355179i
$613$	14.3029	−	27.2519i	0.577688	−	1.10069i	−0.404807	−	0.914402i	$-0.632661\pi$
$613$	14.3029	−	27.2519i	0.577688	−	1.10069i	0.982495	−	0.186290i	$-0.0596465\pi$
$614$	−0.635218	+	0.333388i	−0.0256353	+	0.0134545i
$615$	−9.19763	−	24.2522i	−0.370884	−	0.977941i
$616$	−2.93605	−	2.02661i	−0.118297	−	0.0816545i
$617$	−3.58225	−	6.82540i	−0.144216	−	0.274780i	0.802624	−	0.596485i	$-0.203436\pi$
$617$	−3.58225	−	6.82540i	−0.144216	−	0.274780i	−0.946840	+	0.321705i	$0.895744\pi$
$618$	7.32255	−	29.7087i	0.294556	−	1.19506i
$619$	−11.3073	−	12.7633i	−0.454480	−	0.513002i	0.475950	−	0.879473i	$-0.342104\pi$
$619$	−11.3073	−	12.7633i	−0.454480	−	0.513002i	−0.930430	+	0.366471i	$0.880566\pi$
$620$	0.721064	+	0.638807i	0.0289586	+	0.0256551i
$621$	−4.70330	−	6.81391i	−0.188737	−	0.273433i
$622$	−14.1161	−	26.8960i	−0.566004	−	1.07843i
$623$	13.6439	−	35.9760i	0.546631	−	1.44135i
$624$	9.31413	+	2.81005i	0.372864	+	0.112492i
$625$	8.26322	+	21.7883i	0.330529	+	0.871533i
$626$	16.4185	−	18.5327i	0.656216	−	0.740715i
$627$	2.90034	+	2.56948i	0.115828	+	0.102615i
$628$	−1.84192	+	0.453993i	−0.0735006	+	0.0181163i
$629$	−9.57935	−	38.8650i	−0.381954	−	1.54965i
$630$	12.6346	+	1.53412i	0.503375	+	0.0611207i
$631$	−44.8828	+	17.0218i	−1.78676	+	0.677627i	−0.788737	+	0.614731i	$0.789264\pi$
$631$	−44.8828	+	17.0218i	−1.78676	+	0.677627i	−0.998020	+	0.0628963i	$0.979966\pi$
$632$	−5.97017	−	0.724910i	−0.237481	−	0.0288354i
$633$	3.54758	−	5.13956i	0.141004	−	0.204279i
$634$	−51.4158	+	12.6729i	−2.04198	+	0.503304i
$635$	19.9217	+	22.4869i	0.790567	+	0.892366i
$636$	−2.95752	−	24.3574i	−0.117273	−	0.965833i
$637$	−0.729658	−	2.26895i	−0.0289101	−	0.0898991i
$638$	−0.669687	+	5.51537i	−0.0265131	+	0.218355i
$639$	−0.212543	+	0.146708i	−0.00840809	+	0.00580368i
$640$	−6.52039	+	17.1929i	−0.257741	+	0.679607i
$641$	−0.607232	−	5.00101i	−0.0239842	−	0.197528i	0.975792	−	0.218703i	$-0.0701825\pi$
$641$	−0.607232	−	5.00101i	−0.0239842	−	0.197528i	−0.999776	+	0.0211747i	$0.993259\pi$
$642$	3.07673	−	5.86221i	0.121429	−	0.231363i
$643$	18.7801	−	21.1983i	0.740614	−	0.835980i	−0.250622	−	0.968085i	$-0.580635\pi$
$643$	18.7801	−	21.1983i	0.740614	−	0.835980i	0.991236	+	0.132105i	$0.0421736\pi$
$644$	−47.4731	−	32.7683i	−1.87070	−	1.29125i
$645$	5.20267	−	3.59114i	0.204855	−	0.141401i
$646$	32.7329	+	17.1795i	1.28786	+	0.675919i
$647$	−3.41827	+	28.1520i	−0.134386	+	1.10677i	0.756965	+	0.653455i	$0.226681\pi$
$647$	−3.41827	+	28.1520i	−0.134386	+	1.10677i	−0.891351	+	0.453313i	$0.850242\pi$
$648$	0.904550	+	0.624366i	0.0355341	+	0.0245274i
$649$	2.00178	+	2.90007i	0.0785766	+	0.113838i
$650$	2.32797	−	0.748636i	0.0913103	−	0.0293639i
$651$	−0.278129	+	0.402939i	−0.0109007	+	0.0157924i
$652$	46.0084	−	17.4487i	1.80183	−	0.683343i
$653$	−1.48592			−0.0581487			−0.0290743	−	0.999577i	$-0.509256\pi$
$653$	−1.48592			−0.0581487			−0.0290743	+	0.999577i	$0.509256\pi$
$654$	12.0889			0.472715
$655$	−14.4553	+	5.48219i	−0.564817	+	0.214207i
$656$	7.74151	+	31.4085i	0.302255	+	1.22630i
$657$		−	0.520353i		−	0.0203009i
$658$	−12.6533	+	51.3365i	−0.493278	+	2.00131i
$659$	−11.7262	+	30.9193i	−0.456786	+	1.20445i	0.486857	+	0.873482i	$0.338143\pi$
$659$	−11.7262	+	30.9193i	−0.456786	+	1.20445i	−0.943643	+	0.330965i	$0.892626\pi$
$660$	−5.65492	−	2.96793i	−0.220118	−	0.115527i
$661$	2.38783	+	0.905584i	0.0928758	+	0.0352231i	0.400605	−	0.916251i	$-0.368800\pi$
$661$	2.38783	+	0.905584i	0.0928758	+	0.0352231i	−0.307729	+	0.951474i	$0.599569\pi$
$662$	0.0131606	+	0.00690722i	0.000511501	+	0.000268457i
$663$	−3.25189	+	18.6992i	−0.126293	+	0.726218i
$664$	9.39385	−	4.93027i	0.364552	−	0.191332i
$665$	−19.6423	+	2.38501i	−0.761696	+	0.0924867i
$666$	5.73086	+	15.1110i	0.222066	+	0.585540i
$667$	−2.22462	+	18.3214i	−0.0861378	+	0.709409i
$668$	32.1826	+	12.2053i	1.24518	+	0.472235i
$669$	−22.3805	−	8.48781i	−0.865280	−	0.328158i
$670$	−4.62713	+	3.19388i	−0.178762	+	0.123390i
$671$	6.13512	+	11.6895i	0.236844	+	0.451268i
$672$	−21.3195	−	5.25477i	−0.822416	−	0.202707i
$673$	0.701610	−	0.621572i	0.0270451	−	0.0239598i	−0.649492	−	0.760369i	$-0.725018\pi$
$673$	0.701610	−	0.621572i	0.0270451	−	0.0239598i	0.676537	+	0.736409i	$0.263480\pi$
$674$	−9.98860	−	1.21284i	−0.384746	−	0.0467167i
$675$	−0.319112			−0.0122826
$676$	8.40565	+	31.6248i	0.323294	+	1.21634i
$677$	20.4301			0.785191			0.392595	−	0.919711i	$-0.371577\pi$
$677$	20.4301			0.785191			0.392595	+	0.919711i	$0.371577\pi$
$678$	39.5981	+	4.80808i	1.52076	+	0.184653i
$679$	−6.46895	+	5.73099i	−0.248256	+	0.219935i
$680$	−12.1540	−	2.99570i	−0.466086	−	0.114880i
$681$	11.1283	+	21.2031i	0.426436	+	0.812506i
$682$	0.362840	−	0.250451i	0.0138939	−	0.00959025i
$683$	34.3232	+	13.0171i	1.31334	+	0.498084i	0.909103	−	0.416570i	$-0.136768\pi$
$683$	34.3232	+	13.0171i	1.31334	+	0.498084i	0.404236	+	0.914655i	$0.367537\pi$
$684$	−7.77660	−	2.94927i	−0.297346	−	0.112768i
$685$	−0.778307	+	6.40993i	−0.0297376	+	0.244911i
$686$	−13.2233	−	34.8669i	−0.504867	−	1.33122i
$687$	−1.04781	+	0.127227i	−0.0399763	+	0.00485401i
$688$	−6.98111	+	3.66397i	−0.266152	+	0.139688i
$689$	−27.4686	+	21.9249i	−1.04647	+	0.835271i
$690$	−33.7107	−	17.6927i	−1.28334	−	0.673551i
$691$	−18.5866	−	7.04895i	−0.707066	−	0.268155i	−0.0252529	−	0.999681i	$-0.508039\pi$
$691$	−18.5866	−	7.04895i	−0.707066	−	0.268155i	−0.681813	+	0.731526i	$0.738808\pi$
$692$	44.3455	+	23.2743i	1.68576	+	0.884756i
$693$	1.15100	−	3.03494i	0.0437230	−	0.115288i
$694$	14.9299	−	60.5729i	0.566730	−	2.29932i
$695$			45.5711i			1.72861i
$696$	−0.586334	−	2.37885i	−0.0222249	−	0.0901700i
$697$	−59.0076	+	22.3786i	−2.23507	+	0.847652i
$698$	1.20680			0.0456779
$699$	19.9717			0.755400
$700$	−2.07880	+	0.788386i	−0.0785713	+	0.0297982i
$701$	14.5911	−	21.1388i	0.551097	−	0.798401i	−0.444133	−	0.895961i	$-0.646488\pi$
$701$	14.5911	−	21.1388i	0.551097	−	0.798401i	0.995230	+	0.0975595i	$0.0311036\pi$
$702$	0.393345	−	7.65298i	0.0148459	−	0.288843i
$703$	−14.2726	−	20.6775i	−0.538302	−	0.779865i
$704$	11.0640	+	7.63696i	0.416992	+	0.287829i
$705$	−2.34391	+	19.3038i	−0.0882768	+	0.727025i
$706$	14.3777	+	7.54599i	0.541111	+	0.283997i
$707$	16.0401	−	11.0717i	0.603251	−	0.416394i
$708$	−6.22485	−	4.29670i	−0.233944	−	0.161480i
$709$	12.3525	−	13.9431i	0.463910	−	0.523646i	−0.469271	−	0.883054i	$-0.655483\pi$
$709$	12.3525	−	13.9431i	0.463910	−	0.523646i	0.933180	+	0.359409i	$0.117022\pi$
$710$	−0.551882	+	1.05152i	−0.0207118	+	0.0394630i
$711$	−0.659543	−	5.43182i	−0.0247348	−	0.203709i
$712$	5.41796	−	14.2860i	0.203047	−	0.535390i
$713$	1.20532	−	0.831969i	0.0451394	−	0.0311575i
$714$	3.73265	−	30.7411i	0.139691	−	1.15046i
$715$	0.635070	+	9.12588i	0.0237503	+	0.341289i
$716$	1.05000	+	8.64751i	0.0392403	+	0.323173i
$717$	−14.6096	−	16.4909i	−0.545607	−	0.615863i
$718$	1.98980	−	0.490443i	0.0742588	−	0.0183032i
$719$	−17.3277	+	25.1035i	−0.646214	+	0.936203i	0.353785	+	0.935327i	$0.384894\pi$
$719$	−17.3277	+	25.1035i	−0.646214	+	0.936203i	−1.00000		0.000876559i	$0.999721\pi$
$720$	−5.79527	−	0.703673i	−0.215977	−	0.0262243i
$721$	37.2582	−	14.1302i	1.38757	−	0.526235i
$722$	−17.0528	−	2.07059i	−0.634640	−	0.0770592i
$723$	3.04522	+	12.3550i	0.113253	+	0.459486i
$724$	10.9771	−	2.70561i	0.407960	−	0.100553i
$725$	0.532443	+	0.471704i	0.0197744	+	0.0175186i
$726$	13.5649	−	15.3116i	0.503440	−	0.568266i
$727$	17.3002	+	45.6169i	0.641629	+	1.69184i	0.719158	+	0.694846i	$0.244528\pi$
$727$	17.3002	+	45.6169i	0.641629	+	1.69184i	−0.0775291	+	0.996990i	$0.524703\pi$
$728$	−3.35800	−	10.4421i	−0.124456	−	0.387009i
$729$	−0.354605	+	0.935016i	−0.0131335	+	0.0346302i
$730$	−1.11196	−	2.11866i	−0.0411554	−	0.0784151i
$731$	−8.73756	−	12.6585i	−0.323170	−	0.468193i
$732$	−21.2103	−	18.7907i	−0.783955	−	0.694523i
$733$	23.3095	+	26.3109i	0.860955	+	0.971817i	0.999829	−	0.0184930i	$-0.00588684\pi$
$733$	23.3095	+	26.3109i	0.860955	+	0.971817i	−0.138874	+	0.990310i	$0.544348\pi$
$734$	−4.73315	+	19.2031i	−0.174704	+	0.708801i
$735$	0.664632	+	1.26635i	0.0245153	+	0.0467101i
$736$	54.0549	+	37.3114i	1.99249	+	1.37532i
$737$	0.508460	+	1.34070i	0.0187294	+	0.0493853i
$738$	22.5614	−	11.8411i	0.830496	−	0.435878i
$739$	−2.40929	+	4.59051i	−0.0886270	+	0.168865i	−0.925735	−	0.378173i	$-0.876552\pi$
$739$	−2.40929	+	4.59051i	−0.0886270	+	0.168865i	0.837108	+	0.547038i	$0.184245\pi$
$740$	30.9965	+	27.4605i	1.13945	+	1.00947i
$741$	2.25355	+	11.6983i	0.0827864	+	0.429747i
$742$	42.9215	−	38.0251i	1.57570	−	1.39595i
$743$	−9.31639	−	37.7981i	−0.341785	−	1.38668i	−0.850605	−	0.525805i	$-0.823764\pi$
$743$	−9.31639	−	37.7981i	−0.341785	−	1.38668i	0.508820	−	0.860873i	$-0.330082\pi$
$744$	−0.110444	+	0.160006i	−0.00404908	+	0.00586611i
$745$	25.0540	−	22.1959i	0.917909	−	0.813196i
$746$		−	22.7372i		−	0.832467i
$747$	6.40073	+	7.22493i	0.234190	+	0.264346i
$748$	−7.22124	+	13.7589i	−0.264035	+	0.503076i
$749$	8.55910	−	1.03926i	0.312743	−	0.0379739i
$750$	−21.6572	+	11.3666i	−0.790809	+	0.415048i
$751$	−1.13470	−	9.34508i	−0.0414057	−	0.341007i	−0.998660	−	0.0517580i	$-0.983518\pi$
$751$	−1.13470	−	9.34508i	−0.0414057	−	0.341007i	0.957254	−	0.289249i	$-0.0934055\pi$
$752$	5.80385	−	23.5471i	0.211645	−	0.858676i
$753$	2.86375	+	0.705851i	0.104361	+	0.0257227i
$754$	−11.9688	+	12.1877i	−0.435877	+	0.443850i
$755$	−30.1759	+	7.43770i	−1.09821	+	0.270685i
$756$			6.96709i			0.253391i
$757$	27.0257	+	6.66125i	0.982267	+	0.242107i	0.697575	−	0.716512i	$-0.254262\pi$
$757$	27.0257	+	6.66125i	0.982267	+	0.242107i	0.284692	+	0.958619i	$0.408109\pi$
$758$	−16.6600	−	24.1361i	−0.605117	−	0.876664i
$759$	−6.43853	+	7.26760i	−0.233704	+	0.263797i
$760$	−7.79992	+	0.947082i	−0.282933	+	0.0343543i
$761$	−19.0339	+	2.31113i	−0.689978	+	0.0837785i	−0.458013	−	0.888945i	$-0.651439\pi$
$761$	−19.0339	+	2.31113i	−0.689978	+	0.0837785i	−0.231965	+	0.972724i	$0.574516\pi$
$762$	−19.5701	+	22.0901i	−0.708950	+	0.800240i
$763$	8.94330	+	12.9566i	0.323769	+	0.469061i
$764$	−4.32742	−	1.06661i	−0.156560	−	0.0385887i
$765$		−	11.3890i		−	0.411771i
$766$	−0.338932	+	0.0835393i	−0.0122461	+	0.00301840i
$767$	−0.556124	+	10.8200i	−0.0200805	+	0.390689i
$768$	4.72328	+	1.16418i	0.170437	+	0.0420089i
$769$	−4.39331	+	17.8244i	−0.158427	+	0.642763i	0.836997	+	0.547207i	$0.184309\pi$
$769$	−4.39331	+	17.8244i	−0.158427	+	0.642763i	−0.995424	+	0.0955558i	$0.969537\pi$
$770$	−1.79906	−	14.8166i	−0.0648338	−	0.533954i
$771$	10.9416	−	5.74260i	0.394052	−	0.206815i
$772$	−34.3970	+	4.17655i	−1.23797	+	0.150317i
$773$	7.20950	−	13.7366i	0.259308	−	0.494070i	−0.720644	−	0.693306i	$-0.756154\pi$
$773$	7.20950	−	13.7366i	0.259308	−	0.494070i	0.979952	+	0.199236i	$0.0638459\pi$
$774$	4.11809	+	4.64837i	0.148022	+	0.167082i
$775$		−	0.0564478i		−	0.00202767i
$776$	−2.56881	+	2.27576i	−0.0922148	+	0.0816951i
$777$	−11.9560	+	17.3212i	−0.428918	+	0.621394i
$778$	−10.2858	−	41.7310i	−0.368763	−	1.49613i
$779$	−29.6502	+	26.2678i	−1.06233	+	0.941142i
$780$	−8.22063	−	17.8319i	−0.294346	−	0.638484i
$781$	0.226695	+	0.200834i	0.00811179	+	0.00718642i
$782$	−43.0480	+	82.0212i	−1.53939	+	2.93307i
$783$	1.97378	−	1.03592i	0.0705373	−	0.0370208i
$784$	−0.632492	−	1.66774i	−0.0225890	−	0.0595623i
$785$	−1.34192	−	0.926258i	−0.0478951	−	0.0330596i
$786$	−7.05783	−	13.4476i	−0.251745	−	0.479659i
$787$	6.16536	−	25.0138i	0.219771	−	0.891647i	−0.752651	−	0.658420i	$-0.771225\pi$
$787$	6.16536	−	25.0138i	0.219771	−	0.891647i	0.972422	−	0.233228i	$-0.0749287\pi$
$788$	−10.2387	−	11.5571i	−0.364737	−	0.411703i
$789$	−2.22471	−	1.97092i	−0.0792019	−	0.0701668i
$790$	−14.2928	−	20.7067i	−0.508515	−	0.736712i
$791$	24.1412	+	45.9972i	0.858362	+	1.63547i
$792$	0.457061	−	1.20517i	0.0162409	−	0.0428238i
$793$	−6.95432	+	39.9892i	−0.246955	+	1.42006i
$794$	−17.9366	−	47.2950i	−0.636546	−	1.67844i
$795$	13.9849	−	15.7857i	0.495993	−	0.559860i
$796$	−29.2030	−	25.8716i	−1.03507	−	0.916993i
$797$	−28.3600	+	6.99011i	−1.00456	+	0.247602i	−0.707086	−	0.707127i	$-0.749991\pi$
$797$	−28.3600	+	6.99011i	−1.00456	+	0.247602i	−0.297476	+	0.954729i	$0.596145\pi$
$798$	−4.65168	−	18.8726i	−0.164668	−	0.668083i
$799$	46.9680	+	5.70294i	1.66161	+	0.201756i
$800$	2.36702	−	0.897691i	0.0836866	−	0.0317382i
$801$	13.7998	+	1.67560i	0.487591	+	0.0592043i
$802$	−9.32487	+	13.5094i	−0.329273	+	0.477034i
$803$	−0.592488	+	0.146035i	−0.0209084	+	0.00515347i
$804$	−2.04092	−	2.30372i	−0.0719777	−	0.0812460i
$805$	−5.97629	−	49.2192i	−0.210637	−	1.73475i
$806$	1.35374	+	0.0695790i	0.0476834	+	0.00245082i
$807$	−2.99014	+	24.6261i	−0.105258	+	0.866878i
$808$	6.36950	−	4.39655i	0.224078	−	0.154670i
$809$	8.54888	−	22.5416i	0.300563	−	0.792519i	−0.696615	−	0.717445i	$-0.745311\pi$
$809$	8.54888	−	22.5416i	0.300563	−	0.792519i	0.997178	−	0.0750739i	$-0.0239193\pi$
$810$	0.554262	+	4.56476i	0.0194748	+	0.160389i
$811$	−22.9593	+	43.7452i	−0.806209	+	1.53610i	0.0374964	+	0.999297i	$0.488062\pi$
$811$	−22.9593	+	43.7452i	−0.806209	+	1.53610i	−0.843706	+	0.536806i	$0.819631\pi$
$812$	10.2986	−	11.6247i	0.361410	−	0.407947i
$813$	−6.03237	−	4.16384i	−0.211564	−	0.146032i
$814$	15.5975	−	10.7662i	0.546691	−	0.377353i
$815$	37.4491	+	19.6548i	1.31179	+	0.688478i
$816$	−1.71210	+	14.1004i	−0.0599354	+	0.493613i
$817$	−7.94556	−	5.48443i	−0.277980	−	0.191876i
$818$	−6.82793	−	9.89196i	−0.238733	−	0.345864i
$819$	8.49326	−	5.24004i	0.296778	−	0.183102i
$820$	37.0883	−	53.7316i	1.29518	−	1.87639i
$821$	−5.53218	+	2.09808i	−0.193075	+	0.0732235i	−0.449247	−	0.893408i	$-0.648308\pi$
$821$	−5.53218	+	2.09808i	−0.193075	+	0.0732235i	0.256173	+	0.966631i	$0.417538\pi$
$822$	−6.34307			−0.221240
$823$	−41.8958			−1.46040			−0.730199	−	0.683235i	$-0.760572\pi$
$823$	−41.8958			−1.46040			−0.730199	+	0.683235i	$0.760572\pi$
$824$	14.7952	−	5.61106i	0.515414	−	0.195471i
$825$	0.0895575	+	0.363349i	0.00311799	+	0.0126502i
$826$		−	17.6769i		−	0.615057i
$827$	9.58142	−	38.8733i	0.333178	−	1.35176i	−0.530487	−	0.847693i	$-0.677991\pi$
$827$	9.58142	−	38.8733i	0.333178	−	1.35176i	0.863666	−	0.504065i	$-0.168163\pi$
$828$	7.39022	−	19.4864i	0.256828	−	0.677199i
$829$	48.8366	+	25.6314i	1.69617	+	0.890217i	0.981673	+	0.190574i	$0.0610350\pi$
$829$	48.8366	+	25.6314i	1.69617	+	0.890217i	0.714493	+	0.699642i	$0.246657\pi$
$830$	41.5002	+	15.7390i	1.44049	+	0.546308i
$831$	4.18045	+	2.19407i	0.145018	+	0.0761115i
$832$	12.6541	+	39.3493i	0.438702	+	1.36419i
$833$	3.08114	−	1.61711i	0.106755	−	0.0560295i
$834$	−44.4405	+	5.39606i	−1.53885	+	0.186850i
$835$	10.4907	+	27.6616i	0.363045	+	0.957270i
$836$	−1.17565	+	9.68234i	−0.0406607	+	0.334871i
$837$	−0.165395	−	0.0627262i	−0.00571690	−	0.00216813i
$838$	−55.5061	−	21.0507i	−1.91743	−	0.727184i
$839$	3.33860	−	2.30447i	0.115261	−	0.0795592i	−0.509040	−	0.860743i	$-0.669999\pi$
$839$	3.33860	−	2.30447i	0.115261	−	0.0795592i	0.624301	+	0.781184i	$0.285384\pi$
$840$	3.05874	+	5.82795i	0.105537	+	0.201083i
$841$	23.3327	+	5.75101i	0.804577	+	0.198311i
$842$	−52.6044	+	46.6034i	−1.81287	+	1.60606i
$843$	−21.2524	−	2.58050i	−0.731970	−	0.0888773i
$844$	15.7196			0.541091
$845$	−15.5552	+	23.4330i	−0.535116	+	0.806120i
$846$	−19.1025			−0.656757
$847$	26.4457	+	3.21110i	0.908687	+	0.110335i
$848$	−19.6873	+	17.4414i	−0.676065	+	0.598941i
$849$	−23.4601	−	5.78238i	−0.805147	−	0.198451i
$850$	1.65917	+	3.16129i	0.0569091	+	0.108431i
$851$	51.8131	−	35.7640i	1.77613	−	1.22597i
$852$	−0.607831	−	0.230520i	−0.0208240	−	0.00789748i
$853$	49.1694	+	18.6475i	1.68353	+	0.638478i	0.996137	−	0.0878083i	$-0.0279863\pi$
$853$	49.1694	+	18.6475i	1.68353	+	0.638478i	0.687392	+	0.726287i	$0.258756\pi$
$854$	7.98244	−	65.7413i	0.273153	−	2.24962i
$855$	−2.53496	−	6.68415i	−0.0866939	−	0.228593i
$856$	3.39880	−	0.412689i	0.116169	−	0.0141054i
$857$	−25.3380	+	13.2984i	−0.865529	+	0.454265i	−0.838201	−	0.545362i	$-0.816392\pi$
$857$	−25.3380	+	13.2984i	−0.865529	+	0.454265i	−0.0273281	+	0.999627i	$0.508700\pi$
$858$	−8.82428	+	1.69991i	−0.301256	+	0.0580338i
$859$	22.9636	+	12.0522i	0.783509	+	0.411217i	0.808519	−	0.588470i	$-0.200270\pi$
$859$	22.9636	+	12.0522i	0.783509	+	0.411217i	−0.0250102	+	0.999687i	$0.507962\pi$
$860$	14.8786	+	5.64270i	0.507355	+	0.192414i
$861$	29.3818	+	15.4207i	1.00133	+	0.525537i
$862$	28.0452	−	73.9492i	0.955225	−	2.51872i
$863$	−4.49565	+	18.2396i	−0.153034	+	0.620882i	0.843458	+	0.537195i	$0.180516\pi$
$863$	−4.49565	+	18.2396i	−0.153034	+	0.620882i	−0.996492	+	0.0836876i	$0.973330\pi$
$864$		−	7.93303i		−	0.269887i
$865$	10.3017	+	41.7957i	0.350269	+	1.42110i
$866$	75.0898	−	28.4778i	2.55165	−	0.967715i
$867$	−10.7105			−0.363747
$868$	−1.23241			−0.0418308
$869$	−5.99972	+	2.27539i	−0.203527	+	0.0771874i
$870$	5.82273	−	8.43568i	0.197409	−	0.285996i
$871$	−1.27336	+	4.22065i	−0.0431461	+	0.143011i
$872$	3.55136	+	5.14504i	0.120264	+	0.174233i
$873$	−2.56971	−	1.77374i	−0.0869714	−	0.0600320i
$874$	−7.00840	+	57.7194i	−0.237063	+	1.95239i
$875$	−28.2042	−	14.8027i	−0.953476	−	0.500423i
$876$	1.07795	−	0.744052i	0.0364204	−	0.0251392i
$877$	−30.7375	−	21.2166i	−1.03793	−	0.716432i	−0.0780815	−	0.996947i	$-0.524879\pi$
$877$	−30.7375	−	21.2166i	−1.03793	−	0.716432i	−0.959850	+	0.280515i	$0.909495\pi$
$878$	−22.3888	+	25.2717i	−0.755585	+	0.852880i
$879$	8.81614	−	16.7978i	0.297361	−	0.566574i
$880$	0.825199	+	6.79612i	0.0278175	+	0.229097i
$881$	−4.83972	+	12.7613i	−0.163054	+	0.429939i	−0.991496	−	0.130136i	$-0.958459\pi$
$881$	−4.83972	+	12.7613i	−0.163054	+	0.429939i	0.828442	+	0.560075i	$0.189228\pi$
$882$	−1.15623	+	0.798091i	−0.0389325	+	0.0268731i
$883$	4.33041	−	35.6641i	0.145730	−	1.20019i	−0.717929	−	0.696117i	$-0.754910\pi$
$883$	4.33041	−	35.6641i	0.145730	−	1.20019i	0.863658	−	0.504077i	$-0.168167\pi$
$884$	−43.3866	+	20.0015i	−1.45925	+	0.672724i
$885$	−0.783634	−	6.45380i	−0.0263416	−	0.216942i
$886$	8.17673	+	9.22961i	0.274702	+	0.310075i
$887$	17.4366	−	4.29773i	0.585462	−	0.144304i	0.0645512	−	0.997914i	$-0.479438\pi$
$887$	17.4366	−	4.29773i	0.585462	−	0.144304i	0.520911	+	0.853611i	$0.325592\pi$
$888$	−4.74768	+	6.87821i	−0.159322	+	0.230818i
$889$	−38.1534	−	4.63266i	−1.27962	−	0.155374i
$890$	59.7675	−	22.6668i	2.00341	−	0.759794i
$891$	1.16415	+	0.141354i	0.0390006	+	0.00473553i
$892$	−14.4188	−	58.4994i	−0.482777	−	1.95871i
$893$	28.8346	−	7.10709i	0.964913	−	0.237830i
$894$	24.6119	+	21.8043i	0.823146	+	0.729243i
$895$	−4.96501	+	5.60433i	−0.165962	+	0.187332i
$896$	−8.34167	−	21.9952i	−0.278676	−	0.734807i
$897$	−29.3133	+	5.64690i	−0.978741	+	0.188545i
$898$	−18.1642	+	47.8950i	−0.606147	+	1.59828i
$899$	0.183245	+	0.349143i	0.00611155	+	0.0116446i
$900$	−0.456298	−	0.661061i	−0.0152099	−	0.0220354i
$901$	−38.4080	−	34.0265i	−1.27955	−	1.13359i
$902$	−19.8144	−	22.3658i	−0.659747	−	0.744700i
$903$	−1.93546	+	7.85249i	−0.0644082	+	0.261314i
$904$	9.58641	+	18.2654i	0.318839	+	0.607498i
$905$	7.99726	+	5.52011i	0.265838	+	0.183495i
$906$	−10.8263	−	28.5466i	−0.359679	−	0.948397i
$907$	−8.43166	+	4.42528i	−0.279969	+	0.146939i	−0.598863	−	0.800851i	$-0.704381\pi$
$907$	−8.43166	+	4.42528i	−0.279969	+	0.146939i	0.318895	+	0.947790i	$0.396688\pi$
$908$	−28.0114	+	53.3713i	−0.929591	+	1.77119i
$909$	5.27073	+	4.66946i	0.174819	+	0.154876i
$910$	23.3834	−	39.4847i	0.775152	−	1.30891i
$911$	16.1168	−	14.2782i	0.533973	−	0.473059i	−0.352518	−	0.935805i	$-0.614674\pi$
$911$	16.1168	−	14.2782i	0.533973	−	0.473059i	0.886491	+	0.462746i	$0.153136\pi$
$912$	2.13364	+	8.65652i	0.0706519	+	0.286646i
$913$	6.43015	−	9.31569i	0.212807	−	0.308304i
$914$	−43.0376	+	38.1280i	−1.42356	+	1.26116i
$915$		−	24.3560i		−	0.805183i
$916$	−1.76182	−	1.98868i	−0.0582121	−	0.0657079i
$917$	9.19143	−	17.5128i	0.303528	−	0.578324i
$918$	11.1065	−	1.34857i	0.366568	−	0.0445094i
$919$	9.74602	−	5.11510i	0.321491	−	0.168732i	−0.296255	−	0.955109i	$-0.595738\pi$
$919$	9.74602	−	5.11510i	0.321491	−	0.168732i	0.617747	+	0.786377i	$0.288046\pi$
$920$	−2.37317	−	19.5448i	−0.0782412	−	0.644374i
$921$	0.0807784	−	0.327731i	0.00266174	−	0.0107991i
$922$	42.4926	+	10.4735i	1.39942	+	0.344926i
$923$	0.176141	+	0.914356i	0.00579776	+	0.0300964i
$924$	7.93291	−	1.95529i	0.260974	−	0.0643242i
$925$		−	2.42653i		−	0.0797838i
$926$	−5.65180	−	1.39304i	−0.185730	−	0.0457783i
$927$	8.17819	+	11.8482i	0.268607	+	0.389144i
$928$	−11.7264	+	13.2364i	−0.384939	+	0.434506i
$929$	−9.31697	+	1.13128i	−0.305680	+	0.0371162i	−0.271939	−	0.962314i	$-0.587665\pi$
$929$	−9.31697	+	1.13128i	−0.305680	+	0.0371162i	−0.0337404	+	0.999431i	$0.510742\pi$
$930$	−0.807462	+	0.0980437i	−0.0264777	+	0.00321498i
$931$	1.44837	−	1.63487i	0.0474684	−	0.0535808i
$932$	28.5575	+	41.3727i	0.935433	+	1.35521i
$933$	13.8766	+	3.42027i	0.454298	+	0.111974i
$934$		−	5.78227i		−	0.189202i
$935$	−12.9678	+	3.19628i	−0.424093	+	0.104530i
$936$	3.37265	−	2.08081i	0.110239	−	0.0680133i
$937$	23.1919	+	5.71628i	0.757645	+	0.186743i	0.599172	−	0.800620i	$-0.295497\pi$
$937$	23.1919	+	5.71628i	0.757645	+	0.186743i	0.158473	+	0.987363i	$0.449343\pi$
$938$	1.72136	−	6.98382i	0.0562043	−	0.228030i
$939$	1.40420	+	11.5646i	0.0458242	+	0.377396i
$940$	−43.3408	+	22.7470i	−1.41362	+	0.741925i
$941$	58.5964	−	7.11489i	1.91019	−	0.231939i	0.922227	−	0.386650i	$-0.126368\pi$
$941$	58.5964	−	7.11489i	1.91019	−	0.231939i	0.987960	+	0.154711i	$0.0494446\pi$
$942$	0.744383	−	1.41830i	0.0242533	−	0.0462108i
$943$	−65.8212	−	74.2968i	−2.14343	−	2.41944i
$944$			8.10806i			0.263895i
$945$	−4.48235	+	3.97102i	−0.145811	+	0.129177i
$946$	4.13702	−	5.99351i	0.134506	−	0.194866i
$947$	−12.0926	−	49.0615i	−0.392956	−	1.59429i	−0.750817	−	0.660510i	$-0.770340\pi$
$947$	−12.0926	−	49.0615i	−0.392956	−	1.59429i	0.357861	−	0.933775i	$-0.383506\pi$
$948$	10.3093	−	9.13325i	0.334831	−	0.296634i
$949$	−1.71778	−	0.754463i	−0.0557614	−	0.0244909i
$950$	1.67740	+	1.48604i	0.0544219	+	0.0482136i
$951$	11.5789	−	22.0617i	0.375471	−	0.715399i
$952$	14.1799	−	7.44220i	0.459574	−	0.241203i
$953$	15.4667	+	40.7822i	0.501014	+	1.32107i	0.912286	+	0.409553i	$0.134315\pi$
$953$	15.4667	+	40.7822i	0.501014	+	1.32107i	−0.411272	+	0.911512i	$0.634916\pi$
$954$	17.0500	+	11.7688i	0.552014	+	0.381028i
$955$	−1.78027	−	3.39202i	−0.0576082	−	0.109763i
$956$	13.2716	−	53.8451i	0.429235	−	1.74148i
$957$	−1.73346	−	1.95667i	−0.0560349	−	0.0632503i
$958$	−18.5227	−	16.4096i	−0.598440	−	0.530172i
$959$	−4.69255	−	6.79833i	−0.151530	−	0.219530i
$960$	−11.5264	−	21.9617i	−0.372012	−	0.708810i
$961$	−10.9817	+	28.9562i	−0.354247	+	0.934072i
$962$	58.1934	+	2.99100i	1.87623	+	0.0964338i
$963$	1.10461	+	2.91261i	0.0355954	+	0.0938575i
$964$	−21.2398	+	23.9747i	−0.684087	+	0.772174i
$965$	−22.2922	−	19.7492i	−0.717611	−	0.635748i
$966$	47.2905	−	11.6561i	1.52155	−	0.375027i
$967$	−4.49093	−	18.2204i	−0.144419	−	0.585929i	−0.997898	−	0.0648029i	$-0.979358\pi$
$967$	−4.49093	−	18.2204i	−0.144419	−	0.585929i	0.853479	−	0.521127i	$-0.174488\pi$
$968$	10.5015	+	1.27512i	0.337533	+	0.0409839i
$969$	−16.2631	+	6.16779i	−0.522447	+	0.198138i
$970$	−14.2531	−	1.73064i	−0.457640	−	0.0555676i
$971$	22.8997	−	33.1760i	0.734887	−	1.06467i	−0.260189	−	0.965558i	$-0.583785\pi$
$971$	22.8997	−	33.1760i	0.734887	−	1.06467i	0.995076	−	0.0991102i	$-0.0315996\pi$
$972$	−2.44400	+	0.602391i	−0.0783913	+	0.0193217i
$973$	−38.6601	−	43.6382i	−1.23939	−	1.39898i
$974$	−2.28117	−	18.7871i	−0.0730934	−	0.601978i
$975$	−0.462682	+	1.05344i	−0.0148177	+	0.0337372i
$976$	−3.66140	+	30.1544i	−0.117199	+	0.965218i
$977$	−12.3946	+	8.55535i	−0.396537	+	0.273710i	−0.749602	−	0.661889i	$-0.769755\pi$
$977$	−12.3946	+	8.55535i	−0.396537	+	0.273710i	0.353065	+	0.935599i	$0.385140\pi$
$978$	−14.7329	+	38.8473i	−0.471105	+	1.24220i
$979$	−1.96498	−	16.1830i	−0.0628009	−	0.517212i
$980$	−1.67297	+	3.18758i	−0.0534412	+	0.101824i
$981$	−3.77181	+	4.25750i	−0.120425	+	0.135931i
$982$	−28.0750	−	19.3788i	−0.895909	−	0.618401i
$983$	11.8278	−	8.16416i	0.377249	−	0.260396i	−0.364319	−	0.931274i	$-0.618698\pi$
$983$	11.8278	−	8.16416i	0.377249	−	0.260396i	0.741568	+	0.670878i	$0.234083\pi$
$984$	11.6674	+	6.12354i	0.371944	+	0.195211i
$985$	1.59965	−	13.1743i	0.0509691	−	0.419768i
$986$	−20.5247	−	14.1672i	−0.653641	−	0.451176i
$987$	−14.1319	−	20.4735i	−0.449822	−	0.651680i
$988$	−21.0114	+	21.3958i	−0.668462	+	0.680690i
$989$	13.7427	−	19.9098i	0.436994	−	0.633094i
$990$	5.04200	−	1.91218i	0.160245	−	0.0607731i
$991$	−10.6612			−0.338665			−0.169333	−	0.985559i	$-0.554161\pi$
$991$	−10.6612			−0.338665			−0.169333	+	0.985559i	$0.554161\pi$
$992$	1.40328			0.0445541
$993$	−0.00653877	+	0.00247983i	−0.000207502	+	7.86950e-5i
$994$	−0.363582	−	1.47511i	−0.0115321	−	0.0467877i
$995$		−	33.5340i		−	1.06310i
$996$	−5.81453	+	23.5905i	−0.184240	+	0.747492i
$997$	−3.24979	+	8.56899i	−0.102922	+	0.271383i	−0.976579	−	0.215160i	$-0.930973\pi$
$997$	−3.24979	+	8.56899i	−0.102922	+	0.271383i	0.873657	+	0.486542i	$0.161742\pi$
$998$	7.94957	+	4.17226i	0.251639	+	0.132070i
$999$	−7.10988	−	2.69642i	−0.224947	−	0.0853110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.64.3	✓	192
169.103	even	26	inner	507.2.p.b.103.3	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.64.3	✓	192	1.1	even	1	trivial
507.2.p.b.103.3	yes	192	169.103	even	26	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10986 - 0.256183i) q^{2} +(0.748511 - 0.663123i) q^{3} +(2.44400 + 0.602391i) q^{4} +(1.00545 + 1.91572i) q^{5} +(-1.74913 + 1.20734i) q^{6} +(-2.58799 - 0.981496i) q^{7} +(-1.02769 - 0.389750i) q^{8} +(0.120537 - 0.992709i) q^{9} +O(q^{10})\)	\(q+(-2.10986 - 0.256183i) q^{2} +(0.748511 - 0.663123i) q^{3} +(2.44400 + 0.602391i) q^{4} +(1.00545 + 1.91572i) q^{5} +(-1.74913 + 1.20734i) q^{6} +(-2.58799 - 0.981496i) q^{7} +(-1.02769 - 0.389750i) q^{8} +(0.120537 - 0.992709i) q^{9} +(-1.63057 - 4.29947i) q^{10} +(-1.16415 + 0.141354i) q^{11} +(2.22882 - 1.16977i) q^{12} +(-3.10234 - 1.83725i) q^{13} +(5.20886 + 2.73382i) q^{14} +(2.02294 + 0.767200i) q^{15} +(-2.38921 - 1.25395i) q^{16} +(1.86667 - 4.92200i) q^{17} +(-0.508631 + 2.06360i) q^{18} -3.30417i q^{19} +(1.30330 + 5.28768i) q^{20} +(-2.58799 + 0.981496i) q^{21} +2.49241 q^{22} +8.27952 q^{23} +(-1.02769 + 0.389750i) q^{24} +(0.181276 - 0.262624i) q^{25} +(6.07483 + 4.67111i) q^{26} +(-0.568065 - 0.822984i) q^{27} +(-5.73380 - 3.95776i) q^{28} +(-0.268690 + 2.21286i) q^{29} +(-4.07158 - 2.13693i) q^{30} +(0.145578 - 0.100485i) q^{31} +(6.52876 + 4.50648i) q^{32} +(-0.777646 + 0.877781i) q^{33} +(-5.19934 + 9.90652i) q^{34} +(-0.721817 - 5.94470i) q^{35} +(0.892591 - 2.35357i) q^{36} +(6.25798 - 4.31957i) q^{37} +(-0.846475 + 6.97135i) q^{38} +(-3.54046 + 0.682033i) q^{39} +(-0.286632 - 2.36063i) q^{40} +(-7.94989 - 8.97357i) q^{41} +(5.71174 - 1.40782i) q^{42} +(1.65985 - 2.40470i) q^{43} +(-2.93034 - 0.355807i) q^{44} +(2.02294 - 0.767200i) q^{45} +(-17.4686 - 2.12107i) q^{46} +(2.15094 + 8.72672i) q^{47} +(-2.61987 + 0.645741i) q^{48} +(0.494790 + 0.438346i) q^{49} +(-0.449747 + 0.507660i) q^{50} +(-1.86667 - 4.92200i) q^{51} +(-6.47537 - 6.35905i) q^{52} +(3.45657 - 9.11423i) q^{53} +(0.987703 + 1.88191i) q^{54} +(-1.44129 - 2.08806i) q^{55} +(2.27710 + 2.01734i) q^{56} +(-2.19107 - 2.47321i) q^{57} +(1.13380 - 4.60000i) q^{58} +(-1.39645 - 2.66070i) q^{59} +(4.48191 + 3.09364i) q^{60} +(-3.99196 - 10.5259i) q^{61} +(-0.332892 + 0.174715i) q^{62} +(-1.28629 + 2.45082i) q^{63} +(-8.58090 - 7.60201i) q^{64} +(0.400411 - 7.79046i) q^{65} +(1.86560 - 1.65277i) q^{66} +(-0.292614 - 1.18718i) q^{67} +(7.52710 - 10.9049i) q^{68} +(6.19731 - 5.49033i) q^{69} +12.7274i q^{70} +(-0.171258 - 0.193310i) q^{71} +(-0.510782 + 0.973213i) q^{72} +(0.516559 - 0.0627216i) q^{73} +(-14.3101 + 7.51050i) q^{74} +(-0.0384647 - 0.316785i) q^{75} +(1.99041 - 8.07539i) q^{76} +(3.15155 + 0.776788i) q^{77} +(7.64459 - 0.531988i) q^{78} +(5.31272 - 1.30947i) q^{79} -5.83783i q^{80} +(-0.970942 - 0.239316i) q^{81} +(14.4743 + 20.9696i) q^{82} +(-6.40073 + 7.22493i) q^{83} +(-6.91629 + 0.839790i) q^{84} +(11.3060 - 1.37279i) q^{85} +(-4.11809 + 4.64837i) q^{86} +(1.26628 + 1.83453i) q^{87} +(1.25148 + 0.308461i) q^{88} +13.9011i q^{89} +(-4.46467 + 1.10044i) q^{90} +(6.22558 + 7.79972i) q^{91} +(20.2351 + 4.98751i) q^{92} +(0.0423326 - 0.171750i) q^{93} +(-2.30255 - 18.9632i) q^{94} +(6.32986 - 3.32217i) q^{95} +(7.87519 - 0.956221i) q^{96} +(1.45106 - 2.76477i) q^{97} +(-0.931641 - 1.05161i) q^{98} +1.17270i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more