LMFDB - Embedded newform 507.2.m.a.40.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, 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:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.11
Character	$\chi$	$=$	507.40
Dual form			507.2.m.a.469.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36051 + 0.335337i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(-0.0323644 - 0.0169861i) q^{4} +(1.40752 - 2.03915i) q^{5} +(-0.496883 + 1.31017i) q^{6} +(-3.59937 - 3.18876i) q^{7} +(-2.13601 - 1.89234i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(1.36051 + 0.335337i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(-0.0323644 - 0.0169861i) q^{4} +(1.40752 - 2.03915i) q^{5} +(-0.496883 + 1.31017i) q^{6} +(-3.59937 - 3.18876i) q^{7} +(-2.13601 - 1.89234i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(2.59876 - 2.30230i) q^{10} +(4.04071 - 0.995946i) q^{11} +(0.0207634 - 0.0300809i) q^{12} +(0.722232 - 3.53248i) q^{13} +(-3.82768 - 5.54535i) q^{14} +(1.85463 + 1.64306i) q^{15} +(-2.22997 - 3.23067i) q^{16} +(4.68987 + 4.15486i) q^{17} +(-1.24073 - 0.651185i) q^{18} -2.59004 q^{19} +(-0.0801910 + 0.0420875i) q^{20} +(3.59937 - 3.18876i) q^{21} +5.83142 q^{22} -7.25957 q^{23} +(2.13601 - 1.89234i) q^{24} +(-0.403989 - 1.06523i) q^{25} +(2.16718 - 4.56379i) q^{26} +(0.354605 - 0.935016i) q^{27} +(0.0623265 + 0.164342i) q^{28} +(8.40344 + 2.07126i) q^{29} +(1.97227 + 2.85732i) q^{30} +(-0.0560413 + 0.147769i) q^{31} +(0.0733103 + 0.193303i) q^{32} +(0.501630 + 4.13130i) q^{33} +(4.98736 + 7.22544i) q^{34} +(-11.5686 + 2.85140i) q^{35} +(0.0273589 + 0.0242379i) q^{36} +(0.181022 - 0.477315i) q^{37} +(-3.52379 - 0.868536i) q^{38} +(3.41966 + 1.14276i) q^{39} +(-6.86525 + 1.69213i) q^{40} +(-0.591760 + 4.87358i) q^{41} +(5.96630 - 3.13135i) q^{42} +(-0.638186 - 1.68276i) q^{43} +(-0.147692 - 0.0364029i) q^{44} +(-1.85463 + 1.64306i) q^{45} +(-9.87674 - 2.43440i) q^{46} +(5.72595 - 3.00521i) q^{47} +(3.47591 - 1.82430i) q^{48} +(1.94349 + 16.0061i) q^{49} +(-0.192422 - 1.58474i) q^{50} +(-4.68987 + 4.15486i) q^{51} +(-0.0833777 + 0.102058i) q^{52} +(-6.81953 - 6.04158i) q^{53} +(0.795990 - 1.15319i) q^{54} +(3.65652 - 9.64144i) q^{55} +(1.65406 + 13.6224i) q^{56} +(0.312195 - 2.57116i) q^{57} +(10.7384 + 5.63596i) q^{58} +(7.18102 - 10.4035i) q^{59} +(-0.0321146 - 0.0846794i) q^{60} +(2.68656 - 2.38009i) q^{61} +(-0.125797 + 0.182249i) q^{62} +(2.73166 + 3.95749i) q^{63} +(0.981266 + 8.08146i) q^{64} +(-6.18669 - 6.44479i) q^{65} +(-0.702900 + 5.78890i) q^{66} +(8.78396 - 4.61018i) q^{67} +(-0.0812097 - 0.214132i) q^{68} +(0.875044 - 7.20664i) q^{69} -16.6954 q^{70} +(-0.160276 + 1.32000i) q^{71} +(1.62107 + 2.34853i) q^{72} +(-7.43333 + 1.83215i) q^{73} +(0.406344 - 0.588691i) q^{74} +(1.10616 - 0.272644i) q^{75} +(0.0838251 + 0.0439948i) q^{76} +(-17.7198 - 9.30008i) q^{77} +(4.26929 + 2.70148i) q^{78} +(6.23159 - 3.27059i) q^{79} -9.72658 q^{80} +(0.885456 + 0.464723i) q^{81} +(-2.43939 + 6.43214i) q^{82} +(-0.909536 - 7.49070i) q^{83} +(-0.170656 + 0.0420629i) q^{84} +(15.0735 - 3.71529i) q^{85} +(-0.303970 - 2.50342i) q^{86} +(-3.06908 + 8.09251i) q^{87} +(-10.5157 - 5.51905i) q^{88} +5.26004 q^{89} +(-3.07422 + 1.61348i) q^{90} +(-13.8638 + 10.4116i) q^{91} +(0.234951 + 0.123312i) q^{92} +(-0.139936 - 0.0734443i) q^{93} +(8.79799 - 2.16851i) q^{94} +(-3.64555 + 5.28149i) q^{95} +(-0.200731 + 0.0494757i) q^{96} +(5.85340 + 8.48011i) q^{97} +(-2.72328 + 22.4282i) q^{98} -4.16164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	1.36051	+	0.335337i	0.962029	+	0.237119i	0.688898	−	0.724858i	$-0.258095\pi$
$2$	1.36051	+	0.335337i	0.962029	+	0.237119i	0.273131	+	0.961977i	$0.411941\pi$
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$4$	−0.0323644	−	0.0169861i	−0.0161822	−	0.00849307i
$5$	1.40752	−	2.03915i	0.629464	−	0.911936i	−0.370392	−	0.928875i	$-0.620777\pi$
$5$	1.40752	−	2.03915i	0.629464	−	0.911936i	0.999857	+	0.0169390i	$0.00539212\pi$
$6$	−0.496883	+	1.31017i	−0.202852	+	0.534876i
$7$	−3.59937	−	3.18876i	−1.36043	−	1.20524i	−0.956951	−	0.290251i	$-0.906261\pi$
$7$	−3.59937	−	3.18876i	−1.36043	−	1.20524i	−0.403482	−	0.914987i	$-0.632200\pi$
$8$	−2.13601	−	1.89234i	−0.755193	−	0.669043i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	2.59876	−	2.30230i	0.821800	−	0.728051i
$11$	4.04071	−	0.995946i	1.21832	−	0.300289i	0.422804	−	0.906221i	$-0.361046\pi$
$11$	4.04071	−	0.995946i	1.21832	−	0.300289i	0.795516	+	0.605932i	$0.207200\pi$
$12$	0.0207634	−	0.0300809i	0.00599387	−	0.00868362i
$13$	0.722232	−	3.53248i	0.200311	−	0.979732i
$13$	0.722232	−	3.53248i	0.200311	−	0.979732i
$14$	−3.82768	−	5.54535i	−1.02299	−	1.48206i
$15$	1.85463	+	1.64306i	0.478862	+	0.424235i
$16$	−2.22997	−	3.23067i	−0.557493	−	0.807669i
$17$	4.68987	+	4.15486i	1.13746	+	1.00770i	0.999852	+	0.0172159i	$0.00548027\pi$
$17$	4.68987	+	4.15486i	1.13746	+	1.00770i	0.137609	+	0.990487i	$0.456058\pi$
$18$	−1.24073	−	0.651185i	−0.292443	−	0.153486i
$19$	−2.59004			−0.594196			−0.297098	−	0.954847i	$-0.596019\pi$
$19$	−2.59004			−0.594196			−0.297098	+	0.954847i	$0.596019\pi$
$20$	−0.0801910	+	0.0420875i	−0.0179312	+	0.00941104i
$21$	3.59937	−	3.18876i	0.785446	−	0.695845i
$22$	5.83142			1.24326
$23$	−7.25957			−1.51372			−0.756862	−	0.653574i	$-0.773269\pi$
$23$	−7.25957			−1.51372			−0.756862	+	0.653574i	$0.773269\pi$
$24$	2.13601	−	1.89234i	0.436011	−	0.386272i
$25$	−0.403989	−	1.06523i	−0.0807979	−	0.213046i
$26$	2.16718	−	4.56379i	0.425018	−	0.895033i
$27$	0.354605	−	0.935016i	0.0682437	−	0.179944i
$28$	0.0623265	+	0.164342i	0.0117786	+	0.0310576i
$29$	8.40344	+	2.07126i	1.56048	+	0.384624i	0.922676	−	0.385575i	$-0.125997\pi$
$29$	8.40344	+	2.07126i	1.56048	+	0.384624i	0.637804	+	0.770199i	$0.279843\pi$
$30$	1.97227	+	2.85732i	0.360085	+	0.521673i
$31$	−0.0560413	+	0.147769i	−0.0100653	+	0.0265401i	−0.939955	−	0.341299i	$-0.889133\pi$
$31$	−0.0560413	+	0.147769i	−0.0100653	+	0.0265401i	0.929889	+	0.367839i	$0.119902\pi$
$32$	0.0733103	+	0.193303i	0.0129596	+	0.0341715i
$33$	0.501630	+	4.13130i	0.0873226	+	0.719166i
$34$	4.98736	+	7.22544i	0.855325	+	1.23915i
$35$	−11.5686	+	2.85140i	−1.95544	+	0.481974i
$36$	0.0273589	+	0.0242379i	0.00455981	+	0.00403964i
$37$	0.181022	−	0.477315i	0.0297598	−	0.0784701i	−0.919313	−	0.393528i	$-0.871255\pi$
$37$	0.181022	−	0.477315i	0.0297598	−	0.0784701i	0.949073	+	0.315057i	$0.102024\pi$
$38$	−3.52379	−	0.868536i	−0.571634	−	0.140895i
$39$	3.41966	+	1.14276i	0.547584	+	0.182988i
$40$	−6.86525	+	1.69213i	−1.08549	+	0.267550i
$41$	−0.591760	+	4.87358i	−0.0924174	+	0.761126i	0.870657	+	0.491890i	$0.163694\pi$
$41$	−0.591760	+	4.87358i	−0.0924174	+	0.761126i	−0.963074	+	0.269235i	$0.913229\pi$
$42$	5.96630	−	3.13135i	0.920620	−	0.483178i
$43$	−0.638186	−	1.68276i	−0.0973224	−	0.256618i	0.877510	−	0.479559i	$-0.159203\pi$
$43$	−0.638186	−	1.68276i	−0.0973224	−	0.256618i	−0.974832	+	0.222941i	$0.928434\pi$
$44$	−0.147692	−	0.0364029i	−0.0222655	−	0.00548794i
$45$	−1.85463	+	1.64306i	−0.276471	+	0.244932i
$46$	−9.87674	−	2.43440i	−1.45625	−	0.358933i
$47$	5.72595	−	3.00521i	0.835216	−	0.438355i	0.00781660	−	0.999969i	$-0.497512\pi$
$47$	5.72595	−	3.00521i	0.835216	−	0.438355i	0.827399	+	0.561614i	$0.189820\pi$
$48$	3.47591	−	1.82430i	0.501705	−	0.263315i
$49$	1.94349	+	16.0061i	0.277641	+	2.28658i
$50$	−0.192422	−	1.58474i	−0.0272126	−	0.224116i
$51$	−4.68987	+	4.15486i	−0.656713	+	0.581797i
$52$	−0.0833777	+	0.102058i	−0.0115624	+	0.0141530i
$53$	−6.81953	−	6.04158i	−0.936735	−	0.829875i	0.0488932	−	0.998804i	$-0.484431\pi$
$53$	−6.81953	−	6.04158i	−0.936735	−	0.829875i	−0.985628	+	0.168929i	$0.945969\pi$
$54$	0.795990	−	1.15319i	0.108321	−	0.156929i
$55$	3.65652	−	9.64144i	0.493044	−	1.30005i
$56$	1.65406	+	13.6224i	0.221034	+	1.82038i
$57$	0.312195	−	2.57116i	0.0413512	−	0.340558i
$58$	10.7384	+	5.63596i	1.41002	+	0.740038i
$59$	7.18102	−	10.4035i	0.934889	−	1.35442i	−0.000197845	−	1.00000i	$-0.500063\pi$
$59$	7.18102	−	10.4035i	0.934889	−	1.35442i	0.935086	−	0.354420i	$-0.115322\pi$
$60$	−0.0321146	−	0.0846794i	−0.00414598	−	0.0109321i
$61$	2.68656	−	2.38009i	0.343979	−	0.304739i	−0.473390	−	0.880853i	$-0.656970\pi$
$61$	2.68656	−	2.38009i	0.343979	−	0.304739i	0.817369	+	0.576114i	$0.195432\pi$
$62$	−0.125797	+	0.182249i	−0.0159763	+	0.0231456i
$63$	2.73166	+	3.95749i	0.344156	+	0.498596i
$64$	0.981266	+	8.08146i	0.122658	+	1.01018i
$65$	−6.18669	−	6.44479i	−0.767365	−	0.799378i
$66$	−0.702900	+	5.78890i	−0.0865210	+	0.712565i
$67$	8.78396	−	4.61018i	1.07313	−	0.563223i	0.166887	−	0.985976i	$-0.446629\pi$
$67$	8.78396	−	4.61018i	1.07313	−	0.563223i	0.906245	+	0.422753i	$0.138936\pi$
$68$	−0.0812097	−	0.214132i	−0.00984812	−	0.0259674i
$69$	0.875044	−	7.20664i	0.105343	−	0.867577i
$70$	−16.6954			−1.99548
$71$	−0.160276	+	1.32000i	−0.0190213	+	0.156655i	−0.999125	−	0.0418336i	$-0.986680\pi$
$71$	−0.160276	+	1.32000i	−0.0190213	+	0.156655i	0.980103	+	0.198488i	$0.0636032\pi$
$72$	1.62107	+	2.34853i	0.191045	+	0.276777i
$73$	−7.43333	+	1.83215i	−0.870006	+	0.214437i	−0.648956	−	0.760826i	$-0.724794\pi$
$73$	−7.43333	+	1.83215i	−0.870006	+	0.214437i	−0.221049	+	0.975263i	$0.570948\pi$
$74$	0.406344	−	0.588691i	0.0472365	−	0.0684339i
$75$	1.10616	−	0.272644i	0.127729	−	0.0314822i
$76$	0.0838251	+	0.0439948i	0.00961540	+	0.00504655i
$77$	−17.7198	−	9.30008i	−2.01936	−	1.05984i
$78$	4.26929	+	2.70148i	0.483402	+	0.305882i
$79$	6.23159	−	3.27059i	0.701109	−	0.367970i	−0.0761975	−	0.997093i	$-0.524278\pi$
$79$	6.23159	−	3.27059i	0.701109	−	0.367970i	0.777306	+	0.629123i	$0.216586\pi$
$80$	−9.72658			−1.08746
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	−2.43939	+	6.43214i	−0.269385	+	0.710311i
$83$	−0.909536	−	7.49070i	−0.0998345	−	0.822211i	−0.953501	−	0.301391i	$-0.902549\pi$
$83$	−0.909536	−	7.49070i	−0.0998345	−	0.822211i	0.853666	−	0.520820i	$-0.174374\pi$
$84$	−0.170656	+	0.0420629i	−0.0186201	+	0.00458944i
$85$	15.0735	−	3.71529i	1.63495	−	0.402979i
$86$	−0.303970	−	2.50342i	−0.0327780	−	0.269951i
$87$	−3.06908	+	8.09251i	−0.329040	+	0.867608i
$88$	−10.5157	−	5.51905i	−1.12097	−	0.588332i
$89$	5.26004			0.557563			0.278781	−	0.960355i	$-0.410070\pi$
$89$	5.26004			0.557563			0.278781	+	0.960355i	$0.410070\pi$
$90$	−3.07422	+	1.61348i	−0.324051	+	0.170075i
$91$	−13.8638	+	10.4116i	−1.45332	+	1.09144i
$92$	0.234951	+	0.123312i	0.0244954	+	0.0128562i
$93$	−0.139936	−	0.0734443i	−0.0145107	−	0.00761582i
$94$	8.79799	−	2.16851i	0.907444	−	0.223665i
$95$	−3.64555	+	5.28149i	−0.374025	+	0.541869i
$96$	−0.200731	+	0.0494757i	−0.0204870	+	0.00504959i
$97$	5.85340	+	8.48011i	0.594322	+	0.861025i	0.998561	−	0.0536291i	$-0.0170789\pi$
$97$	5.85340	+	8.48011i	0.594322	+	0.861025i	−0.404239	+	0.914654i	$0.632463\pi$
$98$	−2.72328	+	22.4282i	−0.275093	+	2.26559i
$99$	−4.16164			−0.418261
$100$	−0.00501932	+	0.0413378i	−0.000501932	+	0.00413378i
$101$	2.41653	+	6.37185i	0.240453	+	0.634023i	0.999862	−	0.0165902i	$-0.00528108\pi$
$101$	2.41653	+	6.37185i	0.240453	+	0.634023i	−0.759409	+	0.650613i	$0.774512\pi$
$102$	−7.77391	+	4.08006i	−0.769732	+	0.403987i
$103$	−2.09022	+	17.2145i	−0.205955	+	1.69619i	0.412970	+	0.910745i	$0.364491\pi$
$103$	−2.09022	+	17.2145i	−0.205955	+	1.69619i	−0.618925	+	0.785450i	$0.712432\pi$
$104$	−8.22734	+	6.17869i	−0.806757	+	0.605871i
$105$	−1.43617	−	11.8279i	−0.140156	−	1.15429i
$106$	−7.25211	−	10.5065i	−0.704387	−	1.02048i
$107$	−3.76535	+	5.45505i	−0.364010	+	0.527359i	−0.961604	−	0.274439i	$-0.911508\pi$
$107$	−3.76535	+	5.45505i	−0.364010	+	0.527359i	0.597595	+	0.801798i	$0.296123\pi$
$108$	−0.0273589	+	0.0242379i	−0.00263261	+	0.00233229i
$109$	1.90907	+	5.03381i	0.182856	+	0.482151i	0.994831	−	0.101540i	$-0.0323770\pi$
$109$	1.90907	+	5.03381i	0.182856	+	0.482151i	−0.811976	+	0.583691i	$0.801608\pi$
$110$	8.20787	−	11.8912i	0.782590	−	1.13378i
$111$	0.452015	+	0.237236i	0.0429034	+	0.0225174i
$112$	−2.27535	+	18.7392i	−0.215001	+	1.77069i
$113$	1.20325	+	9.90964i	0.113192	+	0.932221i	0.933073	+	0.359687i	$0.117116\pi$
$113$	1.20325	+	9.90964i	0.113192	+	0.932221i	−0.819881	+	0.572534i	$0.805960\pi$
$114$	1.28695	−	3.39340i	0.120534	−	0.317821i
$115$	−10.2180	+	14.8034i	−0.952836	+	1.38042i
$116$	−0.236789	−	0.209777i	−0.0219853	−	0.0194773i
$117$	−1.54662	+	3.25699i	−0.142985	+	0.301108i
$118$	13.2585	−	11.7460i	1.22055	−	1.08131i
$119$	−3.63170	−	29.9098i	−0.332918	−	2.74182i
$120$	−0.852281	−	7.01916i	−0.0778022	−	0.640759i
$121$	5.59542	−	2.93670i	0.508674	−	0.266973i
$122$	4.45324	−	2.33724i	0.403177	−	0.211604i
$123$	−4.76672	−	1.17489i	−0.429801	−	0.105936i
$124$	0.00432376	−	0.00383052i	0.000388286	−	0.000343991i
$125$	9.28798	+	2.28928i	0.830742	+	0.204760i
$126$	2.38937	+	6.30024i	0.212862	+	0.561270i
$127$	4.66699	−	2.44943i	0.414129	−	0.217352i	−0.244773	−	0.969580i	$-0.578713\pi$
$127$	4.66699	−	2.44943i	0.414129	−	0.217352i	0.658902	+	0.752229i	$0.271021\pi$
$128$	−1.32514	+	10.9135i	−0.117127	+	0.964629i
$129$	1.74741	−	0.430698i	0.153851	−	0.0379209i
$130$	−6.25591	−	10.8428i	−0.548680	−	0.950981i
$131$	−15.0402	−	3.70708i	−1.31407	−	0.323889i	−0.480835	−	0.876811i	$-0.659667\pi$
$131$	−15.0402	−	3.70708i	−1.31407	−	0.323889i	−0.833233	+	0.552922i	$0.813513\pi$
$132$	0.0539398	−	0.142228i	0.00469486	−	0.0123793i
$133$	9.32251	+	8.25902i	0.808364	+	0.716148i
$134$	13.4967	−	3.32663i	1.16593	−	0.287377i
$135$	−1.40752	−	2.03915i	−0.121140	−	0.175502i
$136$	−2.15520	−	17.7497i	−0.184807	−	1.52202i
$137$	−0.461093	−	1.21580i	−0.0393938	−	0.103873i	0.913876	−	0.405994i	$-0.133075\pi$
$137$	−0.461093	−	1.21580i	−0.0393938	−	0.103873i	−0.953270	+	0.302121i	$0.902305\pi$
$138$	3.60716	−	9.51130i	0.307062	−	0.809655i
$139$	−2.59146	−	3.75438i	−0.219805	−	0.318442i	0.697533	−	0.716553i	$-0.254281\pi$
$139$	−2.59146	−	3.75438i	−0.219805	−	0.318442i	−0.917337	+	0.398111i	$0.869666\pi$
$140$	0.422844	+	0.104222i	0.0357368	+	0.00880833i
$141$	2.29311	+	6.04644i	0.193115	+	0.509202i
$142$	−0.660701	+	1.74213i	−0.0554448	+	0.146196i
$143$	−0.599822	−	14.9930i	−0.0501596	−	1.25378i
$144$	1.39202	+	3.67046i	0.116002	+	0.305872i
$145$	16.0517	−	14.2205i	1.33302	−	1.18095i
$146$	−10.7275			−0.887817
$147$	−16.1236			−1.32986
$148$	−0.0139664	+	0.0123731i	−0.00114803	+	0.00101707i
$149$	−2.16797	+	1.13784i	−0.177607	+	0.0932152i	−0.551184	−	0.834384i	$-0.685824\pi$
$149$	−2.16797	+	1.13784i	−0.177607	+	0.0932152i	0.373577	+	0.927599i	$0.378131\pi$
$150$	1.59638			0.130344
$151$	16.4934	+	8.65640i	1.34221	+	0.704448i	0.974267	−	0.225399i	$-0.0723685\pi$
$151$	16.4934	+	8.65640i	1.34221	+	0.704448i	0.367947	+	0.929847i	$0.380061\pi$
$152$	5.53235	+	4.90124i	0.448733	+	0.397543i
$153$	−3.55927	−	5.15649i	−0.287750	−	0.416878i
$154$	−20.9894	−	18.5950i	−1.69138	−	1.49843i
$155$	0.222444	+	0.322265i	0.0178671	+	0.0258850i
$156$	−0.0912642	−	0.0950716i	−0.00730699	−	0.00761182i
$157$	−2.80896	+	4.06949i	−0.224180	+	0.324780i	−0.918893	−	0.394506i	$-0.870916\pi$
$157$	−2.80896	+	4.06949i	−0.224180	+	0.324780i	0.694714	+	0.719286i	$0.255531\pi$
$158$	9.57491	−	2.36000i	0.761739	−	0.187752i
$159$	6.81953	−	6.04158i	0.540824	−	0.479128i
$160$	0.497361	+	0.122589i	0.0393199	+	0.00969147i
$161$	26.1299	+	23.1490i	2.05932	+	1.82440i
$162$	1.04884	+	0.929188i	0.0824044	+	0.0730039i
$163$	1.80639	−	4.76307i	0.141488	−	0.373072i	−0.845476	−	0.534013i	$-0.820683\pi$
$163$	1.80639	−	4.76307i	0.141488	−	0.373072i	0.986964	+	0.160940i	$0.0514527\pi$
$164$	0.101935	−	0.147679i	0.00795981	−	0.0115318i
$165$	9.13040	+	4.79200i	0.710801	+	0.373057i
$166$	1.27447	−	10.4962i	0.0989180	−	0.814663i
$167$	−7.95302	−	1.96024i	−0.615423	−	0.151688i	−0.0807322	−	0.996736i	$-0.525726\pi$
$167$	−7.95302	−	1.96024i	−0.615423	−	0.151688i	−0.534691	+	0.845048i	$0.679572\pi$
$168$	−13.7225			−1.05871
$169$	−11.9568	−	5.10254i	−0.919751	−	0.392503i
$170$	21.7536			1.66842
$171$	2.51478	+	0.619838i	0.192310	+	0.0474002i
$172$	−0.00792906	+	0.0653017i	−0.000604585	+	0.00497921i
$173$	2.75861	+	1.44783i	0.209733	+	0.110076i	0.566319	−	0.824186i	$-0.308367\pi$
$173$	2.75861	+	1.44783i	0.209733	+	0.110076i	−0.356586	+	0.934263i	$0.616059\pi$
$174$	−6.88924	+	9.98079i	−0.522272	+	0.756642i
$175$	−1.94267	+	5.12239i	−0.146852	+	0.387216i
$176$	−12.2283	−	10.8333i	−0.921739	−	0.816590i
$177$	9.46207	+	8.38266i	0.711213	+	0.630079i
$178$	7.15635	+	1.76388i	0.536391	+	0.132209i
$179$	−10.1977	+	9.03437i	−0.762212	+	0.675261i	−0.951840	−	0.306595i	$-0.900810\pi$
$179$	−10.1977	+	9.03437i	−0.762212	+	0.675261i	0.189628	+	0.981856i	$0.439272\pi$
$180$	0.0879330	−	0.0216735i	0.00655414	−	0.00161545i
$181$	13.4700	−	19.5146i	1.00122	−	1.45051i	0.111627	−	0.993750i	$-0.464394\pi$
$181$	13.4700	−	19.5146i	1.00122	−	1.45051i	0.889589	−	0.456762i	$-0.150991\pi$
$182$	−22.3533	+	9.51615i	−1.65694	+	0.705384i
$183$	2.03890	+	2.95386i	0.150720	+	0.218356i
$184$	15.5065	+	13.7376i	1.14315	+	1.01275i
$185$	−0.718525	−	1.04096i	−0.0528270	−	0.0765332i
$186$	−0.165757	−	0.146848i	−0.0121539	−	0.0107674i
$187$	23.0884	+	12.1177i	1.68839	+	0.886137i
$188$	−0.236364			−0.0172386
$189$	−4.25790	+	2.23472i	−0.309716	+	0.162552i
$190$	−6.73089	+	5.96305i	−0.488310	+	0.432605i
$191$	3.79318			0.274465			0.137232	−	0.990539i	$-0.456179\pi$
$191$	3.79318			0.274465			0.137232	+	0.990539i	$0.456179\pi$
$192$	−8.14081			−0.587512
$193$	−4.20977	+	3.72953i	−0.303026	+	0.268458i	−0.800908	−	0.598787i	$-0.795650\pi$
$193$	−4.20977	+	3.72953i	−0.303026	+	0.268458i	0.497882	+	0.867245i	$0.334111\pi$
$194$	5.11994	+	13.5002i	0.367590	+	0.969255i
$195$	7.14352	−	5.36475i	0.511558	−	0.384178i
$196$	0.208982	−	0.551039i	0.0149273	−	0.0393599i
$197$	−4.15000	−	10.9427i	−0.295676	−	0.779632i	−0.997719	−	0.0674986i	$-0.978498\pi$
$197$	−4.15000	−	10.9427i	−0.295676	−	0.779632i	0.702044	−	0.712134i	$-0.252271\pi$
$198$	−5.66197	−	1.39555i	−0.402379	−	0.0991774i
$199$	11.8596	+	17.1817i	0.840708	+	1.21798i	0.973921	+	0.226888i	$0.0728551\pi$
$199$	11.8596	+	17.1817i	0.840708	+	1.21798i	−0.133213	+	0.991087i	$0.542529\pi$
$200$	−1.15286	+	3.03983i	−0.0815192	+	0.214949i
$201$	3.51778	+	9.27561i	0.248125	+	0.654251i
$202$	1.15100	+	9.47935i	0.0809841	+	0.666964i
$203$	−23.6423	−	34.2518i	−1.65936	−	2.40400i
$204$	0.222360	−	0.0548068i	0.0155683	−	0.00383724i
$205$	9.10506	+	8.06638i	0.635925	+	0.563380i
$206$	−8.61642	+	22.7196i	−0.600334	+	1.58295i
$207$	7.04862	+	1.73733i	0.489913	+	0.120753i
$208$	−13.0228	+	5.54403i	−0.902971	+	0.384409i
$209$	−10.4656	+	2.57954i	−0.723921	+	0.178431i
$210$	2.01240	−	16.5736i	0.138869	−	1.14369i
$211$	2.43581	−	1.27841i	0.167688	−	0.0880097i	−0.378791	−	0.925482i	$-0.623660\pi$
$211$	2.43581	−	1.27841i	0.167688	−	0.0880097i	0.546479	+	0.837473i	$0.315968\pi$
$212$	0.118087	+	0.311369i	0.00811024	+	0.0213849i
$213$	−1.29105	−	0.318216i	−0.0884614	−	0.0218038i
$214$	−6.95208	+	6.15901i	−0.475235	+	0.421021i
$215$	−4.32966	−	1.06717i	−0.295280	−	0.0727801i
$216$	−2.52681	+	1.32617i	−0.171927	+	0.0902345i
$217$	0.672913	−	0.353172i	0.0456803	−	0.0239749i
$218$	0.909299	+	7.48875i	0.0615855	+	0.507202i
$219$	−0.922804	−	7.59998i	−0.0623573	−	0.513559i
$220$	−0.282112	+	0.249929i	−0.0190200	+	0.0168502i
$221$	18.0641	−	13.5661i	1.21512	−	0.912553i
$222$	0.535419	+	0.474340i	0.0359350	+	0.0318356i
$223$	−3.99632	+	5.78967i	−0.267614	+	0.387705i	−0.933634	−	0.358228i	$-0.883381\pi$
$223$	−3.99632	+	5.78967i	−0.267614	+	0.387705i	0.666020	+	0.745934i	$0.267996\pi$
$224$	0.352528	−	0.929539i	0.0235542	−	0.0621075i
$225$	0.137323	+	1.13096i	0.00915489	+	0.0753973i
$226$	−1.68603	+	13.8857i	−0.112153	+	0.923663i
$227$	−15.3695	−	8.06654i	−1.02011	−	0.535395i	−0.130179	−	0.991490i	$-0.541555\pi$
$227$	−15.3695	−	8.06654i	−1.02011	−	0.535395i	−0.889931	+	0.456095i	$0.849248\pi$
$228$	−0.0537780	+	0.0779109i	−0.00356154	+	0.00515978i
$229$	−6.83729	−	18.0284i	−0.451821	−	1.19135i	−0.946622	−	0.322347i	$-0.895528\pi$
$229$	−6.83729	−	18.0284i	−0.451821	−	1.19135i	0.494801	−	0.869006i	$-0.335241\pi$
$230$	−18.8659	+	16.7137i	−1.24398	+	1.10207i
$231$	11.3682	−	16.4696i	0.747970	−	1.08362i
$232$	−14.0303	−	20.3264i	−0.921134	−	1.33449i
$233$	−1.83470	−	15.1101i	−0.120195	−	0.989894i	−0.920620	−	0.390461i	$-0.872316\pi$
$233$	−1.83470	−	15.1101i	−0.120195	−	0.989894i	0.800425	−	0.599433i	$-0.204607\pi$
$234$	−3.19639	+	3.91254i	−0.208954	+	0.255771i
$235$	1.93134	−	15.9060i	0.125987	−	1.03759i
$236$	−0.409124	+	0.214725i	−0.0266317	+	0.0139774i
$237$	2.49561	+	6.58038i	0.162107	+	0.427442i
$238$	5.08885	−	41.9105i	0.329861	−	2.71665i
$239$	5.33605			0.345160			0.172580	−	0.984995i	$-0.444790\pi$
$239$	5.33605			0.345160			0.172580	+	0.984995i	$0.444790\pi$
$240$	1.17241	−	9.65566i	0.0756787	−	0.623270i
$241$	−1.89545	−	2.74603i	−0.122097	−	0.176887i	0.757169	−	0.653219i	$-0.226582\pi$
$241$	−1.89545	−	2.74603i	−0.122097	−	0.176887i	−0.879266	+	0.476331i	$0.841966\pi$
$242$	8.59742	−	2.11907i	0.552663	−	0.136219i
$243$	−0.568065	+	0.822984i	−0.0364414	+	0.0527944i
$244$	−0.127377	+	0.0313957i	−0.00815450	+	0.00200990i
$245$	35.3743	+	18.5659i	2.25998	+	1.18613i
$246$	−6.09120	−	3.19691i	−0.388361	−	0.203828i
$247$	−1.87061	+	9.14926i	−0.119024	+	0.582153i
$248$	0.399334	−	0.209586i	0.0253577	−	0.0133088i
$249$	7.54572			0.478190
$250$	11.8687	+	6.22920i	0.750645	+	0.393969i
$251$	−0.214017	+	0.564317i	−0.0135086	+	0.0356194i	−0.941601	−	0.336731i	$-0.890679\pi$
$251$	−0.214017	+	0.564317i	−0.0135086	+	0.0356194i	0.928092	+	0.372350i	$0.121448\pi$
$252$	−0.0211859	−	0.174482i	−0.00133459	−	0.0109913i
$253$	−29.3338	+	7.23014i	−1.84420	+	0.454555i
$254$	7.17089	−	1.76747i	0.449942	−	0.110901i
$255$	1.87129	+	15.4114i	0.117185	+	0.965101i
$256$	0.310964	−	0.819945i	0.0194353	−	0.0512466i
$257$	9.72581	+	5.10450i	0.606679	+	0.318410i	0.739942	−	0.672671i	$-0.234853\pi$
$257$	9.72581	+	5.10450i	0.606679	+	0.318410i	−0.133262	+	0.991081i	$0.542545\pi$
$258$	2.52181			0.157001
$259$	−2.17361	+	1.14080i	−0.135061	+	0.0708857i
$260$	0.0907564	+	0.313670i	0.00562847	+	0.0194530i
$261$	−7.66357	−	4.02215i	−0.474363	−	0.248965i
$262$	−19.2193	−	10.0871i	−1.18737	−	0.623180i
$263$	13.3274	−	3.28492i	0.821805	−	0.202557i	0.194074	−	0.980987i	$-0.437830\pi$
$263$	13.3274	−	3.28492i	0.821805	−	0.202557i	0.627731	+	0.778430i	$0.283984\pi$
$264$	6.74633	−	9.77374i	0.415208	−	0.601532i
$265$	−21.9184	+	5.40239i	−1.34643	+	0.331866i
$266$	9.91385	+	14.3627i	0.607857	+	0.880633i
$267$	−0.634027	+	5.22168i	−0.0388018	+	0.319562i
$268$	−0.362597			−0.0221491
$269$	1.08066	−	8.90007i	0.0658893	−	0.542647i	−0.921966	−	0.387271i	$-0.873418\pi$
$269$	1.08066	−	8.90007i	0.0658893	−	0.542647i	0.987855	−	0.155376i	$-0.0496590\pi$
$270$	−1.23116	−	3.24629i	−0.0749257	−	0.197563i
$271$	−19.9316	+	10.4609i	−1.21076	+	0.635455i	−0.944520	−	0.328453i	$-0.893473\pi$
$271$	−19.9316	+	10.4609i	−1.21076	+	0.635455i	−0.266238	+	0.963907i	$0.585781\pi$
$272$	2.96472	−	24.4167i	0.179763	−	1.48048i
$273$	−8.66464	−	15.0177i	−0.524408	−	0.908913i
$274$	−0.219621	−	1.80874i	−0.0132678	−	0.109270i
$275$	−2.69332	−	3.90194i	−0.162413	−	0.235296i
$276$	−0.150733	+	0.218375i	−0.00907307	+	0.0131446i
$277$	20.0979	−	17.8052i	1.20756	−	1.06981i	0.211852	−	0.977302i	$-0.432051\pi$
$277$	20.0979	−	17.8052i	1.20756	−	1.06981i	0.995712	−	0.0925066i	$-0.0294879\pi$
$278$	−2.26674	−	5.97689i	−0.135950	−	0.358470i
$279$	0.0897763	−	0.130063i	0.00537477	−	0.00778669i
$280$	30.1064	+	15.8010i	1.79920	+	0.944293i
$281$	−3.20765	+	26.4174i	−0.191352	+	1.57593i	0.508131	+	0.861280i	$0.330337\pi$
$281$	−3.20765	+	26.4174i	−0.191352	+	1.57593i	−0.699483	+	0.714649i	$0.746586\pi$
$282$	1.09222	+	8.99523i	0.0650407	+	0.535658i
$283$	−11.4147	+	30.0982i	−0.678535	+	1.78915i	−0.0672558	+	0.997736i	$0.521424\pi$
$283$	−11.4147	+	30.0982i	−0.678535	+	1.78915i	−0.611279	+	0.791415i	$0.709345\pi$
$284$	0.0276089	−	0.0399983i	0.00163828	−	0.00237347i
$285$	−4.80356	−	4.25558i	−0.284538	−	0.252079i
$286$	4.21164	−	20.5993i	0.249039	−	1.21806i
$287$	17.6706	−	15.6548i	1.04307	−	0.924075i
$288$	−0.0249195	−	0.205231i	−0.00146840	−	0.0120933i
$289$	2.68288	+	22.0955i	0.157816	+	1.29974i
$290$	26.6072	−	13.9645i	1.56243	−	0.820025i
$291$	−9.12383	+	4.78855i	−0.534848	+	0.280710i
$292$	0.271696	+	0.0669671i	0.0158998	+	0.00391895i
$293$	0.534430	−	0.473463i	0.0312217	−	0.0276600i	−0.647368	−	0.762178i	$-0.724130\pi$
$293$	0.534430	−	0.473463i	0.0312217	−	0.0276600i	0.678589	+	0.734518i	$0.262592\pi$
$294$	−21.9364	−	5.40685i	−1.27936	−	0.315334i
$295$	−11.1069	−	29.2864i	−0.646666	−	1.70512i
$296$	−1.28991	+	0.676995i	−0.0749743	+	0.0393495i
$297$	0.501630	−	4.13130i	0.0291075	−	0.239722i
$298$	−3.33111	+	0.821044i	−0.192966	+	0.0475618i
$299$	−5.24309	+	25.6442i	−0.303216	+	1.48305i
$300$	−0.0404314	−	0.00996544i	−0.00233431	−	0.000575355i
$301$	−3.06885	+	8.09188i	−0.176885	+	0.466408i
$302$	19.5367	+	17.3080i	1.12421	+	0.995963i
$303$	−6.61668	+	1.63086i	−0.380118	+	0.0936907i
$304$	5.77572	+	8.36758i	0.331260	+	0.479914i
$305$	−1.07195	−	8.82834i	−0.0613800	−	0.505509i
$306$	−3.11327	−	8.20903i	−0.177974	−	0.469279i
$307$	9.18358	−	24.2151i	0.524135	−	1.38203i	−0.367816	−	0.929898i	$-0.619894\pi$
$307$	9.18358	−	24.2151i	0.524135	−	1.38203i	0.891951	−	0.452132i	$-0.149336\pi$
$308$	0.415519	+	0.601983i	0.0236764	+	0.0343012i
$309$	−16.8370	−	4.14996i	−0.957825	−	0.236083i
$310$	0.194570	+	0.513040i	0.0110509	+	0.0291387i
$311$	0.658352	−	1.73593i	0.0373317	−	0.0984357i	−0.915054	−	0.403331i	$-0.867852\pi$
$311$	0.658352	−	1.73593i	0.0373317	−	0.0984357i	0.952386	+	0.304895i	$0.0986215\pi$
$312$	−5.14195	−	8.91211i	−0.291105	−	0.504549i
$313$	−8.75097	−	23.0744i	−0.494634	−	1.30424i	−0.917387	−	0.397997i	$-0.869705\pi$
$313$	−8.75097	−	23.0744i	−0.494634	−	1.30424i	0.422753	−	0.906245i	$-0.361064\pi$
$314$	−5.18628	+	4.59464i	−0.292679	+	0.259291i
$315$	11.9148			0.671322
$316$	−0.257236			−0.0144707
$317$	6.92883	−	6.13841i	0.389162	−	0.344767i	−0.445744	−	0.895161i	$-0.647061\pi$
$317$	6.92883	−	6.13841i	0.389162	−	0.344767i	0.834905	+	0.550393i	$0.185522\pi$
$318$	11.3040	−	5.93281i	0.633899	−	0.332696i
$319$	36.0187			2.01666
$320$	17.8605	+	9.37390i	0.998431	+	0.524017i
$321$	−4.96141	−	4.39543i	−0.276919	−	0.245329i
$322$	27.7873	+	40.2569i	1.54853	+	2.24343i
$323$	−12.1470	−	10.7613i	−0.675875	−	0.598773i
$324$	−0.0207634	−	0.0300809i	−0.00115352	−	0.00167116i
$325$	−4.05468	+	0.657737i	−0.224913	+	0.0364847i
$326$	4.05485	−	5.87447i	0.224578	−	0.325357i
$327$	−5.22722	+	1.28839i	−0.289066	+	0.0712483i
$328$	10.4865	−	9.29021i	0.579019	−	0.512966i
$329$	−30.1927	−	7.44183i	−1.66458	−	0.410281i
$330$	10.8151	+	9.58134i	0.595352	+	0.527436i
$331$	7.47204	+	6.61965i	0.410701	+	0.363849i	0.843030	−	0.537867i	$-0.180770\pi$
$331$	7.47204	+	6.61965i	0.410701	+	0.363849i	−0.432329	+	0.901716i	$0.642308\pi$
$332$	−0.0978015	+	0.257881i	−0.00536755	+	0.0141531i
$333$	−0.289991	+	0.420124i	−0.0158914	+	0.0230226i
$334$	−10.1629	−	5.33388i	−0.556087	−	0.291857i
$335$	2.96279	−	24.4008i	0.161875	−	1.33316i
$336$	−18.3283	−	4.51753i	−0.999893	−	0.246451i
$337$	11.3159			0.616417			0.308209	−	0.951319i	$-0.400271\pi$
$337$	11.3159			0.616417			0.308209	+	0.951319i	$0.400271\pi$
$338$	−14.5563	−	10.9516i	−0.791757	−	0.595689i
$339$	−9.98242			−0.542171
$340$	−0.550953	−	0.135798i	−0.0298796	−	0.00736467i
$341$	−0.0792771	+	0.652905i	−0.00429309	+	0.0353568i
$342$	3.21354	+	1.68660i	0.173768	+	0.0912006i
$343$	24.9226	−	36.1067i	1.34570	−	1.94958i
$344$	−1.82118	+	4.80205i	−0.0981913	+	0.258909i
$345$	−13.4638	−	11.9279i	−0.724866	−	0.642175i
$346$	3.26761	+	2.89485i	0.175668	+	0.155628i
$347$	32.3021	+	7.96176i	1.73407	+	0.427410i	0.974748	−	0.223307i	$-0.0716854\pi$
$347$	32.3021	+	7.96176i	1.73407	+	0.427410i	0.759320	+	0.650717i	$0.225532\pi$
$348$	0.236789	−	0.209777i	0.0126932	−	0.0112452i
$349$	0.336363	−	0.0829060i	0.0180051	−	0.00443786i	−0.230303	−	0.973119i	$-0.573972\pi$
$349$	0.336363	−	0.0829060i	0.0180051	−	0.00443786i	0.248308	+	0.968681i	$0.420126\pi$
$350$	−4.36075	+	6.31763i	−0.233092	+	0.337692i
$351$	−3.04681	−	1.92793i	−0.162627	−	0.102905i
$352$	0.488746	+	0.708070i	0.0260502	+	0.0377403i
$353$	17.0953	+	15.1451i	0.909892	+	0.806094i	0.981524	−	0.191337i	$-0.0612825\pi$
$353$	17.0953	+	15.1451i	0.909892	+	0.806094i	−0.0716326	+	0.997431i	$0.522821\pi$
$354$	10.0623	+	14.5777i	0.534803	+	0.774796i
$355$	2.46608	+	2.18475i	0.130886	+	0.115955i
$356$	−0.170238	−	0.0893477i	−0.00902258	−	0.00473542i
$357$	30.1294			1.59462
$358$	−16.9037	+	8.87173i	−0.893387	+	0.468886i
$359$	−4.39204	+	3.89101i	−0.231803	+	0.205360i	−0.771026	−	0.636803i	$-0.780256\pi$
$359$	−4.39204	+	3.89101i	−0.231803	+	0.205360i	0.539223	+	0.842163i	$0.318718\pi$
$360$	7.07072			0.372659
$361$	−12.2917			−0.646931
$362$	24.8701	−	22.0330i	1.30714	−	1.15803i
$363$	2.24084	+	5.90860i	0.117613	+	0.310121i
$364$	0.625547	−	0.101474i	0.0327876	−	0.00531869i
$365$	−6.72656	+	17.7365i	−0.352084	+	0.928370i
$366$	1.78342	+	4.70249i	0.0932208	+	0.245803i
$367$	−30.9920	−	7.63884i	−1.61777	−	0.398744i	−0.676511	−	0.736432i	$-0.736509\pi$
$367$	−30.9920	−	7.63884i	−1.61777	−	0.398744i	−0.941258	+	0.337688i	$0.890355\pi$
$368$	16.1886	+	23.4533i	0.843891	+	1.22259i
$369$	1.74089	−	4.59035i	0.0906271	−	0.238964i
$370$	−0.628491	−	1.65719i	−0.0326737	−	0.0861534i
$371$	5.28085	+	43.4917i	0.274168	+	2.25798i
$372$	0.00328142	+	0.00475396i	0.000170134	+	0.000246481i
$373$	−26.1239	+	6.43897i	−1.35265	+	0.333397i	−0.848031	−	0.529947i	$-0.822212\pi$
$373$	−26.1239	+	6.43897i	−1.35265	+	0.333397i	−0.504615	+	0.863345i	$0.668366\pi$
$374$	27.3486	+	24.2288i	1.41416	+	1.25284i
$375$	−3.39213	+	8.94432i	−0.175169	+	0.461883i
$376$	−17.9176	−	4.41628i	−0.924028	−	0.227752i
$377$	13.3859	−	28.1890i	0.689410	−	1.45181i
$378$	−6.54231	+	1.61253i	−0.336500	+	0.0829398i
$379$	−2.13561	+	17.5883i	−0.109699	+	0.903452i	0.829127	+	0.559060i	$0.188838\pi$
$379$	−2.13561	+	17.5883i	−0.109699	+	0.903452i	−0.938826	+	0.344392i	$0.888085\pi$
$380$	0.207698	−	0.109008i	0.0106547	−	0.00559201i
$381$	1.86902	+	4.92821i	0.0957530	+	0.252480i
$382$	5.16067	+	1.27199i	0.264043	+	0.0650807i
$383$	2.43464	−	2.15691i	0.124404	−	0.110213i	−0.598627	−	0.801028i	$-0.704287\pi$
$383$	2.43464	−	2.15691i	0.124404	−	0.110213i	0.723031	+	0.690815i	$0.242748\pi$
$384$	−10.6742	−	2.63096i	−0.544717	−	0.134261i
$385$	−43.9054	+	23.0433i	−2.23763	+	1.17440i
$386$	−6.97810	+	3.66239i	−0.355176	+	0.186411i
$387$	0.216931	+	1.78659i	0.0110272	+	0.0908173i
$388$	−0.0453972	−	0.373880i	−0.00230470	−	0.0189809i
$389$	−2.44246	+	2.16383i	−0.123838	+	0.109711i	−0.722769	−	0.691090i	$-0.757131\pi$
$389$	−2.44246	+	2.16383i	−0.123838	+	0.109711i	0.598931	+	0.800801i	$0.295592\pi$
$390$	11.5179	−	4.90334i	0.583229	−	0.248290i
$391$	−34.0464	−	30.1625i	−1.72180	−	1.52538i
$392$	26.1376	−	37.8669i	1.32015	−	1.91257i
$393$	5.49294	−	14.4837i	0.277082	−	0.730606i
$394$	−1.97666	−	16.2793i	−0.0995829	−	0.820139i
$395$	2.10189	−	17.3106i	0.105757	−	0.870990i
$396$	0.134689	+	0.0706902i	0.00676837	+	0.00355231i
$397$	4.40992	−	6.38887i	0.221327	−	0.320648i	−0.696553	−	0.717505i	$-0.745284\pi$
$397$	4.40992	−	6.38887i	0.221327	−	0.320648i	0.917880	+	0.396857i	$0.129899\pi$
$398$	10.3736	+	27.3529i	0.519980	+	1.37107i
$399$	−9.32251	+	8.25902i	−0.466709	+	0.413468i
$400$	−2.54053	+	3.68060i	−0.127027	+	0.184030i
$401$	3.67758	+	5.32789i	0.183649	+	0.266062i	0.903986	−	0.427563i	$-0.140628\pi$
$401$	3.67758	+	5.32789i	0.183649	+	0.266062i	−0.720336	+	0.693625i	$0.756012\pi$
$402$	1.67553	+	13.7992i	0.0835679	+	0.688243i
$403$	0.481515	+	0.304688i	0.0239860	+	0.0151776i
$404$	0.0300238	−	0.247269i	0.00149374	−	0.0123021i
$405$	2.19394	−	1.15147i	0.109018	−	0.0572170i
$406$	−20.6798	−	54.5282i	−1.02632	−	2.70619i
$407$	0.256077	−	2.10898i	0.0126932	−	0.104538i
$408$	17.8800			0.885193
$409$	1.40096	−	11.5379i	0.0692730	−	0.570515i	−0.916205	−	0.400710i	$-0.868763\pi$
$409$	1.40096	−	11.5379i	0.0692730	−	0.570515i	0.985478	−	0.169804i	$-0.0543136\pi$
$410$	9.68260	+	14.0277i	0.478190	+	0.692777i
$411$	1.26252	−	0.311182i	0.0622754	−	0.0153495i
$412$	0.360056	−	0.521632i	0.0177387	−	0.0256989i
$413$	−59.0214	+	14.5475i	−2.90425	+	0.715834i
$414$	9.00715	+	4.72732i	0.442677	+	0.232335i
$415$	−16.5549	−	8.68866i	−0.812647	−	0.426510i
$416$	0.735787	−	0.119357i	0.0360749	−	0.00585196i
$417$	4.03937	−	2.12002i	0.197809	−	0.103818i
$418$	−15.1036			−0.738742
$419$	−35.1735	−	18.4605i	−1.71834	−	0.901853i	−0.971565	−	0.236771i	$-0.923911\pi$
$419$	−35.1735	−	18.4605i	−1.71834	−	0.901853i	−0.746771	−	0.665081i	$-0.768397\pi$
$420$	−0.154430	+	0.407198i	−0.00753541	+	0.0198692i
$421$	−0.848369	−	6.98695i	−0.0413470	−	0.340523i	−0.998672	−	0.0515109i	$-0.983596\pi$
$421$	−0.848369	−	6.98695i	−0.0413470	−	0.340523i	0.957325	−	0.289012i	$-0.0933268\pi$
$422$	3.74266	−	0.922483i	0.182190	−	0.0449058i
$423$	−6.27876	+	1.54757i	−0.305284	+	0.0752457i
$424$	3.13387	+	25.8097i	0.152194	+	1.25343i
$425$	2.53124	−	6.67432i	0.122783	−	0.323752i
$426$	−1.64978	−	0.865874i	−0.0799323	−	0.0419517i
$427$	−17.2595			−0.835244
$428$	0.214523	−	0.112591i	0.0103694	−	0.00544227i
$429$	14.9560	+	1.21176i	0.722082	+	0.0585043i
$430$	−5.53270	−	2.90379i	−0.266811	−	0.140033i
$431$	10.7072	+	5.61956i	0.515747	+	0.270685i	0.702452	−	0.711731i	$-0.252089\pi$
$431$	10.7072	+	5.61956i	0.515747	+	0.270685i	−0.186705	+	0.982416i	$0.559781\pi$
$432$	−3.81149	+	0.939448i	−0.183381	+	0.0451992i
$433$	−6.94608	+	10.0631i	−0.333807	+	0.483603i	−0.953564	−	0.301191i	$-0.902616\pi$
$433$	−6.94608	+	10.0631i	−0.333807	+	0.483603i	0.619757	+	0.784794i	$0.287231\pi$
$434$	1.03394	−	0.254843i	0.0496307	−	0.0122329i
$435$	12.1820	+	17.6487i	0.584084	+	0.846192i
$436$	0.0237190	−	0.195344i	0.00113594	−	0.00935527i
$437$	18.8026			0.899450
$438$	1.29306	−	10.6493i	0.0617849	−	0.508844i
$439$	1.40912	+	3.71555i	0.0672537	+	0.177334i	0.964430	−	0.264340i	$-0.0851541\pi$
$439$	1.40912	+	3.71555i	0.0672537	+	0.177334i	−0.897176	+	0.441674i	$0.854385\pi$
$440$	−26.0552	+	13.6748i	−1.24213	+	0.651922i
$441$	1.94349	−	16.0061i	0.0925471	−	0.762194i
$442$	29.1257	−	12.3993i	1.38537	−	0.589773i
$443$	3.86440	+	31.8262i	0.183603	+	1.51211i	0.735116	+	0.677941i	$0.237128\pi$
$443$	3.86440	+	31.8262i	0.183603	+	1.51211i	−0.551513	+	0.834166i	$0.685949\pi$
$444$	−0.0105995	−	0.0153560i	−0.000503029	−	0.000728763i
$445$	7.40363	−	10.7260i	0.350966	−	0.508462i
$446$	−7.37854	+	6.53682i	−0.349384	+	0.309527i
$447$	−0.868221	−	2.28931i	−0.0410655	−	0.108281i
$448$	22.2379	−	32.2171i	1.05064	−	1.52212i
$449$	11.3896	+	5.97774i	0.537510	+	0.282107i	0.711555	−	0.702631i	$-0.247991\pi$
$449$	11.3896	+	5.97774i	0.537510	+	0.282107i	−0.174044	+	0.984738i	$0.555684\pi$
$450$	−0.192422	+	1.58474i	−0.00907085	+	0.0747052i
$451$	2.46269	+	20.2821i	0.115964	+	0.955046i
$452$	0.129384	−	0.341158i	0.00608572	−	0.0160467i
$453$	−10.5813	+	15.3297i	−0.497155	+	0.720253i
$454$	−18.2054	−	16.1286i	−0.854423	−	0.756953i
$455$	1.71729	+	42.9250i	0.0805079	+	2.01236i
$456$	−5.53235	+	4.90124i	−0.259076	+	0.229521i
$457$	3.79297	+	31.2379i	0.177428	+	1.46125i	0.760770	+	0.649022i	$0.224822\pi$
$457$	3.79297	+	31.2379i	0.177428	+	1.46125i	−0.583342	+	0.812226i	$0.698255\pi$
$458$	−3.25663	−	26.8207i	−0.152172	−	1.25325i
$459$	5.54792	−	2.91177i	0.258955	−	0.135910i
$460$	0.582152	−	0.305537i	0.0271430	−	0.0142457i
$461$	−10.9834	−	2.70718i	−0.511550	−	0.126086i	−0.0249123	−	0.999690i	$-0.507931\pi$
$461$	−10.9834	−	2.70718i	−0.511550	−	0.126086i	−0.486638	+	0.873604i	$0.661777\pi$
$462$	20.9894	−	18.5950i	0.976516	−	0.865118i
$463$	−12.4746	−	3.07471i	−0.579744	−	0.142894i	−0.0614704	−	0.998109i	$-0.519579\pi$
$463$	−12.4746	−	3.07471i	−0.579744	−	0.142894i	−0.518274	+	0.855215i	$0.673425\pi$
$464$	−12.0479	−	31.7676i	−0.559309	−	1.47478i
$465$	−0.346728	+	0.181977i	−0.0160791	+	0.00843898i
$466$	2.57083	−	21.1727i	0.119092	−	0.980807i
$467$	−35.2617	+	8.69124i	−1.63172	+	0.402183i	−0.945606	−	0.325313i	$-0.894530\pi$
$467$	−35.2617	+	8.69124i	−1.63172	+	0.402183i	−0.686113	+	0.727495i	$0.740684\pi$
$468$	0.105379	−	0.0791392i	0.00487115	−	0.00365821i
$469$	−46.3175	−	11.4162i	−2.13874	−	0.527152i
$470$	7.96147	−	20.9927i	0.367235	−	0.968320i
$471$	−3.70123	−	3.27900i	−0.170544	−	0.151089i
$472$	−35.0257	+	8.63305i	−1.61219	+	0.397368i
$473$	−4.25466	−	6.16394i	−0.195629	−	0.283418i
$474$	1.18867	+	9.78957i	0.0545974	+	0.449650i
$475$	1.04635	+	2.75900i	0.0480098	+	0.126591i
$476$	−0.390513	+	1.02970i	−0.0178992	+	0.0471962i
$477$	5.17553	+	7.49804i	0.236971	+	0.343312i
$478$	7.25977	+	1.78937i	0.332054	+	0.0818440i
$479$	7.57848	+	19.9828i	0.346269	+	0.913037i	0.989129	+	0.147053i	$0.0469788\pi$
$479$	7.57848	+	19.9828i	0.346269	+	0.913037i	−0.642859	+	0.765984i	$0.722252\pi$
$480$	−0.181645	+	0.478958i	−0.00829092	+	0.0218614i
$481$	−1.55536	−	0.984187i	−0.0709185	−	0.0448751i
$482$	−1.65794	−	4.37163i	−0.0755171	−	0.199122i
$483$	−26.1299	+	23.1490i	−1.18895	+	1.05332i
$484$	−0.230975			−0.0104989
$485$	25.5310			1.15930
$486$	−1.04884	+	0.929188i	−0.0475762	+	0.0421488i
$487$	−26.0922	+	13.6942i	−1.18235	+	0.620545i	−0.937150	−	0.348927i	$-0.886546\pi$
$487$	−26.0922	+	13.6942i	−1.18235	+	0.620545i	−0.245201	+	0.969472i	$0.578854\pi$
$488$	−10.2425			−0.463654
$489$	4.51060	+	2.36735i	0.203977	+	0.107055i
$490$	41.9015	+	37.1215i	1.89291	+	1.67698i
$491$	5.80094	+	8.40411i	0.261793	+	0.379272i	0.931734	−	0.363142i	$-0.118296\pi$
$491$	5.80094	+	8.40411i	0.261793	+	0.379272i	−0.669941	+	0.742414i	$0.733681\pi$
$492$	0.134315	+	0.118993i	0.00605539	+	0.00536461i
$493$	30.8052	+	44.6291i	1.38740	+	2.00999i
$494$	−5.61307	+	11.8204i	−0.252544	+	0.531825i
$495$	−5.85761	+	8.48622i	−0.263280	+	0.381427i
$496$	0.602364	−	0.148469i	0.0270469	−	0.00666647i
$497$	4.78604	−	4.24006i	0.214683	−	0.190193i
$498$	10.2661	+	2.53035i	0.460033	+	0.113388i
$499$	22.1163	+	19.5934i	0.990063	+	0.877120i	0.992422	−	0.122878i	$-0.0392123\pi$
$499$	22.1163	+	19.5934i	0.990063	+	0.877120i	−0.00235850	+	0.999997i	$0.500751\pi$
$500$	−0.261714	−	0.231858i	−0.0117042	−	0.0103690i
$501$	2.90458	−	7.65875i	0.129767	−	0.342168i
$502$	−0.480409	+	0.695993i	−0.0214417	+	0.0310637i
$503$	−25.2052	−	13.2287i	−1.12385	−	0.589840i	−0.202772	−	0.979226i	$-0.564995\pi$
$503$	−25.2052	−	13.2287i	−1.12385	−	0.589840i	−0.921075	+	0.389386i	$0.872687\pi$
$504$	1.65406	−	13.6224i	0.0736779	−	0.606792i
$505$	16.3945	+	4.04088i	0.729546	+	0.179817i
$506$	−42.3336			−1.88196
$507$	6.50656	−	11.2545i	0.288966	−	0.499832i
$508$	−0.192651			−0.00854749
$509$	−12.1714	−	2.99999i	−0.539489	−	0.132972i	−0.0398497	−	0.999206i	$-0.512688\pi$
$509$	−12.1714	−	2.99999i	−0.539489	−	0.132972i	−0.499639	+	0.866234i	$0.666534\pi$
$510$	−2.62211	+	21.5950i	−0.116109	+	0.956242i
$511$	32.5976	+	17.1085i	1.44203	+	0.756837i
$512$	13.1883	−	19.1065i	0.582845	−	0.844397i
$513$	−0.918441	+	2.42173i	−0.0405502	+	0.106922i
$514$	11.5204	+	10.2062i	0.508142	+	0.450175i
$515$	32.1609	+	28.4921i	1.41718	+	1.25551i
$516$	−0.0638698	−	0.0157425i	−0.00281171	−	0.000693025i
$517$	20.1439	−	17.8459i	0.885927	−	0.784863i
$518$	−3.33977	+	0.823180i	−0.146741	+	0.0361685i
$519$	−1.76979	+	2.56398i	−0.0776850	+	0.112546i
$520$	1.01911	+	25.4734i	0.0446909	+	1.11708i
$521$	−1.97041	−	2.85463i	−0.0863252	−	0.125064i	0.777442	−	0.628954i	$-0.216517\pi$
$521$	−1.97041	−	2.85463i	−0.0863252	−	0.125064i	−0.863767	+	0.503891i	$0.831901\pi$
$522$	−9.07762	−	8.04207i	−0.397316	−	0.351992i
$523$	−14.7590	−	21.3821i	−0.645366	−	0.934973i	0.354634	−	0.935005i	$-0.384605\pi$
$523$	−14.7590	−	21.3821i	−0.645366	−	0.934973i	−1.00000		3.16264e-5i	$0.999990\pi$
$524$	0.423798	+	0.375452i	0.0185137	+	0.0164017i
$525$	−4.85088	−	2.54594i	−0.211710	−	0.111114i
$526$	19.2337			0.838630
$527$	−0.876786	+	0.460173i	−0.0381934	+	0.0200454i
$528$	12.2283	−	10.8333i	0.532166	−	0.471458i
$529$	29.7013			1.29136
$530$	−31.6319			−1.37400
$531$	−9.46207	+	8.38266i	−0.410619	+	0.363776i
$532$	−0.161428	−	0.425652i	−0.00699881	−	0.0184543i
$533$	16.7884	+	5.61024i	0.727187	+	0.243006i
$534$	−2.61362	+	6.89156i	−0.113103	+	0.298227i
$535$	5.82385	+	15.3562i	0.251787	+	0.663908i
$536$	−27.4866	−	6.77485i	−1.18724	−	0.292629i
$537$	−7.73931	−	11.2123i	−0.333976	−	0.483847i
$538$	4.45478	−	11.7463i	0.192059	−	0.506418i
$539$	23.7943	+	62.7403i	1.02489	+	2.70242i
$540$	0.0109164	+	0.0899043i	0.000469765	+	0.00386886i
$541$	−6.54040	−	9.47541i	−0.281194	−	0.407380i	0.656782	−	0.754081i	$-0.271917\pi$
$541$	−6.54040	−	9.47541i	−0.281194	−	0.407380i	−0.937976	+	0.346701i	$0.887302\pi$
$542$	−30.6251	+	7.54842i	−1.31546	+	0.324232i
$543$	17.7487	+	15.7240i	0.761671	+	0.674782i
$544$	−0.459334	+	1.21116i	−0.0196938	+	0.0519282i
$545$	12.9518	+	3.19232i	0.554793	+	0.136744i
$546$	−6.75238	−	23.3374i	−0.288975	−	0.998747i
$547$	44.0866	−	10.8664i	1.88501	−	0.464612i	0.885006	−	0.465580i	$-0.154154\pi$
$547$	44.0866	−	10.8664i	1.88501	−	0.464612i	1.00000		0.000968033i	$0.000308134\pi$
$548$	−0.00572880	+	0.0471809i	−0.000244722	+	0.00201547i
$549$	−3.17809	+	1.66799i	−0.135638	+	0.0711881i
$550$	−2.35583	−	6.21182i	−0.100453	−	0.264873i
$551$	−21.7653	−	5.36466i	−0.927231	−	0.228542i
$552$	−15.5065	+	13.7376i	−0.660001	+	0.584710i
$553$	−32.8589	−	8.09899i	−1.39730	−	0.344404i
$554$	33.3142	−	17.4846i	1.41538	−	0.742850i
$555$	1.11998	−	0.587812i	0.0475406	−	0.0249512i
$556$	0.0200986	+	0.165527i	0.000852371	+	0.00701991i
$557$	−4.59005	−	37.8025i	−0.194487	−	1.60174i	−0.683823	−	0.729648i	$-0.739684\pi$
$557$	−4.59005	−	37.8025i	−0.194487	−	1.60174i	0.489336	−	0.872095i	$-0.337239\pi$
$558$	0.165757	−	0.146848i	0.00701705	−	0.00621656i
$559$	−6.40522	+	1.03903i	−0.270912	+	0.0439464i
$560$	35.0095	+	31.0157i	1.47942	+	1.31065i
$561$	−14.8124	+	21.4595i	−0.625380	+	0.906019i
$562$	−13.2228	+	34.8656i	−0.557769	+	1.47072i
$563$	−4.88669	−	40.2455i	−0.205949	−	1.69615i	−0.618962	−	0.785421i	$-0.712447\pi$
$563$	−4.88669	−	40.2455i	−0.205949	−	1.69615i	0.413013	−	0.910725i	$-0.364476\pi$
$564$	0.0284905	−	0.234640i	0.00119967	−	0.00988014i
$565$	21.9009	+	11.4945i	0.921376	+	0.483576i
$566$	−25.6229	+	37.1212i	−1.07701	+	1.56032i
$567$	−1.70519	−	4.49622i	−0.0716113	−	0.188823i
$568$	2.84023	−	2.51623i	0.119173	−	0.105578i
$569$	−16.7324	+	24.2411i	−0.701461	+	1.01624i	0.296661	+	0.954983i	$0.404127\pi$
$569$	−16.7324	+	24.2411i	−0.701461	+	1.01624i	−0.998122	+	0.0612585i	$0.980489\pi$
$570$	−5.10826	−	7.40059i	−0.213961	−	0.309976i
$571$	0.597522	+	4.92103i	0.0250055	+	0.205939i	0.999857	−	0.0169171i	$-0.00538513\pi$
$571$	0.597522	+	4.92103i	0.0250055	+	0.205939i	−0.974851	+	0.222856i	$0.928462\pi$
$572$	−0.235260	+	0.495428i	−0.00983673	+	0.0207149i
$573$	−0.457217	+	3.76552i	−0.0191005	+	0.157307i
$574$	29.2908	−	15.3730i	1.22257	−	0.641656i
$575$	2.93279	+	7.73313i	0.122306	+	0.322494i
$576$	0.981266	−	8.08146i	0.0408861	−	0.336727i
$577$	−7.00414			−0.291586			−0.145793	−	0.989315i	$-0.546573\pi$
$577$	−7.00414			−0.291586			−0.145793	+	0.989315i	$0.546573\pi$
$578$	−3.75934	+	30.9609i	−0.156368	+	1.28780i
$579$	−3.19491	−	4.62862i	−0.132776	−	0.192359i
$580$	−0.761054	+	0.187583i	−0.0316011	+	0.00778896i
$581$	−20.6123	+	29.8621i	−0.855142	+	1.23889i
$582$	−14.0189	+	3.45534i	−0.581101	+	0.143229i
$583$	−33.5728	−	17.6204i	−1.39045	−	0.729762i
$584$	19.3447	+	10.1529i	0.800490	+	0.420130i
$585$	4.46458	+	7.73809i	0.184588	+	0.319931i
$586$	0.885869	−	0.464940i	0.0365949	−	0.0192065i
$587$	−28.9349			−1.19427			−0.597136	−	0.802140i	$-0.703695\pi$
$587$	−28.9349			−1.19427			−0.597136	+	0.802140i	$0.703695\pi$
$588$	0.521831	+	0.273878i	0.0215200	+	0.0112945i
$589$	0.145149	−	0.382728i	0.00598078	−	0.0157700i
$590$	−5.29024	−	43.5690i	−0.217796	−	1.79371i
$591$	11.3631	−	2.80075i	0.467416	−	0.115208i
$592$	−1.94572	+	0.479578i	−0.0799687	+	0.0197105i
$593$	−1.91194	−	15.7462i	−0.0785139	−	0.646620i	−0.977842	−	0.209345i	$-0.932867\pi$
$593$	−1.91194	−	15.7462i	−0.0785139	−	0.646620i	0.899328	−	0.437275i	$-0.144056\pi$
$594$	2.06785	−	5.45247i	0.0848449	−	0.223718i
$595$	−66.1023	−	34.6931i	−2.70993	−	1.42228i
$596$	0.0894924			0.00366575
$597$	−18.4859	+	9.70215i	−0.756578	+	0.397083i
$598$	−15.7328	+	33.1312i	−0.643360	+	1.35483i
$599$	3.65537	+	1.91848i	0.149354	+	0.0783871i	0.537745	−	0.843108i	$-0.319276\pi$
$599$	3.65537	+	1.91848i	0.149354	+	0.0783871i	−0.388390	+	0.921495i	$0.626969\pi$
$600$	−2.87871	−	1.51086i	−0.117523	−	0.0616807i
$601$	−30.7948	+	7.59023i	−1.25615	+	0.309612i	−0.810575	−	0.585635i	$-0.800845\pi$
$601$	−30.7948	+	7.59023i	−1.25615	+	0.309612i	−0.445570	+	0.895247i	$0.646999\pi$
$602$	−6.88871	+	9.98002i	−0.280763	+	0.406755i
$603$	−9.63200	+	2.37408i	−0.392246	+	0.0966798i
$604$	−0.386760	−	0.560318i	−0.0157370	−	0.0227990i
$605$	1.88731	−	15.5434i	0.0767300	−	0.631928i
$606$	−9.54897			−0.387900
$607$	−3.19184	+	26.2872i	−0.129553	+	1.06696i	0.772402	+	0.635134i	$0.219055\pi$
$607$	−3.19184	+	26.2872i	−0.129553	+	1.06696i	−0.901955	+	0.431830i	$0.857868\pi$
$608$	−0.189877	−	0.500664i	−0.00770052	−	0.0203046i
$609$	36.8518	−	19.3413i	1.49331	−	0.783750i
$610$	1.50206	−	12.3705i	0.0608165	−	0.500869i
$611$	−6.48037	−	22.3972i	−0.262168	−	0.906095i
$612$	0.0276047	+	0.227345i	0.00111585	+	0.00918987i
$613$	4.53262	+	6.56663i	0.183071	+	0.265224i	0.903765	−	0.428030i	$-0.140792\pi$
$613$	4.53262	+	6.56663i	0.183071	+	0.265224i	−0.720694	+	0.693253i	$0.756177\pi$
$614$	20.6146	−	29.8654i	0.831938	−	1.20527i
$615$	−9.10506	+	8.06638i	−0.367151	+	0.325268i
$616$	20.2508	+	53.3970i	0.815928	+	2.15143i
$617$	−9.11795	+	13.2096i	−0.367075	+	0.531800i	−0.962383	−	0.271698i	$-0.912415\pi$
$617$	−9.11795	+	13.2096i	−0.367075	+	0.531800i	0.595308	+	0.803498i	$0.297030\pi$
$618$	−21.5154	−	11.2921i	−0.865476	−	0.454237i
$619$	−2.65324	+	21.8514i	−0.106643	+	0.878283i	0.836974	+	0.547243i	$0.184323\pi$
$619$	−2.65324	+	21.8514i	−0.106643	+	0.878283i	−0.943617	+	0.331040i	$0.892601\pi$
$620$	−0.00172521	−	0.0142084i	−6.92860e−5	−	0.000570622i
$621$	−2.57428	+	6.78781i	−0.103302	+	0.272386i
$622$	1.47782	−	2.14099i	0.0592551	−	0.0858459i
$623$	−18.9328	−	16.7730i	−0.758527	−	0.671996i
$624$	−3.93388	−	13.5961i	−0.157481	−	0.544281i
$625$	22.0050	−	19.4947i	0.880201	−	0.779790i
$626$	−4.16812	−	34.3276i	−0.166592	−	1.37201i
$627$	−1.29924	−	10.7002i	−0.0518868	−	0.427326i
$628$	0.160035	−	0.0839929i	0.00638610	−	0.00335168i
$629$	2.83215	−	1.48643i	0.112925	−	0.0592677i
$630$	16.2102	+	3.99546i	0.645831	+	0.159183i
$631$	−1.24458	+	1.10260i	−0.0495461	+	0.0438940i	−0.687532	−	0.726154i	$-0.741306\pi$
$631$	−1.24458	+	1.10260i	−0.0495461	+	0.0438940i	0.637986	+	0.770048i	$0.279768\pi$
$632$	−19.4998	−	4.80627i	−0.775660	−	0.191183i
$633$	0.975488	+	2.57215i	0.0387722	+	0.102234i
$634$	11.4852	−	6.02790i	0.456136	−	0.239398i
$635$	1.57416	−	12.9643i	0.0624685	−	0.514474i
$636$	−0.323333	+	0.0796944i	−0.0128210	+	0.00316009i
$637$	57.9447	+	4.69478i	2.29585	+	0.186014i
$638$	49.0040	+	12.0784i	1.94009	+	0.478188i
$639$	0.471515	−	1.24328i	0.0186528	−	0.0491835i
$640$	20.3892	+	18.0632i	0.805953	+	0.714012i
$641$	35.3534	−	8.71384i	1.39638	−	0.344176i	0.531882	−	0.846818i	$-0.321485\pi$
$641$	35.3534	−	8.71384i	1.39638	−	0.344176i	0.864494	+	0.502643i	$0.167639\pi$
$642$	−5.27612	−	7.64378i	−0.208232	−	0.301676i
$643$	3.30592	+	27.2267i	0.130373	+	1.07372i	0.900204	+	0.435469i	$0.143417\pi$
$643$	3.30592	+	27.2267i	0.130373	+	1.07372i	−0.769831	+	0.638248i	$0.779660\pi$
$644$	−0.452464	−	1.19305i	−0.0178296	−	0.0470127i
$645$	1.58127	−	4.16946i	0.0622623	−	0.164172i
$646$	−12.9175	−	18.7142i	−0.508231	−	0.736300i
$647$	−22.1469	−	5.45871i	−0.870683	−	0.214604i	−0.221429	−	0.975176i	$-0.571072\pi$
$647$	−22.1469	−	5.45871i	−0.870683	−	0.214604i	−0.649253	+	0.760572i	$0.724918\pi$
$648$	−1.01193	−	2.66824i	−0.0397523	−	0.104818i
$649$	18.6551	−	49.1894i	0.732276	−	1.93085i
$650$	−5.73701	−	0.464822i	−0.225024	−	0.0182318i
$651$	0.269486	+	0.710577i	0.0105620	+	0.0278497i
$652$	−0.139369	+	0.123470i	−0.00545811	+	0.00483546i
$653$	0.258114			0.0101008			0.00505039	−	0.999987i	$-0.498392\pi$
$653$	0.258114			0.0101008			0.00505039	+	0.999987i	$0.498392\pi$
$654$	−7.54375			−0.294984
$655$	−28.7287	+	25.4514i	−1.12252	+	0.994470i
$656$	17.0646	−	8.95617i	0.666259	−	0.349680i
$657$	7.65579			0.298681
$658$	−38.5821	−	20.2494i	−1.50409	−	0.789405i
$659$	−4.92151	−	4.36008i	−0.191715	−	0.169844i	0.561805	−	0.827270i	$-0.310107\pi$
$659$	−4.92151	−	4.36008i	−0.191715	−	0.169844i	−0.753520	+	0.657425i	$0.771646\pi$
$660$	−0.214102	−	0.310180i	−0.00833391	−	0.0120738i
$661$	23.9634	+	21.2297i	0.932067	+	0.825739i	0.984946	−	0.172861i	$-0.0553013\pi$
$661$	23.9634	+	21.2297i	0.932067	+	0.825739i	−0.0528790	+	0.998601i	$0.516840\pi$
$662$	7.94601	+	11.5118i	0.308830	+	0.447418i
$663$	11.2898	+	19.5676i	0.438459	+	0.759944i
$664$	−12.2322	+	17.7214i	−0.474700	+	0.687722i
$665$	29.9631	−	7.38523i	1.16192	−	0.286387i
$666$	−0.535419	+	0.474340i	−0.0207471	+	0.0183803i
$667$	−61.0054	−	15.0365i	−2.36214	−	0.582214i
$668$	0.224098	+	0.198533i	0.00867060	+	0.00768148i
$669$	−5.26576	−	4.66505i	−0.203586	−	0.180361i
$670$	12.2134	−	32.2041i	0.471844	−	1.24415i
$671$	8.48519	−	12.2929i	0.327567	−	0.474563i
$672$	0.880269	+	0.462001i	0.0339571	+	0.0178221i
$673$	3.93175	−	32.3809i	0.151558	−	1.24819i	−0.696215	−	0.717833i	$-0.745134\pi$
$673$	3.93175	−	32.3809i	0.151558	−	1.24819i	0.847773	−	0.530359i	$-0.177943\pi$
$674$	15.3955	+	3.79464i	0.593011	+	0.146164i
$675$	−1.13927			−0.0438504
$676$	0.300301	+	0.368240i	0.0115500	+	0.0141631i
$677$	12.9327			0.497045			0.248522	−	0.968626i	$-0.420055\pi$
$677$	12.9327			0.497045			0.248522	+	0.968626i	$0.420055\pi$
$678$	−13.5812	−	3.34747i	−0.521584	−	0.128559i
$679$	5.97252	−	49.1881i	0.229204	−	1.88767i
$680$	−39.2277	−	20.5883i	−1.50432	−	0.789525i
$681$	9.86032	−	14.2851i	0.377848	−	0.547408i
$682$	−0.326801	+	0.861702i	−0.0125138	+	0.0329963i
$683$	11.3288	+	10.0365i	0.433486	+	0.384035i	0.851456	−	0.524426i	$-0.175720\pi$
$683$	11.3288	+	10.0365i	0.433486	+	0.384035i	−0.417970	+	0.908461i	$0.637258\pi$
$684$	−0.0708606	−	0.0627770i	−0.00270942	−	0.00240034i
$685$	−3.12821	−	0.771034i	−0.119523	−	0.0294597i
$686$	46.0155	−	40.7662i	1.75688	−	1.55646i
$687$	18.7211	−	4.61435i	0.714256	−	0.176048i
$688$	−4.01330	+	5.81427i	−0.153006	+	0.221667i
$689$	−26.2670	+	19.7264i	−1.00069	+	0.751516i
$690$	−14.3178	−	20.7429i	−0.545070	−	0.789670i
$691$	35.0228	+	31.0275i	1.33233	+	1.18034i	0.968539	+	0.248863i	$0.0800569\pi$
$691$	35.0228	+	31.0275i	1.33233	+	1.18034i	0.363793	+	0.931480i	$0.381482\pi$
$692$	−0.0646876	−	0.0937162i	−0.00245905	−	0.00356255i
$693$	14.9793	+	13.2705i	0.569015	+	0.504104i
$694$	41.2776	+	21.6642i	1.56688	+	0.822360i
$695$	−11.3033			−0.428758
$696$	21.8694	−	11.4779i	0.828956	−	0.435070i
$697$	−23.0243	+	20.3978i	−0.872109	+	0.772621i
$698$	0.485428			0.0183737
$699$	15.2211			0.575713
$700$	0.149883	−	0.132785i	0.00566503	−	0.00501878i
$701$	−17.1055	−	45.1036i	−0.646067	−	1.70354i	−0.708708	−	0.705502i	$-0.750722\pi$
$701$	−17.1055	−	45.1036i	−0.646067	−	1.70354i	0.0626412	−	0.998036i	$-0.480048\pi$
$702$	−3.49873	−	3.64469i	−0.132051	−	0.137560i
$703$	−0.468854	+	1.23627i	−0.0176832	+	0.0466267i
$704$	12.0137	+	31.6775i	0.452783	+	1.19389i
$705$	15.5572	+	3.83451i	0.585919	+	0.144416i
$706$	18.1797	+	26.3378i	0.684202	+	0.991238i
$707$	11.6204	−	30.6404i	0.437029	−	1.15235i
$708$	−0.163845	−	0.432024i	−0.00615767	−	0.0162364i
$709$	0.777071	+	6.39975i	0.0291835	+	0.240348i	1.00000		0.000523715i	$0.000166704\pi$
$709$	0.777071	+	6.39975i	0.0291835	+	0.240348i	−0.970816	+	0.239824i	$0.922910\pi$
$710$	2.62251	+	3.79935i	0.0984209	+	0.142587i
$711$	−6.83321	+	1.68424i	−0.256266	+	0.0631638i
$712$	−11.2355	−	9.95377i	−0.421068	−	0.373033i
$713$	0.406836	−	1.07274i	0.0152361	−	0.0401744i
$714$	40.9915	+	10.1035i	1.53407	+	0.378114i
$715$	−31.4173	−	19.8799i	−1.17494	−	0.743466i
$716$	0.483501	−	0.119172i	0.0180693	−	0.00445368i
$717$	−0.643190	+	5.29715i	−0.0240204	+	0.197826i
$718$	−7.28023	+	3.82096i	−0.271696	+	0.142597i
$719$	11.8285	+	31.1891i	0.441127	+	1.16316i	0.952699	+	0.303916i	$0.0982941\pi$
$719$	11.8285	+	31.1891i	0.441127	+	1.16316i	−0.511572	+	0.859240i	$0.670937\pi$
$720$	9.44394	+	2.32772i	0.351955	+	0.0867491i
$721$	62.4164	−	55.2961i	2.32451	−	2.05933i
$722$	−16.7230	−	4.12185i	−0.622366	−	0.153399i
$723$	2.95448	−	1.55063i	0.109878	−	0.0576686i
$724$	−0.767426	+	0.402776i	−0.0285212	+	0.0149691i
$725$	−1.18853	−	9.78839i	−0.0441407	−	0.363532i
$726$	1.06732	+	8.79016i	0.0396119	+	0.326234i
$727$	−14.4722	+	12.8213i	−0.536745	+	0.475515i	−0.887407	−	0.460988i	$-0.847495\pi$
$727$	−14.4722	+	12.8213i	−0.536745	+	0.475515i	0.350662	+	0.936502i	$0.385957\pi$
$728$	49.3156	+	3.99563i	1.82776	+	0.148088i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−15.0993	+	21.8751i	−0.558849	+	0.809633i
$731$	3.99862	−	10.5435i	0.147894	−	0.389965i
$732$	−0.0158132	−	0.130233i	−0.000584471	−	0.00481355i
$733$	−0.0487022	+	0.401099i	−0.00179886	+	0.0148149i	−0.993581	−	0.113126i	$-0.963914\pi$
$733$	−0.0487022	+	0.401099i	−0.00179886	+	0.0148149i	0.991782	+	0.127941i	$0.0408367\pi$
$734$	−39.6035	−	20.7855i	−1.46179	−	0.767207i
$735$	−22.6944	+	32.8785i	−0.837096	+	1.21274i
$736$	−0.532201	−	1.40330i	−0.0196172	−	0.0517263i
$737$	30.9020	−	27.3767i	1.13829	−	1.00844i
$738$	3.90781	−	5.66145i	0.143849	−	0.208401i
$739$	17.5591	+	25.4387i	0.645920	+	0.935777i	1.00000		0.000561702i	$0.000178795\pi$
$739$	17.5591	+	25.4387i	0.645920	+	0.935777i	−0.354080	+	0.935215i	$0.615206\pi$
$740$	0.00557267	+	0.0458951i	0.000204856	+	0.00168714i
$741$	−8.85707	−	2.95979i	−0.325373	−	0.108731i
$742$	−7.39969	+	60.9420i	−0.271651	+	2.23725i
$743$	−8.61291	+	4.52041i	−0.315977	+	0.165838i	−0.615254	−	0.788329i	$-0.710947\pi$
$743$	−8.61291	+	4.52041i	−0.315977	+	0.165838i	0.299277	+	0.954166i	$0.403254\pi$
$744$	0.159924	+	0.421685i	0.00586310	+	0.0154597i
$745$	−0.731246	+	6.02235i	−0.0267908	+	0.220642i
$746$	−37.7012			−1.38034
$747$	−0.909536	+	7.49070i	−0.0332782	+	0.274070i
$748$	−0.541409	−	0.784366i	−0.0197959	−	0.0286793i
$749$	30.9477	−	7.62792i	1.13080	−	0.278718i
$750$	−7.61440	+	11.0314i	−0.278039	+	0.402808i
$751$	18.4045	−	4.53631i	0.671591	−	0.165532i	0.111248	−	0.993793i	$-0.464515\pi$
$751$	18.4045	−	4.53631i	0.671591	−	0.165532i	0.560343	+	0.828260i	$0.310669\pi$
$752$	−22.4776	−	11.7971i	−0.819673	−	0.430197i
$753$	−0.534405	−	0.280478i	−0.0194748	−	0.0102212i
$754$	27.6645	−	33.8628i	1.00748	−	1.23321i
$755$	40.8666	−	21.4484i	1.48729	−	0.780589i
$756$	0.175763			0.00639245
$757$	48.0577	+	25.2226i	1.74669	+	0.916732i	0.949948	+	0.312409i	$0.101136\pi$
$757$	48.0577	+	25.2226i	1.74669	+	0.916732i	0.796739	+	0.604323i	$0.206557\pi$
$758$	−8.80354	+	23.2130i	−0.319759	+	0.843135i
$759$	−3.64162	−	29.9914i	−0.132182	−	1.08862i
$760$	17.7813	−	4.38269i	0.644995	−	0.158977i
$761$	−13.9914	+	3.44857i	−0.507187	+	0.125010i	−0.484603	−	0.874734i	$-0.661036\pi$
$761$	−13.9914	+	3.44857i	−0.507187	+	0.125010i	−0.0225849	+	0.999745i	$0.507190\pi$
$762$	0.890224	+	7.33166i	0.0322494	+	0.265598i
$763$	9.18016	−	24.2061i	0.332344	−	0.876320i
$764$	−0.122764	−	0.0644314i	−0.00444144	−	0.00233105i
$765$	−15.5246			−0.561294
$766$	4.03566	−	2.11808i	0.145814	−	0.0765292i
$767$	−31.5637	−	32.8805i	−1.13970	−	1.18725i
$768$	0.776484	+	0.407530i	0.0280190	+	0.0147055i
$769$	−47.1162	−	24.7285i	−1.69905	−	0.891732i	−0.980565	−	0.196192i	$-0.937142\pi$
$769$	−47.1162	−	24.7285i	−1.69905	−	0.891732i	−0.718488	−	0.695540i	$-0.755165\pi$
$770$	−67.4612	+	16.6277i	−2.43113	+	0.599220i
$771$	−6.23960	+	9.03962i	−0.224714	+	0.325554i
$772$	0.199597	−	0.0491962i	0.00718365	−	0.00177061i
$773$	−16.1522	−	23.4005i	−0.580953	−	0.841656i	0.416776	−	0.909009i	$-0.363160\pi$
$773$	−16.1522	−	23.4005i	−0.580953	−	0.841656i	−0.997729	+	0.0673532i	$0.978545\pi$
$774$	−0.303970	+	2.50342i	−0.0109260	+	0.0899836i
$775$	0.180048			0.00646753
$776$	3.54433	−	29.1902i	0.127234	−	1.04787i
$777$	−0.870480	−	2.29527i	−0.0312283	−	0.0823423i
$778$	−4.04862	+	2.12488i	−0.145150	+	0.0761806i
$779$	1.53268	−	12.6228i	0.0549141	−	0.452258i
$780$	−0.322322	+	0.0522860i	−0.0115410	+	0.00187214i
$781$	0.667013	+	5.49335i	0.0238676	+	0.196567i
$782$	−36.2061	−	52.4535i	−1.29473	−	1.87574i
$783$	4.91657	−	7.12287i	0.175704	−	0.254551i
$784$	47.3765	−	41.9719i	1.69202	−	1.49900i
$785$	4.34461	+	11.4558i	0.155066	+	0.408875i
$786$	12.3301	−	17.8633i	0.439802	−	0.637163i
$787$	46.1734	+	24.2337i	1.64590	+	0.863836i	0.994457	+	0.105141i	$0.0335293\pi$
$787$	46.1734	+	24.2337i	1.64590	+	0.863836i	0.651445	+	0.758696i	$0.274163\pi$
$788$	−0.0515612	+	0.424645i	−0.00183679	+	0.0151273i
$789$	1.65452	+	13.6262i	0.0589026	+	0.485106i
$790$	8.66452	−	22.8465i	0.308270	−	0.812841i
$791$	27.2685	−	39.5053i	0.969558	−	1.40465i
$792$	8.88930	+	7.87523i	0.315868	+	0.279834i
$793$	−6.46728	−	11.2092i	−0.229660	−	0.398050i
$794$	8.14217	−	7.21334i	0.288955	−	0.255992i
$795$	−2.72103	−	22.4097i	−0.0965052	−	0.794791i
$796$	−0.0919800	−	0.757523i	−0.00326014	−	0.0268497i
$797$	−22.4179	+	11.7658i	−0.794083	+	0.416767i	−0.812426	−	0.583065i	$-0.801853\pi$
$797$	−22.4179	+	11.7658i	−0.794083	+	0.416767i	0.0183427	+	0.999832i	$0.494161\pi$
$798$	−15.4530	+	8.11034i	−0.547029	+	0.287103i
$799$	39.3402	+	9.69649i	1.39176	+	0.343037i
$800$	0.176297	−	0.156185i	0.00623302	−	0.00552198i
$801$	−5.10719	−	1.25881i	−0.180454	−	0.0444778i
$802$	3.21676	+	8.48190i	0.113588	+	0.299506i
$803$	−28.2112	+	14.8064i	−0.995552	+	0.522506i
$804$	0.0437062	−	0.359953i	0.00154140	−	0.0126946i
$805$	83.9828	−	20.6999i	2.96000	−	0.729576i
$806$	0.552935	+	0.576002i	0.0194763	+	0.0202888i
$807$	8.70492	+	2.14557i	0.306428	+	0.0755277i
$808$	6.89599	−	18.1832i	0.242600	−	0.639684i
$809$	16.0702	+	14.2369i	0.564997	+	0.500544i	0.896580	−	0.442883i	$-0.146044\pi$
$809$	16.0702	+	14.2369i	0.564997	+	0.500544i	−0.331583	+	0.943426i	$0.607583\pi$
$810$	3.37102	−	0.830882i	0.118446	−	0.0291942i
$811$	−17.8792	−	25.9025i	−0.627823	−	0.909559i	0.372002	−	0.928232i	$-0.378671\pi$
$811$	−17.8792	−	25.9025i	−0.627823	−	0.909559i	−0.999826	+	0.0186726i	$0.994056\pi$
$812$	0.183363	+	1.51013i	0.00643478	+	0.0529952i
$813$	−7.98215	−	21.0472i	−0.279946	−	0.738157i
$814$	1.05561	−	2.78342i	0.0369992	−	0.0975590i
$815$	−7.17008	−	10.3876i	−0.251157	−	0.363863i
$816$	23.8813	+	5.88621i	0.836013	+	0.206059i
$817$	1.65293	+	4.35841i	0.0578286	+	0.152481i
$818$	5.77512	−	15.2277i	0.201922	−	0.532426i
$819$	15.9526	−	6.79128i	0.557429	−	0.237307i
$820$	−0.157663	−	0.415723i	−0.00550583	−	0.0145177i
$821$	−17.1747	+	15.2155i	−0.599403	+	0.531024i	−0.907348	−	0.420379i	$-0.861897\pi$
$821$	−17.1747	+	15.2155i	−0.599403	+	0.531024i	0.307946	+	0.951404i	$0.400359\pi$
$822$	1.82202			0.0635503
$823$	25.9022			0.902893			0.451447	−	0.892298i	$-0.350908\pi$
$823$	25.9022			0.902893			0.451447	+	0.892298i	$0.350908\pi$
$824$	37.0404	−	32.8149i	1.29036	−	1.14316i
$825$	4.19814	−	2.20335i	0.146160	−	0.0767109i
$826$	−85.1777			−2.96371
$827$	3.11471	+	1.63473i	0.108309	+	0.0568450i	0.518008	−	0.855376i	$-0.326674\pi$
$827$	3.11471	+	1.63473i	0.108309	+	0.0568450i	−0.409699	+	0.912221i	$0.634366\pi$
$828$	−0.198614	−	0.175956i	−0.00690230	−	0.00611491i
$829$	−0.512655	−	0.742709i	−0.0178052	−	0.0257954i	0.813980	−	0.580893i	$-0.197296\pi$
$829$	−0.512655	−	0.742709i	−0.0178052	−	0.0257954i	−0.831785	+	0.555097i	$0.812681\pi$
$830$	−19.6095	−	17.3725i	−0.680656	−	0.603008i
$831$	15.2528	+	22.0975i	0.529114	+	0.766554i
$832$	29.2562	+	2.37039i	1.01428	+	0.0821785i
$833$	−57.3884	+	83.1414i	−1.98839	+	2.88068i
$834$	6.20654	−	1.52978i	0.214915	−	0.0529718i
$835$	−15.1913	+	13.4583i	−0.525717	+	0.465745i
$836$	0.382529	+	0.0942850i	0.0132301	+	0.00326091i
$837$	0.118294	+	0.104799i	0.00408883	+	0.00362239i
$838$	−41.6635	−	36.9107i	−1.43924	−	1.27506i
$839$	−12.5115	+	32.9902i	−0.431946	+	1.13895i	0.525617	+	0.850721i	$0.323835\pi$
$839$	−12.5115	+	32.9902i	−0.431946	+	1.13895i	−0.957563	+	0.288225i	$0.906935\pi$
$840$	−19.3148	+	27.9823i	−0.666422	+	0.965480i
$841$	40.6495	+	21.3345i	1.40171	+	0.735672i
$842$	1.18876	−	9.79033i	0.0409674	−	0.337397i
$843$	−25.8381	−	6.36853i	−0.889912	−	0.219344i
$844$	−0.100549			−0.00346104
$845$	−27.2343	+	17.1997i	−0.936888	+	0.591688i
$846$	−9.06130			−0.311534
$847$	−29.5044	−	7.27218i	−1.01378	−	0.249875i
$848$	−4.31100	+	35.5043i	−0.148040	+	1.21922i
$849$	−28.5028	−	14.9594i	−0.978215	−	0.513407i
$850$	5.68193	−	8.23170i	0.194889	−	0.282345i
$851$	−1.31414	+	3.46510i	−0.0450481	+	0.118782i
$852$	0.0363788	+	0.0322288i	0.00124632	+	0.00110414i
$853$	−1.79649	−	1.59155i	−0.0615108	−	0.0544938i	0.631807	−	0.775126i	$-0.282313\pi$
$853$	−1.79649	−	1.59155i	−0.0615108	−	0.0544938i	−0.693318	+	0.720632i	$0.743852\pi$
$854$	−23.4817	−	5.78773i	−0.803528	−	0.198052i
$855$	4.80356	−	4.25558i	0.164278	−	0.145538i
$856$	18.3656	−	4.52672i	0.627724	−	0.154720i
$857$	−18.7017	+	27.0941i	−0.638838	+	0.925517i	−0.999976	−	0.00699544i	$-0.997773\pi$
$857$	−18.7017	+	27.0941i	−0.638838	+	0.925517i	0.361137	+	0.932513i	$0.382389\pi$
$858$	19.9415	+	6.66391i	0.680791	+	0.227502i
$859$	8.92313	+	12.9274i	0.304453	+	0.441077i	0.945111	−	0.326750i	$-0.105954\pi$
$859$	8.92313	+	12.9274i	0.304453	+	0.441077i	−0.640658	+	0.767827i	$0.721338\pi$
$860$	0.122000	+	0.108082i	0.00416015	+	0.00368558i
$861$	13.4107	+	19.4288i	0.457036	+	0.662131i
$862$	12.6828	+	11.2360i	0.431979	+	0.382700i
$863$	−17.1256	−	8.98820i	−0.582962	−	0.305962i	0.147341	−	0.989086i	$-0.452929\pi$
$863$	−17.1256	−	8.98820i	−0.582962	−	0.305962i	−0.730303	+	0.683124i	$0.760621\pi$
$864$	0.206738			0.00703337
$865$	6.83515	−	3.58736i	0.232402	−	0.121974i
$866$	−12.8248	+	11.3618i	−0.435803	+	0.386088i
$867$	−22.2578			−0.755914
$868$	−0.0277774			−0.000942827
$869$	21.9227	−	19.4218i	0.743677	−	0.658841i
$870$	10.6556	+	28.0964i	0.361258	+	0.952558i
$871$	−9.94128	−	34.3587i	−0.336847	−	1.16420i
$872$	5.44788	−	14.3649i	0.184488	−	0.486456i
$873$	−3.65388	−	9.63450i	−0.123665	−	0.326078i
$874$	25.5812	+	6.30519i	0.865296	+	0.213276i
$875$	−26.1309	−	37.8571i	−0.883385	−	1.27980i
$876$	−0.0992282	+	0.261643i	−0.00335261	+	0.00884011i
$877$	−12.1039	−	31.9155i	−0.408721	−	1.07771i	−0.968488	−	0.249059i	$-0.919879\pi$
$877$	−12.1039	−	31.9155i	−0.408721	−	1.07771i	0.559767	−	0.828650i	$-0.310891\pi$
$878$	0.671171	+	5.52759i	0.0226509	+	0.186547i
$879$	0.405593	+	0.587603i	0.0136803	+	0.0198193i
$880$	−39.3023	+	9.68714i	−1.32488	+	0.326554i
$881$	−36.3644	−	32.2160i	−1.22515	−	1.08539i	−0.993646	−	0.112551i	$-0.964098\pi$
$881$	−36.3644	−	32.2160i	−1.22515	−	1.08539i	−0.231501	−	0.972835i	$-0.574364\pi$
$882$	8.01157	−	21.1248i	0.269764	−	0.711308i
$883$	28.5365	+	7.03360i	0.960328	+	0.236700i	0.688167	−	0.725552i	$-0.258416\pi$
$883$	28.5365	+	7.03360i	0.960328	+	0.236700i	0.272161	+	0.962252i	$0.412262\pi$
$884$	−0.815070	+	0.132218i	−0.0274138	+	0.00444697i
$885$	30.4116	−	7.49579i	1.02228	−	0.251968i
$886$	−5.41492	+	44.5958i	−0.181918	+	1.49823i
$887$	30.9502	−	16.2439i	1.03921	−	0.545418i	0.143309	−	0.989678i	$-0.454226\pi$
$887$	30.9502	−	16.2439i	1.03921	−	0.545418i	0.895898	+	0.444260i	$0.146533\pi$
$888$	−0.516578	−	1.36210i	−0.0173352	−	0.0457092i
$889$	−24.6089	−	6.06554i	−0.825355	−	0.203432i
$890$	13.6696	−	12.1102i	0.458205	−	0.405934i
$891$	4.04071	+	0.995946i	0.135369	+	0.0333654i
$892$	0.227683	−	0.119497i	0.00762338	−	0.00400106i
$893$	−14.8304	+	7.78362i	−0.496282	+	0.260469i
$894$	−0.413537	−	3.40579i	−0.0138308	−	0.113907i
$895$	4.06894	+	33.5108i	0.136010	+	1.12014i
$896$	39.5703	−	35.0562i	1.32195	−	1.17115i
$897$	−24.8253	−	8.29594i	−0.828892	−	0.276993i
$898$	13.4912	+	11.9522i	0.450207	+	0.398849i
$899$	−0.777008	+	1.12569i	−0.0259147	+	0.0375439i
$900$	0.0147662	−	0.0389354i	0.000492208	−	0.00129785i
$901$	−6.88080	−	56.6685i	−0.229233	−	1.88790i
$902$	−3.45080	+	28.4199i	−0.114899	+	0.946279i
$903$	−7.66297	−	4.02184i	−0.255008	−	0.133838i
$904$	16.1823	−	23.4440i	0.538214	−	0.779737i
$905$	−20.8340	−	54.9347i	−0.692545	−	1.82609i
$906$	−19.5367	+	17.3080i	−0.649063	+	0.575020i
$907$	−19.7800	+	28.6563i	−0.656785	+	0.951518i	0.343140	+	0.939284i	$0.388509\pi$
$907$	−19.7800	+	28.6563i	−0.656785	+	0.951518i	−0.999925	+	0.0122333i	$0.996106\pi$
$908$	0.360405	+	0.522137i	0.0119605	+	0.0173277i
$909$	−0.821421	−	6.76501i	−0.0272448	−	0.224381i
$910$	−12.0579	+	58.9760i	−0.399717	+	1.95504i
$911$	−0.627772	+	5.17017i	−0.0207990	+	0.171295i	−0.999407	−	0.0344396i	$-0.989035\pi$
$911$	−0.627772	+	5.17017i	−0.0207990	+	0.171295i	0.978608	+	0.205735i	$0.0659584\pi$
$912$	−9.00276	+	4.72501i	−0.298111	+	0.156461i
$913$	−11.1355	−	29.3619i	−0.368531	−	0.971737i
$914$	−5.31483	+	43.7715i	−0.175799	+	1.44783i
$915$	8.89318			0.294000
$916$	−0.0849491	+	0.699619i	−0.00280680	+	0.0231160i
$917$	42.3142	+	61.3027i	1.39734	+	2.02439i
$918$	8.52444	−	2.10109i	0.281348	−	0.0693462i
$919$	3.00635	−	4.35545i	0.0991704	−	0.143673i	−0.770257	−	0.637733i	$-0.779872\pi$
$919$	3.00635	−	4.35545i	0.0991704	−	0.143673i	0.869428	+	0.494060i	$0.164488\pi$
$920$	49.8388	−	12.2842i	1.64314	−	0.404997i
$921$	22.9316	+	12.0354i	0.755622	+	0.396581i
$922$	−14.0353	−	7.36630i	−0.462229	−	0.242596i
$923$	4.54709	+	1.51952i	0.149669	+	0.0500155i
$924$	−0.647679	+	0.339928i	−0.0213071	+	0.0111828i
$925$	−0.581582			−0.0191223
$926$	−15.9408	−	8.36638i	−0.523848	−	0.274936i
$927$	6.14918	−	16.2140i	0.201965	−	0.532539i
$928$	0.215677	+	1.77626i	0.00707994	+	0.0583086i
$929$	−30.2199	+	7.44853i	−0.991482	+	0.244378i	−0.701512	−	0.712658i	$-0.747491\pi$
$929$	−30.2199	+	7.44853i	−0.991482	+	0.244378i	−0.289970	+	0.957036i	$0.593645\pi$
$930$	−0.532752	+	0.131312i	−0.0174696	+	0.00430588i
$931$	−5.03372	−	41.4564i	−0.164973	−	1.35868i
$932$	−0.197283	+	0.520192i	−0.00646222	+	0.0170395i
$933$	1.64392	+	0.862796i	0.0538195	+	0.0282467i
$934$	−50.8886			−1.66513
$935$	57.2075	−	30.0248i	1.87088	−	0.981916i
$936$	9.46692	−	4.03022i	0.309436	−	0.131732i
$937$	6.39961	+	3.35878i	0.209066	+	0.109726i	0.566006	−	0.824401i	$-0.308488\pi$
$937$	6.39961	+	3.35878i	0.209066	+	0.109726i	−0.356940	+	0.934127i	$0.616180\pi$
$938$	−59.1873	−	31.0639i	−1.93253	−	1.01427i
$939$	23.9610	−	5.90585i	0.781937	−	0.192730i
$940$	−0.332688	+	0.481981i	−0.0108511	+	0.0157205i
$941$	32.8692	−	8.10154i	1.07151	−	0.264103i	0.336167	−	0.941802i	$-0.390869\pi$
$941$	32.8692	−	8.10154i	1.07151	−	0.264103i	0.735339	+	0.677700i	$0.237023\pi$
$942$	−3.93601	−	5.70229i	−0.128242	−	0.185791i
$943$	4.29592	−	35.3801i	0.139894	−	1.15213i
$944$	−49.6238			−1.61512
$945$	−1.43617	+	11.8279i	−0.0467186	+	0.384762i
$946$	−3.72153	−	9.81286i	−0.120997	−	0.319044i
$947$	−11.5450	+	6.05929i	−0.375163	+	0.196901i	−0.641757	−	0.766908i	$-0.721794\pi$
$947$	−11.5450	+	6.05929i	−0.375163	+	0.196901i	0.266594	+	0.963809i	$0.414102\pi$
$948$	0.0310064	−	0.255361i	0.00100704	−	0.00829373i
$949$	1.10344	+	27.5813i	0.0358191	+	0.895327i
$950$	0.498380	+	4.10453i	0.0161696	+	0.133169i
$951$	5.25847	+	7.61821i	0.170518	+	0.247038i
$952$	−48.8421	+	70.7599i	−1.58298	+	2.29334i
$953$	−12.5239	+	11.0952i	−0.405688	+	0.359409i	−0.841153	−	0.540797i	$-0.818123\pi$
$953$	−12.5239	+	11.0952i	−0.405688	+	0.359409i	0.435465	+	0.900206i	$0.356584\pi$
$954$	4.52701	+	11.9367i	0.146567	+	0.386466i
$955$	5.33899	−	7.73487i	0.172766	−	0.250294i
$956$	−0.172698	−	0.0906389i	−0.00558545	−	0.00293147i
$957$	−4.34158	+	35.7561i	−0.140343	+	1.15583i
$958$	3.60966	+	29.7282i	0.116623	+	0.960475i
$959$	−2.21726	+	5.84644i	−0.0715991	+	0.188791i
$960$	−11.4584	+	16.6004i	−0.369818	+	0.535774i
$961$	23.1851	+	20.5402i	0.747908	+	0.662588i
$962$	−1.78606	−	1.86057i	−0.0575849	−	0.0599872i
$963$	4.96141	−	4.39543i	0.159879	−	0.141641i
$964$	0.0147005	+	0.121070i	0.000473473	+	0.00389940i
$965$	1.67972	+	13.8338i	0.0540722	+	0.445325i
$966$	−43.3127	+	22.7323i	−1.39356	+	0.731399i
$967$	−35.1453	+	18.4457i	−1.13020	+	0.593174i	−0.922875	−	0.385099i	$-0.874167\pi$
$967$	−35.1453	+	18.4457i	−1.13020	+	0.593174i	−0.207323	+	0.978273i	$0.566475\pi$
$968$	−17.5091	−	4.31560i	−0.562764	−	0.138709i
$969$	12.1470	−	10.7613i	0.390217	−	0.345702i
$970$	34.7353	+	8.56149i	1.11528	+	0.274893i
$971$	7.59207	+	20.0187i	0.243641	+	0.642429i	0.999930	−	0.0118085i	$-0.00375885\pi$
$971$	7.59207	+	20.0187i	0.243641	+	0.642429i	−0.756289	+	0.654238i	$0.772990\pi$
$972$	0.0323644	−	0.0169861i	0.00103809	−	0.000544831i
$973$	−2.64420	+	21.7769i	−0.0847691	+	0.698136i
$974$	−40.0910	+	9.88154i	−1.28460	+	0.316625i
$975$	−0.164204	−	4.10440i	−0.00525873	−	0.131446i
$976$	−13.6802	−	3.37188i	−0.437894	−	0.107931i
$977$	−11.8588	+	31.2690i	−0.379395	+	1.00038i	0.600279	+	0.799790i	$0.295056\pi$
$977$	−11.8588	+	31.2690i	−0.379395	+	1.00038i	−0.979675	+	0.200593i	$0.935713\pi$
$978$	5.34288	+	4.73338i	0.170846	+	0.151357i
$979$	21.2543	−	5.23871i	0.679290	−	0.167430i
$980$	−0.829506	−	1.20175i	−0.0264976	−	0.0383884i
$981$	−0.648928	−	5.34441i	−0.0207187	−	0.170634i
$982$	5.07405	+	13.3792i	0.161920	+	0.426947i
$983$	10.0727	−	26.5596i	0.321270	−	0.847119i	−0.672943	−	0.739694i	$-0.734970\pi$
$983$	10.0727	−	26.5596i	0.321270	−	0.847119i	0.994213	−	0.107425i	$-0.0342605\pi$
$984$	7.95846	+	11.5298i	0.253707	+	0.367557i
$985$	−28.1550	−	6.93958i	−0.897092	−	0.221113i
$986$	26.9452	+	71.0487i	0.858110	+	2.26265i
$987$	11.0269	−	29.0755i	0.350990	−	0.925485i
$988$	0.215952	−	0.264336i	0.00687034	−	0.00840963i
$989$	4.63295	+	12.2161i	0.147319	+	0.388449i
$990$	−10.8151	+	9.58134i	−0.343726	+	0.304515i
$991$	−22.1807			−0.704594			−0.352297	−	0.935888i	$-0.614599\pi$
$991$	−22.1807			−0.704594			−0.352297	+	0.935888i	$0.614599\pi$
$992$	−0.0326726			−0.00103736
$993$	−7.47204	+	6.61965i	−0.237118	+	0.210068i
$994$	7.93333	−	4.16373i	0.251630	−	0.132066i
$995$	51.7287			1.63991
$996$	−0.244212	−	0.128173i	−0.00773817	−	0.00406130i
$997$	13.2120	+	11.7048i	0.418427	+	0.370694i	0.845907	−	0.533331i	$-0.179060\pi$
$997$	13.2120	+	11.7048i	0.418427	+	0.370694i	−0.427480	+	0.904025i	$0.640598\pi$
$998$	23.5192	+	34.0735i	0.744488	+	1.07858i
$999$	−0.382106	−	0.338517i	−0.0120893	−	0.0107102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.40.11	✓	180
169.131	even	13	inner	507.2.m.a.469.11	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.40.11	✓	180	1.1	even	1	trivial
507.2.m.a.469.11	yes	180	169.131	even	13	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.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36051 + 0.335337i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(-0.0323644 - 0.0169861i) q^{4} +(1.40752 - 2.03915i) q^{5} +(-0.496883 + 1.31017i) q^{6} +(-3.59937 - 3.18876i) q^{7} +(-2.13601 - 1.89234i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(1.36051 + 0.335337i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(-0.0323644 - 0.0169861i) q^{4} +(1.40752 - 2.03915i) q^{5} +(-0.496883 + 1.31017i) q^{6} +(-3.59937 - 3.18876i) q^{7} +(-2.13601 - 1.89234i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(2.59876 - 2.30230i) q^{10} +(4.04071 - 0.995946i) q^{11} +(0.0207634 - 0.0300809i) q^{12} +(0.722232 - 3.53248i) q^{13} +(-3.82768 - 5.54535i) q^{14} +(1.85463 + 1.64306i) q^{15} +(-2.22997 - 3.23067i) q^{16} +(4.68987 + 4.15486i) q^{17} +(-1.24073 - 0.651185i) q^{18} -2.59004 q^{19} +(-0.0801910 + 0.0420875i) q^{20} +(3.59937 - 3.18876i) q^{21} +5.83142 q^{22} -7.25957 q^{23} +(2.13601 - 1.89234i) q^{24} +(-0.403989 - 1.06523i) q^{25} +(2.16718 - 4.56379i) q^{26} +(0.354605 - 0.935016i) q^{27} +(0.0623265 + 0.164342i) q^{28} +(8.40344 + 2.07126i) q^{29} +(1.97227 + 2.85732i) q^{30} +(-0.0560413 + 0.147769i) q^{31} +(0.0733103 + 0.193303i) q^{32} +(0.501630 + 4.13130i) q^{33} +(4.98736 + 7.22544i) q^{34} +(-11.5686 + 2.85140i) q^{35} +(0.0273589 + 0.0242379i) q^{36} +(0.181022 - 0.477315i) q^{37} +(-3.52379 - 0.868536i) q^{38} +(3.41966 + 1.14276i) q^{39} +(-6.86525 + 1.69213i) q^{40} +(-0.591760 + 4.87358i) q^{41} +(5.96630 - 3.13135i) q^{42} +(-0.638186 - 1.68276i) q^{43} +(-0.147692 - 0.0364029i) q^{44} +(-1.85463 + 1.64306i) q^{45} +(-9.87674 - 2.43440i) q^{46} +(5.72595 - 3.00521i) q^{47} +(3.47591 - 1.82430i) q^{48} +(1.94349 + 16.0061i) q^{49} +(-0.192422 - 1.58474i) q^{50} +(-4.68987 + 4.15486i) q^{51} +(-0.0833777 + 0.102058i) q^{52} +(-6.81953 - 6.04158i) q^{53} +(0.795990 - 1.15319i) q^{54} +(3.65652 - 9.64144i) q^{55} +(1.65406 + 13.6224i) q^{56} +(0.312195 - 2.57116i) q^{57} +(10.7384 + 5.63596i) q^{58} +(7.18102 - 10.4035i) q^{59} +(-0.0321146 - 0.0846794i) q^{60} +(2.68656 - 2.38009i) q^{61} +(-0.125797 + 0.182249i) q^{62} +(2.73166 + 3.95749i) q^{63} +(0.981266 + 8.08146i) q^{64} +(-6.18669 - 6.44479i) q^{65} +(-0.702900 + 5.78890i) q^{66} +(8.78396 - 4.61018i) q^{67} +(-0.0812097 - 0.214132i) q^{68} +(0.875044 - 7.20664i) q^{69} -16.6954 q^{70} +(-0.160276 + 1.32000i) q^{71} +(1.62107 + 2.34853i) q^{72} +(-7.43333 + 1.83215i) q^{73} +(0.406344 - 0.588691i) q^{74} +(1.10616 - 0.272644i) q^{75} +(0.0838251 + 0.0439948i) q^{76} +(-17.7198 - 9.30008i) q^{77} +(4.26929 + 2.70148i) q^{78} +(6.23159 - 3.27059i) q^{79} -9.72658 q^{80} +(0.885456 + 0.464723i) q^{81} +(-2.43939 + 6.43214i) q^{82} +(-0.909536 - 7.49070i) q^{83} +(-0.170656 + 0.0420629i) q^{84} +(15.0735 - 3.71529i) q^{85} +(-0.303970 - 2.50342i) q^{86} +(-3.06908 + 8.09251i) q^{87} +(-10.5157 - 5.51905i) q^{88} +5.26004 q^{89} +(-3.07422 + 1.61348i) q^{90} +(-13.8638 + 10.4116i) q^{91} +(0.234951 + 0.123312i) q^{92} +(-0.139936 - 0.0734443i) q^{93} +(8.79799 - 2.16851i) q^{94} +(-3.64555 + 5.28149i) q^{95} +(-0.200731 + 0.0494757i) q^{96} +(5.85340 + 8.48011i) q^{97} +(-2.72328 + 22.4282i) q^{98} -4.16164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more