LMFDB - Embedded newform 690.2.m.f.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 36 x^{18} - 172 x^{17} + 691 x^{16} - 2342 x^{15} + 7870 x^{14} - 23240 x^{13} + \cdots + 123904 $ x^20 - 6x^19 + 36x^18 - 172x^17 + 691x^16 - 2342x^15 + 7870x^14 - 23240x^13 + 63837x^12 - 154607x^11 + 334467x^10 - 664202x^9 + 1099560x^8 - 1331000x^7 + 1218096x^6 + 395648x^5 - 588544x^4 + 665984x^3 + 2323200x^2 + 991232*x + 123904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			331.1
Root			$0.303318 + 2.10963i$ of defining polynomial
Character	$\chi$	$=$	690.331
Dual form			690.2.m.f.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.730522 + 1.59962i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.730522 + 1.59962i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-0.625973 - 0.183802i) q^{11} +(0.959493 + 0.281733i) q^{12} +(0.849841 + 1.86089i) q^{13} +(-0.250266 + 1.74063i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(4.93249 + 3.16992i) q^{17} +(0.142315 + 0.989821i) q^{18} +(2.65755 - 1.70791i) q^{19} +(0.654861 + 0.755750i) q^{20} +(-1.68730 + 0.495436i) q^{21} -0.652400 q^{22} +(2.51119 + 4.08582i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(1.33969 + 1.54608i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.250266 + 1.74063i) q^{28} +(-3.61833 - 2.32536i) q^{29} +(-0.415415 + 0.909632i) q^{30} +(-3.53648 + 4.08132i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-0.271017 - 0.593443i) q^{33} +(5.62576 + 1.65187i) q^{34} +(-1.68730 - 0.495436i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.47893 - 10.2862i) q^{37} +(2.06873 - 2.38744i) q^{38} +(-0.849841 + 1.86089i) q^{39} +(0.841254 + 0.540641i) q^{40} +(0.146037 + 1.01571i) q^{41} +(-1.47937 + 0.950735i) q^{42} +(-5.55628 - 6.41229i) q^{43} +(-0.625973 + 0.183802i) q^{44} -1.00000 q^{45} +(3.56058 + 3.21283i) q^{46} -1.35362 q^{47} +(0.959493 - 0.281733i) q^{48} +(2.55891 + 2.95313i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.834429 + 5.80358i) q^{51} +(1.72101 + 1.10602i) q^{52} +(-0.253280 + 0.554606i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(0.0928461 - 0.645759i) q^{55} +(0.730522 + 1.59962i) q^{56} +(3.03108 + 0.890004i) q^{57} +(-4.12689 - 1.21176i) q^{58} +(-4.65177 - 10.1860i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(2.73151 - 3.15233i) q^{61} +(-2.24339 + 4.91234i) q^{62} +(-1.47937 - 0.950735i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-1.72101 + 1.10602i) q^{65} +(-0.427231 - 0.493051i) q^{66} +(10.7503 - 3.15658i) q^{67} +5.86326 q^{68} +(-1.44337 + 4.57347i) q^{69} -1.75853 q^{70} +(-0.886216 + 0.260216i) q^{71} +(0.654861 + 0.755750i) q^{72} +(1.24030 - 0.797096i) q^{73} +(-1.47893 - 10.2862i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(1.31231 - 2.87356i) q^{76} +(0.751300 - 0.867046i) q^{77} +(-0.291142 + 2.02494i) q^{78} +(-7.10965 - 15.5680i) q^{79} +(0.959493 + 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.426279 + 0.933421i) q^{82} +(-1.16561 + 8.10697i) q^{83} +(-1.15160 + 1.32901i) q^{84} +(-2.43569 + 5.33341i) q^{85} +(-7.13777 - 4.58716i) q^{86} +(-0.612112 - 4.25733i) q^{87} +(-0.548833 + 0.352714i) q^{88} +(6.40360 + 7.39015i) q^{89} +(-0.959493 + 0.281733i) q^{90} -3.59754 q^{91} +(4.32151 + 2.07956i) q^{92} -5.40036 q^{93} +(-1.29879 + 0.381360i) q^{94} +(2.06873 + 2.38744i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-1.70831 - 11.8816i) q^{97} +(3.28725 + 2.11258i) q^{98} +(0.271017 - 0.593443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	−0.730522	+	1.59962i	−0.276111	+	0.604599i	−0.995986	−	0.0895043i	$-0.971472\pi$
$7$	−0.730522	+	1.59962i	−0.276111	+	0.604599i	0.719875	+	0.694103i	$0.244199\pi$
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	0.415415	+	0.909632i	0.131366	+	0.287651i
$11$	−0.625973	−	0.183802i	−0.188738	−	0.0554184i	0.185998	−	0.982550i	$-0.440448\pi$
$11$	−0.625973	−	0.183802i	−0.188738	−	0.0554184i	−0.374736	+	0.927132i	$0.622266\pi$
$12$	0.959493	+	0.281733i	0.276982	+	0.0813292i
$13$	0.849841	+	1.86089i	0.235703	+	0.516118i	0.990111	−	0.140288i	$-0.0448029\pi$
$13$	0.849841	+	1.86089i	0.235703	+	0.516118i	−0.754407	+	0.656407i	$0.772076\pi$
$14$	−0.250266	+	1.74063i	−0.0668863	+	0.465204i
$15$	−0.654861	+	0.755750i	−0.169084	+	0.195134i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	4.93249	+	3.16992i	1.19630	+	0.768818i	0.978313	−	0.207133i	$-0.0664133\pi$
$17$	4.93249	+	3.16992i	1.19630	+	0.768818i	0.217991	+	0.975951i	$0.430050\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	2.65755	−	1.70791i	0.609684	−	0.391820i	−0.199054	−	0.979988i	$-0.563787\pi$
$19$	2.65755	−	1.70791i	0.609684	−	0.391820i	0.808739	+	0.588168i	$0.200151\pi$
$20$	0.654861	+	0.755750i	0.146431	+	0.168991i
$21$	−1.68730	+	0.495436i	−0.368199	+	0.108113i
$22$	−0.652400			−0.139092
$23$	2.51119	+	4.08582i	0.523620	+	0.851952i
$23$	2.51119	+	4.08582i	0.523620	+	0.851952i
$24$	1.00000			0.204124
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	1.33969	+	1.54608i	0.262735	+	0.303212i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.250266	+	1.74063i	0.0472957	+	0.328949i
$29$	−3.61833	−	2.32536i	−0.671906	−	0.431808i	0.159706	−	0.987165i	$-0.448945\pi$
$29$	−3.61833	−	2.32536i	−0.671906	−	0.431808i	−0.831612	+	0.555357i	$0.812582\pi$
$30$	−0.415415	+	0.909632i	−0.0758441	+	0.166075i
$31$	−3.53648	+	4.08132i	−0.635171	+	0.733027i	−0.978513	−	0.206184i	$-0.933896\pi$
$31$	−3.53648	+	4.08132i	−0.635171	+	0.733027i	0.343342	+	0.939210i	$0.388441\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	−0.271017	−	0.593443i	−0.0471779	−	0.103305i
$34$	5.62576	+	1.65187i	0.964809	+	0.283294i
$35$	−1.68730	−	0.495436i	−0.285206	−	0.0837440i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	1.47893	−	10.2862i	0.243135	−	1.69104i	−0.393062	−	0.919512i	$-0.628584\pi$
$37$	1.47893	−	10.2862i	0.243135	−	1.69104i	0.636197	−	0.771527i	$-0.280507\pi$
$38$	2.06873	−	2.38744i	0.335592	−	0.387294i
$39$	−0.849841	+	1.86089i	−0.136083	+	0.297981i
$40$	0.841254	+	0.540641i	0.133014	+	0.0854828i
$41$	0.146037	+	1.01571i	0.0228071	+	0.158627i	0.998042	−	0.0625438i	$-0.0199213\pi$
$41$	0.146037	+	1.01571i	0.0228071	+	0.158627i	−0.975235	+	0.221171i	$0.929012\pi$
$42$	−1.47937	+	0.950735i	−0.228272	+	0.146702i
$43$	−5.55628	−	6.41229i	−0.847325	−	0.977865i	0.152620	−	0.988285i	$-0.451229\pi$
$43$	−5.55628	−	6.41229i	−0.847325	−	0.977865i	−0.999946	+	0.0104194i	$0.996683\pi$
$44$	−0.625973	+	0.183802i	−0.0943689	+	0.0277092i
$45$	−1.00000			−0.149071
$46$	3.56058	+	3.21283i	0.524979	+	0.473706i
$47$	−1.35362			−0.197446			−0.0987231	−	0.995115i	$-0.531476\pi$
$47$	−1.35362			−0.197446			−0.0987231	+	0.995115i	$0.531476\pi$
$48$	0.959493	−	0.281733i	0.138491	−	0.0406646i
$49$	2.55891	+	2.95313i	0.365558	+	0.421876i
$50$	−0.841254	+	0.540641i	−0.118971	+	0.0764582i
$51$	0.834429	+	5.80358i	0.116843	+	0.812664i
$52$	1.72101	+	1.10602i	0.238660	+	0.153378i
$53$	−0.253280	+	0.554606i	−0.0347907	+	0.0761810i	−0.926229	−	0.376960i	$-0.876969\pi$
$53$	−0.253280	+	0.554606i	−0.0347907	+	0.0761810i	0.891439	+	0.453141i	$0.149697\pi$
$54$	−0.654861	+	0.755750i	−0.0891153	+	0.102844i
$55$	0.0928461	−	0.645759i	0.0125194	−	0.0870741i
$56$	0.730522	+	1.59962i	0.0976200	+	0.213758i
$57$	3.03108	+	0.890004i	0.401476	+	0.117884i
$58$	−4.12689	−	1.21176i	−0.541887	−	0.159112i
$59$	−4.65177	−	10.1860i	−0.605609	−	1.32610i	−0.925537	−	0.378657i	$-0.876386\pi$
$59$	−4.65177	−	10.1860i	−0.605609	−	1.32610i	0.319928	−	0.947442i	$-0.396341\pi$
$60$	−0.142315	+	0.989821i	−0.0183728	+	0.127785i
$61$	2.73151	−	3.15233i	0.349734	−	0.403614i	−0.553440	−	0.832889i	$-0.686685\pi$
$61$	2.73151	−	3.15233i	0.349734	−	0.403614i	0.903174	+	0.429275i	$0.141231\pi$
$62$	−2.24339	+	4.91234i	−0.284911	+	0.623868i
$63$	−1.47937	−	0.950735i	−0.186383	−	0.119781i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−1.72101	+	1.10602i	−0.213464	+	0.137185i
$66$	−0.427231	−	0.493051i	−0.0525885	−	0.0606903i
$67$	10.7503	−	3.15658i	1.31336	−	0.385637i	0.451267	−	0.892389i	$-0.350972\pi$
$67$	10.7503	−	3.15658i	1.31336	−	0.385637i	0.862092	+	0.506752i	$0.169154\pi$
$68$	5.86326			0.711025
$69$	−1.44337	+	4.57347i	−0.173762	+	0.550582i
$70$	−1.75853			−0.210185
$71$	−0.886216	+	0.260216i	−0.105174	+	0.0308820i	−0.333896	−	0.942610i	$-0.608364\pi$
$71$	−0.886216	+	0.260216i	−0.105174	+	0.0308820i	0.228722	+	0.973492i	$0.426545\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	1.24030	−	0.797096i	0.145167	−	0.0932930i	−0.466041	−	0.884763i	$-0.654320\pi$
$73$	1.24030	−	0.797096i	0.145167	−	0.0932930i	0.611208	+	0.791470i	$0.290684\pi$
$74$	−1.47893	−	10.2862i	−0.171922	−	1.19574i
$75$	−0.841254	−	0.540641i	−0.0971396	−	0.0624278i
$76$	1.31231	−	2.87356i	0.150533	−	0.329620i
$77$	0.751300	−	0.867046i	0.0856186	−	0.0988091i
$78$	−0.291142	+	2.02494i	−0.0329654	+	0.229279i
$79$	−7.10965	−	15.5680i	−0.799898	−	1.75153i	−0.645844	−	0.763470i	$-0.723494\pi$
$79$	−7.10965	−	15.5680i	−0.799898	−	1.75153i	−0.154054	−	0.988062i	$-0.549233\pi$
$80$	0.959493	+	0.281733i	0.107275	+	0.0314987i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	0.426279	+	0.933421i	0.0470747	+	0.103079i
$83$	−1.16561	+	8.10697i	−0.127942	+	0.889856i	0.820215	+	0.572055i	$0.193854\pi$
$83$	−1.16561	+	8.10697i	−0.127942	+	0.889856i	−0.948157	+	0.317801i	$0.897056\pi$
$84$	−1.15160	+	1.32901i	−0.125649	+	0.145007i
$85$	−2.43569	+	5.33341i	−0.264187	+	0.578489i
$86$	−7.13777	−	4.58716i	−0.769685	−	0.494647i
$87$	−0.612112	−	4.25733i	−0.0656253	−	0.456434i
$88$	−0.548833	+	0.352714i	−0.0585058	+	0.0375994i
$89$	6.40360	+	7.39015i	0.678781	+	0.783355i	0.985723	−	0.168373i	$-0.0538514\pi$
$89$	6.40360	+	7.39015i	0.678781	+	0.783355i	−0.306943	+	0.951728i	$0.599306\pi$
$90$	−0.959493	+	0.281733i	−0.101139	+	0.0296972i
$91$	−3.59754			−0.377125
$92$	4.32151	+	2.07956i	0.450549	+	0.216809i
$93$	−5.40036			−0.559991
$94$	−1.29879	+	0.381360i	−0.133960	+	0.0393343i
$95$	2.06873	+	2.38744i	0.212247	+	0.244946i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	−1.70831	−	11.8816i	−0.173453	−	1.20639i	−0.871521	−	0.490358i	$-0.836866\pi$
$97$	−1.70831	−	11.8816i	−0.173453	−	1.20639i	0.698069	−	0.716031i	$-0.254043\pi$
$98$	3.28725	+	2.11258i	0.332062	+	0.213403i
$99$	0.271017	−	0.593443i	0.0272382	−	0.0596433i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	−1.23798	+	8.61034i	−0.123184	+	0.856761i	0.830729	+	0.556677i	$0.187924\pi$
$101$	−1.23798	+	8.61034i	−0.123184	+	0.856761i	−0.953913	+	0.300084i	$0.902985\pi$
$102$	2.43569	+	5.33341i	0.241169	+	0.528086i
$103$	−9.97232	−	2.92814i	−0.982602	−	0.288518i	−0.249304	−	0.968425i	$-0.580202\pi$
$103$	−9.97232	−	2.92814i	−0.982602	−	0.288518i	−0.733298	+	0.679907i	$0.762020\pi$
$104$	1.96289	+	0.576358i	0.192478	+	0.0565165i
$105$	−0.730522	−	1.59962i	−0.0712916	−	0.156107i
$106$	−0.0867699	+	0.603498i	−0.00842784	+	0.0586169i
$107$	9.63372	−	11.1179i	0.931327	−	1.07481i	−0.0657063	−	0.997839i	$-0.520930\pi$
$107$	9.63372	−	11.1179i	0.931327	−	1.07481i	0.997033	−	0.0769698i	$-0.0245245\pi$
$108$	−0.415415	+	0.909632i	−0.0399733	+	0.0875294i
$109$	−0.392855	−	0.252473i	−0.0376287	−	0.0241825i	0.521691	−	0.853134i	$-0.325301\pi$
$109$	−0.392855	−	0.252473i	−0.0376287	−	0.0241825i	−0.559320	+	0.828952i	$0.688938\pi$
$110$	−0.0928461	−	0.645759i	−0.00885253	−	0.0615707i
$111$	8.74227	−	5.61832i	0.829780	−	0.533267i
$112$	1.15160	+	1.32901i	0.108816	+	0.125580i
$113$	−2.09664	+	0.615628i	−0.197235	+	0.0579134i	−0.378858	−	0.925455i	$-0.623683\pi$
$113$	−2.09664	+	0.615628i	−0.197235	+	0.0579134i	0.181623	+	0.983368i	$0.441865\pi$
$114$	3.15904			0.295871
$115$	−3.68685	+	3.06711i	−0.343801	+	0.286009i
$116$	−4.30111			−0.399348
$117$	−1.96289	+	0.576358i	−0.181470	+	0.0532843i
$118$	−7.33306	−	8.46280i	−0.675063	−	0.779064i
$119$	−8.67395	+	5.57441i	−0.795139	+	0.511005i
$120$	0.142315	+	0.989821i	0.0129915	+	0.0903579i
$121$	−8.89573	−	5.71694i	−0.808703	−	0.519722i
$122$	1.73275	−	3.79419i	0.156876	−	0.343510i
$123$	−0.671987	+	0.775515i	−0.0605910	+	0.0699258i
$124$	−0.768552	+	5.34539i	−0.0690180	+	0.480031i
$125$	−0.415415	−	0.909632i	−0.0371558	−	0.0813600i
$126$	−1.68730	−	0.495436i	−0.150317	−	0.0441370i
$127$	−6.32810	−	1.85810i	−0.561528	−	0.164880i	−0.0113632	−	0.999935i	$-0.503617\pi$
$127$	−6.32810	−	1.85810i	−0.561528	−	0.164880i	−0.550165	+	0.835056i	$0.685435\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	1.20750	−	8.39832i	0.106314	−	0.739431i
$130$	−1.33969	+	1.54608i	−0.117499	+	0.135601i
$131$	−2.98930	+	6.54565i	−0.261176	+	0.571896i	−0.994107	−	0.108408i	$-0.965425\pi$
$131$	−2.98930	+	6.54565i	−0.261176	+	0.571896i	0.732930	+	0.680304i	$0.238152\pi$
$132$	−0.548833	−	0.352714i	−0.0477698	−	0.0306998i
$133$	0.790599	+	5.49873i	0.0685536	+	0.476801i
$134$	9.42553	−	6.05742i	0.814242	−	0.523282i
$135$	−0.654861	−	0.755750i	−0.0563614	−	0.0650446i
$136$	5.62576	−	1.65187i	0.482405	−	0.141647i
$137$	5.57046			0.475916			0.237958	−	0.971275i	$-0.423522\pi$
$137$	5.57046			0.475916			0.237958	+	0.971275i	$0.423522\pi$
$138$	−0.0964099	+	4.79486i	−0.00820696	+	0.408166i
$139$	16.6350			1.41096			0.705480	−	0.708730i	$-0.250732\pi$
$139$	16.6350			1.41096			0.705480	+	0.708730i	$0.250732\pi$
$140$	−1.68730	+	0.495436i	−0.142603	+	0.0418720i
$141$	−0.886435	−	1.02300i	−0.0746513	−	0.0861522i
$142$	−0.777006	+	0.499352i	−0.0652049	+	0.0419047i
$143$	−0.189941	−	1.32107i	−0.0158837	−	0.110473i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	1.78675	−	3.91243i	0.148381	−	0.324910i
$146$	0.965496	−	1.11424i	0.0799050	−	0.0922153i
$147$	−0.556103	+	3.86778i	−0.0458666	+	0.319009i
$148$	−4.31698	−	9.45286i	−0.354853	−	0.777020i
$149$	−5.09733	−	1.49671i	−0.417590	−	0.122615i	0.0661862	−	0.997807i	$-0.478917\pi$
$149$	−5.09733	−	1.49671i	−0.417590	−	0.122615i	−0.483776	+	0.875192i	$0.660735\pi$
$150$	−0.959493	−	0.281733i	−0.0783423	−	0.0230034i
$151$	−0.166501	−	0.364586i	−0.0135496	−	0.0296696i	0.902736	−	0.430195i	$-0.141555\pi$
$151$	−0.166501	−	0.364586i	−0.0135496	−	0.0296696i	−0.916286	+	0.400525i	$0.868828\pi$
$152$	0.449578	−	3.12688i	0.0364656	−	0.253624i
$153$	−3.83962	+	4.43116i	−0.310415	+	0.358238i
$154$	0.476592	−	1.04359i	0.0384049	−	0.0840949i
$155$	−4.54307	−	2.91966i	−0.364908	−	0.234512i
$156$	0.291142	+	2.02494i	0.0233100	+	0.162125i
$157$	15.3129	−	9.84103i	1.22211	−	0.785400i	0.239462	−	0.970906i	$-0.423029\pi$
$157$	15.3129	−	9.84103i	1.22211	−	0.785400i	0.982643	+	0.185506i	$0.0593925\pi$
$158$	−11.2077	−	12.9343i	−0.891633	−	1.02900i
$159$	−0.585007	+	0.171773i	−0.0463941	+	0.0136225i
$160$	1.00000			0.0790569
$161$	−8.37023	+	1.03217i	−0.659667	+	0.0813467i
$162$	−1.00000			−0.0785674
$163$	−12.7302	+	3.73791i	−0.997103	+	0.292776i	−0.739267	−	0.673413i	$-0.764828\pi$
$163$	−12.7302	+	3.73791i	−0.997103	+	0.292776i	−0.257837	+	0.966189i	$0.583010\pi$
$164$	0.671987	+	0.775515i	0.0524734	+	0.0605575i
$165$	0.548833	−	0.352714i	0.0427266	−	0.0274587i
$166$	1.16561	+	8.10697i	0.0904686	+	0.629223i
$167$	−12.6335	−	8.11907i	−0.977611	−	0.628273i	−0.0487932	−	0.998809i	$-0.515538\pi$
$167$	−12.6335	−	8.11907i	−0.977611	−	0.628273i	−0.928818	+	0.370536i	$0.879174\pi$
$168$	−0.730522	+	1.59962i	−0.0563610	+	0.123413i
$169$	5.77250	−	6.66182i	0.444039	−	0.512448i
$170$	−0.834429	+	5.80358i	−0.0639978	+	0.445114i
$171$	1.31231	+	2.87356i	0.100355	+	0.219747i
$172$	−8.14099	−	2.39041i	−0.620745	−	0.182267i
$173$	9.95965	+	2.92442i	0.757218	+	0.222339i	0.637481	−	0.770466i	$-0.279977\pi$
$173$	9.95965	+	2.92442i	0.757218	+	0.222339i	0.119737	+	0.992806i	$0.461795\pi$
$174$	−1.78675	−	3.91243i	−0.135453	−	0.296600i
$175$	0.250266	−	1.74063i	0.0189183	−	0.131580i
$176$	−0.427231	+	0.493051i	−0.0322037	+	0.0371651i
$177$	4.65177	−	10.1860i	0.349648	−	0.765623i
$178$	8.22626	+	5.28670i	0.616584	+	0.396255i
$179$	1.05235	+	7.31926i	0.0786564	+	0.547067i	0.990604	+	0.136761i	$0.0436691\pi$
$179$	1.05235	+	7.31926i	0.0786564	+	0.547067i	−0.911948	+	0.410306i	$0.865422\pi$
$180$	−0.841254	+	0.540641i	−0.0627033	+	0.0402970i
$181$	−8.28547	−	9.56194i	−0.615854	−	0.710733i	0.359060	−	0.933314i	$-0.383097\pi$
$181$	−8.28547	−	9.56194i	−0.615854	−	0.710733i	−0.974914	+	0.222581i	$0.928552\pi$
$182$	−3.45182	+	1.01355i	−0.255866	+	0.0751290i
$183$	4.17113			0.308339
$184$	4.73234	+	0.777809i	0.348873	+	0.0573408i
$185$	10.3920			0.764032
$186$	−5.18161	+	1.52146i	−0.379934	+	0.111559i
$187$	−2.50496	−	2.89088i	−0.183181	−	0.211402i
$188$	−1.13874	+	0.731824i	−0.0830512	+	0.0533738i
$189$	−0.250266	−	1.74063i	−0.0182041	−	0.126613i
$190$	2.65755	+	1.70791i	0.192799	+	0.123904i
$191$	−7.48261	+	16.3846i	−0.541423	+	1.18555i	0.419251	+	0.907870i	$0.362293\pi$
$191$	−7.48261	+	16.3846i	−0.541423	+	1.18555i	−0.960674	+	0.277680i	$0.910435\pi$
$192$	0.654861	−	0.755750i	0.0472605	−	0.0545415i
$193$	0.991535	−	6.89628i	0.0713723	−	0.496405i	−0.922511	−	0.385970i	$-0.873867\pi$
$193$	0.991535	−	6.89628i	0.0713723	−	0.496405i	0.993883	−	0.110435i	$-0.0352243\pi$
$194$	−4.98653	−	10.9190i	−0.358012	−	0.783937i
$195$	−1.96289	−	0.576358i	−0.140566	−	0.0412738i
$196$	3.74927	+	1.10089i	0.267805	+	0.0786347i
$197$	9.16204	+	20.0621i	0.652768	+	1.42936i	0.889110	+	0.457693i	$0.151324\pi$
$197$	9.16204	+	20.0621i	0.652768	+	1.42936i	−0.236342	+	0.971670i	$0.575949\pi$
$198$	0.0928461	−	0.645759i	0.00659829	−	0.0458921i
$199$	−8.36583	+	9.65468i	−0.593038	+	0.684402i	−0.970356	−	0.241682i	$-0.922301\pi$
$199$	−8.36583	+	9.65468i	−0.593038	+	0.684402i	0.377318	+	0.926084i	$0.376846\pi$
$200$	−0.415415	+	0.909632i	−0.0293743	+	0.0643207i
$201$	9.42553	+	6.05742i	0.664826	+	0.427258i
$202$	1.23798	+	8.61034i	0.0871040	+	0.605822i
$203$	6.36295	−	4.08922i	0.446591	−	0.287007i
$204$	3.83962	+	4.43116i	0.268827	+	0.310243i
$205$	−0.984586	+	0.289101i	−0.0687665	+	0.0201917i
$206$	−10.3933			−0.724137
$207$	−4.40161	+	1.90416i	−0.305933	+	0.132348i
$208$	2.04576			0.141848
$209$	−1.97747	+	0.580638i	−0.136785	+	0.0401636i
$210$	−1.15160	−	1.32901i	−0.0794676	−	0.0917105i
$211$	−14.7117	+	9.45464i	−1.01280	+	0.650884i	−0.938115	−	0.346323i	$-0.887430\pi$
$211$	−14.7117	+	9.45464i	−1.01280	+	0.650884i	−0.0746802	+	0.997208i	$0.523794\pi$
$212$	0.0867699	+	0.603498i	0.00595938	+	0.0414484i
$213$	−0.777006	−	0.499352i	−0.0532396	−	0.0342150i
$214$	6.11121	−	13.3817i	0.417754	−	0.914753i
$215$	5.55628	−	6.41229i	0.378935	−	0.437315i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	−3.94508	−	8.63852i	−0.267810	−	0.586421i
$218$	−0.448071	−	0.131566i	−0.0303472	−	0.00891075i
$219$	1.41463	+	0.415373i	0.0955919	+	0.0280683i
$220$	−0.271017	−	0.593443i	−0.0182719	−	0.0400100i
$221$	−1.70704	+	11.8727i	−0.114828	+	0.798647i
$222$	6.80529	−	7.85372i	0.456741	−	0.527107i
$223$	3.66046	−	8.01530i	0.245123	−	0.536744i	−0.746580	−	0.665296i	$-0.768306\pi$
$223$	3.66046	−	8.01530i	0.245123	−	0.536744i	0.991703	+	0.128552i	$0.0410328\pi$
$224$	1.47937	+	0.950735i	0.0988448	+	0.0635237i
$225$	−0.142315	−	0.989821i	−0.00948766	−	0.0659881i
$226$	−1.83827	+	1.18138i	−0.122280	+	0.0785843i
$227$	−16.6600	−	19.2267i	−1.10576	−	1.27612i	−0.957897	−	0.287112i	$-0.907305\pi$
$227$	−16.6600	−	19.2267i	−1.10576	−	1.27612i	−0.147867	−	0.989007i	$-0.547241\pi$
$228$	3.03108	−	0.890004i	0.200738	−	0.0589420i
$229$	11.3690			0.751286			0.375643	−	0.926764i	$-0.377422\pi$
$229$	11.3690			0.751286			0.375643	+	0.926764i	$0.377422\pi$
$230$	−2.67340	+	3.98157i	−0.176279	+	0.262537i
$231$	1.14727			0.0754846
$232$	−4.12689	+	1.21176i	−0.270943	+	0.0795562i
$233$	12.9388	+	14.9322i	0.847652	+	0.978242i	0.999949	−	0.0100927i	$-0.00321265\pi$
$233$	12.9388	+	14.9322i	0.847652	+	0.978242i	−0.152298	+	0.988335i	$0.548667\pi$
$234$	−1.72101	+	1.10602i	−0.112506	+	0.0723030i
$235$	−0.192641	−	1.33985i	−0.0125665	−	0.0874019i
$236$	−9.42026	−	6.05404i	−0.613207	−	0.394084i
$237$	7.10965	−	15.5680i	0.461821	−	1.01125i
$238$	−6.75210	+	7.79234i	−0.437674	+	0.505102i
$239$	−0.820159	+	5.70433i	−0.0530517	+	0.368982i	0.945950	+	0.324312i	$0.105133\pi$
$239$	−0.820159	+	5.70433i	−0.0530517	+	0.368982i	−0.999002	+	0.0446702i	$0.985776\pi$
$240$	0.415415	+	0.909632i	0.0268149	+	0.0587165i
$241$	1.30912	+	0.384392i	0.0843279	+	0.0247609i	0.323624	−	0.946186i	$-0.395099\pi$
$241$	1.30912	+	0.384392i	0.0843279	+	0.0247609i	−0.239296	+	0.970947i	$0.576917\pi$
$242$	−10.1460	−	2.97915i	−0.652212	−	0.191507i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	0.593613	−	4.12867i	0.0380022	−	0.264311i
$245$	−2.55891	+	2.95313i	−0.163482	+	0.188669i
$246$	−0.426279	+	0.933421i	−0.0271786	+	0.0595128i
$247$	5.43672	+	3.49397i	0.345930	+	0.222316i
$248$	0.768552	+	5.34539i	0.0488031	+	0.339433i
$249$	−6.89015	+	4.42803i	−0.436646	+	0.280615i
$250$	−0.654861	−	0.755750i	−0.0414170	−	0.0477978i
$251$	−15.2911	+	4.48986i	−0.965163	+	0.283397i	−0.726087	−	0.687603i	$-0.758663\pi$
$251$	−15.2911	+	4.48986i	−0.965163	+	0.283397i	−0.239076	+	0.971001i	$0.576845\pi$
$252$	−1.75853			−0.110777
$253$	−0.820956	−	3.01917i	−0.0516131	−	0.189814i
$254$	−6.59526			−0.413823
$255$	−5.62576	+	1.65187i	−0.352298	+	0.103444i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	4.22845	−	2.71746i	0.263764	−	0.169511i	−0.402074	−	0.915607i	$-0.631711\pi$
$257$	4.22845	−	2.71746i	0.263764	−	0.169511i	0.665838	+	0.746096i	$0.268074\pi$
$258$	−1.20750	−	8.39832i	−0.0751754	−	0.522856i
$259$	15.3736	+	9.88000i	0.955268	+	0.613914i
$260$	−0.849841	+	1.86089i	−0.0527049	+	0.115408i
$261$	2.81663	−	3.25056i	0.174345	−	0.201205i
$262$	−1.02409	+	7.12269i	−0.0632683	+	0.440041i
$263$	−0.954210	−	2.08943i	−0.0588391	−	0.128840i	0.877928	−	0.478792i	$-0.158925\pi$
$263$	−0.954210	−	2.08943i	−0.0588391	−	0.128840i	−0.936768	+	0.349952i	$0.886198\pi$
$264$	−0.625973	−	0.183802i	−0.0385260	−	0.0113122i
$265$	−0.585007	−	0.171773i	−0.0359367	−	0.0105520i
$266$	2.30775	+	5.05326i	0.141497	+	0.309835i
$267$	−1.39164	+	9.67904i	−0.0851668	+	0.592348i
$268$	7.33716	−	8.46753i	0.448188	−	0.517237i
$269$	−6.65347	+	14.5691i	−0.405669	+	0.888291i	0.590995	+	0.806675i	$0.298735\pi$
$269$	−6.65347	+	14.5691i	−0.405669	+	0.888291i	−0.996664	+	0.0816160i	$0.973992\pi$
$270$	−0.841254	−	0.540641i	−0.0511971	−	0.0329024i
$271$	1.58204	+	11.0033i	0.0961020	+	0.668404i	0.979746	+	0.200245i	$0.0641737\pi$
$271$	1.58204	+	11.0033i	0.0961020	+	0.668404i	−0.883644	+	0.468160i	$0.844917\pi$
$272$	4.93249	−	3.16992i	0.299076	−	0.192204i
$273$	−2.35589	−	2.71884i	−0.142585	−	0.164552i
$274$	5.34482	−	1.56938i	0.322892	−	0.0948097i
$275$	0.652400			0.0393412
$276$	1.25836	+	4.62780i	0.0757446	+	0.278561i
$277$	−2.18268			−0.131144			−0.0655722	−	0.997848i	$-0.520887\pi$
$277$	−2.18268			−0.131144			−0.0655722	+	0.997848i	$0.520887\pi$
$278$	15.9611	−	4.68661i	0.957285	−	0.281084i
$279$	−3.53648	−	4.08132i	−0.211724	−	0.244342i
$280$	−1.47937	+	0.950735i	−0.0884095	+	0.0568173i
$281$	1.05978	+	7.37095i	0.0632214	+	0.439714i	0.996706	+	0.0810973i	$0.0258425\pi$
$281$	1.05978	+	7.37095i	0.0632214	+	0.439714i	−0.933485	+	0.358617i	$0.883248\pi$
$282$	−1.13874	−	0.731824i	−0.0678110	−	0.0435795i
$283$	−2.51715	+	5.51178i	−0.149629	+	0.327642i	−0.969573	−	0.244802i	$-0.921277\pi$
$283$	−2.51715	+	5.51178i	−0.149629	+	0.327642i	0.819944	+	0.572443i	$0.194004\pi$
$284$	−0.604849	+	0.698033i	−0.0358912	+	0.0414206i
$285$	−0.449578	+	3.12688i	−0.0266307	+	0.185221i
$286$	−0.554436	−	1.21404i	−0.0327845	−	0.0717880i
$287$	−1.73143	−	0.508393i	−0.102203	−	0.0300095i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	7.21900	+	15.8074i	0.424647	+	0.929847i
$290$	0.612112	−	4.25733i	0.0359445	−	0.249999i
$291$	7.86077	−	9.07182i	0.460807	−	0.531799i
$292$	0.612468	−	1.34112i	0.0358420	−	0.0784830i
$293$	21.3265	+	13.7057i	1.24591	+	0.800697i	0.986291	−	0.165014i	$-0.0527669\pi$
$293$	21.3265	+	13.7057i	1.24591	+	0.800697i	0.259618	+	0.965711i	$0.416403\pi$
$294$	0.556103	+	3.86778i	0.0324326	+	0.225574i
$295$	9.42026	−	6.05404i	0.548469	−	0.352480i
$296$	−6.80529	−	7.85372i	−0.395549	−	0.456488i
$297$	0.625973	−	0.183802i	0.0363226	−	0.0106653i
$298$	−5.31253			−0.307746
$299$	−5.46915	+	8.14535i	−0.316289	+	0.471058i
$300$	−1.00000			−0.0577350
$301$	14.3162	−	4.20362i	0.825173	−	0.242293i
$302$	−0.262472	−	0.302909i	−0.0151036	−	0.0174304i
$303$	−7.31797	+	4.70297i	−0.420406	+	0.270179i
$304$	−0.449578	−	3.12688i	−0.0257851	−	0.179339i
$305$	3.50898	+	2.25508i	0.200923	+	0.129126i
$306$	−2.43569	+	5.33341i	−0.139239	+	0.304891i
$307$	21.5039	−	24.8168i	1.22729	−	1.41637i	0.349767	−	0.936837i	$-0.386261\pi$
$307$	21.5039	−	24.8168i	1.22729	−	1.41637i	0.877524	−	0.479532i	$-0.159194\pi$
$308$	0.163273	−	1.13559i	0.00930335	−	0.0647062i
$309$	−4.31754	−	9.45410i	−0.245616	−	0.537825i
$310$	−5.18161	−	1.52146i	−0.294296	−	0.0864130i
$311$	−7.54831	−	2.21638i	−0.428026	−	0.125680i	0.0606223	−	0.998161i	$-0.480691\pi$
$311$	−7.54831	−	2.21638i	−0.428026	−	0.125680i	−0.488648	+	0.872481i	$0.662510\pi$
$312$	0.849841	+	1.86089i	0.0481127	+	0.105352i
$313$	−2.00667	+	13.9567i	−0.113424	+	0.788879i	0.851123	+	0.524966i	$0.175922\pi$
$313$	−2.00667	+	13.9567i	−0.113424	+	0.788879i	−0.964547	+	0.263912i	$0.914987\pi$
$314$	11.9201	−	13.7566i	0.672691	−	0.776327i
$315$	0.730522	−	1.59962i	0.0411602	−	0.0901283i
$316$	−14.3977	−	9.25283i	−0.809933	−	0.520513i
$317$	−0.471244	−	3.27758i	−0.0264677	−	0.184087i	0.972299	−	0.233742i	$-0.0750970\pi$
$317$	−0.471244	−	3.27758i	−0.0264677	−	0.184087i	−0.998766	+	0.0496547i	$0.984188\pi$
$318$	−0.512916	+	0.329631i	−0.0287629	+	0.0184848i
$319$	1.83757	+	2.12067i	0.102884	+	0.118734i
$320$	0.959493	−	0.281733i	0.0536373	−	0.0157493i
$321$	14.7111			0.821094
$322$	−7.74038	+	3.34853i	−0.431355	+	0.186606i
$323$	18.5223			1.03061
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	−1.33969	−	1.54608i	−0.0743126	−	0.0857613i
$326$	−11.1614	+	7.17300i	−0.618173	+	0.397276i
$327$	−0.0664593	−	0.462234i	−0.00367521	−	0.0255616i
$328$	0.863255	+	0.554780i	0.0476653	+	0.0306326i
$329$	0.988851	−	2.16528i	0.0545171	−	0.119376i
$330$	0.427231	−	0.493051i	0.0235183	−	0.0271415i
$331$	−2.39730	+	16.6736i	−0.131767	+	0.916462i	0.811482	+	0.584377i	$0.198661\pi$
$331$	−2.39730	+	16.6736i	−0.131767	+	0.916462i	−0.943249	+	0.332085i	$0.892248\pi$
$332$	3.40239	+	7.45020i	0.186730	+	0.408883i
$333$	9.97101	+	2.92775i	0.546408	+	0.160440i
$334$	−14.4092	−	4.23092i	−0.788435	−	0.231505i
$335$	4.65437	+	10.1917i	0.254296	+	0.556830i
$336$	−0.250266	+	1.74063i	−0.0136531	+	0.0949594i
$337$	3.21511	−	3.71043i	0.175138	−	0.202120i	−0.661393	−	0.750039i	$-0.730034\pi$
$337$	3.21511	−	3.71043i	0.175138	−	0.202120i	0.836531	+	0.547919i	$0.184580\pi$
$338$	3.66182	−	8.01827i	0.199177	−	0.436137i
$339$	−1.83827	−	1.18138i	−0.0998409	−	0.0641638i
$340$	0.834429	+	5.80358i	0.0452532	+	0.314743i
$341$	2.96390	−	1.90478i	0.160504	−	0.103150i
$342$	2.06873	+	2.38744i	0.111864	+	0.129098i
$343$	−18.4043	+	5.40400i	−0.993741	+	0.291789i
$344$	−8.48468			−0.457463
$345$	−4.73234	−	0.777809i	−0.254780	−	0.0418758i
$346$	10.3801			0.558038
$347$	−4.12332	+	1.21072i	−0.221352	+	0.0649947i	−0.390528	−	0.920591i	$-0.627707\pi$
$347$	−4.12332	+	1.21072i	−0.221352	+	0.0649947i	0.169176	+	0.985586i	$0.445889\pi$
$348$	−2.81663	−	3.25056i	−0.150987	−	0.174248i
$349$	1.15348	−	0.741294i	0.0617442	−	0.0396806i	−0.509405	−	0.860527i	$-0.670134\pi$
$349$	1.15348	−	0.741294i	0.0617442	−	0.0396806i	0.571149	+	0.820847i	$0.306498\pi$
$350$	−0.250266	−	1.74063i	−0.0133773	−	0.0930409i
$351$	−1.72101	−	1.10602i	−0.0918605	−	0.0590351i
$352$	−0.271017	+	0.593443i	−0.0144452	+	0.0316306i
$353$	23.5417	−	27.1686i	1.25300	−	1.44604i	0.406494	−	0.913654i	$-0.366751\pi$
$353$	23.5417	−	27.1686i	1.25300	−	1.44604i	0.846504	−	0.532383i	$-0.178703\pi$
$354$	1.59363	−	11.0839i	0.0847002	−	0.589103i
$355$	−0.383690	−	0.840163i	−0.0203641	−	0.0445912i
$356$	9.38247	+	2.75494i	0.497270	+	0.146012i
$357$	−9.89308	−	2.90487i	−0.523598	−	0.153742i
$358$	3.07180	+	6.72630i	0.162349	+	0.355496i
$359$	−0.109490	+	0.761522i	−0.00577868	+	0.0401916i	−0.992507	−	0.122190i	$-0.961008\pi$
$359$	−0.109490	+	0.761522i	−0.00577868	+	0.0401916i	0.986728	+	0.162381i	$0.0519175\pi$
$360$	−0.654861	+	0.755750i	−0.0345142	+	0.0398315i
$361$	−3.74724	+	8.20531i	−0.197223	+	0.431858i
$362$	−10.6438	−	6.84033i	−0.559424	−	0.359520i
$363$	−1.50489	−	10.4667i	−0.0789863	−	0.549362i
$364$	−3.02645	+	1.94498i	−0.158629	+	0.101945i
$365$	0.965496	+	1.11424i	0.0505364	+	0.0583221i
$366$	4.00217	−	1.17514i	0.209197	−	0.0614257i
$367$	22.1668			1.15710			0.578550	−	0.815647i	$-0.303619\pi$
$367$	22.1668			1.15710			0.578550	+	0.815647i	$0.303619\pi$
$368$	4.75978	−	0.586951i	0.248121	−	0.0305970i
$369$	−1.02615			−0.0534194
$370$	9.97101	−	2.92775i	0.518368	−	0.152207i
$371$	−0.702132	−	0.810304i	−0.0364529	−	0.0420689i
$372$	−4.54307	+	2.91966i	−0.235547	+	0.151377i
$373$	4.13771	+	28.7784i	0.214243	+	1.49009i	0.758776	+	0.651351i	$0.225798\pi$
$373$	4.13771	+	28.7784i	0.214243	+	1.49009i	−0.544534	+	0.838739i	$0.683293\pi$
$374$	−3.21795	−	2.06805i	−0.166396	−	0.106936i
$375$	0.415415	−	0.909632i	0.0214519	−	0.0469732i
$376$	−0.886435	+	1.02300i	−0.0457144	+	0.0527572i
$377$	1.25224	−	8.70949i	0.0644934	−	0.448562i
$378$	−0.730522	−	1.59962i	−0.0375740	−	0.0822755i
$379$	22.1766	+	6.51165i	1.13914	+	0.334481i	0.796293	−	0.604911i	$-0.206791\pi$
$379$	22.1766	+	6.51165i	1.13914	+	0.334481i	0.342845	+	0.939392i	$0.388610\pi$
$380$	3.03108	+	0.890004i	0.155491	+	0.0456563i
$381$	−2.73977	−	5.99926i	−0.140363	−	0.307351i
$382$	−2.56343	+	17.8290i	−0.131156	+	0.912213i
$383$	11.7042	−	13.5074i	0.598057	−	0.690194i	−0.373330	−	0.927699i	$-0.621784\pi$
$383$	11.7042	−	13.5074i	0.598057	−	0.690194i	0.971386	+	0.237504i	$0.0763294\pi$
$384$	0.415415	−	0.909632i	0.0211991	−	0.0464195i
$385$	0.965142	+	0.620259i	0.0491882	+	0.0316113i
$386$	−0.991535	−	6.89628i	−0.0504678	−	0.351011i
$387$	7.13777	−	4.58716i	0.362833	−	0.233179i
$388$	−7.86077	−	9.07182i	−0.399070	−	0.460552i
$389$	13.4940	−	3.96221i	0.684175	−	0.200892i	0.0788690	−	0.996885i	$-0.474869\pi$
$389$	13.4940	−	3.96221i	0.684175	−	0.200892i	0.605306	+	0.795993i	$0.293051\pi$
$390$	−2.04576			−0.103591
$391$	−0.565276	+	28.1135i	−0.0285873	+	1.42176i
$392$	3.90756			0.197361
$393$	−6.90444	+	2.02733i	−0.348283	+	0.102265i
$394$	14.4430	+	16.6682i	0.727630	+	0.839730i
$395$	14.3977	−	9.25283i	0.724426	−	0.465561i
$396$	−0.0928461	−	0.645759i	−0.00466569	−	0.0324506i
$397$	4.55474	+	2.92716i	0.228596	+	0.146910i	0.649926	−	0.759998i	$-0.274800\pi$
$397$	4.55474	+	2.92716i	0.228596	+	0.146910i	−0.421330	+	0.906908i	$0.638436\pi$
$398$	−5.30692	+	11.6205i	−0.266012	+	0.582484i
$399$	−3.63793	+	4.19840i	−0.182124	+	0.210183i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	−8.92523	−	19.5435i	−0.445705	−	0.975957i	−0.990516	−	0.137398i	$-0.956126\pi$
$401$	−8.92523	−	19.5435i	−0.445705	−	0.975957i	0.544811	−	0.838559i	$-0.316601\pi$
$402$	10.7503	+	3.15658i	0.536177	+	0.157436i
$403$	−10.6003	−	3.11254i	−0.528041	−	0.155047i
$404$	3.61365	+	7.91279i	0.179786	+	0.393676i
$405$	0.142315	−	0.989821i	0.00707168	−	0.0491846i
$406$	4.95314	−	5.71623i	0.245820	−	0.283692i
$407$	−2.81639	+	6.16704i	−0.139603	+	0.305689i
$408$	4.93249	+	3.16992i	0.244194	+	0.156934i
$409$	−1.26190	−	8.77673i	−0.0623971	−	0.433981i	−0.996943	−	0.0781376i	$-0.975103\pi$
$409$	−1.26190	−	8.77673i	−0.0623971	−	0.433981i	0.934545	−	0.355844i	$-0.115806\pi$
$410$	−0.863255	+	0.554780i	−0.0426331	+	0.0273986i
$411$	3.64787	+	4.20987i	0.179936	+	0.207658i
$412$	−9.97232	+	2.92814i	−0.491301	+	0.144259i
$413$	19.6919			0.968974
$414$	−3.68685	+	3.06711i	−0.181199	+	0.150740i
$415$	−8.19034			−0.402048
$416$	1.96289	−	0.576358i	0.0962388	−	0.0282583i
$417$	10.8936	+	12.5719i	0.533461	+	0.615647i
$418$	−1.73379	+	1.11424i	−0.0848023	+	0.0544991i
$419$	1.12011	+	7.79050i	0.0547207	+	0.380591i	0.998717	+	0.0506355i	$0.0161247\pi$
$419$	1.12011	+	7.79050i	0.0547207	+	0.380591i	−0.943996	+	0.329956i	$0.892966\pi$
$420$	−1.47937	−	0.950735i	−0.0721860	−	0.0463911i
$421$	−7.19189	+	15.7480i	−0.350511	+	0.767513i	0.649463	+	0.760393i	$0.274994\pi$
$421$	−7.19189	+	15.7480i	−0.350511	+	0.767513i	−0.999975	+	0.00711973i	$0.997734\pi$
$422$	−11.4521	+	13.2164i	−0.557479	+	0.643365i
$423$	0.192641	−	1.33985i	0.00936651	−	0.0651455i
$424$	0.253280	+	0.554606i	0.0123004	+	0.0269341i
$425$	−5.62576	−	1.65187i	−0.272889	−	0.0801275i
$426$	−0.886216	−	0.260216i	−0.0429373	−	0.0126075i
$427$	3.04710	+	6.67222i	0.147459	+	0.322891i
$428$	2.09361	−	14.5614i	0.101198	−	0.703850i
$429$	0.874013	−	1.00866i	0.0421977	−	0.0486988i
$430$	3.52466	−	7.71794i	0.169974	−	0.372192i
$431$	5.20559	+	3.34543i	0.250744	+	0.161144i	0.659975	−	0.751287i	$-0.270567\pi$
$431$	5.20559	+	3.34543i	0.250744	+	0.161144i	−0.409231	+	0.912431i	$0.634203\pi$
$432$	0.142315	+	0.989821i	0.00684713	+	0.0476228i
$433$	5.28395	−	3.39579i	0.253930	−	0.163191i	−0.407483	−	0.913213i	$-0.633593\pi$
$433$	5.28395	−	3.39579i	0.253930	−	0.163191i	0.661413	+	0.750022i	$0.269957\pi$
$434$	−6.21903	−	7.17714i	−0.298523	−	0.344514i
$435$	4.12689	−	1.21176i	0.197869	−	0.0580996i
$436$	−0.466988			−0.0223646
$437$	13.6518	+	6.56940i	0.653055	+	0.314257i
$438$	1.47435			0.0704473
$439$	−31.0922	+	9.12948i	−1.48395	+	0.435726i	−0.920604	−	0.390496i	$-0.872303\pi$
$439$	−31.0922	+	9.12948i	−1.48395	+	0.435726i	−0.563343	+	0.826223i	$0.690485\pi$
$440$	−0.427231	−	0.493051i	−0.0203674	−	0.0235053i
$441$	−3.28725	+	2.11258i	−0.156536	+	0.100599i
$442$	1.70704	+	11.8727i	0.0811958	+	0.564729i
$443$	−19.0726	−	12.2572i	−0.906166	−	0.582358i	0.00244658	−	0.999997i	$-0.499221\pi$
$443$	−19.0726	−	12.2572i	−0.906166	−	0.582358i	−0.908613	+	0.417639i	$0.862858\pi$
$444$	4.31698	−	9.45286i	0.204875	−	0.448613i
$445$	−6.40360	+	7.39015i	−0.303560	+	0.350327i
$446$	1.25402	−	8.72189i	0.0593795	−	0.412994i
$447$	−2.20690	−	4.83245i	−0.104383	−	0.228567i
$448$	1.68730	+	0.495436i	0.0797175	+	0.0234072i
$449$	1.27852	+	0.375406i	0.0603369	+	0.0177165i	0.311762	−	0.950160i	$-0.399081\pi$
$449$	1.27852	+	0.375406i	0.0603369	+	0.0177165i	−0.251425	+	0.967877i	$0.580899\pi$
$450$	−0.415415	−	0.909632i	−0.0195829	−	0.0428805i
$451$	0.0952743	−	0.662647i	0.00448629	−	0.0312028i
$452$	−1.43097	+	1.65143i	−0.0673071	+	0.0776766i
$453$	0.166501	−	0.364586i	0.00782289	−	0.0171297i
$454$	−21.4019	−	13.7542i	−1.00444	−	0.645516i
$455$	−0.511984	−	3.56093i	−0.0240022	−	0.166939i
$456$	2.65755	−	1.70791i	0.124451	−	0.0799800i
$457$	14.5578	+	16.8007i	0.680987	+	0.785901i	0.986053	−	0.166430i	$-0.0532239\pi$
$457$	14.5578	+	16.8007i	0.680987	+	0.785901i	−0.305066	+	0.952331i	$0.598678\pi$
$458$	10.9085	−	3.20303i	0.509721	−	0.149668i
$459$	−5.86326			−0.273673
$460$	−1.44337	+	4.57347i	−0.0672976	+	0.213239i
$461$	−6.72518			−0.313223			−0.156611	−	0.987660i	$-0.550057\pi$
$461$	−6.72518			−0.313223			−0.156611	+	0.987660i	$0.550057\pi$
$462$	1.10079	−	0.323222i	0.0512136	−	0.0150377i
$463$	−0.487780	−	0.562929i	−0.0226691	−	0.0261615i	0.744302	−	0.667843i	$-0.232782\pi$
$463$	−0.487780	−	0.562929i	−0.0226691	−	0.0261615i	−0.766971	+	0.641682i	$0.778237\pi$
$464$	−3.61833	+	2.32536i	−0.167977	+	0.107952i
$465$	−0.768552	−	5.34539i	−0.0356407	−	0.247887i
$466$	16.6216	+	10.6821i	0.769982	+	0.494837i
$467$	−5.29982	+	11.6050i	−0.245246	+	0.537015i	−0.991723	−	0.128397i	$-0.959017\pi$
$467$	−5.29982	+	11.6050i	−0.245246	+	0.537015i	0.746476	+	0.665412i	$0.231744\pi$
$468$	−1.33969	+	1.54608i	−0.0619272	+	0.0714678i
$469$	−2.80401	+	19.5023i	−0.129477	+	0.900534i
$470$	−0.562315	−	1.23130i	−0.0259377	−	0.0567956i
$471$	17.4652	+	5.12824i	0.804754	+	0.236297i
$472$	−10.7443	−	3.15481i	−0.494546	−	0.145212i
$473$	2.29949	+	5.03518i	0.105731	+	0.231518i
$474$	2.43566	−	16.9404i	0.111873	−	0.778097i
$475$	−2.06873	+	2.38744i	−0.0949199	+	0.109543i
$476$	−4.28324	+	9.37898i	−0.196322	+	0.429885i
$477$	−0.512916	−	0.329631i	−0.0234848	−	0.0150928i
$478$	0.820159	+	5.70433i	0.0375132	+	0.260910i
$479$	−10.1071	+	6.49541i	−0.461803	+	0.296783i	−0.750779	−	0.660554i	$-0.770322\pi$
$479$	−10.1071	+	6.49541i	−0.461803	+	0.296783i	0.288976	+	0.957336i	$0.406685\pi$
$480$	0.654861	+	0.755750i	0.0298902	+	0.0344951i
$481$	20.3983	−	5.98949i	0.930084	−	0.273097i
$482$	1.36439			0.0621462
$483$	−6.26140	−	5.64987i	−0.284904	−	0.257078i
$484$	−10.5744			−0.480653
$485$	11.5175	−	3.38184i	0.522983	−	0.153562i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	−34.4858	+	22.1627i	−1.56270	+	1.00429i	−0.580987	+	0.813913i	$0.697333\pi$
$487$	−34.4858	+	22.1627i	−1.56270	+	1.00429i	−0.981712	+	0.190373i	$0.939030\pi$
$488$	−0.593613	−	4.12867i	−0.0268716	−	0.186896i
$489$	−11.1614	−	7.17300i	−0.504736	−	0.324374i
$490$	−1.62326	+	3.55444i	−0.0733313	+	0.160573i
$491$	10.8703	−	12.5450i	0.490570	−	0.566148i	−0.455448	−	0.890263i	$-0.650521\pi$
$491$	10.8703	−	12.5450i	0.490570	−	0.566148i	0.946018	+	0.324114i	$0.105066\pi$
$492$	−0.146037	+	1.01571i	−0.00658385	+	0.0457917i
$493$	−10.4762	−	22.9396i	−0.471822	−	1.03315i
$494$	6.20086	+	1.82074i	0.278990	+	0.0819188i
$495$	0.625973	+	0.183802i	0.0281354	+	0.00826129i
$496$	2.24339	+	4.91234i	0.100731	+	0.220571i
$497$	0.231153	−	1.60770i	0.0103686	−	0.0721153i
$498$	−5.36353	+	6.18985i	−0.240346	+	0.277374i
$499$	−3.20822	+	7.02503i	−0.143620	+	0.314484i	−0.967748	−	0.251920i	$-0.918938\pi$
$499$	−3.20822	+	7.02503i	−0.143620	+	0.314484i	0.824128	+	0.566403i	$0.191665\pi$
$500$	−0.841254	−	0.540641i	−0.0376220	−	0.0241782i
$501$	−2.13721	−	14.8646i	−0.0954836	−	0.664103i
$502$	−13.4067	+	8.61598i	−0.598371	+	0.384550i
$503$	−16.1804	−	18.6732i	−0.721449	−	0.832596i	0.270032	−	0.962851i	$-0.412966\pi$
$503$	−16.1804	−	18.6732i	−0.721449	−	0.832596i	−0.991480	+	0.130255i	$0.958420\pi$
$504$	−1.68730	+	0.495436i	−0.0751584	+	0.0220685i
$505$	−8.69889			−0.387095
$506$	−1.63830	−	2.66559i	−0.0728314	−	0.118500i
$507$	8.81486			0.391481
$508$	−6.32810	+	1.85810i	−0.280764	+	0.0824398i
$509$	19.2967	+	22.2695i	0.855309	+	0.987079i	0.999997	−	0.00239785i	$-0.000763262\pi$
$509$	19.2967	+	22.2695i	0.855309	+	0.987079i	−0.144688	+	0.989477i	$0.546218\pi$
$510$	−4.93249	+	3.16992i	−0.218414	+	0.140366i
$511$	0.368980	+	2.56631i	0.0163227	+	0.113527i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	−1.31231	+	2.87356i	−0.0579400	+	0.126871i
$514$	3.29157	−	3.79868i	0.145185	−	0.167553i
$515$	1.47912	−	10.2875i	0.0651780	−	0.453323i
$516$	−3.52466	−	7.71794i	−0.155165	−	0.339763i
$517$	0.847331	+	0.248799i	0.0372656	+	0.0109422i
$518$	17.5344	+	5.14856i	0.770416	+	0.226215i
$519$	4.31205	+	9.44208i	0.189278	+	0.414461i
$520$	−0.291142	+	2.02494i	−0.0127674	+	0.0887995i
$521$	26.8481	−	30.9844i	1.17624	−	1.35745i	0.255721	−	0.966751i	$-0.417687\pi$
$521$	26.8481	−	30.9844i	1.17624	−	1.35745i	0.920518	−	0.390701i	$-0.127767\pi$
$522$	1.78675	−	3.91243i	0.0782038	−	0.171242i
$523$	−9.53263	−	6.12625i	−0.416833	−	0.267882i	0.315370	−	0.948969i	$-0.397871\pi$
$523$	−9.53263	−	6.12625i	−0.416833	−	0.267882i	−0.732203	+	0.681087i	$0.761508\pi$
$524$	1.02409	+	7.12269i	0.0447375	+	0.311156i
$525$	1.47937	−	0.950735i	0.0645651	−	0.0414935i
$526$	−1.50422	−	1.73596i	−0.0655870	−	0.0756915i
$527$	−30.3811	+	8.92070i	−1.32342	+	0.388592i
$528$	−0.652400			−0.0283920
$529$	−10.3878	+	20.5206i	−0.451644	+	0.892198i
$530$	−0.609704			−0.0264839
$531$	10.7443	−	3.15481i	0.466263	−	0.136907i
$532$	3.63793	+	4.19840i	0.157724	+	0.182024i
$533$	−1.76601	+	1.13495i	−0.0764946	+	0.0491601i
$534$	1.39164	+	9.67904i	0.0602220	+	0.418853i
$535$	12.3758	+	7.95342i	0.535051	+	0.343856i
$536$	4.65437	−	10.1917i	0.201038	−	0.440213i
$537$	−4.84238	+	5.58841i	−0.208964	+	0.241158i
$538$	−2.27938	+	15.8534i	−0.0982709	+	0.683489i
$539$	−1.05901	−	2.31891i	−0.0456149	−	0.0998827i
$540$	−0.959493	−	0.281733i	−0.0412900	−	0.0121238i
$541$	−26.4652	−	7.77087i	−1.13783	−	0.334096i	−0.342047	−	0.939683i	$-0.611120\pi$
$541$	−26.4652	−	7.77087i	−1.13783	−	0.334096i	−0.795779	+	0.605587i	$0.792938\pi$
$542$	4.61795	+	10.1119i	0.198358	+	0.434343i
$543$	1.80060	−	12.5235i	0.0772713	−	0.537434i
$544$	3.83962	−	4.43116i	0.164622	−	0.189984i
$545$	0.193994	−	0.424787i	0.00830977	−	0.0181959i
$546$	−3.02645	−	1.94498i	−0.129520	−	0.0832374i
$547$	3.27810	+	22.7997i	0.140162	+	0.974846i	0.931571	+	0.363559i	$0.118439\pi$
$547$	3.27810	+	22.7997i	0.140162	+	0.974846i	−0.791409	+	0.611286i	$0.790652\pi$
$548$	4.68617	−	3.01162i	0.200183	−	0.128650i
$549$	2.73151	+	3.15233i	0.116578	+	0.134538i
$550$	0.625973	−	0.183802i	0.0266916	−	0.00783735i
$551$	−13.5874			−0.578842
$552$	2.51119	+	4.08582i	0.106883	+	0.173904i
$553$	30.0966			1.27984
$554$	−2.09426	+	0.614931i	−0.0889767	+	0.0261259i
$555$	6.80529	+	7.85372i	0.288868	+	0.333372i
$556$	13.9942	−	8.99354i	0.593487	−	0.381411i
$557$	−3.84503	−	26.7427i	−0.162919	−	1.13313i	−0.893095	−	0.449867i	$-0.851471\pi$
$557$	−3.84503	−	26.7427i	−0.162919	−	1.13313i	0.730176	−	0.683259i	$-0.239438\pi$
$558$	−4.54307	−	2.91966i	−0.192324	−	0.123599i
$559$	7.21062	−	15.7891i	0.304977	−	0.667806i
$560$	−1.15160	+	1.32901i	−0.0486638	+	0.0561610i
$561$	0.544381	−	3.78625i	0.0229838	−	0.159856i
$562$	3.09349	+	6.77380i	0.130491	+	0.285736i
$563$	22.6577	+	6.65289i	0.954906	+	0.280386i	0.721828	−	0.692072i	$-0.243302\pi$
$563$	22.6577	+	6.65289i	0.954906	+	0.280386i	0.233078	+	0.972458i	$0.425120\pi$
$564$	−1.29879	−	0.381360i	−0.0546890	−	0.0160581i
$565$	−0.907744	−	1.98768i	−0.0381891	−	0.0836224i
$566$	−0.862336	+	5.99768i	−0.0362467	+	0.252101i
$567$	1.15160	−	1.32901i	0.0483624	−	0.0558132i
$568$	−0.383690	+	0.840163i	−0.0160993	+	0.0352525i
$569$	−25.8349	−	16.6031i	−1.08306	−	0.696038i	−0.127795	−	0.991801i	$-0.540790\pi$
$569$	−25.8349	−	16.6031i	−1.08306	−	0.696038i	−0.955261	+	0.295763i	$0.904426\pi$
$570$	0.449578	+	3.12688i	0.0188308	+	0.130971i
$571$	24.9253	−	16.0185i	1.04309	−	0.670355i	0.0973434	−	0.995251i	$-0.468965\pi$
$571$	24.9253	−	16.0185i	1.04309	−	0.670355i	0.945750	+	0.324895i	$0.105329\pi$
$572$	−0.874013	−	1.00866i	−0.0365443	−	0.0421744i
$573$	−17.2827	+	5.07467i	−0.721997	+	0.211997i
$574$	−1.80452			−0.0753194
$575$	−3.56058	−	3.21283i	−0.148486	−	0.133984i
$576$	1.00000			0.0416667
$577$	26.9941	−	7.92619i	1.12378	−	0.329971i	0.333520	−	0.942743i	$-0.391764\pi$
$577$	26.9941	−	7.92619i	1.12378	−	0.329971i	0.790260	+	0.612772i	$0.209945\pi$
$578$	11.3800	+	13.1333i	0.473347	+	0.546272i
$579$	5.86118	−	3.76675i	0.243582	−	0.156541i
$580$	−0.612112	−	4.25733i	−0.0254166	−	0.176776i
$581$	−12.1166	−	7.78685i	−0.502680	−	0.323053i
$582$	4.98653	−	10.9190i	0.206698	−	0.452606i
$583$	0.260484	−	0.300615i	0.0107882	−	0.0124502i
$584$	0.209822	−	1.45935i	0.00868251	−	0.0603882i
$585$	−0.849841	−	1.86089i	−0.0351366	−	0.0769384i
$586$	24.3240	+	7.14217i	1.00482	+	0.295040i
$587$	−27.4818	−	8.06939i	−1.13430	−	0.333059i	−0.339901	−	0.940461i	$-0.610394\pi$
$587$	−27.4818	−	8.06939i	−1.13430	−	0.333059i	−0.794395	+	0.607402i	$0.792212\pi$
$588$	1.62326	+	3.55444i	0.0669420	+	0.146583i
$589$	−2.42788	+	16.8863i	−0.100039	+	0.695788i
$590$	7.33306	−	8.46280i	0.301897	−	0.348408i
$591$	−9.16204	+	20.0621i	−0.376876	+	0.825243i
$592$	−8.74227	−	5.61832i	−0.359305	−	0.230911i
$593$	5.85648	+	40.7327i	0.240497	+	1.67269i	0.649655	+	0.760229i	$0.274913\pi$
$593$	5.85648	+	40.7327i	0.240497	+	1.67269i	−0.409158	+	0.912463i	$0.634178\pi$
$594$	0.548833	−	0.352714i	0.0225189	−	0.0144720i
$595$	−6.75210	−	7.79234i	−0.276809	−	0.319455i
$596$	−5.09733	+	1.49671i	−0.208795	+	0.0613077i
$597$	−12.7750			−0.522845
$598$	−2.95280	+	9.35624i	−0.120749	+	0.382605i
$599$	−39.0953			−1.59739			−0.798696	−	0.601735i	$-0.794476\pi$
$599$	−39.0953			−1.59739			−0.798696	+	0.601735i	$0.794476\pi$
$600$	−0.959493	+	0.281733i	−0.0391711	+	0.0115017i
$601$	−21.8601	−	25.2279i	−0.891692	−	1.02907i	−0.999391	−	0.0348835i	$-0.988894\pi$
$601$	−21.8601	−	25.2279i	−0.891692	−	1.02907i	0.107700	−	0.994183i	$-0.465651\pi$
$602$	12.5520	−	8.06668i	0.511582	−	0.328774i
$603$	1.59452	+	11.0901i	0.0649338	+	0.451624i
$604$	−0.337179	−	0.216692i	−0.0137196	−	0.00881707i
$605$	4.39275	−	9.61879i	0.178591	−	0.391059i
$606$	−5.69656	+	6.57418i	−0.231407	+	0.267058i
$607$	−0.404499	+	2.81335i	−0.0164181	+	0.114190i	−0.996382	−	0.0849826i	$-0.972917\pi$
$607$	−0.404499	+	2.81335i	−0.0164181	+	0.114190i	0.979964	+	0.199173i	$0.0638256\pi$
$608$	−1.31231	−	2.87356i	−0.0532213	−	0.116538i
$609$	7.25727	+	2.13093i	0.294079	+	0.0863495i
$610$	4.00217	+	1.17514i	0.162043	+	0.0475801i
$611$	−1.15036	−	2.51895i	−0.0465387	−	0.101906i
$612$	−0.834429	+	5.80358i	−0.0337298	+	0.234596i
$613$	−25.1253	+	28.9962i	−1.01480	+	1.17114i	−0.0296326	+	0.999561i	$0.509434\pi$
$613$	−25.1253	+	28.9962i	−1.01480	+	1.17114i	−0.985170	+	0.171583i	$0.945112\pi$
$614$	13.6411	−	29.8699i	0.550511	−	1.20545i
$615$	−0.863255	−	0.554780i	−0.0348098	−	0.0223709i
$616$	−0.163273	−	1.13559i	−0.00657846	−	0.0457542i
$617$	−32.2160	+	20.7040i	−1.29697	+	0.833511i	−0.992878	−	0.119132i	$-0.961989\pi$
$617$	−32.2160	+	20.7040i	−1.29697	+	0.833511i	−0.304091	+	0.952643i	$0.598353\pi$
$618$	−6.80618	−	7.85475i	−0.273785	−	0.315964i
$619$	−35.9212	+	10.5474i	−1.44379	+	0.423936i	−0.907485	−	0.420085i	$-0.862000\pi$
$619$	−35.9212	+	10.5474i	−1.44379	+	0.423936i	−0.536310	+	0.844021i	$0.680182\pi$
$620$	−5.40036			−0.216884
$621$	−4.32151	−	2.07956i	−0.173416	−	0.0834497i
$622$	−7.86698			−0.315437
$623$	−16.4994	+	4.84466i	−0.661035	+	0.194097i
$624$	1.33969	+	1.54608i	0.0536305	+	0.0618929i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	2.00667	+	13.9567i	0.0802026	+	0.557822i
$627$	−1.73379	−	1.11424i	−0.0692408	−	0.0444983i
$628$	7.56160	−	16.5576i	0.301741	−	0.660720i
$629$	39.9012	−	46.0484i	1.59096	−	1.83607i
$630$	0.250266	−	1.74063i	0.00997082	−	0.0693486i
$631$	−5.65323	−	12.3788i	−0.225052	−	0.492794i	0.763099	−	0.646282i	$-0.223677\pi$
$631$	−5.65323	−	12.3788i	−0.225052	−	0.492794i	−0.988151	+	0.153487i	$0.950950\pi$
$632$	−16.4213	−	4.82173i	−0.653204	−	0.191798i
$633$	−16.7795	−	4.92689i	−0.666923	−	0.195826i
$634$	−1.37556	−	3.01205i	−0.0546303	−	0.119624i
$635$	0.938603	−	6.52813i	0.0372473	−	0.259061i
$636$	−0.399271	+	0.460784i	−0.0158321	+	0.0182713i
$637$	−3.32080	+	7.27154i	−0.131575	+	0.288109i
$638$	2.36059	+	1.51706i	0.0934568	+	0.0600610i
$639$	−0.131446	−	0.914228i	−0.00519993	−	0.0361663i
$640$	0.841254	−	0.540641i	0.0332535	−	0.0213707i
$641$	−23.8141	−	27.4829i	−0.940599	−	1.08551i	−0.996203	−	0.0870560i	$-0.972254\pi$
$641$	−23.8141	−	27.4829i	−0.940599	−	1.08551i	0.0556046	−	0.998453i	$-0.482291\pi$
$642$	14.1152	−	4.14460i	0.557082	−	0.163574i
$643$	29.2918			1.15516			0.577578	−	0.816336i	$-0.303998\pi$
$643$	29.2918			1.15516			0.577578	+	0.816336i	$0.303998\pi$
$644$	−6.48345	+	5.39361i	−0.255484	+	0.212538i
$645$	8.48468			0.334084
$646$	17.7720	−	5.21832i	0.699229	−	0.205312i
$647$	1.80816	+	2.08672i	0.0710860	+	0.0820376i	0.790179	−	0.612877i	$-0.209988\pi$
$647$	1.80816	+	2.08672i	0.0710860	+	0.0820376i	−0.719093	+	0.694914i	$0.755442\pi$
$648$	−0.841254	+	0.540641i	−0.0330476	+	0.0212384i
$649$	1.03968	+	7.23114i	0.0408110	+	0.283847i
$650$	−1.72101	−	1.10602i	−0.0675034	−	0.0433818i
$651$	3.94508	−	8.63852i	0.154620	−	0.338570i
$652$	−8.68843	+	10.0270i	−0.340265	+	0.392687i
$653$	1.03177	−	7.17612i	0.0403763	−	0.280823i	−0.959624	−	0.281287i	$-0.909239\pi$
$653$	1.03177	−	7.17612i	0.0403763	−	0.280823i	1.00000		0.000464086i	$0.000147723\pi$
$654$	−0.193994	−	0.424787i	−0.00758575	−	0.0166105i
$655$	−6.90444	−	2.02733i	−0.269779	−	0.0792143i
$656$	0.984586	+	0.289101i	0.0384416	+	0.0112875i
$657$	0.612468	+	1.34112i	0.0238947	+	0.0523220i
$658$	0.338765	−	2.35616i	0.0132064	−	0.0918528i
$659$	15.1973	−	17.5386i	0.592003	−	0.683208i	−0.378138	−	0.925749i	$-0.623435\pi$
$659$	15.1973	−	17.5386i	0.592003	−	0.683208i	0.970141	+	0.242541i	$0.0779809\pi$
$660$	0.271017	−	0.593443i	0.0105493	−	0.0230998i
$661$	−16.3610	−	10.5146i	−0.636370	−	0.408970i	0.182293	−	0.983244i	$-0.441648\pi$
$661$	−16.3610	−	10.5146i	−0.636370	−	0.408970i	−0.818663	+	0.574274i	$0.805284\pi$
$662$	2.39730	+	16.6736i	0.0931736	+	0.648037i
$663$	−10.0907	+	6.48490i	−0.391890	+	0.251853i
$664$	5.36353	+	6.18985i	0.208145	+	0.240213i
$665$	−5.33025	+	1.56510i	−0.206698	+	0.0606921i
$666$	10.3920			0.402680
$667$	0.414670	−	20.6232i	0.0160561	−	0.798535i
$668$	−15.0175			−0.581044
$669$	8.45465	−	2.48251i	0.326876	−	0.0959794i
$670$	7.33716	+	8.46753i	0.283459	+	0.327129i
$671$	−2.28925	+	1.47121i	−0.0883757	+	0.0567956i
$672$	0.250266	+	1.74063i	0.00965420	+	0.0671465i
$673$	−29.1269	−	18.7187i	−1.12276	−	0.721552i	−0.158721	−	0.987323i	$-0.550737\pi$
$673$	−29.1269	−	18.7187i	−1.12276	−	0.721552i	−0.964036	+	0.265771i	$0.914374\pi$
$674$	2.03952	−	4.46593i	0.0785595	−	0.172021i
$675$	0.654861	−	0.755750i	0.0252056	−	0.0290888i
$676$	1.25448	−	8.72513i	0.0482494	−	0.335582i
$677$	−9.48542	−	20.7702i	−0.364554	−	0.798263i	−0.999666	−	0.0258425i	$-0.991773\pi$
$677$	−9.48542	−	20.7702i	−0.364554	−	0.798263i	0.635112	−	0.772420i	$-0.280954\pi$
$678$	−2.09664	−	0.615628i	−0.0805208	−	0.0236431i
$679$	20.2539	+	5.94709i	0.777274	+	0.228228i
$680$	2.43569	+	5.33341i	0.0934043	+	0.204527i
$681$	3.62057	−	25.1816i	0.138740	−	0.964961i
$682$	2.30720	−	2.66265i	0.0883473	−	0.101958i
$683$	20.6172	−	45.1454i	0.788896	−	1.72744i	0.109111	−	0.994030i	$-0.465199\pi$
$683$	20.6172	−	45.1454i	0.788896	−	1.72744i	0.679785	−	0.733412i	$-0.262073\pi$
$684$	2.65755	+	1.70791i	0.101614	+	0.0653034i
$685$	0.792759	+	5.51376i	0.0302898	+	0.210670i
$686$	−16.1363	+	10.3702i	−0.616089	+	0.395936i
$687$	7.44513	+	8.59214i	0.284049	+	0.327810i
$688$	−8.14099	+	2.39041i	−0.310372	+	0.0911335i
$689$	−1.24731			−0.0475187
$690$	−4.75978	+	0.586951i	−0.181202	+	0.0223449i
$691$	30.4511			1.15842			0.579208	−	0.815180i	$-0.303362\pi$
$691$	30.4511			1.15842			0.579208	+	0.815180i	$0.303362\pi$
$692$	9.95965	−	2.92442i	0.378609	−	0.111170i
$693$	0.751300	+	0.867046i	0.0285395	+	0.0329364i
$694$	−3.61520	+	2.32335i	−0.137231	+	0.0881932i
$695$	2.36740	+	16.4656i	0.0898007	+	0.624577i
$696$	−3.61833	−	2.32536i	−0.137152	−	0.0881424i
$697$	−2.49939	+	5.47289i	−0.0946710	+	0.207301i
$698$	0.897906	−	1.03624i	0.0339862	−	0.0392222i
$699$	−2.81188	+	19.5570i	−0.106355	+	0.739715i
$700$	−0.730522	−	1.59962i	−0.0276111	−	0.0604599i
$701$	−2.89118	−	0.848926i	−0.109198	−	0.0320635i	0.226677	−	0.973970i	$-0.427214\pi$
$701$	−2.89118	−	0.848926i	−0.109198	−	0.0320635i	−0.335875	+	0.941907i	$0.609032\pi$
$702$	−1.96289	−	0.576358i	−0.0740847	−	0.0217532i
$703$	−13.6375	−	29.8620i	−0.514348	−	1.12626i
$704$	−0.0928461	+	0.645759i	−0.00349927	+	0.0243380i
$705$	0.886435	−	1.02300i	0.0333851	−	0.0385284i
$706$	14.9338	−	32.7005i	0.562042	−	1.23070i
$707$	−12.8689	−	8.27034i	−0.483985	−	0.311038i
$708$	−1.59363	−	11.0839i	−0.0598921	−	0.416559i
$709$	22.3660	−	14.3737i	0.839972	−	0.539817i	−0.0484603	−	0.998825i	$-0.515431\pi$
$709$	22.3660	−	14.3737i	0.839972	−	0.539817i	0.888432	+	0.459008i	$0.151795\pi$
$710$	−0.604849	−	0.698033i	−0.0226996	−	0.0261967i
$711$	16.4213	−	4.82173i	0.615847	−	0.180829i
$712$	9.77858			0.366468
$713$	−25.5563	−	4.20045i	−0.957092	−	0.157308i
$714$	−10.3107			−0.385870
$715$	1.28059	−	0.376016i	0.0478914	−	0.0140622i
$716$	4.84238	+	5.58841i	0.180968	+	0.208849i
$717$	−4.84813	+	3.11571i	−0.181057	+	0.116358i
$718$	0.109490	+	0.761522i	0.00408614	+	0.0284198i
$719$	−13.5329	−	8.69705i	−0.504691	−	0.324345i	0.263399	−	0.964687i	$-0.415156\pi$
$719$	−13.5329	−	8.69705i	−0.504691	−	0.324345i	−0.768090	+	0.640342i	$0.778793\pi$
$720$	−0.415415	+	0.909632i	−0.0154816	+	0.0339000i
$721$	11.9689	−	13.8129i	0.445745	−	0.514417i
$722$	−1.28375	+	8.92866i	−0.0477761	+	0.332290i
$723$	0.566787	+	1.24109i	0.0210790	+	0.0461567i
$724$	−12.1398	−	3.56455i	−0.451170	−	0.132476i
$725$	4.12689	+	1.21176i	0.153269	+	0.0450038i
$726$	−4.39275	−	9.61879i	−0.163030	−	0.356987i
$727$	−4.50752	+	31.3505i	−0.167175	+	1.16273i	0.717514	+	0.696544i	$0.245280\pi$
$727$	−4.50752	+	31.3505i	−0.167175	+	1.16273i	−0.884689	+	0.466182i	$0.845629\pi$
$728$	−2.35589	+	2.71884i	−0.0873151	+	0.100767i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	1.24030	+	0.797096i	0.0459057	+	0.0295018i
$731$	−7.07986	−	49.2415i	−0.261858	−	1.82126i
$732$	3.50898	−	2.25508i	0.129695	−	0.0833502i
$733$	−23.3263	−	26.9200i	−0.861576	−	0.994312i	−0.999992	−	0.00393800i	$-0.998746\pi$
$733$	−23.3263	−	26.9200i	−0.861576	−	0.994312i	0.138416	−	0.990374i	$-0.455799\pi$
$734$	21.2689	−	6.24512i	0.785050	−	0.230512i
$735$	−3.90756			−0.144132
$736$	4.40161	−	1.90416i	0.162246	−	0.0701883i
$737$	−7.30958			−0.269252
$738$	−0.984586	+	0.289101i	−0.0362431	+	0.0106419i
$739$	−16.9872	−	19.6043i	−0.624886	−	0.721157i	0.351741	−	0.936097i	$-0.385590\pi$
$739$	−16.9872	−	19.6043i	−0.624886	−	0.721157i	−0.976627	+	0.214940i	$0.931044\pi$
$740$	8.74227	−	5.61832i	0.321372	−	0.206533i
$741$	0.919730	+	6.39686i	0.0337871	+	0.234995i
$742$	−0.901980	−	0.579667i	−0.0331127	−	0.0212803i
$743$	3.89337	−	8.52528i	0.142834	−	0.312762i	−0.824672	−	0.565611i	$-0.808640\pi$
$743$	3.89337	−	8.52528i	0.142834	−	0.312762i	0.967506	+	0.252849i	$0.0813676\pi$
$744$	−3.53648	+	4.08132i	−0.129654	+	0.149628i
$745$	0.756052	−	5.25845i	0.0276996	−	0.192655i
$746$	12.0779	+	26.4470i	0.442204	+	0.968292i
$747$	−7.85857	−	2.30749i	−0.287530	−	0.0844265i
$748$	−3.67024	−	1.07768i	−0.134197	−	0.0394039i
$749$	10.7468	+	23.5322i	0.392679	+	0.859846i
$750$	0.142315	−	0.989821i	0.00519660	−	0.0361432i
$751$	−9.38736	+	10.8336i	−0.342550	+	0.395323i	−0.900718	−	0.434404i	$-0.856959\pi$
$751$	−9.38736	+	10.8336i	−0.342550	+	0.395323i	0.558168	+	0.829728i	$0.311504\pi$
$752$	−0.562315	+	1.23130i	−0.0205055	+	0.0449009i
$753$	−13.4067	−	8.61598i	−0.488568	−	0.313984i
$754$	−1.25224	−	8.70949i	−0.0456037	−	0.317181i
$755$	0.337179	−	0.216692i	0.0122712	−	0.00788623i
$756$	−1.15160	−	1.32901i	−0.0418831	−	0.0483357i
$757$	−9.26873	+	2.72154i	−0.336878	+	0.0989162i	−0.445796	−	0.895134i	$-0.647079\pi$
$757$	−9.26873	+	2.72154i	−0.336878	+	0.0989162i	0.108919	+	0.994051i	$0.465261\pi$
$758$	23.1129			0.839497
$759$	1.74413	−	2.59758i	0.0633078	−	0.0942860i
$760$	3.15904			0.114590
$761$	−6.13023	+	1.80000i	−0.222221	+	0.0652499i	−0.390948	−	0.920413i	$-0.627853\pi$
$761$	−6.13023	+	1.80000i	−0.222221	+	0.0652499i	0.168727	+	0.985663i	$0.446034\pi$
$762$	−4.31898	−	4.98436i	−0.156460	−	0.180564i
$763$	0.690849	−	0.443982i	0.0250104	−	0.0160732i
$764$	2.56343	+	17.8290i	0.0927416	+	0.645032i
$765$	−4.93249	−	3.16992i	−0.178334	−	0.114609i
$766$	7.42464	−	16.2577i	0.268263	−	0.587414i
$767$	15.0017	−	17.3129i	0.541680	−	0.625132i
$768$	0.142315	−	0.989821i	0.00513534	−	0.0357171i
$769$	−19.6732	−	43.0783i	−0.709434	−	1.55344i	−0.828144	−	0.560515i	$-0.810603\pi$
$769$	−19.6732	−	43.0783i	−0.709434	−	1.55344i	0.118710	−	0.992929i	$-0.462124\pi$
$770$	1.10079	+	0.323222i	0.0396699	+	0.0116481i
$771$	4.82277	+	1.41609i	0.173688	+	0.0509993i
$772$	−2.89428	−	6.33758i	−0.104167	−	0.228095i
$773$	−3.65270	+	25.4051i	−0.131378	+	0.913757i	0.812382	+	0.583126i	$0.198171\pi$
$773$	−3.65270	+	25.4051i	−0.131378	+	0.913757i	−0.943760	+	0.330631i	$0.892738\pi$
$774$	5.55628	−	6.41229i	0.199716	−	0.230485i
$775$	2.24339	−	4.91234i	0.0805850	−	0.176457i
$776$	−10.0982	−	6.48971i	−0.362504	−	0.232967i
$777$	2.60075	+	18.0886i	0.0933014	+	0.648925i
$778$	11.8311	−	7.60342i	0.424167	−	0.272596i
$779$	2.12283	+	2.44988i	0.0760584	+	0.0877761i
$780$	−1.96289	+	0.576358i	−0.0702829	+	0.0206369i
$781$	0.602575			0.0215618
$782$	7.37811	+	27.1340i	0.263841	+	0.970309i
$783$	4.30111			0.153709
$784$	3.74927	−	1.10089i	0.133903	−	0.0393174i
$785$	11.9201	+	13.7566i	0.425447	+	0.490992i
$786$	−6.05360	+	3.89041i	−0.215925	+	0.138766i
$787$	0.132484	+	0.921444i	0.00472253	+	0.0328459i	0.992046	−	0.125872i	$-0.0401730\pi$
$787$	0.132484	+	0.921444i	0.00472253	+	0.0328459i	−0.987324	+	0.158718i	$0.949264\pi$
$788$	18.5540	+	11.9239i	0.660958	+	0.424772i
$789$	0.954210	−	2.08943i	0.0339708	−	0.0743856i
$790$	11.2077	−	12.9343i	0.398751	−	0.460183i
$791$	0.546868	−	3.80355i	0.0194444	−	0.135239i
$792$	−0.271017	−	0.593443i	−0.00963015	−	0.0210871i
$793$	8.18749	+	2.40406i	0.290746	+	0.0853708i
$794$	5.19492	+	1.52537i	0.184361	+	0.0541332i
$795$	−0.253280	−	0.554606i	−0.00898292	−	0.0196699i
$796$	−1.81807	+	12.6449i	−0.0644397	+	0.448188i
$797$	−9.72113	+	11.2188i	−0.344340	+	0.397390i	−0.901332	−	0.433128i	$-0.857410\pi$
$797$	−9.72113	+	11.2188i	−0.344340	+	0.397390i	0.556992	+	0.830518i	$0.311955\pi$
$798$	−2.30775	+	5.05326i	−0.0816933	+	0.178883i
$799$	−6.67673	−	4.29087i	−0.236206	−	0.151800i
$800$	0.142315	+	0.989821i	0.00503159	+	0.0349955i
$801$	−8.22626	+	5.28670i	−0.290661	+	0.186796i
$802$	−14.0697	−	16.2374i	−0.496820	−	0.573361i
$803$	−0.922905	+	0.270989i	−0.0325686	+	0.00956301i
$804$	11.2042			0.395140
$805$	−2.21288	−	8.13814i	−0.0779937	−	0.286832i
$806$	−11.0479			−0.389144
$807$	−15.3677	+	4.51235i	−0.540967	+	0.158842i
$808$	5.69656	+	6.57418i	0.200404	+	0.231279i
$809$	−44.3059	+	28.4737i	−1.55771	+	1.00108i	−0.574526	+	0.818486i	$0.694814\pi$
$809$	−44.3059	+	28.4737i	−1.55771	+	1.00108i	−0.983188	+	0.182596i	$0.941550\pi$
$810$	−0.142315	−	0.989821i	−0.00500043	−	0.0347788i
$811$	16.1755	+	10.3954i	0.567999	+	0.365031i	0.792901	−	0.609351i	$-0.208570\pi$
$811$	16.1755	+	10.3954i	0.567999	+	0.365031i	−0.224902	+	0.974381i	$0.572206\pi$
$812$	3.14205	−	6.88014i	0.110265	−	0.241446i
$813$	−7.27974	+	8.40127i	−0.255312	+	0.294645i
$814$	−0.964853	+	6.71070i	−0.0338181	+	0.235210i
$815$	−5.51156	−	12.0686i	−0.193061	−	0.422746i
$816$	5.62576	+	1.65187i	0.196941	+	0.0578270i
$817$	−25.7177	−	7.55140i	−0.899749	−	0.264190i
$818$	−3.68348	−	8.06569i	−0.128790	−	0.282010i
$819$	0.511984	−	3.56093i	0.0178902	−	0.124429i
$820$	−0.671987	+	0.775515i	−0.0234668	+	0.0270821i
$821$	−8.90237	+	19.4935i	−0.310695	+	0.680327i	−0.998982	−	0.0451115i	$-0.985636\pi$
$821$	−8.90237	+	19.4935i	−0.310695	+	0.680327i	0.688287	+	0.725438i	$0.258363\pi$
$822$	4.68617	+	3.01162i	0.163449	+	0.105042i
$823$	4.40478	+	30.6359i	0.153541	+	1.06790i	0.910223	+	0.414118i	$0.135910\pi$
$823$	4.40478	+	30.6359i	0.153541	+	1.06790i	−0.756682	+	0.653783i	$0.773181\pi$
$824$	−8.74342	+	5.61906i	−0.304592	+	0.195749i
$825$	0.427231	+	0.493051i	0.0148743	+	0.0171658i
$826$	18.8942	−	5.54784i	0.657414	−	0.193034i
$827$	13.5101			0.469793			0.234897	−	0.972020i	$-0.424525\pi$
$827$	13.5101			0.469793			0.234897	+	0.972020i	$0.424525\pi$
$828$	−2.67340	+	3.98157i	−0.0929072	+	0.138369i
$829$	−33.7770			−1.17312			−0.586562	−	0.809905i	$-0.699519\pi$
$829$	−33.7770			−1.17312			−0.586562	+	0.809905i	$0.699519\pi$
$830$	−7.85857	+	2.30749i	−0.272775	+	0.0800940i
$831$	−1.42935	−	1.64956i	−0.0495836	−	0.0572225i
$832$	1.72101	−	1.10602i	0.0596651	−	0.0383444i
$833$	3.26058	+	22.6778i	0.112972	+	0.785740i
$834$	13.9942	+	8.99354i	0.484580	+	0.311421i
$835$	6.23849	−	13.6604i	0.215892	−	0.472737i
$836$	−1.34964	+	1.55757i	−0.0466782	+	0.0538696i
$837$	0.768552	−	5.34539i	0.0265650	−	0.184764i
$838$	3.26957	+	7.15936i	0.112945	+	0.247316i
$839$	−35.3937	−	10.3925i	−1.22193	−	0.358790i	−0.393729	−	0.919227i	$-0.628815\pi$
$839$	−35.3937	−	10.3925i	−1.22193	−	0.358790i	−0.828197	+	0.560437i	$0.810633\pi$
$840$	−1.68730	−	0.495436i	−0.0582174	−	0.0170942i
$841$	−4.36204	−	9.55153i	−0.150415	−	0.329363i
$842$	−2.46383	+	17.1363i	−0.0849092	+	0.590557i
$843$	−4.87658	+	5.62788i	−0.167958	+	0.193834i
$844$	−7.26471	+	15.9075i	−0.250062	+	0.547559i
$845$	7.41553	+	4.76567i	0.255102	+	0.163944i
$846$	−0.192641	−	1.33985i	−0.00662312	−	0.0460648i
$847$	15.6434	−	10.0534i	0.537515	−	0.345440i
$848$	0.399271	+	0.460784i	0.0137110	+	0.0158234i
$849$	−5.81391	+	1.70712i	−0.199533	+	0.0585881i
$850$	−5.86326			−0.201108
$851$	45.7414	−	19.7880i	1.56799	−	0.678322i
$852$	−0.923629			−0.0316430
$853$	−25.4676	+	7.47796i	−0.871994	+	0.256041i	−0.686963	−	0.726692i	$-0.741057\pi$
$853$	−25.4676	+	7.47796i	−0.871994	+	0.256041i	−0.185031	+	0.982733i	$0.559238\pi$
$854$	4.80345	+	5.54348i	0.164371	+	0.189694i
$855$	−2.65755	+	1.70791i	−0.0908864	+	0.0584091i
$856$	−2.09361	−	14.5614i	−0.0715580	−	0.497697i
$857$	−26.4479	−	16.9970i	−0.903442	−	0.580607i	0.00436700	−	0.999990i	$-0.498610\pi$
$857$	−26.4479	−	16.9970i	−0.903442	−	0.580607i	−0.907809	+	0.419383i	$0.862246\pi$
$858$	0.554436	−	1.21404i	0.0189281	−	0.0414468i
$859$	23.4247	−	27.0336i	0.799241	−	0.922373i	−0.199098	−	0.979979i	$-0.563801\pi$
$859$	23.4247	−	27.0336i	0.799241	−	0.922373i	0.998339	+	0.0576063i	$0.0183468\pi$
$860$	1.20750	−	8.39832i	0.0411753	−	0.286380i
$861$	−0.749627	−	1.64145i	−0.0255472	−	0.0559406i
$862$	5.93724	+	1.74333i	0.202223	+	0.0593781i
$863$	−12.9608	−	3.80563i	−0.441190	−	0.129545i	0.0535905	−	0.998563i	$-0.482933\pi$
$863$	−12.9608	−	3.80563i	−0.441190	−	0.129545i	−0.494781	+	0.869018i	$0.664752\pi$
$864$	0.415415	+	0.909632i	0.0141327	+	0.0309463i
$865$	−1.47724	+	10.2745i	−0.0502278	+	0.349342i
$866$	4.11320	−	4.74689i	0.139772	−	0.161306i
$867$	−7.21900	+	15.8074i	−0.245170	+	0.536848i
$868$	−7.98915	−	5.13432i	−0.271169	−	0.174270i
$869$	1.58902	+	11.0519i	0.0539039	+	0.374910i
$870$	3.61833	−	2.32536i	0.122673	−	0.0788370i
$871$	15.0101	+	17.3226i	0.508597	+	0.586953i
$872$	−0.448071	+	0.131566i	−0.0151736	+	0.00445537i
$873$	12.0037			0.406265
$874$	14.9496	+	2.45713i	0.505679	+	0.0831136i
$875$	1.75853			0.0594493
$876$	1.41463	−	0.415373i	0.0477960	−	0.0140342i
$877$	8.56696	+	9.88680i	0.289286	+	0.333854i	0.881727	−	0.471760i	$-0.156381\pi$
$877$	8.56696	+	9.88680i	0.289286	+	0.333854i	−0.592441	+	0.805614i	$0.701836\pi$
$878$	−27.2606	+	17.5193i	−0.920002	+	0.591249i
$879$	3.60781	+	25.0929i	0.121688	+	0.846361i
$880$	−0.548833	−	0.352714i	−0.0185012	−	0.0118900i
$881$	10.3493	−	22.6618i	0.348676	−	0.763495i	−0.651313	−	0.758810i	$-0.725781\pi$
$881$	10.3493	−	22.6618i	0.348676	−	0.763495i	0.999989	−	0.00468532i	$-0.00149139\pi$
$882$	−2.55891	+	2.95313i	−0.0861628	+	0.0994372i
$883$	−6.90826	+	48.0480i	−0.232482	+	1.61695i	0.454827	+	0.890580i	$0.349701\pi$
$883$	−6.90826	+	48.0480i	−0.232482	+	1.61695i	−0.687309	+	0.726365i	$0.741208\pi$
$884$	4.98283	+	10.9109i	0.167591	+	0.366973i
$885$	10.7443	+	3.15481i	0.361166	+	0.106048i
$886$	−21.7533	−	6.38734i	−0.730816	−	0.214587i
$887$	18.8641	+	41.3065i	0.633393	+	1.38694i	0.905366	+	0.424633i	$0.139597\pi$
$887$	18.8641	+	41.3065i	0.633393	+	1.38694i	−0.271972	+	0.962305i	$0.587676\pi$
$888$	1.47893	−	10.2862i	0.0496296	−	0.345182i
$889$	7.59507	−	8.76518i	0.254730	−	0.293975i
$890$	−4.06217	+	8.89490i	−0.136164	+	0.298158i
$891$	0.548833	+	0.352714i	0.0183866	+	0.0118164i
$892$	−1.25402	−	8.72189i	−0.0419877	−	0.292031i
$893$	−3.59733	+	2.31186i	−0.120380	+	0.0773635i
$894$	−3.47897	−	4.01494i	−0.116354	−	0.134280i
$895$	−7.09499	+	2.08328i	−0.237159	+	0.0696363i
$896$	1.75853			0.0587485
$897$	−9.73738	+	1.20076i	−0.325122	+	0.0400923i
$898$	1.33249			0.0444658
$899$	22.2867	−	6.54396i	0.743302	−	0.218253i
$900$	−0.654861	−	0.755750i	−0.0218287	−	0.0251917i
$901$	−3.00736	+	1.93271i	−0.100190	+	0.0643879i
$902$	−0.0952743	−	0.662647i	−0.00317229	−	0.0220637i
$903$	12.5520	+	8.06668i	0.417705	+	0.268442i
$904$	−0.907744	+	1.98768i	−0.0301911	+	0.0661093i
$905$	8.28547	−	9.56194i	0.275418	−	0.317850i
$906$	0.0570406	−	0.396726i	0.00189505	−	0.0131803i
$907$	−3.03656	−	6.64914i	−0.100827	−	0.220781i	0.852495	−	0.522735i	$-0.175088\pi$
$907$	−3.03656	−	6.64914i	−0.100827	−	0.220781i	−0.953322	+	0.301954i	$0.902361\pi$
$908$	−24.4100	−	7.16743i	−0.810075	−	0.237859i
$909$	−8.34652	−	2.45076i	−0.276837	−	0.0812866i
$910$	−1.49447	−	3.27244i	−0.0495413	−	0.108480i
$911$	−4.09081	+	28.4522i	−0.135535	+	0.942665i	0.802630	+	0.596477i	$0.203433\pi$
$911$	−4.09081	+	28.4522i	−0.135535	+	0.942665i	−0.938165	+	0.346188i	$0.887476\pi$
$912$	2.06873	−	2.38744i	0.0685025	−	0.0790561i
$913$	2.21972	−	4.86050i	0.0734619	−	0.160859i
$914$	18.7014	+	12.0187i	0.618589	+	0.397543i
$915$	0.593613	+	4.12867i	0.0196243	+	0.136490i
$916$	9.56423	−	6.14656i	0.316011	−	0.203088i
$917$	−8.28680	−	9.56347i	−0.273654	−	0.315814i
$918$	−5.62576	+	1.65187i	−0.185678	+	0.0545199i
$919$	15.6211			0.515291			0.257646	−	0.966239i	$-0.417053\pi$
$919$	15.6211			0.515291			0.257646	+	0.966239i	$0.417053\pi$
$920$	−0.0964099	+	4.79486i	−0.00317854	+	0.158082i
$921$	32.8373			1.08203
$922$	−6.45276	+	1.89470i	−0.212510	+	0.0623987i
$923$	−1.23738	−	1.42801i	−0.0407288	−	0.0470035i
$924$	0.965142	−	0.620259i	0.0317509	−	0.0204050i
$925$	1.47893	+	10.2862i	0.0486269	+	0.338208i
$926$	−0.626617	−	0.402702i	−0.0205919	−	0.0132336i
$927$	4.31754	−	9.45410i	0.141807	−	0.310513i
$928$	−2.81663	+	3.25056i	−0.0924604	+	0.106705i
$929$	0.338029	−	2.35104i	0.0110904	−	0.0771353i	−0.983525	−	0.180774i	$-0.942140\pi$
$929$	0.338029	−	2.35104i	0.0110904	−	0.0771353i	0.994615	+	0.103639i	$0.0330487\pi$
$930$	−2.24339	−	4.91234i	−0.0735637	−	0.161082i
$931$	11.8441	+	3.47774i	0.388175	+	0.113978i
$932$	18.9578	+	5.56652i	0.620984	+	0.182337i
$933$	−3.26806	−	7.15606i	−0.106992	−	0.234279i
$934$	−1.81564	+	12.6280i	−0.0594095	+	0.413202i
$935$	2.50496	−	2.89088i	0.0819211	−	0.0945420i
$936$	−0.849841	+	1.86089i	−0.0277779	+	0.0608251i
$937$	−20.1001	−	12.9175i	−0.656641	−	0.421998i	0.169446	−	0.985539i	$-0.445802\pi$
$937$	−20.1001	−	12.9175i	−0.656641	−	0.421998i	−0.826088	+	0.563542i	$0.809438\pi$
$938$	2.80401	+	19.5023i	0.0915543	+	0.636774i
$939$	−11.8619	+	7.62315i	−0.387097	+	0.248772i
$940$	−0.886435	−	1.02300i	−0.0289123	−	0.0333666i
$941$	49.4113	−	14.5085i	1.61076	−	0.472963i	0.652248	−	0.758005i	$-0.273826\pi$
$941$	49.4113	−	14.5085i	1.61076	−	0.472963i	0.958515	+	0.285043i	$0.0920078\pi$
$942$	18.2025			0.593070
$943$	−3.78327	+	3.14732i	−0.123200	+	0.102491i
$944$	−11.1979			−0.364460
$945$	1.68730	−	0.495436i	0.0548879	−	0.0161165i
$946$	3.62492	+	4.18338i	0.117856	+	0.136013i
$947$	−37.1028	+	23.8445i	−1.20568	+	0.774844i	−0.979930	−	0.199342i	$-0.936120\pi$
$947$	−37.1028	+	23.8445i	−1.20568	+	0.774844i	−0.225750	+	0.974185i	$0.572483\pi$
$948$	−2.43566	−	16.9404i	−0.0791065	−	0.550197i
$949$	2.53737	+	1.63067i	0.0823665	+	0.0529337i
$950$	−1.31231	+	2.87356i	−0.0425770	+	0.0932307i
$951$	2.16843	−	2.50250i	0.0703161	−	0.0811491i
$952$	−1.46737	+	10.2058i	−0.0475578	+	0.330772i
$953$	23.7018	+	51.8997i	0.767777	+	1.68120i	0.731486	+	0.681856i	$0.238827\pi$
$953$	23.7018	+	51.8997i	0.767777	+	1.68120i	0.0362910	+	0.999341i	$0.488446\pi$
$954$	−0.585007	−	0.171773i	−0.0189403	−	0.00556137i
$955$	−17.2827	−	5.07467i	−0.559257	−	0.164213i
$956$	2.39403	+	5.24220i	0.0774285	+	0.169545i
$957$	−0.399342	+	2.77748i	−0.0129089	+	0.0897832i
$958$	−7.86768	+	9.07978i	−0.254193	+	0.293355i
$959$	−4.06934	+	8.91061i	−0.131406	+	0.287739i
$960$	0.841254	+	0.540641i	0.0271513	+	0.0174491i
$961$	0.261303	+	1.81740i	0.00842914	+	0.0586259i
$962$	17.8846	−	11.4937i	0.576623	−	0.370573i
$963$	9.63372	+	11.1179i	0.310442	+	0.358270i
$964$	1.30912	−	0.384392i	0.0421639	−	0.0123804i
$965$	6.96719			0.224282
$966$	−7.59952	−	3.65697i	−0.244511	−	0.117661i
$967$	50.3185			1.61813			0.809066	−	0.587717i	$-0.199973\pi$
$967$	50.3185			1.61813			0.809066	+	0.587717i	$0.199973\pi$
$968$	−10.1460	+	2.97915i	−0.326106	+	0.0957534i
$969$	12.1295	+	13.9982i	0.389656	+	0.449687i
$970$	10.0982	−	6.48971i	0.324233	−	0.208372i
$971$	7.38480	+	51.3624i	0.236990	+	1.64830i	0.666695	+	0.745330i	$0.267708\pi$
$971$	7.38480	+	51.3624i	0.236990	+	1.64830i	−0.429706	+	0.902969i	$0.641383\pi$
$972$	−0.841254	−	0.540641i	−0.0269832	−	0.0173411i
$973$	−12.1522	+	26.6096i	−0.389582	+	0.853065i
$974$	−26.8449	+	30.9807i	−0.860166	+	0.992685i
$975$	0.291142	−	2.02494i	0.00932402	−	0.0648500i
$976$	−1.73275	−	3.79419i	−0.0554639	−	0.121449i
$977$	38.7291	+	11.3719i	1.23905	+	0.363819i	0.834660	−	0.550766i	$-0.185664\pi$
$977$	38.7291	+	11.3719i	1.23905	+	0.363819i	0.404394	+	0.914585i	$0.367482\pi$
$978$	−12.7302	−	3.73791i	−0.407066	−	0.119525i
$979$	−2.65016	−	5.80303i	−0.0846993	−	0.185466i
$980$	−0.556103	+	3.86778i	−0.0177641	+	0.123552i
$981$	0.305812	−	0.352926i	0.00976382	−	0.0112680i
$982$	6.89565	−	15.0994i	0.220049	−	0.481840i
$983$	2.93342	+	1.88520i	0.0935616	+	0.0601284i	0.586585	−	0.809888i	$-0.300472\pi$
$983$	2.93342	+	1.88520i	0.0935616	+	0.0601284i	−0.493023	+	0.870016i	$0.664108\pi$
$984$	0.146037	+	1.01571i	0.00465548	+	0.0323796i
$985$	−18.5540	+	11.9239i	−0.591178	+	0.379927i
$986$	−16.5146	−	19.0589i	−0.525933	−	0.606959i
$987$	2.28397	−	0.670634i	0.0726996	−	0.0213465i
$988$	6.46264			0.205604
$989$	12.2466	−	38.8045i	0.389418	−	1.23391i
$990$	0.652400			0.0207346
$991$	18.0191	−	5.29088i	0.572395	−	0.168070i	0.0172901	−	0.999851i	$-0.494496\pi$
$991$	18.0191	−	5.29088i	0.572395	−	0.168070i	0.555105	+	0.831780i	$0.312678\pi$
$992$	3.53648	+	4.08132i	0.112284	+	0.129582i
$993$	−14.1709	+	9.10711i	−0.449701	+	0.289005i
$994$	−0.231153	−	1.60770i	−0.00733172	−	0.0509932i
$995$	−10.7470	−	6.90667i	−0.340703	−	0.218956i
$996$	−3.40239	+	7.45020i	−0.107809	+	0.236068i
$997$	−15.0244	+	17.3391i	−0.475828	+	0.549135i	−0.942023	−	0.335547i	$-0.891079\pi$
$997$	−15.0244	+	17.3391i	−0.475828	+	0.549135i	0.466196	+	0.884682i	$0.345624\pi$
$998$	−1.09909	+	7.64433i	−0.0347910	+	0.241977i
$999$	4.31698	+	9.45286i	0.136583	+	0.299075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.f.331.1	yes	20
23.18	even	11	inner	690.2.m.f.271.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.f.271.1	✓	20	23.18	even	11	inner
690.2.m.f.331.1	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.730522 + 1.59962i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.730522 + 1.59962i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-0.625973 - 0.183802i) q^{11} +(0.959493 + 0.281733i) q^{12} +(0.849841 + 1.86089i) q^{13} +(-0.250266 + 1.74063i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(4.93249 + 3.16992i) q^{17} +(0.142315 + 0.989821i) q^{18} +(2.65755 - 1.70791i) q^{19} +(0.654861 + 0.755750i) q^{20} +(-1.68730 + 0.495436i) q^{21} -0.652400 q^{22} +(2.51119 + 4.08582i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(1.33969 + 1.54608i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.250266 + 1.74063i) q^{28} +(-3.61833 - 2.32536i) q^{29} +(-0.415415 + 0.909632i) q^{30} +(-3.53648 + 4.08132i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-0.271017 - 0.593443i) q^{33} +(5.62576 + 1.65187i) q^{34} +(-1.68730 - 0.495436i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.47893 - 10.2862i) q^{37} +(2.06873 - 2.38744i) q^{38} +(-0.849841 + 1.86089i) q^{39} +(0.841254 + 0.540641i) q^{40} +(0.146037 + 1.01571i) q^{41} +(-1.47937 + 0.950735i) q^{42} +(-5.55628 - 6.41229i) q^{43} +(-0.625973 + 0.183802i) q^{44} -1.00000 q^{45} +(3.56058 + 3.21283i) q^{46} -1.35362 q^{47} +(0.959493 - 0.281733i) q^{48} +(2.55891 + 2.95313i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.834429 + 5.80358i) q^{51} +(1.72101 + 1.10602i) q^{52} +(-0.253280 + 0.554606i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(0.0928461 - 0.645759i) q^{55} +(0.730522 + 1.59962i) q^{56} +(3.03108 + 0.890004i) q^{57} +(-4.12689 - 1.21176i) q^{58} +(-4.65177 - 10.1860i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(2.73151 - 3.15233i) q^{61} +(-2.24339 + 4.91234i) q^{62} +(-1.47937 - 0.950735i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-1.72101 + 1.10602i) q^{65} +(-0.427231 - 0.493051i) q^{66} +(10.7503 - 3.15658i) q^{67} +5.86326 q^{68} +(-1.44337 + 4.57347i) q^{69} -1.75853 q^{70} +(-0.886216 + 0.260216i) q^{71} +(0.654861 + 0.755750i) q^{72} +(1.24030 - 0.797096i) q^{73} +(-1.47893 - 10.2862i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(1.31231 - 2.87356i) q^{76} +(0.751300 - 0.867046i) q^{77} +(-0.291142 + 2.02494i) q^{78} +(-7.10965 - 15.5680i) q^{79} +(0.959493 + 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.426279 + 0.933421i) q^{82} +(-1.16561 + 8.10697i) q^{83} +(-1.15160 + 1.32901i) q^{84} +(-2.43569 + 5.33341i) q^{85} +(-7.13777 - 4.58716i) q^{86} +(-0.612112 - 4.25733i) q^{87} +(-0.548833 + 0.352714i) q^{88} +(6.40360 + 7.39015i) q^{89} +(-0.959493 + 0.281733i) q^{90} -3.59754 q^{91} +(4.32151 + 2.07956i) q^{92} -5.40036 q^{93} +(-1.29879 + 0.381360i) q^{94} +(2.06873 + 2.38744i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-1.70831 - 11.8816i) q^{97} +(3.28725 + 2.11258i) q^{98} +(0.271017 - 0.593443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Introduction

L-functions

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