LMFDB - Embedded newform 690.2.m.c.331.2

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} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
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			331.2
Root			$-3.70312 + 1.08733i$ of defining polynomial
Character	$\chi$	$=$	690.331
Dual form			690.2.m.c.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.113936 + 0.249486i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(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} +(-0.113936 + 0.249486i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(1.96472 + 0.576894i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-1.58075 - 3.46136i) q^{13} +(0.0390329 - 0.271480i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(5.21717 + 3.35287i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(1.93180 - 1.24149i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-0.263161 + 0.0772711i) q^{21} -2.04766 q^{22} +(0.871264 + 4.71603i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(2.49189 + 2.87580i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.0390329 + 0.271480i) q^{28} +(6.11682 + 3.93104i) q^{29} +(-0.415415 + 0.909632i) q^{30} +(4.32218 - 4.98807i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(0.850631 + 1.86262i) q^{33} +(-5.95045 - 1.74721i) q^{34} +(0.263161 + 0.0772711i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.53396 - 10.6689i) q^{37} +(-1.50378 + 1.73545i) q^{38} +(1.58075 - 3.46136i) q^{39} +(0.841254 + 0.540641i) q^{40} +(-1.31643 - 9.15600i) q^{41} +(0.230732 - 0.148282i) q^{42} +(7.01851 + 8.09979i) q^{43} +(1.96472 - 0.576894i) q^{44} +1.00000 q^{45} +(-2.16463 - 4.27953i) q^{46} -9.93495 q^{47} +(0.959493 - 0.281733i) q^{48} +(4.53476 + 5.23340i) q^{49} +(0.841254 - 0.540641i) q^{50} +(0.882589 + 6.13854i) q^{51} +(-3.20116 - 2.05726i) q^{52} +(-3.39538 + 7.43485i) q^{53} +(0.654861 - 0.755750i) q^{54} +(0.291413 - 2.02682i) q^{55} +(-0.113936 - 0.249486i) q^{56} +(2.20331 + 0.646951i) q^{57} +(-6.97654 - 2.04850i) q^{58} +(4.77077 + 10.4465i) q^{59} +(0.142315 - 0.989821i) q^{60} +(0.404404 - 0.466707i) q^{61} +(-2.74180 + 6.00371i) q^{62} +(-0.230732 - 0.148282i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-3.20116 + 2.05726i) q^{65} +(-1.34094 - 1.54752i) q^{66} +(3.00834 - 0.883328i) q^{67} +6.20167 q^{68} +(-2.99358 + 3.74680i) q^{69} -0.274271 q^{70} +(15.6810 - 4.60436i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-5.48570 + 3.52544i) q^{73} +(1.53396 + 10.6689i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(0.953931 - 2.08882i) q^{76} +(-0.367780 + 0.424441i) q^{77} +(-0.541540 + 3.76649i) q^{78} +(-1.75046 - 3.83297i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(3.84265 + 8.41423i) q^{82} +(-1.09141 + 7.59096i) q^{83} +(-0.179609 + 0.207280i) q^{84} +(2.57626 - 5.64123i) q^{85} +(-9.01618 - 5.79435i) q^{86} +(1.03478 + 7.19706i) q^{87} +(-1.72261 + 1.10705i) q^{88} +(-10.2662 - 11.8478i) q^{89} +(-0.959493 + 0.281733i) q^{90} +1.04366 q^{91} +(3.28263 + 3.49633i) q^{92} +6.60016 q^{93} +(9.53251 - 2.79900i) q^{94} +(-1.50378 - 1.73545i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(0.334081 + 2.32358i) q^{97} +(-5.82549 - 3.74382i) q^{98} +(-0.850631 + 1.86262i) 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	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 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 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * 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
$7$	−0.113936	+	0.249486i	−0.0430639	+	0.0942968i	−0.929941	−	0.367708i	$-0.880143\pi$
$7$	−0.113936	+	0.249486i	−0.0430639	+	0.0942968i	0.886877	+	0.462005i	$0.152870\pi$
$8$	−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
$11$	1.96472	+	0.576894i	0.592385	+	0.173940i	0.564165	−	0.825662i	$-0.309198\pi$
$11$	1.96472	+	0.576894i	0.592385	+	0.173940i	0.0282198	+	0.999602i	$0.491016\pi$
$12$	0.959493	+	0.281733i	0.276982	+	0.0813292i
$13$	−1.58075	−	3.46136i	−0.438421	−	0.960007i	−0.991885	−	0.127135i	$-0.959422\pi$
$13$	−1.58075	−	3.46136i	−0.438421	−	0.960007i	0.553465	−	0.832873i	$-0.313305\pi$
$14$	0.0390329	−	0.271480i	0.0104320	−	0.0725559i
$15$	0.654861	−	0.755750i	0.169084	−	0.195134i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	5.21717	+	3.35287i	1.26535	+	0.813191i	0.989007	−	0.147868i	$-0.0472410\pi$
$17$	5.21717	+	3.35287i	1.26535	+	0.813191i	0.276343	+	0.961059i	$0.410877\pi$
$18$	−0.142315	−	0.989821i	−0.0335439	−	0.233303i
$19$	1.93180	−	1.24149i	0.443185	−	0.284818i	−0.299956	−	0.953953i	$-0.596972\pi$
$19$	1.93180	−	1.24149i	0.443185	−	0.284818i	0.743140	+	0.669136i	$0.233335\pi$
$20$	−0.654861	−	0.755750i	−0.146431	−	0.168991i
$21$	−0.263161	+	0.0772711i	−0.0574265	+	0.0168619i
$22$	−2.04766			−0.436564
$23$	0.871264	+	4.71603i	0.181671	+	0.983359i
$23$	0.871264	+	4.71603i	0.181671	+	0.983359i
$24$	−1.00000			−0.204124
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	2.49189	+	2.87580i	0.488700	+	0.563990i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.0390329	+	0.271480i	0.00737652	+	0.0513048i
$29$	6.11682	+	3.93104i	1.13586	+	0.729976i	0.966776	−	0.255625i	$-0.0822814\pi$
$29$	6.11682	+	3.93104i	1.13586	+	0.729976i	0.169088	+	0.985601i	$0.445918\pi$
$30$	−0.415415	+	0.909632i	−0.0758441	+	0.166075i
$31$	4.32218	−	4.98807i	0.776287	−	0.895883i	−0.220548	−	0.975376i	$-0.570785\pi$
$31$	4.32218	−	4.98807i	0.776287	−	0.895883i	0.996835	+	0.0794931i	$0.0253302\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	0.850631	+	1.86262i	0.148076	+	0.324241i
$34$	−5.95045	−	1.74721i	−1.02049	−	0.299644i
$35$	0.263161	+	0.0772711i	0.0444824	+	0.0130612i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	1.53396	−	10.6689i	0.252181	−	1.75396i	−0.332879	−	0.942970i	$-0.608020\pi$
$37$	1.53396	−	10.6689i	0.252181	−	1.75396i	0.585060	−	0.810990i	$-0.301071\pi$
$38$	−1.50378	+	1.73545i	−0.243945	+	0.281527i
$39$	1.58075	−	3.46136i	0.253122	−	0.554260i
$40$	0.841254	+	0.540641i	0.133014	+	0.0854828i
$41$	−1.31643	−	9.15600i	−0.205592	−	1.42993i	−0.787321	−	0.616544i	$-0.788532\pi$
$41$	−1.31643	−	9.15600i	−0.205592	−	1.42993i	0.581728	−	0.813383i	$-0.302377\pi$
$42$	0.230732	−	0.148282i	0.0356027	−	0.0228804i
$43$	7.01851	+	8.09979i	1.07031	+	1.23521i	0.970729	+	0.240177i	$0.0772056\pi$
$43$	7.01851	+	8.09979i	1.07031	+	1.23521i	0.0995834	+	0.995029i	$0.468249\pi$
$44$	1.96472	−	0.576894i	0.296193	−	0.0869700i
$45$	1.00000			0.149071
$46$	−2.16463	−	4.27953i	−0.319157	−	0.630982i
$47$	−9.93495			−1.44916			−0.724581	−	0.689190i	$-0.757967\pi$
$47$	−9.93495			−1.44916			−0.724581	+	0.689190i	$0.757967\pi$
$48$	0.959493	−	0.281733i	0.138491	−	0.0406646i
$49$	4.53476	+	5.23340i	0.647823	+	0.747628i
$50$	0.841254	−	0.540641i	0.118971	−	0.0764582i
$51$	0.882589	+	6.13854i	0.123587	+	0.859568i
$52$	−3.20116	−	2.05726i	−0.443921	−	0.285291i
$53$	−3.39538	+	7.43485i	−0.466392	+	1.02126i	0.519592	+	0.854414i	$0.326084\pi$
$53$	−3.39538	+	7.43485i	−0.466392	+	1.02126i	−0.985984	+	0.166841i	$0.946643\pi$
$54$	0.654861	−	0.755750i	0.0891153	−	0.102844i
$55$	0.291413	−	2.02682i	0.0392941	−	0.273297i
$56$	−0.113936	−	0.249486i	−0.0152254	−	0.0333389i
$57$	2.20331	+	0.646951i	0.291836	+	0.0856908i
$58$	−6.97654	−	2.04850i	−0.916065	−	0.268981i
$59$	4.77077	+	10.4465i	0.621102	+	1.36002i	0.914715	+	0.404099i	$0.132415\pi$
$59$	4.77077	+	10.4465i	0.621102	+	1.36002i	−0.293613	+	0.955924i	$0.594858\pi$
$60$	0.142315	−	0.989821i	0.0183728	−	0.127785i
$61$	0.404404	−	0.466707i	0.0517786	−	0.0597557i	−0.729269	−	0.684227i	$-0.760140\pi$
$61$	0.404404	−	0.466707i	0.0517786	−	0.0597557i	0.781048	+	0.624471i	$0.214685\pi$
$62$	−2.74180	+	6.00371i	−0.348209	+	0.762472i
$63$	−0.230732	−	0.148282i	−0.0290694	−	0.0186818i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−3.20116	+	2.05726i	−0.397055	+	0.255172i
$66$	−1.34094	−	1.54752i	−0.165058	−	0.190487i
$67$	3.00834	−	0.883328i	0.367527	−	0.107916i	−0.0927537	−	0.995689i	$-0.529567\pi$
$67$	3.00834	−	0.883328i	0.367527	−	0.107916i	0.460281	+	0.887773i	$0.347749\pi$
$68$	6.20167			0.752062
$69$	−2.99358	+	3.74680i	−0.360384	+	0.451061i
$70$	−0.274271			−0.0327817
$71$	15.6810	−	4.60436i	1.86099	−	0.546437i	0.861759	−	0.507318i	$-0.169363\pi$
$71$	15.6810	−	4.60436i	1.86099	−	0.546437i	0.999235	−	0.0391186i	$-0.0124550\pi$
$72$	−0.654861	−	0.755750i	−0.0771761	−	0.0890659i
$73$	−5.48570	+	3.52544i	−0.642053	+	0.412622i	−0.820754	−	0.571281i	$-0.806447\pi$
$73$	−5.48570	+	3.52544i	−0.642053	+	0.412622i	0.178702	+	0.983903i	$0.442810\pi$
$74$	1.53396	+	10.6689i	0.178319	+	1.24024i
$75$	−0.841254	−	0.540641i	−0.0971396	−	0.0624278i
$76$	0.953931	−	2.08882i	0.109423	−	0.239604i
$77$	−0.367780	+	0.424441i	−0.0419124	+	0.0483695i
$78$	−0.541540	+	3.76649i	−0.0613173	+	0.426472i
$79$	−1.75046	−	3.83297i	−0.196942	−	0.431243i	0.785236	−	0.619197i	$-0.212542\pi$
$79$	−1.75046	−	3.83297i	−0.196942	−	0.431243i	−0.982178	+	0.187954i	$0.939814\pi$
$80$	−0.959493	−	0.281733i	−0.107275	−	0.0314987i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	3.84265	+	8.41423i	0.424350	+	0.929197i
$83$	−1.09141	+	7.59096i	−0.119798	+	0.833216i	0.837979	+	0.545703i	$0.183737\pi$
$83$	−1.09141	+	7.59096i	−0.119798	+	0.833216i	−0.957777	+	0.287512i	$0.907172\pi$
$84$	−0.179609	+	0.207280i	−0.0195970	+	0.0226161i
$85$	2.57626	−	5.64123i	0.279435	−	0.611878i
$86$	−9.01618	−	5.79435i	−0.972240	−	0.624821i
$87$	1.03478	+	7.19706i	0.110940	+	0.771606i
$88$	−1.72261	+	1.10705i	−0.183630	+	0.118012i
$89$	−10.2662	−	11.8478i	−1.08822	−	1.25587i	−0.964651	−	0.263533i	$-0.915112\pi$
$89$	−10.2662	−	11.8478i	−1.08822	−	1.25587i	−0.123566	−	0.992336i	$-0.539433\pi$
$90$	−0.959493	+	0.281733i	−0.101139	+	0.0296972i
$91$	1.04366			0.109406
$92$	3.28263	+	3.49633i	0.342238	+	0.364518i
$93$	6.60016			0.684404
$94$	9.53251	−	2.79900i	0.983204	−	0.288695i
$95$	−1.50378	−	1.73545i	−0.154284	−	0.178054i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	0.334081	+	2.32358i	0.0339207	+	0.235924i	0.999728	−	0.0233386i	$-0.00742959\pi$
$97$	0.334081	+	2.32358i	0.0339207	+	0.235924i	−0.965807	+	0.259263i	$0.916521\pi$
$98$	−5.82549	−	3.74382i	−0.588464	−	0.378183i
$99$	−0.850631	+	1.86262i	−0.0854916	+	0.187200i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	−0.895173	+	6.22607i	−0.0890731	+	0.619517i	0.895568	+	0.444925i	$0.146770\pi$
$101$	−0.895173	+	6.22607i	−0.0890731	+	0.619517i	−0.984641	+	0.174592i	$0.944139\pi$
$102$	−2.57626	−	5.64123i	−0.255088	−	0.558565i
$103$	−5.60118	−	1.64465i	−0.551901	−	0.162053i	−0.00612075	−	0.999981i	$-0.501948\pi$
$103$	−5.60118	−	1.64465i	−0.551901	−	0.162053i	−0.545780	+	0.837929i	$0.683766\pi$
$104$	3.65109	+	1.07206i	0.358019	+	0.105124i
$105$	0.113936	+	0.249486i	0.0111191	+	0.0243473i
$106$	1.16321	−	8.09028i	0.112981	−	0.785797i
$107$	5.20518	−	6.00710i	0.503204	−	0.580728i	−0.446142	−	0.894962i	$-0.647202\pi$
$107$	5.20518	−	6.00710i	0.503204	−	0.580728i	0.949346	+	0.314234i	$0.101748\pi$
$108$	−0.415415	+	0.909632i	−0.0399733	+	0.0875294i
$109$	9.02871	+	5.80240i	0.864793	+	0.555769i	0.896156	−	0.443739i	$-0.146348\pi$
$109$	9.02871	+	5.80240i	0.864793	+	0.555769i	−0.0313626	+	0.999508i	$0.509985\pi$
$110$	0.291413	+	2.02682i	0.0277851	+	0.193250i
$111$	9.06756	−	5.82737i	0.860655	−	0.553109i
$112$	0.179609	+	0.207280i	0.0169715	+	0.0195862i
$113$	−2.04365	+	0.600069i	−0.192250	+	0.0564497i	−0.376440	−	0.926441i	$-0.622852\pi$
$113$	−2.04365	+	0.600069i	−0.192250	+	0.0564497i	0.184190	+	0.982891i	$0.441034\pi$
$114$	−2.29633			−0.215071
$115$	4.54403	−	1.53356i	0.423733	−	0.143005i
$116$	7.27107			0.675102
$117$	3.65109	−	1.07206i	0.337543	−	0.0991116i
$118$	−7.52065	−	8.67930i	−0.692332	−	0.798994i
$119$	−1.43092	+	0.919597i	−0.131172	+	0.0842993i
$120$	0.142315	+	0.989821i	0.0129915	+	0.0903579i
$121$	−5.72647	−	3.68018i	−0.520588	−	0.334562i
$122$	−0.256536	+	0.561736i	−0.0232257	+	0.0508572i
$123$	6.05756	−	6.99080i	0.546192	−	0.630339i
$124$	0.939300	−	6.53298i	0.0843516	−	0.586679i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	0.263161	+	0.0772711i	0.0234443	+	0.00688386i
$127$	−7.01784	−	2.06062i	−0.622733	−	0.182851i	−0.0448807	−	0.998992i	$-0.514291\pi$
$127$	−7.01784	−	2.06062i	−0.622733	−	0.182851i	−0.577852	+	0.816142i	$0.696109\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	−1.52527	+	10.6085i	−0.134292	+	0.934024i
$130$	2.49189	−	2.87580i	0.218553	−	0.252224i
$131$	4.91829	−	10.7696i	0.429713	−	0.940941i	−0.563660	−	0.826007i	$-0.690607\pi$
$131$	4.91829	−	10.7696i	0.429713	−	0.940941i	0.993373	−	0.114934i	$-0.0366657\pi$
$132$	1.72261	+	1.10705i	0.149934	+	0.0963564i
$133$	0.0896324	+	0.623407i	0.00777212	+	0.0540562i
$134$	−2.63762	+	1.69509i	−0.227855	+	0.146434i
$135$	0.654861	+	0.755750i	0.0563614	+	0.0650446i
$136$	−5.95045	+	1.74721i	−0.510247	+	0.149822i
$137$	−1.26942			−0.108454			−0.0542269	−	0.998529i	$-0.517269\pi$
$137$	−1.26942			−0.108454			−0.0542269	+	0.998529i	$0.517269\pi$
$138$	1.81672	−	4.43841i	0.154650	−	0.377823i
$139$	−19.8716			−1.68549			−0.842744	−	0.538315i	$-0.819061\pi$
$139$	−19.8716			−1.68549			−0.842744	+	0.538315i	$0.819061\pi$
$140$	0.263161	−	0.0772711i	0.0222412	−	0.00653060i
$141$	−6.50601	−	7.50833i	−0.547905	−	0.632316i
$142$	−13.7486	+	8.83570i	−1.15376	+	0.741476i
$143$	−1.10889	−	7.71252i	−0.0927303	−	0.644953i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	3.02051	−	6.61400i	0.250840	−	0.549263i
$146$	4.27026	−	4.92814i	0.353409	−	0.407856i
$147$	−0.985498	+	6.85429i	−0.0812825	+	0.565332i
$148$	−4.47761	−	9.80459i	−0.368057	−	0.805932i
$149$	−20.2231	−	5.93803i	−1.65674	−	0.486462i	−0.686201	−	0.727412i	$-0.740723\pi$
$149$	−20.2231	−	5.93803i	−1.65674	−	0.486462i	−0.970538	+	0.240950i	$0.922541\pi$
$150$	0.959493	+	0.281733i	0.0783423	+	0.0230034i
$151$	−7.07600	−	15.4943i	−0.575836	−	1.26091i	−0.943631	−	0.330999i	$-0.892614\pi$
$151$	−7.07600	−	15.4943i	−0.575836	−	1.26091i	0.367795	−	0.929907i	$-0.380113\pi$
$152$	−0.326802	+	2.27296i	−0.0265072	+	0.184361i
$153$	−4.06123	+	4.68691i	−0.328331	+	0.378914i
$154$	0.233303	−	0.510863i	0.0188001	−	0.0411665i
$155$	−5.55240	−	3.56831i	−0.445980	−	0.286614i
$156$	−0.541540	−	3.76649i	−0.0433579	−	0.301561i
$157$	−17.1761	+	11.0384i	−1.37080	+	0.880961i	−0.998881	−	0.0473030i	$-0.984937\pi$
$157$	−17.1761	+	11.0384i	−1.37080	+	0.880961i	−0.371922	+	0.928264i	$0.621301\pi$
$158$	2.75943	+	3.18455i	0.219528	+	0.253349i
$159$	−7.84239	+	2.30273i	−0.621942	+	0.182619i
$160$	1.00000			0.0790569
$161$	−1.27585	−	0.319959i	−0.100551	−	0.0252163i
$162$	1.00000			0.0785674
$163$	1.45761	−	0.427992i	0.114169	−	0.0335229i	−0.224149	−	0.974555i	$-0.571960\pi$
$163$	1.45761	−	0.427992i	0.114169	−	0.0335229i	0.338318	+	0.941032i	$0.390142\pi$
$164$	−6.05756	−	6.99080i	−0.473016	−	0.545890i
$165$	1.72261	−	1.10705i	0.134105	−	0.0861838i
$166$	−1.09141	−	7.59096i	−0.0847102	−	0.589172i
$167$	11.6654	+	7.49687i	0.902692	+	0.580125i	0.907587	−	0.419863i	$-0.137922\pi$
$167$	11.6654	+	7.49687i	0.902692	+	0.580125i	−0.00489549	+	0.999988i	$0.501558\pi$
$168$	0.113936	−	0.249486i	0.00879038	−	0.0192483i
$169$	−0.969028	+	1.11832i	−0.0745406	+	0.0860245i
$170$	−0.882589	+	6.13854i	−0.0676915	+	0.470805i
$171$	0.953931	+	2.08882i	0.0729489	+	0.159736i
$172$	10.2834	+	3.01949i	0.784104	+	0.230234i
$173$	−11.9166	−	3.49904i	−0.906005	−	0.266027i	−0.204647	−	0.978836i	$-0.565605\pi$
$173$	−11.9166	−	3.49904i	−0.906005	−	0.266027i	−0.701358	+	0.712809i	$0.747423\pi$
$174$	−3.02051	−	6.61400i	−0.228984	−	0.501406i
$175$	0.0390329	−	0.271480i	0.00295061	−	0.0205219i
$176$	1.34094	−	1.54752i	0.101077	−	0.116649i
$177$	−4.77077	+	10.4465i	−0.358593	+	0.785210i
$178$	13.1883	+	8.47560i	0.988504	+	0.635273i
$179$	1.80004	+	12.5196i	0.134541	+	0.935755i	0.939530	+	0.342466i	$0.111262\pi$
$179$	1.80004	+	12.5196i	0.134541	+	0.935755i	−0.804989	+	0.593290i	$0.797829\pi$
$180$	0.841254	−	0.540641i	0.0627033	−	0.0402970i
$181$	−9.56843	−	11.0426i	−0.711216	−	0.820787i	0.279006	−	0.960289i	$-0.409995\pi$
$181$	−9.56843	−	11.0426i	−0.711216	−	0.820787i	−0.990222	+	0.139502i	$0.955450\pi$
$182$	−1.00139	+	0.294034i	−0.0742278	+	0.0217953i
$183$	0.617542			0.0456500
$184$	−4.13469	−	2.42988i	−0.304813	−	0.179133i
$185$	−10.7786			−0.792461
$186$	−6.33280	+	1.85948i	−0.464344	+	0.136344i
$187$	8.31603	+	9.59721i	0.608128	+	0.701818i
$188$	−8.35781	+	5.37124i	−0.609556	+	0.391738i
$189$	−0.0390329	−	0.271480i	−0.00283922	−	0.0197472i
$190$	1.93180	+	1.24149i	0.140147	+	0.0900672i
$191$	5.65500	−	12.3827i	0.409181	−	0.895982i	−0.587075	−	0.809533i	$-0.699721\pi$
$191$	5.65500	−	12.3827i	0.409181	−	0.895982i	0.996256	−	0.0864496i	$-0.0275521\pi$
$192$	0.654861	−	0.755750i	0.0472605	−	0.0545415i
$193$	0.0339154	−	0.235887i	0.00244129	−	0.0169795i	−0.988564	−	0.150799i	$-0.951815\pi$
$193$	0.0339154	−	0.235887i	0.00244129	−	0.0169795i	0.991006	+	0.133820i	$0.0427243\pi$
$194$	−0.975176	−	2.13534i	−0.0700136	−	0.153308i
$195$	−3.65109	−	1.07206i	−0.261460	−	0.0767715i
$196$	6.64427	+	1.95093i	0.474591	+	0.139352i
$197$	−9.29138	−	20.3453i	−0.661984	−	1.44954i	−0.880662	−	0.473745i	$-0.842902\pi$
$197$	−9.29138	−	20.3453i	−0.661984	−	1.44954i	0.218679	−	0.975797i	$-0.429825\pi$
$198$	0.291413	−	2.02682i	0.0207098	−	0.144040i
$199$	8.08171	−	9.32679i	0.572897	−	0.661159i	−0.393165	−	0.919468i	$-0.628620\pi$
$199$	8.08171	−	9.32679i	0.572897	−	0.661159i	0.966062	+	0.258309i	$0.0831654\pi$
$200$	0.415415	−	0.909632i	0.0293743	−	0.0643207i
$201$	2.63762	+	1.69509i	0.186043	+	0.119563i
$202$	−0.895173	−	6.22607i	−0.0629842	−	0.438064i
$203$	−1.67767	+	1.07817i	−0.117749	+	0.0756727i
$204$	4.06123	+	4.68691i	0.284343	+	0.328149i
$205$	−8.87546	+	2.60607i	−0.619889	+	0.182016i
$206$	5.83764			0.406728
$207$	−4.79202	+	0.191236i	−0.333068	+	0.0132918i
$208$	−3.80523			−0.263845
$209$	4.51165	−	1.32474i	0.312077	−	0.0916342i
$210$	−0.179609	−	0.207280i	−0.0123942	−	0.0143037i
$211$	−10.8165	+	6.95136i	−0.744640	+	0.478551i	−0.857129	−	0.515102i	$-0.827754\pi$
$211$	−10.8165	+	6.95136i	−0.744640	+	0.478551i	0.112489	+	0.993653i	$0.464118\pi$
$212$	1.16321	+	8.09028i	0.0798893	+	0.555642i
$213$	13.7486	+	8.83570i	0.942040	+	0.605412i
$214$	−3.30194	+	7.23024i	−0.225716	+	0.494249i
$215$	7.01851	−	8.09979i	0.478658	−	0.552401i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	0.751998	+	1.64665i	0.0510489	+	0.111782i
$218$	−10.2977	−	3.02368i	−0.697449	−	0.204789i
$219$	−6.25672	−	1.83714i	−0.422790	−	0.124142i
$220$	−0.850631	−	1.86262i	−0.0573495	−	0.125578i
$221$	3.35845	−	23.3585i	0.225914	−	1.57127i
$222$	−7.05850	+	8.14595i	−0.473736	+	0.546720i
$223$	1.68262	−	3.68443i	0.112677	−	0.246728i	−0.844889	−	0.534941i	$-0.820334\pi$
$223$	1.68262	−	3.68443i	0.112677	−	0.246728i	0.957566	+	0.288213i	$0.0930611\pi$
$224$	−0.230732	−	0.148282i	−0.0154164	−	0.00990752i
$225$	−0.142315	−	0.989821i	−0.00948766	−	0.0659881i
$226$	1.79181	−	1.15152i	0.119189	−	0.0765982i
$227$	−9.95784	−	11.4920i	−0.660925	−	0.762748i	0.322003	−	0.946739i	$-0.395644\pi$
$227$	−9.95784	−	11.4920i	−0.660925	−	0.762748i	−0.982928	+	0.183990i	$0.941098\pi$
$228$	2.20331	−	0.646951i	0.145918	−	0.0428454i
$229$	4.77938			0.315831			0.157915	−	0.987453i	$-0.449523\pi$
$229$	4.77938			0.315831			0.157915	+	0.987453i	$0.449523\pi$
$230$	−3.92791	+	2.75164i	−0.258999	+	0.181438i
$231$	−0.561615			−0.0369516
$232$	−6.97654	+	2.04850i	−0.458032	+	0.134490i
$233$	13.7419	+	15.8590i	0.900260	+	1.03895i	0.999038	+	0.0438454i	$0.0139609\pi$
$233$	13.7419	+	15.8590i	0.900260	+	1.03895i	−0.0987788	+	0.995109i	$0.531494\pi$
$234$	−3.20116	+	2.05726i	−0.209266	+	0.134487i
$235$	1.41389	+	9.83383i	0.0922321	+	0.641488i
$236$	9.66125	+	6.20891i	0.628894	+	0.404166i
$237$	1.75046	−	3.83297i	0.113705	−	0.248978i
$238$	1.11388	−	1.28548i	0.0722020	−	0.0833255i
$239$	−0.842849	+	5.86215i	−0.0545194	+	0.379191i	0.944234	+	0.329275i	$0.106804\pi$
$239$	−0.842849	+	5.86215i	−0.0545194	+	0.379191i	−0.998753	+	0.0499156i	$0.984105\pi$
$240$	−0.415415	−	0.909632i	−0.0268149	−	0.0587165i
$241$	−3.63866	−	1.06841i	−0.234387	−	0.0688222i	0.162430	−	0.986720i	$-0.448067\pi$
$241$	−3.63866	−	1.06841i	−0.234387	−	0.0688222i	−0.396817	+	0.917898i	$0.629885\pi$
$242$	6.53134	+	1.91777i	0.419850	+	0.123279i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	0.0878854	−	0.611256i	0.00562629	−	0.0391317i
$245$	4.53476	−	5.23340i	0.289715	−	0.334349i
$246$	−3.84265	+	8.41423i	−0.244999	+	0.536472i
$247$	−7.35093	−	4.72415i	−0.467728	−	0.300591i
$248$	0.939300	+	6.53298i	0.0596456	+	0.414844i
$249$	−6.45159	+	4.14618i	−0.408853	+	0.262754i
$250$	−0.654861	−	0.755750i	−0.0414170	−	0.0477978i
$251$	−0.177345	+	0.0520733i	−0.0111939	+	0.00328684i	−0.287325	−	0.957833i	$-0.592766\pi$
$251$	−0.177345	+	0.0520733i	−0.0111939	+	0.00328684i	0.276131	+	0.961120i	$0.410948\pi$
$252$	−0.274271			−0.0172775
$253$	−1.00886	+	9.76830i	−0.0634262	+	0.614127i
$254$	7.31412			0.458928
$255$	5.95045	−	1.74721i	0.372632	−	0.109415i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−17.7089	+	11.3808i	−1.10465	+	0.709917i	−0.960121	−	0.279583i	$-0.909804\pi$
$257$	−17.7089	+	11.3808i	−1.10465	+	0.709917i	−0.144531	+	0.989500i	$0.546167\pi$
$258$	−1.52527	−	10.6085i	−0.0949590	−	0.660454i
$259$	2.48697	+	1.59828i	0.154533	+	0.0993122i
$260$	−1.58075	+	3.46136i	−0.0980338	+	0.214664i
$261$	−4.76154	+	5.49511i	−0.294732	+	0.340139i
$262$	−1.68493	+	11.7190i	−0.104095	+	0.724000i
$263$	−8.62142	−	18.8783i	−0.531619	−	1.16408i	−0.964850	−	0.262801i	$-0.915354\pi$
$263$	−8.62142	−	18.8783i	−0.531619	−	1.16408i	0.433231	−	0.901283i	$-0.357374\pi$
$264$	−1.96472	−	0.576894i	−0.120920	−	0.0355054i
$265$	7.84239	+	2.30273i	0.481754	+	0.141456i
$266$	−0.261636	−	0.572902i	−0.0160419	−	0.0351269i
$267$	2.23106	−	15.5174i	0.136539	−	0.949648i
$268$	2.05321	−	2.36953i	0.125420	−	0.144742i
$269$	−6.08869	+	13.3324i	−0.371234	+	0.812889i	0.628160	+	0.778084i	$0.283808\pi$
$269$	−6.08869	+	13.3324i	−0.371234	+	0.812889i	−0.999394	+	0.0348051i	$0.988919\pi$
$270$	−0.841254	−	0.540641i	−0.0511971	−	0.0329024i
$271$	3.65124	+	25.3949i	0.221797	+	1.54263i	0.731236	+	0.682124i	$0.238944\pi$
$271$	3.65124	+	25.3949i	0.221797	+	1.54263i	−0.509440	+	0.860506i	$0.670147\pi$
$272$	5.21717	−	3.35287i	0.316338	−	0.203298i
$273$	0.683455	+	0.788749i	0.0413646	+	0.0477372i
$274$	1.21800	−	0.357637i	0.0735820	−	0.0216056i
$275$	−2.04766			−0.123479
$276$	−0.492686	+	4.77046i	−0.0296562	+	0.287148i
$277$	20.7111			1.24441			0.622206	−	0.782853i	$-0.286237\pi$
$277$	20.7111			1.24441			0.622206	+	0.782853i	$0.286237\pi$
$278$	19.0667	−	5.59848i	1.14354	−	0.335774i
$279$	4.32218	+	4.98807i	0.258762	+	0.298628i
$280$	−0.230732	+	0.148282i	−0.0137889	+	0.00886156i
$281$	0.835093	+	5.80820i	0.0498175	+	0.346488i	0.999451	+	0.0331261i	$0.0105463\pi$
$281$	0.835093	+	5.80820i	0.0498175	+	0.346488i	−0.949634	+	0.313362i	$0.898545\pi$
$282$	8.35781	+	5.37124i	0.497700	+	0.319853i
$283$	7.15024	−	15.6568i	0.425038	−	0.930702i	−0.569069	−	0.822290i	$-0.692696\pi$
$283$	7.15024	−	15.6568i	0.425038	−	0.930702i	0.994106	−	0.108412i	$-0.0345766\pi$
$284$	10.7024	−	12.3512i	0.635071	−	0.732910i
$285$	0.326802	−	2.27296i	0.0193581	−	0.134638i
$286$	3.23684	+	7.08770i	0.191398	+	0.419104i
$287$	2.43428	+	0.714770i	0.143691	+	0.0421915i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	8.91508	+	19.5213i	0.524416	+	1.14831i
$290$	−1.03478	+	7.19706i	−0.0607645	+	0.422626i
$291$	−1.53727	+	1.77410i	−0.0901163	+	0.104000i
$292$	−2.70886	+	5.93159i	−0.158524	+	0.347120i
$293$	−27.0749	−	17.4000i	−1.58173	−	1.01652i	−0.975164	−	0.221485i	$-0.928910\pi$
$293$	−27.0749	−	17.4000i	−1.58173	−	1.01652i	−0.606568	−	0.795032i	$-0.707454\pi$
$294$	−0.985498	−	6.85429i	−0.0574754	−	0.399750i
$295$	9.66125	−	6.20891i	0.562500	−	0.361497i
$296$	7.05850	+	8.14595i	0.410267	+	0.473473i
$297$	−1.96472	+	0.576894i	−0.114005	+	0.0334748i
$298$	21.0768			1.22095
$299$	14.9466	−	10.4706i	0.864384	−	0.605531i
$300$	−1.00000			−0.0577350
$301$	−2.82045	+	0.828158i	−0.162568	+	0.0477342i
$302$	11.1546	+	12.8731i	0.641876	+	0.740764i
$303$	−5.29156	+	3.40068i	−0.303992	+	0.195364i
$304$	−0.326802	−	2.27296i	−0.0187434	−	0.130363i
$305$	−0.519509	−	0.333868i	−0.0297470	−	0.0191172i
$306$	2.57626	−	5.64123i	0.147275	−	0.322488i
$307$	5.13859	−	5.93024i	0.293275	−	0.338457i	−0.589922	−	0.807460i	$-0.700841\pi$
$307$	5.13859	−	5.93024i	0.293275	−	0.338457i	0.883196	+	0.469004i	$0.155387\pi$
$308$	−0.0799262	+	0.555899i	−0.00455422	+	0.0316753i
$309$	−2.42505	−	5.31011i	−0.137956	−	0.302081i
$310$	6.33280	+	1.85948i	0.359679	+	0.105611i
$311$	18.4959	+	5.43089i	1.04881	+	0.307958i	0.760335	−	0.649531i	$-0.225035\pi$
$311$	18.4959	+	5.43089i	1.04881	+	0.307958i	0.288472	+	0.957488i	$0.406853\pi$
$312$	1.58075	+	3.46136i	0.0894922	+	0.195961i
$313$	1.58148	−	10.9994i	0.0893906	−	0.621726i	−0.895044	−	0.445977i	$-0.852856\pi$
$313$	1.58148	−	10.9994i	0.0893906	−	0.621726i	0.984435	−	0.175749i	$-0.0562346\pi$
$314$	13.3705	−	15.4303i	0.754539	−	0.870785i
$315$	−0.113936	+	0.249486i	−0.00641959	+	0.0140569i
$316$	−3.54484	−	2.27813i	−0.199413	−	0.128155i
$317$	2.79910	+	19.4682i	0.157213	+	1.09344i	0.903739	+	0.428085i	$0.140812\pi$
$317$	2.79910	+	19.4682i	0.157213	+	1.09344i	−0.746525	+	0.665357i	$0.768279\pi$
$318$	6.87596	−	4.41891i	0.385585	−	0.247800i
$319$	9.75004	+	11.2521i	0.545897	+	0.629999i
$320$	−0.959493	+	0.281733i	−0.0536373	+	0.0157493i
$321$	7.94853			0.443644
$322$	1.31431	−	0.0524504i	0.0732438	−	0.00292295i
$323$	14.2411			0.792395
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	2.49189	+	2.87580i	0.138225	+	0.159521i
$326$	−1.27798	+	0.821311i	−0.0707810	+	0.0454882i
$327$	1.52739	+	10.6232i	0.0844647	+	0.587465i
$328$	7.78172	+	5.00101i	0.429674	+	0.276135i
$329$	1.13195	−	2.47863i	0.0624065	−	0.136651i
$330$	−1.34094	+	1.54752i	−0.0738160	+	0.0851883i
$331$	−1.96312	+	13.6538i	−0.107903	+	0.750480i	0.861986	+	0.506932i	$0.169220\pi$
$331$	−1.96312	+	13.6538i	−0.107903	+	0.750480i	−0.969889	+	0.243548i	$0.921689\pi$
$332$	3.18582	+	6.97598i	0.174845	+	0.382857i
$333$	10.3420	+	3.03669i	0.566739	+	0.166410i
$334$	−13.3049	−	3.90668i	−0.728014	−	0.213764i
$335$	−1.30247	−	2.85201i	−0.0711614	−	0.155822i
$336$	−0.0390329	+	0.271480i	−0.00212942	+	0.0148104i
$337$	2.99081	−	3.45157i	0.162920	−	0.188019i	−0.668420	−	0.743784i	$-0.733029\pi$
$337$	2.99081	−	3.45157i	0.162920	−	0.188019i	0.831340	+	0.555765i	$0.187575\pi$
$338$	0.614709	−	1.34603i	0.0334358	−	0.0732141i
$339$	−1.79181	−	1.15152i	−0.0973175	−	0.0625422i
$340$	−0.882589	−	6.13854i	−0.0478651	−	0.332909i
$341$	11.3695	−	7.30671i	0.615691	−	0.395681i
$342$	−1.50378	−	1.73545i	−0.0813150	−	0.0938425i
$343$	−3.66446	+	1.07598i	−0.197862	+	0.0580976i
$344$	−10.7176			−0.577852
$345$	4.13469	+	2.42988i	0.222604	+	0.130820i
$346$	12.4197			0.667688
$347$	6.45467	−	1.89526i	0.346505	−	0.101743i	−0.103849	−	0.994593i	$-0.533116\pi$
$347$	6.45467	−	1.89526i	0.346505	−	0.101743i	0.450354	+	0.892850i	$0.351298\pi$
$348$	4.76154	+	5.49511i	0.255245	+	0.294569i
$349$	−19.5020	+	12.5332i	−1.04392	+	0.670886i	−0.945953	−	0.324304i	$-0.894870\pi$
$349$	−19.5020	+	12.5332i	−1.04392	+	0.670886i	−0.0979654	+	0.995190i	$0.531233\pi$
$350$	0.0390329	+	0.271480i	0.00208639	+	0.0145112i
$351$	3.20116	+	2.05726i	0.170865	+	0.109808i
$352$	−0.850631	+	1.86262i	−0.0453388	+	0.0992780i
$353$	−17.0581	+	19.6861i	−0.907913	+	1.04779i	0.0907390	+	0.995875i	$0.471077\pi$
$353$	−17.0581	+	19.6861i	−0.907913	+	1.04779i	−0.998652	+	0.0519123i	$0.983468\pi$
$354$	1.63439	−	11.3675i	0.0868671	−	0.604174i
$355$	−6.78913	−	14.8661i	−0.360330	−	0.789012i
$356$	−15.0419	−	4.41671i	−0.797220	−	0.234085i
$357$	−1.63204	−	0.479210i	−0.0863766	−	0.0253625i
$358$	−5.25429	−	11.5053i	−0.277698	−	0.608074i
$359$	1.95760	−	13.6154i	0.103318	−	0.718592i	−0.870649	−	0.491904i	$-0.836301\pi$
$359$	1.95760	−	13.6154i	0.103318	−	0.718592i	0.973967	−	0.226688i	$-0.0727898\pi$
$360$	−0.654861	+	0.755750i	−0.0345142	+	0.0398315i
$361$	−5.70234	+	12.4864i	−0.300123	+	0.657178i
$362$	12.2919	+	7.89952i	0.646048	+	0.415190i
$363$	−0.968747	−	6.73778i	−0.0508460	−	0.353642i
$364$	0.877986	−	0.564247i	0.0460190	−	0.0295746i
$365$	4.27026	+	4.92814i	0.223515	+	0.257951i
$366$	−0.592527	+	0.173982i	−0.0309719	+	0.00909417i
$367$	4.69407			0.245028			0.122514	−	0.992467i	$-0.460904\pi$
$367$	4.69407			0.245028			0.122514	+	0.992467i	$0.460904\pi$
$368$	4.65178	+	1.16658i	0.242491	+	0.0608121i
$369$	9.25015			0.481544
$370$	10.3420	−	3.03669i	0.537656	−	0.157870i
$371$	−1.46803	−	1.69420i	−0.0762164	−	0.0879585i
$372$	5.55240	−	3.56831i	0.287879	−	0.185008i
$373$	2.41541	+	16.7996i	0.125065	+	0.869849i	0.951682	+	0.307084i	$0.0993532\pi$
$373$	2.41541	+	16.7996i	0.125065	+	0.869849i	−0.826617	+	0.562765i	$0.809738\pi$
$374$	−10.6830	−	6.86556i	−0.552406	−	0.355010i
$375$	−0.415415	+	0.909632i	−0.0214519	+	0.0469732i
$376$	6.50601	−	7.50833i	0.335522	−	0.387213i
$377$	3.93758	−	27.3865i	0.202796	−	1.41047i
$378$	0.113936	+	0.249486i	0.00586025	+	0.0128322i
$379$	25.2732	+	7.42087i	1.29820	+	0.381185i	0.856578	−	0.516018i	$-0.172586\pi$
$379$	25.2732	+	7.42087i	1.29820	+	0.381185i	0.441618	+	0.897203i	$0.354405\pi$
$380$	−2.20331	−	0.646951i	−0.113028	−	0.0331879i
$381$	−3.03839	−	6.65315i	−0.155662	−	0.340851i
$382$	−1.93732	+	13.4743i	−0.0991217	+	0.689407i
$383$	−5.77686	+	6.66685i	−0.295184	+	0.340660i	−0.883897	−	0.467682i	$-0.845089\pi$
$383$	−5.77686	+	6.66685i	−0.295184	+	0.340660i	0.588713	+	0.808342i	$0.299635\pi$
$384$	−0.415415	+	0.909632i	−0.0211991	+	0.0464195i
$385$	0.472461	+	0.303632i	0.0240788	+	0.0154745i
$386$	0.0339154	+	0.235887i	0.00172625	+	0.0120063i
$387$	−9.01618	+	5.79435i	−0.458318	+	0.294543i
$388$	1.53727	+	1.77410i	0.0780430	+	0.0900664i
$389$	−23.6974	+	6.95819i	−1.20151	+	0.352794i	−0.820429	−	0.571748i	$-0.806265\pi$
$389$	−23.6974	+	6.95819i	−1.20151	+	0.352794i	−0.381078	+	0.924543i	$0.624447\pi$
$390$	3.80523			0.192685
$391$	−11.2667	+	27.5256i	−0.569782	+	1.39203i
$392$	−6.92478			−0.349754
$393$	11.3599	−	3.33556i	0.573031	−	0.168257i
$394$	14.6469	+	16.9035i	0.737902	+	0.851585i
$395$	−3.54484	+	2.27813i	−0.178360	+	0.114625i
$396$	0.291413	+	2.02682i	0.0146441	+	0.101852i
$397$	15.3031	+	9.83473i	0.768042	+	0.493591i	0.865046	−	0.501693i	$-0.167289\pi$
$397$	15.3031	+	9.83473i	0.768042	+	0.493591i	−0.0970034	+	0.995284i	$0.530926\pi$
$398$	−5.12668	+	11.2259i	−0.256977	+	0.562702i
$399$	−0.412443	+	0.475984i	−0.0206480	+	0.0238290i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	2.56097	+	5.60774i	0.127889	+	0.280037i	0.962735	−	0.270445i	$-0.0871710\pi$
$401$	2.56097	+	5.60774i	0.127889	+	0.280037i	−0.834847	+	0.550483i	$0.814444\pi$
$402$	−3.00834	−	0.883328i	−0.150042	−	0.0440564i
$403$	−24.0978	−	7.07574i	−1.20039	−	0.352468i
$404$	2.61300	+	5.72167i	0.130001	+	0.284664i
$405$	−0.142315	+	0.989821i	−0.00707168	+	0.0491846i
$406$	1.30595	−	1.50715i	0.0648134	−	0.0747986i
$407$	9.16863	−	20.0765i	0.454472	−	0.995155i
$408$	−5.21717	−	3.35287i	−0.258289	−	0.165992i
$409$	−1.31074	−	9.11641i	−0.0648120	−	0.450777i	−0.996225	−	0.0868125i	$-0.972332\pi$
$409$	−1.31074	−	9.11641i	−0.0648120	−	0.450777i	0.931413	−	0.363965i	$-0.118577\pi$
$410$	7.78172	−	5.00101i	0.384312	−	0.246982i
$411$	−0.831293	−	0.959363i	−0.0410046	−	0.0473219i
$412$	−5.60118	+	1.64465i	−0.275950	+	0.0810263i
$413$	−3.14983			−0.154993
$414$	4.54403	−	1.53356i	0.223327	−	0.0753702i
$415$	7.66901			0.376457
$416$	3.65109	−	1.07206i	0.179009	−	0.0525619i
$417$	−13.0131	−	15.0180i	−0.637256	−	0.735432i
$418$	−3.95567	+	2.54216i	−0.193478	+	0.124341i
$419$	2.41829	+	16.8196i	0.118141	+	0.821690i	0.959600	+	0.281369i	$0.0907884\pi$
$419$	2.41829	+	16.8196i	0.118141	+	0.821690i	−0.841459	+	0.540322i	$0.818303\pi$
$420$	0.230732	+	0.148282i	0.0112585	+	0.00723543i
$421$	−5.70409	+	12.4902i	−0.278000	+	0.608736i	−0.996199	−	0.0871019i	$-0.972239\pi$
$421$	−5.70409	+	12.4902i	−0.278000	+	0.608736i	0.718199	+	0.695838i	$0.244967\pi$
$422$	8.41995	−	9.71714i	0.409877	−	0.473023i
$423$	1.41389	−	9.83383i	0.0687457	−	0.478137i
$424$	−3.39538	−	7.43485i	−0.164894	−	0.361068i
$425$	−5.95045	−	1.74721i	−0.288639	−	0.0847522i
$426$	−15.6810	−	4.60436i	−0.759747	−	0.223082i
$427$	0.0703605	+	0.154068i	0.00340498	+	0.00745587i
$428$	1.13119	−	7.86763i	0.0546783	−	0.380296i
$429$	5.10256	−	5.88867i	0.246354	−	0.284308i
$430$	−4.45223	+	9.74903i	−0.214706	+	0.470140i
$431$	17.3533	+	11.1523i	0.835877	+	0.537186i	0.887140	−	0.461500i	$-0.152688\pi$
$431$	17.3533	+	11.1523i	0.835877	+	0.537186i	−0.0512633	+	0.998685i	$0.516325\pi$
$432$	0.142315	+	0.989821i	0.00684713	+	0.0476228i
$433$	30.6423	−	19.6926i	1.47258	−	0.946367i	0.474774	−	0.880108i	$-0.342530\pi$
$433$	30.6423	−	19.6926i	1.47258	−	0.946367i	0.997802	−	0.0662596i	$-0.0211066\pi$
$434$	−1.18545	−	1.36808i	−0.0569034	−	0.0656701i
$435$	6.97654	−	2.04850i	0.334500	−	0.0982180i
$436$	10.7324			0.513991
$437$	7.53801	+	8.02874i	0.360592	+	0.384067i
$438$	6.52086			0.311579
$439$	33.8911	−	9.95131i	1.61753	−	0.474950i	0.657178	−	0.753735i	$-0.271750\pi$
$439$	33.8911	−	9.95131i	1.61753	−	0.474950i	0.960354	+	0.278785i	$0.0899316\pi$
$440$	1.34094	+	1.54752i	0.0639266	+	0.0737752i
$441$	−5.82549	+	3.74382i	−0.277404	+	0.178277i
$442$	3.35845	+	23.3585i	0.159745	+	1.11105i
$443$	5.03410	+	3.23522i	0.239177	+	0.153710i	0.654739	−	0.755855i	$-0.272779\pi$
$443$	5.03410	+	3.23522i	0.239177	+	0.153710i	−0.415562	+	0.909565i	$0.636415\pi$
$444$	4.47761	−	9.80459i	0.212498	−	0.465305i
$445$	−10.2662	+	11.8478i	−0.486665	+	0.561642i
$446$	−0.576442	+	4.00924i	−0.0272953	+	0.189843i
$447$	−8.75563	−	19.1722i	−0.414127	−	0.906812i
$448$	0.263161	+	0.0772711i	0.0124332	+	0.00365072i
$449$	−12.4213	−	3.64722i	−0.586197	−	0.172123i	−0.0248325	−	0.999692i	$-0.507905\pi$
$449$	−12.4213	−	3.64722i	−0.586197	−	0.172123i	−0.561365	+	0.827569i	$0.689723\pi$
$450$	0.415415	+	0.909632i	0.0195829	+	0.0428805i
$451$	2.69562	−	18.7484i	0.126932	−	0.882828i
$452$	−1.39480	+	1.60969i	−0.0656060	+	0.0757134i
$453$	7.07600	−	15.4943i	0.332459	−	0.727984i
$454$	12.7921	+	8.22101i	0.600365	+	0.385831i
$455$	−0.148529	−	1.03304i	−0.00696314	−	0.0484297i
$456$	−1.93180	+	1.24149i	−0.0904647	+	0.0581381i
$457$	−5.55592	−	6.41187i	−0.259895	−	0.299935i	0.610773	−	0.791805i	$-0.290859\pi$
$457$	−5.55592	−	6.41187i	−0.259895	−	0.299935i	−0.870668	+	0.491871i	$0.836313\pi$
$458$	−4.58579	+	1.34651i	−0.214280	+	0.0629182i
$459$	−6.20167			−0.289469
$460$	2.99358	−	3.74680i	0.139576	−	0.174695i
$461$	−33.7883			−1.57368			−0.786839	−	0.617158i	$-0.788284\pi$
$461$	−33.7883			−1.57368			−0.786839	+	0.617158i	$0.788284\pi$
$462$	0.538866	−	0.158225i	0.0250703	−	0.00736131i
$463$	16.3282	+	18.8438i	0.758838	+	0.875746i	0.995394	−	0.0958722i	$-0.0305640\pi$
$463$	16.3282	+	18.8438i	0.758838	+	0.875746i	−0.236556	+	0.971618i	$0.576019\pi$
$464$	6.11682	−	3.93104i	0.283966	−	0.182494i
$465$	−0.939300	−	6.53298i	−0.0435590	−	0.302960i
$466$	−17.6532	−	11.3450i	−0.817769	−	0.525548i
$467$	−9.41944	+	20.6257i	−0.435880	+	0.954443i	0.556457	+	0.830877i	$0.312161\pi$
$467$	−9.41944	+	20.6257i	−0.435880	+	0.954443i	−0.992336	+	0.123567i	$0.960567\pi$
$468$	2.49189	−	2.87580i	0.115188	−	0.132934i
$469$	−0.122381	+	0.851181i	−0.00565105	+	0.0393039i
$470$	−4.12713	−	9.03715i	−0.190370	−	0.416853i
$471$	−19.5902	−	5.75221i	−0.902670	−	0.265048i
$472$	−11.0192	−	3.23552i	−0.507198	−	0.148927i
$473$	9.11668	+	19.9628i	0.419186	+	0.917888i
$474$	−0.599681	+	4.17087i	−0.0275443	+	0.191574i
$475$	−1.50378	+	1.73545i	−0.0689981	+	0.0796280i
$476$	−0.706595	+	1.54723i	−0.0323867	+	0.0709171i
$477$	−6.87596	−	4.41891i	−0.314829	−	0.202328i
$478$	−0.842849	−	5.86215i	−0.0385510	−	0.268128i
$479$	−14.7593	+	9.48521i	−0.674368	+	0.433390i	−0.832498	−	0.554028i	$-0.813090\pi$
$479$	−14.7593	+	9.48521i	−0.674368	+	0.433390i	0.158130	+	0.987418i	$0.449454\pi$
$480$	0.654861	+	0.755750i	0.0298902	+	0.0344951i
$481$	−39.3537	+	11.5553i	−1.79438	+	0.526876i
$482$	3.79227			0.172733
$483$	−0.593696	−	1.17375i	−0.0270141	−	0.0534076i
$484$	−6.80707			−0.309412
$485$	2.25239	−	0.661360i	0.102276	−	0.0300308i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	−2.10969	+	1.35582i	−0.0955993	+	0.0614379i	−0.587567	−	0.809176i	$-0.699914\pi$
$487$	−2.10969	+	1.35582i	−0.0955993	+	0.0614379i	0.491968	+	0.870613i	$0.336278\pi$
$488$	0.0878854	+	0.611256i	0.00397838	+	0.0276703i
$489$	1.27798	+	0.821311i	0.0577925	+	0.0371410i
$490$	−2.87666	+	6.29900i	−0.129954	+	0.284560i
$491$	15.4753	−	17.8594i	0.698389	−	0.805983i	−0.290145	−	0.956983i	$-0.593704\pi$
$491$	15.4753	−	17.8594i	0.698389	−	0.805983i	0.988534	+	0.150999i	$0.0482491\pi$
$492$	1.31643	−	9.15600i	0.0593494	−	0.412784i
$493$	18.7322	+	41.0178i	0.843656	+	1.84735i
$494$	8.38411	+	2.46180i	0.377219	+	0.110761i
$495$	1.96472	+	0.576894i	0.0883076	+	0.0259294i
$496$	−2.74180	−	6.00371i	−0.123111	−	0.269575i
$497$	−0.637915	+	4.43679i	−0.0286144	+	0.199017i
$498$	5.02214	−	5.79585i	0.225047	−	0.259718i
$499$	−7.63864	+	16.7263i	−0.341952	+	0.748771i	−0.999991	−	0.00421277i	$-0.998659\pi$
$499$	−7.63864	+	16.7263i	−0.341952	+	0.748771i	0.658039	+	0.752984i	$0.271386\pi$
$500$	0.841254	+	0.540641i	0.0376220	+	0.0241782i
$501$	1.97343	+	13.7255i	0.0881662	+	0.613210i
$502$	0.155491	−	0.0999279i	0.00693990	−	0.00446000i
$503$	−26.2043	−	30.2414i	−1.16839	−	1.34840i	−0.925684	−	0.378297i	$-0.876510\pi$
$503$	−26.2043	−	30.2414i	−1.16839	−	1.34840i	−0.242708	−	0.970099i	$-0.578036\pi$
$504$	0.263161	−	0.0772711i	0.0117221	−	0.00344193i
$505$	6.29009			0.279905
$506$	−1.78406	−	9.65684i	−0.0793110	−	0.429299i
$507$	−1.47975			−0.0657179
$508$	−7.01784	+	2.06062i	−0.311366	+	0.0914254i
$509$	7.50352	+	8.65953i	0.332588	+	0.383827i	0.897270	−	0.441481i	$-0.145547\pi$
$509$	7.50352	+	8.65953i	0.332588	+	0.383827i	−0.564683	+	0.825308i	$0.691001\pi$
$510$	−5.21717	+	3.35287i	−0.231020	+	0.148468i
$511$	−0.254528	−	1.77028i	−0.0112597	−	0.0783126i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	−0.953931	+	2.08882i	−0.0421171	+	0.0922235i
$514$	13.7852	−	15.9090i	0.608041	−	0.701716i
$515$	−0.830783	+	5.77823i	−0.0366087	+	0.254619i
$516$	4.45223	+	9.74903i	0.195999	+	0.429177i
$517$	−19.5194	−	5.73141i	−0.858462	−	0.252067i
$518$	−2.83652	−	0.832877i	−0.124629	−	0.0365945i
$519$	−5.15934	−	11.2974i	−0.226470	−	0.495900i
$520$	0.541540	−	3.76649i	0.0237481	−	0.165172i
$521$	15.9886	−	18.4519i	0.700474	−	0.808390i	−0.288342	−	0.957527i	$-0.593104\pi$
$521$	15.9886	−	18.4519i	0.700474	−	0.808390i	0.988817	+	0.149137i	$0.0476496\pi$
$522$	3.02051	−	6.61400i	0.132204	−	0.289487i
$523$	−12.4843	−	8.02319i	−0.545902	−	0.350830i	0.238442	−	0.971157i	$-0.423363\pi$
$523$	−12.4843	−	8.02319i	−0.545902	−	0.350830i	−0.784343	+	0.620327i	$0.787000\pi$
$524$	−1.68493	−	11.7190i	−0.0736066	−	0.511945i
$525$	0.230732	−	0.148282i	0.0100700	−	0.00647157i
$526$	13.5908	+	15.6846i	0.592588	+	0.683883i
$527$	39.2739	−	11.5319i	1.71080	−	0.502336i
$528$	2.04766			0.0891132
$529$	−21.4818	+	8.21781i	−0.933991	+	0.357296i
$530$	−8.17347			−0.355033
$531$	−11.0192	+	3.23552i	−0.478191	+	0.140409i
$532$	0.412443	+	0.475984i	0.0178817	+	0.0206365i
$533$	−29.6112	+	19.0300i	−1.28260	+	0.824280i
$534$	2.23106	+	15.5174i	0.0965475	+	0.671502i
$535$	−6.68673	−	4.29730i	−0.289093	−	0.185788i
$536$	−1.30247	+	2.85201i	−0.0562581	+	0.123188i
$537$	−8.28287	+	9.55894i	−0.357432	+	0.412499i
$538$	2.08589	−	14.5077i	0.0899292	−	0.625471i
$539$	5.89043	+	12.8982i	0.253719	+	0.555566i
$540$	0.959493	+	0.281733i	0.0412900	+	0.0121238i
$541$	4.25053	+	1.24807i	0.182745	+	0.0536587i	0.371824	−	0.928303i	$-0.378732\pi$
$541$	4.25053	+	1.24807i	0.182745	+	0.0536587i	−0.189080	+	0.981962i	$0.560551\pi$
$542$	−10.6579	−	23.3376i	−0.457796	−	1.00243i
$543$	2.07942	−	14.4627i	0.0892364	−	0.620653i
$544$	−4.06123	+	4.68691i	−0.174124	+	0.200949i
$545$	4.45842	−	9.76258i	0.190978	−	0.418183i
$546$	−0.877986	−	0.564247i	−0.0375743	−	0.0241476i
$547$	−3.58590	−	24.9405i	−0.153322	−	1.06638i	−0.910601	−	0.413286i	$-0.864381\pi$
$547$	−3.58590	−	24.9405i	−0.153322	−	1.06638i	0.757279	−	0.653091i	$-0.226528\pi$
$548$	−1.06790	+	0.686300i	−0.0456186	+	0.0293173i
$549$	0.404404	+	0.466707i	0.0172595	+	0.0199186i
$550$	1.96472	−	0.576894i	0.0837759	−	0.0245988i
$551$	16.6968			0.711307
$552$	−0.871264	−	4.71603i	−0.0370835	−	0.200727i
$553$	1.15571			0.0491459
$554$	−19.8722	+	5.83500i	−0.844289	+	0.247906i
$555$	−7.05850	−	8.14595i	−0.299617	−	0.345776i
$556$	−16.7171	+	10.7434i	−0.708961	+	0.455622i
$557$	−1.61892	−	11.2599i	−0.0685960	−	0.477096i	−0.994944	−	0.100428i	$-0.967979\pi$
$557$	−1.61892	−	11.2599i	−0.0685960	−	0.477096i	0.926348	−	0.376668i	$-0.122930\pi$
$558$	−5.55240	−	3.56831i	−0.235052	−	0.151059i
$559$	16.9418	−	37.0973i	0.716560	−	1.56905i
$560$	0.179609	−	0.207280i	0.00758988	−	0.00875919i
$561$	−1.80725	+	12.5697i	−0.0763020	+	0.530692i
$562$	−2.43763	−	5.33766i	−0.102825	−	0.225155i
$563$	−13.2219	−	3.88231i	−0.557239	−	0.163620i	−0.00902631	−	0.999959i	$-0.502873\pi$
$563$	−13.2219	−	3.88231i	−0.557239	−	0.163620i	−0.548212	+	0.836339i	$0.684691\pi$
$564$	−9.53251	−	2.79900i	−0.401391	−	0.117859i
$565$	0.884802	+	1.93745i	0.0372239	+	0.0815090i
$566$	−2.44956	+	17.0371i	−0.102963	+	0.716122i
$567$	0.179609	−	0.207280i	0.00754289	−	0.00870496i
$568$	−6.78913	+	14.8661i	−0.284866	+	0.623769i
$569$	−3.32291	−	2.13551i	−0.139304	−	0.0895251i	0.469133	−	0.883128i	$-0.344567\pi$
$569$	−3.32291	−	2.13551i	−0.139304	−	0.0895251i	−0.608436	+	0.793603i	$0.708203\pi$
$570$	0.326802	+	2.27296i	0.0136882	+	0.0952038i
$571$	−22.6708	+	14.5697i	−0.948744	+	0.609721i	−0.920861	−	0.389890i	$-0.872513\pi$
$571$	−22.6708	+	14.5697i	−0.948744	+	0.609721i	−0.0278831	+	0.999611i	$0.508877\pi$
$572$	−5.10256	−	5.88867i	−0.213349	−	0.246218i
$573$	13.0615	−	3.83519i	0.545651	−	0.160218i
$574$	−2.53705			−0.105894
$575$	−2.16463	−	4.27953i	−0.0902713	−	0.178469i
$576$	1.00000			0.0416667
$577$	−23.0050	+	6.75488i	−0.957711	+	0.281209i	−0.722994	−	0.690854i	$-0.757235\pi$
$577$	−23.0050	+	6.75488i	−0.957711	+	0.281209i	−0.234717	+	0.972064i	$0.575416\pi$
$578$	−14.0537	−	16.2189i	−0.584558	−	0.674616i
$579$	0.200481	−	0.128842i	0.00833172	−	0.00535447i
$580$	−1.03478	−	7.19706i	−0.0429670	−	0.298842i
$581$	−1.76948	−	1.13718i	−0.0734106	−	0.0471781i
$582$	0.975176	−	2.13534i	0.0404224	−	0.0885126i
$583$	−10.9601	+	12.6486i	−0.453921	+	0.523852i
$584$	0.928016	−	6.45449i	0.0384016	−	0.267089i
$585$	−1.58075	−	3.46136i	−0.0653559	−	0.143109i
$586$	30.8803	+	9.06727i	1.27565	+	0.374566i
$587$	−23.0679	−	6.77335i	−0.952114	−	0.279566i	−0.231447	−	0.972847i	$-0.574346\pi$
$587$	−23.0679	−	6.77335i	−0.952114	−	0.279566i	−0.720667	+	0.693281i	$0.756164\pi$
$588$	2.87666	+	6.29900i	0.118631	+	0.259766i
$589$	2.15695	−	15.0019i	0.0888754	−	0.618142i
$590$	−7.52065	+	8.67930i	−0.309620	+	0.357321i
$591$	9.29138	−	20.3453i	0.382196	−	0.836893i
$592$	−9.06756	−	5.82737i	−0.372674	−	0.239503i
$593$	−0.281829	−	1.96016i	−0.0115733	−	0.0804942i	0.983216	−	0.182444i	$-0.0584009\pi$
$593$	−0.281829	−	1.96016i	−0.0115733	−	0.0804942i	−0.994790	+	0.101950i	$0.967492\pi$
$594$	1.72261	−	1.10705i	0.0706793	−	0.0454229i
$595$	1.11388	+	1.28548i	0.0456645	+	0.0526997i
$596$	−20.2231	+	5.93803i	−0.828369	+	0.243231i
$597$	12.3411			0.505088
$598$	−11.3912	+	14.2574i	−0.465822	+	0.583029i
$599$	−5.64718			−0.230738			−0.115369	−	0.993323i	$-0.536805\pi$
$599$	−5.64718			−0.230738			−0.115369	+	0.993323i	$0.536805\pi$
$600$	0.959493	−	0.281733i	0.0391711	−	0.0115017i
$601$	18.2646	+	21.0785i	0.745030	+	0.859810i	0.994077	−	0.108681i	$-0.0346627\pi$
$601$	18.2646	+	21.0785i	0.745030	+	0.859810i	−0.249047	+	0.968491i	$0.580117\pi$
$602$	2.47288	−	1.58922i	0.100787	−	0.0647719i
$603$	0.446206	+	3.10343i	0.0181709	+	0.126381i
$604$	−14.3295	−	9.20904i	−0.583061	−	0.374710i
$605$	−2.82776	+	6.19193i	−0.114965	+	0.251738i
$606$	4.11913	−	4.75373i	0.167328	−	0.193107i
$607$	3.39469	−	23.6106i	0.137786	−	0.958324i	−0.797219	−	0.603690i	$-0.793696\pi$
$607$	3.39469	−	23.6106i	0.137786	−	0.958324i	0.935005	−	0.354634i	$-0.115394\pi$
$608$	0.953931	+	2.08882i	0.0386870	+	0.0847127i
$609$	−1.91346	−	0.561844i	−0.0775375	−	0.0227671i
$610$	0.592527	+	0.173982i	0.0239907	+	0.00704431i
$611$	15.7047	+	34.3884i	0.635342	+	1.39121i
$612$	−0.882589	+	6.13854i	−0.0356765	+	0.248136i
$613$	21.1442	−	24.4017i	0.854005	−	0.985574i	−0.145988	−	0.989286i	$-0.546636\pi$
$613$	21.1442	−	24.4017i	0.854005	−	0.985574i	0.999993	+	0.00371234i	$0.00118168\pi$
$614$	−3.25969	+	7.13773i	−0.131551	+	0.288056i
$615$	−7.78172	−	5.00101i	−0.313789	−	0.201660i
$616$	−0.0799262	−	0.555899i	−0.00322032	−	0.0223978i
$617$	6.53351	−	4.19883i	0.263029	−	0.169039i	−0.402479	−	0.915429i	$-0.631851\pi$
$617$	6.53351	−	4.19883i	0.263029	−	0.169039i	0.665508	+	0.746391i	$0.268215\pi$
$618$	3.82284	+	4.41180i	0.153777	+	0.177469i
$619$	2.27530	−	0.668090i	0.0914522	−	0.0268528i	−0.235686	−	0.971829i	$-0.575734\pi$
$619$	2.27530	−	0.668090i	0.0914522	−	0.0268528i	0.327139	+	0.944976i	$0.393916\pi$
$620$	−6.60016			−0.265069
$621$	−3.28263	−	3.49633i	−0.131727	−	0.140303i
$622$	−19.2768			−0.772928
$623$	4.12556	−	1.21138i	0.165287	−	0.0485327i
$624$	−2.49189	−	2.87580i	−0.0997556	−	0.115124i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	1.58148	+	10.9994i	0.0632087	+	0.439626i
$627$	3.95567	+	2.54216i	0.157974	+	0.101524i
$628$	−8.48164	+	18.5722i	−0.338454	+	0.741112i
$629$	43.7745	−	50.5184i	1.74540	−	2.01430i
$630$	0.0390329	−	0.271480i	0.00155511	−	0.0108160i
$631$	15.3454	+	33.6017i	0.610890	+	1.33766i	0.921963	+	0.387277i	$0.126584\pi$
$631$	15.3454	+	33.6017i	0.610890	+	1.33766i	−0.311073	+	0.950386i	$0.600688\pi$
$632$	4.04308	+	1.18715i	0.160825	+	0.0472224i
$633$	−12.3368	−	3.62241i	−0.490344	−	0.143978i
$634$	−8.17054	−	17.8910i	−0.324493	−	0.710541i
$635$	−1.04091	+	7.23967i	−0.0413071	+	0.287297i
$636$	−5.35249	+	6.17710i	−0.212240	+	0.244938i
$637$	10.9463	−	23.9691i	0.433709	−	0.949691i
$638$	−12.5252	−	8.04945i	−0.495877	−	0.318681i
$639$	2.32585	+	16.1767i	0.0920093	+	0.639939i
$640$	0.841254	−	0.540641i	0.0332535	−	0.0213707i
$641$	−27.8189	−	32.1047i	−1.09878	−	1.26806i	−0.960685	−	0.277640i	$-0.910448\pi$
$641$	−27.8189	−	32.1047i	−1.09878	−	1.26806i	−0.138095	−	0.990419i	$-0.544098\pi$
$642$	−7.62656	+	2.23936i	−0.300996	+	0.0883805i
$643$	22.0187			0.868334			0.434167	−	0.900832i	$-0.357043\pi$
$643$	22.0187			0.868334			0.434167	+	0.900832i	$0.357043\pi$
$644$	−1.24630	+	0.420610i	−0.0491110	+	0.0165744i
$645$	10.7176			0.422003
$646$	−13.6642	+	4.01218i	−0.537611	+	0.157857i
$647$	22.3577	+	25.8022i	0.878973	+	1.01439i	0.999764	+	0.0217106i	$0.00691124\pi$
$647$	22.3577	+	25.8022i	0.878973	+	1.01439i	−0.120792	+	0.992678i	$0.538543\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	3.34669	+	23.2767i	0.131369	+	0.913692i
$650$	−3.20116	−	2.05726i	−0.125560	−	0.0806924i
$651$	−0.751998	+	1.64665i	−0.0294731	+	0.0645371i
$652$	0.994827	−	1.14809i	0.0389604	−	0.0449627i
$653$	4.33323	−	30.1382i	0.169572	−	1.17940i	−0.710198	−	0.704002i	$-0.751395\pi$
$653$	4.33323	−	30.1382i	0.169572	−	1.17940i	0.879770	−	0.475399i	$-0.157696\pi$
$654$	−4.45842	−	9.76258i	−0.174338	−	0.381747i
$655$	−11.3599	−	3.33556i	−0.443868	−	0.130331i
$656$	−8.87546	−	2.60607i	−0.346528	−	0.101750i
$657$	−2.70886	−	5.93159i	−0.105683	−	0.231413i
$658$	−0.387790	+	2.69714i	−0.0151176	+	0.105145i
$659$	−21.8892	+	25.2615i	−0.852683	+	0.984049i	−0.999987	−	0.00504224i	$-0.998395\pi$
$659$	−21.8892	+	25.2615i	−0.852683	+	0.984049i	0.147304	+	0.989091i	$0.452940\pi$
$660$	0.850631	−	1.86262i	0.0331108	−	0.0725024i
$661$	−28.0732	−	18.0415i	−1.09192	−	0.701734i	−0.134639	−	0.990895i	$-0.542987\pi$
$661$	−28.0732	−	18.0415i	−1.09192	−	0.701734i	−0.957281	+	0.289161i	$0.906624\pi$
$662$	−1.96312	−	13.6538i	−0.0762987	−	0.530669i
$663$	19.8525	−	12.7584i	0.771008	−	0.495497i
$664$	−5.02214	−	5.79585i	−0.194897	−	0.224923i
$665$	0.604306	−	0.177440i	0.0234340	−	0.00688083i
$666$	−10.7786			−0.417663
$667$	−13.2095	+	32.2720i	−0.511475	+	1.24958i
$668$	13.8666			0.536516
$669$	3.88639	−	1.14115i	0.150257	−	0.0441193i
$670$	2.05321	+	2.36953i	0.0793225	+	0.0915431i
$671$	1.06378	−	0.683651i	0.0410668	−	0.0263920i
$672$	−0.0390329	−	0.271480i	−0.00150573	−	0.0104725i
$673$	−19.0402	−	12.2364i	−0.733947	−	0.471679i	0.119516	−	0.992832i	$-0.461866\pi$
$673$	−19.0402	−	12.2364i	−0.733947	−	0.471679i	−0.853463	+	0.521153i	$0.825502\pi$
$674$	−1.89724	+	4.15437i	−0.0730788	+	0.160020i
$675$	0.654861	−	0.755750i	0.0252056	−	0.0290888i
$676$	−0.210590	+	1.46469i	−0.00809962	+	0.0563341i
$677$	−14.2852	−	31.2803i	−0.549026	−	1.20220i	−0.957235	−	0.289311i	$-0.906574\pi$
$677$	−14.2852	−	31.2803i	−0.549026	−	1.20220i	0.408209	−	0.912888i	$-0.366153\pi$
$678$	2.04365	+	0.600069i	0.0784858	+	0.0230455i
$679$	−0.617765	−	0.181392i	−0.0237076	−	0.00696119i
$680$	2.57626	+	5.64123i	0.0987952	+	0.216331i
$681$	2.16405	−	15.0513i	0.0829264	−	0.576766i
$682$	−8.85038	+	10.2139i	−0.338899	+	0.391110i
$683$	−11.0432	+	24.1812i	−0.422555	+	0.925266i	0.571922	+	0.820308i	$0.306198\pi$
$683$	−11.0432	+	24.1812i	−0.422555	+	0.925266i	−0.994477	+	0.104958i	$0.966529\pi$
$684$	1.93180	+	1.24149i	0.0738641	+	0.0474696i
$685$	0.180657	+	1.25650i	0.00690256	+	0.0480083i
$686$	3.21289	−	2.06480i	0.122669	−	0.0788343i
$687$	3.12983	+	3.61202i	0.119411	+	0.137807i
$688$	10.2834	−	3.01949i	0.392052	−	0.115117i
$689$	31.1019			1.18489
$690$	−4.65178	−	1.16658i	−0.177090	−	0.0444109i
$691$	−10.8084			−0.411169			−0.205585	−	0.978639i	$-0.565910\pi$
$691$	−10.8084			−0.411169			−0.205585	+	0.978639i	$0.565910\pi$
$692$	−11.9166	+	3.49904i	−0.453003	+	0.133014i
$693$	−0.367780	−	0.424441i	−0.0139708	−	0.0161232i
$694$	−5.65925	+	3.63698i	−0.214822	+	0.138058i
$695$	2.82802	+	19.6693i	0.107273	+	0.746101i
$696$	−6.11682	−	3.93104i	−0.231857	−	0.149006i
$697$	23.8308	−	52.1823i	0.902657	−	1.97654i
$698$	15.1810	−	17.5198i	0.574610	−	0.663136i
$699$	−2.98639	+	20.7708i	−0.112956	+	0.785624i
$700$	−0.113936	−	0.249486i	−0.00430639	−	0.00942968i
$701$	−3.43683	−	1.00914i	−0.129807	−	0.0381148i	0.216184	−	0.976353i	$-0.430639\pi$
$701$	−3.43683	−	1.00914i	−0.129807	−	0.0381148i	−0.345991	+	0.938238i	$0.612457\pi$
$702$	−3.65109	−	1.07206i	−0.137801	−	0.0404622i
$703$	−10.2821	−	22.5146i	−0.387796	−	0.849154i
$704$	0.291413	−	2.02682i	0.0109830	−	0.0763887i
$705$	−6.50601	+	7.50833i	−0.245030	+	0.282780i
$706$	10.8209	−	23.6945i	0.407251	−	0.891756i
$707$	−1.45132	−	0.932708i	−0.0545826	−	0.0350781i
$708$	1.63439	+	11.3675i	0.0614243	+	0.427215i
$709$	13.0160	−	8.36490i	0.488828	−	0.314150i	−0.272906	−	0.962041i	$-0.587985\pi$
$709$	13.0160	−	8.36490i	0.488828	−	0.314150i	0.761734	+	0.647890i	$0.224348\pi$
$710$	10.7024	+	12.3512i	0.401654	+	0.463533i
$711$	4.04308	−	1.18715i	0.151627	−	0.0445218i
$712$	15.6769			0.587518
$713$	27.2896	+	16.0376i	1.02200	+	0.600613i
$714$	1.70094			0.0636560
$715$	−7.47620	+	2.19521i	−0.279594	+	0.0820962i
$716$	8.28287	+	9.55894i	0.309545	+	0.357234i
$717$	−4.98226	+	3.20191i	−0.186066	+	0.119577i
$718$	1.95760	+	13.6154i	0.0730568	+	0.508121i
$719$	21.5744	+	13.8650i	0.804590	+	0.517078i	0.877111	−	0.480288i	$-0.159468\pi$
$719$	21.5744	+	13.8650i	0.804590	+	0.517078i	−0.0725208	+	0.997367i	$0.523104\pi$
$720$	0.415415	−	0.909632i	0.0154816	−	0.0339000i
$721$	1.04850	−	1.21003i	0.0390480	−	0.0450638i
$722$	1.95354	−	13.5871i	0.0727031	−	0.505661i
$723$	−1.57537	−	3.44957i	−0.0585886	−	0.128291i
$724$	−14.0195	−	4.11651i	−0.521032	−	0.152989i
$725$	−6.97654	−	2.04850i	−0.259102	−	0.0760793i
$726$	2.82776	+	6.19193i	0.104948	+	0.229804i
$727$	6.18891	−	43.0448i	0.229534	−	1.59644i	−0.470543	−	0.882377i	$-0.655942\pi$
$727$	6.18891	−	43.0448i	0.229534	−	1.59644i	0.700077	−	0.714067i	$-0.253149\pi$
$728$	−0.683455	+	0.788749i	−0.0253305	+	0.0292330i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−5.48570	−	3.52544i	−0.203035	−	0.130483i
$731$	9.45920	+	65.7902i	0.349861	+	2.43334i
$732$	0.519509	−	0.333868i	0.0192016	−	0.0123401i
$733$	−2.87457	−	3.31743i	−0.106175	−	0.122532i	0.700175	−	0.713971i	$-0.253105\pi$
$733$	−2.87457	−	3.31743i	−0.106175	−	0.122532i	−0.806349	+	0.591439i	$0.798560\pi$
$734$	−4.50392	+	1.32247i	−0.166243	+	0.0488133i
$735$	6.92478			0.255424
$736$	−4.79202	+	0.191236i	−0.176636	+	0.00704904i
$737$	6.42013			0.236488
$738$	−8.87546	+	2.60607i	−0.326710	+	0.0959307i
$739$	−1.85617	−	2.14214i	−0.0682805	−	0.0787999i	0.720582	−	0.693370i	$-0.243875\pi$
$739$	−1.85617	−	2.14214i	−0.0682805	−	0.0787999i	−0.788862	+	0.614570i	$0.789329\pi$
$740$	−9.06756	+	5.82737i	−0.333330	+	0.214218i
$741$	−1.24356	−	8.64912i	−0.0456832	−	0.317733i
$742$	1.88588	+	1.21198i	0.0692328	+	0.0444932i
$743$	−5.36678	+	11.7516i	−0.196888	+	0.431125i	−0.982165	−	0.188020i	$-0.939793\pi$
$743$	−5.36678	+	11.7516i	−0.196888	+	0.431125i	0.785277	+	0.619144i	$0.212520\pi$
$744$	−4.32218	+	4.98807i	−0.158459	+	0.182871i
$745$	−2.99955	+	20.8623i	−0.109895	+	0.764336i
$746$	−7.05056	−	15.4386i	−0.258139	−	0.565246i
$747$	−7.35837	−	2.16061i	−0.269229	−	0.0790526i
$748$	12.1845	+	3.57770i	0.445511	+	0.130814i
$749$	0.905627	+	1.98305i	0.0330909	+	0.0724589i
$750$	0.142315	−	0.989821i	0.00519660	−	0.0361432i
$751$	−5.45142	+	6.29128i	−0.198925	+	0.229572i	−0.846444	−	0.532477i	$-0.821261\pi$
$751$	−5.45142	+	6.29128i	−0.198925	+	0.229572i	0.647519	+	0.762049i	$0.275807\pi$
$752$	−4.12713	+	9.03715i	−0.150501	+	0.329551i
$753$	−0.155491	−	0.0999279i	−0.00566640	−	0.00364158i
$754$	3.93758	+	27.3865i	0.143398	+	0.997356i
$755$	−14.3295	+	9.20904i	−0.521506	+	0.335151i
$756$	−0.179609	−	0.207280i	−0.00653233	−	0.00753871i
$757$	15.6271	−	4.58853i	0.567976	−	0.166773i	0.0148785	−	0.999889i	$-0.495264\pi$
$757$	15.6271	−	4.58853i	0.567976	−	0.166773i	0.553098	+	0.833116i	$0.313446\pi$
$758$	−26.3401			−0.956717
$759$	−8.04305	+	5.63443i	−0.291944	+	0.204517i
$760$	2.29633			0.0832967
$761$	−15.8768	+	4.66184i	−0.575532	+	0.168992i	−0.556529	−	0.830828i	$-0.687867\pi$
$761$	−15.8768	+	4.66184i	−0.575532	+	0.168992i	−0.0190029	+	0.999819i	$0.506049\pi$
$762$	4.78973	+	5.52764i	0.173513	+	0.200245i
$763$	−2.47631	+	1.59143i	−0.0896486	+	0.0576137i
$764$	−1.93732	−	13.4743i	−0.0700896	−	0.487484i
$765$	5.21717	+	3.35287i	0.188627	+	0.121223i
$766$	3.66459	−	8.02433i	0.132407	−	0.289931i
$767$	28.6178	−	33.0267i	1.03333	−	1.19252i
$768$	0.142315	−	0.989821i	0.00513534	−	0.0357171i
$769$	6.03742	+	13.2201i	0.217715	+	0.476729i	0.986703	−	0.162534i	$-0.0519668\pi$
$769$	6.03742	+	13.2201i	0.217715	+	0.476729i	−0.768988	+	0.639263i	$0.779239\pi$
$770$	−0.538866	−	0.158225i	−0.0194194	−	0.00570205i
$771$	−20.1979	−	5.93065i	−0.727411	−	0.213587i
$772$	−0.0989987	−	0.216777i	−0.00356304	−	0.00780197i
$773$	−7.32974	+	50.9794i	−0.263632	+	1.83360i	0.241308	+	0.970448i	$0.422423\pi$
$773$	−7.32974	+	50.9794i	−0.263632	+	1.83360i	−0.504941	+	0.863154i	$0.668486\pi$
$774$	7.01851	−	8.09979i	0.252275	−	0.291141i
$775$	−2.74180	+	6.00371i	−0.0984885	+	0.215660i
$776$	−1.97482	−	1.26914i	−0.0708920	−	0.0455595i
$777$	0.420721	+	2.92618i	0.0150933	+	0.104976i
$778$	20.7772	−	13.3527i	0.744897	−	0.478717i
$779$	−13.9102	−	16.0532i	−0.498384	−	0.575165i
$780$	−3.65109	+	1.07206i	−0.130730	+	0.0383858i
$781$	33.4650			1.19747
$782$	3.05547	−	29.5848i	0.109264	−	1.05795i
$783$	−7.27107			−0.259847
$784$	6.64427	−	1.95093i	0.237295	−	0.0696762i
$785$	13.3705	+	15.4303i	0.477213	+	0.550733i
$786$	−9.96000	+	6.40090i	−0.355261	+	0.228313i
$787$	3.07962	+	21.4192i	0.109777	+	0.763514i	0.968129	+	0.250453i	$0.0805794\pi$
$787$	3.07962	+	21.4192i	0.109777	+	0.763514i	−0.858352	+	0.513061i	$0.828511\pi$
$788$	−18.8159	−	12.0922i	−0.670289	−	0.430768i
$789$	8.62142	−	18.8783i	0.306931	−	0.672084i
$790$	2.75943	−	3.18455i	0.0981760	−	0.113301i
$791$	0.0831370	−	0.578231i	0.00295601	−	0.0205595i
$792$	−0.850631	−	1.86262i	−0.0302258	−	0.0661854i
$793$	−2.25470	−	0.662040i	−0.0800668	−	0.0235097i
$794$	−17.4540	−	5.12496i	−0.619420	−	0.181878i
$795$	3.39538	+	7.43485i	0.120422	+	0.263687i
$796$	1.75632	−	12.2155i	0.0622512	−	0.432967i
$797$	4.09205	−	4.72248i	0.144948	−	0.167279i	−0.678633	−	0.734477i	$-0.737427\pi$
$797$	4.09205	−	4.72248i	0.144948	−	0.167279i	0.823581	+	0.567199i	$0.191973\pi$
$798$	0.261636	−	0.572902i	0.00926180	−	0.0202805i
$799$	−51.8323	−	33.3106i	−1.83370	−	1.17845i
$800$	−0.142315	−	0.989821i	−0.00503159	−	0.0349955i
$801$	13.1883	−	8.47560i	0.465985	−	0.299470i
$802$	−4.03712	−	4.65908i	−0.142556	−	0.164518i
$803$	−12.8117	+	3.76185i	−0.452114	+	0.132753i
$804$	3.13534			0.110575
$805$	−0.135130	+	1.30840i	−0.00476269	+	0.0461150i
$806$	25.1151			0.884641
$807$	−14.0632	+	4.12932i	−0.495047	+	0.145359i
$808$	−4.11913	−	4.75373i	−0.144911	−	0.167236i
$809$	18.1317	−	11.6525i	0.637477	−	0.409681i	−0.181594	−	0.983374i	$-0.558126\pi$
$809$	18.1317	−	11.6525i	0.637477	−	0.409681i	0.819071	+	0.573692i	$0.194489\pi$
$810$	−0.142315	−	0.989821i	−0.00500043	−	0.0347788i
$811$	13.5566	+	8.71230i	0.476037	+	0.305930i	0.756569	−	0.653914i	$-0.226874\pi$
$811$	13.5566	+	8.71230i	0.476037	+	0.305930i	−0.280532	+	0.959845i	$0.590511\pi$
$812$	−0.828440	+	1.81403i	−0.0290725	+	0.0636600i
$813$	−16.8011	+	19.3895i	−0.589242	+	0.680021i
$814$	−3.14103	+	21.8464i	−0.110093	+	0.765715i
$815$	−0.631075	−	1.38186i	−0.0221056	−	0.0484045i
$816$	5.95045	+	1.74721i	0.208308	+	0.0611646i
$817$	23.6142	+	6.93374i	0.826155	+	0.242581i
$818$	3.82604	+	8.37785i	0.133774	+	0.292925i
$819$	−0.148529	+	1.03304i	−0.00519002	+	0.0360974i
$820$	−6.05756	+	6.99080i	−0.211539	+	0.244129i
$821$	−4.55883	+	9.98244i	−0.159104	+	0.348390i	−0.972349	−	0.233532i	$-0.924972\pi$
$821$	−4.55883	+	9.98244i	−0.159104	+	0.348390i	0.813245	+	0.581922i	$0.197699\pi$
$822$	1.06790	+	0.686300i	0.0372474	+	0.0239375i
$823$	−4.26647	−	29.6739i	−0.148720	−	1.03437i	−0.918319	−	0.395841i	$-0.870453\pi$
$823$	−4.26647	−	29.6739i	−0.148720	−	1.03437i	0.769599	−	0.638527i	$-0.220456\pi$
$824$	4.91094	−	3.15607i	0.171081	−	0.109947i
$825$	−1.34094	−	1.54752i	−0.0466854	−	0.0538778i
$826$	3.02224	−	0.887409i	0.105157	−	0.0308769i
$827$	12.1458			0.422350			0.211175	−	0.977448i	$-0.432271\pi$
$827$	12.1458			0.422350			0.211175	+	0.977448i	$0.432271\pi$
$828$	−3.92791	+	2.75164i	−0.136504	+	0.0956260i
$829$	19.6625			0.682906			0.341453	−	0.939899i	$-0.389081\pi$
$829$	19.6625			0.682906			0.341453	+	0.939899i	$0.389081\pi$
$830$	−7.35837	+	2.16061i	−0.255413	+	0.0749959i
$831$	13.5629	+	15.6524i	0.470492	+	0.542977i
$832$	−3.20116	+	2.05726i	−0.110980	+	0.0713227i
$833$	6.11173	+	42.5080i	0.211759	+	1.47282i
$834$	16.7171	+	10.7434i	0.578864	+	0.372013i
$835$	5.76041	−	12.6135i	0.199347	−	0.436509i
$836$	3.07923	−	3.55362i	0.106497	−	0.122905i
$837$	−0.939300	+	6.53298i	−0.0324670	+	0.225813i
$838$	−7.05896	−	15.4570i	−0.243848	−	0.533952i
$839$	−26.8791	−	7.89242i	−0.927970	−	0.272476i	−0.217383	−	0.976086i	$-0.569752\pi$
$839$	−26.8791	−	7.89242i	−0.927970	−	0.272476i	−0.710586	+	0.703610i	$0.751570\pi$
$840$	−0.263161	−	0.0772711i	−0.00907993	−	0.00266611i
$841$	9.91533	+	21.7115i	0.341908	+	0.748674i
$842$	1.95413	−	13.5913i	0.0673439	−	0.468387i
$843$	−3.84268	+	4.43469i	−0.132349	+	0.152739i
$844$	−5.34125	+	11.6957i	−0.183853	+	0.402583i
$845$	1.24484	+	0.800012i	0.0428239	+	0.0275212i
$846$	1.41389	+	9.83383i	0.0486106	+	0.338094i
$847$	1.57061	−	1.00937i	0.0539667	−	0.0346823i
$848$	5.35249	+	6.17710i	0.183805	+	0.212122i
$849$	16.5151	−	4.84926i	0.566795	−	0.166426i
$850$	6.20167			0.212715
$851$	51.6514	−	2.06126i	1.77059	−	0.0706590i
$852$	16.3430			0.559902
$853$	46.9616	−	13.7892i	1.60794	−	0.472132i	0.650195	−	0.759767i	$-0.274687\pi$
$853$	46.9616	−	13.7892i	1.60794	−	0.472132i	0.957740	+	0.287635i	$0.0928689\pi$
$854$	−0.110916	−	0.128004i	−0.00379548	−	0.00438022i
$855$	1.93180	−	1.24149i	0.0660661	−	0.0424581i
$856$	1.13119	+	7.86763i	0.0386634	+	0.268910i
$857$	−25.6621	−	16.4920i	−0.876599	−	0.563356i	0.0231655	−	0.999732i	$-0.492626\pi$
$857$	−25.6621	−	16.4920i	−0.876599	−	0.563356i	−0.899765	+	0.436376i	$0.856262\pi$
$858$	−3.23684	+	7.08770i	−0.110504	+	0.241970i
$859$	−20.9085	+	24.1297i	−0.713389	+	0.823294i	−0.990496	−	0.137545i	$-0.956079\pi$
$859$	−20.9085	+	24.1297i	−0.713389	+	0.823294i	0.277107	+	0.960839i	$0.410624\pi$
$860$	1.52527	−	10.6085i	0.0520112	−	0.361746i
$861$	1.05393	+	2.30778i	0.0359178	+	0.0786490i
$862$	−19.7923	−	5.81154i	−0.674128	−	0.197942i
$863$	20.3488	+	5.97495i	0.692681	+	0.203390i	0.609079	−	0.793110i	$-0.291539\pi$
$863$	20.3488	+	5.97495i	0.692681	+	0.203390i	0.0836023	+	0.996499i	$0.473357\pi$
$864$	−0.415415	−	0.909632i	−0.0141327	−	0.0309463i
$865$	−1.76751	+	12.2933i	−0.0600972	+	0.417985i
$866$	−23.8530	+	27.5279i	−0.810559	+	0.935436i
$867$	−8.91508	+	19.5213i	−0.302772	+	0.662978i
$868$	1.52286	+	0.978686i	0.0516894	+	0.0332188i
$869$	−1.22795	−	8.54055i	−0.0416552	−	0.289718i
$870$	−6.11682	+	3.93104i	−0.207379	+	0.133275i
$871$	−7.81294	−	9.01661i	−0.264731	−	0.305516i
$872$	−10.2977	+	3.02368i	−0.348724	+	0.102395i
$873$	−2.34748			−0.0794500
$874$	−9.49462	−	5.57982i	−0.321160	−	0.188740i
$875$	−0.274271			−0.00927206
$876$	−6.25672	+	1.83714i	−0.211395	+	0.0620712i
$877$	−14.4525	−	16.6791i	−0.488026	−	0.563212i	0.457311	−	0.889307i	$-0.348813\pi$
$877$	−14.4525	−	16.6791i	−0.488026	−	0.563212i	−0.945337	+	0.326095i	$0.894267\pi$
$878$	−29.7146	+	19.0964i	−1.00282	+	0.644473i
$879$	−4.58026	−	31.8564i	−0.154488	−	1.07449i
$880$	−1.72261	−	1.10705i	−0.0580690	−	0.0373187i
$881$	21.6804	−	47.4735i	0.730432	−	1.59942i	−0.0682481	−	0.997668i	$-0.521741\pi$
$881$	21.6804	−	47.4735i	0.730432	−	1.59942i	0.798680	−	0.601755i	$-0.205532\pi$
$882$	4.53476	−	5.23340i	0.152693	−	0.176218i
$883$	2.37741	−	16.5353i	0.0800063	−	0.556456i	−0.909910	−	0.414805i	$-0.863850\pi$
$883$	2.37741	−	16.5353i	0.0800063	−	0.556456i	0.989917	−	0.141651i	$-0.0452411\pi$
$884$	−9.80327	−	21.4662i	−0.329720	−	0.721985i
$885$	11.0192	+	3.23552i	0.370405	+	0.108761i
$886$	−5.74165	−	1.68590i	−0.192895	−	0.0566390i
$887$	7.46327	+	16.3423i	0.250592	+	0.548720i	0.992566	−	0.121709i	$-0.0388373\pi$
$887$	7.46327	+	16.3423i	0.250592	+	0.548720i	−0.741974	+	0.670429i	$0.766110\pi$
$888$	−1.53396	+	10.6689i	−0.0514763	+	0.358026i
$889$	1.31368	−	1.51607i	0.0440595	−	0.0508474i
$890$	6.51244	−	14.2602i	0.218297	−	0.478005i
$891$	−1.72261	−	1.10705i	−0.0577094	−	0.0370876i
$892$	−0.576442	−	4.00924i	−0.0193007	−	0.134239i
$893$	−19.1923	+	12.3341i	−0.642246	+	0.412747i
$894$	13.8024	+	15.9288i	0.461621	+	0.532739i
$895$	12.1359	−	3.56344i	0.405660	−	0.119113i
$896$	−0.274271			−0.00916276
$897$	17.7011	+	4.43909i	0.591022	+	0.148217i
$898$	12.9457			0.432003
$899$	46.0463	−	13.5204i	1.53573	−	0.450931i
$900$	−0.654861	−	0.755750i	−0.0218287	−	0.0251917i
$901$	−42.6424	+	27.4046i	−1.42062	+	0.912980i
$902$	2.69562	+	18.7484i	0.0897542	+	0.624254i
$903$	−2.47288	−	1.58922i	−0.0822923	−	0.0528860i
$904$	0.884802	−	1.93745i	0.0294281	−	0.0644385i
$905$	−9.56843	+	11.0426i	−0.318066	+	0.367067i
$906$	−2.42413	+	16.8602i	−0.0805363	+	0.560142i
$907$	2.26956	+	4.96963i	0.0753594	+	0.165014i	0.943562	−	0.331196i	$-0.107452\pi$
$907$	2.26956	+	4.96963i	0.0753594	+	0.165014i	−0.868203	+	0.496210i	$0.834725\pi$
$908$	−14.5901	−	4.28404i	−0.484189	−	0.142171i
$909$	−6.03530	−	1.77212i	−0.200178	−	0.0587776i
$910$	0.433554	+	0.949350i	0.0143722	+	0.0314706i
$911$	−3.02092	+	21.0110i	−0.100088	+	0.696125i	0.876562	+	0.481288i	$0.159831\pi$
$911$	−3.02092	+	21.0110i	−0.100088	+	0.696125i	−0.976650	+	0.214837i	$0.931078\pi$
$912$	1.50378	−	1.73545i	0.0497951	−	0.0574666i
$913$	−6.52350	+	14.2845i	−0.215896	+	0.472747i
$914$	7.13729	+	4.58686i	0.236081	+	0.151720i
$915$	−0.0878854	−	0.611256i	−0.00290540	−	0.0202075i
$916$	4.02067	−	2.58393i	0.132847	−	0.0853755i
$917$	2.12648	+	2.45409i	0.0702226	+	0.0810412i
$918$	5.95045	−	1.74721i	0.196394	−	0.0576666i
$919$	−47.9503			−1.58174			−0.790868	−	0.611987i	$-0.790370\pi$
$919$	−47.9503			−1.58174			−0.790868	+	0.611987i	$0.790370\pi$
$920$	−1.81672	+	4.43841i	−0.0598955	+	0.146330i
$921$	7.84684			0.258562
$922$	32.4196	−	9.51927i	1.06768	−	0.313500i
$923$	−40.7250	−	46.9992i	−1.34048	−	1.54700i
$924$	−0.472461	+	0.303632i	−0.0155428	+	0.00998877i
$925$	1.53396	+	10.6689i	0.0504363	+	0.350792i
$926$	−20.9758	−	13.4803i	−0.689306	−	0.442990i
$927$	2.42505	−	5.31011i	0.0796489	−	0.174407i
$928$	−4.76154	+	5.49511i	−0.156305	+	0.180386i
$929$	−0.854231	+	5.94131i	−0.0280264	+	0.194928i	−0.999025	−	0.0441593i	$-0.985939\pi$
$929$	−0.854231	+	5.94131i	−0.0280264	+	0.194928i	0.970998	+	0.239087i	$0.0768482\pi$
$930$	2.74180	+	6.00371i	0.0899073	+	0.196870i
$931$	15.2575	+	4.47999i	0.500043	+	0.146826i
$932$	20.1344	+	5.91199i	0.659524	+	0.193654i
$933$	8.00785	+	17.5348i	0.262165	+	0.574062i
$934$	3.22696	−	22.4440i	0.105589	−	0.734389i
$935$	8.31603	−	9.59721i	0.271963	−	0.313862i
$936$	−1.58075	+	3.46136i	−0.0516684	+	0.113138i
$937$	11.0808	+	7.12119i	0.361994	+	0.232639i	0.708976	−	0.705232i	$-0.249157\pi$
$937$	11.0808	+	7.12119i	0.361994	+	0.232639i	−0.346983	+	0.937872i	$0.612794\pi$
$938$	−0.122381	−	0.851181i	−0.00399589	−	0.0277920i
$939$	9.34848	−	6.00790i	0.305076	−	0.196060i
$940$	6.50601	+	7.50833i	0.212203	+	0.244895i
$941$	−11.3340	+	3.32797i	−0.369478	+	0.108489i	−0.461200	−	0.887296i	$-0.652581\pi$
$941$	−11.3340	+	3.32797i	−0.369478	+	0.108489i	0.0917221	+	0.995785i	$0.470763\pi$
$942$	20.4173			0.665231
$943$	42.0330	−	14.1856i	1.36878	−	0.461948i
$944$	11.4844			0.373784
$945$	−0.263161	+	0.0772711i	−0.00856064	+	0.00251363i
$946$	−14.3716	−	16.5857i	−0.467259	−	0.539246i
$947$	−13.5432	+	8.70370i	−0.440095	+	0.282832i	−0.741866	−	0.670549i	$-0.766059\pi$
$947$	−13.5432	+	8.70370i	−0.440095	+	0.282832i	0.301770	+	0.953381i	$0.402422\pi$
$948$	−0.599681	−	4.17087i	−0.0194767	−	0.135464i
$949$	20.8743	+	13.4151i	0.677609	+	0.435473i
$950$	0.953931	−	2.08882i	0.0309496	−	0.0677702i
$951$	−12.8800	+	14.8644i	−0.417664	+	0.482010i
$952$	0.242069	−	1.68362i	0.00784549	−	0.0545666i
$953$	1.39740	+	3.05988i	0.0452663	+	0.0991193i	0.930914	−	0.365238i	$-0.119013\pi$
$953$	1.39740	+	3.05988i	0.0452663	+	0.0991193i	−0.885648	+	0.464358i	$0.846285\pi$
$954$	7.84239	+	2.30273i	0.253907	+	0.0745537i
$955$	−13.0615	−	3.83519i	−0.422659	−	0.124104i
$956$	2.46027	+	5.38723i	0.0795707	+	0.174235i
$957$	−2.11889	+	14.7372i	−0.0684938	+	0.476385i
$958$	11.4891	−	13.2592i	0.371197	−	0.428384i
$959$	0.144633	−	0.316702i	0.00467044	−	0.0102268i
$960$	−0.841254	−	0.540641i	−0.0271513	−	0.0174491i
$961$	−1.78777	−	12.4342i	−0.0576699	−	0.401103i
$962$	34.5041	−	22.1745i	1.11246	−	0.714933i
$963$	5.20518	+	6.00710i	0.167735	+	0.193576i
$964$	−3.63866	+	1.06841i	−0.117193	+	0.0344111i
$965$	−0.238313			−0.00767156
$966$	0.900331	+	0.958943i	0.0289677	+	0.0308535i
$967$	−7.77693			−0.250089			−0.125045	−	0.992151i	$-0.539907\pi$
$967$	−7.77693			−0.250089			−0.125045	+	0.992151i	$0.539907\pi$
$968$	6.53134	−	1.91777i	0.209925	−	0.0616396i
$969$	9.32593	+	10.7627i	0.299592	+	0.345747i
$970$	−1.97482	+	1.26914i	−0.0634077	+	0.0407497i
$971$	2.45809	+	17.0964i	0.0788837	+	0.548648i	0.990490	+	0.137584i	$0.0439337\pi$
$971$	2.45809	+	17.0964i	0.0788837	+	0.548648i	−0.911606	+	0.411064i	$0.865157\pi$
$972$	−0.841254	−	0.540641i	−0.0269832	−	0.0173411i
$973$	2.26410	−	4.95768i	0.0725837	−	0.158936i
$974$	1.64226	−	1.89527i	0.0526213	−	0.0607282i
$975$	−0.541540	+	3.76649i	−0.0173432	+	0.120624i
$976$	−0.256536	−	0.561736i	−0.00821152	−	0.0179807i
$977$	19.5229	+	5.73243i	0.624592	+	0.183397i	0.578688	−	0.815549i	$-0.303565\pi$
$977$	19.5229	+	5.73243i	0.624592	+	0.183397i	0.0459042	+	0.998946i	$0.485383\pi$
$978$	−1.45761	−	0.427992i	−0.0466091	−	0.0136857i
$979$	−13.3353	−	29.2002i	−0.426198	−	0.933243i
$980$	0.985498	−	6.85429i	0.0314806	−	0.218952i
$981$	−7.02826	+	8.11104i	−0.224395	+	0.258966i
$982$	−9.81683	+	21.4959i	−0.313268	+	0.685960i
$983$	−21.7320	−	13.9663i	−0.693145	−	0.445457i	0.146058	−	0.989276i	$-0.453341\pi$
$983$	−21.7320	−	13.9663i	−0.693145	−	0.445457i	−0.839202	+	0.543819i	$0.816978\pi$
$984$	1.31643	+	9.15600i	0.0419664	+	0.291883i
$985$	−18.8159	+	12.0922i	−0.599524	+	0.385291i
$986$	−29.5295	−	34.0788i	−0.940410	−	1.08529i
$987$	2.61449	−	0.767685i	0.0832203	−	0.0244357i
$988$	−8.73806			−0.277995
$989$	−32.0838	+	40.1565i	−1.02021	+	1.27690i
$990$	−2.04766			−0.0650791
$991$	−47.6997	+	14.0059i	−1.51523	+	0.444912i	−0.930493	−	0.366310i	$-0.880621\pi$
$991$	−47.6997	+	14.0059i	−1.51523	+	0.444912i	−0.584738	+	0.811222i	$0.698803\pi$
$992$	4.32218	+	4.98807i	0.137229	+	0.158371i
$993$	−11.6044	+	7.45770i	−0.368255	+	0.236663i
$994$	−0.637915	−	4.43679i	−0.0202334	−	0.140727i
$995$	−10.3820	−	6.67211i	−0.329132	−	0.211520i
$996$	−3.18582	+	6.97598i	−0.100947	+	0.221042i
$997$	25.8596	−	29.8435i	0.818981	−	0.945154i	−0.180279	−	0.983615i	$-0.557700\pi$
$997$	25.8596	−	29.8435i	0.818981	−	0.945154i	0.999260	+	0.0384612i	$0.0122456\pi$
$998$	2.61688	−	18.2008i	0.0828359	−	0.576136i
$999$	4.47761	+	9.80459i	0.141665	+	0.310203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.c.331.2	yes	20
23.18	even	11	inner	690.2.m.c.271.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.c.271.2	✓	20	23.18	even	11	inner
690.2.m.c.331.2	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)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.113936 + 0.249486i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(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} +(-0.113936 + 0.249486i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(1.96472 + 0.576894i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-1.58075 - 3.46136i) q^{13} +(0.0390329 - 0.271480i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(5.21717 + 3.35287i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(1.93180 - 1.24149i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-0.263161 + 0.0772711i) q^{21} -2.04766 q^{22} +(0.871264 + 4.71603i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(2.49189 + 2.87580i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.0390329 + 0.271480i) q^{28} +(6.11682 + 3.93104i) q^{29} +(-0.415415 + 0.909632i) q^{30} +(4.32218 - 4.98807i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(0.850631 + 1.86262i) q^{33} +(-5.95045 - 1.74721i) q^{34} +(0.263161 + 0.0772711i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.53396 - 10.6689i) q^{37} +(-1.50378 + 1.73545i) q^{38} +(1.58075 - 3.46136i) q^{39} +(0.841254 + 0.540641i) q^{40} +(-1.31643 - 9.15600i) q^{41} +(0.230732 - 0.148282i) q^{42} +(7.01851 + 8.09979i) q^{43} +(1.96472 - 0.576894i) q^{44} +1.00000 q^{45} +(-2.16463 - 4.27953i) q^{46} -9.93495 q^{47} +(0.959493 - 0.281733i) q^{48} +(4.53476 + 5.23340i) q^{49} +(0.841254 - 0.540641i) q^{50} +(0.882589 + 6.13854i) q^{51} +(-3.20116 - 2.05726i) q^{52} +(-3.39538 + 7.43485i) q^{53} +(0.654861 - 0.755750i) q^{54} +(0.291413 - 2.02682i) q^{55} +(-0.113936 - 0.249486i) q^{56} +(2.20331 + 0.646951i) q^{57} +(-6.97654 - 2.04850i) q^{58} +(4.77077 + 10.4465i) q^{59} +(0.142315 - 0.989821i) q^{60} +(0.404404 - 0.466707i) q^{61} +(-2.74180 + 6.00371i) q^{62} +(-0.230732 - 0.148282i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-3.20116 + 2.05726i) q^{65} +(-1.34094 - 1.54752i) q^{66} +(3.00834 - 0.883328i) q^{67} +6.20167 q^{68} +(-2.99358 + 3.74680i) q^{69} -0.274271 q^{70} +(15.6810 - 4.60436i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-5.48570 + 3.52544i) q^{73} +(1.53396 + 10.6689i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(0.953931 - 2.08882i) q^{76} +(-0.367780 + 0.424441i) q^{77} +(-0.541540 + 3.76649i) q^{78} +(-1.75046 - 3.83297i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(3.84265 + 8.41423i) q^{82} +(-1.09141 + 7.59096i) q^{83} +(-0.179609 + 0.207280i) q^{84} +(2.57626 - 5.64123i) q^{85} +(-9.01618 - 5.79435i) q^{86} +(1.03478 + 7.19706i) q^{87} +(-1.72261 + 1.10705i) q^{88} +(-10.2662 - 11.8478i) q^{89} +(-0.959493 + 0.281733i) q^{90} +1.04366 q^{91} +(3.28263 + 3.49633i) q^{92} +6.60016 q^{93} +(9.53251 - 2.79900i) q^{94} +(-1.50378 - 1.73545i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(0.334081 + 2.32358i) q^{97} +(-5.82549 - 3.74382i) q^{98} +(-0.850631 + 1.86262i) 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	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 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 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

L-functions

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