LMFDB - Embedded newform 690.2.m.d.211.1

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} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + \cdots + 7921 $ x^20 - 5x^19 + 8x^18 - 32x^17 + 277x^16 - 1138x^15 + 2950x^14 - 6404x^13 + 24088x^12 - 93423x^11 + 318055x^10 - 798006x^9 + 1869818x^8 - 3381161x^7 + 6172602x^6 - 7296658x^5 + 10759748x^4 - 4308967x^3 + 7994447x^2 + 486652*x + 7921
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			211.1
Root			$-2.75487 + 1.77045i$ of defining polynomial
Character	$\chi$	$=$	690.211
Dual form			690.2.m.d.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(-0.257432 - 1.79048i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(-0.257432 - 1.79048i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.142315 - 0.989821i) q^{10} +(2.50531 - 5.48586i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.456463 + 3.17477i) q^{13} +(1.52174 - 0.977962i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.98566 + 3.44564i) q^{17} +(0.841254 + 0.540641i) q^{18} +(4.90662 - 5.66254i) q^{19} +(0.959493 - 0.281733i) q^{20} +(-0.751442 - 1.64543i) q^{21} +6.03085 q^{22} +(2.37095 - 4.16877i) q^{23} -1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(-3.07749 + 0.903633i) q^{26} +(0.654861 - 0.755750i) q^{27} +(1.52174 + 0.977962i) q^{28} +(4.49513 + 5.18766i) q^{29} +(-0.142315 - 0.989821i) q^{30} +(-7.21804 - 2.11941i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.858280 - 5.96947i) q^{33} +(-1.89397 + 4.14722i) q^{34} +(-0.751442 + 1.64543i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-1.25926 + 0.809276i) q^{37} +(7.18911 + 2.11091i) q^{38} +(0.456463 + 3.17477i) q^{39} +(0.654861 + 0.755750i) q^{40} +(0.128152 + 0.0823581i) q^{41} +(1.18457 - 1.36707i) q^{42} +(-4.19808 + 1.23267i) q^{43} +(2.50531 + 5.48586i) q^{44} -1.00000 q^{45} +(4.77697 + 0.424923i) q^{46} +4.07021 q^{47} +(-0.415415 - 0.909632i) q^{48} +(3.57690 - 1.05027i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(3.83547 + 2.46491i) q^{51} +(-2.10041 - 2.42400i) q^{52} +(-0.323199 - 2.24790i) q^{53} +(0.959493 + 0.281733i) q^{54} +(-5.07348 + 3.26052i) q^{55} +(-0.257432 + 1.79048i) q^{56} +(3.11254 - 6.81552i) q^{57} +(-2.85151 + 6.24394i) q^{58} +(-1.64530 + 11.4433i) q^{59} +(0.841254 - 0.540641i) q^{60} +(-14.6736 - 4.30855i) q^{61} +(-1.07060 - 7.44619i) q^{62} +(-1.18457 - 1.36707i) q^{63} +(0.841254 + 0.540641i) q^{64} +(2.10041 - 2.42400i) q^{65} +(5.78656 - 1.69909i) q^{66} +(-1.63864 - 3.58811i) q^{67} -4.55923 q^{68} +(1.10043 - 4.66787i) q^{69} -1.80889 q^{70} +(1.08051 + 2.36598i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(-1.57119 + 1.81325i) q^{73} +(-1.25926 - 0.809276i) q^{74} +(0.654861 + 0.755750i) q^{75} +(1.06631 + 7.41635i) q^{76} +(-10.4673 - 3.07347i) q^{77} +(-2.69825 + 1.73406i) q^{78} +(0.792412 - 5.51135i) q^{79} +(-0.415415 + 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.0216794 + 0.150784i) q^{82} +(1.26936 - 0.815768i) q^{83} +(1.73562 + 0.509624i) q^{84} +(-0.648846 - 4.51282i) q^{85} +(-2.86522 - 3.30664i) q^{86} +(5.77458 + 3.71110i) q^{87} +(-3.94937 + 4.55781i) q^{88} +(-4.20077 + 1.23346i) q^{89} +(-0.415415 - 0.909632i) q^{90} +5.80187 q^{91} +(1.59790 + 4.52180i) q^{92} -7.52276 q^{93} +(1.69082 + 3.70239i) q^{94} +(-7.18911 + 2.11091i) q^{95} +(0.654861 - 0.755750i) q^{96} +(11.9404 + 7.67364i) q^{97} +(2.44126 + 2.81736i) q^{98} +(-0.858280 - 5.96947i) 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	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 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 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	0.415415	+	0.909632i	0.293743	+	0.643207i
$2$	0.415415	+	0.909632i	0.293743	+	0.643207i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$6$	0.654861	+	0.755750i	0.267346	+	0.308533i
$7$	−0.257432	−	1.79048i	−0.0973003	−	0.676738i	−0.978840	−	0.204628i	$-0.934401\pi$
$7$	−0.257432	−	1.79048i	−0.0973003	−	0.676738i	0.881539	−	0.472110i	$-0.156508\pi$
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.142315	−	0.989821i	0.0450039	−	0.313009i
$11$	2.50531	−	5.48586i	0.755378	−	1.65405i	−0.00107441	−	0.999999i	$-0.500342\pi$
$11$	2.50531	−	5.48586i	0.755378	−	1.65405i	0.756453	−	0.654048i	$-0.226931\pi$
$12$	−0.415415	+	0.909632i	−0.119920	+	0.262588i
$13$	−0.456463	+	3.17477i	−0.126600	+	0.880522i	0.823220	+	0.567723i	$0.192176\pi$
$13$	−0.456463	+	3.17477i	−0.126600	+	0.880522i	−0.949819	+	0.312799i	$0.898733\pi$
$14$	1.52174	−	0.977962i	0.406702	−	0.261371i
$15$	−0.959493	−	0.281733i	−0.247740	−	0.0727430i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	2.98566	+	3.44564i	0.724129	+	0.835690i	0.991797	−	0.127822i	$-0.0407985\pi$
$17$	2.98566	+	3.44564i	0.724129	+	0.835690i	−0.267668	+	0.963511i	$0.586253\pi$
$18$	0.841254	+	0.540641i	0.198285	+	0.127430i
$19$	4.90662	−	5.66254i	1.12566	−	1.29908i	0.176489	−	0.984303i	$-0.443526\pi$
$19$	4.90662	−	5.66254i	1.12566	−	1.29908i	0.949167	−	0.314773i	$-0.101928\pi$
$20$	0.959493	−	0.281733i	0.214549	−	0.0629973i
$21$	−0.751442	−	1.64543i	−0.163978	−	0.359062i
$22$	6.03085			1.28578
$23$	2.37095	−	4.16877i	0.494377	−	0.869248i
$23$	2.37095	−	4.16877i	0.494377	−	0.869248i
$24$	−1.00000			−0.204124
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	−3.07749	+	0.903633i	−0.603546	+	0.177217i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	1.52174	+	0.977962i	0.287581	+	0.184817i
$29$	4.49513	+	5.18766i	0.834725	+	0.963324i	0.999736	−	0.0229681i	$-0.00731161\pi$
$29$	4.49513	+	5.18766i	0.834725	+	0.963324i	−0.165012	+	0.986292i	$0.552766\pi$
$30$	−0.142315	−	0.989821i	−0.0259830	−	0.180716i
$31$	−7.21804	−	2.11941i	−1.29640	−	0.380657i	−0.440477	−	0.897764i	$-0.645191\pi$
$31$	−7.21804	−	2.11941i	−1.29640	−	0.380657i	−0.855921	+	0.517107i	$0.827009\pi$
$32$	0.841254	−	0.540641i	0.148714	−	0.0955727i
$33$	0.858280	−	5.96947i	0.149407	−	1.03915i
$34$	−1.89397	+	4.14722i	−0.324814	+	0.711243i
$35$	−0.751442	+	1.64543i	−0.127017	+	0.278128i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	−1.25926	+	0.809276i	−0.207021	+	0.133044i	−0.640043	−	0.768339i	$-0.721083\pi$
$37$	−1.25926	+	0.809276i	−0.207021	+	0.133044i	0.433022	+	0.901383i	$0.357447\pi$
$38$	7.18911	+	2.11091i	1.16623	+	0.342435i
$39$	0.456463	+	3.17477i	0.0730925	+	0.508370i
$40$	0.654861	+	0.755750i	0.103543	+	0.119494i
$41$	0.128152	+	0.0823581i	0.0200139	+	0.0128622i	0.550610	−	0.834763i	$-0.314395\pi$
$41$	0.128152	+	0.0823581i	0.0200139	+	0.0128622i	−0.530596	+	0.847625i	$0.678032\pi$
$42$	1.18457	−	1.36707i	0.182784	−	0.210944i
$43$	−4.19808	+	1.23267i	−0.640202	+	0.187980i	−0.585693	−	0.810533i	$-0.699177\pi$
$43$	−4.19808	+	1.23267i	−0.640202	+	0.187980i	−0.0545088	+	0.998513i	$0.517359\pi$
$44$	2.50531	+	5.48586i	0.377689	+	0.827024i
$45$	−1.00000			−0.149071
$46$	4.77697	+	0.424923i	0.704326	+	0.0626515i
$47$	4.07021			0.593700			0.296850	−	0.954924i	$-0.404064\pi$
$47$	4.07021			0.593700			0.296850	+	0.954924i	$0.404064\pi$
$48$	−0.415415	−	0.909632i	−0.0599600	−	0.131294i
$49$	3.57690	−	1.05027i	0.510985	−	0.150039i
$50$	−0.654861	+	0.755750i	−0.0926113	+	0.106879i
$51$	3.83547	+	2.46491i	0.537073	+	0.345156i
$52$	−2.10041	−	2.42400i	−0.291274	−	0.336149i
$53$	−0.323199	−	2.24790i	−0.0443947	−	0.308772i	−0.999905	−	0.0138130i	$-0.995603\pi$
$53$	−0.323199	−	2.24790i	−0.0443947	−	0.308772i	0.955510	−	0.294959i	$-0.0953061\pi$
$54$	0.959493	+	0.281733i	0.130570	+	0.0383389i
$55$	−5.07348	+	3.26052i	−0.684107	+	0.439649i
$56$	−0.257432	+	1.79048i	−0.0344009	+	0.239263i
$57$	3.11254	−	6.81552i	0.412267	−	0.902738i
$58$	−2.85151	+	6.24394i	−0.374422	+	0.819870i
$59$	−1.64530	+	11.4433i	−0.214200	+	1.48979i	0.544726	+	0.838614i	$0.316634\pi$
$59$	−1.64530	+	11.4433i	−0.214200	+	1.48979i	−0.758926	+	0.651177i	$0.774275\pi$
$60$	0.841254	−	0.540641i	0.108605	−	0.0697964i
$61$	−14.6736	−	4.30855i	−1.87876	−	0.551654i	−0.996763	−	0.0803993i	$-0.974380\pi$
$61$	−14.6736	−	4.30855i	−1.87876	−	0.551654i	−0.881997	−	0.471254i	$-0.843801\pi$
$62$	−1.07060	−	7.44619i	−0.135966	−	0.945667i
$63$	−1.18457	−	1.36707i	−0.149242	−	0.172235i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	2.10041	−	2.42400i	0.260524	−	0.300660i
$66$	5.78656	−	1.69909i	0.712276	−	0.209143i
$67$	−1.63864	−	3.58811i	−0.200191	−	0.438357i	0.782736	−	0.622354i	$-0.213824\pi$
$67$	−1.63864	−	3.58811i	−0.200191	−	0.438357i	−0.982927	+	0.183997i	$0.941096\pi$
$68$	−4.55923			−0.552888
$69$	1.10043	−	4.66787i	0.132476	−	0.561946i
$70$	−1.80889			−0.216204
$71$	1.08051	+	2.36598i	0.128233	+	0.280790i	0.962849	−	0.270042i	$-0.0870376\pi$
$71$	1.08051	+	2.36598i	0.128233	+	0.280790i	−0.834616	+	0.550832i	$0.814310\pi$
$72$	−0.959493	+	0.281733i	−0.113077	+	0.0332025i
$73$	−1.57119	+	1.81325i	−0.183894	+	0.212225i	−0.840210	−	0.542261i	$-0.817568\pi$
$73$	−1.57119	+	1.81325i	−0.183894	+	0.212225i	0.656316	+	0.754486i	$0.272114\pi$
$74$	−1.25926	−	0.809276i	−0.146386	−	0.0940764i
$75$	0.654861	+	0.755750i	0.0756168	+	0.0872664i
$76$	1.06631	+	7.41635i	0.122314	+	0.850714i
$77$	−10.4673	−	3.07347i	−1.19286	−	0.350254i
$78$	−2.69825	+	1.73406i	−0.305516	+	0.196343i
$79$	0.792412	−	5.51135i	0.0891533	−	0.620075i	−0.895436	−	0.445191i	$-0.853136\pi$
$79$	0.792412	−	5.51135i	0.0891533	−	0.620075i	0.984589	−	0.174884i	$-0.0559551\pi$
$80$	−0.415415	+	0.909632i	−0.0464448	+	0.101700i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−0.0216794	+	0.150784i	−0.00239409	+	0.0166513i
$83$	1.26936	−	0.815768i	0.139330	−	0.0895421i	−0.469119	−	0.883135i	$-0.655428\pi$
$83$	1.26936	−	0.815768i	0.139330	−	0.0895421i	0.608449	+	0.793593i	$0.291792\pi$
$84$	1.73562	+	0.509624i	0.189372	+	0.0556046i
$85$	−0.648846	−	4.51282i	−0.0703772	−	0.489485i
$86$	−2.86522	−	3.30664i	−0.308965	−	0.356564i
$87$	5.77458	+	3.71110i	0.619100	+	0.397871i
$88$	−3.94937	+	4.55781i	−0.421004	+	0.485865i
$89$	−4.20077	+	1.23346i	−0.445280	+	0.130746i	−0.496683	−	0.867932i	$-0.665449\pi$
$89$	−4.20077	+	1.23346i	−0.445280	+	0.130746i	0.0514028	+	0.998678i	$0.483631\pi$
$90$	−0.415415	−	0.909632i	−0.0437886	−	0.0958836i
$91$	5.80187			0.608201
$92$	1.59790	+	4.52180i	0.166593	+	0.471431i
$93$	−7.52276			−0.780074
$94$	1.69082	+	3.70239i	0.174395	+	0.381872i
$95$	−7.18911	+	2.11091i	−0.737587	+	0.216575i
$96$	0.654861	−	0.755750i	0.0668364	−	0.0771334i
$97$	11.9404	+	7.67364i	1.21237	+	0.779140i	0.981053	−	0.193739i	$-0.0620615\pi$
$97$	11.9404	+	7.67364i	1.21237	+	0.779140i	0.231313	+	0.972879i	$0.425698\pi$
$98$	2.44126	+	2.81736i	0.246604	+	0.284597i
$99$	−0.858280	−	5.96947i	−0.0862604	−	0.599954i
$100$	−0.959493	−	0.281733i	−0.0959493	−	0.0281733i
$101$	1.17379	−	0.754352i	0.116797	−	0.0750609i	−0.480938	−	0.876755i	$-0.659704\pi$
$101$	1.17379	−	0.754352i	0.116797	−	0.0750609i	0.597735	+	0.801694i	$0.296067\pi$
$102$	−0.648846	+	4.51282i	−0.0642453	+	0.446836i
$103$	−4.27500	+	9.36095i	−0.421229	+	0.922362i	0.573441	+	0.819247i	$0.305608\pi$
$103$	−4.27500	+	9.36095i	−0.421229	+	0.922362i	−0.994669	+	0.103115i	$0.967119\pi$
$104$	1.33241	−	2.91757i	0.130653	−	0.286091i
$105$	−0.257432	+	1.79048i	−0.0251228	+	0.174733i
$106$	1.91050	−	1.22780i	0.185564	−	0.119255i
$107$	10.0222	+	2.94280i	0.968887	+	0.284491i	0.727630	−	0.685970i	$-0.240622\pi$
$107$	10.0222	+	2.94280i	0.968887	+	0.284491i	0.241258	+	0.970461i	$0.422440\pi$
$108$	0.142315	+	0.989821i	0.0136943	+	0.0952456i
$109$	2.47646	+	2.85799i	0.237202	+	0.273746i	0.861853	−	0.507159i	$-0.169304\pi$
$109$	2.47646	+	2.85799i	0.237202	+	0.273746i	−0.624651	+	0.780904i	$0.714759\pi$
$110$	−5.07348	−	3.26052i	−0.483737	−	0.310879i
$111$	−0.980250	+	1.13127i	−0.0930412	+	0.107375i
$112$	−1.73562	+	0.509624i	−0.164001	+	0.0481550i
$113$	5.30798	+	11.6229i	0.499333	+	1.09339i	0.976686	+	0.214675i	$0.0688691\pi$
$113$	5.30798	+	11.6229i	0.499333	+	1.09339i	−0.477353	+	0.878712i	$0.658404\pi$
$114$	7.49261			0.701748
$115$	−4.24837	+	2.22516i	−0.396163	+	0.207497i
$116$	−6.86425			−0.637330
$117$	1.33241	+	2.91757i	0.123181	+	0.269729i
$118$	−11.0927	+	3.25710i	−1.02116	+	0.299841i
$119$	5.40074	−	6.23279i	0.495085	−	0.571359i
$120$	0.841254	+	0.540641i	0.0767956	+	0.0493535i
$121$	−16.6146	−	19.1743i	−1.51042	−	1.74311i
$122$	−2.17643	−	15.1374i	−0.197045	−	1.37048i
$123$	0.146164	+	0.0429175i	0.0131791	+	0.00386974i
$124$	6.32855	−	4.06711i	0.568320	−	0.365237i
$125$	0.142315	−	0.989821i	0.0127290	−	0.0885323i
$126$	0.751442	−	1.64543i	0.0669437	−	0.146586i
$127$	−7.62632	+	16.6993i	−0.676726	+	1.48182i	0.189348	+	0.981910i	$0.439362\pi$
$127$	−7.62632	+	16.6993i	−0.676726	+	1.48182i	−0.866075	+	0.499914i	$0.833365\pi$
$128$	−0.142315	+	0.989821i	−0.0125790	+	0.0874887i
$129$	−3.68075	+	2.36547i	−0.324072	+	0.208268i
$130$	3.07749	+	0.903633i	0.269914	+	0.0792538i
$131$	−2.71673	−	18.8953i	−0.237362	−	1.65089i	−0.664932	−	0.746904i	$-0.731539\pi$
$131$	−2.71673	−	18.8953i	−0.237362	−	1.65089i	0.427570	−	0.903982i	$-0.359370\pi$
$132$	3.94937	+	4.55781i	0.343748	+	0.396707i
$133$	−11.4018	−	7.32749i	−0.988661	−	0.635374i
$134$	2.58315	−	2.98111i	0.223150	−	0.257529i
$135$	−0.959493	+	0.281733i	−0.0825800	+	0.0242477i
$136$	−1.89397	−	4.14722i	−0.162407	−	0.355621i
$137$	6.11555			0.522487			0.261243	−	0.965273i	$-0.415867\pi$
$137$	6.11555			0.522487			0.261243	+	0.965273i	$0.415867\pi$
$138$	4.70318	−	0.938117i	0.400362	−	0.0798578i
$139$	−20.2563			−1.71812			−0.859059	−	0.511876i	$-0.828951\pi$
$139$	−20.2563			−1.71812			−0.859059	+	0.511876i	$0.828951\pi$
$140$	−0.751442	−	1.64543i	−0.0635084	−	0.139064i
$141$	3.90533	−	1.14671i	0.328888	−	0.0965704i
$142$	−1.70331	+	1.96573i	−0.142939	+	0.164960i
$143$	16.2727	+	10.4579i	1.36079	+	0.874529i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	−0.976885	−	6.79438i	−0.0811259	−	0.564243i
$146$	−2.30209	−	0.675954i	−0.190522	−	0.0559424i
$147$	3.13611	−	2.01546i	0.258662	−	0.166232i
$148$	0.213029	−	1.48165i	0.0175108	−	0.121791i
$149$	−5.18756	+	11.3592i	−0.424982	+	0.930580i	0.569133	+	0.822246i	$0.307279\pi$
$149$	−5.18756	+	11.3592i	−0.424982	+	0.930580i	−0.994115	+	0.108334i	$0.965448\pi$
$150$	−0.415415	+	0.909632i	−0.0339185	+	0.0742711i
$151$	−0.913002	+	6.35007i	−0.0742991	+	0.516761i	0.918353	+	0.395761i	$0.129519\pi$
$151$	−0.913002	+	6.35007i	−0.0742991	+	0.516761i	−0.992652	+	0.121000i	$0.961390\pi$
$152$	−6.30319	+	4.05081i	−0.511256	+	0.328564i
$153$	4.37455	+	1.28448i	0.353661	+	0.103844i
$154$	−1.55254	−	10.7981i	−0.125107	−	0.870138i
$155$	4.92636	+	5.68532i	0.395695	+	0.456656i
$156$	−2.69825	−	1.73406i	−0.216033	−	0.138836i
$157$	−11.0393	+	12.7400i	−0.881032	+	1.01677i	0.118684	+	0.992932i	$0.462133\pi$
$157$	−11.0393	+	12.7400i	−0.881032	+	1.01677i	−0.999716	+	0.0238335i	$0.992413\pi$
$158$	5.34248	−	1.56869i	0.425025	−	0.124799i
$159$	−0.943412	−	2.06578i	−0.0748175	−	0.163827i
$160$	−1.00000			−0.0790569
$161$	−8.07446	−	3.17196i	−0.636356	−	0.249986i
$162$	1.00000			0.0785674
$163$	−4.63074	−	10.1399i	−0.362708	−	0.794219i	−0.999727	−	0.0233710i	$-0.992560\pi$
$163$	−4.63074	−	10.1399i	−0.362708	−	0.794219i	0.637019	−	0.770848i	$-0.280167\pi$
$164$	−0.146164	+	0.0429175i	−0.0114135	+	0.00335129i
$165$	−3.94937	+	4.55781i	−0.307458	+	0.354825i
$166$	1.26936	+	0.815768i	0.0985214	+	0.0633158i
$167$	−5.81633	−	6.71240i	−0.450081	−	0.519421i	0.484683	−	0.874690i	$-0.338935\pi$
$167$	−5.81633	−	6.71240i	−0.450081	−	0.519421i	−0.934764	+	0.355268i	$0.884389\pi$
$168$	0.257432	+	1.79048i	0.0198613	+	0.138139i
$169$	2.60262	+	0.764199i	0.200202	+	0.0587846i
$170$	3.83547	−	2.46491i	0.294167	−	0.189050i
$171$	1.06631	−	7.41635i	0.0815428	−	0.567142i
$172$	1.81757	−	3.97993i	0.138588	−	0.303466i
$173$	4.92287	−	10.7796i	0.374279	−	0.819556i	−0.624964	−	0.780653i	$-0.714886\pi$
$173$	4.92287	−	10.7796i	0.374279	−	0.819556i	0.999243	−	0.0389027i	$-0.0123862\pi$
$174$	−0.976885	+	6.79438i	−0.0740575	+	0.515081i
$175$	1.52174	−	0.977962i	0.115033	−	0.0739270i
$176$	−5.78656	−	1.69909i	−0.436178	−	0.128074i
$177$	1.64530	+	11.4433i	0.123668	+	0.860132i
$178$	−2.86705	−	3.30876i	−0.214895	−	0.248002i
$179$	17.0969	+	10.9875i	1.27789	+	0.821247i	0.990625	−	0.136606i	$-0.0436193\pi$
$179$	17.0969	+	10.9875i	1.27789	+	0.821247i	0.287260	+	0.957853i	$0.407256\pi$
$180$	0.654861	−	0.755750i	0.0488104	−	0.0563302i
$181$	8.20588	−	2.40946i	0.609938	−	0.179094i	0.0378464	−	0.999284i	$-0.487950\pi$
$181$	8.20588	−	2.40946i	0.609938	−	0.179094i	0.572092	+	0.820189i	$0.306132\pi$
$182$	2.41018	+	5.27757i	0.178655	+	0.391199i
$183$	−15.2931			−1.13050
$184$	−3.44939	+	3.33193i	−0.254292	+	0.245633i
$185$	1.49688			0.110053
$186$	−3.12507	−	6.84294i	−0.229141	−	0.501749i
$187$	26.3823	−	7.74653i	1.92926	−	0.566482i
$188$	−2.66542	+	3.07606i	−0.194396	+	0.224344i
$189$	−1.52174	−	0.977962i	−0.110690	−	0.0711362i
$190$	−4.90662	−	5.66254i	−0.355964	−	0.410804i
$191$	0.555314	+	3.86229i	0.0401811	+	0.279466i	0.999999	−	0.00115669i	$-0.000368186\pi$
$191$	0.555314	+	3.86229i	0.0401811	+	0.279466i	−0.959818	+	0.280623i	$0.909459\pi$
$192$	0.959493	+	0.281733i	0.0692454	+	0.0203323i
$193$	1.16524	−	0.748852i	0.0838755	−	0.0539035i	−0.498031	−	0.867159i	$-0.665943\pi$
$193$	1.16524	−	0.748852i	0.0838755	−	0.0539035i	0.581906	+	0.813256i	$0.302307\pi$
$194$	−2.01996	+	14.0491i	−0.145025	+	1.00867i
$195$	1.33241	−	2.91757i	0.0954157	−	0.208931i
$196$	−1.54863	+	3.39102i	−0.110616	+	0.242216i
$197$	−1.22112	+	8.49310i	−0.0870014	+	0.605108i	0.898947	+	0.438058i	$0.144333\pi$
$197$	−1.22112	+	8.49310i	−0.0870014	+	0.605108i	−0.985948	+	0.167051i	$0.946576\pi$
$198$	5.07348	−	3.26052i	0.360556	−	0.231715i
$199$	−18.1015	−	5.31508i	−1.28318	−	0.376776i	−0.432108	−	0.901822i	$-0.642230\pi$
$199$	−18.1015	−	5.31508i	−1.28318	−	0.376776i	−0.851074	+	0.525046i	$0.824048\pi$
$200$	−0.142315	−	0.989821i	−0.0100632	−	0.0699909i
$201$	−2.58315	−	2.98111i	−0.182201	−	0.210271i
$202$	1.17379	+	0.754352i	0.0825879	+	0.0530760i
$203$	8.13121	−	9.38392i	0.570699	−	0.658622i
$204$	−4.37455	+	1.28448i	−0.306280	+	0.0899318i
$205$	−0.0632819	−	0.138568i	−0.00441980	−	0.00967801i
$206$	−10.2909			−0.717002
$207$	−0.259236	−	4.78882i	−0.0180181	−	0.332846i
$208$	3.20741			0.222394
$209$	−18.7713	−	41.1034i	−1.29844	−	2.84318i
$210$	−1.73562	+	0.509624i	−0.119769	+	0.0351674i
$211$	−4.16152	+	4.80265i	−0.286491	+	0.330628i	−0.880693	−	0.473688i	$-0.842922\pi$
$211$	−4.16152	+	4.80265i	−0.286491	+	0.330628i	0.594202	+	0.804316i	$0.297468\pi$
$212$	1.91050	+	1.22780i	0.131213	+	0.0843257i
$213$	1.70331	+	1.96573i	0.116709	+	0.134690i
$214$	1.48653	+	10.3390i	0.101617	+	0.706762i
$215$	4.19808	+	1.23267i	0.286307	+	0.0840673i
$216$	−0.841254	+	0.540641i	−0.0572401	+	0.0367859i
$217$	−1.93660	+	13.4694i	−0.131465	+	0.914360i
$218$	−1.57096	+	3.43992i	−0.106399	+	0.232981i
$219$	−0.996696	+	2.18246i	−0.0673504	+	0.147477i
$220$	0.858280	−	5.96947i	0.0578652	−	0.402461i
$221$	−12.3019	+	7.90597i	−0.827518	+	0.531813i
$222$	−1.43625	−	0.421721i	−0.0963947	−	0.0283040i
$223$	0.581821	+	4.04666i	0.0389616	+	0.270984i	0.999985	−	0.00548315i	$-0.00174535\pi$
$223$	0.581821	+	4.04666i	0.0389616	+	0.270984i	−0.961023	+	0.276467i	$0.910836\pi$
$224$	−1.18457	−	1.36707i	−0.0791476	−	0.0913412i
$225$	0.841254	+	0.540641i	0.0560836	+	0.0360427i
$226$	−8.36751	+	9.65662i	−0.556598	+	0.642349i
$227$	8.27830	−	2.43073i	0.549450	−	0.161333i	0.00478784	−	0.999989i	$-0.498476\pi$
$227$	8.27830	−	2.43073i	0.549450	−	0.161333i	0.544662	+	0.838655i	$0.316658\pi$
$228$	3.11254	+	6.81552i	0.206133	+	0.451369i
$229$	18.0308			1.19151			0.595754	−	0.803167i	$-0.296853\pi$
$229$	18.0308			1.19151			0.595754	+	0.803167i	$0.296853\pi$
$230$	−3.78891	−	2.94009i	−0.249833	−	0.193864i
$231$	−10.9092			−0.717771
$232$	−2.85151	−	6.24394i	−0.187211	−	0.409935i
$233$	−20.3491	+	5.97504i	−1.33312	+	0.391438i	−0.869208	−	0.494446i	$-0.835371\pi$
$233$	−20.3491	+	5.97504i	−1.33312	+	0.391438i	−0.463907	+	0.885884i	$0.653553\pi$
$234$	−2.10041	+	2.42400i	−0.137308	+	0.158462i
$235$	−3.42407	−	2.20052i	−0.223362	−	0.143546i
$236$	−7.57083	−	8.73721i	−0.492819	−	0.568744i
$237$	−0.792412	−	5.51135i	−0.0514727	−	0.358001i
$238$	7.91309	+	2.32349i	0.512930	+	0.150610i
$239$	13.4039	−	8.61416i	0.867025	−	0.557203i	−0.0298161	−	0.999555i	$-0.509492\pi$
$239$	13.4039	−	8.61416i	0.867025	−	0.557203i	0.896842	+	0.442352i	$0.145856\pi$
$240$	−0.142315	+	0.989821i	−0.00918638	+	0.0638927i
$241$	−9.75659	+	21.3639i	−0.628477	+	1.37617i	0.280713	+	0.959792i	$0.409429\pi$
$241$	−9.75659	+	21.3639i	−0.628477	+	1.37617i	−0.909190	+	0.416381i	$0.863298\pi$
$242$	10.5396	−	23.0784i	0.677509	−	1.48354i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	12.8653	−	8.26805i	0.823619	−	0.529308i
$245$	−3.57690	−	1.05027i	−0.228520	−	0.0670994i
$246$	0.0216794	+	0.150784i	0.00138223	+	0.00961362i
$247$	15.7376	+	18.1621i	1.00136	+	1.15563i
$248$	6.32855	+	4.06711i	0.401863	+	0.258262i
$249$	0.988113	−	1.14034i	0.0626191	−	0.0722663i
$250$	0.959493	−	0.281733i	0.0606837	−	0.0178183i
$251$	−1.91423	−	4.19157i	−0.120825	−	0.264569i	0.839549	−	0.543283i	$-0.182819\pi$
$251$	−1.91423	−	4.19157i	−0.120825	−	0.264569i	−0.960374	+	0.278714i	$0.910092\pi$
$252$	1.80889			0.113950
$253$	−16.9293	−	23.4507i	−1.06434	−	1.47433i
$254$	−18.3583			−1.15190
$255$	−1.89397	−	4.14722i	−0.118605	−	0.259709i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−14.5708	+	16.8156i	−0.908904	+	1.04893i	0.0896928	+	0.995969i	$0.471411\pi$
$257$	−14.5708	+	16.8156i	−0.908904	+	1.04893i	−0.998597	+	0.0529613i	$0.983134\pi$
$258$	−3.68075	−	2.36547i	−0.229153	−	0.147268i
$259$	1.77317	+	2.04634i	0.110179	+	0.127154i
$260$	0.456463	+	3.17477i	0.0283086	+	0.196891i
$261$	6.58620	+	1.93388i	0.407676	+	0.119704i
$262$	16.0592	−	10.3206i	0.992138	−	0.637609i
$263$	2.42176	−	16.8437i	0.149332	−	1.03863i	−0.767984	−	0.640469i	$-0.778740\pi$
$263$	2.42176	−	16.8437i	0.149332	−	1.03863i	0.917316	−	0.398159i	$-0.130351\pi$
$264$	−2.50531	+	5.48586i	−0.154191	+	0.337631i
$265$	−0.943412	+	2.06578i	−0.0579534	+	0.126900i
$266$	1.92884	−	13.4154i	0.118265	−	0.822550i
$267$	−3.68310	+	2.36699i	−0.225402	+	0.144857i
$268$	3.78479	+	1.11131i	0.231193	+	0.0678844i
$269$	−1.86775	−	12.9905i	−0.113879	−	0.792044i	−0.964085	−	0.265594i	$-0.914432\pi$
$269$	−1.86775	−	12.9905i	−0.113879	−	0.792044i	0.850206	−	0.526450i	$-0.176477\pi$
$270$	−0.654861	−	0.755750i	−0.0398536	−	0.0459935i
$271$	20.3379	+	13.0704i	1.23544	+	0.793968i	0.984729	−	0.174095i	$-0.0557000\pi$
$271$	20.3379	+	13.0704i	1.23544	+	0.793968i	0.250709	+	0.968063i	$0.419336\pi$
$272$	2.98566	−	3.44564i	0.181032	−	0.208922i
$273$	5.56685	−	1.63458i	0.336921	−	0.0989290i
$274$	2.54049	+	5.56290i	0.153477	+	0.336067i
$275$	6.03085			0.363674
$276$	2.80711	+	3.88846i	0.168968	+	0.234058i
$277$	−2.67381			−0.160654			−0.0803268	−	0.996769i	$-0.525596\pi$
$277$	−2.67381			−0.160654			−0.0803268	+	0.996769i	$0.525596\pi$
$278$	−8.41478	−	18.4258i	−0.504685	−	1.10511i
$279$	−7.21804	+	2.11941i	−0.432133	+	0.126886i
$280$	1.18457	−	1.36707i	0.0707918	−	0.0816981i
$281$	−23.2142	−	14.9188i	−1.38484	−	0.889983i	−0.385377	−	0.922759i	$-0.625929\pi$
$281$	−23.2142	−	14.9188i	−1.38484	−	0.889983i	−0.999463	+	0.0327763i	$0.989565\pi$
$282$	2.66542	+	3.07606i	0.158723	+	0.183176i
$283$	4.44153	+	30.8915i	0.264021	+	1.83631i	0.501793	+	0.864988i	$0.332674\pi$
$283$	4.44153	+	30.8915i	0.264021	+	1.83631i	−0.237771	+	0.971321i	$0.576417\pi$
$284$	−2.49567	−	0.732796i	−0.148091	−	0.0434834i
$285$	−6.30319	+	4.05081i	−0.373369	+	0.239949i
$286$	−2.75286	+	19.1465i	−0.162780	+	1.13216i
$287$	0.114470	−	0.250655i	0.00675697	−	0.0147957i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	−0.538887	+	3.74804i	−0.0316992	+	0.220473i
$290$	5.77458	−	3.71110i	0.339095	−	0.217923i
$291$	13.6187	+	3.99880i	0.798340	+	0.234414i
$292$	−0.341453	−	2.37486i	−0.0199820	−	0.138978i
$293$	15.3733	+	17.7418i	0.898119	+	1.03648i	0.999134	+	0.0415997i	$0.0132454\pi$
$293$	15.3733	+	17.7418i	0.898119	+	1.03648i	−0.101015	+	0.994885i	$0.532209\pi$
$294$	3.13611	+	2.01546i	0.182902	+	0.117544i
$295$	7.57083	−	8.73721i	0.440791	−	0.508700i
$296$	1.43625	−	0.421721i	0.0834803	−	0.0245120i
$297$	−2.50531	−	5.48586i	−0.145373	−	0.318322i
$298$	−12.4877			−0.723391
$299$	12.1526	+	9.43009i	0.702803	+	0.545356i
$300$	−1.00000			−0.0577350
$301$	3.28779	+	7.19926i	0.189505	+	0.414959i
$302$	−6.15550	+	1.80742i	−0.354209	+	0.104005i
$303$	0.913722	−	1.05449i	0.0524920	−	0.0605790i
$304$	−6.30319	−	4.05081i	−0.361513	−	0.232330i
$305$	10.0148	+	11.5577i	0.573447	+	0.661793i
$306$	0.648846	+	4.51282i	0.0370921	+	0.257981i
$307$	−13.9465	−	4.09507i	−0.795969	−	0.233718i	−0.141631	−	0.989920i	$-0.545235\pi$
$307$	−13.9465	−	4.09507i	−0.795969	−	0.233718i	−0.654338	+	0.756202i	$0.727053\pi$
$308$	9.17738	−	5.89794i	0.522930	−	0.336066i
$309$	−1.46455	+	10.1862i	−0.0833154	+	0.579471i
$310$	−3.12507	+	6.84294i	−0.177492	+	0.388653i
$311$	−12.0498	+	26.3854i	−0.683283	+	1.49618i	0.175843	+	0.984418i	$0.443735\pi$
$311$	−12.0498	+	26.3854i	−0.683283	+	1.49618i	−0.859126	+	0.511763i	$0.828992\pi$
$312$	0.456463	−	3.17477i	0.0258421	−	0.179736i
$313$	20.4900	−	13.1681i	1.15816	−	0.744305i	0.186914	−	0.982376i	$-0.440151\pi$
$313$	20.4900	−	13.1681i	1.15816	−	0.744305i	0.971248	+	0.238071i	$0.0765151\pi$
$314$	−16.1746	−	4.74930i	−0.912788	−	0.268019i
$315$	0.257432	+	1.79048i	0.0145047	+	0.100882i
$316$	3.64628	+	4.20803i	0.205119	+	0.236720i
$317$	20.3002	+	13.0461i	1.14017	+	0.732744i	0.967659	−	0.252263i	$-0.0811750\pi$
$317$	20.3002	+	13.0461i	1.14017	+	0.732744i	0.172513	+	0.985007i	$0.444811\pi$
$318$	1.48720	−	1.71632i	0.0833978	−	0.0962462i
$319$	39.7204	−	11.6630i	2.22392	−	0.653001i
$320$	−0.415415	−	0.909632i	−0.0232224	−	0.0508500i
$321$	10.4454			0.583003
$322$	−0.468930	−	8.66247i	−0.0261324	−	0.482740i
$323$	34.1606			1.90074
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	−3.07749	+	0.903633i	−0.170708	+	0.0501245i
$326$	7.29991	−	8.42454i	0.404304	−	0.466592i
$327$	3.18134	+	2.04452i	0.175928	+	0.113062i
$328$	−0.0997577	−	0.115127i	−0.00550820	−	0.00635680i
$329$	−1.04780	−	7.28763i	−0.0577672	−	0.401780i
$330$	−5.78656	−	1.69909i	−0.318540	−	0.0935317i
$331$	10.5424	−	6.77517i	0.579461	−	0.372397i	−0.217835	−	0.975986i	$-0.569899\pi$
$331$	10.5424	−	6.77517i	0.579461	−	0.372397i	0.797296	+	0.603589i	$0.206263\pi$
$332$	−0.214737	+	1.49353i	−0.0117852	+	0.0819682i
$333$	−0.621828	+	1.36161i	−0.0340759	+	0.0746159i
$334$	3.68963	−	8.07915i	0.201887	−	0.442072i
$335$	−0.561371	+	3.90442i	−0.0306710	+	0.213321i
$336$	−1.52174	+	0.977962i	−0.0830176	+	0.0533522i
$337$	18.8161	+	5.52491i	1.02498	+	0.300961i	0.750668	−	0.660680i	$-0.229732\pi$
$337$	18.8161	+	5.52491i	1.02498	+	0.300961i	0.274311	+	0.961641i	$0.411550\pi$
$338$	0.386029	+	2.68489i	0.0209972	+	0.146039i
$339$	8.36751	+	9.65662i	0.454461	+	0.524476i
$340$	3.83547	+	2.46491i	0.208008	+	0.133678i
$341$	−29.7102	+	34.2873i	−1.60889	+	1.85676i
$342$	7.18911	−	2.11091i	0.388743	−	0.114145i
$343$	−8.06139	−	17.6520i	−0.435274	−	0.953118i
$344$	4.37531			0.235901
$345$	−3.44939	+	3.33193i	−0.185709	+	0.179385i
$346$	11.8505			0.637086
$347$	5.18067	+	11.3441i	0.278113	+	0.608983i	0.996212	−	0.0869585i	$-0.0277148\pi$
$347$	5.18067	+	11.3441i	0.278113	+	0.608983i	−0.718099	+	0.695941i	$0.754987\pi$
$348$	−6.58620	+	1.93388i	−0.353058	+	0.103667i
$349$	8.14883	−	9.40425i	0.436197	−	0.503398i	−0.494506	−	0.869174i	$-0.664651\pi$
$349$	8.14883	−	9.40425i	0.436197	−	0.503398i	0.930703	+	0.365776i	$0.119196\pi$
$350$	1.52174	+	0.977962i	0.0813403	+	0.0522743i
$351$	2.10041	+	2.42400i	0.112112	+	0.129384i
$352$	−0.858280	−	5.96947i	−0.0457465	−	0.318174i
$353$	33.8327	+	9.93418i	1.80073	+	0.528743i	0.997737	−	0.0672394i	$-0.0214191\pi$
$353$	33.8327	+	9.93418i	1.80073	+	0.528743i	0.802997	+	0.595983i	$0.203237\pi$
$354$	−9.72571	+	6.25034i	−0.516916	+	0.332202i
$355$	0.370166	−	2.57456i	0.0196463	−	0.136643i
$356$	1.81873	−	3.98247i	0.0963927	−	0.211071i
$357$	3.42600	−	7.50188i	0.181323	−	0.397042i
$358$	−2.89229	+	20.1163i	−0.152862	+	1.06318i
$359$	−15.7141	+	10.0989i	−0.829361	+	0.532998i	−0.885075	−	0.465449i	$-0.845893\pi$
$359$	−15.7141	+	10.0989i	−0.829361	+	0.532998i	0.0557139	+	0.998447i	$0.482257\pi$
$360$	0.959493	+	0.281733i	0.0505697	+	0.0148486i
$361$	−5.28547	−	36.7612i	−0.278183	−	1.93480i
$362$	5.60057	+	6.46340i	0.294360	+	0.339709i
$363$	−21.3436	−	13.7167i	−1.12025	−	0.719940i
$364$	−3.79942	+	4.38476i	−0.199144	+	0.229824i
$365$	2.30209	−	0.675954i	0.120497	−	0.0353811i
$366$	−6.35297	−	13.9111i	−0.332075	−	0.727143i
$367$	4.48888			0.234318			0.117159	−	0.993113i	$-0.462621\pi$
$367$	4.48888			0.234318			0.117159	+	0.993113i	$0.462621\pi$
$368$	−4.46375	−	1.75354i	−0.232689	−	0.0914095i
$369$	0.152334			0.00793020
$370$	0.621828	+	1.36161i	0.0323273	+	0.0707869i
$371$	−3.94161	+	1.15736i	−0.204638	+	0.0600873i
$372$	4.92636	−	5.68532i	0.255420	−	0.294770i
$373$	12.1755	+	7.82475i	0.630426	+	0.405150i	0.816467	−	0.577392i	$-0.195929\pi$
$373$	12.1755	+	7.82475i	0.630426	+	0.405150i	−0.186041	+	0.982542i	$0.559566\pi$
$374$	18.0061	+	20.7801i	0.931072	+	1.07451i
$375$	−0.142315	−	0.989821i	−0.00734911	−	0.0511142i
$376$	−3.90533	−	1.14671i	−0.201402	−	0.0591370i
$377$	−18.5215	+	11.9030i	−0.953903	+	0.613037i
$378$	0.257432	−	1.79048i	0.0132409	−	0.0920924i
$379$	9.27060	−	20.2998i	0.476199	−	1.04273i	−0.507293	−	0.861774i	$-0.669354\pi$
$379$	9.27060	−	20.2998i	0.476199	−	1.04273i	0.983491	−	0.180956i	$-0.0579190\pi$
$380$	3.11254	−	6.81552i	0.159670	−	0.349629i
$381$	−2.61266	+	18.1715i	−0.133851	+	0.930952i
$382$	−3.28258	+	2.10959i	−0.167951	+	0.107936i
$383$	15.6649	+	4.59964i	0.800441	+	0.235031i	0.656274	−	0.754523i	$-0.272132\pi$
$383$	15.6649	+	4.59964i	0.800441	+	0.235031i	0.144167	+	0.989553i	$0.453950\pi$
$384$	0.142315	+	0.989821i	0.00726247	+	0.0505116i
$385$	7.14399	+	8.24460i	0.364091	+	0.420184i
$386$	1.16524	+	0.748852i	0.0593090	+	0.0381155i
$387$	−2.86522	+	3.30664i	−0.145647	+	0.168086i
$388$	−13.6187	+	3.99880i	−0.691383	+	0.203008i
$389$	−0.885452	−	1.93887i	−0.0448942	−	0.0983046i	0.885856	−	0.463960i	$-0.153572\pi$
$389$	−0.885452	−	1.93887i	−0.0448942	−	0.0983046i	−0.930750	+	0.365656i	$0.880845\pi$
$390$	3.20741			0.162414
$391$	21.4429	−	4.27709i	1.08441	−	0.216302i
$392$	−3.72790			−0.188288
$393$	−7.93009	−	17.3645i	−0.400020	−	0.875922i
$394$	−8.23287	+	2.41739i	−0.414766	+	0.121786i
$395$	−3.64628	+	4.20803i	−0.183464	+	0.211729i
$396$	5.07348	+	3.26052i	0.254952	+	0.163848i
$397$	3.48230	+	4.01879i	0.174772	+	0.201697i	0.836377	−	0.548155i	$-0.184670\pi$
$397$	3.48230	+	4.01879i	0.174772	+	0.201697i	−0.661605	+	0.749853i	$0.730124\pi$
$398$	−2.68487	−	18.6737i	−0.134580	−	0.936027i
$399$	−13.0043	−	3.81842i	−0.651031	−	0.191160i
$400$	0.841254	−	0.540641i	0.0420627	−	0.0270320i
$401$	2.43791	−	16.9560i	0.121743	−	0.846744i	−0.833836	−	0.552012i	$-0.813860\pi$
$401$	2.43791	−	16.9560i	0.121743	−	0.846744i	0.955580	−	0.294733i	$-0.0952306\pi$
$402$	1.63864	−	3.58811i	0.0817277	−	0.178959i
$403$	10.0234	−	21.9482i	0.499300	−	1.09332i
$404$	−0.198571	+	1.38109i	−0.00987927	+	0.0687118i
$405$	−0.841254	+	0.540641i	−0.0418022	+	0.0268647i
$406$	11.9137	+	3.49819i	0.591269	+	0.173612i
$407$	1.28474	+	8.93559i	0.0636824	+	0.442921i
$408$	−2.98566	−	3.44564i	−0.147812	−	0.170584i
$409$	−8.64742	−	5.55736i	−0.427587	−	0.274794i	0.309097	−	0.951031i	$-0.399973\pi$
$409$	−8.64742	−	5.55736i	−0.427587	−	0.274794i	−0.736684	+	0.676237i	$0.763610\pi$
$410$	0.0997577	−	0.115127i	0.00492668	−	0.00568569i
$411$	5.86783	−	1.72295i	0.289439	−	0.0849869i
$412$	−4.27500	−	9.36095i	−0.210614	−	0.461181i
$413$	20.9126			1.02904
$414$	4.24837	−	2.22516i	0.208796	−	0.109360i
$415$	−1.50889			−0.0740685
$416$	1.33241	+	2.91757i	0.0653267	+	0.143045i
$417$	−19.4358	+	5.70686i	−0.951775	+	0.279466i
$418$	29.5911	−	34.1499i	1.44735	−	1.67033i
$419$	15.9831	+	10.2717i	0.780828	+	0.501808i	0.869308	−	0.494270i	$-0.164565\pi$
$419$	15.9831	+	10.2717i	0.780828	+	0.501808i	−0.0884805	+	0.996078i	$0.528201\pi$
$420$	−1.18457	−	1.36707i	−0.0578013	−	0.0667062i
$421$	−4.53963	−	31.5738i	−0.221248	−	1.53881i	−0.733328	−	0.679875i	$-0.762034\pi$
$421$	−4.53963	−	31.5738i	−0.221248	−	1.53881i	0.512080	−	0.858938i	$-0.328875\pi$
$422$	−6.09740	−	1.79036i	−0.296817	−	0.0871532i
$423$	3.42407	−	2.20052i	0.166484	−	0.106993i
$424$	−0.323199	+	2.24790i	−0.0156959	+	0.109167i
$425$	−1.89397	+	4.14722i	−0.0918712	+	0.201170i
$426$	−1.08051	+	2.36598i	−0.0523508	+	0.114632i
$427$	−3.93693	+	27.3819i	−0.190521	+	1.32511i
$428$	−8.78720	+	5.64719i	−0.424745	+	0.272967i
$429$	18.5599	+	5.44968i	0.896080	+	0.263113i
$430$	0.622672	+	4.33078i	0.0300279	+	0.208849i
$431$	3.46434	+	3.99806i	0.166871	+	0.192580i	0.833026	−	0.553234i	$-0.186606\pi$
$431$	3.46434	+	3.99806i	0.166871	+	0.192580i	−0.666155	+	0.745814i	$0.732061\pi$
$432$	−0.841254	−	0.540641i	−0.0404748	−	0.0260116i
$433$	−15.5466	+	17.9417i	−0.747122	+	0.862224i	−0.994286	−	0.106749i	$-0.965956\pi$
$433$	−15.5466	+	17.9417i	−0.747122	+	0.862224i	0.247164	+	0.968974i	$0.420501\pi$
$434$	−13.0567	+	3.83378i	−0.626740	+	0.184027i
$435$	−2.85151	−	6.24394i	−0.136720	−	0.299374i
$436$	−3.78166			−0.181109
$437$	−11.9725	−	33.8801i	−0.572720	−	1.62071i
$438$	−2.39928			−0.114642
$439$	15.5447	+	34.0381i	0.741908	+	1.62455i	0.780391	+	0.625292i	$0.215020\pi$
$439$	15.5447	+	34.0381i	0.741908	+	1.62455i	−0.0384835	+	0.999259i	$0.512253\pi$
$440$	5.78656	−	1.69909i	0.275863	−	0.0810008i
$441$	2.44126	−	2.81736i	0.116250	−	0.134160i
$442$	−12.3019	−	7.90597i	−0.585143	−	0.376049i
$443$	−24.7484	−	28.5612i	−1.17583	−	1.35698i	−0.920792	−	0.390054i	$-0.872456\pi$
$443$	−24.7484	−	28.5612i	−1.17583	−	1.35698i	−0.255041	−	0.966930i	$-0.582089\pi$
$444$	−0.213029	−	1.48165i	−0.0101099	−	0.0703158i
$445$	4.20077	+	1.23346i	0.199135	+	0.0584715i
$446$	−3.43927	+	2.21028i	−0.162854	+	0.104660i
$447$	−1.77718	+	12.3606i	−0.0840577	+	0.584634i
$448$	0.751442	−	1.64543i	0.0355023	−	0.0777391i
$449$	1.64231	−	3.59616i	0.0775055	−	0.169713i	−0.866913	−	0.498460i	$-0.833899\pi$
$449$	1.64231	−	3.59616i	0.0775055	−	0.169713i	0.944418	+	0.328747i	$0.106626\pi$
$450$	−0.142315	+	0.989821i	−0.00670879	+	0.0466606i
$451$	0.772864	−	0.496690i	0.0363927	−	0.0233882i
$452$	−12.2600	−	3.59985i	−0.576660	−	0.169323i
$453$	0.913002	+	6.35007i	0.0428966	+	0.298352i
$454$	5.65000	+	6.52045i	0.265168	+	0.306020i
$455$	−4.88084	−	3.13673i	−0.228817	−	0.147052i
$456$	−4.90662	+	5.66254i	−0.229773	+	0.265173i
$457$	5.14604	−	1.51101i	0.240722	−	0.0706823i	−0.159146	−	0.987255i	$-0.550874\pi$
$457$	5.14604	−	1.51101i	0.240722	−	0.0706823i	0.399868	+	0.916573i	$0.369056\pi$
$458$	7.49026	+	16.4014i	0.349997	+	0.766387i
$459$	4.55923			0.212807
$460$	1.10043	−	4.66787i	0.0513079	−	0.217641i
$461$	0.997262			0.0464471			0.0232236	−	0.999730i	$-0.492607\pi$
$461$	0.997262			0.0464471			0.0232236	+	0.999730i	$0.492607\pi$
$462$	−4.53183	−	9.92333i	−0.210840	−	0.461675i
$463$	−7.93237	+	2.32916i	−0.368649	+	0.108245i	−0.460809	−	0.887499i	$-0.652441\pi$
$463$	−7.93237	+	2.32916i	−0.368649	+	0.108245i	0.0921607	+	0.995744i	$0.470623\pi$
$464$	4.49513	−	5.18766i	0.208681	−	0.240831i
$465$	6.32855	+	4.06711i	0.293479	+	0.188608i
$466$	−13.8884	−	16.0281i	−0.643369	−	0.742487i
$467$	4.19430	+	29.1720i	0.194089	+	1.34992i	0.821044	+	0.570864i	$0.193392\pi$
$467$	4.19430	+	29.1720i	0.194089	+	1.34992i	−0.626955	+	0.779055i	$0.715699\pi$
$468$	−3.07749	−	0.903633i	−0.142257	−	0.0417704i
$469$	−6.00261	+	3.85764i	−0.277175	+	0.178129i
$470$	0.579251	−	4.02878i	0.0267188	−	0.185834i
$471$	−7.00285	+	15.3341i	−0.322674	+	0.706558i
$472$	4.80260	−	10.5162i	0.221058	−	0.484049i
$473$	−3.75524	+	26.1183i	−0.172666	+	1.20092i
$474$	4.68412	−	3.01030i	0.215149	−	0.138268i
$475$	7.18911	+	2.11091i	0.329859	+	0.0968554i
$476$	1.17369	+	8.16322i	0.0537962	+	0.374161i
$477$	−1.48720	−	1.71632i	−0.0680940	−	0.0785847i
$478$	13.4039	+	8.61416i	0.613080	+	0.394002i
$479$	−10.4091	+	12.0128i	−0.475605	+	0.548877i	−0.941962	−	0.335719i	$-0.891021\pi$
$479$	−10.4091	+	12.0128i	−0.475605	+	0.548877i	0.466357	+	0.884596i	$0.345566\pi$
$480$	−0.959493	+	0.281733i	−0.0437947	+	0.0128593i
$481$	−1.99446	−	4.36725i	−0.0909395	−	0.199130i
$482$	−23.4864			−1.06977
$483$	−8.64103	−	0.768641i	−0.393180	−	0.0349744i
$484$	25.3712			1.15324
$485$	−5.89624	−	12.9110i	−0.267734	−	0.586256i
$486$	0.959493	−	0.281733i	0.0435235	−	0.0127796i
$487$	−5.99998	+	6.92434i	−0.271885	+	0.313772i	−0.875229	−	0.483709i	$-0.839289\pi$
$487$	−5.99998	+	6.92434i	−0.271885	+	0.313772i	0.603344	+	0.797481i	$0.293835\pi$
$488$	12.8653	+	8.26805i	0.582387	+	0.374277i
$489$	−7.29991	−	8.42454i	−0.330113	−	0.380971i
$490$	−0.530536	−	3.68996i	−0.0239672	−	0.166695i
$491$	24.6185	+	7.22864i	1.11102	+	0.326224i	0.785221	−	0.619216i	$-0.212549\pi$
$491$	24.6185	+	7.22864i	1.11102	+	0.326224i	0.325797	+	0.945440i	$0.394368\pi$
$492$	−0.128152	+	0.0823581i	−0.00577753	+	0.00371299i
$493$	−4.45384	+	30.9772i	−0.200591	+	1.39514i
$494$	−9.98322	+	21.8602i	−0.449166	+	0.983537i
$495$	−2.50531	+	5.48586i	−0.112605	+	0.246571i
$496$	−1.07060	+	7.44619i	−0.0480714	+	0.334344i
$497$	3.95809	−	2.54371i	0.177545	−	0.114101i
$498$	1.44777	+	0.425104i	0.0648761	+	0.0190493i
$499$	−0.938064	−	6.52438i	−0.0419935	−	0.292071i	−0.999986	−	0.00527820i	$-0.998320\pi$
$499$	−0.938064	−	6.52438i	−0.0419935	−	0.292071i	0.957993	−	0.286793i	$-0.0925892\pi$
$500$	0.654861	+	0.755750i	0.0292863	+	0.0337981i
$501$	−7.47183	−	4.80185i	−0.333817	−	0.214531i
$502$	3.01759	−	3.48248i	0.134682	−	0.155431i
$503$	−22.7662	+	6.68475i	−1.01509	+	0.298058i	−0.746636	−	0.665233i	$-0.768332\pi$
$503$	−22.7662	+	6.68475i	−1.01509	+	0.298058i	−0.268458	+	0.963291i	$0.586514\pi$
$504$	0.751442	+	1.64543i	0.0334719	+	0.0732932i
$505$	−1.39529			−0.0620897
$506$	14.2988	−	25.1412i	0.635661	−	1.11766i
$507$	2.71250			0.120466
$508$	−7.62632	−	16.6993i	−0.338363	−	0.740912i
$509$	−17.2570	+	5.06712i	−0.764904	+	0.224596i	−0.640836	−	0.767678i	$-0.721412\pi$
$509$	−17.2570	+	5.06712i	−0.764904	+	0.224596i	−0.124068	+	0.992274i	$0.539594\pi$
$510$	2.98566	−	3.44564i	0.132207	−	0.152575i
$511$	3.65107	+	2.34640i	0.161514	+	0.103799i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	−1.06631	−	7.41635i	−0.0470787	−	0.327440i
$514$	−21.3490	−	6.26863i	−0.941663	−	0.276497i
$515$	8.65727	−	5.56369i	0.381485	−	0.245166i
$516$	0.622672	−	4.33078i	0.0274116	−	0.190652i
$517$	10.1971	−	22.3286i	0.448468	−	0.982009i
$518$	−1.12482	+	2.46301i	−0.0494218	+	0.108219i
$519$	1.68650	−	11.7299i	0.0740291	−	0.514884i
$520$	−2.69825	+	1.73406i	−0.118326	+	0.0760435i
$521$	−35.0262	−	10.2846i	−1.53453	−	0.450577i	−0.598094	−	0.801426i	$-0.704075\pi$
$521$	−35.0262	−	10.2846i	−1.53453	−	0.450577i	−0.936432	+	0.350849i	$0.885893\pi$
$522$	0.976885	+	6.79438i	0.0427571	+	0.297382i
$523$	0.813710	+	0.939072i	0.0355811	+	0.0410627i	0.773261	−	0.634088i	$-0.218624\pi$
$523$	0.813710	+	0.939072i	0.0355811	+	0.0410627i	−0.737680	+	0.675150i	$0.764079\pi$
$524$	16.0592	+	10.3206i	0.701548	+	0.450857i
$525$	1.18457	−	1.36707i	0.0516990	−	0.0596638i
$526$	16.3276	−	4.79422i	0.711918	−	0.209038i
$527$	−14.2479	−	31.1986i	−0.620648	−	1.35903i
$528$	−6.03085			−0.262459
$529$	−11.7572	−	19.7679i	−0.511183	−	0.859472i
$530$	−2.27101			−0.0986464
$531$	4.80260	+	10.5162i	0.208415	+	0.456366i
$532$	13.0043	−	3.81842i	0.563809	−	0.165549i
$533$	−0.319964	+	0.369258i	−0.0138592	+	0.0159944i
$534$	−3.68310	−	2.36699i	−0.159383	−	0.102429i
$535$	−6.84026	−	7.89408i	−0.295730	−	0.341291i
$536$	0.561371	+	3.90442i	0.0242476	+	0.168645i
$537$	19.4999	+	5.72570i	0.841485	+	0.247082i
$538$	11.0407	−	7.09540i	0.475997	−	0.305905i
$539$	3.19958	−	22.2536i	0.137816	−	0.958530i
$540$	0.415415	−	0.909632i	0.0178766	−	0.0391443i
$541$	6.74473	−	14.7689i	0.289978	−	0.634964i	−0.707440	−	0.706773i	$-0.750150\pi$
$541$	6.74473	−	14.7689i	0.289978	−	0.634964i	0.997418	+	0.0718092i	$0.0228773\pi$
$542$	−3.44056	+	23.9296i	−0.147785	+	1.02786i
$543$	7.19466	−	4.62373i	0.308752	−	0.198423i
$544$	4.37455	+	1.28448i	0.187557	+	0.0550718i
$545$	−0.538186	−	3.74317i	−0.0230534	−	0.160340i
$546$	3.79942	+	4.38476i	0.162600	+	0.187650i
$547$	−24.7409	−	15.9000i	−1.05785	−	0.679836i	−0.108508	−	0.994096i	$-0.534607\pi$
$547$	−24.7409	−	15.9000i	−1.05785	−	0.679836i	−0.949337	+	0.314260i	$0.898244\pi$
$548$	−4.00484	+	4.62183i	−0.171078	+	0.197435i
$549$	−14.6736	+	4.30855i	−0.626253	+	0.183885i
$550$	2.50531	+	5.48586i	0.106827	+	0.233918i
$551$	51.4312			2.19104
$552$	−2.37095	+	4.16877i	−0.100914	+	0.177434i
$553$	−10.0720			−0.428303
$554$	−1.11074	−	2.43218i	−0.0471909	−	0.103334i
$555$	1.43625	−	0.421721i	0.0609654	−	0.0179010i
$556$	13.2651	−	15.3087i	0.562564	−	0.649234i
$557$	−25.0762	−	16.1155i	−1.06251	−	0.682836i	−0.112060	−	0.993701i	$-0.535745\pi$
$557$	−25.0762	−	16.1155i	−1.06251	−	0.682836i	−0.950454	+	0.310865i	$0.899381\pi$
$558$	−4.92636	−	5.68532i	−0.208549	−	0.240679i
$559$	−1.99717	−	13.8906i	−0.0844712	−	0.587510i
$560$	1.73562	+	0.509624i	0.0733434	+	0.0215356i
$561$	23.1311	−	14.8655i	0.976598	−	0.627621i
$562$	3.92714	−	27.3138i	0.165656	−	1.15216i
$563$	14.4864	−	31.7208i	0.610528	−	1.33687i	−0.311684	−	0.950186i	$-0.600893\pi$
$563$	14.4864	−	31.7208i	0.610528	−	1.33687i	0.922212	−	0.386685i	$-0.126380\pi$
$564$	−1.69082	+	3.70239i	−0.0711966	+	0.155899i
$565$	1.81843	−	12.6475i	0.0765021	−	0.532084i
$566$	−26.2548	+	16.8729i	−1.10357	+	0.709223i
$567$	−1.73562	−	0.509624i	−0.0728892	−	0.0214022i
$568$	−0.370166	−	2.57456i	−0.0155318	−	0.108026i
$569$	−5.78494	−	6.67617i	−0.242517	−	0.279880i	0.621422	−	0.783476i	$-0.286555\pi$
$569$	−5.78494	−	6.67617i	−0.242517	−	0.279880i	−0.863939	+	0.503596i	$0.832010\pi$
$570$	−6.30319	−	4.05081i	−0.264012	−	0.169670i
$571$	7.01654	−	8.09752i	0.293633	−	0.338871i	−0.589695	−	0.807626i	$-0.700752\pi$
$571$	7.01654	−	8.09752i	0.293633	−	0.338871i	0.883328	+	0.468756i	$0.155297\pi$
$572$	−18.5599	+	5.44968i	−0.776028	+	0.227862i
$573$	1.62095	+	3.54939i	0.0677163	+	0.148278i
$574$	0.275556			0.0115015
$575$	4.77697	+	0.424923i	0.199213	+	0.0177205i
$576$	1.00000			0.0416667
$577$	−7.89704	−	17.2921i	−0.328758	−	0.719880i	0.671009	−	0.741449i	$-0.265861\pi$
$577$	−7.89704	−	17.2921i	−0.328758	−	0.719880i	−0.999767	+	0.0215693i	$0.993134\pi$
$578$	−3.63320	+	1.06680i	−0.151121	+	0.0443732i
$579$	0.907060	−	1.04680i	0.0376961	−	0.0435036i
$580$	5.77458	+	3.71110i	0.239776	+	0.154095i
$581$	−1.78739	−	2.06276i	−0.0741535	−	0.0855777i
$582$	2.01996	+	14.0491i	0.0837301	+	0.582355i
$583$	−13.1413	−	3.85865i	−0.544259	−	0.159809i
$584$	2.01840	−	1.29715i	0.0835220	−	0.0536763i
$585$	0.456463	−	3.17477i	0.0188724	−	0.131260i
$586$	−9.75216	+	21.3543i	−0.402858	+	0.882136i
$587$	2.75199	−	6.02601i	0.113587	−	0.248720i	−0.844298	−	0.535874i	$-0.819982\pi$
$587$	2.75199	−	6.02601i	0.113587	−	0.248720i	0.957884	+	0.287154i	$0.0927093\pi$
$588$	−0.530536	+	3.68996i	−0.0218789	+	0.152171i
$589$	−47.4174	+	30.4733i	−1.95380	+	1.25563i
$590$	11.0927	+	3.25710i	0.456678	+	0.134093i
$591$	1.22112	+	8.49310i	0.0502303	+	0.349359i
$592$	0.980250	+	1.13127i	0.0402880	+	0.0464949i
$593$	−10.4883	−	6.74040i	−0.430702	−	0.276795i	0.307276	−	0.951621i	$-0.400583\pi$
$593$	−10.4883	−	6.74040i	−0.430702	−	0.276795i	−0.737978	+	0.674825i	$0.764219\pi$
$594$	3.94937	−	4.55781i	0.162045	−	0.187009i
$595$	−7.91309	+	2.32349i	−0.324405	+	0.0952540i
$596$	−5.18756	−	11.3592i	−0.212491	−	0.465290i
$597$	−18.8657			−0.772122
$598$	−3.52954	+	14.9718i	−0.144334	+	0.612243i
$599$	−34.0959			−1.39312			−0.696561	−	0.717498i	$-0.745287\pi$
$599$	−34.0959			−1.39312			−0.696561	+	0.717498i	$0.745287\pi$
$600$	−0.415415	−	0.909632i	−0.0169592	−	0.0371356i
$601$	14.8693	−	4.36602i	0.606532	−	0.178094i	0.0359759	−	0.999353i	$-0.488546\pi$
$601$	14.8693	−	4.36602i	0.606532	−	0.178094i	0.570556	+	0.821259i	$0.306728\pi$
$602$	−5.18288	+	5.98136i	−0.211238	+	0.243782i
$603$	−3.31839	−	2.13260i	−0.135135	−	0.0868461i
$604$	−4.20117	−	4.84841i	−0.170943	−	0.197279i
$605$	3.61069	+	25.1129i	0.146796	+	1.02099i
$606$	1.33877	+	0.393099i	0.0543840	+	0.0159686i
$607$	10.6201	−	6.82512i	0.431056	−	0.277023i	−0.307068	−	0.951687i	$-0.599348\pi$
$607$	10.6201	−	6.82512i	0.431056	−	0.277023i	0.738125	+	0.674664i	$0.235712\pi$
$608$	1.06631	−	7.41635i	0.0432446	−	0.300773i
$609$	5.15808	−	11.2946i	0.209016	−	0.457681i
$610$	−6.35297	+	13.9111i	−0.257224	+	0.563242i
$611$	−1.85790	+	12.9220i	−0.0751624	+	0.522766i
$612$	−3.83547	+	2.46491i	−0.155040	+	0.0996379i
$613$	17.9796	+	5.27930i	0.726191	+	0.213229i	0.623876	−	0.781523i	$-0.285557\pi$
$613$	17.9796	+	5.27930i	0.726191	+	0.213229i	0.102315	+	0.994752i	$0.467375\pi$
$614$	−2.06859	−	14.3873i	−0.0834814	−	0.580626i
$615$	−0.0997577	−	0.115127i	−0.00402262	−	0.00464235i
$616$	9.17738	+	5.89794i	0.369767	+	0.237635i
$617$	−0.276926	+	0.319590i	−0.0111486	+	0.0128662i	−0.761297	−	0.648404i	$-0.775437\pi$
$617$	−0.276926	+	0.319590i	−0.0111486	+	0.0128662i	0.750148	+	0.661270i	$0.229982\pi$
$618$	−9.87407	+	2.89929i	−0.397193	+	0.116626i
$619$	−16.3166	−	35.7283i	−0.655818	−	1.43604i	−0.886368	−	0.462981i	$-0.846780\pi$
$619$	−16.3166	−	35.7283i	−0.655818	−	1.43604i	0.230550	−	0.973061i	$-0.425948\pi$
$620$	−7.52276			−0.302121
$621$	−1.59790	−	4.52180i	−0.0641216	−	0.181454i
$622$	−29.0067			−1.16306
$623$	3.28989	+	7.20387i	0.131807	+	0.288617i
$624$	3.07749	−	0.903633i	0.123198	−	0.0361743i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	20.4900	+	13.1681i	0.818944	+	0.526303i
$627$	−29.5911	−	34.1499i	−1.18175	−	1.36382i
$628$	−2.39907	−	16.6859i	−0.0957333	−	0.665840i
$629$	−6.54819	−	1.92272i	−0.261093	−	0.0766639i
$630$	−1.52174	+	0.977962i	−0.0606275	+	0.0389629i
$631$	−2.96485	+	20.6210i	−0.118029	+	0.820908i	0.841693	+	0.539956i	$0.181559\pi$
$631$	−2.96485	+	20.6210i	−0.118029	+	0.820908i	−0.959722	+	0.280952i	$0.909350\pi$
$632$	−2.31304	+	5.06485i	−0.0920078	+	0.201469i
$633$	−2.63988	+	5.78054i	−0.104926	+	0.229756i
$634$	−3.43418	+	23.8853i	−0.136389	+	0.948604i
$635$	15.4440	−	9.92525i	0.612876	−	0.393872i
$636$	2.17902	+	0.639818i	0.0864037	+	0.0253704i
$637$	1.70165	+	11.8352i	0.0674218	+	0.468929i
$638$	27.1095	+	31.2860i	1.07327	+	1.23862i
$639$	2.18813	+	1.40622i	0.0865610	+	0.0556294i
$640$	0.654861	−	0.755750i	0.0258856	−	0.0298736i
$641$	−15.2572	+	4.47991i	−0.602622	+	0.176946i	−0.568791	−	0.822482i	$-0.692589\pi$
$641$	−15.2572	+	4.47991i	−0.602622	+	0.176946i	−0.0338306	+	0.999428i	$0.510771\pi$
$642$	4.33916	+	9.50143i	0.171253	+	0.374992i
$643$	−21.3814			−0.843201			−0.421601	−	0.906782i	$-0.638532\pi$
$643$	−21.3814			−0.843201			−0.421601	+	0.906782i	$0.638532\pi$
$644$	7.68486	−	4.02507i	0.302826	−	0.158610i
$645$	4.37531			0.172278
$646$	14.1908	+	31.0735i	0.558330	+	1.22257i
$647$	−36.9908	+	10.8615i	−1.45426	+	0.427009i	−0.910947	−	0.412523i	$-0.864648\pi$
$647$	−36.9908	+	10.8615i	−1.45426	+	0.427009i	−0.543311	+	0.839532i	$0.682830\pi$
$648$	−0.654861	+	0.755750i	−0.0257254	+	0.0296886i
$649$	58.6543	+	37.6949i	2.30238	+	1.47965i
$650$	−2.10041	−	2.42400i	−0.0823848	−	0.0950772i
$651$	1.93660	+	13.4694i	0.0759014	+	0.527906i
$652$	10.6957	+	3.14055i	0.418877	+	0.122993i
$653$	8.97512	−	5.76796i	0.351224	−	0.225718i	−0.353118	−	0.935579i	$-0.614879\pi$
$653$	8.97512	−	5.76796i	0.351224	−	0.225718i	0.704342	+	0.709861i	$0.251242\pi$
$654$	−0.538186	+	3.74317i	−0.0210448	+	0.146369i
$655$	−7.93009	+	17.3645i	−0.309854	+	0.678486i
$656$	0.0632819	−	0.138568i	0.00247074	−	0.00541017i
$657$	−0.341453	+	2.37486i	−0.0133213	+	0.0926519i
$658$	6.19379	−	3.98050i	0.241459	−	0.155176i
$659$	−9.59962	−	2.81870i	−0.373948	−	0.109801i	0.0893575	−	0.996000i	$-0.471519\pi$
$659$	−9.59962	−	2.81870i	−0.373948	−	0.109801i	−0.463306	+	0.886199i	$0.653337\pi$
$660$	−0.858280	−	5.96947i	−0.0334085	−	0.232361i
$661$	13.2710	+	15.3155i	0.516181	+	0.595704i	0.952670	−	0.304005i	$-0.0983239\pi$
$661$	13.2710	+	15.3155i	0.516181	+	0.595704i	−0.436490	+	0.899709i	$0.643778\pi$
$662$	10.5424	+	6.77517i	0.409741	+	0.263324i
$663$	−9.57625	+	11.0516i	−0.371911	+	0.429208i
$664$	−1.44777	+	0.425104i	−0.0561844	+	0.0164972i
$665$	5.63026	+	12.3286i	0.218332	+	0.478081i
$666$	−1.49688			−0.0580030
$667$	32.2838	−	6.43947i	1.25004	−	0.249337i
$668$	8.88178			0.343647
$669$	1.69833	+	3.71882i	0.0656612	+	0.143778i
$670$	−3.78479	+	1.11131i	−0.146219	+	0.0429338i
$671$	−60.3979	+	69.7029i	−2.33164	+	2.69085i
$672$	−1.52174	−	0.977962i	−0.0587023	−	0.0377257i
$673$	7.53589	+	8.69688i	0.290487	+	0.335240i	0.882170	−	0.470931i	$-0.156082\pi$
$673$	7.53589	+	8.69688i	0.290487	+	0.335240i	−0.591683	+	0.806171i	$0.701536\pi$
$674$	2.79086	+	19.4109i	0.107500	+	0.747679i
$675$	0.959493	+	0.281733i	0.0369309	+	0.0108439i
$676$	−2.28190	+	1.46649i	−0.0877654	+	0.0564034i
$677$	4.44465	−	30.9132i	0.170822	−	1.18809i	−0.706332	−	0.707881i	$-0.749651\pi$
$677$	4.44465	−	30.9132i	0.170822	−	1.18809i	0.877154	−	0.480210i	$-0.159439\pi$
$678$	−5.30798	+	11.6229i	−0.203852	+	0.446373i
$679$	10.6657	−	23.3545i	0.409311	−	0.896265i
$680$	−0.648846	+	4.51282i	−0.0248821	+	0.173059i
$681$	7.25816	−	4.66453i	0.278133	−	0.178745i
$682$	−43.5309	−	12.7818i	−1.66688	−	0.489441i
$683$	−4.04118	−	28.1070i	−0.154631	−	1.07549i	−0.908327	−	0.418261i	$-0.862640\pi$
$683$	−4.04118	−	28.1070i	−0.154631	−	1.07549i	0.753695	−	0.657224i	$-0.228269\pi$
$684$	4.90662	+	5.66254i	0.187609	+	0.216513i
$685$	−5.14473	−	3.30632i	−0.196570	−	0.126328i
$686$	12.7080	−	14.6658i	0.485193	−	0.559943i
$687$	17.3004	−	5.07986i	0.660052	−	0.193809i
$688$	1.81757	+	3.97993i	0.0692942	+	0.151733i
$689$	7.28407			0.277501
$690$	−4.46375	−	1.75354i	−0.169932	−	0.0667561i
$691$	12.9410			0.492300			0.246150	−	0.969232i	$-0.420834\pi$
$691$	12.9410			0.492300			0.246150	+	0.969232i	$0.420834\pi$
$692$	4.92287	+	10.7796i	0.187139	+	0.409778i
$693$	−10.4673	+	3.07347i	−0.397619	+	0.116751i
$694$	−8.16682	+	9.42501i	−0.310008	+	0.357768i
$695$	17.0407	+	10.9514i	0.646391	+	0.415410i
$696$	−4.49513	−	5.18766i	−0.170387	−	0.196638i
$697$	0.0988415	+	0.687458i	0.00374389	+	0.0260393i
$698$	11.9396	+	3.50577i	0.451919	+	0.132695i
$699$	−17.8415	+	11.4660i	−0.674827	+	0.433685i
$700$	−0.257432	+	1.79048i	−0.00973003	+	0.0676738i
$701$	9.83282	−	21.5309i	0.371381	−	0.813210i	−0.628007	−	0.778208i	$-0.716129\pi$
$701$	9.83282	−	21.5309i	0.371381	−	0.813210i	0.999387	−	0.0350021i	$-0.0111438\pi$
$702$	−1.33241	+	2.91757i	−0.0502885	+	0.110116i
$703$	−1.59614	+	11.1014i	−0.0601996	+	0.418698i
$704$	5.07348	−	3.26052i	0.191214	−	0.122886i
$705$	−3.90533	−	1.14671i	−0.147083	−	0.0431876i
$706$	5.01817	+	34.9021i	0.188861	+	1.31356i
$707$	−1.65283	−	1.90746i	−0.0621609	−	0.0717376i
$708$	−9.72571	−	6.25034i	−0.365515	−	0.234902i
$709$	12.0429	−	13.8983i	0.452282	−	0.521961i	−0.483117	−	0.875556i	$-0.660495\pi$
$709$	12.0429	−	13.8983i	0.452282	−	0.521961i	0.935399	+	0.353595i	$0.115041\pi$
$710$	2.49567	−	0.732796i	0.0936609	−	0.0275013i
$711$	−2.31304	−	5.06485i	−0.0867458	−	0.189947i
$712$	4.37811			0.164077
$713$	−25.9489	+	25.0653i	−0.971794	+	0.938703i
$714$	8.24716			0.308642
$715$	−8.03555	−	17.5954i	−0.300513	−	0.658031i
$716$	−19.4999	+	5.72570i	−0.728747	+	0.213979i
$717$	10.4340	−	12.0415i	0.389667	−	0.449699i
$718$	−15.7141	−	10.0989i	−0.586447	−	0.376886i
$719$	0.720364	+	0.831345i	0.0268651	+	0.0310039i	0.769023	−	0.639221i	$-0.220743\pi$
$719$	0.720364	+	0.831345i	0.0268651	+	0.0310039i	−0.742158	+	0.670225i	$0.766198\pi$
$720$	0.142315	+	0.989821i	0.00530376	+	0.0368885i
$721$	17.8611	+	5.24450i	0.665183	+	0.195315i
$722$	31.2435	−	20.0790i	1.16276	−	0.747263i
$723$	−3.34246	+	23.2473i	−0.124307	+	0.864576i
$724$	−3.55276	+	7.77946i	−0.132037	+	0.289121i
$725$	−2.85151	+	6.24394i	−0.105903	+	0.231894i
$726$	3.61069	−	25.1129i	0.134005	−	0.932028i
$727$	−40.9576	+	26.3218i	−1.51903	+	0.976223i	−0.527052	+	0.849833i	$0.676703\pi$
$727$	−40.9576	+	26.3218i	−1.51903	+	0.976223i	−0.991981	+	0.126390i	$0.959661\pi$
$728$	−5.56685	−	1.63458i	−0.206321	−	0.0605814i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	1.57119	+	1.81325i	0.0581524	+	0.0671115i
$731$	−16.7814	−	10.7847i	−0.620682	−	0.398888i
$732$	10.0148	−	11.5577i	0.370159	−	0.427186i
$733$	−24.1002	+	7.07644i	−0.890160	+	0.261374i	−0.694668	−	0.719331i	$-0.744449\pi$
$733$	−24.1002	+	7.07644i	−0.890160	+	0.261374i	−0.195492	+	0.980705i	$0.562630\pi$
$734$	1.86475	+	4.08323i	0.0688291	+	0.150715i
$735$	−3.72790			−0.137506
$736$	−0.259236	−	4.78882i	−0.00955555	−	0.176518i
$737$	−23.7891			−0.876284
$738$	0.0632819	+	0.138568i	0.00232944	+	0.00510076i
$739$	−26.8247	+	7.87643i	−0.986762	+	0.289739i	−0.735013	−	0.678053i	$-0.762824\pi$
$739$	−26.8247	+	7.87643i	−0.986762	+	0.289739i	−0.251749	+	0.967793i	$0.581006\pi$
$740$	−0.980250	+	1.13127i	−0.0360347	+	0.0415863i
$741$	20.2169	+	12.9926i	0.742688	+	0.477296i
$742$	−2.69018	−	3.10463i	−0.0987596	−	0.113975i
$743$	−5.64692	−	39.2752i	−0.207166	−	1.44087i	−0.782347	−	0.622842i	$-0.785978\pi$
$743$	−5.64692	−	39.2752i	−0.207166	−	1.44087i	0.575182	−	0.818026i	$-0.304931\pi$
$744$	7.21804	+	2.11941i	0.264626	+	0.0777012i
$745$	10.5053	−	6.75134i	0.384884	−	0.247350i
$746$	−2.05974	+	14.3258i	−0.0754123	+	0.524504i
$747$	0.626816	−	1.37253i	0.0229340	−	0.0502184i
$748$	−11.4223	+	25.0113i	−0.417640	+	0.914503i
$749$	2.68897	−	18.7022i	0.0982530	−	0.683364i
$750$	0.841254	−	0.540641i	0.0307182	−	0.0197414i
$751$	−32.4893	−	9.53971i	−1.18555	−	0.348109i	−0.371239	−	0.928537i	$-0.621067\pi$
$751$	−32.4893	−	9.53971i	−1.18555	−	0.348109i	−0.814311	+	0.580429i	$0.802885\pi$
$752$	−0.579251	−	4.02878i	−0.0211231	−	0.146914i
$753$	−3.01759	−	3.48248i	−0.109967	−	0.126909i
$754$	−18.5215	−	11.9030i	−0.674512	−	0.433482i
$755$	4.20117	−	4.84841i	0.152896	−	0.176452i
$756$	1.73562	−	0.509624i	0.0631239	−	0.0185349i
$757$	−15.7239	−	34.4306i	−0.571496	−	1.25140i	−0.945997	−	0.324175i	$-0.894913\pi$
$757$	−15.7239	−	34.4306i	−0.571496	−	1.25140i	0.374501	−	0.927226i	$-0.377814\pi$
$758$	22.3165			0.810571
$759$	−22.8504	−	17.7313i	−0.829416	−	0.643604i
$760$	7.49261			0.271786
$761$	16.8519	+	36.9005i	0.610881	+	1.33764i	0.921970	+	0.387261i	$0.126579\pi$
$761$	16.8519	+	36.9005i	0.610881	+	1.33764i	−0.311089	+	0.950381i	$0.600694\pi$
$762$	−17.6147	+	5.17214i	−0.638112	+	0.187367i
$763$	4.47965	−	5.16980i	0.162174	−	0.187159i
$764$	−3.28258	−	2.10959i	−0.118760	−	0.0763222i
$765$	−2.98566	−	3.44564i	−0.107947	−	0.124577i
$766$	2.32347	+	16.1601i	0.0839504	+	0.583888i
$767$	−35.5788	−	10.4469i	−1.28468	−	0.377215i
$768$	−0.841254	+	0.540641i	−0.0303561	+	0.0195087i
$769$	−4.24349	+	29.5141i	−0.153024	+	1.06431i	0.758089	+	0.652151i	$0.226133\pi$
$769$	−4.24349	+	29.5141i	−0.153024	+	1.06431i	−0.911113	+	0.412156i	$0.864776\pi$
$770$	−4.53183	+	9.92333i	−0.163316	+	0.357612i
$771$	−9.24310	+	20.2396i	−0.332882	+	0.728910i
$772$	−0.197123	+	1.37102i	−0.00709461	+	0.0493441i
$773$	−16.7426	+	10.7598i	−0.602191	+	0.387005i	−0.805922	−	0.592022i	$-0.798330\pi$
$773$	−16.7426	+	10.7598i	−0.602191	+	0.387005i	0.203730	+	0.979027i	$0.434693\pi$
$774$	−4.19808	−	1.23267i	−0.150897	−	0.0443073i
$775$	−1.07060	−	7.44619i	−0.0384571	−	0.267475i
$776$	−9.29483	−	10.7268i	−0.333665	−	0.385070i
$777$	2.27786	+	1.46389i	0.0817179	+	0.0525169i
$778$	1.39583	−	1.61087i	0.0500429	−	0.0577525i
$779$	1.09515	−	0.321564i	0.0392377	−	0.0115212i
$780$	1.33241	+	2.91757i	0.0477078	+	0.104466i
$781$	15.6864			0.561305
$782$	12.7983	+	17.7284i	0.457666	+	0.633966i
$783$	6.86425			0.245308
$784$	−1.54863	−	3.39102i	−0.0553081	−	0.121108i
$785$	16.1746	−	4.74930i	0.577298	−	0.169510i
$786$	12.5010	−	14.4269i	0.445896	−	0.514591i
$787$	7.06040	+	4.53744i	0.251676	+	0.161742i	0.660396	−	0.750917i	$-0.270388\pi$
$787$	7.06040	+	4.53744i	0.251676	+	0.161742i	−0.408720	+	0.912660i	$0.634025\pi$
$788$	−5.61899	−	6.48466i	−0.200168	−	0.231006i
$789$	−2.42176	−	16.8437i	−0.0862170	−	0.599652i
$790$	−5.34248	−	1.56869i	−0.190077	−	0.0558116i
$791$	19.4441	−	12.4959i	0.691351	−	0.444305i
$792$	−0.858280	+	5.96947i	−0.0304976	+	0.212116i
$793$	20.3766	−	44.6185i	0.723594	−	1.58445i
$794$	−2.20902	+	4.83708i	−0.0783952	+	0.171662i
$795$	−0.323199	+	2.24790i	−0.0114627	+	0.0797246i
$796$	15.8708	−	10.1996i	0.562527	−	0.361514i
$797$	−10.7617	−	3.15993i	−0.381200	−	0.111930i	0.0855181	−	0.996337i	$-0.472745\pi$
$797$	−10.7617	−	3.15993i	−0.381200	−	0.111930i	−0.466718	+	0.884406i	$0.654564\pi$
$798$	−1.92884	−	13.4154i	−0.0682803	−	0.474900i
$799$	12.1523	+	14.0244i	0.429916	+	0.496149i
$800$	0.841254	+	0.540641i	0.0297428	+	0.0191145i
$801$	−2.86705	+	3.30876i	−0.101302	+	0.116909i
$802$	16.4365	−	4.82619i	0.580393	−	0.170419i
$803$	6.01092	+	13.1621i	0.212121	+	0.464480i
$804$	3.94457			0.139114
$805$	5.07777	+	7.03381i	0.178968	+	0.247909i
$806$	24.1286			0.849894
$807$	−5.45193	−	11.9381i	−0.191917	−	0.420240i
$808$	−1.33877	+	0.393099i	−0.0470979	+	0.0138292i
$809$	−7.31127	+	8.43766i	−0.257051	+	0.296652i	−0.869576	−	0.493798i	$-0.835608\pi$
$809$	−7.31127	+	8.43766i	−0.257051	+	0.296652i	0.612526	+	0.790451i	$0.290154\pi$
$810$	−0.841254	−	0.540641i	−0.0295586	−	0.0189962i
$811$	8.67749	+	10.0144i	0.304708	+	0.351652i	0.887366	−	0.461066i	$-0.152533\pi$
$811$	8.67749	+	10.0144i	0.304708	+	0.351652i	−0.582658	+	0.812717i	$0.697987\pi$
$812$	1.76708	+	12.2903i	0.0620124	+	0.431306i
$813$	23.1964	+	6.81107i	0.813533	+	0.238875i
$814$	−7.59440	+	4.88062i	−0.266184	+	0.171066i
$815$	−1.58642	+	11.0338i	−0.0555699	+	0.386497i
$816$	1.89397	−	4.14722i	0.0663023	−	0.145182i
$817$	−13.6184	+	29.8200i	−0.476446	+	1.04327i
$818$	1.46288	−	10.1746i	0.0511485	−	0.355746i
$819$	4.88084	−	3.13673i	0.170550	−	0.109606i
$820$	0.146164	+	0.0429175i	0.00510426	+	0.00149874i
$821$	−2.86430	−	19.9217i	−0.0999649	−	0.695271i	−0.976749	−	0.214387i	$-0.931225\pi$
$821$	−2.86430	−	19.9217i	−0.0999649	−	0.695271i	0.876784	−	0.480884i	$-0.159684\pi$
$822$	4.00484	+	4.62183i	0.139685	+	0.161205i
$823$	−44.7999	−	28.7911i	−1.56163	−	1.00360i	−0.982038	−	0.188685i	$-0.939577\pi$
$823$	−44.7999	−	28.7911i	−1.56163	−	1.00360i	−0.579587	−	0.814910i	$-0.696786\pi$
$824$	6.73912	−	7.77736i	0.234768	−	0.270937i
$825$	5.78656	−	1.69909i	0.201462	−	0.0591546i
$826$	8.68740	+	19.0228i	0.302273	+	0.661886i
$827$	40.8236			1.41958			0.709788	−	0.704415i	$-0.248791\pi$
$827$	40.8236			1.41958			0.709788	+	0.704415i	$0.248791\pi$
$828$	3.78891	+	2.94009i	0.131674	+	0.102175i
$829$	2.07606			0.0721044			0.0360522	−	0.999350i	$-0.488522\pi$
$829$	2.07606			0.0721044			0.0360522	+	0.999350i	$0.488522\pi$
$830$	−0.626816	−	1.37253i	−0.0217571	−	0.0476414i
$831$	−2.56550	+	0.753299i	−0.0889963	+	0.0261317i
$832$	−2.10041	+	2.42400i	−0.0728186	+	0.0840371i
$833$	14.2983	+	9.18893i	0.495405	+	0.318378i
$834$	−13.2651	−	15.3087i	−0.459332	−	0.530097i
$835$	1.26401	+	8.79138i	0.0437429	+	0.304238i
$836$	43.3565	+	12.7306i	1.49951	+	0.440297i
$837$	−6.32855	+	4.06711i	−0.218747	+	0.140580i
$838$	−2.70387	+	18.8058i	−0.0934036	+	0.649636i
$839$	13.2963	−	29.1147i	0.459038	−	1.00515i	−0.528668	−	0.848829i	$-0.677308\pi$
$839$	13.2963	−	29.1147i	0.459038	−	1.00515i	0.987706	−	0.156324i	$-0.0499644\pi$
$840$	0.751442	−	1.64543i	0.0259272	−	0.0567726i
$841$	−2.57846	+	17.9336i	−0.0889123	+	0.618398i
$842$	26.8347	−	17.2456i	0.924785	−	0.594323i
$843$	−26.4769	−	7.77433i	−0.911914	−	0.267762i
$844$	−0.904384	−	6.29013i	−0.0311302	−	0.216515i
$845$	−1.77631	−	2.04997i	−0.0611069	−	0.0705211i
$846$	3.42407	+	2.20052i	0.117722	+	0.0756554i
$847$	−30.0540	+	34.6842i	−1.03267	+	1.19176i
$848$	−2.17902	+	0.639818i	−0.0748278	+	0.0219714i
$849$	12.9648	+	28.3889i	0.444949	+	0.974303i
$850$	−4.55923			−0.156380
$851$	0.388045	+	7.16830i	0.0133020	+	0.245726i
$852$	−2.60103			−0.0891099
$853$	14.5265	+	31.8086i	0.497378	+	1.08910i	0.977313	+	0.211801i	$0.0679329\pi$
$853$	14.5265	+	31.8086i	0.497378	+	1.08910i	−0.479935	+	0.877304i	$0.659340\pi$
$854$	−26.5430	+	7.79371i	−0.908281	+	0.266695i
$855$	−4.90662	+	5.66254i	−0.167803	+	0.193655i
$856$	−8.78720	−	5.64719i	−0.300340	−	0.193017i
$857$	3.04747	+	3.51697i	0.104100	+	0.120137i	0.805408	−	0.592720i	$-0.201946\pi$
$857$	3.04747	+	3.51697i	0.104100	+	0.120137i	−0.701309	+	0.712858i	$0.747401\pi$
$858$	2.75286	+	19.1465i	0.0939810	+	0.653652i
$859$	−45.9143	−	13.4816i	−1.56657	−	0.459988i	−0.620573	−	0.784149i	$-0.713100\pi$
$859$	−45.9143	−	13.4816i	−1.56657	−	0.459988i	−0.946002	+	0.324161i	$0.894918\pi$
$860$	−3.68075	+	2.36547i	−0.125512	+	0.0806620i
$861$	0.0392158	−	0.272752i	0.00133647	−	0.00929535i
$862$	−2.19763	+	4.81213i	−0.0748514	+	0.163902i
$863$	−10.9151	+	23.9007i	−0.371554	+	0.813590i	0.627825	+	0.778355i	$0.283945\pi$
$863$	−10.9151	+	23.9007i	−0.371554	+	0.813590i	−0.999379	+	0.0352355i	$0.988782\pi$
$864$	0.142315	−	0.989821i	0.00484165	−	0.0336744i
$865$	−9.96926	+	6.40685i	−0.338965	+	0.217840i
$866$	−22.7787	−	6.68842i	−0.774050	−	0.227282i
$867$	0.538887	+	3.74804i	0.0183016	+	0.127290i
$868$	−8.91126	−	10.2841i	−0.302468	−	0.349067i
$869$	−28.2492	−	18.1547i	−0.958289	−	0.615855i
$870$	4.49513	−	5.18766i	0.152399	−	0.175878i
$871$	12.1394	−	3.56445i	0.411327	−	0.120777i
$872$	−1.57096	−	3.43992i	−0.0531994	−	0.116490i
$873$	14.1936			0.480381
$874$	25.8449	−	24.9648i	0.874217	−	0.844449i
$875$	−1.80889			−0.0611518
$876$	−0.996696	−	2.18246i	−0.0336752	−	0.0737385i
$877$	2.95277	−	0.867010i	0.0997078	−	0.0292769i	−0.231498	−	0.972835i	$-0.574363\pi$
$877$	2.95277	−	0.867010i	0.0997078	−	0.0292769i	0.331206	+	0.943558i	$0.392545\pi$
$878$	−24.5047	+	28.2799i	−0.826993	+	0.954400i
$879$	19.7490	+	12.6919i	0.666118	+	0.428088i
$880$	3.94937	+	4.55781i	0.133133	+	0.153644i
$881$	−7.62556	−	53.0370i	−0.256912	−	1.78686i	−0.554518	−	0.832172i	$-0.687097\pi$
$881$	−7.62556	−	53.0370i	−0.256912	−	1.78686i	0.297606	−	0.954689i	$-0.403812\pi$
$882$	3.57690	+	1.05027i	0.120440	+	0.0353645i
$883$	42.8839	−	27.5598i	1.44316	−	0.927460i	0.443645	−	0.896202i	$-0.353685\pi$
$883$	42.8839	−	27.5598i	1.44316	−	0.927460i	0.999511	−	0.0312580i	$-0.00995135\pi$
$884$	2.08112	−	14.4745i	0.0699956	−	0.486830i
$885$	4.80260	−	10.5162i	0.161438	−	0.353499i
$886$	15.6993	−	34.3767i	0.527429	−	1.15491i
$887$	1.37756	−	9.58117i	0.0462541	−	0.321704i	−0.953537	−	0.301275i	$-0.902588\pi$
$887$	1.37756	−	9.58117i	0.0462541	−	0.321704i	0.999791	−	0.0204290i	$-0.00650322\pi$
$888$	1.25926	−	0.809276i	0.0422579	−	0.0271575i
$889$	31.8631	+	9.35584i	1.06865	+	0.313785i
$890$	0.623070	+	4.33355i	0.0208854	+	0.145261i
$891$	−3.94937	−	4.55781i	−0.132309	−	0.152693i
$892$	−3.43927	−	2.21028i	−0.115155	−	0.0740058i
$893$	19.9709	−	23.0477i	0.668302	−	0.771262i
$894$	−11.9818	+	3.51818i	−0.400732	+	0.117666i
$895$	−8.44255	−	18.4866i	−0.282203	−	0.617939i
$896$	1.80889			0.0604309
$897$	14.3171	+	5.62432i	0.478034	+	0.187791i
$898$	3.95342			0.131927
$899$	−21.4513	−	46.9717i	−0.715439	−	1.56659i
$900$	−0.959493	+	0.281733i	−0.0319831	+	0.00939109i
$901$	6.78047	−	7.82508i	0.225890	−	0.260691i
$902$	0.772864	+	0.496690i	0.0257336	+	0.0165380i
$903$	5.18288	+	5.98136i	0.172475	+	0.199047i
$904$	−1.81843	−	12.6475i	−0.0604802	−	0.420649i
$905$	−8.20588	−	2.40946i	−0.272773	−	0.0800933i
$906$	−5.39695	+	3.46841i	−0.179302	+	0.115230i
$907$	0.229603	−	1.59692i	0.00762384	−	0.0530249i	−0.985654	−	0.168776i	$-0.946018\pi$
$907$	0.229603	−	1.59692i	0.00762384	−	0.0530249i	0.993278	+	0.115751i	$0.0369276\pi$
$908$	−3.58411	+	7.84811i	−0.118943	+	0.260449i
$909$	0.579626	−	1.26920i	0.0192250	−	0.0420968i
$910$	0.825692	−	5.74281i	0.0273714	−	0.190372i
$911$	46.2558	−	29.7268i	1.53252	−	0.984893i	0.543126	−	0.839651i	$-0.317240\pi$
$911$	46.2558	−	29.7268i	1.53252	−	0.984893i	0.989396	−	0.145242i	$-0.0463960\pi$
$912$	−7.18911	−	2.11091i	−0.238055	−	0.0698993i
$913$	−1.29505	−	9.00727i	−0.0428599	−	0.298097i
$914$	3.51221	+	4.05331i	0.116174	+	0.134071i
$915$	12.8653	+	8.26805i	0.425315	+	0.273333i
$916$	−11.8077	+	13.6268i	−0.390136	+	0.450241i
$917$	−33.1322	+	9.72850i	−1.09412	+	0.321263i
$918$	1.89397	+	4.14722i	0.0625104	+	0.136879i
$919$	27.8808			0.919703			0.459851	−	0.887996i	$-0.347903\pi$
$919$	27.8808			0.919703			0.459851	+	0.887996i	$0.347903\pi$
$920$	4.70318	−	0.938117i	0.155059	−	0.0309288i
$921$	−14.5353			−0.478954
$922$	0.414277	+	0.907141i	0.0136435	+	0.0298751i
$923$	−8.00465	+	2.35038i	−0.263476	+	0.0773636i
$924$	7.14399	−	8.24460i	0.235020	−	0.271227i
$925$	−1.25926	−	0.809276i	−0.0414041	−	0.0266088i
$926$	−5.41390	−	6.24798i	−0.177912	−	0.205321i
$927$	1.46455	+	10.1862i	0.0481022	+	0.334558i
$928$	6.58620	+	1.93388i	0.216203	+	0.0634828i
$929$	20.4249	−	13.1263i	0.670121	−	0.430660i	−0.160848	−	0.986979i	$-0.551423\pi$
$929$	20.4249	−	13.1263i	0.670121	−	0.430660i	0.830969	+	0.556319i	$0.187787\pi$
$930$	−1.07060	+	7.44619i	−0.0351064	+	0.244170i
$931$	11.6033	−	25.4076i	0.380282	−	0.832701i
$932$	8.81021	−	19.2917i	0.288588	−	0.631919i
$933$	−4.12809	+	28.7115i	−0.135148	+	0.939972i
$934$	−24.7934	+	15.9338i	−0.811265	+	0.521369i
$935$	−26.3823	−	7.74653i	−0.862792	−	0.253339i
$936$	−0.456463	−	3.17477i	−0.0149199	−	0.103770i
$937$	−16.0914	−	18.5705i	−0.525683	−	0.606671i	0.429361	−	0.903133i	$-0.358739\pi$
$937$	−16.0914	−	18.5705i	−0.525683	−	0.606671i	−0.955045	+	0.296462i	$0.904193\pi$
$938$	−6.00261	−	3.85764i	−0.195992	−	0.125956i
$939$	15.9501	−	18.4074i	0.520512	−	0.600703i
$940$	3.90533	−	1.14671i	0.127378	−	0.0374015i
$941$	−9.21637	−	20.1810i	−0.300445	−	0.657883i	0.697851	−	0.716243i	$-0.254140\pi$
$941$	−9.21637	−	20.1810i	−0.300445	−	0.657883i	−0.998296	+	0.0583606i	$0.981413\pi$
$942$	−16.8575			−0.549247
$943$	0.647173	−	0.338968i	0.0210748	−	0.0110383i
$944$	11.5610			0.376278
$945$	0.751442	+	1.64543i	0.0244444	+	0.0535258i
$946$	−25.3180	+	7.43404i	−0.823160	+	0.241702i
$947$	−4.79416	+	5.53275i	−0.155789	+	0.179790i	−0.828279	−	0.560316i	$-0.810680\pi$
$947$	−4.79416	+	5.53275i	−0.155789	+	0.179790i	0.672489	+	0.740107i	$0.265225\pi$
$948$	4.68412	+	3.01030i	0.152133	+	0.0977700i
$949$	−5.03946	−	5.81585i	−0.163588	−	0.188790i
$950$	1.06631	+	7.41635i	0.0345957	+	0.240618i
$951$	23.1534	+	6.79845i	0.750800	+	0.220455i
$952$	−6.93795	+	4.45875i	−0.224860	+	0.144509i
$953$	−2.36544	+	16.4520i	−0.0766241	+	0.532933i	0.914968	+	0.403527i	$0.132216\pi$
$953$	−2.36544	+	16.4520i	−0.0766241	+	0.532933i	−0.991592	+	0.129405i	$0.958693\pi$
$954$	0.943412	−	2.06578i	0.0305441	−	0.0668822i
$955$	1.62095	−	3.54939i	0.0524528	−	0.114856i
$956$	−2.26754	+	15.7711i	−0.0733373	+	0.510072i
$957$	34.8256	−	22.3811i	1.12575	−	0.723477i
$958$	−15.2513	−	4.47818i	−0.492747	−	0.144684i
$959$	−1.57434	−	10.9498i	−0.0508381	−	0.353587i
$960$	−0.654861	−	0.755750i	−0.0211355	−	0.0243917i
$961$	21.5293	+	13.8360i	0.694494	+	0.446324i
$962$	3.14407	−	3.62845i	0.101369	−	0.116986i
$963$	10.0222	−	2.94280i	0.322962	−	0.0948303i
$964$	−9.75659	−	21.3639i	−0.314238	−	0.688086i
$965$	−1.38512			−0.0445885
$966$	−2.89043	−	8.17946i	−0.0929982	−	0.263170i
$967$	2.47510			0.0795938			0.0397969	−	0.999208i	$-0.487329\pi$
$967$	2.47510			0.0795938			0.0397969	+	0.999208i	$0.487329\pi$
$968$	10.5396	+	23.0784i	0.338755	+	0.741769i
$969$	32.7768	−	9.62414i	1.05294	−	0.309172i
$970$	9.29483	−	10.7268i	0.298439	−	0.344417i
$971$	43.9417	+	28.2396i	1.41015	+	0.906251i	0.999983	−	0.00575710i	$-0.00183255\pi$
$971$	43.9417	+	28.2396i	1.41015	+	0.906251i	0.410171	+	0.912009i	$0.365469\pi$
$972$	0.654861	+	0.755750i	0.0210047	+	0.0242407i
$973$	5.21463	+	36.2686i	0.167173	+	1.16272i
$974$	−8.79108	−	2.58129i	−0.281684	−	0.0827100i
$975$	−2.69825	+	1.73406i	−0.0864131	+	0.0555343i
$976$	−2.17643	+	15.1374i	−0.0696658	+	0.484536i
$977$	−7.17602	+	15.7133i	−0.229581	+	0.502712i	−0.989005	−	0.147884i	$-0.952754\pi$
$977$	−7.17602	+	15.7133i	−0.229581	+	0.502712i	0.759424	+	0.650596i	$0.225481\pi$
$978$	4.63074	−	10.1399i	0.148075	−	0.324239i
$979$	−3.75764	+	26.1350i	−0.120095	+	0.835278i
$980$	3.13611	−	2.01546i	0.100179	−	0.0643814i
$981$	3.62848	+	1.06542i	0.115848	+	0.0340161i
$982$	3.65149	+	25.3967i	0.116524	+	0.810440i
$983$	−2.59338	−	2.99292i	−0.0827160	−	0.0954593i	0.712883	−	0.701283i	$-0.247389\pi$
$983$	−2.59338	−	2.99292i	−0.0827160	−	0.0954593i	−0.795599	+	0.605824i	$0.792844\pi$
$984$	−0.128152	−	0.0823581i	−0.00408533	−	0.00262548i
$985$	5.61899	−	6.48466i	0.179036	−	0.206618i
$986$	−30.0280	+	8.81702i	−0.956287	+	0.280791i
$987$	−3.05852	−	6.69723i	−0.0973538	−	0.213175i
$988$	−24.0319			−0.764557
$989$	−4.81473	+	20.4234i	−0.153100	+	0.649427i
$990$	−6.03085			−0.191673
$991$	−19.6163	−	42.9537i	−0.623132	−	1.36447i	−0.913219	−	0.407469i	$-0.866412\pi$
$991$	−19.6163	−	42.9537i	−0.623132	−	1.36447i	0.290087	−	0.957000i	$-0.406316\pi$
$992$	−7.21804	+	2.11941i	−0.229173	+	0.0672912i
$993$	8.20654	−	9.47085i	0.260427	−	0.300548i
$994$	3.95809	+	2.54371i	0.125543	+	0.0806816i
$995$	12.3544	+	14.2577i	0.391661	+	0.452001i
$996$	0.214737	+	1.49353i	0.00680422	+	0.0473244i
$997$	35.7136	+	10.4865i	1.13106	+	0.332110i	0.793125	−	0.609059i	$-0.208453\pi$
$997$	35.7136	+	10.4865i	1.13106	+	0.332110i	0.337936	+	0.941169i	$0.390271\pi$
$998$	5.54510	−	3.56362i	0.175527	−	0.112804i
$999$	−0.213029	+	1.48165i	−0.00673993	+	0.0468772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.d.211.1	yes	20
23.6	even	11	inner	690.2.m.d.121.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.d.121.1	✓	20	23.6	even	11	inner
690.2.m.d.211.1	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)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(-0.257432 - 1.79048i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(-0.257432 - 1.79048i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.142315 - 0.989821i) q^{10} +(2.50531 - 5.48586i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.456463 + 3.17477i) q^{13} +(1.52174 - 0.977962i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.98566 + 3.44564i) q^{17} +(0.841254 + 0.540641i) q^{18} +(4.90662 - 5.66254i) q^{19} +(0.959493 - 0.281733i) q^{20} +(-0.751442 - 1.64543i) q^{21} +6.03085 q^{22} +(2.37095 - 4.16877i) q^{23} -1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(-3.07749 + 0.903633i) q^{26} +(0.654861 - 0.755750i) q^{27} +(1.52174 + 0.977962i) q^{28} +(4.49513 + 5.18766i) q^{29} +(-0.142315 - 0.989821i) q^{30} +(-7.21804 - 2.11941i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.858280 - 5.96947i) q^{33} +(-1.89397 + 4.14722i) q^{34} +(-0.751442 + 1.64543i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-1.25926 + 0.809276i) q^{37} +(7.18911 + 2.11091i) q^{38} +(0.456463 + 3.17477i) q^{39} +(0.654861 + 0.755750i) q^{40} +(0.128152 + 0.0823581i) q^{41} +(1.18457 - 1.36707i) q^{42} +(-4.19808 + 1.23267i) q^{43} +(2.50531 + 5.48586i) q^{44} -1.00000 q^{45} +(4.77697 + 0.424923i) q^{46} +4.07021 q^{47} +(-0.415415 - 0.909632i) q^{48} +(3.57690 - 1.05027i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(3.83547 + 2.46491i) q^{51} +(-2.10041 - 2.42400i) q^{52} +(-0.323199 - 2.24790i) q^{53} +(0.959493 + 0.281733i) q^{54} +(-5.07348 + 3.26052i) q^{55} +(-0.257432 + 1.79048i) q^{56} +(3.11254 - 6.81552i) q^{57} +(-2.85151 + 6.24394i) q^{58} +(-1.64530 + 11.4433i) q^{59} +(0.841254 - 0.540641i) q^{60} +(-14.6736 - 4.30855i) q^{61} +(-1.07060 - 7.44619i) q^{62} +(-1.18457 - 1.36707i) q^{63} +(0.841254 + 0.540641i) q^{64} +(2.10041 - 2.42400i) q^{65} +(5.78656 - 1.69909i) q^{66} +(-1.63864 - 3.58811i) q^{67} -4.55923 q^{68} +(1.10043 - 4.66787i) q^{69} -1.80889 q^{70} +(1.08051 + 2.36598i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(-1.57119 + 1.81325i) q^{73} +(-1.25926 - 0.809276i) q^{74} +(0.654861 + 0.755750i) q^{75} +(1.06631 + 7.41635i) q^{76} +(-10.4673 - 3.07347i) q^{77} +(-2.69825 + 1.73406i) q^{78} +(0.792412 - 5.51135i) q^{79} +(-0.415415 + 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.0216794 + 0.150784i) q^{82} +(1.26936 - 0.815768i) q^{83} +(1.73562 + 0.509624i) q^{84} +(-0.648846 - 4.51282i) q^{85} +(-2.86522 - 3.30664i) q^{86} +(5.77458 + 3.71110i) q^{87} +(-3.94937 + 4.55781i) q^{88} +(-4.20077 + 1.23346i) q^{89} +(-0.415415 - 0.909632i) q^{90} +5.80187 q^{91} +(1.59790 + 4.52180i) q^{92} -7.52276 q^{93} +(1.69082 + 3.70239i) q^{94} +(-7.18911 + 2.11091i) q^{95} +(0.654861 - 0.755750i) q^{96} +(11.9404 + 7.67364i) q^{97} +(2.44126 + 2.81736i) q^{98} +(-0.858280 - 5.96947i) 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	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 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 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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