LMFDB - Embedded newform 690.2.m.f.271.2

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} - 6 x^{19} + 36 x^{18} - 172 x^{17} + 691 x^{16} - 2342 x^{15} + 7870 x^{14} - 23240 x^{13} + \cdots + 123904 $ x^20 - 6x^19 + 36x^18 - 172x^17 + 691x^16 - 2342x^15 + 7870x^14 - 23240x^13 + 63837x^12 - 154607x^11 + 334467x^10 - 664202x^9 + 1099560x^8 - 1331000x^7 + 1218096x^6 + 395648x^5 - 588544x^4 + 665984x^3 + 2323200x^2 + 991232*x + 123904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.2
Root			$-0.523366 + 3.64009i$ of defining polynomial
Character	$\chi$	$=$	690.271
Dual form			690.2.m.f.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.68256 + 3.68429i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(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} +(1.68256 + 3.68429i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(3.62954 - 1.06573i) q^{11} +(0.959493 - 0.281733i) q^{12} +(-0.305763 + 0.669527i) q^{13} +(0.576419 + 4.00908i) q^{14} +(-0.654861 - 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-2.85864 + 1.83714i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-0.838252 - 0.538712i) q^{19} +(0.654861 - 0.755750i) q^{20} +(3.88624 + 1.14110i) q^{21} +3.78277 q^{22} +(-2.04017 - 4.34024i) q^{23} +1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.482004 + 0.556263i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.576419 + 4.00908i) q^{28} +(2.54660 - 1.63660i) q^{29} +(-0.415415 - 0.909632i) q^{30} +(4.94148 + 5.70277i) q^{31} +(0.142315 + 0.989821i) q^{32} +(1.57142 - 3.44093i) q^{33} +(-3.26043 + 0.957348i) q^{34} +(3.88624 - 1.14110i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.363507 - 2.52825i) q^{37} +(-0.652525 - 0.753053i) q^{38} +(0.305763 + 0.669527i) q^{39} +(0.841254 - 0.540641i) q^{40} +(0.274557 - 1.90959i) q^{41} +(3.40733 + 2.18976i) q^{42} +(-0.0781905 + 0.0902367i) q^{43} +(3.62954 + 1.06573i) q^{44} -1.00000 q^{45} +(-0.734742 - 4.73921i) q^{46} +1.62827 q^{47} +(0.959493 + 0.281733i) q^{48} +(-6.15895 + 7.10781i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(-0.483596 + 3.36348i) q^{51} +(-0.619197 + 0.397934i) q^{52} +(-0.466007 - 1.02041i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-0.538345 - 3.74427i) q^{55} +(-1.68256 + 3.68429i) q^{56} +(-0.956070 + 0.280727i) q^{57} +(2.90453 - 0.852847i) q^{58} +(4.44714 - 9.73788i) q^{59} +(-0.142315 - 0.989821i) q^{60} +(-4.96417 - 5.72896i) q^{61} +(3.13466 + 6.86394i) q^{62} +(3.40733 - 2.18976i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.619197 + 0.397934i) q^{65} +(2.47719 - 2.85883i) q^{66} +(-9.77430 - 2.86999i) q^{67} -3.39807 q^{68} +(-4.61616 - 1.30040i) q^{69} +4.05031 q^{70} +(-7.42629 - 2.18056i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-12.1972 - 7.83869i) q^{73} +(0.363507 - 2.52825i) q^{74} +(-0.841254 + 0.540641i) q^{75} +(-0.413933 - 0.906387i) q^{76} +(10.0334 + 11.5791i) q^{77} +(0.104750 + 0.728549i) q^{78} +(0.110837 - 0.242700i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.801428 - 1.75488i) q^{82} +(1.73881 + 12.0937i) q^{83} +(2.65239 + 3.06102i) q^{84} +(1.41161 + 3.09100i) q^{85} +(-0.100446 + 0.0645527i) q^{86} +(0.430808 - 2.99634i) q^{87} +(3.18227 + 2.04512i) q^{88} +(-10.8605 + 12.5337i) q^{89} +(-0.959493 - 0.281733i) q^{90} -2.98119 q^{91} +(0.630211 - 4.75424i) q^{92} +7.54584 q^{93} +(1.56231 + 0.458737i) q^{94} +(-0.652525 + 0.753053i) q^{95} +(0.841254 + 0.540641i) q^{96} +(-2.48876 + 17.3097i) q^{97} +(-7.91197 + 5.08471i) q^{98} +(-1.57142 - 3.44093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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
$7$	1.68256	+	3.68429i	0.635947	+	1.39253i	0.903333	+	0.428940i	$0.141113\pi$
$7$	1.68256	+	3.68429i	0.635947	+	1.39253i	−0.267386	+	0.963590i	$0.586160\pi$
$8$	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
$11$	3.62954	−	1.06573i	1.09435	−	0.321330i	0.315744	−	0.948844i	$-0.397746\pi$
$11$	3.62954	−	1.06573i	1.09435	−	0.321330i	0.778605	+	0.627515i	$0.215928\pi$
$12$	0.959493	−	0.281733i	0.276982	−	0.0813292i
$13$	−0.305763	+	0.669527i	−0.0848033	+	0.185693i	−0.947283	−	0.320399i	$-0.896183\pi$
$13$	−0.305763	+	0.669527i	−0.0848033	+	0.185693i	0.862479	+	0.506092i	$0.168910\pi$
$14$	0.576419	+	4.00908i	0.154054	+	1.07147i
$15$	−0.654861	−	0.755750i	−0.169084	−	0.195134i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−2.85864	+	1.83714i	−0.693322	+	0.445571i	−0.839265	−	0.543722i	$-0.817015\pi$
$17$	−2.85864	+	1.83714i	−0.693322	+	0.445571i	0.145943	+	0.989293i	$0.453378\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	−0.838252	−	0.538712i	−0.192308	−	0.123589i	0.440944	−	0.897535i	$-0.354644\pi$
$19$	−0.838252	−	0.538712i	−0.192308	−	0.123589i	−0.633252	+	0.773946i	$0.718280\pi$
$20$	0.654861	−	0.755750i	0.146431	−	0.168991i
$21$	3.88624	+	1.14110i	0.848047	+	0.249009i
$22$	3.78277			0.806490
$23$	−2.04017	−	4.34024i	−0.425405	−	0.905003i
$23$	−2.04017	−	4.34024i	−0.425405	−	0.905003i
$24$	1.00000			0.204124
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	−0.482004	+	0.556263i	−0.0945289	+	0.109092i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−0.576419	+	4.00908i	−0.108933	+	0.757645i
$29$	2.54660	−	1.63660i	0.472892	−	0.303909i	−0.282401	−	0.959296i	$-0.591131\pi$
$29$	2.54660	−	1.63660i	0.472892	−	0.303909i	0.755293	+	0.655387i	$0.227495\pi$
$30$	−0.415415	−	0.909632i	−0.0758441	−	0.166075i
$31$	4.94148	+	5.70277i	0.887515	+	1.02425i	0.999534	+	0.0305412i	$0.00972307\pi$
$31$	4.94148	+	5.70277i	0.887515	+	1.02425i	−0.112018	+	0.993706i	$0.535731\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	1.57142	−	3.44093i	0.273549	−	0.598989i
$34$	−3.26043	+	0.957348i	−0.559159	+	0.164184i
$35$	3.88624	−	1.14110i	0.656894	−	0.192882i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−0.363507	−	2.52825i	−0.0597602	−	0.415641i	−0.997639	−	0.0686778i	$-0.978122\pi$
$37$	−0.363507	−	2.52825i	−0.0597602	−	0.415641i	0.937879	−	0.346963i	$-0.112787\pi$
$38$	−0.652525	−	0.753053i	−0.105853	−	0.122161i
$39$	0.305763	+	0.669527i	0.0489612	+	0.107210i
$40$	0.841254	−	0.540641i	0.133014	−	0.0854828i
$41$	0.274557	−	1.90959i	0.0428786	−	0.298227i	−0.957086	−	0.289804i	$-0.906410\pi$
$41$	0.274557	−	1.90959i	0.0428786	−	0.298227i	0.999965	−	0.00842296i	$-0.00268114\pi$
$42$	3.40733	+	2.18976i	0.525763	+	0.337887i
$43$	−0.0781905	+	0.0902367i	−0.0119239	+	0.0137610i	−0.761680	−	0.647953i	$-0.775625\pi$
$43$	−0.0781905	+	0.0902367i	−0.0119239	+	0.0137610i	0.749756	+	0.661714i	$0.230171\pi$
$44$	3.62954	+	1.06573i	0.547174	+	0.160665i
$45$	−1.00000			−0.149071
$46$	−0.734742	−	4.73921i	−0.108332	−	0.698759i
$47$	1.62827			0.237508			0.118754	−	0.992924i	$-0.462110\pi$
$47$	1.62827			0.237508			0.118754	+	0.992924i	$0.462110\pi$
$48$	0.959493	+	0.281733i	0.138491	+	0.0406646i
$49$	−6.15895	+	7.10781i	−0.879850	+	1.01540i
$50$	−0.841254	−	0.540641i	−0.118971	−	0.0764582i
$51$	−0.483596	+	3.36348i	−0.0677170	+	0.470982i
$52$	−0.619197	+	0.397934i	−0.0858672	+	0.0551835i
$53$	−0.466007	−	1.02041i	−0.0640110	−	0.140165i	0.874923	−	0.484263i	$-0.160912\pi$
$53$	−0.466007	−	1.02041i	−0.0640110	−	0.140165i	−0.938934	+	0.344098i	$0.888185\pi$
$54$	−0.654861	−	0.755750i	−0.0891153	−	0.102844i
$55$	−0.538345	−	3.74427i	−0.0725904	−	0.504877i
$56$	−1.68256	+	3.68429i	−0.224841	+	0.492334i
$57$	−0.956070	+	0.280727i	−0.126635	+	0.0371833i
$58$	2.90453	−	0.852847i	0.381383	−	0.111984i
$59$	4.44714	−	9.73788i	0.578968	−	1.26776i	−0.362915	−	0.931822i	$-0.618218\pi$
$59$	4.44714	−	9.73788i	0.578968	−	1.26776i	0.941883	−	0.335941i	$-0.109054\pi$
$60$	−0.142315	−	0.989821i	−0.0183728	−	0.127785i
$61$	−4.96417	−	5.72896i	−0.635597	−	0.733518i	0.342993	−	0.939338i	$-0.388559\pi$
$61$	−4.96417	−	5.72896i	−0.635597	−	0.733518i	−0.978590	+	0.205820i	$0.934014\pi$
$62$	3.13466	+	6.86394i	0.398102	+	0.871721i
$63$	3.40733	−	2.18976i	0.429284	−	0.275884i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	0.619197	+	0.397934i	0.0768020	+	0.0493576i
$66$	2.47719	−	2.85883i	0.304921	−	0.351897i
$67$	−9.77430	−	2.86999i	−1.19412	−	0.350625i	−0.376518	−	0.926409i	$-0.622879\pi$
$67$	−9.77430	−	2.86999i	−1.19412	−	0.350625i	−0.817602	+	0.575784i	$0.804697\pi$
$68$	−3.39807			−0.412077
$69$	−4.61616	−	1.30040i	−0.555721	−	0.156549i
$70$	4.05031			0.484104
$71$	−7.42629	−	2.18056i	−0.881339	−	0.258784i	−0.190408	−	0.981705i	$-0.560981\pi$
$71$	−7.42629	−	2.18056i	−0.881339	−	0.258784i	−0.690931	+	0.722921i	$0.742799\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	−12.1972	−	7.83869i	−1.42758	−	0.917449i	−0.999909	−	0.0135146i	$-0.995698\pi$
$73$	−12.1972	−	7.83869i	−1.42758	−	0.917449i	−0.427670	−	0.903935i	$-0.640666\pi$
$74$	0.363507	−	2.52825i	0.0422568	−	0.293903i
$75$	−0.841254	+	0.540641i	−0.0971396	+	0.0624278i
$76$	−0.413933	−	0.906387i	−0.0474814	−	0.103970i
$77$	10.0334	+	11.5791i	1.14341	+	1.31956i
$78$	0.104750	+	0.728549i	0.0118606	+	0.0824920i
$79$	0.110837	−	0.242700i	0.0124702	−	0.0273058i	−0.903294	−	0.429021i	$-0.858859\pi$
$79$	0.110837	−	0.242700i	0.0124702	−	0.0273058i	0.915765	+	0.401715i	$0.131586\pi$
$80$	0.959493	−	0.281733i	0.107275	−	0.0314987i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	0.801428	−	1.75488i	0.0885029	−	0.193794i
$83$	1.73881	+	12.0937i	0.190860	+	1.32746i	0.829740	+	0.558151i	$0.188489\pi$
$83$	1.73881	+	12.0937i	0.190860	+	1.32746i	−0.638880	+	0.769306i	$0.720602\pi$
$84$	2.65239	+	3.06102i	0.289399	+	0.333984i
$85$	1.41161	+	3.09100i	0.153111	+	0.335266i
$86$	−0.100446	+	0.0645527i	−0.0108314	+	0.00696089i
$87$	0.430808	−	2.99634i	0.0461875	−	0.321241i
$88$	3.18227	+	2.04512i	0.339231	+	0.218011i
$89$	−10.8605	+	12.5337i	−1.15121	+	1.32857i	−0.215210	+	0.976568i	$0.569044\pi$
$89$	−10.8605	+	12.5337i	−1.15121	+	1.32857i	−0.936000	+	0.351999i	$0.885502\pi$
$90$	−0.959493	−	0.281733i	−0.101139	−	0.0296972i
$91$	−2.98119			−0.312514
$92$	0.630211	−	4.75424i	0.0657041	−	0.495664i
$93$	7.54584			0.782467
$94$	1.56231	+	0.458737i	0.161140	+	0.0473151i
$95$	−0.652525	+	0.753053i	−0.0669476	+	0.0772617i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	−2.48876	+	17.3097i	−0.252696	+	1.75754i	0.329188	+	0.944265i	$0.393225\pi$
$97$	−2.48876	+	17.3097i	−0.252696	+	1.75754i	−0.581883	+	0.813272i	$0.697684\pi$
$98$	−7.91197	+	5.08471i	−0.799230	+	0.513634i
$99$	−1.57142	−	3.44093i	−0.157934	−	0.345827i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	−0.300010	−	2.08662i	−0.0298521	−	0.207626i	0.969436	−	0.245343i	$-0.0789006\pi$
$101$	−0.300010	−	2.08662i	−0.0298521	−	0.207626i	−0.999288	+	0.0377169i	$0.987991\pi$
$102$	−1.41161	+	3.09100i	−0.139770	+	0.306054i
$103$	−1.58308	+	0.464833i	−0.155985	+	0.0458014i	−0.358793	−	0.933417i	$-0.616812\pi$
$103$	−1.58308	+	0.464833i	−0.155985	+	0.0458014i	0.202808	+	0.979219i	$0.434993\pi$
$104$	−0.706226	+	0.207367i	−0.0692512	+	0.0203340i
$105$	1.68256	−	3.68429i	0.164201	−	0.359550i
$106$	−0.159647	−	1.11037i	−0.0155063	−	0.107849i
$107$	−2.95400	−	3.40910i	−0.285574	−	0.329570i	0.594779	−	0.803889i	$-0.297240\pi$
$107$	−2.95400	−	3.40910i	−0.285574	−	0.329570i	−0.880353	+	0.474319i	$0.842694\pi$
$108$	−0.415415	−	0.909632i	−0.0399733	−	0.0875294i
$109$	−4.52576	+	2.90853i	−0.433489	+	0.278586i	−0.739133	−	0.673559i	$-0.764765\pi$
$109$	−4.52576	+	2.90853i	−0.433489	+	0.278586i	0.305644	+	0.952146i	$0.401128\pi$
$110$	0.538345	−	3.74427i	0.0513291	−	0.357002i
$111$	−2.14877	−	1.38093i	−0.203952	−	0.131072i
$112$	−2.65239	+	3.06102i	−0.250627	+	0.289239i
$113$	11.4910	+	3.37406i	1.08098	+	0.317405i	0.773272	−	0.634075i	$-0.218619\pi$
$113$	11.4910	+	3.37406i	1.08098	+	0.317405i	0.307711	+	0.951480i	$0.400437\pi$
$114$	−0.996433			−0.0933245
$115$	−4.58641	+	1.40172i	−0.427685	+	0.130711i
$116$	3.02715			0.281064
$117$	0.706226	+	0.207367i	0.0652906	+	0.0191711i
$118$	7.01047	−	8.09052i	0.645366	−	0.744793i
$119$	−11.5784	−	7.44096i	−1.06139	−	0.682112i
$120$	0.142315	−	0.989821i	0.0129915	−	0.0903579i
$121$	2.78402	−	1.78918i	0.253093	−	0.162653i
$122$	−3.14905	−	6.89546i	−0.285102	−	0.624286i
$123$	−1.26337	−	1.45801i	−0.113914	−	0.131464i
$124$	1.07389	+	7.46904i	0.0964378	+	0.670739i
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$	3.88624	−	1.14110i	0.346214	−	0.101658i
$127$	−16.0286	+	4.70643i	−1.42231	+	0.417628i	−0.900285	−	0.435301i	$-0.856642\pi$
$127$	−16.0286	+	4.70643i	−1.42231	+	0.417628i	−0.522027	+	0.852929i	$0.674824\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	0.0169924	+	0.118185i	0.00149610	+	0.0104056i
$130$	0.482004	+	0.556263i	0.0422746	+	0.0487875i
$131$	−5.25020	−	11.4963i	−0.458712	−	1.00444i	−0.987779	−	0.155859i	$-0.950185\pi$
$131$	−5.25020	−	11.4963i	−0.458712	−	1.00444i	0.529067	−	0.848580i	$-0.322542\pi$
$132$	3.18227	−	2.04512i	0.276981	−	0.178005i
$133$	0.574362	−	3.99478i	0.0498035	−	0.346391i
$134$	−8.56980	−	5.50748i	−0.740318	−	0.475773i
$135$	−0.654861	+	0.755750i	−0.0563614	+	0.0650446i
$136$	−3.26043	−	0.957348i	−0.279579	−	0.0820919i
$137$	−1.99019			−0.170033			−0.0850166	−	0.996380i	$-0.527094\pi$
$137$	−1.99019			−0.170033			−0.0850166	+	0.996380i	$0.527094\pi$
$138$	−4.06281	−	2.54824i	−0.345850	−	0.216921i
$139$	−10.2945			−0.873165			−0.436582	−	0.899664i	$-0.643811\pi$
$139$	−10.2945			−0.873165			−0.436582	+	0.899664i	$0.643811\pi$
$140$	3.88624	+	1.14110i	0.328447	+	0.0964408i
$141$	1.06629	−	1.23056i	0.0897978	−	0.103632i
$142$	−6.51114	−	4.18446i	−0.546403	−	0.351152i
$143$	−0.396244	+	2.75594i	−0.0331356	+	0.230463i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−1.25752	−	2.75359i	−0.104432	−	0.228673i
$146$	−9.49475	−	10.9575i	−0.785791	−	0.906852i
$147$	1.33847	+	9.30925i	0.110395	+	0.767814i
$148$	1.06107	−	2.32342i	0.0872195	−	0.190984i
$149$	19.4902	−	5.72284i	1.59670	−	0.468833i	0.642075	−	0.766642i	$-0.278074\pi$
$149$	19.4902	−	5.72284i	1.59670	−	0.468833i	0.954626	+	0.297809i	$0.0962557\pi$
$150$	−0.959493	+	0.281733i	−0.0783423	+	0.0230034i
$151$	6.29961	−	13.7942i	0.512655	−	1.12256i	−0.459491	−	0.888182i	$-0.651968\pi$
$151$	6.29961	−	13.7942i	0.512655	−	1.12256i	0.972146	−	0.234376i	$-0.0753046\pi$
$152$	−0.141807	−	0.986290i	−0.0115021	−	0.0799987i
$153$	2.22526	+	2.56809i	0.179902	+	0.207618i
$154$	6.36473	+	13.9368i	0.512885	+	1.12306i
$155$	6.34797	−	4.07959i	0.509881	−	0.327681i
$156$	−0.104750	+	0.728549i	−0.00838668	+	0.0583306i
$157$	11.0384	+	7.09392i	0.880957	+	0.566157i	0.901086	−	0.433641i	$-0.142771\pi$
$157$	11.0384	+	7.09392i	0.880957	+	0.566157i	−0.0201289	+	0.999797i	$0.506408\pi$
$158$	0.174724	−	0.201642i	0.0139003	−	0.0160418i
$159$	−1.07635	−	0.316044i	−0.0853599	−	0.0250639i
$160$	1.00000			0.0790569
$161$	12.5580	−	14.8193i	0.989709	−	1.16792i
$162$	−1.00000			−0.0785674
$163$	−12.6414	−	3.71186i	−0.990155	−	0.290736i	−0.253745	−	0.967271i	$-0.581662\pi$
$163$	−12.6414	−	3.71186i	−0.990155	−	0.290736i	−0.736410	+	0.676536i	$0.763481\pi$
$164$	1.26337	−	1.45801i	0.0986528	−	0.113851i
$165$	−3.18227	−	2.04512i	−0.247739	−	0.159212i
$166$	−1.73881	+	12.0937i	−0.134958	+	0.938654i
$167$	−7.32595	+	4.70810i	−0.566899	+	0.364324i	−0.792478	−	0.609901i	$-0.791209\pi$
$167$	−7.32595	+	4.70810i	−0.566899	+	0.364324i	0.225578	+	0.974225i	$0.427573\pi$
$168$	1.68256	+	3.68429i	0.129812	+	0.284249i
$169$	8.15841	+	9.41531i	0.627570	+	0.724255i
$170$	0.483596	+	3.36348i	0.0370901	+	0.257968i
$171$	−0.413933	+	0.906387i	−0.0316543	+	0.0693131i
$172$	−0.114564	+	0.0336389i	−0.00873540	+	0.00256495i
$173$	17.1830	−	5.04540i	1.30640	−	0.383594i	0.446835	−	0.894616i	$-0.352551\pi$
$173$	17.1830	−	5.04540i	1.30640	−	0.383594i	0.859568	+	0.511022i	$0.170733\pi$
$174$	1.25752	−	2.75359i	0.0953326	−	0.208749i
$175$	−0.576419	−	4.00908i	−0.0435732	−	0.303058i
$176$	2.47719	+	2.85883i	0.186725	+	0.215492i
$177$	−4.44714	−	9.73788i	−0.334267	−	0.731944i
$178$	−13.9517	+	8.96622i	−1.04573	+	0.672047i
$179$	−0.531650	+	3.69771i	−0.0397374	+	0.276380i	−0.999996	−	0.00273131i	$-0.999131\pi$
$179$	−0.531650	+	3.69771i	−0.0397374	+	0.276380i	0.960259	+	0.279111i	$0.0900397\pi$
$180$	−0.841254	−	0.540641i	−0.0627033	−	0.0402970i
$181$	−1.17344	+	1.35422i	−0.0872213	+	0.100659i	−0.797683	−	0.603078i	$-0.793941\pi$
$181$	−1.17344	+	1.35422i	−0.0872213	+	0.100659i	0.710461	+	0.703736i	$0.248486\pi$
$182$	−2.86043	−	0.839899i	−0.212029	−	0.0622574i
$183$	−7.58050			−0.560367
$184$	1.94411	−	4.38411i	0.143322	−	0.323201i
$185$	−2.55424			−0.187792
$186$	7.24018	+	2.12591i	0.530876	+	0.155879i
$187$	−8.41767	+	9.71451i	−0.615561	+	0.710395i
$188$	1.36979	+	0.880309i	0.0999020	+	0.0642031i
$189$	0.576419	−	4.00908i	0.0419283	−	0.291618i
$190$	−0.838252	+	0.538712i	−0.0608132	+	0.0390823i
$191$	−9.38712	−	20.5549i	−0.679228	−	1.48730i	−0.863459	−	0.504419i	$-0.831707\pi$
$191$	−9.38712	−	20.5549i	−0.679228	−	1.48730i	0.184231	−	0.982883i	$-0.441020\pi$
$192$	0.654861	+	0.755750i	0.0472605	+	0.0545415i
$193$	−1.48070	−	10.2985i	−0.106583	−	0.741300i	−0.971096	−	0.238690i	$-0.923282\pi$
$193$	−1.48070	−	10.2985i	−0.106583	−	0.741300i	0.864513	−	0.502610i	$-0.167627\pi$
$194$	−7.26467	+	15.9074i	−0.521573	+	1.14208i
$195$	0.706226	−	0.207367i	0.0505739	−	0.0148498i
$196$	−9.02401	+	2.64969i	−0.644572	+	0.189263i
$197$	−4.59653	+	10.0650i	−0.327489	+	0.717102i	−0.999730	−	0.0232308i	$-0.992605\pi$
$197$	−4.59653	+	10.0650i	−0.327489	+	0.717102i	0.672241	+	0.740333i	$0.265332\pi$
$198$	−0.538345	−	3.74427i	−0.0382585	−	0.266094i
$199$	15.5112	+	17.9009i	1.09956	+	1.26896i	0.960380	+	0.278695i	$0.0899018\pi$
$199$	15.5112	+	17.9009i	1.09956	+	1.26896i	0.139182	+	0.990267i	$0.455553\pi$
$200$	−0.415415	−	0.909632i	−0.0293743	−	0.0643207i
$201$	−8.56980	+	5.50748i	−0.604467	+	0.388467i
$202$	0.300010	−	2.08662i	0.0211086	−	0.146814i
$203$	10.3145	+	6.62874i	0.723937	+	0.465246i
$204$	−2.22526	+	2.56809i	−0.155800	+	0.179802i
$205$	−1.85108	−	0.543525i	−0.129285	−	0.0379614i
$206$	−1.64991			−0.114955
$207$	−4.00572	+	2.63709i	−0.278417	+	0.183290i
$208$	−0.736041			−0.0510353
$209$	−3.61660	−	1.06193i	−0.250165	−	0.0734551i
$210$	2.65239	−	3.06102i	0.183032	−	0.211230i
$211$	4.24374	+	2.72729i	0.292151	+	0.187754i	0.678504	−	0.734597i	$-0.262629\pi$
$211$	4.24374	+	2.72729i	0.292151	+	0.187754i	−0.386352	+	0.922351i	$0.626265\pi$
$212$	0.159647	−	1.11037i	0.0109646	−	0.0762605i
$213$	−6.51114	+	4.18446i	−0.446136	+	0.286714i
$214$	−1.87389	−	4.10324i	−0.128096	−	0.280492i
$215$	0.0781905	+	0.0902367i	0.00533255	+	0.00615409i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	−12.6963	+	27.8011i	−0.861882	+	1.88726i
$218$	−5.16186	+	1.51566i	−0.349605	+	0.102653i
$219$	−13.9116	+	4.08481i	−0.940058	+	0.276026i
$220$	1.57142	−	3.44093i	0.105945	−	0.231988i
$221$	−0.355947	−	2.47566i	−0.0239436	−	0.166531i
$222$	−1.67267	−	1.93037i	−0.112263	−	0.129558i
$223$	−8.45207	−	18.5074i	−0.565992	−	1.23935i	−0.948904	−	0.315565i	$-0.897806\pi$
$223$	−8.45207	−	18.5074i	−0.565992	−	1.23935i	0.382912	−	0.923785i	$-0.374921\pi$
$224$	−3.40733	+	2.18976i	−0.227662	+	0.146310i
$225$	−0.142315	+	0.989821i	−0.00948766	+	0.0659881i
$226$	10.0750	+	6.47478i	0.670176	+	0.430696i
$227$	2.38706	−	2.75482i	0.158435	−	0.182844i	−0.670982	−	0.741474i	$-0.734127\pi$
$227$	2.38706	−	2.75482i	0.158435	−	0.182844i	0.829417	+	0.558630i	$0.188673\pi$
$228$	−0.956070	−	0.280727i	−0.0633173	−	0.0185916i
$229$	25.5530			1.68859			0.844293	−	0.535881i	$-0.180020\pi$
$229$	25.5530			1.68859			0.844293	+	0.535881i	$0.180020\pi$
$230$	−4.79554	+	0.0528027i	−0.316209	+	0.00348170i
$231$	15.3214			1.00807
$232$	2.90453	+	0.852847i	0.190692	+	0.0559921i
$233$	8.68332	−	10.0211i	0.568863	−	0.656503i	−0.396309	−	0.918117i	$-0.629709\pi$
$233$	8.68332	−	10.0211i	0.568863	−	0.656503i	0.965173	+	0.261614i	$0.0842546\pi$
$234$	0.619197	+	0.397934i	0.0404782	+	0.0260138i
$235$	0.231727	−	1.61170i	0.0151162	−	0.105135i
$236$	9.00586	−	5.78772i	0.586232	−	0.376748i
$237$	−0.110837	−	0.242700i	−0.00719965	−	0.0157650i
$238$	−9.01300	−	10.4016i	−0.584226	−	0.674233i
$239$	−3.70652	−	25.7794i	−0.239755	−	1.66753i	−0.653340	−	0.757064i	$-0.726633\pi$
$239$	−3.70652	−	25.7794i	−0.239755	−	1.66753i	0.413586	−	0.910465i	$-0.364276\pi$
$240$	0.415415	−	0.909632i	0.0268149	−	0.0587165i
$241$	−5.91428	+	1.73659i	−0.380972	+	0.111864i	−0.466611	−	0.884463i	$-0.654525\pi$
$241$	−5.91428	+	1.73659i	−0.380972	+	0.111864i	0.0856386	+	0.996326i	$0.472707\pi$
$242$	3.17532	−	0.932357i	0.204117	−	0.0599342i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	−1.07882	−	7.50334i	−0.0690642	−	0.480352i
$245$	6.15895	+	7.10781i	0.393481	+	0.454101i
$246$	−0.801428	−	1.75488i	−0.0510972	−	0.111887i
$247$	0.616988	−	0.396514i	0.0392580	−	0.0252296i
$248$	−1.07389	+	7.46904i	−0.0681918	+	0.474284i
$249$	10.2785	+	6.60559i	0.651373	+	0.418612i
$250$	−0.654861	+	0.755750i	−0.0414170	+	0.0477978i
$251$	16.8808	+	4.95665i	1.06551	+	0.312861i	0.767066	−	0.641568i	$-0.221716\pi$
$251$	16.8808	+	4.95665i	1.06551	+	0.312861i	0.298440	+	0.954429i	$0.403534\pi$
$252$	4.05031			0.255145
$253$	−12.0304	−	13.5788i	−0.756346	−	0.853694i
$254$	−16.7053			−1.04819
$255$	3.26043	+	0.957348i	0.204176	+	0.0599514i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−11.5286	−	7.40895i	−0.719131	−	0.462158i	0.129203	−	0.991618i	$-0.458758\pi$
$257$	−11.5286	−	7.40895i	−0.719131	−	0.462158i	−0.848335	+	0.529461i	$0.822394\pi$
$258$	−0.0169924	+	0.118185i	−0.00105790	+	0.00735787i
$259$	8.70316	−	5.59318i	0.540788	−	0.347544i
$260$	0.305763	+	0.669527i	0.0189626	+	0.0415223i
$261$	−1.98236	−	2.28777i	−0.122705	−	0.141609i
$262$	−1.79864	−	12.5098i	−0.111120	−	0.772858i
$263$	−3.66873	+	8.03340i	−0.226224	+	0.495361i	−0.988375	−	0.152039i	$-0.951416\pi$
$263$	−3.66873	+	8.03340i	−0.226224	+	0.495361i	0.762151	+	0.647399i	$0.224143\pi$
$264$	3.62954	−	1.06573i	0.223383	−	0.0655912i
$265$	−1.07635	+	0.316044i	−0.0661195	+	0.0194144i
$266$	1.67656	−	3.67114i	0.102796	−	0.225092i
$267$	2.36021	+	16.4156i	0.144443	+	1.00462i
$268$	−6.67103	−	7.69878i	−0.407498	−	0.470278i
$269$	9.45854	+	20.7113i	0.576697	+	1.26279i	0.943154	+	0.332356i	$0.107843\pi$
$269$	9.45854	+	20.7113i	0.576697	+	1.26279i	−0.366457	+	0.930435i	$0.619429\pi$
$270$	−0.841254	+	0.540641i	−0.0511971	+	0.0329024i
$271$	2.68603	−	18.6817i	0.163165	−	1.13483i	−0.729457	−	0.684027i	$-0.760227\pi$
$271$	2.68603	−	18.6817i	0.163165	−	1.13483i	0.892621	−	0.450807i	$-0.148864\pi$
$272$	−2.85864	−	1.83714i	−0.173331	−	0.111393i
$273$	−1.95227	+	2.25303i	−0.118156	+	0.136360i
$274$	−1.90957	−	0.560700i	−0.115361	−	0.0338732i
$275$	−3.78277			−0.228110
$276$	−3.18032	−	3.58965i	−0.191433	−	0.216072i
$277$	22.2071			1.33430			0.667149	−	0.744924i	$-0.267514\pi$
$277$	22.2071			1.33430			0.667149	+	0.744924i	$0.267514\pi$
$278$	−9.87746	−	2.90029i	−0.592411	−	0.173948i
$279$	4.94148	−	5.70277i	0.295838	−	0.341416i
$280$	3.40733	+	2.18976i	0.203627	+	0.130863i
$281$	3.16186	−	21.9912i	0.188621	−	1.31189i	−0.646962	−	0.762522i	$-0.723961\pi$
$281$	3.16186	−	21.9912i	0.188621	−	1.31189i	0.835583	−	0.549364i	$-0.185130\pi$
$282$	1.36979	−	0.880309i	0.0815697	−	0.0524216i
$283$	6.86445	+	15.0311i	0.408049	+	0.893503i	0.996390	+	0.0848903i	$0.0270540\pi$
$283$	6.86445	+	15.0311i	0.408049	+	0.893503i	−0.588341	+	0.808613i	$0.700219\pi$
$284$	−5.06850	−	5.84936i	−0.300760	−	0.347095i
$285$	0.141807	+	0.986290i	0.00839993	+	0.0584228i
$286$	−1.15663	+	2.53267i	−0.0683930	+	0.149760i
$287$	7.49742	−	2.20144i	0.442559	−	0.129947i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−2.26530	+	4.96032i	−0.133253	+	0.291783i
$290$	−0.430808	−	2.99634i	−0.0252979	−	0.175951i
$291$	11.4520	+	13.2163i	0.671330	+	0.774756i
$292$	−6.02306	−	13.1887i	−0.352473	−	0.771808i
$293$	2.26922	−	1.45834i	0.132569	−	0.0851970i	−0.472675	−	0.881237i	$-0.656712\pi$
$293$	2.26922	−	1.45834i	0.132569	−	0.0851970i	0.605245	+	0.796040i	$0.293075\pi$
$294$	−1.33847	+	9.30925i	−0.0780610	+	0.542926i
$295$	−9.00586	−	5.78772i	−0.524342	−	0.336974i
$296$	1.67267	−	1.93037i	0.0972222	−	0.112200i
$297$	−3.62954	−	1.06573i	−0.210607	−	0.0618399i
$298$	20.3130			1.17670
$299$	3.52972	−	0.0388649i	0.204129	−	0.00224762i
$300$	−1.00000			−0.0577350
$301$	−0.464018	−	0.136248i	−0.0267456	−	0.00785320i
$302$	9.93071	−	11.4607i	0.571448	−	0.659487i
$303$	−1.77342	−	1.13971i	−0.101881	−	0.0654746i
$304$	0.141807	−	0.986290i	0.00813320	−	0.0565676i
$305$	−6.37712	+	4.09833i	−0.365153	+	0.234670i
$306$	1.41161	+	3.09100i	0.0806964	+	0.176700i
$307$	4.02705	+	4.64746i	0.229836	+	0.265245i	0.858940	−	0.512076i	$-0.171124\pi$
$307$	4.02705	+	4.64746i	0.229836	+	0.265245i	−0.629104	+	0.777321i	$0.716578\pi$
$308$	2.18046	+	15.1654i	0.124243	+	0.864131i
$309$	−0.685397	+	1.50081i	−0.0389909	+	0.0853782i
$310$	7.24018	−	2.12591i	0.411215	−	0.120744i
$311$	0.953901	−	0.280091i	0.0540908	−	0.0158825i	−0.254575	−	0.967053i	$-0.581936\pi$
$311$	0.953901	−	0.280091i	0.0540908	−	0.0158825i	0.308666	+	0.951170i	$0.400117\pi$
$312$	−0.305763	+	0.669527i	−0.0173104	+	0.0379045i
$313$	2.26018	+	15.7199i	0.127753	+	0.888540i	0.948394	+	0.317096i	$0.102708\pi$
$313$	2.26018	+	15.7199i	0.127753	+	0.888540i	−0.820641	+	0.571444i	$0.806383\pi$
$314$	8.59264	+	9.91643i	0.484911	+	0.559617i
$315$	−1.68256	−	3.68429i	−0.0948014	−	0.207586i
$316$	0.224456	−	0.144249i	0.0126266	−	0.00811463i
$317$	−0.427930	+	2.97632i	−0.0240349	+	0.167167i	−0.998304	−	0.0582232i	$-0.981456\pi$
$317$	−0.427930	+	2.97632i	−0.0240349	+	0.167167i	0.974269	+	0.225390i	$0.0723656\pi$
$318$	−0.943708	−	0.606484i	−0.0529205	−	0.0340099i
$319$	7.49882	−	8.65411i	0.419854	−	0.484537i
$320$	0.959493	+	0.281733i	0.0536373	+	0.0157493i
$321$	−4.51088			−0.251773
$322$	16.2244	−	10.6810i	0.904150	−	0.595229i
$323$	3.38595			0.188399
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	0.482004	−	0.556263i	0.0267368	−	0.0308559i
$326$	−11.0836	−	7.12302i	−0.613865	−	0.394507i
$327$	−0.765622	+	5.32502i	−0.0423390	+	0.294474i
$328$	1.62297	−	1.04302i	0.0896133	−	0.0575910i
$329$	2.73966	+	5.99901i	0.151042	+	0.330736i
$330$	−2.47719	−	2.85883i	−0.136365	−	0.157373i
$331$	−0.346356	−	2.40896i	−0.0190375	−	0.132409i	0.978086	−	0.208200i	$-0.0667606\pi$
$331$	−0.346356	−	2.40896i	−0.0190375	−	0.132409i	−0.997124	+	0.0757919i	$0.975852\pi$
$332$	−5.07557	+	11.1140i	−0.278558	+	0.609957i
$333$	−2.45078	+	0.719614i	−0.134302	+	0.0394346i
$334$	−8.35563	+	2.45343i	−0.457200	+	0.134246i
$335$	−4.23181	+	9.26637i	−0.231208	+	0.506276i
$336$	0.576419	+	4.00908i	0.0314462	+	0.218713i
$337$	13.3299	+	15.3835i	0.726125	+	0.837993i	0.992029	−	0.126006i	$-0.0402160\pi$
$337$	13.3299	+	15.3835i	0.726125	+	0.837993i	−0.265904	+	0.963999i	$0.585671\pi$
$338$	5.17534	+	11.3324i	0.281501	+	0.616402i
$339$	10.0750	−	6.47478i	0.547196	−	0.351662i
$340$	−0.483596	+	3.36348i	−0.0262267	+	0.182411i
$341$	24.0129	+	15.4322i	1.30037	+	0.835699i
$342$	−0.652525	+	0.753053i	−0.0352845	+	0.0407205i
$343$	−9.34632	−	2.74433i	−0.504654	−	0.148180i
$344$	−0.119400			−0.00643763
$345$	−1.94411	+	4.38411i	−0.104667	+	0.236033i
$346$	17.9085			0.962765
$347$	−11.3798	−	3.34141i	−0.610900	−	0.179376i	−0.0383744	−	0.999263i	$-0.512218\pi$
$347$	−11.3798	−	3.34141i	−0.610900	−	0.179376i	−0.572525	+	0.819887i	$0.694036\pi$
$348$	1.98236	−	2.28777i	0.106266	−	0.122637i
$349$	6.34836	+	4.07984i	0.339820	+	0.218389i	0.699409	−	0.714722i	$-0.253447\pi$
$349$	6.34836	+	4.07984i	0.339820	+	0.218389i	−0.359589	+	0.933111i	$0.617083\pi$
$350$	0.576419	−	4.00908i	0.0308109	−	0.214294i
$351$	0.619197	−	0.397934i	0.0330503	−	0.0212401i
$352$	1.57142	+	3.44093i	0.0837570	+	0.183402i
$353$	22.7693	+	26.2772i	1.21189	+	1.39860i	0.892546	+	0.450956i	$0.148917\pi$
$353$	22.7693	+	26.2772i	1.21189	+	1.39860i	0.319343	+	0.947639i	$0.396538\pi$
$354$	−1.52352	−	10.5963i	−0.0809743	−	0.563188i
$355$	−3.21523	+	7.04038i	−0.170647	+	0.373664i
$356$	−15.9126	+	4.67237i	−0.843369	+	0.247635i
$357$	−13.2057	+	3.87755i	−0.698921	+	0.205222i
$358$	−1.55188	+	3.39814i	−0.0820193	+	0.179597i
$359$	−3.29122	−	22.8909i	−0.173704	−	1.20814i	−0.870975	−	0.491328i	$-0.836512\pi$
$359$	−3.29122	−	22.8909i	−0.173704	−	1.20814i	0.697271	−	0.716808i	$-0.254397\pi$
$360$	−0.654861	−	0.755750i	−0.0345142	−	0.0398315i
$361$	−7.48043	−	16.3799i	−0.393707	−	0.862098i
$362$	−1.50744	+	0.968772i	−0.0792292	+	0.0509175i
$363$	0.470972	−	3.27568i	0.0247196	−	0.171929i
$364$	−2.50794	−	1.61175i	−0.131452	−	0.0844789i
$365$	−9.49475	+	10.9575i	−0.496978	+	0.573543i
$366$	−7.27343	−	2.13567i	−0.380189	−	0.111633i
$367$	0.928519			0.0484683			0.0242341	−	0.999706i	$-0.492285\pi$
$367$	0.928519			0.0484683			0.0242341	+	0.999706i	$0.492285\pi$
$368$	3.10051	−	3.65881i	0.161625	−	0.190728i
$369$	−1.92922			−0.100431
$370$	−2.45078	−	0.719614i	−0.127410	−	0.0374109i
$371$	2.97541	−	3.43381i	0.154476	−	0.178275i
$372$	6.34797	+	4.07959i	0.329127	+	0.211517i
$373$	−1.84939	+	12.8628i	−0.0957576	+	0.666009i	0.884245	+	0.467024i	$0.154674\pi$
$373$	−1.84939	+	12.8628i	−0.0957576	+	0.666009i	−0.980002	+	0.198985i	$0.936235\pi$
$374$	−10.8136	+	6.94947i	−0.559157	+	0.359349i
$375$	0.415415	+	0.909632i	0.0214519	+	0.0469732i
$376$	1.06629	+	1.23056i	0.0549897	+	0.0634615i
$377$	0.317093	+	2.20543i	0.0163311	+	0.113585i
$378$	1.68256	−	3.68429i	0.0865414	−	0.189499i
$379$	−2.07347	+	0.608827i	−0.106507	+	0.0312733i	−0.334552	−	0.942377i	$-0.608585\pi$
$379$	−2.07347	+	0.608827i	−0.106507	+	0.0312733i	0.228045	+	0.973651i	$0.426767\pi$
$380$	−0.956070	+	0.280727i	−0.0490454	+	0.0144010i
$381$	−6.93964	+	15.1957i	−0.355529	+	0.778499i
$382$	−3.21588	−	22.3670i	−0.164539	−	1.14439i
$383$	18.3900	+	21.2232i	0.939687	+	1.08446i	0.996290	+	0.0860597i	$0.0274276\pi$
$383$	18.3900	+	21.2232i	0.939687	+	1.08446i	−0.0566031	+	0.998397i	$0.518027\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	12.8892	−	8.28337i	0.656893	−	0.422159i
$386$	1.48070	−	10.2985i	0.0753655	−	0.524178i
$387$	0.100446	+	0.0645527i	0.00510595	+	0.00328140i
$388$	−11.4520	+	13.2163i	−0.581389	+	0.670958i
$389$	−18.4952	−	5.43069i	−0.937746	−	0.275347i	−0.223070	−	0.974802i	$-0.571608\pi$
$389$	−18.4952	−	5.43069i	−0.937746	−	0.275347i	−0.714676	+	0.699455i	$0.753426\pi$
$390$	0.736041			0.0372709
$391$	13.8057	+	8.65912i	0.698186	+	0.437911i
$392$	−9.40498			−0.475023
$393$	−12.1265	−	3.56066i	−0.611701	−	0.179612i
$394$	−7.24598	+	8.36231i	−0.365047	+	0.421287i
$395$	−0.224456	−	0.144249i	−0.0112936	−	0.00725795i
$396$	0.538345	−	3.74427i	0.0270528	−	0.188157i
$397$	−11.3416	+	7.28880i	−0.569218	+	0.365814i	−0.793370	−	0.608740i	$-0.791675\pi$
$397$	−11.3416	+	7.28880i	−0.569218	+	0.365814i	0.224152	+	0.974554i	$0.428039\pi$
$398$	9.83964	+	21.5458i	0.493217	+	1.07999i
$399$	−2.64292	−	3.05010i	−0.132312	−	0.152696i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	−6.96018	+	15.2407i	−0.347575	+	0.761082i	0.652420	+	0.757858i	$0.273754\pi$
$401$	−6.96018	+	15.2407i	−0.347575	+	0.761082i	−0.999995	+	0.00322489i	$0.998973\pi$
$402$	−9.77430	+	2.86999i	−0.487498	+	0.143142i
$403$	−5.32907	+	1.56476i	−0.265460	+	0.0779461i
$404$	0.875725	−	1.91757i	0.0435689	−	0.0954027i
$405$	0.142315	+	0.989821i	0.00707168	+	0.0491846i
$406$	8.02917	+	9.26616i	0.398481	+	0.459872i
$407$	−4.01379	−	8.78898i	−0.198956	−	0.435653i
$408$	−2.85864	+	1.83714i	−0.141524	+	0.0909518i
$409$	3.05599	−	21.2549i	0.151109	−	1.05099i	−0.763256	−	0.646096i	$-0.776401\pi$
$409$	3.05599	−	21.2549i	0.151109	−	1.05099i	0.914365	−	0.404890i	$-0.132690\pi$
$410$	−1.62297	−	1.04302i	−0.0801526	−	0.0515109i
$411$	−1.30330	+	1.50408i	−0.0642868	+	0.0741909i
$412$	−1.58308	−	0.464833i	−0.0779926	−	0.0229007i
$413$	43.3597			2.13359
$414$	−4.58641	+	1.40172i	−0.225410	+	0.0688910i
$415$	12.2181			0.599762
$416$	−0.706226	−	0.207367i	−0.0346256	−	0.0101670i
$417$	−6.74144	+	7.78004i	−0.330130	+	0.380990i
$418$	−3.17092	−	2.03783i	−0.155095	−	0.0996733i
$419$	2.87023	−	19.9629i	0.140220	−	0.975251i	−0.791266	−	0.611473i	$-0.790577\pi$
$419$	2.87023	−	19.9629i	0.140220	−	0.975251i	0.931486	−	0.363778i	$-0.118513\pi$
$420$	3.40733	−	2.18976i	0.166261	−	0.106849i
$421$	1.10890	+	2.42815i	0.0540444	+	0.118341i	0.934728	−	0.355365i	$-0.115643\pi$
$421$	1.10890	+	2.42815i	0.0540444	+	0.118341i	−0.880683	+	0.473706i	$0.842916\pi$
$422$	3.30347	+	3.81241i	0.160811	+	0.185585i
$423$	−0.231727	−	1.61170i	−0.0112669	−	0.0783634i
$424$	0.466007	−	1.02041i	0.0226313	−	0.0495557i
$425$	3.26043	−	0.957348i	0.158154	−	0.0464382i
$426$	−7.42629	+	2.18056i	−0.359805	+	0.105648i
$427$	12.7546	−	27.9287i	0.617240	−	1.35157i
$428$	−0.641966	−	4.46497i	−0.0310306	−	0.215822i
$429$	1.82331	+	2.10422i	0.0880304	+	0.101592i
$430$	0.0496007	+	0.108610i	0.00239196	+	0.00523765i
$431$	−8.79530	+	5.65240i	−0.423655	+	0.272266i	−0.735048	−	0.678015i	$-0.762841\pi$
$431$	−8.79530	+	5.65240i	−0.423655	+	0.272266i	0.311394	+	0.950281i	$0.399204\pi$
$432$	0.142315	−	0.989821i	0.00684713	−	0.0476228i
$433$	24.3123	+	15.6245i	1.16837	+	0.750868i	0.973213	−	0.229904i	$-0.0738412\pi$
$433$	24.3123	+	15.6245i	1.16837	+	0.750868i	0.195160	+	0.980772i	$0.437478\pi$
$434$	−20.0145	+	23.0980i	−0.960726	+	1.10874i
$435$	−2.90453	−	0.852847i	−0.139262	−	0.0408909i
$436$	−5.37978			−0.257645
$437$	−0.627963	+	4.73728i	−0.0300396	+	0.226615i
$438$	−14.4989			−0.692784
$439$	32.9278	+	9.66848i	1.57156	+	0.461451i	0.947455	−	0.319890i	$-0.103646\pi$
$439$	32.9278	+	9.66848i	1.57156	+	0.461451i	0.624104	+	0.781341i	$0.285464\pi$
$440$	2.47719	−	2.85883i	0.118095	−	0.136289i
$441$	7.91197	+	5.08471i	0.376760	+	0.242129i
$442$	0.355947	−	2.47566i	0.0169307	−	0.117755i
$443$	−9.72997	+	6.25307i	−0.462285	+	0.297093i	−0.750976	−	0.660330i	$-0.770416\pi$
$443$	−9.72997	+	6.25307i	−0.462285	+	0.297093i	0.288691	+	0.957422i	$0.406780\pi$
$444$	−1.06107	−	2.32342i	−0.0503562	−	0.110265i
$445$	10.8605	+	12.5337i	0.514837	+	0.594153i
$446$	−2.89555	−	20.1390i	−0.137108	−	0.953609i
$447$	8.43834	−	18.4774i	0.399120	−	0.873950i
$448$	−3.88624	+	1.14110i	−0.183608	+	0.0539120i
$449$	22.9778	−	6.74689i	1.08439	−	0.318405i	0.309756	−	0.950816i	$-0.399753\pi$
$449$	22.9778	−	6.74689i	1.08439	−	0.318405i	0.774633	+	0.632411i	$0.217935\pi$
$450$	−0.415415	+	0.909632i	−0.0195829	+	0.0428805i
$451$	−1.03859	−	7.22353i	−0.0489052	−	0.340143i
$452$	7.84269	+	9.05095i	0.368889	+	0.425721i
$453$	−6.29961	−	13.7942i	−0.295982	−	0.648109i
$454$	3.06649	−	1.97072i	0.143918	−	0.0924902i
$455$	−0.424268	+	2.95085i	−0.0198900	+	0.138338i
$456$	−0.838252	−	0.538712i	−0.0392548	−	0.0252275i
$457$	−4.24160	+	4.89507i	−0.198414	+	0.228982i	−0.846234	−	0.532812i	$-0.821135\pi$
$457$	−4.24160	+	4.89507i	−0.198414	+	0.228982i	0.647820	+	0.761793i	$0.275681\pi$
$458$	24.5179	+	7.19910i	1.14565	+	0.336392i
$459$	3.39807			0.158608
$460$	−4.61616	−	1.30040i	−0.215230	−	0.0606313i
$461$	−33.0764			−1.54052			−0.770260	−	0.637730i	$-0.779874\pi$
$461$	−33.0764			−1.54052			−0.770260	+	0.637730i	$0.779874\pi$
$462$	14.7008	+	4.31653i	0.683941	+	0.200823i
$463$	18.5899	−	21.4539i	0.863945	−	0.997045i	−0.136035	−	0.990704i	$-0.543436\pi$
$463$	18.5899	−	21.4539i	0.863945	−	0.997045i	0.999980	−	0.00634135i	$-0.00201853\pi$
$464$	2.54660	+	1.63660i	0.118223	+	0.0759773i
$465$	1.07389	−	7.46904i	0.0498002	−	0.346368i
$466$	11.1549	−	7.16879i	0.516739	−	0.332088i
$467$	4.00843	+	8.77724i	0.185488	+	0.406162i	0.979417	−	0.201849i	$-0.0646949\pi$
$467$	4.00843	+	8.77724i	0.185488	+	0.406162i	−0.793929	+	0.608011i	$0.791968\pi$
$468$	0.482004	+	0.556263i	0.0222807	+	0.0257133i
$469$	−5.87194	−	40.8403i	−0.271141	−	1.88583i
$470$	0.676408	−	1.48113i	0.0312004	−	0.0683193i
$471$	12.5898	−	3.69670i	0.580108	−	0.170335i
$472$	10.2717	−	3.01603i	0.472791	−	0.138824i
$473$	−0.187628	+	0.410848i	−0.00862715	+	0.0188908i
$474$	−0.0379711	−	0.264095i	−0.00174407	−	0.0121303i
$475$	0.652525	+	0.753053i	0.0299399	+	0.0345525i
$476$	−5.71745	−	12.5195i	−0.262059	−	0.573829i
$477$	−0.943708	+	0.606484i	−0.0432094	+	0.0277690i
$478$	3.70652	−	25.7794i	0.169532	−	1.17912i
$479$	−24.8270	−	15.9554i	−1.13438	−	0.729019i	−0.167907	−	0.985803i	$-0.553701\pi$
$479$	−24.8270	−	15.9554i	−1.13438	−	0.729019i	−0.966469	+	0.256783i	$0.917337\pi$
$480$	0.654861	−	0.755750i	0.0298902	−	0.0344951i
$481$	1.80387	+	0.529665i	0.0822496	+	0.0241507i
$482$	−6.16396			−0.280761
$483$	−2.97593	−	19.1953i	−0.135409	−	0.873415i
$484$	3.30937			0.150426
$485$	16.7794	+	4.92686i	0.761911	+	0.223717i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	21.8124	+	14.0180i	0.988414	+	0.635215i	0.931720	−	0.363176i	$-0.118308\pi$
$487$	21.8124	+	14.0180i	0.988414	+	0.635215i	0.0566937	+	0.998392i	$0.481944\pi$
$488$	1.07882	−	7.50334i	0.0488358	−	0.339660i
$489$	−11.0836	+	7.12302i	−0.501219	+	0.322114i
$490$	3.90697	+	8.55507i	0.176499	+	0.386479i
$491$	17.2212	+	19.8743i	0.777182	+	0.896916i	0.996903	−	0.0786470i	$-0.0250600\pi$
$491$	17.2212	+	19.8743i	0.777182	+	0.896916i	−0.219721	+	0.975563i	$0.570515\pi$
$492$	−0.274557	−	1.90959i	−0.0123780	−	0.0860908i
$493$	−4.27316	+	9.35691i	−0.192453	+	0.421414i
$494$	0.703707	−	0.206627i	0.0316613	−	0.00929659i
$495$	−3.62954	+	1.06573i	−0.163136	+	0.0479010i
$496$	−3.13466	+	6.86394i	−0.140750	+	0.308200i
$497$	−4.46137	−	31.0295i	−0.200120	−	1.39186i
$498$	8.00114	+	9.23380i	0.358540	+	0.413777i
$499$	7.21895	+	15.8073i	0.323165	+	0.707632i	0.999583	−	0.0288859i	$-0.00919596\pi$
$499$	7.21895	+	15.8073i	0.323165	+	0.707632i	−0.676418	+	0.736518i	$0.736469\pi$
$500$	−0.841254	+	0.540641i	−0.0376220	+	0.0241782i
$501$	−1.23933	+	8.61974i	−0.0553692	+	0.385102i
$502$	14.8006	+	9.51174i	0.660581	+	0.424530i
$503$	−27.0043	+	31.1646i	−1.20406	+	1.38956i	−0.304644	+	0.952466i	$0.598537\pi$
$503$	−27.0043	+	31.1646i	−1.20406	+	1.38956i	−0.899416	+	0.437093i	$0.856008\pi$
$504$	3.88624	+	1.14110i	0.173107	+	0.0508288i
$505$	−2.10807			−0.0938080
$506$	−7.71750	−	16.4181i	−0.343085	−	0.729876i
$507$	12.4582			0.553290
$508$	−16.0286	−	4.70643i	−0.711156	−	0.208814i
$509$	−4.86742	+	5.61731i	−0.215745	+	0.248983i	−0.853298	−	0.521424i	$-0.825401\pi$
$509$	−4.86742	+	5.61731i	−0.215745	+	0.248983i	0.637553	+	0.770406i	$0.279947\pi$
$510$	2.85864	+	1.83714i	0.126583	+	0.0813498i
$511$	8.35743	−	58.1272i	0.369711	−	2.57140i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	0.413933	+	0.906387i	0.0182756	+	0.0400180i
$514$	−8.97422	−	10.3568i	−0.395836	−	0.456819i
$515$	0.234807	+	1.63312i	0.0103468	+	0.0719637i
$516$	−0.0496007	+	0.108610i	−0.00218355	+	0.00478130i
$517$	5.90988	−	1.73530i	0.259916	−	0.0763182i
$518$	9.92641	−	2.91466i	0.436141	−	0.128063i
$519$	7.43945	−	16.2901i	0.326555	−	0.715057i
$520$	0.104750	+	0.728549i	0.00459357	+	0.0319490i
$521$	−9.60105	−	11.0802i	−0.420630	−	0.485432i	0.505399	−	0.862886i	$-0.331345\pi$
$521$	−9.60105	−	11.0802i	−0.420630	−	0.485432i	−0.926029	+	0.377453i	$0.876800\pi$
$522$	−1.25752	−	2.75359i	−0.0550403	−	0.120521i
$523$	31.9564	−	20.5371i	1.39735	−	0.898025i	0.397545	−	0.917583i	$-0.369862\pi$
$523$	31.9564	−	20.5371i	1.39735	−	0.898025i	0.999809	+	0.0195579i	$0.00622586\pi$
$524$	1.79864	−	12.5098i	0.0785739	−	0.546493i
$525$	−3.40733	−	2.18976i	−0.148708	−	0.0955690i
$526$	−5.78339	+	6.67439i	−0.252168	+	0.291017i
$527$	−24.6027	−	7.22399i	−1.07171	−	0.314682i
$528$	3.78277			0.164624
$529$	−14.6754	+	17.7097i	−0.638061	+	0.769986i
$530$	−1.12179			−0.0487273
$531$	−10.2717	−	3.01603i	−0.445752	−	0.130885i
$532$	2.64292	−	3.05010i	0.114585	−	0.132238i
$533$	1.19457	+	0.767703i	0.0517426	+	0.0332529i
$534$	−2.36021	+	16.4156i	−0.102136	+	0.710374i
$535$	−3.79480	+	2.43877i	−0.164063	+	0.105437i
$536$	−4.23181	−	9.26637i	−0.182786	−	0.400246i
$537$	2.44638	+	2.82328i	0.105569	+	0.121833i
$538$	3.24035	+	22.5371i	0.139701	+	0.971645i
$539$	−14.7792	+	32.3619i	−0.636584	+	1.39392i
$540$	−0.959493	+	0.281733i	−0.0412900	+	0.0121238i
$541$	−25.4032	+	7.45905i	−1.09217	+	0.320690i	−0.777736	−	0.628591i	$-0.783632\pi$
$541$	−25.4032	+	7.45905i	−1.09217	+	0.320690i	−0.314432	+	0.949280i	$0.601814\pi$
$542$	7.84048	−	17.1683i	0.336777	−	0.737440i
$543$	0.255013	+	1.77366i	0.0109437	+	0.0761149i
$544$	−2.22526	−	2.56809i	−0.0954074	−	0.110106i
$545$	2.23484	+	4.89362i	0.0957300	+	0.209619i
$546$	−2.50794	+	1.61175i	−0.107330	+	0.0689767i
$547$	4.18457	−	29.1043i	0.178919	−	1.24441i	−0.680350	−	0.732887i	$-0.738172\pi$
$547$	4.18457	−	29.1043i	0.178919	−	1.24441i	0.859269	−	0.511523i	$-0.170919\pi$
$548$	−1.67425	−	1.07598i	−0.0715205	−	0.0459634i
$549$	−4.96417	+	5.72896i	−0.211866	+	0.244506i
$550$	−3.62954	−	1.06573i	−0.154764	−	0.0454429i
$551$	−3.01635			−0.128501
$552$	−2.04017	−	4.34024i	−0.0868354	−	0.184733i
$553$	1.08067			0.0459546
$554$	21.3076	+	6.25647i	0.905273	+	0.265812i
$555$	−1.67267	+	1.93037i	−0.0710011	+	0.0819396i
$556$	−8.66025	−	5.56561i	−0.367277	−	0.236034i
$557$	4.16465	−	28.9657i	0.176462	−	1.22732i	−0.688409	−	0.725323i	$-0.741690\pi$
$557$	4.16465	−	28.9657i	0.176462	−	1.22732i	0.864870	−	0.501995i	$-0.167400\pi$
$558$	6.34797	−	4.07959i	0.268731	−	0.172703i
$559$	−0.0365081	−	0.0799416i	−0.00154413	−	0.00338117i
$560$	2.65239	+	3.06102i	0.112084	+	0.129352i
$561$	1.82933	+	12.7233i	0.0772345	+	0.537178i
$562$	9.22942	−	20.2096i	0.389320	−	0.852491i
$563$	−38.6647	+	11.3530i	−1.62952	+	0.478471i	−0.963555	−	0.267509i	$-0.913799\pi$
$563$	−38.6647	+	11.3530i	−1.62952	+	0.478471i	−0.665968	+	0.745980i	$0.731981\pi$
$564$	1.56231	−	0.458737i	0.0657853	−	0.0193163i
$565$	4.97506	−	10.8939i	0.209302	−	0.458308i
$566$	2.35166	+	16.3561i	0.0988475	+	0.687499i
$567$	−2.65239	−	3.06102i	−0.111390	−	0.128551i
$568$	−3.21523	−	7.04038i	−0.134908	−	0.295408i
$569$	5.95587	−	3.82761i	0.249683	−	0.160462i	−0.409813	−	0.912170i	$-0.634406\pi$
$569$	5.95587	−	3.82761i	0.249683	−	0.160462i	0.659496	+	0.751708i	$0.270770\pi$
$570$	−0.141807	+	0.986290i	−0.00593965	+	0.0413112i
$571$	29.4003	+	18.8944i	1.23037	+	0.790708i	0.983948	−	0.178456i	$-0.0571102\pi$
$571$	29.4003	+	18.8944i	1.23037	+	0.790708i	0.246417	+	0.969164i	$0.420747\pi$
$572$	−1.82331	+	2.10422i	−0.0762366	+	0.0879817i
$573$	−21.6816	−	6.36630i	−0.905763	−	0.265956i
$574$	7.81394			0.326148
$575$	0.734742	+	4.73921i	0.0306409	+	0.197639i
$576$	1.00000			0.0416667
$577$	−18.1423	−	5.32706i	−0.755273	−	0.221768i	−0.118643	−	0.992937i	$-0.537854\pi$
$577$	−18.1423	−	5.32706i	−0.755273	−	0.221768i	−0.636631	+	0.771169i	$0.719672\pi$
$578$	−3.57102	+	4.12118i	−0.148535	+	0.171419i
$579$	−8.75271	−	5.62503i	−0.363750	−	0.233768i
$580$	0.430808	−	2.99634i	0.0178883	−	0.124416i
$581$	−41.6311	+	26.7547i	−1.72715	+	1.10997i
$582$	7.26467	+	15.9074i	0.301130	+	0.659383i
$583$	−2.77888	−	3.20700i	−0.115089	−	0.132820i
$584$	−2.06341	−	14.3513i	−0.0853844	−	0.593861i
$585$	0.305763	−	0.669527i	0.0126417	−	0.0276815i
$586$	2.58816	−	0.759952i	0.106916	−	0.0313933i
$587$	−42.8696	+	12.5876i	−1.76942	+	0.519548i	−0.993753	−	0.111599i	$-0.964403\pi$
$587$	−42.8696	+	12.5876i	−1.76942	+	0.519548i	−0.775664	+	0.631146i	$0.782585\pi$
$588$	−3.90697	+	8.55507i	−0.161121	+	0.352805i
$589$	−1.07005	−	7.44239i	−0.0440908	−	0.306658i
$590$	−7.01047	−	8.09052i	−0.288617	−	0.333081i
$591$	4.59653	+	10.0650i	0.189076	+	0.414019i
$592$	2.14877	−	1.38093i	0.0883138	−	0.0567558i
$593$	−5.07624	+	35.3060i	−0.208456	+	1.44984i	0.569741	+	0.821824i	$0.307044\pi$
$593$	−5.07624	+	35.3060i	−0.208456	+	1.44984i	−0.778197	+	0.628020i	$0.783866\pi$
$594$	−3.18227	−	2.04512i	−0.130570	−	0.0839123i
$595$	−9.01300	+	10.4016i	−0.369497	+	0.426422i
$596$	19.4902	+	5.72284i	0.798350	+	0.234417i
$597$	23.6863			0.969415
$598$	3.39769	+	0.957145i	0.138942	+	0.0391406i
$599$	12.5925			0.514518			0.257259	−	0.966343i	$-0.417181\pi$
$599$	12.5925			0.514518			0.257259	+	0.966343i	$0.417181\pi$
$600$	−0.959493	−	0.281733i	−0.0391711	−	0.0115017i
$601$	4.33773	−	5.00601i	0.176940	−	0.204199i	−0.660351	−	0.750957i	$-0.729593\pi$
$601$	4.33773	−	5.00601i	0.176940	−	0.204199i	0.837291	+	0.546758i	$0.184138\pi$
$602$	−0.406837	−	0.261458i	−0.0165814	−	0.0106562i
$603$	−1.44975	+	10.0833i	−0.0590385	+	0.410622i
$604$	12.7573	−	8.19861i	0.519087	−	0.333597i
$605$	−1.37476	−	3.01031i	−0.0558920	−	0.122386i
$606$	−1.38049	−	1.59318i	−0.0560787	−	0.0647183i
$607$	−3.74533	−	26.0493i	−0.152018	−	1.05731i	−0.912831	−	0.408338i	$-0.866108\pi$
$607$	−3.74533	−	26.0493i	−0.152018	−	1.05731i	0.760812	−	0.648972i	$-0.224801\pi$
$608$	0.413933	−	0.906387i	0.0167872	−	0.0367588i
$609$	11.7642	−	3.45429i	0.476711	−	0.139975i
$610$	−7.27343	+	2.13567i	−0.294493	+	0.0864709i
$611$	−0.497864	+	1.09017i	−0.0201414	+	0.0441036i
$612$	0.483596	+	3.36348i	0.0195482	+	0.135961i
$613$	−28.1731	−	32.5135i	−1.13790	−	1.31321i	−0.943155	−	0.332354i	$-0.892157\pi$
$613$	−28.1731	−	32.5135i	−1.13790	−	1.31321i	−0.194746	−	0.980854i	$-0.562388\pi$
$614$	2.55458	+	5.59376i	0.103095	+	0.225746i
$615$	−1.62297	+	1.04302i	−0.0654443	+	0.0420585i
$616$	−2.18046	+	15.1654i	−0.0878533	+	0.611033i
$617$	17.5104	+	11.2533i	0.704943	+	0.453039i	0.843370	−	0.537333i	$-0.180568\pi$
$617$	17.5104	+	11.2533i	0.704943	+	0.453039i	−0.138427	+	0.990373i	$0.544205\pi$
$618$	−1.08046	+	1.24692i	−0.0434625	+	0.0501584i
$619$	18.7517	+	5.50598i	0.753692	+	0.221304i	0.635940	−	0.771739i	$-0.280613\pi$
$619$	18.7517	+	5.50598i	0.753692	+	0.221304i	0.117753	+	0.993043i	$0.462431\pi$
$620$	7.54584			0.303048
$621$	−0.630211	+	4.75424i	−0.0252895	+	0.190781i
$622$	0.994172			0.0398627
$623$	−64.4511	−	18.9245i	−2.58218	−	0.758196i
$624$	−0.482004	+	0.556263i	−0.0192956	+	0.0222683i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	−2.26018	+	15.7199i	−0.0903348	+	0.628293i
$627$	−3.17092	+	2.03783i	−0.126634	+	0.0813829i
$628$	5.45079	+	11.9356i	0.217510	+	0.476281i
$629$	5.68387	+	6.55953i	0.226631	+	0.261546i
$630$	−0.576419	−	4.00908i	−0.0229651	−	0.159726i
$631$	−15.6033	+	34.1664i	−0.621156	+	1.36014i	0.293520	+	0.955953i	$0.405173\pi$
$631$	−15.6033	+	34.1664i	−0.621156	+	1.36014i	−0.914676	+	0.404188i	$0.867554\pi$
$632$	0.256003	−	0.0751693i	0.0101833	−	0.00299007i
$633$	4.84021	−	1.42121i	0.192381	−	0.0564881i
$634$	−1.24912	+	2.73519i	−0.0496089	+	0.108628i
$635$	2.37742	+	16.5353i	0.0943449	+	0.656183i
$636$	−0.734615	−	0.847791i	−0.0291294	−	0.0336171i
$637$	−2.87569	−	6.29688i	−0.113939	−	0.249492i
$638$	9.63321	−	6.19089i	0.381383	−	0.245100i
$639$	−1.10149	+	7.66103i	−0.0435743	+	0.303066i
$640$	0.841254	+	0.540641i	0.0332535	+	0.0213707i
$641$	−19.0330	+	21.9653i	−0.751760	+	0.867577i	−0.994738	−	0.102455i	$-0.967330\pi$
$641$	−19.0330	+	21.9653i	−0.751760	+	0.867577i	0.242978	+	0.970032i	$0.421876\pi$
$642$	−4.32816	−	1.27086i	−0.170819	−	0.0501570i
$643$	−26.9923			−1.06447			−0.532237	−	0.846595i	$-0.678648\pi$
$643$	−26.9923			−1.06447			−0.532237	+	0.846595i	$0.678648\pi$
$644$	18.5764	−	5.67741i	0.732011	−	0.223721i
$645$	0.119400			0.00470138
$646$	3.24880	+	0.953932i	0.127822	+	0.0375320i
$647$	22.9421	−	26.4766i	0.901948	−	1.04090i	−0.0970109	−	0.995283i	$-0.530928\pi$
$647$	22.9421	−	26.4766i	0.901948	−	1.04090i	0.998959	−	0.0456201i	$-0.0145264\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	5.76314	−	40.0835i	0.226223	−	1.57341i
$650$	0.619197	−	0.397934i	0.0242869	−	0.0156083i
$651$	12.6963	+	27.8011i	0.497608	+	1.08961i
$652$	−8.62788	−	9.95710i	−0.337894	−	0.389950i
$653$	2.51307	+	17.4788i	0.0983439	+	0.683997i	0.978033	+	0.208448i	$0.0668413\pi$
$653$	2.51307	+	17.4788i	0.0983439	+	0.683997i	−0.879689	+	0.475549i	$0.842250\pi$
$654$	−2.23484	+	4.89362i	−0.0873891	+	0.191356i
$655$	−12.1265	+	3.56066i	−0.473821	+	0.139127i
$656$	1.85108	−	0.543525i	0.0722724	−	0.0212211i
$657$	−6.02306	+	13.1887i	−0.234982	+	0.514538i
$658$	0.938565	+	6.52786i	0.0365891	+	0.254483i
$659$	−5.73473	−	6.61823i	−0.223393	−	0.257810i	0.632978	−	0.774169i	$-0.281832\pi$
$659$	−5.73473	−	6.61823i	−0.223393	−	0.257810i	−0.856372	+	0.516360i	$0.827287\pi$
$660$	−1.57142	−	3.44093i	−0.0611675	−	0.133938i
$661$	−38.4621	+	24.7181i	−1.49600	+	0.961422i	−0.500595	+	0.865682i	$0.666885\pi$
$661$	−38.4621	+	24.7181i	−1.49600	+	0.961422i	−0.995406	+	0.0957401i	$0.969478\pi$
$662$	0.346356	−	2.40896i	0.0134615	−	0.0936270i
$663$	−2.10408	−	1.35221i	−0.0817156	−	0.0525154i
$664$	−8.00114	+	9.23380i	−0.310504	+	0.358341i
$665$	−3.87238	−	1.13703i	−0.150164	−	0.0440922i
$666$	−2.55424			−0.0989750
$667$	−12.2987	−	7.71392i	−0.476209	−	0.298684i
$668$	−8.70838			−0.336937
$669$	−19.5219	−	5.73215i	−0.754761	−	0.221618i
$670$	−6.67103	+	7.69878i	−0.257724	+	0.297430i
$671$	−24.1232	−	15.5030i	−0.931266	−	0.598488i
$672$	−0.576419	+	4.00908i	−0.0222358	+	0.154654i
$673$	26.1411	−	16.7998i	1.00766	−	0.647587i	0.0708767	−	0.997485i	$-0.477420\pi$
$673$	26.1411	−	16.7998i	1.00766	−	0.647587i	0.936788	+	0.349899i	$0.113784\pi$
$674$	8.45590	+	18.5158i	0.325709	+	0.713203i
$675$	0.654861	+	0.755750i	0.0252056	+	0.0290888i
$676$	1.77299	+	12.3314i	0.0681920	+	0.474286i
$677$	15.6265	−	34.2173i	0.600576	−	1.31508i	−0.328260	−	0.944588i	$-0.606462\pi$
$677$	15.6265	−	34.2173i	0.600576	−	1.31508i	0.928836	−	0.370491i	$-0.120811\pi$
$678$	11.4910	−	3.37406i	0.441309	−	0.129580i
$679$	−67.9615	+	19.9553i	−2.60812	+	0.765814i
$680$	−1.41161	+	3.09100i	−0.0541328	+	0.118534i
$681$	−0.518758	−	3.60804i	−0.0198789	−	0.138261i
$682$	18.6925	+	21.5723i	0.715772	+	0.826045i
$683$	−1.79897	−	3.93919i	−0.0688355	−	0.150729i	0.872087	−	0.489351i	$-0.162766\pi$
$683$	−1.79897	−	3.93919i	−0.0688355	−	0.150729i	−0.940922	+	0.338622i	$0.890039\pi$
$684$	−0.838252	+	0.538712i	−0.0320514	+	0.0205982i
$685$	−0.283233	+	1.96993i	−0.0108218	+	0.0752671i
$686$	−8.19456	−	5.26632i	−0.312870	−	0.201069i
$687$	16.7336	−	19.3116i	0.638428	−	0.736785i
$688$	−0.114564	−	0.0336389i	−0.00436770	−	0.00128247i
$689$	0.825682			0.0314560
$690$	−3.10051	+	3.65881i	−0.118034	+	0.139288i
$691$	10.9614			0.416992			0.208496	−	0.978023i	$-0.433143\pi$
$691$	10.9614			0.416992			0.208496	+	0.978023i	$0.433143\pi$
$692$	17.1830	+	5.04540i	0.653201	+	0.191797i
$693$	10.0334	−	11.5791i	0.381136	−	0.439855i
$694$	−9.97745	−	6.41212i	−0.378739	−	0.243401i
$695$	−1.46505	+	10.1897i	−0.0555727	+	0.386517i
$696$	2.54660	−	1.63660i	0.0965287	−	0.0620352i
$697$	2.72331	+	5.96322i	0.103153	+	0.225873i
$698$	4.94178	+	5.70312i	0.187049	+	0.215866i
$699$	−1.88707	−	13.1248i	−0.0713754	−	0.496427i
$700$	1.68256	−	3.68429i	0.0635947	−	0.139253i
$701$	0.589789	−	0.173178i	0.0222760	−	0.00654083i	−0.270576	−	0.962699i	$-0.587214\pi$
$701$	0.589789	−	0.173178i	0.0222760	−	0.00654083i	0.292852	+	0.956158i	$0.405396\pi$
$702$	0.706226	−	0.207367i	0.0266548	−	0.00782655i
$703$	−1.05729	+	2.31513i	−0.0398763	+	0.0873169i
$704$	0.538345	+	3.74427i	0.0202896	+	0.141117i
$705$	−1.06629	−	1.23056i	−0.0401588	−	0.0463457i
$706$	14.4439	+	31.6277i	0.543602	+	1.19032i
$707$	7.18291	−	4.61617i	0.270141	−	0.173609i
$708$	1.52352	−	10.5963i	0.0572575	−	0.398234i
$709$	−27.8186	−	17.8779i	−1.04475	−	0.671420i	−0.0985925	−	0.995128i	$-0.531434\pi$
$709$	−27.8186	−	17.8779i	−1.04475	−	0.671420i	−0.946157	+	0.323708i	$0.895070\pi$
$710$	−5.06850	+	5.84936i	−0.190217	+	0.219522i
$711$	−0.256003	−	0.0751693i	−0.00960087	−	0.00281907i
$712$	−16.5844			−0.621528
$713$	14.6699	−	33.0818i	0.549394	−	1.23892i
$714$	−13.7632			−0.515076
$715$	2.67149	+	0.784421i	0.0999082	+	0.0293357i
$716$	−2.44638	+	2.82328i	−0.0914256	+	0.105511i
$717$	−21.9100	−	14.0807i	−0.818244	−	0.525854i
$718$	3.29122	−	22.8909i	0.122827	−	0.854281i
$719$	−15.7029	+	10.0917i	−0.585620	+	0.376355i	−0.799645	−	0.600473i	$-0.794979\pi$
$719$	−15.7029	+	10.0917i	−0.585620	+	0.376355i	0.214025	+	0.976828i	$0.431343\pi$
$720$	−0.415415	−	0.909632i	−0.0154816	−	0.0339000i
$721$	−4.37620	−	5.05040i	−0.162978	−	0.188087i
$722$	−2.56268	−	17.8238i	−0.0953731	−	0.663334i
$723$	−2.56060	+	5.60694i	−0.0952299	+	0.208524i
$724$	−1.71931	+	0.504836i	−0.0638977	+	0.0187621i
$725$	−2.90453	+	0.852847i	−0.107872	+	0.0316739i
$726$	1.37476	−	3.01031i	0.0510222	−	0.111723i
$727$	0.195976	+	1.36305i	0.00726836	+	0.0505526i	0.993133	−	0.116992i	$-0.0373252\pi$
$727$	0.195976	+	1.36305i	0.00726836	+	0.0505526i	−0.985864	+	0.167545i	$0.946416\pi$
$728$	−1.95227	−	2.25303i	−0.0723558	−	0.0835030i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−12.1972	+	7.83869i	−0.451440	+	0.290123i
$731$	0.0577415	−	0.401601i	0.00213565	−	0.0148537i
$732$	−6.37712	−	4.09833i	−0.235705	−	0.151479i
$733$	12.5420	−	14.4742i	0.463248	−	0.534617i	−0.475273	−	0.879838i	$-0.657651\pi$
$733$	12.5420	−	14.4742i	0.463248	−	0.534617i	0.938521	+	0.345222i	$0.112196\pi$
$734$	0.890907	+	0.261594i	0.0328840	+	0.00965561i
$735$	9.40498			0.346908
$736$	4.00572	−	2.63709i	0.147653	−	0.0972043i
$737$	−38.5349			−1.41945
$738$	−1.85108	−	0.543525i	−0.0681390	−	0.0200074i
$739$	18.5191	−	21.3721i	0.681235	−	0.786187i	−0.304855	−	0.952399i	$-0.598608\pi$
$739$	18.5191	−	21.3721i	0.681235	−	0.786187i	0.986090	+	0.166212i	$0.0531535\pi$
$740$	−2.14877	−	1.38093i	−0.0789902	−	0.0507639i
$741$	0.104376	−	0.725950i	0.00383434	−	0.0266684i
$742$	3.82231	−	2.45645i	0.140321	−	0.0901790i
$743$	−7.57938	−	16.5965i	−0.278061	−	0.608868i	0.718146	−	0.695893i	$-0.244991\pi$
$743$	−7.57938	−	16.5965i	−0.278061	−	0.608868i	−0.996206	+	0.0870252i	$0.972264\pi$
$744$	4.94148	+	5.70277i	0.181163	+	0.209074i
$745$	−2.89085	−	20.1063i	−0.105912	−	0.736637i
$746$	−5.39833	+	11.8207i	−0.197647	+	0.432787i
$747$	11.7232	−	3.44223i	0.428928	−	0.125945i
$748$	−12.3335	+	3.62143i	−0.450956	+	0.132413i
$749$	7.58982	−	16.6194i	0.277326	−	0.607259i
$750$	0.142315	+	0.989821i	0.00519660	+	0.0361432i
$751$	10.5613	+	12.1884i	0.385386	+	0.444759i	0.914984	−	0.403489i	$-0.132203\pi$
$751$	10.5613	+	12.1884i	0.385386	+	0.444759i	−0.529598	+	0.848249i	$0.677657\pi$
$752$	0.676408	+	1.48113i	0.0246660	+	0.0540111i
$753$	14.8006	−	9.51174i	0.539362	−	0.346627i
$754$	−0.317093	+	2.20543i	−0.0115478	+	0.0803170i
$755$	−12.7573	−	8.19861i	−0.464285	−	0.298378i
$756$	2.65239	−	3.06102i	0.0964664	−	0.111328i
$757$	20.6253	+	6.05613i	0.749639	+	0.220114i	0.634166	−	0.773197i	$-0.281344\pi$
$757$	20.6253	+	6.05613i	0.749639	+	0.220114i	0.115473	+	0.993311i	$0.463162\pi$
$758$	−2.16101			−0.0784914
$759$	−18.1404	+	0.199740i	−0.658456	+	0.00725012i
$760$	−0.996433			−0.0361444
$761$	34.6527	+	10.1749i	1.25616	+	0.368842i	0.841064	−	0.540936i	$-0.181930\pi$
$761$	34.6527	+	10.1749i	1.25616	+	0.368842i	0.415095	+	0.909778i	$0.363748\pi$
$762$	−10.9397	+	12.6250i	−0.396302	+	0.457357i
$763$	−18.3307	−	11.7804i	−0.663616	−	0.426480i
$764$	3.21588	−	22.3670i	0.116347	−	0.809208i
$765$	2.85864	−	1.83714i	0.103354	−	0.0664218i
$766$	11.6658	+	25.5446i	0.421504	+	0.922964i
$767$	5.16000	+	5.95496i	0.186317	+	0.215021i
$768$	0.142315	+	0.989821i	0.00513534	+	0.0357171i
$769$	−16.2865	+	35.6625i	−0.587307	+	1.28602i	0.349749	+	0.936844i	$0.386267\pi$
$769$	−16.2865	+	35.6625i	−0.587307	+	1.28602i	−0.937056	+	0.349180i	$0.886460\pi$
$770$	14.7008	−	4.31653i	0.529779	−	0.155557i
$771$	−13.1489	+	3.86087i	−0.473546	+	0.139046i
$772$	4.32213	−	9.46415i	0.155557	−	0.340622i
$773$	0.687246	+	4.77990i	0.0247185	+	0.171921i	0.998441	−	0.0558166i	$-0.0177762\pi$
$773$	0.687246	+	4.77990i	0.0247185	+	0.171921i	−0.973723	+	0.227738i	$0.926867\pi$
$774$	0.0781905	+	0.0902367i	0.00281050	+	0.00324349i
$775$	−3.13466	−	6.86394i	−0.112600	−	0.246560i
$776$	−14.7116	+	9.45458i	−0.528116	+	0.339400i
$777$	1.47231	−	10.2402i	0.0528190	−	0.367364i
$778$	−16.2161	−	10.4214i	−0.581374	−	0.373626i
$779$	−1.25887	+	1.45281i	−0.0451035	+	0.0520523i
$780$	0.706226	+	0.207367i	0.0252870	+	0.00742492i
$781$	−29.2779			−1.04765
$782$	10.8069	+	12.1979i	0.386456	+	0.436196i
$783$	−3.02715			−0.108182
$784$	−9.02401	−	2.64969i	−0.322286	−	0.0946317i
$785$	8.59264	−	9.91643i	0.306684	−	0.353933i
$786$	−10.6321	−	6.83286i	−0.379236	−	0.243720i
$787$	−5.39805	+	37.5443i	−0.192420	+	1.33831i	0.633159	+	0.774022i	$0.281758\pi$
$787$	−5.39805	+	37.5443i	−0.192420	+	1.33831i	−0.825579	+	0.564287i	$0.809151\pi$
$788$	−9.30840	+	5.98215i	−0.331598	+	0.213105i
$789$	3.66873	+	8.03340i	0.130610	+	0.285997i
$790$	−0.174724	−	0.201642i	−0.00621640	−	0.00717411i
$791$	6.90326	+	48.0132i	0.245452	+	1.70715i
$792$	1.57142	−	3.44093i	0.0558380	−	0.122268i
$793$	5.35355	−	1.57194i	0.190110	−	0.0558213i
$794$	−12.9357	+	3.79826i	−0.459070	+	0.134795i
$795$	−0.466007	+	1.02041i	−0.0165276	+	0.0361904i
$796$	3.37091	+	23.4452i	0.119479	+	0.830993i
$797$	−1.88355	−	2.17374i	−0.0667189	−	0.0769977i	0.721409	−	0.692509i	$-0.243495\pi$
$797$	−1.88355	−	2.17374i	−0.0667189	−	0.0769977i	−0.788128	+	0.615512i	$0.788949\pi$
$798$	−1.67656	−	3.67114i	−0.0593494	−	0.129957i
$799$	−4.65464	+	2.99135i	−0.164669	+	0.105826i
$800$	0.142315	−	0.989821i	0.00503159	−	0.0349955i
$801$	13.9517	+	8.96622i	0.492960	+	0.316806i
$802$	−10.9720	+	12.6624i	−0.387436	+	0.447125i
$803$	−52.6243	−	15.4519i	−1.85707	−	0.545286i
$804$	−10.1869			−0.359266
$805$	−12.8813	−	14.5392i	−0.454005	−	0.512439i
$806$	−5.55405			−0.195633
$807$	21.8466	+	6.41474i	0.769036	+	0.225809i
$808$	1.38049	−	1.59318i	0.0485656	−	0.0560477i
$809$	31.5203	+	20.2569i	1.10820	+	0.712194i	0.960899	−	0.276898i	$-0.0893064\pi$
$809$	31.5203	+	20.2569i	1.10820	+	0.712194i	0.147297	+	0.989092i	$0.452943\pi$
$810$	−0.142315	+	0.989821i	−0.00500043	+	0.0347788i
$811$	−18.2129	+	11.7047i	−0.639542	+	0.411009i	−0.819832	−	0.572605i	$-0.805933\pi$
$811$	−18.2129	+	11.7047i	−0.639542	+	0.411009i	0.180289	+	0.983614i	$0.442297\pi$
$812$	5.09336	+	11.1529i	0.178742	+	0.391390i
$813$	−12.3597	−	14.2639i	−0.433475	−	0.500257i
$814$	−1.37506	−	9.56378i	−0.0481960	−	0.335210i
$815$	−5.47315	+	11.9845i	−0.191716	+	0.419800i
$816$	−3.26043	+	0.957348i	−0.114138	+	0.0335139i
$817$	0.114155	−	0.0335189i	0.00399378	−	0.00117268i
$818$	8.92039	−	19.5329i	0.311894	−	0.682953i
$819$	0.424268	+	2.95085i	0.0148251	+	0.103111i
$820$	−1.26337	−	1.45801i	−0.0441189	−	0.0509159i
$821$	−13.6787	−	29.9521i	−0.477388	−	1.04533i	−0.983173	−	0.182675i	$-0.941524\pi$
$821$	−13.6787	−	29.9521i	−0.477388	−	1.04533i	0.505785	−	0.862660i	$-0.331203\pi$
$822$	−1.67425	+	1.07598i	−0.0583962	+	0.0375290i
$823$	3.22734	−	22.4467i	0.112498	−	0.782442i	−0.852977	−	0.521948i	$-0.825206\pi$
$823$	3.22734	−	22.4467i	0.112498	−	0.782442i	0.965475	−	0.260494i	$-0.0838854\pi$
$824$	−1.38799	−	0.892009i	−0.0483530	−	0.0310746i
$825$	−2.47719	+	2.85883i	−0.0862447	+	0.0995316i
$826$	41.6033	+	12.2158i	1.44756	+	0.425043i
$827$	8.17451			0.284256			0.142128	−	0.989848i	$-0.454606\pi$
$827$	8.17451			0.284256			0.142128	+	0.989848i	$0.454606\pi$
$828$	−4.79554	+	0.0528027i	−0.166657	+	0.00183502i
$829$	−13.1438			−0.456504			−0.228252	−	0.973602i	$-0.573301\pi$
$829$	−13.1438			−0.456504			−0.228252	+	0.973602i	$0.573301\pi$
$830$	11.7232	+	3.44223i	0.406917	+	0.119482i
$831$	14.5426	−	16.7830i	0.504477	−	0.582197i
$832$	−0.619197	−	0.397934i	−0.0214668	−	0.0137959i
$833$	4.54821	−	31.6335i	0.157586	−	1.09604i
$834$	−8.66025	+	5.56561i	−0.299880	+	0.192721i
$835$	3.61759	+	7.92142i	0.125192	+	0.274132i
$836$	−2.46835	−	2.84863i	−0.0853697	−	0.0985219i
$837$	−1.07389	−	7.46904i	−0.0371189	−	0.258168i
$838$	8.37816	−	18.3456i	0.289419	−	0.633739i
$839$	35.2602	−	10.3533i	1.21732	−	0.357437i	0.390867	−	0.920447i	$-0.372175\pi$
$839$	35.2602	−	10.3533i	1.21732	−	0.357437i	0.826450	+	0.563010i	$0.190357\pi$
$840$	3.88624	−	1.14110i	0.134088	−	0.0393718i
$841$	−8.24032	+	18.0438i	−0.284149	+	0.622200i
$842$	0.379892	+	2.64221i	0.0130919	+	0.0910564i
$843$	−14.5493	−	16.7908i	−0.501104	−	0.578304i
$844$	2.09558	+	4.58868i	0.0721328	+	0.157949i
$845$	10.4805	−	6.73543i	0.360542	−	0.231706i
$846$	0.231727	−	1.61170i	0.00796694	−	0.0554113i
$847$	11.2761	+	7.24672i	0.387452	+	0.249000i
$848$	0.734615	−	0.847791i	0.0252268	−	0.0291132i
$849$	15.8550	+	4.65544i	0.544141	+	0.159774i
$850$	3.39807			0.116553
$851$	−10.2316	+	6.73576i	−0.350734	+	0.230899i
$852$	−7.73981			−0.265161
$853$	29.3937	+	8.63077i	1.00642	+	0.295512i	0.743089	−	0.669193i	$-0.233360\pi$
$853$	29.3937	+	8.63077i	1.00642	+	0.295512i	0.263333	+	0.964705i	$0.415178\pi$
$854$	20.1064	−	23.2040i	0.688027	−	0.794026i
$855$	0.838252	+	0.538712i	0.0286676	+	0.0184236i
$856$	0.641966	−	4.46497i	0.0219419	−	0.152610i
$857$	−38.8076	+	24.9401i	−1.32564	+	0.851939i	−0.995752	−	0.0920805i	$-0.970648\pi$
$857$	−38.8076	+	24.9401i	−1.32564	+	0.851939i	−0.329891	+	0.944019i	$0.607012\pi$
$858$	1.15663	+	2.53267i	0.0394867	+	0.0864638i
$859$	36.4276	+	42.0397i	1.24290	+	1.43438i	0.859770	+	0.510681i	$0.170607\pi$
$859$	36.4276	+	42.0397i	1.24290	+	1.43438i	0.383125	+	0.923696i	$0.374848\pi$
$860$	0.0169924	+	0.118185i	0.000579437	+	0.00403007i
$861$	3.24603	−	7.10781i	0.110624	−	0.242234i
$862$	−10.0315	+	2.94551i	−0.341674	+	0.100325i
$863$	26.2094	−	7.69578i	0.892179	−	0.261967i	0.196657	−	0.980472i	$-0.436991\pi$
$863$	26.2094	−	7.69578i	0.892179	−	0.261967i	0.695522	+	0.718505i	$0.255173\pi$
$864$	0.415415	−	0.909632i	0.0141327	−	0.0309463i
$865$	−2.54864	−	17.7262i	−0.0866564	−	0.602708i
$866$	18.9255	+	21.8412i	0.643115	+	0.742194i
$867$	2.26530	+	4.96032i	0.0769337	+	0.168461i
$868$	−25.7112	+	16.5236i	−0.872695	+	0.560847i
$869$	0.143636	−	0.999011i	0.00487252	−	0.0338891i
$870$	−2.54660	−	1.63660i	−0.0863379	−	0.0554860i
$871$	4.91015	−	5.66662i	0.166374	−	0.192006i
$872$	−5.16186	−	1.51566i	−0.174803	−	0.0513267i
$873$	17.4877			0.591870
$874$	−1.93717	+	4.36847i	−0.0655259	+	0.147766i
$875$	−4.05031			−0.136925
$876$	−13.9116	−	4.08481i	−0.470029	−	0.138013i
$877$	4.66713	−	5.38615i	0.157598	−	0.181877i	−0.671460	−	0.741041i	$-0.734332\pi$
$877$	4.66713	−	5.38615i	0.157598	−	0.181877i	0.829057	+	0.559164i	$0.188878\pi$
$878$	28.8701	+	18.5537i	0.974318	+	0.626156i
$879$	0.383884	−	2.66997i	0.0129481	−	0.0900558i
$880$	3.18227	−	2.04512i	0.107274	−	0.0689410i
$881$	−8.41600	−	18.4285i	−0.283542	−	0.620871i	0.713249	−	0.700910i	$-0.247223\pi$
$881$	−8.41600	−	18.4285i	−0.283542	−	0.620871i	−0.996792	+	0.0800394i	$0.974495\pi$
$882$	6.15895	+	7.10781i	0.207383	+	0.239332i
$883$	5.28457	+	36.7550i	0.177840	+	1.23690i	0.861749	+	0.507336i	$0.169370\pi$
$883$	5.28457	+	36.7550i	0.177840	+	1.23690i	−0.683909	+	0.729568i	$0.739721\pi$
$884$	1.03900	−	2.27510i	0.0349455	−	0.0765199i
$885$	−10.2717	+	3.01603i	−0.345278	+	0.101383i
$886$	−11.0975	+	3.25853i	−0.372829	+	0.109472i
$887$	16.7709	−	36.7232i	0.563113	−	1.23304i	−0.387271	−	0.921966i	$-0.626582\pi$
$887$	16.7709	−	36.7232i	0.563113	−	1.23304i	0.950384	−	0.311079i	$-0.100690\pi$
$888$	−0.363507	−	2.52825i	−0.0121985	−	0.0848424i
$889$	−44.3090	−	51.1353i	−1.48608	−	1.71502i
$890$	6.88942	+	15.0857i	0.230934	+	0.505675i
$891$	−3.18227	+	2.04512i	−0.106610	+	0.0685141i
$892$	2.89555	−	20.1390i	0.0969501	−	0.674303i
$893$	−1.36490	−	0.877169i	−0.0456747	−	0.0293533i
$894$	13.3022	−	15.3516i	0.444892	−	0.513433i
$895$	3.58441	+	1.05248i	0.119814	+	0.0351804i
$896$	−4.05031			−0.135311
$897$	2.28210	−	2.69303i	0.0761971	−	0.0899177i
$898$	23.9478			0.799150
$899$	21.9171	+	6.43545i	0.730977	+	0.214634i
$900$	−0.654861	+	0.755750i	−0.0218287	+	0.0251917i
$901$	3.20679	+	2.06088i	0.106834	+	0.0686578i
$902$	1.03859	−	7.22353i	0.0345812	−	0.240517i
$903$	−0.406837	+	0.261458i	−0.0135387	+	0.00870078i
$904$	4.97506	+	10.8939i	0.165468	+	0.362324i
$905$	1.17344	+	1.35422i	0.0390065	+	0.0450160i
$906$	−2.15815	−	15.0103i	−0.0716997	−	0.498683i
$907$	−23.4716	+	51.3957i	−0.779362	+	1.70657i	−0.0745004	+	0.997221i	$0.523736\pi$
$907$	−23.4716	+	51.3957i	−0.779362	+	1.70657i	−0.704862	+	0.709345i	$0.748991\pi$
$908$	3.49749	−	1.02696i	0.116068	−	0.0340807i
$909$	−2.02268	+	0.593913i	−0.0670881	+	0.0196988i
$910$	−1.23843	+	2.71179i	−0.0410536	+	0.0898949i
$911$	−6.18678	−	43.0300i	−0.204977	−	1.42565i	−0.789241	−	0.614084i	$-0.789526\pi$
$911$	−6.18678	−	43.0300i	−0.204977	−	1.42565i	0.584263	−	0.811564i	$-0.301383\pi$
$912$	−0.652525	−	0.753053i	−0.0216072	−	0.0249361i
$913$	19.1997	+	42.0415i	0.635418	+	1.39137i
$914$	−5.44888	+	3.50179i	−0.180233	+	0.115829i
$915$	−1.07882	+	7.50334i	−0.0356646	+	0.248053i
$916$	21.4965	+	13.8150i	0.710265	+	0.456460i
$917$	33.5220	−	38.6865i	1.10699	−	1.27754i
$918$	3.26043	+	0.957348i	0.107610	+	0.0315972i
$919$	34.8758			1.15045			0.575223	−	0.817997i	$-0.304915\pi$
$919$	34.8758			1.15045			0.575223	+	0.817997i	$0.304915\pi$
$920$	−4.06281	−	2.54824i	−0.133947	−	0.0840131i
$921$	6.14947			0.202632
$922$	−31.7366	−	9.31869i	−1.04519	−	0.306895i
$923$	3.73062	−	4.30537i	0.122795	−	0.141713i
$924$	12.8892	+	8.28337i	0.424023	+	0.272503i
$925$	−0.363507	+	2.52825i	−0.0119520	+	0.0831282i
$926$	23.8811	−	15.3475i	0.784782	−	0.504349i
$927$	0.685397	+	1.50081i	0.0225114	+	0.0492931i
$928$	1.98236	+	2.28777i	0.0650742	+	0.0750997i
$929$	−1.55988	−	10.8492i	−0.0511781	−	0.355951i	−0.999278	−	0.0379803i	$-0.987908\pi$
$929$	−1.55988	−	10.8492i	−0.0511781	−	0.355951i	0.948100	−	0.317971i	$-0.103001\pi$
$930$	3.13466	−	6.86394i	0.102789	−	0.225077i
$931$	8.99182	−	2.64024i	0.294695	−	0.0865302i
$932$	12.7227	−	3.73572i	0.416745	−	0.122367i
$933$	0.412994	−	0.904331i	0.0135208	−	0.0296065i
$934$	1.37323	+	9.55100i	0.0449334	+	0.312518i
$935$	8.41767	+	9.71451i	0.275287	+	0.317698i
$936$	0.305763	+	0.669527i	0.00999416	+	0.0218842i
$937$	−42.4402	+	27.2747i	−1.38646	+	0.891025i	−0.999517	−	0.0310785i	$-0.990106\pi$
$937$	−42.4402	+	27.2747i	−1.38646	+	0.891025i	−0.386944	+	0.922103i	$0.626469\pi$
$938$	5.87194	−	40.8403i	0.191726	−	1.33348i
$939$	13.3604	+	8.58620i	0.436000	+	0.280200i
$940$	1.06629	−	1.23056i	0.0347785	−	0.0401366i
$941$	−7.27742	−	2.13684i	−0.237237	−	0.0696591i	0.160953	−	0.986962i	$-0.448543\pi$
$941$	−7.27742	−	2.13684i	−0.237237	−	0.0696591i	−0.398190	+	0.917303i	$0.630361\pi$
$942$	13.1213			0.427516
$943$	−8.84821	+	2.70424i	−0.288137	+	0.0880621i
$944$	10.7053			0.348428
$945$	−3.88624	−	1.14110i	−0.126419	−	0.0371201i
$946$	−0.295777	+	0.341345i	−0.00961654	+	0.0110981i
$947$	−36.6332	−	23.5427i	−1.19042	−	0.765036i	−0.213146	−	0.977020i	$-0.568371\pi$
$947$	−36.6332	−	23.5427i	−1.19042	−	0.765036i	−0.977273	+	0.211985i	$0.932007\pi$
$948$	0.0379711	−	0.264095i	0.00123325	−	0.00857741i
$949$	8.97767	−	5.76960i	0.291428	−	0.187289i
$950$	0.413933	+	0.906387i	0.0134298	+	0.0294071i
$951$	1.96912	+	2.27248i	0.0638529	+	0.0736902i
$952$	−1.95871	−	13.6231i	−0.0634822	−	0.441529i
$953$	2.35370	−	5.15389i	0.0762439	−	0.166951i	−0.867672	−	0.497138i	$-0.834384\pi$
$953$	2.35370	−	5.15389i	0.0762439	−	0.166951i	0.943916	+	0.330187i	$0.107112\pi$
$954$	−1.07635	+	0.316044i	−0.0348480	+	0.0102323i
$955$	−21.6816	+	6.36630i	−0.701601	+	0.206009i
$956$	10.8193	−	23.6909i	0.349920	−	0.766218i
$957$	−1.62965	−	11.3345i	−0.0526791	−	0.366391i
$958$	−19.3262	−	22.3037i	−0.624402	−	0.720598i
$959$	−3.34860	−	7.33242i	−0.108132	−	0.236776i
$960$	0.841254	−	0.540641i	0.0271513	−	0.0174491i
$961$	−3.69161	+	25.6757i	−0.119084	+	0.828249i
$962$	1.58158	+	1.01642i	0.0509922	+	0.0327707i
$963$	−2.95400	+	3.40910i	−0.0951913	+	0.109857i
$964$	−5.91428	−	1.73659i	−0.190486	−	0.0559318i
$965$	−10.4044			−0.334929
$966$	2.55255	−	19.2561i	0.0821269	−	0.619556i
$967$	23.9838			0.771266			0.385633	−	0.922652i	$-0.373983\pi$
$967$	23.9838			0.771266			0.385633	+	0.922652i	$0.373983\pi$
$968$	3.17532	+	0.932357i	0.102059	+	0.0299671i
$969$	2.21733	−	2.55893i	0.0712308	−	0.0822047i
$970$	14.7116	+	9.45458i	0.472362	+	0.303568i
$971$	−0.356699	+	2.48089i	−0.0114470	+	0.0796156i	−0.994744	−	0.102392i	$-0.967350\pi$
$971$	−0.356699	+	2.48089i	−0.0114470	+	0.0796156i	0.983297	+	0.182008i	$0.0582595\pi$
$972$	−0.841254	+	0.540641i	−0.0269832	+	0.0173411i
$973$	−17.3210	−	37.9278i	−0.555287	−	1.21591i
$974$	16.9795	+	19.5954i	0.544059	+	0.627878i
$975$	−0.104750	−	0.728549i	−0.00335467	−	0.0233323i
$976$	3.14905	−	6.89546i	0.100799	−	0.220718i
$977$	−14.0217	+	4.11714i	−0.448593	+	0.131719i	−0.498223	−	0.867049i	$-0.666014\pi$
$977$	−14.0217	+	4.11714i	−0.448593	+	0.131719i	0.0496298	+	0.998768i	$0.484196\pi$
$978$	−12.6414	+	3.71186i	−0.404229	+	0.118692i
$979$	−26.0611	+	57.0659i	−0.832917	+	1.82383i
$980$	1.33847	+	9.30925i	0.0427558	+	0.297373i
$981$	3.52300	+	4.06576i	0.112481	+	0.129810i
$982$	10.9244	+	23.9211i	0.348611	+	0.763351i
$983$	−10.7158	+	6.88663i	−0.341781	+	0.219649i	−0.700259	−	0.713889i	$-0.746932\pi$
$983$	−10.7158	+	6.88663i	−0.341781	+	0.219649i	0.358478	+	0.933538i	$0.383296\pi$
$984$	0.274557	−	1.90959i	0.00875256	−	0.0608754i
$985$	9.30840	+	5.98215i	0.296590	+	0.190607i
$986$	−6.73621	+	7.77400i	−0.214525	+	0.247575i
$987$	6.32785	+	1.85802i	0.201418	+	0.0591415i
$988$	0.733415			0.0233331
$989$	0.551171	+	0.155268i	0.0175262	+	0.00493722i
$990$	−3.78277			−0.120224
$991$	45.9610	+	13.4954i	1.46000	+	0.428694i	0.912834	−	0.408330i	$-0.133889\pi$
$991$	45.9610	+	13.4954i	1.46000	+	0.428694i	0.547165	+	0.837025i	$0.315707\pi$
$992$	−4.94148	+	5.70277i	−0.156892	+	0.181063i
$993$	−2.04739	−	1.31578i	−0.0649719	−	0.0417549i
$994$	4.46137	−	31.0295i	0.141506	−	0.984196i
$995$	19.9262	−	12.8058i	0.631702	−	0.405970i
$996$	5.07557	+	11.1140i	0.160826	+	0.352159i
$997$	5.09312	+	5.87777i	0.161301	+	0.186151i	0.830647	−	0.556800i	$-0.187971\pi$
$997$	5.09312	+	5.87777i	0.161301	+	0.186151i	−0.669346	+	0.742951i	$0.733426\pi$
$998$	2.47310	+	17.2008i	0.0782847	+	0.544482i
$999$	−1.06107	+	2.32342i	−0.0335708	+	0.0735098i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.f.271.2	✓	20	1.1	even	1	trivial
690.2.m.f.331.2	yes	20	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.68256 + 3.68429i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(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} +(1.68256 + 3.68429i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(3.62954 - 1.06573i) q^{11} +(0.959493 - 0.281733i) q^{12} +(-0.305763 + 0.669527i) q^{13} +(0.576419 + 4.00908i) q^{14} +(-0.654861 - 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-2.85864 + 1.83714i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-0.838252 - 0.538712i) q^{19} +(0.654861 - 0.755750i) q^{20} +(3.88624 + 1.14110i) q^{21} +3.78277 q^{22} +(-2.04017 - 4.34024i) q^{23} +1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.482004 + 0.556263i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.576419 + 4.00908i) q^{28} +(2.54660 - 1.63660i) q^{29} +(-0.415415 - 0.909632i) q^{30} +(4.94148 + 5.70277i) q^{31} +(0.142315 + 0.989821i) q^{32} +(1.57142 - 3.44093i) q^{33} +(-3.26043 + 0.957348i) q^{34} +(3.88624 - 1.14110i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.363507 - 2.52825i) q^{37} +(-0.652525 - 0.753053i) q^{38} +(0.305763 + 0.669527i) q^{39} +(0.841254 - 0.540641i) q^{40} +(0.274557 - 1.90959i) q^{41} +(3.40733 + 2.18976i) q^{42} +(-0.0781905 + 0.0902367i) q^{43} +(3.62954 + 1.06573i) q^{44} -1.00000 q^{45} +(-0.734742 - 4.73921i) q^{46} +1.62827 q^{47} +(0.959493 + 0.281733i) q^{48} +(-6.15895 + 7.10781i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(-0.483596 + 3.36348i) q^{51} +(-0.619197 + 0.397934i) q^{52} +(-0.466007 - 1.02041i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-0.538345 - 3.74427i) q^{55} +(-1.68256 + 3.68429i) q^{56} +(-0.956070 + 0.280727i) q^{57} +(2.90453 - 0.852847i) q^{58} +(4.44714 - 9.73788i) q^{59} +(-0.142315 - 0.989821i) q^{60} +(-4.96417 - 5.72896i) q^{61} +(3.13466 + 6.86394i) q^{62} +(3.40733 - 2.18976i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.619197 + 0.397934i) q^{65} +(2.47719 - 2.85883i) q^{66} +(-9.77430 - 2.86999i) q^{67} -3.39807 q^{68} +(-4.61616 - 1.30040i) q^{69} +4.05031 q^{70} +(-7.42629 - 2.18056i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-12.1972 - 7.83869i) q^{73} +(0.363507 - 2.52825i) q^{74} +(-0.841254 + 0.540641i) q^{75} +(-0.413933 - 0.906387i) q^{76} +(10.0334 + 11.5791i) q^{77} +(0.104750 + 0.728549i) q^{78} +(0.110837 - 0.242700i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.801428 - 1.75488i) q^{82} +(1.73881 + 12.0937i) q^{83} +(2.65239 + 3.06102i) q^{84} +(1.41161 + 3.09100i) q^{85} +(-0.100446 + 0.0645527i) q^{86} +(0.430808 - 2.99634i) q^{87} +(3.18227 + 2.04512i) q^{88} +(-10.8605 + 12.5337i) q^{89} +(-0.959493 - 0.281733i) q^{90} -2.98119 q^{91} +(0.630211 - 4.75424i) q^{92} +7.54584 q^{93} +(1.56231 + 0.458737i) q^{94} +(-0.652525 + 0.753053i) q^{95} +(0.841254 + 0.540641i) q^{96} +(-2.48876 + 17.3097i) q^{97} +(-7.91197 + 5.08471i) q^{98} +(-1.57142 - 3.44093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Introduction

L-functions

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