LMFDB - Embedded newform 690.2.m.c.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			331.1
Root			$2.17335 - 0.638152i$ of defining polynomial
Character	$\chi$	$=$	690.331
Dual form			690.2.m.c.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.838100 + 1.83518i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.838100 + 1.83518i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-5.73181 - 1.68301i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-0.0306387 - 0.0670895i) q^{13} +(0.287120 - 1.99697i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-0.312496 - 0.200829i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(-6.48890 + 4.17016i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-1.93578 + 0.568396i) q^{21} +5.97379 q^{22} +(0.340220 - 4.78375i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(0.0482989 + 0.0557399i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.287120 + 1.99697i) q^{28} +(-0.668061 - 0.429337i) q^{29} +(-0.415415 + 0.909632i) q^{30} +(-2.98961 + 3.45019i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-2.48160 - 5.43395i) q^{33} +(0.356418 + 0.104654i) q^{34} +(1.93578 + 0.568396i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.0113045 + 0.0786248i) q^{37} +(5.05118 - 5.82937i) q^{38} +(0.0306387 - 0.0670895i) q^{39} +(0.841254 + 0.540641i) q^{40} +(1.61139 + 11.2075i) q^{41} +(1.69723 - 1.09074i) q^{42} +(-1.84339 - 2.12739i) q^{43} +(-5.73181 + 1.68301i) q^{44} +1.00000 q^{45} +(1.02130 + 4.68582i) q^{46} -8.45028 q^{47} +(0.959493 - 0.281733i) q^{48} +(1.91854 + 2.21411i) q^{49} +(0.841254 - 0.540641i) q^{50} +(-0.0528649 - 0.367684i) q^{51} +(-0.0620462 - 0.0398747i) q^{52} +(2.07782 - 4.54979i) q^{53} +(0.654861 - 0.755750i) q^{54} +(-0.850159 + 5.91299i) q^{55} +(-0.838100 - 1.83518i) q^{56} +(-7.40092 - 2.17311i) q^{57} +(0.761958 + 0.223731i) q^{58} +(-4.25158 - 9.30966i) q^{59} +(0.142315 - 0.989821i) q^{60} +(3.03477 - 3.50231i) q^{61} +(1.89648 - 4.15271i) q^{62} +(-1.69723 - 1.09074i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-0.0620462 + 0.0398747i) q^{65} +(3.91200 + 4.51469i) q^{66} +(5.57751 - 1.63771i) q^{67} -0.371465 q^{68} +(3.83811 - 2.87557i) q^{69} -2.01750 q^{70} +(-6.26701 + 1.84016i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-10.0145 + 6.43591i) q^{73} +(-0.0113045 - 0.0786248i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(-3.20425 + 7.01633i) q^{76} +(7.89247 - 9.10839i) q^{77} +(-0.0104964 + 0.0730038i) q^{78} +(-1.92908 - 4.22410i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-4.70362 - 10.2995i) q^{82} +(1.38220 - 9.61343i) q^{83} +(-1.32118 + 1.52473i) q^{84} +(-0.154312 + 0.337896i) q^{85} +(2.36808 + 1.52187i) q^{86} +(-0.113016 - 0.786042i) q^{87} +(5.02547 - 3.22968i) q^{88} +(-9.26532 - 10.6927i) q^{89} +(-0.959493 + 0.281733i) q^{90} +0.148800 q^{91} +(-2.30008 - 4.20828i) q^{92} -4.56526 q^{93} +(8.10799 - 2.38072i) q^{94} +(5.05118 + 5.82937i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(2.04051 + 14.1921i) q^{97} +(-2.46461 - 1.58391i) q^{98} +(2.48160 - 5.43395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	−0.838100	+	1.83518i	−0.316772	+	0.693634i	−0.999307	−	0.0372189i	$-0.988150\pi$
$7$	−0.838100	+	1.83518i	−0.316772	+	0.693634i	0.682535	+	0.730853i	$0.260877\pi$
$8$	−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
$11$	−5.73181	−	1.68301i	−1.72821	−	0.507447i	−0.741639	−	0.670800i	$-0.765951\pi$
$11$	−5.73181	−	1.68301i	−1.72821	−	0.507447i	−0.986568	+	0.163353i	$0.947769\pi$
$12$	0.959493	+	0.281733i	0.276982	+	0.0813292i
$13$	−0.0306387	−	0.0670895i	−0.00849765	−	0.0186073i	0.905336	−	0.424697i	$-0.139619\pi$
$13$	−0.0306387	−	0.0670895i	−0.00849765	−	0.0186073i	−0.913833	+	0.406090i	$0.866892\pi$
$14$	0.287120	−	1.99697i	0.0767361	−	0.533711i
$15$	0.654861	−	0.755750i	0.169084	−	0.195134i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−0.312496	−	0.200829i	−0.0757914	−	0.0487082i	0.502196	−	0.864754i	$-0.332525\pi$
$17$	−0.312496	−	0.200829i	−0.0757914	−	0.0487082i	−0.577988	+	0.816045i	$0.696162\pi$
$18$	−0.142315	−	0.989821i	−0.0335439	−	0.233303i
$19$	−6.48890	+	4.17016i	−1.48866	+	0.956701i	−0.492388	+	0.870376i	$0.663876\pi$
$19$	−6.48890	+	4.17016i	−1.48866	+	0.956701i	−0.996267	+	0.0863249i	$0.972488\pi$
$20$	−0.654861	−	0.755750i	−0.146431	−	0.168991i
$21$	−1.93578	+	0.568396i	−0.422421	+	0.124034i
$22$	5.97379			1.27362
$23$	0.340220	−	4.78375i	0.0709409	−	0.997481i
$23$	0.340220	−	4.78375i	0.0709409	−	0.997481i
$24$	−1.00000			−0.204124
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	0.0482989	+	0.0557399i	0.00947220	+	0.0109315i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.287120	+	1.99697i	0.0542606	+	0.377391i
$29$	−0.668061	−	0.429337i	−0.124056	−	0.0797258i	0.477141	−	0.878827i	$-0.341673\pi$
$29$	−0.668061	−	0.429337i	−0.124056	−	0.0797258i	−0.601197	+	0.799101i	$0.705309\pi$
$30$	−0.415415	+	0.909632i	−0.0758441	+	0.166075i
$31$	−2.98961	+	3.45019i	−0.536950	+	0.619673i	−0.957792	−	0.287461i	$-0.907189\pi$
$31$	−2.98961	+	3.45019i	−0.536950	+	0.619673i	0.420843	+	0.907134i	$0.361734\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	−2.48160	−	5.43395i	−0.431992	−	0.945930i
$34$	0.356418	+	0.104654i	0.0611251	+	0.0179480i
$35$	1.93578	+	0.568396i	0.327206	+	0.0960764i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−0.0113045	+	0.0786248i	−0.00185846	+	0.0129258i	−0.990730	−	0.135849i	$-0.956624\pi$
$37$	−0.0113045	+	0.0786248i	−0.00185846	+	0.0129258i	0.988871	+	0.148775i	$0.0475329\pi$
$38$	5.05118	−	5.82937i	0.819410	−	0.945649i
$39$	0.0306387	−	0.0670895i	0.00490612	−	0.0107429i
$40$	0.841254	+	0.540641i	0.133014	+	0.0854828i
$41$	1.61139	+	11.2075i	0.251657	+	1.75031i	0.588267	+	0.808667i	$0.299811\pi$
$41$	1.61139	+	11.2075i	0.251657	+	1.75031i	−0.336610	+	0.941644i	$0.609280\pi$
$42$	1.69723	−	1.09074i	0.261888	−	0.168305i
$43$	−1.84339	−	2.12739i	−0.281115	−	0.324424i	0.597578	−	0.801810i	$-0.296130\pi$
$43$	−1.84339	−	2.12739i	−0.281115	−	0.324424i	−0.878693	+	0.477386i	$0.841584\pi$
$44$	−5.73181	+	1.68301i	−0.864103	+	0.253724i
$45$	1.00000			0.149071
$46$	1.02130	+	4.68582i	0.150582	+	0.690887i
$47$	−8.45028			−1.23260			−0.616300	−	0.787511i	$-0.711369\pi$
$47$	−8.45028			−1.23260			−0.616300	+	0.787511i	$0.711369\pi$
$48$	0.959493	−	0.281733i	0.138491	−	0.0406646i
$49$	1.91854	+	2.21411i	0.274077	+	0.316302i
$50$	0.841254	−	0.540641i	0.118971	−	0.0764582i
$51$	−0.0528649	−	0.367684i	−0.00740257	−	0.0514860i
$52$	−0.0620462	−	0.0398747i	−0.00860427	−	0.00552963i
$53$	2.07782	−	4.54979i	0.285410	−	0.624961i	−0.711570	−	0.702615i	$-0.752016\pi$
$53$	2.07782	−	4.54979i	0.285410	−	0.624961i	0.996980	+	0.0776539i	$0.0247429\pi$
$54$	0.654861	−	0.755750i	0.0891153	−	0.102844i
$55$	−0.850159	+	5.91299i	−0.114635	+	0.797307i
$56$	−0.838100	−	1.83518i	−0.111996	−	0.245237i
$57$	−7.40092	−	2.17311i	−0.980276	−	0.287835i
$58$	0.761958	+	0.223731i	0.100050	+	0.0293773i
$59$	−4.25158	−	9.30966i	−0.553508	−	1.21201i	−0.955124	−	0.296206i	$-0.904279\pi$
$59$	−4.25158	−	9.30966i	−0.553508	−	1.21201i	0.401616	−	0.915808i	$-0.368449\pi$
$60$	0.142315	−	0.989821i	0.0183728	−	0.127785i
$61$	3.03477	−	3.50231i	0.388563	−	0.448425i	−0.527443	−	0.849590i	$-0.676849\pi$
$61$	3.03477	−	3.50231i	0.388563	−	0.448425i	0.916006	+	0.401165i	$0.131395\pi$
$62$	1.89648	−	4.15271i	0.240853	−	0.527394i
$63$	−1.69723	−	1.09074i	−0.213831	−	0.137421i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−0.0620462	+	0.0398747i	−0.00769589	+	0.00494585i
$66$	3.91200	+	4.51469i	0.481534	+	0.555720i
$67$	5.57751	−	1.63771i	0.681402	−	0.200078i	0.0773276	−	0.997006i	$-0.475361\pi$
$67$	5.57751	−	1.63771i	0.681402	−	0.200078i	0.604074	+	0.796928i	$0.293543\pi$
$68$	−0.371465			−0.0450467
$69$	3.83811	−	2.87557i	0.462054	−	0.346178i
$70$	−2.01750			−0.241137
$71$	−6.26701	+	1.84016i	−0.743758	+	0.218387i	−0.631590	−	0.775302i	$-0.717597\pi$
$71$	−6.26701	+	1.84016i	−0.743758	+	0.218387i	−0.112167	+	0.993689i	$0.535779\pi$
$72$	−0.654861	−	0.755750i	−0.0771761	−	0.0890659i
$73$	−10.0145	+	6.43591i	−1.17211	+	0.753266i	−0.973919	−	0.226898i	$-0.927142\pi$
$73$	−10.0145	+	6.43591i	−1.17211	+	0.753266i	−0.198187	+	0.980164i	$0.563505\pi$
$74$	−0.0113045	−	0.0786248i	−0.00131413	−	0.00913995i
$75$	−0.841254	−	0.540641i	−0.0971396	−	0.0624278i
$76$	−3.20425	+	7.01633i	−0.367553	+	0.804828i
$77$	7.89247	−	9.10839i	0.899430	−	1.03800i
$78$	−0.0104964	+	0.0730038i	−0.00118848	+	0.00826605i
$79$	−1.92908	−	4.22410i	−0.217038	−	0.475248i	0.769527	−	0.638614i	$-0.220492\pi$
$79$	−1.92908	−	4.22410i	−0.217038	−	0.475248i	−0.986565	+	0.163366i	$0.947765\pi$
$80$	−0.959493	−	0.281733i	−0.107275	−	0.0314987i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−4.70362	−	10.2995i	−0.519428	−	1.13739i
$83$	1.38220	−	9.61343i	0.151717	−	1.05521i	−0.761625	−	0.648018i	$-0.775598\pi$
$83$	1.38220	−	9.61343i	0.151717	−	1.05521i	0.913342	−	0.407194i	$-0.133493\pi$
$84$	−1.32118	+	1.52473i	−0.144153	+	0.166361i
$85$	−0.154312	+	0.337896i	−0.0167375	+	0.0366500i
$86$	2.36808	+	1.52187i	0.255356	+	0.164108i
$87$	−0.113016	−	0.786042i	−0.0121166	−	0.0842726i
$88$	5.02547	−	3.22968i	0.535717	−	0.344285i
$89$	−9.26532	−	10.6927i	−0.982122	−	1.13343i	−0.991053	−	0.133469i	$-0.957388\pi$
$89$	−9.26532	−	10.6927i	−0.982122	−	1.13343i	0.00893107	−	0.999960i	$-0.497157\pi$
$90$	−0.959493	+	0.281733i	−0.101139	+	0.0296972i
$91$	0.148800			0.0155985
$92$	−2.30008	−	4.20828i	−0.239800	−	0.438744i
$93$	−4.56526			−0.473395
$94$	8.10799	−	2.38072i	0.836275	−	0.245552i
$95$	5.05118	+	5.82937i	0.518240	+	0.598081i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	2.04051	+	14.1921i	0.207183	+	1.44099i	0.782293	+	0.622911i	$0.214050\pi$
$97$	2.04051	+	14.1921i	0.207183	+	1.44099i	−0.575110	+	0.818076i	$0.695041\pi$
$98$	−2.46461	−	1.58391i	−0.248964	−	0.159999i
$99$	2.48160	−	5.43395i	0.249410	−	0.546133i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	−2.39031	+	16.6250i	−0.237845	+	1.65425i	0.424778	+	0.905297i	$0.360352\pi$
$101$	−2.39031	+	16.6250i	−0.237845	+	1.65425i	−0.662624	+	0.748953i	$0.730557\pi$
$102$	0.154312	+	0.337896i	0.0152792	+	0.0334567i
$103$	6.79230	+	1.99440i	0.669265	+	0.196514i	0.598676	−	0.800991i	$-0.295694\pi$
$103$	6.79230	+	1.99440i	0.669265	+	0.196514i	0.0705895	+	0.997505i	$0.477512\pi$
$104$	0.0707669	+	0.0207790i	0.00693927	+	0.00203755i
$105$	0.838100	+	1.83518i	0.0817902	+	0.179096i
$106$	−0.711829	+	4.95088i	−0.0691389	+	0.480872i
$107$	2.53730	−	2.92820i	0.245290	−	0.283080i	−0.619732	−	0.784813i	$-0.712759\pi$
$107$	2.53730	−	2.92820i	0.245290	−	0.283080i	0.865022	+	0.501734i	$0.167304\pi$
$108$	−0.415415	+	0.909632i	−0.0399733	+	0.0875294i
$109$	4.59687	+	2.95423i	0.440300	+	0.282964i	0.741950	−	0.670455i	$-0.233901\pi$
$109$	4.59687	+	2.95423i	0.440300	+	0.282964i	−0.301650	+	0.953419i	$0.597537\pi$
$110$	−0.850159	−	5.91299i	−0.0810595	−	0.563781i
$111$	−0.0668236	+	0.0429449i	−0.00634261	+	0.00407615i
$112$	1.32118	+	1.52473i	0.124840	+	0.144073i
$113$	−1.44506	+	0.424309i	−0.135940	+	0.0399156i	−0.348995	−	0.937125i	$-0.613477\pi$
$113$	−1.44506	+	0.424309i	−0.135940	+	0.0399156i	0.213055	+	0.977040i	$0.431659\pi$
$114$	7.71337			0.722423
$115$	−4.78348	+	0.344041i	−0.446061	+	0.0320820i
$116$	−0.794125			−0.0737327
$117$	0.0707669	−	0.0207790i	0.00654241	−	0.00192102i
$118$	6.70219	+	7.73474i	0.616987	+	0.712041i
$119$	0.630461	−	0.405172i	0.0577942	−	0.0371421i
$120$	0.142315	+	0.989821i	0.0129915	+	0.0903579i
$121$	20.7673	+	13.3464i	1.88794	+	1.21331i
$122$	−1.92513	+	4.21544i	−0.174293	+	0.381648i
$123$	−7.41480	+	8.55713i	−0.668570	+	0.771571i
$124$	−0.649704	+	4.51879i	−0.0583452	+	0.405800i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	1.93578	+	0.568396i	0.172453	+	0.0506367i
$127$	−8.89288	−	2.61118i	−0.789115	−	0.231705i	−0.137748	−	0.990467i	$-0.543986\pi$
$127$	−8.89288	−	2.61118i	−0.789115	−	0.231705i	−0.651368	+	0.758762i	$0.725804\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	0.400608	−	2.78629i	0.0352715	−	0.245319i
$130$	0.0482989	−	0.0557399i	0.00423610	−	0.00488872i
$131$	−4.86149	+	10.6452i	−0.424750	+	0.930073i	0.569399	+	0.822061i	$0.307176\pi$
$131$	−4.86149	+	10.6452i	−0.424750	+	0.930073i	−0.994150	+	0.108012i	$0.965551\pi$
$132$	−5.02547	−	3.22968i	−0.437411	−	0.281107i
$133$	−2.21466	−	15.4033i	−0.192036	−	1.33564i
$134$	−4.89019	+	3.14273i	−0.422448	+	0.271491i
$135$	0.654861	+	0.755750i	0.0563614	+	0.0650446i
$136$	0.356418	−	0.104654i	0.0305626	−	0.00897398i
$137$	7.55051			0.645084			0.322542	−	0.946555i	$-0.395463\pi$
$137$	7.55051			0.645084			0.322542	+	0.946555i	$0.395463\pi$
$138$	−2.87250	+	3.84041i	−0.244524	+	0.326917i
$139$	−0.250893			−0.0212804			−0.0106402	−	0.999943i	$-0.503387\pi$
$139$	−0.250893			−0.0212804			−0.0106402	+	0.999943i	$0.503387\pi$
$140$	1.93578	−	0.568396i	0.163603	−	0.0480382i
$141$	−5.53376	−	6.38630i	−0.466026	−	0.537823i
$142$	5.49472	−	3.53124i	0.461107	−	0.296335i
$143$	0.0627031	+	0.436109i	0.00524349	+	0.0364693i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	−0.329892	+	0.722362i	−0.0273960	+	0.0599889i
$146$	7.79561	−	8.99661i	0.645169	−	0.744565i
$147$	−0.416939	+	2.89987i	−0.0343885	+	0.239177i
$148$	0.0329978	+	0.0722551i	0.00271240	+	0.00593933i
$149$	−1.88251	−	0.552756i	−0.154222	−	0.0452835i	0.203711	−	0.979031i	$-0.434700\pi$
$149$	−1.88251	−	0.552756i	−0.154222	−	0.0452835i	−0.357932	+	0.933748i	$0.616518\pi$
$150$	0.959493	+	0.281733i	0.0783423	+	0.0230034i
$151$	−0.240281	−	0.526141i	−0.0195538	−	0.0428168i	0.899603	−	0.436708i	$-0.143856\pi$
$151$	−0.240281	−	0.526141i	−0.0195538	−	0.0428168i	−0.919157	+	0.393892i	$0.871129\pi$
$152$	1.09773	−	7.63486i	0.0890374	−	0.619269i
$153$	0.243258	−	0.280734i	0.0196662	−	0.0226960i
$154$	−5.00663	+	10.9630i	−0.403446	+	0.883424i
$155$	3.84054	+	2.46817i	0.308480	+	0.198248i
$156$	−0.0104964	−	0.0730038i	−0.000840381	−	0.00584498i
$157$	4.07850	−	2.62109i	0.325500	−	0.209186i	−0.367677	−	0.929953i	$-0.619847\pi$
$157$	4.07850	−	2.62109i	0.325500	−	0.209186i	0.693177	+	0.720768i	$0.256211\pi$
$158$	3.04100	+	3.50951i	0.241929	+	0.279201i
$159$	4.79918	−	1.40917i	0.380600	−	0.111754i
$160$	1.00000			0.0790569
$161$	8.49391	+	4.63363i	0.669414	+	0.365181i
$162$	1.00000			0.0785674
$163$	17.0111	−	4.99492i	1.33241	−	0.391232i	0.463457	−	0.886120i	$-0.346609\pi$
$163$	17.0111	−	4.99492i	1.33241	−	0.391232i	0.868957	+	0.494888i	$0.164791\pi$
$164$	7.41480	+	8.55713i	0.578998	+	0.668200i
$165$	−5.02547	+	3.22968i	−0.391233	+	0.251430i
$166$	1.38220	+	9.61343i	0.107280	+	0.746147i
$167$	21.6118	+	13.8890i	1.67237	+	1.07477i	0.895447	+	0.445168i	$0.146856\pi$
$167$	21.6118	+	13.8890i	1.67237	+	1.07477i	0.776921	+	0.629598i	$0.216780\pi$
$168$	0.838100	−	1.83518i	0.0646608	−	0.141587i
$169$	8.50963	−	9.82063i	0.654587	−	0.755433i
$170$	0.0528649	−	0.367684i	0.00405456	−	0.0282001i
$171$	−3.20425	−	7.01633i	−0.245035	−	0.536552i
$172$	−2.70092	−	0.793060i	−0.205943	−	0.0604703i
$173$	13.8527	+	4.06752i	1.05320	+	0.309248i	0.762110	−	0.647448i	$-0.224164\pi$
$173$	13.8527	+	4.06752i	1.05320	+	0.309248i	0.291091	+	0.956695i	$0.405982\pi$
$174$	0.329892	+	0.722362i	0.0250090	+	0.0547621i
$175$	0.287120	−	1.99697i	0.0217042	−	0.150956i
$176$	−3.91200	+	4.51469i	−0.294878	+	0.340308i
$177$	4.25158	−	9.30966i	0.319568	−	0.699757i
$178$	11.9025	+	7.64928i	0.892130	+	0.573337i
$179$	2.82566	+	19.6529i	0.211199	+	1.46892i	0.769160	+	0.639057i	$0.220675\pi$
$179$	2.82566	+	19.6529i	0.211199	+	1.46892i	−0.557960	+	0.829868i	$0.688416\pi$
$180$	0.841254	−	0.540641i	0.0627033	−	0.0402970i
$181$	−0.954620	−	1.10169i	−0.0709564	−	0.0818880i	0.719161	−	0.694843i	$-0.244526\pi$
$181$	−0.954620	−	1.10169i	−0.0709564	−	0.0818880i	−0.790118	+	0.612955i	$0.789981\pi$
$182$	−0.142772	+	0.0419217i	−0.0105830	+	0.00310745i
$183$	4.63422			0.342572
$184$	3.39252	+	3.38981i	0.250100	+	0.249900i
$185$	0.0794333			0.00584005
$186$	4.38034	−	1.28618i	0.321182	−	0.0943075i
$187$	1.45317	+	1.67705i	0.106266	+	0.122638i
$188$	−7.10883	+	4.56857i	−0.518465	+	0.333197i
$189$	−0.287120	−	1.99697i	−0.0208849	−	0.145258i
$190$	−6.48890	−	4.17016i	−0.470754	−	0.302535i
$191$	−2.64539	+	5.79259i	−0.191414	+	0.419137i	−0.980869	−	0.194671i	$-0.937636\pi$
$191$	−2.64539	+	5.79259i	−0.191414	+	0.419137i	0.789455	+	0.613808i	$0.210363\pi$
$192$	0.654861	−	0.755750i	0.0472605	−	0.0545415i
$193$	3.21055	−	22.3298i	0.231100	−	1.60734i	−0.462260	−	0.886745i	$-0.652961\pi$
$193$	3.21055	−	22.3298i	0.231100	−	1.60734i	0.693360	−	0.720592i	$-0.256130\pi$
$194$	−5.95623	−	13.0423i	−0.427632	−	0.936384i
$195$	−0.0707669	−	0.0207790i	−0.00506773	−	0.00148802i
$196$	2.81102	+	0.825390i	0.200787	+	0.0589564i
$197$	5.87529	+	12.8651i	0.418597	+	0.916600i	0.995041	+	0.0994636i	$0.0317127\pi$
$197$	5.87529	+	12.8651i	0.418597	+	0.916600i	−0.576444	+	0.817137i	$0.695560\pi$
$198$	−0.850159	+	5.91299i	−0.0604182	+	0.420218i
$199$	5.86875	−	6.77290i	0.416025	−	0.480118i	−0.508597	−	0.861005i	$-0.669836\pi$
$199$	5.86875	−	6.77290i	0.416025	−	0.480118i	0.924622	+	0.380887i	$0.124381\pi$
$200$	0.415415	−	0.909632i	0.0293743	−	0.0643207i
$201$	4.89019	+	3.14273i	0.344927	+	0.221671i
$202$	−2.39031	−	16.6250i	−0.168182	−	1.16973i
$203$	1.34781	−	0.866187i	0.0945979	−	0.0607944i
$204$	−0.243258	−	0.280734i	−0.0170314	−	0.0196553i
$205$	10.8641	−	3.18998i	0.758779	−	0.222798i
$206$	−7.07905			−0.493221
$207$	4.68664	+	1.01756i	0.325744	+	0.0707250i
$208$	−0.0737545			−0.00511395
$209$	44.2116	−	12.9817i	3.05818	−	0.897962i
$210$	−1.32118	−	1.52473i	−0.0911702	−	0.105216i
$211$	−1.45062	+	0.932254i	−0.0998645	+	0.0641790i	−0.589620	−	0.807681i	$-0.700722\pi$
$211$	−1.45062	+	0.932254i	−0.0998645	+	0.0641790i	0.489755	+	0.871860i	$0.337086\pi$
$212$	−0.711829	−	4.95088i	−0.0488886	−	0.340028i
$213$	−5.49472	−	3.53124i	−0.376492	−	0.241957i
$214$	−1.60955	+	3.52442i	−0.110027	+	0.240925i
$215$	−1.84339	+	2.12739i	−0.125718	+	0.145087i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	−3.82614	−	8.37809i	−0.259736	−	0.568742i
$218$	−5.24297	−	1.53947i	−0.355099	−	0.104266i
$219$	−11.4220	−	3.35381i	−0.771829	−	0.226629i
$220$	2.48160	+	5.43395i	0.167310	+	0.366357i
$221$	−0.00389903	+	0.0271183i	−0.000262277	+	0.00182418i
$222$	0.0520178	−	0.0600317i	0.00349120	−	0.00402906i
$223$	−9.47762	+	20.7531i	−0.634668	+	1.38973i	0.269686	+	0.962948i	$0.413080\pi$
$223$	−9.47762	+	20.7531i	−0.634668	+	1.38973i	−0.904355	+	0.426782i	$0.859647\pi$
$224$	−1.69723	−	1.09074i	−0.113401	−	0.0728783i
$225$	−0.142315	−	0.989821i	−0.00948766	−	0.0659881i
$226$	1.26699	−	0.814243i	0.0842787	−	0.0541626i
$227$	−13.4480	−	15.5198i	−0.892575	−	1.03009i	−0.999359	−	0.0358044i	$-0.988601\pi$
$227$	−13.4480	−	15.5198i	−0.892575	−	1.03009i	0.106784	−	0.994282i	$-0.465945\pi$
$228$	−7.40092	+	2.17311i	−0.490138	+	0.143918i
$229$	−22.5078			−1.48736			−0.743680	−	0.668536i	$-0.766921\pi$
$229$	−22.5078			−1.48736			−0.743680	+	0.668536i	$0.766921\pi$
$230$	4.49278	−	1.67777i	0.296245	−	0.110629i
$231$	12.0521			0.792972
$232$	0.761958	−	0.223731i	0.0500250	−	0.0146887i
$233$	−6.62106	−	7.64111i	−0.433760	−	0.500586i	0.496220	−	0.868197i	$-0.334721\pi$
$233$	−6.62106	−	7.64111i	−0.433760	−	0.500586i	−0.929979	+	0.367611i	$0.880176\pi$
$234$	−0.0620462	+	0.0398747i	−0.00405609	+	0.00260669i
$235$	1.20260	+	8.36427i	0.0784490	+	0.545625i
$236$	−8.60984	−	5.53321i	−0.560453	−	0.360181i
$237$	1.92908	−	4.22410i	0.125307	−	0.274385i
$238$	−0.490772	+	0.566381i	−0.0318120	+	0.0367131i
$239$	−1.00595	+	6.99651i	−0.0650692	+	0.452566i	0.931074	+	0.364829i	$0.118873\pi$
$239$	−1.00595	+	6.99651i	−0.0650692	+	0.452566i	−0.996144	+	0.0877371i	$0.972036\pi$
$240$	−0.415415	−	0.909632i	−0.0268149	−	0.0587165i
$241$	−4.22424	−	1.24035i	−0.272108	−	0.0798980i	0.142832	−	0.989747i	$-0.454379\pi$
$241$	−4.22424	−	1.24035i	−0.272108	−	0.0798980i	−0.414940	+	0.909849i	$0.636197\pi$
$242$	−23.6862	−	6.95490i	−1.52261	−	0.447078i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	0.659519	−	4.58705i	0.0422214	−	0.293656i
$245$	1.91854	−	2.21411i	0.122571	−	0.141455i
$246$	4.70362	−	10.2995i	0.299892	−	0.656672i
$247$	0.478585	+	0.307568i	0.0304517	+	0.0195701i
$248$	−0.649704	−	4.51879i	−0.0412563	−	0.286944i
$249$	8.17050	−	5.25086i	0.517784	−	0.332760i
$250$	−0.654861	−	0.755750i	−0.0414170	−	0.0477978i
$251$	−25.7554	+	7.56246i	−1.62567	+	0.477338i	−0.962533	−	0.271164i	$-0.912591\pi$
$251$	−25.7554	+	7.56246i	−1.62567	+	0.477338i	−0.663132	+	0.748502i	$0.730773\pi$
$252$	−2.01750			−0.127091
$253$	−10.0012	+	26.8470i	−0.628769	+	1.68785i
$254$	9.26831			0.581545
$255$	−0.356418	+	0.104654i	−0.0223197	+	0.00655367i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−12.2867	+	7.89616i	−0.766421	+	0.492549i	−0.864502	−	0.502629i	$-0.832366\pi$
$257$	−12.2867	+	7.89616i	−0.766421	+	0.492549i	0.0980808	+	0.995178i	$0.468730\pi$
$258$	0.400608	+	2.78629i	0.0249408	+	0.173467i
$259$	−0.134817	−	0.0866414i	−0.00837709	−	0.00538363i
$260$	−0.0306387	+	0.0670895i	−0.00190013	+	0.00416071i
$261$	0.520041	−	0.600160i	0.0321898	−	0.0371490i
$262$	1.66547	−	11.5836i	0.102893	−	0.715638i
$263$	11.3966	+	24.9550i	0.702743	+	1.53879i	0.836614	+	0.547793i	$0.184532\pi$
$263$	11.3966	+	24.9550i	0.702743	+	1.53879i	−0.133871	+	0.990999i	$0.542741\pi$
$264$	5.73181	+	1.68301i	0.352769	+	0.103582i
$265$	−4.79918	−	1.40917i	−0.294811	−	0.0865644i
$266$	6.46457	+	14.1554i	0.396368	+	0.867926i
$267$	2.01355	−	14.0045i	0.123227	−	0.857063i
$268$	3.80669	−	4.39316i	0.232531	−	0.268355i
$269$	6.93199	−	15.1789i	0.422651	−	0.925476i	−0.571812	−	0.820385i	$-0.693759\pi$
$269$	6.93199	−	15.1789i	0.422651	−	0.925476i	0.994463	−	0.105091i	$-0.0335135\pi$
$270$	−0.841254	−	0.540641i	−0.0511971	−	0.0329024i
$271$	2.34034	+	16.2774i	0.142166	+	0.988784i	0.928593	+	0.371101i	$0.121020\pi$
$271$	2.34034	+	16.2774i	0.142166	+	0.988784i	−0.786427	+	0.617683i	$0.788071\pi$
$272$	−0.312496	+	0.200829i	−0.0189478	+	0.0121770i
$273$	0.0974431	+	0.112455i	0.00589753	+	0.00680611i
$274$	−7.24467	+	2.12723i	−0.437666	+	0.128510i
$275$	5.97379			0.360233
$276$	1.67418	−	4.49412i	0.100774	−	0.270514i
$277$	−5.02057			−0.301657			−0.150828	−	0.988560i	$-0.548194\pi$
$277$	−5.02057			−0.301657			−0.150828	+	0.988560i	$0.548194\pi$
$278$	0.240730	−	0.0706847i	0.0144380	−	0.00423938i
$279$	−2.98961	−	3.45019i	−0.178983	−	0.206558i
$280$	−1.69723	+	1.09074i	−0.101429	+	0.0651844i
$281$	1.90945	+	13.2805i	0.113908	+	0.792250i	0.964055	+	0.265704i	$0.0856043\pi$
$281$	1.90945	+	13.2805i	0.113908	+	0.792250i	−0.850146	+	0.526547i	$0.823487\pi$
$282$	7.10883	+	4.56857i	0.423325	+	0.272054i
$283$	7.17453	−	15.7100i	0.426482	−	0.933865i	−0.567403	−	0.823440i	$-0.692052\pi$
$283$	7.17453	−	15.7100i	0.426482	−	0.933865i	0.993885	−	0.110424i	$-0.0352210\pi$
$284$	−4.27728	+	4.93625i	−0.253810	+	0.292912i
$285$	−1.09773	+	7.63486i	−0.0650237	+	0.452250i
$286$	−0.183029	−	0.400778i	−0.0108228	−	0.0236985i
$287$	−21.9182	−	6.43578i	−1.29379	−	0.379892i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	−7.00473	−	15.3382i	−0.412043	−	0.902249i
$290$	0.113016	−	0.786042i	0.00663652	−	0.0461580i
$291$	−9.38940	+	10.8360i	−0.550417	+	0.635215i
$292$	−4.94519	+	10.8285i	−0.289396	+	0.633688i
$293$	−2.63104	−	1.69087i	−0.153707	−	0.0987816i	0.461526	−	0.887126i	$-0.347302\pi$
$293$	−2.63104	−	1.69087i	−0.153707	−	0.0987816i	−0.615234	+	0.788345i	$0.710938\pi$
$294$	−0.416939	−	2.89987i	−0.0243164	−	0.169124i
$295$	−8.60984	+	5.53321i	−0.501284	+	0.322156i
$296$	−0.0520178	−	0.0600317i	−0.00302347	−	0.00348927i
$297$	5.73181	−	1.68301i	0.332593	−	0.0976582i
$298$	1.96199			0.113655
$299$	−0.331363	+	0.123743i	−0.0191632	+	0.00715623i
$300$	−1.00000			−0.0577350
$301$	5.44910	−	1.60000i	0.314081	−	0.0922224i
$302$	0.378779	+	0.437134i	0.0217963	+	0.0251542i
$303$	−14.1297	+	9.08058i	−0.811728	+	0.521666i
$304$	1.09773	+	7.63486i	0.0629589	+	0.437889i
$305$	−3.89856	−	2.50545i	−0.223231	−	0.143462i
$306$	−0.154312	+	0.337896i	−0.00882143	+	0.0193162i
$307$	15.5194	−	17.9104i	0.885741	−	1.02220i	−0.113848	−	0.993498i	$-0.536318\pi$
$307$	15.5194	−	17.9104i	0.885741	−	1.02220i	0.999588	−	0.0287008i	$-0.00913701\pi$
$308$	1.71520	−	11.9295i	0.0977324	−	0.679744i
$309$	2.94074	+	6.43933i	0.167293	+	0.366321i
$310$	−4.38034	−	1.28618i	−0.248786	−	0.0730503i
$311$	−24.8130	−	7.28575i	−1.40701	−	0.413137i	−0.511928	−	0.859028i	$-0.671068\pi$
$311$	−24.8130	−	7.28575i	−1.40701	−	0.413137i	−0.895087	+	0.445892i	$0.852887\pi$
$312$	0.0306387	+	0.0670895i	0.00173458	+	0.00379819i
$313$	1.73224	−	12.0480i	0.0979120	−	0.680993i	−0.880457	−	0.474126i	$-0.842764\pi$
$313$	1.73224	−	12.0480i	0.0979120	−	0.680993i	0.978369	−	0.206867i	$-0.0663268\pi$
$314$	−3.17484	+	3.66396i	−0.179167	+	0.206769i
$315$	−0.838100	+	1.83518i	−0.0472216	+	0.103401i
$316$	−3.90656	−	2.51060i	−0.219761	−	0.141232i
$317$	−0.278428	−	1.93651i	−0.0156381	−	0.108765i	0.980507	−	0.196482i	$-0.0629519\pi$
$317$	−0.278428	−	1.93651i	−0.0156381	−	0.108765i	−0.996145	+	0.0877173i	$0.972043\pi$
$318$	−4.20777	+	2.70417i	−0.235960	+	0.151642i
$319$	3.10662	+	3.58523i	0.173937	+	0.200734i
$320$	−0.959493	+	0.281733i	−0.0536373	+	0.0157493i
$321$	3.87456			0.216257
$322$	−9.45529	−	2.05292i	−0.526923	−	0.114405i
$323$	2.86524			0.159426
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	0.0482989	+	0.0557399i	0.00267914	+	0.00309190i
$326$	−14.9148	+	9.58517i	−0.826055	+	0.530874i
$327$	0.777653	+	5.40869i	0.0430043	+	0.299101i
$328$	−9.52527	−	6.12152i	−0.525945	−	0.338004i
$329$	7.08218	−	15.5078i	0.390453	−	0.854973i
$330$	3.91200	−	4.51469i	0.215349	−	0.248526i
$331$	−0.206656	+	1.43732i	−0.0113588	+	0.0790024i	−0.994712	−	0.102700i	$-0.967252\pi$
$331$	−0.206656	+	1.43732i	−0.0113588	+	0.0790024i	0.983354	+	0.181703i	$0.0581608\pi$
$332$	−4.03463	−	8.83461i	−0.221429	−	0.484862i
$333$	−0.0762157	−	0.0223790i	−0.00417660	−	0.00122636i
$334$	−24.6493	−	7.23769i	−1.34875	−	0.396029i
$335$	−2.41480	−	5.28767i	−0.131935	−	0.288896i
$336$	−0.287120	+	1.99697i	−0.0156637	+	0.108943i
$337$	−4.85318	+	5.60087i	−0.264369	+	0.305099i	−0.872378	−	0.488832i	$-0.837423\pi$
$337$	−4.85318	+	5.60087i	−0.264369	+	0.305099i	0.608009	+	0.793930i	$0.291969\pi$
$338$	−5.39814	+	11.8203i	−0.293620	+	0.642938i
$339$	−1.26699	−	0.814243i	−0.0688133	−	0.0442236i
$340$	0.0528649	+	0.367684i	0.00286700	+	0.0199404i
$341$	22.9426	−	14.7443i	1.24241	−	0.798449i
$342$	5.05118	+	5.82937i	0.273137	+	0.315216i
$343$	−19.2217	+	5.64399i	−1.03787	+	0.304747i
$344$	2.81494			0.151771
$345$	−3.39252	−	3.38981i	−0.182647	−	0.182501i
$346$	−14.4375			−0.776166
$347$	−0.315279	+	0.0925741i	−0.0169250	+	0.00496964i	−0.290184	−	0.956971i	$-0.593717\pi$
$347$	−0.315279	+	0.0925741i	−0.0169250	+	0.00496964i	0.273259	+	0.961940i	$0.411898\pi$
$348$	−0.520041	−	0.600160i	−0.0278771	−	0.0321719i
$349$	−26.4816	+	17.0187i	−1.41753	+	0.910990i	−0.417530	+	0.908663i	$0.637104\pi$
$349$	−26.4816	+	17.0187i	−1.41753	+	0.910990i	−0.999997	+	0.00232660i	$0.999259\pi$
$350$	0.287120	+	1.99697i	0.0153472	+	0.106742i
$351$	0.0620462	+	0.0398747i	0.00331178	+	0.00212835i
$352$	2.48160	−	5.43395i	0.132270	−	0.289631i
$353$	14.4247	−	16.6469i	0.767747	−	0.886028i	−0.228414	−	0.973564i	$-0.573354\pi$
$353$	14.4247	−	16.6469i	0.767747	−	0.886028i	0.996161	+	0.0875365i	$0.0278994\pi$
$354$	−1.45653	+	10.1304i	−0.0774135	+	0.538423i
$355$	2.71332	+	5.94134i	0.144008	+	0.315334i
$356$	−13.5754	−	3.98610i	−0.719496	−	0.211263i
$357$	0.719073	+	0.211139i	0.0380574	+	0.0111747i
$358$	−8.24805	−	18.0607i	−0.435923	−	0.954538i
$359$	−4.97166	+	34.5786i	−0.262394	+	1.82499i	0.252338	+	0.967639i	$0.418801\pi$
$359$	−4.97166	+	34.5786i	−0.262394	+	1.82499i	−0.514732	+	0.857351i	$0.672108\pi$
$360$	−0.654861	+	0.755750i	−0.0345142	+	0.0398315i
$361$	16.8227	−	36.8365i	0.885403	−	1.93876i
$362$	1.22633	+	0.788117i	0.0644547	+	0.0414225i
$363$	3.51321	+	24.4349i	0.184396	+	1.28250i
$364$	0.125178	−	0.0804472i	0.00656113	−	0.00421658i
$365$	7.79561	+	8.99661i	0.408041	+	0.470904i
$366$	−4.44651	+	1.30561i	−0.232423	+	0.0682454i
$367$	−8.20213			−0.428148			−0.214074	−	0.976817i	$-0.568673\pi$
$367$	−8.20213			−0.428148			−0.214074	+	0.976817i	$0.568673\pi$
$368$	−4.21012	−	2.29672i	−0.219468	−	0.119725i
$369$	−11.3227			−0.589437
$370$	−0.0762157	+	0.0223790i	−0.00396227	+	0.00116343i
$371$	6.60827	+	7.62635i	0.343084	+	0.395940i
$372$	−3.84054	+	2.46817i	−0.199123	+	0.127968i
$373$	−0.00130909	−	0.00910492i	−6.77821e−5	−	0.000471435i	0.989788	−	0.142551i	$-0.0455303\pi$
$373$	−0.00130909	−	0.00910492i	−6.77821e−5	−	0.000471435i	−0.989855	+	0.142079i	$0.954621\pi$
$374$	−1.86679	−	1.19971i	−0.0965292	−	0.0620355i
$375$	−0.415415	+	0.909632i	−0.0214519	+	0.0469732i
$376$	5.53376	−	6.38630i	0.285382	−	0.329348i
$377$	−0.00833542	+	0.0579742i	−0.000429296	+	0.00298582i
$378$	0.838100	+	1.83518i	0.0431072	+	0.0943916i
$379$	−8.69553	−	2.55324i	−0.446659	−	0.131151i	0.0506650	−	0.998716i	$-0.483866\pi$
$379$	−8.69553	−	2.55324i	−0.446659	−	0.131151i	−0.497324	+	0.867565i	$0.665684\pi$
$380$	7.40092	+	2.17311i	0.379659	+	0.111478i
$381$	−3.85019	−	8.43075i	−0.197251	−	0.431920i
$382$	0.906270	−	6.30324i	0.0463688	−	0.322502i
$383$	21.2647	−	24.5407i	1.08657	−	1.25397i	0.121333	−	0.992612i	$-0.461283\pi$
$383$	21.2647	−	24.5407i	1.08657	−	1.25397i	0.965241	−	0.261362i	$-0.0841715\pi$
$384$	−0.415415	+	0.909632i	−0.0211991	+	0.0464195i
$385$	−10.1389	−	6.51587i	−0.516726	−	0.332080i
$386$	3.21055	+	22.3298i	0.163412	+	1.13656i
$387$	2.36808	−	1.52187i	0.120376	−	0.0773611i
$388$	9.38940	+	10.8360i	0.476675	+	0.550112i
$389$	−20.5226	+	6.02597i	−1.04054	+	0.305529i	−0.756988	−	0.653429i	$-0.773330\pi$
$389$	−20.5226	+	6.02597i	−1.04054	+	0.305529i	−0.283548	+	0.958958i	$0.591512\pi$
$390$	0.0737545			0.00373470
$391$	−1.06703	+	1.42658i	−0.0539622	+	0.0721450i
$392$	−2.92969			−0.147972
$393$	−11.2287	+	3.29704i	−0.566412	+	0.166314i
$394$	−9.26182	−	10.6887i	−0.466604	−	0.538489i
$395$	−3.90656	+	2.51060i	−0.196561	+	0.126322i
$396$	−0.850159	−	5.91299i	−0.0427221	−	0.297139i
$397$	−3.72715	−	2.39529i	−0.187060	−	0.120216i	0.443759	−	0.896146i	$-0.353645\pi$
$397$	−3.72715	−	2.39529i	−0.187060	−	0.120216i	−0.630819	+	0.775930i	$0.717281\pi$
$398$	−3.72288	+	8.15197i	−0.186611	+	0.408621i
$399$	10.1908	−	11.7608i	0.510176	−	0.588775i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	−0.0816134	−	0.178708i	−0.00407558	−	0.00892427i	0.907583	−	0.419872i	$-0.137925\pi$
$401$	−0.0816134	−	0.178708i	−0.00407558	−	0.00892427i	−0.911659	+	0.410948i	$0.865198\pi$
$402$	−5.57751	−	1.63771i	−0.278181	−	0.0816813i
$403$	0.323069	+	0.0948618i	0.0160932	+	0.00472540i
$404$	6.97730	+	15.2781i	0.347133	+	0.760116i
$405$	−0.142315	+	0.989821i	−0.00707168	+	0.0491846i
$406$	−1.04918	+	1.21082i	−0.0520701	+	0.0600921i
$407$	0.197122	−	0.431637i	0.00977098	−	0.0213955i
$408$	0.312496	+	0.200829i	0.0154709	+	0.00994251i
$409$	−3.50140	−	24.3528i	−0.173133	−	1.20417i	−0.872214	−	0.489125i	$-0.837316\pi$
$409$	−3.50140	−	24.3528i	−0.173133	−	1.20417i	0.699080	−	0.715043i	$-0.253593\pi$
$410$	−9.52527	+	6.12152i	−0.470420	+	0.302320i
$411$	4.94454	+	5.70630i	0.243896	+	0.281471i
$412$	6.79230	−	1.99440i	0.334633	−	0.0982570i
$413$	20.6482			1.01603
$414$	−4.78348	+	0.344041i	−0.235095	+	0.0169087i
$415$	−9.71229			−0.476758
$416$	0.0707669	−	0.0207790i	0.00346963	−	0.00101878i
$417$	−0.164300	−	0.189612i	−0.00804580	−	0.00928534i
$418$	−38.7633	+	24.9117i	−1.89598	+	1.21847i
$419$	−2.31748	−	16.1184i	−0.113216	−	0.787435i	−0.964756	−	0.263146i	$-0.915240\pi$
$419$	−2.31748	−	16.1184i	−0.113216	−	0.787435i	0.851540	−	0.524290i	$-0.175669\pi$
$420$	1.69723	+	1.09074i	0.0828163	+	0.0532228i
$421$	14.1499	−	30.9839i	0.689623	−	1.51006i	−0.162492	−	0.986710i	$-0.551953\pi$
$421$	14.1499	−	30.9839i	0.689623	−	1.51006i	0.852115	−	0.523354i	$-0.175319\pi$
$422$	1.12921	−	1.30318i	0.0549691	−	0.0634377i
$423$	1.20260	−	8.36427i	0.0584724	−	0.406685i
$424$	2.07782	+	4.54979i	0.100908	+	0.220957i
$425$	0.356418	+	0.104654i	0.0172888	+	0.00507645i
$426$	6.26701	+	1.84016i	0.303638	+	0.0891561i
$427$	3.88394	+	8.50465i	0.187957	+	0.411569i
$428$	0.551407	−	3.83512i	0.0266533	−	0.185378i
$429$	−0.288528	+	0.332979i	−0.0139303	+	0.0160764i
$430$	1.16937	−	2.56056i	0.0563920	−	0.123481i
$431$	−26.6726	−	17.1414i	−1.28477	−	0.825673i	−0.293303	−	0.956019i	$-0.594755\pi$
$431$	−26.6726	−	17.1414i	−1.28477	−	0.825673i	−0.991468	+	0.130347i	$0.958391\pi$
$432$	0.142315	+	0.989821i	0.00684713	+	0.0476228i
$433$	−21.8348	+	14.0323i	−1.04931	+	0.674352i	−0.947273	−	0.320429i	$-0.896173\pi$
$433$	−21.8348	+	14.0323i	−1.04931	+	0.674352i	−0.102039	+	0.994780i	$0.532537\pi$
$434$	6.03154	+	6.96077i	0.289523	+	0.334127i
$435$	−0.761958	+	0.223731i	−0.0365331	+	0.0107271i
$436$	5.46431			0.261693
$437$	17.7413	+	32.4600i	0.848684	+	1.55277i
$438$	11.9042			0.568806
$439$	3.60288	−	1.05790i	0.171956	−	0.0504909i	−0.194621	−	0.980878i	$-0.562348\pi$
$439$	3.60288	−	1.05790i	0.171956	−	0.0504909i	0.366577	+	0.930388i	$0.380530\pi$
$440$	−3.91200	−	4.51469i	−0.186497	−	0.215229i
$441$	−2.46461	+	1.58391i	−0.117363	+	0.0754243i
$442$	−0.00389903	−	0.0271183i	−0.000185458	−	0.00128989i
$443$	−21.2089	−	13.6302i	−1.00767	−	0.647588i	−0.0708786	−	0.997485i	$-0.522580\pi$
$443$	−21.2089	−	13.6302i	−1.00767	−	0.647588i	−0.936788	+	0.349897i	$0.886217\pi$
$444$	−0.0329978	+	0.0722551i	−0.00156601	+	0.00342908i
$445$	−9.26532	+	10.6927i	−0.439218	+	0.506885i
$446$	3.24689	−	22.5826i	0.153745	−	1.06932i
$447$	−0.815039	−	1.78469i	−0.0385500	−	0.0844128i
$448$	1.93578	+	0.568396i	0.0914569	+	0.0268542i
$449$	2.29478	+	0.673807i	0.108297	+	0.0317989i	0.335432	−	0.942064i	$-0.391118\pi$
$449$	2.29478	+	0.673807i	0.108297	+	0.0317989i	−0.227135	+	0.973863i	$0.572936\pi$
$450$	0.415415	+	0.909632i	0.0195829	+	0.0428805i
$451$	9.62611	−	66.9510i	0.453276	−	3.15260i
$452$	−0.986266	+	1.13821i	−0.0463901	+	0.0535370i
$453$	0.240281	−	0.526141i	0.0112894	−	0.0247203i
$454$	17.2757	+	11.1024i	0.810789	+	0.521062i
$455$	−0.0211764	−	0.147285i	−0.000992765	−	0.00690484i
$456$	6.48890	−	4.17016i	0.303870	−	0.195286i
$457$	−8.06335	−	9.30560i	−0.377188	−	0.435298i	0.535137	−	0.844765i	$-0.320260\pi$
$457$	−8.06335	−	9.30560i	−0.377188	−	0.435298i	−0.912325	+	0.409468i	$0.865714\pi$
$458$	21.5961	−	6.34119i	1.00912	−	0.296304i
$459$	0.371465			0.0173385
$460$	−3.83811	+	2.87557i	−0.178953	+	0.134074i
$461$	13.0189			0.606352			0.303176	−	0.952935i	$-0.401953\pi$
$461$	13.0189			0.606352			0.303176	+	0.952935i	$0.401953\pi$
$462$	−11.5639	+	3.39548i	−0.538003	+	0.157972i
$463$	20.6654	+	23.8491i	0.960403	+	1.10836i	0.994049	+	0.108930i	$0.0347424\pi$
$463$	20.6654	+	23.8491i	0.960403	+	1.10836i	−0.0336468	+	0.999434i	$0.510712\pi$
$464$	−0.668061	+	0.429337i	−0.0310139	+	0.0199314i
$465$	0.649704	+	4.51879i	0.0301293	+	0.209554i
$466$	8.50561	+	5.46622i	0.394015	+	0.253218i
$467$	−16.2174	+	35.5111i	−0.750450	+	1.64326i	0.0151061	+	0.999886i	$0.495191\pi$
$467$	−16.2174	+	35.5111i	−0.750450	+	1.64326i	−0.765556	+	0.643370i	$0.777536\pi$
$468$	0.0482989	−	0.0557399i	0.00223262	−	0.00257658i
$469$	−1.66902	+	11.6083i	−0.0770684	+	0.536022i
$470$	−3.51037	−	7.68665i	−0.161921	−	0.354559i
$471$	4.65174	+	1.36587i	0.214341	+	0.0629361i
$472$	9.81996	+	2.88340i	0.452000	+	0.132719i
$473$	6.98556	+	15.2963i	0.321197	+	0.703322i
$474$	−0.660873	+	4.59648i	−0.0303549	+	0.211123i
$475$	5.05118	−	5.82937i	0.231764	−	0.267470i
$476$	0.311324	−	0.681706i	0.0142695	−	0.0312459i
$477$	4.20777	+	2.70417i	0.192661	+	0.123815i
$478$	−1.00595	−	6.99651i	−0.0460109	−	0.320013i
$479$	−7.93628	+	5.10034i	−0.362618	+	0.233040i	−0.709244	−	0.704963i	$-0.750964\pi$
$479$	−7.93628	+	5.10034i	−0.362618	+	0.233040i	0.346626	+	0.938003i	$0.387327\pi$
$480$	0.654861	+	0.755750i	0.0298902	+	0.0344951i
$481$	0.00562125	−	0.00165055i	0.000256307	−	7.52586e-5i
$482$	4.40258			0.200532
$483$	2.06047	+	9.45365i	0.0937546	+	0.430156i
$484$	24.6862			1.12210
$485$	13.7572	−	4.03949i	0.624684	−	0.183424i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	−14.3787	+	9.24065i	−0.651563	+	0.418734i	−0.824237	−	0.566245i	$-0.808396\pi$
$487$	−14.3787	+	9.24065i	−0.651563	+	0.418734i	0.172674	+	0.984979i	$0.444759\pi$
$488$	0.659519	+	4.58705i	0.0298550	+	0.207646i
$489$	14.9148	+	9.58517i	0.674471	+	0.433456i
$490$	−1.21704	+	2.66494i	−0.0549802	+	0.120390i
$491$	11.5938	−	13.3800i	0.523221	−	0.603830i	−0.431213	−	0.902250i	$-0.641914\pi$
$491$	11.5938	−	13.3800i	0.523221	−	0.603830i	0.954435	+	0.298420i	$0.0964598\pi$
$492$	−1.61139	+	11.2075i	−0.0726471	+	0.505271i
$493$	0.122543	+	0.268332i	0.00551906	+	0.0120851i
$494$	−0.545851	−	0.160276i	−0.0245590	−	0.00721118i
$495$	−5.73181	−	1.68301i	−0.257626	−	0.0756458i
$496$	1.89648	+	4.15271i	0.0851544	+	0.186462i
$497$	1.87535	−	13.0434i	0.0841210	−	0.585074i
$498$	−6.36020	+	7.34006i	−0.285007	+	0.328916i
$499$	5.86140	−	12.8347i	0.262392	−	0.574559i	−0.731880	−	0.681433i	$-0.761357\pi$
$499$	5.86140	−	12.8347i	0.262392	−	0.574559i	0.994273	+	0.106874i	$0.0340842\pi$
$500$	0.841254	+	0.540641i	0.0376220	+	0.0241782i
$501$	3.65606	+	25.4285i	0.163341	+	1.13606i
$502$	22.5815	−	14.5123i	1.00786	−	0.647714i
$503$	4.81035	+	5.55144i	0.214483	+	0.247527i	0.852788	−	0.522257i	$-0.174910\pi$
$503$	4.81035	+	5.55144i	0.214483	+	0.247527i	−0.638305	+	0.769783i	$0.720364\pi$
$504$	1.93578	−	0.568396i	0.0862264	−	0.0253183i
$505$	16.7960			0.747411
$506$	2.03241	−	28.5771i	0.0903515	−	1.27041i
$507$	12.9946			0.577109
$508$	−8.89288	+	2.61118i	−0.394558	+	0.115853i
$509$	9.12448	+	10.5302i	0.404435	+	0.466743i	0.921033	−	0.389485i	$-0.127347\pi$
$509$	9.12448	+	10.5302i	0.404435	+	0.466743i	−0.516597	+	0.856228i	$0.672802\pi$
$510$	0.312496	−	0.200829i	0.0138376	−	0.00889286i
$511$	−3.41794	−	23.7723i	−0.151201	−	1.05163i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	3.20425	−	7.01633i	0.141471	−	0.309778i
$514$	9.56436	−	11.0379i	0.421866	−	0.486859i
$515$	1.00745	−	7.00700i	0.0443937	−	0.308765i
$516$	−1.16937	−	2.56056i	−0.0514786	−	0.112722i
$517$	48.4354	+	14.2219i	2.13019	+	0.625479i
$518$	0.153765	+	0.0451496i	0.00675606	+	0.00198376i
$519$	5.99756	+	13.1328i	0.263264	+	0.576467i
$520$	0.0104964	−	0.0730038i	0.000460296	−	0.00320143i
$521$	−18.4975	+	21.3472i	−0.810388	+	0.935238i	−0.998903	−	0.0468327i	$-0.985087\pi$
$521$	−18.4975	+	21.3472i	−0.810388	+	0.935238i	0.188515	+	0.982070i	$0.439633\pi$
$522$	−0.329892	+	0.722362i	−0.0144390	+	0.0316169i
$523$	−23.0784	−	14.8316i	−1.00915	−	0.648541i	−0.0719767	−	0.997406i	$-0.522931\pi$
$523$	−23.0784	−	14.8316i	−1.00915	−	0.648541i	−0.937173	+	0.348865i	$0.886567\pi$
$524$	1.66547	+	11.5836i	0.0727565	+	0.506032i
$525$	1.69723	−	1.09074i	0.0740732	−	0.0476039i
$526$	−17.9656	−	20.7334i	−0.783336	−	0.904018i
$527$	1.62714	−	0.477771i	0.0708793	−	0.0208120i
$528$	−5.97379			−0.259976
$529$	−22.7685	−	3.25506i	−0.989935	−	0.141524i
$530$	5.00179			0.217264
$531$	9.81996	−	2.88340i	0.426150	−	0.125129i
$532$	−10.1908	−	11.7608i	−0.441826	−	0.509894i
$533$	0.702532	−	0.451490i	0.0304300	−	0.0195562i
$534$	2.01355	+	14.0045i	0.0871347	+	0.606035i
$535$	−3.25949	−	2.09475i	−0.140920	−	0.0905637i
$536$	−2.41480	+	5.28767i	−0.104303	+	0.228393i
$537$	−13.0022	+	15.0054i	−0.561088	+	0.647530i
$538$	−2.37479	+	16.5170i	−0.102385	+	0.712101i
$539$	−7.27033	−	15.9198i	−0.313155	−	0.685715i
$540$	0.959493	+	0.281733i	0.0412900	+	0.0121238i
$541$	−15.9962	−	4.69692i	−0.687732	−	0.201936i	−0.0808474	−	0.996726i	$-0.525763\pi$
$541$	−15.9962	−	4.69692i	−0.687732	−	0.201936i	−0.606884	+	0.794790i	$0.707581\pi$
$542$	−6.83143	−	14.9587i	−0.293435	−	0.642533i
$543$	0.207459	−	1.44291i	0.00890291	−	0.0619211i
$544$	0.243258	−	0.280734i	0.0104296	−	0.0120364i
$545$	2.26996	−	4.97051i	0.0972343	−	0.212913i
$546$	−0.125178	−	0.0804472i	−0.00535714	−	0.00344282i
$547$	5.23151	+	36.3859i	0.223683	+	1.55575i	0.723934	+	0.689870i	$0.242332\pi$
$547$	5.23151	+	36.3859i	0.223683	+	1.55575i	−0.500250	+	0.865881i	$0.666759\pi$
$548$	6.35190	−	4.08212i	0.271340	−	0.174379i
$549$	3.03477	+	3.50231i	0.129521	+	0.149475i
$550$	−5.73181	+	1.68301i	−0.244405	+	0.0717639i
$551$	6.12538			0.260950
$552$	−0.340220	+	4.78375i	−0.0144807	+	0.203610i
$553$	9.36875			0.398400
$554$	4.81720	−	1.41446i	0.204663	−	0.0600945i
$555$	0.0520178	+	0.0600317i	0.00220803	+	0.00254820i
$556$	−0.211064	+	0.135643i	−0.00895113	+	0.00575254i
$557$	2.96334	+	20.6105i	0.125561	+	0.873295i	0.951085	+	0.308929i	$0.0999705\pi$
$557$	2.96334	+	20.6105i	0.125561	+	0.873295i	−0.825524	+	0.564367i	$0.809120\pi$
$558$	3.84054	+	2.46817i	0.162583	+	0.104486i
$559$	−0.0862462	+	0.188853i	−0.00364783	+	0.00798762i
$560$	1.32118	−	1.52473i	0.0558301	−	0.0644314i
$561$	−0.315804	+	2.19647i	−0.0133333	+	0.0927349i
$562$	−5.57367	−	12.2046i	−0.235111	−	0.514821i
$563$	−30.6779	−	9.00784i	−1.29292	−	0.379635i	−0.438271	−	0.898843i	$-0.644409\pi$
$563$	−30.6779	−	9.00784i	−1.29292	−	0.379635i	−0.854648	+	0.519208i	$0.826227\pi$
$564$	−8.10799	−	2.38072i	−0.341408	−	0.100246i
$565$	0.625644	+	1.36997i	0.0263211	+	0.0576351i
$566$	−2.45789	+	17.0950i	−0.103313	+	0.718555i
$567$	1.32118	−	1.52473i	0.0554844	−	0.0640324i
$568$	2.71332	−	5.94134i	0.113848	−	0.249293i
$569$	−6.48020	−	4.16457i	−0.271664	−	0.174588i	0.397715	−	0.917509i	$-0.369803\pi$
$569$	−6.48020	−	4.16457i	−0.271664	−	0.174588i	−0.669379	+	0.742921i	$0.733440\pi$
$570$	−1.09773	−	7.63486i	−0.0459787	−	0.319789i
$571$	22.1270	−	14.2201i	0.925985	−	0.595095i	0.0115969	−	0.999933i	$-0.496309\pi$
$571$	22.1270	−	14.2201i	0.925985	−	0.595095i	0.914388	+	0.404838i	$0.132672\pi$
$572$	0.288528	+	0.332979i	0.0120640	+	0.0139225i
$573$	−6.11011	+	1.79409i	−0.255254	+	0.0749492i
$574$	22.8436			0.953472
$575$	1.02130	+	4.68582i	0.0425911	+	0.195412i
$576$	1.00000			0.0416667
$577$	−22.9505	+	6.73887i	−0.955440	+	0.280543i	−0.722050	−	0.691841i	$-0.756800\pi$
$577$	−22.9505	+	6.73887i	−0.955440	+	0.280543i	−0.233390	+	0.972383i	$0.574982\pi$
$578$	11.0423	+	12.7435i	0.459298	+	0.530058i
$579$	18.9782	−	12.1966i	0.788708	−	0.506872i
$580$	0.113016	+	0.786042i	0.00469273	+	0.0326386i
$581$	16.4840	+	10.5936i	0.683871	+	0.439497i
$582$	5.95623	−	13.0423i	0.246894	−	0.540622i
$583$	−19.5670	+	22.5815i	−0.810382	+	0.935231i
$584$	1.69415	−	11.7831i	0.0701043	−	0.487586i
$585$	−0.0306387	−	0.0670895i	−0.00126676	−	0.00277381i
$586$	3.00084	+	0.881126i	0.123964	+	0.0363990i
$587$	21.8387	+	6.41241i	0.901378	+	0.264668i	0.699407	−	0.714723i	$-0.253447\pi$
$587$	21.8387	+	6.41241i	0.901378	+	0.264668i	0.201970	+	0.979392i	$0.435266\pi$
$588$	1.21704	+	2.66494i	0.0501898	+	0.109900i
$589$	5.01141	−	34.8551i	0.206491	−	1.43618i
$590$	6.70219	−	7.73474i	0.275925	−	0.318434i
$591$	−5.87529	+	12.8651i	−0.241677	+	0.529199i
$592$	0.0668236	+	0.0429449i	0.00274643	+	0.00176502i
$593$	−4.18744	−	29.1243i	−0.171958	−	1.19599i	−0.874742	−	0.484588i	$-0.838969\pi$
$593$	−4.18744	−	29.1243i	−0.171958	−	1.19599i	0.702785	−	0.711402i	$-0.251940\pi$
$594$	−5.02547	+	3.22968i	−0.206198	+	0.132515i
$595$	−0.490772	−	0.566381i	−0.0201197	−	0.0232194i
$596$	−1.88251	+	0.552756i	−0.0771108	+	0.0226418i
$597$	8.96183			0.366783
$598$	0.283078	−	0.212086i	0.0115759	−	0.00867284i
$599$	−33.3375			−1.36213			−0.681066	−	0.732222i	$-0.738484\pi$
$599$	−33.3375			−1.36213			−0.681066	+	0.732222i	$0.738484\pi$
$600$	0.959493	−	0.281733i	0.0391711	−	0.0115017i
$601$	21.6850	+	25.0258i	0.884548	+	1.02082i	0.999623	+	0.0274664i	$0.00874394\pi$
$601$	21.6850	+	25.0258i	0.884548	+	1.02082i	−0.115074	+	0.993357i	$0.536711\pi$
$602$	−4.77760	+	3.07038i	−0.194720	+	0.125139i
$603$	0.827273	+	5.75381i	0.0336892	+	0.234313i
$604$	−0.486590	−	0.312713i	−0.0197991	−	0.0127241i
$605$	10.2550	−	22.4554i	0.416926	−	0.912940i
$606$	10.9990	−	12.6935i	0.446805	−	0.515640i
$607$	2.16273	−	15.0421i	0.0877826	−	0.610541i	−0.897680	−	0.440648i	$-0.854749\pi$
$607$	2.16273	−	15.0421i	0.0877826	−	0.610541i	0.985463	−	0.169893i	$-0.0543422\pi$
$608$	−3.20425	−	7.01633i	−0.129949	−	0.284550i
$609$	1.53725	+	0.451377i	0.0622925	+	0.0182907i
$610$	4.44651	+	1.30561i	0.180034	+	0.0528627i
$611$	0.258906	+	0.566925i	0.0104742	+	0.0229353i
$612$	0.0528649	−	0.367684i	0.00213694	−	0.0148627i
$613$	2.08038	−	2.40089i	0.0840259	−	0.0969710i	−0.712180	−	0.701997i	$-0.752292\pi$
$613$	2.08038	−	2.40089i	0.0840259	−	0.0969710i	0.796206	+	0.605026i	$0.206837\pi$
$614$	−9.84485	+	21.5572i	−0.397306	+	0.869978i
$615$	9.52527	+	6.12152i	0.384096	+	0.246843i
$616$	1.71520	+	11.9295i	0.0691072	+	0.480651i
$617$	−14.1401	+	9.08731i	−0.569260	+	0.365841i	−0.793386	−	0.608719i	$-0.791684\pi$
$617$	−14.1401	+	9.08731i	−0.569260	+	0.365841i	0.224126	+	0.974560i	$0.428047\pi$
$618$	−4.63579	−	5.34999i	−0.186479	−	0.215208i
$619$	−13.9307	+	4.09042i	−0.559922	+	0.164408i	−0.549434	−	0.835537i	$-0.685157\pi$
$619$	−13.9307	+	4.09042i	−0.559922	+	0.164408i	−0.0104881	+	0.999945i	$0.503339\pi$
$620$	4.56526			0.183345
$621$	2.30008	+	4.20828i	0.0922990	+	0.168873i
$622$	25.8605			1.03691
$623$	27.3884	−	8.04196i	1.09729	−	0.322194i
$624$	−0.0482989	−	0.0557399i	−0.00193350	−	0.00223138i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	1.73224	+	12.0480i	0.0692342	+	0.481535i
$627$	38.7633	+	24.9117i	1.54806	+	0.994877i
$628$	2.01398	−	4.41000i	0.0803666	−	0.175978i
$629$	0.0193228	−	0.0222997i	0.000770449	−	0.000889146i
$630$	0.287120	−	1.99697i	0.0114391	−	0.0795610i
$631$	12.6182	+	27.6299i	0.502321	+	1.09993i	0.975708	+	0.219075i	$0.0703039\pi$
$631$	12.6182	+	27.6299i	0.502321	+	1.09993i	−0.473387	+	0.880854i	$0.656969\pi$
$632$	4.45564	+	1.30829i	0.177236	+	0.0520411i
$633$	−1.65450	−	0.485806i	−0.0657606	−	0.0193090i
$634$	0.812727	+	1.77962i	0.0322775	+	0.0706779i
$635$	−1.31902	+	9.17397i	−0.0523436	+	0.364058i
$636$	3.27547	−	3.78010i	0.129881	−	0.149891i
$637$	0.0897621	−	0.196551i	0.00355650	−	0.00778765i
$638$	−3.99086	−	2.56477i	−0.157999	−	0.101540i
$639$	−0.929542	−	6.46511i	−0.0367721	−	0.255756i
$640$	0.841254	−	0.540641i	0.0332535	−	0.0213707i
$641$	−13.4442	−	15.5154i	−0.531013	−	0.612821i	0.425341	−	0.905033i	$-0.360154\pi$
$641$	−13.4442	−	15.5154i	−0.531013	−	0.612821i	−0.956354	+	0.292212i	$0.905609\pi$
$642$	−3.71761	+	1.09159i	−0.146723	+	0.0430816i
$643$	39.2588			1.54822			0.774108	−	0.633053i	$-0.218199\pi$
$643$	39.2588			1.54822			0.774108	+	0.633053i	$0.218199\pi$
$644$	9.65066	−	0.694103i	0.380289	−	0.0273515i
$645$	−2.81494			−0.110838
$646$	−2.74918	+	0.807232i	−0.108165	+	0.0317601i
$647$	24.9112	+	28.7491i	0.979362	+	1.13024i	0.991472	+	0.130318i	$0.0415997\pi$
$647$	24.9112	+	28.7491i	0.979362	+	1.13024i	−0.0121101	+	0.999927i	$0.503855\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	8.70098	+	60.5167i	0.341543	+	2.37549i
$650$	−0.0620462	−	0.0398747i	−0.00243365	−	0.00156401i
$651$	3.82614	−	8.37809i	0.149958	−	0.328363i
$652$	11.6102	−	13.3989i	0.454691	−	0.524741i
$653$	6.01026	−	41.8023i	0.235200	−	1.63585i	−0.439846	−	0.898073i	$-0.644967\pi$
$653$	6.01026	−	41.8023i	0.235200	−	1.63585i	0.675045	−	0.737776i	$-0.264124\pi$
$654$	−2.26996	−	4.97051i	−0.0887623	−	0.194362i
$655$	11.2287	+	3.29704i	0.438741	+	0.128826i
$656$	10.8641	+	3.18998i	0.424170	+	0.124548i
$657$	−4.94519	−	10.8285i	−0.192930	−	0.422459i
$658$	−2.42625	+	16.8749i	−0.0945850	+	0.657853i
$659$	21.5044	−	24.8174i	0.837693	−	0.966749i	−0.162106	−	0.986773i	$-0.551829\pi$
$659$	21.5044	−	24.8174i	0.837693	−	0.966749i	0.999800	+	0.0200240i	$0.00637425\pi$
$660$	−2.48160	+	5.43395i	−0.0965963	+	0.211516i
$661$	−16.5944	−	10.6646i	−0.645449	−	0.414805i	0.176552	−	0.984291i	$-0.443506\pi$
$661$	−16.5944	−	10.6646i	−0.645449	−	0.414805i	−0.822001	+	0.569487i	$0.807142\pi$
$662$	−0.206656	−	1.43732i	−0.00803191	−	0.0558632i
$663$	−0.0230480	+	0.0148120i	−0.000895110	+	0.000575252i
$664$	6.36020	+	7.34006i	0.246824	+	0.284850i
$665$	−14.9314	+	4.38424i	−0.579013	+	0.170014i
$666$	0.0794333			0.00307798
$667$	−2.28113	+	3.04977i	−0.0883255	+	0.118087i
$668$	25.6899			0.993974
$669$	−21.8907	+	6.42768i	−0.846342	+	0.248508i
$670$	3.80669	+	4.39316i	0.147065	+	0.169722i
$671$	−23.2892	+	14.9670i	−0.899069	+	0.577796i
$672$	−0.287120	−	1.99697i	−0.0110759	−	0.0770346i
$673$	−1.74987	−	1.12457i	−0.0674524	−	0.0433491i	0.506480	−	0.862252i	$-0.330946\pi$
$673$	−1.74987	−	1.12457i	−0.0674524	−	0.0433491i	−0.573932	+	0.818903i	$0.694583\pi$
$674$	3.07864	−	6.74129i	0.118585	−	0.259665i
$675$	0.654861	−	0.755750i	0.0252056	−	0.0290888i
$676$	1.84932	−	12.8623i	0.0711276	−	0.494704i
$677$	−0.849760	−	1.86072i	−0.0326589	−	0.0715131i	0.892599	−	0.450850i	$-0.148879\pi$
$677$	−0.849760	−	1.86072i	−0.0326589	−	0.0715131i	−0.925258	+	0.379337i	$0.876152\pi$
$678$	1.44506	+	0.424309i	0.0554973	+	0.0162955i
$679$	−27.7552	−	8.14967i	−1.06515	−	0.312755i
$680$	−0.154312	−	0.337896i	−0.00591759	−	0.0129577i
$681$	2.92253	−	20.3266i	0.111992	−	0.778919i
$682$	−17.8593	+	20.6107i	−0.683868	+	0.789226i
$683$	−2.91096	+	6.37410i	−0.111385	+	0.243898i	−0.957113	−	0.289716i	$-0.906439\pi$
$683$	−2.91096	+	6.37410i	−0.111385	+	0.243898i	0.845728	+	0.533614i	$0.179166\pi$
$684$	−6.48890	−	4.17016i	−0.248109	−	0.159450i
$685$	−1.07455	−	7.47366i	−0.0410565	−	0.285554i
$686$	16.8530	−	10.8307i	0.643449	−	0.413520i
$687$	−14.7395	−	17.0103i	−0.562347	−	0.648983i
$688$	−2.70092	+	0.793060i	−0.102971	+	0.0302351i
$689$	−0.368904			−0.0140541
$690$	4.21012	+	2.29672i	0.160276	+	0.0874345i
$691$	−11.4821			−0.436799			−0.218400	−	0.975859i	$-0.570084\pi$
$691$	−11.4821			−0.436799			−0.218400	+	0.975859i	$0.570084\pi$
$692$	13.8527	−	4.06752i	0.526600	−	0.154624i
$693$	7.89247	+	9.10839i	0.299810	+	0.345999i
$694$	0.276426	−	0.177648i	0.0104930	−	0.00674344i
$695$	0.0357058	+	0.248339i	0.00135440	+	0.00942004i
$696$	0.668061	+	0.429337i	0.0253228	+	0.0162740i
$697$	1.74723	−	3.82590i	0.0661811	−	0.144916i
$698$	20.6142	−	23.7900i	0.780259	−	0.900466i
$699$	1.43889	−	10.0077i	0.0544239	−	0.378527i
$700$	−0.838100	−	1.83518i	−0.0316772	−	0.0693634i
$701$	−20.6263	−	6.05642i	−0.779043	−	0.228748i	−0.132050	−	0.991243i	$-0.542156\pi$
$701$	−20.6263	−	6.05642i	−0.779043	−	0.228748i	−0.646994	+	0.762495i	$0.723974\pi$
$702$	−0.0707669	−	0.0207790i	−0.00267093	−	0.000784255i
$703$	−0.254524	−	0.557330i	−0.00959956	−	0.0210201i
$704$	−0.850159	+	5.91299i	−0.0320416	+	0.222854i
$705$	−5.53376	+	6.38630i	−0.208413	+	0.240522i
$706$	−9.15037	+	20.0365i	−0.344379	+	0.754085i
$707$	−28.5066	−	18.3201i	−1.07210	−	0.688998i
$708$	−1.45653	−	10.1304i	−0.0547396	−	0.380722i
$709$	−3.97251	+	2.55298i	−0.149191	+	0.0958792i	−0.613107	−	0.790000i	$-0.710080\pi$
$709$	−3.97251	+	2.55298i	−0.149191	+	0.0958792i	0.463916	+	0.885879i	$0.346444\pi$
$710$	−4.27728	−	4.93625i	−0.160524	−	0.185254i
$711$	4.45564	−	1.30829i	0.167099	−	0.0490648i
$712$	14.1485			0.530239
$713$	15.4877	+	15.4754i	0.580020	+	0.579557i
$714$	−0.749430			−0.0280467
$715$	0.422747	−	0.124130i	0.0158098	−	0.00464219i
$716$	13.0022	+	15.0054i	0.485916	+	0.560777i
$717$	−5.94636	+	3.82149i	−0.222071	+	0.142716i
$718$	−4.97166	−	34.5786i	−0.185541	−	1.29046i
$719$	24.1225	+	15.5026i	0.899619	+	0.578150i	0.906677	−	0.421825i	$-0.138610\pi$
$719$	24.1225	+	15.5026i	0.899619	+	0.578150i	−0.00705810	+	0.999975i	$0.502247\pi$
$720$	0.415415	−	0.909632i	0.0154816	−	0.0339000i
$721$	−9.35272	+	10.7936i	−0.348313	+	0.401975i
$722$	−5.76319	+	40.0838i	−0.214484	+	1.49177i
$723$	−1.82890	−	4.00473i	−0.0680174	−	0.148937i
$724$	−1.39870	−	0.410694i	−0.0519821	−	0.0152633i
$725$	0.761958	+	0.223731i	0.0282984	+	0.00830916i
$726$	−10.2550	−	22.4554i	−0.380599	−	0.833396i
$727$	−5.27724	+	36.7040i	−0.195722	+	1.36128i	0.620803	+	0.783967i	$0.286807\pi$
$727$	−5.27724	+	36.7040i	−0.195722	+	1.36128i	−0.816525	+	0.577310i	$0.804102\pi$
$728$	−0.0974431	+	0.112455i	−0.00361148	+	0.00416787i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−10.0145	−	6.43591i	−0.370652	−	0.238204i
$731$	0.148812	+	1.03501i	0.00550400	+	0.0382811i
$732$	3.89856	−	2.50545i	0.144095	−	0.0926041i
$733$	−17.1962	−	19.8455i	−0.635158	−	0.733011i	0.343353	−	0.939206i	$-0.388437\pi$
$733$	−17.1962	−	19.8455i	−0.635158	−	0.733011i	−0.978511	+	0.206195i	$0.933892\pi$
$734$	7.86989	−	2.31081i	0.290483	−	0.0852934i
$735$	2.92969			0.108063
$736$	4.68664	+	1.01756i	0.172752	+	0.0375076i
$737$	−34.7255			−1.27913
$738$	10.8641	−	3.18998i	0.399912	−	0.117425i
$739$	24.6804	+	28.4827i	0.907884	+	1.04775i	0.998653	+	0.0518825i	$0.0165221\pi$
$739$	24.6804	+	28.4827i	0.907884	+	1.04775i	−0.0907687	+	0.995872i	$0.528932\pi$
$740$	0.0668236	−	0.0429449i	0.00245648	−	0.00157869i
$741$	0.0809623	+	0.563105i	0.00297422	+	0.0206862i
$742$	−8.48918	−	5.45566i	−0.311648	−	0.200284i
$743$	−19.2440	+	42.1384i	−0.705993	+	1.54591i	0.126557	+	0.991959i	$0.459607\pi$
$743$	−19.2440	+	42.1384i	−0.705993	+	1.54591i	−0.832550	+	0.553950i	$0.813120\pi$
$744$	2.98961	−	3.45019i	0.109604	−	0.126490i
$745$	−0.279220	+	1.94202i	−0.0102298	+	0.0711500i
$746$	0.00382121	+	0.00836729i	0.000139905	+	0.000306348i
$747$	9.31887	+	2.73627i	0.340960	+	0.100115i
$748$	2.12917	+	0.625179i	0.0778500	+	0.0228588i
$749$	3.24727	+	7.11053i	0.118653	+	0.259813i
$750$	0.142315	−	0.989821i	0.00519660	−	0.0361432i
$751$	17.4554	−	20.1446i	0.636957	−	0.735088i	−0.341876	−	0.939745i	$-0.611062\pi$
$751$	17.4554	−	20.1446i	0.636957	−	0.735088i	0.978834	+	0.204657i	$0.0656079\pi$
$752$	−3.51037	+	7.68665i	−0.128010	+	0.280303i
$753$	−22.5815	−	14.5123i	−0.822916	−	0.528856i
$754$	−0.00833542	−	0.0579742i	−0.000303558	−	0.00211129i
$755$	−0.486590	+	0.312713i	−0.0177088	+	0.0113808i
$756$	−1.32118	−	1.52473i	−0.0480509	−	0.0554537i
$757$	−18.9883	+	5.57547i	−0.690142	+	0.202644i	−0.607953	−	0.793973i	$-0.708009\pi$
$757$	−18.9883	+	5.57547i	−0.690142	+	0.202644i	−0.0821889	+	0.996617i	$0.526191\pi$
$758$	9.06263			0.329170
$759$	−26.8390	+	10.0226i	−0.974192	+	0.363798i
$760$	−7.71337			−0.279793
$761$	−35.4102	+	10.3974i	−1.28362	+	0.376904i	−0.851234	−	0.524786i	$-0.824145\pi$
$761$	−35.4102	+	10.3974i	−1.28362	+	0.376904i	−0.432383	+	0.901690i	$0.642327\pi$
$762$	6.06945	+	7.00452i	0.219873	+	0.253747i
$763$	−9.27419	+	5.96016i	−0.335748	+	0.215772i
$764$	0.906270	+	6.30324i	0.0327877	+	0.228043i
$765$	−0.312496	−	0.200829i	−0.0112983	−	0.00726099i
$766$	−13.4894	+	29.5376i	−0.487391	+	1.06724i
$767$	−0.494317	+	0.570472i	−0.0178488	+	0.0205986i
$768$	0.142315	−	0.989821i	0.00513534	−	0.0357171i
$769$	3.86694	+	8.46742i	0.139445	+	0.305343i	0.966451	−	0.256851i	$-0.0826849\pi$
$769$	3.86694	+	8.46742i	0.139445	+	0.305343i	−0.827006	+	0.562194i	$0.809958\pi$
$770$	11.5639	+	3.39548i	0.416735	+	0.122364i
$771$	−14.0136	−	4.11476i	−0.504687	−	0.148189i
$772$	−9.37154	−	20.5208i	−0.337289	−	0.738560i
$773$	−5.79090	+	40.2766i	−0.208284	+	1.44865i	0.570469	+	0.821319i	$0.306761\pi$
$773$	−5.79090	+	40.2766i	−0.208284	+	1.44865i	−0.778754	+	0.627330i	$0.784148\pi$
$774$	−1.84339	+	2.12739i	−0.0662594	+	0.0764675i
$775$	1.89648	−	4.15271i	0.0681235	−	0.149170i
$776$	−12.0619	−	7.75172i	−0.432997	−	0.278270i
$777$	−0.0228069	−	0.158626i	−0.000818194	−	0.00569066i
$778$	17.9935	−	11.5638i	0.645100	−	0.414581i
$779$	−57.1931	−	66.0043i	−2.04915	−	2.36485i
$780$	−0.0707669	+	0.0207790i	−0.00253386	+	0.000744009i
$781$	39.0184			1.39619
$782$	0.621897	−	1.66941i	0.0222390	−	0.0596979i
$783$	0.794125			0.0283797
$784$	2.81102	−	0.825390i	0.100394	−	0.0294782i
$785$	−3.17484	−	3.66396i	−0.113315	−	0.130772i
$786$	9.84496	−	6.32697i	0.351158	−	0.225676i
$787$	2.67731	+	18.6211i	0.0954358	+	0.663771i	0.980241	+	0.197809i	$0.0633825\pi$
$787$	2.67731	+	18.6211i	0.0954358	+	0.663771i	−0.884805	+	0.465962i	$0.845708\pi$
$788$	11.8980	+	7.64639i	0.423849	+	0.272391i
$789$	−11.3966	+	24.9550i	−0.405729	+	0.888422i
$790$	3.04100	−	3.50951i	0.108194	−	0.124863i
$791$	0.432423	−	3.00757i	0.0153752	−	0.106937i
$792$	2.48160	+	5.43395i	0.0881799	+	0.193087i
$793$	−0.327950	−	0.0962948i	−0.0116458	−	0.00341953i
$794$	4.25100	+	1.24821i	0.150862	+	0.0442972i
$795$	−2.07782	−	4.54979i	−0.0736926	−	0.161364i
$796$	1.27540	−	8.87061i	0.0452054	−	0.314411i
$797$	14.6719	−	16.9323i	0.519705	−	0.599771i	−0.433852	−	0.900984i	$-0.642846\pi$
$797$	14.6719	−	16.9323i	0.519705	−	0.599771i	0.953557	+	0.301213i	$0.0973915\pi$
$798$	−6.46457	+	14.1554i	−0.228843	+	0.501097i
$799$	2.64068	+	1.69706i	0.0934205	+	0.0600377i
$800$	−0.142315	−	0.989821i	−0.00503159	−	0.0349955i
$801$	11.9025	−	7.64928i	0.420554	−	0.270274i
$802$	0.128655	+	0.148476i	0.00454298	+	0.00524288i
$803$	68.2328	−	20.0350i	2.40788	−	0.707018i
$804$	5.81298			0.205008
$805$	3.37765	−	9.06689i	0.119047	−	0.319566i
$806$	−0.336709			−0.0118601
$807$	16.0110	−	4.70124i	0.563612	−	0.165492i
$808$	−10.9990	−	12.6935i	−0.386944	−	0.446557i
$809$	−11.8310	+	7.60335i	−0.415957	+	0.267320i	−0.731837	−	0.681480i	$-0.761337\pi$
$809$	−11.8310	+	7.60335i	−0.415957	+	0.267320i	0.315880	+	0.948799i	$0.397700\pi$
$810$	−0.142315	−	0.989821i	−0.00500043	−	0.0347788i
$811$	−39.5235	−	25.4002i	−1.38786	−	0.891922i	−0.388297	−	0.921534i	$-0.626936\pi$
$811$	−39.5235	−	25.4002i	−1.38786	−	0.891922i	−0.999561	+	0.0296120i	$0.990573\pi$
$812$	0.665556	−	1.45737i	0.0233564	−	0.0511435i
$813$	−10.7691	+	12.4282i	−0.377688	+	0.435875i
$814$	−0.0675310	+	0.469688i	−0.00236696	+	0.0164626i
$815$	−7.36501	−	16.1271i	−0.257985	−	0.564908i
$816$	−0.356418	−	0.104654i	−0.0124771	−	0.00366361i
$817$	20.8332	+	6.11717i	0.728860	+	0.214013i
$818$	10.2205	+	22.3799i	0.357353	+	0.782494i
$819$	−0.0211764	+	0.147285i	−0.000739964	+	0.00514656i
$820$	7.41480	−	8.55713i	0.258936	−	0.298828i
$821$	12.8924	−	28.2305i	0.449949	−	0.985252i	−0.539715	−	0.841848i	$-0.681468\pi$
$821$	12.8924	−	28.2305i	0.449949	−	0.985252i	0.989664	−	0.143404i	$-0.0458047\pi$
$822$	−6.35190	−	4.08212i	−0.221548	−	0.142380i
$823$	−1.84225	−	12.8131i	−0.0642166	−	0.446637i	−0.996409	−	0.0846728i	$-0.973015\pi$
$823$	−1.84225	−	12.8131i	−0.0642166	−	0.446637i	0.932192	−	0.361964i	$-0.117894\pi$
$824$	−5.95528	+	3.82723i	−0.207462	+	0.133328i
$825$	3.91200	+	4.51469i	0.136198	+	0.157181i
$826$	−19.8118	+	5.81726i	−0.689340	+	0.202408i
$827$	−38.4115			−1.33570			−0.667850	−	0.744296i	$-0.732785\pi$
$827$	−38.4115			−1.33570			−0.667850	+	0.744296i	$0.732785\pi$
$828$	4.49278	−	1.67777i	0.156135	−	0.0583064i
$829$	9.11177			0.316465			0.158232	−	0.987402i	$-0.449420\pi$
$829$	9.11177			0.316465			0.158232	+	0.987402i	$0.449420\pi$
$830$	9.31887	−	2.73627i	0.323463	−	0.0949773i
$831$	−3.28777	−	3.79429i	−0.114052	−	0.131623i
$832$	−0.0620462	+	0.0398747i	−0.00215107	+	0.00138241i
$833$	−0.154878	−	1.07720i	−0.00536620	−	0.0373228i
$834$	0.211064	+	0.135643i	0.00730856	+	0.00469693i
$835$	10.6720	−	23.3684i	0.369319	−	0.808697i
$836$	30.1747	−	34.8235i	1.04361	−	1.20439i
$837$	0.649704	−	4.51879i	0.0224571	−	0.156192i
$838$	6.76468	+	14.8126i	0.233682	+	0.511692i
$839$	31.6068	+	9.28059i	1.09119	+	0.320402i	0.777346	−	0.629073i	$-0.216566\pi$
$839$	31.6068	+	9.28059i	1.09119	+	0.320402i	0.313842	+	0.949475i	$0.398384\pi$
$840$	−1.93578	−	0.568396i	−0.0667907	−	0.0196115i
$841$	−11.7851	−	25.8057i	−0.406381	−	0.889851i
$842$	−4.84753	+	33.7153i	−0.167057	+	1.16191i
$843$	−8.78633	+	10.1400i	−0.302617	+	0.349239i
$844$	−0.716321	+	1.56852i	−0.0246568	+	0.0539908i
$845$	−10.9317	−	7.02539i	−0.376063	−	0.241681i
$846$	1.20260	+	8.36427i	0.0413463	+	0.287570i
$847$	−41.8981	+	26.9263i	−1.43964	+	0.925198i
$848$	−3.27547	−	3.78010i	−0.112480	−	0.129809i
$849$	16.5712	−	4.86573i	0.568721	−	0.166992i
$850$	−0.371465			−0.0127411
$851$	0.372275	+	0.0808279i	0.0127614	+	0.00277074i
$852$	−6.53159			−0.223769
$853$	−15.3707	+	4.51324i	−0.526282	+	0.154530i	−0.534071	−	0.845439i	$-0.679339\pi$
$853$	−15.3707	+	4.51324i	−0.526282	+	0.154530i	0.00778965	+	0.999970i	$0.497520\pi$
$854$	−6.12265	−	7.06592i	−0.209513	−	0.241791i
$855$	−6.48890	+	4.17016i	−0.221916	+	0.142617i
$856$	0.551407	+	3.83512i	0.0188467	+	0.131082i
$857$	6.37636	+	4.09784i	0.217812	+	0.139980i	0.644998	−	0.764185i	$-0.276858\pi$
$857$	6.37636	+	4.09784i	0.217812	+	0.139980i	−0.427185	+	0.904164i	$0.640495\pi$
$858$	0.183029	−	0.400778i	0.00624852	−	0.0136824i
$859$	6.82273	−	7.87385i	0.232788	−	0.268652i	−0.627322	−	0.778760i	$-0.715849\pi$
$859$	6.82273	−	7.87385i	0.232788	−	0.268652i	0.860110	+	0.510108i	$0.170394\pi$
$860$	−0.400608	+	2.78629i	−0.0136606	+	0.0950116i
$861$	−9.48956	−	20.7792i	−0.323403	−	0.708155i
$862$	30.4214	+	8.93254i	1.03616	+	0.304243i
$863$	−39.9700	−	11.7362i	−1.36059	−	0.399506i	−0.481622	−	0.876379i	$-0.659952\pi$
$863$	−39.9700	−	11.7362i	−1.36059	−	0.399506i	−0.878972	+	0.476873i	$0.841770\pi$
$864$	−0.415415	−	0.909632i	−0.0141327	−	0.0309463i
$865$	2.05467	−	14.2906i	0.0698610	−	0.485894i
$866$	16.9969	−	19.6155i	0.577579	−	0.666562i
$867$	7.00473	−	15.3382i	0.237893	−	0.520914i
$868$	−7.74829	−	4.97953i	−0.262994	−	0.169016i
$869$	3.94792	+	27.4584i	0.133924	+	0.931462i
$870$	0.668061	−	0.429337i	0.0226494	−	0.0145559i
$871$	−0.280761	−	0.324015i	−0.00951321	−	0.0109788i
$872$	−5.24297	+	1.53947i	−0.177549	+	0.0521332i
$873$	−14.3380			−0.485268
$874$	−26.1677	−	26.1469i	−0.885137	−	0.884431i
$875$	−2.01750			−0.0682040
$876$	−11.4220	+	3.35381i	−0.385914	+	0.113315i
$877$	24.8656	+	28.6965i	0.839653	+	0.969011i	0.999837	−	0.0180760i	$-0.00575410\pi$
$877$	24.8656	+	28.6965i	0.839653	+	0.969011i	−0.160184	+	0.987087i	$0.551209\pi$
$878$	−3.15889	+	2.03010i	−0.106608	+	0.0685125i
$879$	−0.445094	−	3.09569i	−0.0150126	−	0.104415i
$880$	5.02547	+	3.22968i	0.169409	+	0.108872i
$881$	−8.82932	+	19.3335i	−0.297467	+	0.651362i	−0.998064	−	0.0621950i	$-0.980190\pi$
$881$	−8.82932	+	19.3335i	−0.297467	+	0.651362i	0.700597	+	0.713557i	$0.252917\pi$
$882$	1.91854	−	2.21411i	0.0646006	−	0.0745531i
$883$	1.53932	−	10.7062i	0.0518024	−	0.360293i	−0.947389	−	0.320085i	$-0.896289\pi$
$883$	1.53932	−	10.7062i	0.0518024	−	0.360293i	0.999191	−	0.0402087i	$-0.0128023\pi$
$884$	0.0113812	+	0.0249214i	0.000382791	+	0.000838196i
$885$	−9.81996	−	2.88340i	−0.330094	−	0.0969245i
$886$	24.1899	+	7.10279i	0.812675	+	0.238623i
$887$	−12.7846	−	27.9944i	−0.429265	−	0.939958i	−0.993445	−	0.114307i	$-0.963535\pi$
$887$	−12.7846	−	27.9944i	−0.429265	−	0.939958i	0.564181	−	0.825651i	$-0.309192\pi$
$888$	0.0113045	−	0.0786248i	0.000379356	−	0.00263848i
$889$	12.2451	−	14.1316i	0.410688	−	0.473959i
$890$	5.87751	−	12.8700i	0.197015	−	0.431402i
$891$	5.02547	+	3.22968i	0.168360	+	0.108198i
$892$	3.24689	+	22.5826i	0.108714	+	0.756121i
$893$	54.8330	−	35.2390i	1.83492	−	1.17923i
$894$	1.28483	+	1.48277i	0.0429711	+	0.0495913i
$895$	19.0507	−	5.59379i	0.636795	−	0.186980i
$896$	−2.01750			−0.0674000
$897$	−0.310515	−	0.169393i	−0.0103678	−	0.00565587i
$898$	−2.39166			−0.0798106
$899$	3.47853	−	1.02139i	0.116016	−	0.0340653i
$900$	−0.654861	−	0.755750i	−0.0218287	−	0.0251917i
$901$	−1.56304	+	1.00450i	−0.0520724	+	0.0334649i
$902$	9.62611	+	66.9510i	0.320514	+	2.22923i
$903$	4.77760	+	3.07038i	0.158989	+	0.102176i
$904$	0.625644	−	1.36997i	0.0208086	−	0.0455645i
$905$	−0.954620	+	1.10169i	−0.0317326	+	0.0366214i
$906$	−0.0823165	+	0.572524i	−0.00273478	+	0.0190208i
$907$	1.52548	+	3.34033i	0.0506527	+	0.110914i	0.933266	−	0.359185i	$-0.116945\pi$
$907$	1.52548	+	3.34033i	0.0506527	+	0.110914i	−0.882614	+	0.470099i	$0.844218\pi$
$908$	−19.7038	−	5.78557i	−0.653894	−	0.192001i
$909$	−16.1156	−	4.73197i	−0.534521	−	0.156950i
$910$	0.0618136	+	0.135353i	0.00204910	+	0.00448691i
$911$	4.85265	−	33.7509i	0.160776	−	1.11822i	−0.736401	−	0.676546i	$-0.763476\pi$
$911$	4.85265	−	33.7509i	0.160776	−	1.11822i	0.897176	−	0.441673i	$-0.145615\pi$
$912$	−5.05118	+	5.82937i	−0.167261	+	0.193030i
$913$	−24.1021	+	52.7761i	−0.797661	+	1.74663i
$914$	10.3584	+	6.65695i	0.342626	+	0.220192i
$915$	−0.659519	−	4.58705i	−0.0218030	−	0.151643i
$916$	−18.9348	+	12.1687i	−0.625623	+	0.402064i
$917$	−15.4614	−	17.8434i	−0.510581	−	0.589242i
$918$	−0.356418	+	0.104654i	−0.0117635	+	0.00345409i
$919$	30.8116			1.01638			0.508191	−	0.861244i	$-0.330314\pi$
$919$	30.8116			1.01638			0.508191	+	0.861244i	$0.330314\pi$
$920$	2.87250	−	3.84041i	0.0947036	−	0.126615i
$921$	23.6988			0.780903
$922$	−12.4916	+	3.66786i	−0.411388	+	0.120794i
$923$	0.315469	+	0.364070i	0.0103838	+	0.0119835i
$924$	10.1389	−	6.51587i	0.333545	−	0.214356i
$925$	−0.0113045	−	0.0786248i	−0.000371691	−	0.00258517i
$926$	−26.5474	−	17.0610i	−0.872401	−	0.560658i
$927$	−2.94074	+	6.43933i	−0.0965867	+	0.211495i
$928$	0.520041	−	0.600160i	0.0170712	−	0.0197012i
$929$	−0.410444	+	2.85470i	−0.0134662	+	0.0936596i	−0.995446	−	0.0953257i	$-0.969611\pi$
$929$	−0.410444	+	2.85470i	−0.0134662	+	0.0936596i	0.981980	+	0.188985i	$0.0605198\pi$
$930$	−1.89648	−	4.15271i	−0.0621880	−	0.136173i
$931$	−21.6824	−	6.36653i	−0.710613	−	0.208655i
$932$	−9.70108	−	2.84849i	−0.317770	−	0.0933055i
$933$	−10.7428	−	23.5235i	−0.351705	−	0.770126i
$934$	5.55582	−	38.6416i	0.181792	−	1.26439i
$935$	1.45317	−	1.67705i	0.0475238	−	0.0548453i
$936$	−0.0306387	+	0.0670895i	−0.00100146	+	0.00219289i
$937$	−1.09632	−	0.704564i	−0.0358153	−	0.0230171i	0.522611	−	0.852571i	$-0.324958\pi$
$937$	−1.09632	−	0.704564i	−0.0358153	−	0.0230171i	−0.558426	+	0.829554i	$0.688595\pi$
$938$	−1.66902	−	11.6083i	−0.0544956	−	0.379025i
$939$	10.2396	−	6.58062i	0.334158	−	0.214750i
$940$	5.53376	+	6.38630i	0.180491	+	0.208298i
$941$	−3.13833	+	0.921498i	−0.102307	+	0.0300400i	−0.332485	−	0.943108i	$-0.607887\pi$
$941$	−3.13833	+	0.921498i	−0.102307	+	0.0300400i	0.230179	+	0.973148i	$0.426069\pi$
$942$	−4.84812			−0.157960
$943$	54.1619	−	3.89548i	1.76375	−	0.126854i
$944$	−10.2345			−0.333106
$945$	−1.93578	+	0.568396i	−0.0629708	+	0.0184899i
$946$	−11.0121	−	12.7086i	−0.358033	−	0.413192i
$947$	14.1793	−	9.11249i	0.460766	−	0.296116i	−0.289589	−	0.957151i	$-0.593519\pi$
$947$	14.1793	−	9.11249i	0.460766	−	0.296116i	0.750355	+	0.661035i	$0.229882\pi$
$948$	−0.660873	−	4.59648i	−0.0214642	−	0.149287i
$949$	0.738613	+	0.474677i	0.0239764	+	0.0154087i
$950$	−3.20425	+	7.01633i	−0.103960	+	0.227640i
$951$	1.28118	−	1.47857i	0.0415452	−	0.0479458i
$952$	−0.106655	+	0.741802i	−0.00345671	+	0.0240419i
$953$	−5.04354	−	11.0438i	−0.163376	−	0.357744i	0.810183	−	0.586176i	$-0.199367\pi$
$953$	−5.04354	−	11.0438i	−0.163376	−	0.357744i	−0.973560	+	0.228432i	$0.926640\pi$
$954$	−4.79918	−	1.40917i	−0.155379	−	0.0456234i
$955$	6.11011	+	1.79409i	0.197719	+	0.0580554i
$956$	2.93634	+	6.42969i	0.0949681	+	0.207951i
$957$	−0.675133	+	4.69565i	−0.0218239	+	0.151789i
$958$	6.17787	−	7.12965i	0.199598	−	0.230348i
$959$	−6.32809	+	13.8566i	−0.204345	+	0.447452i
$960$	−0.841254	−	0.540641i	−0.0271513	−	0.0174491i
$961$	1.44569	+	10.0550i	0.0466352	+	0.324355i
$962$	−0.00492854	+	0.00316738i	−0.000158903	+	0.000102120i
$963$	2.53730	+	2.92820i	0.0817633	+	0.0943598i
$964$	−4.22424	+	1.24035i	−0.136054	+	0.0399490i
$965$	−22.5595			−0.726215
$966$	−4.64041	−	8.49021i	−0.149303	−	0.273168i
$967$	8.27862			0.266223			0.133111	−	0.991101i	$-0.457503\pi$
$967$	8.27862			0.266223			0.133111	+	0.991101i	$0.457503\pi$
$968$	−23.6862	+	6.95490i	−0.761304	+	0.223539i
$969$	1.87634	+	2.16541i	0.0602766	+	0.0695629i
$970$	−12.0619	+	7.75172i	−0.387285	+	0.248893i
$971$	1.28318	+	8.92473i	0.0411793	+	0.286408i	0.999997	+	0.00238653i	$0.000759656\pi$
$971$	1.28318	+	8.92473i	0.0411793	+	0.286408i	−0.958818	+	0.284022i	$0.908331\pi$
$972$	−0.841254	−	0.540641i	−0.0269832	−	0.0173411i
$973$	0.210273	−	0.460434i	0.00674105	−	0.0147608i
$974$	11.1929	−	12.9173i	0.358644	−	0.413897i
$975$	−0.0104964	+	0.0730038i	−0.000336153	+	0.00233799i
$976$	−1.92513	−	4.21544i	−0.0616218	−	0.134933i
$977$	−6.38493	−	1.87479i	−0.204272	−	0.0599797i	0.177996	−	0.984031i	$-0.443039\pi$
$977$	−6.38493	−	1.87479i	−0.204272	−	0.0599797i	−0.382268	+	0.924052i	$0.624857\pi$
$978$	−17.0111	−	4.99492i	−0.543956	−	0.159720i
$979$	35.1110	+	76.8825i	1.12215	+	2.45717i
$980$	0.416939	−	2.89987i	0.0133186	−	0.0926330i
$981$	−3.57836	+	4.12965i	−0.114248	+	0.131850i
$982$	−7.35461	+	16.1043i	−0.234695	+	0.513910i
$983$	−34.4008	−	22.1080i	−1.09721	−	0.705137i	−0.138744	−	0.990328i	$-0.544306\pi$
$983$	−34.4008	−	22.1080i	−1.09721	−	0.705137i	−0.958471	+	0.285192i	$0.907943\pi$
$984$	−1.61139	−	11.2075i	−0.0513692	−	0.357281i
$985$	11.8980	−	7.64639i	0.379102	−	0.243634i
$986$	−0.193177	−	0.222938i	−0.00615201	−	0.00709980i
$987$	16.3579	−	4.80310i	0.520677	−	0.152884i
$988$	0.568896			0.0180990
$989$	−10.8041	+	8.09455i	−0.343549	+	0.257392i
$990$	5.97379			0.189860
$991$	−31.1200	+	9.13767i	−0.988560	+	0.290268i	−0.735754	−	0.677249i	$-0.763172\pi$
$991$	−31.1200	+	9.13767i	−0.988560	+	0.290268i	−0.252807	+	0.967517i	$0.581354\pi$
$992$	−2.98961	−	3.45019i	−0.0949202	−	0.109544i
$993$	−1.22159	+	0.785066i	−0.0387659	+	0.0249133i
$994$	1.87535	+	13.0434i	0.0594825	+	0.413710i
$995$	−7.53917	−	4.84513i	−0.239008	−	0.153601i
$996$	4.03463	−	8.83461i	0.127842	−	0.279935i
$997$	−12.6539	+	14.6034i	−0.400755	+	0.462495i	−0.919878	−	0.392204i	$-0.871713\pi$
$997$	−12.6539	+	14.6034i	−0.400755	+	0.462495i	0.519124	+	0.854699i	$0.326258\pi$
$998$	−2.00803	+	13.9661i	−0.0635630	+	0.442090i
$999$	−0.0329978	−	0.0722551i	−0.00104400	−	0.00228605i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.838100 + 1.83518i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.838100 + 1.83518i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.415415 + 0.909632i) q^{10} +(-5.73181 - 1.68301i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-0.0306387 - 0.0670895i) q^{13} +(0.287120 - 1.99697i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-0.312496 - 0.200829i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(-6.48890 + 4.17016i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-1.93578 + 0.568396i) q^{21} +5.97379 q^{22} +(0.340220 - 4.78375i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(0.0482989 + 0.0557399i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.287120 + 1.99697i) q^{28} +(-0.668061 - 0.429337i) q^{29} +(-0.415415 + 0.909632i) q^{30} +(-2.98961 + 3.45019i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-2.48160 - 5.43395i) q^{33} +(0.356418 + 0.104654i) q^{34} +(1.93578 + 0.568396i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.0113045 + 0.0786248i) q^{37} +(5.05118 - 5.82937i) q^{38} +(0.0306387 - 0.0670895i) q^{39} +(0.841254 + 0.540641i) q^{40} +(1.61139 + 11.2075i) q^{41} +(1.69723 - 1.09074i) q^{42} +(-1.84339 - 2.12739i) q^{43} +(-5.73181 + 1.68301i) q^{44} +1.00000 q^{45} +(1.02130 + 4.68582i) q^{46} -8.45028 q^{47} +(0.959493 - 0.281733i) q^{48} +(1.91854 + 2.21411i) q^{49} +(0.841254 - 0.540641i) q^{50} +(-0.0528649 - 0.367684i) q^{51} +(-0.0620462 - 0.0398747i) q^{52} +(2.07782 - 4.54979i) q^{53} +(0.654861 - 0.755750i) q^{54} +(-0.850159 + 5.91299i) q^{55} +(-0.838100 - 1.83518i) q^{56} +(-7.40092 - 2.17311i) q^{57} +(0.761958 + 0.223731i) q^{58} +(-4.25158 - 9.30966i) q^{59} +(0.142315 - 0.989821i) q^{60} +(3.03477 - 3.50231i) q^{61} +(1.89648 - 4.15271i) q^{62} +(-1.69723 - 1.09074i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-0.0620462 + 0.0398747i) q^{65} +(3.91200 + 4.51469i) q^{66} +(5.57751 - 1.63771i) q^{67} -0.371465 q^{68} +(3.83811 - 2.87557i) q^{69} -2.01750 q^{70} +(-6.26701 + 1.84016i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-10.0145 + 6.43591i) q^{73} +(-0.0113045 - 0.0786248i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(-3.20425 + 7.01633i) q^{76} +(7.89247 - 9.10839i) q^{77} +(-0.0104964 + 0.0730038i) q^{78} +(-1.92908 - 4.22410i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-4.70362 - 10.2995i) q^{82} +(1.38220 - 9.61343i) q^{83} +(-1.32118 + 1.52473i) q^{84} +(-0.154312 + 0.337896i) q^{85} +(2.36808 + 1.52187i) q^{86} +(-0.113016 - 0.786042i) q^{87} +(5.02547 - 3.22968i) q^{88} +(-9.26532 - 10.6927i) q^{89} +(-0.959493 + 0.281733i) q^{90} +0.148800 q^{91} +(-2.30008 - 4.20828i) q^{92} -4.56526 q^{93} +(8.10799 - 2.38072i) q^{94} +(5.05118 + 5.82937i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(2.04051 + 14.1921i) q^{97} +(-2.46461 - 1.58391i) q^{98} +(2.48160 - 5.43395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

L-functions

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