LMFDB - Embedded newform 418.2.n.c.159.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			159.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	418.159
Dual form			418.2.n.c.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.669131 - 0.743145i) q^{2} +(-0.209057 + 1.98904i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(2.56082 - 0.544320i) q^{5} +(1.33826 + 1.48629i) q^{6} +(0.190983 - 0.138757i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(0.669131 - 0.743145i) q^{2} +(-0.209057 + 1.98904i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(2.56082 - 0.544320i) q^{5} +(1.33826 + 1.48629i) q^{6} +(0.190983 - 0.138757i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.30902 - 2.26728i) q^{10} +(3.04508 + 1.31433i) q^{11} +2.00000 q^{12} +(-4.74803 - 1.00922i) q^{13} +(0.0246758 - 0.234775i) q^{14} +(0.547318 + 5.20738i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(7.45156 - 1.58388i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-3.89452 + 1.95774i) q^{19} +(-0.809017 - 2.48990i) q^{20} +(0.236068 + 0.408882i) q^{21} +(3.01430 - 1.38348i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.33826 - 1.48629i) q^{24} +(1.69381 - 0.754131i) q^{25} +(-3.92705 + 2.85317i) q^{26} +(-1.23607 + 3.80423i) q^{27} +(-0.157960 - 0.175433i) q^{28} +(0.233733 + 2.22382i) q^{29} +(4.23607 + 3.07768i) q^{30} +(0.972136 + 2.99193i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.25085 + 5.78204i) q^{33} +(3.80902 - 6.59741i) q^{34} +(0.413545 - 0.459289i) q^{35} +(-0.104528 + 0.994522i) q^{36} +(4.54508 - 3.30220i) q^{37} +(-1.15106 + 4.20417i) q^{38} +(3.00000 - 9.23305i) q^{39} +(-2.39169 - 1.06485i) q^{40} +(0.830403 - 7.90075i) q^{41} +(0.461819 + 0.0981626i) q^{42} +(-1.35410 - 2.34537i) q^{43} +(0.988830 - 3.16579i) q^{44} -2.61803 q^{45} +(-0.309017 - 0.951057i) q^{46} +(0.913545 - 0.406737i) q^{47} +(-0.209057 - 1.98904i) q^{48} +(-2.14590 + 6.60440i) q^{49} +(0.572949 - 1.76336i) q^{50} +(1.59260 + 15.1526i) q^{51} +(-0.507392 + 4.82751i) q^{52} +(-10.9905 - 2.33611i) q^{53} +(2.00000 + 3.46410i) q^{54} +(8.51334 + 1.70826i) q^{55} -0.236068 q^{56} +(-3.07985 - 8.15564i) q^{57} +(1.80902 + 1.31433i) q^{58} +(-4.30116 - 1.91500i) q^{59} +(5.12165 - 1.08864i) q^{60} +(-9.27020 - 10.2956i) q^{61} +(2.87392 + 1.27955i) q^{62} +(-0.215659 + 0.0960175i) q^{63} +(0.309017 + 0.951057i) q^{64} -12.7082 q^{65} +(2.12165 + 6.28479i) q^{66} +(1.66312 - 2.88061i) q^{67} +(-2.35410 - 7.24518i) q^{68} +(1.61803 + 1.17557i) q^{69} +(-0.0646021 - 0.614648i) q^{70} +(-9.12244 + 1.93903i) q^{71} +(0.669131 + 0.743145i) q^{72} +(-6.17916 - 2.75114i) q^{73} +(0.587244 - 5.58726i) q^{74} +(1.14590 + 3.52671i) q^{75} +(2.35410 + 3.66854i) q^{76} +(0.763932 - 0.171513i) q^{77} +(-4.85410 - 8.40755i) q^{78} +(-6.49606 + 7.21460i) q^{79} +(-2.39169 + 1.06485i) q^{80} +(-10.0490 - 4.47410i) q^{81} +(-5.31576 - 5.90374i) q^{82} +(0.781153 - 2.40414i) q^{83} +(0.381966 - 0.277515i) q^{84} +(18.2200 - 8.11207i) q^{85} +(-2.64902 - 0.563067i) q^{86} -4.47214 q^{87} +(-1.69098 - 2.85317i) q^{88} +(-0.645898 + 1.11873i) q^{89} +(-1.75181 + 1.94558i) q^{90} +(-1.04683 + 0.466079i) q^{91} +(-0.913545 - 0.406737i) q^{92} +(-6.15431 + 1.30814i) q^{93} +(0.309017 - 0.951057i) q^{94} +(-8.90753 + 7.13329i) q^{95} +(-1.61803 - 1.17557i) q^{96} +(4.13545 - 4.59289i) q^{97} +(3.47214 + 6.01392i) q^{98} +(-2.70528 - 1.91872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 8 * q + q^2 + 2 * q^3 + q^4 + q^5 + 2 * q^6 + 6 * q^7 - 2 * q^8 + q^9	\( 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9} + 6 q^{10} + 2 q^{11} + 16 q^{12} - 6 q^{13} - 3 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 2 q^{18} - 4 q^{19} - 2 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} - 18 q^{26} + 8 q^{27} + 7 q^{28} - 5 q^{29} + 16 q^{30} - 28 q^{31} - 4 q^{32} + 18 q^{33} + 26 q^{34} - 3 q^{35} + q^{36} + 14 q^{37} - 13 q^{38} + 24 q^{39} - 4 q^{40} - 19 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} - 12 q^{45} + 2 q^{46} + q^{47} + 2 q^{48} - 44 q^{49} + 18 q^{50} - 18 q^{51} + 9 q^{52} + 4 q^{53} + 16 q^{54} + 14 q^{55} + 16 q^{56} - 26 q^{57} + 10 q^{58} - 13 q^{59} + 2 q^{60} - 3 q^{61} - q^{62} - 3 q^{63} - 2 q^{64} - 48 q^{65} - 22 q^{66} - 18 q^{67} + 8 q^{68} + 4 q^{69} + 2 q^{70} - 16 q^{71} + q^{72} - 4 q^{73} - 7 q^{74} + 36 q^{75} - 8 q^{76} + 24 q^{77} - 12 q^{78} + 12 q^{79} - 4 q^{80} - 11 q^{81} + 21 q^{82} - 34 q^{83} + 12 q^{84} + 31 q^{85} - 19 q^{86} - 18 q^{88} - 32 q^{89} + q^{90} + 3 q^{91} - q^{92} + 28 q^{93} - 2 q^{94} - 38 q^{95} - 4 q^{96} - 30 q^{97} - 8 q^{98} - q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 + q^4 + q^5 + 2 * q^6 + 6 * q^7 - 2 * q^8 + q^9 + 6 * q^10 + 2 * q^11 + 16 * q^12 - 6 * q^13 - 3 * q^14 - 8 * q^15 + q^16 - 4 * q^17 - 2 * q^18 - 4 * q^19 - 2 * q^20 - 16 * q^21 - q^22 + 4 * q^23 + 2 * q^24 + 6 * q^25 - 18 * q^26 + 8 * q^27 + 7 * q^28 - 5 * q^29 + 16 * q^30 - 28 * q^31 - 4 * q^32 + 18 * q^33 + 26 * q^34 - 3 * q^35 + q^36 + 14 * q^37 - 13 * q^38 + 24 * q^39 - 4 * q^40 - 19 * q^41 + 14 * q^42 + 16 * q^43 + 4 * q^44 - 12 * q^45 + 2 * q^46 + q^47 + 2 * q^48 - 44 * q^49 + 18 * q^50 - 18 * q^51 + 9 * q^52 + 4 * q^53 + 16 * q^54 + 14 * q^55 + 16 * q^56 - 26 * q^57 + 10 * q^58 - 13 * q^59 + 2 * q^60 - 3 * q^61 - q^62 - 3 * q^63 - 2 * q^64 - 48 * q^65 - 22 * q^66 - 18 * q^67 + 8 * q^68 + 4 * q^69 + 2 * q^70 - 16 * q^71 + q^72 - 4 * q^73 - 7 * q^74 + 36 * q^75 - 8 * q^76 + 24 * q^77 - 12 * q^78 + 12 * q^79 - 4 * q^80 - 11 * q^81 + 21 * q^82 - 34 * q^83 + 12 * q^84 + 31 * q^85 - 19 * q^86 - 18 * q^88 - 32 * q^89 + q^90 + 3 * q^91 - q^92 + 28 * q^93 - 2 * q^94 - 38 * q^95 - 4 * q^96 - 30 * q^97 - 8 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.669131	−	0.743145i	0.473147	−	0.525483i
$2$	0.669131	−	0.743145i	0.473147	−	0.525483i
$3$	−0.209057	+	1.98904i	−0.120699	+	1.14837i	0.751674	+	0.659535i	$0.229247\pi$
$3$	−0.209057	+	1.98904i	−0.120699	+	1.14837i	−0.872373	+	0.488840i	$0.837420\pi$
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	2.56082	−	0.544320i	1.14524	−	0.243427i	0.404056	−	0.914734i	$-0.367600\pi$
$5$	2.56082	−	0.544320i	1.14524	−	0.243427i	0.741179	+	0.671307i	$0.234267\pi$
$6$	1.33826	+	1.48629i	0.546343	+	0.606775i
$7$	0.190983	−	0.138757i	0.0721848	−	0.0524453i	−0.551108	−	0.834434i	$-0.685795\pi$
$7$	0.190983	−	0.138757i	0.0721848	−	0.0524453i	0.623292	+	0.781989i	$0.285795\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	1.30902	−	2.26728i	0.413948	−	0.716978i
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$12$	2.00000			0.577350
$13$	−4.74803	−	1.00922i	−1.31687	−	0.279909i	−0.504680	−	0.863307i	$-0.668389\pi$
$13$	−4.74803	−	1.00922i	−1.31687	−	0.279909i	−0.812186	+	0.583398i	$0.801723\pi$
$14$	0.0246758	−	0.234775i	0.00659489	−	0.0627462i
$15$	0.547318	+	5.20738i	0.141317	+	1.34454i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	7.45156	−	1.58388i	1.80727	−	0.384147i	0.824042	−	0.566529i	$-0.191714\pi$
$17$	7.45156	−	1.58388i	1.80727	−	0.384147i	0.983228	+	0.182383i	$0.0583809\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	−3.89452	+	1.95774i	−0.893463	+	0.449136i
$19$	−3.89452	+	1.95774i	−0.893463	+	0.449136i
$20$	−0.809017	−	2.48990i	−0.180902	−	0.556758i
$21$	0.236068	+	0.408882i	0.0515143	+	0.0892253i
$22$	3.01430	−	1.38348i	0.642650	−	0.294959i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	1.33826	−	1.48629i	0.273171	−	0.303388i
$25$	1.69381	−	0.754131i	0.338761	−	0.150826i
$26$	−3.92705	+	2.85317i	−0.770158	+	0.559553i
$27$	−1.23607	+	3.80423i	−0.237881	+	0.732124i
$28$	−0.157960	−	0.175433i	−0.0298517	−	0.0331537i
$29$	0.233733	+	2.22382i	0.0434031	+	0.412953i	0.994554	+	0.104225i	$0.0332364\pi$
$29$	0.233733	+	2.22382i	0.0434031	+	0.412953i	−0.951151	+	0.308727i	$0.900097\pi$
$30$	4.23607	+	3.07768i	0.773397	+	0.561906i
$31$	0.972136	+	2.99193i	0.174601	+	0.537366i	0.999615	−	0.0277460i	$-0.00883297\pi$
$31$	0.972136	+	2.99193i	0.174601	+	0.537366i	−0.825014	+	0.565112i	$0.808833\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.25085	+	5.78204i	−0.565901	+	1.00652i
$34$	3.80902	−	6.59741i	0.653241	−	1.13145i
$35$	0.413545	−	0.459289i	0.0699019	−	0.0776340i
$36$	−0.104528	+	0.994522i	−0.0174214	+	0.165754i
$37$	4.54508	−	3.30220i	0.747207	−	0.542878i	−0.147753	−	0.989024i	$-0.547204\pi$
$37$	4.54508	−	3.30220i	0.747207	−	0.542878i	0.894960	+	0.446146i	$0.147204\pi$
$38$	−1.15106	+	4.20417i	−0.186726	+	0.682007i
$39$	3.00000	−	9.23305i	0.480384	−	1.47847i
$40$	−2.39169	−	1.06485i	−0.378160	−	0.168368i
$41$	0.830403	−	7.90075i	0.129687	−	1.23389i	−0.715190	−	0.698930i	$-0.753660\pi$
$41$	0.830403	−	7.90075i	0.129687	−	1.23389i	0.844877	−	0.534960i	$-0.179673\pi$
$42$	0.461819	+	0.0981626i	0.0712602	+	0.0151468i
$43$	−1.35410	−	2.34537i	−0.206499	−	0.357666i	0.744111	−	0.668056i	$-0.232874\pi$
$43$	−1.35410	−	2.34537i	−0.206499	−	0.357666i	−0.950609	+	0.310390i	$0.899540\pi$
$44$	0.988830	−	3.16579i	0.149072	−	0.477261i
$45$	−2.61803			−0.390273
$46$	−0.309017	−	0.951057i	−0.0455621	−	0.140226i
$47$	0.913545	−	0.406737i	0.133254	−	0.0593286i	−0.339026	−	0.940777i	$-0.610098\pi$
$47$	0.913545	−	0.406737i	0.133254	−	0.0593286i	0.472281	+	0.881448i	$0.343431\pi$
$48$	−0.209057	−	1.98904i	−0.0301748	−	0.287094i
$49$	−2.14590	+	6.60440i	−0.306557	+	0.943485i
$50$	0.572949	−	1.76336i	0.0810272	−	0.249376i
$51$	1.59260	+	15.1526i	0.223009	+	2.12179i
$52$	−0.507392	+	4.82751i	−0.0703626	+	0.669455i
$53$	−10.9905	−	2.33611i	−1.50967	−	0.320889i	−0.622603	−	0.782538i	$-0.713925\pi$
$53$	−10.9905	−	2.33611i	−1.50967	−	0.320889i	−0.887063	+	0.461649i	$0.847258\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	8.51334	+	1.70826i	1.14794	+	0.230342i
$56$	−0.236068			−0.0315459
$57$	−3.07985	−	8.15564i	−0.407936	−	1.08024i
$58$	1.80902	+	1.31433i	0.237536	+	0.172580i
$59$	−4.30116	−	1.91500i	−0.559963	−	0.249312i	0.107182	−	0.994239i	$-0.465817\pi$
$59$	−4.30116	−	1.91500i	−0.559963	−	0.249312i	−0.667145	+	0.744928i	$0.732484\pi$
$60$	5.12165	−	1.08864i	0.661202	−	0.140543i
$61$	−9.27020	−	10.2956i	−1.18693	−	1.31822i	−0.936743	−	0.350019i	$-0.886175\pi$
$61$	−9.27020	−	10.2956i	−1.18693	−	1.31822i	−0.250185	−	0.968198i	$-0.580492\pi$
$62$	2.87392	+	1.27955i	0.364988	+	0.162503i
$63$	−0.215659	+	0.0960175i	−0.0271705	+	0.0120971i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−12.7082			−1.57626
$66$	2.12165	+	6.28479i	0.261157	+	0.773604i
$67$	1.66312	−	2.88061i	0.203182	−	0.351922i	−0.746370	−	0.665532i	$-0.768205\pi$
$67$	1.66312	−	2.88061i	0.203182	−	0.351922i	0.949552	+	0.313609i	$0.101538\pi$
$68$	−2.35410	−	7.24518i	−0.285477	−	0.878607i
$69$	1.61803	+	1.17557i	0.194788	+	0.141522i
$70$	−0.0646021	−	0.614648i	−0.00772143	−	0.0734645i
$71$	−9.12244	+	1.93903i	−1.08263	+	0.230121i	−0.714489	−	0.699647i	$-0.753341\pi$
$71$	−9.12244	+	1.93903i	−1.08263	+	0.230121i	−0.368146	+	0.929768i	$0.620007\pi$
$72$	0.669131	+	0.743145i	0.0788578	+	0.0875805i
$73$	−6.17916	−	2.75114i	−0.723216	−	0.321996i	0.0119081	−	0.999929i	$-0.496209\pi$
$73$	−6.17916	−	2.75114i	−0.723216	−	0.321996i	−0.735124	+	0.677933i	$0.762876\pi$
$74$	0.587244	−	5.58726i	0.0682658	−	0.649506i
$75$	1.14590	+	3.52671i	0.132317	+	0.407230i
$76$	2.35410	+	3.66854i	0.270034	+	0.420811i
$77$	0.763932	−	0.171513i	0.0870581	−	0.0195458i
$78$	−4.85410	−	8.40755i	−0.549619	−	0.951968i
$79$	−6.49606	+	7.21460i	−0.730863	+	0.811706i	−0.987965	−	0.154678i	$-0.950566\pi$
$79$	−6.49606	+	7.21460i	−0.730863	+	0.811706i	0.257101	+	0.966384i	$0.417233\pi$
$80$	−2.39169	+	1.06485i	−0.267399	+	0.119054i
$81$	−10.0490	−	4.47410i	−1.11656	−	0.497123i
$82$	−5.31576	−	5.90374i	−0.587027	−	0.651960i
$83$	0.781153	−	2.40414i	0.0857427	−	0.263889i	−0.898988	−	0.437973i	$-0.855697\pi$
$83$	0.781153	−	2.40414i	0.0857427	−	0.263889i	0.984731	+	0.174084i	$0.0556965\pi$
$84$	0.381966	−	0.277515i	0.0416759	−	0.0302793i
$85$	18.2200	−	8.11207i	1.97624	−	0.879877i
$86$	−2.64902	−	0.563067i	−0.285652	−	0.0607171i
$87$	−4.47214			−0.479463
$88$	−1.69098	−	2.85317i	−0.180259	−	0.304149i
$89$	−0.645898	+	1.11873i	−0.0684651	+	0.118585i	−0.898226	−	0.439534i	$-0.855143\pi$
$89$	−0.645898	+	1.11873i	−0.0684651	+	0.118585i	0.829761	+	0.558119i	$0.188477\pi$
$90$	−1.75181	+	1.94558i	−0.184657	+	0.205082i
$91$	−1.04683	+	0.466079i	−0.109738	+	0.0488583i
$92$	−0.913545	−	0.406737i	−0.0952437	−	0.0424052i
$93$	−6.15431	+	1.30814i	−0.638172	+	0.135648i
$94$	0.309017	−	0.951057i	0.0318727	−	0.0980940i
$95$	−8.90753	+	7.13329i	−0.913894	+	0.731860i
$96$	−1.61803	−	1.17557i	−0.165140	−	0.119981i
$97$	4.13545	−	4.59289i	0.419892	−	0.466337i	−0.495672	−	0.868510i	$-0.665078\pi$
$97$	4.13545	−	4.59289i	0.419892	−	0.466337i	0.915564	+	0.402173i	$0.131745\pi$
$98$	3.47214	+	6.01392i	0.350739	+	0.607497i
$99$	−2.70528	−	1.91872i	−0.271891	−	0.192838i
$100$	−0.927051	−	1.60570i	−0.0927051	−	0.160570i
$101$	−7.07794	−	1.50446i	−0.704282	−	0.149700i	−0.158170	−	0.987412i	$-0.550559\pi$
$101$	−7.07794	−	1.50446i	−0.704282	−	0.149700i	−0.546112	+	0.837712i	$0.683893\pi$
$102$	12.3262	+	8.95554i	1.22048	+	0.886730i
$103$	7.23607	−	5.25731i	0.712991	−	0.518018i	−0.171146	−	0.985246i	$-0.554747\pi$
$103$	7.23607	−	5.25731i	0.712991	−	0.518018i	0.884137	+	0.467227i	$0.154747\pi$
$104$	3.24803	+	3.60730i	0.318495	+	0.353725i
$105$	0.827091	+	0.918578i	0.0807158	+	0.0896440i
$106$	−9.09017	+	6.60440i	−0.882915	+	0.641476i
$107$	4.11803	+	2.99193i	0.398105	+	0.289240i	0.768769	−	0.639527i	$-0.220870\pi$
$107$	4.11803	+	2.99193i	0.398105	+	0.289240i	−0.370663	+	0.928767i	$0.620870\pi$
$108$	3.91259	+	0.831647i	0.376489	+	0.0800252i
$109$	−9.54508	−	16.5326i	−0.914253	−	1.58353i	−0.807991	−	0.589195i	$-0.799445\pi$
$109$	−9.54508	−	16.5326i	−0.914253	−	1.58353i	−0.106263	−	0.994338i	$-0.533888\pi$
$110$	6.96602	−	5.18359i	0.664184	−	0.494236i
$111$	5.61803	+	9.73072i	0.533240	+	0.923599i
$112$	−0.157960	+	0.175433i	−0.0149258	+	0.0165768i
$113$	14.5902	+	10.6004i	1.37253	+	0.997200i	0.997535	+	0.0701721i	$0.0223548\pi$
$113$	14.5902	+	10.6004i	1.37253	+	0.997200i	0.374993	+	0.927028i	$0.377645\pi$
$114$	−8.12165	−	3.16841i	−0.760662	−	0.296749i
$115$	0.809017	−	2.48990i	0.0754412	−	0.232184i
$116$	2.18720	−	0.464905i	0.203077	−	0.0431653i
$117$	4.43444	+	1.97434i	0.409964	+	0.182528i
$118$	−4.30116	+	1.91500i	−0.395954	+	0.176290i
$119$	1.20335	−	1.33645i	0.110311	−	0.122512i
$120$	2.61803	−	4.53457i	0.238993	−	0.413948i
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$	−13.8541			−1.25429
$123$	15.5413	+	3.30341i	1.40132	+	0.297859i
$124$	2.87392	−	1.27955i	0.258086	−	0.114907i
$125$	−6.66312	+	4.84104i	−0.595967	+	0.432996i
$126$	−0.0729490	+	0.224514i	−0.00649881	+	0.0200013i
$127$	13.0897	+	14.5376i	1.16153	+	1.29001i	0.949864	+	0.312663i	$0.101221\pi$
$127$	13.0897	+	14.5376i	1.16153	+	1.29001i	0.211662	+	0.977343i	$0.432112\pi$
$128$	0.913545	+	0.406737i	0.0807468	+	0.0359508i
$129$	4.94813	−	2.20305i	0.435659	−	0.193968i
$130$	−8.50345	+	9.44404i	−0.745802	+	0.828297i
$131$	2.73607	+	4.73901i	0.239051	+	0.414049i	0.960442	−	0.278479i	$-0.0898302\pi$
$131$	2.73607	+	4.73901i	0.239051	+	0.414049i	−0.721391	+	0.692528i	$0.756497\pi$
$132$	6.09017	+	2.62866i	0.530081	+	0.228795i
$133$	−0.472136	+	0.914287i	−0.0409394	+	0.0792788i
$134$	−1.02786	−	3.16344i	−0.0887939	−	0.273280i
$135$	−1.09464	+	10.4148i	−0.0942113	+	0.896361i
$136$	−6.95942	−	3.09853i	−0.596765	−	0.265697i
$137$	12.0674	+	13.4022i	1.03099	+	1.14503i	0.989300	+	0.145897i	$0.0466067\pi$
$137$	12.0674	+	13.4022i	1.03099	+	1.14503i	0.0416875	+	0.999131i	$0.486727\pi$
$138$	1.95630	−	0.415823i	0.166531	−	0.0353972i
$139$	−1.71598	−	16.3265i	−0.145548	−	1.38479i	−0.786679	−	0.617362i	$-0.788201\pi$
$139$	−1.71598	−	16.3265i	−0.145548	−	1.38479i	0.641131	−	0.767431i	$-0.278465\pi$
$140$	−0.500000	−	0.363271i	−0.0422577	−	0.0307020i
$141$	0.618034	+	1.90211i	0.0520479	+	0.160187i
$142$	−4.66312	+	8.07676i	−0.391320	+	0.677787i
$143$	−13.1317	−	9.31364i	−1.09813	−	0.778846i
$144$	1.00000			0.0833333
$145$	1.80902	+	5.56758i	0.150231	+	0.462363i
$146$	−6.17916	+	2.75114i	−0.511391	+	0.227686i
$147$	−12.6878	−	5.64898i	−1.04647	−	0.465920i
$148$	−3.75920	−	4.17501i	−0.309004	−	0.343184i
$149$	−2.04449	+	0.434571i	−0.167492	+	0.0356014i	−0.290894	−	0.956755i	$-0.593953\pi$
$149$	−2.04449	+	0.434571i	−0.167492	+	0.0356014i	0.123403	+	0.992357i	$0.460619\pi$
$150$	3.38761	+	1.50826i	0.276597	+	0.123149i
$151$	−9.89919	−	7.19218i	−0.805584	−	0.585291i	0.106963	−	0.994263i	$-0.465887\pi$
$151$	−9.89919	−	7.19218i	−0.805584	−	0.585291i	−0.912547	+	0.408972i	$0.865887\pi$
$152$	4.30146	+	0.705295i	0.348894	+	0.0572070i
$153$	−7.61803			−0.615882
$154$	0.383711	−	0.682477i	0.0309203	−	0.0549956i
$155$	4.11803	+	7.13264i	0.330768	+	0.572908i
$156$	−9.49606	−	2.01845i	−0.760293	−	0.161605i
$157$	−0.667097	+	6.34700i	−0.0532401	+	0.506546i	0.935111	+	0.354355i	$0.115300\pi$
$157$	−0.667097	+	6.34700i	−0.0532401	+	0.506546i	−0.988351	+	0.152191i	$0.951367\pi$
$158$	1.01478	+	9.65502i	0.0807319	+	0.768112i
$159$	6.94427	−	21.3723i	0.550717	−	1.69493i
$160$	−0.809017	+	2.48990i	−0.0639584	+	0.196844i
$161$	−0.0246758	−	0.234775i	−0.00194473	−	0.0185028i
$162$	−10.0490	+	4.47410i	−0.789524	+	0.351519i
$163$	4.00000	+	12.3107i	0.313304	+	0.964251i	0.976447	+	0.215758i	$0.0692223\pi$
$163$	4.00000	+	12.3107i	0.313304	+	0.964251i	−0.663143	+	0.748493i	$0.730778\pi$
$164$	−7.94427			−0.620343
$165$	−5.17758	+	16.5763i	−0.403074	+	1.29046i
$166$	−1.26393	−	2.18919i	−0.0981002	−	0.169914i
$167$	−16.6285	−	3.53450i	−1.28675	−	0.273508i	−0.486770	−	0.873530i	$-0.661825\pi$
$167$	−16.6285	−	3.53450i	−1.28675	−	0.273508i	−0.799983	+	0.600023i	$0.795158\pi$
$168$	0.0493516	−	0.469550i	0.00380756	−	0.0362265i
$169$	9.64915	+	4.29608i	0.742242	+	0.330467i
$170$	6.16312	−	18.9681i	0.472690	−	1.45479i
$171$	4.21645	−	1.10524i	0.322440	−	0.0845200i
$172$	−2.19098	+	1.59184i	−0.167061	+	0.121377i
$173$	1.99907	−	19.0198i	0.151986	−	1.44605i	−0.606874	−	0.794798i	$-0.707577\pi$
$173$	1.99907	−	19.0198i	0.151986	−	1.44605i	0.758860	−	0.651254i	$-0.225757\pi$
$174$	−2.99244	+	3.32344i	−0.226857	+	0.251950i
$175$	0.218847	−	0.379054i	0.0165433	−	0.0286538i
$176$	−3.25181	−	0.652498i	−0.245114	−	0.0491839i
$177$	4.70820	−	8.15485i	0.353890	−	0.612956i
$178$	0.399187	+	1.22857i	0.0299203	+	0.0920853i
$179$	−9.47214	−	6.88191i	−0.707981	−	0.514378i	0.174541	−	0.984650i	$-0.444156\pi$
$179$	−9.47214	−	6.88191i	−0.707981	−	0.514378i	−0.882522	+	0.470272i	$0.844156\pi$
$180$	0.273659	+	2.60369i	0.0203973	+	0.194068i
$181$	10.1949	+	11.3226i	0.757782	+	0.841603i	0.991419	−	0.130721i	$-0.0417293\pi$
$181$	10.1949	+	11.3226i	0.757782	+	0.841603i	−0.233637	+	0.972324i	$0.575063\pi$
$182$	−0.354102	+	1.08981i	−0.0262478	+	0.0807824i
$183$	22.4164	−	16.2865i	1.65707	−	1.20393i
$184$	−0.913545	+	0.406737i	−0.0673475	+	0.0299850i
$185$	9.84171	−	10.9303i	0.723577	−	0.803614i
$186$	−3.14590	+	5.44886i	−0.230668	+	0.399529i
$187$	24.7724	+	4.97075i	1.81154	+	0.363497i
$188$	−0.500000	−	0.866025i	−0.0364662	−	0.0631614i
$189$	0.291796	+	0.898056i	0.0212250	+	0.0653240i
$190$	−0.659238	+	11.3927i	−0.0478262	+	0.826512i
$191$	11.0902	−	8.05748i	0.802457	−	0.583019i	−0.109177	−	0.994022i	$-0.534822\pi$
$191$	11.0902	−	8.05748i	0.802457	−	0.583019i	0.911634	+	0.411004i	$0.134822\pi$
$192$	−1.95630	+	0.415823i	−0.141183	+	0.0300095i
$193$	18.0140	−	3.82899i	1.29667	−	0.275616i	0.492657	−	0.870224i	$-0.336026\pi$
$193$	18.0140	−	3.82899i	1.29667	−	0.275616i	0.804016	+	0.594607i	$0.202692\pi$
$194$	−0.646021	−	6.14648i	−0.0463816	−	0.441292i
$195$	2.65674	−	25.2772i	0.190253	−	1.81014i
$196$	6.79252	+	1.44380i	0.485180	+	0.103128i
$197$	5.43769			0.387420			0.193710	−	0.981059i	$-0.437948\pi$
$197$	5.43769			0.387420			0.193710	+	0.981059i	$0.437948\pi$
$198$	−3.23607	+	0.726543i	−0.229977	+	0.0516331i
$199$	−7.07295	+	12.2507i	−0.501388	+	0.868430i	0.498611	+	0.866826i	$0.333844\pi$
$199$	−7.07295	+	12.2507i	−0.501388	+	0.868430i	−0.999999	+	0.00160354i	$0.999490\pi$
$200$	−1.81359	−	0.385489i	−0.128240	−	0.0272582i
$201$	5.38197	+	3.91023i	0.379615	+	0.275806i
$202$	−5.85410	+	4.25325i	−0.411893	+	0.299258i
$203$	0.353210	+	0.392279i	0.0247905	+	0.0275326i
$204$	14.9031	−	3.16776i	1.04343	−	0.221787i
$205$	−2.17402	−	20.6844i	−0.151840	−	1.44466i
$206$	0.934931	−	8.89527i	0.0651397	−	0.619763i
$207$	−0.669131	+	0.743145i	−0.0465078	+	0.0516521i
$208$	4.85410			0.336571
$209$	−14.4322	+	0.842810i	−0.998299	+	0.0582984i
$210$	1.23607			0.0852968
$211$	13.4429	−	14.9299i	0.925451	−	1.02782i	−0.0740821	−	0.997252i	$-0.523603\pi$
$211$	13.4429	−	14.9299i	0.925451	−	1.02782i	0.999533	−	0.0305650i	$-0.00973064\pi$
$212$	−1.17449	+	11.1745i	−0.0806642	+	0.767469i
$213$	−1.94971	−	18.5503i	−0.133592	−	1.27105i
$214$	4.97894	−	1.05831i	0.340353	−	0.0723443i
$215$	−4.74425	−	5.26902i	−0.323555	−	0.359344i
$216$	3.23607	−	2.35114i	0.220187	−	0.159975i
$217$	0.600813	+	0.436516i	0.0407858	+	0.0296327i
$218$	−18.6730	−	3.96907i	−1.26470	−	0.268819i
$219$	6.76393	−	11.7155i	0.457064	−	0.791658i
$220$	0.809017	−	8.64527i	0.0545439	−	0.582864i
$221$	−36.9787			−2.48746
$222$	10.9905	+	2.33611i	0.737636	+	0.156789i
$223$	−1.20499	+	11.4647i	−0.0806921	+	0.767734i	0.877107	+	0.480295i	$0.159470\pi$
$223$	−1.20499	+	11.4647i	−0.0806921	+	0.767734i	−0.957799	+	0.287439i	$0.907196\pi$
$224$	0.0246758	+	0.234775i	0.00164872	+	0.0156865i
$225$	−1.81359	+	0.385489i	−0.120906	+	0.0256993i
$226$	17.6403	−	3.74957i	1.17342	−	0.249418i
$227$	−5.66312	+	4.11450i	−0.375874	+	0.273089i	−0.759643	−	0.650341i	$-0.774626\pi$
$227$	−5.66312	+	4.11450i	−0.375874	+	0.273089i	0.383768	+	0.923429i	$0.374626\pi$
$228$	−7.78903	+	3.91548i	−0.515841	+	0.259309i
$229$	1.63525	+	5.03280i	0.108061	+	0.332577i	0.990437	−	0.137969i	$-0.0440573\pi$
$229$	1.63525	+	5.03280i	0.108061	+	0.332577i	−0.882376	+	0.470545i	$0.844057\pi$
$230$	−1.30902	−	2.26728i	−0.0863140	−	0.149500i
$231$	0.181442	+	1.55535i	0.0119380	+	0.102335i
$232$	1.11803	−	1.93649i	0.0734025	−	0.127137i
$233$	−11.2776	+	12.5250i	−0.738820	+	0.820543i	−0.989040	−	0.147646i	$-0.952830\pi$
$233$	−11.2776	+	12.5250i	−0.738820	+	0.820543i	0.250220	+	0.968189i	$0.419497\pi$
$234$	4.43444	−	1.97434i	0.289889	−	0.129067i
$235$	2.11803	−	1.53884i	0.138165	−	0.100383i
$236$	−1.45492	+	4.47777i	−0.0947069	+	0.291478i
$237$	−12.9921	−	14.4292i	−0.843928	−	0.937277i
$238$	−0.187981	−	1.78852i	−0.0121850	−	0.115933i
$239$	7.82624	+	5.68609i	0.506237	+	0.367803i	0.811394	−	0.584499i	$-0.198709\pi$
$239$	7.82624	+	5.68609i	0.506237	+	0.367803i	−0.305157	+	0.952302i	$0.598709\pi$
$240$	−1.61803	−	4.97980i	−0.104444	−	0.321444i
$241$	−5.16312	+	8.94278i	−0.332586	+	0.576055i	−0.983018	−	0.183509i	$-0.941254\pi$
$241$	−5.16312	+	8.94278i	−0.332586	+	0.576055i	0.650432	+	0.759564i	$0.274588\pi$
$242$	10.9971	−	0.251049i	0.706923	−	0.0161380i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−9.27020	+	10.2956i	−0.593464	+	0.659109i
$245$	−1.90036	+	18.0807i	−0.121410	+	1.15514i
$246$	12.8541	−	9.33905i	0.819548	−	0.595436i
$247$	20.4671	−	5.36496i	1.30229	−	0.341364i
$248$	0.972136	−	2.99193i	0.0617307	−	0.189988i
$249$	4.61864	+	2.05635i	0.292694	+	0.130316i
$250$	−0.860904	+	8.19095i	−0.0544483	+	0.518041i
$251$	13.8368	+	2.94110i	0.873370	+	0.185640i	0.622727	−	0.782439i	$-0.286025\pi$
$251$	13.8368	+	2.94110i	0.873370	+	0.185640i	0.250643	+	0.968080i	$0.419358\pi$
$252$	0.118034	+	0.204441i	0.00743544	+	0.0128786i
$253$	2.66078	−	1.97996i	0.167282	−	0.124479i
$254$	19.5623			1.22745
$255$	12.3262	+	37.9363i	0.771899	+	2.37566i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	−1.46340	−	13.9233i	−0.0912843	−	0.868512i	−0.940346	−	0.340219i	$-0.889499\pi$
$257$	−1.46340	−	13.9233i	−0.0912843	−	0.868512i	0.849062	−	0.528293i	$-0.177168\pi$
$258$	1.67376	−	5.15131i	0.104204	−	0.320707i
$259$	0.409830	−	1.26133i	0.0254656	−	0.0783751i
$260$	1.32837	+	12.6386i	0.0823819	+	0.783812i
$261$	0.233733	−	2.22382i	0.0144677	−	0.137651i
$262$	5.35256	+	1.13772i	0.330682	+	0.0702886i
$263$	3.89919	+	6.75359i	0.240434	+	0.416444i	0.960838	−	0.277111i	$-0.0893769\pi$
$263$	3.89919	+	6.75359i	0.240434	+	0.416444i	−0.720404	+	0.693555i	$0.756044\pi$
$264$	6.02859	−	2.76696i	0.371034	−	0.170295i
$265$	−29.4164			−1.80704
$266$	0.363527	+	0.962643i	0.0222893	+	0.0590234i
$267$	−2.09017	−	1.51860i	−0.127916	−	0.0929366i
$268$	−3.03867	−	1.35290i	−0.185616	−	0.0826417i
$269$	−0.319109	+	0.0678287i	−0.0194564	+	0.00413559i	−0.217630	−	0.976031i	$-0.569832\pi$
$269$	−0.319109	+	0.0678287i	−0.0194564	+	0.00413559i	0.198173	+	0.980167i	$0.436499\pi$
$270$	7.00723	+	7.78231i	0.426446	+	0.473617i
$271$	0.348943	+	0.155360i	0.0211968	+	0.00943742i	0.417308	−	0.908765i	$-0.362974\pi$
$271$	0.348943	+	0.155360i	0.0211968	+	0.00943742i	−0.396111	+	0.918203i	$0.629640\pi$
$272$	−6.95942	+	3.09853i	−0.421977	+	0.187876i
$273$	−0.708204	−	2.17963i	−0.0428625	−	0.131917i
$274$	18.0344			1.08950
$275$	6.14896	−	0.0701768i	0.370796	−	0.00423182i
$276$	1.00000	−	1.73205i	0.0601929	−	0.104257i
$277$	4.45492	+	13.7108i	0.267670	+	0.823803i	0.991066	+	0.133370i	$0.0425800\pi$
$277$	4.45492	+	13.7108i	0.267670	+	0.823803i	−0.723396	+	0.690433i	$0.757420\pi$
$278$	−13.2812	−	9.64932i	−0.796551	−	0.578728i
$279$	−0.328836	−	3.12866i	−0.0196869	−	0.187308i
$280$	−0.604528	+	0.128496i	−0.0361275	+	0.00767913i
$281$	11.0823	+	12.3082i	0.661117	+	0.734245i	0.976690	−	0.214656i	$-0.0688632\pi$
$281$	11.0823	+	12.3082i	0.661117	+	0.734245i	−0.315572	+	0.948902i	$0.602196\pi$
$282$	1.82709	+	0.813473i	0.108802	+	0.0484416i
$283$	−2.11525	+	20.1252i	−0.125738	+	1.19632i	0.731661	+	0.681668i	$0.238745\pi$
$283$	−2.11525	+	20.1252i	−0.125738	+	1.19632i	−0.857400	+	0.514651i	$0.827921\pi$
$284$	2.88197	+	8.86978i	0.171013	+	0.526325i
$285$	−12.3262	−	19.2087i	−0.730143	−	1.13783i
$286$	−15.7082	+	3.52671i	−0.928846	+	0.208539i
$287$	−0.937694	−	1.62413i	−0.0553503	−	0.0958696i
$288$	0.669131	−	0.743145i	0.0394289	−	0.0437902i
$289$	37.4868	−	16.6902i	2.20511	−	0.981777i
$290$	5.34799	+	2.38108i	0.314045	+	0.139822i
$291$	8.27091	+	9.18578i	0.484849	+	0.538480i
$292$	−2.09017	+	6.43288i	−0.122318	+	0.376456i
$293$	−6.80902	+	4.94704i	−0.397787	+	0.289009i	−0.768639	−	0.639683i	$-0.779066\pi$
$293$	−6.80902	+	4.94704i	−0.397787	+	0.289009i	0.370852	+	0.928692i	$0.379066\pi$
$294$	−12.6878	+	5.64898i	−0.739968	+	0.329455i
$295$	−12.0569	−	2.56277i	−0.701979	−	0.149210i
$296$	−5.61803			−0.326542
$297$	−8.76393	+	9.95959i	−0.508535	+	0.577914i
$298$	−1.04508	+	1.81014i	−0.0605401	+	0.104859i
$299$	−3.24803	+	3.60730i	−0.187838	+	0.208616i
$300$	3.38761	−	1.50826i	0.195584	−	0.0870796i
$301$	−0.584048	−	0.260035i	−0.0336640	−	0.0149882i
$302$	−11.9687	+	2.54402i	−0.688720	+	0.146392i
$303$	4.47214	−	13.7638i	0.256917	−	0.790711i
$304$	3.40238	−	2.72467i	0.195140	−	0.156271i
$305$	−29.3435	−	21.3193i	−1.68020	−	1.22074i
$306$	−5.09746	+	5.66130i	−0.291402	+	0.323635i
$307$	12.6353	+	21.8849i	0.721132	+	1.24904i	0.960546	+	0.278120i	$0.0897113\pi$
$307$	12.6353	+	21.8849i	0.721132	+	1.24904i	−0.239414	+	0.970918i	$0.576955\pi$
$308$	−0.250426	−	0.741819i	−0.0142694	−	0.0422691i
$309$	8.94427	+	15.4919i	0.508822	+	0.881305i
$310$	8.05609	+	1.71237i	0.457555	+	0.0972564i
$311$	−3.69098	−	2.68166i	−0.209296	−	0.152063i	0.478199	−	0.878252i	$-0.341290\pi$
$311$	−3.69098	−	2.68166i	−0.209296	−	0.152063i	−0.687495	+	0.726189i	$0.741290\pi$
$312$	−7.85410	+	5.70634i	−0.444651	+	0.323058i
$313$	−15.3527	−	17.0509i	−0.867787	−	0.963775i	0.131835	−	0.991272i	$-0.457913\pi$
$313$	−15.3527	−	17.0509i	−0.867787	−	0.963775i	−0.999622	+	0.0274968i	$0.991246\pi$
$314$	4.27037	+	4.74273i	0.240991	+	0.267647i
$315$	−0.500000	+	0.363271i	−0.0281718	+	0.0204680i
$316$	7.85410	+	5.70634i	0.441828	+	0.321007i
$317$	14.3868	+	3.05801i	0.808043	+	0.171755i	0.593369	−	0.804931i	$-0.297798\pi$
$317$	14.3868	+	3.05801i	0.808043	+	0.171755i	0.214674	+	0.976686i	$0.431131\pi$
$318$	−11.2361	−	19.4614i	−0.630087	−	1.09134i
$319$	−2.21109	+	7.07892i	−0.123797	+	0.396343i
$320$	1.30902	+	2.26728i	0.0731763	+	0.126745i
$321$	−6.81198	+	7.56547i	−0.380207	+	0.422263i
$322$	−0.190983	−	0.138757i	−0.0106431	−	0.00773264i
$323$	−25.9194	+	20.7567i	−1.44219	+	1.15493i
$324$	−3.39919	+	10.4616i	−0.188844	+	0.581201i
$325$	−8.80333	+	1.87121i	−0.488321	+	0.103796i
$326$	11.8252	+	5.26491i	0.654936	+	0.291596i
$327$	34.8795	−	15.5293i	1.92884	−	0.858775i
$328$	−5.31576	+	5.90374i	−0.293513	+	0.325980i
$329$	0.118034	−	0.204441i	0.00650742	−	0.0112712i
$330$	8.85410	+	14.9394i	0.487402	+	0.822386i
$331$	−17.0344			−0.936298			−0.468149	−	0.883650i	$-0.655079\pi$
$331$	−17.0344			−0.936298			−0.468149	+	0.883650i	$0.655079\pi$
$332$	−2.47262	−	0.525572i	−0.135703	−	0.0288445i
$333$	−5.13233	+	2.28506i	−0.281250	+	0.125221i
$334$	−13.7533	+	9.99235i	−0.752546	+	0.546757i
$335$	2.69098	−	8.28199i	0.147024	−	0.452494i
$336$	−0.315921	−	0.350865i	−0.0172349	−	0.0191413i
$337$	21.0115	+	9.35494i	1.14457	+	0.509596i	0.889323	−	0.457279i	$-0.151176\pi$
$337$	21.0115	+	9.35494i	1.14457	+	0.509596i	0.255249	+	0.966875i	$0.417843\pi$
$338$	9.64915	−	4.29608i	0.524844	−	0.233676i
$339$	−24.1348	+	26.8044i	−1.31082	+	1.45582i
$340$	−9.97214	−	17.2722i	−0.540815	−	0.936719i
$341$	−0.972136	+	10.3884i	−0.0526441	+	0.562562i
$342$	2.00000	−	3.87298i	0.108148	−	0.209427i
$343$	1.01722	+	3.13068i	0.0549248	+	0.169041i
$344$	−0.283084	+	2.69337i	−0.0152629	+	0.145217i
$345$	4.78339	+	2.12970i	0.257529	+	0.114659i
$346$	−12.7969	−	14.2124i	−0.687964	−	0.764061i
$347$	−0.747238	+	0.158830i	−0.0401139	+	0.00852646i	−0.227925	−	0.973679i	$-0.573194\pi$
$347$	−0.747238	+	0.158830i	−0.0401139	+	0.00852646i	0.187811	+	0.982205i	$0.439861\pi$
$348$	0.467465	+	4.44764i	0.0250588	+	0.238418i
$349$	−24.8435	−	18.0498i	−1.32984	−	0.966185i	−0.999753	−	0.0222347i	$-0.992922\pi$
$349$	−24.8435	−	18.0498i	−1.32984	−	0.966185i	−0.330087	−	0.943950i	$-0.607078\pi$
$350$	−0.135255	−	0.416272i	−0.00722968	−	0.0222507i
$351$	9.70820	−	16.8151i	0.518186	−	0.897524i
$352$	−2.66078	+	1.97996i	−0.141820	+	0.105532i
$353$	4.00000			0.212899			0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000			0.212899			0.106449	+	0.994318i	$0.466052\pi$
$354$	−2.90983	−	8.95554i	−0.154656	−	0.475981i
$355$	−22.3055	+	9.93105i	−1.18385	+	0.527085i
$356$	1.18011	+	0.525421i	0.0625459	+	0.0278472i
$357$	2.40669	+	2.67290i	0.127376	+	0.141465i
$358$	−11.4524	+	2.43427i	−0.605276	+	0.128655i
$359$	0.748797	+	0.333386i	0.0395200	+	0.0175954i	0.426401	−	0.904534i	$-0.359781\pi$
$359$	0.748797	+	0.333386i	0.0395200	+	0.0175954i	−0.386881	+	0.922129i	$0.626448\pi$
$360$	2.11803	+	1.53884i	0.111630	+	0.0811041i
$361$	11.3345	−	15.2489i	0.596554	−	0.802573i
$362$	15.2361			0.800790
$363$	−17.4986	+	13.3341i	−0.918439	+	0.699859i
$364$	0.572949	+	0.992377i	0.0300307	+	0.0520147i
$365$	−17.3212	−	3.68174i	−0.906635	−	0.192711i
$366$	2.89630	−	27.5564i	0.151392	−	1.44040i
$367$	−2.53113	−	24.0821i	−0.132124	−	1.25708i	−0.836785	−	0.547532i	$-0.815567\pi$
$367$	−2.53113	−	24.0821i	−0.132124	−	1.25708i	0.704660	−	0.709545i	$-0.251099\pi$
$368$	−0.309017	+	0.951057i	−0.0161086	+	0.0495772i
$369$	−2.45492	+	7.55545i	−0.127798	+	0.393321i
$370$	−1.53743	−	14.6276i	−0.0799270	−	0.760454i
$371$	−2.42316	+	1.07886i	−0.125804	+	0.0560116i
$372$	1.94427	+	5.98385i	0.100806	+	0.310248i
$373$	29.3607			1.52024			0.760119	−	0.649784i	$-0.225141\pi$
$373$	29.3607			1.52024			0.760119	+	0.649784i	$0.225141\pi$
$374$	20.2699	−	15.0834i	1.04813	−	0.779943i
$375$	−8.23607	−	14.2653i	−0.425309	−	0.736656i
$376$	−0.978148	−	0.207912i	−0.0504441	−	0.0107222i
$377$	1.13456	−	10.7946i	0.0584329	−	0.555952i
$378$	0.862635	+	0.384070i	0.0443692	+	0.0197544i
$379$	−0.208204	+	0.640786i	−0.0106947	+	0.0329150i	−0.956261	−	0.292513i	$-0.905508\pi$
$379$	−0.208204	+	0.640786i	−0.0106947	+	0.0329150i	0.945567	+	0.325428i	$0.105508\pi$
$380$	8.02530	+	8.11311i	0.411689	+	0.416194i
$381$	−31.6525	+	22.9969i	−1.62161	+	1.17817i
$382$	1.43290	−	13.6331i	0.0733134	−	0.697531i
$383$	13.8938	−	15.4306i	0.709939	−	0.788467i	−0.274986	−	0.961448i	$-0.588673\pi$
$383$	13.8938	−	15.4306i	0.709939	−	0.788467i	0.984925	+	0.172981i	$0.0553399\pi$
$384$	−1.00000	+	1.73205i	−0.0510310	+	0.0883883i
$385$	1.86294	−	0.855039i	0.0949441	−	0.0435768i
$386$	9.20820	−	15.9491i	0.468685	−	0.811787i
$387$	0.836881	+	2.57565i	0.0425411	+	0.130928i
$388$	−5.00000	−	3.63271i	−0.253837	−	0.184423i
$389$	−1.12874	−	10.7392i	−0.0572293	−	0.544500i	−0.985147	−	0.171714i	$-0.945069\pi$
$389$	−1.12874	−	10.7392i	−0.0572293	−	0.544500i	0.927918	−	0.372786i	$-0.121597\pi$
$390$	−17.0069	−	18.8881i	−0.861178	−	0.956435i
$391$	2.35410	−	7.24518i	0.119052	−	0.366405i
$392$	5.61803	−	4.08174i	0.283754	−	0.206159i
$393$	−9.99809	+	4.45144i	−0.504337	+	0.224545i
$394$	3.63853	−	4.04099i	0.183306	−	0.203582i
$395$	−12.7082	+	22.0113i	−0.639419	+	1.10751i
$396$	−1.62543	+	2.89102i	−0.0816807	+	0.145279i
$397$	9.47214	+	16.4062i	0.475393	+	0.823405i	0.999603	−	0.0281845i	$-0.00897259\pi$
$397$	9.47214	+	16.4062i	0.475393	+	0.823405i	−0.524210	+	0.851589i	$0.675639\pi$
$398$	4.37132	+	13.4535i	0.219115	+	0.674365i
$399$	−1.71985	−	1.13024i	−0.0861004	−	0.0565826i
$400$	−1.50000	+	1.08981i	−0.0750000	+	0.0544907i
$401$	−1.03266	+	0.219498i	−0.0515685	+	0.0109612i	−0.233624	−	0.972327i	$-0.575058\pi$
$401$	−1.03266	+	0.219498i	−0.0515685	+	0.0109612i	0.182055	+	0.983288i	$0.441725\pi$
$402$	6.50710	−	1.38313i	0.324545	−	0.0689841i
$403$	−1.59620	−	15.1869i	−0.0795125	−	0.756511i
$404$	−0.756375	+	7.19643i	−0.0376311	+	0.358036i
$405$	−28.1691	−	5.98752i	−1.39973	−	0.297522i
$406$	0.527864			0.0261975
$407$	18.1803	−	4.08174i	0.901166	−	0.202324i
$408$	7.61803	−	13.1948i	0.377149	−	0.653241i
$409$	2.38442	+	0.506825i	0.117902	+	0.0250609i	0.266485	−	0.963839i	$-0.414138\pi$
$409$	2.38442	+	0.506825i	0.117902	+	0.0250609i	−0.148583	+	0.988900i	$0.547471\pi$
$410$	−16.8262	−	12.2250i	−0.830989	−	0.603749i
$411$	−29.1803	+	21.2008i	−1.43936	+	1.04576i
$412$	−5.98489	−	6.64689i	−0.294854	−	0.327469i
$413$	−1.08717	+	0.231085i	−0.0534960	+	0.0113709i
$414$	0.104528	+	0.994522i	0.00513729	+	0.0488781i
$415$	0.691773	−	6.58178i	0.0339578	−	0.323087i
$416$	3.24803	−	3.60730i	0.159248	−	0.176862i
$417$	32.8328			1.60783
$418$	−9.03073	+	11.2892i	−0.441707	+	0.552173i
$419$	−2.34752			−0.114684			−0.0573420	−	0.998355i	$-0.518263\pi$
$419$	−2.34752			−0.114684			−0.0573420	+	0.998355i	$0.518263\pi$
$420$	0.827091	−	0.918578i	0.0403579	−	0.0448220i
$421$	−1.19916	+	11.4093i	−0.0584437	+	0.556055i	0.925647	+	0.378388i	$0.123522\pi$
$421$	−1.19916	+	11.4093i	−0.0584437	+	0.556055i	−0.984091	+	0.177667i	$0.943145\pi$
$422$	−2.09999	−	19.9801i	−0.102226	−	0.972617i
$423$	−0.978148	+	0.207912i	−0.0475592	+	0.0101090i
$424$	7.51840	+	8.35003i	0.365126	+	0.405513i
$425$	11.4271	−	8.30224i	0.554293	−	0.402718i
$426$	−15.0902	−	10.9637i	−0.731121	−	0.531191i
$427$	−3.19904	−	0.679977i	−0.154812	−	0.0329064i
$428$	2.54508	−	4.40822i	0.123021	−	0.213079i
$429$	21.2705	−	24.1724i	1.02695	−	1.16706i
$430$	−7.09017			−0.341918
$431$	12.2541	+	2.60469i	0.590259	+	0.125463i	0.493352	−	0.869830i	$-0.335772\pi$
$431$	12.2541	+	2.60469i	0.590259	+	0.125463i	0.0969075	+	0.995293i	$0.469105\pi$
$432$	0.418114	−	3.97809i	0.0201165	−	0.191396i
$433$	1.91561	+	18.2258i	0.0920585	+	0.875878i	0.938936	+	0.344091i	$0.111813\pi$
$433$	1.91561	+	18.2258i	0.0920585	+	0.875878i	−0.846878	+	0.531787i	$0.821521\pi$
$434$	0.726417	−	0.154405i	0.0348691	−	0.00741166i
$435$	−11.4524	+	2.43427i	−0.549098	+	0.116714i
$436$	−15.4443	+	11.2209i	−0.739646	+	0.537385i
$437$	−0.251807	+	4.35162i	−0.0120455	+	0.208166i
$438$	−4.18034	−	12.8658i	−0.199744	−	0.614750i
$439$	−8.91641	−	15.4437i	−0.425557	−	0.737086i	0.570915	−	0.821009i	$-0.306588\pi$
$439$	−8.91641	−	15.4437i	−0.425557	−	0.737086i	−0.996472	+	0.0839227i	$0.973255\pi$
$440$	−5.88335	−	6.38603i	−0.280478	−	0.304442i
$441$	3.47214	−	6.01392i	0.165340	−	0.286377i
$442$	−24.7436	+	27.4805i	−1.17693	+	1.30712i
$443$	−35.8245	+	15.9501i	−1.70207	+	0.757812i	−0.703168	+	0.711024i	$0.748232\pi$
$443$	−35.8245	+	15.9501i	−1.70207	+	0.757812i	−0.998905	+	0.0467877i	$0.985102\pi$
$444$	9.09017	−	6.60440i	0.431400	−	0.313431i
$445$	−1.04508	+	3.21644i	−0.0495418	+	0.152474i
$446$	7.71365	+	8.56687i	0.365252	+	0.405653i
$447$	−0.436965	−	4.15744i	−0.0206677	−	0.196640i
$448$	0.190983	+	0.138757i	0.00902310	+	0.00655567i
$449$	−1.88197	−	5.79210i	−0.0888155	−	0.273346i	0.896777	−	0.442482i	$-0.145902\pi$
$449$	−1.88197	−	5.79210i	−0.0888155	−	0.273346i	−0.985593	+	0.169137i	$0.945902\pi$
$450$	−0.927051	+	1.60570i	−0.0437016	+	0.0756934i
$451$	12.9128	−	22.9670i	0.608041	−	1.08148i
$452$	9.01722	−	15.6183i	0.424134	−	0.734622i
$453$	16.3751	−	18.1863i	0.769367	−	0.854469i
$454$	−0.731699	+	6.96165i	−0.0343403	+	0.326727i
$455$	−2.42705	+	1.76336i	−0.113782	+	0.0826674i
$456$	−2.30211	+	8.40835i	−0.107806	+	0.393757i
$457$	−7.69098	+	23.6704i	−0.359769	+	1.10726i	0.593423	+	0.804891i	$0.297776\pi$
$457$	−7.69098	+	23.6704i	−0.359769	+	1.10726i	−0.953192	+	0.302365i	$0.902224\pi$
$458$	4.83430	+	2.15237i	0.225892	+	0.100574i
$459$	−3.18521	+	30.3052i	−0.148673	+	1.41453i
$460$	−2.56082	−	0.544320i	−0.119399	−	0.0253790i
$461$	13.8262	+	23.9477i	0.643952	+	1.11536i	0.984542	+	0.175146i	$0.0560397\pi$
$461$	13.8262	+	23.9477i	0.643952	+	1.11536i	−0.340590	+	0.940212i	$0.610627\pi$
$462$	1.27726	+	0.905894i	0.0594235	+	0.0421460i
$463$	−2.70820			−0.125861			−0.0629305	−	0.998018i	$-0.520045\pi$
$463$	−2.70820			−0.125861			−0.0629305	+	0.998018i	$0.520045\pi$
$464$	−0.690983	−	2.12663i	−0.0320781	−	0.0987262i
$465$	−15.0480	+	6.69982i	−0.697836	+	0.310697i
$466$	1.76173	+	16.7618i	0.0816107	+	0.776474i
$467$	8.14590	−	25.0705i	0.376947	−	1.16012i	−0.565208	−	0.824948i	$-0.691204\pi$
$467$	8.14590	−	25.0705i	0.376947	−	1.16012i	0.942156	−	0.335176i	$-0.108796\pi$
$468$	1.50000	−	4.61653i	0.0693375	−	0.213399i
$469$	−0.0820777	−	0.780917i	−0.00378999	−	0.0360594i
$470$	0.273659	−	2.60369i	0.0126230	−	0.120099i
$471$	−12.4850	−	2.65377i	−0.575279	−	0.122279i
$472$	2.35410	+	4.07742i	0.108356	+	0.187679i
$473$	−1.04077	−	8.92160i	−0.0478545	−	0.410215i
$474$	−19.4164			−0.891825
$475$	−5.12017	+	6.25301i	−0.234929	+	0.286908i
$476$	−1.45492	−	1.05706i	−0.0666859	−	0.0484502i
$477$	10.2647	+	4.57012i	0.469986	+	0.209251i
$478$	9.46237	−	2.01129i	0.432799	−	0.0919942i
$479$	−14.6090	−	16.2249i	−0.667502	−	0.741337i	0.310352	−	0.950622i	$-0.399553\pi$
$479$	−14.6090	−	16.2249i	−0.667502	−	0.741337i	−0.977855	+	0.209285i	$0.932886\pi$
$480$	−4.78339	−	2.12970i	−0.218331	−	0.0972071i
$481$	−24.9129	+	11.0919i	−1.13593	+	0.505748i
$482$	3.19098	+	9.82084i	0.145345	+	0.447327i
$483$	0.472136			0.0214829
$484$	7.17195	−	8.34045i	0.325998	−	0.379111i
$485$	8.09017	−	14.0126i	0.367356	−	0.636279i
$486$	−3.09017	−	9.51057i	−0.140173	−	0.431408i
$487$	−25.8435	−	18.7764i	−1.17108	−	0.850839i	−0.179941	−	0.983677i	$-0.557591\pi$
$487$	−25.8435	−	18.7764i	−1.17108	−	0.850839i	−0.991138	+	0.132839i	$0.957591\pi$
$488$	1.44815	+	13.7782i	0.0655546	+	0.623710i
$489$	−25.3228	+	5.38253i	−1.14514	+	0.243406i
$490$	12.1650	+	13.5106i	0.549560	+	0.610348i
$491$	−26.6067	−	11.8460i	−1.20074	−	0.534605i	−0.293802	−	0.955866i	$-0.594921\pi$
$491$	−26.6067	−	11.8460i	−1.20074	−	0.534605i	−0.906939	+	0.421262i	$0.861587\pi$
$492$	1.66081	−	15.8015i	0.0748749	−	0.712387i
$493$	5.26393	+	16.2007i	0.237076	+	0.729644i
$494$	9.70820	−	18.7999i	0.436793	−	0.845846i
$495$	−7.97214	−	3.44095i	−0.358321	−	0.154659i
$496$	−1.57295	−	2.72443i	−0.0706275	−	0.122330i
$497$	−1.47318	+	1.63613i	−0.0660809	+	0.0733903i
$498$	4.61864	−	2.05635i	0.206966	−	0.0921472i
$499$	−24.8110	−	11.0466i	−1.11069	−	0.494513i	−0.232394	−	0.972622i	$-0.574656\pi$
$499$	−24.8110	−	11.0466i	−1.11069	−	0.494513i	−0.878301	+	0.478109i	$0.841322\pi$
$500$	5.51101	+	6.12059i	0.246460	+	0.273721i
$501$	10.5066	−	32.3359i	0.469399	−	1.44466i
$502$	11.4443	−	8.31475i	0.510783	−	0.371105i
$503$	26.4734	−	11.7867i	1.18039	−	0.525543i	0.279734	−	0.960078i	$-0.409754\pi$
$503$	26.4734	−	11.7867i	1.18039	−	0.525543i	0.900655	+	0.434534i	$0.143087\pi$
$504$	0.230909	+	0.0490813i	0.0102855	+	0.00218625i
$505$	−18.9443			−0.843009
$506$	0.309017	−	3.30220i	0.0137375	−	0.146801i
$507$	−10.5623	+	18.2945i	−0.469088	+	0.812485i
$508$	13.0897	−	14.5376i	0.580763	−	0.645003i
$509$	−9.94718	+	4.42877i	−0.440901	+	0.196302i	−0.615167	−	0.788397i	$-0.710911\pi$
$509$	−9.94718	+	4.42877i	−0.440901	+	0.196302i	0.174266	+	0.984699i	$0.444245\pi$
$510$	36.4400	+	16.2241i	1.61359	+	0.718417i
$511$	−1.56185	+	0.331983i	−0.0690924	+	0.0146860i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−2.63379	−	17.2355i	−0.116285	−	0.760967i
$514$	−11.3262	−	8.22899i	−0.499579	−	0.362965i
$515$	15.6686	−	17.4018i	0.690443	−	0.766814i
$516$	−2.70820	−	4.69075i	−0.119222	−	0.206499i
$517$	3.31641	−	0.0378495i	0.145855	−	0.00166462i
$518$	−0.663119	−	1.14856i	−0.0291358	−	0.0504646i
$519$	37.4134	+	7.95246i	1.64227	+	0.349074i
$520$	10.2812	+	7.46969i	0.450858	+	0.327568i
$521$	−10.4271	+	7.57570i	−0.456817	+	0.331897i	−0.792282	−	0.610156i	$-0.791107\pi$
$521$	−10.4271	+	7.57570i	−0.456817	+	0.331897i	0.335464	+	0.942053i	$0.391107\pi$
$522$	−1.49622	−	1.66172i	−0.0654878	−	0.0727316i
$523$	15.2178	+	16.9011i	0.665428	+	0.739033i	0.977479	−	0.211033i	$-0.0676827\pi$
$523$	15.2178	+	16.9011i	0.665428	+	0.739033i	−0.312051	+	0.950065i	$0.601016\pi$
$524$	4.42705	−	3.21644i	0.193397	−	0.140511i
$525$	0.708204	+	0.514540i	0.0309086	+	0.0224564i
$526$	7.62796	+	1.62137i	0.332595	+	0.0706952i
$527$	11.9828	+	20.7548i	0.521978	+	0.904093i
$528$	1.97766	−	6.33158i	0.0860666	−	0.275547i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−19.6834	+	21.8607i	−0.854993	+	0.949566i
$531$	3.80902	+	2.76741i	0.165297	+	0.120095i
$532$	0.958630	+	0.373980i	0.0415619	+	0.0162141i
$533$	−11.9164	+	36.6749i	−0.516157	+	1.58857i
$534$	−2.52713	+	0.537159i	−0.109360	+	0.0232451i
$535$	12.1741	+	5.42027i	0.526333	+	0.234339i
$536$	−3.03867	+	1.35290i	−0.131251	+	0.0584365i
$537$	15.6686	−	17.4018i	0.676152	−	0.750942i
$538$	−0.163119	+	0.282530i	−0.00703256	+	0.0121807i
$539$	−15.2148	+	17.2905i	−0.655347	+	0.744756i
$540$	10.4721			0.450649
$541$	17.5858	+	3.73798i	0.756074	+	0.160709i	0.569793	−	0.821788i	$-0.307023\pi$
$541$	17.5858	+	3.73798i	0.756074	+	0.160709i	0.186281	+	0.982497i	$0.440357\pi$
$542$	0.348943	−	0.155360i	0.0149884	−	0.00667327i
$543$	−24.6525	+	17.9111i	−1.05794	+	0.768638i
$544$	−2.35410	+	7.24518i	−0.100931	+	0.310635i
$545$	−33.4423	−	37.1414i	−1.43251	−	1.59096i
$546$	−2.09366	−	0.932157i	−0.0896004	−	0.0398927i
$547$	11.1782	−	4.97686i	0.477946	−	0.212795i	−0.153601	−	0.988133i	$-0.549087\pi$
$547$	11.1782	−	4.97686i	0.477946	−	0.212795i	0.631547	+	0.775338i	$0.282420\pi$
$548$	12.0674	−	13.4022i	0.515494	−	0.572514i
$549$	6.92705	+	11.9980i	0.295639	+	0.512062i
$550$	4.06231	−	4.61653i	0.173217	−	0.196849i
$551$	−5.26393	−	8.20311i	−0.224251	−	0.349464i
$552$	−0.618034	−	1.90211i	−0.0263053	−	0.0809593i
$553$	−0.239558	+	2.27924i	−0.0101870	+	0.0969232i
$554$	13.1700	+	5.86368i	0.559542	+	0.249124i
$555$	19.6834	+	21.8607i	0.835515	+	0.927933i
$556$	−16.0577	+	3.41316i	−0.680997	+	0.144750i
$557$	−2.36200	−	22.4730i	−0.100081	−	0.952210i	−0.923195	−	0.384333i	$-0.874432\pi$
$557$	−2.36200	−	22.4730i	−0.100081	−	0.952210i	0.823113	−	0.567877i	$-0.192235\pi$
$558$	−2.54508	−	1.84911i	−0.107742	−	0.0782792i
$559$	4.06231	+	12.5025i	0.171817	+	0.528799i
$560$	−0.309017	+	0.535233i	−0.0130584	+	0.0226177i
$561$	−15.0659	+	48.2342i	−0.636082	+	2.03645i
$562$	16.5623			0.698639
$563$	8.38197	+	25.7970i	0.353258	+	1.08722i	0.957013	+	0.290046i	$0.0936705\pi$
$563$	8.38197	+	25.7970i	0.353258	+	1.08722i	−0.603755	+	0.797170i	$0.706329\pi$
$564$	1.82709	−	0.813473i	0.0769344	−	0.0342534i
$565$	43.1328	+	19.2040i	1.81461	+	0.807918i
$566$	13.5406	+	15.0383i	0.569153	+	0.632108i
$567$	−2.54000	+	0.539894i	−0.106670	+	0.0226734i
$568$	8.51994	+	3.79332i	0.357489	+	0.159164i
$569$	36.0344	+	26.1806i	1.51064	+	1.09755i	0.965891	+	0.258948i	$0.0833759\pi$
$569$	36.0344	+	26.1806i	1.51064	+	1.09755i	0.544751	+	0.838598i	$0.316624\pi$
$570$	−22.5227	−	3.69297i	−0.943374	−	0.154682i
$571$	−28.0344			−1.17320			−0.586602	−	0.809875i	$-0.699535\pi$
$571$	−28.0344			−1.17320			−0.586602	+	0.809875i	$0.699535\pi$
$572$	−7.88998	+	14.0333i	−0.329897	+	0.586762i
$573$	13.7082	+	23.7433i	0.572668	+	0.991891i
$574$	−1.83441	−	0.389915i	−0.0765666	−	0.0162747i
$575$	0.193806	−	1.84395i	0.00808229	−	0.0768978i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	4.46149	−	13.7311i	0.185734	−	0.571632i	−0.814226	−	0.580548i	$-0.802838\pi$
$577$	4.46149	−	13.7311i	0.185734	−	0.571632i	0.999960	+	0.00891658i	$0.00283827\pi$
$578$	12.6803	−	39.0261i	0.527433	−	1.62327i
$579$	3.85008	+	36.6310i	0.160004	+	1.52233i
$580$	5.34799	−	2.38108i	0.222063	−	0.0988689i
$581$	−0.184405	−	0.567541i	−0.00765042	−	0.0235456i
$582$	12.3607			0.512367
$583$	−30.3967	−	21.5588i	−1.25890	−	0.892875i
$584$	3.38197	+	5.85774i	0.139947	+	0.242395i
$585$	12.4305	+	2.64218i	0.513938	+	0.109241i
$586$	−0.879754	+	8.37030i	−0.0363423	+	0.345774i
$587$	−38.5337	−	17.1563i	−1.59045	−	0.708116i	−0.595033	−	0.803701i	$-0.702861\pi$
$587$	−38.5337	−	17.1563i	−1.59045	−	0.708116i	−0.995421	+	0.0955854i	$0.969528\pi$
$588$	−4.29180	+	13.2088i	−0.176991	+	0.544721i
$589$	−9.64341	−	9.74892i	−0.397350	−	0.401697i
$590$	−9.97214	+	7.24518i	−0.410546	+	0.298279i
$591$	−1.13679	+	10.8158i	−0.0467612	+	0.444903i
$592$	−3.75920	+	4.17501i	−0.154502	+	0.171592i
$593$	13.7639	−	23.8398i	0.565217	−	0.978984i	−0.431813	−	0.901963i	$-0.642126\pi$
$593$	13.7639	−	23.8398i	0.565217	−	0.978984i	0.997029	−	0.0770211i	$-0.0245409\pi$
$594$	1.53720	+	13.1771i	0.0630723	+	0.540665i
$595$	2.35410	−	4.07742i	0.0965088	−	0.167158i
$596$	0.645898	+	1.98787i	0.0264570	+	0.0814263i
$597$	−22.8885	−	16.6295i	−0.936766	−	0.680600i
$598$	0.507392	+	4.82751i	0.0207488	+	0.197412i
$599$	22.0671	+	24.5080i	0.901636	+	1.00137i	0.999981	+	0.00621572i	$0.00197854\pi$
$599$	22.0671	+	24.5080i	0.901636	+	1.00137i	−0.0983448	+	0.995152i	$0.531355\pi$
$600$	1.14590	−	3.52671i	0.0467811	−	0.143977i
$601$	8.61803	−	6.26137i	0.351537	−	0.255407i	−0.397977	−	0.917396i	$-0.630287\pi$
$601$	8.61803	−	6.26137i	0.351537	−	0.255407i	0.749514	+	0.661989i	$0.230287\pi$
$602$	−0.584048	+	0.260035i	−0.0238040	+	0.0105982i
$603$	−2.22569	+	2.47188i	−0.0906370	+	0.100663i
$604$	−6.11803	+	10.5967i	−0.248939	+	0.431175i
$605$	23.6786	+	16.3911i	0.962673	+	0.666394i
$606$	−7.23607	−	12.5332i	−0.293945	−	0.509128i
$607$	−13.1287	−	40.4059i	−0.532877	−	1.64003i	−0.748193	−	0.663481i	$-0.769078\pi$
$607$	−13.1287	−	40.4059i	−0.532877	−	1.64003i	0.215316	−	0.976544i	$-0.430922\pi$
$608$	0.251807	−	4.35162i	0.0102121	−	0.176481i
$609$	−0.854102	+	0.620541i	−0.0346100	+	0.0251456i
$610$	−35.4779	+	7.54106i	−1.43646	+	0.305329i
$611$	−4.74803	+	1.00922i	−0.192085	+	0.0408289i
$612$	0.796301	+	7.57630i	0.0321886	+	0.306254i
$613$	2.64149	−	25.1321i	0.106689	−	1.01507i	−0.801921	−	0.597430i	$-0.796189\pi$
$613$	2.64149	−	25.1321i	0.106689	−	1.01507i	0.908610	−	0.417645i	$-0.137145\pi$
$614$	24.7183	+	5.25403i	0.997549	+	0.212036i
$615$	41.5967			1.67734
$616$	−0.718847	−	0.310271i	−0.0289632	−	0.0125012i
$617$	18.5623	−	32.1509i	0.747290	−	1.29434i	−0.201827	−	0.979421i	$-0.564688\pi$
$617$	18.5623	−	32.1509i	0.747290	−	1.29434i	0.949117	−	0.314924i	$-0.101979\pi$
$618$	17.4976	+	3.71924i	0.703858	+	0.149610i
$619$	1.71885	+	1.24882i	0.0690863	+	0.0501941i	0.621792	−	0.783182i	$-0.286405\pi$
$619$	1.71885	+	1.24882i	0.0690863	+	0.0501941i	−0.552706	+	0.833376i	$0.686405\pi$
$620$	6.66312	−	4.84104i	0.267597	−	0.194421i
$621$	2.67652	+	2.97258i	0.107405	+	0.119285i
$622$	−4.46261	+	0.948557i	−0.178934	+	0.0380337i
$623$	0.0318761	+	0.303281i	0.00127709	+	0.0121507i
$624$	−1.01478	+	9.65502i	−0.0406239	+	0.386510i
$625$	−20.6312	+	22.9132i	−0.825247	+	0.916530i
$626$	−22.9443			−0.917038
$627$	1.34077	−	28.8826i	0.0535454	−	1.15346i
$628$	6.38197			0.254668
$629$	28.6377	−	31.8054i	1.14186	−	1.26816i
$630$	−0.0646021	+	0.614648i	−0.00257381	+	0.0244882i
$631$	−0.454440	−	4.32371i	−0.0180910	−	0.172124i	0.981746	−	0.190198i	$-0.0609131\pi$
$631$	−0.454440	−	4.32371i	−0.0180910	−	0.172124i	−0.999837	+	0.0180743i	$0.994246\pi$
$632$	9.49606	−	2.01845i	0.377733	−	0.0802896i
$633$	26.8859	+	29.8598i	1.06862	+	1.18682i
$634$	11.8992	−	8.64527i	0.472577	−	0.343347i
$635$	41.4336	+	30.1033i	1.64424	+	1.19461i
$636$	−21.9811	−	4.67222i	−0.871606	−	0.185266i
$637$	16.8541	−	29.1922i	0.667784	−	1.15664i
$638$	3.78115	+	6.37988i	0.149697	+	0.252582i
$639$	9.32624			0.368940
$640$	2.56082	+	0.544320i	0.101225	+	0.0215161i
$641$	−0.919681	+	8.75018i	−0.0363252	+	0.345611i	0.961231	+	0.275744i	$0.0889242\pi$
$641$	−0.919681	+	8.75018i	−0.0363252	+	0.345611i	−0.997556	+	0.0698671i	$0.977742\pi$
$642$	1.06414	+	10.1246i	0.0419981	+	0.399585i
$643$	34.8189	−	7.40098i	1.37312	−	0.291866i	0.538471	−	0.842644i	$-0.319002\pi$
$643$	34.8189	−	7.40098i	1.37312	−	0.291866i	0.834652	+	0.550778i	$0.185669\pi$
$644$	−0.230909	+	0.0490813i	−0.00909910	+	0.00193407i
$645$	11.4721	−	8.33499i	0.451715	−	0.328190i
$646$	−1.91827	+	33.1508i	−0.0754734	+	1.30430i
$647$	2.95492	+	9.09429i	0.116170	+	0.357534i	0.992189	−	0.124742i	$-0.0398104\pi$
$647$	2.95492	+	9.09429i	0.116170	+	0.357534i	−0.876020	+	0.482276i	$0.839810\pi$
$648$	5.50000	+	9.52628i	0.216060	+	0.374228i
$649$	−10.5805	−	11.4845i	−0.415319	−	0.450805i
$650$	−4.50000	+	7.79423i	−0.176505	+	0.305715i
$651$	−0.993854	+	1.10379i	−0.0389522	+	0.0432608i
$652$	11.8252	−	5.26491i	0.463110	−	0.206190i
$653$	36.5066	−	26.5236i	1.42861	−	1.03795i	0.438340	−	0.898809i	$-0.355567\pi$
$653$	36.5066	−	26.5236i	1.42861	−	1.03795i	0.990273	−	0.139139i	$-0.0444334\pi$
$654$	11.7984	−	36.3117i	0.461353	−	1.41990i
$655$	9.58612	+	10.6465i	0.374561	+	0.415992i
$656$	0.830403	+	7.90075i	0.0324218	+	0.308473i
$657$	5.47214	+	3.97574i	0.213488	+	0.155108i
$658$	−0.0729490	−	0.224514i	−0.00284385	−	0.00875247i
$659$	−19.6631	+	34.0575i	−0.765966	+	1.32669i	0.173768	+	0.984787i	$0.444406\pi$
$659$	−19.6631	+	34.0575i	−0.765966	+	1.32669i	−0.939734	+	0.341906i	$0.888928\pi$
$660$	17.0267	+	3.41652i	0.662763	+	0.132988i
$661$	−0.427051	+	0.739674i	−0.0166104	+	0.0287700i	−0.874211	−	0.485546i	$-0.838621\pi$
$661$	−0.427051	+	0.739674i	−0.0166104	+	0.0287700i	0.857601	+	0.514316i	$0.171954\pi$
$662$	−11.3983	+	12.6591i	−0.443006	+	0.492008i
$663$	7.73066	−	73.5523i	0.300234	−	2.85653i
$664$	−2.04508	+	1.48584i	−0.0793647	+	0.0576618i
$665$	−0.711392	+	2.59832i	−0.0275866	+	0.100759i
$666$	−1.73607	+	5.34307i	−0.0672713	+	0.207040i
$667$	2.04275	+	0.909491i	0.0790956	+	0.0352156i
$668$	−1.77698	+	16.9069i	−0.0687536	+	0.654147i
$669$	−22.5519	−	4.79356i	−0.871907	−	0.185330i
$670$	−4.35410	−	7.54153i	−0.168214	−	0.291355i
$671$	−14.6968	−	43.5351i	−0.567362	−	1.68065i
$672$	−0.472136			−0.0182130
$673$	−1.27051	−	3.91023i	−0.0489746	−	0.150728i	0.923579	−	0.383409i	$-0.125250\pi$
$673$	−1.27051	−	3.91023i	−0.0489746	−	0.150728i	−0.972553	+	0.232681i	$0.925250\pi$
$674$	21.0115	−	9.35494i	0.809334	−	0.360339i
$675$	0.775226	+	7.37578i	0.0298385	+	0.283894i
$676$	3.26393	−	10.0453i	0.125536	−	0.386360i
$677$	−5.76393	+	17.7396i	−0.221526	+	0.681787i	0.777100	+	0.629377i	$0.216690\pi$
$677$	−5.76393	+	17.7396i	−0.221526	+	0.681787i	−0.998626	+	0.0524092i	$0.983310\pi$
$678$	3.77022	+	35.8713i	0.144795	+	1.37763i
$679$	0.152505	−	1.45099i	0.00585260	−	0.0556838i
$680$	−19.5084	−	4.14665i	−0.748115	−	0.159017i
$681$	−7.00000	−	12.1244i	−0.268241	−	0.464606i
$682$	7.06958	+	7.67362i	0.270708	+	0.293838i
$683$	1.29180			0.0494292			0.0247146	−	0.999695i	$-0.492132\pi$
$683$	1.29180			0.0494292			0.0247146	+	0.999695i	$0.492132\pi$
$684$	−1.53993	−	4.07782i	−0.0588806	−	0.155919i
$685$	38.1976	+	27.7522i	1.45945	+	1.06036i
$686$	3.00721	+	1.33889i	0.114816	+	0.0511192i
$687$	−10.3523	+	2.20045i	−0.394965	+	0.0839525i
$688$	1.81214	+	2.01259i	0.0690873	+	0.0767292i
$689$	49.8257	+	22.1838i	1.89821	+	0.845137i
$690$	4.78339	−	2.12970i	0.182100	−	0.0810763i
$691$	−4.48936	−	13.8168i	−0.170783	−	0.525617i	0.828633	−	0.559793i	$-0.189119\pi$
$691$	−4.48936	−	13.8168i	−0.170783	−	0.525617i	−0.999416	+	0.0341762i	$0.989119\pi$
$692$	−19.1246			−0.727009
$693$	−0.782898	+	0.00893505i	−0.0297398	+	0.000339414i
$694$	−0.381966	+	0.661585i	−0.0144992	+	0.0251134i
$695$	−13.2812	−	40.8752i	−0.503783	−	1.55048i
$696$	3.61803	+	2.62866i	0.137141	+	0.0996389i
$697$	−6.32603	−	60.1882i	−0.239616	−	2.27979i
$698$	−30.0372	+	6.38459i	−1.13692	+	0.241660i
$699$	−22.5552	−	25.0501i	−0.853116	−	0.947481i
$700$	−0.399853	−	0.178026i	−0.0151130	−	0.00672876i
$701$	0.492141	−	4.68241i	0.0185879	−	0.176852i	−0.981289	−	0.192541i	$-0.938327\pi$
$701$	0.492141	−	4.68241i	0.0185879	−	0.176852i	0.999877	+	0.0156883i	$0.00499396\pi$
$702$	−6.00000	−	18.4661i	−0.226455	−	0.696958i
$703$	−11.2361	+	21.7586i	−0.423776	+	0.820639i
$704$	−0.309017	+	3.30220i	−0.0116465	+	0.124456i
$705$	2.61803	+	4.53457i	0.0986009	+	0.170782i
$706$	2.67652	−	2.97258i	0.100732	−	0.111874i
$707$	−1.56052	+	0.694789i	−0.0586895	+	0.0261302i
$708$	−8.60232	−	3.83000i	−0.323295	−	0.143940i
$709$	32.7874	+	36.4141i	1.23136	+	1.36756i	0.906727	+	0.421719i	$0.138573\pi$
$709$	32.7874	+	36.4141i	1.23136	+	1.36756i	0.324630	+	0.945841i	$0.394760\pi$
$710$	−7.54508	+	23.2214i	−0.283162	+	0.871483i
$711$	7.85410	−	5.70634i	0.294552	−	0.214004i
$712$	1.18011	−	0.525421i	0.0442267	−	0.0196910i
$713$	3.07715	+	0.654069i	0.115240	+	0.0244951i
$714$	3.59675			0.134605
$715$	−38.6976	−	16.7027i	−1.44721	−	0.624647i
$716$	−5.85410	+	10.1396i	−0.218778	+	0.378935i
$717$	−12.9460	+	14.3780i	−0.483478	+	0.536957i
$718$	0.748797	−	0.333386i	0.0279448	−	0.0124418i
$719$	13.5190	+	6.01904i	0.504173	+	0.224472i	0.643031	−	0.765840i	$-0.277677\pi$
$719$	13.5190	+	6.01904i	0.504173	+	0.224472i	−0.138858	+	0.990312i	$0.544343\pi$
$720$	2.56082	−	0.544320i	0.0954363	−	0.0202856i
$721$	0.652476	−	2.00811i	0.0242995	−	0.0747861i
$722$	−3.74786	−	18.6267i	−0.139481	−	0.693214i
$723$	−16.7082	−	12.1392i	−0.621385	−	0.451462i
$724$	10.1949	−	11.3226i	0.378891	−	0.420801i
$725$	2.07295	+	3.59045i	0.0769874	+	0.133346i
$726$	−1.79968	+	21.9263i	−0.0667924	+	0.813760i
$727$	−5.71885	−	9.90533i	−0.212100	−	0.367368i	0.740271	−	0.672308i	$-0.234697\pi$
$727$	−5.71885	−	9.90533i	−0.212100	−	0.367368i	−0.952372	+	0.304940i	$0.901364\pi$
$728$	1.12086	+	0.238246i	0.0415417	+	0.00882997i
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$	−14.3262	+	10.4086i	−0.530238	+	0.385240i
$731$	−13.8050	−	15.3320i	−0.510595	−	0.567073i
$732$	−18.5404	−	20.5912i	−0.685273	−	0.761073i
$733$	−20.5172	+	14.9066i	−0.757821	+	0.550589i	−0.898241	−	0.439503i	$-0.855155\pi$
$733$	−20.5172	+	14.9066i	−0.757821	+	0.550589i	0.140420	+	0.990092i	$0.455155\pi$
$734$	−19.5902	−	14.2331i	−0.723086	−	0.525353i
$735$	−35.5661	−	7.55981i	−1.31188	−	0.278848i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	8.85040	−	6.58581i	0.326009	−	0.242591i
$738$	3.97214	+	6.87994i	0.146216	+	0.253254i
$739$	25.3151	−	28.1153i	0.931231	−	1.03424i	−0.0681007	−	0.997678i	$-0.521694\pi$
$739$	25.3151	−	28.1153i	0.931231	−	1.03424i	0.999332	−	0.0365582i	$-0.0116394\pi$
$740$	−11.8992	−	8.64527i	−0.437423	−	0.317806i
$741$	6.39235	+	41.8315i	0.234829	+	1.53672i
$742$	−0.819660	+	2.52265i	−0.0300907	+	0.0926096i
$743$	−10.8686	+	2.31020i	−0.398732	+	0.0847531i	−0.402913	−	0.915238i	$-0.632002\pi$
$743$	−10.8686	+	2.31020i	−0.398732	+	0.0847531i	0.00418135	+	0.999991i	$0.498669\pi$
$744$	5.74784	+	2.55910i	0.210726	+	0.0938213i
$745$	−4.99904	+	2.22572i	−0.183151	+	0.0815440i
$746$	19.6461	−	21.8192i	0.719296	−	0.798859i
$747$	−1.26393	+	2.18919i	−0.0462449	+	0.0800984i
$748$	2.35410	−	25.1563i	0.0860745	−	0.919804i
$749$	1.20163			0.0439065
$750$	−16.1122	−	3.42475i	−0.588334	−	0.125054i
$751$	24.0308	−	10.6992i	0.876895	−	0.390419i	0.0816172	−	0.996664i	$-0.473992\pi$
$751$	24.0308	−	10.6992i	0.876895	−	0.390419i	0.795278	+	0.606245i	$0.207325\pi$
$752$	−0.809017	+	0.587785i	−0.0295018	+	0.0214343i
$753$	−8.74265	+	26.9071i	−0.318600	+	0.980549i
$754$	−7.26281	−	8.06617i	−0.264496	−	0.293753i
$755$	−29.2649	−	13.0296i	−1.06506	−	0.474195i
$756$	0.862635	−	0.384070i	0.0313737	−	0.0139685i
$757$	27.3598	−	30.3861i	0.994408	−	1.10440i	−0.000127207	−	1.00000i	$-0.500040\pi$
$757$	27.3598	−	30.3861i	0.994408	−	1.10440i	0.994535	−	0.104402i	$-0.0332928\pi$
$758$	0.336881	+	0.583495i	0.0122361	+	0.0211935i
$759$	3.38197	+	5.70634i	0.122758	+	0.207127i
$760$	11.3992	−	0.535233i	0.413492	−	0.0194149i
$761$	−4.87132	−	14.9924i	−0.176585	−	0.543474i	0.823117	−	0.567872i	$-0.192233\pi$
$761$	−4.87132	−	14.9924i	−0.176585	−	0.543474i	−0.999702	+	0.0243981i	$0.992233\pi$
$762$	−4.08964	+	38.9103i	−0.148152	+	1.40957i
$763$	−4.11696	−	1.83299i	−0.149044	−	0.0663587i
$764$	−9.17258	−	10.1872i	−0.331852	−	0.368559i
$765$	−19.5084	+	4.14665i	−0.705329	+	0.149922i
$766$	−2.17042	−	20.6502i	−0.0784205	−	0.746122i
$767$	18.4894	+	13.4333i	0.667612	+	0.485048i
$768$	0.618034	+	1.90211i	0.0223014	+	0.0686366i
$769$	−12.6353	+	21.8849i	−0.455639	+	0.789190i	−0.998725	−	0.0504874i	$-0.983923\pi$
$769$	−12.6353	+	21.8849i	−0.455639	+	0.789190i	0.543086	+	0.839677i	$0.317256\pi$
$770$	0.611130	−	1.95656i	0.0220236	−	0.0705097i
$771$	28.0000			1.00840
$772$	−5.69098	−	17.5150i	−0.204823	−	0.630380i
$773$	30.3941	−	13.5323i	1.09320	−	0.486724i	0.220702	−	0.975341i	$-0.429165\pi$
$773$	30.3941	−	13.5323i	1.09320	−	0.486724i	0.872498	+	0.488617i	$0.162498\pi$
$774$	2.47407	+	1.10153i	0.0889285	+	0.0395935i
$775$	3.90292	+	4.33463i	0.140197	+	0.155704i
$776$	−6.04528	+	1.28496i	−0.217013	+	0.0461276i
$777$	2.42316	+	1.07886i	0.0869303	+	0.0387039i
$778$	−8.73607	−	6.34712i	−0.313203	−	0.227555i
$779$	12.2336	+	32.3953i	0.438314	+	1.16068i
$780$	−25.4164			−0.910053
$781$	−30.3271	−	6.08535i	−1.08519	−	0.217751i
$782$	−3.80902	−	6.59741i	−0.136210	−	0.235923i
$783$	−8.74882	−	1.85962i	−0.312657	−	0.0664574i
$784$	0.725874	−	6.90623i	0.0259241	−	0.246651i
$785$	1.74648	+	16.6167i	0.0623346	+	0.593075i
$786$	−3.38197	+	10.4086i	−0.120631	+	0.371263i
$787$	−12.1074	+	37.2627i	−0.431582	+	1.32827i	0.464967	+	0.885328i	$0.346066\pi$
$787$	−12.1074	+	37.2627i	−0.431582	+	1.32827i	−0.896549	+	0.442945i	$0.853934\pi$
$788$	−0.568394	−	5.40791i	−0.0202482	−	0.192649i
$789$	−14.2483	+	6.34377i	−0.507254	+	0.225844i
$790$	7.85410	+	24.1724i	0.279436	+	0.860017i
$791$	4.25735			0.151374
$792$	1.06082	+	3.14240i	0.0376947	+	0.111660i
$793$	33.6246	+	58.2395i	1.19404	+	2.06815i
$794$	18.5303	+	3.93874i	0.657616	+	0.139780i
$795$	6.14970	−	58.5105i	0.218108	−	2.07515i
$796$	12.9229	+	5.75366i	0.458041	+	0.203933i
$797$	3.70820	−	11.4127i	0.131351	−	0.404258i	−0.863653	−	0.504086i	$-0.831829\pi$
$797$	3.70820	−	11.4127i	0.131351	−	0.404258i	0.995005	+	0.0998284i	$0.0318294\pi$
$798$	−1.99074	+	0.521825i	−0.0704713	+	0.0184724i
$799$	6.16312	−	4.47777i	0.218035	−	0.158412i
$800$	−0.193806	+	1.84395i	−0.00685209	+	0.0651933i
$801$	0.864380	−	0.959992i	0.0305414	−	0.0339196i
$802$	−0.527864	+	0.914287i	−0.0186395	+	0.0322846i
$803$	−15.2002	−	16.4989i	−0.536402	−	0.582233i
$804$	3.32624	−	5.76121i	0.117307	−	0.203182i
$805$	−0.190983	−	0.587785i	−0.00673127	−	0.0207167i
$806$	−12.3541	−	8.97578i	−0.435155	−	0.316158i
$807$	−0.0682023	−	0.648902i	−0.00240083	−	0.0228424i
$808$	4.84187	+	5.37745i	0.170337	+	0.189178i
$809$	−1.02786	+	3.16344i	−0.0361378	+	0.111221i	−0.967498	−	0.252878i	$-0.918623\pi$
$809$	−1.02786	+	3.16344i	−0.0361378	+	0.111221i	0.931360	+	0.364099i	$0.118623\pi$
$810$	−23.2984	+	16.9273i	−0.818621	+	0.594763i
$811$	25.4775	−	11.3433i	0.894634	−	0.398317i	0.0926757	−	0.995696i	$-0.470458\pi$
$811$	25.4775	−	11.3433i	0.894634	−	0.398317i	0.801959	+	0.597379i	$0.203791\pi$
$812$	0.353210	−	0.392279i	0.0123952	−	0.0137663i
$813$	−0.381966	+	0.661585i	−0.0133961	+	0.0232028i
$814$	9.13170	−	16.2418i	0.320066	−	0.569276i
$815$	16.9443	+	29.3483i	0.593532	+	1.02803i
$816$	−4.70820	−	14.4904i	−0.164820	−	0.507264i
$817$	9.86520	+	6.48312i	0.345140	+	0.226816i
$818$	1.97214	−	1.43284i	0.0689541	−	0.0500981i
$819$	1.12086	−	0.238246i	0.0391659	−	0.00832497i
$820$	−20.3439	+	4.32423i	−0.710439	+	0.151008i
$821$	0.923281	+	8.78443i	0.0322227	+	0.306579i	0.998749	+	0.0500100i	$0.0159253\pi$
$821$	0.923281	+	8.78443i	0.0322227	+	0.306579i	−0.966526	+	0.256569i	$0.917408\pi$
$822$	−3.77022	+	35.8713i	−0.131502	+	1.25116i
$823$	−32.2580	−	6.85666i	−1.12444	−	0.239008i	−0.392087	−	0.919928i	$-0.628247\pi$
$823$	−32.2580	−	6.85666i	−1.12444	−	0.239008i	−0.732358	+	0.680920i	$0.761580\pi$
$824$	−8.94427			−0.311588
$825$	−1.14590	+	12.2452i	−0.0398950	+	0.426324i
$826$	−0.555728	+	0.962549i	−0.0193363	+	0.0334914i
$827$	−7.85887	−	1.67045i	−0.273280	−	0.0580874i	0.0692333	−	0.997600i	$-0.477945\pi$
$827$	−7.85887	−	1.67045i	−0.273280	−	0.0580874i	−0.342513	+	0.939513i	$0.611278\pi$
$828$	0.809017	+	0.587785i	0.0281153	+	0.0204269i
$829$	13.9894	−	10.1639i	0.485870	−	0.353006i	−0.317724	−	0.948183i	$-0.602918\pi$
$829$	13.9894	−	10.1639i	0.485870	−	0.353006i	0.803594	+	0.595178i	$0.202918\pi$
$830$	−4.42833	−	4.91816i	−0.153710	−	0.170712i
$831$	−28.2027	+	5.99468i	−0.978343	+	0.207953i
$832$	−0.507392	−	4.82751i	−0.0175906	−	0.167364i
$833$	−5.52973	+	52.6119i	−0.191594	+	1.82289i
$834$	21.9694	−	24.3995i	0.760740	−	0.844887i
$835$	−44.5066			−1.54021
$836$	2.34677	+	14.2651i	0.0811648	+	0.493368i
$837$	−12.5836			−0.434953
$838$	−1.57080	+	1.74455i	−0.0542624	+	0.0602645i
$839$	−0.315810	+	3.00474i	−0.0109030	+	0.103735i	−0.998620	−	0.0525187i	$-0.983275\pi$
$839$	−0.315810	+	3.00474i	−0.0109030	+	0.103735i	0.987717	+	0.156254i	$0.0499417\pi$
$840$	−0.129204	−	1.22930i	−0.00445797	−	0.0424148i
$841$	23.4755	−	4.98988i	0.809501	−	0.172065i
$842$	7.67636	+	8.52546i	0.264545	+	0.293807i
$843$	−26.7984	+	19.4702i	−0.922985	+	0.670588i
$844$	−16.2533	−	11.8087i	−0.559461	−	0.406472i
$845$	27.0482	+	5.74927i	0.930486	+	0.197781i
$846$	−0.500000	+	0.866025i	−0.0171904	+	0.0297746i
$847$	2.55166	+	0.481784i	0.0876762	+	0.0165543i
$848$	11.2361			0.385848
$849$	−39.5877	−	8.41463i	−1.35865	−	0.288789i
$850$	1.47642	−	14.0472i	0.0506409	−	0.481816i
$851$	−0.587244	−	5.58726i	−0.0201305	−	0.191529i
$852$	−18.2449	+	3.87807i	−0.625059	+	0.132860i
$853$	−14.9576	+	3.17934i	−0.512140	+	0.108859i	−0.456731	−	0.889605i	$-0.650980\pi$
$853$	−14.9576	+	3.17934i	−0.512140	+	0.108859i	−0.0554091	+	0.998464i	$0.517646\pi$
$854$	−2.64590	+	1.92236i	−0.0905408	+	0.0657817i
$855$	10.1960	−	5.12543i	0.348695	−	0.175286i
$856$	−1.57295	−	4.84104i	−0.0537623	−	0.165463i
$857$	−13.2705	−	22.9852i	−0.453312	−	0.785159i	0.545277	−	0.838256i	$-0.316424\pi$
$857$	−13.2705	−	22.9852i	−0.453312	−	0.785159i	−0.998589	+	0.0530963i	$0.983091\pi$
$858$	−3.73087	−	31.9816i	−0.127370	−	1.09183i
$859$	−7.38854	+	12.7973i	−0.252094	+	0.436639i	−0.964102	−	0.265532i	$-0.914453\pi$
$859$	−7.38854	+	12.7973i	−0.252094	+	0.436639i	0.712008	+	0.702171i	$0.247786\pi$
$860$	−4.74425	+	5.26902i	−0.161778	+	0.179672i
$861$	3.42650	−	1.52558i	0.116775	−	0.0519916i
$862$	10.1353	−	7.36369i	0.345208	−	0.250808i
$863$	17.6418	−	54.2960i	0.600535	−	1.84826i	0.0755557	−	0.997142i	$-0.475927\pi$
$863$	17.6418	−	54.2960i	0.600535	−	1.84826i	0.524979	−	0.851115i	$-0.324073\pi$
$864$	−2.67652	−	2.97258i	−0.0910571	−	0.101129i
$865$	−5.23362	−	49.7946i	−0.177949	−	1.69307i
$866$	14.8262	+	10.7719i	0.503816	+	0.366044i
$867$	25.3607	+	78.0521i	0.861294	+	2.65079i
$868$	0.371323	−	0.643150i	0.0126035	−	0.0218299i
$869$	−29.2634	+	13.4311i	−0.992693	+	0.455620i
$870$	−5.85410	+	10.1396i	−0.198473	+	0.343765i
$871$	−10.8037	+	11.9987i	−0.366070	+	0.406562i
$872$	−1.99547	+	18.9856i	−0.0675750	+	0.642933i
$873$	−5.00000	+	3.63271i	−0.169224	+	0.122949i
$874$	3.06539	+	3.09893i	0.103688	+	0.104823i
$875$	−0.600813	+	1.84911i	−0.0203112	+	0.0625114i
$876$	−12.3583	−	5.50228i	−0.417549	−	0.185905i
$877$	1.00758	−	9.58652i	0.0340237	−	0.323714i	−0.964251	−	0.264992i	$-0.914631\pi$
$877$	1.00758	−	9.58652i	0.0340237	−	0.323714i	0.998274	−	0.0587220i	$-0.0187025\pi$
$878$	−17.4431	−	3.70765i	−0.588677	−	0.125127i
$879$	−8.41641	−	14.5776i	−0.283878	−	0.491692i
$880$	−8.68247	+	0.0990912i	−0.292686	+	0.00334036i
$881$	10.5836			0.356570			0.178285	−	0.983979i	$-0.442945\pi$
$881$	10.5836			0.356570			0.178285	+	0.983979i	$0.442945\pi$
$882$	−2.14590	−	6.60440i	−0.0722561	−	0.222382i
$883$	9.78243	−	4.35542i	0.329205	−	0.146572i	−0.235477	−	0.971880i	$-0.575665\pi$
$883$	9.78243	−	4.35542i	0.329205	−	0.146572i	0.564682	+	0.825308i	$0.308999\pi$
$884$	3.86533	+	36.7761i	0.130005	+	1.23692i
$885$	7.61803	−	23.4459i	0.256077	−	0.788125i
$886$	−12.1180	+	37.2955i	−0.407113	+	1.25297i
$887$	0.614145	+	5.84320i	0.0206210	+	0.196196i	0.999982	−	0.00592095i	$-0.00188471\pi$
$887$	0.614145	+	5.84320i	0.0206210	+	0.196196i	−0.979361	+	0.202116i	$0.935218\pi$
$888$	1.17449	−	11.1745i	0.0394133	−	0.374992i
$889$	4.51712	+	0.960143i	0.151499	+	0.0322022i
$890$	1.69098	+	2.92887i	0.0566819	+	0.0981759i
$891$	−24.7196	−	26.8317i	−0.828138	−	0.898896i
$892$	11.5279			0.385981
$893$	−2.76153	+	3.37253i	−0.0924112	+	0.112857i
$894$	−3.38197	−	2.45714i	−0.113110	−	0.0821791i
$895$	−28.0024	−	12.4675i	−0.936018	−	0.416742i
$896$	0.230909	−	0.0490813i	0.00771414	−	0.00163969i
$897$	−6.49606	−	7.21460i	−0.216897	−	0.240889i
$898$	−5.56365	−	2.47710i	−0.185661	−	0.0826617i
$899$	−6.42628	+	2.86117i	−0.214329	+	0.0954252i
$900$	0.572949	+	1.76336i	0.0190983	+	0.0587785i
$901$	−85.5967			−2.85164
$902$	−8.42747	−	24.9640i	−0.280604	−	0.831212i
$903$	0.639320	−	1.10734i	0.0212752	−	0.0368498i
$904$	−5.57295	−	17.1518i	−0.185354	−	0.570459i
$905$	32.2705	+	23.4459i	1.07271	+	0.779368i
$906$	−2.55803	−	24.3381i	−0.0849850	−	0.808578i
$907$	−25.8391	+	5.49228i	−0.857975	+	0.182368i	−0.615837	−	0.787874i	$-0.711182\pi$
$907$	−25.8391	+	5.49228i	−0.857975	+	0.182368i	−0.242138	+	0.970242i	$0.577849\pi$
$908$	4.68391	+	5.20201i	0.155441	+	0.172635i
$909$	6.61048	+	2.94317i	0.219256	+	0.0976189i
$910$	−0.313585	+	2.98357i	−0.0103953	+	0.0989042i
$911$	13.6803	+	42.1038i	0.453250	+	1.39496i	0.873178	+	0.487402i	$0.162055\pi$
$911$	13.6803	+	42.1038i	0.453250	+	1.39496i	−0.419928	+	0.907558i	$0.637945\pi$
$912$	4.70820	+	7.33708i	0.155904	+	0.242955i
$913$	5.53851	−	6.29412i	0.183298	−	0.208305i
$914$	12.4443	+	21.5541i	0.411620	+	0.712947i
$915$	48.5394	−	53.9085i	1.60466	−	1.78216i
$916$	4.83430	−	2.15237i	0.159730	−	0.0711162i
$917$	1.18011	+	0.525421i	0.0389708	+	0.0173509i
$918$	20.3898	+	22.6452i	0.672965	+	0.747403i
$919$	−10.7295	+	33.0220i	−0.353933	+	1.08929i	0.602692	+	0.797974i	$0.294095\pi$
$919$	−10.7295	+	33.0220i	−0.353933	+	1.08929i	−0.956625	+	0.291321i	$0.905905\pi$
$920$	−2.11803	+	1.53884i	−0.0698295	+	0.0507341i
$921$	−46.1715	+	20.5569i	−1.52140	+	0.677372i
$922$	27.0482	+	5.74927i	0.890785	+	0.189342i
$923$	45.2705			1.49010
$924$	1.52786	−	0.343027i	0.0502630	−	0.0112848i
$925$	5.20820	−	9.02087i	0.171245	−	0.296605i
$926$	−1.81214	+	2.01259i	−0.0595507	+	0.0661377i
$927$	−8.17100	+	3.63796i	−0.268371	+	0.119486i
$928$	−2.04275	−	0.909491i	−0.0670565	−	0.0298555i
$929$	−30.5535	+	6.49434i	−1.00243	+	0.213073i	−0.679756	−	0.733439i	$-0.737914\pi$
$929$	−30.5535	+	6.49434i	−1.00243	+	0.213073i	−0.322672	+	0.946511i	$0.604581\pi$
$930$	−5.09017	+	15.6659i	−0.166913	+	0.513706i
$931$	−4.57245	−	29.9220i	−0.149856	−	0.980655i
$932$	13.6353	+	9.90659i	0.446638	+	0.324501i
$933$	6.10556	−	6.78091i	0.199887	−	0.221997i
$934$	−13.1803	−	22.8290i	−0.431274	−	0.746988i
$935$	66.1434	−	0.754880i	2.16312	−	0.0246872i
$936$	−2.42705	−	4.20378i	−0.0793306	−	0.137405i
$937$	3.64799	+	0.775405i	0.119175	+	0.0253314i	0.267113	−	0.963665i	$-0.413930\pi$
$937$	3.64799	+	0.775405i	0.119175	+	0.0253314i	−0.147938	+	0.988997i	$0.547264\pi$
$938$	−0.635255	−	0.461540i	−0.0207418	−	0.0150698i
$939$	37.1246	−	26.9726i	1.21152	−	0.880218i
$940$	−1.75181	−	1.94558i	−0.0571376	−	0.0634578i
$941$	1.02234	+	1.13542i	0.0333274	+	0.0370138i	0.759578	−	0.650416i	$-0.225405\pi$
$941$	1.02234	+	1.13542i	0.0333274	+	0.0370138i	−0.726251	+	0.687430i	$0.758739\pi$
$942$	−10.3262	+	7.50245i	−0.336447	+	0.244443i
$943$	−6.42705	−	4.66953i	−0.209294	−	0.152061i
$944$	4.60532	+	0.978891i	0.149890	+	0.0318602i
$945$	1.23607	+	2.14093i	0.0402093	+	0.0696445i
$946$	−7.32645	−	5.19627i	−0.238203	−	0.168945i
$947$	−15.1631	−	26.2633i	−0.492735	−	0.853442i	0.507230	−	0.861811i	$-0.330670\pi$
$947$	−15.1631	−	26.2633i	−0.492735	−	0.853442i	−0.999965	+	0.00836850i	$0.997336\pi$
$948$	−12.9921	+	14.4292i	−0.421964	+	0.468639i
$949$	26.5623	+	19.2986i	0.862249	+	0.626461i
$950$	1.22083	+	7.98910i	0.0396090	+	0.259201i
$951$	−9.09017	+	27.9767i	−0.294769	+	0.907206i
$952$	−1.75908	+	0.373903i	−0.0570120	+	0.0121183i
$953$	4.19934	+	1.86967i	0.136030	+	0.0605644i	0.473623	−	0.880728i	$-0.342946\pi$
$953$	4.19934	+	1.86967i	0.136030	+	0.0605644i	−0.337593	+	0.941292i	$0.609613\pi$
$954$	10.2647	−	4.57012i	0.332331	−	0.147963i
$955$	24.0141	−	26.6704i	0.777079	−	0.863033i
$956$	4.83688	−	8.37772i	0.156436	−	0.270955i
$957$	−13.6180	−	5.87785i	−0.440209	−	0.190004i
$958$	−21.8328			−0.705386
$959$	4.16432	+	0.885154i	0.134473	+	0.0285831i
$960$	−4.78339	+	2.12970i	−0.154383	+	0.0687358i
$961$	17.0729	−	12.4042i	0.550740	−	0.400136i
$962$	−8.42705	+	25.9358i	−0.271699	+	0.836204i
$963$	−3.40599	−	3.78273i	−0.109756	−	0.121897i
$964$	9.43349	+	4.20006i	0.303832	+	0.135275i
$965$	44.0464	−	19.6107i	1.41790	−	0.631291i
$966$	0.315921	−	0.350865i	0.0101646	−	0.0112889i
$967$	−2.51722	−	4.35995i	−0.0809484	−	0.140207i	0.822709	−	0.568462i	$-0.192462\pi$
$967$	−2.51722	−	4.35995i	−0.0809484	−	0.140207i	−0.903658	+	0.428256i	$0.859128\pi$
$968$	−1.39919	−	10.9106i	−0.0449716	−	0.350682i
$969$	−35.8673	−	55.8942i	−1.15222	−	1.79558i
$970$	−5.00000	−	15.3884i	−0.160540	−	0.494092i
$971$	−5.32873	+	50.6994i	−0.171007	+	1.62702i	0.486574	+	0.873639i	$0.338246\pi$
$971$	−5.32873	+	50.6994i	−0.171007	+	1.62702i	−0.657581	+	0.753384i	$0.728420\pi$
$972$	−9.13545	−	4.06737i	−0.293020	−	0.130461i
$973$	−2.59314	−	2.87997i	−0.0831323	−	0.0923277i
$974$	−31.2462	+	6.64159i	−1.00119	+	0.212810i
$975$	−1.88151	−	17.9014i	−0.0602566	−	0.573303i
$976$	11.2082	+	8.14324i	0.358766	+	0.260659i
$977$	−14.8820	−	45.8020i	−0.476116	−	1.46534i	−0.844446	−	0.535640i	$-0.820070\pi$
$977$	−14.8820	−	45.8020i	−0.476116	−	1.46534i	0.368330	−	0.929695i	$-0.379930\pi$
$978$	−12.9443	+	22.4201i	−0.413912	+	0.716917i
$979$	−3.43719	+	2.55770i	−0.109853	+	0.0817445i
$980$	18.1803			0.580750
$981$	5.89919	+	18.1558i	0.188347	+	0.579671i
$982$	−26.6067	+	11.8460i	−0.849053	+	0.378023i
$983$	8.98272	+	3.99937i	0.286504	+	0.127560i	0.544957	−	0.838464i	$-0.316546\pi$
$983$	8.98272	+	3.99937i	0.286504	+	0.127560i	−0.258453	+	0.966024i	$0.583213\pi$
$984$	−10.6315	−	11.8075i	−0.338920	−	0.376409i
$985$	13.9250	−	2.95984i	0.443687	−	0.0943085i
$986$	15.5617	+	6.92853i	0.495587	+	0.220649i
$987$	0.381966	+	0.277515i	0.0121581	+	0.00883339i
$988$	−7.47496	−	19.7942i	−0.237810	−	0.629736i
$989$	−2.70820			−0.0861159
$990$	−7.89153	+	3.62200i	−0.250809	+	0.115115i
$991$	15.6353	+	27.0811i	0.496670	+	0.860258i	0.999993	−	0.00384062i	$-0.00122251\pi$
$991$	15.6353	+	27.0811i	0.496670	+	0.860258i	−0.503322	+	0.864099i	$0.667889\pi$
$992$	−3.07715	−	0.654069i	−0.0976997	−	0.0207667i
$993$	3.56117	−	33.8823i	0.113010	−	1.07522i
$994$	0.230133	+	2.18957i	0.00729936	+	0.0694488i
$995$	−11.4443	+	35.2218i	−0.362808	+	1.11661i
$996$	1.56231	−	4.80828i	0.0495036	−	0.152356i
$997$	−0.507392	−	4.82751i	−0.0160693	−	0.152889i	0.983545	−	0.180664i	$-0.0578245\pi$
$997$	−0.507392	−	4.82751i	−0.0160693	−	0.152889i	−0.999614	+	0.0277748i	$0.991158\pi$
$998$	−24.8110	+	11.0466i	−0.785379	+	0.349673i
$999$	6.94427	+	21.3723i	0.219707	+	0.676189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.c.159.1	yes	8
11.9	even	5	inner	418.2.n.c.273.1	yes	8
19.11	even	3	inner	418.2.n.c.49.1	✓	8
209.163	even	15	inner	418.2.n.c.163.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.c.49.1	✓	8	19.11	even	3	inner
418.2.n.c.159.1	yes	8	1.1	even	1	trivial
418.2.n.c.163.1	yes	8	209.163	even	15	inner
418.2.n.c.273.1	yes	8	11.9	even	5	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.669131 - 0.743145i) q^{2} +(-0.209057 + 1.98904i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(2.56082 - 0.544320i) q^{5} +(1.33826 + 1.48629i) q^{6} +(0.190983 - 0.138757i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.669131 - 0.743145i) q^{2} +(-0.209057 + 1.98904i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(2.56082 - 0.544320i) q^{5} +(1.33826 + 1.48629i) q^{6} +(0.190983 - 0.138757i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.30902 - 2.26728i) q^{10} +(3.04508 + 1.31433i) q^{11} +2.00000 q^{12} +(-4.74803 - 1.00922i) q^{13} +(0.0246758 - 0.234775i) q^{14} +(0.547318 + 5.20738i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(7.45156 - 1.58388i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-3.89452 + 1.95774i) q^{19} +(-0.809017 - 2.48990i) q^{20} +(0.236068 + 0.408882i) q^{21} +(3.01430 - 1.38348i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.33826 - 1.48629i) q^{24} +(1.69381 - 0.754131i) q^{25} +(-3.92705 + 2.85317i) q^{26} +(-1.23607 + 3.80423i) q^{27} +(-0.157960 - 0.175433i) q^{28} +(0.233733 + 2.22382i) q^{29} +(4.23607 + 3.07768i) q^{30} +(0.972136 + 2.99193i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.25085 + 5.78204i) q^{33} +(3.80902 - 6.59741i) q^{34} +(0.413545 - 0.459289i) q^{35} +(-0.104528 + 0.994522i) q^{36} +(4.54508 - 3.30220i) q^{37} +(-1.15106 + 4.20417i) q^{38} +(3.00000 - 9.23305i) q^{39} +(-2.39169 - 1.06485i) q^{40} +(0.830403 - 7.90075i) q^{41} +(0.461819 + 0.0981626i) q^{42} +(-1.35410 - 2.34537i) q^{43} +(0.988830 - 3.16579i) q^{44} -2.61803 q^{45} +(-0.309017 - 0.951057i) q^{46} +(0.913545 - 0.406737i) q^{47} +(-0.209057 - 1.98904i) q^{48} +(-2.14590 + 6.60440i) q^{49} +(0.572949 - 1.76336i) q^{50} +(1.59260 + 15.1526i) q^{51} +(-0.507392 + 4.82751i) q^{52} +(-10.9905 - 2.33611i) q^{53} +(2.00000 + 3.46410i) q^{54} +(8.51334 + 1.70826i) q^{55} -0.236068 q^{56} +(-3.07985 - 8.15564i) q^{57} +(1.80902 + 1.31433i) q^{58} +(-4.30116 - 1.91500i) q^{59} +(5.12165 - 1.08864i) q^{60} +(-9.27020 - 10.2956i) q^{61} +(2.87392 + 1.27955i) q^{62} +(-0.215659 + 0.0960175i) q^{63} +(0.309017 + 0.951057i) q^{64} -12.7082 q^{65} +(2.12165 + 6.28479i) q^{66} +(1.66312 - 2.88061i) q^{67} +(-2.35410 - 7.24518i) q^{68} +(1.61803 + 1.17557i) q^{69} +(-0.0646021 - 0.614648i) q^{70} +(-9.12244 + 1.93903i) q^{71} +(0.669131 + 0.743145i) q^{72} +(-6.17916 - 2.75114i) q^{73} +(0.587244 - 5.58726i) q^{74} +(1.14590 + 3.52671i) q^{75} +(2.35410 + 3.66854i) q^{76} +(0.763932 - 0.171513i) q^{77} +(-4.85410 - 8.40755i) q^{78} +(-6.49606 + 7.21460i) q^{79} +(-2.39169 + 1.06485i) q^{80} +(-10.0490 - 4.47410i) q^{81} +(-5.31576 - 5.90374i) q^{82} +(0.781153 - 2.40414i) q^{83} +(0.381966 - 0.277515i) q^{84} +(18.2200 - 8.11207i) q^{85} +(-2.64902 - 0.563067i) q^{86} -4.47214 q^{87} +(-1.69098 - 2.85317i) q^{88} +(-0.645898 + 1.11873i) q^{89} +(-1.75181 + 1.94558i) q^{90} +(-1.04683 + 0.466079i) q^{91} +(-0.913545 - 0.406737i) q^{92} +(-6.15431 + 1.30814i) q^{93} +(0.309017 - 0.951057i) q^{94} +(-8.90753 + 7.13329i) q^{95} +(-1.61803 - 1.17557i) q^{96} +(4.13545 - 4.59289i) q^{97} +(3.47214 + 6.01392i) q^{98} +(-2.70528 - 1.91872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 8 * q + q^2 + 2 * q^3 + q^4 + q^5 + 2 * q^6 + 6 * q^7 - 2 * q^8 + q^9	\( 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9} + 6 q^{10} + 2 q^{11} + 16 q^{12} - 6 q^{13} - 3 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 2 q^{18} - 4 q^{19} - 2 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} - 18 q^{26} + 8 q^{27} + 7 q^{28} - 5 q^{29} + 16 q^{30} - 28 q^{31} - 4 q^{32} + 18 q^{33} + 26 q^{34} - 3 q^{35} + q^{36} + 14 q^{37} - 13 q^{38} + 24 q^{39} - 4 q^{40} - 19 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} - 12 q^{45} + 2 q^{46} + q^{47} + 2 q^{48} - 44 q^{49} + 18 q^{50} - 18 q^{51} + 9 q^{52} + 4 q^{53} + 16 q^{54} + 14 q^{55} + 16 q^{56} - 26 q^{57} + 10 q^{58} - 13 q^{59} + 2 q^{60} - 3 q^{61} - q^{62} - 3 q^{63} - 2 q^{64} - 48 q^{65} - 22 q^{66} - 18 q^{67} + 8 q^{68} + 4 q^{69} + 2 q^{70} - 16 q^{71} + q^{72} - 4 q^{73} - 7 q^{74} + 36 q^{75} - 8 q^{76} + 24 q^{77} - 12 q^{78} + 12 q^{79} - 4 q^{80} - 11 q^{81} + 21 q^{82} - 34 q^{83} + 12 q^{84} + 31 q^{85} - 19 q^{86} - 18 q^{88} - 32 q^{89} + q^{90} + 3 q^{91} - q^{92} + 28 q^{93} - 2 q^{94} - 38 q^{95} - 4 q^{96} - 30 q^{97} - 8 q^{98} - q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 + q^4 + q^5 + 2 * q^6 + 6 * q^7 - 2 * q^8 + q^9 + 6 * q^10 + 2 * q^11 + 16 * q^12 - 6 * q^13 - 3 * q^14 - 8 * q^15 + q^16 - 4 * q^17 - 2 * q^18 - 4 * q^19 - 2 * q^20 - 16 * q^21 - q^22 + 4 * q^23 + 2 * q^24 + 6 * q^25 - 18 * q^26 + 8 * q^27 + 7 * q^28 - 5 * q^29 + 16 * q^30 - 28 * q^31 - 4 * q^32 + 18 * q^33 + 26 * q^34 - 3 * q^35 + q^36 + 14 * q^37 - 13 * q^38 + 24 * q^39 - 4 * q^40 - 19 * q^41 + 14 * q^42 + 16 * q^43 + 4 * q^44 - 12 * q^45 + 2 * q^46 + q^47 + 2 * q^48 - 44 * q^49 + 18 * q^50 - 18 * q^51 + 9 * q^52 + 4 * q^53 + 16 * q^54 + 14 * q^55 + 16 * q^56 - 26 * q^57 + 10 * q^58 - 13 * q^59 + 2 * q^60 - 3 * q^61 - q^62 - 3 * q^63 - 2 * q^64 - 48 * q^65 - 22 * q^66 - 18 * q^67 + 8 * q^68 + 4 * q^69 + 2 * q^70 - 16 * q^71 + q^72 - 4 * q^73 - 7 * q^74 + 36 * q^75 - 8 * q^76 + 24 * q^77 - 12 * q^78 + 12 * q^79 - 4 * q^80 - 11 * q^81 + 21 * q^82 - 34 * q^83 + 12 * q^84 + 31 * q^85 - 19 * q^86 - 18 * q^88 - 32 * q^89 + q^90 + 3 * q^91 - q^92 + 28 * q^93 - 2 * q^94 - 38 * q^95 - 4 * q^96 - 30 * q^97 - 8 * q^98 - q^99

Introduction

L-functions

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