LMFDB - Embedded newform 104.2.s.a.69.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(69,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("104.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.s (of order $6$, degree $2$, 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:	$0.830444181021$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	104.69
Dual form			104.2.s.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.36603 - 1.36603i) q^{3} +2.00000i q^{4} -0.267949 q^{5} +(1.00000 + 3.73205i) q^{6} +(-3.00000 + 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.23205 + 3.86603i) q^{9} +(0.267949 + 0.267949i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(2.73205 - 4.73205i) q^{12} +(-2.59808 + 2.50000i) q^{13} +(4.73205 + 1.26795i) q^{14} +(0.633975 + 0.366025i) q^{15} -4.00000 q^{16} +(-3.23205 - 5.59808i) q^{17} +(1.63397 - 6.09808i) q^{18} +(-2.36603 - 4.09808i) q^{19} -0.535898i q^{20} +9.46410 q^{21} +(2.73205 - 0.732051i) q^{22} +(1.09808 - 1.90192i) q^{23} +(-7.46410 + 2.00000i) q^{24} -4.92820 q^{25} +(5.09808 + 0.0980762i) q^{26} -4.00000i q^{27} +(-3.46410 - 6.00000i) q^{28} +(2.59808 + 1.50000i) q^{29} +(-0.267949 - 1.00000i) q^{30} +1.26795i q^{31} +(4.00000 + 4.00000i) q^{32} +(4.73205 - 2.73205i) q^{33} +(-2.36603 + 8.83013i) q^{34} +(0.803848 - 0.464102i) q^{35} +(-7.73205 + 4.46410i) q^{36} +(-3.86603 + 6.69615i) q^{37} +(-1.73205 + 6.46410i) q^{38} +(9.56218 - 2.36603i) q^{39} +(-0.535898 + 0.535898i) q^{40} +(-1.03590 - 0.598076i) q^{41} +(-9.46410 - 9.46410i) q^{42} +(8.19615 - 4.73205i) q^{43} +(-3.46410 - 2.00000i) q^{44} +(-0.598076 - 1.03590i) q^{45} +(-3.00000 + 0.803848i) q^{46} +3.26795i q^{47} +(9.46410 + 5.46410i) q^{48} +(2.50000 - 4.33013i) q^{49} +(4.92820 + 4.92820i) q^{50} +17.6603i q^{51} +(-5.00000 - 5.19615i) q^{52} -9.92820i q^{53} +(-4.00000 + 4.00000i) q^{54} +(0.267949 - 0.464102i) q^{55} +(-2.53590 + 9.46410i) q^{56} +12.9282i q^{57} +(-1.09808 - 4.09808i) q^{58} +(-3.73205 - 6.46410i) q^{59} +(-0.732051 + 1.26795i) q^{60} +(0.866025 - 0.500000i) q^{61} +(1.26795 - 1.26795i) q^{62} +(-13.3923 - 7.73205i) q^{63} -8.00000i q^{64} +(0.696152 - 0.669873i) q^{65} +(-7.46410 - 2.00000i) q^{66} +(-5.36603 + 9.29423i) q^{67} +(11.1962 - 6.46410i) q^{68} +(-5.19615 + 3.00000i) q^{69} +(-1.26795 - 0.339746i) q^{70} +(-11.0263 + 6.36603i) q^{71} +(12.1962 + 3.26795i) q^{72} +1.73205i q^{73} +(10.5622 - 2.83013i) q^{74} +(11.6603 + 6.73205i) q^{75} +(8.19615 - 4.73205i) q^{76} -6.92820i q^{77} +(-11.9282 - 7.19615i) q^{78} +10.3923 q^{79} +1.07180 q^{80} +(1.23205 - 2.13397i) q^{81} +(0.437822 + 1.63397i) q^{82} +5.46410 q^{83} +18.9282i q^{84} +(0.866025 + 1.50000i) q^{85} +(-12.9282 - 3.46410i) q^{86} +(-4.09808 - 7.09808i) q^{87} +(1.46410 + 5.46410i) q^{88} +(-0.464102 - 0.267949i) q^{89} +(-0.437822 + 1.63397i) q^{90} +(3.46410 - 12.0000i) q^{91} +(3.80385 + 2.19615i) q^{92} +(1.73205 - 3.00000i) q^{93} +(3.26795 - 3.26795i) q^{94} +(0.633975 + 1.09808i) q^{95} +(-4.00000 - 14.9282i) q^{96} +(5.19615 - 3.00000i) q^{97} +(-6.83013 + 1.83013i) q^{98} -8.92820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 6 q^{3} - 8 q^{5} + 4 q^{6} - 12 q^{7} + 8 q^{8} + 2 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{14} + 6 q^{15} - 16 q^{16} - 6 q^{17} + 10 q^{18} - 6 q^{19} + 24 q^{21} + 4 q^{22} - 6 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^5 + 4 * q^6 - 12 * q^7 + 8 * q^8 + 2 * q^9 + 8 * q^10 - 4 * q^11 + 4 * q^12 + 12 * q^14 + 6 * q^15 - 16 * q^16 - 6 * q^17 + 10 * q^18 - 6 * q^19 + 24 * q^21 + 4 * q^22 - 6 * q^23 - 16 * q^24 + 8 * q^25 + 10 * q^26 - 8 * q^30 + 16 * q^32 + 12 * q^33 - 6 * q^34 + 24 * q^35 - 24 * q^36 - 12 * q^37 + 14 * q^39 - 16 * q^40 - 18 * q^41 - 24 * q^42 + 12 * q^43 + 8 * q^45 - 12 * q^46 + 24 * q^48 + 10 * q^49 - 8 * q^50 - 20 * q^52 - 16 * q^54 + 8 * q^55 - 24 * q^56 + 6 * q^58 - 8 * q^59 + 4 * q^60 + 12 * q^62 - 12 * q^63 - 18 * q^65 - 16 * q^66 - 18 * q^67 + 24 * q^68 - 12 * q^70 - 6 * q^71 + 28 * q^72 + 18 * q^74 + 12 * q^75 + 12 * q^76 - 20 * q^78 + 32 * q^80 - 2 * q^81 + 26 * q^82 + 8 * q^83 - 24 * q^86 - 6 * q^87 - 8 * q^88 + 12 * q^89 - 26 * q^90 + 36 * q^92 + 20 * q^94 + 6 * q^95 - 16 * q^96 - 10 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−2.36603	−	1.36603i	−1.36603	−	0.788675i	−0.375608	−	0.926779i	$-0.622566\pi$
$3$	−2.36603	−	1.36603i	−1.36603	−	0.788675i	−0.990418	+	0.138104i	$0.955899\pi$
$4$			2.00000i			1.00000i
$5$	−0.267949			−0.119831			−0.0599153	−	0.998203i	$-0.519083\pi$
$5$	−0.267949			−0.119831			−0.0599153	+	0.998203i	$0.519083\pi$
$6$	1.00000	+	3.73205i	0.408248	+	1.52360i
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	2.23205	+	3.86603i	0.744017	+	1.28868i
$10$	0.267949	+	0.267949i	0.0847330	+	0.0847330i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	2.73205	−	4.73205i	0.788675	−	1.36603i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$14$	4.73205	+	1.26795i	1.26469	+	0.338874i
$15$	0.633975	+	0.366025i	0.163692	+	0.0945074i
$16$	−4.00000			−1.00000
$17$	−3.23205	−	5.59808i	−0.783887	−	1.35773i	−0.929661	−	0.368415i	$-0.879901\pi$
$17$	−3.23205	−	5.59808i	−0.783887	−	1.35773i	0.145774	−	0.989318i	$-0.453433\pi$
$18$	1.63397	−	6.09808i	0.385132	−	1.43733i
$19$	−2.36603	−	4.09808i	−0.542803	−	0.940163i	−0.998742	−	0.0501517i	$-0.984030\pi$
$19$	−2.36603	−	4.09808i	−0.542803	−	0.940163i	0.455938	−	0.890011i	$-0.349304\pi$
$20$		−	0.535898i		−	0.119831i
$21$	9.46410			2.06524
$22$	2.73205	−	0.732051i	0.582475	−	0.156074i
$23$	1.09808	−	1.90192i	0.228965	−	0.396579i	−0.728537	−	0.685007i	$-0.759799\pi$
$23$	1.09808	−	1.90192i	0.228965	−	0.396579i	0.957502	+	0.288428i	$0.0931326\pi$
$24$	−7.46410	+	2.00000i	−1.52360	+	0.408248i
$25$	−4.92820			−0.985641
$26$	5.09808	+	0.0980762i	0.999815	+	0.0192343i
$27$		−	4.00000i		−	0.769800i
$28$	−3.46410	−	6.00000i	−0.654654	−	1.13389i
$29$	2.59808	+	1.50000i	0.482451	+	0.278543i	0.721437	−	0.692480i	$-0.243482\pi$
$29$	2.59808	+	1.50000i	0.482451	+	0.278543i	−0.238987	+	0.971023i	$0.576815\pi$
$30$	−0.267949	−	1.00000i	−0.0489206	−	0.182574i
$31$			1.26795i			0.227730i	0.993496	+	0.113865i	$0.0363232\pi$
$31$			1.26795i			0.227730i	−0.993496	+	0.113865i	$0.963677\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	4.73205	−	2.73205i	0.823744	−	0.475589i
$34$	−2.36603	+	8.83013i	−0.405770	+	1.51435i
$35$	0.803848	−	0.464102i	0.135875	−	0.0784475i
$36$	−7.73205	+	4.46410i	−1.28868	+	0.744017i
$37$	−3.86603	+	6.69615i	−0.635571	+	1.10084i	0.350823	+	0.936442i	$0.385902\pi$
$37$	−3.86603	+	6.69615i	−0.635571	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−1.73205	+	6.46410i	−0.280976	+	1.04862i
$39$	9.56218	−	2.36603i	1.53117	−	0.378867i
$40$	−0.535898	+	0.535898i	−0.0847330	+	0.0847330i
$41$	−1.03590	−	0.598076i	−0.161780	−	0.0934038i	0.416924	−	0.908941i	$-0.363108\pi$
$41$	−1.03590	−	0.598076i	−0.161780	−	0.0934038i	−0.578704	+	0.815538i	$0.696441\pi$
$42$	−9.46410	−	9.46410i	−1.46034	−	1.46034i
$43$	8.19615	−	4.73205i	1.24990	−	0.721631i	0.278812	−	0.960346i	$-0.410059\pi$
$43$	8.19615	−	4.73205i	1.24990	−	0.721631i	0.971090	+	0.238715i	$0.0767261\pi$
$44$	−3.46410	−	2.00000i	−0.522233	−	0.301511i
$45$	−0.598076	−	1.03590i	−0.0891559	−	0.154423i
$46$	−3.00000	+	0.803848i	−0.442326	+	0.118521i
$47$			3.26795i			0.476679i	0.971182	+	0.238340i	$0.0766032\pi$
$47$			3.26795i			0.476679i	−0.971182	+	0.238340i	$0.923397\pi$
$48$	9.46410	+	5.46410i	1.36603	+	0.788675i
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$	4.92820	+	4.92820i	0.696953	+	0.696953i
$51$			17.6603i			2.47293i
$52$	−5.00000	−	5.19615i	−0.693375	−	0.720577i
$53$		−	9.92820i		−	1.36374i	−0.731472	−	0.681872i	$-0.761166\pi$
$53$		−	9.92820i		−	1.36374i	0.731472	−	0.681872i	$-0.238834\pi$
$54$	−4.00000	+	4.00000i	−0.544331	+	0.544331i
$55$	0.267949	−	0.464102i	0.0361303	−	0.0625794i
$56$	−2.53590	+	9.46410i	−0.338874	+	1.26469i
$57$			12.9282i			1.71238i
$58$	−1.09808	−	4.09808i	−0.144184	−	0.538104i
$59$	−3.73205	−	6.46410i	−0.485872	−	0.841554i	0.513997	−	0.857792i	$-0.328164\pi$
$59$	−3.73205	−	6.46410i	−0.485872	−	0.841554i	−0.999868	+	0.0162379i	$0.994831\pi$
$60$	−0.732051	+	1.26795i	−0.0945074	+	0.163692i
$61$	0.866025	−	0.500000i	0.110883	−	0.0640184i	−0.443533	−	0.896258i	$-0.646275\pi$
$61$	0.866025	−	0.500000i	0.110883	−	0.0640184i	0.554416	+	0.832240i	$0.312942\pi$
$62$	1.26795	−	1.26795i	0.161030	−	0.161030i
$63$	−13.3923	−	7.73205i	−1.68727	−	0.974147i
$64$		−	8.00000i		−	1.00000i
$65$	0.696152	−	0.669873i	0.0863471	−	0.0830875i
$66$	−7.46410	−	2.00000i	−0.918767	−	0.246183i
$67$	−5.36603	+	9.29423i	−0.655564	+	1.13547i	0.326188	+	0.945305i	$0.394236\pi$
$67$	−5.36603	+	9.29423i	−0.655564	+	1.13547i	−0.981752	+	0.190166i	$0.939097\pi$
$68$	11.1962	−	6.46410i	1.35773	−	0.783887i
$69$	−5.19615	+	3.00000i	−0.625543	+	0.361158i
$70$	−1.26795	−	0.339746i	−0.151549	−	0.0406074i
$71$	−11.0263	+	6.36603i	−1.30858	+	0.755508i	−0.981859	−	0.189613i	$-0.939277\pi$
$71$	−11.0263	+	6.36603i	−1.30858	+	0.755508i	−0.326720	+	0.945121i	$0.605943\pi$
$72$	12.1962	+	3.26795i	1.43733	+	0.385132i
$73$			1.73205i			0.202721i	0.994850	+	0.101361i	$0.0323196\pi$
$73$			1.73205i			0.202721i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	10.5622	−	2.83013i	1.22783	−	0.328996i
$75$	11.6603	+	6.73205i	1.34641	+	0.777350i
$76$	8.19615	−	4.73205i	0.940163	−	0.542803i
$77$		−	6.92820i		−	0.789542i
$78$	−11.9282	−	7.19615i	−1.35060	−	0.814804i
$79$	10.3923			1.16923			0.584613	−	0.811312i	$-0.301246\pi$
$79$	10.3923			1.16923			0.584613	+	0.811312i	$0.301246\pi$
$80$	1.07180			0.119831
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	0.437822	+	1.63397i	0.0483494	+	0.180442i
$83$	5.46410			0.599763			0.299882	−	0.953976i	$-0.403053\pi$
$83$	5.46410			0.599763			0.299882	+	0.953976i	$0.403053\pi$
$84$			18.9282i			2.06524i
$85$	0.866025	+	1.50000i	0.0939336	+	0.162698i
$86$	−12.9282	−	3.46410i	−1.39408	−	0.373544i
$87$	−4.09808	−	7.09808i	−0.439360	−	0.760994i
$88$	1.46410	+	5.46410i	0.156074	+	0.582475i
$89$	−0.464102	−	0.267949i	−0.0491947	−	0.0284026i	0.475201	−	0.879877i	$-0.342375\pi$
$89$	−0.464102	−	0.267949i	−0.0491947	−	0.0284026i	−0.524396	+	0.851475i	$0.675709\pi$
$90$	−0.437822	+	1.63397i	−0.0461505	+	0.172236i
$91$	3.46410	−	12.0000i	0.363137	−	1.25794i
$92$	3.80385	+	2.19615i	0.396579	+	0.228965i
$93$	1.73205	−	3.00000i	0.179605	−	0.311086i
$94$	3.26795	−	3.26795i	0.337063	−	0.337063i
$95$	0.633975	+	1.09808i	0.0650444	+	0.112660i
$96$	−4.00000	−	14.9282i	−0.408248	−	1.52360i
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	−0.212445	−	0.977173i	$-0.568143\pi$
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	0.740034	+	0.672569i	$0.234809\pi$
$98$	−6.83013	+	1.83013i	−0.689947	+	0.184871i
$99$	−8.92820			−0.897318
$100$		−	9.85641i		−	0.985641i
$101$	−15.9904	−	9.23205i	−1.59110	−	0.918623i	−0.993118	−	0.117115i	$-0.962635\pi$
$101$	−15.9904	−	9.23205i	−1.59110	−	0.918623i	−0.597984	−	0.801508i	$-0.704031\pi$
$102$	17.6603	−	17.6603i	1.74863	−	1.74863i
$103$	−4.19615			−0.413459			−0.206730	−	0.978398i	$-0.566282\pi$
$103$	−4.19615			−0.413459			−0.206730	+	0.978398i	$0.566282\pi$
$104$	−0.196152	+	10.1962i	−0.0192343	+	0.999815i
$105$	−2.53590			−0.247478
$106$	−9.92820	+	9.92820i	−0.964312	+	0.964312i
$107$	0.294229	+	0.169873i	0.0284442	+	0.0164222i	0.514155	−	0.857697i	$-0.328106\pi$
$107$	0.294229	+	0.169873i	0.0284442	+	0.0164222i	−0.485710	+	0.874120i	$0.661439\pi$
$108$	8.00000			0.769800
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	−0.732051	+	0.196152i	−0.0697983	+	0.0187024i
$111$	18.2942	−	10.5622i	1.73641	−	1.00252i
$112$	12.0000	−	6.92820i	1.13389	−	0.654654i
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	0.927914	−	0.372794i	$-0.121600\pi$
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	−0.786806	+	0.617200i	$0.788267\pi$
$114$	12.9282	−	12.9282i	1.21084	−	1.21084i
$115$	−0.294229	+	0.509619i	−0.0274370	+	0.0475222i
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	−15.4641	−	4.46410i	−1.42966	−	0.412706i
$118$	−2.73205	+	10.1962i	−0.251506	+	0.938632i
$119$	19.3923	+	11.1962i	1.77769	+	1.02635i
$120$	2.00000	−	0.535898i	0.182574	−	0.0489206i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.36603	−	0.366025i	−0.123674	−	0.0331384i
$123$	1.63397	+	2.83013i	0.147331	+	0.255184i
$124$	−2.53590			−0.227730
$125$	2.66025			0.237940
$126$	5.66025	+	21.1244i	0.504256	+	1.88191i
$127$	−8.83013	+	15.2942i	−0.783547	+	1.35714i	0.146316	+	0.989238i	$0.453258\pi$
$127$	−8.83013	+	15.2942i	−0.783547	+	1.35714i	−0.929863	+	0.367905i	$0.880075\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	−25.8564			−2.27653
$130$	−1.36603	−	0.0262794i	−0.119808	−	0.00230486i
$131$			7.26795i			0.635004i	0.948258	+	0.317502i	$0.102844\pi$
$131$			7.26795i			0.635004i	−0.948258	+	0.317502i	$0.897156\pi$
$132$	5.46410	+	9.46410i	0.475589	+	0.823744i
$133$	14.1962	+	8.19615i	1.23096	+	0.710697i
$134$	14.6603	−	3.92820i	1.26645	−	0.339345i
$135$			1.07180i			0.0922456i
$136$	−17.6603	−	4.73205i	−1.51435	−	0.405770i
$137$	−15.2321	+	8.79423i	−1.30136	+	0.751342i	−0.980638	−	0.195831i	$-0.937260\pi$
$137$	−15.2321	+	8.79423i	−1.30136	+	0.751342i	−0.320724	+	0.947173i	$0.603926\pi$
$138$	8.19615	+	2.19615i	0.697703	+	0.186949i
$139$	2.19615	−	1.26795i	0.186275	−	0.107546i	−0.403962	−	0.914776i	$-0.632367\pi$
$139$	2.19615	−	1.26795i	0.186275	−	0.107546i	0.590238	+	0.807230i	$0.299034\pi$
$140$	0.928203	+	1.60770i	0.0784475	+	0.135875i
$141$	4.46410	−	7.73205i	0.375945	−	0.651156i
$142$	17.3923	+	4.66025i	1.45953	+	0.391080i
$143$	−1.73205	−	7.00000i	−0.144841	−	0.585369i
$144$	−8.92820	−	15.4641i	−0.744017	−	1.28868i
$145$	−0.696152	−	0.401924i	−0.0578123	−	0.0333780i
$146$	1.73205	−	1.73205i	0.143346	−	0.143346i
$147$	−11.8301	+	6.83013i	−0.975732	+	0.563339i
$148$	−13.3923	−	7.73205i	−1.10084	−	0.635571i
$149$	4.13397	+	7.16025i	0.338668	+	0.586591i	0.984183	−	0.177157i	$-0.0566902\pi$
$149$	4.13397	+	7.16025i	0.338668	+	0.586591i	−0.645514	+	0.763748i	$0.723357\pi$
$150$	−4.92820	−	18.3923i	−0.402386	−	1.50173i
$151$		−	8.19615i		−	0.666993i	−0.942751	−	0.333497i	$-0.891771\pi$
$151$		−	8.19615i		−	0.666993i	0.942751	−	0.333497i	$-0.108229\pi$
$152$	−12.9282	−	3.46410i	−1.04862	−	0.280976i
$153$	14.4282	−	24.9904i	1.16645	−	2.02035i
$154$	−6.92820	+	6.92820i	−0.558291	+	0.558291i
$155$		−	0.339746i		−	0.0272891i
$156$	4.73205	+	19.1244i	0.378867	+	1.53117i
$157$			9.92820i			0.792357i	0.918174	+	0.396178i	$0.129664\pi$
$157$			9.92820i			0.792357i	−0.918174	+	0.396178i	$0.870336\pi$
$158$	−10.3923	−	10.3923i	−0.826767	−	0.826767i
$159$	−13.5622	+	23.4904i	−1.07555	+	1.86291i
$160$	−1.07180	−	1.07180i	−0.0847330	−	0.0847330i
$161$			7.60770i			0.599570i
$162$	−3.36603	+	0.901924i	−0.264460	+	0.0708618i
$163$	−2.19615	−	3.80385i	−0.172016	−	0.297940i	0.767109	−	0.641517i	$-0.221695\pi$
$163$	−2.19615	−	3.80385i	−0.172016	−	0.297940i	−0.939125	+	0.343577i	$0.888361\pi$
$164$	1.19615	−	2.07180i	0.0934038	−	0.161780i
$165$	−1.26795	+	0.732051i	−0.0987097	+	0.0569901i
$166$	−5.46410	−	5.46410i	−0.424097	−	0.424097i
$167$	−7.73205	−	4.46410i	−0.598324	−	0.345443i	0.170058	−	0.985434i	$-0.445605\pi$
$167$	−7.73205	−	4.46410i	−0.598324	−	0.345443i	−0.768382	+	0.639992i	$0.778938\pi$
$168$	18.9282	−	18.9282i	1.46034	−	1.46034i
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$	0.633975	−	2.36603i	0.0486236	−	0.181466i
$171$	10.5622	−	18.2942i	0.807710	−	1.39899i
$172$	9.46410	+	16.3923i	0.721631	+	1.24990i
$173$	−4.39230	+	2.53590i	−0.333941	+	0.192801i	−0.657589	−	0.753377i	$-0.728424\pi$
$173$	−4.39230	+	2.53590i	−0.333941	+	0.192801i	0.323649	+	0.946177i	$0.395090\pi$
$174$	−3.00000	+	11.1962i	−0.227429	+	0.848778i
$175$	14.7846	−	8.53590i	1.11761	−	0.645253i
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$			20.3923i			1.53278i
$178$	0.196152	+	0.732051i	0.0147022	+	0.0548695i
$179$	−12.0000	−	6.92820i	−0.896922	−	0.517838i	−0.0207218	−	0.999785i	$-0.506596\pi$
$179$	−12.0000	−	6.92820i	−0.896922	−	0.517838i	−0.876200	+	0.481947i	$0.839930\pi$
$180$	2.07180	−	1.19615i	0.154423	−	0.0891559i
$181$			11.5359i			0.857457i	0.903433	+	0.428728i	$0.141038\pi$
$181$			11.5359i			0.857457i	−0.903433	+	0.428728i	$0.858962\pi$
$182$	−15.4641	+	8.53590i	−1.14628	+	0.632723i
$183$	−2.73205			−0.201959
$184$	−1.60770	−	6.00000i	−0.118521	−	0.442326i
$185$	1.03590	−	1.79423i	0.0761608	−	0.131914i
$186$	−4.73205	+	1.26795i	−0.346971	+	0.0929705i
$187$	12.9282			0.945404
$188$	−6.53590			−0.476679
$189$	6.92820	+	12.0000i	0.503953	+	0.872872i
$190$	0.464102	−	1.73205i	0.0336695	−	0.125656i
$191$	−7.09808	−	12.2942i	−0.513599	−	0.889579i	−0.999876	−	0.0157743i	$-0.994979\pi$
$191$	−7.09808	−	12.2942i	−0.513599	−	0.889579i	0.486277	−	0.873805i	$-0.338355\pi$
$192$	−10.9282	+	18.9282i	−0.788675	+	1.36603i
$193$	21.6962	+	12.5263i	1.56172	+	0.901661i	0.997083	+	0.0763241i	$0.0243184\pi$
$193$	21.6962	+	12.5263i	1.56172	+	0.901661i	0.564640	+	0.825337i	$0.309015\pi$
$194$	−8.19615	−	2.19615i	−0.588449	−	0.157675i
$195$	−2.56218	+	0.633975i	−0.183481	+	0.0453999i
$196$	8.66025	+	5.00000i	0.618590	+	0.357143i
$197$	9.73205	−	16.8564i	0.693380	−	1.20097i	−0.277344	−	0.960771i	$-0.589454\pi$
$197$	9.73205	−	16.8564i	0.693380	−	1.20097i	0.970724	−	0.240199i	$-0.0772125\pi$
$198$	8.92820	+	8.92820i	0.634500	+	0.634500i
$199$	−4.56218	−	7.90192i	−0.323404	−	0.560153i	0.657784	−	0.753207i	$-0.271494\pi$
$199$	−4.56218	−	7.90192i	−0.323404	−	0.560153i	−0.981188	+	0.193054i	$0.938161\pi$
$200$	−9.85641	+	9.85641i	−0.696953	+	0.696953i
$201$	25.3923	−	14.6603i	1.79104	−	1.03405i
$202$	6.75833	+	25.2224i	0.475514	+	1.77464i
$203$	−10.3923			−0.729397
$204$	−35.3205			−2.47293
$205$	0.277568	+	0.160254i	0.0193862	+	0.0111926i
$206$	4.19615	+	4.19615i	0.292360	+	0.292360i
$207$	9.80385			0.681415
$208$	10.3923	−	10.0000i	0.720577	−	0.693375i
$209$	9.46410			0.654646
$210$	2.53590	+	2.53590i	0.174994	+	0.174994i
$211$	2.24167	+	1.29423i	0.154323	+	0.0890984i	0.575173	−	0.818032i	$-0.304935\pi$
$211$	2.24167	+	1.29423i	0.154323	+	0.0890984i	−0.420850	+	0.907130i	$0.638268\pi$
$212$	19.8564			1.36374
$213$	34.7846			2.38340
$214$	−0.124356	−	0.464102i	−0.00850078	−	0.0317253i
$215$	−2.19615	+	1.26795i	−0.149776	+	0.0864734i
$216$	−8.00000	−	8.00000i	−0.544331	−	0.544331i
$217$	−2.19615	−	3.80385i	−0.149085	−	0.258222i
$218$	6.00000	+	6.00000i	0.406371	+	0.406371i
$219$	2.36603	−	4.09808i	0.159881	−	0.276922i
$220$	0.928203	+	0.535898i	0.0625794	+	0.0361303i
$221$	22.3923	+	6.46410i	1.50627	+	0.434823i
$222$	−28.8564	−	7.73205i	−1.93672	−	0.518941i
$223$	−16.9019	−	9.75833i	−1.13184	−	0.653466i	−0.187440	−	0.982276i	$-0.560019\pi$
$223$	−16.9019	−	9.75833i	−1.13184	−	0.653466i	−0.944396	+	0.328810i	$0.893352\pi$
$224$	−18.9282	−	5.07180i	−1.26469	−	0.338874i
$225$	−11.0000	−	19.0526i	−0.733333	−	1.27017i
$226$	1.09808	−	4.09808i	0.0730429	−	0.272600i
$227$	6.02628	+	10.4378i	0.399978	+	0.692783i	0.993723	−	0.111871i	$-0.0356844\pi$
$227$	6.02628	+	10.4378i	0.399978	+	0.692783i	−0.593745	+	0.804654i	$0.702351\pi$
$228$	−25.8564			−1.71238
$229$	0.928203			0.0613374			0.0306687	−	0.999530i	$-0.490236\pi$
$229$	0.928203			0.0613374			0.0306687	+	0.999530i	$0.490236\pi$
$230$	0.803848	−	0.215390i	0.0530041	−	0.0142024i
$231$	−9.46410	+	16.3923i	−0.622692	+	1.07853i
$232$	8.19615	−	2.19615i	0.538104	−	0.144184i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	11.0000	+	19.9282i	0.719092	+	1.30275i
$235$		−	0.875644i		−	0.0571207i
$236$	12.9282	−	7.46410i	0.841554	−	0.485872i
$237$	−24.5885	−	14.1962i	−1.59719	−	0.922139i
$238$	−8.19615	−	30.5885i	−0.531278	−	1.98276i
$239$			2.39230i			0.154745i	0.997002	+	0.0773727i	$0.0246531\pi$
$239$			2.39230i			0.154745i	−0.997002	+	0.0773727i	$0.975347\pi$
$240$	−2.53590	−	1.46410i	−0.163692	−	0.0945074i
$241$	−0.696152	+	0.401924i	−0.0448431	+	0.0258902i	−0.522254	−	0.852790i	$-0.674909\pi$
$241$	−0.696152	+	0.401924i	−0.0448431	+	0.0258902i	0.477411	+	0.878680i	$0.341575\pi$
$242$	2.56218	−	9.56218i	0.164703	−	0.614680i
$243$	−16.2224	+	9.36603i	−1.04067	+	0.600831i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	−0.669873	+	1.16025i	−0.0427966	+	0.0741259i
$246$	1.19615	−	4.46410i	0.0762639	−	0.284621i
$247$	16.3923	+	4.73205i	1.04302	+	0.301093i
$248$	2.53590	+	2.53590i	0.161030	+	0.161030i
$249$	−12.9282	−	7.46410i	−0.819292	−	0.473018i
$250$	−2.66025	−	2.66025i	−0.168249	−	0.168249i
$251$	1.90192	−	1.09808i	0.120048	−	0.0693100i	−0.438773	−	0.898598i	$-0.644587\pi$
$251$	1.90192	−	1.09808i	0.120048	−	0.0693100i	0.558822	+	0.829288i	$0.311254\pi$
$252$	15.4641	−	26.7846i	0.974147	−	1.68727i
$253$	2.19615	+	3.80385i	0.138071	+	0.239146i
$254$	24.1244	−	6.46410i	1.51370	−	0.405594i
$255$		−	4.73205i		−	0.296333i
$256$	16.0000			1.00000
$257$	2.42820	−	4.20577i	0.151467	−	0.262349i	−0.780300	−	0.625406i	$-0.784934\pi$
$257$	2.42820	−	4.20577i	0.151467	−	0.262349i	0.931767	+	0.363057i	$0.118267\pi$
$258$	25.8564	+	25.8564i	1.60975	+	1.60975i
$259$		−	26.7846i		−	1.66431i
$260$	1.33975	+	1.39230i	0.0830875	+	0.0863471i
$261$			13.3923i			0.828963i
$262$	7.26795	−	7.26795i	0.449015	−	0.449015i
$263$	2.19615	−	3.80385i	0.135421	−	0.234555i	−0.790337	−	0.612672i	$-0.790095\pi$
$263$	2.19615	−	3.80385i	0.135421	−	0.234555i	0.925758	+	0.378116i	$0.123428\pi$
$264$	4.00000	−	14.9282i	0.246183	−	0.918767i
$265$			2.66025i			0.163418i
$266$	−6.00000	−	22.3923i	−0.367884	−	1.37296i
$267$	0.732051	+	1.26795i	0.0448008	+	0.0775972i
$268$	−18.5885	−	10.7321i	−1.13547	−	0.655564i
$269$	2.19615	−	1.26795i	0.133902	−	0.0773082i	−0.431553	−	0.902088i	$-0.642034\pi$
$269$	2.19615	−	1.26795i	0.133902	−	0.0773082i	0.565455	+	0.824779i	$0.308701\pi$
$270$	1.07180	−	1.07180i	0.0652275	−	0.0652275i
$271$	−15.0000	−	8.66025i	−0.911185	−	0.526073i	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−15.0000	−	8.66025i	−0.911185	−	0.526073i	−0.880812	+	0.473466i	$0.843003\pi$
$272$	12.9282	+	22.3923i	0.783887	+	1.35773i
$273$	−24.5885	+	23.6603i	−1.48816	+	1.43198i
$274$	24.0263	+	6.43782i	1.45148	+	0.388923i
$275$	4.92820	−	8.53590i	0.297182	−	0.514734i
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	−17.5981	+	10.1603i	−1.05737	+	0.610471i	−0.924702	−	0.380691i	$-0.875686\pi$
$277$	−17.5981	+	10.1603i	−1.05737	+	0.610471i	−0.132663	+	0.991161i	$0.542353\pi$
$278$	−3.46410	−	0.928203i	−0.207763	−	0.0556699i
$279$	−4.90192	+	2.83013i	−0.293471	+	0.169435i
$280$	0.679492	−	2.53590i	0.0406074	−	0.151549i
$281$		−	6.66025i		−	0.397317i	−0.980069	−	0.198659i	$-0.936341\pi$
$281$		−	6.66025i		−	0.397317i	0.980069	−	0.198659i	$-0.0636585\pi$
$282$	−12.1962	+	3.26795i	−0.726270	+	0.194604i
$283$	−9.33975	−	5.39230i	−0.555190	−	0.320539i	0.196022	−	0.980599i	$-0.437197\pi$
$283$	−9.33975	−	5.39230i	−0.555190	−	0.320539i	−0.751213	+	0.660060i	$0.770531\pi$
$284$	−12.7321	−	22.0526i	−0.755508	−	1.30858i
$285$		−	3.46410i		−	0.205196i
$286$	−5.26795	+	8.73205i	−0.311500	+	0.516337i
$287$	4.14359			0.244589
$288$	−6.53590	+	24.3923i	−0.385132	+	1.43733i
$289$	−12.3923	+	21.4641i	−0.728959	+	1.26259i
$290$	0.294229	+	1.09808i	0.0172777	+	0.0644813i
$291$	−16.3923			−0.960934
$292$	−3.46410			−0.202721
$293$	−6.59808	−	11.4282i	−0.385464	−	0.667643i	0.606370	−	0.795183i	$-0.292625\pi$
$293$	−6.59808	−	11.4282i	−0.385464	−	0.667643i	−0.991833	+	0.127540i	$0.959292\pi$
$294$	18.6603	+	5.00000i	1.08829	+	0.291606i
$295$	1.00000	+	1.73205i	0.0582223	+	0.100844i
$296$	5.66025	+	21.1244i	0.328996	+	1.22783i
$297$	6.92820	+	4.00000i	0.402015	+	0.232104i
$298$	3.02628	−	11.2942i	0.175308	−	0.654257i
$299$	1.90192	+	7.68653i	0.109991	+	0.444524i
$300$	−13.4641	+	23.3205i	−0.777350	+	1.34641i
$301$	−16.3923	+	28.3923i	−0.944837	+	1.63651i
$302$	−8.19615	+	8.19615i	−0.471636	+	0.471636i
$303$	25.2224	+	43.6865i	1.44899	+	2.50973i
$304$	9.46410	+	16.3923i	0.542803	+	0.940163i
$305$	−0.232051	+	0.133975i	−0.0132872	+	0.00767136i
$306$	−39.4186	+	10.5622i	−2.25341	+	0.603800i
$307$	8.19615			0.467779			0.233890	−	0.972263i	$-0.424855\pi$
$307$	8.19615			0.467779			0.233890	+	0.972263i	$0.424855\pi$
$308$	13.8564			0.789542
$309$	9.92820	+	5.73205i	0.564796	+	0.326085i
$310$	−0.339746	+	0.339746i	−0.0192963	+	0.0192963i
$311$	12.5885			0.713826			0.356913	−	0.934138i	$-0.383829\pi$
$311$	12.5885			0.713826			0.356913	+	0.934138i	$0.383829\pi$
$312$	14.3923	−	23.8564i	0.814804	−	1.35060i
$313$	−9.46410			−0.534943			−0.267471	−	0.963566i	$-0.586188\pi$
$313$	−9.46410			−0.534943			−0.267471	+	0.963566i	$0.586188\pi$
$314$	9.92820	−	9.92820i	0.560281	−	0.560281i
$315$	3.58846	+	2.07180i	0.202187	+	0.116733i
$316$			20.7846i			1.16923i
$317$	−14.8038			−0.831467			−0.415733	−	0.909486i	$-0.636475\pi$
$317$	−14.8038			−0.831467			−0.415733	+	0.909486i	$0.636475\pi$
$318$	37.0526	−	9.92820i	2.07780	−	0.556746i
$319$	−5.19615	+	3.00000i	−0.290929	+	0.167968i
$320$			2.14359i			0.119831i
$321$	−0.464102	−	0.803848i	−0.0259036	−	0.0448664i
$322$	7.60770	−	7.60770i	0.423960	−	0.423960i
$323$	−15.2942	+	26.4904i	−0.850994	+	1.47396i
$324$	4.26795	+	2.46410i	0.237108	+	0.136895i
$325$	12.8038	−	12.3205i	0.710230	−	0.683419i
$326$	−1.60770	+	6.00000i	−0.0890420	+	0.332309i
$327$	14.1962	+	8.19615i	0.785049	+	0.453248i
$328$	−3.26795	+	0.875644i	−0.180442	+	0.0483494i
$329$	−5.66025	−	9.80385i	−0.312060	−	0.540504i
$330$	2.00000	+	0.535898i	0.110096	+	0.0295002i
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$			10.9282i			0.599763i
$333$	−34.5167			−1.89150
$334$	3.26795	+	12.1962i	0.178814	+	0.667344i
$335$	1.43782	−	2.49038i	0.0785566	−	0.136064i
$336$	−37.8564			−2.06524
$337$	15.2487			0.830650			0.415325	−	0.909673i	$-0.363668\pi$
$337$	15.2487			0.830650			0.415325	+	0.909673i	$0.363668\pi$
$338$	−13.4904	+	12.4904i	−0.733780	+	0.679387i
$339$		−	8.19615i		−	0.445154i
$340$	−3.00000	+	1.73205i	−0.162698	+	0.0939336i
$341$	−2.19615	−	1.26795i	−0.118928	−	0.0686633i
$342$	−28.8564	+	7.73205i	−1.56038	+	0.418101i
$343$		−	6.92820i		−	0.374088i
$344$	6.92820	−	25.8564i	0.373544	−	1.39408i
$345$	1.39230	−	0.803848i	0.0749592	−	0.0432777i
$346$	6.92820	+	1.85641i	0.372463	+	0.0998010i
$347$	−4.09808	+	2.36603i	−0.219996	+	0.127015i	−0.605949	−	0.795504i	$-0.707206\pi$
$347$	−4.09808	+	2.36603i	−0.219996	+	0.127015i	0.385952	+	0.922519i	$0.373873\pi$
$348$	14.1962	−	8.19615i	0.760994	−	0.439360i
$349$	14.6603	−	25.3923i	0.784745	−	1.35922i	−0.144406	−	0.989519i	$-0.546127\pi$
$349$	14.6603	−	25.3923i	0.784745	−	1.35922i	0.929151	−	0.369700i	$-0.120540\pi$
$350$	−23.3205	−	6.24871i	−1.24653	−	0.334008i
$351$	10.0000	+	10.3923i	0.533761	+	0.554700i
$352$	−10.9282	+	2.92820i	−0.582475	+	0.156074i
$353$	18.8205	+	10.8660i	1.00171	+	0.578340i	0.908755	−	0.417330i	$-0.137034\pi$
$353$	18.8205	+	10.8660i	1.00171	+	0.578340i	0.0929594	+	0.995670i	$0.470367\pi$
$354$	20.3923	−	20.3923i	1.08384	−	1.08384i
$355$	2.95448	−	1.70577i	0.156808	−	0.0905329i
$356$	0.535898	−	0.928203i	0.0284026	−	0.0491947i
$357$	−30.5885	−	52.9808i	−1.61891	−	2.80404i
$358$	5.07180	+	18.9282i	0.268053	+	1.00039i
$359$		−	26.9282i		−	1.42122i	−0.703588	−	0.710608i	$-0.748420\pi$
$359$		−	26.9282i		−	1.42122i	0.703588	−	0.710608i	$-0.251580\pi$
$360$	−3.26795	−	0.875644i	−0.172236	−	0.0461505i
$361$	−1.69615	+	2.93782i	−0.0892712	+	0.154622i
$362$	11.5359	−	11.5359i	0.606313	−	0.606313i
$363$		−	19.1244i		−	1.00377i
$364$	24.0000	+	6.92820i	1.25794	+	0.363137i
$365$		−	0.464102i		−	0.0242922i
$366$	2.73205	+	2.73205i	0.142807	+	0.142807i
$367$	8.90192	−	15.4186i	0.464677	−	0.804844i	−0.534510	−	0.845162i	$-0.679504\pi$
$367$	8.90192	−	15.4186i	0.464677	−	0.804844i	0.999187	+	0.0403184i	$0.0128372\pi$
$368$	−4.39230	+	7.60770i	−0.228965	+	0.396579i
$369$		−	5.33975i		−	0.277976i
$370$	−2.83013	+	0.758330i	−0.147131	+	0.0394237i
$371$	17.1962	+	29.7846i	0.892780	+	1.54634i
$372$	6.00000	+	3.46410i	0.311086	+	0.179605i
$373$	−13.6699	+	7.89230i	−0.707799	+	0.408648i	−0.810246	−	0.586090i	$-0.800666\pi$
$373$	−13.6699	+	7.89230i	−0.707799	+	0.408648i	0.102446	+	0.994739i	$0.467333\pi$
$374$	−12.9282	−	12.9282i	−0.668501	−	0.668501i
$375$	−6.29423	−	3.63397i	−0.325033	−	0.187658i
$376$	6.53590	+	6.53590i	0.337063	+	0.337063i
$377$	−10.5000	+	2.59808i	−0.540778	+	0.133808i
$378$	5.07180	−	18.9282i	0.260865	−	0.973562i
$379$	−8.02628	+	13.9019i	−0.412282	+	0.714094i	−0.995139	−	0.0984811i	$-0.968602\pi$
$379$	−8.02628	+	13.9019i	−0.412282	+	0.714094i	0.582857	+	0.812575i	$0.301935\pi$
$380$	−2.19615	+	1.26795i	−0.112660	+	0.0650444i
$381$	41.7846	−	24.1244i	2.14069	−	1.23593i
$382$	−5.19615	+	19.3923i	−0.265858	+	0.992197i
$383$	−17.3205	+	10.0000i	−0.885037	+	0.510976i	−0.872316	−	0.488943i	$-0.837383\pi$
$383$	−17.3205	+	10.0000i	−0.885037	+	0.510976i	−0.0127209	+	0.999919i	$0.504049\pi$
$384$	29.8564	−	8.00000i	1.52360	−	0.408248i
$385$			1.85641i			0.0946112i
$386$	−9.16987	−	34.2224i	−0.466734	−	1.74188i
$387$	36.5885	+	21.1244i	1.85990	+	1.07381i
$388$	6.00000	+	10.3923i	0.304604	+	0.527589i
$389$			36.7128i			1.86141i	0.365766	+	0.930707i	$0.380807\pi$
$389$			36.7128i			1.86141i	−0.365766	+	0.930707i	$0.619193\pi$
$390$	3.19615	+	1.92820i	0.161843	+	0.0976384i
$391$	−14.1962			−0.717930
$392$	−3.66025	−	13.6603i	−0.184871	−	0.689947i
$393$	9.92820	−	17.1962i	0.500812	−	0.867431i
$394$	−26.5885	+	7.12436i	−1.33951	+	0.358920i
$395$	−2.78461			−0.140109
$396$		−	17.8564i		−	0.897318i
$397$	−12.1244	−	21.0000i	−0.608504	−	1.05396i	−0.991487	−	0.130204i	$-0.958437\pi$
$397$	−12.1244	−	21.0000i	−0.608504	−	1.05396i	0.382983	−	0.923755i	$-0.374897\pi$
$398$	−3.33975	+	12.4641i	−0.167406	+	0.624769i
$399$	−22.3923	−	38.7846i	−1.12102	−	1.94166i
$400$	19.7128			0.985641
$401$	−5.42820	−	3.13397i	−0.271072	−	0.156503i	0.358303	−	0.933605i	$-0.383355\pi$
$401$	−5.42820	−	3.13397i	−0.271072	−	0.156503i	−0.629374	+	0.777102i	$0.716689\pi$
$402$	−40.0526	−	10.7321i	−1.99764	−	0.535266i
$403$	−3.16987	−	3.29423i	−0.157903	−	0.164097i
$404$	18.4641	−	31.9808i	0.918623	−	1.59110i
$405$	−0.330127	+	0.571797i	−0.0164041	+	0.0284128i
$406$	10.3923	+	10.3923i	0.515761	+	0.515761i
$407$	−7.73205	−	13.3923i	−0.383264	−	0.663832i
$408$	35.3205	+	35.3205i	1.74863	+	1.74863i
$409$	−9.69615	+	5.59808i	−0.479444	+	0.276807i	−0.720185	−	0.693782i	$-0.755943\pi$
$409$	−9.69615	+	5.59808i	−0.479444	+	0.276807i	0.240741	+	0.970589i	$0.422610\pi$
$410$	−0.117314	−	0.437822i	−0.00579373	−	0.0216225i
$411$	48.0526			2.37026
$412$		−	8.39230i		−	0.413459i
$413$	22.3923	+	12.9282i	1.10185	+	0.636155i
$414$	−9.80385	−	9.80385i	−0.481833	−	0.481833i
$415$	−1.46410			−0.0718699
$416$	−20.3923	−	0.392305i	−0.999815	−	0.0192343i
$417$	−6.92820			−0.339276
$418$	−9.46410	−	9.46410i	−0.462904	−	0.462904i
$419$	22.0981	+	12.7583i	1.07956	+	0.623285i	0.930778	−	0.365585i	$-0.119131\pi$
$419$	22.0981	+	12.7583i	1.07956	+	0.623285i	0.148784	+	0.988870i	$0.452464\pi$
$420$		−	5.07180i		−	0.247478i
$421$	5.87564			0.286361			0.143181	−	0.989697i	$-0.454267\pi$
$421$	5.87564			0.286361			0.143181	+	0.989697i	$0.454267\pi$
$422$	−0.947441	−	3.53590i	−0.0461207	−	0.172125i
$423$	−12.6340	+	7.29423i	−0.614285	+	0.354658i
$424$	−19.8564	−	19.8564i	−0.964312	−	0.964312i
$425$	15.9282	+	27.5885i	0.772631	+	1.33824i
$426$	−34.7846	−	34.7846i	−1.68532	−	1.68532i
$427$	−1.73205	+	3.00000i	−0.0838198	+	0.145180i
$428$	−0.339746	+	0.588457i	−0.0164222	+	0.0284442i
$429$	−5.46410	+	18.9282i	−0.263809	+	0.913862i
$430$	3.46410	+	0.928203i	0.167054	+	0.0447619i
$431$	8.53590	+	4.92820i	0.411160	+	0.237383i	0.691288	−	0.722579i	$-0.257044\pi$
$431$	8.53590	+	4.92820i	0.411160	+	0.237383i	−0.280128	+	0.959963i	$0.590377\pi$
$432$			16.0000i			0.769800i
$433$	−10.5000	−	18.1865i	−0.504598	−	0.873989i	−0.999986	−	0.00531724i	$-0.998307\pi$
$433$	−10.5000	−	18.1865i	−0.504598	−	0.873989i	0.495388	−	0.868672i	$-0.335026\pi$
$434$	−1.60770	+	6.00000i	−0.0771718	+	0.288009i
$435$	1.09808	+	1.90192i	0.0526487	+	0.0911903i
$436$		−	12.0000i		−	0.574696i
$437$	−10.3923			−0.497131
$438$	−6.46410	+	1.73205i	−0.308867	+	0.0827606i
$439$	−18.1962	+	31.5167i	−0.868455	+	1.50421i	−0.00487976	+	0.999988i	$0.501553\pi$
$439$	−18.1962	+	31.5167i	−0.868455	+	1.50421i	−0.863575	+	0.504220i	$0.831780\pi$
$440$	−0.392305	−	1.46410i	−0.0187024	−	0.0697983i
$441$	22.3205			1.06288
$442$	−15.9282	−	28.8564i	−0.757627	−	1.37256i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	21.1244	+	36.5885i	1.00252	+	1.73641i
$445$	0.124356	+	0.0717968i	0.00589502	+	0.00340349i
$446$	7.14359	+	26.6603i	0.338259	+	1.26240i
$447$		−	22.5885i		−	1.06840i
$448$	13.8564	+	24.0000i	0.654654	+	1.13389i
$449$	11.5359	−	6.66025i	0.544413	−	0.314317i	−0.202453	−	0.979292i	$-0.564891\pi$
$449$	11.5359	−	6.66025i	0.544413	−	0.314317i	0.746865	+	0.664975i	$0.231558\pi$
$450$	−8.05256	+	30.0526i	−0.379601	+	1.41669i
$451$	2.07180	−	1.19615i	0.0975571	−	0.0563246i
$452$	−5.19615	+	3.00000i	−0.244406	+	0.141108i
$453$	−11.1962	+	19.3923i	−0.526041	+	0.911130i
$454$	4.41154	−	16.4641i	0.207044	−	0.772699i
$455$	−0.928203	+	3.21539i	−0.0435148	+	0.150740i
$456$	25.8564	+	25.8564i	1.21084	+	1.21084i
$457$	−3.69615	−	2.13397i	−0.172899	−	0.0998231i	0.411053	−	0.911611i	$-0.365161\pi$
$457$	−3.69615	−	2.13397i	−0.172899	−	0.0998231i	−0.583952	+	0.811788i	$0.698494\pi$
$458$	−0.928203	−	0.928203i	−0.0433721	−	0.0433721i
$459$	−22.3923	+	12.9282i	−1.04518	+	0.603437i
$460$	−1.01924	−	0.588457i	−0.0475222	−	0.0274370i
$461$	5.66987	+	9.82051i	0.264072	+	0.457387i	0.967320	−	0.253558i	$-0.0816009\pi$
$461$	5.66987	+	9.82051i	0.264072	+	0.457387i	−0.703248	+	0.710945i	$0.748268\pi$
$462$	25.8564	−	6.92820i	1.20295	−	0.322329i
$463$			4.39230i			0.204128i	0.994778	+	0.102064i	$0.0325446\pi$
$463$			4.39230i			0.204128i	−0.994778	+	0.102064i	$0.967455\pi$
$464$	−10.3923	−	6.00000i	−0.482451	−	0.278543i
$465$	−0.464102	+	0.803848i	−0.0215222	+	0.0372775i
$466$		0			0
$467$		−	27.4641i		−	1.27089i	−0.772147	−	0.635444i	$-0.780817\pi$
$467$		−	27.4641i		−	1.27089i	0.772147	−	0.635444i	$-0.219183\pi$
$468$	8.92820	−	30.9282i	0.412706	−	1.42966i
$469$		−	37.1769i		−	1.71667i
$470$	−0.875644	+	0.875644i	−0.0403905	+	0.0403905i
$471$	13.5622	−	23.4904i	0.624912	−	1.08238i
$472$	−20.3923	−	5.46410i	−0.938632	−	0.251506i
$473$			18.9282i			0.870320i
$474$	10.3923	+	38.7846i	0.477334	+	1.78144i
$475$	11.6603	+	20.1962i	0.535009	+	0.926663i
$476$	−22.3923	+	38.7846i	−1.02635	+	1.77769i
$477$	38.3827	−	22.1603i	1.75742	−	1.01465i
$478$	2.39230	−	2.39230i	0.109421	−	0.109421i
$479$	28.3468	+	16.3660i	1.29520	+	0.747783i	0.979571	−	0.201100i	$-0.0644518\pi$
$479$	28.3468	+	16.3660i	1.29520	+	0.747783i	0.315627	+	0.948883i	$0.397785\pi$
$480$	1.07180	+	4.00000i	0.0489206	+	0.182574i
$481$	−6.69615	−	27.0622i	−0.305318	−	1.23393i
$482$	1.09808	+	0.294229i	0.0500160	+	0.0134017i
$483$	10.3923	−	18.0000i	0.472866	−	0.819028i
$484$	−12.1244	+	7.00000i	−0.551107	+	0.318182i
$485$	−1.39230	+	0.803848i	−0.0632213	+	0.0365008i
$486$	25.5885	+	6.85641i	1.16072	+	0.311013i
$487$	9.80385	−	5.66025i	0.444255	−	0.256491i	−0.261146	−	0.965299i	$-0.584100\pi$
$487$	9.80385	−	5.66025i	0.444255	−	0.256491i	0.705401	+	0.708809i	$0.250767\pi$
$488$	0.732051	−	2.73205i	0.0331384	−	0.123674i
$489$			12.0000i			0.542659i
$490$	1.83013	−	0.490381i	0.0826767	−	0.0221532i
$491$	−24.5885	−	14.1962i	−1.10966	−	0.640663i	−0.170920	−	0.985285i	$-0.554674\pi$
$491$	−24.5885	−	14.1962i	−1.10966	−	0.640663i	−0.938742	+	0.344622i	$0.888007\pi$
$492$	−5.66025	+	3.26795i	−0.255184	+	0.147331i
$493$		−	19.3923i		−	0.873385i
$494$	−11.6603	−	21.1244i	−0.524620	−	0.950430i
$495$	2.39230			0.107526
$496$		−	5.07180i		−	0.227730i
$497$	22.0526	−	38.1962i	0.989192	−	1.71333i
$498$	5.46410	+	20.3923i	0.244852	+	0.913801i
$499$	−33.1244			−1.48285			−0.741425	−	0.671036i	$-0.765850\pi$
$499$	−33.1244			−1.48285			−0.741425	+	0.671036i	$0.765850\pi$
$500$			5.32051i			0.237940i
$501$	12.1962	+	21.1244i	0.544884	+	0.943767i
$502$	−3.00000	−	0.803848i	−0.133897	−	0.0358775i
$503$	16.3923	+	28.3923i	0.730897	+	1.26595i	0.956500	+	0.291731i	$0.0942312\pi$
$503$	16.3923	+	28.3923i	0.730897	+	1.26595i	−0.225604	+	0.974219i	$0.572435\pi$
$504$	−42.2487	+	11.3205i	−1.88191	+	0.504256i
$505$	4.28461	+	2.47372i	0.190663	+	0.110079i
$506$	1.60770	−	6.00000i	0.0714708	−	0.266733i
$507$	−18.9282	+	30.0526i	−0.840631	+	1.33468i
$508$	−30.5885	−	17.6603i	−1.35714	−	0.783547i
$509$	−16.0622	+	27.8205i	−0.711944	+	1.23312i	0.252183	+	0.967680i	$0.418851\pi$
$509$	−16.0622	+	27.8205i	−0.711944	+	1.23312i	−0.964127	+	0.265443i	$0.914482\pi$
$510$	−4.73205	+	4.73205i	−0.209539	+	0.209539i
$511$	−3.00000	−	5.19615i	−0.132712	−	0.229864i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−16.3923	+	9.46410i	−0.723738	+	0.417850i
$514$	−6.63397	+	1.77757i	−0.292612	+	0.0784052i
$515$	1.12436			0.0495450
$516$		−	51.7128i		−	2.27653i
$517$	−5.66025	−	3.26795i	−0.248938	−	0.143724i
$518$	−26.7846	+	26.7846i	−1.17685	+	1.17685i
$519$	13.8564			0.608229
$520$	0.0525589	−	2.73205i	0.00230486	−	0.119808i
$521$	−39.2487			−1.71952			−0.859759	−	0.510701i	$-0.829386\pi$
$521$	−39.2487			−1.71952			−0.859759	+	0.510701i	$0.829386\pi$
$522$	13.3923	−	13.3923i	0.586165	−	0.586165i
$523$	11.1962	+	6.46410i	0.489574	+	0.282655i	0.724398	−	0.689382i	$-0.242118\pi$
$523$	11.1962	+	6.46410i	0.489574	+	0.282655i	−0.234824	+	0.972038i	$0.575451\pi$
$524$	−14.5359			−0.635004
$525$	−46.6410			−2.03558
$526$	−6.00000	+	1.60770i	−0.261612	+	0.0700988i
$527$	7.09808	−	4.09808i	0.309197	−	0.178515i
$528$	−18.9282	+	10.9282i	−0.823744	+	0.475589i
$529$	9.08846	+	15.7417i	0.395150	+	0.684420i
$530$	2.66025	−	2.66025i	0.115554	−	0.115554i
$531$	16.6603	−	28.8564i	0.722993	−	1.25226i
$532$	−16.3923	+	28.3923i	−0.710697	+	1.23096i
$533$	4.18653	−	1.03590i	0.181339	−	0.0448697i
$534$	0.535898	−	2.00000i	0.0231906	−	0.0865485i
$535$	−0.0788383	−	0.0455173i	−0.00340848	−	0.00196789i
$536$	7.85641	+	29.3205i	0.339345	+	1.26645i
$537$	18.9282	+	32.7846i	0.816812	+	1.41476i
$538$	−3.46410	−	0.928203i	−0.149348	−	0.0400177i
$539$	5.00000	+	8.66025i	0.215365	+	0.373024i
$540$	−2.14359			−0.0922456
$541$	23.4449			1.00797			0.503987	−	0.863711i	$-0.331866\pi$
$541$	23.4449			1.00797			0.503987	+	0.863711i	$0.331866\pi$
$542$	6.33975	+	23.6603i	0.272315	+	1.01629i
$543$	15.7583	−	27.2942i	0.676255	−	1.17131i
$544$	9.46410	−	35.3205i	0.405770	−	1.51435i
$545$	1.60770			0.0688661
$546$	48.2487	+	0.928203i	2.06485	+	0.0397234i
$547$		−	12.5885i		−	0.538244i	−0.963106	−	0.269122i	$-0.913267\pi$
$547$		−	12.5885i		−	0.538244i	0.963106	−	0.269122i	$-0.0867334\pi$
$548$	−17.5885	−	30.4641i	−0.751342	−	1.30136i
$549$	3.86603	+	2.23205i	0.164998	+	0.0952616i
$550$	−13.4641	+	3.60770i	−0.574111	+	0.153833i
$551$		−	14.1962i		−	0.604776i
$552$	−4.39230	+	16.3923i	−0.186949	+	0.697703i
$553$	−31.1769	+	18.0000i	−1.32578	+	0.765438i
$554$	27.7583	+	7.43782i	1.17934	+	0.316003i
$555$	−4.90192	+	2.83013i	−0.208075	+	0.120132i
$556$	2.53590	+	4.39230i	0.107546	+	0.186275i
$557$	7.59808	−	13.1603i	0.321941	−	0.557618i	−0.658948	−	0.752189i	$-0.728998\pi$
$557$	7.59808	−	13.1603i	0.321941	−	0.557618i	0.980888	+	0.194571i	$0.0623315\pi$
$558$	7.73205	+	2.07180i	0.327324	+	0.0877062i
$559$	−9.46410	+	32.7846i	−0.400289	+	1.38664i
$560$	−3.21539	+	1.85641i	−0.135875	+	0.0784475i
$561$	−30.5885	−	17.6603i	−1.29145	−	0.745617i
$562$	−6.66025	+	6.66025i	−0.280946	+	0.280946i
$563$	37.9808	−	21.9282i	1.60070	−	0.924164i	0.609351	−	0.792901i	$-0.291430\pi$
$563$	37.9808	−	21.9282i	1.60070	−	0.924164i	0.991348	−	0.131263i	$-0.0419031\pi$
$564$	15.4641	+	8.92820i	0.651156	+	0.375945i
$565$	−0.401924	−	0.696152i	−0.0169091	−	0.0292874i
$566$	3.94744	+	14.7321i	0.165923	+	0.619234i
$567$			8.53590i			0.358474i
$568$	−9.32051	+	34.7846i	−0.391080	+	1.45953i
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	−0.496928	−	0.867792i	$-0.665539\pi$
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	0.999994	−	0.00354413i	$-0.00112814\pi$
$570$	−3.46410	+	3.46410i	−0.145095	+	0.145095i
$571$			18.3923i			0.769694i	0.922980	+	0.384847i	$0.125746\pi$
$571$			18.3923i			0.769694i	−0.922980	+	0.384847i	$0.874254\pi$
$572$	14.0000	−	3.46410i	0.585369	−	0.144841i
$573$			38.7846i			1.62025i
$574$	−4.14359	−	4.14359i	−0.172950	−	0.172950i
$575$	−5.41154	+	9.37307i	−0.225677	+	0.390884i
$576$	30.9282	−	17.8564i	1.28868	−	0.744017i
$577$		−	37.7321i		−	1.57081i	−0.618985	−	0.785403i	$-0.712456\pi$
$577$		−	37.7321i		−	1.57081i	0.618985	−	0.785403i	$-0.287544\pi$
$578$	33.8564	−	9.07180i	1.40824	−	0.377337i
$579$	−34.2224	−	59.2750i	−1.42224	−	2.46338i
$580$	0.803848	−	1.39230i	0.0333780	−	0.0578123i
$581$	−16.3923	+	9.46410i	−0.680067	+	0.392637i
$582$	16.3923	+	16.3923i	0.679483	+	0.679483i
$583$	17.1962	+	9.92820i	0.712192	+	0.411184i
$584$	3.46410	+	3.46410i	0.143346	+	0.143346i
$585$	4.14359	+	1.19615i	0.171317	+	0.0494548i
$586$	−4.83013	+	18.0263i	−0.199531	+	0.744659i
$587$	−8.58846	+	14.8756i	−0.354484	+	0.613984i	−0.987029	−	0.160539i	$-0.948677\pi$
$587$	−8.58846	+	14.8756i	−0.354484	+	0.613984i	0.632546	+	0.774523i	$0.282010\pi$
$588$	−13.6603	−	23.6603i	−0.563339	−	0.975732i
$589$	5.19615	−	3.00000i	0.214104	−	0.123613i
$590$	0.732051	−	2.73205i	0.0301381	−	0.112477i
$591$	−46.0526	+	26.5885i	−1.89435	+	1.09370i
$592$	15.4641	−	26.7846i	0.635571	−	1.10084i
$593$		−	29.5885i		−	1.21505i	−0.794300	−	0.607526i	$-0.792162\pi$
$593$		−	29.5885i		−	1.21505i	0.794300	−	0.607526i	$-0.207838\pi$
$594$	−2.92820	−	10.9282i	−0.120146	−	0.448390i
$595$	−5.19615	−	3.00000i	−0.213021	−	0.122988i
$596$	−14.3205	+	8.26795i	−0.586591	+	0.338668i
$597$			24.9282i			1.02024i
$598$	5.78461	−	9.58846i	0.236550	−	0.392101i
$599$	−16.7321			−0.683653			−0.341827	−	0.939763i	$-0.611046\pi$
$599$	−16.7321			−0.683653			−0.341827	+	0.939763i	$0.611046\pi$
$600$	36.7846	−	9.85641i	1.50173	−	0.402386i
$601$	−19.9641	+	34.5788i	−0.814353	+	1.41050i	0.0954391	+	0.995435i	$0.469574\pi$
$601$	−19.9641	+	34.5788i	−0.814353	+	1.41050i	−0.909792	+	0.415065i	$0.863759\pi$
$602$	44.7846	−	12.0000i	1.82528	−	0.489083i
$603$	−47.9090			−1.95100
$604$	16.3923			0.666993
$605$	−0.937822	−	1.62436i	−0.0381279	−	0.0660394i
$606$	18.4641	−	68.9090i	0.750053	−	2.79924i
$607$	14.2942	+	24.7583i	0.580185	+	1.00491i	0.995457	+	0.0952124i	$0.0303530\pi$
$607$	14.2942	+	24.7583i	0.580185	+	1.00491i	−0.415272	+	0.909697i	$0.636314\pi$
$608$	6.92820	−	25.8564i	0.280976	−	1.04862i
$609$	24.5885	+	14.1962i	0.996375	+	0.575257i
$610$	0.366025	+	0.0980762i	0.0148199	+	0.00397099i
$611$	−8.16987	−	8.49038i	−0.330518	−	0.343484i
$612$	49.9808	+	28.8564i	2.02035	+	1.16645i
$613$	2.25833	−	3.91154i	0.0912131	−	0.157986i	−0.816809	−	0.576909i	$-0.804259\pi$
$613$	2.25833	−	3.91154i	0.0912131	−	0.157986i	0.908022	+	0.418923i	$0.137592\pi$
$614$	−8.19615	−	8.19615i	−0.330770	−	0.330770i
$615$	−0.437822	−	0.758330i	−0.0176547	−	0.0305788i
$616$	−13.8564	−	13.8564i	−0.558291	−	0.558291i
$617$	−12.3564	+	7.13397i	−0.497450	+	0.287203i	−0.727660	−	0.685938i	$-0.759392\pi$
$617$	−12.3564	+	7.13397i	−0.497450	+	0.287203i	0.230210	+	0.973141i	$0.426059\pi$
$618$	−4.19615	−	15.6603i	−0.168794	−	0.629948i
$619$	−24.2487			−0.974638			−0.487319	−	0.873224i	$-0.662025\pi$
$619$	−24.2487			−0.974638			−0.487319	+	0.873224i	$0.662025\pi$
$620$	0.679492			0.0272891
$621$	−7.60770	−	4.39230i	−0.305286	−	0.176257i
$622$	−12.5885	−	12.5885i	−0.504751	−	0.504751i
$623$	1.85641			0.0743754
$624$	−38.2487	+	9.46410i	−1.53117	+	0.378867i
$625$	23.9282			0.957128
$626$	9.46410	+	9.46410i	0.378262	+	0.378262i
$627$	−22.3923	−	12.9282i	−0.894263	−	0.516303i
$628$	−19.8564			−0.792357
$629$	49.9808			1.99286
$630$	−1.51666	−	5.66025i	−0.0604252	−	0.225510i
$631$	26.7846	−	15.4641i	1.06628	−	0.615616i	0.139116	−	0.990276i	$-0.455574\pi$
$631$	26.7846	−	15.4641i	1.06628	−	0.615616i	0.927162	+	0.374660i	$0.122241\pi$
$632$	20.7846	−	20.7846i	0.826767	−	0.826767i
$633$	−3.53590	−	6.12436i	−0.140539	−	0.243421i
$634$	14.8038	+	14.8038i	0.587936	+	0.587936i
$635$	2.36603	−	4.09808i	0.0938929	−	0.162627i
$636$	−46.9808	−	27.1244i	−1.86291	−	1.07555i
$637$	4.33013	+	17.5000i	0.171566	+	0.693375i
$638$	8.19615	+	2.19615i	0.324489	+	0.0869465i
$639$	−49.2224	−	28.4186i	−1.94721	−	1.12422i
$640$	2.14359	−	2.14359i	0.0847330	−	0.0847330i
$641$	13.9641	+	24.1865i	0.551549	+	0.955311i	0.998163	+	0.0605840i	$0.0192963\pi$
$641$	13.9641	+	24.1865i	0.551549	+	0.955311i	−0.446614	+	0.894727i	$0.647370\pi$
$642$	−0.339746	+	1.26795i	−0.0134087	+	0.0500420i
$643$	−1.39230	−	2.41154i	−0.0549071	−	0.0951020i	0.837265	−	0.546797i	$-0.184153\pi$
$643$	−1.39230	−	2.41154i	−0.0549071	−	0.0951020i	−0.892173	+	0.451695i	$0.850820\pi$
$644$	−15.2154			−0.599570
$645$	6.92820			0.272798
$646$	41.7846	−	11.1962i	1.64399	−	0.440507i
$647$	−6.16987	+	10.6865i	−0.242563	+	0.420131i	−0.961444	−	0.275002i	$-0.911321\pi$
$647$	−6.16987	+	10.6865i	−0.242563	+	0.420131i	0.718881	+	0.695133i	$0.244655\pi$
$648$	−1.80385	−	6.73205i	−0.0708618	−	0.264460i
$649$	14.9282			0.585983
$650$	−25.1244	−	0.483340i	−0.985458	−	0.0189581i
$651$			12.0000i			0.470317i
$652$	7.60770	−	4.39230i	0.297940	−	0.172016i
$653$	−31.1769	−	18.0000i	−1.22005	−	0.704394i	−0.255119	−	0.966910i	$-0.582115\pi$
$653$	−31.1769	−	18.0000i	−1.22005	−	0.704394i	−0.964928	+	0.262515i	$0.915448\pi$
$654$	−6.00000	−	22.3923i	−0.234619	−	0.875608i
$655$		−	1.94744i		−	0.0760928i
$656$	4.14359	+	2.39230i	0.161780	+	0.0934038i
$657$	−6.69615	+	3.86603i	−0.261242	+	0.150828i
$658$	−4.14359	+	15.4641i	−0.161534	+	0.602853i
$659$	14.7846	−	8.53590i	0.575927	−	0.332511i	−0.183586	−	0.983004i	$-0.558771\pi$
$659$	14.7846	−	8.53590i	0.575927	−	0.332511i	0.759513	+	0.650492i	$0.225437\pi$
$660$	−1.46410	−	2.53590i	−0.0569901	−	0.0987097i
$661$	6.06218	−	10.5000i	0.235791	−	0.408403i	−0.723711	−	0.690103i	$-0.757565\pi$
$661$	6.06218	−	10.5000i	0.235791	−	0.408403i	0.959502	+	0.281701i	$0.0908985\pi$
$662$	−4.39230	+	16.3923i	−0.170712	+	0.637105i
$663$	−44.1506	−	45.8827i	−1.71467	−	1.78194i
$664$	10.9282	−	10.9282i	0.424097	−	0.424097i
$665$	−3.80385	−	2.19615i	−0.147507	−	0.0851631i
$666$	34.5167	+	34.5167i	1.33749	+	1.33749i
$667$	5.70577	−	3.29423i	0.220928	−	0.127553i
$668$	8.92820	−	15.4641i	0.345443	−	0.598324i
$669$	26.6603	+	46.1769i	1.03074	+	1.78530i
$670$	−3.92820	+	1.05256i	−0.151760	+	0.0406639i
$671$			2.00000i			0.0772091i
$672$	37.8564	+	37.8564i	1.46034	+	1.46034i
$673$	5.50000	−	9.52628i	0.212009	−	0.367211i	−0.740334	−	0.672239i	$-0.765333\pi$
$673$	5.50000	−	9.52628i	0.212009	−	0.367211i	0.952343	+	0.305028i	$0.0986659\pi$
$674$	−15.2487	−	15.2487i	−0.587358	−	0.587358i
$675$			19.7128i			0.758747i
$676$	25.9808	+	1.00000i	0.999260	+	0.0384615i
$677$			19.8564i			0.763144i	0.924339	+	0.381572i	$0.124617\pi$
$677$			19.8564i			0.763144i	−0.924339	+	0.381572i	$0.875383\pi$
$678$	−8.19615	+	8.19615i	−0.314771	+	0.314771i
$679$	−10.3923	+	18.0000i	−0.398820	+	0.690777i
$680$	4.73205	+	1.26795i	0.181466	+	0.0486236i
$681$		−	32.9282i		−	1.26181i
$682$	0.928203	+	3.46410i	0.0355427	+	0.132647i
$683$	−7.36603	−	12.7583i	−0.281853	−	0.488184i	0.689988	−	0.723821i	$-0.257616\pi$
$683$	−7.36603	−	12.7583i	−0.281853	−	0.488184i	−0.971841	+	0.235637i	$0.924282\pi$
$684$	36.5885	+	21.1244i	1.39899	+	0.807710i
$685$	4.08142	−	2.35641i	0.155943	−	0.0900337i
$686$	−6.92820	+	6.92820i	−0.264520	+	0.264520i
$687$	−2.19615	−	1.26795i	−0.0837884	−	0.0483753i
$688$	−32.7846	+	18.9282i	−1.24990	+	0.721631i
$689$	24.8205	+	25.7942i	0.945586	+	0.982682i
$690$	−2.19615	−	0.588457i	−0.0836061	−	0.0224022i
$691$	−9.00000	+	15.5885i	−0.342376	+	0.593013i	−0.984873	−	0.173275i	$-0.944565\pi$
$691$	−9.00000	+	15.5885i	−0.342376	+	0.593013i	0.642497	+	0.766288i	$0.277898\pi$
$692$	−5.07180	−	8.78461i	−0.192801	−	0.333941i
$693$	26.7846	−	15.4641i	1.01746	−	0.587433i
$694$	6.46410	+	1.73205i	0.245374	+	0.0657477i
$695$	−0.588457	+	0.339746i	−0.0223215	+	0.0128873i
$696$	−22.3923	−	6.00000i	−0.848778	−	0.227429i
$697$			7.73205i			0.292872i
$698$	−40.0526	+	10.7321i	−1.51601	+	0.406214i
$699$		0			0
$700$	17.0718	+	29.5692i	0.645253	+	1.11761i
$701$		−	32.7846i		−	1.23826i	−0.785289	−	0.619129i	$-0.787486\pi$
$701$		−	32.7846i		−	1.23826i	0.785289	−	0.619129i	$-0.212514\pi$
$702$	0.392305	−	20.3923i	0.0148066	−	0.769658i
$703$	36.5885			1.37996
$704$	13.8564	+	8.00000i	0.522233	+	0.301511i
$705$	−1.19615	+	2.07180i	−0.0450497	+	0.0780284i
$706$	−7.95448	−	29.6865i	−0.299371	−	1.11727i
$707$	63.9615			2.40552
$708$	−40.7846			−1.53278
$709$	−15.4019	−	26.6769i	−0.578431	−	1.00187i	−0.995659	−	0.0930708i	$-0.970332\pi$
$709$	−15.4019	−	26.6769i	−0.578431	−	1.00187i	0.417228	−	0.908802i	$-0.363002\pi$
$710$	−4.66025	−	1.24871i	−0.174896	−	0.0468633i
$711$	23.1962	+	40.1769i	0.869924	+	1.50675i
$712$	−1.46410	+	0.392305i	−0.0548695	+	0.0147022i
$713$	2.41154	+	1.39230i	0.0903130	+	0.0521422i
$714$	−22.3923	+	83.5692i	−0.838011	+	3.12750i
$715$	0.464102	+	1.87564i	0.0173564	+	0.0701451i
$716$	13.8564	−	24.0000i	0.517838	−	0.896922i
$717$	3.26795	−	5.66025i	0.122044	−	0.211386i
$718$	−26.9282	+	26.9282i	−1.00495	+	1.00495i
$719$	−10.8564	−	18.8038i	−0.404876	−	0.701265i	0.589431	−	0.807818i	$-0.299352\pi$
$719$	−10.8564	−	18.8038i	−0.404876	−	0.701265i	−0.994307	+	0.106553i	$0.966019\pi$
$720$	2.39230	+	4.14359i	0.0891559	+	0.154423i
$721$	12.5885	−	7.26795i	0.468819	−	0.270673i
$722$	4.63397	−	1.24167i	0.172459	−	0.0462102i
$723$	2.19615			0.0816758
$724$	−23.0718			−0.857457
$725$	−12.8038	−	7.39230i	−0.475523	−	0.274543i
$726$	−19.1244	+	19.1244i	−0.709771	+	0.709771i
$727$	−34.3923			−1.27554			−0.637770	−	0.770227i	$-0.720143\pi$
$727$	−34.3923			−1.27554			−0.637770	+	0.770227i	$0.720143\pi$
$728$	−17.0718	−	30.9282i	−0.632723	−	1.14628i
$729$	43.7846			1.62165
$730$	−0.464102	+	0.464102i	−0.0171772	+	0.0171772i
$731$	−52.9808	−	30.5885i	−1.95956	−	1.13135i
$732$		−	5.46410i		−	0.201959i
$733$	−43.0526			−1.59018			−0.795091	−	0.606490i	$-0.792577\pi$
$733$	−43.0526			−1.59018			−0.795091	+	0.606490i	$0.792577\pi$
$734$	−24.3205	+	6.51666i	−0.897686	+	0.240534i
$735$	3.16987	−	1.83013i	0.116923	−	0.0675053i
$736$	12.0000	−	3.21539i	0.442326	−	0.118521i
$737$	−10.7321	−	18.5885i	−0.395320	−	0.684715i
$738$	−5.33975	+	5.33975i	−0.196559	+	0.196559i
$739$	−2.53590	+	4.39230i	−0.0932845	+	0.161574i	−0.908891	−	0.417033i	$-0.863070\pi$
$739$	−2.53590	+	4.39230i	−0.0932845	+	0.161574i	0.815607	+	0.578607i	$0.196403\pi$
$740$	3.58846	+	2.07180i	0.131914	+	0.0761608i
$741$	−32.3205	−	33.5885i	−1.18732	−	1.23390i
$742$	12.5885	−	46.9808i	0.462137	−	1.72472i
$743$	1.26795	+	0.732051i	0.0465165	+	0.0268563i	0.523078	−	0.852285i	$-0.324784\pi$
$743$	1.26795	+	0.732051i	0.0465165	+	0.0268563i	−0.476561	+	0.879141i	$0.658117\pi$
$744$	−2.53590	−	9.46410i	−0.0929705	−	0.346971i
$745$	−1.10770	−	1.91858i	−0.0405828	−	0.0702915i
$746$	21.5622	+	5.77757i	0.789447	+	0.211532i
$747$	12.1962	+	21.1244i	0.446234	+	0.772900i
$748$			25.8564i			0.945404i
$749$	−1.17691			−0.0430035
$750$	2.66025	+	9.92820i	0.0971387	+	0.362527i
$751$	7.80385	−	13.5167i	0.284766	−	0.493230i	−0.687786	−	0.725913i	$-0.741417\pi$
$751$	7.80385	−	13.5167i	0.284766	−	0.493230i	0.972553	+	0.232683i	$0.0747506\pi$
$752$		−	13.0718i		−	0.476679i
$753$	−6.00000			−0.218652
$754$	13.0981	+	7.90192i	0.477004	+	0.287771i
$755$			2.19615i			0.0799262i
$756$	−24.0000	+	13.8564i	−0.872872	+	0.503953i
$757$	35.6603	+	20.5885i	1.29609	+	0.748300i	0.979727	−	0.200337i	$-0.0642036\pi$
$757$	35.6603	+	20.5885i	1.29609	+	0.748300i	0.316367	+	0.948637i	$0.397537\pi$
$758$	21.9282	−	5.87564i	0.796468	−	0.213413i
$759$		−	12.0000i		−	0.435572i
$760$	3.46410	+	0.928203i	0.125656	+	0.0336695i
$761$	16.8564	−	9.73205i	0.611044	−	0.352787i	−0.162330	−	0.986737i	$-0.551901\pi$
$761$	16.8564	−	9.73205i	0.611044	−	0.352787i	0.773374	+	0.633950i	$0.218568\pi$
$762$	−65.9090	−	17.6603i	−2.38763	−	0.639764i
$763$	18.0000	−	10.3923i	0.651644	−	0.376227i
$764$	24.5885	−	14.1962i	0.889579	−	0.513599i
$765$	−3.86603	+	6.69615i	−0.139776	+	0.242100i
$766$	27.3205	+	7.32051i	0.987130	+	0.264501i
$767$	25.8564	+	7.46410i	0.933621	+	0.269513i

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.36603 - 1.36603i) q^{3} +2.00000i q^{4} -0.267949 q^{5} +(1.00000 + 3.73205i) q^{6} +(-3.00000 + 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.23205 + 3.86603i) q^{9} +(0.267949 + 0.267949i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(2.73205 - 4.73205i) q^{12} +(-2.59808 + 2.50000i) q^{13} +(4.73205 + 1.26795i) q^{14} +(0.633975 + 0.366025i) q^{15} -4.00000 q^{16} +(-3.23205 - 5.59808i) q^{17} +(1.63397 - 6.09808i) q^{18} +(-2.36603 - 4.09808i) q^{19} -0.535898i q^{20} +9.46410 q^{21} +(2.73205 - 0.732051i) q^{22} +(1.09808 - 1.90192i) q^{23} +(-7.46410 + 2.00000i) q^{24} -4.92820 q^{25} +(5.09808 + 0.0980762i) q^{26} -4.00000i q^{27} +(-3.46410 - 6.00000i) q^{28} +(2.59808 + 1.50000i) q^{29} +(-0.267949 - 1.00000i) q^{30} +1.26795i q^{31} +(4.00000 + 4.00000i) q^{32} +(4.73205 - 2.73205i) q^{33} +(-2.36603 + 8.83013i) q^{34} +(0.803848 - 0.464102i) q^{35} +(-7.73205 + 4.46410i) q^{36} +(-3.86603 + 6.69615i) q^{37} +(-1.73205 + 6.46410i) q^{38} +(9.56218 - 2.36603i) q^{39} +(-0.535898 + 0.535898i) q^{40} +(-1.03590 - 0.598076i) q^{41} +(-9.46410 - 9.46410i) q^{42} +(8.19615 - 4.73205i) q^{43} +(-3.46410 - 2.00000i) q^{44} +(-0.598076 - 1.03590i) q^{45} +(-3.00000 + 0.803848i) q^{46} +3.26795i q^{47} +(9.46410 + 5.46410i) q^{48} +(2.50000 - 4.33013i) q^{49} +(4.92820 + 4.92820i) q^{50} +17.6603i q^{51} +(-5.00000 - 5.19615i) q^{52} -9.92820i q^{53} +(-4.00000 + 4.00000i) q^{54} +(0.267949 - 0.464102i) q^{55} +(-2.53590 + 9.46410i) q^{56} +12.9282i q^{57} +(-1.09808 - 4.09808i) q^{58} +(-3.73205 - 6.46410i) q^{59} +(-0.732051 + 1.26795i) q^{60} +(0.866025 - 0.500000i) q^{61} +(1.26795 - 1.26795i) q^{62} +(-13.3923 - 7.73205i) q^{63} -8.00000i q^{64} +(0.696152 - 0.669873i) q^{65} +(-7.46410 - 2.00000i) q^{66} +(-5.36603 + 9.29423i) q^{67} +(11.1962 - 6.46410i) q^{68} +(-5.19615 + 3.00000i) q^{69} +(-1.26795 - 0.339746i) q^{70} +(-11.0263 + 6.36603i) q^{71} +(12.1962 + 3.26795i) q^{72} +1.73205i q^{73} +(10.5622 - 2.83013i) q^{74} +(11.6603 + 6.73205i) q^{75} +(8.19615 - 4.73205i) q^{76} -6.92820i q^{77} +(-11.9282 - 7.19615i) q^{78} +10.3923 q^{79} +1.07180 q^{80} +(1.23205 - 2.13397i) q^{81} +(0.437822 + 1.63397i) q^{82} +5.46410 q^{83} +18.9282i q^{84} +(0.866025 + 1.50000i) q^{85} +(-12.9282 - 3.46410i) q^{86} +(-4.09808 - 7.09808i) q^{87} +(1.46410 + 5.46410i) q^{88} +(-0.464102 - 0.267949i) q^{89} +(-0.437822 + 1.63397i) q^{90} +(3.46410 - 12.0000i) q^{91} +(3.80385 + 2.19615i) q^{92} +(1.73205 - 3.00000i) q^{93} +(3.26795 - 3.26795i) q^{94} +(0.633975 + 1.09808i) q^{95} +(-4.00000 - 14.9282i) q^{96} +(5.19615 - 3.00000i) q^{97} +(-6.83013 + 1.83013i) q^{98} -8.92820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{5} + 4 q^{6} - 12 q^{7} + 8 q^{8} + 2 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{14} + 6 q^{15} - 16 q^{16} - 6 q^{17} + 10 q^{18} - 6 q^{19} + 24 q^{21} + 4 q^{22} - 6 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^5 + 4 * q^6 - 12 * q^7 + 8 * q^8 + 2 * q^9 + 8 * q^10 - 4 * q^11 + 4 * q^12 + 12 * q^14 + 6 * q^15 - 16 * q^16 - 6 * q^17 + 10 * q^18 - 6 * q^19 + 24 * q^21 + 4 * q^22 - 6 * q^23 - 16 * q^24 + 8 * q^25 + 10 * q^26 - 8 * q^30 + 16 * q^32 + 12 * q^33 - 6 * q^34 + 24 * q^35 - 24 * q^36 - 12 * q^37 + 14 * q^39 - 16 * q^40 - 18 * q^41 - 24 * q^42 + 12 * q^43 + 8 * q^45 - 12 * q^46 + 24 * q^48 + 10 * q^49 - 8 * q^50 - 20 * q^52 - 16 * q^54 + 8 * q^55 - 24 * q^56 + 6 * q^58 - 8 * q^59 + 4 * q^60 + 12 * q^62 - 12 * q^63 - 18 * q^65 - 16 * q^66 - 18 * q^67 + 24 * q^68 - 12 * q^70 - 6 * q^71 + 28 * q^72 + 18 * q^74 + 12 * q^75 + 12 * q^76 - 20 * q^78 + 32 * q^80 - 2 * q^81 + 26 * q^82 + 8 * q^83 - 24 * q^86 - 6 * q^87 - 8 * q^88 + 12 * q^89 - 26 * q^90 + 36 * q^92 + 20 * q^94 + 6 * q^95 - 16 * q^96 - 10 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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