LMFDB - Embedded newform 928.2.k.e.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [928,2,Mod(191,928)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(928, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("928.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 928 = 2^{5} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	928.k (of order $4$, 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:	$7.41011730757$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 23x^{8} + 153x^{6} + 273x^{4} + 103x^{2} + 9 $ x^10 + 23x^8 + 153x^6 + 273x^4 + 103x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.2
Root			$0.356878i$ of defining polynomial
Character	$\chi$	$=$	928.191
Dual form			928.2.k.e.447.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13340 - 1.13340i) q^{3} -1.87777i q^{5} -4.61854i q^{7} -0.430814i q^{9} +O(q^{10})$	\(q+(-1.13340 - 1.13340i) q^{3} -1.87777i q^{5} -4.61854i q^{7} -0.430814i q^{9} +(-3.65429 - 3.65429i) q^{11} +2.02701i q^{13} +(-2.12826 + 2.12826i) q^{15} +(-0.117094 + 0.117094i) q^{17} +(5.13944 + 5.13944i) q^{19} +(-5.23465 + 5.23465i) q^{21} -6.35174i q^{23} +1.47397 q^{25} +(-3.88848 + 3.88848i) q^{27} +(-5.38389 - 0.117094i) q^{29} +(3.45813 + 3.45813i) q^{31} +8.28354i q^{33} -8.67257 q^{35} +(6.78256 + 6.78256i) q^{37} +(2.29741 - 2.29741i) q^{39} +(3.99487 + 3.99487i) q^{41} +(-6.36805 - 6.36805i) q^{43} -0.808970 q^{45} +(4.12826 - 4.12826i) q^{47} -14.3309 q^{49} +0.265428 q^{51} +4.67647 q^{53} +(-6.86193 + 6.86193i) q^{55} -11.6501i q^{57} -1.40380i q^{59} +(4.85319 - 4.85319i) q^{61} -1.98973 q^{63} +3.80627 q^{65} -14.5233 q^{67} +(-7.19906 + 7.19906i) q^{69} +2.02234 q^{71} +(-10.2101 - 10.2101i) q^{73} +(-1.67060 - 1.67060i) q^{75} +(-16.8775 + 16.8775i) q^{77} +(3.68131 + 3.68131i) q^{79} +7.52196 q^{81} +7.22364i q^{83} +(0.219876 + 0.219876i) q^{85} +(5.96938 + 6.23481i) q^{87} +(-4.43325 + 4.43325i) q^{89} +9.36185 q^{91} -7.83888i q^{93} +(9.65069 - 9.65069i) q^{95} +(-6.88021 - 6.88021i) q^{97} +(-1.57432 + 1.57432i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3}+O(q^{10}) $ 10 * q - 2 * q^3	$ 10 q - 2 q^{3} - 14 q^{11} + 14 q^{15} + 6 q^{17} - 12 q^{19} - 28 q^{21} + 2 q^{25} - 2 q^{27} - 28 q^{29} + 14 q^{31} + 4 q^{35} + 10 q^{37} + 6 q^{39} + 14 q^{41} - 30 q^{43} - 36 q^{45} + 6 q^{47} - 42 q^{49} - 56 q^{51} + 4 q^{53} - 42 q^{55} - 26 q^{61} + 32 q^{63} - 36 q^{65} - 56 q^{67} + 16 q^{69} - 36 q^{71} - 22 q^{73} + 8 q^{75} + 28 q^{77} - 6 q^{79} - 54 q^{81} - 16 q^{85} + 58 q^{87} + 58 q^{89} + 20 q^{91} + 52 q^{95} + 26 q^{97} - 68 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 - 14 * q^11 + 14 * q^15 + 6 * q^17 - 12 * q^19 - 28 * q^21 + 2 * q^25 - 2 * q^27 - 28 * q^29 + 14 * q^31 + 4 * q^35 + 10 * q^37 + 6 * q^39 + 14 * q^41 - 30 * q^43 - 36 * q^45 + 6 * q^47 - 42 * q^49 - 56 * q^51 + 4 * q^53 - 42 * q^55 - 26 * q^61 + 32 * q^63 - 36 * q^65 - 56 * q^67 + 16 * q^69 - 36 * q^71 - 22 * q^73 + 8 * q^75 + 28 * q^77 - 6 * q^79 - 54 * q^81 - 16 * q^85 + 58 * q^87 + 58 * q^89 + 20 * q^91 + 52 * q^95 + 26 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/928\mathbb{Z}\right)^\times$.

$n$	$321$	$581$	$639$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.13340	−	1.13340i	−0.654368	−	0.654368i	0.299674	−	0.954042i	$-0.403122\pi$
$3$	−1.13340	−	1.13340i	−0.654368	−	0.654368i	−0.954042	+	0.299674i	$0.903122\pi$
$4$		0			0
$5$		−	1.87777i		−	0.839765i	−0.907578	−	0.419883i	$-0.862071\pi$
$5$		−	1.87777i		−	0.839765i	0.907578	−	0.419883i	$-0.137929\pi$
$6$		0			0
$7$		−	4.61854i		−	1.74564i	−0.488038	−	0.872822i	$-0.662287\pi$
$7$		−	4.61854i		−	1.74564i	0.488038	−	0.872822i	$-0.337713\pi$
$8$		0			0
$9$		−	0.430814i		−	0.143605i
$10$		0			0
$11$	−3.65429	−	3.65429i	−1.10181	−	1.10181i	−0.994192	−	0.107619i	$-0.965677\pi$
$11$	−3.65429	−	3.65429i	−1.10181	−	1.10181i	−0.107619	−	0.994192i	$-0.534323\pi$
$12$		0			0
$13$			2.02701i			0.562192i	0.959680	+	0.281096i	$0.0906980\pi$
$13$			2.02701i			0.562192i	−0.959680	+	0.281096i	$0.909302\pi$
$14$		0			0
$15$	−2.12826	+	2.12826i	−0.549516	+	0.549516i
$16$		0			0
$17$	−0.117094	+	0.117094i	−0.0283994	+	0.0283994i	−0.721164	−	0.692764i	$-0.756393\pi$
$17$	−0.117094	+	0.117094i	−0.0283994	+	0.0283994i	0.692764	+	0.721164i	$0.256393\pi$
$18$		0			0
$19$	5.13944	+	5.13944i	1.17907	+	1.17907i	0.979982	+	0.199085i	$0.0637971\pi$
$19$	5.13944	+	5.13944i	1.17907	+	1.17907i	0.199085	+	0.979982i	$0.436203\pi$
$20$		0			0
$21$	−5.23465	+	5.23465i	−1.14229	+	1.14229i
$22$		0			0
$23$		−	6.35174i		−	1.32443i	−0.749314	−	0.662215i	$-0.769617\pi$
$23$		−	6.35174i		−	1.32443i	0.749314	−	0.662215i	$-0.230383\pi$
$24$		0			0
$25$	1.47397			0.294794
$26$		0			0
$27$	−3.88848	+	3.88848i	−0.748338	+	0.748338i
$28$		0			0
$29$	−5.38389	−	0.117094i	−0.999764	−	0.0217438i
$29$	−5.38389	−	0.117094i	−0.999764	−	0.0217438i
$30$		0			0
$31$	3.45813	+	3.45813i	0.621098	+	0.621098i	0.945812	−	0.324714i	$-0.105268\pi$
$31$	3.45813	+	3.45813i	0.621098	+	0.621098i	−0.324714	+	0.945812i	$0.605268\pi$
$32$		0			0
$33$			8.28354i			1.44198i
$34$		0			0
$35$	−8.67257			−1.46593
$36$		0			0
$37$	6.78256	+	6.78256i	1.11505	+	1.11505i	0.992458	+	0.122588i	$0.0391194\pi$
$37$	6.78256	+	6.78256i	1.11505	+	1.11505i	0.122588	+	0.992458i	$0.460881\pi$
$38$		0			0
$39$	2.29741	−	2.29741i	0.367881	−	0.367881i
$40$		0			0
$41$	3.99487	+	3.99487i	0.623893	+	0.623893i	0.946525	−	0.322631i	$-0.104567\pi$
$41$	3.99487	+	3.99487i	0.623893	+	0.623893i	−0.322631	+	0.946525i	$0.604567\pi$
$42$		0			0
$43$	−6.36805	−	6.36805i	−0.971118	−	0.971118i	0.0284761	−	0.999594i	$-0.490935\pi$
$43$	−6.36805	−	6.36805i	−0.971118	−	0.971118i	−0.999594	+	0.0284761i	$0.990935\pi$
$44$		0			0
$45$	−0.808970			−0.120594
$46$		0			0
$47$	4.12826	−	4.12826i	0.602169	−	0.602169i	−0.338718	−	0.940888i	$-0.609993\pi$
$47$	4.12826	−	4.12826i	0.602169	−	0.602169i	0.940888	+	0.338718i	$0.109993\pi$
$48$		0			0
$49$	−14.3309			−2.04728
$50$		0			0
$51$	0.265428			0.0371674
$52$		0			0
$53$	4.67647			0.642363			0.321182	−	0.947018i	$-0.395920\pi$
$53$	4.67647			0.642363			0.321182	+	0.947018i	$0.395920\pi$
$54$		0			0
$55$	−6.86193	+	6.86193i	−0.925262	+	0.925262i
$56$		0			0
$57$		−	11.6501i		−	1.54309i
$58$		0			0
$59$		−	1.40380i		−	0.182759i	−0.995816	−	0.0913796i	$-0.970872\pi$
$59$		−	1.40380i		−	0.182759i	0.995816	−	0.0913796i	$-0.0291277\pi$
$60$		0			0
$61$	4.85319	−	4.85319i	0.621388	−	0.621388i	−0.324499	−	0.945886i	$-0.605196\pi$
$61$	4.85319	−	4.85319i	0.621388	−	0.621388i	0.945886	+	0.324499i	$0.105196\pi$
$62$		0			0
$63$	−1.98973			−0.250683
$64$		0			0
$65$	3.80627			0.472110
$66$		0			0
$67$	−14.5233			−1.77431			−0.887153	−	0.461475i	$-0.847321\pi$
$67$	−14.5233			−1.77431			−0.887153	+	0.461475i	$0.847321\pi$
$68$		0			0
$69$	−7.19906	+	7.19906i	−0.866665	+	0.866665i
$70$		0			0
$71$	2.02234			0.240008			0.120004	−	0.992773i	$-0.461709\pi$
$71$	2.02234			0.240008			0.120004	+	0.992773i	$0.461709\pi$
$72$		0			0
$73$	−10.2101	−	10.2101i	−1.19500	−	1.19500i	−0.975646	−	0.219353i	$-0.929605\pi$
$73$	−10.2101	−	10.2101i	−1.19500	−	1.19500i	−0.219353	−	0.975646i	$-0.570395\pi$
$74$		0			0
$75$	−1.67060	−	1.67060i	−0.192904	−	0.192904i
$76$		0			0
$77$	−16.8775	+	16.8775i	−1.92337	+	1.92337i
$78$		0			0
$79$	3.68131	+	3.68131i	0.414179	+	0.414179i	0.883192	−	0.469012i	$-0.155390\pi$
$79$	3.68131	+	3.68131i	0.414179	+	0.414179i	−0.469012	+	0.883192i	$0.655390\pi$
$80$		0			0
$81$	7.52196			0.835773
$82$		0			0
$83$			7.22364i			0.792897i	0.918057	+	0.396449i	$0.129758\pi$
$83$			7.22364i			0.792897i	−0.918057	+	0.396449i	$0.870242\pi$
$84$		0			0
$85$	0.219876	+	0.219876i	0.0238489	+	0.0238489i
$86$		0			0
$87$	5.96938	+	6.23481i	0.639985	+	0.668442i
$88$		0			0
$89$	−4.43325	+	4.43325i	−0.469923	+	0.469923i	−0.901890	−	0.431966i	$-0.857820\pi$
$89$	−4.43325	+	4.43325i	−0.469923	+	0.469923i	0.431966	+	0.901890i	$0.357820\pi$
$90$		0			0
$91$	9.36185			0.981388
$92$		0			0
$93$		−	7.83888i		−	0.812854i
$94$		0			0
$95$	9.65069	−	9.65069i	0.990140	−	0.990140i
$96$		0			0
$97$	−6.88021	−	6.88021i	−0.698579	−	0.698579i	0.265525	−	0.964104i	$-0.414455\pi$
$97$	−6.88021	−	6.88021i	−0.698579	−	0.698579i	−0.964104	+	0.265525i	$0.914455\pi$
$98$		0			0
$99$	−1.57432	+	1.57432i	−0.158225	+	0.158225i
$100$		0			0
$101$	3.20887	−	3.20887i	0.319294	−	0.319294i	−0.529202	−	0.848496i	$-0.677509\pi$
$101$	3.20887	−	3.20887i	0.319294	−	0.319294i	0.848496	+	0.529202i	$0.177509\pi$
$102$		0			0
$103$			5.18245i			0.510642i	0.966856	+	0.255321i	$0.0821812\pi$
$103$			5.18245i			0.510642i	−0.966856	+	0.255321i	$0.917819\pi$
$104$		0			0
$105$	9.82948	+	9.82948i	0.959259	+	0.959259i
$106$		0			0
$107$		−	11.0878i		−	1.07190i	−0.844249	−	0.535951i	$-0.819953\pi$
$107$		−	11.0878i		−	1.07190i	0.844249	−	0.535951i	$-0.180047\pi$
$108$		0			0
$109$		−	5.68734i		−	0.544749i	−0.962191	−	0.272374i	$-0.912191\pi$
$109$		−	5.68734i		−	0.544749i	0.962191	−	0.272374i	$-0.0878089\pi$
$110$		0			0
$111$		−	15.3747i		−	1.45930i
$112$		0			0
$113$	3.37409	+	3.37409i	0.317407	+	0.317407i	0.847771	−	0.530363i	$-0.177944\pi$
$113$	3.37409	+	3.37409i	0.317407	+	0.317407i	−0.530363	+	0.847771i	$0.677944\pi$
$114$		0			0
$115$	−11.9271			−1.11221
$116$		0			0
$117$	0.873266			0.0807334
$118$		0			0
$119$	0.540803	+	0.540803i	0.0495753	+	0.0495753i
$120$		0			0
$121$			15.7077i			1.42797i
$122$		0			0
$123$		−	9.05555i		−	0.816512i
$124$		0			0
$125$		−	12.1566i		−	1.08732i
$126$		0			0
$127$	12.8011	+	12.8011i	1.13592	+	1.13592i	0.989175	+	0.146742i	$0.0468788\pi$
$127$	12.8011	+	12.8011i	1.13592	+	1.13592i	0.146742	+	0.989175i	$0.453121\pi$
$128$		0			0
$129$			14.4351i			1.27094i
$130$		0			0
$131$	−5.31102	+	5.31102i	−0.464026	+	0.464026i	−0.899973	−	0.435947i	$-0.856414\pi$
$131$	−5.31102	+	5.31102i	−0.464026	+	0.464026i	0.435947	+	0.899973i	$0.356414\pi$
$132$		0			0
$133$	23.7367	−	23.7367i	2.05823	−	2.05823i
$134$		0			0
$135$	7.30168	+	7.30168i	0.628429	+	0.628429i
$136$		0			0
$137$	9.46539	−	9.46539i	0.808683	−	0.808683i	−0.175751	−	0.984435i	$-0.556235\pi$
$137$	9.46539	−	9.46539i	0.808683	−	0.808683i	0.984435	+	0.175751i	$0.0562355\pi$
$138$		0			0
$139$			9.86283i			0.836555i	0.908319	+	0.418277i	$0.137366\pi$
$139$			9.86283i			0.836555i	−0.908319	+	0.418277i	$0.862634\pi$
$140$		0			0
$141$	−9.35794			−0.788081
$142$		0			0
$143$	7.40730	−	7.40730i	0.619430	−	0.619430i
$144$		0			0
$145$	−0.219876	+	10.1097i	−0.0182597	+	0.839567i
$146$		0			0
$147$	16.2427	+	16.2427i	1.33967	+	1.33967i
$148$		0			0
$149$		−	14.2223i		−	1.16514i	−0.812782	−	0.582568i	$-0.802048\pi$
$149$		−	14.2223i		−	1.16514i	0.812782	−	0.582568i	$-0.197952\pi$
$150$		0			0
$151$	−13.3872			−1.08944			−0.544719	−	0.838618i	$-0.683364\pi$
$151$	−13.3872			−1.08944			−0.544719	+	0.838618i	$0.683364\pi$
$152$		0			0
$153$	0.0504456	+	0.0504456i	0.00407829	+	0.00407829i
$154$		0			0
$155$	6.49358	−	6.49358i	0.521577	−	0.521577i
$156$		0			0
$157$	7.15558	+	7.15558i	0.571077	+	0.571077i	0.932429	−	0.361352i	$-0.117685\pi$
$157$	7.15558	+	7.15558i	0.571077	+	0.571077i	−0.361352	+	0.932429i	$0.617685\pi$
$158$		0			0
$159$	−5.30031	−	5.30031i	−0.420342	−	0.420342i
$160$		0			0
$161$	−29.3358			−2.31198
$162$		0			0
$163$	−2.50628	+	2.50628i	−0.196307	+	0.196307i	−0.798415	−	0.602108i	$-0.794328\pi$
$163$	−2.50628	+	2.50628i	−0.196307	+	0.196307i	0.602108	+	0.798415i	$0.294328\pi$
$164$		0			0
$165$	15.5546			1.21092
$166$		0			0
$167$	18.2463			1.41194			0.705969	−	0.708243i	$-0.250512\pi$
$167$	18.2463			1.41194			0.705969	+	0.708243i	$0.250512\pi$
$168$		0			0
$169$	8.89122			0.683940
$170$		0			0
$171$	2.21414	−	2.21414i	0.169320	−	0.169320i
$172$		0			0
$173$		−	16.2028i		−	1.23188i	−0.787794	−	0.615939i	$-0.788777\pi$
$173$		−	16.2028i		−	1.23188i	0.787794	−	0.615939i	$-0.211223\pi$
$174$		0			0
$175$		−	6.80760i		−	0.514606i
$176$		0			0
$177$	−1.59107	+	1.59107i	−0.119592	+	0.119592i
$178$		0			0
$179$	−1.43472			−0.107236			−0.0536180	−	0.998562i	$-0.517075\pi$
$179$	−1.43472			−0.107236			−0.0536180	+	0.998562i	$0.517075\pi$
$180$		0			0
$181$	−1.11486			−0.0828666			−0.0414333	−	0.999141i	$-0.513192\pi$
$181$	−1.11486			−0.0828666			−0.0414333	+	0.999141i	$0.513192\pi$
$182$		0			0
$183$	−11.0012			−0.813232
$184$		0			0
$185$	12.7361	−	12.7361i	0.936377	−	0.936377i
$186$		0			0
$187$	0.855790			0.0625816
$188$		0			0
$189$	17.9591	+	17.9591i	1.30633	+	1.30633i
$190$		0			0
$191$	−7.82058	−	7.82058i	−0.565877	−	0.565877i	0.365093	−	0.930971i	$-0.381037\pi$
$191$	−7.82058	−	7.82058i	−0.565877	−	0.565877i	−0.930971	+	0.365093i	$0.881037\pi$
$192$		0			0
$193$	10.9652	−	10.9652i	0.789289	−	0.789289i	−0.192089	−	0.981378i	$-0.561526\pi$
$193$	10.9652	−	10.9652i	0.789289	−	0.789289i	0.981378	+	0.192089i	$0.0615261\pi$
$194$		0			0
$195$	−4.31402	−	4.31402i	−0.308934	−	0.308934i
$196$		0			0
$197$	−6.22392			−0.443436			−0.221718	−	0.975111i	$-0.571166\pi$
$197$	−6.22392			−0.443436			−0.221718	+	0.975111i	$0.571166\pi$
$198$		0			0
$199$			0.403965i			0.0286363i	0.999897	+	0.0143182i	$0.00455777\pi$
$199$			0.403965i			0.0286363i	−0.999897	+	0.0143182i	$0.995442\pi$
$200$		0			0
$201$	16.4607	+	16.4607i	1.16105	+	1.16105i
$202$		0			0
$203$	−0.540803	+	24.8657i	−0.0379569	+	1.74523i
$204$		0			0
$205$	7.50145	−	7.50145i	0.523924	−	0.523924i
$206$		0			0
$207$	−2.73642			−0.190194
$208$		0			0
$209$		−	37.5620i		−	2.59822i
$210$		0			0
$211$	8.13629	−	8.13629i	0.560126	−	0.560126i	−0.369217	−	0.929343i	$-0.620374\pi$
$211$	8.13629	−	8.13629i	0.560126	−	0.560126i	0.929343	+	0.369217i	$0.120374\pi$
$212$		0			0
$213$	−2.29212	−	2.29212i	−0.157053	−	0.157053i
$214$		0			0
$215$	−11.9577	+	11.9577i	−0.815511	+	0.815511i
$216$		0			0
$217$	15.9715	−	15.9715i	1.08422	−	1.08422i
$218$		0			0
$219$			23.1442i			1.56394i
$220$		0			0
$221$	−0.237351	−	0.237351i	−0.0159659	−	0.0159659i
$222$		0			0
$223$		−	8.71556i		−	0.583637i	−0.956474	−	0.291819i	$-0.905740\pi$
$223$		−	8.71556i		−	0.583637i	0.956474	−	0.291819i	$-0.0942604\pi$
$224$		0			0
$225$		−	0.635008i		−	0.0423338i
$226$		0			0
$227$		−	12.0214i		−	0.797889i	−0.916975	−	0.398945i	$-0.869377\pi$
$227$		−	12.0214i		−	0.797889i	0.916975	−	0.398945i	$-0.130623\pi$
$228$		0			0
$229$	−2.94281	−	2.94281i	−0.194466	−	0.194466i	0.603157	−	0.797623i	$-0.293909\pi$
$229$	−2.94281	−	2.94281i	−0.194466	−	0.194466i	−0.797623	+	0.603157i	$0.793909\pi$
$230$		0			0
$231$	38.2579			2.51718
$232$		0			0
$233$	−23.1681			−1.51779			−0.758897	−	0.651211i	$-0.774261\pi$
$233$	−23.1681			−1.51779			−0.758897	+	0.651211i	$0.774261\pi$
$234$		0			0
$235$	−7.75194	−	7.75194i	−0.505681	−	0.505681i
$236$		0			0
$237$		−	8.34478i		−	0.542052i
$238$		0			0
$239$			22.5443i			1.45827i	0.684370	+	0.729135i	$0.260077\pi$
$239$			22.5443i			1.45827i	−0.684370	+	0.729135i	$0.739923\pi$
$240$		0			0
$241$		−	1.29184i		−	0.0832148i	−0.999134	−	0.0416074i	$-0.986752\pi$
$241$		−	1.29184i		−	0.0832148i	0.999134	−	0.0416074i	$-0.0132479\pi$
$242$		0			0
$243$	3.14006	+	3.14006i	0.201435	+	0.201435i
$244$		0			0
$245$			26.9102i			1.71923i
$246$		0			0
$247$	−10.4177	+	10.4177i	−0.662863	+	0.662863i
$248$		0			0
$249$	8.18727	−	8.18727i	0.518847	−	0.518847i
$250$		0			0
$251$	10.1769	+	10.1769i	0.642359	+	0.642359i	0.951135	−	0.308776i	$-0.0999193\pi$
$251$	10.1769	+	10.1769i	0.642359	+	0.642359i	−0.308776	+	0.951135i	$0.599919\pi$
$252$		0			0
$253$	−23.2111	+	23.2111i	−1.45927	+	1.45927i
$254$		0			0
$255$		−	0.498413i		−	0.0312119i
$256$		0			0
$257$	−1.16708			−0.0728003			−0.0364001	−	0.999337i	$-0.511589\pi$
$257$	−1.16708			−0.0728003			−0.0364001	+	0.999337i	$0.511589\pi$
$258$		0			0
$259$	31.3255	−	31.3255i	1.94647	−	1.94647i
$260$		0			0
$261$	−0.0504456	+	2.31946i	−0.00312251	+	0.143571i
$262$		0			0
$263$	−4.35144	−	4.35144i	−0.268321	−	0.268321i	0.560102	−	0.828424i	$-0.310762\pi$
$263$	−4.35144	−	4.35144i	−0.268321	−	0.268321i	−0.828424	+	0.560102i	$0.810762\pi$
$264$		0			0
$265$		−	8.78135i		−	0.539434i
$266$		0			0
$267$	10.0493			0.615006
$268$		0			0
$269$	−10.4925	−	10.4925i	−0.639742	−	0.639742i	0.310750	−	0.950492i	$-0.399420\pi$
$269$	−10.4925	−	10.4925i	−0.639742	−	0.639742i	−0.950492	+	0.310750i	$0.899420\pi$
$270$		0			0
$271$	−9.74634	+	9.74634i	−0.592048	+	0.592048i	−0.938184	−	0.346136i	$-0.887494\pi$
$271$	−9.74634	+	9.74634i	−0.592048	+	0.592048i	0.346136	+	0.938184i	$0.387494\pi$
$272$		0			0
$273$	−10.6107	−	10.6107i	−0.642189	−	0.642189i
$274$		0			0
$275$	−5.38633	−	5.38633i	−0.324808	−	0.324808i
$276$		0			0
$277$	18.0550			1.08482			0.542408	−	0.840115i	$-0.317513\pi$
$277$	18.0550			1.08482			0.542408	+	0.840115i	$0.317513\pi$
$278$		0			0
$279$	1.48981	−	1.48981i	0.0891926	−	0.0891926i
$280$		0			0
$281$	−15.3507			−0.915748			−0.457874	−	0.889017i	$-0.651389\pi$
$281$	−15.3507			−0.915748			−0.457874	+	0.889017i	$0.651389\pi$
$282$		0			0
$283$	2.78389			0.165485			0.0827425	−	0.996571i	$-0.473632\pi$
$283$	2.78389			0.165485			0.0827425	+	0.996571i	$0.473632\pi$
$284$		0			0
$285$	−21.8762			−1.29583
$286$		0			0
$287$	18.4505	−	18.4505i	1.08910	−	1.08910i
$288$		0			0
$289$			16.9726i			0.998387i
$290$		0			0
$291$			15.5960i			0.914256i
$292$		0			0
$293$	2.11953	−	2.11953i	0.123824	−	0.123824i	−0.642479	−	0.766303i	$-0.722094\pi$
$293$	2.11953	−	2.11953i	0.123824	−	0.123824i	0.766303	+	0.642479i	$0.222094\pi$
$294$		0			0
$295$	−2.63602			−0.153475
$296$		0			0
$297$	28.4193			1.64905
$298$		0			0
$299$	12.8751			0.744585
$300$		0			0
$301$	−29.4111	+	29.4111i	−1.69523	+	1.69523i
$302$		0			0
$303$	−7.27385			−0.417872
$304$		0			0
$305$	−9.11319	−	9.11319i	−0.521820	−	0.521820i
$306$		0			0
$307$	9.74951	+	9.74951i	0.556434	+	0.556434i	0.928290	−	0.371856i	$-0.121279\pi$
$307$	9.74951	+	9.74951i	0.556434	+	0.556434i	−0.371856	+	0.928290i	$0.621279\pi$
$308$		0			0
$309$	5.87379	−	5.87379i	0.334148	−	0.334148i
$310$		0			0
$311$	−12.7465	−	12.7465i	−0.722788	−	0.722788i	0.246384	−	0.969172i	$-0.420757\pi$
$311$	−12.7465	−	12.7465i	−0.722788	−	0.722788i	−0.969172	+	0.246384i	$0.920757\pi$
$312$		0			0
$313$	0.166591			0.00941625			0.00470813	−	0.999989i	$-0.498501\pi$
$313$	0.166591			0.00941625			0.00470813	+	0.999989i	$0.498501\pi$
$314$		0			0
$315$			3.73626i			0.210515i
$316$		0			0
$317$	10.8755	+	10.8755i	0.610831	+	0.610831i	0.943163	−	0.332332i	$-0.107835\pi$
$317$	10.8755	+	10.8755i	0.610831	+	0.610831i	−0.332332	+	0.943163i	$0.607835\pi$
$318$		0			0
$319$	19.2464	+	20.1022i	1.07759	+	1.12551i
$320$		0			0
$321$	−12.5669	+	12.5669i	−0.701419	+	0.701419i
$322$		0			0
$323$	−1.20359			−0.0669697
$324$		0			0
$325$			2.98776i			0.165731i
$326$		0			0
$327$	−6.44603	+	6.44603i	−0.356466	+	0.356466i
$328$		0			0
$329$	−19.0666	−	19.0666i	−1.05117	−	1.05117i
$330$		0			0
$331$	−20.2753	+	20.2753i	−1.11443	+	1.11443i	−0.121885	+	0.992544i	$0.538894\pi$
$331$	−20.2753	+	20.2753i	−1.11443	+	1.11443i	−0.992544	+	0.121885i	$0.961106\pi$
$332$		0			0
$333$	2.92202	−	2.92202i	0.160126	−	0.160126i
$334$		0			0
$335$			27.2715i			1.49000i
$336$		0			0
$337$	−13.3139	−	13.3139i	−0.725255	−	0.725255i	0.244415	−	0.969671i	$-0.421404\pi$
$337$	−13.3139	−	13.3139i	−0.725255	−	0.725255i	−0.969671	+	0.244415i	$0.921404\pi$
$338$		0			0
$339$		−	7.64837i		−	0.415402i
$340$		0			0
$341$		−	25.2740i		−	1.36867i
$342$		0			0
$343$			33.8582i			1.82817i
$344$		0			0
$345$	13.5182	+	13.5182i	0.727795	+	0.727795i
$346$		0			0
$347$	24.0375			1.29040			0.645200	−	0.764014i	$-0.276774\pi$
$347$	24.0375			1.29040			0.645200	+	0.764014i	$0.276774\pi$
$348$		0			0
$349$	−1.69411			−0.0906839			−0.0453419	−	0.998972i	$-0.514438\pi$
$349$	−1.69411			−0.0906839			−0.0453419	+	0.998972i	$0.514438\pi$
$350$		0			0
$351$	−7.88200	−	7.88200i	−0.420710	−	0.420710i
$352$		0			0
$353$			15.2039i			0.809220i	0.914489	+	0.404610i	$0.132593\pi$
$353$			15.2039i			0.809220i	−0.914489	+	0.404610i	$0.867407\pi$
$354$		0			0
$355$		−	3.79750i		−	0.201550i
$356$		0			0
$357$		−	1.22589i		−	0.0648810i
$358$		0			0
$359$	−7.55485	−	7.55485i	−0.398730	−	0.398730i	0.479055	−	0.877785i	$-0.340979\pi$
$359$	−7.55485	−	7.55485i	−0.398730	−	0.398730i	−0.877785	+	0.479055i	$0.840979\pi$
$360$		0			0
$361$			33.8276i			1.78040i
$362$		0			0
$363$	17.8031	−	17.8031i	0.934421	−	0.934421i
$364$		0			0
$365$	−19.1722	+	19.1722i	−1.00352	+	1.00352i
$366$		0			0
$367$	−21.5582	−	21.5582i	−1.12533	−	1.12533i	−0.990927	−	0.134402i	$-0.957089\pi$
$367$	−21.5582	−	21.5582i	−1.12533	−	1.12533i	−0.134402	−	0.990927i	$-0.542911\pi$
$368$		0			0
$369$	1.72104	−	1.72104i	0.0895940	−	0.0895940i
$370$		0			0
$371$		−	21.5985i		−	1.12134i
$372$		0			0
$373$	1.51653			0.0785228			0.0392614	−	0.999229i	$-0.487500\pi$
$373$	1.51653			0.0785228			0.0392614	+	0.999229i	$0.487500\pi$
$374$		0			0
$375$	−13.7783	+	13.7783i	−0.711510	+	0.711510i
$376$		0			0
$377$	0.237351	−	10.9132i	0.0122242	−	0.562060i
$378$		0			0
$379$	−17.7612	−	17.7612i	−0.912329	−	0.912329i	0.0841260	−	0.996455i	$-0.473190\pi$
$379$	−17.7612	−	17.7612i	−0.912329	−	0.912329i	−0.996455	+	0.0841260i	$0.973190\pi$
$380$		0			0
$381$		−	29.0176i		−	1.48662i
$382$		0			0
$383$	−30.7163			−1.56953			−0.784766	−	0.619793i	$-0.787217\pi$
$383$	−30.7163			−1.56953			−0.784766	+	0.619793i	$0.787217\pi$
$384$		0			0
$385$	31.6921	+	31.6921i	1.61518	+	1.61518i
$386$		0			0
$387$	−2.74344	+	2.74344i	−0.139457	+	0.139457i
$388$		0			0
$389$	13.9093	+	13.9093i	0.705229	+	0.705229i	0.965528	−	0.260299i	$-0.0838211\pi$
$389$	13.9093	+	13.9093i	0.705229	+	0.705229i	−0.260299	+	0.965528i	$0.583821\pi$
$390$		0			0
$391$	0.743750	+	0.743750i	0.0376131	+	0.0376131i
$392$		0			0
$393$	12.0390			0.607288
$394$		0			0
$395$	6.91265	−	6.91265i	0.347813	−	0.347813i
$396$		0			0
$397$	23.2779			1.16828			0.584141	−	0.811652i	$-0.301431\pi$
$397$	23.2779			1.16828			0.584141	+	0.811652i	$0.301431\pi$
$398$		0			0
$399$	−53.8063			−2.69368
$400$		0			0
$401$	−23.3061			−1.16385			−0.581924	−	0.813243i	$-0.697700\pi$
$401$	−23.3061			−1.16385			−0.581924	+	0.813243i	$0.697700\pi$
$402$		0			0
$403$	−7.00968	+	7.00968i	−0.349177	+	0.349177i
$404$		0			0
$405$		−	14.1245i		−	0.701853i
$406$		0			0
$407$		−	49.5709i		−	2.45714i
$408$		0			0
$409$	13.1630	−	13.1630i	0.650869	−	0.650869i	−0.302333	−	0.953202i	$-0.597766\pi$
$409$	13.1630	−	13.1630i	0.650869	−	0.650869i	0.953202	+	0.302333i	$0.0977656\pi$
$410$		0			0
$411$	−21.4561			−1.05835
$412$		0			0
$413$	−6.48351			−0.319033
$414$		0			0
$415$	13.5643			0.665848
$416$		0			0
$417$	11.1785	−	11.1785i	0.547415	−	0.547415i
$418$		0			0
$419$	−5.70332			−0.278626			−0.139313	−	0.990248i	$-0.544489\pi$
$419$	−5.70332			−0.278626			−0.139313	+	0.990248i	$0.544489\pi$
$420$		0			0
$421$	−15.4789	−	15.4789i	−0.754397	−	0.754397i	0.220899	−	0.975297i	$-0.429101\pi$
$421$	−15.4789	−	15.4789i	−0.754397	−	0.754397i	−0.975297	+	0.220899i	$0.929101\pi$
$422$		0			0
$423$	−1.77851	−	1.77851i	−0.0864743	−	0.0864743i
$424$		0			0
$425$	−0.172593	+	0.172593i	−0.00837199	+	0.00837199i
$426$		0			0
$427$	−22.4147	−	22.4147i	−1.08472	−	1.08472i
$428$		0			0
$429$	−16.7909			−0.810670
$430$		0			0
$431$			9.59910i			0.462372i	0.972910	+	0.231186i	$0.0742606\pi$
$431$			9.59910i			0.462372i	−0.972910	+	0.231186i	$0.925739\pi$
$432$		0			0
$433$	11.7314	+	11.7314i	0.563776	+	0.563776i	0.930378	−	0.366602i	$-0.119479\pi$
$433$	11.7314	+	11.7314i	0.563776	+	0.563776i	−0.366602	+	0.930378i	$0.619479\pi$
$434$		0			0
$435$	11.7076	−	11.2091i	0.561334	−	0.537437i
$436$		0			0
$437$	32.6444	−	32.6444i	1.56159	−	1.56159i
$438$		0			0
$439$	10.5216			0.502170			0.251085	−	0.967965i	$-0.419213\pi$
$439$	10.5216			0.502170			0.251085	+	0.967965i	$0.419213\pi$
$440$		0			0
$441$			6.17396i			0.293998i
$442$		0			0
$443$	3.38252	−	3.38252i	0.160708	−	0.160708i	−0.622172	−	0.782881i	$-0.713750\pi$
$443$	3.38252	−	3.38252i	0.160708	−	0.160708i	0.782881	+	0.622172i	$0.213750\pi$
$444$		0			0
$445$	8.32463	+	8.32463i	0.394625	+	0.394625i
$446$		0			0
$447$	−16.1195	+	16.1195i	−0.762429	+	0.762429i
$448$		0			0
$449$	7.41696	−	7.41696i	0.350028	−	0.350028i	−0.510092	−	0.860120i	$-0.670389\pi$
$449$	7.41696	−	7.41696i	0.350028	−	0.350028i	0.860120	+	0.510092i	$0.170389\pi$
$450$		0			0
$451$		−	29.1968i		−	1.37482i
$452$		0			0
$453$	15.1731	+	15.1731i	0.712894	+	0.712894i
$454$		0			0
$455$		−	17.5794i		−	0.824136i
$456$		0			0
$457$		−	5.96799i		−	0.279171i	−0.990210	−	0.139585i	$-0.955423\pi$
$457$		−	5.96799i		−	0.279171i	0.990210	−	0.139585i	$-0.0445770\pi$
$458$		0			0
$459$		−	0.910634i		−	0.0425048i
$460$		0			0
$461$	8.39522	+	8.39522i	0.391005	+	0.391005i	0.875045	−	0.484041i	$-0.160831\pi$
$461$	8.39522	+	8.39522i	0.391005	+	0.391005i	−0.484041	+	0.875045i	$0.660831\pi$
$462$		0			0
$463$	10.2011			0.474087			0.237043	−	0.971499i	$-0.423822\pi$
$463$	10.2011			0.474087			0.237043	+	0.971499i	$0.423822\pi$
$464$		0			0
$465$	−14.7196			−0.682606
$466$		0			0
$467$	−3.03744	−	3.03744i	−0.140556	−	0.140556i	0.633328	−	0.773884i	$-0.281689\pi$
$467$	−3.03744	−	3.03744i	−0.140556	−	0.140556i	−0.773884	+	0.633328i	$0.781689\pi$
$468$		0			0
$469$			67.0766i			3.09731i
$470$		0			0
$471$		−	16.2203i		−	0.747390i
$472$		0			0
$473$			46.5414i			2.13998i
$474$		0			0
$475$	7.57538	+	7.57538i	0.347582	+	0.347582i
$476$		0			0
$477$		−	2.01469i		−	0.0922463i
$478$		0			0
$479$	9.00259	−	9.00259i	0.411339	−	0.411339i	−0.470866	−	0.882205i	$-0.656058\pi$
$479$	9.00259	−	9.00259i	0.411339	−	0.411339i	0.882205	+	0.470866i	$0.156058\pi$
$480$		0			0
$481$	−13.7483	+	13.7483i	−0.626870	+	0.626870i
$482$		0			0
$483$	33.2492	+	33.2492i	1.51289	+	1.51289i
$484$		0			0
$485$	−12.9195	+	12.9195i	−0.586642	+	0.586642i
$486$		0			0
$487$		−	6.90676i		−	0.312975i	−0.987680	−	0.156488i	$-0.949983\pi$
$487$		−	6.90676i		−	0.312975i	0.987680	−	0.156488i	$-0.0500171\pi$
$488$		0			0
$489$	5.68123			0.256914
$490$		0			0
$491$	−15.2194	+	15.2194i	−0.686842	+	0.686842i	−0.961533	−	0.274690i	$-0.911425\pi$
$491$	−15.2194	+	15.2194i	−0.686842	+	0.686842i	0.274690	+	0.961533i	$0.411425\pi$
$492$		0			0
$493$	0.644131	−	0.616710i	0.0290102	−	0.0277752i
$494$		0			0
$495$	2.95621	+	2.95621i	0.132872	+	0.132872i
$496$		0			0
$497$		−	9.34027i		−	0.418968i
$498$		0			0
$499$	8.94029			0.400222			0.200111	−	0.979773i	$-0.435870\pi$
$499$	8.94029			0.400222			0.200111	+	0.979773i	$0.435870\pi$
$500$		0			0
$501$	−20.6803	−	20.6803i	−0.923927	−	0.923927i
$502$		0			0
$503$	24.0347	−	24.0347i	1.07166	−	1.07166i	0.0744288	−	0.997226i	$-0.476287\pi$
$503$	24.0347	−	24.0347i	1.07166	−	1.07166i	0.997226	−	0.0744288i	$-0.0237133\pi$
$504$		0			0
$505$	−6.02552	−	6.02552i	−0.268132	−	0.268132i
$506$		0			0
$507$	−10.0773	−	10.0773i	−0.447548	−	0.447548i
$508$		0			0
$509$	−21.6977			−0.961735			−0.480867	−	0.876793i	$-0.659678\pi$
$509$	−21.6977			−0.961735			−0.480867	+	0.876793i	$0.659678\pi$
$510$		0			0
$511$	−47.1556	+	47.1556i	−2.08604	+	2.08604i
$512$		0			0
$513$	−39.9692			−1.76468
$514$		0			0
$515$	9.73147			0.428820
$516$		0			0
$517$	−30.1718			−1.32695
$518$		0			0
$519$	−18.3643	+	18.3643i	−0.806102	+	0.806102i
$520$		0			0
$521$			28.3550i			1.24226i	0.783709	+	0.621128i	$0.213325\pi$
$521$			28.3550i			1.24226i	−0.783709	+	0.621128i	$0.786675\pi$
$522$		0			0
$523$		−	31.2190i		−	1.36511i	−0.730833	−	0.682556i	$-0.760868\pi$
$523$		−	31.2190i		−	1.36511i	0.730833	−	0.682556i	$-0.239132\pi$
$524$		0			0
$525$	−7.71573	+	7.71573i	−0.336742	+	0.336742i
$526$		0			0
$527$	−0.809851			−0.0352777
$528$		0			0
$529$	−17.3447			−0.754115
$530$		0			0
$531$	−0.604777			−0.0262451
$532$		0			0
$533$	−8.09765	+	8.09765i	−0.350748	+	0.350748i
$534$		0			0
$535$	−20.8204			−0.900146
$536$		0			0
$537$	1.62611	+	1.62611i	0.0701718	+	0.0701718i
$538$		0			0
$539$	52.3694	+	52.3694i	2.25571	+	2.25571i
$540$		0			0
$541$	0.803209	−	0.803209i	0.0345326	−	0.0345326i	−0.689630	−	0.724162i	$-0.742227\pi$
$541$	0.803209	−	0.803209i	0.0345326	−	0.0345326i	0.724162	+	0.689630i	$0.242227\pi$
$542$		0			0
$543$	1.26358	+	1.26358i	0.0542252	+	0.0542252i
$544$		0			0
$545$	−10.6795			−0.457461
$546$		0			0
$547$			17.4159i			0.744649i	0.928103	+	0.372325i	$0.121439\pi$
$547$			17.4159i			0.744649i	−0.928103	+	0.372325i	$0.878561\pi$
$548$		0			0
$549$	−2.09082	−	2.09082i	−0.0892341	−	0.0892341i
$550$		0			0
$551$	−27.0684	−	28.2720i	−1.15315	−	1.20443i
$552$		0			0
$553$	17.0023	−	17.0023i	0.723010	−	0.723010i
$554$		0			0
$555$	−28.8702			−1.22547
$556$		0			0
$557$		−	4.46415i		−	0.189152i	−0.995518	−	0.0945761i	$-0.969850\pi$
$557$		−	4.46415i		−	0.189152i	0.995518	−	0.0945761i	$-0.0301496\pi$
$558$		0			0
$559$	12.9081	−	12.9081i	0.545955	−	0.545955i
$560$		0			0
$561$	−0.969952	−	0.969952i	−0.0409514	−	0.0409514i
$562$		0			0
$563$	19.7864	−	19.7864i	0.833896	−	0.833896i	−0.154152	−	0.988047i	$-0.549264\pi$
$563$	19.7864	−	19.7864i	0.833896	−	0.833896i	0.988047	+	0.154152i	$0.0492644\pi$
$564$		0			0
$565$	6.33576	−	6.33576i	0.266548	−	0.266548i
$566$		0			0
$567$		−	34.7405i		−	1.45896i
$568$		0			0
$569$	−14.5991	−	14.5991i	−0.612026	−	0.612026i	0.331448	−	0.943474i	$-0.392463\pi$
$569$	−14.5991	−	14.5991i	−0.612026	−	0.612026i	−0.943474	+	0.331448i	$0.892463\pi$
$570$		0			0
$571$		−	4.89118i		−	0.204689i	−0.994749	−	0.102345i	$-0.967366\pi$
$571$		−	4.89118i		−	0.204689i	0.994749	−	0.102345i	$-0.0326345\pi$
$572$		0			0
$573$			17.7277i			0.740584i
$574$		0			0
$575$		−	9.36229i		−	0.390435i
$576$		0			0
$577$	−18.6225	−	18.6225i	−0.775265	−	0.775265i	0.203757	−	0.979022i	$-0.434685\pi$
$577$	−18.6225	−	18.6225i	−0.775265	−	0.775265i	−0.979022	+	0.203757i	$0.934685\pi$
$578$		0			0
$579$	−24.8558			−1.03297
$580$		0			0
$581$	33.3627			1.38412
$582$		0			0
$583$	−17.0892	−	17.0892i	−0.707763	−	0.707763i
$584$		0			0
$585$		−	1.63979i		−	0.0677971i
$586$		0			0
$587$		−	30.8014i		−	1.27131i	−0.771973	−	0.635656i	$-0.780730\pi$
$587$		−	30.8014i		−	1.27131i	0.771973	−	0.635656i	$-0.219270\pi$
$588$		0			0
$589$			35.5457i			1.46463i
$590$		0			0
$591$	7.05418	+	7.05418i	0.290170	+	0.290170i
$592$		0			0
$593$		−	0.859810i		−	0.0353082i	−0.999844	−	0.0176541i	$-0.994380\pi$
$593$		−	0.859810i		−	0.0353082i	0.999844	−	0.0176541i	$-0.00561976\pi$
$594$		0			0
$595$	1.01550	−	1.01550i	0.0416316	−	0.0416316i
$596$		0			0
$597$	0.457854	−	0.457854i	0.0187387	−	0.0187387i
$598$		0			0
$599$	14.8795	+	14.8795i	0.607960	+	0.607960i	0.942413	−	0.334453i	$-0.108551\pi$
$599$	14.8795	+	14.8795i	0.607960	+	0.607960i	−0.334453	+	0.942413i	$0.608551\pi$
$600$		0			0
$601$	12.7547	−	12.7547i	0.520274	−	0.520274i	−0.397380	−	0.917654i	$-0.630081\pi$
$601$	12.7547	−	12.7547i	0.520274	−	0.520274i	0.917654	+	0.397380i	$0.130081\pi$
$602$		0			0
$603$			6.25685i			0.254799i
$604$		0			0
$605$	29.4955			1.19916
$606$		0			0
$607$	25.6300	−	25.6300i	1.04029	−	1.04029i	0.0411375	−	0.999153i	$-0.486902\pi$
$607$	25.6300	−	25.6300i	1.04029	−	1.04029i	0.999153	−	0.0411375i	$-0.0130982\pi$
$608$		0			0
$609$	28.7957	−	27.5698i	1.16686	−	1.11719i
$610$		0			0
$611$	8.36805	+	8.36805i	0.338535	+	0.338535i
$612$		0			0
$613$		−	29.3524i		−	1.18553i	−0.805374	−	0.592767i	$-0.798036\pi$
$613$		−	29.3524i		−	1.18553i	0.805374	−	0.592767i	$-0.201964\pi$
$614$		0			0
$615$	−17.0043			−0.685678
$616$		0			0
$617$	32.4589	+	32.4589i	1.30675	+	1.30675i	0.923749	+	0.382999i	$0.125109\pi$
$617$	32.4589	+	32.4589i	1.30675	+	1.30675i	0.382999	+	0.923749i	$0.374891\pi$
$618$		0			0
$619$	−7.45209	+	7.45209i	−0.299525	+	0.299525i	−0.840828	−	0.541303i	$-0.817931\pi$
$619$	−7.45209	+	7.45209i	−0.299525	+	0.299525i	0.541303	+	0.840828i	$0.317931\pi$
$620$		0			0
$621$	24.6986	+	24.6986i	0.991122	+	0.991122i
$622$		0			0
$623$	20.4751	+	20.4751i	0.820319	+	0.820319i
$624$		0			0
$625$	−15.4575			−0.618302
$626$		0			0
$627$	−42.5727	+	42.5727i	−1.70019	+	1.70019i
$628$		0			0
$629$	−1.58839			−0.0633333
$630$		0			0
$631$	11.9343			0.475097			0.237548	−	0.971376i	$-0.423656\pi$
$631$	11.9343			0.475097			0.237548	+	0.971376i	$0.423656\pi$
$632$		0			0
$633$	−18.4433			−0.733057
$634$		0			0
$635$	24.0376	−	24.0376i	0.953904	−	0.953904i
$636$		0			0
$637$		−	29.0490i		−	1.15096i
$638$		0			0
$639$		−	0.871253i		−	0.0344662i
$640$		0			0
$641$	−19.7465	+	19.7465i	−0.779940	+	0.779940i	−0.979820	−	0.199880i	$-0.935945\pi$
$641$	−19.7465	+	19.7465i	−0.779940	+	0.779940i	0.199880	+	0.979820i	$0.435945\pi$
$642$		0			0
$643$	19.5916			0.772616			0.386308	−	0.922370i	$-0.373750\pi$
$643$	19.5916			0.772616			0.386308	+	0.922370i	$0.373750\pi$
$644$		0			0
$645$	27.1058			1.06729
$646$		0			0
$647$	16.5461			0.650495			0.325247	−	0.945629i	$-0.394552\pi$
$647$	16.5461			0.650495			0.325247	+	0.945629i	$0.394552\pi$
$648$		0			0
$649$	−5.12990	+	5.12990i	−0.201366	+	0.201366i
$650$		0			0
$651$	−36.2042			−1.41895
$652$		0			0
$653$	−35.9120	−	35.9120i	−1.40535	−	1.40535i	−0.781730	−	0.623617i	$-0.785663\pi$
$653$	−35.9120	−	35.9120i	−1.40535	−	1.40535i	−0.623617	−	0.781730i	$-0.714337\pi$
$654$		0			0
$655$	9.97288	+	9.97288i	0.389673	+	0.389673i
$656$		0			0
$657$	−4.39864	+	4.39864i	−0.171607	+	0.171607i
$658$		0			0
$659$	−21.6276	−	21.6276i	−0.842492	−	0.842492i	0.146690	−	0.989182i	$-0.453138\pi$
$659$	−21.6276	−	21.6276i	−0.842492	−	0.842492i	−0.989182	+	0.146690i	$0.953138\pi$
$660$		0			0
$661$	−1.74975			−0.0680575			−0.0340287	−	0.999421i	$-0.510834\pi$
$661$	−1.74975			−0.0680575			−0.0340287	+	0.999421i	$0.510834\pi$
$662$		0			0
$663$			0.538026i			0.0208952i
$664$		0			0
$665$	−44.5721	−	44.5721i	−1.72843	−	1.72843i
$666$		0			0
$667$	−0.743750	+	34.1971i	−0.0287981	+	1.32412i
$668$		0			0
$669$	−9.87821	+	9.87821i	−0.381914	+	0.381914i
$670$		0			0
$671$	−35.4700			−1.36930
$672$		0			0
$673$			48.7095i			1.87761i	0.344446	+	0.938806i	$0.388067\pi$
$673$			48.7095i			1.87761i	−0.344446	+	0.938806i	$0.611933\pi$
$674$		0			0
$675$	−5.73151	+	5.73151i	−0.220606	+	0.220606i
$676$		0			0
$677$	11.2703	+	11.2703i	0.433153	+	0.433153i	0.889699	−	0.456547i	$-0.150914\pi$
$677$	11.2703	+	11.2703i	0.433153	+	0.433153i	−0.456547	+	0.889699i	$0.650914\pi$
$678$		0			0
$679$	−31.7765	+	31.7765i	−1.21947	+	1.21947i
$680$		0			0
$681$	−13.6251	+	13.6251i	−0.522113	+	0.522113i
$682$		0			0
$683$		−	33.0026i		−	1.26281i	−0.775454	−	0.631404i	$-0.782479\pi$
$683$		−	33.0026i		−	1.26281i	0.775454	−	0.631404i	$-0.217521\pi$
$684$		0			0
$685$	−17.7739	−	17.7739i	−0.679104	−	0.679104i
$686$		0			0
$687$			6.67075i			0.254505i
$688$		0			0
$689$			9.47928i			0.361132i
$690$		0			0
$691$		−	24.0492i		−	0.914873i	−0.889242	−	0.457437i	$-0.848768\pi$
$691$		−	24.0492i		−	0.914873i	0.889242	−	0.457437i	$-0.151232\pi$
$692$		0			0
$693$	7.27106	+	7.27106i	0.276205	+	0.276205i
$694$		0			0
$695$	18.5202			0.702509
$696$		0			0
$697$	−0.935548			−0.0354364
$698$		0			0
$699$	26.2587	+	26.2587i	0.993196	+	0.993196i
$700$		0			0
$701$		−	17.2843i		−	0.652819i	−0.945228	−	0.326410i	$-0.894161\pi$
$701$		−	17.2843i		−	0.652819i	0.945228	−	0.326410i	$-0.105839\pi$
$702$		0			0
$703$			69.7170i			2.62943i
$704$		0			0
$705$			17.5721i			0.661803i
$706$		0			0
$707$	−14.8203	−	14.8203i	−0.557374	−	0.557374i
$708$		0			0
$709$		−	39.1739i		−	1.47121i	−0.677413	−	0.735603i	$-0.736899\pi$
$709$		−	39.1739i		−	1.47121i	0.677413	−	0.735603i	$-0.263101\pi$
$710$		0			0
$711$	1.58596	−	1.58596i	0.0594781	−	0.0594781i
$712$		0			0
$713$	21.9652	−	21.9652i	0.822601	−	0.822601i
$714$		0			0
$715$	−13.9092	−	13.9092i	−0.520176	−	0.520176i
$716$		0			0
$717$	25.5517	−	25.5517i	0.954245	−	0.954245i
$718$		0			0
$719$		−	35.6490i		−	1.32948i	−0.747073	−	0.664742i	$-0.768541\pi$
$719$		−	35.6490i		−	1.32948i	0.747073	−	0.664742i	$-0.231459\pi$
$720$		0			0
$721$	23.9354			0.891400
$722$		0			0
$723$	−1.46417	+	1.46417i	−0.0544531	+	0.0544531i
$724$		0			0
$725$	−7.93570	−	0.172593i	−0.294725	−	0.00640994i
$726$		0			0
$727$	35.7780	+	35.7780i	1.32693	+	1.32693i	0.908031	+	0.418902i	$0.137585\pi$
$727$	35.7780	+	35.7780i	1.32693	+	1.32693i	0.418902	+	0.908031i	$0.362415\pi$
$728$		0			0
$729$		−	29.6838i		−	1.09940i
$730$		0			0
$731$	1.49132			0.0551584
$732$		0			0
$733$	−2.91038	−	2.91038i	−0.107497	−	0.107497i	0.651312	−	0.758810i	$-0.274219\pi$
$733$	−2.91038	−	2.91038i	−0.107497	−	0.107497i	−0.758810	+	0.651312i	$0.774219\pi$
$734$		0			0
$735$	30.5000	−	30.5000i	1.12501	−	1.12501i
$736$		0			0
$737$	53.0725	+	53.0725i	1.95495	+	1.95495i
$738$		0			0
$739$	29.2116	+	29.2116i	1.07457	+	1.07457i	0.996986	+	0.0775789i	$0.0247190\pi$
$739$	29.2116	+	29.2116i	1.07457	+	1.07457i	0.0775789	+	0.996986i	$0.475281\pi$
$740$		0			0
$741$	23.6148			0.867513
$742$		0			0
$743$	−25.4269	+	25.4269i	−0.932822	+	0.932822i	−0.997881	−	0.0650595i	$-0.979276\pi$
$743$	−25.4269	+	25.4269i	−0.932822	+	0.932822i	0.0650595	+	0.997881i	$0.479276\pi$
$744$		0			0
$745$	−26.7063			−0.978441
$746$		0			0
$747$	3.11204			0.113864
$748$		0			0
$749$	−51.2097			−1.87116
$750$		0			0
$751$	−17.8866	+	17.8866i	−0.652690	+	0.652690i	−0.953640	−	0.300950i	$-0.902696\pi$
$751$	−17.8866	+	17.8866i	−0.652690	+	0.652690i	0.300950	+	0.953640i	$0.402696\pi$
$752$		0			0
$753$		−	23.0689i		−	0.840678i
$754$		0			0
$755$			25.1382i			0.914873i
$756$		0			0
$757$	13.6836	−	13.6836i	0.497338	−	0.497338i	−0.413270	−	0.910608i	$-0.635614\pi$
$757$	13.6836	−	13.6836i	0.497338	−	0.497338i	0.910608	+	0.413270i	$0.135614\pi$
$758$		0			0
$759$	52.6149			1.90980
$760$		0			0
$761$	36.0021			1.30508			0.652538	−	0.757756i	$-0.273704\pi$
$761$	36.0021			1.30508			0.652538	+	0.757756i	$0.273704\pi$
$762$		0			0
$763$	−26.2672			−0.950938
$764$		0			0
$765$	0.0947254	−	0.0947254i	0.00342481	−	0.00342481i
$766$		0			0
$767$	2.84552			0.102746
$768$		0			0
$769$	26.9265	+	26.9265i	0.970994	+	0.970994i	0.999591	−	0.0285966i	$-0.00910382\pi$
$769$	26.9265	+	26.9265i	0.970994	+	0.970994i	−0.0285966	+	0.999591i	$0.509104\pi$
$770$		0			0
$771$	1.32276	+	1.32276i	0.0476382	+	0.0476382i
$772$		0			0
$773$	−33.3516	+	33.3516i	−1.19957	+	1.19957i	−0.225281	+	0.974294i	$0.572330\pi$
$773$	−33.3516	+	33.3516i	−1.19957	+	1.19957i	−0.974294	+	0.225281i	$0.927670\pi$
$774$		0			0
$775$	5.09719	+	5.09719i	0.183096	+	0.183096i
$776$		0			0
$777$	−71.0086			−2.54742
$778$		0			0
$779$			41.0627i			1.47122i
$780$		0			0
$781$	−7.39023	−	7.39023i	−0.264443	−	0.264443i
$782$		0			0
$783$	21.3905	−	20.4798i	0.764433	−	0.731890i
$784$		0			0
$785$	13.4365	−	13.4365i	0.479571	−	0.479571i
$786$		0			0
$787$	−6.46870			−0.230584			−0.115292	−	0.993332i	$-0.536780\pi$
$787$	−6.46870			−0.230584			−0.115292	+	0.993332i	$0.536780\pi$
$788$		0			0
$789$			9.86384i			0.351162i
$790$		0			0
$791$	15.5834	−	15.5834i	0.554080	−	0.554080i
$792$		0			0
$793$	9.83749	+	9.83749i	0.349339	+	0.349339i
$794$		0			0
$795$	−9.95278	+	9.95278i	−0.352989	+	0.352989i
$796$		0			0
$797$	23.6210	−	23.6210i	0.836698	−	0.836698i	−0.151725	−	0.988423i	$-0.548483\pi$
$797$	23.6210	−	23.6210i	0.836698	−	0.836698i	0.988423	+	0.151725i	$0.0484828\pi$
$798$		0			0
$799$			0.966789i			0.0342025i
$800$		0			0
$801$	1.90990	+	1.90990i	0.0674832	+	0.0674832i
$802$		0			0
$803$			74.6212i			2.63332i
$804$		0			0
$805$			55.0859i			1.94152i
$806$		0			0
$807$			23.7845i			0.837254i
$808$		0			0
$809$	9.92186	+	9.92186i	0.348834	+	0.348834i	0.859675	−	0.510841i	$-0.170666\pi$
$809$	9.92186	+	9.92186i	0.348834	+	0.348834i	−0.510841	+	0.859675i	$0.670666\pi$
$810$		0			0
$811$	18.3418			0.644068			0.322034	−	0.946728i	$-0.395634\pi$
$811$	18.3418			0.644068			0.322034	+	0.946728i	$0.395634\pi$
$812$		0			0
$813$	22.0930			0.774835
$814$		0			0
$815$	4.70622	+	4.70622i	0.164852	+	0.164852i
$816$		0			0
$817$		−	65.4564i		−	2.29003i
$818$		0			0
$819$		−	4.03321i		−	0.140932i
$820$		0			0
$821$			21.2252i			0.740765i	0.928879	+	0.370382i	$0.120773\pi$
$821$			21.2252i			0.740765i	−0.928879	+	0.370382i	$0.879227\pi$
$822$		0			0
$823$	−2.92578	−	2.92578i	−0.101986	−	0.101986i	0.654272	−	0.756259i	$-0.272975\pi$
$823$	−2.92578	−	2.92578i	−0.101986	−	0.101986i	−0.756259	+	0.654272i	$0.772975\pi$
$824$		0			0
$825$			12.2097i			0.425088i
$826$		0			0
$827$	29.2586	−	29.2586i	1.01742	−	1.01742i	0.0175740	−	0.999846i	$-0.494406\pi$
$827$	29.2586	−	29.2586i	1.01742	−	1.01742i	0.999846	−	0.0175740i	$-0.00559427\pi$
$828$		0			0
$829$	16.1371	−	16.1371i	0.560466	−	0.560466i	−0.368974	−	0.929440i	$-0.620291\pi$
$829$	16.1371	−	16.1371i	0.560466	−	0.560466i	0.929440	+	0.368974i	$0.120291\pi$
$830$		0			0
$831$	−20.4635	−	20.4635i	−0.709870	−	0.709870i
$832$		0			0
$833$	1.67806	−	1.67806i	0.0581414	−	0.0581414i
$834$		0			0
$835$		−	34.2623i		−	1.18570i
$836$		0			0
$837$	−26.8937			−0.929584
$838$		0			0
$839$	−2.55730	+	2.55730i	−0.0882879	+	0.0882879i	−0.749871	−	0.661584i	$-0.769885\pi$
$839$	−2.55730	+	2.55730i	−0.0882879	+	0.0882879i	0.661584	+	0.749871i	$0.269885\pi$
$840$		0			0
$841$	28.9726	+	1.26084i	0.999054	+	0.0434773i
$842$		0			0
$843$	17.3985	+	17.3985i	0.599236	+	0.599236i
$844$		0			0
$845$		−	16.6957i		−	0.574349i
$846$		0			0
$847$	72.5467			2.49274
$848$		0			0
$849$	−3.15526	−	3.15526i	−0.108288	−	0.108288i
$850$		0			0
$851$	43.0811	−	43.0811i	1.47680	−	1.47680i
$852$		0			0
$853$	−13.5144	−	13.5144i	−0.462725	−	0.462725i	0.436822	−	0.899548i	$-0.356104\pi$
$853$	−13.5144	−	13.5144i	−0.462725	−	0.462725i	−0.899548	+	0.436822i	$0.856104\pi$
$854$		0			0
$855$	−4.15765	−	4.15765i	−0.142189	−	0.142189i
$856$		0			0
$857$	35.5099			1.21300			0.606498	−	0.795085i	$-0.292574\pi$
$857$	35.5099			1.21300			0.606498	+	0.795085i	$0.292574\pi$
$858$		0			0
$859$	15.5054	−	15.5054i	0.529036	−	0.529036i	−0.391249	−	0.920285i	$-0.627957\pi$
$859$	15.5054	−	15.5054i	0.529036	−	0.529036i	0.920285	+	0.391249i	$0.127957\pi$
$860$		0			0
$861$	−41.8235			−1.42534
$862$		0			0
$863$	23.9502			0.815276			0.407638	−	0.913144i	$-0.366353\pi$
$863$	23.9502			0.815276			0.407638	+	0.913144i	$0.366353\pi$
$864$		0			0
$865$	−30.4252			−1.03449
$866$		0			0
$867$	19.2367	−	19.2367i	0.653313	−	0.653313i
$868$		0			0
$869$		−	26.9051i		−	0.912695i
$870$		0			0
$871$		−	29.4390i		−	0.997502i
$872$		0			0
$873$	−2.96409	+	2.96409i	−0.100319	+	0.100319i
$874$		0			0
$875$	−56.1460			−1.89808
$876$		0			0
$877$	−9.15943			−0.309292			−0.154646	−	0.987970i	$-0.549424\pi$
$877$	−9.15943			−0.309292			−0.154646	+	0.987970i	$0.549424\pi$
$878$		0			0
$879$	−4.80454			−0.162053
$880$		0			0
$881$	1.60816	−	1.60816i	0.0541803	−	0.0541803i	−0.679498	−	0.733678i	$-0.737802\pi$
$881$	1.60816	−	1.60816i	0.0541803	−	0.0541803i	0.733678	+	0.679498i	$0.237802\pi$
$882$		0			0
$883$	−21.5780			−0.726156			−0.363078	−	0.931759i	$-0.618274\pi$
$883$	−21.5780			−0.726156			−0.363078	+	0.931759i	$0.618274\pi$
$884$		0			0
$885$	2.98766	+	2.98766i	0.100429	+	0.100429i
$886$		0			0
$887$	18.9686	+	18.9686i	0.636904	+	0.636904i	0.949790	−	0.312887i	$-0.101296\pi$
$887$	18.9686	+	18.9686i	0.636904	+	0.636904i	−0.312887	+	0.949790i	$0.601296\pi$
$888$		0			0
$889$	59.1226	−	59.1226i	1.98291	−	1.98291i
$890$		0			0
$891$	−27.4874	−	27.4874i	−0.920864	−	0.920864i
$892$		0			0
$893$	42.4339			1.42000
$894$		0			0
$895$			2.69408i			0.0900530i
$896$		0			0
$897$	−14.5926	−	14.5926i	−0.487232	−	0.487232i
$898$		0			0
$899$	−18.2133	−	19.0231i	−0.607446	−	0.634457i
$900$		0			0
$901$	−0.547586	+	0.547586i	−0.0182427	+	0.0182427i
$902$		0			0
$903$	66.6690			2.21861
$904$		0			0
$905$			2.09344i			0.0695885i
$906$		0			0
$907$	−17.6167	+	17.6167i	−0.584953	+	0.584953i	−0.936260	−	0.351307i	$-0.885737\pi$
$907$	−17.6167	+	17.6167i	−0.584953	+	0.584953i	0.351307	+	0.936260i	$0.385737\pi$
$908$		0			0
$909$	−1.38242	−	1.38242i	−0.0458521	−	0.0458521i
$910$		0			0
$911$	−0.266941	+	0.266941i	−0.00884414	+	0.00884414i	−0.711515	−	0.702671i	$-0.751991\pi$
$911$	−0.266941	+	0.266941i	−0.00884414	+	0.00884414i	0.702671	+	0.711515i	$0.251991\pi$
$912$		0			0
$913$	26.3973	−	26.3973i	0.873623	−	0.873623i
$914$		0			0
$915$			20.6578i			0.682924i
$916$		0			0
$917$	24.5292	+	24.5292i	0.810024	+	0.810024i
$918$		0			0
$919$			29.2241i			0.964016i	0.876167	+	0.482008i	$0.160092\pi$
$919$			29.2241i			0.964016i	−0.876167	+	0.482008i	$0.839908\pi$
$920$		0			0
$921$		−	22.1002i		−	0.728225i
$922$		0			0
$923$			4.09931i			0.134931i
$924$		0			0
$925$	9.99730	+	9.99730i	0.328709	+	0.328709i
$926$		0			0
$927$	2.23267			0.0733306
$928$		0			0
$929$	0.693550			0.0227546			0.0113773	−	0.999935i	$-0.496378\pi$
$929$	0.693550			0.0227546			0.0113773	+	0.999935i	$0.496378\pi$
$930$		0			0
$931$	−73.6529	−	73.6529i	−2.41388	−	2.41388i
$932$		0			0
$933$			28.8937i			0.945939i
$934$		0			0
$935$		−	1.60698i		−	0.0525538i
$936$		0			0
$937$		−	29.0078i		−	0.947642i	−0.880621	−	0.473821i	$-0.842874\pi$
$937$		−	29.0078i		−	0.947642i	0.880621	−	0.473821i	$-0.157126\pi$
$938$		0			0
$939$	−0.188814	−	0.188814i	−0.00616170	−	0.00616170i
$940$		0			0
$941$			26.9516i			0.878596i	0.898341	+	0.439298i	$0.144773\pi$
$941$			26.9516i			0.878596i	−0.898341	+	0.439298i	$0.855227\pi$
$942$		0			0
$943$	25.3744	−	25.3744i	0.826303	−	0.826303i
$944$		0			0
$945$	33.7231	−	33.7231i	1.09701	−	1.09701i
$946$		0			0
$947$	26.1687	+	26.1687i	0.850369	+	0.850369i	0.990178	−	0.139809i	$-0.0446489\pi$
$947$	26.1687	+	26.1687i	0.850369	+	0.850369i	−0.139809	+	0.990178i	$0.544649\pi$
$948$		0			0
$949$	20.6960	−	20.6960i	0.671819	−	0.671819i
$950$		0			0
$951$		−	24.6526i		−	0.799417i
$952$		0			0
$953$	−50.8766			−1.64806			−0.824028	−	0.566549i	$-0.808278\pi$
$953$	−50.8766			−1.64806			−0.824028	+	0.566549i	$0.808278\pi$
$954$		0			0
$955$	−14.6853	+	14.6853i	−0.475204	+	0.475204i
$956$		0			0
$957$	0.969952	−	44.5977i	0.0313541	−	1.44164i
$958$		0			0
$959$	−43.7163	−	43.7163i	−1.41167	−	1.41167i
$960$		0			0
$961$		−	7.08268i		−	0.228474i
$962$		0			0
$963$	−4.77680			−0.153930
$964$		0			0
$965$	−20.5901	−	20.5901i	−0.662817	−	0.662817i
$966$		0			0
$967$	−6.66999	+	6.66999i	−0.214493	+	0.214493i	−0.806173	−	0.591680i	$-0.798465\pi$
$967$	−6.66999	+	6.66999i	−0.214493	+	0.214493i	0.591680	+	0.806173i	$0.298465\pi$
$968$		0			0
$969$	1.36415	+	1.36415i	0.0438228	+	0.0438228i
$970$		0			0
$971$	3.20264	+	3.20264i	0.102778	+	0.102778i	0.756626	−	0.653848i	$-0.226846\pi$
$971$	3.20264	+	3.20264i	0.102778	+	0.102778i	−0.653848	+	0.756626i	$0.726846\pi$
$972$		0			0
$973$	45.5519			1.46033
$974$		0			0
$975$	3.38633	−	3.38633i	0.108449	−	0.108449i
$976$		0			0
$977$	30.4986			0.975737			0.487868	−	0.872917i	$-0.337775\pi$
$977$	30.4986			0.975737			0.487868	+	0.872917i	$0.337775\pi$
$978$		0			0
$979$	32.4008			1.03553
$980$		0			0
$981$	−2.45019			−0.0782284
$982$		0			0
$983$	4.79423	−	4.79423i	0.152912	−	0.152912i	−0.626505	−	0.779417i	$-0.715515\pi$
$983$	4.79423	−	4.79423i	0.152912	−	0.152912i	0.779417	+	0.626505i	$0.215515\pi$
$984$		0			0
$985$			11.6871i			0.372382i
$986$		0			0
$987$			43.2200i			1.37571i
$988$		0			0
$989$	−40.4482	+	40.4482i	−1.28618	+	1.28618i
$990$		0			0
$991$	19.9596			0.634037			0.317018	−	0.948419i	$-0.397318\pi$
$991$	19.9596			0.634037			0.317018	+	0.948419i	$0.397318\pi$
$992$		0			0
$993$	45.9599			1.45849
$994$		0			0
$995$	0.758555			0.0240478
$996$		0			0
$997$	18.0474	−	18.0474i	0.571566	−	0.571566i	−0.361000	−	0.932566i	$-0.617564\pi$
$997$	18.0474	−	18.0474i	0.571566	−	0.571566i	0.932566	+	0.361000i	$0.117564\pi$
$998$		0			0
$999$	−52.7477			−1.66886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	928.2.k.e.191.2	✓	10
4.3	odd	2		928.2.k.f.191.4	yes	10
29.12	odd	4		928.2.k.f.447.4	yes	10
116.99	even	4	inner	928.2.k.e.447.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
928.2.k.e.191.2	✓	10	1.1	even	1	trivial
928.2.k.e.447.2	yes	10	116.99	even	4	inner
928.2.k.f.191.4	yes	10	4.3	odd	2
928.2.k.f.447.4	yes	10	29.12	odd	4

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:	\( N \)	\(=\)	\( 928 = 2^{5} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	928.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13340 - 1.13340i) q^{3} -1.87777i q^{5} -4.61854i q^{7} -0.430814i q^{9} +O(q^{10})\)	\(q+(-1.13340 - 1.13340i) q^{3} -1.87777i q^{5} -4.61854i q^{7} -0.430814i q^{9} +(-3.65429 - 3.65429i) q^{11} +2.02701i q^{13} +(-2.12826 + 2.12826i) q^{15} +(-0.117094 + 0.117094i) q^{17} +(5.13944 + 5.13944i) q^{19} +(-5.23465 + 5.23465i) q^{21} -6.35174i q^{23} +1.47397 q^{25} +(-3.88848 + 3.88848i) q^{27} +(-5.38389 - 0.117094i) q^{29} +(3.45813 + 3.45813i) q^{31} +8.28354i q^{33} -8.67257 q^{35} +(6.78256 + 6.78256i) q^{37} +(2.29741 - 2.29741i) q^{39} +(3.99487 + 3.99487i) q^{41} +(-6.36805 - 6.36805i) q^{43} -0.808970 q^{45} +(4.12826 - 4.12826i) q^{47} -14.3309 q^{49} +0.265428 q^{51} +4.67647 q^{53} +(-6.86193 + 6.86193i) q^{55} -11.6501i q^{57} -1.40380i q^{59} +(4.85319 - 4.85319i) q^{61} -1.98973 q^{63} +3.80627 q^{65} -14.5233 q^{67} +(-7.19906 + 7.19906i) q^{69} +2.02234 q^{71} +(-10.2101 - 10.2101i) q^{73} +(-1.67060 - 1.67060i) q^{75} +(-16.8775 + 16.8775i) q^{77} +(3.68131 + 3.68131i) q^{79} +7.52196 q^{81} +7.22364i q^{83} +(0.219876 + 0.219876i) q^{85} +(5.96938 + 6.23481i) q^{87} +(-4.43325 + 4.43325i) q^{89} +9.36185 q^{91} -7.83888i q^{93} +(9.65069 - 9.65069i) q^{95} +(-6.88021 - 6.88021i) q^{97} +(-1.57432 + 1.57432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3}+O(q^{10}) \) 10 * q - 2 * q^3	\( 10 q - 2 q^{3} - 14 q^{11} + 14 q^{15} + 6 q^{17} - 12 q^{19} - 28 q^{21} + 2 q^{25} - 2 q^{27} - 28 q^{29} + 14 q^{31} + 4 q^{35} + 10 q^{37} + 6 q^{39} + 14 q^{41} - 30 q^{43} - 36 q^{45} + 6 q^{47} - 42 q^{49} - 56 q^{51} + 4 q^{53} - 42 q^{55} - 26 q^{61} + 32 q^{63} - 36 q^{65} - 56 q^{67} + 16 q^{69} - 36 q^{71} - 22 q^{73} + 8 q^{75} + 28 q^{77} - 6 q^{79} - 54 q^{81} - 16 q^{85} + 58 q^{87} + 58 q^{89} + 20 q^{91} + 52 q^{95} + 26 q^{97} - 68 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 - 14 * q^11 + 14 * q^15 + 6 * q^17 - 12 * q^19 - 28 * q^21 + 2 * q^25 - 2 * q^27 - 28 * q^29 + 14 * q^31 + 4 * q^35 + 10 * q^37 + 6 * q^39 + 14 * q^41 - 30 * q^43 - 36 * q^45 + 6 * q^47 - 42 * q^49 - 56 * q^51 + 4 * q^53 - 42 * q^55 - 26 * q^61 + 32 * q^63 - 36 * q^65 - 56 * q^67 + 16 * q^69 - 36 * q^71 - 22 * q^73 + 8 * q^75 + 28 * q^77 - 6 * q^79 - 54 * q^81 - 16 * q^85 + 58 * q^87 + 58 * q^89 + 20 * q^91 + 52 * q^95 + 26 * q^97 - 68 * q^99

Introduction

L-functions

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Database

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