LMFDB - Embedded newform 1216.2.t.b.353.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(353,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1216.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.t (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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.4
Root			$2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	1216.353
Dual form			1216.2.t.b.1185.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.59808 + 1.50000i) q^{3} +(2.73861 + 1.58114i) q^{5} -3.16228 q^{7} +(3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(2.59808 + 1.50000i) q^{3} +(2.73861 + 1.58114i) q^{5} -3.16228 q^{7} +(3.00000 + 5.19615i) q^{9} +3.00000i q^{11} +(5.47723 - 3.16228i) q^{13} +(4.74342 + 8.21584i) q^{15} +(-2.00000 + 3.46410i) q^{17} +(2.59808 - 3.50000i) q^{19} +(-8.21584 - 4.74342i) q^{21} +(-4.74342 - 8.21584i) q^{23} +(2.50000 + 4.33013i) q^{25} +9.00000i q^{27} +(-2.73861 + 1.58114i) q^{29} -3.16228 q^{31} +(-4.50000 + 7.79423i) q^{33} +(-8.66025 - 5.00000i) q^{35} +3.16228i q^{37} +18.9737 q^{39} +(1.50000 - 2.59808i) q^{41} +(8.66025 + 5.00000i) q^{43} +18.9737i q^{45} +(-1.58114 - 2.73861i) q^{47} +3.00000 q^{49} +(-10.3923 + 6.00000i) q^{51} +(-4.74342 + 8.21584i) q^{55} +(12.0000 - 5.19615i) q^{57} +(-6.06218 - 3.50000i) q^{59} +(-2.73861 + 1.58114i) q^{61} +(-9.48683 - 16.4317i) q^{63} +20.0000 q^{65} +(-4.33013 + 2.50000i) q^{67} -28.4605i q^{69} +(3.50000 - 6.06218i) q^{73} +15.0000i q^{75} -9.48683i q^{77} +(-3.16228 + 5.47723i) q^{79} +(-4.50000 + 7.79423i) q^{81} -7.00000i q^{83} +(-10.9545 + 6.32456i) q^{85} -9.48683 q^{87} +(-4.00000 - 6.92820i) q^{89} +(-17.3205 + 10.0000i) q^{91} +(-8.21584 - 4.74342i) q^{93} +(12.6491 - 5.47723i) q^{95} +(4.50000 - 7.79423i) q^{97} +(-15.5885 + 9.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 24 q^{9}+O(q^{10}) $ 8 * q + 24 * q^9	$ 8 q + 24 q^{9} - 16 q^{17} + 20 q^{25} - 36 q^{33} + 12 q^{41} + 24 q^{49} + 96 q^{57} + 160 q^{65} + 28 q^{73} - 36 q^{81} - 32 q^{89} + 36 q^{97}+O(q^{100}) $ 8 * q + 24 * q^9 - 16 * q^17 + 20 * q^25 - 36 * q^33 + 12 * q^41 + 24 * q^49 + 96 * q^57 + 160 * q^65 + 28 * q^73 - 36 * q^81 - 32 * q^89 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	2.59808	+	1.50000i	1.50000	+	0.866025i	1.00000			$0$
$3$	2.59808	+	1.50000i	1.50000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$4$		0			0
$5$	2.73861	+	1.58114i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$5$	2.73861	+	1.58114i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$6$		0			0
$7$	−3.16228			−1.19523			−0.597614	−	0.801784i	$-0.703885\pi$
$7$	−3.16228			−1.19523			−0.597614	+	0.801784i	$0.703885\pi$
$8$		0			0
$9$	3.00000	+	5.19615i	1.00000	+	1.73205i
$10$		0			0
$11$			3.00000i			0.904534i	0.891883	+	0.452267i	$0.149385\pi$
$11$			3.00000i			0.904534i	−0.891883	+	0.452267i	$0.850615\pi$
$12$		0			0
$13$	5.47723	−	3.16228i	1.51911	−	0.877058i	0.519362	−	0.854554i	$-0.326170\pi$
$13$	5.47723	−	3.16228i	1.51911	−	0.877058i	0.999747	−	0.0225039i	$-0.00716381\pi$
$14$		0			0
$15$	4.74342	+	8.21584i	1.22474	+	2.12132i
$16$		0			0
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	2.59808	−	3.50000i	0.596040	−	0.802955i
$19$	2.59808	−	3.50000i	0.596040	−	0.802955i
$20$		0			0
$21$	−8.21584	−	4.74342i	−1.79284	−	1.03510i
$22$		0			0
$23$	−4.74342	−	8.21584i	−0.989071	−	1.71312i	−0.622224	−	0.782839i	$-0.713771\pi$
$23$	−4.74342	−	8.21584i	−0.989071	−	1.71312i	−0.366847	−	0.930281i	$-0.619563\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$		0			0
$27$			9.00000i			1.73205i
$28$		0			0
$29$	−2.73861	+	1.58114i	−0.508548	+	0.293610i	−0.732236	−	0.681051i	$-0.761523\pi$
$29$	−2.73861	+	1.58114i	−0.508548	+	0.293610i	0.223689	+	0.974661i	$0.428190\pi$
$30$		0			0
$31$	−3.16228			−0.567962			−0.283981	−	0.958830i	$-0.591655\pi$
$31$	−3.16228			−0.567962			−0.283981	+	0.958830i	$0.591655\pi$
$32$		0			0
$33$	−4.50000	+	7.79423i	−0.783349	+	1.35680i
$34$		0			0
$35$	−8.66025	−	5.00000i	−1.46385	−	0.845154i
$36$		0			0
$37$			3.16228i			0.519875i	0.965625	+	0.259938i	$0.0837020\pi$
$37$			3.16228i			0.519875i	−0.965625	+	0.259938i	$0.916298\pi$
$38$		0			0
$39$	18.9737			3.03822
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	8.66025	+	5.00000i	1.32068	+	0.762493i	0.983836	−	0.179069i	$-0.0573086\pi$
$43$	8.66025	+	5.00000i	1.32068	+	0.762493i	0.336840	+	0.941562i	$0.390642\pi$
$44$		0			0
$45$			18.9737i			2.82843i
$46$		0			0
$47$	−1.58114	−	2.73861i	−0.230633	−	0.399468i	0.727362	−	0.686254i	$-0.240746\pi$
$47$	−1.58114	−	2.73861i	−0.230633	−	0.399468i	−0.957995	+	0.286787i	$0.907413\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$	−10.3923	+	6.00000i	−1.45521	+	0.840168i
$52$		0			0
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$	−4.74342	+	8.21584i	−0.639602	+	1.10782i
$56$		0			0
$57$	12.0000	−	5.19615i	1.58944	−	0.688247i
$58$		0			0
$59$	−6.06218	−	3.50000i	−0.789228	−	0.455661i	0.0504625	−	0.998726i	$-0.483930\pi$
$59$	−6.06218	−	3.50000i	−0.789228	−	0.455661i	−0.839691	+	0.543065i	$0.817264\pi$
$60$		0			0
$61$	−2.73861	+	1.58114i	−0.350643	+	0.202444i	−0.664969	−	0.746871i	$-0.731555\pi$
$61$	−2.73861	+	1.58114i	−0.350643	+	0.202444i	0.314325	+	0.949315i	$0.398222\pi$
$62$		0			0
$63$	−9.48683	−	16.4317i	−1.19523	−	2.07020i
$64$		0			0
$65$	20.0000			2.48069
$66$		0			0
$67$	−4.33013	+	2.50000i	−0.529009	+	0.305424i	−0.740613	−	0.671932i	$-0.765465\pi$
$67$	−4.33013	+	2.50000i	−0.529009	+	0.305424i	0.211604	+	0.977356i	$0.432131\pi$
$68$		0			0
$69$		−	28.4605i		−	3.42624i
$70$		0			0
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$		0			0
$75$			15.0000i			1.73205i
$76$		0			0
$77$		−	9.48683i		−	1.08112i
$78$		0			0
$79$	−3.16228	+	5.47723i	−0.355784	+	0.616236i	−0.987252	−	0.159166i	$-0.949119\pi$
$79$	−3.16228	+	5.47723i	−0.355784	+	0.616236i	0.631468	+	0.775402i	$0.282453\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$		−	7.00000i		−	0.768350i	−0.923260	−	0.384175i	$-0.874486\pi$
$83$		−	7.00000i		−	0.768350i	0.923260	−	0.384175i	$-0.125514\pi$
$84$		0			0
$85$	−10.9545	+	6.32456i	−1.18818	+	0.685994i
$86$		0			0
$87$	−9.48683			−1.01710
$88$		0			0
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	0.572327	−	0.820025i	$-0.306041\pi$
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	−0.996326	+	0.0856373i	$0.972707\pi$
$90$		0			0
$91$	−17.3205	+	10.0000i	−1.81568	+	1.04828i
$92$		0			0
$93$	−8.21584	−	4.74342i	−0.851943	−	0.491869i
$94$		0			0
$95$	12.6491	−	5.47723i	1.29777	−	0.561951i
$96$		0			0
$97$	4.50000	−	7.79423i	0.456906	−	0.791384i	−0.541890	−	0.840450i	$-0.682291\pi$
$97$	4.50000	−	7.79423i	0.456906	−	0.791384i	0.998796	+	0.0490655i	$0.0156243\pi$
$98$		0			0
$99$	−15.5885	+	9.00000i	−1.56670	+	0.904534i
$100$		0			0
$101$	8.21584	−	4.74342i	0.817506	−	0.471988i	−0.0320494	−	0.999486i	$-0.510203\pi$
$101$	8.21584	−	4.74342i	0.817506	−	0.471988i	0.849556	+	0.527499i	$0.176870\pi$
$102$		0			0
$103$	6.32456			0.623177			0.311588	−	0.950217i	$-0.399139\pi$
$103$	6.32456			0.623177			0.311588	+	0.950217i	$0.399139\pi$
$104$		0			0
$105$	−15.0000	−	25.9808i	−1.46385	−	2.53546i
$106$		0			0
$107$			6.00000i			0.580042i	0.957020	+	0.290021i	$0.0936623\pi$
$107$			6.00000i			0.580042i	−0.957020	+	0.290021i	$0.906338\pi$
$108$		0			0
$109$	16.4317	+	9.48683i	1.57387	+	0.908674i	0.995688	+	0.0927654i	$0.0295707\pi$
$109$	16.4317	+	9.48683i	1.57387	+	0.908674i	0.578181	+	0.815908i	$0.303763\pi$
$110$		0			0
$111$	−4.74342	+	8.21584i	−0.450225	+	0.779813i
$112$		0			0
$113$	−13.0000			−1.22294			−0.611469	−	0.791269i	$-0.709421\pi$
$113$	−13.0000			−1.22294			−0.611469	+	0.791269i	$0.709421\pi$
$114$		0			0
$115$		−	30.0000i		−	2.79751i
$116$		0			0
$117$	32.8634	+	18.9737i	3.03822	+	1.75412i
$118$		0			0
$119$	6.32456	−	10.9545i	0.579771	−	1.00419i
$120$		0			0
$121$	2.00000			0.181818
$122$		0			0
$123$	7.79423	−	4.50000i	0.702782	−	0.405751i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	3.16228	+	5.47723i	0.280607	+	0.486025i	0.971534	−	0.236899i	$-0.0761310\pi$
$127$	3.16228	+	5.47723i	0.280607	+	0.486025i	−0.690928	+	0.722924i	$0.742798\pi$
$128$		0			0
$129$	15.0000	+	25.9808i	1.32068	+	2.28748i
$130$		0			0
$131$	−7.79423	−	4.50000i	−0.680985	−	0.393167i	0.119241	−	0.992865i	$-0.461954\pi$
$131$	−7.79423	−	4.50000i	−0.680985	−	0.393167i	−0.800226	+	0.599699i	$0.795287\pi$
$132$		0			0
$133$	−8.21584	+	11.0680i	−0.712404	+	0.959715i
$134$		0			0
$135$	−14.2302	+	24.6475i	−1.22474	+	2.12132i
$136$		0			0
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$		0			0
$139$	9.52628	−	5.50000i	0.808008	−	0.466504i	−0.0382553	−	0.999268i	$-0.512180\pi$
$139$	9.52628	−	5.50000i	0.808008	−	0.466504i	0.846264	+	0.532764i	$0.178847\pi$
$140$		0			0
$141$		−	9.48683i		−	0.798935i
$142$		0			0
$143$	9.48683	+	16.4317i	0.793329	+	1.37409i
$144$		0			0
$145$	−10.0000			−0.830455
$146$		0			0
$147$	7.79423	+	4.50000i	0.642857	+	0.371154i
$148$		0			0
$149$	8.21584	+	4.74342i	0.673068	+	0.388596i	0.797238	−	0.603665i	$-0.206294\pi$
$149$	8.21584	+	4.74342i	0.673068	+	0.388596i	−0.124170	+	0.992261i	$0.539627\pi$
$150$		0			0
$151$	−3.16228			−0.257343			−0.128671	−	0.991687i	$-0.541071\pi$
$151$	−3.16228			−0.257343			−0.128671	+	0.991687i	$0.541071\pi$
$152$		0			0
$153$	−24.0000			−1.94029
$154$		0			0
$155$	−8.66025	−	5.00000i	−0.695608	−	0.401610i
$156$		0			0
$157$	−5.47723	−	3.16228i	−0.437130	−	0.252377i	0.265249	−	0.964180i	$-0.414546\pi$
$157$	−5.47723	−	3.16228i	−0.437130	−	0.252377i	−0.702380	+	0.711803i	$0.747879\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	15.0000	+	25.9808i	1.18217	+	2.04757i
$162$		0			0
$163$		−	5.00000i		−	0.391630i	−0.980641	−	0.195815i	$-0.937265\pi$
$163$		−	5.00000i		−	0.391630i	0.980641	−	0.195815i	$-0.0627352\pi$
$164$		0			0
$165$	−24.6475	+	14.2302i	−1.91881	+	1.10782i
$166$		0			0
$167$	−3.16228	−	5.47723i	−0.244704	−	0.423840i	0.717344	−	0.696719i	$-0.245358\pi$
$167$	−3.16228	−	5.47723i	−0.244704	−	0.423840i	−0.962048	+	0.272879i	$0.912024\pi$
$168$		0			0
$169$	13.5000	−	23.3827i	1.03846	−	1.79867i
$170$		0			0
$171$	25.9808	+	3.00000i	1.98680	+	0.229416i
$172$		0			0
$173$	−10.9545	−	6.32456i	−0.832851	−	0.480847i	0.0219765	−	0.999758i	$-0.493004\pi$
$173$	−10.9545	−	6.32456i	−0.832851	−	0.480847i	−0.854828	+	0.518911i	$0.826337\pi$
$174$		0			0
$175$	−7.90569	−	13.6931i	−0.597614	−	1.03510i
$176$		0			0
$177$	−10.5000	−	18.1865i	−0.789228	−	1.36698i
$178$		0			0
$179$		−	3.00000i		−	0.224231i	−0.993695	−	0.112115i	$-0.964237\pi$
$179$		−	3.00000i		−	0.224231i	0.993695	−	0.112115i	$-0.0357626\pi$
$180$		0			0
$181$	−8.21584	+	4.74342i	−0.610678	+	0.352575i	−0.773231	−	0.634125i	$-0.781361\pi$
$181$	−8.21584	+	4.74342i	−0.610678	+	0.352575i	0.162552	+	0.986700i	$0.448027\pi$
$182$		0			0
$183$	−9.48683			−0.701287
$184$		0			0
$185$	−5.00000	+	8.66025i	−0.367607	+	0.636715i
$186$		0			0
$187$	−10.3923	−	6.00000i	−0.759961	−	0.438763i
$188$		0			0
$189$		−	28.4605i		−	2.07020i
$190$		0			0
$191$	6.32456			0.457629			0.228814	−	0.973470i	$-0.426515\pi$
$191$	6.32456			0.457629			0.228814	+	0.973470i	$0.426515\pi$
$192$		0			0
$193$	−4.00000	+	6.92820i	−0.287926	+	0.498703i	−0.973315	−	0.229475i	$-0.926299\pi$
$193$	−4.00000	+	6.92820i	−0.287926	+	0.498703i	0.685388	+	0.728178i	$0.259632\pi$
$194$		0			0
$195$	51.9615	+	30.0000i	3.72104	+	2.14834i
$196$		0			0
$197$		−	22.1359i		−	1.57712i	−0.614957	−	0.788560i	$-0.710827\pi$
$197$		−	22.1359i		−	1.57712i	0.614957	−	0.788560i	$-0.289173\pi$
$198$		0			0
$199$	3.16228	+	5.47723i	0.224168	+	0.388270i	0.956069	−	0.293140i	$-0.0947003\pi$
$199$	3.16228	+	5.47723i	0.224168	+	0.388270i	−0.731902	+	0.681410i	$0.761367\pi$
$200$		0			0
$201$	−15.0000			−1.05802
$202$		0			0
$203$	8.66025	−	5.00000i	0.607831	−	0.350931i
$204$		0			0
$205$	8.21584	−	4.74342i	0.573819	−	0.331295i
$206$		0			0
$207$	28.4605	−	49.2950i	1.97814	−	3.42624i
$208$		0			0
$209$	10.5000	+	7.79423i	0.726300	+	0.539138i
$210$		0			0
$211$	13.8564	+	8.00000i	0.953914	+	0.550743i	0.894295	−	0.447478i	$-0.147678\pi$
$211$	13.8564	+	8.00000i	0.953914	+	0.550743i	0.0596196	+	0.998221i	$0.481011\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	15.8114	+	27.3861i	1.07833	+	1.86772i
$216$		0			0
$217$	10.0000			0.678844
$218$		0			0
$219$	18.1865	−	10.5000i	1.22893	−	0.709524i
$220$		0			0
$221$			25.2982i			1.70174i
$222$		0			0
$223$	−7.90569	+	13.6931i	−0.529404	+	0.916955i	0.470007	+	0.882662i	$0.344251\pi$
$223$	−7.90569	+	13.6931i	−0.529404	+	0.916955i	−0.999412	+	0.0342929i	$0.989082\pi$
$224$		0			0
$225$	−15.0000	+	25.9808i	−1.00000	+	1.73205i
$226$		0			0
$227$		−	11.0000i		−	0.730096i	−0.930989	−	0.365048i	$-0.881053\pi$
$227$		−	11.0000i		−	0.730096i	0.930989	−	0.365048i	$-0.118947\pi$
$228$		0			0
$229$			25.2982i			1.67175i	0.548917	+	0.835877i	$0.315040\pi$
$229$			25.2982i			1.67175i	−0.548917	+	0.835877i	$0.684960\pi$
$230$		0			0
$231$	14.2302	−	24.6475i	0.936282	−	1.62169i
$232$		0			0
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	−0.812700	−	0.582683i	$-0.802003\pi$
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	0.910968	+	0.412477i	$0.135336\pi$
$234$		0			0
$235$		−	10.0000i		−	0.652328i
$236$		0			0
$237$	−16.4317	+	9.48683i	−1.06735	+	0.616236i
$238$		0			0
$239$	−6.32456			−0.409101			−0.204551	−	0.978856i	$-0.565573\pi$
$239$	−6.32456			−0.409101			−0.204551	+	0.978856i	$0.565573\pi$
$240$		0			0
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.21584	+	4.74342i	0.524891	+	0.303046i
$246$		0			0
$247$	3.16228	−	27.3861i	0.201211	−	1.74254i
$248$		0			0
$249$	10.5000	−	18.1865i	0.665410	−	1.15252i
$250$		0			0
$251$	−6.06218	+	3.50000i	−0.382641	+	0.220918i	−0.678967	−	0.734169i	$-0.737572\pi$
$251$	−6.06218	+	3.50000i	−0.382641	+	0.220918i	0.296326	+	0.955087i	$0.404239\pi$
$252$		0			0
$253$	24.6475	−	14.2302i	1.54958	−	0.894648i
$254$		0			0
$255$	−37.9473			−2.37635
$256$		0			0
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	−0.981901	−	0.189396i	$-0.939347\pi$
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	0.326929	−	0.945049i	$-0.393986\pi$
$258$		0			0
$259$		−	10.0000i		−	0.621370i
$260$		0			0
$261$	−16.4317	−	9.48683i	−1.01710	−	0.587220i
$262$		0			0
$263$	−4.74342	+	8.21584i	−0.292492	+	0.506610i	−0.974398	−	0.224829i	$-0.927818\pi$
$263$	−4.74342	+	8.21584i	−0.292492	+	0.506610i	0.681907	+	0.731439i	$0.261151\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	24.0000i		−	1.46878i
$268$		0			0
$269$	−21.9089	−	12.6491i	−1.33581	−	0.771230i	−0.349626	−	0.936889i	$-0.613691\pi$
$269$	−21.9089	−	12.6491i	−1.33581	−	0.771230i	−0.986183	+	0.165659i	$0.947025\pi$
$270$		0			0
$271$	−11.0680	+	19.1703i	−0.672331	+	1.16451i	0.304910	+	0.952381i	$0.401374\pi$
$271$	−11.0680	+	19.1703i	−0.672331	+	1.16451i	−0.977241	+	0.212131i	$0.931960\pi$
$272$		0			0
$273$	−60.0000			−3.63137
$274$		0			0
$275$	−12.9904	+	7.50000i	−0.783349	+	0.452267i
$276$		0			0
$277$		−	28.4605i		−	1.71003i	−0.518607	−	0.855013i	$-0.673549\pi$
$277$		−	28.4605i		−	1.71003i	0.518607	−	0.855013i	$-0.326451\pi$
$278$		0			0
$279$	−9.48683	−	16.4317i	−0.567962	−	0.983739i
$280$		0			0
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	0.996887	+	0.0788417i	$0.0251222\pi$
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	−0.430165	+	0.902750i	$0.641545\pi$
$282$		0			0
$283$	12.9904	+	7.50000i	0.772198	+	0.445829i	0.833658	−	0.552281i	$-0.186242\pi$
$283$	12.9904	+	7.50000i	0.772198	+	0.445829i	−0.0614601	+	0.998110i	$0.519576\pi$
$284$		0			0
$285$	41.0792	+	4.74342i	2.43332	+	0.280976i
$286$		0			0
$287$	−4.74342	+	8.21584i	−0.279995	+	0.484966i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	23.3827	−	13.5000i	1.37072	−	0.791384i
$292$		0			0
$293$			15.8114i			0.923711i	0.886955	+	0.461856i	$0.152816\pi$
$293$			15.8114i			0.923711i	−0.886955	+	0.461856i	$0.847184\pi$
$294$		0			0
$295$	−11.0680	−	19.1703i	−0.644402	−	1.11614i
$296$		0			0
$297$	−27.0000			−1.56670
$298$		0			0
$299$	−51.9615	−	30.0000i	−3.00501	−	1.73494i
$300$		0			0
$301$	−27.3861	−	15.8114i	−1.57851	−	0.911353i
$302$		0			0
$303$	28.4605			1.63501
$304$		0			0
$305$	−10.0000			−0.572598
$306$		0			0
$307$	18.1865	+	10.5000i	1.03796	+	0.599267i	0.919255	−	0.393663i	$-0.128792\pi$
$307$	18.1865	+	10.5000i	1.03796	+	0.599267i	0.118705	+	0.992930i	$0.462126\pi$
$308$		0			0
$309$	16.4317	+	9.48683i	0.934765	+	0.539687i
$310$		0			0
$311$	−22.1359			−1.25521			−0.627607	−	0.778530i	$-0.715966\pi$
$311$	−22.1359			−1.25521			−0.627607	+	0.778530i	$0.715966\pi$
$312$		0			0
$313$	1.50000	+	2.59808i	0.0847850	+	0.146852i	0.905300	−	0.424774i	$-0.139646\pi$
$313$	1.50000	+	2.59808i	0.0847850	+	0.146852i	−0.820515	+	0.571626i	$0.806313\pi$
$314$		0			0
$315$		−	60.0000i		−	3.38062i
$316$		0			0
$317$	−27.3861	+	15.8114i	−1.53816	+	0.888056i	−0.539211	+	0.842170i	$0.681278\pi$
$317$	−27.3861	+	15.8114i	−1.53816	+	0.888056i	−0.998947	+	0.0458856i	$0.985389\pi$
$318$		0			0
$319$	−4.74342	−	8.21584i	−0.265580	−	0.459999i
$320$		0			0
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$		0			0
$323$	6.92820	+	16.0000i	0.385496	+	0.890264i
$324$		0			0
$325$	27.3861	+	15.8114i	1.51911	+	0.877058i
$326$		0			0
$327$	28.4605	+	49.2950i	1.57387	+	2.72602i
$328$		0			0
$329$	5.00000	+	8.66025i	0.275659	+	0.477455i
$330$		0			0
$331$			29.0000i			1.59398i	0.603990	+	0.796992i	$0.293577\pi$
$331$			29.0000i			1.59398i	−0.603990	+	0.796992i	$0.706423\pi$
$332$		0			0
$333$	−16.4317	+	9.48683i	−0.900450	+	0.519875i
$334$		0			0
$335$	−15.8114			−0.863868
$336$		0			0
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	−0.293783	−	0.955872i	$-0.594914\pi$
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	0.974701	−	0.223513i	$-0.0717525\pi$
$338$		0			0
$339$	−33.7750	−	19.5000i	−1.83441	−	1.05909i
$340$		0			0
$341$		−	9.48683i		−	0.513741i
$342$		0			0
$343$	12.6491			0.682988
$344$		0			0
$345$	45.0000	−	77.9423i	2.42272	−	4.19627i
$346$		0			0
$347$	4.33013	+	2.50000i	0.232453	+	0.134207i	0.611703	−	0.791087i	$-0.290485\pi$
$347$	4.33013	+	2.50000i	0.232453	+	0.134207i	−0.379250	+	0.925294i	$0.623818\pi$
$348$		0			0
$349$		−	12.6491i		−	0.677091i	−0.940950	−	0.338546i	$-0.890065\pi$
$349$		−	12.6491i		−	0.677091i	0.940950	−	0.338546i	$-0.109935\pi$
$350$		0			0
$351$	28.4605	+	49.2950i	1.51911	+	2.63117i
$352$		0			0
$353$	−13.0000			−0.691920			−0.345960	−	0.938249i	$-0.612447\pi$
$353$	−13.0000			−0.691920			−0.345960	+	0.938249i	$0.612447\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	32.8634	−	18.9737i	1.73931	−	1.00419i
$358$		0			0
$359$	−4.74342	+	8.21584i	−0.250348	+	0.433615i	−0.963622	−	0.267270i	$-0.913878\pi$
$359$	−4.74342	+	8.21584i	−0.250348	+	0.433615i	0.713274	+	0.700886i	$0.247212\pi$
$360$		0			0
$361$	−5.50000	−	18.1865i	−0.289474	−	0.957186i
$362$		0			0
$363$	5.19615	+	3.00000i	0.272727	+	0.157459i
$364$		0			0
$365$	19.1703	−	11.0680i	1.00342	−	0.579324i
$366$		0			0
$367$	−1.58114	−	2.73861i	−0.0825348	−	0.142954i	0.821803	−	0.569771i	$-0.192968\pi$
$367$	−1.58114	−	2.73861i	−0.0825348	−	0.142954i	−0.904338	+	0.426817i	$0.859635\pi$
$368$		0			0
$369$	18.0000			0.937043
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.0000	+	17.3205i	−0.515026	+	0.892052i
$378$		0			0
$379$		−	32.0000i		−	1.64373i	−0.569683	−	0.821865i	$-0.692934\pi$
$379$		−	32.0000i		−	1.64373i	0.569683	−	0.821865i	$-0.307066\pi$
$380$		0			0
$381$			18.9737i			0.972050i
$382$		0			0
$383$	14.2302	−	24.6475i	0.727132	−	1.25943i	−0.230959	−	0.972964i	$-0.574186\pi$
$383$	14.2302	−	24.6475i	0.727132	−	1.25943i	0.958091	−	0.286466i	$-0.0924804\pi$
$384$		0			0
$385$	15.0000	−	25.9808i	0.764471	−	1.32410i
$386$		0			0
$387$			60.0000i			3.04997i
$388$		0			0
$389$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$389$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$390$		0			0
$391$	37.9473			1.91908
$392$		0			0
$393$	−13.5000	−	23.3827i	−0.680985	−	1.17950i
$394$		0			0
$395$	−17.3205	+	10.0000i	−0.871489	+	0.503155i
$396$		0			0
$397$	13.6931	+	7.90569i	0.687235	+	0.396775i	0.802575	−	0.596551i	$-0.203463\pi$
$397$	13.6931	+	7.90569i	0.687235	+	0.396775i	−0.115340	+	0.993326i	$0.536796\pi$
$398$		0			0
$399$	−37.9473	+	16.4317i	−1.89974	+	0.822613i
$400$		0			0
$401$	6.50000	−	11.2583i	0.324595	−	0.562214i	−0.656836	−	0.754034i	$-0.728105\pi$
$401$	6.50000	−	11.2583i	0.324595	−	0.562214i	0.981430	+	0.191820i	$0.0614388\pi$
$402$		0			0
$403$	−17.3205	+	10.0000i	−0.862796	+	0.498135i
$404$		0			0
$405$	−24.6475	+	14.2302i	−1.22474	+	0.707107i
$406$		0			0
$407$	−9.48683			−0.470245
$408$		0			0
$409$	−4.50000	−	7.79423i	−0.222511	−	0.385400i	0.733059	−	0.680165i	$-0.238092\pi$
$409$	−4.50000	−	7.79423i	−0.222511	−	0.385400i	−0.955570	+	0.294765i	$0.904759\pi$
$410$		0			0
$411$			27.0000i			1.33181i
$412$		0			0
$413$	19.1703	+	11.0680i	0.943308	+	0.544619i
$414$		0			0
$415$	11.0680	−	19.1703i	0.543305	−	0.941033i
$416$		0			0
$417$	33.0000			1.61602
$418$		0			0
$419$		−	18.0000i		−	0.879358i	−0.898155	−	0.439679i	$-0.855092\pi$
$419$		−	18.0000i		−	0.879358i	0.898155	−	0.439679i	$-0.144908\pi$
$420$		0			0
$421$	−24.6475	−	14.2302i	−1.20125	−	0.693540i	−0.240414	−	0.970670i	$-0.577283\pi$
$421$	−24.6475	−	14.2302i	−1.20125	−	0.693540i	−0.960832	+	0.277130i	$0.910617\pi$
$422$		0			0
$423$	9.48683	−	16.4317i	0.461266	−	0.798935i
$424$		0			0
$425$	−20.0000			−0.970143
$426$		0			0
$427$	8.66025	−	5.00000i	0.419099	−	0.241967i
$428$		0			0
$429$			56.9210i			2.74817i
$430$		0			0
$431$	6.32456	+	10.9545i	0.304643	+	0.527657i	0.977182	−	0.212405i	$-0.0681295\pi$
$431$	6.32456	+	10.9545i	0.304643	+	0.527657i	−0.672539	+	0.740062i	$0.734796\pi$
$432$		0			0
$433$	14.0000	+	24.2487i	0.672797	+	1.16532i	0.977108	+	0.212746i	$0.0682406\pi$
$433$	14.0000	+	24.2487i	0.672797	+	1.16532i	−0.304311	+	0.952573i	$0.598426\pi$
$434$		0			0
$435$	−25.9808	−	15.0000i	−1.24568	−	0.719195i
$436$		0			0
$437$	−41.0792	−	4.74342i	−1.96508	−	0.226908i
$438$		0			0
$439$	7.90569	−	13.6931i	0.377318	−	0.653534i	−0.613353	−	0.789809i	$-0.710180\pi$
$439$	7.90569	−	13.6931i	0.377318	−	0.653534i	0.990671	+	0.136275i	$0.0435130\pi$
$440$		0			0
$441$	9.00000	+	15.5885i	0.428571	+	0.742307i
$442$		0			0
$443$	−30.3109	+	17.5000i	−1.44011	+	0.831450i	−0.997857	−	0.0654382i	$-0.979155\pi$
$443$	−30.3109	+	17.5000i	−1.44011	+	0.831450i	−0.442257	+	0.896888i	$0.645822\pi$
$444$		0			0
$445$		−	25.2982i		−	1.19925i
$446$		0			0
$447$	14.2302	+	24.6475i	0.673068	+	1.16579i
$448$		0			0
$449$	17.0000			0.802280			0.401140	−	0.916017i	$-0.368614\pi$
$449$	17.0000			0.802280			0.401140	+	0.916017i	$0.368614\pi$
$450$		0			0
$451$	7.79423	+	4.50000i	0.367016	+	0.211897i
$452$		0			0
$453$	−8.21584	−	4.74342i	−0.386014	−	0.222865i
$454$		0			0
$455$	−63.2456			−2.96500
$456$		0			0
$457$	−31.0000			−1.45012			−0.725059	−	0.688686i	$-0.758188\pi$
$457$	−31.0000			−1.45012			−0.725059	+	0.688686i	$0.758188\pi$
$458$		0			0
$459$	−31.1769	−	18.0000i	−1.45521	−	0.840168i
$460$		0			0
$461$	27.3861	+	15.8114i	1.27550	+	0.736410i	0.976017	−	0.217692i	$-0.0698529\pi$
$461$	27.3861	+	15.8114i	1.27550	+	0.736410i	0.299482	+	0.954102i	$0.403186\pi$
$462$		0			0
$463$	31.6228			1.46964			0.734818	−	0.678265i	$-0.237268\pi$
$463$	31.6228			1.46964			0.734818	+	0.678265i	$0.237268\pi$
$464$		0			0
$465$	−15.0000	−	25.9808i	−0.695608	−	1.20483i
$466$		0			0
$467$		−	21.0000i		−	0.971764i	−0.874024	−	0.485882i	$-0.838498\pi$
$467$		−	21.0000i		−	0.971764i	0.874024	−	0.485882i	$-0.161502\pi$
$468$		0			0
$469$	13.6931	−	7.90569i	0.632287	−	0.365051i
$470$		0			0
$471$	−9.48683	−	16.4317i	−0.437130	−	0.757132i
$472$		0			0
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$		0			0
$475$	21.6506	+	2.50000i	0.993399	+	0.114708i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.48683	−	16.4317i	−0.433464	−	0.750782i	0.563704	−	0.825977i	$-0.309376\pi$
$479$	−9.48683	−	16.4317i	−0.433464	−	0.750782i	−0.997169	+	0.0751941i	$0.976042\pi$
$480$		0			0
$481$	10.0000	+	17.3205i	0.455961	+	0.789747i
$482$		0			0
$483$			90.0000i			4.09514i
$484$		0			0
$485$	24.6475	−	14.2302i	1.11919	−	0.646162i
$486$		0			0
$487$	9.48683			0.429889			0.214945	−	0.976626i	$-0.431043\pi$
$487$	9.48683			0.429889			0.214945	+	0.976626i	$0.431043\pi$
$488$		0			0
$489$	7.50000	−	12.9904i	0.339162	−	0.587445i
$490$		0			0
$491$	−15.5885	−	9.00000i	−0.703497	−	0.406164i	0.105151	−	0.994456i	$-0.466467\pi$
$491$	−15.5885	−	9.00000i	−0.703497	−	0.406164i	−0.808649	+	0.588292i	$0.799801\pi$
$492$		0			0
$493$		−	12.6491i		−	0.569687i
$494$		0			0
$495$	−56.9210			−2.55841
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−11.2583	−	6.50000i	−0.503992	−	0.290980i	0.226369	−	0.974042i	$-0.427315\pi$
$499$	−11.2583	−	6.50000i	−0.503992	−	0.290980i	−0.730361	+	0.683062i	$0.760648\pi$
$500$		0			0
$501$		−	18.9737i		−	0.847681i
$502$		0			0
$503$	−1.58114	−	2.73861i	−0.0704995	−	0.122109i	0.828621	−	0.559810i	$-0.189126\pi$
$503$	−1.58114	−	2.73861i	−0.0704995	−	0.122109i	−0.899120	+	0.437702i	$0.855793\pi$
$504$		0			0
$505$	30.0000			1.33498
$506$		0			0
$507$	70.1481	−	40.5000i	3.11538	−	1.79867i
$508$		0			0
$509$	−27.3861	+	15.8114i	−1.21387	+	0.700827i	−0.963600	−	0.267349i	$-0.913852\pi$
$509$	−27.3861	+	15.8114i	−1.21387	+	0.700827i	−0.250269	+	0.968176i	$0.580519\pi$
$510$		0			0
$511$	−11.0680	+	19.1703i	−0.489618	+	0.848044i
$512$		0			0
$513$	31.5000	+	23.3827i	1.39076	+	1.03237i
$514$		0			0
$515$	17.3205	+	10.0000i	0.763233	+	0.440653i
$516$		0			0
$517$	8.21584	−	4.74342i	0.361332	−	0.208615i
$518$		0			0
$519$	−18.9737	−	32.8634i	−0.832851	−	1.44254i
$520$		0			0
$521$	−33.0000			−1.44576			−0.722878	−	0.690976i	$-0.757181\pi$
$521$	−33.0000			−1.44576			−0.722878	+	0.690976i	$0.757181\pi$
$522$		0			0
$523$	−19.0526	+	11.0000i	−0.833110	+	0.480996i	−0.854916	−	0.518766i	$-0.826392\pi$
$523$	−19.0526	+	11.0000i	−0.833110	+	0.480996i	0.0218062	+	0.999762i	$0.493058\pi$
$524$		0			0
$525$		−	47.4342i		−	2.07020i
$526$		0			0
$527$	6.32456	−	10.9545i	0.275502	−	0.477183i
$528$		0			0
$529$	−33.5000	+	58.0237i	−1.45652	+	2.52277i
$530$		0			0
$531$		−	42.0000i		−	1.82264i
$532$		0			0
$533$		−	18.9737i		−	0.821841i
$534$		0			0
$535$	−9.48683	+	16.4317i	−0.410152	+	0.710403i
$536$		0			0
$537$	4.50000	−	7.79423i	0.194189	−	0.336346i
$538$		0			0
$539$			9.00000i			0.387657i
$540$		0			0
$541$	−21.9089	+	12.6491i	−0.941937	+	0.543828i	−0.890567	−	0.454852i	$-0.849692\pi$
$541$	−21.9089	+	12.6491i	−0.941937	+	0.543828i	−0.0513702	+	0.998680i	$0.516359\pi$
$542$		0			0
$543$	−28.4605			−1.22136
$544$		0			0
$545$	30.0000	+	51.9615i	1.28506	+	2.22579i
$546$		0			0
$547$	22.5167	−	13.0000i	0.962743	−	0.555840i	0.0657267	−	0.997838i	$-0.479063\pi$
$547$	22.5167	−	13.0000i	0.962743	−	0.555840i	0.897016	+	0.441998i	$0.145730\pi$
$548$		0			0
$549$	−16.4317	−	9.48683i	−0.701287	−	0.404888i
$550$		0			0
$551$	−1.58114	+	13.6931i	−0.0673588	+	0.583344i
$552$		0			0
$553$	10.0000	−	17.3205i	0.425243	−	0.736543i
$554$		0			0
$555$	−25.9808	+	15.0000i	−1.10282	+	0.636715i
$556$		0			0
$557$	−16.4317	+	9.48683i	−0.696232	+	0.401970i	−0.805943	−	0.591994i	$-0.798341\pi$
$557$	−16.4317	+	9.48683i	−0.696232	+	0.401970i	0.109710	+	0.993964i	$0.465008\pi$
$558$		0			0
$559$	63.2456			2.67500
$560$		0			0
$561$	−18.0000	−	31.1769i	−0.759961	−	1.31629i
$562$		0			0
$563$		−	3.00000i		−	0.126435i	−0.998000	−	0.0632175i	$-0.979864\pi$
$563$		−	3.00000i		−	0.126435i	0.998000	−	0.0632175i	$-0.0201362\pi$
$564$		0			0
$565$	−35.6020	−	20.5548i	−1.49779	−	0.864747i
$566$		0			0
$567$	14.2302	−	24.6475i	0.597614	−	1.03510i
$568$		0			0
$569$	12.0000			0.503066			0.251533	−	0.967849i	$-0.419065\pi$
$569$	12.0000			0.503066			0.251533	+	0.967849i	$0.419065\pi$
$570$		0			0
$571$			29.0000i			1.21361i	0.794850	+	0.606806i	$0.207550\pi$
$571$			29.0000i			1.21361i	−0.794850	+	0.606806i	$0.792450\pi$
$572$		0			0
$573$	16.4317	+	9.48683i	0.686443	+	0.396318i
$574$		0			0
$575$	23.7171	−	41.0792i	0.989071	−	1.71312i
$576$		0			0
$577$	−45.0000			−1.87337			−0.936687	−	0.350167i	$-0.886125\pi$
$577$	−45.0000			−1.87337			−0.936687	+	0.350167i	$0.886125\pi$
$578$		0			0
$579$	−20.7846	+	12.0000i	−0.863779	+	0.498703i
$580$		0			0
$581$			22.1359i			0.918354i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	60.0000	+	103.923i	2.48069	+	4.29669i
$586$		0			0
$587$	29.4449	+	17.0000i	1.21532	+	0.701665i	0.963913	−	0.266217i	$-0.0857736\pi$
$587$	29.4449	+	17.0000i	1.21532	+	0.701665i	0.251406	+	0.967882i	$0.419107\pi$
$588$		0			0
$589$	−8.21584	+	11.0680i	−0.338528	+	0.456048i
$590$		0			0
$591$	33.2039	−	57.5109i	1.36583	−	2.36568i
$592$		0			0
$593$	17.5000	+	30.3109i	0.718639	+	1.24472i	0.961539	+	0.274668i	$0.0885679\pi$
$593$	17.5000	+	30.3109i	0.718639	+	1.24472i	−0.242900	+	0.970051i	$0.578099\pi$
$594$		0			0
$595$	34.6410	−	20.0000i	1.42014	−	0.819920i
$596$		0			0
$597$			18.9737i			0.776540i
$598$		0			0
$599$	14.2302	+	24.6475i	0.581432	+	1.00707i	0.995310	+	0.0967377i	$0.0308408\pi$
$599$	14.2302	+	24.6475i	0.581432	+	1.00707i	−0.413878	+	0.910333i	$0.635826\pi$
$600$		0			0
$601$	−31.0000			−1.26452			−0.632258	−	0.774758i	$-0.717872\pi$
$601$	−31.0000			−1.26452			−0.632258	+	0.774758i	$0.717872\pi$
$602$		0			0
$603$	−25.9808	−	15.0000i	−1.05802	−	0.610847i
$604$		0			0
$605$	5.47723	+	3.16228i	0.222681	+	0.128565i
$606$		0			0
$607$	−22.1359			−0.898470			−0.449235	−	0.893414i	$-0.648303\pi$
$607$	−22.1359			−0.898470			−0.449235	+	0.893414i	$0.648303\pi$
$608$		0			0
$609$	30.0000			1.21566
$610$		0			0
$611$	−17.3205	−	10.0000i	−0.700713	−	0.404557i
$612$		0			0
$613$	−16.4317	−	9.48683i	−0.663669	−	0.383170i	0.130004	−	0.991513i	$-0.458501\pi$
$613$	−16.4317	−	9.48683i	−0.663669	−	0.383170i	−0.793674	+	0.608344i	$0.791834\pi$
$614$		0			0
$615$	28.4605			1.14764
$616$		0			0
$617$	10.5000	+	18.1865i	0.422714	+	0.732162i	0.996204	−	0.0870504i	$-0.0277441\pi$
$617$	10.5000	+	18.1865i	0.422714	+	0.732162i	−0.573490	+	0.819213i	$0.694411\pi$
$618$		0			0
$619$			14.0000i			0.562708i	0.959604	+	0.281354i	$0.0907834\pi$
$619$			14.0000i			0.562708i	−0.959604	+	0.281354i	$0.909217\pi$
$620$		0			0
$621$	73.9425	−	42.6907i	2.96721	−	1.71312i
$622$		0			0
$623$	12.6491	+	21.9089i	0.506776	+	0.877762i
$624$		0			0
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$		0			0
$627$	15.5885	+	36.0000i	0.622543	+	1.43770i
$628$		0			0
$629$	−10.9545	−	6.32456i	−0.436783	−	0.252177i
$630$		0			0
$631$	−1.58114	−	2.73861i	−0.0629441	−	0.109022i	0.832836	−	0.553520i	$-0.186716\pi$
$631$	−1.58114	−	2.73861i	−0.0629441	−	0.109022i	−0.895780	+	0.444497i	$0.853382\pi$
$632$		0			0
$633$	24.0000	+	41.5692i	0.953914	+	1.65223i
$634$		0			0
$635$			20.0000i			0.793676i
$636$		0			0
$637$	16.4317	−	9.48683i	0.651047	−	0.375882i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	−0.736725	−	0.676192i	$-0.763629\pi$
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	0.953962	+	0.299927i	$0.0969622\pi$
$642$		0			0
$643$	37.2391	+	21.5000i	1.46857	+	0.847877i	0.999380	−	0.0352216i	$-0.0112137\pi$
$643$	37.2391	+	21.5000i	1.46857	+	0.847877i	0.469187	+	0.883099i	$0.344547\pi$
$644$		0			0
$645$			94.8683i			3.73544i
$646$		0			0
$647$	25.2982			0.994576			0.497288	−	0.867586i	$-0.334329\pi$
$647$	25.2982			0.994576			0.497288	+	0.867586i	$0.334329\pi$
$648$		0			0
$649$	10.5000	−	18.1865i	0.412161	−	0.713884i
$650$		0			0
$651$	25.9808	+	15.0000i	1.01827	+	0.587896i
$652$		0			0
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$	−14.2302	−	24.6475i	−0.556022	−	0.963058i
$656$		0			0
$657$	42.0000			1.63858
$658$		0			0
$659$	−15.5885	+	9.00000i	−0.607240	+	0.350590i	−0.771885	−	0.635763i	$-0.780686\pi$
$659$	−15.5885	+	9.00000i	−0.607240	+	0.350590i	0.164644	+	0.986353i	$0.447352\pi$
$660$		0			0
$661$	−13.6931	+	7.90569i	−0.532598	+	0.307496i	−0.742074	−	0.670318i	$-0.766158\pi$
$661$	−13.6931	+	7.90569i	−0.532598	+	0.307496i	0.209475	+	0.977814i	$0.432824\pi$
$662$		0			0
$663$	−37.9473	+	65.7267i	−1.47375	+	2.55261i
$664$		0			0
$665$	−40.0000	+	17.3205i	−1.55113	+	0.671660i
$666$		0			0
$667$	25.9808	+	15.0000i	1.00598	+	0.580802i
$668$		0			0
$669$	−41.0792	+	23.7171i	−1.58821	+	0.916955i
$670$		0			0
$671$	−4.74342	−	8.21584i	−0.183118	−	0.317169i
$672$		0			0
$673$	−20.0000			−0.770943			−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000			−0.770943			−0.385472	+	0.922720i	$0.625961\pi$
$674$		0			0
$675$	−38.9711	+	22.5000i	−1.50000	+	0.866025i
$676$		0			0
$677$			31.6228i			1.21536i	0.794181	+	0.607681i	$0.207900\pi$
$677$			31.6228i			1.21536i	−0.794181	+	0.607681i	$0.792100\pi$
$678$		0			0
$679$	−14.2302	+	24.6475i	−0.546107	+	0.945885i
$680$		0			0
$681$	16.5000	−	28.5788i	0.632281	−	1.09514i
$682$		0			0
$683$			38.0000i			1.45403i	0.686622	+	0.727015i	$0.259093\pi$
$683$			38.0000i			1.45403i	−0.686622	+	0.727015i	$0.740907\pi$
$684$		0			0
$685$			28.4605i			1.08742i
$686$		0			0
$687$	−37.9473	+	65.7267i	−1.44778	+	2.50763i
$688$		0			0
$689$		0			0
$690$		0			0
$691$			6.00000i			0.228251i	0.993466	+	0.114125i	$0.0364066\pi$
$691$			6.00000i			0.228251i	−0.993466	+	0.114125i	$0.963593\pi$
$692$		0			0
$693$	49.2950	−	28.4605i	1.87256	−	1.08112i
$694$		0			0
$695$	34.7851			1.31947
$696$		0			0
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$		0			0
$699$	7.79423	−	4.50000i	0.294805	−	0.170206i
$700$		0			0
$701$	35.6020	+	20.5548i	1.34467	+	0.776344i	0.987488	−	0.157692i	$-0.0504052\pi$
$701$	35.6020	+	20.5548i	1.34467	+	0.776344i	0.357179	+	0.934036i	$0.383739\pi$
$702$		0			0
$703$	11.0680	+	8.21584i	0.417436	+	0.309866i
$704$		0			0
$705$	15.0000	−	25.9808i	0.564933	−	0.978492i
$706$		0			0
$707$	−25.9808	+	15.0000i	−0.977107	+	0.564133i
$708$		0			0
$709$	13.6931	−	7.90569i	0.514254	−	0.296905i	−0.220327	−	0.975426i	$-0.570712\pi$
$709$	13.6931	−	7.90569i	0.514254	−	0.296905i	0.734580	+	0.678522i	$0.237379\pi$
$710$		0			0
$711$	−37.9473			−1.42314
$712$		0			0
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$		0			0
$715$			60.0000i			2.24387i
$716$		0			0
$717$	−16.4317	−	9.48683i	−0.613652	−	0.354292i
$718$		0			0
$719$	−18.9737	+	32.8634i	−0.707598	+	1.22560i	0.258147	+	0.966106i	$0.416888\pi$
$719$	−18.9737	+	32.8634i	−0.707598	+	1.22560i	−0.965746	+	0.259491i	$0.916445\pi$
$720$		0			0
$721$	−20.0000			−0.744839
$722$		0			0
$723$		−	39.0000i		−	1.45043i
$724$		0			0
$725$	−13.6931	−	7.90569i	−0.508548	−	0.293610i
$726$		0			0
$727$	−22.1359	+	38.3406i	−0.820977	+	1.42197i	0.0839790	+	0.996468i	$0.473237\pi$
$727$	−22.1359	+	38.3406i	−0.820977	+	1.42197i	−0.904956	+	0.425506i	$0.860096\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−34.6410	+	20.0000i	−1.28124	+	0.739727i
$732$		0			0
$733$		−	41.1096i		−	1.51842i	−0.650847	−	0.759209i	$-0.725586\pi$
$733$		−	41.1096i		−	1.51842i	0.650847	−	0.759209i	$-0.274414\pi$
$734$		0			0
$735$	14.2302	+	24.6475i	0.524891	+	0.909137i
$736$		0			0
$737$	−7.50000	−	12.9904i	−0.276266	−	0.478507i
$738$		0			0
$739$	11.2583	+	6.50000i	0.414144	+	0.239106i	0.692569	−	0.721352i	$-0.256479\pi$
$739$	11.2583	+	6.50000i	0.414144	+	0.239106i	−0.278425	+	0.960458i	$0.589812\pi$
$740$		0			0
$741$	49.2950	−	66.4078i	1.81090	−	2.43955i
$742$		0			0
$743$	−14.2302	+	24.6475i	−0.522057	+	0.904230i	0.477614	+	0.878570i	$0.341502\pi$
$743$	−14.2302	+	24.6475i	−0.522057	+	0.904230i	−0.999671	+	0.0256596i	$0.991831\pi$
$744$		0			0
$745$	15.0000	+	25.9808i	0.549557	+	0.951861i
$746$		0			0
$747$	36.3731	−	21.0000i	1.33082	−	0.768350i
$748$		0			0
$749$		−	18.9737i		−	0.693283i
$750$		0			0
$751$	−25.2982	−	43.8178i	−0.923145	−	1.59893i	−0.794517	−	0.607241i	$-0.792276\pi$
$751$	−25.2982	−	43.8178i	−0.923145	−	1.59893i	−0.128628	−	0.991693i	$-0.541057\pi$
$752$		0			0
$753$	−21.0000			−0.765283
$754$		0			0
$755$	−8.66025	−	5.00000i	−0.315179	−	0.181969i
$756$		0			0
$757$	21.9089	+	12.6491i	0.796293	+	0.459740i	0.842173	−	0.539207i	$-0.181276\pi$
$757$	21.9089	+	12.6491i	0.796293	+	0.459740i	−0.0458805	+	0.998947i	$0.514609\pi$
$758$		0			0
$759$	85.3815			3.09915
$760$		0			0
$761$	−17.0000			−0.616250			−0.308125	−	0.951346i	$-0.599701\pi$
$761$	−17.0000			−0.616250			−0.308125	+	0.951346i	$0.599701\pi$
$762$		0			0
$763$	−51.9615	−	30.0000i	−1.88113	−	1.08607i
$764$		0			0
$765$	−65.7267	−	37.9473i	−2.37635	−	1.37199i
$766$		0			0
$767$	−44.2719			−1.59857
$768$		0			0
$769$	−4.00000	−	6.92820i	−0.144244	−	0.249837i	0.784847	−	0.619690i	$-0.212742\pi$
$769$	−4.00000	−	6.92820i	−0.144244	−	0.249837i	−0.929091	+	0.369852i	$0.879408\pi$
$770$		0			0
$771$		−	63.0000i		−	2.26889i
$772$		0			0
$773$	30.1247	−	17.3925i	1.08351	−	0.625566i	0.151670	−	0.988431i	$-0.451535\pi$
$773$	30.1247	−	17.3925i	1.08351	−	0.625566i	0.931842	+	0.362865i	$0.118202\pi$
$774$		0			0
$775$	−7.90569	−	13.6931i	−0.283981	−	0.491869i
$776$		0			0
$777$	15.0000	−	25.9808i	0.538122	−	0.932055i
$778$		0			0
$779$	−5.19615	−	12.0000i	−0.186171	−	0.429945i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−14.2302	−	24.6475i	−0.508548	−	0.880830i
$784$		0			0
$785$	−10.0000	−	17.3205i	−0.356915	−	0.618195i
$786$		0			0
$787$		−	31.0000i		−	1.10503i	−0.833503	−	0.552515i	$-0.813668\pi$
$787$		−	31.0000i		−	1.10503i	0.833503	−	0.552515i	$-0.186332\pi$
$788$		0			0
$789$	−24.6475	+	14.2302i	−0.877475	+	0.506610i
$790$		0			0
$791$	41.1096			1.46169
$792$		0			0
$793$	−10.0000	+	17.3205i	−0.355110	+	0.615069i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			28.4605i			1.00812i	0.863668	+	0.504061i	$0.168161\pi$
$797$			28.4605i			1.00812i	−0.863668	+	0.504061i	$0.831839\pi$
$798$		0			0
$799$	12.6491			0.447493
$800$		0			0
$801$	24.0000	−	41.5692i	0.847998	−	1.46878i
$802$		0			0
$803$	18.1865	+	10.5000i	0.641789	+	0.370537i
$804$		0			0
$805$			94.8683i			3.34367i
$806$		0			0
$807$	−37.9473	−	65.7267i	−1.33581	−	2.31369i
$808$		0			0
$809$	13.0000			0.457056			0.228528	−	0.973537i	$-0.426609\pi$
$809$	13.0000			0.457056			0.228528	+	0.973537i	$0.426609\pi$
$810$		0			0
$811$	−1.73205	+	1.00000i	−0.0608205	+	0.0351147i	−0.530102	−	0.847934i	$-0.677846\pi$
$811$	−1.73205	+	1.00000i	−0.0608205	+	0.0351147i	0.469281	+	0.883049i	$0.344513\pi$
$812$		0			0
$813$	−57.5109	+	33.2039i	−2.01699	+	1.16451i
$814$		0			0
$815$	7.90569	−	13.6931i	0.276924	−	0.479647i
$816$		0			0
$817$	40.0000	−	17.3205i	1.39942	−	0.605968i
$818$		0			0
$819$	−103.923	−	60.0000i	−3.63137	−	2.09657i
$820$		0			0
$821$	21.9089	−	12.6491i	0.764626	−	0.441457i	−0.0663282	−	0.997798i	$-0.521128\pi$
$821$	21.9089	−	12.6491i	0.764626	−	0.441457i	0.830954	+	0.556341i	$0.187795\pi$
$822$		0			0
$823$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$823$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$	−45.0000			−1.56670
$826$		0			0
$827$	4.33013	−	2.50000i	0.150573	−	0.0869335i	−0.422820	−	0.906213i	$-0.638960\pi$
$827$	4.33013	−	2.50000i	0.150573	−	0.0869335i	0.573394	+	0.819280i	$0.305627\pi$
$828$		0			0
$829$			12.6491i			0.439322i	0.975576	+	0.219661i	$0.0704951\pi$
$829$			12.6491i			0.439322i	−0.975576	+	0.219661i	$0.929505\pi$
$830$		0			0
$831$	42.6907	−	73.9425i	1.48093	−	2.56504i
$832$		0			0
$833$	−6.00000	+	10.3923i	−0.207888	+	0.360072i
$834$		0			0
$835$		−	20.0000i		−	0.692129i
$836$		0			0
$837$		−	28.4605i		−	0.983739i
$838$		0			0
$839$	17.3925	−	30.1247i	0.600457	−	1.04002i	−0.392295	−	0.919839i	$-0.628319\pi$
$839$	17.3925	−	30.1247i	0.600457	−	1.04002i	0.992752	−	0.120182i	$-0.0383479\pi$
$840$		0			0
$841$	−9.50000	+	16.4545i	−0.327586	+	0.567396i
$842$		0			0
$843$			57.0000i			1.96318i
$844$		0			0
$845$	73.9425	−	42.6907i	2.54370	−	1.46861i
$846$		0			0
$847$	−6.32456			−0.217314
$848$		0			0
$849$	22.5000	+	38.9711i	0.772198	+	1.33749i
$850$		0			0
$851$	25.9808	−	15.0000i	0.890609	−	0.514193i
$852$		0			0
$853$	5.47723	+	3.16228i	0.187537	+	0.108274i	0.590829	−	0.806797i	$-0.298801\pi$
$853$	5.47723	+	3.16228i	0.187537	+	0.108274i	−0.403292	+	0.915071i	$0.632134\pi$
$854$		0			0
$855$	66.4078	+	49.2950i	2.27110	+	1.68585i
$856$		0			0
$857$	−17.5000	+	30.3109i	−0.597789	+	1.03540i	0.395358	+	0.918527i	$0.370620\pi$
$857$	−17.5000	+	30.3109i	−0.597789	+	1.03540i	−0.993147	+	0.116873i	$0.962713\pi$
$858$		0			0
$859$	−19.9186	+	11.5000i	−0.679613	+	0.392375i	−0.799709	−	0.600387i	$-0.795013\pi$
$859$	−19.9186	+	11.5000i	−0.679613	+	0.392375i	0.120096	+	0.992762i	$0.461680\pi$
$860$		0			0
$861$	−24.6475	+	14.2302i	−0.839985	+	0.484966i
$862$		0			0
$863$	53.7587			1.82997			0.914984	−	0.403490i	$-0.132203\pi$
$863$	53.7587			1.82997			0.914984	+	0.403490i	$0.132203\pi$
$864$		0			0
$865$	−20.0000	−	34.6410i	−0.680020	−	1.17783i
$866$		0			0
$867$			3.00000i			0.101885i
$868$		0			0
$869$	−16.4317	−	9.48683i	−0.557406	−	0.321819i
$870$		0			0
$871$	−15.8114	+	27.3861i	−0.535748	+	0.927944i
$872$		0			0
$873$	54.0000			1.82762
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.73861	+	1.58114i	0.0924764	+	0.0533913i	0.545525	−	0.838095i	$-0.316330\pi$
$877$	2.73861	+	1.58114i	0.0924764	+	0.0533913i	−0.453049	+	0.891486i	$0.649664\pi$
$878$		0			0
$879$	−23.7171	+	41.0792i	−0.799957	+	1.38557i
$880$		0			0
$881$	−59.0000			−1.98776			−0.993880	−	0.110463i	$-0.964767\pi$
$881$	−59.0000			−1.98776			−0.993880	+	0.110463i	$0.964767\pi$
$882$		0			0
$883$	−37.2391	+	21.5000i	−1.25320	+	0.723533i	−0.971743	−	0.236043i	$-0.924150\pi$
$883$	−37.2391	+	21.5000i	−1.25320	+	0.723533i	−0.281453	+	0.959575i	$0.590816\pi$
$884$		0			0
$885$		−	66.4078i		−	2.23227i
$886$		0			0
$887$	3.16228	+	5.47723i	0.106179	+	0.183907i	0.914219	−	0.405220i	$-0.132805\pi$
$887$	3.16228	+	5.47723i	0.106179	+	0.183907i	−0.808040	+	0.589127i	$0.799472\pi$
$888$		0			0
$889$	−10.0000	−	17.3205i	−0.335389	−	0.580911i
$890$		0			0
$891$	−23.3827	−	13.5000i	−0.783349	−	0.452267i
$892$		0			0
$893$	−13.6931	−	1.58114i	−0.458221	−	0.0529108i
$894$		0			0
$895$	4.74342	−	8.21584i	0.158555	−	0.274625i
$896$		0			0
$897$	−90.0000	−	155.885i	−3.00501	−	5.20483i
$898$		0			0
$899$	8.66025	−	5.00000i	0.288836	−	0.166759i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−47.4342	−	82.1584i	−1.57851	−	2.73406i
$904$		0			0
$905$	−30.0000			−0.997234
$906$		0			0
$907$	0.866025	+	0.500000i	0.0287559	+	0.0166022i	0.514309	−	0.857605i	$-0.328048\pi$
$907$	0.866025	+	0.500000i	0.0287559	+	0.0166022i	−0.485553	+	0.874207i	$0.661382\pi$
$908$		0			0
$909$	49.2950	+	28.4605i	1.63501	+	0.943975i
$910$		0			0
$911$	−28.4605			−0.942938			−0.471469	−	0.881883i	$-0.656276\pi$
$911$	−28.4605			−0.942938			−0.471469	+	0.881883i	$0.656276\pi$
$912$		0			0
$913$	21.0000			0.694999
$914$		0			0
$915$	−25.9808	−	15.0000i	−0.858898	−	0.495885i
$916$		0			0
$917$	24.6475	+	14.2302i	0.813933	+	0.469924i
$918$		0			0
$919$	−31.6228			−1.04314			−0.521570	−	0.853209i	$-0.674653\pi$
$919$	−31.6228			−1.04314			−0.521570	+	0.853209i	$0.674653\pi$
$920$		0			0
$921$	31.5000	+	54.5596i	1.03796	+	1.79780i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−13.6931	+	7.90569i	−0.450225	+	0.259938i
$926$		0			0
$927$	18.9737	+	32.8634i	0.623177	+	1.07937i
$928$		0			0
$929$	6.50000	−	11.2583i	0.213258	−	0.369374i	−0.739474	−	0.673185i	$-0.764926\pi$
$929$	6.50000	−	11.2583i	0.213258	−	0.369374i	0.952732	+	0.303811i	$0.0982592\pi$
$930$		0			0
$931$	7.79423	−	10.5000i	0.255446	−	0.344124i
$932$		0			0
$933$	−57.5109	−	33.2039i	−1.88282	−	1.08705i
$934$		0			0
$935$	−18.9737	−	32.8634i	−0.620505	−	1.07475i
$936$		0			0
$937$	−0.500000	−	0.866025i	−0.0163343	−	0.0282918i	0.857743	−	0.514079i	$-0.171866\pi$
$937$	−0.500000	−	0.866025i	−0.0163343	−	0.0282918i	−0.874077	+	0.485787i	$0.838533\pi$
$938$		0			0
$939$			9.00000i			0.293704i
$940$		0			0
$941$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$941$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$942$		0			0
$943$	−28.4605			−0.926801
$944$		0			0
$945$	45.0000	−	77.9423i	1.46385	−	2.53546i
$946$		0			0
$947$	−25.9808	−	15.0000i	−0.844261	−	0.487435i	0.0144491	−	0.999896i	$-0.495401\pi$
$947$	−25.9808	−	15.0000i	−0.844261	−	0.487435i	−0.858710	+	0.512461i	$0.828734\pi$
$948$		0			0
$949$		−	44.2719i		−	1.43713i
$950$		0			0
$951$	−94.8683			−3.07632
$952$		0			0
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	−0.718604	−	0.695419i	$-0.755219\pi$
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	0.961553	+	0.274620i	$0.0885520\pi$
$954$		0			0
$955$	17.3205	+	10.0000i	0.560478	+	0.323592i
$956$		0			0
$957$		−	28.4605i		−	0.919997i
$958$		0			0
$959$	−14.2302	−	24.6475i	−0.459519	−	0.795910i
$960$		0			0
$961$	−21.0000			−0.677419
$962$		0			0
$963$	−31.1769	+	18.0000i	−1.00466	+	0.580042i
$964$		0			0
$965$	−21.9089	+	12.6491i	−0.705273	+	0.407189i
$966$		0			0
$967$	−3.16228	+	5.47723i	−0.101692	+	0.176136i	−0.912382	−	0.409340i	$-0.865759\pi$
$967$	−3.16228	+	5.47723i	−0.101692	+	0.176136i	0.810690	+	0.585476i	$0.199092\pi$
$968$		0			0
$969$	−6.00000	+	51.9615i	−0.192748	+	1.66924i
$970$		0			0
$971$	0.866025	+	0.500000i	0.0277921	+	0.0160458i	0.513832	−	0.857891i	$-0.328226\pi$
$971$	0.866025	+	0.500000i	0.0277921	+	0.0160458i	−0.486040	+	0.873937i	$0.661559\pi$
$972$		0			0
$973$	−30.1247	+	17.3925i	−0.965755	+	0.557579i
$974$		0			0
$975$	47.4342	+	82.1584i	1.51911	+	2.63117i
$976$		0			0
$977$	35.0000			1.11975			0.559875	−	0.828577i	$-0.310849\pi$
$977$	35.0000			1.11975			0.559875	+	0.828577i	$0.310849\pi$
$978$		0			0
$979$	20.7846	−	12.0000i	0.664279	−	0.383522i
$980$		0			0
$981$			113.842i			3.63470i
$982$		0			0
$983$	18.9737	−	32.8634i	0.605166	−	1.04818i	−0.386859	−	0.922139i	$-0.626440\pi$
$983$	18.9737	−	32.8634i	0.605166	−	1.04818i	0.992025	−	0.126039i	$-0.0402266\pi$
$984$		0			0
$985$	35.0000	−	60.6218i	1.11519	−	1.93157i
$986$		0			0
$987$			30.0000i			0.954911i
$988$		0			0
$989$		−	94.8683i		−	3.01664i
$990$		0			0
$991$	−12.6491	+	21.9089i	−0.401812	+	0.695959i	−0.993945	−	0.109881i	$-0.964953\pi$
$991$	−12.6491	+	21.9089i	−0.401812	+	0.695959i	0.592132	+	0.805841i	$0.298286\pi$
$992$		0			0
$993$	−43.5000	+	75.3442i	−1.38043	+	2.39098i
$994$		0			0
$995$			20.0000i			0.634043i
$996$		0			0
$997$	−35.6020	+	20.5548i	−1.12753	+	0.650977i	−0.943311	−	0.331909i	$-0.892307\pi$
$997$	−35.6020	+	20.5548i	−1.12753	+	0.650977i	−0.184214	+	0.982886i	$0.558974\pi$
$998$		0			0
$999$	−28.4605			−0.900450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.t.b.353.4	yes	8
4.3	odd	2	inner	1216.2.t.b.353.2	yes	8
8.3	odd	2	inner	1216.2.t.b.353.3	yes	8
8.5	even	2	inner	1216.2.t.b.353.1	✓	8
19.7	even	3	inner	1216.2.t.b.1185.1	yes	8
76.7	odd	6	inner	1216.2.t.b.1185.3	yes	8
152.45	even	6	inner	1216.2.t.b.1185.4	yes	8
152.83	odd	6	inner	1216.2.t.b.1185.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.t.b.353.1	✓	8	8.5	even	2	inner
1216.2.t.b.353.2	yes	8	4.3	odd	2	inner
1216.2.t.b.353.3	yes	8	8.3	odd	2	inner
1216.2.t.b.353.4	yes	8	1.1	even	1	trivial
1216.2.t.b.1185.1	yes	8	19.7	even	3	inner
1216.2.t.b.1185.2	yes	8	152.83	odd	6	inner
1216.2.t.b.1185.3	yes	8	76.7	odd	6	inner
1216.2.t.b.1185.4	yes	8	152.45	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.59808 + 1.50000i) q^{3} +(2.73861 + 1.58114i) q^{5} -3.16228 q^{7} +(3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(2.59808 + 1.50000i) q^{3} +(2.73861 + 1.58114i) q^{5} -3.16228 q^{7} +(3.00000 + 5.19615i) q^{9} +3.00000i q^{11} +(5.47723 - 3.16228i) q^{13} +(4.74342 + 8.21584i) q^{15} +(-2.00000 + 3.46410i) q^{17} +(2.59808 - 3.50000i) q^{19} +(-8.21584 - 4.74342i) q^{21} +(-4.74342 - 8.21584i) q^{23} +(2.50000 + 4.33013i) q^{25} +9.00000i q^{27} +(-2.73861 + 1.58114i) q^{29} -3.16228 q^{31} +(-4.50000 + 7.79423i) q^{33} +(-8.66025 - 5.00000i) q^{35} +3.16228i q^{37} +18.9737 q^{39} +(1.50000 - 2.59808i) q^{41} +(8.66025 + 5.00000i) q^{43} +18.9737i q^{45} +(-1.58114 - 2.73861i) q^{47} +3.00000 q^{49} +(-10.3923 + 6.00000i) q^{51} +(-4.74342 + 8.21584i) q^{55} +(12.0000 - 5.19615i) q^{57} +(-6.06218 - 3.50000i) q^{59} +(-2.73861 + 1.58114i) q^{61} +(-9.48683 - 16.4317i) q^{63} +20.0000 q^{65} +(-4.33013 + 2.50000i) q^{67} -28.4605i q^{69} +(3.50000 - 6.06218i) q^{73} +15.0000i q^{75} -9.48683i q^{77} +(-3.16228 + 5.47723i) q^{79} +(-4.50000 + 7.79423i) q^{81} -7.00000i q^{83} +(-10.9545 + 6.32456i) q^{85} -9.48683 q^{87} +(-4.00000 - 6.92820i) q^{89} +(-17.3205 + 10.0000i) q^{91} +(-8.21584 - 4.74342i) q^{93} +(12.6491 - 5.47723i) q^{95} +(4.50000 - 7.79423i) q^{97} +(-15.5885 + 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 24 q^{9}+O(q^{10}) \) 8 * q + 24 * q^9	\( 8 q + 24 q^{9} - 16 q^{17} + 20 q^{25} - 36 q^{33} + 12 q^{41} + 24 q^{49} + 96 q^{57} + 160 q^{65} + 28 q^{73} - 36 q^{81} - 32 q^{89} + 36 q^{97}+O(q^{100}) \) 8 * q + 24 * q^9 - 16 * q^17 + 20 * q^25 - 36 * q^33 + 12 * q^41 + 24 * q^49 + 96 * q^57 + 160 * q^65 + 28 * q^73 - 36 * q^81 - 32 * q^89 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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