LMFDB - Embedded newform 1380.2.r.c.737.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.4
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57061 - 0.730184i) q^{3} +(-0.115647 + 2.23308i) q^{5} +(-0.487335 - 0.487335i) q^{7} +(1.93366 + 2.29368i) q^{9} +O(q^{10})$	\(q+(-1.57061 - 0.730184i) q^{3} +(-0.115647 + 2.23308i) q^{5} +(-0.487335 - 0.487335i) q^{7} +(1.93366 + 2.29368i) q^{9} +5.43048i q^{11} +(1.32721 - 1.32721i) q^{13} +(1.81219 - 3.42286i) q^{15} +(1.95078 - 1.95078i) q^{17} -1.37492i q^{19} +(0.409571 + 1.12126i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-4.97325 - 0.516499i) q^{25} +(-1.36223 - 5.01441i) q^{27} -0.502711 q^{29} -10.3420 q^{31} +(3.96525 - 8.52919i) q^{33} +(1.14462 - 1.03190i) q^{35} +(-0.339633 - 0.339633i) q^{37} +(-3.05363 + 1.11542i) q^{39} +11.7428i q^{41} +(3.29965 - 3.29965i) q^{43} +(-5.34558 + 4.05275i) q^{45} +(-7.09842 + 7.09842i) q^{47} -6.52501i q^{49} +(-4.48836 + 1.63950i) q^{51} +(7.61463 + 7.61463i) q^{53} +(-12.1267 - 0.628021i) q^{55} +(-1.00394 + 2.15947i) q^{57} -12.4440 q^{59} -0.391005 q^{61} +(0.175448 - 2.06013i) q^{63} +(2.81026 + 3.11724i) q^{65} +(7.74226 + 7.74226i) q^{67} +(-0.594274 - 1.62691i) q^{69} -9.80460i q^{71} +(-4.21064 + 4.21064i) q^{73} +(7.43392 + 4.44261i) q^{75} +(2.64646 - 2.64646i) q^{77} +13.0490i q^{79} +(-1.52191 + 8.87039i) q^{81} +(-10.9511 - 10.9511i) q^{83} +(4.13064 + 4.58185i) q^{85} +(0.789566 + 0.367072i) q^{87} -0.737166 q^{89} -1.29359 q^{91} +(16.2433 + 7.55157i) q^{93} +(3.07029 + 0.159006i) q^{95} +(-0.383944 - 0.383944i) q^{97} +(-12.4558 + 10.5007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{3}+O(q^{10}) $ 80 * q + 8 * q^3	$ 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) $ 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$1$

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
$3$	−1.57061	−	0.730184i	−0.906795	−	0.421572i
$3$	−1.57061	−	0.730184i	−0.906795	−	0.421572i
$4$		0			0
$5$	−0.115647	+	2.23308i	−0.0517191	+	0.998662i
$5$	−0.115647	+	2.23308i	−0.0517191	+	0.998662i
$6$		0			0
$7$	−0.487335	−	0.487335i	−0.184195	−	0.184195i	0.608986	−	0.793181i	$-0.291577\pi$
$7$	−0.487335	−	0.487335i	−0.184195	−	0.184195i	−0.793181	+	0.608986i	$0.791577\pi$
$8$		0			0
$9$	1.93366	+	2.29368i	0.644554	+	0.764559i
$10$		0			0
$11$			5.43048i			1.63735i	0.574256	+	0.818676i	$0.305291\pi$
$11$			5.43048i			1.63735i	−0.574256	+	0.818676i	$0.694709\pi$
$12$		0			0
$13$	1.32721	−	1.32721i	0.368101	−	0.368101i	−0.498684	−	0.866784i	$-0.666183\pi$
$13$	1.32721	−	1.32721i	0.368101	−	0.368101i	0.866784	+	0.498684i	$0.166183\pi$
$14$		0			0
$15$	1.81219	−	3.42286i	0.467907	−	0.883778i
$16$		0			0
$17$	1.95078	−	1.95078i	0.473135	−	0.473135i	−0.429793	−	0.902927i	$-0.641413\pi$
$17$	1.95078	−	1.95078i	0.473135	−	0.473135i	0.902927	+	0.429793i	$0.141413\pi$
$18$		0			0
$19$		−	1.37492i		−	0.315428i	−0.987485	−	0.157714i	$-0.949588\pi$
$19$		−	1.37492i		−	0.315428i	0.987485	−	0.157714i	$-0.0504124\pi$
$20$		0			0
$21$	0.409571	+	1.12126i	0.0893758	+	0.244679i
$22$		0			0
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−4.97325	−	0.516499i	−0.994650	−	0.103300i
$26$		0			0
$27$	−1.36223	−	5.01441i	−0.262161	−	0.965024i
$28$		0			0
$29$	−0.502711			−0.0933512			−0.0466756	−	0.998910i	$-0.514863\pi$
$29$	−0.502711			−0.0933512			−0.0466756	+	0.998910i	$0.514863\pi$
$30$		0			0
$31$	−10.3420			−1.85748			−0.928739	−	0.370735i	$-0.879106\pi$
$31$	−10.3420			−1.85748			−0.928739	+	0.370735i	$0.879106\pi$
$32$		0			0
$33$	3.96525	−	8.52919i	0.690262	−	1.48474i
$34$		0			0
$35$	1.14462	−	1.03190i	0.193475	−	0.174422i
$36$		0			0
$37$	−0.339633	−	0.339633i	−0.0558353	−	0.0558353i	0.678638	−	0.734473i	$-0.262571\pi$
$37$	−0.339633	−	0.339633i	−0.0558353	−	0.0558353i	−0.734473	+	0.678638i	$0.762571\pi$
$38$		0			0
$39$	−3.05363	+	1.11542i	−0.488973	+	0.178611i
$40$		0			0
$41$			11.7428i			1.83392i	0.398975	+	0.916962i	$0.369366\pi$
$41$			11.7428i			1.83392i	−0.398975	+	0.916962i	$0.630634\pi$
$42$		0			0
$43$	3.29965	−	3.29965i	0.503192	−	0.503192i	−0.409236	−	0.912428i	$-0.634205\pi$
$43$	3.29965	−	3.29965i	0.503192	−	0.503192i	0.912428	+	0.409236i	$0.134205\pi$
$44$		0			0
$45$	−5.34558	+	4.05275i	−0.796871	+	0.604149i
$46$		0			0
$47$	−7.09842	+	7.09842i	−1.03541	+	1.03541i	−0.0360609	+	0.999350i	$0.511481\pi$
$47$	−7.09842	+	7.09842i	−1.03541	+	1.03541i	−0.999350	+	0.0360609i	$0.988519\pi$
$48$		0			0
$49$		−	6.52501i		−	0.932144i
$50$		0			0
$51$	−4.48836	+	1.63950i	−0.628496	+	0.229576i
$52$		0			0
$53$	7.61463	+	7.61463i	1.04595	+	1.04595i	0.998892	+	0.0470574i	$0.0149844\pi$
$53$	7.61463	+	7.61463i	1.04595	+	1.04595i	0.0470574	+	0.998892i	$0.485016\pi$
$54$		0			0
$55$	−12.1267	−	0.628021i	−1.63516	−	0.0846823i
$56$		0			0
$57$	−1.00394	+	2.15947i	−0.132976	+	0.286028i
$58$		0			0
$59$	−12.4440			−1.62007			−0.810037	−	0.586379i	$-0.800553\pi$
$59$	−12.4440			−1.62007			−0.810037	+	0.586379i	$0.800553\pi$
$60$		0			0
$61$	−0.391005			−0.0500631			−0.0250315	−	0.999687i	$-0.507969\pi$
$61$	−0.391005			−0.0500631			−0.0250315	+	0.999687i	$0.507969\pi$
$62$		0			0
$63$	0.175448	−	2.06013i	0.0221044	−	0.259552i
$64$		0			0
$65$	2.81026	+	3.11724i	0.348570	+	0.386646i
$66$		0			0
$67$	7.74226	+	7.74226i	0.945868	+	0.945868i	0.998608	−	0.0527405i	$-0.0167956\pi$
$67$	7.74226	+	7.74226i	0.945868	+	0.945868i	−0.0527405	+	0.998608i	$0.516796\pi$
$68$		0			0
$69$	−0.594274	−	1.62691i	−0.0715422	−	0.195857i
$70$		0			0
$71$		−	9.80460i		−	1.16359i	−0.813335	−	0.581796i	$-0.802350\pi$
$71$		−	9.80460i		−	1.16359i	0.813335	−	0.581796i	$-0.197650\pi$
$72$		0			0
$73$	−4.21064	+	4.21064i	−0.492818	+	0.492818i	−0.909193	−	0.416375i	$-0.863300\pi$
$73$	−4.21064	+	4.21064i	−0.492818	+	0.492818i	0.416375	+	0.909193i	$0.363300\pi$
$74$		0			0
$75$	7.43392	+	4.44261i	0.858395	+	0.512989i
$76$		0			0
$77$	2.64646	−	2.64646i	0.301593	−	0.301593i
$78$		0			0
$79$			13.0490i			1.46813i	0.679078	+	0.734066i	$0.262380\pi$
$79$			13.0490i			1.46813i	−0.679078	+	0.734066i	$0.737620\pi$
$80$		0			0
$81$	−1.52191	+	8.87039i	−0.169101	+	0.985599i
$82$		0			0
$83$	−10.9511	−	10.9511i	−1.20204	−	1.20204i	−0.973545	−	0.228496i	$-0.926619\pi$
$83$	−10.9511	−	10.9511i	−1.20204	−	1.20204i	−0.228496	−	0.973545i	$-0.573381\pi$
$84$		0			0
$85$	4.13064	+	4.58185i	0.448031	+	0.496971i
$86$		0			0
$87$	0.789566	+	0.367072i	0.0846504	+	0.0393543i
$88$		0			0
$89$	−0.737166			−0.0781395			−0.0390697	−	0.999236i	$-0.512439\pi$
$89$	−0.737166			−0.0781395			−0.0390697	+	0.999236i	$0.512439\pi$
$90$		0			0
$91$	−1.29359			−0.135605
$92$		0			0
$93$	16.2433	+	7.55157i	1.68435	+	0.783061i
$94$		0			0
$95$	3.07029	+	0.159006i	0.315006	+	0.0163136i
$96$		0			0
$97$	−0.383944	−	0.383944i	−0.0389836	−	0.0389836i	0.687346	−	0.726330i	$-0.258775\pi$
$97$	−0.383944	−	0.383944i	−0.0389836	−	0.0389836i	−0.726330	+	0.687346i	$0.758775\pi$
$98$		0			0
$99$	−12.4558	+	10.5007i	−1.25185	+	1.05536i
$100$		0			0
$101$			13.5153i			1.34483i	0.740176	+	0.672413i	$0.234742\pi$
$101$			13.5153i			1.34483i	−0.740176	+	0.672413i	$0.765258\pi$
$102$		0			0
$103$	−6.91724	+	6.91724i	−0.681576	+	0.681576i	−0.960355	−	0.278779i	$-0.910070\pi$
$103$	−6.91724	+	6.91724i	−0.681576	+	0.681576i	0.278779	+	0.960355i	$0.410070\pi$
$104$		0			0
$105$	−2.55122	+	0.784932i	−0.248974	+	0.0766016i
$106$		0			0
$107$	−7.70048	+	7.70048i	−0.744433	+	0.744433i	−0.973428	−	0.228994i	$-0.926456\pi$
$107$	−7.70048	+	7.70048i	−0.744433	+	0.744433i	0.228994	+	0.973428i	$0.426456\pi$
$108$		0			0
$109$		−	12.9825i		−	1.24350i	−0.783217	−	0.621748i	$-0.786423\pi$
$109$		−	12.9825i		−	1.24350i	0.783217	−	0.621748i	$-0.213577\pi$
$110$		0			0
$111$	0.285438	+	0.781427i	0.0270926	+	0.0741698i
$112$		0			0
$113$	−5.25351	−	5.25351i	−0.494209	−	0.494209i	0.415420	−	0.909630i	$-0.363634\pi$
$113$	−5.25351	−	5.25351i	−0.494209	−	0.494209i	−0.909630	+	0.415420i	$0.863634\pi$
$114$		0			0
$115$	−1.66080	+	1.49725i	−0.154870	+	0.139619i
$116$		0			0
$117$	5.61055	+	0.477815i	0.518695	+	0.0441740i
$118$		0			0
$119$	−1.90137			−0.174298
$120$		0			0
$121$	−18.4901			−1.68092
$122$		0			0
$123$	8.57444	−	18.4435i	0.773131	−	1.66299i
$124$		0			0
$125$	1.72852	−	11.0459i	0.154604	−	0.987977i
$126$		0			0
$127$	−6.21795	−	6.21795i	−0.551754	−	0.551754i	0.375193	−	0.926947i	$-0.377576\pi$
$127$	−6.21795	−	6.21795i	−0.551754	−	0.551754i	−0.926947	+	0.375193i	$0.877576\pi$
$128$		0			0
$129$	−7.59183	+	2.77313i	−0.668424	+	0.244160i
$130$		0			0
$131$		−	1.76777i		−	0.154451i	−0.997014	−	0.0772256i	$-0.975394\pi$
$131$		−	1.76777i		−	0.154451i	0.997014	−	0.0772256i	$-0.0246062\pi$
$132$		0			0
$133$	−0.670046	+	0.670046i	−0.0581003	+	0.0581003i
$134$		0			0
$135$	11.3551	−	2.46206i	0.977291	−	0.211900i
$136$		0			0
$137$	−8.56496	+	8.56496i	−0.731754	+	0.731754i	−0.970967	−	0.239213i	$-0.923111\pi$
$137$	−8.56496	+	8.56496i	−0.731754	+	0.731754i	0.239213	+	0.970967i	$0.423111\pi$
$138$		0			0
$139$			4.41225i			0.374242i	0.982337	+	0.187121i	$0.0599157\pi$
$139$			4.41225i			0.374242i	−0.982337	+	0.187121i	$0.940084\pi$
$140$		0			0
$141$	16.3320	−	5.96572i	1.37541	−	0.502405i
$142$		0			0
$143$	7.20737	+	7.20737i	0.602710	+	0.602710i
$144$		0			0
$145$	0.0581373	−	1.12259i	0.00482804	−	0.0932262i
$146$		0			0
$147$	−4.76446	+	10.2483i	−0.392966	+	0.845264i
$148$		0			0
$149$	−8.24767			−0.675676			−0.337838	−	0.941204i	$-0.609696\pi$
$149$	−8.24767			−0.675676			−0.337838	+	0.941204i	$0.609696\pi$
$150$		0			0
$151$	−11.5290			−0.938214			−0.469107	−	0.883141i	$-0.655424\pi$
$151$	−11.5290			−0.938214			−0.469107	+	0.883141i	$0.655424\pi$
$152$		0			0
$153$	8.24662	+	0.702313i	0.666700	+	0.0567786i
$154$		0			0
$155$	1.19603	−	23.0945i	0.0960671	−	1.85499i
$156$		0			0
$157$	9.21886	+	9.21886i	0.735745	+	0.735745i	0.971752	−	0.236006i	$-0.0758386\pi$
$157$	9.21886	+	9.21886i	0.735745	+	0.735745i	−0.236006	+	0.971752i	$0.575839\pi$
$158$		0			0
$159$	−6.39956	−	17.5197i	−0.507518	−	1.38940i
$160$		0			0
$161$		−	0.689196i		−	0.0543162i
$162$		0			0
$163$	7.02252	−	7.02252i	0.550046	−	0.550046i	−0.376408	−	0.926454i	$-0.622841\pi$
$163$	7.02252	−	7.02252i	0.550046	−	0.550046i	0.926454	+	0.376408i	$0.122841\pi$
$164$		0			0
$165$	18.5878	+	9.84109i	1.44706	+	0.766128i
$166$		0			0
$167$	−13.5641	+	13.5641i	−1.04962	+	1.04962i	−0.0509174	+	0.998703i	$0.516215\pi$
$167$	−13.5641	+	13.5641i	−1.04962	+	1.04962i	−0.998703	+	0.0509174i	$0.983785\pi$
$168$		0			0
$169$			9.47705i			0.729004i
$170$		0			0
$171$	3.15362	−	2.65863i	0.241163	−	0.203310i
$172$		0			0
$173$	4.85200	+	4.85200i	0.368891	+	0.368891i	0.867073	−	0.498182i	$-0.165999\pi$
$173$	4.85200	+	4.85200i	0.368891	+	0.368891i	−0.498182	+	0.867073i	$0.665999\pi$
$174$		0			0
$175$	2.17193	+	2.67535i	0.164183	+	0.202237i
$176$		0			0
$177$	19.5448	+	9.08644i	1.46908	+	0.682978i
$178$		0			0
$179$	22.5228			1.68343			0.841715	−	0.539921i	$-0.181546\pi$
$179$	22.5228			1.68343			0.841715	+	0.539921i	$0.181546\pi$
$180$		0			0
$181$	−3.68485			−0.273893			−0.136947	−	0.990578i	$-0.543729\pi$
$181$	−3.68485			−0.273893			−0.136947	+	0.990578i	$0.543729\pi$
$182$		0			0
$183$	0.614119	+	0.285506i	0.0453970	+	0.0211052i
$184$		0			0
$185$	0.797704	−	0.719148i	0.0586483	−	0.0528728i
$186$		0			0
$187$	10.5937	+	10.5937i	0.774688	+	0.774688i
$188$		0			0
$189$	−1.77984	+	3.10756i	−0.129464	+	0.226042i
$190$		0			0
$191$		−	11.7564i		−	0.850663i	−0.905038	−	0.425331i	$-0.860158\pi$
$191$		−	11.7564i		−	0.850663i	0.905038	−	0.425331i	$-0.139842\pi$
$192$		0			0
$193$	7.57761	−	7.57761i	0.545448	−	0.545448i	−0.379673	−	0.925121i	$-0.623963\pi$
$193$	7.57761	−	7.57761i	0.545448	−	0.545448i	0.925121	+	0.379673i	$0.123963\pi$
$194$		0			0
$195$	−2.13768	−	6.94799i	−0.153083	−	0.497556i
$196$		0			0
$197$	1.75116	−	1.75116i	0.124765	−	0.124765i	−0.641967	−	0.766732i	$-0.721881\pi$
$197$	1.75116	−	1.75116i	0.124765	−	0.124765i	0.766732	+	0.641967i	$0.221881\pi$
$198$		0			0
$199$			8.55734i			0.606614i	0.952893	+	0.303307i	$0.0980907\pi$
$199$			8.55734i			0.606614i	−0.952893	+	0.303307i	$0.901909\pi$
$200$		0			0
$201$	−6.50683	−	17.8134i	−0.458956	−	1.25646i
$202$		0			0
$203$	0.244989	+	0.244989i	0.0171949	+	0.0171949i
$204$		0			0
$205$	−26.2226	−	1.35803i	−1.83147	−	0.0948489i
$206$		0			0
$207$	−0.254569	+	2.98918i	−0.0176938	+	0.207762i
$208$		0			0
$209$	7.46646			0.516466
$210$		0			0
$211$	−2.41990			−0.166593			−0.0832965	−	0.996525i	$-0.526545\pi$
$211$	−2.41990			−0.166593			−0.0832965	+	0.996525i	$0.526545\pi$
$212$		0			0
$213$	−7.15917	+	15.3993i	−0.490538	+	1.05514i
$214$		0			0
$215$	6.98677	+	7.74996i	0.476494	+	0.528543i
$216$		0			0
$217$	5.04002	+	5.04002i	0.342139	+	0.342139i
$218$		0			0
$219$	9.68783	−	3.53875i	0.654643	−	0.239126i
$220$		0			0
$221$		−	5.17818i		−	0.348322i
$222$		0			0
$223$	18.3766	−	18.3766i	1.23059	−	1.23059i	0.266849	−	0.963738i	$-0.414017\pi$
$223$	18.3766	−	18.3766i	1.23059	−	1.23059i	0.963738	−	0.266849i	$-0.0859826\pi$
$224$		0			0
$225$	−8.43190	−	12.4058i	−0.562127	−	0.827051i
$226$		0			0
$227$	13.9621	−	13.9621i	0.926695	−	0.926695i	−0.0707957	−	0.997491i	$-0.522554\pi$
$227$	13.9621	−	13.9621i	0.926695	−	0.926695i	0.997491	+	0.0707957i	$0.0225538\pi$
$228$		0			0
$229$			0.648926i			0.0428823i	0.999770	+	0.0214411i	$0.00682545\pi$
$229$			0.648926i			0.0428823i	−0.999770	+	0.0214411i	$0.993175\pi$
$230$		0			0
$231$	−6.08898	+	2.22417i	−0.400626	+	0.146340i
$232$		0			0
$233$	−1.01509	−	1.01509i	−0.0665008	−	0.0665008i	0.673074	−	0.739575i	$-0.264973\pi$
$233$	−1.01509	−	1.01509i	−0.0665008	−	0.0665008i	−0.739575	+	0.673074i	$0.764973\pi$
$234$		0			0
$235$	−15.0304	−	16.6722i	−0.980474	−	1.08758i
$236$		0			0
$237$	9.52821	−	20.4950i	0.618924	−	1.33129i
$238$		0			0
$239$	11.7980			0.763150			0.381575	−	0.924338i	$-0.375382\pi$
$239$	11.7980			0.763150			0.381575	+	0.924338i	$0.375382\pi$
$240$		0			0
$241$	−10.2831			−0.662395			−0.331197	−	0.943562i	$-0.607453\pi$
$241$	−10.2831			−0.662395			−0.331197	+	0.943562i	$0.607453\pi$
$242$		0			0
$243$	8.86735	−	12.8207i	0.568841	−	0.822448i
$244$		0			0
$245$	14.5708	+	0.754600i	0.930897	+	0.0482096i
$246$		0			0
$247$	−1.82480	−	1.82480i	−0.116109	−	0.116109i
$248$		0			0
$249$	9.20365	+	25.1963i	0.583258	+	1.59675i
$250$		0			0
$251$		−	11.8989i		−	0.751053i	−0.926812	−	0.375526i	$-0.877462\pi$
$251$		−	11.8989i		−	0.751053i	0.926812	−	0.375526i	$-0.122538\pi$
$252$		0			0
$253$	−3.83993	+	3.83993i	−0.241414	+	0.241414i
$254$		0			0
$255$	−3.14205	−	10.2125i	−0.196763	−	0.639529i
$256$		0			0
$257$	15.2707	−	15.2707i	0.952562	−	0.952562i	−0.0463623	−	0.998925i	$-0.514763\pi$
$257$	15.2707	−	15.2707i	0.952562	−	0.952562i	0.998925	+	0.0463623i	$0.0147629\pi$
$258$		0			0
$259$			0.331030i			0.0205692i
$260$		0			0
$261$	−0.972074	−	1.15306i	−0.0601699	−	0.0713725i
$262$		0			0
$263$	−16.7897	−	16.7897i	−1.03529	−	1.03529i	−0.999354	−	0.0359406i	$-0.988557\pi$
$263$	−16.7897	−	16.7897i	−1.03529	−	1.03529i	−0.0359406	−	0.999354i	$-0.511443\pi$
$264$		0			0
$265$	−17.8846	+	16.1234i	−1.09865	+	0.990454i
$266$		0			0
$267$	1.15780	+	0.538267i	0.0708565	+	0.0329414i
$268$		0			0
$269$	1.60643			0.0979458			0.0489729	−	0.998800i	$-0.484405\pi$
$269$	1.60643			0.0979458			0.0489729	+	0.998800i	$0.484405\pi$
$270$		0			0
$271$	0.893742			0.0542909			0.0271455	−	0.999631i	$-0.491358\pi$
$271$	0.893742			0.0542909			0.0271455	+	0.999631i	$0.491358\pi$
$272$		0			0
$273$	2.03173	+	0.944558i	0.122966	+	0.0571672i
$274$		0			0
$275$	2.80484	−	27.0071i	0.169138	−	1.62859i
$276$		0			0
$277$	−22.1959	−	22.1959i	−1.33362	−	1.33362i	−0.902103	−	0.431521i	$-0.857977\pi$
$277$	−22.1959	−	22.1959i	−1.33362	−	1.33362i	−0.431521	−	0.902103i	$-0.642023\pi$
$278$		0			0
$279$	−19.9979	−	23.7212i	−1.19724	−	1.42015i
$280$		0			0
$281$			23.4654i			1.39983i	0.714226	+	0.699916i	$0.246779\pi$
$281$			23.4654i			1.39983i	−0.714226	+	0.699916i	$0.753221\pi$
$282$		0			0
$283$	−7.33218	+	7.33218i	−0.435853	+	0.435853i	−0.890614	−	0.454761i	$-0.849725\pi$
$283$	−7.33218	+	7.33218i	−0.435853	+	0.435853i	0.454761	+	0.890614i	$0.349725\pi$
$284$		0			0
$285$	−4.70615	−	2.49162i	−0.278768	−	0.147591i
$286$		0			0
$287$	5.72270	−	5.72270i	0.337800	−	0.337800i
$288$		0			0
$289$			9.38889i			0.552287i
$290$		0			0
$291$	0.322678	+	0.883377i	0.0189157	+	0.0517845i
$292$		0			0
$293$	−4.65660	−	4.65660i	−0.272041	−	0.272041i	0.557880	−	0.829921i	$-0.311615\pi$
$293$	−4.65660	−	4.65660i	−0.272041	−	0.272041i	−0.829921	+	0.557880i	$0.811615\pi$
$294$		0			0
$295$	1.43912	−	27.7885i	0.0837888	−	1.61791i
$296$		0			0
$297$	27.2307	−	7.39756i	1.58008	−	0.429250i
$298$		0			0
$299$	1.87695			0.108547
$300$		0			0
$301$	−3.21607			−0.185371
$302$		0			0
$303$	9.86868	−	21.2274i	0.566941	−	1.21948i
$304$		0			0
$305$	0.0452187	−	0.873144i	0.00258922	−	0.0499961i
$306$		0			0
$307$	−2.85598	−	2.85598i	−0.162999	−	0.162999i	0.620895	−	0.783894i	$-0.286769\pi$
$307$	−2.85598	−	2.85598i	−0.162999	−	0.162999i	−0.783894	+	0.620895i	$0.786769\pi$
$308$		0			0
$309$	15.9152	−	5.81346i	0.905383	−	0.330716i
$310$		0			0
$311$			10.2612i			0.581860i	0.956744	+	0.290930i	$0.0939647\pi$
$311$			10.2612i			0.581860i	−0.956744	+	0.290930i	$0.906035\pi$
$312$		0			0
$313$	5.54456	−	5.54456i	0.313397	−	0.313397i	−0.532827	−	0.846224i	$-0.678870\pi$
$313$	5.54456	−	5.54456i	0.313397	−	0.313397i	0.846224	+	0.532827i	$0.178870\pi$
$314$		0			0
$315$	4.58014	+	0.630038i	0.258061	+	0.0354986i
$316$		0			0
$317$	−8.96233	+	8.96233i	−0.503374	+	0.503374i	−0.912485	−	0.409110i	$-0.865839\pi$
$317$	−8.96233	+	8.96233i	−0.503374	+	0.503374i	0.409110	+	0.912485i	$0.365839\pi$
$318$		0			0
$319$		−	2.72997i		−	0.152849i
$320$		0			0
$321$	17.7173	−	6.47172i	0.988881	−	0.361216i
$322$		0			0
$323$	−2.68217	−	2.68217i	−0.149240	−	0.149240i
$324$		0			0
$325$	−7.28603	+	5.91503i	−0.404156	+	0.328107i
$326$		0			0
$327$	−9.47961	+	20.3905i	−0.524224	+	1.12760i
$328$		0			0
$329$	6.91862			0.381436
$330$		0			0
$331$	32.2067			1.77024			0.885120	−	0.465362i	$-0.154076\pi$
$331$	32.2067			1.77024			0.885120	+	0.465362i	$0.154076\pi$
$332$		0			0
$333$	0.122273	−	1.43574i	0.00670053	−	0.0786782i
$334$		0			0
$335$	−18.1844	+	16.3937i	−0.993521	+	0.895682i
$336$		0			0
$337$	7.35004	+	7.35004i	0.400382	+	0.400382i	0.878368	−	0.477986i	$-0.158633\pi$
$337$	7.35004	+	7.35004i	0.400382	+	0.400382i	−0.477986	+	0.878368i	$0.658633\pi$
$338$		0			0
$339$	4.41521	+	12.0873i	0.239801	+	0.656491i
$340$		0			0
$341$		−	56.1620i		−	3.04134i
$342$		0			0
$343$	−6.59121	+	6.59121i	−0.355892	+	0.355892i
$344$		0			0
$345$	3.70174	−	1.13891i	0.199295	−	0.0613169i
$346$		0			0
$347$	9.26157	−	9.26157i	0.497187	−	0.497187i	−0.413374	−	0.910561i	$-0.635650\pi$
$347$	9.26157	−	9.26157i	0.497187	−	0.497187i	0.910561	+	0.413374i	$0.135650\pi$
$348$		0			0
$349$			22.6270i			1.21120i	0.795771	+	0.605598i	$0.207066\pi$
$349$			22.6270i			1.21120i	−0.795771	+	0.605598i	$0.792934\pi$
$350$		0			0
$351$	−8.46312	−	4.84720i	−0.451728	−	0.258724i
$352$		0			0
$353$	−0.949187	−	0.949187i	−0.0505201	−	0.0505201i	0.681395	−	0.731916i	$-0.261373\pi$
$353$	−0.949187	−	0.949187i	−0.0505201	−	0.0505201i	−0.731916	+	0.681395i	$0.761373\pi$
$354$		0			0
$355$	21.8944	+	1.13388i	1.16203	+	0.0601799i
$356$		0			0
$357$	2.98632	+	1.38835i	0.158053	+	0.0734793i
$358$		0			0
$359$	7.58292			0.400211			0.200106	−	0.979774i	$-0.435871\pi$
$359$	7.58292			0.400211			0.200106	+	0.979774i	$0.435871\pi$
$360$		0			0
$361$	17.1096			0.900505
$362$		0			0
$363$	29.0409	+	13.5012i	1.52425	+	0.708629i
$364$		0			0
$365$	−8.91572	−	9.88962i	−0.466670	−	0.517646i
$366$		0			0
$367$	9.02010	+	9.02010i	0.470846	+	0.470846i	0.902188	−	0.431343i	$-0.141960\pi$
$367$	9.02010	+	9.02010i	0.470846	+	0.470846i	−0.431343	+	0.902188i	$0.641960\pi$
$368$		0			0
$369$	−26.9343	+	22.7067i	−1.40214	+	1.18206i
$370$		0			0
$371$		−	7.42175i		−	0.385318i
$372$		0			0
$373$	17.1625	−	17.1625i	0.888643	−	0.888643i	−0.105750	−	0.994393i	$-0.533724\pi$
$373$	17.1625	−	17.1625i	0.888643	−	0.888643i	0.994393	+	0.105750i	$0.0337244\pi$
$374$		0			0
$375$	−10.7804	+	16.0867i	−0.556697	+	0.830715i
$376$		0			0
$377$	−0.667202	+	0.667202i	−0.0343626	+	0.0343626i
$378$		0			0
$379$			34.8380i			1.78951i	0.446559	+	0.894754i	$0.352649\pi$
$379$			34.8380i			1.78951i	−0.446559	+	0.894754i	$0.647351\pi$
$380$		0			0
$381$	5.22575	+	14.3063i	0.267723	+	0.732931i
$382$		0			0
$383$	8.38826	+	8.38826i	0.428620	+	0.428620i	0.888158	−	0.459538i	$-0.151985\pi$
$383$	8.38826	+	8.38826i	0.428620	+	0.428620i	−0.459538	+	0.888158i	$0.651985\pi$
$384$		0			0
$385$	5.60370	+	6.21581i	0.285591	+	0.316787i
$386$		0			0
$387$	13.9487	+	1.18793i	0.709054	+	0.0603857i
$388$		0			0
$389$	3.62136			0.183610			0.0918051	−	0.995777i	$-0.470736\pi$
$389$	3.62136			0.183610			0.0918051	+	0.995777i	$0.470736\pi$
$390$		0			0
$391$	2.75882			0.139520
$392$		0			0
$393$	−1.29080	+	2.77649i	−0.0651123	+	0.140056i
$394$		0			0
$395$	−29.1395	−	1.50909i	−1.46617	−	0.0759304i
$396$		0			0
$397$	−5.36228	−	5.36228i	−0.269125	−	0.269125i	0.559622	−	0.828748i	$-0.310946\pi$
$397$	−5.36228	−	5.36228i	−0.269125	−	0.269125i	−0.828748	+	0.559622i	$0.810946\pi$
$398$		0			0
$399$	1.54164	−	0.563127i	0.0771786	−	0.0281916i
$400$		0			0
$401$			1.28350i			0.0640951i	0.999486	+	0.0320476i	$0.0102028\pi$
$401$			1.28350i			0.0640951i	−0.999486	+	0.0320476i	$0.989797\pi$
$402$		0			0
$403$	−13.7260	+	13.7260i	−0.683739	+	0.683739i
$404$		0			0
$405$	−19.6322	−	4.42437i	−0.975534	−	0.219849i
$406$		0			0
$407$	1.84437	−	1.84437i	0.0914220	−	0.0914220i
$408$		0			0
$409$			9.38788i			0.464201i	0.972692	+	0.232100i	$0.0745598\pi$
$409$			9.38788i			0.464201i	−0.972692	+	0.232100i	$0.925440\pi$
$410$		0			0
$411$	19.7063	−	7.19825i	0.972038	−	0.355064i
$412$		0			0
$413$	6.06441	+	6.06441i	0.298410	+	0.298410i
$414$		0			0
$415$	25.7211	−	23.1882i	1.26260	−	1.13826i
$416$		0			0
$417$	3.22176	−	6.92995i	0.157770	−	0.339361i
$418$		0			0
$419$	−2.81130			−0.137341			−0.0686704	−	0.997639i	$-0.521876\pi$
$419$	−2.81130			−0.137341			−0.0686704	+	0.997639i	$0.521876\pi$
$420$		0			0
$421$	−16.1992			−0.789501			−0.394750	−	0.918788i	$-0.629169\pi$
$421$	−16.1992			−0.789501			−0.394750	+	0.918788i	$0.629169\pi$
$422$		0			0
$423$	−30.0074	−	2.55554i	−1.45901	−	0.124255i
$424$		0			0
$425$	−10.7093	+	8.69416i	−0.519478	+	0.421729i
$426$		0			0
$427$	0.190551	+	0.190551i	0.00922139	+	0.00922139i
$428$		0			0
$429$	−6.05729	−	16.5827i	−0.292449	−	0.800620i
$430$		0			0
$431$			37.3260i			1.79793i	0.438019	+	0.898966i	$0.355680\pi$
$431$			37.3260i			1.79793i	−0.438019	+	0.898966i	$0.644320\pi$
$432$		0			0
$433$	22.9782	−	22.9782i	1.10426	−	1.10426i	0.110371	−	0.993890i	$-0.464796\pi$
$433$	22.9782	−	22.9782i	1.10426	−	1.10426i	0.993890	−	0.110371i	$-0.0352038\pi$
$434$		0			0
$435$	−0.911011	+	1.72071i	−0.0436796	+	0.0825017i
$436$		0			0
$437$	0.972214	−	0.972214i	0.0465073	−	0.0465073i
$438$		0			0
$439$			37.5015i			1.78985i	0.446219	+	0.894924i	$0.352770\pi$
$439$			37.5015i			1.78985i	−0.446219	+	0.894924i	$0.647230\pi$
$440$		0			0
$441$	14.9663	−	12.6172i	0.712679	−	0.600817i
$442$		0			0
$443$	14.1195	+	14.1195i	0.670836	+	0.670836i	0.957909	−	0.287073i	$-0.0926821\pi$
$443$	14.1195	+	14.1195i	0.670836	+	0.670836i	−0.287073	+	0.957909i	$0.592682\pi$
$444$		0			0
$445$	0.0852513	−	1.64615i	0.00404130	−	0.0780349i
$446$		0			0
$447$	12.9539	+	6.02232i	0.612699	+	0.284846i
$448$		0			0
$449$	9.65812			0.455795			0.227897	−	0.973685i	$-0.426815\pi$
$449$	9.65812			0.455795			0.227897	+	0.973685i	$0.426815\pi$
$450$		0			0
$451$	−63.7693			−3.00278
$452$		0			0
$453$	18.1076	+	8.41827i	0.850768	+	0.395525i
$454$		0			0
$455$	0.149600	−	2.88868i	0.00701336	−	0.135423i
$456$		0			0
$457$	22.6672	+	22.6672i	1.06033	+	1.06033i	0.998060	+	0.0622659i	$0.0198327\pi$
$457$	22.6672	+	22.6672i	1.06033	+	1.06033i	0.0622659	+	0.998060i	$0.480167\pi$
$458$		0			0
$459$	−12.4394	−	7.12462i	−0.580624	−	0.332549i
$460$		0			0
$461$		−	10.9774i		−	0.511268i	−0.966774	−	0.255634i	$-0.917716\pi$
$461$		−	10.9774i		−	0.511268i	0.966774	−	0.255634i	$-0.0822842\pi$
$462$		0			0
$463$	3.41246	−	3.41246i	0.158590	−	0.158590i	−0.623351	−	0.781942i	$-0.714229\pi$
$463$	3.41246	−	3.41246i	0.158590	−	0.158590i	0.781942	+	0.623351i	$0.214229\pi$
$464$		0			0
$465$	−18.7417	+	35.3992i	−0.869126	+	1.64160i
$466$		0			0
$467$	−12.4955	+	12.4955i	−0.578222	+	0.578222i	−0.934413	−	0.356191i	$-0.884075\pi$
$467$	−12.4955	+	12.4955i	−0.578222	+	0.578222i	0.356191	+	0.934413i	$0.384075\pi$
$468$		0			0
$469$		−	7.54615i		−	0.348449i
$470$		0			0
$471$	−7.74781	−	21.2107i	−0.357000	−	0.977340i
$472$		0			0
$473$	17.9187	+	17.9187i	0.823902	+	0.823902i
$474$		0			0
$475$	−0.710143	+	6.83781i	−0.0325836	+	0.313740i
$476$		0			0
$477$	−2.74138	+	32.1896i	−0.125519	+	1.47386i
$478$		0			0
$479$	−21.0901			−0.963630			−0.481815	−	0.876273i	$-0.660022\pi$
$479$	−21.0901			−0.963630			−0.481815	+	0.876273i	$0.660022\pi$
$480$		0			0
$481$	−0.901525			−0.0411060
$482$		0			0
$483$	−0.503240	+	1.08246i	−0.0228982	+	0.0492537i
$484$		0			0
$485$	0.901777	−	0.812973i	0.0409476	−	0.0369152i
$486$		0			0
$487$	10.0481	+	10.0481i	0.455322	+	0.455322i	0.897116	−	0.441794i	$-0.145658\pi$
$487$	10.0481	+	10.0481i	0.455322	+	0.455322i	−0.441794	+	0.897116i	$0.645658\pi$
$488$		0			0
$489$	−16.1574	+	5.90194i	−0.730663	+	0.266895i
$490$		0			0
$491$			1.49925i			0.0676601i	0.999428	+	0.0338300i	$0.0107705\pi$
$491$			1.49925i			0.0676601i	−0.999428	+	0.0338300i	$0.989230\pi$
$492$		0			0
$493$	−0.980681	+	0.980681i	−0.0441677	+	0.0441677i
$494$		0			0
$495$	−22.0084	−	29.0291i	−0.989204	−	1.30476i
$496$		0			0
$497$	−4.77813	+	4.77813i	−0.214328	+	0.214328i
$498$		0			0
$499$			16.4046i			0.734370i	0.930148	+	0.367185i	$0.119678\pi$
$499$			16.4046i			0.734370i	−0.930148	+	0.367185i	$0.880322\pi$
$500$		0			0
$501$	31.2082	−	11.3997i	1.39428	−	0.509300i
$502$		0			0
$503$	0.758120	+	0.758120i	0.0338029	+	0.0338029i	0.723806	−	0.690003i	$-0.242391\pi$
$503$	0.758120	+	0.758120i	0.0338029	+	0.0338029i	−0.690003	+	0.723806i	$0.742391\pi$
$504$		0			0
$505$	−30.1807	−	1.56301i	−1.34303	−	0.0695531i
$506$		0			0
$507$	6.91999	−	14.8848i	0.307328	−	0.661057i
$508$		0			0
$509$	29.4163			1.30386			0.651928	−	0.758281i	$-0.273960\pi$
$509$	29.4163			1.30386			0.651928	+	0.758281i	$0.273960\pi$
$510$		0			0
$511$	4.10398			0.181550
$512$		0			0
$513$	−6.89440	+	1.87295i	−0.304395	+	0.0826929i
$514$		0			0
$515$	−14.6468	−	16.2467i	−0.645413	−	0.715914i
$516$		0			0
$517$	−38.5478	−	38.5478i	−1.69533	−	1.69533i
$518$		0			0
$519$	−4.07777	−	11.1635i	−0.178994	−	0.490022i
$520$		0			0
$521$			27.6239i			1.21022i	0.796140	+	0.605112i	$0.206872\pi$
$521$			27.6239i			1.21022i	−0.796140	+	0.605112i	$0.793128\pi$
$522$		0			0
$523$	28.2518	−	28.2518i	1.23536	−	1.23536i	0.273488	−	0.961875i	$-0.411823\pi$
$523$	28.2518	−	28.2518i	1.23536	−	1.23536i	0.961875	−	0.273488i	$-0.0881773\pi$
$524$		0			0
$525$	−1.45777	−	5.78785i	−0.0636223	−	0.252603i
$526$		0			0
$527$	−20.1750	+	20.1750i	−0.878837	+	0.878837i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	−24.0625	−	28.5426i	−1.04423	−	1.23864i
$532$		0			0
$533$	15.5852	+	15.5852i	0.675068	+	0.675068i
$534$		0			0
$535$	−16.3052	−	18.0863i	−0.704936	−	0.781939i
$536$		0			0
$537$	−35.3746	−	16.4458i	−1.52653	−	0.709688i
$538$		0			0
$539$	35.4339			1.52625
$540$		0			0
$541$	−18.5842			−0.798995			−0.399498	−	0.916734i	$-0.630815\pi$
$541$	−18.5842			−0.798995			−0.399498	+	0.916734i	$0.630815\pi$
$542$		0			0
$543$	5.78749	+	2.69062i	0.248365	+	0.115466i
$544$		0			0
$545$	28.9909	+	1.50139i	1.24183	+	0.0643125i
$546$		0			0
$547$	28.2988	+	28.2988i	1.20997	+	1.20997i	0.971036	+	0.238932i	$0.0767974\pi$
$547$	28.2988	+	28.2988i	1.20997	+	1.20997i	0.238932	+	0.971036i	$0.423203\pi$
$548$		0			0
$549$	−0.756072	−	0.896840i	−0.0322684	−	0.0382762i
$550$		0			0
$551$			0.691187i			0.0294456i
$552$		0			0
$553$	6.35926	−	6.35926i	0.270423	−	0.270423i
$554$		0			0
$555$	−1.77800	+	0.547034i	−0.0754717	+	0.0232203i
$556$		0			0
$557$	−17.7309	+	17.7309i	−0.751284	+	0.751284i	−0.974719	−	0.223435i	$-0.928273\pi$
$557$	−17.7309	+	17.7309i	−0.751284	+	0.751284i	0.223435	+	0.974719i	$0.428273\pi$
$558$		0			0
$559$		−	8.75863i		−	0.370451i
$560$		0			0
$561$	−8.90326	−	24.3740i	−0.375896	−	1.02907i
$562$		0			0
$563$	−13.9647	−	13.9647i	−0.588542	−	0.588542i	0.348694	−	0.937236i	$-0.386625\pi$
$563$	−13.9647	−	13.9647i	−0.588542	−	0.588542i	−0.937236	+	0.348694i	$0.886625\pi$
$564$		0			0
$565$	12.3390	−	11.1239i	0.519108	−	0.467988i
$566$		0			0
$567$	5.06453	−	3.58117i	0.212690	−	0.150395i
$568$		0			0
$569$	−41.9194			−1.75735			−0.878677	−	0.477417i	$-0.841573\pi$
$569$	−41.9194			−1.75735			−0.878677	+	0.477417i	$0.841573\pi$
$570$		0			0
$571$	40.9292			1.71283			0.856417	−	0.516285i	$-0.172685\pi$
$571$	40.9292			1.71283			0.856417	+	0.516285i	$0.172685\pi$
$572$		0			0
$573$	−8.58433	+	18.4648i	−0.358616	+	0.771376i
$574$		0			0
$575$	−3.15140	−	3.88184i	−0.131422	−	0.161884i
$576$		0			0
$577$	−16.0638	−	16.0638i	−0.668747	−	0.668747i	0.288679	−	0.957426i	$-0.406784\pi$
$577$	−16.0638	−	16.0638i	−0.668747	−	0.668747i	−0.957426	+	0.288679i	$0.906784\pi$
$578$		0			0
$579$	−17.4346	+	6.36845i	−0.724556	+	0.264664i
$580$		0			0
$581$			10.6737i			0.442821i
$582$		0			0
$583$	−41.3511	+	41.3511i	−1.71259	+	1.71259i
$584$		0			0
$585$	−1.71584	+	12.4735i	−0.0709413	+	0.515716i
$586$		0			0
$587$	−22.3462	+	22.3462i	−0.922326	+	0.922326i	−0.997193	−	0.0748676i	$-0.976147\pi$
$587$	−22.3462	+	22.3462i	−0.922326	+	0.922326i	0.0748676	+	0.997193i	$0.476147\pi$
$588$		0			0
$589$			14.2194i			0.585900i
$590$		0			0
$591$	−4.02906	+	1.47173i	−0.165734	+	0.0605387i
$592$		0			0
$593$	−26.2111	−	26.2111i	−1.07636	−	1.07636i	−0.996833	−	0.0795297i	$-0.974658\pi$
$593$	−26.2111	−	26.2111i	−1.07636	−	1.07636i	−0.0795297	−	0.996833i	$-0.525342\pi$
$594$		0			0
$595$	0.219889	−	4.24590i	0.00901455	−	0.174065i
$596$		0			0
$597$	6.24844	−	13.4403i	0.255731	−	0.550074i
$598$		0			0
$599$	21.3581			0.872669			0.436334	−	0.899785i	$-0.356276\pi$
$599$	21.3581			0.872669			0.436334	+	0.899785i	$0.356276\pi$
$600$		0			0
$601$	28.0092			1.14252			0.571259	−	0.820770i	$-0.306455\pi$
$601$	28.0092			1.14252			0.571259	+	0.820770i	$0.306455\pi$
$602$		0			0
$603$	−2.78733	+	32.7292i	−0.113509	+	1.33283i
$604$		0			0
$605$	2.13833	−	41.2898i	0.0869357	−	1.67867i
$606$		0			0
$607$	−11.7422	−	11.7422i	−0.476603	−	0.476603i	0.427440	−	0.904044i	$-0.359415\pi$
$607$	−11.7422	−	11.7422i	−0.476603	−	0.476603i	−0.904044	+	0.427440i	$0.859415\pi$
$608$		0			0
$609$	−0.205896	−	0.563670i	−0.00834333	−	0.0228411i
$610$		0			0
$611$			18.8421i			0.762271i
$612$		0			0
$613$	29.3491	−	29.3491i	1.18540	−	1.18540i	0.207072	−	0.978326i	$-0.433607\pi$
$613$	29.3491	−	29.3491i	1.18540	−	1.18540i	0.978326	−	0.207072i	$-0.0663934\pi$
$614$		0			0
$615$	40.1941	+	21.2803i	1.62078	+	0.858105i
$616$		0			0
$617$	2.52626	−	2.52626i	0.101703	−	0.101703i	−0.654424	−	0.756128i	$-0.727089\pi$
$617$	2.52626	−	2.52626i	0.101703	−	0.101703i	0.756128	+	0.654424i	$0.227089\pi$
$618$		0			0
$619$		−	10.2265i		−	0.411037i	−0.978653	−	0.205518i	$-0.934112\pi$
$619$		−	10.2265i		−	0.411037i	0.978653	−	0.205518i	$-0.0658880\pi$
$620$		0			0
$621$	2.58248	−	4.50897i	0.103631	−	0.180939i
$622$		0			0
$623$	0.359247	+	0.359247i	0.0143929	+	0.0143929i
$624$		0			0
$625$	24.4665	+	5.13736i	0.978658	+	0.205494i
$626$		0			0
$627$	−11.7269	−	5.45190i	−0.468329	−	0.217728i
$628$		0			0
$629$	−1.32510			−0.0528352
$630$		0			0
$631$	−1.94592			−0.0774657			−0.0387328	−	0.999250i	$-0.512332\pi$
$631$	−1.94592			−0.0774657			−0.0387328	+	0.999250i	$0.512332\pi$
$632$		0			0
$633$	3.80074	+	1.76698i	0.151066	+	0.0702310i
$634$		0			0
$635$	14.6042	−	13.1661i	0.579552	−	0.522479i
$636$		0			0
$637$	−8.66003	−	8.66003i	−0.343123	−	0.343123i
$638$		0			0
$639$	22.4886	−	18.9588i	0.889635	−	0.749998i
$640$		0			0
$641$			23.0657i			0.911039i	0.890226	+	0.455519i	$0.150546\pi$
$641$			23.0657i			0.911039i	−0.890226	+	0.455519i	$0.849454\pi$
$642$		0			0
$643$	−6.46011	+	6.46011i	−0.254762	+	0.254762i	−0.822920	−	0.568158i	$-0.807656\pi$
$643$	−6.46011	+	6.46011i	−0.254762	+	0.254762i	0.568158	+	0.822920i	$0.307656\pi$
$644$		0			0
$645$	−5.31462	−	17.2738i	−0.209263	−	0.680157i
$646$		0			0
$647$	−22.5825	+	22.5825i	−0.887811	+	0.887811i	−0.994313	−	0.106502i	$-0.966035\pi$
$647$	−22.5825	+	22.5825i	−0.887811	+	0.887811i	0.106502	+	0.994313i	$0.466035\pi$
$648$		0			0
$649$		−	67.5771i		−	2.65263i
$650$		0			0
$651$	−4.23578	−	11.5961i	−0.166013	−	0.454486i
$652$		0			0
$653$	22.7937	+	22.7937i	0.891988	+	0.891988i	0.994710	−	0.102722i	$-0.0327552\pi$
$653$	22.7937	+	22.7937i	0.891988	+	0.891988i	−0.102722	+	0.994710i	$0.532755\pi$
$654$		0			0
$655$	3.94757	+	0.204439i	0.154244	+	0.00798807i
$656$		0			0
$657$	−17.7998	−	1.51590i	−0.694436	−	0.0591407i
$658$		0			0
$659$	7.42769			0.289342			0.144671	−	0.989480i	$-0.453788\pi$
$659$	7.42769			0.289342			0.144671	+	0.989480i	$0.453788\pi$
$660$		0			0
$661$	−9.28586			−0.361178			−0.180589	−	0.983559i	$-0.557800\pi$
$661$	−9.28586			−0.361178			−0.180589	+	0.983559i	$0.557800\pi$
$662$		0			0
$663$	−3.78103	+	8.13293i	−0.146843	+	0.315857i
$664$		0			0
$665$	−1.41877	−	1.57375i	−0.0550177	−	0.0610275i
$666$		0			0
$667$	−0.355471	−	0.355471i	−0.0137639	−	0.0137639i
$668$		0			0
$669$	−42.2808	+	15.4442i	−1.63467	+	0.597109i
$670$		0			0
$671$		−	2.12335i		−	0.0819709i
$672$		0			0
$673$	−15.2296	+	15.2296i	−0.587058	+	0.587058i	−0.936833	−	0.349776i	$-0.886258\pi$
$673$	−15.2296	+	15.2296i	−0.587058	+	0.587058i	0.349776	+	0.936833i	$0.386258\pi$
$674$		0			0
$675$	4.18477	+	25.6415i	0.161072	+	0.986943i
$676$		0			0
$677$	−2.26932	+	2.26932i	−0.0872171	+	0.0872171i	−0.749369	−	0.662152i	$-0.769643\pi$
$677$	−2.26932	+	2.26932i	−0.0872171	+	0.0872171i	0.662152	+	0.749369i	$0.269643\pi$
$678$		0			0
$679$			0.374218i			0.0143612i
$680$		0			0
$681$	−32.1239	+	11.7341i	−1.23099	+	0.449653i
$682$		0			0
$683$	28.4712	+	28.4712i	1.08942	+	1.08942i	0.995588	+	0.0938301i	$0.0299111\pi$
$683$	28.4712	+	28.4712i	1.08942	+	1.08942i	0.0938301	+	0.995588i	$0.470089\pi$
$684$		0			0
$685$	−18.1357	−	20.1167i	−0.692929	−	0.768620i
$686$		0			0
$687$	0.473836	−	1.01921i	0.0180780	−	0.0388854i
$688$		0			0
$689$	20.2124			0.770029
$690$		0			0
$691$	−2.57058			−0.0977894			−0.0488947	−	0.998804i	$-0.515570\pi$
$691$	−2.57058			−0.0977894			−0.0488947	+	0.998804i	$0.515570\pi$
$692$		0			0
$693$	11.1875	+	0.952768i	0.424978	+	0.0361927i
$694$		0			0
$695$	−9.85289	−	0.510266i	−0.373742	−	0.0193555i
$696$		0			0
$697$	22.9077	+	22.9077i	0.867693	+	0.867693i
$698$		0			0
$699$	0.853113	+	2.33552i	0.0322677	+	0.0883374i
$700$		0			0
$701$		−	31.8570i		−	1.20322i	−0.798789	−	0.601611i	$-0.794526\pi$
$701$		−	31.8570i		−	1.20322i	0.798789	−	0.601611i	$-0.205474\pi$
$702$		0			0
$703$	−0.466967	+	0.466967i	−0.0176120	+	0.0176120i
$704$		0			0
$705$	11.4332	+	37.1606i	0.430598	+	1.39955i
$706$		0			0
$707$	6.58649	−	6.58649i	0.247711	−	0.247711i
$708$		0			0
$709$			7.58040i			0.284688i	0.989817	+	0.142344i	$0.0454639\pi$
$709$			7.58040i			0.284688i	−0.989817	+	0.142344i	$0.954536\pi$
$710$		0			0
$711$	−29.9303	+	25.2324i	−1.12247	+	0.946290i
$712$		0			0
$713$	−7.31290	−	7.31290i	−0.273870	−	0.273870i
$714$		0			0
$715$	−16.9281	+	15.2611i	−0.633075	+	0.570732i
$716$		0			0
$717$	−18.5301	−	8.61472i	−0.692020	−	0.321723i
$718$		0			0
$719$	−26.9617			−1.00550			−0.502750	−	0.864432i	$-0.667679\pi$
$719$	−26.9617			−1.00550			−0.502750	+	0.864432i	$0.667679\pi$
$720$		0			0
$721$	6.74202			0.251086
$722$		0			0
$723$	16.1508	+	7.50858i	0.600656	+	0.279247i
$724$		0			0
$725$	2.50011	+	0.259650i	0.0928518	+	0.00964315i
$726$		0			0
$727$	−7.01344	−	7.01344i	−0.260114	−	0.260114i	0.564986	−	0.825100i	$-0.308881\pi$
$727$	−7.01344	−	7.01344i	−0.260114	−	0.260114i	−0.825100	+	0.564986i	$0.808881\pi$
$728$		0			0
$729$	−23.2887	+	13.6616i	−0.862543	+	0.505984i
$730$		0			0
$731$		−	12.8738i		−	0.476155i
$732$		0			0
$733$	−6.50240	+	6.50240i	−0.240172	+	0.240172i	−0.816921	−	0.576749i	$-0.804321\pi$
$733$	−6.50240	+	6.50240i	−0.240172	+	0.240172i	0.576749	+	0.816921i	$0.304321\pi$
$734$		0			0
$735$	−22.3342	−	11.8246i	−0.823808	−	0.436156i
$736$		0			0
$737$	−42.0442	+	42.0442i	−1.54872	+	1.54872i
$738$		0			0
$739$		−	36.5707i		−	1.34528i	−0.739972	−	0.672638i	$-0.765161\pi$
$739$		−	36.5707i		−	1.34528i	0.739972	−	0.672638i	$-0.234839\pi$
$740$		0			0
$741$	1.53362	+	4.19849i	0.0563388	+	0.154236i
$742$		0			0
$743$	−21.8635	−	21.8635i	−0.802092	−	0.802092i	0.181330	−	0.983422i	$-0.441960\pi$
$743$	−21.8635	−	21.8635i	−0.802092	−	0.802092i	−0.983422	+	0.181330i	$0.941960\pi$
$744$		0			0
$745$	0.953822	−	18.4177i	0.0349453	−	0.674772i
$746$		0			0
$747$	3.94257	−	46.2941i	0.144251	−	1.69381i
$748$		0			0
$749$	7.50543			0.274242
$750$		0			0
$751$	27.6083			1.00744			0.503720	−	0.863867i	$-0.331964\pi$
$751$	27.6083			1.00744			0.503720	+	0.863867i	$0.331964\pi$
$752$		0			0
$753$	−8.68840	+	18.6886i	−0.316623	+	0.681051i
$754$		0			0
$755$	1.33329	−	25.7450i	0.0485236	−	0.936958i
$756$		0			0
$757$	−18.7617	−	18.7617i	−0.681906	−	0.681906i	0.278524	−	0.960429i	$-0.410155\pi$
$757$	−18.7617	−	18.7617i	−0.681906	−	0.681906i	−0.960429	+	0.278524i	$0.910155\pi$
$758$		0			0
$759$	8.83491	−	3.22719i	0.320687	−	0.117140i
$760$		0			0
$761$		−	1.42287i		−	0.0515790i	−0.999667	−	0.0257895i	$-0.991790\pi$
$761$		−	1.42287i		−	0.0515790i	0.999667	−	0.0257895i	$-0.00820996\pi$
$762$		0			0
$763$	−6.32682	+	6.32682i	−0.229046	+	0.229046i
$764$		0			0
$765$	−2.52202	+	18.3341i	−0.0911837	+	0.662871i
$766$		0			0
$767$	−16.5158	+	16.5158i	−0.596350	+	0.596350i
$768$		0			0
$769$		−	38.4186i		−	1.38541i	−0.721221	−	0.692705i	$-0.756419\pi$
$769$		−	38.4186i		−	1.38541i	0.721221	−	0.692705i	$-0.243581\pi$
$770$		0			0
$771$	−35.1349	+	12.8340i	−1.26535	+	0.462205i
$772$		0			0
$773$	5.86582	+	5.86582i	0.210979	+	0.210979i	0.804683	−	0.593704i	$-0.202335\pi$
$773$	5.86582	+	5.86582i	0.210979	+	0.210979i	−0.593704	+	0.804683i	$0.702335\pi$
$774$		0			0
$775$	51.4334	+	5.34163i	1.84754	+	0.191877i
$776$		0			0
$777$	0.241713	−	0.519921i	0.00867141	−	0.0186521i
$778$		0			0
$779$	16.1454			0.578470
$780$		0			0
$781$	53.2437			1.90521
$782$		0			0
$783$	0.684809	+	2.52080i	0.0244731	+	0.0900861i
$784$		0			0
$785$	−21.6525	+	19.5203i	−0.772812	+	0.696708i
$786$		0			0
$787$	26.8238	+	26.8238i	0.956167	+	0.956167i	0.999079	−	0.0429122i	$-0.0136636\pi$
$787$	26.8238	+	26.8238i	0.956167	+	0.956167i	−0.0429122	+	0.999079i	$0.513664\pi$
$788$		0			0
$789$	14.1105	+	38.6296i	0.502348	+	1.37525i
$790$		0			0
$791$			5.12044i			0.182062i
$792$		0			0
$793$	−0.518944	+	0.518944i	−0.0184283	+	0.0184283i
$794$		0			0
$795$	39.8630	−	12.2646i	1.41379	−	0.434980i
$796$		0			0
$797$	17.0179	−	17.0179i	0.602804	−	0.602804i	−0.338252	−	0.941056i	$-0.609836\pi$
$797$	17.0179	−	17.0179i	0.602804	−	0.602804i	0.941056	+	0.338252i	$0.109836\pi$
$798$		0			0
$799$			27.6950i			0.979777i
$800$		0			0
$801$	−1.42543	−	1.69082i	−0.0503651	−	0.0597422i
$802$		0			0
$803$	−22.8658	−	22.8658i	−0.806916	−	0.806916i
$804$		0			0
$805$	1.53903	+	0.0797037i	0.0542436	+	0.00280919i
$806$		0			0
$807$	−2.52308	−	1.17299i	−0.0888167	−	0.0412912i
$808$		0			0
$809$	32.2597			1.13419			0.567096	−	0.823652i	$-0.308067\pi$
$809$	32.2597			1.13419			0.567096	+	0.823652i	$0.308067\pi$
$810$		0			0
$811$	−21.6363			−0.759753			−0.379876	−	0.925037i	$-0.624033\pi$
$811$	−21.6363			−0.759753			−0.379876	+	0.925037i	$0.624033\pi$
$812$		0			0
$813$	−1.40372	−	0.652596i	−0.0492307	−	0.0228876i
$814$		0			0
$815$	14.8697	+	16.4939i	0.520862	+	0.577758i
$816$		0			0
$817$	−4.53675	−	4.53675i	−0.158721	−	0.158721i
$818$		0			0
$819$	−2.50136	−	2.96707i	−0.0874046	−	0.103678i
$820$		0			0
$821$			13.4641i			0.469901i	0.972007	+	0.234951i	$0.0754928\pi$
$821$			13.4641i			0.469901i	−0.972007	+	0.234951i	$0.924507\pi$
$822$		0			0
$823$	−8.25526	+	8.25526i	−0.287760	+	0.287760i	−0.836194	−	0.548434i	$-0.815224\pi$
$823$	−8.25526	+	8.25526i	−0.287760	+	0.287760i	0.548434	+	0.836194i	$0.315224\pi$
$824$		0			0
$825$	−24.1255	+	40.3698i	−0.839943	+	1.40550i
$826$		0			0
$827$	2.97743	−	2.97743i	0.103536	−	0.103536i	−0.653441	−	0.756977i	$-0.726675\pi$
$827$	2.97743	−	2.97743i	0.103536	−	0.103536i	0.756977	+	0.653441i	$0.226675\pi$
$828$		0			0
$829$			26.2712i			0.912437i	0.889868	+	0.456219i	$0.150797\pi$
$829$			26.2712i			0.912437i	−0.889868	+	0.456219i	$0.849203\pi$
$830$		0			0
$831$	18.6541	+	51.0684i	0.647105	+	1.77154i
$832$		0			0
$833$	−12.7289	−	12.7289i	−0.441030	−	0.441030i
$834$		0			0
$835$	−28.7210	−	31.8583i	−0.993930	−	1.10250i
$836$		0			0
$837$	14.0882	+	51.8590i	0.486959	+	1.79251i
$838$		0			0
$839$	16.4407			0.567595			0.283797	−	0.958884i	$-0.408406\pi$
$839$	16.4407			0.567595			0.283797	+	0.958884i	$0.408406\pi$
$840$		0			0
$841$	−28.7473			−0.991286
$842$		0			0
$843$	17.1341	−	36.8552i	0.590130	−	1.26936i
$844$		0			0
$845$	−21.1630	−	1.09600i	−0.728028	−	0.0377034i
$846$		0			0
$847$	9.01089	+	9.01089i	0.309618	+	0.309618i
$848$		0			0
$849$	16.8699	−	6.16218i	0.578972	−	0.211486i
$850$		0			0
$851$		−	0.480313i		−	0.0164649i
$852$		0			0
$853$	−10.6096	+	10.6096i	−0.363267	+	0.363267i	−0.865014	−	0.501747i	$-0.832691\pi$
$853$	−10.6096	+	10.6096i	−0.363267	+	0.363267i	0.501747	+	0.865014i	$0.332691\pi$
$854$		0			0
$855$	5.57220	+	7.34973i	0.190565	+	0.251355i
$856$		0			0
$857$	28.1041	−	28.1041i	0.960017	−	0.960017i	−0.0392137	−	0.999231i	$-0.512485\pi$
$857$	28.1041	−	28.1041i	0.960017	−	0.960017i	0.999231	+	0.0392137i	$0.0124853\pi$
$858$		0			0
$859$		−	11.0079i		−	0.375583i	−0.982209	−	0.187792i	$-0.939867\pi$
$859$		−	11.0079i		−	0.375583i	0.982209	−	0.187792i	$-0.0601330\pi$
$860$		0			0
$861$	−13.1668	+	4.80953i	−0.448723	+	0.163908i
$862$		0			0
$863$	−28.2772	−	28.2772i	−0.962569	−	0.962569i	0.0367556	−	0.999324i	$-0.488298\pi$
$863$	−28.2772	−	28.2772i	−0.962569	−	0.962569i	−0.999324	+	0.0367556i	$0.988298\pi$
$864$		0			0
$865$	−11.3960	+	10.2738i	−0.387476	+	0.349318i
$866$		0			0
$867$	6.85562	−	14.7463i	0.232829	−	0.500811i
$868$		0			0
$869$	−70.8626			−2.40385
$870$		0			0
$871$	20.5511			0.696349
$872$		0			0
$873$	0.138226	−	1.62306i	0.00467823	−	0.0549322i
$874$		0			0
$875$	−6.22543	+	4.54069i	−0.210458	+	0.153503i
$876$		0			0
$877$	18.6847	+	18.6847i	0.630938	+	0.630938i	0.948303	−	0.317365i	$-0.102798\pi$
$877$	18.6847	+	18.6847i	0.630938	+	0.630938i	−0.317365	+	0.948303i	$0.602798\pi$
$878$		0			0
$879$	3.91354	+	10.7139i	0.132001	+	0.361371i
$880$		0			0
$881$			14.6367i			0.493122i	0.969127	+	0.246561i	$0.0793005\pi$
$881$			14.6367i			0.493122i	−0.969127	+	0.246561i	$0.920699\pi$
$882$		0			0
$883$	23.5534	−	23.5534i	0.792634	−	0.792634i	−0.189287	−	0.981922i	$-0.560618\pi$
$883$	23.5534	−	23.5534i	0.792634	−	0.792634i	0.981922	+	0.189287i	$0.0606177\pi$
$884$		0			0
$885$	−22.5510	+	42.5941i	−0.758043	+	1.43179i
$886$		0			0
$887$	−24.8756	+	24.8756i	−0.835240	+	0.835240i	−0.988228	−	0.152988i	$-0.951110\pi$
$887$	−24.8756	+	24.8756i	−0.835240	+	0.835240i	0.152988	+	0.988228i	$0.451110\pi$
$888$		0			0
$889$			6.06045i			0.203261i
$890$		0			0
$891$	−48.1705	−	8.26469i	−1.61377	−	0.276878i
$892$		0			0
$893$	9.75974	+	9.75974i	0.326597	+	0.326597i
$894$		0			0
$895$	−2.60470	+	50.2950i	−0.0870655	+	1.68118i
$896$		0			0
$897$	−2.94797	−	1.37052i	−0.0984298	−	0.0457604i
$898$		0			0
$899$	5.19904			0.173398
$900$		0			0
$901$	29.7090			0.989750
$902$		0			0
$903$	5.05121	+	2.34833i	0.168094	+	0.0781474i
$904$		0			0
$905$	0.426144	−	8.22856i	0.0141655	−	0.273526i
$906$		0			0
$907$	14.3814	+	14.3814i	0.477525	+	0.477525i	0.904339	−	0.426814i	$-0.140364\pi$
$907$	14.3814	+	14.3814i	0.477525	+	0.477525i	−0.426814	+	0.904339i	$0.640364\pi$
$908$		0			0
$909$	−30.9998	+	26.1341i	−1.02820	+	0.866812i
$910$		0			0
$911$			41.4243i			1.37245i	0.727390	+	0.686224i	$0.240733\pi$
$911$			41.4243i			1.37245i	−0.727390	+	0.686224i	$0.759267\pi$
$912$		0			0
$913$	59.4698	−	59.4698i	1.96816	−	1.96816i
$914$		0			0
$915$	−0.708578	+	1.33836i	−0.0234249	+	0.0442447i
$916$		0			0
$917$	−0.861499	+	0.861499i	−0.0284492	+	0.0284492i
$918$		0			0
$919$		−	39.8812i		−	1.31556i	−0.753210	−	0.657780i	$-0.771495\pi$
$919$		−	39.8812i		−	1.31556i	0.753210	−	0.657780i	$-0.228505\pi$
$920$		0			0
$921$	2.40025	+	6.57104i	0.0790910	+	0.216523i
$922$		0			0
$923$	−13.0127	−	13.0127i	−0.428319	−	0.428319i
$924$		0			0
$925$	1.51366	+	1.86450i	0.0497688	+	0.0613044i
$926$		0			0
$927$	−29.2415	−	2.49031i	−0.960417	−	0.0817926i
$928$		0			0
$929$	12.6973			0.416586			0.208293	−	0.978067i	$-0.433209\pi$
$929$	12.6973			0.416586			0.208293	+	0.978067i	$0.433209\pi$
$930$		0			0
$931$	−8.97135			−0.294024
$932$		0			0
$933$	7.49258	−	16.1164i	0.245296	−	0.527628i
$934$		0			0
$935$	−24.8817	+	22.4314i	−0.813717	+	0.733585i
$936$		0			0
$937$	−7.87724	−	7.87724i	−0.257338	−	0.257338i	0.566632	−	0.823971i	$-0.308246\pi$
$937$	−7.87724	−	7.87724i	−0.257338	−	0.257338i	−0.823971	+	0.566632i	$0.808246\pi$
$938$		0			0
$939$	−12.7569	+	4.65982i	−0.416307	+	0.152067i
$940$		0			0
$941$		−	23.1023i		−	0.753113i	−0.926394	−	0.376556i	$-0.877108\pi$
$941$		−	23.1023i		−	0.753113i	0.926394	−	0.376556i	$-0.122892\pi$
$942$		0			0
$943$	−8.30344	+	8.30344i	−0.270397	+	0.270397i
$944$		0			0
$945$	−6.73359	−	4.33389i	−0.219044	−	0.140981i
$946$		0			0
$947$	13.9428	−	13.9428i	0.453079	−	0.453079i	−0.443296	−	0.896375i	$-0.646191\pi$
$947$	13.9428	−	13.9428i	0.453079	−	0.453079i	0.896375	+	0.443296i	$0.146191\pi$
$948$		0			0
$949$			11.1768i			0.362813i
$950$		0			0
$951$	20.6205	−	7.53221i	0.668666	−	0.244249i
$952$		0			0
$953$	−21.4710	−	21.4710i	−0.695514	−	0.695514i	0.267925	−	0.963440i	$-0.413662\pi$
$953$	−21.4710	−	21.4710i	−0.695514	−	0.695514i	−0.963440	+	0.267925i	$0.913662\pi$
$954$		0			0
$955$	26.2529	+	1.35960i	0.849524	+	0.0439955i
$956$		0			0
$957$	−1.99338	+	4.28772i	−0.0644368	+	0.138602i
$958$		0			0
$959$	8.34801			0.269571
$960$		0			0
$961$	75.9569			2.45022
$962$		0			0
$963$	−32.5525	−	2.77229i	−1.04899	−	0.0893359i
$964$		0			0
$965$	16.0450	+	17.7977i	0.516508	+	0.572928i
$966$		0			0
$967$	15.7964	+	15.7964i	0.507977	+	0.507977i	0.913905	−	0.405928i	$-0.133052\pi$
$967$	15.7964	+	15.7964i	0.507977	+	0.507977i	−0.405928	+	0.913905i	$0.633052\pi$
$968$		0			0
$969$	2.25417	+	6.17113i	0.0724145	+	0.198245i
$970$		0			0
$971$		−	2.15190i		−	0.0690576i	−0.999404	−	0.0345288i	$-0.989007\pi$
$971$		−	2.15190i		−	0.0690576i	0.999404	−	0.0345288i	$-0.0109930\pi$
$972$		0			0
$973$	2.15025	−	2.15025i	0.0689337	−	0.0689337i
$974$		0			0
$975$	15.7626	−	3.97009i	0.504807	−	0.127144i
$976$		0			0
$977$	20.0570	−	20.0570i	0.641680	−	0.641680i	−0.309288	−	0.950968i	$-0.600091\pi$
$977$	20.0570	−	20.0570i	0.641680	−	0.641680i	0.950968	+	0.309288i	$0.100091\pi$
$978$		0			0
$979$		−	4.00317i		−	0.127942i
$980$		0			0
$981$	29.7776	−	25.1037i	0.950726	−	0.801500i
$982$		0			0
$983$	13.8521	+	13.8521i	0.441812	+	0.441812i	0.892621	−	0.450808i	$-0.148864\pi$
$983$	13.8521	+	13.8521i	0.441812	+	0.441812i	−0.450808	+	0.892621i	$0.648864\pi$
$984$		0			0
$985$	3.70795	+	4.11299i	0.118145	+	0.131051i
$986$		0			0
$987$	−10.8665	−	5.05187i	−0.345884	−	0.160803i
$988$		0			0
$989$	4.66641			0.148383
$990$		0			0
$991$	−46.9182			−1.49040			−0.745202	−	0.666839i	$-0.767647\pi$
$991$	−46.9182			−1.49040			−0.745202	+	0.666839i	$0.767647\pi$
$992$		0			0
$993$	−50.5843	−	23.5168i	−1.60525	−	0.746284i
$994$		0			0
$995$	−19.1092	−	0.989634i	−0.605802	−	0.0313735i
$996$		0			0
$997$	−2.71029	−	2.71029i	−0.0858358	−	0.0858358i	0.662885	−	0.748721i	$-0.269332\pi$
$997$	−2.71029	−	2.71029i	−0.0858358	−	0.0858358i	−0.748721	+	0.662885i	$0.769332\pi$
$998$		0			0
$999$	−1.24040	+	2.16572i	−0.0392446	+	0.0685203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.4	✓	80
3.2	odd	2	inner	1380.2.r.c.737.23	yes	80
5.3	odd	4	inner	1380.2.r.c.1013.23	yes	80
15.8	even	4	inner	1380.2.r.c.1013.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.4	✓	80	1.1	even	1	trivial
1380.2.r.c.737.23	yes	80	3.2	odd	2	inner
1380.2.r.c.1013.4	yes	80	15.8	even	4	inner
1380.2.r.c.1013.23	yes	80	5.3	odd	4	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57061 - 0.730184i) q^{3} +(-0.115647 + 2.23308i) q^{5} +(-0.487335 - 0.487335i) q^{7} +(1.93366 + 2.29368i) q^{9} +O(q^{10})\)	\(q+(-1.57061 - 0.730184i) q^{3} +(-0.115647 + 2.23308i) q^{5} +(-0.487335 - 0.487335i) q^{7} +(1.93366 + 2.29368i) q^{9} +5.43048i q^{11} +(1.32721 - 1.32721i) q^{13} +(1.81219 - 3.42286i) q^{15} +(1.95078 - 1.95078i) q^{17} -1.37492i q^{19} +(0.409571 + 1.12126i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-4.97325 - 0.516499i) q^{25} +(-1.36223 - 5.01441i) q^{27} -0.502711 q^{29} -10.3420 q^{31} +(3.96525 - 8.52919i) q^{33} +(1.14462 - 1.03190i) q^{35} +(-0.339633 - 0.339633i) q^{37} +(-3.05363 + 1.11542i) q^{39} +11.7428i q^{41} +(3.29965 - 3.29965i) q^{43} +(-5.34558 + 4.05275i) q^{45} +(-7.09842 + 7.09842i) q^{47} -6.52501i q^{49} +(-4.48836 + 1.63950i) q^{51} +(7.61463 + 7.61463i) q^{53} +(-12.1267 - 0.628021i) q^{55} +(-1.00394 + 2.15947i) q^{57} -12.4440 q^{59} -0.391005 q^{61} +(0.175448 - 2.06013i) q^{63} +(2.81026 + 3.11724i) q^{65} +(7.74226 + 7.74226i) q^{67} +(-0.594274 - 1.62691i) q^{69} -9.80460i q^{71} +(-4.21064 + 4.21064i) q^{73} +(7.43392 + 4.44261i) q^{75} +(2.64646 - 2.64646i) q^{77} +13.0490i q^{79} +(-1.52191 + 8.87039i) q^{81} +(-10.9511 - 10.9511i) q^{83} +(4.13064 + 4.58185i) q^{85} +(0.789566 + 0.367072i) q^{87} -0.737166 q^{89} -1.29359 q^{91} +(16.2433 + 7.55157i) q^{93} +(3.07029 + 0.159006i) q^{95} +(-0.383944 - 0.383944i) q^{97} +(-12.4558 + 10.5007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 80 * q + 8 * q^3	\( 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) \) 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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