LMFDB - Embedded newform 1088.2.o.w.769.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1088,2,Mod(769,1088)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1088, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1088.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1088.o (of order $4$, degree $2$, not 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:	$8.68772373992$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 544)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			769.6
Root			$-0.204810 - 1.39930i$ of defining polynomial
Character	$\chi$	$=$	1088.769
Dual form			1088.2.o.w.897.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.08397 - 2.08397i) q^{3} +(-2.48929 + 2.48929i) q^{5} +(0.409620 + 0.409620i) q^{7} -5.68585i q^{9} +O(q^{10})$	\(q+(2.08397 - 2.08397i) q^{3} +(-2.48929 + 2.48929i) q^{5} +(0.409620 + 0.409620i) q^{7} -5.68585i q^{9} +(3.51325 + 3.51325i) q^{11} +4.68585 q^{13} +10.3752i q^{15} +(-2.19656 + 3.48929i) q^{17} +7.51663i q^{19} +1.70727 q^{21} +(-1.83890 - 1.83890i) q^{23} -7.39312i q^{25} +(-5.59722 - 5.59722i) q^{27} +(0.196558 - 0.196558i) q^{29} +(5.18760 - 5.18760i) q^{31} +14.6430 q^{33} -2.03932 q^{35} +(0.489289 - 0.489289i) q^{37} +(9.76515 - 9.76515i) q^{39} +(1.00000 + 1.00000i) q^{41} -2.52946i q^{43} +(14.1537 + 14.1537i) q^{45} +1.63848 q^{47} -6.66442i q^{49} +(2.69401 + 11.8491i) q^{51} +2.97858i q^{53} -17.4910 q^{55} +(15.6644 + 15.6644i) q^{57} -7.02650i q^{59} +(4.48929 + 4.48929i) q^{61} +(2.32903 - 2.32903i) q^{63} +(-11.6644 + 11.6644i) q^{65} -0.490134 q^{67} -7.66442 q^{69} +(-5.39680 + 5.39680i) q^{71} +(7.39312 - 7.39312i) q^{73} +(-15.4070 - 15.4070i) q^{75} +2.87819i q^{77} +(9.35553 + 9.35553i) q^{79} -6.27131 q^{81} -1.30937i q^{83} +(-3.21798 - 14.1537i) q^{85} -0.819240i q^{87} -0.335577 q^{89} +(1.91942 + 1.91942i) q^{91} -21.6216i q^{93} +(-18.7111 - 18.7111i) q^{95} +(1.29273 - 1.29273i) q^{97} +(19.9758 - 19.9758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 8 q^{13} - 8 q^{17} + 32 q^{21} - 16 q^{29} + 8 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} + 80 q^{57} + 24 q^{61} - 32 q^{65} + 16 q^{69} + 52 q^{73} - 4 q^{81} - 80 q^{85} - 112 q^{89} + 4 q^{97}+O(q^{100}) $ 12 * q + 8 * q^13 - 8 * q^17 + 32 * q^21 - 16 * q^29 + 8 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 + 80 * q^57 + 24 * q^61 - 32 * q^65 + 16 * q^69 + 52 * q^73 - 4 * q^81 - 80 * q^85 - 112 * q^89 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1088\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.08397	−	2.08397i	1.20318	−	1.20318i	0.229985	−	0.973194i	$-0.426132\pi$
$3$	2.08397	−	2.08397i	1.20318	−	1.20318i	0.973194	−	0.229985i	$-0.0738679\pi$
$4$		0			0
$5$	−2.48929	+	2.48929i	−1.11324	+	1.11324i	−0.120535	+	0.992709i	$0.538461\pi$
$5$	−2.48929	+	2.48929i	−1.11324	+	1.11324i	−0.992709	+	0.120535i	$0.961539\pi$
$6$		0			0
$7$	0.409620	+	0.409620i	0.154822	+	0.154822i	0.780268	−	0.625446i	$-0.215083\pi$
$7$	0.409620	+	0.409620i	0.154822	+	0.154822i	−0.625446	+	0.780268i	$0.715083\pi$
$8$		0			0
$9$		−	5.68585i		−	1.89528i
$10$		0			0
$11$	3.51325	+	3.51325i	1.05928	+	1.05928i	0.998128	+	0.0611564i	$0.0194789\pi$
$11$	3.51325	+	3.51325i	1.05928	+	1.05928i	0.0611564	+	0.998128i	$0.480521\pi$
$12$		0			0
$13$	4.68585			1.29962			0.649810	−	0.760097i	$-0.274848\pi$
$13$	4.68585			1.29962			0.649810	+	0.760097i	$0.274848\pi$
$14$		0			0
$15$			10.3752i			2.67886i
$16$		0			0
$17$	−2.19656	+	3.48929i	−0.532743	+	0.846277i
$17$	−2.19656	+	3.48929i	−0.532743	+	0.846277i
$18$		0			0
$19$			7.51663i			1.72443i	0.506539	+	0.862217i	$0.330925\pi$
$19$			7.51663i			1.72443i	−0.506539	+	0.862217i	$0.669075\pi$
$20$		0			0
$21$	1.70727			0.372557
$22$		0			0
$23$	−1.83890	−	1.83890i	−0.383437	−	0.383437i	0.488902	−	0.872339i	$-0.337398\pi$
$23$	−1.83890	−	1.83890i	−0.383437	−	0.383437i	−0.872339	+	0.488902i	$0.837398\pi$
$24$		0			0
$25$		−	7.39312i		−	1.47862i
$26$		0			0
$27$	−5.59722	−	5.59722i	−1.07719	−	1.07719i
$28$		0			0
$29$	0.196558	−	0.196558i	0.0364998	−	0.0364998i	−0.688621	−	0.725121i	$-0.741784\pi$
$29$	0.196558	−	0.196558i	0.0364998	−	0.0364998i	0.725121	+	0.688621i	$0.241784\pi$
$30$		0			0
$31$	5.18760	−	5.18760i	0.931720	−	0.931720i	−0.0660933	−	0.997813i	$-0.521054\pi$
$31$	5.18760	−	5.18760i	0.931720	−	0.931720i	0.997813	+	0.0660933i	$0.0210535\pi$
$32$		0			0
$33$	14.6430			2.54902
$34$		0			0
$35$	−2.03932			−0.344709
$36$		0			0
$37$	0.489289	−	0.489289i	0.0804385	−	0.0804385i	−0.665743	−	0.746181i	$-0.731885\pi$
$37$	0.489289	−	0.489289i	0.0804385	−	0.0804385i	0.746181	+	0.665743i	$0.231885\pi$
$38$		0			0
$39$	9.76515	−	9.76515i	1.56368	−	1.56368i
$40$		0			0
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$		−	2.52946i		−	0.385739i	−0.981224	−	0.192869i	$-0.938221\pi$
$43$		−	2.52946i		−	0.385739i	0.981224	−	0.192869i	$-0.0617793\pi$
$44$		0			0
$45$	14.1537	+	14.1537i	2.10991	+	2.10991i
$46$		0			0
$47$	1.63848			0.238997			0.119498	−	0.992834i	$-0.461871\pi$
$47$	1.63848			0.238997			0.119498	+	0.992834i	$0.461871\pi$
$48$		0			0
$49$		−	6.66442i		−	0.952060i
$50$		0			0
$51$	2.69401	+	11.8491i	0.377237	+	1.65921i
$52$		0			0
$53$			2.97858i			0.409139i	0.978852	+	0.204570i	$0.0655794\pi$
$53$			2.97858i			0.409139i	−0.978852	+	0.204570i	$0.934421\pi$
$54$		0			0
$55$	−17.4910			−2.35848
$56$		0			0
$57$	15.6644	+	15.6644i	2.07480	+	2.07480i
$58$		0			0
$59$		−	7.02650i		−	0.914772i	−0.889268	−	0.457386i	$-0.848786\pi$
$59$		−	7.02650i		−	0.914772i	0.889268	−	0.457386i	$-0.151214\pi$
$60$		0			0
$61$	4.48929	+	4.48929i	0.574795	+	0.574795i	0.933464	−	0.358670i	$-0.116770\pi$
$61$	4.48929	+	4.48929i	0.574795	+	0.574795i	−0.358670	+	0.933464i	$0.616770\pi$
$62$		0			0
$63$	2.32903	−	2.32903i	0.293431	−	0.293431i
$64$		0			0
$65$	−11.6644	+	11.6644i	−1.44679	+	1.44679i
$66$		0			0
$67$	−0.490134			−0.0598794			−0.0299397	−	0.999552i	$-0.509532\pi$
$67$	−0.490134			−0.0598794			−0.0299397	+	0.999552i	$0.509532\pi$
$68$		0			0
$69$	−7.66442			−0.922688
$70$		0			0
$71$	−5.39680	+	5.39680i	−0.640482	+	0.640482i	−0.950674	−	0.310192i	$-0.899607\pi$
$71$	−5.39680	+	5.39680i	−0.640482	+	0.640482i	0.310192	+	0.950674i	$0.399607\pi$
$72$		0			0
$73$	7.39312	−	7.39312i	0.865299	−	0.865299i	−0.126649	−	0.991948i	$-0.540422\pi$
$73$	7.39312	−	7.39312i	0.865299	−	0.865299i	0.991948	+	0.126649i	$0.0404222\pi$
$74$		0			0
$75$	−15.4070	−	15.4070i	−1.77905	−	1.77905i
$76$		0			0
$77$			2.87819i			0.328001i
$78$		0			0
$79$	9.35553	+	9.35553i	1.05258	+	1.05258i	0.998539	+	0.0540411i	$0.0172102\pi$
$79$	9.35553	+	9.35553i	1.05258	+	1.05258i	0.0540411	+	0.998539i	$0.482790\pi$
$80$		0			0
$81$	−6.27131			−0.696812
$82$		0			0
$83$		−	1.30937i		−	0.143722i	−0.997415	−	0.0718612i	$-0.977106\pi$
$83$		−	1.30937i		−	0.143722i	0.997415	−	0.0718612i	$-0.0228939\pi$
$84$		0			0
$85$	−3.21798	−	14.1537i	−0.349039	−	1.53519i
$86$		0			0
$87$		−	0.819240i		−	0.0878317i
$88$		0			0
$89$	−0.335577			−0.0355711			−0.0177855	−	0.999842i	$-0.505662\pi$
$89$	−0.335577			−0.0355711			−0.0177855	+	0.999842i	$0.505662\pi$
$90$		0			0
$91$	1.91942	+	1.91942i	0.201209	+	0.201209i
$92$		0			0
$93$		−	21.6216i		−	2.24205i
$94$		0			0
$95$	−18.7111	−	18.7111i	−1.91972	−	1.91972i
$96$		0			0
$97$	1.29273	−	1.29273i	0.131257	−	0.131257i	−0.638426	−	0.769683i	$-0.720414\pi$
$97$	1.29273	−	1.29273i	0.131257	−	0.131257i	0.769683	+	0.638426i	$0.220414\pi$
$98$		0			0
$99$	19.9758	−	19.9758i	2.00764	−	2.00764i
$100$		0			0
$101$	12.6858			1.26229			0.631144	−	0.775665i	$-0.282586\pi$
$101$	12.6858			1.26229			0.631144	+	0.775665i	$0.282586\pi$
$102$		0			0
$103$	−17.8918			−1.76293			−0.881467	−	0.472245i	$-0.843444\pi$
$103$	−17.8918			−1.76293			−0.881467	+	0.472245i	$0.843444\pi$
$104$		0			0
$105$	−4.24989	+	4.24989i	−0.414746	+	0.414746i
$106$		0			0
$107$	−6.25190	+	6.25190i	−0.604394	+	0.604394i	−0.941476	−	0.337081i	$-0.890560\pi$
$107$	−6.25190	+	6.25190i	−0.604394	+	0.604394i	0.337081	+	0.941476i	$0.390560\pi$
$108$		0			0
$109$	−7.86098	−	7.86098i	−0.752945	−	0.752945i	0.222082	−	0.975028i	$-0.428715\pi$
$109$	−7.86098	−	7.86098i	−0.752945	−	0.752945i	−0.975028	+	0.222082i	$0.928715\pi$
$110$		0			0
$111$		−	2.03932i		−	0.193564i
$112$		0			0
$113$	−7.29273	−	7.29273i	−0.686042	−	0.686042i	0.275312	−	0.961355i	$-0.411219\pi$
$113$	−7.29273	−	7.29273i	−0.686042	−	0.686042i	−0.961355	+	0.275312i	$0.911219\pi$
$114$		0			0
$115$	9.15511			0.853719
$116$		0			0
$117$		−	26.6430i		−	2.46315i
$118$		0			0
$119$	−2.32903	+	0.529528i	−0.213502	+	0.0485418i
$120$		0			0
$121$			13.6858i			1.24417i
$122$		0			0
$123$	4.16794			0.375810
$124$		0			0
$125$	5.95715	+	5.95715i	0.532824	+	0.532824i
$126$		0			0
$127$			12.9939i			1.15303i	0.817088	+	0.576513i	$0.195587\pi$
$127$			12.9939i			1.15303i	−0.817088	+	0.576513i	$0.804413\pi$
$128$		0			0
$129$	−5.27131	−	5.27131i	−0.464113	−	0.464113i
$130$		0			0
$131$	−12.4592	+	12.4592i	−1.08856	+	1.08856i	−0.0928854	+	0.995677i	$0.529609\pi$
$131$	−12.4592	+	12.4592i	−1.08856	+	1.08856i	−0.995677	+	0.0928854i	$0.970391\pi$
$132$		0			0
$133$	−3.07896	+	3.07896i	−0.266980	+	0.266980i
$134$		0			0
$135$	27.8662			2.39834
$136$		0			0
$137$	−14.6430			−1.25104			−0.625518	−	0.780210i	$-0.715112\pi$
$137$	−14.6430			−1.25104			−0.625518	+	0.780210i	$0.715112\pi$
$138$		0			0
$139$	−6.86195	+	6.86195i	−0.582023	+	0.582023i	−0.935459	−	0.353436i	$-0.885013\pi$
$139$	−6.86195	+	6.86195i	−0.582023	+	0.582023i	0.353436	+	0.935459i	$0.385013\pi$
$140$		0			0
$141$	3.41454	−	3.41454i	0.287556	−	0.287556i
$142$		0			0
$143$	16.4625	+	16.4625i	1.37667	+	1.37667i
$144$		0			0
$145$			0.978577i			0.0812664i
$146$		0			0
$147$	−13.8884	−	13.8884i	−1.14550	−	1.14550i
$148$		0			0
$149$	−0.0428457			−0.00351006			−0.00175503	−	0.999998i	$-0.500559\pi$
$149$	−0.0428457			−0.00351006			−0.00175503	+	0.999998i	$0.500559\pi$
$150$		0			0
$151$		−	21.5696i		−	1.75531i	−0.479291	−	0.877656i	$-0.659106\pi$
$151$		−	21.5696i		−	1.75531i	0.479291	−	0.877656i	$-0.340894\pi$
$152$		0			0
$153$	19.8396	+	12.4893i	1.60393	+	1.00970i
$154$		0			0
$155$			25.8269i			2.07446i
$156$		0			0
$157$	0.628308			0.0501444			0.0250722	−	0.999686i	$-0.492018\pi$
$157$	0.628308			0.0501444			0.0250722	+	0.999686i	$0.492018\pi$
$158$		0			0
$159$	6.20726	+	6.20726i	0.492268	+	0.492268i
$160$		0			0
$161$		−	1.50650i		−	0.118729i
$162$		0			0
$163$	−1.47393	−	1.47393i	−0.115447	−	0.115447i	0.647023	−	0.762470i	$-0.276014\pi$
$163$	−1.47393	−	1.47393i	−0.115447	−	0.115447i	−0.762470	+	0.647023i	$0.776014\pi$
$164$		0			0
$165$	−36.4507	+	36.4507i	−2.83768	+	2.83768i
$166$		0			0
$167$	−3.26818	+	3.26818i	−0.252900	+	0.252900i	−0.822158	−	0.569259i	$-0.807230\pi$
$167$	−3.26818	+	3.26818i	−0.252900	+	0.252900i	0.569259	+	0.822158i	$0.307230\pi$
$168$		0			0
$169$	8.95715			0.689012
$170$		0			0
$171$	42.7384			3.26829
$172$		0			0
$173$	0.196558	−	0.196558i	0.0149440	−	0.0149440i	−0.699595	−	0.714539i	$-0.746636\pi$
$173$	0.196558	−	0.196558i	0.0149440	−	0.0149440i	0.714539	+	0.699595i	$0.246636\pi$
$174$		0			0
$175$	3.02837	−	3.02837i	0.228923	−	0.228923i
$176$		0			0
$177$	−14.6430	−	14.6430i	−1.10064	−	1.10064i
$178$		0			0
$179$		−	3.67780i		−	0.274892i	−0.990509	−	0.137446i	$-0.956111\pi$
$179$		−	3.67780i		−	0.274892i	0.990509	−	0.137446i	$-0.0438893\pi$
$180$		0			0
$181$	−8.88240	−	8.88240i	−0.660224	−	0.660224i	0.295209	−	0.955433i	$-0.404611\pi$
$181$	−8.88240	−	8.88240i	−0.660224	−	0.660224i	−0.955433	+	0.295209i	$0.904611\pi$
$182$		0			0
$183$	18.7111			1.38316
$184$		0			0
$185$			2.43596i			0.179095i
$186$		0			0
$187$	−19.9758	+	4.54169i	−1.46077	+	0.332121i
$188$		0			0
$189$		−	4.58546i		−	0.333543i
$190$		0			0
$191$	−13.8132			−0.999487			−0.499743	−	0.866174i	$-0.666572\pi$
$191$	−13.8132			−0.999487			−0.499743	+	0.866174i	$0.666572\pi$
$192$		0			0
$193$	9.58546	+	9.58546i	0.689977	+	0.689977i	0.962227	−	0.272250i	$-0.0877677\pi$
$193$	9.58546	+	9.58546i	0.689977	+	0.689977i	−0.272250	+	0.962227i	$0.587768\pi$
$194$		0			0
$195$			48.6166i			3.48151i
$196$		0			0
$197$	1.21798	+	1.21798i	0.0867775	+	0.0867775i	0.749163	−	0.662386i	$-0.230456\pi$
$197$	1.21798	+	1.21798i	0.0867775	+	0.0867775i	−0.662386	+	0.749163i	$0.730456\pi$
$198$		0			0
$199$	3.47738	−	3.47738i	0.246505	−	0.246505i	−0.573030	−	0.819535i	$-0.694232\pi$
$199$	3.47738	−	3.47738i	0.246505	−	0.246505i	0.819535	+	0.573030i	$0.194232\pi$
$200$		0			0
$201$	−1.02142	+	1.02142i	−0.0720456	+	0.0720456i
$202$		0			0
$203$	0.161028			0.0113019
$204$		0			0
$205$	−4.97858			−0.347719
$206$		0			0
$207$	−10.4557	+	10.4557i	−0.726722	+	0.726722i
$208$		0			0
$209$	−26.4078	+	26.4078i	−1.82667	+	1.82667i
$210$		0			0
$211$	−5.43266	−	5.43266i	−0.374000	−	0.374000i	0.494932	−	0.868932i	$-0.335193\pi$
$211$	−5.43266	−	5.43266i	−0.374000	−	0.374000i	−0.868932	+	0.494932i	$0.835193\pi$
$212$		0			0
$213$			22.4935i			1.54123i
$214$		0			0
$215$	6.29655	+	6.29655i	0.429421	+	0.429421i
$216$		0			0
$217$	4.24989			0.288501
$218$		0			0
$219$		−	30.8140i		−	2.08222i
$220$		0			0
$221$	−10.2927	+	16.3503i	−0.692364	+	1.09984i
$222$		0			0
$223$		−	14.2140i		−	0.951842i	−0.879488	−	0.475921i	$-0.842115\pi$
$223$		−	14.2140i		−	0.951842i	0.879488	−	0.475921i	$-0.157885\pi$
$224$		0			0
$225$	−42.0361			−2.80241
$226$		0			0
$227$	−4.82262	−	4.82262i	−0.320089	−	0.320089i	0.528712	−	0.848801i	$-0.322675\pi$
$227$	−4.82262	−	4.82262i	−0.320089	−	0.320089i	−0.848801	+	0.528712i	$0.822675\pi$
$228$		0			0
$229$		−	18.2499i		−	1.20599i	−0.797746	−	0.602993i	$-0.793975\pi$
$229$		−	18.2499i		−	1.20599i	0.797746	−	0.602993i	$-0.206025\pi$
$230$		0			0
$231$	5.99806	+	5.99806i	0.394644	+	0.394644i
$232$		0			0
$233$	11.6858	−	11.6858i	0.765565	−	0.765565i	−0.211757	−	0.977322i	$-0.567919\pi$
$233$	11.6858	−	11.6858i	0.765565	−	0.765565i	0.977322	+	0.211757i	$0.0679186\pi$
$234$		0			0
$235$	−4.07865	+	4.07865i	−0.266062	+	0.266062i
$236$		0			0
$237$	38.9933			2.53289
$238$		0			0
$239$	19.5303			1.26331			0.631655	−	0.775249i	$-0.282376\pi$
$239$	19.5303			1.26331			0.631655	+	0.775249i	$0.282376\pi$
$240$		0			0
$241$	16.5640	−	16.5640i	1.06698	−	1.06698i	0.0693942	−	0.997589i	$-0.477893\pi$
$241$	16.5640	−	16.5640i	1.06698	−	1.06698i	0.997589	−	0.0693942i	$-0.0221066\pi$
$242$		0			0
$243$	3.72245	−	3.72245i	0.238795	−	0.238795i
$244$		0			0
$245$	16.5897	+	16.5897i	1.05988	+	1.05988i
$246$		0			0
$247$			35.2218i			2.24111i
$248$		0			0
$249$	−2.72869	−	2.72869i	−0.172924	−	0.172924i
$250$		0			0
$251$	27.3760			1.72796			0.863980	−	0.503525i	$-0.167964\pi$
$251$	27.3760			1.72796			0.863980	+	0.503525i	$0.167964\pi$
$252$		0			0
$253$		−	12.9210i		−	0.812339i
$254$		0			0
$255$	−36.2021	−	22.7897i	−2.26706	−	1.42715i
$256$		0			0
$257$		−	22.6002i		−	1.40976i	−0.709327	−	0.704879i	$-0.751001\pi$
$257$		−	22.6002i		−	1.40976i	0.709327	−	0.704879i	$-0.248999\pi$
$258$		0			0
$259$	0.400845			0.0249073
$260$		0			0
$261$	−1.11760	−	1.11760i	−0.0691775	−	0.0691775i
$262$		0			0
$263$			29.9055i			1.84405i	0.387128	+	0.922026i	$0.373467\pi$
$263$			29.9055i			1.84405i	−0.387128	+	0.922026i	$0.626533\pi$
$264$		0			0
$265$	−7.41454	−	7.41454i	−0.455471	−	0.455471i
$266$		0			0
$267$	−0.699331	+	0.699331i	−0.0427984	+	0.0427984i
$268$		0			0
$269$	20.2541	−	20.2541i	1.23491	−	1.23491i	0.272860	−	0.962054i	$-0.412030\pi$
$269$	20.2541	−	20.2541i	1.23491	−	1.23491i	0.962054	−	0.272860i	$-0.0879697\pi$
$270$		0			0
$271$	−19.5303			−1.18638			−0.593191	−	0.805062i	$-0.702132\pi$
$271$	−19.5303			−1.18638			−0.593191	+	0.805062i	$0.702132\pi$
$272$		0			0
$273$	8.00000			0.484182
$274$		0			0
$275$	25.9739	−	25.9739i	1.56628	−	1.56628i
$276$		0			0
$277$	−14.5468	+	14.5468i	−0.874034	+	0.874034i	−0.992909	−	0.118875i	$-0.962071\pi$
$277$	−14.5468	+	14.5468i	−0.874034	+	0.874034i	0.118875	+	0.992909i	$0.462071\pi$
$278$		0			0
$279$	−29.4959	−	29.4959i	−1.76587	−	1.76587i
$280$		0			0
$281$		−	5.60688i		−	0.334479i	−0.985916	−	0.167239i	$-0.946515\pi$
$281$		−	5.60688i		−	0.334479i	0.985916	−	0.167239i	$-0.0534853\pi$
$282$		0			0
$283$	10.2106	+	10.2106i	0.606960	+	0.606960i	0.942150	−	0.335191i	$-0.108801\pi$
$283$	10.2106	+	10.2106i	0.606960	+	0.606960i	−0.335191	+	0.942150i	$0.608801\pi$
$284$		0			0
$285$	−77.9865			−4.61952
$286$		0			0
$287$			0.819240i			0.0483582i
$288$		0			0
$289$	−7.35027	−	15.3288i	−0.432369	−	0.901697i
$290$		0			0
$291$		−	5.38802i		−	0.315851i
$292$		0			0
$293$	−17.3288			−1.01236			−0.506181	−	0.862427i	$-0.668943\pi$
$293$	−17.3288			−1.01236			−0.506181	+	0.862427i	$0.668943\pi$
$294$		0			0
$295$	17.4910	+	17.4910i	1.01836	+	1.01836i
$296$		0			0
$297$		−	39.3288i		−	2.28209i
$298$		0			0
$299$	−8.61681	−	8.61681i	−0.498323	−	0.498323i
$300$		0			0
$301$	1.03612	−	1.03612i	0.0597207	−	0.0597207i
$302$		0			0
$303$	26.4369	−	26.4369i	1.51876	−	1.51876i
$304$		0			0
$305$	−22.3503			−1.27977
$306$		0			0
$307$	−18.5500			−1.05871			−0.529353	−	0.848401i	$-0.677565\pi$
$307$	−18.5500			−1.05871			−0.529353	+	0.848401i	$0.677565\pi$
$308$		0			0
$309$	−37.2860	+	37.2860i	−2.12113	+	2.12113i
$310$		0			0
$311$	4.08742	−	4.08742i	0.231776	−	0.231776i	−0.581657	−	0.813434i	$-0.697596\pi$
$311$	4.08742	−	4.08742i	0.231776	−	0.231776i	0.813434	+	0.581657i	$0.197596\pi$
$312$		0			0
$313$	6.60688	+	6.60688i	0.373443	+	0.373443i	0.868730	−	0.495286i	$-0.164937\pi$
$313$	6.60688	+	6.60688i	0.373443	+	0.373443i	−0.495286	+	0.868730i	$0.664937\pi$
$314$		0			0
$315$			11.5953i			0.653320i
$316$		0			0
$317$	5.21798	+	5.21798i	0.293071	+	0.293071i	0.838292	−	0.545221i	$-0.183554\pi$
$317$	5.21798	+	5.21798i	0.293071	+	0.293071i	−0.545221	+	0.838292i	$0.683554\pi$
$318$		0			0
$319$	1.38111			0.0773274
$320$		0			0
$321$			26.0575i			1.45439i
$322$		0			0
$323$	−26.2277	−	16.5107i	−1.45935	−	0.918681i
$324$		0			0
$325$		−	34.6430i		−	1.92165i
$326$		0			0
$327$	−32.7641			−1.81186
$328$		0			0
$329$	0.671153	+	0.671153i	0.0370019	+	0.0370019i
$330$		0			0
$331$		−	18.2209i		−	1.00151i	−0.865588	−	0.500757i	$-0.833055\pi$
$331$		−	18.2209i		−	1.00151i	0.865588	−	0.500757i	$-0.166945\pi$
$332$		0			0
$333$	−2.78202	−	2.78202i	−0.152454	−	0.152454i
$334$		0			0
$335$	1.22008	−	1.22008i	0.0666603	−	0.0666603i
$336$		0			0
$337$	13.9357	−	13.9357i	0.759128	−	0.759128i	−0.217036	−	0.976164i	$-0.569639\pi$
$337$	13.9357	−	13.9357i	0.759128	−	0.759128i	0.976164	+	0.217036i	$0.0696389\pi$
$338$		0			0
$339$	−30.3956			−1.65086
$340$		0			0
$341$	36.4507			1.97391
$342$		0			0
$343$	5.59722	−	5.59722i	0.302221	−	0.302221i
$344$		0			0
$345$	19.0790	−	19.0790i	1.02718	−	1.02718i
$346$		0			0
$347$	3.51325	+	3.51325i	0.188601	+	0.188601i	0.795091	−	0.606490i	$-0.207423\pi$
$347$	3.51325	+	3.51325i	0.188601	+	0.188601i	−0.606490	+	0.795091i	$0.707423\pi$
$348$		0			0
$349$			10.9786i			0.587670i	0.955856	+	0.293835i	$0.0949316\pi$
$349$			10.9786i			0.587670i	−0.955856	+	0.293835i	$0.905068\pi$
$350$		0			0
$351$	−26.2277	−	26.2277i	−1.39993	−	1.39993i
$352$		0			0
$353$	−22.9357			−1.22075			−0.610373	−	0.792114i	$-0.708980\pi$
$353$	−22.9357			−1.22075			−0.610373	+	0.792114i	$0.708980\pi$
$354$		0			0
$355$		−	26.8684i		−	1.42602i
$356$		0			0
$357$	−3.75011	+	5.95715i	−0.198477	+	0.315286i
$358$		0			0
$359$			0.161028i			0.00849872i	0.999991	+	0.00424936i	$0.00135262\pi$
$359$			0.161028i			0.00849872i	−0.999991	+	0.00424936i	$0.998647\pi$
$360$		0			0
$361$	−37.4998			−1.97367
$362$		0			0
$363$	28.5209	+	28.5209i	1.49696	+	1.49696i
$364$		0			0
$365$			36.8072i			1.92658i
$366$		0			0
$367$	−0.0805139	−	0.0805139i	−0.00420279	−	0.00420279i	0.705002	−	0.709205i	$-0.250946\pi$
$367$	−0.0805139	−	0.0805139i	−0.00420279	−	0.00420279i	−0.709205	+	0.705002i	$0.750946\pi$
$368$		0			0
$369$	5.68585	−	5.68585i	0.295993	−	0.295993i
$370$		0			0
$371$	−1.22008	+	1.22008i	−0.0633436	+	0.0633436i
$372$		0			0
$373$	−18.8438			−0.975693			−0.487847	−	0.872929i	$-0.662217\pi$
$373$	−18.8438			−0.975693			−0.487847	+	0.872929i	$0.662217\pi$
$374$		0			0
$375$	24.8290			1.28217
$376$		0			0
$377$	0.921039	−	0.921039i	0.0474359	−	0.0474359i
$378$		0			0
$379$	−10.7489	+	10.7489i	−0.552136	+	0.552136i	−0.927057	−	0.374921i	$-0.877670\pi$
$379$	−10.7489	+	10.7489i	−0.552136	+	0.552136i	0.374921	+	0.927057i	$0.377670\pi$
$380$		0			0
$381$	27.0790	+	27.0790i	1.38730	+	1.38730i
$382$		0			0
$383$		−	24.8466i		−	1.26960i	−0.772676	−	0.634801i	$-0.781082\pi$
$383$		−	24.8466i		−	1.26960i	0.772676	−	0.634801i	$-0.218918\pi$
$384$		0			0
$385$	−7.16465	−	7.16465i	−0.365145	−	0.365145i
$386$		0			0
$387$	−14.3821			−0.731083
$388$		0			0
$389$		−	32.2070i		−	1.63296i	−0.577372	−	0.816481i	$-0.695922\pi$
$389$		−	32.2070i		−	1.63296i	0.577372	−	0.816481i	$-0.304078\pi$
$390$		0			0
$391$	10.4557	−	2.37720i	0.528768	−	0.120220i
$392$		0			0
$393$			51.9290i			2.61947i
$394$		0			0
$395$	−46.5772			−2.34356
$396$		0			0
$397$	−14.2541	−	14.2541i	−0.715393	−	0.715393i	0.252265	−	0.967658i	$-0.418824\pi$
$397$	−14.2541	−	14.2541i	−0.715393	−	0.715393i	−0.967658	+	0.252265i	$0.918824\pi$
$398$		0			0
$399$			12.8329i			0.642449i
$400$		0			0
$401$	13.3503	+	13.3503i	0.666681	+	0.666681i	0.956946	−	0.290266i	$-0.0937436\pi$
$401$	13.3503	+	13.3503i	0.666681	+	0.666681i	−0.290266	+	0.956946i	$0.593744\pi$
$402$		0			0
$403$	24.3083	−	24.3083i	1.21088	−	1.21088i
$404$		0			0
$405$	15.6111	−	15.6111i	0.775722	−	0.775722i
$406$		0			0
$407$	3.43799			0.170415
$408$		0			0
$409$	22.3503			1.10515			0.552575	−	0.833463i	$-0.313645\pi$
$409$	22.3503			1.10515			0.552575	+	0.833463i	$0.313645\pi$
$410$		0			0
$411$	−30.5155	+	30.5155i	−1.50522	+	1.50522i
$412$		0			0
$413$	2.87819	−	2.87819i	0.141627	−	0.141627i
$414$		0			0
$415$	3.25941	+	3.25941i	0.159998	+	0.159998i
$416$		0			0
$417$			28.6002i			1.40056i
$418$		0			0
$419$	11.9690	+	11.9690i	0.584725	+	0.584725i	0.936198	−	0.351473i	$-0.114319\pi$
$419$	11.9690	+	11.9690i	0.584725	+	0.584725i	−0.351473	+	0.936198i	$0.614319\pi$
$420$		0			0
$421$	21.3864			1.04231			0.521154	−	0.853462i	$-0.325502\pi$
$421$	21.3864			1.04231			0.521154	+	0.853462i	$0.325502\pi$
$422$		0			0
$423$		−	9.31614i		−	0.452966i
$424$		0			0
$425$	25.7967	+	16.2394i	1.25132	+	0.787727i
$426$		0			0
$427$			3.67780i			0.177981i
$428$		0			0
$429$	68.6148			3.31276
$430$		0			0
$431$	−5.67773	−	5.67773i	−0.273487	−	0.273487i	0.557015	−	0.830502i	$-0.311946\pi$
$431$	−5.67773	−	5.67773i	−0.273487	−	0.273487i	−0.830502	+	0.557015i	$0.811946\pi$
$432$		0			0
$433$		−	35.0361i		−	1.68373i	−0.539690	−	0.841864i	$-0.681458\pi$
$433$		−	35.0361i		−	1.68373i	0.539690	−	0.841864i	$-0.318542\pi$
$434$		0			0
$435$	2.03932	+	2.03932i	0.0977781	+	0.0977781i
$436$		0			0
$437$	13.8223	−	13.8223i	0.661212	−	0.661212i
$438$		0			0
$439$	−6.61688	+	6.61688i	−0.315806	+	0.315806i	−0.847154	−	0.531348i	$-0.821686\pi$
$439$	−6.61688	+	6.61688i	−0.315806	+	0.315806i	0.531348	+	0.847154i	$0.321686\pi$
$440$		0			0
$441$	−37.8929			−1.80442
$442$		0			0
$443$	−27.1362			−1.28928			−0.644641	−	0.764486i	$-0.722993\pi$
$443$	−27.1362			−1.28928			−0.644641	+	0.764486i	$0.722993\pi$
$444$		0			0
$445$	0.835347	−	0.835347i	0.0395993	−	0.0395993i
$446$		0			0
$447$	−0.0892891	+	0.0892891i	−0.00422323	+	0.00422323i
$448$		0			0
$449$	23.4507	+	23.4507i	1.10670	+	1.10670i	0.993581	+	0.113124i	$0.0360857\pi$
$449$	23.4507	+	23.4507i	1.10670	+	1.10670i	0.113124	+	0.993581i	$0.463914\pi$
$450$		0			0
$451$			7.02650i			0.330865i
$452$		0			0
$453$	−44.9504	−	44.9504i	−2.11196	−	2.11196i
$454$		0			0
$455$	−9.55596			−0.447990
$456$		0			0
$457$		−	13.0790i		−	0.611808i	−0.952062	−	0.305904i	$-0.901041\pi$
$457$		−	13.0790i		−	0.611808i	0.952062	−	0.305904i	$-0.0989587\pi$
$458$		0			0
$459$	31.8249	−	7.23570i	1.48546	−	0.337733i
$460$		0			0
$461$		−	1.80765i		−	0.0841908i	−0.999114	−	0.0420954i	$-0.986597\pi$
$461$		−	1.80765i		−	0.0841908i	0.999114	−	0.0420954i	$-0.0134033\pi$
$462$		0			0
$463$	14.4714			0.672543			0.336271	−	0.941765i	$-0.390834\pi$
$463$	14.4714			0.672543			0.336271	+	0.941765i	$0.390834\pi$
$464$		0			0
$465$	53.8223	+	53.8223i	2.49595	+	2.49595i
$466$		0			0
$467$			16.2709i			0.752927i	0.926431	+	0.376464i	$0.122860\pi$
$467$			16.2709i			0.752927i	−0.926431	+	0.376464i	$0.877140\pi$
$468$		0			0
$469$	−0.200768	−	0.200768i	−0.00927062	−	0.00927062i
$470$		0			0
$471$	1.30937	−	1.30937i	0.0603327	−	0.0603327i
$472$		0			0
$473$	8.88661	−	8.88661i	0.408607	−	0.408607i
$474$		0			0
$475$	55.5713			2.54979
$476$		0			0
$477$	16.9357			0.775434
$478$		0			0
$479$	22.3495	−	22.3495i	1.02117	−	1.02117i	0.0214027	−	0.999771i	$-0.493187\pi$
$479$	22.3495	−	22.3495i	1.02117	−	1.02117i	0.999771	−	0.0214027i	$-0.00681321\pi$
$480$		0			0
$481$	2.29273	−	2.29273i	0.104540	−	0.104540i
$482$		0			0
$483$	−3.13950	−	3.13950i	−0.142852	−	0.142852i
$484$		0			0
$485$			6.43596i			0.292242i
$486$		0			0
$487$	26.1472	+	26.1472i	1.18484	+	1.18484i	0.978475	+	0.206368i	$0.0661643\pi$
$487$	26.1472	+	26.1472i	1.18484	+	1.18484i	0.206368	+	0.978475i	$0.433836\pi$
$488$		0			0
$489$	−6.14323			−0.277806
$490$		0			0
$491$			4.23967i			0.191334i	0.995413	+	0.0956669i	$0.0304984\pi$
$491$			4.23967i			0.191334i	−0.995413	+	0.0956669i	$0.969502\pi$
$492$		0			0
$493$	0.254096	+	1.11760i	0.0114439	+	0.0503340i
$494$		0			0
$495$			99.4510i			4.46999i
$496$		0			0
$497$	−4.42127			−0.198321
$498$		0			0
$499$	23.1635	+	23.1635i	1.03694	+	1.03694i	0.999291	+	0.0376481i	$0.0119866\pi$
$499$	23.1635	+	23.1635i	1.03694	+	1.03694i	0.0376481	+	0.999291i	$0.488013\pi$
$500$		0			0
$501$			13.6216i			0.608567i
$502$		0			0
$503$	−19.6108	−	19.6108i	−0.874403	−	0.874403i	0.118545	−	0.992949i	$-0.462177\pi$
$503$	−19.6108	−	19.6108i	−0.874403	−	0.874403i	−0.992949	+	0.118545i	$0.962177\pi$
$504$		0			0
$505$	−31.5787	+	31.5787i	−1.40524	+	1.40524i
$506$		0			0
$507$	18.6664	−	18.6664i	0.829005	−	0.829005i
$508$		0			0
$509$	−2.20077			−0.0975473			−0.0487737	−	0.998810i	$-0.515531\pi$
$509$	−2.20077			−0.0975473			−0.0487737	+	0.998810i	$0.515531\pi$
$510$		0			0
$511$	6.05673			0.267934
$512$		0			0
$513$	42.0722	−	42.0722i	1.85753	−	1.85753i
$514$		0			0
$515$	44.5379	−	44.5379i	1.96258	−	1.96258i
$516$		0			0
$517$	5.75639	+	5.75639i	0.253166	+	0.253166i
$518$		0			0
$519$		−	0.819240i		−	0.0359606i
$520$		0			0
$521$	−7.14950	−	7.14950i	−0.313225	−	0.313225i	0.532932	−	0.846158i	$-0.321090\pi$
$521$	−7.14950	−	7.14950i	−0.313225	−	0.313225i	−0.846158	+	0.532932i	$0.821090\pi$
$522$		0			0
$523$	−10.7043			−0.468066			−0.234033	−	0.972229i	$-0.575192\pi$
$523$	−10.7043			−0.468066			−0.234033	+	0.972229i	$0.575192\pi$
$524$		0			0
$525$		−	12.6220i		−	0.550871i
$526$		0			0
$527$	6.70617	+	29.4959i	0.292125	+	1.28486i
$528$		0			0
$529$		−	16.2369i		−	0.705951i
$530$		0			0
$531$	−39.9516			−1.73375
$532$		0			0
$533$	4.68585	+	4.68585i	0.202967	+	0.202967i
$534$		0			0
$535$		−	31.1256i		−	1.34568i
$536$		0			0
$537$	−7.66442	−	7.66442i	−0.330744	−	0.330744i
$538$		0			0
$539$	23.4138	−	23.4138i	1.00850	−	1.00850i
$540$		0			0
$541$	6.53213	−	6.53213i	0.280838	−	0.280838i	−0.552605	−	0.833443i	$-0.686366\pi$
$541$	6.53213	−	6.53213i	0.280838	−	0.280838i	0.833443	+	0.552605i	$0.186366\pi$
$542$		0			0
$543$	−37.0213			−1.58874
$544$		0			0
$545$	39.1365			1.67642
$546$		0			0
$547$	−20.3766	+	20.3766i	−0.871242	+	0.871242i	−0.992608	−	0.121366i	$-0.961273\pi$
$547$	−20.3766	+	20.3766i	−0.871242	+	0.871242i	0.121366	+	0.992608i	$0.461273\pi$
$548$		0			0
$549$	25.5254	−	25.5254i	1.08940	−	1.08940i
$550$		0			0
$551$	1.47745	+	1.47745i	0.0629415	+	0.0629415i
$552$		0			0
$553$			7.66442i			0.325924i
$554$		0			0
$555$	5.07646	+	5.07646i	0.215484	+	0.215484i
$556$		0			0
$557$	−3.31415			−0.140425			−0.0702126	−	0.997532i	$-0.522368\pi$
$557$	−3.31415			−0.140425			−0.0702126	+	0.997532i	$0.522368\pi$
$558$		0			0
$559$		−	11.8526i		−	0.501314i
$560$		0			0
$561$	−32.1642	+	51.0937i	−1.35797	+	2.15718i
$562$		0			0
$563$			13.3055i			0.560760i	0.959889	+	0.280380i	$0.0904605\pi$
$563$			13.3055i			0.560760i	−0.959889	+	0.280380i	$0.909540\pi$
$564$		0			0
$565$	36.3074			1.52746
$566$		0			0
$567$	−2.56885	−	2.56885i	−0.107882	−	0.107882i
$568$		0			0
$569$		−	14.6283i		−	0.613251i	−0.951830	−	0.306625i	$-0.900800\pi$
$569$		−	14.6283i		−	0.613251i	0.951830	−	0.306625i	$-0.0991998\pi$
$570$		0			0
$571$	−16.5554	−	16.5554i	−0.692820	−	0.692820i	0.270031	−	0.962852i	$-0.412966\pi$
$571$	−16.5554	−	16.5554i	−0.692820	−	0.692820i	−0.962852	+	0.270031i	$0.912966\pi$
$572$		0			0
$573$	−28.7862	+	28.7862i	−1.20256	+	1.20256i
$574$		0			0
$575$	−13.5952	+	13.5952i	−0.566959	+	0.566959i
$576$		0			0
$577$	−4.60015			−0.191507			−0.0957535	−	0.995405i	$-0.530526\pi$
$577$	−4.60015			−0.191507			−0.0957535	+	0.995405i	$0.530526\pi$
$578$		0			0
$579$	39.9516			1.66033
$580$		0			0
$581$	0.536345	−	0.536345i	0.0222513	−	0.0222513i
$582$		0			0
$583$	−10.4645	+	10.4645i	−0.433395	+	0.433395i
$584$		0			0
$585$	66.3221	+	66.3221i	2.74208	+	2.74208i
$586$		0			0
$587$			12.9939i			0.536317i	0.963375	+	0.268159i	$0.0864152\pi$
$587$			12.9939i			0.536317i	−0.963375	+	0.268159i	$0.913585\pi$
$588$		0			0
$589$	38.9933	+	38.9933i	1.60669	+	1.60669i
$590$		0			0
$591$	5.07646			0.208818
$592$		0			0
$593$			41.6707i			1.71121i	0.517629	+	0.855605i	$0.326815\pi$
$593$			41.6707i			1.71121i	−0.517629	+	0.855605i	$0.673185\pi$
$594$		0			0
$595$	4.47949	−	7.11579i	0.183641	−	0.291719i
$596$		0			0
$597$		−	14.4935i		−	0.593179i
$598$		0			0
$599$	30.3063			1.23828			0.619142	−	0.785279i	$-0.287481\pi$
$599$	30.3063			1.23828			0.619142	+	0.785279i	$0.287481\pi$
$600$		0			0
$601$	−11.3503	−	11.3503i	−0.462987	−	0.462987i	0.436646	−	0.899633i	$-0.356166\pi$
$601$	−11.3503	−	11.3503i	−0.462987	−	0.462987i	−0.899633	+	0.436646i	$0.856166\pi$
$602$		0			0
$603$			2.78682i			0.113488i
$604$		0			0
$605$	−34.0680	−	34.0680i	−1.38506	−	1.38506i
$606$		0			0
$607$	−0.289711	+	0.289711i	−0.0117590	+	0.0117590i	−0.712962	−	0.701203i	$-0.752647\pi$
$607$	−0.289711	+	0.289711i	−0.0117590	+	0.0117590i	0.701203	+	0.712962i	$0.252647\pi$
$608$		0			0
$609$	0.335577	−	0.335577i	0.0135983	−	0.0135983i
$610$		0			0
$611$	7.67766			0.310605
$612$		0			0
$613$	−21.5296			−0.869573			−0.434786	−	0.900534i	$-0.643176\pi$
$613$	−21.5296			−0.869573			−0.434786	+	0.900534i	$0.643176\pi$
$614$		0			0
$615$	−10.3752	+	10.3752i	−0.418368	+	0.418368i
$616$		0			0
$617$	18.6644	−	18.6644i	0.751401	−	0.751401i	−0.223339	−	0.974741i	$-0.571696\pi$
$617$	18.6644	−	18.6644i	0.751401	−	0.751401i	0.974741	+	0.223339i	$0.0716958\pi$
$618$		0			0
$619$	7.84221	+	7.84221i	0.315205	+	0.315205i	0.846922	−	0.531717i	$-0.178453\pi$
$619$	7.84221	+	7.84221i	0.315205	+	0.315205i	−0.531717	+	0.846922i	$0.678453\pi$
$620$		0			0
$621$			20.5855i			0.826066i
$622$		0			0
$623$	−0.137459	−	0.137459i	−0.00550717	−	0.00550717i
$624$		0			0
$625$	7.30742			0.292297
$626$		0			0
$627$			110.066i			4.39562i
$628$		0			0
$629$	0.632518	+	2.78202i	0.0252202	+	0.110926i
$630$		0			0
$631$			9.39493i			0.374006i	0.982359	+	0.187003i	$0.0598774\pi$
$631$			9.39493i			0.374006i	−0.982359	+	0.187003i	$0.940123\pi$
$632$		0			0
$633$	−22.6430			−0.899978
$634$		0			0
$635$	−32.3457	−	32.3457i	−1.28360	−	1.28360i
$636$		0			0
$637$		−	31.2285i		−	1.23732i
$638$		0			0
$639$	30.6853	+	30.6853i	1.21389	+	1.21389i
$640$		0			0
$641$	13.0575	−	13.0575i	0.515742	−	0.515742i	−0.400538	−	0.916280i	$-0.631177\pi$
$641$	13.0575	−	13.0575i	0.515742	−	0.515742i	0.916280	+	0.400538i	$0.131177\pi$
$642$		0			0
$643$	4.45240	−	4.45240i	0.175585	−	0.175585i	−0.613843	−	0.789428i	$-0.710377\pi$
$643$	4.45240	−	4.45240i	0.175585	−	0.175585i	0.789428	+	0.613843i	$0.210377\pi$
$644$		0			0
$645$	26.2436			1.03334
$646$		0			0
$647$	−28.5244			−1.12141			−0.560705	−	0.828016i	$-0.689470\pi$
$647$	−28.5244			−1.12141			−0.560705	+	0.828016i	$0.689470\pi$
$648$		0			0
$649$	24.6858	−	24.6858i	0.969004	−	0.969004i
$650$		0			0
$651$	8.85663	−	8.85663i	0.347119	−	0.347119i
$652$		0			0
$653$	0.867711	+	0.867711i	0.0339562	+	0.0339562i	0.723881	−	0.689925i	$-0.242356\pi$
$653$	0.867711	+	0.867711i	0.0339562	+	0.0339562i	−0.689925	+	0.723881i	$0.742356\pi$
$654$		0			0
$655$		−	62.0289i		−	2.42367i
$656$		0			0
$657$	−42.0361	−	42.0361i	−1.63999	−	1.63999i
$658$		0			0
$659$	−18.3102			−0.713265			−0.356633	−	0.934245i	$-0.616075\pi$
$659$	−18.3102			−0.713265			−0.356633	+	0.934245i	$0.616075\pi$
$660$		0			0
$661$			21.5212i			0.837077i	0.908199	+	0.418539i	$0.137458\pi$
$661$			21.5212i			0.837077i	−0.908199	+	0.418539i	$0.862542\pi$
$662$		0			0
$663$	12.6237	+	55.5232i	0.490265	+	2.15634i
$664$		0			0
$665$		−	15.3288i		−	0.594427i
$666$		0			0
$667$	−0.722900			−0.0279908
$668$		0			0
$669$	−29.6216	−	29.6216i	−1.14524	−	1.14524i
$670$		0			0
$671$			31.5440i			1.21774i
$672$		0			0
$673$	−15.0575	−	15.0575i	−0.580425	−	0.580425i	0.354595	−	0.935020i	$-0.384619\pi$
$673$	−15.0575	−	15.0575i	−0.580425	−	0.580425i	−0.935020	+	0.354595i	$0.884619\pi$
$674$		0			0
$675$	−41.3809	+	41.3809i	−1.59275	+	1.59275i
$676$		0			0
$677$	8.34606	−	8.34606i	0.320765	−	0.320765i	−0.528295	−	0.849061i	$-0.677169\pi$
$677$	8.34606	−	8.34606i	0.320765	−	0.320765i	0.849061	+	0.528295i	$0.177169\pi$
$678$		0			0
$679$	1.05906			0.0406429
$680$		0			0
$681$	−20.1004			−0.770248
$682$		0			0
$683$	1.59383	−	1.59383i	0.0609864	−	0.0609864i	−0.675956	−	0.736942i	$-0.736269\pi$
$683$	1.59383	−	1.59383i	0.0609864	−	0.0609864i	0.736942	+	0.675956i	$0.236269\pi$
$684$		0			0
$685$	36.4507	−	36.4507i	1.39271	−	1.39271i
$686$		0			0
$687$	−38.0322	−	38.0322i	−1.45102	−	1.45102i
$688$		0			0
$689$			13.9572i			0.531725i
$690$		0			0
$691$	−4.82262	−	4.82262i	−0.183461	−	0.183461i	0.609401	−	0.792862i	$-0.291410\pi$
$691$	−4.82262	−	4.82262i	−0.183461	−	0.183461i	−0.792862	+	0.609401i	$0.791410\pi$
$692$		0			0
$693$	16.3650			0.621654
$694$		0			0
$695$		−	34.1627i		−	1.29587i
$696$		0			0
$697$	−5.68585	+	1.29273i	−0.215367	+	0.0489657i
$698$		0			0
$699$		−	48.7059i		−	1.84222i
$700$		0			0
$701$	−31.2285			−1.17948			−0.589741	−	0.807592i	$-0.700770\pi$
$701$	−31.2285			−1.17948			−0.589741	+	0.807592i	$0.700770\pi$
$702$		0			0
$703$	3.67780	+	3.67780i	0.138711	+	0.138711i
$704$		0			0
$705$			16.9995i			0.640240i
$706$		0			0
$707$	5.19637	+	5.19637i	0.195430	+	0.195430i
$708$		0			0
$709$	−31.7178	+	31.7178i	−1.19119	+	1.19119i	−0.214450	+	0.976735i	$0.568796\pi$
$709$	−31.7178	+	31.7178i	−1.19119	+	1.19119i	−0.976735	+	0.214450i	$0.931204\pi$
$710$		0			0
$711$	53.1941	−	53.1941i	1.99494	−	1.99494i
$712$		0			0
$713$	−19.0790			−0.714513
$714$		0			0
$715$	−81.9601			−3.06513
$716$		0			0
$717$	40.7005	−	40.7005i	1.51999	−	1.51999i
$718$		0			0
$719$	33.0056	−	33.0056i	1.23090	−	1.23090i	0.267284	−	0.963618i	$-0.413874\pi$
$719$	33.0056	−	33.0056i	1.23090	−	1.23090i	0.963618	−	0.267284i	$-0.0861260\pi$
$720$		0			0
$721$	−7.32885	−	7.32885i	−0.272941	−	0.272941i
$722$		0			0
$723$		−	69.0379i		−	2.56755i
$724$		0			0
$725$	−1.45317	−	1.45317i	−0.0539695	−	0.0539695i
$726$		0			0
$727$	−12.5931			−0.467052			−0.233526	−	0.972351i	$-0.575026\pi$
$727$	−12.5931			−0.467052			−0.233526	+	0.972351i	$0.575026\pi$
$728$		0			0
$729$		−	34.3288i		−	1.27144i
$730$		0			0
$731$	8.82601	+	5.55610i	0.326442	+	0.205500i
$732$		0			0
$733$		−	4.82065i		−	0.178055i	−0.996029	−	0.0890275i	$-0.971624\pi$
$733$		−	4.82065i		−	0.178055i	0.996029	−	0.0890275i	$-0.0283759\pi$
$734$		0			0
$735$	69.1447			2.55044
$736$		0			0
$737$	−1.72196	−	1.72196i	−0.0634293	−	0.0634293i
$738$		0			0
$739$		−	3.67780i		−	0.135290i	−0.997709	−	0.0676451i	$-0.978451\pi$
$739$		−	3.67780i		−	0.135290i	0.997709	−	0.0676451i	$-0.0215486\pi$
$740$		0			0
$741$	73.4011	+	73.4011i	2.69646	+	2.69646i
$742$		0			0
$743$	−17.6197	+	17.6197i	−0.646403	+	0.646403i	−0.952122	−	0.305719i	$-0.901103\pi$
$743$	−17.6197	+	17.6197i	−0.646403	+	0.646403i	0.305719	+	0.952122i	$0.401103\pi$
$744$		0			0
$745$	0.106655	−	0.106655i	0.00390755	−	0.00390755i
$746$		0			0
$747$	−7.44489			−0.272394
$748$		0			0
$749$	−5.12181			−0.187147
$750$		0			0
$751$	−12.0942	+	12.0942i	−0.441323	+	0.441323i	−0.892457	−	0.451133i	$-0.851020\pi$
$751$	−12.0942	+	12.0942i	−0.441323	+	0.441323i	0.451133	+	0.892457i	$0.351020\pi$
$752$		0			0
$753$	57.0508	−	57.0508i	2.07905	−	2.07905i
$754$		0			0
$755$	53.6930	+	53.6930i	1.95409	+	1.95409i
$756$		0			0
$757$		−	44.5229i		−	1.61821i	−0.587663	−	0.809106i	$-0.699952\pi$
$757$		−	44.5229i		−	1.61821i	0.587663	−	0.809106i	$-0.300048\pi$
$758$		0			0
$759$	−26.9270	−	26.9270i	−0.977389	−	0.977389i
$760$		0			0
$761$	−28.6002			−1.03675			−0.518377	−	0.855152i	$-0.673464\pi$
$761$	−28.6002			−1.03675			−0.518377	+	0.855152i	$0.673464\pi$
$762$		0			0
$763$		−	6.44003i		−	0.233145i
$764$		0			0
$765$	−80.4758	+	18.2969i	−2.90961	+	0.661527i
$766$		0			0
$767$		−	32.9251i		−	1.18886i
$768$		0			0
$769$	−4.77154			−0.172066			−0.0860330	−	0.996292i	$-0.527419\pi$
$769$	−4.77154			−0.172066			−0.0860330	+	0.996292i	$0.527419\pi$
$770$		0			0
$771$	−47.0980	−	47.0980i	−1.69619	−	1.69619i
$772$		0			0
$773$			39.7367i			1.42923i	0.699519	+	0.714614i	$0.253398\pi$
$773$			39.7367i			1.42923i	−0.699519	+	0.714614i	$0.746602\pi$
$774$		0			0
$775$	−38.3525	−	38.3525i	−1.37766	−	1.37766i
$776$		0			0
$777$	0.835347	−	0.835347i	0.0299679	−	0.0299679i
$778$		0			0
$779$	−7.51663	+	7.51663i	−0.269311	+	0.269311i
$780$		0			0
$781$	−37.9206			−1.35691
$782$		0			0
$783$	−2.20035			−0.0786341
$784$		0			0
$785$	−1.56404	+	1.56404i	−0.0558229	+	0.0558229i
$786$		0			0
$787$	33.6691	−	33.6691i	1.20017	−	1.20017i	0.226059	−	0.974114i	$-0.427416\pi$
$787$	33.6691	−	33.6691i	1.20017	−	1.20017i	0.974114	−	0.226059i	$-0.0725843\pi$
$788$		0			0
$789$	62.3221	+	62.3221i	2.21873	+	2.21873i
$790$		0			0
$791$		−	5.97449i		−	0.212429i
$792$		0			0
$793$	21.0361	+	21.0361i	0.747014	+	0.747014i
$794$		0			0
$795$	−30.9033			−1.09603
$796$		0			0
$797$		−	11.6497i		−	0.412655i	−0.978483	−	0.206327i	$-0.933849\pi$
$797$		−	11.6497i		−	0.412655i	0.978483	−	0.206327i	$-0.0661512\pi$
$798$		0			0
$799$	−3.59901	+	5.71713i	−0.127324	+	0.202257i
$800$		0			0
$801$			1.90804i			0.0674172i
$802$		0			0
$803$	51.9477			1.83320
$804$		0			0
$805$	3.75011	+	3.75011i	0.132174	+	0.132174i
$806$		0			0
$807$		−	84.4178i		−	2.97165i
$808$		0			0
$809$	17.2070	+	17.2070i	0.604967	+	0.604967i	0.941627	−	0.336659i	$-0.109297\pi$
$809$	17.2070	+	17.2070i	0.604967	+	0.604967i	−0.336659	+	0.941627i	$0.609297\pi$
$810$		0			0
$811$	17.7273	−	17.7273i	0.622489	−	0.622489i	−0.323678	−	0.946167i	$-0.604920\pi$
$811$	17.7273	−	17.7273i	0.622489	−	0.622489i	0.946167	+	0.323678i	$0.104920\pi$
$812$		0			0
$813$	−40.7005	+	40.7005i	−1.42743	+	1.42743i
$814$		0			0
$815$	7.33805			0.257041
$816$		0			0
$817$	19.0130			0.665181
$818$		0			0
$819$	10.9135	−	10.9135i	0.381349	−	0.381349i
$820$		0			0
$821$	−5.61110	+	5.61110i	−0.195829	+	0.195829i	−0.798209	−	0.602380i	$-0.794219\pi$
$821$	−5.61110	+	5.61110i	−0.195829	+	0.195829i	0.602380	+	0.798209i	$0.294219\pi$
$822$		0			0
$823$	−20.3889	−	20.3889i	−0.710714	−	0.710714i	0.255971	−	0.966685i	$-0.417605\pi$
$823$	−20.3889	−	20.3889i	−0.710714	−	0.710714i	−0.966685	+	0.255971i	$0.917605\pi$
$824$		0			0
$825$		−	108.257i		−	3.76904i
$826$		0			0
$827$	4.68516	+	4.68516i	0.162919	+	0.162919i	0.783859	−	0.620939i	$-0.213249\pi$
$827$	4.68516	+	4.68516i	0.162919	+	0.162919i	−0.620939	+	0.783859i	$0.713249\pi$
$828$		0			0
$829$	−36.1579			−1.25582			−0.627908	−	0.778287i	$-0.716089\pi$
$829$	−36.1579			−1.25582			−0.627908	+	0.778287i	$0.716089\pi$
$830$		0			0
$831$			60.6302i			2.10324i
$832$		0			0
$833$	23.2541	+	14.6388i	0.805707	+	0.507204i
$834$		0			0
$835$		−	16.2709i		−	0.563078i
$836$		0			0
$837$	−58.0722			−2.00727
$838$		0			0
$839$	3.26818	+	3.26818i	0.112830	+	0.112830i	0.761268	−	0.648438i	$-0.224577\pi$
$839$	3.26818	+	3.26818i	0.112830	+	0.112830i	−0.648438	+	0.761268i	$0.724577\pi$
$840$		0			0
$841$			28.9227i			0.997336i
$842$		0			0
$843$	−11.6846	−	11.6846i	−0.402438	−	0.402438i
$844$		0			0
$845$	−22.2969	+	22.2969i	−0.767038	+	0.767038i
$846$		0			0
$847$	−5.60599	+	5.60599i	−0.192624	+	0.192624i
$848$		0			0
$849$	42.5573			1.46056
$850$		0			0
$851$	−1.79951			−0.0616863
$852$		0			0
$853$	10.7967	−	10.7967i	0.369672	−	0.369672i	−0.497685	−	0.867358i	$-0.665817\pi$
$853$	10.7967	−	10.7967i	0.369672	−	0.369672i	0.867358	+	0.497685i	$0.165817\pi$
$854$		0			0
$855$	−106.388	+	106.388i	−3.63840	+	3.63840i
$856$		0			0
$857$	−7.20077	−	7.20077i	−0.245974	−	0.245974i	0.573342	−	0.819316i	$-0.305647\pi$
$857$	−7.20077	−	7.20077i	−0.245974	−	0.245974i	−0.819316	+	0.573342i	$0.805647\pi$
$858$		0			0
$859$			56.3835i			1.92378i	0.273435	+	0.961890i	$0.411840\pi$
$859$			56.3835i			1.92378i	−0.273435	+	0.961890i	$0.588160\pi$
$860$		0			0
$861$	1.70727	+	1.70727i	0.0581836	+	0.0581836i
$862$		0			0
$863$	−2.20035			−0.0749008			−0.0374504	−	0.999298i	$-0.511924\pi$
$863$	−2.20035			−0.0749008			−0.0374504	+	0.999298i	$0.511924\pi$
$864$		0			0
$865$			0.978577i			0.0332726i
$866$		0			0
$867$	−47.2626	−	16.6271i	−1.60512	−	0.564686i
$868$		0			0
$869$			65.7367i			2.22996i
$870$		0			0
$871$	−2.29669			−0.0778204
$872$		0			0
$873$	−7.35027	−	7.35027i	−0.248769	−	0.248769i
$874$		0			0
$875$			4.88034i			0.164985i
$876$		0			0
$877$	36.7539	+	36.7539i	1.24109	+	1.24109i	0.959549	+	0.281541i	$0.0908454\pi$
$877$	36.7539	+	36.7539i	1.24109	+	1.24109i	0.281541	+	0.959549i	$0.409155\pi$
$878$		0			0
$879$	−36.1128	+	36.1128i	−1.21805	+	1.21805i
$880$		0			0
$881$	−34.2432	+	34.2432i	−1.15368	+	1.15368i	−0.167872	+	0.985809i	$0.553690\pi$
$881$	−34.2432	+	34.2432i	−1.15368	+	1.15368i	−0.985809	+	0.167872i	$0.946310\pi$
$882$		0			0
$883$	−4.15039			−0.139672			−0.0698358	−	0.997558i	$-0.522248\pi$
$883$	−4.15039			−0.139672			−0.0698358	+	0.997558i	$0.522248\pi$
$884$		0			0
$885$	72.9013			2.45055
$886$		0			0
$887$	−8.13545	+	8.13545i	−0.273162	+	0.273162i	−0.830372	−	0.557210i	$-0.811872\pi$
$887$	−8.13545	+	8.13545i	−0.273162	+	0.273162i	0.557210	+	0.830372i	$0.311872\pi$
$888$		0			0
$889$	−5.32258	+	5.32258i	−0.178513	+	0.178513i
$890$		0			0
$891$	−22.0327	−	22.0327i	−0.738122	−	0.738122i
$892$		0			0
$893$			12.3158i			0.412134i
$894$		0			0
$895$	9.15511	+	9.15511i	0.306022	+	0.306022i
$896$		0			0
$897$	−35.9143			−1.19914
$898$		0			0
$899$		−	2.03932i		−	0.0680152i
$900$		0			0
$901$	−10.3931	−	6.54262i	−0.346245	−	0.217966i
$902$		0			0
$903$		−	4.31846i		−	0.143709i
$904$		0			0
$905$	44.2217			1.46998
$906$		0			0
$907$	7.59190	+	7.59190i	0.252085	+	0.252085i	0.821825	−	0.569740i	$-0.192956\pi$
$907$	7.59190	+	7.59190i	0.252085	+	0.252085i	−0.569740	+	0.821825i	$0.692956\pi$
$908$		0			0
$909$		−	72.1298i		−	2.39239i
$910$		0			0
$911$	33.3347	+	33.3347i	1.10443	+	1.10443i	0.993870	+	0.110559i	$0.0352640\pi$
$911$	33.3347	+	33.3347i	1.10443	+	1.10443i	0.110559	+	0.993870i	$0.464736\pi$
$912$		0			0
$913$	4.60015	−	4.60015i	0.152243	−	0.152243i
$914$		0			0
$915$	−46.5772	+	46.5772i	−1.53980	+	1.53980i
$916$		0			0
$917$	−10.2070			−0.337066
$918$		0			0
$919$	37.4221			1.23444			0.617221	−	0.786790i	$-0.288258\pi$
$919$	37.4221			1.23444			0.617221	+	0.786790i	$0.288258\pi$
$920$		0			0
$921$	−38.6577	+	38.6577i	−1.27381	+	1.27381i
$922$		0			0
$923$	−25.2886	+	25.2886i	−0.832383	+	0.832383i
$924$		0			0
$925$	−3.61737	−	3.61737i	−0.118938	−	0.118938i
$926$		0			0
$927$			101.730i			3.34126i
$928$		0			0
$929$	−24.9572	−	24.9572i	−0.818818	−	0.818818i	0.167119	−	0.985937i	$-0.446554\pi$
$929$	−24.9572	−	24.9572i	−0.818818	−	0.818818i	−0.985937	+	0.167119i	$0.946554\pi$
$930$		0			0
$931$	50.0940			1.64177
$932$		0			0
$933$		−	17.0361i		−	0.557737i
$934$		0			0
$935$	38.4200	−	61.0311i	1.25647	−	1.99593i
$936$		0			0
$937$			52.4653i			1.71397i	0.515343	+	0.856984i	$0.327665\pi$
$937$			52.4653i			1.71397i	−0.515343	+	0.856984i	$0.672335\pi$
$938$		0			0
$939$	27.5371			0.898638
$940$		0			0
$941$	22.5897	+	22.5897i	0.736402	+	0.736402i	0.971880	−	0.235478i	$-0.0756654\pi$
$941$	22.5897	+	22.5897i	0.736402	+	0.736402i	−0.235478	+	0.971880i	$0.575665\pi$
$942$		0			0
$943$		−	3.67780i		−	0.119766i
$944$		0			0
$945$	11.4145	+	11.4145i	0.371315	+	0.371315i
$946$		0			0
$947$	28.4316	−	28.4316i	0.923902	−	0.923902i	−0.0734004	−	0.997303i	$-0.523385\pi$
$947$	28.4316	−	28.4316i	0.923902	−	0.923902i	0.997303	+	0.0734004i	$0.0233851\pi$
$948$		0			0
$949$	34.6430	−	34.6430i	1.12456	−	1.12456i
$950$		0			0
$951$	21.7482			0.705234
$952$		0			0
$953$	−31.8652			−1.03221			−0.516107	−	0.856524i	$-0.672619\pi$
$953$	−31.8652			−1.03221			−0.516107	+	0.856524i	$0.672619\pi$
$954$		0			0
$955$	34.3850	−	34.3850i	1.11267	−	1.11267i
$956$		0			0
$957$	2.87819	−	2.87819i	0.0930388	−	0.0930388i
$958$		0			0
$959$	−5.99806	−	5.99806i	−0.193688	−	0.193688i
$960$		0			0
$961$		−	22.8223i		−	0.736205i
$962$		0			0
$963$	35.5474	+	35.5474i	1.14550	+	1.14550i
$964$		0			0
$965$	−47.7220			−1.53622
$966$		0			0
$967$		−	7.27682i		−	0.234007i	−0.993132	−	0.117003i	$-0.962671\pi$
$967$		−	7.27682i		−	0.234007i	0.993132	−	0.117003i	$-0.0373288\pi$
$968$		0			0
$969$	−89.0655	+	20.2499i	−2.86120	+	0.650520i
$970$		0			0
$971$		−	41.7336i		−	1.33929i	−0.742680	−	0.669647i	$-0.766446\pi$
$971$		−	41.7336i		−	1.33929i	0.742680	−	0.669647i	$-0.233554\pi$
$972$		0			0
$973$	−5.62158			−0.180220
$974$		0			0
$975$	−72.1949	−	72.1949i	−2.31209	−	2.31209i
$976$		0			0
$977$		−	5.45738i		−	0.174597i	−0.996182	−	0.0872986i	$-0.972177\pi$
$977$		−	5.45738i		−	0.174597i	0.996182	−	0.0872986i	$-0.0278234\pi$
$978$		0			0
$979$	−1.17896	−	1.17896i	−0.0376799	−	0.0376799i
$980$		0			0
$981$	−44.6963	+	44.6963i	−1.42704	+	1.42704i
$982$		0			0
$983$	−17.5715	+	17.5715i	−0.560444	+	0.560444i	−0.929433	−	0.368990i	$-0.879704\pi$
$983$	−17.5715	+	17.5715i	−0.560444	+	0.560444i	0.368990	+	0.929433i	$0.379704\pi$
$984$		0			0
$985$	−6.06381			−0.193209
$986$		0			0
$987$	2.79732			0.0890398
$988$		0			0
$989$	−4.65142	+	4.65142i	−0.147907	+	0.147907i
$990$		0			0
$991$	4.99595	−	4.99595i	0.158702	−	0.158702i	−0.623290	−	0.781991i	$-0.714204\pi$
$991$	4.99595	−	4.99595i	0.158702	−	0.158702i	0.781991	+	0.623290i	$0.214204\pi$
$992$		0			0
$993$	−37.9718	−	37.9718i	−1.20500	−	1.20500i
$994$		0			0
$995$			17.3124i			0.548840i
$996$		0			0
$997$	9.71775	+	9.71775i	0.307764	+	0.307764i	0.844042	−	0.536277i	$-0.180170\pi$
$997$	9.71775	+	9.71775i	0.307764	+	0.307764i	−0.536277	+	0.844042i	$0.680170\pi$
$998$		0			0
$999$	−5.47731			−0.173294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.2.o.w.769.6		12
4.3	odd	2	inner	1088.2.o.w.769.1		12
8.3	odd	2		544.2.o.i.225.6	yes	12
8.5	even	2		544.2.o.i.225.1	✓	12
17.13	even	4	inner	1088.2.o.w.897.6		12
68.47	odd	4	inner	1088.2.o.w.897.1		12
136.13	even	4		544.2.o.i.353.1	yes	12
136.43	odd	8		9248.2.a.bv.1.11		12
136.59	odd	8		9248.2.a.bv.1.2		12
136.77	even	8		9248.2.a.bv.1.1		12
136.93	even	8		9248.2.a.bv.1.12		12
136.115	odd	4		544.2.o.i.353.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.o.i.225.1	✓	12	8.5	even	2
544.2.o.i.225.6	yes	12	8.3	odd	2
544.2.o.i.353.1	yes	12	136.13	even	4
544.2.o.i.353.6	yes	12	136.115	odd	4
1088.2.o.w.769.1		12	4.3	odd	2	inner
1088.2.o.w.769.6		12	1.1	even	1	trivial
1088.2.o.w.897.1		12	68.47	odd	4	inner
1088.2.o.w.897.6		12	17.13	even	4	inner
9248.2.a.bv.1.1		12	136.77	even	8
9248.2.a.bv.1.2		12	136.59	odd	8
9248.2.a.bv.1.11		12	136.43	odd	8
9248.2.a.bv.1.12		12	136.93	even	8

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:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.08397 - 2.08397i) q^{3} +(-2.48929 + 2.48929i) q^{5} +(0.409620 + 0.409620i) q^{7} -5.68585i q^{9} +O(q^{10})\)	\(q+(2.08397 - 2.08397i) q^{3} +(-2.48929 + 2.48929i) q^{5} +(0.409620 + 0.409620i) q^{7} -5.68585i q^{9} +(3.51325 + 3.51325i) q^{11} +4.68585 q^{13} +10.3752i q^{15} +(-2.19656 + 3.48929i) q^{17} +7.51663i q^{19} +1.70727 q^{21} +(-1.83890 - 1.83890i) q^{23} -7.39312i q^{25} +(-5.59722 - 5.59722i) q^{27} +(0.196558 - 0.196558i) q^{29} +(5.18760 - 5.18760i) q^{31} +14.6430 q^{33} -2.03932 q^{35} +(0.489289 - 0.489289i) q^{37} +(9.76515 - 9.76515i) q^{39} +(1.00000 + 1.00000i) q^{41} -2.52946i q^{43} +(14.1537 + 14.1537i) q^{45} +1.63848 q^{47} -6.66442i q^{49} +(2.69401 + 11.8491i) q^{51} +2.97858i q^{53} -17.4910 q^{55} +(15.6644 + 15.6644i) q^{57} -7.02650i q^{59} +(4.48929 + 4.48929i) q^{61} +(2.32903 - 2.32903i) q^{63} +(-11.6644 + 11.6644i) q^{65} -0.490134 q^{67} -7.66442 q^{69} +(-5.39680 + 5.39680i) q^{71} +(7.39312 - 7.39312i) q^{73} +(-15.4070 - 15.4070i) q^{75} +2.87819i q^{77} +(9.35553 + 9.35553i) q^{79} -6.27131 q^{81} -1.30937i q^{83} +(-3.21798 - 14.1537i) q^{85} -0.819240i q^{87} -0.335577 q^{89} +(1.91942 + 1.91942i) q^{91} -21.6216i q^{93} +(-18.7111 - 18.7111i) q^{95} +(1.29273 - 1.29273i) q^{97} +(19.9758 - 19.9758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 8 q^{13} - 8 q^{17} + 32 q^{21} - 16 q^{29} + 8 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} + 80 q^{57} + 24 q^{61} - 32 q^{65} + 16 q^{69} + 52 q^{73} - 4 q^{81} - 80 q^{85} - 112 q^{89} + 4 q^{97}+O(q^{100}) \) 12 * q + 8 * q^13 - 8 * q^17 + 32 * q^21 - 16 * q^29 + 8 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 + 80 * q^57 + 24 * q^61 - 32 * q^65 + 16 * q^69 + 52 * q^73 - 4 * q^81 - 80 * q^85 - 112 * q^89 + 4 * q^97

Introduction

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Modular forms

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