LMFDB - Embedded newform 1344.2.u.a.1231.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(559,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1344.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.u (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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1231.19
Character	$\chi$	$=$	1344.1231
Dual form			1344.2.u.a.559.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(1.90169 - 1.90169i) q^{5} +(-2.22978 + 1.42411i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(1.90169 - 1.90169i) q^{5} +(-2.22978 + 1.42411i) q^{7} -1.00000i q^{9} +(3.56463 - 3.56463i) q^{11} +(1.66932 + 1.66932i) q^{13} -2.68940i q^{15} -7.15496i q^{17} +(-3.10260 + 3.10260i) q^{19} +(-0.569692 + 2.58369i) q^{21} -3.63389 q^{23} -2.23286i q^{25} +(-0.707107 - 0.707107i) q^{27} +(5.29845 - 5.29845i) q^{29} +0.906641 q^{31} -5.04114i q^{33} +(-1.53213 + 6.94857i) q^{35} +(2.51619 + 2.51619i) q^{37} +2.36078 q^{39} -2.37705 q^{41} +(1.93434 - 1.93434i) q^{43} +(-1.90169 - 1.90169i) q^{45} +0.550905 q^{47} +(2.94382 - 6.35090i) q^{49} +(-5.05932 - 5.05932i) q^{51} +(3.05130 + 3.05130i) q^{53} -13.5576i q^{55} +4.38774i q^{57} +(-9.17593 - 9.17593i) q^{59} +(-5.62319 - 5.62319i) q^{61} +(1.42411 + 2.22978i) q^{63} +6.34907 q^{65} +(-1.68616 - 1.68616i) q^{67} +(-2.56955 + 2.56955i) q^{69} +11.6715 q^{71} +8.41083 q^{73} +(-1.57887 - 1.57887i) q^{75} +(-2.87190 + 13.0247i) q^{77} +12.6448i q^{79} -1.00000 q^{81} +(3.82605 - 3.82605i) q^{83} +(-13.6065 - 13.6065i) q^{85} -7.49314i q^{87} -14.6937 q^{89} +(-6.09951 - 1.34492i) q^{91} +(0.641092 - 0.641092i) q^{93} +11.8004i q^{95} +6.22825i q^{97} +(-3.56463 - 3.56463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	1.90169	−	1.90169i	0.850462	−	0.850462i	−0.139728	−	0.990190i	$-0.544623\pi$
$5$	1.90169	−	1.90169i	0.850462	−	0.850462i	0.990190	+	0.139728i	$0.0446227\pi$
$6$		0			0
$7$	−2.22978	+	1.42411i	−0.842777	+	0.538263i
$7$	−2.22978	+	1.42411i	−0.842777	+	0.538263i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	3.56463	−	3.56463i	1.07477	−	1.07477i	0.0778065	−	0.996968i	$-0.475208\pi$
$11$	3.56463	−	3.56463i	1.07477	−	1.07477i	0.996968	−	0.0778065i	$-0.0247916\pi$
$12$		0			0
$13$	1.66932	+	1.66932i	0.462986	+	0.462986i	0.899633	−	0.436647i	$-0.143834\pi$
$13$	1.66932	+	1.66932i	0.462986	+	0.462986i	−0.436647	+	0.899633i	$0.643834\pi$
$14$		0			0
$15$		−	2.68940i		−	0.694400i
$16$		0			0
$17$		−	7.15496i		−	1.73533i	−0.497147	−	0.867667i	$-0.665619\pi$
$17$		−	7.15496i		−	1.73533i	0.497147	−	0.867667i	$-0.334381\pi$
$18$		0			0
$19$	−3.10260	+	3.10260i	−0.711785	+	0.711785i	−0.966908	−	0.255123i	$-0.917884\pi$
$19$	−3.10260	+	3.10260i	−0.711785	+	0.711785i	0.255123	+	0.966908i	$0.417884\pi$
$20$		0			0
$21$	−0.569692	+	2.58369i	−0.124317	+	0.563807i
$22$		0			0
$23$	−3.63389			−0.757719			−0.378860	−	0.925454i	$-0.623684\pi$
$23$	−3.63389			−0.757719			−0.378860	+	0.925454i	$0.623684\pi$
$24$		0			0
$25$		−	2.23286i		−	0.446572i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	5.29845	−	5.29845i	0.983898	−	0.983898i	−0.0159747	−	0.999872i	$-0.505085\pi$
$29$	5.29845	−	5.29845i	0.983898	−	0.983898i	0.999872	+	0.0159747i	$0.00508512\pi$
$30$		0			0
$31$	0.906641			0.162838			0.0814188	−	0.996680i	$-0.474055\pi$
$31$	0.906641			0.162838			0.0814188	+	0.996680i	$0.474055\pi$
$32$		0			0
$33$		−	5.04114i		−	0.877550i
$34$		0			0
$35$	−1.53213	+	6.94857i	−0.258977	+	1.17452i
$36$		0			0
$37$	2.51619	+	2.51619i	0.413660	+	0.413660i	0.883011	−	0.469352i	$-0.155512\pi$
$37$	2.51619	+	2.51619i	0.413660	+	0.413660i	−0.469352	+	0.883011i	$0.655512\pi$
$38$		0			0
$39$	2.36078			0.378027
$40$		0			0
$41$	−2.37705			−0.371232			−0.185616	−	0.982622i	$-0.559428\pi$
$41$	−2.37705			−0.371232			−0.185616	+	0.982622i	$0.559428\pi$
$42$		0			0
$43$	1.93434	−	1.93434i	0.294984	−	0.294984i	−0.544062	−	0.839045i	$-0.683114\pi$
$43$	1.93434	−	1.93434i	0.294984	−	0.294984i	0.839045	+	0.544062i	$0.183114\pi$
$44$		0			0
$45$	−1.90169	−	1.90169i	−0.283487	−	0.283487i
$46$		0			0
$47$	0.550905			0.0803577			0.0401789	−	0.999193i	$-0.487207\pi$
$47$	0.550905			0.0803577			0.0401789	+	0.999193i	$0.487207\pi$
$48$		0			0
$49$	2.94382	−	6.35090i	0.420545	−	0.907272i
$50$		0			0
$51$	−5.05932	−	5.05932i	−0.708447	−	0.708447i
$52$		0			0
$53$	3.05130	+	3.05130i	0.419128	+	0.419128i	0.884903	−	0.465775i	$-0.154224\pi$
$53$	3.05130	+	3.05130i	0.419128	+	0.419128i	−0.465775	+	0.884903i	$0.654224\pi$
$54$		0			0
$55$		−	13.5576i		−	1.82811i
$56$		0			0
$57$			4.38774i			0.581170i
$58$		0			0
$59$	−9.17593	−	9.17593i	−1.19460	−	1.19460i	−0.975760	−	0.218845i	$-0.929771\pi$
$59$	−9.17593	−	9.17593i	−1.19460	−	1.19460i	−0.218845	−	0.975760i	$-0.570229\pi$
$60$		0			0
$61$	−5.62319	−	5.62319i	−0.719976	−	0.719976i	0.248624	−	0.968600i	$-0.420022\pi$
$61$	−5.62319	−	5.62319i	−0.719976	−	0.719976i	−0.968600	+	0.248624i	$0.920022\pi$
$62$		0			0
$63$	1.42411	+	2.22978i	0.179421	+	0.280926i
$64$		0			0
$65$	6.34907			0.787505
$66$		0			0
$67$	−1.68616	−	1.68616i	−0.205997	−	0.205997i	0.596567	−	0.802564i	$-0.296531\pi$
$67$	−1.68616	−	1.68616i	−0.205997	−	0.205997i	−0.802564	+	0.596567i	$0.796531\pi$
$68$		0			0
$69$	−2.56955	+	2.56955i	−0.309338	+	0.309338i
$70$		0			0
$71$	11.6715			1.38515			0.692577	−	0.721344i	$-0.256475\pi$
$71$	11.6715			1.38515			0.692577	+	0.721344i	$0.256475\pi$
$72$		0			0
$73$	8.41083			0.984414			0.492207	−	0.870478i	$-0.336190\pi$
$73$	8.41083			0.984414			0.492207	+	0.870478i	$0.336190\pi$
$74$		0			0
$75$	−1.57887	−	1.57887i	−0.182312	−	0.182312i
$76$		0			0
$77$	−2.87190	+	13.0247i	−0.327283	+	1.48431i
$78$		0			0
$79$			12.6448i			1.42265i	0.702862	+	0.711327i	$0.251905\pi$
$79$			12.6448i			1.42265i	−0.702862	+	0.711327i	$0.748095\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	3.82605	−	3.82605i	0.419964	−	0.419964i	−0.465227	−	0.885191i	$-0.654027\pi$
$83$	3.82605	−	3.82605i	0.419964	−	0.419964i	0.885191	+	0.465227i	$0.154027\pi$
$84$		0			0
$85$	−13.6065	−	13.6065i	−1.47584	−	1.47584i
$86$		0			0
$87$		−	7.49314i		−	0.803349i
$88$		0			0
$89$	−14.6937			−1.55753			−0.778765	−	0.627315i	$-0.784154\pi$
$89$	−14.6937			−1.55753			−0.778765	+	0.627315i	$0.784154\pi$
$90$		0			0
$91$	−6.09951	−	1.34492i	−0.639403	−	0.140986i
$92$		0			0
$93$	0.641092	−	0.641092i	0.0664782	−	0.0664782i
$94$		0			0
$95$			11.8004i			1.21069i
$96$		0			0
$97$			6.22825i			0.632383i	0.948695	+	0.316191i	$0.102404\pi$
$97$			6.22825i			0.632383i	−0.948695	+	0.316191i	$0.897596\pi$
$98$		0			0
$99$	−3.56463	−	3.56463i	−0.358258	−	0.358258i
$100$		0			0
$101$	−13.7348	+	13.7348i	−1.36666	+	1.36666i	−0.501512	+	0.865150i	$0.667223\pi$
$101$	−13.7348	+	13.7348i	−1.36666	+	1.36666i	−0.865150	+	0.501512i	$0.832777\pi$
$102$		0			0
$103$		−	2.12589i		−	0.209471i	−0.994500	−	0.104735i	$-0.966600\pi$
$103$		−	2.12589i		−	0.209471i	0.994500	−	0.104735i	$-0.0333995\pi$
$104$		0			0
$105$	3.83000	+	5.99676i	0.373770	+	0.585224i
$106$		0			0
$107$	9.07831	−	9.07831i	0.877634	−	0.877634i	−0.115656	−	0.993289i	$-0.536897\pi$
$107$	9.07831	−	9.07831i	0.877634	−	0.877634i	0.993289	+	0.115656i	$0.0368969\pi$
$108$		0			0
$109$	−7.77089	+	7.77089i	−0.744316	+	0.744316i	−0.973405	−	0.229090i	$-0.926425\pi$
$109$	−7.77089	+	7.77089i	−0.744316	+	0.744316i	0.229090	+	0.973405i	$0.426425\pi$
$110$		0			0
$111$	3.55843			0.337752
$112$		0			0
$113$	7.32742			0.689306			0.344653	−	0.938730i	$-0.387997\pi$
$113$	7.32742			0.689306			0.344653	+	0.938730i	$0.387997\pi$
$114$		0			0
$115$	−6.91054	+	6.91054i	−0.644412	+	0.644412i
$116$		0			0
$117$	1.66932	−	1.66932i	0.154329	−	0.154329i
$118$		0			0
$119$	10.1895	+	15.9540i	0.934066	+	1.46250i
$120$		0			0
$121$		−	14.4131i		−	1.31028i
$122$		0			0
$123$	−1.68083	+	1.68083i	−0.151555	+	0.151555i
$124$		0			0
$125$	5.26224	+	5.26224i	0.470669	+	0.470669i
$126$		0			0
$127$		−	14.6589i		−	1.30076i	−0.759608	−	0.650382i	$-0.774609\pi$
$127$		−	14.6589i		−	1.30076i	0.759608	−	0.650382i	$-0.225391\pi$
$128$		0			0
$129$		−	2.73556i		−	0.240853i
$130$		0			0
$131$	5.52527	−	5.52527i	0.482745	−	0.482745i	−0.423262	−	0.906007i	$-0.639115\pi$
$131$	5.52527	−	5.52527i	0.482745	−	0.482745i	0.906007	+	0.423262i	$0.139115\pi$
$132$		0			0
$133$	2.49966	−	11.3365i	0.216748	−	0.983004i
$134$		0			0
$135$	−2.68940			−0.231467
$136$		0			0
$137$		−	3.43937i		−	0.293845i	−0.989148	−	0.146923i	$-0.953063\pi$
$137$		−	3.43937i		−	0.293845i	0.989148	−	0.146923i	$-0.0469368\pi$
$138$		0			0
$139$	5.21179	+	5.21179i	0.442058	+	0.442058i	0.892703	−	0.450645i	$-0.148806\pi$
$139$	5.21179	+	5.21179i	0.442058	+	0.442058i	−0.450645	+	0.892703i	$0.648806\pi$
$140$		0			0
$141$	0.389548	−	0.389548i	0.0328059	−	0.0328059i
$142$		0			0
$143$	11.9010			0.995212
$144$		0			0
$145$		−	20.1520i		−	1.67354i
$146$		0			0
$147$	−2.40917	−	6.57236i	−0.198705	−	0.542079i
$148$		0			0
$149$	8.38511	+	8.38511i	0.686935	+	0.686935i	0.961553	−	0.274618i	$-0.0885514\pi$
$149$	8.38511	+	8.38511i	0.686935	+	0.686935i	−0.274618	+	0.961553i	$0.588551\pi$
$150$		0			0
$151$	−3.21093			−0.261302			−0.130651	−	0.991428i	$-0.541707\pi$
$151$	−3.21093			−0.261302			−0.130651	+	0.991428i	$0.541707\pi$
$152$		0			0
$153$	−7.15496			−0.578444
$154$		0			0
$155$	1.72415	−	1.72415i	0.138487	−	0.138487i
$156$		0			0
$157$	0.574508	+	0.574508i	0.0458508	+	0.0458508i	0.729660	−	0.683810i	$-0.239678\pi$
$157$	0.574508	+	0.574508i	0.0458508	+	0.0458508i	−0.683810	+	0.729660i	$0.739678\pi$
$158$		0			0
$159$	4.31519			0.342217
$160$		0			0
$161$	8.10277	−	5.17507i	0.638588	−	0.407852i
$162$		0			0
$163$	13.8383	+	13.8383i	1.08390	+	1.08390i	0.996142	+	0.0877597i	$0.0279708\pi$
$163$	13.8383	+	13.8383i	1.08390	+	1.08390i	0.0877597	+	0.996142i	$0.472029\pi$
$164$		0			0
$165$	−9.58670	−	9.58670i	−0.746323	−	0.746323i
$166$		0			0
$167$			9.71401i			0.751692i	0.926682	+	0.375846i	$0.122648\pi$
$167$			9.71401i			0.751692i	−0.926682	+	0.375846i	$0.877352\pi$
$168$		0			0
$169$		−	7.42674i		−	0.571287i
$170$		0			0
$171$	3.10260	+	3.10260i	0.237262	+	0.237262i
$172$		0			0
$173$	3.57505	+	3.57505i	0.271806	+	0.271806i	0.829827	−	0.558021i	$-0.188439\pi$
$173$	3.57505	+	3.57505i	0.271806	+	0.271806i	−0.558021	+	0.829827i	$0.688439\pi$
$174$		0			0
$175$	3.17984	+	4.97879i	0.240374	+	0.376361i
$176$		0			0
$177$	−12.9767			−0.975391
$178$		0			0
$179$	−12.0824	−	12.0824i	−0.903078	−	0.903078i	0.0926229	−	0.995701i	$-0.470475\pi$
$179$	−12.0824	−	12.0824i	−0.903078	−	0.903078i	−0.995701	+	0.0926229i	$0.970475\pi$
$180$		0			0
$181$	−14.7072	+	14.7072i	−1.09318	+	1.09318i	−0.0979893	+	0.995187i	$0.531241\pi$
$181$	−14.7072	+	14.7072i	−1.09318	+	1.09318i	−0.995187	+	0.0979893i	$0.968759\pi$
$182$		0			0
$183$	−7.95239			−0.587858
$184$		0			0
$185$	9.57005			0.703604
$186$		0			0
$187$	−25.5048	−	25.5048i	−1.86509	−	1.86509i
$188$		0			0
$189$	2.58369	+	0.569692i	0.187936	+	0.0414390i
$190$		0			0
$191$		−	4.83855i		−	0.350105i	−0.984559	−	0.175052i	$-0.943991\pi$
$191$		−	4.83855i		−	0.350105i	0.984559	−	0.175052i	$-0.0560095\pi$
$192$		0			0
$193$	23.3996			1.68434			0.842169	−	0.539213i	$-0.181278\pi$
$193$	23.3996			1.68434			0.842169	+	0.539213i	$0.181278\pi$
$194$		0			0
$195$	4.48947	−	4.48947i	0.321497	−	0.321497i
$196$		0			0
$197$	5.84458	+	5.84458i	0.416409	+	0.416409i	0.883964	−	0.467555i	$-0.154865\pi$
$197$	5.84458	+	5.84458i	0.416409	+	0.416409i	−0.467555	+	0.883964i	$0.654865\pi$
$198$		0			0
$199$		−	4.28359i		−	0.303655i	−0.988407	−	0.151828i	$-0.951484\pi$
$199$		−	4.28359i		−	0.303655i	0.988407	−	0.151828i	$-0.0485159\pi$
$200$		0			0
$201$	−2.38459			−0.168196
$202$		0			0
$203$	−4.26879	+	19.3600i	−0.299610	+	1.35880i
$204$		0			0
$205$	−4.52041	+	4.52041i	−0.315719	+	0.315719i
$206$		0			0
$207$			3.63389i			0.252573i
$208$		0			0
$209$			22.1192i			1.53002i
$210$		0			0
$211$	5.34715	+	5.34715i	0.368113	+	0.368113i	0.866789	−	0.498676i	$-0.166180\pi$
$211$	5.34715	+	5.34715i	0.368113	+	0.368113i	−0.498676	+	0.866789i	$0.666180\pi$
$212$		0			0
$213$	8.25301	−	8.25301i	0.565487	−	0.565487i
$214$		0			0
$215$		−	7.35702i		−	0.501745i
$216$		0			0
$217$	−2.02161	+	1.29116i	−0.137236	+	0.0876495i
$218$		0			0
$219$	5.94736	−	5.94736i	0.401885	−	0.401885i
$220$		0			0
$221$	11.9439	−	11.9439i	0.803435	−	0.803435i
$222$		0			0
$223$	28.4331			1.90402			0.952009	−	0.306070i	$-0.0990142\pi$
$223$	28.4331			1.90402			0.952009	+	0.306070i	$0.0990142\pi$
$224$		0			0
$225$	−2.23286			−0.148857
$226$		0			0
$227$	−19.1228	+	19.1228i	−1.26923	+	1.26923i	−0.322739	+	0.946488i	$0.604604\pi$
$227$	−19.1228	+	19.1228i	−1.26923	+	1.26923i	−0.946488	+	0.322739i	$0.895396\pi$
$228$		0			0
$229$	2.11755	−	2.11755i	0.139932	−	0.139932i	−0.633671	−	0.773603i	$-0.718453\pi$
$229$	2.11755	−	2.11755i	0.139932	−	0.139932i	0.773603	+	0.633671i	$0.218453\pi$
$230$		0			0
$231$	7.17914	+	11.2406i	0.472353	+	0.739579i
$232$		0			0
$233$			23.1104i			1.51401i	0.653408	+	0.757006i	$0.273339\pi$
$233$			23.1104i			1.51401i	−0.653408	+	0.757006i	$0.726661\pi$
$234$		0			0
$235$	1.04765	−	1.04765i	0.0683412	−	0.0683412i
$236$		0			0
$237$	8.94124	+	8.94124i	0.580796	+	0.580796i
$238$		0			0
$239$			9.94538i			0.643313i	0.946856	+	0.321657i	$0.104240\pi$
$239$			9.94538i			0.643313i	−0.946856	+	0.321657i	$0.895760\pi$
$240$		0			0
$241$			11.4287i			0.736187i	0.929789	+	0.368093i	$0.119989\pi$
$241$			11.4287i			0.736187i	−0.929789	+	0.368093i	$0.880011\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−6.47922	−	17.6757i	−0.413942	−	1.12926i
$246$		0			0
$247$	−10.3585			−0.659093
$248$		0			0
$249$		−	5.41086i		−	0.342899i
$250$		0			0
$251$	11.4020	+	11.4020i	0.719687	+	0.719687i	0.968541	−	0.248854i	$-0.0800540\pi$
$251$	11.4020	+	11.4020i	0.719687	+	0.719687i	−0.248854	+	0.968541i	$0.580054\pi$
$252$		0			0
$253$	−12.9535	+	12.9535i	−0.814378	+	0.814378i
$254$		0			0
$255$	−19.2425			−1.20501
$256$		0			0
$257$			8.41347i			0.524818i	0.964957	+	0.262409i	$0.0845169\pi$
$257$			8.41347i			0.524818i	−0.964957	+	0.262409i	$0.915483\pi$
$258$		0			0
$259$	−9.19389	−	2.02721i	−0.571280	−	0.125965i
$260$		0			0
$261$	−5.29845	−	5.29845i	−0.327966	−	0.327966i
$262$		0			0
$263$	6.67247			0.411442			0.205721	−	0.978611i	$-0.434046\pi$
$263$	6.67247			0.411442			0.205721	+	0.978611i	$0.434046\pi$
$264$		0			0
$265$	11.6053			0.712906
$266$		0			0
$267$	−10.3900	+	10.3900i	−0.635859	+	0.635859i
$268$		0			0
$269$	1.02225	+	1.02225i	0.0623274	+	0.0623274i	0.737583	−	0.675256i	$-0.235967\pi$
$269$	1.02225	+	1.02225i	0.0623274	+	0.0623274i	−0.675256	+	0.737583i	$0.735967\pi$
$270$		0			0
$271$	5.47375			0.332507			0.166253	−	0.986083i	$-0.446833\pi$
$271$	5.47375			0.332507			0.166253	+	0.986083i	$0.446833\pi$
$272$		0			0
$273$	−5.26401	+	3.36201i	−0.318592	+	0.203478i
$274$		0			0
$275$	−7.95932	−	7.95932i	−0.479965	−	0.479965i
$276$		0			0
$277$	9.91118	+	9.91118i	0.595505	+	0.595505i	0.939113	−	0.343608i	$-0.111649\pi$
$277$	9.91118	+	9.91118i	0.595505	+	0.595505i	−0.343608	+	0.939113i	$0.611649\pi$
$278$		0			0
$279$		−	0.906641i		−	0.0542792i
$280$		0			0
$281$			19.6432i			1.17182i	0.810378	+	0.585908i	$0.199262\pi$
$281$			19.6432i			1.17182i	−0.810378	+	0.585908i	$0.800738\pi$
$282$		0			0
$283$	20.3051	+	20.3051i	1.20701	+	1.20701i	0.971990	+	0.235022i	$0.0755162\pi$
$283$	20.3051	+	20.3051i	1.20701	+	1.20701i	0.235022	+	0.971990i	$0.424484\pi$
$284$		0			0
$285$	8.34412	+	8.34412i	0.494263	+	0.494263i
$286$		0			0
$287$	5.30028	−	3.38518i	0.312866	−	0.199821i
$288$		0			0
$289$	−34.1935			−2.01138
$290$		0			0
$291$	4.40404	+	4.40404i	0.258169	+	0.258169i
$292$		0			0
$293$	−11.7526	+	11.7526i	−0.686597	+	0.686597i	−0.961478	−	0.274881i	$-0.911361\pi$
$293$	−11.7526	+	11.7526i	−0.686597	+	0.686597i	0.274881	+	0.961478i	$0.411361\pi$
$294$		0			0
$295$	−34.8996			−2.03193
$296$		0			0
$297$	−5.04114			−0.292517
$298$		0			0
$299$	−6.06613	−	6.06613i	−0.350814	−	0.350814i
$300$		0			0
$301$	−1.55843	+	7.06785i	−0.0898264	+	0.407384i
$302$		0			0
$303$			19.4239i			1.11588i
$304$		0			0
$305$	−21.3871			−1.22462
$306$		0			0
$307$	−19.0195	+	19.0195i	−1.08550	+	1.08550i	−0.0895163	+	0.995985i	$0.528532\pi$
$307$	−19.0195	+	19.0195i	−1.08550	+	1.08550i	−0.995985	+	0.0895163i	$0.971468\pi$
$308$		0			0
$309$	−1.50323	−	1.50323i	−0.0855160	−	0.0855160i
$310$		0			0
$311$		−	13.7113i		−	0.777499i	−0.921344	−	0.388749i	$-0.872907\pi$
$311$		−	13.7113i		−	0.777499i	0.921344	−	0.388749i	$-0.127093\pi$
$312$		0			0
$313$	−4.84337			−0.273764			−0.136882	−	0.990587i	$-0.543708\pi$
$313$	−4.84337			−0.273764			−0.136882	+	0.990587i	$0.543708\pi$
$314$		0			0
$315$	6.94857	+	1.53213i	0.391508	+	0.0863257i
$316$		0			0
$317$	−2.72533	+	2.72533i	−0.153070	+	0.153070i	−0.779488	−	0.626418i	$-0.784520\pi$
$317$	−2.72533	+	2.72533i	−0.153070	+	0.153070i	0.626418	+	0.779488i	$0.284520\pi$
$318$		0			0
$319$		−	37.7740i		−	2.11494i
$320$		0			0
$321$		−	12.8387i		−	0.716585i
$322$		0			0
$323$	22.1990	+	22.1990i	1.23518	+	1.23518i
$324$		0			0
$325$	3.72736	−	3.72736i	0.206757	−	0.206757i
$326$		0			0
$327$			10.9897i			0.607731i
$328$		0			0
$329$	−1.22839	+	0.784549i	−0.0677236	+	0.0432536i
$330$		0			0
$331$	−6.93803	+	6.93803i	−0.381349	+	0.381349i	−0.871588	−	0.490239i	$-0.836909\pi$
$331$	−6.93803	+	6.93803i	−0.381349	+	0.381349i	0.490239	+	0.871588i	$0.336909\pi$
$332$		0			0
$333$	2.51619	−	2.51619i	0.137887	−	0.137887i
$334$		0			0
$335$	−6.41310			−0.350385
$336$		0			0
$337$	2.95698			0.161077			0.0805384	−	0.996752i	$-0.474336\pi$
$337$	2.95698			0.161077			0.0805384	+	0.996752i	$0.474336\pi$
$338$		0			0
$339$	5.18127	−	5.18127i	0.281408	−	0.281408i
$340$		0			0
$341$	3.23184	−	3.23184i	0.175014	−	0.175014i
$342$		0			0
$343$	2.48033	+	18.3534i	0.133925	+	0.990991i
$344$		0			0
$345$			9.77299i			0.526160i
$346$		0			0
$347$	3.16858	−	3.16858i	0.170098	−	0.170098i	−0.616924	−	0.787023i	$-0.711622\pi$
$347$	3.16858	−	3.16858i	0.170098	−	0.170098i	0.787023	+	0.616924i	$0.211622\pi$
$348$		0			0
$349$	11.0951	+	11.0951i	0.593908	+	0.593908i	0.938685	−	0.344777i	$-0.112045\pi$
$349$	11.0951	+	11.0951i	0.593908	+	0.593908i	−0.344777	+	0.938685i	$0.612045\pi$
$350$		0			0
$351$		−	2.36078i		−	0.126009i
$352$		0			0
$353$		−	30.8984i		−	1.64455i	−0.569087	−	0.822277i	$-0.692703\pi$
$353$		−	30.8984i		−	1.64455i	0.569087	−	0.822277i	$-0.307297\pi$
$354$		0			0
$355$	22.1956	−	22.1956i	1.17802	−	1.17802i
$356$		0			0
$357$	18.4862	+	4.07613i	0.978393	+	0.215732i
$358$		0			0
$359$	−0.943215			−0.0497810			−0.0248905	−	0.999690i	$-0.507924\pi$
$359$	−0.943215			−0.0497810			−0.0248905	+	0.999690i	$0.507924\pi$
$360$		0			0
$361$		−	0.252238i		−	0.0132757i
$362$		0			0
$363$	−10.1916	−	10.1916i	−0.534921	−	0.534921i
$364$		0			0
$365$	15.9948	−	15.9948i	0.837207	−	0.837207i
$366$		0			0
$367$	−3.56906			−0.186304			−0.0931518	−	0.995652i	$-0.529694\pi$
$367$	−3.56906			−0.186304			−0.0931518	+	0.995652i	$0.529694\pi$
$368$		0			0
$369$			2.37705i			0.123744i
$370$		0			0
$371$	−11.1491	−	2.45833i	−0.578833	−	0.127630i
$372$		0			0
$373$	−0.693026	−	0.693026i	−0.0358835	−	0.0358835i	0.688937	−	0.724821i	$-0.258077\pi$
$373$	−0.693026	−	0.693026i	−0.0358835	−	0.0358835i	−0.724821	+	0.688937i	$0.758077\pi$
$374$		0			0
$375$	7.44194			0.384300
$376$		0			0
$377$	17.6896			0.911062
$378$		0			0
$379$	−6.55229	+	6.55229i	−0.336569	+	0.336569i	−0.855074	−	0.518506i	$-0.826489\pi$
$379$	−6.55229	+	6.55229i	−0.336569	+	0.336569i	0.518506	+	0.855074i	$0.326489\pi$
$380$		0			0
$381$	−10.3654	−	10.3654i	−0.531034	−	0.531034i
$382$		0			0
$383$	−25.4405			−1.29995			−0.649975	−	0.759956i	$-0.725221\pi$
$383$	−25.4405			−1.29995			−0.649975	+	0.759956i	$0.725221\pi$
$384$		0			0
$385$	19.3076	+	30.2305i	0.984005	+	1.54069i
$386$		0			0
$387$	−1.93434	−	1.93434i	−0.0983278	−	0.0983278i
$388$		0			0
$389$	−11.6405	−	11.6405i	−0.590199	−	0.590199i	0.347486	−	0.937685i	$-0.387035\pi$
$389$	−11.6405	−	11.6405i	−0.590199	−	0.590199i	−0.937685	+	0.347486i	$0.887035\pi$
$390$		0			0
$391$			26.0004i			1.31490i
$392$		0			0
$393$		−	7.81392i		−	0.394160i
$394$		0			0
$395$	24.0465	+	24.0465i	1.20991	+	1.20991i
$396$		0			0
$397$	−18.3501	−	18.3501i	−0.920963	−	0.920963i	0.0761349	−	0.997098i	$-0.475742\pi$
$397$	−18.3501	−	18.3501i	−0.920963	−	0.920963i	−0.997098	+	0.0761349i	$0.975742\pi$
$398$		0			0
$399$	−6.24862	−	9.78368i	−0.312822	−	0.489797i
$400$		0			0
$401$	22.2529			1.11126			0.555630	−	0.831430i	$-0.312477\pi$
$401$	22.2529			1.11126			0.555630	+	0.831430i	$0.312477\pi$
$402$		0			0
$403$	1.51347	+	1.51347i	0.0753916	+	0.0753916i
$404$		0			0
$405$	−1.90169	+	1.90169i	−0.0944958	+	0.0944958i
$406$		0			0
$407$	17.9386			0.889182
$408$		0			0
$409$	27.1395			1.34196			0.670981	−	0.741475i	$-0.265873\pi$
$409$	27.1395			1.34196			0.670981	+	0.741475i	$0.265873\pi$
$410$		0			0
$411$	−2.43200	−	2.43200i	−0.119962	−	0.119962i
$412$		0			0
$413$	33.5278	+	7.39274i	1.64980	+	0.363773i
$414$		0			0
$415$		−	14.5519i		−	0.714327i
$416$		0			0
$417$	7.37059			0.360939
$418$		0			0
$419$	14.0335	−	14.0335i	0.685582	−	0.685582i	−0.275670	−	0.961252i	$-0.588900\pi$
$419$	14.0335	−	14.0335i	0.685582	−	0.685582i	0.961252	+	0.275670i	$0.0888997\pi$
$420$		0			0
$421$	18.7350	+	18.7350i	0.913087	+	0.913087i	0.996514	−	0.0834270i	$-0.0265866\pi$
$421$	18.7350	+	18.7350i	0.913087	+	0.913087i	−0.0834270	+	0.996514i	$0.526587\pi$
$422$		0			0
$423$		−	0.550905i		−	0.0267859i
$424$		0			0
$425$	−15.9760			−0.774952
$426$		0			0
$427$	20.5465	+	4.53042i	0.994315	+	0.219242i
$428$		0			0
$429$	8.41528	−	8.41528i	0.406294	−	0.406294i
$430$		0			0
$431$			24.5106i			1.18063i	0.807172	+	0.590317i	$0.200997\pi$
$431$			24.5106i			1.18063i	−0.807172	+	0.590317i	$0.799003\pi$
$432$		0			0
$433$			10.3532i			0.497542i	0.968562	+	0.248771i	$0.0800267\pi$
$433$			10.3532i			0.497542i	−0.968562	+	0.248771i	$0.919973\pi$
$434$		0			0
$435$	−14.2496	−	14.2496i	−0.683218	−	0.683218i
$436$		0			0
$437$	11.2745	−	11.2745i	0.539333	−	0.539333i
$438$		0			0
$439$		−	21.8589i		−	1.04327i	−0.853170	−	0.521634i	$-0.825323\pi$
$439$		−	21.8589i		−	1.04327i	0.853170	−	0.521634i	$-0.174677\pi$
$440$		0			0
$441$	−6.35090	−	2.94382i	−0.302424	−	0.140182i
$442$		0			0
$443$	−8.82244	+	8.82244i	−0.419167	+	0.419167i	−0.884916	−	0.465750i	$-0.845785\pi$
$443$	−8.82244	+	8.82244i	−0.419167	+	0.419167i	0.465750	+	0.884916i	$0.345785\pi$
$444$		0			0
$445$	−27.9429	+	27.9429i	−1.32462	+	1.32462i
$446$		0			0
$447$	11.8583			0.560880
$448$		0			0
$449$	−15.3552			−0.724657			−0.362329	−	0.932050i	$-0.618018\pi$
$449$	−15.3552			−0.724657			−0.362329	+	0.932050i	$0.618018\pi$
$450$		0			0
$451$	−8.47328	+	8.47328i	−0.398991	+	0.398991i
$452$		0			0
$453$	−2.27047	+	2.27047i	−0.106676	+	0.106676i
$454$		0			0
$455$	−14.1570	+	9.04177i	−0.663691	+	0.423885i
$456$		0			0
$457$		−	34.0509i		−	1.59283i	−0.604748	−	0.796417i	$-0.706726\pi$
$457$		−	34.0509i		−	1.59283i	0.604748	−	0.796417i	$-0.293274\pi$
$458$		0			0
$459$	−5.05932	+	5.05932i	−0.236149	+	0.236149i
$460$		0			0
$461$	−17.5033	−	17.5033i	−0.815210	−	0.815210i	0.170200	−	0.985410i	$-0.445559\pi$
$461$	−17.5033	−	17.5033i	−0.815210	−	0.815210i	−0.985410	+	0.170200i	$0.945559\pi$
$462$		0			0
$463$		−	0.0530223i		−	0.00246416i	−0.999999	−	0.00123208i	$-0.999608\pi$
$463$		−	0.0530223i		−	0.00246416i	0.999999	−	0.00123208i	$-0.000392183\pi$
$464$		0			0
$465$		−	2.43832i		−	0.113074i
$466$		0			0
$467$	8.39635	−	8.39635i	0.388537	−	0.388537i	−0.485629	−	0.874165i	$-0.661409\pi$
$467$	8.39635	−	8.39635i	0.388537	−	0.388537i	0.874165	+	0.485629i	$0.161409\pi$
$468$		0			0
$469$	6.16103	+	1.35848i	0.284490	+	0.0627288i
$470$		0			0
$471$	0.812478			0.0374370
$472$		0			0
$473$		−	13.7904i		−	0.634082i
$474$		0			0
$475$	6.92768	+	6.92768i	0.317864	+	0.317864i
$476$		0			0
$477$	3.05130	−	3.05130i	0.139709	−	0.139709i
$478$		0			0
$479$	−36.9533			−1.68844			−0.844220	−	0.535997i	$-0.819936\pi$
$479$	−36.9533			−1.68844			−0.844220	+	0.535997i	$0.819936\pi$
$480$		0			0
$481$			8.40067i			0.383037i
$482$		0			0
$483$	2.07020	−	9.38885i	0.0941974	−	0.427208i
$484$		0			0
$485$	11.8442	+	11.8442i	0.537818	+	0.537818i
$486$		0			0
$487$	−14.6233			−0.662647			−0.331324	−	0.943517i	$-0.607495\pi$
$487$	−14.6233			−0.662647			−0.331324	+	0.943517i	$0.607495\pi$
$488$		0			0
$489$	19.5703			0.885002
$490$		0			0
$491$	−6.45924	+	6.45924i	−0.291502	+	0.291502i	−0.837673	−	0.546172i	$-0.816085\pi$
$491$	−6.45924	+	6.45924i	−0.291502	+	0.291502i	0.546172	+	0.837673i	$0.316085\pi$
$492$		0			0
$493$	−37.9102	−	37.9102i	−1.70739	−	1.70739i
$494$		0			0
$495$	−13.5576			−0.609370
$496$		0			0
$497$	−26.0249	+	16.6215i	−1.16738	+	0.745578i
$498$		0			0
$499$	−0.0937570	−	0.0937570i	−0.00419714	−	0.00419714i	0.705005	−	0.709202i	$-0.250945\pi$
$499$	−0.0937570	−	0.0937570i	−0.00419714	−	0.00419714i	−0.709202	+	0.705005i	$0.750945\pi$
$500$		0			0
$501$	6.86884	+	6.86884i	0.306877	+	0.306877i
$502$		0			0
$503$		−	8.91797i		−	0.397633i	−0.980037	−	0.198816i	$-0.936290\pi$
$503$		−	8.91797i		−	0.397633i	0.980037	−	0.198816i	$-0.0637097\pi$
$504$		0			0
$505$			52.2387i			2.32459i
$506$		0			0
$507$	−5.25150	−	5.25150i	−0.233227	−	0.233227i
$508$		0			0
$509$	−8.24799	−	8.24799i	−0.365586	−	0.365586i	0.500279	−	0.865864i	$-0.333231\pi$
$509$	−8.24799	−	8.24799i	−0.365586	−	0.365586i	−0.865864	+	0.500279i	$0.833231\pi$
$510$		0			0
$511$	−18.7543	+	11.9780i	−0.829641	+	0.529874i
$512$		0			0
$513$	4.38774			0.193723
$514$		0			0
$515$	−4.04279	−	4.04279i	−0.178147	−	0.178147i
$516$		0			0
$517$	1.96377	−	1.96377i	0.0863664	−	0.0863664i
$518$		0			0
$519$	5.05588			0.221929
$520$		0			0
$521$	22.1437			0.970135			0.485068	−	0.874477i	$-0.338795\pi$
$521$	22.1437			0.970135			0.485068	+	0.874477i	$0.338795\pi$
$522$		0			0
$523$	−1.49811	−	1.49811i	−0.0655079	−	0.0655079i	0.673594	−	0.739102i	$-0.264750\pi$
$523$	−1.49811	−	1.49811i	−0.0655079	−	0.0655079i	−0.739102	+	0.673594i	$0.764750\pi$
$524$		0			0
$525$	5.76902	+	1.27204i	0.251781	+	0.0555166i
$526$		0			0
$527$		−	6.48698i		−	0.282577i
$528$		0			0
$529$	−9.79482			−0.425862
$530$		0			0
$531$	−9.17593	+	9.17593i	−0.398202	+	0.398202i
$532$		0			0
$533$	−3.96805	−	3.96805i	−0.171875	−	0.171875i
$534$		0			0
$535$		−	34.5283i		−	1.49279i
$536$		0			0
$537$	−17.0870			−0.737360
$538$		0			0
$539$	−12.1450	−	33.1322i	−0.523121	−	1.42710i
$540$		0			0
$541$	3.10477	−	3.10477i	0.133485	−	0.133485i	−0.637208	−	0.770692i	$-0.719911\pi$
$541$	3.10477	−	3.10477i	0.133485	−	0.133485i	0.770692	+	0.637208i	$0.219911\pi$
$542$		0			0
$543$			20.7991i			0.892575i
$544$		0			0
$545$			29.5557i			1.26603i
$546$		0			0
$547$	1.79963	+	1.79963i	0.0769465	+	0.0769465i	0.744533	−	0.667586i	$-0.232672\pi$
$547$	1.79963	+	1.79963i	0.0769465	+	0.0769465i	−0.667586	+	0.744533i	$0.732672\pi$
$548$		0			0
$549$	−5.62319	+	5.62319i	−0.239992	+	0.239992i
$550$		0			0
$551$			32.8779i			1.40065i
$552$		0			0
$553$	−18.0076	−	28.1951i	−0.765762	−	1.19898i
$554$		0			0
$555$	6.76704	−	6.76704i	0.287245	−	0.287245i
$556$		0			0
$557$	−11.8995	+	11.8995i	−0.504196	+	0.504196i	−0.912739	−	0.408543i	$-0.866037\pi$
$557$	−11.8995	+	11.8995i	−0.504196	+	0.504196i	0.408543	+	0.912739i	$0.366037\pi$
$558$		0			0
$559$	6.45806			0.273147
$560$		0			0
$561$	−36.0692			−1.52284
$562$		0			0
$563$	0.635961	−	0.635961i	0.0268026	−	0.0268026i	−0.693578	−	0.720381i	$-0.743967\pi$
$563$	0.635961	−	0.635961i	0.0268026	−	0.0268026i	0.720381	+	0.693578i	$0.243967\pi$
$564$		0			0
$565$	13.9345	−	13.9345i	0.586229	−	0.586229i
$566$		0			0
$567$	2.22978	−	1.42411i	0.0936419	−	0.0598070i
$568$		0			0
$569$		−	0.425156i		−	0.0178235i	−0.999960	−	0.00891174i	$-0.997163\pi$
$569$		−	0.425156i		−	0.0178235i	0.999960	−	0.00891174i	$-0.00283673\pi$
$570$		0			0
$571$	20.0961	−	20.0961i	0.840997	−	0.840997i	−0.147992	−	0.988989i	$-0.547281\pi$
$571$	20.0961	−	20.0961i	0.840997	−	0.840997i	0.988989	+	0.147992i	$0.0472809\pi$
$572$		0			0
$573$	−3.42137	−	3.42137i	−0.142930	−	0.142930i
$574$		0			0
$575$			8.11398i			0.338376i
$576$		0			0
$577$			10.2508i			0.426748i	0.976971	+	0.213374i	$0.0684453\pi$
$577$			10.2508i			0.426748i	−0.976971	+	0.213374i	$0.931555\pi$
$578$		0			0
$579$	16.5460	−	16.5460i	0.687628	−	0.687628i
$580$		0			0
$581$	−3.08252	+	13.9800i	−0.127885	+	0.579987i
$582$		0			0
$583$	21.7535			0.900937
$584$		0			0
$585$		−	6.34907i		−	0.262502i
$586$		0			0
$587$	19.3706	+	19.3706i	0.799510	+	0.799510i	0.983018	−	0.183508i	$-0.0587454\pi$
$587$	19.3706	+	19.3706i	0.799510	+	0.799510i	−0.183508	+	0.983018i	$0.558745\pi$
$588$		0			0
$589$	−2.81294	+	2.81294i	−0.115905	+	0.115905i
$590$		0			0
$591$	8.26548			0.339997
$592$		0			0
$593$		−	33.1941i		−	1.36312i	−0.731764	−	0.681559i	$-0.761302\pi$
$593$		−	33.1941i		−	1.36312i	0.731764	−	0.681559i	$-0.238698\pi$
$594$		0			0
$595$	49.7167	+	10.9623i	2.03819	+	0.449412i
$596$		0			0
$597$	−3.02895	−	3.02895i	−0.123967	−	0.123967i
$598$		0			0
$599$	1.68554			0.0688694			0.0344347	−	0.999407i	$-0.489037\pi$
$599$	1.68554			0.0688694			0.0344347	+	0.999407i	$0.489037\pi$
$600$		0			0
$601$	2.90830			0.118632			0.0593160	−	0.998239i	$-0.481108\pi$
$601$	2.90830			0.118632			0.0593160	+	0.998239i	$0.481108\pi$
$602$		0			0
$603$	−1.68616	+	1.68616i	−0.0686656	+	0.0686656i
$604$		0			0
$605$	−27.4093	−	27.4093i	−1.11435	−	1.11435i
$606$		0			0
$607$	−21.5383			−0.874213			−0.437106	−	0.899410i	$-0.643997\pi$
$607$	−21.5383			−0.874213			−0.437106	+	0.899410i	$0.643997\pi$
$608$		0			0
$609$	10.6711	+	16.7080i	0.432413	+	0.677044i
$610$		0			0
$611$	0.919637	+	0.919637i	0.0372045	+	0.0372045i
$612$		0			0
$613$	19.8687	+	19.8687i	0.802488	+	0.802488i	0.983484	−	0.180996i	$-0.0579321\pi$
$613$	19.8687	+	19.8687i	0.802488	+	0.802488i	−0.180996	+	0.983484i	$0.557932\pi$
$614$		0			0
$615$			6.39282i			0.257783i
$616$		0			0
$617$		−	31.7899i		−	1.27981i	−0.768453	−	0.639906i	$-0.778973\pi$
$617$		−	31.7899i		−	1.27981i	0.768453	−	0.639906i	$-0.221027\pi$
$618$		0			0
$619$	14.2152	+	14.2152i	0.571358	+	0.571358i	0.932508	−	0.361150i	$-0.117616\pi$
$619$	14.2152	+	14.2152i	0.571358	+	0.571358i	−0.361150	+	0.932508i	$0.617616\pi$
$620$		0			0
$621$	2.56955	+	2.56955i	0.103113	+	0.103113i
$622$		0			0
$623$	32.7637	−	20.9255i	1.31265	−	0.838362i
$624$		0			0
$625$	31.1786			1.24715
$626$		0			0
$627$	15.6406	+	15.6406i	0.624627	+	0.624627i
$628$		0			0
$629$	18.0033	−	18.0033i	0.717837	−	0.717837i
$630$		0			0
$631$	−7.63145			−0.303803			−0.151902	−	0.988396i	$-0.548540\pi$
$631$	−7.63145			−0.303803			−0.151902	+	0.988396i	$0.548540\pi$
$632$		0			0
$633$	7.56202			0.300563
$634$		0			0
$635$	−27.8766	−	27.8766i	−1.10625	−	1.10625i
$636$		0			0
$637$	15.5159	−	5.68752i	0.614761	−	0.225348i
$638$		0			0
$639$		−	11.6715i		−	0.461718i
$640$		0			0
$641$	−24.3462			−0.961616			−0.480808	−	0.876826i	$-0.659657\pi$
$641$	−24.3462			−0.961616			−0.480808	+	0.876826i	$0.659657\pi$
$642$		0			0
$643$	21.6002	−	21.6002i	0.851829	−	0.851829i	−0.138529	−	0.990358i	$-0.544237\pi$
$643$	21.6002	−	21.6002i	0.851829	−	0.851829i	0.990358	+	0.138529i	$0.0442374\pi$
$644$		0			0
$645$	−5.20220	−	5.20220i	−0.204836	−	0.204836i
$646$		0			0
$647$		−	34.5047i		−	1.35652i	−0.734823	−	0.678259i	$-0.762735\pi$
$647$		−	34.5047i		−	1.35652i	0.734823	−	0.678259i	$-0.237265\pi$
$648$		0			0
$649$	−65.4175			−2.56786
$650$		0			0
$651$	−0.516507	+	2.34248i	−0.0202435	+	0.0918090i
$652$		0			0
$653$	10.7862	−	10.7862i	0.422097	−	0.422097i	−0.463828	−	0.885925i	$-0.653525\pi$
$653$	10.7862	−	10.7862i	0.422097	−	0.422097i	0.885925	+	0.463828i	$0.153525\pi$
$654$		0			0
$655$		−	21.0147i		−	0.821113i
$656$		0			0
$657$		−	8.41083i		−	0.328138i
$658$		0			0
$659$	14.5491	+	14.5491i	0.566754	+	0.566754i	0.931217	−	0.364464i	$-0.118748\pi$
$659$	14.5491	+	14.5491i	0.566754	+	0.566754i	−0.364464	+	0.931217i	$0.618748\pi$
$660$		0			0
$661$	−25.2625	+	25.2625i	−0.982596	+	0.982596i	−0.999851	−	0.0172555i	$-0.994507\pi$
$661$	−25.2625	+	25.2625i	−0.982596	+	0.982596i	0.0172555	+	0.999851i	$0.494507\pi$
$662$		0			0
$663$		−	16.8913i		−	0.656002i
$664$		0			0
$665$	−16.8050	−	26.3122i	−0.651671	−	1.02034i
$666$		0			0
$667$	−19.2540	+	19.2540i	−0.745518	+	0.745518i
$668$		0			0
$669$	20.1052	−	20.1052i	0.777312	−	0.777312i
$670$		0			0
$671$	−40.0891			−1.54762
$672$		0			0
$673$	10.5919			0.408287			0.204144	−	0.978941i	$-0.434559\pi$
$673$	10.5919			0.408287			0.204144	+	0.978941i	$0.434559\pi$
$674$		0			0
$675$	−1.57887	+	1.57887i	−0.0607708	+	0.0607708i
$676$		0			0
$677$	27.0595	−	27.0595i	1.03998	−	1.03998i	0.0408138	−	0.999167i	$-0.487005\pi$
$677$	27.0595	−	27.0595i	1.03998	−	1.03998i	0.999167	−	0.0408138i	$-0.0129951\pi$
$678$		0			0
$679$	−8.86971	−	13.8876i	−0.340388	−	0.532957i
$680$		0			0
$681$			27.0438i			1.03632i
$682$		0			0
$683$	−28.1993	+	28.1993i	−1.07901	+	1.07901i	−0.0824168	+	0.996598i	$0.526264\pi$
$683$	−28.1993	+	28.1993i	−1.07901	+	1.07901i	−0.996598	+	0.0824168i	$0.973736\pi$
$684$		0			0
$685$	−6.54062	−	6.54062i	−0.249904	−	0.249904i
$686$		0			0
$687$		−	2.99467i		−	0.114254i
$688$		0			0
$689$			10.1872i			0.388101i
$690$		0			0
$691$	−2.94281	+	2.94281i	−0.111950	+	0.111950i	−0.760863	−	0.648913i	$-0.775224\pi$
$691$	−2.94281	+	2.94281i	−0.111950	+	0.111950i	0.648913	+	0.760863i	$0.275224\pi$
$692$		0			0
$693$	13.0247	+	2.87190i	0.494769	+	0.109094i
$694$		0			0
$695$	19.8224			0.751908
$696$		0			0
$697$			17.0077i			0.644211i
$698$		0			0
$699$	16.3415	+	16.3415i	0.618093	+	0.618093i
$700$		0			0
$701$	14.0610	−	14.0610i	0.531077	−	0.531077i	−0.389816	−	0.920893i	$-0.627461\pi$
$701$	14.0610	−	14.0610i	0.531077	−	0.531077i	0.920893	+	0.389816i	$0.127461\pi$
$702$		0			0
$703$	−15.6135			−0.588873
$704$		0			0
$705$		−	1.48160i		−	0.0558004i
$706$		0			0
$707$	11.0657	−	50.1854i	0.416167	−	1.88742i
$708$		0			0
$709$	−17.0650	−	17.0650i	−0.640890	−	0.640890i	0.309884	−	0.950774i	$-0.399710\pi$
$709$	−17.0650	−	17.0650i	−0.640890	−	0.640890i	−0.950774	+	0.309884i	$0.899710\pi$
$710$		0			0
$711$	12.6448			0.474218
$712$		0			0
$713$	−3.29464			−0.123385
$714$		0			0
$715$	22.6320	−	22.6320i	0.846390	−	0.846390i
$716$		0			0
$717$	7.03245	+	7.03245i	0.262632	+	0.262632i
$718$		0			0
$719$	−4.08011			−0.152162			−0.0760812	−	0.997102i	$-0.524241\pi$
$719$	−4.08011			−0.152162			−0.0760812	+	0.997102i	$0.524241\pi$
$720$		0			0
$721$	3.02751	+	4.74027i	0.112750	+	0.176537i
$722$		0			0
$723$	8.08131	+	8.08131i	0.300547	+	0.300547i
$724$		0			0
$725$	−11.8307	−	11.8307i	−0.439382	−	0.439382i
$726$		0			0
$727$		−	29.7494i		−	1.10334i	−0.834061	−	0.551672i	$-0.813990\pi$
$727$		−	29.7494i		−	1.10334i	0.834061	−	0.551672i	$-0.186010\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−13.8401	−	13.8401i	−0.511895	−	0.511895i
$732$		0			0
$733$	12.3461	+	12.3461i	0.456014	+	0.456014i	0.897345	−	0.441330i	$-0.145493\pi$
$733$	12.3461	+	12.3461i	0.456014	+	0.456014i	−0.441330	+	0.897345i	$0.645493\pi$
$734$		0			0
$735$	−17.0801	−	7.91709i	−0.630009	−	0.292026i
$736$		0			0
$737$	−12.0210			−0.442801
$738$		0			0
$739$	12.7621	+	12.7621i	0.469462	+	0.469462i	0.901740	−	0.432278i	$-0.142290\pi$
$739$	12.7621	+	12.7621i	0.469462	+	0.469462i	−0.432278	+	0.901740i	$0.642290\pi$
$740$		0			0
$741$	−7.32454	+	7.32454i	−0.269074	+	0.269074i
$742$		0			0
$743$	14.3254			0.525547			0.262774	−	0.964858i	$-0.415363\pi$
$743$	14.3254			0.525547			0.262774	+	0.964858i	$0.415363\pi$
$744$		0			0
$745$	31.8918			1.16843
$746$		0			0
$747$	−3.82605	−	3.82605i	−0.139988	−	0.139988i
$748$		0			0
$749$	−7.31409	+	33.1711i	−0.267251	+	1.21205i
$750$		0			0
$751$		−	51.1794i		−	1.86756i	−0.357846	−	0.933781i	$-0.616489\pi$
$751$		−	51.1794i		−	1.86756i	0.357846	−	0.933781i	$-0.383511\pi$
$752$		0			0
$753$	16.1248			0.587622
$754$		0			0
$755$	−6.10620	+	6.10620i	−0.222227	+	0.222227i
$756$		0			0
$757$	−14.4521	−	14.4521i	−0.525271	−	0.525271i	0.393888	−	0.919159i	$-0.371130\pi$
$757$	−14.4521	−	14.4521i	−0.525271	−	0.525271i	−0.919159	+	0.393888i	$0.871130\pi$
$758$		0			0
$759$			18.3190i			0.664936i
$760$		0			0
$761$	6.59268			0.238985			0.119492	−	0.992835i	$-0.461873\pi$
$761$	6.59268			0.238985			0.119492	+	0.992835i	$0.461873\pi$
$762$		0			0
$763$	6.26074	−	28.3939i	0.226654	−	1.02793i
$764$		0			0
$765$	−13.6065	+	13.6065i	−0.491945	+	0.491945i
$766$		0			0
$767$		−	30.6351i		−	1.10617i
$768$		0			0
$769$		−	2.21522i		−	0.0798829i	−0.999202	−	0.0399414i	$-0.987283\pi$
$769$		−	2.21522i		−	0.0798829i	0.999202	−	0.0399414i	$-0.0127171\pi$
$770$		0			0
$771$	5.94922	+	5.94922i	0.214256	+	0.214256i
$772$		0			0
$773$	−17.1592	+	17.1592i	−0.617173	+	0.617173i	−0.944805	−	0.327633i	$-0.893749\pi$
$773$	−17.1592	+	17.1592i	−0.617173	+	0.617173i	0.327633	+	0.944805i	$0.393749\pi$
$774$		0			0
$775$		−	2.02440i		−	0.0727188i
$776$		0			0
$777$	−7.93452	+	5.06760i	−0.284649	+	0.181799i
$778$		0			0
$779$	7.37502	−	7.37502i	0.264237	−	0.264237i
$780$		0			0
$781$	41.6046	−	41.6046i	1.48873	−	1.48873i
$782$		0			0
$783$	−7.49314			−0.267783
$784$		0			0
$785$	2.18508			0.0779887
$786$		0			0
$787$	−18.9133	+	18.9133i	−0.674188	+	0.674188i	−0.958679	−	0.284491i	$-0.908175\pi$
$787$	−18.9133	+	18.9133i	−0.674188	+	0.674188i	0.284491	+	0.958679i	$0.408175\pi$
$788$		0			0
$789$	4.71815	−	4.71815i	0.167970	−	0.167970i
$790$		0			0
$791$	−16.3385	+	10.4351i	−0.580931	+	0.371028i
$792$		0			0
$793$		−	18.7738i		−	0.666678i
$794$		0			0
$795$	8.20616	−	8.20616i	0.291043	−	0.291043i
$796$		0			0
$797$	−0.285537	−	0.285537i	−0.0101142	−	0.0101142i	0.702032	−	0.712146i	$-0.252277\pi$
$797$	−0.285537	−	0.285537i	−0.0101142	−	0.0101142i	−0.712146	+	0.702032i	$0.752277\pi$
$798$		0			0
$799$		−	3.94170i		−	0.139447i
$800$		0			0
$801$			14.6937i			0.519177i
$802$		0			0
$803$	29.9815	−	29.9815i	1.05802	−	1.05802i
$804$		0			0
$805$	5.56760	−	25.2504i	0.196232	−	0.889958i
$806$		0			0
$807$	1.44567			0.0508901
$808$		0			0
$809$			20.9610i			0.736948i	0.929638	+	0.368474i	$0.120120\pi$
$809$			20.9610i			0.736948i	−0.929638	+	0.368474i	$0.879880\pi$
$810$		0			0
$811$	−8.09740	−	8.09740i	−0.284338	−	0.284338i	0.550498	−	0.834836i	$-0.314438\pi$
$811$	−8.09740	−	8.09740i	−0.284338	−	0.284338i	−0.834836	+	0.550498i	$0.814438\pi$
$812$		0			0
$813$	3.87053	−	3.87053i	0.135745	−	0.135745i
$814$		0			0
$815$	52.6325			1.84363
$816$		0			0
$817$			12.0029i			0.419930i
$818$		0			0
$819$	−1.34492	+	6.09951i	−0.0469952	+	0.213134i
$820$		0			0
$821$	−33.6935	−	33.6935i	−1.17591	−	1.17591i	−0.980776	−	0.195136i	$-0.937485\pi$
$821$	−33.6935	−	33.6935i	−1.17591	−	1.17591i	−0.195136	−	0.980776i	$-0.562515\pi$
$822$		0			0
$823$	46.3245			1.61477			0.807386	−	0.590023i	$-0.200882\pi$
$823$	46.3245			1.61477			0.807386	+	0.590023i	$0.200882\pi$
$824$		0			0
$825$	−11.2562			−0.391890
$826$		0			0
$827$	13.5597	−	13.5597i	0.471516	−	0.471516i	−0.430889	−	0.902405i	$-0.641800\pi$
$827$	13.5597	−	13.5597i	0.471516	−	0.471516i	0.902405	+	0.430889i	$0.141800\pi$
$828$		0			0
$829$	−19.5380	−	19.5380i	−0.678582	−	0.678582i	0.281097	−	0.959679i	$-0.409302\pi$
$829$	−19.5380	−	19.5380i	−0.678582	−	0.678582i	−0.959679	+	0.281097i	$0.909302\pi$
$830$		0			0
$831$	14.0165			0.486228
$832$		0			0
$833$	−45.4405	−	21.0629i	−1.57442	−	0.729786i
$834$		0			0
$835$	18.4730	+	18.4730i	0.639286	+	0.639286i
$836$		0			0
$837$	−0.641092	−	0.641092i	−0.0221594	−	0.0221594i
$838$		0			0
$839$		−	1.94803i		−	0.0672534i	−0.999434	−	0.0336267i	$-0.989294\pi$
$839$		−	1.94803i		−	0.0672534i	0.999434	−	0.0336267i	$-0.0107057\pi$
$840$		0			0
$841$		−	27.1472i		−	0.936109i
$842$		0			0
$843$	13.8898	+	13.8898i	0.478392	+	0.478392i
$844$		0			0
$845$	−14.1234	−	14.1234i	−0.485858	−	0.485858i
$846$		0			0
$847$	20.5259	+	32.1380i	0.705277	+	1.10428i
$848$		0			0
$849$	28.7157			0.985521
$850$		0			0
$851$	−9.14358	−	9.14358i	−0.313438	−	0.313438i
$852$		0			0
$853$	15.1509	−	15.1509i	0.518756	−	0.518756i	−0.398439	−	0.917195i	$-0.630448\pi$
$853$	15.1509	−	15.1509i	0.518756	−	0.518756i	0.917195	+	0.398439i	$0.130448\pi$
$854$		0			0
$855$	11.8004			0.403564
$856$		0			0
$857$	−28.4917			−0.973259			−0.486629	−	0.873609i	$-0.661774\pi$
$857$	−28.4917			−0.973259			−0.486629	+	0.873609i	$0.661774\pi$
$858$		0			0
$859$	−4.12583	−	4.12583i	−0.140772	−	0.140772i	0.633209	−	0.773981i	$-0.281737\pi$
$859$	−4.12583	−	4.12583i	−0.140772	−	0.140772i	−0.773981	+	0.633209i	$0.781737\pi$
$860$		0			0
$861$	1.35418	−	6.14155i	0.0461505	−	0.209303i
$862$		0			0
$863$		−	13.9231i		−	0.473949i	−0.971516	−	0.236974i	$-0.923844\pi$
$863$		−	13.9231i		−	0.473949i	0.971516	−	0.236974i	$-0.0761557\pi$
$864$		0			0
$865$	13.5973			0.462321
$866$		0			0
$867$	−24.1784	+	24.1784i	−0.821143	+	0.821143i
$868$		0			0
$869$	45.0740	+	45.0740i	1.52903	+	1.52903i
$870$		0			0
$871$		−	5.62947i		−	0.190747i
$872$		0			0
$873$	6.22825			0.210794
$874$		0			0
$875$	−19.2276	−	4.23961i	−0.650013	−	0.143325i
$876$		0			0
$877$	28.6830	−	28.6830i	0.968557	−	0.968557i	−0.0309635	−	0.999521i	$-0.509858\pi$
$877$	28.6830	−	28.6830i	0.968557	−	0.968557i	0.999521	+	0.0309635i	$0.00985756\pi$
$878$		0			0
$879$			16.6208i			0.560604i
$880$		0			0
$881$			4.92697i			0.165994i	0.996550	+	0.0829969i	$0.0264492\pi$
$881$			4.92697i			0.165994i	−0.996550	+	0.0829969i	$0.973551\pi$
$882$		0			0
$883$	−33.0133	−	33.0133i	−1.11099	−	1.11099i	−0.993017	−	0.117971i	$-0.962361\pi$
$883$	−33.0133	−	33.0133i	−1.11099	−	1.11099i	−0.117971	−	0.993017i	$-0.537639\pi$
$884$		0			0
$885$	−24.6777	+	24.6777i	−0.829533	+	0.829533i
$886$		0			0
$887$		−	6.48099i		−	0.217610i	−0.994063	−	0.108805i	$-0.965298\pi$
$887$		−	6.48099i		−	0.217610i	0.994063	−	0.108805i	$-0.0347025\pi$
$888$		0			0
$889$	20.8758	+	32.6860i	0.700153	+	1.09625i
$890$		0			0
$891$	−3.56463	+	3.56463i	−0.119419	+	0.119419i
$892$		0			0
$893$	−1.70924	+	1.70924i	−0.0571974	+	0.0571974i
$894$		0			0
$895$	−45.9539			−1.53607
$896$		0			0
$897$	−8.57881			−0.286438
$898$		0			0
$899$	4.80379	−	4.80379i	0.160216	−	0.160216i
$900$		0			0
$901$	21.8319	−	21.8319i	0.727327	−	0.727327i
$902$		0			0
$903$	3.89575	+	6.09970i	0.129642	+	0.202985i
$904$		0			0
$905$			55.9371i			1.85941i
$906$		0			0
$907$	−33.5078	+	33.5078i	−1.11261	+	1.11261i	−0.119810	+	0.992797i	$0.538229\pi$
$907$	−33.5078	+	33.5078i	−1.11261	+	1.11261i	−0.992797	+	0.119810i	$0.961771\pi$
$908$		0			0
$909$	13.7348	+	13.7348i	0.455554	+	0.455554i
$910$		0			0
$911$		−	12.4867i		−	0.413702i	−0.978372	−	0.206851i	$-0.933679\pi$
$911$		−	12.4867i		−	0.413702i	0.978372	−	0.206851i	$-0.0663215\pi$
$912$		0			0
$913$		−	27.2769i		−	0.902733i
$914$		0			0
$915$	−15.1230	+	15.1230i	−0.499951	+	0.499951i
$916$		0			0
$917$	−4.45153	+	20.1887i	−0.147002	+	0.666691i
$918$		0			0
$919$	23.3667			0.770796			0.385398	−	0.922751i	$-0.374064\pi$
$919$	23.3667			0.770796			0.385398	+	0.922751i	$0.374064\pi$
$920$		0			0
$921$			26.8977i			0.886308i
$922$		0			0
$923$	19.4835	+	19.4835i	0.641308	+	0.641308i
$924$		0			0
$925$	5.61831	−	5.61831i	0.184729	−	0.184729i
$926$		0			0
$927$	−2.12589			−0.0698235
$928$		0			0
$929$		−	22.6572i		−	0.743357i	−0.928361	−	0.371679i	$-0.878782\pi$
$929$		−	22.6572i		−	0.743357i	0.928361	−	0.371679i	$-0.121218\pi$
$930$		0			0
$931$	10.5708	+	28.8378i	0.346445	+	0.945120i
$932$		0			0
$933$	−9.69538	−	9.69538i	−0.317413	−	0.317413i
$934$		0			0
$935$	−97.0044			−3.17238
$936$		0			0
$937$	23.8889			0.780417			0.390208	−	0.920727i	$-0.372403\pi$
$937$	23.8889			0.780417			0.390208	+	0.920727i	$0.372403\pi$
$938$		0			0
$939$	−3.42478	+	3.42478i	−0.111764	+	0.111764i
$940$		0			0
$941$	13.2546	+	13.2546i	0.432088	+	0.432088i	0.889338	−	0.457250i	$-0.151166\pi$
$941$	13.2546	+	13.2546i	0.432088	+	0.432088i	−0.457250	+	0.889338i	$0.651166\pi$
$942$		0			0
$943$	8.63793			0.281290
$944$		0			0
$945$	5.99676	−	3.83000i	0.195075	−	0.124590i
$946$		0			0
$947$	−7.30455	−	7.30455i	−0.237366	−	0.237366i	0.578393	−	0.815759i	$-0.303680\pi$
$947$	−7.30455	−	7.30455i	−0.237366	−	0.237366i	−0.815759	+	0.578393i	$0.803680\pi$
$948$		0			0
$949$	14.0404	+	14.0404i	0.455770	+	0.455770i
$950$		0			0
$951$			3.85421i			0.124981i
$952$		0			0
$953$		−	27.8206i		−	0.901198i	−0.892726	−	0.450599i	$-0.851210\pi$
$953$		−	27.8206i		−	0.901198i	0.892726	−	0.450599i	$-0.148790\pi$
$954$		0			0
$955$	−9.20142	−	9.20142i	−0.297751	−	0.297751i
$956$		0			0
$957$	−26.7102	−	26.7102i	−0.863419	−	0.863419i
$958$		0			0
$959$	4.89804	+	7.66903i	0.158166	+	0.247646i
$960$		0			0
$961$	−30.1780			−0.973484
$962$		0			0
$963$	−9.07831	−	9.07831i	−0.292545	−	0.292545i
$964$		0			0
$965$	44.4988	−	44.4988i	1.43247	−	1.43247i
$966$		0			0
$967$	−23.9412			−0.769898			−0.384949	−	0.922938i	$-0.625781\pi$
$967$	−23.9412			−0.769898			−0.384949	+	0.922938i	$0.625781\pi$
$968$		0			0
$969$	31.3941			1.00852
$970$		0			0
$971$	−18.4212	−	18.4212i	−0.591165	−	0.591165i	0.346781	−	0.937946i	$-0.387275\pi$
$971$	−18.4212	−	18.4212i	−0.591165	−	0.591165i	−0.937946	+	0.346781i	$0.887275\pi$
$972$		0			0
$973$	−19.0433	−	4.19897i	−0.610500	−	0.134613i
$974$		0			0
$975$		−	5.27129i		−	0.168816i
$976$		0			0
$977$	41.8758			1.33973			0.669863	−	0.742484i	$-0.266353\pi$
$977$	41.8758			1.33973			0.669863	+	0.742484i	$0.266353\pi$
$978$		0			0
$979$	−52.3776	+	52.3776i	−1.67399	+	1.67399i
$980$		0			0
$981$	7.77089	+	7.77089i	0.248105	+	0.248105i
$982$		0			0
$983$		−	28.1376i		−	0.897450i	−0.893670	−	0.448725i	$-0.851878\pi$
$983$		−	28.1376i		−	0.897450i	0.893670	−	0.448725i	$-0.148122\pi$
$984$		0			0
$985$	22.2292			0.708281
$986$		0			0
$987$	−0.313846	+	1.42337i	−0.00998983	+	0.0453063i
$988$		0			0
$989$	−7.02917	+	7.02917i	−0.223515	+	0.223515i
$990$		0			0
$991$			57.5245i			1.82733i	0.406473	+	0.913663i	$0.366758\pi$
$991$			57.5245i			1.82733i	−0.406473	+	0.913663i	$0.633242\pi$
$992$		0			0
$993$			9.81186i			0.311370i
$994$		0			0
$995$	−8.14606	−	8.14606i	−0.258248	−	0.258248i
$996$		0			0
$997$	−31.2570	+	31.2570i	−0.989919	+	0.989919i	−0.999950	−	0.0100311i	$-0.996807\pi$
$997$	−31.2570	+	31.2570i	−0.989919	+	0.989919i	0.0100311	+	0.999950i	$0.496807\pi$
$998$		0			0
$999$		−	3.55843i		−	0.112584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.u.a.1231.19		64
4.3	odd	2		336.2.u.a.139.3	✓	64
7.6	odd	2	inner	1344.2.u.a.1231.14		64
16.3	odd	4	inner	1344.2.u.a.559.14		64
16.13	even	4		336.2.u.a.307.4	yes	64
28.27	even	2		336.2.u.a.139.4	yes	64
112.13	odd	4		336.2.u.a.307.3	yes	64
112.83	even	4	inner	1344.2.u.a.559.19		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.3	✓	64	4.3	odd	2
336.2.u.a.139.4	yes	64	28.27	even	2
336.2.u.a.307.3	yes	64	112.13	odd	4
336.2.u.a.307.4	yes	64	16.13	even	4
1344.2.u.a.559.14		64	16.3	odd	4	inner
1344.2.u.a.559.19		64	112.83	even	4	inner
1344.2.u.a.1231.14		64	7.6	odd	2	inner
1344.2.u.a.1231.19		64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.90169 - 1.90169i) q^{5} +(-2.22978 + 1.42411i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.90169 - 1.90169i) q^{5} +(-2.22978 + 1.42411i) q^{7} -1.00000i q^{9} +(3.56463 - 3.56463i) q^{11} +(1.66932 + 1.66932i) q^{13} -2.68940i q^{15} -7.15496i q^{17} +(-3.10260 + 3.10260i) q^{19} +(-0.569692 + 2.58369i) q^{21} -3.63389 q^{23} -2.23286i q^{25} +(-0.707107 - 0.707107i) q^{27} +(5.29845 - 5.29845i) q^{29} +0.906641 q^{31} -5.04114i q^{33} +(-1.53213 + 6.94857i) q^{35} +(2.51619 + 2.51619i) q^{37} +2.36078 q^{39} -2.37705 q^{41} +(1.93434 - 1.93434i) q^{43} +(-1.90169 - 1.90169i) q^{45} +0.550905 q^{47} +(2.94382 - 6.35090i) q^{49} +(-5.05932 - 5.05932i) q^{51} +(3.05130 + 3.05130i) q^{53} -13.5576i q^{55} +4.38774i q^{57} +(-9.17593 - 9.17593i) q^{59} +(-5.62319 - 5.62319i) q^{61} +(1.42411 + 2.22978i) q^{63} +6.34907 q^{65} +(-1.68616 - 1.68616i) q^{67} +(-2.56955 + 2.56955i) q^{69} +11.6715 q^{71} +8.41083 q^{73} +(-1.57887 - 1.57887i) q^{75} +(-2.87190 + 13.0247i) q^{77} +12.6448i q^{79} -1.00000 q^{81} +(3.82605 - 3.82605i) q^{83} +(-13.6065 - 13.6065i) q^{85} -7.49314i q^{87} -14.6937 q^{89} +(-6.09951 - 1.34492i) q^{91} +(0.641092 - 0.641092i) q^{93} +11.8004i q^{95} +6.22825i q^{97} +(-3.56463 - 3.56463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Introduction

L-functions

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