LMFDB - Embedded newform 1680.2.bl.d.463.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(127,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.11
Character	$\chi$	$=$	1680.463
Dual form			1680.2.bl.d.127.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{3} +(-1.55110 + 1.61062i) q^{5} +(-0.707107 - 0.707107i) q^{7} -1.00000i q^{9} -1.41421i q^{11} +(-1.61475 - 1.61475i) q^{13} +(0.0420883 + 2.23567i) q^{15} +(-3.57816 + 3.57816i) q^{17} +6.00216 q^{19} -1.00000 q^{21} +(-4.89228 + 4.89228i) q^{23} +(-0.188191 - 4.99646i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.96341i q^{29} +2.23185i q^{31} +(-1.00000 - 1.00000i) q^{33} +(2.23567 - 0.0420883i) q^{35} +(-4.13524 + 4.13524i) q^{37} -2.28360 q^{39} -0.725814 q^{41} +(-6.42894 + 6.42894i) q^{43} +(1.61062 + 1.55110i) q^{45} +(1.55062 + 1.55062i) q^{47} +1.00000i q^{49} +5.06028i q^{51} +(1.39823 + 1.39823i) q^{53} +(2.27776 + 2.19358i) q^{55} +(4.24417 - 4.24417i) q^{57} -10.5113 q^{59} -14.6812 q^{61} +(-0.707107 + 0.707107i) q^{63} +(5.10538 - 0.0961128i) q^{65} +(6.19032 + 6.19032i) q^{67} +6.91872i q^{69} -0.835192i q^{71} +(-9.04739 - 9.04739i) q^{73} +(-3.66610 - 3.39996i) q^{75} +(-1.00000 + 1.00000i) q^{77} -0.726792 q^{79} -1.00000 q^{81} +(-9.93860 + 9.93860i) q^{83} +(-0.212978 - 11.3131i) q^{85} +(2.09545 + 2.09545i) q^{87} -9.21415i q^{89} +2.28360i q^{91} +(1.57816 + 1.57816i) q^{93} +(-9.30994 + 9.66720i) q^{95} +(8.98296 - 8.98296i) q^{97} -1.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{13} - 8 q^{17} - 24 q^{21} + 8 q^{25} - 24 q^{33} + 24 q^{37} + 32 q^{41} + 8 q^{45} - 16 q^{53} - 8 q^{57} - 32 q^{61} + 32 q^{65} - 48 q^{73} - 24 q^{77} - 24 q^{81} + 72 q^{85} - 40 q^{93}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q - 16 * q^13 - 8 * q^17 - 24 * q^21 + 8 * q^25 - 24 * q^33 + 24 * q^37 + 32 * q^41 + 8 * q^45 - 16 * q^53 - 8 * q^57 - 32 * q^61 + 32 * q^65 - 48 * q^73 - 24 * q^77 - 24 * q^81 + 72 * q^85 - 40 * q^93 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−1.55110	+	1.61062i	−0.693672	+	0.720291i
$5$	−1.55110	+	1.61062i	−0.693672	+	0.720291i
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	1.41421i		−	0.426401i	−0.977008	−	0.213201i	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$		0			0
$13$	−1.61475	−	1.61475i	−0.447851	−	0.447851i	0.446789	−	0.894640i	$-0.352568\pi$
$13$	−1.61475	−	1.61475i	−0.447851	−	0.447851i	−0.894640	+	0.446789i	$0.852568\pi$
$14$		0			0
$15$	0.0420883	+	2.23567i	0.0108671	+	0.577248i
$16$		0			0
$17$	−3.57816	+	3.57816i	−0.867831	+	0.867831i	−0.992232	−	0.124401i	$-0.960299\pi$
$17$	−3.57816	+	3.57816i	−0.867831	+	0.867831i	0.124401	+	0.992232i	$0.460299\pi$
$18$		0			0
$19$	6.00216			1.37699			0.688495	−	0.725241i	$-0.258272\pi$
$19$	6.00216			1.37699			0.688495	+	0.725241i	$0.258272\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−4.89228	+	4.89228i	−1.02011	+	1.02011i	−0.0203164	+	0.999794i	$0.506467\pi$
$23$	−4.89228	+	4.89228i	−1.02011	+	1.02011i	−0.999794	+	0.0203164i	$0.993533\pi$
$24$		0			0
$25$	−0.188191	−	4.99646i	−0.0376382	−	0.999291i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			2.96341i			0.550291i	0.961403	+	0.275146i	$0.0887261\pi$
$29$			2.96341i			0.550291i	−0.961403	+	0.275146i	$0.911274\pi$
$30$		0			0
$31$			2.23185i			0.400853i	0.979709	+	0.200426i	$0.0642327\pi$
$31$			2.23185i			0.400853i	−0.979709	+	0.200426i	$0.935767\pi$
$32$		0			0
$33$	−1.00000	−	1.00000i	−0.174078	−	0.174078i
$34$		0			0
$35$	2.23567	−	0.0420883i	0.377898	−	0.00711421i
$36$		0			0
$37$	−4.13524	+	4.13524i	−0.679830	+	0.679830i	−0.959962	−	0.280132i	$-0.909622\pi$
$37$	−4.13524	+	4.13524i	−0.679830	+	0.679830i	0.280132	+	0.959962i	$0.409622\pi$
$38$		0			0
$39$	−2.28360			−0.365669
$40$		0			0
$41$	−0.725814			−0.113353			−0.0566765	−	0.998393i	$-0.518050\pi$
$41$	−0.725814			−0.113353			−0.0566765	+	0.998393i	$0.518050\pi$
$42$		0			0
$43$	−6.42894	+	6.42894i	−0.980404	+	0.980404i	−0.999812	−	0.0194081i	$-0.993822\pi$
$43$	−6.42894	+	6.42894i	−0.980404	+	0.980404i	0.0194081	+	0.999812i	$0.493822\pi$
$44$		0			0
$45$	1.61062	+	1.55110i	0.240097	+	0.231224i
$46$		0			0
$47$	1.55062	+	1.55062i	0.226181	+	0.226181i	0.811095	−	0.584914i	$-0.198872\pi$
$47$	1.55062	+	1.55062i	0.226181	+	0.226181i	−0.584914	+	0.811095i	$0.698872\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$			5.06028i			0.708581i
$52$		0			0
$53$	1.39823	+	1.39823i	0.192061	+	0.192061i	0.796586	−	0.604525i	$-0.206637\pi$
$53$	1.39823	+	1.39823i	0.192061	+	0.192061i	−0.604525	+	0.796586i	$0.706637\pi$
$54$		0			0
$55$	2.27776	+	2.19358i	0.307133	+	0.295783i
$56$		0			0
$57$	4.24417	−	4.24417i	0.562154	−	0.562154i
$58$		0			0
$59$	−10.5113			−1.36846			−0.684230	−	0.729266i	$-0.739862\pi$
$59$	−10.5113			−1.36846			−0.684230	+	0.729266i	$0.739862\pi$
$60$		0			0
$61$	−14.6812			−1.87974			−0.939871	−	0.341531i	$-0.889055\pi$
$61$	−14.6812			−1.87974			−0.939871	+	0.341531i	$0.889055\pi$
$62$		0			0
$63$	−0.707107	+	0.707107i	−0.0890871	+	0.0890871i
$64$		0			0
$65$	5.10538	−	0.0961128i	0.633245	−	0.0119213i
$66$		0			0
$67$	6.19032	+	6.19032i	0.756268	+	0.756268i	0.975641	−	0.219373i	$-0.0704013\pi$
$67$	6.19032	+	6.19032i	0.756268	+	0.756268i	−0.219373	+	0.975641i	$0.570401\pi$
$68$		0			0
$69$			6.91872i			0.832916i
$70$		0			0
$71$		−	0.835192i		−	0.0991190i	−0.998771	−	0.0495595i	$-0.984218\pi$
$71$		−	0.835192i		−	0.0991190i	0.998771	−	0.0495595i	$-0.0157817\pi$
$72$		0			0
$73$	−9.04739	−	9.04739i	−1.05892	−	1.05892i	−0.998152	−	0.0607650i	$-0.980646\pi$
$73$	−9.04739	−	9.04739i	−1.05892	−	1.05892i	−0.0607650	−	0.998152i	$-0.519354\pi$
$74$		0			0
$75$	−3.66610	−	3.39996i	−0.423325	−	0.392593i
$76$		0			0
$77$	−1.00000	+	1.00000i	−0.113961	+	0.113961i
$78$		0			0
$79$	−0.726792			−0.0817704			−0.0408852	−	0.999164i	$-0.513018\pi$
$79$	−0.726792			−0.0817704			−0.0408852	+	0.999164i	$0.513018\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−9.93860	+	9.93860i	−1.09090	+	1.09090i	−0.0954704	+	0.995432i	$0.530436\pi$
$83$	−9.93860	+	9.93860i	−1.09090	+	1.09090i	−0.995432	+	0.0954704i	$0.969564\pi$
$84$		0			0
$85$	−0.212978	−	11.3131i	−0.0231007	−	1.22708i
$86$		0			0
$87$	2.09545	+	2.09545i	0.224655	+	0.224655i
$88$		0			0
$89$		−	9.21415i		−	0.976698i	−0.872648	−	0.488349i	$-0.837599\pi$
$89$		−	9.21415i		−	0.976698i	0.872648	−	0.488349i	$-0.162401\pi$
$90$		0			0
$91$			2.28360i			0.239386i
$92$		0			0
$93$	1.57816	+	1.57816i	0.163647	+	0.163647i
$94$		0			0
$95$	−9.30994	+	9.66720i	−0.955180	+	0.991834i
$96$		0			0
$97$	8.98296	−	8.98296i	0.912082	−	0.912082i	−0.0843542	−	0.996436i	$-0.526883\pi$
$97$	8.98296	−	8.98296i	0.912082	−	0.912082i	0.996436	+	0.0843542i	$0.0268827\pi$
$98$		0			0
$99$	−1.41421			−0.142134
$100$		0			0
$101$	−18.0106			−1.79212			−0.896061	−	0.443930i	$-0.853584\pi$
$101$	−18.0106			−1.79212			−0.896061	+	0.443930i	$0.853584\pi$
$102$		0			0
$103$	−5.98632	+	5.98632i	−0.589850	+	0.589850i	−0.937591	−	0.347741i	$-0.886949\pi$
$103$	−5.98632	+	5.98632i	−0.589850	+	0.589850i	0.347741	+	0.937591i	$0.386949\pi$
$104$		0			0
$105$	1.55110	−	1.61062i	0.151372	−	0.157180i
$106$		0			0
$107$	10.6607	+	10.6607i	1.03061	+	1.03061i	0.999516	+	0.0310948i	$0.00989936\pi$
$107$	10.6607	+	10.6607i	1.03061	+	1.03061i	0.0310948	+	0.999516i	$0.490101\pi$
$108$		0			0
$109$		−	4.38582i		−	0.420085i	−0.977692	−	0.210043i	$-0.932640\pi$
$109$		−	4.38582i		−	0.420085i	0.977692	−	0.210043i	$-0.0673603\pi$
$110$		0			0
$111$			5.84812i			0.555079i
$112$		0			0
$113$	0.104299	+	0.104299i	0.00981165	+	0.00981165i	0.711996	−	0.702184i	$-0.247792\pi$
$113$	0.104299	+	0.104299i	0.00981165	+	0.00981165i	−0.702184	+	0.711996i	$0.747792\pi$
$114$		0			0
$115$	−0.291197	−	15.4680i	−0.0271543	−	1.44240i
$116$		0			0
$117$	−1.61475	+	1.61475i	−0.149284	+	0.149284i
$118$		0			0
$119$	5.06028			0.463875
$120$		0			0
$121$	9.00000			0.818182
$122$		0			0
$123$	−0.513228	+	0.513228i	−0.0462762	+	0.0462762i
$124$		0			0
$125$	8.33929	+	7.44689i	0.745889	+	0.666070i
$126$		0			0
$127$	1.48671	+	1.48671i	0.131924	+	0.131924i	0.769985	−	0.638061i	$-0.220263\pi$
$127$	1.48671	+	1.48671i	0.131924	+	0.131924i	−0.638061	+	0.769985i	$0.720263\pi$
$128$		0			0
$129$			9.09189i			0.800496i
$130$		0			0
$131$			3.49202i			0.305099i	0.988296	+	0.152550i	$0.0487484\pi$
$131$			3.49202i			0.305099i	−0.988296	+	0.152550i	$0.951252\pi$
$132$		0			0
$133$	−4.24417	−	4.24417i	−0.368016	−	0.368016i
$134$		0			0
$135$	2.23567	−	0.0420883i	0.192416	−	0.00362238i
$136$		0			0
$137$	−1.97582	+	1.97582i	−0.168806	+	0.168806i	−0.786454	−	0.617649i	$-0.788085\pi$
$137$	−1.97582	+	1.97582i	−0.168806	+	0.168806i	0.617649	+	0.786454i	$0.288085\pi$
$138$		0			0
$139$	17.1492			1.45457			0.727287	−	0.686333i	$-0.240781\pi$
$139$	17.1492			1.45457			0.727287	+	0.686333i	$0.240781\pi$
$140$		0			0
$141$	2.19291			0.184676
$142$		0			0
$143$	−2.28360	+	2.28360i	−0.190964	+	0.190964i
$144$		0			0
$145$	−4.77292	−	4.59654i	−0.396370	−	0.381722i
$146$		0			0
$147$	0.707107	+	0.707107i	0.0583212	+	0.0583212i
$148$		0			0
$149$			13.4912i			1.10525i	0.833432	+	0.552623i	$0.186373\pi$
$149$			13.4912i			1.10525i	−0.833432	+	0.552623i	$0.813627\pi$
$150$		0			0
$151$		−	9.12096i		−	0.742253i	−0.928582	−	0.371126i	$-0.878972\pi$
$151$		−	9.12096i		−	0.742253i	0.928582	−	0.371126i	$-0.121028\pi$
$152$		0			0
$153$	3.57816	+	3.57816i	0.289277	+	0.289277i
$154$		0			0
$155$	−3.59467	−	3.46182i	−0.288731	−	0.278060i
$156$		0			0
$157$	−7.39702	+	7.39702i	−0.590346	+	0.590346i	−0.937725	−	0.347379i	$-0.887072\pi$
$157$	−7.39702	+	7.39702i	−0.590346	+	0.590346i	0.347379	+	0.937725i	$0.387072\pi$
$158$		0			0
$159$	1.97739			0.156818
$160$		0			0
$161$	6.91872			0.545272
$162$		0			0
$163$	5.82118	−	5.82118i	0.455950	−	0.455950i	−0.441373	−	0.897324i	$-0.645509\pi$
$163$	5.82118	−	5.82118i	0.455950	−	0.455950i	0.897324	+	0.441373i	$0.145509\pi$
$164$		0			0
$165$	3.16172	−	0.0595218i	0.246139	−	0.00463376i
$166$		0			0
$167$	7.29832	+	7.29832i	0.564761	+	0.564761i	0.930656	−	0.365895i	$-0.119237\pi$
$167$	7.29832	+	7.29832i	0.564761	+	0.564761i	−0.365895	+	0.930656i	$0.619237\pi$
$168$		0			0
$169$		−	7.78516i		−	0.598859i
$170$		0			0
$171$		−	6.00216i		−	0.458997i
$172$		0			0
$173$	13.4781	+	13.4781i	1.02472	+	1.02472i	0.999687	+	0.0250318i	$0.00796869\pi$
$173$	13.4781	+	13.4781i	1.02472	+	1.02472i	0.0250318	+	0.999687i	$0.492031\pi$
$174$		0			0
$175$	−3.39996	+	3.66610i	−0.257013	+	0.277131i
$176$		0			0
$177$	−7.43264	+	7.43264i	−0.558672	+	0.558672i
$178$		0			0
$179$	11.1988			0.837035			0.418517	−	0.908209i	$-0.362550\pi$
$179$	11.1988			0.837035			0.418517	+	0.908209i	$0.362550\pi$
$180$		0			0
$181$	5.30087			0.394010			0.197005	−	0.980402i	$-0.436878\pi$
$181$	5.30087			0.394010			0.197005	+	0.980402i	$0.436878\pi$
$182$		0			0
$183$	−10.3812	+	10.3812i	−0.767401	+	0.767401i
$184$		0			0
$185$	−0.246137	−	13.0745i	−0.0180964	−	0.961254i
$186$		0			0
$187$	5.06028	+	5.06028i	0.370044	+	0.370044i
$188$		0			0
$189$			1.00000i			0.0727393i
$190$		0			0
$191$		−	14.5504i		−	1.05283i	−0.850228	−	0.526414i	$-0.823536\pi$
$191$		−	14.5504i		−	1.05283i	0.850228	−	0.526414i	$-0.176464\pi$
$192$		0			0
$193$	−10.7376	−	10.7376i	−0.772908	−	0.772908i	0.205706	−	0.978614i	$-0.434051\pi$
$193$	−10.7376	−	10.7376i	−0.772908	−	0.772908i	−0.978614	+	0.205706i	$0.934051\pi$
$194$		0			0
$195$	3.54209	−	3.67801i	0.253654	−	0.263388i
$196$		0			0
$197$	10.8500	−	10.8500i	0.773029	−	0.773029i	−0.205606	−	0.978635i	$-0.565917\pi$
$197$	10.8500	−	10.8500i	0.773029	−	0.773029i	0.978635	+	0.205606i	$0.0659165\pi$
$198$		0			0
$199$	−5.17932			−0.367152			−0.183576	−	0.983006i	$-0.558767\pi$
$199$	−5.17932			−0.367152			−0.183576	+	0.983006i	$0.558767\pi$
$200$		0			0
$201$	8.75443			0.617490
$202$		0			0
$203$	2.09545	−	2.09545i	0.147072	−	0.147072i
$204$		0			0
$205$	1.12581	−	1.16901i	0.0786298	−	0.0816472i
$206$		0			0
$207$	4.89228	+	4.89228i	0.340037	+	0.340037i
$208$		0			0
$209$		−	8.48834i		−	0.587151i
$210$		0			0
$211$		−	0.114377i		−	0.00787404i	−0.999992	−	0.00393702i	$-0.998747\pi$
$211$		−	0.114377i		−	0.00787404i	0.999992	−	0.00393702i	$-0.00125320\pi$
$212$		0			0
$213$	−0.590570	−	0.590570i	−0.0404652	−	0.0404652i
$214$		0			0
$215$	−0.382662	−	20.3265i	−0.0260973	−	1.38625i
$216$		0			0
$217$	1.57816	−	1.57816i	0.107132	−	0.107132i
$218$		0			0
$219$	−12.7949			−0.864602
$220$		0			0
$221$	11.5557			0.777318
$222$		0			0
$223$	4.06175	−	4.06175i	0.271995	−	0.271995i	−0.557908	−	0.829903i	$-0.688396\pi$
$223$	4.06175	−	4.06175i	0.271995	−	0.271995i	0.829903	+	0.557908i	$0.188396\pi$
$224$		0			0
$225$	−4.99646	+	0.188191i	−0.333097	+	0.0125461i
$226$		0			0
$227$	−10.8517	−	10.8517i	−0.720256	−	0.720256i	0.248401	−	0.968657i	$-0.420095\pi$
$227$	−10.8517	−	10.8517i	−0.720256	−	0.720256i	−0.968657	+	0.248401i	$0.920095\pi$
$228$		0			0
$229$			13.7823i			0.910758i	0.890298	+	0.455379i	$0.150496\pi$
$229$			13.7823i			0.910758i	−0.890298	+	0.455379i	$0.849504\pi$
$230$		0			0
$231$			1.41421i			0.0930484i
$232$		0			0
$233$	0.730251	+	0.730251i	0.0478403	+	0.0478403i	0.730622	−	0.682782i	$-0.239230\pi$
$233$	0.730251	+	0.730251i	0.0478403	+	0.0478403i	−0.682782	+	0.730622i	$0.739230\pi$
$234$		0			0
$235$	−4.90262	+	0.0922957i	−0.319812	+	0.00602071i
$236$		0			0
$237$	−0.513919	+	0.513919i	−0.0333826	+	0.0333826i
$238$		0			0
$239$	20.8853			1.35096			0.675479	−	0.737380i	$-0.263937\pi$
$239$	20.8853			1.35096			0.675479	+	0.737380i	$0.263937\pi$
$240$		0			0
$241$	−23.3064			−1.50130			−0.750649	−	0.660702i	$-0.770259\pi$
$241$	−23.3064			−1.50130			−0.750649	+	0.660702i	$0.770259\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−1.61062	−	1.55110i	−0.102899	−	0.0990960i
$246$		0			0
$247$	−9.69199	−	9.69199i	−0.616687	−	0.616687i
$248$		0			0
$249$			14.0553i			0.890718i
$250$		0			0
$251$			5.35719i			0.338143i	0.985604	+	0.169071i	$0.0540769\pi$
$251$			5.35719i			0.338143i	−0.985604	+	0.169071i	$0.945923\pi$
$252$		0			0
$253$	6.91872	+	6.91872i	0.434976	+	0.434976i
$254$		0			0
$255$	−8.15019	−	7.84899i	−0.510385	−	0.491523i
$256$		0			0
$257$	−19.5888	+	19.5888i	−1.22191	+	1.22191i	−0.254963	+	0.966951i	$0.582063\pi$
$257$	−19.5888	+	19.5888i	−1.22191	+	1.22191i	−0.966951	+	0.254963i	$0.917937\pi$
$258$		0			0
$259$	5.84812			0.363384
$260$		0			0
$261$	2.96341			0.183430
$262$		0			0
$263$	−7.94724	+	7.94724i	−0.490048	+	0.490048i	−0.908321	−	0.418273i	$-0.862635\pi$
$263$	−7.94724	+	7.94724i	−0.490048	+	0.490048i	0.418273	+	0.908321i	$0.362635\pi$
$264$		0			0
$265$	−4.42080	+	0.0832251i	−0.271568	+	0.00511248i
$266$		0			0
$267$	−6.51539	−	6.51539i	−0.398735	−	0.398735i
$268$		0			0
$269$			15.2625i			0.930572i	0.885160	+	0.465286i	$0.154049\pi$
$269$			15.2625i			0.930572i	−0.885160	+	0.465286i	$0.845951\pi$
$270$		0			0
$271$		−	9.82831i		−	0.597028i	−0.954405	−	0.298514i	$-0.903509\pi$
$271$		−	9.82831i		−	0.597028i	0.954405	−	0.298514i	$-0.0964909\pi$
$272$		0			0
$273$	1.61475	+	1.61475i	0.0977291	+	0.0977291i
$274$		0			0
$275$	−7.06606	+	0.266142i	−0.426099	+	0.0160490i
$276$		0			0
$277$	3.70220	−	3.70220i	0.222444	−	0.222444i	−0.587083	−	0.809527i	$-0.699724\pi$
$277$	3.70220	−	3.70220i	0.222444	−	0.222444i	0.809527	+	0.587083i	$0.199724\pi$
$278$		0			0
$279$	2.23185			0.133618
$280$		0			0
$281$	18.0878			1.07903			0.539515	−	0.841976i	$-0.318608\pi$
$281$	18.0878			1.07903			0.539515	+	0.841976i	$0.318608\pi$
$282$		0			0
$283$	1.40931	−	1.40931i	0.0837747	−	0.0837747i	−0.663978	−	0.747752i	$-0.731133\pi$
$283$	1.40931	−	1.40931i	0.0837747	−	0.0837747i	0.747752	+	0.663978i	$0.231133\pi$
$284$		0			0
$285$	0.252621	+	13.4189i	0.0149639	+	0.794865i
$286$		0			0
$287$	0.513228	+	0.513228i	0.0302949	+	0.0302949i
$288$		0			0
$289$		−	8.60644i		−	0.506261i
$290$		0			0
$291$		−	12.7038i		−	0.744712i
$292$		0			0
$293$	−18.9056	−	18.9056i	−1.10447	−	1.10447i	−0.993864	−	0.110610i	$-0.964719\pi$
$293$	−18.9056	−	18.9056i	−1.10447	−	1.10447i	−0.110610	−	0.993864i	$-0.535281\pi$
$294$		0			0
$295$	16.3041	−	16.9298i	0.949263	−	0.985690i
$296$		0			0
$297$	−1.00000	+	1.00000i	−0.0580259	+	0.0580259i
$298$		0			0
$299$	15.7996			0.913715
$300$		0			0
$301$	9.09189			0.524048
$302$		0			0
$303$	−12.7354	+	12.7354i	−0.731631	+	0.731631i
$304$		0			0
$305$	22.7721	−	23.6459i	1.30392	−	1.35396i
$306$		0			0
$307$	10.3811	+	10.3811i	0.592482	+	0.592482i	0.938301	−	0.345819i	$-0.112399\pi$
$307$	10.3811	+	10.3811i	0.592482	+	0.592482i	−0.345819	+	0.938301i	$0.612399\pi$
$308$		0			0
$309$			8.46594i			0.481610i
$310$		0			0
$311$		−	30.5873i		−	1.73445i	−0.497921	−	0.867223i	$-0.665903\pi$
$311$		−	30.5873i		−	1.73445i	0.497921	−	0.867223i	$-0.334097\pi$
$312$		0			0
$313$	−18.9098	−	18.9098i	−1.06884	−	1.06884i	−0.997448	−	0.0713959i	$-0.977255\pi$
$313$	−18.9098	−	18.9098i	−1.06884	−	1.06884i	−0.0713959	−	0.997448i	$-0.522745\pi$
$314$		0			0
$315$	−0.0420883	−	2.23567i	−0.00237140	−	0.125966i
$316$		0			0
$317$	−15.0516	+	15.0516i	−0.845384	+	0.845384i	−0.989553	−	0.144169i	$-0.953949\pi$
$317$	−15.0516	+	15.0516i	−0.845384	+	0.845384i	0.144169	+	0.989553i	$0.453949\pi$
$318$		0			0
$319$	4.19089			0.234645
$320$		0			0
$321$	15.0765			0.841491
$322$		0			0
$323$	−21.4767	+	21.4767i	−1.19500	+	1.19500i
$324$		0			0
$325$	−7.76415	+	8.37191i	−0.430677	+	0.464390i
$326$		0			0
$327$	−3.10124	−	3.10124i	−0.171499	−	0.171499i
$328$		0			0
$329$		−	2.19291i		−	0.120899i
$330$		0			0
$331$		−	23.9966i		−	1.31897i	−0.751716	−	0.659487i	$-0.770773\pi$
$331$		−	23.9966i		−	1.31897i	0.751716	−	0.659487i	$-0.229227\pi$
$332$		0			0
$333$	4.13524	+	4.13524i	0.226610	+	0.226610i
$334$		0			0
$335$	−19.5720	+	0.368459i	−1.06933	+	0.0201310i
$336$		0			0
$337$	20.5553	−	20.5553i	1.11972	−	1.11972i	0.127935	−	0.991783i	$-0.459165\pi$
$337$	20.5553	−	20.5553i	1.11972	−	1.11972i	0.991783	−	0.127935i	$-0.0408350\pi$
$338$		0			0
$339$	0.147501			0.00801118
$340$		0			0
$341$	3.15632			0.170924
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	−11.1434	−	10.7316i	−0.599942	−	0.577771i
$346$		0			0
$347$	−4.14820	−	4.14820i	−0.222687	−	0.222687i	0.586942	−	0.809629i	$-0.300332\pi$
$347$	−4.14820	−	4.14820i	−0.222687	−	0.222687i	−0.809629	+	0.586942i	$0.800332\pi$
$348$		0			0
$349$			16.3686i			0.876192i	0.898928	+	0.438096i	$0.144347\pi$
$349$			16.3686i			0.876192i	−0.898928	+	0.438096i	$0.855653\pi$
$350$		0			0
$351$			2.28360i			0.121890i
$352$		0			0
$353$	12.6727	+	12.6727i	0.674500	+	0.674500i	0.958750	−	0.284250i	$-0.0917446\pi$
$353$	12.6727	+	12.6727i	0.674500	+	0.674500i	−0.284250	+	0.958750i	$0.591745\pi$
$354$		0			0
$355$	1.34518	+	1.29546i	0.0713945	+	0.0687561i
$356$		0			0
$357$	3.57816	−	3.57816i	0.189376	−	0.189376i
$358$		0			0
$359$	5.73841			0.302861			0.151431	−	0.988468i	$-0.451612\pi$
$359$	5.73841			0.302861			0.151431	+	0.988468i	$0.451612\pi$
$360$		0			0
$361$	17.0260			0.896103
$362$		0			0
$363$	6.36396	−	6.36396i	0.334021	−	0.334021i
$364$		0			0
$365$	28.6053	−	0.538517i	1.49727	−	0.0281873i
$366$		0			0
$367$	4.94124	+	4.94124i	0.257931	+	0.257931i	0.824212	−	0.566281i	$-0.191618\pi$
$367$	4.94124	+	4.94124i	0.257931	+	0.257931i	−0.566281	+	0.824212i	$0.691618\pi$
$368$		0			0
$369$			0.725814i			0.0377843i
$370$		0			0
$371$		−	1.97739i		−	0.102661i
$372$		0			0
$373$	−23.7378	−	23.7378i	−1.22909	−	1.22909i	−0.964307	−	0.264788i	$-0.914698\pi$
$373$	−23.7378	−	23.7378i	−1.22909	−	1.22909i	−0.264788	−	0.964307i	$-0.585302\pi$
$374$		0			0
$375$	11.1625	−	0.631026i	0.576430	−	0.0325860i
$376$		0			0
$377$	4.78516	−	4.78516i	0.246449	−	0.246449i
$378$		0			0
$379$	−19.9989			−1.02728			−0.513638	−	0.858007i	$-0.671702\pi$
$379$	−19.9989			−1.02728			−0.513638	+	0.858007i	$0.671702\pi$
$380$		0			0
$381$	2.10252			0.107715
$382$		0			0
$383$	6.05490	−	6.05490i	0.309391	−	0.309391i	−0.535282	−	0.844673i	$-0.679795\pi$
$383$	6.05490	−	6.05490i	0.309391	−	0.309391i	0.844673	+	0.535282i	$0.179795\pi$
$384$		0			0
$385$	−0.0595218	−	3.16172i	−0.00303351	−	0.161136i
$386$		0			0
$387$	6.42894	+	6.42894i	0.326801	+	0.326801i
$388$		0			0
$389$		−	4.79071i		−	0.242899i	−0.992598	−	0.121449i	$-0.961246\pi$
$389$		−	4.79071i		−	0.242899i	0.992598	−	0.121449i	$-0.0387542\pi$
$390$		0			0
$391$		−	35.0107i		−	1.77057i
$392$		0			0
$393$	2.46923	+	2.46923i	0.124556	+	0.124556i
$394$		0			0
$395$	1.12732	−	1.17058i	0.0567219	−	0.0588985i
$396$		0			0
$397$	15.5416	−	15.5416i	0.780009	−	0.780009i	−0.199823	−	0.979832i	$-0.564037\pi$
$397$	15.5416	−	15.5416i	0.780009	−	0.780009i	0.979832	+	0.199823i	$0.0640367\pi$
$398$		0			0
$399$	−6.00216			−0.300484
$400$		0			0
$401$	−31.5637			−1.57622			−0.788109	−	0.615536i	$-0.788940\pi$
$401$	−31.5637			−1.57622			−0.788109	+	0.615536i	$0.788940\pi$
$402$		0			0
$403$	3.60389	−	3.60389i	0.179522	−	0.179522i
$404$		0			0
$405$	1.55110	−	1.61062i	0.0770747	−	0.0800323i
$406$		0			0
$407$	5.84812	+	5.84812i	0.289880	+	0.289880i
$408$		0			0
$409$			15.8757i			0.785001i	0.919752	+	0.392500i	$0.128390\pi$
$409$			15.8757i			0.785001i	−0.919752	+	0.392500i	$0.871610\pi$
$410$		0			0
$411$			2.79423i			0.137829i
$412$		0			0
$413$	7.43264	+	7.43264i	0.365736	+	0.365736i
$414$		0			0
$415$	−0.591563	−	31.4230i	−0.0290387	−	1.54250i
$416$		0			0
$417$	12.1263	−	12.1263i	0.593828	−	0.593828i
$418$		0			0
$419$	−11.3966			−0.556759			−0.278379	−	0.960471i	$-0.589797\pi$
$419$	−11.3966			−0.556759			−0.278379	+	0.960471i	$0.589797\pi$
$420$		0			0
$421$	−19.0104			−0.926509			−0.463255	−	0.886225i	$-0.653318\pi$
$421$	−19.0104			−0.926509			−0.463255	+	0.886225i	$0.653318\pi$
$422$		0			0
$423$	1.55062	−	1.55062i	0.0753938	−	0.0753938i
$424$		0			0
$425$	18.5515	+	17.2047i	0.899880	+	0.834553i
$426$		0			0
$427$	10.3812	+	10.3812i	0.502382	+	0.502382i
$428$		0			0
$429$			3.22950i			0.155922i
$430$		0			0
$431$			12.5216i			0.603145i	0.953443	+	0.301573i	$0.0975115\pi$
$431$			12.5216i			0.603145i	−0.953443	+	0.301573i	$0.902488\pi$
$432$		0			0
$433$	9.12057	+	9.12057i	0.438307	+	0.438307i	0.891442	−	0.453135i	$-0.149694\pi$
$433$	9.12057	+	9.12057i	0.438307	+	0.438307i	−0.453135	+	0.891442i	$0.649694\pi$
$434$		0			0
$435$	−6.62521	+	0.124725i	−0.317655	+	0.00598009i
$436$		0			0
$437$	−29.3642	+	29.3642i	−1.40468	+	1.40468i
$438$		0			0
$439$	14.2206			0.678714			0.339357	−	0.940658i	$-0.389791\pi$
$439$	14.2206			0.678714			0.339357	+	0.940658i	$0.389791\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	21.4454	−	21.4454i	1.01890	−	1.01890i	0.0190862	−	0.999818i	$-0.493924\pi$
$443$	21.4454	−	21.4454i	1.01890	−	1.01890i	0.999818	−	0.0190862i	$-0.00607569\pi$
$444$		0			0
$445$	14.8405	+	14.2921i	0.703507	+	0.677508i
$446$		0			0
$447$	9.53974	+	9.53974i	0.451214	+	0.451214i
$448$		0			0
$449$		−	5.43568i		−	0.256526i	−0.991740	−	0.128263i	$-0.959060\pi$
$449$		−	5.43568i		−	0.256526i	0.991740	−	0.128263i	$-0.0409401\pi$
$450$		0			0
$451$			1.02646i			0.0483339i
$452$		0			0
$453$	−6.44949	−	6.44949i	−0.303023	−	0.303023i
$454$		0			0
$455$	−3.67801	−	3.54209i	−0.172428	−	0.166056i
$456$		0			0
$457$	−20.5758	+	20.5758i	−0.962497	+	0.962497i	−0.999322	−	0.0368249i	$-0.988276\pi$
$457$	−20.5758	+	20.5758i	−0.962497	+	0.962497i	0.0368249	+	0.999322i	$0.488276\pi$
$458$		0			0
$459$	5.06028			0.236194
$460$		0			0
$461$	9.31329			0.433763			0.216882	−	0.976198i	$-0.430411\pi$
$461$	9.31329			0.433763			0.216882	+	0.976198i	$0.430411\pi$
$462$		0			0
$463$	10.9363	−	10.9363i	0.508254	−	0.508254i	−0.405736	−	0.913990i	$-0.632985\pi$
$463$	10.9363	−	10.9363i	0.508254	−	0.508254i	0.913990	+	0.405736i	$0.132985\pi$
$464$		0			0
$465$	−4.98969	+	0.0939348i	−0.231391	+	0.00435612i
$466$		0			0
$467$	−24.4209	−	24.4209i	−1.13006	−	1.13006i	−0.990166	−	0.139897i	$-0.955323\pi$
$467$	−24.4209	−	24.4209i	−1.13006	−	1.13006i	−0.139897	−	0.990166i	$-0.544677\pi$
$468$		0			0
$469$		−	8.75443i		−	0.404242i
$470$		0			0
$471$			10.4610i			0.482016i
$472$		0			0
$473$	9.09189	+	9.09189i	0.418045	+	0.418045i
$474$		0			0
$475$	−1.12955	−	29.9895i	−0.0518275	−	1.37601i
$476$		0			0
$477$	1.39823	−	1.39823i	0.0640205	−	0.0640205i
$478$		0			0
$479$	17.4478			0.797210			0.398605	−	0.917123i	$-0.369494\pi$
$479$	17.4478			0.797210			0.398605	+	0.917123i	$0.369494\pi$
$480$		0			0
$481$	13.3548			0.608925
$482$		0			0
$483$	4.89228	−	4.89228i	0.222606	−	0.222606i
$484$		0			0
$485$	0.534682	+	28.4016i	0.0242787	+	1.28965i
$486$		0			0
$487$	20.2887	+	20.2887i	0.919370	+	0.919370i	0.996983	−	0.0776138i	$-0.0247301\pi$
$487$	20.2887	+	20.2887i	0.919370	+	0.919370i	−0.0776138	+	0.996983i	$0.524730\pi$
$488$		0			0
$489$		−	8.23240i		−	0.372282i
$490$		0			0
$491$		−	26.4431i		−	1.19336i	−0.802479	−	0.596680i	$-0.796486\pi$
$491$		−	26.4431i		−	1.19336i	0.802479	−	0.596680i	$-0.203514\pi$
$492$		0			0
$493$	−10.6035	−	10.6035i	−0.477560	−	0.477560i
$494$		0			0
$495$	2.19358	−	2.27776i	0.0985943	−	0.102378i
$496$		0			0
$497$	−0.590570	+	0.590570i	−0.0264907	+	0.0264907i
$498$		0			0
$499$	37.0718			1.65956			0.829782	−	0.558088i	$-0.188465\pi$
$499$	37.0718			1.65956			0.829782	+	0.558088i	$0.188465\pi$
$500$		0			0
$501$	10.3214			0.461126
$502$		0			0
$503$	−11.7610	+	11.7610i	−0.524395	+	0.524395i	−0.918896	−	0.394500i	$-0.870918\pi$
$503$	−11.7610	+	11.7610i	−0.524395	+	0.524395i	0.394500	+	0.918896i	$0.370918\pi$
$504$		0			0
$505$	27.9362	−	29.0082i	1.24315	−	1.29085i
$506$		0			0
$507$	−5.50494	−	5.50494i	−0.244483	−	0.244483i
$508$		0			0
$509$			3.76912i			0.167063i	0.996505	+	0.0835316i	$0.0266200\pi$
$509$			3.76912i			0.167063i	−0.996505	+	0.0835316i	$0.973380\pi$
$510$		0			0
$511$			12.7949i			0.566015i
$512$		0			0
$513$	−4.24417	−	4.24417i	−0.187385	−	0.187385i
$514$		0			0
$515$	−0.356316	−	18.9271i	−0.0157012	−	0.834026i
$516$		0			0
$517$	2.19291	−	2.19291i	0.0964440	−	0.0964440i
$518$		0			0
$519$	19.0609			0.836679
$520$		0			0
$521$	21.2629			0.931544			0.465772	−	0.884905i	$-0.345777\pi$
$521$	21.2629			0.931544			0.465772	+	0.884905i	$0.345777\pi$
$522$		0			0
$523$	−27.7278	+	27.7278i	−1.21245	+	1.21245i	−0.242237	+	0.970217i	$0.577881\pi$
$523$	−27.7278	+	27.7278i	−1.21245	+	1.21245i	−0.970217	+	0.242237i	$0.922119\pi$
$524$		0			0
$525$	0.188191	+	4.99646i	0.00821333	+	0.218063i
$526$		0			0
$527$	−7.98593	−	7.98593i	−0.347872	−	0.347872i
$528$		0			0
$529$		−	24.8687i		−	1.08125i
$530$		0			0
$531$			10.5113i			0.456153i
$532$		0			0
$533$	1.17201	+	1.17201i	0.0507653	+	0.0507653i
$534$		0			0
$535$	−33.7062	+	0.634545i	−1.45725	+	0.0274338i
$536$		0			0
$537$	7.91872	−	7.91872i	0.341718	−	0.341718i
$538$		0			0
$539$	1.41421			0.0609145
$540$		0			0
$541$	37.1578			1.59754			0.798769	−	0.601638i	$-0.205485\pi$
$541$	37.1578			1.59754			0.798769	+	0.601638i	$0.205485\pi$
$542$		0			0
$543$	3.74828	−	3.74828i	0.160854	−	0.160854i
$544$		0			0
$545$	7.06388	+	6.80283i	0.302584	+	0.291401i
$546$		0			0
$547$	28.0433	+	28.0433i	1.19904	+	1.19904i	0.974453	+	0.224591i	$0.0721048\pi$
$547$	28.0433	+	28.0433i	1.19904	+	1.19904i	0.224591	+	0.974453i	$0.427895\pi$
$548$		0			0
$549$			14.6812i			0.626580i
$550$		0			0
$551$			17.7869i			0.757746i
$552$		0			0
$553$	0.513919	+	0.513919i	0.0218541	+	0.0218541i
$554$		0			0
$555$	−9.41909	−	9.07100i	−0.399818	−	0.385043i
$556$		0			0
$557$	11.2200	−	11.2200i	0.475406	−	0.475406i	−0.428253	−	0.903659i	$-0.640871\pi$
$557$	11.2200	−	11.2200i	0.475406	−	0.475406i	0.903659	+	0.428253i	$0.140871\pi$
$558$		0			0
$559$	20.7622			0.878150
$560$		0			0
$561$	7.15632			0.302140
$562$		0			0
$563$	−3.56969	+	3.56969i	−0.150444	+	0.150444i	−0.778317	−	0.627872i	$-0.783926\pi$
$563$	−3.56969	+	3.56969i	−0.150444	+	0.150444i	0.627872	+	0.778317i	$0.283926\pi$
$564$		0			0
$565$	−0.329765	+	0.00620808i	−0.0138733	+	0.000261176i
$566$		0			0
$567$	0.707107	+	0.707107i	0.0296957	+	0.0296957i
$568$		0			0
$569$		−	18.6617i		−	0.782340i	−0.920318	−	0.391170i	$-0.872070\pi$
$569$		−	18.6617i		−	0.782340i	0.920318	−	0.391170i	$-0.127930\pi$
$570$		0			0
$571$			38.8423i			1.62550i	0.582613	+	0.812750i	$0.302030\pi$
$571$			38.8423i			1.62550i	−0.582613	+	0.812750i	$0.697970\pi$
$572$		0			0
$573$	−10.2887	−	10.2887i	−0.429815	−	0.429815i
$574$		0			0
$575$	25.3647	+	23.5234i	1.05778	+	0.980992i
$576$		0			0
$577$	−18.1788	+	18.1788i	−0.756792	+	0.756792i	−0.975737	−	0.218945i	$-0.929738\pi$
$577$	−18.1788	+	18.1788i	−0.756792	+	0.756792i	0.218945	+	0.975737i	$0.429738\pi$
$578$		0			0
$579$	−15.1852			−0.631077
$580$		0			0
$581$	14.0553			0.583112
$582$		0			0
$583$	1.97739	−	1.97739i	0.0818953	−	0.0818953i
$584$		0			0
$585$	−0.0961128	−	5.10538i	−0.00397377	−	0.211082i
$586$		0			0
$587$	1.52090	+	1.52090i	0.0627744	+	0.0627744i	0.737797	−	0.675023i	$-0.235866\pi$
$587$	1.52090	+	1.52090i	0.0627744	+	0.0627744i	−0.675023	+	0.737797i	$0.735866\pi$
$588$		0			0
$589$			13.3960i			0.551971i
$590$		0			0
$591$		−	15.3442i		−	0.631175i
$592$		0			0
$593$	−20.0796	−	20.0796i	−0.824572	−	0.824572i	0.162188	−	0.986760i	$-0.448145\pi$
$593$	−20.0796	−	20.0796i	−0.824572	−	0.824572i	−0.986760	+	0.162188i	$0.948145\pi$
$594$		0			0
$595$	−7.84899	+	8.15019i	−0.321777	+	0.334125i
$596$		0			0
$597$	−3.66233	+	3.66233i	−0.149889	+	0.149889i
$598$		0			0
$599$	9.16616			0.374519			0.187260	−	0.982310i	$-0.440039\pi$
$599$	9.16616			0.374519			0.187260	+	0.982310i	$0.440039\pi$
$600$		0			0
$601$	37.4953			1.52946			0.764732	−	0.644349i	$-0.222872\pi$
$601$	37.4953			1.52946			0.764732	+	0.644349i	$0.222872\pi$
$602$		0			0
$603$	6.19032	−	6.19032i	0.252089	−	0.252089i
$604$		0			0
$605$	−13.9599	+	14.4956i	−0.567550	+	0.589329i
$606$		0			0
$607$	−27.1447	−	27.1447i	−1.10177	−	1.10177i	−0.994197	−	0.107572i	$-0.965692\pi$
$607$	−27.1447	−	27.1447i	−1.10177	−	1.10177i	−0.107572	−	0.994197i	$-0.534308\pi$
$608$		0			0
$609$		−	2.96341i		−	0.120083i
$610$		0			0
$611$		−	5.00773i		−	0.202591i
$612$		0			0
$613$	14.5477	+	14.5477i	0.587578	+	0.587578i	0.936975	−	0.349397i	$-0.113614\pi$
$613$	14.5477	+	14.5477i	0.587578	+	0.587578i	−0.349397	+	0.936975i	$0.613614\pi$
$614$		0			0
$615$	−0.0305482	−	1.62268i	−0.00123182	−	0.0654328i
$616$		0			0
$617$	−19.0257	+	19.0257i	−0.765945	+	0.765945i	−0.977390	−	0.211445i	$-0.932183\pi$
$617$	−19.0257	+	19.0257i	−0.765945	+	0.765945i	0.211445	+	0.977390i	$0.432183\pi$
$618$		0			0
$619$	−13.7336			−0.552001			−0.276001	−	0.961157i	$-0.589009\pi$
$619$	−13.7336			−0.552001			−0.276001	+	0.961157i	$0.589009\pi$
$620$		0			0
$621$	6.91872			0.277639
$622$		0			0
$623$	−6.51539	+	6.51539i	−0.261034	+	0.261034i
$624$		0			0
$625$	−24.9292	+	1.88058i	−0.997167	+	0.0752231i
$626$		0			0
$627$	−6.00216	−	6.00216i	−0.239703	−	0.239703i
$628$		0			0
$629$		−	29.5931i		−	1.17995i
$630$		0			0
$631$			2.27096i			0.0904053i	0.998978	+	0.0452026i	$0.0143934\pi$
$631$			2.27096i			0.0904053i	−0.998978	+	0.0452026i	$0.985607\pi$
$632$		0			0
$633$	−0.0808768	−	0.0808768i	−0.00321456	−	0.00321456i
$634$		0			0
$635$	−4.70055	+	0.0884915i	−0.186536	+	0.00351168i
$636$		0			0
$637$	1.61475	−	1.61475i	0.0639787	−	0.0639787i
$638$		0			0
$639$	−0.835192			−0.0330397
$640$		0			0
$641$	−27.4488			−1.08416			−0.542082	−	0.840326i	$-0.682364\pi$
$641$	−27.4488			−1.08416			−0.542082	+	0.840326i	$0.682364\pi$
$642$		0			0
$643$	−0.260735	+	0.260735i	−0.0102824	+	0.0102824i	−0.712229	−	0.701947i	$-0.752314\pi$
$643$	−0.260735	+	0.260735i	−0.0102824	+	0.0102824i	0.701947	+	0.712229i	$0.252314\pi$
$644$		0			0
$645$	−14.6436	−	14.1024i	−0.576590	−	0.555282i
$646$		0			0
$647$	−11.7253	−	11.7253i	−0.460970	−	0.460970i	0.438003	−	0.898973i	$-0.355686\pi$
$647$	−11.7253	−	11.7253i	−0.460970	−	0.460970i	−0.898973	+	0.438003i	$0.855686\pi$
$648$		0			0
$649$			14.8653i			0.583513i
$650$		0			0
$651$		−	2.23185i		−	0.0874732i
$652$		0			0
$653$	−10.0706	−	10.0706i	−0.394093	−	0.394093i	0.482050	−	0.876144i	$-0.339892\pi$
$653$	−10.0706	−	10.0706i	−0.394093	−	0.394093i	−0.876144	+	0.482050i	$0.839892\pi$
$654$		0			0
$655$	−5.62432	−	5.41647i	−0.219760	−	0.211639i
$656$		0			0
$657$	−9.04739	+	9.04739i	−0.352972	+	0.352972i
$658$		0			0
$659$	0.987258			0.0384581			0.0192291	−	0.999815i	$-0.493879\pi$
$659$	0.987258			0.0384581			0.0192291	+	0.999815i	$0.493879\pi$
$660$		0			0
$661$	−35.5698			−1.38351			−0.691753	−	0.722134i	$-0.743161\pi$
$661$	−35.5698			−1.38351			−0.691753	+	0.722134i	$0.743161\pi$
$662$		0			0
$663$	8.17109	−	8.17109i	0.317339	−	0.317339i
$664$		0			0
$665$	13.4189	−	0.252621i	0.520361	−	0.00979620i
$666$		0			0
$667$	−14.4978	−	14.4978i	−0.561358	−	0.561358i
$668$		0			0
$669$		−	5.74418i		−	0.222083i
$670$		0			0
$671$			20.7624i			0.801524i
$672$		0			0
$673$	5.77671	+	5.77671i	0.222676	+	0.222676i	0.809624	−	0.586948i	$-0.199671\pi$
$673$	5.77671	+	5.77671i	0.222676	+	0.222676i	−0.586948	+	0.809624i	$0.699671\pi$
$674$		0			0
$675$	−3.39996	+	3.66610i	−0.130864	+	0.141108i
$676$		0			0
$677$	0.223962	−	0.223962i	0.00860756	−	0.00860756i	−0.702790	−	0.711397i	$-0.748063\pi$
$677$	0.223962	−	0.223962i	0.00860756	−	0.00860756i	0.711397	+	0.702790i	$0.248063\pi$
$678$		0			0
$679$	−12.7038			−0.487528
$680$		0			0
$681$	−15.3467			−0.588086
$682$		0			0
$683$	−22.6071	+	22.6071i	−0.865036	+	0.865036i	−0.991918	−	0.126882i	$-0.959503\pi$
$683$	−22.6071	+	22.6071i	−0.865036	+	0.865036i	0.126882	+	0.991918i	$0.459503\pi$
$684$		0			0
$685$	−0.117604	−	6.24698i	−0.00449343	−	0.238685i
$686$		0			0
$687$	9.74554	+	9.74554i	0.371815	+	0.371815i
$688$		0			0
$689$		−	4.51558i		−	0.172030i
$690$		0			0
$691$			44.6726i			1.69943i	0.527245	+	0.849713i	$0.323225\pi$
$691$			44.6726i			1.69943i	−0.527245	+	0.849713i	$0.676775\pi$
$692$		0			0
$693$	1.00000	+	1.00000i	0.0379869	+	0.0379869i
$694$		0			0
$695$	−26.6001	+	27.6208i	−1.00900	+	1.04772i
$696$		0			0
$697$	2.59708	−	2.59708i	0.0983713	−	0.0983713i
$698$		0			0
$699$	1.03273			0.0390615
$700$		0			0
$701$	−39.2966			−1.48421			−0.742105	−	0.670283i	$-0.766173\pi$
$701$	−39.2966			−1.48421			−0.742105	+	0.670283i	$0.766173\pi$
$702$		0			0
$703$	−24.8204	+	24.8204i	−0.936119	+	0.936119i
$704$		0			0
$705$	−3.40142	+	3.53194i	−0.128105	+	0.133021i
$706$		0			0
$707$	12.7354	+	12.7354i	0.478965	+	0.478965i
$708$		0			0
$709$			33.4616i			1.25668i	0.777940	+	0.628339i	$0.216265\pi$
$709$			33.4616i			1.25668i	−0.777940	+	0.628339i	$0.783735\pi$
$710$		0			0
$711$			0.726792i			0.0272568i
$712$		0			0
$713$	−10.9188	−	10.9188i	−0.408914	−	0.408914i
$714$		0			0
$715$	−0.135924	−	7.22010i	−0.00508327	−	0.270017i
$716$		0			0
$717$	14.7681	−	14.7681i	0.551526	−	0.551526i
$718$		0			0
$719$	48.2614			1.79985			0.899923	−	0.436050i	$-0.143623\pi$
$719$	48.2614			1.79985			0.899923	+	0.436050i	$0.143623\pi$
$720$		0			0
$721$	8.46594			0.315288
$722$		0			0
$723$	−16.4801	+	16.4801i	−0.612902	+	0.612902i
$724$		0			0
$725$	14.8065	−	0.557687i	0.549901	−	0.0207120i
$726$		0			0
$727$	−28.9489	−	28.9489i	−1.07366	−	1.07366i	−0.997062	−	0.0765933i	$-0.975596\pi$
$727$	−28.9489	−	28.9489i	−1.07366	−	1.07366i	−0.0765933	−	0.997062i	$-0.524404\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	46.0075i		−	1.70165i
$732$		0			0
$733$	−18.6714	−	18.6714i	−0.689645	−	0.689645i	0.272508	−	0.962153i	$-0.412147\pi$
$733$	−18.6714	−	18.6714i	−0.689645	−	0.689645i	−0.962153	+	0.272508i	$0.912147\pi$
$734$		0			0
$735$	−2.23567	+	0.0420883i	−0.0824640	+	0.00155245i
$736$		0			0
$737$	8.75443	−	8.75443i	0.322474	−	0.322474i
$738$		0			0
$739$	4.23603			0.155825			0.0779124	−	0.996960i	$-0.475175\pi$
$739$	4.23603			0.155825			0.0779124	+	0.996960i	$0.475175\pi$
$740$		0			0
$741$	−13.7065			−0.503523
$742$		0			0
$743$	−3.72467	+	3.72467i	−0.136645	+	0.136645i	−0.772121	−	0.635476i	$-0.780804\pi$
$743$	−3.72467	+	3.72467i	−0.136645	+	0.136645i	0.635476	+	0.772121i	$0.280804\pi$
$744$		0			0
$745$	−21.7292	−	20.9262i	−0.796098	−	0.766678i
$746$		0			0
$747$	9.93860	+	9.93860i	0.363634	+	0.363634i
$748$		0			0
$749$		−	15.0765i		−	0.550885i
$750$		0			0
$751$		−	33.7435i		−	1.23132i	−0.788013	−	0.615658i	$-0.788890\pi$
$751$		−	33.7435i		−	1.23132i	0.788013	−	0.615658i	$-0.211110\pi$
$752$		0			0
$753$	3.78811	+	3.78811i	0.138046	+	0.138046i
$754$		0			0
$755$	14.6904	+	14.1475i	0.534638	+	0.514880i
$756$		0			0
$757$	−0.0265074	+	0.0265074i	−0.000963429	+	0.000963429i	−0.707588	−	0.706625i	$-0.750217\pi$
$757$	−0.0265074	+	0.0265074i	−0.000963429	+	0.000963429i	0.706625	+	0.707588i	$0.250217\pi$
$758$		0			0
$759$	9.78455			0.355157
$760$		0			0
$761$	14.2629			0.517029			0.258514	−	0.966007i	$-0.416767\pi$
$761$	14.2629			0.517029			0.258514	+	0.966007i	$0.416767\pi$
$762$		0			0
$763$	−3.10124	+	3.10124i	−0.112272	+	0.112272i
$764$		0			0
$765$	−11.3131	+	0.212978i	−0.409027	+	0.00770025i
$766$		0			0
$767$	16.9732	+	16.9732i	0.612866	+	0.612866i
$768$		0			0
$769$		−	36.1710i		−	1.30436i	−0.758065	−	0.652179i	$-0.773855\pi$
$769$		−	36.1710i		−	1.30436i	0.758065	−	0.652179i	$-0.226145\pi$
$770$		0			0
$771$			27.7027i			0.997689i
$772$		0			0
$773$	−3.14281	−	3.14281i	−0.113039	−	0.113039i	0.648325	−	0.761364i	$-0.275470\pi$
$773$	−3.14281	−	3.14281i	−0.113039	−	0.113039i	−0.761364	+	0.648325i	$0.775470\pi$
$774$		0			0
$775$	11.1514	−	0.420015i	0.400569	−	0.0150874i
$776$		0			0
$777$	4.13524	−	4.13524i	0.148351	−	0.148351i
$778$		0			0
$779$	−4.35645			−0.156086
$780$		0			0
$781$	−1.18114			−0.0422645
$782$		0			0
$783$	2.09545	−	2.09545i	0.0748852	−	0.0748852i
$784$		0			0
$785$	−0.440284	−	23.3873i	−0.0157144	−	0.834728i
$786$		0			0
$787$	24.9347	+	24.9347i	0.888826	+	0.888826i	0.994410	−	0.105585i	$-0.0336714\pi$
$787$	24.9347	+	24.9347i	0.888826	+	0.888826i	−0.105585	+	0.994410i	$0.533671\pi$
$788$		0			0
$789$			11.2391i			0.400122i
$790$		0			0
$791$		−	0.147501i		−	0.00524455i
$792$		0			0
$793$	23.7065	+	23.7065i	0.841844	+	0.841844i
$794$		0			0
$795$	−3.06713	+	3.18483i	−0.108780	+	0.112954i
$796$		0			0
$797$	−13.2467	+	13.2467i	−0.469222	+	0.469222i	−0.901662	−	0.432441i	$-0.857652\pi$
$797$	−13.2467	+	13.2467i	−0.469222	+	0.469222i	0.432441	+	0.901662i	$0.357652\pi$
$798$		0			0
$799$	−11.0967			−0.392574
$800$		0			0
$801$	−9.21415			−0.325566
$802$		0			0
$803$	−12.7949	+	12.7949i	−0.451524	+	0.451524i
$804$		0			0
$805$	−10.7316	+	11.1434i	−0.378240	+	0.392754i
$806$		0			0
$807$	10.7922	+	10.7922i	0.379904	+	0.379904i
$808$		0			0
$809$		−	20.2321i		−	0.711324i	−0.934615	−	0.355662i	$-0.884255\pi$
$809$		−	20.2321i		−	0.711324i	0.934615	−	0.355662i	$-0.115745\pi$
$810$		0			0
$811$			56.5075i			1.98425i	0.125270	+	0.992123i	$0.460020\pi$
$811$			56.5075i			1.98425i	−0.125270	+	0.992123i	$0.539980\pi$
$812$		0			0
$813$	−6.94967	−	6.94967i	−0.243735	−	0.243735i
$814$		0			0
$815$	0.346487	+	18.4049i	0.0121369	+	0.644697i
$816$		0			0
$817$	−38.5875	+	38.5875i	−1.35001	+	1.35001i
$818$		0			0
$819$	2.28360			0.0797955
$820$		0			0
$821$	−51.2877			−1.78995			−0.894976	−	0.446114i	$-0.852807\pi$
$821$	−51.2877			−1.78995			−0.894976	+	0.446114i	$0.852807\pi$
$822$		0			0
$823$	−29.1306	+	29.1306i	−1.01543	+	1.01543i	−0.0155490	+	0.999879i	$0.504950\pi$
$823$	−29.1306	+	29.1306i	−1.01543	+	1.01543i	−0.999879	+	0.0155490i	$0.995050\pi$
$824$		0			0
$825$	−4.80827	+	5.18465i	−0.167402	+	0.180506i
$826$		0			0
$827$	24.3500	+	24.3500i	0.846731	+	0.846731i	0.989724	−	0.142993i	$-0.0456726\pi$
$827$	24.3500	+	24.3500i	0.846731	+	0.846731i	−0.142993	+	0.989724i	$0.545673\pi$
$828$		0			0
$829$			39.9876i			1.38883i	0.719575	+	0.694414i	$0.244336\pi$
$829$			39.9876i			1.38883i	−0.719575	+	0.694414i	$0.755664\pi$
$830$		0			0
$831$		−	5.23570i		−	0.181625i
$832$		0			0
$833$	−3.57816	−	3.57816i	−0.123976	−	0.123976i
$834$		0			0
$835$	−23.0752	+	0.434409i	−0.798552	+	0.0150334i
$836$		0			0
$837$	1.57816	−	1.57816i	0.0545492	−	0.0545492i
$838$		0			0
$839$	6.30454			0.217657			0.108829	−	0.994061i	$-0.465290\pi$
$839$	6.30454			0.217657			0.108829	+	0.994061i	$0.465290\pi$
$840$		0			0
$841$	20.2182			0.697180
$842$		0			0
$843$	12.7900	−	12.7900i	0.440512	−	0.440512i
$844$		0			0
$845$	12.5389	+	12.0756i	0.431353	+	0.415412i
$846$		0			0
$847$	−6.36396	−	6.36396i	−0.218668	−	0.218668i
$848$		0			0
$849$		−	1.99306i		−	0.0684017i
$850$		0			0
$851$		−	40.4615i		−	1.38700i
$852$		0			0
$853$	−9.48627	−	9.48627i	−0.324804	−	0.324804i	0.525803	−	0.850607i	$-0.323765\pi$
$853$	−9.48627	−	9.48627i	−0.324804	−	0.324804i	−0.850607	+	0.525803i	$0.823765\pi$
$854$		0			0
$855$	9.66720	+	9.30994i	0.330611	+	0.318393i
$856$		0			0
$857$	−18.6693	+	18.6693i	−0.637732	+	0.637732i	−0.949996	−	0.312264i	$-0.898913\pi$
$857$	−18.6693	+	18.6693i	−0.637732	+	0.637732i	0.312264	+	0.949996i	$0.398913\pi$
$858$		0			0
$859$	−40.0484			−1.36643			−0.683217	−	0.730216i	$-0.739420\pi$
$859$	−40.0484			−1.36643			−0.683217	+	0.730216i	$0.739420\pi$
$860$		0			0
$861$	0.725814			0.0247357
$862$		0			0
$863$	−28.8750	+	28.8750i	−0.982916	+	0.982916i	−0.999856	−	0.0169409i	$-0.994607\pi$
$863$	−28.8750	+	28.8750i	−0.982916	+	0.982916i	0.0169409	+	0.999856i	$0.494607\pi$
$864$		0			0
$865$	−42.6138	+	0.802238i	−1.44891	+	0.0272769i
$866$		0			0
$867$	−6.08567	−	6.08567i	−0.206680	−	0.206680i
$868$		0			0
$869$			1.02784i			0.0348670i
$870$		0			0
$871$		−	19.9916i		−	0.677391i
$872$		0			0
$873$	−8.98296	−	8.98296i	−0.304027	−	0.304027i
$874$		0			0
$875$	−0.631026	−	11.1625i	−0.0213326	−	0.377362i
$876$		0			0
$877$	16.1481	−	16.1481i	0.545281	−	0.545281i	−0.379791	−	0.925072i	$-0.624004\pi$
$877$	16.1481	−	16.1481i	0.545281	−	0.545281i	0.925072	+	0.379791i	$0.124004\pi$
$878$		0			0
$879$	−26.7365			−0.901799
$880$		0			0
$881$	10.1767			0.342862			0.171431	−	0.985196i	$-0.445161\pi$
$881$	10.1767			0.342862			0.171431	+	0.985196i	$0.445161\pi$
$882$		0			0
$883$	2.70918	−	2.70918i	0.0911711	−	0.0911711i	−0.660050	−	0.751221i	$-0.729465\pi$
$883$	2.70918	−	2.70918i	0.0911711	−	0.0911711i	0.751221	+	0.660050i	$0.229465\pi$
$884$		0			0
$885$	−0.442404	−	23.4999i	−0.0148712	−	0.789941i
$886$		0			0
$887$	−21.2973	−	21.2973i	−0.715093	−	0.715093i	0.252503	−	0.967596i	$-0.418746\pi$
$887$	−21.2973	−	21.2973i	−0.715093	−	0.715093i	−0.967596	+	0.252503i	$0.918746\pi$
$888$		0			0
$889$		−	2.10252i		−	0.0705163i
$890$		0			0
$891$			1.41421i			0.0473779i
$892$		0			0
$893$	9.30708	+	9.30708i	0.311450	+	0.311450i
$894$		0			0
$895$	−17.3704	+	18.0370i	−0.580628	+	0.602909i
$896$		0			0
$897$	11.1720	−	11.1720i	0.373022	−	0.373022i
$898$		0			0
$899$	−6.61390			−0.220586
$900$		0			0
$901$	−10.0062			−0.333354
$902$		0			0
$903$	6.42894	−	6.42894i	0.213942	−	0.213942i
$904$		0			0
$905$	−8.22216	+	8.53768i	−0.273314	+	0.283802i
$906$		0			0
$907$	29.0336	+	29.0336i	0.964044	+	0.964044i	0.999376	−	0.0353317i	$-0.0112488\pi$
$907$	29.0336	+	29.0336i	0.964044	+	0.964044i	−0.0353317	+	0.999376i	$0.511249\pi$
$908$		0			0
$909$			18.0106i			0.597374i
$910$		0			0
$911$			12.7765i			0.423304i	0.977345	+	0.211652i	$0.0678844\pi$
$911$			12.7765i			0.423304i	−0.977345	+	0.211652i	$0.932116\pi$
$912$		0			0
$913$	14.0553	+	14.0553i	0.465162	+	0.465162i
$914$		0			0
$915$	−0.617908	−	32.8225i	−0.0204274	−	1.08508i
$916$		0			0
$917$	2.46923	−	2.46923i	0.0815413	−	0.0815413i
$918$		0			0
$919$	−40.6251			−1.34010			−0.670050	−	0.742316i	$-0.733727\pi$
$919$	−40.6251			−1.34010			−0.670050	+	0.742316i	$0.733727\pi$
$920$		0			0
$921$	14.6811			0.483760
$922$		0			0
$923$	−1.34863	+	1.34863i	−0.0443906	+	0.0443906i
$924$		0			0
$925$	21.4398	+	19.8834i	0.704936	+	0.653761i
$926$		0			0
$927$	5.98632	+	5.98632i	0.196617	+	0.196617i
$928$		0			0
$929$		−	39.3360i		−	1.29057i	−0.763940	−	0.645287i	$-0.776738\pi$
$929$		−	39.3360i		−	1.29057i	0.763940	−	0.645287i	$-0.223262\pi$
$930$		0			0
$931$			6.00216i			0.196713i
$932$		0			0
$933$	−21.6285	−	21.6285i	−0.708084	−	0.708084i
$934$		0			0
$935$	−15.9992	+	0.301197i	−0.523229	+	0.00985019i
$936$		0			0
$937$	−6.86324	+	6.86324i	−0.224212	+	0.224212i	−0.810270	−	0.586057i	$-0.800679\pi$
$937$	−6.86324	+	6.86324i	−0.224212	+	0.224212i	0.586057	+	0.810270i	$0.300679\pi$
$938$		0			0
$939$	−26.7425			−0.872707
$940$		0			0
$941$	−54.5433			−1.77806			−0.889030	−	0.457848i	$-0.848620\pi$
$941$	−54.5433			−1.77806			−0.889030	+	0.457848i	$0.848620\pi$
$942$		0			0
$943$	3.55088	−	3.55088i	0.115633	−	0.115633i
$944$		0			0
$945$	−1.61062	−	1.55110i	−0.0523935	−	0.0504572i
$946$		0			0
$947$	0.550590	+	0.550590i	0.0178918	+	0.0178918i	0.715996	−	0.698104i	$-0.245973\pi$
$947$	0.550590	+	0.550590i	0.0178918	+	0.0178918i	−0.698104	+	0.715996i	$0.745973\pi$
$948$		0			0
$949$			29.2186i			0.948474i
$950$		0			0
$951$			21.2862i			0.690253i
$952$		0			0
$953$	20.5746	+	20.5746i	0.666478	+	0.666478i	0.956899	−	0.290421i	$-0.0937954\pi$
$953$	20.5746	+	20.5746i	0.666478	+	0.666478i	−0.290421	+	0.956899i	$0.593795\pi$
$954$		0			0
$955$	23.4351	+	22.5691i	0.758342	+	0.730317i
$956$		0			0
$957$	2.96341	−	2.96341i	0.0957934	−	0.0957934i
$958$		0			0
$959$	2.79423			0.0902304
$960$		0			0
$961$	26.0188			0.839317
$962$		0			0
$963$	10.6607	−	10.6607i	0.343537	−	0.343537i
$964$		0			0
$965$	33.9492	−	0.639120i	1.09286	−	0.0205740i
$966$		0			0
$967$	2.85635	+	2.85635i	0.0918540	+	0.0918540i	0.751541	−	0.659687i	$-0.229311\pi$
$967$	2.85635	+	2.85635i	0.0918540	+	0.0918540i	−0.659687	+	0.751541i	$0.729311\pi$
$968$		0			0
$969$			30.3726i			0.975709i
$970$		0			0
$971$		−	2.39615i		−	0.0768962i	−0.999261	−	0.0384481i	$-0.987759\pi$
$971$		−	2.39615i		−	0.0768962i	0.999261	−	0.0384481i	$-0.0122414\pi$
$972$		0			0
$973$	−12.1263	−	12.1263i	−0.388751	−	0.388751i
$974$		0			0
$975$	0.429753	+	11.4099i	0.0137631	+	0.365410i
$976$		0			0
$977$	−28.1571	+	28.1571i	−0.900824	+	0.900824i	−0.995507	−	0.0946834i	$-0.969816\pi$
$977$	−28.1571	+	28.1571i	−0.900824	+	0.900824i	0.0946834	+	0.995507i	$0.469816\pi$
$978$		0			0
$979$	−13.0308			−0.416466
$980$		0			0
$981$	−4.38582			−0.140028
$982$		0			0
$983$	9.34594	−	9.34594i	0.298089	−	0.298089i	−0.542176	−	0.840265i	$-0.682399\pi$
$983$	9.34594	−	9.34594i	0.298089	−	0.298089i	0.840265	+	0.542176i	$0.182399\pi$
$984$		0			0
$985$	0.645810	+	34.3046i	0.0205772	+	1.09303i
$986$		0			0
$987$	−1.55062	−	1.55062i	−0.0493568	−	0.0493568i
$988$		0			0
$989$		−	62.9043i		−	2.00024i
$990$		0			0
$991$			10.5891i			0.336373i	0.985755	+	0.168186i	$0.0537910\pi$
$991$			10.5891i			0.336373i	−0.985755	+	0.168186i	$0.946209\pi$
$992$		0			0
$993$	−16.9682	−	16.9682i	−0.538469	−	0.538469i
$994$		0			0
$995$	8.03363	−	8.34191i	0.254683	−	0.264456i
$996$		0			0
$997$	−1.26993	+	1.26993i	−0.0402192	+	0.0402192i	−0.726930	−	0.686711i	$-0.759054\pi$
$997$	−1.26993	+	1.26993i	−0.0402192	+	0.0402192i	0.686711	+	0.726930i	$0.259054\pi$
$998$		0			0
$999$	5.84812			0.185026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bl.d.463.11	yes	24
4.3	odd	2	inner	1680.2.bl.d.463.5	yes	24
5.2	odd	4	inner	1680.2.bl.d.127.5	✓	24
20.7	even	4	inner	1680.2.bl.d.127.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.bl.d.127.5	✓	24	5.2	odd	4	inner
1680.2.bl.d.127.10	yes	24	20.7	even	4	inner
1680.2.bl.d.463.5	yes	24	4.3	odd	2	inner
1680.2.bl.d.463.11	yes	24	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-1.55110 + 1.61062i) q^{5} +(-0.707107 - 0.707107i) q^{7} -1.00000i q^{9} -1.41421i q^{11} +(-1.61475 - 1.61475i) q^{13} +(0.0420883 + 2.23567i) q^{15} +(-3.57816 + 3.57816i) q^{17} +6.00216 q^{19} -1.00000 q^{21} +(-4.89228 + 4.89228i) q^{23} +(-0.188191 - 4.99646i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.96341i q^{29} +2.23185i q^{31} +(-1.00000 - 1.00000i) q^{33} +(2.23567 - 0.0420883i) q^{35} +(-4.13524 + 4.13524i) q^{37} -2.28360 q^{39} -0.725814 q^{41} +(-6.42894 + 6.42894i) q^{43} +(1.61062 + 1.55110i) q^{45} +(1.55062 + 1.55062i) q^{47} +1.00000i q^{49} +5.06028i q^{51} +(1.39823 + 1.39823i) q^{53} +(2.27776 + 2.19358i) q^{55} +(4.24417 - 4.24417i) q^{57} -10.5113 q^{59} -14.6812 q^{61} +(-0.707107 + 0.707107i) q^{63} +(5.10538 - 0.0961128i) q^{65} +(6.19032 + 6.19032i) q^{67} +6.91872i q^{69} -0.835192i q^{71} +(-9.04739 - 9.04739i) q^{73} +(-3.66610 - 3.39996i) q^{75} +(-1.00000 + 1.00000i) q^{77} -0.726792 q^{79} -1.00000 q^{81} +(-9.93860 + 9.93860i) q^{83} +(-0.212978 - 11.3131i) q^{85} +(2.09545 + 2.09545i) q^{87} -9.21415i q^{89} +2.28360i q^{91} +(1.57816 + 1.57816i) q^{93} +(-9.30994 + 9.66720i) q^{95} +(8.98296 - 8.98296i) q^{97} -1.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{13} - 8 q^{17} - 24 q^{21} + 8 q^{25} - 24 q^{33} + 24 q^{37} + 32 q^{41} + 8 q^{45} - 16 q^{53} - 8 q^{57} - 32 q^{61} + 32 q^{65} - 48 q^{73} - 24 q^{77} - 24 q^{81} + 72 q^{85} - 40 q^{93}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q - 16 * q^13 - 8 * q^17 - 24 * q^21 + 8 * q^25 - 24 * q^33 + 24 * q^37 + 32 * q^41 + 8 * q^45 - 16 * q^53 - 8 * q^57 - 32 * q^61 + 32 * q^65 - 48 * q^73 - 24 * q^77 - 24 * q^81 + 72 * q^85 - 40 * q^93 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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