LMFDB - Embedded newform 1248.2.ca.b.49.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1248,2,Mod(49,1248)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1248, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1248.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.19
Character	$\chi$	$=$	1248.49
Dual form			1248.2.ca.b.433.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{3} +0.112463 q^{5} +(-0.0378844 - 0.0218726i) q^{7} +(0.500000 - 0.866025i) q^{9} +(3.10283 + 5.37427i) q^{11} +(-1.35237 - 3.34232i) q^{13} +(0.0973959 - 0.0562315i) q^{15} +(1.70610 - 2.95506i) q^{17} +(3.27166 - 5.66668i) q^{19} -0.0437452 q^{21} +(2.27419 + 3.93902i) q^{23} -4.98735 q^{25} -1.00000i q^{27} +(5.22044 - 3.01402i) q^{29} +7.66040i q^{31} +(5.37427 + 3.10283i) q^{33} +(-0.00426060 - 0.00245986i) q^{35} +(5.07408 + 8.78857i) q^{37} +(-2.84235 - 2.21835i) q^{39} +(2.01283 - 1.16211i) q^{41} +(8.02853 + 4.63527i) q^{43} +(0.0562315 - 0.0973959i) q^{45} -6.65732i q^{47} +(-3.49904 - 6.06052i) q^{49} -3.41220i q^{51} -11.2461i q^{53} +(0.348954 + 0.604406i) q^{55} -6.54332i q^{57} +(1.11081 - 1.92397i) q^{59} +(8.56334 + 4.94405i) q^{61} +(-0.0378844 + 0.0218726i) q^{63} +(-0.152092 - 0.375887i) q^{65} +(-2.26023 - 3.91483i) q^{67} +(3.93902 + 2.27419i) q^{69} +(-2.64086 - 1.52470i) q^{71} +4.71199i q^{73} +(-4.31917 + 2.49368i) q^{75} -0.271468i q^{77} -8.01847 q^{79} +(-0.500000 - 0.866025i) q^{81} +2.86994 q^{83} +(0.191873 - 0.332335i) q^{85} +(3.01402 - 5.22044i) q^{87} +(3.35627 - 1.93775i) q^{89} +(-0.0218715 + 0.156202i) q^{91} +(3.83020 + 6.63410i) q^{93} +(0.367941 - 0.637292i) q^{95} +(-0.971031 - 0.560625i) q^{97} +6.20567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) $ 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	0.112463			0.0502950			0.0251475	−	0.999684i	$-0.491994\pi$
$5$	0.112463			0.0502950			0.0251475	+	0.999684i	$0.491994\pi$
$6$		0			0
$7$	−0.0378844	−	0.0218726i	−0.0143190	−	0.00826706i	0.492823	−	0.870129i	$-0.335965\pi$
$7$	−0.0378844	−	0.0218726i	−0.0143190	−	0.00826706i	−0.507142	+	0.861862i	$0.669298\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	3.10283	+	5.37427i	0.935540	+	1.62040i	0.773669	+	0.633590i	$0.218420\pi$
$11$	3.10283	+	5.37427i	0.935540	+	1.62040i	0.161871	+	0.986812i	$0.448247\pi$
$12$		0			0
$13$	−1.35237	−	3.34232i	−0.375080	−	0.926993i
$13$	−1.35237	−	3.34232i	−0.375080	−	0.926993i
$14$		0			0
$15$	0.0973959	−	0.0562315i	0.0251475	−	0.0145189i
$16$		0			0
$17$	1.70610	−	2.95506i	0.413791	−	0.716706i	−0.581510	−	0.813539i	$-0.697538\pi$
$17$	1.70610	−	2.95506i	0.413791	−	0.716706i	0.995301	+	0.0968330i	$0.0308713\pi$
$18$		0			0
$19$	3.27166	−	5.66668i	0.750570	−	1.30003i	−0.196976	−	0.980408i	$-0.563112\pi$
$19$	3.27166	−	5.66668i	0.750570	−	1.30003i	0.947547	−	0.319618i	$-0.103555\pi$
$20$		0			0
$21$	−0.0437452			−0.00954598
$22$		0			0
$23$	2.27419	+	3.93902i	0.474202	+	0.821342i	0.999564	−	0.0295369i	$-0.00940324\pi$
$23$	2.27419	+	3.93902i	0.474202	+	0.821342i	−0.525362	+	0.850879i	$0.676070\pi$
$24$		0			0
$25$	−4.98735			−0.997470
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	5.22044	−	3.01402i	0.969411	−	0.559690i	0.0703545	−	0.997522i	$-0.477587\pi$
$29$	5.22044	−	3.01402i	0.969411	−	0.559690i	0.899057	+	0.437832i	$0.144254\pi$
$30$		0			0
$31$			7.66040i			1.37585i	0.725782	+	0.687925i	$0.241478\pi$
$31$			7.66040i			1.37585i	−0.725782	+	0.687925i	$0.758522\pi$
$32$		0			0
$33$	5.37427	+	3.10283i	0.935540	+	0.540134i
$34$		0			0
$35$	−0.00426060	−	0.00245986i	−0.000720173	−	0.000415792i
$36$		0			0
$37$	5.07408	+	8.78857i	0.834174	+	1.44483i	0.894701	+	0.446665i	$0.147388\pi$
$37$	5.07408	+	8.78857i	0.834174	+	1.44483i	−0.0605274	+	0.998167i	$0.519278\pi$
$38$		0			0
$39$	−2.84235	−	2.21835i	−0.455140	−	0.355220i
$40$		0			0
$41$	2.01283	−	1.16211i	0.314352	−	0.181491i	−0.334520	−	0.942389i	$-0.608574\pi$
$41$	2.01283	−	1.16211i	0.314352	−	0.181491i	0.648872	+	0.760897i	$0.275241\pi$
$42$		0			0
$43$	8.02853	+	4.63527i	1.22434	+	0.706873i	0.965840	−	0.259139i	$-0.0834388\pi$
$43$	8.02853	+	4.63527i	1.22434	+	0.706873i	0.258499	+	0.966011i	$0.416772\pi$
$44$		0			0
$45$	0.0562315	−	0.0973959i	0.00838250	−	0.0145189i
$46$		0			0
$47$		−	6.65732i		−	0.971070i	−0.874217	−	0.485535i	$-0.838625\pi$
$47$		−	6.65732i		−	0.971070i	0.874217	−	0.485535i	$-0.161375\pi$
$48$		0			0
$49$	−3.49904	−	6.06052i	−0.499863	−	0.865789i
$50$		0			0
$51$		−	3.41220i		−	0.477804i
$52$		0			0
$53$		−	11.2461i		−	1.54477i	−0.635153	−	0.772387i	$-0.719063\pi$
$53$		−	11.2461i		−	1.54477i	0.635153	−	0.772387i	$-0.280937\pi$
$54$		0			0
$55$	0.348954	+	0.604406i	0.0470530	+	0.0814981i
$56$		0			0
$57$		−	6.54332i		−	0.866684i
$58$		0			0
$59$	1.11081	−	1.92397i	0.144615	−	0.250480i	−0.784614	−	0.619984i	$-0.787139\pi$
$59$	1.11081	−	1.92397i	0.144615	−	0.250480i	0.929229	+	0.369504i	$0.120472\pi$
$60$		0			0
$61$	8.56334	+	4.94405i	1.09642	+	0.633021i	0.935279	−	0.353910i	$-0.115148\pi$
$61$	8.56334	+	4.94405i	1.09642	+	0.633021i	0.161144	+	0.986931i	$0.448481\pi$
$62$		0			0
$63$	−0.0378844	+	0.0218726i	−0.00477299	+	0.00275569i
$64$		0			0
$65$	−0.152092	−	0.375887i	−0.0188646	−	0.0466231i
$66$		0			0
$67$	−2.26023	−	3.91483i	−0.276131	−	0.478273i	0.694289	−	0.719696i	$-0.255719\pi$
$67$	−2.26023	−	3.91483i	−0.276131	−	0.478273i	−0.970420	+	0.241424i	$0.922386\pi$
$68$		0			0
$69$	3.93902	+	2.27419i	0.474202	+	0.273781i
$70$		0			0
$71$	−2.64086	−	1.52470i	−0.313413	−	0.180949i	0.335040	−	0.942204i	$-0.391250\pi$
$71$	−2.64086	−	1.52470i	−0.313413	−	0.180949i	−0.648453	+	0.761255i	$0.724584\pi$
$72$		0			0
$73$			4.71199i			0.551496i	0.961230	+	0.275748i	$0.0889256\pi$
$73$			4.71199i			0.551496i	−0.961230	+	0.275748i	$0.911074\pi$
$74$		0			0
$75$	−4.31917	+	2.49368i	−0.498735	+	0.287945i
$76$		0			0
$77$		−	0.271468i		−	0.0309367i
$78$		0			0
$79$	−8.01847			−0.902149			−0.451074	−	0.892486i	$-0.648959\pi$
$79$	−8.01847			−0.902149			−0.451074	+	0.892486i	$0.648959\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	2.86994			0.315017			0.157509	−	0.987518i	$-0.449654\pi$
$83$	2.86994			0.315017			0.157509	+	0.987518i	$0.449654\pi$
$84$		0			0
$85$	0.191873	−	0.332335i	0.0208116	−	0.0360467i
$86$		0			0
$87$	3.01402	−	5.22044i	0.323137	−	0.559690i
$88$		0			0
$89$	3.35627	−	1.93775i	0.355764	−	0.205401i	−0.311457	−	0.950260i	$-0.600817\pi$
$89$	3.35627	−	1.93775i	0.355764	−	0.205401i	0.667221	+	0.744860i	$0.267484\pi$
$90$		0			0
$91$	−0.0218715	+	0.156202i	−0.00229275	+	0.0163744i
$92$		0			0
$93$	3.83020	+	6.63410i	0.397173	+	0.687925i
$94$		0			0
$95$	0.367941	−	0.637292i	0.0377499	−	0.0653848i
$96$		0			0
$97$	−0.971031	−	0.560625i	−0.0985932	−	0.0569228i	0.449893	−	0.893083i	$-0.351462\pi$
$97$	−0.971031	−	0.560625i	−0.0985932	−	0.0569228i	−0.548486	+	0.836160i	$0.684796\pi$
$98$		0			0
$99$	6.20567			0.623693
$100$		0			0
$101$	2.33138	−	1.34602i	0.231981	−	0.133934i	−0.379505	−	0.925190i	$-0.623906\pi$
$101$	2.33138	−	1.34602i	0.231981	−	0.133934i	0.611485	+	0.791256i	$0.290572\pi$
$102$		0			0
$103$	−8.58090			−0.845501			−0.422750	−	0.906246i	$-0.638935\pi$
$103$	−8.58090			−0.845501			−0.422750	+	0.906246i	$0.638935\pi$
$104$		0			0
$105$	−0.00491972			−0.000480115
$106$		0			0
$107$	9.46960	−	5.46727i	0.915460	−	0.528541i	0.0332764	−	0.999446i	$-0.489406\pi$
$107$	9.46960	−	5.46727i	0.915460	−	0.528541i	0.882184	+	0.470905i	$0.156073\pi$
$108$		0			0
$109$	−1.35607			−0.129888			−0.0649438	−	0.997889i	$-0.520687\pi$
$109$	−1.35607			−0.129888			−0.0649438	+	0.997889i	$0.520687\pi$
$110$		0			0
$111$	8.78857	+	5.07408i	0.834174	+	0.481611i
$112$		0			0
$113$	−4.54900	+	7.87909i	−0.427934	+	0.741203i	−0.996689	−	0.0813038i	$-0.974092\pi$
$113$	−4.54900	+	7.87909i	−0.427934	+	0.741203i	0.568756	+	0.822506i	$0.307425\pi$
$114$		0			0
$115$	0.255763	+	0.442994i	0.0238500	+	0.0413094i
$116$		0			0
$117$	−3.57072	−	0.499974i	−0.330113	−	0.0462226i
$118$		0			0
$119$	−0.129269	+	0.0746337i	−0.0118501	+	0.00684166i
$120$		0			0
$121$	−13.7552	+	23.8246i	−1.25047	+	2.16588i
$122$		0			0
$123$	1.16211	−	2.01283i	0.104784	−	0.181491i
$124$		0			0
$125$	−1.12321			−0.100463
$126$		0			0
$127$	−2.71600	−	4.70425i	−0.241006	−	0.417435i	0.719995	−	0.693979i	$-0.244144\pi$
$127$	−2.71600	−	4.70425i	−0.241006	−	0.417435i	−0.961001	+	0.276545i	$0.910811\pi$
$128$		0			0
$129$	9.27055			0.816226
$130$		0			0
$131$			12.9469i			1.13118i	0.824688	+	0.565588i	$0.191351\pi$
$131$			12.9469i			1.13118i	−0.824688	+	0.565588i	$0.808649\pi$
$132$		0			0
$133$	−0.247890	+	0.143119i	−0.0214948	+	0.0124100i
$134$		0			0
$135$		−	0.112463i		−	0.00967928i
$136$		0			0
$137$	−8.11473	−	4.68504i	−0.693289	−	0.400270i	0.111554	−	0.993758i	$-0.464417\pi$
$137$	−8.11473	−	4.68504i	−0.693289	−	0.400270i	−0.804843	+	0.593488i	$0.797750\pi$
$138$		0			0
$139$	−11.5652	−	6.67714i	−0.980944	−	0.566348i	−0.0783887	−	0.996923i	$-0.524978\pi$
$139$	−11.5652	−	6.67714i	−0.980944	−	0.566348i	−0.902555	+	0.430575i	$0.858311\pi$
$140$		0			0
$141$	−3.32866	−	5.76541i	−0.280324	−	0.485535i
$142$		0			0
$143$	13.7663	−	17.6387i	1.15120	−	1.47502i
$144$		0			0
$145$	0.587106	−	0.338966i	0.0487565	−	0.0281496i
$146$		0			0
$147$	−6.06052	−	3.49904i	−0.499863	−	0.288596i
$148$		0			0
$149$	−3.72048	+	6.44406i	−0.304794	+	0.527918i	−0.977215	−	0.212250i	$-0.931921\pi$
$149$	−3.72048	+	6.44406i	−0.304794	+	0.527918i	0.672422	+	0.740168i	$0.265254\pi$
$150$		0			0
$151$			5.32718i			0.433520i	0.976225	+	0.216760i	$0.0695489\pi$
$151$			5.32718i			0.433520i	−0.976225	+	0.216760i	$0.930451\pi$
$152$		0			0
$153$	−1.70610	−	2.95506i	−0.137930	−	0.238902i
$154$		0			0
$155$			0.861512i			0.0691983i
$156$		0			0
$157$		−	0.685882i		−	0.0547394i	−0.999625	−	0.0273697i	$-0.991287\pi$
$157$		−	0.685882i		−	0.0547394i	0.999625	−	0.0273697i	$-0.00871313\pi$
$158$		0			0
$159$	−5.62306	−	9.73943i	−0.445938	−	0.772387i
$160$		0			0
$161$		−	0.198970i		−	0.0156810i
$162$		0			0
$163$	−2.13178	+	3.69236i	−0.166974	+	0.289208i	−0.937355	−	0.348377i	$-0.886733\pi$
$163$	−2.13178	+	3.69236i	−0.166974	+	0.289208i	0.770380	+	0.637584i	$0.220066\pi$
$164$		0			0
$165$	0.604406	+	0.348954i	0.0470530	+	0.0271660i
$166$		0			0
$167$	18.7011	−	10.7971i	1.44713	−	0.835502i	0.448823	−	0.893621i	$-0.351843\pi$
$167$	18.7011	−	10.7971i	1.44713	−	0.835502i	0.998310	+	0.0581186i	$0.0185102\pi$
$168$		0			0
$169$	−9.34220	+	9.04010i	−0.718631	+	0.695392i
$170$		0			0
$171$	−3.27166	−	5.66668i	−0.250190	−	0.433342i
$172$		0			0
$173$	−8.50417	−	4.90988i	−0.646560	−	0.373291i	0.140577	−	0.990070i	$-0.455104\pi$
$173$	−8.50417	−	4.90988i	−0.646560	−	0.373291i	−0.787137	+	0.616778i	$0.788438\pi$
$174$		0			0
$175$	0.188943	+	0.109086i	0.0142828	+	0.00824615i
$176$		0			0
$177$		−	2.22161i		−	0.166987i
$178$		0			0
$179$	−17.9739	+	10.3772i	−1.34343	+	0.775631i	−0.987309	−	0.158808i	$-0.949235\pi$
$179$	−17.9739	+	10.3772i	−1.34343	+	0.775631i	−0.356123	+	0.934439i	$0.615901\pi$
$180$		0			0
$181$		−	15.8357i		−	1.17706i	−0.808476	−	0.588530i	$-0.799707\pi$
$181$		−	15.8357i		−	1.17706i	0.808476	−	0.588530i	$-0.200293\pi$
$182$		0			0
$183$	9.88810			0.730949
$184$		0			0
$185$	0.570647	+	0.988389i	0.0419548	+	0.0726678i
$186$		0			0
$187$	21.1750			1.54847
$188$		0			0
$189$	−0.0218726	+	0.0378844i	−0.00159100	+	0.00275569i
$190$		0			0
$191$	−5.91519	+	10.2454i	−0.428008	+	0.741332i	−0.996696	−	0.0812216i	$-0.974118\pi$
$191$	−5.91519	+	10.2454i	−0.428008	+	0.741332i	0.568688	+	0.822553i	$0.307451\pi$
$192$		0			0
$193$	7.37552	−	4.25826i	0.530901	−	0.306516i	−0.210482	−	0.977598i	$-0.567503\pi$
$193$	7.37552	−	4.25826i	0.530901	−	0.306516i	0.741383	+	0.671082i	$0.234170\pi$
$194$		0			0
$195$	−0.319659	−	0.249482i	−0.0228912	−	0.0178658i
$196$		0			0
$197$	4.62690	+	8.01403i	0.329653	+	0.570976i	0.982443	−	0.186563i	$-0.0597349\pi$
$197$	4.62690	+	8.01403i	0.329653	+	0.570976i	−0.652790	+	0.757539i	$0.726402\pi$
$198$		0			0
$199$	−4.56241	+	7.90232i	−0.323420	+	0.560181i	−0.981191	−	0.193037i	$-0.938166\pi$
$199$	−4.56241	+	7.90232i	−0.323420	+	0.560181i	0.657771	+	0.753218i	$0.271499\pi$
$200$		0			0
$201$	−3.91483	−	2.26023i	−0.276131	−	0.159424i
$202$		0			0
$203$	−0.263698			−0.0185080
$204$		0			0
$205$	0.226370	−	0.130695i	0.0158103	−	0.00912810i
$206$		0			0
$207$	4.54839			0.316135
$208$		0			0
$209$	40.6057			2.80875
$210$		0			0
$211$	−17.9433	+	10.3596i	−1.23527	+	0.713184i	−0.968124	−	0.250472i	$-0.919414\pi$
$211$	−17.9433	+	10.3596i	−1.23527	+	0.713184i	−0.267147	+	0.963656i	$0.586081\pi$
$212$		0			0
$213$	−3.04941			−0.208942
$214$		0			0
$215$	0.902913	+	0.521297i	0.0615781	+	0.0355522i
$216$		0			0
$217$	0.167553	−	0.290210i	0.0113742	−	0.0197007i
$218$		0			0
$219$	2.35599	+	4.08070i	0.159203	+	0.275748i
$220$		0			0
$221$	−12.1840	−	1.70601i	−0.819586	−	0.114759i
$222$		0			0
$223$	1.91875	−	1.10779i	0.128489	−	0.0741830i	−0.434378	−	0.900731i	$-0.643032\pi$
$223$	1.91875	−	1.10779i	0.128489	−	0.0741830i	0.562867	+	0.826548i	$0.309698\pi$
$224$		0			0
$225$	−2.49368	+	4.31917i	−0.166245	+	0.287945i
$226$		0			0
$227$	−4.67656	+	8.10005i	−0.310394	+	0.537619i	−0.978448	−	0.206494i	$-0.933794\pi$
$227$	−4.67656	+	8.10005i	−0.310394	+	0.537619i	0.668053	+	0.744113i	$0.267128\pi$
$228$		0			0
$229$	−6.14279			−0.405927			−0.202963	−	0.979186i	$-0.565057\pi$
$229$	−6.14279			−0.405927			−0.202963	+	0.979186i	$0.565057\pi$
$230$		0			0
$231$	−0.135734	−	0.235098i	−0.00893065	−	0.0154683i
$232$		0			0
$233$	−25.5816			−1.67591			−0.837953	−	0.545742i	$-0.816248\pi$
$233$	−25.5816			−1.67591			−0.837953	+	0.545742i	$0.816248\pi$
$234$		0			0
$235$		−	0.748703i		−	0.0488400i
$236$		0			0
$237$	−6.94420	+	4.00924i	−0.451074	+	0.260428i
$238$		0			0
$239$			24.4002i			1.57831i	0.614191	+	0.789157i	$0.289482\pi$
$239$			24.4002i			1.57831i	−0.614191	+	0.789157i	$0.710518\pi$
$240$		0			0
$241$	13.3295	+	7.69576i	0.858626	+	0.495728i	0.863552	−	0.504260i	$-0.168235\pi$
$241$	13.3295	+	7.69576i	0.858626	+	0.495728i	−0.00492624	+	0.999988i	$0.501568\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−0.393513	−	0.681585i	−0.0251406	−	0.0435448i
$246$		0			0
$247$	−23.3644	−	3.27149i	−1.48664	−	0.208160i
$248$		0			0
$249$	2.48544	−	1.43497i	0.157509	−	0.0909376i
$250$		0			0
$251$	−7.67751	−	4.43261i	−0.484600	−	0.279784i	0.237732	−	0.971331i	$-0.423596\pi$
$251$	−7.67751	−	4.43261i	−0.484600	−	0.279784i	−0.722331	+	0.691547i	$0.756929\pi$
$252$		0			0
$253$	−14.1129	+	24.4442i	−0.887270	+	1.53680i
$254$		0			0
$255$		−	0.383747i		−	0.0240312i
$256$		0			0
$257$	−1.86412	−	3.22876i	−0.116281	−	0.201404i	0.802010	−	0.597310i	$-0.203764\pi$
$257$	−1.86412	−	3.22876i	−0.116281	−	0.201404i	−0.918291	+	0.395906i	$0.870431\pi$
$258$		0			0
$259$		−	0.443933i		−	0.0275847i
$260$		0			0
$261$		−	6.02804i		−	0.373127i
$262$		0			0
$263$	3.86616	+	6.69639i	0.238398	+	0.412917i	0.960255	−	0.279125i	$-0.0900445\pi$
$263$	3.86616	+	6.69639i	0.238398	+	0.412917i	−0.721857	+	0.692042i	$0.756711\pi$
$264$		0			0
$265$		−	1.26477i		−	0.0776944i
$266$		0			0
$267$	1.93775	−	3.35627i	0.118588	−	0.205401i
$268$		0			0
$269$	12.9358	+	7.46846i	0.788707	+	0.455360i	0.839507	−	0.543349i	$-0.182844\pi$
$269$	12.9358	+	7.46846i	0.788707	+	0.455360i	−0.0508004	+	0.998709i	$0.516177\pi$
$270$		0			0
$271$	−25.4780	+	14.7097i	−1.54768	+	0.893552i	−0.549359	+	0.835586i	$0.685128\pi$
$271$	−25.4780	+	14.7097i	−1.54768	+	0.893552i	−0.998319	+	0.0579660i	$0.981539\pi$
$272$		0			0
$273$	0.0591596	+	0.146210i	0.00358050	+	0.00884905i
$274$		0			0
$275$	−15.4749	−	26.8034i	−0.933173	−	1.61630i
$276$		0			0
$277$	−15.7963	−	9.12000i	−0.949108	−	0.547968i	−0.0563041	−	0.998414i	$-0.517932\pi$
$277$	−15.7963	−	9.12000i	−0.949108	−	0.547968i	−0.892804	+	0.450446i	$0.851265\pi$
$278$		0			0
$279$	6.63410	+	3.83020i	0.397173	+	0.229308i
$280$		0			0
$281$		−	14.2985i		−	0.852976i	−0.904493	−	0.426488i	$-0.859751\pi$
$281$		−	14.2985i		−	0.852976i	0.904493	−	0.426488i	$-0.140249\pi$
$282$		0			0
$283$	−19.3766	+	11.1871i	−1.15182	+	0.665004i	−0.949330	−	0.314280i	$-0.898237\pi$
$283$	−19.3766	+	11.1871i	−1.15182	+	0.665004i	−0.202491	+	0.979284i	$0.564904\pi$
$284$		0			0
$285$		−	0.735882i		−	0.0435899i
$286$		0			0
$287$	−0.101673			−0.00600160
$288$		0			0
$289$	2.67843	+	4.63918i	0.157555	+	0.272893i
$290$		0			0
$291$	−1.12125			−0.0657288
$292$		0			0
$293$	7.40233	−	12.8212i	0.432449	−	0.749024i	−0.564635	−	0.825341i	$-0.690983\pi$
$293$	7.40233	−	12.8212i	0.432449	−	0.749024i	0.997084	+	0.0763174i	$0.0243162\pi$
$294$		0			0
$295$	0.124925	−	0.216376i	0.00727340	−	0.0125979i
$296$		0			0
$297$	5.37427	−	3.10283i	0.311847	−	0.180045i
$298$		0			0
$299$	10.0899	−	12.9281i	0.583515	−	0.747651i
$300$		0			0
$301$	−0.202771	−	0.351209i	−0.0116875	−	0.0202434i
$302$		0			0
$303$	1.34602	−	2.33138i	0.0773269	−	0.133934i
$304$		0			0
$305$	0.963060	+	0.556023i	0.0551446	+	0.0318378i
$306$		0			0
$307$	3.92702			0.224127			0.112063	−	0.993701i	$-0.464254\pi$
$307$	3.92702			0.224127			0.112063	+	0.993701i	$0.464254\pi$
$308$		0			0
$309$	−7.43127	+	4.29045i	−0.422750	+	0.244075i
$310$		0			0
$311$	−5.57194			−0.315956			−0.157978	−	0.987443i	$-0.550498\pi$
$311$	−5.57194			−0.315956			−0.157978	+	0.987443i	$0.550498\pi$
$312$		0			0
$313$	−3.34250			−0.188929			−0.0944647	−	0.995528i	$-0.530114\pi$
$313$	−3.34250			−0.188929			−0.0944647	+	0.995528i	$0.530114\pi$
$314$		0			0
$315$	−0.00426060	+	0.00245986i	−0.000240058	+	0.000138597i
$316$		0			0
$317$	−9.69504			−0.544528			−0.272264	−	0.962223i	$-0.587772\pi$
$317$	−9.69504			−0.544528			−0.272264	+	0.962223i	$0.587772\pi$
$318$		0			0
$319$	32.3963	+	18.7040i	1.81385	+	1.04722i
$320$		0			0
$321$	5.46727	−	9.46960i	0.305153	−	0.528541i
$322$		0			0
$323$	−11.1636	−	19.3359i	−0.621158	−	1.07588i
$324$		0			0
$325$	6.74474	+	16.6693i	0.374131	+	0.924648i
$326$		0			0
$327$	−1.17439	+	0.678033i	−0.0649438	+	0.0374953i
$328$		0			0
$329$	−0.145613	+	0.252209i	−0.00802790	+	0.0139047i
$330$		0			0
$331$	−9.32657	+	16.1541i	−0.512635	+	0.887909i	0.487258	+	0.873258i	$0.337997\pi$
$331$	−9.32657	+	16.1541i	−0.512635	+	0.887909i	−0.999893	+	0.0146513i	$0.995336\pi$
$332$		0			0
$333$	10.1482			0.556116
$334$		0			0
$335$	−0.254192	−	0.440274i	−0.0138880	−	0.0240547i
$336$		0			0
$337$	−3.77708			−0.205751			−0.102875	−	0.994694i	$-0.532804\pi$
$337$	−3.77708			−0.205751			−0.102875	+	0.994694i	$0.532804\pi$
$338$		0			0
$339$			9.09799i			0.494135i
$340$		0			0
$341$	−41.1691	+	23.7690i	−2.22943	+	1.28716i
$342$		0			0
$343$			0.612349i			0.0330637i
$344$		0			0
$345$	0.442994	+	0.255763i	0.0238500	+	0.0137698i
$346$		0			0
$347$	3.29621	+	1.90307i	0.176950	+	0.102162i	0.585859	−	0.810413i	$-0.300757\pi$
$347$	3.29621	+	1.90307i	0.176950	+	0.102162i	−0.408909	+	0.912575i	$0.634091\pi$
$348$		0			0
$349$	−6.84360	−	11.8535i	−0.366330	−	0.634502i	0.622659	−	0.782493i	$-0.286052\pi$
$349$	−6.84360	−	11.8535i	−0.366330	−	0.634502i	−0.988989	+	0.147992i	$0.952719\pi$
$350$		0			0
$351$	−3.34232	+	1.35237i	−0.178400	+	0.0721841i
$352$		0			0
$353$	19.0118	−	10.9765i	1.01190	−	0.584220i	0.100151	−	0.994972i	$-0.468067\pi$
$353$	19.0118	−	10.9765i	1.01190	−	0.584220i	0.911747	+	0.410753i	$0.134734\pi$
$354$		0			0
$355$	−0.297000	−	0.171473i	−0.0157631	−	0.00910083i
$356$		0			0
$357$	−0.0746337	+	0.129269i	−0.00395004	+	0.00684166i
$358$		0			0
$359$		−	28.3255i		−	1.49496i	−0.664282	−	0.747482i	$-0.731263\pi$
$359$		−	28.3255i		−	1.49496i	0.664282	−	0.747482i	$-0.268737\pi$
$360$		0			0
$361$	−11.9075	−	20.6244i	−0.626712	−	1.08550i
$362$		0			0
$363$			27.5103i			1.44392i
$364$		0			0
$365$			0.529925i			0.0277375i
$366$		0			0
$367$	−6.66461	−	11.5434i	−0.347890	−	0.602562i	0.637985	−	0.770049i	$-0.279768\pi$
$367$	−6.66461	−	11.5434i	−0.347890	−	0.602562i	−0.985874	+	0.167487i	$0.946435\pi$
$368$		0			0
$369$		−	2.32422i		−	0.120994i
$370$		0			0
$371$	−0.245982	+	0.426053i	−0.0127707	+	0.0221196i
$372$		0			0
$373$	12.5046	+	7.21954i	0.647464	+	0.373813i	0.787484	−	0.616335i	$-0.211383\pi$
$373$	12.5046	+	7.21954i	0.647464	+	0.373813i	−0.140020	+	0.990149i	$0.544717\pi$
$374$		0			0
$375$	−0.972727	+	0.561604i	−0.0502314	+	0.0290011i
$376$		0			0
$377$	−17.1338	−	13.3723i	−0.882435	−	0.688709i
$378$		0			0
$379$	−7.32609	−	12.6892i	−0.376316	−	0.651799i	0.614207	−	0.789145i	$-0.289476\pi$
$379$	−7.32609	−	12.6892i	−0.376316	−	0.651799i	−0.990523	+	0.137346i	$0.956143\pi$
$380$		0			0
$381$	−4.70425	−	2.71600i	−0.241006	−	0.139145i
$382$		0			0
$383$	−27.6336	−	15.9543i	−1.41201	−	0.815224i	−0.416433	−	0.909167i	$-0.636720\pi$
$383$	−27.6336	−	15.9543i	−1.41201	−	0.815224i	−0.995578	+	0.0939422i	$0.970053\pi$
$384$		0			0
$385$		−	0.0305301i		−	0.00155596i
$386$		0			0
$387$	8.02853	−	4.63527i	0.408113	−	0.235624i
$388$		0			0
$389$			10.8562i			0.550429i	0.961383	+	0.275214i	$0.0887488\pi$
$389$			10.8562i			0.550429i	−0.961383	+	0.275214i	$0.911251\pi$
$390$		0			0
$391$	15.5200			0.784881
$392$		0			0
$393$	6.47345	+	11.2123i	0.326542	+	0.565588i
$394$		0			0
$395$	−0.901782			−0.0453736
$396$		0			0
$397$	14.8260	−	25.6793i	0.744093	−	1.28881i	−0.206524	−	0.978442i	$-0.566215\pi$
$397$	14.8260	−	25.6793i	0.744093	−	1.28881i	0.950617	−	0.310366i	$-0.100452\pi$
$398$		0			0
$399$	−0.143119	+	0.247890i	−0.00716493	+	0.0124100i
$400$		0			0
$401$	18.5432	−	10.7059i	0.926001	−	0.534627i	0.0404563	−	0.999181i	$-0.487119\pi$
$401$	18.5432	−	10.7059i	0.926001	−	0.534627i	0.885545	+	0.464554i	$0.153786\pi$
$402$		0			0
$403$	25.6035	−	10.3597i	1.27540	−	0.516053i
$404$		0			0
$405$	−0.0562315	−	0.0973959i	−0.00279417	−	0.00483964i
$406$		0			0
$407$	−31.4881	+	54.5389i	−1.56081	+	2.70339i
$408$		0			0
$409$	−18.0981	−	10.4490i	−0.894896	−	0.516668i	−0.0193551	−	0.999813i	$-0.506161\pi$
$409$	−18.0981	−	10.4490i	−0.894896	−	0.516668i	−0.875541	+	0.483144i	$0.839495\pi$
$410$		0			0
$411$	−9.37009			−0.462192
$412$		0			0
$413$	−0.0841646	+	0.0485925i	−0.00414147	+	0.00239108i
$414$		0			0
$415$	0.322762			0.0158438
$416$		0			0
$417$	−13.3543			−0.653962
$418$		0			0
$419$	3.61754	−	2.08859i	0.176728	−	0.102034i	−0.409026	−	0.912523i	$-0.634132\pi$
$419$	3.61754	−	2.08859i	0.176728	−	0.102034i	0.585755	+	0.810488i	$0.300798\pi$
$420$		0			0
$421$	−26.9125			−1.31164			−0.655818	−	0.754919i	$-0.727676\pi$
$421$	−26.9125			−1.31164			−0.655818	+	0.754919i	$0.727676\pi$
$422$		0			0
$423$	−5.76541	−	3.32866i	−0.280324	−	0.161845i
$424$		0			0
$425$	−8.50893	+	14.7379i	−0.412744	+	0.714893i
$426$		0			0
$427$	−0.216278	−	0.374605i	−0.0104664	−	0.0181284i
$428$		0			0
$429$	3.10267	−	22.1587i	0.149798	−	1.06983i
$430$		0			0
$431$	20.0200	−	11.5585i	0.964329	−	0.556756i	0.0668263	−	0.997765i	$-0.478713\pi$
$431$	20.0200	−	11.5585i	0.964329	−	0.556756i	0.897503	+	0.441009i	$0.145379\pi$
$432$		0			0
$433$	−8.79268	+	15.2294i	−0.422549	+	0.731877i	−0.996188	−	0.0872315i	$-0.972198\pi$
$433$	−8.79268	+	15.2294i	−0.422549	+	0.731877i	0.573639	+	0.819108i	$0.305531\pi$
$434$		0			0
$435$	0.338966	−	0.587106i	0.0162522	−	0.0281496i
$436$		0			0
$437$	29.7616			1.42369
$438$		0			0
$439$	8.91367	+	15.4389i	0.425426	+	0.736860i	0.996460	−	0.0840668i	$-0.0267909\pi$
$439$	8.91367	+	15.4389i	0.425426	+	0.736860i	−0.571034	+	0.820926i	$0.693458\pi$
$440$		0			0
$441$	−6.99809			−0.333242
$442$		0			0
$443$			5.80167i			0.275646i	0.990457	+	0.137823i	$0.0440105\pi$
$443$			5.80167i			0.275646i	−0.990457	+	0.137823i	$0.955990\pi$
$444$		0			0
$445$	0.377457	−	0.217925i	0.0178932	−	0.0103306i
$446$		0			0
$447$			7.44096i			0.351945i
$448$		0			0
$449$	13.5058	+	7.79756i	0.637377	+	0.367990i	0.783603	−	0.621261i	$-0.213380\pi$
$449$	13.5058	+	7.79756i	0.637377	+	0.367990i	−0.146227	+	0.989251i	$0.546713\pi$
$450$		0			0
$451$	12.4910	+	7.21167i	0.588178	+	0.339584i
$452$		0			0
$453$	2.66359	+	4.61348i	0.125146	+	0.216760i
$454$		0			0
$455$	−0.00245973	+	0.0175669i	−0.000115314	+	0.000823550i
$456$		0			0
$457$	−9.66544	+	5.58035i	−0.452130	+	0.261038i	−0.708729	−	0.705480i	$-0.750731\pi$
$457$	−9.66544	+	5.58035i	−0.452130	+	0.261038i	0.256599	+	0.966518i	$0.417398\pi$
$458$		0			0
$459$	−2.95506	−	1.70610i	−0.137930	−	0.0796340i
$460$		0			0
$461$	−1.29055	+	2.23530i	−0.0601070	+	0.104108i	−0.894513	−	0.447042i	$-0.852478\pi$
$461$	−1.29055	+	2.23530i	−0.0601070	+	0.104108i	0.834406	+	0.551150i	$0.185811\pi$
$462$		0			0
$463$		−	18.5594i		−	0.862530i	−0.902225	−	0.431265i	$-0.858067\pi$
$463$		−	18.5594i		−	0.862530i	0.902225	−	0.431265i	$-0.141933\pi$
$464$		0			0
$465$	0.430756	+	0.746092i	0.0199758	+	0.0345992i
$466$		0			0
$467$			29.7896i			1.37850i	0.724525	+	0.689249i	$0.242059\pi$
$467$			29.7896i			1.37850i	−0.724525	+	0.689249i	$0.757941\pi$
$468$		0			0
$469$			0.197748i			0.00913117i
$470$		0			0
$471$	−0.342941	−	0.593991i	−0.0158019	−	0.0273697i
$472$		0			0
$473$			57.5299i			2.64523i
$474$		0			0
$475$	−16.3169	+	28.2617i	−0.748672	+	1.29674i
$476$		0			0
$477$	−9.73943	−	5.62306i	−0.445938	−	0.257462i
$478$		0			0
$479$	−5.33480	+	3.08005i	−0.243753	+	0.140731i	−0.616901	−	0.787041i	$-0.711612\pi$
$479$	−5.33480	+	3.08005i	−0.243753	+	0.140731i	0.373147	+	0.927772i	$0.378279\pi$
$480$		0			0
$481$	22.5122	−	28.8446i	1.02647	−	1.31520i
$482$		0			0
$483$	−0.0994850	−	0.172313i	−0.00452673	−	0.00784052i
$484$		0			0
$485$	−0.109205	−	0.0630496i	−0.00495875	−	0.00286293i
$486$		0			0
$487$	1.79547	+	1.03662i	0.0813607	+	0.0469736i	0.540128	−	0.841583i	$-0.318376\pi$
$487$	1.79547	+	1.03662i	0.0813607	+	0.0469736i	−0.458768	+	0.888556i	$0.651709\pi$
$488$		0			0
$489$			4.26357i			0.192805i
$490$		0			0
$491$	11.4247	−	6.59605i	0.515589	−	0.297676i	−0.219539	−	0.975604i	$-0.570455\pi$
$491$	11.4247	−	6.59605i	0.515589	−	0.297676i	0.735128	+	0.677928i	$0.237122\pi$
$492$		0			0
$493$		−	20.5689i		−	0.926377i
$494$		0			0
$495$	0.697908			0.0313687
$496$		0			0
$497$	0.0666984	+	0.115525i	0.00299183	+	0.00518201i
$498$		0			0
$499$	25.3564			1.13511			0.567554	−	0.823336i	$-0.307890\pi$
$499$	25.3564			1.13511			0.567554	+	0.823336i	$0.307890\pi$
$500$		0			0
$501$	10.7971	−	18.7011i	0.482377	−	0.835502i
$502$		0			0
$503$	6.42317	−	11.1253i	0.286395	−	0.496051i	−0.686552	−	0.727081i	$-0.740876\pi$
$503$	6.42317	−	11.1253i	0.286395	−	0.496051i	0.972947	+	0.231030i	$0.0742097\pi$
$504$		0			0
$505$	0.262194	−	0.151378i	0.0116675	−	0.00673621i
$506$		0			0
$507$	−3.57053	+	12.5001i	−0.158573	+	0.555147i
$508$		0			0
$509$	12.2833	+	21.2754i	0.544449	+	0.943014i	0.998641	+	0.0521099i	$0.0165946\pi$
$509$	12.2833	+	21.2754i	0.544449	+	0.943014i	−0.454192	+	0.890904i	$0.650072\pi$
$510$		0			0
$511$	0.103063	−	0.178511i	0.00455926	−	0.00789686i
$512$		0			0
$513$	−5.66668	−	3.27166i	−0.250190	−	0.144447i
$514$		0			0
$515$	−0.965034			−0.0425245
$516$		0			0
$517$	35.7782	−	20.6566i	1.57352	−	0.908475i
$518$		0			0
$519$	−9.81976			−0.431040
$520$		0			0
$521$	−2.81245			−0.123216			−0.0616078	−	0.998100i	$-0.519623\pi$
$521$	−2.81245			−0.123216			−0.0616078	+	0.998100i	$0.519623\pi$
$522$		0			0
$523$	−9.12262	+	5.26694i	−0.398904	+	0.230307i	−0.686011	−	0.727591i	$-0.740640\pi$
$523$	−9.12262	+	5.26694i	−0.398904	+	0.230307i	0.287107	+	0.957899i	$0.407307\pi$
$524$		0			0
$525$	0.218173			0.00952183
$526$		0			0
$527$	22.6369	+	13.0694i	0.986080	+	0.569313i
$528$		0			0
$529$	1.15609	−	2.00240i	0.0502646	−	0.0870608i
$530$		0			0
$531$	−1.11081	−	1.92397i	−0.0482049	−	0.0834934i
$532$		0			0
$533$	−6.60624	−	5.15593i	−0.286148	−	0.223328i
$534$		0			0
$535$	1.06498	−	0.614866i	0.0460431	−	0.0265830i
$536$		0			0
$537$	−10.3772	+	17.9739i	−0.447811	+	0.775631i
$538$		0			0
$539$	21.7139	−	37.6096i	0.935284	−	1.61996i
$540$		0			0
$541$	−33.5743			−1.44347			−0.721737	−	0.692167i	$-0.756656\pi$
$541$	−33.5743			−1.44347			−0.721737	+	0.692167i	$0.756656\pi$
$542$		0			0
$543$	−7.91786	−	13.7141i	−0.339788	−	0.588530i
$544$		0			0
$545$	−0.152507			−0.00653270
$546$		0			0
$547$		−	27.3023i		−	1.16736i	−0.811984	−	0.583680i	$-0.801612\pi$
$547$		−	27.3023i		−	1.16736i	0.811984	−	0.583680i	$-0.198388\pi$
$548$		0			0
$549$	8.56334	−	4.94405i	0.365475	−	0.211007i
$550$		0			0
$551$		−	39.4434i		−	1.68035i
$552$		0			0
$553$	0.303775	+	0.175385i	0.0129178	+	0.00745812i
$554$		0			0
$555$	0.988389	+	0.570647i	0.0419548	+	0.0242226i
$556$		0			0
$557$	13.2914	+	23.0215i	0.563176	+	0.975450i	0.997217	+	0.0745568i	$0.0237542\pi$
$557$	13.2914	+	23.0215i	0.563176	+	0.975450i	−0.434040	+	0.900893i	$0.642912\pi$
$558$		0			0
$559$	4.63503	−	33.1025i	0.196041	−	1.40009i
$560$		0			0
$561$	18.3381	−	10.5875i	0.774235	−	0.447005i
$562$		0			0
$563$	27.8800	+	16.0965i	1.17500	+	0.678387i	0.954853	−	0.297079i	$-0.0960125\pi$
$563$	27.8800	+	16.0965i	1.17500	+	0.678387i	0.220148	+	0.975466i	$0.429346\pi$
$564$		0			0
$565$	−0.511594	+	0.886107i	−0.0215229	+	0.0372788i
$566$		0			0
$567$			0.0437452i			0.00183713i
$568$		0			0
$569$	−11.7985	−	20.4356i	−0.494618	−	0.856704i	0.505363	−	0.862907i	$-0.331359\pi$
$569$	−11.7985	−	20.4356i	−0.494618	−	0.856704i	−0.999981	+	0.00620347i	$0.998025\pi$
$570$		0			0
$571$		−	26.6763i		−	1.11637i	−0.829717	−	0.558184i	$-0.811498\pi$
$571$		−	26.6763i		−	1.11637i	0.829717	−	0.558184i	$-0.188502\pi$
$572$		0			0
$573$			11.8304i			0.494221i
$574$		0			0
$575$	−11.3422	−	19.6453i	−0.473003	−	0.819265i
$576$		0			0
$577$			25.7891i			1.07361i	0.843705	+	0.536806i	$0.180369\pi$
$577$			25.7891i			1.07361i	−0.843705	+	0.536806i	$0.819631\pi$
$578$		0			0
$579$	4.25826	−	7.37552i	0.176967	−	0.306516i
$580$		0			0
$581$	−0.108726	−	0.0627731i	−0.00451072	−	0.00260427i
$582$		0			0
$583$	60.4396	−	34.8948i	2.50315	−	1.44520i
$584$		0			0
$585$	−0.401574	−	0.0562286i	−0.0166030	−	0.00232477i
$586$		0			0
$587$	−3.12213	−	5.40768i	−0.128864	−	0.223199i	0.794373	−	0.607431i	$-0.207800\pi$
$587$	−3.12213	−	5.40768i	−0.128864	−	0.223199i	−0.923237	+	0.384232i	$0.874466\pi$
$588$		0			0
$589$	43.4091	+	25.0622i	1.78864	+	1.03267i
$590$		0			0
$591$	8.01403	+	4.62690i	0.329653	+	0.190325i
$592$		0			0
$593$		−	18.9712i		−	0.779053i	−0.921015	−	0.389526i	$-0.872639\pi$
$593$		−	18.9712i		−	0.779053i	0.921015	−	0.389526i	$-0.127361\pi$
$594$		0			0
$595$	−0.0145380	+	0.00839354i	−0.000596001	+	0.000344102i
$596$		0			0
$597$			9.12481i			0.373454i
$598$		0			0
$599$	−3.88163			−0.158599			−0.0792995	−	0.996851i	$-0.525268\pi$
$599$	−3.88163			−0.158599			−0.0792995	+	0.996851i	$0.525268\pi$
$600$		0			0
$601$	−14.9897	−	25.9630i	−0.611444	−	1.05905i	−0.990997	−	0.133883i	$-0.957256\pi$
$601$	−14.9897	−	25.9630i	−0.611444	−	1.05905i	0.379553	−	0.925170i	$-0.376078\pi$
$602$		0			0
$603$	−4.52046			−0.184087
$604$		0			0
$605$	−1.54695	+	2.67939i	−0.0628924	+	0.108933i
$606$		0			0
$607$	−12.6058	+	21.8339i	−0.511654	+	0.886210i	0.488255	+	0.872701i	$0.337634\pi$
$607$	−12.6058	+	21.8339i	−0.511654	+	0.886210i	−0.999909	+	0.0135094i	$0.995700\pi$
$608$		0			0
$609$	−0.228369	+	0.131849i	−0.00925398	+	0.00534279i
$610$		0			0
$611$	−22.2509	+	9.00315i	−0.900175	+	0.364229i
$612$		0			0
$613$	−7.25898	−	12.5729i	−0.293187	−	0.507816i	0.681374	−	0.731935i	$-0.261383\pi$
$613$	−7.25898	−	12.5729i	−0.293187	−	0.507816i	−0.974562	+	0.224120i	$0.928049\pi$
$614$		0			0
$615$	0.130695	−	0.226370i	0.00527011	−	0.00912810i
$616$		0			0
$617$	11.3549	+	6.55573i	0.457130	+	0.263924i	0.710837	−	0.703357i	$-0.248317\pi$
$617$	11.3549	+	6.55573i	0.457130	+	0.263924i	−0.253707	+	0.967281i	$0.581650\pi$
$618$		0			0
$619$	−6.58321			−0.264602			−0.132301	−	0.991210i	$-0.542236\pi$
$619$	−6.58321			−0.264602			−0.132301	+	0.991210i	$0.542236\pi$
$620$		0			0
$621$	3.93902	−	2.27419i	0.158067	−	0.0912603i
$622$		0			0
$623$	−0.169534			−0.00679224
$624$		0			0
$625$	24.8104			0.992418
$626$		0			0
$627$	35.1656	−	20.3028i	1.40438	−	0.810817i
$628$		0			0
$629$	34.6276			1.38069
$630$		0			0
$631$	12.8951	+	7.44499i	0.513346	+	0.296381i	0.734208	−	0.678925i	$-0.237554\pi$
$631$	12.8951	+	7.44499i	0.513346	+	0.296381i	−0.220862	+	0.975305i	$0.570887\pi$
$632$		0			0
$633$	−10.3596	+	17.9433i	−0.411757	+	0.713184i
$634$		0			0
$635$	−0.305450	−	0.529054i	−0.0121214	−	0.0209949i
$636$		0			0
$637$	−15.5242	+	19.8910i	−0.615091	+	0.788109i
$638$		0			0
$639$	−2.64086	+	1.52470i	−0.104471	+	0.0603163i
$640$		0			0
$641$	−8.56846	+	14.8410i	−0.338434	+	0.586185i	−0.984138	−	0.177403i	$-0.943230\pi$
$641$	−8.56846	+	14.8410i	−0.338434	+	0.586185i	0.645705	+	0.763587i	$0.276564\pi$
$642$		0			0
$643$	14.2230	−	24.6349i	0.560899	−	0.971505i	−0.436520	−	0.899695i	$-0.643789\pi$
$643$	14.2230	−	24.6349i	0.560899	−	0.971505i	0.997418	−	0.0718101i	$-0.0228776\pi$
$644$		0			0
$645$	1.04259			0.0410521
$646$		0			0
$647$	−7.39125	−	12.8020i	−0.290580	−	0.503299i	0.683367	−	0.730075i	$-0.260515\pi$
$647$	−7.39125	−	12.8020i	−0.290580	−	0.503299i	−0.973947	+	0.226776i	$0.927182\pi$
$648$		0			0
$649$	13.7866			0.541172
$650$		0			0
$651$		−	0.335106i		−	0.0131338i
$652$		0			0
$653$	30.7907	−	17.7770i	1.20493	−	0.695669i	0.243286	−	0.969955i	$-0.421775\pi$
$653$	30.7907	−	17.7770i	1.20493	−	0.695669i	0.961648	+	0.274285i	$0.0884413\pi$
$654$		0			0
$655$			1.45605i			0.0568925i
$656$		0			0
$657$	4.08070	+	2.35599i	0.159203	+	0.0919161i
$658$		0			0
$659$	−12.1452	−	7.01204i	−0.473110	−	0.273150i	0.244431	−	0.969667i	$-0.421399\pi$
$659$	−12.1452	−	7.01204i	−0.473110	−	0.273150i	−0.717541	+	0.696517i	$0.754732\pi$
$660$		0			0
$661$	20.7687	+	35.9725i	0.807810	+	1.39917i	0.914377	+	0.404863i	$0.132681\pi$
$661$	20.7687	+	35.9725i	0.807810	+	1.39917i	−0.106567	+	0.994306i	$0.533986\pi$
$662$		0			0
$663$	−11.4047	+	4.61456i	−0.442921	+	0.179215i
$664$		0			0
$665$	−0.0278785	+	0.0160956i	−0.00108108	+	0.000624162i
$666$		0			0
$667$	23.7446	+	13.7089i	0.919394	+	0.530812i
$668$		0			0
$669$	1.10779	−	1.91875i	0.0428296	−	0.0741830i
$670$		0			0
$671$			61.3623i			2.36886i
$672$		0			0
$673$	16.6927	+	28.9126i	0.643455	+	1.11450i	0.984656	+	0.174507i	$0.0558332\pi$
$673$	16.6927	+	28.9126i	0.643455	+	1.11450i	−0.341200	+	0.939991i	$0.610833\pi$
$674$		0			0
$675$			4.98735i			0.191963i
$676$		0			0
$677$		−	29.9211i		−	1.14996i	−0.818167	−	0.574980i	$-0.805010\pi$
$677$		−	29.9211i		−	1.14996i	0.818167	−	0.574980i	$-0.194990\pi$
$678$		0			0
$679$	0.0245246	+	0.0424779i	0.000941169	+	0.00163015i
$680$		0			0
$681$			9.35313i			0.358413i
$682$		0			0
$683$	1.87235	−	3.24301i	0.0716436	−	0.124090i	−0.827978	−	0.560760i	$-0.810509\pi$
$683$	1.87235	−	3.24301i	0.0716436	−	0.124090i	0.899622	+	0.436670i	$0.143842\pi$
$684$		0			0
$685$	−0.912608	−	0.526894i	−0.0348690	−	0.0201316i
$686$		0			0
$687$	−5.31981	+	3.07139i	−0.202963	+	0.117181i
$688$		0			0
$689$	−37.5881	+	15.2089i	−1.43199	+	0.579413i
$690$		0			0
$691$	3.30629	+	5.72665i	0.125777	+	0.217852i	0.922036	−	0.387103i	$-0.126524\pi$
$691$	3.30629	+	5.72665i	0.125777	+	0.217852i	−0.796259	+	0.604955i	$0.793191\pi$
$692$		0			0
$693$	−0.235098	−	0.135734i	−0.00893065	−	0.00515611i
$694$		0			0
$695$	−1.30065	−	0.750932i	−0.0493366	−	0.0284845i
$696$		0			0
$697$		−	7.93072i		−	0.300397i
$698$		0			0
$699$	−22.1543	+	12.7908i	−0.837953	+	0.483793i
$700$		0			0
$701$		−	27.7966i		−	1.04986i	−0.851145	−	0.524931i	$-0.824091\pi$
$701$		−	27.7966i		−	1.04986i	0.851145	−	0.524931i	$-0.175909\pi$
$702$		0			0
$703$	66.4027			2.50442
$704$		0			0
$705$	−0.374351	−	0.648396i	−0.0140989	−	0.0244200i
$706$		0			0
$707$	−0.117764			−0.00442896
$708$		0			0
$709$	−3.80578	+	6.59181i	−0.142929	+	0.247561i	−0.928598	−	0.371086i	$-0.878985\pi$
$709$	−3.80578	+	6.59181i	−0.142929	+	0.247561i	0.785669	+	0.618647i	$0.212319\pi$
$710$		0			0
$711$	−4.00924	+	6.94420i	−0.150358	+	0.260428i
$712$		0			0
$713$	−30.1745	+	17.4212i	−1.13004	+	0.652431i
$714$		0			0
$715$	1.54820	−	1.98370i	0.0578996	−	0.0741861i
$716$		0			0
$717$	12.2001	+	21.1312i	0.455620	+	0.789157i
$718$		0			0
$719$	−9.68786	+	16.7799i	−0.361296	+	0.625783i	−0.988174	−	0.153334i	$-0.950999\pi$
$719$	−9.68786	+	16.7799i	−0.361296	+	0.625783i	0.626878	+	0.779117i	$0.284332\pi$
$720$		0			0
$721$	0.325082	+	0.187686i	0.0121067	+	0.00698981i
$722$		0			0
$723$	15.3915			0.572417
$724$		0			0
$725$	−26.0362	+	15.0320i	−0.966959	+	0.558274i
$726$		0			0
$727$	−44.4404			−1.64820			−0.824102	−	0.566441i	$-0.808320\pi$
$727$	−44.4404			−1.64820			−0.824102	+	0.566441i	$0.808320\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	27.3950	−	15.8165i	1.01324	−	0.584994i
$732$		0			0
$733$	38.2441			1.41258			0.706288	−	0.707924i	$-0.250368\pi$
$733$	38.2441			1.41258			0.706288	+	0.707924i	$0.250368\pi$
$734$		0			0
$735$	−0.681585	−	0.393513i	−0.0251406	−	0.0145149i
$736$		0			0
$737$	14.0262	−	24.2941i	0.516663	−	0.894886i
$738$		0			0
$739$	11.2629	+	19.5080i	0.414313	+	0.717612i	0.995356	−	0.0962612i	$-0.0306884\pi$
$739$	11.2629	+	19.5080i	0.414313	+	0.717612i	−0.581043	+	0.813873i	$0.697355\pi$
$740$		0			0
$741$	−21.8699	+	8.84898i	−0.803410	+	0.325076i
$742$		0			0
$743$	−5.01591	+	2.89594i	−0.184016	+	0.106242i	−0.589178	−	0.808003i	$-0.700548\pi$
$743$	−5.01591	+	2.89594i	−0.184016	+	0.106242i	0.405162	+	0.914245i	$0.367215\pi$
$744$		0			0
$745$	−0.418417	+	0.724719i	−0.0153296	+	0.0265516i
$746$		0			0
$747$	1.43497	−	2.48544i	0.0525028	−	0.0909376i
$748$		0			0
$749$	−0.478334			−0.0174779
$750$		0			0
$751$	−21.1123	−	36.5675i	−0.770398	−	1.33437i	−0.937345	−	0.348403i	$-0.886724\pi$
$751$	−21.1123	−	36.5675i	−0.770398	−	1.33437i	0.166947	−	0.985966i	$-0.446609\pi$
$752$		0			0
$753$	−8.86522			−0.323067
$754$		0			0
$755$			0.599111i			0.0218039i
$756$		0			0
$757$	23.6590	−	13.6595i	0.859900	−	0.496463i	−0.00407907	−	0.999992i	$-0.501298\pi$
$757$	23.6590	−	13.6595i	0.859900	−	0.496463i	0.863979	+	0.503528i	$0.167965\pi$
$758$		0			0
$759$			28.2258i			1.02453i
$760$		0			0
$761$	47.5882	+	27.4750i	1.72507	+	0.995969i	0.907383	+	0.420305i	$0.138077\pi$
$761$	47.5882	+	27.4750i	1.72507	+	0.995969i	0.817686	+	0.575664i	$0.195256\pi$
$762$		0			0
$763$	0.0513738	+	0.0296607i	0.00185986	+	0.00107379i
$764$		0			0
$765$	−0.191873	−	0.332335i	−0.00693720	−	0.0120156i
$766$		0			0
$767$	−7.93276	−	1.11075i	−0.286435	−	0.0401068i
$768$		0			0
$769$	34.0582	−	19.6635i	1.22817	−	0.709085i	0.261524	−	0.965197i	$-0.415775\pi$
$769$	34.0582	−	19.6635i	1.22817	−	0.709085i	0.966647	+	0.256112i	$0.0824416\pi$
$770$		0			0
$771$	−3.22876	−	1.86412i	−0.116281	−	0.0671347i
$772$		0			0
$773$	24.7532	−	42.8738i	0.890310	−	1.54206i	0.0508062	−	0.998709i	$-0.483821\pi$
$773$	24.7532	−	42.8738i	0.890310	−	1.54206i	0.839504	−	0.543354i	$-0.182846\pi$
$774$		0			0
$775$		−	38.2051i		−	1.37237i
$776$		0			0
$777$	−0.221967	−	0.384458i	−0.00796301	−	0.0137923i
$778$		0			0
$779$		−	15.2081i		−	0.544888i
$780$		0			0
$781$		−	18.9236i		−	0.677140i
$782$		0			0
$783$	−3.01402	−	5.22044i	−0.107712	−	0.186563i
$784$		0			0
$785$		−	0.0771364i		−	0.00275312i
$786$		0			0
$787$	−5.27752	+	9.14093i	−0.188123	+	0.325839i	−0.944625	−	0.328153i	$-0.893574\pi$
$787$	−5.27752	+	9.14093i	−0.188123	+	0.325839i	0.756501	+	0.653992i	$0.226907\pi$
$788$		0			0
$789$	6.69639	+	3.86616i	0.238398	+	0.137639i
$790$		0			0
$791$	0.344672	−	0.198997i	0.0122551	−	0.00707551i
$792$		0			0
$793$	4.94379	−	35.3076i	0.175559	−	1.25381i
$794$		0			0
$795$	−0.632386	−	1.09533i	−0.0224284	−	0.0388472i
$796$		0			0
$797$	−2.33710	−	1.34933i	−0.0827844	−	0.0477956i	0.458036	−	0.888933i	$-0.348553\pi$
$797$	−2.33710	−	1.34933i	−0.0827844	−	0.0477956i	−0.540821	+	0.841138i	$0.681886\pi$
$798$		0			0
$799$	−19.6728	−	11.3581i	−0.695972	−	0.401820i
$800$		0			0
$801$		−	3.87549i		−	0.136934i
$802$		0			0
$803$	−25.3235	+	14.6205i	−0.893646	+	0.515947i
$804$		0			0
$805$		−	0.0223768i		−	0.000788678i
$806$		0			0
$807$	14.9369			0.525804
$808$		0			0
$809$	−18.6291	−	32.2665i	−0.654963	−	1.13443i	−0.981903	−	0.189384i	$-0.939351\pi$
$809$	−18.6291	−	32.2665i	−0.654963	−	1.13443i	0.326940	−	0.945045i	$-0.393983\pi$
$810$		0			0
$811$	−23.8133			−0.836198			−0.418099	−	0.908401i	$-0.637304\pi$
$811$	−23.8133			−0.836198			−0.418099	+	0.908401i	$0.637304\pi$
$812$		0			0
$813$	−14.7097	+	25.4780i	−0.515893	+	0.893552i
$814$		0			0
$815$	−0.239747	+	0.415254i	−0.00839797	+	0.0145457i
$816$		0			0
$817$	52.5332	−	30.3301i	1.83791	−	1.06112i
$818$		0			0
$819$	0.124339	+	0.0970421i	0.00434475	+	0.00339093i
$820$		0			0
$821$	23.2659	+	40.2977i	0.811985	+	1.40640i	0.911473	+	0.411360i	$0.134946\pi$
$821$	23.2659	+	40.2977i	0.811985	+	1.40640i	−0.0994882	+	0.995039i	$0.531721\pi$
$822$		0			0
$823$	−2.01612	+	3.49203i	−0.0702776	+	0.121724i	−0.899023	−	0.437902i	$-0.855722\pi$
$823$	−2.01612	+	3.49203i	−0.0702776	+	0.121724i	0.828745	+	0.559626i	$0.189055\pi$
$824$		0			0
$825$	−26.8034	−	15.4749i	−0.933173	−	0.538768i
$826$		0			0
$827$	44.3039			1.54060			0.770299	−	0.637682i	$-0.220107\pi$
$827$	44.3039			1.54060			0.770299	+	0.637682i	$0.220107\pi$
$828$		0			0
$829$	11.6419	−	6.72147i	0.404341	−	0.233446i	−0.284014	−	0.958820i	$-0.591666\pi$
$829$	11.6419	−	6.72147i	0.404341	−	0.233446i	0.688355	+	0.725374i	$0.258333\pi$
$830$		0			0
$831$	−18.2400			−0.632738
$832$		0			0
$833$	−23.8789			−0.827355
$834$		0			0
$835$	2.10318	−	1.21427i	0.0727835	−	0.0420216i
$836$		0			0
$837$	7.66040			0.264782
$838$		0			0
$839$	12.2305	+	7.06127i	0.422243	+	0.243782i	0.696037	−	0.718006i	$-0.254945\pi$
$839$	12.2305	+	7.06127i	0.422243	+	0.243782i	−0.273793	+	0.961789i	$0.588278\pi$
$840$		0			0
$841$	3.66866	−	6.35430i	0.126505	−	0.219114i
$842$		0			0
$843$	−7.14924	−	12.3828i	−0.246233	−	0.426488i
$844$		0			0
$845$	−1.05065	+	1.01668i	−0.0361435	+	0.0349747i
$846$		0			0
$847$	1.04221	−	0.601722i	0.0358109	−	0.0206754i
$848$		0			0
$849$	−11.1871	+	19.3766i	−0.383941	+	0.665004i
$850$		0			0
$851$	−23.0789	+	39.9738i	−0.791134	+	1.37028i
$852$		0			0
$853$	−40.7923			−1.39670			−0.698350	−	0.715756i	$-0.746082\pi$
$853$	−40.7923			−1.39670			−0.698350	+	0.715756i	$0.746082\pi$
$854$		0			0
$855$	−0.367941	−	0.637292i	−0.0125833	−	0.0217949i
$856$		0			0
$857$	−28.0604			−0.958526			−0.479263	−	0.877671i	$-0.659096\pi$
$857$	−28.0604			−0.958526			−0.479263	+	0.877671i	$0.659096\pi$
$858$		0			0
$859$		−	2.43440i		−	0.0830607i	−0.999137	−	0.0415303i	$-0.986777\pi$
$859$		−	2.43440i		−	0.0830607i	0.999137	−	0.0415303i	$-0.0132233\pi$
$860$		0			0
$861$	−0.0880518	+	0.0508367i	−0.00300080	+	0.00173251i
$862$		0			0
$863$		−	17.4046i		−	0.592459i	−0.955117	−	0.296230i	$-0.904271\pi$
$863$		−	17.4046i		−	0.592459i	0.955117	−	0.296230i	$-0.0957294\pi$
$864$		0			0
$865$	−0.956404	−	0.552180i	−0.0325187	−	0.0187747i
$866$		0			0
$867$	4.63918	+	2.67843i	0.157555	+	0.0909643i
$868$		0			0
$869$	−24.8800	−	43.0934i	−0.843996	−	1.46184i
$870$		0			0
$871$	−10.0280	+	12.8487i	−0.339784	+	0.435362i
$872$		0			0
$873$	−0.971031	+	0.560625i	−0.0328644	+	0.0189743i
$874$		0			0
$875$	0.0425521	+	0.0245675i	0.00143852	+	0.000830532i
$876$		0			0
$877$	−12.6152	+	21.8502i	−0.425986	+	0.737829i	−0.996512	−	0.0834505i	$-0.973406\pi$
$877$	−12.6152	+	21.8502i	−0.425986	+	0.737829i	0.570526	+	0.821279i	$0.306739\pi$
$878$		0			0
$879$		−	14.8047i		−	0.499349i
$880$		0			0
$881$	−24.7204	−	42.8169i	−0.832850	−	1.44254i	−0.895769	−	0.444520i	$-0.853374\pi$
$881$	−24.7204	−	42.8169i	−0.832850	−	1.44254i	0.0629186	−	0.998019i	$-0.479959\pi$
$882$		0			0
$883$		−	30.3032i		−	1.01978i	−0.860238	−	0.509892i	$-0.829685\pi$
$883$		−	30.3032i		−	1.01978i	0.860238	−	0.509892i	$-0.170315\pi$
$884$		0			0
$885$		−	0.249850i		−	0.00839860i
$886$		0			0
$887$	14.7503	+	25.5482i	0.495265	+	0.857824i	0.999985	−	0.00545876i	$-0.00173759\pi$
$887$	14.7503	+	25.5482i	0.495265	+	0.857824i	−0.504720	+	0.863283i	$0.668404\pi$
$888$		0			0
$889$			0.237624i			0.00796965i
$890$		0			0
$891$	3.10283	−	5.37427i	0.103949	−	0.180045i
$892$		0			0
$893$	−37.7249	−	21.7805i	−1.26242	−	0.728857i
$894$		0			0
$895$	−2.02140	+	1.16706i	−0.0675679	+	0.0390104i
$896$		0			0
$897$	2.27407	−	16.2410i	0.0759292	−	0.542271i
$898$		0			0
$899$	23.0886	+	39.9907i	0.770049	+	1.33376i
$900$		0			0
$901$	−33.2329	−	19.1870i	−1.10715	−	0.639213i
$902$		0			0
$903$	−0.351209	−	0.202771i	−0.0116875	−	0.00674779i
$904$		0			0
$905$		−	1.78093i		−	0.0592002i
$906$		0			0
$907$	22.0489	−	12.7299i	0.732121	−	0.422690i	−0.0870764	−	0.996202i	$-0.527752\pi$
$907$	22.0489	−	12.7299i	0.732121	−	0.422690i	0.819198	+	0.573511i	$0.194419\pi$
$908$		0			0
$909$		−	2.69204i		−	0.0892894i
$910$		0			0
$911$	29.6321			0.981755			0.490877	−	0.871229i	$-0.336676\pi$
$911$	29.6321			0.981755			0.490877	+	0.871229i	$0.336676\pi$
$912$		0			0
$913$	8.90495	+	15.4238i	0.294711	+	0.510454i
$914$		0			0
$915$	1.11205			0.0367631
$916$		0			0
$917$	0.283182	−	0.490486i	0.00935150	−	0.0161973i
$918$		0			0
$919$	−8.72730	+	15.1161i	−0.287887	+	0.498635i	−0.973305	−	0.229515i	$-0.926286\pi$
$919$	−8.72730	+	15.1161i	−0.287887	+	0.498635i	0.685418	+	0.728150i	$0.259619\pi$
$920$		0			0
$921$	3.40090	−	1.96351i	0.112063	−	0.0646999i
$922$		0			0
$923$	−1.52462	+	10.8886i	−0.0501836	+	0.358402i
$924$		0			0
$925$	−25.3062	−	43.8317i	−0.832064	−	1.44118i
$926$		0			0
$927$	−4.29045	+	7.43127i	−0.140917	+	0.244075i
$928$		0			0
$929$	34.5218	+	19.9311i	1.13262	+	0.653920i	0.944593	−	0.328244i	$-0.106457\pi$
$929$	34.5218	+	19.9311i	1.13262	+	0.653920i	0.188029	+	0.982163i	$0.439790\pi$
$930$		0			0
$931$	−45.7907			−1.50073
$932$		0			0
$933$	−4.82545	+	2.78597i	−0.157978	+	0.0912086i
$934$		0			0
$935$	2.38141			0.0778803
$936$		0			0
$937$	12.4580			0.406986			0.203493	−	0.979076i	$-0.434771\pi$
$937$	12.4580			0.406986			0.203493	+	0.979076i	$0.434771\pi$
$938$		0			0
$939$	−2.89469	+	1.67125i	−0.0944647	+	0.0545392i
$940$		0			0
$941$	−32.3676			−1.05515			−0.527577	−	0.849507i	$-0.676899\pi$
$941$	−32.3676			−1.05515			−0.527577	+	0.849507i	$0.676899\pi$
$942$		0			0
$943$	9.15515	+	5.28573i	0.298133	+	0.172127i
$944$		0			0
$945$	−0.00245986	+	0.00426060i	−8.00192e−5	+	0.000138597i
$946$		0			0
$947$	14.2367	+	24.6587i	0.462630	+	0.801299i	0.999091	−	0.0426262i	$-0.0135724\pi$
$947$	14.2367	+	24.6587i	0.462630	+	0.801299i	−0.536461	+	0.843925i	$0.680239\pi$
$948$		0			0
$949$	15.7490	−	6.37235i	0.511233	−	0.206855i
$950$		0			0
$951$	−8.39615	+	4.84752i	−0.272264	+	0.157192i
$952$		0			0
$953$	−5.10449	+	8.84123i	−0.165350	+	0.286395i	−0.936780	−	0.349920i	$-0.886209\pi$
$953$	−5.10449	+	8.84123i	−0.165350	+	0.286395i	0.771429	+	0.636315i	$0.219542\pi$
$954$		0			0
$955$	−0.665240	+	1.15223i	−0.0215267	+	0.0372853i
$956$		0			0
$957$	37.4080			1.20923
$958$		0			0
$959$	0.204948	+	0.354981i	0.00661812	+	0.0114629i
$960$		0			0
$961$	−27.6818			−0.892961
$962$		0			0
$963$		−	10.9345i		−	0.352361i
$964$		0			0
$965$	0.829473	−	0.478896i	0.0267017	−	0.0154162i
$966$		0			0
$967$			12.0250i			0.386700i	0.981130	+	0.193350i	$0.0619352\pi$
$967$			12.0250i			0.386700i	−0.981130	+	0.193350i	$0.938065\pi$
$968$		0			0
$969$	−19.3359	−	11.1636i	−0.621158	−	0.358626i
$970$		0			0
$971$	1.94279	+	1.12167i	0.0623471	+	0.0359961i	0.530850	−	0.847466i	$-0.321873\pi$
$971$	1.94279	+	1.12167i	0.0623471	+	0.0359961i	−0.468502	+	0.883462i	$0.655206\pi$
$972$		0			0
$973$	0.292093	+	0.505920i	0.00936407	+	0.0162190i
$974$		0			0
$975$	14.1758	+	11.0637i	0.453988	+	0.354322i
$976$		0			0
$977$	−32.6677	+	18.8607i	−1.04513	+	0.603408i	−0.921283	−	0.388893i	$-0.872857\pi$
$977$	−32.6677	+	18.8607i	−1.04513	+	0.603408i	−0.123850	+	0.992301i	$0.539524\pi$
$978$		0			0
$979$	20.8279	+	12.0250i	0.665663	+	0.384321i
$980$		0			0
$981$	−0.678033	+	1.17439i	−0.0216479	+	0.0374953i
$982$		0			0
$983$			26.2704i			0.837895i	0.908011	+	0.418947i	$0.137601\pi$
$983$			26.2704i			0.837895i	−0.908011	+	0.418947i	$0.862399\pi$
$984$		0			0
$985$	0.520355	+	0.901282i	0.0165799	+	0.0287172i
$986$		0			0
$987$			0.291226i			0.00926982i
$988$		0			0
$989$			42.1660i			1.34080i
$990$		0			0
$991$	19.5606	+	33.8799i	0.621362	+	1.07623i	0.989232	+	0.146354i	$0.0467538\pi$
$991$	19.5606	+	33.8799i	0.621362	+	1.07623i	−0.367870	+	0.929877i	$0.619913\pi$
$992$		0			0
$993$			18.6531i			0.591940i
$994$		0			0
$995$	−0.513102	+	0.888719i	−0.0162664	+	0.0281743i
$996$		0			0
$997$	9.80345	+	5.66002i	0.310478	+	0.179255i	0.647140	−	0.762371i	$-0.275965\pi$
$997$	9.80345	+	5.66002i	0.310478	+	0.179255i	−0.336662	+	0.941625i	$0.609298\pi$
$998$		0			0
$999$	8.78857	−	5.07408i	0.278058	−	0.160537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.ca.b.49.19		48
4.3	odd	2		312.2.bk.b.205.9	✓	48
8.3	odd	2		312.2.bk.b.205.18	yes	48
8.5	even	2	inner	1248.2.ca.b.49.6		48
12.11	even	2		936.2.dg.e.829.16		48
13.4	even	6	inner	1248.2.ca.b.433.6		48
24.11	even	2		936.2.dg.e.829.7		48
52.43	odd	6		312.2.bk.b.277.18	yes	48
104.43	odd	6		312.2.bk.b.277.9	yes	48
104.69	even	6	inner	1248.2.ca.b.433.19		48
156.95	even	6		936.2.dg.e.901.7		48
312.251	even	6		936.2.dg.e.901.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.9	✓	48	4.3	odd	2
312.2.bk.b.205.18	yes	48	8.3	odd	2
312.2.bk.b.277.9	yes	48	104.43	odd	6
312.2.bk.b.277.18	yes	48	52.43	odd	6
936.2.dg.e.829.7		48	24.11	even	2
936.2.dg.e.829.16		48	12.11	even	2
936.2.dg.e.901.7		48	156.95	even	6
936.2.dg.e.901.16		48	312.251	even	6
1248.2.ca.b.49.6		48	8.5	even	2	inner
1248.2.ca.b.49.19		48	1.1	even	1	trivial
1248.2.ca.b.433.6		48	13.4	even	6	inner
1248.2.ca.b.433.19		48	104.69	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +0.112463 q^{5} +(-0.0378844 - 0.0218726i) q^{7} +(0.500000 - 0.866025i) q^{9} +(3.10283 + 5.37427i) q^{11} +(-1.35237 - 3.34232i) q^{13} +(0.0973959 - 0.0562315i) q^{15} +(1.70610 - 2.95506i) q^{17} +(3.27166 - 5.66668i) q^{19} -0.0437452 q^{21} +(2.27419 + 3.93902i) q^{23} -4.98735 q^{25} -1.00000i q^{27} +(5.22044 - 3.01402i) q^{29} +7.66040i q^{31} +(5.37427 + 3.10283i) q^{33} +(-0.00426060 - 0.00245986i) q^{35} +(5.07408 + 8.78857i) q^{37} +(-2.84235 - 2.21835i) q^{39} +(2.01283 - 1.16211i) q^{41} +(8.02853 + 4.63527i) q^{43} +(0.0562315 - 0.0973959i) q^{45} -6.65732i q^{47} +(-3.49904 - 6.06052i) q^{49} -3.41220i q^{51} -11.2461i q^{53} +(0.348954 + 0.604406i) q^{55} -6.54332i q^{57} +(1.11081 - 1.92397i) q^{59} +(8.56334 + 4.94405i) q^{61} +(-0.0378844 + 0.0218726i) q^{63} +(-0.152092 - 0.375887i) q^{65} +(-2.26023 - 3.91483i) q^{67} +(3.93902 + 2.27419i) q^{69} +(-2.64086 - 1.52470i) q^{71} +4.71199i q^{73} +(-4.31917 + 2.49368i) q^{75} -0.271468i q^{77} -8.01847 q^{79} +(-0.500000 - 0.866025i) q^{81} +2.86994 q^{83} +(0.191873 - 0.332335i) q^{85} +(3.01402 - 5.22044i) q^{87} +(3.35627 - 1.93775i) q^{89} +(-0.0218715 + 0.156202i) q^{91} +(3.83020 + 6.63410i) q^{93} +(0.367941 - 0.637292i) q^{95} +(-0.971031 - 0.560625i) q^{97} +6.20567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) \) 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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