LMFDB - Embedded newform 324.3.f.s.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,3,Mod(55,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.55"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5x^{14} + x^{12} + 40x^{10} - 80x^{8} + 640x^{6} + 256x^{4} - 20480x^{2} + 65536 $ x^16 - 5x^14 + x^12 + 40x^10 - 80x^8 + 640x^6 + 256x^4 - 20480x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.1
Root			$-1.30766 + 1.51328i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.s.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96437 - 0.375825i) q^{2} +(3.71751 + 1.47652i) q^{4} +(0.447399 + 0.774917i) q^{5} +(-1.36976 - 0.790831i) q^{7} +(-6.74766 - 4.29756i) q^{8} +(-0.587624 - 1.69037i) q^{10} +(-10.7156 - 6.18667i) q^{11} +(5.77492 + 10.0025i) q^{13} +(2.39350 + 2.06828i) q^{14} +(11.6398 + 10.9780i) q^{16} -26.0958 q^{17} -21.4313i q^{19} +(0.519030 + 3.54136i) q^{20} +(18.7244 + 16.1801i) q^{22} +(23.8038 - 13.7431i) q^{23} +(12.0997 - 20.9572i) q^{25} +(-7.58492 - 21.8189i) q^{26} +(-3.92442 - 4.96240i) q^{28} +(-4.74875 + 8.22508i) q^{29} +(-42.5991 + 24.5946i) q^{31} +(-18.7391 - 25.9393i) q^{32} +(51.2619 + 9.80747i) q^{34} -1.41527i q^{35} -20.4502 q^{37} +(-8.05440 + 42.0990i) q^{38} +(0.311362 - 7.15160i) q^{40} +(-2.62685 - 4.54983i) q^{41} +(-69.3777 - 40.0552i) q^{43} +(-30.7007 - 38.8209i) q^{44} +(-51.9244 + 18.0505i) q^{46} +(-52.3525 - 30.2257i) q^{47} +(-23.2492 - 40.2687i) q^{49} +(-31.6445 + 36.6205i) q^{50} +(6.69952 + 45.7110i) q^{52} -12.4121 q^{53} -11.0716i q^{55} +(5.84403 + 11.2229i) q^{56} +(12.4195 - 14.3724i) q^{58} +(26.1762 - 15.1129i) q^{59} +(28.4244 - 49.2325i) q^{61} +(92.9237 - 32.3031i) q^{62} +(27.0619 + 57.9970i) q^{64} +(-5.16738 + 8.95017i) q^{65} +(-61.1591 + 35.3102i) q^{67} +(-97.0116 - 38.5310i) q^{68} +(-0.531892 + 2.78011i) q^{70} +71.5006i q^{71} +31.9003 q^{73} +(40.1717 + 7.68568i) q^{74} +(31.6437 - 79.6710i) q^{76} +(9.78523 + 16.9485i) q^{77} +(-83.8284 - 48.3983i) q^{79} +(-3.29938 + 13.9314i) q^{80} +(3.45017 + 9.92480i) q^{82} +(21.4313 + 12.3733i) q^{83} +(-11.6752 - 20.2221i) q^{85} +(121.230 + 104.757i) q^{86} +(45.7178 + 87.7967i) q^{88} +68.1254 q^{89} -18.2679i q^{91} +(108.783 - 15.9435i) q^{92} +(91.4802 + 79.0499i) q^{94} +(16.6075 - 9.58832i) q^{95} +(-50.4502 + 87.3823i) q^{97} +(30.5360 + 87.8404i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{4} - 100 q^{10} + 32 q^{13} + 46 q^{16} + 36 q^{22} - 48 q^{25} + 360 q^{28} + 122 q^{34} - 448 q^{37} - 154 q^{40} - 408 q^{46} + 232 q^{49} - 154 q^{52} + 86 q^{58} + 32 q^{61} - 20 q^{64}+ \cdots - 928 q^{97}+O(q^{100}) $ 16 * q + 10 * q^4 - 100 * q^10 + 32 * q^13 + 46 * q^16 + 36 * q^22 - 48 * q^25 + 360 * q^28 + 122 * q^34 - 448 * q^37 - 154 * q^40 - 408 * q^46 + 232 * q^49 - 154 * q^52 + 86 * q^58 + 32 * q^61 - 20 * q^64 + 492 * q^70 + 752 * q^73 - 516 * q^76 + 176 * q^82 - 368 * q^85 - 516 * q^88 + 672 * q^94 - 928 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.96437	−	0.375825i	−0.982186	−	0.187912i
$2$	−1.96437	−	0.375825i	−0.982186	−	0.187912i
$3$		0			0
$3$		0			0
$4$	3.71751	+	1.47652i	0.929378	+	0.369130i
$5$	0.447399	+	0.774917i	0.0894797	+	0.154983i	0.907291	−	0.420503i	$-0.138146\pi$
$5$	0.447399	+	0.774917i	0.0894797	+	0.154983i	−0.817812	+	0.575486i	$0.804813\pi$
$6$		0			0
$7$	−1.36976	−	0.790831i	−0.195680	−	0.112976i	0.398959	−	0.916969i	$-0.369372\pi$
$7$	−1.36976	−	0.790831i	−0.195680	−	0.112976i	−0.594639	+	0.803993i	$0.702705\pi$
$8$	−6.74766	−	4.29756i	−0.843458	−	0.537196i
$9$		0			0
$10$	−0.587624	−	1.69037i	−0.0587624	−	0.169037i
$11$	−10.7156	−	6.18667i	−0.974148	−	0.562425i	−0.0736499	−	0.997284i	$-0.523465\pi$
$11$	−10.7156	−	6.18667i	−0.974148	−	0.562425i	−0.900498	+	0.434859i	$0.856798\pi$
$12$		0			0
$13$	5.77492	+	10.0025i	0.444224	+	0.769419i	0.997998	−	0.0632482i	$-0.0201460\pi$
$13$	5.77492	+	10.0025i	0.444224	+	0.769419i	−0.553773	+	0.832667i	$0.686813\pi$
$14$	2.39350	+	2.06828i	0.170965	+	0.147734i
$15$		0			0
$16$	11.6398	+	10.9780i	0.727487	+	0.686122i
$17$	−26.0958			−1.53505			−0.767525	−	0.641019i	$-0.778512\pi$
$17$	−26.0958			−1.53505			−0.767525	+	0.641019i	$0.778512\pi$
$18$		0			0
$19$		−	21.4313i		−	1.12796i	−0.825788	−	0.563981i	$-0.809269\pi$
$19$		−	21.4313i		−	1.12796i	0.825788	−	0.563981i	$-0.190731\pi$
$20$	0.519030	+	3.54136i	0.0259515	+	0.177068i
$21$		0			0
$22$	18.7244	+	16.1801i	0.851108	+	0.735460i
$23$	23.8038	−	13.7431i	1.03495	−	0.597526i	0.116548	−	0.993185i	$-0.462817\pi$
$23$	23.8038	−	13.7431i	1.03495	−	0.597526i	0.918398	+	0.395659i	$0.129484\pi$
$24$		0			0
$25$	12.0997	−	20.9572i	0.483987	−	0.838290i
$26$	−7.58492	−	21.8189i	−0.291728	−	0.839188i
$27$		0			0
$28$	−3.92442	−	4.96240i	−0.140158	−	0.177229i
$29$	−4.74875	+	8.22508i	−0.163750	+	0.283624i	−0.936211	−	0.351439i	$-0.885692\pi$
$29$	−4.74875	+	8.22508i	−0.163750	+	0.283624i	0.772461	+	0.635063i	$0.219026\pi$
$30$		0			0
$31$	−42.5991	+	24.5946i	−1.37416	+	0.793374i	−0.991449	−	0.130493i	$-0.958344\pi$
$31$	−42.5991	+	24.5946i	−1.37416	+	0.793374i	−0.382714	+	0.923867i	$0.625011\pi$
$32$	−18.7391	−	25.9393i	−0.585596	−	0.810603i
$33$		0			0
$34$	51.2619	+	9.80747i	1.50770	+	0.288455i
$35$		−	1.41527i		−	0.0404362i
$36$		0			0
$37$	−20.4502			−0.552707			−0.276354	−	0.961056i	$-0.589126\pi$
$37$	−20.4502			−0.552707			−0.276354	+	0.961056i	$0.589126\pi$
$38$	−8.05440	+	42.0990i	−0.211958	+	1.10787i
$39$		0			0
$40$	0.311362	−	7.15160i	0.00778405	−	0.178790i
$41$	−2.62685	−	4.54983i	−0.0640695	−	0.110972i	0.832211	−	0.554459i	$-0.187075\pi$
$41$	−2.62685	−	4.54983i	−0.0640695	−	0.110972i	−0.896281	+	0.443487i	$0.853741\pi$
$42$		0			0
$43$	−69.3777	−	40.0552i	−1.61343	−	0.931516i	−0.988567	−	0.150785i	$-0.951820\pi$
$43$	−69.3777	−	40.0552i	−1.61343	−	0.931516i	−0.624867	−	0.780731i	$-0.714847\pi$
$44$	−30.7007	−	38.8209i	−0.697744	−	0.882292i
$45$		0			0
$46$	−51.9244	+	18.0505i	−1.12879	+	0.392403i
$47$	−52.3525	−	30.2257i	−1.11388	−	0.643101i	−0.174051	−	0.984737i	$-0.555686\pi$
$47$	−52.3525	−	30.2257i	−1.11388	−	0.643101i	−0.939832	+	0.341636i	$0.889019\pi$
$48$		0			0
$49$	−23.2492	−	40.2687i	−0.474473	−	0.821811i
$50$	−31.6445	+	36.6205i	−0.632890	+	0.732409i
$51$		0			0
$52$	6.69952	+	45.7110i	0.128837	+	0.879058i
$53$	−12.4121			−0.234190			−0.117095	−	0.993121i	$-0.537358\pi$
$53$	−12.4121			−0.234190			−0.117095	+	0.993121i	$0.537358\pi$
$54$		0			0
$55$		−	11.0716i		−	0.201302i
$56$	5.84403	+	11.2229i	0.104358	+	0.200409i
$57$		0			0
$58$	12.4195	−	14.3724i	0.214129	−	0.247800i
$59$	26.1762	−	15.1129i	0.443665	−	0.256150i	−0.261486	−	0.965207i	$-0.584212\pi$
$59$	26.1762	−	15.1129i	0.443665	−	0.256150i	0.705151	+	0.709057i	$0.250879\pi$
$60$		0			0
$61$	28.4244	−	49.2325i	0.465974	−	0.807091i	−0.533271	−	0.845945i	$-0.679037\pi$
$61$	28.4244	−	49.2325i	0.465974	−	0.807091i	0.999245	+	0.0388538i	$0.0123707\pi$
$62$	92.9237	−	32.3031i	1.49877	−	0.521018i
$63$		0			0
$64$	27.0619	+	57.9970i	0.422842	+	0.906203i
$65$	−5.16738	+	8.95017i	−0.0794982	+	0.137695i
$66$		0			0
$67$	−61.1591	+	35.3102i	−0.912822	+	0.527018i	−0.881338	−	0.472486i	$-0.843357\pi$
$67$	−61.1591	+	35.3102i	−0.912822	+	0.527018i	−0.0314841	+	0.999504i	$0.510023\pi$
$68$	−97.0116	−	38.5310i	−1.42664	−	0.566633i
$69$		0			0
$70$	−0.531892	+	2.78011i	−0.00759846	+	0.0397159i
$71$			71.5006i			1.00705i	0.863981	+	0.503525i	$0.167964\pi$
$71$			71.5006i			1.00705i	−0.863981	+	0.503525i	$0.832036\pi$
$72$		0			0
$73$	31.9003			0.436991			0.218495	−	0.975838i	$-0.429885\pi$
$73$	31.9003			0.436991			0.218495	+	0.975838i	$0.429885\pi$
$74$	40.1717	+	7.68568i	0.542861	+	0.103861i
$75$		0			0
$76$	31.6437	−	79.6710i	0.416364	−	1.04830i
$77$	9.78523	+	16.9485i	0.127081	+	0.220111i
$78$		0			0
$79$	−83.8284	−	48.3983i	−1.06112	−	0.612637i	−0.135377	−	0.990794i	$-0.543225\pi$
$79$	−83.8284	−	48.3983i	−1.06112	−	0.612637i	−0.925742	+	0.378157i	$0.876558\pi$
$80$	−3.29938	+	13.9314i	−0.0412422	+	0.174142i
$81$		0			0
$82$	3.45017	+	9.92480i	0.0420752	+	0.121034i
$83$	21.4313	+	12.3733i	0.258208	+	0.149076i	0.623517	−	0.781810i	$-0.285703\pi$
$83$	21.4313	+	12.3733i	0.258208	+	0.149076i	−0.365309	+	0.930886i	$0.619037\pi$
$84$		0			0
$85$	−11.6752	−	20.2221i	−0.137356	−	0.237907i
$86$	121.230	+	104.757i	1.40965	+	1.21811i
$87$		0			0
$88$	45.7178	+	87.7967i	0.519521	+	0.997690i
$89$	68.1254			0.765454			0.382727	−	0.923861i	$-0.374985\pi$
$89$	68.1254			0.765454			0.382727	+	0.923861i	$0.374985\pi$
$90$		0			0
$91$		−	18.2679i		−	0.200747i
$92$	108.783	−	15.9435i	1.18242	−	0.173298i
$93$		0			0
$94$	91.4802	+	79.0499i	0.973193	+	0.840957i
$95$	16.6075	−	9.58832i	0.174815	−	0.100930i
$96$		0			0
$97$	−50.4502	+	87.3823i	−0.520105	+	0.900848i	0.479622	+	0.877475i	$0.340774\pi$
$97$	−50.4502	+	87.3823i	−0.520105	+	0.900848i	−0.999727	+	0.0233727i	$0.992560\pi$
$98$	30.5360	+	87.8404i	0.311592	+	0.896331i
$99$		0			0
$100$	75.9244	−	60.0434i	0.759244	−	0.600434i
$101$	99.1297	−	171.698i	0.981482	−	1.69998i	0.324851	−	0.945765i	$-0.394686\pi$
$101$	99.1297	−	171.698i	0.981482	−	1.69998i	0.656631	−	0.754212i	$-0.271981\pi$
$102$		0			0
$103$	60.5425	−	34.9542i	0.587791	−	0.339361i	−0.176433	−	0.984313i	$-0.556456\pi$
$103$	60.5425	−	34.9542i	0.587791	−	0.339361i	0.764224	+	0.644951i	$0.223122\pi$
$104$	4.01899	−	92.3112i	0.0386441	−	0.887608i
$105$		0			0
$106$	24.3819	+	4.66476i	0.230018	+	0.0440072i
$107$			153.959i			1.43887i	0.694559	+	0.719435i	$0.255599\pi$
$107$			153.959i			1.43887i	−0.694559	+	0.719435i	$0.744401\pi$
$108$		0			0
$109$	103.447			0.949054			0.474527	−	0.880241i	$-0.342619\pi$
$109$	103.447			0.949054			0.474527	+	0.880241i	$0.342619\pi$
$110$	−4.16099	+	21.7488i	−0.0378272	+	0.197716i
$111$		0			0
$112$	−7.26200	−	24.2423i	−0.0648393	−	0.216449i
$113$	61.5453	+	106.600i	0.544649	+	0.943360i	0.998629	+	0.0523479i	$0.0166705\pi$
$113$	61.5453	+	106.600i	0.544649	+	0.943360i	−0.453980	+	0.891012i	$0.649996\pi$
$114$		0			0
$115$	21.2995	+	12.2973i	0.185213	+	0.106933i
$116$	−29.7980	+	23.5652i	−0.256880	+	0.203148i
$117$		0			0
$118$	−57.0997	+	19.8496i	−0.483895	+	0.168217i
$119$	35.7450	+	20.6374i	0.300379	+	0.173424i
$120$		0			0
$121$	16.0498	+	27.7991i	0.132643	+	0.229745i
$122$	−74.3389	+	86.0284i	−0.609335	+	0.705151i
$123$		0			0
$124$	−194.677	+	28.5323i	−1.56998	+	0.230099i
$125$	44.0234			0.352187
$126$		0			0
$127$			4.74499i			0.0373621i	0.999825	+	0.0186811i	$0.00594671\pi$
$127$			4.74499i			0.0373621i	−0.999825	+	0.0186811i	$0.994053\pi$
$128$	−31.3629	−	124.098i	−0.245022	−	0.969517i
$129$		0			0
$130$	13.5143	−	15.6394i	0.103957	−	0.120303i
$131$	−24.9506	+	14.4052i	−0.190463	+	0.109964i	−0.592199	−	0.805792i	$-0.701740\pi$
$131$	−24.9506	+	14.4052i	−0.190463	+	0.109964i	0.401737	+	0.915755i	$0.368407\pi$
$132$		0			0
$133$	−16.9485	+	29.3557i	−0.127432	+	0.220719i
$134$	133.410	−	46.3773i	0.995594	−	0.346099i
$135$		0			0
$136$	176.086	+	112.149i	1.29475	+	0.824622i
$137$	−68.7037	+	118.998i	−0.501487	+	0.868601i	0.498511	+	0.866883i	$0.333880\pi$
$137$	−68.7037	+	118.998i	−0.501487	+	0.868601i	−0.999999	+	0.00171795i	$0.999453\pi$
$138$		0			0
$139$	122.318	−	70.6204i	0.879987	−	0.508061i	0.00933283	−	0.999956i	$-0.497029\pi$
$139$	122.318	−	70.6204i	0.879987	−	0.508061i	0.870654	+	0.491896i	$0.163696\pi$
$140$	2.08967	−	5.26127i	0.0149262	−	0.0375805i
$141$		0			0
$142$	26.8717	−	140.454i	0.189237	−	0.989110i
$143$		−	142.910i		−	0.999371i
$144$		0			0
$145$	−8.49834			−0.0586093
$146$	−62.6641	−	11.9889i	−0.429206	−	0.0821160i
$147$		0			0
$148$	−76.0237	−	30.1951i	−0.513674	−	0.204021i
$149$	−69.9596	−	121.174i	−0.469528	−	0.813246i	0.529865	−	0.848082i	$-0.322242\pi$
$149$	−69.9596	−	121.174i	−0.469528	−	0.813246i	−0.999393	+	0.0348361i	$0.988909\pi$
$150$		0			0
$151$	64.5152	+	37.2479i	0.427253	+	0.246675i	0.698176	−	0.715926i	$-0.253995\pi$
$151$	64.5152	+	37.2479i	0.427253	+	0.246675i	−0.270923	+	0.962601i	$0.587329\pi$
$152$	−92.1022	+	144.611i	−0.605936	+	0.951388i
$153$		0			0
$154$	−12.8522	−	36.9707i	−0.0834555	−	0.240069i
$155$	−38.1175	−	22.0072i	−0.245920	−	0.141982i
$156$		0			0
$157$	26.7749	+	46.3755i	0.170541	+	0.295385i	0.938609	−	0.344983i	$-0.112115\pi$
$157$	26.7749	+	46.3755i	0.170541	+	0.295385i	−0.768068	+	0.640368i	$0.778782\pi$
$158$	146.481	+	126.577i	0.927094	+	0.801121i
$159$		0			0
$160$	11.7170	−	26.1264i	0.0732311	−	0.163290i
$161$	−43.4739			−0.270024
$162$		0			0
$163$			204.823i			1.25658i	0.777979	+	0.628290i	$0.216245\pi$
$163$			204.823i			1.25658i	−0.777979	+	0.628290i	$0.783755\pi$
$164$	−3.04742	−	20.7927i	−0.0185818	−	0.126784i
$165$		0			0
$166$	−37.4488	−	32.3602i	−0.225595	−	0.194941i
$167$	−152.234	+	87.8922i	−0.911579	+	0.526300i	−0.880939	−	0.473230i	$-0.843088\pi$
$167$	−152.234	+	87.8922i	−0.911579	+	0.526300i	−0.0306401	+	0.999530i	$0.509755\pi$
$168$		0			0
$169$	17.8007	−	30.8317i	0.105329	−	0.182436i
$170$	15.3346	+	44.1116i	0.0902032	+	0.259480i
$171$		0			0
$172$	−198.770	−	251.343i	−1.15564	−	1.46130i
$173$	−15.4863	+	26.8231i	−0.0895163	+	0.155047i	−0.907307	−	0.420469i	$-0.861865\pi$
$173$	−15.4863	+	26.8231i	−0.0895163	+	0.155047i	0.817790	+	0.575516i	$0.195199\pi$
$174$		0			0
$175$	−33.1473	+	19.1376i	−0.189413	+	0.109358i
$176$	−56.8106	−	189.647i	−0.322788	−	1.07754i
$177$		0			0
$178$	−133.824	−	25.6032i	−0.751818	−	0.143838i
$179$		−	250.115i		−	1.39729i	−0.715467	−	0.698646i	$-0.753786\pi$
$179$		−	250.115i		−	1.39729i	0.715467	−	0.698646i	$-0.246214\pi$
$180$		0			0
$181$	−263.196			−1.45412			−0.727061	−	0.686573i	$-0.759114\pi$
$181$	−263.196			−1.45412			−0.727061	+	0.686573i	$0.759114\pi$
$182$	−6.86554	+	35.8850i	−0.0377228	+	0.197170i
$183$		0			0
$184$	−219.682	−	9.56435i	−1.19392	−	0.0519802i
$185$	−9.14938	−	15.8472i	−0.0494561	−	0.0856605i
$186$		0			0
$187$	279.634	+	161.446i	1.49537	+	0.863350i
$188$	−149.992	−	189.664i	−0.797831	−	1.00885i
$189$		0			0
$190$	−36.2267	+	12.5935i	−0.190667	+	0.0662817i
$191$	268.880	+	155.238i	1.40775	+	0.812764i	0.995171	−	0.0981584i	$-0.0312952\pi$
$191$	268.880	+	155.238i	1.40775	+	0.812764i	0.412578	+	0.910922i	$0.364629\pi$
$192$		0			0
$193$	−88.0498	−	152.507i	−0.456217	−	0.790191i	0.542541	−	0.840030i	$-0.317462\pi$
$193$	−88.0498	−	152.507i	−0.456217	−	0.790191i	−0.998757	+	0.0498390i	$0.984129\pi$
$194$	131.943	−	152.691i	0.680120	−	0.787066i
$195$		0			0
$196$	−26.9715	−	184.027i	−0.137610	−	0.938915i
$197$	117.920			0.598581			0.299290	−	0.954162i	$-0.403250\pi$
$197$	117.920			0.598581			0.299290	+	0.954162i	$0.403250\pi$
$198$		0			0
$199$		−	100.118i		−	0.503104i	−0.967844	−	0.251552i	$-0.919059\pi$
$199$		−	100.118i		−	0.503104i	0.967844	−	0.251552i	$-0.0809409\pi$
$200$	−171.710	+	89.4133i	−0.858548	+	0.447066i
$201$		0			0
$202$	−259.256	+	300.023i	−1.28344	+	1.48526i
$203$	13.0093	−	7.51092i	0.0640852	−	0.0369996i
$204$		0			0
$205$	2.35050	−	4.07118i	0.0114658	−	0.0198594i
$206$	−132.065	+	45.9097i	−0.641090	+	0.222863i
$207$		0			0
$208$	−42.5876	+	179.823i	−0.204748	+	0.864534i
$209$	−132.588	+	229.650i	−0.634393	+	1.09880i
$210$		0			0
$211$	−7.60194	+	4.38898i	−0.0360282	+	0.0208009i	−0.517906	−	0.855438i	$-0.673288\pi$
$211$	−7.60194	+	4.38898i	−0.0360282	+	0.0208009i	0.481878	+	0.876238i	$0.339955\pi$
$212$	−46.1420	−	18.3267i	−0.217651	−	0.0864465i
$213$		0			0
$214$	57.8617	−	302.433i	0.270382	−	1.41324i
$215$		−	71.6826i		−	0.333407i
$216$		0			0
$217$	77.8007			0.358528
$218$	−203.208	−	38.8779i	−0.932147	−	0.178339i
$219$		0			0
$220$	16.3475	−	41.1589i	0.0743067	−	0.187086i
$221$	−150.701	−	261.022i	−0.681907	−	1.18110i
$222$		0			0
$223$	303.809	+	175.404i	1.36237	+	0.786566i	0.989939	−	0.141493i	$-0.0451902\pi$
$223$	303.809	+	175.404i	1.36237	+	0.786566i	0.372433	+	0.928059i	$0.378524\pi$
$224$	5.15443	+	50.3500i	0.0230108	+	0.224777i
$225$		0			0
$226$	−80.8351	−	232.532i	−0.357678	−	1.02890i
$227$	−15.4606	−	8.92619i	−0.0681084	−	0.0393224i	0.465559	−	0.885017i	$-0.345853\pi$
$227$	−15.4606	−	8.92619i	−0.0681084	−	0.0393224i	−0.533668	+	0.845694i	$0.679187\pi$
$228$		0			0
$229$	207.672	+	359.698i	0.906864	+	1.57074i	0.818395	+	0.574656i	$0.194864\pi$
$229$	207.672	+	359.698i	0.906864	+	1.57074i	0.0884695	+	0.996079i	$0.471802\pi$
$230$	−37.2186	−	32.1613i	−0.161820	−	0.139832i
$231$		0			0
$232$	67.3908	−	35.0920i	0.290478	−	0.151259i
$233$	−311.712			−1.33782			−0.668909	−	0.743344i	$-0.733238\pi$
$233$	−311.712			−1.33782			−0.668909	+	0.743344i	$0.733238\pi$
$234$		0			0
$235$		−	54.0918i		−	0.230178i
$236$	119.625	−	17.5325i	0.506885	−	0.0742904i
$237$		0			0
$238$	−62.4605	−	53.9734i	−0.262439	−	0.226779i
$239$	−38.1175	+	22.0072i	−0.159488	+	0.0920802i	−0.577620	−	0.816306i	$-0.696018\pi$
$239$	−38.1175	+	22.0072i	−0.159488	+	0.0920802i	0.418132	+	0.908386i	$0.362685\pi$
$240$		0			0
$241$	−59.4003	+	102.884i	−0.246474	+	0.426906i	−0.962545	−	0.271122i	$-0.912605\pi$
$241$	−59.4003	+	102.884i	−0.246474	+	0.426906i	0.716071	+	0.698028i	$0.245939\pi$
$242$	−21.0802	−	60.6397i	−0.0871084	−	0.250577i
$243$		0			0
$244$	178.361	−	141.053i	0.730987	−	0.578087i
$245$	20.8033	−	36.0324i	0.0849114	−	0.147071i
$246$		0			0
$247$	214.365	−	123.764i	0.867875	−	0.501068i
$248$	393.141	+	17.1163i	1.58525	+	0.0690174i
$249$		0			0
$250$	−86.4784	−	16.5451i	−0.345914	−	0.0661804i
$251$		−	342.026i		−	1.36265i	−0.731980	−	0.681326i	$-0.761403\pi$
$251$		−	342.026i		−	1.36265i	0.731980	−	0.681326i	$-0.238597\pi$
$252$		0			0
$253$	−340.096			−1.34425
$254$	1.78328	−	9.32092i	0.00702080	−	0.0366965i
$255$		0			0
$256$	14.9691	+	255.562i	0.0584732	+	0.998289i
$257$	101.121	+	175.146i	0.393466	+	0.681503i	0.992904	−	0.118918i	$-0.0379427\pi$
$257$	101.121	+	175.146i	0.393466	+	0.681503i	−0.599438	+	0.800421i	$0.704609\pi$
$258$		0			0
$259$	28.0118	+	16.1726i	0.108154	+	0.0624426i
$260$	−32.4249	+	25.6426i	−0.124711	+	0.0986254i
$261$		0			0
$262$	54.4261	−	18.9202i	0.207733	−	0.0722144i
$263$	−300.038	−	173.227i	−1.14083	−	0.658657i	−0.194192	−	0.980963i	$-0.562209\pi$
$263$	−300.038	−	173.227i	−1.14083	−	0.658657i	−0.946635	+	0.322306i	$0.895542\pi$
$264$		0			0
$265$	−5.55315	−	9.61833i	−0.0209553	−	0.0362956i
$266$	44.3258	−	51.2958i	0.166638	−	0.192841i
$267$		0			0
$268$	−279.496	+	40.9636i	−1.04289	+	0.152849i
$269$	−123.174			−0.457896			−0.228948	−	0.973439i	$-0.573529\pi$
$269$	−123.174			−0.457896			−0.228948	+	0.973439i	$0.573529\pi$
$270$		0			0
$271$			247.528i			0.913386i	0.889624	+	0.456693i	$0.150966\pi$
$271$			247.528i			0.913386i	−0.889624	+	0.456693i	$0.849034\pi$
$272$	−303.750	−	286.479i	−1.11673	−	1.05323i
$273$		0			0
$274$	179.682	−	207.936i	0.655774	−	0.758892i
$275$	−259.311	+	149.713i	−0.942950	+	0.544412i
$276$		0			0
$277$	115.900	−	200.745i	0.418413	−	0.724712i	−0.577367	−	0.816485i	$-0.695920\pi$
$277$	115.900	−	200.745i	0.418413	−	0.724712i	0.995780	+	0.0917724i	$0.0292532\pi$
$278$	−266.819	+	92.7546i	−0.959782	+	0.333650i
$279$		0			0
$280$	−6.08220	+	9.54974i	−0.0217222	+	0.0341062i
$281$	−86.1134	+	149.153i	−0.306453	+	0.530793i	−0.977584	−	0.210546i	$-0.932476\pi$
$281$	−86.1134	+	149.153i	−0.306453	+	0.530793i	0.671130	+	0.741339i	$0.265809\pi$
$282$		0			0
$283$	39.8596	−	23.0129i	0.140846	−	0.0813178i	−0.427921	−	0.903816i	$-0.640754\pi$
$283$	39.8596	−	23.0129i	0.140846	−	0.0813178i	0.568767	+	0.822498i	$0.307420\pi$
$284$	−105.572	+	265.804i	−0.371732	+	0.935930i
$285$		0			0
$286$	−53.7091	+	280.729i	−0.187794	+	0.981568i
$287$			8.30957i			0.0289532i
$288$		0			0
$289$	391.993			1.35638
$290$	16.6939	+	3.19389i	0.0575652	+	0.0110134i
$291$		0			0
$292$	118.590	+	47.1014i	0.406130	+	0.161306i
$293$	21.2320	+	36.7749i	0.0724642	+	0.125512i	0.899981	−	0.435930i	$-0.143580\pi$
$293$	21.2320	+	36.7749i	0.0724642	+	0.125512i	−0.827517	+	0.561441i	$0.810247\pi$
$294$		0			0
$295$	23.4224	+	13.5230i	0.0793981	+	0.0458405i
$296$	137.991	+	87.8859i	0.466185	+	0.296912i
$297$		0			0
$298$	91.8866	+	264.323i	0.308344	+	0.886988i
$299$	274.929	+	158.731i	0.919496	+	0.530872i
$300$		0			0
$301$	63.3538	+	109.732i	0.210478	+	0.364558i
$302$	−112.733	−	97.4151i	−0.373289	−	0.322567i
$303$		0			0
$304$	235.271	−	249.455i	0.773919	−	0.820577i
$305$	50.8682			0.166781
$306$		0			0
$307$		−	304.625i		−	0.992264i	−0.868247	−	0.496132i	$-0.834753\pi$
$307$		−	304.625i		−	0.992264i	0.868247	−	0.496132i	$-0.165247\pi$
$308$	11.3519	+	77.4544i	0.0368568	+	0.251475i
$309$		0			0
$310$	66.6062	+	57.5558i	0.214859	+	0.185664i
$311$	338.155	−	195.234i	1.08732	−	0.627762i	0.154455	−	0.988000i	$-0.450638\pi$
$311$	338.155	−	195.234i	1.08732	−	0.627762i	0.932861	+	0.360238i	$0.117304\pi$
$312$		0			0
$313$	−274.194	+	474.919i	−0.876020	+	1.51731i	−0.0203485	+	0.999793i	$0.506478\pi$
$313$	−274.194	+	474.919i	−0.876020	+	1.51731i	−0.855672	+	0.517519i	$0.826856\pi$
$314$	−35.1668	−	101.161i	−0.111996	−	0.322170i
$315$		0			0
$316$	−240.172	−	303.696i	−0.760038	−	0.961062i
$317$	284.932	−	493.517i	0.898841	−	1.55684i	0.0698622	−	0.997557i	$-0.477744\pi$
$317$	284.932	−	493.517i	0.898841	−	1.55684i	0.828978	−	0.559281i	$-0.188923\pi$
$318$		0			0
$319$	101.772	−	58.7580i	0.319034	−	0.184194i
$320$	−32.8354	+	46.9185i	−0.102611	+	0.146620i
$321$		0			0
$322$	85.3989	+	16.3386i	0.265214	+	0.0507409i
$323$			559.267i			1.73148i
$324$		0			0
$325$	279.498			0.859995
$326$	76.9774	−	402.348i	0.236127	−	1.23420i
$327$		0			0
$328$	−1.82812	+	41.9898i	−0.00557355	+	0.128018i
$329$	47.8069	+	82.8040i	0.145310	+	0.251684i
$330$		0			0
$331$	−139.372	−	80.4664i	−0.421063	−	0.243101i	0.274469	−	0.961596i	$-0.411498\pi$
$331$	−139.372	−	80.4664i	−0.421063	−	0.243101i	−0.695532	+	0.718495i	$0.744831\pi$
$332$	61.4015	+	77.6417i	0.184944	+	0.233861i
$333$		0			0
$334$	332.076	−	115.440i	0.994238	−	0.345628i
$335$	−54.7250	−	31.5955i	−0.163358	−	0.0943149i
$336$		0			0
$337$	−23.1512	−	40.0990i	−0.0686978	−	0.118988i	0.829631	−	0.558313i	$-0.188551\pi$
$337$	−23.1512	−	40.0990i	−0.0686978	−	0.118988i	−0.898328	+	0.439325i	$0.855218\pi$
$338$	−46.5544	+	53.8749i	−0.137735	+	0.159393i
$339$		0			0
$340$	−13.5445	−	92.4147i	−0.0398368	−	0.271808i
$341$	608.635			1.78485
$342$		0			0
$343$			151.046i			0.440368i
$344$	295.997	+	568.434i	0.860457	+	1.65242i
$345$		0			0
$346$	40.5017	−	46.8704i	0.117057	−	0.135464i
$347$	179.557	−	103.667i	0.517455	−	0.298753i	−0.218438	−	0.975851i	$-0.570096\pi$
$347$	179.557	−	103.667i	0.517455	−	0.298753i	0.735893	+	0.677098i	$0.236763\pi$
$348$		0			0
$349$	196.746	−	340.774i	0.563742	−	0.976429i	−0.433424	−	0.901190i	$-0.642695\pi$
$349$	196.746	−	340.774i	0.563742	−	0.976429i	0.997166	−	0.0752391i	$-0.0239720\pi$
$350$	72.3060	−	25.1358i	0.206588	−	0.0718165i
$351$		0			0
$352$	40.3231	+	393.888i	0.114554	+	1.11900i
$353$	−129.501	+	224.302i	−0.366858	+	0.635417i	−0.989073	−	0.147430i	$-0.952900\pi$
$353$	−129.501	+	224.302i	−0.366858	+	0.635417i	0.622214	+	0.782847i	$0.286233\pi$
$354$		0			0
$355$	−55.4070	+	31.9893i	−0.156076	+	0.0901106i
$356$	253.257	+	100.588i	0.711396	+	0.282552i
$357$		0			0
$358$	−93.9996	+	491.320i	−0.262569	+	1.37240i
$359$			219.981i			0.612760i	0.951909	+	0.306380i	$0.0991177\pi$
$359$			219.981i			0.612760i	−0.951909	+	0.306380i	$0.900882\pi$
$360$		0			0
$361$	−98.2990			−0.272296
$362$	517.015	+	98.9156i	1.42822	+	0.273247i
$363$		0			0
$364$	26.9730	−	67.9113i	0.0741015	−	0.186569i
$365$	14.2722	+	24.7201i	0.0391018	+	0.0677263i
$366$		0			0
$367$	−459.138	−	265.083i	−1.25106	−	0.722298i	−0.279738	−	0.960076i	$-0.590248\pi$
$367$	−459.138	−	265.083i	−1.25106	−	0.722298i	−0.971319	+	0.237778i	$0.923581\pi$
$368$	427.942	+	101.350i	1.16289	+	0.275407i
$369$		0			0
$370$	12.0170	+	34.5683i	0.0324784	+	0.0934279i
$371$	17.0016	+	9.81586i	0.0458263	+	0.0264578i
$372$		0			0
$373$	−254.595	−	440.971i	−0.682560	−	1.18223i	−0.974197	−	0.225699i	$-0.927533\pi$
$373$	−254.595	−	440.971i	−0.682560	−	1.18223i	0.291638	−	0.956529i	$-0.405800\pi$
$374$	−488.629	−	422.234i	−1.30649	−	1.12897i
$375$		0			0
$376$	223.360	+	428.941i	0.594042	+	1.14080i
$377$	−109.695			−0.290967
$378$		0			0
$379$		−	9.48997i		−	0.0250395i	−0.999922	−	0.0125198i	$-0.996015\pi$
$379$		−	9.48997i		−	0.0250395i	0.999922	−	0.0125198i	$-0.00398527\pi$
$380$	75.8957	−	11.1235i	0.199726	−	0.0292723i
$381$		0			0
$382$	−469.838	−	405.997i	−1.22994	−	1.06282i
$383$	−342.979	+	198.019i	−0.895507	+	0.517021i	−0.875740	−	0.482784i	$-0.839626\pi$
$383$	−342.979	+	198.019i	−0.895507	+	0.517021i	−0.0197669	+	0.999805i	$0.506292\pi$
$384$		0			0
$385$	−8.75579	+	15.1655i	−0.0227423	+	0.0393909i
$386$	115.647	+	332.671i	0.299603	+	0.861843i
$387$		0			0
$388$	−316.571	+	250.354i	−0.815904	+	0.645242i
$389$	309.142	−	535.450i	0.794710	−	1.37648i	−0.128313	−	0.991734i	$-0.540956\pi$
$389$	309.142	−	535.450i	0.794710	−	1.37648i	0.923023	−	0.384745i	$-0.125711\pi$
$390$		0			0
$391$	−621.179	+	358.638i	−1.58869	+	0.917233i
$392$	−16.1800	+	371.635i	−0.0412755	+	0.948048i
$393$		0			0
$394$	−231.640	−	44.3174i	−0.587918	−	0.112481i
$395$		−	86.6134i		−	0.219274i
$396$		0			0
$397$	−377.151			−0.950003			−0.475001	−	0.879985i	$-0.657552\pi$
$397$	−377.151			−0.950003			−0.475001	+	0.879985i	$0.657552\pi$
$398$	−37.6267	+	196.668i	−0.0945394	+	0.494141i
$399$		0			0
$400$	370.905	−	111.108i	0.927263	−	0.277770i
$401$	121.905	+	211.146i	0.304003	+	0.526549i	0.977039	−	0.213061i	$-0.0683433\pi$
$401$	121.905	+	211.146i	0.304003	+	0.526549i	−0.673036	+	0.739610i	$0.735010\pi$
$402$		0			0
$403$	−492.012	−	284.063i	−1.22087	−	0.704872i
$404$	622.031	−	491.921i	1.53968	−	1.21763i
$405$		0			0
$406$	−28.3779	+	9.86503i	−0.0698963	+	0.0242981i
$407$	219.136	+	126.518i	0.538419	+	0.310856i
$408$		0			0
$409$	−256.349	−	444.009i	−0.626770	−	1.08560i	−0.988196	−	0.153196i	$-0.951043\pi$
$409$	−256.349	−	444.009i	−0.626770	−	1.08560i	0.361426	−	0.932401i	$-0.382290\pi$
$410$	−6.14730	+	7.11393i	−0.0149934	+	0.0173511i
$411$		0			0
$412$	276.678	−	40.5506i	0.671548	−	0.0984238i
$413$	−47.8069			−0.115755
$414$		0			0
$415$			22.1433i			0.0533573i
$416$	151.240	−	337.234i	0.363557	−	0.810659i
$417$		0			0
$418$	346.760	−	401.287i	0.829570	−	0.960017i
$419$	364.016	−	210.165i	0.868774	−	0.501587i	0.00183316	−	0.999998i	$-0.499416\pi$
$419$	364.016	−	210.165i	0.868774	−	0.501587i	0.866941	+	0.498412i	$0.166083\pi$
$420$		0			0
$421$	55.4244	−	95.9979i	0.131649	−	0.228024i	−0.792663	−	0.609660i	$-0.791306\pi$
$421$	55.4244	−	95.9979i	0.131649	−	0.228024i	0.924313	+	0.381636i	$0.124639\pi$
$422$	16.5825	−	5.76459i	0.0392951	−	0.0136602i
$423$		0			0
$424$	83.7525	+	53.3417i	0.197529	+	0.125806i
$425$	−315.751	+	546.897i	−0.742944	+	1.28682i
$426$		0			0
$427$	−77.8693	+	44.9578i	−0.182364	+	0.105288i
$428$	−227.324	+	572.345i	−0.531130	+	1.33725i
$429$		0			0
$430$	−26.9401	+	140.811i	−0.0626514	+	0.327468i
$431$			621.316i			1.44157i	0.693160	+	0.720784i	$0.256218\pi$
$431$			621.316i			1.44157i	−0.693160	+	0.720784i	$0.743782\pi$
$432$		0			0
$433$	431.797			0.997223			0.498611	−	0.866826i	$-0.333844\pi$
$433$	431.797			0.997223			0.498611	+	0.866826i	$0.333844\pi$
$434$	−152.829	−	29.2394i	−0.352142	−	0.0673719i
$435$		0			0
$436$	384.565	+	152.741i	0.882030	+	0.350324i
$437$	−294.532	−	510.145i	−0.673986	−	1.16738i
$438$		0			0
$439$	−261.073	−	150.731i	−0.594700	−	0.343350i	0.172253	−	0.985053i	$-0.444895\pi$
$439$	−261.073	−	150.731i	−0.594700	−	0.343350i	−0.766954	+	0.641702i	$0.778229\pi$
$440$	−47.5811	+	74.7077i	−0.108139	+	0.169790i
$441$		0			0
$442$	197.935	+	569.382i	0.447816	+	1.28820i
$443$	−566.703	−	327.186i	−1.27924	−	0.738569i	−0.302530	−	0.953140i	$-0.597831\pi$
$443$	−566.703	−	327.186i	−1.27924	−	0.738569i	−0.976708	+	0.214571i	$0.931165\pi$
$444$		0			0
$445$	30.4792	+	52.7916i	0.0684926	+	0.118633i
$446$	−530.873	−	458.738i	−1.19030	−	1.02856i
$447$		0			0
$448$	8.79758	−	100.843i	0.0196375	−	0.225097i
$449$	384.567			0.856497			0.428248	−	0.903661i	$-0.359131\pi$
$449$	384.567			0.856497			0.428248	+	0.903661i	$0.359131\pi$
$450$		0			0
$451$			65.0058i			0.144137i
$452$	71.3991	+	487.158i	0.157963	+	1.07778i
$453$		0			0
$454$	27.0157	+	23.3448i	0.0595060	+	0.0514204i
$455$	14.1561	−	8.17305i	0.0311124	−	0.0179627i
$456$		0			0
$457$	14.2492	−	24.6803i	0.0311798	−	0.0540050i	−0.850014	−	0.526759i	$-0.823407\pi$
$457$	14.2492	−	24.6803i	0.0311798	−	0.0540050i	0.881194	+	0.472754i	$0.156740\pi$
$458$	−272.761	−	784.629i	−0.595549	−	1.71316i
$459$		0			0
$460$	61.0241	+	77.1645i	0.132661	+	0.167749i
$461$	226.004	−	391.450i	0.490247	−	0.849133i	−0.509690	−	0.860358i	$-0.670240\pi$
$461$	226.004	−	391.450i	0.490247	−	0.849133i	0.999937	+	0.0112254i	$0.00357324\pi$
$462$		0			0
$463$	−83.6919	+	48.3195i	−0.180760	+	0.104362i	−0.587650	−	0.809115i	$-0.699947\pi$
$463$	−83.6919	+	48.3195i	−0.180760	+	0.104362i	0.406890	+	0.913477i	$0.366613\pi$
$464$	−145.569	+	43.6066i	−0.313726	+	0.0939797i
$465$		0			0
$466$	612.317	+	117.149i	1.31399	+	0.251393i
$467$			197.791i			0.423536i	0.977320	+	0.211768i	$0.0679222\pi$
$467$			197.791i			0.423536i	−0.977320	+	0.211768i	$0.932078\pi$
$468$		0			0
$469$	111.698			0.238161
$470$	−20.3290	+	106.256i	−0.0432533	+	0.226077i
$471$		0			0
$472$	−241.577	−	10.5176i	−0.511816	−	0.0222831i
$473$	495.617	+	858.434i	1.04782	+	1.81487i
$474$		0			0
$475$	−449.140	−	259.311i	−0.945558	−	0.545918i
$476$	102.411	+	129.498i	0.215149	+	0.272055i
$477$		0			0
$478$	83.1478	−	28.9047i	0.173949	−	0.0604702i
$479$	−425.780	−	245.824i	−0.888893	−	0.513203i	−0.0153129	−	0.999883i	$-0.504874\pi$
$479$	−425.780	−	245.824i	−0.888893	−	0.513203i	−0.873580	+	0.486680i	$0.838208\pi$
$480$		0			0
$481$	−118.098	−	204.552i	−0.245526	−	0.425264i
$482$	155.351	−	179.779i	0.322305	−	0.372986i
$483$		0			0
$484$	18.6195	+	127.041i	0.0384701	+	0.262482i
$485$	−90.2853			−0.186155
$486$		0			0
$487$		−	566.388i		−	1.16301i	−0.813542	−	0.581507i	$-0.802463\pi$
$487$		−	566.388i		−	1.16301i	0.813542	−	0.581507i	$-0.197537\pi$
$488$	−403.378	+	210.049i	−0.826595	+	0.430428i
$489$		0			0
$490$	−54.4073	+	62.9626i	−0.111035	+	0.128495i
$491$	−289.007	+	166.858i	−0.588608	+	0.339833i	−0.764547	−	0.644568i	$-0.777037\pi$
$491$	−289.007	+	166.858i	−0.588608	+	0.339833i	0.175939	+	0.984401i	$0.443704\pi$
$492$		0			0
$493$	123.923	−	214.641i	0.251365	−	0.435376i
$494$	−467.606	+	162.554i	−0.946571	+	0.329057i
$495$		0			0
$496$	−765.842	−	181.375i	−1.54404	−	0.365675i
$497$	56.5449	−	97.9386i	0.113772	−	0.197060i
$498$		0			0
$499$	−24.0391	+	13.8790i	−0.0481745	+	0.0278135i	−0.523894	−	0.851784i	$-0.675521\pi$
$499$	−24.0391	+	13.8790i	−0.0481745	+	0.0278135i	0.475719	+	0.879597i	$0.342188\pi$
$500$	163.658	+	65.0014i	0.327315	+	0.130003i
$501$		0			0
$502$	−128.542	+	671.866i	−0.256059	+	1.33838i
$503$		−	494.752i		−	0.983602i	−0.870708	−	0.491801i	$-0.836339\pi$
$503$		−	494.752i		−	0.983602i	0.870708	−	0.491801i	$-0.163661\pi$
$504$		0			0
$505$	177.402			0.351291
$506$	668.076	+	127.817i	1.32031	+	0.252602i
$507$		0			0
$508$	−7.00606	+	17.6395i	−0.0137915	+	0.0347235i
$509$	−282.874	−	489.952i	−0.555744	−	0.962577i	−0.997845	−	0.0656120i	$-0.979100\pi$
$509$	−282.874	−	489.952i	−0.555744	−	0.962577i	0.442101	−	0.896965i	$-0.354233\pi$
$510$		0			0
$511$	−43.6958	−	25.2278i	−0.0855104	−	0.0493694i
$512$	66.6415	−	507.644i	0.130159	−	0.991493i
$513$		0			0
$514$	−132.814	−	382.056i	−0.258394	−	0.743299i
$515$	54.1732	+	31.2769i	0.105191	+	0.0607319i
$516$		0			0
$517$	373.993	+	647.776i	0.723391	+	1.25295i
$518$	−48.9475	−	42.2966i	−0.0944933	−	0.0816536i
$519$		0			0
$520$	73.3316	−	38.1855i	0.141022	−	0.0734337i
$521$	−896.794			−1.72129			−0.860647	−	0.509203i	$-0.829940\pi$
$521$	−896.794			−1.72129			−0.860647	+	0.509203i	$0.829940\pi$
$522$		0			0
$523$			216.764i			0.414463i	0.978292	+	0.207231i	$0.0664453\pi$
$523$			216.764i			0.414463i	−0.978292	+	0.207231i	$0.933555\pi$
$524$	−114.024	+	16.7116i	−0.217602	+	0.0318924i
$525$		0			0
$526$	524.283	+	453.043i	0.996735	+	0.861299i
$527$	1111.66	−	641.817i	2.10941	−	1.21787i
$528$		0			0
$529$	113.246	−	196.148i	0.214075	−	0.370789i
$530$	7.29364	+	20.9810i	0.0137616	+	0.0395868i
$531$		0			0
$532$	−106.350	+	84.1053i	−0.199907	+	0.158093i
$533$	30.3397	−	52.5498i	0.0569224	−	0.0985926i
$534$		0			0
$535$	−119.306	+	68.8811i	−0.223001	+	0.128750i
$536$	564.429	+	24.5737i	1.05304	+	0.0458465i
$537$		0			0
$538$	241.960	+	46.2919i	0.449739	+	0.0860444i
$539$			575.340i			1.06742i
$540$		0			0
$541$	−639.646			−1.18234			−0.591170	−	0.806547i	$-0.701334\pi$
$541$	−639.646			−1.18234			−0.591170	+	0.806547i	$0.701334\pi$
$542$	93.0270	−	486.236i	0.171636	−	0.897114i
$543$		0			0
$544$	489.012	+	676.908i	0.898919	+	1.24432i
$545$	46.2820	+	80.1627i	0.0849211	+	0.147088i
$546$		0			0
$547$	514.201	+	296.874i	0.940039	+	0.542732i	0.889973	−	0.456014i	$-0.150723\pi$
$547$	514.201	+	296.874i	0.940039	+	0.542732i	0.0500666	+	0.998746i	$0.484057\pi$
$548$	−431.110	+	340.935i	−0.786697	+	0.622145i
$549$		0			0
$550$	565.650	−	196.637i	1.02845	−	0.357522i
$551$	176.274	+	101.772i	0.319916	+	0.184704i
$552$		0			0
$553$	76.5498	+	132.588i	0.138426	+	0.239762i
$554$	−303.116	+	350.780i	−0.547141	+	0.633177i
$555$		0			0
$556$	558.992	−	81.9272i	1.00538	−	0.147351i
$557$	−426.623			−0.765929			−0.382965	−	0.923763i	$-0.625097\pi$
$557$	−426.623			−0.765929			−0.382965	+	0.923763i	$0.625097\pi$
$558$		0			0
$559$		−	925.262i		−	1.65521i
$560$	15.5367	−	16.4734i	0.0277442	−	0.0294168i
$561$		0			0
$562$	225.214	−	260.628i	0.400737	−	0.463751i
$563$	285.960	−	165.099i	0.507922	−	0.293249i	−0.224057	−	0.974576i	$-0.571930\pi$
$563$	285.960	−	165.099i	0.507922	−	0.293249i	0.731979	+	0.681327i	$0.238597\pi$
$564$		0			0
$565$	−55.0706	+	95.3851i	−0.0974701	+	0.168823i
$566$	−86.9478	+	30.2257i	−0.153618	+	0.0534023i
$567$		0			0
$568$	307.278	−	482.462i	0.540983	−	0.849404i
$569$	−399.264	+	691.545i	−0.701694	+	1.21537i	0.266178	+	0.963924i	$0.414239\pi$
$569$	−399.264	+	691.545i	−0.701694	+	1.21537i	−0.967872	+	0.251445i	$0.919094\pi$
$570$		0			0
$571$	−694.050	+	400.710i	−1.21550	+	0.701768i	−0.963952	−	0.266077i	$-0.914272\pi$
$571$	−694.050	+	400.710i	−1.21550	+	0.701768i	−0.251547	+	0.967845i	$0.580939\pi$
$572$	211.009	−	531.270i	0.368898	−	0.928794i
$573$		0			0
$574$	3.12294	−	16.3231i	0.00544067	−	0.0284374i
$575$		−	665.148i		−	1.15678i
$576$		0			0
$577$	345.694			0.599124			0.299562	−	0.954077i	$-0.403160\pi$
$577$	345.694			0.599124			0.299562	+	0.954077i	$0.403160\pi$
$578$	−770.021	−	147.321i	−1.33222	−	0.254880i
$579$		0			0
$580$	−31.5927	−	12.5480i	−0.0544702	−	0.0216344i
$581$	−19.5705	−	33.8970i	−0.0336841	−	0.0583425i
$582$		0			0
$583$	133.003	+	76.7894i	0.228136	+	0.131714i
$584$	−215.253	−	137.094i	−0.368583	−	0.234750i
$585$		0			0
$586$	−27.8866	−	80.2191i	−0.0475881	−	0.136893i
$587$	−284.262	−	164.119i	−0.484262	−	0.279589i	0.237929	−	0.971283i	$-0.423531\pi$
$587$	−284.262	−	164.119i	−0.484262	−	0.279589i	−0.722191	+	0.691694i	$0.756865\pi$
$588$		0			0
$589$	527.093	+	912.952i	0.894895	+	1.55000i
$590$	−40.9281	−	35.3668i	−0.0693697	−	0.0599438i
$591$		0			0
$592$	−238.036	−	224.501i	−0.402087	−	0.379225i
$593$	−529.415			−0.892774			−0.446387	−	0.894840i	$-0.647289\pi$
$593$	−529.415			−0.892774			−0.446387	+	0.894840i	$0.647289\pi$
$594$		0			0
$595$			36.9326i			0.0620716i
$596$	−81.1605	−	553.761i	−0.136175	−	0.929129i
$597$		0			0
$598$	−480.409	−	415.131i	−0.803359	−	0.694199i
$599$	−697.426	+	402.659i	−1.16432	+	0.672219i	−0.952335	−	0.305054i	$-0.901325\pi$
$599$	−697.426	+	402.659i	−1.16432	+	0.672219i	−0.211983	+	0.977273i	$0.567992\pi$
$600$		0			0
$601$	55.9502	−	96.9085i	0.0930951	−	0.161245i	−0.815717	−	0.578451i	$-0.803657\pi$
$601$	55.9502	−	96.9085i	0.0930951	−	0.161245i	0.908812	+	0.417206i	$0.136991\pi$
$602$	−83.2104	−	239.364i	−0.138223	−	0.397615i
$603$		0			0
$604$	184.839	+	233.727i	0.306025	+	0.386966i
$605$	−14.3613	+	24.8746i	−0.0237378	+	0.0411150i
$606$		0			0
$607$	757.195	−	437.167i	1.24744	−	0.720209i	0.276840	−	0.960916i	$-0.410713\pi$
$607$	757.195	−	437.167i	1.24744	−	0.720209i	0.970598	+	0.240707i	$0.0773793\pi$
$608$	−555.912	+	401.602i	−0.914329	+	0.660530i
$609$		0			0
$610$	−99.9240	−	19.1175i	−0.163810	−	0.0313402i
$611$		−	698.204i		−	1.14272i
$612$		0			0
$613$	−152.804			−0.249272			−0.124636	−	0.992203i	$-0.539776\pi$
$613$	−152.804			−0.249272			−0.124636	+	0.992203i	$0.539776\pi$
$614$	−114.486	+	598.397i	−0.186459	+	0.974588i
$615$		0			0
$616$	6.80991	−	156.415i	0.0110551	−	0.253921i
$617$	−35.7056	−	61.8439i	−0.0578697	−	0.100233i	0.835639	−	0.549279i	$-0.185097\pi$
$617$	−35.7056	−	61.8439i	−0.0578697	−	0.100233i	−0.893509	+	0.449045i	$0.851764\pi$
$618$		0			0
$619$	278.744	+	160.933i	0.450313	+	0.259988i	0.707962	−	0.706250i	$-0.249615\pi$
$619$	278.744	+	160.933i	0.450313	+	0.259988i	−0.257649	+	0.966239i	$0.582948\pi$
$620$	−109.208	−	138.093i	−0.176143	−	0.222731i
$621$		0			0
$622$	−737.636	+	256.425i	−1.18591	+	0.412259i
$623$	−93.3155	−	53.8757i	−0.149784	−	0.0864779i
$624$		0			0
$625$	−282.796	−	489.817i	−0.452473	−	0.783706i
$626$	717.106	−	829.868i	1.14554	−	1.32567i
$627$		0			0
$628$	31.0617	+	211.935i	0.0494614	+	0.337476i
$629$	533.664			0.848433
$630$		0			0
$631$			642.307i			1.01792i	0.860790	+	0.508960i	$0.169970\pi$
$631$			642.307i			1.01792i	−0.860790	+	0.508960i	$0.830030\pi$
$632$	357.651	+	686.834i	0.565903	+	1.08676i
$633$		0			0
$634$	−745.189	+	862.367i	−1.17538	+	1.36020i
$635$	−3.67697	+	2.12290i	−0.00579051	+	0.00334315i
$636$		0			0
$637$	268.524	−	465.097i	0.421545	−	0.730137i
$638$	−222.000	+	77.1741i	−0.347963	+	0.120963i
$639$		0			0
$640$	82.1341	−	79.8250i	0.128335	−	0.124727i
$641$	49.5994	−	85.9086i	0.0773781	−	0.134023i	−0.824740	−	0.565512i	$-0.808678\pi$
$641$	49.5994	−	85.9086i	0.0773781	−	0.134023i	0.902118	+	0.431490i	$0.142012\pi$
$642$		0			0
$643$	443.661	−	256.148i	0.689986	−	0.398364i	−0.113621	−	0.993524i	$-0.536245\pi$
$643$	443.661	−	256.148i	0.689986	−	0.398364i	0.803607	+	0.595161i	$0.202912\pi$
$644$	−161.615	−	64.1900i	−0.250955	−	0.0996740i
$645$		0			0
$646$	210.186	−	1098.61i	0.325366	−	1.70063i
$647$			142.728i			0.220600i	0.993898	+	0.110300i	$0.0351811\pi$
$647$			142.728i			0.220600i	−0.993898	+	0.110300i	$0.964819\pi$
$648$		0			0
$649$	−373.993			−0.576261
$650$	−549.039	−	105.042i	−0.844675	−	0.161604i
$651$		0			0
$652$	−302.425	+	761.431i	−0.463841	+	1.16784i
$653$	−110.883	−	192.055i	−0.169805	−	0.294111i	0.768546	−	0.639795i	$-0.220981\pi$
$653$	−110.883	−	192.055i	−0.169805	−	0.294111i	−0.938351	+	0.345683i	$0.887647\pi$
$654$		0			0
$655$	−22.3257	−	12.8898i	−0.0340851	−	0.0196790i
$656$	19.3719	−	81.7965i	0.0295304	−	0.124690i
$657$		0			0
$658$	−62.7907	−	180.625i	−0.0954266	−	0.274506i
$659$	−112.969	−	65.2229i	−0.171425	−	0.0989725i	0.411832	−	0.911260i	$-0.364889\pi$
$659$	−112.969	−	65.2229i	−0.171425	−	0.0989725i	−0.583258	+	0.812287i	$0.698222\pi$
$660$		0			0
$661$	−358.875	−	621.589i	−0.542927	−	0.940377i	−0.998734	−	0.0502983i	$-0.983983\pi$
$661$	−358.875	−	621.589i	−0.542927	−	0.940377i	0.455807	−	0.890078i	$-0.349351\pi$
$662$	243.537	+	210.445i	0.367881	+	0.317893i
$663$		0			0
$664$	−91.4357	−	175.593i	−0.137704	−	0.264448i
$665$	−30.3310			−0.0456105
$666$		0			0
$667$			261.050i			0.391380i
$668$	−695.705	+	101.964i	−1.04147	+	0.152641i
$669$		0			0
$670$	95.6259	+	82.6323i	0.142725	+	0.123332i
$671$	−609.171	+	351.705i	−0.907856	+	0.524151i
$672$		0			0
$673$	−529.947	+	917.895i	−0.787440	+	1.36389i	0.140091	+	0.990139i	$0.455260\pi$
$673$	−529.947	+	917.895i	−0.787440	+	1.36389i	−0.927531	+	0.373747i	$0.878073\pi$
$674$	30.4073	+	87.4701i	0.0451147	+	0.129778i
$675$		0			0
$676$	111.698	−	88.3340i	0.165233	−	0.130672i
$677$	214.576	−	371.656i	0.316951	−	0.548975i	−0.662899	−	0.748709i	$-0.730674\pi$
$677$	214.576	−	371.656i	0.316951	−	0.548975i	0.979850	+	0.199733i	$0.0640076\pi$
$678$		0			0
$679$	138.209	−	79.7951i	0.203548	−	0.117519i
$680$	−8.12525	+	186.627i	−0.0119489	+	0.274452i
$681$		0			0
$682$	−1195.58	−	228.740i	−1.75306	−	0.335396i
$683$		−	565.979i		−	0.828667i	−0.910125	−	0.414333i	$-0.864015\pi$
$683$		−	565.979i		−	0.828667i	0.910125	−	0.414333i	$-0.135985\pi$
$684$		0			0
$685$	−122.952			−0.179492
$686$	56.7669	−	296.711i	0.0827505	−	0.432523i
$687$		0			0
$688$	−367.817	−	1227.86i	−0.534617	−	1.78468i
$689$	−71.6787	−	124.151i	−0.104033	−	0.180190i
$690$		0			0
$691$	751.509	+	433.884i	1.08757	+	0.627907i	0.932928	−	0.360064i	$-0.117245\pi$
$691$	751.509	+	433.884i	1.08757	+	0.627907i	0.154639	+	0.987971i	$0.450578\pi$
$692$	−97.1754	+	76.8493i	−0.140427	+	0.111054i
$693$		0			0
$694$	−391.677	+	136.159i	−0.564376	+	0.196194i
$695$	109.450	+	63.1910i	0.157482	+	0.0909223i
$696$		0			0
$697$	68.5498	+	118.732i	0.0983498	+	0.170347i
$698$	−514.553	+	595.464i	−0.737182	+	0.853101i
$699$		0			0
$700$	−151.482	+	22.2016i	−0.216403	+	0.0317166i
$701$	405.608			0.578613			0.289307	−	0.957237i	$-0.406575\pi$
$701$	405.608			0.578613			0.289307	+	0.957237i	$0.406575\pi$
$702$		0			0
$703$			438.273i			0.623432i
$704$	68.8235	−	788.898i	0.0977606	−	1.12059i
$705$		0			0
$706$	338.686	−	391.943i	0.479726	−	0.555161i
$707$	−271.568	+	156.790i	−0.384113	+	0.221768i
$708$		0			0
$709$	−185.318	+	320.980i	−0.261380	+	0.452723i	−0.966609	−	0.256257i	$-0.917511\pi$
$709$	−185.318	+	320.980i	−0.261380	+	0.452723i	0.705229	+	0.708979i	$0.250844\pi$
$710$	120.862	−	42.0155i	0.170229	−	0.0591767i
$711$		0			0
$712$	−459.687	−	292.773i	−0.645628	−	0.411199i
$713$	−676.012	+	1170.89i	−0.948123	+	1.64220i
$714$		0			0
$715$	110.743	−	63.9378i	0.154886	−	0.0894235i
$716$	369.300	−	929.807i	0.515782	−	1.29861i
$717$		0			0
$718$	82.6742	−	432.124i	0.115145	−	0.601844i
$719$		−	24.6557i		−	0.0342916i	−0.999853	−	0.0171458i	$-0.994542\pi$
$719$		−	24.6557i		−	0.0342916i	0.999853	−	0.0171458i	$-0.00545795\pi$
$720$		0			0
$721$	−110.572			−0.153359
$722$	193.096	+	36.9432i	0.267446	+	0.0511679i
$723$		0			0
$724$	−978.434	−	388.614i	−1.35143	−	0.536760i
$725$	114.917	+	199.042i	0.158506	+	0.274540i
$726$		0			0
$727$	497.628	+	287.306i	0.684495	+	0.395193i	0.801546	−	0.597933i	$-0.204011\pi$
$727$	497.628	+	287.306i	0.684495	+	0.395193i	−0.117052	+	0.993126i	$0.537344\pi$
$728$	−78.5076	+	123.266i	−0.107840	+	0.169321i
$729$		0			0
$730$	−18.7454	−	53.9233i	−0.0256786	−	0.0738676i
$731$	1810.47	+	1045.27i	2.47670	+	1.42992i
$732$		0			0
$733$	105.096	+	182.032i	0.143378	+	0.248339i	0.928767	−	0.370665i	$-0.120870\pi$
$733$	105.096	+	182.032i	0.143378	+	0.248339i	−0.785388	+	0.619003i	$0.787537\pi$
$734$	802.293	+	693.278i	1.09304	+	0.944520i
$735$		0			0
$736$	−802.547	−	359.920i	−1.09042	−	0.489021i
$737$	873.811			1.18563
$738$		0			0
$739$		−	270.937i		−	0.366627i	−0.983055	−	0.183313i	$-0.941318\pi$
$739$		−	270.937i		−	0.366627i	0.983055	−	0.183313i	$-0.0586823\pi$
$740$	−10.6142	−	72.4213i	−0.0143436	−	0.0978667i
$741$		0			0
$742$	−29.7083	−	25.6716i	−0.0400382	−	0.0345978i
$743$	−402.764	+	232.536i	−0.542078	+	0.312969i	−0.745921	−	0.666035i	$-0.767990\pi$
$743$	−402.764	+	232.536i	−0.542078	+	0.312969i	0.203842	+	0.979004i	$0.434657\pi$
$744$		0			0
$745$	62.5997	−	108.426i	0.0840264	−	0.145538i
$746$	334.391	+	961.914i	0.448245	+	1.28943i
$747$		0			0
$748$	801.162	+	1013.06i	1.07107	+	1.35436i
$749$	121.756	−	210.887i	0.162558	−	0.281558i
$750$		0			0
$751$	−784.590	+	452.983i	−1.04473	+	0.603174i	−0.921169	−	0.389164i	$-0.872764\pi$
$751$	−784.590	+	452.983i	−1.04473	+	0.603174i	−0.123559	+	0.992337i	$0.539431\pi$
$752$	−277.555	−	926.544i	−0.369089	−	1.23211i
$753$		0			0
$754$	215.481	+	41.2260i	0.285784	+	0.0546763i
$755$			66.6586i			0.0882896i
$756$		0			0
$757$	−263.196			−0.347683			−0.173841	−	0.984774i	$-0.555618\pi$
$757$	−263.196			−0.347683			−0.173841	+	0.984774i	$0.555618\pi$
$758$	−3.56657	+	18.6418i	−0.00470523	+	0.0245934i
$759$		0			0
$760$	−153.268	−	6.67288i	−0.201668	−	0.00878010i
$761$	−540.155	−	935.576i	−0.709797	−	1.22940i	−0.964932	−	0.262499i	$-0.915453\pi$
$761$	−540.155	−	935.576i	−0.709797	−	1.22940i	0.255136	−	0.966905i	$-0.417880\pi$
$762$		0			0
$763$	−141.697	−	81.8090i	−0.185711	−	0.107220i
$764$	770.353	+	974.105i	1.00832	+	1.27501i
$765$		0			0
$766$	748.159	−	260.083i	0.976708	−	0.339534i
$767$	302.331	+	174.551i	0.394174	+	0.227576i
$768$		0			0
$769$	−256.050	−	443.491i	−0.332965	−	0.576712i	0.650127	−	0.759826i	$-0.274716\pi$
$769$	−256.050	−	443.491i	−0.332965	−	0.576712i	−0.983092	+	0.183114i	$0.941382\pi$
$770$	22.8992	−	26.5000i	0.0297392	−	0.0344156i
$771$		0			0
$772$	−102.147	−	696.953i	−0.132315	−	0.902789i
$773$	546.612			0.707130			0.353565	−	0.935410i	$-0.384969\pi$
$773$	546.612			0.707130			0.353565	+	0.935410i	$0.384969\pi$
$774$		0			0
$775$			1190.35i			1.53593i
$776$	715.952	−	372.813i	0.922618	−	0.480429i
$777$		0			0
$778$	−808.506	+	935.640i	−1.03921	+	1.20262i
$779$	−97.5087	+	56.2967i	−0.125172	+	0.0722679i
$780$		0			0
$781$	442.350	−	766.174i	0.566390	−	0.981016i
$782$	1355.01	−	471.044i	1.73275	−	0.602358i
$783$		0			0
$784$	171.453	−	723.948i	0.218690	−	0.923403i
$785$	−23.9581	+	41.4967i	−0.0305199	+	0.0528620i
$786$		0			0
$787$	1130.11	−	652.469i	1.43597	−	0.829058i	0.438404	−	0.898778i	$-0.355544\pi$
$787$	1130.11	−	652.469i	1.43597	−	0.829058i	0.997567	+	0.0697202i	$0.0222107\pi$
$788$	438.371	+	174.112i	0.556308	+	0.220954i
$789$		0			0
$790$	−32.5515	+	170.141i	−0.0412044	+	0.215368i
$791$		−	194.688i		−	0.246129i
$792$		0			0
$793$	656.595			0.827988
$794$	740.865	+	141.743i	0.933079	+	0.178517i
$795$		0			0
$796$	147.826	−	372.189i	0.185711	−	0.467574i
$797$	−80.6972	−	139.772i	−0.101251	−	0.175372i	0.810949	−	0.585117i	$-0.198951\pi$
$797$	−80.6972	−	139.772i	−0.101251	−	0.175372i	−0.912200	+	0.409744i	$0.865618\pi$
$798$		0			0
$799$	1366.18	+	788.766i	1.70987	+	0.987192i
$800$	−770.353	+	78.8624i	−0.962941	+	0.0985781i
$801$		0			0
$802$	−160.113	−	460.585i	−0.199643	−	0.574295i
$803$	−341.832	−	197.357i	−0.425694	−	0.245774i
$804$		0			0
$805$	−19.4502	−	33.6887i	−0.0241617	−	0.0418493i
$806$	859.737	+	742.916i	1.06667	+	0.921733i
$807$		0			0
$808$	−1406.78	+	732.542i	−1.74106	+	0.906611i
$809$	−144.054			−0.178064			−0.0890319	−	0.996029i	$-0.528377\pi$
$809$	−144.054			−0.178064			−0.0890319	+	0.996029i	$0.528377\pi$
$810$		0			0
$811$		−	219.215i		−	0.270302i	−0.990825	−	0.135151i	$-0.956848\pi$
$811$		−	219.215i		−	0.270302i	0.990825	−	0.135151i	$-0.0431520\pi$
$812$	59.4523	−	8.71347i	0.0732171	−	0.0107309i
$813$		0			0
$814$	−382.917	−	330.886i	−0.470414	−	0.406494i
$815$	−158.721	+	91.6374i	−0.194749	+	0.112439i
$816$		0			0
$817$	−858.434	+	1486.85i	−1.05071	+	1.81989i
$818$	336.695	+	968.541i	0.411607	+	1.18404i
$819$		0			0
$820$	14.7492	−	11.6641i	0.0179868	−	0.0142245i
$821$	721.409	−	1249.52i	0.878696	−	1.52195i	0.0259228	−	0.999664i	$-0.491748\pi$
$821$	721.409	−	1249.52i	0.878696	−	1.52195i	0.852773	−	0.522282i	$-0.174919\pi$
$822$		0			0
$823$	1087.17	−	627.676i	1.32098	−	0.762668i	0.337095	−	0.941471i	$-0.390556\pi$
$823$	1087.17	−	627.676i	1.32098	−	0.762668i	0.983885	+	0.178803i	$0.0572225\pi$
$824$	−558.738	−	24.3260i	−0.678080	−	0.0295218i
$825$		0			0
$826$	93.9105	+	17.9670i	0.113693	+	0.0217518i
$827$			518.447i			0.626901i	0.949605	+	0.313451i	$0.101485\pi$
$827$			518.447i			0.626901i	−0.949605	+	0.313451i	$0.898515\pi$
$828$		0			0
$829$	481.382			0.580678			0.290339	−	0.956924i	$-0.406232\pi$
$829$	481.382			0.580678			0.290339	+	0.956924i	$0.406232\pi$
$830$	8.32199	−	43.4976i	0.0100265	−	0.0524068i
$831$		0			0
$832$	−423.832	+	605.613i	−0.509414	+	0.727900i
$833$	606.707	+	1050.85i	0.728340	+	1.26152i
$834$		0			0
$835$	−136.218	−	78.6457i	−0.163136	−	0.0941864i
$836$	−831.980	+	657.956i	−0.995191	+	0.787028i
$837$		0			0
$838$	−794.048	+	276.036i	−0.947552	+	0.329398i
$839$	545.035	+	314.676i	0.649625	+	0.375061i	0.788312	−	0.615275i	$-0.210955\pi$
$839$	545.035	+	314.676i	0.649625	+	0.375061i	−0.138688	+	0.990336i	$0.544288\pi$
$840$		0			0
$841$	375.399	+	650.210i	0.446372	+	0.773139i
$842$	−144.953	+	167.746i	−0.172153	+	0.199223i
$843$		0			0
$844$	−34.7407	+	5.09168i	−0.0411620	+	0.00603280i
$845$	31.8560			0.0376994
$846$		0			0
$847$		−	50.7708i		−	0.0599420i
$848$	−144.474	−	136.259i	−0.170370	−	0.160683i
$849$		0			0
$850$	825.790	−	955.642i	0.971518	−	1.12428i
$851$	−486.791	+	281.049i	−0.572022	+	0.330257i
$852$		0			0
$853$	−399.502	+	691.957i	−0.468349	+	0.811204i	−0.999346	−	0.0361697i	$-0.988484\pi$
$853$	−399.502	+	691.957i	−0.468349	+	0.811204i	0.530997	+	0.847374i	$0.321818\pi$
$854$	169.860	−	59.0487i	0.198900	−	0.0691437i
$855$		0			0
$856$	661.650	−	1038.86i	0.772955	−	1.21363i
$857$	414.961	−	718.734i	0.484202	−	0.838663i	−0.515633	−	0.856810i	$-0.672443\pi$
$857$	414.961	−	718.734i	0.484202	−	0.838663i	0.999835	+	0.0181465i	$0.00577652\pi$
$858$		0			0
$859$	778.288	−	449.344i	0.906039	−	0.523102i	0.0268844	−	0.999639i	$-0.491441\pi$
$859$	778.288	−	449.344i	0.906039	−	0.523102i	0.879155	+	0.476537i	$0.158108\pi$
$860$	105.841	−	266.481i	0.123071	−	0.309861i
$861$		0			0
$862$	233.506	−	1220.50i	0.270888	−	1.41589i
$863$			604.060i			0.699953i	0.936758	+	0.349977i	$0.113810\pi$
$863$			604.060i			0.699953i	−0.936758	+	0.349977i	$0.886190\pi$
$864$		0			0
$865$	−27.7142			−0.0320396
$866$	−848.210	−	162.280i	−0.979458	−	0.187390i
$867$		0			0
$868$	289.225	+	114.874i	0.333208	+	0.132343i
$869$	598.849	+	1037.24i	0.689125	+	1.19360i
$870$		0			0
$871$	−706.377	−	407.827i	−0.810996	−	0.468229i
$872$	−698.024	−	444.570i	−0.800487	−	0.509827i
$873$		0			0
$874$	386.846	+	1112.81i	0.442615	+	1.27323i
$875$	−60.3015	−	34.8151i	−0.0689160	−	0.0397887i
$876$		0			0
$877$	55.2700	+	95.7304i	0.0630216	+	0.109157i	0.895815	−	0.444428i	$-0.146593\pi$
$877$	55.2700	+	95.7304i	0.0630216	+	0.109157i	−0.832793	+	0.553584i	$0.813260\pi$
$878$	456.197	+	394.209i	0.519587	+	0.448985i
$879$		0			0
$880$	121.544	−	128.871i	0.138118	−	0.146445i
$881$	1020.91			1.15881			0.579407	−	0.815039i	$-0.303284\pi$
$881$	1020.91			1.15881			0.579407	+	0.815039i	$0.303284\pi$
$882$		0			0
$883$			194.702i			0.220501i	0.993904	+	0.110250i	$0.0351653\pi$
$883$			194.702i			0.220501i	−0.993904	+	0.110250i	$0.964835\pi$
$884$	−174.830	−	1192.87i	−0.197771	−	1.34940i
$885$		0			0
$886$	990.250	+	855.696i	1.11766	+	0.965797i
$887$	830.680	−	479.593i	0.936505	−	0.540692i	0.0476422	−	0.998864i	$-0.484829\pi$
$887$	830.680	−	479.593i	0.936505	−	0.540692i	0.888863	+	0.458173i	$0.151496\pi$
$888$		0			0
$889$	3.75248	−	6.49949i	0.00422102	−	0.00731101i
$890$	−40.0321	−	115.157i	−0.0449799	−	0.129390i
$891$		0			0
$892$	870.426	+	1100.65i	0.975814	+	1.23391i
$893$	−647.776	+	1121.98i	−0.725393	+	1.25642i
$894$		0			0
$895$	193.819	−	111.901i	0.216557	−	0.125029i
$896$	−55.1811	+	194.787i	−0.0615861	+	0.217397i
$897$		0			0
$898$	−755.433	−	144.530i	−0.841239	−	0.160946i
$899$		−	467.175i		−	0.519660i
$900$		0			0
$901$	323.904			0.359493
$902$	24.4308	−	127.696i	0.0270851	−	0.141569i
$903$		0			0
$904$	42.8318	−	983.794i	0.0473803	−	1.08827i
$905$	−117.754	−	203.955i	−0.130114	−	0.225365i
$906$		0			0
$907$	402.841	+	232.581i	0.444147	+	0.256428i	0.705355	−	0.708854i	$-0.250788\pi$
$907$	402.841	+	232.581i	0.444147	+	0.256428i	−0.261208	+	0.965283i	$0.584121\pi$
$908$	−44.2953	−	56.0111i	−0.0487834	−	0.0616863i
$909$		0			0
$910$	−30.8796	+	10.7347i	−0.0339336	+	0.0117964i
$911$	116.567	+	67.3003i	0.127956	+	0.0738751i	0.562612	−	0.826721i	$-0.309797\pi$
$911$	116.567	+	67.3003i	0.127956	+	0.0738751i	−0.434656	+	0.900597i	$0.643130\pi$
$912$		0			0
$913$	−153.100	−	265.176i	−0.167689	−	0.290445i
$914$	−37.2661	+	43.1261i	−0.0407726	+	0.0471839i
$915$		0			0
$916$	240.921	+	1643.81i	0.263015	+	1.79456i
$917$	45.5684			0.0496929
$918$		0			0
$919$		−	105.178i		−	0.114448i	−0.998361	−	0.0572241i	$-0.981775\pi$
$919$		−	105.178i		−	0.114448i	0.998361	−	0.0572241i	$-0.0182250\pi$
$920$	−90.8737	−	174.514i	−0.0987757	−	0.189689i
$921$		0			0
$922$	−591.072	+	684.016i	−0.641076	+	0.741883i
$923$	−715.181	+	412.910i	−0.774844	+	0.447356i
$924$		0			0
$925$	−247.440	+	428.579i	−0.267503	+	0.463329i
$926$	182.562	−	63.4640i	0.197151	−	0.0685357i
$927$		0			0
$928$	302.340	−	30.9511i	0.325798	−	0.0333525i
$929$	258.654	−	448.002i	0.278422	−	0.482241i	−0.692571	−	0.721350i	$-0.743522\pi$
$929$	258.654	−	448.002i	0.278422	−	0.482241i	0.970993	+	0.239109i	$0.0768554\pi$
$930$		0			0
$931$	−863.010	+	498.259i	−0.926971	+	0.535187i
$932$	−1158.79	−	460.248i	−1.24334	−	0.493828i
$933$		0			0
$934$	74.3349	−	388.536i	0.0795877	−	0.415991i
$935$			288.924i			0.309009i
$936$		0			0
$937$	367.880			0.392615			0.196308	−	0.980542i	$-0.437105\pi$
$937$	367.880			0.392615			0.196308	+	0.980542i	$0.437105\pi$
$938$	−219.416	−	41.9788i	−0.233919	−	0.0447535i
$939$		0			0
$940$	79.8676	−	201.087i	0.0849655	−	0.213922i
$941$	−637.454	−	1104.10i	−0.677422	−	1.17333i	−0.975755	−	0.218867i	$-0.929764\pi$
$941$	−637.454	−	1104.10i	−0.677422	−	1.17333i	0.298333	−	0.954462i	$-0.403569\pi$
$942$		0			0
$943$	−125.058	−	72.2021i	−0.132617	−	0.0765664i
$944$	470.594	+	111.451i	0.498511	+	0.118063i
$945$		0			0
$946$	−650.955	−	1872.55i	−0.688113	−	1.97944i
$947$	−624.238	−	360.404i	−0.659174	−	0.380574i	0.132788	−	0.991144i	$-0.457607\pi$
$947$	−624.238	−	360.404i	−0.659174	−	0.380574i	−0.791962	+	0.610570i	$0.790940\pi$
$948$		0			0
$949$	184.222	+	319.081i	0.194122	+	0.336229i
$950$	784.823	+	678.181i	0.826129	+	0.713875i
$951$		0			0
$952$	−152.505	−	292.871i	−0.160194	−	0.307638i
$953$	−513.654			−0.538986			−0.269493	−	0.963002i	$-0.586856\pi$
$953$	−513.654			−0.538986			−0.269493	+	0.963002i	$0.586856\pi$
$954$		0			0
$955$			277.813i			0.290904i
$956$	−174.196	+	25.5306i	−0.182214	+	0.0267057i
$957$		0			0
$958$	744.003	+	642.908i	0.776621	+	0.671094i
$959$	188.215	−	108.666i	0.196262	−	0.113312i
$960$		0			0
$961$	729.287	−	1263.16i	0.758884	−	1.31443i
$962$	155.113	+	446.200i	0.161240	+	0.463825i
$963$		0			0
$964$	−372.732	+	294.768i	−0.386652	+	0.305776i
$965$	78.7868	−	136.463i	0.0816443	−	0.141412i
$966$		0			0
$967$	−10.1344	+	5.85110i	−0.0104803	+	0.00605078i	−0.505231	−	0.862984i	$-0.668593\pi$
$967$	−10.1344	+	5.85110i	−0.0104803	+	0.00605078i	0.494751	+	0.869035i	$0.335259\pi$
$968$	11.1697	−	256.554i	0.0115389	−	0.265035i
$969$		0			0
$970$	177.354	+	33.9315i	0.182839	+	0.0349809i
$971$		−	743.634i		−	0.765843i	−0.923781	−	0.382922i	$-0.874918\pi$
$971$		−	743.634i		−	0.765843i	0.923781	−	0.382922i	$-0.125082\pi$
$972$		0			0
$973$	−223.395			−0.229594
$974$	−212.862	+	1112.60i	−0.218545	+	1.14230i
$975$		0			0
$976$	871.327	−	261.014i	0.892753	−	0.267433i
$977$	478.872	+	829.430i	0.490145	+	0.848956i	0.999936	−	0.0113423i	$-0.00361043\pi$
$977$	478.872	+	829.430i	0.490145	+	0.848956i	−0.509791	+	0.860299i	$0.670277\pi$
$978$		0			0
$979$	−730.007	−	421.470i	−0.745666	−	0.430510i
$980$	130.539	−	103.234i	0.133203	−	0.105341i
$981$		0			0
$982$	630.426	−	219.155i	0.641982	−	0.223173i
$983$	−467.058	−	269.656i	−0.475135	−	0.274320i	0.243252	−	0.969963i	$-0.421786\pi$
$983$	−467.058	−	269.656i	−0.475135	−	0.274320i	−0.718387	+	0.695644i	$0.755119\pi$
$984$		0			0
$985$	52.7575	+	91.3786i	0.0535609	+	0.0927701i
$986$	−324.098	+	375.061i	−0.328699	+	0.380386i
$987$		0			0
$988$	979.644	−	143.579i	0.991543	−	0.145323i
$989$	−2201.93			−2.22642
$990$		0			0
$991$		−	114.353i		−	0.115391i	−0.998334	−	0.0576956i	$-0.981625\pi$
$991$		−	114.353i		−	0.115391i	0.998334	−	0.0576956i	$-0.0183753\pi$
$992$	1436.23	+	644.110i	1.44782	+	0.649305i
$993$		0			0
$994$	−147.883	+	171.137i	−0.148776	+	0.172170i
$995$	77.5829	−	44.7925i	0.0779728	−	0.0450176i
$996$		0			0
$997$	1.86796	−	3.23541i	0.00187358	−	0.00324514i	−0.865087	−	0.501622i	$-0.832737\pi$
$997$	1.86796	−	3.23541i	0.00187358	−	0.00324514i	0.866961	+	0.498377i	$0.166070\pi$
$998$	52.4377	−	18.2290i	0.0525428	−	0.0182655i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.s.55.1		16
3.2	odd	2	inner	324.3.f.s.55.8		16
4.3	odd	2	inner	324.3.f.s.55.6		16
9.2	odd	6		324.3.d.h.163.3	✓	8
9.4	even	3	inner	324.3.f.s.271.6		16
9.5	odd	6	inner	324.3.f.s.271.3		16
9.7	even	3		324.3.d.h.163.6	yes	8
12.11	even	2	inner	324.3.f.s.55.3		16
36.7	odd	6		324.3.d.h.163.5	yes	8
36.11	even	6		324.3.d.h.163.4	yes	8
36.23	even	6	inner	324.3.f.s.271.8		16
36.31	odd	6	inner	324.3.f.s.271.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.h.163.3	✓	8	9.2	odd	6
324.3.d.h.163.4	yes	8	36.11	even	6
324.3.d.h.163.5	yes	8	36.7	odd	6
324.3.d.h.163.6	yes	8	9.7	even	3
324.3.f.s.55.1		16	1.1	even	1	trivial
324.3.f.s.55.3		16	12.11	even	2	inner
324.3.f.s.55.6		16	4.3	odd	2	inner
324.3.f.s.55.8		16	3.2	odd	2	inner
324.3.f.s.271.1		16	36.31	odd	6	inner
324.3.f.s.271.3		16	9.5	odd	6	inner
324.3.f.s.271.6		16	9.4	even	3	inner
324.3.f.s.271.8		16	36.23	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.96437 - 0.375825i) q^{2} +(3.71751 + 1.47652i) q^{4} +(0.447399 + 0.774917i) q^{5} +(-1.36976 - 0.790831i) q^{7} +(-6.74766 - 4.29756i) q^{8} +(-0.587624 - 1.69037i) q^{10} +(-10.7156 - 6.18667i) q^{11} +(5.77492 + 10.0025i) q^{13} +(2.39350 + 2.06828i) q^{14} +(11.6398 + 10.9780i) q^{16} -26.0958 q^{17} -21.4313i q^{19} +(0.519030 + 3.54136i) q^{20} +(18.7244 + 16.1801i) q^{22} +(23.8038 - 13.7431i) q^{23} +(12.0997 - 20.9572i) q^{25} +(-7.58492 - 21.8189i) q^{26} +(-3.92442 - 4.96240i) q^{28} +(-4.74875 + 8.22508i) q^{29} +(-42.5991 + 24.5946i) q^{31} +(-18.7391 - 25.9393i) q^{32} +(51.2619 + 9.80747i) q^{34} -1.41527i q^{35} -20.4502 q^{37} +(-8.05440 + 42.0990i) q^{38} +(0.311362 - 7.15160i) q^{40} +(-2.62685 - 4.54983i) q^{41} +(-69.3777 - 40.0552i) q^{43} +(-30.7007 - 38.8209i) q^{44} +(-51.9244 + 18.0505i) q^{46} +(-52.3525 - 30.2257i) q^{47} +(-23.2492 - 40.2687i) q^{49} +(-31.6445 + 36.6205i) q^{50} +(6.69952 + 45.7110i) q^{52} -12.4121 q^{53} -11.0716i q^{55} +(5.84403 + 11.2229i) q^{56} +(12.4195 - 14.3724i) q^{58} +(26.1762 - 15.1129i) q^{59} +(28.4244 - 49.2325i) q^{61} +(92.9237 - 32.3031i) q^{62} +(27.0619 + 57.9970i) q^{64} +(-5.16738 + 8.95017i) q^{65} +(-61.1591 + 35.3102i) q^{67} +(-97.0116 - 38.5310i) q^{68} +(-0.531892 + 2.78011i) q^{70} +71.5006i q^{71} +31.9003 q^{73} +(40.1717 + 7.68568i) q^{74} +(31.6437 - 79.6710i) q^{76} +(9.78523 + 16.9485i) q^{77} +(-83.8284 - 48.3983i) q^{79} +(-3.29938 + 13.9314i) q^{80} +(3.45017 + 9.92480i) q^{82} +(21.4313 + 12.3733i) q^{83} +(-11.6752 - 20.2221i) q^{85} +(121.230 + 104.757i) q^{86} +(45.7178 + 87.7967i) q^{88} +68.1254 q^{89} -18.2679i q^{91} +(108.783 - 15.9435i) q^{92} +(91.4802 + 79.0499i) q^{94} +(16.6075 - 9.58832i) q^{95} +(-50.4502 + 87.3823i) q^{97} +(30.5360 + 87.8404i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{4} - 100 q^{10} + 32 q^{13} + 46 q^{16} + 36 q^{22} - 48 q^{25} + 360 q^{28} + 122 q^{34} - 448 q^{37} - 154 q^{40} - 408 q^{46} + 232 q^{49} - 154 q^{52} + 86 q^{58} + 32 q^{61} - 20 q^{64}+ \cdots - 928 q^{97}+O(q^{100}) \) 16 * q + 10 * q^4 - 100 * q^10 + 32 * q^13 + 46 * q^16 + 36 * q^22 - 48 * q^25 + 360 * q^28 + 122 * q^34 - 448 * q^37 - 154 * q^40 - 408 * q^46 + 232 * q^49 - 154 * q^52 + 86 * q^58 + 32 * q^61 - 20 * q^64 + 492 * q^70 + 752 * q^73 - 516 * q^76 + 176 * q^82 - 368 * q^85 - 516 * q^88 + 672 * q^94 - 928 * q^97

Introduction

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