LMFDB - Embedded newform 225.3.r.a.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(28,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("225.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.r (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	225.73
Dual form			225.3.r.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.312579 - 1.97355i) q^{2} +(0.00704800 + 0.00229003i) q^{4} +(-4.93389 + 0.810386i) q^{5} +(3.91191 - 3.91191i) q^{7} +(3.63528 - 7.13464i) q^{8} +O(q^{10})$	\(q+(0.312579 - 1.97355i) q^{2} +(0.00704800 + 0.00229003i) q^{4} +(-4.93389 + 0.810386i) q^{5} +(3.91191 - 3.91191i) q^{7} +(3.63528 - 7.13464i) q^{8} +(0.0571038 + 9.99057i) q^{10} +(2.73590 - 1.98775i) q^{11} +(-3.13886 - 19.8180i) q^{13} +(-6.49755 - 8.94311i) q^{14} +(-12.9202 - 9.38711i) q^{16} +(-17.7107 - 9.02407i) q^{17} +(-5.87938 + 1.91032i) q^{19} +(-0.0366299 - 0.00558718i) q^{20} +(-3.06773 - 6.02076i) q^{22} +(13.6608 + 2.16366i) q^{23} +(23.6865 - 7.99671i) q^{25} -40.0928 q^{26} +(0.0365295 - 0.0186127i) q^{28} +(29.3129 + 9.52435i) q^{29} +(-0.774840 - 2.38471i) q^{31} +(0.0838425 - 0.0838425i) q^{32} +(-23.3454 + 32.1322i) q^{34} +(-16.1308 + 22.4711i) q^{35} +(-33.6313 + 5.32667i) q^{37} +(1.93234 + 12.2003i) q^{38} +(-12.1543 + 38.1475i) q^{40} +(-29.0354 - 21.0954i) q^{41} +(23.3347 + 23.3347i) q^{43} +(0.0238347 - 0.00774436i) q^{44} +(8.54016 - 26.2839i) q^{46} +(19.2067 + 37.6953i) q^{47} +18.3940i q^{49} +(-8.37796 - 49.2461i) q^{50} +(0.0232612 - 0.146865i) q^{52} +(73.4897 - 37.4449i) q^{53} +(-11.8878 + 12.0245i) q^{55} +(-13.6892 - 42.1309i) q^{56} +(27.9594 - 54.8733i) q^{58} +(-1.53534 + 2.11322i) q^{59} +(21.8447 - 15.8711i) q^{61} +(-4.94854 + 0.783771i) q^{62} +(-37.6877 - 51.8727i) q^{64} +(31.5470 + 95.2360i) q^{65} +(67.8430 + 34.5677i) q^{67} +(-0.104160 - 0.104160i) q^{68} +(39.3056 + 38.8588i) q^{70} +(-22.6659 + 69.7586i) q^{71} +(51.6598 + 8.18211i) q^{73} +68.0379i q^{74} -0.0458126 q^{76} +(2.92671 - 18.4785i) q^{77} +(-37.4103 - 12.1554i) q^{79} +(71.3543 + 35.8446i) q^{80} +(-50.7087 + 50.7087i) q^{82} +(22.8152 - 44.7773i) q^{83} +(94.6958 + 30.1712i) q^{85} +(53.3460 - 38.7581i) q^{86} +(-4.23611 - 26.7457i) q^{88} +(41.7155 + 57.4164i) q^{89} +(-89.8050 - 65.2472i) q^{91} +(0.0913265 + 0.0465332i) q^{92} +(80.3971 - 26.1226i) q^{94} +(27.4601 - 14.1899i) q^{95} +(-1.26842 - 2.48942i) q^{97} +(36.3014 + 5.74957i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} - 10 q^{4} + 10 q^{5} - 10 q^{7} + 10 q^{8}+O(q^{10}) $ 32 * q + 10 * q^2 - 10 * q^4 + 10 * q^5 - 10 * q^7 + 10 * q^8	$ 32 q + 10 q^{2} - 10 q^{4} + 10 q^{5} - 10 q^{7} + 10 q^{8} - 10 q^{10} + 6 q^{11} - 10 q^{13} + 10 q^{14} + 2 q^{16} - 60 q^{17} + 90 q^{19} - 130 q^{20} + 70 q^{22} - 10 q^{23} - 40 q^{25} - 4 q^{26} - 250 q^{28} + 110 q^{29} - 6 q^{31} + 290 q^{32} - 260 q^{34} + 120 q^{35} + 50 q^{37} - 320 q^{38} + 440 q^{40} + 86 q^{41} + 230 q^{43} - 340 q^{44} - 6 q^{46} - 70 q^{47} + 100 q^{50} - 320 q^{52} + 190 q^{53} - 250 q^{55} + 70 q^{56} - 640 q^{58} + 260 q^{59} + 114 q^{61} - 60 q^{62} + 340 q^{64} - 360 q^{65} + 270 q^{67} - 710 q^{68} + 310 q^{70} + 66 q^{71} + 30 q^{73} - 80 q^{76} + 250 q^{77} - 210 q^{79} + 850 q^{80} + 30 q^{82} + 600 q^{85} + 6 q^{86} + 190 q^{88} + 10 q^{89} - 6 q^{91} + 30 q^{92} + 790 q^{94} - 310 q^{95} + 270 q^{97} - 170 q^{98}+O(q^{100}) $ 32 * q + 10 * q^2 - 10 * q^4 + 10 * q^5 - 10 * q^7 + 10 * q^8 - 10 * q^10 + 6 * q^11 - 10 * q^13 + 10 * q^14 + 2 * q^16 - 60 * q^17 + 90 * q^19 - 130 * q^20 + 70 * q^22 - 10 * q^23 - 40 * q^25 - 4 * q^26 - 250 * q^28 + 110 * q^29 - 6 * q^31 + 290 * q^32 - 260 * q^34 + 120 * q^35 + 50 * q^37 - 320 * q^38 + 440 * q^40 + 86 * q^41 + 230 * q^43 - 340 * q^44 - 6 * q^46 - 70 * q^47 + 100 * q^50 - 320 * q^52 + 190 * q^53 - 250 * q^55 + 70 * q^56 - 640 * q^58 + 260 * q^59 + 114 * q^61 - 60 * q^62 + 340 * q^64 - 360 * q^65 + 270 * q^67 - 710 * q^68 + 310 * q^70 + 66 * q^71 + 30 * q^73 - 80 * q^76 + 250 * q^77 - 210 * q^79 + 850 * q^80 + 30 * q^82 + 600 * q^85 + 6 * q^86 + 190 * q^88 + 10 * q^89 - 6 * q^91 + 30 * q^92 + 790 * q^94 - 310 * q^95 + 270 * q^97 - 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	0.312579	−	1.97355i	0.156289	−	0.986773i	−0.777483	−	0.628905i	$-0.783504\pi$
$2$	0.312579	−	1.97355i	0.156289	−	0.986773i	0.933772	−	0.357868i	$-0.116496\pi$
$3$		0			0
$3$		0			0
$4$	0.00704800	+	0.00229003i	0.00176200	+	0.000572509i
$5$	−4.93389	+	0.810386i	−0.986778	+	0.162077i
$5$	−4.93389	+	0.810386i	−0.986778	+	0.162077i
$6$		0			0
$7$	3.91191	−	3.91191i	0.558844	−	0.558844i	−0.370134	−	0.928978i	$-0.620688\pi$
$7$	3.91191	−	3.91191i	0.558844	−	0.558844i	0.928978	+	0.370134i	$0.120688\pi$
$8$	3.63528	−	7.13464i	0.454410	−	0.891830i
$9$		0			0
$10$	0.0571038	+	9.99057i	0.00571038	+	0.999057i
$11$	2.73590	−	1.98775i	0.248719	−	0.180705i	−0.456440	−	0.889754i	$-0.650876\pi$
$11$	2.73590	−	1.98775i	0.248719	−	0.180705i	0.705159	+	0.709049i	$0.250876\pi$
$12$		0			0
$13$	−3.13886	−	19.8180i	−0.241451	−	1.52446i	−0.748845	−	0.662746i	$-0.769391\pi$
$13$	−3.13886	−	19.8180i	−0.241451	−	1.52446i	0.507394	−	0.861714i	$-0.330609\pi$
$14$	−6.49755	−	8.94311i	−0.464111	−	0.638793i
$15$		0			0
$16$	−12.9202	−	9.38711i	−0.807515	−	0.586694i
$17$	−17.7107	−	9.02407i	−1.04181	−	0.530828i	−0.152579	−	0.988291i	$-0.548758\pi$
$17$	−17.7107	−	9.02407i	−1.04181	−	0.530828i	−0.889228	+	0.457464i	$0.848758\pi$
$18$		0			0
$19$	−5.87938	+	1.91032i	−0.309441	+	0.100543i	−0.459621	−	0.888115i	$-0.652015\pi$
$19$	−5.87938	+	1.91032i	−0.309441	+	0.100543i	0.150180	+	0.988659i	$0.452015\pi$
$20$	−0.0366299	−	0.00558718i	−0.00183149	−	0.000279359i
$21$		0			0
$22$	−3.06773	−	6.02076i	−0.139442	−	0.273671i
$23$	13.6608	+	2.16366i	0.593948	+	0.0940721i	0.446170	−	0.894948i	$-0.352788\pi$
$23$	13.6608	+	2.16366i	0.593948	+	0.0940721i	0.147778	+	0.989021i	$0.452788\pi$
$24$		0			0
$25$	23.6865	−	7.99671i	0.947462	−	0.319868i
$26$	−40.0928			−1.54203
$27$		0			0
$28$	0.0365295	−	0.0186127i	0.00130463	−	0.000664740i
$29$	29.3129	+	9.52435i	1.01079	+	0.328426i	0.767170	−	0.641444i	$-0.221664\pi$
$29$	29.3129	+	9.52435i	1.01079	+	0.328426i	0.243622	+	0.969870i	$0.421664\pi$
$30$		0			0
$31$	−0.774840	−	2.38471i	−0.0249948	−	0.0769262i	0.937781	−	0.347227i	$-0.112877\pi$
$31$	−0.774840	−	2.38471i	−0.0249948	−	0.0769262i	−0.962776	+	0.270301i	$0.912877\pi$
$32$	0.0838425	−	0.0838425i	0.00262008	−	0.00262008i
$33$		0			0
$34$	−23.3454	+	32.1322i	−0.686630	+	0.945065i
$35$	−16.1308	+	22.4711i	−0.460879	+	0.642031i
$36$		0			0
$37$	−33.6313	+	5.32667i	−0.908954	+	0.143964i	−0.593367	−	0.804932i	$-0.702202\pi$
$37$	−33.6313	+	5.32667i	−0.908954	+	0.143964i	−0.315587	+	0.948897i	$0.602202\pi$
$38$	1.93234	+	12.2003i	0.0508512	+	0.321062i
$39$		0			0
$40$	−12.1543	+	38.1475i	−0.303857	+	0.953688i
$41$	−29.0354	−	21.0954i	−0.708180	−	0.514523i	0.174406	−	0.984674i	$-0.444200\pi$
$41$	−29.0354	−	21.0954i	−0.708180	−	0.514523i	−0.882586	+	0.470151i	$0.844200\pi$
$42$		0			0
$43$	23.3347	+	23.3347i	0.542667	+	0.542667i	0.924310	−	0.381643i	$-0.124642\pi$
$43$	23.3347	+	23.3347i	0.542667	+	0.542667i	−0.381643	+	0.924310i	$0.624642\pi$
$44$	0.0238347	−	0.00774436i	0.000541697	−	0.000176008i
$45$		0			0
$46$	8.54016	−	26.2839i	0.185656	−	0.571389i
$47$	19.2067	+	37.6953i	0.408654	+	0.802029i	0.999990	−	0.00439647i	$-0.00139944\pi$
$47$	19.2067	+	37.6953i	0.408654	+	0.802029i	−0.591336	+	0.806425i	$0.701399\pi$
$48$		0			0
$49$			18.3940i			0.375387i
$50$	−8.37796	−	49.2461i	−0.167559	−	0.984922i
$51$		0			0
$52$	0.0232612	−	0.146865i	0.000447330	−	0.00282433i
$53$	73.4897	−	37.4449i	1.38660	−	0.706507i	0.408134	−	0.912922i	$-0.366180\pi$
$53$	73.4897	−	37.4449i	1.38660	−	0.706507i	0.978465	+	0.206415i	$0.0661797\pi$
$54$		0			0
$55$	−11.8878	+	12.0245i	−0.216142	+	0.218627i
$56$	−13.6892	−	42.1309i	−0.244449	−	0.752338i
$57$		0			0
$58$	27.9594	−	54.8733i	0.482058	−	0.946092i
$59$	−1.53534	+	2.11322i	−0.0260228	+	0.0358173i	−0.821830	−	0.569733i	$-0.807047\pi$
$59$	−1.53534	+	2.11322i	−0.0260228	+	0.0358173i	0.795807	+	0.605550i	$0.207047\pi$
$60$		0			0
$61$	21.8447	−	15.8711i	0.358110	−	0.260182i	−0.394153	−	0.919045i	$-0.628962\pi$
$61$	21.8447	−	15.8711i	0.358110	−	0.260182i	0.752264	+	0.658862i	$0.228962\pi$
$62$	−4.94854	+	0.783771i	−0.0798151	+	0.0126415i
$63$		0			0
$64$	−37.6877	−	51.8727i	−0.588870	−	0.810510i
$65$	31.5470	+	95.2360i	0.485338	+	1.46517i
$66$		0			0
$67$	67.8430	+	34.5677i	1.01258	+	0.515936i	0.879868	−	0.475218i	$-0.157631\pi$
$67$	67.8430	+	34.5677i	1.01258	+	0.515936i	0.132714	+	0.991154i	$0.457631\pi$
$68$	−0.104160	−	0.104160i	−0.00153176	−	0.00153176i
$69$		0			0
$70$	39.3056	+	38.8588i	0.561508	+	0.555126i
$71$	−22.6659	+	69.7586i	−0.319239	+	0.982516i	0.654736	+	0.755858i	$0.272780\pi$
$71$	−22.6659	+	69.7586i	−0.319239	+	0.982516i	−0.973974	+	0.226658i	$0.927220\pi$
$72$		0			0
$73$	51.6598	+	8.18211i	0.707669	+	0.112084i	0.499886	−	0.866091i	$-0.333375\pi$
$73$	51.6598	+	8.18211i	0.707669	+	0.112084i	0.207783	+	0.978175i	$0.433375\pi$
$74$			68.0379i			0.919431i
$75$		0			0
$76$	−0.0458126			−0.000602797
$77$	2.92671	−	18.4785i	0.0380092	−	0.239981i
$78$		0			0
$79$	−37.4103	−	12.1554i	−0.473548	−	0.153865i	0.0625131	−	0.998044i	$-0.480088\pi$
$79$	−37.4103	−	12.1554i	−0.473548	−	0.153865i	−0.536061	+	0.844179i	$0.680088\pi$
$80$	71.3543	+	35.8446i	0.891928	+	0.448057i
$81$		0			0
$82$	−50.7087	+	50.7087i	−0.618399	+	0.618399i
$83$	22.8152	−	44.7773i	0.274881	−	0.539485i	−0.711754	−	0.702429i	$-0.752099\pi$
$83$	22.8152	−	44.7773i	0.274881	−	0.539485i	0.986635	+	0.162944i	$0.0520989\pi$
$84$		0			0
$85$	94.6958	+	30.1712i	1.11407	+	0.354956i
$86$	53.3460	−	38.7581i	0.620302	−	0.450676i
$87$		0			0
$88$	−4.23611	−	26.7457i	−0.0481376	−	0.303929i
$89$	41.7155	+	57.4164i	0.468713	+	0.645128i	0.976287	−	0.216480i	$-0.0694576\pi$
$89$	41.7155	+	57.4164i	0.468713	+	0.645128i	−0.507574	+	0.861608i	$0.669458\pi$
$90$		0			0
$91$	−89.8050	−	65.2472i	−0.986868	−	0.717002i
$92$	0.0913265	+	0.0465332i	0.000992679	+	0.000505795i
$93$		0			0
$94$	80.3971	−	26.1226i	0.855288	−	0.277900i
$95$	27.4601	−	14.1899i	0.289054	−	0.149367i
$96$		0			0
$97$	−1.26842	−	2.48942i	−0.0130765	−	0.0256642i	0.884376	−	0.466775i	$-0.154584\pi$
$97$	−1.26842	−	2.48942i	−0.0130765	−	0.0256642i	−0.897452	+	0.441111i	$0.854584\pi$
$98$	36.3014	+	5.74957i	0.370422	+	0.0586691i
$99$		0			0
$100$	0.185256	−	0.00211783i	0.00185256	−	2.11783e-5i
$101$	53.7631			0.532308			0.266154	−	0.963931i	$-0.414247\pi$
$101$	53.7631			0.532308			0.266154	+	0.963931i	$0.414247\pi$
$102$		0			0
$103$	104.783	−	53.3894i	1.01731	−	0.518344i	0.135911	−	0.990721i	$-0.456604\pi$
$103$	104.783	−	53.3894i	1.01731	−	0.518344i	0.881397	+	0.472377i	$0.156604\pi$
$104$	−152.805	−	49.6493i	−1.46928	−	0.477397i
$105$		0			0
$106$	−50.9278	−	156.740i	−0.480451	−	1.47868i
$107$	−1.86245	+	1.86245i	−0.0174060	+	0.0174060i	−0.715756	−	0.698350i	$-0.753918\pi$
$107$	−1.86245	+	1.86245i	−0.0174060	+	0.0174060i	0.698350	+	0.715756i	$0.253918\pi$
$108$		0			0
$109$	−77.7078	+	106.956i	−0.712915	+	0.981244i	0.286814	+	0.957986i	$0.407404\pi$
$109$	−77.7078	+	106.956i	−0.712915	+	0.981244i	−0.999730	+	0.0232574i	$0.992596\pi$
$110$	20.0150	+	27.2197i	0.181954	+	0.247452i
$111$		0			0
$112$	−87.2643	+	13.8213i	−0.779145	+	0.123405i
$113$	−6.99224	−	44.1473i	−0.0618782	−	0.390684i	−0.999118	−	0.0419974i	$-0.986628\pi$
$113$	−6.99224	−	44.1473i	−0.0618782	−	0.390684i	0.937239	−	0.348686i	$-0.113372\pi$
$114$		0			0
$115$	−69.1543	+	0.395270i	−0.601342	+	0.00343713i
$116$	0.184787	+	0.134255i	0.00159299	+	0.00115737i
$117$		0			0
$118$	3.69062	+	3.69062i	0.0312765	+	0.0312765i
$119$	−104.584	+	33.9814i	−0.878858	+	0.285558i
$120$		0			0
$121$	−33.8570	+	104.201i	−0.279810	+	0.861167i
$122$	−24.4942	−	48.0726i	−0.200772	−	0.394037i
$123$		0			0
$124$		−	0.0185819i		−	0.000149854i
$125$	−110.386	+	58.6502i	−0.883091	+	0.469201i
$126$		0			0
$127$	−26.6349	+	168.166i	−0.209724	+	1.32415i	0.628069	+	0.778158i	$0.283845\pi$
$127$	−26.6349	+	168.166i	−0.209724	+	1.32415i	−0.837793	+	0.545988i	$0.816155\pi$
$128$	−113.731	+	57.9488i	−0.888522	+	0.452725i
$129$		0			0
$130$	197.814	−	32.4907i	1.52164	−	0.249928i
$131$	−16.2028	−	49.8672i	−0.123686	−	0.380665i	0.869974	−	0.493098i	$-0.164136\pi$
$131$	−16.2028	−	49.8672i	−0.123686	−	0.380665i	−0.993659	+	0.112433i	$0.964136\pi$
$132$		0			0
$133$	−15.5266	+	30.4726i	−0.116741	+	0.229117i
$134$	89.4273	−	123.086i	0.667368	−	0.918553i
$135$		0			0
$136$	−128.767	+	93.5547i	−0.946816	+	0.687902i
$137$	−50.3103	+	7.96837i	−0.367228	+	0.0581633i	−0.337322	−	0.941389i	$-0.609521\pi$
$137$	−50.3103	+	7.96837i	−0.367228	+	0.0581633i	−0.0299067	+	0.999553i	$0.509521\pi$
$138$		0			0
$139$	−69.7880	−	96.0549i	−0.502072	−	0.691043i	0.480485	−	0.877003i	$-0.340461\pi$
$139$	−69.7880	−	96.0549i	−0.502072	−	0.691043i	−0.982557	+	0.185960i	$0.940461\pi$
$140$	−0.165149	+	0.121436i	−0.00117964	+	0.000867401i
$141$		0			0
$142$	130.587	+	66.5374i	0.919626	+	0.468573i
$143$	−47.9808	−	47.9808i	−0.335530	−	0.335530i
$144$		0			0
$145$	−152.345	−	23.2373i	−1.05066	−	0.160257i
$146$	32.2955	−	99.3955i	0.221202	−	0.680791i
$147$		0			0
$148$	−0.249232	−	0.0394744i	−0.00168400	−	0.000266719i
$149$		−	64.0597i		−	0.429931i	−0.976622	−	0.214965i	$-0.931036\pi$
$149$		−	64.0597i		−	0.429931i	0.976622	−	0.214965i	$-0.0689639\pi$
$150$		0			0
$151$	227.547			1.50693			0.753467	−	0.657486i	$-0.228380\pi$
$151$	227.547			1.50693			0.753467	+	0.657486i	$0.228380\pi$
$152$	−7.74370	+	48.8918i	−0.0509454	+	0.321657i
$153$		0			0
$154$	−35.5533	−	11.5520i	−0.230866	−	0.0750129i
$155$	5.75551	+	11.1380i	0.0371323	+	0.0718580i
$156$		0			0
$157$	−65.7370	+	65.7370i	−0.418707	+	0.418707i	−0.884758	−	0.466051i	$-0.845676\pi$
$157$	−65.7370	+	65.7370i	−0.418707	+	0.418707i	0.466051	+	0.884758i	$0.345676\pi$
$158$	−35.6828	+	70.0315i	−0.225841	+	0.443237i
$159$		0			0
$160$	−0.345725	+	0.481614i	−0.00216078	+	0.00301009i
$161$	61.9038	−	44.9757i	0.384496	−	0.279352i
$162$		0			0
$163$	−19.9218	−	125.781i	−0.122220	−	0.771664i	−0.970319	−	0.241827i	$-0.922253\pi$
$163$	−19.9218	−	125.781i	−0.122220	−	0.771664i	0.848100	−	0.529837i	$-0.177747\pi$
$164$	−0.156332	−	0.215173i	−0.000953245	−	0.00131203i
$165$		0			0
$166$	−81.2384	−	59.0232i	−0.489388	−	0.355561i
$167$	71.6764	+	36.5209i	0.429200	+	0.218688i	0.655226	−	0.755433i	$-0.272573\pi$
$167$	71.6764	+	36.5209i	0.429200	+	0.218688i	−0.226026	+	0.974121i	$0.572573\pi$
$168$		0			0
$169$	−222.171	+	72.1878i	−1.31462	+	0.427147i
$170$	89.1442	−	177.456i	0.524378	−	1.04386i
$171$		0			0
$172$	0.111026	+	0.217900i	0.000645498	+	0.00126686i
$173$	−168.729	−	26.7241i	−0.975314	−	0.154474i	−0.351619	−	0.936143i	$-0.614369\pi$
$173$	−168.729	−	26.7241i	−0.975314	−	0.154474i	−0.623694	+	0.781669i	$0.714369\pi$
$174$		0			0
$175$	61.3772	−	123.942i	0.350727	−	0.708240i
$176$	−54.0078			−0.306862
$177$		0			0
$178$	126.353	−	64.3802i	0.709850	−	0.361687i
$179$	−250.316	−	81.3326i	−1.39841	−	0.454372i	−0.489736	−	0.871871i	$-0.662907\pi$
$179$	−250.316	−	81.3326i	−1.39841	−	0.454372i	−0.908677	+	0.417499i	$0.862907\pi$
$180$		0			0
$181$	−42.4512	−	130.651i	−0.234537	−	0.721830i	−0.997183	−	0.0750137i	$-0.976100\pi$
$181$	−42.4512	−	130.651i	−0.234537	−	0.721830i	0.762646	−	0.646817i	$-0.223900\pi$
$182$	−156.839	+	156.839i	−0.861755	+	0.861755i
$183$		0			0
$184$	65.0978	−	89.5994i	0.353792	−	0.486953i
$185$	161.616	−	53.5356i	0.873602	−	0.289381i
$186$		0			0
$187$	−66.3925	+	10.5155i	−0.355040	+	0.0562328i
$188$	0.0490455	+	0.309661i	0.000260880	+	0.00164713i
$189$		0			0
$190$	−19.4210	−	58.6292i	−0.102216	−	0.308575i
$191$	153.497	+	111.522i	0.803651	+	0.583886i	0.911983	−	0.410228i	$-0.134551\pi$
$191$	153.497	+	111.522i	0.803651	+	0.583886i	−0.108332	+	0.994115i	$0.534551\pi$
$192$		0			0
$193$	46.3256	+	46.3256i	0.240029	+	0.240029i	0.816862	−	0.576833i	$-0.195712\pi$
$193$	46.3256	+	46.3256i	0.240029	+	0.240029i	−0.576833	+	0.816862i	$0.695712\pi$
$194$	−5.30947	+	1.72515i	−0.0273684	+	0.00889254i
$195$		0			0
$196$	−0.0421228	+	0.129641i	−0.000214912	+	0.000661433i
$197$	124.210	+	243.776i	0.630508	+	1.23744i	0.956407	+	0.292038i	$0.0943332\pi$
$197$	124.210	+	243.776i	0.630508	+	1.23744i	−0.325899	+	0.945405i	$0.605667\pi$
$198$		0			0
$199$		−	198.243i		−	0.996197i	−0.867120	−	0.498099i	$-0.834032\pi$
$199$		−	198.243i		−	0.996197i	0.867120	−	0.498099i	$-0.165968\pi$
$200$	29.0536	−	198.065i	0.145268	−	0.990326i
$201$		0			0
$202$	16.8052	−	106.104i	0.0831941	−	0.525267i
$203$	151.928	−	77.4111i	0.748413	−	0.381336i
$204$		0			0
$205$	160.353	+	80.5527i	0.782209	+	0.392940i
$206$	−72.6137	−	223.482i	−0.352494	−	1.08486i
$207$		0			0
$208$	−145.479	+	285.518i	−0.699417	+	1.37268i
$209$	−12.2882	+	16.9132i	−0.0587950	+	0.0809244i
$210$		0			0
$211$	304.272	−	221.067i	1.44205	−	1.04771i	0.454440	−	0.890777i	$-0.349839\pi$
$211$	304.272	−	221.067i	1.44205	−	1.04771i	0.987609	−	0.156933i	$-0.0501605\pi$
$212$	0.603706	−	0.0956176i	0.00284767	−	0.000451026i
$213$		0			0
$214$	3.09346	+	4.25778i	0.0144554	+	0.0198962i
$215$	−134.041	−	96.2207i	−0.623446	−	0.447538i
$216$		0			0
$217$	−12.3599	−	6.29767i	−0.0569579	−	0.0290215i
$218$	186.792	+	186.792i	0.856844	+	0.856844i
$219$		0			0
$220$	−0.111322	+	0.0575251i	−0.000506008	+	0.000261478i
$221$	−123.247	+	379.316i	−0.557680	+	1.71636i
$222$		0			0
$223$	−385.310	−	61.0271i	−1.72785	−	0.273664i	−0.788104	−	0.615542i	$-0.788937\pi$
$223$	−385.310	−	61.0271i	−1.72785	−	0.273664i	−0.939744	+	0.341878i	$0.888937\pi$
$224$		−	0.655968i		−	0.00292843i
$225$		0			0
$226$	−89.3123			−0.395187
$227$	65.9806	−	416.585i	0.290663	−	1.83518i	−0.220127	−	0.975471i	$-0.570647\pi$
$227$	65.9806	−	416.585i	0.290663	−	1.83518i	0.510790	−	0.859706i	$-0.329353\pi$
$228$		0			0
$229$	272.802	+	88.6388i	1.19128	+	0.387069i	0.836544	−	0.547899i	$-0.184572\pi$
$229$	272.802	+	88.6388i	1.19128	+	0.387069i	0.354731	+	0.934968i	$0.384572\pi$
$230$	−20.8361	+	136.603i	−0.0905917	+	0.593925i
$231$		0			0
$232$	174.514	−	174.514i	0.752214	−	0.752214i
$233$	−87.8729	+	172.460i	−0.377137	+	0.740173i	−0.999080	−	0.0428897i	$-0.986344\pi$
$233$	−87.8729	+	172.460i	−0.377137	+	0.740173i	0.621943	+	0.783063i	$0.286344\pi$
$234$		0			0
$235$	−125.312	−	170.420i	−0.533241	−	0.725191i
$236$	−0.0156605	+	0.0113780i	−6.63579e−5	+	4.82118e-5i
$237$		0			0
$238$	34.3731	+	217.023i	0.144425	+	0.911863i
$239$	34.9983	+	48.1710i	0.146436	+	0.201552i	0.875934	−	0.482431i	$-0.160246\pi$
$239$	34.9983	+	48.1710i	0.146436	+	0.201552i	−0.729498	+	0.683983i	$0.760246\pi$
$240$		0			0
$241$	361.028	+	262.302i	1.49804	+	1.08839i	0.971153	+	0.238457i	$0.0766416\pi$
$241$	361.028	+	262.302i	1.49804	+	1.08839i	0.526889	+	0.849934i	$0.323358\pi$
$242$	195.063	+	99.3895i	0.806045	+	0.410701i
$243$		0			0
$244$	0.190307	−	0.0618346i	0.000779948	−	0.000253420i
$245$	−14.9062	−	90.7539i	−0.0608417	−	0.370424i
$246$		0			0
$247$	56.3133	+	110.521i	0.227989	+	0.447454i
$248$	−19.8308	−	3.14089i	−0.0799630	−	0.0126649i
$249$		0			0
$250$	81.2443	+	236.185i	0.324977	+	0.944742i
$251$	274.930			1.09534			0.547669	−	0.836695i	$-0.315515\pi$
$251$	274.930			1.09534			0.547669	+	0.836695i	$0.315515\pi$
$252$		0			0
$253$	41.6755	−	21.2347i	0.164725	−	0.0839316i
$254$	323.559	+	105.131i	1.27385	+	0.413900i
$255$		0			0
$256$	−0.439685	−	1.35321i	−0.00171752	−	0.00528598i
$257$	−160.142	+	160.142i	−0.623121	+	0.623121i	−0.946328	−	0.323207i	$-0.895239\pi$
$257$	−160.142	+	160.142i	−0.623121	+	0.623121i	0.323207	+	0.946328i	$0.395239\pi$
$258$		0			0
$259$	−110.725	+	152.400i	−0.427510	+	0.588417i
$260$	0.00424949	+	0.743468i	1.63442e−5	+	0.00285949i
$261$		0			0
$262$	−103.480	+	16.3896i	−0.394961	+	0.0625557i
$263$	−65.5157	−	413.650i	−0.249109	−	1.57281i	−0.722127	−	0.691760i	$-0.756836\pi$
$263$	−65.5157	−	413.650i	−0.249109	−	1.57281i	0.473018	−	0.881053i	$-0.343164\pi$
$264$		0			0
$265$	−332.245	+	244.304i	−1.25376	+	0.921902i
$266$	55.2858	+	40.1675i	0.207841	+	0.151005i
$267$		0			0
$268$	0.398996	+	0.398996i	0.00148879	+	0.00148879i
$269$	11.6319	−	3.77942i	0.0432412	−	0.0140499i	−0.287317	−	0.957836i	$-0.592763\pi$
$269$	11.6319	−	3.77942i	0.0432412	−	0.0140499i	0.330558	+	0.943786i	$0.392763\pi$
$270$		0			0
$271$	−161.855	+	498.138i	−0.597250	+	1.83815i	−0.0540612	+	0.998538i	$0.517217\pi$
$271$	−161.855	+	498.138i	−0.597250	+	1.83815i	−0.543189	+	0.839610i	$0.682783\pi$
$272$	144.117	+	282.846i	0.529842	+	1.03987i
$273$		0			0
$274$			101.780i			0.371461i
$275$	48.9087	−	68.9612i	0.177850	−	0.250768i
$276$		0			0
$277$	68.2890	−	431.160i	0.246531	−	1.55653i	−0.484871	−	0.874586i	$-0.661133\pi$
$277$	68.2890	−	431.160i	0.246531	−	1.55653i	0.731402	−	0.681947i	$-0.238867\pi$
$278$	−211.383	+	107.705i	−0.760371	+	0.387428i
$279$		0			0
$280$	101.683	+	196.776i	0.363154	+	0.702771i
$281$	−31.8261	−	97.9506i	−0.113260	−	0.348579i	0.878320	−	0.478073i	$-0.158665\pi$
$281$	−31.8261	−	97.9506i	−0.113260	−	0.348579i	−0.991580	+	0.129494i	$0.958665\pi$
$282$		0			0
$283$	96.0529	−	188.514i	0.339409	−	0.666129i	−0.656710	−	0.754143i	$-0.728052\pi$
$283$	96.0529	−	188.514i	0.339409	−	0.666129i	0.996119	+	0.0880149i	$0.0280523\pi$
$284$	−0.319499	+	0.439753i	−0.00112500	+	0.00154843i
$285$		0			0
$286$	−109.690	+	79.6946i	−0.383532	+	0.278652i
$287$	−196.107	+	31.0603i	−0.683300	+	0.108224i
$288$		0			0
$289$	62.3663	+	85.8398i	0.215800	+	0.297024i
$290$	−93.4798	+	293.397i	−0.322344	+	1.01171i
$291$		0			0
$292$	0.345361	+	0.175970i	0.00118274	+	0.000602638i
$293$	192.127	+	192.127i	0.655724	+	0.655724i	0.954365	−	0.298642i	$-0.0965335\pi$
$293$	192.127	+	192.127i	0.655724	+	0.655724i	−0.298642	+	0.954365i	$0.596534\pi$
$294$		0			0
$295$	5.86270	−	11.6706i	0.0198736	−	0.0395614i
$296$	−84.2553	+	259.311i	−0.284646	+	0.876051i
$297$		0			0
$298$	−126.425	−	20.0237i	−0.424244	−	0.0671937i
$299$		−	277.521i		−	0.928163i
$300$		0			0
$301$	182.566			0.606532
$302$	71.1264	−	449.075i	0.235518	−	1.48700i
$303$		0			0
$304$	93.8954	+	30.5085i	0.308866	+	0.100357i
$305$	−94.9178	+	96.0091i	−0.311206	+	0.314784i
$306$		0			0
$307$	−37.7886	+	37.7886i	−0.123090	+	0.123090i	−0.765968	−	0.642878i	$-0.777740\pi$
$307$	−37.7886	+	37.7886i	−0.123090	+	0.123090i	0.642878	+	0.765968i	$0.277740\pi$
$308$	0.0629438	−	0.123534i	0.000204363	−	0.000401085i
$309$		0			0
$310$	23.7804	−	7.87727i	0.0767109	−	0.0254105i
$311$	−208.182	+	151.253i	−0.669396	+	0.486345i	−0.869823	−	0.493364i	$-0.835767\pi$
$311$	−208.182	+	151.253i	−0.669396	+	0.486345i	0.200427	+	0.979709i	$0.435767\pi$
$312$		0			0
$313$	−75.0087	−	473.586i	−0.239644	−	1.51306i	−0.754798	−	0.655957i	$-0.772265\pi$
$313$	−75.0087	−	473.586i	−0.239644	−	1.51306i	0.515154	−	0.857098i	$-0.327735\pi$
$314$	109.187	+	150.283i	0.347729	+	0.478608i
$315$		0			0
$316$	−0.235832	−	0.171342i	−0.000746303	−	0.000542221i
$317$	175.952	+	89.6519i	0.555053	+	0.282814i	0.708933	−	0.705276i	$-0.249177\pi$
$317$	175.952	+	89.6519i	0.555053	+	0.282814i	−0.153880	+	0.988090i	$0.549177\pi$
$318$		0			0
$319$	99.1295	−	32.2091i	0.310751	−	0.100969i
$320$	227.984	+	225.392i	0.712449	+	0.704351i
$321$		0			0
$322$	−69.4119	−	136.228i	−0.215565	−	0.423070i
$323$	121.367	+	19.2226i	0.375749	+	0.0595128i
$324$		0			0
$325$	−232.827	−	444.319i	−0.716392	−	1.36714i
$326$	−254.462			−0.780559
$327$		0			0
$328$	−256.060	+	130.469i	−0.780671	+	0.397772i
$329$	222.596	+	72.3257i	0.676582	+	0.219835i
$330$		0			0
$331$	−91.8385	−	282.650i	−0.277458	−	0.853927i	−0.988559	−	0.150837i	$-0.951803\pi$
$331$	−91.8385	−	282.650i	−0.277458	−	0.853927i	0.711101	−	0.703090i	$-0.248197\pi$
$332$	0.263343	−	0.263343i	0.000793201	−	0.000793201i
$333$		0			0
$334$	94.4803	−	130.041i	0.282875	−	0.389344i
$335$	−362.743	−	115.574i	−1.08282	−	0.344998i
$336$		0			0
$337$	316.947	−	50.1994i	0.940495	−	0.148960i	0.332681	−	0.943039i	$-0.392047\pi$
$337$	316.947	−	50.1994i	0.940495	−	0.148960i	0.607814	+	0.794080i	$0.292047\pi$
$338$	73.0199	+	461.030i	0.216035	+	1.36399i
$339$		0			0
$340$	0.598323	+	0.429504i	0.00175977	+	0.00126325i
$341$	−6.86010	−	4.98416i	−0.0201176	−	0.0146163i
$342$		0			0
$343$	263.639	+	263.639i	0.768627	+	0.768627i
$344$	251.313	−	81.6564i	0.730560	−	0.237373i
$345$		0			0
$346$	−105.482	+	324.642i	−0.304863	+	0.938270i
$347$	−207.859	−	407.947i	−0.599019	−	1.17564i	−0.969106	−	0.246643i	$-0.920672\pi$
$347$	−207.859	−	407.947i	−0.599019	−	1.17564i	0.370088	−	0.928997i	$-0.379328\pi$
$348$		0			0
$349$			275.249i			0.788680i	0.918965	+	0.394340i	$0.129027\pi$
$349$			275.249i			0.788680i	−0.918965	+	0.394340i	$0.870973\pi$
$350$	−225.420	−	159.872i	−0.644057	−	0.456778i
$351$		0			0
$352$	0.0627271	−	0.396043i	0.000178202	−	0.00112512i
$353$	365.927	−	186.449i	1.03662	−	0.528184i	0.149036	−	0.988832i	$-0.452383\pi$
$353$	365.927	−	186.449i	1.03662	−	0.528184i	0.887583	+	0.460648i	$0.152383\pi$
$354$		0			0
$355$	55.2999	−	362.549i	0.155774	−	1.02127i
$356$	0.162525	+	0.500201i	0.000456531	+	0.00140506i
$357$		0			0
$358$	−238.757	+	468.587i	−0.666919	+	1.30890i
$359$	80.6575	−	111.015i	0.224673	−	0.309235i	−0.681768	−	0.731568i	$-0.738789\pi$
$359$	80.6575	−	111.015i	0.224673	−	0.309235i	0.906441	+	0.422333i	$0.138789\pi$
$360$		0			0
$361$	−261.137	+	189.727i	−0.723372	+	0.525561i
$362$	−271.116	+	42.9405i	−0.748938	+	0.118620i
$363$		0			0
$364$	−0.483528	−	0.665519i	−0.00132837	−	0.00182835i
$365$	−261.515	+	1.49476i	−0.716478	+	0.00409522i
$366$		0			0
$367$	−468.126	−	238.522i	−1.27555	−	0.649924i	−0.320745	−	0.947166i	$-0.603933\pi$
$367$	−468.126	−	238.522i	−1.27555	−	0.649924i	−0.954802	+	0.297242i	$0.903933\pi$
$368$	−156.190	−	156.190i	−0.424430	−	0.424430i
$369$		0			0
$370$	−55.1370	−	335.692i	−0.149019	−	0.907274i
$371$	141.004	−	433.966i	0.380065	−	1.16972i
$372$		0			0
$373$	171.238	+	27.1214i	0.459083	+	0.0727116i	0.381693	−	0.924289i	$-0.375341\pi$
$373$	171.238	+	27.1214i	0.459083	+	0.0727116i	0.0773903	+	0.997001i	$0.475341\pi$
$374$			134.316i			0.359132i
$375$		0			0
$376$	338.765			0.900970
$377$	96.7442	−	610.819i	0.256616	−	1.62021i
$378$		0			0
$379$	474.193	+	154.074i	1.25117	+	0.406529i	0.858339	−	0.513083i	$-0.171497\pi$
$379$	474.193	+	154.074i	1.25117	+	0.406529i	0.392829	+	0.919612i	$0.371497\pi$
$380$	0.226034	−	0.0371259i	0.000594827	−	9.76996e-5i
$381$		0			0
$382$	268.074	−	268.074i	0.701765	−	0.701765i
$383$	−46.0664	+	90.4105i	−0.120278	+	0.236059i	−0.943293	−	0.331960i	$-0.892290\pi$
$383$	−46.0664	+	90.4105i	−0.120278	+	0.236059i	0.823015	+	0.568019i	$0.192290\pi$
$384$		0			0
$385$	0.534668	+	93.5427i	0.00138875	+	0.242968i
$386$	105.906	−	76.9453i	0.274368	−	0.199340i
$387$		0			0
$388$	−0.00323899	−	0.0204502i	−8.34792e−6	−	5.27067e-5i
$389$	40.2289	+	55.3703i	0.103416	+	0.142340i	0.857589	−	0.514336i	$-0.171962\pi$
$389$	40.2289	+	55.3703i	0.103416	+	0.142340i	−0.754172	+	0.656676i	$0.771962\pi$
$390$		0			0
$391$	−222.418	−	161.596i	−0.568843	−	0.413289i
$392$	131.234	+	66.8673i	0.334782	+	0.170580i
$393$		0			0
$394$	519.929	−	168.935i	1.31962	−	0.428769i
$395$	194.429	+	29.6564i	0.492225	+	0.0750794i
$396$		0			0
$397$	−44.2700	−	86.8847i	−0.111511	−	0.218853i	0.828506	−	0.559980i	$-0.189191\pi$
$397$	−44.2700	−	86.8847i	−0.111511	−	0.218853i	−0.940017	+	0.341127i	$0.889191\pi$
$398$	−391.242	−	61.9667i	−0.983021	−	0.155695i
$399$		0			0
$400$	−381.102	−	119.029i	−0.952755	−	0.297572i
$401$	−145.737			−0.363435			−0.181717	−	0.983351i	$-0.558166\pi$
$401$	−145.737			−0.363435			−0.181717	+	0.983351i	$0.558166\pi$
$402$		0			0
$403$	−44.8281	+	22.8410i	−0.111236	+	0.0566775i
$404$	0.378922	+	0.123119i	0.000937927	+	0.000304751i
$405$		0			0
$406$	−105.285	−	324.034i	−0.259323	−	0.798113i
$407$	−81.4239	+	81.4239i	−0.200059	+	0.200059i
$408$		0			0
$409$	59.1584	−	81.4246i	0.144642	−	0.199082i	−0.730549	−	0.682860i	$-0.760736\pi$
$409$	59.1584	−	81.4246i	0.144642	−	0.199082i	0.875191	+	0.483778i	$0.160736\pi$
$410$	209.098	−	291.285i	0.509994	−	0.710451i
$411$		0			0
$412$	0.860772	−	0.136333i	0.00208925	−	0.000330905i
$413$	2.26060	+	14.2728i	0.00547360	+	0.0345590i
$414$		0			0
$415$	−76.2806	+	239.415i	−0.183809	+	0.576904i
$416$	−1.92476	−	1.39842i	−0.00462682	−	0.00336158i
$417$		0			0
$418$	29.5380	+	29.5380i	0.0706650	+	0.0706650i
$419$	−330.195	+	107.287i	−0.788054	+	0.256054i	−0.675275	−	0.737566i	$-0.735975\pi$
$419$	−330.195	+	107.287i	−0.788054	+	0.256054i	−0.112779	+	0.993620i	$0.535975\pi$
$420$		0			0
$421$	−78.9442	+	242.965i	−0.187516	+	0.577115i	−0.999983	−	0.00589274i	$-0.998124\pi$
$421$	−78.9442	+	242.965i	−0.187516	+	0.577115i	0.812467	+	0.583008i	$0.198124\pi$
$422$	−341.176	−	669.596i	−0.808475	−	1.58672i
$423$		0			0
$424$		−	660.445i		−	1.55765i
$425$	−491.669	−	72.1214i	−1.15687	−	0.169697i
$426$		0			0
$427$	23.3682	−	147.541i	0.0547264	−	0.345529i
$428$	−0.0173916	+	0.00886145i	−4.06345e−5	+	2.07043e-5i
$429$		0			0
$430$	−231.794	+	234.459i	−0.539056	+	0.545254i
$431$	−69.5257	−	213.978i	−0.161312	−	0.496469i	0.837433	−	0.546540i	$-0.184055\pi$
$431$	−69.5257	−	213.978i	−0.161312	−	0.496469i	−0.998746	+	0.0500709i	$0.984055\pi$
$432$		0			0
$433$	17.7029	−	34.7439i	0.0408843	−	0.0802399i	−0.869661	−	0.493650i	$-0.835662\pi$
$433$	17.7029	−	34.7439i	0.0408843	−	0.0802399i	0.910545	+	0.413410i	$0.135662\pi$
$434$	−16.2922	+	22.4243i	−0.0375396	+	0.0516688i
$435$		0			0
$436$	−0.792616	+	0.575870i	−0.00181793	+	0.00132080i
$437$	−84.4503	+	13.3756i	−0.193250	+	0.0306078i
$438$		0			0
$439$	134.972	+	185.773i	0.307454	+	0.423174i	0.934585	−	0.355740i	$-0.115771\pi$
$439$	134.972	+	185.773i	0.307454	+	0.423174i	−0.627131	+	0.778914i	$0.715771\pi$
$440$	42.5749	+	128.528i	0.0967610	+	0.292108i
$441$		0			0
$442$	710.073	+	361.800i	1.60650	+	0.818553i
$443$	−514.933	−	514.933i	−1.16238	−	1.16238i	−0.983954	−	0.178423i	$-0.942900\pi$
$443$	−514.933	−	514.933i	−1.16238	−	1.16238i	−0.178423	−	0.983954i	$-0.557100\pi$
$444$		0			0
$445$	−252.349	−	249.481i	−0.567077	−	0.560631i
$446$	−240.880	+	741.351i	−0.540089	+	1.66222i
$447$		0			0
$448$	−350.352	−	55.4903i	−0.782035	−	0.123862i
$449$			747.530i			1.66488i	0.554117	+	0.832439i	$0.313056\pi$
$449$			747.530i			1.66488i	−0.554117	+	0.832439i	$0.686944\pi$
$450$		0			0
$451$	−121.371			−0.269114
$452$	0.0518174	−	0.327162i	0.000114640	−	0.000723811i
$453$		0			0
$454$	−801.526	−	260.432i	−1.76548	−	0.573638i
$455$	495.963	+	249.146i	1.09003	+	0.547573i
$456$		0			0
$457$	−131.867	+	131.867i	−0.288549	+	0.288549i	−0.836506	−	0.547957i	$-0.815406\pi$
$457$	−131.867	+	131.867i	−0.288549	+	0.288549i	0.547957	+	0.836506i	$0.315406\pi$
$458$	260.205	−	510.681i	0.568133	−	1.11502i
$459$		0			0
$460$	−0.488305	−	0.155580i	−0.00106153	−	0.000338217i
$461$	146.995	−	106.798i	0.318861	−	0.231666i	−0.416828	−	0.908985i	$-0.636858\pi$
$461$	146.995	−	106.798i	0.318861	−	0.231666i	0.735689	+	0.677319i	$0.236858\pi$
$462$		0			0
$463$	70.5369	+	445.353i	0.152348	+	0.961885i	0.938857	+	0.344307i	$0.111886\pi$
$463$	70.5369	+	445.353i	0.152348	+	0.961885i	−0.786510	+	0.617578i	$0.788114\pi$
$464$	−289.324	−	398.221i	−0.623544	−	0.858234i
$465$		0			0
$466$	312.891	+	227.329i	0.671440	+	0.487830i
$467$	340.453	+	173.469i	0.729021	+	0.371455i	0.778772	−	0.627307i	$-0.215843\pi$
$467$	340.453	+	173.469i	0.729021	+	0.371455i	−0.0497511	+	0.998762i	$0.515843\pi$
$468$		0			0
$469$	400.621	−	130.170i	0.854203	−	0.277547i
$470$	−375.501	+	194.039i	−0.798939	+	0.412848i
$471$		0			0
$472$	9.49566	+	18.6363i	0.0201179	+	0.0394837i
$473$	110.225	+	17.4579i	0.233034	+	0.0369089i
$474$		0			0
$475$	−123.986	+	92.2647i	−0.261023	+	0.194241i
$476$	−0.814927			−0.00171203
$477$		0			0
$478$	106.007	−	54.0135i	0.221773	−	0.112999i
$479$	333.071	+	108.221i	0.695347	+	0.225932i	0.635302	−	0.772264i	$-0.280876\pi$
$479$	333.071	+	108.221i	0.695347	+	0.225932i	0.0600450	+	0.998196i	$0.480876\pi$
$480$		0			0
$481$	211.128	+	649.784i	0.438935	+	1.35090i
$482$	630.515	−	630.515i	1.30812	−	1.30812i
$483$		0			0
$484$	−0.477249	+	0.656877i	−0.000986052	+	0.00135718i
$485$	8.27566	+	11.2546i	0.0170632	+	0.0232054i
$486$		0			0
$487$	−798.213	+	126.425i	−1.63904	+	0.259599i	−0.906835	−	0.421485i	$-0.861509\pi$
$487$	−798.213	+	126.425i	−1.63904	+	0.259599i	−0.732206	+	0.681084i	$0.761509\pi$
$488$	−33.8231	−	213.550i	−0.0693095	−	0.437603i
$489$		0			0
$490$	−183.766	+	1.05037i	−0.375033	+	0.00214360i
$491$	426.270	+	309.703i	0.868166	+	0.630760i	0.930094	−	0.367321i	$-0.119725\pi$
$491$	426.270	+	309.703i	0.868166	+	0.630760i	−0.0619282	+	0.998081i	$0.519725\pi$
$492$		0			0
$493$	−433.205	−	433.205i	−0.878713	−	0.878713i
$494$	235.721	−	76.5903i	0.477168	−	0.155041i
$495$		0			0
$496$	−12.3744	+	38.0846i	−0.0249484	+	0.0767834i
$497$	184.222	+	361.556i	0.370668	+	0.727477i
$498$		0			0
$499$			568.734i			1.13975i	0.821732	+	0.569874i	$0.193008\pi$
$499$			568.734i			1.13975i	−0.821732	+	0.569874i	$0.806992\pi$
$500$	−0.912315	+	0.160578i	−0.00182463	+	0.000321155i
$501$		0			0
$502$	85.9373	−	542.587i	0.171190	−	1.08085i
$503$	−165.934	+	84.5473i	−0.329888	+	0.168086i	−0.611087	−	0.791563i	$-0.709268\pi$
$503$	−165.934	+	84.5473i	−0.329888	+	0.168086i	0.281200	+	0.959649i	$0.409268\pi$
$504$		0			0
$505$	−265.261	+	43.5689i	−0.525270	+	0.0862750i
$506$	−28.8808	−	88.8860i	−0.0570767	−	0.175664i
$507$		0			0
$508$	−0.572830	+	1.12424i	−0.00112762	+	0.00221308i
$509$	−321.853	+	442.992i	−0.632324	+	0.870319i	−0.998177	−	0.0603538i	$-0.980777\pi$
$509$	−321.853	+	442.992i	−0.632324	+	0.870319i	0.365854	+	0.930672i	$0.380777\pi$
$510$		0			0
$511$	234.096	−	170.081i	0.458114	−	0.332839i
$512$	−507.095	+	80.3159i	−0.990419	+	0.156867i
$513$		0			0
$514$	265.991	+	366.105i	0.517492	+	0.712266i
$515$	−473.720	+	348.332i	−0.919845	+	0.676373i
$516$		0			0
$517$	127.477	+	64.9526i	0.246570	+	0.125634i
$518$	266.158	+	266.158i	0.513818	+	0.513818i
$519$		0			0
$520$	794.157	+	121.133i	1.52723	+	0.232949i
$521$	−140.714	+	433.072i	−0.270084	+	0.831233i	0.720395	+	0.693564i	$0.243961\pi$
$521$	−140.714	+	433.072i	−0.270084	+	0.831233i	−0.990478	+	0.137668i	$0.956039\pi$
$522$		0			0
$523$	946.845	+	149.965i	1.81041	+	0.286741i	0.967788	−	0.251765i	$-0.0810109\pi$
$523$	946.845	+	149.965i	1.81041	+	0.286741i	0.842622	+	0.538506i	$0.181011\pi$
$524$		−	0.388569i		−	0.000741544i
$525$		0			0
$526$	−836.836			−1.59094
$527$	−7.79682	+	49.2272i	−0.0147947	+	0.0934103i
$528$		0			0
$529$	−321.173	−	104.355i	−0.607132	−	0.197269i
$530$	378.292	+	732.066i	0.713759	+	1.38126i
$531$		0			0
$532$	−0.179214	+	0.179214i	−0.000336869	+	0.000336869i
$533$	−326.931	+	641.638i	−0.613379	+	1.20382i
$534$		0			0
$535$	7.67980	−	10.6984i	0.0143548	−	0.0199970i
$536$	493.257	−	358.372i	0.920255	−	0.668604i
$537$		0			0
$538$	−3.82299	−	24.1374i	−0.00710593	−	0.0448651i
$539$	36.5626	+	50.3242i	0.0678342	+	0.0933658i
$540$		0			0
$541$	134.635	+	97.8182i	0.248864	+	0.180810i	0.705223	−	0.708986i	$-0.250847\pi$
$541$	134.635	+	97.8182i	0.248864	+	0.180810i	−0.456359	+	0.889796i	$0.650847\pi$
$542$	932.506	+	475.136i	1.72049	+	0.876634i
$543$		0			0
$544$	−2.24151	+	0.728311i	−0.00412043	+	0.00133881i
$545$	296.726	−	590.680i	0.544452	−	1.08382i
$546$		0			0
$547$	−107.533	−	211.046i	−0.196587	−	0.385824i	0.771579	−	0.636134i	$-0.219467\pi$
$547$	−107.533	−	211.046i	−0.196587	−	0.385824i	−0.968166	+	0.250310i	$0.919467\pi$
$548$	−0.372835	−	0.0590513i	−0.000680356	−	0.000107758i
$549$		0			0
$550$	−120.810	−	118.079i	−0.219655	−	0.214690i
$551$	−190.536			−0.345801
$552$		0			0
$553$	−193.896	+	98.7951i	−0.350626	+	0.178653i
$554$	−829.567	−	269.543i	−1.49741	−	0.486539i
$555$		0			0
$556$	−0.271897	−	0.836812i	−0.000489023	−	0.00150506i
$557$	−443.386	+	443.386i	−0.796026	+	0.796026i	−0.982466	−	0.186441i	$-0.940305\pi$
$557$	−443.386	+	443.386i	−0.796026	+	0.796026i	0.186441	+	0.982466i	$0.440305\pi$
$558$		0			0
$559$	389.202	−	535.691i	0.696247	−	0.958302i
$560$	419.352	−	138.911i	0.748843	−	0.248055i
$561$		0			0
$562$	−203.258	+	32.1929i	−0.361669	+	0.0572828i
$563$	78.6829	+	496.784i	0.139757	+	0.882388i	0.953550	+	0.301234i	$0.0973986\pi$
$563$	78.6829	+	496.784i	0.139757	+	0.882388i	−0.813794	+	0.581154i	$0.802601\pi$
$564$		0			0
$565$	70.2753	+	212.151i	0.124381	+	0.375489i
$566$	−342.018	−	248.490i	−0.604272	−	0.439029i
$567$		0			0
$568$	415.305	+	415.305i	0.731172	+	0.731172i
$569$	780.470	−	253.590i	1.37165	−	0.445677i	0.471736	−	0.881740i	$-0.343627\pi$
$569$	780.470	−	253.590i	1.37165	−	0.445677i	0.899916	+	0.436063i	$0.143627\pi$
$570$		0			0
$571$	119.477	−	367.712i	0.209241	−	0.643979i	−0.790271	−	0.612757i	$-0.790060\pi$
$571$	119.477	−	367.712i	0.209241	−	0.643979i	0.999512	−	0.0312214i	$-0.00993968\pi$
$572$	−0.228291	−	0.448047i	−0.000399110	−	0.000783298i
$573$		0			0
$574$			396.735i			0.691176i
$575$	340.879	−	57.9919i	0.592834	−	0.100855i
$576$		0			0
$577$	24.2091	−	152.850i	0.0419568	−	0.264905i	−0.957788	−	0.287474i	$-0.907185\pi$
$577$	24.2091	−	152.850i	0.0419568	−	0.264905i	0.999745	+	0.0225689i	$0.00718452\pi$
$578$	188.903	−	96.2510i	0.326822	−	0.166524i
$579$		0			0
$580$	−1.02052	−	0.512653i	−0.00175951	−	0.000883884i
$581$	−85.9137	−	264.415i	−0.147872	−	0.455104i
$582$		0			0
$583$	126.630	−	248.525i	0.217204	−	0.426286i
$584$	246.174	−	338.830i	0.421531	−	0.580188i
$585$		0			0
$586$	439.226	−	319.117i	0.749533	−	0.544568i
$587$	−587.344	+	93.0261i	−1.00059	+	0.158477i	−0.635174	−	0.772369i	$-0.719072\pi$
$587$	−587.344	+	93.0261i	−1.00059	+	0.158477i	−0.365412	+	0.930846i	$0.619072\pi$
$588$		0			0
$589$	9.11115	+	12.5404i	0.0154688	+	0.0212910i
$590$	−21.2000	−	15.2183i	−0.0359321	−	0.0257937i
$591$		0			0
$592$	484.527	+	246.879i	0.818457	+	0.417025i
$593$	151.299	+	151.299i	0.255142	+	0.255142i	0.823075	−	0.567933i	$-0.192257\pi$
$593$	151.299	+	151.299i	0.255142	+	0.255142i	−0.567933	+	0.823075i	$0.692257\pi$
$594$		0			0
$595$	488.468	−	252.414i	0.820955	−	0.424225i
$596$	0.146699	−	0.451493i	0.000246139	−	0.000757539i
$597$		0			0
$598$	−547.700	−	86.7472i	−0.915886	−	0.145062i
$599$		−	471.606i		−	0.787322i	−0.919256	−	0.393661i	$-0.871208\pi$
$599$		−	471.606i		−	0.787322i	0.919256	−	0.393661i	$-0.128792\pi$
$600$		0			0
$601$	12.2283			0.0203466			0.0101733	−	0.999948i	$-0.496762\pi$
$601$	12.2283			0.0203466			0.0101733	+	0.999948i	$0.496762\pi$
$602$	57.0664	−	360.303i	0.0947946	−	0.598510i
$603$		0			0
$604$	1.60375	+	0.521091i	0.00265522	+	0.000862733i
$605$	82.6037	−	541.555i	0.136535	−	0.895132i
$606$		0			0
$607$	−786.089	+	786.089i	−1.29504	+	1.29504i	−0.363411	+	0.931629i	$0.618388\pi$
$607$	−786.089	+	786.089i	−1.29504	+	1.29504i	−0.931629	+	0.363411i	$0.881612\pi$
$608$	−0.332775	+	0.653108i	−0.000547327	+	0.00107419i
$609$		0			0
$610$	159.809	+	217.335i	0.261982	+	0.356287i
$611$	686.758	−	498.959i	1.12399	−	0.816627i
$612$		0			0
$613$	−9.63893	−	60.8578i	−0.0157242	−	0.0992786i	0.978578	−	0.205876i	$-0.0660044\pi$
$613$	−9.63893	−	60.8578i	−0.0157242	−	0.0992786i	−0.994302	+	0.106597i	$0.966004\pi$
$614$	62.7656	+	86.3895i	0.102224	+	0.140700i
$615$		0			0
$616$	−121.198	−	88.0555i	−0.196750	−	0.142947i
$617$	−139.850	−	71.2571i	−0.226661	−	0.115490i	0.336973	−	0.941514i	$-0.390597\pi$
$617$	−139.850	−	71.2571i	−0.226661	−	0.115490i	−0.563634	+	0.826025i	$0.690597\pi$
$618$		0			0
$619$	−972.585	+	316.012i	−1.57122	+	0.510520i	−0.959776	−	0.280767i	$-0.909411\pi$
$619$	−972.585	+	316.012i	−1.57122	+	0.510520i	−0.611444	+	0.791287i	$0.709411\pi$
$620$	0.0150585	+	0.0916809i	2.42879e−5	+	0.000147872i
$621$		0			0
$622$	233.432	+	458.136i	0.375292	+	0.736552i
$623$	387.795	+	61.4207i	0.622463	+	0.0985885i
$624$		0			0
$625$	497.105	−	378.829i	0.795368	−	0.606126i
$626$	−958.090			−1.53050
$627$		0			0
$628$	−0.613854	+	0.312774i	−0.000977475	+	0.000498048i
$629$	643.703	+	209.152i	1.02338	+	0.332515i
$630$		0			0
$631$	80.5107	+	247.786i	0.127592	+	0.392688i	0.994364	−	0.106016i	$-0.0338094\pi$
$631$	80.5107	+	247.786i	0.127592	+	0.392688i	−0.866772	+	0.498704i	$0.833809\pi$
$632$	−222.721	+	222.721i	−0.352407	+	0.352407i
$633$		0			0
$634$	231.931	−	319.226i	0.365822	−	0.503510i
$635$	−4.86583	−	851.299i	−0.00766272	−	1.34063i
$636$		0			0
$637$	364.531	−	57.7361i	0.572263	−	0.0906375i
$638$	−32.5804	−	205.704i	−0.0510664	−	0.322421i
$639$		0			0
$640$	514.175	−	378.079i	0.803398	−	0.590748i
$641$	947.896	+	688.686i	1.47878	+	1.07439i	0.977948	+	0.208847i	$0.0669711\pi$
$641$	947.896	+	688.686i	1.47878	+	1.07439i	0.500828	+	0.865547i	$0.333029\pi$
$642$		0			0
$643$	−268.108	−	268.108i	−0.416965	−	0.416965i	0.467191	−	0.884156i	$-0.345266\pi$
$643$	−268.108	−	268.108i	−0.416965	−	0.416965i	−0.884156	+	0.467191i	$0.845266\pi$
$644$	0.539294	−	0.175227i	0.000837413	−	0.000272092i
$645$		0			0
$646$	75.8735	−	233.515i	0.117451	−	0.361478i
$647$	540.483	+	1060.76i	0.835368	+	1.63950i	0.766828	+	0.641853i	$0.221834\pi$
$647$	540.483	+	1060.76i	0.835368	+	1.63950i	0.0685400	+	0.997648i	$0.478166\pi$
$648$		0			0
$649$			8.83345i			0.0136109i
$650$	−949.661	+	320.611i	−1.46102	+	0.493247i
$651$		0			0
$652$	0.147635	−	0.932128i	0.000226433	−	0.00142964i
$653$	−402.175	+	204.918i	−0.615888	+	0.313810i	−0.733958	−	0.679195i	$-0.762329\pi$
$653$	−402.175	+	204.918i	−0.615888	+	0.313810i	0.118070	+	0.993005i	$0.462329\pi$
$654$		0			0
$655$	120.355	+	232.909i	0.183747	+	0.355586i
$656$	177.119	+	545.117i	0.269999	+	0.830971i
$657$		0			0
$658$	212.317	−	416.695i	0.322670	−	0.633275i
$659$	−190.013	+	261.531i	−0.288336	+	0.396860i	−0.928473	−	0.371401i	$-0.878878\pi$
$659$	−190.013	+	261.531i	−0.288336	+	0.396860i	0.640137	+	0.768261i	$0.278878\pi$
$660$		0			0
$661$	346.646	−	251.853i	0.524427	−	0.381018i	−0.293842	−	0.955854i	$-0.594934\pi$
$661$	346.646	−	251.853i	0.524427	−	0.381018i	0.818269	+	0.574836i	$0.194934\pi$
$662$	−586.529	+	92.8971i	−0.885996	+	0.140328i
$663$		0			0
$664$	−236.530	−	325.556i	−0.356220	−	0.490295i
$665$	51.9118	−	162.931i	0.0780628	−	0.245009i
$666$		0			0
$667$	379.831	+	193.533i	0.569462	+	0.290155i
$668$	0.421541	+	0.421541i	0.000631049	+	0.000631049i
$669$		0			0
$670$	−341.477	+	679.764i	−0.509668	+	1.01457i
$671$	28.2173	−	86.8438i	0.0420525	−	0.129424i
$672$		0			0
$673$	−326.867	−	51.7706i	−0.485686	−	0.0769252i	−0.0912108	−	0.995832i	$-0.529074\pi$
$673$	−326.867	−	51.7706i	−0.485686	−	0.0769252i	−0.394476	+	0.918906i	$0.629074\pi$
$674$		−	641.200i		−	0.951336i
$675$		0			0
$676$	−1.73118			−0.00256091
$677$	−163.559	+	1032.67i	−0.241593	+	1.52536i	0.506776	+	0.862078i	$0.330837\pi$
$677$	−163.559	+	1032.67i	−0.241593	+	1.52536i	−0.748369	+	0.663282i	$0.769163\pi$
$678$		0			0
$679$	−14.7004	−	4.77643i	−0.0216500	−	0.00703451i
$680$	559.507	−	565.939i	0.822804	−	0.832264i
$681$		0			0
$682$	−11.9808	+	11.9808i	−0.0175671	+	0.0175671i
$683$	76.1595	−	149.471i	0.111507	−	0.218845i	−0.828508	−	0.559977i	$-0.810810\pi$
$683$	76.1595	−	149.471i	0.111507	−	0.218845i	0.940016	+	0.341131i	$0.110810\pi$
$684$		0			0
$685$	241.768	−	80.0858i	0.352946	−	0.116914i
$686$	602.712	−	437.896i	0.878588	−	0.638332i
$687$		0			0
$688$	−82.4447	−	520.535i	−0.119832	−	0.756592i
$689$	−972.756	−	1338.88i	−1.41184	−	1.94323i
$690$		0			0
$691$	−159.959	−	116.217i	−0.231489	−	0.168187i	0.465994	−	0.884788i	$-0.345697\pi$
$691$	−159.959	−	116.217i	−0.231489	−	0.168187i	−0.697483	+	0.716601i	$0.745697\pi$
$692$	−1.12801	−	0.574747i	−0.00163007	−	0.000830560i
$693$		0			0
$694$	−870.075	+	282.704i	−1.25371	+	0.407355i
$695$	422.168	+	417.369i	0.607436	+	0.600531i
$696$		0			0
$697$	323.871	+	635.633i	0.464665	+	0.911956i
$698$	543.217	+	86.0371i	0.778248	+	0.123262i
$699$		0			0
$700$	0.716418	−	0.732987i	0.00102345	−	0.00104712i
$701$	−317.355			−0.452718			−0.226359	−	0.974044i	$-0.572682\pi$
$701$	−317.355			−0.452718			−0.226359	+	0.974044i	$0.572682\pi$
$702$		0			0
$703$	187.555	−	95.5642i	0.266793	−	0.135938i
$704$	−206.220	−	67.0049i	−0.292926	−	0.0951774i
$705$		0			0
$706$	−253.584	−	780.453i	−0.359185	−	1.10546i
$707$	210.316	−	210.316i	0.297477	−	0.297477i
$708$		0			0
$709$	−600.695	+	826.785i	−0.847242	+	1.16613i	0.137221	+	0.990540i	$0.456183\pi$
$709$	−600.695	+	826.785i	−0.847242	+	1.16613i	−0.984464	+	0.175588i	$0.943817\pi$
$710$	−698.222	−	222.462i	−0.983412	−	0.313327i
$711$		0			0
$712$	561.293	−	88.9001i	0.788333	−	0.124860i
$713$	−5.42523	−	34.2536i	−0.00760902	−	0.0480415i
$714$		0			0
$715$	275.615	+	197.849i	0.385476	+	0.276712i
$716$	−1.57797	−	1.14646i	−0.00220387	−	0.00160121i
$717$		0			0
$718$	−193.882	−	193.882i	−0.270031	−	0.270031i
$719$	−1129.58	+	367.024i	−1.57105	+	0.510464i	−0.959730	−	0.280923i	$-0.909360\pi$
$719$	−1129.58	+	367.024i	−1.57105	+	0.510464i	−0.611316	+	0.791387i	$0.709360\pi$
$720$		0			0
$721$	201.046	−	618.755i	0.278843	−	0.858190i
$722$	292.810	+	574.672i	0.405554	+	0.795944i
$723$		0			0
$724$		−	1.01805i		−	0.00140614i
$725$	770.486	−	8.80813i	1.06274	−	0.0121491i
$726$		0			0
$727$	39.2430	−	247.771i	0.0539794	−	0.340813i	−0.945887	−	0.324495i	$-0.894806\pi$
$727$	39.2430	−	247.771i	0.0539794	−	0.340813i	0.999867	−	0.0163178i	$-0.00519433\pi$
$728$	−791.981	+	403.535i	−1.08789	+	0.554306i
$729$		0			0
$730$	−78.7940	+	516.578i	−0.107937	+	0.707641i
$731$	−202.701	−	623.848i	−0.277292	−	0.853417i
$732$		0			0
$733$	−119.145	+	233.835i	−0.162544	+	0.319011i	−0.957885	−	0.287151i	$-0.907292\pi$
$733$	−119.145	+	233.835i	−0.162544	+	0.319011i	0.795341	+	0.606162i	$0.207292\pi$
$734$	−617.060	+	849.311i	−0.840682	+	1.15710i
$735$		0			0
$736$	1.32676	−	0.963949i	0.00180267	−	0.00130971i
$737$	254.324	−	40.2810i	0.345080	−	0.0546553i
$738$		0			0
$739$	−419.335	−	577.165i	−0.567435	−	0.781008i	0.424813	−	0.905281i	$-0.360340\pi$
$739$	−419.335	−	577.165i	−0.567435	−	0.781008i	−0.992248	+	0.124273i	$0.960340\pi$
$740$	1.26167	−	0.00721142i	0.00170496	−	9.74516e-6i
$741$		0			0
$742$	−812.376	−	413.926i	−1.09485	−	0.557852i
$743$	9.34501	+	9.34501i	0.0125774	+	0.0125774i	0.713368	−	0.700790i	$-0.247169\pi$
$743$	9.34501	+	9.34501i	0.0125774	+	0.0125774i	−0.700790	+	0.713368i	$0.747169\pi$
$744$		0			0
$745$	51.9131	+	316.064i	0.0696820	+	0.424246i
$746$	107.051	−	329.468i	0.143500	−	0.441647i
$747$		0			0
$748$	−0.492015	−	0.0779276i	−0.000657774	−	0.000104181i
$749$			14.5714i			0.0194545i
$750$		0			0
$751$	−175.040			−0.233076			−0.116538	−	0.993186i	$-0.537180\pi$
$751$	−175.040			−0.233076			−0.116538	+	0.993186i	$0.537180\pi$
$752$	105.694	−	667.329i	0.140551	−	0.887405i
$753$		0			0
$754$	−1175.24	−	381.858i	−1.55867	−	0.506443i
$755$	−1122.69	+	184.401i	−1.48701	+	0.244240i
$756$		0			0
$757$	−331.826	+	331.826i	−0.438343	+	0.438343i	−0.891454	−	0.453111i	$-0.850314\pi$
$757$	−331.826	+	331.826i	−0.438343	+	0.438343i	0.453111	+	0.891454i	$0.350314\pi$
$758$	452.296	−	887.680i	0.596696	−	1.17108i
$759$		0			0
$760$	−1.41466	−	247.502i	−0.00186140	−	0.325661i
$761$	−854.871	+	621.100i	−1.12335	+	0.816163i	−0.984714	−	0.174180i	$-0.944273\pi$
$761$	−854.871	+	621.100i	−1.12335	+	0.816163i	−0.138638	+	0.990343i	$0.544273\pi$
$762$		0			0
$763$	114.415	+	722.386i	0.149954	+	0.946770i
$764$	0.826459	+	1.13752i	0.00108175	+	0.00148891i
$765$		0			0
$766$	164.030	+	119.175i	0.214138	+	0.155581i
$767$	46.6990	+	23.7943i	0.0608853	+	0.0310226i
$768$		0			0
$769$	−407.934	+	132.546i	−0.530474	+	0.172361i	−0.561993	−	0.827142i	$-0.689965\pi$
$769$	−407.934	+	132.546i	−0.530474	+	0.172361i	0.0315195	+	0.999503i	$0.489965\pi$
$770$	184.778	+	28.1843i	0.239971	+	0.0366030i
$771$		0			0
$772$	0.220416	+	0.432590i	0.000285512	+	0.000560350i
$773$	−209.109	−	33.1196i	−0.270516	−	0.0428456i	0.0197025	−	0.999806i	$-0.493728\pi$
$773$	−209.109	−	33.1196i	−0.270516	−	0.0428456i	−0.290219	+	0.956960i	$0.593728\pi$
$774$		0			0
$775$	−37.4231	−	50.2894i	−0.0482879	−	0.0648896i
$776$	−22.3722			−0.0288302
$777$		0			0
$778$	121.851	−	62.0859i	0.156620	−	0.0798020i
$779$	211.009	+	68.5610i	0.270872	+	0.0880116i
$780$		0			0
$781$	76.6509	+	235.907i	0.0981445	+	0.302058i
$782$	−388.440	+	388.440i	−0.496727	+	0.496727i
$783$		0			0
$784$	172.666	−	237.655i	0.220238	−	0.303131i
$785$	271.067	−	377.611i	0.345308	−	0.481034i
$786$		0			0
$787$	−506.378	+	80.2023i	−0.643428	+	0.101909i	−0.469617	−	0.882870i	$-0.655608\pi$
$787$	−506.378	+	80.2023i	−0.643428	+	0.101909i	−0.173811	+	0.984779i	$0.555608\pi$
$788$	0.317178	+	2.00258i	0.000402510	+	0.00254135i
$789$		0			0
$790$	119.303	−	374.445i	0.151016	−	0.473980i
$791$	−200.053	−	145.347i	−0.252911	−	0.183751i
$792$		0			0
$793$	−383.101	−	383.101i	−0.483104	−	0.483104i
$794$	−185.309	+	60.2105i	−0.233386	+	0.0758318i
$795$		0			0
$796$	0.453984	−	1.39722i	0.000570332	−	0.00175530i
$797$	−607.216	−	1191.73i	−0.761878	−	1.49527i	−0.865640	−	0.500667i	$-0.833088\pi$
$797$	−607.216	−	1191.73i	−0.761878	−	1.49527i	0.103762	−	0.994602i	$-0.466912\pi$
$798$		0			0
$799$		−	840.935i		−	1.05248i
$800$	1.31547	−	2.65640i	0.00164434	−	0.00332050i
$801$		0			0
$802$	−45.5544	+	287.619i	−0.0568010	+	0.358628i
$803$	157.600	−	80.3014i	0.196264	−	0.100002i
$804$		0			0
$805$	−268.979	+	272.071i	−0.334135	+	0.337977i
$806$	31.0655	+	95.6099i	0.0385428	+	0.118623i
$807$		0			0
$808$	195.444	−	383.580i	0.241886	−	0.474728i
$809$	82.9765	−	114.207i	0.102567	−	0.141171i	−0.754649	−	0.656129i	$-0.772193\pi$
$809$	82.9765	−	114.207i	0.102567	−	0.141171i	0.857215	+	0.514958i	$0.172193\pi$
$810$		0			0
$811$	105.885	−	76.9299i	0.130561	−	0.0948581i	−0.520588	−	0.853808i	$-0.674287\pi$
$811$	105.885	−	76.9299i	0.130561	−	0.0948581i	0.651149	+	0.758950i	$0.274287\pi$
$812$	1.24806	−	0.197674i	0.00153702	−	0.000243440i
$813$		0			0
$814$	135.242	+	186.145i	0.166145	+	0.228680i
$815$	200.223	+	604.447i	0.245673	+	0.741652i
$816$		0			0
$817$	−181.770	−	92.6165i	−0.222485	−	0.113362i
$818$	−142.203	−	142.203i	−0.173843	−	0.173843i
$819$		0			0
$820$	0.945699	+	0.934950i	0.00115329	+	0.00114018i
$821$	223.412	−	687.591i	0.272122	−	0.837504i	−0.717845	−	0.696203i	$-0.754871\pi$
$821$	223.412	−	687.591i	0.272122	−	0.837504i	0.989967	−	0.141301i	$-0.0451287\pi$
$822$		0			0
$823$	1267.47	+	200.748i	1.54006	+	0.243922i	0.867996	−	0.496571i	$-0.165408\pi$
$823$	1267.47	+	200.748i	1.54006	+	0.243922i	0.672065	+	0.740492i	$0.265408\pi$
$824$		−	941.672i		−	1.14281i
$825$		0			0
$826$	28.8747			0.0349573
$827$	26.4921	−	167.265i	0.0320340	−	0.202255i	−0.966481	−	0.256740i	$-0.917352\pi$
$827$	26.4921	−	167.265i	0.0320340	−	0.202255i	0.998515	+	0.0544850i	$0.0173517\pi$
$828$		0			0
$829$	1291.17	+	419.527i	1.55751	+	0.506064i	0.956140	−	0.292910i	$-0.0946235\pi$
$829$	1291.17	+	419.527i	1.55751	+	0.506064i	0.601366	+	0.798974i	$0.294624\pi$
$830$	448.653	+	225.379i	0.540546	+	0.271541i
$831$		0			0
$832$	−909.715	+	909.715i	−1.09341	+	1.09341i
$833$	165.988	−	325.771i	0.199266	−	0.391081i
$834$		0			0
$835$	−383.239	−	122.105i	−0.458969	−	0.146233i
$836$	−0.125339	+	0.0910640i	−0.000149927	+	0.000108928i
$837$		0			0
$838$	108.523	+	685.190i	0.129503	+	0.817649i
$839$	678.477	+	933.843i	0.808673	+	1.11304i	0.991527	+	0.129903i	$0.0414666\pi$
$839$	678.477	+	933.843i	0.808673	+	1.11304i	−0.182853	+	0.983140i	$0.558533\pi$
$840$		0			0
$841$	88.1522	+	64.0464i	0.104818	+	0.0761550i
$842$	454.827	+	231.746i	0.540175	+	0.275233i
$843$		0			0
$844$	2.65076	−	0.861285i	0.00314071	−	0.00102048i
$845$	1037.67	−	536.211i	1.22801	−	0.634569i
$846$		0			0
$847$	275.180	+	540.071i	0.324888	+	0.637628i
$848$	−1301.00	−	206.059i	−1.53420	−	0.242994i
$849$		0			0
$850$	−296.020	+	947.788i	−0.348259	+	1.11504i
$851$	−470.955			−0.553414
$852$		0			0
$853$	83.5286	−	42.5599i	0.0979233	−	0.0498944i	−0.404343	−	0.914607i	$-0.632500\pi$
$853$	83.5286	−	42.5599i	0.0979233	−	0.0498944i	0.502266	+	0.864713i	$0.332500\pi$
$854$	−283.874	−	92.2364i	−0.332406	−	0.108005i
$855$		0			0
$856$	6.51737	+	20.0584i	0.00761374	+	0.0234327i
$857$	−178.447	+	178.447i	−0.208223	+	0.208223i	−0.803512	−	0.595289i	$-0.797038\pi$
$857$	−178.447	+	178.447i	−0.208223	+	0.208223i	0.595289	+	0.803512i	$0.297038\pi$
$858$		0			0
$859$	−192.730	+	265.270i	−0.224366	+	0.308813i	−0.906328	−	0.422574i	$-0.861127\pi$
$859$	−192.730	+	265.270i	−0.224366	+	0.308813i	0.681963	+	0.731387i	$0.261127\pi$
$860$	−0.724372	−	0.985122i	−0.000842293	−	0.00114549i
$861$		0			0
$862$	−444.028	+	70.3271i	−0.515113	+	0.0815860i
$863$	−18.8095	−	118.758i	−0.0217954	−	0.137611i	0.974391	−	0.224860i	$-0.0721925\pi$
$863$	−18.8095	−	118.758i	−0.0217954	−	0.137611i	−0.996187	+	0.0872489i	$0.972192\pi$
$864$		0			0
$865$	854.148	−	4.88211i	0.987455	−	0.00564406i
$866$	−63.0351	−	45.7977i	−0.0727888	−	0.0528842i
$867$		0			0
$868$	−0.0726905	−	0.0726905i	−8.37449e−5	−	8.37449e-5i
$869$	−126.513	+	41.1065i	−0.145584	+	0.0473033i
$870$		0			0
$871$	472.113	−	1453.01i	0.542036	−	1.66821i
$872$	480.600	+	943.230i	0.551147	+	1.08169i
$873$		0			0
$874$			170.847i			0.195478i
$875$	−202.387	+	661.255i	−0.231300	+	0.755720i
$876$		0			0
$877$	142.712	−	901.047i	0.162727	−	1.02742i	−0.762218	−	0.647320i	$-0.775890\pi$
$877$	142.712	−	901.047i	0.162727	−	1.02742i	0.924945	−	0.380100i	$-0.124110\pi$
$878$	408.822	−	208.305i	0.465628	−	0.237249i
$879$		0			0
$880$	266.469	−	43.7672i	0.302805	−	0.0497354i
$881$	−422.625	−	1300.71i	−0.479710	−	1.47640i	−0.839498	−	0.543363i	$-0.817151\pi$
$881$	−422.625	−	1300.71i	−0.479710	−	1.47640i	0.359788	−	0.933034i	$-0.382849\pi$
$882$		0			0
$883$	700.304	−	1374.42i	0.793096	−	1.55654i	−0.0372608	−	0.999306i	$-0.511863\pi$
$883$	700.304	−	1374.42i	0.793096	−	1.55654i	0.830357	−	0.557232i	$-0.188137\pi$
$884$	−1.73729	+	2.39118i	−0.00196527	+	0.00270496i
$885$		0			0
$886$	−1177.20	+	855.287i	−1.32867	+	0.965335i
$887$	−359.608	+	56.9563i	−0.405421	+	0.0642123i	−0.355815	−	0.934557i	$-0.615797\pi$
$887$	−359.608	+	56.9563i	−0.405421	+	0.0642123i	−0.0496060	+	0.998769i	$0.515797\pi$
$888$		0			0
$889$	553.658	+	762.045i	0.622787	+	0.857193i
$890$	−571.241	+	420.040i	−0.641843	+	0.471955i
$891$		0			0
$892$	−2.57591	−	1.31249i	−0.00288779	−	0.00147140i
$893$	−184.934	−	184.934i	−0.207093	−	0.207093i
$894$		0			0
$895$	1300.94	+	198.434i	1.45357	+	0.221713i
$896$	−218.214	+	671.595i	−0.243543	+	0.749548i
$897$		0			0
$898$	1475.29	+	233.662i	1.64286	+	0.260203i
$899$		−	77.2828i		−	0.0859653i
$900$		0			0
$901$	−1639.46			−1.81960
$902$	−37.9379	+	239.530i	−0.0420597	+	0.265555i
$903$		0			0
$904$	−340.394	−	110.601i	−0.376542	−	0.122346i
$905$	315.327	+	610.217i	0.348428	+	0.674273i
$906$		0			0
$907$	45.1187	−	45.1187i	0.0497450	−	0.0497450i	−0.681797	−	0.731542i	$-0.738801\pi$
$907$	45.1187	−	45.1187i	0.0497450	−	0.0497450i	0.731542	+	0.681797i	$0.238801\pi$
$908$	1.41903	−	2.78500i	0.00156280	−	0.00306718i
$909$		0			0
$910$	646.728	−	900.929i	0.710690	−	0.990032i
$911$	274.452	−	199.401i	0.301265	−	0.218882i	−0.426874	−	0.904311i	$-0.640385\pi$
$911$	274.452	−	199.401i	0.301265	−	0.218882i	0.728139	+	0.685429i	$0.240385\pi$
$912$		0			0
$913$	−26.5860	−	167.857i	−0.0291193	−	0.183852i
$914$	219.027	+	301.465i	0.239636	+	0.329830i
$915$		0			0
$916$	1.71972	+	1.24945i	0.00187743	+	0.00136403i
$917$	−258.460	−	131.692i	−0.281853	−	0.143611i
$918$		0			0
$919$	−240.689	+	78.2047i	−0.261903	+	0.0850976i	−0.437025	−	0.899449i	$-0.643968\pi$
$919$	−240.689	+	78.2047i	−0.261903	+	0.0850976i	0.175122	+	0.984547i	$0.443968\pi$
$920$	−248.575	+	494.828i	−0.270190	+	0.537856i
$921$		0			0
$922$	−164.823	−	323.484i	−0.178767	−	0.350851i
$923$	1453.62	+	230.231i	1.57489	+	0.249437i
$924$		0			0
$925$	−754.013	+	395.110i	−0.815150	+	0.427146i
$926$	900.972			0.972972
$927$		0			0
$928$	3.25622	−	1.65912i	0.00350885	−	0.00178785i
$929$	658.494	+	213.958i	0.708820	+	0.230310i	0.641169	−	0.767399i	$-0.278450\pi$
$929$	658.494	+	213.958i	0.708820	+	0.230310i	0.0676508	+	0.997709i	$0.478450\pi$
$930$		0			0
$931$	−35.1385	−	108.145i	−0.0377427	−	0.116160i
$932$	−1.01427	+	1.01427i	−0.00108827	+	0.00108827i
$933$		0			0
$934$	448.768	−	617.676i	0.480480	−	0.661324i
$935$	319.052	−	105.686i	0.341232	−	0.113033i
$936$		0			0
$937$	218.653	−	34.6312i	0.233354	−	0.0369596i	−0.0386622	−	0.999252i	$-0.512310\pi$
$937$	218.653	−	34.6312i	0.233354	−	0.0369596i	0.272016	+	0.962293i	$0.412310\pi$
$938$	−131.670	−	831.333i	−0.140373	−	0.886282i
$939$		0			0
$940$	−0.492930	−	1.48809i	−0.000524394	−	0.00158307i
$941$	−164.559	−	119.559i	−0.174876	−	0.127055i	0.496904	−	0.867805i	$-0.334470\pi$
$941$	−164.559	−	119.559i	−0.174876	−	0.127055i	−0.671780	+	0.740750i	$0.734470\pi$
$942$		0			0
$943$	−351.003	−	351.003i	−0.372220	−	0.372220i
$944$	39.6741	−	12.8909i	0.0420276	−	0.0136556i
$945$		0			0
$946$	68.9080	−	212.077i	0.0728415	−	0.224183i
$947$	−544.018	−	1067.69i	−0.574464	−	1.12745i	−0.977237	−	0.212150i	$-0.931954\pi$
$947$	−544.018	−	1067.69i	−0.574464	−	1.12745i	0.402773	−	0.915300i	$-0.368046\pi$
$948$		0			0
$949$		−	1049.48i		−	1.10588i
$950$	143.333	+	273.532i	0.150877	+	0.287928i
$951$		0			0
$952$	−137.747	+	869.701i	−0.144692	+	0.913552i
$953$	863.782	−	440.119i	0.906382	−	0.461825i	0.0623115	−	0.998057i	$-0.480153\pi$
$953$	863.782	−	440.119i	0.906382	−	0.461825i	0.844071	+	0.536232i	$0.180153\pi$
$954$		0			0
$955$	−847.715	−	425.847i	−0.887660	−	0.445913i
$956$	0.136355	+	0.419657i	0.000142631	+	0.000438972i
$957$		0			0
$958$	317.691	−	623.504i	0.331619	−	0.650839i
$959$	−165.638	+	227.981i	−0.172719	+	0.237728i
$960$		0			0
$961$	772.379	−	561.166i	0.803724	−	0.583940i
$962$	1348.37	−	213.561i	1.40164	−	0.221997i
$963$		0			0
$964$	1.94385	+	2.67547i	0.00201644	+	0.00277539i
$965$	−266.107	−	191.024i	−0.275758	−	0.197952i
$966$		0			0
$967$	394.896	+	201.209i	0.408372	+	0.208076i	0.646095	−	0.763257i	$-0.276401\pi$
$967$	394.896	+	201.209i	0.408372	+	0.208076i	−0.237723	+	0.971333i	$0.576401\pi$
$968$	620.359	+	620.359i	0.640866	+	0.640866i
$969$		0			0
$970$	24.7983	−	12.8144i	0.0255653	−	0.0132108i
$971$	−53.8408	+	165.705i	−0.0554488	+	0.170654i	−0.974946	−	0.222444i	$-0.928597\pi$
$971$	−53.8408	+	165.705i	−0.0554488	+	0.170654i	0.919497	+	0.393098i	$0.128597\pi$
$972$		0			0
$973$	−648.762	−	102.754i	−0.666765	−	0.105605i
$974$			1614.83i			1.65793i
$975$		0			0
$976$	−431.223			−0.441827
$977$	257.214	−	1623.99i	0.263269	−	1.66222i	−0.402020	−	0.915631i	$-0.631692\pi$
$977$	257.214	−	1623.99i	0.263269	−	1.66222i	0.665289	−	0.746586i	$-0.268308\pi$
$978$		0			0
$979$	228.259	+	74.1659i	0.233155	+	0.0757568i
$980$	0.102770	−	0.673769i	0.000104868	−	0.000687520i
$981$		0			0
$982$	744.456	−	744.456i	0.758102	−	0.758102i
$983$	−378.134	+	742.129i	−0.384673	+	0.754964i	−0.999430	−	0.0337529i	$-0.989254\pi$
$983$	−378.134	+	742.129i	−0.384673	+	0.754964i	0.614757	+	0.788717i	$0.289254\pi$
$984$		0			0
$985$	−810.392	−	1102.11i	−0.822733	−	1.11889i
$986$	−990.361	+	719.540i	−1.00442	+	0.729756i
$987$		0			0
$988$	0.143799	+	0.907912i	0.000145546	+	0.000918940i
$989$	268.282	+	369.259i	0.271266	+	0.373366i
$990$		0			0
$991$	−238.832	−	173.522i	−0.241001	−	0.175098i	0.460728	−	0.887541i	$-0.347588\pi$
$991$	−238.832	−	173.522i	−0.241001	−	0.175098i	−0.701729	+	0.712444i	$0.747588\pi$
$992$	−0.264905	−	0.134976i	−0.000267041	−	0.000136064i
$993$		0			0
$994$	771.132	−	250.556i	0.775786	−	0.252068i
$995$	160.654	+	978.111i	0.161461	+	0.983026i
$996$		0			0
$997$	410.202	+	805.068i	0.411437	+	0.807490i	1.00000		0.000961470i	$-0.000306045\pi$
$997$	410.202	+	805.068i	0.411437	+	0.807490i	−0.588563	+	0.808451i	$0.700306\pi$
$998$	1122.42	+	177.774i	1.12467	+	0.178131i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.r.a.73.3		32
3.2	odd	2		25.3.f.a.23.2	yes	32
12.11	even	2		400.3.bg.c.273.4		32
15.2	even	4		125.3.f.a.32.2		32
15.8	even	4		125.3.f.b.32.3		32
15.14	odd	2		125.3.f.c.93.3		32
25.12	odd	20	inner	225.3.r.a.37.3		32
75.38	even	20		125.3.f.c.82.3		32
75.41	odd	10		125.3.f.a.43.2		32
75.59	odd	10		125.3.f.b.43.3		32
75.62	even	20		25.3.f.a.12.2	✓	32
300.287	odd	20		400.3.bg.c.337.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.12.2	✓	32	75.62	even	20
25.3.f.a.23.2	yes	32	3.2	odd	2
125.3.f.a.32.2		32	15.2	even	4
125.3.f.a.43.2		32	75.41	odd	10
125.3.f.b.32.3		32	15.8	even	4
125.3.f.b.43.3		32	75.59	odd	10
125.3.f.c.82.3		32	75.38	even	20
125.3.f.c.93.3		32	15.14	odd	2
225.3.r.a.37.3		32	25.12	odd	20	inner
225.3.r.a.73.3		32	1.1	even	1	trivial
400.3.bg.c.273.4		32	12.11	even	2
400.3.bg.c.337.4		32	300.287	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.312579 - 1.97355i) q^{2} +(0.00704800 + 0.00229003i) q^{4} +(-4.93389 + 0.810386i) q^{5} +(3.91191 - 3.91191i) q^{7} +(3.63528 - 7.13464i) q^{8} +O(q^{10})\)	\(q+(0.312579 - 1.97355i) q^{2} +(0.00704800 + 0.00229003i) q^{4} +(-4.93389 + 0.810386i) q^{5} +(3.91191 - 3.91191i) q^{7} +(3.63528 - 7.13464i) q^{8} +(0.0571038 + 9.99057i) q^{10} +(2.73590 - 1.98775i) q^{11} +(-3.13886 - 19.8180i) q^{13} +(-6.49755 - 8.94311i) q^{14} +(-12.9202 - 9.38711i) q^{16} +(-17.7107 - 9.02407i) q^{17} +(-5.87938 + 1.91032i) q^{19} +(-0.0366299 - 0.00558718i) q^{20} +(-3.06773 - 6.02076i) q^{22} +(13.6608 + 2.16366i) q^{23} +(23.6865 - 7.99671i) q^{25} -40.0928 q^{26} +(0.0365295 - 0.0186127i) q^{28} +(29.3129 + 9.52435i) q^{29} +(-0.774840 - 2.38471i) q^{31} +(0.0838425 - 0.0838425i) q^{32} +(-23.3454 + 32.1322i) q^{34} +(-16.1308 + 22.4711i) q^{35} +(-33.6313 + 5.32667i) q^{37} +(1.93234 + 12.2003i) q^{38} +(-12.1543 + 38.1475i) q^{40} +(-29.0354 - 21.0954i) q^{41} +(23.3347 + 23.3347i) q^{43} +(0.0238347 - 0.00774436i) q^{44} +(8.54016 - 26.2839i) q^{46} +(19.2067 + 37.6953i) q^{47} +18.3940i q^{49} +(-8.37796 - 49.2461i) q^{50} +(0.0232612 - 0.146865i) q^{52} +(73.4897 - 37.4449i) q^{53} +(-11.8878 + 12.0245i) q^{55} +(-13.6892 - 42.1309i) q^{56} +(27.9594 - 54.8733i) q^{58} +(-1.53534 + 2.11322i) q^{59} +(21.8447 - 15.8711i) q^{61} +(-4.94854 + 0.783771i) q^{62} +(-37.6877 - 51.8727i) q^{64} +(31.5470 + 95.2360i) q^{65} +(67.8430 + 34.5677i) q^{67} +(-0.104160 - 0.104160i) q^{68} +(39.3056 + 38.8588i) q^{70} +(-22.6659 + 69.7586i) q^{71} +(51.6598 + 8.18211i) q^{73} +68.0379i q^{74} -0.0458126 q^{76} +(2.92671 - 18.4785i) q^{77} +(-37.4103 - 12.1554i) q^{79} +(71.3543 + 35.8446i) q^{80} +(-50.7087 + 50.7087i) q^{82} +(22.8152 - 44.7773i) q^{83} +(94.6958 + 30.1712i) q^{85} +(53.3460 - 38.7581i) q^{86} +(-4.23611 - 26.7457i) q^{88} +(41.7155 + 57.4164i) q^{89} +(-89.8050 - 65.2472i) q^{91} +(0.0913265 + 0.0465332i) q^{92} +(80.3971 - 26.1226i) q^{94} +(27.4601 - 14.1899i) q^{95} +(-1.26842 - 2.48942i) q^{97} +(36.3014 + 5.74957i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} - 10 q^{4} + 10 q^{5} - 10 q^{7} + 10 q^{8}+O(q^{10}) \) 32 * q + 10 * q^2 - 10 * q^4 + 10 * q^5 - 10 * q^7 + 10 * q^8	\( 32 q + 10 q^{2} - 10 q^{4} + 10 q^{5} - 10 q^{7} + 10 q^{8} - 10 q^{10} + 6 q^{11} - 10 q^{13} + 10 q^{14} + 2 q^{16} - 60 q^{17} + 90 q^{19} - 130 q^{20} + 70 q^{22} - 10 q^{23} - 40 q^{25} - 4 q^{26} - 250 q^{28} + 110 q^{29} - 6 q^{31} + 290 q^{32} - 260 q^{34} + 120 q^{35} + 50 q^{37} - 320 q^{38} + 440 q^{40} + 86 q^{41} + 230 q^{43} - 340 q^{44} - 6 q^{46} - 70 q^{47} + 100 q^{50} - 320 q^{52} + 190 q^{53} - 250 q^{55} + 70 q^{56} - 640 q^{58} + 260 q^{59} + 114 q^{61} - 60 q^{62} + 340 q^{64} - 360 q^{65} + 270 q^{67} - 710 q^{68} + 310 q^{70} + 66 q^{71} + 30 q^{73} - 80 q^{76} + 250 q^{77} - 210 q^{79} + 850 q^{80} + 30 q^{82} + 600 q^{85} + 6 q^{86} + 190 q^{88} + 10 q^{89} - 6 q^{91} + 30 q^{92} + 790 q^{94} - 310 q^{95} + 270 q^{97} - 170 q^{98}+O(q^{100}) \) 32 * q + 10 * q^2 - 10 * q^4 + 10 * q^5 - 10 * q^7 + 10 * q^8 - 10 * q^10 + 6 * q^11 - 10 * q^13 + 10 * q^14 + 2 * q^16 - 60 * q^17 + 90 * q^19 - 130 * q^20 + 70 * q^22 - 10 * q^23 - 40 * q^25 - 4 * q^26 - 250 * q^28 + 110 * q^29 - 6 * q^31 + 290 * q^32 - 260 * q^34 + 120 * q^35 + 50 * q^37 - 320 * q^38 + 440 * q^40 + 86 * q^41 + 230 * q^43 - 340 * q^44 - 6 * q^46 - 70 * q^47 + 100 * q^50 - 320 * q^52 + 190 * q^53 - 250 * q^55 + 70 * q^56 - 640 * q^58 + 260 * q^59 + 114 * q^61 - 60 * q^62 + 340 * q^64 - 360 * q^65 + 270 * q^67 - 710 * q^68 + 310 * q^70 + 66 * q^71 + 30 * q^73 - 80 * q^76 + 250 * q^77 - 210 * q^79 + 850 * q^80 + 30 * q^82 + 600 * q^85 + 6 * q^86 + 190 * q^88 + 10 * q^89 - 6 * q^91 + 30 * q^92 + 790 * q^94 - 310 * q^95 + 270 * q^97 - 170 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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