LMFDB - Embedded newform 300.3.l.g.107.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(107,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("300.107");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.l (of order $4$, degree $2$, 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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.17
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75394 - 0.961083i) q^{2} +(-0.903948 - 2.86057i) q^{3} +(2.15264 - 3.37137i) q^{4} +(-4.33472 - 4.14852i) q^{6} +(7.30016 - 7.30016i) q^{7} +(0.535443 - 7.98206i) q^{8} +(-7.36576 + 5.17162i) q^{9} +O(q^{10})$	\(q+(1.75394 - 0.961083i) q^{2} +(-0.903948 - 2.86057i) q^{3} +(2.15264 - 3.37137i) q^{4} +(-4.33472 - 4.14852i) q^{6} +(7.30016 - 7.30016i) q^{7} +(0.535443 - 7.98206i) q^{8} +(-7.36576 + 5.17162i) q^{9} +4.41713 q^{11} +(-11.5899 - 3.11024i) q^{12} +(-7.53253 + 7.53253i) q^{13} +(5.78801 - 19.8201i) q^{14} +(-6.73229 - 14.5147i) q^{16} +(0.350578 - 0.350578i) q^{17} +(-7.94877 + 16.1498i) q^{18} +9.24359 q^{19} +(-27.4816 - 14.2837i) q^{21} +(7.74740 - 4.24523i) q^{22} +(-17.9810 + 17.9810i) q^{23} +(-23.3173 + 5.68370i) q^{24} +(-5.97225 + 20.4510i) q^{26} +(21.4521 + 16.3954i) q^{27} +(-8.89693 - 40.3261i) q^{28} +5.52099 q^{29} -48.1716i q^{31} +(-25.7579 - 18.9877i) q^{32} +(-3.99285 - 12.6355i) q^{33} +(0.277960 - 0.951830i) q^{34} +(1.57963 + 35.9653i) q^{36} +(-3.39462 - 3.39462i) q^{37} +(16.2127 - 8.88386i) q^{38} +(28.3564 + 14.7383i) q^{39} +33.0983i q^{41} +(-61.9290 + 1.35933i) q^{42} +(-1.45103 - 1.45103i) q^{43} +(9.50848 - 14.8918i) q^{44} +(-14.2565 + 48.8190i) q^{46} +(27.8943 + 27.8943i) q^{47} +(-35.4347 + 32.3787i) q^{48} -57.5846i q^{49} +(-1.31976 - 0.685951i) q^{51} +(9.18014 + 41.6098i) q^{52} +(52.6835 + 52.6835i) q^{53} +(53.3830 + 8.13943i) q^{54} +(-54.3615 - 62.1791i) q^{56} +(-8.35573 - 26.4420i) q^{57} +(9.68351 - 5.30613i) q^{58} +24.6578i q^{59} +46.1739 q^{61} +(-46.2969 - 84.4904i) q^{62} +(-16.0176 + 91.5248i) q^{63} +(-63.4266 - 8.54787i) q^{64} +(-19.1470 - 18.3245i) q^{66} +(32.1110 - 32.1110i) q^{67} +(-0.427261 - 1.93660i) q^{68} +(67.6900 + 35.1822i) q^{69} +116.455 q^{71} +(37.3362 + 61.5630i) q^{72} +(72.2123 - 72.2123i) q^{73} +(-9.21650 - 2.69147i) q^{74} +(19.8981 - 31.1636i) q^{76} +(32.2457 - 32.2457i) q^{77} +(63.9003 - 1.40260i) q^{78} -55.9466 q^{79} +(27.5087 - 76.1858i) q^{81} +(31.8102 + 58.0526i) q^{82} +(46.5302 - 46.5302i) q^{83} +(-107.314 + 61.9031i) q^{84} +(-3.93959 - 1.15047i) q^{86} +(-4.99069 - 15.7932i) q^{87} +(2.36512 - 35.2578i) q^{88} -33.2025 q^{89} +109.977i q^{91} +(21.9141 + 99.3275i) q^{92} +(-137.798 + 43.5447i) q^{93} +(75.7338 + 22.1163i) q^{94} +(-31.0319 + 90.8462i) q^{96} +(24.6341 + 24.6341i) q^{97} +(-55.3436 - 101.000i) q^{98} +(-32.5355 + 22.8437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.75394	−	0.961083i	0.876972	−	0.480541i
$2$	1.75394	−	0.961083i	0.876972	−	0.480541i
$3$	−0.903948	−	2.86057i	−0.301316	−	0.953524i
$3$	−0.903948	−	2.86057i	−0.301316	−	0.953524i
$4$	2.15264	−	3.37137i	0.538160	−	0.842843i
$5$		0			0
$5$		0			0
$6$	−4.33472	−	4.14852i	−0.722454	−	0.691419i
$7$	7.30016	−	7.30016i	1.04288	−	1.04288i	0.0438411	−	0.999039i	$-0.486040\pi$
$7$	7.30016	−	7.30016i	1.04288	−	1.04288i	0.999039	−	0.0438411i	$-0.0139595\pi$
$8$	0.535443	−	7.98206i	0.0669303	−	0.997758i
$9$	−7.36576	+	5.17162i	−0.818417	+	0.574624i
$10$		0			0
$11$	4.41713			0.401557			0.200779	−	0.979637i	$-0.435653\pi$
$11$	4.41713			0.401557			0.200779	+	0.979637i	$0.435653\pi$
$12$	−11.5899	−	3.11024i	−0.965827	−	0.259187i
$13$	−7.53253	+	7.53253i	−0.579426	+	0.579426i	−0.934745	−	0.355319i	$-0.884372\pi$
$13$	−7.53253	+	7.53253i	−0.579426	+	0.579426i	0.355319	+	0.934745i	$0.384372\pi$
$14$	5.78801	−	19.8201i	0.413429	−	1.41572i
$15$		0			0
$16$	−6.73229	−	14.5147i	−0.420768	−	0.907168i
$17$	0.350578	−	0.350578i	0.0206223	−	0.0206223i	−0.696720	−	0.717343i	$-0.745358\pi$
$17$	0.350578	−	0.350578i	0.0206223	−	0.0206223i	0.717343	+	0.696720i	$0.245358\pi$
$18$	−7.94877	+	16.1498i	−0.441598	+	0.897213i
$19$	9.24359			0.486505			0.243252	−	0.969963i	$-0.421786\pi$
$19$	9.24359			0.486505			0.243252	+	0.969963i	$0.421786\pi$
$20$		0			0
$21$	−27.4816	−	14.2837i	−1.30865	−	0.680175i
$22$	7.74740	−	4.24523i	0.352154	−	0.192965i
$23$	−17.9810	+	17.9810i	−0.781785	+	0.781785i	−0.980132	−	0.198347i	$-0.936443\pi$
$23$	−17.9810	+	17.9810i	−0.781785	+	0.781785i	0.198347	+	0.980132i	$0.436443\pi$
$24$	−23.3173	+	5.68370i	−0.971553	+	0.236821i
$25$		0			0
$26$	−5.97225	+	20.4510i	−0.229702	+	0.786578i
$27$	21.4521	+	16.3954i	0.794520	+	0.607237i
$28$	−8.89693	−	40.3261i	−0.317748	−	1.44022i
$29$	5.52099			0.190379			0.0951895	−	0.995459i	$-0.469654\pi$
$29$	5.52099			0.190379			0.0951895	+	0.995459i	$0.469654\pi$
$30$		0			0
$31$		−	48.1716i		−	1.55392i	−0.629548	−	0.776962i	$-0.716760\pi$
$31$		−	48.1716i		−	1.55392i	0.629548	−	0.776962i	$-0.283240\pi$
$32$	−25.7579	−	18.9877i	−0.804934	−	0.593365i
$33$	−3.99285	−	12.6355i	−0.120996	−	0.382894i
$34$	0.277960	−	0.951830i	0.00817530	−	0.0279950i
$35$		0			0
$36$	1.57963	+	35.9653i	0.0438785	+	0.999037i
$37$	−3.39462	−	3.39462i	−0.0917466	−	0.0917466i	0.659744	−	0.751491i	$-0.270665\pi$
$37$	−3.39462	−	3.39462i	−0.0917466	−	0.0917466i	−0.751491	+	0.659744i	$0.770665\pi$
$38$	16.2127	−	8.88386i	0.426651	−	0.233786i
$39$	28.3564	+	14.7383i	0.727087	+	0.377906i
$40$		0			0
$41$			33.0983i			0.807276i	0.914919	+	0.403638i	$0.132254\pi$
$41$			33.0983i			0.807276i	−0.914919	+	0.403638i	$0.867746\pi$
$42$	−61.9290	+	1.35933i	−1.47450	+	0.0323650i
$43$	−1.45103	−	1.45103i	−0.0337449	−	0.0337449i	0.690033	−	0.723778i	$-0.257596\pi$
$43$	−1.45103	−	1.45103i	−0.0337449	−	0.0337449i	−0.723778	+	0.690033i	$0.757596\pi$
$44$	9.50848	−	14.8918i	0.216102	−	0.338449i
$45$		0			0
$46$	−14.2565	+	48.8190i	−0.309923	+	1.06128i
$47$	27.8943	+	27.8943i	0.593496	+	0.593496i	0.938574	−	0.345078i	$-0.112147\pi$
$47$	27.8943	+	27.8943i	0.593496	+	0.593496i	−0.345078	+	0.938574i	$0.612147\pi$
$48$	−35.4347	+	32.3787i	−0.738223	+	0.674557i
$49$		−	57.5846i		−	1.17520i
$50$		0			0
$51$	−1.31976	−	0.685951i	−0.0258776	−	0.0134500i
$52$	9.18014	+	41.6098i	0.176541	+	0.800188i
$53$	52.6835	+	52.6835i	0.994028	+	0.994028i	0.999982	−	0.00595455i	$-0.00189540\pi$
$53$	52.6835	+	52.6835i	0.994028	+	0.994028i	−0.00595455	+	0.999982i	$0.501895\pi$
$54$	53.3830	+	8.13943i	0.988575	+	0.150730i
$55$		0			0
$56$	−54.3615	−	62.1791i	−0.970741	−	1.11034i
$57$	−8.35573	−	26.4420i	−0.146592	−	0.463894i
$58$	9.68351	−	5.30613i	0.166957	−	0.0914850i
$59$			24.6578i			0.417929i	0.977923	+	0.208964i	$0.0670093\pi$
$59$			24.6578i			0.417929i	−0.977923	+	0.208964i	$0.932991\pi$
$60$		0			0
$61$	46.1739			0.756950			0.378475	−	0.925612i	$-0.376449\pi$
$61$	46.1739			0.756950			0.378475	+	0.925612i	$0.376449\pi$
$62$	−46.2969	−	84.4904i	−0.746725	−	1.36275i
$63$	−16.0176	+	91.5248i	−0.254247	+	1.45277i
$64$	−63.4266	−	8.54787i	−0.991041	−	0.133560i
$65$		0			0
$66$	−19.1470	−	18.3245i	−0.290106	−	0.277644i
$67$	32.1110	−	32.1110i	0.479269	−	0.479269i	−0.425629	−	0.904898i	$-0.639947\pi$
$67$	32.1110	−	32.1110i	0.479269	−	0.479269i	0.904898	+	0.425629i	$0.139947\pi$
$68$	−0.427261	−	1.93660i	−0.00628325	−	0.0284794i
$69$	67.6900	+	35.1822i	0.981015	+	0.509887i
$70$		0			0
$71$	116.455			1.64021			0.820103	−	0.572216i	$-0.193916\pi$
$71$	116.455			1.64021			0.820103	+	0.572216i	$0.193916\pi$
$72$	37.3362	+	61.5630i	0.518559	+	0.855042i
$73$	72.2123	−	72.2123i	0.989210	−	0.989210i	−0.0107324	−	0.999942i	$-0.503416\pi$
$73$	72.2123	−	72.2123i	0.989210	−	0.989210i	0.999942	+	0.0107324i	$0.00341629\pi$
$74$	−9.21650	−	2.69147i	−0.124547	−	0.0363712i
$75$		0			0
$76$	19.8981	−	31.1636i	0.261817	−	0.410047i
$77$	32.2457	−	32.2457i	0.418776	−	0.418776i
$78$	63.9003	−	1.40260i	0.819234	−	0.0179821i
$79$	−55.9466			−0.708185			−0.354092	−	0.935210i	$-0.615210\pi$
$79$	−55.9466			−0.708185			−0.354092	+	0.935210i	$0.615210\pi$
$80$		0			0
$81$	27.5087	−	76.1858i	0.339614	−	0.940565i
$82$	31.8102	+	58.0526i	0.387929	+	0.707958i
$83$	46.5302	−	46.5302i	0.560605	−	0.560605i	−0.368874	−	0.929479i	$-0.620257\pi$
$83$	46.5302	−	46.5302i	0.560605	−	0.560605i	0.929479	+	0.368874i	$0.120257\pi$
$84$	−107.314	+	61.9031i	−1.27754	+	0.736941i
$85$		0			0
$86$	−3.93959	−	1.15047i	−0.0458092	−	0.0133775i
$87$	−4.99069	−	15.7932i	−0.0573642	−	0.181531i
$88$	2.36512	−	35.2578i	0.0268763	−	0.400657i
$89$	−33.2025			−0.373062			−0.186531	−	0.982449i	$-0.559724\pi$
$89$	−33.2025			−0.373062			−0.186531	+	0.982449i	$0.559724\pi$
$90$		0			0
$91$			109.977i			1.20854i
$92$	21.9141	+	99.3275i	0.238196	+	1.07965i
$93$	−137.798	+	43.5447i	−1.48170	+	0.468222i
$94$	75.7338	+	22.1163i	0.805679	+	0.235280i
$95$		0			0
$96$	−31.0319	+	90.8462i	−0.323248	+	0.946314i
$97$	24.6341	+	24.6341i	0.253959	+	0.253959i	0.822592	−	0.568632i	$-0.192527\pi$
$97$	24.6341	+	24.6341i	0.253959	+	0.253959i	−0.568632	+	0.822592i	$0.692527\pi$
$98$	−55.3436	−	101.000i	−0.564730	−	1.03061i
$99$	−32.5355	+	22.8437i	−0.328641	+	0.230744i
$100$		0			0
$101$			12.2683i			0.121468i	0.998154	+	0.0607342i	$0.0193442\pi$
$101$			12.2683i			0.121468i	−0.998154	+	0.0607342i	$0.980656\pi$
$102$	−2.97404	+	0.0652797i	−0.0291573	+	0.000639997i
$103$	−21.2333	−	21.2333i	−0.206149	−	0.206149i	0.596479	−	0.802628i	$-0.296566\pi$
$103$	−21.2333	−	21.2333i	−0.206149	−	0.206149i	−0.802628	+	0.596479i	$0.796566\pi$
$104$	56.0919	+	64.1584i	0.539345	+	0.616907i
$105$		0			0
$106$	143.037	+	41.7707i	1.34941	+	0.394063i
$107$	77.4288	+	77.4288i	0.723634	+	0.723634i	0.969343	−	0.245710i	$-0.0790210\pi$
$107$	77.4288	+	77.4288i	0.723634	+	0.723634i	−0.245710	+	0.969343i	$0.579021\pi$
$108$	101.454	−	37.0294i	0.939385	−	0.342865i
$109$			62.5243i			0.573618i	0.957988	+	0.286809i	$0.0925945\pi$
$109$			62.5243i			0.573618i	−0.957988	+	0.286809i	$0.907406\pi$
$110$		0			0
$111$	−6.64201	+	12.7791i	−0.0598379	+	0.115127i
$112$	−155.106	−	56.8128i	−1.38488	−	0.507257i
$113$	−64.0685	−	64.0685i	−0.566977	−	0.566977i	0.364303	−	0.931280i	$-0.381307\pi$
$113$	−64.0685	−	64.0685i	−0.566977	−	0.566977i	−0.931280	+	0.364303i	$0.881307\pi$
$114$	−40.0684	−	38.3472i	−0.351477	−	0.336379i
$115$		0			0
$116$	11.8847	−	18.6133i	0.102454	−	0.160460i
$117$	16.5274	−	94.4382i	0.141260	−	0.807164i
$118$	23.6982	+	43.2484i	0.200832	+	0.366512i
$119$		−	5.11856i		−	0.0430131i
$120$		0			0
$121$	−101.489			−0.838752
$122$	80.9865	−	44.3770i	0.663824	−	0.363746i
$123$	94.6801	−	29.9191i	0.769757	−	0.243245i
$124$	−162.404	−	103.696i	−1.30971	−	0.836259i
$125$		0			0
$126$	59.8690	+	175.924i	0.475151	+	1.39622i
$127$	−36.2102	+	36.2102i	−0.285120	+	0.285120i	−0.835147	−	0.550027i	$-0.814617\pi$
$127$	−36.2102	+	36.2102i	−0.285120	+	0.285120i	0.550027	+	0.835147i	$0.314617\pi$
$128$	−119.462	+	45.9657i	−0.933296	+	0.359107i
$129$	−2.83912	+	5.46244i	−0.0220087	+	0.0423445i
$130$		0			0
$131$	−78.8270			−0.601733			−0.300866	−	0.953666i	$-0.597276\pi$
$131$	−78.8270			−0.601733			−0.300866	+	0.953666i	$0.597276\pi$
$132$	−51.1942	−	13.7383i	−0.387835	−	0.104078i
$133$	67.4797	−	67.4797i	0.507366	−	0.507366i
$134$	25.4596	−	87.1822i	0.189997	−	0.650614i
$135$		0			0
$136$	−2.61062	−	2.98605i	−0.0191958	−	0.0219563i
$137$	−178.746	+	178.746i	−1.30472	+	1.30472i	−0.379544	+	0.925174i	$0.623919\pi$
$137$	−178.746	+	178.746i	−1.30472	+	1.30472i	−0.925174	+	0.379544i	$0.876081\pi$
$138$	152.538	−	3.34817i	1.10534	−	0.0242621i
$139$	15.4896			0.111436			0.0557180	−	0.998447i	$-0.482255\pi$
$139$	15.4896			0.111436			0.0557180	+	0.998447i	$0.482255\pi$
$140$		0			0
$141$	54.5787	−	105.009i	0.387083	−	0.744743i
$142$	204.255	−	111.922i	1.43841	−	0.788187i
$143$	−33.2722	+	33.2722i	−0.232672	+	0.232672i
$144$	124.653	+	72.0949i	0.865645	+	0.500659i
$145$		0			0
$146$	57.2544	−	196.058i	0.392153	−	1.34287i
$147$	−164.725	+	52.0535i	−1.12058	+	0.354105i
$148$	−18.7519	+	4.13714i	−0.126702	+	0.0279536i
$149$	−209.818			−1.40817			−0.704086	−	0.710115i	$-0.748643\pi$
$149$	−209.818			−1.40817			−0.704086	+	0.710115i	$0.748643\pi$
$150$		0			0
$151$		−	144.169i		−	0.954759i	−0.878697	−	0.477380i	$-0.841587\pi$
$151$		−	144.169i		−	0.954759i	0.878697	−	0.477380i	$-0.158413\pi$
$152$	4.94941	−	73.7829i	0.0325619	−	0.485414i
$153$	−0.769217	+	4.39533i	−0.00502756	+	0.0287277i
$154$	25.5664	−	87.5480i	0.166016	−	0.568494i
$155$		0			0
$156$	110.729	−	63.8735i	0.709804	−	0.409446i
$157$	161.893	+	161.893i	1.03117	+	1.03117i	0.999498	+	0.0316669i	$0.0100816\pi$
$157$	161.893	+	161.893i	1.03117	+	1.03117i	0.0316669	+	0.999498i	$0.489918\pi$
$158$	−98.1272	+	53.7693i	−0.621058	+	0.340312i
$159$	103.082	−	198.328i	0.648313	−	1.24735i
$160$		0			0
$161$			262.529i			1.63061i
$162$	−24.9721	−	160.064i	−0.154149	−	0.988048i
$163$	19.4060	+	19.4060i	0.119055	+	0.119055i	0.764124	−	0.645069i	$-0.223171\pi$
$163$	19.4060	+	19.4060i	0.119055	+	0.119055i	−0.645069	+	0.764124i	$0.723171\pi$
$164$	111.587	+	71.2487i	0.680406	+	0.434443i
$165$		0			0
$166$	36.8920	−	126.331i	0.222241	−	0.761029i
$167$	−183.816	−	183.816i	−1.10069	−	1.10069i	−0.994327	−	0.106366i	$-0.966078\pi$
$167$	−183.816	−	183.816i	−1.10069	−	1.10069i	−0.106366	−	0.994327i	$-0.533922\pi$
$168$	−128.728	+	211.712i	−0.766238	+	1.26019i
$169$			55.5219i			0.328532i
$170$		0			0
$171$	−68.0861	+	47.8043i	−0.398164	+	0.279558i
$172$	−8.01551	+	1.76842i	−0.0466018	+	0.0102815i
$173$	198.939	+	198.939i	1.14993	+	1.14993i	0.986565	+	0.163370i	$0.0522364\pi$
$173$	198.939	+	198.939i	1.14993	+	1.14993i	0.163370	+	0.986565i	$0.447764\pi$
$174$	−23.9320	−	22.9039i	−0.137540	−	0.131632i
$175$		0			0
$176$	−29.7374	−	64.1133i	−0.168962	−	0.364280i
$177$	70.5354	−	22.2894i	0.398505	−	0.125929i
$178$	−58.2353	+	31.9103i	−0.327165	+	0.179272i
$179$			167.155i			0.933828i	0.884303	+	0.466914i	$0.154634\pi$
$179$			167.155i			0.933828i	−0.884303	+	0.466914i	$0.845366\pi$
$180$		0			0
$181$	46.3698			0.256187			0.128093	−	0.991762i	$-0.459114\pi$
$181$	46.3698			0.256187			0.128093	+	0.991762i	$0.459114\pi$
$182$	105.697	+	192.894i	0.580755	+	1.05986i
$183$	−41.7388	−	132.084i	−0.228081	−	0.721770i
$184$	133.898	+	153.154i	0.727707	+	0.832357i
$185$		0			0
$186$	−199.841	+	208.811i	−1.07441	+	1.12264i
$187$	1.54855	−	1.54855i	0.00828102	−	0.00828102i
$188$	154.089	−	33.9957i	0.819620	−	0.180828i
$189$	276.292	−	36.9143i	1.46186	−	0.195314i
$190$		0			0
$191$	−299.293			−1.56698			−0.783490	−	0.621405i	$-0.786562\pi$
$191$	−299.293			−1.56698			−0.783490	+	0.621405i	$0.786562\pi$
$192$	32.8825	+	189.163i	0.171263	+	0.985225i
$193$	−207.042	+	207.042i	−1.07276	+	1.07276i	−0.0756225	+	0.997137i	$0.524094\pi$
$193$	−207.042	+	207.042i	−1.07276	+	1.07276i	−0.997137	+	0.0756225i	$0.975906\pi$
$194$	66.8821	+	19.5314i	0.344753	+	0.100677i
$195$		0			0
$196$	−194.139	−	123.959i	−0.990505	−	0.632443i
$197$	5.31992	−	5.31992i	0.0270047	−	0.0270047i	−0.693476	−	0.720480i	$-0.743921\pi$
$197$	5.31992	−	5.31992i	0.0270047	−	0.0270047i	0.720480	+	0.693476i	$0.243921\pi$
$198$	−35.1107	+	71.3359i	−0.177327	+	0.360282i
$199$	61.5955			0.309525			0.154762	−	0.987952i	$-0.450539\pi$
$199$	61.5955			0.309525			0.154762	+	0.987952i	$0.450539\pi$
$200$		0			0
$201$	−120.883	−	62.8292i	−0.601406	−	0.312583i
$202$	11.7909	+	21.5179i	0.0583706	+	0.106524i
$203$	40.3041	−	40.3041i	0.198542	−	0.198542i
$204$	−5.15356	+	2.97280i	−0.0252626	+	0.0145725i
$205$		0			0
$206$	−57.6491	−	16.8351i	−0.279850	−	0.0817237i
$207$	39.4529	−	225.435i	0.190594	−	1.08906i
$208$	160.044	+	58.6212i	0.769440	+	0.281833i
$209$	40.8301			0.195360
$210$		0			0
$211$			184.930i			0.876444i	0.898867	+	0.438222i	$0.144392\pi$
$211$			184.930i			0.876444i	−0.898867	+	0.438222i	$0.855608\pi$
$212$	291.024	−	64.2070i	1.37275	−	0.302863i
$213$	−105.269	−	333.127i	−0.494220	−	1.56398i
$214$	210.221	+	61.3903i	0.982343	+	0.286871i
$215$		0			0
$216$	142.356	−	162.453i	0.659053	−	0.752096i
$217$	−351.661	−	351.661i	−1.62056	−	1.62056i
$218$	60.0911	+	109.664i	0.275647	+	0.503047i
$219$	−271.845	−	141.292i	−1.24130	−	0.645171i
$220$		0			0
$221$			5.28149i			0.0238981i
$222$	0.632098	+	28.7974i	0.00284729	+	0.129718i
$223$	−206.560	−	206.560i	−0.926280	−	0.926280i	0.0711833	−	0.997463i	$-0.477322\pi$
$223$	−206.560	−	206.560i	−0.926280	−	0.926280i	−0.997463	+	0.0711833i	$0.977322\pi$
$224$	−326.650	+	49.4235i	−1.45826	+	0.220641i
$225$		0			0
$226$	−173.948	−	50.7974i	−0.769680	−	0.224767i
$227$	−174.751	−	174.751i	−0.769827	−	0.769827i	0.208249	−	0.978076i	$-0.433224\pi$
$227$	−174.751	−	174.751i	−0.769827	−	0.769827i	−0.978076	+	0.208249i	$0.933224\pi$
$228$	−107.133	−	28.7498i	−0.469880	−	0.126096i
$229$		−	287.354i		−	1.25482i	−0.778689	−	0.627410i	$-0.784115\pi$
$229$		−	287.354i		−	1.25482i	0.778689	−	0.627410i	$-0.215885\pi$
$230$		0			0
$231$	−121.390	−	63.0928i	−0.525497	−	0.273129i
$232$	2.95617	−	44.0689i	0.0127421	−	0.189952i
$233$	1.51498	+	1.51498i	0.00650206	+	0.00650206i	0.710350	−	0.703848i	$-0.248537\pi$
$233$	1.51498	+	1.51498i	0.00650206	+	0.00650206i	−0.703848	+	0.710350i	$0.748537\pi$
$234$	−61.7748	−	181.524i	−0.263995	−	0.775742i
$235$		0			0
$236$	83.1306	+	53.0794i	0.352248	+	0.224913i
$237$	50.5728	+	160.039i	0.213387	+	0.675271i
$238$	−4.91936	−	8.97766i	−0.0206696	−	0.0377213i
$239$		−	271.429i		−	1.13569i	−0.823137	−	0.567843i	$-0.807778\pi$
$239$		−	271.429i		−	1.13569i	0.823137	−	0.567843i	$-0.192222\pi$
$240$		0			0
$241$	122.522			0.508390			0.254195	−	0.967153i	$-0.418190\pi$
$241$	122.522			0.508390			0.254195	+	0.967153i	$0.418190\pi$
$242$	−178.006	+	97.5393i	−0.735562	+	0.403055i
$243$	−242.801	−	9.82275i	−0.999183	−	0.0404229i
$244$	99.3959	−	155.669i	0.407360	−	0.637990i
$245$		0			0
$246$	137.309	−	143.472i	0.558166	−	0.583219i
$247$	−69.6277	+	69.6277i	−0.281893	+	0.281893i
$248$	−384.509	−	25.7931i	−1.55044	−	0.104005i
$249$	−175.164	−	91.0422i	−0.703470	−	0.365631i
$250$		0			0
$251$	335.099			1.33506			0.667529	−	0.744584i	$-0.267352\pi$
$251$	335.099			1.33506			0.667529	+	0.744584i	$0.267352\pi$
$252$	274.084	+	251.021i	1.08764	+	0.996115i
$253$	−79.4246	+	79.4246i	−0.313931	+	0.313931i
$254$	−28.7097	+	98.3118i	−0.113030	+	0.387054i
$255$		0			0
$256$	−165.353	+	195.434i	−0.645909	+	0.763415i
$257$	−11.3695	+	11.3695i	−0.0442393	+	0.0442393i	−0.728880	−	0.684641i	$-0.759959\pi$
$257$	−11.3695	+	11.3695i	−0.0442393	+	0.0442393i	0.684641	+	0.728880i	$0.259959\pi$
$258$	0.270190	+	12.3094i	0.00104725	+	0.0477110i
$259$	−49.5626			−0.191361
$260$		0			0
$261$	−40.6663	+	28.5525i	−0.155809	+	0.109396i
$262$	−138.258	+	75.7593i	−0.527703	+	0.289158i
$263$	211.355	−	211.355i	0.803631	−	0.803631i	−0.180030	−	0.983661i	$-0.557620\pi$
$263$	211.355	−	211.355i	0.803631	−	0.803631i	0.983661	+	0.180030i	$0.0576196\pi$
$264$	−102.995	+	25.1056i	−0.390134	+	0.0950970i
$265$		0			0
$266$	53.5020	−	183.209i	0.201135	−	0.688756i
$267$	30.0133	+	94.9781i	0.112409	+	0.355723i
$268$	−39.1347	−	177.382i	−0.146025	−	0.661871i
$269$	−174.453			−0.648523			−0.324261	−	0.945968i	$-0.605116\pi$
$269$	−174.453			−0.648523			−0.324261	+	0.945968i	$0.605116\pi$
$270$		0			0
$271$		−	189.665i		−	0.699869i	−0.936774	−	0.349935i	$-0.886204\pi$
$271$		−	189.665i		−	0.699869i	0.936774	−	0.349935i	$-0.113796\pi$
$272$	−7.44873	−	2.72834i	−0.0273850	−	0.0100307i
$273$	314.598	−	99.4138i	1.15237	−	0.364153i
$274$	−141.721	+	485.301i	−0.517230	+	1.77117i
$275$		0			0
$276$	264.324	−	152.474i	0.957697	−	0.552441i
$277$	−46.8665	−	46.8665i	−0.169193	−	0.169193i	0.617431	−	0.786625i	$-0.288173\pi$
$277$	−46.8665	−	46.8665i	−0.169193	−	0.169193i	−0.786625	+	0.617431i	$0.788173\pi$
$278$	27.1679	−	14.8868i	0.0977263	−	0.0535496i
$279$	249.125	+	354.821i	0.892922	+	1.27176i
$280$		0			0
$281$			266.157i			0.947179i	0.880746	+	0.473590i	$0.157042\pi$
$281$			266.157i			0.947179i	−0.880746	+	0.473590i	$0.842958\pi$
$282$	−5.19408	−	236.634i	−0.0184187	−	0.839128i
$283$	370.389	+	370.389i	1.30880	+	1.30880i	0.922285	+	0.386512i	$0.126320\pi$
$283$	370.389	+	370.389i	1.30880	+	1.30880i	0.386512	+	0.922285i	$0.373680\pi$
$284$	250.685	−	392.612i	0.882693	−	1.38244i
$285$		0			0
$286$	−26.3802	+	90.3348i	−0.0922385	+	0.315856i
$287$	241.623	+	241.623i	0.841891	+	0.841891i
$288$	287.923	+	6.64869i	0.999733	+	0.0230857i
$289$			288.754i			0.999149i
$290$		0			0
$291$	48.1996	−	92.7354i	0.165634	−	0.318678i
$292$	−88.0074	−	398.902i	−0.301395	−	1.36610i
$293$	−50.2973	−	50.2973i	−0.171663	−	0.171663i	0.616047	−	0.787710i	$-0.288733\pi$
$293$	−50.2973	−	50.2973i	−0.171663	−	0.171663i	−0.787710	+	0.616047i	$0.788733\pi$
$294$	−238.891	+	249.613i	−0.812553	+	0.849025i
$295$		0			0
$296$	−28.9137	+	25.2785i	−0.0976815	+	0.0854003i
$297$	94.7565	+	72.4206i	0.319045	+	0.243840i
$298$	−368.008	+	201.652i	−1.23493	+	0.676685i
$299$		−	270.886i		−	0.905972i
$300$		0			0
$301$	−21.1855			−0.0703838
$302$	−138.558	−	252.864i	−0.458801	−	0.837297i
$303$	35.0944	−	11.0899i	0.115823	−	0.0366004i
$304$	−62.2305	−	134.168i	−0.204706	−	0.441342i
$305$		0			0
$306$	2.87512	+	8.44845i	0.00939580	+	0.0276093i
$307$	−295.562	+	295.562i	−0.962741	+	0.962741i	−0.999330	−	0.0365891i	$-0.988351\pi$
$307$	−295.562	+	295.562i	−0.962741	+	0.962741i	0.0365891	+	0.999330i	$0.488351\pi$
$308$	−39.2989	−	178.126i	−0.127594	−	0.578330i
$309$	−41.5457	+	79.9333i	−0.134452	+	0.258684i
$310$		0			0
$311$	−168.540			−0.541930			−0.270965	−	0.962589i	$-0.587343\pi$
$311$	−168.540			−0.541930			−0.270965	+	0.962589i	$0.587343\pi$
$312$	132.826	−	218.451i	0.425723	−	0.700163i
$313$	−139.822	+	139.822i	−0.446717	+	0.446717i	−0.894262	−	0.447545i	$-0.852299\pi$
$313$	−139.822	+	139.822i	−0.446717	+	0.446717i	0.447545	+	0.894262i	$0.352299\pi$
$314$	439.544	+	128.359i	1.39982	+	0.408786i
$315$		0			0
$316$	−120.433	+	188.617i	−0.381117	+	0.596888i
$317$	168.037	−	168.037i	0.530086	−	0.530086i	−0.390512	−	0.920598i	$-0.627702\pi$
$317$	168.037	−	168.037i	0.530086	−	0.530086i	0.920598	+	0.390512i	$0.127702\pi$
$318$	−9.80996	−	446.926i	−0.0308489	−	1.40543i
$319$	24.3869			0.0764480
$320$		0			0
$321$	151.499	−	291.482i	0.471960	−	0.908045i
$322$	252.312	+	460.461i	0.783578	+	1.43000i
$323$	3.24061	−	3.24061i	0.0100328	−	0.0100328i
$324$	−197.634	−	256.743i	−0.609982	−	0.792415i
$325$		0			0
$326$	52.6878	+	15.3863i	0.161619	+	0.0471971i
$327$	178.855	−	56.5187i	0.546958	−	0.172840i
$328$	264.193	+	17.7222i	0.805465	+	0.0540312i
$329$	407.266			1.23789
$330$		0			0
$331$			278.549i			0.841538i	0.907168	+	0.420769i	$0.138240\pi$
$331$			278.549i			0.841538i	−0.907168	+	0.420769i	$0.861760\pi$
$332$	−56.7079	−	257.034i	−0.170807	−	0.774197i
$333$	42.5597	+	7.44827i	0.127807	+	0.0223672i
$334$	−499.065	−	145.740i	−1.49421	−	0.436349i
$335$		0			0
$336$	−22.3091	+	495.049i	−0.0663963	+	1.47336i
$337$	371.125	+	371.125i	1.10126	+	1.10126i	0.994259	+	0.107001i	$0.0341248\pi$
$337$	371.125	+	371.125i	1.10126	+	1.10126i	0.107001	+	0.994259i	$0.465875\pi$
$338$	53.3611	+	97.3823i	0.157873	+	0.288113i
$339$	−125.358	+	241.187i	−0.369787	+	0.711466i
$340$		0			0
$341$		−	212.780i		−	0.623989i
$342$	−73.4752	+	149.282i	−0.214840	+	0.436498i
$343$	−62.6689	−	62.6689i	−0.182708	−	0.182708i
$344$	−12.3592	+	10.8053i	−0.0359278	+	0.0314107i
$345$		0			0
$346$	540.124	+	157.731i	1.56105	+	0.455869i
$347$	160.180	+	160.180i	0.461613	+	0.461613i	0.899184	−	0.437571i	$-0.144161\pi$
$347$	160.180	+	160.180i	0.461613	+	0.461613i	−0.437571	+	0.899184i	$0.644161\pi$
$348$	−63.9879	−	17.1716i	−0.183873	−	0.0493437i
$349$			395.209i			1.13240i	0.824266	+	0.566202i	$0.191588\pi$
$349$			395.209i			1.13240i	−0.824266	+	0.566202i	$0.808412\pi$
$350$		0			0
$351$	−285.087	+	38.0893i	−0.812214	+	0.108517i
$352$	−113.776	−	83.8710i	−0.323227	−	0.238270i
$353$	−143.113	−	143.113i	−0.405418	−	0.405418i	0.474719	−	0.880137i	$-0.342550\pi$
$353$	−143.113	−	143.113i	−0.405418	−	0.405418i	−0.880137	+	0.474719i	$0.842550\pi$
$354$	102.293	−	106.885i	0.288964	−	0.301934i
$355$		0			0
$356$	−71.4730	+	111.938i	−0.200767	+	0.314432i
$357$	−14.6420	+	4.62691i	−0.0410140	+	0.0129605i
$358$	160.650	+	293.181i	0.448743	+	0.818941i
$359$			388.897i			1.08328i	0.840611	+	0.541639i	$0.182196\pi$
$359$			388.897i			1.08328i	−0.840611	+	0.541639i	$0.817804\pi$
$360$		0			0
$361$	−275.556			−0.763313
$362$	81.3301	−	44.5652i	0.224669	−	0.123108i
$363$	91.7408	+	290.317i	0.252729	+	0.799770i
$364$	370.774	+	236.742i	1.01861	+	0.650389i
$365$		0			0
$366$	−200.151	−	191.553i	−0.546861	−	0.523370i
$367$	361.520	−	361.520i	0.985069	−	0.985069i	−0.0148215	−	0.999890i	$-0.504718\pi$
$367$	361.520	−	361.520i	0.985069	−	0.985069i	0.999890	+	0.0148215i	$0.00471801\pi$
$368$	382.043	+	139.936i	1.03816	+	0.380260i
$369$	−171.172	−	243.794i	−0.463880	−	0.660688i
$370$		0			0
$371$	769.195			2.07330
$372$	−149.825	+	558.306i	−0.402756	+	1.50082i
$373$	104.714	−	104.714i	0.280735	−	0.280735i	−0.552667	−	0.833402i	$-0.686390\pi$
$373$	104.714	−	104.714i	0.280735	−	0.280735i	0.833402	+	0.552667i	$0.186390\pi$
$374$	1.22779	−	4.20435i	0.00328285	−	0.0112416i
$375$		0			0
$376$	237.590	−	207.718i	0.631888	−	0.552442i
$377$	−41.5870	+	41.5870i	−0.110310	+	0.110310i
$378$	449.124	−	330.286i	1.18816	−	0.873771i
$379$	−40.1346			−0.105896			−0.0529480	−	0.998597i	$-0.516862\pi$
$379$	−40.1346			−0.105896			−0.0529480	+	0.998597i	$0.516862\pi$
$380$		0			0
$381$	136.314	+	70.8499i	0.357780	+	0.185958i
$382$	−524.943	+	287.645i	−1.37420	+	0.752998i
$383$	−340.574	+	340.574i	−0.889226	+	0.889226i	−0.994449	−	0.105223i	$-0.966444\pi$
$383$	−340.574	+	340.574i	−0.889226	+	0.889226i	0.105223	+	0.994449i	$0.466444\pi$
$384$	239.476	+	300.179i	0.623635	+	0.781716i
$385$		0			0
$386$	−164.156	+	562.126i	−0.425275	+	1.45628i
$387$	18.1921	+	3.18376i	0.0470081	+	0.00822678i
$388$	136.079	−	30.0223i	0.350719	−	0.0773771i
$389$	98.4019			0.252961			0.126481	−	0.991969i	$-0.459632\pi$
$389$	98.4019			0.252961			0.126481	+	0.991969i	$0.459632\pi$
$390$		0			0
$391$			12.6075i			0.0322443i
$392$	−459.644	−	30.8332i	−1.17256	−	0.0786562i
$393$	71.2555	+	225.490i	0.181312	+	0.573767i
$394$	4.21796	−	14.4437i	0.0107055	−	0.0366592i
$395$		0			0
$396$	6.97741	+	158.863i	0.0176197	+	0.401170i
$397$	−323.459	−	323.459i	−0.814758	−	0.814758i	0.170585	−	0.985343i	$-0.445434\pi$
$397$	−323.459	−	323.459i	−0.814758	−	0.814758i	−0.985343	+	0.170585i	$0.945434\pi$
$398$	108.035	−	59.1983i	0.271445	−	0.148740i
$399$	−254.029	−	132.032i	−0.636663	−	0.330908i
$400$		0			0
$401$		−	648.291i		−	1.61669i	−0.588712	−	0.808343i	$-0.700365\pi$
$401$		−	648.291i		−	1.61669i	0.588712	−	0.808343i	$-0.299635\pi$
$402$	−272.405	+	5.97925i	−0.677625	+	0.0148738i
$403$	362.854	+	362.854i	0.900383	+	0.900383i
$404$	41.3610	+	26.4092i	0.102379	+	0.0653694i
$405$		0			0
$406$	31.9556	−	109.427i	0.0787083	−	0.269524i
$407$	−14.9945	−	14.9945i	−0.0368415	−	0.0368415i
$408$	−6.18196	+	10.1671i	−0.0151519	+	0.0249194i
$409$		−	13.9598i		−	0.0341315i	−0.999854	−	0.0170658i	$-0.994568\pi$
$409$		−	13.9598i		−	0.0341315i	0.999854	−	0.0170658i	$-0.00543247\pi$
$410$		0			0
$411$	672.894	+	349.740i	1.63721	+	0.850948i
$412$	−117.293	+	25.8777i	−0.284692	+	0.0628100i
$413$	180.006	+	180.006i	0.435849	+	0.435849i
$414$	−147.464	−	433.318i	−0.356192	−	1.04666i
$415$		0			0
$416$	337.047	−	50.9968i	0.810210	−	0.122588i
$417$	−14.0018	−	44.3092i	−0.0335775	−	0.106257i
$418$	71.6138	−	39.2411i	0.171325	−	0.0938783i
$419$			317.783i			0.758433i	0.925308	+	0.379216i	$0.123806\pi$
$419$			317.783i			0.758433i	−0.925308	+	0.379216i	$0.876194\pi$
$420$		0			0
$421$	−56.9987			−0.135389			−0.0676944	−	0.997706i	$-0.521564\pi$
$421$	−56.9987			−0.135389			−0.0676944	+	0.997706i	$0.521564\pi$
$422$	177.733	+	324.356i	0.421168	+	0.768617i
$423$	−349.722	−	61.2040i	−0.826765	−	0.144690i
$424$	448.732	−	392.314i	1.05833	−	0.925268i
$425$		0			0
$426$	−504.798	−	483.114i	−1.18497	−	1.13407i
$427$	337.077	−	337.077i	0.789408	−	0.789408i
$428$	427.718	−	94.3649i	0.999340	−	0.220479i
$429$	125.254	+	65.1011i	0.291967	+	0.151751i
$430$		0			0
$431$	−146.371			−0.339607			−0.169803	−	0.985478i	$-0.554313\pi$
$431$	−146.371			−0.339607			−0.169803	+	0.985478i	$0.554313\pi$
$432$	93.5530	−	421.749i	0.216558	−	0.976270i
$433$	425.454	−	425.454i	0.982572	−	0.982572i	−0.0172788	−	0.999851i	$-0.505500\pi$
$433$	425.454	−	425.454i	0.982572	−	0.982572i	0.999851	+	0.0172788i	$0.00550028\pi$
$434$	−954.768	−	278.818i	−2.19993	−	0.642438i
$435$		0			0
$436$	210.793	+	134.592i	0.483470	+	0.308698i
$437$	−166.210	+	166.210i	−0.380342	+	0.380342i
$438$	−612.594	+	13.4463i	−1.39862	+	0.0306994i
$439$	679.724			1.54835			0.774173	−	0.632974i	$-0.218166\pi$
$439$	679.724			1.54835			0.774173	+	0.632974i	$0.218166\pi$
$440$		0			0
$441$	297.806	+	424.154i	0.675296	+	0.961801i
$442$	5.07595	+	9.26343i	0.0114840	+	0.0209580i
$443$	−192.731	+	192.731i	−0.435059	+	0.435059i	−0.890345	−	0.455286i	$-0.849537\pi$
$443$	−192.731	+	192.731i	−0.435059	+	0.435059i	0.455286	+	0.890345i	$0.349537\pi$
$444$	28.7854	+	49.9015i	0.0648319	+	0.112391i
$445$		0			0
$446$	−560.817	−	163.774i	−1.25744	−	0.367206i
$447$	189.664	+	600.199i	0.424305	+	1.34273i
$448$	−525.425	+	400.623i	−1.17282	+	0.894249i
$449$	−167.799			−0.373717			−0.186859	−	0.982387i	$-0.559831\pi$
$449$	−167.799			−0.373717			−0.186859	+	0.982387i	$0.559831\pi$
$450$		0			0
$451$			146.199i			0.324167i
$452$	−353.915	+	78.0822i	−0.782997	+	0.172748i
$453$	−412.405	+	130.321i	−0.910386	+	0.287684i
$454$	−474.453	−	138.553i	−1.04505	−	0.305183i
$455$		0			0
$456$	−215.535	+	52.5378i	−0.472666	+	0.115214i
$457$	124.480	+	124.480i	0.272385	+	0.272385i	0.830060	−	0.557674i	$-0.188306\pi$
$457$	124.480	+	124.480i	0.272385	+	0.272385i	−0.557674	+	0.830060i	$0.688306\pi$
$458$	−276.171	−	504.002i	−0.602993	−	1.10044i
$459$	13.2685	−	1.77275i	0.0289074	−	0.00386220i
$460$		0			0
$461$			355.022i			0.770114i	0.922893	+	0.385057i	$0.125818\pi$
$461$			355.022i			0.770114i	−0.922893	+	0.385057i	$0.874182\pi$
$462$	−273.548	+	6.00434i	−0.592096	+	0.0129964i
$463$	−244.127	−	244.127i	−0.527272	−	0.527272i	0.392486	−	0.919758i	$-0.371615\pi$
$463$	−244.127	−	244.127i	−0.527272	−	0.527272i	−0.919758	+	0.392486i	$0.871615\pi$
$464$	−37.1689	−	80.1355i	−0.0801054	−	0.172706i
$465$		0			0
$466$	4.11321	+	1.20117i	0.00882663	+	0.00257762i
$467$	184.217	+	184.217i	0.394468	+	0.394468i	0.876277	−	0.481808i	$-0.160020\pi$
$467$	184.217	+	184.217i	0.394468	+	0.394468i	−0.481808	+	0.876277i	$0.660020\pi$
$468$	−282.809	−	259.011i	−0.604292	−	0.553443i
$469$		−	468.831i		−	0.999639i
$470$		0			0
$471$	316.764	−	609.449i	0.672535	−	1.29395i
$472$	196.820	+	13.2028i	0.416992	+	0.0279721i
$473$	−6.40939	−	6.40939i	−0.0135505	−	0.0135505i
$474$	242.513	+	232.095i	0.511631	+	0.489653i
$475$		0			0
$476$	−17.2566	−	11.0184i	−0.0362533	−	0.0231479i
$477$	−660.512	−	115.595i	−1.38472	−	0.242337i
$478$	−260.866	−	476.071i	−0.545744	−	0.995965i
$479$			178.759i			0.373192i	0.982437	+	0.186596i	$0.0597455\pi$
$479$			178.759i			0.373192i	−0.982437	+	0.186596i	$0.940254\pi$
$480$		0			0
$481$	51.1402			0.106321
$482$	214.897	−	117.754i	0.445844	−	0.244302i
$483$	750.983	−	237.313i	1.55483	−	0.491330i
$484$	−218.469	+	342.157i	−0.451383	+	0.706936i
$485$		0			0
$486$	−435.301	+	216.124i	−0.895680	+	0.444699i
$487$	11.7814	−	11.7814i	0.0241918	−	0.0241918i	−0.694907	−	0.719099i	$-0.744555\pi$
$487$	11.7814	−	11.7814i	0.0241918	−	0.0241918i	0.719099	+	0.694907i	$0.244555\pi$
$488$	24.7235	−	368.563i	0.0506629	−	0.755253i
$489$	37.9703	−	73.0543i	0.0776488	−	0.149395i
$490$		0			0
$491$	−741.254			−1.50968			−0.754842	−	0.655907i	$-0.772286\pi$
$491$	−741.254			−1.50968			−0.754842	+	0.655907i	$0.772286\pi$
$492$	102.944	−	383.607i	0.209235	−	0.779689i
$493$	1.93554	−	1.93554i	0.00392605	−	0.00392605i
$494$	−55.2051	+	189.041i	−0.111751	+	0.382674i
$495$		0			0
$496$	−699.197	+	324.305i	−1.40967	+	0.653841i
$497$	850.137	−	850.137i	1.71054	−	1.71054i
$498$	−394.727	+	8.66419i	−0.792625	+	0.0173980i
$499$	−659.372			−1.32139			−0.660693	−	0.750656i	$-0.729738\pi$
$499$	−659.372			−1.32139			−0.660693	+	0.750656i	$0.729738\pi$
$500$		0			0
$501$	−359.659	+	691.978i	−0.717881	+	1.38119i
$502$	587.746	−	322.058i	1.17081	−	0.641550i
$503$	−138.296	+	138.296i	−0.274942	+	0.274942i	−0.831086	−	0.556144i	$-0.812280\pi$
$503$	−138.296	+	138.296i	−0.274942	+	0.274942i	0.556144	+	0.831086i	$0.312280\pi$
$504$	721.980	+	176.859i	1.43250	+	0.350911i
$505$		0			0
$506$	−62.9727	+	215.640i	−0.124452	+	0.426166i
$507$	158.824	−	50.1889i	0.313263	−	0.0989919i
$508$	44.1306	+	200.026i	0.0868712	+	0.393751i
$509$	0.354751			0.000696957			0.000348478	−	1.00000i	$-0.499889\pi$
$509$	0.354751			0.000696957			0.000348478		1.00000i	$0.499889\pi$
$510$		0			0
$511$		−	1054.32i		−	2.06325i
$512$	−102.191	+	501.698i	−0.199592	+	0.979879i
$513$	198.294	+	151.553i	0.386538	+	0.295424i
$514$	−9.01444	+	30.8685i	−0.0175378	+	0.0600555i
$515$		0			0
$516$	12.3043	+	21.3304i	0.0238455	+	0.0413380i
$517$	123.213	+	123.213i	0.238323	+	0.238323i
$518$	−86.9300	+	47.6338i	−0.167819	+	0.0919571i
$519$	389.249	−	748.909i	0.749997	−	1.44298i
$520$		0			0
$521$		−	594.299i		−	1.14069i	−0.821406	−	0.570345i	$-0.806810\pi$
$521$		−	594.299i		−	1.14069i	0.821406	−	0.570345i	$-0.193190\pi$
$522$	−43.8851	+	89.1631i	−0.0840711	+	0.170810i
$523$	−543.498	−	543.498i	−1.03919	−	1.03919i	−0.999200	−	0.0399922i	$-0.987267\pi$
$523$	−543.498	−	543.498i	−1.03919	−	1.03919i	−0.0399922	−	0.999200i	$-0.512733\pi$
$524$	−169.686	+	265.755i	−0.323829	+	0.507166i
$525$		0			0
$526$	167.575	−	573.834i	0.318584	−	1.09094i
$527$	−16.8879	−	16.8879i	−0.0320454	−	0.0320454i
$528$	−156.520	+	143.021i	−0.296439	+	0.270873i
$529$		−	117.636i		−	0.222375i
$530$		0			0
$531$	−127.521	−	181.623i	−0.240152	−	0.342040i
$532$	−82.2396	−	372.759i	−0.154586	−	0.700674i
$533$	−249.314	−	249.314i	−0.467756	−	0.467756i
$534$	143.924	+	137.741i	0.269520	+	0.257942i
$535$		0			0
$536$	−239.118	−	273.506i	−0.446116	−	0.510272i
$537$	478.160	−	151.100i	0.890428	−	0.281377i
$538$	−305.980	+	167.663i	−0.568736	+	0.311642i
$539$		−	254.359i		−	0.471908i
$540$		0			0
$541$	−446.978			−0.826206			−0.413103	−	0.910684i	$-0.635555\pi$
$541$	−446.978			−0.826206			−0.413103	+	0.910684i	$0.635555\pi$
$542$	−182.283	−	332.661i	−0.336316	−	0.613766i
$543$	−41.9159	−	132.644i	−0.0771932	−	0.244280i
$544$	−15.6868	+	2.37349i	−0.0288361	+	0.00436303i
$545$		0			0
$546$	456.243	−	476.721i	0.835610	−	0.873116i
$547$	−492.299	+	492.299i	−0.899998	+	0.899998i	−0.995435	−	0.0954376i	$-0.969575\pi$
$547$	−492.299	+	492.299i	−0.899998	+	0.899998i	0.0954376	+	0.995435i	$0.469575\pi$
$548$	217.844	+	987.397i	0.397525	+	1.80182i
$549$	−340.106	+	238.794i	−0.619501	+	0.434962i
$550$		0			0
$551$	51.0338			0.0926203
$552$	317.070	−	521.468i	0.574403	−	0.944688i
$553$	−408.419	+	408.419i	−0.738552	+	0.738552i
$554$	−127.244	−	37.1587i	−0.229682	−	0.0670734i
$555$		0			0
$556$	33.3436	−	52.2212i	0.0599704	−	0.0939231i
$557$	−367.436	+	367.436i	−0.659670	+	0.659670i	−0.955302	−	0.295632i	$-0.904470\pi$
$557$	−367.436	+	367.436i	−0.659670	+	0.659670i	0.295632	+	0.955302i	$0.404470\pi$
$558$	777.964	+	382.905i	1.39420	+	0.686210i
$559$	21.8599			0.0391053
$560$		0			0
$561$	−5.82955	−	3.02993i	−0.0103914	−	0.00540095i
$562$	255.799	+	466.825i	0.455159	+	0.830650i
$563$	129.412	−	129.412i	0.229861	−	0.229861i	−0.582773	−	0.812635i	$-0.698032\pi$
$563$	129.412	−	129.412i	0.229861	−	0.229861i	0.812635	+	0.582773i	$0.198032\pi$
$564$	−236.535	−	410.051i	−0.419389	−	0.727041i
$565$		0			0
$566$	1005.62	+	293.667i	1.77671	+	0.518847i
$567$	−355.350	−	756.986i	−0.626720	−	1.33507i
$568$	62.3547	−	929.548i	0.109779	−	1.63653i
$569$	658.832			1.15788			0.578939	−	0.815371i	$-0.303467\pi$
$569$	658.832			1.15788			0.578939	+	0.815371i	$0.303467\pi$
$570$		0			0
$571$		−	153.311i		−	0.268496i	−0.990948	−	0.134248i	$-0.957138\pi$
$571$		−	153.311i		−	0.268496i	0.990948	−	0.134248i	$-0.0428618\pi$
$572$	40.5498	+	183.796i	0.0708913	+	0.321321i
$573$	270.545	+	856.149i	0.472156	+	1.49415i
$574$	656.012	+	191.573i	1.14288	+	0.333751i
$575$		0			0
$576$	511.391	−	265.057i	0.887832	−	0.460168i
$577$	−379.812	−	379.812i	−0.658252	−	0.658252i	0.296714	−	0.954966i	$-0.404109\pi$
$577$	−379.812	−	379.812i	−0.658252	−	0.658252i	−0.954966	+	0.296714i	$0.904109\pi$
$578$	277.517	+	506.459i	0.480133	+	0.876226i
$579$	779.416	+	405.105i	1.34614	+	0.699662i
$580$		0			0
$581$		−	679.356i		−	1.16929i
$582$	−4.58700	−	208.977i	−0.00788144	−	0.359066i
$583$	232.710	+	232.710i	0.399159	+	0.399159i
$584$	−537.738	−	615.069i	−0.920784	−	1.05320i
$585$		0			0
$586$	−136.559	−	39.8788i	−0.233035	−	0.0680525i
$587$	80.3753	+	80.3753i	0.136925	+	0.136925i	0.772247	−	0.635322i	$-0.219133\pi$
$587$	80.3753	+	80.3753i	0.136925	+	0.136925i	−0.635322	+	0.772247i	$0.719133\pi$
$588$	−179.102	+	667.401i	−0.304595	+	1.13504i
$589$		−	445.279i		−	0.755992i
$590$		0			0
$591$	−20.0270	−	10.4091i	−0.0338866	−	0.0176127i
$592$	−26.4184	+	72.1255i	−0.0446256	+	0.121834i
$593$	−417.804	−	417.804i	−0.704559	−	0.704559i	0.260826	−	0.965386i	$-0.416005\pi$
$593$	−417.804	−	417.804i	−0.704559	−	0.704559i	−0.965386	+	0.260826i	$0.916005\pi$
$594$	235.800	+	35.9529i	0.396969	+	0.0605268i
$595$		0			0
$596$	−451.662	+	707.373i	−0.757822	+	1.18687i
$597$	−55.6791	−	176.198i	−0.0932648	−	0.295140i
$598$	−260.344	−	475.118i	−0.435357	−	0.794512i
$599$		−	806.349i		−	1.34616i	−0.739570	−	0.673080i	$-0.764971\pi$
$599$		−	806.349i		−	1.34616i	0.739570	−	0.673080i	$-0.235029\pi$
$600$		0			0
$601$	687.797			1.14442			0.572211	−	0.820107i	$-0.306086\pi$
$601$	687.797			1.14442			0.572211	+	0.820107i	$0.306086\pi$
$602$	−37.1582	+	20.3610i	−0.0617246	+	0.0338223i
$603$	−70.4560	+	402.588i	−0.116842	+	0.667641i
$604$	−486.046	−	310.343i	−0.804712	−	0.513813i
$605$		0			0
$606$	50.8953	−	53.1797i	0.0839856	−	0.0877553i
$607$	232.895	−	232.895i	0.383682	−	0.383682i	−0.488745	−	0.872427i	$-0.662545\pi$
$607$	232.895	−	232.895i	0.383682	−	0.383682i	0.872427	+	0.488745i	$0.162545\pi$
$608$	−238.095	−	175.514i	−0.391604	−	0.288675i
$609$	−151.726	−	78.8600i	−0.249139	−	0.129491i
$610$		0			0
$611$	−420.230			−0.687774
$612$	13.1625	+	12.0549i	0.0215073	+	0.0196975i
$613$	575.631	−	575.631i	0.939038	−	0.939038i	−0.0592074	−	0.998246i	$-0.518857\pi$
$613$	575.631	−	575.631i	0.939038	−	0.939038i	0.998246	+	0.0592074i	$0.0188573\pi$
$614$	−234.339	+	802.458i	−0.381660	+	1.30693i
$615$		0			0
$616$	−240.122	−	274.653i	−0.389808	−	0.445865i
$617$	−475.711	+	475.711i	−0.771007	+	0.771007i	−0.978283	−	0.207275i	$-0.933540\pi$
$617$	−475.711	+	475.711i	−0.771007	+	0.771007i	0.207275	+	0.978283i	$0.433540\pi$
$618$	3.95377	+	180.127i	0.00639768	+	0.291468i
$619$	−215.170			−0.347610			−0.173805	−	0.984780i	$-0.555606\pi$
$619$	−215.170			−0.347610			−0.173805	+	0.984780i	$0.555606\pi$
$620$		0			0
$621$	−680.537	+	90.9238i	−1.09587	+	0.146415i
$622$	−295.610	+	161.981i	−0.475258	+	0.260420i
$623$	−242.383	+	242.383i	−0.389058	+	0.389058i
$624$	23.0193	−	510.807i	0.0368899	−	0.818601i
$625$		0			0
$626$	−110.860	+	379.622i	−0.177092	+	0.606424i
$627$	−36.9083	−	116.798i	−0.0588649	−	0.186280i
$628$	894.298	−	197.304i	1.42404	−	0.314178i
$629$	−2.38016			−0.00378405
$630$		0			0
$631$			710.672i			1.12626i	0.826367	+	0.563132i	$0.190404\pi$
$631$			710.672i			1.12626i	−0.826367	+	0.563132i	$0.809596\pi$
$632$	−29.9562	+	446.569i	−0.0473990	+	0.706597i
$633$	529.005	−	167.167i	0.835711	−	0.264087i
$634$	133.230	−	456.225i	0.210142	−	0.719598i
$635$		0			0
$636$	−446.739	−	774.456i	−0.702420	−	1.21770i
$637$	433.758	+	433.758i	0.680939	+	0.680939i
$638$	42.7733	−	23.4379i	0.0670428	−	0.0367364i
$639$	−857.776	+	602.259i	−1.34237	+	0.942502i
$640$		0			0
$641$			445.381i			0.694822i	0.937713	+	0.347411i	$0.112939\pi$
$641$			445.381i			0.694822i	−0.937713	+	0.347411i	$0.887061\pi$
$642$	−14.4177	−	656.847i	−0.0224574	−	1.02313i
$643$	−310.249	−	310.249i	−0.482502	−	0.482502i	0.423428	−	0.905930i	$-0.360827\pi$
$643$	−310.249	−	310.249i	−0.482502	−	0.482502i	−0.905930	+	0.423428i	$0.860827\pi$
$644$	885.083	+	565.130i	1.37435	+	0.877531i
$645$		0			0
$646$	2.56935	−	8.79833i	0.00397732	−	0.0136197i
$647$	−797.318	−	797.318i	−1.23233	−	1.23233i	−0.963066	−	0.269265i	$-0.913219\pi$
$647$	−797.318	−	797.318i	−1.23233	−	1.23233i	−0.269265	−	0.963066i	$-0.586781\pi$
$648$	−593.390	−	260.369i	−0.915725	−	0.401805i
$649$			108.917i			0.167822i
$650$		0			0
$651$	−688.068	+	1323.83i	−1.05694	+	2.03354i
$652$	107.199	−	23.6507i	0.164416	−	0.0362741i
$653$	−686.842	−	686.842i	−1.05183	−	1.05183i	−0.998582	−	0.0532438i	$-0.983044\pi$
$653$	−686.842	−	686.842i	−1.05183	−	1.05183i	−0.0532438	−	0.998582i	$-0.516956\pi$
$654$	259.383	−	271.026i	0.396610	−	0.414412i
$655$		0			0
$656$	480.412	−	222.827i	0.732335	−	0.339676i
$657$	−158.444	+	905.353i	−0.241163	+	1.37801i
$658$	714.322	−	391.416i	1.08560	−	0.594858i
$659$			633.604i			0.961463i	0.876868	+	0.480732i	$0.159629\pi$
$659$			633.604i			0.961463i	−0.876868	+	0.480732i	$0.840371\pi$
$660$		0			0
$661$	893.706			1.35205			0.676026	−	0.736878i	$-0.263701\pi$
$661$	893.706			1.35205			0.676026	+	0.736878i	$0.263701\pi$
$662$	267.709	+	488.560i	0.404394	+	0.738006i
$663$	15.1081	−	4.77419i	0.0227875	−	0.00720089i
$664$	−346.493	−	396.322i	−0.521827	−	0.596870i
$665$		0			0
$666$	81.8057	−	27.8395i	0.122831	−	0.0418011i
$667$	−99.2732	+	99.2732i	−0.148835	+	0.148835i
$668$	−1015.40	+	224.022i	−1.52006	+	0.335362i
$669$	−404.161	+	777.601i	−0.604128	+	1.16233i
$670$		0			0
$671$	203.956			0.303959
$672$	436.654	+	889.729i	0.649782	+	1.32400i
$673$	−656.768	+	656.768i	−0.975881	+	0.975881i	−0.999716	−	0.0238351i	$-0.992412\pi$
$673$	−656.768	+	656.768i	−0.975881	+	0.975881i	0.0238351	+	0.999716i	$0.492412\pi$
$674$	1007.61	+	294.250i	1.49498	+	0.436573i
$675$		0			0
$676$	187.185	+	119.519i	0.276901	+	0.176803i
$677$	119.083	−	119.083i	0.175898	−	0.175898i	−0.613667	−	0.789565i	$-0.710306\pi$
$677$	119.083	−	119.083i	0.175898	−	0.175898i	0.789565	+	0.613667i	$0.210306\pi$
$678$	11.9299	+	543.508i	0.0175957	+	0.801634i
$679$	359.665			0.529698
$680$		0			0
$681$	−341.922	+	657.853i	−0.502088	+	0.966010i
$682$	−204.499	−	373.205i	−0.299853	−	0.547221i
$683$	894.185	−	894.185i	1.30920	−	1.30920i	0.387211	−	0.921991i	$-0.373439\pi$
$683$	894.185	−	894.185i	1.30920	−	1.30920i	0.921991	−	0.387211i	$-0.126561\pi$
$684$	14.6014	+	332.449i	0.0213471	+	0.486036i
$685$		0			0
$686$	−170.148	−	49.6878i	−0.248029	−	0.0724312i
$687$	−821.996	+	259.753i	−1.19650	+	0.378097i
$688$	−11.2925	+	30.8300i	−0.0164135	+	0.0448111i
$689$	−793.680			−1.15193
$690$		0			0
$691$			957.776i			1.38607i	0.720903	+	0.693036i	$0.243728\pi$
$691$			957.776i			1.38607i	−0.720903	+	0.693036i	$0.756272\pi$
$692$	1098.94	−	242.453i	1.58806	−	0.350365i
$693$	−70.7516	+	404.277i	−0.102095	+	0.583372i
$694$	434.892	+	127.000i	0.626646	+	0.182998i
$695$		0			0
$696$	−128.734	+	31.3796i	−0.184963	+	0.0450857i
$697$	11.6036	+	11.6036i	0.0166478	+	0.0166478i
$698$	379.829	+	693.175i	0.544167	+	0.993087i
$699$	2.96425	−	5.70317i	0.00424070	−	0.00815905i
$700$		0			0
$701$			236.408i			0.337244i	0.985681	+	0.168622i	$0.0539317\pi$
$701$			236.408i			0.337244i	−0.985681	+	0.168622i	$0.946068\pi$
$702$	−463.420	+	340.799i	−0.660143	+	0.485469i
$703$	−31.3785	−	31.3785i	−0.0446352	−	0.0446352i
$704$	−280.163	−	37.7570i	−0.397959	−	0.0536322i
$705$		0			0
$706$	−388.555	−	113.469i	−0.550361	−	0.160720i
$707$	89.5606	+	89.5606i	0.126677	+	0.126677i
$708$	76.6916	−	285.782i	0.108322	−	0.403647i
$709$			3.07348i			0.00433495i	0.999998	+	0.00216747i	$0.000689929\pi$
$709$			3.07348i			0.00433495i	−0.999998	+	0.00216747i	$0.999310\pi$
$710$		0			0
$711$	412.089	−	289.334i	0.579591	−	0.406940i
$712$	−17.7780	+	265.024i	−0.0249691	+	0.372225i
$713$	866.177	+	866.177i	1.21483	+	1.21483i
$714$	−21.2344	+	22.1875i	−0.0297401	+	0.0310750i
$715$		0			0
$716$	563.542	+	359.825i	0.787070	+	0.502549i
$717$	−776.442	+	245.358i	−1.08290	+	0.342200i
$718$	373.762	+	682.103i	0.520560	+	0.950004i
$719$		−	893.990i		−	1.24338i	−0.783264	−	0.621690i	$-0.786447\pi$
$719$		−	893.990i		−	1.24338i	0.783264	−	0.621690i	$-0.213553\pi$
$720$		0			0
$721$	−310.013			−0.429977
$722$	−483.310	+	264.832i	−0.669404	+	0.366803i
$723$	−110.753	−	350.483i	−0.153186	−	0.484762i
$724$	99.8175	−	156.330i	0.137869	−	0.215925i
$725$		0			0
$726$	439.926	+	421.029i	0.605959	+	0.579929i
$727$	319.871	−	319.871i	0.439988	−	0.439988i	−0.452020	−	0.892008i	$-0.649296\pi$
$727$	319.871	−	319.871i	0.439988	−	0.439988i	0.892008	+	0.452020i	$0.149296\pi$
$728$	877.846	+	58.8866i	1.20583	+	0.0808881i
$729$	191.381	+	703.430i	0.262526	+	0.964925i
$730$		0			0
$731$	−1.01740			−0.00139179
$732$	−535.153	−	143.612i	−0.731083	−	0.196191i
$733$	577.382	−	577.382i	0.787698	−	0.787698i	−0.193419	−	0.981116i	$-0.561958\pi$
$733$	577.382	−	577.382i	0.787698	−	0.787698i	0.981116	+	0.193419i	$0.0619576\pi$
$734$	286.635	−	981.537i	0.390511	−	1.33724i
$735$		0			0
$736$	804.572	−	121.735i	1.09317	−	0.165401i
$737$	141.838	−	141.838i	0.192454	−	0.192454i
$738$	−534.532	−	263.091i	−0.724298	−	0.356492i
$739$	−1125.12			−1.52248			−0.761242	−	0.648468i	$-0.775410\pi$
$739$	−1125.12			−1.52248			−0.761242	+	0.648468i	$0.775410\pi$
$740$		0			0
$741$	262.115	+	136.235i	0.353731	+	0.183853i
$742$	1349.13	−	739.260i	1.81823	−	0.996308i
$743$	−63.1774	+	63.1774i	−0.0850302	+	0.0850302i	−0.748343	−	0.663312i	$-0.769150\pi$
$743$	−63.1774	+	63.1774i	−0.0850302	+	0.0850302i	0.663312	+	0.748343i	$0.269150\pi$
$744$	273.793	+	1123.23i	0.368001	+	1.50972i
$745$		0			0
$746$	83.0237	−	284.302i	0.111292	−	0.381101i
$747$	−102.094	+	583.367i	−0.136672	+	0.780947i
$748$	−1.88727	−	8.55421i	−0.00252308	−	0.0114361i
$749$	1130.49			1.50933
$750$		0			0
$751$		−	705.259i		−	0.939093i	−0.882908	−	0.469547i	$-0.844417\pi$
$751$		−	705.259i		−	0.939093i	0.882908	−	0.469547i	$-0.155583\pi$
$752$	217.085	−	592.670i	0.288677	−	0.788125i
$753$	−302.912	−	958.576i	−0.402274	−	1.27301i
$754$	−32.9728	+	112.910i	−0.0437304	+	0.149748i
$755$		0			0
$756$	470.306	−	1010.95i	0.622098	−	1.33723i
$757$	555.302	+	555.302i	0.733556	+	0.733556i	0.971322	−	0.237766i	$-0.0764152\pi$
$757$	555.302	+	555.302i	0.733556	+	0.733556i	−0.237766	+	0.971322i	$0.576415\pi$
$758$	−70.3938	+	38.5727i	−0.0928679	+	0.0508874i
$759$	298.996	+	155.404i	0.393934	+	0.204749i
$760$		0			0
$761$		−	1189.64i		−	1.56326i	−0.623745	−	0.781628i	$-0.714390\pi$
$761$		−	1189.64i		−	1.56326i	0.623745	−	0.781628i	$-0.285610\pi$
$762$	307.180	−	6.74255i	0.403123	−	0.00884849i
$763$	456.438	+	456.438i	0.598214	+	0.598214i
$764$	−644.270	+	1009.03i	−0.843285	+	1.32072i
$765$		0			0
$766$	−270.028	+	924.666i	−0.352516	+	1.20714i
$767$	−185.736	−	185.736i	−0.242159	−	0.242159i
$768$	708.524	+	296.341i	0.922557	+	0.385861i
$769$			900.882i			1.17150i	0.810492	+	0.585749i	$0.199200\pi$
$769$			900.882i			1.17150i	−0.810492	+	0.585749i	$0.800800\pi$
$770$		0			0
$771$	42.8007	+	22.2459i	0.0555133	+	0.0288533i
$772$	252.329	+	1143.70i	0.326851	+	1.48148i
$773$	−464.010	−	464.010i	−0.600272	−	0.600272i	0.340113	−	0.940385i	$-0.389535\pi$
$773$	−464.010	−	464.010i	−0.600272	−	0.600272i	−0.940385	+	0.340113i	$0.889535\pi$
$774$	34.9678	−	11.9000i	0.0451781	−	0.0153747i
$775$		0			0
$776$	209.821	−	183.440i	0.270387	−	0.236392i
$777$	44.8020	+	141.777i	0.0576602	+	0.182468i
$778$	172.591	−	94.5724i	0.221840	−	0.121558i
$779$			305.947i			0.392744i
$780$		0			0
$781$	514.395			0.658636
$782$	12.1169	+	22.1129i	0.0154947	+	0.0282774i
$783$	118.437	+	90.5189i	0.151260	+	0.115605i
$784$	−835.823	+	387.676i	−1.06610	+	0.494485i
$785$		0			0
$786$	341.693	+	327.015i	0.434724	+	0.416050i
$787$	−511.685	+	511.685i	−0.650172	+	0.650172i	−0.953034	−	0.302862i	$-0.902058\pi$
$787$	−511.685	+	511.685i	−0.650172	+	0.650172i	0.302862	+	0.953034i	$0.402058\pi$
$788$	−6.48355	−	29.3873i	−0.00822786	−	0.0372935i
$789$	−795.650	−	413.542i	−1.00843	−	0.524135i
$790$		0			0
$791$	−935.420			−1.18258
$792$	164.919	+	271.932i	0.208231	+	0.343348i
$793$	−347.807	+	347.807i	−0.438596	+	0.438596i
$794$	−878.200	−	256.458i	−1.10604	−	0.322995i
$795$		0			0
$796$	132.593	−	207.661i	0.166574	−	0.260881i
$797$	606.760	−	606.760i	0.761305	−	0.761305i	−0.215253	−	0.976558i	$-0.569058\pi$
$797$	606.760	−	606.760i	0.761305	−	0.761305i	0.976558	+	0.215253i	$0.0690576\pi$
$798$	−572.446	+	12.5651i	−0.717351	+	0.0157457i
$799$	19.5583			0.0244785
$800$		0			0
$801$	244.561	−	171.711i	0.305320	−	0.214370i
$802$	−623.062	−	1137.07i	−0.776885	−	1.41779i
$803$	318.971	−	318.971i	0.397224	−	0.397224i
$804$	−472.037	+	272.291i	−0.587111	+	0.338671i
$805$		0			0
$806$	985.160	+	287.693i	1.22228	+	0.356939i
$807$	157.696	+	499.034i	0.195410	+	0.618382i
$808$	97.9264	+	6.56897i	0.121196	+	0.00812992i
$809$	−9.70812			−0.0120001			−0.00600007	−	0.999982i	$-0.501910\pi$
$809$	−9.70812			−0.0120001			−0.00600007	+	0.999982i	$0.501910\pi$
$810$		0			0
$811$		−	109.279i		−	0.134747i	−0.997728	−	0.0673733i	$-0.978538\pi$
$811$		−	109.279i		−	0.134747i	0.997728	−	0.0673733i	$-0.0214618\pi$
$812$	−49.1199	−	222.640i	−0.0604925	−	0.274188i
$813$	−542.549	+	171.447i	−0.667342	+	0.210882i
$814$	−40.7104	−	11.8886i	−0.0500128	−	0.0146051i
$815$		0			0
$816$	−1.07136	+	23.7739i	−0.00131294	+	0.0291347i
$817$	−13.4127	−	13.4127i	−0.0164171	−	0.0164171i
$818$	−13.4165	−	24.4847i	−0.0164016	−	0.0299324i
$819$	−568.761	−	810.066i	−0.694458	−	0.989092i
$820$		0			0
$821$		−	219.704i		−	0.267606i	−0.991008	−	0.133803i	$-0.957281\pi$
$821$		−	219.704i		−	0.267606i	0.991008	−	0.133803i	$-0.0427189\pi$
$822$	1516.35	−	33.2836i	1.84471	−	0.0404910i
$823$	1.99663	+	1.99663i	0.00242604	+	0.00242604i	0.708319	−	0.705893i	$-0.249454\pi$
$823$	1.99663	+	1.99663i	0.00242604	+	0.00242604i	−0.705893	+	0.708319i	$0.749454\pi$
$824$	−180.855	+	158.117i	−0.219484	+	0.191889i
$825$		0			0
$826$	488.721	+	142.720i	0.591672	+	0.172784i
$827$	−917.802	−	917.802i	−1.10980	−	1.10980i	−0.993177	−	0.116620i	$-0.962794\pi$
$827$	−917.802	−	917.802i	−1.10980	−	1.10980i	−0.116620	−	0.993177i	$-0.537206\pi$
$828$	−675.098	−	618.291i	−0.815335	−	0.746728i
$829$		−	1134.07i		−	1.36800i	−0.729482	−	0.684000i	$-0.760239\pi$
$829$		−	1134.07i		−	1.36800i	0.729482	−	0.684000i	$-0.239761\pi$
$830$		0			0
$831$	−91.7003	+	176.430i	−0.110349	+	0.212311i
$832$	542.150	−	413.376i	0.651623	−	0.496846i
$833$	−20.1879	−	20.1879i	−0.0242352	−	0.0242352i
$834$	−67.1432	−	64.2589i	−0.0805074	−	0.0770491i
$835$		0			0
$836$	87.8926	−	137.654i	0.105135	−	0.164657i
$837$	789.794	−	1033.38i	0.943601	−	1.23462i
$838$	305.416	+	557.374i	0.364458	+	0.665124i
$839$		−	624.895i		−	0.744809i	−0.928070	−	0.372405i	$-0.878533\pi$
$839$		−	624.895i		−	0.744809i	0.928070	−	0.372405i	$-0.121467\pi$
$840$		0			0
$841$	−810.519			−0.963756
$842$	−99.9726	+	54.7805i	−0.118732	+	0.0650600i
$843$	761.362	−	240.592i	0.903158	−	0.285400i
$844$	623.467	+	398.087i	0.738705	+	0.471667i
$845$		0			0
$846$	−672.214	+	228.763i	−0.794579	+	0.270405i
$847$	−740.886	+	740.886i	−0.874717	+	0.874717i
$848$	410.004	−	1119.36i	0.483496	−	1.32001i
$849$	724.713	−	1394.34i	0.853608	−	1.64233i
$850$		0			0
$851$	122.078			0.143452
$852$	−1349.70	−	362.202i	−1.58415	−	0.425119i
$853$	462.091	−	462.091i	0.541724	−	0.541724i	−0.382310	−	0.924034i	$-0.624871\pi$
$853$	462.091	−	462.091i	0.541724	−	0.541724i	0.924034	+	0.382310i	$0.124871\pi$
$854$	267.255	−	915.173i	0.312945	−	1.07163i
$855$		0			0
$856$	659.500	−	576.583i	0.770444	−	0.673578i
$857$	343.527	−	343.527i	0.400848	−	0.400848i	−0.477684	−	0.878532i	$-0.658524\pi$
$857$	343.527	−	343.527i	0.400848	−	0.400848i	0.878532	+	0.477684i	$0.158524\pi$
$858$	282.256	−	6.19546i	0.328969	−	0.00722082i
$859$	1108.16			1.29006			0.645028	−	0.764159i	$-0.276846\pi$
$859$	1108.16			1.29006			0.645028	+	0.764159i	$0.276846\pi$
$860$		0			0
$861$	472.765	−	909.594i	0.549089	−	1.05644i
$862$	−256.726	+	140.674i	−0.297826	+	0.163195i
$863$	247.757	−	247.757i	0.287089	−	0.287089i	−0.548839	−	0.835928i	$-0.684930\pi$
$863$	247.757	−	247.757i	0.287089	−	0.287089i	0.835928	+	0.548839i	$0.184930\pi$
$864$	−241.249	−	829.636i	−0.279223	−	0.960226i
$865$		0			0
$866$	337.326	−	1155.12i	0.389522	−	1.33385i
$867$	826.002	−	261.019i	0.952713	−	0.301060i
$868$	−1942.58	+	428.580i	−2.23799	+	0.493756i
$869$	−247.123			−0.284377
$870$		0			0
$871$			483.754i			0.555401i
$872$	499.073	+	33.4782i	0.572332	+	0.0383924i
$873$	−308.846	−	54.0505i	−0.353776	−	0.0619135i
$874$	−131.781	+	451.263i	−0.150779	+	0.516320i
$875$		0			0
$876$	−1061.53	+	612.338i	−1.21180	+	0.699016i
$877$	−477.322	−	477.322i	−0.544266	−	0.544266i	0.380510	−	0.924777i	$-0.375748\pi$
$877$	−477.322	−	477.322i	−0.544266	−	0.544266i	−0.924777	+	0.380510i	$0.875748\pi$
$878$	1192.20	−	653.271i	1.35786	−	0.744044i
$879$	−98.4130	+	189.345i	−0.111960	+	0.215410i
$880$		0			0
$881$			907.230i			1.02977i	0.857259	+	0.514886i	$0.172166\pi$
$881$			907.230i			1.02977i	−0.857259	+	0.514886i	$0.827834\pi$
$882$	929.982	+	457.727i	1.05440	+	0.518965i
$883$	−55.2196	−	55.2196i	−0.0625364	−	0.0625364i	0.675147	−	0.737683i	$-0.264080\pi$
$883$	−55.2196	−	55.2196i	−0.0625364	−	0.0625364i	−0.737683	+	0.675147i	$0.764080\pi$
$884$	17.8059	+	11.3691i	0.0201424	+	0.0128610i
$885$		0			0
$886$	−152.809	+	523.270i	−0.172471	+	0.590599i
$887$	587.061	+	587.061i	0.661850	+	0.661850i	0.955816	−	0.293966i	$-0.0949753\pi$
$887$	587.061	+	587.061i	0.661850	+	0.661850i	−0.293966	+	0.955816i	$0.594975\pi$
$888$	98.4474	+	59.8594i	0.110864	+	0.0674092i
$889$			528.681i			0.594692i
$890$		0			0
$891$	121.510	−	336.522i	0.136374	−	0.377691i
$892$	−1141.04	+	251.742i	−1.27920	+	0.282222i
$893$	257.844	+	257.844i	0.288739	+	0.288739i
$894$	909.501	+	870.432i	1.01734	+	0.973637i
$895$		0			0
$896$	−536.534	+	1207.65i	−0.598810	+	1.34782i
$897$	−774.888	+	244.867i	−0.863867	+	0.272984i
$898$	−294.310	+	161.269i	−0.327740	+	0.179587i
$899$		−	265.955i		−	0.295834i
$900$		0			0
$901$	36.9394			0.0409982
$902$	140.510	+	256.426i	0.155776	+	0.284286i
$903$	19.1506	+	60.6027i	0.0212078	+	0.0671126i
$904$	−545.703	+	477.093i	−0.603654	+	0.527758i
$905$		0			0
$906$	−598.086	+	624.931i	−0.660139	+	0.689769i
$907$	570.349	−	570.349i	0.628831	−	0.628831i	−0.318943	−	0.947774i	$-0.603328\pi$
$907$	570.349	−	570.349i	0.628831	−	0.628831i	0.947774	+	0.318943i	$0.103328\pi$
$908$	−965.325	+	212.974i	−1.06313	+	0.234553i
$909$	−63.4470	−	90.3654i	−0.0697987	−	0.0994118i
$910$		0			0
$911$	809.153			0.888203			0.444102	−	0.895976i	$-0.353523\pi$
$911$	809.153			0.888203			0.444102	+	0.895976i	$0.353523\pi$
$912$	−327.544	+	299.296i	−0.359149	+	0.328175i
$913$	205.530	−	205.530i	0.225115	−	0.225115i
$914$	337.967	+	98.6954i	0.369767	+	0.107982i
$915$		0			0
$916$	−968.776	−	618.569i	−1.05762	−	0.675293i
$917$	−575.450	+	575.450i	−0.627535	+	0.627535i
$918$	21.5685	−	15.8614i	0.0234951	−	0.0172783i
$919$	−683.390			−0.743623			−0.371812	−	0.928308i	$-0.621263\pi$
$919$	−683.390			−0.743623			−0.371812	+	0.928308i	$0.621263\pi$
$920$		0			0
$921$	1112.65	+	578.303i	1.20809	+	0.627908i
$922$	341.206	+	622.689i	0.370071	+	0.675368i
$923$	−877.198	+	877.198i	−0.950377	+	0.950377i
$924$	−474.018	+	273.434i	−0.513006	+	0.295924i
$925$		0			0
$926$	−662.811	−	193.559i	−0.715778	−	0.209027i
$927$	266.210	+	46.5889i	0.287174	+	0.0502577i
$928$	−142.209	−	104.831i	−0.153242	−	0.112964i
$929$	533.625			0.574408			0.287204	−	0.957869i	$-0.407274\pi$
$929$	533.625			0.574408			0.287204	+	0.957869i	$0.407274\pi$
$930$		0			0
$931$		−	532.289i		−	0.571739i
$932$	8.36876	−	1.84635i	0.00897936	−	0.00198107i
$933$	152.352	+	482.122i	0.163292	+	0.516744i
$934$	500.153	+	146.058i	0.535496	+	0.156379i
$935$		0			0
$936$	−744.962	−	182.489i	−0.795899	−	0.194967i
$937$	−757.665	−	757.665i	−0.808607	−	0.808607i	0.175816	−	0.984423i	$-0.443744\pi$
$937$	−757.665	−	757.665i	−0.808607	−	0.808607i	−0.984423	+	0.175816i	$0.943744\pi$
$938$	−450.585	−	822.303i	−0.480368	−	0.876656i
$939$	526.364	+	273.580i	0.560558	+	0.291352i
$940$		0			0
$941$			1555.04i			1.65254i	0.563277	+	0.826268i	$0.309540\pi$
$941$			1555.04i			1.65254i	−0.563277	+	0.826268i	$0.690460\pi$
$942$	−30.1454	−	1373.38i	−0.0320015	−	1.45794i
$943$	−595.142	−	595.142i	−0.631116	−	0.631116i
$944$	357.900	−	166.003i	0.379132	−	0.175851i
$945$		0			0
$946$	−17.4017	−	5.08176i	−0.0183950	−	0.00537184i
$947$	385.141	+	385.141i	0.406696	+	0.406696i	0.880585	−	0.473889i	$-0.157150\pi$
$947$	385.141	+	385.141i	0.406696	+	0.406696i	−0.473889	+	0.880585i	$0.657150\pi$
$948$	648.417	+	174.007i	0.683984	+	0.183552i
$949$			1087.88i			1.14635i
$950$		0			0
$951$	−632.579	−	328.786i	−0.665173	−	0.345726i
$952$	−40.8566	−	2.74069i	−0.0429166	−	0.00287888i
$953$	450.513	+	450.513i	0.472731	+	0.472731i	0.902797	−	0.430066i	$-0.141510\pi$
$953$	450.513	+	450.513i	0.472731	+	0.472731i	−0.430066	+	0.902797i	$0.641510\pi$
$954$	−1269.60	+	432.060i	−1.33082	+	0.452893i
$955$		0			0
$956$	−915.088	−	584.289i	−0.957205	−	0.611181i
$957$	−22.0445	−	69.7606i	−0.0230350	−	0.0728951i
$958$	171.802	+	313.533i	0.179334	+	0.327279i
$959$			2609.75i			2.72133i
$960$		0			0
$961$	−1359.51			−1.41468
$962$	89.6971	−	49.1500i	0.0932403	−	0.0510915i
$963$	−970.754	−	169.889i	−1.00805	−	0.176417i
$964$	263.746	−	413.067i	0.273595	−	0.428493i
$965$		0			0
$966$	1089.11	−	1137.99i	1.12744	−	1.17804i
$967$	577.404	−	577.404i	0.597108	−	0.597108i	−0.342434	−	0.939542i	$-0.611251\pi$
$967$	577.404	−	577.404i	0.597108	−	0.597108i	0.939542	+	0.342434i	$0.111251\pi$
$968$	−54.3415	+	810.091i	−0.0561379	+	0.836871i
$969$	−12.1993	−	6.34065i	−0.0125896	−	0.00654350i
$970$		0			0
$971$	983.651			1.01303			0.506514	−	0.862231i	$-0.330934\pi$
$971$	983.651			1.01303			0.506514	+	0.862231i	$0.330934\pi$
$972$	−555.780	+	797.429i	−0.571790	+	0.820400i
$973$	113.077	−	113.077i	0.116214	−	0.116214i
$974$	9.34100	−	31.9868i	0.00959035	−	0.0328406i
$975$		0			0
$976$	−310.856	−	670.201i	−0.318500	−	0.686681i
$977$	−734.412	+	734.412i	−0.751702	+	0.751702i	−0.974797	−	0.223095i	$-0.928384\pi$
$977$	−734.412	+	734.412i	−0.751702	+	0.751702i	0.223095	+	0.974797i	$0.428384\pi$
$978$	−3.61351	−	164.626i	−0.00369479	−	0.168329i
$979$	−146.660			−0.149806
$980$		0			0
$981$	−323.352	−	460.539i	−0.329615	−	0.469459i
$982$	−1300.12	+	712.407i	−1.32395	+	0.725465i
$983$	−421.808	+	421.808i	−0.429103	+	0.429103i	−0.888323	−	0.459220i	$-0.848129\pi$
$983$	−421.808	+	421.808i	−0.429103	+	0.429103i	0.459220	+	0.888323i	$0.348129\pi$
$984$	−188.121	−	771.762i	−0.191180	−	0.784311i
$985$		0			0
$986$	1.53462	−	5.25504i	0.00155640	−	0.00532966i
$987$	−368.147	−	1165.01i	−0.372996	−	1.18036i
$988$	84.8574	+	384.624i	0.0858881	+	0.389296i
$989$	52.1821			0.0527625
$990$		0			0
$991$			1077.21i			1.08699i	0.839411	+	0.543496i	$0.182900\pi$
$991$			1077.21i			1.08699i	−0.839411	+	0.543496i	$0.817100\pi$
$992$	−914.667	+	1240.80i	−0.922044	+	1.25081i
$993$	796.810	−	251.794i	0.802427	−	0.253569i
$994$	674.040	−	2308.14i	0.678109	−	2.32208i
$995$		0			0
$996$	−684.002	+	394.562i	−0.686749	+	0.396147i
$997$	999.351	+	999.351i	1.00236	+	1.00236i	0.999997	+	0.00236078i	$0.000751461\pi$
$997$	999.351	+	999.351i	1.00236	+	1.00236i	0.00236078	+	0.999997i	$0.499249\pi$
$998$	−1156.50	+	633.711i	−1.15882	+	0.634981i
$999$	−17.1654	−	128.478i	−0.0171826	−	0.128607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.l.g.107.17		40
3.2	odd	2	inner	300.3.l.g.107.4		40
4.3	odd	2	inner	300.3.l.g.107.14		40
5.2	odd	4		60.3.l.a.23.14	yes	40
5.3	odd	4	inner	300.3.l.g.143.7		40
5.4	even	2		60.3.l.a.47.4	yes	40
12.11	even	2	inner	300.3.l.g.107.7		40
15.2	even	4		60.3.l.a.23.7	yes	40
15.8	even	4	inner	300.3.l.g.143.14		40
15.14	odd	2		60.3.l.a.47.17	yes	40
20.3	even	4	inner	300.3.l.g.143.4		40
20.7	even	4		60.3.l.a.23.17	yes	40
20.19	odd	2		60.3.l.a.47.7	yes	40
60.23	odd	4	inner	300.3.l.g.143.17		40
60.47	odd	4		60.3.l.a.23.4	✓	40
60.59	even	2		60.3.l.a.47.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.4	✓	40	60.47	odd	4
60.3.l.a.23.7	yes	40	15.2	even	4
60.3.l.a.23.14	yes	40	5.2	odd	4
60.3.l.a.23.17	yes	40	20.7	even	4
60.3.l.a.47.4	yes	40	5.4	even	2
60.3.l.a.47.7	yes	40	20.19	odd	2
60.3.l.a.47.14	yes	40	60.59	even	2
60.3.l.a.47.17	yes	40	15.14	odd	2
300.3.l.g.107.4		40	3.2	odd	2	inner
300.3.l.g.107.7		40	12.11	even	2	inner
300.3.l.g.107.14		40	4.3	odd	2	inner
300.3.l.g.107.17		40	1.1	even	1	trivial
300.3.l.g.143.4		40	20.3	even	4	inner
300.3.l.g.143.7		40	5.3	odd	4	inner
300.3.l.g.143.14		40	15.8	even	4	inner
300.3.l.g.143.17		40	60.23	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.75394 - 0.961083i) q^{2} +(-0.903948 - 2.86057i) q^{3} +(2.15264 - 3.37137i) q^{4} +(-4.33472 - 4.14852i) q^{6} +(7.30016 - 7.30016i) q^{7} +(0.535443 - 7.98206i) q^{8} +(-7.36576 + 5.17162i) q^{9} +O(q^{10})\)	\(q+(1.75394 - 0.961083i) q^{2} +(-0.903948 - 2.86057i) q^{3} +(2.15264 - 3.37137i) q^{4} +(-4.33472 - 4.14852i) q^{6} +(7.30016 - 7.30016i) q^{7} +(0.535443 - 7.98206i) q^{8} +(-7.36576 + 5.17162i) q^{9} +4.41713 q^{11} +(-11.5899 - 3.11024i) q^{12} +(-7.53253 + 7.53253i) q^{13} +(5.78801 - 19.8201i) q^{14} +(-6.73229 - 14.5147i) q^{16} +(0.350578 - 0.350578i) q^{17} +(-7.94877 + 16.1498i) q^{18} +9.24359 q^{19} +(-27.4816 - 14.2837i) q^{21} +(7.74740 - 4.24523i) q^{22} +(-17.9810 + 17.9810i) q^{23} +(-23.3173 + 5.68370i) q^{24} +(-5.97225 + 20.4510i) q^{26} +(21.4521 + 16.3954i) q^{27} +(-8.89693 - 40.3261i) q^{28} +5.52099 q^{29} -48.1716i q^{31} +(-25.7579 - 18.9877i) q^{32} +(-3.99285 - 12.6355i) q^{33} +(0.277960 - 0.951830i) q^{34} +(1.57963 + 35.9653i) q^{36} +(-3.39462 - 3.39462i) q^{37} +(16.2127 - 8.88386i) q^{38} +(28.3564 + 14.7383i) q^{39} +33.0983i q^{41} +(-61.9290 + 1.35933i) q^{42} +(-1.45103 - 1.45103i) q^{43} +(9.50848 - 14.8918i) q^{44} +(-14.2565 + 48.8190i) q^{46} +(27.8943 + 27.8943i) q^{47} +(-35.4347 + 32.3787i) q^{48} -57.5846i q^{49} +(-1.31976 - 0.685951i) q^{51} +(9.18014 + 41.6098i) q^{52} +(52.6835 + 52.6835i) q^{53} +(53.3830 + 8.13943i) q^{54} +(-54.3615 - 62.1791i) q^{56} +(-8.35573 - 26.4420i) q^{57} +(9.68351 - 5.30613i) q^{58} +24.6578i q^{59} +46.1739 q^{61} +(-46.2969 - 84.4904i) q^{62} +(-16.0176 + 91.5248i) q^{63} +(-63.4266 - 8.54787i) q^{64} +(-19.1470 - 18.3245i) q^{66} +(32.1110 - 32.1110i) q^{67} +(-0.427261 - 1.93660i) q^{68} +(67.6900 + 35.1822i) q^{69} +116.455 q^{71} +(37.3362 + 61.5630i) q^{72} +(72.2123 - 72.2123i) q^{73} +(-9.21650 - 2.69147i) q^{74} +(19.8981 - 31.1636i) q^{76} +(32.2457 - 32.2457i) q^{77} +(63.9003 - 1.40260i) q^{78} -55.9466 q^{79} +(27.5087 - 76.1858i) q^{81} +(31.8102 + 58.0526i) q^{82} +(46.5302 - 46.5302i) q^{83} +(-107.314 + 61.9031i) q^{84} +(-3.93959 - 1.15047i) q^{86} +(-4.99069 - 15.7932i) q^{87} +(2.36512 - 35.2578i) q^{88} -33.2025 q^{89} +109.977i q^{91} +(21.9141 + 99.3275i) q^{92} +(-137.798 + 43.5447i) q^{93} +(75.7338 + 22.1163i) q^{94} +(-31.0319 + 90.8462i) q^{96} +(24.6341 + 24.6341i) q^{97} +(-55.3436 - 101.000i) q^{98} +(-32.5355 + 22.8437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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