LMFDB - Embedded newform 300.3.l.g.107.14

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			107.14
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.961083 - 1.75394i) q^{2} +(0.903948 + 2.86057i) q^{3} +(-2.15264 - 3.37137i) q^{4} +(5.88605 + 1.16377i) q^{6} +(-7.30016 + 7.30016i) q^{7} +(-7.98206 + 0.535443i) q^{8} +(-7.36576 + 5.17162i) q^{9} +O(q^{10})$	\(q+(0.961083 - 1.75394i) q^{2} +(0.903948 + 2.86057i) q^{3} +(-2.15264 - 3.37137i) q^{4} +(5.88605 + 1.16377i) q^{6} +(-7.30016 + 7.30016i) q^{7} +(-7.98206 + 0.535443i) q^{8} +(-7.36576 + 5.17162i) q^{9} -4.41713 q^{11} +(7.69818 - 9.20533i) 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} +(1.99163 + 17.8895i) q^{18} -9.24359 q^{19} +(-27.4816 - 14.2837i) q^{21} +(-4.24523 + 7.74740i) q^{22} +(17.9810 - 17.9810i) q^{23} +(-8.74704 - 22.3493i) q^{24} +(5.97225 + 20.4510i) q^{26} +(-21.4521 - 16.3954i) q^{27} +(40.3261 + 8.89693i) q^{28} +5.52099 q^{29} +48.1716i q^{31} +(18.9877 + 25.7579i) q^{32} +(-3.99285 - 12.6355i) q^{33} +(-0.277960 - 0.951830i) q^{34} +(33.2913 + 13.7001i) q^{36} +(-3.39462 - 3.39462i) q^{37} +(-8.88386 + 16.2127i) q^{38} +(-28.3564 - 14.7383i) q^{39} +33.0983i q^{41} +(-51.4649 + 34.4734i) 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} +(-47.6060 - 6.13767i) q^{48} -57.5846i q^{49} +(1.31976 + 0.685951i) q^{51} +(41.6098 + 9.18014i) q^{52} +(52.6835 + 52.6835i) q^{53} +(-49.3738 + 21.8684i) q^{54} +(54.3615 - 62.1791i) q^{56} +(-8.35573 - 26.4420i) q^{57} +(5.30613 - 9.68351i) q^{58} -24.6578i q^{59} +46.1739 q^{61} +(84.4904 + 46.2969i) q^{62} +(16.0176 - 91.5248i) q^{63} +(63.4266 - 8.54787i) q^{64} +(-25.9995 - 5.14054i) q^{66} +(-32.1110 + 32.1110i) q^{67} +(-1.93660 - 0.427261i) q^{68} +(67.6900 + 35.1822i) q^{69} -116.455 q^{71} +(56.0248 - 45.2241i) 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} +(-53.1031 + 35.5707i) q^{78} +55.9466 q^{79} +(27.5087 - 76.1858i) q^{81} +(58.0526 + 31.8102i) q^{82} +(-46.5302 + 46.5302i) q^{83} +(11.0024 + 123.398i) q^{84} +(3.93959 - 1.15047i) q^{86} +(4.99069 + 15.7932i) q^{87} +(35.2578 - 2.36512i) q^{88} -33.2025 q^{89} -109.977i q^{91} +(-99.3275 - 21.9141i) q^{92} +(-137.798 + 43.5447i) q^{93} +(-75.7338 + 22.1163i) q^{94} +(-56.5184 + 77.5994i) q^{96} +(24.6341 + 24.6341i) q^{97} +(-101.000 - 55.3436i) 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 $

$2$	0.961083	−	1.75394i	0.480541	−	0.876972i
$2$	0.961083	−	1.75394i	0.480541	−	0.876972i
$3$	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
$6$	5.88605	+	1.16377i	0.981009	+	0.193962i
$7$	−7.30016	+	7.30016i	−1.04288	+	1.04288i	−0.0438411	+	0.999039i	$0.513960\pi$
$7$	−7.30016	+	7.30016i	−1.04288	+	1.04288i	−0.999039	+	0.0438411i	$0.986040\pi$
$8$	−7.98206	+	0.535443i	−0.997758	+	0.0669303i
$9$	−7.36576	+	5.17162i	−0.818417	+	0.574624i
$10$		0			0
$11$	−4.41713			−0.401557			−0.200779	−	0.979637i	$-0.564347\pi$
$11$	−4.41713			−0.401557			−0.200779	+	0.979637i	$0.564347\pi$
$12$	7.69818	−	9.20533i	0.641515	−	0.767111i
$13$	−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	$0.245358\pi$
$18$	1.99163	+	17.8895i	0.110646	+	0.993860i
$19$	−9.24359			−0.486505			−0.243252	−	0.969963i	$-0.578214\pi$
$19$	−9.24359			−0.486505			−0.243252	+	0.969963i	$0.578214\pi$
$20$		0			0
$21$	−27.4816	−	14.2837i	−1.30865	−	0.680175i
$22$	−4.24523	+	7.74740i	−0.192965	+	0.352154i
$23$	17.9810	−	17.9810i	0.781785	−	0.781785i	−0.198347	−	0.980132i	$-0.563557\pi$
$23$	17.9810	−	17.9810i	0.781785	−	0.781785i	0.980132	+	0.198347i	$0.0635573\pi$
$24$	−8.74704	−	22.3493i	−0.364460	−	0.931219i
$25$		0			0
$26$	5.97225	+	20.4510i	0.229702	+	0.786578i
$27$	−21.4521	−	16.3954i	−0.794520	−	0.607237i
$28$	40.3261	+	8.89693i	1.44022	+	0.317748i
$29$	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	$0.283240\pi$
$31$			48.1716i			1.55392i	−0.629548	+	0.776962i	$0.716760\pi$
$32$	18.9877	+	25.7579i	0.593365	+	0.804934i
$33$	−3.99285	−	12.6355i	−0.120996	−	0.382894i
$34$	−0.277960	−	0.951830i	−0.00817530	−	0.0279950i
$35$		0			0
$36$	33.2913	+	13.7001i	0.924757	+	0.380557i
$37$	−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	$0.770665\pi$
$38$	−8.88386	+	16.2127i	−0.233786	+	0.426651i
$39$	−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	$0.867746\pi$
$42$	−51.4649	+	34.4734i	−1.22535	+	0.820795i
$43$	1.45103	+	1.45103i	0.0337449	+	0.0337449i	0.723778	−	0.690033i	$-0.242404\pi$
$43$	1.45103	+	1.45103i	0.0337449	+	0.0337449i	−0.690033	+	0.723778i	$0.742404\pi$
$44$	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	0.345078	−	0.938574i	$-0.387853\pi$
$47$	−27.8943	−	27.8943i	−0.593496	−	0.593496i	−0.938574	+	0.345078i	$0.887853\pi$
$48$	−47.6060	−	6.13767i	−0.991791	−	0.127868i
$49$		−	57.5846i		−	1.17520i
$50$		0			0
$51$	1.31976	+	0.685951i	0.0258776	+	0.0134500i
$52$	41.6098	+	9.18014i	0.800188	+	0.176541i
$53$	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	$0.501895\pi$
$54$	−49.3738	+	21.8684i	−0.914330	+	0.404970i
$55$		0			0
$56$	54.3615	−	62.1791i	0.970741	−	1.11034i
$57$	−8.35573	−	26.4420i	−0.146592	−	0.463894i
$58$	5.30613	−	9.68351i	0.0914850	−	0.166957i
$59$		−	24.6578i		−	0.417929i	−0.977923	−	0.208964i	$-0.932991\pi$
$59$		−	24.6578i		−	0.417929i	0.977923	−	0.208964i	$-0.0670093\pi$
$60$		0			0
$61$	46.1739			0.756950			0.378475	−	0.925612i	$-0.376449\pi$
$61$	46.1739			0.756950			0.378475	+	0.925612i	$0.376449\pi$
$62$	84.4904	+	46.2969i	1.36275	+	0.746725i
$63$	16.0176	−	91.5248i	0.254247	−	1.45277i
$64$	63.4266	−	8.54787i	0.991041	−	0.133560i
$65$		0			0
$66$	−25.9995	−	5.14054i	−0.393931	−	0.0778869i
$67$	−32.1110	+	32.1110i	−0.479269	+	0.479269i	−0.904898	−	0.425629i	$-0.860053\pi$
$67$	−32.1110	+	32.1110i	−0.479269	+	0.479269i	0.425629	+	0.904898i	$0.360053\pi$
$68$	−1.93660	−	0.427261i	−0.0284794	−	0.00628325i
$69$	67.6900	+	35.1822i	0.981015	+	0.509887i
$70$		0			0
$71$	−116.455			−1.64021			−0.820103	−	0.572216i	$-0.806084\pi$
$71$	−116.455			−1.64021			−0.820103	+	0.572216i	$0.806084\pi$
$72$	56.0248	−	45.2241i	0.778122	−	0.628113i
$73$	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
$78$	−53.1031	+	35.5707i	−0.680808	+	0.456035i
$79$	55.9466			0.708185			0.354092	−	0.935210i	$-0.384790\pi$
$79$	55.9466			0.708185			0.354092	+	0.935210i	$0.384790\pi$
$80$		0			0
$81$	27.5087	−	76.1858i	0.339614	−	0.940565i
$82$	58.0526	+	31.8102i	0.707958	+	0.387929i
$83$	−46.5302	+	46.5302i	−0.560605	+	0.560605i	−0.929479	−	0.368874i	$-0.879743\pi$
$83$	−46.5302	+	46.5302i	−0.560605	+	0.560605i	0.368874	+	0.929479i	$0.379743\pi$
$84$	11.0024	+	123.398i	0.130981	+	1.46903i
$85$		0			0
$86$	3.93959	−	1.15047i	0.0458092	−	0.0133775i
$87$	4.99069	+	15.7932i	0.0573642	+	0.181531i
$88$	35.2578	−	2.36512i	0.400657	−	0.0268763i
$89$	−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
$92$	−99.3275	−	21.9141i	−1.07965	−	0.238196i
$93$	−137.798	+	43.5447i	−1.48170	+	0.468222i
$94$	−75.7338	+	22.1163i	−0.805679	+	0.235280i
$95$		0			0
$96$	−56.5184	+	77.5994i	−0.588733	+	0.808327i
$97$	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	$0.692527\pi$
$98$	−101.000	−	55.3436i	−1.03061	−	0.564730i
$99$	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	$0.980656\pi$
$102$	2.47152	−	1.65553i	0.0242306	−	0.0162307i
$103$	21.2333	+	21.2333i	0.206149	+	0.206149i	0.802628	−	0.596479i	$-0.203434\pi$
$103$	21.2333	+	21.2333i	0.206149	+	0.206149i	−0.596479	+	0.802628i	$0.703434\pi$
$104$	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	0.245710	−	0.969343i	$-0.420979\pi$
$107$	−77.4288	−	77.4288i	−0.723634	−	0.723634i	−0.969343	+	0.245710i	$0.920979\pi$
$108$	−9.09647	+	107.616i	−0.0842266	+	0.996447i
$109$			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
$112$	−56.8128	−	155.106i	−0.507257	−	1.38488i
$113$	−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	$0.881307\pi$
$114$	−54.4083	−	10.7574i	−0.477266	−	0.0943636i
$115$		0			0
$116$	−11.8847	−	18.6133i	−0.102454	−	0.160460i
$117$	16.5274	−	94.4382i	0.141260	−	0.807164i
$118$	−43.2484	−	23.6982i	−0.366512	−	0.200832i
$119$			5.11856i			0.0430131i
$120$		0			0
$121$	−101.489			−0.838752
$122$	44.3770	−	80.9865i	0.363746	−	0.663824i
$123$	−94.6801	+	29.9191i	−0.769757	+	0.243245i
$124$	162.404	−	103.696i	1.30971	−	0.836259i
$125$		0			0
$126$	−145.135	−	116.057i	−1.15187	−	0.921086i
$127$	36.2102	−	36.2102i	0.285120	−	0.285120i	−0.550027	−	0.835147i	$-0.685383\pi$
$127$	36.2102	−	36.2102i	0.285120	−	0.285120i	0.835147	+	0.550027i	$0.185383\pi$
$128$	45.9657	−	119.462i	0.359107	−	0.933296i
$129$	−2.83912	+	5.46244i	−0.0220087	+	0.0423445i
$130$		0			0
$131$	78.8270			0.601733			0.300866	−	0.953666i	$-0.402724\pi$
$131$	78.8270			0.601733			0.300866	+	0.953666i	$0.402724\pi$
$132$	−34.0038	+	40.6611i	−0.257605	+	0.308039i
$133$	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	$0.876081\pi$
$138$	126.763	−	84.9116i	0.918575	−	0.615301i
$139$	−15.4896			−0.111436			−0.0557180	−	0.998447i	$-0.517745\pi$
$139$	−15.4896			−0.111436			−0.0557180	+	0.998447i	$0.517745\pi$
$140$		0			0
$141$	54.5787	−	105.009i	0.387083	−	0.744743i
$142$	−111.922	+	204.255i	−0.788187	+	1.43841i
$143$	33.2722	−	33.2722i	0.232672	−	0.232672i
$144$	−25.4761	−	141.729i	−0.176917	−	0.984226i
$145$		0			0
$146$	−57.2544	−	196.058i	−0.392153	−	1.34287i
$147$	164.725	−	52.0535i	1.12058	−	0.354105i
$148$	−4.13714	+	18.7519i	−0.0279536	+	0.126702i
$149$	−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	$0.158413\pi$
$151$			144.169i			0.954759i	−0.878697	+	0.477380i	$0.841587\pi$
$152$	73.7829	−	4.94941i	0.485414	−	0.0325619i
$153$	−0.769217	+	4.39533i	−0.00502756	+	0.0287277i
$154$	−25.5664	−	87.5480i	−0.166016	−	0.568494i
$155$		0			0
$156$	11.3526	+	127.326i	0.0727733	+	0.816194i
$157$	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	$0.489918\pi$
$158$	53.7693	−	98.1272i	0.340312	−	0.621058i
$159$	−103.082	+	198.328i	−0.648313	+	1.24735i
$160$		0			0
$161$			262.529i			1.63061i
$162$	−107.187	−	121.470i	−0.661651	−	0.749812i
$163$	−19.4060	−	19.4060i	−0.119055	−	0.119055i	0.645069	−	0.764124i	$-0.276829\pi$
$163$	−19.4060	−	19.4060i	−0.119055	−	0.119055i	−0.764124	+	0.645069i	$0.776829\pi$
$164$	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	$0.0339216\pi$
$167$	183.816	+	183.816i	1.10069	+	1.10069i	0.106366	+	0.994327i	$0.466078\pi$
$168$	227.008	+	99.2983i	1.35124	+	0.591061i
$169$			55.5219i			0.328532i
$170$		0			0
$171$	68.0861	−	47.8043i	0.398164	−	0.279558i
$172$	1.76842	−	8.01551i	0.0102815	−	0.0466018i
$173$	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	$0.447764\pi$
$174$	32.4969	+	6.42518i	0.186764	+	0.0369263i
$175$		0			0
$176$	29.7374	−	64.1133i	0.168962	−	0.364280i
$177$	70.5354	−	22.2894i	0.398505	−	0.125929i
$178$	−31.9103	+	58.2353i	−0.179272	+	0.327165i
$179$		−	167.155i		−	0.933828i	−0.884303	−	0.466914i	$-0.845366\pi$
$179$		−	167.155i		−	0.933828i	0.884303	−	0.466914i	$-0.154634\pi$
$180$		0			0
$181$	46.3698			0.256187			0.128093	−	0.991762i	$-0.459114\pi$
$181$	46.3698			0.256187			0.128093	+	0.991762i	$0.459114\pi$
$182$	−192.894	−	105.697i	−1.05986	−	0.580755i
$183$	41.7388	+	132.084i	0.228081	+	0.721770i
$184$	−133.898	+	153.154i	−0.727707	+	0.832357i
$185$		0			0
$186$	−56.0609	+	283.541i	−0.301403	+	1.52441i
$187$	−1.54855	+	1.54855i	−0.00828102	+	0.00828102i
$188$	−33.9957	+	154.089i	−0.180828	+	0.819620i
$189$	276.292	−	36.9143i	1.46186	−	0.195314i
$190$		0			0
$191$	299.293			1.56698			0.783490	−	0.621405i	$-0.213438\pi$
$191$	299.293			1.56698			0.783490	+	0.621405i	$0.213438\pi$
$192$	81.7862	+	173.710i	0.425970	+	0.904737i
$193$	−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	$0.243921\pi$
$198$	−8.79727	−	79.0201i	−0.0444307	−	0.399091i
$199$	−61.5955			−0.309525			−0.154762	−	0.987952i	$-0.549461\pi$
$199$	−61.5955			−0.309525			−0.154762	+	0.987952i	$0.549461\pi$
$200$		0			0
$201$	−120.883	−	62.8292i	−0.601406	−	0.312583i
$202$	21.5179	+	11.7909i	0.106524	+	0.0583706i
$203$	−40.3041	+	40.3041i	−0.198542	+	0.198542i
$204$	−0.528374	−	5.92601i	−0.00259007	−	0.0290490i
$205$		0			0
$206$	57.6491	−	16.8351i	0.279850	−	0.0817237i
$207$	−39.4529	+	225.435i	−0.190594	+	1.08906i
$208$	−58.6212	−	160.044i	−0.281833	−	0.769440i
$209$	40.8301			0.195360
$210$		0			0
$211$		−	184.930i		−	0.876444i	−0.898867	−	0.438222i	$-0.855608\pi$
$211$		−	184.930i		−	0.876444i	0.898867	−	0.438222i	$-0.144392\pi$
$212$	64.2070	−	291.024i	0.302863	−	1.37275i
$213$	−105.269	−	333.127i	−0.494220	−	1.56398i
$214$	−210.221	+	61.3903i	−0.982343	+	0.286871i
$215$		0			0
$216$	180.010	+	119.383i	0.833381	+	0.552698i
$217$	−351.661	−	351.661i	−1.62056	−	1.62056i
$218$	109.664	+	60.0911i	0.503047	+	0.275647i
$219$	271.845	+	141.292i	1.24130	+	0.645171i
$220$		0			0
$221$			5.28149i			0.0238981i
$222$	−16.0304	−	23.9315i	−0.0722089	−	0.107800i
$223$	206.560	+	206.560i	0.926280	+	0.926280i	0.997463	−	0.0711833i	$-0.0226775\pi$
$223$	206.560	+	206.560i	0.926280	+	0.926280i	−0.0711833	+	0.997463i	$0.522678\pi$
$224$	−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	0.978076	−	0.208249i	$-0.0667763\pi$
$227$	174.751	+	174.751i	0.769827	+	0.769827i	−0.208249	+	0.978076i	$0.566776\pi$
$228$	−71.1588	+	85.0903i	−0.312100	+	0.373203i
$229$		−	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
$232$	−44.0689	+	2.95617i	−0.189952	+	0.0127421i
$233$	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	$0.748537\pi$
$234$	−149.755	−	119.751i	−0.639979	−	0.511757i
$235$		0			0
$236$	−83.1306	+	53.0794i	−0.352248	+	0.224913i
$237$	50.5728	+	160.039i	0.213387	+	0.675271i
$238$	8.97766	+	4.91936i	0.0377213	+	0.0206696i
$239$			271.429i			1.13569i	0.823137	+	0.567843i	$0.192222\pi$
$239$			271.429i			1.13569i	−0.823137	+	0.567843i	$0.807778\pi$
$240$		0			0
$241$	122.522			0.508390			0.254195	−	0.967153i	$-0.418190\pi$
$241$	122.522			0.508390			0.254195	+	0.967153i	$0.418190\pi$
$242$	−97.5393	+	178.006i	−0.403055	+	0.735562i
$243$	242.801	+	9.82275i	0.999183	+	0.0404229i
$244$	−99.3959	−	155.669i	−0.407360	−	0.637990i
$245$		0			0
$246$	−38.5189	+	194.818i	−0.156581	+	0.791945i
$247$	69.6277	−	69.6277i	0.281893	−	0.281893i
$248$	−25.7931	−	384.509i	−0.104005	−	1.55044i
$249$	−175.164	−	91.0422i	−0.703470	−	0.365631i
$250$		0			0
$251$	−335.099			−1.33506			−0.667529	−	0.744584i	$-0.732648\pi$
$251$	−335.099			−1.33506			−0.667529	+	0.744584i	$0.732648\pi$
$252$	−343.044	+	143.019i	−1.36129	+	0.567535i
$253$	−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	$0.259959\pi$
$258$	6.85218	+	10.2295i	0.0265588	+	0.0396493i
$259$	49.5626			0.191361
$260$		0			0
$261$	−40.6663	+	28.5525i	−0.155809	+	0.109396i
$262$	75.7593	−	138.258i	0.289158	−	0.527703i
$263$	−211.355	+	211.355i	−0.803631	+	0.803631i	−0.983661	−	0.180030i	$-0.942380\pi$
$263$	−211.355	+	211.355i	−0.803631	+	0.803631i	0.180030	+	0.983661i	$0.442380\pi$
$264$	38.6368	+	98.7195i	0.146352	+	0.373938i
$265$		0			0
$266$	−53.5020	−	183.209i	−0.201135	−	0.688756i
$267$	−30.0133	−	94.9781i	−0.112409	−	0.355723i
$268$	177.382	+	39.1347i	0.661871	+	0.146025i
$269$	−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	$0.113796\pi$
$271$			189.665i			0.699869i	−0.936774	+	0.349935i	$0.886204\pi$
$272$	2.72834	+	7.44873i	0.0100307	+	0.0273850i
$273$	314.598	−	99.4138i	1.15237	−	0.364153i
$274$	141.721	+	485.301i	0.517230	+	1.77117i
$275$		0			0
$276$	−27.1001	−	303.943i	−0.0981888	−	1.10124i
$277$	−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	$0.788173\pi$
$278$	−14.8868	+	27.1679i	−0.0535496	+	0.0977263i
$279$	−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	$0.842958\pi$
$282$	−131.725	−	196.650i	−0.467109	−	0.697341i
$283$	−370.389	−	370.389i	−1.30880	−	1.30880i	−0.922285	−	0.386512i	$-0.873680\pi$
$283$	−370.389	−	370.389i	−1.30880	−	1.30880i	−0.386512	−	0.922285i	$-0.626320\pi$
$284$	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
$288$	−273.068	−	91.5292i	−0.948154	−	0.317810i
$289$			288.754i			0.999149i
$290$		0			0
$291$	−48.1996	+	92.7354i	−0.165634	+	0.318678i
$292$	−398.902	−	88.0074i	−1.36610	−	0.301395i
$293$	−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	$0.788733\pi$
$294$	67.0154	−	338.946i	0.227944	−	1.15288i
$295$		0			0
$296$	28.9137	+	25.2785i	0.0976815	+	0.0854003i
$297$	94.7565	+	72.4206i	0.319045	+	0.243840i
$298$	−201.652	+	368.008i	−0.676685	+	1.23493i
$299$			270.886i			0.905972i
$300$		0			0
$301$	−21.1855			−0.0703838
$302$	252.864	+	138.558i	0.837297	+	0.458801i
$303$	−35.0944	+	11.0899i	−0.115823	+	0.0366004i
$304$	62.2305	−	134.168i	0.204706	−	0.441342i
$305$		0			0
$306$	6.96989	+	5.57344i	0.0227774	+	0.0182139i
$307$	295.562	−	295.562i	0.962741	−	0.962741i	−0.0365891	−	0.999330i	$-0.511649\pi$
$307$	295.562	−	295.562i	0.962741	−	0.962741i	0.999330	+	0.0365891i	$0.0116493\pi$
$308$	−178.126	−	39.2989i	−0.578330	−	0.127594i
$309$	−41.5457	+	79.9333i	−0.134452	+	0.258684i
$310$		0			0
$311$	168.540			0.541930			0.270965	−	0.962589i	$-0.412657\pi$
$311$	168.540			0.541930			0.270965	+	0.962589i	$0.412657\pi$
$312$	234.234	+	102.459i	0.750750	+	0.328395i
$313$	−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	$0.127702\pi$
$318$	248.786	+	371.409i	0.782346	+	1.16795i
$319$	−24.3869			−0.0764480
$320$		0			0
$321$	151.499	−	291.482i	0.471960	−	0.908045i
$322$	460.461	+	252.312i	1.43000	+	0.783578i
$323$	−3.24061	+	3.24061i	−0.0100328	+	0.0100328i
$324$	−316.067	+	71.2584i	−0.975515	+	0.219933i
$325$		0			0
$326$	−52.6878	+	15.3863i	−0.161619	+	0.0471971i
$327$	−178.855	+	56.5187i	−0.546958	+	0.172840i
$328$	−17.7222	−	264.193i	−0.0540312	−	0.805465i
$329$	407.266			1.23789
$330$		0			0
$331$		−	278.549i		−	0.841538i	−0.907168	−	0.420769i	$-0.861760\pi$
$331$		−	278.549i		−	0.841538i	0.907168	−	0.420769i	$-0.138240\pi$
$332$	257.034	+	56.7079i	0.774197	+	0.170807i
$333$	42.5597	+	7.44827i	0.127807	+	0.0223672i
$334$	499.065	−	145.740i	1.49421	−	0.436349i
$335$		0			0
$336$	392.337	−	302.725i	1.16767	−	0.900968i
$337$	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	$0.465875\pi$
$338$	97.3823	+	53.3611i	0.288113	+	0.157873i
$339$	125.358	−	241.187i	0.369787	−	0.711466i
$340$		0			0
$341$		−	212.780i		−	0.623989i
$342$	−18.4098	−	165.363i	−0.0538298	−	0.483518i
$343$	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	0.437571	−	0.899184i	$-0.355839\pi$
$347$	−160.180	−	160.180i	−0.461613	−	0.461613i	−0.899184	+	0.437571i	$0.855839\pi$
$348$	42.5016	−	50.8225i	0.122131	−	0.146042i
$349$			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
$352$	−83.8710	−	113.776i	−0.238270	−	0.323227i
$353$	−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	$0.842550\pi$
$354$	28.6961	−	145.137i	0.0810624	−	0.409992i
$355$		0			0
$356$	71.4730	+	111.938i	0.200767	+	0.314432i
$357$	−14.6420	+	4.62691i	−0.0410140	+	0.0129605i
$358$	−293.181	−	160.650i	−0.818941	−	0.448743i
$359$		−	388.897i		−	1.08328i	−0.840611	−	0.541639i	$-0.817804\pi$
$359$		−	388.897i		−	1.08328i	0.840611	−	0.541639i	$-0.182196\pi$
$360$		0			0
$361$	−275.556			−0.763313
$362$	44.5652	−	81.3301i	0.123108	−	0.224669i
$363$	−91.7408	−	290.317i	−0.252729	−	0.799770i
$364$	−370.774	+	236.742i	−1.01861	+	0.650389i
$365$		0			0
$366$	271.782	+	53.7360i	0.742575	+	0.146820i
$367$	−361.520	+	361.520i	−0.985069	+	0.985069i	−0.999890	−	0.0148215i	$-0.995282\pi$
$367$	−361.520	+	361.520i	−0.985069	+	0.985069i	0.0148215	+	0.999890i	$0.495282\pi$
$368$	139.936	+	382.043i	0.380260	+	1.03816i
$369$	−171.172	−	243.794i	−0.463880	−	0.660688i
$370$		0			0
$371$	−769.195			−2.07330
$372$	443.436	+	370.834i	1.19203	+	0.996865i
$373$	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
$378$	200.794	−	520.079i	0.531202	−	1.37587i
$379$	40.1346			0.105896			0.0529480	−	0.998597i	$-0.483138\pi$
$379$	40.1346			0.105896			0.0529480	+	0.998597i	$0.483138\pi$
$380$		0			0
$381$	136.314	+	70.8499i	0.357780	+	0.185958i
$382$	287.645	−	524.943i	0.752998	−	1.37420i
$383$	340.574	−	340.574i	0.889226	−	0.889226i	−0.105223	−	0.994449i	$-0.533556\pi$
$383$	340.574	−	340.574i	0.889226	−	0.889226i	0.994449	+	0.105223i	$0.0335556\pi$
$384$	383.280	+	23.5010i	0.998125	+	0.0612004i
$385$		0			0
$386$	164.156	+	562.126i	0.425275	+	1.45628i
$387$	−18.1921	−	3.18376i	−0.0470081	−	0.00822678i
$388$	30.0223	−	136.079i	0.0773771	−	0.350719i
$389$	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
$392$	30.8332	+	459.644i	0.0786562	+	1.17256i
$393$	71.2555	+	225.490i	0.181312	+	0.573767i
$394$	−4.21796	−	14.4437i	−0.0107055	−	0.0366592i
$395$		0			0
$396$	−147.052	−	60.5149i	−0.371343	−	0.152816i
$397$	−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	$0.945434\pi$
$398$	−59.1983	+	108.035i	−0.148740	+	0.271445i
$399$	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	$-0.299635\pi$
$402$	−226.377	+	151.637i	−0.563127	+	0.377207i
$403$	−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
$408$	−10.9017	−	4.76864i	−0.0267198	−	0.0116879i
$409$		−	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
$412$	25.8777	−	117.293i	0.0628100	−	0.284692i
$413$	180.006	+	180.006i	0.435849	+	0.435849i
$414$	357.483	+	285.860i	0.863486	+	0.690483i
$415$		0			0
$416$	−337.047	−	50.9968i	−0.810210	−	0.122588i
$417$	−14.0018	−	44.3092i	−0.0335775	−	0.106257i
$418$	39.2411	−	71.6138i	0.0938783	−	0.171325i
$419$		−	317.783i		−	0.758433i	−0.925308	−	0.379216i	$-0.876194\pi$
$419$		−	317.783i		−	0.758433i	0.925308	−	0.379216i	$-0.123806\pi$
$420$		0			0
$421$	−56.9987			−0.135389			−0.0676944	−	0.997706i	$-0.521564\pi$
$421$	−56.9987			−0.135389			−0.0676944	+	0.997706i	$0.521564\pi$
$422$	−324.356	−	177.733i	−0.768617	−	0.421168i
$423$	349.722	+	61.2040i	0.826765	+	0.144690i
$424$	−448.732	−	392.314i	−1.05833	−	0.925268i
$425$		0			0
$426$	−685.458	−	135.527i	−1.60906	−	0.318138i
$427$	−337.077	+	337.077i	−0.789408	+	0.789408i
$428$	−94.3649	+	427.718i	−0.220479	+	0.999340i
$429$	125.254	+	65.1011i	0.291967	+	0.151751i
$430$		0			0
$431$	146.371			0.339607			0.169803	−	0.985478i	$-0.445687\pi$
$431$	146.371			0.339607			0.169803	+	0.985478i	$0.445687\pi$
$432$	382.396	−	200.991i	0.885175	−	0.465258i
$433$	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
$438$	509.084	−	341.007i	1.16229	−	0.778555i
$439$	−679.724			−1.54835			−0.774173	−	0.632974i	$-0.781834\pi$
$439$	−679.724			−1.54835			−0.774173	+	0.632974i	$0.781834\pi$
$440$		0			0
$441$	297.806	+	424.154i	0.675296	+	0.961801i
$442$	9.26343	+	5.07595i	0.0209580	+	0.0114840i
$443$	192.731	−	192.731i	0.435059	−	0.435059i	−0.455286	−	0.890345i	$-0.650463\pi$
$443$	192.731	−	192.731i	0.435059	−	0.435059i	0.890345	+	0.455286i	$0.150463\pi$
$444$	−57.3811	+	5.11620i	−0.129237	+	0.0115230i
$445$		0			0
$446$	560.817	−	163.774i	1.25744	−	0.367206i
$447$	−189.664	−	600.199i	−0.424305	−	1.34273i
$448$	−400.623	+	525.425i	−0.894249	+	1.17282i
$449$	−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
$452$	−78.0822	+	353.915i	−0.172748	+	0.782997i
$453$	−412.405	+	130.321i	−0.910386	+	0.287684i
$454$	474.453	−	138.553i	1.04505	−	0.305183i
$455$		0			0
$456$	80.8541	+	206.587i	0.177312	+	0.453043i
$457$	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	$0.688306\pi$
$458$	−504.002	−	276.171i	−1.10044	−	0.602993i
$459$	−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	$0.874182\pi$
$462$	227.327	−	152.273i	0.492049	−	0.329596i
$463$	244.127	+	244.127i	0.527272	+	0.527272i	0.919758	−	0.392486i	$-0.128385\pi$
$463$	244.127	+	244.127i	0.527272	+	0.527272i	−0.392486	+	0.919758i	$0.628385\pi$
$464$	−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	0.481808	−	0.876277i	$-0.339980\pi$
$467$	−184.217	−	184.217i	−0.394468	−	0.394468i	−0.876277	+	0.481808i	$0.839980\pi$
$468$	−353.964	+	147.571i	−0.756333	+	0.315323i
$469$		−	468.831i		−	0.999639i
$470$		0			0
$471$	−316.764	+	609.449i	−0.672535	+	1.29395i
$472$	13.2028	+	196.820i	0.0279721	+	0.416992i
$473$	−6.40939	−	6.40939i	−0.0135505	−	0.0135505i
$474$	329.305	+	65.1092i	0.694736	+	0.137361i
$475$		0			0
$476$	17.2566	−	11.0184i	0.0362533	−	0.0231479i
$477$	−660.512	−	115.595i	−1.38472	−	0.242337i
$478$	476.071	+	260.866i	0.995965	+	0.545744i
$479$		−	178.759i		−	0.373192i	−0.982437	−	0.186596i	$-0.940254\pi$
$479$		−	178.759i		−	0.373192i	0.982437	−	0.186596i	$-0.0597455\pi$
$480$		0			0
$481$	51.1402			0.106321
$482$	117.754	−	214.897i	0.244302	−	0.445844i
$483$	−750.983	+	237.313i	−1.55483	+	0.491330i
$484$	218.469	+	342.157i	0.451383	+	0.706936i
$485$		0			0
$486$	250.581	−	416.420i	0.515598	−	0.856830i
$487$	−11.7814	+	11.7814i	−0.0241918	+	0.0241918i	−0.719099	−	0.694907i	$-0.755445\pi$
$487$	−11.7814	+	11.7814i	−0.0241918	+	0.0241918i	0.694907	+	0.719099i	$0.255445\pi$
$488$	−368.563	+	24.7235i	−0.755253	+	0.0506629i
$489$	37.9703	−	73.0543i	0.0776488	−	0.149395i
$490$		0			0
$491$	741.254			1.50968			0.754842	−	0.655907i	$-0.227714\pi$
$491$	741.254			1.50968			0.754842	+	0.655907i	$0.227714\pi$
$492$	304.681	+	254.797i	0.619270	+	0.517879i
$493$	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
$498$	−328.030	+	219.729i	−0.658695	+	0.441223i
$499$	659.372			1.32139			0.660693	−	0.750656i	$-0.270262\pi$
$499$	659.372			1.32139			0.660693	+	0.750656i	$0.270262\pi$
$500$		0			0
$501$	−359.659	+	691.978i	−0.717881	+	1.38119i
$502$	−322.058	+	587.746i	−0.641550	+	1.17081i
$503$	138.296	−	138.296i	0.274942	−	0.274942i	−0.556144	−	0.831086i	$-0.687720\pi$
$503$	138.296	−	138.296i	0.274942	−	0.274942i	0.831086	+	0.556144i	$0.187720\pi$
$504$	−78.8468	+	739.133i	−0.156442	+	1.46653i
$505$		0			0
$506$	62.9727	+	215.640i	0.124452	+	0.426166i
$507$	−158.824	+	50.1889i	−0.313263	+	0.0989919i
$508$	−200.026	−	44.1306i	−0.393751	−	0.0868712i
$509$	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
$512$	−501.698	+	102.191i	−0.979879	+	0.199592i
$513$	198.294	+	151.553i	0.386538	+	0.295424i
$514$	9.01444	+	30.8685i	0.0175378	+	0.0600555i
$515$		0			0
$516$	24.5275	−	2.18692i	0.0475339	−	0.00423821i
$517$	123.213	+	123.213i	0.238323	+	0.238323i
$518$	47.6338	−	86.9300i	0.0919571	−	0.167819i
$519$	−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	$-0.193190\pi$
$522$	10.9958	+	98.7676i	0.0210647	+	0.189210i
$523$	543.498	+	543.498i	1.03919	+	1.03919i	0.999200	+	0.0399922i	$0.0127333\pi$
$523$	543.498	+	543.498i	1.03919	+	1.03919i	0.0399922	+	0.999200i	$0.487267\pi$
$524$	−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
$528$	210.282	+	27.1109i	0.398261	+	0.0513463i
$529$		−	117.636i		−	0.222375i
$530$		0			0
$531$	127.521	+	181.623i	0.240152	+	0.342040i
$532$	−372.759	−	82.2396i	−0.700674	−	0.154586i
$533$	−249.314	−	249.314i	−0.467756	−	0.467756i
$534$	−195.432	−	38.6402i	−0.365977	−	0.0723599i
$535$		0			0
$536$	239.118	−	273.506i	0.446116	−	0.510272i
$537$	478.160	−	151.100i	0.890428	−	0.281377i
$538$	−167.663	+	305.980i	−0.311642	+	0.568736i
$539$			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	$0.635555\pi$
$542$	332.661	+	182.283i	0.613766	+	0.336316i
$543$	41.9159	+	132.644i	0.0771932	+	0.244280i
$544$	15.6868	+	2.37349i	0.0288361	+	0.00436303i
$545$		0			0
$546$	127.989	−	647.333i	0.234412	−	1.18559i
$547$	492.299	−	492.299i	0.899998	−	0.899998i	−0.0954376	−	0.995435i	$-0.530425\pi$
$547$	492.299	−	492.299i	0.899998	−	0.899998i	0.995435	+	0.0954376i	$0.0304250\pi$
$548$	987.397	+	217.844i	1.80182	+	0.397525i
$549$	−340.106	+	238.794i	−0.619501	+	0.434962i
$550$		0			0
$551$	−51.0338			−0.0926203
$552$	−559.144	−	244.582i	−1.01294	−	0.443084i
$553$	−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	$0.404470\pi$
$558$	−861.765	+	95.9400i	−1.54438	+	0.171935i
$559$	−21.8599			−0.0391053
$560$		0			0
$561$	−5.82955	−	3.02993i	−0.0103914	−	0.00540095i
$562$	466.825	+	255.799i	0.830650	+	0.455159i
$563$	−129.412	+	129.412i	−0.229861	+	0.229861i	−0.812635	−	0.582773i	$-0.801968\pi$
$563$	−129.412	+	129.412i	−0.229861	+	0.229861i	0.582773	+	0.812635i	$0.301968\pi$
$564$	−471.512	+	42.0409i	−0.836014	+	0.0745405i
$565$		0			0
$566$	−1005.62	+	293.667i	−1.77671	+	0.518847i
$567$	355.350	+	756.986i	0.626720	+	1.33507i
$568$	929.548	−	62.3547i	1.63653	−	0.109779i
$569$	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	$0.0428618\pi$
$571$			153.311i			0.268496i	−0.990948	+	0.134248i	$0.957138\pi$
$572$	−183.796	−	40.5498i	−0.321321	−	0.0708913i
$573$	270.545	+	856.149i	0.472156	+	1.49415i
$574$	−656.012	+	191.573i	−1.14288	+	0.333751i
$575$		0			0
$576$	−422.979	+	390.980i	−0.734338	+	0.678784i
$577$	−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	$0.904109\pi$
$578$	506.459	+	277.517i	0.876226	+	0.480133i
$579$	−779.416	−	405.105i	−1.34614	−	0.699662i
$580$		0			0
$581$		−	679.356i		−	1.16929i
$582$	116.329	+	173.666i	0.199878	+	0.298395i
$583$	−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	0.635322	−	0.772247i	$-0.280867\pi$
$587$	−80.3753	−	80.3753i	−0.136925	−	0.136925i	−0.772247	+	0.635322i	$0.780867\pi$
$588$	−530.085	−	443.297i	−0.901505	−	0.753906i
$589$		−	445.279i		−	0.755992i
$590$		0			0
$591$	20.0270	+	10.4091i	0.0338866	+	0.0176127i
$592$	72.1255	−	26.4184i	0.121834	−	0.0446256i
$593$	−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	$0.916005\pi$
$594$	218.091	−	96.5953i	0.367156	−	0.162618i
$595$		0			0
$596$	451.662	+	707.373i	0.757822	+	1.18687i
$597$	−55.6791	−	176.198i	−0.0932648	−	0.295140i
$598$	475.118	+	260.344i	0.794512	+	0.435357i
$599$			806.349i			1.34616i	0.739570	+	0.673080i	$0.235029\pi$
$599$			806.349i			1.34616i	−0.739570	+	0.673080i	$0.764971\pi$
$600$		0			0
$601$	687.797			1.14442			0.572211	−	0.820107i	$-0.306086\pi$
$601$	687.797			1.14442			0.572211	+	0.820107i	$0.306086\pi$
$602$	−20.3610	+	37.1582i	−0.0338223	+	0.0617246i
$603$	70.4560	−	402.588i	0.116842	−	0.667641i
$604$	486.046	−	310.343i	0.804712	−	0.513813i
$605$		0			0
$606$	−14.2775	+	72.2119i	−0.0235603	+	0.119162i
$607$	−232.895	+	232.895i	−0.383682	+	0.383682i	−0.872427	−	0.488745i	$-0.837455\pi$
$607$	−232.895	+	232.895i	−0.383682	+	0.383682i	0.488745	+	0.872427i	$0.337455\pi$
$608$	−175.514	−	238.095i	−0.288675	−	0.391604i
$609$	−151.726	−	78.8600i	−0.249139	−	0.129491i
$610$		0			0
$611$	420.230			0.687774
$612$	16.4741	−	6.86825i	0.0269185	−	0.0112226i
$613$	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	$0.433540\pi$
$618$	100.270	+	149.691i	0.162249	+	0.242219i
$619$	215.170			0.347610			0.173805	−	0.984780i	$-0.444394\pi$
$619$	215.170			0.347610			0.173805	+	0.984780i	$0.444394\pi$
$620$		0			0
$621$	−680.537	+	90.9238i	−1.09587	+	0.146415i
$622$	161.981	−	295.610i	0.260420	−	0.475258i
$623$	242.383	−	242.383i	0.389058	−	0.389058i
$624$	404.826	−	312.361i	0.648759	−	0.500579i
$625$		0			0
$626$	110.860	+	379.622i	0.177092	+	0.606424i
$627$	36.9083	+	116.798i	0.0588649	+	0.186280i
$628$	197.304	−	894.298i	0.314178	−	1.42404i
$629$	−2.38016			−0.00378405
$630$		0			0
$631$		−	710.672i		−	1.12626i	−0.826367	−	0.563132i	$-0.809596\pi$
$631$		−	710.672i		−	1.12626i	0.826367	−	0.563132i	$-0.190404\pi$
$632$	−446.569	+	29.9562i	−0.706597	+	0.0473990i
$633$	529.005	−	167.167i	0.835711	−	0.264087i
$634$	−133.230	−	456.225i	−0.210142	−	0.719598i
$635$		0			0
$636$	890.535	−	79.4018i	1.40021	−	0.124846i
$637$	433.758	+	433.758i	0.680939	+	0.680939i
$638$	−23.4379	+	42.7733i	−0.0367364	+	0.0670428i
$639$	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	$0.887061\pi$
$642$	−365.641	−	545.860i	−0.569534	−	0.850249i
$643$	310.249	+	310.249i	0.482502	+	0.482502i	0.905930	−	0.423428i	$-0.139173\pi$
$643$	310.249	+	310.249i	0.482502	+	0.482502i	−0.423428	+	0.905930i	$0.639173\pi$
$644$	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	$0.0867806\pi$
$647$	797.318	+	797.318i	1.23233	+	1.23233i	0.269265	+	0.963066i	$0.413219\pi$
$648$	−178.783	+	622.849i	−0.275900	+	0.961186i
$649$			108.917i			0.167822i
$650$		0			0
$651$	688.068	−	1323.83i	1.05694	−	2.03354i
$652$	−23.6507	+	107.199i	−0.0362741	+	0.164416i
$653$	−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	$-0.516956\pi$
$654$	−72.7642	+	368.022i	−0.111260	+	0.562724i
$655$		0			0
$656$	−480.412	−	222.827i	−0.732335	−	0.339676i
$657$	−158.444	+	905.353i	−0.241163	+	1.37801i
$658$	391.416	−	714.322i	0.594858	−	1.08560i
$659$		−	633.604i		−	0.961463i	−0.876868	−	0.480732i	$-0.840371\pi$
$659$		−	633.604i		−	0.961463i	0.876868	−	0.480732i	$-0.159629\pi$
$660$		0			0
$661$	893.706			1.35205			0.676026	−	0.736878i	$-0.263701\pi$
$661$	893.706			1.35205			0.676026	+	0.736878i	$0.263701\pi$
$662$	−488.560	−	267.709i	−0.738006	−	0.404394i
$663$	−15.1081	+	4.77419i	−0.0227875	+	0.00720089i
$664$	346.493	−	396.322i	0.521827	−	0.596870i
$665$		0			0
$666$	53.9672	−	67.4889i	0.0810319	−	0.101335i
$667$	99.2732	−	99.2732i	0.148835	−	0.148835i
$668$	224.022	−	1015.40i	0.335362	−	1.52006i
$669$	−404.161	+	777.601i	−0.604128	+	1.16233i
$670$		0			0
$671$	−203.956			−0.303959
$672$	−153.895	−	979.081i	−0.229010	−	1.45697i
$673$	−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	$0.210306\pi$
$678$	−302.549	−	451.672i	−0.446238	−	0.666182i
$679$	−359.665			−0.529698
$680$		0			0
$681$	−341.922	+	657.853i	−0.502088	+	0.966010i
$682$	−373.205	−	204.499i	−0.547221	−	0.299853i
$683$	−894.185	+	894.185i	−1.30920	+	1.30920i	−0.387211	+	0.921991i	$0.626561\pi$
$683$	−894.185	+	894.185i	−1.30920	+	1.30920i	−0.921991	+	0.387211i	$0.873439\pi$
$684$	−307.731	−	126.638i	−0.449899	−	0.185143i
$685$		0			0
$686$	170.148	−	49.6878i	0.248029	−	0.0724312i
$687$	821.996	−	259.753i	1.19650	−	0.378097i
$688$	−30.8300	+	11.2925i	−0.0448111	+	0.0164135i
$689$	−793.680			−1.15193
$690$		0			0
$691$		−	957.776i		−	1.38607i	−0.720903	−	0.693036i	$-0.756272\pi$
$691$		−	957.776i		−	1.38607i	0.720903	−	0.693036i	$-0.243728\pi$
$692$	242.453	−	1098.94i	0.350365	−	1.58806i
$693$	−70.7516	+	404.277i	−0.102095	+	0.583372i
$694$	−434.892	+	127.000i	−0.626646	+	0.182998i
$695$		0			0
$696$	−48.2923	−	123.390i	−0.0693855	−	0.177285i
$697$	11.6036	+	11.6036i	0.0166478	+	0.0166478i
$698$	693.175	+	379.829i	0.993087	+	0.544167i
$699$	−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	$0.946068\pi$
$702$	207.186	−	536.634i	0.295137	−	0.764436i
$703$	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
$708$	−226.983	−	189.820i	−0.320598	−	0.268108i
$709$			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
$712$	265.024	−	17.7780i	0.372225	−	0.0249691i
$713$	866.177	+	866.177i	1.21483	+	1.21483i
$714$	−5.95684	+	30.1281i	−0.00834291	+	0.0421962i
$715$		0			0
$716$	−563.542	+	359.825i	−0.787070	+	0.502549i
$717$	−776.442	+	245.358i	−1.08290	+	0.342200i
$718$	−682.103	−	373.762i	−0.950004	−	0.520560i
$719$			893.990i			1.24338i	0.783264	+	0.621690i	$0.213553\pi$
$719$			893.990i			1.24338i	−0.783264	+	0.621690i	$0.786447\pi$
$720$		0			0
$721$	−310.013			−0.429977
$722$	−264.832	+	483.310i	−0.366803	+	0.669404i
$723$	110.753	+	350.483i	0.153186	+	0.484762i
$724$	−99.8175	−	156.330i	−0.137869	−	0.215925i
$725$		0			0
$726$	−597.370	−	118.110i	−0.822823	−	0.162686i
$727$	−319.871	+	319.871i	−0.439988	+	0.439988i	−0.892008	−	0.452020i	$-0.850704\pi$
$727$	−319.871	+	319.871i	−0.439988	+	0.439988i	0.452020	+	0.892008i	$0.350704\pi$
$728$	58.8866	+	877.846i	0.0808881	+	1.20583i
$729$	191.381	+	703.430i	0.262526	+	0.964925i
$730$		0			0
$731$	1.01740			0.00139179
$732$	355.455	−	425.046i	0.485595	−	0.580664i
$733$	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
$738$	−592.111	+	65.9195i	−0.802319	+	0.0893218i
$739$	1125.12			1.52248			0.761242	−	0.648468i	$-0.224590\pi$
$739$	1125.12			1.52248			0.761242	+	0.648468i	$0.224590\pi$
$740$		0			0
$741$	262.115	+	136.235i	0.353731	+	0.183853i
$742$	−739.260	+	1349.13i	−0.996308	+	1.81823i
$743$	63.1774	−	63.1774i	0.0850302	−	0.0850302i	−0.663312	−	0.748343i	$-0.730850\pi$
$743$	63.1774	−	63.1774i	0.0850302	−	0.0850302i	0.748343	+	0.663312i	$0.230850\pi$
$744$	1076.60	−	421.359i	1.44704	−	0.566343i
$745$		0			0
$746$	−83.0237	−	284.302i	−0.111292	−	0.381101i
$747$	102.094	−	583.367i	0.136672	−	0.780947i
$748$	8.55421	+	1.88727i	0.0114361	+	0.00252308i
$749$	1130.49			1.50933
$750$		0			0
$751$			705.259i			0.939093i	0.882908	+	0.469547i	$0.155583\pi$
$751$			705.259i			0.939093i	−0.882908	+	0.469547i	$0.844417\pi$
$752$	592.670	−	217.085i	0.788125	−	0.288677i
$753$	−302.912	−	958.576i	−0.402274	−	1.27301i
$754$	32.9728	+	112.910i	0.0437304	+	0.149748i
$755$		0			0
$756$	−719.210	−	852.021i	−0.951336	−	1.12701i
$757$	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	$0.576415\pi$
$758$	38.5727	−	70.3938i	0.0508874	−	0.0928679i
$759$	−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	$-0.285610\pi$
$762$	255.276	−	170.995i	0.335008	−	0.224403i
$763$	−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
$768$	409.583	−	649.666i	0.533312	−	0.845919i
$769$			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
$772$	1143.70	+	252.329i	1.48148	+	0.326851i
$773$	−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	$0.889535\pi$
$774$	−23.0683	+	28.8481i	−0.0298040	+	0.0372715i
$775$		0			0
$776$	−209.821	−	183.440i	−0.270387	−	0.236392i
$777$	44.8020	+	141.777i	0.0576602	+	0.182468i
$778$	94.5724	−	172.591i	0.121558	−	0.221840i
$779$		−	305.947i		−	0.392744i
$780$		0			0
$781$	514.395			0.658636
$782$	−22.1129	−	12.1169i	−0.0282774	−	0.0154947i
$783$	−118.437	−	90.5189i	−0.151260	−	0.115605i
$784$	835.823	+	387.676i	1.06610	+	0.494485i
$785$		0			0
$786$	463.980	+	91.7368i	0.590305	+	0.116713i
$787$	511.685	−	511.685i	0.650172	−	0.650172i	−0.302862	−	0.953034i	$-0.597942\pi$
$787$	511.685	−	511.685i	0.650172	−	0.650172i	0.953034	+	0.302862i	$0.0979422\pi$
$788$	−29.3873	−	6.48355i	−0.0372935	−	0.00822786i
$789$	−795.650	−	413.542i	−1.00843	−	0.524135i
$790$		0			0
$791$	935.420			1.18258
$792$	−247.469	+	199.761i	−0.312461	+	0.252223i
$793$	−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	$0.0690576\pi$
$798$	475.720	−	318.658i	0.596141	−	0.399321i
$799$	−19.5583			−0.0244785
$800$		0			0
$801$	244.561	−	171.711i	0.305320	−	0.214370i
$802$	−1137.07	−	623.062i	−1.41779	−	0.776885i
$803$	−318.971	+	318.971i	−0.397224	+	0.397224i
$804$	48.3960	+	542.789i	0.0601941	+	0.675110i
$805$		0			0
$806$	−985.160	+	287.693i	−1.22228	+	0.356939i
$807$	−157.696	−	499.034i	−0.195410	−	0.618382i
$808$	−6.56897	−	97.9264i	−0.00812992	−	0.121196i
$809$	−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	$0.0214618\pi$
$811$			109.279i			0.134747i	−0.997728	+	0.0673733i	$0.978538\pi$
$812$	222.640	+	49.1199i	0.274188	+	0.0604925i
$813$	−542.549	+	171.447i	−0.667342	+	0.210882i
$814$	40.7104	−	11.8886i	0.0500128	−	0.0146051i
$815$		0			0
$816$	−18.8414	+	14.5379i	−0.0230899	+	0.0178160i
$817$	−13.4127	−	13.4127i	−0.0164171	−	0.0164171i
$818$	−24.4847	−	13.4165i	−0.0299324	−	0.0164016i
$819$	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	$-0.0427189\pi$
$822$	−1260.13	+	844.090i	−1.53301	+	1.02687i
$823$	−1.99663	−	1.99663i	−0.00242604	−	0.00242604i	0.705893	−	0.708319i	$-0.250546\pi$
$823$	−1.99663	−	1.99663i	−0.00242604	−	0.00242604i	−0.708319	+	0.705893i	$0.750546\pi$
$824$	−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	$0.0372061\pi$
$827$	917.802	+	917.802i	1.10980	+	1.10980i	0.116620	+	0.993177i	$0.462794\pi$
$828$	844.953	−	352.270i	1.02048	−	0.425447i
$829$		−	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
$832$	−413.376	+	542.150i	−0.496846	+	0.651623i
$833$	−20.1879	−	20.1879i	−0.0242352	−	0.0242352i
$834$	−91.1727	−	18.0264i	−0.109320	−	0.0216144i
$835$		0			0
$836$	−87.8926	−	137.654i	−0.105135	−	0.164657i
$837$	789.794	−	1033.38i	0.943601	−	1.23462i
$838$	−557.374	−	305.416i	−0.665124	−	0.364458i
$839$			624.895i			0.744809i	0.928070	+	0.372405i	$0.121467\pi$
$839$			624.895i			0.744809i	−0.928070	+	0.372405i	$0.878533\pi$
$840$		0			0
$841$	−810.519			−0.963756
$842$	−54.7805	+	99.9726i	−0.0650600	+	0.118732i
$843$	−761.362	+	240.592i	−0.903158	+	0.285400i
$844$	−623.467	+	398.087i	−0.738705	+	0.471667i
$845$		0			0
$846$	443.460	−	554.570i	0.524184	−	0.655520i
$847$	740.886	−	740.886i	0.874717	−	0.874717i
$848$	−1119.36	+	410.004i	−1.32001	+	0.483496i
$849$	724.713	−	1394.34i	0.853608	−	1.64233i
$850$		0			0
$851$	−122.078			−0.143452
$852$	−896.488	+	1072.00i	−1.05222	+	1.25822i
$853$	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	$0.158524\pi$
$858$	234.563	−	157.120i	0.273383	−	0.183124i
$859$	−1108.16			−1.29006			−0.645028	−	0.764159i	$-0.723154\pi$
$859$	−1108.16			−1.29006			−0.645028	+	0.764159i	$0.723154\pi$
$860$		0			0
$861$	472.765	−	909.594i	0.549089	−	1.05644i
$862$	140.674	−	256.726i	0.163195	−	0.297826i
$863$	−247.757	+	247.757i	−0.287089	+	0.287089i	−0.835928	−	0.548839i	$-0.815070\pi$
$863$	−247.757	+	247.757i	−0.287089	+	0.287089i	0.548839	+	0.835928i	$0.315070\pi$
$864$	14.9863	−	863.870i	0.0173452	−	0.999850i
$865$		0			0
$866$	−337.326	−	1155.12i	−0.389522	−	1.33385i
$867$	−826.002	+	261.019i	−0.952713	+	0.301060i
$868$	−428.580	+	1942.58i	−0.493756	+	2.23799i
$869$	−247.123			−0.284377
$870$		0			0
$871$		−	483.754i		−	0.555401i
$872$	−33.4782	−	499.073i	−0.0383924	−	0.572332i
$873$	−308.846	−	54.0505i	−0.353776	−	0.0619135i
$874$	131.781	+	451.263i	0.150779	+	0.516320i
$875$		0			0
$876$	−108.835	−	1220.64i	−0.124240	−	1.39343i
$877$	−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	$0.875748\pi$
$878$	−653.271	+	1192.20i	−0.744044	+	1.35786i
$879$	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	$0.827834\pi$
$882$	1030.16	−	114.687i	1.16798	−	0.130031i
$883$	55.2196	+	55.2196i	0.0625364	+	0.0625364i	0.737683	−	0.675147i	$-0.235920\pi$
$883$	55.2196	+	55.2196i	0.0625364	+	0.0625364i	−0.675147	+	0.737683i	$0.735920\pi$
$884$	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	0.293966	−	0.955816i	$-0.405025\pi$
$887$	−587.061	−	587.061i	−0.661850	−	0.661850i	−0.955816	+	0.293966i	$0.905025\pi$
$888$	−46.1744	+	105.560i	−0.0519982	+	0.118874i
$889$			528.681i			0.594692i
$890$		0			0
$891$	−121.510	+	336.522i	−0.136374	+	0.377691i
$892$	251.742	−	1141.04i	0.282222	−	1.27920i
$893$	257.844	+	257.844i	0.288739	+	0.288739i
$894$	−1235.00	−	244.180i	−1.38143	−	0.273132i
$895$		0			0
$896$	536.534	+	1207.65i	0.598810	+	1.34782i
$897$	−774.888	+	244.867i	−0.863867	+	0.272984i
$898$	−161.269	+	294.310i	−0.179587	+	0.327740i
$899$			265.955i			0.295834i
$900$		0			0
$901$	36.9394			0.0409982
$902$	−256.426	−	140.510i	−0.284286	−	0.155776i
$903$	−19.1506	−	60.6027i	−0.0212078	−	0.0671126i
$904$	545.703	+	477.093i	0.603654	+	0.527758i
$905$		0			0
$906$	−167.780	+	848.584i	−0.185187	+	0.936627i
$907$	−570.349	+	570.349i	−0.628831	+	0.628831i	−0.947774	−	0.318943i	$-0.896672\pi$
$907$	−570.349	+	570.349i	−0.628831	+	0.628831i	0.318943	+	0.947774i	$0.396672\pi$
$908$	212.974	−	965.325i	0.234553	−	1.06313i
$909$	−63.4470	−	90.3654i	−0.0697987	−	0.0994118i
$910$		0			0
$911$	−809.153			−0.888203			−0.444102	−	0.895976i	$-0.646477\pi$
$911$	−809.153			−0.888203			−0.444102	+	0.895976i	$0.646477\pi$
$912$	440.050	+	56.7341i	0.482511	+	0.0622084i
$913$	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
$918$	−9.64283	+	24.9760i	−0.0105042	+	0.0272069i
$919$	683.390			0.743623			0.371812	−	0.928308i	$-0.378737\pi$
$919$	683.390			0.743623			0.371812	+	0.928308i	$0.378737\pi$
$920$		0			0
$921$	1112.65	+	578.303i	1.20809	+	0.627908i
$922$	622.689	+	341.206i	0.675368	+	0.370071i
$923$	877.198	−	877.198i	0.950377	−	0.950377i
$924$	−48.5991	−	545.066i	−0.0525964	−	0.589898i
$925$		0			0
$926$	662.811	−	193.559i	0.715778	−	0.209027i
$927$	−266.210	−	46.5889i	−0.287174	−	0.0502577i
$928$	104.831	+	142.209i	0.112964	+	0.153242i
$929$	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
$932$	1.84635	−	8.36876i	0.00198107	−	0.00897936i
$933$	152.352	+	482.122i	0.163292	+	0.516744i
$934$	−500.153	+	146.058i	−0.535496	+	0.156379i
$935$		0			0
$936$	−81.3566	+	762.661i	−0.0869195	+	0.814809i
$937$	−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	$0.943744\pi$
$938$	−822.303	−	450.585i	−0.876656	−	0.480368i
$939$	−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	$0.690460\pi$
$942$	764.504	+	1141.32i	0.811575	+	1.21159i
$943$	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	0.473889	−	0.880585i	$-0.342850\pi$
$947$	−385.141	−	385.141i	−0.406696	−	0.406696i	−0.880585	+	0.473889i	$0.842850\pi$
$948$	430.687	−	515.007i	0.454311	−	0.543256i
$949$			1087.88i			1.14635i
$950$		0			0
$951$	632.579	+	328.786i	0.665173	+	0.345726i
$952$	−2.74069	−	40.8566i	−0.00287888	−	0.0429166i
$953$	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	$0.641510\pi$
$954$	−837.554	+	1047.41i	−0.877939	+	1.09791i
$955$		0			0
$956$	915.088	−	584.289i	0.957205	−	0.611181i
$957$	−22.0445	−	69.7606i	−0.0230350	−	0.0728951i
$958$	−313.533	−	171.802i	−0.327279	−	0.179334i
$959$		−	2609.75i		−	2.72133i
$960$		0			0
$961$	−1359.51			−1.41468
$962$	49.1500	−	89.6971i	0.0510915	−	0.0932403i
$963$	970.754	+	169.889i	1.00805	+	0.176417i
$964$	−263.746	−	413.067i	−0.273595	−	0.428493i
$965$		0			0
$966$	−305.524	+	1545.26i	−0.316278	+	1.59965i
$967$	−577.404	+	577.404i	−0.597108	+	0.597108i	−0.939542	−	0.342434i	$-0.888749\pi$
$967$	−577.404	+	577.404i	−0.597108	+	0.597108i	0.342434	+	0.939542i	$0.388749\pi$
$968$	810.091	−	54.3415i	0.836871	−	0.0561379i
$969$	−12.1993	−	6.34065i	−0.0125896	−	0.00654350i
$970$		0			0
$971$	−983.651			−1.01303			−0.506514	−	0.862231i	$-0.669066\pi$
$971$	−983.651			−1.01303			−0.506514	+	0.862231i	$0.669066\pi$
$972$	−489.548	−	839.718i	−0.503650	−	0.863908i
$973$	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	$0.428384\pi$
$978$	−91.6406	−	136.809i	−0.0937020	−	0.139886i
$979$	146.660			0.149806
$980$		0			0
$981$	−323.352	−	460.539i	−0.329615	−	0.469459i
$982$	712.407	−	1300.12i	0.725465	−	1.32395i
$983$	421.808	−	421.808i	0.429103	−	0.429103i	−0.459220	−	0.888323i	$-0.651871\pi$
$983$	421.808	−	421.808i	0.429103	−	0.429103i	0.888323	+	0.459220i	$0.151871\pi$
$984$	739.722	−	289.512i	0.751750	−	0.294220i
$985$		0			0
$986$	−1.53462	−	5.25504i	−0.00155640	−	0.00532966i
$987$	368.147	+	1165.01i	0.372996	+	1.18036i
$988$	−384.624	−	84.8574i	−0.389296	−	0.0858881i
$989$	52.1821			0.0527625
$990$		0			0
$991$		−	1077.21i		−	1.08699i	−0.839411	−	0.543496i	$-0.817100\pi$
$991$		−	1077.21i		−	1.08699i	0.839411	−	0.543496i	$-0.182900\pi$
$992$	−1240.80	+	914.667i	−1.25081	+	0.922044i
$993$	796.810	−	251.794i	0.802427	−	0.253569i
$994$	−674.040	−	2308.14i	−0.678109	−	2.32208i
$995$		0			0
$996$	70.1280	+	786.524i	0.0704096	+	0.789683i
$997$	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	$0.499249\pi$
$998$	633.711	−	1156.50i	0.634981	−	1.15882i
$999$	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.107.14		40
3.2	odd	2	inner	300.3.l.g.107.7		40
4.3	odd	2	inner	300.3.l.g.107.17		40
5.2	odd	4		60.3.l.a.23.17	yes	40
5.3	odd	4	inner	300.3.l.g.143.4		40
5.4	even	2		60.3.l.a.47.7	yes	40
12.11	even	2	inner	300.3.l.g.107.4		40
15.2	even	4		60.3.l.a.23.4	✓	40
15.8	even	4	inner	300.3.l.g.143.17		40
15.14	odd	2		60.3.l.a.47.14	yes	40
20.3	even	4	inner	300.3.l.g.143.7		40
20.7	even	4		60.3.l.a.23.14	yes	40
20.19	odd	2		60.3.l.a.47.4	yes	40
60.23	odd	4	inner	300.3.l.g.143.14		40
60.47	odd	4		60.3.l.a.23.7	yes	40
60.59	even	2		60.3.l.a.47.17	yes	40

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

\(f(q)\)	\(=\)	\(q+(0.961083 - 1.75394i) q^{2} +(0.903948 + 2.86057i) q^{3} +(-2.15264 - 3.37137i) q^{4} +(5.88605 + 1.16377i) q^{6} +(-7.30016 + 7.30016i) q^{7} +(-7.98206 + 0.535443i) q^{8} +(-7.36576 + 5.17162i) q^{9} +O(q^{10})\)	\(q+(0.961083 - 1.75394i) q^{2} +(0.903948 + 2.86057i) q^{3} +(-2.15264 - 3.37137i) q^{4} +(5.88605 + 1.16377i) q^{6} +(-7.30016 + 7.30016i) q^{7} +(-7.98206 + 0.535443i) q^{8} +(-7.36576 + 5.17162i) q^{9} -4.41713 q^{11} +(7.69818 - 9.20533i) 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} +(1.99163 + 17.8895i) q^{18} -9.24359 q^{19} +(-27.4816 - 14.2837i) q^{21} +(-4.24523 + 7.74740i) q^{22} +(17.9810 - 17.9810i) q^{23} +(-8.74704 - 22.3493i) q^{24} +(5.97225 + 20.4510i) q^{26} +(-21.4521 - 16.3954i) q^{27} +(40.3261 + 8.89693i) q^{28} +5.52099 q^{29} +48.1716i q^{31} +(18.9877 + 25.7579i) q^{32} +(-3.99285 - 12.6355i) q^{33} +(-0.277960 - 0.951830i) q^{34} +(33.2913 + 13.7001i) q^{36} +(-3.39462 - 3.39462i) q^{37} +(-8.88386 + 16.2127i) q^{38} +(-28.3564 - 14.7383i) q^{39} +33.0983i q^{41} +(-51.4649 + 34.4734i) 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} +(-47.6060 - 6.13767i) q^{48} -57.5846i q^{49} +(1.31976 + 0.685951i) q^{51} +(41.6098 + 9.18014i) q^{52} +(52.6835 + 52.6835i) q^{53} +(-49.3738 + 21.8684i) q^{54} +(54.3615 - 62.1791i) q^{56} +(-8.35573 - 26.4420i) q^{57} +(5.30613 - 9.68351i) q^{58} -24.6578i q^{59} +46.1739 q^{61} +(84.4904 + 46.2969i) q^{62} +(16.0176 - 91.5248i) q^{63} +(63.4266 - 8.54787i) q^{64} +(-25.9995 - 5.14054i) q^{66} +(-32.1110 + 32.1110i) q^{67} +(-1.93660 - 0.427261i) q^{68} +(67.6900 + 35.1822i) q^{69} -116.455 q^{71} +(56.0248 - 45.2241i) 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} +(-53.1031 + 35.5707i) q^{78} +55.9466 q^{79} +(27.5087 - 76.1858i) q^{81} +(58.0526 + 31.8102i) q^{82} +(-46.5302 + 46.5302i) q^{83} +(11.0024 + 123.398i) q^{84} +(3.93959 - 1.15047i) q^{86} +(4.99069 + 15.7932i) q^{87} +(35.2578 - 2.36512i) q^{88} -33.2025 q^{89} -109.977i q^{91} +(-99.3275 - 21.9141i) q^{92} +(-137.798 + 43.5447i) q^{93} +(-75.7338 + 22.1163i) q^{94} +(-56.5184 + 77.5994i) q^{96} +(24.6341 + 24.6341i) q^{97} +(-101.000 - 55.3436i) 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

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Representations

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Database

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