LMFDB - Embedded newform 225.4.k.d.49.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,4,Mod(49,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.49"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.9
Character	$\chi$	$=$	225.49
Dual form			225.4.k.d.124.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35984 - 0.785104i) q^{2} +(3.43441 + 3.89934i) q^{3} +(-2.76722 + 4.79297i) q^{4} +(7.73164 + 2.60611i) q^{6} +(29.6525 - 17.1199i) q^{7} +21.2519i q^{8} +(-3.40971 + 26.7838i) q^{9} +(13.4480 + 23.2926i) q^{11} +(-28.1932 + 5.67066i) q^{12} +(-16.8771 - 9.74401i) q^{13} +(26.8818 - 46.5607i) q^{14} +(-5.45281 - 9.44454i) q^{16} +29.1232i q^{17} +(16.3915 + 39.0987i) q^{18} -47.1006 q^{19} +(168.595 + 56.8286i) q^{21} +(36.5743 + 21.1162i) q^{22} +(98.0485 + 56.6083i) q^{23} +(-82.8684 + 72.9877i) q^{24} -30.6003 q^{26} +(-116.150 + 78.6910i) q^{27} +189.498i q^{28} +(40.6219 + 70.3593i) q^{29} +(5.41811 - 9.38445i) q^{31} +(-162.067 - 93.5697i) q^{32} +(-44.6399 + 132.435i) q^{33} +(22.8648 + 39.6029i) q^{34} +(-118.939 - 90.4594i) q^{36} +410.002i q^{37} +(-64.0493 + 36.9789i) q^{38} +(-19.9677 - 99.2746i) q^{39} +(221.755 - 384.091i) q^{41} +(273.879 - 55.0869i) q^{42} +(-294.012 + 169.748i) q^{43} -148.854 q^{44} +177.774 q^{46} +(204.591 - 118.121i) q^{47} +(18.1003 - 53.6988i) q^{48} +(414.681 - 718.249i) q^{49} +(-113.561 + 100.021i) q^{51} +(93.4055 - 53.9277i) q^{52} -609.634i q^{53} +(-96.1643 + 198.197i) q^{54} +(363.830 + 630.173i) q^{56} +(-161.763 - 183.661i) q^{57} +(110.479 + 63.7849i) q^{58} +(7.77272 - 13.4627i) q^{59} +(-30.5255 - 52.8717i) q^{61} -17.0151i q^{62} +(357.430 + 852.582i) q^{63} -206.603 q^{64} +(43.2718 + 215.137i) q^{66} +(-187.832 - 108.445i) q^{67} +(-139.587 - 80.5903i) q^{68} +(116.003 + 576.740i) q^{69} +65.4315 q^{71} +(-569.208 - 72.4627i) q^{72} -711.811i q^{73} +(321.895 + 557.538i) q^{74} +(130.338 - 225.752i) q^{76} +(797.534 + 460.457i) q^{77} +(-105.094 - 119.321i) q^{78} +(-478.876 - 829.438i) q^{79} +(-705.748 - 182.650i) q^{81} -696.404i q^{82} +(452.446 - 261.220i) q^{83} +(-738.918 + 650.814i) q^{84} +(-266.540 + 461.660i) q^{86} +(-134.842 + 400.041i) q^{87} +(-495.012 + 285.796i) q^{88} +1602.24 q^{89} -667.266 q^{91} +(-542.644 + 313.296i) q^{92} +(55.2011 - 11.1029i) q^{93} +(185.474 - 321.251i) q^{94} +(-191.745 - 953.312i) q^{96} +(694.499 - 400.969i) q^{97} -1302.27i q^{98} +(-669.719 + 280.768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41}+ \cdots - 4640 q^{99}+O(q^{100}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.35984	−	0.785104i	0.480776	−	0.277576i	−0.239964	−	0.970782i	$-0.577136\pi$
$2$	1.35984	−	0.785104i	0.480776	−	0.277576i	0.720740	+	0.693206i	$0.243802\pi$
$3$	3.43441	+	3.89934i	0.660952	+	0.750428i
$3$	3.43441	+	3.89934i	0.660952	+	0.750428i
$4$	−2.76722	+	4.79297i	−0.345903	+	0.599121i
$5$		0			0
$5$		0			0
$6$	7.73164	+	2.60611i	0.526071	+	0.177324i
$7$	29.6525	−	17.1199i	1.60109	−	0.924387i	0.609815	−	0.792544i	$-0.291244\pi$
$7$	29.6525	−	17.1199i	1.60109	−	0.924387i	0.991271	−	0.131844i	$-0.0420897\pi$
$8$			21.2519i			0.939210i
$9$	−3.40971	+	26.7838i	−0.126285	+	0.991994i
$10$		0			0
$11$	13.4480	+	23.2926i	0.368611	+	0.638453i	0.989349	−	0.145565i	$-0.0465000\pi$
$11$	13.4480	+	23.2926i	0.368611	+	0.638453i	−0.620737	+	0.784019i	$0.713167\pi$
$12$	−28.1932	+	5.67066i	−0.678223	+	0.136415i
$13$	−16.8771	−	9.74401i	−0.360067	−	0.207885i	0.309043	−	0.951048i	$-0.399991\pi$
$13$	−16.8771	−	9.74401i	−0.360067	−	0.207885i	−0.669110	+	0.743163i	$0.733325\pi$
$14$	26.8818	−	46.5607i	0.513176	−	0.888847i
$15$		0			0
$16$	−5.45281	−	9.44454i	−0.0852001	−	0.147571i
$17$			29.1232i			0.415495i	0.978182	+	0.207747i	$0.0666132\pi$
$17$			29.1232i			0.415495i	−0.978182	+	0.207747i	$0.933387\pi$
$18$	16.3915	+	39.0987i	0.214639	+	0.511981i
$19$	−47.1006			−0.568717			−0.284358	−	0.958718i	$-0.591781\pi$
$19$	−47.1006			−0.568717			−0.284358	+	0.958718i	$0.591781\pi$
$20$		0			0
$21$	168.595	+	56.8286i	1.75193	+	0.590525i
$22$	36.5743	+	21.1162i	0.354439	+	0.204636i
$23$	98.0485	+	56.6083i	0.888892	+	0.513202i	0.873580	−	0.486680i	$-0.161792\pi$
$23$	98.0485	+	56.6083i	0.888892	+	0.513202i	0.0153124	+	0.999883i	$0.495126\pi$
$24$	−82.8684	+	72.9877i	−0.704810	+	0.620773i
$25$		0			0
$26$	−30.6003			−0.230816
$27$	−116.150	+	78.6910i	−0.827889	+	0.560892i
$28$			189.498i			1.27899i
$29$	40.6219	+	70.3593i	0.260114	+	0.450531i	0.966272	−	0.257524i	$-0.0829065\pi$
$29$	40.6219	+	70.3593i	0.260114	+	0.450531i	−0.706158	+	0.708054i	$0.749573\pi$
$30$		0			0
$31$	5.41811	−	9.38445i	0.0313910	−	0.0543708i	−0.849903	−	0.526939i	$-0.823340\pi$
$31$	5.41811	−	9.38445i	0.0313910	−	0.0543708i	0.881294	+	0.472568i	$0.156673\pi$
$32$	−162.067	−	93.5697i	−0.895304	−	0.516904i
$33$	−44.6399	+	132.435i	−0.235479	+	0.698603i
$34$	22.8648	+	39.6029i	0.115332	+	0.199760i
$35$		0			0
$36$	−118.939	−	90.4594i	−0.550642	−	0.418794i
$37$			410.002i			1.82173i	0.412706	+	0.910864i	$0.364584\pi$
$37$			410.002i			1.82173i	−0.412706	+	0.910864i	$0.635416\pi$
$38$	−64.0493	+	36.9789i	−0.273426	+	0.157862i
$39$	−19.9677	−	99.2746i	−0.0819843	−	0.407606i
$40$		0			0
$41$	221.755	−	384.091i	0.844691	−	1.46305i	−0.0411978	−	0.999151i	$-0.513117\pi$
$41$	221.755	−	384.091i	0.844691	−	1.46305i	0.885889	−	0.463897i	$-0.153549\pi$
$42$	273.879	−	55.0869i	1.00620	−	0.202383i
$43$	−294.012	+	169.748i	−1.04271	+	0.602007i	−0.920599	−	0.390510i	$-0.872299\pi$
$43$	−294.012	+	169.748i	−1.04271	+	0.602007i	−0.122108	+	0.992517i	$0.538965\pi$
$44$	−148.854			−0.510015
$45$		0			0
$46$	177.774			0.569811
$47$	204.591	−	118.121i	0.634950	−	0.366589i	−0.147716	−	0.989030i	$-0.547192\pi$
$47$	204.591	−	118.121i	0.634950	−	0.366589i	0.782667	+	0.622441i	$0.213859\pi$
$48$	18.1003	−	53.6988i	0.0544283	−	0.161474i
$49$	414.681	−	718.249i	1.20898	−	2.09402i
$50$		0			0
$51$	−113.561	+	100.021i	−0.311799	+	0.274622i
$52$	93.4055	−	53.9277i	0.249096	−	0.143816i
$53$		−	609.634i		−	1.57999i	−0.613111	−	0.789997i	$-0.710082\pi$
$53$		−	609.634i		−	1.57999i	0.613111	−	0.789997i	$-0.289918\pi$
$54$	−96.1643	+	198.197i	−0.242339	+	0.499466i
$55$		0			0
$56$	363.830	+	630.173i	0.868194	+	1.50376i
$57$	−161.763	−	183.661i	−0.375894	−	0.426781i
$58$	110.479	+	63.7849i	0.250113	+	0.144403i
$59$	7.77272	−	13.4627i	0.0171512	−	0.0297068i	−0.857322	−	0.514780i	$-0.827874\pi$
$59$	7.77272	−	13.4627i	0.0171512	−	0.0297068i	0.874474	+	0.485073i	$0.161207\pi$
$60$		0			0
$61$	−30.5255	−	52.8717i	−0.0640719	−	0.110976i	0.832210	−	0.554461i	$-0.187075\pi$
$61$	−30.5255	−	52.8717i	−0.0640719	−	0.110976i	−0.896282	+	0.443485i	$0.853742\pi$
$62$		−	17.0151i		−	0.0348536i
$63$	357.430	+	852.582i	0.714793	+	1.70500i
$64$	−206.603			−0.403521
$65$		0			0
$66$	43.2718	+	215.137i	0.0807029	+	0.401235i
$67$	−187.832	−	108.445i	−0.342497	−	0.197741i	0.318879	−	0.947796i	$-0.396694\pi$
$67$	−187.832	−	108.445i	−0.342497	−	0.197741i	−0.661376	+	0.750055i	$0.730027\pi$
$68$	−139.587	−	80.5903i	−0.248932	−	0.143721i
$69$	116.003	+	576.740i	0.202394	+	1.00625i
$70$		0			0
$71$	65.4315			0.109370			0.0546852	−	0.998504i	$-0.482584\pi$
$71$	65.4315			0.109370			0.0546852	+	0.998504i	$0.482584\pi$
$72$	−569.208	−	72.4627i	−0.931691	−	0.118609i
$73$		−	711.811i		−	1.14125i	−0.821211	−	0.570624i	$-0.806701\pi$
$73$		−	711.811i		−	1.14125i	0.821211	−	0.570624i	$-0.193299\pi$
$74$	321.895	+	557.538i	0.505669	+	0.875844i
$75$		0			0
$76$	130.338	−	225.752i	0.196721	−	0.340730i
$77$	797.534	+	460.457i	1.18036	+	0.681479i
$78$	−105.094	−	119.321i	−0.152558	−	0.173211i
$79$	−478.876	−	829.438i	−0.681997	−	1.18125i	−0.974370	−	0.224949i	$-0.927778\pi$
$79$	−478.876	−	829.438i	−0.681997	−	1.18125i	0.292373	−	0.956304i	$-0.405555\pi$
$80$		0			0
$81$	−705.748	−	182.650i	−0.968104	−	0.250549i
$82$		−	696.404i		−	0.937865i
$83$	452.446	−	261.220i	0.598343	−	0.345453i	−0.170047	−	0.985436i	$-0.554392\pi$
$83$	452.446	−	261.220i	0.598343	−	0.345453i	0.768389	+	0.639983i	$0.221058\pi$
$84$	−738.918	+	650.814i	−0.959792	+	0.845352i
$85$		0			0
$86$	−266.540	+	461.660i	−0.334206	+	0.578862i
$87$	−134.842	+	400.041i	−0.166168	+	0.492976i
$88$	−495.012	+	285.796i	−0.599642	+	0.346204i
$89$	1602.24			1.90828			0.954141	−	0.299359i	$-0.0967728\pi$
$89$	1602.24			1.90828			0.954141	+	0.299359i	$0.0967728\pi$
$90$		0			0
$91$	−667.266			−0.768664
$92$	−542.644	+	313.296i	−0.614941	+	0.355036i
$93$	55.2011	−	11.1029i	0.0615494	−	0.0123798i
$94$	185.474	−	321.251i	0.203513	−	0.352494i
$95$		0			0
$96$	−191.745	−	953.312i	−0.203854	−	1.01351i
$97$	694.499	−	400.969i	0.726966	−	0.419714i	−0.0903455	−	0.995910i	$-0.528797\pi$
$97$	694.499	−	400.969i	0.726966	−	0.419714i	0.817311	+	0.576197i	$0.195464\pi$
$98$		−	1302.27i		−	1.34234i
$99$	−669.719	+	280.768i	−0.679892	+	0.285033i
$100$		0			0
$101$	−293.065	−	507.604i	−0.288724	−	0.500084i	0.684782	−	0.728748i	$-0.259898\pi$
$101$	−293.065	−	507.604i	−0.288724	−	0.500084i	−0.973505	+	0.228664i	$0.926564\pi$
$102$	−75.8984	+	225.170i	−0.0736770	+	0.218580i
$103$	−710.725	−	410.337i	−0.679901	−	0.392541i	0.119917	−	0.992784i	$-0.461737\pi$
$103$	−710.725	−	410.337i	−0.679901	−	0.392541i	−0.799818	+	0.600243i	$0.795071\pi$
$104$	207.079	−	358.671i	0.195248	−	0.338179i
$105$		0			0
$106$	−478.626	−	829.005i	−0.438569	−	0.759623i
$107$		−	1358.33i		−	1.22724i	−0.789600	−	0.613621i	$-0.789712\pi$
$107$		−	1358.33i		−	1.22724i	0.789600	−	0.613621i	$-0.210288\pi$
$108$	−55.7517	−	774.457i	−0.0496732	−	0.690020i
$109$	−489.495			−0.430139			−0.215069	−	0.976599i	$-0.568998\pi$
$109$	−489.495			−0.430139			−0.215069	+	0.976599i	$0.568998\pi$
$110$		0			0
$111$	−1598.74	+	1408.11i	−1.36708	+	1.20407i
$112$	−323.379	−	186.703i	−0.272825	−	0.157516i
$113$	690.797	+	398.832i	0.575086	+	0.332026i	0.759178	−	0.650883i	$-0.225601\pi$
$113$	690.797	+	398.832i	0.575086	+	0.332026i	−0.184092	+	0.982909i	$0.558935\pi$
$114$	−364.165	−	122.750i	−0.299185	−	0.100847i
$115$		0			0
$116$	−449.640			−0.359897
$117$	318.528	−	418.810i	0.251692	−	0.330932i
$118$		−	24.4096i		−	0.0190431i
$119$	498.586	+	863.576i	0.384078	+	0.665243i
$120$		0			0
$121$	303.803	−	526.202i	0.228251	−	0.395343i
$122$	−83.0196	−	47.9314i	−0.0616085	−	0.0355697i
$123$	2259.30	−	454.427i	1.65621	−	0.333124i
$124$	29.9862	+	51.9377i	0.0217165	+	0.0376141i
$125$		0			0
$126$	1155.41	+	878.756i	0.816924	+	0.621316i
$127$			1728.22i			1.20752i	0.797167	+	0.603759i	$0.206331\pi$
$127$			1728.22i			1.20752i	−0.797167	+	0.603759i	$0.793669\pi$
$128$	1015.59	−	586.352i	0.701301	−	0.404896i
$129$	−1671.66	−	563.469i	−1.14094	−	0.384579i
$130$		0			0
$131$	−319.551	+	553.478i	−0.213124	+	0.369142i	−0.952691	−	0.303942i	$-0.901697\pi$
$131$	−319.551	+	553.478i	−0.213124	+	0.369142i	0.739566	+	0.673084i	$0.235031\pi$
$132$	−511.226	−	580.434i	−0.337095	−	0.382729i
$133$	−1396.65	+	806.357i	−0.910564	+	0.525715i
$134$	−340.562			−0.219553
$135$		0			0
$136$	−618.923			−0.390237
$137$	−2456.00	+	1417.97i	−1.53161	+	0.884274i	−0.532319	+	0.846544i	$0.678679\pi$
$137$	−2456.00	+	1417.97i	−1.53161	+	0.884274i	−0.999288	+	0.0377300i	$0.987987\pi$
$138$	610.548	+	693.201i	0.376618	+	0.427603i
$139$	87.4981	−	151.551i	0.0533920	−	0.0924777i	−0.838094	−	0.545526i	$-0.816330\pi$
$139$	87.4981	−	151.551i	0.0533920	−	0.0924777i	0.891486	+	0.453048i	$0.149663\pi$
$140$		0			0
$141$	1163.24	+	392.096i	0.694770	+	0.234187i
$142$	88.9764	−	51.3706i	0.0525827	−	0.0303586i
$143$		−	524.150i		−	0.306515i
$144$	271.554	−	113.844i	0.157149	−	0.0658820i
$145$		0			0
$146$	−558.846	−	967.949i	−0.316784	−	0.548685i
$147$	4224.88	−	849.776i	2.37049	−	0.476791i
$148$	−1965.13	−	1134.57i	−1.09144	−	0.630141i
$149$	511.766	−	886.405i	0.281379	−	0.487363i	−0.690345	−	0.723480i	$-0.742541\pi$
$149$	511.766	−	886.405i	0.281379	−	0.487363i	0.971725	+	0.236117i	$0.0758748\pi$
$150$		0			0
$151$	436.998	+	756.902i	0.235512	+	0.407920i	0.959421	−	0.281976i	$-0.0909898\pi$
$151$	436.998	+	756.902i	0.235512	+	0.407920i	−0.723909	+	0.689895i	$0.757656\pi$
$152$		−	1000.98i		−	0.534145i
$153$	−780.031	−	99.3015i	−0.412168	−	0.0524709i
$154$	1446.03			0.756650
$155$		0			0
$156$	531.075	+	179.010i	0.272564	+	0.0918736i
$157$	−107.000	−	61.7762i	−0.0543917	−	0.0314031i	0.472558	−	0.881300i	$-0.343331\pi$
$157$	−107.000	−	61.7762i	−0.0543917	−	0.0314031i	−0.526949	+	0.849897i	$0.676664\pi$
$158$	−1302.39	−	751.936i	−0.655776	−	0.378613i
$159$	2377.17	−	2093.73i	1.18567	−	1.04430i
$160$		0			0
$161$	3876.51			1.89759
$162$	−1103.10	+	305.711i	−0.534988	+	0.148265i
$163$			1410.89i			0.677972i	0.940791	+	0.338986i	$0.110084\pi$
$163$			1410.89i			0.677972i	−0.940791	+	0.338986i	$0.889916\pi$
$164$	1227.29	+	2125.73i	0.584362	+	1.01214i
$165$		0			0
$166$	410.170	−	710.435i	0.191779	−	0.332172i
$167$	1756.04	+	1013.85i	0.813692	+	0.469786i	0.848236	−	0.529618i	$-0.177665\pi$
$167$	1756.04	+	1013.85i	0.813692	+	0.469786i	−0.0345441	+	0.999403i	$0.510998\pi$
$168$	−1207.72	+	3582.97i	−0.554627	+	1.64543i
$169$	−908.608	−	1573.76i	−0.413568	−	0.716320i
$170$		0			0
$171$	160.599	−	1261.53i	0.0718206	−	0.564164i
$172$		−	1878.92i		−	0.832944i
$173$	−2341.71	+	1351.99i	−1.02912	+	0.594160i	−0.916731	−	0.399505i	$-0.869182\pi$
$173$	−2341.71	+	1351.99i	−1.02912	+	0.594160i	−0.112384	+	0.993665i	$0.535849\pi$
$174$	130.710	+	649.858i	0.0569487	+	0.283135i
$175$		0			0
$176$	146.659	−	254.020i	0.0628115	−	0.108793i
$177$	79.1905	−	15.9281i	0.0336289	−	0.00676399i
$178$	2178.79	−	1257.93i	0.917456	−	0.529694i
$179$	750.694			0.313461			0.156730	−	0.987641i	$-0.449905\pi$
$179$	750.694			0.313461			0.156730	+	0.987641i	$0.449905\pi$
$180$		0			0
$181$	−1134.08			−0.465722			−0.232861	−	0.972510i	$-0.574809\pi$
$181$	−1134.08			−0.465722			−0.232861	+	0.972510i	$0.574809\pi$
$182$	−907.375	+	523.873i	−0.369556	+	0.213363i
$183$	101.328	−	300.612i	0.0409309	−	0.121431i
$184$	−1203.03	+	2083.72i	−0.482005	+	0.834857i
$185$		0			0
$186$	66.3478	−	58.4369i	0.0261551	−	0.0230366i
$187$	−678.355	+	391.649i	−0.265274	+	0.153156i
$188$			1307.46i			0.507216i
$189$	−2096.95	+	4321.85i	−0.807040	+	1.66333i
$190$		0			0
$191$	267.627	+	463.544i	0.101387	+	0.175607i	0.912256	−	0.409620i	$-0.134339\pi$
$191$	267.627	+	463.544i	0.101387	+	0.175607i	−0.810870	+	0.585227i	$0.801005\pi$
$192$	−709.558	−	805.615i	−0.266708	−	0.302814i
$193$	2272.06	+	1311.77i	0.847391	+	0.489241i	0.859770	−	0.510682i	$-0.170607\pi$
$193$	2272.06	+	1311.77i	0.847391	+	0.489241i	−0.0123786	+	0.999923i	$0.503940\pi$
$194$	629.605	−	1090.51i	0.233005	−	0.403577i
$195$		0			0
$196$	2295.03	+	3975.11i	0.836382	+	1.44866i
$197$			2954.08i			1.06837i	0.845367	+	0.534186i	$0.179382\pi$
$197$			2954.08i			1.06837i	−0.845367	+	0.534186i	$0.820618\pi$
$198$	−690.279	+	907.599i	−0.247758	+	0.325759i
$199$	−2639.35			−0.940192			−0.470096	−	0.882615i	$-0.655781\pi$
$199$	−2639.35			−0.940192			−0.470096	+	0.882615i	$0.655781\pi$
$200$		0			0
$201$	−222.228	−	1104.86i	−0.0779838	−	0.387717i
$202$	−797.044	−	460.174i	−0.277623	−	0.160286i
$203$	2409.09	+	1390.89i	0.832929	+	0.480892i
$204$	−165.148	−	821.076i	−0.0566797	−	0.281798i
$205$		0			0
$206$	−1288.63			−0.435841
$207$	−1850.50	+	2433.10i	−0.621348	+	0.816966i
$208$			212.529i			0.0708473i
$209$	−633.409	−	1097.10i	−0.209635	−	0.363099i
$210$		0			0
$211$	995.327	−	1723.96i	0.324745	−	0.562474i	−0.656716	−	0.754138i	$-0.728055\pi$
$211$	995.327	−	1723.96i	0.324745	−	0.562474i	0.981461	+	0.191664i	$0.0613883\pi$
$212$	2921.96	+	1686.99i	0.946607	+	0.546524i
$213$	224.718	+	255.140i	0.0722885	+	0.0820746i
$214$	−1066.43	−	1847.12i	−0.340654	−	0.590029i
$215$		0			0
$216$	−1672.33	−	2468.40i	−0.526796	−	0.777562i
$217$		−	371.030i		−	0.116070i
$218$	−665.635	+	384.305i	−0.206800	+	0.119396i
$219$	2775.59	−	2444.65i	0.856425	−	0.754310i
$220$		0			0
$221$	283.777	−	491.516i	0.0863751	−	0.149606i
$222$	−1068.51	+	3169.99i	−0.323035	+	0.958359i
$223$	584.481	−	337.450i	0.175515	−	0.101333i	−0.409669	−	0.912234i	$-0.634356\pi$
$223$	584.481	−	337.450i	0.175515	−	0.101333i	0.585184	+	0.810901i	$0.301022\pi$
$224$	−6407.61			−1.91128
$225$		0			0
$226$	1252.50			0.368650
$227$	1638.39	−	945.926i	0.479048	−	0.276579i	−0.240972	−	0.970532i	$-0.577466\pi$
$227$	1638.39	−	945.926i	0.479048	−	0.276579i	0.720020	+	0.693954i	$0.244133\pi$
$228$	1327.92	−	267.092i	0.385717	−	0.0775815i
$229$	1704.26	−	2951.86i	0.491792	−	0.851810i	−0.508163	−	0.861261i	$-0.669675\pi$
$229$	1704.26	−	2951.86i	0.491792	−	0.851810i	0.999955	+	0.00945146i	$0.00300854\pi$
$230$		0			0
$231$	943.580	+	4691.25i	0.268758	+	1.33620i
$232$	−1495.27	+	863.294i	−0.423143	+	0.244302i
$233$			2841.86i			0.799041i	0.916724	+	0.399521i	$0.130823\pi$
$233$			2841.86i			0.799041i	−0.916724	+	0.399521i	$0.869177\pi$
$234$	104.338	−	819.593i	0.0291486	−	0.228968i
$235$		0			0
$236$	43.0177	+	74.5088i	0.0118653	+	0.0205513i
$237$	1589.60	−	4715.93i	0.435679	−	1.29254i
$238$	1356.00	+	782.884i	0.369311	+	0.213222i
$239$	809.803	−	1402.62i	0.219171	−	0.379615i	−0.735384	−	0.677651i	$-0.762998\pi$
$239$	809.803	−	1402.62i	0.219171	−	0.379615i	0.954555	+	0.298036i	$0.0963315\pi$
$240$		0			0
$241$	−13.3504	−	23.1235i	−0.00356835	−	0.00618057i	0.864236	−	0.503087i	$-0.167803\pi$
$241$	−13.3504	−	23.1235i	−0.00356835	−	0.00618057i	−0.867804	+	0.496907i	$0.834469\pi$
$242$		−	954.068i		−	0.253429i
$243$	−1711.61	−	3379.24i	−0.451851	−	0.892093i
$244$	337.883			0.0886506
$245$		0			0
$246$	2715.52	−	2391.73i	0.703801	−	0.619884i
$247$	794.923	+	458.949i	0.204776	+	0.118228i
$248$	199.437	+	115.145i	0.0510657	+	0.0294828i
$249$	2572.47	+	867.107i	0.654714	+	0.220685i
$250$		0			0
$251$	−427.354			−0.107467			−0.0537337	−	0.998555i	$-0.517112\pi$
$251$	−427.354			−0.107467			−0.0537337	+	0.998555i	$0.517112\pi$
$252$	−5075.49	−	646.133i	−1.26875	−	0.161518i
$253$			3045.07i			0.756689i
$254$	1356.83	+	2350.10i	0.335178	+	0.580546i
$255$		0			0
$256$	1747.11	−	3026.08i	0.426540	−	0.738789i
$257$	−3326.88	−	1920.77i	−0.807490	−	0.466204i	0.0385936	−	0.999255i	$-0.487712\pi$
$257$	−3326.88	−	1920.77i	−0.807490	−	0.466204i	−0.846083	+	0.533051i	$0.821046\pi$
$258$	−2715.58	+	546.200i	−0.655288	+	0.131802i
$259$	7019.19	+	12157.6i	1.68398	+	2.91674i
$260$		0			0
$261$	−2023.00	+	848.107i	−0.479772	+	0.201136i
$262$			1003.52i			0.236633i
$263$	691.845	−	399.437i	0.162209	−	0.0936514i	−0.416698	−	0.909045i	$-0.636813\pi$
$263$	691.845	−	399.437i	0.162209	−	0.0936514i	0.578907	+	0.815394i	$0.303479\pi$
$264$	−2814.49	−	948.684i	−0.656135	−	0.221165i
$265$		0			0
$266$	−1266.15	+	2193.03i	−0.291852	+	0.505502i
$267$	5502.74	+	6247.68i	1.26128	+	1.43203i
$268$	1039.54	−	600.181i	0.236941	−	0.136798i
$269$	−7934.42			−1.79840			−0.899201	−	0.437536i	$-0.855851\pi$
$269$	−7934.42			−1.79840			−0.899201	+	0.437536i	$0.855851\pi$
$270$		0			0
$271$	−2309.09			−0.517592			−0.258796	−	0.965932i	$-0.583326\pi$
$271$	−2309.09			−0.517592			−0.258796	+	0.965932i	$0.583326\pi$
$272$	275.055	−	158.803i	0.0613150	−	0.0354002i
$273$	−2291.66	−	2601.90i	−0.508050	−	0.576828i
$274$	−2226.51	+	3856.43i	−0.490907	+	0.850276i
$275$		0			0
$276$	−3085.31	−	1039.97i	−0.672875	−	0.226807i
$277$	659.307	−	380.651i	0.143011	−	0.0825672i	−0.426787	−	0.904352i	$-0.640355\pi$
$277$	659.307	−	380.651i	0.143011	−	0.0825672i	0.569798	+	0.821785i	$0.307021\pi$
$278$		−	274.781i		−	0.0592815i
$279$	232.877	+	177.116i	0.0499713	+	0.0380059i
$280$		0			0
$281$	643.638	+	1114.81i	0.136641	+	0.236670i	0.926223	−	0.376975i	$-0.123036\pi$
$281$	643.638	+	1114.81i	0.136641	+	0.236670i	−0.789582	+	0.613645i	$0.789703\pi$
$282$	1889.66	−	380.079i	0.399034	−	0.0802601i
$283$	−2361.22	−	1363.25i	−0.495972	−	0.286350i	0.231076	−	0.972936i	$-0.425775\pi$
$283$	−2361.22	−	1363.25i	−0.495972	−	0.286350i	−0.727049	+	0.686586i	$0.759109\pi$
$284$	−181.064	+	313.611i	−0.0378315	+	0.0655261i
$285$		0			0
$286$	−411.512	−	712.760i	−0.0850813	−	0.147365i
$287$		−	15185.7i		−	3.12329i
$288$	3058.76	−	4021.74i	0.625830	−	0.822859i
$289$	4064.84			0.827364
$290$		0			0
$291$	3948.71	+	1331.00i	0.795454	+	0.268125i
$292$	3411.69	+	1969.74i	0.683746	+	0.394761i
$293$	−83.4622	−	48.1869i	−0.0166414	−	0.00960789i	0.491656	−	0.870789i	$-0.336392\pi$
$293$	−83.4622	−	48.1869i	−0.0166414	−	0.00960789i	−0.508298	+	0.861181i	$0.669725\pi$
$294$	5078.00	−	4472.53i	1.00733	−	0.887223i
$295$		0			0
$296$	−8713.33			−1.71099
$297$	−3394.90	−	1647.19i	−0.663273	−	0.321817i
$298$		−	1607.16i		−	0.312417i
$299$	−1103.18	−	1910.77i	−0.213374	−	0.369575i
$300$		0			0
$301$	−5812.13	+	10066.9i	−1.11298	+	1.92773i
$302$	1188.50	+	686.178i	0.226458	+	0.130745i
$303$	972.815	−	2886.08i	0.184445	−	0.547198i
$304$	256.831	+	444.844i	0.0484547	+	0.0839261i
$305$		0			0
$306$	−1138.68	+	477.372i	−0.212726	+	0.0891814i
$307$			5258.02i			0.977495i	0.872425	+	0.488747i	$0.162546\pi$
$307$			5258.02i			0.977495i	−0.872425	+	0.488747i	$0.837454\pi$
$308$	−4413.91	+	2548.37i	−0.816577	+	0.471451i
$309$	−840.874	−	4180.62i	−0.154808	−	0.769668i
$310$		0			0
$311$	2615.66	−	4530.45i	0.476914	−	0.826039i	−0.522736	−	0.852495i	$-0.675089\pi$
$311$	2615.66	−	4530.45i	0.476914	−	0.826039i	0.999650	+	0.0264555i	$0.00842202\pi$
$312$	2109.77	−	424.351i	0.382828	−	0.0770005i
$313$	3457.74	−	1996.33i	0.624419	−	0.360509i	−0.154168	−	0.988045i	$-0.549270\pi$
$313$	3457.74	−	1996.33i	0.624419	−	0.360509i	0.778588	+	0.627536i	$0.215936\pi$
$314$	−194.003			−0.0348670
$315$		0			0
$316$	5300.63			0.943619
$317$	−4099.40	+	2366.79i	−0.726325	+	0.419344i	−0.817076	−	0.576529i	$-0.804407\pi$
$317$	−4099.40	+	2366.79i	−0.726325	+	0.419344i	0.0907509	+	0.995874i	$0.471073\pi$
$318$	1588.78	−	4713.47i	0.280170	−	0.831189i
$319$	−1092.57	+	1892.38i	−0.191762	+	0.332141i
$320$		0			0
$321$	5296.60	−	4665.07i	0.920958	−	0.811148i
$322$	5271.44	−	3043.47i	0.912317	−	0.526726i
$323$		−	1371.72i		−	0.236299i
$324$	2828.40	−	2877.19i	0.484979	−	0.493346i
$325$		0			0
$326$	1107.70	+	1918.59i	0.188189	+	0.325953i
$327$	−1681.12	−	1908.71i	−0.284301	−	0.322788i
$328$	8162.67	+	4712.72i	1.37411	+	0.793343i
$329$	4044.43	−	7005.15i	0.677740	−	1.17388i
$330$		0			0
$331$	−4684.92	−	8114.52i	−0.777965	−	1.34747i	−0.933113	−	0.359583i	$-0.882919\pi$
$331$	−4684.92	−	8114.52i	−0.777965	−	1.34747i	0.155148	−	0.987891i	$-0.450415\pi$
$332$			2891.42i			0.477973i
$333$	−10981.4	−	1397.99i	−1.80714	−	0.230058i
$334$	3183.92			0.521605
$335$		0			0
$336$	−382.597	−	1902.18i	−0.0621201	−	0.308846i
$337$	−4718.83	−	2724.41i	−0.762762	−	0.440381i	0.0675246	−	0.997718i	$-0.478490\pi$
$337$	−4718.83	−	2724.41i	−0.762762	−	0.440381i	−0.830287	+	0.557337i	$0.811823\pi$
$338$	−2471.13	−	1426.71i	−0.397667	−	0.229593i
$339$	817.296	+	4063.40i	0.130942	+	0.651014i
$340$		0			0
$341$	291.451			0.0462843
$342$	−772.047	−	1841.57i	−0.122069	−	0.291172i
$343$		−	16653.0i		−	2.62150i
$344$	−3607.47	−	6248.31i	−0.565411	−	0.979321i
$345$		0			0
$346$	−2122.90	+	3676.98i	−0.329850	+	0.571316i
$347$	3375.38	+	1948.77i	0.522189	+	0.301486i	0.737830	−	0.674987i	$-0.235851\pi$
$347$	3375.38	+	1948.77i	0.522189	+	0.301486i	−0.215641	+	0.976473i	$0.569184\pi$
$348$	−1544.25	−	1753.30i	−0.237874	−	0.270077i
$349$	−3129.53	−	5420.51i	−0.480000	−	0.831384i	0.519737	−	0.854326i	$-0.326030\pi$
$349$	−3129.53	−	5420.51i	−0.480000	−	0.831384i	−0.999737	+	0.0229422i	$0.992697\pi$
$350$		0			0
$351$	2727.04	−	196.314i	0.414697	−	0.0298532i
$352$		−	5033.30i		−	0.762147i
$353$	−296.931	+	171.433i	−0.0447706	+	0.0258483i	−0.522218	−	0.852812i	$-0.674895\pi$
$353$	−296.931	+	171.433i	−0.0447706	+	0.0258483i	0.477448	+	0.878660i	$0.341562\pi$
$354$	95.1813	−	83.8324i	0.0142905	−	0.0125866i
$355$		0			0
$356$	−4433.75	+	7679.48i	−0.660080	+	1.14329i
$357$	−1655.03	+	4910.03i	−0.245360	+	0.727917i
$358$	1020.82	−	589.373i	0.150705	−	0.0870093i
$359$	−10448.9			−1.53613			−0.768066	−	0.640371i	$-0.778781\pi$
$359$	−10448.9			−1.53613			−0.768066	+	0.640371i	$0.778781\pi$
$360$		0			0
$361$	−4640.53			−0.676561
$362$	−1542.17	+	890.373i	−0.223908	+	0.129273i
$363$	3095.22	−	622.561i	0.447540	−	0.0900164i
$364$	1846.47	−	3198.18i	0.265883	−	0.460523i
$365$		0			0
$366$	−98.2222	−	488.337i	−0.0140278	−	0.0697426i
$367$	−4480.58	+	2586.87i	−0.637288	+	0.367938i	−0.783569	−	0.621305i	$-0.786603\pi$
$367$	−4480.58	+	2586.87i	−0.637288	+	0.367938i	0.146281	+	0.989243i	$0.453270\pi$
$368$		−	1234.70i		−	0.174900i
$369$	9531.32	+	7249.09i	1.34466	+	1.02269i
$370$		0			0
$371$	−10436.9	−	18077.2i	−1.46053	−	2.52970i
$372$	−99.5378	+	295.302i	−0.0138731	+	0.0411577i
$373$	1819.58	+	1050.53i	0.252585	+	0.145830i	0.620947	−	0.783852i	$-0.286748\pi$
$373$	1819.58	+	1050.53i	0.252585	+	0.145830i	−0.368362	+	0.929682i	$0.620081\pi$
$374$	−614.970	+	1065.16i	−0.0850250	+	0.147268i
$375$		0			0
$376$	2510.29	+	4347.95i	0.344304	+	0.596352i
$377$		−	1583.28i		−	0.216295i
$378$	541.593	+	7523.36i	0.0736945	+	1.02370i
$379$	−11242.6			−1.52374			−0.761868	−	0.647732i	$-0.775718\pi$
$379$	−11242.6			−1.52374			−0.761868	+	0.647732i	$0.775718\pi$
$380$		0			0
$381$	−6738.92	+	5935.41i	−0.906155	+	0.798111i
$382$	727.862	+	420.231i	0.0974886	+	0.0562851i
$383$	5884.53	+	3397.44i	0.785080	+	0.453266i	0.838227	−	0.545321i	$-0.183592\pi$
$383$	5884.53	+	3397.44i	0.785080	+	0.453266i	−0.0531478	+	0.998587i	$0.516925\pi$
$384$	5774.34	+	1946.37i	0.767372	+	0.258659i
$385$		0			0
$386$	4119.52			0.543207
$387$	−3544.01	−	8453.56i	−0.465509	−	1.11038i
$388$			4438.28i			0.580721i
$389$	3524.70	+	6104.96i	0.459407	+	0.795717i	0.998930	−	0.0462544i	$-0.0147285\pi$
$389$	3524.70	+	6104.96i	0.459407	+	0.795717i	−0.539522	+	0.841971i	$0.681395\pi$
$390$		0			0
$391$	−1648.62	+	2855.49i	−0.213233	+	0.369330i
$392$	15264.2	+	8812.77i	1.96673	+	1.13549i
$393$	−3255.67	+	654.832i	−0.417879	+	0.0840506i
$394$	2319.26	+	4017.08i	0.296555	+	0.513648i
$395$		0			0
$396$	507.550	−	3986.89i	0.0644074	−	0.505931i
$397$			3011.36i			0.380694i	0.981717	+	0.190347i	$0.0609614\pi$
$397$			3011.36i			0.380694i	−0.981717	+	0.190347i	$0.939039\pi$
$398$	−3589.09	+	2072.16i	−0.452022	+	0.260975i
$399$	−7940.93	−	2676.66i	−0.996350	−	0.335841i
$400$		0			0
$401$	2084.07	−	3609.72i	0.259535	−	0.449528i	−0.706582	−	0.707631i	$-0.749764\pi$
$401$	2084.07	−	3609.72i	0.259535	−	0.449528i	0.966118	+	0.258103i	$0.0830973\pi$
$402$	−1169.63	−	1327.97i	−0.145114	−	0.164758i
$403$	−182.884	+	105.588i	−0.0226058	+	0.0130514i
$404$	3243.91			0.399481
$405$		0			0
$406$	4367.96			0.533937
$407$	−9550.03	+	5513.71i	−1.16309	+	0.671510i
$408$	−2125.63	−	2413.39i	−0.257928	−	0.292845i
$409$	−6302.68	+	10916.6i	−0.761974	+	1.31978i	0.179858	+	0.983693i	$0.442436\pi$
$409$	−6302.68	+	10916.6i	−0.761974	+	1.31978i	−0.941832	+	0.336085i	$0.890897\pi$
$410$		0			0
$411$	−13964.1	−	4706.88i	−1.67590	−	0.564899i
$412$	3933.47	−	2270.99i	0.470359	−	0.271562i
$413$		−	532.272i		−	0.0634175i
$414$	−606.156	+	4761.46i	−0.0719588	+	0.565249i
$415$		0			0
$416$	1823.49	+	3158.37i	0.214913	+	0.372240i
$417$	891.454	−	179.303i	0.104687	−	0.0210564i
$418$	−1722.67	−	994.584i	−0.201575	−	0.116380i
$419$	−2572.24	+	4455.24i	−0.299909	+	0.519458i	−0.976115	−	0.217255i	$-0.930290\pi$
$419$	−2572.24	+	4455.24i	−0.299909	+	0.519458i	0.676206	+	0.736713i	$0.263623\pi$
$420$		0			0
$421$	1685.03	+	2918.56i	0.195068	+	0.337867i	0.946923	−	0.321461i	$-0.104174\pi$
$421$	1685.03	+	2918.56i	0.195068	+	0.337867i	−0.751855	+	0.659329i	$0.770841\pi$
$422$		−	3125.74i		−	0.360566i
$423$	2466.13	+	5882.49i	0.283469	+	0.676162i
$424$	12955.9			1.48395
$425$		0			0
$426$	505.893	+	170.522i	0.0575366	+	0.0193939i
$427$	−1810.31	−	1045.19i	−0.205169	−	0.118454i
$428$	6510.45	+	3758.81i	0.735267	+	0.424507i
$429$	2043.84	−	1800.14i	0.230017	−	0.202592i
$430$		0			0
$431$	14948.3			1.67061			0.835306	−	0.549785i	$-0.185290\pi$
$431$	14948.3			1.67061			0.835306	+	0.549785i	$0.185290\pi$
$432$	1376.54	+	667.893i	0.153308	+	0.0743843i
$433$			14011.1i			1.55504i	0.628858	+	0.777520i	$0.283523\pi$
$433$			14011.1i			1.55504i	−0.628858	+	0.777520i	$0.716477\pi$
$434$	−291.297	−	504.542i	−0.0322182	−	0.0558036i
$435$		0			0
$436$	1354.54	−	2346.13i	0.148786	−	0.257705i
$437$	−4618.14	−	2666.29i	−0.505528	−	0.291867i
$438$	1855.06	−	5503.46i	0.202370	−	0.600378i
$439$	−2391.10	−	4141.50i	−0.259956	−	0.450257i	0.706274	−	0.707939i	$-0.250375\pi$
$439$	−2391.10	−	4141.50i	−0.259956	−	0.450257i	−0.966230	+	0.257681i	$0.917041\pi$
$440$		0			0
$441$	17823.5	+	13555.8i	1.92458	+	1.46375i
$442$		−	891.178i		−	0.0959027i
$443$	−4134.42	+	2387.01i	−0.443413	+	0.256005i	−0.705044	−	0.709163i	$-0.749073\pi$
$443$	−4134.42	+	2387.01i	−0.443413	+	0.256005i	0.261631	+	0.965168i	$0.415740\pi$
$444$	−2324.99	−	11559.3i	−0.248511	−	1.23554i
$445$		0			0
$446$	529.867	−	917.757i	0.0562555	−	0.0974374i
$447$	5214.01	−	1048.72i	0.551709	−	0.110969i
$448$	−6126.30	+	3537.02i	−0.646072	+	0.373010i
$449$	855.812			0.0899516			0.0449758	−	0.998988i	$-0.485679\pi$
$449$	855.812			0.0899516			0.0449758	+	0.998988i	$0.485679\pi$
$450$		0			0
$451$	11928.7			1.24545
$452$	−3823.18	+	2207.31i	−0.397848	+	0.229697i
$453$	−1450.59	+	4303.51i	−0.150452	+	0.446350i
$454$	1485.30	−	2572.62i	0.153543	−	0.265945i
$455$		0			0
$456$	3903.15	−	3437.76i	0.400837	−	0.353044i
$457$	−11620.3	+	6708.99i	−1.18944	+	0.686725i	−0.958180	−	0.286166i	$-0.907619\pi$
$457$	−11620.3	+	6708.99i	−1.18944	+	0.686725i	−0.231263	+	0.972891i	$0.574286\pi$
$458$		−	5352.08i		−	0.546040i
$459$	−2291.73	−	3382.65i	−0.233048	−	0.343984i
$460$		0			0
$461$	7942.99	+	13757.7i	0.802477	+	1.38993i	0.917981	+	0.396625i	$0.129819\pi$
$461$	7942.99	+	13757.7i	0.802477	+	1.38993i	−0.115503	+	0.993307i	$0.536848\pi$
$462$	4966.24	+	5638.55i	0.500109	+	0.567812i
$463$	5682.32	+	3280.69i	0.570367	+	0.329302i	0.757296	−	0.653072i	$-0.226520\pi$
$463$	5682.32	+	3280.69i	0.570367	+	0.329302i	−0.186929	+	0.982373i	$0.559853\pi$
$464$	443.007	−	767.311i	0.0443235	−	0.0767705i
$465$		0			0
$466$	2231.16	+	3864.48i	0.221795	+	0.384160i
$467$		−	6792.37i		−	0.673048i	−0.941675	−	0.336524i	$-0.890749\pi$
$467$		−	6792.37i		−	0.673048i	0.941675	−	0.336524i	$-0.109251\pi$
$468$	1125.91	+	2685.64i	0.111207	+	0.265264i
$469$	−7426.25			−0.731156
$470$		0			0
$471$	−126.593	−	629.392i	−0.0123845	−	0.0615730i
$472$	286.109	+	165.185i	0.0279009	+	0.0161086i
$473$	−7907.74	−	4565.54i	−0.768707	−	0.443813i
$474$	−1540.89	−	7660.92i	−0.149315	−	0.742358i
$475$		0			0
$476$	−5518.79			−0.531415
$477$	16328.3	+	2078.67i	1.56734	+	0.199530i
$478$		−	2543.12i		−	0.243346i
$479$	8826.24	+	15287.5i	0.841923	+	1.45825i	0.888267	+	0.459328i	$0.151910\pi$
$479$	8826.24	+	15287.5i	0.841923	+	1.45825i	−0.0463438	+	0.998926i	$0.514757\pi$
$480$		0			0
$481$	3995.07	−	6919.66i	0.378710	−	0.655945i
$482$	−36.3088	−	20.9629i	−0.00343116	−	0.00198098i
$483$	13313.5	+	15115.8i	1.25422	+	1.42401i
$484$	1681.38	+	2912.23i	0.157906	+	0.273501i
$485$		0			0
$486$	−4980.58	−	3251.44i	−0.464863	−	0.303474i
$487$		−	5318.16i		−	0.494844i	−0.968908	−	0.247422i	$-0.920417\pi$
$487$		−	5318.16i		−	0.494844i	0.968908	−	0.247422i	$-0.0795833\pi$
$488$	1123.62	−	648.724i	0.104230	−	0.0601770i
$489$	−5501.54	+	4845.57i	−0.508769	+	0.448107i
$490$		0			0
$491$	−5434.98	+	9413.66i	−0.499546	+	0.865239i	−1.00000		0.000523887i	$-0.999833\pi$
$491$	−5434.98	+	9413.66i	−0.499546	+	0.865239i	0.500454	+	0.865763i	$0.333167\pi$
$492$	−4073.93	+	12086.3i	−0.373307	+	1.10750i
$493$	−2049.09	+	1183.04i	−0.187193	+	0.108076i
$494$	1441.29			0.131269
$495$		0			0
$496$	−118.176			−0.0106981
$497$	1940.21	−	1120.18i	0.175111	−	0.101101i
$498$	4178.92	−	840.531i	0.376028	−	0.0756328i
$499$	5185.25	−	8981.12i	0.465178	−	0.805711i	−0.534032	−	0.845464i	$-0.679324\pi$
$499$	5185.25	−	8981.12i	0.465178	−	0.805711i	0.999210	+	0.0397529i	$0.0126571\pi$
$500$		0			0
$501$	2077.61	+	10329.4i	0.185271	+	0.921123i
$502$	−581.133	+	335.517i	−0.0516678	+	0.0298304i
$503$			12396.4i			1.09886i	0.835538	+	0.549432i	$0.185156\pi$
$503$			12396.4i			1.09886i	−0.835538	+	0.549432i	$0.814844\pi$
$504$	−18119.0	+	7596.07i	−1.60136	+	0.671341i
$505$		0			0
$506$	2390.70	+	4140.82i	0.210039	+	0.363798i
$507$	3016.08	−	8947.89i	0.264199	−	0.783806i
$508$	−8283.30	−	4782.37i	−0.723449	−	0.417684i
$509$	2780.52	−	4816.00i	0.242130	−	0.419382i	−0.719190	−	0.694813i	$-0.755487\pi$
$509$	2780.52	−	4816.00i	0.242130	−	0.419382i	0.961321	+	0.275431i	$0.0888205\pi$
$510$		0			0
$511$	−12186.1	−	21107.0i	−1.05496	−	1.82724i
$512$			3894.99i			0.336203i
$513$	5470.72	−	3706.39i	0.470834	−	0.318989i
$514$	−6032.03			−0.517629
$515$		0			0
$516$	7326.55	−	6452.98i	0.625065	−	0.550536i
$517$	5502.68	+	3176.97i	0.468100	+	0.270258i
$518$	19090.0	+	11021.6i	1.61924	+	0.934868i
$519$	−13314.2	−	4487.85i	−1.12607	−	0.379566i
$520$		0			0
$521$	−2613.39			−0.219760			−0.109880	−	0.993945i	$-0.535047\pi$
$521$	−2613.39			−0.219760			−0.109880	+	0.993945i	$0.535047\pi$
$522$	−2085.11	+	2741.56i	−0.174833	+	0.229875i
$523$			2927.73i			0.244781i	0.992482	+	0.122391i	$0.0390561\pi$
$523$			2927.73i			0.244781i	−0.992482	+	0.122391i	$0.960944\pi$
$524$	−1768.53	−	3063.19i	−0.147440	−	0.255374i
$525$		0			0
$526$	627.199	−	1086.34i	0.0519908	−	0.0900508i
$527$	273.305	+	157.793i	0.0225908	+	0.0130428i
$528$	1494.20	−	300.537i	0.123156	−	0.0247712i
$529$	325.506	+	563.793i	0.0267532	+	0.0463379i
$530$		0			0
$531$	334.081	+	254.087i	0.0273030	+	0.0207654i
$532$		−	8925.48i		−	0.727384i
$533$	−7485.18	+	4321.57i	−0.608291	+	0.351197i
$534$	12387.9	+	4175.62i	1.00389	+	0.338383i
$535$		0			0
$536$	2304.66	−	3991.78i	0.185720	−	0.321677i
$537$	2578.19	+	2927.21i	0.207183	+	0.235230i
$538$	−10789.5	+	6229.35i	−0.864629	+	0.499194i
$539$	22306.5			1.78258
$540$		0			0
$541$	−4023.02			−0.319710			−0.159855	−	0.987140i	$-0.551103\pi$
$541$	−4023.02			−0.319710			−0.159855	+	0.987140i	$0.551103\pi$
$542$	−3140.00	+	1812.88i	−0.248846	+	0.143671i
$543$	−3894.90	−	4422.17i	−0.307820	−	0.349491i
$544$	2725.05	−	4719.92i	0.214771	−	0.371994i
$545$		0			0
$546$	−5159.06	−	1738.97i	−0.404372	−	0.136302i
$547$	2862.68	−	1652.77i	0.223765	−	0.129191i	−0.383927	−	0.923363i	$-0.625429\pi$
$547$	2862.68	−	1652.77i	0.223765	−	0.129191i	0.607692	+	0.794172i	$0.292095\pi$
$548$		−	15695.4i		−	1.22349i
$549$	1520.19	−	637.312i	0.118179	−	0.0495443i
$550$		0			0
$551$	−1913.32	−	3313.96i	−0.147931	−	0.256224i
$552$	−12256.8	+	2465.29i	−0.945082	+	0.190090i
$553$	−28399.8	−	16396.6i	−2.18387	−	1.26086i
$554$	597.702	−	1035.25i	0.0458374	−	0.0793927i
$555$		0			0
$556$	484.253	+	838.752i	0.0369369	+	0.0639766i
$557$			6472.87i			0.492396i	0.969220	+	0.246198i	$0.0791813\pi$
$557$			6472.87i			0.492396i	−0.969220	+	0.246198i	$0.920819\pi$
$558$	455.731	+	58.0166i	0.0345746	+	0.00440150i
$559$	6616.10			0.500593
$560$		0			0
$561$	−3856.92	−	1300.06i	−0.290266	−	0.0978404i
$562$	1750.49	+	1010.65i	0.131388	+	0.0758569i
$563$	−17801.4	−	10277.6i	−1.33257	−	0.769362i	−0.346881	−	0.937909i	$-0.612759\pi$
$563$	−17801.4	−	10277.6i	−1.33257	−	0.769362i	−0.985694	+	0.168547i	$0.946093\pi$
$564$	−5098.25	+	4490.37i	−0.380629	+	0.335246i
$565$		0			0
$566$	−4281.18			−0.317936
$567$	−24054.2	+	6666.29i	−1.78162	+	0.493753i
$568$			1390.54i			0.102722i
$569$	635.311	+	1100.39i	0.0468078	+	0.0810735i	0.888480	−	0.458915i	$-0.151762\pi$
$569$	635.311	+	1100.39i	0.0468078	+	0.0810735i	−0.841672	+	0.539989i	$0.818429\pi$
$570$		0			0
$571$	8376.66	−	14508.8i	0.613927	−	1.06335i	−0.376645	−	0.926358i	$-0.622922\pi$
$571$	8376.66	−	14508.8i	0.613927	−	1.06335i	0.990572	−	0.136995i	$-0.0437444\pi$
$572$	2512.23	+	1450.44i	0.183639	+	0.106024i
$573$	−888.376	+	2635.57i	−0.0647686	+	0.192151i
$574$	−11922.4	−	20650.1i	−0.866951	−	1.50160i
$575$		0			0
$576$	704.455	−	5533.62i	0.0509588	−	0.400291i
$577$		−	7800.01i		−	0.562770i	−0.959595	−	0.281385i	$-0.909206\pi$
$577$		−	7800.01i		−	0.562770i	0.959595	−	0.281385i	$-0.0907939\pi$
$578$	5527.53	−	3191.32i	0.397777	−	0.229657i
$579$	2688.12	+	13364.7i	0.192944	+	0.959271i
$580$		0			0
$581$	8944.12	−	15491.7i	0.638665	−	1.10620i
$582$	6414.58	−	1290.20i	0.456861	−	0.0918912i
$583$	14200.0	−	8198.35i	1.00875	−	0.582403i
$584$	15127.3			1.07187
$585$		0			0
$586$	−151.327			−0.0106677
$587$	−2051.83	+	1184.62i	−0.144273	+	0.0832958i	−0.570399	−	0.821368i	$-0.693211\pi$
$587$	−2051.83	+	1184.62i	−0.144273	+	0.0832958i	0.426126	+	0.904664i	$0.359878\pi$
$588$	−7618.24	+	22601.2i	−0.534304	+	1.58514i
$589$	−255.196	+	442.013i	−0.0178526	+	0.0309216i
$590$		0			0
$591$	−11519.0	+	10145.5i	−0.801737	+	0.706143i
$592$	3872.28	−	2235.66i	0.268834	−	0.155212i
$593$		−	11974.3i		−	0.829218i	−0.910000	−	0.414609i	$-0.863918\pi$
$593$		−	11974.3i		−	0.829218i	0.910000	−	0.414609i	$-0.136082\pi$
$594$	−5909.74	+	425.431i	−0.408215	+	0.0293866i
$595$		0			0
$596$	2832.34	+	4905.76i	0.194660	+	0.337160i
$597$	−9064.59	−	10291.7i	−0.621422	−	0.705547i
$598$	−3000.31	−	1732.23i	−0.205170	−	0.118455i
$599$	11099.7	−	19225.3i	0.757134	−	1.31139i	−0.187173	−	0.982327i	$-0.559932\pi$
$599$	11099.7	−	19225.3i	0.757134	−	1.31139i	0.944307	−	0.329067i	$-0.106734\pi$
$600$		0			0
$601$	5749.47	+	9958.38i	0.390226	+	0.675891i	0.992479	−	0.122414i	$-0.0390635\pi$
$601$	5749.47	+	9958.38i	0.390226	+	0.675891i	−0.602253	+	0.798305i	$0.705730\pi$
$602$			18252.5i			1.23574i
$603$	3545.02	−	4661.09i	0.239410	−	0.314783i
$604$	−4837.08			−0.325858
$605$		0			0
$606$	−943.000	−	4688.37i	−0.0632125	−	0.314277i
$607$	13226.8	+	7636.51i	0.884448	+	0.510636i	0.872122	−	0.489288i	$-0.162743\pi$
$607$	13226.8	+	7636.51i	0.884448	+	0.510636i	0.0123257	+	0.999924i	$0.496077\pi$
$608$	7633.47	+	4407.19i	0.509175	+	0.293972i
$609$	2850.24	+	14170.7i	0.189651	+	0.942900i
$610$		0			0
$611$	−4603.88			−0.304833
$612$	2634.47	−	3463.87i	0.174007	−	0.228789i
$613$			16440.8i			1.08326i	0.840617	+	0.541630i	$0.182192\pi$
$613$			16440.8i			1.08326i	−0.840617	+	0.541630i	$0.817808\pi$
$614$	4128.09	+	7150.07i	0.271329	+	0.469956i
$615$		0			0
$616$	−9785.58	+	16949.1i	−0.640052	+	1.10860i
$617$	−8105.25	−	4679.57i	−0.528857	−	0.305336i	0.211694	−	0.977336i	$-0.432102\pi$
$617$	−8105.25	−	4679.57i	−0.528857	−	0.305336i	−0.740551	+	0.672000i	$0.765435\pi$
$618$	−4425.68	−	5024.81i	−0.288070	−	0.327067i
$619$	−12742.3	−	22070.3i	−0.827392	−	1.43308i	−0.900078	−	0.435729i	$-0.856490\pi$
$619$	−12742.3	−	22070.3i	−0.827392	−	1.43308i	0.0726861	−	0.997355i	$-0.476843\pi$
$620$		0			0
$621$	−15842.9	+	1140.50i	−1.02376	+	0.0736982i
$622$		−	8214.25i		−	0.529520i
$623$	47510.4	−	27430.2i	3.05532	−	1.76399i
$624$	−828.723	+	729.911i	−0.0531658	+	0.0468266i
$625$		0			0
$626$	3134.65	−	5429.38i	0.200137	−	0.346648i
$627$	2102.57	−	6237.75i	0.133921	−	0.397307i
$628$	592.183	−	341.897i	0.0376285	−	0.0217248i
$629$	−11940.6			−0.756919
$630$		0			0
$631$	−21733.8			−1.37117			−0.685585	−	0.727993i	$-0.740454\pi$
$631$	−21733.8			−1.37117			−0.685585	+	0.727993i	$0.740454\pi$
$632$	17627.1	−	10177.0i	1.10945	−	0.640539i
$633$	10140.6	−	2039.65i	0.636737	−	0.128071i
$634$	−3716.35	+	6436.91i	−0.232800	+	0.403222i
$635$		0			0
$636$	3457.03	+	17187.5i	0.215535	+	1.07159i
$637$	−13997.3	+	8081.32i	−0.870631	+	0.502659i
$638$			3431.12i			0.212914i
$639$	−223.102	+	1752.51i	−0.0138119	+	0.108495i
$640$		0			0
$641$	10162.4	+	17601.8i	0.626195	+	1.08460i	0.988308	+	0.152468i	$0.0487220\pi$
$641$	10162.4	+	17601.8i	0.626195	+	1.08460i	−0.362113	+	0.932134i	$0.617945\pi$
$642$	3539.97	−	10502.1i	0.217619	−	0.645617i
$643$	5826.13	+	3363.72i	0.357325	+	0.206302i	0.667907	−	0.744245i	$-0.267190\pi$
$643$	5826.13	+	3363.72i	0.357325	+	0.206302i	−0.310581	+	0.950547i	$0.600524\pi$
$644$	−10727.2	+	18580.0i	−0.656382	+	1.13689i
$645$		0			0
$646$	−1076.94	−	1865.32i	−0.0655910	−	0.113607i
$647$			6724.69i			0.408616i	0.978907	+	0.204308i	$0.0654945\pi$
$647$			6724.69i			0.408616i	−0.978907	+	0.204308i	$0.934506\pi$
$648$	3881.66	−	14998.5i	0.235318	−	0.909253i
$649$	418.110			0.0252885
$650$		0			0
$651$	1446.77	−	1274.27i	0.0871021	−	0.0767166i
$652$	−6762.35	−	3904.25i	−0.406187	−	0.234512i
$653$	−26670.4	−	15398.2i	−1.59831	−	0.922782i	−0.991814	−	0.127693i	$-0.959243\pi$
$653$	−26670.4	−	15398.2i	−1.59831	−	0.922782i	−0.606492	−	0.795089i	$-0.707424\pi$
$654$	−3784.60	−	1275.68i	−0.226283	−	0.0762737i
$655$		0			0
$656$	−4836.75			−0.287871
$657$	19065.0	+	2427.07i	1.13211	+	0.144123i
$658$		−	12701.2i		−	0.752498i
$659$	8267.16	+	14319.1i	0.488684	+	0.846426i	0.999915	−	0.0130174i	$-0.00414369\pi$
$659$	8267.16	+	14319.1i	0.488684	+	0.846426i	−0.511231	+	0.859443i	$0.670810\pi$
$660$		0			0
$661$	−968.527	+	1677.54i	−0.0569914	+	0.0987121i	−0.893114	−	0.449831i	$-0.851484\pi$
$661$	−968.527	+	1677.54i	−0.0569914	+	0.0987121i	0.836122	+	0.548543i	$0.184817\pi$
$662$	−12741.5	−	7356.30i	−0.748054	−	0.431889i
$663$	2891.19	−	581.523i	0.169358	−	0.0340641i
$664$	5551.42	+	9615.35i	0.324453	+	0.561970i
$665$		0			0
$666$	−16030.6	+	6720.53i	−0.932691	+	0.391014i
$667$			9198.16i			0.533964i
$668$	−9718.72	+	5611.10i	−0.562917	+	0.325000i
$669$	3323.18	+	1120.15i	0.192050	+	0.0647346i
$670$		0			0
$671$	821.013	−	1422.04i	0.0472352	−	0.0818138i
$672$	−22006.3	−	24985.5i	−1.26326	−	1.43428i
$673$	398.881	−	230.294i	0.0228465	−	0.0131905i	−0.488533	−	0.872545i	$-0.662468\pi$
$673$	398.881	−	230.294i	0.0228465	−	0.0131905i	0.511380	+	0.859355i	$0.329135\pi$
$674$	−8555.80			−0.488957
$675$		0			0
$676$	10057.3			0.572217
$677$	25166.4	−	14529.8i	1.42869	−	0.824854i	0.431671	−	0.902031i	$-0.357924\pi$
$677$	25166.4	−	14529.8i	1.42869	−	0.824854i	0.997017	+	0.0771775i	$0.0245908\pi$
$678$	4301.59	+	4883.92i	0.243660	+	0.276646i
$679$	13729.1	−	23779.5i	0.775956	−	1.34400i
$680$		0			0
$681$	9315.39	+	3139.95i	0.524180	+	0.176686i
$682$	396.327	−	228.820i	0.0222524	−	0.0128474i
$683$		−	14366.9i		−	0.804881i	−0.915446	−	0.402440i	$-0.868162\pi$
$683$		−	14366.9i		−	0.804881i	0.915446	−	0.402440i	$-0.131838\pi$
$684$	5602.08	+	4260.69i	0.313159	+	0.238175i
$685$		0			0
$686$	−13074.3	−	22645.4i	−0.727667	−	1.26036i
$687$	17363.4	−	3492.41i	0.964273	−	0.193950i
$688$	3206.38	+	1851.21i	0.177678	+	0.102582i
$689$	−5940.28	+	10288.9i	−0.328457	+	0.568904i
$690$		0			0
$691$	6353.97	+	11005.4i	0.349807	+	0.605883i	0.986215	−	0.165469i	$-0.0529139\pi$
$691$	6353.97	+	11005.4i	0.349807	+	0.605883i	−0.636408	+	0.771352i	$0.719581\pi$
$692$		−	14965.0i		−	0.822087i
$693$	−15052.1	+	19791.0i	−0.825085	+	1.08485i
$694$	6119.97			0.334742
$695$		0			0
$696$	−8501.63	−	2865.66i	−0.463008	−	0.156067i
$697$	11186.0	+	6458.22i	0.607889	+	0.350965i
$698$	−8511.33	−	4914.02i	−0.461545	−	0.266473i
$699$	−11081.4	+	9760.11i	−0.599623	+	0.528128i
$700$		0			0
$701$	5959.06			0.321071			0.160535	−	0.987030i	$-0.448678\pi$
$701$	5959.06			0.321071			0.160535	+	0.987030i	$0.448678\pi$
$702$	3554.21	−	2407.97i	0.191090	−	0.129463i
$703$		−	19311.4i		−	1.03605i
$704$	−2778.40	−	4812.32i	−0.148743	−	0.257630i
$705$		0			0
$706$	−269.186	+	466.243i	−0.0143498	+	0.0248545i
$707$	−17380.2	−	10034.5i	−0.924542	−	0.533785i
$708$	−142.795	+	423.634i	−0.00757989	+	0.0224875i
$709$	225.912	+	391.292i	0.0119666	+	0.0207268i	0.871947	−	0.489601i	$-0.162857\pi$
$709$	225.912	+	391.292i	0.0119666	+	0.0207268i	−0.859980	+	0.510328i	$0.829524\pi$
$710$		0			0
$711$	23848.4	−	9998.00i	1.25792	−	0.527362i
$712$			34050.6i			1.79228i
$713$	1062.48	−	613.421i	0.0558065	−	0.0322199i
$714$	1604.31	+	7976.23i	0.0840892	+	0.418071i
$715$		0			0
$716$	−2077.34	+	3598.05i	−0.108427	+	0.187801i
$717$	8250.48	−	1659.47i	0.429735	−	0.0864352i
$718$	−14208.8	+	8203.47i	−0.738536	+	0.426394i
$719$	13488.4			0.699627			0.349814	−	0.936819i	$-0.386245\pi$
$719$	13488.4			0.699627			0.349814	+	0.936819i	$0.386245\pi$
$720$		0			0
$721$	−28099.7			−1.45144
$722$	−6310.39	+	3643.30i	−0.325275	+	0.187797i
$723$	44.3159	−	131.473i	0.00227957	−	0.00676285i
$724$	3138.26	−	5435.62i	0.161094	−	0.279024i
$725$		0			0
$726$	3720.23	−	3276.66i	0.190180	−	0.167504i
$727$	25273.3	−	14591.6i	1.28932	−	0.744389i	0.310787	−	0.950480i	$-0.399407\pi$
$727$	25273.3	−	14591.6i	1.28932	−	0.744389i	0.978533	+	0.206090i	$0.0660741\pi$
$728$		−	14180.7i		−	0.721938i
$729$	7298.46	−	18279.9i	0.370800	−	0.928713i
$730$		0			0
$731$	−4943.60	−	8562.57i	−0.250131	−	0.433239i
$732$	1160.43	+	1317.52i	0.0585938	+	0.0665259i
$733$	10836.1	+	6256.24i	0.546032	+	0.315252i	0.747520	−	0.664239i	$-0.231244\pi$
$733$	10836.1	+	6256.24i	0.546032	+	0.315252i	−0.201488	+	0.979491i	$0.564578\pi$
$734$	−4061.92	+	7035.45i	−0.204262	+	0.353792i
$735$		0			0
$736$	−10593.6	−	18348.7i	−0.530553	−	0.918945i
$737$		−	5833.46i		−	0.291558i
$738$	18652.4	+	2374.53i	0.930357	+	0.118439i
$739$	32248.2			1.60524			0.802619	−	0.596492i	$-0.203439\pi$
$739$	32248.2			1.60524			0.802619	+	0.596492i	$0.203439\pi$
$740$		0			0
$741$	940.490	+	4675.89i	0.0466259	+	0.231813i
$742$	−28384.9	−	16388.1i	−1.40437	−	0.810815i
$743$	16011.9	+	9244.50i	0.790607	+	0.456457i	0.840176	−	0.542313i	$-0.182451\pi$
$743$	16011.9	+	9244.50i	0.790607	+	0.456457i	−0.0495691	+	0.998771i	$0.515785\pi$
$744$	235.959	+	1173.13i	0.0116272	+	0.0578078i
$745$		0			0
$746$	3299.12			0.161916
$747$	5453.77	+	13008.9i	0.267126	+	0.637178i
$748$		−	4335.12i		−	0.211908i
$749$	−23254.5	−	40278.0i	−1.13445	−	1.96492i
$750$		0			0
$751$	1026.10	−	1777.26i	0.0498575	−	0.0863558i	−0.840020	−	0.542556i	$-0.817457\pi$
$751$	1026.10	−	1777.26i	0.0498575	−	0.0863558i	0.889877	+	0.456200i	$0.150790\pi$
$752$	−2231.19	−	1288.18i	−0.108196	−	0.0624668i
$753$	−1467.71	−	1666.40i	−0.0710308	−	0.0806466i
$754$	−1243.04	−	2153.01i	−0.0600384	−	0.103990i
$755$		0			0
$756$	−14911.8	−	22010.1i	−0.717377	−	1.05886i
$757$			10118.9i			0.485834i	0.970047	+	0.242917i	$0.0781043\pi$
$757$			10118.9i			0.485834i	−0.970047	+	0.242917i	$0.921896\pi$
$758$	−15288.2	+	8826.65i	−0.732576	+	0.422953i
$759$	−11873.8	+	10458.0i	−0.567841	+	0.500135i
$760$		0			0
$761$	−13652.0	+	23646.0i	−0.650309	+	1.12637i	0.332739	+	0.943019i	$0.392027\pi$
$761$	−13652.0	+	23646.0i	−0.650309	+	1.12637i	−0.983048	+	0.183349i	$0.941306\pi$
$762$	−4503.94	+	13362.0i	−0.214121	+	0.635240i
$763$	−14514.8	+	8380.10i	−0.688689	+	0.397615i
$764$	−2962.34			−0.140280
$765$		0			0
$766$	10669.4			0.503264
$767$	−262.362	+	151.475i	−0.0123512	+	0.00713096i
$768$	17800.0	−	3580.22i	0.836330	−	0.168216i
$769$	−11236.9	+	19462.9i	−0.526935	+	0.912679i	0.472572	+	0.881292i	$0.343326\pi$
$769$	−11236.9	+	19462.9i	−0.526935	+	0.912679i	−0.999507	+	0.0313867i	$0.990008\pi$
$770$		0			0
$771$	−3936.10	−	19569.3i	−0.183859	−	0.914102i
$772$	−12574.6	+	7259.94i	−0.586230	+	0.338460i
$773$			35405.6i			1.64741i	0.567015	+	0.823707i	$0.308098\pi$
$773$			35405.6i			1.64741i	−0.567015	+	0.823707i	$0.691902\pi$
$774$	−11456.2	−	8713.08i	−0.532022	−	0.404632i
$775$		0			0
$776$	8521.35	+	14759.4i	0.394200	+	0.682774i
$777$	−23299.9	+	69124.4i	−1.07578	+	3.19154i
$778$	9586.07	+	5534.52i	0.441744	+	0.255041i
$779$	−10444.8	+	18090.9i	−0.480390	+	0.832060i
$780$		0			0
$781$	879.923	+	1524.07i	0.0403151	+	0.0698278i
$782$			5177.34i			0.236754i
$783$	−10254.9	−	4975.62i	−0.468044	−	0.227093i
$784$	−9044.71			−0.412022
$785$		0			0
$786$	−3913.08	+	3446.50i	−0.177576	+	0.156403i
$787$	10548.2	+	6090.02i	0.477769	+	0.275840i	0.719486	−	0.694507i	$-0.244377\pi$
$787$	10548.2	+	6090.02i	0.477769	+	0.275840i	−0.241718	+	0.970347i	$0.577711\pi$
$788$	−14158.8	−	8174.59i	−0.640085	−	0.369553i
$789$	3933.62	+	1325.91i	0.177491	+	0.0598272i
$790$		0			0
$791$	27311.8			1.22768
$792$	−5966.86	−	14232.8i	−0.267706	−	0.638562i
$793$			1189.76i			0.0532783i
$794$	2364.23	+	4094.97i	0.105672	+	0.183029i
$795$		0			0
$796$	7303.65	−	12650.3i	0.325215	−	0.563289i
$797$	−1985.86	−	1146.54i	−0.0882596	−	0.0509567i	0.455221	−	0.890379i	$-0.349560\pi$
$797$	−1985.86	−	1146.54i	−0.0882596	−	0.0509567i	−0.543480	+	0.839422i	$0.682894\pi$
$798$	−12899.9	+	2594.63i	−0.572243	+	0.115099i
$799$	3440.05	+	5958.35i	0.152316	+	0.263819i
$800$		0			0
$801$	−5463.16	+	42914.1i	−0.240988	+	1.89300i
$802$		−	6544.86i		−	0.288164i
$803$	16579.9	−	9572.43i	0.728634	−	0.420677i
$804$	5910.53	+	1992.27i	0.259264	+	0.0873905i
$805$		0			0
$806$	−165.796	+	287.167i	−0.00724554	+	0.0125496i
$807$	−27250.0	−	30939.0i	−1.18866	−	1.34957i
$808$	10787.5	−	6228.19i	0.469684	−	0.271172i
$809$	25264.0			1.09794			0.548972	−	0.835841i	$-0.315019\pi$
$809$	25264.0			1.09794			0.548972	+	0.835841i	$0.315019\pi$
$810$		0			0
$811$	18781.2			0.813190			0.406595	−	0.913608i	$-0.366716\pi$
$811$	18781.2			0.813190			0.406595	+	0.913608i	$0.366716\pi$
$812$	−13333.0	+	7697.78i	−0.576225	+	0.332684i
$813$	−7930.37	−	9003.94i	−0.342103	−	0.388416i
$814$	−8657.68	+	14995.5i	−0.372790	+	0.645692i
$815$		0			0
$816$	1563.88	+	527.139i	0.0670916	+	0.0226147i
$817$	13848.1	−	7995.23i	0.593005	−	0.342372i
$818$			19793.0i			0.846023i
$819$	2275.18	−	17871.9i	0.0970711	−	0.762510i
$820$		0			0
$821$	−15787.4	−	27344.6i	−0.671114	−	1.16240i	−0.977588	−	0.210525i	$-0.932483\pi$
$821$	−15787.4	−	27344.6i	−0.671114	−	1.16240i	0.306474	−	0.951879i	$-0.400851\pi$
$822$	−22684.3	+	4562.63i	−0.962537	+	0.193601i
$823$	−819.484	−	473.129i	−0.0347089	−	0.0200392i	0.482545	−	0.875871i	$-0.339712\pi$
$823$	−819.484	−	473.129i	−0.0347089	−	0.0200392i	−0.517254	+	0.855832i	$0.673046\pi$
$824$	8720.45	−	15104.3i	0.368679	−	0.638570i
$825$		0			0
$826$	−417.889	−	723.806i	−0.0176032	−	0.0304896i
$827$			35044.7i			1.47355i	0.676139	+	0.736774i	$0.263652\pi$
$827$			35044.7i			1.47355i	−0.676139	+	0.736774i	$0.736348\pi$
$828$	−6541.00	−	15602.3i	−0.274536	−	0.654853i
$829$	−31029.2			−1.29999			−0.649993	−	0.759940i	$-0.725228\pi$
$829$	−31029.2			−1.29999			−0.649993	+	0.759940i	$0.725228\pi$
$830$		0			0
$831$	3748.62	+	1263.55i	0.156484	+	0.0527463i
$832$	3486.86	+	2013.14i	0.145295	+	0.0838860i
$833$	20917.7	+	12076.8i	0.870055	+	0.502327i
$834$	1071.46	−	943.708i	0.0444865	−	0.0391822i
$835$		0			0
$836$	7011.13			0.290054
$837$	109.160	+	1516.36i	0.00450790	+	0.0626200i
$838$			8077.90i			0.332991i
$839$	−10599.9	−	18359.6i	−0.436175	−	0.755477i	0.561216	−	0.827669i	$-0.310334\pi$
$839$	−10599.9	−	18359.6i	−0.436175	−	0.755477i	−0.997391	+	0.0721924i	$0.977000\pi$
$840$		0			0
$841$	8894.22	−	15405.2i	0.364681	−	0.631647i
$842$	4582.76	+	2645.86i	0.187568	+	0.108292i
$843$	−2136.52	+	6338.49i	−0.0872904	+	0.258967i
$844$	5508.58	+	9541.14i	0.224660	+	0.389123i
$845$		0			0
$846$	7971.91	+	6063.08i	0.323972	+	0.246398i
$847$		−	20804.3i		−	0.843971i
$848$	−5757.71	+	3324.22i	−0.233161	+	0.134616i
$849$	−2793.61	−	13889.2i	−0.112929	−	0.561455i
$850$		0			0
$851$	−23209.5	+	40200.1i	−0.934915	+	1.61932i
$852$	−1844.72	+	371.040i	−0.0741774	+	0.0149197i
$853$	−9508.84	+	5489.93i	−0.381684	+	0.220365i	−0.678551	−	0.734554i	$-0.737392\pi$
$853$	−9508.84	+	5489.93i	−0.381684	+	0.220365i	0.296867	+	0.954919i	$0.404058\pi$
$854$	−3282.32			−0.131521
$855$		0			0
$856$	28867.2			1.15264
$857$	38810.4	−	22407.2i	1.54695	−	0.893133i	0.548580	−	0.836098i	$-0.315169\pi$
$857$	38810.4	−	22407.2i	1.54695	−	0.893133i	0.998372	−	0.0570348i	$-0.0181646\pi$
$858$	1365.99	−	4052.54i	0.0543523	−	0.161249i
$859$	18693.1	−	32377.4i	0.742492	−	1.28603i	−0.208866	−	0.977944i	$-0.566977\pi$
$859$	18693.1	−	32377.4i	0.742492	−	1.28603i	0.951358	−	0.308089i	$-0.0996895\pi$
$860$		0			0
$861$	59214.2	−	52153.9i	2.34380	−	2.06434i
$862$	20327.3	−	11736.0i	0.803191	−	0.463722i
$863$			30536.3i			1.20448i	0.798314	+	0.602241i	$0.205725\pi$
$863$			30536.3i			1.20448i	−0.798314	+	0.602241i	$0.794275\pi$
$864$	26187.2	−	1885.16i	1.03114	−	0.0742299i
$865$		0			0
$866$	11000.2	+	19052.9i	0.431643	+	0.747627i
$867$	13960.3	+	15850.2i	0.546848	+	0.620877i
$868$	1778.34	+	1026.72i	0.0695399	+	0.0401489i
$869$	12879.8	−	22308.6i	0.502784	−	0.870847i
$870$		0			0
$871$	2113.37	+	3660.47i	0.0822146	+	0.142400i
$872$		−	10402.7i		−	0.403991i
$873$	8371.45	+	19968.5i	0.324548	+	0.774149i
$874$	−8373.25			−0.324061
$875$		0			0
$876$	4036.44	+	20068.2i	0.155683	+	0.774021i
$877$	−29728.4	−	17163.7i	−1.14465	−	0.660864i	−0.197072	−	0.980389i	$-0.563143\pi$
$877$	−29728.4	−	17163.7i	−1.14465	−	0.660864i	−0.947578	+	0.319525i	$0.896477\pi$
$878$	−6503.02	−	3754.52i	−0.249962	−	0.144315i
$879$	−98.7460	−	490.941i	−0.00378910	−	0.0188385i
$880$		0			0
$881$	−18009.6			−0.688718			−0.344359	−	0.938838i	$-0.611904\pi$
$881$	−18009.6			−0.688718			−0.344359	+	0.938838i	$0.611904\pi$
$882$	34879.9	+	4440.37i	1.33159	+	0.169518i
$883$			29074.4i			1.10808i	0.832491	+	0.554039i	$0.186914\pi$
$883$			29074.4i			1.10808i	−0.832491	+	0.554039i	$0.813086\pi$
$884$	1570.55	+	2720.27i	0.0597548	+	0.103498i
$885$		0			0
$886$	−3748.10	+	6491.90i	−0.142122	+	0.246162i
$887$	28494.5	+	16451.3i	1.07864	+	0.622752i	0.930528	−	0.366220i	$-0.119348\pi$
$887$	28494.5	+	16451.3i	1.07864	+	0.622752i	0.148109	+	0.988971i	$0.452681\pi$
$888$	−29925.1	−	33976.2i	−1.13088	−	1.28397i
$889$	29586.9	+	51246.1i	1.11621	+	1.93334i
$890$		0			0
$891$	−5236.50	−	18895.0i	−0.196890	−	0.710444i
$892$			3735.20i			0.140206i
$893$	−9636.36	+	5563.56i	−0.361107	+	0.208485i
$894$	6266.86	−	5519.64i	0.234446	−	0.206493i
$895$		0			0
$896$	20076.6	−	34773.7i	0.748562	−	1.29655i
$897$	3661.96	−	10864.1i	0.136309	−	0.404393i
$898$	1163.77	−	671.902i	0.0432466	−	0.0249684i
$899$	880.377			0.0326610
$900$		0			0
$901$	17754.5			0.656479
$902$	16221.1	−	9365.24i	0.598783	−	0.345708i
$903$	−59215.5	+	11910.4i	−2.18225	+	0.438928i
$904$	−8475.93	+	14680.7i	−0.311842	+	0.540127i
$905$		0			0
$906$	1406.13	+	6990.96i	0.0515625	+	0.256357i
$907$	−706.517	+	407.908i	−0.0258649	+	0.0149331i	−0.512877	−	0.858462i	$-0.671420\pi$
$907$	−706.517	+	407.908i	−0.0258649	+	0.0149331i	0.487012	+	0.873395i	$0.338087\pi$
$908$			10470.4i			0.382677i
$909$	14594.8	−	6118.63i	0.532542	−	0.223259i
$910$		0			0
$911$	−7921.41	−	13720.3i	−0.288088	−	0.498983i	0.685265	−	0.728293i	$-0.259686\pi$
$911$	−7921.41	−	13720.3i	−0.288088	−	0.498983i	−0.973353	+	0.229311i	$0.926353\pi$
$912$	−852.536	+	2529.24i	−0.0309543	+	0.0918329i
$913$	12169.0	+	7025.77i	0.441112	+	0.254676i
$914$	−10534.5	+	18246.3i	−0.381237	+	0.660322i
$915$		0			0
$916$	9432.11	+	16336.9i	0.340225	+	0.589286i
$917$			21882.7i			0.788037i
$918$	−5772.12	−	2800.61i	−0.207526	−	0.100691i
$919$	−23848.4			−0.856025			−0.428013	−	0.903773i	$-0.640786\pi$
$919$	−23848.4			−0.856025			−0.428013	+	0.903773i	$0.640786\pi$
$920$		0			0
$921$	−20502.8	+	18058.2i	−0.733540	+	0.646077i
$922$	21602.4	+	12472.2i	0.771624	+	0.445498i
$923$	−1104.30	−	637.566i	−0.0393807	−	0.0227364i
$924$	−25096.1	−	8459.19i	−0.893508	−	0.301176i
$925$		0			0
$926$	10302.7			0.365625
$927$	13413.8	−	17636.8i	0.475260	−	0.624886i
$928$		−	15203.9i		−	0.537816i
$929$	−19796.0	−	34287.7i	−0.699123	−	1.21092i	−0.968771	−	0.247958i	$-0.920240\pi$
$929$	−19796.0	−	34287.7i	−0.699123	−	1.21092i	0.269647	−	0.962959i	$-0.413093\pi$
$930$		0			0
$931$	−19531.7	+	33830.0i	−0.687569	+	1.19090i
$932$	−13621.0	−	7864.07i	−0.478723	−	0.276391i
$933$	26649.0	−	5360.07i	0.935100	−	0.188082i
$934$	−5332.72	−	9236.54i	−0.186822	−	0.323585i
$935$		0			0
$936$	8900.51	+	6769.33i	0.310814	+	0.236391i
$937$			10255.0i			0.357540i	0.983891	+	0.178770i	$0.0572118\pi$
$937$			10255.0i			0.357540i	−0.983891	+	0.178770i	$0.942788\pi$
$938$	−10098.5	+	5830.38i	−0.351523	+	0.202952i
$939$	19659.7	+	6626.71i	0.683247	+	0.230303i
$940$		0			0
$941$	11947.2	−	20693.1i	0.413886	−	0.716871i	−0.581425	−	0.813600i	$-0.697505\pi$
$941$	11947.2	−	20693.1i	0.413886	−	0.716871i	0.995311	+	0.0967289i	$0.0308380\pi$
$942$	−666.286	−	756.484i	−0.0230454	−	0.0261652i
$943$	43485.5	−	25106.4i	1.50168	−	0.866995i
$944$	−169.533			−0.00584514
$945$		0			0
$946$	−14337.7			−0.492768
$947$	−31399.7	+	18128.6i	−1.07746	+	0.622072i	−0.930210	−	0.367028i	$-0.880375\pi$
$947$	−31399.7	+	18128.6i	−1.07746	+	0.622072i	−0.147250	+	0.989099i	$0.547042\pi$
$948$	18204.5	+	20668.9i	0.623686	+	0.708118i
$949$	−6935.89	+	12013.3i	−0.237248	+	0.410926i
$950$		0			0
$951$	−23307.9	−	7856.43i	−0.794754	−	0.267889i
$952$	−18352.6	+	10595.9i	−0.624803	+	0.360730i
$953$			46736.7i			1.58861i	0.607516	+	0.794307i	$0.292166\pi$
$953$			46736.7i			1.58861i	−0.607516	+	0.794307i	$0.707834\pi$
$954$	23835.9	−	9992.78i	0.808927	−	0.339128i
$955$		0			0
$956$	4481.81	+	7762.72i	0.151623	+	0.262620i
$957$	−11131.4	+	2238.92i	−0.375994	+	0.0756259i
$958$	24004.6	+	13859.0i	0.809553	+	0.467396i
$959$	−48551.0	+	84092.9i	−1.63482	+	2.83160i
$960$		0			0
$961$	14836.8	+	25698.1i	0.498029	+	0.862612i
$962$		−	12546.2i		−	0.420484i
$963$	36381.4	+	4631.51i	1.21742	+	0.154983i
$964$	147.774			0.00493721
$965$		0			0
$966$	29971.8	+	10102.6i	0.998268	+	0.336488i
$967$	−38414.3	−	22178.5i	−1.27748	−	0.737552i	−0.301094	−	0.953595i	$-0.597352\pi$
$967$	−38414.3	−	22178.5i	−1.27748	−	0.737552i	−0.976384	+	0.216043i	$0.930685\pi$
$968$	11182.8	+	6456.39i	0.371310	+	0.214376i
$969$	5348.80	−	4711.04i	0.177325	−	0.156182i
$970$		0			0
$971$	−650.540			−0.0215003			−0.0107502	−	0.999942i	$-0.503422\pi$
$971$	−650.540			−0.0215003			−0.0107502	+	0.999942i	$0.503422\pi$
$972$	20933.0	+	1147.42i	0.690769	+	0.0378639i
$973$		−	5991.83i		−	0.197420i
$974$	−4175.31	−	7231.85i	−0.137357	−	0.237909i
$975$		0			0
$976$	−332.899	+	576.598i	−0.0109179	+	0.0189103i
$977$	−44751.9	−	25837.5i	−1.46544	−	0.846075i	−0.466190	−	0.884684i	$-0.654374\pi$
$977$	−44751.9	−	25837.5i	−1.46544	−	0.846075i	−0.999254	+	0.0386096i	$0.987707\pi$
$978$	−3676.94	+	10908.5i	−0.120220	+	0.356662i
$979$	21546.9	+	37320.3i	0.703414	+	1.21835i
$980$		0			0
$981$	1669.03	−	13110.5i	0.0543202	−	0.426695i
$982$			17068.1i			0.554649i
$983$	−20368.0	+	11759.5i	−0.660874	+	0.381556i	−0.792610	−	0.609729i	$-0.791278\pi$
$983$	−20368.0	+	11759.5i	−0.660874	+	0.381556i	0.131736	+	0.991285i	$0.457945\pi$
$984$	9657.43	+	48014.4i	0.312874	+	1.55553i
$985$		0			0
$986$	−1857.62	+	3217.49i	−0.0599987	+	0.103921i
$987$	41205.7	−	8287.95i	1.32887	−	0.267283i
$988$	−4399.46	+	2540.03i	−0.141665	+	0.0817905i
$989$	−38436.6			−1.23581
$990$		0			0
$991$	−27732.9			−0.888966			−0.444483	−	0.895787i	$-0.646613\pi$
$991$	−27732.9			−0.888966			−0.444483	+	0.895787i	$0.646613\pi$
$992$	−1756.20	+	1013.94i	−0.0562090	+	0.0324523i
$993$	15551.3	−	46136.6i	0.496986	−	1.47442i
$994$	1758.92	−	3046.53i	0.0561262	−	0.0972135i
$995$		0			0
$996$	−11274.6	+	9930.30i	−0.358685	+	0.315917i
$997$	−29728.7	+	17163.9i	−0.944351	+	0.545221i	−0.891322	−	0.453372i	$-0.850221\pi$
$997$	−29728.7	+	17163.9i	−0.944351	+	0.545221i	−0.0530293	+	0.998593i	$0.516888\pi$
$998$		−	16283.9i		−	0.516489i
$999$	−32263.5	−	47621.6i	−1.02179	−	1.50819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.d.49.9		28
5.2	odd	4		225.4.e.d.76.5		14
5.3	odd	4		45.4.e.c.31.3	yes	14
5.4	even	2	inner	225.4.k.d.49.6		28
9.7	even	3	inner	225.4.k.d.124.6		28
15.8	even	4		135.4.e.c.91.5		14
45.7	odd	12		225.4.e.d.151.5		14
45.13	odd	12		405.4.a.m.1.5		7
45.22	odd	12		2025.4.a.bb.1.3		7
45.23	even	12		405.4.a.n.1.3		7
45.32	even	12		2025.4.a.ba.1.5		7
45.34	even	6	inner	225.4.k.d.124.9		28
45.38	even	12		135.4.e.c.46.5		14
45.43	odd	12		45.4.e.c.16.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.3	✓	14	45.43	odd	12
45.4.e.c.31.3	yes	14	5.3	odd	4
135.4.e.c.46.5		14	45.38	even	12
135.4.e.c.91.5		14	15.8	even	4
225.4.e.d.76.5		14	5.2	odd	4
225.4.e.d.151.5		14	45.7	odd	12
225.4.k.d.49.6		28	5.4	even	2	inner
225.4.k.d.49.9		28	1.1	even	1	trivial
225.4.k.d.124.6		28	9.7	even	3	inner
225.4.k.d.124.9		28	45.34	even	6	inner
405.4.a.m.1.5		7	45.13	odd	12
405.4.a.n.1.3		7	45.23	even	12
2025.4.a.ba.1.5		7	45.32	even	12
2025.4.a.bb.1.3		7	45.22	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35984 - 0.785104i) q^{2} +(3.43441 + 3.89934i) q^{3} +(-2.76722 + 4.79297i) q^{4} +(7.73164 + 2.60611i) q^{6} +(29.6525 - 17.1199i) q^{7} +21.2519i q^{8} +(-3.40971 + 26.7838i) q^{9} +(13.4480 + 23.2926i) q^{11} +(-28.1932 + 5.67066i) q^{12} +(-16.8771 - 9.74401i) q^{13} +(26.8818 - 46.5607i) q^{14} +(-5.45281 - 9.44454i) q^{16} +29.1232i q^{17} +(16.3915 + 39.0987i) q^{18} -47.1006 q^{19} +(168.595 + 56.8286i) q^{21} +(36.5743 + 21.1162i) q^{22} +(98.0485 + 56.6083i) q^{23} +(-82.8684 + 72.9877i) q^{24} -30.6003 q^{26} +(-116.150 + 78.6910i) q^{27} +189.498i q^{28} +(40.6219 + 70.3593i) q^{29} +(5.41811 - 9.38445i) q^{31} +(-162.067 - 93.5697i) q^{32} +(-44.6399 + 132.435i) q^{33} +(22.8648 + 39.6029i) q^{34} +(-118.939 - 90.4594i) q^{36} +410.002i q^{37} +(-64.0493 + 36.9789i) q^{38} +(-19.9677 - 99.2746i) q^{39} +(221.755 - 384.091i) q^{41} +(273.879 - 55.0869i) q^{42} +(-294.012 + 169.748i) q^{43} -148.854 q^{44} +177.774 q^{46} +(204.591 - 118.121i) q^{47} +(18.1003 - 53.6988i) q^{48} +(414.681 - 718.249i) q^{49} +(-113.561 + 100.021i) q^{51} +(93.4055 - 53.9277i) q^{52} -609.634i q^{53} +(-96.1643 + 198.197i) q^{54} +(363.830 + 630.173i) q^{56} +(-161.763 - 183.661i) q^{57} +(110.479 + 63.7849i) q^{58} +(7.77272 - 13.4627i) q^{59} +(-30.5255 - 52.8717i) q^{61} -17.0151i q^{62} +(357.430 + 852.582i) q^{63} -206.603 q^{64} +(43.2718 + 215.137i) q^{66} +(-187.832 - 108.445i) q^{67} +(-139.587 - 80.5903i) q^{68} +(116.003 + 576.740i) q^{69} +65.4315 q^{71} +(-569.208 - 72.4627i) q^{72} -711.811i q^{73} +(321.895 + 557.538i) q^{74} +(130.338 - 225.752i) q^{76} +(797.534 + 460.457i) q^{77} +(-105.094 - 119.321i) q^{78} +(-478.876 - 829.438i) q^{79} +(-705.748 - 182.650i) q^{81} -696.404i q^{82} +(452.446 - 261.220i) q^{83} +(-738.918 + 650.814i) q^{84} +(-266.540 + 461.660i) q^{86} +(-134.842 + 400.041i) q^{87} +(-495.012 + 285.796i) q^{88} +1602.24 q^{89} -667.266 q^{91} +(-542.644 + 313.296i) q^{92} +(55.2011 - 11.1029i) q^{93} +(185.474 - 321.251i) q^{94} +(-191.745 - 953.312i) q^{96} +(694.499 - 400.969i) q^{97} -1302.27i q^{98} +(-669.719 + 280.768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41}+ \cdots - 4640 q^{99}+O(q^{100}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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