LMFDB - Embedded newform 225.4.k.d.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

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")

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

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			49.6
Character	$\chi$	$=$	225.49
Dual form			225.4.k.d.124.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35984 + 0.785104i) q^{2} +(-3.43441 - 3.89934i) q^{3} +(-2.76722 + 4.79297i) q^{4} +(7.73164 + 2.60611i) q^{6} +(-29.6525 + 17.1199i) q^{7} -21.2519i q^{8} +(-3.40971 + 26.7838i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.720740	−	0.693206i	$-0.756198\pi$
$2$	−1.35984	+	0.785104i	−0.480776	+	0.277576i	0.239964	+	0.970782i	$0.422864\pi$
$3$	−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	$0.708756\pi$
$7$	−29.6525	+	17.1199i	−1.60109	+	0.924387i	−0.991271	+	0.131844i	$0.957910\pi$
$8$		−	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	0.669110	−	0.743163i	$-0.266675\pi$
$13$	16.8771	+	9.74401i	0.360067	+	0.207885i	−0.309043	+	0.951048i	$0.600009\pi$
$14$	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	$-0.933387\pi$
$17$		−	29.1232i		−	0.415495i	0.978182	−	0.207747i	$-0.0666132\pi$
$18$	−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	−0.0153124	−	0.999883i	$-0.504874\pi$
$23$	−98.0485	−	56.6083i	−0.888892	−	0.513202i	−0.873580	+	0.486680i	$0.838208\pi$
$24$	−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	$-0.635416\pi$
$37$		−	410.002i		−	1.82173i	0.412706	−	0.910864i	$-0.364584\pi$
$38$	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	0.122108	−	0.992517i	$-0.461035\pi$
$43$	294.012	−	169.748i	1.04271	−	0.602007i	0.920599	+	0.390510i	$0.127701\pi$
$44$	−148.854			−0.510015
$45$		0			0
$46$	177.774			0.569811
$47$	−204.591	+	118.121i	−0.634950	+	0.366589i	−0.782667	−	0.622441i	$-0.786141\pi$
$47$	−204.591	+	118.121i	−0.634950	+	0.366589i	0.147716	+	0.989030i	$0.452808\pi$
$48$	−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	$0.289918\pi$
$53$			609.634i			1.57999i	−0.613111	+	0.789997i	$0.710082\pi$
$54$	−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	0.661376	−	0.750055i	$-0.269973\pi$
$67$	187.832	+	108.445i	0.342497	+	0.197741i	−0.318879	+	0.947796i	$0.603306\pi$
$68$	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	$0.193299\pi$
$73$			711.811i			1.14125i	−0.821211	+	0.570624i	$0.806701\pi$
$74$	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	−0.768389	−	0.639983i	$-0.778942\pi$
$83$	−452.446	+	261.220i	−0.598343	+	0.345453i	0.170047	+	0.985436i	$0.445608\pi$
$84$	−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	−0.817311	−	0.576197i	$-0.804536\pi$
$97$	−694.499	+	400.969i	−0.726966	+	0.419714i	0.0903455	+	0.995910i	$0.471203\pi$
$98$			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	0.799818	−	0.600243i	$-0.204929\pi$
$103$	710.725	+	410.337i	0.679901	+	0.392541i	−0.119917	+	0.992784i	$0.538263\pi$
$104$	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	$0.210288\pi$
$107$			1358.33i			1.22724i	−0.789600	+	0.613621i	$0.789712\pi$
$108$	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	0.184092	−	0.982909i	$-0.441065\pi$
$113$	−690.797	−	398.832i	−0.575086	−	0.332026i	−0.759178	+	0.650883i	$0.774399\pi$
$114$	−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	$-0.793669\pi$
$127$		−	1728.22i		−	1.20752i	0.797167	−	0.603759i	$-0.206331\pi$
$128$	−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	$-0.321321\pi$
$137$	2456.00	−	1417.97i	1.53161	−	0.884274i	0.999288	−	0.0377300i	$-0.0120127\pi$
$138$	−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	0.526949	−	0.849897i	$-0.323336\pi$
$157$	107.000	+	61.7762i	0.0543917	+	0.0314031i	−0.472558	+	0.881300i	$0.656669\pi$
$158$	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	$-0.889916\pi$
$163$		−	1410.89i		−	0.677972i	0.940791	−	0.338986i	$-0.110084\pi$
$164$	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	0.0345441	−	0.999403i	$-0.489002\pi$
$167$	−1756.04	−	1013.85i	−0.813692	−	0.469786i	−0.848236	+	0.529618i	$0.822335\pi$
$168$	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	0.112384	−	0.993665i	$-0.464151\pi$
$173$	2341.71	−	1351.99i	1.02912	−	0.594160i	0.916731	+	0.399505i	$0.130818\pi$
$174$	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	0.0123786	−	0.999923i	$-0.496060\pi$
$193$	−2272.06	−	1311.77i	−0.847391	−	0.489241i	−0.859770	+	0.510682i	$0.829393\pi$
$194$	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	$-0.820618\pi$
$197$		−	2954.08i		−	1.06837i	0.845367	−	0.534186i	$-0.179382\pi$
$198$	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	−0.585184	−	0.810901i	$-0.698978\pi$
$223$	−584.481	+	337.450i	−0.175515	+	0.101333i	0.409669	+	0.912234i	$0.365644\pi$
$224$	−6407.61			−1.91128
$225$		0			0
$226$	1252.50			0.368650
$227$	−1638.39	+	945.926i	−0.479048	+	0.276579i	−0.720020	−	0.693954i	$-0.755867\pi$
$227$	−1638.39	+	945.926i	−0.479048	+	0.276579i	0.240972	+	0.970532i	$0.422534\pi$
$228$	−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	$-0.869177\pi$
$233$		−	2841.86i		−	0.799041i	0.916724	−	0.399521i	$-0.130823\pi$
$234$	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	0.846083	−	0.533051i	$-0.178954\pi$
$257$	3326.88	+	1920.77i	0.807490	+	0.466204i	−0.0385936	+	0.999255i	$0.512288\pi$
$258$	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	−0.578907	−	0.815394i	$-0.696521\pi$
$263$	−691.845	+	399.437i	−0.162209	+	0.0936514i	0.416698	+	0.909045i	$0.363187\pi$
$264$	−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	−0.569798	−	0.821785i	$-0.692979\pi$
$277$	−659.307	+	380.651i	−0.143011	+	0.0825672i	0.426787	+	0.904352i	$0.359645\pi$
$278$			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	0.727049	−	0.686586i	$-0.240891\pi$
$283$	2361.22	+	1363.25i	0.495972	+	0.286350i	−0.231076	+	0.972936i	$0.574225\pi$
$284$	−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	0.508298	−	0.861181i	$-0.330275\pi$
$293$	83.4622	+	48.1869i	0.0166414	+	0.00960789i	−0.491656	+	0.870789i	$0.663608\pi$
$294$	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	$-0.837454\pi$
$307$		−	5258.02i		−	0.977495i	0.872425	−	0.488747i	$-0.162546\pi$
$308$	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	−0.778588	−	0.627536i	$-0.784064\pi$
$313$	−3457.74	+	1996.33i	−0.624419	+	0.360509i	0.154168	+	0.988045i	$0.450730\pi$
$314$	−194.003			−0.0348670
$315$		0			0
$316$	5300.63			0.943619
$317$	4099.40	−	2366.79i	0.726325	−	0.419344i	−0.0907509	−	0.995874i	$-0.528927\pi$
$317$	4099.40	−	2366.79i	0.726325	−	0.419344i	0.817076	+	0.576529i	$0.195593\pi$
$318$	−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	0.830287	−	0.557337i	$-0.188177\pi$
$337$	4718.83	+	2724.41i	0.762762	+	0.440381i	−0.0675246	+	0.997718i	$0.521510\pi$
$338$	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	0.215641	−	0.976473i	$-0.430816\pi$
$347$	−3375.38	−	1948.77i	−0.522189	−	0.301486i	−0.737830	+	0.674987i	$0.764149\pi$
$348$	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	−0.477448	−	0.878660i	$-0.658438\pi$
$353$	296.931	−	171.433i	0.0447706	−	0.0258483i	0.522218	+	0.852812i	$0.325105\pi$
$354$	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	−0.146281	−	0.989243i	$-0.546730\pi$
$367$	4480.58	−	2586.87i	0.637288	−	0.367938i	0.783569	+	0.621305i	$0.213397\pi$
$368$			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	0.368362	−	0.929682i	$-0.379919\pi$
$373$	−1819.58	−	1050.53i	−0.252585	−	0.145830i	−0.620947	+	0.783852i	$0.713252\pi$
$374$	−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	0.0531478	−	0.998587i	$-0.483075\pi$
$383$	−5884.53	−	3397.44i	−0.785080	−	0.453266i	−0.838227	+	0.545321i	$0.816408\pi$
$384$	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	$-0.939039\pi$
$397$		−	3011.36i		−	0.380694i	0.981717	−	0.190347i	$-0.0609614\pi$
$398$	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	$-0.716477\pi$
$433$		−	14011.1i		−	1.55504i	0.628858	−	0.777520i	$-0.283523\pi$
$434$	−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	−0.261631	−	0.965168i	$-0.584260\pi$
$443$	4134.42	−	2387.01i	0.443413	−	0.256005i	0.705044	+	0.709163i	$0.250927\pi$
$444$	−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	0.231263	−	0.972891i	$-0.425714\pi$
$457$	11620.3	−	6708.99i	1.18944	−	0.686725i	0.958180	+	0.286166i	$0.0923810\pi$
$458$			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	0.186929	−	0.982373i	$-0.440147\pi$
$463$	−5682.32	−	3280.69i	−0.570367	−	0.329302i	−0.757296	+	0.653072i	$0.773480\pi$
$464$	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	$0.109251\pi$
$467$			6792.37i			0.673048i	−0.941675	+	0.336524i	$0.890749\pi$
$468$	−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	$0.0795833\pi$
$487$			5318.16i			0.494844i	−0.968908	+	0.247422i	$0.920417\pi$
$488$	−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	$-0.814844\pi$
$503$		−	12396.4i		−	1.09886i	0.835538	−	0.549432i	$-0.185156\pi$
$504$	−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	$-0.960944\pi$
$523$		−	2927.73i		−	0.244781i	0.992482	−	0.122391i	$-0.0390561\pi$
$524$	−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	−0.607692	−	0.794172i	$-0.707905\pi$
$547$	−2862.68	+	1652.77i	−0.223765	+	0.129191i	0.383927	+	0.923363i	$0.374571\pi$
$548$			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	$-0.920819\pi$
$557$		−	6472.87i		−	0.492396i	0.969220	−	0.246198i	$-0.0791813\pi$
$558$	−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	0.985694	−	0.168547i	$-0.0539074\pi$
$563$	17801.4	+	10277.6i	1.33257	+	0.769362i	0.346881	+	0.937909i	$0.387241\pi$
$564$	−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	$0.0907939\pi$
$577$			7800.01i			0.562770i	−0.959595	+	0.281385i	$0.909206\pi$
$578$	−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	−0.426126	−	0.904664i	$-0.640122\pi$
$587$	2051.83	−	1184.62i	0.144273	−	0.0832958i	0.570399	+	0.821368i	$0.306789\pi$
$588$	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	$0.136082\pi$
$593$			11974.3i			0.829218i	−0.910000	+	0.414609i	$0.863918\pi$
$594$	−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	−0.0123257	−	0.999924i	$-0.503923\pi$
$607$	−13226.8	−	7636.51i	−0.884448	−	0.510636i	−0.872122	+	0.489288i	$0.837257\pi$
$608$	−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	$-0.817808\pi$
$613$		−	16440.8i		−	1.08326i	0.840617	−	0.541630i	$-0.182192\pi$
$614$	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	0.740551	−	0.672000i	$-0.234565\pi$
$617$	8105.25	+	4679.57i	0.528857	+	0.305336i	−0.211694	+	0.977336i	$0.567898\pi$
$618$	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	0.310581	−	0.950547i	$-0.399476\pi$
$643$	−5826.13	−	3363.72i	−0.357325	−	0.206302i	−0.667907	+	0.744245i	$0.732810\pi$
$644$	−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	$-0.934506\pi$
$647$		−	6724.69i		−	0.408616i	0.978907	−	0.204308i	$-0.0654945\pi$
$648$	−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	$0.0407572\pi$
$653$	26670.4	+	15398.2i	1.59831	+	0.922782i	0.606492	+	0.795089i	$0.292576\pi$
$654$	−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	−0.511380	−	0.859355i	$-0.670865\pi$
$673$	−398.881	+	230.294i	−0.0228465	+	0.0131905i	0.488533	+	0.872545i	$0.337532\pi$
$674$	−8555.80			−0.488957
$675$		0			0
$676$	10057.3			0.572217
$677$	−25166.4	+	14529.8i	−1.42869	+	0.824854i	−0.997017	−	0.0771775i	$-0.975409\pi$
$677$	−25166.4	+	14529.8i	−1.42869	+	0.824854i	−0.431671	+	0.902031i	$0.642076\pi$
$678$	−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	$0.131838\pi$
$683$			14366.9i			0.804881i	−0.915446	+	0.402440i	$0.868162\pi$
$684$	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	−0.978533	−	0.206090i	$-0.933926\pi$
$727$	−25273.3	+	14591.6i	−1.28932	+	0.744389i	−0.310787	+	0.950480i	$0.600593\pi$
$728$			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	0.201488	−	0.979491i	$-0.435422\pi$
$733$	−10836.1	−	6256.24i	−0.546032	−	0.315252i	−0.747520	+	0.664239i	$0.768756\pi$
$734$	−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	0.0495691	−	0.998771i	$-0.484215\pi$
$743$	−16011.9	−	9244.50i	−0.790607	−	0.456457i	−0.840176	+	0.542313i	$0.817549\pi$
$744$	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	$-0.921896\pi$
$757$		−	10118.9i		−	0.485834i	0.970047	−	0.242917i	$-0.0781043\pi$
$758$	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	$-0.691902\pi$
$773$		−	35405.6i		−	1.64741i	0.567015	−	0.823707i	$-0.308098\pi$
$774$	−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	0.241718	−	0.970347i	$-0.422289\pi$
$787$	−10548.2	−	6090.02i	−0.477769	−	0.275840i	−0.719486	+	0.694507i	$0.755623\pi$
$788$	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	0.543480	−	0.839422i	$-0.317106\pi$
$797$	1985.86	+	1146.54i	0.0882596	+	0.0509567i	−0.455221	+	0.890379i	$0.650440\pi$
$798$	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	0.517254	−	0.855832i	$-0.326954\pi$
$823$	819.484	+	473.129i	0.0347089	+	0.0200392i	−0.482545	+	0.875871i	$0.660288\pi$
$824$	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	$-0.736348\pi$
$827$		−	35044.7i		−	1.47355i	0.676139	−	0.736774i	$-0.263652\pi$
$828$	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	−0.296867	−	0.954919i	$-0.595942\pi$
$853$	9508.84	−	5489.93i	0.381684	−	0.220365i	0.678551	+	0.734554i	$0.262608\pi$
$854$	−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	$0.684831\pi$
$857$	−38810.4	+	22407.2i	−1.54695	+	0.893133i	−0.998372	+	0.0570348i	$0.981835\pi$
$858$	−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	$-0.794275\pi$
$863$		−	30536.3i		−	1.20448i	0.798314	−	0.602241i	$-0.205725\pi$
$864$	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	0.947578	−	0.319525i	$-0.103523\pi$
$877$	29728.4	+	17163.7i	1.14465	+	0.660864i	0.197072	+	0.980389i	$0.436857\pi$
$878$	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	$-0.813086\pi$
$883$		−	29074.4i		−	1.10808i	0.832491	−	0.554039i	$-0.186914\pi$
$884$	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	−0.148109	−	0.988971i	$-0.547319\pi$
$887$	−28494.5	−	16451.3i	−1.07864	−	0.622752i	−0.930528	+	0.366220i	$0.880652\pi$
$888$	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	−0.487012	−	0.873395i	$-0.661913\pi$
$907$	706.517	−	407.908i	0.0258649	−	0.0149331i	0.512877	+	0.858462i	$0.328580\pi$
$908$		−	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	$-0.942788\pi$
$937$		−	10255.0i		−	0.357540i	0.983891	−	0.178770i	$-0.0572118\pi$
$938$	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	0.147250	−	0.989099i	$-0.452958\pi$
$947$	31399.7	−	18128.6i	1.07746	−	0.622072i	0.930210	+	0.367028i	$0.119625\pi$
$948$	−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	$-0.707834\pi$
$953$		−	46736.7i		−	1.58861i	0.607516	−	0.794307i	$-0.292166\pi$
$954$	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	0.976384	−	0.216043i	$-0.0693150\pi$
$967$	38414.3	+	22178.5i	1.27748	+	0.737552i	0.301094	+	0.953595i	$0.402648\pi$
$968$	−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	0.999254	−	0.0386096i	$-0.0122929\pi$
$977$	44751.9	+	25837.5i	1.46544	+	0.846075i	0.466190	+	0.884684i	$0.345626\pi$
$978$	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	−0.131736	−	0.991285i	$-0.542055\pi$
$983$	20368.0	−	11759.5i	0.660874	−	0.381556i	0.792610	+	0.609729i	$0.208722\pi$
$984$	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	0.0530293	−	0.998593i	$-0.483112\pi$
$997$	29728.7	−	17163.9i	0.944351	−	0.545221i	0.891322	+	0.453372i	$0.149779\pi$
$998$			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.49.6		28
5.2	odd	4		45.4.e.c.31.3	yes	14
5.3	odd	4		225.4.e.d.76.5		14
5.4	even	2	inner	225.4.k.d.49.9		28
9.7	even	3	inner	225.4.k.d.124.9		28
15.2	even	4		135.4.e.c.91.5		14
45.2	even	12		135.4.e.c.46.5		14
45.7	odd	12		45.4.e.c.16.3	✓	14
45.13	odd	12		2025.4.a.bb.1.3		7
45.22	odd	12		405.4.a.m.1.5		7
45.23	even	12		2025.4.a.ba.1.5		7
45.32	even	12		405.4.a.n.1.3		7
45.34	even	6	inner	225.4.k.d.124.6		28
45.43	odd	12		225.4.e.d.151.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.3	✓	14	45.7	odd	12
45.4.e.c.31.3	yes	14	5.2	odd	4
135.4.e.c.46.5		14	45.2	even	12
135.4.e.c.91.5		14	15.2	even	4
225.4.e.d.76.5		14	5.3	odd	4
225.4.e.d.151.5		14	45.43	odd	12
225.4.k.d.49.6		28	1.1	even	1	trivial
225.4.k.d.49.9		28	5.4	even	2	inner
225.4.k.d.124.6		28	45.34	even	6	inner
225.4.k.d.124.9		28	9.7	even	3	inner
405.4.a.m.1.5		7	45.22	odd	12
405.4.a.n.1.3		7	45.32	even	12
2025.4.a.ba.1.5		7	45.23	even	12
2025.4.a.bb.1.3		7	45.13	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.35984 + 0.785104i) q^{2} +(-3.43441 - 3.89934i) q^{3} +(-2.76722 + 4.79297i) q^{4} +(7.73164 + 2.60611i) q^{6} +(-29.6525 + 17.1199i) q^{7} -21.2519i q^{8} +(-3.40971 + 26.7838i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) \) 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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