LMFDB - Embedded newform 225.4.k.e.49.19

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 = [48,0,0,96] 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.19
Character	$\chi$	$=$	225.49
Dual form			225.4.k.e.124.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.15215 - 1.81989i) q^{2} +(-0.391700 + 5.18137i) q^{3} +(2.62402 - 4.54493i) q^{4} +(8.19483 + 17.0453i) q^{6} +(3.22208 - 1.86027i) q^{7} +10.0166i q^{8} +(-26.6931 - 4.05909i) q^{9} +(14.0066 + 24.2602i) q^{11} +(22.5211 + 15.3762i) q^{12} +(37.7951 + 21.8210i) q^{13} +(6.77099 - 11.7277i) q^{14} +(39.2212 + 67.9331i) q^{16} +87.3128i q^{17} +(-91.5278 + 35.7838i) q^{18} -38.5062 q^{19} +(8.37666 + 17.4235i) q^{21} +(88.3019 + 50.9811i) q^{22} +(-100.413 - 57.9733i) q^{23} +(-51.8995 - 3.92349i) q^{24} +158.848 q^{26} +(31.4873 - 136.717i) q^{27} -19.5255i q^{28} +(98.0246 + 169.784i) q^{29} +(-86.7675 + 150.286i) q^{31} +(177.865 + 102.690i) q^{32} +(-131.187 + 63.0708i) q^{33} +(158.900 + 275.223i) q^{34} +(-88.4915 + 110.667i) q^{36} -181.738i q^{37} +(-121.377 + 70.0772i) q^{38} +(-127.867 + 187.283i) q^{39} +(124.893 - 216.320i) q^{41} +(58.1133 + 39.6767i) q^{42} +(398.985 - 230.354i) q^{43} +147.015 q^{44} -422.021 q^{46} +(284.395 - 164.196i) q^{47} +(-367.349 + 176.610i) q^{48} +(-164.579 + 285.059i) q^{49} +(-452.400 - 34.2005i) q^{51} +(198.350 - 114.517i) q^{52} -667.821i q^{53} +(-149.558 - 488.256i) q^{54} +(18.6335 + 32.2742i) q^{56} +(15.0829 - 199.515i) q^{57} +(617.976 + 356.788i) q^{58} +(55.5587 - 96.2305i) q^{59} +(-218.973 - 379.272i) q^{61} +631.630i q^{62} +(-93.5586 + 36.5778i) q^{63} +120.003 q^{64} +(-298.740 + 437.555i) q^{66} +(-134.100 - 77.4225i) q^{67} +(396.831 + 229.110i) q^{68} +(339.713 - 497.567i) q^{69} +912.989 q^{71} +(40.6581 - 267.374i) q^{72} -975.779i q^{73} +(-330.743 - 572.863i) q^{74} +(-101.041 + 175.008i) q^{76} +(90.2611 + 52.1123i) q^{77} +(-62.2207 + 823.048i) q^{78} +(428.020 + 741.352i) q^{79} +(696.048 + 216.700i) q^{81} -909.164i q^{82} +(-59.2542 + 34.2104i) q^{83} +(101.169 + 7.64816i) q^{84} +(838.439 - 1452.22i) q^{86} +(-918.107 + 441.397i) q^{87} +(-243.004 + 140.298i) q^{88} -665.452 q^{89} +162.372 q^{91} +(-526.970 + 304.246i) q^{92} +(-744.699 - 508.441i) q^{93} +(597.637 - 1035.14i) q^{94} +(-601.747 + 881.361i) q^{96} +(-1215.62 + 701.837i) q^{97} +1198.06i q^{98} +(-275.407 - 704.435i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 26 q^{6} + 122 q^{9} - 58 q^{11} - 138 q^{14} - 384 q^{16} + 300 q^{19} - 120 q^{21} - 684 q^{24} - 616 q^{26} + 212 q^{29} - 120 q^{31} - 216 q^{34} + 2606 q^{36} + 820 q^{39} + 706 q^{41}+ \cdots + 3394 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 - 26 * q^6 + 122 * q^9 - 58 * q^11 - 138 * q^14 - 384 * q^16 + 300 * q^19 - 120 * q^21 - 684 * q^24 - 616 * q^26 + 212 * q^29 - 120 * q^31 - 216 * q^34 + 2606 * q^36 + 820 * q^39 + 706 * q^41 - 2284 * q^44 + 1080 * q^46 + 1332 * q^49 - 2738 * q^51 + 4256 * q^54 + 1140 * q^56 + 964 * q^59 - 804 * q^61 - 3900 * q^64 + 4082 * q^66 - 5712 * q^69 - 3776 * q^71 + 20 * q^74 + 924 * q^76 + 516 * q^79 + 6142 * q^81 + 5406 * q^84 - 3904 * q^86 + 2952 * q^89 - 2472 * q^91 + 126 * q^94 - 20848 * q^96 + 3394 * 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 $

$2$	3.15215	−	1.81989i	1.11445	−	0.643429i	0.174473	−	0.984662i	$-0.444178\pi$
$2$	3.15215	−	1.81989i	1.11445	−	0.643429i	0.939979	+	0.341233i	$0.110844\pi$
$3$	−0.391700	+	5.18137i	−0.0753828	+	0.997155i
$3$	−0.391700	+	5.18137i	−0.0753828	+	0.997155i
$4$	2.62402	−	4.54493i	0.328002	−	0.568116i
$5$		0			0
$5$		0			0
$6$	8.19483	+	17.0453i	0.557588	+	1.15978i
$7$	3.22208	−	1.86027i	0.173976	−	0.100445i	−0.410483	−	0.911868i	$-0.634640\pi$
$7$	3.22208	−	1.86027i	0.173976	−	0.100445i	0.584459	+	0.811423i	$0.301307\pi$
$8$			10.0166i			0.442674i
$9$	−26.6931	−	4.05909i	−0.988635	−	0.150337i
$10$		0			0
$11$	14.0066	+	24.2602i	0.383923	+	0.664975i	0.991619	−	0.129195i	$-0.0412393\pi$
$11$	14.0066	+	24.2602i	0.383923	+	0.664975i	−0.607696	+	0.794170i	$0.707906\pi$
$12$	22.5211	+	15.3762i	0.541774	+	0.369895i
$13$	37.7951	+	21.8210i	0.806344	+	0.465543i	0.845685	−	0.533683i	$-0.179192\pi$
$13$	37.7951	+	21.8210i	0.806344	+	0.465543i	−0.0393404	+	0.999226i	$0.512526\pi$
$14$	6.77099	−	11.7277i	0.129259	−	0.223883i
$15$		0			0
$16$	39.2212	+	67.9331i	0.612831	+	1.06146i
$17$			87.3128i			1.24567i	0.782351	+	0.622837i	$0.214020\pi$
$17$			87.3128i			1.24567i	−0.782351	+	0.622837i	$0.785980\pi$
$18$	−91.5278	+	35.7838i	−1.19852	+	0.468574i
$19$	−38.5062			−0.464944			−0.232472	−	0.972603i	$-0.574681\pi$
$19$	−38.5062			−0.464944			−0.232472	+	0.972603i	$0.574681\pi$
$20$		0			0
$21$	8.37666	+	17.4235i	0.0870446	+	0.181053i
$22$	88.3019	+	50.9811i	0.855728	+	0.494055i
$23$	−100.413	−	57.9733i	−0.910327	−	0.525577i	−0.0297904	−	0.999556i	$-0.509484\pi$
$23$	−100.413	−	57.9733i	−0.910327	−	0.525577i	−0.880536	+	0.473979i	$0.842817\pi$
$24$	−51.8995	−	3.92349i	−0.441414	−	0.0333700i
$25$		0			0
$26$	158.848			1.19818
$27$	31.4873	−	136.717i	0.224435	−	0.974489i
$28$		−	19.5255i		−	0.131785i
$29$	98.0246	+	169.784i	0.627679	+	1.08717i	0.988016	+	0.154350i	$0.0493285\pi$
$29$	98.0246	+	169.784i	0.627679	+	1.08717i	−0.360337	+	0.932822i	$0.617338\pi$
$30$		0			0
$31$	−86.7675	+	150.286i	−0.502707	+	0.870713i	0.497289	+	0.867585i	$0.334329\pi$
$31$	−86.7675	+	150.286i	−0.502707	+	0.870713i	−0.999995	+	0.00312811i	$0.999004\pi$
$32$	177.865	+	102.690i	0.982575	+	0.567290i
$33$	−131.187	+	63.0708i	−0.692024	+	0.332703i
$34$	158.900	+	275.223i	0.801503	+	1.38824i
$35$		0			0
$36$	−88.4915	+	110.667i	−0.409683	+	0.512349i
$37$		−	181.738i		−	0.807499i	−0.914870	−	0.403749i	$-0.867707\pi$
$37$		−	181.738i		−	0.807499i	0.914870	−	0.403749i	$-0.132293\pi$
$38$	−121.377	+	70.0772i	−0.518158	+	0.299159i
$39$	−127.867	+	187.283i	−0.525003	+	0.768956i
$40$		0			0
$41$	124.893	−	216.320i	0.475730	−	0.823989i	−0.523883	−	0.851790i	$-0.675517\pi$
$41$	124.893	−	216.320i	0.475730	−	0.823989i	0.999613	+	0.0278012i	$0.00885054\pi$
$42$	58.1133	+	39.6767i	0.213502	+	0.145768i
$43$	398.985	−	230.354i	1.41499	−	0.816945i	0.419138	−	0.907923i	$-0.362332\pi$
$43$	398.985	−	230.354i	1.41499	−	0.816945i	0.995853	+	0.0909774i	$0.0289991\pi$
$44$	147.015			0.503711
$45$		0			0
$46$	−422.021			−1.35269
$47$	284.395	−	164.196i	0.882624	−	0.509583i	0.0111016	−	0.999938i	$-0.496466\pi$
$47$	284.395	−	164.196i	0.882624	−	0.509583i	0.871523	+	0.490355i	$0.163133\pi$
$48$	−367.349	+	176.610i	−1.10463	+	0.531072i
$49$	−164.579	+	285.059i	−0.479822	+	0.831075i
$50$		0			0
$51$	−452.400	−	34.2005i	−1.24213	−	0.0939024i
$52$	198.350	−	114.517i	0.528965	−	0.305398i
$53$		−	667.821i		−	1.73080i	−0.501083	−	0.865399i	$-0.667065\pi$
$53$		−	667.821i		−	1.73080i	0.501083	−	0.865399i	$-0.332935\pi$
$54$	−149.558	−	488.256i	−0.376893	−	1.23043i
$55$		0			0
$56$	18.6335	+	32.2742i	0.0444645	+	0.0770147i
$57$	15.0829	−	199.515i	0.0350488	−	0.463621i
$58$	617.976	+	356.788i	1.39904	+	0.807735i
$59$	55.5587	−	96.2305i	0.122595	−	0.212341i	−0.798195	−	0.602399i	$-0.794212\pi$
$59$	55.5587	−	96.2305i	0.122595	−	0.212341i	0.920790	+	0.390058i	$0.127545\pi$
$60$		0			0
$61$	−218.973	−	379.272i	−0.459617	−	0.796080i	0.539324	−	0.842098i	$-0.318680\pi$
$61$	−218.973	−	379.272i	−0.459617	−	0.796080i	−0.998941	+	0.0460189i	$0.985347\pi$
$62$			631.630i			1.29382i
$63$	−93.5586	+	36.5778i	−0.187100	+	0.0731487i
$64$	120.003			0.234381
$65$		0			0
$66$	−298.740	+	437.555i	−0.557156	+	0.816050i
$67$	−134.100	−	77.4225i	−0.244521	−	0.141174i	0.372732	−	0.927939i	$-0.378421\pi$
$67$	−134.100	−	77.4225i	−0.244521	−	0.141174i	−0.617253	+	0.786765i	$0.711754\pi$
$68$	396.831	+	229.110i	0.707688	+	0.408584i
$69$	339.713	−	497.567i	0.592705	−	0.868117i
$70$		0			0
$71$	912.989			1.52608			0.763041	−	0.646350i	$-0.223705\pi$
$71$	912.989			1.52608			0.763041	+	0.646350i	$0.223705\pi$
$72$	40.6581	−	267.374i	0.0665501	−	0.437643i
$73$		−	975.779i		−	1.56447i	−0.622984	−	0.782234i	$-0.714080\pi$
$73$		−	975.779i		−	1.56447i	0.622984	−	0.782234i	$-0.285920\pi$
$74$	−330.743	−	572.863i	−0.519568	−	0.899919i
$75$		0			0
$76$	−101.041	+	175.008i	−0.152503	+	0.264142i
$77$	90.2611	+	52.1123i	0.133587	+	0.0771265i
$78$	−62.2207	+	823.048i	−0.0903218	+	1.19477i
$79$	428.020	+	741.352i	0.609570	+	1.05581i	0.991311	+	0.131536i	$0.0419910\pi$
$79$	428.020	+	741.352i	0.609570	+	1.05581i	−0.381742	+	0.924269i	$0.624676\pi$
$80$		0			0
$81$	696.048	+	216.700i	0.954798	+	0.297256i
$82$		−	909.164i		−	1.22439i
$83$	−59.2542	+	34.2104i	−0.0783614	+	0.0452420i	−0.538669	−	0.842518i	$-0.681073\pi$
$83$	−59.2542	+	34.2104i	−0.0783614	+	0.0452420i	0.460307	+	0.887760i	$0.347739\pi$
$84$	101.169	+	7.64816i	0.131410	+	0.00993431i
$85$		0			0
$86$	838.439	−	1452.22i	1.05129	−	1.82089i
$87$	−918.107	+	441.397i	−1.13140	+	0.543939i
$88$	−243.004	+	140.298i	−0.294367	+	0.169953i
$89$	−665.452			−0.792559			−0.396280	−	0.918130i	$-0.629699\pi$
$89$	−665.452			−0.792559			−0.396280	+	0.918130i	$0.629699\pi$
$90$		0			0
$91$	162.372			0.187046
$92$	−526.970	+	304.246i	−0.597178	+	0.344781i
$93$	−744.699	−	508.441i	−0.830340	−	0.566913i
$94$	597.637	−	1035.14i	0.655762	−	1.13581i
$95$		0			0
$96$	−601.747	+	881.361i	−0.639745	+	0.937016i
$97$	−1215.62	+	701.837i	−1.27245	+	0.734646i	−0.975448	−	0.220232i	$-0.929319\pi$
$97$	−1215.62	+	701.837i	−1.27245	+	0.734646i	−0.296997	+	0.954878i	$0.595985\pi$
$98$			1198.06i			1.23492i
$99$	−275.407	−	704.435i	−0.279590	−	0.715135i
$100$		0			0
$101$	327.589	+	567.401i	0.322736	+	0.558995i	0.981051	−	0.193747i	$-0.0620641\pi$
$101$	327.589	+	567.401i	0.322736	+	0.558995i	−0.658316	+	0.752742i	$0.728731\pi$
$102$	−1488.27	+	715.514i	−1.44471	+	0.694573i
$103$	219.557	+	126.762i	0.210035	+	0.121264i	0.601328	−	0.799002i	$-0.294639\pi$
$103$	219.557	+	126.762i	0.210035	+	0.121264i	−0.391293	+	0.920266i	$0.627972\pi$
$104$	−218.572	+	378.577i	−0.206084	+	0.356948i
$105$		0			0
$106$	−1215.36	−	2105.07i	−1.11365	−	1.92889i
$107$			1132.73i			1.02341i	0.859161	+	0.511706i	$0.170986\pi$
$107$			1132.73i			1.02341i	−0.859161	+	0.511706i	$0.829014\pi$
$108$	−538.746	−	501.856i	−0.480008	−	0.447140i
$109$	−1514.68			−1.33101			−0.665506	−	0.746392i	$-0.731784\pi$
$109$	−1514.68			−1.33101			−0.665506	+	0.746392i	$0.731784\pi$
$110$		0			0
$111$	941.649	+	71.1866i	0.805201	+	0.0608715i
$112$	252.748	+	145.924i	0.213236	+	0.123112i
$113$	1448.02	+	836.016i	1.20547	+	0.695980i	0.961767	−	0.273869i	$-0.0883034\pi$
$113$	1448.02	+	836.016i	1.20547	+	0.695980i	0.243706	+	0.969849i	$0.421637\pi$
$114$	−315.552	−	656.350i	−0.259247	−	0.539235i
$115$		0			0
$116$	1028.87			0.823521
$117$	−920.297	−	735.885i	−0.727192	−	0.581475i
$118$		−	404.443i		−	0.315526i
$119$	162.426	+	281.329i	0.125122	+	0.216718i
$120$		0			0
$121$	273.129	−	473.073i	0.205206	−	0.355427i
$122$	−1380.47	−	797.015i	−1.02444	−	0.591462i
$123$	1071.91	+	731.847i	0.785782	+	0.536491i
$124$	455.359	+	788.705i	0.329778	+	0.571192i
$125$		0			0
$126$	−228.343	+	285.565i	−0.161447	+	0.201906i
$127$		−	547.016i		−	0.382203i	−0.981570	−	0.191102i	$-0.938794\pi$
$127$		−	547.016i		−	0.382203i	0.981570	−	0.191102i	$-0.0612060\pi$
$128$	−1044.65	+	603.131i	−0.721369	+	0.416482i
$129$	1037.27	+	2157.52i	0.707955	+	1.47255i
$130$		0			0
$131$	−633.985	+	1098.09i	−0.422836	+	0.732374i	−0.996216	−	0.0869161i	$-0.972299\pi$
$131$	−633.985	+	1098.09i	−0.422836	+	0.732374i	0.573379	+	0.819290i	$0.305632\pi$
$132$	−57.5856	+	761.736i	−0.0379711	+	0.502277i
$133$	−124.070	+	71.6321i	−0.0808892	+	0.0467014i
$134$	−563.602			−0.363342
$135$		0			0
$136$	−874.575			−0.551428
$137$	805.788	−	465.222i	0.502504	−	0.290121i	−0.227243	−	0.973838i	$-0.572971\pi$
$137$	805.788	−	465.222i	0.502504	−	0.290121i	0.729747	+	0.683717i	$0.239638\pi$
$138$	165.306	−	2186.65i	0.101969	−	1.34884i
$139$	1565.13	−	2710.89i	0.955057	−	1.65421i	0.220818	−	0.975315i	$-0.429127\pi$
$139$	1565.13	−	2710.89i	0.955057	−	1.65421i	0.734238	−	0.678892i	$-0.237539\pi$
$140$		0			0
$141$	739.361	+	1537.87i	0.441599	+	0.918527i
$142$	2877.87	−	1661.54i	1.70075	−	0.981926i
$143$			1222.56i			0.714932i
$144$	−771.191	−	1972.55i	−0.446291	−	1.14152i
$145$		0			0
$146$	−1775.81	−	3075.80i	−1.00662	−	1.74353i
$147$	−1412.53	−	964.401i	−0.792540	−	0.541105i
$148$	−825.984	−	476.882i	−0.458753	−	0.264861i
$149$	−815.678	+	1412.80i	−0.448476	+	0.776784i	−0.998287	−	0.0585055i	$-0.981366\pi$
$149$	−815.678	+	1412.80i	−0.448476	+	0.776784i	0.549811	+	0.835289i	$0.314700\pi$
$150$		0			0
$151$	−910.818	−	1577.58i	−0.490870	−	0.850211i	0.509075	−	0.860722i	$-0.329988\pi$
$151$	−910.818	−	1577.58i	−0.490870	−	0.850211i	−0.999945	+	0.0105108i	$0.996654\pi$
$152$		−	385.700i		−	0.205819i
$153$	354.410	−	2330.65i	0.187270	−	1.23152i
$154$	379.355			0.198502
$155$		0			0
$156$	515.663	+	1072.58i	0.264654	+	0.550482i
$157$	2455.34	+	1417.59i	1.24814	+	0.720612i	0.970738	−	0.240142i	$-0.0771941\pi$
$157$	2455.34	+	1417.59i	1.24814	+	0.720612i	0.277400	+	0.960755i	$0.410527\pi$
$158$	2698.36	+	1557.90i	1.35867	+	0.784430i
$159$	3460.23	+	261.586i	1.72587	+	0.130472i
$160$		0			0
$161$	−431.385			−0.211167
$162$	2588.41	−	583.663i	1.25534	−	0.283067i
$163$		−	3048.62i		−	1.46495i	−0.680796	−	0.732473i	$-0.738366\pi$
$163$		−	3048.62i		−	1.46495i	0.680796	−	0.732473i	$-0.261634\pi$
$164$	−655.440	−	1135.26i	−0.312081	−	0.540540i
$165$		0			0
$166$	−124.519	+	215.673i	−0.0582200	+	0.100840i
$167$	2457.71	+	1418.96i	1.13882	+	0.657500i	0.946139	−	0.323761i	$-0.104947\pi$
$167$	2457.71	+	1418.96i	1.13882	+	0.657500i	0.192685	+	0.981261i	$0.438281\pi$
$168$	−174.523	+	83.9053i	−0.0801474	+	0.0385324i
$169$	−146.186	−	253.202i	−0.0665391	−	0.115249i
$170$		0			0
$171$	1027.85	+	156.300i	0.459660	+	0.0698981i
$172$		−	2417.81i		−	1.07184i
$173$	−442.135	+	255.267i	−0.194306	+	0.112183i	−0.593997	−	0.804467i	$-0.702451\pi$
$173$	−442.135	+	255.267i	−0.194306	+	0.112183i	0.399691	+	0.916650i	$0.369117\pi$
$174$	−2090.71	+	3062.20i	−0.910900	+	1.33417i
$175$		0			0
$176$	−1098.71	+	1903.03i	−0.470561	+	0.815035i
$177$	476.843	+	325.563i	0.202496	+	0.138253i
$178$	−2097.60	+	1211.05i	−0.883269	+	0.509956i
$179$	2274.36			0.949687			0.474843	−	0.880070i	$-0.342505\pi$
$179$	2274.36			0.949687			0.474843	+	0.880070i	$0.342505\pi$
$180$		0			0
$181$	−975.489			−0.400594			−0.200297	−	0.979735i	$-0.564191\pi$
$181$	−975.489			−0.400594			−0.200297	+	0.979735i	$0.564191\pi$
$182$	511.820	−	295.500i	0.208454	−	0.120351i
$183$	2050.92	−	986.019i	0.828462	−	0.398298i
$184$	580.694	−	1005.79i	0.232659	−	0.402978i
$185$		0			0
$186$	−3272.71	−	247.410i	−1.29014	−	0.0975321i
$187$	−2118.23	+	1222.96i	−0.828342	+	0.478244i
$188$		−	1723.41i		−	0.668578i
$189$	−152.876	−	499.089i	−0.0588364	−	0.192081i
$190$		0			0
$191$	940.013	+	1628.15i	0.356110	+	0.616800i	0.987307	−	0.158822i	$-0.0507696\pi$
$191$	940.013	+	1628.15i	0.356110	+	0.616800i	−0.631198	+	0.775622i	$0.717436\pi$
$192$	−47.0053	+	621.781i	−0.0176683	+	0.233714i
$193$	−531.360	−	306.781i	−0.198177	−	0.114418i	0.397628	−	0.917547i	$-0.369834\pi$
$193$	−531.360	−	306.781i	−0.198177	−	0.114418i	−0.595805	+	0.803129i	$0.703167\pi$
$194$	−2554.53	+	4424.58i	−0.945386	+	1.63746i
$195$		0			0
$196$	863.715	+	1496.00i	0.314765	+	0.545189i
$197$		−	68.3454i		−	0.0247178i	−0.999924	−	0.0123589i	$-0.996066\pi$
$197$		−	68.3454i		−	0.0247178i	0.999924	−	0.0123589i	$-0.00393406\pi$
$198$	−2150.12	−	1719.27i	−0.771728	−	0.617087i
$199$	−2174.87			−0.774736			−0.387368	−	0.921925i	$-0.626616\pi$
$199$	−2174.87			−0.774736			−0.387368	+	0.921925i	$0.626616\pi$
$200$		0			0
$201$	453.681	−	664.493i	0.159205	−	0.233183i
$202$	2065.22	+	1192.35i	0.719347	+	0.415315i
$203$	631.687	+	364.705i	0.218403	+	0.126095i
$204$	−1342.54	+	1966.38i	−0.460769	+	0.674874i
$205$		0			0
$206$	922.769			0.312099
$207$	2445.01	+	1955.08i	0.820967	+	0.656459i
$208$			3423.39i			1.14120i
$209$	−539.343	−	934.169i	−0.178503	−	0.309176i
$210$		0			0
$211$	237.521	−	411.398i	0.0774957	−	0.134227i	−0.824673	−	0.565610i	$-0.808641\pi$
$211$	237.521	−	411.398i	0.0774957	−	0.134227i	0.902169	+	0.431383i	$0.141974\pi$
$212$	−3035.20	−	1752.37i	−0.983295	−	0.567705i
$213$	−357.618	+	4730.53i	−0.115040	+	1.52174i
$214$	2061.44	+	3570.53i	0.658493	+	1.14054i
$215$		0			0
$216$	1369.44	+	315.395i	0.431381	+	0.0993514i
$217$			645.644i			0.201978i
$218$	−4774.50	+	2756.56i	−1.48335	+	0.856412i
$219$	5055.87	+	382.213i	1.56002	+	0.117934i
$220$		0			0
$221$	−1905.25	+	3300.00i	−0.579915	+	1.00444i
$222$	3097.77	−	1489.31i	0.936525	−	0.450252i
$223$	−2568.93	+	1483.17i	−0.771427	+	0.445384i	−0.833384	−	0.552695i	$-0.813599\pi$
$223$	−2568.93	+	1483.17i	−0.771427	+	0.445384i	0.0619561	+	0.998079i	$0.480266\pi$
$224$	764.129			0.227926
$225$		0			0
$226$	6085.84			1.79126
$227$	2452.78	−	1416.11i	0.717167	−	0.414056i	−0.0965423	−	0.995329i	$-0.530778\pi$
$227$	2452.78	−	1416.11i	0.717167	−	0.414056i	0.813709	+	0.581273i	$0.197445\pi$
$228$	−867.204	−	592.081i	−0.251895	−	0.171980i
$229$	−2146.22	+	3717.37i	−0.619330	+	1.07271i	0.370278	+	0.928921i	$0.379262\pi$
$229$	−2146.22	+	3717.37i	−0.619330	+	1.07271i	−0.989608	+	0.143790i	$0.954071\pi$
$230$		0			0
$231$	−305.368	+	447.263i	−0.0869772	+	0.127393i
$232$	−1700.65	+	981.870i	−0.481263	+	0.277857i
$233$		−	4267.52i		−	1.19989i	−0.800041	−	0.599945i	$-0.795189\pi$
$233$		−	4267.52i		−	1.19989i	0.800041	−	0.599945i	$-0.204811\pi$
$234$	−4240.14	−	644.776i	−1.18456	−	0.180130i
$235$		0			0
$236$	−291.574	−	505.021i	−0.0804231	−	0.139297i
$237$	−4008.87	+	1927.34i	−1.09875	+	0.528246i
$238$	1023.98	+	591.194i	0.278885	+	0.161014i
$239$	1292.52	−	2238.70i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$239$	1292.52	−	2238.70i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$240$		0			0
$241$	1952.49	+	3381.82i	0.521872	+	0.903909i	0.999676	+	0.0254427i	$0.00809954\pi$
$241$	1952.49	+	3381.82i	0.521872	+	0.903909i	−0.477804	+	0.878466i	$0.658567\pi$
$242$		−	1988.26i		−	0.528141i
$243$	−1395.44	+	3521.60i	−0.368385	+	0.929673i
$244$	−2298.36			−0.603021
$245$		0			0
$246$	4710.71	+	356.120i	1.22091	+	0.0922983i
$247$	−1455.35	−	840.245i	−0.374905	−	0.216452i
$248$	−1505.35	−	869.112i	−0.385442	−	0.222535i
$249$	−154.047	−	320.418i	−0.0392062	−	0.0815489i
$250$		0			0
$251$	1466.63			0.368815			0.184408	−	0.982850i	$-0.440963\pi$
$251$	1466.63			0.368815			0.184408	+	0.982850i	$0.440963\pi$
$252$	−79.2558	+	521.198i	−0.0198121	+	0.130287i
$253$		−	3248.04i		−	0.807126i
$254$	−995.510	−	1724.27i	−0.245921	−	0.425947i
$255$		0			0
$256$	−2675.28	+	4633.72i	−0.653144	+	1.13128i
$257$	3851.51	+	2223.67i	0.934828	+	0.539723i	0.888335	−	0.459195i	$-0.151862\pi$
$257$	3851.51	+	2223.67i	0.934828	+	0.539723i	0.0464928	+	0.998919i	$0.485196\pi$
$258$	7196.06	+	4913.09i	1.73646	+	1.18557i
$259$	−338.081	−	585.574i	−0.0811094	−	0.140486i
$260$		0			0
$261$	−1927.42	−	4929.95i	−0.457104	−	1.16918i
$262$			4615.14i			1.08826i
$263$	1520.00	−	877.572i	0.356377	−	0.205754i	−0.311113	−	0.950373i	$-0.600702\pi$
$263$	1520.00	−	877.572i	0.356377	−	0.205754i	0.667490	+	0.744618i	$0.267369\pi$
$264$	−631.752	−	1314.05i	−0.147279	−	0.306341i
$265$		0			0
$266$	−260.725	+	451.589i	−0.0600981	+	0.104093i
$267$	260.658	−	3447.95i	0.0597453	−	0.790304i
$268$	−703.760	+	406.316i	−0.160407	+	0.0926108i
$269$	3412.93			0.773569			0.386785	−	0.922170i	$-0.373586\pi$
$269$	3412.93			0.773569			0.386785	+	0.922170i	$0.373586\pi$
$270$		0			0
$271$	206.271			0.0462365			0.0231183	−	0.999733i	$-0.492641\pi$
$271$	206.271			0.0462365			0.0231183	+	0.999733i	$0.492641\pi$
$272$	−5931.43	+	3424.51i	−1.32223	+	0.763388i
$273$	−63.6012	+	841.309i	−0.0141001	+	0.186514i
$274$	1693.31	−	2932.89i	0.373345	−	0.646652i
$275$		0			0
$276$	−1370.00	−	2849.60i	−0.298783	−	0.621469i
$277$	−4593.09	+	2651.82i	−0.996289	+	0.575208i	−0.907148	−	0.420811i	$-0.861746\pi$
$277$	−4593.09	+	2651.82i	−0.996289	+	0.575208i	−0.0891411	+	0.996019i	$0.528412\pi$
$278$		−	11393.5i		−	2.45805i
$279$	2926.12	−	3659.40i	0.627893	−	0.785242i
$280$		0			0
$281$	−1424.58	−	2467.44i	−0.302431	−	0.523825i	0.674255	−	0.738498i	$-0.264465\pi$
$281$	−1424.58	−	2467.44i	−0.302431	−	0.523825i	−0.976686	+	0.214673i	$0.931131\pi$
$282$	5129.34	+	3502.04i	1.08315	+	0.739516i
$283$	6993.19	+	4037.52i	1.46891	+	0.848077i	0.999393	−	0.0348448i	$-0.0110937\pi$
$283$	6993.19	+	4037.52i	1.46891	+	0.848077i	0.469520	+	0.882922i	$0.344427\pi$
$284$	2395.70	−	4149.47i	0.500558	−	0.866992i
$285$		0			0
$286$	2224.92	+	3853.67i	0.460008	+	0.796757i
$287$		−	929.336i		−	0.191139i
$288$	−4330.95	−	3463.10i	−0.886124	−	0.708560i
$289$	−2710.53			−0.551705
$290$		0			0
$291$	−3160.32	−	6573.47i	−0.636636	−	1.32420i
$292$	−4434.85	−	2560.46i	−0.888800	−	0.513149i
$293$	−2271.46	−	1311.43i	−0.452900	−	0.261482i	0.256154	−	0.966636i	$-0.417545\pi$
$293$	−2271.46	−	1311.43i	−0.452900	−	0.261482i	−0.709054	+	0.705154i	$0.750878\pi$
$294$	−6207.60	−	469.282i	−1.23141	−	0.0930920i
$295$		0			0
$296$	1820.39			0.357459
$297$	3757.81	−	1151.06i	0.734176	−	0.224886i
$298$			5937.79i			1.15425i
$299$	−2530.07	−	4382.22i	−0.489358	−	0.847593i
$300$		0			0
$301$	857.042	−	1484.44i	0.164116	−	0.284258i
$302$	−5742.06	−	3315.18i	−1.09410	−	0.631680i
$303$	−3068.23	+	1475.11i	−0.581733	+	0.279679i
$304$	−1510.26	−	2615.85i	−0.284932	−	0.493517i
$305$		0			0
$306$	−3124.39	−	7991.55i	−0.583690	−	1.49296i
$307$		−	1699.16i		−	0.315883i	−0.987448	−	0.157941i	$-0.949514\pi$
$307$		−	1699.16i		−	0.315883i	0.987448	−	0.157941i	$-0.0504857\pi$
$308$	473.693	−	273.487i	0.0876337	−	0.0505953i
$309$	−742.799	+	1087.96i	−0.136752	+	0.200296i
$310$		0			0
$311$	−2409.47	+	4173.32i	−0.439319	+	0.760924i	−0.997637	−	0.0687036i	$-0.978114\pi$
$311$	−2409.47	+	4173.32i	−0.439319	+	0.760924i	0.558318	+	0.829627i	$0.311447\pi$
$312$	−1875.93	−	1280.79i	−0.340397	−	0.232405i
$313$	5210.40	−	3008.23i	0.940925	−	0.543243i	0.0506747	−	0.998715i	$-0.483863\pi$
$313$	5210.40	−	3008.23i	0.940925	−	0.543243i	0.890250	+	0.455472i	$0.150529\pi$
$314$	10319.5			1.85465
$315$		0			0
$316$	4492.52			0.799760
$317$	6301.82	−	3638.36i	1.11655	−	0.644639i	0.176030	−	0.984385i	$-0.443674\pi$
$317$	6301.82	−	3638.36i	1.11655	−	0.644639i	0.940517	+	0.339746i	$0.110341\pi$
$318$	11383.2	−	5472.69i	2.00735	−	0.965072i
$319$	−2745.99	+	4756.19i	−0.481962	+	0.834782i
$320$		0			0
$321$	−5869.08	−	443.690i	−1.02050	−	0.0771476i
$322$	−1359.79	+	785.074i	−0.235335	+	0.135871i
$323$		−	3362.09i		−	0.579169i
$324$	2811.33	−	2594.86i	0.482052	−	0.444936i
$325$		0			0
$326$	−5548.16	−	9609.69i	−0.942589	−	1.63261i
$327$	593.302	−	7848.13i	0.100335	−	1.32723i
$328$	2166.79	+	1250.99i	0.364758	+	0.210593i
$329$	610.898	−	1058.11i	0.102370	−	0.177311i
$330$		0			0
$331$	797.088	+	1380.60i	0.132362	+	0.229258i	0.924587	−	0.380972i	$-0.124410\pi$
$331$	797.088	+	1380.60i	0.132362	+	0.229258i	−0.792224	+	0.610230i	$0.791077\pi$
$332$			359.075i			0.0593579i
$333$	−737.688	+	4851.15i	−0.121397	+	0.798322i
$334$	10329.4			1.69222
$335$		0			0
$336$	−855.088	+	1252.42i	−0.138836	+	0.203349i
$337$	−7271.96	−	4198.47i	−1.17546	−	0.678650i	−0.220497	−	0.975388i	$-0.570768\pi$
$337$	−7271.96	−	4198.47i	−1.17546	−	0.678650i	−0.954959	+	0.296738i	$0.904101\pi$
$338$	−921.602	−	532.087i	−0.148309	−	0.0856264i
$339$	−4898.90	+	7175.27i	−0.784872	+	1.14958i
$340$		0			0
$341$	−4861.28			−0.772003
$342$	3524.39	−	1377.90i	0.557243	−	0.217861i
$343$			2500.79i			0.393673i
$344$	2307.36	+	3996.46i	0.361640	+	0.626379i
$345$		0			0
$346$	−929.117	+	1609.28i	−0.144363	+	0.250044i
$347$	−9024.74	−	5210.44i	−1.39618	−	0.806083i	−0.402188	−	0.915557i	$-0.631750\pi$
$347$	−9024.74	−	5210.44i	−1.39618	−	0.806083i	−0.993990	+	0.109474i	$0.965083\pi$
$348$	−403.010	+	5330.97i	−0.0620793	+	0.821178i
$349$	−3953.71	−	6848.03i	−0.606411	−	1.05033i	−0.991827	−	0.127591i	$-0.959275\pi$
$349$	−3953.71	−	6848.03i	−0.606411	−	1.05033i	0.385416	−	0.922743i	$-0.374058\pi$
$350$		0			0
$351$	4173.37	−	4480.15i	0.634639	−	0.681290i
$352$			5753.39i			0.871184i
$353$	−4333.56	+	2501.98i	−0.653406	+	0.377244i	−0.789760	−	0.613416i	$-0.789795\pi$
$353$	−4333.56	+	2501.98i	−0.653406	+	0.377244i	0.136354	+	0.990660i	$0.456462\pi$
$354$	2095.57	+	158.421i	0.314628	+	0.0237852i
$355$		0			0
$356$	−1746.16	+	3024.43i	−0.259961	+	0.450266i
$357$	−1521.29	+	731.390i	−0.225533	+	0.108429i
$358$	7169.13	−	4139.10i	1.05838	−	0.611056i
$359$	2385.12			0.350646			0.175323	−	0.984511i	$-0.443903\pi$
$359$	2385.12			0.350646			0.175323	+	0.984511i	$0.443903\pi$
$360$		0			0
$361$	−5376.27			−0.783827
$362$	−3074.88	+	1775.28i	−0.446443	+	0.257754i
$363$	2344.18	+	1600.48i	0.338946	+	0.231415i
$364$	426.067	−	737.970i	0.0613516	−	0.106264i
$365$		0			0
$366$	4670.36	−	6840.53i	0.667004	−	0.976941i
$367$	1565.78	−	904.006i	0.222706	−	0.128580i	−0.384496	−	0.923126i	$-0.625625\pi$
$367$	1565.78	−	904.006i	0.222706	−	0.128580i	0.607203	+	0.794547i	$0.292292\pi$
$368$		−	9095.14i		−	1.28836i
$369$	−4211.84	+	5267.32i	−0.594199	+	0.743104i
$370$		0			0
$371$	−1242.33	−	2151.78i	−0.173850	−	0.301118i
$372$	−4264.93	+	2050.45i	−0.594426	+	0.285781i
$373$	−10854.5	−	6266.85i	−1.50677	−	0.869933i	−0.999969	−	0.00786860i	$-0.997495\pi$
$373$	−10854.5	−	6266.85i	−1.50677	−	0.869933i	−0.506799	−	0.862064i	$-0.669171\pi$
$374$	−4451.30	+	7709.89i	−0.615432	+	1.06596i
$375$		0			0
$376$	1644.68	+	2848.67i	0.225579	+	0.390715i
$377$			8555.98i			1.16885i
$378$	−1390.18	−	1294.98i	−0.189161	−	0.176208i
$379$	−5221.98			−0.707745			−0.353872	−	0.935294i	$-0.615135\pi$
$379$	−5221.98			−0.707745			−0.353872	+	0.935294i	$0.615135\pi$
$380$		0			0
$381$	2834.29	+	214.266i	0.381116	+	0.0288115i
$382$	5926.12	+	3421.44i	0.793734	+	0.458263i
$383$	7411.18	+	4278.85i	0.988756	+	0.570859i	0.904902	−	0.425619i	$-0.139944\pi$
$383$	7411.18	+	4278.85i	0.988756	+	0.570859i	0.0838538	+	0.996478i	$0.473277\pi$
$384$	−2715.85	−	5648.98i	−0.360919	−	0.750712i
$385$		0			0
$386$	−2233.23			−0.294478
$387$	−11585.2	+	4529.36i	−1.52173	+	0.594936i
$388$			7366.52i			0.963862i
$389$	−2730.66	−	4729.65i	−0.355913	−	0.616459i	0.631361	−	0.775489i	$-0.282497\pi$
$389$	−2730.66	−	4729.65i	−0.355913	−	0.616459i	−0.987274	+	0.159030i	$0.949163\pi$
$390$		0			0
$391$	5061.82	−	8767.32i	0.654698	−	1.13397i
$392$	−2855.31	−	1648.51i	−0.367895	−	0.212404i
$393$	−5441.30	−	3715.04i	−0.698416	−	0.476842i
$394$	−124.381	−	215.435i	−0.0159042	−	0.0275468i
$395$		0			0
$396$	−3924.28	−	596.745i	−0.497986	−	0.0757261i
$397$			1998.55i			0.252656i	0.991989	+	0.126328i	$0.0403191\pi$
$397$			1998.55i			0.252656i	−0.991989	+	0.126328i	$0.959681\pi$
$398$	−6855.51	+	3958.03i	−0.863406	+	0.498488i
$399$	−322.554	−	670.912i	−0.0404709	−	0.0841795i
$400$		0			0
$401$	246.083	−	426.228i	0.0306454	−	0.0530793i	−0.850296	−	0.526305i	$-0.823577\pi$
$401$	246.083	−	426.228i	0.0306454	−	0.0530793i	0.880941	+	0.473225i	$0.156910\pi$
$402$	220.763	−	2920.23i	0.0273897	−	0.362308i
$403$	−6558.78	+	3786.71i	−0.810709	+	0.468063i
$404$	3438.40			0.423432
$405$		0			0
$406$	2654.89			0.324532
$407$	4408.99	−	2545.53i	0.536966	−	0.310018i
$408$	342.571	−	4531.49i	0.0415681	−	0.549859i
$409$	−4000.23	+	6928.60i	−0.483615	+	0.837646i	−0.999823	−	0.0188177i	$-0.994010\pi$
$409$	−4000.23	+	6928.60i	−0.483615	+	0.837646i	0.516208	+	0.856463i	$0.327343\pi$
$410$		0			0
$411$	2094.86	+	4357.31i	0.251415	+	0.522945i
$412$	1152.24	−	665.249i	0.137784	−	0.0795496i
$413$		−	413.417i		−	0.0492565i
$414$	11265.1	+	1713.02i	1.33731	+	0.203358i
$415$		0			0
$416$	4481.62	+	7762.40i	0.528196	+	0.914863i
$417$	13433.1	+	9171.39i	1.57751	+	1.07704i
$418$	−3400.17	−	1963.09i	−0.397866	−	0.229708i
$419$	2752.47	−	4767.41i	0.320923	−	0.555855i	−0.659756	−	0.751480i	$-0.729340\pi$
$419$	2752.47	−	4767.41i	0.320923	−	0.555855i	0.980679	+	0.195625i	$0.0626735\pi$
$420$		0			0
$421$	5202.28	+	9010.61i	0.602241	+	1.04311i	0.992481	+	0.122399i	$0.0390588\pi$
$421$	5202.28	+	9010.61i	0.602241	+	1.04311i	−0.390240	+	0.920713i	$0.627608\pi$
$422$		−	1729.05i		−	0.199452i
$423$	−8257.89	+	3228.52i	−0.949202	+	0.371101i
$424$	6689.28			0.766179
$425$		0			0
$426$	7481.79	+	15562.1i	0.850925	+	1.76993i
$427$	−1411.10	−	814.698i	−0.159925	−	0.0923326i
$428$	5148.17	+	2972.30i	0.581417	+	0.335681i
$429$	−6334.51	−	478.875i	−0.712897	−	0.0538935i
$430$		0			0
$431$	6446.05			0.720406			0.360203	−	0.932874i	$-0.382707\pi$
$431$	6446.05			0.720406			0.360203	+	0.932874i	$0.382707\pi$
$432$	10522.6	−	3223.17i	1.17192	−	0.358970i
$433$			6307.26i			0.700018i	0.936746	+	0.350009i	$0.113821\pi$
$433$			6307.26i			0.700018i	−0.936746	+	0.350009i	$0.886179\pi$
$434$	1175.00	+	2035.17i	0.129958	+	0.225095i
$435$		0			0
$436$	−3974.56	+	6884.13i	−0.436575	+	0.756170i
$437$	3866.52	+	2232.34i	0.423251	+	0.244364i
$438$	16632.4	−	7996.34i	1.81445	−	0.872329i
$439$	−3947.14	−	6836.64i	−0.429127	−	0.743269i	0.567669	−	0.823257i	$-0.307845\pi$
$439$	−3947.14	−	6836.64i	−0.429127	−	0.743269i	−0.996796	+	0.0799877i	$0.974512\pi$
$440$		0			0
$441$	5550.20	−	6941.08i	0.599309	−	0.749495i
$442$			13869.4i			1.49254i
$443$	−7602.99	+	4389.59i	−0.815415	+	0.470780i	−0.848833	−	0.528661i	$-0.822694\pi$
$443$	−7602.99	+	4389.59i	−0.815415	+	0.470780i	0.0334178	+	0.999441i	$0.489361\pi$
$444$	2794.44	−	4092.93i	0.298690	−	0.437482i
$445$		0			0
$446$	−5398.43	+	9350.36i	−0.573146	+	0.992718i
$447$	−7000.71	−	4779.72i	−0.740766	−	0.505756i
$448$	386.661	−	223.239i	0.0407768	−	0.0235425i
$449$	−16514.2			−1.73575			−0.867874	−	0.496784i	$-0.834514\pi$
$449$	−16514.2			−1.73575			−0.867874	+	0.496784i	$0.834514\pi$
$450$		0			0
$451$	6997.29			0.730576
$452$	7599.27	−	4387.44i	0.790796	−	0.456566i
$453$	8530.81	−	4101.34i	0.884795	−	0.425382i
$454$	5154.35	−	8927.60i	0.532832	−	0.922892i
$455$		0			0
$456$	1998.46	+	151.079i	0.205233	+	0.0155152i
$457$	13420.7	−	7748.44i	1.37373	−	0.793121i	0.382332	−	0.924025i	$-0.375121\pi$
$457$	13420.7	−	7748.44i	1.37373	−	0.793121i	0.991395	+	0.130904i	$0.0417879\pi$
$458$			15623.6i			1.59398i
$459$	11937.1	+	2749.25i	1.21390	+	0.279573i
$460$		0			0
$461$	7641.45	+	13235.4i	0.772012	+	1.33716i	0.936459	+	0.350778i	$0.114083\pi$
$461$	7641.45	+	13235.4i	0.772012	+	1.33716i	−0.164446	+	0.986386i	$0.552584\pi$
$462$	−148.593	+	1965.58i	−0.0149636	+	0.197937i
$463$	−11821.0	−	6824.87i	−1.18654	−	0.685051i	−0.229025	−	0.973421i	$-0.573554\pi$
$463$	−11821.0	−	6824.87i	−1.18654	−	0.685051i	−0.957519	+	0.288369i	$0.906887\pi$
$464$	−7689.28	+	13318.2i	−0.769323	+	1.33251i
$465$		0			0
$466$	−7766.42	−	13451.8i	−0.772044	−	1.33722i
$467$		−	6841.24i		−	0.677891i	−0.940806	−	0.338945i	$-0.889930\pi$
$467$		−	6841.24i		−	0.677891i	0.940806	−	0.338945i	$-0.110070\pi$
$468$	−5759.42	+	2251.71i	−0.568866	+	0.222405i
$469$	−576.107			−0.0567210
$470$		0			0
$471$	−8306.82	+	12166.8i	−0.812650	+	1.19026i
$472$	963.899	+	556.507i	0.0939980	+	0.0542698i
$473$	11176.9	+	6452.96i	1.08650	+	0.627289i
$474$	−9129.00	+	13371.0i	−0.884618	+	1.29567i
$475$		0			0
$476$	1704.83			0.164161
$477$	−2710.74	+	17826.2i	−0.260202	+	1.71113i
$478$		−	9408.96i		−	0.900326i
$479$	−2888.63	−	5003.25i	−0.275542	−	0.477254i	0.694729	−	0.719271i	$-0.255524\pi$
$479$	−2888.63	−	5003.25i	−0.275542	−	0.477254i	−0.970272	+	0.242018i	$0.922191\pi$
$480$		0			0
$481$	3965.70	−	6868.79i	0.375926	−	0.651122i
$482$	12309.1	+	7106.66i	1.16320	+	0.671576i
$483$	168.974	−	2235.16i	0.0159183	−	0.210566i
$484$	−1433.39	−	2482.70i	−0.134616	−	0.233161i
$485$		0			0
$486$	2010.29	+	13640.1i	0.187631	+	1.27311i
$487$		−	17699.8i		−	1.64693i	−0.567370	−	0.823463i	$-0.692039\pi$
$487$		−	17699.8i		−	1.64693i	0.567370	−	0.823463i	$-0.307961\pi$
$488$	3799.01	−	2193.36i	0.352404	−	0.203460i
$489$	15796.0	+	1194.15i	1.46078	+	0.110432i
$490$		0			0
$491$	6045.50	−	10471.1i	0.555661	−	0.962433i	−0.442191	−	0.896921i	$-0.645799\pi$
$491$	6045.50	−	10471.1i	0.555661	−	0.962433i	0.997852	−	0.0655120i	$-0.0208681\pi$
$492$	6138.91	−	2951.40i	0.562528	−	0.270446i
$493$	−14824.3	+	8558.80i	−1.35426	+	0.781884i
$494$	−6116.63			−0.557085
$495$		0			0
$496$	−13612.5			−1.23230
$497$	2941.73	−	1698.41i	0.265502	−	0.153288i
$498$	−1068.71	−	729.656i	−0.0961643	−	0.0656560i
$499$	−8153.68	+	14122.6i	−0.731481	+	1.26696i	0.224769	+	0.974412i	$0.427837\pi$
$499$	−8153.68	+	14122.6i	−0.731481	+	1.26696i	−0.956250	+	0.292550i	$0.905496\pi$
$500$		0			0
$501$	−8314.85	+	12178.5i	−0.741477	+	1.08602i
$502$	4623.02	−	2669.10i	0.411027	−	0.237307i
$503$			8574.88i			0.760109i	0.924964	+	0.380054i	$0.124095\pi$
$503$			8574.88i			0.760109i	−0.924964	+	0.380054i	$0.875905\pi$
$504$	−366.384	−	937.135i	−0.0323810	−	0.0828241i
$505$		0			0
$506$	−5911.09	−	10238.3i	−0.519328	−	0.899503i
$507$	1369.20	−	658.266i	0.119937	−	0.0576620i
$508$	−2486.15	−	1435.38i	−0.217136	−	0.125364i
$509$	2027.21	−	3511.23i	0.176532	−	0.305762i	−0.764159	−	0.645028i	$-0.776846\pi$
$509$	2027.21	−	3511.23i	0.176532	−	0.305762i	0.940690	+	0.339267i	$0.110179\pi$
$510$		0			0
$511$	−1815.21	−	3144.04i	−0.157143	−	0.272180i
$512$			9824.79i			0.848044i
$513$	−1212.46	+	5264.46i	−0.104350	+	0.453083i
$514$	16187.4			1.38909
$515$		0			0
$516$	12527.6	+	947.057i	1.06879	+	0.0807982i
$517$	7966.84	+	4599.66i	0.677720	+	0.391282i
$518$	−2131.36	−	1230.54i	−0.180785	−	0.104376i
$519$	−1149.45	−	2390.85i	−0.0972161	−	0.202210i
$520$		0			0
$521$	−22757.9			−1.91371			−0.956854	−	0.290570i	$-0.906155\pi$
$521$	−22757.9			−1.91371			−0.956854	+	0.290570i	$0.906155\pi$
$522$	−15047.5	−	12032.2i	−1.26170	−	1.00888i
$523$		−	12468.0i		−	1.04242i	−0.853428	−	0.521211i	$-0.825480\pi$
$523$		−	12468.0i		−	1.04242i	0.853428	−	0.521211i	$-0.174520\pi$
$524$	3327.18	+	5762.84i	0.277382	+	0.480440i
$525$		0			0
$526$	3194.17	−	5532.47i	0.264777	−	0.458607i
$527$	−13121.9	−	7575.92i	−1.08463	−	0.626209i
$528$	−9429.92	−	6438.26i	−0.777244	−	0.530661i
$529$	638.318	+	1105.60i	0.0524631	+	0.0908687i
$530$		0			0
$531$	−1873.64	+	2343.18i	−0.153125	+	0.191498i
$532$			751.855i			0.0612726i
$533$	9440.65	−	5450.56i	0.767205	−	0.442946i
$534$	−5453.27	−	11342.8i	−0.441921	−	0.919198i
$535$		0			0
$536$	775.507	−	1343.22i	0.0624941	−	0.108243i
$537$	−890.869	+	11784.3i	−0.0715900	+	0.946985i
$538$	10758.1	−	6211.17i	0.862106	−	0.497737i
$539$	−9220.77			−0.736859
$540$		0			0
$541$	−22965.1			−1.82504			−0.912519	−	0.409034i	$-0.865866\pi$
$541$	−22965.1			−1.82504			−0.912519	+	0.409034i	$0.865866\pi$
$542$	650.198	−	375.392i	0.0515284	−	0.0297499i
$543$	382.099	−	5054.37i	0.0301979	−	0.399454i
$544$	−8966.20	+	15529.9i	−0.706659	+	1.22397i
$545$		0			0
$546$	1330.61	+	2767.68i	0.104295	+	0.216933i
$547$	8818.73	−	5091.50i	0.689327	−	0.397983i	−0.114033	−	0.993477i	$-0.536377\pi$
$547$	8818.73	−	5091.50i	0.689327	−	0.397983i	0.803360	+	0.595494i	$0.203044\pi$
$548$		−	4883.00i		−	0.380641i
$549$	4305.58	+	11012.8i	0.334713	+	0.856129i
$550$		0			0
$551$	−3774.56	−	6537.73i	−0.291836	−	0.505475i
$552$	4983.92	+	3402.76i	0.384293	+	0.262375i
$553$	2758.23	+	1592.47i	0.212101	+	0.122457i
$554$	−9652.07	+	16717.9i	−0.740211	+	1.28208i
$555$		0			0
$556$	−8213.87	−	14226.8i	−0.626521	−	1.08517i
$557$			4498.86i			0.342231i	0.985251	+	0.171116i	$0.0547372\pi$
$557$			4498.86i			0.342231i	−0.985251	+	0.171116i	$0.945263\pi$
$558$	2563.84	−	16860.2i	0.194509	−	1.27912i
$559$	20106.2			1.52129
$560$		0			0
$561$	−5506.89	−	11454.3i	−0.414440	−	0.862037i
$562$	−8980.94	−	5185.15i	−0.674089	−	0.389186i
$563$	10428.8	+	6021.09i	0.780680	+	0.450726i	0.836671	−	0.547705i	$-0.184498\pi$
$563$	10428.8	+	6021.09i	0.780680	+	0.450726i	−0.0559910	+	0.998431i	$0.517832\pi$
$564$	8929.62	+	675.060i	0.666675	+	0.0503992i
$565$		0			0
$566$	29391.4			2.18271
$567$	2645.84	−	596.613i	0.195970	−	0.0441894i
$568$			9145.01i			0.675557i
$569$	1745.67	+	3023.58i	0.128615	+	0.222768i	0.923140	−	0.384463i	$-0.125613\pi$
$569$	1745.67	+	3023.58i	0.128615	+	0.222768i	−0.794525	+	0.607231i	$0.792280\pi$
$570$		0			0
$571$	8050.10	−	13943.2i	0.589993	−	1.02190i	−0.404239	−	0.914653i	$-0.632464\pi$
$571$	8050.10	−	13943.2i	0.589993	−	1.02190i	0.994233	−	0.107245i	$-0.0342029\pi$
$572$	5556.43	+	3208.01i	0.406164	+	0.234499i
$573$	−8804.25	+	4232.81i	−0.641890	+	0.308600i
$574$	−1691.29	−	2929.40i	−0.122985	−	0.213016i
$575$		0			0
$576$	−3203.26	−	487.104i	−0.231718	−	0.0352361i
$577$		−	5196.41i		−	0.374921i	−0.982272	−	0.187460i	$-0.939974\pi$
$577$		−	5196.41i		−	0.374921i	0.982272	−	0.187460i	$-0.0600256\pi$
$578$	−8543.98	+	4932.87i	−0.614849	+	0.354983i
$579$	1797.68	−	2633.01i	0.129031	−	0.188988i
$580$		0			0
$581$	−127.281	+	220.458i	−0.00908868	+	0.0157421i
$582$	−21924.8	−	14969.1i	−1.56153	−	1.06613i
$583$	16201.5	−	9353.92i	1.15094	−	0.664494i
$584$	9773.95			0.692550
$585$		0			0
$586$	−9546.61			−0.672981
$587$	−3375.07	+	1948.60i	−0.237315	+	0.137014i	−0.613942	−	0.789351i	$-0.710417\pi$
$587$	−3375.07	+	1948.60i	−0.237315	+	0.137014i	0.376627	+	0.926365i	$0.377084\pi$
$588$	−8089.63	+	3889.24i	−0.567365	+	0.272771i
$589$	3341.09	−	5786.94i	0.233730	−	0.404833i
$590$		0			0
$591$	354.123	+	26.7709i	0.0246475	+	0.00186330i
$592$	12346.0	−	7127.96i	0.857124	−	0.494861i
$593$			3023.70i			0.209390i	0.994504	+	0.104695i	$0.0333867\pi$
$593$			3023.70i			0.209390i	−0.994504	+	0.104695i	$0.966613\pi$
$594$	9750.38	−	10467.1i	0.673506	−	0.723015i
$595$		0			0
$596$	4280.71	+	7414.40i	0.294202	+	0.509573i
$597$	851.897	−	11268.8i	0.0584017	−	0.772532i
$598$	−15950.3	−	9208.93i	−1.09073	−	0.629734i
$599$	8314.74	−	14401.6i	0.567164	−	0.982356i	−0.429681	−	0.902981i	$-0.641374\pi$
$599$	8314.74	−	14401.6i	0.567164	−	0.982356i	0.996845	−	0.0793757i	$-0.0252927\pi$
$600$		0			0
$601$	1479.34	+	2562.29i	0.100405	+	0.173907i	0.911852	−	0.410520i	$-0.134653\pi$
$601$	1479.34	+	2562.29i	0.100405	+	0.173907i	−0.811446	+	0.584427i	$0.801319\pi$
$602$		−	6238.89i		−	0.422389i
$603$	3265.28	+	2610.97i	0.220518	+	0.176330i
$604$	−9560.01			−0.644025
$605$		0			0
$606$	−6986.97	+	10233.6i	−0.468360	+	0.685993i
$607$	−6072.88	−	3506.18i	−0.406080	−	0.234451i	0.283024	−	0.959113i	$-0.408662\pi$
$607$	−6072.88	−	3506.18i	−0.406080	−	0.234451i	−0.689104	+	0.724662i	$0.741996\pi$
$608$	−6848.92	−	3954.22i	−0.456843	−	0.263758i
$609$	−2137.10	+	3130.15i	−0.142200	+	0.208276i
$610$		0			0
$611$	14331.7			0.948932
$612$	−9662.68	−	7726.44i	−0.638220	−	0.510332i
$613$		−	8462.75i		−	0.557597i	−0.960350	−	0.278799i	$-0.910064\pi$
$613$		−	8462.75i		−	0.557597i	0.960350	−	0.278799i	$-0.0899362\pi$
$614$	−3092.28	−	5355.99i	−0.203248	−	0.352036i
$615$		0			0
$616$	−521.986	+	904.106i	−0.0341419	+	0.0591355i
$617$	7286.24	+	4206.71i	0.475418	+	0.274483i	0.718505	−	0.695522i	$-0.244827\pi$
$617$	7286.24	+	4206.71i	0.475418	+	0.274483i	−0.243087	+	0.970005i	$0.578160\pi$
$618$	−361.449	+	4781.21i	−0.0235269	+	0.311211i
$619$	−560.233	−	970.351i	−0.0363775	−	0.0630076i	0.847263	−	0.531173i	$-0.178249\pi$
$619$	−560.233	−	970.351i	−0.0363775	−	0.0630076i	−0.883641	+	0.468165i	$0.844915\pi$
$620$		0			0
$621$	−11087.7	+	11902.7i	−0.716478	+	0.769146i
$622$			17539.9i			1.13068i
$623$	−2144.14	+	1237.92i	−0.137886	+	0.0796088i
$624$	−17737.8	−	1340.94i	−1.13795	−	0.0860266i
$625$		0			0
$626$	10949.3	−	18964.7i	0.699077	−	1.21084i
$627$	5051.53	−	2428.62i	0.321752	−	0.154688i
$628$	12885.7	−	7439.57i	0.818783	−	0.472725i
$629$	15868.0			1.00588
$630$		0			0
$631$	7709.69			0.486399			0.243200	−	0.969976i	$-0.421803\pi$
$631$	7709.69			0.486399			0.243200	+	0.969976i	$0.421803\pi$
$632$	−7425.80	+	4287.29i	−0.467377	+	0.269840i
$633$	2038.57	+	1391.83i	0.128003	+	0.0873936i
$634$	13242.8	−	22937.3i	0.829559	−	1.43684i
$635$		0			0
$636$	10268.6	−	15040.1i	0.640214	−	0.937702i
$637$	−12440.5	+	7182.55i	−0.773803	+	0.446755i
$638$			19989.6i			1.24043i
$639$	−24370.5	−	3705.90i	−1.50874	−	0.229426i
$640$		0			0
$641$	−10149.8	−	17580.0i	−0.625419	−	1.08326i	−0.988460	−	0.151484i	$-0.951595\pi$
$641$	−10149.8	−	17580.0i	−0.625419	−	1.08326i	0.363041	−	0.931773i	$-0.381739\pi$
$642$	−19307.7	+	9282.53i	−1.18694	+	0.570642i
$643$	27596.1	+	15932.6i	1.69251	+	0.977169i	0.952484	+	0.304587i	$0.0985186\pi$
$643$	27596.1	+	15932.6i	1.69251	+	0.977169i	0.740023	+	0.672582i	$0.234815\pi$
$644$	−1131.96	+	1960.61i	−0.0692632	+	0.119967i
$645$		0			0
$646$	−6118.64	−	10597.8i	−0.372654	−	0.645456i
$647$			22400.4i			1.36113i	0.732689	+	0.680563i	$0.238265\pi$
$647$			22400.4i			1.36113i	−0.732689	+	0.680563i	$0.761735\pi$
$648$	−2170.59	+	6972.01i	−0.131587	+	0.422664i
$649$	3112.76			0.188269
$650$		0			0
$651$	−3345.32	−	252.899i	−0.201403	−	0.0152257i
$652$	−13855.8	−	7999.63i	−0.832260	−	0.480506i
$653$	8956.65	+	5171.12i	0.536755	+	0.309895i	0.743763	−	0.668444i	$-0.233039\pi$
$653$	8956.65	+	5171.12i	0.536755	+	0.309895i	−0.207008	+	0.978339i	$0.566373\pi$
$654$	−12412.6	−	25818.2i	−0.742157	−	1.54369i
$655$		0			0
$656$	19593.7			1.16617
$657$	−3960.77	+	26046.6i	−0.235197	+	1.54669i
$658$		−	4447.07i		−	0.263472i
$659$	118.705	+	205.603i	0.00701682	+	0.0121535i	0.869512	−	0.493911i	$-0.164433\pi$
$659$	118.705	+	205.603i	0.00701682	+	0.0121535i	−0.862496	+	0.506064i	$0.831100\pi$
$660$		0			0
$661$	−14411.8	+	24962.0i	−0.848042	+	1.46885i	0.0349116	+	0.999390i	$0.488885\pi$
$661$	−14411.8	+	24962.0i	−0.848042	+	1.46885i	−0.882953	+	0.469461i	$0.844448\pi$
$662$	5025.08	+	2901.23i	0.295023	+	0.170332i
$663$	−16352.2	−	11164.4i	−0.957869	−	0.653983i
$664$	−342.671	−	593.524i	−0.0200274	−	0.0346885i
$665$		0			0
$666$	6503.26	+	16634.0i	0.378373	+	0.967801i
$667$		−	22731.2i		−	1.31958i
$668$	12898.2	−	7446.76i	0.747073	−	0.431323i
$669$	−6678.61	−	13891.5i	−0.385964	−	0.802807i
$670$		0			0
$671$	6134.15	−	10624.7i	0.352915	−	0.611267i
$672$	−299.309	+	3959.23i	−0.0171817	+	0.227278i
$673$	6721.08	−	3880.42i	0.384961	−	0.222257i	−0.295014	−	0.955493i	$-0.595324\pi$
$673$	6721.08	−	3880.42i	0.384961	−	0.222257i	0.679974	+	0.733236i	$0.261991\pi$
$674$	−30563.0			−1.74665
$675$		0			0
$676$	−1534.38			−0.0872998
$677$	−20432.4	+	11796.7i	−1.15994	+	0.669693i	−0.951290	−	0.308296i	$-0.900241\pi$
$677$	−20432.4	+	11796.7i	−1.15994	+	0.669693i	−0.208653	+	0.977990i	$0.566908\pi$
$678$	−2383.82	+	31533.0i	−0.135030	+	1.78616i
$679$	−2611.21	+	4522.75i	−0.147583	+	0.255622i
$680$		0			0
$681$	6376.65	+	13263.5i	0.358816	+	0.746339i
$682$	−15323.5	+	8847.01i	−0.860361	+	0.496729i
$683$		−	4383.39i		−	0.245572i	−0.992433	−	0.122786i	$-0.960817\pi$
$683$		−	4383.39i		−	0.245572i	0.992433	−	0.122786i	$-0.0391829\pi$
$684$	3407.48	−	4261.38i	0.190480	−	0.238214i
$685$		0			0
$686$	4551.17	+	7882.86i	0.253301	+	0.438730i
$687$	−18420.4	−	12576.5i	−1.02297	−	0.698432i
$688$	31297.3	+	18069.5i	1.73430	+	1.00130i
$689$	14572.5	−	25240.4i	0.805761	−	1.39562i
$690$		0			0
$691$	8876.26	+	15374.1i	0.488667	+	0.846396i	0.999915	−	0.0130375i	$-0.00415008\pi$
$691$	8876.26	+	15374.1i	0.488667	+	0.846396i	−0.511248	+	0.859433i	$0.670817\pi$
$692$			2679.30i			0.147185i
$693$	−2197.82	−	1757.42i	−0.120474	−	0.0963330i
$694$	−37929.7			−2.07463
$695$		0			0
$696$	−4421.28	−	9196.28i	−0.240788	−	0.500839i
$697$	18887.5	+	10904.7i	1.02642	+	0.592605i
$698$	−24925.3	−	14390.7i	−1.35163	−	0.780364i
$699$	22111.6	+	1671.59i	1.19648	+	0.0904510i
$700$		0			0
$701$	15650.2			0.843223			0.421611	−	0.906777i	$-0.361465\pi$
$701$	15650.2			0.843223			0.421611	+	0.906777i	$0.361465\pi$
$702$	5001.69	−	21717.2i	0.268912	−	1.16761i
$703$			6998.03i			0.375442i
$704$	1680.84	+	2911.30i	0.0899845	+	0.155858i
$705$		0			0
$706$	−9106.68	+	15773.2i	−0.485460	+	0.840841i
$707$	2111.04	+	1218.81i	0.112297	+	0.0648345i
$708$	2730.91	−	1312.93i	0.144963	−	0.0696936i
$709$	6608.80	+	11446.8i	0.350069	+	0.606337i	0.986261	−	0.165194i	$-0.0528249\pi$
$709$	6608.80	+	11446.8i	0.350069	+	0.606337i	−0.636192	+	0.771530i	$0.719492\pi$
$710$		0			0
$711$	−8415.98	−	21526.4i	−0.443916	−	1.13545i
$712$		−	6665.54i		−	0.350845i
$713$	17425.1	−	10060.4i	0.915254	−	0.528422i
$714$	−3464.29	+	5074.04i	−0.181579	+	0.265954i
$715$		0			0
$716$	5967.97	−	10336.8i	0.311499	−	0.539533i
$717$	11093.3	+	7573.90i	0.577804	+	0.394495i
$718$	7518.26	−	4340.67i	0.390779	−	0.225616i
$719$	14824.5			0.768932			0.384466	−	0.923139i	$-0.374386\pi$
$719$	14824.5			0.768932			0.384466	+	0.923139i	$0.374386\pi$
$720$		0			0
$721$	943.243			0.0487215
$722$	−16946.8	+	9784.23i	−0.873537	+	0.504337i
$723$	−18287.2	+	8791.93i	−0.940677	+	0.452248i
$724$	−2559.70	+	4433.53i	−0.131396	+	0.227584i
$725$		0			0
$726$	10301.9	+	778.802i	0.526639	+	0.0398127i
$727$	−6252.78	+	3610.05i	−0.318986	+	0.184167i	−0.650941	−	0.759129i	$-0.725625\pi$
$727$	−6252.78	+	3610.05i	−0.318986	+	0.184167i	0.331954	+	0.943295i	$0.392292\pi$
$728$			1626.41i			0.0828005i
$729$	−17700.1	−	8609.71i	−0.899258	−	0.437419i
$730$		0			0
$731$	20112.9	+	34836.5i	1.01765	+	1.76262i
$732$	900.267	−	11908.6i	0.0454574	−	0.601305i
$733$	−1612.51	−	930.981i	−0.0812542	−	0.0469121i	0.458822	−	0.888528i	$-0.348271\pi$
$733$	−1612.51	−	930.981i	−0.0812542	−	0.0469121i	−0.540077	+	0.841616i	$0.681605\pi$
$734$	3290.39	−	5699.12i	0.165464	−	0.286592i
$735$		0			0
$736$	−11906.6	−	20622.9i	−0.596310	−	1.03284i
$737$		−	4337.71i		−	0.216800i
$738$	−3690.38	+	24268.4i	−0.184071	+	1.21048i
$739$	29412.7			1.46409			0.732046	−	0.681255i	$-0.238566\pi$
$739$	29412.7			1.46409			0.732046	+	0.681255i	$0.238566\pi$
$740$		0			0
$741$	4923.68	−	7211.57i	0.244097	−	0.357522i
$742$	−7832.00	−	4521.81i	−0.387496	−	0.223721i
$743$	−29810.5	−	17211.1i	−1.47192	−	0.849816i	−0.472422	−	0.881373i	$-0.656620\pi$
$743$	−29810.5	−	17211.1i	−1.47192	−	0.849816i	−0.999502	+	0.0315568i	$0.989953\pi$
$744$	5092.84	−	7459.32i	0.250958	−	0.367570i
$745$		0			0
$746$	−45619.9			−2.23896
$747$	1720.54	−	672.666i	0.0842724	−	0.0329472i
$748$			12836.3i			0.627460i
$749$	2107.18	+	3649.75i	0.102797	+	0.178049i
$750$		0			0
$751$	14688.2	−	25440.7i	0.713689	−	1.23615i	−0.249773	−	0.968304i	$-0.580356\pi$
$751$	14688.2	−	25440.7i	0.713689	−	1.23615i	0.963463	−	0.267842i	$-0.0863105\pi$
$752$	22308.7	+	12879.9i	1.08180	+	0.624577i
$753$	−574.478	+	7599.13i	−0.0278023	+	0.367766i
$754$	15571.0	+	26969.7i	0.752071	+	1.30262i
$755$		0			0
$756$	−2669.47	−	614.807i	−0.128423	−	0.0295771i
$757$		−	6235.27i		−	0.299372i	−0.988734	−	0.149686i	$-0.952174\pi$
$757$		−	6235.27i		−	0.299372i	0.988734	−	0.149686i	$-0.0478263\pi$
$758$	−16460.5	+	9503.45i	−0.788748	+	0.455384i
$759$	16829.3	+	1272.26i	0.804829	+	0.0608434i
$760$		0			0
$761$	13985.1	−	24222.9i	0.666176	−	1.15385i	−0.312789	−	0.949823i	$-0.601263\pi$
$761$	13985.1	−	24222.9i	0.666176	−	1.15385i	0.978965	−	0.204028i	$-0.0654034\pi$
$762$	9324.04	−	4482.71i	0.443274	−	0.213112i
$763$	−4880.44	+	2817.72i	−0.231565	+	0.133694i
$764$	9866.44			0.467219
$765$		0			0
$766$	31148.2			1.46923
$767$	4199.69	−	2424.69i	0.197708	−	0.114147i
$768$	−22961.1	−	15676.6i	−1.07882	−	0.736565i
$769$	−4534.05	+	7853.21i	−0.212616	+	0.368263i	−0.952533	−	0.304437i	$-0.901532\pi$
$769$	−4534.05	+	7853.21i	−0.212616	+	0.368263i	0.739916	+	0.672699i	$0.234865\pi$
$770$		0			0
$771$	−13030.3	+	19085.1i	−0.608658	+	0.891482i
$772$	−2788.60	+	1610.00i	−0.130005	+	0.0750584i
$773$		−	31339.8i		−	1.45823i	−0.684389	−	0.729117i	$-0.739931\pi$
$773$		−	31339.8i		−	1.45823i	0.684389	−	0.729117i	$-0.260069\pi$
$774$	−28275.2	+	35361.0i	−1.31309	+	1.64215i
$775$		0			0
$776$	−7029.99	−	12176.3i	−0.325209	−	0.563278i
$777$	3166.50	−	1522.35i	0.146200	−	0.0702884i
$778$	−17214.9	−	9939.03i	−0.793296	−	0.458010i
$779$	−4809.14	+	8329.68i	−0.221188	+	0.383109i
$780$		0			0
$781$	12787.9	+	22149.3i	0.585899	+	1.01481i
$782$		−	36847.8i		−	1.68501i
$783$	26298.8	−	8055.60i	1.20031	−	0.367667i
$784$	−25819.9			−1.17620
$785$		0			0
$786$	−23912.7	−	1807.75i	−1.08516	−	0.0820361i
$787$	8729.01	+	5039.70i	0.395369	+	0.228267i	0.684484	−	0.729028i	$-0.260028\pi$
$787$	8729.01	+	5039.70i	0.395369	+	0.228267i	−0.289115	+	0.957294i	$0.593361\pi$
$788$	−310.625	−	179.340i	−0.0140426	−	0.00810750i
$789$	3951.64	+	8219.42i	0.178304	+	0.370873i
$790$		0			0
$791$	6220.87			0.279632
$792$	7056.02	−	2758.63i	0.316572	−	0.123767i
$793$		−	19112.9i		−	0.855886i
$794$	3637.15	+	6299.72i	0.162566	+	0.281573i
$795$		0			0
$796$	−5706.90	+	9884.63i	−0.254115	+	0.440140i
$797$	−6608.47	−	3815.40i	−0.293706	−	0.169571i	0.345906	−	0.938269i	$-0.387572\pi$
$797$	−6608.47	−	3815.40i	−0.293706	−	0.169571i	−0.639612	+	0.768698i	$0.720905\pi$
$798$	−2237.72	−	1527.80i	−0.0992664	−	0.0677739i
$799$	14336.4	+	24831.4i	0.634775	+	1.09946i
$800$		0			0
$801$	17763.0	+	2701.13i	0.783552	+	0.119151i
$802$		−	1791.38i		−	0.0788725i
$803$	23672.6	−	13667.4i	1.04033	−	0.600636i
$804$	−1829.61	−	3805.59i	−0.0802554	−	0.166931i
$805$		0			0
$806$	−13782.8	+	23872.5i	−0.602331	+	1.04327i
$807$	−1336.85	+	17683.7i	−0.0583138	+	0.771368i
$808$	−5683.41	+	3281.32i	−0.247452	+	0.142867i
$809$	2066.39			0.0898028			0.0449014	−	0.998991i	$-0.485703\pi$
$809$	2066.39			0.0898028			0.0449014	+	0.998991i	$0.485703\pi$
$810$		0			0
$811$	−27700.4			−1.19937			−0.599687	−	0.800235i	$-0.704708\pi$
$811$	−27700.4			−1.19937			−0.599687	+	0.800235i	$0.704708\pi$
$812$	3315.11	−	1913.98i	0.143273	−	0.0827187i
$813$	−80.7966	+	1068.77i	−0.00348544	+	0.0461049i
$814$	9265.18	−	16047.8i	0.398949	−	0.691000i
$815$		0			0
$816$	−15420.3	−	32074.3i	−0.661543	−	1.37601i
$817$	−15363.4	+	8870.06i	−0.657892	+	0.379834i
$818$			29119.9i			1.24469i
$819$	−4334.22	−	659.082i	−0.184921	−	0.0281199i
$820$		0			0
$821$	−8551.54	−	14811.7i	−0.363521	−	0.629637i	0.625017	−	0.780612i	$-0.285092\pi$
$821$	−8551.54	−	14811.7i	−0.363521	−	0.629637i	−0.988538	+	0.150974i	$0.951759\pi$
$822$	14533.1	+	9922.46i	0.616668	+	0.421029i
$823$	7958.91	+	4595.08i	0.337096	+	0.194623i	0.658987	−	0.752154i	$-0.270985\pi$
$823$	7958.91	+	4595.08i	0.337096	+	0.194623i	−0.321891	+	0.946777i	$0.604318\pi$
$824$	−1269.72	+	2199.21i	−0.0536804	+	0.0929771i
$825$		0			0
$826$	−752.374	−	1303.15i	−0.0316930	−	0.0548940i
$827$		−	9902.35i		−	0.416371i	−0.978089	−	0.208185i	$-0.933244\pi$
$827$		−	9902.35i		−	0.416371i	0.978089	−	0.208185i	$-0.0667557\pi$
$828$	15301.4	−	5982.27i	0.642224	−	0.251085i
$829$	−26858.5			−1.12525			−0.562626	−	0.826711i	$-0.690209\pi$
$829$	−26858.5			−1.12525			−0.562626	+	0.826711i	$0.690209\pi$
$830$		0			0
$831$	−11941.0	−	24837.2i	−0.498468	−	1.03682i
$832$	4535.54	+	2618.59i	0.188992	+	0.109115i
$833$	−24889.3	−	14369.8i	−1.03525	−	0.597701i
$834$	59033.9	+	4462.84i	2.45105	+	0.185294i
$835$		0			0
$836$	−5660.98			−0.234197
$837$	17814.5	+	16594.7i	0.735676	+	0.685300i
$838$		−	20036.8i		−	0.825965i
$839$	−4650.27	−	8054.51i	−0.191353	−	0.331433i	0.754346	−	0.656477i	$-0.227954\pi$
$839$	−4650.27	−	8054.51i	−0.191353	−	0.331433i	−0.945699	+	0.325044i	$0.894621\pi$
$840$		0			0
$841$	−7023.13	+	12164.4i	−0.287963	+	0.498767i
$842$	32796.7	+	18935.2i	1.34234	+	0.774999i
$843$	13342.7	−	6414.75i	0.545133	−	0.262083i
$844$	−1246.52	−	2159.03i	−0.0508375	−	0.0880532i
$845$		0			0
$846$	−20154.5	+	25205.2i	−0.819063	+	1.02432i
$847$		−	2032.37i		−	0.0824477i
$848$	45367.2	−	26192.8i	1.83716	−	1.06069i
$849$	−23659.1	+	34652.8i	−0.956395	+	1.40080i
$850$		0			0
$851$	−10535.9	+	18248.8i	−0.424403	+	0.735088i
$852$	20561.5	+	14038.3i	0.826792	+	0.564490i
$853$	−19238.4	+	11107.3i	−0.772227	+	0.445845i	−0.833668	−	0.552265i	$-0.813764\pi$
$853$	−19238.4	+	11107.3i	−0.772227	+	0.445845i	0.0614415	+	0.998111i	$0.480430\pi$
$854$	−5930.65			−0.237638
$855$		0			0
$856$	−11346.1			−0.453037
$857$	29746.2	−	17174.0i	1.18566	−	0.684541i	0.228343	−	0.973581i	$-0.426669\pi$
$857$	29746.2	−	17174.0i	1.18566	−	0.684541i	0.957317	+	0.289040i	$0.0933360\pi$
$858$	−20838.8	+	10018.6i	−0.829167	+	0.398637i
$859$	5589.12	−	9680.65i	0.222001	−	0.384516i	−0.733415	−	0.679781i	$-0.762075\pi$
$859$	5589.12	−	9680.65i	0.222001	−	0.384516i	0.955415	+	0.295265i	$0.0954080\pi$
$860$		0			0
$861$	4815.23	+	364.021i	0.190595	+	0.0144086i
$862$	20318.9	−	11731.1i	0.802858	−	0.463531i
$863$			33684.0i			1.32864i	0.747448	+	0.664321i	$0.231279\pi$
$863$			33684.0i			1.32864i	−0.747448	+	0.664321i	$0.768721\pi$
$864$	19640.0	−	21083.7i	0.773342	−	0.830189i
$865$		0			0
$866$	11478.5	+	19881.4i	0.450412	+	0.780136i
$867$	1061.71	−	14044.2i	0.0415891	−	0.550135i
$868$	2934.41	+	1694.18i	0.114747	+	0.0662492i
$869$	−11990.2	+	20767.7i	−0.468056	+	0.810697i
$870$		0			0
$871$	−3378.87	−	5852.38i	−0.131445	−	0.227670i
$872$		−	15171.9i		−	0.589204i
$873$	35297.4	−	13799.9i	1.36843	−	0.535002i
$874$	16250.4			0.628924
$875$		0			0
$876$	15003.8	−	21975.6i	0.578689	−	0.847589i
$877$	−4684.60	−	2704.66i	−0.180374	−	0.104139i	0.407095	−	0.913386i	$-0.366542\pi$
$877$	−4684.60	−	2704.66i	−0.180374	−	0.104139i	−0.587468	+	0.809247i	$0.699875\pi$
$878$	−24883.9	−	14366.7i	−0.956482	−	0.552225i
$879$	7684.71	−	11255.6i	0.294879	−	0.431901i
$880$		0			0
$881$	−41501.3			−1.58708			−0.793538	−	0.608520i	$-0.791763\pi$
$881$	−41501.3			−1.58708			−0.793538	+	0.608520i	$0.791763\pi$
$882$	4863.04	−	31980.1i	0.185654	−	1.22089i
$883$		−	10532.8i		−	0.401423i	−0.979650	−	0.200711i	$-0.935675\pi$
$883$		−	10532.8i		−	0.401423i	0.979650	−	0.200711i	$-0.0643253\pi$
$884$	9998.84	+	17318.5i	0.380427	+	0.658919i
$885$		0			0
$886$	−15977.2	+	27673.2i	−0.605827	+	1.04932i
$887$	−25982.9	−	15001.2i	−0.983564	−	0.567861i	−0.0802195	−	0.996777i	$-0.525562\pi$
$887$	−25982.9	−	15001.2i	−0.983564	−	0.567861i	−0.903344	+	0.428916i	$0.858895\pi$
$888$	−713.046	+	9432.09i	−0.0269462	+	0.356442i
$889$	−1017.60	−	1762.53i	−0.0383905	−	0.0664943i
$890$		0			0
$891$	4492.11	+	19921.5i	0.168902	+	0.749040i
$892$			15567.5i			0.584347i
$893$	−10951.0	+	6322.56i	−0.410371	+	0.236928i
$894$	−30765.9	−	2325.83i	−1.15097	−	0.0870106i
$895$		0			0
$896$	−2243.97	+	3886.68i	−0.0836673	+	0.144916i
$897$	23696.9	−	11392.7i	0.882070	−	0.424072i
$898$	−52055.0	+	30054.0i	−1.93441	+	1.11683i
$899$	−34021.4			−1.26215
$900$		0			0
$901$	58309.4			2.15601
$902$	22056.5	−	12734.3i	0.814192	−	0.470074i
$903$	7355.72	+	5022.10i	0.271078	+	0.185078i
$904$	−8374.01	+	14504.2i	−0.308092	+	0.533632i
$905$		0			0
$906$	19426.3	−	28453.2i	0.712359	−	1.04337i
$907$	951.200	−	549.175i	0.0348226	−	0.0201048i	−0.482488	−	0.875903i	$-0.660267\pi$
$907$	951.200	−	549.175i	0.0348226	−	0.0201048i	0.517310	+	0.855798i	$0.326933\pi$
$908$		−	14863.6i		−	0.543245i
$909$	−6441.25	−	16475.4i	−0.235031	−	0.601161i
$910$		0			0
$911$	18420.8	+	31905.7i	0.669931	+	1.16036i	0.977923	+	0.208966i	$0.0670098\pi$
$911$	18420.8	+	31905.7i	0.669931	+	1.16036i	−0.307992	+	0.951389i	$0.599657\pi$
$912$	14145.2	−	6800.59i	0.513592	−	0.246919i
$913$	−1659.90	−	958.346i	−0.0601696	−	0.0347389i
$914$	28202.6	−	48848.4i	1.02063	−	1.76779i
$915$		0			0
$916$	11263.5	+	19508.9i	0.406283	+	0.703703i
$917$			4717.54i			0.169888i
$918$	42631.0	−	13058.3i	1.53271	−	0.469486i
$919$	−46004.8			−1.65131			−0.825657	−	0.564172i	$-0.809196\pi$
$919$	−46004.8			−1.65131			−0.825657	+	0.564172i	$0.809196\pi$
$920$		0			0
$921$	8803.96	+	665.561i	0.314984	+	0.0238121i
$922$	48173.9	+	27813.2i	1.72074	+	0.993470i
$923$	34506.5	+	19922.3i	1.23055	+	0.710457i
$924$	1231.49	+	2561.50i	0.0438453	+	0.0911983i
$925$		0			0
$926$	−49682.1			−1.76313
$927$	−5346.14	−	4274.87i	−0.189418	−	0.151462i
$928$			40264.8i			1.42431i
$929$	25451.4	+	44083.2i	0.898853	+	1.55686i	0.828963	+	0.559304i	$0.188932\pi$
$929$	25451.4	+	44083.2i	0.898853	+	1.55686i	0.0698903	+	0.997555i	$0.477735\pi$
$930$		0			0
$931$	6337.31	−	10976.5i	0.223090	−	0.386404i
$932$	−19395.6	−	11198.0i	−0.681677	−	0.393566i
$933$	−20679.7	−	14119.0i	−0.725641	−	0.495430i
$934$	−12450.3	−	21564.6i	−0.436175	−	0.755477i
$935$		0			0
$936$	7371.04	−	9218.21i	0.257404	−	0.321909i
$937$			26913.6i			0.938343i	0.883107	+	0.469172i	$0.155447\pi$
$937$			26913.6i			0.938343i	−0.883107	+	0.469172i	$0.844553\pi$
$938$	−1815.97	+	1048.45i	−0.0632129	+	0.0364960i
$939$	13545.8	+	28175.3i	0.470768	+	0.979199i
$940$		0			0
$941$	−10780.5	+	18672.3i	−0.373468	+	0.646865i	−0.990096	−	0.140389i	$-0.955165\pi$
$941$	−10780.5	+	18672.3i	−0.373468	+	0.646865i	0.616629	+	0.787254i	$0.288498\pi$
$942$	−4042.14	+	53468.9i	−0.139809	+	1.84938i
$943$	−25081.6	+	14480.9i	−0.866140	+	0.500066i
$944$	8716.32			0.300521
$945$		0			0
$946$	46974.8			1.61446
$947$	−24741.5	+	14284.5i	−0.848987	+	0.490163i	−0.860309	−	0.509773i	$-0.829729\pi$
$947$	−24741.5	+	14284.5i	−0.848987	+	0.490163i	0.0113221	+	0.999936i	$0.496396\pi$
$948$	−1759.72	+	23277.4i	−0.0602881	+	0.797485i
$949$	21292.5	−	36879.7i	0.728328	−	1.26150i
$950$		0			0
$951$	16383.2	+	34077.2i	0.558636	+	1.16196i
$952$	−2817.95	+	1626.95i	−0.0959353	+	0.0553883i
$953$		−	3807.33i		−	0.129414i	−0.997904	−	0.0647069i	$-0.979389\pi$
$953$		−	3807.33i		−	0.129414i	0.997904	−	0.0647069i	$-0.0206113\pi$
$954$	23897.2	+	61124.2i	0.811006	+	2.07439i
$955$		0			0
$956$	−6783.17	−	11748.8i	−0.229480	−	0.397472i
$957$	−23568.0	−	16091.0i	−0.796075	−	0.543519i
$958$	−18210.8	−	10514.0i	−0.614158	−	0.354584i
$959$	1730.88	−	2997.97i	0.0582825	−	0.100948i
$960$		0			0
$961$	−161.700	−	280.072i	−0.00542781	−	0.00940124i
$962$		−	28868.6i		−	0.967526i
$963$	4597.84	−	30236.1i	0.153856	−	1.01178i
$964$	20493.5			0.684701
$965$		0			0
$966$	−3535.13	−	7353.07i	−0.117744	−	0.244908i
$967$	15506.5	+	8952.67i	0.515672	+	0.297723i	0.735162	−	0.677891i	$-0.237106\pi$
$967$	15506.5	+	8952.67i	0.515672	+	0.297723i	−0.219490	+	0.975615i	$0.570439\pi$
$968$	4738.57	+	2735.81i	0.157338	+	0.0908392i
$969$	17420.2	+	1316.93i	0.577521	+	0.0436594i
$970$		0			0
$971$	−8567.95			−0.283170			−0.141585	−	0.989926i	$-0.545220\pi$
$971$	−8567.95			−0.283170			−0.141585	+	0.989926i	$0.545220\pi$
$972$	12343.8	+	15582.9i	0.407331	+	0.514221i
$973$		−	11646.3i		−	0.383723i
$974$	−32211.7	−	55792.2i	−1.05968	−	1.83542i
$975$		0			0
$976$	17176.8	−	29751.0i	0.563335	−	0.975725i
$977$	−16991.7	−	9810.17i	−0.556411	−	0.321244i	0.195293	−	0.980745i	$-0.437434\pi$
$977$	−16991.7	−	9810.17i	−0.556411	−	0.321244i	−0.751704	+	0.659501i	$0.770768\pi$
$978$	51964.6	−	24982.9i	1.69902	−	0.816837i
$979$	−9320.74	−	16144.0i	−0.304282	−	0.527032i
$980$		0			0
$981$	40431.7	+	6148.23i	1.31589	+	0.200100i
$982$		−	44008.6i		−	1.43011i
$983$	−40994.4	+	23668.1i	−1.33013	+	0.767951i	−0.985319	−	0.170721i	$-0.945390\pi$
$983$	−40994.4	+	23668.1i	−1.33013	+	0.767951i	−0.344811	+	0.938672i	$0.612057\pi$
$984$	−7330.59	+	10736.9i	−0.237491	+	0.347845i
$985$		0			0
$986$	−31152.2	+	53957.2i	−1.00617	+	1.74275i
$987$	5243.14	+	3579.74i	0.169089	+	0.115445i
$988$	−7637.71	+	4409.64i	−0.245939	+	0.141993i
$989$	−53417.6			−1.71747
$990$		0			0
$991$	13735.8			0.440294			0.220147	−	0.975467i	$-0.429346\pi$
$991$	13735.8			0.440294			0.220147	+	0.975467i	$0.429346\pi$
$992$	−30865.8	+	17820.4i	−0.987894	+	0.570361i
$993$	−7465.60	+	3589.23i	−0.238584	+	0.114704i
$994$	6181.84	−	10707.3i	0.197259	−	0.341663i
$995$		0			0
$996$	−1860.50	−	140.650i	−0.0591890	−	0.00447456i
$997$	−31066.6	+	17936.3i	−0.986850	+	0.569758i	−0.904331	−	0.426831i	$-0.859630\pi$
$997$	−31066.6	+	17936.3i	−0.986850	+	0.569758i	−0.0825187	+	0.996590i	$0.526296\pi$
$998$			59355.3i			1.88262i
$999$	−24846.6	−	5722.43i	−0.786899	−	0.181231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.e.49.19		48
5.2	odd	4		225.4.e.f.76.10	yes	24
5.3	odd	4		225.4.e.e.76.3	✓	24
5.4	even	2	inner	225.4.k.e.49.6		48
9.7	even	3	inner	225.4.k.e.124.6		48
45.7	odd	12		225.4.e.f.151.10	yes	24
45.13	odd	12		2025.4.a.bi.1.10		12
45.22	odd	12		2025.4.a.bf.1.3		12
45.23	even	12		2025.4.a.be.1.3		12
45.32	even	12		2025.4.a.bj.1.10		12
45.34	even	6	inner	225.4.k.e.124.19		48
45.43	odd	12		225.4.e.e.151.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.3	✓	24	5.3	odd	4
225.4.e.e.151.3	yes	24	45.43	odd	12
225.4.e.f.76.10	yes	24	5.2	odd	4
225.4.e.f.151.10	yes	24	45.7	odd	12
225.4.k.e.49.6		48	5.4	even	2	inner
225.4.k.e.49.19		48	1.1	even	1	trivial
225.4.k.e.124.6		48	9.7	even	3	inner
225.4.k.e.124.19		48	45.34	even	6	inner
2025.4.a.be.1.3		12	45.23	even	12
2025.4.a.bf.1.3		12	45.22	odd	12
2025.4.a.bi.1.10		12	45.13	odd	12
2025.4.a.bj.1.10		12	45.32	even	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+(3.15215 - 1.81989i) q^{2} +(-0.391700 + 5.18137i) q^{3} +(2.62402 - 4.54493i) q^{4} +(8.19483 + 17.0453i) q^{6} +(3.22208 - 1.86027i) q^{7} +10.0166i q^{8} +(-26.6931 - 4.05909i) q^{9} +(14.0066 + 24.2602i) q^{11} +(22.5211 + 15.3762i) q^{12} +(37.7951 + 21.8210i) q^{13} +(6.77099 - 11.7277i) q^{14} +(39.2212 + 67.9331i) q^{16} +87.3128i q^{17} +(-91.5278 + 35.7838i) q^{18} -38.5062 q^{19} +(8.37666 + 17.4235i) q^{21} +(88.3019 + 50.9811i) q^{22} +(-100.413 - 57.9733i) q^{23} +(-51.8995 - 3.92349i) q^{24} +158.848 q^{26} +(31.4873 - 136.717i) q^{27} -19.5255i q^{28} +(98.0246 + 169.784i) q^{29} +(-86.7675 + 150.286i) q^{31} +(177.865 + 102.690i) q^{32} +(-131.187 + 63.0708i) q^{33} +(158.900 + 275.223i) q^{34} +(-88.4915 + 110.667i) q^{36} -181.738i q^{37} +(-121.377 + 70.0772i) q^{38} +(-127.867 + 187.283i) q^{39} +(124.893 - 216.320i) q^{41} +(58.1133 + 39.6767i) q^{42} +(398.985 - 230.354i) q^{43} +147.015 q^{44} -422.021 q^{46} +(284.395 - 164.196i) q^{47} +(-367.349 + 176.610i) q^{48} +(-164.579 + 285.059i) q^{49} +(-452.400 - 34.2005i) q^{51} +(198.350 - 114.517i) q^{52} -667.821i q^{53} +(-149.558 - 488.256i) q^{54} +(18.6335 + 32.2742i) q^{56} +(15.0829 - 199.515i) q^{57} +(617.976 + 356.788i) q^{58} +(55.5587 - 96.2305i) q^{59} +(-218.973 - 379.272i) q^{61} +631.630i q^{62} +(-93.5586 + 36.5778i) q^{63} +120.003 q^{64} +(-298.740 + 437.555i) q^{66} +(-134.100 - 77.4225i) q^{67} +(396.831 + 229.110i) q^{68} +(339.713 - 497.567i) q^{69} +912.989 q^{71} +(40.6581 - 267.374i) q^{72} -975.779i q^{73} +(-330.743 - 572.863i) q^{74} +(-101.041 + 175.008i) q^{76} +(90.2611 + 52.1123i) q^{77} +(-62.2207 + 823.048i) q^{78} +(428.020 + 741.352i) q^{79} +(696.048 + 216.700i) q^{81} -909.164i q^{82} +(-59.2542 + 34.2104i) q^{83} +(101.169 + 7.64816i) q^{84} +(838.439 - 1452.22i) q^{86} +(-918.107 + 441.397i) q^{87} +(-243.004 + 140.298i) q^{88} -665.452 q^{89} +162.372 q^{91} +(-526.970 + 304.246i) q^{92} +(-744.699 - 508.441i) q^{93} +(597.637 - 1035.14i) q^{94} +(-601.747 + 881.361i) q^{96} +(-1215.62 + 701.837i) q^{97} +1198.06i q^{98} +(-275.407 - 704.435i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 26 q^{6} + 122 q^{9} - 58 q^{11} - 138 q^{14} - 384 q^{16} + 300 q^{19} - 120 q^{21} - 684 q^{24} - 616 q^{26} + 212 q^{29} - 120 q^{31} - 216 q^{34} + 2606 q^{36} + 820 q^{39} + 706 q^{41}+ \cdots + 3394 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 - 26 * q^6 + 122 * q^9 - 58 * q^11 - 138 * q^14 - 384 * q^16 + 300 * q^19 - 120 * q^21 - 684 * q^24 - 616 * q^26 + 212 * q^29 - 120 * q^31 - 216 * q^34 + 2606 * q^36 + 820 * q^39 + 706 * q^41 - 2284 * q^44 + 1080 * q^46 + 1332 * q^49 - 2738 * q^51 + 4256 * q^54 + 1140 * q^56 + 964 * q^59 - 804 * q^61 - 3900 * q^64 + 4082 * q^66 - 5712 * q^69 - 3776 * q^71 + 20 * q^74 + 924 * q^76 + 516 * q^79 + 6142 * q^81 + 5406 * q^84 - 3904 * q^86 + 2952 * q^89 - 2472 * q^91 + 126 * q^94 - 20848 * q^96 + 3394 * q^99

Introduction

L-functions

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Database

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