LMFDB - Embedded newform 225.4.k.d.124.14

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			124.14
Character	$\chi$	$=$	225.124
Dual form			225.4.k.d.49.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.66357 + 2.69252i) q^{2} +(-3.19791 - 4.09553i) q^{3} +(10.4993 + 18.1853i) q^{4} +(-3.88642 - 27.7102i) q^{6} +(10.8861 + 6.28510i) q^{7} +69.9976i q^{8} +(-6.54673 + 26.1943i) q^{9} +O(q^{10})$	\(q+(4.66357 + 2.69252i) q^{2} +(-3.19791 - 4.09553i) q^{3} +(10.4993 + 18.1853i) q^{4} +(-3.88642 - 27.7102i) q^{6} +(10.8861 + 6.28510i) q^{7} +69.9976i q^{8} +(-6.54673 + 26.1943i) q^{9} +(-6.41534 + 11.1117i) q^{11} +(40.9026 - 101.155i) q^{12} +(51.8442 - 29.9322i) q^{13} +(33.8455 + 58.6220i) q^{14} +(-104.475 + 180.957i) q^{16} +110.011i q^{17} +(-101.060 + 104.532i) q^{18} +12.0872 q^{19} +(-9.07201 - 64.6836i) q^{21} +(-59.8368 + 34.5468i) q^{22} +(-58.6485 + 33.8608i) q^{23} +(286.677 - 223.846i) q^{24} +322.372 q^{26} +(128.215 - 56.9547i) q^{27} +263.956i q^{28} +(99.9790 - 173.169i) q^{29} +(-38.3143 - 66.3624i) q^{31} +(-489.500 + 282.613i) q^{32} +(66.0240 - 9.26000i) q^{33} +(-296.206 + 513.044i) q^{34} +(-545.086 + 155.967i) q^{36} +22.4815i q^{37} +(56.3694 + 32.5449i) q^{38} +(-288.381 - 116.609i) q^{39} +(-43.8807 - 76.0037i) q^{41} +(131.854 - 326.083i) q^{42} +(-103.412 - 59.7050i) q^{43} -269.426 q^{44} -364.682 q^{46} +(210.579 + 121.578i) q^{47} +(1075.22 - 150.801i) q^{48} +(-92.4951 - 160.206i) q^{49} +(450.553 - 351.805i) q^{51} +(1088.65 + 628.534i) q^{52} -293.518i q^{53} +(751.293 + 79.6094i) q^{54} +(-439.942 + 762.002i) q^{56} +(-38.6537 - 49.5034i) q^{57} +(932.519 - 538.390i) q^{58} +(-290.692 - 503.493i) q^{59} +(386.847 - 670.038i) q^{61} -412.648i q^{62} +(-235.902 + 244.007i) q^{63} -1372.15 q^{64} +(332.840 + 134.586i) q^{66} +(200.431 - 115.719i) q^{67} +(-2000.58 + 1155.03i) q^{68} +(326.231 + 131.913i) q^{69} -744.342 q^{71} +(-1833.54 - 458.255i) q^{72} -264.839i q^{73} +(-60.5317 + 104.844i) q^{74} +(126.907 + 219.809i) q^{76} +(-139.676 + 80.6421i) q^{77} +(-1030.92 - 1320.28i) q^{78} +(279.858 - 484.729i) q^{79} +(-643.281 - 342.974i) q^{81} -472.598i q^{82} +(1057.32 + 610.443i) q^{83} +(1081.04 - 844.108i) q^{84} +(-321.513 - 556.878i) q^{86} +(-1028.94 + 144.311i) q^{87} +(-777.792 - 449.059i) q^{88} +255.905 q^{89} +752.509 q^{91} +(-1231.53 - 711.027i) q^{92} +(-149.263 + 369.138i) q^{93} +(654.699 + 1133.97i) q^{94} +(2722.83 + 1100.99i) q^{96} +(908.909 + 524.759i) q^{97} -996.177i q^{98} +(-249.064 - 240.791i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	4.66357	+	2.69252i	1.64882	+	0.951948i	0.977541	+	0.210745i	$0.0675890\pi$
$2$	4.66357	+	2.69252i	1.64882	+	0.951948i	0.671281	+	0.741203i	$0.265744\pi$
$3$	−3.19791	−	4.09553i	−0.615438	−	0.788185i
$3$	−3.19791	−	4.09553i	−0.615438	−	0.788185i
$4$	10.4993	+	18.1853i	1.31241	+	2.27316i
$5$		0			0
$5$		0			0
$6$	−3.88642	−	27.7102i	−0.264437	−	1.88544i
$7$	10.8861	+	6.28510i	0.587795	+	0.339363i	0.764225	−	0.644950i	$-0.223122\pi$
$7$	10.8861	+	6.28510i	0.587795	+	0.339363i	−0.176430	+	0.984313i	$0.556455\pi$
$8$			69.9976i			3.09349i
$9$	−6.54673	+	26.1943i	−0.242471	+	0.970159i
$10$		0			0
$11$	−6.41534	+	11.1117i	−0.175845	+	0.304573i	−0.940454	−	0.339922i	$-0.889599\pi$
$11$	−6.41534	+	11.1117i	−0.175845	+	0.304573i	0.764608	+	0.644495i	$0.222933\pi$
$12$	40.9026	−	101.155i	0.983964	−	2.43341i
$13$	51.8442	−	29.9322i	1.10608	−	0.638593i	0.168266	−	0.985742i	$-0.446183\pi$
$13$	51.8442	−	29.9322i	1.10608	−	0.638593i	0.937810	+	0.347148i	$0.112850\pi$
$14$	33.8455	+	58.6220i	0.646113	+	1.11910i
$15$		0			0
$16$	−104.475	+	180.957i	−1.63243	+	2.82745i
$17$			110.011i			1.56950i	0.619810	+	0.784752i	$0.287210\pi$
$17$			110.011i			1.56950i	−0.619810	+	0.784752i	$0.712790\pi$
$18$	−101.060	+	104.532i	−1.32333	+	1.36880i
$19$	12.0872			0.145947			0.0729733	−	0.997334i	$-0.476751\pi$
$19$	12.0872			0.145947			0.0729733	+	0.997334i	$0.476751\pi$
$20$		0			0
$21$	−9.07201	−	64.6836i	−0.0942702	−	0.672148i
$22$	−59.8368	+	34.5468i	−0.579875	+	0.334791i
$23$	−58.6485	+	33.8608i	−0.531699	+	0.306976i	−0.741708	−	0.670723i	$-0.765984\pi$
$23$	−58.6485	+	33.8608i	−0.531699	+	0.306976i	0.210009	+	0.977699i	$0.432651\pi$
$24$	286.677	−	223.846i	2.43824	−	1.90385i
$25$		0			0
$26$	322.372			2.43163
$27$	128.215	−	56.9547i	0.913891	−	0.405960i
$28$			263.956i			1.78154i
$29$	99.9790	−	173.169i	0.640194	−	1.10885i	−0.345195	−	0.938531i	$-0.612187\pi$
$29$	99.9790	−	173.169i	0.640194	−	1.10885i	0.985389	−	0.170318i	$-0.0544794\pi$
$30$		0			0
$31$	−38.3143	−	66.3624i	−0.221982	−	0.384485i	0.733427	−	0.679768i	$-0.237919\pi$
$31$	−38.3143	−	66.3624i	−0.221982	−	0.384485i	−0.955410	+	0.295283i	$0.904586\pi$
$32$	−489.500	+	282.613i	−2.70413	+	1.56123i
$33$	66.0240	−	9.26000i	0.348282	−	0.0488473i
$34$	−296.206	+	513.044i	−1.49409	+	2.58783i
$35$		0			0
$36$	−545.086	+	155.967i	−2.52355	+	0.722069i
$37$			22.4815i			0.0998900i	0.998752	+	0.0499450i	$0.0159046\pi$
$37$			22.4815i			0.0998900i	−0.998752	+	0.0499450i	$0.984095\pi$
$38$	56.3694	+	32.5449i	0.240640	+	0.138934i
$39$	−288.381	−	116.609i	−1.18405	−	0.478778i
$40$		0			0
$41$	−43.8807	−	76.0037i	−0.167147	−	0.289507i	0.770269	−	0.637719i	$-0.220122\pi$
$41$	−43.8807	−	76.0037i	−0.167147	−	0.289507i	−0.937416	+	0.348213i	$0.886789\pi$
$42$	131.854	−	326.083i	0.484415	−	1.19799i
$43$	−103.412	−	59.7050i	−0.366749	−	0.211743i	0.305288	−	0.952260i	$-0.401247\pi$
$43$	−103.412	−	59.7050i	−0.366749	−	0.211743i	−0.672037	+	0.740517i	$0.734581\pi$
$44$	−269.426			−0.923124
$45$		0			0
$46$	−364.682			−1.16890
$47$	210.579	+	121.578i	0.653533	+	0.377317i	0.789808	−	0.613354i	$-0.210180\pi$
$47$	210.579	+	121.578i	0.653533	+	0.377317i	−0.136276	+	0.990671i	$0.543513\pi$
$48$	1075.22	−	150.801i	3.23321	−	0.453465i
$49$	−92.4951	−	160.206i	−0.269665	−	0.467073i
$50$		0			0
$51$	450.553	−	351.805i	1.23706	−	0.965932i
$52$	1088.65	+	628.534i	2.90325	+	1.67619i
$53$		−	293.518i		−	0.760712i	−0.924840	−	0.380356i	$-0.875801\pi$
$53$		−	293.518i		−	0.760712i	0.924840	−	0.380356i	$-0.124199\pi$
$54$	751.293	+	79.6094i	1.89330	+	0.200620i
$55$		0			0
$56$	−439.942	+	762.002i	−1.04982	+	1.81834i
$57$	−38.6537	−	49.5034i	−0.0898212	−	0.115033i
$58$	932.519	−	538.390i	2.11113	−	1.21886i
$59$	−290.692	−	503.493i	−0.641438	−	1.11100i	−0.985112	−	0.171914i	$-0.945005\pi$
$59$	−290.692	−	503.493i	−0.641438	−	1.11100i	0.343674	−	0.939089i	$-0.388328\pi$
$60$		0			0
$61$	386.847	−	670.038i	0.811977	−	1.40639i	−0.0995008	−	0.995037i	$-0.531725\pi$
$61$	386.847	−	670.038i	0.811977	−	1.40639i	0.911478	−	0.411349i	$-0.134942\pi$
$62$		−	412.648i		−	0.845263i
$63$	−235.902	+	244.007i	−0.471760	+	0.487968i
$64$	−1372.15			−2.67998
$65$		0			0
$66$	332.840	+	134.586i	0.620755	+	0.251006i
$67$	200.431	−	115.719i	0.365471	−	0.211005i	−0.306007	−	0.952029i	$-0.598993\pi$
$67$	200.431	−	115.719i	0.365471	−	0.211005i	0.671478	+	0.741024i	$0.265660\pi$
$68$	−2000.58	+	1155.03i	−3.56773	+	2.05983i
$69$	326.231	+	131.913i	0.569182	+	0.230152i
$70$		0			0
$71$	−744.342			−1.24418			−0.622092	−	0.782944i	$-0.713717\pi$
$71$	−744.342			−1.24418			−0.622092	+	0.782944i	$0.713717\pi$
$72$	−1833.54	−	458.255i	−3.00117	−	0.750082i
$73$		−	264.839i		−	0.424616i	−0.977203	−	0.212308i	$-0.931902\pi$
$73$		−	264.839i		−	0.424616i	0.977203	−	0.212308i	$-0.0680981\pi$
$74$	−60.5317	+	104.844i	−0.0950901	+	0.164701i
$75$		0			0
$76$	126.907	+	219.809i	0.191542	+	0.331760i
$77$	−139.676	+	80.6421i	−0.206722	+	0.119351i
$78$	−1030.92	−	1320.28i	−1.49652	−	1.91657i
$79$	279.858	−	484.729i	0.398564	−	0.690333i	−0.594985	−	0.803737i	$-0.702842\pi$
$79$	279.858	−	484.729i	0.398564	−	0.690333i	0.993549	+	0.113404i	$0.0361755\pi$
$80$		0			0
$81$	−643.281	−	342.974i	−0.882415	−	0.470471i
$82$		−	472.598i		−	0.636460i
$83$	1057.32	+	610.443i	1.39826	+	0.807288i	0.994211	−	0.107448i	$-0.0342680\pi$
$83$	1057.32	+	610.443i	1.39826	+	0.807288i	0.404052	+	0.914736i	$0.367601\pi$
$84$	1081.04	−	844.108i	1.40418	−	1.09643i
$85$		0			0
$86$	−321.513	−	556.878i	−0.403136	−	0.698252i
$87$	−1028.94	+	144.311i	−1.26798	+	0.177837i
$88$	−777.792	−	449.059i	−0.942193	−	0.543975i
$89$	255.905			0.304785			0.152392	−	0.988320i	$-0.451302\pi$
$89$	255.905			0.304785			0.152392	+	0.988320i	$0.451302\pi$
$90$		0			0
$91$	752.509			0.866861
$92$	−1231.53	−	711.027i	−1.39561	−	0.805757i
$93$	−149.263	+	369.138i	−0.166429	+	0.411590i
$94$	654.699	+	1133.97i	0.718373	+	1.24426i
$95$		0			0
$96$	2722.83	+	1100.99i	2.89476	+	1.17051i
$97$	908.909	+	524.759i	0.951400	+	0.549291i	0.893515	−	0.449032i	$-0.148231\pi$
$97$	908.909	+	524.759i	0.951400	+	0.549291i	0.0578842	+	0.998323i	$0.481565\pi$
$98$		−	996.177i		−	1.02683i
$99$	−249.064	−	240.791i	−0.252847	−	0.244448i
$100$		0			0
$101$	−44.3635	+	76.8398i	−0.0437062	+	0.0757014i	−0.887051	−	0.461671i	$-0.847250\pi$
$101$	−44.3635	+	76.8398i	−0.0437062	+	0.0757014i	0.843345	+	0.537373i	$0.180583\pi$
$102$	3048.43	−	427.548i	2.95921	−	0.415035i
$103$	−1337.20	+	772.035i	−1.27921	+	0.738552i	−0.976703	−	0.214595i	$-0.931157\pi$
$103$	−1337.20	+	772.035i	−1.27921	+	0.738552i	−0.302507	+	0.953147i	$0.597824\pi$
$104$	2095.19	+	3628.97i	1.97548	+	3.42163i
$105$		0			0
$106$	790.301	−	1368.84i	0.724158	−	1.25428i
$107$			585.772i			0.529240i	0.964353	+	0.264620i	$0.0852466\pi$
$107$			585.772i			0.529240i	−0.964353	+	0.264620i	$0.914753\pi$
$108$	2381.90	+	1733.65i	2.12221	+	1.54463i
$109$	−1367.04			−1.20127			−0.600634	−	0.799524i	$-0.705085\pi$
$109$	−1367.04			−1.20127			−0.600634	+	0.799524i	$0.705085\pi$
$110$		0			0
$111$	92.0735	−	71.8937i	0.0787318	−	0.0614761i
$112$	−2274.66	+	1313.28i	−1.91907	+	1.10797i
$113$	147.596	−	85.2146i	0.122873	−	0.0709408i	−0.437304	−	0.899314i	$-0.644067\pi$
$113$	147.596	−	85.2146i	0.122873	−	0.0709408i	0.560177	+	0.828373i	$0.310733\pi$
$114$	−46.9758	−	334.938i	−0.0385937	−	0.275174i
$115$		0			0
$116$	4198.83			3.36079
$117$	444.644	+	1553.98i	0.351345	+	1.22791i
$118$		−	3130.77i		−	2.44246i
$119$	−691.429	+	1197.59i	−0.532632	+	0.922546i
$120$		0			0
$121$	583.187	+	1010.11i	0.438157	+	0.758910i
$122$	3608.17	−	2083.18i	2.67761	−	1.54592i
$123$	−170.949	+	422.768i	−0.125316	+	0.309916i
$124$	804.545	−	1393.51i	0.582664	−	1.00920i
$125$		0			0
$126$	−1757.14	+	502.775i	−1.24237	+	0.355482i
$127$		−	1809.74i		−	1.26447i	−0.774775	−	0.632237i	$-0.782137\pi$
$127$		−	1809.74i		−	1.26447i	0.774775	−	0.632237i	$-0.217863\pi$
$128$	−2483.13	−	1433.63i	−1.71468	−	0.989973i
$129$	86.1791	+	614.459i	0.0588190	+	0.419381i
$130$		0			0
$131$	619.147	+	1072.39i	0.412940	+	0.715232i	0.995210	−	0.0977630i	$-0.0311687\pi$
$131$	619.147	+	1072.39i	0.412940	+	0.715232i	−0.582270	+	0.812995i	$0.697835\pi$
$132$	861.600	+	1103.44i	0.568126	+	0.727593i
$133$	131.582	+	75.9691i	0.0857867	+	0.0495290i
$134$	1246.30			0.803462
$135$		0			0
$136$	−7700.50			−4.85524
$137$	438.367	+	253.091i	0.273374	+	0.157832i	0.630420	−	0.776254i	$-0.282883\pi$
$137$	438.367	+	253.091i	0.273374	+	0.157832i	−0.357046	+	0.934087i	$0.616216\pi$
$138$	1166.22	+	1493.57i	0.719387	+	0.921311i
$139$	−106.840	−	185.052i	−0.0651946	−	0.112920i	0.831586	−	0.555396i	$-0.187433\pi$
$139$	−106.840	−	185.052i	−0.0651946	−	0.112920i	−0.896780	+	0.442476i	$0.854100\pi$
$140$		0			0
$141$	−175.487	−	1251.23i	−0.104813	−	0.747320i
$142$	−3471.29	−	2004.15i	−2.05144	−	1.18440i
$143$			768.103i			0.449175i
$144$	−4056.06	−	3921.33i	−2.34726	−	2.26929i
$145$		0			0
$146$	713.082	−	1235.09i	0.404213	−	0.700117i
$147$	−360.338	+	891.141i	−0.202178	+	0.500001i
$148$	−408.832	+	236.039i	−0.227066	+	0.131097i
$149$	−452.655	−	784.022i	−0.248879	−	0.431071i	0.714336	−	0.699803i	$-0.246729\pi$
$149$	−452.655	−	784.022i	−0.248879	−	0.431071i	−0.963215	+	0.268732i	$0.913395\pi$
$150$		0			0
$151$	−679.335	+	1176.64i	−0.366116	+	0.634131i	−0.988955	−	0.148219i	$-0.952646\pi$
$151$	−679.335	+	1176.64i	−0.366116	+	0.634131i	0.622839	+	0.782350i	$0.285979\pi$
$152$			846.073i			0.451484i
$153$	−2881.66	−	720.211i	−1.52267	−	0.380560i
$154$	−868.521			−0.454464
$155$		0			0
$156$	−907.235	−	6468.60i	−0.465622	−	3.31989i
$157$	−1646.61	+	950.670i	−0.837030	+	0.483259i	−0.856254	−	0.516556i	$-0.827214\pi$
$157$	−1646.61	+	950.670i	−0.837030	+	0.483259i	0.0192236	+	0.999815i	$0.493881\pi$
$158$	2610.28	−	1507.05i	1.31432	−	0.758824i
$159$	−1202.11	+	938.643i	−0.599582	+	0.468172i
$160$		0			0
$161$	−851.273			−0.416706
$162$	−2076.53	−	3331.53i	−1.00708	−	1.61574i
$163$		−	2325.15i		−	1.11730i	−0.829404	−	0.558649i	$-0.811320\pi$
$163$		−	2325.15i		−	1.11730i	0.829404	−	0.558649i	$-0.188680\pi$
$164$	921.432	−	1595.97i	0.438730	−	0.759903i
$165$		0			0
$166$	3287.26	+	5693.69i	1.53699	+	2.66215i
$167$	−1702.43	+	982.901i	−0.788853	+	0.455444i	−0.839558	−	0.543269i	$-0.817186\pi$
$167$	−1702.43	+	982.901i	−0.788853	+	0.455444i	0.0507059	+	0.998714i	$0.483853\pi$
$168$	4527.70	−	635.019i	2.07928	−	0.291624i
$169$	693.379	−	1200.97i	0.315603	−	0.546640i
$170$		0			0
$171$	−79.1314	+	316.615i	−0.0353879	+	0.141591i
$172$		−	2507.44i		−	1.11157i
$173$	1990.04	+	1148.95i	0.874567	+	0.504932i	0.868863	−	0.495052i	$-0.164851\pi$
$173$	1990.04	+	1148.95i	0.874567	+	0.504932i	0.00570381	+	0.999984i	$0.498184\pi$
$174$	−5187.10	−	2097.43i	−2.25996	−	0.913828i
$175$		0			0
$176$	−1340.49	−	2321.80i	−0.574110	−	0.994387i
$177$	−1132.46	+	2800.66i	−0.480911	+	1.18933i
$178$	1193.43	+	689.027i	0.502536	+	0.290139i
$179$	873.696			0.364822			0.182411	−	0.983222i	$-0.441610\pi$
$179$	873.696			0.364822			0.182411	+	0.983222i	$0.441610\pi$
$180$		0			0
$181$	1494.20			0.613609			0.306805	−	0.951772i	$-0.400740\pi$
$181$	1494.20			0.613609			0.306805	+	0.951772i	$0.400740\pi$
$182$	3509.38	+	2026.14i	1.42930	+	0.825206i
$183$	−3981.26	+	558.380i	−1.60821	+	0.225555i
$184$	−2370.17	−	4105.26i	−0.949627	−	1.64480i
$185$		0			0
$186$	−1690.01	+	1319.61i	−0.666224	+	0.520207i
$187$	−1222.41	−	705.758i	−0.478028	−	0.275990i
$188$			5105.91i			1.98078i
$189$	1753.73	+	185.831i	0.674948	+	0.0715196i
$190$		0			0
$191$	−2525.13	+	4373.65i	−0.956607	+	1.65689i	−0.225959	+	0.974137i	$0.572551\pi$
$191$	−2525.13	+	4373.65i	−0.956607	+	1.65689i	−0.730648	+	0.682754i	$0.760782\pi$
$192$	4388.02	+	5619.68i	1.64936	+	2.11232i
$193$	4470.08	−	2580.80i	1.66717	−	0.962539i	0.698011	−	0.716087i	$-0.254069\pi$
$193$	4470.08	−	2580.80i	1.66717	−	0.962539i	0.969155	−	0.246452i	$-0.0792647\pi$
$194$	2825.84	+	4894.50i	1.04579	+	1.81137i
$195$		0			0
$196$	1942.26	−	3364.10i	0.707822	−	1.22598i
$197$		−	374.025i		−	0.135270i	−0.997710	−	0.0676350i	$-0.978455\pi$
$197$		−	374.025i		−	0.135270i	0.997710	−	0.0676350i	$-0.0215453\pi$
$198$	−513.194	−	1793.55i	−0.184197	−	0.643748i
$199$	−603.342			−0.214924			−0.107462	−	0.994209i	$-0.534272\pi$
$199$	−603.342			−0.214924			−0.107462	+	0.994209i	$0.534272\pi$
$200$		0			0
$201$	−1114.89	−	450.813i	−0.391236	−	0.158198i
$202$	−413.785	+	238.899i	−0.144128	+	0.0832121i
$203$	2176.76	−	1256.76i	0.752606	−	0.434517i
$204$	11128.2	+	4499.73i	3.81925	+	1.54433i
$205$		0			0
$206$	−8314.87			−2.81225
$207$	−503.002	−	1757.93i	−0.168894	−	0.590265i
$208$			12508.7i			4.16983i
$209$	−77.5434	+	134.309i	−0.0256640	+	0.0444514i
$210$		0			0
$211$	−1205.91	−	2088.69i	−0.393450	−	0.681476i	0.599452	−	0.800411i	$-0.295385\pi$
$211$	−1205.91	−	2088.69i	−0.393450	−	0.681476i	−0.992902	+	0.118935i	$0.962052\pi$
$212$	5337.70	−	3081.72i	1.72922	−	0.998366i
$213$	2380.34	+	3048.47i	0.765719	+	0.980648i
$214$	−1577.20	+	2731.79i	−0.503809	+	0.872623i
$215$		0			0
$216$	3986.69	+	8974.76i	1.25583	+	2.82711i
$217$		−	963.237i		−	0.301331i
$218$	−6375.27	−	3680.76i	−1.98068	−	1.14354i
$219$	−1084.65	+	846.930i	−0.334676	+	0.261325i
$220$		0			0
$221$	3292.87	+	5703.42i	1.00227	+	1.73599i
$222$	622.966	−	87.3724i	0.188337	−	0.0264146i
$223$	−4746.93	−	2740.64i	−1.42546	−	0.822990i	−0.428703	−	0.903446i	$-0.641029\pi$
$223$	−4746.93	−	2740.64i	−1.42546	−	0.822990i	−0.996758	+	0.0804554i	$0.974363\pi$
$224$	−7105.00			−2.11930
$225$		0			0
$226$	917.766			0.270128
$227$	−4739.30	−	2736.24i	−1.38572	−	0.800046i	−0.392891	−	0.919585i	$-0.628525\pi$
$227$	−4739.30	−	2736.24i	−1.38572	−	0.800046i	−0.992830	+	0.119539i	$0.961858\pi$
$228$	494.397	−	1222.68i	0.143606	−	0.355148i
$229$	1637.99	+	2837.08i	0.472670	+	0.818689i	0.999511	−	0.0312750i	$-0.00995677\pi$
$229$	1637.99	+	2837.08i	0.472670	+	0.818689i	−0.526840	+	0.849964i	$0.676623\pi$
$230$		0			0
$231$	776.945	+	314.162i	0.221295	+	0.0894820i
$232$	12121.4	+	6998.29i	3.43021	+	1.98043i
$233$			3446.21i			0.968965i	0.874801	+	0.484483i	$0.160992\pi$
$233$			3446.21i			0.968965i	−0.874801	+	0.484483i	$0.839008\pi$
$234$	−2110.48	+	8444.31i	−0.589601	+	2.35907i
$235$		0			0
$236$	6104.11	−	10572.6i	1.68366	−	2.91618i
$237$	−2880.18	+	403.952i	−0.789401	+	0.110715i
$238$	−6449.06	+	3723.37i	−1.75643	+	1.01408i
$239$	−862.406	−	1493.73i	−0.233408	−	0.404274i	0.725401	−	0.688326i	$-0.241654\pi$
$239$	−862.406	−	1493.73i	−0.233408	−	0.404274i	−0.958809	+	0.284053i	$0.908321\pi$
$240$		0			0
$241$	2787.86	−	4828.71i	0.745152	−	1.29064i	−0.204972	−	0.978768i	$-0.565710\pi$
$241$	2787.86	−	4828.71i	0.745152	−	1.29064i	0.950124	−	0.311873i	$-0.100956\pi$
$242$			6280.96i			1.66841i
$243$	652.496	+	3731.37i	0.172254	+	0.985053i
$244$	16246.4			4.26259
$245$		0			0
$246$	−1935.54	+	1511.33i	−0.501649	+	0.391702i
$247$	626.649	−	361.796i	0.161428	−	0.0932006i
$248$	4645.21	−	2681.91i	1.18940	−	0.686700i
$249$	−881.123	−	6282.42i	−0.224253	−	1.59893i
$250$		0			0
$251$	−1356.38			−0.341090			−0.170545	−	0.985350i	$-0.554553\pi$
$251$	−1356.38			−0.341090			−0.170545	+	0.985350i	$0.554553\pi$
$252$	−6914.14	−	1728.05i	−1.72837	−	0.431971i
$253$		−	868.913i		−	0.215921i
$254$	4872.75	−	8439.84i	1.20371	−	2.08489i
$255$		0			0
$256$	−2231.56	−	3865.18i	−0.544815	−	0.943647i
$257$	3540.16	−	2043.91i	0.859256	−	0.496092i	−0.00450688	−	0.999990i	$-0.501435\pi$
$257$	3540.16	−	2043.91i	0.859256	−	0.496092i	0.863763	+	0.503898i	$0.168101\pi$
$258$	−1252.54	+	3097.61i	−0.302246	+	0.747476i
$259$	−141.298	+	244.736i	−0.0338990	+	0.0587148i
$260$		0			0
$261$	3881.49	+	3752.57i	0.920530	+	0.889954i
$262$			6668.25i			1.57239i
$263$	372.616	+	215.130i	0.0873631	+	0.0504391i	0.543045	−	0.839704i	$-0.317271\pi$
$263$	372.616	+	215.130i	0.0873631	+	0.0504391i	−0.455682	+	0.890143i	$0.650605\pi$
$264$	648.178	+	4621.52i	0.151108	+	1.07741i
$265$		0			0
$266$	409.096	+	708.575i	0.0942980	+	0.163329i
$267$	−818.360	−	1048.06i	−0.187576	−	0.240227i
$268$	4208.76	+	2429.93i	0.959295	+	0.553849i
$269$	−3467.85			−0.786017			−0.393008	−	0.919535i	$-0.628566\pi$
$269$	−3467.85			−0.786017			−0.393008	+	0.919535i	$0.628566\pi$
$270$		0			0
$271$	−55.4415			−0.0124274			−0.00621371	−	0.999981i	$-0.501978\pi$
$271$	−55.4415			−0.0124274			−0.00621371	+	0.999981i	$0.501978\pi$
$272$	−19907.2	−	11493.4i	−4.43769	−	2.56210i
$273$	−2406.46	−	3081.92i	−0.533499	−	0.683247i
$274$	1362.90	+	2360.62i	0.300497	+	0.520475i
$275$		0			0
$276$	1026.31	+	7317.59i	0.223828	+	1.59589i
$277$	−1362.72	−	786.769i	−0.295589	−	0.170658i	0.344871	−	0.938650i	$-0.387923\pi$
$277$	−1362.72	−	786.769i	−0.295589	−	0.170658i	−0.640460	+	0.767992i	$0.721256\pi$
$278$		−	1150.67i		−	0.248247i
$279$	1989.15	−	569.160i	0.426836	−	0.122132i
$280$		0			0
$281$	−4073.23	+	7055.04i	−0.864727	+	1.49775i	0.00259078	+	0.999997i	$0.499175\pi$
$281$	−4073.23	+	7055.04i	−0.864727	+	1.49775i	−0.867318	+	0.497755i	$0.834158\pi$
$282$	2550.55	−	6307.68i	0.538592	−	1.33198i
$283$	2683.21	−	1549.15i	0.563605	−	0.325398i	−0.190986	−	0.981593i	$-0.561168\pi$
$283$	2683.21	−	1549.15i	0.563605	−	0.325398i	0.754591	+	0.656195i	$0.227835\pi$
$284$	−7815.05	−	13536.1i	−1.63288	−	2.82823i
$285$		0			0
$286$	−2068.13	+	3582.10i	−0.427591	+	0.740609i
$287$		−	1103.18i		−	0.226894i
$288$	−4198.22	−	14672.3i	−0.858967	−	3.00199i
$289$	−7189.39			−1.46334
$290$		0			0
$291$	−757.445	−	5400.60i	−0.152585	−	1.08793i
$292$	4816.16	−	2780.61i	0.965221	−	0.557271i
$293$	105.794	−	61.0799i	0.0210939	−	0.0121786i	−0.489416	−	0.872050i	$-0.662790\pi$
$293$	105.794	−	61.0799i	0.0210939	−	0.0121786i	0.510510	+	0.859872i	$0.329457\pi$
$294$	−4079.87	+	3185.69i	−0.809330	+	0.631949i
$295$		0			0
$296$	−1573.65			−0.309008
$297$	−189.682	+	1790.07i	−0.0370588	+	0.349733i
$298$		−	4875.12i		−	0.947679i
$299$	−2027.06	+	3510.97i	−0.392066	+	0.679078i
$300$		0			0
$301$	−750.504	−	1299.91i	−0.143715	−	0.248922i
$302$	−6336.25	+	3658.24i	−1.20732	+	0.697046i
$303$	456.570	−	64.0349i	0.0865652	−	0.0121410i
$304$	−1262.81	+	2187.25i	−0.238247	+	0.412657i
$305$		0			0
$306$	−11499.6	−	11117.7i	−2.14833	−	2.07697i
$307$			1928.53i			0.358525i	0.983801	+	0.179263i	$0.0573712\pi$
$307$			1928.53i			0.358525i	−0.983801	+	0.179263i	$0.942629\pi$
$308$	−2933.00	−	1693.37i	−0.542608	−	0.313275i
$309$	7438.15	+	3007.66i	1.36939	+	0.553721i
$310$		0			0
$311$	−3969.65	−	6875.63i	−0.723788	−	1.25364i	−0.959471	−	0.281807i	$-0.909066\pi$
$311$	−3969.65	−	6875.63i	−0.723788	−	1.25364i	0.235683	−	0.971830i	$-0.424267\pi$
$312$	8162.33	−	20186.0i	1.48109	−	3.66285i
$313$	5853.37	+	3379.44i	1.05703	+	0.610279i	0.924611	−	0.380914i	$-0.124391\pi$
$313$	5853.37	+	3379.44i	1.05703	+	0.610279i	0.132424	+	0.991193i	$0.457724\pi$
$314$	−10238.8			−1.84015
$315$		0			0
$316$	11753.2			2.09232
$317$	7295.60	+	4212.12i	1.29262	+	0.746297i	0.979119	−	0.203290i	$-0.0651634\pi$
$317$	7295.60	+	4212.12i	1.29262	+	0.746297i	0.313505	+	0.949587i	$0.398497\pi$
$318$	−8133.44	+	1140.73i	−1.43428	+	0.201161i
$319$	1282.80	+	2221.87i	0.225150	+	0.389972i
$320$		0			0
$321$	2399.05	−	1873.25i	0.417139	−	0.325715i
$322$	−3969.97	−	2292.06i	−0.687074	−	0.396683i
$323$			1329.72i			0.229064i
$324$	−516.912	−	15299.2i	−0.0886337	−	2.62332i
$325$		0			0
$326$	6260.49	−	10843.5i	1.06361	−	1.84222i
$327$	4371.66	+	5598.73i	0.739307	+	0.946822i
$328$	5320.08	−	3071.55i	0.895586	−	0.517067i
$329$	1528.25	+	2647.01i	0.256095	+	0.443570i
$330$		0			0
$331$	−128.837	+	223.153i	−0.0213944	+	0.0370562i	−0.876524	−	0.481357i	$-0.840144\pi$
$331$	−128.837	+	223.153i	−0.0213944	+	0.0370562i	0.855130	+	0.518414i	$0.173477\pi$
$332$			25636.9i			4.23797i
$333$	−588.886	−	147.180i	−0.0969091	−	0.0242205i
$334$	−10585.9			−1.73424
$335$		0			0
$336$	12652.7	+	5116.20i	2.05435	+	0.830690i
$337$	9612.47	−	5549.76i	1.55378	−	0.897077i	0.555954	−	0.831213i	$-0.312353\pi$
$337$	9612.47	−	5549.76i	1.55378	−	0.897077i	0.997829	−	0.0658636i	$-0.0209802\pi$
$338$	6467.25	−	3733.87i	1.04075	−	0.600874i
$339$	−820.997	−	331.975i	−0.131535	−	0.0531870i
$340$		0			0
$341$	983.198			0.156138
$342$	−1221.53	+	1263.49i	−0.193136	+	0.199772i
$343$		−	6636.94i		−	1.04478i
$344$	4179.21	−	7238.60i	0.655023	−	1.13453i
$345$		0			0
$346$	6187.14	+	10716.4i	0.961337	+	1.66508i
$347$	−8562.02	+	4943.28i	−1.32459	+	0.764753i	−0.984457	−	0.175624i	$-0.943806\pi$
$347$	−8562.02	+	4943.28i	−1.32459	+	0.764753i	−0.340134	+	0.940377i	$0.610472\pi$
$348$	−13427.5	−	17196.4i	−2.06836	−	2.64892i
$349$	3029.60	−	5247.42i	0.464673	−	0.804837i	−0.534514	−	0.845160i	$-0.679505\pi$
$349$	3029.60	−	5247.42i	0.464673	−	0.804837i	0.999187	+	0.0403230i	$0.0128387\pi$
$350$		0			0
$351$	4942.43	−	6790.54i	0.751589	−	1.03263i
$352$		−	7252.23i		−	1.09814i
$353$	7877.96	+	4548.34i	1.18782	+	0.685790i	0.957811	−	0.287398i	$-0.0927902\pi$
$353$	7877.96	+	4548.34i	1.18782	+	0.685790i	0.230012	+	0.973188i	$0.426123\pi$
$354$	−12822.2	+	10011.9i	−1.92511	+	1.50318i
$355$		0			0
$356$	2686.81	+	4653.70i	0.400002	+	0.692824i
$357$	7115.90	−	998.020i	1.05494	−	0.147957i
$358$	4074.55	+	2352.44i	0.601527	+	0.347291i
$359$	8804.63			1.29440			0.647201	−	0.762319i	$-0.275939\pi$
$359$	8804.63			1.29440			0.647201	+	0.762319i	$0.275939\pi$
$360$		0			0
$361$	−6712.90			−0.978700
$362$	6968.33	+	4023.17i	1.01173	+	0.584124i
$363$	2271.95	−	5618.70i	0.328503	−	0.812411i
$364$	7900.80	+	13684.6i	1.13768	+	1.97051i
$365$		0			0
$366$	−20070.3	−	8115.56i	−2.86638	−	1.15904i
$367$	7493.17	+	4326.18i	1.06578	+	0.615326i	0.927025	−	0.375001i	$-0.122358\pi$
$367$	7493.17	+	4326.18i	1.06578	+	0.615326i	0.138752	+	0.990327i	$0.455691\pi$
$368$		−	14150.5i		−	2.00447i
$369$	2278.14	−	651.849i	0.321396	−	0.0919619i
$370$		0			0
$371$	1844.79	−	3195.27i	0.258158	−	0.447143i
$372$	−8280.04	+	1161.29i	−1.15403	+	0.161855i
$373$	−10321.8	+	5959.31i	−1.43283	+	0.827243i	−0.997336	−	0.0729500i	$-0.976759\pi$
$373$	−10321.8	+	5959.31i	−1.43283	+	0.827243i	−0.435491	+	0.900193i	$0.643425\pi$
$374$	−3800.53	−	6582.70i	−0.525456	−	0.910116i
$375$		0			0
$376$	−8510.14	+	14740.0i	−1.16723	+	2.02170i
$377$		−	11970.4i		−	1.63529i
$378$	7678.30	+	5588.59i	1.04479	+	0.760439i
$379$	−5052.23			−0.684738			−0.342369	−	0.939566i	$-0.611229\pi$
$379$	−5052.23			−0.684738			−0.342369	+	0.939566i	$0.611229\pi$
$380$		0			0
$381$	−7411.83	+	5787.38i	−0.996640	+	0.778206i
$382$	−23552.2	+	13597.9i	−3.15455	+	1.82128i
$383$	−4616.24	+	2665.19i	−0.615871	+	0.355573i	−0.775260	−	0.631642i	$-0.782381\pi$
$383$	−4616.24	+	2665.19i	−0.615871	+	0.355573i	0.159388	+	0.987216i	$0.449048\pi$
$384$	2069.33	+	14754.4i	0.275000	+	1.96076i
$385$		0			0
$386$	27795.4			3.66515
$387$	2240.94	−	2317.93i	0.294350	−	0.304463i
$388$			22038.4i			2.88358i
$389$	1669.76	−	2892.11i	0.217635	−	0.376955i	−0.736449	−	0.676493i	$-0.763499\pi$
$389$	1669.76	−	2892.11i	0.217635	−	0.376955i	0.954085	+	0.299537i	$0.0968324\pi$
$390$		0			0
$391$	−3725.05	−	6451.98i	−0.481800	−	0.834503i
$392$	11214.0	−	6474.43i	1.44488	−	0.834205i
$393$	2412.04	−	5965.15i	0.309597	−	0.765654i
$394$	1007.07	−	1744.29i	0.128770	−	0.223036i
$395$		0			0
$396$	1763.86	−	7057.42i	0.223831	−	0.895577i
$397$		−	9041.65i		−	1.14304i	−0.820588	−	0.571520i	$-0.806354\pi$
$397$		−	9041.65i		−	1.14304i	0.820588	−	0.571520i	$-0.193646\pi$
$398$	−2813.73	−	1624.51i	−0.354371	−	0.204596i
$399$	−109.655	−	781.842i	−0.0137584	−	0.0980978i
$400$		0			0
$401$	835.978	+	1447.96i	0.104107	+	0.180318i	0.913373	−	0.407124i	$-0.133468\pi$
$401$	835.978	+	1447.96i	0.104107	+	0.180318i	−0.809266	+	0.587442i	$0.800135\pi$
$402$	−3985.56	−	5104.26i	−0.494482	−	0.633277i
$403$	−3972.75	−	2293.67i	−0.491059	−	0.283513i
$404$	−1863.14			−0.229442
$405$		0			0
$406$	13535.3			1.65455
$407$	−249.807	−	144.226i	−0.0304238	−	0.0175652i
$408$	24625.5	+	31537.6i	2.98810	+	3.82683i
$409$	236.363	+	409.393i	0.0285755	+	0.0494943i	0.879960	−	0.475049i	$-0.157570\pi$
$409$	236.363	+	409.393i	0.0285755	+	0.0494943i	−0.851384	+	0.524543i	$0.824236\pi$
$410$		0			0
$411$	−365.316	−	2604.71i	−0.0438436	−	0.312605i
$412$	−28079.4	−	16211.6i	−3.35770	−	1.93857i
$413$		−	7308.11i		−	0.870722i
$414$	2387.48	−	9552.59i	0.283425	−	1.13402i
$415$		0			0
$416$	−16918.5	+	29303.7i	−1.99398	+	3.45368i
$417$	−416.222	+	1029.35i	−0.0488789	+	0.120881i
$418$	−723.258	+	417.573i	−0.0846309	+	0.0488617i
$419$	6269.65	+	10859.3i	0.731008	+	1.26614i	0.956453	+	0.291887i	$0.0942830\pi$
$419$	6269.65	+	10859.3i	0.731008	+	1.26614i	−0.225445	+	0.974256i	$0.572384\pi$
$420$		0			0
$421$	3375.88	−	5847.19i	0.390808	−	0.676900i	−0.601748	−	0.798686i	$-0.705529\pi$
$421$	3375.88	−	5847.19i	0.390808	−	0.676900i	0.992556	+	0.121786i	$0.0388623\pi$
$422$		−	12987.7i		−	1.49818i
$423$	−4563.24	+	4720.02i	−0.524521	+	0.542542i
$424$	20545.5			2.35325
$425$		0			0
$426$	2892.82	+	20625.9i	0.329009	+	2.34584i
$427$	8422.51	−	4862.74i	0.954552	−	0.551111i
$428$	−10652.4	+	6150.18i	−1.20305	+	0.694580i
$429$	3145.79	−	2456.32i	0.354033	−	0.276439i
$430$		0			0
$431$	7535.06			0.842114			0.421057	−	0.907034i	$-0.361659\pi$
$431$	7535.06			0.842114			0.421057	+	0.907034i	$0.361659\pi$
$432$	−3089.01	+	29151.8i	−0.344028	+	3.24668i
$433$		−	5135.13i		−	0.569928i	−0.958538	−	0.284964i	$-0.908018\pi$
$433$		−	5135.13i		−	0.569928i	0.958538	−	0.284964i	$-0.0919816\pi$
$434$	2593.53	−	4492.13i	0.286851	−	0.496841i
$435$		0			0
$436$	−14352.9	−	24859.9i	−1.57656	−	2.73068i
$437$	−708.895	+	409.281i	−0.0775996	+	0.0448022i
$438$	−7338.74	+	1029.27i	−0.800590	+	0.112284i
$439$	8486.60	−	14699.2i	0.922650	−	1.59808i	0.127353	−	0.991857i	$-0.459352\pi$
$439$	8486.60	−	14699.2i	0.922650	−	1.59808i	0.795297	−	0.606220i	$-0.207315\pi$
$440$		0			0
$441$	4802.02	−	1374.02i	0.518521	−	0.148366i
$442$			35464.4i			3.81645i
$443$	−9831.39	−	5676.15i	−1.05441	−	0.608763i	−0.130529	−	0.991445i	$-0.541667\pi$
$443$	−9831.39	−	5676.15i	−1.05441	−	0.608763i	−0.923880	+	0.382681i	$0.875001\pi$
$444$	2274.11	+	919.550i	0.243073	+	0.0982881i
$445$		0			0
$446$	−14758.4	−	25562.3i	−1.56689	−	2.71393i
$447$	−1763.43	+	4361.09i	−0.186594	+	0.461460i
$448$	−14937.4	−	8624.10i	−1.57528	−	0.909488i
$449$	−11059.8			−1.16246			−0.581230	−	0.813740i	$-0.697428\pi$
$449$	−11059.8			−1.16246			−0.581230	+	0.813740i	$0.697428\pi$
$450$		0			0
$451$	1126.04			0.117568
$452$	3099.30	+	1789.38i	0.322520	+	0.186207i
$453$	6991.42	−	980.562i	0.725134	−	0.101702i
$454$	−14734.7	−	25521.3i	−1.52320	−	2.63827i
$455$		0			0
$456$	3465.12	−	2705.67i	0.355853	−	0.277861i
$457$	308.897	+	178.342i	0.0316184	+	0.0182549i	0.515726	−	0.856754i	$-0.327522\pi$
$457$	308.897	+	178.342i	0.0316184	+	0.0182549i	−0.484107	+	0.875009i	$0.660856\pi$
$458$			17641.3i			1.79983i
$459$	6265.63	+	14105.1i	0.637156	+	1.43435i
$460$		0			0
$461$	−5159.88	+	8937.17i	−0.521300	+	0.902918i	0.478393	+	0.878146i	$0.341219\pi$
$461$	−5159.88	+	8937.17i	−0.521300	+	0.902918i	−0.999693	+	0.0247726i	$0.992114\pi$
$462$	2777.45	+	3557.05i	0.279694	+	0.358201i
$463$	−15734.4	+	9084.27i	−1.57935	+	0.911839i	−0.584403	+	0.811464i	$0.698671\pi$
$463$	−15734.4	+	9084.27i	−1.57935	+	0.911839i	−0.994950	+	0.100376i	$0.967996\pi$
$464$	20890.7	+	36183.7i	2.09014	+	3.62023i
$465$		0			0
$466$	−9278.98	+	16071.7i	−0.922404	+	1.59765i
$467$		−	3817.15i		−	0.378237i	−0.981954	−	0.189118i	$-0.939437\pi$
$467$		−	3817.15i		−	0.378237i	0.981954	−	0.189118i	$-0.0605630\pi$
$468$	−23591.1	+	24401.6i	−2.33013	+	2.41018i
$469$	2909.22			0.286429
$470$		0			0
$471$	9159.21	+	3703.58i	0.896038	+	0.362318i
$472$	35243.3	−	20347.7i	3.43687	−	1.98428i
$473$	1326.85	−	766.056i	0.128982	−	0.0744679i
$474$	−14519.6	−	5871.08i	−1.40698	−	0.568919i
$475$		0			0
$476$	−29038.0			−2.79613
$477$	7688.48	+	1921.58i	0.738012	+	0.184451i
$478$		−	9288.17i		−	0.888768i
$479$	1453.28	−	2517.16i	0.138627	−	0.240109i	−0.788350	−	0.615227i	$-0.789064\pi$
$479$	1453.28	−	2517.16i	0.138627	−	0.240109i	0.926977	+	0.375118i	$0.122398\pi$
$480$		0			0
$481$	672.921	+	1165.53i	0.0637891	+	0.110486i
$482$	26002.7	−	15012.7i	2.45725	−	1.41869i
$483$	2722.29	+	3486.41i	0.256457	+	0.328442i
$484$	−12246.1	+	21210.8i	−1.15008	+	1.99200i
$485$		0			0
$486$	−7003.82	+	19158.4i	−0.653703	+	1.78815i
$487$		−	10411.1i		−	0.968734i	−0.874865	−	0.484367i	$-0.839050\pi$
$487$		−	10411.1i		−	0.968734i	0.874865	−	0.484367i	$-0.160950\pi$
$488$	46901.0	+	27078.3i	4.35064	+	2.51184i
$489$	−9522.70	+	7435.61i	−0.880637	+	0.687628i
$490$		0			0
$491$	−7316.26	−	12672.1i	−0.672460	−	1.16474i	−0.977204	−	0.212301i	$-0.931904\pi$
$491$	−7316.26	−	12672.1i	−0.672460	−	1.16474i	0.304744	−	0.952434i	$-0.401429\pi$
$492$	−9482.99	+	1330.01i	−0.868956	+	0.121873i
$493$	19050.4	+	10998.8i	1.74034	+	1.00479i
$494$	3896.57			0.354888
$495$		0			0
$496$	16011.6			1.44948
$497$	−8102.99	−	4678.26i	−0.731325	−	0.422231i
$498$	12806.3	−	31671.0i	1.15234	−	2.84982i
$499$	4083.42	+	7072.69i	0.366330	+	0.634503i	0.988989	−	0.147991i	$-0.0472807\pi$
$499$	4083.42	+	7072.69i	0.366330	+	0.634503i	−0.622658	+	0.782494i	$0.713947\pi$
$500$		0			0
$501$	9469.74	+	3829.14i	0.844464	+	0.341464i
$502$	−6325.56	−	3652.06i	−0.562397	−	0.324700i
$503$		−	8080.38i		−	0.716275i	−0.933669	−	0.358137i	$-0.883412\pi$
$503$		−	8080.38i		−	0.716275i	0.933669	−	0.358137i	$-0.116588\pi$
$504$	−17079.9	−	16512.6i	−1.50952	−	1.45938i
$505$		0			0
$506$	2339.56	−	4052.24i	0.205546	−	0.356016i
$507$	−7135.96	+	1000.83i	−0.625087	+	0.0876698i
$508$	32910.6	−	19000.9i	2.87435	−	1.65951i
$509$	58.0903	+	100.615i	0.00505856	+	0.00876169i	0.868544	−	0.495613i	$-0.165056\pi$
$509$	58.0903	+	100.615i	0.00505856	+	0.00876169i	−0.863485	+	0.504374i	$0.831723\pi$
$510$		0			0
$511$	1664.54	−	2883.06i	0.144099	−	0.249587i
$512$		−	1095.90i		−	0.0945947i
$513$	1549.76	−	688.421i	0.133379	−	0.0592486i
$514$	22013.0			1.88901
$515$		0			0
$516$	−10269.3	+	8018.57i	−0.876124	+	0.684104i
$517$	−2701.87	+	1559.92i	−0.229841	+	0.132699i
$518$	−1317.91	+	760.895i	−0.111787	+	0.0645402i
$519$	−1658.41	−	11824.5i	−0.140263	−	1.00007i
$520$		0			0
$521$	−14479.3			−1.21756			−0.608780	−	0.793339i	$-0.708341\pi$
$521$	−14479.3			−1.21756			−0.608780	+	0.793339i	$0.708341\pi$
$522$	7997.79	+	27951.3i	0.670601	+	2.34367i
$523$			6841.05i			0.571966i	0.958235	+	0.285983i	$0.0923201\pi$
$523$			6841.05i			0.571966i	−0.958235	+	0.285983i	$0.907680\pi$
$524$	−13001.2	+	22518.7i	−1.08389	+	1.87736i
$525$		0			0
$526$	1158.48	+	2006.55i	0.0960308	+	0.166330i
$527$	7300.58	−	4214.99i	0.603450	−	0.348402i
$528$	−5222.22	+	12914.9i	−0.430432	+	1.06449i
$529$	−3790.40	+	6565.16i	−0.311531	+	0.539588i
$530$		0			0
$531$	15091.7	−	4318.23i	1.23338	−	0.352910i
$532$			3190.48i			0.260009i
$533$	−4549.92	−	2626.90i	−0.369754	−	0.213478i
$534$	−994.552	−	7091.17i	−0.0805964	−	0.574654i
$535$		0			0
$536$	8100.05	+	14029.7i	0.652741	+	1.13058i
$537$	−2794.00	−	3578.25i	−0.224525	−	0.287547i
$538$	−16172.6	−	9337.24i	−1.29600	−	0.748247i
$539$	2373.55			0.189677
$540$		0			0
$541$	−12746.0			−1.01293			−0.506465	−	0.862261i	$-0.669048\pi$
$541$	−12746.0			−1.01293			−0.506465	+	0.862261i	$0.669048\pi$
$542$	−258.555	−	149.277i	−0.0204906	−	0.0118303i
$543$	−4778.33	−	6119.56i	−0.377639	−	0.483638i
$544$	−31090.5	−	53850.3i	−2.45036	−	4.24414i
$545$		0			0
$546$	−2924.56	−	20852.2i	−0.229230	−	1.63442i
$547$	4313.28	+	2490.27i	0.337152	+	0.194655i	0.659012	−	0.752132i	$-0.270975\pi$
$547$	4313.28	+	2490.27i	0.337152	+	0.194655i	−0.321860	+	0.946787i	$0.604308\pi$
$548$			10629.1i			0.828563i
$549$	15018.6	+	14519.7i	1.16754	+	1.12876i
$550$		0			0
$551$	1208.46	−	2093.12i	0.0934342	−	0.161833i
$552$	−9233.61	+	22835.4i	−0.711972	+	1.76076i
$553$	6093.14	−	3517.88i	0.468547	−	0.270516i
$554$	−4236.77	−	7338.31i	−0.324916	−	0.562771i
$555$		0			0
$556$	2243.48	−	3885.83i	0.171124	−	0.296395i
$557$			635.610i			0.0483513i	0.999708	+	0.0241756i	$0.00769610\pi$
$557$			635.610i			0.0483513i	−0.999708	+	0.0241756i	$0.992304\pi$
$558$	10809.0	+	2701.49i	0.820039	+	0.204952i
$559$	−7148.42			−0.540869
$560$		0			0
$561$	1018.70	+	7263.36i	0.0766660	+	0.546630i
$562$	−37991.6	+	21934.4i	−2.85156	+	1.64635i
$563$	−6527.82	+	3768.84i	−0.488659	+	0.282127i	−0.724018	−	0.689781i	$-0.757707\pi$
$563$	−6527.82	+	3768.84i	−0.488659	+	0.282127i	0.235359	+	0.971908i	$0.424373\pi$
$564$	20911.4	−	16328.2i	1.56122	−	1.21905i
$565$		0			0
$566$	16684.5			1.23905
$567$	−4847.20	−	7776.73i	−0.359018	−	0.576000i
$568$		−	52102.2i		−	3.84887i
$569$	−1129.18	+	1955.79i	−0.0831943	+	0.144097i	−0.904620	−	0.426218i	$-0.859846\pi$
$569$	−1129.18	+	1955.79i	−0.0831943	+	0.144097i	0.821426	+	0.570315i	$0.193179\pi$
$570$		0			0
$571$	−5688.66	−	9853.06i	−0.416923	−	0.722132i	0.578705	−	0.815537i	$-0.303558\pi$
$571$	−5688.66	−	9853.06i	−0.416923	−	0.722132i	−0.995628	+	0.0934047i	$0.970225\pi$
$572$	−13968.2	+	8064.52i	−1.02105	+	0.589501i
$573$	25987.5	−	3644.81i	1.89467	−	0.265731i
$574$	2970.33	−	5144.76i	0.215991	−	0.374108i
$575$		0			0
$576$	8983.10	−	35942.5i	0.649819	−	2.60001i
$577$			25027.9i			1.80576i	0.429890	+	0.902881i	$0.358553\pi$
$577$			25027.9i			1.80576i	−0.429890	+	0.902881i	$0.641447\pi$
$578$	−33528.3	−	19357.5i	−2.41279	−	1.39302i
$579$	−24864.6	−	10054.2i	−1.78470	−	0.721652i
$580$		0			0
$581$	7673.39	+	13290.7i	0.547928	+	0.949039i
$582$	11008.8	−	27225.5i	0.784071	−	1.93906i
$583$	3261.48	+	1883.02i	0.231692	+	0.133768i
$584$	18538.1			1.31355
$585$		0			0
$586$	657.835			0.0463736
$587$	128.396	+	74.1295i	0.00902806	+	0.00521235i	0.504507	−	0.863407i	$-0.331674\pi$
$587$	128.396	+	74.1295i	0.00902806	+	0.00521235i	−0.495479	+	0.868620i	$0.665008\pi$
$588$	−19988.9	+	2803.49i	−1.40192	+	0.196622i
$589$	−463.112	−	802.133i	−0.0323976	−	0.0561143i
$590$		0			0
$591$	−1531.83	+	1196.10i	−0.106618	+	0.0832503i
$592$	−4068.17	−	2348.76i	−0.282434	−	0.163063i
$593$		−	27452.6i		−	1.90109i	−0.310590	−	0.950544i	$-0.600527\pi$
$593$		−	27452.6i		−	1.90109i	0.310590	−	0.950544i	$-0.399473\pi$
$594$	−5704.40	+	7837.42i	−0.394031	+	0.541369i
$595$		0			0
$596$	9505.10	−	16463.3i	0.653262	−	1.13148i
$597$	1929.43	+	2471.01i	0.132272	+	0.169400i
$598$	−18906.7	+	10915.8i	−1.29289	+	0.746453i
$599$	−1906.00	−	3301.29i	−0.130012	−	0.225187i	0.793669	−	0.608350i	$-0.208168\pi$
$599$	−1906.00	−	3301.29i	−0.130012	−	0.225187i	−0.923681	+	0.383163i	$0.874835\pi$
$600$		0			0
$601$	−11584.3	+	20064.6i	−0.786247	+	1.36182i	0.142004	+	0.989866i	$0.454646\pi$
$601$	−11584.3	+	20064.6i	−0.786247	+	1.36182i	−0.928251	+	0.371954i	$0.878688\pi$
$602$		−	8082.97i		−	0.547238i
$603$	1719.01	+	6007.73i	0.116092	+	0.405728i
$604$	−28530.1			−1.92197
$605$		0			0
$606$	2301.66	+	930.691i	0.154288	+	0.0623873i
$607$	−6367.69	+	3676.39i	−0.425794	+	0.245832i	−0.697553	−	0.716533i	$-0.745728\pi$
$607$	−6367.69	+	3676.39i	−0.425794	+	0.245832i	0.271759	+	0.962365i	$0.412395\pi$
$608$	−5916.67	+	3415.99i	−0.394659	+	0.227856i
$609$	−12108.2	−	4896.01i	−0.805662	−	0.325774i
$610$		0			0
$611$	14556.4			0.963809
$612$	−17158.1	−	59965.4i	−1.13329	−	3.96072i
$613$			19902.6i			1.31135i	0.755043	+	0.655676i	$0.227616\pi$
$613$			19902.6i			1.31135i	−0.755043	+	0.655676i	$0.772384\pi$
$614$	−5192.61	+	8993.86i	−0.341297	+	0.591144i
$615$		0			0
$616$	−5644.76	−	9777.01i	−0.369211	−	0.639492i
$617$	−21724.4	+	12542.6i	−1.41749	+	0.818390i	−0.996078	−	0.0884785i	$-0.971800\pi$
$617$	−21724.4	+	12542.6i	−1.41749	+	0.818390i	−0.421414	+	0.906868i	$0.638466\pi$
$618$	26590.2	+	34053.8i	1.73077	+	2.21658i
$619$	−1565.52	+	2711.56i	−0.101654	+	0.176069i	−0.912366	−	0.409375i	$-0.865747\pi$
$619$	−1565.52	+	2711.56i	−0.101654	+	0.176069i	0.810712	+	0.585445i	$0.199080\pi$
$620$		0			0
$621$	−5591.11	+	7681.78i	−0.361294	+	0.496391i
$622$		−	42753.3i		−	2.75603i
$623$	2785.81	+	1608.39i	0.179151	+	0.103433i
$624$	51229.9	−	40001.8i	3.28660	−	2.56627i
$625$		0			0
$626$	18198.4	+	31520.6i	1.16191	+	2.01248i
$627$	798.043	−	111.927i	0.0508306	−	0.00712910i
$628$	−34576.4	−	19962.7i	−2.19705	−	1.26847i
$629$	−2473.21			−0.156778
$630$		0			0
$631$	−22527.2			−1.42123			−0.710614	−	0.703582i	$-0.751583\pi$
$631$	−22527.2			−1.42123			−0.710614	+	0.703582i	$0.751583\pi$
$632$	33929.9	+	19589.4i	2.13553	+	1.23295i
$633$	−4697.92	+	11618.3i	−0.294985	+	0.729518i
$634$	22682.4	+	39287.0i	1.42087	+	2.46102i
$635$		0			0
$636$	−29690.8	−	12005.6i	−1.85113	−	0.748513i
$637$	−9590.66	−	5537.17i	−0.596540	−	0.344412i
$638$			13815.8i			0.857325i
$639$	4873.00	−	19497.5i	0.301679	−	1.20706i
$640$		0			0
$641$	3462.88	−	5997.88i	0.213378	−	0.369582i	−0.739391	−	0.673276i	$-0.764887\pi$
$641$	3462.88	−	5997.88i	0.213378	−	0.369582i	0.952770	+	0.303694i	$0.0982200\pi$
$642$	16231.9	−	2276.55i	0.997852	−	0.139951i
$643$	−12959.7	+	7482.26i	−0.794835	+	0.458898i	−0.841662	−	0.540005i	$-0.818422\pi$
$643$	−12959.7	+	7482.26i	−0.794835	+	0.458898i	0.0468271	+	0.998903i	$0.485089\pi$
$644$	−8937.75	−	15480.6i	−0.546889	−	0.947240i
$645$		0			0
$646$	−3580.29	+	6201.25i	−0.218057	+	0.377685i
$647$			2371.74i			0.144115i	0.997400	+	0.0720577i	$0.0229566\pi$
$647$			2371.74i			0.144115i	−0.997400	+	0.0720577i	$0.977043\pi$
$648$	24007.3	−	45028.1i	1.45540	−	2.72974i
$649$	7459.55			0.451176
$650$		0			0
$651$	−3944.97	+	3080.35i	−0.237505	+	0.185451i
$652$	42283.4	−	24412.4i	2.53980	−	1.46635i
$653$	−13831.9	+	7985.85i	−0.828919	+	0.478577i	−0.853482	−	0.521122i	$-0.825514\pi$
$653$	−13831.9	+	7985.85i	−0.828919	+	0.478577i	0.0245632	+	0.999698i	$0.492180\pi$
$654$	5312.87	+	37880.9i	0.317660	+	2.26492i
$655$		0			0
$656$	18337.8			1.09142
$657$	6937.25	+	1733.83i	0.411945	+	0.102957i
$658$			16459.4i			0.975158i
$659$	−3421.46	+	5926.15i	−0.202248	+	0.350304i	−0.949252	−	0.314515i	$-0.898158\pi$
$659$	−3421.46	+	5926.15i	−0.202248	+	0.350304i	0.747005	+	0.664819i	$0.231491\pi$
$660$		0			0
$661$	6695.50	+	11597.0i	0.393986	+	0.682404i	0.992971	−	0.118356i	$-0.0377624\pi$
$661$	6695.50	+	11597.0i	0.393986	+	0.682404i	−0.598985	+	0.800760i	$0.704429\pi$
$662$	−1201.68	+	693.793i	−0.0705511	+	0.0407327i
$663$	12828.2	−	31725.1i	0.751443	−	1.85837i
$664$	−42729.6	+	74009.8i	−2.49733	+	4.32551i
$665$		0			0
$666$	−2350.03	−	2271.97i	−0.136729	−	0.132188i
$667$			13541.5i			0.786098i
$668$	−35748.7	−	20639.5i	−2.07060	−	1.19546i
$669$	3955.88	+	28205.5i	0.228615	+	1.63003i
$670$		0			0
$671$	4963.51	+	8597.05i	0.285565	+	0.494613i
$672$	22721.2	+	29098.7i	1.30430	+	1.67040i
$673$	27628.1	+	15951.1i	1.58244	+	0.913624i	0.994502	+	0.104720i	$0.0333947\pi$
$673$	27628.1	+	15951.1i	1.58244	+	0.913624i	0.587941	+	0.808904i	$0.299939\pi$
$674$	59771.3			3.41588
$675$		0			0
$676$	29119.9			1.65680
$677$	−10271.7	−	5930.38i	−0.583123	−	0.336666i	0.179251	−	0.983803i	$-0.442633\pi$
$677$	−10271.7	−	5930.38i	−0.583123	−	0.336666i	−0.762373	+	0.647137i	$0.775966\pi$
$678$	−2934.93	−	3758.74i	−0.166247	−	0.212911i
$679$	6596.33	+	11425.2i	0.372818	+	0.645741i
$680$		0			0
$681$	3949.53	+	28160.2i	0.222241	+	1.58458i
$682$	4585.22	+	2647.28i	0.257444	+	0.148636i
$683$			7639.34i			0.427981i	0.976836	+	0.213991i	$0.0686462\pi$
$683$			7639.34i			0.427981i	−0.976836	+	0.213991i	$0.931354\pi$
$684$	−6588.55	+	1885.20i	−0.368303	+	0.105384i
$685$		0			0
$686$	17870.1	−	30951.9i	0.994580	−	1.72266i
$687$	6381.21	−	15781.2i	0.354379	−	0.876405i
$688$	21608.0	−	12475.4i	1.19738	−	0.691309i
$689$	−8785.64	−	15217.2i	−0.485786	−	0.841406i
$690$		0			0
$691$	7863.00	−	13619.1i	0.432883	−	0.749776i	−0.564237	−	0.825613i	$-0.690829\pi$
$691$	7863.00	−	13619.1i	0.432883	−	0.749776i	0.997120	+	0.0758369i	$0.0241628\pi$
$692$			48252.6i			2.65071i
$693$	−1197.94	−	4186.66i	−0.0656652	−	0.229492i
$694$	−53239.5			−2.91202
$695$		0			0
$696$	−10101.4	−	72023.4i	−0.550135	−	3.92247i
$697$	8361.23	−	4827.36i	0.454382	−	0.262338i
$698$	28257.5	−	16314.5i	1.53232	−	0.884688i
$699$	14114.1	−	11020.7i	0.763724	−	0.596338i
$700$		0			0
$701$	−6338.17			−0.341497			−0.170748	−	0.985315i	$-0.554619\pi$
$701$	−6338.17			−0.341497			−0.170748	+	0.985315i	$0.554619\pi$
$702$	41333.0	−	18360.6i	2.22224	−	0.987146i
$703$			271.737i			0.0145786i
$704$	8802.82	−	15246.9i	0.471262	−	0.816250i
$705$		0			0
$706$	24493.0	+	42423.1i	1.30567	+	2.26149i
$707$	−965.892	+	557.658i	−0.0513806	+	0.0296646i
$708$	−62820.9	+	8810.76i	−3.33468	+	0.467696i
$709$	17191.8	−	29777.1i	0.910651	−	1.57729i	0.0975047	−	0.995235i	$-0.468914\pi$
$709$	17191.8	−	29777.1i	0.910651	−	1.57729i	0.813147	−	0.582059i	$-0.197753\pi$
$710$		0			0
$711$	10865.0	+	10504.1i	0.573092	+	0.554056i
$712$			17912.7i			0.942847i
$713$	4494.16	+	2594.70i	0.236055	+	0.136287i
$714$	35872.7	+	14505.3i	1.88025	+	0.760292i
$715$		0			0
$716$	9173.18	+	15888.4i	0.478796	+	0.829299i
$717$	−3359.72	+	8308.83i	−0.174995	+	0.432774i
$718$	41061.0	+	23706.6i	2.13424	+	1.23220i
$719$	988.886			0.0512924			0.0256462	−	0.999671i	$-0.491836\pi$
$719$	988.886			0.0512924			0.0256462	+	0.999671i	$0.491836\pi$
$720$		0			0
$721$	−19409.3			−1.00255
$722$	−31306.1	−	18074.6i	−1.61370	−	0.931671i
$723$	−28691.4	+	4024.03i	−1.47586	+	0.206992i
$724$	15688.1	+	27172.5i	0.805307	+	1.39483i
$725$		0			0
$726$	25723.8	−	20085.9i	1.31502	−	1.02680i
$727$	−11857.5	−	6845.92i	−0.604910	−	0.349245i	0.166061	−	0.986116i	$-0.446895\pi$
$727$	−11857.5	−	6845.92i	−0.604910	−	0.349245i	−0.770971	+	0.636871i	$0.780229\pi$
$728$			52673.8i			2.68162i
$729$	13195.3	−	14604.9i	0.670392	−	0.742007i
$730$		0			0
$731$	6568.20	−	11376.5i	0.332331	−	0.575614i
$732$	−51954.7	−	66537.8i	−2.62336	−	3.35971i
$733$	−2166.74	+	1250.97i	−0.109182	+	0.0630363i	−0.553597	−	0.832785i	$-0.686745\pi$
$733$	−2166.74	+	1250.97i	−0.109182	+	0.0630363i	0.444415	+	0.895821i	$0.353412\pi$
$734$	23296.6	+	40350.9i	1.17152	+	2.02913i
$735$		0			0
$736$	19139.0	−	33149.7i	0.958521	−	1.66021i
$737$			2969.51i			0.148417i
$738$	12379.4	+	3093.97i	0.617468	+	0.154323i
$739$	−26453.1			−1.31677			−0.658384	−	0.752682i	$-0.728760\pi$
$739$	−26453.1			−1.31677			−0.658384	+	0.752682i	$0.728760\pi$
$740$		0			0
$741$	−3485.72	−	1409.47i	−0.172808	−	0.0698760i
$742$	17206.6	−	9934.24i	0.851313	−	0.491506i
$743$	−18085.0	+	10441.4i	−0.892967	+	0.515555i	−0.874912	−	0.484282i	$-0.839081\pi$
$743$	−18085.0	+	10441.4i	−0.892967	+	0.515555i	−0.0180555	+	0.999837i	$0.505748\pi$
$744$	−25838.8	−	10448.1i	−1.27325	−	0.514845i
$745$		0			0
$746$	−64182.2			−3.14997
$747$	−22912.1	+	23699.3i	−1.12224	+	1.16079i
$748$		−	29639.8i		−	1.44885i
$749$	−3681.64	+	6376.78i	−0.179605	+	0.311085i
$750$		0			0
$751$	8847.65	+	15324.6i	0.429901	+	0.744610i	0.996864	−	0.0791332i	$-0.0252152\pi$
$751$	8847.65	+	15324.6i	0.429901	+	0.744610i	−0.566963	+	0.823743i	$0.691882\pi$
$752$	−44000.6	+	25403.7i	−2.13369	+	1.23189i
$753$	4337.57	+	5555.08i	0.209920	+	0.268842i
$754$	32230.4	−	55824.8i	1.55672	−	2.69631i
$755$		0			0
$756$	15033.5	+	33843.2i	0.723233	+	1.62813i
$757$		−	7755.61i		−	0.372368i	−0.982515	−	0.186184i	$-0.940388\pi$
$757$		−	7755.61i		−	0.372368i	0.982515	−	0.186184i	$-0.0596120\pi$
$758$	−23561.4	−	13603.2i	−1.12901	−	0.651835i
$759$	−3558.66	+	2778.71i	−0.170186	+	0.132886i
$760$		0			0
$761$	−8527.15	−	14769.5i	−0.406188	−	0.703538i	0.588271	−	0.808664i	$-0.299809\pi$
$761$	−8527.15	−	14769.5i	−0.406188	−	0.703538i	−0.994459	+	0.105126i	$0.966476\pi$
$762$	−50148.2	+	7033.40i	−2.38409	+	0.334374i
$763$	−14881.7	−	8591.95i	−0.706099	−	0.407667i
$764$	−106048.			−5.02184
$765$		0			0
$766$	−28704.2			−1.35395
$767$	−30141.3	−	17402.1i	−1.41896	−	0.819236i
$768$	−8693.61	+	21499.9i	−0.408468	+	1.01017i
$769$	−5024.16	−	8702.11i	−0.235599	−	0.408070i	0.723847	−	0.689960i	$-0.242372\pi$
$769$	−5024.16	−	8702.11i	−0.235599	−	0.408070i	−0.959447	+	0.281890i	$0.909039\pi$
$770$		0			0
$771$	−19692.0	−	7962.57i	−0.919831	−	0.371939i
$772$	93865.1	+	54193.0i	4.37601	+	2.52649i
$773$			7293.24i			0.339352i	0.985500	+	0.169676i	$0.0542722\pi$
$773$			7293.24i			0.339352i	−0.985500	+	0.169676i	$0.945728\pi$
$774$	16691.9	−	4776.09i	0.775164	−	0.221800i
$775$		0			0
$776$	−36731.9	+	63621.5i	−1.69922	+	2.94314i
$777$	1454.18	−	203.952i	0.0671409	−	0.00941665i
$778$	15574.1	−	8991.70i	0.717684	−	0.414355i
$779$	−530.394	−	918.670i	−0.0243945	−	0.0422526i
$780$		0			0
$781$	4775.21	−	8270.90i	0.218784	−	0.378945i
$782$		−	40119.0i		−	1.83460i
$783$	2956.07	−	27897.1i	0.134919	−	1.27326i
$784$	38653.8			1.76083
$785$		0			0
$786$	27310.0	−	21324.5i	1.23933	−	0.967708i
$787$	−24643.8	+	14228.1i	−1.11621	+	0.644445i	−0.940431	−	0.339985i	$-0.889578\pi$
$787$	−24643.8	+	14228.1i	−1.11621	+	0.644445i	−0.175780	+	0.984429i	$0.556245\pi$
$788$	6801.75	−	3926.99i	0.307490	−	0.177530i
$789$	−310.522	−	2214.03i	−0.0140112	−	0.0999004i
$790$		0			0
$791$	2142.33			0.0962989
$792$	16854.8	−	17433.9i	0.756197	−	0.782178i
$793$		−	46316.7i		−	2.07409i
$794$	24344.8	−	42166.4i	1.08812	−	1.88467i
$795$		0			0
$796$	−6334.66	−	10971.9i	−0.282068	−	0.488556i
$797$	−3534.65	+	2040.73i	−0.157094	+	0.0906981i	−0.576486	−	0.817107i	$-0.695576\pi$
$797$	−3534.65	+	2040.73i	−0.157094	+	0.0906981i	0.419392	+	0.907805i	$0.362243\pi$
$798$	1593.74	−	3941.42i	0.0706988	−	0.174843i
$799$	−13374.9	+	23165.9i	−0.592201	+	1.02572i
$800$		0			0
$801$	−1675.34	+	6703.24i	−0.0739015	+	0.295689i
$802$			9003.54i			0.396416i
$803$	2942.81	+	1699.03i	0.129327	+	0.0746668i
$804$	−3507.40	−	25007.8i	−0.153851	−	1.09696i
$805$		0			0
$806$	−12351.5	−	21393.4i	−0.539779	−	0.934925i
$807$	11089.9	+	14202.7i	0.483745	+	0.619527i
$808$	−5378.60	−	3105.34i	−0.234181	−	0.135205i
$809$	−14209.7			−0.617536			−0.308768	−	0.951137i	$-0.599917\pi$
$809$	−14209.7			−0.617536			−0.308768	+	0.951137i	$0.599917\pi$
$810$		0			0
$811$	4901.79			0.212238			0.106119	−	0.994353i	$-0.466158\pi$
$811$	4901.79			0.212238			0.106119	+	0.994353i	$0.466158\pi$
$812$	45708.9	+	26390.0i	1.97545	+	1.14053i
$813$	177.297	+	227.062i	0.00764831	+	0.00979511i
$814$	−776.663	−	1345.22i	−0.0334423	−	0.0579237i
$815$		0			0
$816$	16589.8	+	118286.i	0.711714	+	5.07454i
$817$	−1249.96	−	721.665i	−0.0535258	−	0.0309031i
$818$			2545.64i			0.108810i
$819$	−4926.47	+	19711.4i	−0.210189	+	0.840992i
$820$		0			0
$821$	7259.82	−	12574.4i	0.308611	−	0.534530i	−0.669448	−	0.742859i	$-0.733469\pi$
$821$	7259.82	−	12574.4i	0.308611	−	0.534530i	0.978059	+	0.208329i	$0.0668026\pi$
$822$	5309.54	−	13130.9i	0.225294	−	0.557167i
$823$	−33260.9	+	19203.2i	−1.40875	+	0.813344i	−0.995268	−	0.0971672i	$-0.969022\pi$
$823$	−33260.9	+	19203.2i	−1.40875	+	0.813344i	−0.413485	+	0.910511i	$0.635688\pi$
$824$	−54040.6	−	93601.1i	−2.28470	−	3.95722i
$825$		0			0
$826$	19677.2	−	34081.9i	0.828882	−	1.43567i
$827$			10446.4i			0.439248i	0.975585	+	0.219624i	$0.0704830\pi$
$827$			10446.4i			0.439248i	−0.975585	+	0.219624i	$0.929517\pi$
$828$	26687.4	−	27604.3i	1.12011	−	1.15859i
$829$	6474.00			0.271232			0.135616	−	0.990761i	$-0.456699\pi$
$829$	6474.00			0.271232			0.135616	+	0.990761i	$0.456699\pi$
$830$		0			0
$831$	1135.63	+	8097.09i	0.0474064	+	0.338008i
$832$	−71138.0	+	41071.6i	−2.96426	+	1.71142i
$833$	17624.4	−	10175.5i	0.733073	−	0.423240i
$834$	−4712.61	+	3679.75i	−0.195665	+	0.152781i
$835$		0			0
$836$	−3256.60			−0.134727
$837$	−8692.13	−	6326.49i	−0.358953	−	0.261261i
$838$			67524.5i			2.78353i
$839$	7919.71	−	13717.3i	0.325886	−	0.564452i	−0.655805	−	0.754930i	$-0.727671\pi$
$839$	7919.71	−	13717.3i	0.325886	−	0.564452i	0.981691	+	0.190478i	$0.0610039\pi$
$840$		0			0
$841$	−7797.09	−	13505.0i	−0.319697	−	0.553731i
$842$	31487.3	−	18179.2i	1.28875	−	0.744058i
$843$	41919.9	−	5879.36i	1.71269	−	0.240209i
$844$	25322.3	−	43859.5i	1.03274	−	1.78875i
$845$		0			0
$846$	−33989.7	+	9725.57i	−1.38131	+	0.395239i
$847$			14661.5i			0.594778i
$848$	53114.0	+	30665.4i	2.15087	+	1.24181i
$849$	−14925.3	−	6035.12i	−0.603338	−	0.243963i
$850$		0			0
$851$	−761.239	−	1318.51i	−0.0306639	−	0.0531114i
$852$	−30445.5	+	75293.9i	−1.22423	+	3.02761i
$853$	16316.2	+	9420.17i	0.654931	+	0.378125i	0.790343	−	0.612665i	$-0.209902\pi$
$853$	16316.2	+	9420.17i	0.654931	+	0.378125i	−0.135412	+	0.990789i	$0.543236\pi$
$854$	52372.0			2.09852
$855$		0			0
$856$	−41002.6			−1.63720
$857$	7842.91	+	4528.11i	0.312612	+	0.180487i	0.648095	−	0.761560i	$-0.275566\pi$
$857$	7842.91	+	4528.11i	0.312612	+	0.180487i	−0.335483	+	0.942046i	$0.608899\pi$
$858$	21284.3	−	2985.17i	0.846893	−	0.118778i
$859$	11027.7	+	19100.6i	0.438022	+	0.758676i	0.997537	−	0.0701440i	$-0.0223459\pi$
$859$	11027.7	+	19100.6i	0.438022	+	0.758676i	−0.559515	+	0.828820i	$0.689013\pi$
$860$		0			0
$861$	−4518.10	+	3527.87i	−0.178835	+	0.139639i
$862$	35140.3	+	20288.3i	1.38850	+	0.801649i
$863$			13105.6i			0.516941i	0.966019	+	0.258471i	$0.0832185\pi$
$863$			13105.6i			0.516941i	−0.966019	+	0.258471i	$0.916781\pi$
$864$	−46665.2	+	64114.6i	−1.83748	+	2.52456i
$865$		0			0
$866$	13826.4	−	23948.1i	0.542542	−	0.939710i
$867$	22991.0	+	29444.4i	0.900596	+	1.15338i
$868$	17516.7	−	10113.3i	0.684973	−	0.395470i
$869$	3590.78	+	6219.41i	0.140171	+	0.242784i
$870$		0			0
$871$	6927.46	−	11998.7i	0.269492	−	0.466775i
$872$		−	95689.2i		−	3.71611i
$873$	−19696.1	+	20372.8i	−0.763586	+	0.789821i
$874$	−4407.98			−0.170597
$875$		0			0
$876$	−26789.7	−	10832.6i	−1.03327	−	0.417807i
$877$	31802.4	−	18361.1i	1.22450	−	0.706967i	0.258628	−	0.965977i	$-0.416730\pi$
$877$	31802.4	−	18361.1i	1.22450	−	0.706967i	0.965875	+	0.259010i	$0.0833962\pi$
$878$	79155.8	−	45700.6i	3.04257	−	1.75663i
$879$	−588.473	−	237.952i	−0.0225810	−	0.00913076i
$880$		0			0
$881$	36054.4			1.37878			0.689390	−	0.724390i	$-0.257879\pi$
$881$	36054.4			1.37878			0.689390	+	0.724390i	$0.257879\pi$
$882$	26094.1	+	6521.70i	0.996186	+	0.248976i
$883$			13524.6i			0.515446i	0.966219	+	0.257723i	$0.0829721\pi$
$883$			13524.6i			0.515446i	−0.966219	+	0.257723i	$0.917028\pi$
$884$	−69145.6	+	119764.i	−2.63079	+	4.55666i
$885$		0			0
$886$	−30566.3	−	52942.3i	−1.15902	−	2.00749i
$887$	34407.4	−	19865.1i	1.30246	−	0.751978i	0.321639	−	0.946863i	$-0.395766\pi$
$887$	34407.4	−	19865.1i	1.30246	−	0.751978i	0.980826	+	0.194884i	$0.0624331\pi$
$888$	5032.39	+	6444.92i	0.190176	+	0.243556i
$889$	11374.4	−	19701.0i	0.429116	−	0.743251i
$890$		0			0
$891$	7937.89	−	4947.65i	0.298462	−	0.186030i
$892$		−	115099.i		−	4.32040i
$893$	2545.30	+	1469.53i	0.0953810	+	0.0550682i
$894$	−19966.2	+	15590.2i	−0.746946	+	0.583238i
$895$		0			0
$896$	−18021.1	−	31213.4i	−0.671921	−	1.16380i
$897$	20861.6	−	2925.88i	0.776532	−	0.108910i
$898$	−51578.2	−	29778.7i	−1.91669	−	1.10660i
$899$	−15322.5			−0.568447
$900$		0			0
$901$	32290.1			1.19394
$902$	5251.37	+	3031.88i	0.193849	+	0.111919i
$903$	−2923.78	+	7230.71i	−0.107749	+	0.266471i
$904$	5964.81	+	10331.4i	0.219454	+	0.380106i
$905$		0			0
$906$	35245.2	+	14251.6i	1.29243	+	0.522602i
$907$	19938.0	+	11511.2i	0.729912	+	0.421415i	0.818390	−	0.574663i	$-0.194867\pi$
$907$	19938.0	+	11511.2i	0.729912	+	0.421415i	−0.0884783	+	0.996078i	$0.528200\pi$
$908$		−	114914.i		−	4.19995i
$909$	−1722.33	−	1665.12i	−0.0628449	−	0.0607574i
$910$		0			0
$911$	−15940.1	+	27609.1i	−0.579714	+	1.00409i	0.415798	+	0.909457i	$0.363502\pi$
$911$	−15940.1	+	27609.1i	−0.579714	+	1.00409i	−0.995512	+	0.0946365i	$0.969831\pi$
$912$	12996.3	−	1822.76i	0.471877	−	0.0661817i
$913$	−13566.1	+	7832.41i	−0.491756	+	0.283916i
$914$	960.376	+	1663.42i	0.0347554	+	0.0601981i
$915$		0			0
$916$	−34395.5	+	59574.7i	−1.24067	+	2.14891i
$917$			15565.6i			0.560547i
$918$	−8757.89	+	82650.4i	−0.314873	+	2.97153i
$919$	−38459.6			−1.38049			−0.690243	−	0.723578i	$-0.742496\pi$
$919$	−38459.6			−1.38049			−0.690243	+	0.723578i	$0.742496\pi$
$920$		0			0
$921$	7898.37	−	6167.28i	0.282584	−	0.220650i
$922$	−48126.9	+	27786.1i	−1.71906	+	0.992501i
$923$	−38589.8	+	22279.8i	−1.37616	+	0.794528i
$924$	2444.23	+	17427.4i	0.0870231	+	0.620477i
$925$		0			0
$926$	−97838.1			−3.47209
$927$	−11468.6	−	40081.4i	−0.406341	−	1.42011i
$928$			113021.i			3.99796i
$929$	−18600.5	+	32217.1i	−0.656903	+	1.13779i	0.324509	+	0.945882i	$0.394801\pi$
$929$	−18600.5	+	32217.1i	−0.656903	+	1.13779i	−0.981413	+	0.191908i	$0.938533\pi$
$930$		0			0
$931$	−1118.00	−	1936.44i	−0.0393567	−	0.0681678i
$932$	−62670.3	+	36182.7i	−2.20261	+	1.27168i
$933$	−15464.8	+	38245.5i	−0.542651	+	1.34201i
$934$	10277.7	−	17801.5i	0.360062	−	0.623645i
$935$		0			0
$936$	−108775.	+	31124.0i	−3.79852	+	1.08688i
$937$			23593.7i			0.822595i	0.911501	+	0.411298i	$0.134924\pi$
$937$			23593.7i			0.822595i	−0.911501	+	0.411298i	$0.865076\pi$
$938$	13567.4	+	7833.12i	0.472271	+	0.272666i
$939$	−4877.94	−	34779.8i	−0.169527	−	1.20873i
$940$		0			0
$941$	−18285.8	−	31672.0i	−0.633477	−	1.09721i	−0.986836	−	0.161726i	$-0.948294\pi$
$941$	−18285.8	−	31672.0i	−0.633477	−	1.09721i	0.353359	−	0.935488i	$-0.385039\pi$
$942$	32742.7	+	41933.2i	1.13250	+	1.45038i
$943$	5147.08	+	2971.67i	0.177744	+	0.102620i
$944$	121481.			4.18841
$945$		0			0
$946$	8250.48			0.283558
$947$	28502.4	+	16455.9i	0.978039	+	0.564671i	0.901678	−	0.432409i	$-0.142336\pi$
$947$	28502.4	+	16455.9i	0.978039	+	0.564671i	0.0763615	+	0.997080i	$0.475670\pi$
$948$	−37585.8	−	48135.8i	−1.28769	−	1.64913i
$949$	−7927.21	−	13730.3i	−0.271157	−	0.469658i
$950$		0			0
$951$	−6079.83	−	43349.3i	−0.207310	−	1.47813i
$952$	−83828.5	−	48398.4i	−2.85388	−	1.64769i
$953$		−	21564.5i		−	0.732993i	−0.930419	−	0.366497i	$-0.880557\pi$
$953$		−	21564.5i		−	0.732993i	0.930419	−	0.366497i	$-0.119443\pi$
$954$	30681.9	+	29662.8i	1.04126	+	1.00668i
$955$		0			0
$956$	18109.3	−	31366.2i	0.612653	−	1.06115i
$957$	4997.47	−	12359.1i	0.168804	−	0.417464i
$958$	13555.0	−	7825.98i	0.457142	−	0.263931i
$959$	3181.41	+	5510.36i	0.107125	+	0.185546i
$960$		0			0
$961$	11959.5	−	20714.5i	0.401448	−	0.695328i
$962$			7247.40i			0.242895i
$963$	−15343.9	−	3834.89i	−0.513447	−	0.128326i
$964$	117082.			3.91178
$965$		0			0
$966$	3308.40	+	23589.0i	0.110193	+	0.785675i
$967$	−25776.2	+	14881.9i	−0.857193	+	0.494901i	−0.863071	−	0.505082i	$-0.831462\pi$
$967$	−25776.2	+	14881.9i	−0.857193	+	0.494901i	0.00587841	+	0.999983i	$0.498129\pi$
$968$	−70705.2	+	40821.7i	−2.34768	+	1.35543i
$969$	5445.91	−	4252.33i	0.180545	−	0.140975i
$970$		0			0
$971$	29812.3			0.985297			0.492648	−	0.870228i	$-0.336029\pi$
$971$	29812.3			0.985297			0.492648	+	0.870228i	$0.336029\pi$
$972$	−61005.4	+	51042.6i	−2.01311	+	1.68435i
$973$		−	2686.00i		−	0.0884986i
$974$	28032.1	−	48553.1i	0.922184	−	1.59727i
$975$		0			0
$976$	80831.9	+	140005.i	2.65099	+	4.59165i
$977$	4988.07	−	2879.87i	0.163339	−	0.0943041i	−0.416102	−	0.909318i	$-0.636604\pi$
$977$	4988.07	−	2879.87i	0.163339	−	0.0943041i	0.579441	+	0.815014i	$0.303271\pi$
$978$	−64430.3	+	9036.49i	−2.10660	+	0.295455i
$979$	−1641.72	+	2843.54i	−0.0535950	+	0.0928292i
$980$		0			0
$981$	8949.61	−	35808.5i	0.291273	−	1.16542i
$982$		−	78796.5i		−	2.56059i
$983$	15286.6	+	8825.70i	0.495998	+	0.286364i	0.727059	−	0.686575i	$-0.240887\pi$
$983$	15286.6	+	8825.70i	0.495998	+	0.286364i	−0.231062	+	0.972939i	$0.574220\pi$
$984$	−29592.7	−	11966.0i	−0.958722	−	0.387665i
$985$		0			0
$986$	59228.7	+	102587.i	1.91301	+	3.31343i
$987$	5953.70	−	14723.9i	0.192005	−	0.474841i
$988$	13158.7	+	7597.20i	0.423720	+	0.244635i
$989$	8086.63			0.260000
$990$		0			0
$991$	−5186.45			−0.166249			−0.0831246	−	0.996539i	$-0.526490\pi$
$991$	−5186.45			−0.166249			−0.0831246	+	0.996539i	$0.526490\pi$
$992$	37509.7	+	21656.2i	1.20054	+	0.693131i
$993$	1325.94	−	185.966i	0.0423740	−	0.00594305i
$994$	−25192.6	−	43634.8i	−0.803884	−	1.39237i
$995$		0			0
$996$	104996.	−	81984.4i	3.34030	−	2.60821i
$997$	−13951.9	−	8055.12i	−0.443190	−	0.255876i	0.261760	−	0.965133i	$-0.415697\pi$
$997$	−13951.9	−	8055.12i	−0.443190	−	0.255876i	−0.704950	+	0.709257i	$0.749030\pi$
$998$			43978.6i			1.39491i
$999$	1280.42	+	2882.47i	0.0405514	+	0.0912885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.d.124.14		28
5.2	odd	4		45.4.e.c.16.1	✓	14
5.3	odd	4		225.4.e.d.151.7		14
5.4	even	2	inner	225.4.k.d.124.1		28
9.4	even	3	inner	225.4.k.d.49.1		28
15.2	even	4		135.4.e.c.46.7		14
45.2	even	12		405.4.a.n.1.1		7
45.4	even	6	inner	225.4.k.d.49.14		28
45.7	odd	12		405.4.a.m.1.7		7
45.13	odd	12		225.4.e.d.76.7		14
45.22	odd	12		45.4.e.c.31.1	yes	14
45.32	even	12		135.4.e.c.91.7		14
45.38	even	12		2025.4.a.ba.1.7		7
45.43	odd	12		2025.4.a.bb.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.1	✓	14	5.2	odd	4
45.4.e.c.31.1	yes	14	45.22	odd	12
135.4.e.c.46.7		14	15.2	even	4
135.4.e.c.91.7		14	45.32	even	12
225.4.e.d.76.7		14	45.13	odd	12
225.4.e.d.151.7		14	5.3	odd	4
225.4.k.d.49.1		28	9.4	even	3	inner
225.4.k.d.49.14		28	45.4	even	6	inner
225.4.k.d.124.1		28	5.4	even	2	inner
225.4.k.d.124.14		28	1.1	even	1	trivial
405.4.a.m.1.7		7	45.7	odd	12
405.4.a.n.1.1		7	45.2	even	12
2025.4.a.ba.1.7		7	45.38	even	12
2025.4.a.bb.1.1		7	45.43	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)

\(f(q)\)	\(=\)	\(q+(4.66357 + 2.69252i) q^{2} +(-3.19791 - 4.09553i) q^{3} +(10.4993 + 18.1853i) q^{4} +(-3.88642 - 27.7102i) q^{6} +(10.8861 + 6.28510i) q^{7} +69.9976i q^{8} +(-6.54673 + 26.1943i) q^{9} +O(q^{10})\)	\(q+(4.66357 + 2.69252i) q^{2} +(-3.19791 - 4.09553i) q^{3} +(10.4993 + 18.1853i) q^{4} +(-3.88642 - 27.7102i) q^{6} +(10.8861 + 6.28510i) q^{7} +69.9976i q^{8} +(-6.54673 + 26.1943i) q^{9} +(-6.41534 + 11.1117i) q^{11} +(40.9026 - 101.155i) q^{12} +(51.8442 - 29.9322i) q^{13} +(33.8455 + 58.6220i) q^{14} +(-104.475 + 180.957i) q^{16} +110.011i q^{17} +(-101.060 + 104.532i) q^{18} +12.0872 q^{19} +(-9.07201 - 64.6836i) q^{21} +(-59.8368 + 34.5468i) q^{22} +(-58.6485 + 33.8608i) q^{23} +(286.677 - 223.846i) q^{24} +322.372 q^{26} +(128.215 - 56.9547i) q^{27} +263.956i q^{28} +(99.9790 - 173.169i) q^{29} +(-38.3143 - 66.3624i) q^{31} +(-489.500 + 282.613i) q^{32} +(66.0240 - 9.26000i) q^{33} +(-296.206 + 513.044i) q^{34} +(-545.086 + 155.967i) q^{36} +22.4815i q^{37} +(56.3694 + 32.5449i) q^{38} +(-288.381 - 116.609i) q^{39} +(-43.8807 - 76.0037i) q^{41} +(131.854 - 326.083i) q^{42} +(-103.412 - 59.7050i) q^{43} -269.426 q^{44} -364.682 q^{46} +(210.579 + 121.578i) q^{47} +(1075.22 - 150.801i) q^{48} +(-92.4951 - 160.206i) q^{49} +(450.553 - 351.805i) q^{51} +(1088.65 + 628.534i) q^{52} -293.518i q^{53} +(751.293 + 79.6094i) q^{54} +(-439.942 + 762.002i) q^{56} +(-38.6537 - 49.5034i) q^{57} +(932.519 - 538.390i) q^{58} +(-290.692 - 503.493i) q^{59} +(386.847 - 670.038i) q^{61} -412.648i q^{62} +(-235.902 + 244.007i) q^{63} -1372.15 q^{64} +(332.840 + 134.586i) q^{66} +(200.431 - 115.719i) q^{67} +(-2000.58 + 1155.03i) q^{68} +(326.231 + 131.913i) q^{69} -744.342 q^{71} +(-1833.54 - 458.255i) q^{72} -264.839i q^{73} +(-60.5317 + 104.844i) q^{74} +(126.907 + 219.809i) q^{76} +(-139.676 + 80.6421i) q^{77} +(-1030.92 - 1320.28i) q^{78} +(279.858 - 484.729i) q^{79} +(-643.281 - 342.974i) q^{81} -472.598i q^{82} +(1057.32 + 610.443i) q^{83} +(1081.04 - 844.108i) q^{84} +(-321.513 - 556.878i) q^{86} +(-1028.94 + 144.311i) q^{87} +(-777.792 - 449.059i) q^{88} +255.905 q^{89} +752.509 q^{91} +(-1231.53 - 711.027i) q^{92} +(-149.263 + 369.138i) q^{93} +(654.699 + 1133.97i) q^{94} +(2722.83 + 1100.99i) q^{96} +(908.909 + 524.759i) q^{97} -996.177i q^{98} +(-249.064 - 240.791i) 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

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