LMFDB - Embedded newform 124.5.o.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, 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:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	124.13
Dual form			124.5.o.a.105.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.78469 + 6.25452i) q^{3} +(-8.17325 - 14.1565i) q^{5} +(16.4871 + 18.3107i) q^{7} +(22.8350 - 25.3609i) q^{9} +O(q^{10})$	\(q+(2.78469 + 6.25452i) q^{3} +(-8.17325 - 14.1565i) q^{5} +(16.4871 + 18.3107i) q^{7} +(22.8350 - 25.3609i) q^{9} +(30.4863 + 143.427i) q^{11} +(158.932 + 16.7044i) q^{13} +(65.7820 - 90.5412i) q^{15} +(-8.31215 + 39.1056i) q^{17} +(65.5333 + 623.508i) q^{19} +(-68.6135 + 154.108i) q^{21} +(-590.526 + 191.873i) q^{23} +(178.896 - 309.857i) q^{25} +(749.627 + 243.569i) q^{27} +(305.995 + 421.165i) q^{29} +(-734.024 + 620.266i) q^{31} +(-812.170 + 590.076i) q^{33} +(124.463 - 383.057i) q^{35} +(169.328 + 97.7618i) q^{37} +(338.098 + 1040.56i) q^{39} +(1968.66 + 876.503i) q^{41} +(3155.91 - 331.699i) q^{43} +(-545.657 - 115.983i) q^{45} +(389.423 + 282.932i) q^{47} +(187.513 - 1784.07i) q^{49} +(-267.734 + 56.9085i) q^{51} +(-2438.93 - 2196.02i) q^{53} +(1781.24 - 1603.84i) q^{55} +(-3717.26 + 2146.16i) q^{57} +(-3437.39 + 1530.43i) q^{59} -430.679i q^{61} +840.859 q^{63} +(-1062.51 - 2386.44i) q^{65} +(-3094.99 - 5360.69i) q^{67} +(-2844.51 - 3159.15i) q^{69} +(459.499 - 510.325i) q^{71} +(-77.4438 - 364.345i) q^{73} +(2436.18 + 256.053i) q^{75} +(-2123.62 + 2922.91i) q^{77} +(1912.50 - 8997.63i) q^{79} +(275.134 + 2617.73i) q^{81} +(2525.08 - 5671.42i) q^{83} +(621.535 - 201.949i) q^{85} +(-1782.09 + 3086.67i) q^{87} +(-5028.80 - 1633.96i) q^{89} +(2314.45 + 3185.57i) q^{91} +(-5923.50 - 2863.72i) q^{93} +(8291.06 - 6023.81i) q^{95} +(-4628.10 + 14243.8i) q^{97} +(4333.58 + 2501.99i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{11}{30}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.78469	+	6.25452i	0.309410	+	0.694947i	0.999588	−	0.0286927i	$-0.00913443\pi$
$3$	2.78469	+	6.25452i	0.309410	+	0.694947i	−0.690178	+	0.723640i	$0.742468\pi$
$4$		0			0
$5$	−8.17325	−	14.1565i	−0.326930	−	0.566259i	0.654971	−	0.755654i	$-0.272681\pi$
$5$	−8.17325	−	14.1565i	−0.326930	−	0.566259i	−0.981901	+	0.189395i	$0.939347\pi$
$6$		0			0
$7$	16.4871	+	18.3107i	0.336471	+	0.373688i	0.887508	−	0.460792i	$-0.152435\pi$
$7$	16.4871	+	18.3107i	0.336471	+	0.373688i	−0.551038	+	0.834480i	$0.685768\pi$
$8$		0			0
$9$	22.8350	−	25.3609i	0.281914	−	0.313097i
$10$		0			0
$11$	30.4863	+	143.427i	0.251952	+	1.18534i	0.904123	+	0.427271i	$0.140525\pi$
$11$	30.4863	+	143.427i	0.251952	+	1.18534i	−0.652171	+	0.758072i	$0.726142\pi$
$12$		0			0
$13$	158.932	+	16.7044i	0.940425	+	0.0988427i	0.562320	−	0.826920i	$-0.309909\pi$
$13$	158.932	+	16.7044i	0.940425	+	0.0988427i	0.378105	+	0.925763i	$0.376576\pi$
$14$		0			0
$15$	65.7820	−	90.5412i	0.292365	−	0.402405i
$16$		0			0
$17$	−8.31215	+	39.1056i	−0.0287618	+	0.135313i	−0.990186	−	0.139757i	$-0.955368\pi$
$17$	−8.31215	+	39.1056i	−0.0287618	+	0.135313i	0.961424	+	0.275070i	$0.0887012\pi$
$18$		0			0
$19$	65.5333	+	623.508i	0.181533	+	1.72717i	0.584016	+	0.811742i	$0.301480\pi$
$19$	65.5333	+	623.508i	0.181533	+	1.72717i	−0.402483	+	0.915427i	$0.631853\pi$
$20$		0			0
$21$	−68.6135	+	154.108i	−0.155586	+	0.349452i
$22$		0			0
$23$	−590.526	+	191.873i	−1.11631	+	0.362710i	−0.808357	−	0.588693i	$-0.799643\pi$
$23$	−590.526	+	191.873i	−1.11631	+	0.362710i	−0.307949	+	0.951403i	$0.599643\pi$
$24$		0			0
$25$	178.896	−	309.857i	0.286234	−	0.495771i
$26$		0			0
$27$	749.627	+	243.569i	1.02830	+	0.334113i
$28$		0			0
$29$	305.995	+	421.165i	0.363846	+	0.500791i	0.951215	−	0.308528i	$-0.0998363\pi$
$29$	305.995	+	421.165i	0.363846	+	0.500791i	−0.587369	+	0.809319i	$0.699836\pi$
$30$		0			0
$31$	−734.024	+	620.266i	−0.763812	+	0.645438i
$31$	−734.024	+	620.266i	−0.763812	+	0.645438i
$32$		0			0
$33$	−812.170	+	590.076i	−0.745794	+	0.541851i
$34$		0			0
$35$	124.463	−	383.057i	0.101602	−	0.312699i
$36$		0			0
$37$	169.328	+	97.7618i	0.123688	+	0.0714111i	0.560567	−	0.828109i	$-0.310583\pi$
$37$	169.328	+	97.7618i	0.123688	+	0.0714111i	−0.436880	+	0.899520i	$0.643916\pi$
$38$		0			0
$39$	338.098	+	1040.56i	0.222287	+	0.684129i
$40$		0			0
$41$	1968.66	+	876.503i	1.17112	+	0.521418i	0.897757	−	0.440492i	$-0.145196\pi$
$41$	1968.66	+	876.503i	1.17112	+	0.521418i	0.273367	+	0.961910i	$0.411863\pi$
$42$		0			0
$43$	3155.91	−	331.699i	1.70682	−	0.179394i	0.799737	−	0.600351i	$-0.204972\pi$
$43$	3155.91	−	331.699i	1.70682	−	0.179394i	0.907081	+	0.420957i	$0.138306\pi$
$44$		0			0
$45$	−545.657	−	115.983i	−0.269460	−	0.0572756i
$46$		0			0
$47$	389.423	+	282.932i	0.176289	+	0.128082i	0.672431	−	0.740160i	$-0.265250\pi$
$47$	389.423	+	282.932i	0.176289	+	0.128082i	−0.496142	+	0.868242i	$0.665250\pi$
$48$		0			0
$49$	187.513	−	1784.07i	0.0780979	−	0.743052i
$50$		0			0
$51$	−267.734	+	56.9085i	−0.102935	+	0.0218795i
$52$		0			0
$53$	−2438.93	−	2196.02i	−0.868255	−	0.781780i	0.108957	−	0.994046i	$-0.465249\pi$
$53$	−2438.93	−	2196.02i	−0.868255	−	0.781780i	−0.977212	+	0.212266i	$0.931916\pi$
$54$		0			0
$55$	1781.24	−	1603.84i	0.588841	−	0.530194i
$56$		0			0
$57$	−3717.26	+	2146.16i	−1.14412	+	0.660560i
$58$		0			0
$59$	−3437.39	+	1530.43i	−0.987473	+	0.439651i	−0.835952	−	0.548803i	$-0.815084\pi$
$59$	−3437.39	+	1530.43i	−0.987473	+	0.439651i	−0.151521	+	0.988454i	$0.548417\pi$
$60$		0			0
$61$		−	430.679i		−	0.115743i	−0.998324	−	0.0578715i	$-0.981569\pi$
$61$		−	430.679i		−	0.115743i	0.998324	−	0.0578715i	$-0.0184314\pi$
$62$		0			0
$63$	840.859			0.211857
$64$		0			0
$65$	−1062.51	−	2386.44i	−0.251482	−	0.564839i
$66$		0			0
$67$	−3094.99	−	5360.69i	−0.689462	−	1.19418i	−0.972012	−	0.234930i	$-0.924514\pi$
$67$	−3094.99	−	5360.69i	−0.689462	−	1.19418i	0.282551	−	0.959252i	$-0.408820\pi$
$68$		0			0
$69$	−2844.51	−	3159.15i	−0.597460	−	0.663547i
$70$		0			0
$71$	459.499	−	510.325i	0.0911524	−	0.101235i	−0.695843	−	0.718194i	$-0.744969\pi$
$71$	459.499	−	510.325i	0.0911524	−	0.101235i	0.786995	+	0.616959i	$0.211636\pi$
$72$		0			0
$73$	−77.4438	−	364.345i	−0.0145325	−	0.0683702i	0.970284	−	0.241970i	$-0.0777935\pi$
$73$	−77.4438	−	364.345i	−0.0145325	−	0.0683702i	−0.984816	+	0.173600i	$0.944460\pi$
$74$		0			0
$75$	2436.18	+	256.053i	0.433098	+	0.0455205i
$76$		0			0
$77$	−2123.62	+	2922.91i	−0.358174	+	0.492985i
$78$		0			0
$79$	1912.50	−	8997.63i	0.306442	−	1.44170i	−0.507953	−	0.861385i	$-0.669598\pi$
$79$	1912.50	−	8997.63i	0.306442	−	1.44170i	0.814395	−	0.580311i	$-0.197069\pi$
$80$		0			0
$81$	275.134	+	2617.73i	0.0419348	+	0.398983i
$82$		0			0
$83$	2525.08	−	5671.42i	0.366538	−	0.823257i	−0.632285	−	0.774736i	$-0.717883\pi$
$83$	2525.08	−	5671.42i	0.366538	−	0.823257i	0.998822	−	0.0485206i	$-0.0154507\pi$
$84$		0			0
$85$	621.535	−	201.949i	0.0860256	−	0.0279514i
$86$		0			0
$87$	−1782.09	+	3086.67i	−0.235446	+	0.407804i
$88$		0			0
$89$	−5028.80	−	1633.96i	−0.634869	−	0.206282i	−0.0261385	−	0.999658i	$-0.508321\pi$
$89$	−5028.80	−	1633.96i	−0.634869	−	0.206282i	−0.608731	+	0.793377i	$0.708321\pi$
$90$		0			0
$91$	2314.45	+	3185.57i	0.279489	+	0.384684i
$92$		0			0
$93$	−5923.50	−	2863.72i	−0.684877	−	0.331104i
$94$		0			0
$95$	8291.06	−	6023.81i	0.918677	−	0.667458i
$96$		0			0
$97$	−4628.10	+	14243.8i	−0.491880	+	1.51385i	0.329882	+	0.944022i	$0.392991\pi$
$97$	−4628.10	+	14243.8i	−0.491880	+	1.51385i	−0.821763	+	0.569830i	$0.807009\pi$
$98$		0			0
$99$	4333.58	+	2501.99i	0.442157	+	0.255279i
$100$		0			0
$101$	−4310.84	−	13267.4i	−0.422590	−	1.30060i	−0.905283	−	0.424809i	$-0.860341\pi$
$101$	−4310.84	−	13267.4i	−0.422590	−	1.30060i	0.482692	−	0.875790i	$-0.339659\pi$
$102$		0			0
$103$	−1524.60	−	678.794i	−0.143708	−	0.0639829i	0.333623	−	0.942707i	$-0.391729\pi$
$103$	−1524.60	−	678.794i	−0.143708	−	0.0639829i	−0.477331	+	0.878724i	$0.658396\pi$
$104$		0			0
$105$	2742.43	−	288.241i	0.248746	−	0.0261443i
$106$		0			0
$107$	7718.72	+	1640.66i	0.674183	+	0.143302i	0.532267	−	0.846577i	$-0.321340\pi$
$107$	7718.72	+	1640.66i	0.674183	+	0.143302i	0.141916	+	0.989879i	$0.454674\pi$
$108$		0			0
$109$	6341.73	+	4607.54i	0.533771	+	0.387807i	0.821766	−	0.569825i	$-0.192989\pi$
$109$	6341.73	+	4607.54i	0.533771	+	0.387807i	−0.287996	+	0.957632i	$0.592989\pi$
$110$		0			0
$111$	−139.926	+	1331.30i	−0.0113567	+	0.108052i
$112$		0			0
$113$	−621.530	+	132.110i	−0.0486749	+	0.0103462i	−0.232185	−	0.972672i	$-0.574587\pi$
$113$	−621.530	+	132.110i	−0.0486749	+	0.0103462i	0.183510	+	0.983018i	$0.441254\pi$
$114$		0			0
$115$	7542.76	+	6791.53i	0.570341	+	0.513538i
$116$		0			0
$117$	4052.85	−	3649.21i	0.296066	−	0.266579i
$118$		0			0
$119$	−853.095	+	492.534i	−0.0602426	+	0.0347811i
$120$		0			0
$121$	−6266.54	+	2790.04i	−0.428013	+	0.190564i
$122$		0			0
$123$			14753.8i			0.975201i
$124$		0			0
$125$	−16065.2			−1.02817
$126$		0			0
$127$	7525.04	+	16901.5i	0.466553	+	1.04790i	0.981637	+	0.190756i	$0.0610941\pi$
$127$	7525.04	+	16901.5i	0.466553	+	1.04790i	−0.515084	+	0.857140i	$0.672239\pi$
$128$		0			0
$129$	10862.8	+	18815.0i	0.652776	+	1.13064i
$130$		0			0
$131$	−2028.19	−	2252.54i	−0.118186	−	0.131259i	0.681148	−	0.732146i	$-0.261481\pi$
$131$	−2028.19	−	2252.54i	−0.118186	−	0.131259i	−0.799334	+	0.600887i	$0.794814\pi$
$132$		0			0
$133$	−10336.4	+	11479.8i	−0.584343	+	0.648978i
$134$		0			0
$135$	−2678.81	−	12602.8i	−0.146986	−	0.691513i
$136$		0			0
$137$	2873.49	+	302.016i	0.153098	+	0.0160912i	0.180767	−	0.983526i	$-0.442142\pi$
$137$	2873.49	+	302.016i	0.153098	+	0.0160912i	−0.0276696	+	0.999617i	$0.508809\pi$
$138$		0			0
$139$	16534.4	−	22757.7i	0.855774	−	1.17787i	−0.126786	−	0.991930i	$-0.540466\pi$
$139$	16534.4	−	22757.7i	0.855774	−	1.17787i	0.982561	−	0.185942i	$-0.0595338\pi$
$140$		0			0
$141$	−685.183	+	3223.53i	−0.0344642	+	0.162141i
$142$		0			0
$143$	2449.38	+	23304.3i	0.119780	+	1.13963i
$144$		0			0
$145$	3461.25	−	7774.09i	0.164625	−	0.369755i
$146$		0			0
$147$	11680.7	−	3795.27i	0.540546	−	0.175634i
$148$		0			0
$149$	−17414.5	+	30162.8i	−0.784401	+	1.35862i	0.144955	+	0.989438i	$0.453696\pi$
$149$	−17414.5	+	30162.8i	−0.784401	+	1.35862i	−0.929356	+	0.369185i	$0.879637\pi$
$150$		0			0
$151$	−15916.3	−	5171.53i	−0.698054	−	0.226811i	−0.0615715	−	0.998103i	$-0.519611\pi$
$151$	−15916.3	−	5171.53i	−0.698054	−	0.226811i	−0.636482	+	0.771291i	$0.719611\pi$
$152$		0			0
$153$	801.944	+	1103.78i	0.0342579	+	0.0471520i
$154$		0			0
$155$	14780.1	+	5321.60i	0.615198	+	0.221503i
$156$		0			0
$157$	−5463.52	+	3969.48i	−0.221653	+	0.161040i	−0.693070	−	0.720870i	$-0.743743\pi$
$157$	−5463.52	+	3969.48i	−0.221653	+	0.161040i	0.471417	+	0.881910i	$0.343743\pi$
$158$		0			0
$159$	6943.39	−	21369.6i	0.274649	−	0.845282i
$160$		0			0
$161$	−13249.4	−	7649.53i	−0.511144	−	0.295109i
$162$		0			0
$163$	8079.48	+	24866.1i	0.304094	+	0.935906i	0.980014	+	0.198930i	$0.0637467\pi$
$163$	8079.48	+	24866.1i	0.304094	+	0.935906i	−0.675920	+	0.736975i	$0.736253\pi$
$164$		0			0
$165$	14991.5	+	6674.63i	0.550650	+	0.245165i
$166$		0			0
$167$	−13654.2	+	1435.12i	−0.489592	+	0.0514581i	−0.346108	−	0.938195i	$-0.612497\pi$
$167$	−13654.2	+	1435.12i	−0.489592	+	0.0514581i	−0.143483	+	0.989653i	$0.545830\pi$
$168$		0			0
$169$	−2956.58	−	628.440i	−0.103518	−	0.0220034i
$170$		0			0
$171$	17309.2	+	12575.9i	0.591949	+	0.430076i
$172$		0			0
$173$	3939.18	−	37478.8i	0.131617	−	1.25226i	−0.706873	−	0.707340i	$-0.749895\pi$
$173$	3939.18	−	37478.8i	0.131617	−	1.25226i	0.838491	−	0.544916i	$-0.183439\pi$
$174$		0			0
$175$	8623.18	−	1832.91i	0.281573	−	0.0598502i
$176$		0			0
$177$	−19144.2	−	17237.5i	−0.611068	−	0.550208i
$178$		0			0
$179$	−31321.7	+	28202.2i	−0.977551	+	0.880191i	−0.992811	−	0.119693i	$-0.961809\pi$
$179$	−31321.7	+	28202.2i	−0.977551	+	0.880191i	0.0152601	+	0.999884i	$0.495142\pi$
$180$		0			0
$181$	40213.9	−	23217.5i	1.22749	−	0.708693i	0.260987	−	0.965342i	$-0.415952\pi$
$181$	40213.9	−	23217.5i	1.22749	−	0.708693i	0.966505	+	0.256649i	$0.0826186\pi$
$182$		0			0
$183$	2693.69	−	1199.31i	0.0804352	−	0.0358121i
$184$		0			0
$185$		−	3196.12i		−	0.0933857i
$186$		0			0
$187$	−5862.18			−0.167639
$188$		0			0
$189$	7899.23	+	17742.0i	0.221137	+	0.496681i
$190$		0			0
$191$	−29228.8	−	50625.8i	−0.801206	−	1.38773i	−0.918823	−	0.394671i	$-0.870859\pi$
$191$	−29228.8	−	50625.8i	−0.801206	−	1.38773i	0.117616	−	0.993059i	$-0.462475\pi$
$192$		0			0
$193$	23864.1	+	26503.7i	0.640663	+	0.711529i	0.972785	−	0.231708i	$-0.0744313\pi$
$193$	23864.1	+	26503.7i	0.640663	+	0.711529i	−0.332122	+	0.943236i	$0.607765\pi$
$194$		0			0
$195$	11967.3	−	13291.0i	0.314722	−	0.349534i
$196$		0			0
$197$	−11156.6	−	52487.8i	−0.287475	−	1.35246i	−0.850479	−	0.526009i	$-0.823688\pi$
$197$	−11156.6	−	52487.8i	−0.287475	−	1.35246i	0.563004	−	0.826454i	$-0.309646\pi$
$198$		0			0
$199$	19767.0	+	2077.60i	0.499155	+	0.0524633i	0.350761	−	0.936465i	$-0.385923\pi$
$199$	19767.0	+	2077.60i	0.499155	+	0.0524633i	0.148394	+	0.988928i	$0.452590\pi$
$200$		0			0
$201$	24909.9	−	34285.6i	0.616567	−	0.848632i
$202$		0			0
$203$	−2666.90	+	12546.8i	−0.0647164	+	0.304467i
$204$		0			0
$205$	−3682.13	−	35033.2i	−0.0876177	−	0.833626i
$206$		0			0
$207$	−8618.60	+	19357.7i	−0.201139	+	0.451765i
$208$		0			0
$209$	−87429.7	+	28407.6i	−2.00155	+	0.650343i
$210$		0			0
$211$	1151.89	−	1995.13i	0.0258730	−	0.0448133i	−0.852799	−	0.522239i	$-0.825097\pi$
$211$	1151.89	−	1995.13i	0.0258730	−	0.0448133i	0.878672	+	0.477426i	$0.158430\pi$
$212$		0			0
$213$	4471.40	+	1452.85i	0.0985564	+	0.0320229i
$214$		0			0
$215$	−30489.7	−	41965.5i	−0.659593	−	0.907852i
$216$		0			0
$217$	−23459.4	−	3214.15i	−0.498193	−	0.0682569i
$218$		0			0
$219$	2063.14	−	1498.96i	0.0430171	−	0.0312538i
$220$		0			0
$221$	−1974.30	+	6076.27i	−0.0404230	+	0.124409i
$222$		0			0
$223$	−23448.2	−	13537.8i	−0.471519	−	0.272232i	0.245356	−	0.969433i	$-0.421095\pi$
$223$	−23448.2	−	13537.8i	−0.471519	−	0.272232i	−0.716875	+	0.697201i	$0.754428\pi$
$224$		0			0
$225$	−3773.15	−	11612.6i	−0.0745314	−	0.229384i
$226$		0			0
$227$	−65803.8	−	29297.7i	−1.27702	−	0.568568i	−0.347622	−	0.937635i	$-0.613011\pi$
$227$	−65803.8	−	29297.7i	−1.27702	−	0.568568i	−0.929403	+	0.369067i	$0.879677\pi$
$228$		0			0
$229$	19379.5	−	2036.86i	0.369548	−	0.0388411i	0.0820655	−	0.996627i	$-0.473848\pi$
$229$	19379.5	−	2036.86i	0.369548	−	0.0388411i	0.287483	+	0.957786i	$0.407182\pi$
$230$		0			0
$231$	−24195.0	−	5142.81i	−0.453421	−	0.0963776i
$232$		0			0
$233$	33195.5	+	24118.0i	0.611460	+	0.444252i	0.849928	−	0.526899i	$-0.176645\pi$
$233$	33195.5	+	24118.0i	0.611460	+	0.444252i	−0.238468	+	0.971150i	$0.576645\pi$
$234$		0			0
$235$	822.476	−	7825.33i	0.0148932	−	0.141699i
$236$		0			0
$237$	61601.6	−	13093.8i	1.09672	−	0.233115i
$238$		0			0
$239$	−44081.5	−	39691.2i	−0.771722	−	0.694862i	0.186002	−	0.982549i	$-0.440447\pi$
$239$	−44081.5	−	39691.2i	−0.771722	−	0.694862i	−0.957724	+	0.287688i	$0.907114\pi$
$240$		0			0
$241$	15819.5	−	14243.9i	0.272369	−	0.245243i	−0.521614	−	0.853181i	$-0.674670\pi$
$241$	15819.5	−	14243.9i	0.272369	−	0.245243i	0.793984	+	0.607939i	$0.208003\pi$
$242$		0			0
$243$	39684.6	−	22911.9i	0.672062	−	0.388015i
$244$		0			0
$245$	−26788.7	+	11927.1i	−0.446292	+	0.198702i
$246$		0			0
$247$			100190.i			1.64222i
$248$		0			0
$249$	42503.6			0.685530
$250$		0			0
$251$	12971.0	+	29133.4i	0.205886	+	0.462428i	0.986745	−	0.162280i	$-0.0518848\pi$
$251$	12971.0	+	29133.4i	0.205886	+	0.462428i	−0.780859	+	0.624708i	$0.785218\pi$
$252$		0			0
$253$	−45522.6	−	78847.5i	−0.711191	−	1.23182i
$254$		0			0
$255$	2993.88	+	3325.04i	0.0460419	+	0.0511347i
$256$		0			0
$257$	−57288.3	+	63625.1i	−0.867361	+	0.963302i	−0.999610	−	0.0279148i	$-0.991113\pi$
$257$	−57288.3	+	63625.1i	−0.867361	+	0.963302i	0.132250	+	0.991216i	$0.457780\pi$
$258$		0			0
$259$	1001.64	+	4712.33i	0.0149318	+	0.0702484i
$260$		0			0
$261$	17668.5	+	1857.04i	0.259370	+	0.0272609i
$262$		0			0
$263$	−758.215	+	1043.59i	−0.0109618	+	0.0150876i	−0.814463	−	0.580216i	$-0.802968\pi$
$263$	−758.215	+	1043.59i	−0.0109618	+	0.0150876i	0.803501	+	0.595303i	$0.202968\pi$
$264$		0			0
$265$	−11154.0	+	52475.2i	−0.158832	+	0.747244i
$266$		0			0
$267$	−3784.05	−	36002.8i	−0.0530804	−	0.505026i
$268$		0			0
$269$	21550.8	−	48403.8i	0.297823	−	0.668921i	−0.701207	−	0.712958i	$-0.747355\pi$
$269$	21550.8	−	48403.8i	0.297823	−	0.668921i	0.999030	+	0.0440364i	$0.0140218\pi$
$270$		0			0
$271$	56232.7	−	18271.1i	0.765686	−	0.248786i	0.0999686	−	0.994991i	$-0.468126\pi$
$271$	56232.7	−	18271.1i	0.765686	−	0.248786i	0.665717	+	0.746204i	$0.268126\pi$
$272$		0			0
$273$	−13479.2	+	23346.6i	−0.180858	+	0.313255i
$274$		0			0
$275$	49895.6	+	16212.1i	0.659777	+	0.214374i
$276$		0			0
$277$	40117.1	+	55216.5i	0.522841	+	0.719630i	0.986018	−	0.166636i	$-0.0532906\pi$
$277$	40117.1	+	55216.5i	0.522841	+	0.719630i	−0.463177	+	0.886266i	$0.653291\pi$
$278$		0			0
$279$	−1030.97	+	32779.3i	−0.0132445	+	0.421106i
$280$		0			0
$281$	57643.5	−	41880.4i	0.730024	−	0.530394i	−0.159547	−	0.987190i	$-0.551003\pi$
$281$	57643.5	−	41880.4i	0.730024	−	0.530394i	0.889571	+	0.456797i	$0.151003\pi$
$282$		0			0
$283$	9561.31	−	29426.7i	0.119384	−	0.367425i	−0.873453	−	0.486909i	$-0.838124\pi$
$283$	9561.31	−	29426.7i	0.119384	−	0.367425i	0.992836	+	0.119485i	$0.0381242\pi$
$284$		0			0
$285$	60764.1	+	35082.2i	0.748096	+	0.431913i
$286$		0			0
$287$	16408.0	+	50498.5i	0.199201	+	0.613077i
$288$		0			0
$289$	74840.1	+	33320.9i	0.896063	+	0.398953i
$290$		0			0
$291$	−101976.	+	10718.1i	−1.20424	+	0.126571i
$292$		0			0
$293$	126821.	+	26956.7i	1.47726	+	0.314002i	0.874932	−	0.484246i	$-0.160906\pi$
$293$	126821.	+	26956.7i	1.47726	+	0.314002i	0.602329	+	0.798248i	$0.294239\pi$
$294$		0			0
$295$	49760.1	+	36152.8i	0.571791	+	0.415430i
$296$		0			0
$297$	−12080.9	+	114942.i	−0.136958	+	1.30306i
$298$		0			0
$299$	−97058.5	+	20630.4i	−1.08565	+	0.230763i
$300$		0			0
$301$	58105.2	+	52318.2i	0.641331	+	0.577457i
$302$		0			0
$303$	70977.0	−	63907.9i	0.773094	−	0.696097i
$304$		0			0
$305$	−6096.90	+	3520.05i	−0.0655405	+	0.0378398i
$306$		0			0
$307$	−93257.6	+	41521.0i	−0.989481	+	0.440545i	−0.836668	−	0.547710i	$-0.815500\pi$
$307$	−93257.6	+	41521.0i	−0.989481	+	0.440545i	−0.152813	+	0.988255i	$0.548833\pi$
$308$		0			0
$309$		−	11425.9i		−	0.119666i
$310$		0			0
$311$	−113108.			−1.16943			−0.584713	−	0.811240i	$-0.698793\pi$
$311$	−113108.			−1.16943			−0.584713	+	0.811240i	$0.698793\pi$
$312$		0			0
$313$	17594.6	+	39518.2i	0.179594	+	0.403375i	0.980801	−	0.195013i	$-0.0624749\pi$
$313$	17594.6	+	39518.2i	0.179594	+	0.403375i	−0.801207	+	0.598388i	$0.795808\pi$
$314$		0			0
$315$	−6872.55	−	11903.6i	−0.0692623	−	0.119966i
$316$		0			0
$317$	−103748.	−	115223.i	−1.03243	−	1.14663i	−0.989052	−	0.147567i	$-0.952856\pi$
$317$	−103748.	−	115223.i	−1.03243	−	1.14663i	−0.0433743	−	0.999059i	$-0.513811\pi$
$318$		0			0
$319$	−51077.7	+	56727.5i	−0.501937	+	0.557458i
$320$		0			0
$321$	11232.7	+	52845.7i	0.109012	+	0.512861i
$322$		0			0
$323$	−24927.4	−	2619.97i	−0.238930	−	0.0251126i
$324$		0			0
$325$	33608.3	−	46257.8i	0.318185	−	0.437944i
$326$		0			0
$327$	−11158.2	+	52495.1i	−0.104351	+	0.490934i
$328$		0			0
$329$	1239.74	+	11795.3i	0.0114535	+	0.108973i
$330$		0			0
$331$	23941.1	−	53772.6i	0.218518	−	0.490800i	−0.770709	−	0.637187i	$-0.780098\pi$
$331$	23941.1	−	53772.6i	0.218518	−	0.490800i	0.989227	+	0.146387i	$0.0467645\pi$
$332$		0			0
$333$	6345.95	−	2061.92i	0.0572279	−	0.0185945i
$334$		0			0
$335$	−50592.3	+	87628.4i	−0.450811	+	0.780828i
$336$		0			0
$337$	52.0392	+	16.9086i	0.000458217	+	0.000148884i	0.309246	−	0.950982i	$-0.399923\pi$
$337$	52.0392	+	16.9086i	0.000458217	+	0.000148884i	−0.308788	+	0.951131i	$0.599923\pi$
$338$		0			0
$339$	−2557.06	−	3519.49i	−0.0222506	−	0.0306253i
$340$		0			0
$341$	−111340.	−	86368.9i	−0.957510	−	0.742760i
$342$		0			0
$343$	83620.1	−	60753.6i	0.710759	−	0.516397i
$344$		0			0
$345$	−21473.5	+	66088.7i	−0.180412	+	0.555251i
$346$		0			0
$347$	−38696.0	−	22341.1i	−0.321371	−	0.185544i	0.330632	−	0.943760i	$-0.392738\pi$
$347$	−38696.0	−	22341.1i	−0.321371	−	0.185544i	−0.652004	+	0.758216i	$0.726071\pi$
$348$		0			0
$349$	4934.03	+	15185.4i	0.0405089	+	0.124674i	0.969266	−	0.246016i	$-0.0791215\pi$
$349$	4934.03	+	15185.4i	0.0405089	+	0.124674i	−0.928757	+	0.370689i	$0.879121\pi$
$350$		0			0
$351$	115071.	+	51232.9i	0.934010	+	0.415848i
$352$		0			0
$353$	172552.	−	18135.9i	1.38474	−	0.145543i	0.617335	−	0.786700i	$-0.288212\pi$
$353$	172552.	−	18135.9i	1.38474	−	0.145543i	0.767409	+	0.641158i	$0.221546\pi$
$354$		0			0
$355$	−10980.0	−	2333.87i	−0.0871256	−	0.0185191i
$356$		0			0
$357$	−5456.18	−	3964.14i	−0.0428107	−	0.0311038i
$358$		0			0
$359$	−13768.2	+	130996.i	−0.106829	+	1.01641i	0.801456	+	0.598054i	$0.204059\pi$
$359$	−13768.2	+	130996.i	−0.106829	+	1.01641i	−0.908284	+	0.418353i	$0.862607\pi$
$360$		0			0
$361$	−256995.	+	54625.9i	−1.97201	+	0.419164i
$362$		0			0
$363$	−34900.8	−	31424.8i	−0.264863	−	0.238484i
$364$		0			0
$365$	−4524.87	+	4074.21i	−0.0339641	+	0.0305814i
$366$		0			0
$367$	231140.	−	133449.i	1.71610	−	0.990790i	0.790346	−	0.612661i	$-0.209901\pi$
$367$	231140.	−	133449.i	1.71610	−	0.990790i	0.925753	−	0.378129i	$-0.123432\pi$
$368$		0			0
$369$	67183.3	−	29911.9i	0.493411	−	0.219681i
$370$		0			0
$371$		−	80864.5i		−	0.587503i
$372$		0			0
$373$	134544.			0.967046			0.483523	−	0.875332i	$-0.339357\pi$
$373$	134544.			0.967046			0.483523	+	0.875332i	$0.339357\pi$
$374$		0			0
$375$	−44736.7	−	100480.i	−0.318127	−	0.714526i
$376$		0			0
$377$	41597.0	+	72048.0i	0.292670	+	0.506920i
$378$		0			0
$379$	−91135.1	−	101216.i	−0.634464	−	0.704644i	0.337087	−	0.941474i	$-0.390558\pi$
$379$	−91135.1	−	101216.i	−0.634464	−	0.704644i	−0.971551	+	0.236829i	$0.923892\pi$
$380$		0			0
$381$	−84756.0	+	94131.1i	−0.583876	+	0.648460i
$382$		0			0
$383$	11614.8	+	54643.6i	0.0791801	+	0.372513i	0.999841	−	0.0178510i	$-0.00568246\pi$
$383$	11614.8	+	54643.6i	0.0791801	+	0.372513i	−0.920661	+	0.390364i	$0.872349\pi$
$384$		0			0
$385$	58734.9	+	6173.29i	0.396255	+	0.0416481i
$386$		0			0
$387$	63653.1	−	87610.9i	0.425008	−	0.584974i
$388$		0			0
$389$	57162.5	−	268929.i	0.377757	−	1.77721i	−0.219971	−	0.975506i	$-0.570596\pi$
$389$	57162.5	−	268929.i	0.377757	−	1.77721i	0.597728	−	0.801699i	$-0.296070\pi$
$390$		0			0
$391$	−2594.79	−	24687.7i	−0.0169726	−	0.161483i
$392$		0			0
$393$	8440.65	−	18958.0i	0.0546501	−	0.122746i
$394$		0			0
$395$	−143006.	+	46465.5i	−0.916559	+	0.297808i
$396$		0			0
$397$	37352.6	−	64696.6i	0.236995	−	0.410488i	−0.722855	−	0.690999i	$-0.757171\pi$
$397$	37352.6	−	64696.6i	0.236995	−	0.410488i	0.959851	+	0.280511i	$0.0905041\pi$
$398$		0			0
$399$	−100584.	−	32681.8i	−0.631807	−	0.205287i
$400$		0			0
$401$	−160202.	−	220499.i	−0.996276	−	1.37126i	−0.927583	−	0.373618i	$-0.878117\pi$
$401$	−160202.	−	220499.i	−0.996276	−	1.37126i	−0.0686934	−	0.997638i	$-0.521883\pi$
$402$		0			0
$403$	−127021.	+	86318.6i	−0.782105	+	0.531489i
$404$		0			0
$405$	34809.0	−	25290.3i	0.212218	−	0.154185i
$406$		0			0
$407$	−8859.45	+	27266.6i	−0.0534833	+	0.164605i
$408$		0			0
$409$	2669.31	+	1541.13i	0.0159571	+	0.00921281i	0.507957	−	0.861382i	$-0.330401\pi$
$409$	2669.31	+	1541.13i	0.0159571	+	0.00921281i	−0.492000	+	0.870595i	$0.663734\pi$
$410$		0			0
$411$	6112.82	+	18813.3i	0.0361874	+	0.111373i
$412$		0			0
$413$	−84695.7	−	37708.9i	−0.496548	−	0.221077i
$414$		0			0
$415$	−100925.	+	10607.7i	−0.586009	+	0.0615920i
$416$		0			0
$417$	188382.	+	40041.8i	1.08334	+	0.230272i
$418$		0			0
$419$	199373.	+	144853.i	1.13563	+	0.825087i	0.986505	−	0.163731i	$-0.0523529\pi$
$419$	199373.	+	144853.i	1.13563	+	0.825087i	0.149129	+	0.988818i	$0.452353\pi$
$420$		0			0
$421$	25312.9	−	240837.i	0.142817	−	1.35881i	−0.654872	−	0.755739i	$-0.727278\pi$
$421$	25312.9	−	240837.i	0.142817	−	1.35881i	0.797689	−	0.603069i	$-0.206056\pi$
$422$		0			0
$423$	16067.9	−	3415.34i	0.0898004	−	0.0190877i
$424$		0			0
$425$	10630.1	+	9571.42i	0.0588520	+	0.0529905i
$426$		0			0
$427$	7886.05	−	7100.64i	0.0432518	−	0.0389441i
$428$		0			0
$429$	−138936.	+	80215.0i	−0.754921	+	0.435854i
$430$		0			0
$431$	−77541.1	+	34523.5i	−0.417424	+	0.185849i	−0.604691	−	0.796460i	$-0.706704\pi$
$431$	−77541.1	+	34523.5i	−0.417424	+	0.185849i	0.187268	+	0.982309i	$0.440037\pi$
$432$		0			0
$433$			37138.7i			0.198085i	0.995083	+	0.0990423i	$0.0315779\pi$
$433$			37138.7i			0.198085i	−0.995083	+	0.0990423i	$0.968422\pi$
$434$		0			0
$435$	58261.8			0.307897
$436$		0			0
$437$	−158334.	−	355623.i	−0.829107	−	1.86220i
$438$		0			0
$439$	−62213.8	−	107758.i	−0.322818	−	0.559138i	0.658250	−	0.752799i	$-0.271297\pi$
$439$	−62213.8	−	107758.i	−0.322818	−	0.559138i	−0.981068	+	0.193662i	$0.937964\pi$
$440$		0			0
$441$	−40963.6	−	45494.7i	−0.210631	−	0.233929i
$442$		0			0
$443$	116278.	−	129140.i	0.592503	−	0.658041i	−0.370089	−	0.928996i	$-0.620673\pi$
$443$	116278.	−	129140.i	0.592503	−	0.658041i	0.962592	+	0.270955i	$0.0873395\pi$
$444$		0			0
$445$	17970.6	+	84544.8i	0.0907489	+	0.426940i
$446$		0			0
$447$	−237148.	−	24925.2i	−1.18687	−	0.124745i
$448$		0			0
$449$	23892.5	−	32885.2i	0.118514	−	0.163120i	−0.745638	−	0.666351i	$-0.767855\pi$
$449$	23892.5	−	32885.2i	0.118514	−	0.163120i	0.864152	+	0.503231i	$0.167855\pi$
$450$		0			0
$451$	−65696.8	+	309079.i	−0.322992	+	1.51956i
$452$		0			0
$453$	−11976.6	−	113950.i	−0.0583631	−	0.555288i
$454$		0			0
$455$	26179.8	−	58800.8i	0.126457	−	0.284028i
$456$		0			0
$457$	−284865.	+	92558.2i	−1.36398	+	0.443183i	−0.897368	−	0.441282i	$-0.854524\pi$
$457$	−284865.	+	92558.2i	−1.36398	+	0.443183i	−0.466607	+	0.884465i	$0.654524\pi$
$458$		0			0
$459$	−15755.9	+	27290.0i	−0.0747856	+	0.129532i
$460$		0			0
$461$	18475.0	+	6002.90i	0.0869327	+	0.0282461i	0.352160	−	0.935940i	$-0.385447\pi$
$461$	18475.0	+	6002.90i	0.0869327	+	0.0282461i	−0.265228	+	0.964186i	$0.585447\pi$
$462$		0			0
$463$	3235.96	+	4453.91i	0.0150953	+	0.0207769i	0.816498	−	0.577348i	$-0.195913\pi$
$463$	3235.96	+	4453.91i	0.0150953	+	0.0207769i	−0.801403	+	0.598125i	$0.795913\pi$
$464$		0			0
$465$	7874.07	+	107262.i	0.0364161	+	0.496065i
$466$		0			0
$467$	107867.	−	78369.8i	0.494600	−	0.359348i	−0.312351	−	0.949967i	$-0.601116\pi$
$467$	107867.	−	78369.8i	0.494600	−	0.359348i	0.806950	+	0.590619i	$0.201116\pi$
$468$		0			0
$469$	47130.7	−	145054.i	0.214269	−	0.659451i
$470$		0			0
$471$	−40041.4	−	23117.9i	−0.180496	−	0.104209i
$472$		0			0
$473$	143786.	+	442528.i	0.642680	+	1.97797i
$474$		0			0
$475$	204922.	+	91237.2i	0.908242	+	0.404375i
$476$		0			0
$477$	−111386.	+	11707.1i	−0.489546	+	0.0514534i
$478$		0			0
$479$	281663.	+	59869.3i	1.22761	+	0.260936i	0.775684	−	0.631122i	$-0.217405\pi$
$479$	281663.	+	59869.3i	1.22761	+	0.260936i	0.451922	+	0.892057i	$0.350738\pi$
$480$		0			0
$481$	25278.6	+	18366.0i	0.109261	+	0.0793824i
$482$		0			0
$483$	10948.7	−	104170.i	0.0469320	−	0.446528i
$484$		0			0
$485$	239469.	−	50900.7i	1.01804	−	0.216392i
$486$		0			0
$487$	37877.9	+	34105.4i	0.159709	+	0.143802i	0.745111	−	0.666941i	$-0.232397\pi$
$487$	37877.9	+	34105.4i	0.159709	+	0.143802i	−0.585402	+	0.810743i	$0.699063\pi$
$488$		0			0
$489$	−133027.	+	119778.i	−0.556315	+	0.500908i
$490$		0			0
$491$	74929.7	−	43260.7i	0.310807	−	0.179445i	−0.336480	−	0.941690i	$-0.609237\pi$
$491$	74929.7	−	43260.7i	0.310807	−	0.179445i	0.647288	+	0.762246i	$0.275903\pi$
$492$		0			0
$493$	−19013.4	+	8465.31i	−0.0782286	+	0.0348296i
$494$		0			0
$495$		−	81797.6i		−	0.333834i
$496$		0			0
$497$	16920.2			0.0685004
$498$		0			0
$499$	−100949.	−	226734.i	−0.405414	−	0.910576i	−0.994716	−	0.102663i	$-0.967264\pi$
$499$	−100949.	−	226734.i	−0.405414	−	0.910576i	0.589302	−	0.807913i	$-0.299403\pi$
$500$		0			0
$501$	−46998.8	−	81404.3i	−0.187245	−	0.324318i
$502$		0			0
$503$	158416.	+	175938.i	0.626127	+	0.695384i	0.969854	−	0.243685i	$-0.0783564\pi$
$503$	158416.	+	175938.i	0.626127	+	0.695384i	−0.343728	+	0.939069i	$0.611690\pi$
$504$		0			0
$505$	−152586.	+	169464.i	−0.598319	+	0.664500i
$506$		0			0
$507$	−4302.57	−	20242.0i	−0.0167383	−	0.0787476i
$508$		0			0
$509$	−288658.	−	30339.2i	−1.11416	−	0.117103i	−0.470490	−	0.882405i	$-0.655923\pi$
$509$	−288658.	−	30339.2i	−1.11416	−	0.117103i	−0.643671	+	0.765302i	$0.722590\pi$
$510$		0			0
$511$	5394.60	−	7425.02i	0.0206594	−	0.0284352i
$512$		0			0
$513$	−102741.	+	483361.i	−0.390401	+	1.83669i
$514$		0			0
$515$	2851.57	+	27130.9i	0.0107515	+	0.102294i
$516$		0			0
$517$	−28708.0	+	64479.1i	−0.107404	+	0.241234i
$518$		0			0
$519$	245381.	−	79729.2i	0.910976	−	0.295994i
$520$		0			0
$521$	−196797.	+	340862.i	−0.725007	+	1.25575i	0.233964	+	0.972245i	$0.424830\pi$
$521$	−196797.	+	340862.i	−0.725007	+	1.25575i	−0.958971	+	0.283504i	$0.908503\pi$
$522$		0			0
$523$	213861.	+	69487.7i	0.781859	+	0.254041i	0.672634	−	0.739976i	$-0.265163\pi$
$523$	213861.	+	69487.7i	0.781859	+	0.254041i	0.109225	+	0.994017i	$0.465163\pi$
$524$		0			0
$525$	35476.9	+	48829.8i	0.128714	+	0.177160i
$526$		0			0
$527$	−18154.6	−	33860.2i	−0.0653679	−	0.121918i
$528$		0			0
$529$	85509.0	−	62125.9i	0.305563	−	0.222004i
$530$		0			0
$531$	−39680.0	+	122123.i	−0.140729	+	0.433119i
$532$		0			0
$533$	298241.	+	172190.i	1.04982	+	0.606111i
$534$		0			0
$535$	−39861.0	−	122679.i	−0.139264	−	0.428612i
$536$		0			0
$537$	−263613.	−	117368.i	−0.914150	−	0.407006i
$538$		0			0
$539$	261599.	−	27495.2i	0.900448	−	0.0946409i
$540$		0			0
$541$	−98978.6	−	21038.6i	−0.338179	−	0.0718822i	0.0356920	−	0.999363i	$-0.488636\pi$
$541$	−98978.6	−	21038.6i	−0.338179	−	0.0718822i	−0.373871	+	0.927481i	$0.621970\pi$
$542$		0			0
$543$	257198.	+	186865.i	0.872303	+	0.633765i
$544$		0			0
$545$	13394.0	−	127435.i	0.0450937	−	0.429038i
$546$		0			0
$547$	378466.	−	80445.5i	1.26489	−	0.268860i	0.473839	−	0.880612i	$-0.342868\pi$
$547$	378466.	−	80445.5i	1.26489	−	0.268860i	0.791050	+	0.611751i	$0.209535\pi$
$548$		0			0
$549$	−10922.4	−	9834.58i	−0.0362388	−	0.0326296i
$550$		0			0
$551$	−242547.	+	218390.i	−0.798901	+	0.719334i
$552$		0			0
$553$	196285.	−	113325.i	0.641854	−	0.370575i
$554$		0			0
$555$	19990.2	−	8900.23i	0.0648981	−	0.0288945i
$556$		0			0
$557$			325196.i			1.04818i	0.851664	+	0.524089i	$0.175594\pi$
$557$			325196.i			1.04818i	−0.851664	+	0.524089i	$0.824406\pi$
$558$		0			0
$559$	507115.			1.62287
$560$		0			0
$561$	−16324.4	−	36665.2i	−0.0518694	−	0.116501i
$562$		0			0
$563$	62420.6	+	108116.i	0.196930	+	0.341092i	0.947531	−	0.319663i	$-0.103570\pi$
$563$	62420.6	+	108116.i	0.196930	+	0.341092i	−0.750602	+	0.660755i	$0.770236\pi$
$564$		0			0
$565$	6950.13	+	7718.91i	0.0217719	+	0.0241801i
$566$		0			0
$567$	−43396.3	+	48196.5i	−0.134985	+	0.149917i
$568$		0			0
$569$	77395.3	+	364116.i	0.239051	+	1.12465i	0.919879	+	0.392202i	$0.128287\pi$
$569$	77395.3	+	364116.i	0.239051	+	1.12465i	−0.680828	+	0.732443i	$0.738380\pi$
$570$		0			0
$571$	−595558.	−	62595.7i	−1.82664	−	0.191987i	−0.871949	−	0.489597i	$-0.837144\pi$
$571$	−595558.	−	62595.7i	−1.82664	−	0.191987i	−0.954688	+	0.297609i	$0.903811\pi$
$572$		0			0
$573$	235247.	−	323789.i	0.716497	−	0.986174i
$574$		0			0
$575$	−46189.4	+	217304.i	−0.139703	+	0.657252i
$576$		0			0
$577$	40796.5	+	388152.i	0.122538	+	1.16587i	0.867036	+	0.498246i	$0.166022\pi$
$577$	40796.5	+	388152.i	0.122538	+	1.16587i	−0.744498	+	0.667625i	$0.767311\pi$
$578$		0			0
$579$	−99314.1	+	223063.i	−0.296247	+	0.665381i
$580$		0			0
$581$	145479.	−	47268.9i	0.430971	−	0.140031i
$582$		0			0
$583$	240614.	−	416755.i	0.707919	−	1.22615i
$584$		0			0
$585$	−84784.9	−	27548.3i	−0.247746	−	0.0804976i
$586$		0			0
$587$	−101061.	−	139099.i	−0.293298	−	0.403690i	0.636784	−	0.771042i	$-0.280264\pi$
$587$	−101061.	−	139099.i	−0.293298	−	0.403690i	−0.930082	+	0.367353i	$0.880264\pi$
$588$		0			0
$589$	−434844.	−	417022.i	−1.25344	−	1.20207i
$590$		0			0
$591$	297218.	−	215942.i	0.850943	−	0.618246i
$592$		0			0
$593$	98626.6	−	303541.i	0.280469	−	0.863194i	−0.707252	−	0.706962i	$-0.750065\pi$
$593$	98626.6	−	303541.i	0.280469	−	0.863194i	0.987720	−	0.156232i	$-0.0499348\pi$
$594$		0			0
$595$	13945.1	+	8051.21i	0.0393902	+	0.0227419i
$596$		0			0
$597$	42050.7	+	129419.i	0.117984	+	0.363119i
$598$		0			0
$599$	−143587.	−	63929.1i	−0.400186	−	0.178174i	0.196767	−	0.980450i	$-0.436956\pi$
$599$	−143587.	−	63929.1i	−0.400186	−	0.178174i	−0.596953	+	0.802276i	$0.703622\pi$
$600$		0			0
$601$	−624997.	+	65689.9i	−1.73033	+	0.181865i	−0.916716	−	0.399539i	$-0.869170\pi$
$601$	−624997.	+	65689.9i	−1.73033	+	0.181865i	−0.813615	+	0.581404i	$0.802504\pi$
$602$		0			0
$603$	−206626.	−	43919.7i	−0.568264	−	0.120788i
$604$		0			0
$605$	90715.2	+	65908.4i	0.247839	+	0.180065i
$606$		0			0
$607$	−15156.3	+	144202.i	−0.0411353	+	0.391376i	0.954512	+	0.298173i	$0.0963773\pi$
$607$	−15156.3	+	144202.i	−0.0411353	+	0.391376i	−0.995647	+	0.0932032i	$0.970289\pi$
$608$		0			0
$609$	−85900.5	+	18258.7i	−0.231612	+	0.0492306i
$610$		0			0
$611$	57165.5	+	51472.0i	0.153127	+	0.137876i
$612$		0			0
$613$	−470860.	+	423965.i	−1.25306	+	1.12826i	−0.266676	+	0.963786i	$0.585925\pi$
$613$	−470860.	+	423965.i	−1.25306	+	1.12826i	−0.986382	+	0.164472i	$0.947408\pi$
$614$		0			0
$615$	208862.	−	120587.i	0.552216	−	0.318822i
$616$		0			0
$617$	168730.	−	75123.5i	0.443223	−	0.197336i	−0.172976	−	0.984926i	$-0.555338\pi$
$617$	168730.	−	75123.5i	0.443223	−	0.197336i	0.616199	+	0.787590i	$0.288672\pi$
$618$		0			0
$619$			242794.i			0.633659i	0.948482	+	0.316830i	$0.102618\pi$
$619$			242794.i			0.633659i	−0.948482	+	0.316830i	$0.897382\pi$
$620$		0			0
$621$	−489408.			−1.26908
$622$		0			0
$623$	−52991.2	−	119020.i	−0.136530	−	0.306651i
$624$		0			0
$625$	19494.8	+	33766.0i	0.0499067	+	0.0864410i
$626$		0			0
$627$	−421141.	−	467725.i	−1.07125	−	1.18975i
$628$		0			0
$629$	−5230.51	+	5809.08i	−0.0132204	+	0.0146827i
$630$		0			0
$631$	50399.3	+	237110.i	0.126580	+	0.595513i	0.995016	+	0.0997118i	$0.0317921\pi$
$631$	50399.3	+	237110.i	0.126580	+	0.595513i	−0.868436	+	0.495801i	$0.834875\pi$
$632$		0			0
$633$	15686.3	+	1648.69i	0.0391483	+	0.00411465i
$634$		0			0
$635$	177762.	−	244668.i	0.440851	−	0.606779i
$636$		0			0
$637$	59603.6	−	280413.i	0.146890	−	0.691065i
$638$		0			0
$639$	−2449.62	−	23306.6i	−0.00599926	−	0.0570791i
$640$		0			0
$641$	−50082.6	+	112487.i	−0.121891	+	0.273771i	−0.964177	−	0.265259i	$-0.914543\pi$
$641$	−50082.6	+	112487.i	−0.121891	+	0.273771i	0.842286	+	0.539030i	$0.181209\pi$
$642$		0			0
$643$	391117.	−	127082.i	0.945985	−	0.307369i	0.204902	−	0.978782i	$-0.434312\pi$
$643$	391117.	−	127082.i	0.945985	−	0.307369i	0.741083	+	0.671413i	$0.234312\pi$
$644$		0			0
$645$	177569.	−	307559.i	0.426824	−	0.739281i
$646$		0			0
$647$	−730807.	−	237454.i	−1.74580	−	0.567244i	−0.750221	−	0.661188i	$-0.770053\pi$
$647$	−730807.	−	237454.i	−1.74580	−	0.567244i	−0.995578	+	0.0939433i	$0.970053\pi$
$648$		0			0
$649$	−324297.	−	446356.i	−0.769934	−	1.05972i
$650$		0			0
$651$	−45224.3	−	155678.i	−0.106711	−	0.367337i
$652$		0			0
$653$	548010.	−	398152.i	1.28517	−	0.933734i	0.285478	−	0.958385i	$-0.407848\pi$
$653$	548010.	−	398152.i	1.28517	−	0.933734i	0.999696	+	0.0246516i	$0.00784765\pi$
$654$		0			0
$655$	−15311.1	+	47122.6i	−0.0356881	+	0.109837i
$656$		0			0
$657$	−11008.5	−	6355.78i	−0.0255034	−	0.0147244i
$658$		0			0
$659$	145775.	+	448649.i	0.335670	+	1.03309i	0.966391	+	0.257076i	$0.0827590\pi$
$659$	145775.	+	448649.i	0.335670	+	1.03309i	−0.630722	+	0.776009i	$0.717241\pi$
$660$		0			0
$661$	314162.	+	139874.i	0.719037	+	0.320136i	0.733434	−	0.679761i	$-0.237916\pi$
$661$	314162.	+	139874.i	0.719037	+	0.320136i	−0.0143974	+	0.999896i	$0.504583\pi$
$662$		0			0
$663$	−43502.0	+	4572.25i	−0.0989652	+	0.0104017i
$664$		0			0
$665$	246995.	+	52500.5i	0.558529	+	0.118719i
$666$		0			0
$667$	−261508.	−	189997.i	−0.587805	−	0.427065i
$668$		0			0
$669$	19376.6	−	184356.i	0.0432937	−	0.411912i
$670$		0			0
$671$	61770.8	−	13129.8i	0.137195	−	0.0291617i
$672$		0			0
$673$	−325811.	−	293361.i	−0.719341	−	0.647698i	0.225870	−	0.974157i	$-0.427478\pi$
$673$	−325811.	−	293361.i	−0.719341	−	0.647698i	−0.945211	+	0.326460i	$0.894144\pi$
$674$		0			0
$675$	209577.	−	188704.i	0.459977	−	0.414165i
$676$		0			0
$677$	293374.	−	169380.i	0.640095	−	0.369559i	−0.144556	−	0.989497i	$-0.546176\pi$
$677$	293374.	−	169380.i	0.640095	−	0.369559i	0.784651	+	0.619938i	$0.212842\pi$
$678$		0			0
$679$	−337119.	+	150095.i	−0.731212	+	0.325557i
$680$		0			0
$681$		−	493157.i		−	1.06339i
$682$		0			0
$683$	878338.			1.88287			0.941434	−	0.337196i	$-0.109479\pi$
$683$	878338.			1.88287			0.941434	+	0.337196i	$0.109479\pi$
$684$		0			0
$685$	−19210.3	−	43146.9i	−0.0409404	−	0.0919536i
$686$		0			0
$687$	66705.5	+	115537.i	0.141334	+	0.244798i
$688$		0			0
$689$	−350940.	−	389758.i	−0.739255	−	0.821026i
$690$		0			0
$691$	−594777.	+	660567.i	−1.24566	+	1.38344i	−0.351192	+	0.936304i	$0.614223\pi$
$691$	−594777.	+	660567.i	−1.24566	+	1.38344i	−0.894465	+	0.447138i	$0.852443\pi$
$692$		0			0
$693$	25634.6	+	120601.i	0.0533778	+	0.251123i
$694$		0			0
$695$	−457308.	−	48065.0i	−0.946759	−	0.0995084i
$696$		0			0
$697$	−50640.0	+	69699.9i	−0.104238	+	0.143472i
$698$		0			0
$699$	−58407.0	+	274783.i	−0.119539	+	0.562388i
$700$		0			0
$701$	89582.0	+	852316.i	0.182299	+	1.73446i	0.577960	+	0.816065i	$0.303849\pi$
$701$	89582.0	+	852316.i	0.182299	+	1.73446i	−0.395661	+	0.918397i	$0.629485\pi$
$702$		0			0
$703$	−49858.6	+	111984.i	−0.100886	+	0.226593i
$704$		0			0
$705$	51234.1	−	16647.0i	0.103081	−	0.0334932i
$706$		0			0
$707$	171863.	−	297675.i	0.343830	−	0.595531i
$708$		0			0
$709$	−485633.	−	157792.i	−0.966086	−	0.313900i	−0.216851	−	0.976205i	$-0.569579\pi$
$709$	−485633.	−	157792.i	−0.966086	−	0.313900i	−0.749235	+	0.662305i	$0.769579\pi$
$710$		0			0
$711$	−184516.	−	253964.i	−0.365001	−	0.502381i
$712$		0			0
$713$	314447.	−	507123.i	0.618541	−	0.997548i
$714$		0			0
$715$	309887.	−	225146.i	0.606166	−	0.440406i
$716$		0			0
$717$	125496.	−	386237.i	0.244113	−	0.751303i
$718$		0			0
$719$	290837.	+	167915.i	0.562590	+	0.324812i	0.754185	−	0.656662i	$-0.228032\pi$
$719$	290837.	+	167915.i	0.562590	+	0.324812i	−0.191594	+	0.981474i	$0.561366\pi$
$720$		0			0
$721$	−12706.9	−	39107.8i	−0.0244438	−	0.0752303i
$722$		0			0
$723$	133141.	+	59278.4i	0.254705	+	0.113402i
$724$		0			0
$725$	185242.	−	19469.8i	0.352423	−	0.0370411i
$726$		0			0
$727$	−535879.	−	113905.i	−1.01391	−	0.215513i	−0.329145	−	0.944279i	$-0.606760\pi$
$727$	−535879.	−	113905.i	−1.01391	−	0.215513i	−0.684762	+	0.728767i	$0.740094\pi$
$728$		0			0
$729$	426298.	+	309723.i	0.802155	+	0.582799i
$730$		0			0
$731$	−13261.1	+	126171.i	−0.0248167	+	0.236115i
$732$		0			0
$733$	902189.	−	191766.i	1.67915	−	0.356914i	0.732897	−	0.680340i	$-0.238168\pi$
$733$	902189.	−	191766.i	1.67915	−	0.356914i	0.946254	+	0.323426i	$0.104835\pi$
$734$		0			0
$735$	−149197.	−	134337.i	−0.276175	−	0.248669i
$736$		0			0
$737$	674510.	−	607331.i	1.24180	−	1.11813i
$738$		0			0
$739$	−163640.	+	94477.8i	−0.299641	+	0.172998i	−0.642282	−	0.766469i	$-0.722012\pi$
$739$	−163640.	+	94477.8i	−0.299641	+	0.172998i	0.342641	+	0.939467i	$0.388679\pi$
$740$		0			0
$741$	−626641.	+	278998.i	−1.14125	+	0.508119i
$742$		0			0
$743$			320601.i			0.580747i	0.956913	+	0.290373i	$0.0937795\pi$
$743$			320601.i			0.580747i	−0.956913	+	0.290373i	$0.906221\pi$
$744$		0			0
$745$	569332.			1.02578
$746$		0			0
$747$	−86171.9	−	193545.i	−0.154427	−	0.346850i
$748$		0			0
$749$	97217.2	+	168385.i	0.173292	+	0.300151i
$750$		0			0
$751$	−624478.	−	693553.i	−1.10723	−	1.22970i	−0.971014	−	0.239022i	$-0.923173\pi$
$751$	−624478.	−	693553.i	−1.10723	−	1.22970i	−0.136214	−	0.990679i	$-0.543493\pi$
$752$		0			0
$753$	−146095.	+	162255.i	−0.257659	+	0.286160i
$754$		0			0
$755$	56877.4	+	267587.i	0.0997806	+	0.469431i
$756$		0			0
$757$	−910603.	−	95708.2i	−1.58905	−	0.167016i	−0.731654	−	0.681676i	$-0.761252\pi$
$757$	−910603.	−	95708.2i	−1.58905	−	0.167016i	−0.857394	+	0.514660i	$0.827918\pi$
$758$		0			0
$759$	366387.	−	504289.i	0.635999	−	0.875378i
$760$		0			0
$761$	−236490.	+	1.11260e6i	−0.408360	+	1.92118i	−0.0196906	+	0.999806i	$0.506268\pi$
$761$	−236490.	+	1.11260e6i	−0.408360	+	1.92118i	−0.388670	+	0.921377i	$0.627065\pi$
$762$		0			0
$763$	20189.1	+	192086.i	0.0346791	+	0.329950i
$764$		0			0
$765$	9071.17	−	20374.2i	0.0155003	−	0.0348143i
$766$		0			0
$767$	−571876.	+	185814.i	−0.972100	+	0.315855i
$768$		0			0
$769$	−128471.	+	222518.i	−0.217246	+	0.376281i	−0.953965	−	0.299918i	$-0.903041\pi$
$769$	−128471.	+	222518.i	−0.217246	+	0.376281i	0.736719	+	0.676199i	$0.236374\pi$
$770$		0			0
$771$	−557475.	−	181135.i	−0.937814	−	0.304714i
$772$		0			0
$773$	−184615.	−	254101.i	−0.308964	−	0.425252i	0.626094	−	0.779748i	$-0.284653\pi$
$773$	−184615.	−	254101.i	−0.308964	−	0.425252i	−0.935058	+	0.354495i	$0.884653\pi$
$774$		0			0
$775$	60879.9	+	338406.i	0.101361	+	0.563423i
$776$		0			0
$777$	−26684.1	+	19387.2i	−0.0441989	+	0.0321123i
$778$		0			0
$779$	−417494.	+	1.28492e6i	−0.687980	+	2.11738i
$780$		0			0
$781$	87202.6	+	50346.4i	0.142964	+	0.0825404i
$782$		0			0
$783$	126799.	+	390248.i	0.206820	+	0.636527i
$784$		0			0
$785$	100849.	+	44900.7i	0.163655	+	0.0728641i
$786$		0			0
$787$	1.18546e6	−	124597.i	1.91399	−	0.201168i	0.928550	−	0.371207i	$-0.121056\pi$
$787$	1.18546e6	−	124597.i	1.91399	−	0.201168i	0.985437	+	0.170038i	$0.0543891\pi$
$788$		0			0
$789$	−8638.58	−	1836.19i	−0.0138768	−	0.00294960i
$790$		0			0
$791$	−12666.2	−	9202.56i	−0.0202439	−	0.0147081i
$792$		0			0
$793$	7194.25	−	68448.7i	0.0114403	−	0.108848i
$794$		0			0
$795$	−359268.	+	76364.7i	−0.568439	+	0.120826i
$796$		0			0
$797$	287536.	+	258899.i	0.452664	+	0.407581i	0.863674	−	0.504050i	$-0.168157\pi$
$797$	287536.	+	258899.i	0.452664	+	0.407581i	−0.411010	+	0.911631i	$0.634824\pi$
$798$		0			0
$799$	−14301.2	+	12876.8i	−0.0224016	+	0.0201705i
$800$		0			0
$801$	−156271.	+	90223.4i	−0.243565	+	0.140622i
$802$		0			0
$803$	49895.7	−	22215.0i	0.0773806	−	0.0344521i
$804$		0			0
$805$			250086.i			0.385920i
$806$		0			0
$807$	362755.			0.557014
$808$		0			0
$809$	−501529.	−	1.12645e6i	−0.766300	−	1.72114i	−0.689721	−	0.724075i	$-0.742267\pi$
$809$	−501529.	−	1.12645e6i	−0.766300	−	1.72114i	−0.0765794	−	0.997063i	$-0.524400\pi$
$810$		0			0
$811$	−403527.	−	698929.i	−0.613523	−	1.06265i	−0.990642	−	0.136488i	$-0.956419\pi$
$811$	−403527.	−	698929.i	−0.613523	−	1.06265i	0.377119	−	0.926165i	$-0.376915\pi$
$812$		0			0
$813$	270868.	+	300829.i	0.409804	+	0.455134i
$814$		0			0
$815$	285980.	−	317613.i	0.430548	−	0.478172i
$816$		0			0
$817$	413634.	+	1.94600e6i	0.619687	+	2.91540i
$818$		0			0
$819$	133639.	+	14046.1i	0.199235	+	0.0209405i
$820$		0			0
$821$	292470.	−	402551.i	0.433906	−	0.597220i	−0.534939	−	0.844891i	$-0.679665\pi$
$821$	292470.	−	402551.i	0.433906	−	0.597220i	0.968844	+	0.247671i	$0.0796653\pi$
$822$		0			0
$823$	−36399.3	+	171245.i	−0.0537394	+	0.252824i	−0.996814	−	0.0797561i	$-0.974586\pi$
$823$	−36399.3	+	171245.i	−0.0537394	+	0.252824i	0.943075	+	0.332580i	$0.107919\pi$
$824$		0			0
$825$	37545.2	+	357219.i	0.0551628	+	0.524839i
$826$		0			0
$827$	−267949.	+	601823.i	−0.391779	+	0.879950i	0.604727	+	0.796432i	$0.293282\pi$
$827$	−267949.	+	601823.i	−0.391779	+	0.879950i	−0.996506	+	0.0835172i	$0.973385\pi$
$828$		0			0
$829$	704794.	−	229002.i	1.02554	−	0.333219i	0.252515	−	0.967593i	$-0.418742\pi$
$829$	704794.	−	229002.i	1.02554	−	0.333219i	0.773026	+	0.634374i	$0.218742\pi$
$830$		0			0
$831$	−233639.	+	404674.i	−0.338332	+	0.586008i
$832$		0			0
$833$	68208.3	+	22162.2i	0.0982986	+	0.0319392i
$834$		0			0
$835$	131915.	+	181566.i	0.189201	+	0.260412i
$836$		0			0
$837$	−701322.	+	286183.i	−1.00107	+	0.408501i
$838$		0			0
$839$	479311.	−	348240.i	0.680916	−	0.494715i	−0.192745	−	0.981249i	$-0.561739\pi$
$839$	479311.	−	348240.i	0.680916	−	0.494715i	0.873662	+	0.486534i	$0.161739\pi$
$840$		0			0
$841$	134814.	−	414916.i	0.190609	−	0.586635i
$842$		0			0
$843$	422461.	+	243908.i	0.594473	+	0.343219i
$844$		0			0
$845$	15268.3	+	46991.1i	0.0213835	+	0.0658116i
$846$		0			0
$847$	−154405.	−	68745.3i	−0.215225	−	0.0958245i
$848$		0			0
$849$	210675.	−	22142.8i	0.292279	−	0.0307198i
$850$		0			0
$851$	−118751.	−	25241.2i	−0.163975	−	0.0348539i
$852$		0			0
$853$	937924.	+	681442.i	1.28905	+	0.936549i	0.999786	−	0.0207000i	$-0.00658948\pi$
$853$	937924.	+	681442.i	1.28905	+	0.936549i	0.289264	+	0.957249i	$0.406589\pi$
$854$		0			0
$855$	36557.6	−	347822.i	0.0500087	−	0.475801i
$856$		0			0
$857$	1.21585e6	−	258437.i	1.65546	−	0.351878i	0.716947	−	0.697128i	$-0.245539\pi$
$857$	1.21585e6	−	258437.i	1.65546	−	0.351878i	0.938511	+	0.345249i	$0.112206\pi$
$858$		0			0
$859$	−710510.	−	639746.i	−0.962906	−	0.867005i	0.0282638	−	0.999600i	$-0.491002\pi$
$859$	−710510.	−	639746.i	−0.962906	−	0.867005i	−0.991170	+	0.132596i	$0.957669\pi$
$860$		0			0
$861$	−270153.	+	243247.i	−0.364421	+	0.328126i
$862$		0			0
$863$	−65194.7	+	37640.2i	−0.0875368	+	0.0505394i	−0.543129	−	0.839649i	$-0.682761\pi$
$863$	−65194.7	+	37640.2i	−0.0875368	+	0.0505394i	0.455593	+	0.890188i	$0.349427\pi$
$864$		0			0
$865$	−562763.	+	250558.i	−0.752131	+	0.334870i
$866$		0			0
$867$			560878.i			0.746156i
$868$		0			0
$869$	1.34880e6			1.78611
$870$		0			0
$871$	−402346.	−	903684.i	−0.530351	−	1.19119i
$872$		0			0
$873$	255553.	+	442631.i	0.335315	+	0.580783i
$874$		0			0
$875$	−264868.	−	294166.i	−0.345950	−	0.384216i
$876$		0			0
$877$	−391570.	+	434883.i	−0.509109	+	0.565422i	−0.941823	−	0.336109i	$-0.890889\pi$
$877$	−391570.	+	434883.i	−0.509109	+	0.565422i	0.432715	+	0.901531i	$0.357556\pi$
$878$		0			0
$879$	184557.	+	868273.i	0.238865	+	1.12377i
$880$		0			0
$881$	1.16186e6	+	122117.i	1.49693	+	0.157334i	0.817298	−	0.576215i	$-0.195471\pi$
$881$	1.16186e6	+	122117.i	1.49693	+	0.157334i	0.679637	+	0.733549i	$0.262138\pi$
$882$		0			0
$883$	708566.	−	975257.i	0.908780	−	1.25083i	−0.0588015	−	0.998270i	$-0.518728\pi$
$883$	708566.	−	975257.i	0.908780	−	1.25083i	0.967582	−	0.252559i	$-0.0812721\pi$
$884$		0			0
$885$	−87552.1	+	411900.i	−0.111784	+	0.525903i
$886$		0			0
$887$	45489.1	+	432800.i	0.0578176	+	0.550097i	0.984640	+	0.174597i	$0.0558624\pi$
$887$	45489.1	+	432800.i	0.0578176	+	0.550097i	−0.926822	+	0.375500i	$0.877471\pi$
$888$		0			0
$889$	−185413.	+	416445.i	−0.234605	+	0.526932i
$890$		0			0
$891$	−367064.	+	119266.i	−0.462366	+	0.150232i
$892$		0			0
$893$	−150890.	+	261350.i	−0.189216	+	0.327732i
$894$		0			0
$895$	655244.	+	212902.i	0.818007	+	0.265786i
$896$		0			0
$897$	−399311.	−	549605.i	−0.496280	−	0.683071i
$898$		0			0
$899$	−485842.	−	119347.i	−0.601140	−	0.147670i
$900$		0			0
$901$	106149.	−	77122.0i	0.130758	−	0.0950012i
$902$		0			0
$903$	−165420.	+	509111.i	−0.202868	+	0.624362i
$904$		0			0
$905$	−657356.	−	379524.i	−0.802608	−	0.463386i
$906$		0			0
$907$	−209732.	−	645489.i	−0.254947	−	0.784647i	−0.993840	−	0.110824i	$-0.964651\pi$
$907$	−209732.	−	645489.i	−0.254947	−	0.784647i	0.738893	−	0.673823i	$-0.235349\pi$
$908$		0			0
$909$	−434912.	−	193635.i	−0.526348	−	0.234345i
$910$		0			0
$911$	−772835.	+	81228.2i	−0.931215	+	0.0978747i	−0.557973	−	0.829859i	$-0.688421\pi$
$911$	−772835.	+	81228.2i	−0.931215	+	0.0978747i	−0.373242	+	0.927734i	$0.621754\pi$
$912$		0			0
$913$	890412.	+	189263.i	1.06819	+	0.227051i
$914$		0			0
$915$	−38994.2	−	28331.0i	−0.0465756	−	0.0338391i
$916$		0			0
$917$	7806.66	−	74275.5i	0.00928382	−	0.0883297i
$918$		0			0
$919$	−578445.	+	122952.i	−0.684906	+	0.145581i	−0.537206	−	0.843451i	$-0.680520\pi$
$919$	−578445.	+	122952.i	−0.684906	+	0.145581i	−0.147700	+	0.989032i	$0.547187\pi$
$920$		0			0
$921$	−519388.	−	467659.i	−0.612311	−	0.551328i
$922$		0			0
$923$	81553.7	−	73431.3i	0.0957283	−	0.0861941i
$924$		0			0
$925$	60584.4	−	34978.4i	0.0708072	−	0.0408805i
$926$		0			0
$927$	−52029.1	+	23164.8i	−0.0605461	+	0.0269569i
$928$		0			0
$929$		−	1.03490e6i		−	1.19913i	−0.800325	−	0.599566i	$-0.795340\pi$
$929$		−	1.03490e6i		−	1.19913i	0.800325	−	0.599566i	$-0.204660\pi$
$930$		0			0
$931$	1.12467e6			1.29755
$932$		0			0
$933$	−314971.	−	707437.i	−0.361833	−	0.812689i
$934$		0			0
$935$	47913.1	+	82987.9i	0.0548064	+	0.0949274i
$936$		0			0
$937$	−482078.	−	535402.i	−0.549083	−	0.609819i	0.403171	−	0.915125i	$-0.367908\pi$
$937$	−482078.	−	535402.i	−0.549083	−	0.609819i	−0.952254	+	0.305306i	$0.901241\pi$
$938$		0			0
$939$	−198172.	+	220092.i	−0.224756	+	0.249617i
$940$		0			0
$941$	−86155.6	−	405330.i	−0.0972981	−	0.457752i	−0.999643	−	0.0267359i	$-0.991489\pi$
$941$	−86155.6	−	405330.i	−0.0972981	−	0.457752i	0.902344	−	0.431016i	$-0.141845\pi$
$942$		0			0
$943$	−1.33072e6	−	139864.i	−1.49646	−	0.157284i
$944$		0			0
$945$	186601.	−	256835.i	0.208954	−	0.287601i
$946$		0			0
$947$	−317439.	+	1.49343e6i	−0.353965	+	1.66527i	0.336329	+	0.941744i	$0.390814\pi$
$947$	−317439.	+	1.49343e6i	−0.353965	+	1.66527i	−0.690294	+	0.723529i	$0.742519\pi$
$948$		0			0
$949$	−6222.13	−	59199.6i	−0.00690886	−	0.0657335i
$950$		0			0
$951$	431762.	−	969753.i	0.477401	−	1.07226i
$952$		0			0
$953$	334373.	−	108644.i	0.368168	−	0.119625i	−0.119089	−	0.992884i	$-0.537997\pi$
$953$	334373.	−	108644.i	0.368168	−	0.119625i	0.487257	+	0.873259i	$0.337997\pi$
$954$		0			0
$955$	−477788.	+	827554.i	−0.523877	+	0.907381i
$956$		0			0
$957$	−497039.	−	161498.i	−0.542708	−	0.176337i
$958$		0			0
$959$	41845.2	+	57595.0i	0.0454997	+	0.0626250i
$960$		0			0
$961$	154061.	−	910580.i	0.166819	−	0.985988i
$962$		0			0
$963$	217866.	−	158289.i	0.234929	−	0.170686i
$964$		0			0
$965$	180153.	−	554453.i	0.193458	−	0.595402i
$966$		0			0
$967$	−423023.	−	244232.i	−0.452388	−	0.261186i	0.256450	−	0.966557i	$-0.417447\pi$
$967$	−423023.	−	244232.i	−0.452388	−	0.261186i	−0.708838	+	0.705371i	$0.750780\pi$
$968$		0			0
$969$	−53028.4	−	163205.i	−0.0564756	−	0.173814i
$970$		0			0
$971$	−382435.	−	170271.i	−0.405620	−	0.180594i	0.193777	−	0.981046i	$-0.437926\pi$
$971$	−382435.	−	170271.i	−0.405620	−	0.180594i	−0.599397	+	0.800452i	$0.704593\pi$
$972$		0			0
$973$	689314.	−	72449.8i	0.728100	−	0.0765264i
$974$		0			0
$975$	382909.	+	81389.9i	0.402797	+	0.0856172i
$976$		0			0
$977$	−438069.	−	318276.i	−0.458937	−	0.333437i	0.334177	−	0.942510i	$-0.391542\pi$
$977$	−438069.	−	318276.i	−0.458937	−	0.333437i	−0.793114	+	0.609073i	$0.791542\pi$
$978$		0			0
$979$	81043.4	−	771077.i	0.0845576	−	0.804511i
$980$		0			0
$981$	261665.	−	55618.6i	0.271899	−	0.0577939i
$982$		0			0
$983$	−679658.	−	611967.i	−0.703369	−	0.633317i	0.237775	−	0.971320i	$-0.423582\pi$
$983$	−679658.	−	611967.i	−0.703369	−	0.633317i	−0.941145	+	0.338003i	$0.890248\pi$
$984$		0			0
$985$	−651856.	+	586934.i	−0.671861	+	0.604946i
$986$		0			0
$987$	−70321.9	+	40600.4i	−0.0721866	+	0.0416769i
$988$		0			0
$989$	−1.80000e6	+	801411.i	−1.84026	+	0.819337i
$990$		0			0
$991$			667636.i			0.679817i	0.940458	+	0.339909i	$0.110396\pi$
$991$			667636.i			0.679817i	−0.940458	+	0.339909i	$0.889604\pi$
$992$		0			0
$993$	402990.			0.408692
$994$		0			0
$995$	−132149.	−	296812.i	−0.133481	−	0.299803i
$996$		0			0
$997$	154925.	+	268338.i	0.155859	+	0.269956i	0.933371	−	0.358912i	$-0.116852\pi$
$997$	154925.	+	268338.i	0.155859	+	0.269956i	−0.777512	+	0.628868i	$0.783519\pi$
$998$		0			0
$999$	103121.	+	114528.i	0.103328	+	0.114757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.13.8	✓	88
31.12	odd	30	inner	124.5.o.a.105.8	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.13.8	✓	88	1.1	even	1	trivial
124.5.o.a.105.8	yes	88	31.12	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.78469 + 6.25452i) q^{3} +(-8.17325 - 14.1565i) q^{5} +(16.4871 + 18.3107i) q^{7} +(22.8350 - 25.3609i) q^{9} +O(q^{10})\)	\(q+(2.78469 + 6.25452i) q^{3} +(-8.17325 - 14.1565i) q^{5} +(16.4871 + 18.3107i) q^{7} +(22.8350 - 25.3609i) q^{9} +(30.4863 + 143.427i) q^{11} +(158.932 + 16.7044i) q^{13} +(65.7820 - 90.5412i) q^{15} +(-8.31215 + 39.1056i) q^{17} +(65.5333 + 623.508i) q^{19} +(-68.6135 + 154.108i) q^{21} +(-590.526 + 191.873i) q^{23} +(178.896 - 309.857i) q^{25} +(749.627 + 243.569i) q^{27} +(305.995 + 421.165i) q^{29} +(-734.024 + 620.266i) q^{31} +(-812.170 + 590.076i) q^{33} +(124.463 - 383.057i) q^{35} +(169.328 + 97.7618i) q^{37} +(338.098 + 1040.56i) q^{39} +(1968.66 + 876.503i) q^{41} +(3155.91 - 331.699i) q^{43} +(-545.657 - 115.983i) q^{45} +(389.423 + 282.932i) q^{47} +(187.513 - 1784.07i) q^{49} +(-267.734 + 56.9085i) q^{51} +(-2438.93 - 2196.02i) q^{53} +(1781.24 - 1603.84i) q^{55} +(-3717.26 + 2146.16i) q^{57} +(-3437.39 + 1530.43i) q^{59} -430.679i q^{61} +840.859 q^{63} +(-1062.51 - 2386.44i) q^{65} +(-3094.99 - 5360.69i) q^{67} +(-2844.51 - 3159.15i) q^{69} +(459.499 - 510.325i) q^{71} +(-77.4438 - 364.345i) q^{73} +(2436.18 + 256.053i) q^{75} +(-2123.62 + 2922.91i) q^{77} +(1912.50 - 8997.63i) q^{79} +(275.134 + 2617.73i) q^{81} +(2525.08 - 5671.42i) q^{83} +(621.535 - 201.949i) q^{85} +(-1782.09 + 3086.67i) q^{87} +(-5028.80 - 1633.96i) q^{89} +(2314.45 + 3185.57i) q^{91} +(-5923.50 - 2863.72i) q^{93} +(8291.06 - 6023.81i) q^{95} +(-4628.10 + 14243.8i) q^{97} +(4333.58 + 2501.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more