LMFDB - Embedded newform 124.5.o.a.13.9

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			13.9
Character	$\chi$	$=$	124.13
Dual form			124.5.o.a.105.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.39298 + 7.62076i) q^{3} +(-15.4750 - 26.8035i) q^{5} +(11.7917 + 13.0960i) q^{7} +(7.63586 - 8.48048i) q^{9} +O(q^{10})$	\(q+(3.39298 + 7.62076i) q^{3} +(-15.4750 - 26.8035i) q^{5} +(11.7917 + 13.0960i) q^{7} +(7.63586 - 8.48048i) q^{9} +(-24.4372 - 114.968i) q^{11} +(-167.657 - 17.6215i) q^{13} +(151.757 - 208.876i) q^{15} +(45.1519 - 212.423i) q^{17} +(-25.0500 - 238.335i) q^{19} +(-59.7923 + 134.296i) q^{21} +(764.251 - 248.320i) q^{23} +(-166.453 + 288.306i) q^{25} +(733.164 + 238.219i) q^{27} +(224.160 + 308.529i) q^{29} +(108.939 - 954.805i) q^{31} +(793.229 - 576.315i) q^{33} +(168.542 - 518.719i) q^{35} +(-1394.73 - 805.246i) q^{37} +(-434.570 - 1337.47i) q^{39} +(-471.066 - 209.732i) q^{41} +(-1730.32 + 181.863i) q^{43} +(-345.472 - 73.4323i) q^{45} +(-326.009 - 236.859i) q^{47} +(218.512 - 2079.00i) q^{49} +(1772.03 - 376.656i) q^{51} +(2260.25 + 2035.14i) q^{53} +(-2703.38 + 2434.14i) q^{55} +(1731.30 - 999.566i) q^{57} +(-2547.73 + 1134.32i) q^{59} +6463.39i q^{61} +201.099 q^{63} +(2122.19 + 4766.51i) q^{65} +(-381.288 - 660.410i) q^{67} +(4485.48 + 4981.63i) q^{69} +(-2889.46 + 3209.08i) q^{71} +(-782.045 - 3679.23i) q^{73} +(-2761.88 - 290.286i) q^{75} +(1217.46 - 1675.69i) q^{77} +(32.2655 - 151.797i) q^{79} +(575.579 + 5476.27i) q^{81} +(531.673 - 1194.16i) q^{83} +(-6392.42 + 2077.02i) q^{85} +(-1590.66 + 2755.10i) q^{87} +(-7133.99 - 2317.97i) q^{89} +(-1746.19 - 2403.42i) q^{91} +(7645.98 - 2409.44i) q^{93} +(-6000.57 + 4359.67i) q^{95} +(940.834 - 2895.59i) q^{97} +(-1161.58 - 670.640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.39298	+	7.62076i	0.376998	+	0.846752i	0.998016	+	0.0629555i	$0.0200526\pi$
$3$	3.39298	+	7.62076i	0.376998	+	0.846752i	−0.621018	+	0.783796i	$0.713281\pi$
$4$		0			0
$5$	−15.4750	−	26.8035i	−0.619001	−	1.07214i	−0.989668	−	0.143376i	$-0.954204\pi$
$5$	−15.4750	−	26.8035i	−0.619001	−	1.07214i	0.370667	−	0.928766i	$-0.379129\pi$
$6$		0			0
$7$	11.7917	+	13.0960i	0.240646	+	0.267264i	0.851354	−	0.524591i	$-0.175782\pi$
$7$	11.7917	+	13.0960i	0.240646	+	0.267264i	−0.610708	+	0.791856i	$0.709115\pi$
$8$		0			0
$9$	7.63586	−	8.48048i	0.0942698	−	0.104697i
$10$		0			0
$11$	−24.4372	−	114.968i	−0.201960	−	0.950149i	−0.956011	−	0.293332i	$-0.905236\pi$
$11$	−24.4372	−	114.968i	−0.201960	−	0.950149i	0.754050	−	0.656817i	$-0.228098\pi$
$12$		0			0
$13$	−167.657	−	17.6215i	−0.992056	−	0.104269i	−0.405429	−	0.914127i	$-0.632878\pi$
$13$	−167.657	−	17.6215i	−0.992056	−	0.104269i	−0.586627	+	0.809857i	$0.699545\pi$
$14$		0			0
$15$	151.757	−	208.876i	0.674476	−	0.928336i
$16$		0			0
$17$	45.1519	−	212.423i	0.156235	−	0.735028i	−0.828363	−	0.560192i	$-0.810727\pi$
$17$	45.1519	−	212.423i	0.156235	−	0.735028i	0.984598	−	0.174836i	$-0.0559395\pi$
$18$		0			0
$19$	−25.0500	−	238.335i	−0.0693906	−	0.660207i	−0.972835	−	0.231501i	$-0.925636\pi$
$19$	−25.0500	−	238.335i	−0.0693906	−	0.660207i	0.903444	−	0.428706i	$-0.141030\pi$
$20$		0			0
$21$	−59.7923	+	134.296i	−0.135584	+	0.304526i
$22$		0			0
$23$	764.251	−	248.320i	1.44471	−	0.469414i	0.521347	−	0.853345i	$-0.325430\pi$
$23$	764.251	−	248.320i	1.44471	−	0.469414i	0.923362	+	0.383930i	$0.125430\pi$
$24$		0			0
$25$	−166.453	+	288.306i	−0.266325	+	0.461289i
$26$		0			0
$27$	733.164	+	238.219i	1.00571	+	0.326776i
$28$		0			0
$29$	224.160	+	308.529i	0.266539	+	0.366860i	0.921218	−	0.389048i	$-0.127196\pi$
$29$	224.160	+	308.529i	0.266539	+	0.366860i	−0.654678	+	0.755908i	$0.727196\pi$
$30$		0			0
$31$	108.939	−	954.805i	0.113360	−	0.993554i
$31$	108.939	−	954.805i	0.113360	−	0.993554i
$32$		0			0
$33$	793.229	−	576.315i	0.728402	−	0.529215i
$34$		0			0
$35$	168.542	−	518.719i	0.137585	−	0.423444i
$36$		0			0
$37$	−1394.73	−	805.246i	−1.01879	−	0.588200i	−0.105039	−	0.994468i	$-0.533497\pi$
$37$	−1394.73	−	805.246i	−1.01879	−	0.588200i	−0.913754	+	0.406268i	$0.866830\pi$
$38$		0			0
$39$	−434.570	−	1337.47i	−0.285713	−	0.879335i
$40$		0			0
$41$	−471.066	−	209.732i	−0.280230	−	0.124766i	0.261809	−	0.965120i	$-0.415681\pi$
$41$	−471.066	−	209.732i	−0.280230	−	0.124766i	−0.542039	+	0.840353i	$0.682348\pi$
$42$		0			0
$43$	−1730.32	+	181.863i	−0.935811	+	0.0983577i	−0.560143	−	0.828396i	$-0.689254\pi$
$43$	−1730.32	+	181.863i	−0.935811	+	0.0983577i	−0.375669	+	0.926754i	$0.622587\pi$
$44$		0			0
$45$	−345.472	−	73.4323i	−0.170603	−	0.0362629i
$46$		0			0
$47$	−326.009	−	236.859i	−0.147582	−	0.107225i	0.511544	−	0.859257i	$-0.329074\pi$
$47$	−326.009	−	236.859i	−0.147582	−	0.107225i	−0.659126	+	0.752032i	$0.729074\pi$
$48$		0			0
$49$	218.512	−	2079.00i	0.0910087	−	0.865890i
$50$		0			0
$51$	1772.03	−	376.656i	0.681287	−	0.144812i
$52$		0			0
$53$	2260.25	+	2035.14i	0.804646	+	0.724506i	0.964914	−	0.262567i	$-0.0845691\pi$
$53$	2260.25	+	2035.14i	0.804646	+	0.724506i	−0.160268	+	0.987074i	$0.551236\pi$
$54$		0			0
$55$	−2703.38	+	2434.14i	−0.893681	+	0.804674i
$56$		0			0
$57$	1731.30	−	999.566i	0.532871	−	0.307653i
$58$		0			0
$59$	−2547.73	+	1134.32i	−0.731897	+	0.325861i	−0.738626	−	0.674116i	$-0.764525\pi$
$59$	−2547.73	+	1134.32i	−0.731897	+	0.325861i	0.00672874	+	0.999977i	$0.497858\pi$
$60$		0			0
$61$			6463.39i			1.73700i	0.495687	+	0.868501i	$0.334916\pi$
$61$			6463.39i			1.73700i	−0.495687	+	0.868501i	$0.665084\pi$
$62$		0			0
$63$	201.099			0.0506675
$64$		0			0
$65$	2122.19	+	4766.51i	0.502293	+	1.12817i
$66$		0			0
$67$	−381.288	−	660.410i	−0.0849383	−	0.147117i	0.820427	−	0.571752i	$-0.193736\pi$
$67$	−381.288	−	660.410i	−0.0849383	−	0.147117i	−0.905365	+	0.424634i	$0.860403\pi$
$68$		0			0
$69$	4485.48	+	4981.63i	0.942130	+	1.04634i
$70$		0			0
$71$	−2889.46	+	3209.08i	−0.573193	+	0.636595i	−0.958125	−	0.286350i	$-0.907558\pi$
$71$	−2889.46	+	3209.08i	−0.573193	+	0.636595i	0.384932	+	0.922945i	$0.374225\pi$
$72$		0			0
$73$	−782.045	−	3679.23i	−0.146753	−	0.690417i	−0.988583	−	0.150675i	$-0.951855\pi$
$73$	−782.045	−	3679.23i	−0.146753	−	0.690417i	0.841831	−	0.539742i	$-0.181478\pi$
$74$		0			0
$75$	−2761.88	−	290.286i	−0.491002	−	0.0516063i
$76$		0			0
$77$	1217.46	−	1675.69i	0.205340	−	0.282626i
$78$		0			0
$79$	32.2655	−	151.797i	0.00516993	−	0.0243226i	−0.975487	−	0.220057i	$-0.929376\pi$
$79$	32.2655	−	151.797i	0.00516993	−	0.0243226i	0.980657	+	0.195734i	$0.0627090\pi$
$80$		0			0
$81$	575.579	+	5476.27i	0.0877274	+	0.834670i
$82$		0			0
$83$	531.673	−	1194.16i	0.0771770	−	0.173342i	−0.870836	−	0.491573i	$-0.836422\pi$
$83$	531.673	−	1194.16i	0.0771770	−	0.173342i	0.948013	+	0.318231i	$0.103089\pi$
$84$		0			0
$85$	−6392.42	+	2077.02i	−0.884764	+	0.287477i
$86$		0			0
$87$	−1590.66	+	2755.10i	−0.210154	+	0.363998i
$88$		0			0
$89$	−7133.99	−	2317.97i	−0.900642	−	0.292636i	−0.178140	−	0.984005i	$-0.557008\pi$
$89$	−7133.99	−	2317.97i	−0.900642	−	0.292636i	−0.722502	+	0.691369i	$0.757008\pi$
$90$		0			0
$91$	−1746.19	−	2403.42i	−0.210867	−	0.290233i
$92$		0			0
$93$	7645.98	−	2409.44i	0.884030	−	0.278580i
$94$		0			0
$95$	−6000.57	+	4359.67i	−0.664883	+	0.483066i
$96$		0			0
$97$	940.834	−	2895.59i	0.0999930	−	0.307747i	−0.888530	−	0.458819i	$-0.848273\pi$
$97$	940.834	−	2895.59i	0.0999930	−	0.307747i	0.988523	+	0.151072i	$0.0482726\pi$
$98$		0			0
$99$	−1161.58	−	670.640i	−0.118517	−	0.0684257i
$100$		0			0
$101$	782.101	+	2407.06i	0.0766691	+	0.235963i	0.982045	−	0.188648i	$-0.0604107\pi$
$101$	782.101	+	2407.06i	0.0766691	+	0.235963i	−0.905376	+	0.424612i	$0.860411\pi$
$102$		0			0
$103$	825.205	+	367.405i	0.0777834	+	0.0346314i	0.445260	−	0.895402i	$-0.353111\pi$
$103$	825.205	+	367.405i	0.0777834	+	0.0346314i	−0.367476	+	0.930033i	$0.619778\pi$
$104$		0			0
$105$	4524.89	−	475.585i	0.410421	−	0.0431370i
$106$		0			0
$107$	−3240.83	−	688.860i	−0.283067	−	0.0601677i	0.0641903	−	0.997938i	$-0.479554\pi$
$107$	−3240.83	−	688.860i	−0.283067	−	0.0601677i	−0.347257	+	0.937770i	$0.612887\pi$
$108$		0			0
$109$	14193.4	+	10312.1i	1.19463	+	0.867951i	0.993746	−	0.111664i	$-0.0356180\pi$
$109$	14193.4	+	10312.1i	1.19463	+	0.867951i	0.200886	+	0.979615i	$0.435618\pi$
$110$		0			0
$111$	1404.31	−	13361.1i	0.113977	−	1.08441i
$112$		0			0
$113$	12763.2	−	2712.90i	0.999547	−	0.212460i	0.321049	−	0.947063i	$-0.395965\pi$
$113$	12763.2	−	2712.90i	0.999547	−	0.212460i	0.678498	+	0.734602i	$0.262631\pi$
$114$		0			0
$115$	−18482.7	−	16641.9i	−1.39756	−	1.25836i
$116$		0			0
$117$	−1429.65	+	1287.26i	−0.104438	+	0.0940361i
$118$		0			0
$119$	3314.30	−	1913.51i	0.234044	−	0.135126i
$120$		0			0
$121$	754.743	−	336.033i	0.0515500	−	0.0229515i
$122$		0			0
$123$		−	4301.50i		−	0.284322i
$124$		0			0
$125$	−9040.31			−0.578580
$126$		0			0
$127$	8153.41	+	18312.9i	0.505513	+	1.13540i	0.968495	+	0.249033i	$0.0801126\pi$
$127$	8153.41	+	18312.9i	0.505513	+	1.13540i	−0.462982	+	0.886367i	$0.653221\pi$
$128$		0			0
$129$	−7256.87	−	12569.3i	−0.436084	−	0.755319i
$130$		0			0
$131$	−8334.21	−	9256.08i	−0.485648	−	0.539367i	0.449661	−	0.893199i	$-0.351545\pi$
$131$	−8334.21	−	9256.08i	−0.485648	−	0.539367i	−0.935309	+	0.353833i	$0.884878\pi$
$132$		0			0
$133$	2825.84	−	3138.42i	0.159751	−	0.177422i
$134$		0			0
$135$	−4960.61	−	23337.9i	−0.272187	−	1.28054i
$136$		0			0
$137$	34550.8	+	3631.44i	1.84085	+	0.193481i	0.960014	−	0.279950i	$-0.0903180\pi$
$137$	34550.8	+	3631.44i	1.84085	+	0.193481i	0.880831	+	0.473431i	$0.156985\pi$
$138$		0			0
$139$	19603.0	−	26981.2i	1.01459	−	1.39647i	0.0986674	−	0.995120i	$-0.468542\pi$
$139$	19603.0	−	26981.2i	1.01459	−	1.39647i	0.915926	−	0.401347i	$-0.131458\pi$
$140$		0			0
$141$	698.906	−	3288.09i	0.0351545	−	0.165389i
$142$		0			0
$143$	2071.17	+	19705.9i	0.101285	+	0.963660i
$144$		0			0
$145$	4800.80	−	10782.8i	0.228338	−	0.512855i
$146$		0			0
$147$	16585.0	−	5388.79i	0.767504	−	0.249377i
$148$		0			0
$149$	−15462.4	+	26781.7i	−0.696474	+	1.20633i	0.273207	+	0.961955i	$0.411915\pi$
$149$	−15462.4	+	26781.7i	−0.696474	+	1.20633i	−0.969681	+	0.244373i	$0.921418\pi$
$150$		0			0
$151$	−9780.62	−	3177.91i	−0.428956	−	0.139376i	0.0865788	−	0.996245i	$-0.472407\pi$
$151$	−9780.62	−	3177.91i	−0.428956	−	0.139376i	−0.515534	+	0.856869i	$0.672407\pi$
$152$		0			0
$153$	−1456.68	−	2004.94i	−0.0622272	−	0.0856484i
$154$		0			0
$155$	−27278.0	+	11855.7i	−1.13540	+	0.493473i
$156$		0			0
$157$	22516.1	−	16358.9i	0.913468	−	0.663674i	−0.0284214	−	0.999596i	$-0.509048\pi$
$157$	22516.1	−	16358.9i	0.913468	−	0.663674i	0.941890	+	0.335923i	$0.109048\pi$
$158$		0			0
$159$	−7840.32	+	24130.0i	−0.310127	+	0.954473i
$160$		0			0
$161$	12263.8	+	7080.49i	0.473121	+	0.273157i
$162$		0			0
$163$	−5972.39	−	18381.1i	−0.224788	−	0.691826i	−0.998313	−	0.0580607i	$-0.981508\pi$
$163$	−5972.39	−	18381.1i	−0.224788	−	0.691826i	0.773525	−	0.633766i	$-0.218492\pi$
$164$		0			0
$165$	−27722.5	−	12342.9i	−1.01827	−	0.453365i
$166$		0			0
$167$	33978.6	−	3571.29i	1.21835	−	0.128054i	0.526551	−	0.850143i	$-0.323485\pi$
$167$	33978.6	−	3571.29i	1.21835	−	0.128054i	0.691800	+	0.722089i	$0.256818\pi$
$168$		0			0
$169$	−138.358	−	29.4088i	−0.00484429	−	0.00102969i
$170$		0			0
$171$	−2212.47	−	1607.45i	−0.0756633	−	0.0549726i
$172$		0			0
$173$	−1177.82	+	11206.2i	−0.0393539	+	0.374427i	0.957065	+	0.289873i	$0.0936132\pi$
$173$	−1177.82	+	11206.2i	−0.0393539	+	0.374427i	−0.996419	+	0.0845539i	$0.973053\pi$
$174$		0			0
$175$	−5738.40	+	1219.73i	−0.187376	+	0.0398281i
$176$		0			0
$177$	−17288.8	−	15566.9i	−0.551847	−	0.496886i
$178$		0			0
$179$	45518.3	−	40984.8i	1.42063	−	1.27914i	0.513621	−	0.858017i	$-0.328304\pi$
$179$	45518.3	−	40984.8i	1.42063	−	1.27914i	0.907005	−	0.421120i	$-0.138363\pi$
$180$		0			0
$181$	−5271.23	+	3043.35i	−0.160900	+	0.0928954i	−0.578288	−	0.815833i	$-0.696279\pi$
$181$	−5271.23	+	3043.35i	−0.160900	+	0.0928954i	0.417388	+	0.908728i	$0.362946\pi$
$182$		0			0
$183$	−49256.0	+	21930.2i	−1.47081	+	0.654847i
$184$		0			0
$185$			49844.8i			1.45639i
$186$		0			0
$187$	−25525.3			−0.729940
$188$		0			0
$189$	5525.51	+	12410.5i	0.154685	+	0.347428i
$190$		0			0
$191$	−8247.63	−	14285.3i	−0.226080	−	0.391582i	0.730563	−	0.682846i	$-0.239258\pi$
$191$	−8247.63	−	14285.3i	−0.226080	−	0.391582i	−0.956643	+	0.291263i	$0.905924\pi$
$192$		0			0
$193$	−8856.06	−	9835.65i	−0.237753	−	0.264051i	0.612447	−	0.790512i	$-0.290185\pi$
$193$	−8856.06	−	9835.65i	−0.237753	−	0.264051i	−0.850200	+	0.526461i	$0.823519\pi$
$194$		0			0
$195$	−29123.9	+	32345.4i	−0.765915	+	0.850634i
$196$		0			0
$197$	−272.066	−	1279.97i	−0.00701038	−	0.0329812i	0.974503	−	0.224373i	$-0.0720333\pi$
$197$	−272.066	−	1279.97i	−0.00701038	−	0.0329812i	−0.981514	+	0.191392i	$0.938700\pi$
$198$		0			0
$199$	37104.7	+	3899.87i	0.936965	+	0.0984790i	0.560687	−	0.828028i	$-0.310537\pi$
$199$	37104.7	+	3899.87i	0.936965	+	0.0984790i	0.376278	+	0.926507i	$0.377204\pi$
$200$		0			0
$201$	3739.13	−	5146.47i	0.0925504	−	0.127385i
$202$		0			0
$203$	−1397.27	+	6573.65i	−0.0339070	+	0.159520i
$204$		0			0
$205$	1668.20	+	15871.9i	0.0396954	+	0.377677i
$206$		0			0
$207$	3729.84	−	8377.35i	0.0870461	−	0.195509i
$208$		0			0
$209$	−26788.7	+	8704.19i	−0.613281	+	0.199267i
$210$		0			0
$211$	−36089.5	+	62508.9i	−0.810618	+	1.40403i	0.101814	+	0.994803i	$0.467535\pi$
$211$	−36089.5	+	62508.9i	−0.810618	+	1.40403i	−0.912432	+	0.409228i	$0.865798\pi$
$212$		0			0
$213$	−34259.5	−	11131.6i	−0.755131	−	0.245357i
$214$		0			0
$215$	31651.3	+	43564.2i	0.684722	+	0.942439i
$216$		0			0
$217$	13788.7	−	9832.07i	0.292821	−	0.208798i
$218$		0			0
$219$	25385.1	−	18443.4i	0.529287	−	0.384549i
$220$		0			0
$221$	−11313.3	+	34818.7i	−0.231635	+	0.712899i
$222$		0			0
$223$	−26350.4	−	15213.4i	−0.529880	−	0.305926i	0.211088	−	0.977467i	$-0.432299\pi$
$223$	−26350.4	−	15213.4i	−0.529880	−	0.305926i	−0.740968	+	0.671541i	$0.765633\pi$
$224$		0			0
$225$	1173.96	+	3613.07i	0.0231893	+	0.0713692i
$226$		0			0
$227$	83160.9	+	37025.6i	1.61387	+	0.718539i	0.997616	−	0.0690122i	$-0.0219847\pi$
$227$	83160.9	+	37025.6i	1.61387	+	0.718539i	0.616249	+	0.787551i	$0.288651\pi$
$228$		0			0
$229$	−17628.1	+	1852.79i	−0.336151	+	0.0353309i	−0.271100	−	0.962551i	$-0.587387\pi$
$229$	−17628.1	+	1852.79i	−0.336151	+	0.0353309i	−0.0650504	+	0.997882i	$0.520721\pi$
$230$		0			0
$231$	16900.9	+	3592.39i	0.316727	+	0.0673225i
$232$		0			0
$233$	62543.7	+	45440.7i	1.15205	+	0.837015i	0.988752	−	0.149562i	$-0.0477863\pi$
$233$	62543.7	+	45440.7i	1.15205	+	0.837015i	0.163299	+	0.986577i	$0.447786\pi$
$234$		0			0
$235$	−1303.67	+	12403.6i	−0.0236065	+	0.224601i
$236$		0			0
$237$	1266.29	−	269.158i	0.0225443	−	0.00479193i
$238$		0			0
$239$	16443.3	+	14805.7i	0.287869	+	0.259198i	0.800394	−	0.599474i	$-0.204623\pi$
$239$	16443.3	+	14805.7i	0.287869	+	0.259198i	−0.512526	+	0.858672i	$0.671290\pi$
$240$		0			0
$241$	−11702.6	+	10537.0i	−0.201487	+	0.181420i	−0.763697	−	0.645575i	$-0.776618\pi$
$241$	−11702.6	+	10537.0i	−0.201487	+	0.181420i	0.562210	+	0.826994i	$0.309951\pi$
$242$		0			0
$243$	14296.3	−	8253.98i	0.242109	−	0.139782i
$244$		0			0
$245$	−59106.1	+	26315.7i	−0.984691	+	0.438413i
$246$		0			0
$247$			40400.0i			0.662198i
$248$		0			0
$249$	10904.3			0.175874
$250$		0			0
$251$	28603.6	+	64244.7i	0.454018	+	1.01974i	0.985031	+	0.172378i	$0.0551449\pi$
$251$	28603.6	+	64244.7i	0.454018	+	1.01974i	−0.531013	+	0.847364i	$0.678188\pi$
$252$		0			0
$253$	−47225.1	−	81796.2i	−0.737788	−	1.27789i
$254$		0			0
$255$	−37517.9	−	41667.8i	−0.576976	−	0.640797i
$256$		0			0
$257$	−50631.4	+	56231.8i	−0.766573	+	0.851366i	−0.992432	−	0.122794i	$-0.960814\pi$
$257$	−50631.4	+	56231.8i	−0.766573	+	0.851366i	0.225859	+	0.974160i	$0.427481\pi$
$258$		0			0
$259$	−5900.67	−	27760.5i	−0.0879634	−	0.413835i
$260$		0			0
$261$	4328.12	+	454.904i	0.0635358	+	0.00667788i
$262$		0			0
$263$	60857.1	−	83762.6i	0.879832	−	1.21099i	−0.0966352	−	0.995320i	$-0.530808\pi$
$263$	60857.1	−	83762.6i	0.879832	−	1.21099i	0.976467	−	0.215665i	$-0.0691920\pi$
$264$		0			0
$265$	19571.5	−	92076.6i	0.278697	−	1.31116i
$266$		0			0
$267$	−6540.77	−	62231.3i	−0.0917501	−	0.872944i
$268$		0			0
$269$	33187.8	−	74541.1i	0.458642	−	1.03013i	−0.525182	−	0.850990i	$-0.676003\pi$
$269$	33187.8	−	74541.1i	0.458642	−	1.03013i	0.983824	−	0.179137i	$-0.0573307\pi$
$270$		0			0
$271$	−91525.7	+	29738.5i	−1.24625	+	0.404931i	−0.856575	−	0.516023i	$-0.827412\pi$
$271$	−91525.7	+	29738.5i	−1.24625	+	0.404931i	−0.389673	+	0.920953i	$0.627412\pi$
$272$		0			0
$273$	12391.1	−	21462.1i	0.166259	−	0.287969i
$274$		0			0
$275$	37213.6	+	12091.4i	0.492081	+	0.159887i
$276$		0			0
$277$	−80556.1	−	110876.i	−1.04988	−	1.44503i	−0.888915	−	0.458073i	$-0.848540\pi$
$277$	−80556.1	−	110876.i	−1.04988	−	1.44503i	−0.160963	−	0.986960i	$-0.551460\pi$
$278$		0			0
$279$	−7265.36	−	8214.61i	−0.0933359	−	0.105531i
$280$		0			0
$281$	−39468.3	+	28675.4i	−0.499846	+	0.363159i	−0.808958	−	0.587866i	$-0.799968\pi$
$281$	−39468.3	+	28675.4i	−0.499846	+	0.363159i	0.309112	+	0.951026i	$0.399968\pi$
$282$		0			0
$283$	11674.0	−	35928.8i	0.145763	−	0.448611i	−0.851346	−	0.524605i	$-0.824213\pi$
$283$	11674.0	−	35928.8i	0.145763	−	0.448611i	0.997108	+	0.0759940i	$0.0242130\pi$
$284$		0			0
$285$	−53583.8	−	30936.6i	−0.659696	−	0.380876i
$286$		0			0
$287$	−2808.01	−	8642.15i	−0.0340906	−	0.104920i
$288$		0			0
$289$	33215.3	+	14788.4i	0.397688	+	0.177062i
$290$		0			0
$291$	25258.8	−	2654.81i	0.298282	−	0.0313507i
$292$		0			0
$293$	43692.6	+	9287.16i	0.508948	+	0.108180i	0.455226	−	0.890376i	$-0.349558\pi$
$293$	43692.6	+	9287.16i	0.508948	+	0.108180i	0.0537214	+	0.998556i	$0.482892\pi$
$294$		0			0
$295$	69830.2	+	50734.6i	0.802415	+	0.582989i
$296$		0			0
$297$	9471.14	−	90111.9i	0.107372	−	1.02157i
$298$		0			0
$299$	−132508.	+	28165.5i	−1.48218	+	0.315047i
$300$		0			0
$301$	−22785.0	−	20515.7i	−0.251487	−	0.226440i
$302$		0			0
$303$	−15690.0	+	14127.3i	−0.170898	+	0.153877i
$304$		0			0
$305$	173242.	−	100021.i	1.86231	−	1.07521i
$306$		0			0
$307$	16794.3	−	7477.31i	0.178191	−	0.0793357i	−0.315702	−	0.948858i	$-0.602240\pi$
$307$	16794.3	−	7477.31i	0.178191	−	0.0793357i	0.493893	+	0.869523i	$0.335573\pi$
$308$		0			0
$309$			7535.29i			0.0789192i
$310$		0			0
$311$	136613.			1.41244			0.706221	−	0.707992i	$-0.250399\pi$
$311$	136613.			1.41244			0.706221	+	0.707992i	$0.250399\pi$
$312$		0			0
$313$	−15874.6	−	35654.9i	−0.162037	−	0.363940i	0.814220	−	0.580556i	$-0.197165\pi$
$313$	−15874.6	−	35654.9i	−0.162037	−	0.363940i	−0.976257	+	0.216616i	$0.930498\pi$
$314$		0			0
$315$	−3112.02	−	5390.18i	−0.0313633	−	0.0543228i
$316$		0			0
$317$	88338.9	+	98110.3i	0.879091	+	0.976329i	0.999866	−	0.0163509i	$-0.00520488\pi$
$317$	88338.9	+	98110.3i	0.879091	+	0.976329i	−0.120776	+	0.992680i	$0.538538\pi$
$318$		0			0
$319$	29993.2	−	33310.8i	0.294741	−	0.327343i
$320$		0			0
$321$	−5746.45	−	27034.9i	−0.0557685	−	0.262370i
$322$		0			0
$323$	−51758.9	−	5440.08i	−0.496112	−	0.0521435i
$324$		0			0
$325$	32987.5	−	45403.5i	0.312308	−	0.429855i
$326$		0			0
$327$	−30428.2	+	143154.i	−0.284565	+	1.33877i
$328$		0			0
$329$	−742.284	−	7062.36i	−0.00685769	−	0.0652466i
$330$		0			0
$331$	−15002.9	+	33697.0i	−0.136936	+	0.307564i	−0.968977	−	0.247150i	$-0.920506\pi$
$331$	−15002.9	+	33697.0i	−0.136936	+	0.307564i	0.832041	+	0.554714i	$0.187172\pi$
$332$		0			0
$333$	−17478.8	+	5679.21i	−0.157624	+	0.0512152i
$334$		0			0
$335$	−11800.9	+	20439.7i	−0.105154	+	0.182132i
$336$		0			0
$337$	84149.1	+	27341.7i	0.740951	+	0.240750i	0.655083	−	0.755557i	$-0.272634\pi$
$337$	84149.1	+	27341.7i	0.740951	+	0.240750i	0.0858681	+	0.996307i	$0.472634\pi$
$338$		0			0
$339$	63979.8	+	88060.6i	0.556728	+	0.766271i
$340$		0			0
$341$	−112434.	+	10808.2i	−0.966919	+	0.0929492i
$342$		0			0
$343$	64033.7	−	46523.2i	0.544277	−	0.395440i
$344$		0			0
$345$	64112.4	−	197318.i	0.538647	−	1.65778i
$346$		0			0
$347$	6952.24	+	4013.88i	0.0577385	+	0.0333354i	0.528591	−	0.848876i	$-0.322720\pi$
$347$	6952.24	+	4013.88i	0.0577385	+	0.0333354i	−0.470853	+	0.882212i	$0.656054\pi$
$348$		0			0
$349$	28699.2	+	88327.2i	0.235624	+	0.725176i	0.997038	+	0.0769103i	$0.0245055\pi$
$349$	28699.2	+	88327.2i	0.235624	+	0.725176i	−0.761414	+	0.648266i	$0.775494\pi$
$350$		0			0
$351$	−118723.	−	52858.7i	−0.963650	−	0.429045i
$352$		0			0
$353$	−187231.	+	19678.8i	−1.50255	+	0.157924i	−0.819767	−	0.572698i	$-0.805897\pi$
$353$	−187231.	+	19678.8i	−1.50255	+	0.157924i	−0.682782	+	0.730622i	$0.739230\pi$
$354$		0			0
$355$	130729.	+	27787.3i	1.03733	+	0.220491i
$356$		0			0
$357$	25827.8	+	18765.0i	0.202652	+	0.147235i
$358$		0			0
$359$	−727.669	+	6923.31i	−0.00564605	+	0.0537186i	−0.996982	−	0.0776310i	$-0.975264\pi$
$359$	−727.669	+	6923.31i	−0.00564605	+	0.0537186i	0.991336	+	0.131350i	$0.0419311\pi$
$360$		0			0
$361$	71297.2	−	15154.7i	0.547089	−	0.116287i
$362$		0			0
$363$	5121.66	+	4611.57i	0.0388685	+	0.0349973i
$364$		0			0
$365$	−86514.3	+	77897.9i	−0.649385	+	0.584709i
$366$		0			0
$367$	151444.	−	87436.3i	1.12440	−	0.649172i	0.181879	−	0.983321i	$-0.441782\pi$
$367$	151444.	−	87436.3i	1.12440	−	0.649172i	0.942520	+	0.334149i	$0.108449\pi$
$368$		0			0
$369$	−5375.62	+	2393.38i	−0.0394799	+	0.0175776i
$370$		0			0
$371$			53597.8i			0.389403i
$372$		0			0
$373$	−253327.			−1.82081			−0.910405	−	0.413718i	$-0.864230\pi$
$373$	−253327.			−1.82081			−0.910405	+	0.413718i	$0.864230\pi$
$374$		0			0
$375$	−30673.6	−	68894.0i	−0.218123	−	0.489913i
$376$		0			0
$377$	−32145.3	−	55677.2i	−0.226170	−	0.391737i
$378$		0			0
$379$	−94600.1	−	105064.i	−0.658587	−	0.731435i	0.317634	−	0.948213i	$-0.397112\pi$
$379$	−94600.1	−	105064.i	−0.658587	−	0.731435i	−0.976221	+	0.216778i	$0.930445\pi$
$380$		0			0
$381$	−111894.	+	124271.i	−0.770825	+	0.856087i
$382$		0			0
$383$	−11709.0	−	55086.5i	−0.0798219	−	0.375532i	0.920046	−	0.391811i	$-0.128151\pi$
$383$	−11709.0	−	55086.5i	−0.0798219	−	0.375532i	−0.999867	+	0.0162788i	$0.994818\pi$
$384$		0			0
$385$	−63754.8	−	6700.89i	−0.430121	−	0.0452076i
$386$		0			0
$387$	−11670.1	+	16062.6i	−0.0779210	+	0.107249i
$388$		0			0
$389$	−48657.9	+	228917.i	−0.321554	+	1.51279i	0.459414	+	0.888222i	$0.348059\pi$
$389$	−48657.9	+	228917.i	−0.321554	+	1.51279i	−0.780968	+	0.624571i	$0.785274\pi$
$390$		0			0
$391$	−18241.6	−	173557.i	−0.119319	−	1.13524i
$392$		0			0
$393$	42260.5	−	94918.7i	0.273621	−	0.614564i
$394$		0			0
$395$	−4568.02	+	1484.24i	−0.0292775	+	0.00951283i
$396$		0			0
$397$	−116189.	+	201245.i	−0.737195	+	1.27686i	0.216558	+	0.976270i	$0.430517\pi$
$397$	−116189.	+	201245.i	−0.737195	+	1.27686i	−0.953754	+	0.300590i	$0.902817\pi$
$398$		0			0
$399$	33505.2	+	10886.5i	0.210458	+	0.0683820i
$400$		0			0
$401$	−56130.4	−	77256.8i	−0.349067	−	0.480450i	0.597995	−	0.801500i	$-0.295964\pi$
$401$	−56130.4	−	77256.8i	−0.349067	−	0.480450i	−0.947062	+	0.321050i	$0.895964\pi$
$402$		0			0
$403$	−35089.6	+	158161.i	−0.216057	+	0.973841i
$404$		0			0
$405$	137876.	−	100173.i	0.840581	−	0.610718i
$406$		0			0
$407$	−58494.3	+	180027.i	−0.353122	+	1.08680i
$408$		0			0
$409$	94213.0	+	54393.9i	0.563202	+	0.325165i	0.754430	−	0.656381i	$-0.227914\pi$
$409$	94213.0	+	54393.9i	0.563202	+	0.325165i	−0.191228	+	0.981546i	$0.561247\pi$
$410$		0			0
$411$	89556.0	+	275625.i	0.530165	+	1.63168i
$412$		0			0
$413$	−44897.0	−	19989.5i	−0.263219	−	0.117193i
$414$		0			0
$415$	−40235.3	+	4228.90i	−0.233620	+	0.0245545i
$416$		0			0
$417$	272130.	+	57842.9i	1.56496	+	0.332643i
$418$		0			0
$419$	61340.4	+	44566.4i	0.349396	+	0.253851i	0.748616	−	0.663004i	$-0.230719\pi$
$419$	61340.4	+	44566.4i	0.349396	+	0.253851i	−0.399219	+	0.916855i	$0.630719\pi$
$420$		0			0
$421$	−30563.1	+	290788.i	−0.172438	+	1.64064i	0.476054	+	0.879416i	$0.342067\pi$
$421$	−30563.1	+	290788.i	−0.172438	+	1.64064i	−0.648492	+	0.761221i	$0.724600\pi$
$422$		0			0
$423$	−4498.03	+	956.087i	−0.0251386	+	0.00534338i
$424$		0			0
$425$	53727.1	+	48376.1i	0.297451	+	0.267826i
$426$		0			0
$427$	−84644.3	+	76214.0i	−0.464239	+	0.418003i
$428$		0			0
$429$	−143146.	+	82645.6i	−0.777796	+	0.449061i
$430$		0			0
$431$	212131.	−	94446.7i	1.14196	−	0.508431i	0.253473	−	0.967342i	$-0.418427\pi$
$431$	212131.	−	94446.7i	1.14196	−	0.508431i	0.888482	+	0.458911i	$0.151760\pi$
$432$		0			0
$433$		−	107182.i		−	0.571670i	−0.958279	−	0.285835i	$-0.907729\pi$
$433$		−	107182.i		−	0.571670i	0.958279	−	0.285835i	$-0.0922709\pi$
$434$		0			0
$435$	98462.0			0.520343
$436$		0			0
$437$	−78327.8	−	175927.i	−0.410160	−	0.921234i
$438$		0			0
$439$	−46893.4	−	81221.7i	−0.243323	−	0.421447i	0.718336	−	0.695696i	$-0.244904\pi$
$439$	−46893.4	−	81221.7i	−0.243323	−	0.421447i	−0.961659	+	0.274249i	$0.911571\pi$
$440$		0			0
$441$	−15962.4	−	17728.0i	−0.0820769	−	0.0911556i
$442$		0			0
$443$	−47203.3	+	52424.6i	−0.240528	+	0.267133i	−0.851307	−	0.524668i	$-0.824190\pi$
$443$	−47203.3	+	52424.6i	−0.240528	+	0.267133i	0.610779	+	0.791801i	$0.290856\pi$
$444$		0			0
$445$	48268.8	+	227087.i	0.243751	+	1.14676i
$446$		0			0
$447$	−256561.	−	26965.6i	−1.28403	−	0.134957i
$448$		0			0
$449$	−18601.9	+	25603.3i	−0.0922708	+	0.127000i	−0.852656	−	0.522472i	$-0.825010\pi$
$449$	−18601.9	+	25603.3i	−0.0922708	+	0.127000i	0.760386	+	0.649472i	$0.225010\pi$
$450$		0			0
$451$	−12601.0	+	59282.8i	−0.0619513	+	0.291458i
$452$		0			0
$453$	−8967.32	−	85318.4i	−0.0436985	−	0.415763i
$454$		0			0
$455$	−37397.9	+	83997.1i	−0.180644	+	0.405734i
$456$		0			0
$457$	−55264.2	+	17956.4i	−0.264613	+	0.0859781i	−0.438319	−	0.898820i	$-0.644426\pi$
$457$	−55264.2	+	17956.4i	−0.264613	+	0.0859781i	0.173705	+	0.984798i	$0.444426\pi$
$458$		0			0
$459$	83707.1	−	144985.i	0.397317	−	0.688173i
$460$		0			0
$461$	77273.3	+	25107.6i	0.363603	+	0.118142i	0.485120	−	0.874448i	$-0.338776\pi$
$461$	77273.3	+	25107.6i	0.363603	+	0.118142i	−0.121517	+	0.992589i	$0.538776\pi$
$462$		0			0
$463$	−197939.	−	272439.i	−0.923355	−	1.27089i	−0.962396	−	0.271651i	$-0.912430\pi$
$463$	−197939.	−	272439.i	−0.923355	−	1.27089i	0.0390411	−	0.999238i	$-0.487570\pi$
$464$		0			0
$465$	−182903.	−	167653.i	−0.845893	−	0.775364i
$466$		0			0
$467$	215815.	−	156799.i	0.989575	−	0.718969i	0.0297472	−	0.999557i	$-0.490530\pi$
$467$	215815.	−	156799.i	0.989575	−	0.718969i	0.959828	+	0.280589i	$0.0905298\pi$
$468$		0			0
$469$	4152.69	−	12780.7i	0.0188792	−	0.0581042i
$470$		0			0
$471$	201064.	+	116084.i	0.906342	+	0.523277i
$472$		0			0
$473$	63192.6	+	194487.i	0.282451	+	0.869296i
$474$		0			0
$475$	72882.9	+	32449.6i	0.323027	+	0.143821i
$476$		0			0
$477$	34517.9	−	3627.98i	0.151708	−	0.0159451i
$478$		0			0
$479$	−256867.	−	54598.8i	−1.11953	−	0.237965i	−0.389267	−	0.921125i	$-0.627272\pi$
$479$	−256867.	−	54598.8i	−1.11953	−	0.237965i	−0.730268	+	0.683161i	$0.760605\pi$
$480$		0			0
$481$	219647.	+	159583.i	0.949368	+	0.689756i
$482$		0			0
$483$	−12348.0	+	117483.i	−0.0529301	+	0.503596i
$484$		0			0
$485$	−92171.5	+	19591.7i	−0.391844	+	0.0832890i
$486$		0			0
$487$	10108.3	+	9101.56i	0.0426207	+	0.0383759i	0.690166	−	0.723651i	$-0.257538\pi$
$487$	10108.3	+	9101.56i	0.0426207	+	0.0383759i	−0.647545	+	0.762027i	$0.724204\pi$
$488$		0			0
$489$	119814.	−	107881.i	0.501061	−	0.451157i
$490$		0			0
$491$	311585.	−	179894.i	1.29245	−	0.746196i	0.313361	−	0.949634i	$-0.398545\pi$
$491$	311585.	−	179894.i	1.29245	−	0.746196i	0.979088	+	0.203438i	$0.0652116\pi$
$492$		0			0
$493$	75660.0	−	33686.0i	0.311295	−	0.138598i
$494$		0			0
$495$			41512.7i			0.169422i
$496$		0			0
$497$	−76097.5			−0.308076
$498$		0			0
$499$	−143606.	−	322545.i	−0.576730	−	1.29536i	−0.932630	−	0.360833i	$-0.882492\pi$
$499$	−143606.	−	322545.i	−0.576730	−	1.29536i	0.355900	−	0.934524i	$-0.384174\pi$
$500$		0			0
$501$	142505.	+	246826.i	0.567746	+	0.983365i
$502$		0			0
$503$	−144952.	−	160985.i	−0.572912	−	0.636283i	0.385147	−	0.922855i	$-0.374151\pi$
$503$	−144952.	−	160985.i	−0.572912	−	0.636283i	−0.958059	+	0.286572i	$0.907484\pi$
$504$		0			0
$505$	52414.7	−	58212.4i	0.205528	−	0.228262i
$506$		0			0
$507$	−245.328	−	1154.18i	−0.000954400	−	0.00449010i
$508$		0			0
$509$	−90260.9	−	9486.80i	−0.348389	−	0.0366171i	−0.0712818	−	0.997456i	$-0.522709\pi$
$509$	−90260.9	−	9486.80i	−0.348389	−	0.0366171i	−0.277107	+	0.960839i	$0.589376\pi$
$510$		0			0
$511$	38961.5	−	53625.9i	0.149209	−	0.205368i
$512$		0			0
$513$	38410.2	−	180706.i	0.145953	−	0.686654i
$514$		0			0
$515$	−2922.32	−	27804.0i	−0.0110183	−	0.104832i
$516$		0			0
$517$	−19264.5	+	43268.8i	−0.0720736	+	0.161880i
$518$		0			0
$519$	−89396.4	+	29046.7i	−0.331883	+	0.107835i
$520$		0			0
$521$	173073.	−	299771.i	0.637608	−	1.10437i	−0.348349	−	0.937365i	$-0.613257\pi$
$521$	173073.	−	299771.i	0.637608	−	1.10437i	0.985956	−	0.167004i	$-0.0534092\pi$
$522$		0			0
$523$	−441671.	−	143508.i	−1.61471	−	0.524652i	−0.644028	−	0.765002i	$-0.722738\pi$
$523$	−441671.	−	143508.i	−1.61471	−	0.524652i	−0.970686	+	0.240350i	$0.922738\pi$
$524$		0			0
$525$	−28765.6	−	39592.5i	−0.104365	−	0.143646i
$526$		0			0
$527$	−197904.	−	66252.6i	−0.712579	−	0.238551i
$528$		0			0
$529$	296021.	−	215072.i	1.05782	−	0.768549i
$530$		0			0
$531$	−9834.52	+	30267.5i	−0.0348790	+	0.107346i
$532$		0			0
$533$	75282.0	+	43464.1i	0.264994	+	0.152995i
$534$		0			0
$535$	31688.1	+	97525.9i	0.110710	+	0.340732i
$536$		0			0
$537$	466779.	+	207823.i	1.61868	+	0.720685i
$538$		0			0
$539$	−244359.	+	25683.1i	−0.841105	+	0.0884036i
$540$		0			0
$541$	429090.	+	91205.9i	1.46607	+	0.311622i	0.870693	−	0.491826i	$-0.163670\pi$
$541$	429090.	+	91205.9i	1.46607	+	0.311622i	0.595374	+	0.803448i	$0.297004\pi$
$542$		0			0
$543$	−41077.8	−	29844.8i	−0.139318	−	0.101221i
$544$		0			0
$545$	56757.8	−	540014.i	0.191088	−	1.81808i
$546$		0			0
$547$	−131255.	+	27899.0i	−0.438672	+	0.0932426i	−0.421953	−	0.906618i	$-0.638655\pi$
$547$	−131255.	+	27899.0i	−0.438672	+	0.0932426i	−0.0167188	+	0.999860i	$0.505322\pi$
$548$		0			0
$549$	54812.6	+	49353.5i	0.181859	+	0.163747i
$550$		0			0
$551$	67918.0	−	61153.7i	0.223708	−	0.201428i
$552$		0			0
$553$	2368.40	−	1367.39i	0.00774469	−	0.00447140i
$554$		0			0
$555$	−379856.	+	169123.i	−1.23320	+	0.549055i
$556$		0			0
$557$		−	467827.i		−	1.50791i	−0.656927	−	0.753954i	$-0.728144\pi$
$557$		−	467827.i		−	1.50791i	0.656927	−	0.753954i	$-0.271856\pi$
$558$		0			0
$559$	293305.			0.938633
$560$		0			0
$561$	−86606.8	−	194522.i	−0.275186	−	0.618078i
$562$		0			0
$563$	−223266.	−	386709.i	−0.704380	−	1.22002i	−0.966915	−	0.255099i	$-0.917892\pi$
$563$	−223266.	−	386709.i	−0.704380	−	1.22002i	0.262535	−	0.964922i	$-0.415441\pi$
$564$		0			0
$565$	−270227.	−	300117.i	−0.846508	−	0.940143i
$566$		0			0
$567$	−64930.0	+	72112.0i	−0.201966	+	0.224306i
$568$		0			0
$569$	109103.	+	513287.i	0.336985	+	1.58539i	0.741562	+	0.670885i	$0.234085\pi$
$569$	109103.	+	513287.i	0.336985	+	1.58539i	−0.404577	+	0.914504i	$0.632581\pi$
$570$		0			0
$571$	−319468.	−	33577.5i	−0.979841	−	0.102985i	−0.398955	−	0.916971i	$-0.630627\pi$
$571$	−319468.	−	33577.5i	−0.979841	−	0.102985i	−0.580886	+	0.813985i	$0.697294\pi$
$572$		0			0
$573$	80881.0	−	111323.i	0.246341	−	0.339060i
$574$		0			0
$575$	−55620.0	+	261672.i	−0.168227	+	0.791446i
$576$		0			0
$577$	52296.4	+	497567.i	0.157080	+	1.49451i	0.734803	+	0.678280i	$0.237275\pi$
$577$	52296.4	+	497567.i	0.157080	+	1.49451i	−0.577723	+	0.816233i	$0.696059\pi$
$578$		0			0
$579$	44906.7	−	100862.i	0.133954	−	0.300865i
$580$		0			0
$581$	21907.9	−	7118.32i	0.0649006	−	0.0210875i
$582$		0			0
$583$	178742.	−	309590.i	0.525883	−	0.910855i
$584$		0			0
$585$	56627.0	+	18399.2i	0.165467	+	0.0537635i
$586$		0			0
$587$	−49191.8	−	67706.8i	−0.142763	−	0.196497i	0.731647	−	0.681683i	$-0.238752\pi$
$587$	−49191.8	−	67706.8i	−0.142763	−	0.196497i	−0.874411	+	0.485186i	$0.838752\pi$
$588$		0			0
$589$	−230292.	−	2046.18i	−0.663818	−	0.00589811i
$590$		0			0
$591$	8831.22	−	6416.26i	0.0252840	−	0.0183699i
$592$		0			0
$593$	118606.	−	365032.i	0.337285	−	1.03806i	−0.628300	−	0.777971i	$-0.716249\pi$
$593$	118606.	−	365032.i	0.337285	−	1.03806i	0.965585	−	0.260087i	$-0.0837511\pi$
$594$		0			0
$595$	−102578.	−	59223.3i	−0.289747	−	0.167286i
$596$		0			0
$597$	96175.8	+	295999.i	0.269847	+	0.830503i
$598$		0			0
$599$	260948.	+	116182.i	0.727279	+	0.323806i	0.736764	−	0.676149i	$-0.236353\pi$
$599$	260948.	+	116182.i	0.727279	+	0.323806i	−0.00948530	+	0.999955i	$0.503019\pi$
$600$		0			0
$601$	683206.	−	71807.8i	1.89148	−	0.198803i	0.913407	−	0.407048i	$-0.133442\pi$
$601$	683206.	−	71807.8i	1.89148	−	0.198803i	0.978077	+	0.208245i	$0.0667751\pi$
$602$		0			0
$603$	−8512.06	−	1809.29i	−0.0234099	−	0.00497593i
$604$		0			0
$605$	−20686.6	−	15029.7i	−0.0565168	−	0.0410619i
$606$		0			0
$607$	−3914.42	+	37243.2i	−0.0106240	+	0.101081i	−0.998549	−	0.0538529i	$-0.982850\pi$
$607$	−3914.42	+	37243.2i	−0.0106240	+	0.101081i	0.987925	+	0.154934i	$0.0495165\pi$
$608$		0			0
$609$	−54837.2	+	11656.0i	−0.147857	+	0.0314279i
$610$		0			0
$611$	50484.0	+	45456.0i	0.135229	+	0.121761i
$612$		0			0
$613$	−298630.	+	268887.i	−0.794716	+	0.715565i	−0.962802	−	0.270207i	$-0.912908\pi$
$613$	−298630.	+	268887.i	−0.794716	+	0.715565i	0.168087	+	0.985772i	$0.446241\pi$
$614$		0			0
$615$	−115296.	+	66565.9i	−0.304833	+	0.175996i
$616$		0			0
$617$	−337023.	+	150052.i	−0.885296	+	0.394159i	−0.798449	−	0.602062i	$-0.794346\pi$
$617$	−337023.	+	150052.i	−0.885296	+	0.394159i	−0.0868472	+	0.996222i	$0.527679\pi$
$618$		0			0
$619$			484894.i			1.26551i	0.774353	+	0.632754i	$0.218076\pi$
$619$			484894.i			1.26551i	−0.774353	+	0.632754i	$0.781924\pi$
$620$		0			0
$621$	619476.			1.60635
$622$		0			0
$623$	−53765.4	−	120759.i	−0.138525	−	0.311131i
$624$		0			0
$625$	243932.	+	422503.i	0.624467	+	1.08161i
$626$		0			0
$627$	−157226.	−	174617.i	−0.399936	−	0.444174i
$628$		0			0
$629$	−234028.	+	259914.i	−0.591515	+	0.656944i
$630$		0			0
$631$	138303.	+	650664.i	0.347354	+	1.63417i	0.711396	+	0.702791i	$0.248063\pi$
$631$	138303.	+	650664.i	0.347354	+	1.63417i	−0.364042	+	0.931383i	$0.618603\pi$
$632$		0			0
$633$	−598817.	−	62938.2i	−1.49447	−	0.157075i
$634$		0			0
$635$	364675.	−	501933.i	0.904397	−	1.24480i
$636$		0			0
$637$	−73270.3	+	344710.i	−0.180571	+	0.849522i
$638$		0			0
$639$	5150.96	+	49008.1i	0.0126150	+	0.120023i
$640$		0			0
$641$	−125550.	+	281990.i	−0.305563	+	0.686305i	−0.999429	−	0.0337989i	$-0.989239\pi$
$641$	−125550.	+	281990.i	−0.305563	+	0.686305i	0.693866	+	0.720104i	$0.255906\pi$
$642$		0			0
$643$	332385.	−	107998.i	0.803933	−	0.261214i	0.121907	−	0.992542i	$-0.461099\pi$
$643$	332385.	−	107998.i	0.803933	−	0.261214i	0.682026	+	0.731328i	$0.261099\pi$
$644$		0			0
$645$	−224601.	+	389020.i	−0.539873	+	0.935087i
$646$		0			0
$647$	234889.	+	76320.0i	0.561117	+	0.182318i	0.575824	−	0.817574i	$-0.304681\pi$
$647$	234889.	+	76320.0i	0.561117	+	0.182318i	−0.0147066	+	0.999892i	$0.504681\pi$
$648$		0			0
$649$	192670.	+	265188.i	0.457431	+	0.629600i
$650$		0			0
$651$	121713.	+	71720.1i	0.287193	+	0.169231i
$652$		0			0
$653$	−62067.6	+	45094.8i	−0.145559	+	0.105755i	−0.658181	−	0.752859i	$-0.728674\pi$
$653$	−62067.6	+	45094.8i	−0.145559	+	0.105755i	0.512623	+	0.858614i	$0.328674\pi$
$654$		0			0
$655$	−119123.	+	366624.i	−0.277661	+	0.854553i
$656$		0			0
$657$	−37173.2	−	21462.0i	−0.0861192	−	0.0497209i
$658$		0			0
$659$	−152078.	−	468048.i	−0.350183	−	1.07775i	−0.958750	−	0.284251i	$-0.908255\pi$
$659$	−152078.	−	468048.i	−0.350183	−	1.07775i	0.608567	−	0.793503i	$-0.291745\pi$
$660$		0			0
$661$	−468112.	−	208417.i	−1.07139	−	0.477013i	−0.206226	−	0.978504i	$-0.566118\pi$
$661$	−468112.	−	208417.i	−1.07139	−	0.477013i	−0.865163	+	0.501491i	$0.832785\pi$
$662$		0			0
$663$	−303731.	+	31923.4i	−0.690974	+	0.0726243i
$664$		0			0
$665$	−127851.	−	27175.5i	−0.289108	−	0.0614517i
$666$		0			0
$667$	247928.	+	180130.i	0.557281	+	0.404888i
$668$		0			0
$669$	26531.4	−	252429.i	0.0592799	−	0.564011i
$670$		0			0
$671$	743083.	−	157947.i	1.65041	−	0.350806i
$672$		0			0
$673$	−132747.	−	119526.i	−0.293085	−	0.263895i	0.509450	−	0.860500i	$-0.329849\pi$
$673$	−132747.	−	119526.i	−0.293085	−	0.263895i	−0.802535	+	0.596606i	$0.796516\pi$
$674$		0			0
$675$	−190718.	+	171723.i	−0.418585	+	0.376895i
$676$		0			0
$677$	−278482.	+	160782.i	−0.607603	+	0.350800i	−0.772027	−	0.635590i	$-0.780757\pi$
$677$	−278482.	+	160782.i	−0.607603	+	0.350800i	0.164424	+	0.986390i	$0.447423\pi$
$678$		0			0
$679$	49014.5	−	21822.7i	0.106313	−	0.0473335i
$680$		0			0
$681$			759377.i			1.63743i
$682$		0			0
$683$	580889.			1.24524			0.622618	−	0.782526i	$-0.286069\pi$
$683$	580889.			1.24524			0.622618	+	0.782526i	$0.286069\pi$
$684$		0			0
$685$	−437340.	−	982281.i	−0.932047	−	2.09341i
$686$		0			0
$687$	−73931.4	−	128053.i	−0.156645	−	0.271316i
$688$		0			0
$689$	−343086.	−	381035.i	−0.722710	−	0.802651i
$690$		0			0
$691$	107850.	−	119779.i	0.225872	−	0.250857i	−0.619547	−	0.784959i	$-0.712684\pi$
$691$	107850.	−	119779.i	0.225872	−	0.250857i	0.845420	+	0.534103i	$0.179350\pi$
$692$		0			0
$693$	−4914.31	−	23120.0i	−0.0102328	−	0.0481417i
$694$		0			0
$695$	−1.02655e6	−	107894.i	−2.12525	−	0.223372i
$696$		0			0
$697$	−65821.5	+	90595.6i	−0.135489	+	0.186484i
$698$		0			0
$699$	−134083.	+	630811.i	−0.274422	+	1.29105i
$700$		0			0
$701$	74679.4	+	710527.i	0.151972	+	1.44592i	0.758922	+	0.651181i	$0.225726\pi$
$701$	74679.4	+	710527.i	0.151972	+	1.44592i	−0.606950	+	0.794740i	$0.707607\pi$
$702$		0			0
$703$	−156980.	+	352583.i	−0.317639	+	0.713430i
$704$		0			0
$705$	−98948.2	+	32150.2i	−0.199081	+	0.0646853i
$706$		0			0
$707$	−22300.5	+	38625.6i	−0.0446145	+	0.0772745i
$708$		0			0
$709$	−691332.	−	224627.i	−1.37529	−	0.446859i	−0.474172	−	0.880432i	$-0.657252\pi$
$709$	−691332.	−	224627.i	−1.37529	−	0.446859i	−0.901118	+	0.433574i	$0.857252\pi$
$710$		0			0
$711$	−1040.94	−	1432.73i	−0.00205914	−	0.00283417i
$712$		0			0
$713$	−153840.	−	756763.i	−0.302616	−	1.48861i
$714$		0			0
$715$	496136.	−	360464.i	0.970484	−	0.705098i
$716$		0			0
$717$	−57038.4	+	175546.i	−0.110950	+	0.341470i
$718$		0			0
$719$	152574.	+	88088.4i	0.295136	+	0.170397i	0.640256	−	0.768162i	$-0.278828\pi$
$719$	152574.	+	88088.4i	0.295136	+	0.170397i	−0.345120	+	0.938559i	$0.612162\pi$
$720$		0			0
$721$	4919.01	+	15139.2i	0.00946253	+	0.0291227i
$722$		0			0
$723$	−120007.	−	53430.5i	−0.229578	−	0.102215i
$724$		0			0
$725$	−126263.	+	13270.8i	−0.240215	+	0.0252476i
$726$		0			0
$727$	−619580.	−	131696.i	−1.17227	−	0.249174i	−0.419687	−	0.907669i	$-0.637860\pi$
$727$	−619580.	−	131696.i	−1.17227	−	0.249174i	−0.752585	+	0.658495i	$0.771193\pi$
$728$		0			0
$729$	472248.	+	343108.i	0.888617	+	0.645618i
$730$		0			0
$731$	−39495.1	+	375771.i	−0.0739109	+	0.703215i
$732$		0			0
$733$	803915.	−	170877.i	1.49624	−	0.318036i	0.614179	−	0.789167i	$-0.289487\pi$
$733$	803915.	−	170877.i	1.49624	−	0.318036i	0.882063	+	0.471131i	$0.156154\pi$
$734$		0			0
$735$	−401092.	−	361145.i	−0.742453	−	0.668508i
$736$		0			0
$737$	−66608.5	+	59974.5i	−0.122629	+	0.110416i
$738$		0			0
$739$	584253.	−	337318.i	1.06982	−	0.617662i	0.141690	−	0.989911i	$-0.454746\pi$
$739$	584253.	−	337318.i	1.06982	−	0.617662i	0.928133	+	0.372249i	$0.121413\pi$
$740$		0			0
$741$	−307879.	+	137077.i	−0.560717	+	0.249647i
$742$		0			0
$743$		−	202389.i		−	0.366613i	−0.983056	−	0.183307i	$-0.941320\pi$
$743$		−	202389.i		−	0.366613i	0.983056	−	0.183307i	$-0.0586801\pi$
$744$		0			0
$745$	957126.			1.72447
$746$		0			0
$747$	−6067.24	−	13627.2i	−0.0108730	−	0.0244212i
$748$		0			0
$749$	−29193.5	−	50564.6i	−0.0520382	−	0.0901328i
$750$		0			0
$751$	415707.	+	461689.i	0.737067	+	0.818596i	0.988807	−	0.149199i	$-0.0476695\pi$
$751$	415707.	+	461689.i	0.737067	+	0.818596i	−0.251740	+	0.967795i	$0.581003\pi$
$752$		0			0
$753$	−392542.	+	435962.i	−0.692304	+	0.768881i
$754$		0			0
$755$	66176.0	+	311334.i	0.116093	+	0.546175i
$756$		0			0
$757$	906256.	+	95251.3i	1.58146	+	0.166218i	0.854127	−	0.520064i	$-0.174092\pi$
$757$	906256.	+	95251.3i	1.58146	+	0.166218i	0.727335	+	0.686282i	$0.240759\pi$
$758$		0			0
$759$	463116.	−	637424.i	0.803908	−	1.10648i
$760$		0			0
$761$	47192.4	−	222023.i	0.0814898	−	0.383379i	−0.918436	−	0.395570i	$-0.870547\pi$
$761$	47192.4	−	222023.i	0.0814898	−	0.383379i	0.999926	+	0.0121906i	$0.00388048\pi$
$762$		0			0
$763$	32316.8	+	307473.i	0.0555110	+	0.528152i
$764$		0			0
$765$	−31197.5	+	70070.6i	−0.0533085	+	0.119733i
$766$		0			0
$767$	447135.	−	145283.i	0.760060	−	0.246959i
$768$		0			0
$769$	−495750.	+	858664.i	−0.838320	+	1.45201i	0.0529778	+	0.998596i	$0.483129\pi$
$769$	−495750.	+	858664.i	−0.838320	+	1.45201i	−0.891298	+	0.453418i	$0.850205\pi$
$770$		0			0
$771$	−600321.	−	195056.i	−1.00989	−	0.328134i
$772$		0			0
$773$	−667707.	−	919020.i	−1.11745	−	1.53803i	−0.809963	−	0.586481i	$-0.800513\pi$
$773$	−667707.	−	919020.i	−1.11745	−	1.53803i	−0.307484	−	0.951553i	$-0.599487\pi$
$774$		0			0
$775$	257142.	+	190338.i	0.428125	+	0.316901i
$776$		0			0
$777$	191535.	−	139158.i	0.317253	−	0.230498i
$778$		0			0
$779$	−38186.3	+	117525.i	−0.0629263	+	0.193667i
$780$		0			0
$781$	439552.	+	253775.i	0.720623	+	0.416052i
$782$		0			0
$783$	90848.1	+	279602.i	0.148181	+	0.456054i
$784$		0			0
$785$	−786913.	−	350356.i	−1.27699	−	0.568553i
$786$		0			0
$787$	−54531.7	+	5731.51i	−0.0880439	+	0.00925379i	−0.148448	−	0.988920i	$-0.547428\pi$
$787$	−54531.7	+	5731.51i	−0.0880439	+	0.00925379i	0.0604040	+	0.998174i	$0.480761\pi$
$788$		0			0
$789$	844822.	+	179573.i	1.35710	+	0.288460i
$790$		0			0
$791$	186027.	+	135157.i	0.297320	+	0.216016i
$792$		0			0
$793$	113895.	−	1.08364e6i	0.181116	−	1.72320i
$794$		0			0
$795$	768100.	−	163265.i	1.21530	−	0.258320i
$796$		0			0
$797$	−117858.	−	106120.i	−0.185542	−	0.167063i	0.571125	−	0.820863i	$-0.306507\pi$
$797$	−117858.	−	106120.i	−0.185542	−	0.167063i	−0.756667	+	0.653800i	$0.773174\pi$
$798$		0			0
$799$	−65034.3	+	58557.1i	−0.101871	+	0.0917247i
$800$		0			0
$801$	−74131.6	+	42799.9i	−0.115542	+	0.0667080i
$802$		0			0
$803$	−403883.	+	179820.i	−0.626361	+	0.278874i
$804$		0			0
$805$		−	438284.i		−	0.676338i
$806$		0			0
$807$	680666.			1.04517
$808$		0			0
$809$	−216051.	−	485257.i	−0.330110	−	0.741439i	0.669890	−	0.742461i	$-0.266341\pi$
$809$	−216051.	−	485257.i	−0.330110	−	0.741439i	−0.999999	+	0.00102204i	$0.999675\pi$
$810$		0			0
$811$	381178.	+	660221.i	0.579544	+	1.00380i	0.995532	+	0.0944298i	$0.0301028\pi$
$811$	381178.	+	660221.i	0.579544	+	1.00380i	−0.415987	+	0.909370i	$0.636564\pi$
$812$		0			0
$813$	−537175.	−	596594.i	−0.812709	−	0.902605i
$814$		0			0
$815$	−400257.	+	444530.i	−0.602592	+	0.669246i
$816$		0			0
$817$	86688.8	+	407839.i	0.129873	+	0.611004i
$818$		0			0
$819$	−33715.8	−	3543.67i	−0.0502650	−	0.00528307i
$820$		0			0
$821$	630220.	−	867424.i	0.934988	−	1.28690i	−0.0228935	−	0.999738i	$-0.507288\pi$
$821$	630220.	−	867424.i	0.934988	−	1.28690i	0.957882	−	0.287163i	$-0.0927121\pi$
$822$		0			0
$823$	−277072.	+	1.30352e6i	−0.409066	+	1.92450i	−0.0289108	+	0.999582i	$0.509204\pi$
$823$	−277072.	+	1.30352e6i	−0.409066	+	1.92450i	−0.380155	+	0.924923i	$0.624129\pi$
$824$		0			0
$825$	34119.2	+	324622.i	0.0501292	+	0.476947i
$826$		0			0
$827$	114703.	−	257626.i	0.167711	−	0.376686i	−0.810064	−	0.586341i	$-0.800568\pi$
$827$	114703.	−	257626.i	0.167711	−	0.376686i	0.977775	+	0.209656i	$0.0672344\pi$
$828$		0			0
$829$	270685.	−	87951.0i	0.393873	−	0.127977i	−0.105383	−	0.994432i	$-0.533607\pi$
$829$	270685.	−	87951.0i	0.393873	−	0.127977i	0.499256	+	0.866455i	$0.333607\pi$
$830$		0			0
$831$	571634.	−	990099.i	0.827782	−	1.43376i
$832$		0			0
$833$	−431762.	−	140288.i	−0.622235	−	0.202176i
$834$		0			0
$835$	−621543.	−	855481.i	−0.891453	−	1.22698i
$836$		0			0
$837$	307324.	−	674078.i	0.438677	−	0.962186i
$838$		0			0
$839$	711162.	−	516689.i	1.01029	−	0.734016i	0.0460170	−	0.998941i	$-0.485347\pi$
$839$	711162.	−	516689.i	1.01029	−	0.734016i	0.964269	+	0.264925i	$0.0853471\pi$
$840$		0			0
$841$	173619.	−	534345.i	0.245474	−	0.755491i
$842$		0			0
$843$	−352444.	−	203484.i	−0.495947	−	0.286335i
$844$		0			0
$845$	1352.83	+	4163.58i	0.00189465	+	0.00583114i
$846$		0			0
$847$	13300.3	+	5921.70i	0.0185394	+	0.00825428i
$848$		0			0
$849$	313415.	−	32941.2i	0.434814	−	0.0457008i
$850$		0			0
$851$	−1.26588e6	−	269071.i	−1.74797	−	0.371542i
$852$		0			0
$853$	−991297.	−	720219.i	−1.36240	−	0.989844i	−0.998288	−	0.0584902i	$-0.981371\pi$
$853$	−991297.	−	720219.i	−1.36240	−	0.989844i	−0.364115	−	0.931354i	$-0.618629\pi$
$854$		0			0
$855$	−8847.41	+	84177.5i	−0.0121027	+	0.115150i
$856$		0			0
$857$	333954.	−	70984.1i	0.454700	−	0.0966494i	0.0251323	−	0.999684i	$-0.491999\pi$
$857$	333954.	−	70984.1i	0.454700	−	0.0966494i	0.429568	+	0.903035i	$0.358666\pi$
$858$		0			0
$859$	−715256.	−	644019.i	−0.969337	−	0.872795i	0.0225717	−	0.999745i	$-0.492815\pi$
$859$	−715256.	−	644019.i	−0.969337	−	0.872795i	−0.991909	+	0.126950i	$0.959481\pi$
$860$		0			0
$861$	56332.3	−	50721.8i	0.0759891	−	0.0684209i
$862$		0			0
$863$	487988.	−	281740.i	0.655221	−	0.378292i	−0.135233	−	0.990814i	$-0.543178\pi$
$863$	487988.	−	281740.i	0.655221	−	0.378292i	0.790454	+	0.612522i	$0.209845\pi$
$864$		0			0
$865$	318594.	−	141847.i	0.425799	−	0.189578i
$866$		0			0
$867$			303303.i			0.403495i
$868$		0			0
$869$	−18240.3			−0.0241542
$870$		0			0
$871$	52288.4	+	117442.i	0.0689237	+	0.154805i
$872$		0			0
$873$	−17371.9	−	30089.0i	−0.0227939	−	0.0394802i
$874$		0			0
$875$	−106600.	−	118391.i	−0.139233	−	0.154634i
$876$		0			0
$877$	−593707.	+	659378.i	−0.771921	+	0.857305i	−0.993020	−	0.117946i	$-0.962369\pi$
$877$	−593707.	+	659378.i	−0.771921	+	0.857305i	0.221099	+	0.975251i	$0.429036\pi$
$878$		0			0
$879$	77473.2	+	364483.i	0.100271	+	0.471736i
$880$		0			0
$881$	−1.07245e6	−	112719.i	−1.38174	−	0.145226i	−0.615679	−	0.787997i	$-0.711118\pi$
$881$	−1.07245e6	−	112719.i	−1.38174	−	0.145226i	−0.766059	+	0.642771i	$0.777785\pi$
$882$		0			0
$883$	458189.	−	630643.i	0.587656	−	0.808839i	−0.406853	−	0.913494i	$-0.633374\pi$
$883$	458189.	−	630643.i	0.587656	−	0.808839i	0.994509	+	0.104655i	$0.0333738\pi$
$884$		0			0
$885$	−149704.	+	704301.i	−0.191138	+	0.899232i
$886$		0			0
$887$	123698.	+	1.17691e6i	0.157223	+	1.49587i	0.734099	+	0.679042i	$0.237605\pi$
$887$	123698.	+	1.17691e6i	0.157223	+	1.49587i	−0.576876	+	0.816831i	$0.695729\pi$
$888$		0			0
$889$	−143682.	+	322716.i	−0.181802	+	0.408335i
$890$		0			0
$891$	615531.	−	199998.i	0.775344	−	0.251924i
$892$		0			0
$893$	−48285.3	+	83632.5i	−0.0605496	+	0.104875i
$894$		0			0
$895$	−1.80294e6	−	585809.i	−2.25079	−	0.731325i
$896$		0			0
$897$	−664241.	−	914249.i	−0.825545	−	1.13626i
$898$		0			0
$899$	319005.	−	180418.i	0.394710	−	0.223234i
$900$		0			0
$901$	534365.	−	388239.i	0.658247	−	0.478244i
$902$		0			0
$903$	79036.1	−	243248.i	0.0969282	−	0.298314i
$904$		0			0
$905$	163145.	+	94191.8i	0.199194	+	0.115005i
$906$		0			0
$907$	345172.	+	1.06233e6i	0.419586	+	1.29135i	0.908084	+	0.418788i	$0.137545\pi$
$907$	345172.	+	1.06233e6i	0.419586	+	1.29135i	−0.488498	+	0.872565i	$0.662455\pi$
$908$		0			0
$909$	26385.0	+	11747.4i	0.0319323	+	0.0142172i
$910$		0			0
$911$	964235.	−	101345.i	1.16184	−	0.122114i	0.496078	−	0.868278i	$-0.334773\pi$
$911$	964235.	−	101345.i	1.16184	−	0.122114i	0.665762	+	0.746164i	$0.268106\pi$
$912$		0			0
$913$	−150282.	−	31943.5i	−0.180288	−	0.0383214i
$914$		0			0
$915$	1.35004e6	+	980864.i	1.61252	+	1.17157i
$916$		0			0
$917$	22943.1	−	218289.i	0.0272843	−	0.259593i
$918$		0			0
$919$	−107754.	+	22903.9i	−0.127586	+	0.0271193i	−0.271262	−	0.962506i	$-0.587441\pi$
$919$	−107754.	+	22903.9i	−0.127586	+	0.0271193i	0.143676	+	0.989625i	$0.454108\pi$
$920$		0			0
$921$	113966.	+	102615.i	0.134355	+	0.120974i
$922$		0			0
$923$	540989.	−	487109.i	0.635017	−	0.571772i
$924$		0			0
$925$	464314.	−	268072.i	0.542661	−	0.313305i
$926$		0			0
$927$	9416.91	−	4192.68i	0.0109584	−	0.00487901i
$928$		0			0
$929$			315102.i			0.365107i	0.983196	+	0.182553i	$0.0584362\pi$
$929$			315102.i			0.365107i	−0.983196	+	0.182553i	$0.941564\pi$
$930$		0			0
$931$	−500972.			−0.577982
$932$		0			0
$933$	463525.	+	1.04109e6i	0.532488	+	1.19599i
$934$		0			0
$935$	395004.	+	684168.i	0.451834	+	0.782599i
$936$		0			0
$937$	−363728.	−	403961.i	−0.414284	−	0.460109i	0.499497	−	0.866315i	$-0.333518\pi$
$937$	−363728.	−	403961.i	−0.414284	−	0.460109i	−0.913781	+	0.406207i	$0.866851\pi$
$938$		0			0
$939$	217855.	−	241953.i	0.247079	−	0.274410i
$940$		0			0
$941$	340347.	+	1.60120e6i	0.384363	+	1.80829i	0.565406	+	0.824813i	$0.308720\pi$
$941$	340347.	+	1.60120e6i	0.384363	+	1.80829i	−0.181043	+	0.983475i	$0.557947\pi$
$942$		0			0
$943$	−412094.	−	43312.8i	−0.463418	−	0.0487072i
$944$		0			0
$945$	247138.	−	340156.i	0.276742	−	0.380903i
$946$		0			0
$947$	−94104.5	+	442727.i	−0.104933	+	0.493669i	0.894025	+	0.448017i	$0.147870\pi$
$947$	−94104.5	+	442727.i	−0.104933	+	0.493669i	−0.998957	+	0.0456517i	$0.985464\pi$
$948$		0			0
$949$	66282.1	+	630632.i	0.0735976	+	0.700235i
$950$		0			0
$951$	−447943.	+	1.00610e6i	−0.495293	+	1.11245i
$952$		0			0
$953$	−1.01369e6	+	329368.i	−1.11614	+	0.362656i	−0.808294	−	0.588780i	$-0.799609\pi$
$953$	−1.01369e6	+	329368.i	−1.11614	+	0.362656i	−0.307847	+	0.951436i	$0.599609\pi$
$954$		0			0
$955$	−255265.	+	442132.i	−0.279888	+	0.484780i
$956$		0			0
$957$	355620.	+	115548.i	0.388295	+	0.126165i
$958$		0			0
$959$	359854.	+	495297.i	0.391282	+	0.538553i
$960$		0			0
$961$	−899785.	−	208032.i	−0.974299	−	0.225259i
$962$		0			0
$963$	−30588.4	+	22223.8i	−0.0329840	+	0.0239643i
$964$		0			0
$965$	−126583.	+	389581.i	−0.135931	+	0.418353i
$966$		0			0
$967$	−310494.	−	179264.i	−0.332048	−	0.191708i	0.324702	−	0.945816i	$-0.394736\pi$
$967$	−310494.	−	179264.i	−0.332048	−	0.191708i	−0.656750	+	0.754108i	$0.728069\pi$
$968$		0			0
$969$	−134159.	−	412900.i	−0.142881	−	0.439742i
$970$		0			0
$971$	371880.	+	165572.i	0.394425	+	0.175609i	0.594358	−	0.804200i	$-0.297406\pi$
$971$	371880.	+	165572.i	0.394425	+	0.175609i	−0.199934	+	0.979809i	$0.564073\pi$
$972$		0			0
$973$	584495.	−	61432.9i	0.617384	−	0.0648897i
$974$		0			0
$975$	457935.	+	97337.1i	0.481720	+	0.102393i
$976$		0			0
$977$	995104.	+	722986.i	1.04251	+	0.757427i	0.970774	−	0.239997i	$-0.0771465\pi$
$977$	995104.	+	722986.i	1.04251	+	0.757427i	0.0717347	+	0.997424i	$0.477147\pi$
$978$		0			0
$979$	−92158.1	+	876825.i	−0.0961541	+	0.914846i
$980$		0			0
$981$	195831.	−	41625.1i	0.203490	−	0.0432531i
$982$		0			0
$983$	−756601.	−	681246.i	−0.782996	−	0.705013i	0.177250	−	0.984166i	$-0.443280\pi$
$983$	−756601.	−	681246.i	−0.782996	−	0.705013i	−0.960247	+	0.279153i	$0.909946\pi$
$984$		0			0
$985$	−30097.5	+	27099.9i	−0.0310211	+	0.0279315i
$986$		0			0
$987$	51302.0	−	29619.2i	0.0526623	−	0.0304046i
$988$		0			0
$989$	−1.27724e6	+	568662.i	−1.30580	+	0.581382i
$990$		0			0
$991$			1.20301e6i			1.22496i	0.790487	+	0.612479i	$0.209828\pi$
$991$			1.20301e6i			1.22496i	−0.790487	+	0.612479i	$0.790172\pi$
$992$		0			0
$993$	−307702.			−0.312055
$994$		0			0
$995$	−469667.	−	1.05489e6i	−0.474399	−	1.06552i
$996$		0			0
$997$	−844034.	−	1.46191e6i	−0.849121	−	1.47072i	−0.881994	−	0.471261i	$-0.843799\pi$
$997$	−844034.	−	1.46191e6i	−0.849121	−	1.47072i	0.0328725	−	0.999460i	$-0.489534\pi$
$998$		0			0
$999$	−830739.	−	922629.i	−0.832403	−	0.924477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.13.9	✓	88
31.12	odd	30	inner	124.5.o.a.105.9	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.13.9	✓	88	1.1	even	1	trivial
124.5.o.a.105.9	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)

\(f(q)\)	\(=\)	\(q+(3.39298 + 7.62076i) q^{3} +(-15.4750 - 26.8035i) q^{5} +(11.7917 + 13.0960i) q^{7} +(7.63586 - 8.48048i) q^{9} +O(q^{10})\)	\(q+(3.39298 + 7.62076i) q^{3} +(-15.4750 - 26.8035i) q^{5} +(11.7917 + 13.0960i) q^{7} +(7.63586 - 8.48048i) q^{9} +(-24.4372 - 114.968i) q^{11} +(-167.657 - 17.6215i) q^{13} +(151.757 - 208.876i) q^{15} +(45.1519 - 212.423i) q^{17} +(-25.0500 - 238.335i) q^{19} +(-59.7923 + 134.296i) q^{21} +(764.251 - 248.320i) q^{23} +(-166.453 + 288.306i) q^{25} +(733.164 + 238.219i) q^{27} +(224.160 + 308.529i) q^{29} +(108.939 - 954.805i) q^{31} +(793.229 - 576.315i) q^{33} +(168.542 - 518.719i) q^{35} +(-1394.73 - 805.246i) q^{37} +(-434.570 - 1337.47i) q^{39} +(-471.066 - 209.732i) q^{41} +(-1730.32 + 181.863i) q^{43} +(-345.472 - 73.4323i) q^{45} +(-326.009 - 236.859i) q^{47} +(218.512 - 2079.00i) q^{49} +(1772.03 - 376.656i) q^{51} +(2260.25 + 2035.14i) q^{53} +(-2703.38 + 2434.14i) q^{55} +(1731.30 - 999.566i) q^{57} +(-2547.73 + 1134.32i) q^{59} +6463.39i q^{61} +201.099 q^{63} +(2122.19 + 4766.51i) q^{65} +(-381.288 - 660.410i) q^{67} +(4485.48 + 4981.63i) q^{69} +(-2889.46 + 3209.08i) q^{71} +(-782.045 - 3679.23i) q^{73} +(-2761.88 - 290.286i) q^{75} +(1217.46 - 1675.69i) q^{77} +(32.2655 - 151.797i) q^{79} +(575.579 + 5476.27i) q^{81} +(531.673 - 1194.16i) q^{83} +(-6392.42 + 2077.02i) q^{85} +(-1590.66 + 2755.10i) q^{87} +(-7133.99 - 2317.97i) q^{89} +(-1746.19 - 2403.42i) q^{91} +(7645.98 - 2409.44i) q^{93} +(-6000.57 + 4359.67i) q^{95} +(940.834 - 2895.59i) q^{97} +(-1161.58 - 670.640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 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

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