LMFDB - Embedded newform 147.6.c.d.146.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.12
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.31267i q^{2} +(-14.0092 - 6.83685i) q^{3} -37.1006 q^{4} +28.6894 q^{5} +(56.8325 - 116.454i) q^{6} -42.3992i q^{8} +(149.515 + 191.558i) q^{9} +O(q^{10})$	\(q+8.31267i q^{2} +(-14.0092 - 6.83685i) q^{3} -37.1006 q^{4} +28.6894 q^{5} +(56.8325 - 116.454i) q^{6} -42.3992i q^{8} +(149.515 + 191.558i) q^{9} +238.485i q^{10} +596.643i q^{11} +(519.749 + 253.651i) q^{12} -602.209i q^{13} +(-401.915 - 196.145i) q^{15} -834.767 q^{16} -154.570 q^{17} +(-1592.36 + 1242.87i) q^{18} +2867.88i q^{19} -1064.39 q^{20} -4959.70 q^{22} -3786.52i q^{23} +(-289.877 + 593.979i) q^{24} -2301.92 q^{25} +5005.96 q^{26} +(-784.934 - 3705.78i) q^{27} +2851.02i q^{29} +(1630.49 - 3340.99i) q^{30} -3228.71i q^{31} -8295.92i q^{32} +(4079.16 - 8358.48i) q^{33} -1284.89i q^{34} +(-5547.09 - 7106.89i) q^{36} -10451.4 q^{37} -23839.8 q^{38} +(-4117.21 + 8436.46i) q^{39} -1216.41i q^{40} +6923.92 q^{41} +3809.47 q^{43} -22135.8i q^{44} +(4289.49 + 5495.66i) q^{45} +31476.1 q^{46} -15764.1 q^{47} +(11694.4 + 5707.18i) q^{48} -19135.1i q^{50} +(2165.40 + 1056.77i) q^{51} +22342.3i q^{52} +4787.21i q^{53} +(30804.9 - 6524.90i) q^{54} +17117.3i q^{55} +(19607.3 - 40176.7i) q^{57} -23699.6 q^{58} -33460.6 q^{59} +(14911.3 + 7277.08i) q^{60} -45173.2i q^{61} +26839.2 q^{62} +42248.7 q^{64} -17277.0i q^{65} +(69481.4 + 33908.7i) q^{66} -49587.7 q^{67} +5734.62 q^{68} +(-25887.9 + 53046.1i) q^{69} +35931.1i q^{71} +(8121.89 - 6339.32i) q^{72} -26728.5i q^{73} -86879.5i q^{74} +(32248.1 + 15737.9i) q^{75} -106400. i q^{76} +(-70129.5 - 34225.0i) q^{78} +6057.73 q^{79} -23948.9 q^{80} +(-14339.6 + 57281.4i) q^{81} +57556.3i q^{82} -36200.9 q^{83} -4434.51 q^{85} +31666.9i q^{86} +(19492.0 - 39940.5i) q^{87} +25297.2 q^{88} -76316.2 q^{89} +(-45683.6 + 35657.1i) q^{90} +140482. i q^{92} +(-22074.2 + 45231.6i) q^{93} -131042. i q^{94} +82277.7i q^{95} +(-56718.0 + 116219. i) q^{96} -51925.1i q^{97} +(-114291. + 89207.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) $ 40 * q - 640 * q^4 + 440 * q^9	$ 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) $ 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			8.31267i			1.46949i	0.678345	+	0.734744i	$0.262697\pi$
$2$			8.31267i			1.46949i	−0.678345	+	0.734744i	$0.737303\pi$
$3$	−14.0092	−	6.83685i	−0.898690	−	0.438584i
$3$	−14.0092	−	6.83685i	−0.898690	−	0.438584i
$4$	−37.1006			−1.15939
$5$	28.6894			0.513211			0.256605	−	0.966516i	$-0.417396\pi$
$5$	28.6894			0.513211			0.256605	+	0.966516i	$0.417396\pi$
$6$	56.8325	−	116.454i	0.644494	−	1.32061i
$7$		0			0
$7$		0			0
$8$		−	42.3992i		−	0.234225i
$9$	149.515	+	191.558i	0.615288	+	0.788302i
$10$			238.485i			0.754157i
$11$			596.643i			1.48673i	0.668885	+	0.743366i	$0.266772\pi$
$11$			596.643i			1.48673i	−0.668885	+	0.743366i	$0.733228\pi$
$12$	519.749	+	253.651i	1.04193	+	0.508491i
$13$		−	602.209i		−	0.988300i	−0.869377	−	0.494150i	$-0.835479\pi$
$13$		−	602.209i		−	0.988300i	0.869377	−	0.494150i	$-0.164521\pi$
$14$		0			0
$15$	−401.915	−	196.145i	−0.461217	−	0.225086i
$16$	−834.767			−0.815202
$17$	−154.570			−0.129719			−0.0648593	−	0.997894i	$-0.520660\pi$
$17$	−154.570			−0.129719			−0.0648593	+	0.997894i	$0.520660\pi$
$18$	−1592.36	+	1242.87i	−1.15840	+	0.904158i
$19$			2867.88i			1.82254i	0.411808	+	0.911271i	$0.364898\pi$
$19$			2867.88i			1.82254i	−0.411808	+	0.911271i	$0.635102\pi$
$20$	−1064.39			−0.595013
$21$		0			0
$22$	−4959.70			−2.18473
$23$		−	3786.52i		−	1.49252i	−0.665653	−	0.746261i	$-0.731847\pi$
$23$		−	3786.52i		−	1.49252i	0.665653	−	0.746261i	$-0.268153\pi$
$24$	−289.877	+	593.979i	−0.102727	+	0.210496i
$25$	−2301.92			−0.736615
$26$	5005.96			1.45229
$27$	−784.934	−	3705.78i	−0.207216	−	0.978295i
$28$		0			0
$29$			2851.02i			0.629515i	0.949172	+	0.314757i	$0.101923\pi$
$29$			2851.02i			0.629515i	−0.949172	+	0.314757i	$0.898077\pi$
$30$	1630.49	−	3340.99i	0.330761	−	0.677753i
$31$		−	3228.71i		−	0.603426i	−0.953399	−	0.301713i	$-0.902442\pi$
$31$		−	3228.71i		−	0.603426i	0.953399	−	0.301713i	$-0.0975585\pi$
$32$		−	8295.92i		−	1.43215i
$33$	4079.16	−	8358.48i	0.652057	−	1.33611i
$34$		−	1284.89i		−	0.190620i
$35$		0			0
$36$	−5547.09	−	7106.89i	−0.713360	−	0.913952i
$37$	−10451.4			−1.25508			−0.627541	−	0.778584i	$-0.715938\pi$
$37$	−10451.4			−1.25508			−0.627541	+	0.778584i	$0.715938\pi$
$38$	−23839.8			−2.67820
$39$	−4117.21	+	8436.46i	−0.433453	+	0.888175i
$40$		−	1216.41i		−	0.120207i
$41$	6923.92			0.643269			0.321634	−	0.946864i	$-0.395768\pi$
$41$	6923.92			0.643269			0.321634	+	0.946864i	$0.395768\pi$
$42$		0			0
$43$	3809.47			0.314191			0.157095	−	0.987583i	$-0.449787\pi$
$43$	3809.47			0.314191			0.157095	+	0.987583i	$0.449787\pi$
$44$		−	22135.8i		−	1.72371i
$45$	4289.49	+	5495.66i	0.315772	+	0.404565i
$46$	31476.1			2.19324
$47$	−15764.1			−1.04094			−0.520470	−	0.853880i	$-0.674243\pi$
$47$	−15764.1			−1.04094			−0.520470	+	0.853880i	$0.674243\pi$
$48$	11694.4	+	5707.18i	0.732614	+	0.357535i
$49$		0			0
$50$		−	19135.1i		−	1.08245i
$51$	2165.40	+	1056.77i	0.116577	+	0.0568925i
$52$			22342.3i			1.14583i
$53$			4787.21i			0.234095i	0.993126	+	0.117048i	$0.0373430\pi$
$53$			4787.21i			0.234095i	−0.993126	+	0.117048i	$0.962657\pi$
$54$	30804.9	−	6524.90i	1.43759	−	0.304501i
$55$			17117.3i			0.763007i
$56$		0			0
$57$	19607.3	−	40176.7i	0.799338	−	1.63790i
$58$	−23699.6			−0.925063
$59$	−33460.6			−1.25142			−0.625711	−	0.780055i	$-0.715191\pi$
$59$	−33460.6			−1.25142			−0.625711	+	0.780055i	$0.715191\pi$
$60$	14911.3	+	7277.08i	0.534732	+	0.260963i
$61$		−	45173.2i		−	1.55438i	−0.629267	−	0.777189i	$-0.716645\pi$
$61$		−	45173.2i		−	1.55438i	0.629267	−	0.777189i	$-0.283355\pi$
$62$	26839.2			0.886727
$63$		0			0
$64$	42248.7			1.28933
$65$		−	17277.0i		−	0.507206i
$66$	69481.4	+	33908.7i	1.96340	+	0.958190i
$67$	−49587.7			−1.34954			−0.674772	−	0.738026i	$-0.735758\pi$
$67$	−49587.7			−1.34954			−0.674772	+	0.738026i	$0.735758\pi$
$68$	5734.62			0.150395
$69$	−25887.9	+	53046.1i	−0.654597	+	1.34132i
$70$		0			0
$71$			35931.1i			0.845911i	0.906150	+	0.422956i	$0.139007\pi$
$71$			35931.1i			0.845911i	−0.906150	+	0.422956i	$0.860993\pi$
$72$	8121.89	−	6339.32i	0.184640	−	0.144116i
$73$		−	26728.5i		−	0.587039i	−0.955953	−	0.293520i	$-0.905173\pi$
$73$		−	26728.5i		−	0.587039i	0.955953	−	0.293520i	$-0.0948266\pi$
$74$		−	86879.5i		−	1.84433i
$75$	32248.1	+	15737.9i	0.661988	+	0.323068i
$76$		−	106400.i		−	2.11304i
$77$		0			0
$78$	−70129.5	−	34225.0i	−1.30516	−	0.636953i
$79$	6057.73			0.109205			0.0546025	−	0.998508i	$-0.482611\pi$
$79$	6057.73			0.109205			0.0546025	+	0.998508i	$0.482611\pi$
$80$	−23948.9			−0.418370
$81$	−14339.6	+	57281.4i	−0.242842	+	0.970066i
$82$			57556.3i			0.945275i
$83$	−36200.9			−0.576799			−0.288399	−	0.957510i	$-0.593123\pi$
$83$	−36200.9			−0.576799			−0.288399	+	0.957510i	$0.593123\pi$
$84$		0			0
$85$	−4434.51			−0.0665730
$86$			31666.9i			0.461700i
$87$	19492.0	−	39940.5i	0.276095	−	0.565738i
$88$	25297.2			0.348230
$89$	−76316.2			−1.02127			−0.510636	−	0.859797i	$-0.670590\pi$
$89$	−76316.2			−1.02127			−0.510636	+	0.859797i	$0.670590\pi$
$90$	−45683.6	+	35657.1i	−0.594504	+	0.464023i
$91$		0			0
$92$			140482.i			1.73042i
$93$	−22074.2	+	45231.6i	−0.264653	+	0.542293i
$94$		−	131042.i		−	1.52965i
$95$			82277.7i			0.935348i
$96$	−56718.0	+	116219.i	−0.628120	+	1.28706i
$97$		−	51925.1i		−	0.560336i	−0.959951	−	0.280168i	$-0.909610\pi$
$97$		−	51925.1i		−	0.560336i	0.959951	−	0.280168i	$-0.0903901\pi$
$98$		0			0
$99$	−114291.	+	89207.0i	−1.17199	+	0.914768i
$100$	85402.5			0.854025
$101$	−90390.5			−0.881697			−0.440848	−	0.897582i	$-0.645322\pi$
$101$	−90390.5			−0.881697			−0.440848	+	0.897582i	$0.645322\pi$
$102$	−8784.58	+	18000.2i	−0.0836028	+	0.171308i
$103$			11908.8i			0.110605i	0.998470	+	0.0553023i	$0.0176123\pi$
$103$			11908.8i			0.110605i	−0.998470	+	0.0553023i	$0.982388\pi$
$104$	−25533.2			−0.231484
$105$		0			0
$106$	−39794.5			−0.344000
$107$			109078.i			0.921038i	0.887650	+	0.460519i	$0.152337\pi$
$107$			109078.i			0.921038i	−0.887650	+	0.460519i	$0.847663\pi$
$108$	29121.5	+	137486.i	0.240245	+	1.13423i
$109$	−74014.4			−0.596692			−0.298346	−	0.954458i	$-0.596435\pi$
$109$	−74014.4			−0.596692			−0.298346	+	0.954458i	$0.596435\pi$
$110$	−142291.			−1.12123
$111$	146416.	+	71455.0i	1.12793	+	0.550459i
$112$		0			0
$113$			138601.i			1.02110i	0.859848	+	0.510551i	$0.170558\pi$
$113$			138601.i			1.02110i	−0.859848	+	0.510551i	$0.829442\pi$
$114$	333976.	+	162989.i	2.40687	+	1.17462i
$115$		−	108633.i		−	0.765979i
$116$		−	105775.i		−	0.729854i
$117$	115358.	−	90039.2i	0.779079	−	0.608089i
$118$		−	278147.i		−	1.83895i
$119$		0			0
$120$	−8316.39	+	17040.9i	−0.0527207	+	0.108029i
$121$	−194932.			−1.21037
$122$	375510.			2.28414
$123$	−96998.5	−	47337.8i	−0.578099	−	0.282127i
$124$			119787.i			0.699608i
$125$	−155695.			−0.891249
$126$		0			0
$127$	339064.			1.86540			0.932702	−	0.360649i	$-0.117445\pi$
$127$	339064.			1.86540			0.932702	+	0.360649i	$0.117445\pi$
$128$			85730.6i			0.462499i
$129$	−53367.6	−	26044.8i	−0.282360	−	0.137799i
$130$	143618.			0.745333
$131$	170248.			0.866769			0.433384	−	0.901209i	$-0.357319\pi$
$131$	170248.			0.866769			0.433384	+	0.901209i	$0.357319\pi$
$132$	−151339.	+	310104.i	−0.755990	+	1.54908i
$133$		0			0
$134$		−	412207.i		−	1.98314i
$135$	−22519.2	−	106316.i	−0.106346	−	0.502072i
$136$			6553.63i			0.0303833i
$137$			104318.i			0.474850i	0.971406	+	0.237425i	$0.0763033\pi$
$137$			104318.i			0.474850i	−0.971406	+	0.237425i	$0.923697\pi$
$138$	−440955.	−	215198.i	−1.97105	−	0.961922i
$139$			388744.i			1.70658i	0.521435	+	0.853291i	$0.325397\pi$
$139$			388744.i			1.70658i	−0.521435	+	0.853291i	$0.674603\pi$
$140$		0			0
$141$	220843.	+	107777.i	0.935483	+	0.456540i
$142$	−298684.			−1.24306
$143$	359303.			1.46934
$144$	−124810.	−	159906.i	−0.501584	−	0.642626i
$145$			81794.0i			0.323074i
$146$	222185.			0.862647
$147$		0			0
$148$	387754.			1.45513
$149$			49118.5i			0.181250i	0.995885	+	0.0906252i	$0.0288865\pi$
$149$			49118.5i			0.181250i	−0.995885	+	0.0906252i	$0.971113\pi$
$150$	−130824.	+	268068.i	−0.474744	+	0.972783i
$151$	495080.			1.76698			0.883492	−	0.468446i	$-0.155186\pi$
$151$	495080.			1.76698			0.883492	+	0.468446i	$0.155186\pi$
$152$	121596.			0.426884
$153$	−23110.5	−	29609.0i	−0.0798143	−	0.102257i
$154$		0			0
$155$		−	92629.5i		−	0.309685i
$156$	152751.	−	312997.i	0.502541	−	1.02974i
$157$		−	5516.25i		−	0.0178606i	−0.999960	−	0.00893028i	$-0.997157\pi$
$157$		−	5516.25i		−	0.0178606i	0.999960	−	0.00893028i	$-0.00284263\pi$
$158$			50356.0i			0.160475i
$159$	32729.4	−	67065.0i	0.102671	−	0.210379i
$160$		−	238005.i		−	0.734997i
$161$		0			0
$162$	−476162.	−	119200.i	−1.42550	−	0.356853i
$163$	−140177.			−0.413246			−0.206623	−	0.978421i	$-0.566247\pi$
$163$	−140177.			−0.413246			−0.206623	+	0.978421i	$0.566247\pi$
$164$	−256881.			−0.745801
$165$	117028.	−	239800.i	0.334643	−	0.685707i
$166$		−	300927.i		−	0.847599i
$167$	64511.8			0.178998			0.0894990	−	0.995987i	$-0.471473\pi$
$167$	64511.8			0.178998			0.0894990	+	0.995987i	$0.471473\pi$
$168$		0			0
$169$	8637.76			0.0232640
$170$		−	36862.6i		−	0.0978281i
$171$	−549365.	+	428791.i	−1.43671	+	1.12139i
$172$	−141334.			−0.364271
$173$	300332.			0.762932			0.381466	−	0.924383i	$-0.375419\pi$
$173$	300332.			0.762932			0.381466	+	0.924383i	$0.375419\pi$
$174$	332013.	+	162031.i	0.831345	+	0.405718i
$175$		0			0
$176$		−	498058.i		−	1.21199i
$177$	468756.	+	228765.i	1.12464	+	0.548854i
$178$		−	634392.i		−	1.50075i
$179$			691500.i			1.61309i	0.591170	+	0.806547i	$0.298666\pi$
$179$			691500.i			1.61309i	−0.591170	+	0.806547i	$0.701334\pi$
$180$	−159142.	−	203892.i	−0.366104	−	0.469050i
$181$		−	468406.i		−	1.06274i	−0.847141	−	0.531368i	$-0.821678\pi$
$181$		−	468406.i		−	1.06274i	0.847141	−	0.531368i	$-0.178322\pi$
$182$		0			0
$183$	−308843.	+	632840.i	−0.681725	+	1.39690i
$184$	−160546.			−0.349586
$185$	−299845.			−0.644122
$186$	−375995.	−	183495.i	−0.796893	−	0.388905i
$187$		−	92222.9i		−	0.192857i
$188$	584859.			1.20686
$189$		0			0
$190$	−683948.			−1.37448
$191$		−	633679.i		−	1.25686i	−0.777867	−	0.628429i	$-0.783698\pi$
$191$		−	633679.i		−	1.25686i	0.777867	−	0.628429i	$-0.216302\pi$
$192$	−591871.	−	288848.i	−1.15871	−	0.565479i
$193$	−96756.0			−0.186975			−0.0934877	−	0.995620i	$-0.529802\pi$
$193$	−96756.0			−0.186975			−0.0934877	+	0.995620i	$0.529802\pi$
$194$	431637.			0.823406
$195$	−118120.	+	242036.i	−0.222453	+	0.455821i
$196$		0			0
$197$			132572.i			0.243381i	0.992568	+	0.121690i	$0.0388315\pi$
$197$			132572.i			0.243381i	−0.992568	+	0.121690i	$0.961168\pi$
$198$	−741549.	−	950067.i	−1.34424	−	1.72223i
$199$			904468.i			1.61905i	0.587085	+	0.809525i	$0.300275\pi$
$199$			904468.i			1.61905i	−0.587085	+	0.809525i	$0.699725\pi$
$200$			97599.6i			0.172533i
$201$	694684.	+	339024.i	1.21282	+	0.591889i
$202$		−	751386.i		−	1.29564i
$203$		0			0
$204$	−80337.4	−	39206.7i	−0.135158	−	0.0659607i
$205$	198643.			0.330132
$206$	−98993.6			−0.162532
$207$	725337.	−	566142.i	1.17656	−	0.918331i
$208$			502704.i			0.805664i
$209$	−1.71110e6			−2.70963
$210$		0			0
$211$	−588017.			−0.909250			−0.454625	−	0.890683i	$-0.650227\pi$
$211$	−588017.			−0.909250			−0.454625	+	0.890683i	$0.650227\pi$
$212$		−	177608.i		−	0.271408i
$213$	245656.	−	503366.i	0.371003	−	0.760212i
$214$	−906729.			−1.35345
$215$	109291.			0.161246
$216$	−157122.	+	33280.6i	−0.229141	+	0.0485352i
$217$		0			0
$218$		−	615258.i		−	0.876831i
$219$	−182739.	+	374445.i	−0.257466	+	0.527567i
$220$		−	635061.i		−	0.884624i
$221$			93083.2i			0.128201i
$222$	−593982.	+	1.21711e6i	−0.808892	+	1.65748i
$223$		−	635944.i		−	0.856361i	−0.903693	−	0.428181i	$-0.859155\pi$
$223$		−	635944.i		−	0.856361i	0.903693	−	0.428181i	$-0.140845\pi$
$224$		0			0
$225$	−344172.	−	440950.i	−0.453230	−	0.580675i
$226$	−1.15214e6			−1.50050
$227$	497480.			0.640783			0.320392	−	0.947285i	$-0.396185\pi$
$227$	497480.			0.640783			0.320392	+	0.947285i	$0.396185\pi$
$228$	−727441.	+	1.49058e6i	−0.926746	+	1.89897i
$229$		−	405801.i		−	0.511357i	−0.966762	−	0.255678i	$-0.917701\pi$
$229$		−	405801.i		−	0.511357i	0.966762	−	0.255678i	$-0.0822988\pi$
$230$	903030.			1.12560
$231$		0			0
$232$	120881.			0.147448
$233$		−	928226.i		−	1.12012i	−0.828453	−	0.560059i	$-0.810778\pi$
$233$		−	928226.i		−	1.12012i	0.828453	−	0.560059i	$-0.189222\pi$
$234$	748467.	+	958930.i	0.893579	+	1.14485i
$235$	−452263.			−0.534222
$236$	1.24141e6			1.45089
$237$	−84864.0	−	41415.8i	−0.0981414	−	0.0478956i
$238$		0			0
$239$			864544.i			0.979022i	0.871997	+	0.489511i	$0.162825\pi$
$239$			864544.i			0.979022i	−0.871997	+	0.489511i	$0.837175\pi$
$240$	335505.	+	163735.i	0.375985	+	0.183491i
$241$			122190.i			0.135516i	0.997702	+	0.0677581i	$0.0215846\pi$
$241$			122190.i			0.135516i	−0.997702	+	0.0677581i	$0.978415\pi$
$242$		−	1.62040e6i		−	1.77863i
$243$	592510.	−	704429.i	0.643695	−	0.765282i
$244$			1.67595e6i			1.80213i
$245$		0			0
$246$	393504.	−	806317.i	0.414583	−	0.849509i
$247$	1.72706e6			1.80122
$248$	−136895.			−0.141337
$249$	507146.	+	247500.i	0.518364	+	0.252975i
$250$		−	1.29424e6i		−	1.30968i
$251$	756161.			0.757582			0.378791	−	0.925482i	$-0.376340\pi$
$251$	756161.			0.757582			0.378791	+	0.925482i	$0.376340\pi$
$252$		0			0
$253$	2.25920e6			2.21898
$254$			2.81853e6i			2.74119i
$255$	62123.8	+	30318.0i	0.0598285	+	0.0291978i
$256$	639309.			0.609693
$257$	−1.78378e6			−1.68464			−0.842322	−	0.538975i	$-0.818812\pi$
$257$	−1.78378e6			−1.68464			−0.842322	+	0.538975i	$0.818812\pi$
$258$	216502.	−	443628.i	0.202494	−	0.414925i
$259$		0			0
$260$			640985.i			0.588051i
$261$	−546135.	+	426271.i	−0.496248	+	0.387333i
$262$			1.41521e6i			1.27371i
$263$			676904.i			0.603445i	0.953396	+	0.301722i	$0.0975616\pi$
$263$			676904.i			0.603445i	−0.953396	+	0.301722i	$0.902438\pi$
$264$	−354393.	−	172953.i	−0.312950	−	0.152728i
$265$			137342.i			0.120140i
$266$		0			0
$267$	1.06913e6	+	521763.i	0.917808	+	0.447914i
$268$	1.83973e6			1.56465
$269$	−712094.			−0.600008			−0.300004	−	0.953938i	$-0.596988\pi$
$269$	−712094.			−0.600008			−0.300004	+	0.953938i	$0.596988\pi$
$270$	883773.	−	187195.i	0.737788	−	0.156273i
$271$			862143.i			0.713110i	0.934274	+	0.356555i	$0.116049\pi$
$271$			862143.i			0.713110i	−0.934274	+	0.356555i	$0.883951\pi$
$272$	129030.			0.105747
$273$		0			0
$274$	−867158.			−0.697785
$275$		−	1.37342e6i		−	1.09515i
$276$	960455.	−	1.96804e6i	0.758935	−	1.55511i
$277$	2.21137e6			1.73165			0.865827	−	0.500343i	$-0.166793\pi$
$277$	2.21137e6			1.73165			0.865827	+	0.500343i	$0.166793\pi$
$278$	−3.23151e6			−2.50780
$279$	618483.	−	482740.i	0.475683	−	0.371281i
$280$		0			0
$281$		−	289037.i		−	0.218367i	−0.994022	−	0.109184i	$-0.965176\pi$
$281$		−	289037.i		−	0.218367i	0.994022	−	0.109184i	$-0.0348237\pi$
$282$	−895916.	+	1.83580e6i	−0.670880	+	1.37468i
$283$			40696.5i			0.0302058i	0.999886	+	0.0151029i	$0.00480759\pi$
$283$			40696.5i			0.0302058i	−0.999886	+	0.0151029i	$0.995192\pi$
$284$		−	1.33306e6i		−	0.980743i
$285$	562520.	−	1.15264e6i	0.410229	−	0.840588i
$286$			2.98677e6i			2.15917i
$287$		0			0
$288$	1.58915e6	−	1.24036e6i	1.12897	−	0.881187i
$289$	−1.39597e6			−0.983173
$290$	−679927.			−0.474753
$291$	−355004.	+	727429.i	−0.245754	+	0.503568i
$292$			991642.i			0.680609i
$293$	−1.21635e6			−0.827735			−0.413867	−	0.910337i	$-0.635822\pi$
$293$	−1.21635e6			−0.827735			−0.413867	+	0.910337i	$0.635822\pi$
$294$		0			0
$295$	−959964.			−0.642243
$296$			443133.i			0.293971i
$297$	2.21103e6	−	468325.i	1.45446	−	0.308075i
$298$	−408306.			−0.266345
$299$	−2.28028e6			−1.47506
$300$	−1.19642e6	−	583884.i	−0.767504	−	0.374562i
$301$		0			0
$302$			4.11544e6i			2.59656i
$303$	1.26630e6	+	617986.i	0.792372	+	0.386698i
$304$		−	2.39401e6i		−	1.48574i
$305$		−	1.29599e6i		−	0.797723i
$306$	246130.	−	192110.i	0.150266	−	0.117286i
$307$			805016.i			0.487482i	0.969840	+	0.243741i	$0.0783746\pi$
$307$			805016.i			0.487482i	−0.969840	+	0.243741i	$0.921625\pi$
$308$		0			0
$309$	81418.4	−	166832.i	0.0485094	−	0.0993993i
$310$	769999.			0.455078
$311$	−668977.			−0.392202			−0.196101	−	0.980584i	$-0.562828\pi$
$311$	−668977.			−0.392202			−0.196101	+	0.980584i	$0.562828\pi$
$312$	357699.	+	174566.i	0.208033	+	0.101525i
$313$			237126.i			0.136810i	0.997658	+	0.0684050i	$0.0217910\pi$
$313$			237126.i			0.136810i	−0.997658	+	0.0684050i	$0.978209\pi$
$314$	45854.8			0.0262458
$315$		0			0
$316$	−224745.			−0.126611
$317$			1.14227e6i			0.638442i	0.947680	+	0.319221i	$0.103421\pi$
$317$			1.14227e6i			0.638442i	−0.947680	+	0.319221i	$0.896579\pi$
$318$	557489.	+	272069.i	0.309150	+	0.150873i
$319$	−1.70104e6			−0.935919
$320$	1.21209e6			0.661698
$321$	745750.	−	1.52809e6i	0.403953	−	0.827728i
$322$		0			0
$323$		−	443288.i		−	0.236417i
$324$	532005.	−	2.12517e6i	0.281549	−	1.12469i
$325$			1.38624e6i			0.727996i
$326$		−	1.16525e6i		−	0.607259i
$327$	1.03688e6	+	506025.i	0.536241	+	0.261699i
$328$		−	293569.i		−	0.150669i
$329$		0			0
$330$	1.99338e6	+	972819.i	1.00764	+	0.491753i
$331$	−696277.			−0.349311			−0.174655	−	0.984630i	$-0.555881\pi$
$331$	−696277.			−0.349311			−0.174655	+	0.984630i	$0.555881\pi$
$332$	1.34307e6			0.668736
$333$	−1.56265e6	−	2.00205e6i	−0.772237	−	0.989384i
$334$			536266.i			0.263035i
$335$	−1.42264e6			−0.692601
$336$		0			0
$337$	−1.61811e6			−0.776129			−0.388064	−	0.921632i	$-0.626856\pi$
$337$	−1.61811e6			−0.776129			−0.388064	+	0.921632i	$0.626856\pi$
$338$			71802.9i			0.0341861i
$339$	947591.	−	1.94168e6i	0.447839	−	0.917654i
$340$	164523.			0.0771842
$341$	1.92638e6			0.897133
$342$	−3.56440e6	−	4.56669e6i	−1.64786	−	2.11123i
$343$		0			0
$344$		−	161519.i		−	0.0735913i
$345$	−742707.	+	1.52186e6i	−0.335946	+	0.688378i
$346$			2.49656e6i			1.12112i
$347$			2.51564e6i			1.12157i	0.827962	+	0.560784i	$0.189500\pi$
$347$			2.51564e6i			1.12157i	−0.827962	+	0.560784i	$0.810500\pi$
$348$	−723165.	+	1.48182e6i	−0.320102	+	0.655913i
$349$			1.89408e6i			0.832405i	0.909272	+	0.416203i	$0.136639\pi$
$349$			1.89408e6i			0.832405i	−0.909272	+	0.416203i	$0.863361\pi$
$350$		0			0
$351$	−2.23165e6	+	472694.i	−0.966849	+	0.204792i
$352$	4.94970e6			2.12923
$353$	−1.44725e6			−0.618170			−0.309085	−	0.951034i	$-0.600023\pi$
$353$	−1.44725e6			−0.618170			−0.309085	+	0.951034i	$0.600023\pi$
$354$	−1.90165e6	+	3.89662e6i	−0.806534	+	1.65265i
$355$			1.03084e6i			0.434131i
$356$	2.83137e6			1.18406
$357$		0			0
$358$	−5.74821e6			−2.37042
$359$			1.62602e6i			0.665871i	0.942950	+	0.332935i	$0.108039\pi$
$359$			1.62602e6i			0.665871i	−0.942950	+	0.332935i	$0.891961\pi$
$360$	233012.	−	181871.i	0.0947592	−	0.0739617i
$361$	−5.74865e6			−2.32166
$362$	3.89370e6			1.56168
$363$	2.73084e6	+	1.33272e6i	1.08775	+	0.530850i
$364$		0			0
$365$		−	766823.i		−	0.301275i
$366$	−5.26060e6	−	2.56731e6i	−2.05273	−	1.00179i
$367$			1.54281e6i			0.597926i	0.954265	+	0.298963i	$0.0966407\pi$
$367$			1.54281e6i			0.597926i	−0.954265	+	0.298963i	$0.903359\pi$
$368$			3.16086e6i			1.21671i
$369$	1.03523e6	+	1.32633e6i	0.395795	+	0.507090i
$370$		−	2.49252e6i		−	0.946528i
$371$		0			0
$372$	818964.	−	1.67812e6i	0.306837	−	0.628731i
$373$	−1.13818e6			−0.423583			−0.211792	−	0.977315i	$-0.567930\pi$
$373$	−1.13818e6			−0.423583			−0.211792	+	0.977315i	$0.567930\pi$
$374$	766619.			0.283400
$375$	2.18116e6	+	1.06446e6i	0.800957	+	0.390888i
$376$			668387.i			0.243814i
$377$	1.71691e6			0.622149
$378$		0			0
$379$	1.94081e6			0.694041			0.347021	−	0.937858i	$-0.387193\pi$
$379$	1.94081e6			0.694041			0.347021	+	0.937858i	$0.387193\pi$
$380$		−	3.05255e6i		−	1.08444i
$381$	−4.75002e6	−	2.31813e6i	−1.67642	−	0.818136i
$382$	5.26757e6			1.84694
$383$	−2.86380e6			−0.997577			−0.498788	−	0.866724i	$-0.666222\pi$
$383$	−2.86380e6			−0.997577			−0.498788	+	0.866724i	$0.666222\pi$
$384$	586127.	−	1.20102e6i	0.202845	−	0.415643i
$385$		0			0
$386$		−	804301.i		−	0.274758i
$387$	569573.	+	729733.i	0.193318	+	0.247677i
$388$			1.92645e6i			0.649649i
$389$		−	31571.4i		−	0.0105784i	−0.999986	−	0.00528921i	$-0.998316\pi$
$389$		−	31571.4i		−	0.0105784i	0.999986	−	0.00528921i	$-0.00168361\pi$
$390$	−2.01197e6	−	981894.i	−0.669823	−	0.326891i
$391$			585282.i			0.193608i
$392$		0			0
$393$	−2.38503e6	−	1.16396e6i	−0.778957	−	0.380151i
$394$	−1.10203e6			−0.357645
$395$	173792.			0.0560452
$396$	4.24027e6	−	3.30963e6i	1.35880	−	1.06058i
$397$			2.27723e6i			0.725153i	0.931954	+	0.362577i	$0.118103\pi$
$397$			2.27723e6i			0.725153i	−0.931954	+	0.362577i	$0.881897\pi$
$398$	−7.51855e6			−2.37917
$399$		0			0
$400$	1.92157e6			0.600490
$401$		−	3.57091e6i		−	1.10897i	−0.832195	−	0.554483i	$-0.812916\pi$
$401$		−	3.57091e6i		−	1.10897i	0.832195	−	0.554483i	$-0.187084\pi$
$402$	−2.81820e6	+	5.77468e6i	−0.869773	+	1.78223i
$403$	−1.94435e6			−0.596366
$404$	3.35354e6			1.02223
$405$	−411393.	+	1.64337e6i	−0.124629	+	0.497848i
$406$		0			0
$407$		−	6.23578e6i		−	1.86597i
$408$	44806.2	−	91811.1i	0.0133256	−	0.0273052i
$409$		−	3.74275e6i		−	1.10632i	−0.833074	−	0.553162i	$-0.813421\pi$
$409$		−	3.74275e6i		−	1.10632i	0.833074	−	0.553162i	$-0.186579\pi$
$410$			1.65125e6i			0.485125i
$411$	713204.	−	1.46140e6i	0.208261	−	0.426743i
$412$		−	441821.i		−	0.128234i
$413$		0			0
$414$	4.70615e6	+	6.02949e6i	1.34948	+	1.72894i
$415$	−1.03858e6			−0.296019
$416$	−4.99587e6			−1.41540
$417$	2.65779e6	−	5.44599e6i	0.748480	−	1.53369i
$418$		−	1.42238e7i		−	3.98177i
$419$	7.09739e6			1.97498			0.987492	−	0.157671i	$-0.0503984\pi$
$419$	7.09739e6			1.97498			0.987492	+	0.157671i	$0.0503984\pi$
$420$		0			0
$421$	−135000.			−0.0371218			−0.0185609	−	0.999828i	$-0.505908\pi$
$421$	−135000.			−0.0371218			−0.0185609	+	0.999828i	$0.505908\pi$
$422$		−	4.88799e6i		−	1.33613i
$423$	−2.35698e6	−	3.01974e6i	−0.640478	−	0.820576i
$424$	202974.			0.0548309
$425$	355807.			0.0955526
$426$	4.18432e6	+	2.04205e6i	1.11712	+	0.545184i
$427$		0			0
$428$		−	4.04685e6i		−	1.06784i
$429$	−5.03355e6	−	2.45650e6i	−1.32048	−	0.644428i
$430$			908503.i			0.236949i
$431$		−	2.63730e6i		−	0.683859i	−0.939726	−	0.341929i	$-0.888920\pi$
$431$		−	2.63730e6i		−	0.683859i	0.939726	−	0.341929i	$-0.111080\pi$
$432$	655237.	+	3.09346e6i	0.168923	+	0.797508i
$433$			2.75069e6i			0.705054i	0.935802	+	0.352527i	$0.114678\pi$
$433$			2.75069e6i			0.705054i	−0.935802	+	0.352527i	$0.885322\pi$
$434$		0			0
$435$	559213.	−	1.14587e6i	0.141695	−	0.290343i
$436$	2.74597e6			0.691800
$437$	1.08593e7			2.72018
$438$	−3.11264e6	−	1.51905e6i	−0.775252	−	0.378343i
$439$		−	5.35729e6i		−	1.32673i	−0.748294	−	0.663367i	$-0.769127\pi$
$439$		−	5.35729e6i		−	1.32673i	0.748294	−	0.663367i	$-0.230873\pi$
$440$	725760.			0.178715
$441$		0			0
$442$	−773770.			−0.188389
$443$			5.29243e6i			1.28129i	0.767839	+	0.640643i	$0.221332\pi$
$443$			5.29243e6i			1.28129i	−0.767839	+	0.640643i	$0.778668\pi$
$444$	−5.43213e6	−	2.65102e6i	−1.30771	−	0.638198i
$445$	−2.18946e6			−0.524128
$446$	5.28640e6			1.25841
$447$	335816.	−	688110.i	0.0794936	−	0.162888i
$448$		0			0
$449$			1.16335e6i			0.272329i	0.990686	+	0.136164i	$0.0434775\pi$
$449$			1.16335e6i			0.272329i	−0.990686	+	0.136164i	$0.956522\pi$
$450$	3.66548e6	−	2.86099e6i	0.853295	−	0.666016i
$451$			4.13111e6i			0.956368i
$452$		−	5.14216e6i		−	1.18386i
$453$	−6.93567e6	−	3.38479e6i	−1.58797	−	0.774971i
$454$			4.13539e6i			0.941623i
$455$		0			0
$456$	−1.70346e6	−	831334.i	−0.383637	−	0.187225i
$457$	−409259.			−0.0916659			−0.0458330	−	0.998949i	$-0.514594\pi$
$457$	−409259.			−0.0916659			−0.0458330	+	0.998949i	$0.514594\pi$
$458$	3.37329e6			0.751432
$459$	121327.	+	572801.i	0.0268798	+	0.126903i
$460$			4.03034e6i			0.888070i
$461$	−2.86383e6			−0.627618			−0.313809	−	0.949486i	$-0.601605\pi$
$461$	−2.86383e6			−0.627618			−0.313809	+	0.949486i	$0.601605\pi$
$462$		0			0
$463$	2.99670e6			0.649666			0.324833	−	0.945771i	$-0.394692\pi$
$463$	2.99670e6			0.649666			0.324833	+	0.945771i	$0.394692\pi$
$464$		−	2.37994e6i		−	0.513181i
$465$	−633294.	+	1.29766e6i	−0.135823	+	0.278311i
$466$	7.71604e6			1.64600
$467$	−105621.			−0.0224109			−0.0112054	−	0.999937i	$-0.503567\pi$
$467$	−105621.			−0.0224109			−0.0112054	+	0.999937i	$0.503567\pi$
$468$	−4.27983e6	+	3.34050e6i	−0.903258	+	0.705013i
$469$		0			0
$470$		−	3.75952e6i		−	0.785032i
$471$	−37713.8	+	77278.2i	−0.00783335	+	0.0160511i
$472$			1.41870e6i			0.293114i
$473$			2.27289e6i			0.467118i
$474$	344276.	−	705446.i	0.0703819	−	0.144218i
$475$		−	6.60164e6i		−	1.34251i
$476$		0			0
$477$	−917026.	+	715760.i	−0.184538	+	0.144036i
$478$	−7.18668e6			−1.43866
$479$	−8.07904e6			−1.60887			−0.804435	−	0.594040i	$-0.797532\pi$
$479$	−8.07904e6			−1.60887			−0.804435	+	0.594040i	$0.797532\pi$
$480$	−1.62720e6	+	3.33425e6i	−0.322358	+	0.660534i
$481$			6.29395e6i			1.24040i
$482$	−1.01572e6			−0.199139
$483$		0			0
$484$	7.23207e6			1.40330
$485$		−	1.48970e6i		−	0.287570i
$486$	5.85569e6	+	4.92534e6i	1.12457	+	0.945901i
$487$	7.09512e6			1.35562			0.677809	−	0.735238i	$-0.262930\pi$
$487$	7.09512e6			1.35562			0.677809	+	0.735238i	$0.262930\pi$
$488$	−1.91531e6			−0.364074
$489$	1.96377e6	+	958370.i	0.371380	+	0.181243i
$490$		0			0
$491$		−	681193.i		−	0.127516i	−0.997965	−	0.0637582i	$-0.979691\pi$
$491$		−	681193.i		−	0.127516i	0.997965	−	0.0637582i	$-0.0203087\pi$
$492$	3.59870e6	+	1.75626e6i	0.670244	+	0.327096i
$493$		−	440682.i		−	0.0816597i
$494$			1.43565e7i			2.64687i
$495$	−3.27895e6	+	2.55929e6i	−0.601480	+	0.469469i
$496$			2.69522e6i			0.491914i
$497$		0			0
$498$	−2.05739e6	+	4.21574e6i	−0.371743	+	0.761728i
$499$	−542586.			−0.0975477			−0.0487738	−	0.998810i	$-0.515531\pi$
$499$	−542586.			−0.0975477			−0.0487738	+	0.998810i	$0.515531\pi$
$500$	5.77636e6			1.03331
$501$	−903759.	−	441058.i	−0.160864	−	0.0785057i
$502$			6.28572e6i			1.11326i
$503$	5.66978e6			0.999186			0.499593	−	0.866260i	$-0.333483\pi$
$503$	5.66978e6			0.999186			0.499593	+	0.866260i	$0.333483\pi$
$504$		0			0
$505$	−2.59324e6			−0.452496
$506$			1.87800e7i			3.26076i
$507$	−121008.	−	59055.1i	−0.0209071	−	0.0102032i
$508$	−1.25795e7			−2.16273
$509$	2.37966e6			0.407118			0.203559	−	0.979063i	$-0.434749\pi$
$509$	2.37966e6			0.407118			0.203559	+	0.979063i	$0.434749\pi$
$510$	−252024.	+	516415.i	−0.0429059	+	0.0879171i
$511$		0			0
$512$			8.05775e6i			1.35843i
$513$	1.06277e7	−	2.25110e6i	1.78298	−	0.377660i
$514$		−	1.48280e7i		−	2.47556i
$515$			341654.i			0.0567635i
$516$	1.97997e6	+	966276.i	0.327366	+	0.159763i
$517$		−	9.40557e6i		−	1.54760i
$518$		0			0
$519$	−4.20741e6	−	2.05332e6i	−0.685640	−	0.334610i
$520$	−732530.			−0.118800
$521$	8.77252e6			1.41589			0.707946	−	0.706267i	$-0.249622\pi$
$521$	8.77252e6			1.41589			0.707946	+	0.706267i	$0.249622\pi$
$522$	−3.54345e6	−	4.53984e6i	−0.569180	−	0.729230i
$523$			1.07432e7i			1.71744i	0.512449	+	0.858718i	$0.328739\pi$
$523$			1.07432e7i			1.71744i	−0.512449	+	0.858718i	$0.671261\pi$
$524$	−6.31629e6			−1.00492
$525$		0			0
$526$	−5.62688e6			−0.886754
$527$			499060.i			0.0782756i
$528$	−3.40515e6	+	6.97738e6i	−0.531558	+	1.08920i
$529$	−7.90141e6			−1.22762
$530$	−1.14168e6			−0.176545
$531$	−5.00286e6	−	6.40963e6i	−0.769985	−	0.986499i
$532$		0			0
$533$		−	4.16964e6i		−	0.635742i
$534$	−4.33724e6	+	8.88732e6i	−0.658204	+	1.34871i
$535$			3.12938e6i			0.472687i
$536$			2.10248e6i			0.316097i
$537$	4.72768e6	−	9.68736e6i	0.707477	−	1.44967i
$538$		−	5.91941e6i		−	0.881703i
$539$		0			0
$540$	835476.	+	3.94440e6i	0.123296	+	0.582098i
$541$	3.38361e6			0.497036			0.248518	−	0.968627i	$-0.420057\pi$
$541$	3.38361e6			0.497036			0.248518	+	0.968627i	$0.420057\pi$
$542$	−7.16672e6			−1.04791
$543$	−3.20242e6	+	6.56198e6i	−0.466099	+	0.955071i
$544$			1.28230e6i			0.185777i
$545$	−2.12343e6			−0.306229
$546$		0			0
$547$	−1.83202e6			−0.261796			−0.130898	−	0.991396i	$-0.541786\pi$
$547$	−1.83202e6			−0.261796			−0.130898	+	0.991396i	$0.541786\pi$
$548$		−	3.87024e6i		−	0.550537i
$549$	8.65327e6	−	6.75407e6i	1.22532	−	0.956390i
$550$	1.14168e7			1.60931
$551$	−8.17640e6			−1.14732
$552$	2.24911e6	+	1.09763e6i	0.314169	+	0.153323i
$553$		0			0
$554$			1.83824e7i			2.54464i
$555$	4.20059e6	+	2.05000e6i	0.578866	+	0.282501i
$556$		−	1.44226e7i		−	1.97860i
$557$		−	1.23898e7i		−	1.69210i	−0.533100	−	0.846052i	$-0.678973\pi$
$557$		−	1.23898e7i		−	1.69210i	0.533100	−	0.846052i	$-0.321027\pi$
$558$	4.01286e6	+	5.14125e6i	0.545593	+	0.699009i
$559$		−	2.29410e6i		−	0.310515i
$560$		0			0
$561$	−630514.	+	1.29197e6i	−0.0845839	+	0.173318i
$562$	2.40267e6			0.320888
$563$	−3.30552e6			−0.439511			−0.219755	−	0.975555i	$-0.570526\pi$
$563$	−3.30552e6			−0.439511			−0.219755	+	0.975555i	$0.570526\pi$
$564$	−8.19340e6	−	3.99859e6i	−1.08459	−	0.529309i
$565$			3.97636e6i			0.524040i
$566$	−338297.			−0.0443871
$567$		0			0
$568$	1.52345e6			0.198133
$569$		−	1.15798e6i		−	0.149941i	−0.997186	−	0.0749707i	$-0.976114\pi$
$569$		−	1.15798e6i		−	0.149941i	0.997186	−	0.0749707i	$-0.0238863\pi$
$570$	9.58156e6	+	4.67605e6i	1.23523	+	0.602826i
$571$	−1.36048e6			−0.174623			−0.0873116	−	0.996181i	$-0.527828\pi$
$571$	−1.36048e6			−0.174623			−0.0873116	+	0.996181i	$0.527828\pi$
$572$	−1.33304e7			−1.70354
$573$	−4.33237e6	+	8.87734e6i	−0.551238	+	1.12953i
$574$		0			0
$575$			8.71628e6i			1.09941i
$576$	6.31682e6	+	8.09306e6i	0.793309	+	1.01638i
$577$			1.00712e7i			1.25934i	0.776864	+	0.629669i	$0.216809\pi$
$577$			1.00712e7i			1.25934i	−0.776864	+	0.629669i	$0.783191\pi$
$578$		−	1.16042e7i		−	1.44476i
$579$	1.35547e6	+	661506.i	0.168033	+	0.0820045i
$580$		−	3.03460e6i		−	0.374569i
$581$		0			0
$582$	−6.04688e6	−	2.95104e6i	−0.739987	−	0.361133i
$583$	−2.85626e6			−0.348037
$584$	−1.13327e6			−0.137499
$585$	3.30953e6	−	2.58317e6i	0.399832	−	0.312078i
$586$		−	1.01112e7i		−	1.21635i
$587$	−1.48152e7			−1.77465			−0.887326	−	0.461142i	$-0.847440\pi$
$587$	−1.48152e7			−1.77465			−0.887326	+	0.461142i	$0.847440\pi$
$588$		0			0
$589$	9.25955e6			1.09977
$590$		−	7.97986e6i		−	0.943768i
$591$	906375.	−	1.85723e6i	0.106743	−	0.218724i
$592$	8.72452e6			1.02315
$593$	−633754.			−0.0740089			−0.0370044	−	0.999315i	$-0.511782\pi$
$593$	−633754.			−0.0740089			−0.0370044	+	0.999315i	$0.511782\pi$
$594$	3.89303e6	+	1.83795e7i	0.452712	+	2.13731i
$595$		0			0
$596$		−	1.82232e6i		−	0.210140i
$597$	6.18371e6	−	1.26709e7i	0.710090	−	1.45502i
$598$		−	1.89552e7i		−	2.16758i
$599$			186824.i			0.0212748i	0.999943	+	0.0106374i	$0.00338605\pi$
$599$			186824.i			0.0212748i	−0.999943	+	0.0106374i	$0.996614\pi$
$600$	667274.	−	1.36729e6i	0.0756704	−	0.155054i
$601$			1.26979e7i			1.43399i	0.697081	+	0.716993i	$0.254482\pi$
$601$			1.26979e7i			1.43399i	−0.697081	+	0.716993i	$0.745518\pi$
$602$		0			0
$603$	−7.41411e6	−	9.49890e6i	−0.830358	−	1.06385i
$604$	−1.83677e7			−2.04863
$605$	−5.59246e6			−0.621176
$606$	−5.13712e6	+	1.05263e7i	−0.568248	+	1.16438i
$607$		−	3.88730e6i		−	0.428229i	−0.976809	−	0.214115i	$-0.931313\pi$
$607$		−	3.88730e6i		−	0.428229i	0.976809	−	0.214115i	$-0.0686866\pi$
$608$	2.37917e7			2.61016
$609$		0			0
$610$	1.07731e7			1.17224
$611$			9.49331e6i			1.02876i
$612$	857412.	+	1.09851e6i	0.0925360	+	0.118556i
$613$	5.19662e6			0.558560			0.279280	−	0.960210i	$-0.409904\pi$
$613$	5.19662e6			0.558560			0.279280	+	0.960210i	$0.409904\pi$
$614$	−6.69183e6			−0.716348
$615$	−2.78282e6	−	1.35809e6i	−0.296687	−	0.144791i
$616$		0			0
$617$			6.06374e6i			0.641250i	0.947206	+	0.320625i	$0.103893\pi$
$617$			6.06374e6i			0.641250i	−0.947206	+	0.320625i	$0.896107\pi$
$618$	1.38682e6	+	676804.i	0.146066	+	0.0712840i
$619$			1.09722e7i			1.15098i	0.817810	+	0.575489i	$0.195188\pi$
$619$			1.09722e7i			1.15098i	−0.817810	+	0.575489i	$0.804812\pi$
$620$			3.43661e6i			0.359046i
$621$	−1.40320e7	+	2.97217e6i	−1.46013	+	0.309275i
$622$		−	5.56099e6i		−	0.576336i
$623$		0			0
$624$	3.43691e6	−	7.04247e6i	0.353351	−	0.724042i
$625$	2.72672e6			0.279216
$626$	−1.97115e6			−0.201040
$627$	2.39712e7	+	1.16985e7i	2.43512	+	1.18840i
$628$			204656.i			0.0207074i
$629$	1.61548e6			0.162807
$630$		0			0
$631$	6.89261e6			0.689144			0.344572	−	0.938760i	$-0.388024\pi$
$631$	6.89261e6			0.689144			0.344572	+	0.938760i	$0.388024\pi$
$632$		−	256843.i		−	0.0255785i
$633$	8.23764e6	+	4.02018e6i	0.817134	+	0.398783i
$634$	−9.49533e6			−0.938182
$635$	9.72754e6			0.957345
$636$	−1.21428e6	+	2.48815e6i	−0.119035	+	0.243912i
$637$		0			0
$638$		−	1.41402e7i		−	1.37532i
$639$	−6.88287e6	+	5.37224e6i	−0.666834	+	0.520479i
$640$			2.45955e6i			0.237359i
$641$		−	1.67005e7i		−	1.60541i	−0.596378	−	0.802704i	$-0.703394\pi$
$641$		−	1.67005e7i		−	1.60541i	0.596378	−	0.802704i	$-0.296606\pi$
$642$	1.27025e7	+	6.19917e6i	1.21634	+	0.593603i
$643$		−	1.70411e7i		−	1.62544i	−0.582658	−	0.812718i	$-0.697987\pi$
$643$		−	1.70411e7i		−	1.62544i	0.582658	−	0.812718i	$-0.302013\pi$
$644$		0			0
$645$	−1.53108e6	−	747208.i	−0.144910	−	0.0707200i
$646$	3.68491e6			0.347412
$647$	−1.38647e7			−1.30212			−0.651059	−	0.759027i	$-0.725675\pi$
$647$	−1.38647e7			−1.30212			−0.651059	+	0.759027i	$0.725675\pi$
$648$	2.42869e6	+	607986.i	0.227213	+	0.0568795i
$649$		−	1.99640e7i		−	1.86053i
$650$	−1.15233e7			−1.06978
$651$		0			0
$652$	5.20065e6			0.479114
$653$		−	6.67502e6i		−	0.612590i	−0.951937	−	0.306295i	$-0.900911\pi$
$653$		−	6.67502e6i		−	0.612590i	0.951937	−	0.306295i	$-0.0990894\pi$
$654$	−4.20642e6	+	8.61926e6i	−0.384564	+	0.787999i
$655$	4.88430e6			0.444835
$656$	−5.77986e6			−0.524394
$657$	5.12004e6	−	3.99631e6i	0.462765	−	0.361198i
$658$		0			0
$659$		−	1.29602e7i		−	1.16251i	−0.813720	−	0.581257i	$-0.802561\pi$
$659$		−	1.29602e7i		−	1.16251i	0.813720	−	0.581257i	$-0.197439\pi$
$660$	−4.34182e6	+	8.89669e6i	−0.387982	+	0.795003i
$661$			7.30288e6i			0.650116i	0.945694	+	0.325058i	$0.105384\pi$
$661$			7.30288e6i			0.650116i	−0.945694	+	0.325058i	$0.894616\pi$
$662$		−	5.78792e6i		−	0.513308i
$663$	636396.	−	1.30402e6i	0.0562268	−	0.115213i
$664$			1.53489e6i			0.135101i
$665$		0			0
$666$	1.66424e7	−	1.29898e7i	1.45389	−	1.13479i
$667$	1.07955e7			0.939565
$668$	−2.39342e6			−0.207529
$669$	−4.34786e6	+	8.90907e6i	−0.375586	+	0.769603i
$670$		−	1.18259e7i		−	1.01777i
$671$	2.69523e7			2.31094
$672$		0			0
$673$	1.11430e7			0.948343			0.474172	−	0.880432i	$-0.342748\pi$
$673$	1.11430e7			0.948343			0.474172	+	0.880432i	$0.342748\pi$
$674$		−	1.34508e7i		−	1.14051i
$675$	1.80686e6	+	8.53041e6i	0.152638	+	0.720627i
$676$	−320466.			−0.0269721
$677$	2.00933e7			1.68492			0.842462	−	0.538755i	$-0.181105\pi$
$677$	2.00933e7			1.68492			0.842462	+	0.538755i	$0.181105\pi$
$678$	1.61406e7	+	7.87702e6i	1.34848	+	0.658093i
$679$		0			0
$680$			188020.i			0.0155930i
$681$	−6.96930e6	−	3.40120e6i	−0.575866	−	0.281037i
$682$			1.60134e7i			1.31833i
$683$			8.29698e6i			0.680563i	0.940324	+	0.340281i	$0.110522\pi$
$683$			8.29698e6i			0.680563i	−0.940324	+	0.340281i	$0.889478\pi$
$684$	2.03817e7	−	1.59084e7i	1.66572	−	1.30013i
$685$			2.99280e6i			0.243698i
$686$		0			0
$687$	−2.77440e6	+	5.68494e6i	−0.224273	+	0.459551i
$688$	−3.18002e6			−0.256129
$689$	2.88290e6			0.231356
$690$	−1.26507e7	−	6.17388e6i	−1.01156	−	0.493669i
$691$			1.57491e7i			1.25476i	0.778714	+	0.627379i	$0.215872\pi$
$691$			1.57491e7i			1.25476i	−0.778714	+	0.627379i	$0.784128\pi$
$692$	−1.11425e7			−0.884538
$693$		0			0
$694$	−2.09117e7			−1.64813
$695$			1.11528e7i			0.875836i
$696$	−1.69345e6	−	826446.i	−0.132510	−	0.0646683i
$697$	−1.07023e6			−0.0834439
$698$	−1.57449e7			−1.22321
$699$	−6.34614e6	+	1.30037e7i	−0.491266	+	1.00664i
$700$		0			0
$701$			2.29309e7i			1.76249i	0.472661	+	0.881244i	$0.343293\pi$
$701$			2.29309e7i			1.76249i	−0.472661	+	0.881244i	$0.656707\pi$
$702$	−3.92935e6	−	1.85510e7i	−0.300939	−	1.42077i
$703$		−	2.99735e7i		−	2.28744i
$704$			2.52074e7i			1.91689i
$705$	6.33584e6	+	3.09206e6i	0.480100	+	0.234301i
$706$		−	1.20306e7i		−	0.908393i
$707$		0			0
$708$	−1.73911e7	−	8.48732e6i	−1.30390	−	0.636337i
$709$	−2.17299e7			−1.62346			−0.811730	−	0.584032i	$-0.801474\pi$
$709$	−2.17299e7			−1.62346			−0.811730	+	0.584032i	$0.801474\pi$
$710$	−8.56904e6			−0.637949
$711$	905722.	+	1.16040e6i	0.0671925	+	0.0860866i
$712$			3.23575e6i			0.239207i
$713$	−1.22256e7			−0.900628
$714$		0			0
$715$	1.03082e7			0.754079
$716$		−	2.56550e7i		−	1.87021i
$717$	5.91076e6	−	1.21116e7i	0.429384	−	0.879838i
$718$	−1.35166e7			−0.978489
$719$	1.34764e7			0.972188			0.486094	−	0.873907i	$-0.338421\pi$
$719$	1.34764e7			0.972188			0.486094	+	0.873907i	$0.338421\pi$
$720$	−3.58072e6	−	4.58760e6i	−0.257418	−	0.329802i
$721$		0			0
$722$		−	4.77867e7i		−	3.41165i
$723$	835392.	−	1.71178e6i	0.0594353	−	0.121787i
$724$			1.73781e7i			1.23213i
$725$		−	6.56283e6i		−	0.463710i
$726$	−1.10785e7	+	2.27005e7i	−0.780077	+	1.59843i
$727$			1.58371e6i			0.111132i	0.998455	+	0.0555660i	$0.0176963\pi$
$727$			1.58371e6i			0.111132i	−0.998455	+	0.0555660i	$0.982304\pi$
$728$		0			0
$729$	−1.31167e7	+	5.81758e6i	−0.914123	+	0.405437i
$730$	6.37435e6			0.442720
$731$	−588829.			−0.0407564
$732$	1.14582e7	−	2.34787e7i	0.790387	−	1.61956i
$733$			3.52576e6i			0.242378i	0.992629	+	0.121189i	$0.0386707\pi$
$733$			3.52576e6i			0.242378i	−0.992629	+	0.121189i	$0.961329\pi$
$734$	−1.28249e7			−0.878644
$735$		0			0
$736$	−3.14127e7			−2.13752
$737$		−	2.95862e7i		−	2.00641i
$738$	−1.10253e7	+	8.60552e6i	−0.745163	+	0.581616i
$739$	95770.3			0.00645089			0.00322545	−	0.999995i	$-0.498973\pi$
$739$	95770.3			0.00645089			0.00322545	+	0.999995i	$0.498973\pi$
$740$	1.11244e7			0.746789
$741$	−2.41948e7	−	1.18077e7i	−1.61874	−	0.789985i
$742$		0			0
$743$			1.57924e7i			1.04949i	0.851260	+	0.524744i	$0.175839\pi$
$743$			1.57924e7i			1.04949i	−0.851260	+	0.524744i	$0.824161\pi$
$744$	1.91778e6	+	935928.i	0.127019	+	0.0619883i
$745$			1.40918e6i			0.0930197i
$746$		−	9.46132e6i		−	0.622450i
$747$	−5.41258e6	−	6.93456e6i	−0.354897	−	0.454692i
$748$			3.42152e6i			0.223597i
$749$		0			0
$750$	−8.84853e6	+	1.81313e7i	−0.574405	+	1.17700i
$751$	2.72481e6			0.176294			0.0881469	−	0.996107i	$-0.471906\pi$
$751$	2.72481e6			0.176294			0.0881469	+	0.996107i	$0.471906\pi$
$752$	1.31594e7			0.848577
$753$	−1.05932e7	−	5.16976e6i	−0.680832	−	0.332264i
$754$			1.42721e7i			0.914240i
$755$	1.42035e7			0.906835
$756$		0			0
$757$	−2.81384e7			−1.78468			−0.892340	−	0.451363i	$-0.850938\pi$
$757$	−2.81384e7			−1.78468			−0.892340	+	0.451363i	$0.850938\pi$
$758$			1.61333e7i			1.01988i
$759$	−3.16496e7	−	1.54458e7i	−1.99418	−	0.973210i
$760$	3.48851e6			0.219082
$761$	7.69113e6			0.481425			0.240712	−	0.970596i	$-0.422619\pi$
$761$	7.69113e6			0.481425			0.240712	+	0.970596i	$0.422619\pi$
$762$	1.92699e7	−	3.94853e7i	1.20224	−	2.46348i
$763$		0			0
$764$			2.35099e7i			1.45719i
$765$	−663025.	−	849463.i	−0.0409615	−	0.0524796i
$766$		−	2.38059e7i		−	1.46593i
$767$			2.01503e7i			1.23678i
$768$	−8.95621e6	−	4.37086e6i	−0.547925	−	0.267402i
$769$			2.03103e7i			1.23851i	0.785189	+	0.619256i	$0.212566\pi$
$769$			2.03103e7i			1.23851i	−0.785189	+	0.619256i	$0.787434\pi$
$770$		0			0
$771$	2.49893e7	+	1.21954e7i	1.51397	+	0.738858i
$772$	3.58970e6			0.216778
$773$	5.09102e6			0.306447			0.153224	−	0.988192i	$-0.451035\pi$
$773$	5.09102e6			0.306447			0.153224	+	0.988192i	$0.451035\pi$
$774$	−6.06603e6	+	4.73468e6i	−0.363959	+	0.284078i
$775$			7.43223e6i			0.444493i
$776$	−2.20158e6			−0.131245
$777$		0			0
$778$	262443.			0.0155448
$779$			1.98570e7i			1.17238i
$780$	4.38232e6	−	8.97969e6i	0.257910	−	0.528475i
$781$	−2.14380e7			−1.25764
$782$	−4.86526e6			−0.284504
$783$	1.05653e7	−	2.23786e6i	0.615851	−	0.130446i
$784$		0			0
$785$		−	158258.i		−	0.00916623i
$786$	9.67561e6	−	1.98260e7i	0.558627	−	1.14467i
$787$			2.99826e7i			1.72557i	0.505570	+	0.862785i	$0.331282\pi$
$787$			2.99826e7i			1.72557i	−0.505570	+	0.862785i	$0.668718\pi$
$788$		−	4.91850e6i		−	0.282174i
$789$	4.62789e6	−	9.48288e6i	0.264661	−	0.542310i
$790$			1.44468e6i			0.0823577i
$791$		0			0
$792$	3.78231e6	+	4.84587e6i	0.214261	+	0.274510i
$793$	−2.72037e7			−1.53619
$794$	−1.89298e7			−1.06560
$795$	938987.	−	1.92405e6i	0.0526916	−	0.107969i
$796$		−	3.35563e7i		−	1.87711i
$797$	4.32382e6			0.241113			0.120557	−	0.992706i	$-0.461532\pi$
$797$	4.32382e6			0.241113			0.120557	+	0.992706i	$0.461532\pi$
$798$		0			0
$799$	2.43666e6			0.135029
$800$			1.90965e7i			1.05495i
$801$	−1.14104e7	−	1.46189e7i	−0.628377	−	0.805072i
$802$	2.96838e7			1.62961
$803$	1.59474e7			0.872770
$804$	−2.57732e7	−	1.25780e7i	−1.40614	−	0.686231i
$805$		0			0
$806$		−	1.61628e7i		−	0.876352i
$807$	9.97587e6	+	4.86848e6i	0.539221	+	0.263154i
$808$			3.83248e6i			0.206515i
$809$			1.57334e7i			0.845183i	0.906320	+	0.422592i	$0.138880\pi$
$809$			1.57334e7i			0.845183i	−0.906320	+	0.422592i	$0.861120\pi$
$810$	−1.36608e7	−	3.41977e6i	−0.731582	−	0.183141i
$811$			1.11819e7i			0.596986i	0.954412	+	0.298493i	$0.0964839\pi$
$811$			1.11819e7i			0.596986i	−0.954412	+	0.298493i	$0.903516\pi$
$812$		0			0
$813$	5.89435e6	−	1.20779e7i	0.312759	−	0.640865i
$814$	5.18360e7			2.74202
$815$	−4.02159e6			−0.212082
$816$	−1.80760e6	−	882156.i	−0.0950336	−	0.0463789i
$817$			1.09251e7i			0.572626i
$818$	3.11123e7			1.62573
$819$		0			0
$820$	−7.36976e6			−0.382753
$821$			3.36479e7i			1.74221i	0.491098	+	0.871104i	$0.336596\pi$
$821$			3.36479e7i			1.74221i	−0.491098	+	0.871104i	$0.663404\pi$
$822$	1.21482e7	+	5.92863e6i	0.627093	+	0.306038i
$823$	−2.56786e6			−0.132151			−0.0660756	−	0.997815i	$-0.521048\pi$
$823$	−2.56786e6			−0.132151			−0.0660756	+	0.997815i	$0.521048\pi$
$824$	504922.			0.0259063
$825$	−9.38990e6	+	1.92406e7i	−0.480315	+	0.984199i
$826$		0			0
$827$		−	1.70261e7i		−	0.865670i	−0.901473	−	0.432835i	$-0.857513\pi$
$827$		−	1.70261e7i		−	0.865670i	0.901473	−	0.432835i	$-0.142487\pi$
$828$	−2.69104e7	+	2.10042e7i	−1.36409	+	1.06471i
$829$		−	1.40793e7i		−	0.711534i	−0.934575	−	0.355767i	$-0.884220\pi$
$829$		−	1.40793e7i		−	0.711534i	0.934575	−	0.355767i	$-0.115780\pi$
$830$		−	8.63339e6i		−	0.434997i
$831$	−3.09795e7	−	1.51188e7i	−1.55622	−	0.759476i
$832$		−	2.54426e7i		−	1.27424i
$833$		0			0
$834$	4.52708e7	+	2.20933e7i	2.25374	+	1.09988i
$835$	1.85080e6			0.0918637
$836$	6.34828e7			3.14153
$837$	−1.19649e7	+	2.53432e6i	−0.590329	+	0.125040i
$838$			5.89983e7i			2.90221i
$839$	−2.69718e7			−1.32283			−0.661415	−	0.750020i	$-0.730044\pi$
$839$	−2.69718e7			−1.32283			−0.661415	+	0.750020i	$0.730044\pi$
$840$		0			0
$841$	1.23828e7			0.603711
$842$		−	1.12221e6i		−	0.0545501i
$843$	−1.97610e6	+	4.04918e6i	−0.0957725	+	0.196245i
$844$	2.18157e7			1.05418
$845$	247812.			0.0119393
$846$	2.51021e7	−	1.95928e7i	1.20583	−	0.941174i
$847$		0			0
$848$		−	3.99620e6i		−	0.190835i
$849$	278236.	−	570125.i	0.0132478	−	0.0271457i
$850$			2.95771e6i			0.140413i
$851$			3.95746e7i			1.87324i
$852$	−9.11396e6	+	1.86751e7i	−0.430138	+	0.881384i
$853$			1.62151e7i			0.763038i	0.924361	+	0.381519i	$0.124599\pi$
$853$			1.62151e7i			0.763038i	−0.924361	+	0.381519i	$0.875401\pi$
$854$		0			0
$855$	−1.57609e7	+	1.23017e7i	−0.737337	+	0.575508i
$856$	4.62482e6			0.215730
$857$	1.96169e7			0.912384			0.456192	−	0.889881i	$-0.349213\pi$
$857$	1.96169e7			0.912384			0.456192	+	0.889881i	$0.349213\pi$
$858$	2.04201e7	−	4.18423e7i	0.946978	−	1.94043i
$859$		−	2.81262e7i		−	1.30055i	−0.759698	−	0.650276i	$-0.774653\pi$
$859$		−	2.81262e7i		−	1.30055i	0.759698	−	0.650276i	$-0.225347\pi$
$860$	−4.05477e6			−0.186948
$861$		0			0
$862$	2.19230e7			1.00492
$863$			4.00585e6i			0.183091i	0.995801	+	0.0915457i	$0.0291808\pi$
$863$			4.00585e6i			0.183091i	−0.995801	+	0.0915457i	$0.970819\pi$
$864$	−3.07428e7	+	6.51175e6i	−1.40107	+	0.296765i
$865$	8.61632e6			0.391545
$866$	−2.28656e7			−1.03607
$867$	1.95563e7	+	9.54401e6i	0.883568	+	0.431204i
$868$		0			0
$869$			3.61430e6i			0.162359i
$870$	9.52523e6	+	4.64856e6i	0.426655	+	0.208219i
$871$			2.98622e7i			1.33375i
$872$			3.13815e6i			0.139760i
$873$	9.94665e6	−	7.76358e6i	0.441714	−	0.344768i
$874$			9.02699e7i			3.99728i
$875$		0			0
$876$	6.77971e6	−	1.38921e7i	0.298504	−	0.611657i
$877$	1.41023e7			0.619143			0.309572	−	0.950876i	$-0.399814\pi$
$877$	1.41023e7			0.619143			0.309572	+	0.950876i	$0.399814\pi$
$878$	4.45334e7			1.94962
$879$	1.70401e7	+	8.31604e6i	0.743877	+	0.363031i
$880$		−	1.42890e7i		−	0.622005i
$881$	−1.87759e7			−0.815007			−0.407504	−	0.913204i	$-0.633601\pi$
$881$	−1.87759e7			−0.815007			−0.407504	+	0.913204i	$0.633601\pi$
$882$		0			0
$883$	1.01234e7			0.436943			0.218471	−	0.975843i	$-0.429893\pi$
$883$	1.01234e7			0.436943			0.218471	+	0.975843i	$0.429893\pi$
$884$		−	3.45344e6i		−	0.148635i
$885$	1.34483e7	+	6.56313e6i	0.577178	+	0.281678i
$886$	−4.39942e7			−1.88283
$887$	−1.94114e7			−0.828413			−0.414206	−	0.910183i	$-0.635941\pi$
$887$	−1.94114e7			−0.828413			−0.414206	+	0.910183i	$0.635941\pi$
$888$	3.02963e6	−	6.20794e6i	0.128931	−	0.264189i
$889$		0			0
$890$		−	1.82003e7i		−	0.770200i
$891$	−3.41766e7	−	8.55559e6i	−1.44223	−	0.361040i
$892$			2.35939e7i			0.992858i
$893$		−	4.52097e7i		−	1.89716i
$894$	5.72003e6	+	2.79153e6i	0.239362	+	0.116815i
$895$			1.98387e7i			0.827857i
$896$		0			0
$897$	3.19448e7	+	1.55899e7i	1.32562	+	0.646938i
$898$	−9.67053e6			−0.400184
$899$	9.20512e6			0.379866
$900$	1.27690e7	+	1.63595e7i	0.525471	+	0.673230i
$901$		−	739958.i		−	0.0303665i
$902$	−3.43405e7			−1.40537
$903$		0			0
$904$	5.87656e6			0.239167
$905$		−	1.34383e7i		−	0.545408i
$906$	2.81366e7	−	5.76539e7i	1.13881	−	2.33350i
$907$	−1.87347e7			−0.756185			−0.378092	−	0.925768i	$-0.623420\pi$
$907$	−1.87347e7			−0.756185			−0.378092	+	0.925768i	$0.623420\pi$
$908$	−1.84568e7			−0.742919
$909$	−1.35147e7	−	1.73150e7i	−0.542497	−	0.695044i
$910$		0			0
$911$			2.02958e6i			0.0810236i	0.999179	+	0.0405118i	$0.0128988\pi$
$911$			2.02958e6i			0.0810236i	−0.999179	+	0.0405118i	$0.987101\pi$
$912$	−1.63675e7	+	3.35382e7i	−0.651622	+	1.33522i
$913$		−	2.15990e7i		−	0.857546i
$914$		−	3.40204e6i		−	0.134702i
$915$	−8.86050e6	+	1.81558e7i	−0.349869	+	0.716906i
$916$			1.50554e7i			0.592863i
$917$		0			0
$918$	−4.76151e6	+	1.00855e6i	−0.186482	+	0.0394995i
$919$	2.94646e7			1.15083			0.575416	−	0.817861i	$-0.304840\pi$
$919$	2.94646e7			1.15083			0.575416	+	0.817861i	$0.304840\pi$
$920$	−4.60595e6			−0.179411
$921$	5.50377e6	−	1.12776e7i	0.213802	−	0.438095i
$922$		−	2.38061e7i		−	0.922277i
$923$	2.16380e7			0.836014
$924$		0			0
$925$	2.40584e7			0.924512
$926$			2.49106e7i			0.954676i
$927$	−2.28121e6	+	1.78054e6i	−0.0871899	+	0.0680537i
$928$	2.36519e7			0.901561
$929$	−1.47816e6			−0.0561930			−0.0280965	−	0.999605i	$-0.508945\pi$
$929$	−1.47816e6			−0.0561930			−0.0280965	+	0.999605i	$0.508945\pi$
$930$	−1.07871e7	−	5.26437e6i	−0.408974	−	0.199590i
$931$		0			0
$932$			3.44377e7i			1.29866i
$933$	9.37183e6	+	4.57370e6i	0.352468	+	0.172014i
$934$		−	877995.i		−	0.0329325i
$935$		−	2.64582e6i		−	0.0989762i
$936$	−3.81759e6	−	4.89107e6i	−0.142429	−	0.182480i
$937$		−	1.66834e7i		−	0.620777i	−0.950610	−	0.310389i	$-0.899541\pi$
$937$		−	1.66834e7i		−	0.620777i	0.950610	−	0.310389i	$-0.100459\pi$
$938$		0			0
$939$	1.62119e6	−	3.32194e6i	0.0600027	−	0.122950i
$940$	1.67792e7			0.619373
$941$	−1.64592e7			−0.605946			−0.302973	−	0.952999i	$-0.597979\pi$
$941$	−1.64592e7			−0.605946			−0.302973	+	0.952999i	$0.597979\pi$
$942$	−642389.	−	313502.i	−0.0235869	−	0.0115110i
$943$		−	2.62176e7i		−	0.960093i
$944$	2.79318e7			1.02016
$945$		0			0
$946$	−1.88938e7			−0.686423
$947$		−	4.15381e6i		−	0.150512i	−0.997164	−	0.0752561i	$-0.976023\pi$
$947$		−	4.15381e6i		−	0.150512i	0.997164	−	0.0752561i	$-0.0239774\pi$
$948$	3.14850e6	+	1.53655e6i	0.113784	+	0.0555298i
$949$	−1.60961e7			−0.580171
$950$	5.48773e7			1.97280
$951$	7.80954e6	−	1.60023e7i	0.280010	−	0.573761i
$952$		0			0
$953$		−	1.75643e7i		−	0.626468i	−0.949676	−	0.313234i	$-0.898588\pi$
$953$		−	1.75643e7i		−	0.626468i	0.949676	−	0.313234i	$-0.101412\pi$
$954$	−5.94988e6	−	7.62294e6i	−0.211659	−	0.271176i
$955$		−	1.81799e7i		−	0.645033i
$956$		−	3.20751e7i		−	1.13507i
$957$	2.38302e7	+	1.16298e7i	0.841102	+	0.410479i
$958$		−	6.71585e7i		−	2.36421i
$959$		0			0
$960$	−1.69804e7	−	8.28687e6i	−0.594661	−	0.290210i
$961$	1.82046e7			0.635877
$962$	−5.23196e7			−1.82275
$963$	−2.08947e7	+	1.63088e7i	−0.726056	+	0.566703i
$964$		−	4.53330e6i		−	0.157117i
$965$	−2.77587e6			−0.0959578
$966$		0			0
$967$	−3.80768e7			−1.30946			−0.654732	−	0.755861i	$-0.727219\pi$
$967$	−3.80768e7			−1.30946			−0.654732	+	0.755861i	$0.727219\pi$
$968$			8.26495e6i			0.283499i
$969$	−3.03069e6	+	6.21010e6i	−0.103689	+	0.212466i
$970$	1.23834e7			0.422581
$971$	−1.44742e7			−0.492660			−0.246330	−	0.969186i	$-0.579225\pi$
$971$	−1.44742e7			−0.492660			−0.246330	+	0.969186i	$0.579225\pi$
$972$	−2.19825e7	+	2.61347e7i	−0.746295	+	0.887262i
$973$		0			0
$974$			5.89794e7i			1.99206i
$975$	9.47749e6	−	1.94201e7i	0.319287	−	0.654243i
$976$			3.77091e7i			1.26713i
$977$			1.12581e7i			0.377335i	0.982041	+	0.188667i	$0.0604168\pi$
$977$			1.12581e7i			0.377335i	−0.982041	+	0.188667i	$0.939583\pi$
$978$	−7.96662e6	+	1.63242e7i	−0.266334	+	0.545738i
$979$		−	4.55335e7i		−	1.51836i
$980$		0			0
$981$	−1.10663e7	−	1.41780e7i	−0.367137	−	0.470373i
$982$	5.66253e6			0.187384
$983$	−2.53659e7			−0.837273			−0.418636	−	0.908154i	$-0.637492\pi$
$983$	−2.53659e7			−0.837273			−0.418636	+	0.908154i	$0.637492\pi$
$984$	−2.00709e6	+	4.11266e6i	−0.0660812	+	0.135405i
$985$			3.80341e6i			0.124906i
$986$	3.66324e6			0.119998
$987$		0			0
$988$	−6.40750e7			−2.08832
$989$		−	1.44247e7i		−	0.468937i
$990$	−2.12746e7	−	2.72568e7i	−0.689879	−	0.883867i
$991$	7.36046e6			0.238079			0.119039	−	0.992890i	$-0.462019\pi$
$991$	7.36046e6			0.238079			0.119039	+	0.992890i	$0.462019\pi$
$992$	−2.67851e7			−0.864199
$993$	9.75428e6	+	4.76034e6i	0.313922	+	0.153202i
$994$		0			0
$995$			2.59486e7i			0.830914i
$996$	−1.88154e7	−	9.18240e6i	−0.600987	−	0.293297i
$997$		−	4.08061e7i		−	1.30013i	−0.759878	−	0.650066i	$-0.774741\pi$
$997$		−	4.08061e7i		−	1.30013i	0.759878	−	0.650066i	$-0.225259\pi$
$998$		−	4.51034e6i		−	0.143345i
$999$	8.20369e6	+	3.87307e7i	0.260073	+	1.22784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.12	yes	40
3.2	odd	2	inner	147.6.c.d.146.29	yes	40
7.6	odd	2	inner	147.6.c.d.146.30	yes	40
21.20	even	2	inner	147.6.c.d.146.11	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.11	✓	40	21.20	even	2	inner
147.6.c.d.146.12	yes	40	1.1	even	1	trivial
147.6.c.d.146.29	yes	40	3.2	odd	2	inner
147.6.c.d.146.30	yes	40	7.6	odd	2	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+8.31267i q^{2} +(-14.0092 - 6.83685i) q^{3} -37.1006 q^{4} +28.6894 q^{5} +(56.8325 - 116.454i) q^{6} -42.3992i q^{8} +(149.515 + 191.558i) q^{9} +O(q^{10})\)	\(q+8.31267i q^{2} +(-14.0092 - 6.83685i) q^{3} -37.1006 q^{4} +28.6894 q^{5} +(56.8325 - 116.454i) q^{6} -42.3992i q^{8} +(149.515 + 191.558i) q^{9} +238.485i q^{10} +596.643i q^{11} +(519.749 + 253.651i) q^{12} -602.209i q^{13} +(-401.915 - 196.145i) q^{15} -834.767 q^{16} -154.570 q^{17} +(-1592.36 + 1242.87i) q^{18} +2867.88i q^{19} -1064.39 q^{20} -4959.70 q^{22} -3786.52i q^{23} +(-289.877 + 593.979i) q^{24} -2301.92 q^{25} +5005.96 q^{26} +(-784.934 - 3705.78i) q^{27} +2851.02i q^{29} +(1630.49 - 3340.99i) q^{30} -3228.71i q^{31} -8295.92i q^{32} +(4079.16 - 8358.48i) q^{33} -1284.89i q^{34} +(-5547.09 - 7106.89i) q^{36} -10451.4 q^{37} -23839.8 q^{38} +(-4117.21 + 8436.46i) q^{39} -1216.41i q^{40} +6923.92 q^{41} +3809.47 q^{43} -22135.8i q^{44} +(4289.49 + 5495.66i) q^{45} +31476.1 q^{46} -15764.1 q^{47} +(11694.4 + 5707.18i) q^{48} -19135.1i q^{50} +(2165.40 + 1056.77i) q^{51} +22342.3i q^{52} +4787.21i q^{53} +(30804.9 - 6524.90i) q^{54} +17117.3i q^{55} +(19607.3 - 40176.7i) q^{57} -23699.6 q^{58} -33460.6 q^{59} +(14911.3 + 7277.08i) q^{60} -45173.2i q^{61} +26839.2 q^{62} +42248.7 q^{64} -17277.0i q^{65} +(69481.4 + 33908.7i) q^{66} -49587.7 q^{67} +5734.62 q^{68} +(-25887.9 + 53046.1i) q^{69} +35931.1i q^{71} +(8121.89 - 6339.32i) q^{72} -26728.5i q^{73} -86879.5i q^{74} +(32248.1 + 15737.9i) q^{75} -106400. i q^{76} +(-70129.5 - 34225.0i) q^{78} +6057.73 q^{79} -23948.9 q^{80} +(-14339.6 + 57281.4i) q^{81} +57556.3i q^{82} -36200.9 q^{83} -4434.51 q^{85} +31666.9i q^{86} +(19492.0 - 39940.5i) q^{87} +25297.2 q^{88} -76316.2 q^{89} +(-45683.6 + 35657.1i) q^{90} +140482. i q^{92} +(-22074.2 + 45231.6i) q^{93} -131042. i q^{94} +82277.7i q^{95} +(-56718.0 + 116219. i) q^{96} -51925.1i q^{97} +(-114291. + 89207.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) \) 40 * q - 640 * q^4 + 440 * q^9	\( 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) \) 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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