LMFDB - Embedded newform 162.7.d.g.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 485774x^{12} + 87183614355x^{8} + 6839940225440174x^{4} + 198392288899684017121 $ x^16 + 485774x^12 + 87183614355x^8 + 6839940225440174*x^4 + 198392288899684017121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.5
Root			$-12.7063 + 11.9992i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.7.d.g.53.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-148.146 + 85.5319i) q^{5} +(-280.419 + 485.701i) q^{7} +181.019i q^{8} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-148.146 + 85.5319i) q^{5} +(-280.419 + 485.701i) q^{7} +181.019i q^{8} -967.683 q^{10} +(-190.829 - 110.175i) q^{11} +(-1890.50 - 3274.44i) q^{13} +(-2747.54 + 1586.29i) q^{14} +(-512.000 + 886.810i) q^{16} +2662.46i q^{17} +10334.0 q^{19} +(-4740.66 - 2737.02i) q^{20} +(-623.246 - 1079.49i) q^{22} +(12804.8 - 7392.86i) q^{23} +(6818.90 - 11810.7i) q^{25} -21388.5i q^{26} -17946.8 q^{28} +(-12880.3 - 7436.43i) q^{29} +(-7915.51 - 13710.1i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-7530.58 + 13043.4i) q^{34} -95939.2i q^{35} +26550.4 q^{37} +(50626.0 + 29229.0i) q^{38} +(-15482.9 - 26817.2i) q^{40} +(-98677.0 + 56971.2i) q^{41} +(26049.5 - 45119.0i) q^{43} -7051.22i q^{44} +83640.6 q^{46} +(-10009.8 - 5779.19i) q^{47} +(-98445.5 - 170513. i) q^{49} +(66811.3 - 38573.5i) q^{50} +(60495.9 - 104782. i) q^{52} +137651. i q^{53} +37694.0 q^{55} +(-87921.2 - 50761.3i) q^{56} +(-42066.8 - 72861.8i) q^{58} +(-252344. + 145691. i) q^{59} +(141109. - 244408. i) q^{61} -89553.8i q^{62} -32768.0 q^{64} +(560138. + 323396. i) q^{65} +(-188957. - 327283. i) q^{67} +(-73784.4 + 42599.4i) q^{68} +(271357. - 470004. i) q^{70} -521287. i q^{71} -611614. q^{73} +(130070. + 75095.8i) q^{74} +(165344. + 286384. i) q^{76} +(107024. - 61790.6i) q^{77} +(87787.4 - 152052. i) q^{79} -175169. i q^{80} -644556. q^{82} +(314364. + 181498. i) q^{83} +(-227725. - 394432. i) q^{85} +(255232. - 147358. i) q^{86} +(19943.9 - 34543.8i) q^{88} +1.23323e6i q^{89} +2.12053e6 q^{91} +(409754. + 236571. i) q^{92} +(-32692.0 - 56624.3i) q^{94} +(-1.53094e6 + 883886. i) q^{95} +(624144. - 1.08105e6i) q^{97} -1.11378e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 256 q^{4} - 964 q^{7}+O(q^{10}) $ 16 * q + 256 * q^4 - 964 * q^7	$ 16 q + 256 q^{4} - 964 q^{7} - 1536 q^{10} - 4540 q^{13} - 8192 q^{16} - 47368 q^{19} - 27072 q^{22} + 32392 q^{25} - 61696 q^{28} - 77056 q^{31} + 52608 q^{34} - 22696 q^{37} - 24576 q^{40} + 226604 q^{43} - 325440 q^{46} - 1298088 q^{49} + 145280 q^{52} - 2921832 q^{55} - 867456 q^{58} + 327476 q^{61} - 524288 q^{64} - 1713292 q^{67} + 176352 q^{70} - 4378432 q^{73} - 757888 q^{76} + 1326884 q^{79} - 2317632 q^{82} - 3483180 q^{85} + 866304 q^{88} + 2260648 q^{91} + 26400 q^{94} + 2200064 q^{97}+O(q^{100}) $ 16 * q + 256 * q^4 - 964 * q^7 - 1536 * q^10 - 4540 * q^13 - 8192 * q^16 - 47368 * q^19 - 27072 * q^22 + 32392 * q^25 - 61696 * q^28 - 77056 * q^31 + 52608 * q^34 - 22696 * q^37 - 24576 * q^40 + 226604 * q^43 - 325440 * q^46 - 1298088 * q^49 + 145280 * q^52 - 2921832 * q^55 - 867456 * q^58 + 327476 * q^61 - 524288 * q^64 - 1713292 * q^67 + 176352 * q^70 - 4378432 * q^73 - 757888 * q^76 + 1326884 * q^79 - 2317632 * q^82 - 3483180 * q^85 + 866304 * q^88 + 2260648 * q^91 + 26400 * q^94 + 2200064 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	−148.146	+	85.5319i	−1.18516	+	0.684255i	−0.957204	−	0.289415i	$-0.906539\pi$
$5$	−148.146	+	85.5319i	−1.18516	+	0.684255i	−0.227961	+	0.973670i	$0.573206\pi$
$6$		0			0
$7$	−280.419	+	485.701i	−0.817549	+	1.41604i	0.0899339	+	0.995948i	$0.471334\pi$
$7$	−280.419	+	485.701i	−0.817549	+	1.41604i	−0.907483	+	0.420089i	$0.861999\pi$
$8$			181.019i			0.353553i
$9$		0			0
$10$	−967.683			−0.967683
$11$	−190.829	−	110.175i	−0.143373	−	0.0827764i	0.426598	−	0.904442i	$-0.359712\pi$
$11$	−190.829	−	110.175i	−0.143373	−	0.0827764i	−0.569971	+	0.821665i	$0.693045\pi$
$12$		0			0
$13$	−1890.50	−	3274.44i	−0.860491	−	1.49041i	−0.871456	−	0.490473i	$-0.836824\pi$
$13$	−1890.50	−	3274.44i	−0.860491	−	1.49041i	0.0109657	−	0.999940i	$-0.496509\pi$
$14$	−2747.54	+	1586.29i	−1.00129	+	0.578094i
$15$		0			0
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$			2662.46i			0.541922i	0.962590	+	0.270961i	$0.0873415\pi$
$17$			2662.46i			0.541922i	−0.962590	+	0.270961i	$0.912659\pi$
$18$		0			0
$19$	10334.0			1.50663			0.753317	−	0.657658i	$-0.228453\pi$
$19$	10334.0			1.50663			0.753317	+	0.657658i	$0.228453\pi$
$20$	−4740.66	−	2737.02i	−0.592582	−	0.342127i
$21$		0			0
$22$	−623.246	−	1079.49i	−0.0585317	−	0.101380i
$23$	12804.8	−	7392.86i	1.05242	−	0.607615i	0.129095	−	0.991632i	$-0.458793\pi$
$23$	12804.8	−	7392.86i	1.05242	−	0.607615i	0.923326	+	0.384017i	$0.125460\pi$
$24$		0			0
$25$	6818.90	−	11810.7i	0.436410	−	0.755884i
$26$		−	21388.5i		−	1.21692i
$27$		0			0
$28$	−17946.8			−0.817549
$29$	−12880.3	−	7436.43i	−0.528118	−	0.304909i	0.212132	−	0.977241i	$-0.431959\pi$
$29$	−12880.3	−	7436.43i	−0.528118	−	0.304909i	−0.740250	+	0.672332i	$0.765293\pi$
$30$		0			0
$31$	−7915.51	−	13710.1i	−0.265701	−	0.460208i	0.702046	−	0.712132i	$-0.252270\pi$
$31$	−7915.51	−	13710.1i	−0.265701	−	0.460208i	−0.967747	+	0.251923i	$0.918937\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−7530.58	+	13043.4i	−0.191598	+	0.331858i
$35$		−	95939.2i		−	2.23765i
$36$		0			0
$37$	26550.4			0.524162			0.262081	−	0.965046i	$-0.415591\pi$
$37$	26550.4			0.524162			0.262081	+	0.965046i	$0.415591\pi$
$38$	50626.0	+	29229.0i	0.922621	+	0.532675i
$39$		0			0
$40$	−15482.9	−	26817.2i	−0.241921	−	0.419019i
$41$	−98677.0	+	56971.2i	−1.43174	+	0.826616i	−0.997254	−	0.0740621i	$-0.976404\pi$
$41$	−98677.0	+	56971.2i	−1.43174	+	0.826616i	−0.434487	+	0.900678i	$0.643070\pi$
$42$		0			0
$43$	26049.5	−	45119.0i	0.327637	−	0.567485i	−0.654405	−	0.756144i	$-0.727081\pi$
$43$	26049.5	−	45119.0i	0.327637	−	0.567485i	0.982043	+	0.188660i	$0.0604143\pi$
$44$		−	7051.22i		−	0.0827764i
$45$		0			0
$46$	83640.6			0.859298
$47$	−10009.8	−	5779.19i	−0.0964126	−	0.0556639i	0.451018	−	0.892515i	$-0.351061\pi$
$47$	−10009.8	−	5779.19i	−0.0964126	−	0.0556639i	−0.547431	+	0.836851i	$0.684394\pi$
$48$		0			0
$49$	−98445.5	−	170513.i	−0.836773	−	1.44933i
$50$	66811.3	−	38573.5i	0.534490	−	0.308588i
$51$		0			0
$52$	60495.9	−	104782.i	0.430245	−	0.745207i
$53$			137651.i			0.924595i	0.886725	+	0.462298i	$0.152975\pi$
$53$			137651.i			0.924595i	−0.886725	+	0.462298i	$0.847025\pi$
$54$		0			0
$55$	37694.0			0.226561
$56$	−87921.2	−	50761.3i	−0.500645	−	0.289047i
$57$		0			0
$58$	−42066.8	−	72861.8i	−0.215603	−	0.373436i
$59$	−252344.	+	145691.i	−1.22868	+	0.709377i	−0.966753	−	0.255712i	$-0.917690\pi$
$59$	−252344.	+	145691.i	−1.22868	+	0.709377i	−0.261923	+	0.965089i	$0.584357\pi$
$60$		0			0
$61$	141109.	−	244408.i	0.621678	−	1.07678i	−0.367495	−	0.930025i	$-0.619785\pi$
$61$	141109.	−	244408.i	0.621678	−	1.07678i	0.989173	−	0.146752i	$-0.0468821\pi$
$62$		−	89553.8i		−	0.375759i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	560138.	+	323396.i	2.03965	+	1.17759i
$66$		0			0
$67$	−188957.	−	327283.i	−0.628258	−	1.08818i	−0.987901	−	0.155085i	$-0.950435\pi$
$67$	−188957.	−	327283.i	−0.628258	−	1.08818i	0.359643	−	0.933090i	$-0.382899\pi$
$68$	−73784.4	+	42599.4i	−0.234659	+	0.135481i
$69$		0			0
$70$	271357.	−	470004.i	0.791128	−	1.37027i
$71$		−	521287.i		−	1.45647i	−0.685328	−	0.728235i	$-0.740341\pi$
$71$		−	521287.i		−	1.45647i	0.685328	−	0.728235i	$-0.259659\pi$
$72$		0			0
$73$	−611614.			−1.57221			−0.786103	−	0.618096i	$-0.787904\pi$
$73$	−611614.			−1.57221			−0.786103	+	0.618096i	$0.787904\pi$
$74$	130070.	+	75095.8i	0.320982	+	0.185319i
$75$		0			0
$76$	165344.	+	286384.i	0.376658	+	0.652391i
$77$	107024.	−	61790.6i	0.234429	−	0.135348i
$78$		0			0
$79$	87787.4	−	152052.i	0.178054	−	0.308398i	−0.763160	−	0.646209i	$-0.776353\pi$
$79$	87787.4	−	152052.i	0.178054	−	0.308398i	0.941214	+	0.337811i	$0.109687\pi$
$80$		−	175169.i		−	0.342127i
$81$		0			0
$82$	−644556.			−1.16901
$83$	314364.	+	181498.i	0.549792	+	0.317422i	0.749038	−	0.662527i	$-0.230516\pi$
$83$	314364.	+	181498.i	0.549792	+	0.317422i	−0.199246	+	0.979949i	$0.563849\pi$
$84$		0			0
$85$	−227725.	−	394432.i	−0.370813	−	0.642267i
$86$	255232.	−	147358.i	0.401272	−	0.231675i
$87$		0			0
$88$	19943.9	−	34543.8i	0.0292659	−	0.0506900i
$89$			1.23323e6i			1.74934i	0.484719	+	0.874670i	$0.338922\pi$
$89$			1.23323e6i			1.74934i	−0.484719	+	0.874670i	$0.661078\pi$
$90$		0			0
$91$	2.12053e6			2.81397
$92$	409754.	+	236571.i	0.526210	+	0.303808i
$93$		0			0
$94$	−32692.0	−	56624.3i	−0.0393603	−	0.0681740i
$95$	−1.53094e6	+	883886.i	−1.78561	+	1.03092i
$96$		0			0
$97$	624144.	−	1.08105e6i	0.683863	−	1.18449i	−0.289929	−	0.957048i	$-0.593632\pi$
$97$	624144.	−	1.08105e6i	0.683863	−	1.18449i	0.973793	−	0.227438i	$-0.0730349\pi$
$98$		−	1.11378e6i		−	1.18338i
$99$		0			0
$100$	436410.			0.436410
$101$	−915242.	−	528415.i	−0.888324	−	0.512874i	−0.0149303	−	0.999889i	$-0.504753\pi$
$101$	−915242.	−	528415.i	−0.888324	−	0.512874i	−0.873394	+	0.487014i	$0.838086\pi$
$102$		0			0
$103$	144795.	+	250792.i	0.132508	+	0.229511i	0.924643	−	0.380836i	$-0.124364\pi$
$103$	144795.	+	250792.i	0.132508	+	0.229511i	−0.792135	+	0.610346i	$0.791030\pi$
$104$	592737.	−	342217.i	0.526941	−	0.304229i
$105$		0			0
$106$	−389336.	+	674349.i	−0.326894	+	0.566197i
$107$			811508.i			0.662432i	0.943555	+	0.331216i	$0.107459\pi$
$107$			811508.i			0.662432i	−0.943555	+	0.331216i	$0.892541\pi$
$108$		0			0
$109$	−595882.			−0.460130			−0.230065	−	0.973175i	$-0.573894\pi$
$109$	−595882.			−0.460130			−0.230065	+	0.973175i	$0.573894\pi$
$110$	184662.	+	106615.i	0.138739	+	0.0801013i
$111$		0			0
$112$	−287149.	−	497357.i	−0.204387	−	0.354009i
$113$	−557538.	+	321895.i	−0.386402	+	0.223089i	−0.680600	−	0.732655i	$-0.738281\pi$
$113$	−557538.	+	321895.i	−0.386402	+	0.223089i	0.294198	+	0.955745i	$0.404948\pi$
$114$		0			0
$115$	−1.26465e6	+	2.19044e6i	−0.831528	+	1.44025i
$116$		−	475931.i		−	0.304909i
$117$		0			0
$118$	−1.64831e6			−1.00321
$119$	−1.29316e6	−	746606.i	−0.767382	−	0.443048i
$120$		0			0
$121$	−861503.	−	1.49217e6i	−0.486296	−	0.842290i
$122$	1.38258e6	−	798234.i	0.761397	−	0.439593i
$123$		0			0
$124$	253296.	−	438722.i	0.132851	−	0.230104i
$125$		−	339938.i		−	0.174048i
$126$		0			0
$127$	−53251.0			−0.0259966			−0.0129983	−	0.999916i	$-0.504138\pi$
$127$	−53251.0			−0.0259966			−0.0129983	+	0.999916i	$0.504138\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	1.82940e6	+	3.16862e6i	0.832682	+	1.44225i
$131$	1.50264e6	−	867552.i	0.668409	−	0.385906i	−0.127064	−	0.991894i	$-0.540556\pi$
$131$	1.50264e6	−	867552.i	0.668409	−	0.385906i	0.795474	+	0.605988i	$0.207222\pi$
$132$		0			0
$133$	−2.89785e6	+	5.01923e6i	−1.23175	+	2.13345i
$134$		−	2.13780e6i		−	0.888491i
$135$		0			0
$136$	−481957.			−0.191598
$137$	−1.84002e6	−	1.06233e6i	−0.715583	−	0.413142i	0.0975419	−	0.995231i	$-0.468902\pi$
$137$	−1.84002e6	−	1.06233e6i	−0.715583	−	0.413142i	−0.813125	+	0.582089i	$0.802235\pi$
$138$		0			0
$139$	1.49299e6	+	2.58593e6i	0.555918	+	0.962879i	0.997831	+	0.0658211i	$0.0209667\pi$
$139$	1.49299e6	+	2.58593e6i	0.555918	+	0.962879i	−0.441913	+	0.897058i	$0.645700\pi$
$140$	2.65874e6	−	1.53503e6i	0.968930	−	0.559412i
$141$		0			0
$142$	1.47442e6	−	2.55377e6i	0.514940	−	0.891902i
$143$			833145.i			0.284913i
$144$		0			0
$145$	2.54421e6			0.834542
$146$	−2.99629e6	−	1.72991e6i	−0.962775	−	0.555858i
$147$		0			0
$148$	424806.	+	735786.i	0.131041	+	0.226969i
$149$	1.37292e6	−	792654.i	0.415036	−	0.239621i	−0.277915	−	0.960606i	$-0.589643\pi$
$149$	1.37292e6	−	792654.i	0.415036	−	0.239621i	0.692951	+	0.720985i	$0.256310\pi$
$150$		0			0
$151$	−100324.	+	173767.i	−0.0291390	+	0.0504703i	−0.880227	−	0.474553i	$-0.842610\pi$
$151$	−100324.	+	173767.i	−0.0291390	+	0.0504703i	0.851088	+	0.525023i	$0.175943\pi$
$152$			1.87065e6i			0.532675i
$153$		0			0
$154$	699081.			0.191410
$155$	2.34530e6	+	1.35406e6i	0.629800	+	0.363615i
$156$		0			0
$157$	−525225.	−	909716.i	−0.135721	−	0.235075i	0.790152	−	0.612911i	$-0.210002\pi$
$157$	−525225.	−	909716.i	−0.135721	−	0.235075i	−0.925873	+	0.377836i	$0.876668\pi$
$158$	860137.	−	496600.i	0.218070	−	0.125903i
$159$		0			0
$160$	495453.	−	858151.i	0.120960	−	0.209509i
$161$			8.29240e6i			1.98702i
$162$		0			0
$163$	−2.04370e6			−0.471905			−0.235953	−	0.971765i	$-0.575821\pi$
$163$	−2.04370e6			−0.471905			−0.235953	+	0.971765i	$0.575821\pi$
$164$	−3.15766e6	−	1.82308e6i	−0.715870	−	0.413308i
$165$		0			0
$166$	1.02671e6	+	1.77831e6i	0.224451	+	0.388761i
$167$	−5.92645e6	+	3.42164e6i	−1.27246	+	0.734657i	−0.975451	−	0.220217i	$-0.929323\pi$
$167$	−5.92645e6	+	3.42164e6i	−1.27246	+	0.734657i	−0.297012	+	0.954874i	$0.595990\pi$
$168$		0			0
$169$	−4.73456e6	+	8.20050e6i	−0.980888	+	1.69895i
$170$		−	2.57642e6i		−	0.524409i
$171$		0			0
$172$	1.66717e6			0.327637
$173$	−1.08913e6	−	628810.i	−0.210350	−	0.121445i	0.391124	−	0.920338i	$-0.372086\pi$
$173$	−1.08913e6	−	628810.i	−0.210350	−	0.121445i	−0.601474	+	0.798892i	$0.705420\pi$
$174$		0			0
$175$	3.82430e6	+	6.62389e6i	0.713573	+	1.23594i
$176$	195409.	−	112820.i	0.0358432	−	0.0206941i
$177$		0			0
$178$	−3.48810e6	+	6.04157e6i	−0.618485	+	1.07125i
$179$			8.25586e6i			1.43947i	0.694248	+	0.719736i	$0.255737\pi$
$179$			8.25586e6i			1.43947i	−0.694248	+	0.719736i	$0.744263\pi$
$180$		0			0
$181$	2.62711e6			0.443040			0.221520	−	0.975156i	$-0.428898\pi$
$181$	2.62711e6			0.443040			0.221520	+	0.975156i	$0.428898\pi$
$182$	1.03884e7	+	5.99776e6i	1.72320	+	0.994890i
$183$		0			0
$184$	1.33825e6	+	2.31792e6i	0.214825	+	0.372087i
$185$	−3.93332e6	+	2.27090e6i	−0.621218	+	0.358661i
$186$		0			0
$187$	293338.	−	508076.i	0.0448584	−	0.0776970i
$188$		−	369868.i		−	0.0556639i
$189$		0			0
$190$	−1.00000e7			−1.45794
$191$	−1.27253e6	−	734698.i	−0.182629	−	0.105441i	0.405898	−	0.913918i	$-0.366959\pi$
$191$	−1.27253e6	−	734698.i	−0.182629	−	0.105441i	−0.588527	+	0.808477i	$0.700292\pi$
$192$		0			0
$193$	81598.8	+	141333.i	0.0113504	+	0.0196595i	0.871645	−	0.490138i	$-0.163054\pi$
$193$	81598.8	+	141333.i	0.0113504	+	0.0196595i	−0.860294	+	0.509798i	$0.829720\pi$
$194$	6.11533e6	−	3.53069e6i	0.837558	−	0.483564i
$195$		0			0
$196$	3.15026e6	−	5.45640e6i	0.418386	−	0.724667i
$197$		−	1.03528e7i		−	1.35413i	−0.735923	−	0.677065i	$-0.763252\pi$
$197$		−	1.03528e7i		−	1.35413i	0.735923	−	0.677065i	$-0.236748\pi$
$198$		0			0
$199$	−6.96701e6			−0.884071			−0.442035	−	0.896998i	$-0.645743\pi$
$199$	−6.96701e6			−0.884071			−0.442035	+	0.896998i	$0.645743\pi$
$200$	2.13796e6	+	1.23435e6i	0.267245	+	0.154294i
$201$		0			0
$202$	−2.98917e6	−	5.17739e6i	−0.362657	−	0.628140i
$203$	7.22375e6	−	4.17064e6i	0.863525	−	0.498556i
$204$		0			0
$205$	9.74571e6	−	1.68801e7i	1.13123	−	1.95935i
$206$			1.63817e6i			0.187395i
$207$		0			0
$208$	3.87174e6			0.430245
$209$	−1.97203e6	−	1.13855e6i	−0.216010	−	0.124714i
$210$		0			0
$211$	−6.08632e6	−	1.05418e7i	−0.647900	−	1.12220i	−0.983624	−	0.180235i	$-0.942314\pi$
$211$	−6.08632e6	−	1.05418e7i	−0.647900	−	1.12220i	0.335724	−	0.941960i	$-0.391019\pi$
$212$	−3.81470e6	+	2.20242e6i	−0.400362	+	0.231149i
$213$		0			0
$214$	−2.29529e6	+	3.97556e6i	−0.234205	+	0.405655i
$215$			8.91224e6i			0.896750i
$216$		0			0
$217$	8.87865e6			0.868896
$218$	−2.91921e6	−	1.68541e6i	−0.281771	−	0.162681i
$219$		0			0
$220$	603104.	+	1.04461e6i	0.0566401	+	0.0981036i
$221$	8.71807e6	−	5.03338e6i	0.807688	−	0.466319i
$222$		0			0
$223$	7.85859e6	−	1.36115e7i	0.708647	−	1.22741i	−0.256712	−	0.966488i	$-0.582639\pi$
$223$	7.85859e6	−	1.36115e7i	0.708647	−	1.22741i	0.965359	−	0.260925i	$-0.0840274\pi$
$224$		−	3.24872e6i		−	0.289047i
$225$		0			0
$226$	−3.64183e6			−0.315496
$227$	−130354.	−	75259.9i	−0.0111441	−	0.00643407i	0.494418	−	0.869225i	$-0.335381\pi$
$227$	−130354.	−	75259.9i	−0.0111441	−	0.00643407i	−0.505562	+	0.862790i	$0.668715\pi$
$228$		0			0
$229$	6.30714e6	+	1.09243e7i	0.525201	+	0.909675i	0.999569	+	0.0293486i	$0.00934330\pi$
$229$	6.30714e6	+	1.09243e7i	0.525201	+	0.909675i	−0.474368	+	0.880327i	$0.657323\pi$
$230$	−1.23910e7	+	7.15394e6i	−1.01841	+	0.587979i
$231$		0			0
$232$	1.34614e6	−	2.33158e6i	0.107802	−	0.186718i
$233$		−	1.73833e7i		−	1.37425i	−0.726542	−	0.687123i	$-0.758874\pi$
$233$		−	1.73833e7i		−	1.37425i	0.726542	−	0.687123i	$-0.241126\pi$
$234$		0			0
$235$	1.97722e6			0.152353
$236$	−8.07502e6	−	4.66211e6i	−0.614338	−	0.354688i
$237$		0			0
$238$	−4.22344e6	−	7.31522e6i	−0.313282	−	0.542621i
$239$	−1.09822e7	+	6.34059e6i	−0.804445	+	0.464447i	−0.845023	−	0.534730i	$-0.820413\pi$
$239$	−1.09822e7	+	6.34059e6i	−0.804445	+	0.464447i	0.0405780	+	0.999176i	$0.487080\pi$
$240$		0			0
$241$	−4.99488e6	+	8.65139e6i	−0.356840	+	0.618066i	−0.987431	−	0.158050i	$-0.949479\pi$
$241$	−4.99488e6	+	8.65139e6i	−0.356840	+	0.618066i	0.630591	+	0.776116i	$0.282813\pi$
$242$		−	9.74680e6i		−	0.687727i
$243$		0			0
$244$	9.03098e6			0.621678
$245$	2.91685e7	+	1.68405e7i	1.98343	+	1.14513i
$246$		0			0
$247$	−1.95364e7	−	3.38380e7i	−1.29644	−	2.24551i
$248$	2.48179e6	−	1.43286e6i	0.162708	−	0.0939396i
$249$		0			0
$250$	961489.	−	1.66535e6i	0.0615353	−	0.106582i
$251$		−	1.92884e7i		−	1.21976i	−0.792493	−	0.609881i	$-0.791217\pi$
$251$		−	1.92884e7i		−	1.21976i	0.792493	−	0.609881i	$-0.208783\pi$
$252$		0			0
$253$	−3.25804e6			−0.201185
$254$	−260876.	−	150617.i	−0.0159196	−	0.00919119i
$255$		0			0
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.32457e7	+	7.64740e6i	−0.780324	+	0.450520i	−0.836545	−	0.547898i	$-0.815428\pi$
$257$	−1.32457e7	+	7.64740e6i	−0.780324	+	0.450520i	0.0562210	+	0.998418i	$0.482095\pi$
$258$		0			0
$259$	−7.44524e6	+	1.28955e7i	−0.428528	+	0.742233i
$260$			2.06973e7i			1.17759i
$261$		0			0
$262$	9.81523e6			0.545754
$263$	−1.90796e7	−	1.10156e7i	−1.04882	−	0.605537i	−0.126502	−	0.991966i	$-0.540375\pi$
$263$	−1.90796e7	−	1.10156e7i	−1.04882	−	0.605537i	−0.922319	+	0.386429i	$0.873708\pi$
$264$		0			0
$265$	−1.17735e7	−	2.03924e7i	−0.632659	−	1.09580i
$266$	−2.83930e7	+	1.63927e7i	−1.50858	+	0.870976i
$267$		0			0
$268$	6.04662e6	−	1.04731e7i	0.314129	−	0.544088i
$269$		−	1.44503e7i		−	0.742368i	−0.928559	−	0.371184i	$-0.878952\pi$
$269$		−	1.44503e7i		−	0.742368i	0.928559	−	0.371184i	$-0.121048\pi$
$270$		0			0
$271$	−8.83074e6			−0.443700			−0.221850	−	0.975081i	$-0.571209\pi$
$271$	−8.83074e6			−0.443700			−0.221850	+	0.975081i	$0.571209\pi$
$272$	−2.36110e6	−	1.36318e6i	−0.117330	−	0.0677403i
$273$		0			0
$274$	−6.00947e6	−	1.04087e7i	−0.292135	−	0.505994i
$275$	−2.60249e6	+	1.50255e6i	−0.125139	+	0.0722488i
$276$		0			0
$277$	1.22908e7	−	2.12883e7i	0.578283	−	1.00162i	−0.417394	−	0.908726i	$-0.637056\pi$
$277$	1.22908e7	−	2.12883e7i	0.578283	−	1.00162i	0.995676	−	0.0928895i	$-0.0296103\pi$
$278$			1.68912e7i			0.786187i
$279$		0			0
$280$	1.73668e7			0.791128
$281$	2.87160e7	+	1.65792e7i	1.29421	+	0.747213i	0.979398	−	0.201940i	$-0.0647247\pi$
$281$	2.87160e7	+	1.65792e7i	1.29421	+	0.747213i	0.314813	+	0.949154i	$0.398058\pi$
$282$		0			0
$283$	1.90735e7	+	3.30363e7i	0.841533	+	1.45758i	0.888599	+	0.458685i	$0.151680\pi$
$283$	1.90735e7	+	3.30363e7i	0.841533	+	1.45758i	−0.0470661	+	0.998892i	$0.514987\pi$
$284$	1.44463e7	−	8.34059e6i	0.630670	−	0.364117i
$285$		0			0
$286$	−2.35649e6	+	4.08156e6i	−0.100732	+	0.174473i
$287$		−	6.39033e7i		−	2.70320i
$288$		0			0
$289$	1.70489e7			0.706320
$290$	1.24640e7	+	7.19610e6i	0.511051	+	0.295055i
$291$		0			0
$292$	−9.78583e6	−	1.69496e7i	−0.393051	−	0.680785i
$293$	3.00232e7	−	1.73339e7i	1.19359	−	0.689118i	0.234470	−	0.972123i	$-0.424665\pi$
$293$	3.00232e7	−	1.73339e7i	1.19359	−	0.689118i	0.959118	+	0.283005i	$0.0913313\pi$
$294$		0			0
$295$	2.49225e7	−	4.31670e7i	0.970789	−	1.68146i
$296$			4.80613e6i			0.185319i
$297$		0			0
$298$	8.96786e6			0.338875
$299$	−4.84149e7	−	2.79524e7i	−1.81120	−	1.04569i
$300$		0			0
$301$	1.46095e7	+	2.53045e7i	0.535719	+	0.927893i
$302$	−982972.	+	567519.i	−0.0356879	+	0.0206044i
$303$		0			0
$304$	−5.29101e6	+	9.16429e6i	−0.188329	+	0.326196i
$305$			4.82773e7i			1.70154i
$306$		0			0
$307$	−4.85387e7			−1.67754			−0.838770	−	0.544486i	$-0.816725\pi$
$307$	−4.85387e7			−1.67754			−0.838770	+	0.544486i	$0.816725\pi$
$308$	3.42478e6	+	1.97730e6i	0.117214	+	0.0676738i
$309$		0			0
$310$	7.65970e6	+	1.32670e7i	0.257115	+	0.445336i
$311$	2.67899e7	−	1.54672e7i	0.890616	−	0.514197i	0.0164719	−	0.999864i	$-0.494757\pi$
$311$	2.67899e7	−	1.54672e7i	0.890616	−	0.514197i	0.874144	+	0.485667i	$0.161423\pi$
$312$		0			0
$313$	−359747.	+	623100.i	−0.0117318	+	0.0203201i	−0.871832	−	0.489806i	$-0.837068\pi$
$313$	−359747.	+	623100.i	−0.0117318	+	0.0203201i	0.860100	+	0.510126i	$0.170401\pi$
$314$		−	5.94224e6i		−	0.191938i
$315$		0			0
$316$	5.61839e6			0.178054
$317$	6.46139e6	+	3.73049e6i	0.202838	+	0.117108i	0.597978	−	0.801512i	$-0.295971\pi$
$317$	6.46139e6	+	3.73049e6i	0.202838	+	0.117108i	−0.395141	+	0.918621i	$0.629304\pi$
$318$		0			0
$319$	1.63862e6	+	2.83818e6i	0.0504785	+	0.0874314i
$320$	4.85443e6	−	2.80271e6i	0.148146	−	0.0855319i
$321$		0			0
$322$	−2.34544e7	+	4.06243e7i	−0.702518	+	1.21680i
$323$			2.75139e7i			0.816478i
$324$		0			0
$325$	−5.15645e7			−1.50211
$326$	−1.00121e7	−	5.78046e6i	−0.288982	−	0.166844i
$327$		0			0
$328$	−1.03129e7	−	1.78624e7i	−0.292253	−	0.506197i
$329$	5.61391e6	−	3.24119e6i	0.157644	−	0.0910159i
$330$		0			0
$331$	−742285.	+	1.28568e6i	−0.0204685	+	0.0354525i	−0.876078	−	0.482169i	$-0.839849\pi$
$331$	−742285.	+	1.28568e6i	−0.0204685	+	0.0354525i	0.855610	+	0.517622i	$0.173182\pi$
$332$			1.16159e7i			0.317422i
$333$		0			0
$334$	−3.87114e7			−1.03896
$335$	5.59862e7	+	3.23237e7i	1.48918	+	0.859778i
$336$		0			0
$337$	−3.93257e6	−	6.81142e6i	−0.102751	−	0.177970i	0.810066	−	0.586339i	$-0.199431\pi$
$337$	−3.93257e6	−	6.81142e6i	−0.102751	−	0.177970i	−0.912817	+	0.408368i	$0.866098\pi$
$338$	−4.63890e7	+	2.67827e7i	−1.20134	+	0.693592i
$339$		0			0
$340$	7.28722e6	−	1.26218e7i	0.185406	−	0.321133i
$341$			3.48838e6i			0.0879752i
$342$		0			0
$343$	4.44420e7			1.10131
$344$	8.16741e6	+	4.71546e6i	0.200636	+	0.115837i
$345$		0			0
$346$	−3.55709e6	−	6.16105e6i	−0.0858749	−	0.148740i
$347$	−1.58793e7	+	9.16793e6i	−0.380052	+	0.219423i	−0.677841	−	0.735208i	$-0.737084\pi$
$347$	−1.58793e7	+	9.16793e6i	−0.380052	+	0.219423i	0.297789	+	0.954632i	$0.403751\pi$
$348$		0			0
$349$	−3.21650e7	+	5.57114e7i	−0.756672	+	1.31059i	0.187867	+	0.982194i	$0.439842\pi$
$349$	−3.21650e7	+	5.57114e7i	−0.756672	+	1.31059i	−0.944539	+	0.328399i	$0.893491\pi$
$350$			4.32670e7i			1.00914i
$351$		0			0
$352$	1.27641e6			0.0292659
$353$	−2.06487e7	−	1.19216e7i	−0.469429	−	0.271025i	0.246572	−	0.969124i	$-0.420696\pi$
$353$	−2.06487e7	−	1.19216e7i	−0.469429	−	0.271025i	−0.716000	+	0.698100i	$0.754029\pi$
$354$		0			0
$355$	4.45866e7	+	7.72263e7i	0.996597	+	1.72616i
$356$	−3.41763e7	+	1.97317e7i	−0.757486	+	0.437335i
$357$		0			0
$358$	−2.33511e7	+	4.04453e7i	−0.508930	+	0.881493i
$359$			1.50510e7i			0.325298i	0.986684	+	0.162649i	$0.0520038\pi$
$359$			1.50510e7i			0.325298i	−0.986684	+	0.162649i	$0.947996\pi$
$360$		0			0
$361$	5.97456e7			1.26994
$362$	1.28702e7	+	7.43059e6i	0.271305	+	0.156638i
$363$		0			0
$364$	3.39285e7	+	5.87658e7i	0.703493	+	1.21849i
$365$	9.06080e7	−	5.23125e7i	1.86332	−	1.07579i
$366$		0			0
$367$	−8.97392e6	+	1.55433e7i	−0.181545	+	0.314445i	−0.942407	−	0.334469i	$-0.891443\pi$
$367$	−8.97392e6	+	1.55433e7i	−0.181545	+	0.314445i	0.760862	+	0.648914i	$0.224776\pi$
$368$			1.51406e7i			0.303808i
$369$		0			0
$370$	−2.56923e7			−0.507223
$371$	−6.68572e7	−	3.86000e7i	−1.30926	−	0.755902i
$372$		0			0
$373$	4.33400e6	+	7.50671e6i	0.0835147	+	0.144652i	0.904757	−	0.425927i	$-0.140052\pi$
$373$	4.33400e6	+	7.50671e6i	0.0835147	+	0.144652i	−0.821243	+	0.570579i	$0.806719\pi$
$374$	2.87411e6	−	1.65937e6i	0.0549400	−	0.0317197i
$375$		0			0
$376$	1.04614e6	−	1.81198e6i	0.0196801	−	0.0340870i
$377$			5.62342e7i			1.04949i
$378$		0			0
$379$	−1.03648e7			−0.190390			−0.0951950	−	0.995459i	$-0.530347\pi$
$379$	−1.03648e7			−0.190390			−0.0951950	+	0.995459i	$0.530347\pi$
$380$	−4.89899e7	−	2.82844e7i	−0.892804	−	0.515461i
$381$		0			0
$382$	−4.15608e6	−	7.19854e6i	−0.0745579	−	0.129138i
$383$	−2.16952e6	+	1.25257e6i	−0.0386160	+	0.0222950i	−0.519184	−	0.854663i	$-0.673764\pi$
$383$	−2.16952e6	+	1.25257e6i	−0.0386160	+	0.0222950i	0.480568	+	0.876958i	$0.340431\pi$
$384$		0			0
$385$	−1.05701e7	+	1.83080e7i	−0.185224	+	0.320818i
$386$			923185.i			0.0160519i
$387$		0			0
$388$	3.99452e7			0.683863
$389$	2.13002e6	+	1.22977e6i	0.0361855	+	0.0208917i	0.517984	−	0.855391i	$-0.326683\pi$
$389$	2.13002e6	+	1.22977e6i	0.0361855	+	0.0208917i	−0.481798	+	0.876282i	$0.660016\pi$
$390$		0			0
$391$	1.96832e7	+	3.40923e7i	0.329280	+	0.570330i
$392$	3.08661e7	−	1.78205e7i	0.512417	−	0.295844i
$393$		0			0
$394$	2.92822e7	−	5.07183e7i	0.478757	−	0.829232i
$395$			3.00345e7i			0.487336i
$396$		0			0
$397$	1.17180e6			0.0187275			0.00936376	−	0.999956i	$-0.497019\pi$
$397$	1.17180e6			0.0187275			0.00936376	+	0.999956i	$0.497019\pi$
$398$	−3.41312e7	−	1.97057e7i	−0.541380	−	0.312566i
$399$		0			0
$400$	6.98255e6	+	1.20941e7i	0.109102	+	0.188971i
$401$	1.52455e7	−	8.80198e6i	0.236433	−	0.136505i	−0.377103	−	0.926171i	$-0.623080\pi$
$401$	1.52455e7	−	8.80198e6i	0.236433	−	0.136505i	0.613536	+	0.789667i	$0.289746\pi$
$402$		0			0
$403$	−2.99285e7	+	5.18377e7i	−0.457267	+	0.792010i
$404$		−	3.38186e7i		−	0.512874i
$405$		0			0
$406$	4.71854e7			0.705065
$407$	−5.06659e6	−	2.92520e6i	−0.0751507	−	0.0433883i
$408$		0			0
$409$	−3.22649e7	−	5.58844e7i	−0.471585	−	0.816809i	0.527887	−	0.849315i	$-0.322985\pi$
$409$	−3.22649e7	−	5.58844e7i	−0.471585	−	0.816809i	−0.999472	+	0.0325057i	$0.989651\pi$
$410$	9.54880e7	−	5.51300e7i	1.38547	−	0.799902i
$411$		0			0
$412$	−4.63344e6	+	8.02536e6i	−0.0662540	+	0.114755i
$413$		−	1.63418e8i		−	2.31980i
$414$		0			0
$415$	−6.20954e7			−0.868791
$416$	1.89676e7	+	1.09509e7i	0.263470	+	0.152115i
$417$		0			0
$418$	−6.44062e6	−	1.11555e7i	−0.0881859	−	0.152742i
$419$	−9.58989e7	+	5.53672e7i	−1.30368	+	0.752681i	−0.981033	−	0.193838i	$-0.937906\pi$
$419$	−9.58989e7	+	5.53672e7i	−1.30368	+	0.752681i	−0.322648	+	0.946519i	$0.604573\pi$
$420$		0			0
$421$	−1.58451e7	+	2.74445e7i	−0.212348	+	0.367798i	−0.952449	−	0.304698i	$-0.901444\pi$
$421$	−1.58451e7	+	2.74445e7i	−0.212348	+	0.367798i	0.740101	+	0.672496i	$0.234778\pi$
$422$		−	6.88589e7i		−	0.916268i
$423$		0			0
$424$	−2.49175e7			−0.326894
$425$	3.14455e7	+	1.81551e7i	0.409630	+	0.236500i
$426$		0			0
$427$	7.91394e7	+	1.37074e8i	1.01650	+	1.76064i
$428$	−2.24892e7	+	1.29841e7i	−0.286841	+	0.165608i
$429$		0			0
$430$	−2.52076e7	+	4.36609e7i	−0.317049	+	0.549145i
$431$		−	9.48759e6i		−	0.118502i	−0.998243	−	0.0592508i	$-0.981129\pi$
$431$		−	9.48759e6i		−	0.118502i	0.998243	−	0.0592508i	$-0.0188712\pi$
$432$		0			0
$433$	−1.03139e8			−1.27045			−0.635225	−	0.772327i	$-0.719092\pi$
$433$	−1.03139e8			−1.27045			−0.635225	+	0.772327i	$0.719092\pi$
$434$	4.34963e7	+	2.51126e7i	0.532088	+	0.307201i
$435$		0			0
$436$	−9.53411e6	−	1.65136e7i	−0.115033	−	0.199242i
$437$	1.32325e8	−	7.63978e7i	1.58561	−	0.915454i
$438$		0			0
$439$	2.31397e7	−	4.00791e7i	0.273504	−	0.473723i	−0.696252	−	0.717797i	$-0.745151\pi$
$439$	2.31397e7	−	4.00791e7i	0.273504	−	0.473723i	0.969757	+	0.244074i	$0.0784839\pi$
$440$			6.82335e6i			0.0801013i
$441$		0			0
$442$	5.69462e7			0.659475
$443$	−6.29030e7	−	3.63171e7i	−0.723536	−	0.417734i	0.0925165	−	0.995711i	$-0.470509\pi$
$443$	−6.29030e7	−	3.63171e7i	−0.723536	−	0.417734i	−0.816053	+	0.577977i	$0.803842\pi$
$444$		0			0
$445$	−1.05480e8	−	1.82698e8i	−1.19699	−	2.07325i
$446$	7.69981e7	−	4.44549e7i	0.867912	−	0.501089i
$447$		0			0
$448$	9.18878e6	−	1.59154e7i	0.102194	−	0.177005i
$449$			1.26263e7i			0.139488i	0.997565	+	0.0697439i	$0.0222182\pi$
$449$			1.26263e7i			0.139488i	−0.997565	+	0.0697439i	$0.977782\pi$
$450$		0			0
$451$	2.51073e7			0.273697
$452$	−1.78412e7	−	1.03006e7i	−0.193201	−	0.111545i
$453$		0			0
$454$	−425734.	−	737393.i	−0.00454957	−	0.00788009i
$455$	−3.14147e8	+	1.81373e8i	−3.33502	+	1.92547i
$456$		0			0
$457$	−7.41175e7	+	1.28375e8i	−0.776555	+	1.34503i	0.157361	+	0.987541i	$0.449701\pi$
$457$	−7.41175e7	+	1.28375e8i	−0.776555	+	1.34503i	−0.933916	+	0.357492i	$0.883632\pi$
$458$			7.13571e7i			0.742747i
$459$		0			0
$460$	−8.09376e7			−0.831528
$461$	−1.04144e8	−	6.01278e7i	−1.06300	−	0.613723i	−0.136739	−	0.990607i	$-0.543662\pi$
$461$	−1.04144e8	−	6.01278e7i	−1.06300	−	0.613723i	−0.926260	+	0.376884i	$0.876995\pi$
$462$		0			0
$463$	−6.27212e7	−	1.08636e8i	−0.631934	−	1.09454i	−0.987156	−	0.159760i	$-0.948928\pi$
$463$	−6.27212e7	−	1.08636e8i	−0.631934	−	1.09454i	0.355222	−	0.934782i	$-0.384405\pi$
$464$	1.31894e7	−	7.61490e6i	0.132029	−	0.0762273i
$465$		0			0
$466$	4.91674e7	−	8.51604e7i	0.485869	−	0.841550i
$467$			7.20089e7i			0.707027i	0.935429	+	0.353513i	$0.115013\pi$
$467$			7.20089e7i			0.707027i	−0.935429	+	0.353513i	$0.884987\pi$
$468$		0			0
$469$	2.11949e8			2.05453
$470$	9.68636e6	+	5.59242e6i	0.0932968	+	0.0538649i
$471$		0			0
$472$	−2.63729e7	−	4.56792e7i	−0.250803	−	0.434403i
$473$	−9.94200e6	+	5.74002e6i	−0.0939486	+	0.0542413i
$474$		0			0
$475$	7.04665e7	−	1.22052e8i	0.657509	−	1.13884i
$476$		−	4.77828e7i		−	0.443048i
$477$		0			0
$478$	−7.17356e7			−0.656827
$479$	3.68659e7	+	2.12845e7i	0.335443	+	0.193668i	0.658255	−	0.752795i	$-0.271295\pi$
$479$	3.68659e7	+	2.12845e7i	0.335443	+	0.193668i	−0.322812	+	0.946463i	$0.604628\pi$
$480$		0			0
$481$	−5.01934e7	−	8.69376e7i	−0.451037	−	0.781218i
$482$	−4.89396e7	+	2.82553e7i	−0.437038	+	0.252324i
$483$		0			0
$484$	2.75681e7	−	4.77494e7i	0.243148	−	0.421145i
$485$			2.13537e8i			1.87175i
$486$		0			0
$487$	9.50256e7			0.822723			0.411362	−	0.911472i	$-0.365053\pi$
$487$	9.50256e7			0.822723			0.411362	+	0.911472i	$0.365053\pi$
$488$	4.42426e7	+	2.55435e7i	0.380698	+	0.219796i
$489$		0			0
$490$	9.52640e7	+	1.65002e8i	0.809731	+	1.40249i
$491$	1.16209e8	−	6.70932e7i	0.981735	−	0.566805i	0.0789417	−	0.996879i	$-0.474846\pi$
$491$	1.16209e8	−	6.70932e7i	0.981735	−	0.566805i	0.902794	+	0.430074i	$0.141513\pi$
$492$		0			0
$493$	1.97992e7	−	3.42932e7i	0.165237	−	0.286199i
$494$		−	2.21029e8i		−	1.83345i
$495$		0			0
$496$	1.62110e7			0.132851
$497$	2.53189e8	+	1.46179e8i	2.06241	+	1.19074i
$498$		0			0
$499$	−1.53110e6	−	2.65195e6i	−0.0123226	−	0.0213434i	0.859798	−	0.510634i	$-0.170589\pi$
$499$	−1.53110e6	−	2.65195e6i	−0.0123226	−	0.0213434i	−0.872121	+	0.489290i	$0.837256\pi$
$500$	9.42063e6	−	5.43901e6i	0.0753651	−	0.0435120i
$501$		0			0
$502$	5.45559e7	−	9.44936e7i	0.431251	−	0.746949i
$503$		−	6.21612e7i		−	0.488445i	−0.969719	−	0.244223i	$-0.921467\pi$
$503$		−	6.21612e7i		−	0.488445i	0.969719	−	0.244223i	$-0.0785327\pi$
$504$		0			0
$505$	1.80785e8			1.40375
$506$	−1.59611e7	−	9.21514e6i	−0.123200	−	0.0711296i
$507$		0			0
$508$	−852016.	−	1.47574e6i	−0.00649915	−	0.0112569i
$509$	−2.24463e8	+	1.29594e8i	−1.70212	+	0.982721i	−0.758514	+	0.651657i	$0.774074\pi$
$509$	−2.24463e8	+	1.29594e8i	−1.70212	+	0.982721i	−0.943608	+	0.331064i	$0.892592\pi$
$510$		0			0
$511$	1.71509e8	−	2.97061e8i	1.28535	−	2.22630i
$512$		−	5.93164e6i		−	0.0441942i
$513$		0			0
$514$	−8.65204e7			−0.637132
$515$	−4.29015e7	−	2.47692e7i	−0.314088	−	0.181339i
$516$		0			0
$517$	1.27345e6	+	2.20568e6i	0.00921531	+	0.0159614i
$518$	−7.29482e7	+	4.21167e7i	−0.524838	+	0.303015i
$519$		0			0
$520$	−5.85409e7	+	1.01396e8i	−0.416341	+	0.721123i
$521$		−	6.34248e7i		−	0.448483i	−0.974534	−	0.224241i	$-0.928010\pi$
$521$		−	6.34248e7i		−	0.448483i	0.974534	−	0.224241i	$-0.0719904\pi$
$522$		0			0
$523$	−2.12228e8			−1.48353			−0.741766	−	0.670659i	$-0.766011\pi$
$523$	−2.12228e8			−1.48353			−0.741766	+	0.670659i	$0.766011\pi$
$524$	4.80846e7	+	2.77617e7i	0.334205	+	0.192953i
$525$		0			0
$526$	−6.23136e7	−	1.07930e8i	−0.428179	−	0.741629i
$527$	3.65026e7	−	2.10748e7i	0.249397	−	0.143990i
$528$		0			0
$529$	3.52907e7	−	6.11253e7i	0.238393	−	0.412909i
$530$		−	1.33202e8i		−	0.894715i
$531$		0			0
$532$	−1.85463e8			−1.23175
$533$	3.73097e8	+	2.15408e8i	2.46400	+	1.42259i
$534$		0			0
$535$	−6.94098e7	−	1.20221e8i	−0.453272	−	0.785091i
$536$	5.92445e7	−	3.42048e7i	0.384728	−	0.222123i
$537$		0			0
$538$	4.08716e7	−	7.07916e7i	0.262467	−	0.454606i
$539$			4.33851e7i			0.277060i
$540$		0			0
$541$	960703.			0.00606733			0.00303366	−	0.999995i	$-0.499034\pi$
$541$	960703.			0.00606733			0.00303366	+	0.999995i	$0.499034\pi$
$542$	−4.32616e7	−	2.49771e7i	−0.271710	−	0.156872i
$543$		0			0
$544$	−7.71132e6	−	1.33564e7i	−0.0478996	−	0.0829646i
$545$	8.82772e7	−	5.09669e7i	0.545330	−	0.314846i
$546$		0			0
$547$	−1.28973e8	+	2.23388e8i	−0.788021	+	1.36489i	0.139157	+	0.990270i	$0.455561\pi$
$547$	−1.28973e8	+	2.23388e8i	−0.788021	+	1.36489i	−0.927178	+	0.374622i	$0.877773\pi$
$548$		−	6.79894e7i		−	0.413142i
$549$		0			0
$550$	−1.69994e7			−0.102175
$551$	−1.33105e8	−	7.68480e7i	−0.795680	−	0.459386i
$552$		0			0
$553$	4.92346e7	+	8.52767e7i	0.291135	+	0.504261i
$554$	1.20425e8	−	6.95272e7i	0.708249	−	0.408908i
$555$		0			0
$556$	−4.77755e7	+	8.27496e7i	−0.277959	+	0.481440i
$557$			7.25922e7i			0.420073i	0.977694	+	0.210036i	$0.0673583\pi$
$557$			7.25922e7i			0.420073i	−0.977694	+	0.210036i	$0.932642\pi$
$558$		0			0
$559$	−1.96986e8			−1.12772
$560$	8.50798e7	+	4.91208e7i	0.484465	+	0.279706i
$561$		0			0
$562$	9.37861e7	+	1.62442e8i	0.528360	+	0.915146i
$563$	−1.40634e8	+	8.11948e7i	−0.788068	+	0.454991i	−0.839282	−	0.543696i	$-0.817024\pi$
$563$	−1.40634e8	+	8.11948e7i	−0.788068	+	0.454991i	0.0512139	+	0.998688i	$0.483691\pi$
$564$		0			0
$565$	5.50646e7	−	9.53746e7i	0.305300	−	0.528795i
$566$			2.15792e8i			1.19011i
$567$		0			0
$568$	9.43629e7			0.514940
$569$	−1.35419e8	−	7.81841e7i	−0.735093	−	0.424406i	0.0851898	−	0.996365i	$-0.472850\pi$
$569$	−1.35419e8	−	7.81841e7i	−0.735093	−	0.424406i	−0.820282	+	0.571959i	$0.806184\pi$
$570$		0			0
$571$	−7.72913e6	−	1.33872e7i	−0.0415166	−	0.0719089i	0.844520	−	0.535523i	$-0.179886\pi$
$571$	−7.72913e6	−	1.33872e7i	−0.0415166	−	0.0719089i	−0.886037	+	0.463614i	$0.846552\pi$
$572$	−2.30888e7	+	1.33303e7i	−0.123371	+	0.0712283i
$573$		0			0
$574$	1.80746e8	−	3.13061e8i	0.955724	−	1.65536i
$575$		−	2.01645e8i		−	1.06068i
$576$		0			0
$577$	8.55108e7			0.445137			0.222568	−	0.974917i	$-0.428556\pi$
$577$	8.55108e7			0.445137			0.222568	+	0.974917i	$0.428556\pi$
$578$	8.35220e7	+	4.82214e7i	0.432531	+	0.249722i
$579$		0			0
$580$	4.07073e7	+	7.05071e7i	0.208636	+	0.361367i
$581$	−1.76307e8	+	1.01791e8i	−0.898963	+	0.519017i
$582$		0			0
$583$	1.51657e7	−	2.62678e7i	0.0765347	−	0.132562i
$584$		−	1.10714e8i		−	0.555858i
$585$		0			0
$586$	1.96111e8			0.974561
$587$	−2.77326e8	−	1.60114e8i	−1.37112	−	0.791617i	−0.380051	−	0.924965i	$-0.624094\pi$
$587$	−2.77326e8	−	1.60114e8i	−1.37112	−	0.791617i	−0.991069	+	0.133349i	$0.957427\pi$
$588$		0			0
$589$	−8.17989e7	−	1.41680e8i	−0.400315	−	0.693365i
$590$	2.44189e8	−	1.40983e8i	1.18897	−	0.686451i
$591$		0			0
$592$	−1.35938e7	+	2.35452e7i	−0.0655203	+	0.113484i
$593$			2.07242e8i			0.993832i	0.867799	+	0.496916i	$0.165534\pi$
$593$			2.07242e8i			0.993832i	−0.867799	+	0.496916i	$0.834466\pi$
$594$		0			0
$595$	2.55435e8			1.21263
$596$	4.39333e7	+	2.53649e7i	0.207518	+	0.119810i
$597$		0			0
$598$	−1.58122e8	−	2.73876e8i	−0.739418	−	1.28071i
$599$	−2.43794e8	+	1.40755e8i	−1.13434	+	0.654911i	−0.945023	−	0.327005i	$-0.893961\pi$
$599$	−2.43794e8	+	1.40755e8i	−1.13434	+	0.654911i	−0.189317	+	0.981916i	$0.560627\pi$
$600$		0			0
$601$	−4.57960e7	+	7.93211e7i	−0.210962	+	0.365397i	−0.952016	−	0.306049i	$-0.900993\pi$
$601$	−4.57960e7	+	7.93211e7i	−0.210962	+	0.365397i	0.741054	+	0.671446i	$0.234326\pi$
$602$			1.65288e8i			0.757621i
$603$		0			0
$604$	−6.42075e6			−0.0291390
$605$	2.55256e8	+	1.47372e8i	1.15268	+	0.665501i
$606$		0			0
$607$	−6.45204e7	−	1.11753e8i	−0.288490	−	0.499680i	0.684959	−	0.728581i	$-0.259820\pi$
$607$	−6.45204e7	−	1.11753e8i	−0.288490	−	0.499680i	−0.973450	+	0.228902i	$0.926487\pi$
$608$	−5.18411e7	+	2.99305e7i	−0.230655	+	0.133169i
$609$		0			0
$610$	−1.36549e8	+	2.36509e8i	−0.601587	+	1.04198i
$611$			4.37022e7i			0.191593i
$612$		0			0
$613$	−3.34072e7			−0.145030			−0.0725151	−	0.997367i	$-0.523103\pi$
$613$	−3.34072e7			−0.145030			−0.0725151	+	0.997367i	$0.523103\pi$
$614$	−2.37790e8	−	1.37288e8i	−1.02728	−	0.593100i
$615$		0			0
$616$	1.11853e7	+	1.93735e7i	0.0478526	+	0.0828831i
$617$	3.57455e8	−	2.06377e8i	1.52183	−	0.878628i	0.522160	−	0.852848i	$-0.325126\pi$
$617$	3.57455e8	−	2.06377e8i	1.52183	−	0.878628i	0.999668	−	0.0257801i	$-0.00820697\pi$
$618$		0			0
$619$	−1.96903e7	+	3.41046e7i	−0.0830196	+	0.143794i	−0.904546	−	0.426377i	$-0.859790\pi$
$619$	−1.96903e7	+	3.41046e7i	−0.0830196	+	0.143794i	0.821526	+	0.570171i	$0.193123\pi$
$620$			8.66596e7i			0.363615i
$621$		0			0
$622$	1.74991e8			0.727185
$623$	−5.98981e8	−	3.45822e8i	−2.47713	−	1.43017i
$624$		0			0
$625$	1.35621e8	+	2.34902e8i	0.555503	+	0.962159i
$626$	−3.52479e6	+	2.03504e6i	−0.0143685	+	0.00829563i
$627$		0			0
$628$	1.68072e7	−	2.91109e7i	0.0678603	−	0.117538i
$629$			7.06894e7i			0.284055i
$630$		0			0
$631$	−3.58330e8			−1.42625			−0.713124	−	0.701038i	$-0.752720\pi$
$631$	−3.58330e8			−1.42625			−0.713124	+	0.701038i	$0.752720\pi$
$632$	2.75244e7	+	1.58912e7i	0.109035	+	0.0629515i
$633$		0			0
$634$	2.11028e7	+	3.65511e7i	0.0828081	+	0.143428i
$635$	7.88890e6	−	4.55466e6i	0.0308103	−	0.0177883i
$636$		0			0
$637$	−3.72222e8	+	6.44707e8i	−1.44007	+	2.49428i
$638$			1.85389e7i			0.0713874i
$639$		0			0
$640$	3.17090e7			0.120960
$641$	2.56183e8	+	1.47908e8i	0.972696	+	0.561586i	0.900057	−	0.435772i	$-0.143525\pi$
$641$	2.56183e8	+	1.47908e8i	0.972696	+	0.561586i	0.0726388	+	0.997358i	$0.476858\pi$
$642$		0			0
$643$	3.45261e7	+	5.98010e7i	0.129872	+	0.224945i	0.923627	−	0.383293i	$-0.125210\pi$
$643$	3.45261e7	+	5.98010e7i	0.129872	+	0.224945i	−0.793755	+	0.608238i	$0.791877\pi$
$644$	−2.29806e8	+	1.32678e8i	−0.860406	+	0.496755i
$645$		0			0
$646$	−7.78210e7	+	1.34790e8i	−0.288669	+	0.499989i
$647$			7.16195e7i			0.264435i	0.991221	+	0.132217i	$0.0422097\pi$
$647$			7.16195e7i			0.264435i	−0.991221	+	0.132217i	$0.957790\pi$
$648$		0			0
$649$	6.42063e7			0.234879
$650$	−2.52613e8	−	1.45846e8i	−0.919848	−	0.531074i
$651$		0			0
$652$	−3.26992e7	−	5.66367e7i	−0.117976	−	0.204341i
$653$	4.34310e8	−	2.50749e8i	1.55977	−	0.900533i	0.562490	−	0.826804i	$-0.309843\pi$
$653$	4.34310e8	−	2.50749e8i	1.55977	−	0.900533i	0.997278	−	0.0737286i	$-0.0234899\pi$
$654$		0			0
$655$	−1.48407e8	+	2.57048e8i	−0.528116	+	0.914724i
$656$		−	1.16677e8i		−	0.413308i
$657$		0			0
$658$	3.66699e7			0.128716
$659$	3.11452e8	+	1.79817e8i	1.08827	+	0.628310i	0.933114	−	0.359581i	$-0.117080\pi$
$659$	3.11452e8	+	1.79817e8i	1.08827	+	0.628310i	0.155151	+	0.987891i	$0.450414\pi$
$660$		0			0
$661$	1.95636e8	+	3.38851e8i	0.677398	+	1.17329i	0.975762	+	0.218835i	$0.0702257\pi$
$661$	1.95636e8	+	3.38851e8i	0.677398	+	1.17329i	−0.298364	+	0.954452i	$0.596441\pi$
$662$	−7.27288e6	+	4.19900e6i	−0.0250687	+	0.0144734i
$663$		0			0
$664$	−3.28546e7	+	5.69059e7i	−0.112226	+	0.194381i
$665$		−	9.91435e8i		−	3.37131i
$666$		0			0
$667$	−2.19906e8			−0.741070
$668$	−1.89646e8	−	1.09492e8i	−0.636231	−	0.367328i
$669$		0			0
$670$	1.82850e8	+	3.16706e8i	0.607955	+	1.05301i
$671$	−5.38555e7	+	3.10935e7i	−0.178264	+	0.102921i
$672$		0			0
$673$	1.50865e8	−	2.61306e8i	0.494929	−	0.857242i	−0.505054	−	0.863088i	$-0.668527\pi$
$673$	1.50865e8	−	2.61306e8i	0.494929	−	0.857242i	0.999983	+	0.00584556i	$0.00186071\pi$
$674$		−	4.44920e7i		−	0.145312i
$675$		0			0
$676$	−3.03012e8			−0.980888
$677$	−4.86730e7	−	2.81013e7i	−0.156863	−	0.0905652i	0.419514	−	0.907749i	$-0.362201\pi$
$677$	−4.86730e7	−	2.81013e7i	−0.156863	−	0.0905652i	−0.576377	+	0.817184i	$0.695534\pi$
$678$		0			0
$679$	3.50044e8	+	6.06294e8i	1.11818	+	1.93675i
$680$	7.13998e7	−	4.12227e7i	0.227076	−	0.131102i
$681$		0			0
$682$	−9.86662e6	+	1.70895e7i	−0.0311039	+	0.0538736i
$683$			1.47922e8i			0.464270i	0.972684	+	0.232135i	$0.0745711\pi$
$683$			1.47922e8i			0.464270i	−0.972684	+	0.232135i	$0.925429\pi$
$684$		0			0
$685$	3.63454e8			1.13078
$686$	2.17720e8	+	1.25701e8i	0.674414	+	0.389373i
$687$		0			0
$688$	2.66746e7	+	4.62018e7i	0.0819093	+	0.141871i
$689$	4.50730e8	−	2.60229e8i	1.37803	−	0.795606i
$690$		0			0
$691$	1.13616e7	−	1.96789e7i	0.0344355	−	0.0596441i	−0.848294	−	0.529526i	$-0.822370\pi$
$691$	1.13616e7	−	1.96789e7i	0.0344355	−	0.0596441i	0.882730	+	0.469881i	$0.155703\pi$
$692$		−	4.02438e7i		−	0.121445i
$693$		0			0
$694$	−1.03723e8			−0.310311
$695$	−4.42358e8	−	2.55396e8i	−1.31771	−	0.760780i
$696$		0			0
$697$	−1.51684e8	−	2.62724e8i	−0.447962	−	0.775892i
$698$	−3.15151e8	+	1.81953e8i	−0.926730	+	0.535048i
$699$		0			0
$700$	−1.22378e8	+	2.11964e8i	−0.356786	+	0.617972i
$701$			5.55648e8i			1.61304i	0.591205	+	0.806521i	$0.298652\pi$
$701$			5.55648e8i			1.61304i	−0.591205	+	0.806521i	$0.701348\pi$
$702$		0			0
$703$	2.74372e8			0.789720
$704$	6.25310e6	+	3.61023e6i	0.0179216	+	0.0103470i
$705$		0			0
$706$	−6.74385e7	−	1.16807e8i	−0.191643	−	0.331936i
$707$	5.13303e8	−	2.96356e8i	1.45250	−	0.838600i
$708$		0			0
$709$	3.40215e7	−	5.89270e7i	0.0954585	−	0.165339i	−0.814341	−	0.580386i	$-0.802902\pi$
$709$	3.40215e7	−	5.89270e7i	0.0954585	−	0.165339i	0.909800	+	0.415047i	$0.136235\pi$
$710$			5.04440e8i			1.40940i
$711$		0			0
$712$	−2.23239e8			−0.618485
$713$	−2.02713e8	−	1.17036e8i	−0.559259	−	0.322889i
$714$		0			0
$715$	−7.12605e7	−	1.23427e8i	−0.194953	−	0.337669i
$716$	−2.28793e8	+	1.32094e8i	−0.623310	+	0.359868i
$717$		0			0
$718$	−4.25706e7	+	7.37344e7i	−0.115010	+	0.199203i
$719$			1.29526e8i			0.348474i	0.984704	+	0.174237i	$0.0557459\pi$
$719$			1.29526e8i			0.348474i	−0.984704	+	0.174237i	$0.944254\pi$
$720$		0			0
$721$	−1.62413e8			−0.433327
$722$	2.92692e8	+	1.68986e8i	0.777678	+	0.448993i
$723$		0			0
$724$	4.20338e7	+	7.28046e7i	0.110760	+	0.191842i
$725$	−1.75659e8	+	1.01417e8i	−0.460952	+	0.266130i
$726$		0			0
$727$	3.05350e8	−	5.28882e8i	0.794684	−	1.37643i	−0.128355	−	0.991728i	$-0.540970\pi$
$727$	3.05350e8	−	5.28882e8i	0.794684	−	1.37643i	0.923039	−	0.384705i	$-0.125697\pi$
$728$			3.83857e8i			0.994890i
$729$		0			0
$730$	5.91849e8			1.52140
$731$	1.20128e8	+	6.93557e7i	0.307532	+	0.177554i
$732$		0			0
$733$	5.49347e7	+	9.51497e7i	0.139487	+	0.241599i	0.927303	−	0.374312i	$-0.122121\pi$
$733$	5.49347e7	+	9.51497e7i	0.139487	+	0.241599i	−0.787815	+	0.615911i	$0.788788\pi$
$734$	−8.79261e7	+	5.07642e7i	−0.222346	+	0.128372i
$735$		0			0
$736$	−4.28240e7	+	7.41733e7i	−0.107412	+	0.186043i
$737$			8.32736e7i			0.208020i
$738$		0			0
$739$	−3.13732e8			−0.777366			−0.388683	−	0.921372i	$-0.627070\pi$
$739$	−3.13732e8			−0.777366			−0.388683	+	0.921372i	$0.627070\pi$
$740$	−1.25866e8	−	7.26689e7i	−0.310609	−	0.179330i
$741$		0			0
$742$	−2.18355e8	−	3.78201e8i	−0.534504	−	0.925787i
$743$	2.69001e8	−	1.55308e8i	0.655824	−	0.378640i	−0.134860	−	0.990865i	$-0.543059\pi$
$743$	2.69001e8	−	1.55308e8i	0.655824	−	0.378640i	0.790684	+	0.612225i	$0.209725\pi$
$744$		0			0
$745$	−1.35594e8	+	2.34856e8i	−0.327924	+	0.567981i
$746$			4.90336e7i			0.118108i
$747$		0			0
$748$	1.87736e7			0.0448584
$749$	−3.94150e8	−	2.27562e8i	−0.938028	−	0.541571i
$750$		0			0
$751$	2.78681e8	+	4.82690e8i	0.657942	+	1.13959i	0.981148	+	0.193260i	$0.0619061\pi$
$751$	2.78681e8	+	4.82690e8i	0.657942	+	1.13959i	−0.323206	+	0.946329i	$0.604761\pi$
$752$	1.02501e7	−	5.91789e6i	0.0241032	−	0.0139160i
$753$		0			0
$754$	−1.59054e8	+	2.75490e8i	−0.371049	+	0.642676i
$755$		−	3.43237e7i		−	0.0797541i
$756$		0			0
$757$	1.72743e7			0.0398210			0.0199105	−	0.999802i	$-0.493662\pi$
$757$	1.72743e7			0.0398210			0.0199105	+	0.999802i	$0.493662\pi$
$758$	−5.07770e7	−	2.93161e7i	−0.116590	−	0.0673130i
$759$		0			0
$760$	−1.60000e8	−	2.77129e8i	−0.364486	−	0.631308i
$761$	−3.28749e7	+	1.89803e7i	−0.0745951	+	0.0430675i	−0.536834	−	0.843688i	$-0.680380\pi$
$761$	−3.28749e7	+	1.89803e7i	−0.0745951	+	0.0430675i	0.462239	+	0.886756i	$0.347046\pi$
$762$		0			0
$763$	1.67097e8	−	2.89420e8i	0.376179	−	0.651561i
$764$		−	4.70206e7i		−	0.105441i
$765$		0			0
$766$	−1.41713e7			−0.0315299
$767$	9.54113e8	+	5.50857e8i	2.11453	+	1.22082i
$768$		0			0
$769$	7.19828e7	+	1.24678e8i	0.158289	+	0.274164i	0.934252	−	0.356614i	$-0.116069\pi$
$769$	7.19828e7	+	1.24678e8i	0.158289	+	0.274164i	−0.775963	+	0.630778i	$0.782736\pi$
$770$	−1.03566e8	+	5.97937e7i	−0.226853	+	0.130973i
$771$		0			0
$772$	−2.61116e6	+	4.52267e6i	−0.00567521	+	0.00982975i
$773$			2.81284e8i			0.608984i	0.952515	+	0.304492i	$0.0984867\pi$
$773$			2.81284e8i			0.608984i	−0.952515	+	0.304492i	$0.901513\pi$
$774$		0			0
$775$	−2.15900e8			−0.463819
$776$	1.95691e8	+	1.12982e8i	0.418779	+	0.241782i
$777$		0			0
$778$	6.95662e6	+	1.20492e7i	0.0147727	+	0.0255870i
$779$	−1.01973e9	+	5.88740e8i	−2.15711	+	1.24541i
$780$		0			0
$781$	−5.74329e7	+	9.94768e7i	−0.120561	+	0.208818i
$782$			2.22690e8i			0.465673i
$783$		0			0
$784$	2.01616e8			0.418386
$785$	1.55619e8	+	8.98469e7i	0.321703	+	0.185735i
$786$		0			0
$787$	1.40890e8	+	2.44028e8i	0.289038	+	0.500628i	0.973580	−	0.228345i	$-0.0733313\pi$
$787$	1.40890e8	+	2.44028e8i	0.289038	+	0.500628i	−0.684542	+	0.728973i	$0.739998\pi$
$788$	2.86906e8	−	1.65645e8i	0.586355	−	0.338532i
$789$		0			0
$790$	−8.49503e7	+	1.47138e8i	−0.172299	+	0.298431i
$791$		−	3.61062e8i		−	0.729546i
$792$		0			0
$793$	−1.06707e9			−2.13979
$794$	5.74060e6	+	3.31434e6i	0.0114682	+	0.00662118i
$795$		0			0
$796$	−1.11472e8	−	1.93075e8i	−0.221018	−	0.382814i
$797$	−1.66240e8	+	9.59787e7i	−0.328368	+	0.189583i	−0.655116	−	0.755528i	$-0.727380\pi$
$797$	−1.66240e8	+	9.59787e7i	−0.328368	+	0.189583i	0.326748	+	0.945111i	$0.394047\pi$
$798$		0			0
$799$	1.53869e7	−	2.66509e7i	0.0301655	−	0.0522481i
$800$			7.89986e7i			0.154294i
$801$		0			0
$802$	9.95830e7			0.193047
$803$	1.16714e8	+	6.73849e7i	0.225412	+	0.130141i
$804$		0			0
$805$	−7.09264e8	−	1.22848e9i	−1.35963	−	2.35495i
$806$	−2.93238e8	+	1.69301e8i	−0.560036	+	0.323337i
$807$		0			0
$808$	9.56533e7	−	1.65676e8i	0.181328	−	0.314070i
$809$		−	3.02304e8i		−	0.570950i	−0.958386	−	0.285475i	$-0.907849\pi$
$809$		−	3.02304e8i		−	0.570950i	0.958386	−	0.285475i	$-0.0921513\pi$
$810$		0			0
$811$	−4.85058e8			−0.909351			−0.454675	−	0.890657i	$-0.650245\pi$
$811$	−4.85058e8			−0.909351			−0.454675	+	0.890657i	$0.650245\pi$
$812$	2.31160e8	+	1.33460e8i	0.431762	+	0.249278i
$813$		0			0
$814$	−1.65474e7	−	2.86610e7i	−0.0306801	−	0.0531395i
$815$	3.02765e8	−	1.74802e8i	0.559285	−	0.322903i
$816$		0			0
$817$	2.69195e8	−	4.66260e8i	0.493629	−	0.854991i
$818$		−	3.65035e8i		−	0.666922i
$819$		0			0
$820$	6.23725e8			1.13123
$821$	−7.89614e7	−	4.55884e7i	−0.142687	−	0.0823806i	0.426957	−	0.904272i	$-0.359586\pi$
$821$	−7.89614e7	−	4.55884e7i	−0.142687	−	0.0823806i	−0.569644	+	0.821891i	$0.692919\pi$
$822$		0			0
$823$	−4.68746e7	−	8.11892e7i	−0.0840888	−	0.145646i	0.820914	−	0.571052i	$-0.193465\pi$
$823$	−4.68746e7	−	8.11892e7i	−0.0840888	−	0.145646i	−0.905003	+	0.425406i	$0.860131\pi$
$824$	−4.53983e7	+	2.62107e7i	−0.0811443	+	0.0468487i
$825$		0			0
$826$	4.62217e8	−	8.00583e8i	0.820173	−	1.42058i
$827$		−	7.81578e8i		−	1.38183i	−0.722934	−	0.690917i	$-0.757207\pi$
$827$		−	7.81578e8i		−	1.38183i	0.722934	−	0.690917i	$-0.242793\pi$
$828$		0			0
$829$	5.47882e8			0.961663			0.480832	−	0.876813i	$-0.340335\pi$
$829$	5.47882e8			0.961663			0.480832	+	0.876813i	$0.340335\pi$
$830$	−3.04204e8	−	1.75632e8i	−0.532024	−	0.307164i
$831$		0			0
$832$	6.19478e7	+	1.07297e8i	0.107561	+	0.186302i
$833$	4.53984e8	−	2.62108e8i	0.785426	−	0.453466i
$834$		0			0
$835$	5.85318e8	−	1.01380e9i	1.00538	−	1.74138i
$836$		−	7.28673e7i		−	0.124714i
$837$		0			0
$838$	−6.26409e8			−1.06445
$839$	4.63674e7	+	2.67702e7i	0.0785103	+	0.0453279i	0.538741	−	0.842471i	$-0.318900\pi$
$839$	4.63674e7	+	2.67702e7i	0.0785103	+	0.0453279i	−0.460231	+	0.887799i	$0.652233\pi$
$840$		0			0
$841$	−1.86811e8	−	3.23566e8i	−0.314061	−	0.543969i
$842$	−1.55250e8	+	8.96334e7i	−0.260073	+	0.150153i
$843$		0			0
$844$	1.94762e8	−	3.37338e8i	0.323950	−	0.561098i
$845$		−	1.61982e9i		−	2.68471i
$846$		0			0
$847$	9.66329e8			1.59028
$848$	−1.22070e8	−	7.04773e7i	−0.200181	−	0.115574i
$849$		0			0
$850$	1.02701e8	+	1.77883e8i	0.167231	+	0.289652i
$851$	3.39973e8	−	1.96283e8i	0.551639	−	0.318489i
$852$		0			0
$853$	1.29396e8	−	2.24121e8i	0.208485	−	0.361107i	−0.742752	−	0.669566i	$-0.766480\pi$
$853$	1.29396e8	−	2.24121e8i	0.208485	−	0.361107i	0.951238	+	0.308459i	$0.0998134\pi$
$854$			8.95360e8i			1.43755i
$855$		0			0
$856$	−1.46899e8			−0.234205
$857$	5.78169e8	+	3.33806e8i	0.918571	+	0.530337i	0.883179	−	0.469037i	$-0.155399\pi$
$857$	5.78169e8	+	3.33806e8i	0.918571	+	0.530337i	0.0353918	+	0.999374i	$0.488732\pi$
$858$		0			0
$859$	5.71527e8	+	9.89914e8i	0.901690	+	1.56177i	0.825299	+	0.564696i	$0.191006\pi$
$859$	5.71527e8	+	9.89914e8i	0.901690	+	1.56177i	0.0763913	+	0.997078i	$0.475660\pi$
$860$	−2.46983e8	+	1.42596e8i	−0.388304	+	0.224187i
$861$		0			0
$862$	2.68350e7	−	4.64795e7i	0.0418966	−	0.0725671i
$863$		−	1.78293e8i		−	0.277396i	−0.990335	−	0.138698i	$-0.955708\pi$
$863$		−	1.78293e8i		−	0.277396i	0.990335	−	0.138698i	$-0.0442918\pi$
$864$		0			0
$865$	2.15133e8			0.332398
$866$	−5.05274e8	−	2.91720e8i	−0.777988	−	0.449172i
$867$		0			0
$868$	1.42058e8	+	2.46052e8i	0.217224	+	0.376243i
$869$	−3.35048e7	+	1.93440e7i	−0.0510561	+	0.0294773i
$870$		0			0
$871$	−7.14445e8	+	1.23745e9i	−1.08122	+	1.87273i
$872$		−	1.07866e8i		−	0.162681i
$873$		0			0
$874$	8.64342e8			1.29465
$875$	1.65108e8	+	9.53251e7i	0.246459	+	0.142293i
$876$		0			0
$877$	−4.64920e8	−	8.05265e8i	−0.689254	−	1.19382i	−0.972079	−	0.234652i	$-0.924605\pi$
$877$	−4.64920e8	−	8.05265e8i	−0.689254	−	1.19382i	0.282825	−	0.959172i	$-0.408728\pi$
$878$	2.26722e8	−	1.30898e8i	0.334973	−	0.193397i
$879$		0			0
$880$	−1.92993e7	+	3.34274e7i	−0.0283201	+	0.0490518i
$881$			5.01442e8i			0.733319i	0.930355	+	0.366660i	$0.119499\pi$
$881$			5.01442e8i			0.733319i	−0.930355	+	0.366660i	$0.880501\pi$
$882$		0			0
$883$	8.14295e8			1.18277			0.591384	−	0.806390i	$-0.298582\pi$
$883$	8.14295e8			1.18277			0.591384	+	0.806390i	$0.298582\pi$
$884$	2.78978e8	+	1.61068e8i	0.403844	+	0.233159i
$885$		0			0
$886$	−2.05440e8	−	3.55833e8i	−0.295382	−	0.511617i
$887$	−3.43598e8	+	1.98377e8i	−0.492357	+	0.284262i	−0.725552	−	0.688168i	$-0.758415\pi$
$887$	−3.43598e8	+	1.98377e8i	−0.492357	+	0.284262i	0.233195	+	0.972430i	$0.425082\pi$
$888$		0			0
$889$	1.49326e7	−	2.58641e7i	0.0212535	−	0.0368122i
$890$		−	1.19338e9i		−	1.69281i
$891$		0			0
$892$	5.02950e8			0.708647
$893$	−1.03442e8	−	5.97221e7i	−0.145258	−	0.0838650i
$894$		0			0
$895$	−7.06139e8	−	1.22307e9i	−0.984966	−	1.70601i
$896$	9.00313e7	−	5.19796e7i	0.125161	−	0.0722618i
$897$		0			0
$898$	−3.57125e7	+	6.18559e7i	−0.0493164	+	0.0854185i
$899$			2.35453e8i			0.324059i
$900$		0			0
$901$	−3.66491e8			−0.501059
$902$	1.23000e8	+	7.10141e7i	0.167605	+	0.0967665i
$903$		0			0
$904$	−5.82692e7	−	1.00925e8i	−0.0788740	−	0.136614i
$905$	−3.89195e8	+	2.24702e8i	−0.525075	+	0.303152i
$906$		0			0
$907$	4.40034e8	−	7.62161e8i	0.589745	−	1.02147i	−0.404520	−	0.914529i	$-0.632562\pi$
$907$	4.40034e8	−	7.62161e8i	0.589745	−	1.02147i	0.994266	−	0.106939i	$-0.0341051\pi$
$908$		−	4.81663e6i		−	0.00643407i
$909$		0			0
$910$	−2.05200e9			−2.72303
$911$	−4.37526e8	−	2.52606e8i	−0.578693	−	0.334109i	0.181921	−	0.983313i	$-0.441769\pi$
$911$	−4.37526e8	−	2.52606e8i	−0.578693	−	0.334109i	−0.760614	+	0.649205i	$0.775102\pi$
$912$		0			0
$913$	−3.99932e7	−	6.92703e7i	−0.0525501	−	0.0910195i
$914$	−7.26200e8	+	4.19272e8i	−0.951082	+	0.549107i
$915$		0			0
$916$	−2.01828e8	+	3.49577e8i	−0.262601	+	0.454838i
$917$			9.73114e8i			1.26199i
$918$		0			0
$919$	−2.68525e8			−0.345969			−0.172985	−	0.984925i	$-0.555341\pi$
$919$	−2.68525e8			−0.345969			−0.172985	+	0.984925i	$0.555341\pi$
$920$	−3.96512e8	−	2.28926e8i	−0.509205	−	0.293989i
$921$		0			0
$922$	−3.40134e8	−	5.89129e8i	−0.433968	−	0.751654i
$923$	−1.70692e9	+	9.85491e8i	−2.17074	+	1.25328i
$924$		0			0
$925$	1.81044e8	−	3.13578e8i	0.228749	−	0.396206i
$926$		−	7.09610e8i		−	0.893690i
$927$		0			0
$928$	8.61528e7			0.107802
$929$	−6.07506e8	−	3.50744e8i	−0.757711	−	0.437465i	0.0707624	−	0.997493i	$-0.477457\pi$
$929$	−6.07506e8	−	3.50744e8i	−0.757711	−	0.437465i	−0.828473	+	0.560029i	$0.810790\pi$
$930$		0			0
$931$	−1.01734e9	−	1.76208e9i	−1.26071	−	2.18361i
$932$	4.81740e8	−	2.78133e8i	0.595066	−	0.343561i
$933$		0			0
$934$	−2.03672e8	+	3.52770e8i	−0.249972	+	0.432964i
$935$			1.00359e8i			0.122778i
$936$		0			0
$937$	5.16722e8			0.628114			0.314057	−	0.949404i	$-0.398312\pi$
$937$	5.16722e8			0.628114			0.314057	+	0.949404i	$0.398312\pi$
$938$	1.03833e9	+	5.99481e8i	1.25814	+	0.726385i
$939$		0			0
$940$	3.16355e7	+	5.47943e7i	0.0380883	+	0.0659708i
$941$	−7.16202e7	+	4.13499e7i	−0.0859541	+	0.0496256i	−0.542361	−	0.840146i	$-0.682469\pi$
$941$	−7.16202e7	+	4.13499e7i	−0.0859541	+	0.0496256i	0.456407	+	0.889771i	$0.349136\pi$
$942$		0			0
$943$	−8.42360e8	+	1.45901e9i	−1.00453	+	1.73990i
$944$		−	2.98375e8i		−	0.354688i
$945$		0			0
$946$	−6.49409e7			−0.0767087
$947$	4.08951e8	+	2.36108e8i	0.481527	+	0.278010i	0.721053	−	0.692880i	$-0.243659\pi$
$947$	4.08951e8	+	2.36108e8i	0.481527	+	0.278010i	−0.239525	+	0.970890i	$0.576992\pi$
$948$		0			0
$949$	1.15626e9	+	2.00269e9i	1.35287	+	2.34324i
$950$	6.90428e8	−	3.98619e8i	0.805281	−	0.464929i
$951$		0			0
$952$	1.35150e8	−	2.34087e8i	0.156641	−	0.271310i
$953$			9.55129e8i			1.10353i	0.834000	+	0.551764i	$0.186045\pi$
$953$			9.55129e8i			1.10353i	−0.834000	+	0.551764i	$0.813955\pi$
$954$		0			0
$955$	2.51360e8			0.288593
$956$	−3.51431e8	−	2.02899e8i	−0.402223	−	0.232223i
$957$		0			0
$958$	1.20404e8	+	2.08545e8i	0.136944	+	0.237194i
$959$	1.03195e9	−	5.95798e8i	1.17005	−	0.675528i
$960$		0			0
$961$	3.18441e8	−	5.51556e8i	0.358805	−	0.621469i
$962$		−	5.67874e8i		−	0.637862i
$963$		0			0
$964$	−3.19672e8			−0.356840
$965$	−2.41770e7	−	1.39586e7i	−0.0269042	−	0.0155332i
$966$		0			0
$967$	−4.56862e7	−	7.91307e7i	−0.0505249	−	0.0875116i	0.839657	−	0.543117i	$-0.182756\pi$
$967$	−4.56862e7	−	7.91307e7i	−0.0505249	−	0.0875116i	−0.890182	+	0.455606i	$0.849423\pi$
$968$	2.70111e8	−	1.55949e8i	0.297794	−	0.171932i
$969$		0			0
$970$	−6.03973e8	+	1.04611e9i	−0.661763	+	1.14621i
$971$		−	1.09426e8i		−	0.119526i	−0.998213	−	0.0597630i	$-0.980966\pi$
$971$		−	1.09426e8i		−	0.119526i	0.998213	−	0.0597630i	$-0.0190345\pi$
$972$		0			0
$973$	−1.67465e9			−1.81796
$974$	4.65529e8	+	2.68773e8i	0.503813	+	0.290877i
$975$		0			0
$976$	1.44496e8	+	2.50274e8i	0.155419	+	0.269194i
$977$	−5.11653e8	+	2.95403e8i	−0.548645	+	0.316760i	−0.748575	−	0.663050i	$-0.769262\pi$
$977$	−5.11653e8	+	2.95403e8i	−0.548645	+	0.316760i	0.199930	+	0.979810i	$0.435928\pi$
$978$		0			0
$979$	1.35872e8	−	2.35337e8i	0.144804	−	0.250808i
$980$			1.07779e9i			1.14513i
$981$		0			0
$982$	7.59072e8			0.801584
$983$	−1.34739e9	−	7.77917e8i	−1.41851	−	0.818978i	−0.422344	−	0.906436i	$-0.638793\pi$
$983$	−1.34739e9	−	7.77917e8i	−1.41851	−	0.818978i	−0.996168	+	0.0874573i	$0.972126\pi$
$984$		0			0
$985$	8.85497e8	+	1.53373e9i	0.926570	+	1.60487i
$986$	1.93992e8	−	1.12001e8i	0.202373	−	0.116840i
$987$		0			0
$988$	6.25165e8	−	1.08282e9i	0.648222	−	1.12275i
$989$		−	7.70320e8i		−	0.796310i
$990$		0			0
$991$	1.71185e9			1.75891			0.879456	−	0.475979i	$-0.157906\pi$
$991$	1.71185e9			1.75891			0.879456	+	0.475979i	$0.157906\pi$
$992$	7.94172e7	+	4.58515e7i	0.0813541	+	0.0469698i
$993$		0			0
$994$	8.26912e8	+	1.43225e9i	0.841977	+	1.45835i
$995$	1.03213e9	−	5.95901e8i	1.04777	−	0.604930i
$996$		0			0
$997$	3.57012e8	−	6.18363e8i	0.360244	−	0.623961i	−0.627757	−	0.778410i	$-0.716027\pi$
$997$	3.57012e8	−	6.18363e8i	0.360244	−	0.623961i	0.988001	+	0.154448i	$0.0493600\pi$
$998$		−	1.73225e7i		−	0.0174268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.g.107.5		16
3.2	odd	2	inner	162.7.d.g.107.4		16
9.2	odd	6		162.7.b.b.161.8	yes	8
9.4	even	3	inner	162.7.d.g.53.4		16
9.5	odd	6	inner	162.7.d.g.53.5		16
9.7	even	3		162.7.b.b.161.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.b.161.1	✓	8	9.7	even	3
162.7.b.b.161.8	yes	8	9.2	odd	6
162.7.d.g.53.4		16	9.4	even	3	inner
162.7.d.g.53.5		16	9.5	odd	6	inner
162.7.d.g.107.4		16	3.2	odd	2	inner
162.7.d.g.107.5		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-148.146 + 85.5319i) q^{5} +(-280.419 + 485.701i) q^{7} +181.019i q^{8} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-148.146 + 85.5319i) q^{5} +(-280.419 + 485.701i) q^{7} +181.019i q^{8} -967.683 q^{10} +(-190.829 - 110.175i) q^{11} +(-1890.50 - 3274.44i) q^{13} +(-2747.54 + 1586.29i) q^{14} +(-512.000 + 886.810i) q^{16} +2662.46i q^{17} +10334.0 q^{19} +(-4740.66 - 2737.02i) q^{20} +(-623.246 - 1079.49i) q^{22} +(12804.8 - 7392.86i) q^{23} +(6818.90 - 11810.7i) q^{25} -21388.5i q^{26} -17946.8 q^{28} +(-12880.3 - 7436.43i) q^{29} +(-7915.51 - 13710.1i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-7530.58 + 13043.4i) q^{34} -95939.2i q^{35} +26550.4 q^{37} +(50626.0 + 29229.0i) q^{38} +(-15482.9 - 26817.2i) q^{40} +(-98677.0 + 56971.2i) q^{41} +(26049.5 - 45119.0i) q^{43} -7051.22i q^{44} +83640.6 q^{46} +(-10009.8 - 5779.19i) q^{47} +(-98445.5 - 170513. i) q^{49} +(66811.3 - 38573.5i) q^{50} +(60495.9 - 104782. i) q^{52} +137651. i q^{53} +37694.0 q^{55} +(-87921.2 - 50761.3i) q^{56} +(-42066.8 - 72861.8i) q^{58} +(-252344. + 145691. i) q^{59} +(141109. - 244408. i) q^{61} -89553.8i q^{62} -32768.0 q^{64} +(560138. + 323396. i) q^{65} +(-188957. - 327283. i) q^{67} +(-73784.4 + 42599.4i) q^{68} +(271357. - 470004. i) q^{70} -521287. i q^{71} -611614. q^{73} +(130070. + 75095.8i) q^{74} +(165344. + 286384. i) q^{76} +(107024. - 61790.6i) q^{77} +(87787.4 - 152052. i) q^{79} -175169. i q^{80} -644556. q^{82} +(314364. + 181498. i) q^{83} +(-227725. - 394432. i) q^{85} +(255232. - 147358. i) q^{86} +(19943.9 - 34543.8i) q^{88} +1.23323e6i q^{89} +2.12053e6 q^{91} +(409754. + 236571. i) q^{92} +(-32692.0 - 56624.3i) q^{94} +(-1.53094e6 + 883886. i) q^{95} +(624144. - 1.08105e6i) q^{97} -1.11378e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 256 q^{4} - 964 q^{7}+O(q^{10}) \) 16 * q + 256 * q^4 - 964 * q^7	\( 16 q + 256 q^{4} - 964 q^{7} - 1536 q^{10} - 4540 q^{13} - 8192 q^{16} - 47368 q^{19} - 27072 q^{22} + 32392 q^{25} - 61696 q^{28} - 77056 q^{31} + 52608 q^{34} - 22696 q^{37} - 24576 q^{40} + 226604 q^{43} - 325440 q^{46} - 1298088 q^{49} + 145280 q^{52} - 2921832 q^{55} - 867456 q^{58} + 327476 q^{61} - 524288 q^{64} - 1713292 q^{67} + 176352 q^{70} - 4378432 q^{73} - 757888 q^{76} + 1326884 q^{79} - 2317632 q^{82} - 3483180 q^{85} + 866304 q^{88} + 2260648 q^{91} + 26400 q^{94} + 2200064 q^{97}+O(q^{100}) \) 16 * q + 256 * q^4 - 964 * q^7 - 1536 * q^10 - 4540 * q^13 - 8192 * q^16 - 47368 * q^19 - 27072 * q^22 + 32392 * q^25 - 61696 * q^28 - 77056 * q^31 + 52608 * q^34 - 22696 * q^37 - 24576 * q^40 + 226604 * q^43 - 325440 * q^46 - 1298088 * q^49 + 145280 * q^52 - 2921832 * q^55 - 867456 * q^58 + 327476 * q^61 - 524288 * q^64 - 1713292 * q^67 + 176352 * q^70 - 4378432 * q^73 - 757888 * q^76 + 1326884 * q^79 - 2317632 * q^82 - 3483180 * q^85 + 866304 * q^88 + 2260648 * q^91 + 26400 * q^94 + 2200064 * q^97

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