LMFDB - Embedded newform 162.7.d.g.53.6

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			53.6
Root			$-13.5806 + 14.2877i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.7.d.g.107.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-117.830 - 68.0293i) q^{5} +(93.5265 + 161.993i) q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-117.830 - 68.0293i) q^{5} +(93.5265 + 161.993i) q^{7} -181.019i q^{8} -769.663 q^{10} +(1594.47 - 920.566i) q^{11} +(290.764 - 503.618i) q^{13} +(916.369 + 529.066i) q^{14} +(-512.000 - 886.810i) q^{16} -1756.70i q^{17} -7719.53 q^{19} +(-3770.56 + 2176.94i) q^{20} +(5207.51 - 9019.66i) q^{22} +(-12733.9 - 7351.95i) q^{23} +(1443.46 + 2500.14i) q^{25} -3289.62i q^{26} +5985.70 q^{28} +(-27624.7 + 15949.1i) q^{29} +(-17013.4 + 29468.1i) q^{31} +(-5016.55 - 2896.31i) q^{32} +(-4968.71 - 8606.05i) q^{34} -25450.2i q^{35} -77087.6 q^{37} +(-37817.8 + 21834.1i) q^{38} +(-12314.6 + 21329.5i) q^{40} +(9833.91 + 5677.61i) q^{41} +(25148.9 + 43559.1i) q^{43} -58916.2i q^{44} -83177.8 q^{46} +(-22409.7 + 12938.2i) q^{47} +(41330.1 - 71585.8i) q^{49} +(14143.0 + 8165.44i) q^{50} +(-9304.44 - 16115.8i) q^{52} -195102. i q^{53} -250502. q^{55} +(29323.8 - 16930.1i) q^{56} +(-90221.9 + 156269. i) q^{58} +(331853. + 191596. i) q^{59} +(-223218. - 386625. i) q^{61} +192485. i q^{62} -32768.0 q^{64} +(-68521.5 + 39560.9i) q^{65} +(-232362. + 402462. i) q^{67} +(-48683.2 - 28107.3i) q^{68} +(-71983.9 - 124680. i) q^{70} -248916. i q^{71} -545587. q^{73} +(-377651. + 218037. i) q^{74} +(-123513. + 213930. i) q^{76} +(298250. + 172195. i) q^{77} +(-55131.4 - 95490.5i) q^{79} +139324. i q^{80} +64234.8 q^{82} +(41039.3 - 23694.1i) q^{83} +(-119507. + 206993. i) q^{85} +(246408. + 142263. i) q^{86} +(-166640. - 288629. i) q^{88} -37879.5i q^{89} +108776. q^{91} +(-407486. + 235262. i) q^{92} +(-73189.6 + 126768. i) q^{94} +(909594. + 525154. i) q^{95} +(448580. + 776964. i) q^{97} -467596. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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
$5$	−117.830	−	68.0293i	−0.942641	−	0.544234i	−0.0518538	−	0.998655i	$-0.516513\pi$
$5$	−117.830	−	68.0293i	−0.942641	−	0.544234i	−0.890787	+	0.454421i	$0.849846\pi$
$6$		0			0
$7$	93.5265	+	161.993i	0.272672	+	0.472282i	0.969545	−	0.244913i	$-0.0787593\pi$
$7$	93.5265	+	161.993i	0.272672	+	0.472282i	−0.696873	+	0.717194i	$0.745426\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$	−769.663			−0.769663
$11$	1594.47	−	920.566i	1.19795	−	0.691635i	0.237849	−	0.971302i	$-0.423558\pi$
$11$	1594.47	−	920.566i	1.19795	−	0.691635i	0.960097	+	0.279668i	$0.0902242\pi$
$12$		0			0
$13$	290.764	−	503.618i	0.132346	−	0.229230i	−0.792235	−	0.610217i	$-0.791082\pi$
$13$	290.764	−	503.618i	0.132346	−	0.229230i	0.924580	+	0.380987i	$0.124416\pi$
$14$	916.369	+	529.066i	0.333954	+	0.192808i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$		−	1756.70i		−	0.357562i	−0.983889	−	0.178781i	$-0.942785\pi$
$17$		−	1756.70i		−	0.357562i	0.983889	−	0.178781i	$-0.0572154\pi$
$18$		0			0
$19$	−7719.53			−1.12546			−0.562730	−	0.826641i	$-0.690249\pi$
$19$	−7719.53			−1.12546			−0.562730	+	0.826641i	$0.690249\pi$
$20$	−3770.56	+	2176.94i	−0.471321	+	0.272117i
$21$		0			0
$22$	5207.51	−	9019.66i	0.489059	−	0.847076i
$23$	−12733.9	−	7351.95i	−1.04660	−	0.604253i	−0.124902	−	0.992169i	$-0.539862\pi$
$23$	−12733.9	−	7351.95i	−1.04660	−	0.604253i	−0.921695	+	0.387916i	$0.873195\pi$
$24$		0			0
$25$	1443.46	+	2500.14i	0.0923814	+	0.160009i
$26$		−	3289.62i		−	0.187165i
$27$		0			0
$28$	5985.70			0.272672
$29$	−27624.7	+	15949.1i	−1.13267	+	0.653948i	−0.944605	−	0.328209i	$-0.893555\pi$
$29$	−27624.7	+	15949.1i	−1.13267	+	0.653948i	−0.188065	+	0.982156i	$0.560222\pi$
$30$		0			0
$31$	−17013.4	+	29468.1i	−0.571092	+	0.989160i	0.425362	+	0.905023i	$0.360147\pi$
$31$	−17013.4	+	29468.1i	−0.571092	+	0.989160i	−0.996454	+	0.0841371i	$0.973187\pi$
$32$	−5016.55	−	2896.31i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−4968.71	−	8606.05i	−0.126417	−	0.218961i
$35$		−	25450.2i		−	0.593590i
$36$		0			0
$37$	−77087.6			−1.52188			−0.760939	−	0.648824i	$-0.775261\pi$
$37$	−77087.6			−1.52188			−0.760939	+	0.648824i	$0.775261\pi$
$38$	−37817.8	+	21834.1i	−0.689201	+	0.397910i
$39$		0			0
$40$	−12314.6	+	21329.5i	−0.192416	+	0.333274i
$41$	9833.91	+	5677.61i	0.142684	+	0.0823785i	0.569642	−	0.821893i	$-0.307082\pi$
$41$	9833.91	+	5677.61i	0.142684	+	0.0823785i	−0.426959	+	0.904271i	$0.640415\pi$
$42$		0			0
$43$	25148.9	+	43559.1i	0.316310	+	0.547865i	0.979715	−	0.200395i	$-0.0642227\pi$
$43$	25148.9	+	43559.1i	0.316310	+	0.547865i	−0.663405	+	0.748260i	$0.730889\pi$
$44$		−	58916.2i		−	0.691635i
$45$		0			0
$46$	−83177.8			−0.854543
$47$	−22409.7	+	12938.2i	−0.215845	+	0.124618i	−0.604025	−	0.796966i	$-0.706437\pi$
$47$	−22409.7	+	12938.2i	−0.215845	+	0.124618i	0.388180	+	0.921584i	$0.373104\pi$
$48$		0			0
$49$	41330.1	−	71585.8i	0.351300	−	0.608469i
$50$	14143.0	+	8165.44i	0.113144	+	0.0653235i
$51$		0			0
$52$	−9304.44	−	16115.8i	−0.0661729	−	0.114615i
$53$		−	195102.i		−	1.31049i	−0.755416	−	0.655246i	$-0.772565\pi$
$53$		−	195102.i		−	1.31049i	0.755416	−	0.655246i	$-0.227435\pi$
$54$		0			0
$55$	−250502.			−1.50564
$56$	29323.8	−	16930.1i	0.166977	−	0.0964041i
$57$		0			0
$58$	−90221.9	+	156269.i	−0.462411	+	0.800919i
$59$	331853.	+	191596.i	1.61581	+	0.932888i	0.987988	+	0.154530i	$0.0493864\pi$
$59$	331853.	+	191596.i	1.61581	+	0.932888i	0.627821	+	0.778358i	$0.283947\pi$
$60$		0			0
$61$	−223218.	−	386625.i	−0.983421	−	1.70333i	−0.648753	−	0.760999i	$-0.724709\pi$
$61$	−223218.	−	386625.i	−0.983421	−	1.70333i	−0.334667	−	0.942336i	$-0.608624\pi$
$62$			192485.i			0.807646i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	−68521.5	+	39560.9i	−0.249509	+	0.144054i
$66$		0			0
$67$	−232362.	+	402462.i	−0.772574	+	1.33814i	0.163574	+	0.986531i	$0.447698\pi$
$67$	−232362.	+	402462.i	−0.772574	+	1.33814i	−0.936148	+	0.351606i	$0.885636\pi$
$68$	−48683.2	−	28107.3i	−0.154829	−	0.0893906i
$69$		0			0
$70$	−71983.9	−	124680.i	−0.209866	−	0.363498i
$71$		−	248916.i		−	0.695469i	−0.937593	−	0.347734i	$-0.886951\pi$
$71$		−	248916.i		−	0.695469i	0.937593	−	0.347734i	$-0.113049\pi$
$72$		0			0
$73$	−545587.			−1.40248			−0.701238	−	0.712928i	$-0.747369\pi$
$73$	−545587.			−1.40248			−0.701238	+	0.712928i	$0.747369\pi$
$74$	−377651.	+	218037.i	−0.931956	+	0.538065i
$75$		0			0
$76$	−123513.	+	213930.i	−0.281365	+	0.487339i
$77$	298250.	+	172195.i	0.653293	+	0.377179i
$78$		0			0
$79$	−55131.4	−	95490.5i	−0.111820	−	0.193677i	0.804684	−	0.593703i	$-0.202335\pi$
$79$	−55131.4	−	95490.5i	−0.111820	−	0.193677i	−0.916504	+	0.400026i	$0.869001\pi$
$80$			139324.i			0.272117i
$81$		0			0
$82$	64234.8			0.116501
$83$	41039.3	−	23694.1i	0.0717738	−	0.0414386i	−0.463684	−	0.886001i	$-0.653473\pi$
$83$	41039.3	−	23694.1i	0.0717738	−	0.0414386i	0.535457	+	0.844562i	$0.320139\pi$
$84$		0			0
$85$	−119507.	+	206993.i	−0.194598	+	0.337053i
$86$	246408.	+	142263.i	0.387399	+	0.223665i
$87$		0			0
$88$	−166640.	−	288629.i	−0.244530	−	0.423538i
$89$		−	37879.5i		−	0.0537321i	−0.999639	−	0.0268661i	$-0.991447\pi$
$89$		−	37879.5i		−	0.0537321i	0.999639	−	0.0268661i	$-0.00855276\pi$
$90$		0			0
$91$	108776.			0.144348
$92$	−407486.	+	235262.i	−0.523298	+	0.302126i
$93$		0			0
$94$	−73189.6	+	126768.i	−0.0881183	+	0.152625i
$95$	909594.	+	525154.i	1.06091	+	0.612514i
$96$		0			0
$97$	448580.	+	776964.i	0.491502	+	0.851306i	0.999952	−	0.00978529i	$-0.00311481\pi$
$97$	448580.	+	776964.i	0.491502	+	0.851306i	−0.508450	+	0.861091i	$0.669781\pi$
$98$		−	467596.i		−	0.496813i
$99$		0			0
$100$	92381.4			0.0923814
$101$	1.47984e6	−	854386.i	1.43632	−	0.829259i	0.438727	−	0.898621i	$-0.355430\pi$
$101$	1.47984e6	−	854386.i	1.43632	−	0.829259i	0.997592	+	0.0693619i	$0.0220963\pi$
$102$		0			0
$103$	278688.	−	482702.i	0.255039	−	0.441740i	−0.709867	−	0.704336i	$-0.751245\pi$
$103$	278688.	−	482702.i	0.255039	−	0.441740i	0.964906	+	0.262595i	$0.0845784\pi$
$104$	−91164.5	−	52633.9i	−0.0810449	−	0.0467913i
$105$		0			0
$106$	−551832.	−	955801.i	−0.463329	−	0.802509i
$107$		−	1.53518e6i		−	1.25316i	−0.779356	−	0.626581i	$-0.784454\pi$
$107$		−	1.53518e6i		−	1.25316i	0.779356	−	0.626581i	$-0.215546\pi$
$108$		0			0
$109$	−2.28491e6			−1.76437			−0.882186	−	0.470901i	$-0.843929\pi$
$109$	−2.28491e6			−1.76437			−0.882186	+	0.470901i	$0.843929\pi$
$110$	−1.22720e6	+	708525.i	−0.922015	+	0.532326i
$111$		0			0
$112$	95771.2	−	165881.i	0.0681680	−	0.118070i
$113$	−1.47659e6	−	852507.i	−1.02335	−	0.590830i	−0.108276	−	0.994121i	$-0.534533\pi$
$113$	−1.47659e6	−	852507.i	−1.02335	−	0.590830i	−0.915072	+	0.403291i	$0.867866\pi$
$114$		0			0
$115$	1.00029e6	+	1.73256e6i	0.657710	+	1.13919i
$116$			1.02074e6i			0.653948i
$117$		0			0
$118$	2.16766e6			1.31930
$119$	284573.	−	164298.i	0.168870	−	0.0974972i
$120$		0			0
$121$	809101.	−	1.40140e6i	0.456717	−	0.791056i
$122$	−2.18708e6	−	1.26271e6i	−1.20444	−	0.695384i
$123$		0			0
$124$	544429.	+	942978.i	0.285546	+	0.494580i
$125$			1.73312e6i			0.887360i
$126$		0			0
$127$	1.75851e6			0.858489			0.429244	−	0.903188i	$-0.358780\pi$
$127$	1.75851e6			0.858489			0.429244	+	0.903188i	$0.358780\pi$
$128$	−160530.	+	92681.9i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−223790.	+	387616.i	−0.101862	+	0.176430i
$131$	−1.22794e6	−	708949.i	−0.546213	−	0.315356i	0.201380	−	0.979513i	$-0.435457\pi$
$131$	−1.22794e6	−	708949.i	−0.546213	−	0.315356i	−0.747593	+	0.664157i	$0.768791\pi$
$132$		0			0
$133$	−721981.	−	1.25051e6i	−0.306882	−	0.531535i
$134$			2.62887e6i			1.09258i
$135$		0			0
$136$	−317997.			−0.126417
$137$	1.28048e6	−	739284.i	0.497978	−	0.287508i	−0.229900	−	0.973214i	$-0.573840\pi$
$137$	1.28048e6	−	739284.i	0.497978	−	0.287508i	0.727878	+	0.685706i	$0.240507\pi$
$138$		0			0
$139$	1.64557e6	−	2.85022e6i	0.612735	−	1.06129i	−0.378042	−	0.925788i	$-0.623403\pi$
$139$	1.64557e6	−	2.85022e6i	0.612735	−	1.06129i	0.990777	−	0.135500i	$-0.0432641\pi$
$140$	−705295.	−	407203.i	−0.257032	−	0.148397i
$141$		0			0
$142$	−704041.	−	1.21943e6i	−0.245885	−	0.425886i
$143$		−	1.07067e6i		−	0.366140i
$144$		0			0
$145$	4.34003e6			1.42360
$146$	−2.67282e6	+	1.54315e6i	−0.858837	+	0.495850i
$147$		0			0
$148$	−1.23340e6	+	2.13632e6i	−0.380469	+	0.658992i
$149$	−139618.	−	80608.4i	−0.0422068	−	0.0243681i	0.478748	−	0.877952i	$-0.341091\pi$
$149$	−139618.	−	80608.4i	−0.0422068	−	0.0243681i	−0.520955	+	0.853584i	$0.674424\pi$
$150$		0			0
$151$	2.22056e6	+	3.84612e6i	0.644957	+	1.11710i	0.984311	+	0.176440i	$0.0564583\pi$
$151$	2.22056e6	+	3.84612e6i	0.644957	+	1.11710i	−0.339354	+	0.940659i	$0.610208\pi$
$152$			1.39738e6i			0.397910i
$153$		0			0
$154$	1.94816e6			0.533411
$155$	4.00938e6	−	2.31482e6i	1.07667	−	0.621615i
$156$		0			0
$157$	2.99149e6	−	5.18141e6i	0.773016	−	1.33890i	−0.162888	−	0.986645i	$-0.552081\pi$
$157$	2.99149e6	−	5.18141e6i	0.773016	−	1.33890i	0.935903	−	0.352258i	$-0.114586\pi$
$158$	−540176.	−	311871.i	−0.136951	−	0.0790684i
$159$		0			0
$160$	394068.	+	682545.i	0.0962079	+	0.166637i
$161$		−	2.75041e6i		−	0.659052i
$162$		0			0
$163$	1.87134e6			0.432105			0.216052	−	0.976382i	$-0.430682\pi$
$163$	1.87134e6			0.432105			0.216052	+	0.976382i	$0.430682\pi$
$164$	314685.	−	181684.i	0.0713419	−	0.0411893i
$165$		0			0
$166$	134034.	−	232153.i	0.0293015	−	0.0507517i
$167$	79864.4	+	46109.7i	0.0171476	+	0.00990019i	0.508549	−	0.861033i	$-0.330182\pi$
$167$	79864.4	+	46109.7i	0.0171476	+	0.00990019i	−0.491402	+	0.870933i	$0.663515\pi$
$168$		0			0
$169$	2.24432e6	+	3.88727e6i	0.464969	+	0.805350i
$170$			1.35207e6i			0.275202i
$171$		0			0
$172$	1.60953e6			0.316310
$173$	6.52524e6	−	3.76735e6i	1.26026	−	0.727609i	0.287131	−	0.957891i	$-0.407298\pi$
$173$	6.52524e6	−	3.76735e6i	1.26026	−	0.727609i	0.973124	+	0.230283i	$0.0739651\pi$
$174$		0			0
$175$	−270003.	+	467660.i	−0.0503796	+	0.0872601i
$176$	−1.63273e6	−	942659.i	−0.299487	−	0.172909i
$177$		0			0
$178$	−107139.	−	185571.i	−0.0189972	−	0.0329041i
$179$			4.33502e6i			0.755844i	0.925838	+	0.377922i	$0.123361\pi$
$179$			4.33502e6i			0.755844i	−0.925838	+	0.377922i	$0.876639\pi$
$180$		0			0
$181$	3.65501e6			0.616387			0.308193	−	0.951324i	$-0.400276\pi$
$181$	3.65501e6			0.616387			0.308193	+	0.951324i	$0.400276\pi$
$182$	532894.	−	307666.i	0.0883948	−	0.0510347i
$183$		0			0
$184$	−1.33084e6	+	2.30509e6i	−0.213636	+	0.370028i
$185$	9.08325e6	+	5.24421e6i	1.43458	+	0.828257i
$186$		0			0
$187$	−1.61716e6	−	2.80100e6i	−0.247302	−	0.428340i
$188$			828046.i			0.124618i
$189$		0			0
$190$	5.94144e6			0.866225
$191$	3.13643e6	−	1.81082e6i	0.450128	−	0.259881i	−0.257756	−	0.966210i	$-0.582983\pi$
$191$	3.13643e6	−	1.81082e6i	0.450128	−	0.259881i	0.707884	+	0.706328i	$0.249650\pi$
$192$		0			0
$193$	−3.25471e6	+	5.63733e6i	−0.452731	+	0.784154i	−0.998555	−	0.0537465i	$-0.982884\pi$
$193$	−3.25471e6	+	5.63733e6i	−0.452731	+	0.784154i	0.545823	+	0.837900i	$0.316217\pi$
$194$	4.39517e6	+	2.53755e6i	0.601964	+	0.347544i
$195$		0			0
$196$	−1.32256e6	−	2.29075e6i	−0.175650	−	0.304235i
$197$			6.32938e6i			0.827871i	0.910306	+	0.413935i	$0.135846\pi$
$197$			6.32938e6i			0.827871i	−0.910306	+	0.413935i	$0.864154\pi$
$198$		0			0
$199$	−8.27329e6			−1.04983			−0.524915	−	0.851155i	$-0.675903\pi$
$199$	−8.27329e6			−1.04983			−0.524915	+	0.851155i	$0.675903\pi$
$200$	452574.	−	261294.i	0.0565718	−	0.0326617i
$201$		0			0
$202$	4.83314e6	−	8.37124e6i	0.586374	−	1.01563i
$203$	−5.16729e6	−	2.98333e6i	−0.617695	−	0.356627i
$204$		0			0
$205$	−772487.	−	1.33799e6i	−0.0896664	−	0.155307i
$206$		−	3.15299e6i		−	0.360679i
$207$		0			0
$208$	−595484.			−0.0661729
$209$	−1.23085e7	+	7.10634e6i	−1.34824	+	0.778407i
$210$		0			0
$211$	−4.38392e6	+	7.59317e6i	−0.466676	+	0.808306i	−0.999275	−	0.0380610i	$-0.987882\pi$
$211$	−4.38392e6	+	7.59317e6i	−0.466676	+	0.808306i	0.532599	+	0.846367i	$0.321215\pi$
$212$	−5.40683e6	−	3.12163e6i	−0.567460	−	0.327623i
$213$		0			0
$214$	−4.34214e6	−	7.52081e6i	−0.443060	−	0.767402i
$215$		−	6.84343e6i		−	0.688587i
$216$		0			0
$217$	−6.36482e6			−0.622883
$218$	−1.11937e7	+	6.46271e6i	−1.08045	+	0.623800i
$219$		0			0
$220$	−4.00802e6	+	6.94210e6i	−0.376411	+	0.651963i
$221$	−884707.	−	510786.i	−0.0819639	−	0.0473219i
$222$		0			0
$223$	−6.10907e6	−	1.05812e7i	−0.550885	−	0.954160i	−0.998211	−	0.0597895i	$-0.980957\pi$
$223$	−6.10907e6	−	1.05812e7i	−0.550885	−	0.954160i	0.447326	−	0.894371i	$-0.352376\pi$
$224$		−	1.08353e6i		−	0.0964041i
$225$		0			0
$226$	−9.64502e6			−0.835560
$227$	1.94621e6	−	1.12364e6i	0.166384	−	0.0960618i	−0.414496	−	0.910051i	$-0.636042\pi$
$227$	1.94621e6	−	1.12364e6i	0.166384	−	0.0960618i	0.580880	+	0.813989i	$0.302709\pi$
$228$		0			0
$229$	2.60330e6	−	4.50905e6i	0.216779	−	0.375473i	−0.737042	−	0.675847i	$-0.763778\pi$
$229$	2.60330e6	−	4.50905e6i	0.216779	−	0.375473i	0.953822	+	0.300374i	$0.0971115\pi$
$230$	9.80085e6	+	5.65852e6i	0.805527	+	0.465071i
$231$		0			0
$232$	2.88710e6	+	5.00061e6i	0.231205	+	0.400460i
$233$		−	1.44501e6i		−	0.114236i	−0.998367	−	0.0571179i	$-0.981809\pi$
$233$		−	1.44501e6i		−	0.114236i	0.998367	−	0.0571179i	$-0.0181911\pi$
$234$		0			0
$235$	3.52071e6			0.271286
$236$	1.06193e7	−	6.13106e6i	0.807905	−	0.466444i
$237$		0			0
$238$	929412.	−	1.60979e6i	0.0689410	−	0.119409i
$239$	−3.67560e6	−	2.12211e6i	−0.269237	−	0.155444i	0.359304	−	0.933221i	$-0.383014\pi$
$239$	−3.67560e6	−	2.12211e6i	−0.269237	−	0.155444i	−0.628541	+	0.777777i	$0.716348\pi$
$240$		0			0
$241$	4.31829e6	+	7.47950e6i	0.308504	+	0.534345i	0.978035	−	0.208439i	$-0.0668383\pi$
$241$	4.31829e6	+	7.47950e6i	0.308504	+	0.534345i	−0.669531	+	0.742784i	$0.733505\pi$
$242$		−	9.15394e6i		−	0.645895i
$243$		0			0
$244$	−1.42859e7			−0.983421
$245$	−9.73986e6	+	5.62331e6i	−0.662299	+	0.382379i
$246$		0			0
$247$	−2.24456e6	+	3.88769e6i	−0.148950	+	0.257989i
$248$	5.33429e6	+	3.07975e6i	0.349721	+	0.201911i
$249$		0			0
$250$	4.90202e6	+	8.49054e6i	0.313729	+	0.543395i
$251$		−	1.25318e7i		−	0.792488i	−0.918145	−	0.396244i	$-0.870313\pi$
$251$		−	1.25318e7i		−	0.792488i	0.918145	−	0.396244i	$-0.129687\pi$
$252$		0			0
$253$	−2.70718e7			−1.67169
$254$	8.61492e6	−	4.97383e6i	0.525715	−	0.303522i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	8.47075e6	+	4.89059e6i	0.499025	+	0.288112i	0.728311	−	0.685247i	$-0.240306\pi$
$257$	8.47075e6	+	4.89059e6i	0.499025	+	0.288112i	−0.229286	+	0.973359i	$0.573639\pi$
$258$		0			0
$259$	−7.20974e6	−	1.24876e7i	−0.414973	−	0.718755i
$260$			2.53190e6i			0.144054i
$261$		0			0
$262$	−8.02084e6			−0.445981
$263$	−2.49518e7	+	1.44059e7i	−1.37162	+	0.791907i	−0.991133	−	0.132877i	$-0.957578\pi$
$263$	−2.49518e7	+	1.44059e7i	−1.37162	+	0.791907i	−0.380491	+	0.924784i	$0.624245\pi$
$264$		0			0
$265$	−1.32727e7	+	2.29889e7i	−0.713214	+	1.23532i
$266$	−7.07394e6	−	4.08414e6i	−0.375852	−	0.216998i
$267$		0			0
$268$	7.43557e6	+	1.28788e7i	0.386287	+	0.669069i
$269$		−	2.21154e7i		−	1.13616i	−0.822974	−	0.568079i	$-0.807687\pi$
$269$		−	2.21154e7i		−	1.13616i	0.822974	−	0.568079i	$-0.192313\pi$
$270$		0			0
$271$	−2.22233e7			−1.11661			−0.558303	−	0.829637i	$-0.688547\pi$
$271$	−2.22233e7			−1.11661			−0.558303	+	0.829637i	$0.688547\pi$
$272$	−1.55786e6	+	899432.i	−0.0774145	+	0.0446953i
$273$		0			0
$274$	4.18202e6	−	7.24348e6i	0.203299	−	0.352124i
$275$	4.60309e6	+	2.65760e6i	0.221336	+	0.127788i
$276$		0			0
$277$	6.46408e6	+	1.11961e7i	0.304136	+	0.526778i	0.977068	−	0.212925i	$-0.0682991\pi$
$277$	6.46408e6	+	1.11961e7i	0.304136	+	0.526778i	−0.672933	+	0.739704i	$0.734966\pi$
$278$		−	1.86175e7i		−	0.866538i
$279$		0			0
$280$	−4.60697e6			−0.209866
$281$	−2.53279e7	+	1.46231e7i	−1.14151	+	0.659053i	−0.946805	−	0.321809i	$-0.895709\pi$
$281$	−2.53279e7	+	1.46231e7i	−1.14151	+	0.659053i	−0.194708	+	0.980861i	$0.562376\pi$
$282$		0			0
$283$	1.19308e7	−	2.06647e7i	0.526392	−	0.911738i	−0.473135	−	0.880990i	$-0.656878\pi$
$283$	1.19308e7	−	2.06647e7i	0.526392	−	0.911738i	0.999527	−	0.0307479i	$-0.00978891\pi$
$284$	−6.89816e6	−	3.98266e6i	−0.301147	−	0.173867i
$285$		0			0
$286$	−3.02831e6	−	5.24518e6i	−0.129450	−	0.224214i
$287$			2.12403e6i			0.0898493i
$288$		0			0
$289$	2.10516e7			0.872149
$290$	2.12617e7	−	1.22755e7i	0.871775	−	0.503319i
$291$		0			0
$292$	−8.72939e6	+	1.51197e7i	−0.350619	+	0.607290i
$293$	−1.34014e7	−	7.73732e6i	−0.532780	−	0.307601i	0.209368	−	0.977837i	$-0.432859\pi$
$293$	−1.34014e7	−	7.73732e6i	−0.532780	−	0.307601i	−0.742148	+	0.670236i	$0.766193\pi$
$294$		0			0
$295$	−2.60682e7	−	4.51515e7i	−1.01542	−	1.75876i
$296$			1.39544e7i			0.538065i
$297$		0			0
$298$	−911980.			−0.0344617
$299$	−7.40514e6	+	4.27536e6i	−0.277025	+	0.159941i
$300$		0			0
$301$	−4.70417e6	+	8.14786e6i	−0.172498	+	0.298775i
$302$	2.17569e7	+	1.25614e7i	0.789908	+	0.456054i
$303$		0			0
$304$	3.95240e6	+	6.84576e6i	0.140683	+	0.243669i
$305$			6.07414e7i			2.14084i
$306$		0			0
$307$	4.16301e7			1.43877			0.719386	−	0.694610i	$-0.244423\pi$
$307$	4.16301e7			1.43877			0.719386	+	0.694610i	$0.244423\pi$
$308$	9.54399e6	−	5.51023e6i	0.326646	−	0.188589i
$309$		0			0
$310$	1.30946e7	−	2.26805e7i	0.439548	−	0.761320i
$311$	1.62082e6	+	935779.i	0.0538831	+	0.0311094i	0.526700	−	0.850052i	$-0.323429\pi$
$311$	1.62082e6	+	935779.i	0.0538831	+	0.0311094i	−0.472816	+	0.881161i	$0.656763\pi$
$312$		0			0
$313$	−2.38943e6	−	4.13861e6i	−0.0779222	−	0.134965i	0.824431	−	0.565962i	$-0.191495\pi$
$313$	−2.38943e6	−	4.13861e6i	−0.0779222	−	0.134965i	−0.902353	+	0.430997i	$0.858162\pi$
$314$		−	3.38448e7i		−	1.09321i
$315$		0			0
$316$	−3.52841e6			−0.111820
$317$	−1.02526e7	+	5.91932e6i	−0.321851	+	0.185821i	−0.652217	−	0.758032i	$-0.726161\pi$
$317$	−1.02526e7	+	5.91932e6i	−0.321851	+	0.185821i	0.330366	+	0.943853i	$0.392828\pi$
$318$		0			0
$319$	−2.93644e7	+	5.08607e7i	−0.904586	+	1.56679i
$320$	3.86106e6	+	2.22918e6i	0.117830	+	0.0680293i
$321$		0			0
$322$	−7.77933e6	−	1.34742e7i	−0.233010	−	0.403585i
$323$			1.35609e7i			0.402422i
$324$		0			0
$325$	1.67882e6			0.0489052
$326$	9.16764e6	−	5.29294e6i	0.264609	−	0.152772i
$327$		0			0
$328$	1.02776e6	−	1.78013e6i	0.0291252	−	0.0504463i
$329$	−4.19180e6	−	2.42013e6i	−0.117710	−	0.0679597i
$330$		0			0
$331$	1.25355e7	+	2.17121e7i	0.345667	+	0.598713i	0.985475	−	0.169822i	$-0.0543193\pi$
$331$	1.25355e7	+	2.17121e7i	0.345667	+	0.598713i	−0.639808	+	0.768535i	$0.720986\pi$
$332$		−	1.51642e6i		−	0.0414386i
$333$		0			0
$334$	521672.			0.0140010
$335$	5.47584e7	−	3.16148e7i	1.45652	−	0.840922i
$336$		0			0
$337$	2.67588e7	−	4.63476e7i	0.699160	−	1.21098i	−0.269598	−	0.962973i	$-0.586891\pi$
$337$	2.67588e7	−	4.63476e7i	0.699160	−	1.21098i	0.968758	−	0.248008i	$-0.0797760\pi$
$338$	2.19897e7	+	1.26958e7i	0.569469	+	0.328783i
$339$		0			0
$340$	3.82423e6	+	6.62376e6i	0.0972988	+	0.168526i
$341$			6.26478e7i			1.57995i
$342$		0			0
$343$	3.74684e7			0.928503
$344$	7.88504e6	−	4.55243e6i	0.193700	−	0.111832i
$345$		0			0
$346$	2.13114e7	−	3.69124e7i	0.514497	−	0.891135i
$347$	−5.49315e7	−	3.17147e7i	−1.31472	−	0.759053i	−0.331845	−	0.943334i	$-0.607671\pi$
$347$	−5.49315e7	−	3.17147e7i	−1.31472	−	0.759053i	−0.982874	+	0.184281i	$0.941004\pi$
$348$		0			0
$349$	2.43032e6	+	4.20944e6i	0.0571725	+	0.0990257i	0.893195	−	0.449669i	$-0.148458\pi$
$349$	2.43032e6	+	4.20944e6i	0.0571725	+	0.0990257i	−0.836023	+	0.548695i	$0.815125\pi$
$350$			3.05474e6i			0.0712476i
$351$		0			0
$352$	−1.06650e7			−0.244530
$353$	8.47117e6	−	4.89083e6i	0.192584	−	0.111188i	−0.400608	−	0.916250i	$-0.631201\pi$
$353$	8.47117e6	−	4.89083e6i	0.192584	−	0.111188i	0.593191	+	0.805061i	$0.297868\pi$
$354$		0			0
$355$	−1.69336e7	+	2.93298e7i	−0.378498	+	0.655577i
$356$	−1.04975e6	−	606072.i	−0.0232667	−	0.0134330i
$357$		0			0
$358$	1.22613e7	+	2.12372e7i	0.267231	+	0.462858i
$359$		−	5.87733e7i		−	1.27027i	−0.772400	−	0.635136i	$-0.780944\pi$
$359$		−	5.87733e7i		−	1.27027i	0.772400	−	0.635136i	$-0.219056\pi$
$360$		0			0
$361$	1.25453e7			0.266661
$362$	1.79058e7	−	1.03379e7i	0.377458	−	0.217926i
$363$		0			0
$364$	1.74042e6	−	3.01450e6i	0.0360870	−	0.0625045i
$365$	6.42865e7	+	3.71159e7i	1.32203	+	0.763275i
$366$		0			0
$367$	2.75133e7	+	4.76545e7i	0.556602	+	0.964063i	0.997777	+	0.0666417i	$0.0212285\pi$
$367$	2.75133e7	+	4.76545e7i	0.556602	+	0.964063i	−0.441175	+	0.897421i	$0.645438\pi$
$368$			1.50568e7i			0.302126i
$369$		0			0
$370$	5.93315e7			1.17133
$371$	3.16051e7	−	1.82472e7i	0.618922	−	0.357335i
$372$		0			0
$373$	2.58036e7	−	4.46932e7i	0.497226	−	0.861221i	−0.502769	−	0.864421i	$-0.667685\pi$
$373$	2.58036e7	−	4.46932e7i	0.497226	−	0.861221i	0.999995	+	0.00319984i	$0.00101854\pi$
$374$	−1.58449e7	−	9.14804e6i	−0.302882	−	0.174869i
$375$		0			0
$376$	2.34207e6	+	4.05658e6i	0.0440591	+	0.0763127i
$377$			1.85497e7i			0.346189i
$378$		0			0
$379$	9.95306e7			1.82826			0.914132	−	0.405416i	$-0.132873\pi$
$379$	9.95306e7			1.82826			0.914132	+	0.405416i	$0.132873\pi$
$380$	2.91070e7	−	1.68049e7i	0.530453	−	0.306257i
$381$		0			0
$382$	1.02435e7	−	1.77423e7i	0.183764	−	0.318288i
$383$	−9.15360e6	−	5.28484e6i	−0.162928	−	0.0940665i	0.416319	−	0.909219i	$-0.363320\pi$
$383$	−9.15360e6	−	5.28484e6i	−0.162928	−	0.0940665i	−0.579247	+	0.815152i	$0.696653\pi$
$384$		0			0
$385$	−2.34285e7	−	4.05794e7i	−0.410547	−	0.711088i
$386$			3.68229e7i			0.640259i
$387$		0			0
$388$	2.87091e7			0.491502
$389$	1.20743e7	−	6.97111e6i	0.205123	−	0.118428i	−0.393920	−	0.919145i	$-0.628881\pi$
$389$	1.20743e7	−	6.97111e6i	0.205123	−	0.118428i	0.599043	+	0.800717i	$0.295548\pi$
$390$		0			0
$391$	−1.29152e7	+	2.23698e7i	−0.216058	+	0.374223i
$392$	−1.29584e7	−	7.48154e6i	−0.215126	−	0.124203i
$393$		0			0
$394$	1.79022e7	+	3.10075e7i	0.292697	+	0.506965i
$395$			1.50022e7i			0.243424i
$396$		0			0
$397$	2.16064e7			0.345312			0.172656	−	0.984982i	$-0.444765\pi$
$397$	2.16064e7			0.345312			0.172656	+	0.984982i	$0.444765\pi$
$398$	−4.05307e7	+	2.34004e7i	−0.642887	+	0.371171i
$399$		0			0
$400$	1.47810e6	−	2.56015e6i	0.0230953	−	0.0400023i
$401$	−8.98952e7	−	5.19010e7i	−1.39413	−	0.804902i	−0.400361	−	0.916357i	$-0.631115\pi$
$401$	−8.98952e7	−	5.19010e7i	−1.39413	−	0.804902i	−0.993769	+	0.111456i	$0.964449\pi$
$402$		0			0
$403$	9.89376e6	+	1.71365e7i	0.151163	+	0.261822i
$404$		−	5.46807e7i		−	0.829259i
$405$		0			0
$406$	−3.37526e7			−0.504346
$407$	−1.22914e8	+	7.09642e7i	−1.82313	+	1.05258i
$408$		0			0
$409$	4.56865e7	−	7.91314e7i	0.667757	−	1.15659i	−0.310773	−	0.950484i	$-0.600588\pi$
$409$	4.56865e7	−	7.91314e7i	0.667757	−	1.15659i	0.978530	−	0.206104i	$-0.0660787\pi$
$410$	−7.56880e6	−	4.36985e6i	−0.109818	−	0.0634037i
$411$		0			0
$412$	−8.91801e6	−	1.54465e7i	−0.127519	−	0.220870i
$413$			7.16771e7i			1.01749i
$414$		0			0
$415$	−6.44756e6			−0.0902092
$416$	−2.91726e6	+	1.68428e6i	−0.0405225	+	0.0233957i
$417$		0			0
$418$	−4.01995e7	+	6.96276e7i	−0.550417	+	0.953350i
$419$	−7.16784e7	−	4.13835e7i	−0.974420	−	0.562582i	−0.0738392	−	0.997270i	$-0.523525\pi$
$419$	−7.16784e7	−	4.13835e7i	−0.974420	−	0.562582i	−0.900581	+	0.434688i	$0.856859\pi$
$420$		0			0
$421$	4.08739e7	+	7.07957e7i	0.547772	+	0.948770i	0.998427	+	0.0560711i	$0.0178573\pi$
$421$	4.08739e7	+	7.07957e7i	0.547772	+	0.948770i	−0.450654	+	0.892698i	$0.648809\pi$
$422$			4.95984e7i			0.659979i
$423$		0			0
$424$	−3.53173e7			−0.463329
$425$	4.39201e6	−	2.53573e6i	0.0572133	−	0.0330321i
$426$		0			0
$427$	4.17536e7	−	7.23193e7i	0.536303	−	0.928904i
$428$	−4.25441e7	−	2.45629e7i	−0.542635	−	0.313291i
$429$		0			0
$430$	−1.93562e7	−	3.35258e7i	−0.243452	−	0.421672i
$431$		−	1.53458e8i		−	1.91672i	−0.285569	−	0.958358i	$-0.592183\pi$
$431$		−	1.53458e8i		−	1.91672i	0.285569	−	0.958358i	$-0.407817\pi$
$432$		0			0
$433$	−1.15843e8			−1.42694			−0.713468	−	0.700688i	$-0.752876\pi$
$433$	−1.15843e8			−1.42694			−0.713468	+	0.700688i	$0.752876\pi$
$434$	−3.11811e7	+	1.80024e7i	−0.381437	+	0.220223i
$435$		0			0
$436$	−3.65586e7	+	6.33214e7i	−0.441093	+	0.763995i
$437$	9.83001e7	+	5.67536e7i	1.17790	+	0.680063i
$438$		0			0
$439$	−2.11334e7	−	3.66042e7i	−0.249791	−	0.432651i	0.713677	−	0.700475i	$-0.247029\pi$
$439$	−2.11334e7	−	3.66042e7i	−0.249791	−	0.432651i	−0.963468	+	0.267825i	$0.913695\pi$
$440$			4.53456e7i			0.532326i
$441$		0			0
$442$	−5.77888e6			−0.0669232
$443$	1.44742e8	−	8.35670e7i	1.66489	−	0.961222i	0.694556	−	0.719439i	$-0.255601\pi$
$443$	1.44742e8	−	8.35670e7i	1.66489	−	0.961222i	0.970330	−	0.241783i	$-0.0777323\pi$
$444$		0			0
$445$	−2.57691e6	+	4.46334e6i	−0.0292428	+	0.0506501i
$446$	−5.98564e7	−	3.45581e7i	−0.674693	−	0.389534i
$447$		0			0
$448$	−3.06468e6	−	5.30818e6i	−0.0340840	−	0.0590352i
$449$			8.56152e7i			0.945827i	0.881109	+	0.472914i	$0.156798\pi$
$449$			8.56152e7i			0.945827i	−0.881109	+	0.472914i	$0.843202\pi$
$450$		0			0
$451$	2.09065e7			0.227903
$452$	−4.72507e7	+	2.72802e7i	−0.511674	+	0.295415i
$453$		0			0
$454$	6.35628e6	−	1.10094e7i	0.0679259	−	0.117651i
$455$	−1.28171e7	−	7.39998e6i	−0.136068	−	0.0785591i
$456$		0			0
$457$	3.32696e6	+	5.76247e6i	0.0348577	+	0.0603754i	0.882928	−	0.469508i	$-0.155569\pi$
$457$	3.32696e6	+	5.76247e6i	0.0348577	+	0.0603754i	−0.848070	+	0.529884i	$0.822236\pi$
$458$		−	2.94530e7i		−	0.306572i
$459$		0			0
$460$	6.40189e7			0.657710
$461$	−2.00718e7	+	1.15885e7i	−0.204873	+	0.118283i	−0.598926	−	0.800804i	$-0.704406\pi$
$461$	−2.00718e7	+	1.15885e7i	−0.204873	+	0.118283i	0.394054	+	0.919087i	$0.371072\pi$
$462$		0			0
$463$	1.88019e6	−	3.25658e6i	0.0189434	−	0.0328109i	−0.856398	−	0.516316i	$-0.827303\pi$
$463$	1.88019e6	−	3.25658e6i	0.0189434	−	0.0328109i	0.875342	+	0.483505i	$0.160636\pi$
$464$	2.82877e7	+	1.63319e7i	0.283168	+	0.163487i
$465$		0			0
$466$	−4.08710e6	−	7.07906e6i	−0.0403885	−	0.0699549i
$467$		−	1.12748e8i		−	1.10703i	−0.832839	−	0.553515i	$-0.813286\pi$
$467$		−	1.12748e8i		−	1.10703i	0.832839	−	0.553515i	$-0.186714\pi$
$468$		0			0
$469$	−8.69279e7			−0.842637
$470$	1.72479e7	−	9.95807e6i	0.166128	−	0.0959139i
$471$		0			0
$472$	3.46825e7	−	6.00719e7i	0.329826	−	0.571275i
$473$	8.01980e7	+	4.63024e7i	0.757845	+	0.437542i
$474$		0			0
$475$	−1.11428e7	−	1.92999e7i	−0.103972	−	0.180084i
$476$		−	1.05151e7i		−	0.0974972i
$477$		0			0
$478$	−2.40089e7			−0.219831
$479$	4.10687e7	−	2.37110e7i	0.373684	−	0.215746i	−0.301383	−	0.953503i	$-0.597448\pi$
$479$	4.10687e7	−	2.37110e7i	0.373684	−	0.215746i	0.675067	+	0.737757i	$0.264115\pi$
$480$		0			0
$481$	−2.24143e7	+	3.88227e7i	−0.201414	+	0.348859i
$482$	4.23105e7	+	2.44280e7i	0.377839	+	0.218145i
$483$		0			0
$484$	−2.58912e7	−	4.48450e7i	−0.228358	−	0.395528i
$485$		−	1.22066e8i		−	1.06997i
$486$		0			0
$487$	−2.03528e8			−1.76213			−0.881064	−	0.472997i	$-0.843172\pi$
$487$	−2.03528e8			−1.76213			−0.881064	+	0.472997i	$0.843172\pi$
$488$	−6.99865e7	+	4.04067e7i	−0.602220	+	0.347692i
$489$		0			0
$490$	−3.18102e7	+	5.50970e7i	−0.270383	+	0.468316i
$491$	1.25165e8	+	7.22639e7i	1.05740	+	0.610488i	0.924711	−	0.380670i	$-0.124307\pi$
$491$	1.25165e8	+	7.22639e7i	1.05740	+	0.610488i	0.132685	+	0.991158i	$0.457640\pi$
$492$		0			0
$493$	2.80179e7	+	4.85284e7i	0.233827	+	0.405000i
$494$			2.53943e7i			0.210647i
$495$		0			0
$496$	3.48434e7			0.285546
$497$	4.03226e7	−	2.32802e7i	0.328457	−	0.189635i
$498$		0			0
$499$	−7.67169e7	+	1.32878e8i	−0.617433	+	1.06942i	0.372520	+	0.928024i	$0.378494\pi$
$499$	−7.67169e7	+	1.32878e8i	−0.617433	+	1.06942i	−0.989952	+	0.141401i	$0.954839\pi$
$500$	4.80298e7	+	2.77300e7i	0.384238	+	0.221840i
$501$		0			0
$502$	−3.54453e7	−	6.13931e7i	−0.280187	−	0.485298i
$503$		−	1.94112e8i		−	1.52527i	−0.646827	−	0.762637i	$-0.723905\pi$
$503$		−	1.94112e8i		−	1.52527i	0.646827	−	0.762637i	$-0.276095\pi$
$504$		0			0
$505$	−2.32493e8			−1.80524
$506$	−1.32624e8	+	7.65706e7i	−1.02370	+	0.591031i
$507$		0			0
$508$	2.81362e7	−	4.87334e7i	0.214622	−	0.371737i
$509$	2.25878e7	+	1.30410e7i	0.171285	+	0.0988915i	0.583192	−	0.812335i	$-0.301804\pi$
$509$	2.25878e7	+	1.30410e7i	0.171285	+	0.0988915i	−0.411907	+	0.911226i	$0.635137\pi$
$510$		0			0
$511$	−5.10268e7	−	8.83811e7i	−0.382416	−	0.662364i
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	5.53307e7			0.407453
$515$	−6.56757e7	+	3.79179e7i	−0.480820	+	0.277602i
$516$		0			0
$517$	−2.38210e7	+	4.12591e7i	−0.172380	+	0.298572i
$518$	−7.06407e7	−	4.07844e7i	−0.508237	−	0.293430i
$519$		0			0
$520$	7.16128e6	+	1.24037e7i	0.0509308	+	0.0882148i
$521$			2.12883e8i			1.50532i	0.658409	+	0.752660i	$0.271230\pi$
$521$			2.12883e8i			1.50532i	−0.658409	+	0.752660i	$0.728770\pi$
$522$		0			0
$523$	1.36075e8			0.951204			0.475602	−	0.879661i	$-0.342230\pi$
$523$	1.36075e8			0.951204			0.475602	+	0.879661i	$0.342230\pi$
$524$	−3.92940e7	+	2.26864e7i	−0.273106	+	0.157678i
$525$		0			0
$526$	−8.14923e7	+	1.41149e8i	−0.559963	+	0.969885i
$527$	5.17667e7	+	2.98875e7i	0.353686	+	0.204201i
$528$		0			0
$529$	3.40843e7	+	5.90357e7i	0.230243	+	0.398793i
$530$			1.50163e8i			1.00864i
$531$		0			0
$532$	−4.62068e7			−0.306882
$533$	5.71869e6	−	3.30169e6i	0.0377672	−	0.0218049i
$534$		0			0
$535$	−1.04437e8	+	1.80890e8i	−0.682014	+	1.18128i
$536$	7.28534e7	+	4.20619e7i	0.473103	+	0.273146i
$537$		0			0
$538$	−6.25519e7	−	1.08343e8i	−0.401693	−	0.695752i
$539$		−	1.52188e8i		−	0.971884i
$540$		0			0
$541$	2.00376e7			0.126547			0.0632737	−	0.997996i	$-0.479846\pi$
$541$	2.00376e7			0.126547			0.0632737	+	0.997996i	$0.479846\pi$
$542$	−1.08871e8	+	6.28569e7i	−0.683779	+	0.394780i
$543$		0			0
$544$	−5.08796e6	+	8.81260e6i	−0.0316043	+	0.0547403i
$545$	2.69232e8	+	1.55441e8i	1.66317	+	0.960231i
$546$		0			0
$547$	−6.63316e7	−	1.14890e8i	−0.405283	−	0.701971i	0.589071	−	0.808081i	$-0.299494\pi$
$547$	−6.63316e7	−	1.14890e8i	−0.405283	−	0.701971i	−0.994354	+	0.106110i	$0.966160\pi$
$548$		−	4.73142e7i		−	0.287508i
$549$		0			0
$550$	3.00673e7			0.180720
$551$	2.13250e8	−	1.23120e8i	1.27478	−	0.735992i
$552$		0			0
$553$	1.03125e7	−	1.78618e7i	0.0609802	−	0.105621i
$554$	6.33348e7	+	3.65663e7i	0.372488	+	0.215056i
$555$		0			0
$556$	−5.26583e7	−	9.12069e7i	−0.306368	−	0.530644i
$557$			2.15296e8i			1.24586i	0.782276	+	0.622932i	$0.214059\pi$
$557$			2.15296e8i			1.24586i	−0.782276	+	0.622932i	$0.785941\pi$
$558$		0			0
$559$	2.92495e7			0.167449
$560$	−2.25695e7	+	1.30305e7i	−0.128516	+	0.0741987i
$561$		0			0
$562$	−8.27207e7	+	1.43276e8i	−0.466021	+	0.807171i
$563$	−2.33324e8	−	1.34709e8i	−1.30748	−	0.754871i	−0.325801	−	0.945438i	$-0.605634\pi$
$563$	−2.33324e8	−	1.34709e8i	−1.30748	−	0.754871i	−0.981674	+	0.190567i	$0.938967\pi$
$564$		0			0
$565$	1.15991e8	+	2.00902e8i	0.643100	+	1.11388i
$566$		−	1.34981e8i		−	0.744431i
$567$		0			0
$568$	−4.50586e7			−0.245885
$569$	−1.95776e8	+	1.13032e8i	−1.06273	+	0.613568i	−0.926187	−	0.377065i	$-0.876933\pi$
$569$	−1.95776e8	+	1.13032e8i	−1.06273	+	0.613568i	−0.136545	+	0.990634i	$0.543600\pi$
$570$		0			0
$571$	6.00918e7	−	1.04082e8i	0.322780	−	0.559072i	−0.658280	−	0.752773i	$-0.728716\pi$
$571$	6.00918e7	−	1.04082e8i	0.322780	−	0.559072i	0.981061	+	0.193701i	$0.0620492\pi$
$572$	−2.96712e7	−	1.71307e7i	−0.158543	−	0.0915349i
$573$		0			0
$574$	6.00766e6	+	1.04056e7i	0.0317665	+	0.0550212i
$575$		−	4.24489e7i		−	0.223287i
$576$		0			0
$577$	−1.67233e8			−0.870549			−0.435275	−	0.900298i	$-0.643349\pi$
$577$	−1.67233e8			−0.870549			−0.435275	+	0.900298i	$0.643349\pi$
$578$	1.03131e8	−	5.95428e7i	0.534080	−	0.308351i
$579$		0			0
$580$	6.94405e7	−	1.20274e8i	0.355901	−	0.616438i
$581$	7.67653e6	+	4.43205e6i	0.0391414	+	0.0225983i
$582$		0			0
$583$	−1.79604e8	−	3.11084e8i	−0.906382	−	1.56990i
$584$			9.87617e7i			0.495850i
$585$		0			0
$586$	−8.75377e7			−0.435013
$587$	2.21281e8	−	1.27757e8i	1.09403	−	0.631639i	0.159384	−	0.987217i	$-0.449049\pi$
$587$	2.21281e8	−	1.27757e8i	1.09403	−	0.631639i	0.934647	+	0.355578i	$0.115716\pi$
$588$		0			0
$589$	1.31336e8	−	2.27480e8i	0.642741	−	1.11326i
$590$	−2.55415e8	−	1.47464e8i	−1.24363	−	0.718009i
$591$		0			0
$592$	3.94689e7	+	6.83621e7i	0.190235	+	0.329496i
$593$		−	3.31215e8i		−	1.58835i	−0.607689	−	0.794175i	$-0.707903\pi$
$593$		−	3.31215e8i		−	1.58835i	0.607689	−	0.794175i	$-0.292097\pi$
$594$		0			0
$595$	−4.47084e7			−0.212245
$596$	−4.46777e6	+	2.57947e6i	−0.0211034	+	0.0121840i
$597$		0			0
$598$	−2.41851e7	+	4.18898e7i	−0.113095	+	0.195887i
$599$	3.13732e7	+	1.81133e7i	0.145975	+	0.0842786i	0.571209	−	0.820805i	$-0.306475\pi$
$599$	3.13732e7	+	1.81133e7i	0.145975	+	0.0842786i	−0.425234	+	0.905084i	$0.639808\pi$
$600$		0			0
$601$	5.63630e7	+	9.76236e7i	0.259640	+	0.449709i	0.966145	−	0.257998i	$-0.0830629\pi$
$601$	5.63630e7	+	9.76236e7i	0.259640	+	0.449709i	−0.706506	+	0.707707i	$0.749730\pi$
$602$			5.32216e7i			0.243949i
$603$		0			0
$604$	1.42116e8			0.644957
$605$	−1.90673e8	+	1.10085e8i	−0.861040	+	0.497121i
$606$		0			0
$607$	7.15829e7	−	1.23985e8i	0.320069	−	0.554376i	−0.660433	−	0.750885i	$-0.729627\pi$
$607$	7.15829e7	−	1.23985e8i	0.320069	−	0.554376i	0.980502	+	0.196509i	$0.0629606\pi$
$608$	3.87255e7	+	2.23582e7i	0.172300	+	0.0994776i
$609$		0			0
$610$	1.71803e8	+	2.97571e8i	0.756903	+	1.31099i
$611$			1.50479e7i			0.0659707i
$612$		0			0
$613$	1.40379e7			0.0609425			0.0304712	−	0.999536i	$-0.490299\pi$
$613$	1.40379e7			0.0609425			0.0304712	+	0.999536i	$0.490299\pi$
$614$	2.03945e8	−	1.17748e8i	0.881065	−	0.508683i
$615$		0			0
$616$	3.11706e7	−	5.39890e7i	0.133353	−	0.230974i
$617$	5.99838e7	+	3.46316e7i	0.255375	+	0.147441i	0.622223	−	0.782840i	$-0.286230\pi$
$617$	5.99838e7	+	3.46316e7i	0.255375	+	0.147441i	−0.366848	+	0.930281i	$0.619563\pi$
$618$		0			0
$619$	1.07174e8	+	1.85630e8i	0.451873	+	0.782666i	0.998502	−	0.0547082i	$-0.0174228\pi$
$619$	1.07174e8	+	1.85630e8i	0.451873	+	0.782666i	−0.546630	+	0.837374i	$0.684090\pi$
$620$		−	1.48148e8i		−	0.621615i
$621$		0			0
$622$	1.05871e7			0.0439954
$623$	6.13620e6	−	3.54274e6i	0.0253767	−	0.0146512i
$624$		0			0
$625$	1.40457e8	−	2.43279e8i	0.575313	−	0.996471i
$626$	−2.34115e7	−	1.35167e7i	−0.0954349	−	0.0550993i
$627$		0			0
$628$	−9.57276e7	−	1.65805e8i	−0.386508	−	0.669451i
$629$			1.35420e8i			0.544166i
$630$		0			0
$631$	−8.19880e7			−0.326334			−0.163167	−	0.986598i	$-0.552171\pi$
$631$	−8.19880e7			−0.326334			−0.163167	+	0.986598i	$0.552171\pi$
$632$	−1.72856e7	+	9.97986e6i	−0.0684753	+	0.0395342i
$633$		0			0
$634$	−3.34848e7	+	5.79973e7i	−0.131395	+	0.227583i
$635$	−2.07206e8	−	1.19630e8i	−0.809247	−	0.467219i
$636$		0			0
$637$	−2.40346e7	−	4.16291e7i	−0.0929861	−	0.161057i
$638$			3.32221e8i			1.27928i
$639$		0			0
$640$	2.52203e7			0.0962079
$641$	5.35983e7	−	3.09450e7i	0.203506	−	0.117494i	−0.394784	−	0.918774i	$-0.629181\pi$
$641$	5.35983e7	−	3.09450e7i	0.203506	−	0.117494i	0.598290	+	0.801280i	$0.295847\pi$
$642$		0			0
$643$	−7.51419e7	+	1.30150e8i	−0.282650	+	0.489564i	−0.972037	−	0.234829i	$-0.924547\pi$
$643$	−7.51419e7	+	1.30150e8i	−0.282650	+	0.489564i	0.689387	+	0.724394i	$0.257880\pi$
$644$	−7.62215e7	−	4.40065e7i	−0.285378	−	0.164763i
$645$		0			0
$646$	3.83561e7	+	6.64347e7i	0.142278	+	0.246432i
$647$			1.70289e8i			0.628745i	0.949300	+	0.314372i	$0.101794\pi$
$647$			1.70289e8i			0.628745i	−0.949300	+	0.314372i	$0.898206\pi$
$648$		0			0
$649$	7.05505e8			2.58087
$650$	8.22452e6	−	4.74843e6i	0.0299482	−	0.0172906i
$651$		0			0
$652$	2.99414e7	−	5.18600e7i	0.108026	−	0.187107i
$653$	−1.42742e8	−	8.24121e7i	−0.512639	−	0.295972i	0.221279	−	0.975211i	$-0.428977\pi$
$653$	−1.42742e8	−	8.24121e7i	−0.512639	−	0.295972i	−0.733918	+	0.679238i	$0.762310\pi$
$654$		0			0
$655$	9.64586e7	+	1.67071e8i	0.343255	+	0.594535i
$656$		−	1.16277e7i		−	0.0411893i
$657$		0			0
$658$	−2.73807e7			−0.0961096
$659$	1.45357e8	−	8.39220e7i	0.507902	−	0.293237i	−0.224069	−	0.974573i	$-0.571934\pi$
$659$	1.45357e8	−	8.39220e7i	0.507902	−	0.293237i	0.731971	+	0.681336i	$0.238601\pi$
$660$		0			0
$661$	6.41135e6	−	1.11048e7i	0.0221996	−	0.0384508i	−0.854712	−	0.519102i	$-0.826266\pi$
$661$	6.41135e6	−	1.11048e7i	0.0221996	−	0.0384508i	0.876912	+	0.480651i	$0.159600\pi$
$662$	1.22822e8	+	7.09115e7i	0.423354	+	0.244424i
$663$		0			0
$664$	−4.28908e6	−	7.42891e6i	−0.0146508	−	0.0253759i
$665$			1.96463e8i			0.668062i
$666$		0			0
$667$	4.69029e8			1.58060
$668$	2.55566e6	−	1.47551e6i	0.00857381	−	0.00495009i
$669$		0			0
$670$	1.78840e8	−	3.09760e8i	0.594622	−	1.02991i
$671$	−7.11827e8	−	4.10973e8i	−2.35617	−	1.36034i
$672$		0			0
$673$	2.60954e8	+	4.51986e8i	0.856089	+	1.48279i	0.875631	+	0.482981i	$0.160446\pi$
$673$	2.60954e8	+	4.51986e8i	0.856089	+	1.48279i	−0.0195422	+	0.999809i	$0.506221\pi$
$674$		−	3.02741e8i		−	0.988762i
$675$		0			0
$676$	1.43636e8			0.464969
$677$	−3.44693e8	+	1.99008e8i	−1.11088	+	0.641366i	−0.939057	−	0.343763i	$-0.888298\pi$
$677$	−3.44693e8	+	1.99008e8i	−1.11088	+	0.641366i	−0.171821	+	0.985128i	$0.554965\pi$
$678$		0			0
$679$	−8.39083e7	+	1.45333e8i	−0.268038	+	0.464255i
$680$	3.74697e7	+	2.16331e7i	0.119166	+	0.0688006i
$681$		0			0
$682$	1.77195e8	+	3.06910e8i	0.558596	+	0.967516i
$683$			1.35724e8i			0.425986i	0.977054	+	0.212993i	$0.0683211\pi$
$683$			1.35724e8i			0.425986i	−0.977054	+	0.212993i	$0.931679\pi$
$684$		0			0
$685$	−2.01172e8			−0.625886
$686$	1.83557e8	−	1.05977e8i	0.568590	−	0.328275i
$687$		0			0
$688$	2.57524e7	−	4.46045e7i	0.0790775	−	0.136966i
$689$	−9.82569e7	−	5.67286e7i	−0.300404	−	0.173438i
$690$		0			0
$691$	−2.53179e8	−	4.38519e8i	−0.767350	−	1.32909i	−0.938995	−	0.343930i	$-0.888242\pi$
$691$	−2.53179e8	−	4.38519e8i	−0.767350	−	1.32909i	0.171646	−	0.985159i	$-0.445092\pi$
$692$		−	2.41110e8i		−	0.727609i
$693$		0			0
$694$	−3.58811e8			−1.07346
$695$	−3.87796e8	+	2.23894e8i	−1.15518	+	0.666943i
$696$		0			0
$697$	9.97388e6	−	1.72753e7i	0.0294554	−	0.0510183i
$698$	2.38122e7	+	1.37480e7i	0.0700218	+	0.0404271i
$699$		0			0
$700$	8.64011e6	+	1.49651e7i	0.0251898	+	0.0436301i
$701$			3.25042e8i			0.943595i	0.881707	+	0.471798i	$0.156395\pi$
$701$			3.25042e8i			0.943595i	−0.881707	+	0.471798i	$0.843605\pi$
$702$		0			0
$703$	5.95081e8			1.71281
$704$	−5.22475e7	+	3.01651e7i	−0.149743	+	0.0864543i
$705$		0			0
$706$	2.76667e7	−	4.79202e7i	0.0786219	−	0.136177i
$707$	2.76809e8	+	1.59816e8i	0.783288	+	0.452231i
$708$		0			0
$709$	−1.66726e8	−	2.88778e8i	−0.467805	−	0.810261i	0.531519	−	0.847047i	$-0.321622\pi$
$709$	−1.66726e8	−	2.88778e8i	−0.467805	−	0.810261i	−0.999323	+	0.0367854i	$0.988288\pi$
$710$			1.91581e8i			0.535277i
$711$		0			0
$712$	−6.85692e6			−0.0189972
$713$	4.33295e8	−	2.50163e8i	1.19541	−	0.690168i
$714$		0			0
$715$	−7.28368e7	+	1.26157e8i	−0.199266	+	0.345138i
$716$	1.20136e8	+	6.93603e7i	0.327290	+	0.188961i
$717$		0			0
$718$	−1.66236e8	−	2.87929e8i	−0.449109	−	0.777880i
$719$		−	2.30851e8i		−	0.621076i	−0.950561	−	0.310538i	$-0.899491\pi$
$719$		−	2.30851e8i		−	0.621076i	0.950561	−	0.310538i	$-0.100509\pi$
$720$		0			0
$721$	1.04259e8			0.278168
$722$	6.14593e7	−	3.54835e7i	0.163296	−	0.0942790i
$723$		0			0
$724$	5.84802e7	−	1.01291e8i	0.154097	−	0.266903i
$725$	−7.97503e7	−	4.60438e7i	−0.209275	−	0.120825i
$726$		0			0
$727$	1.78802e8	+	3.09693e8i	0.465337	+	0.805988i	0.999217	−	0.0395726i	$-0.0125996\pi$
$727$	1.78802e8	+	3.09693e8i	0.465337	+	0.805988i	−0.533879	+	0.845561i	$0.679266\pi$
$728$		−	1.96906e7i		−	0.0510347i
$729$		0			0
$730$	4.19918e8			1.07943
$731$	7.65204e7	−	4.41791e7i	0.195896	−	0.113101i
$732$		0			0
$733$	2.02434e7	−	3.50626e7i	0.0514010	−	0.0890291i	−0.839180	−	0.543854i	$-0.816965\pi$
$733$	2.02434e7	−	3.50626e7i	0.0514010	−	0.0890291i	0.890581	+	0.454825i	$0.150298\pi$
$734$	2.69574e8	+	1.55639e8i	0.681695	+	0.393577i
$735$		0			0
$736$	4.25870e7	+	7.37629e7i	0.106818	+	0.185014i
$737$			8.55616e8i			2.13736i
$738$		0			0
$739$	2.40793e7			0.0596638			0.0298319	−	0.999555i	$-0.490503\pi$
$739$	2.40793e7			0.0596638			0.0298319	+	0.999555i	$0.490503\pi$
$740$	2.90664e8	−	1.67815e8i	0.717292	−	0.414129i
$741$		0			0
$742$	1.03222e8	−	1.78786e8i	0.252674	−	0.437644i
$743$	2.87546e8	+	1.66015e8i	0.701038	+	0.404744i	0.807734	−	0.589547i	$-0.200694\pi$
$743$	2.87546e8	+	1.66015e8i	0.701038	+	0.404744i	−0.106696	+	0.994292i	$0.534027\pi$
$744$		0			0
$745$	1.09675e7	+	1.89962e7i	0.0265239	+	0.0459407i
$746$		−	2.91935e8i		−	0.703184i
$747$		0			0
$748$	−1.03498e8			−0.247302
$749$	2.48688e8	−	1.43580e8i	0.591846	−	0.341702i
$750$		0			0
$751$	4.32825e7	−	7.49676e7i	0.102186	−	0.176992i	−0.810399	−	0.585879i	$-0.800750\pi$
$751$	4.32825e7	−	7.49676e7i	0.102186	−	0.176992i	0.912585	+	0.408887i	$0.134083\pi$
$752$	2.29475e7	+	1.32487e7i	0.0539612	+	0.0311545i
$753$		0			0
$754$	5.24665e7	+	9.08747e7i	0.122396	+	0.211997i
$755$		−	6.04251e8i		−	1.40403i
$756$		0			0
$757$	−4.37394e8			−1.00829			−0.504145	−	0.863619i	$-0.668192\pi$
$757$	−4.37394e8			−1.00829			−0.504145	+	0.863619i	$0.668192\pi$
$758$	4.87598e8	−	2.81515e8i	1.11958	−	0.646389i
$759$		0			0
$760$	9.50631e7	−	1.64654e8i	0.216556	−	0.375087i
$761$	2.97123e8	+	1.71544e8i	0.674190	+	0.389244i	0.797662	−	0.603104i	$-0.206070\pi$
$761$	2.97123e8	+	1.71544e8i	0.674190	+	0.389244i	−0.123473	+	0.992348i	$0.539403\pi$
$762$		0			0
$763$	−2.13700e8	−	3.70139e8i	−0.481095	−	0.833281i
$764$		−	1.15893e8i		−	0.259881i
$765$		0			0
$766$	−5.97911e7			−0.133030
$767$	1.92982e8	−	1.11418e8i	0.427691	−	0.246928i
$768$		0			0
$769$	−3.29473e8	+	5.70664e8i	−0.724504	+	1.25488i	0.234673	+	0.972074i	$0.424598\pi$
$769$	−3.29473e8	+	5.70664e8i	−0.724504	+	1.25488i	−0.959178	+	0.282804i	$0.908735\pi$
$770$	−2.29552e8	−	1.32532e8i	−0.502815	−	0.290301i
$771$		0			0
$772$	1.04151e8	+	1.80394e8i	0.226366	+	0.392077i
$773$			7.79814e8i			1.68831i	0.536098	+	0.844156i	$0.319898\pi$
$773$			7.79814e8i			1.68831i	−0.536098	+	0.844156i	$0.680102\pi$
$774$		0			0
$775$	−9.82326e7			−0.211033
$776$	1.40646e8	−	8.12017e7i	0.300982	−	0.173772i
$777$		0			0
$778$	3.94346e7	−	6.83027e7i	0.0837411	−	0.145044i
$779$	−7.59132e7	−	4.38285e7i	−0.160585	−	0.0927138i
$780$		0			0
$781$	−2.29143e8	−	3.96888e8i	−0.481010	−	0.833134i
$782$			1.46119e8i			0.305552i
$783$		0			0
$784$	−8.46440e7			−0.175650
$785$	−7.04975e8	+	4.07017e8i	−1.45735	+	0.841403i
$786$		0			0
$787$	7.13858e7	−	1.23644e8i	0.146449	−	0.253658i	−0.783463	−	0.621438i	$-0.786549\pi$
$787$	7.13858e7	−	1.23644e8i	0.146449	−	0.253658i	0.929913	+	0.367780i	$0.119882\pi$
$788$	1.75405e8	+	1.01270e8i	0.358479	+	0.206968i
$789$		0			0
$790$	4.24326e7	+	7.34955e7i	0.0860635	+	0.149066i
$791$		−	3.18928e8i		−	0.644412i
$792$		0			0
$793$	−2.59615e8			−0.520607
$794$	1.05849e8	−	6.11122e7i	0.211459	−	0.122086i
$795$		0			0
$796$	−1.32373e8	+	2.29276e8i	−0.262458	+	0.454590i
$797$	1.65761e8	+	9.57019e7i	0.327421	+	0.189037i	0.654695	−	0.755893i	$-0.272797\pi$
$797$	1.65761e8	+	9.57019e7i	0.327421	+	0.189037i	−0.327275	+	0.944929i	$0.606130\pi$
$798$		0			0
$799$	2.27286e7	+	3.93671e7i	0.0445587	+	0.0771780i
$800$		−	1.67228e7i		−	0.0326617i
$801$		0			0
$802$	−5.87193e8			−1.13830
$803$	−8.69920e8	+	5.02248e8i	−1.68009	+	0.970000i
$804$		0			0
$805$	−1.87108e8	+	3.24081e8i	−0.358678	+	0.621249i
$806$	9.69386e7	+	5.59676e7i	0.185136	+	0.106889i
$807$		0			0
$808$	−1.54660e8	−	2.67880e8i	−0.293187	−	0.507815i
$809$		−	9.44320e8i		−	1.78350i	−0.452527	−	0.891751i	$-0.649477\pi$
$809$		−	9.44320e8i		−	1.78350i	0.452527	−	0.891751i	$-0.350523\pi$
$810$		0			0
$811$	−2.09243e8			−0.392273			−0.196137	−	0.980577i	$-0.562840\pi$
$811$	−2.09243e8			−0.392273			−0.196137	+	0.980577i	$0.562840\pi$
$812$	−1.65353e8	+	9.54667e7i	−0.308848	+	0.178313i
$813$		0			0
$814$	−4.01434e8	+	6.95305e8i	−0.744288	+	1.28915i
$815$	−2.20500e8	−	1.27306e8i	−0.407320	−	0.235166i
$816$		0			0
$817$	−1.94137e8	−	3.36256e8i	−0.355994	−	0.616600i
$818$		−	5.16884e8i		−	0.944351i
$819$		0			0
$820$	−4.94392e7			−0.0896664
$821$	−1.46942e7	+	8.48369e6i	−0.0265531	+	0.0153305i	−0.513218	−	0.858258i	$-0.671547\pi$
$821$	−1.46942e7	+	8.48369e6i	−0.0265531	+	0.0153305i	0.486665	+	0.873589i	$0.338213\pi$
$822$		0			0
$823$	−5.62432e7	+	9.74161e7i	−0.100895	+	0.174756i	−0.912054	−	0.410071i	$-0.865504\pi$
$823$	−5.62432e7	+	9.74161e7i	−0.100895	+	0.174756i	0.811158	+	0.584826i	$0.198837\pi$
$824$	−8.73783e7	−	5.04479e7i	−0.156179	−	0.0901699i
$825$		0			0
$826$	2.02733e8	+	3.51145e8i	0.359737	+	0.623083i
$827$			6.84539e8i			1.21027i	0.796123	+	0.605135i	$0.206881\pi$
$827$			6.84539e8i			1.21027i	−0.796123	+	0.605135i	$0.793119\pi$
$828$		0			0
$829$	5.25177e8			0.921812			0.460906	−	0.887449i	$-0.347525\pi$
$829$	5.25177e8			0.921812			0.460906	+	0.887449i	$0.347525\pi$
$830$	−3.15864e7	+	1.82364e7i	−0.0552416	+	0.0318938i
$831$		0			0
$832$	−9.52775e6	+	1.65025e7i	−0.0165432	+	0.0286537i
$833$	−1.25755e8	−	7.26047e7i	−0.217566	−	0.125612i
$834$		0			0
$835$	−6.27362e6	−	1.08662e7i	−0.0107760	−	0.0186646i
$836$			4.54806e8i			0.778407i
$837$		0			0
$838$	−4.68201e8			−0.795611
$839$	−2.47051e8	+	1.42635e8i	−0.418312	+	0.241512i	−0.694355	−	0.719633i	$-0.744310\pi$
$839$	−2.47051e8	+	1.42635e8i	−0.418312	+	0.241512i	0.276043	+	0.961145i	$0.410977\pi$
$840$		0			0
$841$	2.11338e8	−	3.66048e8i	0.355295	−	0.615390i
$842$	4.00481e8	+	2.31218e8i	0.670881	+	0.387334i
$843$		0			0
$844$	1.40285e8	+	2.42982e8i	0.233338	+	0.404153i
$845$		−	6.10717e8i		−	1.01221i
$846$		0			0
$847$	3.02690e8			0.498135
$848$	−1.73019e8	+	9.98923e7i	−0.283730	+	0.163812i
$849$		0			0
$850$	1.43442e7	−	2.48450e7i	0.0233572	−	0.0404559i
$851$	9.81630e8	+	5.66744e8i	1.59279	+	0.919599i
$852$		0			0
$853$	−2.98362e8	−	5.16778e8i	−0.480724	−	0.832639i	0.519031	−	0.854755i	$-0.326293\pi$
$853$	−2.98362e8	−	5.16778e8i	−0.480724	−	0.832639i	−0.999755	+	0.0221165i	$0.992960\pi$
$854$		−	4.72388e8i		−	0.758447i
$855$		0			0
$856$	−2.77897e8			−0.443060
$857$	−2.88589e8	+	1.66617e8i	−0.458497	+	0.264713i	−0.711412	−	0.702775i	$-0.751944\pi$
$857$	−2.88589e8	+	1.66617e8i	−0.458497	+	0.264713i	0.252915	+	0.967488i	$0.418611\pi$
$858$		0			0
$859$	−5.14017e8	+	8.90303e8i	−0.810957	+	1.40462i	0.101238	+	0.994862i	$0.467720\pi$
$859$	−5.14017e8	+	8.90303e8i	−0.810957	+	1.40462i	−0.912195	+	0.409756i	$0.865614\pi$
$860$	−1.89651e8	−	1.09495e8i	−0.298167	−	0.172147i
$861$		0			0
$862$	−4.34045e8	−	7.51788e8i	−0.677661	−	1.17374i
$863$		−	7.49705e6i		−	0.0116643i	−0.999983	−	0.00583214i	$-0.998144\pi$
$863$		−	7.49705e6i		−	0.0116643i	0.999983	−	0.00583214i	$-0.00185644\pi$
$864$		0			0
$865$	−1.02516e9			−1.58396
$866$	−5.67510e8	+	3.27652e8i	−0.873816	+	0.504498i
$867$		0			0
$868$	−1.01837e8	+	1.76387e8i	−0.155721	+	0.269716i
$869$	−1.75810e8	−	1.01504e8i	−0.267908	−	0.154677i
$870$		0			0
$871$	1.35125e8	+	2.34043e8i	0.204494	+	0.354194i
$872$			4.13613e8i			0.623800i
$873$		0			0
$874$	6.42094e8			0.961754
$875$	−2.80753e8	+	1.62093e8i	−0.419084	+	0.241958i
$876$		0			0
$877$	1.37626e8	−	2.38375e8i	0.204033	−	0.353396i	−0.745791	−	0.666180i	$-0.767928\pi$
$877$	1.37626e8	−	2.38375e8i	0.204033	−	0.353396i	0.949824	+	0.312784i	$0.101262\pi$
$878$	−2.07065e8	−	1.19549e8i	−0.305930	−	0.176629i
$879$		0			0
$880$	1.28257e8	+	2.22147e8i	0.188206	+	0.325982i
$881$		−	4.00012e8i		−	0.584986i	−0.956268	−	0.292493i	$-0.905515\pi$
$881$		−	4.00012e8i		−	0.584986i	0.956268	−	0.292493i	$-0.0944848\pi$
$882$		0			0
$883$	−1.04179e9			−1.51320			−0.756601	−	0.653877i	$-0.773141\pi$
$883$	−1.04179e9			−1.51320			−0.756601	+	0.653877i	$0.773141\pi$
$884$	−2.83106e7	+	1.63451e7i	−0.0409819	+	0.0236609i
$885$		0			0
$886$	4.72727e8	−	8.18786e8i	0.679687	−	1.17725i
$887$	−4.27176e8	−	2.46630e8i	−0.612119	−	0.353407i	0.161675	−	0.986844i	$-0.448310\pi$
$887$	−4.27176e8	−	2.46630e8i	−0.612119	−	0.353407i	−0.773794	+	0.633437i	$0.781644\pi$
$888$		0			0
$889$	1.64468e8	+	2.84866e8i	0.234086	+	0.405449i
$890$			2.91544e7i			0.0413556i
$891$		0			0
$892$	−3.90981e8			−0.550885
$893$	1.72992e8	−	9.98771e7i	0.242925	−	0.140253i
$894$		0			0
$895$	2.94908e8	−	5.10796e8i	0.411356	−	0.712489i
$896$	−3.00276e7	−	1.73364e7i	−0.0417442	−	0.0241010i
$897$		0			0
$898$	2.42156e8	+	4.19427e8i	0.334400	+	0.579199i
$899$		−	1.08540e9i		−	1.49386i
$900$		0			0
$901$	−3.42737e8			−0.468582
$902$	1.02420e8	−	5.91324e7i	0.139562	−	0.0805760i
$903$		0			0
$904$	−1.54320e8	+	2.67291e8i	−0.208890	+	0.361808i
$905$	−4.30671e8	−	2.48648e8i	−0.581031	−	0.335459i
$906$		0			0
$907$	4.77246e8	+	8.26615e8i	0.639618	+	1.10785i	0.985517	+	0.169579i	$0.0542407\pi$
$907$	4.77246e8	+	8.26615e8i	0.639618	+	1.10785i	−0.345899	+	0.938272i	$0.612426\pi$
$908$		−	7.19131e7i		−	0.0960618i
$909$		0			0
$910$	−8.37213e7			−0.111099
$911$	−8.83047e7	+	5.09828e7i	−0.116796	+	0.0674323i	−0.557260	−	0.830338i	$-0.688147\pi$
$911$	−8.83047e7	+	5.09828e7i	−0.116796	+	0.0674323i	0.440464	+	0.897770i	$0.354814\pi$
$912$		0			0
$913$	4.36239e7	−	7.55587e7i	0.0573207	−	0.0992824i
$914$	3.25974e7	+	1.88201e7i	0.0426918	+	0.0246481i
$915$		0			0
$916$	−8.33056e7	−	1.44290e8i	−0.108390	−	0.187736i
$917$		−	2.65222e8i		−	0.343955i
$918$		0			0
$919$	−7.10292e8			−0.915146			−0.457573	−	0.889172i	$-0.651281\pi$
$919$	−7.10292e8			−0.915146			−0.457573	+	0.889172i	$0.651281\pi$
$920$	3.13627e8	−	1.81073e8i	0.402763	−	0.232536i
$921$		0			0
$922$	−6.55544e7	+	1.13543e8i	−0.0836390	+	0.144867i
$923$	−1.25358e8	−	7.23757e7i	−0.159422	−	0.0920424i
$924$		0			0
$925$	−1.11273e8	−	1.92730e8i	−0.140593	−	0.243514i
$926$		−	2.12719e7i		−	0.0267900i
$927$		0			0
$928$	1.84774e8			0.231205
$929$	3.30778e8	−	1.90975e8i	0.412562	−	0.238193i	−0.279328	−	0.960196i	$-0.590112\pi$
$929$	3.30778e8	−	1.90975e8i	0.412562	−	0.238193i	0.691890	+	0.722003i	$0.256778\pi$
$930$		0			0
$931$	−3.19049e8	+	5.52609e8i	−0.395374	+	0.684808i
$932$	−4.00452e7	−	2.31201e7i	−0.0494656	−	0.0285590i
$933$		0			0
$934$	−3.18900e8	−	5.52351e8i	−0.391394	−	0.677914i
$935$			4.40057e8i			0.538361i
$936$		0			0
$937$	−5.56713e8			−0.676726			−0.338363	−	0.941016i	$-0.609873\pi$
$937$	−5.56713e8			−0.676726			−0.338363	+	0.941016i	$0.609873\pi$
$938$	−4.25858e8	+	2.45869e8i	−0.516008	+	0.297917i
$939$		0			0
$940$	5.63314e7	−	9.75688e7i	0.0678214	−	0.117470i
$941$	5.51171e8	+	3.18219e8i	0.661481	+	0.381906i	0.792841	−	0.609428i	$-0.208601\pi$
$941$	5.51171e8	+	3.18219e8i	0.661481	+	0.381906i	−0.131360	+	0.991335i	$0.541934\pi$
$942$		0			0
$943$	−8.34830e7	−	1.44597e8i	−0.0995549	−	0.172434i
$944$		−	3.92388e8i		−	0.466444i
$945$		0			0
$946$	5.23851e8			0.618778
$947$	1.02466e9	−	5.91587e8i	1.20651	−	0.696577i	0.244512	−	0.969646i	$-0.421372\pi$
$947$	1.02466e9	−	5.91587e8i	1.20651	−	0.696577i	0.961994	+	0.273069i	$0.0880389\pi$
$948$		0			0
$949$	−1.58637e8	+	2.74767e8i	−0.185612	+	0.321489i
$950$	−1.09177e8	−	6.30334e7i	−0.127339	−	0.0735190i
$951$		0			0
$952$	−2.97412e7	−	5.15132e7i	−0.0344705	−	0.0597046i
$953$			1.06040e8i			0.122516i	0.998122	+	0.0612579i	$0.0195112\pi$
$953$			1.06040e8i			0.122516i	−0.998122	+	0.0612579i	$0.980489\pi$
$954$		0			0
$955$	−4.92755e8			−0.565745
$956$	−1.17619e8	+	6.79075e7i	−0.134619	+	0.0777220i
$957$		0			0
$958$	1.34130e8	−	2.32320e8i	0.152556	−	0.264234i
$959$	2.39517e8	+	1.38285e8i	0.271570	+	0.156791i
$960$		0			0
$961$	−1.35160e8	−	2.34103e8i	−0.152292	−	0.263777i
$962$			2.53589e8i			0.284842i
$963$		0			0
$964$	2.76371e8			0.308504
$965$	7.67006e8	−	4.42831e8i	0.853527	−	0.492784i
$966$		0			0
$967$	2.05165e8	−	3.55357e8i	0.226895	−	0.392993i	−0.729991	−	0.683456i	$-0.760476\pi$
$967$	2.05165e8	−	3.55357e8i	0.226895	−	0.392993i	0.956886	+	0.290463i	$0.0938093\pi$
$968$	−2.53681e8	−	1.46463e8i	−0.279681	−	0.161474i
$969$		0			0
$970$	−3.45256e8	−	5.98001e8i	−0.378291	−	0.655219i
$971$			1.16518e9i			1.27273i	0.771389	+	0.636364i	$0.219562\pi$
$971$			1.16518e9i			1.27273i	−0.771389	+	0.636364i	$0.780438\pi$
$972$		0			0
$973$	6.15619e8			0.668303
$974$	−9.97080e8	+	5.75664e8i	−1.07908	+	0.623006i
$975$		0			0
$976$	−2.28575e8	+	3.95904e8i	−0.245855	+	0.425834i
$977$	−2.55899e8	−	1.47743e8i	−0.274401	−	0.158425i	0.356485	−	0.934301i	$-0.383975\pi$
$977$	−2.55899e8	−	1.47743e8i	−0.274401	−	0.158425i	−0.630886	+	0.775876i	$0.717308\pi$
$978$		0			0
$979$	−3.48705e7	−	6.03975e7i	−0.0371630	−	0.0643682i
$980$			3.59892e8i			0.382379i
$981$		0			0
$982$	8.17573e8			0.863360
$983$	7.84506e8	−	4.52935e8i	0.825916	−	0.476843i	−0.0265364	−	0.999648i	$-0.508448\pi$
$983$	7.84506e8	−	4.52935e8i	0.825916	−	0.476843i	0.852452	+	0.522805i	$0.175114\pi$
$984$		0			0
$985$	4.30583e8	−	7.45792e8i	0.450555	−	0.780385i
$986$	2.74518e8	+	1.58493e8i	0.286378	+	0.165341i
$987$		0			0
$988$	7.18259e7	+	1.24406e8i	0.0744750	+	0.128994i
$989$		−	7.39572e8i		−	0.764525i
$990$		0			0
$991$	1.78268e9			1.83169			0.915847	−	0.401529i	$-0.131521\pi$
$991$	1.78268e9			1.83169			0.915847	+	0.401529i	$0.131521\pi$
$992$	1.70697e8	−	9.85521e7i	0.174860	−	0.100956i
$993$		0			0
$994$	1.31693e8	−	2.28099e8i	0.134092	−	0.232254i
$995$	9.74843e8	+	5.62826e8i	0.989613	+	0.571353i
$996$		0			0
$997$	9.06831e8	+	1.57068e9i	0.915041	+	1.58490i	0.806841	+	0.590769i	$0.201176\pi$
$997$	9.06831e8	+	1.57068e9i	0.915041	+	1.58490i	0.108201	+	0.994129i	$0.465491\pi$
$998$			8.67953e8i			0.873182i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.g.53.6		16
3.2	odd	2	inner	162.7.d.g.53.3		16
9.2	odd	6	inner	162.7.d.g.107.6		16
9.4	even	3		162.7.b.b.161.7	yes	8
9.5	odd	6		162.7.b.b.161.2	✓	8
9.7	even	3	inner	162.7.d.g.107.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.b.161.2	✓	8	9.5	odd	6
162.7.b.b.161.7	yes	8	9.4	even	3
162.7.d.g.53.3		16	3.2	odd	2	inner
162.7.d.g.53.6		16	1.1	even	1	trivial
162.7.d.g.107.3		16	9.7	even	3	inner
162.7.d.g.107.6		16	9.2	odd	6	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-117.830 - 68.0293i) q^{5} +(93.5265 + 161.993i) q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-117.830 - 68.0293i) q^{5} +(93.5265 + 161.993i) q^{7} -181.019i q^{8} -769.663 q^{10} +(1594.47 - 920.566i) q^{11} +(290.764 - 503.618i) q^{13} +(916.369 + 529.066i) q^{14} +(-512.000 - 886.810i) q^{16} -1756.70i q^{17} -7719.53 q^{19} +(-3770.56 + 2176.94i) q^{20} +(5207.51 - 9019.66i) q^{22} +(-12733.9 - 7351.95i) q^{23} +(1443.46 + 2500.14i) q^{25} -3289.62i q^{26} +5985.70 q^{28} +(-27624.7 + 15949.1i) q^{29} +(-17013.4 + 29468.1i) q^{31} +(-5016.55 - 2896.31i) q^{32} +(-4968.71 - 8606.05i) q^{34} -25450.2i q^{35} -77087.6 q^{37} +(-37817.8 + 21834.1i) q^{38} +(-12314.6 + 21329.5i) q^{40} +(9833.91 + 5677.61i) q^{41} +(25148.9 + 43559.1i) q^{43} -58916.2i q^{44} -83177.8 q^{46} +(-22409.7 + 12938.2i) q^{47} +(41330.1 - 71585.8i) q^{49} +(14143.0 + 8165.44i) q^{50} +(-9304.44 - 16115.8i) q^{52} -195102. i q^{53} -250502. q^{55} +(29323.8 - 16930.1i) q^{56} +(-90221.9 + 156269. i) q^{58} +(331853. + 191596. i) q^{59} +(-223218. - 386625. i) q^{61} +192485. i q^{62} -32768.0 q^{64} +(-68521.5 + 39560.9i) q^{65} +(-232362. + 402462. i) q^{67} +(-48683.2 - 28107.3i) q^{68} +(-71983.9 - 124680. i) q^{70} -248916. i q^{71} -545587. q^{73} +(-377651. + 218037. i) q^{74} +(-123513. + 213930. i) q^{76} +(298250. + 172195. i) q^{77} +(-55131.4 - 95490.5i) q^{79} +139324. i q^{80} +64234.8 q^{82} +(41039.3 - 23694.1i) q^{83} +(-119507. + 206993. i) q^{85} +(246408. + 142263. i) q^{86} +(-166640. - 288629. i) q^{88} -37879.5i q^{89} +108776. q^{91} +(-407486. + 235262. i) q^{92} +(-73189.6 + 126768. i) q^{94} +(909594. + 525154. i) q^{95} +(448580. + 776964. i) q^{97} -467596. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 256 q^{4} - 964 q^{7}+O(q^{10}) \) 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

Introduction

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