LMFDB - Embedded newform 27.8.c.a.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,8,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, 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:	$8.43439568807$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 375 x^{10} - 1820 x^{9} + 50808 x^{8} - 192378 x^{7} + 3002887 x^{6} + \cdots + 754412211 $ x^12 - 6x^11 + 375x^10 - 1820x^9 + 50808x^8 - 192378x^7 + 3002887x^6 - 8342916x^5 + 72369348x^4 - 131054670x^3 + 513267363x^2 - 449098992*x + 754412211
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{21} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.5
Root			$0.500000 - 6.17443i$ of defining polynomial
Character	$\chi$	$=$	27.10
Dual form			27.8.c.a.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.09721 + 10.5607i) q^{2} +(-10.3519 + 17.9301i) q^{4} +(246.026 - 426.130i) q^{5} +(-382.311 - 662.182i) q^{7} +1308.41 q^{8} +O(q^{10})$	\(q+(6.09721 + 10.5607i) q^{2} +(-10.3519 + 17.9301i) q^{4} +(246.026 - 426.130i) q^{5} +(-382.311 - 662.182i) q^{7} +1308.41 q^{8} +6000.29 q^{10} +(-36.3512 - 62.9621i) q^{11} +(-3010.77 + 5214.80i) q^{13} +(4662.06 - 8074.93i) q^{14} +(9302.72 + 16112.8i) q^{16} +5989.93 q^{17} +18676.2 q^{19} +(5093.69 + 8822.53i) q^{20} +(443.281 - 767.786i) q^{22} +(12139.5 - 21026.3i) q^{23} +(-81995.2 - 142020. i) q^{25} -73429.1 q^{26} +15830.6 q^{28} +(43378.1 + 75133.0i) q^{29} +(-105890. + 183406. i) q^{31} +(-29702.8 + 51446.7i) q^{32} +(36521.9 + 63257.8i) q^{34} -376234. q^{35} -327978. q^{37} +(113873. + 197233. i) q^{38} +(321904. - 557554. i) q^{40} +(196036. - 339545. i) q^{41} +(343611. + 595152. i) q^{43} +1505.22 q^{44} +296069. q^{46} +(320755. + 555563. i) q^{47} +(119448. - 206890. i) q^{49} +(999884. - 1.73185e6i) q^{50} +(-62334.5 - 107966. i) q^{52} +814485. q^{53} -35773.3 q^{55} +(-500221. - 866408. i) q^{56} +(-528971. + 916204. i) q^{58} +(-1.25863e6 + 2.18002e6i) q^{59} +(221621. + 383858. i) q^{61} -2.58252e6 q^{62} +1.65708e6 q^{64} +(1.48145e6 + 2.56595e6i) q^{65} +(-296048. + 512770. i) q^{67} +(-62007.4 + 107400. i) q^{68} +(-2.29398e6 - 3.97329e6i) q^{70} -1.48821e6 q^{71} -5.41341e6 q^{73} +(-1.99975e6 - 3.46367e6i) q^{74} +(-193334. + 334865. i) q^{76} +(-27794.9 + 48142.2i) q^{77} +(444736. + 770305. i) q^{79} +9.15485e6 q^{80} +4.78109e6 q^{82} +(-1.69323e6 - 2.93276e6i) q^{83} +(1.47368e6 - 2.55249e6i) q^{85} +(-4.19014e6 + 7.25754e6i) q^{86} +(-47562.4 - 82380.4i) q^{88} -1.17388e6 q^{89} +4.60420e6 q^{91} +(251335. + 435325. i) q^{92} +(-3.91142e6 + 6.77477e6i) q^{94} +(4.59483e6 - 7.95847e6i) q^{95} +(4.30014e6 + 7.44806e6i) q^{97} +2.91320e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8}+O(q^{10}) $ 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8} + 252 q^{10} + 8460 q^{11} - 1848 q^{13} + 16272 q^{14} - 12417 q^{16} - 30564 q^{17} + 24432 q^{19} + 40788 q^{20} - 35001 q^{22} + 51588 q^{23} + 4746 q^{25} - 536472 q^{26} + 75516 q^{28} + 414648 q^{29} + 8196 q^{31} + 1048977 q^{32} - 106623 q^{34} - 2210616 q^{35} + 139344 q^{37} + 1952685 q^{38} + 305496 q^{40} + 1731582 q^{41} + 408372 q^{43} - 5169114 q^{44} - 1684008 q^{46} + 1631484 q^{47} - 179010 q^{49} + 1654461 q^{50} + 681594 q^{52} - 2835648 q^{53} - 16056 q^{55} + 1784466 q^{56} - 948384 q^{58} + 2055636 q^{59} - 2723196 q^{61} + 1026828 q^{62} + 7178178 q^{64} + 1387620 q^{65} + 3806556 q^{67} - 2142639 q^{68} + 953442 q^{70} - 2408400 q^{71} - 10670052 q^{73} - 9846504 q^{74} - 6727827 q^{76} - 3478824 q^{77} + 6020916 q^{79} + 38072448 q^{80} + 9403002 q^{82} - 9605052 q^{83} - 1698624 q^{85} - 34278561 q^{86} - 16459029 q^{88} + 24630264 q^{89} + 13570104 q^{91} - 39143394 q^{92} + 12602808 q^{94} - 10422072 q^{95} + 9977226 q^{97} + 95833314 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	6.09721	+	10.5607i	0.538922	+	0.933441i	0.998962	+	0.0455426i	$0.0145017\pi$
$2$	6.09721	+	10.5607i	0.538922	+	0.933441i	−0.460040	+	0.887898i	$0.652165\pi$
$3$		0			0
$3$		0			0
$4$	−10.3519	+	17.9301i	−0.0808745	+	0.140079i
$5$	246.026	−	426.130i	0.880210	−	1.52457i	0.0291025	−	0.999576i	$-0.490735\pi$
$5$	246.026	−	426.130i	0.880210	−	1.52457i	0.851107	−	0.524992i	$-0.175932\pi$
$6$		0			0
$7$	−382.311	−	662.182i	−0.421283	−	0.729683i	0.574783	−	0.818306i	$-0.305087\pi$
$7$	−382.311	−	662.182i	−0.421283	−	0.729683i	−0.996065	+	0.0886232i	$0.971753\pi$
$8$	1308.41			0.903504
$9$		0			0
$10$	6000.29			1.89746
$11$	−36.3512	−	62.9621i	−0.00823463	−	0.0142628i	0.861879	−	0.507114i	$-0.169288\pi$
$11$	−36.3512	−	62.9621i	−0.00823463	−	0.0142628i	−0.870113	+	0.492852i	$0.835955\pi$
$12$		0			0
$13$	−3010.77	+	5214.80i	−0.380080	+	0.658318i	−0.991073	−	0.133318i	$-0.957437\pi$
$13$	−3010.77	+	5214.80i	−0.380080	+	0.658318i	0.610993	+	0.791636i	$0.290770\pi$
$14$	4662.06	−	8074.93i	0.454077	−	0.786485i
$15$		0			0
$16$	9302.72	+	16112.8i	0.567793	+	0.983446i
$17$	5989.93			0.295700			0.147850	−	0.989010i	$-0.452765\pi$
$17$	5989.93			0.295700			0.147850	+	0.989010i	$0.452765\pi$
$18$		0			0
$19$	18676.2			0.624670			0.312335	−	0.949972i	$-0.398889\pi$
$19$	18676.2			0.624670			0.312335	+	0.949972i	$0.398889\pi$
$20$	5093.69	+	8822.53i	0.142373	+	0.246597i
$21$		0			0
$22$	443.281	−	767.786i	0.00887565	−	0.0153731i
$23$	12139.5	−	21026.3i	0.208043	−	0.360342i	−0.743055	−	0.669231i	$-0.766624\pi$
$23$	12139.5	−	21026.3i	0.208043	−	0.360342i	0.951098	+	0.308889i	$0.0999571\pi$
$24$		0			0
$25$	−81995.2	−	142020.i	−1.04954	−	1.81785i
$26$	−73429.1			−0.819335
$27$		0			0
$28$	15830.6			0.136284
$29$	43378.1	+	75133.0i	0.330276	+	0.572055i	0.982566	−	0.185914i	$-0.0595247\pi$
$29$	43378.1	+	75133.0i	0.330276	+	0.572055i	−0.652290	+	0.757970i	$0.726191\pi$
$30$		0			0
$31$	−105890.	+	183406.i	−0.638392	+	1.10573i	0.347394	+	0.937719i	$0.387067\pi$
$31$	−105890.	+	183406.i	−0.638392	+	1.10573i	−0.985786	+	0.168008i	$0.946267\pi$
$32$	−29702.8	+	51446.7i	−0.160241	+	0.277545i
$33$		0			0
$34$	36521.9	+	63257.8i	0.159359	+	0.276018i
$35$	−376234.			−1.48327
$36$		0			0
$37$	−327978.			−1.06448			−0.532242	−	0.846592i	$-0.678650\pi$
$37$	−327978.			−1.06448			−0.532242	+	0.846592i	$0.678650\pi$
$38$	113873.	+	197233.i	0.336648	+	0.583092i
$39$		0			0
$40$	321904.	−	557554.i	0.795273	−	1.37745i
$41$	196036.	−	339545.i	0.444214	−	0.769402i	−0.553783	−	0.832661i	$-0.686816\pi$
$41$	196036.	−	339545.i	0.444214	−	0.769402i	0.997997	+	0.0632592i	$0.0201495\pi$
$42$		0			0
$43$	343611.	+	595152.i	0.659064	+	1.14153i	0.980858	+	0.194723i	$0.0623809\pi$
$43$	343611.	+	595152.i	0.659064	+	1.14153i	−0.321794	+	0.946810i	$0.604286\pi$
$44$	1505.22			0.00266388
$45$		0			0
$46$	296069.			0.448477
$47$	320755.	+	555563.i	0.450641	+	0.780533i	0.998426	−	0.0560862i	$-0.0178622\pi$
$47$	320755.	+	555563.i	0.450641	+	0.780533i	−0.547785	+	0.836619i	$0.684529\pi$
$48$		0			0
$49$	119448.	−	206890.i	0.145042	−	0.251220i
$50$	999884.	−	1.73185e6i	1.13124	−	1.95936i
$51$		0			0
$52$	−62334.5	−	107966.i	−0.0614776	−	0.106482i
$53$	814485.			0.751480			0.375740	−	0.926725i	$-0.377389\pi$
$53$	814485.			0.751480			0.375740	+	0.926725i	$0.377389\pi$
$54$		0			0
$55$	−35773.3			−0.0289928
$56$	−500221.	−	866408.i	−0.380631	−	0.659272i
$57$		0			0
$58$	−528971.	+	916204.i	−0.355986	+	0.616587i
$59$	−1.25863e6	+	2.18002e6i	−0.797843	+	1.38190i	0.123176	+	0.992385i	$0.460692\pi$
$59$	−1.25863e6	+	2.18002e6i	−0.797843	+	1.38190i	−0.921018	+	0.389519i	$0.872641\pi$
$60$		0			0
$61$	221621.	+	383858.i	0.125013	+	0.216529i	0.921738	−	0.387813i	$-0.126769\pi$
$61$	221621.	+	383858.i	0.125013	+	0.216529i	−0.796725	+	0.604342i	$0.793436\pi$
$62$	−2.58252e6			−1.37617
$63$		0			0
$64$	1.65708e6			0.790157
$65$	1.48145e6	+	2.56595e6i	0.669101	+	1.15892i
$66$		0			0
$67$	−296048.	+	512770.i	−0.120254	+	0.208286i	−0.919868	−	0.392228i	$-0.871704\pi$
$67$	−296048.	+	512770.i	−0.120254	+	0.208286i	0.799614	+	0.600515i	$0.205038\pi$
$68$	−62007.4	+	107400.i	−0.0239145	+	0.0414212i
$69$		0			0
$70$	−2.29398e6	−	3.97329e6i	−0.799367	−	1.38454i
$71$	−1.48821e6			−0.493469			−0.246734	−	0.969083i	$-0.579357\pi$
$71$	−1.48821e6			−0.493469			−0.246734	+	0.969083i	$0.579357\pi$
$72$		0			0
$73$	−5.41341e6			−1.62870			−0.814350	−	0.580374i	$-0.802906\pi$
$73$	−5.41341e6			−1.62870			−0.814350	+	0.580374i	$0.802906\pi$
$74$	−1.99975e6	−	3.46367e6i	−0.573674	−	0.993633i
$75$		0			0
$76$	−193334.	+	334865.i	−0.0505198	+	0.0875029i
$77$	−27794.9	+	48142.2i	−0.00693821	+	0.0120173i
$78$		0			0
$79$	444736.	+	770305.i	0.101486	+	0.175779i	0.912297	−	0.409529i	$-0.134307\pi$
$79$	444736.	+	770305.i	0.101486	+	0.175779i	−0.810811	+	0.585308i	$0.800974\pi$
$80$	9.15485e6			1.99911
$81$		0			0
$82$	4.78109e6			0.957588
$83$	−1.69323e6	−	2.93276e6i	−0.325044	−	0.562993i	0.656477	−	0.754346i	$-0.272046\pi$
$83$	−1.69323e6	−	2.93276e6i	−0.325044	−	0.562993i	−0.981521	+	0.191353i	$0.938713\pi$
$84$		0			0
$85$	1.47368e6	−	2.55249e6i	0.260278	−	0.450814i
$86$	−4.19014e6	+	7.25754e6i	−0.710369	+	1.23040i
$87$		0			0
$88$	−47562.4	−	82380.4i	−0.00744002	−	0.0128865i
$89$	−1.17388e6			−0.176506			−0.0882531	−	0.996098i	$-0.528128\pi$
$89$	−1.17388e6			−0.176506			−0.0882531	+	0.996098i	$0.528128\pi$
$90$		0			0
$91$	4.60420e6			0.640485
$92$	251335.	+	435325.i	0.0336508	+	0.0582849i
$93$		0			0
$94$	−3.91142e6	+	6.77477e6i	−0.485721	+	0.841293i
$95$	4.59483e6	−	7.95847e6i	0.549840	−	0.952351i
$96$		0			0
$97$	4.30014e6	+	7.44806e6i	0.478390	+	0.828595i	0.999693	−	0.0247763i	$-0.00788736\pi$
$97$	4.30014e6	+	7.44806e6i	0.478390	+	0.828595i	−0.521303	+	0.853371i	$0.674554\pi$
$98$	2.91320e6			0.312665
$99$		0			0
$100$	3.39523e6			0.339523
$101$	−3.28828e6	−	5.69546e6i	−0.317573	−	0.550052i	0.662408	−	0.749143i	$-0.269534\pi$
$101$	−3.28828e6	−	5.69546e6i	−0.317573	−	0.550052i	−0.979981	+	0.199091i	$0.936201\pi$
$102$		0			0
$103$	2.66960e6	−	4.62388e6i	0.240722	−	0.416943i	−0.720198	−	0.693768i	$-0.755949\pi$
$103$	2.66960e6	−	4.62388e6i	0.240722	−	0.416943i	0.960920	+	0.276826i	$0.0892824\pi$
$104$	−3.93933e6	+	6.82312e6i	−0.343404	+	0.594793i
$105$		0			0
$106$	4.96609e6	+	8.60151e6i	0.404989	+	0.701462i
$107$	1.38339e7			1.09170			0.545849	−	0.837884i	$-0.316207\pi$
$107$	1.38339e7			1.09170			0.545849	+	0.837884i	$0.316207\pi$
$108$		0			0
$109$	−1.19308e7			−0.882420			−0.441210	−	0.897404i	$-0.645451\pi$
$109$	−1.19308e7			−0.882420			−0.441210	+	0.897404i	$0.645451\pi$
$110$	−218118.	−	377791.i	−0.0156249	−	0.0270631i
$111$		0			0
$112$	7.11307e6	−	1.23202e7i	0.478403	−	0.828618i
$113$	1.25307e6	−	2.17039e6i	0.0816962	−	0.141502i	−0.822282	−	0.569080i	$-0.807300\pi$
$113$	1.25307e6	−	2.17039e6i	0.0816962	−	0.141502i	0.903979	+	0.427578i	$0.140633\pi$
$114$		0			0
$115$	−5.97328e6	−	1.03460e7i	−0.366244	−	0.634353i
$116$	−1.79619e6			−0.106844
$117$		0			0
$118$	−3.06966e7			−1.71990
$119$	−2.29002e6	−	3.96643e6i	−0.124573	−	0.215767i
$120$		0			0
$121$	9.74094e6	−	1.68718e7i	0.499864	−	0.865791i
$122$	−2.70254e6	+	4.68093e6i	−0.134745	+	0.233385i
$123$		0			0
$124$	−2.19232e6	−	3.79722e6i	−0.103259	−	0.178850i
$125$	−4.22503e7			−1.93484
$126$		0			0
$127$	2.27606e7			0.985986			0.492993	−	0.870033i	$-0.335903\pi$
$127$	2.27606e7			0.985986			0.492993	+	0.870033i	$0.335903\pi$
$128$	1.39055e7	+	2.40851e7i	0.586074	+	1.01511i
$129$		0			0
$130$	−1.80655e7	+	3.12903e7i	−0.721187	+	1.24913i
$131$	−3.88505e6	+	6.72910e6i	−0.150990	+	0.261522i	−0.931592	−	0.363507i	$-0.881579\pi$
$131$	−3.88505e6	+	6.72910e6i	−0.150990	+	0.261522i	0.780602	+	0.625028i	$0.214913\pi$
$132$		0			0
$133$	−7.14011e6	−	1.23670e7i	−0.263162	−	0.455811i
$134$	−7.22026e6			−0.259231
$135$		0			0
$136$	7.83731e6			0.267166
$137$	1.22187e7	+	2.11634e7i	0.405979	+	0.703176i	0.994435	−	0.105353i	$-0.0335973\pi$
$137$	1.22187e7	+	2.11634e7i	0.405979	+	0.703176i	−0.588456	+	0.808529i	$0.700264\pi$
$138$		0			0
$139$	−2.68721e7	+	4.65439e7i	−0.848693	+	1.46998i	0.0336822	+	0.999433i	$0.489277\pi$
$139$	−2.68721e7	+	4.65439e7i	−0.848693	+	1.46998i	−0.882375	+	0.470547i	$0.844057\pi$
$140$	3.89475e6	−	6.74590e6i	0.119959	−	0.207774i
$141$		0			0
$142$	−9.07392e6	−	1.57165e7i	−0.265941	−	0.460624i
$143$	437779.			0.0125193
$144$		0			0
$145$	4.26886e7			1.16285
$146$	−3.30067e7	−	5.71693e7i	−0.877743	−	1.52029i
$147$		0			0
$148$	3.39521e6	−	5.88067e6i	0.0860896	−	0.149112i
$149$	3.89683e7	−	6.74951e7i	0.965072	−	1.67155i	0.255651	−	0.966769i	$-0.417710\pi$
$149$	3.89683e7	−	6.74951e7i	0.965072	−	1.67155i	0.709421	−	0.704785i	$-0.248956\pi$
$150$		0			0
$151$	8.31411e6	+	1.44005e7i	0.196515	+	0.340375i	0.947396	−	0.320063i	$-0.103704\pi$
$151$	8.31411e6	+	1.44005e7i	0.196515	+	0.340375i	−0.750881	+	0.660438i	$0.770371\pi$
$152$	2.44362e7			0.564392
$153$		0			0
$154$	−677885.			−0.0149566
$155$	5.21032e7	+	9.02454e7i	1.12384	+	1.94654i
$156$		0			0
$157$	4.17495e7	−	7.23123e7i	0.860999	−	1.49129i	−0.00996687	−	0.999950i	$-0.503173\pi$
$157$	4.17495e7	−	7.23123e7i	0.860999	−	1.49129i	0.870966	−	0.491344i	$-0.163494\pi$
$158$	−5.42329e6	+	9.39342e6i	−0.109386	+	0.189463i
$159$		0			0
$160$	1.46153e7	+	2.53145e7i	0.282091	+	0.488595i
$161$	−1.85643e7			−0.350580
$162$		0			0
$163$	4.57178e6			0.0826855			0.0413427	−	0.999145i	$-0.486836\pi$
$163$	4.57178e6			0.0826855			0.0413427	+	0.999145i	$0.486836\pi$
$164$	4.05871e6	+	7.02988e6i	0.0718512	+	0.124450i
$165$		0			0
$166$	2.06480e7	−	3.57633e7i	0.350347	−	0.606819i
$167$	2.65043e7	−	4.59068e7i	0.440361	−	0.762728i	−0.557355	−	0.830274i	$-0.688184\pi$
$167$	2.65043e7	−	4.59068e7i	0.440361	−	0.762728i	0.997716	+	0.0675463i	$0.0215170\pi$
$168$		0			0
$169$	1.32448e7	+	2.29407e7i	0.211078	+	0.365598i
$170$	3.59413e7			0.561078
$171$		0			0
$172$	−1.42282e7			−0.213206
$173$	−5.34551e7	−	9.25870e7i	−0.784925	−	1.35953i	−0.929044	−	0.369969i	$-0.879368\pi$
$173$	−5.34551e7	−	9.25870e7i	−0.784925	−	1.35953i	0.144119	−	0.989560i	$-0.453965\pi$
$174$		0			0
$175$	−6.26953e7	+	1.08592e8i	−0.884305	+	1.53166i
$176$	676330.	−	1.17144e6i	0.00935113	−	0.0161966i
$177$		0			0
$178$	−7.15742e6	−	1.23970e7i	−0.0951232	−	0.164758i
$179$	−7.20180e7			−0.938545			−0.469273	−	0.883053i	$-0.655484\pi$
$179$	−7.20180e7			−0.938545			−0.469273	+	0.883053i	$0.655484\pi$
$180$		0			0
$181$	−1.33646e8			−1.67525			−0.837626	−	0.546245i	$-0.816057\pi$
$181$	−1.33646e8			−1.67525			−0.837626	+	0.546245i	$0.816057\pi$
$182$	2.80727e7	+	4.86234e7i	0.345172	+	0.597855i
$183$		0			0
$184$	1.58835e7	−	2.75111e7i	0.187968	−	0.325570i
$185$	−8.06912e7	+	1.39761e8i	−0.936969	+	1.62288i
$186$		0			0
$187$	−217741.	−	377139.i	−0.00243498	−	0.00421750i
$188$	−1.32817e7			−0.145781
$189$		0			0
$190$	1.12063e8			1.18528
$191$	4.43499e7	+	7.68163e7i	0.460549	+	0.797695i	0.998988	−	0.0449697i	$-0.0143191\pi$
$191$	4.43499e7	+	7.68163e7i	0.460549	+	0.797695i	−0.538439	+	0.842664i	$0.680986\pi$
$192$		0			0
$193$	8.42985e6	−	1.46009e7i	0.0844052	−	0.146194i	−0.820732	−	0.571313i	$-0.806434\pi$
$193$	8.42985e6	−	1.46009e7i	0.0844052	−	0.146194i	0.905138	+	0.425119i	$0.139768\pi$
$194$	−5.24377e7	+	9.08248e7i	−0.515630	+	0.893097i
$195$		0			0
$196$	2.47304e6	+	4.28343e6i	0.0234603	+	0.0406345i
$197$	−2.48035e7			−0.231143			−0.115572	−	0.993299i	$-0.536870\pi$
$197$	−2.48035e7			−0.231143			−0.115572	+	0.993299i	$0.536870\pi$
$198$		0			0
$199$	−9.25824e7			−0.832804			−0.416402	−	0.909181i	$-0.636709\pi$
$199$	−9.25824e7			−0.832804			−0.416402	+	0.909181i	$0.636709\pi$
$200$	−1.07284e8	−	1.85821e8i	−0.948263	−	1.64244i
$201$		0			0
$202$	4.00986e7	−	6.94528e7i	0.342294	−	0.592871i
$203$	3.31678e7	−	5.74484e7i	0.278279	−	0.481994i
$204$		0			0
$205$	−9.64600e7	−	1.67074e8i	−0.782004	−	1.35447i
$206$	6.51084e7			0.518922
$207$		0			0
$208$	−1.12033e8			−0.863228
$209$	−678901.	−	1.17589e6i	−0.00514392	−	0.00890953i
$210$		0			0
$211$	1.28115e7	−	2.21902e7i	0.0938883	−	0.162619i	−0.815256	−	0.579101i	$-0.803404\pi$
$211$	1.28115e7	−	2.21902e7i	0.0938883	−	0.162619i	0.909144	+	0.416482i	$0.136737\pi$
$212$	−8.43149e6	+	1.46038e7i	−0.0607755	+	0.105266i
$213$		0			0
$214$	8.43484e7	+	1.46096e8i	0.588340	+	1.01904i
$215$	3.38149e8			2.32046
$216$		0			0
$217$	1.61931e8			1.07577
$218$	−7.27443e7	−	1.25997e8i	−0.475556	−	0.823686i
$219$		0			0
$220$	370323.	−	641418.i	0.00234478	−	0.00406127i
$221$	−1.80343e7	+	3.12363e7i	−0.112390	+	0.194664i
$222$		0			0
$223$	3.29902e7	+	5.71407e7i	0.199213	+	0.345047i	0.948274	−	0.317454i	$-0.102828\pi$
$223$	3.29902e7	+	5.71407e7i	0.199213	+	0.345047i	−0.749060	+	0.662502i	$0.769495\pi$
$224$	4.54228e7			0.270026
$225$		0			0
$226$	3.05610e7			0.176112
$227$	7.69680e7	+	1.33313e8i	0.436737	+	0.756451i	0.997436	−	0.0715693i	$-0.0228007\pi$
$227$	7.69680e7	+	1.33313e8i	0.436737	+	0.756451i	−0.560699	+	0.828020i	$0.689467\pi$
$228$		0			0
$229$	−1.17115e8	+	2.02849e8i	−0.644448	+	1.11622i	0.339981	+	0.940432i	$0.389580\pi$
$229$	−1.17115e8	+	2.02849e8i	−0.644448	+	1.11622i	−0.984429	+	0.175784i	$0.943754\pi$
$230$	7.28406e7	−	1.26164e8i	0.394754	−	0.683734i
$231$		0			0
$232$	5.67565e7	+	9.83051e7i	0.298406	+	0.516854i
$233$	−3.26423e8			−1.69058			−0.845289	−	0.534310i	$-0.820571\pi$
$233$	−3.26423e8			−1.69058			−0.845289	+	0.534310i	$0.820571\pi$
$234$		0			0
$235$	3.15656e8			1.58663
$236$	−2.60586e7	−	4.51348e7i	−0.129050	−	0.223521i
$237$		0			0
$238$	2.79254e7	−	4.83683e7i	0.134270	−	0.232563i
$239$	3.21140e6	−	5.56230e6i	0.0152160	−	0.0263549i	−0.858317	−	0.513120i	$-0.828490\pi$
$239$	3.21140e6	−	5.56230e6i	0.0152160	−	0.0263549i	0.873533	+	0.486765i	$0.161823\pi$
$240$		0			0
$241$	−1.10637e7	−	1.91628e7i	−0.0509142	−	0.0881860i	0.839445	−	0.543445i	$-0.182880\pi$
$241$	−1.10637e7	−	1.91628e7i	−0.0509142	−	0.0881860i	−0.890359	+	0.455259i	$0.849547\pi$
$242$	2.37570e8			1.07755
$243$		0			0
$244$	−9.17681e6			−0.0404415
$245$	−5.87747e7	−	1.01801e8i	−0.255334	−	0.442252i
$246$		0			0
$247$	−5.62296e7	+	9.73925e7i	−0.237425	+	0.411231i
$248$	−1.38547e8	+	2.39971e8i	−0.576790	+	0.999029i
$249$		0			0
$250$	−2.57609e8	−	4.46191e8i	−1.04273	−	1.80606i
$251$	−1.36869e8			−0.546320			−0.273160	−	0.961969i	$-0.588069\pi$
$251$	−1.36869e8			−0.546320			−0.273160	+	0.961969i	$0.588069\pi$
$252$		0			0
$253$	−1.76514e6			−0.00685264
$254$	1.38776e8	+	2.40367e8i	0.531370	+	0.920359i
$255$		0			0
$256$	−6.35166e7	+	1.10014e8i	−0.236618	+	0.409834i
$257$	7.45226e7	−	1.29077e8i	0.273856	−	0.474332i	−0.695990	−	0.718051i	$-0.745034\pi$
$257$	7.45226e7	−	1.29077e8i	0.273856	−	0.474332i	0.969846	+	0.243719i	$0.0783676\pi$
$258$		0			0
$259$	1.25390e8	+	2.17181e8i	0.448449	+	0.776736i
$260$	−6.13436e7			−0.216453
$261$		0			0
$262$	−9.47518e7			−0.325487
$263$	−7.57912e7	−	1.31274e8i	−0.256906	−	0.444974i	0.708506	−	0.705705i	$-0.249370\pi$
$263$	−7.57912e7	−	1.31274e8i	−0.256906	−	0.444974i	−0.965411	+	0.260731i	$0.916036\pi$
$264$		0			0
$265$	2.00385e8	−	3.47076e8i	0.661460	−	1.14568i
$266$	8.70695e7	−	1.50809e8i	0.283648	−	0.491293i
$267$		0			0
$268$	−6.12933e6	−	1.06163e7i	−0.0194510	−	0.0336901i
$269$	2.38302e8			0.746440			0.373220	−	0.927743i	$-0.378254\pi$
$269$	2.38302e8			0.746440			0.373220	+	0.927743i	$0.378254\pi$
$270$		0			0
$271$	−3.13440e8			−0.956670			−0.478335	−	0.878178i	$-0.658759\pi$
$271$	−3.13440e8			−0.956670			−0.478335	+	0.878178i	$0.658759\pi$
$272$	5.57227e7	+	9.65145e7i	0.167896	+	0.290805i
$273$		0			0
$274$	−1.49000e8	+	2.58076e8i	−0.437582	+	0.757915i
$275$	−5.96124e6	+	1.03252e7i	−0.0172851	+	0.0299387i
$276$		0			0
$277$	−1.66427e8	−	2.88261e8i	−0.470485	−	0.814903i	0.528946	−	0.848656i	$-0.322588\pi$
$277$	−1.66427e8	−	2.88261e8i	−0.470485	−	0.814903i	−0.999430	+	0.0337524i	$0.989254\pi$
$278$	−6.55380e8			−1.82952
$279$		0			0
$280$	−4.92270e8			−1.34014
$281$	4.94112e7	+	8.55828e7i	0.132848	+	0.230099i	0.924773	−	0.380519i	$-0.124255\pi$
$281$	4.94112e7	+	8.55828e7i	0.132848	+	0.230099i	−0.791926	+	0.610618i	$0.790921\pi$
$282$		0			0
$283$	2.53690e8	−	4.39404e8i	0.665351	−	1.15242i	−0.313839	−	0.949476i	$-0.601615\pi$
$283$	2.53690e8	−	4.39404e8i	0.665351	−	1.15242i	0.979190	−	0.202946i	$-0.0650514\pi$
$284$	1.54058e7	−	2.66837e7i	0.0399090	−	0.0691244i
$285$		0			0
$286$	2.66923e6	+	4.62325e6i	0.00674692	+	0.0116860i
$287$	−2.99787e8			−0.748559
$288$		0			0
$289$	−3.74459e8			−0.912562
$290$	2.60281e8	+	4.50820e8i	0.626686	+	1.08545i
$291$		0			0
$292$	5.60393e7	−	9.70628e7i	0.131720	−	0.228146i
$293$	6.24969e7	−	1.08248e8i	0.145152	−	0.251410i	−0.784278	−	0.620410i	$-0.786966\pi$
$293$	6.24969e7	−	1.08248e8i	0.145152	−	0.251410i	0.929429	+	0.369000i	$0.120300\pi$
$294$		0			0
$295$	6.19313e8	+	1.07268e9i	1.40454	+	2.43273i
$296$	−4.29132e8			−0.961766
$297$		0			0
$298$	9.50392e8			2.08040
$299$	7.30985e7	+	1.26610e8i	0.158146	+	0.273918i
$300$		0			0
$301$	2.62733e8	−	4.55066e8i	0.555305	−	0.961816i
$302$	−1.01386e8	+	1.75605e8i	−0.211813	+	0.366871i
$303$		0			0
$304$	1.73739e8	+	3.00925e8i	0.354683	+	0.614329i
$305$	2.18098e8			0.440152
$306$		0			0
$307$	−2.20914e8			−0.435751			−0.217875	−	0.975977i	$-0.569913\pi$
$307$	−2.20914e8			−0.435751			−0.217875	+	0.975977i	$0.569913\pi$
$308$	−575462.	−	996729.i	−0.00112225	−	0.00194379i
$309$		0			0
$310$	−6.35368e8	+	1.10049e9i	−1.21132	+	2.09807i
$311$	1.30787e8	−	2.26529e8i	0.246548	−	0.427034i	−0.716018	−	0.698082i	$-0.754037\pi$
$311$	1.30787e8	−	2.26529e8i	0.246548	−	0.427034i	0.962566	+	0.271048i	$0.0873703\pi$
$312$		0			0
$313$	−4.13617e8	−	7.16405e8i	−0.762418	−	1.32055i	−0.941601	−	0.336731i	$-0.890679\pi$
$313$	−4.13617e8	−	7.16405e8i	−0.762418	−	1.32055i	0.179183	−	0.983816i	$-0.442654\pi$
$314$	1.01822e9			1.85605
$315$		0			0
$316$	−1.84155e7			−0.0328306
$317$	−4.16356e8	−	7.21150e8i	−0.734104	−	1.27151i	−0.955115	−	0.296234i	$-0.904269\pi$
$317$	−4.16356e8	−	7.21150e8i	−0.734104	−	1.27151i	0.221012	−	0.975271i	$-0.429064\pi$
$318$		0			0
$319$	3.15369e6	−	5.46235e6i	0.00543940	−	0.00942132i
$320$	4.07685e8	−	7.06131e8i	0.695504	−	1.20465i
$321$		0			0
$322$	−1.13190e8	−	1.96051e8i	−0.188936	−	0.327246i
$323$	1.11869e8			0.184715
$324$		0			0
$325$	9.87473e8			1.59564
$326$	2.78751e7	+	4.82811e7i	0.0445610	+	0.0771820i
$327$		0			0
$328$	2.56496e8	−	4.44265e8i	0.401350	−	0.695158i
$329$	2.45256e8	−	4.24796e8i	0.379694	−	0.657650i
$330$		0			0
$331$	−3.34251e8	−	5.78940e8i	−0.506612	−	0.877477i	−0.999971	−	0.00765136i	$-0.997564\pi$
$331$	−3.34251e8	−	5.78940e8i	−0.506612	−	0.877477i	0.493359	−	0.869826i	$-0.335769\pi$
$332$	7.01128e7			0.105151
$333$		0			0
$334$	6.46410e8			0.949282
$335$	1.45671e8	+	2.52310e8i	0.211698	+	0.366671i
$336$		0			0
$337$	−4.65964e8	+	8.07074e8i	−0.663205	+	1.14871i	0.316563	+	0.948571i	$0.397471\pi$
$337$	−4.65964e8	+	8.07074e8i	−0.663205	+	1.14871i	−0.979769	+	0.200134i	$0.935862\pi$
$338$	−1.61513e8	+	2.79749e8i	−0.227509	+	0.394058i
$339$		0			0
$340$	3.05109e7	+	5.28464e7i	0.0420996	+	0.0729187i
$341$	1.53968e7			0.0210277
$342$		0			0
$343$	−8.12364e8			−1.08698
$344$	4.49586e8	+	7.78706e8i	0.595468	+	1.03138i
$345$		0			0
$346$	6.51854e8	−	1.12904e9i	0.846027	−	1.46536i
$347$	−5.45857e8	+	9.45452e8i	−0.701335	+	1.21475i	0.266662	+	0.963790i	$0.414079\pi$
$347$	−5.45857e8	+	9.45452e8i	−0.701335	+	1.21475i	−0.967998	+	0.250959i	$0.919254\pi$
$348$		0			0
$349$	4.85765e8	+	8.41369e8i	0.611698	+	1.05949i	0.990954	+	0.134200i	$0.0428466\pi$
$349$	4.85765e8	+	8.41369e8i	0.611698	+	1.05949i	−0.379256	+	0.925292i	$0.623820\pi$
$350$	−1.52907e9			−1.90629
$351$		0			0
$352$	4.31892e6			0.00527808
$353$	−2.93516e8	−	5.08385e8i	−0.355157	−	0.615150i	0.631988	−	0.774978i	$-0.282239\pi$
$353$	−2.93516e8	−	5.08385e8i	−0.355157	−	0.615150i	−0.987145	+	0.159828i	$0.948906\pi$
$354$		0			0
$355$	−3.66138e8	+	6.34170e8i	−0.434356	+	0.752326i
$356$	1.21520e7	−	2.10478e7i	0.0142749	−	0.0247248i
$357$		0			0
$358$	−4.39109e8	−	7.60559e8i	−0.505803	−	0.876077i
$359$	1.33975e9			1.52824			0.764121	−	0.645073i	$-0.223173\pi$
$359$	1.33975e9			1.52824			0.764121	+	0.645073i	$0.223173\pi$
$360$		0			0
$361$	−5.45072e8			−0.609788
$362$	−8.14866e8	−	1.41139e9i	−0.902830	−	1.56375i
$363$		0			0
$364$	−4.76623e7	+	8.25535e7i	−0.0517989	+	0.0897183i
$365$	−1.33184e9	+	2.30682e9i	−1.43360	+	2.48306i
$366$		0			0
$367$	−2.85734e8	−	4.94906e8i	−0.301739	−	0.522627i	0.674791	−	0.738009i	$-0.264234\pi$
$367$	−2.85734e8	−	4.94906e8i	−0.301739	−	0.522627i	−0.976530	+	0.215382i	$0.930900\pi$
$368$	4.51722e8			0.472503
$369$		0			0
$370$	−1.96797e9			−2.01981
$371$	−3.11387e8	−	5.39337e8i	−0.316586	−	0.548342i
$372$		0			0
$373$	−7.53182e7	+	1.30455e8i	−0.0751483	+	0.130161i	−0.901151	−	0.433506i	$-0.857276\pi$
$373$	−7.53182e7	+	1.30455e8i	−0.0751483	+	0.130161i	0.826002	+	0.563667i	$0.190610\pi$
$374$	2.65523e6	−	4.59899e6i	0.00262453	−	0.00454581i
$375$		0			0
$376$	4.19680e8	+	7.26907e8i	0.407156	+	0.705215i
$377$	−5.22405e8			−0.502126
$378$		0			0
$379$	1.71164e9			1.61501			0.807507	−	0.589859i	$-0.200817\pi$
$379$	1.71164e9			1.61501			0.807507	+	0.589859i	$0.200817\pi$
$380$	9.51307e7	+	1.64771e8i	0.0889361	+	0.154042i
$381$		0			0
$382$	−5.40822e8	+	9.36730e8i	−0.496400	+	0.859791i
$383$	4.58409e8	−	7.93987e8i	0.416924	−	0.722134i	−0.578704	−	0.815538i	$-0.696441\pi$
$383$	4.58409e8	−	7.93987e8i	0.416924	−	0.722134i	0.995628	+	0.0934036i	$0.0297747\pi$
$384$		0			0
$385$	1.36765e7	+	2.36885e7i	0.0122142	+	0.0211556i
$386$	2.05594e8			0.181951
$387$		0			0
$388$	−1.78059e8			−0.154758
$389$	7.94949e8	+	1.37689e9i	0.684725	+	1.18598i	0.973523	+	0.228588i	$0.0734108\pi$
$389$	7.94949e8	+	1.37689e9i	0.684725	+	1.18598i	−0.288799	+	0.957390i	$0.593256\pi$
$390$		0			0
$391$	7.27149e7	−	1.25946e8i	0.0615184	−	0.106553i
$392$	1.56288e8	−	2.70698e8i	0.131046	−	0.226978i
$393$		0			0
$394$	−1.51232e8	−	2.61941e8i	−0.124568	−	0.215758i
$395$	4.37666e8			0.357317
$396$		0			0
$397$	6.55542e8			0.525816			0.262908	−	0.964821i	$-0.415318\pi$
$397$	6.55542e8			0.525816			0.262908	+	0.964821i	$0.415318\pi$
$398$	−5.64494e8	−	9.77733e8i	−0.448817	−	0.777373i
$399$		0			0
$400$	1.52556e9	−	2.64234e9i	1.19184	−	2.06433i
$401$	−2.56666e8	+	4.44558e8i	−0.198775	+	0.344289i	−0.948132	−	0.317878i	$-0.897030\pi$
$401$	−2.56666e8	+	4.44558e8i	−0.198775	+	0.344289i	0.749356	+	0.662167i	$0.230363\pi$
$402$		0			0
$403$	−6.37618e8	−	1.10439e9i	−0.485280	−	0.840530i
$404$	1.36160e8			0.102734
$405$		0			0
$406$	8.08925e8			0.599884
$407$	1.19224e7	+	2.06502e7i	0.00876563	+	0.0151825i
$408$		0			0
$409$	−3.72327e8	+	6.44890e8i	−0.269087	+	0.466073i	−0.968626	−	0.248521i	$-0.920055\pi$
$409$	−3.72327e8	+	6.44890e8i	−0.269087	+	0.466073i	0.699539	+	0.714594i	$0.253389\pi$
$410$	1.17627e9	−	2.03737e9i	0.842879	−	1.45991i
$411$		0			0
$412$	5.52710e7	+	9.57322e7i	0.0389365	+	0.0674400i
$413$	1.92476e9			1.34447
$414$		0			0
$415$	−1.66631e9			−1.14443
$416$	−1.78856e8	−	3.09788e8i	−0.121808	−	0.210979i
$417$		0			0
$418$	8.27880e6	−	1.43393e7i	0.00554435	−	0.00960309i
$419$	−1.45041e8	+	2.51218e8i	−0.0963256	+	0.166841i	−0.910161	−	0.414255i	$-0.864042\pi$
$419$	−1.45041e8	+	2.51218e8i	−0.0963256	+	0.166841i	0.813836	+	0.581095i	$0.197376\pi$
$420$		0			0
$421$	1.47482e9	+	2.55446e9i	0.963277	+	1.66844i	0.714174	+	0.699968i	$0.246802\pi$
$421$	1.47482e9	+	2.55446e9i	0.963277	+	1.66844i	0.249103	+	0.968477i	$0.419864\pi$
$422$	3.12458e8			0.202394
$423$		0			0
$424$	1.06568e9			0.678966
$425$	−4.91146e8	−	8.50690e8i	−0.310348	−	0.537539i
$426$		0			0
$427$	1.69456e8	−	2.93507e8i	0.105332	−	0.182440i
$428$	−1.43208e8	+	2.48043e8i	−0.0882905	+	0.152924i
$429$		0			0
$430$	2.06177e9	+	3.57109e9i	1.25055	+	2.16601i
$431$	−2.38896e9			−1.43727			−0.718636	−	0.695386i	$-0.755233\pi$
$431$	−2.38896e9			−1.43727			−0.718636	+	0.695386i	$0.755233\pi$
$432$		0			0
$433$	−7.65843e8			−0.453348			−0.226674	−	0.973971i	$-0.572785\pi$
$433$	−7.65843e8			−0.453348			−0.226674	+	0.973971i	$0.572785\pi$
$434$	9.87327e8	+	1.71010e9i	0.579758	+	1.00417i
$435$		0			0
$436$	1.23506e8	−	2.13919e8i	0.0713652	−	0.123608i
$437$	2.26720e8	−	3.92690e8i	0.129958	−	0.225095i
$438$		0			0
$439$	−7.30743e8	−	1.26568e9i	−0.412229	−	0.714002i	0.582904	−	0.812541i	$-0.301916\pi$
$439$	−7.30743e8	−	1.26568e9i	−0.412229	−	0.714002i	−0.995133	+	0.0985390i	$0.968583\pi$
$440$	−4.68063e7			−0.0261951
$441$		0			0
$442$	−4.39835e8			−0.242277
$443$	5.28061e8	+	9.14628e8i	0.288583	+	0.499841i	0.973472	−	0.228807i	$-0.0734825\pi$
$443$	5.28061e8	+	9.14628e8i	0.288583	+	0.499841i	−0.684889	+	0.728648i	$0.740149\pi$
$444$		0			0
$445$	−2.88806e8	+	5.00227e8i	−0.155363	+	0.269096i
$446$	−4.02297e8	+	6.96798e8i	−0.214721	+	0.371907i
$447$		0			0
$448$	−6.33520e8	−	1.09729e9i	−0.332880	−	0.576564i
$449$	1.04312e9			0.543844			0.271922	−	0.962319i	$-0.412341\pi$
$449$	1.04312e9			0.543844			0.271922	+	0.962319i	$0.412341\pi$
$450$		0			0
$451$	−2.85046e7			−0.0146318
$452$	2.59434e7	+	4.49354e7i	0.0132143	+	0.0228878i
$453$		0			0
$454$	−9.38581e8	+	1.62567e9i	−0.470735	+	0.815336i
$455$	1.13275e9	−	1.96198e9i	0.563761	−	0.976463i
$456$		0			0
$457$	−5.50466e8	−	9.53435e8i	−0.269789	−	0.467288i	0.699018	−	0.715104i	$-0.253621\pi$
$457$	−5.50466e8	−	9.53435e8i	−0.269789	−	0.467288i	−0.968807	+	0.247816i	$0.920287\pi$
$458$	−2.85630e9			−1.38923
$459$		0			0
$460$	2.47340e8			0.118479
$461$	−7.03782e8	−	1.21899e9i	−0.334568	−	0.579489i	0.648834	−	0.760930i	$-0.275257\pi$
$461$	−7.03782e8	−	1.21899e9i	−0.334568	−	0.579489i	−0.983402	+	0.181441i	$0.941924\pi$
$462$		0			0
$463$	7.99386e8	−	1.38458e9i	0.374303	−	0.648312i	−0.615920	−	0.787809i	$-0.711215\pi$
$463$	7.99386e8	−	1.38458e9i	0.374303	−	0.648312i	0.990222	+	0.139497i	$0.0445487\pi$
$464$	−8.07069e8	+	1.39788e9i	−0.375057	+	0.649618i
$465$		0			0
$466$	−1.99027e9	−	3.44725e9i	−0.911090	−	1.57805i
$467$	−3.79693e9			−1.72514			−0.862568	−	0.505941i	$-0.831145\pi$
$467$	−3.79693e9			−1.72514			−0.862568	+	0.505941i	$0.831145\pi$
$468$		0			0
$469$	4.52729e8			0.202644
$470$	1.92462e9	+	3.33354e9i	0.855072	+	1.48103i
$471$		0			0
$472$	−1.64681e9	+	2.85237e9i	−0.720854	+	1.24856i
$473$	2.49813e7	−	4.32690e7i	0.0108543	−	0.0188002i
$474$		0			0
$475$	−1.53136e9	−	2.65239e9i	−0.655615	−	1.13556i
$476$	9.48244e7			0.0402991
$477$		0			0
$478$	7.83222e7			0.0328010
$479$	−4.24901e8	−	7.35951e8i	−0.176650	−	0.305967i	0.764081	−	0.645120i	$-0.223193\pi$
$479$	−4.24901e8	−	7.35951e8i	−0.176650	−	0.305967i	−0.940731	+	0.339153i	$0.889859\pi$
$480$		0			0
$481$	9.87466e8	−	1.71034e9i	0.404589	−	0.700769i
$482$	1.34915e8	−	2.33679e8i	0.0548776	−	0.0950508i
$483$		0			0
$484$	2.01675e8	+	3.49312e8i	0.0808525	+	0.140041i
$485$	4.23179e9			1.68433
$486$		0			0
$487$	4.25514e9			1.66941			0.834704	−	0.550699i	$-0.185639\pi$
$487$	4.25514e9			1.66941			0.834704	+	0.550699i	$0.185639\pi$
$488$	2.89972e8	+	5.02246e8i	0.112950	+	0.195635i
$489$		0			0
$490$	7.16724e8	−	1.24140e9i	0.275211	−	0.476679i
$491$	1.48617e8	−	2.57412e8i	0.0566608	−	0.0981394i	−0.836304	−	0.548266i	$-0.815288\pi$
$491$	1.48617e8	−	2.57412e8i	0.0566608	−	0.0981394i	0.892965	+	0.450127i	$0.148621\pi$
$492$		0			0
$493$	2.59832e8	+	4.50042e8i	0.0976626	+	0.169157i
$494$	−1.37137e9			−0.511814
$495$		0			0
$496$	−3.94025e9			−1.44990
$497$	5.68958e8	+	9.85465e8i	0.207890	+	0.360076i
$498$		0			0
$499$	−2.14364e9	+	3.71289e9i	−0.772323	+	1.33770i	0.163963	+	0.986466i	$0.447572\pi$
$499$	−2.14364e9	+	3.71289e9i	−0.772323	+	1.33770i	−0.936287	+	0.351237i	$0.885761\pi$
$500$	4.37372e8	−	7.57550e8i	0.156479	−	0.271029i
$501$		0			0
$502$	−8.34519e8	−	1.44543e9i	−0.294424	−	0.509957i
$503$	−4.73073e9			−1.65745			−0.828725	−	0.559657i	$-0.810933\pi$
$503$	−4.73073e9			−1.65745			−0.828725	+	0.559657i	$0.810933\pi$
$504$		0			0
$505$	−3.23601e9			−1.11812
$506$	−1.07624e7	−	1.86411e7i	−0.00369304	−	0.00639653i
$507$		0			0
$508$	−2.35616e8	+	4.08099e8i	−0.0797411	+	0.138116i
$509$	2.28469e9	−	3.95719e9i	0.767917	−	1.33007i	−0.170774	−	0.985310i	$-0.554627\pi$
$509$	2.28469e9	−	3.95719e9i	0.767917	−	1.33007i	0.938691	−	0.344761i	$-0.112040\pi$
$510$		0			0
$511$	2.06961e9	+	3.58466e9i	0.686143	+	1.18843i
$512$	2.01072e9			0.662073
$513$		0			0
$514$	1.81752e9			0.590348
$515$	−1.31358e9	−	2.27519e9i	−0.423772	−	0.733994i
$516$		0			0
$517$	2.33196e7	−	4.03908e7i	0.00742172	−	0.0128548i
$518$	−1.52905e9	+	2.64840e9i	−0.483358	+	0.837201i
$519$		0			0
$520$	1.93836e9	+	3.35733e9i	0.604535	+	1.04709i
$521$	6.44901e8			0.199784			0.0998920	−	0.994998i	$-0.468150\pi$
$521$	6.44901e8			0.199784			0.0998920	+	0.994998i	$0.468150\pi$
$522$		0			0
$523$	3.91443e9			1.19650			0.598250	−	0.801309i	$-0.295863\pi$
$523$	3.91443e9			1.19650			0.598250	+	0.801309i	$0.295863\pi$
$524$	−8.04355e7	−	1.39318e8i	−0.0244224	−	0.0423008i
$525$		0			0
$526$	9.24230e8	−	1.60081e9i	0.276904	−	0.479612i
$527$	−6.34272e8	+	1.09859e9i	−0.188772	+	0.326963i
$528$		0			0
$529$	1.40768e9	+	2.43817e9i	0.413436	+	0.716092i
$530$	4.88715e9			1.42590
$531$		0			0
$532$	2.95656e8			0.0851325
$533$	1.18044e9	+	2.04458e9i	0.337674	+	0.584869i
$534$		0			0
$535$	3.40351e9	−	5.89505e9i	0.960923	−	1.66437i
$536$	−3.87353e8	+	6.70915e8i	−0.108650	+	0.188188i
$537$		0			0
$538$	1.45298e9	+	2.51663e9i	0.402273	+	0.696758i
$539$	−1.73683e7			−0.00477746
$540$		0			0
$541$	−1.40475e9			−0.381424			−0.190712	−	0.981646i	$-0.561080\pi$
$541$	−1.40475e9			−0.381424			−0.190712	+	0.981646i	$0.561080\pi$
$542$	−1.91111e9	−	3.31014e9i	−0.515571	−	0.892995i
$543$		0			0
$544$	−1.77918e8	+	3.08163e8i	−0.0473831	+	0.0820699i
$545$	−2.93528e9	+	5.08405e9i	−0.776714	+	1.34531i
$546$		0			0
$547$	−9.00133e8	−	1.55908e9i	−0.235153	−	0.407297i	0.724164	−	0.689628i	$-0.242226\pi$
$547$	−9.00133e8	−	1.55908e9i	−0.235153	−	0.407297i	−0.959317	+	0.282330i	$0.908893\pi$
$548$	−5.05949e8			−0.131333
$549$		0			0
$550$	−1.45388e8			−0.0372613
$551$	8.10137e8	+	1.40320e9i	0.206314	+	0.357346i
$552$		0			0
$553$	3.40055e8	−	5.88992e8i	0.0855088	−	0.148106i
$554$	2.02948e9	−	3.51517e9i	0.507109	−	0.878339i
$555$		0			0
$556$	−5.56357e8	−	9.63639e8i	−0.137275	−	0.237768i
$557$	4.72476e9			1.15847			0.579237	−	0.815159i	$-0.303351\pi$
$557$	4.72476e9			1.15847			0.579237	+	0.815159i	$0.303351\pi$
$558$		0			0
$559$	−4.13813e9			−1.00199
$560$	−3.50000e9	−	6.06218e9i	−0.842190	−	1.45872i
$561$		0			0
$562$	−6.02541e8	+	1.04363e9i	−0.143189	+	0.248011i
$563$	3.54792e9	−	6.14517e9i	0.837903	−	1.45129i	−0.0537414	−	0.998555i	$-0.517115\pi$
$563$	3.54792e9	−	6.14517e9i	0.837903	−	1.45129i	0.891645	−	0.452736i	$-0.149552\pi$
$564$		0			0
$565$	−6.16577e8	−	1.06794e9i	−0.143820	−	0.249103i
$566$	6.18720e9			1.43429
$567$		0			0
$568$	−1.94719e9			−0.445851
$569$	8.39936e8	+	1.45481e9i	0.191141	+	0.331066i	0.945629	−	0.325249i	$-0.105448\pi$
$569$	8.39936e8	+	1.45481e9i	0.191141	+	0.331066i	−0.754488	+	0.656314i	$0.772115\pi$
$570$		0			0
$571$	−4.38381e8	+	7.59299e8i	−0.0985430	+	0.170681i	−0.911082	−	0.412226i	$-0.864752\pi$
$571$	−4.38381e8	+	7.59299e8i	−0.0985430	+	0.170681i	0.812539	+	0.582907i	$0.198085\pi$
$572$	−4.53186e6	+	7.84941e6i	−0.00101249	+	0.00175368i
$573$		0			0
$574$	−1.82786e9	−	3.16595e9i	−0.403415	−	0.698736i
$575$	−3.98153e9			−0.873398
$576$		0			0
$577$	2.89693e9			0.627801			0.313901	−	0.949456i	$-0.398364\pi$
$577$	2.89693e9			0.627801			0.313901	+	0.949456i	$0.398364\pi$
$578$	−2.28316e9	−	3.95454e9i	−0.491800	−	0.851822i
$579$		0			0
$580$	−4.41909e8	+	7.65409e8i	−0.0940448	+	0.162890i
$581$	−1.29468e9	+	2.24245e9i	−0.273871	+	0.474359i
$582$		0			0
$583$	−2.96075e7	−	5.12816e7i	−0.00618816	−	0.0107182i
$584$	−7.08298e9			−1.47154
$585$		0			0
$586$	1.52423e9			0.312902
$587$	4.41296e9	+	7.64348e9i	0.900527	+	1.55976i	0.826811	+	0.562480i	$0.190153\pi$
$587$	4.41296e9	+	7.64348e9i	0.900527	+	1.55976i	0.0737164	+	0.997279i	$0.476514\pi$
$588$		0			0
$589$	−1.97761e9	+	3.42533e9i	−0.398784	+	0.690714i
$590$	−7.55217e9	+	1.30807e10i	−1.51387	+	2.62211i
$591$		0			0
$592$	−3.05109e9	−	5.28465e9i	−0.604407	−	1.04686i
$593$	−9.92029e8			−0.195359			−0.0976794	−	0.995218i	$-0.531142\pi$
$593$	−9.92029e8			−0.195359			−0.0976794	+	0.995218i	$0.531142\pi$
$594$		0			0
$595$	−2.25362e9			−0.438602
$596$	8.06795e8	+	1.39741e9i	0.156099	+	0.270372i
$597$		0			0
$598$	−8.91394e8	+	1.54394e9i	−0.170457	+	0.295241i
$599$	−1.70026e9	+	2.94494e9i	−0.323238	+	0.559864i	−0.981154	−	0.193227i	$-0.938105\pi$
$599$	−1.70026e9	+	2.94494e9i	−0.323238	+	0.559864i	0.657916	+	0.753091i	$0.271438\pi$
$600$		0			0
$601$	1.81983e9	+	3.15203e9i	0.341956	+	0.592284i	0.984796	−	0.173716i	$-0.0555774\pi$
$601$	1.81983e9	+	3.15203e9i	0.341956	+	0.592284i	−0.642840	+	0.766000i	$0.722244\pi$
$602$	6.40775e9			1.19706
$603$		0			0
$604$	−3.44268e8			−0.0635723
$605$	−4.79305e9	−	8.30181e9i	−0.879971	−	1.52415i
$606$		0			0
$607$	1.98545e9	−	3.43890e9i	0.360328	−	0.624106i	−0.627687	−	0.778466i	$-0.715998\pi$
$607$	1.98545e9	−	3.43890e9i	0.360328	−	0.624106i	0.988015	+	0.154360i	$0.0493315\pi$
$608$	−5.54735e8	+	9.60828e8i	−0.100097	+	0.173374i
$609$		0			0
$610$	1.32979e9	+	2.30326e9i	0.237208	+	0.410855i
$611$	−3.86287e9			−0.685119
$612$		0			0
$613$	4.76405e7			0.00835342			0.00417671	−	0.999991i	$-0.498671\pi$
$613$	4.76405e7			0.00835342			0.00417671	+	0.999991i	$0.498671\pi$
$614$	−1.34696e9	−	2.33300e9i	−0.234836	−	0.406748i
$615$		0			0
$616$	−3.63672e7	+	6.29899e7i	−0.00626870	+	0.0108577i
$617$	−3.46592e9	+	6.00314e9i	−0.594046	+	1.02892i	0.399635	+	0.916674i	$0.369137\pi$
$617$	−3.46592e9	+	6.00314e9i	−0.594046	+	1.02892i	−0.993681	+	0.112243i	$0.964196\pi$
$618$		0			0
$619$	−2.51972e9	−	4.36428e9i	−0.427007	−	0.739598i	0.569598	−	0.821923i	$-0.307099\pi$
$619$	−2.51972e9	−	4.36428e9i	−0.427007	−	0.739598i	−0.996606	+	0.0823251i	$0.973765\pi$
$620$	−2.15748e9			−0.363559
$621$		0			0
$622$	3.18973e9			0.531481
$623$	4.48789e8	+	7.77325e8i	0.0743590	+	0.128794i
$624$		0			0
$625$	−3.98879e9	+	6.90879e9i	−0.653524	+	1.13194i
$626$	5.04382e9	−	8.73615e9i	0.821768	−	1.42334i
$627$		0			0
$628$	8.64376e8	+	1.49714e9i	0.139266	+	0.241215i
$629$	−1.96457e9			−0.314768
$630$		0			0
$631$	−1.18639e10			−1.87986			−0.939929	−	0.341370i	$-0.889109\pi$
$631$	−1.18639e10			−1.87986			−0.939929	+	0.341370i	$0.889109\pi$
$632$	5.81898e8	+	1.00788e9i	0.0916932	+	0.158817i
$633$		0			0
$634$	5.07722e9	−	8.79400e9i	0.791250	−	1.37048i
$635$	5.59970e9	−	9.69897e9i	0.867874	−	1.50320i
$636$		0			0
$637$	7.19261e8	+	1.24580e9i	0.110255	+	0.190967i
$638$	7.69148e7			0.0117257
$639$		0			0
$640$	1.36845e10			2.06347
$641$	2.29953e9	+	3.98290e9i	0.344854	+	0.597304i	0.985327	−	0.170676i	$-0.0545951\pi$
$641$	2.29953e9	+	3.98290e9i	0.344854	+	0.597304i	−0.640473	+	0.767980i	$0.721262\pi$
$642$		0			0
$643$	−3.09719e9	+	5.36450e9i	−0.459441	+	0.795776i	−0.998931	−	0.0462161i	$-0.985284\pi$
$643$	−3.09719e9	+	5.36450e9i	−0.459441	+	0.795776i	0.539490	+	0.841992i	$0.318617\pi$
$644$	1.92176e8	−	3.32859e8i	0.0283530	−	0.0491088i
$645$		0			0
$646$	6.82089e8	+	1.18141e9i	0.0995468	+	0.172420i
$647$	1.03256e10			1.49882			0.749408	−	0.662108i	$-0.230338\pi$
$647$	1.03256e10			1.49882			0.749408	+	0.662108i	$0.230338\pi$
$648$		0			0
$649$	1.83011e8			0.0262797
$650$	6.02083e9	+	1.04284e10i	0.859924	+	1.48943i
$651$		0			0
$652$	−4.73268e7	+	8.19724e7i	−0.00668714	+	0.0115825i
$653$	3.06685e9	−	5.31193e9i	0.431018	−	0.746546i	−0.565943	−	0.824444i	$-0.691488\pi$
$653$	3.06685e9	−	5.31193e9i	0.431018	−	0.746546i	0.996961	+	0.0778987i	$0.0248211\pi$
$654$		0			0
$655$	1.91165e9	+	3.31107e9i	0.265805	+	0.460388i
$656$	7.29468e9			1.00889
$657$		0			0
$658$	5.98151e9			0.818503
$659$	−2.92489e9	−	5.06606e9i	−0.398117	−	0.689559i	0.595377	−	0.803447i	$-0.297003\pi$
$659$	−2.92489e9	−	5.06606e9i	−0.398117	−	0.689559i	−0.993494	+	0.113888i	$0.963670\pi$
$660$		0			0
$661$	2.28026e9	−	3.94953e9i	0.307100	−	0.531912i	−0.670627	−	0.741795i	$-0.733975\pi$
$661$	2.28026e9	−	3.94953e9i	0.307100	−	0.531912i	0.977727	+	0.209883i	$0.0673082\pi$
$662$	4.07600e9	−	7.05984e9i	0.546049	−	0.945784i
$663$		0			0
$664$	−2.21545e9	−	3.83726e9i	−0.293679	−	0.508667i
$665$	−7.02661e9			−0.926553
$666$		0			0
$667$	2.10636e9			0.274847
$668$	5.48742e8	+	9.50449e8i	0.0712280	+	0.123370i
$669$		0			0
$670$	−1.77637e9	+	3.07677e9i	−0.228177	+	0.395215i
$671$	1.61123e7	−	2.79074e7i	0.00205888	−	0.00356608i
$672$		0			0
$673$	−3.07073e9	−	5.31866e9i	−0.388319	−	0.672589i	0.603904	−	0.797057i	$-0.293611\pi$
$673$	−3.07073e9	−	5.31866e9i	−0.388319	−	0.672589i	−0.992224	+	0.124468i	$0.960278\pi$
$674$	−1.13643e10			−1.42966
$675$		0			0
$676$	−5.48438e8			−0.0682833
$677$	−3.41352e9	−	5.91238e9i	−0.422807	−	0.732322i	0.573406	−	0.819271i	$-0.305622\pi$
$677$	−3.41352e9	−	5.91238e9i	−0.422807	−	0.732322i	−0.996213	+	0.0869487i	$0.972288\pi$
$678$		0			0
$679$	3.28798e9	−	5.69495e9i	0.403074	−	0.698145i
$680$	1.92818e9	−	3.33971e9i	0.235162	−	0.407313i
$681$		0			0
$682$	9.38778e7	+	1.62601e8i	0.0113323	+	0.0196281i
$683$	3.50763e9			0.421251			0.210625	−	0.977567i	$-0.432450\pi$
$683$	3.50763e9			0.421251			0.210625	+	0.977567i	$0.432450\pi$
$684$		0			0
$685$	1.20245e10			1.42939
$686$	−4.95316e9	−	8.57912e9i	−0.585798	−	1.01463i
$687$		0			0
$688$	−6.39304e9	+	1.10731e10i	−0.748424	+	1.29631i
$689$	−2.45222e9	+	4.24738e9i	−0.285623	+	0.494713i
$690$		0			0
$691$	5.14789e9	+	8.91640e9i	0.593548	+	1.02805i	0.993750	+	0.111628i	$0.0356065\pi$
$691$	5.14789e9	+	8.91640e9i	0.593548	+	1.02805i	−0.400202	+	0.916427i	$0.631060\pi$
$692$	2.21345e9			0.253921
$693$		0			0
$694$	−1.33128e10			−1.51186
$695$	1.32225e10	+	2.29020e10i	1.49406	+	2.58778i
$696$		0			0
$697$	1.17424e9	−	2.03385e9i	0.131354	−	0.227512i
$698$	−5.92362e9	+	1.02600e10i	−0.659315	+	1.14197i
$699$		0			0
$700$	−1.29804e9	−	2.24826e9i	−0.143035	−	0.247745i
$701$	−4.56518e9			−0.500548			−0.250274	−	0.968175i	$-0.580521\pi$
$701$	−4.56518e9			−0.500548			−0.250274	+	0.968175i	$0.580521\pi$
$702$		0			0
$703$	−6.12538e9			−0.664951
$704$	−6.02368e7	−	1.04333e8i	−0.00650665	−	0.0112699i
$705$		0			0
$706$	3.57926e9	−	6.19945e9i	0.382804	−	0.663036i
$707$	−2.51429e9	+	4.35487e9i	−0.267576	+	0.463455i
$708$		0			0
$709$	−1.81226e6	−	3.13892e6i	−0.000190967	−	0.000330764i	0.865930	−	0.500165i	$-0.166727\pi$
$709$	−1.81226e6	−	3.13892e6i	−0.000190967	−	0.000330764i	−0.866121	+	0.499835i	$0.833394\pi$
$710$	−8.92968e9			−0.936336
$711$		0			0
$712$	−1.53593e9			−0.159474
$713$	2.57090e9	+	4.45292e9i	0.265626	+	0.460079i
$714$		0			0
$715$	1.07705e8	−	1.86551e8i	0.0110196	−	0.0190865i
$716$	7.45525e8	−	1.29129e9i	0.0759044	−	0.131470i
$717$		0			0
$718$	8.16872e9	+	1.41486e10i	0.823604	+	1.42652i
$719$	−1.69128e10			−1.69693			−0.848467	−	0.529248i	$-0.822474\pi$
$719$	−1.69128e10			−1.69693			−0.848467	+	0.529248i	$0.822474\pi$
$720$		0			0
$721$	−4.08247e9			−0.405648
$722$	−3.32342e9	−	5.75633e9i	−0.328628	−	0.569201i
$723$		0			0
$724$	1.38349e9	−	2.39628e9i	0.135485	−	0.234667i
$725$	7.11359e9	−	1.23211e10i	0.693275	−	1.20079i
$726$		0			0
$727$	3.66555e9	+	6.34892e9i	0.353809	+	0.612815i	0.986913	−	0.161251i	$-0.0515530\pi$
$727$	3.66555e9	+	6.34892e9i	0.353809	+	0.612815i	−0.633104	+	0.774066i	$0.718220\pi$
$728$	6.02419e9			0.578681
$729$		0			0
$730$	−3.24820e10			−3.09039
$731$	2.05821e9	+	3.56492e9i	0.194885	+	0.337551i
$732$		0			0
$733$	4.41256e9	−	7.64277e9i	0.413834	−	0.716782i	−0.581471	−	0.813567i	$-0.697523\pi$
$733$	4.41256e9	−	7.64277e9i	0.413834	−	0.716782i	0.995305	+	0.0967852i	$0.0308560\pi$
$734$	3.48436e9	−	6.03509e9i	0.325227	−	0.563311i
$735$		0			0
$736$	7.21155e8	+	1.24908e9i	0.0666740	+	0.115483i
$737$	4.30467e7			0.00396099
$738$		0			0
$739$	3.03900e9			0.276997			0.138499	−	0.990363i	$-0.455772\pi$
$739$	3.03900e9			0.276997			0.138499	+	0.990363i	$0.455772\pi$
$740$	−1.67062e9	−	2.89360e9i	−0.151554	−	0.262499i
$741$		0			0
$742$	3.79718e9	−	6.57690e9i	0.341230	−	0.591028i
$743$	2.81244e9	−	4.87129e9i	0.251549	−	0.435696i	−0.712403	−	0.701770i	$-0.752393\pi$
$743$	2.81244e9	−	4.87129e9i	0.251549	−	0.435696i	0.963953	+	0.266074i	$0.0857267\pi$
$744$		0			0
$745$	−1.91744e10	−	3.32111e10i	−1.69893	−	2.94264i
$746$	−1.83692e9			−0.161996
$747$		0			0
$748$	9.01616e6			0.000787709
$749$	−5.28886e9	−	9.16058e9i	−0.459913	−	0.796593i
$750$		0			0
$751$	−7.17434e9	+	1.24263e10i	−0.618077	+	1.07054i	0.371760	+	0.928329i	$0.378755\pi$
$751$	−7.17434e9	+	1.24263e10i	−0.618077	+	1.07054i	−0.989836	+	0.142211i	$0.954579\pi$
$752$	−5.96778e9	+	1.03365e10i	−0.511742	+	0.886362i
$753$		0			0
$754$	−3.18521e9	−	5.51695e9i	−0.270607	−	0.468705i
$755$	8.18195e9			0.691899
$756$		0			0
$757$	7.36333e9			0.616934			0.308467	−	0.951235i	$-0.400184\pi$
$757$	7.36333e9			0.616934			0.308467	+	0.951235i	$0.400184\pi$
$758$	1.04362e10	+	1.80761e10i	0.870367	+	1.50752i
$759$		0			0
$760$	6.01194e9	−	1.04130e10i	0.496783	−	0.860454i
$761$	−1.08583e10	+	1.88070e10i	−0.893128	+	1.54694i	−0.0570229	+	0.998373i	$0.518161\pi$
$761$	−1.08583e10	+	1.88070e10i	−0.893128	+	1.54694i	−0.836105	+	0.548570i	$0.815173\pi$
$762$		0			0
$763$	4.56126e9	+	7.90033e9i	0.371748	+	0.643887i
$764$	−1.83643e9			−0.148987
$765$		0			0
$766$	1.11801e10			0.898759
$767$	−7.57890e9	−	1.31270e10i	−0.606488	−	1.05047i
$768$		0			0
$769$	2.45142e9	−	4.24599e9i	0.194391	−	0.336695i	−0.752310	−	0.658810i	$-0.771060\pi$
$769$	2.45142e9	−	4.24599e9i	0.194391	−	0.336695i	0.946701	+	0.322115i	$0.104394\pi$
$770$	−1.66777e8	+	2.88867e8i	−0.0131650	+	0.0228024i
$771$		0			0
$772$	1.74531e8	+	3.02296e8i	0.0136525	+	0.0236467i
$773$	2.31850e10			1.80542			0.902712	−	0.430245i	$-0.141573\pi$
$773$	2.31850e10			1.80542			0.902712	+	0.430245i	$0.141573\pi$
$774$		0			0
$775$	3.47298e10			2.68007
$776$	5.62637e9	+	9.74515e9i	0.432227	+	0.748639i
$777$		0			0
$778$	−9.69395e9	+	1.67904e10i	−0.738027	+	1.27830i
$779$	3.66121e9	−	6.34139e9i	0.277487	−	0.480622i
$780$		0			0
$781$	5.40981e7	+	9.37006e7i	0.00406353	+	0.00703824i
$782$	1.77343e9			0.132614
$783$		0			0
$784$	4.44477e9			0.329415
$785$	−2.05429e10	−	3.55814e10i	−1.51572	−	2.62530i
$786$		0			0
$787$	−1.25529e10	+	2.17422e10i	−0.917976	+	1.58998i	−0.115491	+	0.993308i	$0.536844\pi$
$787$	−1.25529e10	+	2.17422e10i	−0.917976	+	1.58998i	−0.802485	+	0.596673i	$0.796489\pi$
$788$	2.56764e8	−	4.44728e8i	0.0186936	−	0.0323782i
$789$		0			0
$790$	2.66854e9	+	4.62205e9i	0.192566	+	0.333534i
$791$	−1.91625e9			−0.137669
$792$		0			0
$793$	−2.66899e9			−0.190060
$794$	3.99698e9	+	6.92296e9i	0.283374	+	0.490818i
$795$		0			0
$796$	9.58407e8	−	1.66001e9i	0.0673526	−	0.116658i
$797$	−5.17723e9	+	8.96722e9i	−0.362237	+	0.627413i	−0.988329	−	0.152336i	$-0.951320\pi$
$797$	−5.17723e9	+	8.96722e9i	−0.362237	+	0.627413i	0.626091	+	0.779750i	$0.284654\pi$
$798$		0			0
$799$	1.92130e9	+	3.32779e9i	0.133254	+	0.230803i
$800$	9.74195e9			0.672714
$801$		0			0
$802$	−6.25978e9			−0.428498
$803$	1.96784e8	+	3.40840e8i	0.0134117	+	0.0232298i
$804$		0			0
$805$	−4.56730e9	+	7.91079e9i	−0.308584	+	0.534484i
$806$	7.77538e9	−	1.34673e10i	0.523057	−	0.905961i
$807$		0			0
$808$	−4.30243e9	−	7.45202e9i	−0.286928	−	0.496975i
$809$	5.38506e9			0.357578			0.178789	−	0.983887i	$-0.442782\pi$
$809$	5.38506e9			0.357578			0.178789	+	0.983887i	$0.442782\pi$
$810$		0			0
$811$	−2.49541e9			−0.164274			−0.0821369	−	0.996621i	$-0.526174\pi$
$811$	−2.49541e9			−0.164274			−0.0821369	+	0.996621i	$0.526174\pi$
$812$	6.86702e8	+	1.18940e9i	0.0450114	+	0.0779620i
$813$		0			0
$814$	−1.45387e8	+	2.51817e8i	−0.00944799	+	0.0163644i
$815$	1.12478e9	−	1.94817e9i	0.0727805	−	0.126060i
$816$		0			0
$817$	6.41735e9	+	1.11152e10i	0.411698	+	0.713081i
$818$	−9.08063e9			−0.580069
$819$		0			0
$820$	3.99419e9			0.252977
$821$	6.60332e9	+	1.14373e10i	0.416448	+	0.721309i	0.995579	−	0.0939250i	$-0.0299414\pi$
$821$	6.60332e9	+	1.14373e10i	0.416448	+	0.721309i	−0.579131	+	0.815234i	$0.696608\pi$
$822$		0			0
$823$	1.17067e10	−	2.02765e10i	0.732039	−	1.26793i	−0.223972	−	0.974596i	$-0.571902\pi$
$823$	1.17067e10	−	2.02765e10i	0.732039	−	1.26793i	0.956011	−	0.293332i	$-0.0947643\pi$
$824$	3.49294e9	−	6.04995e9i	0.217493	−	0.376710i
$825$		0			0
$826$	1.17357e10	+	2.03267e10i	0.724564	+	1.25498i
$827$	5.37135e9			0.330228			0.165114	−	0.986274i	$-0.447201\pi$
$827$	5.37135e9			0.330228			0.165114	+	0.986274i	$0.447201\pi$
$828$		0			0
$829$	1.03977e10			0.633865			0.316933	−	0.948448i	$-0.397347\pi$
$829$	1.03977e10			0.633865			0.316933	+	0.948448i	$0.397347\pi$
$830$	−1.01599e10	−	1.75974e10i	−0.616758	−	1.06826i
$831$		0			0
$832$	−4.98908e9	+	8.64134e9i	−0.300323	+	0.520175i
$833$	7.15486e8	−	1.23926e9i	0.0428888	−	0.0742856i
$834$		0			0
$835$	−1.30415e10	−	2.25886e10i	−0.775221	−	1.34272i
$836$	2.81117e7			0.00166405
$837$		0			0
$838$	−3.53738e9			−0.207648
$839$	1.42421e9	+	2.46681e9i	0.0832546	+	0.144201i	0.904646	−	0.426164i	$-0.140135\pi$
$839$	1.42421e9	+	2.46681e9i	0.0832546	+	0.144201i	−0.821392	+	0.570365i	$0.806802\pi$
$840$		0			0
$841$	4.86162e9	−	8.42058e9i	0.281835	−	0.488153i
$842$	−1.79846e10	+	3.11502e10i	−1.03826	+	1.79832i
$843$		0			0
$844$	2.65248e8	+	4.59422e8i	0.0151863	+	0.0263035i
$845$	1.30343e10			0.743172
$846$		0			0
$847$	−1.48963e10			−0.842337
$848$	7.57693e9	+	1.31236e10i	0.426685	+	0.739041i
$849$		0			0
$850$	5.98924e9	−	1.03737e10i	0.334507	−	0.579383i
$851$	−3.98150e9	+	6.89616e9i	−0.221459	+	0.383578i
$852$		0			0
$853$	7.01620e9	+	1.21524e10i	0.387062	+	0.670411i	0.992053	−	0.125821i	$-0.0401566\pi$
$853$	7.01620e9	+	1.21524e10i	0.387062	+	0.670411i	−0.604991	+	0.796232i	$0.706823\pi$
$854$	4.13284e9			0.227063
$855$		0			0
$856$	1.81005e10			0.986354
$857$	−1.83029e10	−	3.17016e10i	−0.993317	−	1.72048i	−0.596614	−	0.802528i	$-0.703488\pi$
$857$	−1.83029e10	−	3.17016e10i	−0.993317	−	1.72048i	−0.396703	−	0.917947i	$-0.629846\pi$
$858$		0			0
$859$	1.03281e10	−	1.78889e10i	0.555963	−	0.962957i	−0.441865	−	0.897082i	$-0.645683\pi$
$859$	1.03281e10	−	1.78889e10i	0.555963	−	0.962957i	0.997828	−	0.0658750i	$-0.0209839\pi$
$860$	−3.50050e9	+	6.06304e9i	−0.187666	+	0.325047i
$861$		0			0
$862$	−1.45660e10	−	2.52291e10i	−0.774578	−	1.34161i
$863$	1.03926e10			0.550408			0.275204	−	0.961386i	$-0.411255\pi$
$863$	1.03926e10			0.550408			0.275204	+	0.961386i	$0.411255\pi$
$864$		0			0
$865$	−5.26054e10			−2.76359
$866$	−4.66950e9	−	8.08782e9i	−0.244320	−	0.423174i
$867$		0			0
$868$	−1.67630e9	+	2.90343e9i	−0.0870026	+	0.150693i
$869$	3.23333e7	−	5.60029e7i	0.00167140	−	0.00289495i
$870$		0			0
$871$	−1.78266e9	−	3.08766e9i	−0.0914124	−	0.158331i
$872$	−1.56104e10			−0.797270
$873$		0			0
$874$	5.52943e9			0.280150
$875$	1.61527e10	+	2.79774e10i	0.815113	+	1.41182i
$876$		0			0
$877$	2.77558e9	−	4.80744e9i	0.138949	−	0.240666i	−0.788150	−	0.615483i	$-0.788961\pi$
$877$	2.77558e9	−	4.80744e9i	0.138949	−	0.240666i	0.927099	+	0.374817i	$0.122294\pi$
$878$	8.91099e9	−	1.54343e10i	0.444319	−	0.769583i
$879$		0			0
$880$	−3.32789e8	−	5.76408e8i	−0.0164619	−	0.0285129i
$881$	−2.46612e10			−1.21506			−0.607530	−	0.794297i	$-0.707840\pi$
$881$	−2.46612e10			−1.21506			−0.607530	+	0.794297i	$0.707840\pi$
$882$		0			0
$883$	−2.21047e10			−1.08049			−0.540247	−	0.841506i	$-0.681669\pi$
$883$	−2.21047e10			−1.08049			−0.540247	+	0.841506i	$0.681669\pi$
$884$	−3.73379e8	−	6.46712e8i	−0.0181789	−	0.0314868i
$885$		0			0
$886$	−6.43939e9	+	1.11534e10i	−0.311048	+	0.538750i
$887$	5.12066e9	−	8.86925e9i	0.246373	−	0.426731i	−0.716144	−	0.697953i	$-0.754094\pi$
$887$	5.12066e9	−	8.86925e9i	0.246373	−	0.426731i	0.962517	+	0.271222i	$0.0874278\pi$
$888$		0			0
$889$	−8.70163e9	−	1.50717e10i	−0.415379	−	0.719457i
$890$	−7.04365e9			−0.334913
$891$		0			0
$892$	−1.36605e9			−0.0644450
$893$	5.99047e9	+	1.03758e10i	0.281502	+	0.487575i
$894$		0			0
$895$	−1.77183e10	+	3.06890e10i	−0.826117	+	1.43088i
$896$	1.06325e10	−	1.84160e10i	0.493806	−	0.855296i
$897$		0			0
$898$	6.36015e9	+	1.10161e10i	0.293089	+	0.507646i
$899$	−1.83732e10			−0.843383
$900$		0			0
$901$	4.87871e9			0.222212
$902$	−1.73798e8	−	3.01028e8i	−0.00788538	−	0.0136579i
$903$		0			0
$904$	1.63954e9	−	2.83976e9i	0.0738129	−	0.127848i
$905$	−3.28803e10	+	5.69504e10i	−1.47457	+	2.55403i
$906$		0			0
$907$	1.76691e10	+	3.06038e10i	0.786301	+	1.36191i	0.928219	+	0.372035i	$0.121340\pi$
$907$	1.76691e10	+	3.06038e10i	0.786301	+	1.36191i	−0.141917	+	0.989879i	$0.545327\pi$
$908$	−3.18707e9			−0.141283
$909$		0			0
$910$	2.76265e10			1.21529
$911$	1.48603e9	+	2.57388e9i	0.0651200	+	0.112791i	0.896747	−	0.442543i	$-0.145924\pi$
$911$	1.48603e9	+	2.57388e9i	0.0651200	+	0.112791i	−0.831627	+	0.555334i	$0.812590\pi$
$912$		0			0
$913$	−1.23102e8	+	2.13218e8i	−0.00535324	+	0.00927208i
$914$	6.71262e9	−	1.16266e10i	0.290790	−	0.503664i
$915$		0			0
$916$	−2.42473e9	−	4.19976e9i	−0.104239	−	0.180547i
$917$	5.94119e9			0.254437
$918$		0			0
$919$	1.47368e10			0.626323			0.313162	−	0.949700i	$-0.398612\pi$
$919$	1.47368e10			0.626323			0.313162	+	0.949700i	$0.398612\pi$
$920$	−7.81552e9	−	1.35369e10i	−0.330903	−	0.573141i
$921$		0			0
$922$	8.58221e9	−	1.48648e10i	0.360613	−	0.624599i
$923$	4.48065e9	−	7.76071e9i	0.187558	−	0.324859i
$924$		0			0
$925$	2.68927e10	+	4.65794e10i	1.11722	+	1.93508i
$926$	1.94961e10			0.806881
$927$		0			0
$928$	−5.15380e9			−0.211695
$929$	1.66981e10	+	2.89220e10i	0.683303	+	1.18352i	0.973967	+	0.226690i	$0.0727905\pi$
$929$	1.66981e10	+	2.89220e10i	0.683303	+	1.18352i	−0.290664	+	0.956825i	$0.593876\pi$
$930$		0			0
$931$	2.23083e9	−	3.86392e9i	0.0906032	−	0.156929i
$932$	3.37911e9	−	5.85279e9i	0.136724	−	0.236814i
$933$		0			0
$934$	−2.31507e10	−	4.00981e10i	−0.929715	−	1.61031i
$935$	−2.14280e8			−0.00857316
$936$		0			0
$937$	−3.31971e10			−1.31829			−0.659146	−	0.752015i	$-0.729082\pi$
$937$	−3.31971e10			−1.31829			−0.659146	+	0.752015i	$0.729082\pi$
$938$	2.76039e9	+	4.78113e9i	0.109209	+	0.189156i
$939$		0			0
$940$	−3.26765e9	+	5.65974e9i	−0.128318	+	0.222254i
$941$	1.02294e10	−	1.77179e10i	0.400209	−	0.693182i	−0.593542	−	0.804803i	$-0.702271\pi$
$941$	1.02294e10	−	1.77179e10i	0.400209	−	0.693182i	0.993751	+	0.111621i	$0.0356042\pi$
$942$		0			0
$943$	−4.75957e9	−	8.24382e9i	−0.184832	−	0.320138i
$944$	−4.68349e10			−1.81204
$945$		0			0
$946$	6.09266e8			0.0233985
$947$	−4.17354e9	−	7.22878e9i	−0.159691	−	0.276592i	0.775067	−	0.631880i	$-0.217716\pi$
$947$	−4.17354e9	−	7.22878e9i	−0.159691	−	0.276592i	−0.934757	+	0.355287i	$0.884383\pi$
$948$		0			0
$949$	1.62985e10	−	2.82299e10i	0.619037	−	1.07220i
$950$	1.86740e10	−	3.23443e10i	0.706651	−	1.22396i
$951$		0			0
$952$	−2.99629e9	−	5.18973e9i	−0.112552	−	0.194946i
$953$	1.88821e10			0.706686			0.353343	−	0.935494i	$-0.385045\pi$
$953$	1.88821e10			0.706686			0.353343	+	0.935494i	$0.385045\pi$
$954$		0			0
$955$	4.36450e10			1.62152
$956$	6.64883e7	+	1.15161e8i	0.00246117	+	0.00426288i
$957$		0			0
$958$	5.18143e9	−	8.97449e9i	0.190401	−	0.329785i
$959$	9.34270e9	−	1.61820e10i	0.342064	−	0.592472i
$960$		0			0
$961$	−8.66890e9	−	1.50150e10i	−0.315088	−	0.545749i
$962$	2.40832e10			0.872169
$963$		0			0
$964$	4.58121e8			0.0164706
$965$	−4.14793e9	−	7.18442e9i	−0.148589	−	0.257363i
$966$		0			0
$967$	−7.15938e9	+	1.24004e10i	−0.254614	+	0.441005i	−0.964791	−	0.263019i	$-0.915282\pi$
$967$	−7.15938e9	+	1.24004e10i	−0.254614	+	0.441005i	0.710176	+	0.704024i	$0.248615\pi$
$968$	1.27452e10	−	2.20753e10i	0.451630	−	0.782246i
$969$		0			0
$970$	2.58021e10	+	4.46906e10i	0.907724	+	1.57222i
$971$	3.29069e9			0.115350			0.0576752	−	0.998335i	$-0.481631\pi$
$971$	3.29069e9			0.115350			0.0576752	+	0.998335i	$0.481631\pi$
$972$		0			0
$973$	4.10941e10			1.43016
$974$	2.59445e10	+	4.49371e10i	0.899681	+	1.55829i
$975$		0			0
$976$	−4.12335e9	+	7.14186e9i	−0.141963	+	0.245888i
$977$	1.72076e10	−	2.98044e10i	0.590321	−	1.02247i	−0.403868	−	0.914817i	$-0.632334\pi$
$977$	1.72076e10	−	2.98044e10i	0.590321	−	1.02247i	0.994189	−	0.107649i	$-0.0343322\pi$
$978$		0			0
$979$	4.26721e7	+	7.39102e7i	0.00145346	+	0.00251747i
$980$	2.43373e9			0.0826001
$981$		0			0
$982$	3.62459e9			0.122143
$983$	3.77281e8	+	6.53469e8i	0.0126686	+	0.0219426i	0.872290	−	0.488989i	$-0.162634\pi$
$983$	3.77281e8	+	6.53469e8i	0.0126686	+	0.0219426i	−0.859622	+	0.510931i	$0.829301\pi$
$984$		0			0
$985$	−6.10230e9	+	1.05695e10i	−0.203454	+	0.352393i
$986$	−3.16850e9	+	5.48800e9i	−0.105265	+	0.182324i
$987$		0			0
$988$	−1.16417e9	−	2.01640e9i	−0.0384032	−	0.0665162i
$989$	1.66851e10			0.548456
$990$		0			0
$991$	−1.99115e10			−0.649900			−0.324950	−	0.945731i	$-0.605347\pi$
$991$	−1.99115e10			−0.649900			−0.324950	+	0.945731i	$0.605347\pi$
$992$	−6.29043e9	−	1.08953e10i	−0.204592	−	0.354365i
$993$		0			0
$994$	−6.93812e9	+	1.20172e10i	−0.224073	+	0.388106i
$995$	−2.27777e10	+	3.94521e10i	−0.733042	+	1.26967i
$996$		0			0
$997$	3.31127e8	+	5.73529e8i	0.0105818	+	0.0183283i	0.871268	−	0.490808i	$-0.163298\pi$
$997$	3.31127e8	+	5.73529e8i	0.0105818	+	0.0183283i	−0.860686	+	0.509136i	$0.829965\pi$
$998$	−5.22808e10			−1.66489
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.8.c.a.10.5		12
3.2	odd	2		9.8.c.a.4.2	✓	12
4.3	odd	2		432.8.i.c.145.6		12
9.2	odd	6		9.8.c.a.7.2	yes	12
9.4	even	3		81.8.a.c.1.2		6
9.5	odd	6		81.8.a.e.1.5		6
9.7	even	3	inner	27.8.c.a.19.5		12
12.11	even	2		144.8.i.c.49.5		12
36.7	odd	6		432.8.i.c.289.6		12
36.11	even	6		144.8.i.c.97.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.8.c.a.4.2	✓	12	3.2	odd	2
9.8.c.a.7.2	yes	12	9.2	odd	6
27.8.c.a.10.5		12	1.1	even	1	trivial
27.8.c.a.19.5		12	9.7	even	3	inner
81.8.a.c.1.2		6	9.4	even	3
81.8.a.e.1.5		6	9.5	odd	6
144.8.i.c.49.5		12	12.11	even	2
144.8.i.c.97.5		12	36.11	even	6
432.8.i.c.145.6		12	4.3	odd	2
432.8.i.c.289.6		12	36.7	odd	6

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(6.09721 + 10.5607i) q^{2} +(-10.3519 + 17.9301i) q^{4} +(246.026 - 426.130i) q^{5} +(-382.311 - 662.182i) q^{7} +1308.41 q^{8} +O(q^{10})\)	\(q+(6.09721 + 10.5607i) q^{2} +(-10.3519 + 17.9301i) q^{4} +(246.026 - 426.130i) q^{5} +(-382.311 - 662.182i) q^{7} +1308.41 q^{8} +6000.29 q^{10} +(-36.3512 - 62.9621i) q^{11} +(-3010.77 + 5214.80i) q^{13} +(4662.06 - 8074.93i) q^{14} +(9302.72 + 16112.8i) q^{16} +5989.93 q^{17} +18676.2 q^{19} +(5093.69 + 8822.53i) q^{20} +(443.281 - 767.786i) q^{22} +(12139.5 - 21026.3i) q^{23} +(-81995.2 - 142020. i) q^{25} -73429.1 q^{26} +15830.6 q^{28} +(43378.1 + 75133.0i) q^{29} +(-105890. + 183406. i) q^{31} +(-29702.8 + 51446.7i) q^{32} +(36521.9 + 63257.8i) q^{34} -376234. q^{35} -327978. q^{37} +(113873. + 197233. i) q^{38} +(321904. - 557554. i) q^{40} +(196036. - 339545. i) q^{41} +(343611. + 595152. i) q^{43} +1505.22 q^{44} +296069. q^{46} +(320755. + 555563. i) q^{47} +(119448. - 206890. i) q^{49} +(999884. - 1.73185e6i) q^{50} +(-62334.5 - 107966. i) q^{52} +814485. q^{53} -35773.3 q^{55} +(-500221. - 866408. i) q^{56} +(-528971. + 916204. i) q^{58} +(-1.25863e6 + 2.18002e6i) q^{59} +(221621. + 383858. i) q^{61} -2.58252e6 q^{62} +1.65708e6 q^{64} +(1.48145e6 + 2.56595e6i) q^{65} +(-296048. + 512770. i) q^{67} +(-62007.4 + 107400. i) q^{68} +(-2.29398e6 - 3.97329e6i) q^{70} -1.48821e6 q^{71} -5.41341e6 q^{73} +(-1.99975e6 - 3.46367e6i) q^{74} +(-193334. + 334865. i) q^{76} +(-27794.9 + 48142.2i) q^{77} +(444736. + 770305. i) q^{79} +9.15485e6 q^{80} +4.78109e6 q^{82} +(-1.69323e6 - 2.93276e6i) q^{83} +(1.47368e6 - 2.55249e6i) q^{85} +(-4.19014e6 + 7.25754e6i) q^{86} +(-47562.4 - 82380.4i) q^{88} -1.17388e6 q^{89} +4.60420e6 q^{91} +(251335. + 435325. i) q^{92} +(-3.91142e6 + 6.77477e6i) q^{94} +(4.59483e6 - 7.95847e6i) q^{95} +(4.30014e6 + 7.44806e6i) q^{97} +2.91320e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8}+O(q^{10}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8} + 252 q^{10} + 8460 q^{11} - 1848 q^{13} + 16272 q^{14} - 12417 q^{16} - 30564 q^{17} + 24432 q^{19} + 40788 q^{20} - 35001 q^{22} + 51588 q^{23} + 4746 q^{25} - 536472 q^{26} + 75516 q^{28} + 414648 q^{29} + 8196 q^{31} + 1048977 q^{32} - 106623 q^{34} - 2210616 q^{35} + 139344 q^{37} + 1952685 q^{38} + 305496 q^{40} + 1731582 q^{41} + 408372 q^{43} - 5169114 q^{44} - 1684008 q^{46} + 1631484 q^{47} - 179010 q^{49} + 1654461 q^{50} + 681594 q^{52} - 2835648 q^{53} - 16056 q^{55} + 1784466 q^{56} - 948384 q^{58} + 2055636 q^{59} - 2723196 q^{61} + 1026828 q^{62} + 7178178 q^{64} + 1387620 q^{65} + 3806556 q^{67} - 2142639 q^{68} + 953442 q^{70} - 2408400 q^{71} - 10670052 q^{73} - 9846504 q^{74} - 6727827 q^{76} - 3478824 q^{77} + 6020916 q^{79} + 38072448 q^{80} + 9403002 q^{82} - 9605052 q^{83} - 1698624 q^{85} - 34278561 q^{86} - 16459029 q^{88} + 24630264 q^{89} + 13570104 q^{91} - 39143394 q^{92} + 12602808 q^{94} - 10422072 q^{95} + 9977226 q^{97} + 95833314 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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