LMFDB - Embedded newform 54.9.d.a.35.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(17,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("54.17");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.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:	$21.9984449433$
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} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 $ x^16 - 4x^15 - 150208x^14 - 1927740x^13 + 8702363206x^12 + 239206241152x^11 - 241960304158448x^10 - 9458863275320348x^9 + 3259352971808015407x^8 + 150983052056025751536x^7 - 18744835998632687401792x^6 - 866018994869774202180460x^5 + 35643731791394373752805382x^4 + 1485002234815673954960734644x^3 + 16292568366453217677347743656x^2 + 62373298381917691066182105696*x + 81301302751102601946916438161
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{36} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.4
Root			$-197.435 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	54.35
Dual form			54.9.d.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(944.709 - 545.428i) q^{5} +(1250.70 - 2166.27i) q^{7} -1448.15i q^{8} -12341.6 q^{10} +(3212.80 + 1854.91i) q^{11} +(22409.9 + 38815.1i) q^{13} +(-24508.5 + 14150.0i) q^{14} +(-8192.00 + 14189.0i) q^{16} -54543.2i q^{17} +125188. q^{19} +(120923. + 69814.8i) q^{20} +(-20985.9 - 36348.7i) q^{22} +(-266411. + 153812. i) q^{23} +(399671. - 692251. i) q^{25} -507078. i q^{26} +320178. q^{28} +(-400230. - 231073. i) q^{29} +(-140570. - 243475. i) q^{31} +(160530. - 92681.9i) q^{32} +(-308543. + 534412. i) q^{34} -2.72866e6i q^{35} +159985. q^{37} +(-1.22659e6 - 708173. i) q^{38} +(-789864. - 1.36808e6i) q^{40} +(4.49810e6 - 2.59698e6i) q^{41} +(2.49848e6 - 4.32750e6i) q^{43} +474858. i q^{44} +3.48037e6 q^{46} +(306798. + 177130. i) q^{47} +(-246080. - 426223. i) q^{49} +(-7.83192e6 + 4.52176e6i) q^{50} +(-2.86847e6 + 4.96833e6i) q^{52} +958543. i q^{53} +4.04689e6 q^{55} +(-3.13709e6 - 1.81120e6i) q^{56} +(2.61429e6 + 4.52809e6i) q^{58} +(-1.38270e7 + 7.98300e6i) q^{59} +(-5.55708e6 + 9.62514e6i) q^{61} +3.18074e6i q^{62} -2.09715e6 q^{64} +(4.23417e7 + 2.44460e7i) q^{65} +(-1.22942e7 - 2.12942e7i) q^{67} +(6.04618e6 - 3.49076e6i) q^{68} +(-1.54356e7 + 2.67353e7i) q^{70} -1.67264e7i q^{71} +4.77259e6 q^{73} +(-1.56752e6 - 905009. i) q^{74} +(8.01206e6 + 1.38773e7i) q^{76} +(8.03648e6 - 4.63986e6i) q^{77} +(-1.81889e7 + 3.15042e7i) q^{79} +1.78726e7i q^{80} -5.87630e7 q^{82} +(-2.53425e7 - 1.46315e7i) q^{83} +(-2.97494e7 - 5.15274e7i) q^{85} +(-4.89601e7 + 2.82671e7i) q^{86} +(2.68620e6 - 4.65264e6i) q^{88} +6.26485e7i q^{89} +1.12112e8 q^{91} +(-3.41006e7 - 1.96880e7i) q^{92} +(-2.00399e6 - 3.47102e6i) q^{94} +(1.18267e8 - 6.82813e7i) q^{95} +(2.42081e7 - 4.19297e7i) q^{97} +5.56815e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29}+ \cdots - 89415484 q^{97}+O(q^{100}) $ 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7 - 45756 * q^11 - 3370 * q^13 + 94464 * q^14 - 131072 * q^16 + 362180 * q^19 + 112896 * q^20 - 61824 * q^22 - 1311138 * q^23 + 963394 * q^25 - 472576 * q^28 + 2851290 * q^29 + 542438 * q^31 + 220416 * q^34 + 3343328 * q^37 + 1314432 * q^38 - 9218592 * q^41 + 339512 * q^43 + 7417344 * q^46 + 34980606 * q^47 - 2364654 * q^49 - 27744768 * q^50 + 431360 * q^52 - 4584276 * q^55 + 12091392 * q^56 - 7852800 * q^58 - 93924216 * q^59 - 841954 * q^61 - 33554432 * q^64 + 126568134 * q^65 + 29946644 * q^67 + 5476608 * q^68 - 34359552 * q^70 - 7547764 * q^73 - 35124480 * q^74 + 23179520 * q^76 - 9309294 * q^77 + 33813002 * q^79 - 137346048 * q^82 - 114200226 * q^83 - 125696772 * q^85 + 171379584 * q^86 + 7913472 * q^88 + 268578316 * q^91 - 167825664 * q^92 - 11832576 * q^94 + 143949240 * q^95 - 89415484 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−9.79796	−	5.65685i	−0.612372	−	0.353553i
$2$	−9.79796	−	5.65685i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	64.0000	+	110.851i	0.250000	+	0.433013i
$5$	944.709	−	545.428i	1.51153	−	0.872685i	0.511625	−	0.859209i	$-0.329044\pi$
$5$	944.709	−	545.428i	1.51153	−	0.872685i	0.999909	−	0.0134763i	$-0.00428977\pi$
$6$		0			0
$7$	1250.70	−	2166.27i	0.520906	−	0.902236i	−0.478798	−	0.877925i	$-0.658927\pi$
$7$	1250.70	−	2166.27i	0.520906	−	0.902236i	0.999704	−	0.0243111i	$-0.00773922\pi$
$8$		−	1448.15i		−	0.353553i
$9$		0			0
$10$	−12341.6			−1.23416
$11$	3212.80	+	1854.91i	0.219439	+	0.126693i	0.605690	−	0.795700i	$-0.292897\pi$
$11$	3212.80	+	1854.91i	0.219439	+	0.126693i	−0.386252	+	0.922393i	$0.626230\pi$
$12$		0			0
$13$	22409.9	+	38815.1i	0.784633	+	1.35902i	0.929218	+	0.369531i	$0.120482\pi$
$13$	22409.9	+	38815.1i	0.784633	+	1.35902i	−0.144586	+	0.989492i	$0.546185\pi$
$14$	−24508.5	+	14150.0i	−0.637977	+	0.368336i
$15$		0			0
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$		−	54543.2i		−	0.653048i	−0.945189	−	0.326524i	$-0.894123\pi$
$17$		−	54543.2i		−	0.653048i	0.945189	−	0.326524i	$-0.105877\pi$
$18$		0			0
$19$	125188.			0.960616			0.480308	−	0.877100i	$-0.340525\pi$
$19$	125188.			0.960616			0.480308	+	0.877100i	$0.340525\pi$
$20$	120923.	+	69814.8i	0.755767	+	0.436342i
$21$		0			0
$22$	−20985.9	−	36348.7i	−0.0895855	−	0.155167i
$23$	−266411.	+	153812.i	−0.952007	+	0.549642i	−0.893704	−	0.448657i	$-0.851902\pi$
$23$	−266411.	+	153812.i	−0.952007	+	0.549642i	−0.0583033	+	0.998299i	$0.518569\pi$
$24$		0			0
$25$	399671.	−	692251.i	1.02316	−	1.77216i
$26$		−	507078.i		−	1.10964i
$27$		0			0
$28$	320178.			0.520906
$29$	−400230.	−	231073.i	−0.565872	−	0.326706i	0.189627	−	0.981856i	$-0.439272\pi$
$29$	−400230.	−	231073.i	−0.565872	−	0.326706i	−0.755499	+	0.655150i	$0.772605\pi$
$30$		0			0
$31$	−140570.	−	243475.i	−0.152211	−	0.263638i	0.779829	−	0.625993i	$-0.215306\pi$
$31$	−140570.	−	243475.i	−0.152211	−	0.263638i	−0.932040	+	0.362355i	$0.881973\pi$
$32$	160530.	−	92681.9i	0.153093	−	0.0883883i
$33$		0			0
$34$	−308543.	+	534412.i	−0.230887	+	0.399908i
$35$		−	2.72866e6i		−	1.81835i
$36$		0			0
$37$	159985.			0.0853633			0.0426816	−	0.999089i	$-0.486410\pi$
$37$	159985.			0.0853633			0.0426816	+	0.999089i	$0.486410\pi$
$38$	−1.22659e6	−	708173.i	−0.588255	−	0.339629i
$39$		0			0
$40$	−789864.	−	1.36808e6i	−0.308541	−	0.534408i
$41$	4.49810e6	−	2.59698e6i	1.59182	−	0.919038i	0.598825	−	0.800880i	$-0.295635\pi$
$41$	4.49810e6	−	2.59698e6i	1.59182	−	0.919038i	0.992995	−	0.118158i	$-0.0376988\pi$
$42$		0			0
$43$	2.49848e6	−	4.32750e6i	0.730807	−	1.26580i	−0.225731	−	0.974190i	$-0.572477\pi$
$43$	2.49848e6	−	4.32750e6i	0.730807	−	1.26580i	0.956539	−	0.291606i	$-0.0941895\pi$
$44$			474858.i			0.126693i
$45$		0			0
$46$	3.48037e6			0.777311
$47$	306798.	+	177130.i	0.0628725	+	0.0362995i	0.531107	−	0.847305i	$-0.321776\pi$
$47$	306798.	+	177130.i	0.0628725	+	0.0362995i	−0.468234	+	0.883604i	$0.655110\pi$
$48$		0			0
$49$	−246080.	−	426223.i	−0.0426866	−	0.0739354i
$50$	−7.83192e6	+	4.52176e6i	−1.25311	+	0.723482i
$51$		0			0
$52$	−2.86847e6	+	4.96833e6i	−0.392316	+	0.679512i
$53$			958543.i			0.121481i	0.998154	+	0.0607405i	$0.0193462\pi$
$53$			958543.i			0.121481i	−0.998154	+	0.0607405i	$0.980654\pi$
$54$		0			0
$55$	4.04689e6			0.442252
$56$	−3.13709e6	−	1.81120e6i	−0.318989	−	0.184168i
$57$		0			0
$58$	2.61429e6	+	4.52809e6i	0.231016	+	0.400132i
$59$	−1.38270e7	+	7.98300e6i	−1.14109	+	0.658807i	−0.946700	−	0.322118i	$-0.895605\pi$
$59$	−1.38270e7	+	7.98300e6i	−1.14109	+	0.658807i	−0.194387	+	0.980925i	$0.562272\pi$
$60$		0			0
$61$	−5.55708e6	+	9.62514e6i	−0.401354	+	0.695165i	−0.993890	−	0.110379i	$-0.964793\pi$
$61$	−5.55708e6	+	9.62514e6i	−0.401354	+	0.695165i	0.592536	+	0.805544i	$0.298127\pi$
$62$			3.18074e6i			0.215259i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	4.23417e7	+	2.44460e7i	2.37200	+	1.36947i
$66$		0			0
$67$	−1.22942e7	−	2.12942e7i	−0.610102	−	1.05673i	−0.991223	−	0.132202i	$-0.957795\pi$
$67$	−1.22942e7	−	2.12942e7i	−0.610102	−	1.05673i	0.381121	−	0.924525i	$-0.375538\pi$
$68$	6.04618e6	−	3.49076e6i	0.282778	−	0.163262i
$69$		0			0
$70$	−1.54356e7	+	2.67353e7i	−0.642883	+	1.11351i
$71$		−	1.67264e7i		−	0.658215i	−0.944292	−	0.329108i	$-0.893252\pi$
$71$		−	1.67264e7i		−	0.658215i	0.944292	−	0.329108i	$-0.106748\pi$
$72$		0			0
$73$	4.77259e6			0.168059			0.0840297	−	0.996463i	$-0.473221\pi$
$73$	4.77259e6			0.168059			0.0840297	+	0.996463i	$0.473221\pi$
$74$	−1.56752e6	−	905009.i	−0.0522741	−	0.0301805i
$75$		0			0
$76$	8.01206e6	+	1.38773e7i	0.240154	+	0.415959i
$77$	8.03648e6	−	4.63986e6i	0.228614	−	0.131990i
$78$		0			0
$79$	−1.81889e7	+	3.15042e7i	−0.466981	+	0.808835i	−0.999288	−	0.0377164i	$-0.987992\pi$
$79$	−1.81889e7	+	3.15042e7i	−0.466981	+	0.808835i	0.532308	+	0.846551i	$0.321325\pi$
$80$			1.78726e7i			0.436342i
$81$		0			0
$82$	−5.87630e7			−1.29972
$83$	−2.53425e7	−	1.46315e7i	−0.533994	−	0.308302i	0.208647	−	0.977991i	$-0.433094\pi$
$83$	−2.53425e7	−	1.46315e7i	−0.533994	−	0.308302i	−0.742641	+	0.669689i	$0.766427\pi$
$84$		0			0
$85$	−2.97494e7	−	5.15274e7i	−0.569905	−	0.987104i
$86$	−4.89601e7	+	2.82671e7i	−0.895052	+	0.516759i
$87$		0			0
$88$	2.68620e6	−	4.65264e6i	0.0447927	−	0.0775833i
$89$			6.26485e7i			0.998506i	0.866456	+	0.499253i	$0.166392\pi$
$89$			6.26485e7i			0.998506i	−0.866456	+	0.499253i	$0.833608\pi$
$90$		0			0
$91$	1.12112e8			1.63488
$92$	−3.41006e7	−	1.96880e7i	−0.476004	−	0.274821i
$93$		0			0
$94$	−2.00399e6	−	3.47102e6i	−0.0256676	−	0.0444576i
$95$	1.18267e8	−	6.82813e7i	1.45200	−	0.838315i
$96$		0			0
$97$	2.42081e7	−	4.19297e7i	0.273447	−	0.473625i	−0.696295	−	0.717756i	$-0.745169\pi$
$97$	2.42081e7	−	4.19297e7i	0.273447	−	0.473625i	0.969742	+	0.244131i	$0.0785027\pi$
$98$			5.56815e6i			0.0603680i
$99$		0			0
$100$	1.02316e8			1.02316
$101$	−4.53627e7	−	2.61902e7i	−0.435927	−	0.251682i	0.265942	−	0.963989i	$-0.414317\pi$
$101$	−4.53627e7	−	2.61902e7i	−0.435927	−	0.251682i	−0.701868	+	0.712307i	$0.747651\pi$
$102$		0			0
$103$	−3.13984e7	−	5.43835e7i	−0.278970	−	0.483191i	0.692159	−	0.721745i	$-0.256660\pi$
$103$	−3.13984e7	−	5.43835e7i	−0.278970	−	0.483191i	−0.971129	+	0.238555i	$0.923326\pi$
$104$	5.62102e7	−	3.24530e7i	0.480487	−	0.277410i
$105$		0			0
$106$	5.42234e6	−	9.39177e6i	0.0429500	−	0.0743916i
$107$			631989.i			0.00482142i	0.999997	+	0.00241071i	$0.000767353\pi$
$107$			631989.i			0.00482142i	−0.999997	+	0.00241071i	$0.999233\pi$
$108$		0			0
$109$	3.60140e7			0.255132			0.127566	−	0.991830i	$-0.459284\pi$
$109$	3.60140e7			0.255132			0.127566	+	0.991830i	$0.459284\pi$
$110$	−3.96512e7	−	2.28926e7i	−0.270823	−	0.156360i
$111$		0			0
$112$	2.04914e7	+	3.54921e7i	0.130227	+	0.225559i
$113$	−8.33220e7	+	4.81060e7i	−0.511030	+	0.295043i	−0.733257	−	0.679952i	$-0.762001\pi$
$113$	−8.33220e7	+	4.81060e7i	−0.511030	+	0.295043i	0.222227	+	0.974995i	$0.428667\pi$
$114$		0			0
$115$	−1.67787e8	+	2.90616e8i	−0.959328	+	1.66160i
$116$		−	5.91547e7i		−	0.326706i
$117$		0			0
$118$	1.80635e8			0.931694
$119$	−1.18155e8	−	6.82169e7i	−0.589203	−	0.340177i
$120$		0			0
$121$	−1.00298e8	−	1.73721e8i	−0.467898	−	0.810423i
$122$	1.08896e8	−	6.28712e7i	0.491556	−	0.283800i
$123$		0			0
$124$	1.79930e7	−	3.11648e7i	0.0761057	−	0.131819i
$125$		−	4.45852e8i		−	1.82621i
$126$		0			0
$127$	3.67312e8			1.41195			0.705976	−	0.708235i	$-0.250508\pi$
$127$	3.67312e8			1.41195			0.705976	+	0.708235i	$0.250508\pi$
$128$	2.05478e7	+	1.18633e7i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.76575e8	−	4.79041e8i	−0.968364	−	1.67726i
$131$	−2.20534e8	+	1.27325e8i	−0.748841	+	0.432343i	−0.825275	−	0.564731i	$-0.808980\pi$
$131$	−2.20534e8	+	1.27325e8i	−0.748841	+	0.432343i	0.0764341	+	0.997075i	$0.475647\pi$
$132$		0			0
$133$	1.56573e8	−	2.71192e8i	0.500391	−	0.866702i
$134$			2.78187e8i			0.862815i
$135$		0			0
$136$	−7.89870e7			−0.230887
$137$	3.69065e8	+	2.13080e8i	1.04766	+	0.604868i	0.921994	−	0.387205i	$-0.126559\pi$
$137$	3.69065e8	+	2.13080e8i	1.04766	+	0.604868i	0.125668	+	0.992072i	$0.459893\pi$
$138$		0			0
$139$	1.03393e8	+	1.79082e8i	0.276969	+	0.479725i	0.970630	−	0.240577i	$-0.0773366\pi$
$139$	1.03393e8	+	1.79082e8i	0.276969	+	0.479725i	−0.693661	+	0.720302i	$0.744003\pi$
$140$	3.02475e8	−	1.74634e8i	0.787368	−	0.454587i
$141$		0			0
$142$	−9.46185e7	+	1.63884e8i	−0.232714	+	0.403073i
$143$			1.66274e8i			0.397630i
$144$		0			0
$145$	−5.04135e8			−1.14045
$146$	−4.67616e7	−	2.69978e7i	−0.102915	−	0.0594180i
$147$		0			0
$148$	1.02390e7	+	1.77345e7i	0.0213408	+	0.0369634i
$149$	−5.73316e8	+	3.31004e8i	−1.16319	+	0.671565i	−0.952065	−	0.305895i	$-0.901044\pi$
$149$	−5.73316e8	+	3.31004e8i	−1.16319	+	0.671565i	−0.211120	+	0.977460i	$0.567711\pi$
$150$		0			0
$151$	−2.17181e8	+	3.76169e8i	−0.417749	+	0.723562i	−0.995713	−	0.0925004i	$-0.970514\pi$
$151$	−2.17181e8	+	3.76169e8i	−0.417749	+	0.723562i	0.577964	+	0.816062i	$0.303847\pi$
$152$		−	1.81292e8i		−	0.339629i
$153$		0			0
$154$	−1.04988e8			−0.186663
$155$	−2.65596e8	−	1.53342e8i	−0.460145	−	0.265665i
$156$		0			0
$157$	5.96980e8	+	1.03400e9i	0.982565	+	1.70185i	0.652293	+	0.757967i	$0.273807\pi$
$157$	5.96980e8	+	1.03400e9i	0.982565	+	1.70185i	0.330272	+	0.943886i	$0.392860\pi$
$158$	3.56429e8	−	2.05784e8i	0.571932	−	0.330205i
$159$		0			0
$160$	1.01103e8	−	1.75115e8i	0.154270	−	0.267204i
$161$			7.69489e8i			1.14525i
$162$		0			0
$163$	−1.10437e9			−1.56446			−0.782232	−	0.622987i	$-0.785919\pi$
$163$	−1.10437e9			−1.56446			−0.782232	+	0.622987i	$0.785919\pi$
$164$	5.75757e8	+	3.32414e8i	0.795910	+	0.459519i
$165$		0			0
$166$	1.65536e8	+	2.86717e8i	0.218002	+	0.377591i
$167$	−2.37674e8	+	1.37221e8i	−0.305573	+	0.176423i	−0.644944	−	0.764230i	$-0.723119\pi$
$167$	−2.37674e8	+	1.37221e8i	−0.305573	+	0.176423i	0.339371	+	0.940653i	$0.389786\pi$
$168$		0			0
$169$	−5.96541e8	+	1.03324e9i	−0.731297	+	1.26664i
$170$			6.73152e8i			0.805967i
$171$		0			0
$172$	6.39612e8			0.730807
$173$	7.56506e8	+	4.36769e8i	0.844555	+	0.487604i	0.858810	−	0.512294i	$-0.171204\pi$
$173$	7.56506e8	+	4.36769e8i	0.844555	+	0.487604i	−0.0142547	+	0.999898i	$0.504538\pi$
$174$		0			0
$175$	−9.99734e8	−	1.73159e9i	−1.06594	−	1.84626i
$176$	−5.26386e7	+	3.03909e7i	−0.0548597	+	0.0316733i
$177$		0			0
$178$	3.54393e8	−	6.13827e8i	0.353025	−	0.611457i
$179$		−	6.23780e8i		−	0.607602i	−0.952736	−	0.303801i	$-0.901744\pi$
$179$		−	6.23780e8i		−	0.607602i	0.952736	−	0.303801i	$-0.0982558\pi$
$180$		0			0
$181$	1.47088e9			1.37045			0.685227	−	0.728330i	$-0.259703\pi$
$181$	1.47088e9			1.37045			0.685227	+	0.728330i	$0.259703\pi$
$182$	−1.09847e9	−	6.34200e8i	−1.00116	−	0.578017i
$183$		0			0
$184$	2.22744e8	+	3.85804e8i	0.194328	+	0.336585i
$185$	1.51139e8	−	8.72601e7i	0.129030	−	0.0744952i
$186$		0			0
$187$	1.01173e8	−	1.75236e8i	0.0827366	−	0.143304i
$188$			4.53452e7i			0.0362995i
$189$		0			0
$190$	−1.54503e9			−1.18556
$191$	8.99674e8	+	5.19427e8i	0.676007	+	0.390293i	0.798349	−	0.602195i	$-0.205707\pi$
$191$	8.99674e8	+	5.19427e8i	0.676007	+	0.390293i	−0.122342	+	0.992488i	$0.539040\pi$
$192$		0			0
$193$	1.19815e9	+	2.07527e9i	0.863543	+	1.49570i	0.868487	+	0.495712i	$0.165093\pi$
$193$	1.19815e9	+	2.07527e9i	0.863543	+	1.49570i	−0.00494446	+	0.999988i	$0.501574\pi$
$194$	−4.74380e8	+	2.73883e8i	−0.334903	+	0.193356i
$195$		0			0
$196$	3.14982e7	−	5.45565e7i	0.0213433	−	0.0369677i
$197$		−	1.61075e9i		−	1.06945i	−0.845025	−	0.534727i	$-0.820414\pi$
$197$		−	1.61075e9i		−	1.06945i	0.845025	−	0.534727i	$-0.179586\pi$
$198$		0			0
$199$	−5.25183e8			−0.334887			−0.167444	−	0.985882i	$-0.553551\pi$
$199$	−5.25183e8			−0.334887			−0.167444	+	0.985882i	$0.553551\pi$
$200$	−1.00249e9	−	5.78786e8i	−0.626554	−	0.361741i
$201$		0			0
$202$	2.96308e8	+	5.13221e8i	0.177966	+	0.308247i
$203$	−1.00113e9	+	5.78004e8i	−0.589532	+	0.340367i
$204$		0			0
$205$	2.83293e9	−	4.90678e9i	1.60406	−	2.77831i
$206$			7.10464e8i			0.394524i
$207$		0			0
$208$	−7.34327e8			−0.392316
$209$	4.02206e8	+	2.32214e8i	0.210796	+	0.121703i
$210$		0			0
$211$	−8.85159e8	−	1.53314e9i	−0.446572	−	0.773485i	0.551588	−	0.834117i	$-0.314022\pi$
$211$	−8.85159e8	−	1.53314e9i	−0.446572	−	0.773485i	−0.998160	+	0.0606312i	$0.980689\pi$
$212$	−1.06256e8	+	6.13468e7i	−0.0526028	+	0.0303702i
$213$		0			0
$214$	3.57507e6	−	6.19220e6i	0.00170463	−	0.00295250i
$215$		−	5.45097e9i		−	2.55106i
$216$		0			0
$217$	−7.03243e8			−0.317151
$218$	−3.52863e8	−	2.03726e8i	−0.156236	−	0.0902028i
$219$		0			0
$220$	2.59001e8	+	4.48602e8i	0.110563	+	0.191501i
$221$	2.11710e9	−	1.22231e9i	0.887507	−	0.512402i
$222$		0			0
$223$	−2.52764e8	+	4.37800e8i	−0.102210	+	0.177034i	−0.912595	−	0.408865i	$-0.865925\pi$
$223$	−2.52764e8	+	4.37800e8i	−0.102210	+	0.177034i	0.810385	+	0.585898i	$0.199258\pi$
$224$		−	4.63667e8i		−	0.184168i
$225$		0			0
$226$	1.08851e9			0.417254
$227$	−6.53594e8	−	3.77352e8i	−0.246153	−	0.142116i	0.371849	−	0.928293i	$-0.378724\pi$
$227$	−6.53594e8	−	3.77352e8i	−0.246153	−	0.142116i	−0.618001	+	0.786177i	$0.712057\pi$
$228$		0			0
$229$	−2.78927e8	−	4.83115e8i	−0.101426	−	0.175675i	0.810847	−	0.585259i	$-0.199007\pi$
$229$	−2.78927e8	−	4.83115e8i	−0.101426	−	0.175675i	−0.912272	+	0.409584i	$0.865674\pi$
$230$	3.28794e9	−	1.89829e9i	1.17493	−	0.678347i
$231$		0			0
$232$	−3.34630e8	+	5.79595e8i	−0.115508	+	0.200066i
$233$			3.55157e9i			1.20503i	0.798108	+	0.602514i	$0.205834\pi$
$233$			3.55157e9i			1.20503i	−0.798108	+	0.602514i	$0.794166\pi$
$234$		0			0
$235$	3.86446e8			0.126712
$236$	−1.76985e9	−	1.02182e9i	−0.570543	−	0.329403i
$237$		0			0
$238$	7.71787e8	+	1.33677e9i	0.240541	+	0.416629i
$239$	−7.71502e8	+	4.45427e8i	−0.236453	+	0.136516i	−0.613546	−	0.789659i	$-0.710257\pi$
$239$	−7.71502e8	+	4.45427e8i	−0.236453	+	0.136516i	0.377092	+	0.926176i	$0.376924\pi$
$240$		0			0
$241$	1.71946e9	−	2.97819e9i	0.509710	−	0.882844i	−0.490227	−	0.871595i	$-0.663086\pi$
$241$	1.71946e9	−	2.97819e9i	0.509710	−	0.882844i	0.999937	−	0.0112489i	$-0.00358072\pi$
$242$			2.26949e9i			0.661707i
$243$		0			0
$244$	−1.42261e9			−0.401354
$245$	−4.64948e8	−	2.68438e8i	−0.129045	−	0.0745039i
$246$		0			0
$247$	2.80546e9	+	4.85920e9i	0.753731	+	1.30550i
$248$	−3.52589e8	+	2.03568e8i	−0.0932100	+	0.0538148i
$249$		0			0
$250$	−2.52212e9	+	4.36844e9i	−0.645662	+	1.11832i
$251$			6.42022e9i			1.61754i	0.588124	+	0.808770i	$0.299867\pi$
$251$			6.42022e9i			1.61754i	−0.588124	+	0.808770i	$0.700133\pi$
$252$		0			0
$253$	−1.14123e9			−0.278543
$254$	−3.59891e9	−	2.07783e9i	−0.864641	−	0.499201i
$255$		0			0
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	−8.30896e8	+	4.79718e8i	−0.190464	+	0.109965i	−0.592200	−	0.805791i	$-0.701740\pi$
$257$	−8.30896e8	+	4.79718e8i	−0.190464	+	0.109965i	0.401736	+	0.915756i	$0.368407\pi$
$258$		0			0
$259$	2.00092e8	−	3.46570e8i	0.0444663	−	0.0770178i
$260$			6.25817e9i			1.36947i
$261$		0			0
$262$	2.88104e9			0.611426
$263$	2.47754e9	+	1.43041e9i	0.517842	+	0.298976i	0.736051	−	0.676926i	$-0.236688\pi$
$263$	2.47754e9	+	1.43041e9i	0.517842	+	0.298976i	−0.218209	+	0.975902i	$0.570022\pi$
$264$		0			0
$265$	5.22816e8	+	9.05545e8i	0.106015	+	0.183623i
$266$	−3.06819e9	+	1.77142e9i	−0.612851	+	0.353830i
$267$		0			0
$268$	1.57366e9	−	2.72566e9i	0.305051	−	0.528364i
$269$		−	1.20245e9i		−	0.229646i	−0.993386	−	0.114823i	$-0.963370\pi$
$269$		−	1.20245e9i		−	0.229646i	0.993386	−	0.114823i	$-0.0366301\pi$
$270$		0			0
$271$	−8.98794e9			−1.66641			−0.833207	−	0.552961i	$-0.813498\pi$
$271$	−8.98794e9			−1.66641			−0.833207	+	0.552961i	$0.813498\pi$
$272$	7.73911e8	+	4.46818e8i	0.141389	+	0.0816309i
$273$		0			0
$274$	−2.41072e9	−	4.17550e9i	−0.427706	−	0.740809i
$275$	2.56813e9	−	1.48271e9i	0.449041	−	0.259254i
$276$		0			0
$277$	−8.05272e8	+	1.39477e9i	−0.136780	+	0.236911i	−0.926276	−	0.376845i	$-0.877009\pi$
$277$	−8.05272e8	+	1.39477e9i	−0.136780	+	0.236911i	0.789496	+	0.613756i	$0.210342\pi$
$278$		−	2.33952e9i		−	0.391694i
$279$		0			0
$280$	−3.95152e9			−0.642883
$281$	1.00668e10	+	5.81207e9i	1.61461	+	0.932193i	0.988284	+	0.152628i	$0.0487736\pi$
$281$	1.00668e10	+	5.81207e9i	1.61461	+	0.932193i	0.626322	+	0.779565i	$0.284560\pi$
$282$		0			0
$283$	7.70868e8	+	1.33518e9i	0.120181	+	0.208159i	0.919839	−	0.392297i	$-0.128319\pi$
$283$	7.70868e8	+	1.33518e9i	0.120181	+	0.208159i	−0.799658	+	0.600455i	$0.794986\pi$
$284$	1.85414e9	−	1.07049e9i	0.285015	−	0.164554i
$285$		0			0
$286$	9.40585e8	−	1.62914e9i	0.140583	−	0.243498i
$287$		−	1.29921e10i		−	1.91493i
$288$		0			0
$289$	4.00080e9			0.573529
$290$	4.93949e9	+	2.85182e9i	0.698378	+	0.403209i
$291$		0			0
$292$	3.05446e8	+	5.29048e8i	0.0420148	+	0.0727718i
$293$	−4.98204e9	+	2.87638e9i	−0.675984	+	0.390280i	−0.798340	−	0.602207i	$-0.794288\pi$
$293$	−4.98204e9	+	2.87638e9i	−0.675984	+	0.390280i	0.122356	+	0.992486i	$0.460955\pi$
$294$		0			0
$295$	−8.70831e9	+	1.50832e10i	−1.14986	+	1.99162i
$296$		−	2.31682e8i		−	0.0301805i
$297$		0			0
$298$	7.48977e9			0.949737
$299$	−1.19405e10	−	6.89383e9i	−1.49395	−	0.862533i
$300$		0			0
$301$	−6.24969e9	−	1.08248e10i	−0.761364	−	1.31872i
$302$	4.25587e9	−	2.45713e9i	0.511635	−	0.295393i
$303$		0			0
$304$	−1.02554e9	+	1.77629e9i	−0.120077	+	0.207979i
$305$			1.21239e10i			1.40102i
$306$		0			0
$307$	−6.49769e9			−0.731486			−0.365743	−	0.930716i	$-0.619185\pi$
$307$	−6.49769e9			−0.731486			−0.365743	+	0.930716i	$0.619185\pi$
$308$	1.02867e9	+	5.93902e8i	0.114307	+	0.0659952i
$309$		0			0
$310$	1.73487e9	+	3.00488e9i	0.187854	+	0.325372i
$311$	−1.18485e10	+	6.84076e9i	−1.26655	+	0.731245i	−0.974334	−	0.225106i	$-0.927727\pi$
$311$	−1.18485e10	+	6.84076e9i	−1.26655	+	0.731245i	−0.292219	+	0.956351i	$0.594394\pi$
$312$		0			0
$313$	−3.58243e9	+	6.20496e9i	−0.373251	+	0.646489i	−0.990064	−	0.140620i	$-0.955090\pi$
$313$	−3.58243e9	+	6.20496e9i	−0.373251	+	0.646489i	0.616813	+	0.787110i	$0.288424\pi$
$314$		−	1.35081e10i		−	1.38956i
$315$		0			0
$316$	−4.65637e9			−0.466981
$317$	9.86964e9	+	5.69824e9i	0.977382	+	0.564292i	0.901479	−	0.432824i	$-0.142483\pi$
$317$	9.86964e9	+	5.69824e9i	0.977382	+	0.564292i	0.0759031	+	0.997115i	$0.475816\pi$
$318$		0			0
$319$	−8.57241e8	−	1.48478e9i	−0.0827828	−	0.143384i
$320$	−1.98120e9	+	1.14385e9i	−0.188942	+	0.109086i
$321$		0			0
$322$	4.35289e9	−	7.53943e9i	0.404906	−	0.701318i
$323$		−	6.82818e9i		−	0.627328i
$324$		0			0
$325$	3.58263e10			3.21121
$326$	1.08206e10	+	6.24728e9i	0.958035	+	0.553122i
$327$		0			0
$328$	−3.76083e9	−	6.51395e9i	−0.324929	−	0.562793i
$329$	7.67421e8	−	4.43071e8i	0.0655014	−	0.0378172i
$330$		0			0
$331$	8.59454e9	−	1.48862e10i	0.715996	−	1.24014i	−0.246578	−	0.969123i	$-0.579306\pi$
$331$	8.59454e9	−	1.48862e10i	0.715996	−	1.24014i	0.962574	−	0.271018i	$-0.0873604\pi$
$332$		−	3.74566e9i		−	0.308302i
$333$		0			0
$334$	3.10496e9			0.249499
$335$	−2.32290e10	−	1.34112e10i	−1.84438	−	1.06485i
$336$		0			0
$337$	1.61156e9	+	2.79131e9i	0.124947	+	0.216415i	0.921712	−	0.387874i	$-0.126790\pi$
$337$	1.61156e9	+	2.79131e9i	0.124947	+	0.216415i	−0.796765	+	0.604289i	$0.793457\pi$
$338$	1.16898e10	−	6.74909e9i	0.895652	−	0.517105i
$339$		0			0
$340$	3.80792e9	−	6.59551e9i	0.284952	−	0.493552i
$341$		−	1.04298e9i		−	0.0771364i
$342$		0			0
$343$	1.31889e10			0.952870
$344$	−6.26689e9	−	3.61819e9i	−0.447526	−	0.258379i
$345$		0			0
$346$	−4.94148e9	−	8.55889e9i	−0.344788	−	0.597191i
$347$	2.16831e9	−	1.25187e9i	0.149556	−	0.0863461i	−0.423355	−	0.905964i	$-0.639148\pi$
$347$	2.16831e9	−	1.25187e9i	0.149556	−	0.0863461i	0.572911	+	0.819618i	$0.305814\pi$
$348$		0			0
$349$	−8.92317e9	+	1.54554e10i	−0.601475	+	1.04178i	0.391123	+	0.920338i	$0.372087\pi$
$349$	−8.92317e9	+	1.54554e10i	−0.601475	+	1.04178i	−0.992598	+	0.121446i	$0.961247\pi$
$350$			2.26214e10i			1.50746i
$351$		0			0
$352$	6.87667e8			0.0447927
$353$	−2.33322e9	−	1.34709e9i	−0.150265	−	0.0867555i	0.422982	−	0.906138i	$-0.360983\pi$
$353$	−2.33322e9	−	1.34709e9i	−0.150265	−	0.0867555i	−0.573247	+	0.819382i	$0.694317\pi$
$354$		0			0
$355$	−9.12302e9	−	1.58015e10i	−0.574414	−	0.994915i
$356$	−6.94466e9	+	4.00950e9i	−0.432366	+	0.249626i
$357$		0			0
$358$	−3.52863e9	+	6.11177e9i	−0.214820	+	0.372079i
$359$		−	4.46773e8i		−	0.0268973i	−0.999910	−	0.0134487i	$-0.995719\pi$
$359$		−	4.46773e8i		−	0.0268973i	0.999910	−	0.0134487i	$-0.00428097\pi$
$360$		0			0
$361$	−1.31142e9			−0.0772168
$362$	−1.44117e10	−	8.32058e9i	−0.839228	−	0.484529i
$363$		0			0
$364$	7.17516e9	+	1.24277e10i	0.408720	+	0.707924i
$365$	4.50871e9	−	2.60310e9i	0.254028	−	0.146663i
$366$		0			0
$367$	−4.50312e9	+	7.79963e9i	−0.248227	+	0.429942i	−0.963034	−	0.269380i	$-0.913181\pi$
$367$	−4.50312e9	+	7.79963e9i	−0.248227	+	0.429942i	0.714807	+	0.699322i	$0.246515\pi$
$368$		−	5.04012e9i		−	0.274821i
$369$		0			0
$370$	−1.97447e9			−0.105352
$371$	2.07646e9	+	1.19885e9i	0.109605	+	0.0632802i
$372$		0			0
$373$	3.61769e9	+	6.26602e9i	0.186894	+	0.323710i	0.944213	−	0.329335i	$-0.106825\pi$
$373$	3.61769e9	+	6.26602e9i	0.186894	+	0.323710i	−0.757319	+	0.653045i	$0.773491\pi$
$374$	−1.98257e9	+	1.14464e9i	−0.101331	+	0.0585036i
$375$		0			0
$376$	2.56511e8	−	4.44291e8i	0.0128338	−	0.0222288i
$377$		−	2.07133e10i		−	1.02538i
$378$		0			0
$379$	−2.18940e10			−1.06113			−0.530566	−	0.847644i	$-0.678020\pi$
$379$	−2.18940e10			−1.06113			−0.530566	+	0.847644i	$0.678020\pi$
$380$	1.51381e10	+	8.74001e9i	0.726002	+	0.419158i
$381$		0			0
$382$	−5.87664e9	−	1.01786e10i	−0.275979	−	0.478009i
$383$	1.99158e10	−	1.14984e10i	0.925555	−	0.534369i	0.0401518	−	0.999194i	$-0.487216\pi$
$383$	1.99158e10	−	1.14984e10i	0.925555	−	0.534369i	0.885403	+	0.464824i	$0.153883\pi$
$384$		0			0
$385$	5.06142e9	−	8.76664e9i	0.230372	−	0.399016i
$386$		−	2.71112e10i		−	1.22123i
$387$		0			0
$388$	6.19727e9			0.273447
$389$	1.71912e10	+	9.92532e9i	0.750770	+	0.433457i	0.825972	−	0.563711i	$-0.190627\pi$
$389$	1.71912e10	+	9.92532e9i	0.750770	+	0.433457i	−0.0752021	+	0.997168i	$0.523960\pi$
$390$		0			0
$391$	8.38941e9	+	1.45309e10i	0.358942	+	0.621706i
$392$	−6.17236e8	+	3.56362e8i	−0.0261401	+	0.0150920i
$393$		0			0
$394$	−9.11175e9	+	1.57820e10i	−0.378109	+	0.654904i
$395$			3.96830e10i			1.63011i
$396$		0			0
$397$	−2.22799e10			−0.896915			−0.448458	−	0.893804i	$-0.648026\pi$
$397$	−2.22799e10			−0.896915			−0.448458	+	0.893804i	$0.648026\pi$
$398$	5.14572e9	+	2.97089e9i	0.205076	+	0.118401i
$399$		0			0
$400$	6.54821e9	+	1.13418e10i	0.255789	+	0.443040i
$401$	2.03685e10	−	1.17598e10i	0.787738	−	0.454801i	−0.0514274	−	0.998677i	$-0.516377\pi$
$401$	2.03685e10	−	1.17598e10i	0.787738	−	0.454801i	0.839166	+	0.543876i	$0.183044\pi$
$402$		0			0
$403$	6.30033e9	−	1.09125e10i	0.238860	−	0.413718i
$404$		−	6.70469e9i		−	0.251682i
$405$		0			0
$406$	1.30787e10			0.481351
$407$	5.13999e8	+	2.96757e8i	0.0187320	+	0.0108149i
$408$		0			0
$409$	−2.32825e10	−	4.03265e10i	−0.832025	−	1.44111i	−0.896430	−	0.443186i	$-0.853848\pi$
$409$	−2.32825e10	−	4.03265e10i	−0.832025	−	1.44111i	0.0644044	−	0.997924i	$-0.479485\pi$
$410$	−5.55139e10	+	3.20510e10i	−1.96456	+	1.13424i
$411$		0			0
$412$	4.01899e9	−	6.96109e9i	0.139485	−	0.241595i
$413$			3.99372e10i			1.37271i
$414$		0			0
$415$	−3.19217e10			−1.07620
$416$	7.19491e9	+	4.15398e9i	0.240244	+	0.138705i
$417$		0			0
$418$	−2.62720e9	−	4.55044e9i	−0.0860573	−	0.149056i
$419$	−3.95877e9	+	2.28560e9i	−0.128441	+	0.0741556i	−0.562844	−	0.826563i	$-0.690293\pi$
$419$	−3.95877e9	+	2.28560e9i	−0.128441	+	0.0741556i	0.434403	+	0.900719i	$0.356959\pi$
$420$		0			0
$421$	6.62653e9	−	1.14775e10i	0.210939	−	0.365358i	−0.741069	−	0.671428i	$-0.765681\pi$
$421$	6.62653e9	−	1.14775e10i	0.210939	−	0.365358i	0.952009	+	0.306071i	$0.0990144\pi$
$422$			2.00289e10i			0.631548i
$423$		0			0
$424$	1.38812e9			0.0429500
$425$	−3.77576e10	−	2.17993e10i	−1.15731	−	0.668171i
$426$		0			0
$427$	1.39004e10	+	2.40762e10i	0.418135	+	0.724231i
$428$	−7.00568e7	+	4.04473e7i	−0.00208773	+	0.00120535i
$429$		0			0
$430$	−3.08354e10	+	5.34084e10i	−0.901935	+	1.56220i
$431$			2.64178e10i			0.765575i	0.923836	+	0.382787i	$0.125036\pi$
$431$			2.64178e10i			0.765575i	−0.923836	+	0.382787i	$0.874964\pi$
$432$		0			0
$433$	4.70683e10			1.33899			0.669494	−	0.742817i	$-0.266511\pi$
$433$	4.70683e10			1.33899			0.669494	+	0.742817i	$0.266511\pi$
$434$	6.89035e9	+	3.97814e9i	0.194215	+	0.112130i
$435$		0			0
$436$	2.30489e9	+	3.99219e9i	0.0637830	+	0.110475i
$437$	−3.33515e10	+	1.92555e10i	−0.914513	+	0.527995i
$438$		0			0
$439$	−1.60624e10	+	2.78209e10i	−0.432467	+	0.749055i	−0.997085	−	0.0762974i	$-0.975690\pi$
$439$	−1.60624e10	+	2.78209e10i	−0.432467	+	0.749055i	0.564618	+	0.825352i	$0.309023\pi$
$440$		−	5.86052e9i		−	0.156360i
$441$		0			0
$442$	−2.76576e10			−0.724646
$443$	4.36195e10	+	2.51837e10i	1.13257	+	0.653891i	0.944581	−	0.328279i	$-0.106469\pi$
$443$	4.36195e10	+	2.51837e10i	1.13257	+	0.653891i	0.187992	+	0.982171i	$0.439802\pi$
$444$		0			0
$445$	3.41702e10	+	5.91846e10i	0.871381	+	1.50928i
$446$	4.95314e9	−	2.85969e9i	0.125182	−	0.0722737i
$447$		0			0
$448$	−2.62290e9	+	4.54299e9i	−0.0651133	+	0.112780i
$449$		−	2.09633e10i		−	0.515792i	−0.966173	−	0.257896i	$-0.916971\pi$
$449$		−	2.09633e10i		−	0.515792i	0.966173	−	0.257896i	$-0.0830293\pi$
$450$		0			0
$451$	1.92687e10			0.465743
$452$	−1.06652e10	−	6.15757e9i	−0.255515	−	0.147522i
$453$		0			0
$454$	4.26926e9	+	7.39457e9i	0.100491	+	0.174056i
$455$	1.05913e11	−	6.11489e10i	2.47118	−	1.42674i
$456$		0			0
$457$	2.27460e10	−	3.93972e10i	0.521482	−	0.903234i	−0.478206	−	0.878248i	$-0.658713\pi$
$457$	2.27460e10	−	3.93972e10i	0.521482	−	0.903234i	0.999688	−	0.0249858i	$-0.00795405\pi$
$458$			6.31139e9i			0.143438i
$459$		0			0
$460$	−4.29535e10			−0.959328
$461$	−3.76919e10	−	2.17614e10i	−0.834534	−	0.481818i	0.0208685	−	0.999782i	$-0.493357\pi$
$461$	−3.76919e10	−	2.17614e10i	−0.834534	−	0.481818i	−0.855403	+	0.517964i	$0.826690\pi$
$462$		0			0
$463$	−1.88669e10	−	3.26784e10i	−0.410560	−	0.711111i	0.584391	−	0.811472i	$-0.301333\pi$
$463$	−1.88669e10	−	3.26784e10i	−0.410560	−	0.711111i	−0.994951	+	0.100361i	$0.968000\pi$
$464$	6.55737e9	−	3.78590e9i	0.141468	−	0.0816765i
$465$		0			0
$466$	2.00907e10	−	3.47982e10i	0.426042	−	0.737926i
$467$			1.94089e10i			0.408068i	0.978964	+	0.204034i	$0.0654053\pi$
$467$			1.94089e10i			0.408068i	−0.978964	+	0.204034i	$0.934595\pi$
$468$		0			0
$469$	−6.15054e10			−1.27122
$470$	−3.78638e9	−	2.18607e9i	−0.0775949	−	0.0447994i
$471$		0			0
$472$	1.15606e10	+	2.00236e10i	0.232923	+	0.403435i
$473$	1.60543e10	−	9.26894e9i	0.320735	−	0.185176i
$474$		0			0
$475$	5.00342e10	−	8.66618e10i	0.982862	−	1.70237i
$476$		−	1.74635e10i		−	0.340177i
$477$		0			0
$478$	1.00789e10			0.193063
$479$	−1.20390e10	−	6.95073e9i	−0.228691	−	0.132035i	0.381277	−	0.924461i	$-0.375484\pi$
$479$	−1.20390e10	−	6.95073e9i	−0.228691	−	0.132035i	−0.609968	+	0.792426i	$0.708818\pi$
$480$		0			0
$481$	3.58524e9	+	6.20981e9i	0.0669788	+	0.116011i
$482$	−3.36944e10	+	1.94534e10i	−0.624265	+	0.360420i
$483$		0			0
$484$	1.28381e10	−	2.22363e10i	0.233949	−	0.405211i
$485$		−	5.28151e10i		−	0.954534i
$486$		0			0
$487$	3.69205e10			0.656374			0.328187	−	0.944613i	$-0.393562\pi$
$487$	3.69205e10			0.656374			0.328187	+	0.944613i	$0.393562\pi$
$488$	1.39387e10	+	8.04751e9i	0.245778	+	0.141900i
$489$		0			0
$490$	3.03703e9	+	5.26028e9i	0.0526822	+	0.0912483i
$491$	−5.69924e10	+	3.29046e10i	−0.980598	+	0.566149i	−0.902451	−	0.430793i	$-0.858234\pi$
$491$	−5.69924e10	+	3.29046e10i	−0.980598	+	0.566149i	−0.0781474	+	0.996942i	$0.524900\pi$
$492$		0			0
$493$	−1.26035e10	+	2.18298e10i	−0.213355	+	0.369541i
$494$		−	6.34803e10i		−	1.06594i
$495$		0			0
$496$	4.60621e9			0.0761057
$497$	−3.62338e10	−	2.09196e10i	−0.593865	−	0.342868i
$498$		0			0
$499$	−4.81781e9	−	8.34469e9i	−0.0777047	−	0.134589i	0.824555	−	0.565782i	$-0.191426\pi$
$499$	−4.81781e9	−	8.34469e9i	−0.0777047	−	0.134589i	−0.902259	+	0.431194i	$0.858092\pi$
$500$	4.94232e10	−	2.85345e10i	0.790771	−	0.456552i
$501$		0			0
$502$	3.63183e10	−	6.29051e10i	0.571887	−	0.990537i
$503$		−	2.91551e10i		−	0.455452i	−0.973725	−	0.227726i	$-0.926871\pi$
$503$		−	2.91551e10i		−	0.455452i	0.973725	−	0.227726i	$-0.0731291\pi$
$504$		0			0
$505$	−5.71394e10			−0.878558
$506$	1.11818e10	+	6.45579e9i	0.170572	+	0.0984798i
$507$		0			0
$508$	2.35080e10	+	4.07170e10i	0.352988	+	0.611393i
$509$	−6.14696e10	+	3.54895e10i	−0.915776	+	0.528723i	−0.882285	−	0.470716i	$-0.843996\pi$
$509$	−6.14696e10	+	3.54895e10i	−0.915776	+	0.528723i	−0.0334907	+	0.999439i	$0.510662\pi$
$510$		0			0
$511$	5.96906e9	−	1.03387e10i	0.0875432	−	0.151629i
$512$			3.03700e9i			0.0441942i
$513$		0			0
$514$	1.08548e10			0.155514
$515$	−5.93246e10	−	3.42511e10i	−0.843347	−	0.486906i
$516$		0			0
$517$	6.57120e8	+	1.13817e9i	0.00919778	+	0.0159310i
$518$	−3.92099e9	+	2.26378e9i	−0.0544598	+	0.0314424i
$519$		0			0
$520$	3.54015e10	−	6.13173e10i	0.484182	−	0.838628i
$521$		−	6.08836e10i		−	0.826323i	−0.910658	−	0.413161i	$-0.864425\pi$
$521$		−	6.08836e10i		−	0.826323i	0.910658	−	0.413161i	$-0.135575\pi$
$522$		0			0
$523$	2.81890e10			0.376768			0.188384	−	0.982095i	$-0.439675\pi$
$523$	2.81890e10			0.376768			0.188384	+	0.982095i	$0.439675\pi$
$524$	−2.82283e10	−	1.62976e10i	−0.374420	−	0.216172i
$525$		0			0
$526$	−1.61832e10	−	2.80301e10i	−0.211408	−	0.366170i
$527$	−1.32799e10	+	7.66716e9i	−0.172168	+	0.0994012i
$528$		0			0
$529$	8.16093e9	−	1.41351e10i	0.104212	−	0.180500i
$530$		−	1.18300e10i		−	0.149927i
$531$		0			0
$532$	4.00826e10			0.500391
$533$	2.01604e11	+	1.16396e11i	2.49799	+	1.44221i
$534$		0			0
$535$	3.44705e8	+	5.97046e8i	0.00420758	+	0.00728774i
$536$	−3.08374e10	+	1.78040e10i	−0.373610	+	0.215704i
$537$		0			0
$538$	−6.80210e9	+	1.17816e10i	−0.0811921	+	0.140629i
$539$		−	1.82583e9i		−	0.0216324i
$540$		0			0
$541$	−1.20219e11			−1.40341			−0.701703	−	0.712470i	$-0.747577\pi$
$541$	−1.20219e11			−1.40341			−0.701703	+	0.712470i	$0.747577\pi$
$542$	8.80634e10	+	5.08435e10i	1.02047	+	0.589166i
$543$		0			0
$544$	−5.05517e9	−	8.75580e9i	−0.0577218	−	0.0999771i
$545$	3.40227e10	−	1.96430e10i	0.385641	−	0.222650i
$546$		0			0
$547$	−6.82534e10	+	1.18218e11i	−0.762386	+	1.32049i	0.179231	+	0.983807i	$0.442639\pi$
$547$	−6.82534e10	+	1.18218e11i	−0.762386	+	1.32049i	−0.941617	+	0.336685i	$0.890694\pi$
$548$			5.45485e10i			0.604868i
$549$		0			0
$550$	−3.35499e10			−0.366640
$551$	−5.01042e10	−	2.89277e10i	−0.543585	−	0.313839i
$552$		0			0
$553$	4.54977e10	+	7.88043e10i	0.486506	+	0.842654i
$554$	1.57801e10	−	9.11062e9i	0.167521	−	0.0967183i
$555$		0			0
$556$	−1.32343e10	+	2.29225e10i	−0.138485	+	0.239862i
$557$		−	1.72931e10i		−	0.179660i	−0.995957	−	0.0898300i	$-0.971368\pi$
$557$		−	1.72931e10i		−	0.179660i	0.995957	−	0.0898300i	$-0.0286324\pi$
$558$		0			0
$559$	2.23963e11			2.29366
$560$	3.87168e10	+	2.23532e10i	0.393684	+	0.227294i
$561$		0			0
$562$	−6.57561e10	−	1.13893e11i	−0.659160	−	1.14170i
$563$	−4.39485e10	+	2.53737e10i	−0.437432	+	0.252552i	−0.702508	−	0.711676i	$-0.747936\pi$
$563$	−4.39485e10	+	2.53737e10i	−0.437432	+	0.252552i	0.265076	+	0.964228i	$0.414603\pi$
$564$		0			0
$565$	−5.24767e10	+	9.08923e10i	−0.514959	+	0.891936i
$566$		−	1.74427e10i		−	0.169961i
$567$		0			0
$568$	−2.42223e10			−0.232714
$569$	−7.23149e10	−	4.17510e10i	−0.689888	−	0.398307i	0.113682	−	0.993517i	$-0.463735\pi$
$569$	−7.23149e10	−	4.17510e10i	−0.689888	−	0.398307i	−0.803570	+	0.595210i	$0.797069\pi$
$570$		0			0
$571$	6.95426e10	+	1.20451e11i	0.654194	+	1.13310i	0.982095	+	0.188385i	$0.0603254\pi$
$571$	6.95426e10	+	1.20451e11i	0.654194	+	1.13310i	−0.327901	+	0.944712i	$0.606341\pi$
$572$	−1.84316e10	+	1.06415e10i	−0.172179	+	0.0994075i
$573$		0			0
$574$	−7.34946e10	+	1.27296e11i	−0.677030	+	1.17265i
$575$			2.45897e11i			2.24948i
$576$		0			0
$577$	−1.25735e11			−1.13437			−0.567184	−	0.823591i	$-0.691967\pi$
$577$	−1.25735e11			−1.13437			−0.567184	+	0.823591i	$0.691967\pi$
$578$	−3.91997e10	−	2.26319e10i	−0.351213	−	0.202773i
$579$		0			0
$580$	−3.22646e10	−	5.58840e10i	−0.285112	−	0.493828i
$581$	−6.33915e10	+	3.65991e10i	−0.556322	+	0.321193i
$582$		0			0
$583$	−1.77801e9	+	3.07961e9i	−0.0153908	+	0.0266576i
$584$		−	6.91145e9i		−	0.0594180i
$585$		0			0
$586$	6.50851e10			0.551939
$587$	6.44083e10	+	3.71861e10i	0.542487	+	0.313205i	0.746086	−	0.665849i	$-0.231931\pi$
$587$	6.44083e10	+	3.71861e10i	0.542487	+	0.313205i	−0.203599	+	0.979054i	$0.565264\pi$
$588$		0			0
$589$	−1.75978e10	−	3.04803e10i	−0.146217	−	0.253255i
$590$	1.70647e11	−	9.85232e10i	1.40829	−	0.813075i
$591$		0			0
$592$	−1.31059e9	+	2.27001e9i	−0.0106704	+	0.0184817i
$593$			7.64545e10i			0.618279i	0.951017	+	0.309139i	$0.100041\pi$
$593$			7.64545e10i			0.618279i	−0.951017	+	0.309139i	$0.899959\pi$
$594$		0			0
$595$	−1.48830e11			−1.18747
$596$	−7.33844e10	−	4.23685e10i	−0.581593	−	0.335783i
$597$		0			0
$598$	7.79948e10	+	1.35091e11i	0.609903	+	1.05638i
$599$	−6.63143e10	+	3.82866e10i	−0.515110	+	0.297399i	−0.734932	−	0.678141i	$-0.762786\pi$
$599$	−6.63143e10	+	3.82866e10i	−0.515110	+	0.297399i	0.219822	+	0.975540i	$0.429452\pi$
$600$		0			0
$601$	−2.39823e10	+	4.15386e10i	−0.183820	+	0.318386i	−0.943178	−	0.332287i	$-0.892180\pi$
$601$	−2.39823e10	+	4.15386e10i	−0.183820	+	0.318386i	0.759358	+	0.650673i	$0.225513\pi$
$602$			1.41414e11i			1.07673i
$603$		0			0
$604$	−5.55985e10			−0.417749
$605$	−1.89505e11	−	1.09411e11i	−1.41449	−	0.816655i
$606$		0			0
$607$	−1.02320e11	−	1.77223e11i	−0.753710	−	1.30546i	−0.946013	−	0.324128i	$-0.894929\pi$
$607$	−1.02320e11	−	1.77223e11i	−0.753710	−	1.30546i	0.192303	−	0.981336i	$-0.438404\pi$
$608$	2.00965e10	−	1.16027e10i	0.147064	−	0.0849073i
$609$		0			0
$610$	6.85834e10	−	1.18790e11i	0.495336	−	0.857946i
$611$			1.58778e10i			0.113927i
$612$		0			0
$613$	4.26255e10			0.301876			0.150938	−	0.988543i	$-0.451771\pi$
$613$	4.26255e10			0.301876			0.150938	+	0.988543i	$0.451771\pi$
$614$	6.36641e10	+	3.67565e10i	0.447942	+	0.258619i
$615$		0			0
$616$	−6.71924e9	−	1.16381e10i	−0.0466656	−	0.0808273i
$617$	2.80277e9	−	1.61818e9i	0.0193396	−	0.0111657i	−0.490299	−	0.871554i	$-0.663112\pi$
$617$	2.80277e9	−	1.61818e9i	0.0193396	−	0.0111657i	0.509639	+	0.860389i	$0.329779\pi$
$618$		0			0
$619$	7.34200e10	−	1.27167e11i	0.500094	−	0.866189i	−0.499906	−	0.866080i	$-0.666632\pi$
$619$	7.34200e10	−	1.27167e11i	0.500094	−	0.866189i	1.00000		0.000108934i	$-3.46746e-5\pi$
$620$		−	3.92556e10i		−	0.265665i
$621$		0			0
$622$	1.54789e11			1.03414
$623$	1.35713e11	+	7.83542e10i	0.900888	+	0.520128i
$624$		0			0
$625$	−8.70585e10	−	1.50790e11i	−0.570546	−	0.988215i
$626$	7.02011e10	−	4.05306e10i	0.457137	−	0.263928i
$627$		0			0
$628$	−7.64135e10	+	1.32352e11i	−0.491283	+	0.850926i
$629$		−	8.72607e9i		−	0.0557463i
$630$		0			0
$631$	2.39192e11			1.50879			0.754397	−	0.656419i	$-0.227929\pi$
$631$	2.39192e11			1.50879			0.754397	+	0.656419i	$0.227929\pi$
$632$	4.56229e10	+	2.63404e10i	0.285966	+	0.165103i
$633$		0			0
$634$	−6.44682e10	−	1.11662e11i	−0.399014	−	0.691113i
$635$	3.47003e11	−	2.00342e11i	2.13422	−	1.23219i
$636$		0			0
$637$	1.10292e10	−	1.91032e10i	0.0669866	−	0.116024i
$638$			1.93971e10i			0.117073i
$639$		0			0
$640$	2.58823e10			0.154270
$641$	7.33197e8	+	4.23311e8i	0.00434299	+	0.00250742i	0.502170	−	0.864769i	$-0.332535\pi$
$641$	7.33197e8	+	4.23311e8i	0.00434299	+	0.00250742i	−0.497827	+	0.867276i	$0.665869\pi$
$642$		0			0
$643$	5.89225e10	+	1.02057e11i	0.344697	+	0.597033i	0.985299	−	0.170841i	$-0.0546483\pi$
$643$	5.89225e10	+	1.02057e11i	0.344697	+	0.597033i	−0.640602	+	0.767873i	$0.721315\pi$
$644$	−8.52989e10	+	4.92473e10i	−0.495906	+	0.286312i
$645$		0			0
$646$	−3.86260e10	+	6.69022e10i	−0.221794	+	0.384158i
$647$		−	2.63434e11i		−	1.50333i	−0.659546	−	0.751665i	$-0.729251\pi$
$647$		−	2.63434e11i		−	1.50333i	0.659546	−	0.751665i	$-0.270749\pi$
$648$		0			0
$649$	−5.92311e10			−0.333865
$650$	−3.51025e11	−	2.02664e11i	−1.96646	−	1.13534i
$651$		0			0
$652$	−7.06799e10	−	1.22421e11i	−0.391116	−	0.677433i
$653$	−1.08870e11	+	6.28559e10i	−0.598761	+	0.345695i	−0.768554	−	0.639785i	$-0.779024\pi$
$653$	−1.08870e11	+	6.28559e10i	−0.598761	+	0.345695i	0.169793	+	0.985480i	$0.445690\pi$
$654$		0			0
$655$	−1.38893e11	+	2.40570e11i	−0.754599	+	1.30700i
$656$			8.50979e10i			0.459519i
$657$		0			0
$658$	−1.00256e10			−0.0534816
$659$	3.14417e10	+	1.81529e10i	0.166711	+	0.0962506i	0.581034	−	0.813879i	$-0.302648\pi$
$659$	3.14417e10	+	1.81529e10i	0.166711	+	0.0962506i	−0.414323	+	0.910130i	$0.635982\pi$
$660$		0			0
$661$	−6.52457e10	−	1.13009e11i	−0.341779	−	0.591979i	0.642984	−	0.765880i	$-0.277696\pi$
$661$	−6.52457e10	−	1.13009e11i	−0.341779	−	0.591979i	−0.984763	+	0.173901i	$0.944363\pi$
$662$	−1.68418e11	+	9.72361e10i	−0.876912	+	0.506286i
$663$		0			0
$664$	−2.11887e10	+	3.66998e10i	−0.109001	+	0.188796i
$665$		−	3.41597e11i		−	1.74673i
$666$		0			0
$667$	1.42167e11			0.718285
$668$	−3.04222e10	−	1.75643e10i	−0.152787	−	0.0882114i
$669$		0			0
$670$	1.51731e11	+	2.62806e11i	0.752965	+	1.30417i
$671$	−3.57076e10	+	2.06158e10i	−0.176145	+	0.101697i
$672$		0			0
$673$	−1.99070e10	+	3.44799e10i	−0.0970388	+	0.168076i	−0.910458	−	0.413602i	$-0.864270\pi$
$673$	−1.99070e10	+	3.44799e10i	−0.0970388	+	0.168076i	0.813419	+	0.581678i	$0.197604\pi$
$674$		−	3.64655e10i		−	0.176702i
$675$		0			0
$676$	−1.52715e11			−0.731297
$677$	2.31655e11	+	1.33746e11i	1.10277	+	0.636687i	0.936948	−	0.349468i	$-0.113638\pi$
$677$	2.31655e11	+	1.33746e11i	1.10277	+	0.636687i	0.165826	+	0.986155i	$0.446971\pi$
$678$		0			0
$679$	−6.05539e10	−	1.04882e11i	−0.284881	−	0.493428i
$680$	−7.46197e10	+	4.30817e10i	−0.348994	+	0.201492i
$681$		0			0
$682$	−5.90000e9	+	1.02191e10i	−0.0272719	+	0.0472362i
$683$		−	3.82963e10i		−	0.175984i	−0.996121	−	0.0879922i	$-0.971955\pi$
$683$		−	3.82963e10i		−	0.175984i	0.996121	−	0.0879922i	$-0.0280451\pi$
$684$		0			0
$685$	4.64879e11			2.11144
$686$	−1.29225e11	−	7.46079e10i	−0.583511	−	0.336890i
$687$		0			0
$688$	4.09352e10	+	7.09018e10i	0.182702	+	0.316449i
$689$	−3.72059e10	+	2.14809e10i	−0.165096	+	0.0953179i
$690$		0			0
$691$	2.01386e11	−	3.48810e11i	0.883316	−	1.52995i	0.0356843	−	0.999363i	$-0.488639\pi$
$691$	2.01386e11	−	3.48810e11i	0.883316	−	1.52995i	0.847632	−	0.530585i	$-0.178028\pi$
$692$			1.11813e11i			0.487604i
$693$		0			0
$694$	−2.83267e10			−0.122112
$695$	1.95353e11	+	1.12787e11i	0.837297	+	0.483414i
$696$		0			0
$697$	−1.41648e11	−	2.45341e11i	−0.600175	−	1.03953i
$698$	1.74858e11	−	1.00954e11i	0.736653	−	0.425307i
$699$		0			0
$700$	1.27966e11	−	2.21644e11i	0.532969	−	0.923130i
$701$		−	4.49866e11i		−	1.86299i	−0.363750	−	0.931497i	$-0.618504\pi$
$701$		−	4.49866e11i		−	1.86299i	0.363750	−	0.931497i	$-0.381496\pi$
$702$		0			0
$703$	2.00282e10			0.0820013
$704$	−6.73774e9	−	3.89003e9i	−0.0274298	−	0.0158366i
$705$		0			0
$706$	1.52405e10	+	2.63974e10i	0.0613454	+	0.106253i
$707$	−1.13470e11	+	6.55119e10i	−0.454154	+	0.262206i
$708$		0			0
$709$	1.26945e11	−	2.19875e11i	0.502378	−	0.870145i	−0.497618	−	0.867396i	$-0.665792\pi$
$709$	1.26945e11	−	2.19875e11i	0.502378	−	0.870145i	0.999996	−	0.00274839i	$-0.000874840\pi$
$710$			2.06430e11i			0.812345i
$711$		0			0
$712$	9.07247e10			0.353025
$713$	7.48989e10	+	4.32429e10i	0.289813	+	0.167323i
$714$		0			0
$715$	9.06903e10	+	1.57080e11i	0.347006	+	0.601031i
$716$	6.91468e10	−	3.99219e10i	0.263099	−	0.151901i
$717$		0			0
$718$	−2.52733e9	+	4.37746e9i	−0.00950964	+	0.0164712i
$719$			5.21386e11i			1.95094i	0.220134	+	0.975470i	$0.429351\pi$
$719$			5.21386e11i			1.95094i	−0.220134	+	0.975470i	$0.570649\pi$
$720$		0			0
$721$	−1.57079e11			−0.581269
$722$	1.28492e10	+	7.41849e9i	0.0472854	+	0.0273003i
$723$		0			0
$724$	9.41366e10	+	1.63049e11i	0.342613	+	0.593424i
$725$	−3.19921e11	+	1.84706e11i	−1.15795	+	0.668544i
$726$		0			0
$727$	2.86428e9	−	4.96107e9i	0.0102536	−	0.0177598i	−0.860853	−	0.508854i	$-0.830069\pi$
$727$	2.86428e9	−	4.96107e9i	0.0102536	−	0.0177598i	0.871107	+	0.491094i	$0.163403\pi$
$728$		−	1.62355e11i		−	0.578017i
$729$		0			0
$730$	−5.89015e10			−0.207413
$731$	−2.36036e11	−	1.36275e11i	−0.826625	−	0.477252i
$732$		0			0
$733$	1.60850e11	+	2.78600e11i	0.557192	+	0.965084i	0.997729	+	0.0673502i	$0.0214545\pi$
$733$	1.60850e11	+	2.78600e11i	0.557192	+	0.965084i	−0.440538	+	0.897734i	$0.645212\pi$
$734$	8.82427e10	−	5.09469e10i	0.304015	−	0.175523i
$735$		0			0
$736$	−2.85112e10	+	4.93829e10i	−0.0971638	+	0.168293i
$737$		−	9.12190e10i		−	0.309183i
$738$		0			0
$739$	−5.10308e11			−1.71102			−0.855508	−	0.517789i	$-0.826755\pi$
$739$	−5.10308e11			−1.71102			−0.855508	+	0.517789i	$0.826755\pi$
$740$	1.93458e10	+	1.11693e10i	0.0645148	+	0.0372476i
$741$		0			0
$742$	−1.35634e10	−	2.34925e10i	−0.0447459	−	0.0775021i
$743$	3.85768e11	−	2.22723e11i	1.26582	−	0.730819i	0.291622	−	0.956533i	$-0.405805\pi$
$743$	3.85768e11	−	2.22723e11i	1.26582	−	0.730819i	0.974194	+	0.225714i	$0.0724716\pi$
$744$		0			0
$745$	−3.61078e11	+	6.25405e11i	−1.17213	+	2.03019i
$746$		−	8.18589e10i		−	0.264308i
$747$		0			0
$748$	2.59002e10			0.0827366
$749$	1.36906e9	+	7.90426e8i	0.00435005	+	0.00251151i
$750$		0			0
$751$	−2.49914e11	−	4.32864e11i	−0.785654	−	1.36079i	−0.928608	−	0.371063i	$-0.878993\pi$
$751$	−2.49914e11	−	4.32864e11i	−0.785654	−	1.36079i	0.142954	−	0.989729i	$-0.454340\pi$
$752$	−5.02657e9	+	2.90209e9i	−0.0157181	+	0.00907486i
$753$		0			0
$754$	−1.17172e11	+	2.02948e11i	−0.362526	+	0.627913i
$755$			4.73828e11i			1.45825i
$756$		0			0
$757$	4.42799e11			1.34841			0.674207	−	0.738542i	$-0.264485\pi$
$757$	4.42799e11			1.34841			0.674207	+	0.738542i	$0.264485\pi$
$758$	2.14517e11	+	1.23851e11i	0.649808	+	0.375167i
$759$		0			0
$760$	−9.88819e10	−	1.71268e11i	−0.296389	−	0.513361i
$761$	−4.15275e11	+	2.39759e11i	−1.23822	+	0.714885i	−0.968730	−	0.248119i	$-0.920188\pi$
$761$	−4.15275e11	+	2.39759e11i	−1.23822	+	0.714885i	−0.269488	+	0.963004i	$0.586854\pi$
$762$		0			0
$763$	4.50425e10	−	7.80159e10i	0.132900	−	0.230189i
$764$			1.32973e11i			0.390293i
$765$		0			0
$766$	−2.60179e11			−0.755712
$767$	−6.19721e11	−	3.57796e11i	−1.79067	−	1.03384i
$768$		0			0
$769$	1.36289e10	+	2.36059e10i	0.0389722	+	0.0675018i	0.884854	−	0.465869i	$-0.154258\pi$
$769$	1.36289e10	+	2.36059e10i	0.0389722	+	0.0675018i	−0.845881	+	0.533371i	$0.820925\pi$
$770$	−9.91832e10	+	5.72635e10i	−0.282147	+	0.162898i
$771$		0			0
$772$	−1.53364e11	+	2.65634e11i	−0.431771	+	0.747850i
$773$		−	2.36838e11i		−	0.663336i	−0.943396	−	0.331668i	$-0.892389\pi$
$773$		−	2.36838e11i		−	0.663336i	0.943396	−	0.331668i	$-0.107611\pi$
$774$		0			0
$775$	−2.24728e11			−0.622945
$776$	−6.07206e10	−	3.50571e10i	−0.167452	−	0.0966782i
$777$		0			0
$778$	−1.12292e11	−	1.94496e11i	−0.306501	−	0.530875i
$779$	5.63110e11	−	3.25112e11i	1.52913	−	0.882842i
$780$		0			0
$781$	3.10259e10	−	5.37385e10i	0.0833913	−	0.144438i
$782$		−	1.89831e11i		−	0.507621i
$783$		0			0
$784$	8.06354e9			0.0213433
$785$	1.12795e12	+	6.51220e11i	2.97036	+	1.71494i
$786$		0			0
$787$	1.75898e11	+	3.04664e11i	0.458523	+	0.794185i	0.998883	−	0.0472487i	$-0.0150453\pi$
$787$	1.75898e11	+	3.04664e11i	0.458523	+	0.794185i	−0.540360	+	0.841434i	$0.681712\pi$
$788$	1.78553e11	−	1.03088e11i	0.463087	−	0.267363i
$789$		0			0
$790$	2.24481e11	−	3.88813e11i	0.576330	−	0.998234i
$791$			2.40664e11i			0.614759i
$792$		0			0
$793$	−4.98134e11			−1.25966
$794$	2.18298e11	+	1.26034e11i	0.549246	+	0.317107i
$795$		0			0
$796$	−3.36117e10	−	5.82172e10i	−0.0837218	−	0.145010i
$797$	1.21936e11	−	7.03995e10i	0.302202	−	0.174476i	−0.341230	−	0.939980i	$-0.610843\pi$
$797$	1.21936e11	−	7.03995e10i	0.302202	−	0.174476i	0.643432	+	0.765504i	$0.277510\pi$
$798$		0			0
$799$	9.66122e9	−	1.67337e10i	0.0237053	−	0.0410587i
$800$		−	1.48169e11i		−	0.361741i
$801$		0			0
$802$	−2.66093e11			−0.643186
$803$	1.53334e10	+	8.85274e9i	0.0368787	+	0.0212919i
$804$		0			0
$805$	4.19701e11	+	7.26944e11i	0.999440	+	1.73108i
$806$	−1.23461e11	+	7.12801e10i	−0.292542	+	0.168899i
$807$		0			0
$808$	−3.79274e10	+	6.56922e10i	−0.0889832	+	0.154123i
$809$		−	5.70685e10i		−	0.133230i	−0.997779	−	0.0666151i	$-0.978780\pi$
$809$		−	5.70685e10i		−	0.133230i	0.997779	−	0.0666151i	$-0.0212199\pi$
$810$		0			0
$811$	−5.81519e11			−1.34425			−0.672126	−	0.740437i	$-0.734619\pi$
$811$	−5.81519e11			−1.34425			−0.672126	+	0.740437i	$0.734619\pi$
$812$	−1.28145e11	−	7.39845e10i	−0.294766	−	0.170183i
$813$		0			0
$814$	−3.35743e9	−	5.81523e9i	−0.00764731	−	0.0132455i
$815$	−1.04331e12	+	6.02356e11i	−2.36474	+	1.36528i
$816$		0			0
$817$	3.12781e11	−	5.41753e11i	0.702025	−	1.21594i
$818$			5.26823e11i			1.17666i
$819$		0			0
$820$	7.25231e11			1.60406
$821$	−2.88515e11	−	1.66574e11i	−0.635031	−	0.366636i	0.147667	−	0.989037i	$-0.452824\pi$
$821$	−2.88515e11	−	1.66574e11i	−0.635031	−	0.366636i	−0.782698	+	0.622402i	$0.786157\pi$
$822$		0			0
$823$	4.11950e11	+	7.13518e11i	0.897935	+	1.55527i	0.830129	+	0.557571i	$0.188266\pi$
$823$	4.11950e11	+	7.13518e11i	0.897935	+	1.55527i	0.0678057	+	0.997699i	$0.478400\pi$
$824$	−7.87558e10	+	4.54697e10i	−0.170834	+	0.0986309i
$825$		0			0
$826$	2.25919e11	−	3.91303e11i	0.485325	−	0.840608i
$827$		−	8.92051e11i		−	1.90708i	−0.301274	−	0.953538i	$-0.597412\pi$
$827$		−	8.92051e11i		−	1.90708i	0.301274	−	0.953538i	$-0.402588\pi$
$828$		0			0
$829$	−1.53632e11			−0.325284			−0.162642	−	0.986685i	$-0.552002\pi$
$829$	−1.53632e11			−0.325284			−0.162642	+	0.986685i	$0.552002\pi$
$830$	3.12767e11	+	1.80576e11i	0.659036	+	0.380495i
$831$		0			0
$832$	−4.69970e10	−	8.14011e10i	−0.0980791	−	0.169878i
$833$	−2.32475e10	+	1.34220e10i	−0.0482833	+	0.0278764i
$834$		0			0
$835$	−1.49688e11	+	2.59268e11i	−0.307923	+	0.533338i
$836$			5.94467e10i			0.121703i
$837$		0			0
$838$	5.17172e10			0.104872
$839$	−2.64665e11	−	1.52805e11i	−0.534133	−	0.308382i	0.208565	−	0.978009i	$-0.433121\pi$
$839$	−2.64665e11	−	1.52805e11i	−0.534133	−	0.308382i	−0.742698	+	0.669627i	$0.766454\pi$
$840$		0			0
$841$	−1.43334e11	−	2.48261e11i	−0.286526	−	0.496278i
$842$	−1.29853e11	+	7.49706e10i	−0.258347	+	0.149157i
$843$		0			0
$844$	1.13300e11	−	1.96242e11i	0.223286	−	0.386743i
$845$			1.30148e12i			2.55277i
$846$		0			0
$847$	−5.01769e11			−0.974923
$848$	−1.36007e10	−	7.85239e9i	−0.0263014	−	0.0151851i
$849$		0			0
$850$	2.46631e11	+	4.27178e11i	0.472468	+	0.818339i
$851$	−4.26216e10	+	2.46076e10i	−0.0812665	+	0.0469192i
$852$		0			0
$853$	−2.22811e11	+	3.85919e11i	−0.420862	+	0.728955i	−0.996024	−	0.0890849i	$-0.971606\pi$
$853$	−2.22811e11	+	3.85919e11i	−0.420862	+	0.728955i	0.575162	+	0.818040i	$0.304939\pi$
$854$		−	3.14531e11i		−	0.591332i
$855$		0			0
$856$	9.15218e8			0.00170463
$857$	8.02066e10	+	4.63073e10i	0.148692	+	0.0858472i	0.572500	−	0.819905i	$-0.305974\pi$
$857$	8.02066e10	+	4.63073e10i	0.148692	+	0.0858472i	−0.423808	+	0.905752i	$0.639307\pi$
$858$		0			0
$859$	1.29899e11	+	2.24992e11i	0.238580	+	0.413233i	0.960307	−	0.278945i	$-0.0899847\pi$
$859$	1.29899e11	+	2.24992e11i	0.238580	+	0.413233i	−0.721727	+	0.692178i	$0.756651\pi$
$860$	6.04247e11	−	3.48862e11i	1.10464	−	0.637765i
$861$		0			0
$862$	1.49442e11	−	2.58841e11i	0.270672	−	0.468817i
$863$		−	8.28592e10i		−	0.149382i	−0.997207	−	0.0746909i	$-0.976203\pi$
$863$		−	8.28592e10i		−	0.149382i	0.997207	−	0.0746909i	$-0.0237970\pi$
$864$		0			0
$865$	9.52905e11			1.70210
$866$	−4.61173e11	−	2.66259e11i	−0.819960	−	0.473404i
$867$		0			0
$868$	−4.50076e10	−	7.79554e10i	−0.0792878	−	0.137331i
$869$	−1.16875e11	+	6.74778e10i	−0.204947	+	0.118326i
$870$		0			0
$871$	5.51025e11	−	9.54404e11i	0.957412	−	1.65829i
$872$		−	5.21538e10i		−	0.0902028i
$873$		0			0
$874$	4.35703e11			0.746697
$875$	−9.65834e11	−	5.57625e11i	−1.64767	−	0.951283i
$876$		0			0
$877$	−1.71742e11	−	2.97466e11i	−0.290321	−	0.502851i	0.683564	−	0.729890i	$-0.260429\pi$
$877$	−1.71742e11	−	2.97466e11i	−0.290321	−	0.502851i	−0.973886	+	0.227039i	$0.927096\pi$
$878$	3.14758e11	−	1.81726e11i	0.529662	−	0.305800i
$879$		0			0
$880$	−3.31521e10	+	5.74211e10i	−0.0552815	+	0.0957504i
$881$		−	7.74337e11i		−	1.28537i	−0.766132	−	0.642683i	$-0.777821\pi$
$881$		−	7.74337e11i		−	1.28537i	0.766132	−	0.642683i	$-0.222179\pi$
$882$		0			0
$883$	−3.73068e11			−0.613685			−0.306842	−	0.951760i	$-0.599272\pi$
$883$	−3.73068e11			−0.613685			−0.306842	+	0.951760i	$0.599272\pi$
$884$	2.70989e11	+	1.56455e11i	0.443754	+	0.256201i
$885$		0			0
$886$	−2.84922e11	−	4.93499e11i	−0.462371	−	0.800850i
$887$	5.41302e11	−	3.12521e11i	0.874471	−	0.504876i	0.00563925	−	0.999984i	$-0.498205\pi$
$887$	5.41302e11	−	3.12521e11i	0.874471	−	0.504876i	0.868831	+	0.495108i	$0.164872\pi$
$888$		0			0
$889$	4.59395e11	−	7.95696e11i	0.735495	−	1.27391i
$890$		−	7.73184e11i		−	1.23232i
$891$		0			0
$892$	−6.47075e10			−0.102210
$893$	3.84075e10	+	2.21746e10i	0.0603963	+	0.0348698i
$894$		0			0
$895$	−3.40227e11	−	5.89291e11i	−0.530245	−	0.918412i
$896$	5.13981e10	−	2.96747e10i	0.0797472	−	0.0460420i
$897$		0			0
$898$	−1.18587e11	+	2.05398e11i	−0.182360	+	0.315857i
$899$			1.29928e11i			0.198914i
$900$		0			0
$901$	5.22820e10			0.0793329
$902$	−1.88794e11	−	1.09000e11i	−0.285208	−	0.164665i
$903$		0			0
$904$	6.96649e10	+	1.20663e11i	0.104313	+	0.180676i
$905$	1.38956e12	−	8.02262e11i	2.07149	−	1.19597i
$906$		0			0
$907$	−4.55030e11	+	7.88136e11i	−0.672375	+	1.16459i	0.304854	+	0.952399i	$0.401392\pi$
$907$	−4.55030e11	+	7.88136e11i	−0.672375	+	1.16459i	−0.977229	+	0.212188i	$0.931941\pi$
$908$		−	9.66022e10i		−	0.142116i
$909$		0			0
$910$	−1.38364e12			−2.01771
$911$	−9.63591e10	−	5.56330e10i	−0.139901	−	0.0807716i	0.428416	−	0.903582i	$-0.359072\pi$
$911$	−9.63591e10	−	5.56330e10i	−0.139901	−	0.0807716i	−0.568317	+	0.822810i	$0.692405\pi$
$912$		0			0
$913$	−5.42802e10	−	9.40162e10i	−0.0781194	−	0.135307i
$914$	−4.45728e11	+	2.57341e11i	−0.638683	+	0.368744i
$915$		0			0
$916$	3.57026e10	−	6.18388e10i	0.0507129	−	0.0878373i
$917$			6.36980e11i			0.900842i
$918$		0			0
$919$	1.32576e12			1.85867			0.929333	−	0.369243i	$-0.120383\pi$
$919$	1.32576e12			1.85867			0.929333	+	0.369243i	$0.120383\pi$
$920$	4.20856e11	+	2.42982e11i	0.587466	+	0.339174i
$921$		0			0
$922$	2.46202e11	+	4.26435e11i	0.340697	+	0.590105i
$923$	6.49235e11	−	3.74836e11i	0.894530	−	0.516457i
$924$		0			0
$925$	6.39412e10	−	1.10749e11i	0.0873401	−	0.151278i
$926$			4.26909e11i			0.580620i
$927$		0			0
$928$	−8.56652e10			−0.115508
$929$	−1.11339e12	−	6.42815e11i	−1.49480	−	0.863024i	−0.494819	−	0.868996i	$-0.664766\pi$
$929$	−1.11339e12	−	6.42815e11i	−1.49480	−	0.863024i	−0.999982	+	0.00597212i	$0.998099\pi$
$930$		0			0
$931$	−3.08063e10	−	5.33582e10i	−0.0410054	−	0.0710235i
$932$	−3.93696e11	+	2.27301e11i	−0.521792	+	0.301257i
$933$		0			0
$934$	1.09793e11	−	1.90167e11i	0.144274	−	0.249890i
$935$		−	2.20730e11i		−	0.288812i
$936$		0			0
$937$	−3.48380e11			−0.451955			−0.225977	−	0.974133i	$-0.572558\pi$
$937$	−3.48380e11			−0.451955			−0.225977	+	0.974133i	$0.572558\pi$
$938$	6.02628e11	+	3.47927e11i	0.778462	+	0.449446i
$939$		0			0
$940$	2.47326e10	+	4.28380e10i	0.0316780	+	0.0548679i
$941$	−7.29969e11	+	4.21448e11i	−0.930992	+	0.537508i	−0.887125	−	0.461529i	$-0.847301\pi$
$941$	−7.29969e11	+	4.21448e11i	−0.930992	+	0.537508i	−0.0438668	+	0.999037i	$0.513968\pi$
$942$		0			0
$943$	−7.98895e11	+	1.38373e12i	−1.01028	+	1.74986i
$944$		−	2.61587e11i		−	0.329403i
$945$		0			0
$946$	−2.09732e11			−0.261879
$947$	−1.07702e12	−	6.21820e11i	−1.33914	−	0.773152i	−0.352459	−	0.935827i	$-0.614655\pi$
$947$	−1.07702e12	−	6.21820e11i	−1.33914	−	0.773152i	−0.986680	+	0.162675i	$0.947988\pi$
$948$		0			0
$949$	1.06953e11	+	1.85248e11i	0.131865	+	0.228397i
$950$	−9.80466e11	+	5.66072e11i	−1.20376	+	0.694988i
$951$		0			0
$952$	−9.87887e10	+	1.71107e11i	−0.120271	+	0.208315i
$953$			2.58906e11i			0.313885i	0.987608	+	0.156942i	$0.0501637\pi$
$953$			2.58906e11i			0.313885i	−0.987608	+	0.156942i	$0.949836\pi$
$954$		0			0
$955$	1.13324e12			1.36241
$956$	−9.87523e10	−	5.70146e10i	−0.118227	−	0.0682582i
$957$		0			0
$958$	7.86385e10	+	1.36206e11i	0.0933626	+	0.161709i
$959$	9.23177e11	−	5.32996e11i	1.09147	−	0.630159i
$960$		0			0
$961$	3.86925e11	−	6.70175e11i	0.453663	−	0.785768i
$962$		−	8.11246e10i		−	0.0947224i
$963$		0			0
$964$	4.40181e11			0.509710
$965$	2.26382e12	+	1.30701e12i	2.61055	+	1.50720i
$966$		0			0
$967$	−5.06389e11	−	8.77092e11i	−0.579133	−	1.00309i	−0.995579	−	0.0939280i	$-0.970058\pi$
$967$	−5.06389e11	−	8.77092e11i	−0.579133	−	1.00309i	0.416446	−	0.909161i	$-0.363276\pi$
$968$	−2.51575e11	+	1.45247e11i	−0.286528	+	0.165427i
$969$		0			0
$970$	−2.98767e11	+	5.17480e11i	−0.337479	+	0.584530i
$971$			6.44723e11i			0.725265i	0.931932	+	0.362632i	$0.118122\pi$
$971$			6.44723e11i			0.725265i	−0.931932	+	0.362632i	$0.881878\pi$
$972$		0			0
$973$	5.17253e11			0.577100
$974$	−3.61745e11	−	2.08854e11i	−0.401945	−	0.232063i
$975$		0			0
$976$	−9.10472e10	−	1.57698e11i	−0.100338	−	0.173791i
$977$	−1.30863e12	+	7.55535e11i	−1.43627	+	0.829233i	−0.997588	−	0.0694077i	$-0.977889\pi$
$977$	−1.30863e12	+	7.55535e11i	−1.43627	+	0.829233i	−0.438685	+	0.898641i	$0.644556\pi$
$978$		0			0
$979$	−1.16207e11	+	2.01277e11i	−0.126504	+	0.219111i
$980$		−	6.87200e10i		−	0.0745039i
$981$		0			0
$982$	7.44546e11			0.800655
$983$	9.28316e11	+	5.35963e11i	0.994218	+	0.574012i	0.906532	−	0.422136i	$-0.138720\pi$
$983$	9.28316e11	+	5.35963e11i	0.994218	+	0.574012i	0.0876854	+	0.996148i	$0.472053\pi$
$984$		0			0
$985$	−8.78546e11	−	1.52169e12i	−0.933296	−	1.61652i
$986$	2.46976e11	−	1.42592e11i	0.261305	−	0.150865i
$987$		0			0
$988$	−3.59099e11	+	6.21977e11i	−0.376865	+	0.652750i
$989$			1.53719e12i			1.60673i
$990$		0			0
$991$	−8.67927e11			−0.899888			−0.449944	−	0.893057i	$-0.648556\pi$
$991$	−8.67927e11			−0.899888			−0.449944	+	0.893057i	$0.648556\pi$
$992$	−4.51314e10	−	2.60567e10i	−0.0466050	−	0.0269074i
$993$		0			0
$994$	2.36678e11	+	4.09938e11i	0.242445	+	0.419926i
$995$	−4.96146e11	+	2.86450e11i	−0.506194	+	0.292251i
$996$		0			0
$997$	1.19459e11	−	2.06909e11i	0.120903	−	0.209411i	−0.799221	−	0.601037i	$-0.794754\pi$
$997$	1.19459e11	−	2.06909e11i	0.120903	−	0.209411i	0.920124	+	0.391627i	$0.128088\pi$
$998$			1.09015e11i			0.109891i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.9.d.a.35.4		16
3.2	odd	2		18.9.d.a.11.7	yes	16
4.3	odd	2		432.9.q.c.305.8		16
9.2	odd	6		162.9.b.c.161.1		16
9.4	even	3		18.9.d.a.5.7	✓	16
9.5	odd	6	inner	54.9.d.a.17.4		16
9.7	even	3		162.9.b.c.161.16		16
12.11	even	2		144.9.q.b.65.3		16
36.23	even	6		432.9.q.c.17.8		16
36.31	odd	6		144.9.q.b.113.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.7	✓	16	9.4	even	3
18.9.d.a.11.7	yes	16	3.2	odd	2
54.9.d.a.17.4		16	9.5	odd	6	inner
54.9.d.a.35.4		16	1.1	even	1	trivial
144.9.q.b.65.3		16	12.11	even	2
144.9.q.b.113.3		16	36.31	odd	6
162.9.b.c.161.1		16	9.2	odd	6
162.9.b.c.161.16		16	9.7	even	3
432.9.q.c.17.8		16	36.23	even	6
432.9.q.c.305.8		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(944.709 - 545.428i) q^{5} +(1250.70 - 2166.27i) q^{7} -1448.15i q^{8} -12341.6 q^{10} +(3212.80 + 1854.91i) q^{11} +(22409.9 + 38815.1i) q^{13} +(-24508.5 + 14150.0i) q^{14} +(-8192.00 + 14189.0i) q^{16} -54543.2i q^{17} +125188. q^{19} +(120923. + 69814.8i) q^{20} +(-20985.9 - 36348.7i) q^{22} +(-266411. + 153812. i) q^{23} +(399671. - 692251. i) q^{25} -507078. i q^{26} +320178. q^{28} +(-400230. - 231073. i) q^{29} +(-140570. - 243475. i) q^{31} +(160530. - 92681.9i) q^{32} +(-308543. + 534412. i) q^{34} -2.72866e6i q^{35} +159985. q^{37} +(-1.22659e6 - 708173. i) q^{38} +(-789864. - 1.36808e6i) q^{40} +(4.49810e6 - 2.59698e6i) q^{41} +(2.49848e6 - 4.32750e6i) q^{43} +474858. i q^{44} +3.48037e6 q^{46} +(306798. + 177130. i) q^{47} +(-246080. - 426223. i) q^{49} +(-7.83192e6 + 4.52176e6i) q^{50} +(-2.86847e6 + 4.96833e6i) q^{52} +958543. i q^{53} +4.04689e6 q^{55} +(-3.13709e6 - 1.81120e6i) q^{56} +(2.61429e6 + 4.52809e6i) q^{58} +(-1.38270e7 + 7.98300e6i) q^{59} +(-5.55708e6 + 9.62514e6i) q^{61} +3.18074e6i q^{62} -2.09715e6 q^{64} +(4.23417e7 + 2.44460e7i) q^{65} +(-1.22942e7 - 2.12942e7i) q^{67} +(6.04618e6 - 3.49076e6i) q^{68} +(-1.54356e7 + 2.67353e7i) q^{70} -1.67264e7i q^{71} +4.77259e6 q^{73} +(-1.56752e6 - 905009. i) q^{74} +(8.01206e6 + 1.38773e7i) q^{76} +(8.03648e6 - 4.63986e6i) q^{77} +(-1.81889e7 + 3.15042e7i) q^{79} +1.78726e7i q^{80} -5.87630e7 q^{82} +(-2.53425e7 - 1.46315e7i) q^{83} +(-2.97494e7 - 5.15274e7i) q^{85} +(-4.89601e7 + 2.82671e7i) q^{86} +(2.68620e6 - 4.65264e6i) q^{88} +6.26485e7i q^{89} +1.12112e8 q^{91} +(-3.41006e7 - 1.96880e7i) q^{92} +(-2.00399e6 - 3.47102e6i) q^{94} +(1.18267e8 - 6.82813e7i) q^{95} +(2.42081e7 - 4.19297e7i) q^{97} +5.56815e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29}+ \cdots - 89415484 q^{97}+O(q^{100}) \) 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7 - 45756 * q^11 - 3370 * q^13 + 94464 * q^14 - 131072 * q^16 + 362180 * q^19 + 112896 * q^20 - 61824 * q^22 - 1311138 * q^23 + 963394 * q^25 - 472576 * q^28 + 2851290 * q^29 + 542438 * q^31 + 220416 * q^34 + 3343328 * q^37 + 1314432 * q^38 - 9218592 * q^41 + 339512 * q^43 + 7417344 * q^46 + 34980606 * q^47 - 2364654 * q^49 - 27744768 * q^50 + 431360 * q^52 - 4584276 * q^55 + 12091392 * q^56 - 7852800 * q^58 - 93924216 * q^59 - 841954 * q^61 - 33554432 * q^64 + 126568134 * q^65 + 29946644 * q^67 + 5476608 * q^68 - 34359552 * q^70 - 7547764 * q^73 - 35124480 * q^74 + 23179520 * q^76 - 9309294 * q^77 + 33813002 * q^79 - 137346048 * q^82 - 114200226 * q^83 - 125696772 * q^85 + 171379584 * q^86 + 7913472 * q^88 + 268578316 * q^91 - 167825664 * q^92 - 11832576 * q^94 + 143949240 * q^95 - 89415484 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more