LMFDB - Embedded newform 54.9.d.a.17.4

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			17.4
Root			$-197.435 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	54.17
Dual form			54.9.d.a.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−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	0.999909	+	0.0134763i	$0.00428977\pi$
$5$	944.709	+	545.428i	1.51153	+	0.872685i	0.511625	+	0.859209i	$0.329044\pi$
$6$		0			0
$7$	1250.70	+	2166.27i	0.520906	+	0.902236i	0.999704	+	0.0243111i	$0.00773922\pi$
$7$	1250.70	+	2166.27i	0.520906	+	0.902236i	−0.478798	+	0.877925i	$0.658927\pi$
$8$			1448.15i			0.353553i
$9$		0			0
$10$	−12341.6			−1.23416
$11$	3212.80	−	1854.91i	0.219439	−	0.126693i	−0.386252	−	0.922393i	$-0.626230\pi$
$11$	3212.80	−	1854.91i	0.219439	−	0.126693i	0.605690	+	0.795700i	$0.292897\pi$
$12$		0			0
$13$	22409.9	−	38815.1i	0.784633	−	1.35902i	−0.144586	−	0.989492i	$-0.546185\pi$
$13$	22409.9	−	38815.1i	0.784633	−	1.35902i	0.929218	−	0.369531i	$-0.120482\pi$
$14$	−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	$0.105877\pi$
$17$			54543.2i			0.653048i	−0.945189	+	0.326524i	$0.894123\pi$
$18$		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	−0.0583033	−	0.998299i	$-0.518569\pi$
$23$	−266411.	−	153812.i	−0.952007	−	0.549642i	−0.893704	+	0.448657i	$0.851902\pi$
$24$		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	−0.755499	−	0.655150i	$-0.772605\pi$
$29$	−400230.	+	231073.i	−0.565872	+	0.326706i	0.189627	+	0.981856i	$0.439272\pi$
$30$		0			0
$31$	−140570.	+	243475.i	−0.152211	+	0.263638i	−0.932040	−	0.362355i	$-0.881973\pi$
$31$	−140570.	+	243475.i	−0.152211	+	0.263638i	0.779829	+	0.625993i	$0.215306\pi$
$32$	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	0.992995	+	0.118158i	$0.0376988\pi$
$41$	4.49810e6	+	2.59698e6i	1.59182	+	0.919038i	0.598825	+	0.800880i	$0.295635\pi$
$42$		0			0
$43$	2.49848e6	+	4.32750e6i	0.730807	+	1.26580i	0.956539	+	0.291606i	$0.0941895\pi$
$43$	2.49848e6	+	4.32750e6i	0.730807	+	1.26580i	−0.225731	+	0.974190i	$0.572477\pi$
$44$		−	474858.i		−	0.126693i
$45$		0			0
$46$	3.48037e6			0.777311
$47$	306798.	−	177130.i	0.0628725	−	0.0362995i	−0.468234	−	0.883604i	$-0.655110\pi$
$47$	306798.	−	177130.i	0.0628725	−	0.0362995i	0.531107	+	0.847305i	$0.321776\pi$
$48$		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	$-0.980654\pi$
$53$		−	958543.i		−	0.121481i	0.998154	−	0.0607405i	$-0.0193462\pi$
$54$		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	−0.194387	−	0.980925i	$-0.562272\pi$
$59$	−1.38270e7	−	7.98300e6i	−1.14109	−	0.658807i	−0.946700	+	0.322118i	$0.895605\pi$
$60$		0			0
$61$	−5.55708e6	−	9.62514e6i	−0.401354	−	0.695165i	0.592536	−	0.805544i	$-0.298127\pi$
$61$	−5.55708e6	−	9.62514e6i	−0.401354	−	0.695165i	−0.993890	+	0.110379i	$0.964793\pi$
$62$		−	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	0.381121	+	0.924525i	$0.375538\pi$
$67$	−1.22942e7	+	2.12942e7i	−0.610102	+	1.05673i	−0.991223	+	0.132202i	$0.957795\pi$
$68$	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	$0.106748\pi$
$71$			1.67264e7i			0.658215i	−0.944292	+	0.329108i	$0.893252\pi$
$72$		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	0.532308	−	0.846551i	$-0.321325\pi$
$79$	−1.81889e7	−	3.15042e7i	−0.466981	−	0.808835i	−0.999288	+	0.0377164i	$0.987992\pi$
$80$		−	1.78726e7i		−	0.436342i
$81$		0			0
$82$	−5.87630e7			−1.29972
$83$	−2.53425e7	+	1.46315e7i	−0.533994	+	0.308302i	−0.742641	−	0.669689i	$-0.766427\pi$
$83$	−2.53425e7	+	1.46315e7i	−0.533994	+	0.308302i	0.208647	+	0.977991i	$0.433094\pi$
$84$		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	$-0.833608\pi$
$89$		−	6.26485e7i		−	0.998506i	0.866456	−	0.499253i	$-0.166392\pi$
$90$		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	0.969742	−	0.244131i	$-0.0785027\pi$
$97$	2.42081e7	+	4.19297e7i	0.273447	+	0.473625i	−0.696295	+	0.717756i	$0.745169\pi$
$98$		−	5.56815e6i		−	0.0603680i
$99$		0			0
$100$	1.02316e8			1.02316
$101$	−4.53627e7	+	2.61902e7i	−0.435927	+	0.251682i	−0.701868	−	0.712307i	$-0.747651\pi$
$101$	−4.53627e7	+	2.61902e7i	−0.435927	+	0.251682i	0.265942	+	0.963989i	$0.414317\pi$
$102$		0			0
$103$	−3.13984e7	+	5.43835e7i	−0.278970	+	0.483191i	−0.971129	−	0.238555i	$-0.923326\pi$
$103$	−3.13984e7	+	5.43835e7i	−0.278970	+	0.483191i	0.692159	+	0.721745i	$0.256660\pi$
$104$	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	$-0.999233\pi$
$107$		−	631989.i		−	0.00482142i	0.999997	−	0.00241071i	$-0.000767353\pi$
$108$		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	0.222227	−	0.974995i	$-0.428667\pi$
$113$	−8.33220e7	−	4.81060e7i	−0.511030	−	0.295043i	−0.733257	+	0.679952i	$0.762001\pi$
$114$		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	0.0764341	−	0.997075i	$-0.475647\pi$
$131$	−2.20534e8	−	1.27325e8i	−0.748841	−	0.432343i	−0.825275	+	0.564731i	$0.808980\pi$
$132$		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	0.125668	−	0.992072i	$-0.459893\pi$
$137$	3.69065e8	−	2.13080e8i	1.04766	−	0.604868i	0.921994	+	0.387205i	$0.126559\pi$
$138$		0			0
$139$	1.03393e8	−	1.79082e8i	0.276969	−	0.479725i	−0.693661	−	0.720302i	$-0.744003\pi$
$139$	1.03393e8	−	1.79082e8i	0.276969	−	0.479725i	0.970630	+	0.240577i	$0.0773366\pi$
$140$	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	−0.211120	−	0.977460i	$-0.567711\pi$
$149$	−5.73316e8	−	3.31004e8i	−1.16319	−	0.671565i	−0.952065	+	0.305895i	$0.901044\pi$
$150$		0			0
$151$	−2.17181e8	−	3.76169e8i	−0.417749	−	0.723562i	0.577964	−	0.816062i	$-0.303847\pi$
$151$	−2.17181e8	−	3.76169e8i	−0.417749	−	0.723562i	−0.995713	+	0.0925004i	$0.970514\pi$
$152$			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	0.330272	−	0.943886i	$-0.392860\pi$
$157$	5.96980e8	−	1.03400e9i	0.982565	−	1.70185i	0.652293	−	0.757967i	$-0.273807\pi$
$158$	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	0.339371	−	0.940653i	$-0.389786\pi$
$167$	−2.37674e8	−	1.37221e8i	−0.305573	−	0.176423i	−0.644944	+	0.764230i	$0.723119\pi$
$168$		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	−0.0142547	−	0.999898i	$-0.504538\pi$
$173$	7.56506e8	−	4.36769e8i	0.844555	−	0.487604i	0.858810	+	0.512294i	$0.171204\pi$
$174$		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	$0.0982558\pi$
$179$			6.23780e8i			0.607602i	−0.952736	+	0.303801i	$0.901744\pi$
$180$		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	−0.122342	−	0.992488i	$-0.539040\pi$
$191$	8.99674e8	−	5.19427e8i	0.676007	−	0.390293i	0.798349	+	0.602195i	$0.205707\pi$
$192$		0			0
$193$	1.19815e9	−	2.07527e9i	0.863543	−	1.49570i	−0.00494446	−	0.999988i	$-0.501574\pi$
$193$	1.19815e9	−	2.07527e9i	0.863543	−	1.49570i	0.868487	−	0.495712i	$-0.165093\pi$
$194$	−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	$0.179586\pi$
$197$			1.61075e9i			1.06945i	−0.845025	+	0.534727i	$0.820414\pi$
$198$		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	−0.998160	−	0.0606312i	$-0.980689\pi$
$211$	−8.85159e8	+	1.53314e9i	−0.446572	+	0.773485i	0.551588	+	0.834117i	$0.314022\pi$
$212$	−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	0.810385	−	0.585898i	$-0.199258\pi$
$223$	−2.52764e8	−	4.37800e8i	−0.102210	−	0.177034i	−0.912595	+	0.408865i	$0.865925\pi$
$224$			4.63667e8i			0.184168i
$225$		0			0
$226$	1.08851e9			0.417254
$227$	−6.53594e8	+	3.77352e8i	−0.246153	+	0.142116i	−0.618001	−	0.786177i	$-0.712057\pi$
$227$	−6.53594e8	+	3.77352e8i	−0.246153	+	0.142116i	0.371849	+	0.928293i	$0.378724\pi$
$228$		0			0
$229$	−2.78927e8	+	4.83115e8i	−0.101426	+	0.175675i	−0.912272	−	0.409584i	$-0.865674\pi$
$229$	−2.78927e8	+	4.83115e8i	−0.101426	+	0.175675i	0.810847	+	0.585259i	$0.199007\pi$
$230$	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	$-0.794166\pi$
$233$		−	3.55157e9i		−	1.20503i	0.798108	−	0.602514i	$-0.205834\pi$
$234$		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	0.377092	−	0.926176i	$-0.376924\pi$
$239$	−7.71502e8	−	4.45427e8i	−0.236453	−	0.136516i	−0.613546	+	0.789659i	$0.710257\pi$
$240$		0			0
$241$	1.71946e9	+	2.97819e9i	0.509710	+	0.882844i	0.999937	+	0.0112489i	$0.00358072\pi$
$241$	1.71946e9	+	2.97819e9i	0.509710	+	0.882844i	−0.490227	+	0.871595i	$0.663086\pi$
$242$		−	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	$-0.700133\pi$
$251$		−	6.42022e9i		−	1.61754i	0.588124	−	0.808770i	$-0.299867\pi$
$252$		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	0.401736	−	0.915756i	$-0.368407\pi$
$257$	−8.30896e8	−	4.79718e8i	−0.190464	−	0.109965i	−0.592200	+	0.805791i	$0.701740\pi$
$258$		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	−0.218209	−	0.975902i	$-0.570022\pi$
$263$	2.47754e9	−	1.43041e9i	0.517842	−	0.298976i	0.736051	+	0.676926i	$0.236688\pi$
$264$		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	$0.0366301\pi$
$269$			1.20245e9i			0.229646i	−0.993386	+	0.114823i	$0.963370\pi$
$270$		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	0.789496	−	0.613756i	$-0.210342\pi$
$277$	−8.05272e8	−	1.39477e9i	−0.136780	−	0.236911i	−0.926276	+	0.376845i	$0.877009\pi$
$278$			2.33952e9i			0.391694i
$279$		0			0
$280$	−3.95152e9			−0.642883
$281$	1.00668e10	−	5.81207e9i	1.61461	−	0.932193i	0.626322	−	0.779565i	$-0.284560\pi$
$281$	1.00668e10	−	5.81207e9i	1.61461	−	0.932193i	0.988284	−	0.152628i	$-0.0487736\pi$
$282$		0			0
$283$	7.70868e8	−	1.33518e9i	0.120181	−	0.208159i	−0.799658	−	0.600455i	$-0.794986\pi$
$283$	7.70868e8	−	1.33518e9i	0.120181	−	0.208159i	0.919839	+	0.392297i	$0.128319\pi$
$284$	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	0.122356	−	0.992486i	$-0.460955\pi$
$293$	−4.98204e9	−	2.87638e9i	−0.675984	−	0.390280i	−0.798340	+	0.602207i	$0.794288\pi$
$294$		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	−0.292219	−	0.956351i	$-0.594394\pi$
$311$	−1.18485e10	−	6.84076e9i	−1.26655	−	0.731245i	−0.974334	+	0.225106i	$0.927727\pi$
$312$		0			0
$313$	−3.58243e9	−	6.20496e9i	−0.373251	−	0.646489i	0.616813	−	0.787110i	$-0.288424\pi$
$313$	−3.58243e9	−	6.20496e9i	−0.373251	−	0.646489i	−0.990064	+	0.140620i	$0.955090\pi$
$314$			1.35081e10i			1.38956i
$315$		0			0
$316$	−4.65637e9			−0.466981
$317$	9.86964e9	−	5.69824e9i	0.977382	−	0.564292i	0.0759031	−	0.997115i	$-0.475816\pi$
$317$	9.86964e9	−	5.69824e9i	0.977382	−	0.564292i	0.901479	+	0.432824i	$0.142483\pi$
$318$		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	0.962574	+	0.271018i	$0.0873604\pi$
$331$	8.59454e9	+	1.48862e10i	0.715996	+	1.24014i	−0.246578	+	0.969123i	$0.579306\pi$
$332$			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	−0.796765	−	0.604289i	$-0.793457\pi$
$337$	1.61156e9	−	2.79131e9i	0.124947	−	0.216415i	0.921712	+	0.387874i	$0.126790\pi$
$338$	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	0.572911	−	0.819618i	$-0.305814\pi$
$347$	2.16831e9	+	1.25187e9i	0.149556	+	0.0863461i	−0.423355	+	0.905964i	$0.639148\pi$
$348$		0			0
$349$	−8.92317e9	−	1.54554e10i	−0.601475	−	1.04178i	−0.992598	−	0.121446i	$-0.961247\pi$
$349$	−8.92317e9	−	1.54554e10i	−0.601475	−	1.04178i	0.391123	−	0.920338i	$-0.372087\pi$
$350$		−	2.26214e10i		−	1.50746i
$351$		0			0
$352$	6.87667e8			0.0447927
$353$	−2.33322e9	+	1.34709e9i	−0.150265	+	0.0867555i	−0.573247	−	0.819382i	$-0.694317\pi$
$353$	−2.33322e9	+	1.34709e9i	−0.150265	+	0.0867555i	0.422982	+	0.906138i	$0.360983\pi$
$354$		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	$0.00428097\pi$
$359$			4.46773e8i			0.0268973i	−0.999910	+	0.0134487i	$0.995719\pi$
$360$		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	0.714807	−	0.699322i	$-0.246515\pi$
$367$	−4.50312e9	−	7.79963e9i	−0.248227	−	0.429942i	−0.963034	+	0.269380i	$0.913181\pi$
$368$			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	−0.757319	−	0.653045i	$-0.773491\pi$
$373$	3.61769e9	−	6.26602e9i	0.186894	−	0.323710i	0.944213	+	0.329335i	$0.106825\pi$
$374$	−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	0.885403	−	0.464824i	$-0.153883\pi$
$383$	1.99158e10	+	1.14984e10i	0.925555	+	0.534369i	0.0401518	+	0.999194i	$0.487216\pi$
$384$		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	−0.0752021	−	0.997168i	$-0.523960\pi$
$389$	1.71912e10	−	9.92532e9i	0.750770	−	0.433457i	0.825972	+	0.563711i	$0.190627\pi$
$390$		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	0.839166	−	0.543876i	$-0.183044\pi$
$401$	2.03685e10	+	1.17598e10i	0.787738	+	0.454801i	−0.0514274	+	0.998677i	$0.516377\pi$
$402$		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	0.0644044	+	0.997924i	$0.479485\pi$
$409$	−2.32825e10	+	4.03265e10i	−0.832025	+	1.44111i	−0.896430	+	0.443186i	$0.853848\pi$
$410$	−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	0.434403	−	0.900719i	$-0.356959\pi$
$419$	−3.95877e9	−	2.28560e9i	−0.128441	−	0.0741556i	−0.562844	+	0.826563i	$0.690293\pi$
$420$		0			0
$421$	6.62653e9	+	1.14775e10i	0.210939	+	0.365358i	0.952009	−	0.306071i	$-0.0990144\pi$
$421$	6.62653e9	+	1.14775e10i	0.210939	+	0.365358i	−0.741069	+	0.671428i	$0.765681\pi$
$422$		−	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	$-0.874964\pi$
$431$		−	2.64178e10i		−	0.765575i	0.923836	−	0.382787i	$-0.125036\pi$
$432$		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	0.564618	−	0.825352i	$-0.309023\pi$
$439$	−1.60624e10	−	2.78209e10i	−0.432467	−	0.749055i	−0.997085	+	0.0762974i	$0.975690\pi$
$440$			5.86052e9i			0.156360i
$441$		0			0
$442$	−2.76576e10			−0.724646
$443$	4.36195e10	−	2.51837e10i	1.13257	−	0.653891i	0.187992	−	0.982171i	$-0.439802\pi$
$443$	4.36195e10	−	2.51837e10i	1.13257	−	0.653891i	0.944581	+	0.328279i	$0.106469\pi$
$444$		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	$0.0830293\pi$
$449$			2.09633e10i			0.515792i	−0.966173	+	0.257896i	$0.916971\pi$
$450$		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	0.999688	+	0.0249858i	$0.00795405\pi$
$457$	2.27460e10	+	3.93972e10i	0.521482	+	0.903234i	−0.478206	+	0.878248i	$0.658713\pi$
$458$		−	6.31139e9i		−	0.143438i
$459$		0			0
$460$	−4.29535e10			−0.959328
$461$	−3.76919e10	+	2.17614e10i	−0.834534	+	0.481818i	−0.855403	−	0.517964i	$-0.826690\pi$
$461$	−3.76919e10	+	2.17614e10i	−0.834534	+	0.481818i	0.0208685	+	0.999782i	$0.493357\pi$
$462$		0			0
$463$	−1.88669e10	+	3.26784e10i	−0.410560	+	0.711111i	−0.994951	−	0.100361i	$-0.968000\pi$
$463$	−1.88669e10	+	3.26784e10i	−0.410560	+	0.711111i	0.584391	+	0.811472i	$0.301333\pi$
$464$	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	$-0.934595\pi$
$467$		−	1.94089e10i		−	0.408068i	0.978964	−	0.204034i	$-0.0654053\pi$
$468$		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	−0.609968	−	0.792426i	$-0.708818\pi$
$479$	−1.20390e10	+	6.95073e9i	−0.228691	+	0.132035i	0.381277	+	0.924461i	$0.375484\pi$
$480$		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	−0.0781474	−	0.996942i	$-0.524900\pi$
$491$	−5.69924e10	−	3.29046e10i	−0.980598	−	0.566149i	−0.902451	+	0.430793i	$0.858234\pi$
$492$		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	−0.902259	−	0.431194i	$-0.858092\pi$
$499$	−4.81781e9	+	8.34469e9i	−0.0777047	+	0.134589i	0.824555	+	0.565782i	$0.191426\pi$
$500$	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	$0.0731291\pi$
$503$			2.91551e10i			0.455452i	−0.973725	+	0.227726i	$0.926871\pi$
$504$		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	−0.0334907	−	0.999439i	$-0.510662\pi$
$509$	−6.14696e10	−	3.54895e10i	−0.915776	−	0.528723i	−0.882285	+	0.470716i	$0.843996\pi$
$510$		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	$0.135575\pi$
$521$			6.08836e10i			0.826323i	−0.910658	+	0.413161i	$0.864425\pi$
$522$		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	−0.941617	−	0.336685i	$-0.890694\pi$
$547$	−6.82534e10	−	1.18218e11i	−0.762386	−	1.32049i	0.179231	−	0.983807i	$-0.442639\pi$
$548$		−	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	$0.0286324\pi$
$557$			1.72931e10i			0.179660i	−0.995957	+	0.0898300i	$0.971368\pi$
$558$		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	0.265076	−	0.964228i	$-0.414603\pi$
$563$	−4.39485e10	−	2.53737e10i	−0.437432	−	0.252552i	−0.702508	+	0.711676i	$0.747936\pi$
$564$		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	−0.803570	−	0.595210i	$-0.797069\pi$
$569$	−7.23149e10	+	4.17510e10i	−0.689888	+	0.398307i	0.113682	+	0.993517i	$0.463735\pi$
$570$		0			0
$571$	6.95426e10	−	1.20451e11i	0.654194	−	1.13310i	−0.327901	−	0.944712i	$-0.606341\pi$
$571$	6.95426e10	−	1.20451e11i	0.654194	−	1.13310i	0.982095	−	0.188385i	$-0.0603254\pi$
$572$	−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	−0.203599	−	0.979054i	$-0.565264\pi$
$587$	6.44083e10	−	3.71861e10i	0.542487	−	0.313205i	0.746086	+	0.665849i	$0.231931\pi$
$588$		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	$-0.899959\pi$
$593$		−	7.64545e10i		−	0.618279i	0.951017	−	0.309139i	$-0.100041\pi$
$594$		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	0.219822	−	0.975540i	$-0.429452\pi$
$599$	−6.63143e10	−	3.82866e10i	−0.515110	−	0.297399i	−0.734932	+	0.678141i	$0.762786\pi$
$600$		0			0
$601$	−2.39823e10	−	4.15386e10i	−0.183820	−	0.318386i	0.759358	−	0.650673i	$-0.225513\pi$
$601$	−2.39823e10	−	4.15386e10i	−0.183820	−	0.318386i	−0.943178	+	0.332287i	$0.892180\pi$
$602$		−	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	0.192303	+	0.981336i	$0.438404\pi$
$607$	−1.02320e11	+	1.77223e11i	−0.753710	+	1.30546i	−0.946013	+	0.324128i	$0.894929\pi$
$608$	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	0.509639	−	0.860389i	$-0.329779\pi$
$617$	2.80277e9	+	1.61818e9i	0.0193396	+	0.0111657i	−0.490299	+	0.871554i	$0.663112\pi$
$618$		0			0
$619$	7.34200e10	+	1.27167e11i	0.500094	+	0.866189i	1.00000		0.000108934i	$3.46746e-5\pi$
$619$	7.34200e10	+	1.27167e11i	0.500094	+	0.866189i	−0.499906	+	0.866080i	$0.666632\pi$
$620$			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	−0.497827	−	0.867276i	$-0.665869\pi$
$641$	7.33197e8	−	4.23311e8i	0.00434299	−	0.00250742i	0.502170	+	0.864769i	$0.332535\pi$
$642$		0			0
$643$	5.89225e10	−	1.02057e11i	0.344697	−	0.597033i	−0.640602	−	0.767873i	$-0.721315\pi$
$643$	5.89225e10	−	1.02057e11i	0.344697	−	0.597033i	0.985299	+	0.170841i	$0.0546483\pi$
$644$	−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	$0.270749\pi$
$647$			2.63434e11i			1.50333i	−0.659546	+	0.751665i	$0.729251\pi$
$648$		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	0.169793	−	0.985480i	$-0.445690\pi$
$653$	−1.08870e11	−	6.28559e10i	−0.598761	−	0.345695i	−0.768554	+	0.639785i	$0.779024\pi$
$654$		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	−0.414323	−	0.910130i	$-0.635982\pi$
$659$	3.14417e10	−	1.81529e10i	0.166711	−	0.0962506i	0.581034	+	0.813879i	$0.302648\pi$
$660$		0			0
$661$	−6.52457e10	+	1.13009e11i	−0.341779	+	0.591979i	−0.984763	−	0.173901i	$-0.944363\pi$
$661$	−6.52457e10	+	1.13009e11i	−0.341779	+	0.591979i	0.642984	+	0.765880i	$0.277696\pi$
$662$	−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	0.813419	−	0.581678i	$-0.197604\pi$
$673$	−1.99070e10	−	3.44799e10i	−0.0970388	−	0.168076i	−0.910458	+	0.413602i	$0.864270\pi$
$674$			3.64655e10i			0.176702i
$675$		0			0
$676$	−1.52715e11			−0.731297
$677$	2.31655e11	−	1.33746e11i	1.10277	−	0.636687i	0.165826	−	0.986155i	$-0.446971\pi$
$677$	2.31655e11	−	1.33746e11i	1.10277	−	0.636687i	0.936948	+	0.349468i	$0.113638\pi$
$678$		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	$0.0280451\pi$
$683$			3.82963e10i			0.175984i	−0.996121	+	0.0879922i	$0.971955\pi$
$684$		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	0.847632	+	0.530585i	$0.178028\pi$
$691$	2.01386e11	+	3.48810e11i	0.883316	+	1.52995i	0.0356843	+	0.999363i	$0.488639\pi$
$692$		−	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	$0.381496\pi$
$701$			4.49866e11i			1.86299i	−0.363750	+	0.931497i	$0.618504\pi$
$702$		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	0.999996	+	0.00274839i	$0.000874840\pi$
$709$	1.26945e11	+	2.19875e11i	0.502378	+	0.870145i	−0.497618	+	0.867396i	$0.665792\pi$
$710$		−	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	$-0.570649\pi$
$719$		−	5.21386e11i		−	1.95094i	0.220134	−	0.975470i	$-0.429351\pi$
$720$		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	0.871107	−	0.491094i	$-0.163403\pi$
$727$	2.86428e9	+	4.96107e9i	0.0102536	+	0.0177598i	−0.860853	+	0.508854i	$0.830069\pi$
$728$			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	−0.440538	−	0.897734i	$-0.645212\pi$
$733$	1.60850e11	−	2.78600e11i	0.557192	−	0.965084i	0.997729	−	0.0673502i	$-0.0214545\pi$
$734$	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	0.974194	−	0.225714i	$-0.0724716\pi$
$743$	3.85768e11	+	2.22723e11i	1.26582	+	0.730819i	0.291622	+	0.956533i	$0.405805\pi$
$744$		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	0.142954	+	0.989729i	$0.454340\pi$
$751$	−2.49914e11	+	4.32864e11i	−0.785654	+	1.36079i	−0.928608	+	0.371063i	$0.878993\pi$
$752$	−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	−0.269488	−	0.963004i	$-0.586854\pi$
$761$	−4.15275e11	−	2.39759e11i	−1.23822	−	0.714885i	−0.968730	+	0.248119i	$0.920188\pi$
$762$		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	−0.845881	−	0.533371i	$-0.820925\pi$
$769$	1.36289e10	−	2.36059e10i	0.0389722	−	0.0675018i	0.884854	+	0.465869i	$0.154258\pi$
$770$	−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	$0.107611\pi$
$773$			2.36838e11i			0.663336i	−0.943396	+	0.331668i	$0.892389\pi$
$774$		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	−0.540360	−	0.841434i	$-0.681712\pi$
$787$	1.75898e11	−	3.04664e11i	0.458523	−	0.794185i	0.998883	+	0.0472487i	$0.0150453\pi$
$788$	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	0.643432	−	0.765504i	$-0.277510\pi$
$797$	1.21936e11	+	7.03995e10i	0.302202	+	0.174476i	−0.341230	+	0.939980i	$0.610843\pi$
$798$		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	$0.0212199\pi$
$809$			5.70685e10i			0.133230i	−0.997779	+	0.0666151i	$0.978780\pi$
$810$		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	−0.782698	−	0.622402i	$-0.786157\pi$
$821$	−2.88515e11	+	1.66574e11i	−0.635031	+	0.366636i	0.147667	+	0.989037i	$0.452824\pi$
$822$		0			0
$823$	4.11950e11	−	7.13518e11i	0.897935	−	1.55527i	0.0678057	−	0.997699i	$-0.478400\pi$
$823$	4.11950e11	−	7.13518e11i	0.897935	−	1.55527i	0.830129	−	0.557571i	$-0.188266\pi$
$824$	−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	$0.402588\pi$
$827$			8.92051e11i			1.90708i	−0.301274	+	0.953538i	$0.597412\pi$
$828$		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	−0.742698	−	0.669627i	$-0.766454\pi$
$839$	−2.64665e11	+	1.52805e11i	−0.534133	+	0.308382i	0.208565	+	0.978009i	$0.433121\pi$
$840$		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	0.575162	−	0.818040i	$-0.304939\pi$
$853$	−2.22811e11	−	3.85919e11i	−0.420862	−	0.728955i	−0.996024	+	0.0890849i	$0.971606\pi$
$854$			3.14531e11i			0.591332i
$855$		0			0
$856$	9.15218e8			0.00170463
$857$	8.02066e10	−	4.63073e10i	0.148692	−	0.0858472i	−0.423808	−	0.905752i	$-0.639307\pi$
$857$	8.02066e10	−	4.63073e10i	0.148692	−	0.0858472i	0.572500	+	0.819905i	$0.305974\pi$
$858$		0			0
$859$	1.29899e11	−	2.24992e11i	0.238580	−	0.413233i	−0.721727	−	0.692178i	$-0.756651\pi$
$859$	1.29899e11	−	2.24992e11i	0.238580	−	0.413233i	0.960307	+	0.278945i	$0.0899847\pi$
$860$	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	$0.0237970\pi$
$863$			8.28592e10i			0.149382i	−0.997207	+	0.0746909i	$0.976203\pi$
$864$		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	−0.973886	−	0.227039i	$-0.927096\pi$
$877$	−1.71742e11	+	2.97466e11i	−0.290321	+	0.502851i	0.683564	+	0.729890i	$0.260429\pi$
$878$	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	$0.222179\pi$
$881$			7.74337e11i			1.28537i	−0.766132	+	0.642683i	$0.777821\pi$
$882$		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	0.868831	−	0.495108i	$-0.164872\pi$
$887$	5.41302e11	+	3.12521e11i	0.874471	+	0.504876i	0.00563925	+	0.999984i	$0.498205\pi$
$888$		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	−0.977229	−	0.212188i	$-0.931941\pi$
$907$	−4.55030e11	−	7.88136e11i	−0.672375	−	1.16459i	0.304854	−	0.952399i	$-0.401392\pi$
$908$			9.66022e10i			0.142116i
$909$		0			0
$910$	−1.38364e12			−2.01771
$911$	−9.63591e10	+	5.56330e10i	−0.139901	+	0.0807716i	−0.568317	−	0.822810i	$-0.692405\pi$
$911$	−9.63591e10	+	5.56330e10i	−0.139901	+	0.0807716i	0.428416	+	0.903582i	$0.359072\pi$
$912$		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	−0.999982	−	0.00597212i	$-0.998099\pi$
$929$	−1.11339e12	+	6.42815e11i	−1.49480	+	0.863024i	−0.494819	+	0.868996i	$0.664766\pi$
$930$		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	−0.0438668	−	0.999037i	$-0.513968\pi$
$941$	−7.29969e11	−	4.21448e11i	−0.930992	−	0.537508i	−0.887125	+	0.461529i	$0.847301\pi$
$942$		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	−0.986680	−	0.162675i	$-0.947988\pi$
$947$	−1.07702e12	+	6.21820e11i	−1.33914	+	0.773152i	−0.352459	+	0.935827i	$0.614655\pi$
$948$		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	$-0.949836\pi$
$953$		−	2.58906e11i		−	0.313885i	0.987608	−	0.156942i	$-0.0501637\pi$
$954$		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	0.416446	+	0.909161i	$0.363276\pi$
$967$	−5.06389e11	+	8.77092e11i	−0.579133	+	1.00309i	−0.995579	+	0.0939280i	$0.970058\pi$
$968$	−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	$-0.881878\pi$
$971$		−	6.44723e11i		−	0.725265i	0.931932	−	0.362632i	$-0.118122\pi$
$972$		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	−0.438685	−	0.898641i	$-0.644556\pi$
$977$	−1.30863e12	−	7.55535e11i	−1.43627	−	0.829233i	−0.997588	+	0.0694077i	$0.977889\pi$
$978$		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	0.0876854	−	0.996148i	$-0.472053\pi$
$983$	9.28316e11	−	5.35963e11i	0.994218	−	0.574012i	0.906532	+	0.422136i	$0.138720\pi$
$984$		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	0.920124	−	0.391627i	$-0.128088\pi$
$997$	1.19459e11	+	2.06909e11i	0.120903	+	0.209411i	−0.799221	+	0.601037i	$0.794754\pi$
$998$		−	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.17.4		16
3.2	odd	2		18.9.d.a.5.7	✓	16
4.3	odd	2		432.9.q.c.17.8		16
9.2	odd	6	inner	54.9.d.a.35.4		16
9.4	even	3		162.9.b.c.161.1		16
9.5	odd	6		162.9.b.c.161.16		16
9.7	even	3		18.9.d.a.11.7	yes	16
12.11	even	2		144.9.q.b.113.3		16
36.7	odd	6		144.9.q.b.65.3		16
36.11	even	6		432.9.q.c.305.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.7	✓	16	3.2	odd	2
18.9.d.a.11.7	yes	16	9.7	even	3
54.9.d.a.17.4		16	1.1	even	1	trivial
54.9.d.a.35.4		16	9.2	odd	6	inner
144.9.q.b.65.3		16	36.7	odd	6
144.9.q.b.113.3		16	12.11	even	2
162.9.b.c.161.1		16	9.4	even	3
162.9.b.c.161.16		16	9.5	odd	6
432.9.q.c.17.8		16	4.3	odd	2
432.9.q.c.305.8		16	36.11	even	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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

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