LMFDB - Embedded newform 72.22.f.a.35.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,22,Mod(35,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("72.35");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	72.f (of order $2$, degree $1$, 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:	$201.223687887$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.32
Character	$\chi$	$=$	72.35
Dual form			72.22.f.a.35.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-621.545 + 1307.99i) q^{2} +(-1.32452e6 - 1.62595e6i) q^{4} -9.14091e6 q^{5} -8.56630e8i q^{7} +(2.94997e9 - 7.21852e8i) q^{8} +O(q^{10})$	\(q+(-621.545 + 1307.99i) q^{2} +(-1.32452e6 - 1.62595e6i) q^{4} -9.14091e6 q^{5} -8.56630e8i q^{7} +(2.94997e9 - 7.21852e8i) q^{8} +(5.68149e9 - 1.19562e10i) q^{10} +7.02798e10i q^{11} +6.08698e11i q^{13} +(1.12046e12 + 5.32434e11i) q^{14} +(-8.89362e11 + 4.30719e12i) q^{16} +1.35143e13i q^{17} +2.66607e13 q^{19} +(1.21073e13 + 1.48626e13i) q^{20} +(-9.19251e13 - 4.36820e13i) q^{22} +6.73238e13 q^{23} -3.93281e14 q^{25} +(-7.96170e14 - 3.78333e14i) q^{26} +(-1.39284e15 + 1.13462e15i) q^{28} +3.07544e15 q^{29} -3.73440e15i q^{31} +(-5.08097e15 - 3.84038e15i) q^{32} +(-1.76766e16 - 8.39977e15i) q^{34} +7.83038e15i q^{35} -9.88634e15i q^{37} +(-1.65708e16 + 3.48719e16i) q^{38} +(-2.69654e16 + 6.59839e15i) q^{40} -1.48280e17i q^{41} +7.92658e16 q^{43} +(1.14271e17 - 9.30866e16i) q^{44} +(-4.18448e16 + 8.80588e16i) q^{46} +3.94989e17 q^{47} -1.75270e17 q^{49} +(2.44442e17 - 5.14407e17i) q^{50} +(9.89711e17 - 8.06230e17i) q^{52} -4.73280e17 q^{53} -6.42421e17i q^{55} +(-6.18361e17 - 2.52703e18i) q^{56} +(-1.91152e18 + 4.02264e18i) q^{58} +5.97069e18i q^{59} -9.79657e18i q^{61} +(4.88456e18 + 2.32110e18i) q^{62} +(8.18123e18 - 4.25888e18i) q^{64} -5.56405e18i q^{65} -1.69202e19 q^{67} +(2.19736e19 - 1.79000e19i) q^{68} +(-1.02421e19 - 4.86693e18i) q^{70} -2.88571e19 q^{71} -5.35107e19 q^{73} +(1.29312e19 + 6.14480e18i) q^{74} +(-3.53125e19 - 4.33489e19i) q^{76} +6.02038e19 q^{77} +4.29094e19i q^{79} +(8.12958e18 - 3.93716e19i) q^{80} +(1.93949e20 + 9.21629e19i) q^{82} -9.50389e19i q^{83} -1.23533e20i q^{85} +(-4.92673e19 + 1.03679e20i) q^{86} +(5.07316e19 + 2.07323e20i) q^{88} +4.33090e20i q^{89} +5.21429e20 q^{91} +(-8.91715e19 - 1.09465e20i) q^{92} +(-2.45503e20 + 5.16641e20i) q^{94} -2.43703e20 q^{95} -4.63333e20 q^{97} +(1.08938e20 - 2.29251e20i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2424084 q^{4}+O(q^{10}) $ 84 * q + 2424084 * q^4	$ 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 80\!\cdots\!00 q^{25}+ \cdots - 16\!\cdots\!12 q^{97}+O(q^{100}) $ 84 * q + 2424084 * q^4 + 17057181612 * q^10 - 4099708064904 * q^16 + 92015527242864 * q^19 - 236011369239528 * q^22 + 8010864257812500 * q^25 - 3042238700022024 * q^28 + 74414158327329924 * q^34 + 75018327243317184 * q^40 + 707788847336454432 * q^43 - 162639476543943288 * q^46 - 5423745715136249124 * q^49 - 70566629446202808 * q^52 - 14491558288019904108 * q^58 - 28749968749508108064 * q^64 - 13653811098426494352 * q^67 + 140256684870035374392 * q^70 - 71781309378863778384 * q^73 + 376055720386305092400 * q^76 - 368362114062816367548 * q^82 - 592572120184082106720 * q^88 - 522206955652189957200 * q^91 - 528772551789914644488 * q^94 - 1686050813935078492512 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−621.545	+	1307.99i	−0.429198	+	0.903210i
$2$	−621.545	+	1307.99i	−0.429198	+	0.903210i
$3$		0			0
$3$		0			0
$4$	−1.32452e6	−	1.62595e6i	−0.631578	−	0.775312i
$5$	−9.14091e6			−0.418605			−0.209303	−	0.977851i	$-0.567119\pi$
$5$	−9.14091e6			−0.418605			−0.209303	+	0.977851i	$0.567119\pi$
$6$		0			0
$7$		−	8.56630e8i		−	1.14621i	−0.819482	−	0.573105i	$-0.805739\pi$
$7$		−	8.56630e8i		−	1.14621i	0.819482	−	0.573105i	$-0.194261\pi$
$8$	2.94997e9	−	7.21852e8i	0.971342	−	0.237686i
$9$		0			0
$10$	5.68149e9	−	1.19562e10i	0.179664	−	0.378089i
$11$			7.02798e10i			0.816972i	0.912765	+	0.408486i	$0.133943\pi$
$11$			7.02798e10i			0.816972i	−0.912765	+	0.408486i	$0.866057\pi$
$12$		0			0
$13$			6.08698e11i			1.22461i	0.790623	+	0.612303i	$0.209757\pi$
$13$			6.08698e11i			1.22461i	−0.790623	+	0.612303i	$0.790243\pi$
$14$	1.12046e12	+	5.32434e11i	1.03527	+	0.491951i
$15$		0			0
$16$	−8.89362e11	+	4.30719e12i	−0.202218	+	0.979341i
$17$			1.35143e13i			1.62585i	0.582367	+	0.812926i	$0.302127\pi$
$17$			1.35143e13i			1.62585i	−0.582367	+	0.812926i	$0.697873\pi$
$18$		0			0
$19$	2.66607e13			0.997605			0.498802	−	0.866716i	$-0.333773\pi$
$19$	2.66607e13			0.997605			0.498802	+	0.866716i	$0.333773\pi$
$20$	1.21073e13	+	1.48626e13i	0.264382	+	0.324550i
$21$		0			0
$22$	−9.19251e13	−	4.36820e13i	−0.737897	−	0.350643i
$23$	6.73238e13			0.338865			0.169432	−	0.985542i	$-0.445807\pi$
$23$	6.73238e13			0.338865			0.169432	+	0.985542i	$0.445807\pi$
$24$		0			0
$25$	−3.93281e14			−0.824770
$26$	−7.96170e14	−	3.78333e14i	−1.10608	−	0.525599i
$27$		0			0
$28$	−1.39284e15	+	1.13462e15i	−0.888670	+	0.723921i
$29$	3.07544e15			1.35746			0.678732	−	0.734386i	$-0.262530\pi$
$29$	3.07544e15			1.35746			0.678732	+	0.734386i	$0.262530\pi$
$30$		0			0
$31$		−	3.73440e15i		−	0.818320i	−0.912463	−	0.409160i	$-0.865822\pi$
$31$		−	3.73440e15i		−	0.818320i	0.912463	−	0.409160i	$-0.134178\pi$
$32$	−5.08097e15	−	3.84038e15i	−0.797759	−	0.602976i
$33$		0			0
$34$	−1.76766e16	−	8.39977e15i	−1.46849	−	0.697812i
$35$			7.83038e15i			0.479809i
$36$		0			0
$37$		−	9.88634e15i		−	0.338001i	−0.985616	−	0.169000i	$-0.945946\pi$
$37$		−	9.88634e15i		−	0.338001i	0.985616	−	0.169000i	$-0.0540539\pi$
$38$	−1.65708e16	+	3.48719e16i	−0.428170	+	0.901047i
$39$		0			0
$40$	−2.69654e16	+	6.59839e15i	−0.406609	+	0.0994965i
$41$		−	1.48280e17i		−	1.72525i	−0.505840	−	0.862627i	$-0.668817\pi$
$41$		−	1.48280e17i		−	1.72525i	0.505840	−	0.862627i	$-0.331183\pi$
$42$		0			0
$43$	7.92658e16			0.559329			0.279664	−	0.960098i	$-0.409777\pi$
$43$	7.92658e16			0.559329			0.279664	+	0.960098i	$0.409777\pi$
$44$	1.14271e17	−	9.30866e16i	0.633408	−	0.515982i
$45$		0			0
$46$	−4.18448e16	+	8.80588e16i	−0.145440	+	0.306066i
$47$	3.94989e17			1.09536			0.547680	−	0.836688i	$-0.315511\pi$
$47$	3.94989e17			1.09536			0.547680	+	0.836688i	$0.315511\pi$
$48$		0			0
$49$	−1.75270e17			−0.313796
$50$	2.44442e17	−	5.14407e17i	0.353989	−	0.744941i
$51$		0			0
$52$	9.89711e17	−	8.06230e17i	0.949452	−	0.773435i
$53$	−4.73280e17			−0.371725			−0.185862	−	0.982576i	$-0.559508\pi$
$53$	−4.73280e17			−0.371725			−0.185862	+	0.982576i	$0.559508\pi$
$54$		0			0
$55$		−	6.42421e17i		−	0.341989i
$56$	−6.18361e17	−	2.52703e18i	−0.272438	−	1.11336i
$57$		0			0
$58$	−1.91152e18	+	4.02264e18i	−0.582621	+	1.22608i
$59$			5.97069e18i			1.52082i	0.649442	+	0.760411i	$0.275003\pi$
$59$			5.97069e18i			1.52082i	−0.649442	+	0.760411i	$0.724997\pi$
$60$		0			0
$61$		−	9.79657e18i		−	1.75837i	−0.476479	−	0.879186i	$-0.658087\pi$
$61$		−	9.79657e18i		−	1.75837i	0.476479	−	0.879186i	$-0.341913\pi$
$62$	4.88456e18	+	2.32110e18i	0.739115	+	0.351221i
$63$		0			0
$64$	8.18123e18	−	4.25888e18i	0.887011	−	0.461749i
$65$		−	5.56405e18i		−	0.512627i
$66$		0			0
$67$	−1.69202e19			−1.13402			−0.567008	−	0.823712i	$-0.691899\pi$
$67$	−1.69202e19			−1.13402			−0.567008	+	0.823712i	$0.691899\pi$
$68$	2.19736e19	−	1.79000e19i	1.26054	−	1.02685i
$69$		0			0
$70$	−1.02421e19	−	4.86693e18i	−0.433369	−	0.205933i
$71$	−2.88571e19			−1.05206			−0.526030	−	0.850466i	$-0.676320\pi$
$71$	−2.88571e19			−1.05206			−0.526030	+	0.850466i	$0.676320\pi$
$72$		0			0
$73$	−5.35107e19			−1.45731			−0.728653	−	0.684883i	$-0.759853\pi$
$73$	−5.35107e19			−1.45731			−0.728653	+	0.684883i	$0.759853\pi$
$74$	1.29312e19	+	6.14480e18i	0.305286	+	0.145069i
$75$		0			0
$76$	−3.53125e19	−	4.33489e19i	−0.630066	−	0.773455i
$77$	6.02038e19			0.936421
$78$		0			0
$79$			4.29094e19i			0.509880i	0.966957	+	0.254940i	$0.0820557\pi$
$79$			4.29094e19i			0.509880i	−0.966957	+	0.254940i	$0.917944\pi$
$80$	8.12958e18	−	3.93716e19i	0.0846493	−	0.409957i
$81$		0			0
$82$	1.93949e20	+	9.21629e19i	1.55827	+	0.740476i
$83$		−	9.50389e19i		−	0.672328i	−0.941803	−	0.336164i	$-0.890870\pi$
$83$		−	9.50389e19i		−	0.672328i	0.941803	−	0.336164i	$-0.109130\pi$
$84$		0			0
$85$		−	1.23533e20i		−	0.680590i
$86$	−4.92673e19	+	1.03679e20i	−0.240063	+	0.505192i
$87$		0			0
$88$	5.07316e19	+	2.07323e20i	0.194183	+	0.793559i
$89$			4.33090e20i			1.47226i	0.676843	+	0.736128i	$0.263348\pi$
$89$			4.33090e20i			1.47226i	−0.676843	+	0.736128i	$0.736652\pi$
$90$		0			0
$91$	5.21429e20			1.40366
$92$	−8.91715e19	−	1.09465e20i	−0.214020	−	0.262726i
$93$		0			0
$94$	−2.45503e20	+	5.16641e20i	−0.470126	+	0.989341i
$95$	−2.43703e20			−0.417602
$96$		0			0
$97$	−4.63333e20			−0.637955			−0.318977	−	0.947762i	$-0.603339\pi$
$97$	−4.63333e20			−0.637955			−0.318977	+	0.947762i	$0.603339\pi$
$98$	1.08938e20	−	2.29251e20i	0.134681	−	0.283424i
$99$		0			0
$100$	5.20907e20	+	6.39454e20i	0.520907	+	0.639454i
$101$	1.48594e21			1.33853			0.669265	−	0.743024i	$-0.266609\pi$
$101$	1.48594e21			1.33853			0.669265	+	0.743024i	$0.266609\pi$
$102$		0			0
$103$			8.18041e20i			0.599769i	0.953975	+	0.299885i	$0.0969482\pi$
$103$			8.18041e20i			0.599769i	−0.953975	+	0.299885i	$0.903052\pi$
$104$	4.39390e20	+	1.79564e21i	0.291072	+	1.18951i
$105$		0			0
$106$	2.94165e20	−	6.19045e20i	0.159544	−	0.335746i
$107$		−	1.83283e21i		−	0.900725i	−0.892846	−	0.450362i	$-0.851295\pi$
$107$		−	1.83283e21i		−	0.900725i	0.892846	−	0.450362i	$-0.148705\pi$
$108$		0			0
$109$			2.66660e21i			1.07889i	0.842019	+	0.539447i	$0.181367\pi$
$109$			2.66660e21i			1.07889i	−0.842019	+	0.539447i	$0.818633\pi$
$110$	8.40279e20	+	3.99294e20i	0.308888	+	0.146781i
$111$		0			0
$112$	3.68967e21	+	7.61854e20i	1.12253	+	0.231784i
$113$		−	6.00368e21i		−	1.66377i	−0.554946	−	0.831887i	$-0.687261\pi$
$113$		−	6.00368e21i		−	1.66377i	0.554946	−	0.831887i	$-0.312739\pi$
$114$		0			0
$115$	−6.15401e20			−0.141851
$116$	−4.07347e21	−	5.00051e21i	−0.857345	−	1.05246i
$117$		0			0
$118$	−7.80960e21	−	3.71105e21i	−1.37362	−	0.652734i
$119$	1.15768e22			1.86357
$120$		0			0
$121$	2.46101e21			0.332557
$122$	1.28138e22	+	6.08901e21i	1.58818	+	0.754689i
$123$		0			0
$124$	−6.07194e21	+	4.94627e21i	−0.634454	+	0.516833i
$125$	7.95367e21			0.763858
$126$		0			0
$127$			1.28059e22i			1.04105i	0.853846	+	0.520526i	$0.174264\pi$
$127$			1.28059e22i			1.04105i	−0.853846	+	0.520526i	$0.825736\pi$
$128$	4.85564e20	+	1.33480e22i	0.0363531	+	0.999339i
$129$		0			0
$130$	7.27772e21	+	3.45831e21i	0.463010	+	0.220018i
$131$			1.19685e22i			0.702573i	0.936268	+	0.351286i	$0.114256\pi$
$131$			1.19685e22i			0.702573i	−0.936268	+	0.351286i	$0.885744\pi$
$132$		0			0
$133$		−	2.28384e22i		−	1.14346i
$134$	1.05166e22	−	2.21314e22i	0.486717	−	1.02425i
$135$		0			0
$136$	9.75536e21	+	3.98668e22i	0.386442	+	1.57926i
$137$			7.62483e21i			0.279682i	0.990174	+	0.139841i	$0.0446591\pi$
$137$			7.62483e21i			0.279682i	−0.990174	+	0.139841i	$0.955341\pi$
$138$		0			0
$139$	−3.47248e21			−0.109392			−0.0546958	−	0.998503i	$-0.517419\pi$
$139$	−3.47248e21			−0.109392			−0.0546958	+	0.998503i	$0.517419\pi$
$140$	1.27318e22	−	1.03715e22i	0.372002	−	0.303037i
$141$		0			0
$142$	1.79360e22	−	3.77448e22i	0.451542	−	0.950231i
$143$	−4.27791e22			−1.00047
$144$		0			0
$145$	−2.81123e22			−0.568242
$146$	3.32593e22	−	6.99914e22i	0.625473	−	1.31625i
$147$		0			0
$148$	−1.60747e22	+	1.30946e22i	−0.262056	+	0.213474i
$149$	5.75779e22			0.874580			0.437290	−	0.899320i	$-0.355938\pi$
$149$	5.75779e22			0.874580			0.437290	+	0.899320i	$0.355938\pi$
$150$		0			0
$151$			1.42237e23i			1.87826i	0.343561	+	0.939130i	$0.388367\pi$
$151$			1.42237e23i			1.87826i	−0.343561	+	0.939130i	$0.611633\pi$
$152$	7.86481e22	−	1.92451e22i	0.969016	−	0.237117i
$153$		0			0
$154$	−3.74193e22	+	7.87458e22i	−0.401910	+	0.845785i
$155$			3.41358e22i			0.342553i
$156$		0			0
$157$		−	3.31724e22i		−	0.290958i	−0.989361	−	0.145479i	$-0.953528\pi$
$157$		−	3.31724e22i		−	0.290958i	0.989361	−	0.145479i	$-0.0464724\pi$
$158$	−5.61250e22	−	2.66701e22i	−0.460529	−	0.218839i
$159$		0			0
$160$	4.64447e22	+	3.51046e22i	0.333946	+	0.252409i
$161$		−	5.76716e22i		−	0.388410i
$162$		0			0
$163$	2.86744e23			1.69638			0.848192	−	0.529689i	$-0.177691\pi$
$163$	2.86744e23			1.69638			0.848192	+	0.529689i	$0.177691\pi$
$164$	−2.41096e23	+	1.96400e23i	−1.33761	+	1.08963i
$165$		0			0
$166$	1.24310e23	+	5.90710e22i	0.607254	+	0.288562i
$167$	−1.28937e23			−0.591363			−0.295681	−	0.955287i	$-0.595547\pi$
$167$	−1.28937e23			−0.591363			−0.295681	+	0.955287i	$0.595547\pi$
$168$		0			0
$169$	−1.23449e23			−0.499662
$170$	1.61580e23	+	7.67815e22i	0.614716	+	0.292108i
$171$		0			0
$172$	−1.04989e23	−	1.28882e23i	−0.353260	−	0.433654i
$173$	−2.63925e23			−0.835595			−0.417798	−	0.908540i	$-0.637198\pi$
$173$	−2.63925e23			−0.835595			−0.417798	+	0.908540i	$0.637198\pi$
$174$		0			0
$175$			3.36896e23i			0.945359i
$176$	−3.02708e23	−	6.25041e22i	−0.800094	−	0.165206i
$177$		0			0
$178$	−5.66477e23	−	2.69185e23i	−1.32976	−	0.631889i
$179$		−	2.69566e22i		−	0.0596634i	−0.999555	−	0.0298317i	$-0.990503\pi$
$179$		−	2.69566e22i		−	0.0596634i	0.999555	−	0.0298317i	$-0.00949714\pi$
$180$		0			0
$181$		−	1.59898e23i		−	0.314932i	−0.987524	−	0.157466i	$-0.949667\pi$
$181$		−	1.59898e23i		−	0.314932i	0.987524	−	0.157466i	$-0.0503325\pi$
$182$	−3.24092e23	+	6.82023e23i	−0.602446	+	1.26780i
$183$		0			0
$184$	1.98603e23	−	4.85979e22i	0.329154	−	0.0805434i
$185$			9.03701e22i			0.141489i
$186$		0			0
$187$	−9.49784e23			−1.32828
$188$	−5.23169e23	−	6.42231e23i	−0.691806	−	0.849246i
$189$		0			0
$190$	1.51472e23	−	3.18761e23i	0.179234	−	0.377183i
$191$	2.03348e23			0.227714			0.113857	−	0.993497i	$-0.463679\pi$
$191$	2.03348e23			0.227714			0.113857	+	0.993497i	$0.463679\pi$
$192$		0			0
$193$	2.73611e23			0.274651			0.137326	−	0.990526i	$-0.456149\pi$
$193$	2.73611e23			0.274651			0.137326	+	0.990526i	$0.456149\pi$
$194$	2.87982e23	−	6.06034e23i	0.273809	−	0.576208i
$195$		0			0
$196$	2.32147e23	+	2.84979e23i	0.198187	+	0.243290i
$197$	−1.23248e24			−0.997432			−0.498716	−	0.866765i	$-0.666195\pi$
$197$	−1.23248e24			−0.997432			−0.498716	+	0.866765i	$0.666195\pi$
$198$		0			0
$199$		−	2.06155e24i		−	1.50050i	−0.661152	−	0.750252i	$-0.729932\pi$
$199$		−	2.06155e24i		−	1.50050i	0.661152	−	0.750252i	$-0.270068\pi$
$200$	−1.16017e24	+	2.83891e23i	−0.801134	+	0.196036i
$201$		0			0
$202$	−9.23581e23	+	1.94360e24i	−0.574494	+	1.20897i
$203$		−	2.63452e24i		−	1.55594i
$204$		0			0
$205$			1.35542e24i			0.722200i
$206$	−1.06999e24	−	5.08449e23i	−0.541718	−	0.257420i
$207$		0			0
$208$	−2.62178e24	−	5.41353e23i	−1.19931	−	0.247637i
$209$			1.87371e24i			0.815015i
$210$		0			0
$211$	3.34998e23			0.131849			0.0659244	−	0.997825i	$-0.479000\pi$
$211$	3.34998e23			0.131849			0.0659244	+	0.997825i	$0.479000\pi$
$212$	6.26867e23	+	7.69529e23i	0.234773	+	0.288203i
$213$		0			0
$214$	2.39732e24	+	1.13918e24i	0.813544	+	0.386589i
$215$	−7.24562e23			−0.234138
$216$		0			0
$217$	−3.19900e24			−0.937966
$218$	−3.48788e24	−	1.65741e24i	−0.974469	−	0.463059i
$219$		0			0
$220$	−1.04454e24	+	8.50897e23i	−0.265148	+	0.215993i
$221$	−8.22615e24			−1.99103
$222$		0			0
$223$			6.19991e24i			1.36516i	0.730810	+	0.682581i	$0.239143\pi$
$223$			6.19991e24i			1.36516i	−0.730810	+	0.682581i	$0.760857\pi$
$224$	−3.28979e24	+	4.35251e24i	−0.691137	+	0.914399i
$225$		0			0
$226$	7.85275e24	+	3.73156e24i	1.50274	+	0.714088i
$227$			6.02396e24i			1.10055i	0.834983	+	0.550276i	$0.185477\pi$
$227$			6.02396e24i			1.10055i	−0.834983	+	0.550276i	$0.814523\pi$
$228$		0			0
$229$			8.82574e24i			1.47055i	0.677771	+	0.735273i	$0.262946\pi$
$229$			8.82574e24i			1.47055i	−0.677771	+	0.735273i	$0.737054\pi$
$230$	3.82500e23	−	8.04938e23i	0.0608820	−	0.128121i
$231$		0			0
$232$	9.07245e24	−	2.22001e24i	1.31856	−	0.322650i
$233$		−	3.03738e24i		−	0.421951i	−0.977491	−	0.210976i	$-0.932336\pi$
$233$		−	3.03738e24i		−	0.421951i	0.977491	−	0.210976i	$-0.0676641\pi$
$234$		0			0
$235$	−3.61056e24			−0.458524
$236$	9.70803e24	−	7.90828e24i	1.17911	−	0.960519i
$237$		0			0
$238$	−7.19549e24	+	1.51423e25i	−0.799839	+	1.68319i
$239$	−1.90994e24			−0.203162			−0.101581	−	0.994827i	$-0.532390\pi$
$239$	−1.90994e24			−0.203162			−0.101581	+	0.994827i	$0.532390\pi$
$240$		0			0
$241$	7.14356e24			0.696203			0.348101	−	0.937457i	$-0.386827\pi$
$241$	7.14356e24			0.696203			0.348101	+	0.937457i	$0.386827\pi$
$242$	−1.52963e24	+	3.21897e24i	−0.142733	+	0.300369i
$243$		0			0
$244$	−1.59287e25	+	1.29757e25i	−1.36329	+	1.11055i
$245$	1.60212e24			0.131357
$246$		0			0
$247$			1.62283e25i			1.22167i
$248$	−2.69569e24	−	1.10164e25i	−0.194503	−	0.794869i
$249$		0			0
$250$	−4.94356e24	+	1.04033e25i	−0.327846	+	0.689924i
$251$		−	8.23698e24i		−	0.523834i	−0.965090	−	0.261917i	$-0.915645\pi$
$251$		−	8.23698e24i		−	0.523834i	0.965090	−	0.261917i	$-0.0843547\pi$
$252$		0			0
$253$			4.73150e24i			0.276843i
$254$	−1.67500e25	−	7.95947e24i	−0.940289	−	0.446817i
$255$		0			0
$256$	−1.77609e25	−	7.66129e24i	−0.918216	−	0.396080i
$257$		−	9.16966e24i		−	0.455046i	−0.973773	−	0.227523i	$-0.926937\pi$
$257$		−	9.16966e24i		−	0.455046i	0.973773	−	0.227523i	$-0.0730627\pi$
$258$		0			0
$259$	−8.46894e24			−0.387419
$260$	−9.04686e24	+	7.36968e24i	−0.397446	+	0.323764i
$261$		0			0
$262$	−1.56547e25	−	7.43896e24i	−0.634571	−	0.301543i
$263$	1.93641e25			0.754157			0.377079	−	0.926181i	$-0.376929\pi$
$263$	1.93641e25			0.754157			0.377079	+	0.926181i	$0.376929\pi$
$264$		0			0
$265$	4.32621e24			0.155606
$266$	2.98723e25	+	1.41951e25i	1.03279	+	0.490772i
$267$		0			0
$268$	2.24110e25	+	2.75113e25i	0.716220	+	0.879216i
$269$	1.39331e25			0.428202			0.214101	−	0.976811i	$-0.431318\pi$
$269$	1.39331e25			0.428202			0.214101	+	0.976811i	$0.431318\pi$
$270$		0			0
$271$			5.15914e25i			1.46690i	0.679744	+	0.733449i	$0.262091\pi$
$271$			5.15914e25i			1.46690i	−0.679744	+	0.733449i	$0.737909\pi$
$272$	−5.82088e25	−	1.20191e25i	−1.59226	−	0.328776i
$273$		0			0
$274$	−9.97319e24	−	4.73917e24i	−0.252611	−	0.120039i
$275$		−	2.76397e25i		−	0.673814i
$276$		0			0
$277$			8.31335e25i			1.87819i	0.343664	+	0.939093i	$0.388332\pi$
$277$			8.31335e25i			1.87819i	−0.343664	+	0.939093i	$0.611668\pi$
$278$	2.15830e24	−	4.54196e24i	0.0469507	−	0.0988037i
$279$		0			0
$280$	5.65238e24	+	2.30994e25i	0.114044	+	0.466059i
$281$			1.09118e24i			0.0212071i	0.999944	+	0.0106036i	$0.00337528\pi$
$281$			1.09118e24i			0.0212071i	−0.999944	+	0.0106036i	$0.996625\pi$
$282$		0			0
$283$	5.42534e25			0.978745			0.489373	−	0.872075i	$-0.337226\pi$
$283$	5.42534e25			0.978745			0.489373	+	0.872075i	$0.337226\pi$
$284$	3.82217e25	+	4.69201e25i	0.664458	+	0.815674i
$285$		0			0
$286$	2.65892e25	−	5.59546e25i	0.429399	−	0.903634i
$287$	−1.27021e26			−1.97750
$288$		0			0
$289$	−1.13545e26			−1.64340
$290$	1.74731e25	−	3.67706e25i	0.243888	−	0.513242i
$291$		0			0
$292$	7.08758e25	+	8.70056e25i	0.920403	+	1.12987i
$293$	−1.47231e25			−0.184454			−0.0922271	−	0.995738i	$-0.529399\pi$
$293$	−1.47231e25			−0.184454			−0.0922271	+	0.995738i	$0.529399\pi$
$294$		0			0
$295$		−	5.45776e25i		−	0.636624i
$296$	−7.13648e24	−	2.91644e25i	−0.0803380	−	0.328314i
$297$		0			0
$298$	−3.57872e25	+	7.53112e25i	−0.375368	+	0.789930i
$299$			4.09799e25i			0.414976i
$300$		0			0
$301$		−	6.79015e25i		−	0.641108i
$302$	−1.86045e26	−	8.84069e25i	−1.69646	−	0.806145i
$303$		0			0
$304$	−2.37110e25	+	1.14833e26i	−0.201733	+	0.976995i
$305$			8.95496e25i			0.736063i
$306$		0			0
$307$	−1.27760e26			−0.980487			−0.490243	−	0.871586i	$-0.663092\pi$
$307$	−1.27760e26			−0.980487			−0.490243	+	0.871586i	$0.663092\pi$
$308$	−7.97408e25	−	9.78881e25i	−0.591423	−	0.726018i
$309$		0			0
$310$	−4.46493e25	−	2.12170e25i	−0.309397	−	0.147023i
$311$	−1.10157e26			−0.737953			−0.368977	−	0.929439i	$-0.620292\pi$
$311$	−1.10157e26			−0.737953			−0.368977	+	0.929439i	$0.620292\pi$
$312$		0			0
$313$	6.02008e25			0.377040			0.188520	−	0.982069i	$-0.439631\pi$
$313$	6.02008e25			0.377040			0.188520	+	0.982069i	$0.439631\pi$
$314$	4.33892e25	+	2.06182e25i	0.262797	+	0.124879i
$315$		0			0
$316$	6.97684e25	−	5.68342e25i	0.395316	−	0.322029i
$317$	−3.88386e25			−0.212883			−0.106442	−	0.994319i	$-0.533946\pi$
$317$	−3.88386e25			−0.212883			−0.106442	+	0.994319i	$0.533946\pi$
$318$		0			0
$319$			2.16141e26i			1.10901i
$320$	−7.47839e25	+	3.89301e25i	−0.371307	+	0.193290i
$321$		0			0
$322$	7.54338e25	+	3.58455e25i	0.350816	+	0.166705i
$323$			3.60302e26i			1.62196i
$324$		0			0
$325$		−	2.39389e26i		−	1.01002i
$326$	−1.78224e26	+	3.75058e26i	−0.728084	+	1.53219i
$327$		0			0
$328$	−1.07037e26	−	4.37422e26i	−0.410069	−	1.67581i
$329$		−	3.38359e26i		−	1.25551i
$330$		0			0
$331$	−1.22368e26			−0.426064			−0.213032	−	0.977045i	$-0.568334\pi$
$331$	−1.22368e26			−0.426064			−0.213032	+	0.977045i	$0.568334\pi$
$332$	−1.54528e26	+	1.25881e26i	−0.521264	+	0.424628i
$333$		0			0
$334$	8.01400e25	−	1.68648e26i	0.253812	−	0.534125i
$335$	1.54666e26			0.474705
$336$		0			0
$337$	1.54747e26			0.446178			0.223089	−	0.974798i	$-0.428386\pi$
$337$	1.54747e26			0.446178			0.223089	+	0.974798i	$0.428386\pi$
$338$	7.67289e25	−	1.61469e26i	0.214454	−	0.451300i
$339$		0			0
$340$	−2.00859e26	+	1.63622e26i	−0.527670	+	0.429846i
$341$	2.62453e26			0.668545
$342$		0			0
$343$		−	3.28326e26i		−	0.786533i
$344$	2.33832e26	−	5.72182e25i	0.543300	−	0.132945i
$345$		0			0
$346$	1.64041e26	−	3.45210e26i	0.358636	−	0.754718i
$347$		−	5.05152e26i		−	1.07143i	−0.844400	−	0.535713i	$-0.820043\pi$
$347$		−	5.05152e26i		−	1.07143i	0.844400	−	0.535713i	$-0.179957\pi$
$348$		0			0
$349$			4.20691e26i			0.840033i	0.907516	+	0.420017i	$0.137976\pi$
$349$			4.20691e26i			0.840033i	−0.907516	+	0.420017i	$0.862024\pi$
$350$	−4.40657e26	−	2.09396e26i	−0.853858	−	0.405746i
$351$		0			0
$352$	2.69901e26	−	3.57089e26i	0.492614	−	0.651747i
$353$			2.50714e26i			0.444165i	0.975028	+	0.222082i	$0.0712854\pi$
$353$			2.50714e26i			0.444165i	−0.975028	+	0.222082i	$0.928715\pi$
$354$		0			0
$355$	2.63780e26			0.440397
$356$	7.04182e26	−	5.73635e26i	1.14146	−	0.929845i
$357$		0			0
$358$	3.52589e25	+	1.67547e25i	0.0538887	+	0.0256074i
$359$	8.98020e26			1.33289			0.666445	−	0.745554i	$-0.267815\pi$
$359$	8.98020e26			1.33289			0.666445	+	0.745554i	$0.267815\pi$
$360$		0			0
$361$	−3.41722e24			−0.00478462
$362$	2.09144e26	+	9.93836e25i	0.284450	+	0.135168i
$363$		0			0
$364$	−6.90641e26	−	8.47816e26i	−0.886519	−	1.08827i
$365$	4.89137e26			0.610036
$366$		0			0
$367$		−	1.17224e27i		−	1.38046i	−0.723592	−	0.690228i	$-0.757510\pi$
$367$		−	1.17224e27i		−	1.38046i	0.723592	−	0.690228i	$-0.242490\pi$
$368$	−5.98753e25	+	2.89976e26i	−0.0685244	+	0.331864i
$369$		0			0
$370$	−1.18203e26	−	5.61691e25i	−0.127794	−	0.0607267i
$371$			4.05426e26i			0.426075i
$372$		0			0
$373$			9.52010e26i			0.945581i	0.881175	+	0.472791i	$0.156753\pi$
$373$			9.52010e26i			0.945581i	−0.881175	+	0.472791i	$0.843247\pi$
$374$	5.90334e26	−	1.24231e27i	0.570093	−	1.19971i
$375$		0			0
$376$	1.16520e27	−	2.85124e26i	1.06397	−	0.260352i
$377$			1.87201e27i			1.66236i
$378$		0			0
$379$	−6.96225e26			−0.584841			−0.292421	−	0.956290i	$-0.594461\pi$
$379$	−6.96225e26			−0.584841			−0.292421	+	0.956290i	$0.594461\pi$
$380$	3.22789e26	+	3.96248e26i	0.263749	+	0.323772i
$381$		0			0
$382$	−1.26390e26	+	2.65977e26i	−0.0977342	+	0.205673i
$383$	2.33002e27			1.75296			0.876481	−	0.481436i	$-0.159885\pi$
$383$	2.33002e27			1.75296			0.876481	+	0.481436i	$0.159885\pi$
$384$		0			0
$385$	−5.50317e26			−0.391991
$386$	−1.70062e26	+	3.57880e26i	−0.117880	+	0.248068i
$387$		0			0
$388$	6.13692e26	+	7.53355e26i	0.402919	+	0.494614i
$389$	1.26866e26			0.0810727			0.0405364	−	0.999178i	$-0.487093\pi$
$389$	1.26866e26			0.0810727			0.0405364	+	0.999178i	$0.487093\pi$
$390$		0			0
$391$			9.09837e26i			0.550944i
$392$	−5.17039e26	+	1.26519e26i	−0.304804	+	0.0745850i
$393$		0			0
$394$	7.66040e26	−	1.61207e27i	0.428096	−	0.900891i
$395$		−	3.92231e26i		−	0.213438i
$396$		0			0
$397$		−	9.05838e26i		−	0.467466i	−0.972301	−	0.233733i	$-0.924906\pi$
$397$		−	9.05838e26i		−	0.467466i	0.972301	−	0.233733i	$-0.0750942\pi$
$398$	2.69649e27	+	1.28135e27i	1.35527	+	0.644013i
$399$		0			0
$400$	3.49769e26	−	1.69393e27i	0.166783	−	0.807731i
$401$			1.88202e27i			0.874195i	0.899414	+	0.437097i	$0.143993\pi$
$401$			1.88202e27i			0.874195i	−0.899414	+	0.437097i	$0.856007\pi$
$402$		0			0
$403$	2.27312e27			1.00212
$404$	−1.96816e27	−	2.41607e27i	−0.845387	−	1.03778i
$405$		0			0
$406$	3.44592e27	+	1.63747e27i	1.40534	+	0.667806i
$407$	6.94809e26			0.276137
$408$		0			0
$409$	1.99576e27			0.753378			0.376689	−	0.926340i	$-0.377063\pi$
$409$	1.99576e27			0.753378			0.376689	+	0.926340i	$0.377063\pi$
$410$	−1.77287e27	−	8.42453e26i	−0.652299	−	0.309967i
$411$		0			0
$412$	1.33009e27	−	1.08351e27i	0.465008	−	0.378801i
$413$	5.11468e27			1.74318
$414$		0			0
$415$			8.68742e26i			0.281440i
$416$	2.33763e27	−	3.09278e27i	0.738408	−	0.976942i
$417$		0			0
$418$	−2.45079e27	−	1.16459e27i	−0.736130	−	0.349803i
$419$			6.25017e27i			1.83082i	0.402528	+	0.915408i	$0.368132\pi$
$419$			6.25017e27i			1.83082i	−0.402528	+	0.915408i	$0.631868\pi$
$420$		0			0
$421$		−	3.95405e27i		−	1.10174i	−0.834590	−	0.550872i	$-0.814295\pi$
$421$		−	3.95405e27i		−	1.10174i	0.834590	−	0.550872i	$-0.185705\pi$
$422$	−2.08216e26	+	4.38174e26i	−0.0565893	+	0.119087i
$423$		0			0
$424$	−1.39616e27	+	3.41638e26i	−0.361072	+	0.0883538i
$425$		−	5.31493e27i		−	1.34095i
$426$		0			0
$427$	−8.39204e27			−2.01546
$428$	−2.98008e27	+	2.42761e27i	−0.698343	+	0.568878i
$429$		0			0
$430$	4.50348e26	−	9.47719e26i	0.100491	−	0.211476i
$431$	4.37336e27			0.952365			0.476183	−	0.879346i	$-0.342020\pi$
$431$	4.37336e27			0.952365			0.476183	+	0.879346i	$0.342020\pi$
$432$		0			0
$433$	−9.34089e27			−1.93761			−0.968803	−	0.247832i	$-0.920282\pi$
$433$	−9.34089e27			−1.93761			−0.968803	+	0.247832i	$0.920282\pi$
$434$	1.98832e27	−	4.18426e27i	0.402573	−	0.847181i
$435$		0			0
$436$	4.33575e27	−	3.53195e27i	0.836480	−	0.681407i
$437$	1.79490e27			0.338053
$438$		0			0
$439$			5.55087e27i			0.996514i	0.867029	+	0.498257i	$0.166026\pi$
$439$			5.55087e27i			0.996514i	−0.867029	+	0.498257i	$0.833974\pi$
$440$	−4.63733e26	−	1.89512e27i	−0.0812859	−	0.332188i
$441$		0			0
$442$	5.11292e27	−	1.07597e28i	0.854546	−	1.79832i
$443$		−	3.65113e27i		−	0.595921i	−0.954578	−	0.297960i	$-0.903694\pi$
$443$		−	3.65113e27i		−	0.595921i	0.954578	−	0.297960i	$-0.0963063\pi$
$444$		0			0
$445$		−	3.95884e27i		−	0.616294i
$446$	−8.10941e27	−	3.85352e27i	−1.23303	−	0.585925i
$447$		0			0
$448$	−3.64829e27	−	7.00829e27i	−0.529261	−	1.01670i
$449$			8.18341e27i			1.15970i	0.814722	+	0.579852i	$0.196890\pi$
$449$			8.18341e27i			1.15970i	−0.814722	+	0.579852i	$0.803110\pi$
$450$		0			0
$451$	1.04211e28			1.40948
$452$	−9.76167e27	+	7.95197e27i	−1.28994	+	1.05080i
$453$		0			0
$454$	−7.87927e27	−	3.74416e27i	−0.994030	−	0.472355i
$455$	−4.76634e27			−0.587577
$456$		0			0
$457$	−1.24771e27			−0.146890			−0.0734451	−	0.997299i	$-0.523399\pi$
$457$	−1.24771e27			−0.146890			−0.0734451	+	0.997299i	$0.523399\pi$
$458$	−1.15440e28	−	5.48559e27i	−1.32821	−	0.631155i
$459$		0			0
$460$	8.15109e26	+	1.00061e27i	0.0895898	+	0.109978i
$461$	3.85761e27			0.414437			0.207219	−	0.978295i	$-0.433559\pi$
$461$	3.85761e27			0.414437			0.207219	+	0.978295i	$0.433559\pi$
$462$		0			0
$463$			7.26959e27i			0.746293i	0.927772	+	0.373147i	$0.121721\pi$
$463$			7.26959e27i			0.746293i	−0.927772	+	0.373147i	$0.878279\pi$
$464$	−2.73518e27	+	1.32465e28i	−0.274503	+	1.32942i
$465$		0			0
$466$	3.97286e27	+	1.88787e27i	0.381111	+	0.181101i
$467$			8.03132e27i			0.753286i	0.926359	+	0.376643i	$0.122922\pi$
$467$			8.03132e27i			0.753286i	−0.926359	+	0.376643i	$0.877078\pi$
$468$		0			0
$469$			1.44943e28i			1.29982i
$470$	2.24412e27	−	4.72257e27i	0.196797	−	0.414143i
$471$		0			0
$472$	4.30996e27	+	1.76133e28i	0.361478	+	1.47724i
$473$			5.57078e27i			0.456956i
$474$		0			0
$475$	−1.04851e28			−0.822794
$476$	−1.53336e28	−	1.88232e28i	−1.17699	−	1.44485i
$477$		0			0
$478$	1.18712e27	−	2.49818e27i	0.0871967	−	0.183498i
$479$	1.10351e28			0.792961			0.396481	−	0.918043i	$-0.370231\pi$
$479$	1.10351e28			0.792961			0.396481	+	0.918043i	$0.370231\pi$
$480$		0			0
$481$	6.01779e27			0.413918
$482$	−4.44004e27	+	9.34369e27i	−0.298809	+	0.628817i
$483$		0			0
$484$	−3.25964e27	−	4.00147e27i	−0.210036	−	0.257836i
$485$	4.23529e27			0.267051
$486$		0			0
$487$		−	5.03058e27i		−	0.303783i	−0.988397	−	0.151892i	$-0.951464\pi$
$487$		−	5.03058e27i		−	0.303783i	0.988397	−	0.151892i	$-0.0485365\pi$
$488$	−7.07167e27	−	2.88995e28i	−0.417940	−	1.70798i
$489$		0			0
$490$	−9.95792e26	+	2.09556e27i	−0.0563780	+	0.118643i
$491$			2.28402e28i			1.26574i	0.774258	+	0.632871i	$0.218123\pi$
$491$			2.28402e28i			1.26574i	−0.774258	+	0.632871i	$0.781877\pi$
$492$		0			0
$493$			4.15625e28i			2.20704i
$494$	−2.12264e28	−	1.00866e28i	−1.10343	−	0.524340i
$495$		0			0
$496$	1.60848e28	+	3.32124e27i	0.801414	+	0.165479i
$497$			2.47199e28i			1.20588i
$498$		0			0
$499$	−2.77677e28			−1.29863			−0.649313	−	0.760521i	$-0.724943\pi$
$499$	−2.77677e28			−1.29863			−0.649313	+	0.760521i	$0.724943\pi$
$500$	−1.05348e28	−	1.29323e28i	−0.482436	−	0.592228i
$501$		0			0
$502$	1.07739e28	+	5.11965e27i	0.473132	+	0.224828i
$503$	−1.44043e28			−0.619480			−0.309740	−	0.950821i	$-0.600242\pi$
$503$	−1.44043e28			−0.619480			−0.309740	+	0.950821i	$0.600242\pi$
$504$		0			0
$505$	−1.35829e28			−0.560315
$506$	−6.18875e27	−	2.94084e27i	−0.250048	−	0.118820i
$507$		0			0
$508$	2.08218e28	−	1.69617e28i	0.807140	−	0.657506i
$509$	−2.02542e28			−0.769094			−0.384547	−	0.923105i	$-0.625642\pi$
$509$	−2.02542e28			−0.769094			−0.384547	+	0.923105i	$0.625642\pi$
$510$		0			0
$511$			4.58389e28i			1.67038i
$512$	2.10601e28	−	1.84692e28i	0.751840	−	0.659346i
$513$		0			0
$514$	1.19938e28	+	5.69935e27i	0.411002	+	0.195305i
$515$		−	7.47764e27i		−	0.251067i
$516$		0			0
$517$			2.77597e28i			0.894879i
$518$	5.26382e27	−	1.10773e28i	0.166280	−	0.349921i
$519$		0			0
$520$	−4.01643e27	−	1.64138e28i	−0.121844	−	0.497936i
$521$			9.41777e27i			0.279996i	0.990152	+	0.139998i	$0.0447096\pi$
$521$			9.41777e27i			0.279996i	−0.990152	+	0.139998i	$0.955290\pi$
$522$		0			0
$523$	−4.74316e28			−1.35457			−0.677283	−	0.735723i	$-0.736843\pi$
$523$	−4.74316e28			−1.35457			−0.677283	+	0.735723i	$0.736843\pi$
$524$	1.94602e28	−	1.58525e28i	0.544713	−	0.443730i
$525$		0			0
$526$	−1.20357e28	+	2.53280e28i	−0.323683	+	0.681163i
$527$	5.04680e28			1.33047
$528$		0			0
$529$	−3.49391e28			−0.885171
$530$	−2.68894e27	+	5.65864e27i	−0.0667858	+	0.140545i
$531$		0			0
$532$	−3.71340e28	+	3.02498e28i	−0.886542	+	0.722187i
$533$	9.02580e28			2.11276
$534$		0			0
$535$			1.67537e28i			0.377048i
$536$	−4.99139e28	+	1.22139e28i	−1.10152	+	0.269540i
$537$		0			0
$538$	−8.66005e27	+	1.82243e28i	−0.183784	+	0.386757i
$539$		−	1.23179e28i		−	0.256363i
$540$		0			0
$541$			4.11838e28i			0.824433i	0.911086	+	0.412217i	$0.135245\pi$
$541$			4.11838e28i			0.824433i	−0.911086	+	0.412217i	$0.864755\pi$
$542$	−6.74810e28	−	3.20664e28i	−1.32492	−	0.629590i
$543$		0			0
$544$	5.19002e28	−	6.86660e28i	0.980350	−	1.29704i
$545$		−	2.43751e28i		−	0.451631i
$546$		0			0
$547$	9.40507e28			1.67685			0.838426	−	0.545015i	$-0.183476\pi$
$547$	9.40507e28			1.67685			0.838426	+	0.545015i	$0.183476\pi$
$548$	1.23976e28	−	1.00992e28i	0.216841	−	0.176641i
$549$		0			0
$550$	3.61524e28	+	1.71793e28i	0.608596	+	0.289199i
$551$	8.19934e28			1.35421
$552$		0			0
$553$	3.67575e28			0.584429
$554$	−1.08738e29	−	5.16712e28i	−1.69640	−	0.806113i
$555$		0			0
$556$	4.59935e27	+	5.64607e27i	0.0690894	+	0.0848127i
$557$	8.21528e28			1.21100			0.605498	−	0.795847i	$-0.292974\pi$
$557$	8.21528e28			1.21100			0.605498	+	0.795847i	$0.292974\pi$
$558$		0			0
$559$			4.82489e28i			0.684958i
$560$	−3.37269e28	−	6.96404e27i	−0.469897	−	0.0970258i
$561$		0			0
$562$	−1.42726e27	−	6.78220e26i	−0.0191545	−	0.00910205i
$563$			8.17084e28i			1.07629i	0.842853	+	0.538144i	$0.180874\pi$
$563$			8.17084e28i			1.07629i	−0.842853	+	0.538144i	$0.819126\pi$
$564$		0			0
$565$			5.48792e28i			0.696464i
$566$	−3.37209e28	+	7.09629e28i	−0.420075	+	0.884013i
$567$		0			0
$568$	−8.51275e28	+	2.08306e28i	−1.02191	+	0.250060i
$569$			9.39824e28i			1.10756i	0.832663	+	0.553781i	$0.186815\pi$
$569$			9.39824e28i			1.10756i	−0.832663	+	0.553781i	$0.813185\pi$
$570$		0			0
$571$	−1.51570e29			−1.72160			−0.860801	−	0.508942i	$-0.830037\pi$
$571$	−1.51570e29			−1.72160			−0.860801	+	0.508942i	$0.830037\pi$
$572$	5.66617e28	+	6.95566e28i	0.631875	+	0.775676i
$573$		0			0
$574$	7.89496e28	−	1.66143e29i	0.848740	−	1.78610i
$575$	−2.64772e28			−0.279486
$576$		0			0
$577$	−9.58548e28			−0.975591			−0.487796	−	0.872958i	$-0.662199\pi$
$577$	−9.58548e28			−0.975591			−0.487796	+	0.872958i	$0.662199\pi$
$578$	7.05735e28	−	1.48516e29i	0.705342	−	1.48433i
$579$		0			0
$580$	3.72352e28	+	4.57092e28i	0.358889	+	0.440565i
$581$	−8.14132e28			−0.770629
$582$		0			0
$583$		−	3.32620e28i		−	0.303689i
$584$	−1.57855e29	+	3.86268e28i	−1.41554	+	0.346381i
$585$		0			0
$586$	9.15106e27	−	1.92576e28i	0.0791674	−	0.166601i
$587$		−	3.41368e28i		−	0.290083i	−0.989426	−	0.145042i	$-0.953668\pi$
$587$		−	3.41368e28i		−	0.290083i	0.989426	−	0.145042i	$-0.0463316\pi$
$588$		0			0
$589$		−	9.95617e28i		−	0.816360i
$590$	7.13868e28	+	3.39224e28i	0.575005	+	0.273238i
$591$		0			0
$592$	4.25823e28	+	8.79253e27i	0.331018	+	0.0683496i
$593$		−	2.84826e28i		−	0.217523i	−0.994068	−	0.108761i	$-0.965312\pi$
$593$		−	2.84826e28i		−	0.217523i	0.994068	−	0.108761i	$-0.0346885\pi$
$594$		0			0
$595$	−1.05822e29			−0.780099
$596$	−7.62628e28	−	9.36186e28i	−0.552366	−	0.678073i
$597$		0			0
$598$	−5.36012e28	−	2.54708e28i	−0.374811	−	0.178107i
$599$	−7.13826e28			−0.490468			−0.245234	−	0.969464i	$-0.578865\pi$
$599$	−7.13826e28			−0.490468			−0.245234	+	0.969464i	$0.578865\pi$
$600$		0			0
$601$	8.80749e28			0.584346			0.292173	−	0.956365i	$-0.405622\pi$
$601$	8.80749e28			0.584346			0.292173	+	0.956365i	$0.405622\pi$
$602$	8.88144e28	+	4.22038e28i	0.579056	+	0.275162i
$603$		0			0
$604$	2.31271e29	−	1.88396e29i	1.45624	−	1.18627i
$605$	−2.24958e28			−0.139210
$606$		0			0
$607$			2.54245e29i			1.51975i	0.650072	+	0.759873i	$0.274739\pi$
$607$			2.54245e29i			1.51975i	−0.650072	+	0.759873i	$0.725261\pi$
$608$	−1.35462e29	−	1.02387e29i	−0.795849	−	0.601532i
$609$		0			0
$610$	−1.17130e29	−	5.56591e28i	−0.664820	−	0.315917i
$611$			2.40429e29i			1.34139i
$612$		0			0
$613$		−	2.82720e29i		−	1.52413i	−0.647502	−	0.762063i	$-0.724186\pi$
$613$		−	2.82720e29i		−	1.52413i	0.647502	−	0.762063i	$-0.275814\pi$
$614$	7.94085e28	−	1.67109e29i	0.420823	−	0.885586i
$615$		0			0
$616$	1.77599e29	−	4.34582e28i	0.909585	−	0.222574i
$617$			2.83868e29i			1.42930i	0.699484	+	0.714648i	$0.253413\pi$
$617$			2.83868e29i			1.42930i	−0.699484	+	0.714648i	$0.746587\pi$
$618$		0			0
$619$	2.13868e29			1.04087			0.520433	−	0.853903i	$-0.325771\pi$
$619$	2.13868e29			1.04087			0.520433	+	0.853903i	$0.325771\pi$
$620$	5.55031e28	−	4.52135e28i	0.265585	−	0.216349i
$621$		0			0
$622$	6.84676e28	−	1.44084e29i	0.316728	−	0.666527i
$623$	3.70998e29			1.68751
$624$		0			0
$625$	1.14827e29			0.505015
$626$	−3.74175e28	+	7.87420e28i	−0.161825	+	0.340546i
$627$		0			0
$628$	−5.39366e28	+	4.39374e28i	−0.225584	+	0.183763i
$629$	1.33607e29			0.549539
$630$		0			0
$631$		−	4.45573e29i		−	1.77260i	−0.463113	−	0.886299i	$-0.653268\pi$
$631$		−	4.45573e29i		−	1.77260i	0.463113	−	0.886299i	$-0.346732\pi$
$632$	3.09742e28	+	1.26581e29i	0.121191	+	0.495268i
$633$		0			0
$634$	2.41400e28	−	5.08005e28i	0.0913691	−	0.192279i
$635$		−	1.17058e29i		−	0.435790i
$636$		0			0
$637$		−	1.06686e29i		−	0.384277i
$638$	−2.82710e29	−	1.34341e29i	−1.00167	−	0.475985i
$639$		0			0
$640$	−4.43850e27	−	1.22013e29i	−0.0152176	−	0.418328i
$641$		−	8.98916e28i		−	0.303186i	−0.988443	−	0.151593i	$-0.951560\pi$
$641$		−	8.98916e28i		−	0.303186i	0.988443	−	0.151593i	$-0.0484404\pi$
$642$		0			0
$643$	1.88791e28			0.0616262			0.0308131	−	0.999525i	$-0.490190\pi$
$643$	1.88791e28			0.0616262			0.0308131	+	0.999525i	$0.490190\pi$
$644$	−9.37710e28	+	7.63870e28i	−0.301139	+	0.245311i
$645$		0			0
$646$	−4.71270e29	−	2.23944e29i	−1.46497	−	0.696141i
$647$	−5.73966e29			−1.75546			−0.877731	−	0.479155i	$-0.840943\pi$
$647$	−5.73966e29			−1.75546			−0.877731	+	0.479155i	$0.840943\pi$
$648$		0			0
$649$	−4.19619e29			−1.24247
$650$	3.13118e29	+	1.48791e29i	0.912259	+	0.433498i
$651$		0			0
$652$	−3.79797e29	−	4.66230e29i	−1.07140	−	1.31523i
$653$	4.98246e29			1.38311			0.691553	−	0.722326i	$-0.256927\pi$
$653$	4.98246e29			1.38311			0.691553	+	0.722326i	$0.256927\pi$
$654$		0			0
$655$		−	1.09403e29i		−	0.294101i
$656$	6.38671e29	+	1.31875e29i	1.68961	+	0.348877i
$657$		0			0
$658$	4.42570e29	+	2.10305e29i	1.13399	+	0.538863i
$659$		−	4.47292e29i		−	1.12796i	−0.825788	−	0.563981i	$-0.809269\pi$
$659$		−	4.47292e29i		−	1.12796i	0.825788	−	0.563981i	$-0.190731\pi$
$660$		0			0
$661$		−	1.76146e29i		−	0.430286i	−0.976583	−	0.215143i	$-0.930978\pi$
$661$		−	1.76146e29i		−	0.430286i	0.976583	−	0.215143i	$-0.0690218\pi$
$662$	7.60573e28	−	1.60056e29i	0.182866	−	0.384825i
$663$		0			0
$664$	−6.86041e28	−	2.80362e29i	−0.159803	−	0.653061i
$665$			2.08763e29i			0.478660i
$666$		0			0
$667$	2.07051e29			0.459997
$668$	1.70779e29	+	2.09644e29i	0.373492	+	0.458491i
$669$		0			0
$670$	−9.61317e28	+	2.02301e29i	−0.203742	+	0.428758i
$671$	6.88500e29			1.43654
$672$		0			0
$673$	1.19960e29			0.242594			0.121297	−	0.992616i	$-0.461295\pi$
$673$	1.19960e29			0.242594			0.121297	+	0.992616i	$0.461295\pi$
$674$	−9.61821e28	+	2.02407e29i	−0.191499	+	0.402992i
$675$		0			0
$676$	1.63510e29	+	2.00721e29i	0.315575	+	0.387394i
$677$	−1.71924e29			−0.326706			−0.163353	−	0.986568i	$-0.552231\pi$
$677$	−1.71924e29			−0.326706			−0.163353	+	0.986568i	$0.552231\pi$
$678$		0			0
$679$			3.96905e29i			0.731230i
$680$	−8.91728e28	−	3.64419e29i	−0.161767	−	0.661086i
$681$		0			0
$682$	−1.63126e29	+	3.43285e29i	−0.286938	+	0.603836i
$683$			1.02511e29i			0.177563i	0.996051	+	0.0887814i	$0.0282973\pi$
$683$			1.02511e29i			0.177563i	−0.996051	+	0.0887814i	$0.971703\pi$
$684$		0			0
$685$		−	6.96979e28i		−	0.117076i
$686$	4.29447e29	+	2.04069e29i	0.710405	+	0.337578i
$687$		0			0
$688$	−7.04960e28	+	3.41413e29i	−0.113106	+	0.547774i
$689$		−	2.88085e29i		−	0.455217i
$690$		0			0
$691$	−9.64568e29			−1.47847			−0.739236	−	0.673446i	$-0.764813\pi$
$691$	−9.64568e29			−1.47847			−0.739236	+	0.673446i	$0.764813\pi$
$692$	3.49572e29	+	4.29128e29i	0.527744	+	0.647847i
$693$		0			0
$694$	6.60733e29	+	3.13975e29i	0.967724	+	0.459854i
$695$	3.17416e28			0.0457919
$696$		0			0
$697$	2.00391e30			2.80501
$698$	−5.50259e29	−	2.61479e29i	−0.758727	−	0.360541i
$699$		0			0
$700$	5.47776e29	−	4.46225e29i	0.732948	−	0.597068i
$701$	−1.27758e29			−0.168403			−0.0842015	−	0.996449i	$-0.526834\pi$
$701$	−1.27758e29			−0.168403			−0.0842015	+	0.996449i	$0.526834\pi$
$702$		0			0
$703$		−	2.63577e29i		−	0.337191i
$704$	2.99313e29	+	5.74975e29i	0.377236	+	0.724663i
$705$		0			0
$706$	−3.27931e29	−	1.55830e29i	−0.401174	−	0.190635i
$707$		−	1.27290e30i		−	1.53424i
$708$		0			0
$709$			7.70376e29i			0.901399i	0.892676	+	0.450700i	$0.148825\pi$
$709$			7.70376e29i			0.901399i	−0.892676	+	0.450700i	$0.851175\pi$
$710$	−1.63951e29	+	3.45022e29i	−0.189018	+	0.397772i
$711$		0			0
$712$	3.12627e29	+	1.27760e30i	0.349934	+	1.43006i
$713$		−	2.51414e29i		−	0.277300i
$714$		0			0
$715$	3.91040e29			0.418801
$716$	−4.38300e28	+	3.57044e28i	−0.0462578	+	0.0376821i
$717$		0			0
$718$	−5.58160e29	+	1.17460e30i	−0.572074	+	1.20388i
$719$	−2.43997e29			−0.246451			−0.123225	−	0.992379i	$-0.539324\pi$
$719$	−2.43997e29			−0.246451			−0.123225	+	0.992379i	$0.539324\pi$
$720$		0			0
$721$	7.00759e29			0.687461
$722$	2.12396e27	−	4.46969e27i	0.00205355	−	0.00432152i
$723$		0			0
$724$	−2.59985e29	+	2.11787e29i	−0.244171	+	0.198904i
$725$	−1.20951e30			−1.11960
$726$		0			0
$727$		−	7.46599e29i		−	0.671392i	−0.941970	−	0.335696i	$-0.891029\pi$
$727$		−	7.46599e29i		−	0.671392i	0.941970	−	0.335696i	$-0.108971\pi$
$728$	1.53820e30	−	3.76395e29i	1.36343	−	0.333629i
$729$		0			0
$730$	−3.04020e29	+	6.39785e29i	−0.261826	+	0.550991i
$731$			1.07123e30i			0.909386i
$732$		0			0
$733$			7.15780e29i			0.590456i	0.955427	+	0.295228i	$0.0953957\pi$
$733$			7.15780e29i			0.590456i	−0.955427	+	0.295228i	$0.904604\pi$
$734$	1.53328e30	+	7.28599e29i	1.24684	+	0.592489i
$735$		0			0
$736$	−3.42070e29	−	2.58549e29i	−0.270333	−	0.204327i
$737$		−	1.18914e30i		−	0.926459i
$738$		0			0
$739$	−2.47378e30			−1.87324			−0.936622	−	0.350342i	$-0.886065\pi$
$739$	−2.47378e30			−1.87324			−0.936622	+	0.350342i	$0.886065\pi$
$740$	1.46937e29	−	1.19697e29i	0.109698	−	0.0893612i
$741$		0			0
$742$	−5.30293e29	−	2.51991e29i	−0.384835	−	0.182870i
$743$	−2.04663e30			−1.46439			−0.732194	−	0.681096i	$-0.761504\pi$
$743$	−2.04663e30			−1.46439			−0.732194	+	0.681096i	$0.761504\pi$
$744$		0			0
$745$	−5.26314e29			−0.366104
$746$	−1.24522e30	−	5.91717e29i	−0.854059	−	0.405842i
$747$		0			0
$748$	1.25800e30	+	1.54430e30i	0.838910	+	1.02983i
$749$	−1.57006e30			−1.03242
$750$		0			0
$751$		−	6.93466e29i		−	0.443410i	−0.975114	−	0.221705i	$-0.928838\pi$
$751$		−	6.93466e29i		−	0.443410i	0.975114	−	0.221705i	$-0.0711623\pi$
$752$	−3.51288e29	+	1.70129e30i	−0.221501	+	1.07273i
$753$		0			0
$754$	−2.44857e30	−	1.16354e30i	−1.50146	−	0.713481i
$755$		−	1.30018e30i		−	0.786249i
$756$		0			0
$757$		−	2.65899e30i		−	1.56390i	−0.623339	−	0.781952i	$-0.714224\pi$
$757$		−	2.65899e30i		−	1.56390i	0.623339	−	0.781952i	$-0.285776\pi$
$758$	4.32735e29	−	9.10655e29i	0.251013	−	0.528235i
$759$		0			0
$760$	−7.18916e29	+	1.75918e29i	−0.405635	+	0.0992582i
$761$			1.97349e30i			1.09824i	0.835745	+	0.549118i	$0.185036\pi$
$761$			1.97349e30i			1.09824i	−0.835745	+	0.549118i	$0.814964\pi$
$762$		0			0
$763$	2.28429e30			1.23664
$764$	−2.69337e29	−	3.30633e29i	−0.143819	−	0.176549i
$765$		0			0
$766$	−1.44821e30	+	3.04764e30i	−0.752368	+	1.58329i
$767$	−3.63435e30			−1.86241
$768$		0			0
$769$	−1.82104e30			−0.908014			−0.454007	−	0.890998i	$-0.650006\pi$
$769$	−1.82104e30			−0.908014			−0.454007	+	0.890998i	$0.650006\pi$
$770$	3.42047e29	−	7.19809e29i	0.168241	−	0.354050i
$771$		0			0
$772$	−3.62402e29	−	4.44877e29i	−0.173464	−	0.212941i
$773$	6.47814e29			0.305890			0.152945	−	0.988235i	$-0.451124\pi$
$773$	6.47814e29			0.305890			0.152945	+	0.988235i	$0.451124\pi$
$774$		0			0
$775$			1.46867e30i			0.674926i
$776$	−1.36682e30	+	3.34458e29i	−0.619672	+	0.151633i
$777$		0			0
$778$	−7.88530e28	+	1.65939e29i	−0.0347962	+	0.0732257i
$779$		−	3.95326e30i		−	1.72112i
$780$		0			0
$781$		−	2.02807e30i		−	0.859503i
$782$	−1.19006e30	−	5.65505e29i	−0.497619	−	0.236464i
$783$		0			0
$784$	1.55878e29	−	7.54919e29i	0.0634551	−	0.307313i
$785$			3.03226e29i			0.121797i
$786$		0			0
$787$	1.62777e30			0.636587			0.318293	−	0.947992i	$-0.396890\pi$
$787$	1.62777e30			0.636587			0.318293	+	0.947992i	$0.396890\pi$
$788$	1.63244e30	+	2.00394e30i	0.629957	+	0.773321i
$789$		0			0
$790$	5.13034e29	+	2.43789e29i	0.192780	+	0.0916073i
$791$	−5.14294e30			−1.90703
$792$		0			0
$793$	5.96315e30			2.15331
$794$	1.18483e30	+	5.63019e29i	0.422221	+	0.200636i
$795$		0			0
$796$	−3.35197e30	+	2.73056e30i	−1.16336	+	0.947686i
$797$	−2.71983e28			−0.00931600			−0.00465800	−	0.999989i	$-0.501483\pi$
$797$	−2.71983e28			−0.00931600			−0.00465800	+	0.999989i	$0.501483\pi$
$798$		0			0
$799$			5.33801e30i			1.78089i
$800$	1.99825e30	+	1.51035e30i	0.657968	+	0.497316i
$801$		0			0
$802$	−2.46166e30	−	1.16976e30i	−0.789582	−	0.375203i
$803$		−	3.76072e30i		−	1.19058i
$804$		0			0
$805$			5.27171e29i			0.162590i
$806$	−1.41285e30	+	2.97322e30i	−0.430108	+	0.905126i
$807$		0			0
$808$	4.38349e30	−	1.07263e30i	1.30017	−	0.318150i
$809$		−	2.33462e30i		−	0.683530i	−0.939786	−	0.341765i	$-0.888975\pi$
$809$		−	2.33462e30i		−	0.683530i	0.939786	−	0.341765i	$-0.111025\pi$
$810$		0			0
$811$	−4.29570e30			−1.22550			−0.612752	−	0.790275i	$-0.709938\pi$
$811$	−4.29570e30			−1.22550			−0.612752	+	0.790275i	$0.709938\pi$
$812$	−4.28358e30	+	3.48946e30i	−1.20634	+	0.982697i
$813$		0			0
$814$	−4.31855e29	+	9.08803e29i	−0.118517	+	0.249410i
$815$	−2.62110e30			−0.710115
$816$		0			0
$817$	2.11328e30			0.557989
$818$	−1.24045e30	+	2.61043e30i	−0.323348	+	0.680459i
$819$		0			0
$820$	2.20384e30	−	1.79527e30i	0.559931	−	0.456126i
$821$	−4.13604e30			−1.03748			−0.518742	−	0.854931i	$-0.673600\pi$
$821$	−4.13604e30			−1.03748			−0.518742	+	0.854931i	$0.673600\pi$
$822$		0			0
$823$			1.55343e30i			0.379835i	0.981800	+	0.189917i	$0.0608220\pi$
$823$			1.55343e30i			0.379835i	−0.981800	+	0.189917i	$0.939178\pi$
$824$	5.90505e29	+	2.41319e30i	0.142557	+	0.582581i
$825$		0			0
$826$	−3.17900e30	+	6.68994e30i	−0.748170	+	1.57446i
$827$			1.45005e30i			0.336958i	0.985705	+	0.168479i	$0.0538856\pi$
$827$			1.45005e30i			0.336958i	−0.985705	+	0.168479i	$0.946114\pi$
$828$		0			0
$829$		−	4.05819e30i		−	0.919412i	−0.888071	−	0.459706i	$-0.847955\pi$
$829$		−	4.05819e30i		−	0.919412i	0.888071	−	0.459706i	$-0.152045\pi$
$830$	−1.13631e30	−	5.39962e29i	−0.254200	−	0.120794i
$831$		0			0
$832$	2.59237e30	+	4.97990e30i	0.565461	+	1.08624i
$833$		−	2.36865e30i		−	0.510186i
$834$		0			0
$835$	1.17860e30			0.247547
$836$	3.04655e30	−	2.48175e30i	0.631891	−	0.514746i
$837$		0			0
$838$	−8.17515e30	−	3.88476e30i	−1.65361	−	0.785782i
$839$	4.25565e30			0.850091			0.425046	−	0.905172i	$-0.360258\pi$
$839$	4.25565e30			0.850091			0.425046	+	0.905172i	$0.360258\pi$
$840$		0			0
$841$	4.32550e30			0.842710
$842$	5.17185e30	+	2.45762e30i	0.995106	+	0.472866i
$843$		0			0
$844$	−4.43710e29	−	5.44689e29i	−0.0832729	−	0.102224i
$845$	1.12843e30			0.209161
$846$		0			0
$847$		−	2.10817e30i		−	0.381180i
$848$	4.20917e29	−	2.03851e30i	0.0751693	−	0.364045i
$849$		0			0
$850$	6.95187e30	+	3.30347e30i	1.21116	+	0.575534i
$851$		−	6.65586e29i		−	0.114537i
$852$		0			0
$853$		−	5.82384e30i		−	0.977788i	−0.872343	−	0.488894i	$-0.837400\pi$
$853$		−	5.82384e30i		−	0.977788i	0.872343	−	0.488894i	$-0.162600\pi$
$854$	5.21603e30	−	1.09767e31i	0.865032	−	1.82039i
$855$		0			0
$856$	−1.32303e30	−	5.40678e30i	−0.214090	−	0.874912i
$857$			4.29932e30i			0.687229i	0.939111	+	0.343615i	$0.111651\pi$
$857$			4.29932e30i			0.687229i	−0.939111	+	0.343615i	$0.888349\pi$
$858$		0			0
$859$	−9.79229e30			−1.52741			−0.763705	−	0.645565i	$-0.776622\pi$
$859$	−9.79229e30			−1.52741			−0.763705	+	0.645565i	$0.776622\pi$
$860$	9.59694e29	+	1.17810e30i	0.147876	+	0.181530i
$861$		0			0
$862$	−2.71824e30	+	5.72030e30i	−0.408753	+	0.860186i
$863$	2.46176e30			0.365706			0.182853	−	0.983140i	$-0.441467\pi$
$863$	2.46176e30			0.365706			0.182853	+	0.983140i	$0.441467\pi$
$864$		0			0
$865$	2.41251e30			0.349784
$866$	5.80578e30	−	1.22178e31i	0.831616	−	1.75007i
$867$		0			0
$868$	4.23713e30	+	5.20141e30i	0.592399	+	0.727217i
$869$	−3.01566e30			−0.416558
$870$		0			0
$871$		−	1.02993e31i		−	1.38872i
$872$	1.92489e30	+	7.86637e30i	0.256438	+	1.04798i
$873$		0			0
$874$	−1.11561e30	+	2.34771e30i	−0.145092	+	0.305333i
$875$		−	6.81336e30i		−	0.875541i
$876$		0			0
$877$			3.61432e30i			0.453451i	0.973959	+	0.226726i	$0.0728021\pi$
$877$			3.61432e30i			0.453451i	−0.973959	+	0.226726i	$0.927198\pi$
$878$	−7.26047e30	−	3.45011e30i	−0.900062	−	0.427702i
$879$		0			0
$880$	2.76703e30	+	5.71345e29i	0.334923	+	0.0691561i
$881$			1.37063e31i			1.63936i	0.572824	+	0.819679i	$0.305848\pi$
$881$			1.37063e31i			1.63936i	−0.572824	+	0.819679i	$0.694152\pi$
$882$		0			0
$883$	−6.28213e30			−0.733701			−0.366851	−	0.930280i	$-0.619564\pi$
$883$	−6.28213e30			−0.733701			−0.366851	+	0.930280i	$0.619564\pi$
$884$	1.08957e31	+	1.33753e31i	1.25749	+	1.54367i
$885$		0			0
$886$	4.77564e30	+	2.26934e30i	0.538242	+	0.255768i
$887$	1.57890e31			1.75856			0.879280	−	0.476305i	$-0.158024\pi$
$887$	1.57890e31			1.75856			0.879280	+	0.476305i	$0.158024\pi$
$888$		0			0
$889$	1.09700e31			1.19326
$890$	5.17812e30	+	2.46060e30i	0.556643	+	0.264512i
$891$		0			0
$892$	1.00807e31	−	8.21188e30i	1.05843	−	0.862207i
$893$	1.05307e31			1.09274
$894$		0			0
$895$			2.46408e29i			0.0249754i
$896$	1.14343e31	−	4.15949e29i	1.14545	−	0.0416683i
$897$		0			0
$898$	−1.07038e31	−	5.08635e30i	−1.04746	−	0.497743i
$899$		−	1.14849e31i		−	1.11084i
$900$		0			0
$901$		−	6.39607e30i		−	0.604370i
$902$	−6.47719e30	+	1.36307e31i	−0.604948	+	1.27306i
$903$		0			0
$904$	−4.33377e30	−	1.77107e31i	−0.395456	−	1.61609i
$905$			1.46161e30i			0.131832i
$906$		0			0
$907$	−9.40300e30			−0.828686			−0.414343	−	0.910121i	$-0.635989\pi$
$907$	−9.40300e30			−0.828686			−0.414343	+	0.910121i	$0.635989\pi$
$908$	9.79464e30	−	7.97883e30i	0.853271	−	0.695085i
$909$		0			0
$910$	2.96249e30	−	6.23432e30i	0.252187	−	0.530706i
$911$	−1.96936e31			−1.65723			−0.828616	−	0.559818i	$-0.810871\pi$
$911$	−1.96936e31			−1.65723			−0.828616	+	0.559818i	$0.810871\pi$
$912$		0			0
$913$	6.67931e30			0.549273
$914$	7.75506e29	−	1.63199e30i	0.0630449	−	0.132673i
$915$		0			0
$916$	1.43502e31	−	1.16898e31i	1.14013	−	0.928765i
$917$	1.02526e31			0.805296
$918$		0			0
$919$			1.40760e31i			1.08060i	0.841472	+	0.540301i	$0.181689\pi$
$919$			1.40760e31i			1.08060i	−0.841472	+	0.540301i	$0.818311\pi$
$920$	−1.81541e30	+	4.44229e29i	−0.137785	+	0.0337159i
$921$		0			0
$922$	−2.39768e30	+	5.04571e30i	−0.177876	+	0.374324i
$923$		−	1.75653e31i		−	1.28836i
$924$		0			0
$925$			3.88811e30i			0.278773i
$926$	−9.50854e30	−	4.51838e30i	−0.674060	−	0.320307i
$927$		0			0
$928$	−1.56262e31	−	1.18109e31i	−1.08293	−	0.818518i
$929$			1.68648e31i			1.15562i	0.816171	+	0.577811i	$0.196093\pi$
$929$			1.68648e31i			1.15562i	−0.816171	+	0.577811i	$0.803907\pi$
$930$		0			0
$931$	−4.67281e30			−0.313045
$932$	−4.93863e30	+	4.02306e30i	−0.327144	+	0.266495i
$933$		0			0
$934$	−1.05049e31	−	4.99183e30i	−0.680376	−	0.323309i
$935$	8.68189e30			0.556023
$936$		0			0
$937$	1.90911e31			1.19554			0.597771	−	0.801667i	$-0.296053\pi$
$937$	1.90911e31			1.19554			0.597771	+	0.801667i	$0.296053\pi$
$938$	−1.89584e31	−	9.00887e30i	−1.17401	−	0.557880i
$939$		0			0
$940$	4.78224e30	+	5.87058e30i	0.289594	+	0.355499i
$941$	2.69612e31			1.61454			0.807268	−	0.590185i	$-0.200945\pi$
$941$	2.69612e31			1.61454			0.807268	+	0.590185i	$0.200945\pi$
$942$		0			0
$943$		−	9.98281e30i		−	0.584628i
$944$	−2.57169e31	−	5.31011e30i	−1.48940	−	0.307537i
$945$		0			0
$946$	−7.28652e30	−	3.46249e30i	−0.412727	−	0.196124i
$947$			2.07970e31i			1.16500i	0.812831	+	0.582499i	$0.197925\pi$
$947$			2.07970e31i			1.16500i	−0.812831	+	0.582499i	$0.802075\pi$
$948$		0			0
$949$		−	3.25719e31i		−	1.78463i
$950$	6.51698e30	−	1.37144e31i	0.353142	−	0.743156i
$951$		0			0
$952$	3.41511e31	−	8.35673e30i	1.81016	−	0.442944i
$953$			1.56863e31i			0.822328i	0.911561	+	0.411164i	$0.134878\pi$
$953$			1.56863e31i			0.822328i	−0.911561	+	0.411164i	$0.865122\pi$
$954$		0			0
$955$	−1.85878e30			−0.0953221
$956$	2.52975e30	+	3.10547e30i	0.128313	+	0.157514i
$957$		0			0
$958$	−6.85879e30	+	1.44337e31i	−0.340337	+	0.716211i
$959$	6.53166e30			0.320574
$960$		0			0
$961$	6.87975e30			0.330352
$962$	−3.74033e30	+	7.87120e30i	−0.177653	+	0.373855i
$963$		0			0
$964$	−9.46176e30	−	1.16150e31i	−0.439706	−	0.539774i
$965$	−2.50105e30			−0.114970
$966$		0			0
$967$			4.13834e31i			1.86144i	0.365737	+	0.930718i	$0.380817\pi$
$967$			4.13834e31i			1.86144i	−0.365737	+	0.930718i	$0.619183\pi$
$968$	7.25989e30	−	1.77648e30i	0.323027	−	0.0790442i
$969$		0			0
$970$	−2.63242e30	+	5.53971e30i	−0.114618	+	0.241203i
$971$			1.59891e30i			0.0688689i	0.999407	+	0.0344345i	$0.0109630\pi$
$971$			1.59891e30i			0.0688689i	−0.999407	+	0.0344345i	$0.989037\pi$
$972$		0			0
$973$			2.97463e30i			0.125386i
$974$	6.57994e30	+	3.12673e30i	0.274380	+	0.130383i
$975$		0			0
$976$	4.21956e31	+	8.71269e30i	1.72204	+	0.355573i
$977$		−	3.05439e29i		−	0.0123319i	−0.999981	−	0.00616597i	$-0.998037\pi$
$977$		−	3.05439e29i		−	0.0123319i	0.999981	−	0.00616597i	$-0.00196270\pi$
$978$		0			0
$979$	−3.04375e31			−1.20279
$980$	−2.12204e30	−	2.60497e30i	−0.0829621	−	0.101842i
$981$		0			0
$982$	−2.98748e31	−	1.41962e31i	−1.14323	−	0.543253i
$983$	−3.73513e31			−1.41414			−0.707072	−	0.707142i	$-0.749984\pi$
$983$	−3.73513e31			−1.41414			−0.707072	+	0.707142i	$0.749984\pi$
$984$		0			0
$985$	1.12660e31			0.417530
$986$	−5.43633e31	−	2.58330e31i	−1.99342	−	0.947255i
$987$		0			0
$988$	2.63864e31	−	2.14946e31i	0.947178	−	0.771583i
$989$	5.33648e30			0.189537
$990$		0			0
$991$		−	7.12374e30i		−	0.247705i	−0.992301	−	0.123853i	$-0.960475\pi$
$991$		−	7.12374e30i		−	0.247705i	0.992301	−	0.123853i	$-0.0395250\pi$
$992$	−1.43415e31	+	1.89744e31i	−0.493427	+	0.652823i
$993$		0			0
$994$	−3.23333e31	−	1.53645e31i	−1.08916	−	0.517561i
$995$			1.88445e31i			0.628118i
$996$		0			0
$997$		−	7.44835e30i		−	0.243086i	−0.992586	−	0.121543i	$-0.961216\pi$
$997$		−	7.44835e30i		−	0.243086i	0.992586	−	0.121543i	$-0.0387843\pi$
$998$	1.72589e31	−	3.63198e31i	0.557367	−	1.17293i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.22.f.a.35.32	yes	84
3.2	odd	2	inner	72.22.f.a.35.53	yes	84
8.3	odd	2	inner	72.22.f.a.35.54	yes	84
24.11	even	2	inner	72.22.f.a.35.31	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.22.f.a.35.31	✓	84	24.11	even	2	inner
72.22.f.a.35.32	yes	84	1.1	even	1	trivial
72.22.f.a.35.53	yes	84	3.2	odd	2	inner
72.22.f.a.35.54	yes	84	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	72.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-621.545 + 1307.99i) q^{2} +(-1.32452e6 - 1.62595e6i) q^{4} -9.14091e6 q^{5} -8.56630e8i q^{7} +(2.94997e9 - 7.21852e8i) q^{8} +O(q^{10})\)	\(q+(-621.545 + 1307.99i) q^{2} +(-1.32452e6 - 1.62595e6i) q^{4} -9.14091e6 q^{5} -8.56630e8i q^{7} +(2.94997e9 - 7.21852e8i) q^{8} +(5.68149e9 - 1.19562e10i) q^{10} +7.02798e10i q^{11} +6.08698e11i q^{13} +(1.12046e12 + 5.32434e11i) q^{14} +(-8.89362e11 + 4.30719e12i) q^{16} +1.35143e13i q^{17} +2.66607e13 q^{19} +(1.21073e13 + 1.48626e13i) q^{20} +(-9.19251e13 - 4.36820e13i) q^{22} +6.73238e13 q^{23} -3.93281e14 q^{25} +(-7.96170e14 - 3.78333e14i) q^{26} +(-1.39284e15 + 1.13462e15i) q^{28} +3.07544e15 q^{29} -3.73440e15i q^{31} +(-5.08097e15 - 3.84038e15i) q^{32} +(-1.76766e16 - 8.39977e15i) q^{34} +7.83038e15i q^{35} -9.88634e15i q^{37} +(-1.65708e16 + 3.48719e16i) q^{38} +(-2.69654e16 + 6.59839e15i) q^{40} -1.48280e17i q^{41} +7.92658e16 q^{43} +(1.14271e17 - 9.30866e16i) q^{44} +(-4.18448e16 + 8.80588e16i) q^{46} +3.94989e17 q^{47} -1.75270e17 q^{49} +(2.44442e17 - 5.14407e17i) q^{50} +(9.89711e17 - 8.06230e17i) q^{52} -4.73280e17 q^{53} -6.42421e17i q^{55} +(-6.18361e17 - 2.52703e18i) q^{56} +(-1.91152e18 + 4.02264e18i) q^{58} +5.97069e18i q^{59} -9.79657e18i q^{61} +(4.88456e18 + 2.32110e18i) q^{62} +(8.18123e18 - 4.25888e18i) q^{64} -5.56405e18i q^{65} -1.69202e19 q^{67} +(2.19736e19 - 1.79000e19i) q^{68} +(-1.02421e19 - 4.86693e18i) q^{70} -2.88571e19 q^{71} -5.35107e19 q^{73} +(1.29312e19 + 6.14480e18i) q^{74} +(-3.53125e19 - 4.33489e19i) q^{76} +6.02038e19 q^{77} +4.29094e19i q^{79} +(8.12958e18 - 3.93716e19i) q^{80} +(1.93949e20 + 9.21629e19i) q^{82} -9.50389e19i q^{83} -1.23533e20i q^{85} +(-4.92673e19 + 1.03679e20i) q^{86} +(5.07316e19 + 2.07323e20i) q^{88} +4.33090e20i q^{89} +5.21429e20 q^{91} +(-8.91715e19 - 1.09465e20i) q^{92} +(-2.45503e20 + 5.16641e20i) q^{94} -2.43703e20 q^{95} -4.63333e20 q^{97} +(1.08938e20 - 2.29251e20i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2424084 q^{4}+O(q^{10}) \) 84 * q + 2424084 * q^4	\( 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 80\!\cdots\!00 q^{25}+ \cdots - 16\!\cdots\!12 q^{97}+O(q^{100}) \) 84 * q + 2424084 * q^4 + 17057181612 * q^10 - 4099708064904 * q^16 + 92015527242864 * q^19 - 236011369239528 * q^22 + 8010864257812500 * q^25 - 3042238700022024 * q^28 + 74414158327329924 * q^34 + 75018327243317184 * q^40 + 707788847336454432 * q^43 - 162639476543943288 * q^46 - 5423745715136249124 * q^49 - 70566629446202808 * q^52 - 14491558288019904108 * q^58 - 28749968749508108064 * q^64 - 13653811098426494352 * q^67 + 140256684870035374392 * q^70 - 71781309378863778384 * q^73 + 376055720386305092400 * q^76 - 368362114062816367548 * q^82 - 592572120184082106720 * q^88 - 522206955652189957200 * q^91 - 528772551789914644488 * q^94 - 1686050813935078492512 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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