LMFDB - Embedded newform 72.22.f.a.35.41

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			35.41
Character	$\chi$	$=$	72.35
Dual form			72.22.f.a.35.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-145.330 - 1440.84i) q^{2} +(-2.05491e6 + 418795. i) q^{4} +1.63057e7 q^{5} -1.11046e9i q^{7} +(9.02058e8 + 2.89994e9i) q^{8} +O(q^{10})$	\(q+(-145.330 - 1440.84i) q^{2} +(-2.05491e6 + 418795. i) q^{4} +1.63057e7 q^{5} -1.11046e9i q^{7} +(9.02058e8 + 2.89994e9i) q^{8} +(-2.36971e9 - 2.34940e10i) q^{10} -1.11865e11i q^{11} +1.58848e11i q^{13} +(-1.60000e12 + 1.61383e11i) q^{14} +(4.04727e12 - 1.72117e12i) q^{16} +3.55129e12i q^{17} +3.97170e12 q^{19} +(-3.35068e13 + 6.82876e12i) q^{20} +(-1.61180e14 + 1.62574e13i) q^{22} -9.68326e13 q^{23} -2.10961e14 q^{25} +(2.28875e14 - 2.30853e13i) q^{26} +(4.65054e14 + 2.28189e15i) q^{28} +4.54212e14 q^{29} +7.94527e15i q^{31} +(-3.06813e15 - 5.58134e15i) q^{32} +(5.11686e15 - 5.16109e14i) q^{34} -1.81068e16i q^{35} +1.51812e15i q^{37} +(-5.77207e14 - 5.72261e15i) q^{38} +(1.47087e16 + 4.72856e16i) q^{40} -3.00638e16i q^{41} -1.85924e17 q^{43} +(4.68487e16 + 2.29873e17i) q^{44} +(1.40727e16 + 1.39521e17i) q^{46} +2.24282e17 q^{47} -6.74570e17 q^{49} +(3.06589e16 + 3.03961e17i) q^{50} +(-6.65246e16 - 3.26418e17i) q^{52} -3.35928e17 q^{53} -1.82404e18i q^{55} +(3.22026e18 - 1.00170e18i) q^{56} +(-6.60105e16 - 6.54448e17i) q^{58} -4.52223e18i q^{59} -4.11219e18i q^{61} +(1.14479e19 - 1.15469e18i) q^{62} +(-7.59595e18 + 5.23183e18i) q^{64} +2.59013e18i q^{65} +6.73554e18 q^{67} +(-1.48727e18 - 7.29759e18i) q^{68} +(-2.60891e19 + 2.63146e18i) q^{70} -3.53935e19 q^{71} -2.43223e19 q^{73} +(2.18738e18 - 2.20629e17i) q^{74} +(-8.16150e18 + 1.66333e18i) q^{76} -1.24222e20 q^{77} -6.60458e19i q^{79} +(6.59936e19 - 2.80650e19i) q^{80} +(-4.33173e19 + 4.36917e18i) q^{82} -1.15265e20i q^{83} +5.79064e19i q^{85} +(2.70203e19 + 2.67888e20i) q^{86} +(3.24403e20 - 1.00909e20i) q^{88} +3.32918e20i q^{89} +1.76394e20 q^{91} +(1.98982e20 - 4.05530e19i) q^{92} +(-3.25949e19 - 3.23156e20i) q^{94} +6.47615e19 q^{95} -7.05599e20 q^{97} +(9.80351e19 + 9.71950e20i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−145.330	−	1440.84i	−0.100355	−	0.994952i
$2$	−145.330	−	1440.84i	−0.100355	−	0.994952i
$3$		0			0
$3$		0			0
$4$	−2.05491e6	+	418795.i	−0.979858	+	0.199697i
$5$	1.63057e7			0.746715			0.373358	−	0.927688i	$-0.378206\pi$
$5$	1.63057e7			0.746715			0.373358	+	0.927688i	$0.378206\pi$
$6$		0			0
$7$		−	1.11046e9i		−	1.48584i	−0.669379	−	0.742921i	$-0.733440\pi$
$7$		−	1.11046e9i		−	1.48584i	0.669379	−	0.742921i	$-0.266560\pi$
$8$	9.02058e8	+	2.89994e9i	0.297023	+	0.954870i
$9$		0			0
$10$	−2.36971e9	−	2.34940e10i	−0.0749367	−	0.742946i
$11$		−	1.11865e11i		−	1.30039i	−0.759769	−	0.650193i	$-0.774688\pi$
$11$		−	1.11865e11i		−	1.30039i	0.759769	−	0.650193i	$-0.225312\pi$
$12$		0			0
$13$			1.58848e11i			0.319577i	0.987151	+	0.159789i	$0.0510812\pi$
$13$			1.58848e11i			0.319577i	−0.987151	+	0.159789i	$0.948919\pi$
$14$	−1.60000e12	+	1.61383e11i	−1.47834	+	0.149112i
$15$		0			0
$16$	4.04727e12	−	1.72117e12i	0.920242	−	0.391350i
$17$			3.55129e12i			0.427241i	0.976917	+	0.213621i	$0.0685256\pi$
$17$			3.55129e12i			0.427241i	−0.976917	+	0.213621i	$0.931474\pi$
$18$		0			0
$19$	3.97170e12			0.148615			0.0743077	−	0.997235i	$-0.476325\pi$
$19$	3.97170e12			0.148615			0.0743077	+	0.997235i	$0.476325\pi$
$20$	−3.35068e13	+	6.82876e12i	−0.731675	+	0.149117i
$21$		0			0
$22$	−1.61180e14	+	1.62574e13i	−1.29382	+	0.130500i
$23$	−9.68326e13			−0.487393			−0.243696	−	0.969852i	$-0.578360\pi$
$23$	−9.68326e13			−0.487393			−0.243696	+	0.969852i	$0.578360\pi$
$24$		0			0
$25$	−2.10961e14			−0.442416
$26$	2.28875e14	−	2.30853e13i	0.317964	−	0.0320712i
$27$		0			0
$28$	4.65054e14	+	2.28189e15i	0.296718	+	1.45591i
$29$	4.54212e14			0.200484			0.100242	−	0.994963i	$-0.468038\pi$
$29$	4.54212e14			0.200484			0.100242	+	0.994963i	$0.468038\pi$
$30$		0			0
$31$			7.94527e15i			1.74105i	0.492125	+	0.870525i	$0.336220\pi$
$31$			7.94527e15i			1.74105i	−0.492125	+	0.870525i	$0.663780\pi$
$32$	−3.06813e15	−	5.58134e15i	−0.481725	−	0.876322i
$33$		0			0
$34$	5.11686e15	−	5.16109e14i	0.425084	−	0.0428759i
$35$		−	1.81068e16i		−	1.10950i
$36$		0			0
$37$			1.51812e15i			0.0519026i	0.999663	+	0.0259513i	$0.00826149\pi$
$37$			1.51812e15i			0.0519026i	−0.999663	+	0.0259513i	$0.991739\pi$
$38$	−5.77207e14	−	5.72261e15i	−0.0149143	−	0.147865i
$39$		0			0
$40$	1.47087e16	+	4.72856e16i	0.221791	+	0.713016i
$41$		−	3.00638e16i		−	0.349795i	−0.984587	−	0.174898i	$-0.944041\pi$
$41$		−	3.00638e16i		−	0.349795i	0.984587	−	0.174898i	$-0.0559594\pi$
$42$		0			0
$43$	−1.85924e17			−1.31195			−0.655975	−	0.754783i	$-0.727742\pi$
$43$	−1.85924e17			−1.31195			−0.655975	+	0.754783i	$0.727742\pi$
$44$	4.68487e16	+	2.29873e17i	0.259683	+	1.27419i
$45$		0			0
$46$	1.40727e16	+	1.39521e17i	0.0489124	+	0.484932i
$47$	2.24282e17			0.621968			0.310984	−	0.950415i	$-0.399341\pi$
$47$	2.24282e17			0.621968			0.310984	+	0.950415i	$0.399341\pi$
$48$		0			0
$49$	−6.74570e17			−1.20773
$50$	3.06589e16	+	3.03961e17i	0.0443988	+	0.440183i
$51$		0			0
$52$	−6.65246e16	−	3.26418e17i	−0.0638186	−	0.313140i
$53$	−3.35928e17			−0.263846			−0.131923	−	0.991260i	$-0.542115\pi$
$53$	−3.35928e17			−0.263846			−0.131923	+	0.991260i	$0.542115\pi$
$54$		0			0
$55$		−	1.82404e18i		−	0.971018i
$56$	3.22026e18	−	1.00170e18i	1.41879	−	0.441329i
$57$		0			0
$58$	−6.60105e16	−	6.54448e17i	−0.0201196	−	0.199472i
$59$		−	4.52223e18i		−	1.15188i	−0.817493	−	0.575939i	$-0.804637\pi$
$59$		−	4.52223e18i		−	1.15188i	0.817493	−	0.575939i	$-0.195363\pi$
$60$		0			0
$61$		−	4.11219e18i		−	0.738091i	−0.929411	−	0.369045i	$-0.879685\pi$
$61$		−	4.11219e18i		−	0.738091i	0.929411	−	0.369045i	$-0.120315\pi$
$62$	1.14479e19	−	1.15469e18i	1.73226	−	0.174723i
$63$		0			0
$64$	−7.59595e18	+	5.23183e18i	−0.823555	+	0.567237i
$65$			2.59013e18i			0.238633i
$66$		0			0
$67$	6.73554e18			0.451427			0.225713	−	0.974194i	$-0.427529\pi$
$67$	6.73554e18			0.451427			0.225713	+	0.974194i	$0.427529\pi$
$68$	−1.48727e18	−	7.29759e18i	−0.0853188	−	0.418635i
$69$		0			0
$70$	−2.60891e19	+	2.63146e18i	−1.10390	+	0.111344i
$71$	−3.53935e19			−1.29036			−0.645180	−	0.764030i	$-0.723218\pi$
$71$	−3.53935e19			−1.29036			−0.645180	+	0.764030i	$0.723218\pi$
$72$		0			0
$73$	−2.43223e19			−0.662392			−0.331196	−	0.943562i	$-0.607452\pi$
$73$	−2.43223e19			−0.662392			−0.331196	+	0.943562i	$0.607452\pi$
$74$	2.18738e18	−	2.20629e17i	0.0516406	−	0.00520870i
$75$		0			0
$76$	−8.16150e18	+	1.66333e18i	−0.145622	+	0.0296781i
$77$	−1.24222e20			−1.93217
$78$		0			0
$79$		−	6.60458e19i		−	0.784804i	−0.919794	−	0.392402i	$-0.871644\pi$
$79$		−	6.60458e19i		−	0.784804i	0.919794	−	0.392402i	$-0.128356\pi$
$80$	6.59936e19	−	2.80650e19i	0.687159	−	0.292227i
$81$		0			0
$82$	−4.33173e19	+	4.36917e18i	−0.348029	+	0.0351037i
$83$		−	1.15265e20i		−	0.815416i	−0.913112	−	0.407708i	$-0.866328\pi$
$83$		−	1.15265e20i		−	0.815416i	0.913112	−	0.407708i	$-0.133672\pi$
$84$		0			0
$85$			5.79064e19i			0.319027i
$86$	2.70203e19	+	2.67888e20i	0.131661	+	1.30533i
$87$		0			0
$88$	3.24403e20	−	1.00909e20i	1.24170	−	0.386244i
$89$			3.32918e20i			1.13173i	0.824498	+	0.565864i	$0.191457\pi$
$89$			3.32918e20i			1.13173i	−0.824498	+	0.565864i	$0.808543\pi$
$90$		0			0
$91$	1.76394e20			0.474841
$92$	1.98982e20	−	4.05530e19i	0.477576	−	0.0973310i
$93$		0			0
$94$	−3.25949e19	−	3.23156e20i	−0.0624177	−	0.618828i
$95$	6.47615e19			0.110973
$96$		0			0
$97$	−7.05599e20			−0.971527			−0.485764	−	0.874090i	$-0.661458\pi$
$97$	−7.05599e20			−0.971527			−0.485764	+	0.874090i	$0.661458\pi$
$98$	9.80351e19	+	9.71950e20i	0.121202	+	1.20163i
$99$		0			0
$100$	4.33505e20	−	8.83493e19i	0.433505	−	0.0883493i
$101$	−4.33813e20			−0.390777			−0.195388	−	0.980726i	$-0.562597\pi$
$101$	−4.33813e20			−0.390777			−0.195388	+	0.980726i	$0.562597\pi$
$102$		0			0
$103$			1.27275e21i			0.933154i	0.884480	+	0.466577i	$0.154513\pi$
$103$			1.27275e21i			0.933154i	−0.884480	+	0.466577i	$0.845487\pi$
$104$	−4.60649e20	+	1.43290e20i	−0.305155	+	0.0949217i
$105$		0			0
$106$	4.88204e19	+	4.84020e20i	0.0264783	+	0.262514i
$107$			8.28270e20i			0.407045i	0.979070	+	0.203522i	$0.0652390\pi$
$107$			8.28270e20i			0.407045i	−0.979070	+	0.203522i	$0.934761\pi$
$108$		0			0
$109$			4.48776e21i			1.81573i	0.419264	+	0.907865i	$0.362288\pi$
$109$			4.48776e21i			1.81573i	−0.419264	+	0.907865i	$0.637712\pi$
$110$	−2.62816e21	+	2.65088e20i	−0.966116	+	0.0974467i
$111$		0			0
$112$	−1.91129e21	−	4.49432e21i	−0.581483	−	1.36733i
$113$			5.07033e21i			1.40512i	0.711625	+	0.702559i	$0.247959\pi$
$113$			5.07033e21i			1.40512i	−0.711625	+	0.702559i	$0.752041\pi$
$114$		0			0
$115$	−1.57893e21			−0.363944
$116$	−9.33364e20	+	1.90222e20i	−0.196446	+	0.0400360i
$117$		0			0
$118$	−6.51582e21	+	6.57215e20i	−1.14606	+	0.115597i
$119$	3.94356e21			0.634813
$120$		0			0
$121$	−5.11360e21			−0.691004
$122$	−5.92502e21	+	5.97624e20i	−0.734364	+	0.0740712i
$123$		0			0
$124$	−3.32744e21	−	1.63268e22i	−0.347683	−	1.70598i
$125$	−1.12150e22			−1.07707
$126$		0			0
$127$		−	1.94148e22i		−	1.57832i	−0.614189	−	0.789159i	$-0.710517\pi$
$127$		−	1.94148e22i		−	1.57832i	0.614189	−	0.789159i	$-0.289483\pi$
$128$	8.64217e21	+	1.01842e22i	0.647021	+	0.762472i
$129$		0			0
$130$	3.73197e21	−	3.76423e20i	0.237428	−	0.0239481i
$131$			1.87459e22i			1.10042i	0.835027	+	0.550210i	$0.185452\pi$
$131$			1.87459e22i			1.10042i	−0.835027	+	0.550210i	$0.814548\pi$
$132$		0			0
$133$		−	4.41041e21i		−	0.220819i
$134$	−9.78875e20	−	9.70487e21i	−0.0453030	−	0.449148i
$135$		0			0
$136$	−1.02985e22	+	3.20348e21i	−0.407960	+	0.126900i
$137$		−	2.45808e22i		−	0.901634i	−0.892616	−	0.450817i	$-0.851133\pi$
$137$		−	2.45808e22i		−	0.901634i	0.892616	−	0.450817i	$-0.148867\pi$
$138$		0			0
$139$	−3.63179e22			−1.14410			−0.572052	−	0.820217i	$-0.693852\pi$
$139$	−3.63179e22			−1.14410			−0.572052	+	0.820217i	$0.693852\pi$
$140$	7.58305e21	+	3.72079e22i	0.221564	+	1.08715i
$141$		0			0
$142$	5.14373e21	+	5.09965e22i	0.129494	+	1.28385i
$143$	1.77695e22			0.415573
$144$		0			0
$145$	7.40625e21			0.149704
$146$	3.53476e21	+	3.50447e22i	0.0664744	+	0.659048i
$147$		0			0
$148$	−6.35783e20	−	3.11961e21i	−0.0103648	−	0.0508572i
$149$	−1.21824e23			−1.85045			−0.925226	−	0.379417i	$-0.876124\pi$
$149$	−1.21824e23			−1.85045			−0.925226	+	0.379417i	$0.876124\pi$
$150$		0			0
$151$		−	1.36202e23i		−	1.79856i	−0.437377	−	0.899278i	$-0.644092\pi$
$151$		−	1.36202e23i		−	1.79856i	0.437377	−	0.899278i	$-0.355908\pi$
$152$	3.58271e21	+	1.15177e22i	0.0441422	+	0.141909i
$153$		0			0
$154$	1.80531e22	+	1.78984e23i	0.193903	+	1.92241i
$155$			1.29553e23i			1.30007i
$156$		0			0
$157$			1.33706e23i			1.17275i	0.810041	+	0.586374i	$0.199445\pi$
$157$			1.33706e23i			1.17275i	−0.810041	+	0.586374i	$0.800555\pi$
$158$	−9.51617e22	+	9.59843e21i	−0.780842	+	0.0787591i
$159$		0			0
$160$	−5.00281e22	−	9.10078e22i	−0.359711	−	0.654363i
$161$			1.07528e23i			0.724189i
$162$		0			0
$163$	1.99703e23			1.18145			0.590725	−	0.806873i	$-0.298842\pi$
$163$	1.99703e23			1.18145			0.590725	+	0.806873i	$0.298842\pi$
$164$	1.25906e22	+	6.17785e22i	0.0698531	+	0.342749i
$165$		0			0
$166$	−1.66079e23	+	1.67515e22i	−0.811299	+	0.0818312i
$167$	3.55809e23			1.63190			0.815950	−	0.578122i	$-0.196214\pi$
$167$	3.55809e23			1.63190			0.815950	+	0.578122i	$0.196214\pi$
$168$		0			0
$169$	2.21832e23			0.897871
$170$	8.34341e22	−	8.41553e21i	0.317417	−	0.0320161i
$171$		0			0
$172$	3.82058e23	−	7.78642e22i	1.28552	−	0.261993i
$173$	−1.00471e22			−0.0318095			−0.0159048	−	0.999874i	$-0.505063\pi$
$173$	−1.00471e22			−0.0318095			−0.0159048	+	0.999874i	$0.505063\pi$
$174$		0			0
$175$			2.34263e23i			0.657361i
$176$	−1.92540e23	−	4.52749e23i	−0.508905	−	1.19667i
$177$		0			0
$178$	4.79683e23	−	4.83829e22i	1.12602	−	0.113575i
$179$		−	5.41545e23i		−	1.19861i	−0.800521	−	0.599304i	$-0.795444\pi$
$179$		−	5.41545e23i		−	1.19861i	0.800521	−	0.599304i	$-0.204556\pi$
$180$		0			0
$181$		−	1.99303e23i		−	0.392544i	−0.980549	−	0.196272i	$-0.937116\pi$
$181$		−	1.99303e23i		−	0.392544i	0.980549	−	0.196272i	$-0.0628836\pi$
$182$	−2.56352e22	−	2.54156e23i	−0.0476527	−	0.472444i
$183$		0			0
$184$	−8.73486e22	−	2.80809e23i	−0.144767	−	0.465397i
$185$			2.47541e22i			0.0387565i
$186$		0			0
$187$	3.97267e23			0.555578
$188$	−4.60880e23	+	9.39284e22i	−0.609440	+	0.124205i
$189$		0			0
$190$	−9.41178e21	−	9.33112e22i	−0.0111368	−	0.110413i
$191$	5.97999e23			0.669653			0.334827	−	0.942280i	$-0.391322\pi$
$191$	5.97999e23			0.669653			0.334827	+	0.942280i	$0.391322\pi$
$192$		0			0
$193$	−7.77346e23			−0.780301			−0.390151	−	0.920751i	$-0.627577\pi$
$193$	−7.77346e23			−0.780301			−0.390151	+	0.920751i	$0.627577\pi$
$194$	1.02545e23	+	1.01666e24i	0.0974978	+	0.966623i
$195$		0			0
$196$	1.38618e24	−	2.82507e23i	1.18340	−	0.241179i
$197$	−6.47549e23			−0.524056			−0.262028	−	0.965060i	$-0.584391\pi$
$197$	−6.47549e23			−0.524056			−0.262028	+	0.965060i	$0.584391\pi$
$198$		0			0
$199$			2.53895e24i			1.84798i	0.382421	+	0.923988i	$0.375090\pi$
$199$			2.53895e24i			1.84798i	−0.382421	+	0.923988i	$0.624910\pi$
$200$	−1.90299e23	−	6.11773e23i	−0.131408	−	0.422450i
$201$		0			0
$202$	6.30460e22	+	6.25057e23i	0.0392165	+	0.388804i
$203$		−	5.04383e23i		−	0.297887i
$204$		0			0
$205$		−	4.90212e23i		−	0.261197i
$206$	1.83384e24	−	1.84969e23i	0.928444	−	0.0936469i
$207$		0			0
$208$	2.73404e23	+	6.42899e23i	0.125066	+	0.294088i
$209$		−	4.44296e23i		−	0.193257i
$210$		0			0
$211$	1.63403e24			0.643125			0.321563	−	0.946888i	$-0.395792\pi$
$211$	1.63403e24			0.643125			0.321563	+	0.946888i	$0.395792\pi$
$212$	6.90303e23	−	1.40685e23i	0.258531	−	0.0526892i
$213$		0			0
$214$	1.19341e24	−	1.20372e23i	0.404990	−	0.0408490i
$215$	−3.03163e24			−0.979653
$216$		0			0
$217$	8.82289e24			2.58692
$218$	6.46616e24	−	6.52205e23i	1.80656	−	0.182218i
$219$		0			0
$220$	7.63901e23	+	3.74825e24i	0.193910	+	0.951459i
$221$	−5.64115e23			−0.136536
$222$		0			0
$223$			5.60866e24i			1.23497i	0.786581	+	0.617487i	$0.211849\pi$
$223$			5.60866e24i			1.23497i	−0.786581	+	0.617487i	$0.788151\pi$
$224$	−6.19784e24	+	3.40703e24i	−1.30208	+	0.715767i
$225$		0			0
$226$	7.30556e24	−	7.36871e23i	1.39802	−	0.141011i
$227$			1.04509e25i			1.90934i	0.297668	+	0.954670i	$0.403791\pi$
$227$			1.04509e25i			1.90934i	−0.297668	+	0.954670i	$0.596209\pi$
$228$		0			0
$229$		−	9.63833e24i		−	1.60594i	−0.596019	−	0.802970i	$-0.703252\pi$
$229$		−	9.63833e24i		−	1.60594i	0.596019	−	0.802970i	$-0.296748\pi$
$230$	2.29465e23	+	2.27498e24i	0.0365236	+	0.362106i
$231$		0			0
$232$	4.09725e23	+	1.31719e24i	0.0595483	+	0.191436i
$233$			5.20857e24i			0.723572i	0.932261	+	0.361786i	$0.117833\pi$
$233$			5.20857e24i			0.723572i	−0.932261	+	0.361786i	$0.882167\pi$
$234$		0			0
$235$	3.65709e24			0.464433
$236$	1.89389e24	+	9.29277e24i	0.230027	+	1.12868i
$237$		0			0
$238$	−5.73117e23	−	5.68206e24i	−0.0637067	−	0.631608i
$239$	−3.45429e24			−0.367436			−0.183718	−	0.982979i	$-0.558813\pi$
$239$	−3.45429e24			−0.367436			−0.183718	+	0.982979i	$0.558813\pi$
$240$		0			0
$241$	2.19485e24			0.213908			0.106954	−	0.994264i	$-0.465890\pi$
$241$	2.19485e24			0.213908			0.106954	+	0.994264i	$0.465890\pi$
$242$	7.43159e23	+	7.36790e24i	0.0693458	+	0.687515i
$243$		0			0
$244$	1.72216e24	+	8.45018e24i	0.147395	+	0.723224i
$245$	−1.09994e25			−0.901827
$246$		0			0
$247$			6.30896e23i			0.0474941i
$248$	−2.30408e25	+	7.16710e24i	−1.66248	+	0.517131i
$249$		0			0
$250$	1.62988e24	+	1.61591e25i	0.108090	+	1.07164i
$251$			9.76703e24i			0.621138i	0.950551	+	0.310569i	$0.100520\pi$
$251$			9.76703e24i			0.621138i	−0.950551	+	0.310569i	$0.899480\pi$
$252$		0			0
$253$			1.08322e25i			0.633799i
$254$	−2.79737e25	+	2.82155e24i	−1.57035	+	0.158392i
$255$		0			0
$256$	1.34179e25	−	1.39321e25i	0.693691	−	0.720273i
$257$			1.72645e25i			0.856755i	0.903600	+	0.428378i	$0.140915\pi$
$257$			1.72645e25i			0.856755i	−0.903600	+	0.428378i	$0.859085\pi$
$258$		0			0
$259$	1.68581e24			0.0771191
$260$	−1.08473e24	−	5.32248e24i	−0.0476543	−	0.233826i
$261$		0			0
$262$	2.70099e25	−	2.72434e24i	1.09486	−	0.110433i
$263$	2.33601e25			0.909785			0.454893	−	0.890546i	$-0.349678\pi$
$263$	2.33601e25			0.909785			0.454893	+	0.890546i	$0.349678\pi$
$264$		0			0
$265$	−5.47756e24			−0.197018
$266$	−6.35471e24	+	6.40964e23i	−0.219704	+	0.0221603i
$267$		0			0
$268$	−1.38409e25	+	2.82081e24i	−0.442334	+	0.0901486i
$269$	4.42164e25			1.35889			0.679445	−	0.733726i	$-0.262221\pi$
$269$	4.42164e25			1.35889			0.679445	+	0.733726i	$0.262221\pi$
$270$		0			0
$271$		−	1.41966e25i		−	0.403652i	−0.979421	−	0.201826i	$-0.935313\pi$
$271$		−	1.41966e25i		−	0.403652i	0.979421	−	0.201826i	$-0.0646875\pi$
$272$	6.11239e24	+	1.43730e25i	0.167201	+	0.393165i
$273$		0			0
$274$	−3.54171e25	+	3.57233e24i	−0.897082	+	0.0904837i
$275$			2.35992e25i			0.575312i
$276$		0			0
$277$			1.72266e25i			0.389191i	0.980884	+	0.194596i	$0.0623394\pi$
$277$			1.72266e25i			0.389191i	−0.980884	+	0.194596i	$0.937661\pi$
$278$	5.27808e24	+	5.23284e25i	0.114817	+	1.13833i
$279$		0			0
$280$	5.25087e25	−	1.63334e25i	1.05943	−	0.329547i
$281$			8.21760e25i			1.59709i	0.601937	+	0.798544i	$0.294396\pi$
$281$			8.21760e25i			1.59709i	−0.601937	+	0.798544i	$0.705604\pi$
$282$		0			0
$283$	7.40601e25			1.33606			0.668031	−	0.744133i	$-0.267137\pi$
$283$	7.40601e25			1.33606			0.668031	+	0.744133i	$0.267137\pi$
$284$	7.27305e25	−	1.48226e25i	1.26437	−	0.257681i
$285$		0			0
$286$	−2.58244e24	−	2.56031e25i	−0.0417050	−	0.413476i
$287$	−3.33846e25			−0.519740
$288$		0			0
$289$	5.64802e25			0.817465
$290$	−1.07635e24	−	1.06712e25i	−0.0150236	−	0.148949i
$291$		0			0
$292$	4.99802e25	−	1.01861e25i	0.649049	−	0.132278i
$293$	−1.43600e26			−1.79905			−0.899526	−	0.436868i	$-0.856088\pi$
$293$	−1.43600e26			−1.79905			−0.899526	+	0.436868i	$0.856088\pi$
$294$		0			0
$295$		−	7.37382e25i		−	0.860124i
$296$	−4.40247e24	+	1.36944e24i	−0.0495603	+	0.0154163i
$297$		0			0
$298$	1.77047e25	+	1.75530e26i	0.185702	+	1.84111i
$299$		−	1.53816e25i		−	0.155760i
$300$		0			0
$301$			2.06461e26i			1.94935i
$302$	−1.96245e26	+	1.97942e25i	−1.78948	+	0.180495i
$303$		0			0
$304$	1.60745e25	−	6.83599e24i	0.136762	−	0.0581606i
$305$		−	6.70522e25i		−	0.551143i
$306$		0			0
$307$	6.33744e25			0.486363			0.243182	−	0.969981i	$-0.421809\pi$
$307$	6.33744e25			0.486363			0.243182	+	0.969981i	$0.421809\pi$
$308$	2.55264e26	−	5.20235e25i	1.89325	−	0.385848i
$309$		0			0
$310$	1.86666e26	−	1.88280e25i	1.29350	−	0.130469i
$311$	−1.41945e26			−0.950904			−0.475452	−	0.879742i	$-0.657715\pi$
$311$	−1.41945e26			−0.950904			−0.475452	+	0.879742i	$0.657715\pi$
$312$		0			0
$313$	2.07188e25			0.129763			0.0648814	−	0.997893i	$-0.479333\pi$
$313$	2.07188e25			0.129763			0.0648814	+	0.997893i	$0.479333\pi$
$314$	1.92649e26	−	1.94315e25i	1.16683	−	0.117691i
$315$		0			0
$316$	2.76597e25	+	1.35718e26i	0.156723	+	0.768996i
$317$	−3.12103e23			−0.00171071			−0.000855355	−	1.00000i	$-0.500272\pi$
$317$	−3.12103e23			−0.00171071			−0.000855355		1.00000i	$0.500272\pi$
$318$		0			0
$319$		−	5.08105e25i		−	0.260706i
$320$	−1.23858e26	+	8.53088e25i	−0.614961	+	0.423564i
$321$		0			0
$322$	1.54932e26	−	1.56271e25i	0.720533	−	0.0726761i
$323$			1.41047e25i			0.0634946i
$324$		0			0
$325$		−	3.35106e25i		−	0.141386i
$326$	−2.90228e25	−	2.87741e26i	−0.118565	−	1.17549i
$327$		0			0
$328$	8.71833e25	−	2.71193e25i	0.334009	−	0.103897i
$329$		−	2.49056e26i		−	0.924146i
$330$		0			0
$331$	−2.11279e26			−0.735636			−0.367818	−	0.929898i	$-0.619895\pi$
$331$	−2.11279e26			−0.735636			−0.367818	+	0.929898i	$0.619895\pi$
$332$	4.82726e25	+	2.36860e26i	0.162836	+	0.798991i
$333$		0			0
$334$	−5.17096e25	−	5.12665e26i	−0.163770	−	1.62366i
$335$	1.09828e26			0.337087
$336$		0			0
$337$	−1.56530e25			−0.0451320			−0.0225660	−	0.999745i	$-0.507184\pi$
$337$	−1.56530e25			−0.0451320			−0.0225660	+	0.999745i	$0.507184\pi$
$338$	−3.22388e25	−	3.19625e26i	−0.0901060	−	0.893338i
$339$		0			0
$340$	−2.42509e25	−	1.18993e26i	−0.0637089	−	0.312601i
$341$	8.88801e26			2.26404
$342$		0			0
$343$			1.28840e26i			0.308647i
$344$	−1.67715e26	−	5.39170e26i	−0.389679	−	1.25274i
$345$		0			0
$346$	1.46014e24	+	1.44763e25i	0.00319225	+	0.0316489i
$347$			1.30011e26i			0.275753i	0.990449	+	0.137877i	$0.0440277\pi$
$347$			1.30011e26i			0.275753i	−0.990449	+	0.137877i	$0.955972\pi$
$348$		0			0
$349$		−	2.13554e26i		−	0.426424i	−0.977006	−	0.213212i	$-0.931608\pi$
$349$		−	2.13554e26i		−	0.426424i	0.977006	−	0.213212i	$-0.0683924\pi$
$350$	3.37536e26	−	3.40454e25i	0.654042	−	0.0659696i
$351$		0			0
$352$	−6.24359e26	+	3.43217e26i	−1.13956	+	0.626428i
$353$			5.09456e26i			0.902553i	0.892384	+	0.451276i	$0.149031\pi$
$353$			5.09456e26i			0.902553i	−0.892384	+	0.451276i	$0.850969\pi$
$354$		0			0
$355$	−5.77117e26			−0.963532
$356$	−1.39425e26	−	6.84117e26i	−0.226003	−	1.10893i
$357$		0			0
$358$	−7.80281e26	+	7.87026e25i	−1.19256	+	0.120287i
$359$	7.36779e25			0.109357			0.0546784	−	0.998504i	$-0.482587\pi$
$359$	7.36779e25			0.109357			0.0546784	+	0.998504i	$0.482587\pi$
$360$		0			0
$361$	−6.98435e26			−0.977913
$362$	−2.87164e26	+	2.89647e25i	−0.390563	+	0.0393939i
$363$		0			0
$364$	−3.62473e26	+	7.38728e25i	−0.465276	+	0.0948244i
$365$	−3.96593e26			−0.494618
$366$		0			0
$367$			4.97792e26i			0.586211i	0.956080	+	0.293106i	$0.0946888\pi$
$367$			4.97792e26i			0.586211i	−0.956080	+	0.293106i	$0.905311\pi$
$368$	−3.91907e26	+	1.66666e26i	−0.448520	+	0.190741i
$369$		0			0
$370$	3.56668e25	−	3.59751e24i	0.0385608	−	0.00388941i
$371$			3.73034e26i			0.392033i
$372$		0			0
$373$		−	1.55131e27i		−	1.54083i	−0.637541	−	0.770417i	$-0.720048\pi$
$373$		−	1.55131e27i		−	1.54083i	0.637541	−	0.770417i	$-0.279952\pi$
$374$	−5.77347e25	−	5.72399e26i	−0.0557552	−	0.552774i
$375$		0			0
$376$	2.02316e26	+	6.50406e26i	0.184739	+	0.593899i
$377$			7.21504e25i			0.0640700i
$378$		0			0
$379$	−1.10808e27			−0.930807			−0.465404	−	0.885099i	$-0.654091\pi$
$379$	−1.10808e27			−0.930807			−0.465404	+	0.885099i	$0.654091\pi$
$380$	−1.33079e26	+	2.71218e25i	−0.108738	+	0.0221611i
$381$		0			0
$382$	−8.69071e25	−	8.61623e26i	−0.0672032	−	0.666273i
$383$	−1.00156e27			−0.753512			−0.376756	−	0.926313i	$-0.622960\pi$
$383$	−1.00156e27			−0.753512			−0.376756	+	0.926313i	$0.622960\pi$
$384$		0			0
$385$	−2.02552e27			−1.44278
$386$	1.12972e26	+	1.12003e27i	0.0783073	+	0.776362i
$387$		0			0
$388$	1.44994e27	−	2.95502e26i	0.951958	−	0.194011i
$389$	−2.07322e26			−0.132487			−0.0662437	−	0.997803i	$-0.521101\pi$
$389$	−2.07322e26			−0.132487			−0.0662437	+	0.997803i	$0.521101\pi$
$390$		0			0
$391$		−	3.43881e26i		−	0.208234i
$392$	−6.08502e26	−	1.95621e27i	−0.358722	−	1.15322i
$393$		0			0
$394$	9.41082e25	+	9.33017e26i	0.0525917	+	0.521410i
$395$		−	1.07693e27i		−	0.586025i
$396$		0			0
$397$		−	3.03012e27i		−	1.56372i	−0.623452	−	0.781862i	$-0.714270\pi$
$397$		−	3.03012e27i		−	1.56372i	0.623452	−	0.781862i	$-0.285730\pi$
$398$	3.65823e27	−	3.68985e26i	1.83865	−	0.185454i
$399$		0			0
$400$	−8.53814e26	+	3.63100e26i	−0.407130	+	0.173139i
$401$			2.85606e27i			1.32663i	0.748338	+	0.663317i	$0.230852\pi$
$401$			2.85606e27i			1.32663i	−0.748338	+	0.663317i	$0.769148\pi$
$402$		0			0
$403$	−1.26209e27			−0.556399
$404$	8.91448e26	−	1.81679e26i	0.382905	−	0.0780370i
$405$		0			0
$406$	−7.26737e26	+	7.33019e25i	−0.296383	+	0.0298945i
$407$	1.69826e26			0.0674935
$408$		0			0
$409$	−2.73951e27			−1.03414			−0.517068	−	0.855944i	$-0.672977\pi$
$409$	−2.73951e27			−1.03414			−0.517068	+	0.855944i	$0.672977\pi$
$410$	−7.06319e26	+	7.12425e25i	−0.259879	+	0.0262125i
$411$		0			0
$412$	−5.33023e26	−	2.61539e27i	−0.186348	−	0.914359i
$413$	−5.02174e27			−1.71151
$414$		0			0
$415$		−	1.87949e27i		−	0.608883i
$416$	8.86583e26	−	4.87365e26i	0.280053	−	0.153948i
$417$		0			0
$418$	−6.40161e26	+	6.45695e25i	−0.192282	+	0.0193944i
$419$			3.99947e27i			1.17153i	0.810479	+	0.585767i	$0.199207\pi$
$419$			3.99947e27i			1.17153i	−0.810479	+	0.585767i	$0.800793\pi$
$420$		0			0
$421$			5.93177e27i			1.65281i	0.563078	+	0.826404i	$0.309617\pi$
$421$			5.93177e27i			1.65281i	−0.563078	+	0.826404i	$0.690383\pi$
$422$	−2.37474e26	−	2.35439e27i	−0.0645409	−	0.639878i
$423$		0			0
$424$	−3.03027e26	−	9.74173e26i	−0.0783682	−	0.251939i
$425$		−	7.49183e26i		−	0.189018i
$426$		0			0
$427$	−4.56641e27			−1.09669
$428$	−3.46875e26	−	1.70202e27i	−0.0812857	−	0.398846i
$429$		0			0
$430$	4.40586e26	+	4.36811e27i	0.0983133	+	0.974707i
$431$	6.64122e27			1.44623			0.723114	−	0.690729i	$-0.242710\pi$
$431$	6.64122e27			1.44623			0.723114	+	0.690729i	$0.242710\pi$
$432$		0			0
$433$	−1.26150e27			−0.261677			−0.130838	−	0.991404i	$-0.541767\pi$
$433$	−1.26150e27			−0.261677			−0.130838	+	0.991404i	$0.541767\pi$
$434$	−1.28223e27	−	1.27124e28i	−0.259611	−	2.57386i
$435$		0			0
$436$	−1.87945e27	−	9.22194e27i	−0.362596	−	1.77916i
$437$	−3.84590e26			−0.0724341
$438$		0			0
$439$			1.22822e27i			0.220495i	0.993904	+	0.110247i	$0.0351643\pi$
$439$			1.22822e27i			0.220495i	−0.993904	+	0.110247i	$0.964836\pi$
$440$	5.28962e27	−	1.64539e27i	0.927196	−	0.288414i
$441$		0			0
$442$	8.19827e25	+	8.12801e26i	0.0137021	+	0.135847i
$443$			4.92335e27i			0.803566i	0.915735	+	0.401783i	$0.131609\pi$
$443$			4.92335e27i			0.803566i	−0.915735	+	0.401783i	$0.868391\pi$
$444$		0			0
$445$			5.42847e27i			0.845079i
$446$	8.08120e27	−	8.15106e26i	1.22874	−	0.123936i
$447$		0			0
$448$	5.80973e27	+	8.43498e27i	0.842824	+	1.22367i
$449$		−	5.33955e27i		−	0.756690i	−0.925665	−	0.378345i	$-0.876493\pi$
$449$		−	5.33955e27i		−	0.756690i	0.925665	−	0.378345i	$-0.123507\pi$
$450$		0			0
$451$	−3.36310e27			−0.454869
$452$	−2.12343e27	−	1.04191e28i	−0.280598	−	1.37682i
$453$		0			0
$454$	1.50581e28	−	1.51883e27i	1.89970	−	0.191612i
$455$	2.87622e27			0.354571
$456$		0			0
$457$	−6.93225e26			−0.0816120			−0.0408060	−	0.999167i	$-0.512993\pi$
$457$	−6.93225e26			−0.0816120			−0.0408060	+	0.999167i	$0.512993\pi$
$458$	−1.38873e28	+	1.40074e27i	−1.59783	+	0.161164i
$459$		0			0
$460$	3.24455e27	−	6.61246e26i	0.356613	−	0.0726785i
$461$	5.45652e27			0.586214			0.293107	−	0.956080i	$-0.405311\pi$
$461$	5.45652e27			0.586214			0.293107	+	0.956080i	$0.405311\pi$
$462$		0			0
$463$		−	3.88783e27i		−	0.399123i	−0.979885	−	0.199561i	$-0.936048\pi$
$463$		−	3.88783e27i		−	0.399123i	0.979885	−	0.199561i	$-0.0639518\pi$
$464$	1.83832e27	−	7.81777e26i	0.184494	−	0.0784592i
$465$		0			0
$466$	7.50474e27	−	7.56961e26i	0.719919	−	0.0726142i
$467$			7.16230e27i			0.671777i	0.941902	+	0.335888i	$0.109037\pi$
$467$			7.16230e27i			0.671777i	−0.941902	+	0.335888i	$0.890963\pi$
$468$		0			0
$469$		−	7.47953e27i		−	0.670749i
$470$	−5.31484e26	−	5.26929e27i	−0.0466082	−	0.462088i
$471$		0			0
$472$	1.31142e28	−	4.07931e27i	1.09989	−	0.342134i
$473$			2.07985e28i			1.70604i
$474$		0			0
$475$	−8.37873e26			−0.0657499
$476$	−8.10367e27	+	1.65154e27i	−0.622026	+	0.126770i
$477$		0			0
$478$	5.02012e26	+	4.97710e27i	0.0368741	+	0.365581i
$479$	−1.15399e28			−0.829237			−0.414618	−	0.909995i	$-0.636085\pi$
$479$	−1.15399e28			−0.829237			−0.414618	+	0.909995i	$0.636085\pi$
$480$		0			0
$481$	−2.41151e26			−0.0165869
$482$	−3.18978e26	−	3.16244e27i	−0.0214668	−	0.212828i
$483$		0			0
$484$	1.05080e28	−	2.14155e27i	0.677085	−	0.137991i
$485$	−1.15053e28			−0.725454
$486$		0			0
$487$		−	1.47074e28i		−	0.888143i	−0.895991	−	0.444071i	$-0.853534\pi$
$487$		−	1.47074e28i		−	0.888143i	0.895991	−	0.444071i	$-0.146466\pi$
$488$	1.19251e28	−	3.70943e27i	0.704781	−	0.219230i
$489$		0			0
$490$	1.59853e27	+	1.58483e28i	0.0905030	+	0.897274i
$491$			2.27891e28i			1.26291i	0.775413	+	0.631454i	$0.217542\pi$
$491$			2.27891e28i			1.26291i	−0.775413	+	0.631454i	$0.782458\pi$
$492$		0			0
$493$			1.61304e27i			0.0856549i
$494$	9.09022e26	−	9.16880e25i	0.0472543	−	0.00476628i
$495$		0			0
$496$	1.36752e28	+	3.21566e28i	0.681359	+	1.60219i
$497$			3.93030e28i			1.91727i
$498$		0			0
$499$	2.62317e28			1.22679			0.613395	−	0.789776i	$-0.289803\pi$
$499$	2.62317e28			1.22679			0.613395	+	0.789776i	$0.289803\pi$
$500$	2.30459e28	−	4.69680e27i	1.05538	−	0.215089i
$501$		0			0
$502$	1.40728e28	−	1.41944e27i	0.618003	−	0.0623345i
$503$	−3.85150e28			−1.65640			−0.828202	−	0.560430i	$-0.810636\pi$
$503$	−3.85150e28			−1.65640			−0.828202	+	0.560430i	$0.810636\pi$
$504$		0			0
$505$	−7.07364e27			−0.291799
$506$	1.56075e28	−	1.57424e27i	0.630599	−	0.0636050i
$507$		0			0
$508$	8.13084e27	+	3.98957e28i	0.315186	+	1.54653i
$509$	1.78188e28			0.676614			0.338307	−	0.941036i	$-0.390146\pi$
$509$	1.78188e28			0.676614			0.338307	+	0.941036i	$0.390146\pi$
$510$		0			0
$511$			2.70089e28i			0.984209i
$512$	−2.20240e28	−	1.73084e28i	−0.786252	−	0.617906i
$513$		0			0
$514$	2.48755e28	−	2.50905e27i	0.852430	−	0.0859798i
$515$			2.07532e28i			0.696801i
$516$		0			0
$517$		−	2.50894e28i		−	0.808798i
$518$	−2.44999e26	−	2.42899e27i	−0.00773930	−	0.0767298i
$519$		0			0
$520$	−7.51121e27	+	2.33644e27i	−0.227864	+	0.0708794i
$521$			5.09896e28i			1.51595i	0.652283	+	0.757976i	$0.273812\pi$
$521$			5.09896e28i			1.51595i	−0.652283	+	0.757976i	$0.726188\pi$
$522$		0			0
$523$	−2.90651e28			−0.830050			−0.415025	−	0.909810i	$-0.636227\pi$
$523$	−2.90651e28			−0.830050			−0.415025	+	0.909810i	$0.636227\pi$
$524$	−7.85070e27	−	3.85212e28i	−0.219751	−	1.07825i
$525$		0			0
$526$	−3.39492e27	−	3.36582e28i	−0.0913017	−	0.905193i
$527$	−2.82160e28			−0.743848
$528$		0			0
$529$	−3.00950e28			−0.762448
$530$	7.96052e26	+	7.89230e27i	0.0197717	+	0.196023i
$531$		0			0
$532$	1.84706e27	+	9.06299e27i	0.0440969	+	0.216371i
$533$	4.77557e27			0.111786
$534$		0			0
$535$			1.35055e28i			0.303946i
$536$	6.07585e27	+	1.95327e28i	0.134084	+	0.431054i
$537$		0			0
$538$	−6.42596e27	−	6.37089e28i	−0.136372	−	1.35203i
$539$			7.54610e28i			1.57051i
$540$		0			0
$541$		−	1.69364e28i		−	0.339040i	−0.985527	−	0.169520i	$-0.945778\pi$
$541$		−	1.69364e28i		−	0.339040i	0.985527	−	0.169520i	$-0.0542217\pi$
$542$	−2.04551e28	+	2.06319e27i	−0.401614	+	0.0405085i
$543$		0			0
$544$	1.98210e28	−	1.08958e28i	0.374401	−	0.205813i
$545$			7.31761e28i			1.35583i
$546$		0			0
$547$	−6.12464e28			−1.09198			−0.545989	−	0.837793i	$-0.683846\pi$
$547$	−6.12464e28			−1.09198			−0.545989	+	0.837793i	$0.683846\pi$
$548$	1.02943e28	+	5.05114e28i	0.180054	+	0.883473i
$549$		0			0
$550$	3.40027e28	−	3.42966e27i	0.572408	−	0.0577356i
$551$	1.80399e27			0.0297950
$552$		0			0
$553$	−7.33411e28			−1.16609
$554$	2.48209e28	−	2.50354e27i	0.387226	−	0.0390573i
$555$		0			0
$556$	7.46301e28	−	1.52098e28i	1.12106	−	0.228474i
$557$	2.20360e28			0.324828			0.162414	−	0.986723i	$-0.448072\pi$
$557$	2.20360e28			0.324828			0.162414	+	0.986723i	$0.448072\pi$
$558$		0			0
$559$		−	2.95336e28i		−	0.419269i
$560$	−3.11650e28	−	7.32831e28i	−0.434203	−	1.02101i
$561$		0			0
$562$	1.18403e29	−	1.19426e28i	1.58902	−	0.160276i
$563$			1.16331e29i			1.53235i	0.642630	+	0.766177i	$0.277843\pi$
$563$			1.16331e29i			1.53235i	−0.642630	+	0.766177i	$0.722157\pi$
$564$		0			0
$565$			8.26754e28i			1.04922i
$566$	−1.07631e28	−	1.06709e29i	−0.134081	−	1.32932i
$567$		0			0
$568$	−3.19270e28	−	1.02639e29i	−0.383266	−	1.23213i
$569$		−	1.25615e29i		−	1.48035i	−0.672415	−	0.740174i	$-0.734743\pi$
$569$		−	1.25615e29i		−	1.48035i	0.672415	−	0.740174i	$-0.265257\pi$
$570$		0			0
$571$	−6.01329e28			−0.683019			−0.341510	−	0.939878i	$-0.610938\pi$
$571$	−6.01329e28			−0.683019			−0.341510	+	0.939878i	$0.610938\pi$
$572$	−3.65148e28	+	7.44180e27i	−0.407203	+	0.0829888i
$573$		0			0
$574$	4.85178e27	+	4.81020e28i	0.0521586	+	0.517116i
$575$	2.04279e28			0.215631
$576$		0			0
$577$	1.21390e29			1.23548			0.617742	−	0.786381i	$-0.288048\pi$
$577$	1.21390e29			1.23548			0.617742	+	0.786381i	$0.288048\pi$
$578$	−8.20826e27	−	8.13792e28i	−0.0820369	−	0.813338i
$579$		0			0
$580$	−1.52192e28	+	3.10170e27i	−0.146689	+	0.0298955i
$581$	−1.27997e29			−1.21158
$582$		0			0
$583$			3.75787e28i			0.343101i
$584$	−2.19401e28	−	7.05333e28i	−0.196745	−	0.632498i
$585$		0			0
$586$	2.08693e28	+	2.06905e29i	0.180544	+	1.78997i
$587$		−	2.68343e28i		−	0.228029i	−0.993479	−	0.114014i	$-0.963629\pi$
$587$		−	2.68343e28i		−	0.228029i	0.993479	−	0.114014i	$-0.0363710\pi$
$588$		0			0
$589$			3.15563e28i			0.258747i
$590$	−1.06245e29	+	1.07164e28i	−0.855782	+	0.0863179i
$591$		0			0
$592$	2.61296e27	+	6.14426e27i	0.0203121	+	0.0477630i
$593$			1.49316e29i			1.14033i	0.821529	+	0.570167i	$0.193122\pi$
$593$			1.49316e29i			1.14033i	−0.821529	+	0.570167i	$0.806878\pi$
$594$		0			0
$595$	6.43026e28			0.474024
$596$	2.50338e29	−	5.10194e28i	1.81318	−	0.369530i
$597$		0			0
$598$	−2.21625e28	+	2.23541e27i	−0.154973	+	0.0156313i
$599$	7.15442e27			0.0491578			0.0245789	−	0.999698i	$-0.492176\pi$
$599$	7.15442e27			0.0491578			0.0245789	+	0.999698i	$0.492176\pi$
$600$		0			0
$601$	−2.36815e29			−1.57118			−0.785591	−	0.618746i	$-0.787641\pi$
$601$	−2.36815e29			−1.57118			−0.785591	+	0.618746i	$0.787641\pi$
$602$	2.97478e29	−	3.00049e28i	1.93951	−	0.195627i
$603$		0			0
$604$	5.70406e28	+	2.79882e29i	0.359167	+	1.76233i
$605$	−8.33809e28			−0.515983
$606$		0			0
$607$		−	4.40146e28i		−	0.263097i	−0.991310	−	0.131548i	$-0.958005\pi$
$607$		−	4.40146e28i		−	0.263097i	0.991310	−	0.131548i	$-0.0419949\pi$
$608$	−1.21857e28	−	2.21674e28i	−0.0715918	−	0.130235i
$609$		0			0
$610$	−9.66117e28	+	9.74468e27i	−0.548361	+	0.0553101i
$611$			3.56267e28i			0.198767i
$612$		0			0
$613$		−	1.86148e29i		−	1.00351i	−0.865009	−	0.501757i	$-0.832687\pi$
$613$		−	1.86148e29i		−	1.00351i	0.865009	−	0.501757i	$-0.167313\pi$
$614$	−9.21019e27	−	9.13126e28i	−0.0488091	−	0.483908i
$615$		0			0
$616$	−1.12055e29	−	3.60236e29i	−0.573898	−	1.84497i
$617$		−	1.09610e29i		−	0.551896i	−0.961173	−	0.275948i	$-0.911008\pi$
$617$		−	1.09610e29i		−	0.551896i	0.961173	−	0.275948i	$-0.0889918\pi$
$618$		0			0
$619$	1.29036e29			0.627999			0.314000	−	0.949423i	$-0.398331\pi$
$619$	1.29036e29			0.627999			0.314000	+	0.949423i	$0.398331\pi$
$620$	−5.42564e28	−	2.66221e29i	−0.259620	−	1.27388i
$621$		0			0
$622$	2.06289e28	+	2.04521e29i	0.0954282	+	0.946104i
$623$	3.69691e29			1.68157
$624$		0			0
$625$	−8.22755e28			−0.361851
$626$	−3.01107e27	−	2.98526e28i	−0.0130224	−	0.129108i
$627$		0			0
$628$	−5.59954e28	−	2.74754e29i	−0.234194	−	1.14913i
$629$	−5.39131e27			−0.0221749
$630$		0			0
$631$		−	4.81005e29i		−	1.91356i	−0.290820	−	0.956778i	$-0.593928\pi$
$631$		−	4.81005e29i		−	1.91356i	0.290820	−	0.956778i	$-0.406072\pi$
$632$	1.91529e29	−	5.95772e28i	0.749386	−	0.233105i
$633$		0			0
$634$	4.53579e25	+	4.49692e26i	0.000171679	+	0.00170207i
$635$		−	3.16573e29i		−	1.17855i
$636$		0			0
$637$		−	1.07154e29i		−	0.385961i
$638$	−7.32100e28	+	7.38429e27i	−0.259390	+	0.0261632i
$639$		0			0
$640$	1.40917e29	+	1.66061e29i	0.483140	+	0.569350i
$641$		−	2.63338e29i		−	0.888185i	−0.895981	−	0.444093i	$-0.853526\pi$
$641$		−	2.63338e29i		−	0.888185i	0.895981	−	0.444093i	$-0.146474\pi$
$642$		0			0
$643$	−4.17468e29			−1.36272			−0.681362	−	0.731947i	$-0.738612\pi$
$643$	−4.17468e29			−1.36272			−0.681362	+	0.731947i	$0.738612\pi$
$644$	−4.50324e28	−	2.20961e29i	−0.144618	−	0.709602i
$645$		0			0
$646$	2.03227e28	−	2.04983e27i	0.0631741	−	0.00637202i
$647$	1.80457e29			0.551922			0.275961	−	0.961169i	$-0.411004\pi$
$647$	1.80457e29			0.551922			0.275961	+	0.961169i	$0.411004\pi$
$648$		0			0
$649$	−5.05880e29			−1.49789
$650$	−4.82835e28	+	4.87009e27i	−0.140672	+	0.0141888i
$651$		0			0
$652$	−4.10372e29	+	8.36348e28i	−1.15765	+	0.235932i
$653$	−1.58788e29			−0.440788			−0.220394	−	0.975411i	$-0.570734\pi$
$653$	−1.58788e29			−0.440788			−0.220394	+	0.975411i	$0.570734\pi$
$654$		0			0
$655$			3.05666e29i			0.821700i
$656$	−5.17450e28	−	1.21676e29i	−0.136892	−	0.321896i
$657$		0			0
$658$	−3.58851e29	+	3.61953e28i	−0.919480	+	0.0927428i
$659$		−	3.19695e29i		−	0.806193i	−0.915157	−	0.403097i	$-0.867934\pi$
$659$		−	3.19695e29i		−	0.806193i	0.915157	−	0.403097i	$-0.132066\pi$
$660$		0			0
$661$			2.08534e29i			0.509404i	0.967020	+	0.254702i	$0.0819774\pi$
$661$			2.08534e29i			0.509404i	−0.967020	+	0.254702i	$0.918023\pi$
$662$	3.07052e28	+	3.04421e29i	0.0738249	+	0.731923i
$663$		0			0
$664$	3.34263e29	−	1.03976e29i	0.778616	−	0.242197i
$665$		−	7.19149e28i		−	0.164889i
$666$		0			0
$667$	−4.39825e28			−0.0977144
$668$	−7.31155e29	+	1.49011e29i	−1.59903	+	0.325886i
$669$		0			0
$670$	−1.59613e28	−	1.58245e29i	−0.0338284	−	0.335385i
$671$	−4.60011e29			−0.959803
$672$		0			0
$673$	−4.94384e28			−0.0999784			−0.0499892	−	0.998750i	$-0.515919\pi$
$673$	−4.94384e28			−0.0999784			−0.0499892	+	0.998750i	$0.515919\pi$
$674$	2.27485e27	+	2.25536e28i	0.00452923	+	0.0449041i
$675$		0			0
$676$	−4.55845e29	+	9.29022e28i	−0.879785	+	0.179302i
$677$	7.99489e29			1.51926			0.759629	−	0.650356i	$-0.225380\pi$
$677$	7.99489e29			1.51926			0.759629	+	0.650356i	$0.225380\pi$
$678$		0			0
$679$			7.83538e29i			1.44354i
$680$	−1.67925e29	+	5.22350e28i	−0.304630	+	0.0947584i
$681$		0			0
$682$	−1.29169e29	−	1.28062e30i	−0.227208	−	2.25261i
$683$			8.76090e29i			1.51751i	0.651377	+	0.758755i	$0.274192\pi$
$683$			8.76090e29i			1.51751i	−0.651377	+	0.758755i	$0.725808\pi$
$684$		0			0
$685$		−	4.00808e29i		−	0.673264i
$686$	1.85638e29	−	1.87243e28i	0.307089	−	0.0309743i
$687$		0			0
$688$	−7.52485e29	+	3.20008e29i	−1.20731	+	0.513431i
$689$		−	5.33614e28i		−	0.0843190i
$690$		0			0
$691$	7.37190e29			1.12995			0.564976	−	0.825107i	$-0.308885\pi$
$691$	7.37190e29			1.12995			0.564976	+	0.825107i	$0.308885\pi$
$692$	2.06459e28	−	4.20768e27i	0.0311688	−	0.00635227i
$693$		0			0
$694$	1.87326e29	−	1.88945e28i	0.274361	−	0.0276733i
$695$	−5.92190e29			−0.854320
$696$		0			0
$697$	1.06765e29			0.149447
$698$	−3.07698e29	+	3.10358e28i	−0.424271	+	0.0427938i
$699$		0			0
$700$	−9.81081e28	−	4.81389e29i	−0.131273	−	0.644120i
$701$	1.52884e29			0.201523			0.100761	−	0.994911i	$-0.467872\pi$
$701$	1.52884e29			0.201523			0.100761	+	0.994911i	$0.467872\pi$
$702$		0			0
$703$			6.02954e27i			0.00771353i
$704$	5.85261e29	+	8.49724e29i	0.737626	+	1.07094i
$705$		0			0
$706$	7.34047e29	−	7.40392e28i	0.897996	−	0.0905759i
$707$			4.81731e29i			0.580632i
$708$		0			0
$709$		−	1.07083e29i		−	0.125296i	−0.998036	−	0.0626478i	$-0.980046\pi$
$709$		−	1.07083e29i		−	0.125296i	0.998036	−	0.0626478i	$-0.0199545\pi$
$710$	8.38723e28	+	8.31535e29i	0.0966954	+	0.958668i
$711$		0			0
$712$	−9.65443e29	+	3.00312e29i	−1.08065	+	0.336149i
$713$		−	7.69361e29i		−	0.848575i
$714$		0			0
$715$	2.89745e29			0.310315
$716$	2.26796e29	+	1.11283e30i	0.239359	+	1.17447i
$717$		0			0
$718$	−1.07076e28	−	1.06158e29i	−0.0109745	−	0.108805i
$719$	−9.44904e28			−0.0954409			−0.0477204	−	0.998861i	$-0.515196\pi$
$719$	−9.44904e28			−0.0954409			−0.0477204	+	0.998861i	$0.515196\pi$
$720$		0			0
$721$	1.41334e30			1.38652
$722$	1.01503e29	+	1.00634e30i	0.0981387	+	0.972977i
$723$		0			0
$724$	8.34671e28	+	4.09550e29i	0.0783900	+	0.384638i
$725$	−9.58208e28			−0.0886973
$726$		0			0
$727$			2.63722e29i			0.237157i	0.992945	+	0.118578i	$0.0378337\pi$
$727$			2.63722e29i			0.237157i	−0.992945	+	0.118578i	$0.962166\pi$
$728$	1.59117e29	+	5.11531e29i	0.141039	+	0.453411i
$729$		0			0
$730$	5.76368e28	+	5.71428e29i	0.0496375	+	0.492121i
$731$		−	6.60272e29i		−	0.560519i
$732$		0			0
$733$			9.11045e29i			0.751533i	0.926714	+	0.375767i	$0.122621\pi$
$733$			9.11045e29i			0.751533i	−0.926714	+	0.375767i	$0.877379\pi$
$734$	7.17241e29	−	7.23440e28i	0.583252	−	0.0588294i
$735$		0			0
$736$	2.97095e29	+	5.40456e29i	0.234789	+	0.427113i
$737$		−	7.53474e29i		−	0.587029i
$738$		0			0
$739$	8.20104e29			0.621016			0.310508	−	0.950571i	$-0.399501\pi$
$739$	8.20104e29			0.621016			0.310508	+	0.950571i	$0.399501\pi$
$740$	−1.03669e28	−	5.08675e28i	−0.00773956	−	0.0379758i
$741$		0			0
$742$	5.37484e29	−	5.42130e28i	0.390054	−	0.0393426i
$743$	−1.76727e30			−1.26451			−0.632253	−	0.774762i	$-0.717870\pi$
$743$	−1.76727e30			−1.26451			−0.632253	+	0.774762i	$0.717870\pi$
$744$		0			0
$745$	−1.98643e30			−1.38176
$746$	−2.23519e30	+	2.25451e29i	−1.53305	+	0.154631i
$747$		0			0
$748$	−8.16348e29	+	1.66373e29i	−0.544388	+	0.110947i
$749$	9.19758e29			0.604804
$750$		0			0
$751$		−	6.69678e29i		−	0.428200i	−0.976812	−	0.214100i	$-0.931318\pi$
$751$		−	6.69678e29i		−	0.428200i	0.976812	−	0.214100i	$-0.0686818\pi$
$752$	9.07731e29	−	3.86029e29i	0.572361	−	0.243407i
$753$		0			0
$754$	1.03958e29	−	1.04856e28i	0.0637466	−	0.00642976i
$755$		−	2.22087e30i		−	1.34301i
$756$		0			0
$757$		−	1.50830e30i		−	0.887117i	−0.896245	−	0.443559i	$-0.853716\pi$
$757$		−	1.50830e30i		−	0.887117i	0.896245	−	0.443559i	$-0.146284\pi$
$758$	1.61037e29	+	1.59657e30i	0.0934113	+	0.926108i
$759$		0			0
$760$	5.84186e28	+	1.87805e29i	0.0329616	+	0.105965i
$761$		−	3.23153e30i		−	1.79833i	−0.437612	−	0.899164i	$-0.644176\pi$
$761$		−	3.23153e30i		−	1.79833i	0.437612	−	0.899164i	$-0.355824\pi$
$762$		0			0
$763$	4.98346e30			2.69789
$764$	−1.22883e30	+	2.50439e29i	−0.656165	+	0.133728i
$765$		0			0
$766$	1.45557e29	+	1.44309e30i	0.0756188	+	0.749708i
$767$	7.18345e29			0.368114
$768$		0			0
$769$	2.74415e30			1.36830			0.684149	−	0.729342i	$-0.260174\pi$
$769$	2.74415e30			1.36830			0.684149	+	0.729342i	$0.260174\pi$
$770$	2.94369e29	+	2.91846e30i	0.144790	+	1.43550i
$771$		0			0
$772$	1.59738e30	−	3.25549e29i	0.764584	−	0.155824i
$773$	−1.08380e30			−0.511760			−0.255880	−	0.966709i	$-0.582365\pi$
$773$	−1.08380e30			−0.511760			−0.255880	+	0.966709i	$0.582365\pi$
$774$		0			0
$775$		−	1.67614e30i		−	0.770269i
$776$	−6.36492e29	−	2.04620e30i	−0.288566	−	0.927682i
$777$		0			0
$778$	3.01301e28	+	2.98719e29i	0.0132958	+	0.131819i
$779$		−	1.19405e29i		−	0.0519850i
$780$		0			0
$781$			3.95931e30i			1.67797i
$782$	−4.95479e29	+	4.99762e28i	−0.207183	+	0.0208974i
$783$		0			0
$784$	−2.73017e30	+	1.16105e30i	−1.11140	+	0.472643i
$785$			2.18017e30i			0.875708i
$786$		0			0
$787$	3.42912e30			1.34106			0.670530	−	0.741882i	$-0.266067\pi$
$787$	3.42912e30			1.34106			0.670530	+	0.741882i	$0.266067\pi$
$788$	1.33066e30	−	2.71191e29i	0.513500	−	0.104652i
$789$		0			0
$790$	−1.55168e30	+	1.56509e29i	−0.583066	+	0.0588106i
$791$	5.63039e30			2.08778
$792$		0			0
$793$	6.53211e29			0.235877
$794$	−4.36593e30	+	4.40367e29i	−1.55583	+	0.156928i
$795$		0			0
$796$	−1.06330e30	−	5.21731e30i	−0.369036	−	1.81075i
$797$	3.20924e30			1.09923			0.549617	−	0.835417i	$-0.314774\pi$
$797$	3.20924e30			1.09923			0.549617	+	0.835417i	$0.314774\pi$
$798$		0			0
$799$			7.96493e29i			0.265730i
$800$	6.47255e29	+	1.17744e30i	0.213123	+	0.387699i
$801$		0			0
$802$	4.11514e30	−	4.15071e29i	1.31994	−	0.133135i
$803$			2.72082e30i			0.861365i
$804$		0			0
$805$			1.75333e30i			0.540763i
$806$	1.83419e29	+	1.81847e30i	0.0558376	+	0.553591i
$807$		0			0
$808$	−3.91325e29	−	1.25803e30i	−0.116070	−	0.373141i
$809$		−	5.95892e30i		−	1.74465i	−0.488928	−	0.872324i	$-0.662612\pi$
$809$		−	5.95892e30i		−	1.74465i	0.488928	−	0.872324i	$-0.337388\pi$
$810$		0			0
$811$	5.78707e30			1.65097			0.825486	−	0.564422i	$-0.190901\pi$
$811$	5.78707e30			1.65097			0.825486	+	0.564422i	$0.190901\pi$
$812$	2.11233e29	+	1.03646e30i	0.0594872	+	0.291887i
$813$		0			0
$814$	−2.46807e28	−	2.44692e29i	−0.00677332	−	0.0671527i
$815$	3.25631e30			0.882207
$816$		0			0
$817$	−7.38436e29			−0.194976
$818$	3.98132e29	+	3.94720e30i	0.103781	+	1.02892i
$819$		0			0
$820$	2.05299e29	+	1.00734e30i	0.0521603	+	0.255936i
$821$	−6.18104e30			−1.55045			−0.775226	−	0.631684i	$-0.782364\pi$
$821$	−6.18104e30			−1.55045			−0.775226	+	0.631684i	$0.782364\pi$
$822$		0			0
$823$			1.87831e30i			0.459272i	0.973277	+	0.229636i	$0.0737535\pi$
$823$			1.87831e30i			0.459272i	−0.973277	+	0.229636i	$0.926246\pi$
$824$	−3.69091e30	+	1.14810e30i	−0.891042	+	0.277168i
$825$		0			0
$826$	7.29809e29	+	7.23554e30i	0.171759	+	1.70287i
$827$		−	1.15089e30i		−	0.267441i	−0.991019	−	0.133720i	$-0.957308\pi$
$827$		−	1.15089e30i		−	0.267441i	0.991019	−	0.133720i	$-0.0426924\pi$
$828$		0			0
$829$			2.33044e30i			0.527977i	0.964526	+	0.263988i	$0.0850381\pi$
$829$			2.33044e30i			0.527977i	−0.964526	+	0.263988i	$0.914962\pi$
$830$	−2.70805e30	+	2.73145e29i	−0.605809	+	0.0611046i
$831$		0			0
$832$	−8.31064e29	−	1.20660e30i	−0.181276	−	0.263189i
$833$		−	2.39560e30i		−	0.515990i
$834$		0			0
$835$	5.80172e30			1.21856
$836$	1.86069e29	+	9.12988e29i	0.0385930	+	0.189365i
$837$		0			0
$838$	5.76261e30	−	5.81242e29i	1.16562	−	0.117570i
$839$	−2.46941e30			−0.493279			−0.246639	−	0.969107i	$-0.579326\pi$
$839$	−2.46941e30			−0.493279			−0.246639	+	0.969107i	$0.579326\pi$
$840$		0			0
$841$	−4.92653e30			−0.959806
$842$	8.54676e30	−	8.62063e29i	1.64446	−	0.165868i
$843$		0			0
$844$	−3.35779e30	+	6.84326e29i	−0.630171	+	0.128430i
$845$	3.61713e30			0.670454
$846$		0			0
$847$			5.67844e30i			1.02672i
$848$	−1.35959e30	+	5.78191e29i	−0.242802	+	0.103256i
$849$		0			0
$850$	−1.07946e30	+	1.08879e29i	−0.188064	+	0.0189690i
$851$		−	1.47004e29i		−	0.0252970i
$852$		0			0
$853$		−	6.99217e30i		−	1.17394i	−0.809607	−	0.586972i	$-0.800320\pi$
$853$		−	6.99217e30i		−	1.17394i	0.809607	−	0.586972i	$-0.199680\pi$
$854$	6.63636e29	+	6.57948e30i	0.110058	+	1.09115i
$855$		0			0
$856$	−2.40193e30	+	7.47148e29i	−0.388675	+	0.120902i
$857$		−	7.25707e30i		−	1.16001i	−0.814612	−	0.580006i	$-0.803050\pi$
$857$		−	7.25707e30i		−	1.16001i	0.814612	−	0.580006i	$-0.196950\pi$
$858$		0			0
$859$	−1.16920e31			−1.82372			−0.911861	−	0.410499i	$-0.865355\pi$
$859$	−1.16920e31			−1.82372			−0.911861	+	0.410499i	$0.865355\pi$
$860$	6.22973e30	−	1.26963e30i	0.959921	−	0.195634i
$861$		0			0
$862$	−9.65168e29	−	9.56897e30i	−0.145136	−	1.43893i
$863$	−9.99164e30			−1.48431			−0.742153	−	0.670230i	$-0.766195\pi$
$863$	−9.99164e30			−1.48431			−0.742153	+	0.670230i	$0.766195\pi$
$864$		0			0
$865$	−1.63825e29			−0.0237526
$866$	1.83334e29	+	1.81763e30i	0.0262606	+	0.260356i
$867$		0			0
$868$	−1.81302e31	+	3.69498e30i	−2.53482	+	0.516601i
$869$	−7.38824e30			−1.02055
$870$		0			0
$871$			1.06993e30i			0.144266i
$872$	−1.30142e31	+	4.04822e30i	−1.73379	+	0.539313i
$873$		0			0
$874$	5.58925e28	+	5.54135e29i	0.00726914	+	0.0720685i
$875$			1.24538e31i			1.60036i
$876$		0			0
$877$		−	1.48068e31i		−	1.85766i	−0.370507	−	0.928830i	$-0.620816\pi$
$877$		−	1.48068e31i		−	1.85766i	0.370507	−	0.928830i	$-0.379184\pi$
$878$	1.76967e30	−	1.78497e29i	0.219382	−	0.0221278i
$879$		0			0
$880$	−3.13950e30	−	7.38240e30i	−0.380007	−	0.893572i
$881$		−	9.26792e30i		−	1.10850i	−0.832351	−	0.554249i	$-0.813005\pi$
$881$		−	9.26792e30i		−	1.10850i	0.832351	−	0.554249i	$-0.186995\pi$
$882$		0			0
$883$	3.86015e30			0.450834			0.225417	−	0.974262i	$-0.427626\pi$
$883$	3.86015e30			0.450834			0.225417	+	0.974262i	$0.427626\pi$
$884$	1.15921e30	−	2.36249e29i	0.133786	−	0.0272659i
$885$		0			0
$886$	7.09377e30	−	7.15509e29i	0.799509	−	0.0806420i
$887$	−5.26751e30			−0.586688			−0.293344	−	0.956007i	$-0.594768\pi$
$887$	−5.26751e30			−0.586688			−0.293344	+	0.956007i	$0.594768\pi$
$888$		0			0
$889$	−2.15593e31			−2.34513
$890$	7.82158e30	−	7.88919e29i	0.840813	−	0.0848081i
$891$		0			0
$892$	−2.34888e30	−	1.15253e31i	−0.246621	−	1.21010i
$893$	8.90784e29			0.0924340
$894$		0			0
$895$		−	8.83027e30i		−	0.895019i
$896$	1.13092e31	−	9.59677e30i	1.13291	−	0.961371i
$897$		0			0
$898$	−7.69345e30	+	7.75996e29i	−0.752870	+	0.0759377i
$899$			3.60884e30i			0.349052i
$900$		0			0
$901$		−	1.19298e30i		−	0.112726i
$902$	4.88759e29	+	4.84570e30i	0.0456484	+	0.452572i
$903$		0			0
$904$	−1.47037e31	+	4.57374e30i	−1.34171	+	0.417352i
$905$		−	3.24978e30i		−	0.293119i
$906$		0			0
$907$	1.72788e31			1.52278			0.761389	−	0.648295i	$-0.224518\pi$
$907$	1.72788e31			1.52278			0.761389	+	0.648295i	$0.224518\pi$
$908$	−4.37680e30	−	2.14757e31i	−0.381290	−	1.87088i
$909$		0			0
$910$	−4.18001e29	−	4.14419e30i	−0.0355830	−	0.352781i
$911$	1.44748e31			1.21806			0.609030	−	0.793147i	$-0.291559\pi$
$911$	1.44748e31			1.21806			0.609030	+	0.793147i	$0.291559\pi$
$912$		0			0
$913$	−1.28942e31			−1.06036
$914$	1.00746e29	+	9.98829e29i	0.00819019	+	0.0812000i
$915$		0			0
$916$	4.03649e30	+	1.98059e31i	0.320702	+	1.57359i
$917$	2.08165e31			1.63505
$918$		0			0
$919$			1.88347e31i			1.44592i	0.690889	+	0.722961i	$0.257219\pi$
$919$			1.88347e31i			1.44592i	−0.690889	+	0.722961i	$0.742781\pi$
$920$	−1.42428e30	−	4.57879e30i	−0.108100	−	0.347519i
$921$		0			0
$922$	−7.92995e29	−	7.86199e30i	−0.0588296	−	0.583254i
$923$		−	5.62218e30i		−	0.412370i
$924$		0			0
$925$		−	3.20264e29i		−	0.0229626i
$926$	−5.60175e30	+	5.65017e29i	−0.397108	+	0.0400541i
$927$		0			0
$928$	−1.39358e30	−	2.53511e30i	−0.0965780	−	0.175688i
$929$			8.49947e29i			0.0582408i	0.999576	+	0.0291204i	$0.00927062\pi$
$929$			8.49947e29i			0.0582408i	−0.999576	+	0.0291204i	$0.990729\pi$
$930$		0			0
$931$	−2.67919e30			−0.179487
$932$	−2.18133e30	−	1.07032e31i	−0.144495	−	0.708997i
$933$		0			0
$934$	1.03198e31	−	1.04090e30i	0.668385	−	0.0674163i
$935$	6.47772e30			0.414859
$936$		0			0
$937$	−1.87088e31			−1.17160			−0.585802	−	0.810455i	$-0.699220\pi$
$937$	−1.87088e31			−1.17160			−0.585802	+	0.810455i	$0.699220\pi$
$938$	−1.07768e31	+	1.08700e30i	−0.667362	+	0.0673131i
$939$		0			0
$940$	−7.51499e30	+	1.53157e30i	−0.455078	+	0.0927459i
$941$	1.07614e31			0.644435			0.322218	−	0.946666i	$-0.395572\pi$
$941$	1.07614e31			0.644435			0.322218	+	0.946666i	$0.395572\pi$
$942$		0			0
$943$			2.91116e30i			0.170488i
$944$	−7.78354e30	−	1.83027e31i	−0.450787	−	1.06001i
$945$		0			0
$946$	2.99674e31	−	3.02264e30i	1.69743	−	0.171210i
$947$			1.28020e31i			0.717140i	0.933503	+	0.358570i	$0.116735\pi$
$947$			1.28020e31i			0.717140i	−0.933503	+	0.358570i	$0.883265\pi$
$948$		0			0
$949$		−	3.86354e30i		−	0.211685i
$950$	1.21768e29	+	1.20724e30i	0.00659835	+	0.0654180i
$951$		0			0
$952$	3.55732e30	+	1.14361e31i	0.188554	+	0.606164i
$953$			6.97019e30i			0.365400i	0.983169	+	0.182700i	$0.0584838\pi$
$953$			6.97019e30i			0.365400i	−0.983169	+	0.182700i	$0.941516\pi$
$954$		0			0
$955$	9.75081e30			0.500040
$956$	7.09826e30	−	1.44664e30i	0.360035	−	0.0733758i
$957$		0			0
$958$	1.67709e30	+	1.66272e31i	0.0832182	+	0.825050i
$959$	−2.72960e31			−1.33969
$960$		0			0
$961$	−4.23019e31			−2.03125
$962$	3.50464e28	+	3.47460e29i	0.00166458	+	0.0165032i
$963$		0			0
$964$	−4.51023e30	+	9.19194e29i	−0.209599	+	0.0427168i
$965$	−1.26752e31			−0.582663
$966$		0			0
$967$		−	3.09810e31i		−	1.39353i	−0.717297	−	0.696767i	$-0.754621\pi$
$967$		−	3.09810e31i		−	1.39353i	0.717297	−	0.696767i	$-0.245379\pi$
$968$	−4.61277e30	−	1.48291e31i	−0.205244	−	0.659819i
$969$		0			0
$970$	1.67206e30	+	1.65774e31i	0.0728031	+	0.721792i
$971$			1.90715e31i			0.821452i	0.911759	+	0.410726i	$0.134725\pi$
$971$			1.90715e31i			0.821452i	−0.911759	+	0.410726i	$0.865275\pi$
$972$		0			0
$973$			4.03295e31i			1.69996i
$974$	−2.11911e31	+	2.13743e30i	−0.883659	+	0.0891297i
$975$		0			0
$976$	−7.07779e30	−	1.66431e31i	−0.288851	−	0.679222i
$977$		−	2.79068e31i		−	1.12672i	−0.826211	−	0.563361i	$-0.809508\pi$
$977$		−	2.79068e31i		−	1.12672i	0.826211	−	0.563361i	$-0.190492\pi$
$978$		0			0
$979$	3.72420e31			1.47168
$980$	2.26027e31	−	4.60648e30i	0.883662	−	0.180092i
$981$		0			0
$982$	3.28356e31	−	3.31194e30i	1.25653	−	0.126739i
$983$	1.95416e31			0.739856			0.369928	−	0.929060i	$-0.379382\pi$
$983$	1.95416e31			0.739856			0.369928	+	0.929060i	$0.379382\pi$
$984$		0			0
$985$	−1.05588e31			−0.391320
$986$	2.32414e30	−	2.34423e29i	0.0852225	−	0.00859592i
$987$		0			0
$988$	−2.64216e29	−	1.29643e30i	−0.00948443	−	0.0465374i
$989$	1.80035e31			0.639435
$990$		0			0
$991$		−	3.14391e31i		−	1.09319i	−0.837396	−	0.546596i	$-0.815923\pi$
$991$		−	3.14391e31i		−	1.09319i	0.837396	−	0.546596i	$-0.184077\pi$
$992$	4.43453e31	−	2.43771e31i	1.52572	−	0.838707i
$993$		0			0
$994$	5.66295e31	−	5.71190e30i	1.90759	−	0.192408i
$995$			4.13994e31i			1.37991i
$996$		0			0
$997$		−	2.20318e31i		−	0.719036i	−0.933138	−	0.359518i	$-0.882941\pi$
$997$		−	2.20318e31i		−	0.719036i	0.933138	−	0.359518i	$-0.117059\pi$
$998$	−3.81225e30	−	3.77958e31i	−0.123115	−	1.22060i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.22.f.a.35.41	✓	84
3.2	odd	2	inner	72.22.f.a.35.44	yes	84
8.3	odd	2	inner	72.22.f.a.35.43	yes	84
24.11	even	2	inner	72.22.f.a.35.42	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.22.f.a.35.41	✓	84	1.1	even	1	trivial
72.22.f.a.35.42	yes	84	24.11	even	2	inner
72.22.f.a.35.43	yes	84	8.3	odd	2	inner
72.22.f.a.35.44	yes	84	3.2	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)

\(f(q)\)	\(=\)	\(q+(-145.330 - 1440.84i) q^{2} +(-2.05491e6 + 418795. i) q^{4} +1.63057e7 q^{5} -1.11046e9i q^{7} +(9.02058e8 + 2.89994e9i) q^{8} +O(q^{10})\)	\(q+(-145.330 - 1440.84i) q^{2} +(-2.05491e6 + 418795. i) q^{4} +1.63057e7 q^{5} -1.11046e9i q^{7} +(9.02058e8 + 2.89994e9i) q^{8} +(-2.36971e9 - 2.34940e10i) q^{10} -1.11865e11i q^{11} +1.58848e11i q^{13} +(-1.60000e12 + 1.61383e11i) q^{14} +(4.04727e12 - 1.72117e12i) q^{16} +3.55129e12i q^{17} +3.97170e12 q^{19} +(-3.35068e13 + 6.82876e12i) q^{20} +(-1.61180e14 + 1.62574e13i) q^{22} -9.68326e13 q^{23} -2.10961e14 q^{25} +(2.28875e14 - 2.30853e13i) q^{26} +(4.65054e14 + 2.28189e15i) q^{28} +4.54212e14 q^{29} +7.94527e15i q^{31} +(-3.06813e15 - 5.58134e15i) q^{32} +(5.11686e15 - 5.16109e14i) q^{34} -1.81068e16i q^{35} +1.51812e15i q^{37} +(-5.77207e14 - 5.72261e15i) q^{38} +(1.47087e16 + 4.72856e16i) q^{40} -3.00638e16i q^{41} -1.85924e17 q^{43} +(4.68487e16 + 2.29873e17i) q^{44} +(1.40727e16 + 1.39521e17i) q^{46} +2.24282e17 q^{47} -6.74570e17 q^{49} +(3.06589e16 + 3.03961e17i) q^{50} +(-6.65246e16 - 3.26418e17i) q^{52} -3.35928e17 q^{53} -1.82404e18i q^{55} +(3.22026e18 - 1.00170e18i) q^{56} +(-6.60105e16 - 6.54448e17i) q^{58} -4.52223e18i q^{59} -4.11219e18i q^{61} +(1.14479e19 - 1.15469e18i) q^{62} +(-7.59595e18 + 5.23183e18i) q^{64} +2.59013e18i q^{65} +6.73554e18 q^{67} +(-1.48727e18 - 7.29759e18i) q^{68} +(-2.60891e19 + 2.63146e18i) q^{70} -3.53935e19 q^{71} -2.43223e19 q^{73} +(2.18738e18 - 2.20629e17i) q^{74} +(-8.16150e18 + 1.66333e18i) q^{76} -1.24222e20 q^{77} -6.60458e19i q^{79} +(6.59936e19 - 2.80650e19i) q^{80} +(-4.33173e19 + 4.36917e18i) q^{82} -1.15265e20i q^{83} +5.79064e19i q^{85} +(2.70203e19 + 2.67888e20i) q^{86} +(3.24403e20 - 1.00909e20i) q^{88} +3.32918e20i q^{89} +1.76394e20 q^{91} +(1.98982e20 - 4.05530e19i) q^{92} +(-3.25949e19 - 3.23156e20i) q^{94} +6.47615e19 q^{95} -7.05599e20 q^{97} +(9.80351e19 + 9.71950e20i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2424084 q^{4}+O(q^{10}) \) 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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