LMFDB - Embedded newform 300.11.k.c.193.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,11,Mod(157,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("300.157");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	300.k (of order $4$, degree $2$, 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:	$190.607175802$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 63831600 x^{13} + 120528248672 x^{12} - 17600989215600 x^{11} + \cdots + 38\!\cdots\!56 $ x^16 - 63831600x^13 + 120528248672x^12 - 17600989215600x^11 + 2037236579280000x^10 - 3343396831784087400x^9 + 4317664424723438821024x^8 - 1093166020823780215242000x^7 + 122767222860388422207360000x^6 + 17394213048729389505235839600x^5 + 3322978970397292826674840245897x^4 - 837815701799476622071156318691400x^3 + 126631812340115852451399515174580000x^2 + 31278039886234045787552155897225466400*x + 3862835732371990949484385042694585728656
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{12}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.8
Root			$-380.484 + 380.484i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.11.k.c.157.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(99.2043 + 99.2043i) q^{3} +(17583.1 - 17583.1i) q^{7} +19683.0i q^{9} +O(q^{10})$	$q+(99.2043 + 99.2043i) q^{3} +(17583.1 - 17583.1i) q^{7} +19683.0i q^{9} -245351. q^{11} +(25882.8 + 25882.8i) q^{13} +(-1.01646e6 + 1.01646e6i) q^{17} +2.08723e6i q^{19} +3.48864e6 q^{21} +(-4.16272e6 - 4.16272e6i) q^{23} +(-1.95264e6 + 1.95264e6i) q^{27} +2.48858e7i q^{29} +4.39967e7 q^{31} +(-2.43399e7 - 2.43399e7i) q^{33} +(8.21011e7 - 8.21011e7i) q^{37} +5.13538e6i q^{39} +3.41660e7 q^{41} +(-5.69545e7 - 5.69545e7i) q^{43} +(1.56181e8 - 1.56181e8i) q^{47} -3.35854e8i q^{49} -2.01674e8 q^{51} +(-9.10269e7 - 9.10269e7i) q^{53} +(-2.07062e8 + 2.07062e8i) q^{57} +1.50313e8i q^{59} +1.58473e9 q^{61} +(3.46088e8 + 3.46088e8i) q^{63} +(-9.08379e7 + 9.08379e7i) q^{67} -8.25920e8i q^{69} -3.33819e9 q^{71} +(-6.15460e8 - 6.15460e8i) q^{73} +(-4.31403e9 + 4.31403e9i) q^{77} +1.25540e9i q^{79} -3.87420e8 q^{81} +(-2.20145e9 - 2.20145e9i) q^{83} +(-2.46878e9 + 2.46878e9i) q^{87} -5.39933e9i q^{89} +9.10200e8 q^{91} +(4.36467e9 + 4.36467e9i) q^{93} +(6.66166e9 - 6.66166e9i) q^{97} -4.82925e9i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 331104 q^{11} + 555984 q^{21} - 140804816 q^{31} + 29553600 q^{41} + 471062304 q^{51} + 3576862832 q^{61} + 1853192640 q^{71} - 6198727824 q^{81} + 7033272240 q^{91}+O(q^{100}) $ 16 * q - 331104 * q^11 + 555984 * q^21 - 140804816 * q^31 + 29553600 * q^41 + 471062304 * q^51 + 3576862832 * q^61 + 1853192640 * q^71 - 6198727824 * q^81 + 7033272240 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	99.2043	+	99.2043i	0.408248	+	0.408248i
$3$	99.2043	+	99.2043i	0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	17583.1	−	17583.1i	1.04618	−	1.04618i	0.0472951	−	0.998881i	$-0.484940\pi$
$7$	17583.1	−	17583.1i	1.04618	−	1.04618i	0.998881	−	0.0472951i	$-0.0150601\pi$
$8$		0			0
$9$			19683.0i			0.333333i
$10$		0			0
$11$	−245351.			−1.52344			−0.761719	−	0.647908i	$-0.775644\pi$
$11$	−245351.			−1.52344			−0.761719	+	0.647908i	$0.775644\pi$
$12$		0			0
$13$	25882.8	+	25882.8i	0.0697100	+	0.0697100i	0.741102	−	0.671392i	$-0.234303\pi$
$13$	25882.8	+	25882.8i	0.0697100	+	0.0697100i	−0.671392	+	0.741102i	$0.734303\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.01646e6	+	1.01646e6i	−0.715886	+	0.715886i	−0.967760	−	0.251874i	$-0.918953\pi$
$17$	−1.01646e6	+	1.01646e6i	−0.715886	+	0.715886i	0.251874	+	0.967760i	$0.418953\pi$
$18$		0			0
$19$			2.08723e6i			0.842952i	0.906840	+	0.421476i	$0.138488\pi$
$19$			2.08723e6i			0.842952i	−0.906840	+	0.421476i	$0.861512\pi$
$20$		0			0
$21$	3.48864e6			0.854199
$22$		0			0
$23$	−4.16272e6	−	4.16272e6i	−0.646752	−	0.646752i	0.305454	−	0.952207i	$-0.401192\pi$
$23$	−4.16272e6	−	4.16272e6i	−0.646752	−	0.646752i	−0.952207	+	0.305454i	$0.901192\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.95264e6	+	1.95264e6i	−0.136083	+	0.136083i
$28$		0			0
$29$			2.48858e7i			1.21328i	0.794975	+	0.606642i	$0.207484\pi$
$29$			2.48858e7i			1.21328i	−0.794975	+	0.606642i	$0.792516\pi$
$30$		0			0
$31$	4.39967e7			1.53678			0.768391	−	0.639981i	$-0.221058\pi$
$31$	4.39967e7			1.53678			0.768391	+	0.639981i	$0.221058\pi$
$32$		0			0
$33$	−2.43399e7	−	2.43399e7i	−0.621941	−	0.621941i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.21011e7	−	8.21011e7i	1.18397	−	1.18397i	0.205263	−	0.978707i	$-0.434195\pi$
$37$	8.21011e7	−	8.21011e7i	1.18397	−	1.18397i	0.978707	−	0.205263i	$-0.0658049\pi$
$38$		0			0
$39$			5.13538e6i			0.0569180i
$40$		0			0
$41$	3.41660e7			0.294900			0.147450	−	0.989070i	$-0.452893\pi$
$41$	3.41660e7			0.294900			0.147450	+	0.989070i	$0.452893\pi$
$42$		0			0
$43$	−5.69545e7	−	5.69545e7i	−0.387424	−	0.387424i	0.486344	−	0.873767i	$-0.338330\pi$
$43$	−5.69545e7	−	5.69545e7i	−0.387424	−	0.387424i	−0.873767	+	0.486344i	$0.838330\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.56181e8	−	1.56181e8i	0.680989	−	0.680989i	−0.279234	−	0.960223i	$-0.590080\pi$
$47$	1.56181e8	−	1.56181e8i	0.680989	−	0.680989i	0.960223	+	0.279234i	$0.0900805\pi$
$48$		0			0
$49$		−	3.35854e8i		−	1.18897i
$50$		0			0
$51$	−2.01674e8			−0.584518
$52$		0			0
$53$	−9.10269e7	−	9.10269e7i	−0.217666	−	0.217666i	0.589848	−	0.807514i	$-0.299188\pi$
$53$	−9.10269e7	−	9.10269e7i	−0.217666	−	0.217666i	−0.807514	+	0.589848i	$0.799188\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.07062e8	+	2.07062e8i	−0.344134	+	0.344134i
$58$		0			0
$59$			1.50313e8i			0.210251i	0.994459	+	0.105125i	$0.0335244\pi$
$59$			1.50313e8i			0.210251i	−0.994459	+	0.105125i	$0.966476\pi$
$60$		0			0
$61$	1.58473e9			1.87632			0.938160	−	0.346202i	$-0.112529\pi$
$61$	1.58473e9			1.87632			0.938160	+	0.346202i	$0.112529\pi$
$62$		0			0
$63$	3.46088e8	+	3.46088e8i	0.348725	+	0.348725i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−9.08379e7	+	9.08379e7i	−0.0672811	+	0.0672811i	−0.739947	−	0.672666i	$-0.765149\pi$
$67$	−9.08379e7	+	9.08379e7i	−0.0672811	+	0.0672811i	0.672666	+	0.739947i	$0.265149\pi$
$68$		0			0
$69$		−	8.25920e8i		−	0.528071i
$70$		0			0
$71$	−3.33819e9			−1.85020			−0.925100	−	0.379723i	$-0.876019\pi$
$71$	−3.33819e9			−1.85020			−0.925100	+	0.379723i	$0.876019\pi$
$72$		0			0
$73$	−6.15460e8	−	6.15460e8i	−0.296883	−	0.296883i	0.542909	−	0.839792i	$-0.317323\pi$
$73$	−6.15460e8	−	6.15460e8i	−0.296883	−	0.296883i	−0.839792	+	0.542909i	$0.817323\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.31403e9	+	4.31403e9i	−1.59378	+	1.59378i
$78$		0			0
$79$			1.25540e9i			0.407988i	0.978972	+	0.203994i	$0.0653923\pi$
$79$			1.25540e9i			0.407988i	−0.978972	+	0.203994i	$0.934608\pi$
$80$		0			0
$81$	−3.87420e8			−0.111111
$82$		0			0
$83$	−2.20145e9	−	2.20145e9i	−0.558881	−	0.558881i	0.370108	−	0.928989i	$-0.379321\pi$
$83$	−2.20145e9	−	2.20145e9i	−0.558881	−	0.558881i	−0.928989	+	0.370108i	$0.879321\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.46878e9	+	2.46878e9i	−0.495321	+	0.495321i
$88$		0			0
$89$		−	5.39933e9i		−	0.966918i	−0.875367	−	0.483459i	$-0.839380\pi$
$89$		−	5.39933e9i		−	0.966918i	0.875367	−	0.483459i	$-0.160620\pi$
$90$		0			0
$91$	9.10200e8			0.145858
$92$		0			0
$93$	4.36467e9	+	4.36467e9i	0.627388	+	0.627388i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.66166e9	−	6.66166e9i	0.775754	−	0.775754i	−0.203352	−	0.979106i	$-0.565183\pi$
$97$	6.66166e9	−	6.66166e9i	0.775754	−	0.775754i	0.979106	+	0.203352i	$0.0651835\pi$
$98$		0			0
$99$		−	4.82925e9i		−	0.507813i
$100$		0			0
$101$	−6.10333e9			−0.580711			−0.290355	−	0.956919i	$-0.593774\pi$
$101$	−6.10333e9			−0.580711			−0.290355	+	0.956919i	$0.593774\pi$
$102$		0			0
$103$	−6.03828e9	−	6.03828e9i	−0.520868	−	0.520868i	0.396966	−	0.917833i	$-0.370063\pi$
$103$	−6.03828e9	−	6.03828e9i	−0.520868	−	0.520868i	−0.917833	+	0.396966i	$0.870063\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.44897e10	−	1.44897e10i	1.03309	−	1.03309i	0.0336592	−	0.999433i	$-0.489284\pi$
$107$	1.44897e10	−	1.44897e10i	1.03309	−	1.03309i	0.999433	−	0.0336592i	$-0.0107161\pi$
$108$		0			0
$109$		−	2.56984e10i		−	1.67022i	−0.550081	−	0.835111i	$-0.685403\pi$
$109$		−	2.56984e10i		−	1.67022i	0.550081	−	0.835111i	$-0.314597\pi$
$110$		0			0
$111$	1.62896e10			0.966707
$112$		0			0
$113$	−2.51562e10	−	2.51562e10i	−1.36538	−	1.36538i	−0.866904	−	0.498474i	$-0.833894\pi$
$113$	−2.51562e10	−	2.51562e10i	−1.36538	−	1.36538i	−0.498474	−	0.866904i	$-0.666106\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.09452e8	+	5.09452e8i	−0.0232367	+	0.0232367i
$118$		0			0
$119$			3.57448e10i			1.49788i
$120$		0			0
$121$	3.42598e10			1.32086
$122$		0			0
$123$	3.38942e9	+	3.38942e9i	0.120392	+	0.120392i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.56680e10	+	2.56680e10i	−0.776914	+	0.776914i	−0.979305	−	0.202391i	$-0.935129\pi$
$127$	−2.56680e10	+	2.56680e10i	−0.776914	+	0.776914i	0.202391	+	0.979305i	$0.435129\pi$
$128$		0			0
$129$		−	1.13003e10i		−	0.316330i
$130$		0			0
$131$	−3.75211e10			−0.972565			−0.486283	−	0.873802i	$-0.661647\pi$
$131$	−3.75211e10			−0.972565			−0.486283	+	0.873802i	$0.661647\pi$
$132$		0			0
$133$	3.67000e10	+	3.67000e10i	0.881876	+	0.881876i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.09695e9	−	5.09695e9i	0.105611	−	0.105611i	−0.652327	−	0.757938i	$-0.726207\pi$
$137$	5.09695e9	−	5.09695e9i	0.105611	−	0.105611i	0.757938	+	0.652327i	$0.226207\pi$
$138$		0			0
$139$			2.00719e9i			0.0386825i	0.999813	+	0.0193412i	$0.00615689\pi$
$139$			2.00719e9i			0.0386825i	−0.999813	+	0.0193412i	$0.993843\pi$
$140$		0			0
$141$	3.09878e10			0.556025
$142$		0			0
$143$	−6.35038e9	−	6.35038e9i	−0.106199	−	0.106199i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.33182e10	−	3.33182e10i	0.485394	−	0.485394i
$148$		0			0
$149$		−	3.97699e10i		−	0.541531i	−0.962645	−	0.270765i	$-0.912723\pi$
$149$		−	3.97699e10i		−	0.541531i	0.962645	−	0.270765i	$-0.0872768\pi$
$150$		0			0
$151$	−9.92476e10			−1.26426			−0.632128	−	0.774864i	$-0.717819\pi$
$151$	−9.92476e10			−1.26426			−0.632128	+	0.774864i	$0.717819\pi$
$152$		0			0
$153$	−2.00069e10	−	2.00069e10i	−0.238629	−	0.238629i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.76032e10	+	2.76032e10i	−0.289375	+	0.289375i	−0.836833	−	0.547458i	$-0.815596\pi$
$157$	−2.76032e10	+	2.76032e10i	−0.289375	+	0.289375i	0.547458	+	0.836833i	$0.315596\pi$
$158$		0			0
$159$		−	1.80605e10i		−	0.177723i
$160$		0			0
$161$	−1.46387e11			−1.35323
$162$		0			0
$163$	1.34584e11	+	1.34584e11i	1.16965	+	1.16965i	0.982292	+	0.187355i	$0.0599915\pi$
$163$	1.34584e11	+	1.34584e11i	1.16965	+	1.16965i	0.187355	+	0.982292i	$0.440009\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.12320e11	−	1.12320e11i	0.864717	−	0.864717i	−0.127164	−	0.991882i	$-0.540588\pi$
$167$	1.12320e11	−	1.12320e11i	0.864717	−	0.864717i	0.991882	+	0.127164i	$0.0405875\pi$
$168$		0			0
$169$		−	1.36519e11i		−	0.990281i
$170$		0			0
$171$	−4.10830e10			−0.280984
$172$		0			0
$173$	−2.60619e10	−	2.60619e10i	−0.168180	−	0.168180i	0.617999	−	0.786179i	$-0.287944\pi$
$173$	−2.60619e10	−	2.60619e10i	−0.168180	−	0.168180i	−0.786179	+	0.617999i	$0.787944\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.49117e10	+	1.49117e10i	−0.0858345	+	0.0858345i
$178$		0			0
$179$			4.37045e9i			0.0237827i	0.999929	+	0.0118913i	$0.00378522\pi$
$179$			4.37045e9i			0.0237827i	−0.999929	+	0.0118913i	$0.996215\pi$
$180$		0			0
$181$	−1.96965e11			−1.01390			−0.506952	−	0.861974i	$-0.669228\pi$
$181$	−1.96965e11			−1.01390			−0.506952	+	0.861974i	$0.669228\pi$
$182$		0			0
$183$	1.57212e11	+	1.57212e11i	0.766005	+	0.766005i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.49388e11	−	2.49388e11i	1.09061	−	1.09061i
$188$		0			0
$189$			6.86668e10i			0.284733i
$190$		0			0
$191$	2.91592e11			1.14712			0.573559	−	0.819164i	$-0.305562\pi$
$191$	2.91592e11			1.14712			0.573559	+	0.819164i	$0.305562\pi$
$192$		0			0
$193$	−2.04238e11	−	2.04238e11i	−0.762693	−	0.762693i	0.214116	−	0.976808i	$-0.431313\pi$
$193$	−2.04238e11	−	2.04238e11i	−0.762693	−	0.762693i	−0.976808	+	0.214116i	$0.931313\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.68621e10	+	2.68621e10i	−0.0905335	+	0.0905335i	−0.750923	−	0.660390i	$-0.770391\pi$
$197$	−2.68621e10	+	2.68621e10i	−0.0905335	+	0.0905335i	0.660390	+	0.750923i	$0.270391\pi$
$198$		0			0
$199$			1.32496e11i			0.424557i	0.977209	+	0.212278i	$0.0680884\pi$
$199$			1.32496e11i			0.424557i	−0.977209	+	0.212278i	$0.931912\pi$
$200$		0			0
$201$	−1.80230e10			−0.0549348
$202$		0			0
$203$	4.37570e11	+	4.37570e11i	1.26931	+	1.26931i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	8.19348e10	−	8.19348e10i	0.215584	−	0.215584i
$208$		0			0
$209$		−	5.12105e11i		−	1.28418i
$210$		0			0
$211$	3.62184e11			0.865998			0.432999	−	0.901394i	$-0.357455\pi$
$211$	3.62184e11			0.865998			0.432999	+	0.901394i	$0.357455\pi$
$212$		0			0
$213$	−3.31162e11	−	3.31162e11i	−0.755341	−	0.755341i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	7.73598e11	−	7.73598e11i	1.60774	−	1.60774i
$218$		0			0
$219$		−	1.22113e11i		−	0.242404i
$220$		0			0
$221$	−5.26175e10			−0.0998088
$222$		0			0
$223$	−4.84416e11	−	4.84416e11i	−0.878404	−	0.878404i	0.114966	−	0.993369i	$-0.463324\pi$
$223$	−4.84416e11	−	4.84416e11i	−0.878404	−	0.878404i	−0.993369	+	0.114966i	$0.963324\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.13763e11	−	4.13763e11i	0.686471	−	0.686471i	−0.274979	−	0.961450i	$-0.588671\pi$
$227$	4.13763e11	−	4.13763e11i	0.686471	−	0.686471i	0.961450	+	0.274979i	$0.0886709\pi$
$228$		0			0
$229$		−	2.11849e11i		−	0.336395i	−0.985753	−	0.168197i	$-0.946205\pi$
$229$		−	2.11849e11i		−	0.336395i	0.985753	−	0.168197i	$-0.0537946\pi$
$230$		0			0
$231$	−8.55941e11			−1.30132
$232$		0			0
$233$	5.33034e11	+	5.33034e11i	0.776203	+	0.776203i	0.979183	−	0.202980i	$-0.0650625\pi$
$233$	5.33034e11	+	5.33034e11i	0.776203	+	0.776203i	−0.202980	+	0.979183i	$0.565063\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.24541e11	+	1.24541e11i	−0.166560	+	0.166560i
$238$		0			0
$239$		−	1.42513e12i		−	1.82753i	−0.406244	−	0.913765i	$-0.633162\pi$
$239$		−	1.42513e12i		−	1.82753i	0.406244	−	0.913765i	$-0.366838\pi$
$240$		0			0
$241$	−1.05869e12			−1.30221			−0.651107	−	0.758986i	$-0.725695\pi$
$241$	−1.05869e12			−1.30221			−0.651107	+	0.758986i	$0.725695\pi$
$242$		0			0
$243$	−3.84338e10	−	3.84338e10i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.40235e10	+	5.40235e10i	−0.0587622	+	0.0587622i
$248$		0			0
$249$		−	4.36788e11i		−	0.456324i
$250$		0			0
$251$	−1.21882e12			−1.22341			−0.611704	−	0.791087i	$-0.709516\pi$
$251$	−1.21882e12			−1.22341			−0.611704	+	0.791087i	$0.709516\pi$
$252$		0			0
$253$	1.02133e12	+	1.02133e12i	0.985287	+	0.985287i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.16474e11	−	2.16474e11i	0.193081	−	0.193081i	−0.603945	−	0.797026i	$-0.706405\pi$
$257$	2.16474e11	−	2.16474e11i	0.193081	−	0.193081i	0.797026	+	0.603945i	$0.206405\pi$
$258$		0			0
$259$		−	2.88718e12i		−	2.47728i
$260$		0			0
$261$	−4.89828e11			−0.404428
$262$		0			0
$263$	−4.22079e11	−	4.22079e11i	−0.335440	−	0.335440i	0.519208	−	0.854648i	$-0.326227\pi$
$263$	−4.22079e11	−	4.22079e11i	−0.335440	−	0.335440i	−0.854648	+	0.519208i	$0.826227\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	5.35637e11	−	5.35637e11i	0.394743	−	0.394743i
$268$		0			0
$269$		−	1.97700e12i		−	1.40361i	−0.712370	−	0.701804i	$-0.752378\pi$
$269$		−	1.97700e12i		−	1.40361i	0.712370	−	0.701804i	$-0.247622\pi$
$270$		0			0
$271$	−1.14114e12			−0.780718			−0.390359	−	0.920663i	$-0.627649\pi$
$271$	−1.14114e12			−0.780718			−0.390359	+	0.920663i	$0.627649\pi$
$272$		0			0
$273$	9.02958e10	+	9.02958e10i	0.0595462	+	0.0595462i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.80834e10	+	1.80834e10i	−0.0110887	+	0.0110887i	−0.712629	−	0.701541i	$-0.752496\pi$
$277$	−1.80834e10	+	1.80834e10i	−0.0110887	+	0.0110887i	0.701541	+	0.712629i	$0.252496\pi$
$278$		0			0
$279$			8.65988e11i			0.512260i
$280$		0			0
$281$	4.83399e11			0.275914			0.137957	−	0.990438i	$-0.455946\pi$
$281$	4.83399e11			0.275914			0.137957	+	0.990438i	$0.455946\pi$
$282$		0			0
$283$	−1.30550e12	−	1.30550e12i	−0.719192	−	0.719192i	0.249248	−	0.968440i	$-0.419817\pi$
$283$	−1.30550e12	−	1.30550e12i	−0.719192	−	0.719192i	−0.968440	+	0.249248i	$0.919817\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.00744e11	−	6.00744e11i	0.308517	−	0.308517i
$288$		0			0
$289$		−	5.03680e10i		−	0.0249842i
$290$		0			0
$291$	1.32173e12			0.633400
$292$		0			0
$293$	1.79363e11	+	1.79363e11i	0.0830606	+	0.0830606i	0.747416	−	0.664356i	$-0.231294\pi$
$293$	1.79363e11	+	1.79363e11i	0.0830606	+	0.0830606i	−0.664356	+	0.747416i	$0.731294\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.79082e11	−	4.79082e11i	0.207314	−	0.207314i
$298$		0			0
$299$		−	2.15486e11i		−	0.0901702i
$300$		0			0
$301$	−2.00287e12			−0.810626
$302$		0			0
$303$	−6.05477e11	−	6.05477e11i	−0.237074	−	0.237074i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.02370e12	−	2.02370e12i	0.742085	−	0.742085i	−0.230894	−	0.972979i	$-0.574165\pi$
$307$	2.02370e12	−	2.02370e12i	0.742085	−	0.742085i	0.972979	+	0.230894i	$0.0741650\pi$
$308$		0			0
$309$		−	1.19805e12i		−	0.425287i
$310$		0			0
$311$	−4.23387e11			−0.145524			−0.0727622	−	0.997349i	$-0.523181\pi$
$311$	−4.23387e11			−0.145524			−0.0727622	+	0.997349i	$0.523181\pi$
$312$		0			0
$313$	3.30038e12	+	3.30038e12i	1.09861	+	1.09861i	0.994574	+	0.104032i	$0.0331744\pi$
$313$	3.30038e12	+	3.30038e12i	1.09861	+	1.09861i	0.104032	+	0.994574i	$0.466826\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.57425e12	−	3.57425e12i	1.11658	−	1.11658i	0.124336	−	0.992240i	$-0.460320\pi$
$317$	3.57425e12	−	3.57425e12i	1.11658	−	1.11658i	0.992240	−	0.124336i	$-0.0396801\pi$
$318$		0			0
$319$		−	6.10577e12i		−	1.84836i
$320$		0			0
$321$	2.87487e12			0.843517
$322$		0			0
$323$	−2.12158e12	−	2.12158e12i	−0.603457	−	0.603457i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.54940e12	−	2.54940e12i	0.681865	−	0.681865i
$328$		0			0
$329$		−	5.49230e12i		−	1.42487i
$330$		0			0
$331$	−9.13628e11			−0.229948			−0.114974	−	0.993369i	$-0.536678\pi$
$331$	−9.13628e11			−0.229948			−0.114974	+	0.993369i	$0.536678\pi$
$332$		0			0
$333$	1.61600e12	+	1.61600e12i	0.394657	+	0.394657i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	3.53730e12	−	3.53730e12i	0.813808	−	0.813808i	−0.171395	−	0.985202i	$-0.554827\pi$
$337$	3.53730e12	−	3.53730e12i	0.813808	−	0.813808i	0.985202	+	0.171395i	$0.0548274\pi$
$338$		0			0
$339$		−	4.99121e12i		−	1.11483i
$340$		0			0
$341$	−1.07947e13			−2.34119
$342$		0			0
$343$	−9.38566e11	−	9.38566e11i	−0.197694	−	0.197694i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.02321e12	−	4.02321e12i	0.799697	−	0.799697i	−0.183351	−	0.983048i	$-0.558694\pi$
$347$	4.02321e12	−	4.02321e12i	0.799697	−	0.799697i	0.983048	+	0.183351i	$0.0586944\pi$
$348$		0			0
$349$			4.01641e12i			0.775730i	0.921716	+	0.387865i	$0.126787\pi$
$349$			4.01641e12i			0.775730i	−0.921716	+	0.387865i	$0.873213\pi$
$350$		0			0
$351$	−1.01080e11			−0.0189727
$352$		0			0
$353$	−4.80344e11	−	4.80344e11i	−0.0876353	−	0.0876353i	0.661930	−	0.749565i	$-0.269738\pi$
$353$	−4.80344e11	−	4.80344e11i	−0.0876353	−	0.0876353i	−0.749565	+	0.661930i	$0.769738\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.54604e12	+	3.54604e12i	−0.611509	+	0.611509i
$358$		0			0
$359$			1.16724e13i			1.95743i	0.205217	+	0.978716i	$0.434210\pi$
$359$			1.16724e13i			1.95743i	−0.205217	+	0.978716i	$0.565790\pi$
$360$		0			0
$361$	1.77453e12			0.289432
$362$		0			0
$363$	3.39872e12	+	3.39872e12i	0.539240	+	0.539240i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.48825e11	+	3.48825e11i	−0.0523935	+	0.0523935i	−0.732818	−	0.680425i	$-0.761795\pi$
$367$	−3.48825e11	+	3.48825e11i	−0.0523935	+	0.0523935i	0.680425	+	0.732818i	$0.261795\pi$
$368$		0			0
$369$			6.72490e11i			0.0983000i
$370$		0			0
$371$	−3.20107e12			−0.455434
$372$		0			0
$373$	3.19857e12	+	3.19857e12i	0.443008	+	0.443008i	0.893022	−	0.450013i	$-0.148581\pi$
$373$	3.19857e12	+	3.19857e12i	0.443008	+	0.443008i	−0.450013	+	0.893022i	$0.648581\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.44116e11	+	6.44116e11i	−0.0845780	+	0.0845780i
$378$		0			0
$379$		−	8.46898e12i		−	1.08302i	−0.840695	−	0.541508i	$-0.817853\pi$
$379$		−	8.46898e12i		−	1.08302i	0.840695	−	0.541508i	$-0.182147\pi$
$380$		0			0
$381$	−5.09275e12			−0.634348
$382$		0			0
$383$	7.15121e12	+	7.15121e12i	0.867732	+	0.867732i	0.992221	−	0.124489i	$-0.0397293\pi$
$383$	7.15121e12	+	7.15121e12i	0.867732	+	0.867732i	−0.124489	+	0.992221i	$0.539729\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.12104e12	−	1.12104e12i	0.129141	−	0.129141i
$388$		0			0
$389$		−	6.37482e12i		−	0.715682i	−0.933783	−	0.357841i	$-0.883513\pi$
$389$		−	6.37482e12i		−	0.715682i	0.933783	−	0.357841i	$-0.116487\pi$
$390$		0			0
$391$	8.46243e12			0.926001
$392$		0			0
$393$	−3.72225e12	−	3.72225e12i	−0.397048	−	0.397048i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.32306e12	+	2.32306e12i	−0.235563	+	0.235563i	−0.815010	−	0.579447i	$-0.803269\pi$
$397$	−2.32306e12	+	2.32306e12i	−0.235563	+	0.235563i	0.579447	+	0.815010i	$0.303269\pi$
$398$		0			0
$399$			7.28159e12i			0.720049i
$400$		0			0
$401$	−1.57234e13			−1.51644			−0.758219	−	0.652000i	$-0.773930\pi$
$401$	−1.57234e13			−1.51644			−0.758219	+	0.652000i	$0.773930\pi$
$402$		0			0
$403$	1.13876e12	+	1.13876e12i	0.107129	+	0.107129i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.01436e13	+	2.01436e13i	−1.80370	+	1.80370i
$408$		0			0
$409$			4.69349e12i			0.410090i	0.978753	+	0.205045i	$0.0657340\pi$
$409$			4.69349e12i			0.410090i	−0.978753	+	0.205045i	$0.934266\pi$
$410$		0			0
$411$	1.01128e12			0.0862307
$412$		0			0
$413$	2.64297e12	+	2.64297e12i	0.219959	+	0.219959i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.99122e11	+	1.99122e11i	−0.0157920	+	0.0157920i
$418$		0			0
$419$		−	5.55630e12i		−	0.430244i	−0.976587	−	0.215122i	$-0.930985\pi$
$419$		−	5.55630e12i		−	0.430244i	0.976587	−	0.215122i	$-0.0690150\pi$
$420$		0			0
$421$	5.57057e12			0.421201			0.210600	−	0.977572i	$-0.432458\pi$
$421$	5.57057e12			0.421201			0.210600	+	0.977572i	$0.432458\pi$
$422$		0			0
$423$	3.07412e12	+	3.07412e12i	0.226996	+	0.226996i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.78645e13	−	2.78645e13i	1.96296	−	1.96296i
$428$		0			0
$429$		−	1.25997e12i		−	0.0867110i
$430$		0			0
$431$	1.81802e13			1.22240			0.611199	−	0.791477i	$-0.290687\pi$
$431$	1.81802e13			1.22240			0.611199	+	0.791477i	$0.290687\pi$
$432$		0			0
$433$	−7.48843e12	−	7.48843e12i	−0.491984	−	0.491984i	0.416947	−	0.908931i	$-0.363100\pi$
$433$	−7.48843e12	−	7.48843e12i	−0.491984	−	0.491984i	−0.908931	+	0.416947i	$0.863100\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.68856e12	−	8.68856e12i	0.545181	−	0.545181i
$438$		0			0
$439$			1.55826e13i			0.955688i	0.878445	+	0.477844i	$0.158582\pi$
$439$			1.55826e13i			0.955688i	−0.878445	+	0.477844i	$0.841418\pi$
$440$		0			0
$441$	6.61062e12			0.396323
$442$		0			0
$443$	−1.09695e13	−	1.09695e13i	−0.642935	−	0.642935i	0.308341	−	0.951276i	$-0.400226\pi$
$443$	−1.09695e13	−	1.09695e13i	−0.642935	−	0.642935i	−0.951276	+	0.308341i	$0.900226\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	3.94535e12	−	3.94535e12i	0.221079	−	0.221079i
$448$		0			0
$449$		−	8.28951e12i		−	0.454252i	−0.973865	−	0.227126i	$-0.927067\pi$
$449$		−	8.28951e12i		−	0.454252i	0.973865	−	0.227126i	$-0.0729330\pi$
$450$		0			0
$451$	−8.38267e12			−0.449262
$452$		0			0
$453$	−9.84579e12	−	9.84579e12i	−0.516131	−	0.516131i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.58586e13	+	2.58586e13i	−1.29725	+	1.29725i	−0.367048	+	0.930202i	$0.619632\pi$
$457$	−2.58586e13	+	2.58586e13i	−1.29725	+	1.29725i	−0.930202	+	0.367048i	$0.880368\pi$
$458$		0			0
$459$		−	3.96954e12i		−	0.194839i
$460$		0			0
$461$	2.93741e13			1.41078			0.705392	−	0.708817i	$-0.250771\pi$
$461$	2.93741e13			1.41078			0.705392	+	0.708817i	$0.250771\pi$
$462$		0			0
$463$	−1.41383e13	−	1.41383e13i	−0.664494	−	0.664494i	0.291942	−	0.956436i	$-0.405699\pi$
$463$	−1.41383e13	−	1.41383e13i	−0.664494	−	0.664494i	−0.956436	+	0.291942i	$0.905699\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.42118e12	−	5.42118e12i	0.244067	−	0.244067i	−0.574463	−	0.818530i	$-0.694789\pi$
$467$	5.42118e12	−	5.42118e12i	0.244067	−	0.244067i	0.818530	+	0.574463i	$0.194789\pi$
$468$		0			0
$469$			3.19442e12i			0.140776i
$470$		0			0
$471$	−5.47672e12			−0.236274
$472$		0			0
$473$	1.39739e13	+	1.39739e13i	0.590216	+	0.590216i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.79168e12	−	1.79168e12i	0.0725553	−	0.0725553i
$478$		0			0
$479$			2.01084e13i			0.797442i	0.917072	+	0.398721i	$0.130546\pi$
$479$			2.01084e13i			0.797442i	−0.917072	+	0.398721i	$0.869454\pi$
$480$		0			0
$481$	4.25002e12			0.165069
$482$		0			0
$483$	−1.45222e13	−	1.45222e13i	−0.552455	−	0.552455i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.04347e13	+	3.04347e13i	−1.11103	+	1.11103i	−0.118015	+	0.993012i	$0.537653\pi$
$487$	−3.04347e13	+	3.04347e13i	−1.11103	+	1.11103i	−0.993012	+	0.118015i	$0.962347\pi$
$488$		0			0
$489$			2.67026e13i			0.955013i
$490$		0			0
$491$	2.96582e13			1.03929			0.519645	−	0.854382i	$-0.326064\pi$
$491$	2.96582e13			1.03929			0.519645	+	0.854382i	$0.326064\pi$
$492$		0			0
$493$	−2.52953e13	−	2.52953e13i	−0.868572	−	0.868572i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.86956e13	+	5.86956e13i	−1.93564	+	1.93564i
$498$		0			0
$499$			4.43963e13i			1.43497i	0.696572	+	0.717487i	$0.254708\pi$
$499$			4.43963e13i			1.43497i	−0.696572	+	0.717487i	$0.745292\pi$
$500$		0			0
$501$	2.22852e13			0.706039
$502$		0			0
$503$	2.95547e13	+	2.95547e13i	0.917881	+	0.917881i	0.996875	−	0.0789944i	$-0.0251709\pi$
$503$	2.95547e13	+	2.95547e13i	0.917881	+	0.917881i	−0.0789944	+	0.996875i	$0.525171\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.35432e13	−	1.35432e13i	0.404281	−	0.404281i
$508$		0			0
$509$		−	1.33159e13i		−	0.389747i	−0.980828	−	0.194873i	$-0.937570\pi$
$509$		−	1.33159e13i		−	0.389747i	0.980828	−	0.194873i	$-0.0624296\pi$
$510$		0			0
$511$	−2.16434e13			−0.621184
$512$		0			0
$513$	−4.07561e12	−	4.07561e12i	−0.114711	−	0.114711i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−3.83193e13	+	3.83193e13i	−1.03744	+	1.03744i
$518$		0			0
$519$		−	5.17090e12i		−	0.137319i
$520$		0			0
$521$	−1.57642e13			−0.410661			−0.205331	−	0.978693i	$-0.565827\pi$
$521$	−1.57642e13			−0.410661			−0.205331	+	0.978693i	$0.565827\pi$
$522$		0			0
$523$	1.20803e13	+	1.20803e13i	0.308723	+	0.308723i	0.844414	−	0.535691i	$-0.179949\pi$
$523$	1.20803e13	+	1.20803e13i	0.308723	+	0.308723i	−0.535691	+	0.844414i	$0.679949\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.47207e13	+	4.47207e13i	−1.10016	+	1.10016i
$528$		0			0
$529$		−	6.77005e12i		−	0.163423i
$530$		0			0
$531$	−2.95862e12			−0.0700836
$532$		0			0
$533$	8.84313e11	+	8.84313e11i	0.0205575	+	0.0205575i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.33568e11	+	4.33568e11i	−0.00970924	+	0.00970924i
$538$		0			0
$539$			8.24022e13i			1.81132i
$540$		0			0
$541$	5.08818e13			1.09793			0.548966	−	0.835844i	$-0.315021\pi$
$541$	5.08818e13			1.09793			0.548966	+	0.835844i	$0.315021\pi$
$542$		0			0
$543$	−1.95398e13	−	1.95398e13i	−0.413924	−	0.413924i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.49260e13	−	1.49260e13i	0.304794	−	0.304794i	−0.538092	−	0.842886i	$-0.680855\pi$
$547$	1.49260e13	−	1.49260e13i	0.304794	−	0.304794i	0.842886	+	0.538092i	$0.180855\pi$
$548$		0			0
$549$			3.11923e13i			0.625440i
$550$		0			0
$551$	−5.19425e13			−1.02274
$552$		0			0
$553$	2.20738e13	+	2.20738e13i	0.426827	+	0.426827i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.17195e12	+	1.17195e12i	−0.0218592	+	0.0218592i	−0.717952	−	0.696093i	$-0.754920\pi$
$557$	−1.17195e12	+	1.17195e12i	−0.0218592	+	0.0218592i	0.696093	+	0.717952i	$0.254920\pi$
$558$		0			0
$559$		−	2.94829e12i		−	0.0540146i
$560$		0			0
$561$	4.94808e13			0.890477
$562$		0			0
$563$	−5.14141e13	−	5.14141e13i	−0.908951	−	0.908951i	0.0872368	−	0.996188i	$-0.472196\pi$
$563$	−5.14141e13	−	5.14141e13i	−0.908951	−	0.908951i	−0.996188	+	0.0872368i	$0.972196\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−6.81205e12	+	6.81205e12i	−0.116242	+	0.116242i
$568$		0			0
$569$		−	3.04638e13i		−	0.510767i	−0.966840	−	0.255384i	$-0.917798\pi$
$569$		−	3.04638e13i		−	0.510767i	0.966840	−	0.255384i	$-0.0822018\pi$
$570$		0			0
$571$	7.28538e13			1.20025			0.600125	−	0.799906i	$-0.295117\pi$
$571$	7.28538e13			1.20025			0.600125	+	0.799906i	$0.295117\pi$
$572$		0			0
$573$	2.89272e13	+	2.89272e13i	0.468309	+	0.468309i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	7.24079e13	−	7.24079e13i	1.13216	−	1.13216i	0.142339	−	0.989818i	$-0.454538\pi$
$577$	7.24079e13	−	7.24079e13i	1.13216	−	1.13216i	0.989818	−	0.142339i	$-0.0454624\pi$
$578$		0			0
$579$		−	4.05226e13i		−	0.622736i
$580$		0			0
$581$	−7.74167e13			−1.16938
$582$		0			0
$583$	2.23336e13	+	2.23336e13i	0.331600	+	0.331600i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.23536e13	+	8.23536e13i	−1.18166	+	1.18166i	−0.202345	+	0.979314i	$0.564856\pi$
$587$	−8.23536e13	+	8.23536e13i	−1.18166	+	1.18166i	−0.979314	+	0.202345i	$0.935144\pi$
$588$		0			0
$589$			9.18314e13i			1.29543i
$590$		0			0
$591$	−5.32968e12			−0.0739203
$592$		0			0
$593$	5.89458e13	+	5.89458e13i	0.803858	+	0.803858i	0.983696	−	0.179839i	$-0.0575575\pi$
$593$	5.89458e13	+	5.89458e13i	0.803858	+	0.803858i	−0.179839	+	0.983696i	$0.557558\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.31441e13	+	1.31441e13i	−0.173325	+	0.173325i
$598$		0			0
$599$			7.95878e13i			1.03208i	0.856565	+	0.516039i	$0.172594\pi$
$599$			7.95878e13i			1.03208i	−0.856565	+	0.516039i	$0.827406\pi$
$600$		0			0
$601$	1.52648e14			1.94679			0.973396	−	0.229130i	$-0.0735882\pi$
$601$	1.52648e14			1.94679			0.973396	+	0.229130i	$0.0735882\pi$
$602$		0			0
$603$	−1.78796e12	−	1.78796e12i	−0.0224270	−	0.0224270i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−1.73177e13	+	1.73177e13i	−0.210158	+	0.210158i	−0.804335	−	0.594176i	$-0.797478\pi$
$607$	−1.73177e13	+	1.73177e13i	−0.210158	+	0.210158i	0.594176	+	0.804335i	$0.297478\pi$
$608$		0			0
$609$			8.68177e13i			1.03639i
$610$		0			0
$611$	8.08484e12			0.0949435
$612$		0			0
$613$	−7.17442e13	−	7.17442e13i	−0.828866	−	0.828866i	0.158494	−	0.987360i	$-0.449336\pi$
$613$	−7.17442e13	−	7.17442e13i	−0.828866	−	0.828866i	−0.987360	+	0.158494i	$0.949336\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.30842e13	−	3.30842e13i	0.369994	−	0.369994i	−0.497481	−	0.867475i	$-0.665742\pi$
$617$	3.30842e13	−	3.30842e13i	0.369994	−	0.369994i	0.867475	+	0.497481i	$0.165742\pi$
$618$		0			0
$619$			1.50831e14i			1.65973i	0.557965	+	0.829865i	$0.311582\pi$
$619$			1.50831e14i			1.65973i	−0.557965	+	0.829865i	$0.688418\pi$
$620$		0			0
$621$	1.62566e13			0.176024
$622$		0			0
$623$	−9.49369e13	−	9.49369e13i	−1.01157	−	1.01157i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	5.08030e13	−	5.08030e13i	0.524266	−	0.524266i
$628$		0			0
$629$			1.66904e14i			1.69517i
$630$		0			0
$631$	6.51439e13			0.651219			0.325609	−	0.945504i	$-0.394431\pi$
$631$	6.51439e13			0.651219			0.325609	+	0.945504i	$0.394431\pi$
$632$		0			0
$633$	3.59302e13	+	3.59302e13i	0.353542	+	0.353542i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	8.69286e12	−	8.69286e12i	0.0828830	−	0.0828830i
$638$		0			0
$639$		−	6.57055e13i		−	0.616733i
$640$		0			0
$641$	−8.33777e13			−0.770477			−0.385238	−	0.922817i	$-0.625881\pi$
$641$	−8.33777e13			−0.770477			−0.385238	+	0.922817i	$0.625881\pi$
$642$		0			0
$643$	−9.00080e13	−	9.00080e13i	−0.818891	−	0.818891i	0.167056	−	0.985947i	$-0.446574\pi$
$643$	−9.00080e13	−	9.00080e13i	−0.818891	−	0.818891i	−0.985947	+	0.167056i	$0.946574\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.21631e14	+	1.21631e14i	−1.07281	+	1.07281i	−0.0756761	+	0.997132i	$0.524111\pi$
$647$	−1.21631e14	+	1.21631e14i	−1.07281	+	1.07281i	−0.997132	+	0.0756761i	$0.975889\pi$
$648$		0			0
$649$		−	3.68796e13i		−	0.320304i
$650$		0			0
$651$	1.53489e14			1.31272
$652$		0			0
$653$	1.39661e14	+	1.39661e14i	1.17628	+	1.17628i	0.980685	+	0.195595i	$0.0626639\pi$
$653$	1.39661e14	+	1.39661e14i	1.17628	+	1.17628i	0.195595	+	0.980685i	$0.437336\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.21141e13	−	1.21141e13i	0.0989610	−	0.0989610i
$658$		0			0
$659$		−	1.95289e14i		−	1.57127i	−0.618693	−	0.785633i	$-0.712337\pi$
$659$		−	1.95289e14i		−	1.57127i	0.618693	−	0.785633i	$-0.287663\pi$
$660$		0			0
$661$	8.92478e12			0.0707278			0.0353639	−	0.999375i	$-0.488741\pi$
$661$	8.92478e12			0.0707278			0.0353639	+	0.999375i	$0.488741\pi$
$662$		0			0
$663$	−5.21988e12	−	5.21988e12i	−0.0407468	−	0.0407468i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.03593e14	−	1.03593e14i	0.784694	−	0.784694i
$668$		0			0
$669$		−	9.61124e13i		−	0.717214i
$670$		0			0
$671$	−3.88816e14			−2.85846
$672$		0			0
$673$	3.20625e13	+	3.20625e13i	0.232232	+	0.232232i	0.813624	−	0.581392i	$-0.197492\pi$
$673$	3.20625e13	+	3.20625e13i	0.232232	+	0.232232i	−0.581392	+	0.813624i	$0.697492\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.96987e13	+	4.96987e13i	−0.349463	+	0.349463i	−0.859910	−	0.510446i	$-0.829480\pi$
$677$	−4.96987e13	+	4.96987e13i	−0.349463	+	0.349463i	0.510446	+	0.859910i	$0.329480\pi$
$678$		0			0
$679$		−	2.34265e14i		−	1.62315i
$680$		0			0
$681$	8.20942e13			0.560502
$682$		0			0
$683$	2.01777e14	+	2.01777e14i	1.35759	+	1.35759i	0.876883	+	0.480704i	$0.159619\pi$
$683$	2.01777e14	+	2.01777e14i	1.35759	+	1.35759i	0.480704	+	0.876883i	$0.340381\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	2.10163e13	−	2.10163e13i	0.137333	−	0.137333i
$688$		0			0
$689$		−	4.71207e12i		−	0.0303470i
$690$		0			0
$691$	−6.96254e13			−0.441955			−0.220977	−	0.975279i	$-0.570925\pi$
$691$	−6.96254e13			−0.441955			−0.220977	+	0.975279i	$0.570925\pi$
$692$		0			0
$693$	−8.49131e13	−	8.49131e13i	−0.531261	−	0.531261i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−3.47282e13	+	3.47282e13i	−0.211115	+	0.211115i
$698$		0			0
$699$			1.05759e14i			0.633767i
$700$		0			0
$701$	−1.15316e14			−0.681242			−0.340621	−	0.940201i	$-0.610637\pi$
$701$	−1.15316e14			−0.681242			−0.340621	+	0.940201i	$0.610637\pi$
$702$		0			0
$703$	1.71364e14	+	1.71364e14i	0.998029	+	0.998029i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.07315e14	+	1.07315e14i	−0.607526	+	0.607526i
$708$		0			0
$709$		−	5.88271e13i		−	0.328357i	−0.986431	−	0.164178i	$-0.947503\pi$
$709$		−	5.88271e13i		−	0.328357i	0.986431	−	0.164178i	$-0.0524973\pi$
$710$		0			0
$711$	−2.47101e13			−0.135996
$712$		0			0
$713$	−1.83146e14	−	1.83146e14i	−0.993917	−	0.993917i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.41379e14	−	1.41379e14i	0.746086	−	0.746086i
$718$		0			0
$719$		−	1.84801e14i		−	0.961745i	−0.876790	−	0.480873i	$-0.840320\pi$
$719$		−	1.84801e14i		−	0.961745i	0.876790	−	0.480873i	$-0.159680\pi$
$720$		0			0
$721$	−2.12343e14			−1.08984
$722$		0			0
$723$	−1.05026e14	−	1.05026e14i	−0.531627	−	0.531627i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−3.34341e13	+	3.34341e13i	−0.164633	+	0.164633i	−0.784616	−	0.619983i	$-0.787140\pi$
$727$	−3.34341e13	+	3.34341e13i	−0.164633	+	0.164633i	0.619983	+	0.784616i	$0.287140\pi$
$728$		0			0
$729$		−	7.62560e12i		−	0.0370370i
$730$		0			0
$731$	1.15783e14			0.554702
$732$		0			0
$733$	1.34429e13	+	1.34429e13i	0.0635291	+	0.0635291i	0.738157	−	0.674628i	$-0.235696\pi$
$733$	1.34429e13	+	1.34429e13i	0.0635291	+	0.0635291i	−0.674628	+	0.738157i	$0.735696\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.22872e13	−	2.22872e13i	0.102499	−	0.102499i
$738$		0			0
$739$			9.19414e12i			0.0417147i	0.999782	+	0.0208573i	$0.00663958\pi$
$739$			9.19414e12i			0.0417147i	−0.999782	+	0.0208573i	$0.993360\pi$
$740$		0			0
$741$	−1.07187e13			−0.0479791
$742$		0			0
$743$	3.45280e13	+	3.45280e13i	0.152485	+	0.152485i	0.779227	−	0.626742i	$-0.215612\pi$
$743$	3.45280e13	+	3.45280e13i	0.152485	+	0.152485i	−0.626742	+	0.779227i	$0.715612\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.33312e13	−	4.33312e13i	0.186294	−	0.186294i
$748$		0			0
$749$		−	5.09546e14i		−	2.16159i
$750$		0			0
$751$	−2.78104e14			−1.16415			−0.582073	−	0.813136i	$-0.697758\pi$
$751$	−2.78104e14			−1.16415			−0.582073	+	0.813136i	$0.697758\pi$
$752$		0			0
$753$	−1.20912e14	−	1.20912e14i	−0.499454	−	0.499454i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	2.20330e14	−	2.20330e14i	0.886327	−	0.886327i	−0.107841	−	0.994168i	$-0.534394\pi$
$757$	2.20330e14	−	2.20330e14i	0.886327	−	0.886327i	0.994168	+	0.107841i	$0.0343939\pi$
$758$		0			0
$759$			2.02640e14i			0.804483i
$760$		0			0
$761$	4.15151e14			1.62661			0.813303	−	0.581840i	$-0.197667\pi$
$761$	4.15151e14			1.62661			0.813303	+	0.581840i	$0.197667\pi$
$762$		0			0
$763$	−4.51858e14	−	4.51858e14i	−1.74735	−	1.74735i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.89054e12	+	3.89054e12i	−0.0146566	+	0.0146566i
$768$		0			0
$769$		−	3.28902e14i		−	1.22302i	−0.791235	−	0.611512i	$-0.790562\pi$
$769$		−	3.28902e14i		−	1.22302i	0.791235	−	0.611512i	$-0.209438\pi$
$770$		0			0
$771$	4.29503e13			0.157650
$772$		0			0
$773$	3.53823e14	+	3.53823e14i	1.28200	+	1.28200i	0.939527	+	0.342475i	$0.111265\pi$
$773$	3.53823e14	+	3.53823e14i	1.28200	+	1.28200i	0.342475	+	0.939527i	$0.388735\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	2.86421e14	−	2.86421e14i	1.01135	−	1.01135i
$778$		0			0
$779$			7.13124e13i			0.248587i
$780$		0			0
$781$	8.19028e14			2.81867
$782$		0			0
$783$	−4.85931e13	−	4.85931e13i	−0.165107	−	0.165107i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	3.42715e14	−	3.42715e14i	1.13517	−	1.13517i	0.145862	−	0.989305i	$-0.453404\pi$
$787$	3.42715e14	−	3.42715e14i	1.13517	−	1.13517i	0.989305	−	0.145862i	$-0.0465955\pi$
$788$		0			0
$789$		−	8.37441e13i		−	0.273885i
$790$		0			0
$791$	−8.84648e14			−2.85685
$792$		0			0
$793$	4.10174e13	+	4.10174e13i	0.130798	+	0.130798i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.34436e14	+	3.34436e14i	−1.03997	+	1.03997i	−0.0408030	+	0.999167i	$0.512992\pi$
$797$	−3.34436e14	+	3.34436e14i	−1.03997	+	1.03997i	−0.999167	+	0.0408030i	$0.987008\pi$
$798$		0			0
$799$			3.17503e14i			0.975021i
$800$		0			0
$801$	1.06275e14			0.322306
$802$		0			0
$803$	1.51004e14	+	1.51004e14i	0.452283	+	0.452283i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.96127e14	−	1.96127e14i	0.573020	−	0.573020i
$808$		0			0
$809$		−	4.58044e14i		−	1.32180i	−0.750475	−	0.660898i	$-0.770175\pi$
$809$		−	4.58044e14i		−	1.32180i	0.750475	−	0.660898i	$-0.229825\pi$
$810$		0			0
$811$	−2.39895e14			−0.683780			−0.341890	−	0.939740i	$-0.611067\pi$
$811$	−2.39895e14			−0.683780			−0.341890	+	0.939740i	$0.611067\pi$
$812$		0			0
$813$	−1.13206e14	−	1.13206e14i	−0.318727	−	0.318727i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.18877e14	−	1.18877e14i	0.326579	−	0.326579i
$818$		0			0
$819$			1.79155e13i			0.0486193i
$820$		0			0
$821$	−4.01069e14			−1.07523			−0.537617	−	0.843189i	$-0.680675\pi$
$821$	−4.01069e14			−1.07523			−0.537617	+	0.843189i	$0.680675\pi$
$822$		0			0
$823$	−1.07810e14	−	1.07810e14i	−0.285534	−	0.285534i	0.549777	−	0.835311i	$-0.314713\pi$
$823$	−1.07810e14	−	1.07810e14i	−0.285534	−	0.285534i	−0.835311	+	0.549777i	$0.814713\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.85157e14	−	2.85157e14i	0.737150	−	0.737150i	−0.234876	−	0.972025i	$-0.575468\pi$
$827$	2.85157e14	−	2.85157e14i	0.737150	−	0.737150i	0.972025	+	0.234876i	$0.0754683\pi$
$828$		0			0
$829$		−	4.81396e14i		−	1.22950i	−0.788720	−	0.614752i	$-0.789256\pi$
$829$		−	4.81396e14i		−	1.22950i	0.788720	−	0.614752i	$-0.210744\pi$
$830$		0			0
$831$	−3.58790e12			−0.00905388
$832$		0			0
$833$	3.41381e14	+	3.41381e14i	0.851165	+	0.851165i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.59097e13	+	8.59097e13i	−0.209129	+	0.209129i
$838$		0			0
$839$		−	6.74082e14i		−	1.62145i	−0.585430	−	0.810723i	$-0.699074\pi$
$839$		−	6.74082e14i		−	1.62145i	0.585430	−	0.810723i	$-0.300926\pi$
$840$		0			0
$841$	−1.98598e14			−0.472058
$842$		0			0
$843$	4.79553e13	+	4.79553e13i	0.112641	+	0.112641i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	6.02393e14	−	6.02393e14i	1.38186	−	1.38186i
$848$		0			0
$849$		−	2.59023e14i		−	0.587218i
$850$		0			0
$851$	−6.83528e14			−1.53147
$852$		0			0
$853$	2.47427e13	+	2.47427e13i	0.0547900	+	0.0547900i	0.733971	−	0.679181i	$-0.237665\pi$
$853$	2.47427e13	+	2.47427e13i	0.0547900	+	0.0547900i	−0.679181	+	0.733971i	$0.737665\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.73644e14	+	4.73644e14i	−1.02458	+	1.02458i	−0.0248941	+	0.999690i	$0.507925\pi$
$857$	−4.73644e14	+	4.73644e14i	−1.02458	+	1.02458i	−0.999690	+	0.0248941i	$0.992075\pi$
$858$		0			0
$859$		−	9.26066e13i		−	0.198005i	−0.995087	−	0.0990025i	$-0.968435\pi$
$859$		−	9.26066e13i		−	0.198005i	0.995087	−	0.0990025i	$-0.0315652\pi$
$860$		0			0
$861$	1.19193e14			0.251903
$862$		0			0
$863$	5.31608e14	+	5.31608e14i	1.11055	+	1.11055i	0.993076	+	0.117473i	$0.0374795\pi$
$863$	5.31608e14	+	5.31608e14i	1.11055	+	1.11055i	0.117473	+	0.993076i	$0.462521\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	4.99672e12	−	4.99672e12i	0.0101998	−	0.0101998i
$868$		0			0
$869$		−	3.08014e14i		−	0.621544i
$870$		0			0
$871$	−4.70228e12			−0.00938033
$872$		0			0
$873$	1.31122e14	+	1.31122e14i	0.258585	+	0.258585i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.18639e14	−	7.18639e14i	1.38520	−	1.38520i	0.550107	−	0.835094i	$-0.314587\pi$
$877$	7.18639e14	−	7.18639e14i	1.38520	−	1.38520i	0.835094	−	0.550107i	$-0.185413\pi$
$878$		0			0
$879$			3.55872e13i			0.0678187i
$880$		0			0
$881$	−2.44985e14			−0.461593			−0.230797	−	0.973002i	$-0.574133\pi$
$881$	−2.44985e14			−0.461593			−0.230797	+	0.973002i	$0.574133\pi$
$882$		0			0
$883$	−2.71238e14	−	2.71238e14i	−0.505297	−	0.505297i	0.407782	−	0.913079i	$-0.366302\pi$
$883$	−2.71238e14	−	2.71238e14i	−0.505297	−	0.505297i	−0.913079	+	0.407782i	$0.866302\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.10781e14	+	2.10781e14i	−0.383895	+	0.383895i	−0.872503	−	0.488608i	$-0.837505\pi$
$887$	−2.10781e14	+	2.10781e14i	−0.383895	+	0.383895i	0.488608	+	0.872503i	$0.337505\pi$
$888$		0			0
$889$			9.02644e14i			1.62558i
$890$		0			0
$891$	9.50541e13			0.169271
$892$		0			0
$893$	3.25987e14	+	3.25987e14i	0.574041	+	0.574041i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.13771e13	−	2.13771e13i	0.0368118	−	0.0368118i
$898$		0			0
$899$			1.09490e15i			1.86455i
$900$		0			0
$901$	1.85050e14			0.311648
$902$		0			0
$903$	−1.98694e14	−	1.98694e14i	−0.330937	−	0.330937i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−6.15726e14	+	6.15726e14i	−1.00312	+	1.00312i	−0.00312037	+	0.999995i	$0.500993\pi$
$907$	−6.15726e14	+	6.15726e14i	−1.00312	+	1.00312i	−0.999995	+	0.00312037i	$0.999007\pi$
$908$		0			0
$909$		−	1.20132e14i		−	0.193570i
$910$		0			0
$911$	−1.02185e15			−1.62853			−0.814267	−	0.580490i	$-0.802861\pi$
$911$	−1.02185e15			−1.62853			−0.814267	+	0.580490i	$0.802861\pi$
$912$		0			0
$913$	5.40129e14	+	5.40129e14i	0.851420	+	0.851420i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.59736e14	+	6.59736e14i	−1.01747	+	1.01747i
$918$		0			0
$919$		−	1.05732e15i		−	1.61298i	−0.591249	−	0.806489i	$-0.701365\pi$
$919$		−	1.05732e15i		−	1.61298i	0.591249	−	0.806489i	$-0.298635\pi$
$920$		0			0
$921$	4.01519e14			0.605910
$922$		0			0
$923$	−8.64017e13	−	8.64017e13i	−0.128977	−	0.128977i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.18852e14	−	1.18852e14i	0.173623	−	0.173623i
$928$		0			0
$929$			2.32216e14i			0.335594i	0.985822	+	0.167797i	$0.0536653\pi$
$929$			2.32216e14i			0.335594i	−0.985822	+	0.167797i	$0.946335\pi$
$930$		0			0
$931$	7.01006e14			1.00224
$932$		0			0
$933$	−4.20019e13	−	4.20019e13i	−0.0594101	−	0.0594101i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	4.15284e14	−	4.15284e14i	0.574973	−	0.574973i	−0.358541	−	0.933514i	$-0.616726\pi$
$937$	4.15284e14	−	4.15284e14i	0.574973	−	0.574973i	0.933514	+	0.358541i	$0.116726\pi$
$938$		0			0
$939$			6.54823e14i			0.897008i
$940$		0			0
$941$	−6.25302e14			−0.847504			−0.423752	−	0.905778i	$-0.639287\pi$
$941$	−6.25302e14			−0.847504			−0.423752	+	0.905778i	$0.639287\pi$
$942$		0			0
$943$	−1.42223e14	−	1.42223e14i	−0.190727	−	0.190727i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.21564e14	−	2.21564e14i	0.290903	−	0.290903i	−0.546534	−	0.837437i	$-0.684053\pi$
$947$	2.21564e14	−	2.21564e14i	0.290903	−	0.290903i	0.837437	+	0.546534i	$0.184053\pi$
$948$		0			0
$949$		−	3.18597e13i		−	0.0413914i
$950$		0			0
$951$	7.09162e14			0.911681
$952$		0			0
$953$	−7.17069e14	−	7.17069e14i	−0.912213	−	0.912213i	0.0842326	−	0.996446i	$-0.473156\pi$
$953$	−7.17069e14	−	7.17069e14i	−0.912213	−	0.912213i	−0.996446	+	0.0842326i	$0.973156\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	6.05719e14	−	6.05719e14i	0.754591	−	0.754591i
$958$		0			0
$959$		−	1.79240e14i		−	0.220975i
$960$		0			0
$961$	1.11608e15			1.36170
$962$		0			0
$963$	2.85200e14	+	2.85200e14i	0.344364	+	0.344364i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−2.11433e14	+	2.11433e14i	−0.250058	+	0.250058i	−0.820994	−	0.570936i	$-0.806580\pi$
$967$	−2.11433e14	+	2.11433e14i	−0.250058	+	0.250058i	0.570936	+	0.820994i	$0.306580\pi$
$968$		0			0
$969$		−	4.20939e14i		−	0.492721i
$970$		0			0
$971$	−1.45574e15			−1.68651			−0.843255	−	0.537514i	$-0.819363\pi$
$971$	−1.45574e15			−1.68651			−0.843255	+	0.537514i	$0.819363\pi$
$972$		0			0
$973$	3.52925e13	+	3.52925e13i	0.0404687	+	0.0404687i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.31622e14	+	3.31622e14i	−0.372538	+	0.372538i	−0.868401	−	0.495863i	$-0.834852\pi$
$977$	−3.31622e14	+	3.31622e14i	−0.372538	+	0.372538i	0.495863	+	0.868401i	$0.334852\pi$
$978$		0			0
$979$			1.32473e15i			1.47304i
$980$		0			0
$981$	5.05822e14			0.556741
$982$		0			0
$983$	−9.11608e14	−	9.11608e14i	−0.993209	−	0.993209i	0.00676795	−	0.999977i	$-0.497846\pi$
$983$	−9.11608e14	−	9.11608e14i	−0.993209	−	0.993209i	−0.999977	+	0.00676795i	$0.997846\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	5.44860e14	−	5.44860e14i	0.581700	−	0.581700i
$988$		0			0
$989$			4.74171e14i			0.501134i
$990$		0			0
$991$	7.69307e14			0.804881			0.402440	−	0.915446i	$-0.368162\pi$
$991$	7.69307e14			0.804881			0.402440	+	0.915446i	$0.368162\pi$
$992$		0			0
$993$	−9.06358e13	−	9.06358e13i	−0.0938758	−	0.0938758i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.07674e14	−	1.07674e14i	0.109304	−	0.109304i	−0.650340	−	0.759644i	$-0.725373\pi$
$997$	1.07674e14	−	1.07674e14i	0.109304	−	0.109304i	0.759644	+	0.650340i	$0.225373\pi$
$998$		0			0
$999$			3.20628e14i			0.322236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.11.k.c.193.8	yes	16
5.2	odd	4	inner	300.11.k.c.157.8	yes	16
5.3	odd	4	inner	300.11.k.c.157.1	✓	16
5.4	even	2	inner	300.11.k.c.193.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.11.k.c.157.1	✓	16	5.3	odd	4	inner
300.11.k.c.157.8	yes	16	5.2	odd	4	inner
300.11.k.c.193.1	yes	16	5.4	even	2	inner
300.11.k.c.193.8	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	300.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(99.2043 + 99.2043i) q^{3} +(17583.1 - 17583.1i) q^{7} +19683.0i q^{9} +O(q^{10})\)	\(q+(99.2043 + 99.2043i) q^{3} +(17583.1 - 17583.1i) q^{7} +19683.0i q^{9} -245351. q^{11} +(25882.8 + 25882.8i) q^{13} +(-1.01646e6 + 1.01646e6i) q^{17} +2.08723e6i q^{19} +3.48864e6 q^{21} +(-4.16272e6 - 4.16272e6i) q^{23} +(-1.95264e6 + 1.95264e6i) q^{27} +2.48858e7i q^{29} +4.39967e7 q^{31} +(-2.43399e7 - 2.43399e7i) q^{33} +(8.21011e7 - 8.21011e7i) q^{37} +5.13538e6i q^{39} +3.41660e7 q^{41} +(-5.69545e7 - 5.69545e7i) q^{43} +(1.56181e8 - 1.56181e8i) q^{47} -3.35854e8i q^{49} -2.01674e8 q^{51} +(-9.10269e7 - 9.10269e7i) q^{53} +(-2.07062e8 + 2.07062e8i) q^{57} +1.50313e8i q^{59} +1.58473e9 q^{61} +(3.46088e8 + 3.46088e8i) q^{63} +(-9.08379e7 + 9.08379e7i) q^{67} -8.25920e8i q^{69} -3.33819e9 q^{71} +(-6.15460e8 - 6.15460e8i) q^{73} +(-4.31403e9 + 4.31403e9i) q^{77} +1.25540e9i q^{79} -3.87420e8 q^{81} +(-2.20145e9 - 2.20145e9i) q^{83} +(-2.46878e9 + 2.46878e9i) q^{87} -5.39933e9i q^{89} +9.10200e8 q^{91} +(4.36467e9 + 4.36467e9i) q^{93} +(6.66166e9 - 6.66166e9i) q^{97} -4.82925e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 331104 q^{11} + 555984 q^{21} - 140804816 q^{31} + 29553600 q^{41} + 471062304 q^{51} + 3576862832 q^{61} + 1853192640 q^{71} - 6198727824 q^{81} + 7033272240 q^{91}+O(q^{100}) \) 16 * q - 331104 * q^11 + 555984 * q^21 - 140804816 * q^31 + 29553600 * q^41 + 471062304 * q^51 + 3576862832 * q^61 + 1853192640 * q^71 - 6198727824 * q^81 + 7033272240 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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