LMFDB - Embedded newform 300.11.k.c.193.3

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			193.3
Root			$-97.2366 + 97.2366i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.11.k.c.157.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-99.2043 - 99.2043i) q^{3} +(6761.61 - 6761.61i) q^{7} +19683.0i q^{9} +O(q^{10})$	$q+(-99.2043 - 99.2043i) q^{3} +(6761.61 - 6761.61i) q^{7} +19683.0i q^{9} -23043.7 q^{11} +(417304. + 417304. i) q^{13} +(-1.39626e6 + 1.39626e6i) q^{17} +4.30952e6i q^{19} -1.34156e6 q^{21} +(-7.67251e6 - 7.67251e6i) q^{23} +(1.95264e6 - 1.95264e6i) q^{27} -3.32956e6i q^{29} -1.16484e7 q^{31} +(2.28603e6 + 2.28603e6i) q^{33} +(8.35739e7 - 8.35739e7i) q^{37} -8.27967e7i q^{39} -1.04533e8 q^{41} +(1.74002e8 + 1.74002e8i) q^{43} +(-1.83813e8 + 1.83813e8i) q^{47} +1.91037e8i q^{49} +2.77030e8 q^{51} +(-4.56769e8 - 4.56769e8i) q^{53} +(4.27523e8 - 4.27523e8i) q^{57} -9.95847e8i q^{59} -2.16284e8 q^{61} +(1.33089e8 + 1.33089e8i) q^{63} +(-2.33426e8 + 2.33426e8i) q^{67} +1.52229e9i q^{69} +6.18236e8 q^{71} +(7.26897e8 + 7.26897e8i) q^{73} +(-1.55812e8 + 1.55812e8i) q^{77} -1.14188e9i q^{79} -3.87420e8 q^{81} +(4.89705e9 + 4.89705e9i) q^{83} +(-3.30307e8 + 3.30307e8i) q^{87} -8.94942e9i q^{89} +5.64329e9 q^{91} +(1.15557e9 + 1.15557e9i) q^{93} +(3.32848e9 - 3.32848e9i) q^{97} -4.53568e8i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	6761.61	−	6761.61i	0.402309	−	0.402309i	−0.476737	−	0.879046i	$-0.658181\pi$
$7$	6761.61	−	6761.61i	0.402309	−	0.402309i	0.879046	+	0.476737i	$0.158181\pi$
$8$		0			0
$9$			19683.0i			0.333333i
$10$		0			0
$11$	−23043.7			−0.143083			−0.0715415	−	0.997438i	$-0.522792\pi$
$11$	−23043.7			−0.143083			−0.0715415	+	0.997438i	$0.522792\pi$
$12$		0			0
$13$	417304.	+	417304.i	1.12392	+	1.12392i	0.991146	+	0.132774i	$0.0423884\pi$
$13$	417304.	+	417304.i	1.12392	+	1.12392i	0.132774	+	0.991146i	$0.457612\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.39626e6	+	1.39626e6i	−0.983379	+	0.983379i	−0.999864	−	0.0164852i	$-0.994752\pi$
$17$	−1.39626e6	+	1.39626e6i	−0.983379	+	0.983379i	0.0164852	+	0.999864i	$0.494752\pi$
$18$		0			0
$19$			4.30952e6i			1.74045i	0.492656	+	0.870224i	$0.336026\pi$
$19$			4.30952e6i			1.74045i	−0.492656	+	0.870224i	$0.663974\pi$
$20$		0			0
$21$	−1.34156e6			−0.328484
$22$		0			0
$23$	−7.67251e6	−	7.67251e6i	−1.19206	−	1.19206i	−0.976488	−	0.215573i	$-0.930838\pi$
$23$	−7.67251e6	−	7.67251e6i	−1.19206	−	1.19206i	−0.215573	−	0.976488i	$-0.569162\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.95264e6	−	1.95264e6i	0.136083	−	0.136083i
$28$		0			0
$29$		−	3.32956e6i		−	0.162329i	−0.996701	−	0.0811647i	$-0.974136\pi$
$29$		−	3.32956e6i		−	0.162329i	0.996701	−	0.0811647i	$-0.0258640\pi$
$30$		0			0
$31$	−1.16484e7			−0.406872			−0.203436	−	0.979088i	$-0.565211\pi$
$31$	−1.16484e7			−0.406872			−0.203436	+	0.979088i	$0.565211\pi$
$32$		0			0
$33$	2.28603e6	+	2.28603e6i	0.0584134	+	0.0584134i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.35739e7	−	8.35739e7i	1.20521	−	1.20521i	0.232646	−	0.972561i	$-0.425262\pi$
$37$	8.35739e7	−	8.35739e7i	1.20521	−	1.20521i	0.972561	−	0.232646i	$-0.0747383\pi$
$38$		0			0
$39$		−	8.27967e7i		−	0.917677i
$40$		0			0
$41$	−1.04533e8			−0.902263			−0.451132	−	0.892457i	$-0.648980\pi$
$41$	−1.04533e8			−0.902263			−0.451132	+	0.892457i	$0.648980\pi$
$42$		0			0
$43$	1.74002e8	+	1.74002e8i	1.18362	+	1.18362i	0.978800	+	0.204819i	$0.0656605\pi$
$43$	1.74002e8	+	1.74002e8i	1.18362	+	1.18362i	0.204819	+	0.978800i	$0.434339\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.83813e8	+	1.83813e8i	−0.801470	+	0.801470i	−0.983325	−	0.181855i	$-0.941790\pi$
$47$	−1.83813e8	+	1.83813e8i	−0.801470	+	0.801470i	0.181855	+	0.983325i	$0.441790\pi$
$48$		0			0
$49$			1.91037e8i			0.676295i
$50$		0			0
$51$	2.77030e8			0.802925
$52$		0			0
$53$	−4.56769e8	−	4.56769e8i	−1.09224	−	1.09224i	−0.995289	−	0.0969476i	$-0.969092\pi$
$53$	−4.56769e8	−	4.56769e8i	−1.09224	−	1.09224i	−0.0969476	−	0.995289i	$-0.530908\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.27523e8	−	4.27523e8i	0.710535	−	0.710535i
$58$		0			0
$59$		−	9.95847e8i		−	1.39294i	−0.717586	−	0.696470i	$-0.754753\pi$
$59$		−	9.95847e8i		−	1.39294i	0.717586	−	0.696470i	$-0.245247\pi$
$60$		0			0
$61$	−2.16284e8			−0.256080			−0.128040	−	0.991769i	$-0.540869\pi$
$61$	−2.16284e8			−0.256080			−0.128040	+	0.991769i	$0.540869\pi$
$62$		0			0
$63$	1.33089e8	+	1.33089e8i	0.134103	+	0.134103i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.33426e8	+	2.33426e8i	−0.172892	+	0.172892i	−0.788249	−	0.615357i	$-0.789012\pi$
$67$	−2.33426e8	+	2.33426e8i	−0.172892	+	0.172892i	0.615357	+	0.788249i	$0.289012\pi$
$68$		0			0
$69$			1.52229e9i			0.973313i
$70$		0			0
$71$	6.18236e8			0.342659			0.171330	−	0.985214i	$-0.445194\pi$
$71$	6.18236e8			0.342659			0.171330	+	0.985214i	$0.445194\pi$
$72$		0			0
$73$	7.26897e8	+	7.26897e8i	0.350638	+	0.350638i	0.860347	−	0.509709i	$-0.170247\pi$
$73$	7.26897e8	+	7.26897e8i	0.350638	+	0.350638i	−0.509709	+	0.860347i	$0.670247\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.55812e8	+	1.55812e8i	−0.0575636	+	0.0575636i
$78$		0			0
$79$		−	1.14188e9i		−	0.371095i	−0.982635	−	0.185547i	$-0.940594\pi$
$79$		−	1.14188e9i		−	0.371095i	0.982635	−	0.185547i	$-0.0594058\pi$
$80$		0			0
$81$	−3.87420e8			−0.111111
$82$		0			0
$83$	4.89705e9	+	4.89705e9i	1.24321	+	1.24321i	0.958662	+	0.284547i	$0.0918433\pi$
$83$	4.89705e9	+	4.89705e9i	1.24321	+	1.24321i	0.284547	+	0.958662i	$0.408157\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.30307e8	+	3.30307e8i	−0.0662707	+	0.0662707i
$88$		0			0
$89$		−	8.94942e9i		−	1.60267i	−0.598214	−	0.801336i	$-0.704123\pi$
$89$		−	8.94942e9i		−	1.60267i	0.598214	−	0.801336i	$-0.295877\pi$
$90$		0			0
$91$	5.64329e9			0.904326
$92$		0			0
$93$	1.15557e9	+	1.15557e9i	0.166105	+	0.166105i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.32848e9	−	3.32848e9i	0.387604	−	0.387604i	−0.486228	−	0.873832i	$-0.661628\pi$
$97$	3.32848e9	−	3.32848e9i	0.387604	−	0.387604i	0.873832	+	0.486228i	$0.161628\pi$
$98$		0			0
$99$		−	4.53568e8i		−	0.0476943i
$100$		0			0
$101$	−2.14978e9			−0.204544			−0.102272	−	0.994756i	$-0.532611\pi$
$101$	−2.14978e9			−0.204544			−0.102272	+	0.994756i	$0.532611\pi$
$102$		0			0
$103$	−2.01953e8	−	2.01953e8i	−0.0174207	−	0.0174207i	0.698343	−	0.715763i	$-0.253921\pi$
$103$	−2.01953e8	−	2.01953e8i	−0.0174207	−	0.0174207i	−0.715763	+	0.698343i	$0.753921\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.29781e9	−	7.29781e9i	0.520324	−	0.520324i	−0.397345	−	0.917669i	$-0.630069\pi$
$107$	7.29781e9	−	7.29781e9i	0.520324	−	0.520324i	0.917669	+	0.397345i	$0.130069\pi$
$108$		0			0
$109$		−	3.76191e9i		−	0.244498i	−0.992499	−	0.122249i	$-0.960989\pi$
$109$		−	3.76191e9i		−	0.244498i	0.992499	−	0.122249i	$-0.0390107\pi$
$110$		0			0
$111$	−1.65818e10			−0.984048
$112$		0			0
$113$	−1.54184e10	−	1.54184e10i	−0.836851	−	0.836851i	0.151592	−	0.988443i	$-0.451560\pi$
$113$	−1.54184e10	−	1.54184e10i	−0.836851	−	0.836851i	−0.988443	+	0.151592i	$0.951560\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−8.21379e9	+	8.21379e9i	−0.374640	+	0.374640i
$118$		0			0
$119$			1.88819e10i			0.791244i
$120$		0			0
$121$	−2.54064e10			−0.979527
$122$		0			0
$123$	1.03701e10	+	1.03701e10i	0.368347	+	0.368347i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.17773e9	+	8.17773e9i	−0.247522	+	0.247522i	−0.819953	−	0.572431i	$-0.806000\pi$
$127$	−8.17773e9	+	8.17773e9i	−0.247522	+	0.247522i	0.572431	+	0.819953i	$0.306000\pi$
$128$		0			0
$129$		−	3.45235e10i		−	0.966421i
$130$		0			0
$131$	6.21383e10			1.61066			0.805328	−	0.592830i	$-0.201989\pi$
$131$	6.21383e10			1.61066			0.805328	+	0.592830i	$0.201989\pi$
$132$		0			0
$133$	2.91393e10	+	2.91393e10i	0.700198	+	0.700198i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.61816e9	−	9.61816e9i	0.199292	−	0.199292i	−0.600405	−	0.799696i	$-0.704994\pi$
$137$	9.61816e9	−	9.61816e9i	0.199292	−	0.199292i	0.799696	+	0.600405i	$0.204994\pi$
$138$		0			0
$139$		−	6.71930e10i		−	1.29494i	−0.762091	−	0.647470i	$-0.775827\pi$
$139$		−	6.71930e10i		−	1.29494i	0.762091	−	0.647470i	$-0.224173\pi$
$140$		0			0
$141$	3.64701e10			0.654398
$142$		0			0
$143$	−9.61620e9	−	9.61620e9i	−0.160814	−	0.160814i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.89517e10	−	1.89517e10i	0.276096	−	0.276096i
$148$		0			0
$149$		−	1.29414e10i		−	0.176218i	−0.996111	−	0.0881092i	$-0.971918\pi$
$149$		−	1.29414e10i		−	0.176218i	0.996111	−	0.0881092i	$-0.0280824\pi$
$150$		0			0
$151$	−8.95842e10			−1.14116			−0.570580	−	0.821242i	$-0.693282\pi$
$151$	−8.95842e10			−1.14116			−0.570580	+	0.821242i	$0.693282\pi$
$152$		0			0
$153$	−2.74825e10	−	2.74825e10i	−0.327793	−	0.327793i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.59119e10	+	8.59119e10i	−0.900648	+	0.900648i	−0.995492	−	0.0948442i	$-0.969765\pi$
$157$	−8.59119e10	+	8.59119e10i	−0.900648	+	0.900648i	0.0948442	+	0.995492i	$0.469765\pi$
$158$		0			0
$159$			9.06269e10i			0.891808i
$160$		0			0
$161$	−1.03757e11			−0.959153
$162$		0			0
$163$	−5.40970e10	−	5.40970e10i	−0.470149	−	0.470149i	0.431814	−	0.901963i	$-0.357874\pi$
$163$	−5.40970e10	−	5.40970e10i	−0.470149	−	0.470149i	−0.901963	+	0.431814i	$0.857874\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.25444e11	+	1.25444e11i	−0.965752	+	0.965752i	−0.999433	−	0.0336802i	$-0.989277\pi$
$167$	−1.25444e11	+	1.25444e11i	−0.965752	+	0.965752i	0.0336802	+	0.999433i	$0.489277\pi$
$168$		0			0
$169$			2.10426e11i			1.52639i
$170$		0			0
$171$	−8.48243e10			−0.580150
$172$		0			0
$173$	−2.76438e10	−	2.76438e10i	−0.178389	−	0.178389i	0.612264	−	0.790653i	$-0.290259\pi$
$173$	−2.76438e10	−	2.76438e10i	−0.178389	−	0.178389i	−0.790653	+	0.612264i	$0.790259\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.87923e10	+	9.87923e10i	−0.568666	+	0.568666i
$178$		0			0
$179$		−	3.25934e11i		−	1.77364i	−0.462118	−	0.886818i	$-0.652911\pi$
$179$		−	3.25934e11i		−	1.77364i	0.462118	−	0.886818i	$-0.347089\pi$
$180$		0			0
$181$	1.70024e11			0.875218			0.437609	−	0.899165i	$-0.355825\pi$
$181$	1.70024e11			0.875218			0.437609	+	0.899165i	$0.355825\pi$
$182$		0			0
$183$	2.14563e10	+	2.14563e10i	0.104544	+	0.104544i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.21749e10	−	3.21749e10i	0.140705	−	0.140705i
$188$		0			0
$189$		−	2.64060e10i		−	0.109495i
$190$		0			0
$191$	−1.59693e11			−0.628231			−0.314116	−	0.949385i	$-0.601708\pi$
$191$	−1.59693e11			−0.628231			−0.314116	+	0.949385i	$0.601708\pi$
$192$		0			0
$193$	−2.15753e11	−	2.15753e11i	−0.805694	−	0.805694i	0.178285	−	0.983979i	$-0.442945\pi$
$193$	−2.15753e11	−	2.15753e11i	−0.805694	−	0.805694i	−0.983979	+	0.178285i	$0.942945\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.08670e11	+	2.08670e11i	−0.703280	+	0.703280i	−0.965113	−	0.261833i	$-0.915673\pi$
$197$	−2.08670e11	+	2.08670e11i	−0.703280	+	0.703280i	0.261833	+	0.965113i	$0.415673\pi$
$198$		0			0
$199$		−	3.54372e11i		−	1.13552i	−0.823195	−	0.567759i	$-0.807810\pi$
$199$		−	3.54372e11i		−	1.13552i	0.823195	−	0.567759i	$-0.192190\pi$
$200$		0			0
$201$	4.63138e10			0.141166
$202$		0			0
$203$	−2.25132e10	−	2.25132e10i	−0.0653066	−	0.0653066i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.51018e11	−	1.51018e11i	0.397354	−	0.397354i
$208$		0			0
$209$		−	9.93072e10i		−	0.249029i
$210$		0			0
$211$	−1.67815e11			−0.401254			−0.200627	−	0.979668i	$-0.564298\pi$
$211$	−1.67815e11			−0.401254			−0.200627	+	0.979668i	$0.564298\pi$
$212$		0			0
$213$	−6.13317e10	−	6.13317e10i	−0.139890	−	0.139890i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−7.87620e10	+	7.87620e10i	−0.163688	+	0.163688i
$218$		0			0
$219$		−	1.44223e11i		−	0.286294i
$220$		0			0
$221$	−1.16533e12			−2.21048
$222$		0			0
$223$	9.48541e10	+	9.48541e10i	0.172001	+	0.172001i	0.787858	−	0.615857i	$-0.211190\pi$
$223$	9.48541e10	+	9.48541e10i	0.172001	+	0.172001i	−0.615857	+	0.787858i	$0.711190\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.01318e11	+	4.01318e11i	−0.665824	+	0.665824i	−0.956747	−	0.290923i	$-0.906038\pi$
$227$	−4.01318e11	+	4.01318e11i	−0.665824	+	0.665824i	0.290923	+	0.956747i	$0.406038\pi$
$228$		0			0
$229$		−	1.11888e12i		−	1.77667i	−0.459192	−	0.888337i	$-0.651861\pi$
$229$		−	1.11888e12i		−	1.77667i	0.459192	−	0.888337i	$-0.348139\pi$
$230$		0			0
$231$	3.09145e10			0.0470004
$232$		0			0
$233$	−9.62313e10	−	9.62313e10i	−0.140132	−	0.140132i	0.633561	−	0.773693i	$-0.281593\pi$
$233$	−9.62313e10	−	9.62313e10i	−0.140132	−	0.140132i	−0.773693	+	0.633561i	$0.781593\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.13279e11	+	1.13279e11i	−0.151499	+	0.151499i
$238$		0			0
$239$			3.82748e11i			0.490821i	0.969419	+	0.245411i	$0.0789228\pi$
$239$			3.82748e11i			0.490821i	−0.969419	+	0.245411i	$0.921077\pi$
$240$		0			0
$241$	−6.74618e11			−0.829798			−0.414899	−	0.909867i	$-0.636183\pi$
$241$	−6.74618e11			−0.829798			−0.414899	+	0.909867i	$0.636183\pi$
$242$		0			0
$243$	3.84338e10	+	3.84338e10i	0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.79838e12	+	1.79838e12i	−1.95613	+	1.95613i
$248$		0			0
$249$		−	9.71618e11i		−	1.01508i
$250$		0			0
$251$	1.64376e12			1.64994			0.824972	−	0.565173i	$-0.191191\pi$
$251$	1.64376e12			1.64994			0.824972	+	0.565173i	$0.191191\pi$
$252$		0			0
$253$	1.76803e11	+	1.76803e11i	0.170564	+	0.170564i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.38985e11	−	2.38985e11i	0.213160	−	0.213160i	−0.592448	−	0.805608i	$-0.701839\pi$
$257$	2.38985e11	−	2.38985e11i	0.213160	−	0.213160i	0.805608	+	0.592448i	$0.201839\pi$
$258$		0			0
$259$		−	1.13019e12i		−	0.969732i
$260$		0			0
$261$	6.55358e10			0.0541098
$262$		0			0
$263$	−5.46851e10	−	5.46851e10i	−0.0434601	−	0.0434601i	0.685043	−	0.728503i	$-0.259783\pi$
$263$	−5.46851e10	−	5.46851e10i	−0.0434601	−	0.0434601i	−0.728503	+	0.685043i	$0.759783\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−8.87821e11	+	8.87821e11i	−0.654288	+	0.654288i
$268$		0			0
$269$		−	2.13079e12i		−	1.51279i	−0.654114	−	0.756396i	$-0.726958\pi$
$269$		−	2.13079e12i		−	1.51279i	0.654114	−	0.756396i	$-0.273042\pi$
$270$		0			0
$271$	−2.01544e12			−1.37887			−0.689437	−	0.724346i	$-0.742142\pi$
$271$	−2.01544e12			−1.37887			−0.689437	+	0.724346i	$0.742142\pi$
$272$		0			0
$273$	−5.59839e11	−	5.59839e11i	−0.369190	−	0.369190i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	4.75468e11	−	4.75468e11i	0.291556	−	0.291556i	−0.546139	−	0.837695i	$-0.683903\pi$
$277$	4.75468e11	−	4.75468e11i	0.291556	−	0.291556i	0.837695	+	0.546139i	$0.183903\pi$
$278$		0			0
$279$		−	2.29276e11i		−	0.135624i
$280$		0			0
$281$	−2.42181e12			−1.38232			−0.691160	−	0.722702i	$-0.742900\pi$
$281$	−2.42181e12			−1.38232			−0.691160	+	0.722702i	$0.742900\pi$
$282$		0			0
$283$	6.89816e11	+	6.89816e11i	0.380015	+	0.380015i	0.871108	−	0.491092i	$-0.163402\pi$
$283$	6.89816e11	+	6.89816e11i	0.380015	+	0.380015i	−0.491092	+	0.871108i	$0.663402\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.06810e11	+	7.06810e11i	−0.362989	+	0.362989i
$288$		0			0
$289$		−	1.88308e12i		−	0.934068i
$290$		0			0
$291$	−6.60400e11			−0.316477
$292$		0			0
$293$	2.64991e12	+	2.64991e12i	1.22713	+	1.22713i	0.965043	+	0.262092i	$0.0844124\pi$
$293$	2.64991e12	+	2.64991e12i	1.22713	+	1.22713i	0.262092	+	0.965043i	$0.415588\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.49959e10	+	4.49959e10i	−0.0194711	+	0.0194711i
$298$		0			0
$299$		−	6.40353e12i		−	2.67956i
$300$		0			0
$301$	2.35307e12			0.952361
$302$		0			0
$303$	2.13268e11	+	2.13268e11i	0.0835049	+	0.0835049i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.37107e11	+	7.37107e11i	−0.270295	+	0.270295i	−0.829219	−	0.558924i	$-0.811214\pi$
$307$	−7.37107e11	+	7.37107e11i	−0.270295	+	0.270295i	0.558924	+	0.829219i	$0.311214\pi$
$308$		0			0
$309$			4.00693e10i			0.0142239i
$310$		0			0
$311$	−3.20794e12			−1.10261			−0.551307	−	0.834302i	$-0.685871\pi$
$311$	−3.20794e12			−1.10261			−0.551307	+	0.834302i	$0.685871\pi$
$312$		0			0
$313$	−4.09198e12	−	4.09198e12i	−1.36211	−	1.36211i	−0.871224	−	0.490886i	$-0.836673\pi$
$313$	−4.09198e12	−	4.09198e12i	−1.36211	−	1.36211i	−0.490886	−	0.871224i	$-0.663327\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.60534e12	+	3.60534e12i	−1.12629	+	1.12629i	−0.135515	+	0.990775i	$0.543269\pi$
$317$	−3.60534e12	+	3.60534e12i	−1.12629	+	1.12629i	−0.990775	+	0.135515i	$0.956731\pi$
$318$		0			0
$319$			7.67253e10i			0.0232266i
$320$		0			0
$321$	−1.44795e12			−0.424843
$322$		0			0
$323$	−6.01720e12	−	6.01720e12i	−1.71152	−	1.71152i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3.73198e11	+	3.73198e11i	−0.0998160	+	0.0998160i
$328$		0			0
$329$			2.48575e12i			0.644877i
$330$		0			0
$331$	−2.03877e12			−0.513130			−0.256565	−	0.966527i	$-0.582591\pi$
$331$	−2.03877e12			−0.513130			−0.256565	+	0.966527i	$0.582591\pi$
$332$		0			0
$333$	1.64498e12	+	1.64498e12i	0.401736	+	0.401736i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.88007e12	+	3.88007e12i	−0.892669	+	0.892669i	−0.994774	−	0.102105i	$-0.967442\pi$
$337$	−3.88007e12	+	3.88007e12i	−0.892669	+	0.892669i	0.102105	+	0.994774i	$0.467442\pi$
$338$		0			0
$339$			3.05915e12i			0.683286i
$340$		0			0
$341$	2.68422e11			0.0582165
$342$		0			0
$343$	3.20170e12	+	3.20170e12i	0.674389	+	0.674389i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.51054e12	+	2.51054e12i	−0.499023	+	0.499023i	−0.911134	−	0.412111i	$-0.864792\pi$
$347$	−2.51054e12	+	2.51054e12i	−0.499023	+	0.499023i	0.412111	+	0.911134i	$0.364792\pi$
$348$		0			0
$349$		−	8.81109e12i		−	1.70178i	−0.525347	−	0.850888i	$-0.676064\pi$
$349$		−	8.81109e12i		−	1.70178i	0.525347	−	0.850888i	$-0.323936\pi$
$350$		0			0
$351$	1.62969e12			0.305892
$352$		0			0
$353$	−3.64808e12	−	3.64808e12i	−0.665565	−	0.665565i	0.291121	−	0.956686i	$-0.405972\pi$
$353$	−3.64808e12	−	3.64808e12i	−0.665565	−	0.665565i	−0.956686	+	0.291121i	$0.905972\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.87317e12	−	1.87317e12i	0.323024	−	0.323024i
$358$		0			0
$359$		−	4.58712e12i		−	0.769251i	−0.923073	−	0.384626i	$-0.874331\pi$
$359$		−	4.58712e12i		−	0.769251i	0.923073	−	0.384626i	$-0.125669\pi$
$360$		0			0
$361$	−1.24409e13			−2.02916
$362$		0			0
$363$	2.52043e12	+	2.52043e12i	0.399890	+	0.399890i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−9.32116e11	+	9.32116e11i	−0.140004	+	0.140004i	−0.773635	−	0.633631i	$-0.781564\pi$
$367$	−9.32116e11	+	9.32116e11i	−0.140004	+	0.140004i	0.633631	+	0.773635i	$0.281564\pi$
$368$		0			0
$369$		−	2.05752e12i		−	0.300754i
$370$		0			0
$371$	−6.17698e12			−0.878834
$372$		0			0
$373$	2.12809e12	+	2.12809e12i	0.294744	+	0.294744i	0.838951	−	0.544207i	$-0.183169\pi$
$373$	2.12809e12	+	2.12809e12i	0.294744	+	0.294744i	−0.544207	+	0.838951i	$0.683169\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.38944e12	−	1.38944e12i	0.182445	−	0.182445i
$378$		0			0
$379$			9.27243e12i			1.18576i	0.805290	+	0.592881i	$0.202010\pi$
$379$			9.27243e12i			1.18576i	−0.805290	+	0.592881i	$0.797990\pi$
$380$		0			0
$381$	1.62253e12			0.202101
$382$		0			0
$383$	2.88851e12	+	2.88851e12i	0.350494	+	0.350494i	0.860293	−	0.509799i	$-0.170280\pi$
$383$	2.88851e12	+	2.88851e12i	0.350494	+	0.350494i	−0.509799	+	0.860293i	$0.670280\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.42488e12	+	3.42488e12i	−0.394540	+	0.394540i
$388$		0			0
$389$		−	2.70831e12i		−	0.304054i	−0.988376	−	0.152027i	$-0.951420\pi$
$389$		−	2.70831e12i		−	0.304054i	0.988376	−	0.152027i	$-0.0485801\pi$
$390$		0			0
$391$	2.14256e13			2.34449
$392$		0			0
$393$	−6.16439e12	−	6.16439e12i	−0.657548	−	0.657548i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.45343e12	+	5.45343e12i	−0.552990	+	0.552990i	−0.927302	−	0.374313i	$-0.877879\pi$
$397$	−5.45343e12	+	5.45343e12i	−0.552990	+	0.552990i	0.374313	+	0.927302i	$0.377879\pi$
$398$		0			0
$399$		−	5.78149e12i		−	0.571709i
$400$		0			0
$401$	1.02574e13			0.989268			0.494634	−	0.869101i	$-0.335302\pi$
$401$	1.02574e13			0.989268			0.494634	+	0.869101i	$0.335302\pi$
$402$		0			0
$403$	−4.86092e12	−	4.86092e12i	−0.457292	−	0.457292i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.92585e12	+	1.92585e12i	−0.172445	+	0.172445i
$408$		0			0
$409$			7.78823e12i			0.680490i	0.940337	+	0.340245i	$0.110510\pi$
$409$			7.78823e12i			0.680490i	−0.940337	+	0.340245i	$0.889490\pi$
$410$		0			0
$411$	−1.90833e12			−0.162721
$412$		0			0
$413$	−6.73353e12	−	6.73353e12i	−0.560393	−	0.560393i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−6.66584e12	+	6.66584e12i	−0.528657	+	0.528657i
$418$		0			0
$419$			1.40827e13i			1.09047i	0.838282	+	0.545236i	$0.183560\pi$
$419$			1.40827e13i			1.09047i	−0.838282	+	0.545236i	$0.816440\pi$
$420$		0			0
$421$	−1.92635e13			−1.45655			−0.728275	−	0.685285i	$-0.759678\pi$
$421$	−1.92635e13			−1.45655			−0.728275	+	0.685285i	$0.759678\pi$
$422$		0			0
$423$	−3.61800e12	−	3.61800e12i	−0.267157	−	0.267157i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.46243e12	+	1.46243e12i	−0.103023	+	0.103023i
$428$		0			0
$429$			1.90794e12i			0.131304i
$430$		0			0
$431$	−3.20644e11			−0.0215594			−0.0107797	−	0.999942i	$-0.503431\pi$
$431$	−3.20644e11			−0.0215594			−0.0107797	+	0.999942i	$0.503431\pi$
$432$		0			0
$433$	3.98006e12	+	3.98006e12i	0.261487	+	0.261487i	0.825658	−	0.564171i	$-0.190804\pi$
$433$	3.98006e12	+	3.98006e12i	0.261487	+	0.261487i	−0.564171	+	0.825658i	$0.690804\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.30649e13	−	3.30649e13i	2.07472	−	2.07472i
$438$		0			0
$439$		−	9.06335e12i		−	0.555861i	−0.960601	−	0.277931i	$-0.910351\pi$
$439$		−	9.06335e12i		−	0.555861i	0.960601	−	0.277931i	$-0.0896485\pi$
$440$		0			0
$441$	−3.76017e12			−0.225432
$442$		0			0
$443$	1.72736e13	+	1.72736e13i	1.01243	+	1.01243i	0.999922	+	0.0125060i	$0.00398089\pi$
$443$	1.72736e13	+	1.72736e13i	1.01243	+	1.01243i	0.0125060	+	0.999922i	$0.496019\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.28385e12	+	1.28385e12i	−0.0719408	+	0.0719408i
$448$		0			0
$449$		−	3.55160e12i		−	0.194622i	−0.995254	−	0.0973110i	$-0.968976\pi$
$449$		−	3.55160e12i		−	0.194622i	0.995254	−	0.0973110i	$-0.0310241\pi$
$450$		0			0
$451$	2.40882e12			0.129099
$452$		0			0
$453$	8.88714e12	+	8.88714e12i	0.465877	+	0.465877i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.66276e13	−	1.66276e13i	0.834158	−	0.834158i	−0.153925	−	0.988083i	$-0.549191\pi$
$457$	1.66276e13	−	1.66276e13i	0.834158	−	0.834158i	0.988083	+	0.153925i	$0.0491913\pi$
$458$		0			0
$459$			5.45277e12i			0.267642i
$460$		0			0
$461$	−1.85896e13			−0.892824			−0.446412	−	0.894828i	$-0.647298\pi$
$461$	−1.85896e13			−0.892824			−0.446412	+	0.894828i	$0.647298\pi$
$462$		0			0
$463$	−2.19631e12	−	2.19631e12i	−0.103226	−	0.103226i	0.653608	−	0.756833i	$-0.273255\pi$
$463$	−2.19631e12	−	2.19631e12i	−0.103226	−	0.103226i	−0.756833	+	0.653608i	$0.773255\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.49772e11	+	3.49772e11i	−0.0157471	+	0.0157471i	−0.714937	−	0.699189i	$-0.753544\pi$
$467$	−3.49772e11	+	3.49772e11i	−0.0157471	+	0.0157471i	0.699189	+	0.714937i	$0.253544\pi$
$468$		0			0
$469$			3.15667e12i			0.139112i
$470$		0			0
$471$	1.70457e13			0.735376
$472$		0			0
$473$	−4.00964e12	−	4.00964e12i	−0.169356	−	0.169356i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	8.99058e12	−	8.99058e12i	0.364079	−	0.364079i
$478$		0			0
$479$			9.58522e12i			0.380123i	0.981772	+	0.190062i	$0.0608688\pi$
$479$			9.58522e12i			0.380123i	−0.981772	+	0.190062i	$0.939131\pi$
$480$		0			0
$481$	6.97513e13			2.70911
$482$		0			0
$483$	1.02931e13	+	1.02931e13i	0.391573	+	0.391573i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	1.19310e13	−	1.19310e13i	0.435543	−	0.435543i	−0.454966	−	0.890509i	$-0.650348\pi$
$487$	1.19310e13	−	1.19310e13i	0.435543	−	0.435543i	0.890509	+	0.454966i	$0.150348\pi$
$488$		0			0
$489$			1.07333e13i			0.383875i
$490$		0			0
$491$	−1.57312e13			−0.551258			−0.275629	−	0.961264i	$-0.588886\pi$
$491$	−1.57312e13			−0.551258			−0.275629	+	0.961264i	$0.588886\pi$
$492$		0			0
$493$	4.64893e12	+	4.64893e12i	0.159631	+	0.159631i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.18027e12	−	4.18027e12i	0.137855	−	0.137855i
$498$		0			0
$499$		−	1.55193e13i		−	0.501614i	−0.968037	−	0.250807i	$-0.919304\pi$
$499$		−	1.55193e13i		−	0.501614i	0.968037	−	0.250807i	$-0.0806960\pi$
$500$		0			0
$501$	2.48891e13			0.788534
$502$		0			0
$503$	1.43107e13	+	1.43107e13i	0.444449	+	0.444449i	0.893504	−	0.449055i	$-0.148239\pi$
$503$	1.43107e13	+	1.43107e13i	0.444449	+	0.444449i	−0.449055	+	0.893504i	$0.648239\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.08752e13	−	2.08752e13i	0.623147	−	0.623147i
$508$		0			0
$509$			4.97571e13i			1.45635i	0.685391	+	0.728176i	$0.259631\pi$
$509$			4.97571e13i			1.45635i	−0.685391	+	0.728176i	$0.740369\pi$
$510$		0			0
$511$	9.82998e12			0.282129
$512$		0			0
$513$	8.41494e12	+	8.41494e12i	0.236845	+	0.236845i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.23573e12	−	4.23573e12i	0.114677	−	0.114677i
$518$		0			0
$519$			5.48477e12i			0.145654i
$520$		0			0
$521$	−3.53166e12			−0.0920006			−0.0460003	−	0.998941i	$-0.514648\pi$
$521$	−3.53166e12			−0.0920006			−0.0460003	+	0.998941i	$0.514648\pi$
$522$		0			0
$523$	3.83515e13	+	3.83515e13i	0.980108	+	0.980108i	0.999806	−	0.0196982i	$-0.00627055\pi$
$523$	3.83515e13	+	3.83515e13i	0.980108	+	0.980108i	−0.0196982	+	0.999806i	$0.506271\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.62642e13	−	1.62642e13i	0.400110	−	0.400110i
$528$		0			0
$529$			7.63083e13i			1.84202i
$530$		0			0
$531$	1.96013e13			0.464314
$532$		0			0
$533$	−4.36219e13	−	4.36219e13i	−1.01407	−	1.01407i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.23341e13	+	3.23341e13i	−0.724084	+	0.724084i
$538$		0			0
$539$		−	4.40218e12i		−	0.0967663i
$540$		0			0
$541$	−7.71740e12			−0.166527			−0.0832635	−	0.996528i	$-0.526534\pi$
$541$	−7.71740e12			−0.166527			−0.0832635	+	0.996528i	$0.526534\pi$
$542$		0			0
$543$	−1.68671e13	−	1.68671e13i	−0.357306	−	0.357306i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.14494e13	−	3.14494e13i	0.642209	−	0.642209i	−0.308889	−	0.951098i	$-0.599957\pi$
$547$	3.14494e13	−	3.14494e13i	0.642209	−	0.642209i	0.951098	+	0.308889i	$0.0999572\pi$
$548$		0			0
$549$		−	4.25712e12i		−	0.0853600i
$550$		0			0
$551$	1.43488e13			0.282526
$552$		0			0
$553$	−7.72094e12	−	7.72094e12i	−0.149295	−	0.149295i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.91011e13	−	4.91011e13i	0.915831	−	0.915831i	−0.0808916	−	0.996723i	$-0.525777\pi$
$557$	4.91011e13	−	4.91011e13i	0.915831	−	0.915831i	0.996723	+	0.0808916i	$0.0257768\pi$
$558$		0			0
$559$			1.45223e14i			2.66059i
$560$		0			0
$561$	−6.38377e12			−0.114885
$562$		0			0
$563$	−1.65680e13	−	1.65680e13i	−0.292906	−	0.292906i	0.545321	−	0.838227i	$-0.316408\pi$
$563$	−1.65680e13	−	1.65680e13i	−0.292906	−	0.292906i	−0.838227	+	0.545321i	$0.816408\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.61959e12	+	2.61959e12i	−0.0447010	+	0.0447010i
$568$		0			0
$569$		−	7.95051e13i		−	1.33301i	−0.745500	−	0.666505i	$-0.767789\pi$
$569$		−	7.95051e13i		−	1.33301i	0.745500	−	0.666505i	$-0.232211\pi$
$570$		0			0
$571$	3.32905e13			0.548453			0.274227	−	0.961665i	$-0.411578\pi$
$571$	3.32905e13			0.548453			0.274227	+	0.961665i	$0.411578\pi$
$572$		0			0
$573$	1.58423e13	+	1.58423e13i	0.256474	+	0.256474i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	6.02115e12	−	6.02115e12i	0.0941456	−	0.0941456i	−0.658465	−	0.752611i	$-0.728794\pi$
$577$	6.02115e12	−	6.02115e12i	0.0941456	−	0.0941456i	0.752611	+	0.658465i	$0.228794\pi$
$578$		0			0
$579$			4.28073e13i			0.657847i
$580$		0			0
$581$	6.62239e13			1.00031
$582$		0			0
$583$	1.05256e13	+	1.05256e13i	0.156281	+	0.156281i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.05755e13	−	8.05755e13i	1.15615	−	1.15615i	0.170849	−	0.985297i	$-0.445349\pi$
$587$	8.05755e13	−	8.05755e13i	1.15615	−	1.15615i	0.985297	−	0.170849i	$-0.0546509\pi$
$588$		0			0
$589$		−	5.01991e13i		−	0.708140i
$590$		0			0
$591$	4.14019e13			0.574225
$592$		0			0
$593$	3.51354e13	+	3.51354e13i	0.479150	+	0.479150i	0.904860	−	0.425710i	$-0.139976\pi$
$593$	3.51354e13	+	3.51354e13i	0.479150	+	0.479150i	−0.425710	+	0.904860i	$0.639976\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.51553e13	+	3.51553e13i	−0.463574	+	0.463574i
$598$		0			0
$599$			7.91676e13i			1.02663i	0.858201	+	0.513315i	$0.171583\pi$
$599$			7.91676e13i			1.02663i	−0.858201	+	0.513315i	$0.828417\pi$
$600$		0			0
$601$	8.93707e13			1.13979			0.569893	−	0.821719i	$-0.306985\pi$
$601$	8.93707e13			1.13979			0.569893	+	0.821719i	$0.306985\pi$
$602$		0			0
$603$	−4.59453e12	−	4.59453e12i	−0.0576308	−	0.0576308i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.37015e13	+	6.37015e13i	−0.773047	+	0.773047i	−0.978638	−	0.205591i	$-0.934088\pi$
$607$	−6.37015e13	+	6.37015e13i	−0.773047	+	0.773047i	0.205591	+	0.978638i	$0.434088\pi$
$608$		0			0
$609$			4.46682e12i			0.0533226i
$610$		0			0
$611$	−1.53412e14			−1.80158
$612$		0			0
$613$	4.44555e13	+	4.44555e13i	0.513598	+	0.513598i	0.915627	−	0.402029i	$-0.131695\pi$
$613$	4.44555e13	+	4.44555e13i	0.513598	+	0.513598i	−0.402029	+	0.915627i	$0.631695\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.17206e14	−	1.17206e14i	1.31076	−	1.31076i	0.389913	−	0.920852i	$-0.372505\pi$
$617$	1.17206e14	−	1.17206e14i	1.31076	−	1.31076i	0.920852	−	0.389913i	$-0.127495\pi$
$618$		0			0
$619$		−	1.96629e13i		−	0.216369i	−0.994131	−	0.108184i	$-0.965496\pi$
$619$		−	1.96629e13i		−	0.216369i	0.994131	−	0.108184i	$-0.0345037\pi$
$620$		0			0
$621$	−2.99633e13			−0.324438
$622$		0			0
$623$	−6.05124e13	−	6.05124e13i	−0.644770	−	0.644770i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−9.85170e12	+	9.85170e12i	−0.101665	+	0.101665i
$628$		0			0
$629$			2.33381e14i			2.37035i
$630$		0			0
$631$	−1.51432e14			−1.51381			−0.756904	−	0.653526i	$-0.773289\pi$
$631$	−1.51432e14			−1.51381			−0.756904	+	0.653526i	$0.773289\pi$
$632$		0			0
$633$	1.66480e13	+	1.66480e13i	0.163811	+	0.163811i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−7.97203e13	+	7.97203e13i	−0.760102	+	0.760102i
$638$		0			0
$639$			1.21687e13i			0.114220i
$640$		0			0
$641$	3.61881e12			0.0334407			0.0167204	−	0.999860i	$-0.494677\pi$
$641$	3.61881e12			0.0334407			0.0167204	+	0.999860i	$0.494677\pi$
$642$		0			0
$643$	−1.25083e14	−	1.25083e14i	−1.13800	−	1.13800i	−0.988808	−	0.149192i	$-0.952333\pi$
$643$	−1.25083e14	−	1.25083e14i	−1.13800	−	1.13800i	−0.149192	−	0.988808i	$-0.547667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.94985e13	−	6.94985e13i	0.612991	−	0.612991i	−0.330733	−	0.943724i	$-0.607296\pi$
$647$	6.94985e13	−	6.94985e13i	0.612991	−	0.612991i	0.943724	+	0.330733i	$0.107296\pi$
$648$		0			0
$649$			2.29480e13i			0.199306i
$650$		0			0
$651$	1.56271e13			0.133651
$652$		0			0
$653$	−1.21710e14	−	1.21710e14i	−1.02508	−	1.02508i	−0.999677	−	0.0254058i	$-0.991912\pi$
$653$	−1.21710e14	−	1.21710e14i	−1.02508	−	1.02508i	−0.0254058	−	0.999677i	$-0.508088\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.43075e13	+	1.43075e13i	−0.116879	+	0.116879i
$658$		0			0
$659$			9.42173e12i			0.0758060i	0.999281	+	0.0379030i	$0.0120678\pi$
$659$			9.42173e12i			0.0758060i	−0.999281	+	0.0379030i	$0.987932\pi$
$660$		0			0
$661$	1.31255e14			1.04018			0.520092	−	0.854110i	$-0.325898\pi$
$661$	1.31255e14			1.04018			0.520092	+	0.854110i	$0.325898\pi$
$662$		0			0
$663$	1.15605e14	+	1.15605e14i	0.902424	+	0.902424i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.55461e13	+	2.55461e13i	−0.193507	+	0.193507i
$668$		0			0
$669$		−	1.88199e13i		−	0.140438i
$670$		0			0
$671$	4.98398e12			0.0366407
$672$		0			0
$673$	1.06296e13	+	1.06296e13i	0.0769913	+	0.0769913i	0.744554	−	0.667562i	$-0.232662\pi$
$673$	1.06296e13	+	1.06296e13i	0.0769913	+	0.0769913i	−0.667562	+	0.744554i	$0.732662\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.56600e13	+	8.56600e13i	−0.602330	+	0.602330i	−0.940930	−	0.338600i	$-0.890047\pi$
$677$	−8.56600e13	+	8.56600e13i	−0.602330	+	0.602330i	0.338600	+	0.940930i	$0.390047\pi$
$678$		0			0
$679$		−	4.50118e13i		−	0.311873i
$680$		0			0
$681$	7.96249e13			0.543643
$682$		0			0
$683$	−9.53174e13	−	9.53174e13i	−0.641311	−	0.641311i	0.309567	−	0.950878i	$-0.399816\pi$
$683$	−9.53174e13	−	9.53174e13i	−0.641311	−	0.641311i	−0.950878	+	0.309567i	$0.899816\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.10998e14	+	1.10998e14i	−0.725324	+	0.725324i
$688$		0			0
$689$		−	3.81222e14i		−	2.45517i
$690$		0			0
$691$	2.68127e14			1.70196			0.850981	−	0.525196i	$-0.176008\pi$
$691$	2.68127e14			1.70196			0.850981	+	0.525196i	$0.176008\pi$
$692$		0			0
$693$	−3.06685e12	−	3.06685e12i	−0.0191879	−	0.0191879i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.45955e14	−	1.45955e14i	0.887267	−	0.887267i
$698$		0			0
$699$			1.90931e13i			0.114417i
$700$		0			0
$701$	−2.37352e14			−1.40217			−0.701087	−	0.713076i	$-0.747302\pi$
$701$	−2.37352e14			−1.40217			−0.701087	+	0.713076i	$0.747302\pi$
$702$		0			0
$703$	3.60163e14	+	3.60163e14i	2.09760	+	2.09760i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.45360e13	+	1.45360e13i	−0.0822901	+	0.0822901i
$708$		0			0
$709$		−	1.42036e14i		−	0.792807i	−0.918076	−	0.396404i	$-0.870258\pi$
$709$		−	1.42036e14i		−	0.792807i	0.918076	−	0.396404i	$-0.129742\pi$
$710$		0			0
$711$	2.24756e13			0.123698
$712$		0			0
$713$	8.93726e13	+	8.93726e13i	0.485017	+	0.485017i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.79703e13	−	3.79703e13i	0.200377	−	0.200377i
$718$		0			0
$719$		−	2.74318e14i		−	1.42761i	−0.700344	−	0.713806i	$-0.746970\pi$
$719$		−	2.74318e14i		−	1.42761i	0.700344	−	0.713806i	$-0.253030\pi$
$720$		0			0
$721$	−2.73106e12			−0.0140170
$722$		0			0
$723$	6.69250e13	+	6.69250e13i	0.338764	+	0.338764i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−2.03490e14	+	2.03490e14i	−1.00201	+	1.00201i	−0.00200942	+	0.999998i	$0.500640\pi$
$727$	−2.03490e14	+	2.03490e14i	−1.00201	+	1.00201i	−0.999998	+	0.00200942i	$0.999360\pi$
$728$		0			0
$729$		−	7.62560e12i		−	0.0370370i
$730$		0			0
$731$	−4.85903e14			−2.32789
$732$		0			0
$733$	−1.09204e14	−	1.09204e14i	−0.516080	−	0.516080i	0.400303	−	0.916383i	$-0.368905\pi$
$733$	−1.09204e14	−	1.09204e14i	−0.516080	−	0.516080i	−0.916383	+	0.400303i	$0.868905\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.37899e12	−	5.37899e12i	0.0247379	−	0.0247379i
$738$		0			0
$739$			2.20425e14i			1.00009i	0.866000	+	0.500044i	$0.166683\pi$
$739$			2.20425e14i			1.00009i	−0.866000	+	0.500044i	$0.833317\pi$
$740$		0			0
$741$	3.56814e14			1.59717
$742$		0			0
$743$	−6.23312e13	−	6.23312e13i	−0.275272	−	0.275272i	0.555946	−	0.831218i	$-0.312356\pi$
$743$	−6.23312e13	−	6.23312e13i	−0.275272	−	0.275272i	−0.831218	+	0.555946i	$0.812356\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−9.63887e13	+	9.63887e13i	−0.414403	+	0.414403i
$748$		0			0
$749$		−	9.86898e13i		−	0.418662i
$750$		0			0
$751$	−2.82747e14			−1.18358			−0.591790	−	0.806092i	$-0.701579\pi$
$751$	−2.82747e14			−1.18358			−0.591790	+	0.806092i	$0.701579\pi$
$752$		0			0
$753$	−1.63068e14	−	1.63068e14i	−0.673587	−	0.673587i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.96117e14	+	2.96117e14i	−1.19120	+	1.19120i	−0.214469	+	0.976731i	$0.568802\pi$
$757$	−2.96117e14	+	2.96117e14i	−1.19120	+	1.19120i	−0.976731	+	0.214469i	$0.931198\pi$
$758$		0			0
$759$		−	3.50792e13i		−	0.139265i
$760$		0			0
$761$	−3.19464e14			−1.25170			−0.625848	−	0.779945i	$-0.715247\pi$
$761$	−3.19464e14			−1.25170			−0.625848	+	0.779945i	$0.715247\pi$
$762$		0			0
$763$	−2.54365e13	−	2.54365e13i	−0.0983638	−	0.0983638i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.15571e14	−	4.15571e14i	1.56555	−	1.56555i
$768$		0			0
$769$		−	9.28750e13i		−	0.345356i	−0.984978	−	0.172678i	$-0.944758\pi$
$769$		−	9.28750e13i		−	0.345356i	0.984978	−	0.172678i	$-0.0552420\pi$
$770$		0			0
$771$	−4.74168e13			−0.174044
$772$		0			0
$773$	−9.34633e13	−	9.34633e13i	−0.338644	−	0.338644i	0.517213	−	0.855857i	$-0.326970\pi$
$773$	−9.34633e13	−	9.34633e13i	−0.338644	−	0.338644i	−0.855857	+	0.517213i	$0.826970\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.12119e14	+	1.12119e14i	−0.395891	+	0.395891i
$778$		0			0
$779$		−	4.50486e14i		−	1.57034i
$780$		0			0
$781$	−1.42464e13			−0.0490287
$782$		0			0
$783$	−6.50144e12	−	6.50144e12i	−0.0220902	−	0.0220902i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.32899e14	−	1.32899e14i	0.440197	−	0.440197i	−0.451881	−	0.892078i	$-0.649247\pi$
$787$	1.32899e14	−	1.32899e14i	0.440197	−	0.440197i	0.892078	+	0.451881i	$0.149247\pi$
$788$		0			0
$789$			1.08500e13i			0.0354850i
$790$		0			0
$791$	−2.08507e14			−0.673345
$792$		0			0
$793$	−9.02562e13	−	9.02562e13i	−0.287813	−	0.287813i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.90337e13	+	6.90337e13i	−0.214669	+	0.214669i	−0.806248	−	0.591578i	$-0.798505\pi$
$797$	−6.90337e13	+	6.90337e13i	−0.214669	+	0.214669i	0.591578	+	0.806248i	$0.298505\pi$
$798$		0			0
$799$		−	5.13301e14i		−	1.57630i
$800$		0			0
$801$	1.76151e14			0.534224
$802$		0			0
$803$	−1.67504e13	−	1.67504e13i	−0.0501703	−	0.0501703i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.11384e14	+	2.11384e14i	−0.617595	+	0.617595i
$808$		0			0
$809$		−	1.14329e14i		−	0.329925i	−0.986300	−	0.164962i	$-0.947250\pi$
$809$		−	1.14329e14i		−	0.329925i	0.986300	−	0.164962i	$-0.0527503\pi$
$810$		0			0
$811$	2.71081e13			0.0772670			0.0386335	−	0.999253i	$-0.487700\pi$
$811$	2.71081e13			0.0772670			0.0386335	+	0.999253i	$0.487700\pi$
$812$		0			0
$813$	1.99941e14	+	1.99941e14i	0.562923	+	0.562923i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−7.49865e14	+	7.49865e14i	−2.06003	+	2.06003i
$818$		0			0
$819$			1.11077e14i			0.301442i
$820$		0			0
$821$	2.13873e13			0.0573377			0.0286688	−	0.999589i	$-0.490873\pi$
$821$	2.13873e13			0.0573377			0.0286688	+	0.999589i	$0.490873\pi$
$822$		0			0
$823$	5.60357e13	+	5.60357e13i	0.148411	+	0.148411i	0.777408	−	0.628997i	$-0.216534\pi$
$823$	5.60357e13	+	5.60357e13i	0.148411	+	0.148411i	−0.628997	+	0.777408i	$0.716534\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.91606e13	+	5.91606e13i	−0.152934	+	0.152934i	−0.779427	−	0.626493i	$-0.784490\pi$
$827$	−5.91606e13	+	5.91606e13i	−0.152934	+	0.152934i	0.626493	+	0.779427i	$0.284490\pi$
$828$		0			0
$829$		−	5.94836e14i		−	1.51923i	−0.650371	−	0.759617i	$-0.725387\pi$
$829$		−	5.94836e14i		−	1.51923i	0.650371	−	0.759617i	$-0.274613\pi$
$830$		0			0
$831$	−9.43370e13			−0.238055
$832$		0			0
$833$	−2.66736e14	−	2.66736e14i	−0.665054	−	0.665054i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.27451e13	+	2.27451e13i	−0.0553683	+	0.0553683i
$838$		0			0
$839$			4.17759e14i			1.00488i	0.864611	+	0.502442i	$0.167565\pi$
$839$			4.17759e14i			1.00488i	−0.864611	+	0.502442i	$0.832435\pi$
$840$		0			0
$841$	4.09621e14			0.973649
$842$		0			0
$843$	2.40254e14	+	2.40254e14i	0.564330	+	0.564330i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.71788e14	+	1.71788e14i	−0.394073	+	0.394073i
$848$		0			0
$849$		−	1.36866e14i		−	0.310281i
$850$		0			0
$851$	−1.28244e15			−2.87336
$852$		0			0
$853$	1.34595e14	+	1.34595e14i	0.298046	+	0.298046i	0.840248	−	0.542202i	$-0.182409\pi$
$853$	1.34595e14	+	1.34595e14i	0.298046	+	0.298046i	−0.542202	+	0.840248i	$0.682409\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.43571e14	−	5.43571e14i	1.17585	−	1.17585i	0.195058	−	0.980792i	$-0.437510\pi$
$857$	5.43571e14	−	5.43571e14i	1.17585	−	1.17585i	0.980792	−	0.195058i	$-0.0624895\pi$
$858$		0			0
$859$		−	4.19039e13i		−	0.0895960i	−0.998996	−	0.0447980i	$-0.985736\pi$
$859$		−	4.19039e13i		−	0.0895960i	0.998996	−	0.0447980i	$-0.0142644\pi$
$860$		0			0
$861$	1.40237e14			0.296379
$862$		0			0
$863$	−2.11426e14	−	2.11426e14i	−0.441677	−	0.441677i	0.450898	−	0.892575i	$-0.351104\pi$
$863$	−2.11426e14	−	2.11426e14i	−0.441677	−	0.441677i	−0.892575	+	0.450898i	$0.851104\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.86809e14	+	1.86809e14i	−0.381332	+	0.381332i
$868$		0			0
$869$			2.63131e13i			0.0530973i
$870$		0			0
$871$	−1.94819e14			−0.388634
$872$		0			0
$873$	6.55146e13	+	6.55146e13i	0.129201	+	0.129201i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.38505e13	−	3.38505e13i	0.0652480	−	0.0652480i	−0.673730	−	0.738978i	$-0.735309\pi$
$877$	3.38505e13	−	3.38505e13i	0.0652480	−	0.0652480i	0.738978	+	0.673730i	$0.235309\pi$
$878$		0			0
$879$		−	5.25764e14i		−	1.00195i
$880$		0			0
$881$	−1.55559e14			−0.293100			−0.146550	−	0.989203i	$-0.546817\pi$
$881$	−1.55559e14			−0.293100			−0.146550	+	0.989203i	$0.546817\pi$
$882$		0			0
$883$	−1.48149e14	−	1.48149e14i	−0.275991	−	0.275991i	0.555515	−	0.831506i	$-0.312521\pi$
$883$	−1.48149e14	−	1.48149e14i	−0.275991	−	0.275991i	−0.831506	+	0.555515i	$0.812521\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.14374e14	+	2.14374e14i	−0.390439	+	0.390439i	−0.874844	−	0.484405i	$-0.839036\pi$
$887$	−2.14374e14	+	2.14374e14i	−0.390439	+	0.390439i	0.484405	+	0.874844i	$0.339036\pi$
$888$		0			0
$889$			1.10589e14i			0.199161i
$890$		0			0
$891$	8.92758e12			0.0158981
$892$		0			0
$893$	−7.92147e14	−	7.92147e14i	−1.39492	−	1.39492i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−6.35258e14	+	6.35258e14i	−1.09393	+	1.09393i
$898$		0			0
$899$			3.87841e13i			0.0660474i
$900$		0			0
$901$	1.27553e15			2.14817
$902$		0			0
$903$	−2.33434e14	−	2.33434e14i	−0.388800	−	0.388800i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−6.15559e14	+	6.15559e14i	−1.00284	+	1.00284i	−0.00284780	+	0.999996i	$0.500906\pi$
$907$	−6.15559e14	+	6.15559e14i	−1.00284	+	1.00284i	−0.999996	+	0.00284780i	$0.999094\pi$
$908$		0			0
$909$		−	4.23142e13i		−	0.0681815i
$910$		0			0
$911$	1.91025e13			0.0304437			0.0152219	−	0.999884i	$-0.495155\pi$
$911$	1.91025e13			0.0304437			0.0152219	+	0.999884i	$0.495155\pi$
$912$		0			0
$913$	−1.12846e14	−	1.12846e14i	−0.177882	−	0.177882i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.20155e14	−	4.20155e14i	0.647981	−	0.647981i
$918$		0			0
$919$			8.76368e14i			1.33693i	0.743743	+	0.668465i	$0.233048\pi$
$919$			8.76368e14i			1.33693i	−0.743743	+	0.668465i	$0.766952\pi$
$920$		0			0
$921$	1.46248e14			0.220695
$922$		0			0
$923$	2.57992e14	+	2.57992e14i	0.385121	+	0.385121i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.97504e12	−	3.97504e12i	0.00580689	−	0.00580689i
$928$		0			0
$929$		−	7.11580e14i		−	1.02836i	−0.857682	−	0.514180i	$-0.828096\pi$
$929$		−	7.11580e14i		−	1.02836i	0.857682	−	0.514180i	$-0.171904\pi$
$930$		0			0
$931$	−8.23277e14			−1.17706
$932$		0			0
$933$	3.18241e14	+	3.18241e14i	0.450140	+	0.450140i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.26629e14	−	3.26629e14i	0.452228	−	0.452228i	−0.443865	−	0.896093i	$-0.646393\pi$
$937$	3.26629e14	−	3.26629e14i	0.452228	−	0.452228i	0.896093	+	0.443865i	$0.146393\pi$
$938$		0			0
$939$			8.11885e14i			1.11216i
$940$		0			0
$941$	−1.09565e15			−1.48499			−0.742493	−	0.669853i	$-0.766357\pi$
$941$	−1.09565e15			−1.48499			−0.742493	+	0.669853i	$0.766357\pi$
$942$		0			0
$943$	8.02029e14	+	8.02029e14i	1.07555	+	1.07555i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.23879e13	−	2.23879e13i	0.0293944	−	0.0293944i	−0.692257	−	0.721651i	$-0.743383\pi$
$947$	2.23879e13	−	2.23879e13i	0.0293944	−	0.0293944i	0.721651	+	0.692257i	$0.243383\pi$
$948$		0			0
$949$			6.06673e14i			0.788177i
$950$		0			0
$951$	7.15332e14			0.919612
$952$		0			0
$953$	−9.97864e14	−	9.97864e14i	−1.26942	−	1.26942i	−0.946386	−	0.323038i	$-0.895296\pi$
$953$	−9.97864e14	−	9.97864e14i	−1.26942	−	1.26942i	−0.323038	−	0.946386i	$-0.604704\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	7.61148e12	−	7.61148e12i	0.00948221	−	0.00948221i
$958$		0			0
$959$		−	1.30068e14i		−	0.160354i
$960$		0			0
$961$	−6.83943e14			−0.834455
$962$		0			0
$963$	1.43643e14	+	1.43643e14i	0.173441	+	0.173441i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−9.06388e14	+	9.06388e14i	−1.07197	+	1.07197i	−0.0747674	+	0.997201i	$0.523821\pi$
$967$	−9.06388e14	+	9.06388e14i	−1.07197	+	1.07197i	−0.997201	+	0.0747674i	$0.976179\pi$
$968$		0			0
$969$			1.19387e15i			1.39745i
$970$		0			0
$971$	5.05106e14			0.585176			0.292588	−	0.956239i	$-0.405484\pi$
$971$	5.05106e14			0.585176			0.292588	+	0.956239i	$0.405484\pi$
$972$		0			0
$973$	−4.54333e14	−	4.54333e14i	−0.520966	−	0.520966i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.85368e14	−	5.85368e14i	0.657592	−	0.657592i	−0.297218	−	0.954810i	$-0.596059\pi$
$977$	5.85368e14	−	5.85368e14i	0.657592	−	0.657592i	0.954810	+	0.297218i	$0.0960588\pi$
$978$		0			0
$979$			2.06227e14i			0.229315i
$980$		0			0
$981$	7.40456e13			0.0814994
$982$		0			0
$983$	6.38275e14	+	6.38275e14i	0.695409	+	0.695409i	0.963417	−	0.268008i	$-0.0863652\pi$
$983$	6.38275e14	+	6.38275e14i	0.695409	+	0.695409i	−0.268008	+	0.963417i	$0.586365\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.46597e14	−	2.46597e14i	0.263270	−	0.263270i
$988$		0			0
$989$		−	2.67006e15i		−	2.82189i
$990$		0			0
$991$	1.97076e14			0.206189			0.103094	−	0.994672i	$-0.467126\pi$
$991$	1.97076e14			0.206189			0.103094	+	0.994672i	$0.467126\pi$
$992$		0			0
$993$	2.02254e14	+	2.02254e14i	0.209485	+	0.209485i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	9.98412e14	−	9.98412e14i	1.01352	−	1.01352i	0.0136164	−	0.999907i	$-0.495666\pi$
$997$	9.98412e14	−	9.98412e14i	1.01352	−	1.01352i	0.999907	−	0.0136164i	$-0.00433437\pi$
$998$		0			0
$999$		−	3.26379e14i		−	0.328016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.11.k.c.193.3	yes	16
5.2	odd	4	inner	300.11.k.c.157.3	✓	16
5.3	odd	4	inner	300.11.k.c.157.6	yes	16
5.4	even	2	inner	300.11.k.c.193.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.11.k.c.157.3	✓	16	5.2	odd	4	inner
300.11.k.c.157.6	yes	16	5.3	odd	4	inner
300.11.k.c.193.3	yes	16	1.1	even	1	trivial
300.11.k.c.193.6	yes	16	5.4	even	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	300.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-99.2043 - 99.2043i) q^{3} +(6761.61 - 6761.61i) q^{7} +19683.0i q^{9} +O(q^{10})\)	\(q+(-99.2043 - 99.2043i) q^{3} +(6761.61 - 6761.61i) q^{7} +19683.0i q^{9} -23043.7 q^{11} +(417304. + 417304. i) q^{13} +(-1.39626e6 + 1.39626e6i) q^{17} +4.30952e6i q^{19} -1.34156e6 q^{21} +(-7.67251e6 - 7.67251e6i) q^{23} +(1.95264e6 - 1.95264e6i) q^{27} -3.32956e6i q^{29} -1.16484e7 q^{31} +(2.28603e6 + 2.28603e6i) q^{33} +(8.35739e7 - 8.35739e7i) q^{37} -8.27967e7i q^{39} -1.04533e8 q^{41} +(1.74002e8 + 1.74002e8i) q^{43} +(-1.83813e8 + 1.83813e8i) q^{47} +1.91037e8i q^{49} +2.77030e8 q^{51} +(-4.56769e8 - 4.56769e8i) q^{53} +(4.27523e8 - 4.27523e8i) q^{57} -9.95847e8i q^{59} -2.16284e8 q^{61} +(1.33089e8 + 1.33089e8i) q^{63} +(-2.33426e8 + 2.33426e8i) q^{67} +1.52229e9i q^{69} +6.18236e8 q^{71} +(7.26897e8 + 7.26897e8i) q^{73} +(-1.55812e8 + 1.55812e8i) q^{77} -1.14188e9i q^{79} -3.87420e8 q^{81} +(4.89705e9 + 4.89705e9i) q^{83} +(-3.30307e8 + 3.30307e8i) q^{87} -8.94942e9i q^{89} +5.64329e9 q^{91} +(1.15557e9 + 1.15557e9i) q^{93} +(3.32848e9 - 3.32848e9i) q^{97} -4.53568e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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