LMFDB - Embedded newform 300.8.i.c.293.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,8,Mod(257,300)]

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, 2, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("300.257");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	300.i (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:	$93.7155076452$
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} - 8 x^{15} + 132 x^{14} - 784 x^{13} + 5524236 x^{12} - 33135588 x^{11} - 49457570 x^{10} + \cdots + 18\!\cdots\!21 $ x^16 - 8x^15 + 132x^14 - 784x^13 + 5524236x^12 - 33135588x^11 - 49457570x^10 + 551013008x^9 + 10299424335549x^8 - 41201367881396x^7 - 506171935260830x^6 + 1662723272081664x^5 + 7501118196131608896x^4 - 15005055667263471212x^3 - 559914287081811190962x^2 + 567417098903075834864*x + 1831773137685647789586721
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{12}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.2
Root			$-19.4848 + 16.4140i$ of defining polynomial
Character	$\chi$	$=$	300.293
Dual form			300.8.i.c.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-40.5650 + 23.2698i) q^{3} +(208.115 - 208.115i) q^{7} +(1104.03 - 1887.88i) q^{9} +O(q^{10})$	\(q+(-40.5650 + 23.2698i) q^{3} +(208.115 - 208.115i) q^{7} +(1104.03 - 1887.88i) q^{9} -7004.41i q^{11} +(-9873.16 - 9873.16i) q^{13} +(-17509.4 - 17509.4i) q^{17} +24385.0i q^{19} +(-3599.39 + 13285.0i) q^{21} +(15785.8 - 15785.8i) q^{23} +(-854.643 + 102272. i) q^{27} -122497. q^{29} +228108. q^{31} +(162991. + 284134. i) q^{33} +(155115. - 155115. i) q^{37} +(630251. + 170758. i) q^{39} -725519. i q^{41} +(-430632. - 430632. i) q^{43} +(24323.9 + 24323.9i) q^{47} +736919. i q^{49} +(1.11771e6 + 302828. i) q^{51} +(-464100. + 464100. i) q^{53} +(-567434. - 989178. i) q^{57} +78012.9 q^{59} +1.98833e6 q^{61} +(-163130. - 622662. i) q^{63} +(-2.14870e6 + 2.14870e6i) q^{67} +(-273019. + 1.00768e6i) q^{69} -870154. i q^{71} +(3.29108e6 + 3.29108e6i) q^{73} +(-1.45772e6 - 1.45772e6i) q^{77} +450479. i q^{79} +(-2.34519e6 - 4.16856e6i) q^{81} +(-4.28119e6 + 4.28119e6i) q^{83} +(4.96908e6 - 2.85047e6i) q^{87} +5.27320e6 q^{89} -4.10951e6 q^{91} +(-9.25318e6 + 5.30802e6i) q^{93} +(471574. - 471574. i) q^{97} +(-1.32235e7 - 7.73311e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 215904 q^{21} + 872704 q^{31} + 1978560 q^{51} + 12752864 q^{61} + 10696176 q^{81} - 39496704 q^{91}+O(q^{100}) $ 16 * q + 215904 * q^21 + 872704 * q^31 + 1978560 * q^51 + 12752864 * q^61 + 10696176 * q^81 - 39496704 * 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
$3$	−40.5650	+	23.2698i	−0.867415	+	0.497586i
$3$	−40.5650	+	23.2698i	−0.867415	+	0.497586i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	208.115	−	208.115i	0.229330	−	0.229330i	−0.583083	−	0.812413i	$-0.698154\pi$
$7$	208.115	−	208.115i	0.229330	−	0.229330i	0.812413	+	0.583083i	$0.198154\pi$
$8$		0			0
$9$	1104.03	−	1887.88i	0.504817	−	0.863227i
$10$		0			0
$11$		−	7004.41i		−	1.58671i	−0.608760	−	0.793354i	$-0.708333\pi$
$11$		−	7004.41i		−	1.58671i	0.608760	−	0.793354i	$-0.291667\pi$
$12$		0			0
$13$	−9873.16	−	9873.16i	−1.24639	−	1.24639i	−0.957302	−	0.289089i	$-0.906648\pi$
$13$	−9873.16	−	9873.16i	−1.24639	−	1.24639i	−0.289089	−	0.957302i	$-0.593352\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−17509.4	−	17509.4i	−0.864369	−	0.864369i	0.127473	−	0.991842i	$-0.459313\pi$
$17$	−17509.4	−	17509.4i	−0.864369	−	0.864369i	−0.991842	+	0.127473i	$0.959313\pi$
$18$		0			0
$19$			24385.0i			0.815616i	0.913068	+	0.407808i	$0.133707\pi$
$19$			24385.0i			0.815616i	−0.913068	+	0.407808i	$0.866293\pi$
$20$		0			0
$21$	−3599.39	+	13285.0i	−0.0848129	+	0.313036i
$22$		0			0
$23$	15785.8	−	15785.8i	0.270533	−	0.270533i	−0.558782	−	0.829315i	$-0.688731\pi$
$23$	15785.8	−	15785.8i	0.270533	−	0.270533i	0.829315	+	0.558782i	$0.188731\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−854.643	+	102272.i	−0.00835625	+	0.999965i
$28$		0			0
$29$	−122497.			−0.932678			−0.466339	−	0.884606i	$-0.654427\pi$
$29$	−122497.			−0.932678			−0.466339	+	0.884606i	$0.654427\pi$
$30$		0			0
$31$	228108.			1.37523			0.687613	−	0.726078i	$-0.258659\pi$
$31$	228108.			1.37523			0.687613	+	0.726078i	$0.258659\pi$
$32$		0			0
$33$	162991.	+	284134.i	0.789524	+	1.37633i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	155115.	−	155115.i	0.503439	−	0.503439i	−0.409066	−	0.912505i	$-0.634145\pi$
$37$	155115.	−	155115.i	0.503439	−	0.503439i	0.912505	+	0.409066i	$0.134145\pi$
$38$		0			0
$39$	630251.	+	170758.i	1.70132	+	0.460951i
$40$		0			0
$41$		−	725519.i		−	1.64401i	−0.569478	−	0.822007i	$-0.692855\pi$
$41$		−	725519.i		−	1.64401i	0.569478	−	0.822007i	$-0.307145\pi$
$42$		0			0
$43$	−430632.	−	430632.i	−0.825974	−	0.825974i	0.160983	−	0.986957i	$-0.448534\pi$
$43$	−430632.	−	430632.i	−0.825974	−	0.825974i	−0.986957	+	0.160983i	$0.948534\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	24323.9	+	24323.9i	0.0341736	+	0.0341736i	0.723987	−	0.689813i	$-0.242307\pi$
$47$	24323.9	+	24323.9i	0.0341736	+	0.0341736i	−0.689813	+	0.723987i	$0.742307\pi$
$48$		0			0
$49$			736919.i			0.894816i
$50$		0			0
$51$	1.11771e6	+	302828.i	1.17986	+	0.319669i
$52$		0			0
$53$	−464100.	+	464100.i	−0.428200	+	0.428200i	−0.888015	−	0.459815i	$-0.847916\pi$
$53$	−464100.	+	464100.i	−0.428200	+	0.428200i	0.459815	+	0.888015i	$0.347916\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−567434.	−	989178.i	−0.405839	−	0.707477i
$58$		0			0
$59$	78012.9			0.0494521			0.0247260	−	0.999694i	$-0.492129\pi$
$59$	78012.9			0.0494521			0.0247260	+	0.999694i	$0.492129\pi$
$60$		0			0
$61$	1.98833e6			1.12159			0.560795	−	0.827954i	$-0.310495\pi$
$61$	1.98833e6			1.12159			0.560795	+	0.827954i	$0.310495\pi$
$62$		0			0
$63$	−163130.	−	622662.i	−0.0821941	−	0.313733i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.14870e6	+	2.14870e6i	−0.872797	+	0.872797i	−0.992776	−	0.119980i	$-0.961717\pi$
$67$	−2.14870e6	+	2.14870e6i	−0.872797	+	0.872797i	0.119980	+	0.992776i	$0.461717\pi$
$68$		0			0
$69$	−273019.	+	1.00768e6i	−0.100051	+	0.369278i
$70$		0			0
$71$		−	870154.i		−	0.288531i	−0.989539	−	0.144265i	$-0.953918\pi$
$71$		−	870154.i		−	0.288531i	0.989539	−	0.144265i	$-0.0460819\pi$
$72$		0			0
$73$	3.29108e6	+	3.29108e6i	0.990165	+	0.990165i	0.999952	−	0.00978664i	$-0.00311523\pi$
$73$	3.29108e6	+	3.29108e6i	0.990165	+	0.990165i	−0.00978664	+	0.999952i	$0.503115\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.45772e6	−	1.45772e6i	−0.363880	−	0.363880i
$78$		0			0
$79$			450479.i			0.102797i	0.998678	+	0.0513985i	$0.0163679\pi$
$79$			450479.i			0.102797i	−0.998678	+	0.0513985i	$0.983632\pi$
$80$		0			0
$81$	−2.34519e6	−	4.16856e6i	−0.490320	−	0.871542i
$82$		0			0
$83$	−4.28119e6	+	4.28119e6i	−0.821847	+	0.821847i	−0.986373	−	0.164525i	$-0.947391\pi$
$83$	−4.28119e6	+	4.28119e6i	−0.821847	+	0.821847i	0.164525	+	0.986373i	$0.447391\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.96908e6	−	2.85047e6i	0.809019	−	0.464087i
$88$		0			0
$89$	5.27320e6			0.792883			0.396441	−	0.918060i	$-0.370245\pi$
$89$	5.27320e6			0.792883			0.396441	+	0.918060i	$0.370245\pi$
$90$		0			0
$91$	−4.10951e6			−0.571670
$92$		0			0
$93$	−9.25318e6	+	5.30802e6i	−1.19289	+	0.684293i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	471574.	−	471574.i	0.0524624	−	0.0524624i	−0.680389	−	0.732851i	$-0.738189\pi$
$97$	471574.	−	471574.i	0.0524624	−	0.0524624i	0.732851	+	0.680389i	$0.238189\pi$
$98$		0			0
$99$	−1.32235e7	−	7.73311e6i	−1.36969	−	0.800997i
$100$		0			0
$101$			1.64755e7i			1.59116i	0.605848	+	0.795581i	$0.292834\pi$
$101$			1.64755e7i			1.59116i	−0.605848	+	0.795581i	$0.707166\pi$
$102$		0			0
$103$	−1.84694e6	−	1.84694e6i	−0.166541	−	0.166541i	0.618916	−	0.785457i	$-0.287572\pi$
$103$	−1.84694e6	−	1.84694e6i	−0.166541	−	0.166541i	−0.785457	+	0.618916i	$0.787572\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.43575e7	−	1.43575e7i	−1.13301	−	1.13301i	−0.989673	−	0.143340i	$-0.954216\pi$
$107$	−1.43575e7	−	1.43575e7i	−1.13301	−	1.13301i	−0.143340	−	0.989673i	$-0.545784\pi$
$108$		0			0
$109$		−	8.20147e6i		−	0.606595i	−0.952896	−	0.303298i	$-0.901912\pi$
$109$		−	8.20147e6i		−	0.606595i	0.952896	−	0.303298i	$-0.0980876\pi$
$110$		0			0
$111$	−2.68274e6	+	9.90172e6i	−0.186187	+	0.687195i
$112$		0			0
$113$	−1.48391e7	+	1.48391e7i	−0.967457	+	0.967457i	−0.999487	−	0.0320296i	$-0.989803\pi$
$113$	−1.48391e7	+	1.48391e7i	−0.967457	+	0.967457i	0.0320296	+	0.999487i	$0.489803\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.95396e7	+	7.73900e6i	−1.70512	+	0.446719i
$118$		0			0
$119$	−7.28794e6			−0.396452
$120$		0			0
$121$	−2.95746e7			−1.51764
$122$		0			0
$123$	1.68827e7	+	2.94307e7i	0.818038	+	1.42604i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.01955e6	+	3.01955e6i	−0.130807	+	0.130807i	−0.769479	−	0.638672i	$-0.779484\pi$
$127$	−3.01955e6	+	3.01955e6i	−0.130807	+	0.130807i	0.638672	+	0.769479i	$0.279484\pi$
$128$		0			0
$129$	2.74893e7	+	7.44786e6i	1.12746	+	0.305469i
$130$		0			0
$131$		−	2.00934e7i		−	0.780915i	−0.920621	−	0.390458i	$-0.872317\pi$
$131$		−	2.00934e7i		−	0.780915i	0.920621	−	0.390458i	$-0.127683\pi$
$132$		0			0
$133$	5.07490e6	+	5.07490e6i	0.187045	+	0.187045i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.47844e6	−	9.47844e6i	−0.314931	−	0.314931i	0.531886	−	0.846816i	$-0.321484\pi$
$137$	−9.47844e6	−	9.47844e6i	−0.314931	−	0.314931i	−0.846816	+	0.531886i	$0.821484\pi$
$138$		0			0
$139$		−	1.38424e7i		−	0.437180i	−0.975817	−	0.218590i	$-0.929854\pi$
$139$		−	1.38424e7i		−	0.437180i	0.975817	−	0.218590i	$-0.0701458\pi$
$140$		0			0
$141$	−1.55271e6	−	420687.i	−0.0466470	−	0.0126384i
$142$		0			0
$143$	−6.91556e7	+	6.91556e7i	−1.97766	+	1.97766i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.71479e7	−	2.98931e7i	−0.445247	−	0.776176i
$148$		0			0
$149$	−4.65482e7			−1.15279			−0.576396	−	0.817170i	$-0.695542\pi$
$149$	−4.65482e7			−1.15279			−0.576396	+	0.817170i	$0.695542\pi$
$150$		0			0
$151$	4.01802e7			0.949714			0.474857	−	0.880063i	$-0.342500\pi$
$151$	4.01802e7			0.949714			0.474857	+	0.880063i	$0.342500\pi$
$152$		0			0
$153$	−5.23865e7	+	1.37246e7i	−1.18249	+	0.309798i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.05276e7	−	2.05276e7i	0.423340	−	0.423340i	−0.463012	−	0.886352i	$-0.653231\pi$
$157$	2.05276e7	−	2.05276e7i	0.423340	−	0.423340i	0.886352	+	0.463012i	$0.153231\pi$
$158$		0			0
$159$	8.02670e6	−	2.96257e7i	0.158361	−	0.584493i
$160$		0			0
$161$		−	6.57055e6i		−	0.124083i
$162$		0			0
$163$	3.27257e7	+	3.27257e7i	0.591879	+	0.591879i	0.938139	−	0.346260i	$-0.112549\pi$
$163$	3.27257e7	+	3.27257e7i	0.591879	+	0.591879i	−0.346260	+	0.938139i	$0.612549\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.86557e7	−	5.86557e7i	−0.974546	−	0.974546i	0.0251383	−	0.999684i	$-0.491997\pi$
$167$	−5.86557e7	−	5.86557e7i	−0.974546	−	0.974546i	−0.999684	+	0.0251383i	$0.991997\pi$
$168$		0			0
$169$			1.32210e8i			2.10698i
$170$		0			0
$171$	4.60359e7	+	2.69219e7i	0.704061	+	0.411737i
$172$		0			0
$173$	−5.72521e7	+	5.72521e7i	−0.840679	+	0.840679i	−0.988947	−	0.148268i	$-0.952630\pi$
$173$	−5.72521e7	+	5.72521e7i	−0.840679	+	0.840679i	0.148268	+	0.988947i	$0.452630\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.16459e6	+	1.81534e6i	−0.0428954	+	0.0246066i
$178$		0			0
$179$	6.51415e7			0.848930			0.424465	−	0.905444i	$-0.360462\pi$
$179$	6.51415e7			0.848930			0.424465	+	0.905444i	$0.360462\pi$
$180$		0			0
$181$	4.65856e7			0.583951			0.291976	−	0.956426i	$-0.405687\pi$
$181$	4.65856e7			0.583951			0.291976	+	0.956426i	$0.405687\pi$
$182$		0			0
$183$	−8.06566e7	+	4.62681e7i	−0.972885	+	0.558088i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.22643e8	+	1.22643e8i	−1.37150	+	1.37150i
$188$		0			0
$189$	2.11066e7	+	2.14623e7i	0.227406	+	0.231238i
$190$		0			0
$191$		−	1.17412e8i		−	1.21926i	−0.792685	−	0.609631i	$-0.791318\pi$
$191$		−	1.17412e8i		−	1.21926i	0.792685	−	0.609631i	$-0.208682\pi$
$192$		0			0
$193$	1.10869e8	+	1.10869e8i	1.11010	+	1.11010i	0.993136	+	0.116961i	$0.0373153\pi$
$193$	1.10869e8	+	1.10869e8i	1.11010	+	1.11010i	0.116961	+	0.993136i	$0.462685\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.03739e8	−	1.03739e8i	−0.966739	−	0.966739i	0.0327254	−	0.999464i	$-0.489581\pi$
$197$	−1.03739e8	−	1.03739e8i	−0.966739	−	0.966739i	−0.999464	+	0.0327254i	$0.989581\pi$
$198$		0			0
$199$		−	8.08544e7i		−	0.727307i	−0.931534	−	0.363654i	$-0.881529\pi$
$199$		−	8.08544e7i		−	0.727307i	0.931534	−	0.363654i	$-0.118471\pi$
$200$		0			0
$201$	3.71621e7	−	1.37161e8i	0.322786	−	1.19137i
$202$		0			0
$203$	−2.54935e7	+	2.54935e7i	−0.213891	+	0.213891i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.23736e7	−	4.72298e7i	−0.0969616	−	0.370101i
$208$		0			0
$209$	1.70803e8			1.29414
$210$		0			0
$211$	8.34222e6			0.0611355			0.0305677	−	0.999533i	$-0.490268\pi$
$211$	8.34222e6			0.0611355			0.0305677	+	0.999533i	$0.490268\pi$
$212$		0			0
$213$	2.02483e7	+	3.52978e7i	0.143569	+	0.250276i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.74727e7	−	4.74727e7i	0.315381	−	0.315381i
$218$		0			0
$219$	−2.10085e8	−	5.69198e7i	−1.35158	−	0.366192i
$220$		0			0
$221$			3.45746e8i			2.15468i
$222$		0			0
$223$	−1.74036e8	−	1.74036e8i	−1.05092	−	1.05092i	−0.998632	−	0.0522927i	$-0.983347\pi$
$223$	−1.74036e8	−	1.74036e8i	−1.05092	−	1.05092i	−0.0522927	−	0.998632i	$-0.516653\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.22939e7	+	7.22939e7i	0.410215	+	0.410215i	0.881813	−	0.471599i	$-0.156323\pi$
$227$	7.22939e7	+	7.22939e7i	0.410215	+	0.410215i	−0.471599	+	0.881813i	$0.656323\pi$
$228$		0			0
$229$			2.01557e8i			1.10911i	0.832148	+	0.554554i	$0.187111\pi$
$229$			2.01557e8i			1.10911i	−0.832148	+	0.554554i	$0.812889\pi$
$230$		0			0
$231$	9.30535e7	+	2.52116e7i	0.496696	+	0.134573i
$232$		0			0
$233$	−2.06022e8	+	2.06022e8i	−1.06701	+	1.06701i	−0.0694233	+	0.997587i	$0.522116\pi$
$233$	−2.06022e8	+	2.06022e8i	−1.06701	+	1.06701i	−0.997587	+	0.0694233i	$0.977884\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.04826e7	−	1.82737e7i	−0.0511503	−	0.0891676i
$238$		0			0
$239$	−2.20720e8			−1.04580			−0.522899	−	0.852394i	$-0.675150\pi$
$239$	−2.20720e8			−1.04580			−0.522899	+	0.852394i	$0.675150\pi$
$240$		0			0
$241$	−4.25054e8			−1.95607			−0.978035	−	0.208440i	$-0.933161\pi$
$241$	−4.25054e8			−1.95607			−0.978035	+	0.208440i	$0.933161\pi$
$242$		0			0
$243$	1.92134e8	+	1.14526e8i	0.858978	+	0.512012i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.40757e8	−	2.40757e8i	1.01658	−	1.01658i
$248$		0			0
$249$	7.40440e7	−	2.73289e8i	0.303943	−	1.12182i
$250$		0			0
$251$		−	1.74762e8i		−	0.697573i	−0.937202	−	0.348787i	$-0.886594\pi$
$251$		−	1.74762e8i		−	0.697573i	0.937202	−	0.348787i	$-0.113406\pi$
$252$		0			0
$253$	−1.10570e8	−	1.10570e8i	−0.429257	−	0.429257i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.89089e8	+	1.89089e8i	0.694864	+	0.694864i	0.963298	−	0.268434i	$-0.0865061\pi$
$257$	1.89089e8	+	1.89089e8i	0.694864	+	0.694864i	−0.268434	+	0.963298i	$0.586506\pi$
$258$		0			0
$259$		−	6.45635e7i		−	0.230908i
$260$		0			0
$261$	−1.35241e8	+	2.31259e8i	−0.470832	+	0.805112i
$262$		0			0
$263$	3.69233e8	−	3.69233e8i	1.25157	−	1.25157i	0.296556	−	0.955015i	$-0.404162\pi$
$263$	3.69233e8	−	3.69233e8i	1.25157	−	1.25157i	0.955015	−	0.296556i	$-0.0958382\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.13907e8	+	1.22706e8i	−0.687758	+	0.394527i
$268$		0			0
$269$	−8.90340e7			−0.278884			−0.139442	−	0.990230i	$-0.544531\pi$
$269$	−8.90340e7			−0.278884			−0.139442	+	0.990230i	$0.544531\pi$
$270$		0			0
$271$	−1.21578e8			−0.371076			−0.185538	−	0.982637i	$-0.559403\pi$
$271$	−1.21578e8			−0.371076			−0.185538	+	0.982637i	$0.559403\pi$
$272$		0			0
$273$	1.66702e8	−	9.56274e7i	0.495875	−	0.284455i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.68927e8	+	4.68927e8i	−1.32564	+	1.32564i	−0.416511	+	0.909131i	$0.636747\pi$
$277$	−4.68927e8	+	4.68927e8i	−1.32564	+	1.32564i	−0.909131	+	0.416511i	$0.863253\pi$
$278$		0			0
$279$	2.51839e8	−	4.30639e8i	0.694237	−	1.18713i
$280$		0			0
$281$		−	2.39688e8i		−	0.644427i	−0.946667	−	0.322214i	$-0.895573\pi$
$281$		−	2.39688e8i		−	0.644427i	0.946667	−	0.322214i	$-0.104427\pi$
$282$		0			0
$283$	1.76790e8	+	1.76790e8i	0.463665	+	0.463665i	0.899855	−	0.436190i	$-0.143672\pi$
$283$	1.76790e8	+	1.76790e8i	0.463665	+	0.463665i	−0.436190	+	0.899855i	$0.643672\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.50992e8	−	1.50992e8i	−0.377022	−	0.377022i
$288$		0			0
$289$			2.02818e8i			0.494269i
$290$		0			0
$291$	−8.15596e6	+	3.01028e7i	−0.0194021	+	0.0716113i
$292$		0			0
$293$	4.55883e8	−	4.55883e8i	1.05881	−	1.05881i	0.0606464	−	0.998159i	$-0.480684\pi$
$293$	4.55883e8	−	4.55883e8i	1.05881	−	1.05881i	0.998159	−	0.0606464i	$-0.0193162\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	7.16357e8	+	5.98627e6i	1.58665	+	0.0132589i
$298$		0			0
$299$	−3.11712e8			−0.674380
$300$		0			0
$301$	−1.79242e8			−0.378841
$302$		0			0
$303$	−3.83382e8	−	6.68329e8i	−0.791739	−	1.38020i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	4.07641e8	−	4.07641e8i	0.804068	−	0.804068i	−0.179660	−	0.983729i	$-0.557500\pi$
$307$	4.07641e8	−	4.07641e8i	0.804068	−	0.804068i	0.983729	+	0.179660i	$0.0574998\pi$
$308$		0			0
$309$	1.17899e8	+	3.19431e7i	0.227329	+	0.0615918i
$310$		0			0
$311$			8.42251e8i			1.58774i	0.608086	+	0.793871i	$0.291938\pi$
$311$			8.42251e8i			1.58774i	−0.608086	+	0.793871i	$0.708062\pi$
$312$		0			0
$313$	−2.45437e8	−	2.45437e8i	−0.452414	−	0.452414i	0.443741	−	0.896155i	$-0.353651\pi$
$313$	−2.45437e8	−	2.45437e8i	−0.452414	−	0.452414i	−0.896155	+	0.443741i	$0.853651\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.61944e8	+	5.61944e8i	0.990799	+	0.990799i	0.999958	−	0.00915869i	$-0.00291534\pi$
$317$	5.61944e8	+	5.61944e8i	0.990799	+	0.990799i	−0.00915869	+	0.999958i	$0.502915\pi$
$318$		0			0
$319$			8.58018e8i			1.47989i
$320$		0			0
$321$	9.16507e8	+	2.48315e8i	1.54656	+	0.419021i
$322$		0			0
$323$	4.26967e8	−	4.26967e8i	0.704994	−	0.704994i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.90846e8	+	3.32692e8i	0.301833	+	0.526169i
$328$		0			0
$329$	1.01244e7			0.0156741
$330$		0			0
$331$	−2.41804e8			−0.366494			−0.183247	−	0.983067i	$-0.558661\pi$
$331$	−2.41804e8			−0.366494			−0.183247	+	0.983067i	$0.558661\pi$
$332$		0			0
$333$	−1.21586e8	−	4.64090e8i	−0.180438	−	0.688727i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	4.29724e8	−	4.29724e8i	0.611625	−	0.611625i	−0.331744	−	0.943369i	$-0.607637\pi$
$337$	4.29724e8	−	4.29724e8i	0.611625	−	0.611625i	0.943369	+	0.331744i	$0.107637\pi$
$338$		0			0
$339$	2.56644e8	−	9.47248e8i	0.357794	−	1.32058i
$340$		0			0
$341$		−	1.59776e9i		−	2.18208i
$342$		0			0
$343$	3.24756e8	+	3.24756e8i	0.434538	+	0.434538i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.11375e8	+	3.11375e8i	0.400065	+	0.400065i	0.878256	−	0.478191i	$-0.158707\pi$
$347$	3.11375e8	+	3.11375e8i	0.400065	+	0.400065i	−0.478191	+	0.878256i	$0.658707\pi$
$348$		0			0
$349$			8.50967e8i			1.07158i	0.844352	+	0.535789i	$0.179986\pi$
$349$			8.50967e8i			1.07158i	−0.844352	+	0.535789i	$0.820014\pi$
$350$		0			0
$351$	1.01819e9	−	1.00131e9i	1.25676	−	1.23593i
$352$		0			0
$353$	6.66049e8	−	6.66049e8i	0.805925	−	0.805925i	−0.178090	−	0.984014i	$-0.556992\pi$
$353$	6.66049e8	−	6.66049e8i	0.805925	−	0.805925i	0.984014	+	0.178090i	$0.0569917\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.95635e8	−	1.69589e8i	0.343888	−	0.197269i
$358$		0			0
$359$	1.30978e9			1.49406			0.747029	−	0.664791i	$-0.231480\pi$
$359$	1.30978e9			1.49406			0.747029	+	0.664791i	$0.231480\pi$
$360$		0			0
$361$	2.99242e8			0.334770
$362$		0			0
$363$	1.19969e9	−	6.88194e8i	1.31643	−	0.755158i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.61703e8	+	7.61703e8i	−0.804367	+	0.804367i	−0.983775	−	0.179408i	$-0.942582\pi$
$367$	−7.61703e8	+	7.61703e8i	−0.804367	+	0.804367i	0.179408	+	0.983775i	$0.442582\pi$
$368$		0			0
$369$	−1.36969e9	−	8.00998e8i	−1.41916	−	0.829925i
$370$		0			0
$371$			1.93173e8i			0.196398i
$372$		0			0
$373$	−2.12129e7	−	2.12129e7i	−0.0211650	−	0.0211650i	0.696445	−	0.717610i	$-0.254764\pi$
$373$	−2.12129e7	−	2.12129e7i	−0.0211650	−	0.0211650i	−0.717610	+	0.696445i	$0.754764\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.20943e9	+	1.20943e9i	1.16248	+	1.16248i
$378$		0			0
$379$			2.01580e9i			1.90200i	0.309195	+	0.950999i	$0.399940\pi$
$379$			2.01580e9i			1.90200i	−0.309195	+	0.950999i	$0.600060\pi$
$380$		0			0
$381$	5.22237e7	−	1.92752e8i	0.0483760	−	0.178551i
$382$		0			0
$383$	6.64823e8	−	6.64823e8i	0.604658	−	0.604658i	−0.336887	−	0.941545i	$-0.609374\pi$
$383$	6.64823e8	−	6.64823e8i	0.604658	−	0.604658i	0.941545	+	0.336887i	$0.109374\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.28841e9	+	3.37547e8i	−1.12997	+	0.296037i
$388$		0			0
$389$	7.81809e8			0.673406			0.336703	−	0.941611i	$-0.390688\pi$
$389$	7.81809e8			0.673406			0.336703	+	0.941611i	$0.390688\pi$
$390$		0			0
$391$	−5.52800e8			−0.467681
$392$		0			0
$393$	4.67569e8	+	8.15088e8i	0.388572	+	0.677377i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.04364e9	−	1.04364e9i	0.837110	−	0.837110i	−0.151367	−	0.988478i	$-0.548368\pi$
$397$	1.04364e9	−	1.04364e9i	0.837110	−	0.837110i	0.988478	+	0.151367i	$0.0483677\pi$
$398$		0			0
$399$	−3.23955e8	−	8.77713e7i	−0.255317	−	0.0691747i
$400$		0			0
$401$			2.04506e9i			1.58380i	0.610649	+	0.791901i	$0.290909\pi$
$401$			2.04506e9i			1.58380i	−0.610649	+	0.791901i	$0.709091\pi$
$402$		0			0
$403$	−2.25214e9	−	2.25214e9i	−1.71407	−	1.71407i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.08649e9	−	1.08649e9i	−0.798812	−	0.798812i
$408$		0			0
$409$			1.59201e8i			0.115058i	0.998344	+	0.0575288i	$0.0183221\pi$
$409$			1.59201e8i			0.115058i	−0.998344	+	0.0575288i	$0.981678\pi$
$410$		0			0
$411$	6.05054e8	+	1.63931e8i	0.429880	+	0.116470i
$412$		0			0
$413$	1.62357e7	−	1.62357e7i	0.0113408	−	0.0113408i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.22110e8	+	5.61518e8i	0.217535	+	0.379217i
$418$		0			0
$419$	−1.84493e9			−1.22527			−0.612635	−	0.790366i	$-0.709890\pi$
$419$	−1.84493e9			−1.22527			−0.612635	+	0.790366i	$0.709890\pi$
$420$		0			0
$421$	−6.31405e8			−0.412402			−0.206201	−	0.978510i	$-0.566110\pi$
$421$	−6.31405e8			−0.412402			−0.206201	+	0.978510i	$0.566110\pi$
$422$		0			0
$423$	7.27750e7	−	1.90661e7i	0.0467510	−	0.0122482i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4.13802e8	−	4.13802e8i	0.257214	−	0.257214i
$428$		0			0
$429$	1.19606e9	−	4.41453e9i	0.731396	−	2.69951i
$430$		0			0
$431$		−	5.92656e8i		−	0.356560i	−0.983980	−	0.178280i	$-0.942947\pi$
$431$		−	5.92656e8i		−	0.356560i	0.983980	−	0.178280i	$-0.0570532\pi$
$432$		0			0
$433$	4.10579e8	+	4.10579e8i	0.243046	+	0.243046i	0.818109	−	0.575063i	$-0.195022\pi$
$433$	4.10579e8	+	4.10579e8i	0.243046	+	0.243046i	−0.575063	+	0.818109i	$0.695022\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.84938e8	+	3.84938e8i	0.220651	+	0.220651i
$438$		0			0
$439$			2.00227e9i			1.12953i	0.825252	+	0.564764i	$0.191033\pi$
$439$			2.00227e9i			1.12953i	−0.825252	+	0.564764i	$0.808967\pi$
$440$		0			0
$441$	1.39121e9	+	8.13584e8i	0.772428	+	0.451718i
$442$		0			0
$443$	−2.16030e8	+	2.16030e8i	−0.118059	+	0.118059i	−0.763668	−	0.645609i	$-0.776604\pi$
$443$	−2.16030e8	+	2.16030e8i	−0.118059	+	0.118059i	0.645609	+	0.763668i	$0.276604\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.88823e9	−	1.08317e9i	0.999950	−	0.573613i
$448$		0			0
$449$	−5.11732e8			−0.266797			−0.133398	−	0.991062i	$-0.542589\pi$
$449$	−5.11732e8			−0.266797			−0.133398	+	0.991062i	$0.542589\pi$
$450$		0			0
$451$	−5.08183e9			−2.60857
$452$		0			0
$453$	−1.62991e9	+	9.34985e8i	−0.823796	+	0.472564i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.62621e8	+	8.62621e8i	−0.422779	+	0.422779i	−0.886159	−	0.463380i	$-0.846636\pi$
$457$	−8.62621e8	+	8.62621e8i	−0.422779	+	0.422779i	0.463380	+	0.886159i	$0.346636\pi$
$458$		0			0
$459$	1.80569e9	−	1.77576e9i	0.871562	−	0.857116i
$460$		0			0
$461$		−	1.93234e9i		−	0.918609i	−0.888279	−	0.459304i	$-0.848099\pi$
$461$		−	1.93234e9i		−	0.918609i	0.888279	−	0.459304i	$-0.151901\pi$
$462$		0			0
$463$	2.48394e9	+	2.48394e9i	1.16308	+	1.16308i	0.983799	+	0.179276i	$0.0573756\pi$
$463$	2.48394e9	+	2.48394e9i	1.16308	+	1.16308i	0.179276	+	0.983799i	$0.442624\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.66432e9	−	1.66432e9i	−0.756183	−	0.756183i	0.219443	−	0.975625i	$-0.429576\pi$
$467$	−1.66432e9	−	1.66432e9i	−0.756183	−	0.756183i	−0.975625	+	0.219443i	$0.929576\pi$
$468$		0			0
$469$			8.94353e8i			0.400317i
$470$		0			0
$471$	−3.55029e8	+	1.31037e9i	−0.156563	+	0.577859i
$472$		0			0
$473$	−3.01632e9	+	3.01632e9i	−1.31058	+	1.31058i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.63781e8	+	1.38855e9i	0.153471	+	0.585796i
$478$		0			0
$479$	1.04923e8			0.0436213			0.0218106	−	0.999762i	$-0.493057\pi$
$479$	1.04923e8			0.0436213			0.0218106	+	0.999762i	$0.493057\pi$
$480$		0			0
$481$	−3.06295e9			−1.25496
$482$		0			0
$483$	1.52895e8	+	2.66534e8i	0.0617417	+	0.107631i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.88946e9	+	2.88946e9i	−1.13362	+	1.13362i	−0.144044	+	0.989571i	$0.546011\pi$
$487$	−2.88946e9	+	2.88946e9i	−1.13362	+	1.13362i	−0.989571	+	0.144044i	$0.953989\pi$
$488$		0			0
$489$	−2.08904e9	−	5.65998e8i	−0.807915	−	0.218894i
$490$		0			0
$491$			2.35081e9i			0.896258i	0.893969	+	0.448129i	$0.147910\pi$
$491$			2.35081e9i			0.896258i	−0.893969	+	0.448129i	$0.852090\pi$
$492$		0			0
$493$	2.14484e9	+	2.14484e9i	0.806178	+	0.806178i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.81092e8	−	1.81092e8i	−0.0661687	−	0.0661687i
$498$		0			0
$499$			1.74159e9i			0.627471i	0.949510	+	0.313736i	$0.101581\pi$
$499$			1.74159e9i			0.627471i	−0.949510	+	0.313736i	$0.898419\pi$
$500$		0			0
$501$	3.74427e9	+	1.01446e9i	1.33026	+	0.360415i
$502$		0			0
$503$	1.07332e9	−	1.07332e9i	0.376046	−	0.376046i	−0.493628	−	0.869673i	$-0.664329\pi$
$503$	1.07332e9	−	1.07332e9i	0.376046	−	0.376046i	0.869673	+	0.493628i	$0.164329\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.07650e9	−	5.36309e9i	−1.04840	−	1.82763i
$508$		0			0
$509$	−5.65019e9			−1.89911			−0.949556	−	0.313598i	$-0.898466\pi$
$509$	−5.65019e9			−1.89911			−0.949556	+	0.313598i	$0.898466\pi$
$510$		0			0
$511$	1.36985e9			0.454149
$512$		0			0
$513$	−2.49391e9	−	2.08405e7i	−0.815588	−	0.00681549i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	1.70375e8	−	1.70375e8i	0.0542236	−	0.0542236i
$518$		0			0
$519$	9.90186e8	−	3.65468e9i	0.310908	−	1.14753i
$520$		0			0
$521$		−	1.72735e8i		−	0.0535118i	−0.999642	−	0.0267559i	$-0.991482\pi$
$521$		−	1.72735e8i		−	0.0535118i	0.999642	−	0.0267559i	$-0.00851768\pi$
$522$		0			0
$523$	−2.43183e9	−	2.43183e9i	−0.743324	−	0.743324i	0.229892	−	0.973216i	$-0.426163\pi$
$523$	−2.43183e9	−	2.43183e9i	−0.743324	−	0.743324i	−0.973216	+	0.229892i	$0.926163\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.99402e9	−	3.99402e9i	−1.18870	−	1.18870i
$528$		0			0
$529$			2.90644e9i			0.853624i
$530$		0			0
$531$	8.61289e7	−	1.47279e8i	0.0249642	−	0.0426883i
$532$		0			0
$533$	−7.16316e9	+	7.16316e9i	−2.04908	+	2.04908i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−2.64246e9	+	1.51583e9i	−0.736374	+	0.422415i
$538$		0			0
$539$	5.16168e9			1.41981
$540$		0			0
$541$	1.02142e8			0.0277340			0.0138670	−	0.999904i	$-0.495586\pi$
$541$	1.02142e8			0.0277340			0.0138670	+	0.999904i	$0.495586\pi$
$542$		0			0
$543$	−1.88974e9	+	1.08404e9i	−0.506528	+	0.290566i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.32606e9	−	1.32606e9i	0.346425	−	0.346425i	−0.512351	−	0.858776i	$-0.671225\pi$
$547$	1.32606e9	−	1.32606e9i	0.346425	−	0.346425i	0.858776	+	0.512351i	$0.171225\pi$
$548$		0			0
$549$	2.19519e9	−	3.75373e9i	0.566198	−	0.968187i
$550$		0			0
$551$		−	2.98709e9i		−	0.760707i
$552$		0			0
$553$	9.37517e7	+	9.37517e7i	0.0235744	+	0.0235744i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.99637e9	+	2.99637e9i	0.734686	+	0.734686i	0.971544	−	0.236858i	$-0.0761177\pi$
$557$	2.99637e9	+	2.99637e9i	0.734686	+	0.734686i	−0.236858	+	0.971544i	$0.576118\pi$
$558$		0			0
$559$			8.50339e9i			2.05897i
$560$		0			0
$561$	2.12113e9	−	7.82887e9i	0.507221	−	1.87210i
$562$		0			0
$563$	−1.93345e9	+	1.93345e9i	−0.456619	+	0.456619i	−0.897544	−	0.440925i	$-0.854651\pi$
$563$	−1.93345e9	+	1.93345e9i	−0.456619	+	0.456619i	0.440925	+	0.897544i	$0.354651\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.35561e9	−	3.79472e8i	−0.312316	−	0.0874257i
$568$		0			0
$569$	6.47404e9			1.47327			0.736635	−	0.676291i	$-0.236414\pi$
$569$	6.47404e9			1.47327			0.736635	+	0.676291i	$0.236414\pi$
$570$		0			0
$571$	1.26336e9			0.283988			0.141994	−	0.989868i	$-0.454649\pi$
$571$	1.26336e9			0.283988			0.141994	+	0.989868i	$0.454649\pi$
$572$		0			0
$573$	2.73216e9	+	4.76283e9i	0.606688	+	1.05761i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	3.72702e9	−	3.72702e9i	0.807694	−	0.807694i	−0.176591	−	0.984284i	$-0.556507\pi$
$577$	3.72702e9	−	3.72702e9i	0.807694	−	0.807694i	0.984284	+	0.176591i	$0.0565069\pi$
$578$		0			0
$579$	−7.07732e9	−	1.91751e9i	−1.51528	−	0.410546i
$580$		0			0
$581$			1.78196e9i			0.376949i
$582$		0			0
$583$	3.25075e9	+	3.25075e9i	0.679428	+	0.679428i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.89458e9	−	4.89458e9i	−0.998809	−	0.998809i	0.00119025	−	0.999999i	$-0.499621\pi$
$587$	−4.89458e9	−	4.89458e9i	−0.998809	−	0.998809i	−0.999999	+	0.00119025i	$0.999621\pi$
$588$		0			0
$589$			5.56241e9i			1.12166i
$590$		0			0
$591$	6.62214e9	+	1.79418e9i	1.31960	+	0.357528i
$592$		0			0
$593$	−1.78642e9	+	1.78642e9i	−0.351797	+	0.351797i	−0.860778	−	0.508981i	$-0.830022\pi$
$593$	−1.78642e9	+	1.78642e9i	−0.351797	+	0.351797i	0.508981	+	0.860778i	$0.330022\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.88146e9	+	3.27986e9i	0.361898	+	0.630877i
$598$		0			0
$599$	5.07984e9			0.965731			0.482865	−	0.875695i	$-0.339596\pi$
$599$	5.07984e9			0.965731			0.482865	+	0.875695i	$0.339596\pi$
$600$		0			0
$601$	−1.30990e9			−0.246138			−0.123069	−	0.992398i	$-0.539274\pi$
$601$	−1.30990e9			−0.246138			−0.123069	+	0.992398i	$0.539274\pi$
$602$		0			0
$603$	1.68424e9	+	6.42871e9i	0.312819	+	1.19402i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.46174e9	+	6.46174e9i	−1.17271	+	1.17271i	−0.191144	+	0.981562i	$0.561220\pi$
$607$	−6.46174e9	+	6.46174e9i	−1.17271	+	1.17271i	−0.981562	+	0.191144i	$0.938780\pi$
$608$		0			0
$609$	4.40914e8	−	1.62737e9i	0.0791031	−	0.291961i
$610$		0			0
$611$		−	4.80308e8i		−	0.0851874i
$612$		0			0
$613$	−1.40772e9	−	1.40772e9i	−0.246834	−	0.246834i	0.572836	−	0.819670i	$-0.305843\pi$
$613$	−1.40772e9	−	1.40772e9i	−0.246834	−	0.246834i	−0.819670	+	0.572836i	$0.805843\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.28198e8	+	2.28198e8i	0.0391123	+	0.0391123i	0.726392	−	0.687280i	$-0.241196\pi$
$617$	2.28198e8	+	2.28198e8i	0.0391123	+	0.0391123i	−0.687280	+	0.726392i	$0.741196\pi$
$618$		0			0
$619$		−	2.44766e9i		−	0.414795i	−0.978257	−	0.207398i	$-0.933501\pi$
$619$		−	2.44766e9i		−	0.414795i	0.978257	−	0.207398i	$-0.0664994\pi$
$620$		0			0
$621$	1.60096e9	+	1.62794e9i	0.268263	+	0.272784i
$622$		0			0
$623$	1.09743e9	−	1.09743e9i	0.181832	−	0.181832i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−6.92861e9	+	3.97454e9i	−1.12256	+	0.643948i
$628$		0			0
$629$	−5.43193e9			−0.870315
$630$		0			0
$631$	2.12819e9			0.337216			0.168608	−	0.985683i	$-0.446073\pi$
$631$	2.12819e9			0.337216			0.168608	+	0.985683i	$0.446073\pi$
$632$		0			0
$633$	−3.38402e8	+	1.94122e8i	−0.0530298	+	0.0304201i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	7.27572e9	−	7.27572e9i	1.11529	−	1.11529i
$638$		0			0
$639$	−1.64274e9	−	9.60680e8i	−0.249067	−	0.145655i
$640$		0			0
$641$			5.56635e9i			0.834771i	0.908730	+	0.417385i	$0.137053\pi$
$641$			5.56635e9i			0.834771i	−0.908730	+	0.417385i	$0.862947\pi$
$642$		0			0
$643$	−3.31903e9	−	3.31903e9i	−0.492349	−	0.492349i	0.416697	−	0.909046i	$-0.363188\pi$
$643$	−3.31903e9	−	3.31903e9i	−0.492349	−	0.492349i	−0.909046	+	0.416697i	$0.863188\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.59584e9	−	6.59584e9i	−0.957425	−	0.957425i	0.0417046	−	0.999130i	$-0.486721\pi$
$647$	−6.59584e9	−	6.59584e9i	−0.957425	−	0.957425i	−0.999130	+	0.0417046i	$0.986721\pi$
$648$		0			0
$649$		−	5.46434e8i		−	0.0784660i
$650$		0			0
$651$	−8.21049e8	+	3.03041e9i	−0.116637	+	0.430495i
$652$		0			0
$653$	1.48024e7	−	1.48024e7i	0.00208035	−	0.00208035i	−0.706066	−	0.708146i	$-0.749532\pi$
$653$	1.48024e7	−	1.48024e7i	0.00208035	−	0.00208035i	0.708146	+	0.706066i	$0.249532\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	9.84660e9	−	2.57968e9i	1.35459	−	0.354885i
$658$		0			0
$659$	−1.36101e10			−1.85252			−0.926261	−	0.376882i	$-0.876996\pi$
$659$	−1.36101e10			−1.85252			−0.926261	+	0.376882i	$0.876996\pi$
$660$		0			0
$661$	−6.92029e9			−0.932008			−0.466004	−	0.884783i	$-0.654307\pi$
$661$	−6.92029e9			−0.932008			−0.466004	+	0.884783i	$0.654307\pi$
$662$		0			0
$663$	−8.04542e9	−	1.40252e10i	−1.07214	−	1.86900i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.93371e9	+	1.93371e9i	−0.252320	+	0.252320i
$668$		0			0
$669$	1.11095e10	+	3.00998e9i	1.43451	+	0.388662i
$670$		0			0
$671$		−	1.39271e10i		−	1.77964i
$672$		0			0
$673$	2.28430e9	+	2.28430e9i	0.288869	+	0.288869i	0.836633	−	0.547764i	$-0.184521\pi$
$673$	2.28430e9	+	2.28430e9i	0.288869	+	0.288869i	−0.547764	+	0.836633i	$0.684521\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.48446e9	+	8.48446e9i	1.05091	+	1.05091i	0.998633	+	0.0522733i	$0.0166467\pi$
$677$	8.48446e9	+	8.48446e9i	1.05091	+	1.05091i	0.0522733	+	0.998633i	$0.483353\pi$
$678$		0			0
$679$		−	1.96283e8i		−	0.0240624i
$680$		0			0
$681$	−4.61487e9	−	1.25034e9i	−0.559944	−	0.151709i
$682$		0			0
$683$	4.90325e9	−	4.90325e9i	0.588860	−	0.588860i	−0.348463	−	0.937323i	$-0.613296\pi$
$683$	4.90325e9	−	4.90325e9i	0.588860	−	0.588860i	0.937323	+	0.348463i	$0.113296\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−4.69019e9	−	8.17616e9i	−0.551877	−	0.962057i
$688$		0			0
$689$	9.16427e9			1.06741
$690$		0			0
$691$	−1.48616e10			−1.71353			−0.856765	−	0.515707i	$-0.827529\pi$
$691$	−1.48616e10			−1.71353			−0.856765	+	0.515707i	$0.827529\pi$
$692$		0			0
$693$	−4.36138e9	+	1.14263e9i	−0.497803	+	0.130418i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.27034e10	+	1.27034e10i	−1.42103	+	1.42103i
$698$		0			0
$699$	3.56320e9	−	1.31514e10i	0.394611	−	1.45647i
$700$		0			0
$701$			6.00461e9i			0.658372i	0.944265	+	0.329186i	$0.106774\pi$
$701$			6.00461e9i			0.658372i	−0.944265	+	0.329186i	$0.893226\pi$
$702$		0			0
$703$	3.78248e9	+	3.78248e9i	0.410613	+	0.410613i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.42881e9	+	3.42881e9i	0.364901	+	0.364901i
$708$		0			0
$709$			3.62435e9i			0.381916i	0.981598	+	0.190958i	$0.0611595\pi$
$709$			3.62435e9i			0.381916i	−0.981598	+	0.190958i	$0.938840\pi$
$710$		0			0
$711$	8.50449e8	+	4.97345e8i	0.0887370	+	0.0518936i
$712$		0			0
$713$	3.60087e9	−	3.60087e9i	0.372044	−	0.372044i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	8.95348e9	−	5.13610e9i	0.907141	−	0.520375i
$718$		0			0
$719$	−1.29081e10			−1.29512			−0.647562	−	0.762013i	$-0.724211\pi$
$719$	−1.29081e10			−1.29512			−0.647562	+	0.762013i	$0.724211\pi$
$720$		0			0
$721$	−7.68751e8			−0.0763858
$722$		0			0
$723$	1.72423e10	−	9.89092e9i	1.69672	−	0.973313i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.33372e10	−	1.33372e10i	1.28734	−	1.28734i	0.350942	−	0.936397i	$-0.385861\pi$
$727$	1.33372e10	−	1.33372e10i	1.28734	−	1.28734i	0.936397	−	0.350942i	$-0.114139\pi$
$728$		0			0
$729$	−1.04589e10	−	1.74813e8i	−0.999860	−	0.0167119i
$730$		0			0
$731$			1.50802e10i			1.42789i
$732$		0			0
$733$	1.38410e9	+	1.38410e9i	0.129809	+	0.129809i	0.769026	−	0.639217i	$-0.220742\pi$
$733$	1.38410e9	+	1.38410e9i	0.129809	+	0.129809i	−0.639217	+	0.769026i	$0.720742\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.50503e10	+	1.50503e10i	1.38487	+	1.38487i
$738$		0			0
$739$		−	1.46663e10i		−	1.33680i	−0.743804	−	0.668398i	$-0.766980\pi$
$739$		−	1.46663e10i		−	1.33680i	0.743804	−	0.668398i	$-0.233020\pi$
$740$		0			0
$741$	−4.16394e9	+	1.53687e10i	−0.375959	+	1.38763i
$742$		0			0
$743$	1.03403e10	−	1.03403e10i	0.924854	−	0.924854i	−0.0725133	−	0.997367i	$-0.523102\pi$
$743$	1.03403e10	−	1.03403e10i	0.924854	−	0.924854i	0.997367	+	0.0725133i	$0.0231020\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.35578e9	+	1.28089e10i	0.294558	+	1.12432i
$748$		0			0
$749$	−5.97603e9			−0.519668
$750$		0			0
$751$	1.75881e10			1.51524			0.757618	−	0.652698i	$-0.226363\pi$
$751$	1.75881e10			1.51524			0.757618	+	0.652698i	$0.226363\pi$
$752$		0			0
$753$	4.06668e9	+	7.08923e9i	0.347103	+	0.605085i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−5.99031e9	+	5.99031e9i	−0.501896	+	0.501896i	−0.912027	−	0.410131i	$-0.865483\pi$
$757$	−5.99031e9	+	5.99031e9i	−0.501896	+	0.501896i	0.410131	+	0.912027i	$0.365483\pi$
$758$		0			0
$759$	7.05824e9	+	1.91234e9i	0.585936	+	0.158752i
$760$		0			0
$761$		−	1.12357e10i		−	0.924173i	−0.886835	−	0.462087i	$-0.847101\pi$
$761$		−	1.12357e10i		−	0.924173i	0.886835	−	0.462087i	$-0.152899\pi$
$762$		0			0
$763$	−1.70685e9	−	1.70685e9i	−0.139110	−	0.139110i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.70234e8	−	7.70234e8i	−0.0616366	−	0.0616366i
$768$		0			0
$769$			1.11702e9i			0.0885762i	0.999019	+	0.0442881i	$0.0141020\pi$
$769$			1.11702e9i			0.0885762i	−0.999019	+	0.0442881i	$0.985898\pi$
$770$		0			0
$771$	−1.20704e10	−	3.27033e9i	−0.948490	−	0.256981i
$772$		0			0
$773$	3.05235e8	−	3.05235e8i	0.0237687	−	0.0237687i	−0.695123	−	0.718891i	$-0.744650\pi$
$773$	3.05235e8	−	3.05235e8i	0.0237687	−	0.0237687i	0.718891	+	0.695123i	$0.244650\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.50238e9	+	2.61902e9i	0.114896	+	0.200293i
$778$		0			0
$779$	1.76918e10			1.34088
$780$		0			0
$781$	−6.09492e9			−0.457814
$782$		0			0
$783$	1.04691e8	−	1.25280e10i	0.00779369	−	0.932646i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	5.84014e9	−	5.84014e9i	0.427083	−	0.427083i	−0.460551	−	0.887633i	$-0.652348\pi$
$787$	5.84014e9	−	5.84014e9i	0.427083	−	0.427083i	0.887633	+	0.460551i	$0.152348\pi$
$788$		0			0
$789$	−6.38596e9	+	2.35699e10i	−0.462867	+	1.70840i
$790$		0			0
$791$			6.17647e9i			0.443734i
$792$		0			0
$793$	−1.96311e10	−	1.96311e10i	−1.39794	−	1.39794i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.64740e9	+	2.64740e9i	0.185232	+	0.185232i	0.793631	−	0.608399i	$-0.208188\pi$
$797$	2.64740e9	+	2.64740e9i	0.185232	+	0.185232i	−0.608399	+	0.793631i	$0.708188\pi$
$798$		0			0
$799$		−	8.51793e8i		−	0.0590773i
$800$		0			0
$801$	5.82179e9	−	9.95514e9i	0.400260	−	0.684437i
$802$		0			0
$803$	2.30520e10	−	2.30520e10i	1.57110	−	1.57110i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.61166e9	−	2.07180e9i	0.241908	−	0.138768i
$808$		0			0
$809$	1.14300e10			0.758970			0.379485	−	0.925198i	$-0.376101\pi$
$809$	1.14300e10			0.758970			0.379485	+	0.925198i	$0.376101\pi$
$810$		0			0
$811$	1.36707e10			0.899950			0.449975	−	0.893041i	$-0.351433\pi$
$811$	1.36707e10			0.899950			0.449975	+	0.893041i	$0.351433\pi$
$812$		0			0
$813$	4.93182e9	−	2.82910e9i	0.321877	−	0.184642i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.05010e10	−	1.05010e10i	0.673678	−	0.673678i
$818$		0			0
$819$	−4.53704e9	+	7.75825e9i	−0.288588	+	0.493480i
$820$		0			0
$821$		−	1.04807e10i		−	0.660979i	−0.943810	−	0.330489i	$-0.892786\pi$
$821$		−	1.04807e10i		−	0.660979i	0.943810	−	0.330489i	$-0.107214\pi$
$822$		0			0
$823$	−1.74134e10	−	1.74134e10i	−1.08889	−	1.08889i	−0.995643	−	0.0932472i	$-0.970275\pi$
$823$	−1.74134e10	−	1.74134e10i	−1.08889	−	1.08889i	−0.0932472	−	0.995643i	$-0.529725\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.41202e10	−	1.41202e10i	−0.868102	−	0.868102i	0.124160	−	0.992262i	$-0.460376\pi$
$827$	−1.41202e10	−	1.41202e10i	−0.868102	−	0.868102i	−0.992262	+	0.124160i	$0.960376\pi$
$828$		0			0
$829$		−	1.04559e10i		−	0.637413i	−0.947853	−	0.318706i	$-0.896752\pi$
$829$		−	1.04559e10i		−	0.637413i	0.947853	−	0.318706i	$-0.103248\pi$
$830$		0			0
$831$	8.11018e9	−	2.99338e10i	0.490261	−	1.80950i
$832$		0			0
$833$	1.29030e10	−	1.29030e10i	0.773451	−	0.773451i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.94951e8	+	2.33291e10i	−0.0114917	+	1.37518i
$838$		0			0
$839$	1.09527e10			0.640256			0.320128	−	0.947374i	$-0.396274\pi$
$839$	1.09527e10			0.640256			0.320128	+	0.947374i	$0.396274\pi$
$840$		0			0
$841$	−2.24441e9			−0.130112
$842$		0			0
$843$	5.57748e9	+	9.72293e9i	0.320658	+	0.558986i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−6.15492e9	+	6.15492e9i	−0.348041	+	0.348041i
$848$		0			0
$849$	−1.12853e10	−	3.05761e9i	−0.632903	−	0.171477i
$850$		0			0
$851$		−	4.89723e9i		−	0.272394i
$852$		0			0
$853$	7.67601e9	+	7.67601e9i	0.423462	+	0.423462i	0.886394	−	0.462932i	$-0.153203\pi$
$853$	7.67601e9	+	7.67601e9i	0.423462	+	0.423462i	−0.462932	+	0.886394i	$0.653203\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.66912e10	+	1.66912e10i	0.905845	+	0.905845i	0.995934	−	0.0900883i	$-0.0287149\pi$
$857$	1.66912e10	+	1.66912e10i	0.905845	+	0.905845i	−0.0900883	+	0.995934i	$0.528715\pi$
$858$		0			0
$859$		−	4.18465e9i		−	0.225259i	−0.993637	−	0.112630i	$-0.964073\pi$
$859$		−	4.18465e9i		−	0.225259i	0.993637	−	0.112630i	$-0.0359274\pi$
$860$		0			0
$861$	9.63851e9	+	2.61143e9i	0.514635	+	0.139433i
$862$		0			0
$863$	−4.76521e9	+	4.76521e9i	−0.252374	+	0.252374i	−0.821943	−	0.569569i	$-0.807110\pi$
$863$	−4.76521e9	+	4.76521e9i	−0.252374	+	0.252374i	0.569569	+	0.821943i	$0.307110\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.71952e9	−	8.22729e9i	−0.245941	−	0.428736i
$868$		0			0
$869$	3.15534e9			0.163109
$870$		0			0
$871$	4.24288e10			2.17569
$872$		0			0
$873$	−3.69639e8	−	1.41091e9i	−0.0188031	−	0.0717709i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.04742e10	−	1.04742e10i	0.524352	−	0.524352i	−0.394531	−	0.918883i	$-0.629093\pi$
$877$	1.04742e10	−	1.04742e10i	0.524352	−	0.524352i	0.918883	+	0.394531i	$0.129093\pi$
$878$		0			0
$879$	−7.88457e9	+	2.91012e10i	−0.391577	+	1.44527i
$880$		0			0
$881$			2.12337e10i			1.04619i	0.852274	+	0.523095i	$0.175223\pi$
$881$			2.12337e10i			1.04619i	−0.852274	+	0.523095i	$0.824777\pi$
$882$		0			0
$883$	1.40155e10	+	1.40155e10i	0.685087	+	0.685087i	0.961142	−	0.276055i	$-0.0890271\pi$
$883$	1.40155e10	+	1.40155e10i	0.685087	+	0.685087i	−0.276055	+	0.961142i	$0.589027\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.82610e10	+	1.82610e10i	0.878602	+	0.878602i	0.993390	−	0.114788i	$-0.0366189\pi$
$887$	1.82610e10	+	1.82610e10i	0.878602	+	0.878602i	−0.114788	+	0.993390i	$0.536619\pi$
$888$		0			0
$889$			1.25683e9i			0.0599957i
$890$		0			0
$891$	−2.91983e10	+	1.64266e10i	−1.38288	+	0.777995i
$892$		0			0
$893$	−5.93139e8	+	5.93139e8i	−0.0278726	+	0.0278726i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.26446e10	−	7.25347e9i	0.584967	−	0.335562i
$898$		0			0
$899$	−2.79425e10			−1.28264
$900$		0			0
$901$	1.62522e10			0.740245
$902$		0			0
$903$	7.27095e9	−	4.17093e9i	0.328613	−	0.188506i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−2.18663e10	+	2.18663e10i	−0.973083	+	0.973083i	−0.999647	−	0.0265641i	$-0.991543\pi$
$907$	−2.18663e10	+	2.18663e10i	−0.973083	+	0.973083i	0.0265641	+	0.999647i	$0.491543\pi$
$908$		0			0
$909$	3.11037e10	+	1.81895e10i	1.37353	+	0.803245i
$910$		0			0
$911$		−	7.80144e9i		−	0.341869i	−0.985282	−	0.170935i	$-0.945321\pi$
$911$		−	7.80144e9i		−	0.341869i	0.985282	−	0.170935i	$-0.0546787\pi$
$912$		0			0
$913$	2.99872e10	+	2.99872e10i	1.30403	+	1.30403i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.18174e9	−	4.18174e9i	−0.179087	−	0.179087i
$918$		0			0
$919$		−	4.03762e9i		−	0.171602i	−0.996312	−	0.0858008i	$-0.972655\pi$
$919$		−	4.03762e9i		−	0.171602i	0.996312	−	0.0858008i	$-0.0273448\pi$
$920$		0			0
$921$	−7.05022e9	+	2.60216e10i	−0.297368	+	1.09755i
$922$		0			0
$923$	−8.59117e9	+	8.59117e9i	−0.359622	+	0.359622i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−5.52587e9	+	1.44771e9i	−0.227836	+	0.0596900i
$928$		0			0
$929$	5.97159e9			0.244363			0.122181	−	0.992508i	$-0.461011\pi$
$929$	5.97159e9			0.244363			0.122181	+	0.992508i	$0.461011\pi$
$930$		0			0
$931$	−1.79698e10			−0.729826
$932$		0			0
$933$	−1.95990e10	−	3.41659e10i	−0.790038	−	1.37723i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1.91067e10	−	1.91067e10i	0.758746	−	0.758746i	−0.217348	−	0.976094i	$-0.569741\pi$
$937$	1.91067e10	−	1.91067e10i	0.758746	−	0.758746i	0.976094	+	0.217348i	$0.0697407\pi$
$938$		0			0
$939$	1.56674e10	+	4.24489e9i	0.617545	+	0.167316i
$940$		0			0
$941$		−	5.02986e10i		−	1.96785i	−0.178577	−	0.983926i	$-0.557149\pi$
$941$		−	5.02986e10i		−	1.96785i	0.178577	−	0.983926i	$-0.442851\pi$
$942$		0			0
$943$	−1.14529e10	−	1.14529e10i	−0.444760	−	0.444760i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.11199e10	−	1.11199e10i	−0.425478	−	0.425478i	0.461607	−	0.887085i	$-0.347273\pi$
$947$	−1.11199e10	−	1.11199e10i	−0.425478	−	0.425478i	−0.887085	+	0.461607i	$0.847273\pi$
$948$		0			0
$949$		−	6.49866e10i		−	2.46827i
$950$		0			0
$951$	−3.58716e10	−	9.71893e9i	−1.35244	−	0.366426i
$952$		0			0
$953$	−2.33786e10	+	2.33786e10i	−0.874970	+	0.874970i	−0.993009	−	0.118039i	$-0.962339\pi$
$953$	−2.33786e10	+	2.33786e10i	−0.874970	+	0.874970i	0.118039	+	0.993009i	$0.462339\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.99659e10	−	3.48055e10i	−0.736371	−	1.28368i
$958$		0			0
$959$	−3.94522e9			−0.144446
$960$		0			0
$961$	2.45205e10			0.891246
$962$		0			0
$963$	−4.29563e10	+	1.12540e10i	−1.55001	+	0.406083i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−5.62361e9	+	5.62361e9i	−0.199997	+	0.199997i	−0.799999	−	0.600002i	$-0.795166\pi$
$967$	−5.62361e9	+	5.62361e9i	−0.199997	+	0.199997i	0.600002	+	0.799999i	$0.295166\pi$
$968$		0			0
$969$	−7.38447e9	+	2.72553e10i	−0.260727	+	0.962317i
$970$		0			0
$971$			2.42386e10i			0.849650i	0.905275	+	0.424825i	$0.139664\pi$
$971$			2.42386e10i			0.849650i	−0.905275	+	0.424825i	$0.860336\pi$
$972$		0			0
$973$	−2.88082e9	−	2.88082e9i	−0.100259	−	0.100259i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.12025e10	−	2.12025e10i	−0.727371	−	0.727371i	0.242724	−	0.970095i	$-0.421959\pi$
$977$	−2.12025e10	−	2.12025e10i	−0.727371	−	0.727371i	−0.970095	+	0.242724i	$0.921959\pi$
$978$		0			0
$979$		−	3.69356e10i		−	1.25807i
$980$		0			0
$981$	−1.54834e10	−	9.05470e9i	−0.523629	−	0.306219i
$982$		0			0
$983$	−1.22993e10	+	1.22993e10i	−0.412993	+	0.412993i	−0.882780	−	0.469787i	$-0.844331\pi$
$983$	−1.22993e10	+	1.22993e10i	−0.412993	+	0.412993i	0.469787	+	0.882780i	$0.344331\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.10694e8	+	2.35592e8i	−0.0135959	+	0.00779920i
$988$		0			0
$989$	−1.35958e10			−0.446906
$990$		0			0
$991$	−1.44732e10			−0.472397			−0.236199	−	0.971705i	$-0.575902\pi$
$991$	−1.44732e10			−0.472397			−0.236199	+	0.971705i	$0.575902\pi$
$992$		0			0
$993$	9.80879e9	−	5.62674e9i	0.317902	−	0.182362i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.78256e10	+	2.78256e10i	−0.889224	+	0.889224i	−0.994448	−	0.105225i	$-0.966444\pi$
$997$	−2.78256e10	+	2.78256e10i	−0.889224	+	0.889224i	0.105225	+	0.994448i	$0.466444\pi$
$998$		0			0
$999$	1.57314e10	+	1.59965e10i	0.499215	+	0.507629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.8.i.c.293.2	yes	16
3.2	odd	2	inner	300.8.i.c.293.6	yes	16
5.2	odd	4	inner	300.8.i.c.257.6	yes	16
5.3	odd	4	inner	300.8.i.c.257.3	yes	16
5.4	even	2	inner	300.8.i.c.293.7	yes	16
15.2	even	4	inner	300.8.i.c.257.2	✓	16
15.8	even	4	inner	300.8.i.c.257.7	yes	16
15.14	odd	2	inner	300.8.i.c.293.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.8.i.c.257.2	✓	16	15.2	even	4	inner
300.8.i.c.257.3	yes	16	5.3	odd	4	inner
300.8.i.c.257.6	yes	16	5.2	odd	4	inner
300.8.i.c.257.7	yes	16	15.8	even	4	inner
300.8.i.c.293.2	yes	16	1.1	even	1	trivial
300.8.i.c.293.3	yes	16	15.14	odd	2	inner
300.8.i.c.293.6	yes	16	3.2	odd	2	inner
300.8.i.c.293.7	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	300.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-40.5650 + 23.2698i) q^{3} +(208.115 - 208.115i) q^{7} +(1104.03 - 1887.88i) q^{9} +O(q^{10})\)	\(q+(-40.5650 + 23.2698i) q^{3} +(208.115 - 208.115i) q^{7} +(1104.03 - 1887.88i) q^{9} -7004.41i q^{11} +(-9873.16 - 9873.16i) q^{13} +(-17509.4 - 17509.4i) q^{17} +24385.0i q^{19} +(-3599.39 + 13285.0i) q^{21} +(15785.8 - 15785.8i) q^{23} +(-854.643 + 102272. i) q^{27} -122497. q^{29} +228108. q^{31} +(162991. + 284134. i) q^{33} +(155115. - 155115. i) q^{37} +(630251. + 170758. i) q^{39} -725519. i q^{41} +(-430632. - 430632. i) q^{43} +(24323.9 + 24323.9i) q^{47} +736919. i q^{49} +(1.11771e6 + 302828. i) q^{51} +(-464100. + 464100. i) q^{53} +(-567434. - 989178. i) q^{57} +78012.9 q^{59} +1.98833e6 q^{61} +(-163130. - 622662. i) q^{63} +(-2.14870e6 + 2.14870e6i) q^{67} +(-273019. + 1.00768e6i) q^{69} -870154. i q^{71} +(3.29108e6 + 3.29108e6i) q^{73} +(-1.45772e6 - 1.45772e6i) q^{77} +450479. i q^{79} +(-2.34519e6 - 4.16856e6i) q^{81} +(-4.28119e6 + 4.28119e6i) q^{83} +(4.96908e6 - 2.85047e6i) q^{87} +5.27320e6 q^{89} -4.10951e6 q^{91} +(-9.25318e6 + 5.30802e6i) q^{93} +(471574. - 471574. i) q^{97} +(-1.32235e7 - 7.73311e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 215904 q^{21} + 872704 q^{31} + 1978560 q^{51} + 12752864 q^{61} + 10696176 q^{81} - 39496704 q^{91}+O(q^{100}) \) 16 * q + 215904 * q^21 + 872704 * q^31 + 1978560 * q^51 + 12752864 * q^61 + 10696176 * q^81 - 39496704 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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