LMFDB - Embedded newform 300.8.i.c.293.6

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			293.6
Root			$20.4848 - 23.5555i$ of defining polynomial
Character	$\chi$	$=$	300.293
Dual form			300.8.i.c.257.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(23.2698 - 40.5650i) q^{3} +(208.115 - 208.115i) q^{7} +(-1104.03 - 1887.88i) q^{9} +O(q^{10})$	\(q+(23.2698 - 40.5650i) q^{3} +(208.115 - 208.115i) q^{7} +(-1104.03 - 1887.88i) q^{9} +7004.41i q^{11} +(-9873.16 - 9873.16i) q^{13} +(17509.4 + 17509.4i) q^{17} +24385.0i q^{19} +(-3599.39 - 13285.0i) q^{21} +(-15785.8 + 15785.8i) q^{23} +(-102272. + 854.643i) q^{27} +122497. q^{29} +228108. q^{31} +(284134. + 162991. i) q^{33} +(155115. - 155115. i) q^{37} +(-630251. + 170758. i) q^{39} +725519. i q^{41} +(-430632. - 430632. i) q^{43} +(-24323.9 - 24323.9i) q^{47} +736919. i q^{49} +(1.11771e6 - 302828. i) q^{51} +(464100. - 464100. i) q^{53} +(989178. + 567434. i) q^{57} -78012.9 q^{59} +1.98833e6 q^{61} +(-622662. - 163130. i) q^{63} +(-2.14870e6 + 2.14870e6i) q^{67} +(273019. + 1.00768e6i) q^{69} +870154. i q^{71} +(3.29108e6 + 3.29108e6i) q^{73} +(1.45772e6 + 1.45772e6i) q^{77} +450479. i q^{79} +(-2.34519e6 + 4.16856e6i) q^{81} +(4.28119e6 - 4.28119e6i) q^{83} +(2.85047e6 - 4.96908e6i) q^{87} -5.27320e6 q^{89} -4.10951e6 q^{91} +(5.30802e6 - 9.25318e6i) q^{93} +(471574. - 471574. i) q^{97} +(1.32235e7 - 7.73311e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	23.2698	−	40.5650i	0.497586	−	0.867415i
$3$	23.2698	−	40.5650i	0.497586	−	0.867415i
$4$		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	$0.291667\pi$
$11$			7004.41i			1.58671i	−0.608760	+	0.793354i	$0.708333\pi$
$12$		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	0.991842	−	0.127473i	$-0.0406865\pi$
$17$	17509.4	+	17509.4i	0.864369	+	0.864369i	−0.127473	+	0.991842i	$0.540687\pi$
$18$		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	−0.829315	−	0.558782i	$-0.811269\pi$
$23$	−15785.8	+	15785.8i	−0.270533	+	0.270533i	0.558782	+	0.829315i	$0.311269\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−102272.	+	854.643i	−0.999965	+	0.00835625i
$28$		0			0
$29$	122497.			0.932678			0.466339	−	0.884606i	$-0.345573\pi$
$29$	122497.			0.932678			0.466339	+	0.884606i	$0.345573\pi$
$30$		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
$33$	284134.	+	162991.i	1.37633	+	0.789524i
$34$		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	$0.307145\pi$
$41$			725519.i			1.64401i	−0.569478	+	0.822007i	$0.692855\pi$
$42$		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	0.689813	−	0.723987i	$-0.257693\pi$
$47$	−24323.9	−	24323.9i	−0.0341736	−	0.0341736i	−0.723987	+	0.689813i	$0.757693\pi$
$48$		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	−0.459815	−	0.888015i	$-0.652084\pi$
$53$	464100.	−	464100.i	0.428200	−	0.428200i	0.888015	+	0.459815i	$0.152084\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	989178.	+	567434.i	0.707477	+	0.405839i
$58$		0			0
$59$	−78012.9			−0.0494521			−0.0247260	−	0.999694i	$-0.507871\pi$
$59$	−78012.9			−0.0494521			−0.0247260	+	0.999694i	$0.507871\pi$
$60$		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
$63$	−622662.	−	163130.i	−0.313733	−	0.0821941i
$64$		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	$0.0460819\pi$
$71$			870154.i			0.288531i	−0.989539	+	0.144265i	$0.953918\pi$
$72$		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	−0.164525	−	0.986373i	$-0.552609\pi$
$83$	4.28119e6	−	4.28119e6i	0.821847	−	0.821847i	0.986373	+	0.164525i	$0.0526093\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.85047e6	−	4.96908e6i	0.464087	−	0.809019i
$88$		0			0
$89$	−5.27320e6			−0.792883			−0.396441	−	0.918060i	$-0.629755\pi$
$89$	−5.27320e6			−0.792883			−0.396441	+	0.918060i	$0.629755\pi$
$90$		0			0
$91$	−4.10951e6			−0.571670
$92$		0			0
$93$	5.30802e6	−	9.25318e6i	0.684293	−	1.19289i
$94$		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	$-0.707166\pi$
$101$		−	1.64755e7i		−	1.59116i	0.605848	−	0.795581i	$-0.292834\pi$
$102$		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	$0.0457844\pi$
$107$	1.43575e7	+	1.43575e7i	1.13301	+	1.13301i	0.143340	+	0.989673i	$0.454216\pi$
$108$		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	−0.0320296	−	0.999487i	$-0.510197\pi$
$113$	1.48391e7	−	1.48391e7i	0.967457	−	0.967457i	0.999487	+	0.0320296i	$0.0101971\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−7.73900e6	+	2.95396e7i	−0.446719	+	1.70512i
$118$		0			0
$119$	7.28794e6			0.396452
$120$		0			0
$121$	−2.95746e7			−1.51764
$122$		0			0
$123$	2.94307e7	+	1.68827e7i	1.42604	+	0.818038i
$124$		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	$0.127683\pi$
$131$			2.00934e7i			0.780915i	−0.920621	+	0.390458i	$0.872317\pi$
$132$		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	0.846816	−	0.531886i	$-0.178516\pi$
$137$	9.47844e6	+	9.47844e6i	0.314931	+	0.314931i	−0.531886	+	0.846816i	$0.678516\pi$
$138$		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
$147$	2.98931e7	+	1.71479e7i	0.776176	+	0.445247i
$148$		0			0
$149$	4.65482e7			1.15279			0.576396	−	0.817170i	$-0.304458\pi$
$149$	4.65482e7			1.15279			0.576396	+	0.817170i	$0.304458\pi$
$150$		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
$153$	1.37246e7	−	5.23865e7i	0.309798	−	1.18249i
$154$		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	0.999684	−	0.0251383i	$-0.00800260\pi$
$167$	5.86557e7	+	5.86557e7i	0.974546	+	0.974546i	−0.0251383	+	0.999684i	$0.508003\pi$
$168$		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	−0.148268	−	0.988947i	$-0.547370\pi$
$173$	5.72521e7	−	5.72521e7i	0.840679	−	0.840679i	0.988947	+	0.148268i	$0.0473698\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.81534e6	+	3.16459e6i	−0.0246066	+	0.0428954i
$178$		0			0
$179$	−6.51415e7			−0.848930			−0.424465	−	0.905444i	$-0.639538\pi$
$179$	−6.51415e7			−0.848930			−0.424465	+	0.905444i	$0.639538\pi$
$180$		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
$183$	4.62681e7	−	8.06566e7i	0.558088	−	0.972885i
$184$		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	$0.208682\pi$
$191$			1.17412e8i			1.21926i	−0.792685	+	0.609631i	$0.791318\pi$
$192$		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	0.999464	−	0.0327254i	$-0.0104187\pi$
$197$	1.03739e8	+	1.03739e8i	0.966739	+	0.966739i	−0.0327254	+	0.999464i	$0.510419\pi$
$198$		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
$207$	4.72298e7	+	1.23736e7i	0.370101	+	0.0969616i
$208$		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
$213$	3.52978e7	+	2.02483e7i	0.250276	+	0.143569i
$214$		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	0.471599	−	0.881813i	$-0.343677\pi$
$227$	−7.22939e7	−	7.22939e7i	−0.410215	−	0.410215i	−0.881813	+	0.471599i	$0.843677\pi$
$228$		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	$-0.477884\pi$
$233$	2.06022e8	−	2.06022e8i	1.06701	−	1.06701i	0.997587	−	0.0694233i	$-0.0221159\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.82737e7	+	1.04826e7i	0.0891676	+	0.0511503i
$238$		0			0
$239$	2.20720e8			1.04580			0.522899	−	0.852394i	$-0.324850\pi$
$239$	2.20720e8			1.04580			0.522899	+	0.852394i	$0.324850\pi$
$240$		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
$243$	1.14526e8	+	1.92134e8i	0.512012	+	0.858978i
$244$		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	$0.113406\pi$
$251$			1.74762e8i			0.697573i	−0.937202	+	0.348787i	$0.886594\pi$
$252$		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	0.268434	−	0.963298i	$-0.413494\pi$
$257$	−1.89089e8	−	1.89089e8i	−0.694864	−	0.694864i	−0.963298	+	0.268434i	$0.913494\pi$
$258$		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	$0.595838\pi$
$263$	−3.69233e8	+	3.69233e8i	−1.25157	+	1.25157i	−0.955015	+	0.296556i	$0.904162\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.22706e8	+	2.13907e8i	−0.394527	+	0.687758i
$268$		0			0
$269$	8.90340e7			0.278884			0.139442	−	0.990230i	$-0.455469\pi$
$269$	8.90340e7			0.278884			0.139442	+	0.990230i	$0.455469\pi$
$270$		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
$273$	−9.56274e7	+	1.66702e8i	−0.284455	+	0.495875i
$274$		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	$0.104427\pi$
$281$			2.39688e8i			0.644427i	−0.946667	+	0.322214i	$0.895573\pi$
$282$		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	$0.519316\pi$
$293$	−4.55883e8	+	4.55883e8i	−1.05881	+	1.05881i	−0.998159	+	0.0606464i	$0.980684\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.98627e6	−	7.16357e8i	−0.0132589	−	1.58665i
$298$		0			0
$299$	3.11712e8			0.674380
$300$		0			0
$301$	−1.79242e8			−0.378841
$302$		0			0
$303$	−6.68329e8	−	3.83382e8i	−1.38020	−	0.791739i
$304$		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	$-0.708062\pi$
$311$		−	8.42251e8i		−	1.58774i	0.608086	−	0.793871i	$-0.291938\pi$
$312$		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	0.00915869	−	0.999958i	$-0.497085\pi$
$317$	−5.61944e8	−	5.61944e8i	−0.990799	−	0.990799i	−0.999958	+	0.00915869i	$0.997085\pi$
$318$		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
$327$	−3.32692e8	−	1.90846e8i	−0.526169	−	0.301833i
$328$		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
$333$	−4.64090e8	−	1.21586e8i	−0.688727	−	0.180438i
$334$		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	0.478191	−	0.878256i	$-0.341293\pi$
$347$	−3.11375e8	−	3.11375e8i	−0.400065	−	0.400065i	−0.878256	+	0.478191i	$0.841293\pi$
$348$		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	−0.984014	−	0.178090i	$-0.943008\pi$
$353$	−6.66049e8	+	6.66049e8i	−0.805925	+	0.805925i	0.178090	+	0.984014i	$0.443008\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.69589e8	−	2.95635e8i	0.197269	−	0.343888i
$358$		0			0
$359$	−1.30978e9			−1.49406			−0.747029	−	0.664791i	$-0.768520\pi$
$359$	−1.30978e9			−1.49406			−0.747029	+	0.664791i	$0.768520\pi$
$360$		0			0
$361$	2.99242e8			0.334770
$362$		0			0
$363$	−6.88194e8	+	1.19969e9i	−0.755158	+	1.31643i
$364$		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	−0.941545	−	0.336887i	$-0.890626\pi$
$383$	−6.64823e8	+	6.64823e8i	−0.604658	+	0.604658i	0.336887	+	0.941545i	$0.390626\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.37547e8	+	1.28841e9i	−0.296037	+	1.12997i
$388$		0			0
$389$	−7.81809e8			−0.673406			−0.336703	−	0.941611i	$-0.609312\pi$
$389$	−7.81809e8			−0.673406			−0.336703	+	0.941611i	$0.609312\pi$
$390$		0			0
$391$	−5.52800e8			−0.467681
$392$		0			0
$393$	8.15088e8	+	4.67569e8i	0.677377	+	0.388572i
$394$		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	$-0.709091\pi$
$401$		−	2.04506e9i		−	1.58380i	0.610649	−	0.791901i	$-0.290909\pi$
$402$		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
$417$	−5.61518e8	−	3.22110e8i	−0.379217	−	0.217535i
$418$		0			0
$419$	1.84493e9			1.22527			0.612635	−	0.790366i	$-0.290110\pi$
$419$	1.84493e9			1.22527			0.612635	+	0.790366i	$0.290110\pi$
$420$		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
$423$	−1.90661e7	+	7.27750e7i	−0.0122482	+	0.0467510i
$424$		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	$0.0570532\pi$
$431$			5.92656e8i			0.356560i	−0.983980	+	0.178280i	$0.942947\pi$
$432$		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	−0.645609	−	0.763668i	$-0.723396\pi$
$443$	2.16030e8	−	2.16030e8i	0.118059	−	0.118059i	0.763668	+	0.645609i	$0.223396\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.08317e9	−	1.88823e9i	0.573613	−	0.999950i
$448$		0			0
$449$	5.11732e8			0.266797			0.133398	−	0.991062i	$-0.457411\pi$
$449$	5.11732e8			0.266797			0.133398	+	0.991062i	$0.457411\pi$
$450$		0			0
$451$	−5.08183e9			−2.60857
$452$		0			0
$453$	9.34985e8	−	1.62991e9i	0.472564	−	0.823796i
$454$		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	$0.151901\pi$
$461$			1.93234e9i			0.918609i	−0.888279	+	0.459304i	$0.848099\pi$
$462$		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	0.975625	−	0.219443i	$-0.0704239\pi$
$467$	1.66432e9	+	1.66432e9i	0.756183	+	0.756183i	−0.219443	+	0.975625i	$0.570424\pi$
$468$		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
$477$	−1.38855e9	−	3.63781e8i	−0.585796	−	0.153471i
$478$		0			0
$479$	−1.04923e8			−0.0436213			−0.0218106	−	0.999762i	$-0.506943\pi$
$479$	−1.04923e8			−0.0436213			−0.0218106	+	0.999762i	$0.506943\pi$
$480$		0			0
$481$	−3.06295e9			−1.25496
$482$		0			0
$483$	2.66534e8	+	1.52895e8i	0.107631	+	0.0617417i
$484$		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	$-0.852090\pi$
$491$		−	2.35081e9i		−	0.896258i	0.893969	−	0.448129i	$-0.147910\pi$
$492$		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	−0.869673	−	0.493628i	$-0.835671\pi$
$503$	−1.07332e9	+	1.07332e9i	−0.376046	+	0.376046i	0.493628	+	0.869673i	$0.335671\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.36309e9	+	3.07650e9i	1.82763	+	1.04840i
$508$		0			0
$509$	5.65019e9			1.89911			0.949556	−	0.313598i	$-0.101534\pi$
$509$	5.65019e9			1.89911			0.949556	+	0.313598i	$0.101534\pi$
$510$		0			0
$511$	1.36985e9			0.454149
$512$		0			0
$513$	−2.08405e7	−	2.49391e9i	−0.00681549	−	0.815588i
$514$		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	$0.00851768\pi$
$521$			1.72735e8i			0.0535118i	−0.999642	+	0.0267559i	$0.991482\pi$
$522$		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
$537$	−1.51583e9	+	2.64246e9i	−0.422415	+	0.736374i
$538$		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
$543$	1.08404e9	−	1.88974e9i	0.290566	−	0.506528i
$544$		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	0.236858	−	0.971544i	$-0.423882\pi$
$557$	−2.99637e9	−	2.99637e9i	−0.734686	−	0.734686i	−0.971544	+	0.236858i	$0.923882\pi$
$558$		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	−0.440925	−	0.897544i	$-0.645349\pi$
$563$	1.93345e9	−	1.93345e9i	0.456619	−	0.456619i	0.897544	+	0.440925i	$0.145349\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.79472e8	+	1.35561e9i	0.0874257	+	0.312316i
$568$		0			0
$569$	−6.47404e9			−1.47327			−0.736635	−	0.676291i	$-0.763586\pi$
$569$	−6.47404e9			−1.47327			−0.736635	+	0.676291i	$0.763586\pi$
$570$		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
$573$	4.76283e9	+	2.73216e9i	1.05761	+	0.606688i
$574$		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	0.999999	−	0.00119025i	$-0.000378869\pi$
$587$	4.89458e9	+	4.89458e9i	0.998809	+	0.998809i	−0.00119025	+	0.999999i	$0.500379\pi$
$588$		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	−0.508981	−	0.860778i	$-0.669978\pi$
$593$	1.78642e9	−	1.78642e9i	0.351797	−	0.351797i	0.860778	+	0.508981i	$0.169978\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.27986e9	−	1.88146e9i	−0.630877	−	0.361898i
$598$		0			0
$599$	−5.07984e9			−0.965731			−0.482865	−	0.875695i	$-0.660404\pi$
$599$	−5.07984e9			−0.965731			−0.482865	+	0.875695i	$0.660404\pi$
$600$		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
$603$	6.42871e9	+	1.68424e9i	1.19402	+	0.312819i
$604$		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	0.687280	−	0.726392i	$-0.258804\pi$
$617$	−2.28198e8	−	2.28198e8i	−0.0391123	−	0.0391123i	−0.726392	+	0.687280i	$0.758804\pi$
$618$		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
$627$	−3.97454e9	+	6.92861e9i	−0.643948	+	1.12256i
$628$		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
$633$	1.94122e8	−	3.38402e8i	0.0304201	−	0.0530298i
$634$		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	$-0.862947\pi$
$641$		−	5.56635e9i		−	0.834771i	0.908730	−	0.417385i	$-0.137053\pi$
$642$		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	0.999130	−	0.0417046i	$-0.0132788\pi$
$647$	6.59584e9	+	6.59584e9i	0.957425	+	0.957425i	−0.0417046	+	0.999130i	$0.513279\pi$
$648$		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	−0.708146	−	0.706066i	$-0.750468\pi$
$653$	−1.48024e7	+	1.48024e7i	−0.00208035	+	0.00208035i	0.706066	+	0.708146i	$0.250468\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.57968e9	−	9.84660e9i	0.354885	−	1.35459i
$658$		0			0
$659$	1.36101e10			1.85252			0.926261	−	0.376882i	$-0.123004\pi$
$659$	1.36101e10			1.85252			0.926261	+	0.376882i	$0.123004\pi$
$660$		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
$663$	−1.40252e10	−	8.04542e9i	−1.86900	−	1.07214i
$664$		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	$-0.983353\pi$
$677$	−8.48446e9	−	8.48446e9i	−1.05091	−	1.05091i	−0.0522733	−	0.998633i	$-0.516647\pi$
$678$		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	−0.937323	−	0.348463i	$-0.886704\pi$
$683$	−4.90325e9	+	4.90325e9i	−0.588860	+	0.588860i	0.348463	+	0.937323i	$0.386704\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	8.17616e9	+	4.69019e9i	0.962057	+	0.551877i
$688$		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
$693$	1.14263e9	−	4.36138e9i	0.130418	−	0.497803i
$694$		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	$-0.893226\pi$
$701$		−	6.00461e9i		−	0.658372i	0.944265	−	0.329186i	$-0.106774\pi$
$702$		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
$717$	5.13610e9	−	8.95348e9i	0.520375	−	0.907141i
$718$		0			0
$719$	1.29081e10			1.29512			0.647562	−	0.762013i	$-0.275789\pi$
$719$	1.29081e10			1.29512			0.647562	+	0.762013i	$0.275789\pi$
$720$		0			0
$721$	−7.68751e8			−0.0763858
$722$		0			0
$723$	−9.89092e9	+	1.72423e10i	−0.973313	+	1.69672i
$724$		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	−0.997367	−	0.0725133i	$-0.976898\pi$
$743$	−1.03403e10	+	1.03403e10i	−0.924854	+	0.924854i	0.0725133	+	0.997367i	$0.476898\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.28089e10	−	3.35578e9i	−1.12432	−	0.294558i
$748$		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
$753$	7.08923e9	+	4.06668e9i	0.605085	+	0.347103i
$754$		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	$0.152899\pi$
$761$			1.12357e10i			0.924173i	−0.886835	+	0.462087i	$0.847101\pi$
$762$		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	−0.718891	−	0.695123i	$-0.755350\pi$
$773$	−3.05235e8	+	3.05235e8i	−0.0237687	+	0.0237687i	0.695123	+	0.718891i	$0.255350\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2.61902e9	−	1.50238e9i	−0.200293	−	0.114896i
$778$		0			0
$779$	−1.76918e10			−1.34088
$780$		0			0
$781$	−6.09492e9			−0.457814
$782$		0			0
$783$	−1.25280e10	+	1.04691e8i	−0.932646	+	0.00779369i
$784$		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	0.608399	−	0.793631i	$-0.291812\pi$
$797$	−2.64740e9	−	2.64740e9i	−0.185232	−	0.185232i	−0.793631	+	0.608399i	$0.791812\pi$
$798$		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
$807$	2.07180e9	−	3.61166e9i	0.138768	−	0.241908i
$808$		0			0
$809$	−1.14300e10			−0.758970			−0.379485	−	0.925198i	$-0.623899\pi$
$809$	−1.14300e10			−0.758970			−0.379485	+	0.925198i	$0.623899\pi$
$810$		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
$813$	−2.82910e9	+	4.93182e9i	−0.184642	+	0.321877i
$814$		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	$0.107214\pi$
$821$			1.04807e10i			0.660979i	−0.943810	+	0.330489i	$0.892786\pi$
$822$		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	0.992262	−	0.124160i	$-0.0396237\pi$
$827$	1.41202e10	+	1.41202e10i	0.868102	+	0.868102i	−0.124160	+	0.992262i	$0.539624\pi$
$828$		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
$837$	−2.33291e10	+	1.94951e8i	−1.37518	+	0.0114917i
$838$		0			0
$839$	−1.09527e10			−0.640256			−0.320128	−	0.947374i	$-0.603726\pi$
$839$	−1.09527e10			−0.640256			−0.320128	+	0.947374i	$0.603726\pi$
$840$		0			0
$841$	−2.24441e9			−0.130112
$842$		0			0
$843$	9.72293e9	+	5.57748e9i	0.558986	+	0.320658i
$844$		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	0.0900883	−	0.995934i	$-0.471285\pi$
$857$	−1.66912e10	−	1.66912e10i	−0.905845	−	0.905845i	−0.995934	+	0.0900883i	$0.971285\pi$
$858$		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	−0.569569	−	0.821943i	$-0.692890\pi$
$863$	4.76521e9	−	4.76521e9i	0.252374	−	0.252374i	0.821943	+	0.569569i	$0.192890\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	8.22729e9	+	4.71952e9i	0.428736	+	0.245941i
$868$		0			0
$869$	−3.15534e9			−0.163109
$870$		0			0
$871$	4.24288e10			2.17569
$872$		0			0
$873$	−1.41091e9	−	3.69639e8i	−0.0717709	−	0.0188031i
$874$		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	$-0.824777\pi$
$881$		−	2.12337e10i		−	1.04619i	0.852274	−	0.523095i	$-0.175223\pi$
$882$		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	0.114788	−	0.993390i	$-0.463381\pi$
$887$	−1.82610e10	−	1.82610e10i	−0.878602	−	0.878602i	−0.993390	+	0.114788i	$0.963381\pi$
$888$		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
$897$	7.25347e9	−	1.26446e10i	0.335562	−	0.584967i
$898$		0			0
$899$	2.79425e10			1.28264
$900$		0			0
$901$	1.62522e10			0.740245
$902$		0			0
$903$	−4.17093e9	+	7.27095e9i	−0.188506	+	0.328613i
$904$		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	$0.0546787\pi$
$911$			7.80144e9i			0.341869i	−0.985282	+	0.170935i	$0.945321\pi$
$912$		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
$927$	−1.44771e9	+	5.52587e9i	−0.0596900	+	0.227836i
$928$		0			0
$929$	−5.97159e9			−0.244363			−0.122181	−	0.992508i	$-0.538989\pi$
$929$	−5.97159e9			−0.244363			−0.122181	+	0.992508i	$0.538989\pi$
$930$		0			0
$931$	−1.79698e10			−0.729826
$932$		0			0
$933$	−3.41659e10	−	1.95990e10i	−1.37723	−	0.790038i
$934$		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	$0.442851\pi$
$941$			5.02986e10i			1.96785i	−0.178577	+	0.983926i	$0.557149\pi$
$942$		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	0.887085	−	0.461607i	$-0.152727\pi$
$947$	1.11199e10	+	1.11199e10i	0.425478	+	0.425478i	−0.461607	+	0.887085i	$0.652727\pi$
$948$		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	−0.118039	−	0.993009i	$-0.537661\pi$
$953$	2.33786e10	−	2.33786e10i	0.874970	−	0.874970i	0.993009	+	0.118039i	$0.0376609\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	3.48055e10	+	1.99659e10i	1.28368	+	0.736371i
$958$		0			0
$959$	3.94522e9			0.144446
$960$		0			0
$961$	2.45205e10			0.891246
$962$		0			0
$963$	1.12540e10	−	4.29563e10i	0.406083	−	1.55001i
$964$		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	$-0.860336\pi$
$971$		−	2.42386e10i		−	0.849650i	0.905275	−	0.424825i	$-0.139664\pi$
$972$		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	0.970095	−	0.242724i	$-0.0780411\pi$
$977$	2.12025e10	+	2.12025e10i	0.727371	+	0.727371i	−0.242724	+	0.970095i	$0.578041\pi$
$978$		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	−0.469787	−	0.882780i	$-0.655669\pi$
$983$	1.22993e10	−	1.22993e10i	0.412993	−	0.412993i	0.882780	+	0.469787i	$0.155669\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.35592e8	+	4.10694e8i	−0.00779920	+	0.0135959i
$988$		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
$993$	−5.62674e9	+	9.80879e9i	−0.182362	+	0.317902i
$994$		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.293.6	yes	16
3.2	odd	2	inner	300.8.i.c.293.2	yes	16
5.2	odd	4	inner	300.8.i.c.257.2	✓	16
5.3	odd	4	inner	300.8.i.c.257.7	yes	16
5.4	even	2	inner	300.8.i.c.293.3	yes	16
15.2	even	4	inner	300.8.i.c.257.6	yes	16
15.8	even	4	inner	300.8.i.c.257.3	yes	16
15.14	odd	2	inner	300.8.i.c.293.7	yes	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	300.i (of order \(4\), degree \(2\), minimal)

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

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