LMFDB - Embedded newform 300.8.i.c.293.5

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			293.5
Root			$-26.4835 + 30.5542i$ of defining polynomial
Character	$\chi$	$=$	300.293
Dual form			300.8.i.c.257.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.05216 + 46.0669i) q^{3} +(565.187 - 565.187i) q^{7} +(-2057.33 + 741.876i) q^{9} +O(q^{10})$	\(q+(8.05216 + 46.0669i) q^{3} +(565.187 - 565.187i) q^{7} +(-2057.33 + 741.876i) q^{9} -2361.39i q^{11} +(-732.128 - 732.128i) q^{13} +(22896.0 + 22896.0i) q^{17} -38729.0i q^{19} +(30587.4 + 21485.4i) q^{21} +(-23922.4 + 23922.4i) q^{23} +(-50741.9 - 88801.0i) q^{27} -172492. q^{29} -119020. q^{31} +(108782. - 19014.3i) q^{33} +(-93692.5 + 93692.5i) q^{37} +(27831.7 - 39622.1i) q^{39} +673768. i q^{41} +(-265451. - 265451. i) q^{43} +(-218777. - 218777. i) q^{47} +184671. i q^{49} +(-870387. + 1.23911e6i) q^{51} +(-9795.00 + 9795.00i) q^{53} +(1.78413e6 - 311852. i) q^{57} -1.54803e6 q^{59} -394224. q^{61} +(-743474. + 1.58207e6i) q^{63} +(-898446. + 898446. i) q^{67} +(-1.29466e6 - 909405. i) q^{69} +2.33054e6i q^{71} +(-2.64459e6 - 2.64459e6i) q^{73} +(-1.33463e6 - 1.33463e6i) q^{77} -3.05235e6i q^{79} +(3.68221e6 - 3.05256e6i) q^{81} +(-2.34959e6 + 2.34959e6i) q^{83} +(-1.38893e6 - 7.94617e6i) q^{87} +3.61447e6 q^{89} -827578. q^{91} +(-958365. - 5.48287e6i) q^{93} +(3.89118e6 - 3.89118e6i) q^{97} +(1.75186e6 + 4.85815e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	8.05216	+	46.0669i	0.172182	+	0.985065i
$3$	8.05216	+	46.0669i	0.172182	+	0.985065i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	565.187	−	565.187i	0.622800	−	0.622800i	−0.323446	−	0.946247i	$-0.604841\pi$
$7$	565.187	−	565.187i	0.622800	−	0.622800i	0.946247	+	0.323446i	$0.104841\pi$
$8$		0			0
$9$	−2057.33	+	741.876i	−0.940707	+	0.339221i
$10$		0			0
$11$		−	2361.39i		−	0.534926i	−0.963568	−	0.267463i	$-0.913815\pi$
$11$		−	2361.39i		−	0.534926i	0.963568	−	0.267463i	$-0.0861852\pi$
$12$		0			0
$13$	−732.128	−	732.128i	−0.0924241	−	0.0924241i	0.659383	−	0.751807i	$-0.270818\pi$
$13$	−732.128	−	732.128i	−0.0924241	−	0.0924241i	−0.751807	+	0.659383i	$0.770818\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	22896.0	+	22896.0i	1.13029	+	1.13029i	0.990129	+	0.140157i	$0.0447607\pi$
$17$	22896.0	+	22896.0i	1.13029	+	1.13029i	0.140157	+	0.990129i	$0.455239\pi$
$18$		0			0
$19$		−	38729.0i		−	1.29539i	−0.761902	−	0.647693i	$-0.775734\pi$
$19$		−	38729.0i		−	1.29539i	0.761902	−	0.647693i	$-0.224266\pi$
$20$		0			0
$21$	30587.4	+	21485.4i	0.720734	+	0.506264i
$22$		0			0
$23$	−23922.4	+	23922.4i	−0.409975	+	0.409975i	−0.881730	−	0.471755i	$-0.843621\pi$
$23$	−23922.4	+	23922.4i	−0.409975	+	0.409975i	0.471755	+	0.881730i	$0.343621\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−50741.9	−	88801.0i	−0.496128	−	0.868250i
$28$		0			0
$29$	−172492.			−1.31333			−0.656667	−	0.754181i	$-0.728034\pi$
$29$	−172492.			−1.31333			−0.656667	+	0.754181i	$0.728034\pi$
$30$		0			0
$31$	−119020.			−0.717551			−0.358776	−	0.933424i	$-0.616806\pi$
$31$	−119020.			−0.717551			−0.358776	+	0.933424i	$0.616806\pi$
$32$		0			0
$33$	108782.	−	19014.3i	0.526937	−	0.0921046i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−93692.5	+	93692.5i	−0.304088	+	0.304088i	−0.842611	−	0.538523i	$-0.818983\pi$
$37$	−93692.5	+	93692.5i	−0.304088	+	0.304088i	0.538523	+	0.842611i	$0.318983\pi$
$38$		0			0
$39$	27831.7	−	39622.1i	0.0751300	−	0.106958i
$40$		0			0
$41$			673768.i			1.52675i	0.645958	+	0.763373i	$0.276458\pi$
$41$			673768.i			1.52675i	−0.645958	+	0.763373i	$0.723542\pi$
$42$		0			0
$43$	−265451.	−	265451.i	−0.509148	−	0.509148i	0.405117	−	0.914265i	$-0.367231\pi$
$43$	−265451.	−	265451.i	−0.509148	−	0.509148i	−0.914265	+	0.405117i	$0.867231\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−218777.	−	218777.i	−0.307368	−	0.307368i	0.536520	−	0.843888i	$-0.319739\pi$
$47$	−218777.	−	218777.i	−0.307368	−	0.307368i	−0.843888	+	0.536520i	$0.819739\pi$
$48$		0			0
$49$			184671.i			0.224240i
$50$		0			0
$51$	−870387.	+	1.23911e6i	−0.918791	+	1.30802i
$52$		0			0
$53$	−9795.00	+	9795.00i	−0.00903730	+	0.00903730i	−0.711611	−	0.702574i	$-0.752034\pi$
$53$	−9795.00	+	9795.00i	−0.00903730	+	0.00903730i	0.702574	+	0.711611i	$0.252034\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.78413e6	−	311852.i	1.27604	−	0.223042i
$58$		0			0
$59$	−1.54803e6			−0.981292			−0.490646	−	0.871359i	$-0.663239\pi$
$59$	−1.54803e6			−0.981292			−0.490646	+	0.871359i	$0.663239\pi$
$60$		0			0
$61$	−394224.			−0.222376			−0.111188	−	0.993799i	$-0.535466\pi$
$61$	−394224.			−0.222376			−0.111188	+	0.993799i	$0.535466\pi$
$62$		0			0
$63$	−743474.	+	1.58207e6i	−0.374605	+	0.797139i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−898446.	+	898446.i	−0.364947	+	0.364947i	−0.865631	−	0.500683i	$-0.833082\pi$
$67$	−898446.	+	898446.i	−0.364947	+	0.364947i	0.500683	+	0.865631i	$0.333082\pi$
$68$		0			0
$69$	−1.29466e6	−	909405.i	−0.474442	−	0.333262i
$70$		0			0
$71$			2.33054e6i			0.772772i	0.922337	+	0.386386i	$0.126277\pi$
$71$			2.33054e6i			0.772772i	−0.922337	+	0.386386i	$0.873723\pi$
$72$		0			0
$73$	−2.64459e6	−	2.64459e6i	−0.795663	−	0.795663i	0.186745	−	0.982408i	$-0.440206\pi$
$73$	−2.64459e6	−	2.64459e6i	−0.795663	−	0.795663i	−0.982408	+	0.186745i	$0.940206\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.33463e6	−	1.33463e6i	−0.333152	−	0.333152i
$78$		0			0
$79$		−	3.05235e6i		−	0.696530i	−0.937396	−	0.348265i	$-0.886771\pi$
$79$		−	3.05235e6i		−	0.696530i	0.937396	−	0.348265i	$-0.113229\pi$
$80$		0			0
$81$	3.68221e6	−	3.05256e6i	0.769858	−	0.638215i
$82$		0			0
$83$	−2.34959e6	+	2.34959e6i	−0.451044	+	0.451044i	−0.895701	−	0.444657i	$-0.853326\pi$
$83$	−2.34959e6	+	2.34959e6i	−0.451044	+	0.451044i	0.444657	+	0.895701i	$0.353326\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.38893e6	−	7.94617e6i	−0.226133	−	1.29372i
$88$		0			0
$89$	3.61447e6			0.543475			0.271738	−	0.962371i	$-0.412402\pi$
$89$	3.61447e6			0.543475			0.271738	+	0.962371i	$0.412402\pi$
$90$		0			0
$91$	−827578.			−0.115124
$92$		0			0
$93$	−958365.	−	5.48287e6i	−0.123549	−	0.706835i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.89118e6	−	3.89118e6i	0.432892	−	0.432892i	−0.456719	−	0.889611i	$-0.650975\pi$
$97$	3.89118e6	−	3.89118e6i	0.432892	−	0.432892i	0.889611	+	0.456719i	$0.150975\pi$
$98$		0			0
$99$	1.75186e6	+	4.85815e6i	0.181458	+	0.503208i
$100$		0			0
$101$		−	1.34688e7i		−	1.30078i	−0.759599	−	0.650392i	$-0.774605\pi$
$101$		−	1.34688e7i		−	1.30078i	0.759599	−	0.650392i	$-0.225395\pi$
$102$		0			0
$103$	−1.12200e7	−	1.12200e7i	−1.01172	−	1.01172i	−0.999930	−	0.0117938i	$-0.996246\pi$
$103$	−1.12200e7	−	1.12200e7i	−1.01172	−	1.01172i	−0.0117938	−	0.999930i	$-0.503754\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	513749.	+	513749.i	0.0405423	+	0.0405423i	0.727087	−	0.686545i	$-0.240874\pi$
$107$	513749.	+	513749.i	0.0405423	+	0.0405423i	−0.686545	+	0.727087i	$0.740874\pi$
$108$		0			0
$109$			1.44407e7i			1.06806i	0.845466	+	0.534030i	$0.179323\pi$
$109$			1.44407e7i			1.06806i	−0.845466	+	0.534030i	$0.820677\pi$
$110$		0			0
$111$	−5.07056e6	−	3.56170e6i	−0.351905	−	0.247188i
$112$		0			0
$113$	−1.81341e7	+	1.81341e7i	−1.18228	+	1.18228i	−0.203131	+	0.979152i	$0.565112\pi$
$113$	−1.81341e7	+	1.81341e7i	−1.18228	+	1.18228i	−0.979152	+	0.203131i	$0.934888\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.04937e6	+	963077.i	0.118296	+	0.0555918i
$118$		0			0
$119$	2.58810e7			1.40789
$120$		0			0
$121$	1.39110e7			0.713855
$122$		0			0
$123$	−3.10384e7	+	5.42528e6i	−1.50394	+	0.262878i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	2.98952e7	−	2.98952e7i	1.29506	−	1.29506i	0.363438	−	0.931618i	$-0.381603\pi$
$127$	2.98952e7	−	2.98952e7i	1.29506	−	1.29506i	0.931618	−	0.363438i	$-0.118397\pi$
$128$		0			0
$129$	1.00910e7	−	1.43659e7i	0.413878	−	0.589210i
$130$		0			0
$131$		−	1.04475e7i		−	0.406035i	−0.979175	−	0.203018i	$-0.934925\pi$
$131$		−	1.04475e7i		−	0.406035i	0.979175	−	0.203018i	$-0.0650748\pi$
$132$		0			0
$133$	−2.18891e7	−	2.18891e7i	−0.806767	−	0.806767i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.55355e7	−	3.55355e7i	−1.18070	−	1.18070i	−0.979563	−	0.201138i	$-0.935536\pi$
$137$	−3.55355e7	−	3.55355e7i	−1.18070	−	1.18070i	−0.201138	−	0.979563i	$-0.564464\pi$
$138$		0			0
$139$			2.50412e6i			0.0790865i	0.999218	+	0.0395433i	$0.0125903\pi$
$139$			2.50412e6i			0.0790865i	−0.999218	+	0.0395433i	$0.987410\pi$
$140$		0			0
$141$	8.31675e6	−	1.18400e7i	0.249854	−	0.355701i
$142$		0			0
$143$	−1.72884e6	+	1.72884e6i	−0.0494400	+	0.0494400i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−8.50723e6	+	1.48700e6i	−0.220891	+	0.0386100i
$148$		0			0
$149$	−7.78790e7			−1.92872			−0.964358	−	0.264602i	$-0.914759\pi$
$149$	−7.78790e7			−1.92872			−0.964358	+	0.264602i	$0.914759\pi$
$150$		0			0
$151$	−1.59598e7			−0.377231			−0.188615	−	0.982051i	$-0.560400\pi$
$151$	−1.59598e7			−0.377231			−0.188615	+	0.982051i	$0.560400\pi$
$152$		0			0
$153$	−6.40905e7	−	3.01185e7i	−1.44668	−	0.679851i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.04188e7	−	4.04188e7i	0.833555	−	0.833555i	−0.154446	−	0.988001i	$-0.549359\pi$
$157$	4.04188e7	−	4.04188e7i	0.833555	−	0.833555i	0.988001	+	0.154446i	$0.0493593\pi$
$158$		0			0
$159$	−530096.	−	372355.i	−0.0104584	−	0.00734627i
$160$		0			0
$161$			2.70412e7i			0.510665i
$162$		0			0
$163$	−6.56387e7	−	6.56387e7i	−1.18714	−	1.18714i	−0.977854	−	0.209290i	$-0.932885\pi$
$163$	−6.56387e7	−	6.56387e7i	−1.18714	−	1.18714i	−0.209290	−	0.977854i	$-0.567115\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.17012e7	−	2.17012e7i	−0.360559	−	0.360559i	0.503459	−	0.864019i	$-0.332060\pi$
$167$	−2.17012e7	−	2.17012e7i	−0.360559	−	0.360559i	−0.864019	+	0.503459i	$0.832060\pi$
$168$		0			0
$169$		−	6.16765e7i		−	0.982916i
$170$		0			0
$171$	2.87322e7	+	7.96782e7i	0.439422	+	1.21858i
$172$		0			0
$173$	−8.65454e7	+	8.65454e7i	−1.27082	+	1.27082i	−0.325154	+	0.945661i	$0.605416\pi$
$173$	−8.65454e7	+	8.65454e7i	−1.27082	+	1.27082i	−0.945661	+	0.325154i	$0.894584\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.24650e7	−	7.13132e7i	−0.168961	−	0.966637i
$178$		0			0
$179$	5.55469e7			0.723892			0.361946	−	0.932199i	$-0.382112\pi$
$179$	5.55469e7			0.723892			0.361946	+	0.932199i	$0.382112\pi$
$180$		0			0
$181$	−8.21040e7			−1.02917			−0.514587	−	0.857438i	$-0.672055\pi$
$181$	−8.21040e7			−1.02917			−0.514587	+	0.857438i	$0.672055\pi$
$182$		0			0
$183$	−3.17435e6	−	1.81607e7i	−0.0382892	−	0.219055i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	5.40664e7	−	5.40664e7i	0.604619	−	0.604619i
$188$		0			0
$189$	−7.88678e7	−	2.15105e7i	−0.849735	−	0.231758i
$190$		0			0
$191$			1.27821e8i			1.32735i	0.748021	+	0.663675i	$0.231004\pi$
$191$			1.27821e8i			1.32735i	−0.748021	+	0.663675i	$0.768996\pi$
$192$		0			0
$193$	−4.53151e7	−	4.53151e7i	−0.453724	−	0.453724i	0.442864	−	0.896589i	$-0.353962\pi$
$193$	−4.53151e7	−	4.53151e7i	−0.453724	−	0.453724i	−0.896589	+	0.442864i	$0.853962\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.34501e7	+	6.34501e7i	0.591290	+	0.591290i	0.937980	−	0.346690i	$-0.112694\pi$
$197$	6.34501e7	+	6.34501e7i	0.591290	+	0.591290i	−0.346690	+	0.937980i	$0.612694\pi$
$198$		0			0
$199$			2.01928e8i			1.81640i	0.418538	+	0.908199i	$0.362543\pi$
$199$			2.01928e8i			1.81640i	−0.418538	+	0.908199i	$0.637457\pi$
$200$		0			0
$201$	−4.86231e7	−	3.41542e7i	−0.422334	−	0.296659i
$202$		0			0
$203$	−9.74900e7	+	9.74900e7i	−0.817945	+	0.817945i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.14687e7	−	6.69636e7i	0.246594	−	0.524738i
$208$		0			0
$209$	−9.14544e7			−0.692935
$210$		0			0
$211$	−6.55270e6			−0.0480210			−0.0240105	−	0.999712i	$-0.507644\pi$
$211$	−6.55270e6			−0.0480210			−0.0240105	+	0.999712i	$0.507644\pi$
$212$		0			0
$213$	−1.07361e8	+	1.87658e7i	−0.761231	+	0.133057i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.72683e7	+	6.72683e7i	−0.446891	+	0.446891i
$218$		0			0
$219$	1.00534e8	−	1.43123e8i	0.646781	−	0.920779i
$220$		0			0
$221$		−	3.35256e7i		−	0.208931i
$222$		0			0
$223$	−1.30061e8	−	1.30061e8i	−0.785380	−	0.785380i	0.195353	−	0.980733i	$-0.437415\pi$
$223$	−1.30061e8	−	1.30061e8i	−0.785380	−	0.785380i	−0.980733	+	0.195353i	$0.937415\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.84611e8	−	1.84611e8i	−1.04753	−	1.04753i	−0.998812	−	0.0487216i	$-0.984485\pi$
$227$	−1.84611e8	−	1.84611e8i	−1.04753	−	1.04753i	−0.0487216	−	0.998812i	$-0.515515\pi$
$228$		0			0
$229$		−	3.37952e7i		−	0.185965i	−0.995668	−	0.0929825i	$-0.970360\pi$
$229$		−	3.37952e7i		−	0.185965i	0.995668	−	0.0929825i	$-0.0296401\pi$
$230$		0			0
$231$	5.07355e7	−	7.22288e7i	0.270813	−	0.385539i
$232$		0			0
$233$	2.26237e8	−	2.26237e8i	1.17170	−	1.17170i	0.189898	−	0.981804i	$-0.439184\pi$
$233$	2.26237e8	−	2.26237e8i	1.17170	−	1.17170i	0.981804	−	0.189898i	$-0.0608159\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.40612e8	−	2.45780e7i	0.686127	−	0.119930i
$238$		0			0
$239$	2.17366e8			1.02991			0.514954	−	0.857218i	$-0.327809\pi$
$239$	2.17366e8			1.02991			0.514954	+	0.857218i	$0.327809\pi$
$240$		0			0
$241$	1.52613e8			0.702316			0.351158	−	0.936316i	$-0.385788\pi$
$241$	1.52613e8			0.702316			0.351158	+	0.936316i	$0.385788\pi$
$242$		0			0
$243$	1.70272e8	+	1.45048e8i	0.761239	+	0.648471i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.83546e7	+	2.83546e7i	−0.119725	+	0.119725i
$248$		0			0
$249$	−1.27158e8	−	8.93191e7i	−0.521969	−	0.366646i
$250$		0			0
$251$		−	3.18158e8i		−	1.26994i	−0.772535	−	0.634972i	$-0.781012\pi$
$251$		−	3.18158e8i		−	1.26994i	0.772535	−	0.634972i	$-0.218988\pi$
$252$		0			0
$253$	5.64901e7	+	5.64901e7i	0.219306	+	0.219306i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.37997e7	+	2.37997e7i	0.0874591	+	0.0874591i	0.749483	−	0.662024i	$-0.230302\pi$
$257$	2.37997e7	+	2.37997e7i	0.0874591	+	0.0874591i	−0.662024	+	0.749483i	$0.730302\pi$
$258$		0			0
$259$			1.05908e8i			0.378772i
$260$		0			0
$261$	3.54872e8	−	1.27968e8i	1.23546	−	0.445511i
$262$		0			0
$263$	−8.33888e7	+	8.33888e7i	−0.282659	+	0.282659i	−0.834169	−	0.551510i	$-0.814052\pi$
$263$	−8.33888e7	+	8.33888e7i	−0.282659	+	0.282659i	0.551510	+	0.834169i	$0.314052\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.91043e7	+	1.66508e8i	0.0935766	+	0.535358i
$268$		0			0
$269$	−5.61377e6			−0.0175842			−0.00879208	−	0.999961i	$-0.502799\pi$
$269$	−5.61377e6			−0.0175842			−0.00879208	+	0.999961i	$0.502799\pi$
$270$		0			0
$271$	−3.57656e8			−1.09162			−0.545812	−	0.837907i	$-0.683779\pi$
$271$	−3.57656e8			−1.09162			−0.545812	+	0.837907i	$0.683779\pi$
$272$		0			0
$273$	−6.66379e6	−	3.81240e7i	−0.0198222	−	0.113404i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.65642e8	+	2.65642e8i	−0.750962	+	0.750962i	−0.974659	−	0.223697i	$-0.928187\pi$
$277$	−2.65642e8	+	2.65642e8i	−0.750962	+	0.750962i	0.223697	+	0.974659i	$0.428187\pi$
$278$		0			0
$279$	2.44862e8	−	8.82979e7i	0.675005	−	0.243408i
$280$		0			0
$281$		−	4.57465e8i		−	1.22995i	−0.788548	−	0.614973i	$-0.789167\pi$
$281$		−	4.57465e8i		−	1.22995i	0.788548	−	0.614973i	$-0.210833\pi$
$282$		0			0
$283$	3.81936e8	+	3.81936e8i	1.00170	+	1.00170i	0.999999	+	0.00170342i	$0.000542216\pi$
$283$	3.81936e8	+	3.81936e8i	1.00170	+	1.00170i	0.00170342	+	0.999999i	$0.499458\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.80805e8	+	3.80805e8i	0.950858	+	0.950858i
$288$		0			0
$289$			6.38115e8i			1.55509i
$290$		0			0
$291$	2.10587e8	+	1.47922e8i	0.500963	+	0.351891i
$292$		0			0
$293$	−7.69493e6	+	7.69493e6i	−0.0178718	+	0.0178718i	−0.715986	−	0.698114i	$-0.754023\pi$
$293$	−7.69493e6	+	7.69493e6i	−0.0178718	+	0.0178718i	0.698114	+	0.715986i	$0.254023\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.09694e8	+	1.19821e8i	−0.464449	+	0.265391i
$298$		0			0
$299$	3.50285e7			0.0757832
$300$		0			0
$301$	−3.00058e8			−0.634195
$302$		0			0
$303$	6.20468e8	−	1.08453e8i	1.28136	−	0.223971i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.12115e8	−	2.12115e8i	0.418396	−	0.418396i	−0.466254	−	0.884651i	$-0.654397\pi$
$307$	2.12115e8	−	2.12115e8i	0.418396	−	0.418396i	0.884651	+	0.466254i	$0.154397\pi$
$308$		0			0
$309$	4.26525e8	−	6.07216e8i	0.822414	−	1.17082i
$310$		0			0
$311$			8.81144e8i			1.66106i	0.556973	+	0.830531i	$0.311963\pi$
$311$			8.81144e8i			1.66106i	−0.556973	+	0.830531i	$0.688037\pi$
$312$		0			0
$313$	5.14996e8	+	5.14996e8i	0.949289	+	0.949289i	0.998775	−	0.0494862i	$-0.0157584\pi$
$313$	5.14996e8	+	5.14996e8i	0.949289	+	0.949289i	−0.0494862	+	0.998775i	$0.515758\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.34448e8	+	3.34448e8i	0.589687	+	0.589687i	0.937547	−	0.347860i	$-0.113091\pi$
$317$	3.34448e8	+	3.34448e8i	0.589687	+	0.589687i	−0.347860	+	0.937547i	$0.613091\pi$
$318$		0			0
$319$			4.07320e8i			0.702536i
$320$		0			0
$321$	−1.95301e7	+	2.78036e7i	−0.0329561	+	0.0469174i
$322$		0			0
$323$	8.86740e8	−	8.86740e8i	1.46416	−	1.46416i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.65239e8	+	1.16279e8i	−1.05211	+	0.183901i
$328$		0			0
$329$	−2.47299e8			−0.382858
$330$		0			0
$331$	−1.49153e8			−0.226065			−0.113033	−	0.993591i	$-0.536056\pi$
$331$	−1.49153e8			−0.226065			−0.113033	+	0.993591i	$0.536056\pi$
$332$		0			0
$333$	1.23248e8	−	2.62264e8i	0.182904	−	0.389210i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−6.81331e8	+	6.81331e8i	−0.969736	+	0.969736i	−0.999555	−	0.0298192i	$-0.990507\pi$
$337$	−6.81331e8	+	6.81331e8i	−0.969736	+	0.969736i	0.0298192	+	0.999555i	$0.490507\pi$
$338$		0			0
$339$	−9.81401e8	−	6.89364e8i	−1.36819	−	0.961058i
$340$		0			0
$341$			2.81052e8i			0.383836i
$342$		0			0
$343$	5.69829e8	+	5.69829e8i	0.762457	+	0.762457i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.34509e8	−	2.34509e8i	−0.301305	−	0.301305i	0.540219	−	0.841524i	$-0.318341\pi$
$347$	−2.34509e8	−	2.34509e8i	−0.301305	−	0.301305i	−0.841524	+	0.540219i	$0.818341\pi$
$348$		0			0
$349$			6.82894e8i			0.859932i	0.902845	+	0.429966i	$0.141474\pi$
$349$			6.82894e8i			0.859932i	−0.902845	+	0.429966i	$0.858526\pi$
$350$		0			0
$351$	−2.78641e7	+	1.02163e8i	−0.0343931	+	0.126101i
$352$		0			0
$353$	3.59877e7	−	3.59877e7i	0.0435454	−	0.0435454i	−0.684999	−	0.728544i	$-0.740197\pi$
$353$	3.59877e7	−	3.59877e7i	0.0435454	−	0.0435454i	0.728544	+	0.684999i	$0.240197\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.08398e8	+	1.19226e9i	0.242413	+	1.38686i
$358$		0			0
$359$	−7.87990e8			−0.898856			−0.449428	−	0.893317i	$-0.648372\pi$
$359$	−7.87990e8			−0.898856			−0.449428	+	0.893317i	$0.648372\pi$
$360$		0			0
$361$	−6.06066e8			−0.678024
$362$		0			0
$363$	1.12014e8	+	6.40838e8i	0.122913	+	0.703193i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.88227e8	−	2.88227e8i	0.304371	−	0.304371i	−0.538350	−	0.842721i	$-0.680952\pi$
$367$	2.88227e8	−	2.88227e8i	0.304371	−	0.304371i	0.842721	+	0.538350i	$0.180952\pi$
$368$		0			0
$369$	−4.99853e8	−	1.38616e9i	−0.517904	−	1.43622i
$370$		0			0
$371$			1.10720e7i			0.0112569i
$372$		0			0
$373$	9.75486e8	+	9.75486e8i	0.973285	+	0.973285i	0.999652	−	0.0263674i	$-0.00839398\pi$
$373$	9.75486e8	+	9.75486e8i	0.973285	+	0.973285i	−0.0263674	+	0.999652i	$0.508394\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.26286e8	+	1.26286e8i	0.121384	+	0.121384i
$378$		0			0
$379$			2.44236e7i			0.0230448i	0.999934	+	0.0115224i	$0.00366777\pi$
$379$			2.44236e7i			0.0230448i	−0.999934	+	0.0115224i	$0.996332\pi$
$380$		0			0
$381$	1.61790e9	+	1.13646e9i	1.49870	+	1.05273i
$382$		0			0
$383$	8.30215e8	−	8.30215e8i	0.755083	−	0.755083i	−0.220340	−	0.975423i	$-0.570717\pi$
$383$	8.30215e8	−	8.30215e8i	0.755083	−	0.755083i	0.975423	+	0.220340i	$0.0707167\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.43050e8	+	3.49187e8i	0.651673	+	0.306245i
$388$		0			0
$389$	8.85170e8			0.762435			0.381218	−	0.924485i	$-0.375505\pi$
$389$	8.85170e8			0.762435			0.381218	+	0.924485i	$0.375505\pi$
$390$		0			0
$391$	−1.09545e9			−0.926778
$392$		0			0
$393$	4.81285e8	−	8.41250e7i	0.399971	−	0.0699119i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.72503e8	+	4.72503e8i	−0.378999	+	0.378999i	−0.870741	−	0.491742i	$-0.836360\pi$
$397$	−4.72503e8	+	4.72503e8i	−0.378999	+	0.378999i	0.491742	+	0.870741i	$0.336360\pi$
$398$		0			0
$399$	8.32111e8	−	1.18462e9i	0.655807	−	0.933628i
$400$		0			0
$401$			1.26513e9i			0.979784i	0.871783	+	0.489892i	$0.162964\pi$
$401$			1.26513e9i			0.979784i	−0.871783	+	0.489892i	$0.837036\pi$
$402$		0			0
$403$	8.71377e7	+	8.71377e7i	0.0663190	+	0.0663190i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.21245e8	+	2.21245e8i	0.162664	+	0.162664i
$408$		0			0
$409$			2.15154e9i			1.55495i	0.628911	+	0.777477i	$0.283501\pi$
$409$			2.15154e9i			1.55495i	−0.628911	+	0.777477i	$0.716499\pi$
$410$		0			0
$411$	1.35087e9	−	1.92315e9i	0.959772	−	1.36636i
$412$		0			0
$413$	−8.74928e8	+	8.74928e8i	−0.611149	+	0.611149i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.15357e8	+	2.01635e7i	−0.0779054	+	0.0136173i
$418$		0			0
$419$	−7.48977e8			−0.497415			−0.248708	−	0.968579i	$-0.580006\pi$
$419$	−7.48977e8			−0.497415			−0.248708	+	0.968579i	$0.580006\pi$
$420$		0			0
$421$	−2.49357e9			−1.62867			−0.814337	−	0.580392i	$-0.802899\pi$
$421$	−2.49357e9			−1.62867			−0.814337	+	0.580392i	$0.802899\pi$
$422$		0			0
$423$	6.12400e8	+	2.87790e8i	0.393409	+	0.184877i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.22810e8	+	2.22810e8i	−0.138496	+	0.138496i
$428$		0			0
$429$	−9.35633e7	−	6.57215e7i	−0.0572143	−	0.0401890i
$430$		0			0
$431$		−	2.00871e9i		−	1.20850i	−0.796794	−	0.604251i	$-0.793473\pi$
$431$		−	2.00871e9i		−	1.20850i	0.796794	−	0.604251i	$-0.206527\pi$
$432$		0			0
$433$	−2.15215e9	−	2.15215e9i	−1.27399	−	1.27399i	−0.943977	−	0.330011i	$-0.892948\pi$
$433$	−2.15215e9	−	2.15215e9i	−1.27399	−	1.27399i	−0.330011	−	0.943977i	$-0.607052\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.26492e8	+	9.26492e8i	0.531076	+	0.531076i
$438$		0			0
$439$			3.52076e9i			1.98615i	0.117499	+	0.993073i	$0.462512\pi$
$439$			3.52076e9i			1.98615i	−0.117499	+	0.993073i	$0.537488\pi$
$440$		0			0
$441$	−1.37003e8	−	3.79928e8i	−0.0760668	−	0.210944i
$442$		0			0
$443$	4.05454e8	−	4.05454e8i	0.221579	−	0.221579i	−0.587584	−	0.809163i	$-0.699921\pi$
$443$	4.05454e8	−	4.05454e8i	0.221579	−	0.221579i	0.809163	+	0.587584i	$0.199921\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−6.27094e8	−	3.58764e9i	−0.332090	−	1.89991i
$448$		0			0
$449$	3.04161e9			1.58578			0.792888	−	0.609367i	$-0.208576\pi$
$449$	3.04161e9			1.58578			0.792888	+	0.609367i	$0.208576\pi$
$450$		0			0
$451$	1.59103e9			0.816695
$452$		0			0
$453$	−1.28510e8	−	7.35217e8i	−0.0649523	−	0.371597i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.04947e9	+	1.04947e9i	−0.514355	+	0.514355i	−0.915858	−	0.401502i	$-0.868488\pi$
$457$	−1.04947e9	+	1.04947e9i	−0.514355	+	0.514355i	0.401502	+	0.915858i	$0.368488\pi$
$458$		0			0
$459$	8.71401e8	−	3.19497e9i	0.420604	−	1.54214i
$460$		0			0
$461$		−	1.42379e9i		−	0.676851i	−0.940993	−	0.338425i	$-0.890106\pi$
$461$		−	1.42379e9i		−	0.676851i	0.940993	−	0.338425i	$-0.109894\pi$
$462$		0			0
$463$	1.31932e9	+	1.31932e9i	0.617754	+	0.617754i	0.944955	−	0.327201i	$-0.106105\pi$
$463$	1.31932e9	+	1.31932e9i	0.617754	+	0.617754i	−0.327201	+	0.944955i	$0.606105\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.20143e9	−	2.20143e9i	−1.00022	−	1.00022i	−1.00000		0.000219918i	$-0.999930\pi$
$467$	−2.20143e9	−	2.20143e9i	−1.00022	−	1.00022i	−0.000219918	−	1.00000i	$-0.500070\pi$
$468$		0			0
$469$			1.01558e9i			0.454578i
$470$		0			0
$471$	2.18743e9	+	1.53651e9i	0.964629	+	0.677583i
$472$		0			0
$473$	−6.26832e8	+	6.26832e8i	−0.272356	+	0.272356i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.28848e7	−	2.74182e7i	0.00543581	−	0.0115671i
$478$		0			0
$479$	−1.19523e9			−0.496910			−0.248455	−	0.968643i	$-0.579923\pi$
$479$	−1.19523e9			−0.496910			−0.248455	+	0.968643i	$0.579923\pi$
$480$		0			0
$481$	1.37190e8			0.0562101
$482$		0			0
$483$	−1.24571e9	+	2.17740e8i	−0.503038	+	0.0879274i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	2.43704e9	−	2.43704e9i	0.956117	−	0.956117i	−0.0429600	−	0.999077i	$-0.513679\pi$
$487$	2.43704e9	−	2.43704e9i	0.956117	−	0.956117i	0.999077	+	0.0429600i	$0.0136788\pi$
$488$		0			0
$489$	2.49524e9	−	3.55231e9i	0.965009	−	1.37382i
$490$		0			0
$491$		−	3.69275e9i		−	1.40788i	−0.710261	−	0.703938i	$-0.751423\pi$
$491$		−	3.69275e9i		−	1.40788i	0.710261	−	0.703938i	$-0.248577\pi$
$492$		0			0
$493$	−3.94937e9	−	3.94937e9i	−1.48444	−	1.48444i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.31719e9	+	1.31719e9i	0.481283	+	0.481283i
$498$		0			0
$499$			3.10681e9i			1.11934i	0.828715	+	0.559671i	$0.189072\pi$
$499$			3.10681e9i			1.11934i	−0.828715	+	0.559671i	$0.810928\pi$
$500$		0			0
$501$	8.24968e8	−	1.17445e9i	0.293093	−	0.417256i
$502$		0			0
$503$	−3.71686e9	+	3.71686e9i	−1.30223	+	1.30223i	−0.375345	+	0.926885i	$0.622476\pi$
$503$	−3.71686e9	+	3.71686e9i	−1.30223	+	1.30223i	−0.926885	+	0.375345i	$0.877524\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.84125e9	−	4.96629e8i	0.968236	−	0.169240i
$508$		0			0
$509$	−1.98710e9			−0.667894			−0.333947	−	0.942592i	$-0.608381\pi$
$509$	−1.98710e9			−0.667894			−0.333947	+	0.942592i	$0.608381\pi$
$510$		0			0
$511$	−2.98938e9			−0.991078
$512$		0			0
$513$	−3.43918e9	+	1.96518e9i	−1.12472	+	0.642677i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−5.16617e8	+	5.16617e8i	−0.164419	+	0.164419i
$518$		0			0
$519$	−4.68376e9	−	3.29000e9i	−1.47065	−	1.03302i
$520$		0			0
$521$			2.68557e9i			0.831963i	0.909373	+	0.415982i	$0.136562\pi$
$521$			2.68557e9i			0.831963i	−0.909373	+	0.415982i	$0.863438\pi$
$522$		0			0
$523$	−1.83283e9	−	1.83283e9i	−0.560231	−	0.560231i	0.369142	−	0.929373i	$-0.379652\pi$
$523$	−1.83283e9	−	1.83283e9i	−0.560231	−	0.560231i	−0.929373	+	0.369142i	$0.879652\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.72508e9	−	2.72508e9i	−0.811038	−	0.811038i
$528$		0			0
$529$			2.26026e9i			0.663841i
$530$		0			0
$531$	3.18481e9	−	1.14845e9i	0.923108	−	0.332875i
$532$		0			0
$533$	4.93284e8	−	4.93284e8i	0.141108	−	0.141108i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.47272e8	+	2.55887e9i	0.124641	+	0.713081i
$538$		0			0
$539$	4.36080e8			0.119951
$540$		0			0
$541$	−3.09705e9			−0.840925			−0.420463	−	0.907310i	$-0.638132\pi$
$541$	−3.09705e9			−0.840925			−0.420463	+	0.907310i	$0.638132\pi$
$542$		0			0
$543$	−6.61114e8	−	3.78228e9i	−0.177205	−	1.01380i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	5.08212e9	−	5.08212e9i	1.32767	−	1.32767i	0.420267	−	0.907401i	$-0.361936\pi$
$547$	5.08212e9	−	5.08212e9i	1.32767	−	1.32767i	0.907401	−	0.420267i	$-0.138064\pi$
$548$		0			0
$549$	8.11047e8	−	2.92466e8i	0.209191	−	0.0754348i
$550$		0			0
$551$			6.68044e9i			1.70127i
$552$		0			0
$553$	−1.72515e9	−	1.72515e9i	−0.433799	−	0.433799i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.22298e9	−	2.22298e9i	−0.545059	−	0.545059i	0.379949	−	0.925008i	$-0.375942\pi$
$557$	−2.22298e9	−	2.22298e9i	−0.545059	−	0.545059i	−0.925008	+	0.379949i	$0.875942\pi$
$558$		0			0
$559$			3.88688e8i			0.0941151i
$560$		0			0
$561$	2.92602e9	+	2.05532e9i	0.699694	+	0.491485i
$562$		0			0
$563$	3.57065e8	−	3.57065e8i	0.0843273	−	0.0843273i	−0.663685	−	0.748012i	$-0.731008\pi$
$563$	3.57065e8	−	3.57065e8i	0.0843273	−	0.0843273i	0.748012	+	0.663685i	$0.231008\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.55867e8	−	3.80640e9i	0.0819874	−	0.876948i
$568$		0			0
$569$	−2.15255e8			−0.0489848			−0.0244924	−	0.999700i	$-0.507797\pi$
$569$	−2.15255e8			−0.0489848			−0.0244924	+	0.999700i	$0.507797\pi$
$570$		0			0
$571$	−6.21269e9			−1.39654			−0.698270	−	0.715834i	$-0.746047\pi$
$571$	−6.21269e9			−1.39654			−0.698270	+	0.715834i	$0.746047\pi$
$572$		0			0
$573$	−5.88832e9	+	1.02924e9i	−1.30753	+	0.228546i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.09785e9	−	1.09785e9i	0.237918	−	0.237918i	−0.578069	−	0.815988i	$-0.696194\pi$
$577$	1.09785e9	−	1.09785e9i	0.237918	−	0.237918i	0.815988	+	0.578069i	$0.196194\pi$
$578$		0			0
$579$	1.72264e9	−	2.45241e9i	0.368825	−	0.525071i
$580$		0			0
$581$			2.65591e9i			0.561820i
$582$		0			0
$583$	2.31298e7	+	2.31298e7i	0.00483428	+	0.00483428i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.05457e9	−	3.05457e9i	−0.623329	−	0.623329i	0.323052	−	0.946381i	$-0.395291\pi$
$587$	−3.05457e9	−	3.05457e9i	−0.623329	−	0.623329i	−0.946381	+	0.323052i	$0.895291\pi$
$588$		0			0
$589$			4.60952e9i			0.929505i
$590$		0			0
$591$	−2.41204e9	+	3.43386e9i	−0.480650	+	0.684269i
$592$		0			0
$593$	−5.59943e9	+	5.59943e9i	−1.10269	+	1.10269i	−0.108602	+	0.994085i	$0.534637\pi$
$593$	−5.59943e9	+	5.59943e9i	−1.10269	+	1.10269i	−0.994085	+	0.108602i	$0.965363\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.30221e9	+	1.62596e9i	−1.78927	+	0.312751i
$598$		0			0
$599$	7.22831e8			0.137418			0.0687088	−	0.997637i	$-0.478112\pi$
$599$	7.22831e8			0.137418			0.0687088	+	0.997637i	$0.478112\pi$
$600$		0			0
$601$	−1.31712e9			−0.247493			−0.123747	−	0.992314i	$-0.539491\pi$
$601$	−1.31712e9			−0.247493			−0.123747	+	0.992314i	$0.539491\pi$
$602$		0			0
$603$	1.18186e9	−	2.51493e9i	0.219511	−	0.467106i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	1.78474e9	−	1.78474e9i	0.323903	−	0.323903i	−0.526360	−	0.850262i	$-0.676443\pi$
$607$	1.78474e9	−	1.78474e9i	0.323903	−	0.323903i	0.850262	+	0.526360i	$0.176443\pi$
$608$		0			0
$609$	−5.27607e9	−	3.70606e9i	−0.946564	−	0.664894i
$610$		0			0
$611$			3.20345e8i			0.0568164i
$612$		0			0
$613$	−5.53669e9	−	5.53669e9i	−0.970819	−	0.970819i	0.0287671	−	0.999586i	$-0.490842\pi$
$613$	−5.53669e9	−	5.53669e9i	−0.970819	−	0.970819i	−0.999586	+	0.0287671i	$0.990842\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.29818e9	+	6.29818e9i	1.07949	+	1.07949i	0.996555	+	0.0829309i	$0.0264281\pi$
$617$	6.29818e9	+	6.29818e9i	1.07949	+	1.07949i	0.0829309	+	0.996555i	$0.473572\pi$
$618$		0			0
$619$			4.02532e9i			0.682155i	0.940035	+	0.341078i	$0.110792\pi$
$619$			4.02532e9i			0.682155i	−0.940035	+	0.341078i	$0.889208\pi$
$620$		0			0
$621$	3.33820e9	+	9.10465e8i	0.559361	+	0.152561i
$622$		0			0
$623$	2.04285e9	−	2.04285e9i	0.338476	−	0.338476i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.36405e8	−	4.21302e9i	−0.119311	−	0.682586i
$628$		0			0
$629$	−4.29037e9			−0.687413
$630$		0			0
$631$	1.00012e9			0.158471			0.0792357	−	0.996856i	$-0.474752\pi$
$631$	1.00012e9			0.158471			0.0792357	+	0.996856i	$0.474752\pi$
$632$		0			0
$633$	−5.27633e7	−	3.01863e8i	−0.00826836	−	0.0473038i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.35203e8	−	1.35203e8i	0.0207252	−	0.0207252i
$638$		0			0
$639$	−1.72897e9	−	4.79467e9i	−0.262141	−	0.726952i
$640$		0			0
$641$		−	5.84409e9i		−	0.876423i	−0.898872	−	0.438211i	$-0.855612\pi$
$641$		−	5.84409e9i		−	0.876423i	0.898872	−	0.438211i	$-0.144388\pi$
$642$		0			0
$643$	7.70724e9	+	7.70724e9i	1.14330	+	1.14330i	0.987842	+	0.155458i	$0.0496854\pi$
$643$	7.70724e9	+	7.70724e9i	1.14330	+	1.14330i	0.155458	+	0.987842i	$0.450315\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.26457e9	+	1.26457e9i	0.183560	+	0.183560i	0.792905	−	0.609345i	$-0.208568\pi$
$647$	1.26457e9	+	1.26457e9i	0.183560	+	0.183560i	−0.609345	+	0.792905i	$0.708568\pi$
$648$		0			0
$649$			3.65551e9i			0.524918i
$650$		0			0
$651$	−3.64050e9	−	2.55719e9i	−0.517163	−	0.363270i
$652$		0			0
$653$	−4.06128e9	+	4.06128e9i	−0.570777	+	0.570777i	−0.932345	−	0.361569i	$-0.882241\pi$
$653$	−4.06128e9	+	4.06128e9i	−0.570777	+	0.570777i	0.361569	+	0.932345i	$0.382241\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	7.40275e9	+	3.47883e9i	1.01839	+	0.478580i
$658$		0			0
$659$	4.05577e9			0.552045			0.276022	−	0.961151i	$-0.410984\pi$
$659$	4.05577e9			0.552045			0.276022	+	0.961151i	$0.410984\pi$
$660$		0			0
$661$	3.61381e9			0.486698			0.243349	−	0.969939i	$-0.421754\pi$
$661$	3.61381e9			0.486698			0.243349	+	0.969939i	$0.421754\pi$
$662$		0			0
$663$	1.54442e9	−	2.69954e8i	0.205811	−	0.0359742i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.12642e9	−	4.12642e9i	0.538434	−	0.538434i
$668$		0			0
$669$	4.94424e9	−	7.03878e9i	0.638422	−	0.908879i
$670$		0			0
$671$			9.30917e8i			0.118955i
$672$		0			0
$673$	−2.83270e9	−	2.83270e9i	−0.358218	−	0.358218i	0.504938	−	0.863156i	$-0.331515\pi$
$673$	−2.83270e9	−	2.83270e9i	−0.358218	−	0.358218i	−0.863156	+	0.504938i	$0.831515\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.30153e9	+	1.30153e9i	0.161211	+	0.161211i	0.783103	−	0.621892i	$-0.213636\pi$
$677$	1.30153e9	+	1.30153e9i	0.161211	+	0.161211i	−0.621892	+	0.783103i	$0.713636\pi$
$678$		0			0
$679$		−	4.39848e9i		−	0.539211i
$680$		0			0
$681$	7.01796e9	−	9.99100e9i	0.851523	−	1.21226i
$682$		0			0
$683$	6.66517e9	−	6.66517e9i	0.800458	−	0.800458i	−0.182709	−	0.983167i	$-0.558487\pi$
$683$	6.66517e9	−	6.66517e9i	0.800458	−	0.800458i	0.983167	+	0.182709i	$0.0584866\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1.55684e9	−	2.72124e8i	0.183188	−	0.0320198i
$688$		0			0
$689$	1.43424e7			0.00167053
$690$		0			0
$691$	8.08878e9			0.932631			0.466316	−	0.884618i	$-0.345581\pi$
$691$	8.08878e9			0.932631			0.466316	+	0.884618i	$0.345581\pi$
$692$		0			0
$693$	3.73589e9	+	1.75563e9i	0.426410	+	0.200386i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.54266e10	+	1.54266e10i	−1.72566	+	1.72566i
$698$		0			0
$699$	1.22437e10	+	8.60034e9i	1.35595	+	0.952457i
$700$		0			0
$701$		−	9.03327e9i		−	0.990448i	−0.868765	−	0.495224i	$-0.835086\pi$
$701$		−	9.03327e9i		−	0.990448i	0.868765	−	0.495224i	$-0.164914\pi$
$702$		0			0
$703$	3.62862e9	+	3.62862e9i	0.393911	+	0.393911i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.61240e9	−	7.61240e9i	−0.810128	−	0.810128i
$708$		0			0
$709$		−	4.76635e9i		−	0.502255i	−0.967954	−	0.251127i	$-0.919199\pi$
$709$		−	4.76635e9i		−	0.502255i	0.967954	−	0.251127i	$-0.0808013\pi$
$710$		0			0
$711$	2.26447e9	+	6.27968e9i	0.236278	+	0.655230i
$712$		0			0
$713$	2.84724e9	−	2.84724e9i	0.294178	−	0.294178i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.75026e9	+	1.00134e10i	0.177332	+	1.01453i
$718$		0			0
$719$	3.15153e8			0.0316206			0.0158103	−	0.999875i	$-0.494967\pi$
$719$	3.15153e8			0.0316206			0.0158103	+	0.999875i	$0.494967\pi$
$720$		0			0
$721$	−1.26828e10			−1.26020
$722$		0			0
$723$	1.22887e9	+	7.03043e9i	0.120926	+	0.691827i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−9.64502e8	+	9.64502e8i	−0.0930963	+	0.0930963i	−0.752121	−	0.659025i	$-0.770969\pi$
$727$	−9.64502e8	+	9.64502e8i	−0.0930963	+	0.0930963i	0.659025	+	0.752121i	$0.270969\pi$
$728$		0			0
$729$	−5.31088e9	+	9.01186e9i	−0.507715	+	0.861525i
$730$		0			0
$731$		−	1.21555e10i		−	1.15097i
$732$		0			0
$733$	7.00690e9	+	7.00690e9i	0.657147	+	0.657147i	0.954704	−	0.297557i	$-0.0961720\pi$
$733$	7.00690e9	+	7.00690e9i	0.657147	+	0.657147i	−0.297557	+	0.954704i	$0.596172\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.12158e9	+	2.12158e9i	0.195220	+	0.195220i
$738$		0			0
$739$			1.63138e10i			1.48696i	0.668757	+	0.743481i	$0.266826\pi$
$739$			1.63138e10i			1.48696i	−0.668757	+	0.743481i	$0.733174\pi$
$740$		0			0
$741$	−1.53453e9	−	1.07789e9i	−0.138551	−	0.0973223i
$742$		0			0
$743$	9.77965e9	−	9.77965e9i	0.874707	−	0.874707i	−0.118274	−	0.992981i	$-0.537736\pi$
$743$	9.77965e9	−	9.77965e9i	0.874707	−	0.874707i	0.992981	+	0.118274i	$0.0377362\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.09076e9	−	6.57697e9i	0.271296	−	0.577303i
$748$		0			0
$749$	5.80729e8			0.0504995
$750$		0			0
$751$	−1.45113e9			−0.125016			−0.0625082	−	0.998044i	$-0.519910\pi$
$751$	−1.45113e9			−0.125016			−0.0625082	+	0.998044i	$0.519910\pi$
$752$		0			0
$753$	1.46566e10	−	2.56186e9i	1.25098	−	0.218662i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−8.94867e9	+	8.94867e9i	−0.749761	+	0.749761i	−0.974434	−	0.224673i	$-0.927869\pi$
$757$	−8.94867e9	+	8.94867e9i	−0.749761	+	0.749761i	0.224673	+	0.974434i	$0.427869\pi$
$758$		0			0
$759$	−2.14746e9	+	3.05719e9i	−0.178270	+	0.253791i
$760$		0			0
$761$			3.51046e8i			0.0288747i	0.999896	+	0.0144374i	$0.00459572\pi$
$761$			3.51046e8i			0.0288747i	−0.999896	+	0.0144374i	$0.995404\pi$
$762$		0			0
$763$	8.16169e9	+	8.16169e9i	0.665188	+	0.665188i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.13336e9	+	1.13336e9i	0.0906951	+	0.0906951i
$768$		0			0
$769$		−	1.06835e10i		−	0.847170i	−0.905856	−	0.423585i	$-0.860771\pi$
$769$		−	1.06835e10i		−	0.847170i	0.905856	−	0.423585i	$-0.139229\pi$
$770$		0			0
$771$	−9.04739e8	+	1.28802e9i	−0.0710940	+	0.101212i
$772$		0			0
$773$	9.62442e9	−	9.62442e9i	0.749457	−	0.749457i	−0.224921	−	0.974377i	$-0.572212\pi$
$773$	9.62442e9	−	9.62442e9i	0.749457	−	0.749457i	0.974377	+	0.224921i	$0.0722122\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.87884e9	+	8.52784e8i	−0.373115	+	0.0652177i
$778$		0			0
$779$	2.60944e10			1.97772
$780$		0			0
$781$	5.50330e9			0.413376
$782$		0			0
$783$	8.75255e9	+	1.53174e10i	0.651581	+	1.14030i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.14739e9	+	3.14739e9i	−0.230165	+	0.230165i	−0.812762	−	0.582597i	$-0.802037\pi$
$787$	−3.14739e9	+	3.14739e9i	−0.230165	+	0.230165i	0.582597	+	0.812762i	$0.302037\pi$
$788$		0			0
$789$	−4.51293e9	−	3.17001e9i	−0.327106	−	0.229769i
$790$		0			0
$791$			2.04983e10i			1.47265i
$792$		0			0
$793$	2.88623e8	+	2.88623e8i	0.0205529	+	0.0205529i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.69169e10	+	1.69169e10i	1.18363	+	1.18363i	0.978797	+	0.204835i	$0.0656657\pi$
$797$	1.69169e10	+	1.69169e10i	1.18363	+	1.18363i	0.204835	+	0.978797i	$0.434334\pi$
$798$		0			0
$799$		−	1.00182e10i		−	0.694828i
$800$		0			0
$801$	−7.43614e9	+	2.68149e9i	−0.511251	+	0.184358i
$802$		0			0
$803$	−6.24492e9	+	6.24492e9i	−0.425620	+	0.425620i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4.52030e7	−	2.58609e8i	−0.00302768	−	0.0173215i
$808$		0			0
$809$	−1.86006e10			−1.23511			−0.617556	−	0.786527i	$-0.711877\pi$
$809$	−1.86006e10			−1.23511			−0.617556	+	0.786527i	$0.711877\pi$
$810$		0			0
$811$	1.00449e10			0.661263			0.330632	−	0.943760i	$-0.392738\pi$
$811$	1.00449e10			0.661263			0.330632	+	0.943760i	$0.392738\pi$
$812$		0			0
$813$	−2.87991e9	−	1.64761e10i	−0.187958	−	1.07532i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.02806e10	+	1.02806e10i	−0.659543	+	0.659543i
$818$		0			0
$819$	1.70260e9	−	6.13961e8i	0.108297	−	0.0390523i
$820$		0			0
$821$			1.37544e10i			0.867444i	0.901047	+	0.433722i	$0.142800\pi$
$821$			1.37544e10i			0.867444i	−0.901047	+	0.433722i	$0.857200\pi$
$822$		0			0
$823$	1.26443e10	+	1.26443e10i	0.790669	+	0.790669i	0.981603	−	0.190934i	$-0.0611517\pi$
$823$	1.26443e10	+	1.26443e10i	0.790669	+	0.790669i	−0.190934	+	0.981603i	$0.561152\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.86210e10	+	1.86210e10i	1.14481	+	1.14481i	0.987559	+	0.157252i	$0.0502634\pi$
$827$	1.86210e10	+	1.86210e10i	1.14481	+	1.14481i	0.157252	+	0.987559i	$0.449737\pi$
$828$		0			0
$829$		−	1.21215e10i		−	0.738949i	−0.929241	−	0.369475i	$-0.879538\pi$
$829$		−	1.21215e10i		−	0.738949i	0.929241	−	0.369475i	$-0.120462\pi$
$830$		0			0
$831$	−1.43763e10	−	1.00983e10i	−0.869049	−	0.610444i
$832$		0			0
$833$	−4.22823e9	+	4.22823e9i	−0.253455	+	0.253455i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	6.03928e9	+	1.05691e10i	0.355997	+	0.623014i
$838$		0			0
$839$	−3.12593e10			−1.82731			−0.913656	−	0.406488i	$-0.866753\pi$
$839$	−3.12593e10			−1.82731			−0.913656	+	0.406488i	$0.866753\pi$
$840$		0			0
$841$	1.25035e10			0.724847
$842$		0			0
$843$	2.10740e10	−	3.68358e9i	1.21158	−	0.211775i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	7.86232e9	−	7.86232e9i	0.444589	−	0.444589i
$848$		0			0
$849$	−1.45192e10	+	2.06701e10i	−0.814267	+	1.15922i
$850$		0			0
$851$		−	4.48270e9i		−	0.249337i
$852$		0			0
$853$	1.01070e10	+	1.01070e10i	0.557570	+	0.557570i	0.928615	−	0.371045i	$-0.121000\pi$
$853$	1.01070e10	+	1.01070e10i	0.557570	+	0.557570i	−0.371045	+	0.928615i	$0.621000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.22083e9	−	5.22083e9i	−0.283339	−	0.283339i	0.551100	−	0.834439i	$-0.314208\pi$
$857$	−5.22083e9	−	5.22083e9i	−0.283339	−	0.283339i	−0.834439	+	0.551100i	$0.814208\pi$
$858$		0			0
$859$		−	1.06595e10i		−	0.573798i	−0.957961	−	0.286899i	$-0.907376\pi$
$859$		−	1.06595e10i		−	0.573798i	0.957961	−	0.286899i	$-0.0926244\pi$
$860$		0			0
$861$	−1.44762e10	+	2.06088e10i	−0.772936	+	1.10038i
$862$		0			0
$863$	1.81636e10	−	1.81636e10i	0.961978	−	0.961978i	−0.0373248	−	0.999303i	$-0.511884\pi$
$863$	1.81636e10	−	1.81636e10i	0.961978	−	0.961978i	0.999303	+	0.0373248i	$0.0118836\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.93960e10	+	5.13820e9i	−1.53187	+	0.267759i
$868$		0			0
$869$	−7.20779e9			−0.372592
$870$		0			0
$871$	1.31555e9			0.0674599
$872$		0			0
$873$	−5.11864e9	+	1.08922e10i	−0.260378	+	0.554071i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.91061e9	−	4.91061e9i	0.245831	−	0.245831i	−0.573426	−	0.819257i	$-0.694386\pi$
$877$	4.91061e9	−	4.91061e9i	0.245831	−	0.245831i	0.819257	+	0.573426i	$0.194386\pi$
$878$		0			0
$879$	−4.16443e8	−	2.92521e8i	−0.0206821	−	0.0145277i
$880$		0			0
$881$			6.36282e9i			0.313497i	0.987639	+	0.156749i	$0.0501013\pi$
$881$			6.36282e9i			0.313497i	−0.987639	+	0.156749i	$0.949899\pi$
$882$		0			0
$883$	−9.25527e8	−	9.25527e8i	−0.0452404	−	0.0452404i	0.684125	−	0.729365i	$-0.260184\pi$
$883$	−9.25527e8	−	9.25527e8i	−0.0452404	−	0.0452404i	−0.729365	+	0.684125i	$0.760184\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.78070e10	−	2.78070e10i	−1.33789	−	1.33789i	−0.898099	−	0.439794i	$-0.855051\pi$
$887$	−2.78070e10	−	2.78070e10i	−1.33789	−	1.33789i	−0.439794	−	0.898099i	$-0.644949\pi$
$888$		0			0
$889$		−	3.37928e10i		−	1.61312i
$890$		0			0
$891$	−7.20829e9	−	8.69513e9i	−0.341398	−	0.411817i
$892$		0			0
$893$	−8.47301e9	+	8.47301e9i	−0.398160	+	0.398160i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.82055e8	+	1.61366e9i	0.0130485	+	0.0746514i
$898$		0			0
$899$	2.05299e10			0.942385
$900$		0			0
$901$	−4.48533e8			−0.0204295
$902$		0			0
$903$	−2.41612e9	−	1.38228e10i	−0.109197	−	0.624723i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4.17395e9	−	4.17395e9i	0.185747	−	0.185747i	−0.608108	−	0.793855i	$-0.708071\pi$
$907$	4.17395e9	−	4.17395e9i	0.185747	−	0.185747i	0.793855	+	0.608108i	$0.208071\pi$
$908$		0			0
$909$	9.99220e9	+	2.77098e10i	0.441253	+	1.22366i
$910$		0			0
$911$			3.10265e10i			1.35962i	0.733386	+	0.679812i	$0.237939\pi$
$911$			3.10265e10i			1.35962i	−0.733386	+	0.679812i	$0.762061\pi$
$912$		0			0
$913$	5.54830e9	+	5.54830e9i	0.241275	+	0.241275i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.90480e9	−	5.90480e9i	−0.252879	−	0.252879i
$918$		0			0
$919$		−	1.00910e10i		−	0.428876i	−0.976738	−	0.214438i	$-0.931208\pi$
$919$		−	1.00910e10i		−	0.428876i	0.976738	−	0.214438i	$-0.0687920\pi$
$920$		0			0
$921$	1.14795e10	+	8.06352e9i	0.484188	+	0.340107i
$922$		0			0
$923$	1.70625e9	−	1.70625e9i	0.0714228	−	0.0714228i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.14070e10	+	1.47593e10i	1.29493	+	0.608538i
$928$		0			0
$929$	3.63018e10			1.48550			0.742751	−	0.669568i	$-0.233521\pi$
$929$	3.63018e10			1.48550			0.742751	+	0.669568i	$0.233521\pi$
$930$		0			0
$931$	7.15213e9			0.290477
$932$		0			0
$933$	−4.05916e10	+	7.09511e9i	−1.63625	+	0.286005i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.89509e9	+	6.89509e9i	−0.273811	+	0.273811i	−0.830632	−	0.556821i	$-0.812021\pi$
$937$	−6.89509e9	+	6.89509e9i	−0.273811	+	0.273811i	0.556821	+	0.830632i	$0.312021\pi$
$938$		0			0
$939$	−1.95774e10	+	2.78711e10i	−0.771661	+	1.09856i
$940$		0			0
$941$		−	4.05738e10i		−	1.58739i	−0.608319	−	0.793693i	$-0.708156\pi$
$941$		−	4.05738e10i		−	1.58739i	0.608319	−	0.793693i	$-0.291844\pi$
$942$		0			0
$943$	−1.61181e10	−	1.61181e10i	−0.625928	−	0.625928i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.16883e9	+	6.16883e9i	0.236036	+	0.236036i	0.815206	−	0.579171i	$-0.196623\pi$
$947$	6.16883e9	+	6.16883e9i	0.236036	+	0.236036i	−0.579171	+	0.815206i	$0.696623\pi$
$948$		0			0
$949$			3.87236e9i			0.147077i
$950$		0			0
$951$	−1.27140e10	+	1.81000e10i	−0.479346	+	0.682413i
$952$		0			0
$953$	1.73175e10	−	1.73175e10i	0.648125	−	0.648125i	−0.304415	−	0.952540i	$-0.598461\pi$
$953$	1.73175e10	−	1.73175e10i	0.648125	−	0.648125i	0.952540	+	0.304415i	$0.0984608\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.87640e10	+	3.27981e9i	−0.692044	+	0.120964i
$958$		0			0
$959$	−4.01683e10			−1.47068
$960$		0			0
$961$	−1.33469e10			−0.485120
$962$		0			0
$963$	−1.43809e9	−	6.75811e8i	−0.0518912	−	0.0243856i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.11183e10	−	2.11183e10i	0.751045	−	0.751045i	−0.223630	−	0.974674i	$-0.571791\pi$
$967$	2.11183e10	−	2.11183e10i	0.751045	−	0.751045i	0.974674	+	0.223630i	$0.0717906\pi$
$968$		0			0
$969$	4.79896e10	+	3.37092e10i	1.69439	+	1.19019i
$970$		0			0
$971$		−	3.83642e10i		−	1.34480i	−0.740186	−	0.672402i	$-0.765263\pi$
$971$		−	3.83642e10i		−	1.34480i	0.740186	−	0.672402i	$-0.234737\pi$
$972$		0			0
$973$	1.41529e9	+	1.41529e9i	0.0492551	+	0.0492551i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.73015e9	+	5.73015e9i	0.196578	+	0.196578i	0.798531	−	0.601953i	$-0.205611\pi$
$977$	5.73015e9	+	5.73015e9i	0.196578	+	0.196578i	−0.601953	+	0.798531i	$0.705611\pi$
$978$		0			0
$979$		−	8.53517e9i		−	0.290719i
$980$		0			0
$981$	−1.07132e10	−	2.97092e10i	−0.362308	−	1.00473i
$982$		0			0
$983$	−2.73867e10	+	2.73867e10i	−0.919607	+	0.919607i	−0.997001	−	0.0773933i	$-0.975340\pi$
$983$	−2.73867e10	+	2.73867e10i	−0.919607	+	0.919607i	0.0773933	+	0.997001i	$0.475340\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.99129e9	−	1.13923e10i	−0.0659212	−	0.377140i
$988$		0			0
$989$	1.27004e10			0.417476
$990$		0			0
$991$	4.97037e10			1.62230			0.811149	−	0.584840i	$-0.198843\pi$
$991$	4.97037e10			1.62230			0.811149	+	0.584840i	$0.198843\pi$
$992$		0			0
$993$	−1.20100e9	−	6.87102e9i	−0.0389244	−	0.222689i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.87057e10	−	2.87057e10i	0.917349	−	0.917349i	−0.0794873	−	0.996836i	$-0.525328\pi$
$997$	2.87057e10	−	2.87057e10i	0.917349	−	0.917349i	0.996836	+	0.0794873i	$0.0253283\pi$
$998$		0			0
$999$	1.30741e10	+	3.56585e9i	0.414890	+	0.113158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.8.i.c.293.5	yes	16
3.2	odd	2	inner	300.8.i.c.293.8	yes	16
5.2	odd	4	inner	300.8.i.c.257.8	yes	16
5.3	odd	4	inner	300.8.i.c.257.1	✓	16
5.4	even	2	inner	300.8.i.c.293.4	yes	16
15.2	even	4	inner	300.8.i.c.257.5	yes	16
15.8	even	4	inner	300.8.i.c.257.4	yes	16
15.14	odd	2	inner	300.8.i.c.293.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.8.i.c.257.1	✓	16	5.3	odd	4	inner
300.8.i.c.257.4	yes	16	15.8	even	4	inner
300.8.i.c.257.5	yes	16	15.2	even	4	inner
300.8.i.c.257.8	yes	16	5.2	odd	4	inner
300.8.i.c.293.1	yes	16	15.14	odd	2	inner
300.8.i.c.293.4	yes	16	5.4	even	2	inner
300.8.i.c.293.5	yes	16	1.1	even	1	trivial
300.8.i.c.293.8	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(8.05216 + 46.0669i) q^{3} +(565.187 - 565.187i) q^{7} +(-2057.33 + 741.876i) q^{9} +O(q^{10})\)	\(q+(8.05216 + 46.0669i) q^{3} +(565.187 - 565.187i) q^{7} +(-2057.33 + 741.876i) q^{9} -2361.39i q^{11} +(-732.128 - 732.128i) q^{13} +(22896.0 + 22896.0i) q^{17} -38729.0i q^{19} +(30587.4 + 21485.4i) q^{21} +(-23922.4 + 23922.4i) q^{23} +(-50741.9 - 88801.0i) q^{27} -172492. q^{29} -119020. q^{31} +(108782. - 19014.3i) q^{33} +(-93692.5 + 93692.5i) q^{37} +(27831.7 - 39622.1i) q^{39} +673768. i q^{41} +(-265451. - 265451. i) q^{43} +(-218777. - 218777. i) q^{47} +184671. i q^{49} +(-870387. + 1.23911e6i) q^{51} +(-9795.00 + 9795.00i) q^{53} +(1.78413e6 - 311852. i) q^{57} -1.54803e6 q^{59} -394224. q^{61} +(-743474. + 1.58207e6i) q^{63} +(-898446. + 898446. i) q^{67} +(-1.29466e6 - 909405. i) q^{69} +2.33054e6i q^{71} +(-2.64459e6 - 2.64459e6i) q^{73} +(-1.33463e6 - 1.33463e6i) q^{77} -3.05235e6i q^{79} +(3.68221e6 - 3.05256e6i) q^{81} +(-2.34959e6 + 2.34959e6i) q^{83} +(-1.38893e6 - 7.94617e6i) q^{87} +3.61447e6 q^{89} -827578. q^{91} +(-958365. - 5.48287e6i) q^{93} +(3.89118e6 - 3.89118e6i) q^{97} +(1.75186e6 + 4.85815e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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

Representations

Groups

Database

Properties

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