LMFDB - Embedded newform 252.9.bg.a.29.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(29,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("252.29");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.bg (of order $6$, 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:	$102.659409735$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	252.29
Dual form			252.9.bg.a.113.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-55.8369 + 58.6791i) q^{3} +(-400.624 + 231.301i) q^{5} +(453.746 - 785.912i) q^{7} +(-325.483 - 6552.92i) q^{9} +O(q^{10})$	\(q+(-55.8369 + 58.6791i) q^{3} +(-400.624 + 231.301i) q^{5} +(453.746 - 785.912i) q^{7} +(-325.483 - 6552.92i) q^{9} +(-6952.17 - 4013.84i) q^{11} +(-22709.6 - 39334.1i) q^{13} +(8797.10 - 36423.4i) q^{15} -39548.2i q^{17} +85581.2 q^{19} +(20780.8 + 70508.3i) q^{21} +(-19367.3 + 11181.7i) q^{23} +(-88312.6 + 152962. i) q^{25} +(402694. + 346796. i) q^{27} +(226160. + 130574. i) q^{29} +(-275706. - 477537. i) q^{31} +(623716. - 183827. i) q^{33} +419807. i q^{35} +102685. q^{37} +(3.57612e6 + 863717. i) q^{39} +(109076. - 62975.1i) q^{41} +(2.37202e6 - 4.10847e6i) q^{43} +(1.64609e6 + 2.54998e6i) q^{45} +(2.84800e6 + 1.64429e6i) q^{47} +(-411772. - 713209. i) q^{49} +(2.32065e6 + 2.20825e6i) q^{51} -1.92409e6i q^{53} +3.71361e6 q^{55} +(-4.77859e6 + 5.02183e6i) q^{57} +(-4.21966e6 + 2.43622e6i) q^{59} +(-3.06263e6 + 5.30464e6i) q^{61} +(-5.29770e6 - 2.71756e6i) q^{63} +(1.81960e7 + 1.05055e7i) q^{65} +(-6.01071e6 - 1.04109e7i) q^{67} +(425276. - 1.76081e6i) q^{69} -1.39735e7i q^{71} -1.49769e7 q^{73} +(-4.04457e6 - 1.37230e7i) q^{75} +(-6.30904e6 + 3.64253e6i) q^{77} +(-1.43774e7 + 2.49023e7i) q^{79} +(-4.28348e7 + 4.26573e6i) q^{81} +(7.19554e7 + 4.15435e7i) q^{83} +(9.14752e6 + 1.58440e7i) q^{85} +(-2.02900e7 + 5.98006e6i) q^{87} -1.42252e7i q^{89} -4.12175e7 q^{91} +(4.34160e7 + 1.04860e7i) q^{93} +(-3.42859e7 + 1.97950e7i) q^{95} +(1.02387e7 - 1.77339e7i) q^{97} +(-2.40395e7 + 4.68635e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 42 q^{3} - 882 q^{5} - 14642 q^{9}+O(q^{10}) $ 96 * q - 42 * q^3 - 882 * q^5 - 14642 * q^9	$ 96 q - 42 q^{3} - 882 q^{5} - 14642 q^{9} - 6102 q^{11} - 63218 q^{15} - 354144 q^{19} + 81634 q^{21} - 689760 q^{23} + 4088394 q^{25} - 2939076 q^{27} - 1902474 q^{29} + 613830 q^{31} - 3732526 q^{33} + 4437300 q^{37} - 2690876 q^{39} + 8275176 q^{41} - 2941680 q^{43} + 7299362 q^{45} - 7663950 q^{47} - 39530064 q^{49} - 23625052 q^{51} + 8608908 q^{55} + 28697652 q^{57} + 38291778 q^{59} + 7577556 q^{63} + 42391494 q^{65} + 47903562 q^{67} - 52586968 q^{69} - 32396448 q^{73} + 245976220 q^{75} + 11461314 q^{79} - 16224230 q^{81} - 104964174 q^{83} + 108387294 q^{85} - 213493700 q^{87} - 12590844 q^{91} - 88124258 q^{93} + 293841792 q^{95} + 9277590 q^{97} - 77959808 q^{99}+O(q^{100}) $ 96 * q - 42 * q^3 - 882 * q^5 - 14642 * q^9 - 6102 * q^11 - 63218 * q^15 - 354144 * q^19 + 81634 * q^21 - 689760 * q^23 + 4088394 * q^25 - 2939076 * q^27 - 1902474 * q^29 + 613830 * q^31 - 3732526 * q^33 + 4437300 * q^37 - 2690876 * q^39 + 8275176 * q^41 - 2941680 * q^43 + 7299362 * q^45 - 7663950 * q^47 - 39530064 * q^49 - 23625052 * q^51 + 8608908 * q^55 + 28697652 * q^57 + 38291778 * q^59 + 7577556 * q^63 + 42391494 * q^65 + 47903562 * q^67 - 52586968 * q^69 - 32396448 * q^73 + 245976220 * q^75 + 11461314 * q^79 - 16224230 * q^81 - 104964174 * q^83 + 108387294 * q^85 - 213493700 * q^87 - 12590844 * q^91 - 88124258 * q^93 + 293841792 * q^95 + 9277590 * q^97 - 77959808 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	−55.8369	+	58.6791i	−0.689344	+	0.724434i
$3$	−55.8369	+	58.6791i	−0.689344	+	0.724434i
$4$		0			0
$5$	−400.624	+	231.301i	−0.640999	+	0.370081i	−0.784999	−	0.619497i	$-0.787337\pi$
$5$	−400.624	+	231.301i	−0.640999	+	0.370081i	0.144000	+	0.989578i	$0.454003\pi$
$6$		0			0
$7$	453.746	−	785.912i	0.188982	−	0.327327i
$7$	453.746	−	785.912i	0.188982	−	0.327327i
$8$		0			0
$9$	−325.483	−	6552.92i	−0.0496088	−	0.998769i
$10$		0			0
$11$	−6952.17	−	4013.84i	−0.474843	−	0.274150i	0.243422	−	0.969920i	$-0.421730\pi$
$11$	−6952.17	−	4013.84i	−0.474843	−	0.274150i	−0.718265	+	0.695770i	$0.755063\pi$
$12$		0			0
$13$	−22709.6	−	39334.1i	−0.795125	−	1.37720i	−0.922760	−	0.385376i	$-0.874072\pi$
$13$	−22709.6	−	39334.1i	−0.795125	−	1.37720i	0.127635	−	0.991821i	$-0.459261\pi$
$14$		0			0
$15$	8797.10	−	36423.4i	0.173770	−	0.719474i
$16$		0			0
$17$		−	39548.2i		−	0.473512i	−0.971569	−	0.236756i	$-0.923916\pi$
$17$		−	39548.2i		−	0.473512i	0.971569	−	0.236756i	$-0.0760842\pi$
$18$		0			0
$19$	85581.2			0.656695			0.328348	−	0.944557i	$-0.393508\pi$
$19$	85581.2			0.656695			0.328348	+	0.944557i	$0.393508\pi$
$20$		0			0
$21$	20780.8	+	70508.3i	0.106853	+	0.362546i
$22$		0			0
$23$	−19367.3	+	11181.7i	−0.0692081	+	0.0399573i	−0.534205	−	0.845355i	$-0.679389\pi$
$23$	−19367.3	+	11181.7i	−0.0692081	+	0.0399573i	0.464997	+	0.885312i	$0.346056\pi$
$24$		0			0
$25$	−88312.6	+	152962.i	−0.226080	+	0.391583i
$26$		0			0
$27$	402694.	+	346796.i	0.757739	+	0.652557i
$28$		0			0
$29$	226160.	+	130574.i	0.319760	+	0.184614i	0.651286	−	0.758833i	$-0.274230\pi$
$29$	226160.	+	130574.i	0.319760	+	0.184614i	−0.331525	+	0.943446i	$0.607563\pi$
$30$		0			0
$31$	−275706.	−	477537.i	−0.298538	−	0.517083i	0.677264	−	0.735740i	$-0.263166\pi$
$31$	−275706.	−	477537.i	−0.298538	−	0.517083i	−0.975802	+	0.218658i	$0.929832\pi$
$32$		0			0
$33$	623716.	−	183827.i	0.525934	−	0.155008i
$34$		0			0
$35$			419807.i			0.279755i
$36$		0			0
$37$	102685.			0.0547900			0.0273950	−	0.999625i	$-0.491279\pi$
$37$	102685.			0.0547900			0.0273950	+	0.999625i	$0.491279\pi$
$38$		0			0
$39$	3.57612e6	+	863717.i	1.54580	+	0.373347i
$40$		0			0
$41$	109076.	−	62975.1i	0.0386006	−	0.0222861i	−0.480576	−	0.876953i	$-0.659572\pi$
$41$	109076.	−	62975.1i	0.0386006	−	0.0222861i	0.519176	+	0.854667i	$0.326239\pi$
$42$		0			0
$43$	2.37202e6	−	4.10847e6i	0.693818	−	1.20173i	−0.276760	−	0.960939i	$-0.589261\pi$
$43$	2.37202e6	−	4.10847e6i	0.693818	−	1.20173i	0.970578	−	0.240788i	$-0.0774060\pi$
$44$		0			0
$45$	1.64609e6	+	2.54998e6i	0.401424	+	0.621850i
$46$		0			0
$47$	2.84800e6	+	1.64429e6i	0.583645	+	0.336967i	0.762580	−	0.646893i	$-0.223932\pi$
$47$	2.84800e6	+	1.64429e6i	0.583645	+	0.336967i	−0.178936	+	0.983861i	$0.557265\pi$
$48$		0			0
$49$	−411772.	−	713209.i	−0.0714286	−	0.123718i
$50$		0			0
$51$	2.32065e6	+	2.20825e6i	0.343028	+	0.326413i
$52$		0			0
$53$		−	1.92409e6i		−	0.243850i	−0.992539	−	0.121925i	$-0.961093\pi$
$53$		−	1.92409e6i		−	0.243850i	0.992539	−	0.121925i	$-0.0389067\pi$
$54$		0			0
$55$	3.71361e6			0.405831
$56$		0			0
$57$	−4.77859e6	+	5.02183e6i	−0.452689	+	0.475732i
$58$		0			0
$59$	−4.21966e6	+	2.43622e6i	−0.348232	+	0.201052i	−0.663906	−	0.747816i	$-0.731103\pi$
$59$	−4.21966e6	+	2.43622e6i	−0.348232	+	0.201052i	0.315674	+	0.948868i	$0.397769\pi$
$60$		0			0
$61$	−3.06263e6	+	5.30464e6i	−0.221195	+	0.383121i	−0.955171	−	0.296054i	$-0.904329\pi$
$61$	−3.06263e6	+	5.30464e6i	−0.221195	+	0.383121i	0.733976	+	0.679175i	$0.237662\pi$
$62$		0			0
$63$	−5.29770e6	−	2.71756e6i	−0.336299	−	0.172511i
$64$		0			0
$65$	1.81960e7	+	1.05055e7i	1.01935	+	0.588521i
$66$		0			0
$67$	−6.01071e6	−	1.04109e7i	−0.298282	−	0.516639i	0.677461	−	0.735558i	$-0.263080\pi$
$67$	−6.01071e6	−	1.04109e7i	−0.298282	−	0.516639i	−0.975743	+	0.218920i	$0.929747\pi$
$68$		0			0
$69$	425276.	−	1.76081e6i	0.0187618	−	0.0776810i
$70$		0			0
$71$		−	1.39735e7i		−	0.549886i	−0.961461	−	0.274943i	$-0.911341\pi$
$71$		−	1.39735e7i		−	0.549886i	0.961461	−	0.274943i	$-0.0886590\pi$
$72$		0			0
$73$	−1.49769e7			−0.527388			−0.263694	−	0.964606i	$-0.584941\pi$
$73$	−1.49769e7			−0.527388			−0.263694	+	0.964606i	$0.584941\pi$
$74$		0			0
$75$	−4.04457e6	−	1.37230e7i	−0.127828	−	0.433715i
$76$		0			0
$77$	−6.30904e6	+	3.64253e6i	−0.179474	+	0.103619i
$78$		0			0
$79$	−1.43774e7	+	2.49023e7i	−0.369123	+	0.639340i	−0.989429	−	0.145020i	$-0.953675\pi$
$79$	−1.43774e7	+	2.49023e7i	−0.369123	+	0.639340i	0.620306	+	0.784360i	$0.287009\pi$
$80$		0			0
$81$	−4.28348e7	+	4.26573e6i	−0.995078	+	0.0990954i
$82$		0			0
$83$	7.19554e7	+	4.15435e7i	1.51618	+	0.875368i	0.999820	+	0.0189976i	$0.00604748\pi$
$83$	7.19554e7	+	4.15435e7i	1.51618	+	0.875368i	0.516362	+	0.856370i	$0.327286\pi$
$84$		0			0
$85$	9.14752e6	+	1.58440e7i	0.175238	+	0.303521i
$86$		0			0
$87$	−2.02900e7	+	5.98006e6i	−0.354165	+	0.104383i
$88$		0			0
$89$		−	1.42252e7i		−	0.226724i	−0.993554	−	0.113362i	$-0.963838\pi$
$89$		−	1.42252e7i		−	0.226724i	0.993554	−	0.113362i	$-0.0361620\pi$
$90$		0			0
$91$	−4.12175e7			−0.601058
$92$		0			0
$93$	4.34160e7	+	1.04860e7i	0.580387	+	0.140177i
$94$		0			0
$95$	−3.42859e7	+	1.97950e7i	−0.420941	+	0.243030i
$96$		0			0
$97$	1.02387e7	−	1.77339e7i	0.115653	−	0.200317i	−0.802387	−	0.596803i	$-0.796437\pi$
$97$	1.02387e7	−	1.77339e7i	0.115653	−	0.200317i	0.918041	+	0.396486i	$0.129771\pi$
$98$		0			0
$99$	−2.40395e7	+	4.68635e7i	−0.250257	+	0.487858i
$100$		0			0
$101$	−7.62871e7	−	4.40444e7i	−0.733104	−	0.423258i	0.0864527	−	0.996256i	$-0.472447\pi$
$101$	−7.62871e7	−	4.40444e7i	−0.733104	−	0.423258i	−0.819557	+	0.572998i	$0.805780\pi$
$102$		0			0
$103$	−4.54390e7	−	7.87026e7i	−0.403719	−	0.699262i	0.590452	−	0.807073i	$-0.298949\pi$
$103$	−4.54390e7	−	7.87026e7i	−0.403719	−	0.699262i	−0.994171	+	0.107810i	$0.965616\pi$
$104$		0			0
$105$	−2.46339e7	−	2.34407e7i	−0.202664	−	0.192847i
$106$		0			0
$107$			1.36669e8i			1.04264i	0.853361	+	0.521321i	$0.174561\pi$
$107$			1.36669e8i			1.04264i	−0.853361	+	0.521321i	$0.825439\pi$
$108$		0			0
$109$	−3.36953e6			−0.0238706			−0.0119353	−	0.999929i	$-0.503799\pi$
$109$	−3.36953e6			−0.0238706			−0.0119353	+	0.999929i	$0.503799\pi$
$110$		0			0
$111$	−5.73362e6	+	6.02548e6i	−0.0377692	+	0.0396917i
$112$		0			0
$113$	−1.06974e8	+	6.17615e7i	−0.656092	+	0.378795i	−0.790786	−	0.612092i	$-0.790328\pi$
$113$	−1.06974e8	+	6.17615e7i	−0.656092	+	0.378795i	0.134694	+	0.990887i	$0.456995\pi$
$114$		0			0
$115$	5.17266e6	−	8.95932e6i	0.0295749	−	0.0512252i
$116$		0			0
$117$	−2.50362e8	+	1.61617e8i	−1.33606	+	0.862467i
$118$		0			0
$119$	−3.10814e7	−	1.79449e7i	−0.154993	−	0.0894854i
$120$		0			0
$121$	−7.49577e7	−	1.29830e8i	−0.349683	−	0.605669i
$122$		0			0
$123$	−2.39515e6	+	9.91683e6i	−0.0104643	+	0.0433264i
$124$		0			0
$125$		−	2.62411e8i		−	1.07483i
$126$		0			0
$127$	−3.41583e8			−1.31305			−0.656525	−	0.754304i	$-0.727974\pi$
$127$	−3.41583e8			−1.31305			−0.656525	+	0.754304i	$0.727974\pi$
$128$		0			0
$129$	1.08635e8	+	3.68592e8i	0.392293	+	1.33103i
$130$		0			0
$131$	−1.34858e8	+	7.78605e7i	−0.457923	+	0.264382i	−0.711171	−	0.703019i	$-0.751835\pi$
$131$	−1.34858e8	+	7.78605e7i	−0.457923	+	0.264382i	0.253247	+	0.967402i	$0.418501\pi$
$132$		0			0
$133$	3.88322e7	−	6.72593e7i	0.124104	−	0.214954i
$134$		0			0
$135$	−2.41543e8	−	4.57915e7i	−0.727209	−	0.137864i
$136$		0			0
$137$	2.03243e7	+	1.17343e7i	0.0576945	+	0.0333099i	0.528570	−	0.848890i	$-0.322728\pi$
$137$	2.03243e7	+	1.17343e7i	0.0576945	+	0.0333099i	−0.470875	+	0.882200i	$0.656062\pi$
$138$		0			0
$139$	1.20972e8	+	2.09529e8i	0.324060	+	0.561288i	0.981322	−	0.192374i	$-0.0616188\pi$
$139$	1.20972e8	+	2.09529e8i	0.324060	+	0.561288i	−0.657262	+	0.753662i	$0.728285\pi$
$140$		0			0
$141$	−2.55509e8	+	7.53059e7i	−0.646443	+	0.190525i
$142$		0			0
$143$			3.64610e8i			0.871936i
$144$		0			0
$145$	−1.20807e8			−0.273288
$146$		0			0
$147$	6.48425e7	+	1.56610e7i	0.138864	+	0.0335390i
$148$		0			0
$149$	−4.38973e8	+	2.53441e8i	−0.890620	+	0.514200i	−0.874145	−	0.485665i	$-0.838578\pi$
$149$	−4.38973e8	+	2.53441e8i	−0.890620	+	0.514200i	−0.0164747	+	0.999864i	$0.505244\pi$
$150$		0			0
$151$	−2.61007e8	+	4.52078e8i	−0.502047	+	0.869572i	0.497950	+	0.867206i	$0.334086\pi$
$151$	−2.61007e8	+	4.52078e8i	−0.502047	+	0.869572i	−0.999997	+	0.00236568i	$0.999247\pi$
$152$		0			0
$153$	−2.59156e8	+	1.28723e7i	−0.472929	+	0.0234904i
$154$		0			0
$155$	2.20909e8	+	1.27542e8i	0.382725	+	0.220966i
$156$		0			0
$157$	1.01267e8	+	1.75400e8i	0.166675	+	0.288689i	0.937249	−	0.348661i	$-0.113364\pi$
$157$	1.01267e8	+	1.75400e8i	0.166675	+	0.288689i	−0.770574	+	0.637351i	$0.780030\pi$
$158$		0			0
$159$	1.12904e8	+	1.07435e8i	0.176653	+	0.168096i
$160$		0			0
$161$			2.02946e7i			0.0302049i
$162$		0			0
$163$	−6.59020e8			−0.933572			−0.466786	−	0.884370i	$-0.654588\pi$
$163$	−6.59020e8			−0.933572			−0.466786	+	0.884370i	$0.654588\pi$
$164$		0			0
$165$	−2.07356e8	+	2.17912e8i	−0.279758	+	0.293998i
$166$		0			0
$167$	4.26769e8	−	2.46395e8i	0.548689	−	0.316786i	−0.199904	−	0.979816i	$-0.564063\pi$
$167$	4.26769e8	−	2.46395e8i	0.548689	−	0.316786i	0.748593	+	0.663030i	$0.230730\pi$
$168$		0			0
$169$	−6.23583e8	+	1.08008e9i	−0.764447	+	1.32406i
$170$		0			0
$171$	−2.78553e7	−	5.60807e8i	−0.0325779	−	0.655887i
$172$		0			0
$173$	−1.71480e8	−	9.90043e7i	−0.191439	−	0.110527i	0.401217	−	0.915983i	$-0.368587\pi$
$173$	−1.71480e8	−	9.90043e7i	−0.191439	−	0.110527i	−0.592656	+	0.805456i	$0.701921\pi$
$174$		0			0
$175$	8.01431e7	+	1.38812e8i	0.0854503	+	0.148004i
$176$		0			0
$177$	9.26572e7	−	3.83637e8i	0.0944031	−	0.390865i
$178$		0			0
$179$		−	3.27098e8i		−	0.318615i	−0.987229	−	0.159308i	$-0.949074\pi$
$179$		−	3.27098e8i		−	0.318615i	0.987229	−	0.159308i	$-0.0509261\pi$
$180$		0			0
$181$	9.16279e8			0.853716			0.426858	−	0.904319i	$-0.359620\pi$
$181$	9.16279e8			0.853716			0.426858	+	0.904319i	$0.359620\pi$
$182$		0			0
$183$	−1.40264e8	−	4.75907e8i	−0.125066	−	0.424344i
$184$		0			0
$185$	−4.11382e7	+	2.37512e7i	−0.0351203	+	0.0202767i
$186$		0			0
$187$	−1.58740e8	+	2.74946e8i	−0.129814	+	0.224844i
$188$		0			0
$189$	4.55272e8	−	1.59125e8i	0.356799	−	0.124707i
$190$		0			0
$191$	−5.59132e8	−	3.22815e8i	−0.420127	−	0.242561i	0.275004	−	0.961443i	$-0.411321\pi$
$191$	−5.59132e8	−	3.22815e8i	−0.420127	−	0.242561i	−0.695132	+	0.718882i	$0.744654\pi$
$192$		0			0
$193$	1.14409e9	+	1.98163e9i	0.824579	+	1.42821i	0.902241	+	0.431232i	$0.141921\pi$
$193$	1.14409e9	+	1.98163e9i	0.824579	+	1.42821i	−0.0776624	+	0.996980i	$0.524746\pi$
$194$		0			0
$195$	−1.63246e9	+	4.81133e8i	−1.12903	+	0.332757i
$196$		0			0
$197$			2.00718e9i			1.33267i	0.745654	+	0.666333i	$0.232137\pi$
$197$			2.00718e9i			1.33267i	−0.745654	+	0.666333i	$0.767863\pi$
$198$		0			0
$199$	2.12358e8			0.135412			0.0677059	−	0.997705i	$-0.478432\pi$
$199$	2.12358e8			0.135412			0.0677059	+	0.997705i	$0.478432\pi$
$200$		0			0
$201$	9.46519e8	+	2.28606e8i	0.579889	+	0.140057i
$202$		0			0
$203$	2.05239e8	−	1.18495e8i	0.120858	−	0.0697774i
$204$		0			0
$205$	−2.91324e7	+	5.04587e7i	−0.0164953	+	0.0285707i
$206$		0			0
$207$	7.95765e7	+	1.23273e8i	0.0433415	+	0.0671407i
$208$		0			0
$209$	−5.94975e8	−	3.43509e8i	−0.311827	−	0.180033i
$210$		0			0
$211$	−8.33143e8	−	1.44305e9i	−0.420329	−	0.728032i	0.575642	−	0.817702i	$-0.304752\pi$
$211$	−8.33143e8	−	1.44305e9i	−0.420329	−	0.728032i	−0.995972	+	0.0896699i	$0.971419\pi$
$212$		0			0
$213$	8.19955e8	+	7.80238e8i	0.398356	+	0.379061i
$214$		0			0
$215$			2.19460e9i			1.02707i
$216$		0			0
$217$	−5.00402e8			−0.225673
$218$		0			0
$219$	8.36263e8	−	8.78832e8i	0.363552	−	0.382058i
$220$		0			0
$221$	−1.55559e9	+	8.98122e8i	−0.652119	+	0.376501i
$222$		0			0
$223$	−4.55245e8	+	7.88508e8i	−0.184088	+	0.318850i	−0.943269	−	0.332030i	$-0.892267\pi$
$223$	−4.55245e8	+	7.88508e8i	−0.184088	+	0.318850i	0.759181	+	0.650880i	$0.225600\pi$
$224$		0			0
$225$	1.03109e9	+	5.28919e8i	0.402316	+	0.206376i
$226$		0			0
$227$	−3.12584e9	−	1.80471e9i	−1.17724	−	0.679678i	−0.221863	−	0.975078i	$-0.571214\pi$
$227$	−3.12584e9	−	1.80471e9i	−1.17724	−	0.679678i	−0.955374	+	0.295400i	$0.904547\pi$
$228$		0			0
$229$	−1.33393e9	−	2.31043e9i	−0.485054	−	0.840138i	0.514799	−	0.857311i	$-0.327867\pi$
$229$	−1.33393e9	−	2.31043e9i	−0.485054	−	0.840138i	−0.999853	+	0.0171730i	$0.994533\pi$
$230$		0			0
$231$	1.38537e8	−	5.73597e8i	0.0486539	−	0.201446i
$232$		0			0
$233$			4.80289e9i			1.62959i	0.579746	+	0.814797i	$0.303152\pi$
$233$			4.80289e9i			1.62959i	−0.579746	+	0.814797i	$0.696848\pi$
$234$		0			0
$235$	−1.52130e9			−0.498821
$236$		0			0
$237$	−6.58460e8	−	2.23412e9i	−0.208707	−	0.708131i
$238$		0			0
$239$	−1.61400e9	+	9.31841e8i	−0.494665	+	0.285595i	−0.726508	−	0.687158i	$-0.758858\pi$
$239$	−1.61400e9	+	9.31841e8i	−0.494665	+	0.285595i	0.231843	+	0.972753i	$0.425524\pi$
$240$		0			0
$241$	−1.26160e9	+	2.18516e9i	−0.373985	+	0.647761i	−0.990175	−	0.139837i	$-0.955342\pi$
$241$	−1.26160e9	+	2.18516e9i	−0.373985	+	0.647761i	0.616190	+	0.787598i	$0.288675\pi$
$242$		0			0
$243$	2.14145e9	−	2.75170e9i	0.614163	−	0.789179i
$244$		0			0
$245$	3.29931e8	+	1.90486e8i	0.0915713	+	0.0528687i
$246$		0			0
$247$	−1.94351e9	−	3.36626e9i	−0.522155	−	0.904399i
$248$		0			0
$249$	−6.45550e9	+	1.90262e9i	−1.67932	+	0.494943i
$250$		0			0
$251$		−	5.55306e9i		−	1.39906i	−0.714601	−	0.699532i	$-0.753392\pi$
$251$		−	5.55306e9i		−	1.39906i	0.714601	−	0.699532i	$-0.246608\pi$
$252$		0			0
$253$	1.79526e8			0.0438173
$254$		0			0
$255$	−1.44048e9	−	3.47909e8i	−0.340680	−	0.0822821i
$256$		0			0
$257$	2.71679e9	−	1.56854e9i	0.622764	−	0.359553i	−0.155181	−	0.987886i	$-0.549596\pi$
$257$	2.71679e9	−	1.56854e9i	0.622764	−	0.359553i	0.777944	+	0.628333i	$0.216263\pi$
$258$		0			0
$259$	4.65931e7	−	8.07015e7i	0.0103543	−	0.0179342i
$260$		0			0
$261$	7.82028e8	−	1.52451e9i	0.168523	−	0.328525i
$262$		0			0
$263$	4.55088e7	+	2.62745e7i	0.00951202	+	0.00549177i	0.504748	−	0.863266i	$-0.331585\pi$
$263$	4.55088e7	+	2.62745e7i	0.00951202	+	0.00549177i	−0.495236	+	0.868758i	$0.664919\pi$
$264$		0			0
$265$	4.45044e8	+	7.70838e8i	0.0902442	+	0.156307i
$266$		0			0
$267$	8.34721e8	+	7.94289e8i	0.164246	+	0.156291i
$268$		0			0
$269$			9.43434e8i			0.180178i	0.995934	+	0.0900891i	$0.0287152\pi$
$269$			9.43434e8i			0.180178i	−0.995934	+	0.0900891i	$0.971285\pi$
$270$		0			0
$271$	−6.24158e9			−1.15722			−0.578612	−	0.815603i	$-0.696405\pi$
$271$	−6.24158e9			−1.15722			−0.578612	+	0.815603i	$0.696405\pi$
$272$		0			0
$273$	2.30146e9	−	2.41861e9i	0.414336	−	0.435427i
$274$		0			0
$275$	1.22793e9	−	7.08945e8i	0.214705	−	0.123960i
$276$		0			0
$277$	−4.42633e9	+	7.66663e9i	−0.751839	+	1.30222i	0.195092	+	0.980785i	$0.437500\pi$
$277$	−4.42633e9	+	7.66663e9i	−0.751839	+	1.30222i	−0.946931	+	0.321438i	$0.895834\pi$
$278$		0			0
$279$	−3.03952e9	+	1.96211e9i	−0.501636	+	0.323822i
$280$		0			0
$281$	8.65124e9	+	4.99480e9i	1.38756	+	0.801110i	0.993040	−	0.117775i	$-0.0375762\pi$
$281$	8.65124e9	+	4.99480e9i	1.38756	+	0.801110i	0.394524	+	0.918886i	$0.370910\pi$
$282$		0			0
$283$	−6.36426e8	−	1.10232e9i	−0.0992206	−	0.171855i	0.812142	−	0.583460i	$-0.198302\pi$
$283$	−6.36426e8	−	1.10232e9i	−0.0992206	−	0.171855i	−0.911362	+	0.411605i	$0.864968\pi$
$284$		0			0
$285$	7.52866e8	−	3.11716e9i	0.114114	−	0.472475i
$286$		0			0
$287$		−	1.14299e8i		−	0.0168467i
$288$		0			0
$289$	5.41170e9			0.775786
$290$		0			0
$291$	4.68916e8	+	1.59101e9i	0.0653917	+	0.221871i
$292$		0			0
$293$	1.08123e10	−	6.24247e9i	1.46706	−	0.847005i	0.467735	−	0.883869i	$-0.345070\pi$
$293$	1.08123e10	−	6.24247e9i	1.46706	−	0.847005i	0.999320	+	0.0368635i	$0.0117367\pi$
$294$		0			0
$295$	1.12700e9	−	1.95202e9i	0.148811	−	0.257748i
$296$		0			0
$297$	−1.40761e9	−	4.02733e9i	−0.180908	−	0.517597i
$298$		0			0
$299$	8.79644e8	+	5.07863e8i	0.110058	+	0.0635421i
$300$		0			0
$301$	−2.15260e9	−	3.72840e9i	−0.262238	−	0.454210i
$302$		0			0
$303$	6.84412e9	−	2.01716e9i	0.811983	−	0.239315i
$304$		0			0
$305$		−	2.83356e9i		−	0.327440i
$306$		0			0
$307$	1.21693e10			1.36998			0.684989	−	0.728554i	$-0.259807\pi$
$307$	1.21693e10			1.36998			0.684989	+	0.728554i	$0.259807\pi$
$308$		0			0
$309$	7.15537e9	+	1.72819e9i	0.784871	+	0.189565i
$310$		0			0
$311$	1.06804e10	−	6.16634e9i	1.14168	−	0.659152i	0.194838	−	0.980836i	$-0.437582\pi$
$311$	1.06804e10	−	6.16634e9i	1.14168	−	0.659152i	0.946847	+	0.321683i	$0.104249\pi$
$312$		0			0
$313$	−1.56084e9	+	2.70346e9i	−0.162623	+	0.281671i	−0.935809	−	0.352509i	$-0.885329\pi$
$313$	−1.56084e9	+	2.70346e9i	−0.162623	+	0.281671i	0.773186	+	0.634180i	$0.218662\pi$
$314$		0			0
$315$	2.75096e9	−	1.36640e8i	0.279410	−	0.0138783i
$316$		0			0
$317$	1.39437e10	+	8.05041e9i	1.38083	+	0.797225i	0.992258	−	0.124191i	$-0.0396336\pi$
$317$	1.39437e10	+	8.05041e9i	1.38083	+	0.797225i	0.388576	+	0.921416i	$0.372967\pi$
$318$		0			0
$319$	−1.04820e9	−	1.81554e9i	−0.101224	−	0.175325i
$320$		0			0
$321$	−8.01963e9	−	7.63118e9i	−0.755325	−	0.718739i
$322$		0			0
$323$		−	3.38458e9i		−	0.310953i
$324$		0			0
$325$	8.02216e9			0.719048
$326$		0			0
$327$	1.88144e8	−	1.97721e8i	0.0164551	−	0.0172927i
$328$		0			0
$329$	2.58454e9	−	1.49218e9i	0.220597	−	0.127362i
$330$		0			0
$331$	−3.73129e8	+	6.46278e8i	−0.0310847	+	0.0538403i	−0.881149	−	0.472838i	$-0.843229\pi$
$331$	−3.73129e8	+	6.46278e8i	−0.0310847	+	0.0538403i	0.850065	+	0.526679i	$0.176563\pi$
$332$		0			0
$333$	−3.34223e7	−	6.72888e8i	−0.00271807	−	0.0547225i
$334$		0			0
$335$	4.81607e9	+	2.78056e9i	0.382396	+	0.220777i
$336$		0			0
$337$	−5.01091e9	−	8.67915e9i	−0.388505	−	0.672911i	0.603743	−	0.797179i	$-0.293675\pi$
$337$	−5.01091e9	−	8.67915e9i	−0.388505	−	0.672911i	−0.992249	+	0.124268i	$0.960342\pi$
$338$		0			0
$339$	2.34899e9	−	9.72572e9i	0.177862	−	0.736416i
$340$		0			0
$341$			4.42655e9i			0.327377i
$342$		0			0
$343$	−7.47359e8			−0.0539949
$344$		0			0
$345$	2.36900e8	+	8.03788e8i	0.0167220	+	0.0567368i
$346$		0			0
$347$	−3.10339e9	+	1.79174e9i	−0.214051	+	0.123583i	−0.603193	−	0.797595i	$-0.706105\pi$
$347$	−3.10339e9	+	1.79174e9i	−0.214051	+	0.123583i	0.389141	+	0.921178i	$0.372772\pi$
$348$		0			0
$349$	6.93023e9	−	1.20035e10i	0.467139	−	0.809109i	−0.532156	−	0.846646i	$-0.678618\pi$
$349$	6.93023e9	−	1.20035e10i	0.467139	−	0.809109i	0.999295	+	0.0375376i	$0.0119514\pi$
$350$		0			0
$351$	4.49590e9	−	2.37152e10i	0.296202	−	1.56242i
$352$		0			0
$353$	1.94139e10	+	1.12086e10i	1.25030	+	0.721859i	0.971168	−	0.238394i	$-0.0766211\pi$
$353$	1.94139e10	+	1.12086e10i	1.25030	+	0.721859i	0.279129	+	0.960254i	$0.409954\pi$
$354$		0			0
$355$	3.23208e9	+	5.59813e9i	0.203502	+	0.352476i
$356$		0			0
$357$	2.78848e9	−	8.21845e8i	0.171670	−	0.0505961i
$358$		0			0
$359$			1.35324e10i			0.814699i	0.913272	+	0.407350i	$0.133547\pi$
$359$			1.35324e10i			0.814699i	−0.913272	+	0.407350i	$0.866453\pi$
$360$		0			0
$361$	−9.65942e9			−0.568751
$362$		0			0
$363$	1.18037e10	+	2.85088e9i	0.679819	+	0.164192i
$364$		0			0
$365$	6.00011e9	−	3.46416e9i	0.338055	−	0.195176i
$366$		0			0
$367$	−2.44874e9	+	4.24134e9i	−0.134983	+	0.233797i	−0.925591	−	0.378526i	$-0.876431\pi$
$367$	−2.44874e9	+	4.24134e9i	−0.134983	+	0.233797i	0.790608	+	0.612322i	$0.209765\pi$
$368$		0			0
$369$	−4.48174e8	−	6.94270e8i	−0.0241736	−	0.0374475i
$370$		0			0
$371$	−1.51217e9	−	8.73050e8i	−0.0798186	−	0.0460833i
$372$		0			0
$373$	−5.94330e9	−	1.02941e10i	−0.307038	−	0.531805i	0.670675	−	0.741751i	$-0.266005\pi$
$373$	−5.94330e9	−	1.02941e10i	−0.307038	−	0.531805i	−0.977713	+	0.209946i	$0.932671\pi$
$374$		0			0
$375$	1.53980e10	+	1.46522e10i	0.778646	+	0.740931i
$376$		0			0
$377$		−	1.18611e10i		−	0.587164i
$378$		0			0
$379$	−1.90592e10			−0.923734			−0.461867	−	0.886949i	$-0.652820\pi$
$379$	−1.90592e10			−0.923734			−0.461867	+	0.886949i	$0.652820\pi$
$380$		0			0
$381$	1.90729e10	−	2.00438e10i	0.905144	−	0.951218i
$382$		0			0
$383$	−8.05045e9	+	4.64793e9i	−0.374132	+	0.216005i	−0.675262	−	0.737578i	$-0.735970\pi$
$383$	−8.05045e9	+	4.64793e9i	−0.374132	+	0.216005i	0.301130	+	0.953583i	$0.402636\pi$
$384$		0			0
$385$	1.68504e9	−	2.91857e9i	0.0766949	−	0.132840i
$386$		0			0
$387$	−2.76945e10	−	1.42065e10i	−1.23467	−	0.633347i
$388$		0			0
$389$	2.24840e10	+	1.29811e10i	0.981917	+	0.566910i	0.902848	−	0.429959i	$-0.141472\pi$
$389$	2.24840e10	+	1.29811e10i	0.981917	+	0.566910i	0.0790687	+	0.996869i	$0.474805\pi$
$390$		0			0
$391$	4.42216e8	+	7.65941e8i	0.0189203	+	0.0327709i
$392$		0			0
$393$	2.96128e9	−	1.22609e10i	0.124139	−	0.513986i
$394$		0			0
$395$		−	1.33020e10i		−	0.546422i
$396$		0			0
$397$	1.87729e9			0.0755734			0.0377867	−	0.999286i	$-0.487969\pi$
$397$	1.87729e9			0.0755734			0.0377867	+	0.999286i	$0.487969\pi$
$398$		0			0
$399$	1.77845e9	+	6.03419e9i	0.0701697	+	0.238082i
$400$		0			0
$401$	−1.46427e10	+	8.45397e9i	−0.566297	+	0.326951i	−0.755669	−	0.654954i	$-0.772688\pi$
$401$	−1.46427e10	+	8.45397e9i	−0.566297	+	0.326951i	0.189372	+	0.981905i	$0.439355\pi$
$402$		0			0
$403$	−1.25223e10	+	2.16893e10i	−0.474750	+	0.822291i
$404$		0			0
$405$	1.61740e10	−	1.16167e10i	0.601170	−	0.431779i
$406$		0			0
$407$	−7.13885e8	−	4.12162e8i	−0.0260166	−	0.0150207i
$408$		0			0
$409$	5.39617e9	+	9.34643e9i	0.192838	+	0.334005i	0.946190	−	0.323613i	$-0.104898\pi$
$409$	5.39617e9	+	9.34643e9i	0.192838	+	0.334005i	−0.753352	+	0.657618i	$0.771564\pi$
$410$		0			0
$411$	−1.82340e9	+	5.37410e8i	−0.0639022	+	0.0188338i
$412$		0			0
$413$			4.42170e9i			0.151981i
$414$		0			0
$415$	−3.84361e10			−1.29583
$416$		0			0
$417$	−1.90497e10	−	4.60094e9i	−0.630005	−	0.152161i
$418$		0			0
$419$	2.04636e9	−	1.18147e9i	0.0663935	−	0.0383323i	−0.466436	−	0.884555i	$-0.654462\pi$
$419$	2.04636e9	−	1.18147e9i	0.0663935	−	0.0383323i	0.532829	+	0.846223i	$0.321129\pi$
$420$		0			0
$421$	−2.03621e9	+	3.52682e9i	−0.0648178	+	0.112268i	−0.896613	−	0.442815i	$-0.853980\pi$
$421$	−2.03621e9	+	3.52682e9i	−0.0648178	+	0.112268i	0.831795	+	0.555082i	$0.187313\pi$
$422$		0			0
$423$	9.84795e9	−	1.91979e10i	0.307599	−	0.599643i
$424$		0			0
$425$	6.04937e9	+	3.49261e9i	0.185419	+	0.107052i
$426$		0			0
$427$	2.77932e9	+	4.81392e9i	0.0836039	+	0.144806i
$428$		0			0
$429$	−2.13950e10	−	2.03587e10i	−0.631660	−	0.601064i
$430$		0			0
$431$			3.07178e10i			0.890187i	0.895484	+	0.445093i	$0.146829\pi$
$431$			3.07178e10i			0.890187i	−0.895484	+	0.445093i	$0.853171\pi$
$432$		0			0
$433$	−4.94562e10			−1.40692			−0.703460	−	0.710735i	$-0.748362\pi$
$433$	−4.94562e10			−1.40692			−0.703460	+	0.710735i	$0.748362\pi$
$434$		0			0
$435$	6.74549e9	−	7.08886e9i	0.188389	−	0.197979i
$436$		0			0
$437$	−1.65747e9	+	9.56943e8i	−0.0454486	+	0.0262398i
$438$		0			0
$439$	−3.14826e10	+	5.45294e10i	−0.847642	+	1.46816i	0.0356652	+	0.999364i	$0.488645\pi$
$439$	−3.14826e10	+	5.45294e10i	−0.847642	+	1.46816i	−0.883307	+	0.468795i	$0.844688\pi$
$440$		0			0
$441$	−4.53958e9	+	2.93044e9i	−0.120022	+	0.0774781i
$442$		0			0
$443$	1.17501e10	+	6.78395e9i	0.305090	+	0.176144i	0.644727	−	0.764413i	$-0.276971\pi$
$443$	1.17501e10	+	6.78395e9i	0.305090	+	0.176144i	−0.339637	+	0.940557i	$0.610304\pi$
$444$		0			0
$445$	3.29029e9	+	5.69895e9i	0.0839062	+	0.145330i
$446$		0			0
$447$	9.63917e9	−	3.99099e10i	0.241440	−	0.999656i
$448$		0			0
$449$		−	1.62678e10i		−	0.400261i	−0.979769	−	0.200130i	$-0.935863\pi$
$449$		−	1.62678e10i		−	0.400261i	0.979769	−	0.200130i	$-0.0641366\pi$
$450$		0			0
$451$	−1.01109e9			−0.0244390
$452$		0			0
$453$	−1.19537e10	−	4.05583e10i	−0.283864	−	0.963134i
$454$		0			0
$455$	1.65127e10	−	9.53364e9i	0.385277	−	0.222440i
$456$		0			0
$457$	−2.34634e10	+	4.06398e10i	−0.537931	+	0.931723i	0.461085	+	0.887356i	$0.347460\pi$
$457$	−2.34634e10	+	4.06398e10i	−0.537931	+	0.931723i	−0.999015	+	0.0443672i	$0.985873\pi$
$458$		0			0
$459$	1.37151e10	−	1.59258e10i	0.308994	−	0.358799i
$460$		0			0
$461$	5.55426e10	+	3.20676e10i	1.22977	+	0.710006i	0.966981	−	0.254848i	$-0.0820255\pi$
$461$	5.55426e10	+	3.20676e10i	1.22977	+	0.710006i	0.262786	+	0.964854i	$0.415359\pi$
$462$		0			0
$463$	−8.02066e9	−	1.38922e10i	−0.174536	−	0.302306i	0.765464	−	0.643478i	$-0.222509\pi$
$463$	−8.02066e9	−	1.38922e10i	−0.174536	−	0.302306i	−0.940001	+	0.341172i	$0.889176\pi$
$464$		0			0
$465$	−1.98189e10	+	5.84121e9i	−0.423905	+	0.124937i
$466$		0			0
$467$			1.51060e10i			0.317601i	0.987311	+	0.158800i	$0.0507627\pi$
$467$			1.51060e10i			0.317601i	−0.987311	+	0.158800i	$0.949237\pi$
$468$		0			0
$469$	−1.09093e10			−0.225480
$470$		0			0
$471$	−1.59468e10	−	3.85151e9i	−0.324032	−	0.0782614i
$472$		0			0
$473$	−3.29814e10	+	1.90418e10i	−0.658908	+	0.380421i
$474$		0			0
$475$	−7.55790e9	+	1.30907e10i	−0.148466	+	0.257150i
$476$		0			0
$477$	−1.26084e10	+	6.26260e8i	−0.243550	+	0.0120971i
$478$		0			0
$479$	−9.40599e9	−	5.43055e9i	−0.178674	−	0.103158i	0.407995	−	0.912984i	$-0.366228\pi$
$479$	−9.40599e9	−	5.43055e9i	−0.178674	−	0.103158i	−0.586670	+	0.809826i	$0.699561\pi$
$480$		0			0
$481$	−2.33194e9	−	4.03903e9i	−0.0435649	−	0.0754566i
$482$		0			0
$483$	−1.19087e9	−	1.13319e9i	−0.0218814	−	0.0208216i
$484$		0			0
$485$			9.47286e9i			0.171204i
$486$		0			0
$487$	−9.58248e10			−1.70358			−0.851789	−	0.523885i	$-0.824482\pi$
$487$	−9.58248e10			−1.70358			−0.851789	+	0.523885i	$0.824482\pi$
$488$		0			0
$489$	3.67976e10	−	3.86707e10i	0.643553	−	0.676311i
$490$		0			0
$491$	7.03751e10	−	4.06311e10i	1.21086	−	0.699089i	0.247911	−	0.968783i	$-0.420256\pi$
$491$	7.03751e10	−	4.06311e10i	1.21086	−	0.699089i	0.962946	+	0.269694i	$0.0869226\pi$
$492$		0			0
$493$	5.16396e9	−	8.94423e9i	0.0874168	−	0.151410i
$494$		0			0
$495$	−1.20872e9	−	2.43350e10i	−0.0201328	−	0.405332i
$496$		0			0
$497$	−1.09820e10	−	6.34044e9i	−0.179992	−	0.103919i
$498$		0			0
$499$	5.30537e10	+	9.18916e10i	0.855684	+	1.48209i	0.876009	+	0.482294i	$0.160196\pi$
$499$	5.30537e10	+	9.18916e10i	0.855684	+	1.48209i	−0.0203258	+	0.999793i	$0.506470\pi$
$500$		0			0
$501$	−9.37119e9	+	3.88003e10i	−0.148745	+	0.615864i
$502$		0			0
$503$			1.01433e11i			1.58455i	0.610166	+	0.792274i	$0.291103\pi$
$503$			1.01433e11i			1.58455i	−0.610166	+	0.792274i	$0.708897\pi$
$504$		0			0
$505$	4.07500e10			0.626558
$506$		0			0
$507$	−2.85591e10	−	9.68995e10i	−0.432228	−	1.46653i
$508$		0			0
$509$	−3.26742e10	+	1.88645e10i	−0.486782	+	0.281044i	−0.723238	−	0.690598i	$-0.757347\pi$
$509$	−3.26742e10	+	1.88645e10i	−0.486782	+	0.281044i	0.236457	+	0.971642i	$0.424014\pi$
$510$		0			0
$511$	−6.79571e9	+	1.17705e10i	−0.0996670	+	0.172628i
$512$		0			0
$513$	3.44630e10	+	2.96792e10i	0.497604	+	0.428531i
$514$		0			0
$515$	3.64079e10	+	2.10201e10i	0.517567	+	0.298818i
$516$		0			0
$517$	−1.31999e10	−	2.28628e10i	−0.184760	−	0.320013i
$518$		0			0
$519$	1.53844e10	−	4.53424e9i	0.212037	−	0.0624935i
$520$		0			0
$521$			1.24657e11i			1.69187i	0.533286	+	0.845935i	$0.320957\pi$
$521$			1.24657e11i			1.69187i	−0.533286	+	0.845935i	$0.679043\pi$
$522$		0			0
$523$	−7.05599e10			−0.943085			−0.471543	−	0.881843i	$-0.656303\pi$
$523$	−7.05599e10			−0.943085			−0.471543	+	0.881843i	$0.656303\pi$
$524$		0			0
$525$	−1.26203e10	−	3.04810e9i	−0.166124	−	0.0401228i
$526$		0			0
$527$	−1.88857e10	+	1.09037e10i	−0.244845	+	0.141361i
$528$		0			0
$529$	−3.89054e10	+	6.73862e10i	−0.496807	+	0.860495i
$530$		0			0
$531$	1.73378e10	+	2.68581e10i	0.218080	+	0.337830i
$532$		0			0
$533$	−4.95414e9	−	2.86028e9i	−0.0613846	−	0.0354404i
$534$		0			0
$535$	−3.16116e10	−	5.47530e10i	−0.385862	−	0.668332i
$536$		0			0
$537$	1.91939e10	+	1.82642e10i	0.230816	+	0.219635i
$538$		0			0
$539$			6.61114e9i			0.0783287i
$540$		0			0
$541$	4.44289e10			0.518652			0.259326	−	0.965790i	$-0.416500\pi$
$541$	4.44289e10			0.518652			0.259326	+	0.965790i	$0.416500\pi$
$542$		0			0
$543$	−5.11622e10	+	5.37665e10i	−0.588504	+	0.618461i
$544$		0			0
$545$	1.34992e9	−	7.79375e8i	0.0153010	−	0.00883406i
$546$		0			0
$547$	−3.81423e10	+	6.60643e10i	−0.426047	+	0.737934i	−0.996518	−	0.0833834i	$-0.973427\pi$
$547$	−3.81423e10	+	6.60643e10i	−0.426047	+	0.737934i	0.570471	+	0.821318i	$0.306761\pi$
$548$		0			0
$549$	3.57577e10	+	1.83426e10i	0.393623	+	0.201917i
$550$		0			0
$551$	1.93551e10	+	1.11747e10i	0.209985	+	0.121235i
$552$		0			0
$553$	1.30474e10	+	2.25987e10i	0.139515	+	0.241648i
$554$		0			0
$555$	9.03332e8	−	3.74014e9i	0.00952084	−	0.0394200i
$556$		0			0
$557$			1.78608e10i			0.185558i	0.995687	+	0.0927790i	$0.0295750\pi$
$557$			1.78608e10i			0.185558i	−0.995687	+	0.0927790i	$0.970425\pi$
$558$		0			0
$559$	−2.15471e11			−2.20669
$560$		0			0
$561$	−7.27003e9	−	2.46668e10i	−0.0733981	−	0.249036i
$562$		0			0
$563$	−5.69188e10	+	3.28621e10i	−0.566529	+	0.327086i	−0.755762	−	0.654846i	$-0.772733\pi$
$563$	−5.69188e10	+	3.28621e10i	−0.566529	+	0.327086i	0.189233	+	0.981932i	$0.439400\pi$
$564$		0			0
$565$	2.85709e10	−	4.94863e10i	0.280370	−	0.485614i
$566$		0			0
$567$	−1.60837e10	+	3.56000e10i	−0.155615	+	0.344443i
$568$		0			0
$569$	1.26536e11	+	7.30558e10i	1.20716	+	0.696956i	0.962139	−	0.272560i	$-0.0878705\pi$
$569$	1.26536e11	+	7.30558e10i	1.20716	+	0.696956i	0.245025	+	0.969517i	$0.421204\pi$
$570$		0			0
$571$	−8.27854e9	−	1.43389e10i	−0.0778770	−	0.134887i	0.824457	−	0.565925i	$-0.191481\pi$
$571$	−8.27854e9	−	1.43389e10i	−0.0778770	−	0.134887i	−0.902334	+	0.431038i	$0.858147\pi$
$572$		0			0
$573$	5.01627e10	−	1.47844e10i	0.465332	−	0.137147i
$574$		0			0
$575$		−	3.94994e9i		−	0.0361343i
$576$		0			0
$577$	2.01444e10			0.181740			0.0908699	−	0.995863i	$-0.471035\pi$
$577$	2.01444e10			0.181740			0.0908699	+	0.995863i	$0.471035\pi$
$578$		0			0
$579$	−1.80163e11	−	4.35135e10i	−1.60306	−	0.387177i
$580$		0			0
$581$	6.52990e10	−	3.77004e10i	0.573063	−	0.330858i
$582$		0			0
$583$	−7.72299e9	+	1.33766e10i	−0.0668516	+	0.115790i
$584$		0			0
$585$	6.29190e10	−	1.22656e11i	0.537228	−	1.04729i
$586$		0			0
$587$	−4.84952e10	−	2.79987e10i	−0.408457	−	0.235823i	0.281670	−	0.959511i	$-0.409112\pi$
$587$	−4.84952e10	−	2.79987e10i	−0.408457	−	0.235823i	−0.690126	+	0.723689i	$0.742445\pi$
$588$		0			0
$589$	−2.35952e10	−	4.08682e10i	−0.196048	−	0.339566i
$590$		0			0
$591$	−1.17780e11	−	1.12075e11i	−0.965429	−	0.918666i
$592$		0			0
$593$		−	2.00356e9i		−	0.0162026i	−0.999967	−	0.00810128i	$-0.997421\pi$
$593$		−	2.00356e9i		−	0.0162026i	0.999967	−	0.00810128i	$-0.00257875\pi$
$594$		0			0
$595$	1.66026e10			0.132467
$596$		0			0
$597$	−1.18574e10	+	1.24610e10i	−0.0933453	+	0.0980968i
$598$		0			0
$599$	−1.38430e10	+	7.99229e9i	−0.107529	+	0.0620817i	−0.552800	−	0.833314i	$-0.686441\pi$
$599$	−1.38430e10	+	7.99229e9i	−0.107529	+	0.0620817i	0.445271	+	0.895396i	$0.353107\pi$
$600$		0			0
$601$	−4.43450e10	+	7.68078e10i	−0.339897	+	0.588718i	−0.984413	−	0.175872i	$-0.943725\pi$
$601$	−4.43450e10	+	7.68078e10i	−0.339897	+	0.588718i	0.644516	+	0.764591i	$0.277059\pi$
$602$		0			0
$603$	−6.62651e10	+	4.27763e10i	−0.501205	+	0.323544i
$604$		0			0
$605$	6.00597e10	+	3.46755e10i	0.448293	+	0.258822i
$606$		0			0
$607$	5.07066e9	+	8.78264e9i	0.0373516	+	0.0646949i	0.884097	−	0.467304i	$-0.154775\pi$
$607$	5.07066e9	+	8.78264e9i	0.0373516	+	0.0646949i	−0.846745	+	0.531999i	$0.821441\pi$
$608$		0			0
$609$	−4.50673e9	+	1.86596e10i	−0.0327637	+	0.135654i
$610$		0			0
$611$		−	1.49365e11i		−	1.07172i
$612$		0			0
$613$	−1.76970e11			−1.25331			−0.626654	−	0.779298i	$-0.715576\pi$
$613$	−1.76970e11			−1.25331			−0.626654	+	0.779298i	$0.715576\pi$
$614$		0			0
$615$	−1.33421e9	−	4.52692e9i	−0.00932664	−	0.0316448i
$616$		0			0
$617$	1.96652e11	−	1.13537e11i	1.35693	−	0.783424i	0.367721	−	0.929936i	$-0.380138\pi$
$617$	1.96652e11	−	1.13537e11i	1.35693	−	0.783424i	0.989209	+	0.146513i	$0.0468049\pi$
$618$		0			0
$619$	−2.07891e10	+	3.60078e10i	−0.141603	+	0.245264i	−0.928101	−	0.372330i	$-0.878559\pi$
$619$	−2.07891e10	+	3.60078e10i	−0.141603	+	0.245264i	0.786497	+	0.617594i	$0.211892\pi$
$620$		0			0
$621$	−1.16768e10	−	2.21368e9i	−0.0785161	−	0.0148850i
$622$		0			0
$623$	−1.11797e10	−	6.45462e9i	−0.0742128	−	0.0428468i
$624$		0			0
$625$	2.61986e10	+	4.53773e10i	0.171695	+	0.297385i
$626$		0			0
$627$	5.33784e10	−	1.57321e10i	0.345378	−	0.101793i
$628$		0			0
$629$		−	4.06102e9i		−	0.0259437i
$630$		0			0
$631$	−2.11713e11			−1.33546			−0.667729	−	0.744405i	$-0.732733\pi$
$631$	−2.11713e11			−1.33546			−0.667729	+	0.744405i	$0.732733\pi$
$632$		0			0
$633$	1.31197e11	+	3.16871e10i	0.817163	+	0.197364i
$634$		0			0
$635$	1.36846e11	−	7.90083e10i	0.841664	−	0.485935i
$636$		0			0
$637$	−1.87023e10	+	3.23933e10i	−0.113589	+	0.196742i
$638$		0			0
$639$	−9.15674e10	+	4.54815e9i	−0.549209	+	0.0272792i
$640$		0			0
$641$	2.83588e11	+	1.63730e11i	1.67980	+	0.969831i	0.961788	+	0.273795i	$0.0882791\pi$
$641$	2.83588e11	+	1.63730e11i	1.67980	+	0.969831i	0.718008	+	0.696035i	$0.245054\pi$
$642$		0			0
$643$	−8.87088e10	−	1.53648e11i	−0.518946	−	0.898842i	−0.999758	−	0.0220175i	$-0.992991\pi$
$643$	−8.87088e10	−	1.53648e11i	−0.518946	−	0.898842i	0.480811	−	0.876824i	$-0.340342\pi$
$644$		0			0
$645$	−1.28777e11	−	1.22540e11i	−0.744048	−	0.708008i
$646$		0			0
$647$			3.42977e11i			1.95726i	0.205637	+	0.978628i	$0.434074\pi$
$647$			3.42977e11i			1.95726i	−0.205637	+	0.978628i	$0.565926\pi$
$648$		0			0
$649$	3.91144e10			0.220474
$650$		0			0
$651$	2.79409e10	−	2.93632e10i	0.155567	−	0.163485i
$652$		0			0
$653$	−1.80626e11	+	1.04284e11i	−0.993406	+	0.573543i	−0.906291	−	0.422655i	$-0.861098\pi$
$653$	−1.80626e11	+	1.04284e11i	−0.993406	+	0.573543i	−0.0871151	+	0.996198i	$0.527765\pi$
$654$		0			0
$655$	3.60184e10	−	6.23856e10i	0.195686	−	0.338937i
$656$		0			0
$657$	4.87473e9	+	9.81424e10i	0.0261631	+	0.526739i
$658$		0			0
$659$	1.72409e10	+	9.95401e9i	0.0914150	+	0.0527784i	0.545011	−	0.838429i	$-0.316526\pi$
$659$	1.72409e10	+	9.95401e9i	0.0914150	+	0.0527784i	−0.453596	+	0.891208i	$0.649859\pi$
$660$		0			0
$661$	1.22202e11	+	2.11660e11i	0.640135	+	1.10875i	0.985402	+	0.170242i	$0.0544550\pi$
$661$	1.22202e11	+	2.11660e11i	0.640135	+	1.10875i	−0.345267	+	0.938504i	$0.612212\pi$
$662$		0			0
$663$	3.41585e10	−	1.41429e11i	0.176784	−	0.731956i
$664$		0			0
$665$			3.59276e10i			0.183714i
$666$		0			0
$667$	−5.84014e9			−0.0295067
$668$		0			0
$669$	−2.08495e10	−	7.07413e10i	−0.104086	−	0.353157i
$670$		0			0
$671$	4.25839e10	−	2.45858e10i	0.210066	−	0.121282i
$672$		0			0
$673$	−8.42884e10	+	1.45992e11i	−0.410873	+	0.711653i	−0.994985	−	0.100020i	$-0.968109\pi$
$673$	−8.42884e10	+	1.45992e11i	−0.410873	+	0.711653i	0.584113	+	0.811673i	$0.301443\pi$
$674$		0			0
$675$	−8.86095e10	+	3.09704e10i	−0.426840	+	0.149187i
$676$		0			0
$677$	1.31907e11	+	7.61567e10i	0.627934	+	0.362538i	0.779952	−	0.625840i	$-0.215244\pi$
$677$	1.31907e11	+	7.61567e10i	0.627934	+	0.362538i	−0.152018	+	0.988378i	$0.548577\pi$
$678$		0			0
$679$	−9.29154e9	−	1.60934e10i	−0.0437128	−	0.0757128i
$680$		0			0
$681$	2.80436e11	−	8.26526e10i	1.30390	−	0.384298i
$682$		0			0
$683$		−	2.17469e11i		−	0.999342i	−0.866215	−	0.499671i	$-0.833454\pi$
$683$		−	2.17469e11i		−	0.999342i	0.866215	−	0.499671i	$-0.166546\pi$
$684$		0			0
$685$	−1.08566e10			−0.0493095
$686$		0			0
$687$	2.10056e11	+	5.07335e10i	0.942994	+	0.227755i
$688$		0			0
$689$	−7.56825e10	+	4.36953e10i	−0.335829	+	0.193891i
$690$		0			0
$691$	1.97865e11	−	3.42712e11i	0.867874	−	1.50320i	0.00370854	−	0.999993i	$-0.498820\pi$
$691$	1.97865e11	−	3.42712e11i	0.867874	−	1.50320i	0.864165	−	0.503208i	$-0.167847\pi$
$692$		0			0
$693$	2.59227e10	+	4.01571e10i	0.112395	+	0.174112i
$694$		0			0
$695$	−9.69285e10	−	5.59617e10i	−0.415444	−	0.239857i
$696$		0			0
$697$	−2.49055e9	−	4.31377e9i	−0.0105527	−	0.0182779i
$698$		0			0
$699$	−2.81830e11	−	2.68179e11i	−1.18053	−	1.12335i
$700$		0			0
$701$		−	1.07813e11i		−	0.446475i	−0.974764	−	0.223237i	$-0.928337\pi$
$701$		−	1.07813e11i		−	0.446475i	0.974764	−	0.223237i	$-0.0716625\pi$
$702$		0			0
$703$	8.78792e9			0.0359803
$704$		0			0
$705$	8.49449e10	−	8.92688e10i	0.343859	−	0.361363i
$706$		0			0
$707$	−6.92300e10	+	3.99699e10i	−0.277087	+	0.159976i
$708$		0			0
$709$	−4.56262e10	+	7.90270e10i	−0.180563	+	0.312745i	−0.942073	−	0.335409i	$-0.891125\pi$
$709$	−4.56262e10	+	7.90270e10i	−0.180563	+	0.312745i	0.761509	+	0.648154i	$0.224459\pi$
$710$		0			0
$711$	1.67863e11	+	8.61085e10i	0.656865	+	0.336952i
$712$		0			0
$713$	1.06793e10	+	6.16572e9i	0.0413225	+	0.0238575i
$714$		0			0
$715$	−8.43345e10	−	1.46072e11i	−0.322687	−	0.558910i
$716$		0			0
$717$	3.54409e10	−	1.46739e11i	0.134100	−	0.555225i
$718$		0			0
$719$		−	4.90984e11i		−	1.83718i	−0.395210	−	0.918591i	$-0.629328\pi$
$719$		−	4.90984e11i		−	1.83718i	0.395210	−	0.918591i	$-0.370672\pi$
$720$		0			0
$721$	−8.24711e10			−0.305183
$722$		0			0
$723$	−5.77793e10	−	1.96042e11i	−0.211456	−	0.717458i
$724$		0			0
$725$	−3.99456e10	+	2.30626e10i	−0.144583	+	0.0834750i
$726$		0			0
$727$	1.04866e11	−	1.81633e11i	0.375401	−	0.650214i	−0.614986	−	0.788538i	$-0.710838\pi$
$727$	1.04866e11	−	1.81633e11i	0.375401	−	0.650214i	0.990387	+	0.138324i	$0.0441716\pi$
$728$		0			0
$729$	4.18950e10	+	2.79305e11i	0.148338	+	0.988937i
$730$		0			0
$731$	−1.62482e11	−	9.38093e10i	−0.569032	−	0.328531i
$732$		0			0
$733$	−1.13180e11	−	1.96033e11i	−0.392061	−	0.679069i	0.600660	−	0.799504i	$-0.294904\pi$
$733$	−1.13180e11	−	1.96033e11i	−0.392061	−	0.679069i	−0.992721	+	0.120435i	$0.961571\pi$
$734$		0			0
$735$	−2.95999e10	+	8.72394e9i	−0.101424	+	0.0298926i
$736$		0			0
$737$			9.65040e10i			0.327096i
$738$		0			0
$739$	4.81921e11			1.61584			0.807920	−	0.589292i	$-0.200593\pi$
$739$	4.81921e11			1.61584			0.807920	+	0.589292i	$0.200593\pi$
$740$		0			0
$741$	3.06049e11	+	7.39179e10i	1.01512	+	0.245175i
$742$		0			0
$743$	−3.74545e11	+	2.16244e11i	−1.22899	+	0.709559i	−0.966819	−	0.255462i	$-0.917773\pi$
$743$	−3.74545e11	+	2.16244e11i	−1.22899	+	0.709559i	−0.262173	+	0.965021i	$0.584439\pi$
$744$		0			0
$745$	1.17242e11	−	2.03069e11i	0.380591	−	0.659203i
$746$		0			0
$747$	2.48811e11	−	4.85040e11i	0.799074	−	1.55774i
$748$		0			0
$749$	1.07410e11	+	6.20131e10i	0.341285	+	0.197041i
$750$		0			0
$751$	−5.17169e10	−	8.95763e10i	−0.162582	−	0.281600i	0.773212	−	0.634148i	$-0.218649\pi$
$751$	−5.17169e10	−	8.95763e10i	−0.162582	−	0.281600i	−0.935794	+	0.352547i	$0.885316\pi$
$752$		0			0
$753$	3.25849e11	+	3.10066e11i	1.01353	+	0.964437i
$754$		0			0
$755$		−	2.41484e11i		−	0.743192i
$756$		0			0
$757$	1.41803e11			0.431820			0.215910	−	0.976413i	$-0.430728\pi$
$757$	1.41803e11			0.431820			0.215910	+	0.976413i	$0.430728\pi$
$758$		0			0
$759$	−1.00242e10	+	1.05344e10i	−0.0302052	+	0.0317427i
$760$		0			0
$761$	−1.03381e11	+	5.96872e10i	−0.308250	+	0.177968i	−0.646143	−	0.763216i	$-0.723619\pi$
$761$	−1.03381e11	+	5.96872e10i	−0.308250	+	0.177968i	0.337893	+	0.941184i	$0.390286\pi$
$762$		0			0
$763$	−1.52891e9	+	2.64816e9i	−0.00451112	+	0.00781350i
$764$		0			0
$765$	1.00847e11	−	6.50999e10i	0.294454	−	0.190079i
$766$		0			0
$767$	1.91653e11	+	1.10651e11i	0.553776	+	0.319723i
$768$		0			0
$769$	2.96493e11	+	5.13541e11i	0.847830	+	1.46849i	0.883140	+	0.469109i	$0.155425\pi$
$769$	2.96493e11	+	5.13541e11i	0.847830	+	1.46849i	−0.0353098	+	0.999376i	$0.511242\pi$
$770$		0			0
$771$	−5.96565e10	+	2.47001e11i	−0.168826	+	0.699007i
$772$		0			0
$773$			4.02553e11i			1.12747i	0.825955	+	0.563736i	$0.190636\pi$
$773$			4.02553e11i			1.12747i	−0.825955	+	0.563736i	$0.809364\pi$
$774$		0			0
$775$	9.73932e10			0.269974
$776$		0			0
$777$	2.13389e9	+	7.24016e9i	0.00585446	+	0.0198639i
$778$		0			0
$779$	9.33487e9	−	5.38949e9i	0.0253489	−	0.0146352i
$780$		0			0
$781$	−5.60875e10	+	9.71463e10i	−0.150752	+	0.261109i
$782$		0			0
$783$	4.57910e10	+	1.31013e11i	0.121824	+	0.348551i
$784$		0			0
$785$	−8.11401e10	−	4.68463e10i	−0.213677	−	0.123366i
$786$		0			0
$787$	3.35924e11	+	5.81838e11i	0.875674	+	1.51671i	0.856043	+	0.516905i	$0.172916\pi$
$787$	3.35924e11	+	5.81838e11i	0.875674	+	1.51671i	0.0196315	+	0.999807i	$0.493751\pi$
$788$		0			0
$789$	−4.08284e9	+	1.20333e9i	−0.0105355	+	0.00310511i
$790$		0			0
$791$			1.12096e11i			0.286342i
$792$		0			0
$793$	2.78204e11			0.703511
$794$		0			0
$795$	−7.00820e10	−	1.69264e10i	−0.175444	−	0.0423737i
$796$		0			0
$797$	5.76753e11	−	3.32988e11i	1.42941	−	0.825269i	0.432334	−	0.901713i	$-0.357690\pi$
$797$	5.76753e11	−	3.32988e11i	1.42941	−	0.825269i	0.997074	+	0.0764443i	$0.0243567\pi$
$798$		0			0
$799$	6.50288e10	−	1.12633e11i	0.159558	−	0.276363i
$800$		0			0
$801$	−9.32164e10	+	4.63006e9i	−0.226445	+	0.0112475i
$802$		0			0
$803$	1.04122e11	+	6.01148e10i	0.250426	+	0.144584i
$804$		0			0
$805$	−4.69416e9	−	8.13052e9i	−0.0111783	−	0.0193613i
$806$		0			0
$807$	−5.53599e10	−	5.26784e10i	−0.130527	−	0.124205i
$808$		0			0
$809$		−	8.11128e11i		−	1.89363i	−0.321776	−	0.946816i	$-0.604280\pi$
$809$		−	8.11128e11i		−	1.89363i	0.321776	−	0.946816i	$-0.395720\pi$
$810$		0			0
$811$	1.80161e11			0.416463			0.208231	−	0.978080i	$-0.433229\pi$
$811$	1.80161e11			0.416463			0.208231	+	0.978080i	$0.433229\pi$
$812$		0			0
$813$	3.48510e11	−	3.66251e11i	0.797726	−	0.838332i
$814$		0			0
$815$	2.64019e11	−	1.52432e11i	0.598419	−	0.345497i
$816$		0			0
$817$	2.03001e11	−	3.51608e11i	0.455627	−	0.789169i
$818$		0			0
$819$	1.34156e10	+	2.70095e11i	0.0298178	+	0.600318i
$820$		0			0
$821$	4.70919e11	+	2.71885e11i	1.03651	+	0.598430i	0.918843	−	0.394623i	$-0.129125\pi$
$821$	4.70919e11	+	2.71885e11i	1.03651	+	0.598430i	0.117668	+	0.993053i	$0.462458\pi$
$822$		0			0
$823$	8.85535e10	+	1.53379e11i	0.193022	+	0.334324i	0.946250	−	0.323435i	$-0.104838\pi$
$823$	8.85535e10	+	1.53379e11i	0.193022	+	0.334324i	−0.753228	+	0.657759i	$0.771505\pi$
$824$		0			0
$825$	−2.69634e10	+	1.11639e11i	−0.0582049	+	0.240991i
$826$		0			0
$827$		−	6.08067e10i		−	0.129996i	−0.997885	−	0.0649979i	$-0.979296\pi$
$827$		−	6.08067e10i		−	0.129996i	0.997885	−	0.0649979i	$-0.0207041\pi$
$828$		0			0
$829$	4.60574e11			0.975172			0.487586	−	0.873075i	$-0.337878\pi$
$829$	4.60574e11			0.975172			0.487586	+	0.873075i	$0.337878\pi$
$830$		0			0
$831$	−2.02719e11	−	6.87814e11i	−0.425099	−	1.44234i
$832$		0			0
$833$	−2.82061e10	+	1.62848e10i	−0.0585819	+	0.0338223i
$834$		0			0
$835$	−1.13983e11	+	1.97424e11i	−0.234473	+	0.406119i
$836$		0			0
$837$	5.45826e10	−	2.87915e11i	0.111212	−	0.586627i
$838$		0			0
$839$	−3.96181e11	−	2.28735e11i	−0.799551	−	0.461621i	0.0437630	−	0.999042i	$-0.486065\pi$
$839$	−3.96181e11	−	2.28735e11i	−0.799551	−	0.461621i	−0.843314	+	0.537421i	$0.819399\pi$
$840$		0			0
$841$	−2.16024e11	−	3.74165e11i	−0.431836	−	0.747961i
$842$		0			0
$843$	−7.76149e11	+	2.28753e11i	−1.53686	+	0.452957i
$844$		0			0
$845$		−	5.76941e11i		−	1.13163i
$846$		0			0
$847$	−1.36047e11			−0.264336
$848$		0			0
$849$	1.00219e11	+	2.42053e10i	0.192895	+	0.0465886i
$850$		0			0
$851$	−1.98873e9	+	1.14820e9i	−0.00379191	+	0.00218926i
$852$		0			0
$853$	6.79737e10	−	1.17734e11i	0.128394	−	0.222385i	−0.794661	−	0.607054i	$-0.792351\pi$
$853$	6.79737e10	−	1.17734e11i	0.128394	−	0.222385i	0.923055	+	0.384669i	$0.125684\pi$
$854$		0			0
$855$	1.40874e11	+	2.18230e11i	0.263614	+	0.408366i
$856$		0			0
$857$	−5.97373e11	−	3.44894e11i	−1.10745	−	0.639384i	−0.169279	−	0.985568i	$-0.554144\pi$
$857$	−5.97373e11	−	3.44894e11i	−1.10745	−	0.639384i	−0.938167	+	0.346184i	$0.887477\pi$
$858$		0			0
$859$	−2.65284e11	−	4.59486e11i	−0.487235	−	0.843916i	0.512657	−	0.858594i	$-0.328661\pi$
$859$	−2.65284e11	−	4.59486e11i	−0.487235	−	0.843916i	−0.999892	+	0.0146772i	$0.995328\pi$
$860$		0			0
$861$	6.70697e9	+	6.38210e9i	0.0122043	+	0.0116132i
$862$		0			0
$863$			4.85387e11i			0.875075i	0.899200	+	0.437538i	$0.144149\pi$
$863$			4.85387e11i			0.875075i	−0.899200	+	0.437538i	$0.855851\pi$
$864$		0			0
$865$	9.15990e10			0.163616
$866$		0			0
$867$	−3.02172e11	+	3.17554e11i	−0.534784	+	0.562006i
$868$		0			0
$869$	1.99908e11	−	1.15417e11i	0.350551	−	0.202391i
$870$		0			0
$871$	−2.73001e11	+	4.72852e11i	−0.474342	+	0.821585i
$872$		0			0
$873$	−1.19542e11	−	6.13213e10i	−0.205808	−	0.105573i
$874$		0			0
$875$	−2.06232e11	−	1.19068e11i	−0.351822	−	0.203124i
$876$		0			0
$877$	−5.91665e9	−	1.02479e10i	−0.0100018	−	0.0173236i	0.860981	−	0.508637i	$-0.169850\pi$
$877$	−5.91665e9	−	1.02479e10i	−0.0100018	−	0.0173236i	−0.870983	+	0.491313i	$0.836517\pi$
$878$		0			0
$879$	−2.37421e11	+	9.83015e11i	−0.397707	+	1.64666i
$880$		0			0
$881$		−	2.81659e11i		−	0.467541i	−0.972292	−	0.233770i	$-0.924894\pi$
$881$		−	2.81659e11i		−	0.467541i	0.972292	−	0.233770i	$-0.0751064\pi$
$882$		0			0
$883$	−4.69154e11			−0.771743			−0.385872	−	0.922552i	$-0.626099\pi$
$883$	−4.69154e11			−0.771743			−0.385872	+	0.922552i	$0.626099\pi$
$884$		0			0
$885$	5.16147e10	+	1.75126e11i	0.0841395	+	0.285481i
$886$		0			0
$887$	−4.84361e11	+	2.79646e11i	−0.782482	+	0.451766i	−0.837309	−	0.546730i	$-0.815873\pi$
$887$	−4.84361e11	+	2.79646e11i	−0.782482	+	0.451766i	0.0548272	+	0.998496i	$0.482539\pi$
$888$		0			0
$889$	−1.54992e11	+	2.68454e11i	−0.248143	+	0.429797i
$890$		0			0
$891$	3.14917e11	+	1.42276e11i	0.499672	+	0.225746i
$892$		0			0
$893$	2.43735e11	+	1.40721e11i	0.383277	+	0.221285i
$894$		0			0
$895$	7.56580e10	+	1.31044e11i	0.117913	+	0.204232i
$896$		0			0
$897$	−7.89176e10	+	2.32593e10i	−0.121900	+	0.0359275i
$898$		0			0
$899$		−	1.44000e11i		−	0.220457i
$900$		0			0
$901$	−7.60944e10			−0.115466
$902$		0			0
$903$	3.38974e11	+	8.18701e10i	0.509818	+	0.123133i
$904$		0			0
$905$	−3.67084e11	+	2.11936e11i	−0.547231	+	0.315944i
$906$		0			0
$907$	4.51135e11	−	7.81389e11i	0.666618	−	1.15462i	−0.312225	−	0.950008i	$-0.601074\pi$
$907$	4.51135e11	−	7.81389e11i	0.666618	−	1.15462i	0.978844	−	0.204609i	$-0.0655923\pi$
$908$		0			0
$909$	−2.63789e11	+	5.14239e11i	−0.386368	+	0.753199i
$910$		0			0
$911$	−4.97010e11	−	2.86949e11i	−0.721591	−	0.416611i	0.0937469	−	0.995596i	$-0.470116\pi$
$911$	−4.97010e11	−	2.86949e11i	−0.721591	−	0.416611i	−0.815338	+	0.578985i	$0.803449\pi$
$912$		0			0
$913$	−3.33498e11	−	5.77635e11i	−0.479965	−	0.831324i
$914$		0			0
$915$	1.66271e11	+	1.58217e11i	0.237209	+	0.225719i
$916$		0			0
$917$			1.41316e11i			0.199854i
$918$		0			0
$919$	5.49391e11			0.770229			0.385114	−	0.922869i	$-0.374162\pi$
$919$	5.49391e11			0.770229			0.385114	+	0.922869i	$0.374162\pi$
$920$		0			0
$921$	−6.79498e11	+	7.14086e11i	−0.944386	+	0.992458i
$922$		0			0
$923$	−5.49636e11	+	3.17333e11i	−0.757301	+	0.437228i
$924$		0			0
$925$	−9.06840e9	+	1.57069e10i	−0.0123869	+	0.0214548i
$926$		0			0
$927$	−5.00942e11	+	3.23374e11i	−0.678373	+	0.437912i
$928$		0			0
$929$	−1.11379e12	−	6.43046e11i	−1.49534	−	0.863335i	−0.495355	−	0.868691i	$-0.664962\pi$
$929$	−1.11379e12	−	6.43046e11i	−1.49534	−	0.863335i	−0.999986	+	0.00535552i	$0.998295\pi$
$930$		0			0
$931$	−3.52399e10	−	6.10373e10i	−0.0469068	−	0.0812450i
$932$		0			0
$933$	−2.34525e11	+	9.71026e11i	−0.309502	+	1.28146i
$934$		0			0
$935$		−	1.46867e11i		−	0.192166i
$936$		0			0
$937$	4.78674e10			0.0620985			0.0310493	−	0.999518i	$-0.490115\pi$
$937$	4.78674e10			0.0620985			0.0310493	+	0.999518i	$0.490115\pi$
$938$		0			0
$939$	−7.14840e10	−	2.42541e11i	−0.0919488	−	0.311978i
$940$		0			0
$941$	−1.09787e12	+	6.33857e11i	−1.40021	+	0.808412i	−0.994414	−	0.105551i	$-0.966339\pi$
$941$	−1.09787e12	+	6.33857e11i	−1.40021	+	0.808412i	−0.405797	+	0.913963i	$0.633006\pi$
$942$		0			0
$943$	−1.40834e9	+	2.43931e9i	−0.00178098	+	0.00308476i
$944$		0			0
$945$	−1.45587e11	+	1.69054e11i	−0.182556	+	0.211981i
$946$		0			0
$947$	2.60189e11	+	1.50220e11i	0.323511	+	0.186779i	0.652956	−	0.757396i	$-0.273529\pi$
$947$	2.60189e11	+	1.50220e11i	0.323511	+	0.186779i	−0.329446	+	0.944175i	$0.606862\pi$
$948$		0			0
$949$	3.40119e11	+	5.89103e11i	0.419340	+	0.726317i
$950$		0			0
$951$	−1.25097e12	+	3.68696e11i	−1.52941	+	0.450761i
$952$		0			0
$953$			3.60461e11i			0.437005i	0.975836	+	0.218503i	$0.0701172\pi$
$953$			3.60461e11i			0.437005i	−0.975836	+	0.218503i	$0.929883\pi$
$954$		0			0
$955$	2.98669e11			0.359068
$956$		0			0
$957$	1.65063e11	+	3.98665e10i	0.196789	+	0.0475292i
$958$		0			0
$959$	1.84442e10	−	1.06488e10i	0.0218065	−	0.0125900i
$960$		0			0
$961$	2.74418e11	−	4.75306e11i	0.321750	−	0.557288i
$962$		0			0
$963$	8.95582e11	−	4.44835e10i	1.04136	−	0.0517242i
$964$		0			0
$965$	−9.16703e11	−	5.29259e11i	−1.05711	−	0.610322i
$966$		0			0
$967$	−6.02618e11	−	1.04377e12i	−0.689186	−	1.19370i	−0.972102	−	0.234560i	$-0.924635\pi$
$967$	−6.02618e11	−	1.04377e12i	−0.689186	−	1.19370i	0.282916	−	0.959145i	$-0.408698\pi$
$968$		0			0
$969$	1.98604e11	+	1.88985e11i	0.225265	+	0.214354i
$970$		0			0
$971$		−	1.14027e12i		−	1.28271i	−0.767243	−	0.641356i	$-0.778372\pi$
$971$		−	1.14027e12i		−	1.28271i	0.767243	−	0.641356i	$-0.221628\pi$
$972$		0			0
$973$	2.19562e11			0.244966
$974$		0			0
$975$	−4.47933e11	+	4.70734e11i	−0.495672	+	0.520903i
$976$		0			0
$977$	−1.01897e12	+	5.88305e11i	−1.11837	+	0.645691i	−0.940984	−	0.338451i	$-0.890097\pi$
$977$	−1.01897e12	+	5.88305e11i	−1.11837	+	0.645691i	−0.177385	+	0.984142i	$0.556764\pi$
$978$		0			0
$979$	−5.70975e10	+	9.88958e10i	−0.0621565	+	0.107658i
$980$		0			0
$981$	1.09673e9	+	2.20803e10i	0.00118419	+	0.0238412i
$982$		0			0
$983$	9.86235e11	+	5.69403e11i	1.05625	+	0.609826i	0.924392	−	0.381443i	$-0.124573\pi$
$983$	9.86235e11	+	5.69403e11i	1.05625	+	0.609826i	0.131857	+	0.991269i	$0.457906\pi$
$984$		0			0
$985$	−4.64262e11	−	8.04125e11i	−0.493194	−	0.854238i
$986$		0			0
$987$	−5.67525e10	+	2.34977e11i	−0.0598021	+	0.247604i
$988$		0			0
$989$			1.06093e11i			0.110892i
$990$		0			0
$991$	−5.23286e11			−0.542556			−0.271278	−	0.962501i	$-0.587446\pi$
$991$	−5.23286e11			−0.542556			−0.271278	+	0.962501i	$0.587446\pi$
$992$		0			0
$993$	−1.70887e10	−	5.79810e10i	−0.0175757	−	0.0596333i
$994$		0			0
$995$	−8.50758e10	+	4.91185e10i	−0.0867988	+	0.0501133i
$996$		0			0
$997$	9.53213e10	−	1.65101e11i	0.0964738	−	0.167098i	−0.813749	−	0.581217i	$-0.802577\pi$
$997$	9.53213e10	−	1.65101e11i	0.0964738	−	0.167098i	0.910223	+	0.414119i	$0.135910\pi$
$998$		0			0
$999$	4.13507e10	+	3.56108e10i	0.0415165	+	0.0357536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.bg.a.29.14	✓	96
9.5	odd	6	inner	252.9.bg.a.113.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.9.bg.a.29.14	✓	96	1.1	even	1	trivial
252.9.bg.a.113.14	yes	96	9.5	odd	6	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-55.8369 + 58.6791i) q^{3} +(-400.624 + 231.301i) q^{5} +(453.746 - 785.912i) q^{7} +(-325.483 - 6552.92i) q^{9} +O(q^{10})\)	\(q+(-55.8369 + 58.6791i) q^{3} +(-400.624 + 231.301i) q^{5} +(453.746 - 785.912i) q^{7} +(-325.483 - 6552.92i) q^{9} +(-6952.17 - 4013.84i) q^{11} +(-22709.6 - 39334.1i) q^{13} +(8797.10 - 36423.4i) q^{15} -39548.2i q^{17} +85581.2 q^{19} +(20780.8 + 70508.3i) q^{21} +(-19367.3 + 11181.7i) q^{23} +(-88312.6 + 152962. i) q^{25} +(402694. + 346796. i) q^{27} +(226160. + 130574. i) q^{29} +(-275706. - 477537. i) q^{31} +(623716. - 183827. i) q^{33} +419807. i q^{35} +102685. q^{37} +(3.57612e6 + 863717. i) q^{39} +(109076. - 62975.1i) q^{41} +(2.37202e6 - 4.10847e6i) q^{43} +(1.64609e6 + 2.54998e6i) q^{45} +(2.84800e6 + 1.64429e6i) q^{47} +(-411772. - 713209. i) q^{49} +(2.32065e6 + 2.20825e6i) q^{51} -1.92409e6i q^{53} +3.71361e6 q^{55} +(-4.77859e6 + 5.02183e6i) q^{57} +(-4.21966e6 + 2.43622e6i) q^{59} +(-3.06263e6 + 5.30464e6i) q^{61} +(-5.29770e6 - 2.71756e6i) q^{63} +(1.81960e7 + 1.05055e7i) q^{65} +(-6.01071e6 - 1.04109e7i) q^{67} +(425276. - 1.76081e6i) q^{69} -1.39735e7i q^{71} -1.49769e7 q^{73} +(-4.04457e6 - 1.37230e7i) q^{75} +(-6.30904e6 + 3.64253e6i) q^{77} +(-1.43774e7 + 2.49023e7i) q^{79} +(-4.28348e7 + 4.26573e6i) q^{81} +(7.19554e7 + 4.15435e7i) q^{83} +(9.14752e6 + 1.58440e7i) q^{85} +(-2.02900e7 + 5.98006e6i) q^{87} -1.42252e7i q^{89} -4.12175e7 q^{91} +(4.34160e7 + 1.04860e7i) q^{93} +(-3.42859e7 + 1.97950e7i) q^{95} +(1.02387e7 - 1.77339e7i) q^{97} +(-2.40395e7 + 4.68635e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 42 q^{3} - 882 q^{5} - 14642 q^{9}+O(q^{10}) \) 96 * q - 42 * q^3 - 882 * q^5 - 14642 * q^9	\( 96 q - 42 q^{3} - 882 q^{5} - 14642 q^{9} - 6102 q^{11} - 63218 q^{15} - 354144 q^{19} + 81634 q^{21} - 689760 q^{23} + 4088394 q^{25} - 2939076 q^{27} - 1902474 q^{29} + 613830 q^{31} - 3732526 q^{33} + 4437300 q^{37} - 2690876 q^{39} + 8275176 q^{41} - 2941680 q^{43} + 7299362 q^{45} - 7663950 q^{47} - 39530064 q^{49} - 23625052 q^{51} + 8608908 q^{55} + 28697652 q^{57} + 38291778 q^{59} + 7577556 q^{63} + 42391494 q^{65} + 47903562 q^{67} - 52586968 q^{69} - 32396448 q^{73} + 245976220 q^{75} + 11461314 q^{79} - 16224230 q^{81} - 104964174 q^{83} + 108387294 q^{85} - 213493700 q^{87} - 12590844 q^{91} - 88124258 q^{93} + 293841792 q^{95} + 9277590 q^{97} - 77959808 q^{99}+O(q^{100}) \) 96 * q - 42 * q^3 - 882 * q^5 - 14642 * q^9 - 6102 * q^11 - 63218 * q^15 - 354144 * q^19 + 81634 * q^21 - 689760 * q^23 + 4088394 * q^25 - 2939076 * q^27 - 1902474 * q^29 + 613830 * q^31 - 3732526 * q^33 + 4437300 * q^37 - 2690876 * q^39 + 8275176 * q^41 - 2941680 * q^43 + 7299362 * q^45 - 7663950 * q^47 - 39530064 * q^49 - 23625052 * q^51 + 8608908 * q^55 + 28697652 * q^57 + 38291778 * q^59 + 7577556 * q^63 + 42391494 * q^65 + 47903562 * q^67 - 52586968 * q^69 - 32396448 * q^73 + 245976220 * q^75 + 11461314 * q^79 - 16224230 * q^81 - 104964174 * q^83 + 108387294 * q^85 - 213493700 * q^87 - 12590844 * q^91 - 88124258 * q^93 + 293841792 * q^95 + 9277590 * q^97 - 77959808 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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