LMFDB - Embedded newform 252.8.j.b.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,8,Mod(85,252)]

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, 2, 0]))

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

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

chi := DirichletCharacter("252.85");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	252.j (of order $3$, 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:	$78.7210264220$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	252.85
Dual form			252.8.j.b.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-46.3084 + 6.52189i) q^{3} +(-45.8869 + 79.4784i) q^{5} +(171.500 + 297.047i) q^{7} +(2101.93 - 604.036i) q^{9} +(-1535.50 - 2659.57i) q^{11} +(-3974.55 + 6884.12i) q^{13} +(1606.60 - 3979.78i) q^{15} -20475.4 q^{17} +13970.6 q^{19} +(-9879.19 - 12637.2i) q^{21} +(28826.8 - 49929.5i) q^{23} +(34851.3 + 60364.2i) q^{25} +(-93397.5 + 41680.5i) q^{27} +(72099.5 + 124880. i) q^{29} +(-142832. + 247393. i) q^{31} +(88452.0 + 113146. i) q^{33} -31478.4 q^{35} +369096. q^{37} +(139157. - 344714. i) q^{39} +(-66994.3 + 116038. i) q^{41} +(59715.9 + 103431. i) q^{43} +(-48443.1 + 194775. i) q^{45} +(46477.2 + 80500.9i) q^{47} +(-58824.5 + 101887. i) q^{49} +(948181. - 133538. i) q^{51} -764962. q^{53} +281838. q^{55} +(-646958. + 91115.0i) q^{57} +(447569. - 775213. i) q^{59} +(-1.07113e6 - 1.85524e6i) q^{61} +(539908. + 520779. i) q^{63} +(-364759. - 631781. i) q^{65} +(-804762. + 1.39389e6i) q^{67} +(-1.00929e6 + 2.50016e6i) q^{69} +2.51080e6 q^{71} -3.95286e6 q^{73} +(-2.00760e6 - 2.56807e6i) q^{75} +(526677. - 912232. i) q^{77} +(-704815. - 1.22078e6i) q^{79} +(4.05325e6 - 2.53928e6i) q^{81} +(942751. + 1.63289e6i) q^{83} +(939551. - 1.62735e6i) q^{85} +(-4.15326e6 - 5.31276e6i) q^{87} -5.61469e6 q^{89} -2.72654e6 q^{91} +(5.00086e6 - 1.23879e7i) q^{93} +(-641069. + 1.11036e6i) q^{95} +(-2.61063e6 - 4.52174e6i) q^{97} +(-4.83399e6 - 4.66273e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 82 q^{3} + 179 q^{5} + 7203 q^{7} + 890 q^{9} + 3958 q^{11} - 6177 q^{13} + 20077 q^{15} + 22036 q^{17} + 2094 q^{19} + 686 q^{21} + 91390 q^{23} - 284160 q^{25} - 16247 q^{27} + 180179 q^{29} + 99327 q^{31}+ \cdots - 61176680 q^{99}+O(q^{100}) $ 42 * q + 82 * q^3 + 179 * q^5 + 7203 * q^7 + 890 * q^9 + 3958 * q^11 - 6177 * q^13 + 20077 * q^15 + 22036 * q^17 + 2094 * q^19 + 686 * q^21 + 91390 * q^23 - 284160 * q^25 - 16247 * q^27 + 180179 * q^29 + 99327 * q^31 + 175070 * q^33 + 122794 * q^35 - 151782 * q^37 - 8736 * q^39 - 59940 * q^41 + 360321 * q^43 + 357467 * q^45 + 1348899 * q^47 - 2470629 * q^49 - 1657207 * q^51 + 1010028 * q^53 - 1105080 * q^55 - 1937515 * q^57 - 458041 * q^59 - 1085874 * q^61 - 949424 * q^63 - 1175811 * q^65 + 384222 * q^67 + 3999311 * q^69 - 4838366 * q^71 - 1822650 * q^73 - 1387237 * q^75 - 1357594 * q^77 + 238365 * q^79 - 17003890 * q^81 + 1228174 * q^83 + 356127 * q^85 + 33054031 * q^87 + 34786068 * q^89 - 4237422 * q^91 - 1689051 * q^93 - 12321596 * q^95 + 926001 * q^97 - 61176680 * q^99

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−46.3084	+	6.52189i	−0.990228	+	0.139460i
$3$	−46.3084	+	6.52189i	−0.990228	+	0.139460i
$4$		0			0
$5$	−45.8869	+	79.4784i	−0.164170	+	0.284351i	−0.936360	−	0.351041i	$-0.885828\pi$
$5$	−45.8869	+	79.4784i	−0.164170	+	0.284351i	0.772190	+	0.635391i	$0.219161\pi$
$6$		0			0
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$8$		0			0
$9$	2101.93	−	604.036i	0.961102	−	0.276194i
$10$		0			0
$11$	−1535.50	−	2659.57i	−0.347837	−	0.602472i	0.638028	−	0.770013i	$-0.279751\pi$
$11$	−1535.50	−	2659.57i	−0.347837	−	0.602472i	−0.985865	+	0.167542i	$0.946417\pi$
$12$		0			0
$13$	−3974.55	+	6884.12i	−0.501748	+	0.869053i	0.498250	+	0.867034i	$0.333976\pi$
$13$	−3974.55	+	6884.12i	−0.501748	+	0.869053i	−0.999998	+	0.00201980i	$0.999357\pi$
$14$		0			0
$15$	1606.60	−	3979.78i	0.122910	−	0.304467i
$16$		0			0
$17$	−20475.4			−1.01079			−0.505395	−	0.862888i	$-0.668653\pi$
$17$	−20475.4			−1.01079			−0.505395	+	0.862888i	$0.668653\pi$
$18$		0			0
$19$	13970.6			0.467282			0.233641	−	0.972323i	$-0.424936\pi$
$19$	13970.6			0.467282			0.233641	+	0.972323i	$0.424936\pi$
$20$		0			0
$21$	−9879.19	−	12637.2i	−0.232784	−	0.297773i
$22$		0			0
$23$	28826.8	−	49929.5i	0.494025	−	0.855677i	−0.505951	−	0.862562i	$-0.668858\pi$
$23$	28826.8	−	49929.5i	0.494025	−	0.855677i	0.999976	+	0.00688551i	$0.00219174\pi$
$24$		0			0
$25$	34851.3	+	60364.2i	0.446097	+	0.772662i
$26$		0			0
$27$	−93397.5	+	41680.5i	−0.913192	+	0.407530i
$28$		0			0
$29$	72099.5	+	124880.i	0.548958	+	0.950823i	0.998346	+	0.0574867i	$0.0183087\pi$
$29$	72099.5	+	124880.i	0.548958	+	0.950823i	−0.449388	+	0.893337i	$0.648358\pi$
$30$		0			0
$31$	−142832.	+	247393.i	−0.861114	+	1.49149i	0.00974086	+	0.999953i	$0.496899\pi$
$31$	−142832.	+	247393.i	−0.861114	+	1.49149i	−0.870855	+	0.491540i	$0.836434\pi$
$32$		0			0
$33$	88452.0	+	113146.i	0.428459	+	0.548075i
$34$		0			0
$35$	−31478.4			−0.124101
$36$		0			0
$37$	369096.			1.19794			0.598968	−	0.800773i	$-0.295578\pi$
$37$	369096.			1.19794			0.598968	+	0.800773i	$0.295578\pi$
$38$		0			0
$39$	139157.	−	344714.i	0.375647	−	0.930534i
$40$		0			0
$41$	−66994.3	+	116038.i	−0.151808	+	0.262939i	−0.931892	−	0.362735i	$-0.881843\pi$
$41$	−66994.3	+	116038.i	−0.151808	+	0.262939i	0.780084	+	0.625675i	$0.215176\pi$
$42$		0			0
$43$	59715.9	+	103431.i	0.114538	+	0.198386i	0.917595	−	0.397516i	$-0.130128\pi$
$43$	59715.9	+	103431.i	0.114538	+	0.198386i	−0.803057	+	0.595902i	$0.796794\pi$
$44$		0			0
$45$	−48443.1	+	194775.i	−0.0792480	+	0.318633i
$46$		0			0
$47$	46477.2	+	80500.9i	0.0652977	+	0.113099i	0.896826	−	0.442383i	$-0.145867\pi$
$47$	46477.2	+	80500.9i	0.0652977	+	0.113099i	−0.831528	+	0.555482i	$0.812534\pi$
$48$		0			0
$49$	−58824.5	+	101887.i	−0.0714286	+	0.123718i
$50$		0			0
$51$	948181.	−	133538.i	1.00091	−	0.140965i
$52$		0			0
$53$	−764962.			−0.705788			−0.352894	−	0.935663i	$-0.614802\pi$
$53$	−764962.			−0.705788			−0.352894	+	0.935663i	$0.614802\pi$
$54$		0			0
$55$	281838.			0.228418
$56$		0			0
$57$	−646958.	+	91115.0i	−0.462715	+	0.0651670i
$58$		0			0
$59$	447569.	−	775213.i	0.283712	−	0.491404i	−0.688584	−	0.725157i	$-0.741767\pi$
$59$	447569.	−	775213.i	0.283712	−	0.491404i	0.972296	+	0.233752i	$0.0751005\pi$
$60$		0			0
$61$	−1.07113e6	−	1.85524e6i	−0.604207	−	1.04652i	−0.992176	−	0.124845i	$-0.960157\pi$
$61$	−1.07113e6	−	1.85524e6i	−0.604207	−	1.04652i	0.387969	−	0.921672i	$-0.373177\pi$
$62$		0			0
$63$	539908.	+	520779.i	0.272037	+	0.262399i
$64$		0			0
$65$	−364759.	−	631781.i	−0.164744	−	0.285345i
$66$		0			0
$67$	−804762.	+	1.39389e6i	−0.326893	+	0.566195i	−0.981894	−	0.189433i	$-0.939335\pi$
$67$	−804762.	+	1.39389e6i	−0.326893	+	0.566195i	0.655001	+	0.755628i	$0.272668\pi$
$68$		0			0
$69$	−1.00929e6	+	2.50016e6i	−0.369865	+	0.916211i
$70$		0			0
$71$	2.51080e6			0.832546			0.416273	−	0.909240i	$-0.363336\pi$
$71$	2.51080e6			0.832546			0.416273	+	0.909240i	$0.363336\pi$
$72$		0			0
$73$	−3.95286e6			−1.18927			−0.594636	−	0.803995i	$-0.702704\pi$
$73$	−3.95286e6			−1.18927			−0.594636	+	0.803995i	$0.702704\pi$
$74$		0			0
$75$	−2.00760e6	−	2.56807e6i	−0.549492	−	0.702899i
$76$		0			0
$77$	526677.	−	912232.i	0.131470	−	0.227713i
$78$		0			0
$79$	−704815.	−	1.22078e6i	−0.160835	−	0.278574i	0.774333	−	0.632778i	$-0.218085\pi$
$79$	−704815.	−	1.22078e6i	−0.160835	−	0.278574i	−0.935168	+	0.354204i	$0.884752\pi$
$80$		0			0
$81$	4.05325e6	−	2.53928e6i	0.847434	−	0.530901i
$82$		0			0
$83$	942751.	+	1.63289e6i	0.180977	+	0.313462i	0.942214	−	0.335013i	$-0.108741\pi$
$83$	942751.	+	1.63289e6i	0.180977	+	0.313462i	−0.761236	+	0.648475i	$0.775407\pi$
$84$		0			0
$85$	939551.	−	1.62735e6i	0.165941	−	0.287418i
$86$		0			0
$87$	−4.15326e6	−	5.31276e6i	−0.676195	−	0.864974i
$88$		0			0
$89$	−5.61469e6			−0.844230			−0.422115	−	0.906542i	$-0.638712\pi$
$89$	−5.61469e6			−0.844230			−0.422115	+	0.906542i	$0.638712\pi$
$90$		0			0
$91$	−2.72654e6			−0.379286
$92$		0			0
$93$	5.00086e6	−	1.23879e7i	0.644695	−	1.59701i
$94$		0			0
$95$	−641069.	+	1.11036e6i	−0.0767136	+	0.132872i
$96$		0			0
$97$	−2.61063e6	−	4.52174e6i	−0.290431	−	0.503042i	0.683480	−	0.729969i	$-0.260465\pi$
$97$	−2.61063e6	−	4.52174e6i	−0.290431	−	0.503042i	−0.973912	+	0.226927i	$0.927132\pi$
$98$		0			0
$99$	−4.83399e6	−	4.66273e6i	−0.500706	−	0.482966i
$100$		0			0
$101$	−5.69717e6	−	9.86779e6i	−0.550218	−	0.953005i	−0.998258	−	0.0589920i	$-0.981211\pi$
$101$	−5.69717e6	−	9.86779e6i	−0.550218	−	0.953005i	0.448041	−	0.894013i	$-0.352122\pi$
$102$		0			0
$103$	6.89695e6	−	1.19459e7i	0.621909	−	1.07718i	−0.367221	−	0.930134i	$-0.619691\pi$
$103$	6.89695e6	−	1.19459e7i	0.621909	−	1.07718i	0.989130	−	0.147044i	$-0.0469758\pi$
$104$		0			0
$105$	1.45771e6	−	205299.i	0.122888	−	0.0173071i
$106$		0			0
$107$	−1.19196e7			−0.940629			−0.470314	−	0.882499i	$-0.655859\pi$
$107$	−1.19196e7			−0.940629			−0.470314	+	0.882499i	$0.655859\pi$
$108$		0			0
$109$	−1.73306e7			−1.28180			−0.640900	−	0.767624i	$-0.721439\pi$
$109$	−1.73306e7			−1.28180			−0.640900	+	0.767624i	$0.721439\pi$
$110$		0			0
$111$	−1.70923e7	+	2.40721e6i	−1.18623	+	0.167064i
$112$		0			0
$113$	8.62633e6	−	1.49412e7i	0.562408	−	0.974119i	−0.434878	−	0.900490i	$-0.643208\pi$
$113$	8.62633e6	−	1.49412e7i	0.562408	−	0.974119i	0.997286	−	0.0736297i	$-0.0234583\pi$
$114$		0			0
$115$	2.64554e6	+	4.58222e6i	0.162208	+	0.280953i
$116$		0			0
$117$	−4.19596e6	+	1.68707e7i	−0.242204	+	0.973829i
$118$		0			0
$119$	−3.51153e6	−	6.08214e6i	−0.191021	−	0.330858i
$120$		0			0
$121$	5.02805e6	−	8.70884e6i	0.258018	−	0.446901i
$122$		0			0
$123$	2.34561e6	−	5.81044e6i	0.113655	−	0.281541i
$124$		0			0
$125$	−1.35667e7			−0.621282
$126$		0			0
$127$	4.60487e6			0.199482			0.0997412	−	0.995013i	$-0.468199\pi$
$127$	4.60487e6			0.199482			0.0997412	+	0.995013i	$0.468199\pi$
$128$		0			0
$129$	−3.43991e6	−	4.40026e6i	−0.141086	−	0.180474i
$130$		0			0
$131$	9.05627e6	−	1.56859e7i	0.351965	−	0.609622i	−0.634628	−	0.772817i	$-0.718847\pi$
$131$	9.05627e6	−	1.56859e7i	0.351965	−	0.609622i	0.986594	+	0.163196i	$0.0521801\pi$
$132$		0			0
$133$	2.39596e6	+	4.14993e6i	0.0883079	+	0.152954i
$134$		0			0
$135$	973020.	−	9.33567e6i	0.0340372	−	0.326571i
$136$		0			0
$137$	3.05377e6	+	5.28928e6i	0.101465	+	0.175742i	0.912288	−	0.409549i	$-0.134314\pi$
$137$	3.05377e6	+	5.28928e6i	0.101465	+	0.175742i	−0.810824	+	0.585290i	$0.800981\pi$
$138$		0			0
$139$	8.94249e6	−	1.54888e7i	0.282427	−	0.489178i	−0.689555	−	0.724233i	$-0.742194\pi$
$139$	8.94249e6	−	1.54888e7i	0.282427	−	0.489178i	0.971982	+	0.235055i	$0.0755271\pi$
$140$		0			0
$141$	−2.67730e6	−	3.42475e6i	−0.0804323	−	0.102887i
$142$		0			0
$143$	2.44117e7			0.698107
$144$		0			0
$145$	−1.32337e7			−0.360489
$146$		0			0
$147$	2.05957e6	−	5.10187e6i	0.0534769	−	0.132470i
$148$		0			0
$149$	−5.16644e6	+	8.94854e6i	−0.127950	+	0.221616i	−0.922882	−	0.385083i	$-0.874173\pi$
$149$	−5.16644e6	+	8.94854e6i	−0.127950	+	0.221616i	0.794932	+	0.606698i	$0.207506\pi$
$150$		0			0
$151$	−2.82912e7	−	4.90019e7i	−0.668702	−	1.15823i	−0.978267	−	0.207348i	$-0.933517\pi$
$151$	−2.82912e7	−	4.90019e7i	−0.668702	−	1.15823i	0.309565	−	0.950878i	$-0.399817\pi$
$152$		0			0
$153$	−4.30378e7	+	1.23679e7i	−0.971472	+	0.279174i
$154$		0			0
$155$	−1.31083e7	−	2.27042e7i	−0.282738	−	0.489716i
$156$		0			0
$157$	−1.89733e7	+	3.28628e7i	−0.391286	+	0.677728i	−0.992619	−	0.121271i	$-0.961303\pi$
$157$	−1.89733e7	+	3.28628e7i	−0.391286	+	0.677728i	0.601333	+	0.798998i	$0.294636\pi$
$158$		0			0
$159$	3.54241e7	−	4.98900e6i	0.698891	−	0.0984290i
$160$		0			0
$161$	1.97752e7			0.373448
$162$		0			0
$163$	−5.18200e7			−0.937218			−0.468609	−	0.883406i	$-0.655245\pi$
$163$	−5.18200e7			−0.937218			−0.468609	+	0.883406i	$0.655245\pi$
$164$		0			0
$165$	−1.30514e7	+	1.83811e6i	−0.226185	+	0.0318551i
$166$		0			0
$167$	−1.01593e7	+	1.75964e7i	−0.168793	+	0.292359i	−0.937996	−	0.346646i	$-0.887320\pi$
$167$	−1.01593e7	+	1.75964e7i	−0.168793	+	0.292359i	0.769203	+	0.639005i	$0.220654\pi$
$168$		0			0
$169$	−219774.	−	380660.i	−0.00350246	−	0.00606644i
$170$		0			0
$171$	2.93653e7	−	8.43877e6i	0.449105	−	0.129060i
$172$		0			0
$173$	−5.97784e7	−	1.03539e8i	−0.877774	−	1.52035i	−0.853778	−	0.520638i	$-0.825694\pi$
$173$	−5.97784e7	−	1.03539e8i	−0.877774	−	1.52035i	−0.0239965	−	0.999712i	$-0.507639\pi$
$174$		0			0
$175$	−1.19540e7	+	2.07049e7i	−0.168609	+	0.292039i
$176$		0			0
$177$	−1.56704e7	+	3.88179e7i	−0.212409	+	0.526169i
$178$		0			0
$179$	1.25896e8			1.64069			0.820347	−	0.571867i	$-0.193781\pi$
$179$	1.25896e8			1.64069			0.820347	+	0.571867i	$0.193781\pi$
$180$		0			0
$181$	−1.80186e7			−0.225864			−0.112932	−	0.993603i	$-0.536024\pi$
$181$	−1.80186e7			−0.225864			−0.112932	+	0.993603i	$0.536024\pi$
$182$		0			0
$183$	6.17017e7	+	7.89275e7i	0.744250	+	0.952028i
$184$		0			0
$185$	−1.69367e7	+	2.93352e7i	−0.196665	+	0.340634i
$186$		0			0
$187$	3.14400e7	+	5.44557e7i	0.351590	+	0.608972i
$188$		0			0
$189$	−2.83987e7	−	2.05952e7i	−0.305973	−	0.221896i
$190$		0			0
$191$	−4.15879e7	−	7.20323e7i	−0.431867	−	0.748015i	0.565167	−	0.824976i	$-0.308812\pi$
$191$	−4.15879e7	−	7.20323e7i	−0.431867	−	0.748015i	−0.997034	+	0.0769610i	$0.975478\pi$
$192$		0			0
$193$	6.80545e7	−	1.17874e8i	0.681406	−	1.18023i	−0.293146	−	0.956068i	$-0.594702\pi$
$193$	6.80545e7	−	1.17874e8i	0.681406	−	1.18023i	0.974552	−	0.224162i	$-0.0719646\pi$
$194$		0			0
$195$	2.10118e7	+	2.68778e7i	0.202928	+	0.259581i
$196$		0			0
$197$	−2.04556e8			−1.90625			−0.953127	−	0.302571i	$-0.902155\pi$
$197$	−2.04556e8			−1.90625			−0.953127	+	0.302571i	$0.902155\pi$
$198$		0			0
$199$	4.26491e7			0.383641			0.191820	−	0.981430i	$-0.438561\pi$
$199$	4.26491e7			0.383641			0.191820	+	0.981430i	$0.438561\pi$
$200$		0			0
$201$	2.81764e7	−	6.97973e7i	0.244737	−	0.606251i
$202$		0			0
$203$	−2.47301e7	+	4.28338e7i	−0.207487	+	0.359377i
$204$		0			0
$205$	−6.14832e6	−	1.06492e7i	−0.0498446	−	0.0863333i
$206$		0			0
$207$	3.04327e7	−	1.22361e8i	0.238476	−	0.958839i
$208$		0			0
$209$	−2.14520e7	−	3.71559e7i	−0.162538	−	0.281524i
$210$		0			0
$211$	−3.72208e7	+	6.44683e7i	−0.272770	+	0.472452i	−0.969570	−	0.244814i	$-0.921273\pi$
$211$	−3.72208e7	+	6.44683e7i	−0.272770	+	0.472452i	0.696800	+	0.717266i	$0.254607\pi$
$212$		0			0
$213$	−1.16271e8	+	1.63752e7i	−0.824410	+	0.116107i
$214$		0			0
$215$	−1.09607e7			−0.0752149
$216$		0			0
$217$	−9.79830e7			−0.650941
$218$		0			0
$219$	1.83050e8	−	2.57801e7i	1.17765	−	0.165856i
$220$		0			0
$221$	8.13803e7	−	1.40955e8i	0.507162	−	0.878430i
$222$		0			0
$223$	−5.48551e7	−	9.50119e7i	−0.331246	−	0.573735i	0.651511	−	0.758640i	$-0.274136\pi$
$223$	−5.48551e7	−	9.50119e7i	−0.331246	−	0.573735i	−0.982756	+	0.184905i	$0.940802\pi$
$224$		0			0
$225$	1.09717e8	+	1.05830e8i	0.642149	+	0.619398i
$226$		0			0
$227$	5.91122e7	+	1.02385e8i	0.335418	+	0.580962i	0.983565	−	0.180554i	$-0.0577890\pi$
$227$	5.91122e7	+	1.02385e8i	0.335418	+	0.580962i	−0.648147	+	0.761515i	$0.724456\pi$
$228$		0			0
$229$	−1.24521e8	+	2.15677e8i	−0.685201	+	1.18680i	0.288172	+	0.957579i	$0.406953\pi$
$229$	−1.24521e8	+	2.15677e8i	−0.685201	+	1.18680i	−0.973373	+	0.229225i	$0.926381\pi$
$230$		0			0
$231$	−1.84401e7	+	4.56789e7i	−0.0984286	+	0.243822i
$232$		0			0
$233$	1.00141e7			0.0518643			0.0259321	−	0.999664i	$-0.491745\pi$
$233$	1.00141e7			0.0518643			0.0259321	+	0.999664i	$0.491745\pi$
$234$		0			0
$235$	−8.53078e6			−0.0428796
$236$		0			0
$237$	4.06006e7	+	5.19354e7i	0.198113	+	0.253422i
$238$		0			0
$239$	1.12966e8	−	1.95662e8i	0.535247	−	0.927075i	−0.463904	−	0.885885i	$-0.653552\pi$
$239$	1.12966e8	−	1.95662e8i	0.535247	−	0.927075i	0.999151	−	0.0411896i	$-0.0131148\pi$
$240$		0			0
$241$	−6.60432e7	−	1.14390e8i	−0.303927	−	0.526416i	0.673095	−	0.739556i	$-0.264964\pi$
$241$	−6.60432e7	−	1.14390e8i	−0.303927	−	0.526416i	−0.977022	+	0.213140i	$0.931631\pi$
$242$		0			0
$243$	−1.71138e8	+	1.44025e8i	−0.765113	+	0.643896i
$244$		0			0
$245$	−5.39854e6	−	9.35055e6i	−0.0234528	−	0.0406215i
$246$		0			0
$247$	−5.55270e7	+	9.61755e7i	−0.234458	+	0.406093i
$248$		0			0
$249$	−5.43068e7	−	6.94681e7i	−0.222924	−	0.285159i
$250$		0			0
$251$	4.05102e8			1.61699			0.808493	−	0.588506i	$-0.200284\pi$
$251$	4.05102e8			1.61699			0.808493	+	0.588506i	$0.200284\pi$
$252$		0			0
$253$	−1.77055e8			−0.687361
$254$		0			0
$255$	−3.28957e7	+	8.14876e7i	−0.124236	+	0.307752i
$256$		0			0
$257$	1.32304e8	−	2.29157e8i	0.486191	−	0.842108i	−0.513683	−	0.857980i	$-0.671719\pi$
$257$	1.32304e8	−	2.29157e8i	0.486191	−	0.842108i	0.999874	+	0.0158725i	$0.00505258\pi$
$258$		0			0
$259$	6.33000e7	+	1.09639e8i	0.226389	+	0.392117i
$260$		0			0
$261$	2.26980e8	+	2.18938e8i	0.790216	+	0.762219i
$262$		0			0
$263$	−6.55093e7	−	1.13466e8i	−0.222054	−	0.384608i	0.733378	−	0.679821i	$-0.237943\pi$
$263$	−6.55093e7	−	1.13466e8i	−0.222054	−	0.384608i	−0.955431	+	0.295213i	$0.904609\pi$
$264$		0			0
$265$	3.51017e7	−	6.07979e7i	0.115869	−	0.200691i
$266$		0			0
$267$	2.60007e8	−	3.66184e7i	0.835980	−	0.117736i
$268$		0			0
$269$	1.17427e8			0.367820			0.183910	−	0.982943i	$-0.441124\pi$
$269$	1.17427e8			0.367820			0.183910	+	0.982943i	$0.441124\pi$
$270$		0			0
$271$	1.58598e8			0.484068			0.242034	−	0.970268i	$-0.422185\pi$
$271$	1.58598e8			0.484068			0.242034	+	0.970268i	$0.422185\pi$
$272$		0			0
$273$	1.26262e8	−	1.77822e7i	0.375579	−	0.0528952i
$274$		0			0
$275$	1.07028e8	−	1.85379e8i	0.310338	−	0.537521i
$276$		0			0
$277$	2.53781e8	+	4.39562e8i	0.717432	+	1.24263i	0.962014	+	0.273000i	$0.0880159\pi$
$277$	2.53781e8	+	4.39562e8i	0.717432	+	1.24263i	−0.244582	+	0.969629i	$0.578651\pi$
$278$		0			0
$279$	−1.50789e8	+	6.06278e8i	−0.415677	+	1.67131i
$280$		0			0
$281$	3.34099e8	+	5.78677e8i	0.898263	+	1.55584i	0.829713	+	0.558190i	$0.188504\pi$
$281$	3.34099e8	+	5.78677e8i	0.898263	+	1.55584i	0.0685497	+	0.997648i	$0.478163\pi$
$282$		0			0
$283$	−2.73390e8	+	4.73525e8i	−0.717017	+	1.24191i	0.245159	+	0.969483i	$0.421160\pi$
$283$	−2.73390e8	+	4.73525e8i	−0.717017	+	1.24191i	−0.962176	+	0.272427i	$0.912174\pi$
$284$		0			0
$285$	2.24452e7	−	5.56001e7i	0.0574336	−	0.142272i
$286$		0			0
$287$	−4.59581e7			−0.114756
$288$		0			0
$289$	8.90229e6			0.0216950
$290$		0			0
$291$	1.50384e8	+	1.92368e8i	0.357747	+	0.457622i
$292$		0			0
$293$	−4.18587e8	+	7.25013e8i	−0.972184	+	1.68387i	−0.283254	+	0.959045i	$0.591414\pi$
$293$	−4.18587e8	+	7.25013e8i	−0.972184	+	1.68387i	−0.688930	+	0.724828i	$0.741919\pi$
$294$		0			0
$295$	4.10751e7	+	7.11442e7i	0.0931541	+	0.161348i
$296$		0			0
$297$	2.54264e8	+	1.84397e8i	0.563168	+	0.408418i
$298$		0			0
$299$	2.29147e8	+	3.96894e8i	0.495752	+	0.858668i
$300$		0			0
$301$	−2.04826e7	+	3.54768e7i	−0.0432914	+	0.0749829i
$302$		0			0
$303$	3.28184e8	+	4.19805e8i	0.677747	+	0.866959i
$304$		0			0
$305$	1.96602e8			0.396770
$306$		0			0
$307$	−6.62651e8			−1.30708			−0.653538	−	0.756894i	$-0.726716\pi$
$307$	−6.62651e8			−1.30708			−0.653538	+	0.756894i	$0.726716\pi$
$308$		0			0
$309$	−2.41477e8	+	5.98174e8i	−0.465608	+	1.15338i
$310$		0			0
$311$	2.35442e8	−	4.07797e8i	0.443836	−	0.768746i	−0.554135	−	0.832427i	$-0.686951\pi$
$311$	2.35442e8	−	4.07797e8i	0.443836	−	0.768746i	0.997970	+	0.0636813i	$0.0202841\pi$
$312$		0			0
$313$	−2.63093e8	−	4.55690e8i	−0.484958	−	0.839972i	0.514893	−	0.857255i	$-0.327832\pi$
$313$	−2.63093e8	−	4.55690e8i	−0.484958	−	0.839972i	−0.999851	+	0.0172830i	$0.994498\pi$
$314$		0			0
$315$	−6.61654e7	+	1.90141e7i	−0.119273	+	0.0342759i
$316$		0			0
$317$	−3.16253e8	−	5.47767e8i	−0.557606	−	0.965802i	−0.997696	−	0.0678483i	$-0.978387\pi$
$317$	−3.16253e8	−	5.47767e8i	−0.557606	−	0.965802i	0.440089	−	0.897954i	$-0.354947\pi$
$318$		0			0
$319$	2.21418e8	−	3.83507e8i	0.381896	−	0.661464i
$320$		0			0
$321$	5.51977e8	−	7.77383e7i	0.931437	−	0.131180i
$322$		0			0
$323$	−2.86054e8			−0.472323
$324$		0			0
$325$	−5.54072e8			−0.895312
$326$		0			0
$327$	8.02551e8	−	1.13028e8i	1.26927	−	0.178760i
$328$		0			0
$329$	−1.59417e7	+	2.76118e7i	−0.0246802	+	0.0427474i
$330$		0			0
$331$	−8.08381e7	−	1.40016e8i	−0.122523	−	0.212216i	0.798239	−	0.602341i	$-0.205765\pi$
$331$	−8.08381e7	−	1.40016e8i	−0.122523	−	0.212216i	−0.920762	+	0.390125i	$0.872432\pi$
$332$		0			0
$333$	7.75815e8	−	2.22948e8i	1.15134	−	0.330863i
$334$		0			0
$335$	−7.38560e7	−	1.27922e8i	−0.107332	−	0.185904i
$336$		0			0
$337$	−5.06942e8	+	8.78050e8i	−0.721529	+	1.24973i	0.238858	+	0.971055i	$0.423227\pi$
$337$	−5.06942e8	+	8.78050e8i	−0.721529	+	1.24973i	−0.960387	+	0.278671i	$0.910106\pi$
$338$		0			0
$339$	−3.02026e8	+	7.48164e8i	−0.421061	+	1.04303i
$340$		0			0
$341$	8.77278e8			1.19811
$342$		0			0
$343$	−4.03536e7			−0.0539949
$344$		0			0
$345$	−1.52395e8	−	1.94941e8i	−0.199805	−	0.255586i
$346$		0			0
$347$	7.50068e8	−	1.29916e9i	0.963712	−	1.66920i	0.250676	−	0.968071i	$-0.419347\pi$
$347$	7.50068e8	−	1.29916e9i	0.963712	−	1.66920i	0.713036	−	0.701127i	$-0.247319\pi$
$348$		0			0
$349$	3.91104e8	+	6.77412e8i	0.492496	+	0.853029i	0.999963	−	0.00864285i	$-0.00275114\pi$
$349$	3.91104e8	+	6.77412e8i	0.492496	+	0.853029i	−0.507466	+	0.861672i	$0.669418\pi$
$350$		0			0
$351$	8.42793e7	−	8.08620e8i	0.104027	−	0.998090i
$352$		0			0
$353$	−3.15843e8	−	5.47056e8i	−0.382173	−	0.661943i	0.609200	−	0.793017i	$-0.291491\pi$
$353$	−3.15843e8	−	5.47056e8i	−0.382173	−	0.661943i	−0.991373	+	0.131074i	$0.958157\pi$
$354$		0			0
$355$	−1.15213e8	+	1.99554e8i	−0.136679	+	0.236735i
$356$		0			0
$357$	2.02280e8	+	2.58752e8i	0.235296	+	0.300985i
$358$		0			0
$359$	−3.85095e8			−0.439276			−0.219638	−	0.975581i	$-0.570488\pi$
$359$	−3.85095e8			−0.439276			−0.219638	+	0.975581i	$0.570488\pi$
$360$		0			0
$361$	−6.98693e8			−0.781648
$362$		0			0
$363$	−1.76043e8	+	4.36084e8i	−0.193172	+	0.478517i
$364$		0			0
$365$	1.81384e8	−	3.14167e8i	0.195243	−	0.338170i
$366$		0			0
$367$	3.89735e8	+	6.75042e8i	0.411565	+	0.712852i	0.995061	−	0.0992641i	$-0.0316489\pi$
$367$	3.89735e8	+	6.75042e8i	0.411565	+	0.712852i	−0.583496	+	0.812116i	$0.698316\pi$
$368$		0			0
$369$	−7.07265e7	+	2.84370e8i	−0.0732807	+	0.294640i
$370$		0			0
$371$	−1.31191e8	−	2.27229e8i	−0.133381	−	0.231023i
$372$		0			0
$373$	5.92359e8	−	1.02600e9i	0.591023	−	1.02368i	−0.403072	−	0.915168i	$-0.632058\pi$
$373$	5.92359e8	−	1.02600e9i	0.591023	−	1.02368i	0.994095	−	0.108513i	$-0.0346090\pi$
$374$		0			0
$375$	6.28251e8	−	8.84805e7i	0.615211	−	0.0866439i
$376$		0			0
$377$	−1.14625e9			−1.10175
$378$		0			0
$379$	−3.66625e8			−0.345928			−0.172964	−	0.984928i	$-0.555334\pi$
$379$	−3.66625e8			−0.345928			−0.172964	+	0.984928i	$0.555334\pi$
$380$		0			0
$381$	−2.13244e8	+	3.00325e7i	−0.197533	+	0.0278198i
$382$		0			0
$383$	4.20505e8	−	7.28336e8i	0.382451	−	0.662424i	−0.608961	−	0.793200i	$-0.708414\pi$
$383$	4.20505e8	−	7.28336e8i	0.382451	−	0.662424i	0.991412	+	0.130776i	$0.0417469\pi$
$384$		0			0
$385$	4.83351e7	+	8.37189e7i	0.0431669	+	0.0747672i
$386$		0			0
$387$	1.87995e8	+	1.81334e8i	0.164876	+	0.159034i
$388$		0			0
$389$	−4.86755e8	−	8.43085e8i	−0.419264	−	0.726186i	0.576602	−	0.817025i	$-0.304378\pi$
$389$	−4.86755e8	−	8.43085e8i	−0.419264	−	0.726186i	−0.995866	+	0.0908393i	$0.971045\pi$
$390$		0			0
$391$	−5.90240e8	+	1.02232e9i	−0.499355	+	0.864909i
$392$		0			0
$393$	−3.17079e8	+	7.85454e8i	−0.263508	+	0.652750i
$394$		0			0
$395$	1.29367e8			0.105617
$396$		0			0
$397$	−1.65174e9			−1.32487			−0.662437	−	0.749118i	$-0.730478\pi$
$397$	−1.65174e9			−1.32487			−0.662437	+	0.749118i	$0.730478\pi$
$398$		0			0
$399$	−1.38019e8	−	1.76550e8i	−0.108776	−	0.139144i
$400$		0			0
$401$	1.06679e9	−	1.84774e9i	0.826179	−	1.43098i	−0.0748364	−	0.997196i	$-0.523843\pi$
$401$	1.06679e9	−	1.84774e9i	0.826179	−	1.43098i	0.901015	−	0.433788i	$-0.142823\pi$
$402$		0			0
$403$	−1.13539e9	−	1.96655e9i	−0.864125	−	1.49671i
$404$		0			0
$405$	1.58273e7	+	4.38665e8i	0.0118389	+	0.328126i
$406$		0			0
$407$	−5.66749e8	−	9.81637e8i	−0.416687	−	0.721723i
$408$		0			0
$409$	−3.48584e8	+	6.03766e8i	−0.251928	+	0.436352i	−0.964057	−	0.265697i	$-0.914398\pi$
$409$	−3.48584e8	+	6.03766e8i	−0.251928	+	0.436352i	0.712129	+	0.702049i	$0.247731\pi$
$410$		0			0
$411$	−1.75911e8	−	2.25022e8i	−0.124982	−	0.159874i
$412$		0			0
$413$	3.07033e8			0.214466
$414$		0			0
$415$	−1.73040e8			−0.118844
$416$		0			0
$417$	−3.13095e8	+	7.75585e8i	−0.211447	+	0.523785i
$418$		0			0
$419$	8.85854e8	−	1.53434e9i	0.588319	−	1.01900i	−0.406133	−	0.913814i	$-0.633123\pi$
$419$	8.85854e8	−	1.53434e9i	0.588319	−	1.01900i	0.994453	−	0.105185i	$-0.0335435\pi$
$420$		0			0
$421$	−1.22810e9	−	2.12714e9i	−0.802135	−	1.38934i	−0.918208	−	0.396098i	$-0.870364\pi$
$421$	−1.22810e9	−	2.12714e9i	−0.802135	−	1.38934i	0.116073	−	0.993241i	$-0.462969\pi$
$422$		0			0
$423$	1.46317e8	+	1.41133e8i	0.0939949	+	0.0906647i
$424$		0			0
$425$	−7.13593e8	−	1.23598e9i	−0.450910	−	0.780998i
$426$		0			0
$427$	3.67396e8	−	6.36348e8i	0.228369	−	0.395546i
$428$		0			0
$429$	−1.13047e9	+	1.59210e8i	−0.691285	+	0.0973579i
$430$		0			0
$431$	−5.83620e8			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$431$	−5.83620e8			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$432$		0			0
$433$	−2.28190e9			−1.35079			−0.675397	−	0.737454i	$-0.736028\pi$
$433$	−2.28190e9			−1.35079			−0.675397	+	0.737454i	$0.736028\pi$
$434$		0			0
$435$	6.12830e8	−	8.63086e7i	0.356967	−	0.0502738i
$436$		0			0
$437$	4.02729e8	−	6.97547e8i	0.230849	−	0.399842i
$438$		0			0
$439$	2.40387e7	+	4.16363e7i	0.0135608	+	0.0234880i	0.872726	−	0.488210i	$-0.162350\pi$
$439$	2.40387e7	+	4.16363e7i	0.0135608	+	0.0234880i	−0.859165	+	0.511698i	$0.829017\pi$
$440$		0			0
$441$	−6.21015e7	+	2.49692e8i	−0.0344800	+	0.138634i
$442$		0			0
$443$	1.45047e9	+	2.51229e9i	0.792676	+	1.37295i	0.924305	+	0.381656i	$0.124646\pi$
$443$	1.45047e9	+	2.51229e9i	0.792676	+	1.37295i	−0.131629	+	0.991299i	$0.542021\pi$
$444$		0			0
$445$	2.57641e8	−	4.46246e8i	0.138597	−	0.240057i
$446$		0			0
$447$	1.80888e8	−	4.48087e8i	0.0957930	−	0.237294i
$448$		0			0
$449$	3.68290e8			0.192012			0.0960058	−	0.995381i	$-0.469393\pi$
$449$	3.68290e8			0.192012			0.0960058	+	0.995381i	$0.469393\pi$
$450$		0			0
$451$	4.11480e8			0.211218
$452$		0			0
$453$	1.62971e9	+	2.08468e9i	0.823694	+	1.05365i
$454$		0			0
$455$	1.25112e8	−	2.16701e8i	0.0622673	−	0.107850i
$456$		0			0
$457$	−1.70815e8	−	2.95860e8i	−0.0837181	−	0.145004i	0.821126	−	0.570747i	$-0.193346\pi$
$457$	−1.70815e8	−	2.95860e8i	−0.0837181	−	0.145004i	−0.904844	+	0.425743i	$0.860013\pi$
$458$		0			0
$459$	1.91235e9	−	8.53424e8i	0.923044	−	0.411927i
$460$		0			0
$461$	−1.41140e9	−	2.44462e9i	−0.670961	−	1.16214i	−0.977632	−	0.210323i	$-0.932548\pi$
$461$	−1.41140e9	−	2.44462e9i	−0.670961	−	1.16214i	0.306671	−	0.951816i	$-0.400785\pi$
$462$		0			0
$463$	−8.55758e8	+	1.48222e9i	−0.400698	+	0.694030i	−0.993810	−	0.111090i	$-0.964566\pi$
$463$	−8.55758e8	+	1.48222e9i	−0.400698	+	0.694030i	0.593112	+	0.805120i	$0.297899\pi$
$464$		0			0
$465$	7.55096e8	+	9.65902e8i	0.348271	+	0.445500i
$466$		0			0
$467$	−1.73369e9			−0.787703			−0.393851	−	0.919174i	$-0.628858\pi$
$467$	−1.73369e9			−0.787703			−0.393851	+	0.919174i	$0.628858\pi$
$468$		0			0
$469$	−5.52067e8			−0.247108
$470$		0			0
$471$	6.64296e8	−	1.64556e9i	0.292947	−	0.725674i
$472$		0			0
$473$	1.83388e8	−	3.17637e8i	0.0796814	−	0.138012i
$474$		0			0
$475$	4.86895e8	+	8.43327e8i	0.208453	+	0.361051i
$476$		0			0
$477$	−1.60790e9	+	4.62065e8i	−0.678334	+	0.194934i
$478$		0			0
$479$	−1.95809e9	−	3.39150e9i	−0.814062	−	1.41000i	−0.910000	−	0.414609i	$-0.863918\pi$
$479$	−1.95809e9	−	3.39150e9i	−0.814062	−	1.41000i	0.0959380	−	0.995387i	$-0.469415\pi$
$480$		0			0
$481$	−1.46699e9	+	2.54090e9i	−0.601063	+	1.04107i
$482$		0			0
$483$	−9.15757e8	+	1.28972e8i	−0.369798	+	0.0520810i
$484$		0			0
$485$	4.79174e8			0.190720
$486$		0			0
$487$	−7.60877e8			−0.298513			−0.149256	−	0.988799i	$-0.547688\pi$
$487$	−7.60877e8			−0.298513			−0.149256	+	0.988799i	$0.547688\pi$
$488$		0			0
$489$	2.39970e9	−	3.37964e8i	0.928059	−	0.130704i
$490$		0			0
$491$	−1.19158e9	+	2.06389e9i	−0.454297	+	0.786865i	−0.998647	−	0.0519926i	$-0.983443\pi$
$491$	−1.19158e9	+	2.06389e9i	−0.454297	+	0.786865i	0.544351	+	0.838858i	$0.316776\pi$
$492$		0			0
$493$	−1.47626e9	−	2.55696e9i	−0.554881	−	0.961082i
$494$		0			0
$495$	5.92403e8	−	1.70240e8i	0.219533	−	0.0630876i
$496$		0			0
$497$	4.30602e8	+	7.45825e8i	0.157336	+	0.272515i
$498$		0			0
$499$	−7.01116e8	+	1.21437e9i	−0.252603	+	0.437520i	−0.964242	−	0.265025i	$-0.914620\pi$
$499$	−7.01116e8	+	1.21437e9i	−0.252603	+	0.437520i	0.711639	+	0.702545i	$0.247953\pi$
$500$		0			0
$501$	3.55698e8	−	8.81118e8i	0.126372	−	0.313042i
$502$		0			0
$503$	3.78661e9			1.32667			0.663334	−	0.748323i	$-0.269141\pi$
$503$	3.78661e9			1.32667			0.663334	+	0.748323i	$0.269141\pi$
$504$		0			0
$505$	1.04570e9			0.361317
$506$		0			0
$507$	1.26600e7	+	1.61944e7i	0.00431426	+	0.00551871i
$508$		0			0
$509$	−1.18052e9	+	2.04473e9i	−0.396792	+	0.687264i	−0.993328	−	0.115323i	$-0.963210\pi$
$509$	−1.18052e9	+	2.04473e9i	−0.396792	+	0.687264i	0.596536	+	0.802586i	$0.296543\pi$
$510$		0			0
$511$	−6.77915e8	−	1.17418e9i	−0.224751	−	0.389280i
$512$		0			0
$513$	−1.30482e9	+	5.82303e8i	−0.426718	+	0.190431i
$514$		0			0
$515$	6.32958e8	+	1.09632e9i	0.204197	+	0.353680i
$516$		0			0
$517$	1.42732e8	−	2.47219e8i	0.0454259	−	0.0786800i
$518$		0			0
$519$	3.44351e9	+	4.40486e9i	1.08122	+	1.38308i
$520$		0			0
$521$	1.00498e9			0.311334			0.155667	−	0.987810i	$-0.450247\pi$
$521$	1.00498e9			0.311334			0.155667	+	0.987810i	$0.450247\pi$
$522$		0			0
$523$	1.26287e9			0.386013			0.193006	−	0.981198i	$-0.438176\pi$
$523$	1.26287e9			0.386013			0.193006	+	0.981198i	$0.438176\pi$
$524$		0			0
$525$	4.18535e8	−	1.03677e9i	0.126233	−	0.312699i
$526$		0			0
$527$	2.92455e9	−	5.06546e9i	0.870405	−	1.50759i
$528$		0			0
$529$	4.04438e7	+	7.00506e7i	0.0118784	+	0.0205739i
$530$		0			0
$531$	4.72503e8	−	1.89979e9i	0.136954	−	0.550649i
$532$		0			0
$533$	−5.32544e8	−	9.22393e8i	−0.152339	−	0.263858i
$534$		0			0
$535$	5.46953e8	−	9.47350e8i	0.154423	−	0.267468i
$536$		0			0
$537$	−5.83005e9	+	8.21082e8i	−1.62466	+	0.228811i
$538$		0			0
$539$	3.61301e8			0.0993821
$540$		0			0
$541$	−4.30190e9			−1.16807			−0.584037	−	0.811727i	$-0.698528\pi$
$541$	−4.30190e9			−1.16807			−0.584037	+	0.811727i	$0.698528\pi$
$542$		0			0
$543$	8.34414e8	−	1.17516e8i	0.223657	−	0.0314990i
$544$		0			0
$545$	7.95246e8	−	1.37741e9i	0.210433	−	0.364480i
$546$		0			0
$547$	−1.78578e9	−	3.09306e9i	−0.466522	−	0.808040i	0.532747	−	0.846275i	$-0.321160\pi$
$547$	−1.78578e9	−	3.09306e9i	−0.466522	−	0.808040i	−0.999269	+	0.0382348i	$0.987827\pi$
$548$		0			0
$549$	−3.37206e9	−	3.25259e9i	−0.869746	−	0.838931i
$550$		0			0
$551$	1.00728e9	+	1.74465e9i	0.256518	+	0.444302i
$552$		0			0
$553$	2.41752e8	−	4.18726e8i	0.0607899	−	0.105291i
$554$		0			0
$555$	5.92989e8	−	1.46892e9i	0.147238	−	0.364732i
$556$		0			0
$557$	−3.34906e9			−0.821164			−0.410582	−	0.911824i	$-0.634674\pi$
$557$	−3.34906e9			−0.821164			−0.410582	+	0.911824i	$0.634674\pi$
$558$		0			0
$559$	−9.49375e8			−0.229877
$560$		0			0
$561$	−1.81109e9	−	2.31670e9i	−0.433082	−	0.553988i
$562$		0			0
$563$	1.34927e7	−	2.33700e7i	0.00318654	−	0.00551925i	−0.864428	−	0.502757i	$-0.832319\pi$
$563$	1.34927e7	−	2.33700e7i	0.00318654	−	0.00551925i	0.867614	+	0.497238i	$0.165652\pi$
$564$		0			0
$565$	7.91670e8	+	1.37121e9i	0.184661	+	0.319842i
$566$		0			0
$567$	1.44942e9	+	7.68517e8i	0.333928	+	0.177057i
$568$		0			0
$569$	−1.17902e9	−	2.04212e9i	−0.268304	−	0.464717i	0.700120	−	0.714025i	$-0.253130\pi$
$569$	−1.17902e9	−	2.04212e9i	−0.268304	−	0.464717i	−0.968424	+	0.249309i	$0.919797\pi$
$570$		0			0
$571$	−1.65443e9	+	2.86555e9i	−0.371895	+	0.644142i	−0.989857	−	0.142066i	$-0.954625\pi$
$571$	−1.65443e9	+	2.86555e9i	−0.371895	+	0.644142i	0.617962	+	0.786208i	$0.287959\pi$
$572$		0			0
$573$	2.39565e9	+	3.06447e9i	0.531965	+	0.680478i
$574$		0			0
$575$	4.01861e9			0.881532
$576$		0			0
$577$	1.01622e9			0.220227			0.110114	−	0.993919i	$-0.464879\pi$
$577$	1.01622e9			0.220227			0.110114	+	0.993919i	$0.464879\pi$
$578$		0			0
$579$	−2.38273e9	+	5.90239e9i	−0.510153	+	1.26373i
$580$		0			0
$581$	−3.23364e8	+	5.60082e8i	−0.0684030	+	0.118477i
$582$		0			0
$583$	1.17460e9	+	2.03447e9i	0.245499	+	0.425217i
$584$		0			0
$585$	−1.14832e9	−	1.10763e9i	−0.237146	−	0.228744i
$586$		0			0
$587$	1.29703e9	+	2.24653e9i	0.264678	+	0.458436i	0.967479	−	0.252951i	$-0.0814010\pi$
$587$	1.29703e9	+	2.24653e9i	0.264678	+	0.458436i	−0.702801	+	0.711386i	$0.748068\pi$
$588$		0			0
$589$	−1.99546e9	+	3.45624e9i	−0.402383	+	0.696947i
$590$		0			0
$591$	9.47266e9	−	1.33409e9i	1.88763	−	0.265846i
$592$		0			0
$593$	−4.18460e9			−0.824068			−0.412034	−	0.911169i	$-0.635181\pi$
$593$	−4.18460e9			−0.824068			−0.412034	+	0.911169i	$0.635181\pi$
$594$		0			0
$595$	6.44532e8			0.125440
$596$		0			0
$597$	−1.97501e9	+	2.78153e8i	−0.379891	+	0.0535024i
$598$		0			0
$599$	3.54145e9	−	6.13397e9i	0.673267	−	1.16613i	−0.303705	−	0.952766i	$-0.598224\pi$
$599$	3.54145e9	−	6.13397e9i	0.673267	−	1.16613i	0.976972	−	0.213367i	$-0.0684430\pi$
$600$		0			0
$601$	−1.42107e9	−	2.46137e9i	−0.267027	−	0.462504i	0.701066	−	0.713097i	$-0.252708\pi$
$601$	−1.42107e9	−	2.46137e9i	−0.267027	−	0.462504i	−0.968093	+	0.250593i	$0.919375\pi$
$602$		0			0
$603$	−8.49594e8	+	3.41596e9i	−0.157798	+	0.634457i
$604$		0			0
$605$	4.61443e8	+	7.99242e8i	0.0847177	+	0.146735i
$606$		0			0
$607$	2.03471e9	−	3.52422e9i	0.369268	−	0.639591i	−0.620183	−	0.784457i	$-0.712942\pi$
$607$	2.03471e9	−	3.52422e9i	0.369268	−	0.639591i	0.989451	+	0.144866i	$0.0462752\pi$
$608$		0			0
$609$	8.65854e8	−	2.14485e9i	0.155340	−	0.384802i
$610$		0			0
$611$	−7.38903e8			−0.131052
$612$		0			0
$613$	2.01727e8			0.0353714			0.0176857	−	0.999844i	$-0.494370\pi$
$613$	2.01727e8			0.0353714			0.0176857	+	0.999844i	$0.494370\pi$
$614$		0			0
$615$	3.54172e8	+	4.53048e8i	0.0613975	+	0.0785383i
$616$		0			0
$617$	−5.88263e8	+	1.01890e9i	−0.100826	+	0.174636i	−0.912025	−	0.410134i	$-0.865482\pi$
$617$	−5.88263e8	+	1.01890e9i	−0.100826	+	0.174636i	0.811199	+	0.584770i	$0.198815\pi$
$618$		0			0
$619$	2.92639e9	+	5.06865e9i	0.495923	+	0.858965i	0.999989	−	0.00470078i	$-0.00149631\pi$
$619$	2.92639e9	+	5.06865e9i	0.495923	+	0.858965i	−0.504065	+	0.863665i	$0.668163\pi$
$620$		0			0
$621$	−6.11265e8	+	5.86480e9i	−0.102426	+	0.982727i
$622$		0			0
$623$	−9.62919e8	−	1.66783e9i	−0.159544	−	0.276339i
$624$		0			0
$625$	−2.10022e9	+	3.63770e9i	−0.344101	+	0.596000i
$626$		0			0
$627$	1.23573e9	+	1.58072e9i	0.200211	+	0.256105i
$628$		0			0
$629$	−7.55739e9			−1.21086
$630$		0			0
$631$	3.92237e9			0.621506			0.310753	−	0.950491i	$-0.399419\pi$
$631$	3.92237e9			0.621506			0.310753	+	0.950491i	$0.399419\pi$
$632$		0			0
$633$	1.30318e9	−	3.22817e9i	0.204217	−	0.505876i
$634$		0			0
$635$	−2.11303e8	+	3.65988e8i	−0.0327490	+	0.0567229i
$636$		0			0
$637$	−4.67601e8	−	8.09909e8i	−0.0716783	−	0.124150i
$638$		0			0
$639$	5.27753e9	−	1.51661e9i	0.800161	−	0.229944i
$640$		0			0
$641$	4.20367e9	+	7.28097e9i	0.630414	+	1.09191i	0.987467	+	0.157825i	$0.0504481\pi$
$641$	4.20367e9	+	7.28097e9i	0.630414	+	1.09191i	−0.357053	+	0.934084i	$0.616219\pi$
$642$		0			0
$643$	1.39478e9	−	2.41583e9i	0.206903	−	0.358367i	−0.743834	−	0.668364i	$-0.766995\pi$
$643$	1.39478e9	−	2.41583e9i	0.206903	−	0.358367i	0.950737	+	0.309997i	$0.100328\pi$
$644$		0			0
$645$	5.07573e8	−	7.14845e7i	0.0744799	−	0.0104895i
$646$		0			0
$647$	3.60948e9			0.523938			0.261969	−	0.965076i	$-0.415628\pi$
$647$	3.60948e9			0.523938			0.261969	+	0.965076i	$0.415628\pi$
$648$		0			0
$649$	−2.74898e9			−0.394743
$650$		0			0
$651$	4.53743e9	−	6.39034e8i	0.644580	−	0.0907801i
$652$		0			0
$653$	−2.81141e8	+	4.86951e8i	−0.0395120	+	0.0684368i	−0.885105	−	0.465391i	$-0.845914\pi$
$653$	−2.81141e8	+	4.86951e8i	−0.0395120	+	0.0684368i	0.845593	+	0.533828i	$0.179247\pi$
$654$		0			0
$655$	8.31128e8	+	1.43956e9i	0.115564	+	0.200163i
$656$		0			0
$657$	−8.30863e9	+	2.38767e9i	−1.14301	+	0.328470i
$658$		0			0
$659$	1.84097e9	+	3.18865e9i	0.250580	+	0.434018i	0.963686	−	0.267039i	$-0.0860453\pi$
$659$	1.84097e9	+	3.18865e9i	0.250580	+	0.434018i	−0.713105	+	0.701057i	$0.752712\pi$
$660$		0			0
$661$	3.77126e9	−	6.53201e9i	0.507904	−	0.879715i	−0.492054	−	0.870564i	$-0.663754\pi$
$661$	3.77126e9	−	6.53201e9i	0.507904	−	0.879715i	0.999958	−	0.00915061i	$-0.00291277\pi$
$662$		0			0
$663$	−2.84930e9	+	7.05814e9i	−0.379700	+	0.940574i
$664$		0			0
$665$	−4.39773e8			−0.0579900
$666$		0			0
$667$	8.31359e9			1.08480
$668$		0			0
$669$	3.15991e9	+	4.04209e9i	0.408022	+	0.521932i
$670$		0			0
$671$	−3.28943e9	+	5.69746e9i	−0.420331	+	0.728035i
$672$		0			0
$673$	4.04423e9	+	7.00481e9i	0.511426	+	0.885816i	0.999912	+	0.0132441i	$0.00421586\pi$
$673$	4.04423e9	+	7.00481e9i	0.511426	+	0.885816i	−0.488486	+	0.872572i	$0.662451\pi$
$674$		0			0
$675$	−5.77103e9	−	4.18525e9i	−0.722255	−	0.523791i
$676$		0			0
$677$	6.94533e9	+	1.20297e10i	0.860265	+	1.49002i	0.871673	+	0.490088i	$0.163035\pi$
$677$	6.94533e9	+	1.20297e10i	0.860265	+	1.49002i	−0.0114077	+	0.999935i	$0.503631\pi$
$678$		0			0
$679$	8.95445e8	−	1.55096e9i	0.109773	−	0.190132i
$680$		0			0
$681$	−3.40514e9	−	4.35578e9i	−0.413161	−	0.528507i
$682$		0			0
$683$	−2.24491e9			−0.269604			−0.134802	−	0.990873i	$-0.543040\pi$
$683$	−2.24491e9			−0.269604			−0.134802	+	0.990873i	$0.543040\pi$
$684$		0			0
$685$	−5.60511e8			−0.0666296
$686$		0			0
$687$	4.35974e9	−	1.07997e10i	0.512994	−	1.27076i
$688$		0			0
$689$	3.04038e9	−	5.26608e9i	0.354128	−	0.613367i
$690$		0			0
$691$	6.93214e9	+	1.20068e10i	0.799272	+	1.38438i	0.920091	+	0.391705i	$0.128114\pi$
$691$	6.93214e9	+	1.20068e10i	0.799272	+	1.38438i	−0.120819	+	0.992675i	$0.538552\pi$
$692$		0			0
$693$	5.56018e8	−	2.23558e9i	0.0634633	−	0.255167i
$694$		0			0
$695$	8.20685e8	+	1.42147e9i	0.0927321	+	0.160617i
$696$		0			0
$697$	1.37173e9	−	2.37591e9i	0.153446	−	0.265776i
$698$		0			0
$699$	−4.63739e8	+	6.53112e7i	−0.0513574	+	0.00723298i
$700$		0			0
$701$	−2.56554e9			−0.281298			−0.140649	−	0.990060i	$-0.544919\pi$
$701$	−2.56554e9			−0.281298			−0.140649	+	0.990060i	$0.544919\pi$
$702$		0			0
$703$	5.15651e9			0.559774
$704$		0			0
$705$	3.95046e8	−	5.56368e7i	0.0424606	−	0.00597999i
$706$		0			0
$707$	1.95413e9	−	3.38465e9i	0.207963	−	0.360202i
$708$		0			0
$709$	−2.02093e9	−	3.50035e9i	−0.212956	−	0.368850i	0.739683	−	0.672956i	$-0.234976\pi$
$709$	−2.02093e9	−	3.50035e9i	−0.212956	−	0.368850i	−0.952638	+	0.304106i	$0.901642\pi$
$710$		0			0
$711$	−2.21886e9	−	2.14025e9i	−0.231519	−	0.223317i
$712$		0			0
$713$	8.23480e9	+	1.42631e10i	0.850824	+	1.47367i
$714$		0			0
$715$	−1.12018e9	+	1.94020e9i	−0.114608	+	0.198507i
$716$		0			0
$717$	−3.95517e9	+	9.79756e9i	−0.400727	+	0.992661i
$718$		0			0
$719$	−1.55898e10			−1.56418			−0.782092	−	0.623162i	$-0.785848\pi$
$719$	−1.55898e10			−1.56418			−0.782092	+	0.623162i	$0.785848\pi$
$720$		0			0
$721$	4.73130e9			0.470119
$722$		0			0
$723$	3.80439e9	+	4.86650e9i	0.374370	+	0.478886i
$724$		0			0
$725$	−5.02552e9	+	8.70446e9i	−0.489777	+	0.848318i
$726$		0			0
$727$	6.35805e9	+	1.10125e10i	0.613696	+	1.06295i	0.990612	+	0.136705i	$0.0436513\pi$
$727$	6.35805e9	+	1.10125e10i	0.613696	+	1.06295i	−0.376916	+	0.926248i	$0.623015\pi$
$728$		0			0
$729$	6.98583e9	−	7.78571e9i	0.667838	−	0.744306i
$730$		0			0
$731$	−1.22271e9	−	2.11779e9i	−0.115774	−	0.200527i
$732$		0			0
$733$	−1.06062e10	+	1.83705e10i	−0.994710	+	1.72289i	−0.408396	+	0.912805i	$0.633912\pi$
$733$	−1.06062e10	+	1.83705e10i	−0.994710	+	1.72289i	−0.586314	+	0.810084i	$0.699421\pi$
$734$		0			0
$735$	3.10981e8	+	3.97800e8i	0.0288887	+	0.0369538i
$736$		0			0
$737$	4.94286e9			0.454822
$738$		0			0
$739$	6.18318e9			0.563581			0.281790	−	0.959476i	$-0.409072\pi$
$739$	6.18318e9			0.563581			0.281790	+	0.959476i	$0.409072\pi$
$740$		0			0
$741$	1.94412e9	−	4.81587e9i	0.175533	−	0.434822i
$742$		0			0
$743$	−6.10377e9	+	1.05720e10i	−0.545930	+	0.945579i	0.452618	+	0.891705i	$0.350490\pi$
$743$	−6.10377e9	+	1.05720e10i	−0.545930	+	0.945579i	−0.998548	+	0.0538739i	$0.982843\pi$
$744$		0			0
$745$	−4.74144e8	−	8.21241e8i	−0.0420110	−	0.0727652i
$746$		0			0
$747$	2.96792e9	+	2.86277e9i	0.260514	+	0.251284i
$748$		0			0
$749$	−2.04421e9	−	3.54068e9i	−0.177762	−	0.307893i
$750$		0			0
$751$	7.93530e9	−	1.37443e10i	0.683634	−	1.18409i	−0.290231	−	0.956957i	$-0.593732\pi$
$751$	7.93530e9	−	1.37443e10i	0.683634	−	1.18409i	0.973864	−	0.227131i	$-0.0729347\pi$
$752$		0			0
$753$	−1.87596e10	+	2.64203e9i	−1.60118	+	0.225504i
$754$		0			0
$755$	5.19279e9			0.439123
$756$		0			0
$757$	7.78620e9			0.652364			0.326182	−	0.945307i	$-0.394238\pi$
$757$	7.78620e9			0.652364			0.326182	+	0.945307i	$0.394238\pi$
$758$		0			0
$759$	8.19911e9	−	1.15473e9i	0.680644	−	0.0958593i
$760$		0			0
$761$	−5.85552e9	+	1.01421e10i	−0.481636	+	0.834218i	−0.999778	−	0.0210766i	$-0.993291\pi$
$761$	−5.85552e9	+	1.01421e10i	−0.481636	+	0.834218i	0.518142	+	0.855295i	$0.326624\pi$
$762$		0			0
$763$	−2.97219e9	−	5.14799e9i	−0.242237	−	0.419568i
$764$		0			0
$765$	9.91892e8	−	3.98810e9i	0.0801031	−	0.322070i
$766$		0			0
$767$	3.55777e9	+	6.16224e9i	0.284704	+	0.493123i
$768$		0			0
$769$	1.17564e10	−	2.03626e10i	0.932247	−	1.61470i	0.152776	−	0.988261i	$-0.451179\pi$
$769$	1.17564e10	−	2.03626e10i	0.932247	−	1.61470i	0.779471	−	0.626438i	$-0.215488\pi$
$770$		0			0
$771$	−4.63224e9	+	1.14748e10i	−0.364000	+	0.901682i
$772$		0			0
$773$	1.07195e10			0.834731			0.417366	−	0.908739i	$-0.362953\pi$
$773$	1.07195e10			0.834731			0.417366	+	0.908739i	$0.362953\pi$
$774$		0			0
$775$	−1.99116e10			−1.53656
$776$		0			0
$777$	−3.64637e9	−	4.66436e9i	−0.278861	−	0.356713i
$778$		0			0
$779$	−9.35954e8	+	1.62112e9i	−0.0709371	+	0.122867i
$780$		0			0
$781$	−3.85534e9	−	6.67765e9i	−0.289590	−	0.501585i
$782$		0			0
$783$	−1.19390e10	−	8.65833e9i	−0.888793	−	0.644567i
$784$		0			0
$785$	−1.74125e9	−	3.01594e9i	−0.128475	−	0.222525i
$786$		0			0
$787$	4.17149e9	−	7.22523e9i	0.305056	−	0.528373i	−0.672218	−	0.740353i	$-0.734658\pi$
$787$	4.17149e9	−	7.22523e9i	0.305056	−	0.528373i	0.977274	+	0.211981i	$0.0679915\pi$
$788$		0			0
$789$	3.77364e9	+	4.82716e9i	0.273521	+	0.349882i
$790$		0			0
$791$	5.91766e9			0.425140
$792$		0			0
$793$	1.70289e10			1.21264
$794$		0			0
$795$	−1.22898e9	+	3.04438e9i	−0.0867484	+	0.214889i
$796$		0			0
$797$	3.00916e9	−	5.21201e9i	0.210543	−	0.364671i	−0.741342	−	0.671128i	$-0.765810\pi$
$797$	3.00916e9	−	5.21201e9i	0.210543	−	0.364671i	0.951885	+	0.306457i	$0.0991435\pi$
$798$		0			0
$799$	−9.51639e8	−	1.64829e9i	−0.0660022	−	0.114319i
$800$		0			0
$801$	−1.18017e10	+	3.39148e9i	−0.811391	+	0.233171i
$802$		0			0
$803$	6.06962e9	+	1.05129e10i	0.413673	+	0.716503i
$804$		0			0
$805$	−9.07421e8	+	1.57170e9i	−0.0613089	+	0.106190i
$806$		0			0
$807$	−5.43786e9	+	7.65847e8i	−0.364226	+	0.0512962i
$808$		0			0
$809$	−1.36503e10			−0.906408			−0.453204	−	0.891407i	$-0.649719\pi$
$809$	−1.36503e10			−0.906408			−0.453204	+	0.891407i	$0.649719\pi$
$810$		0			0
$811$	6.05829e8			0.0398820			0.0199410	−	0.999801i	$-0.493652\pi$
$811$	6.05829e8			0.0398820			0.0199410	+	0.999801i	$0.493652\pi$
$812$		0			0
$813$	−7.34444e9	+	1.03436e9i	−0.479338	+	0.0675081i
$814$		0			0
$815$	2.37786e9	−	4.11857e9i	0.153863	−	0.266498i
$816$		0			0
$817$	8.34270e8	+	1.44500e9i	0.0535216	+	0.0927022i
$818$		0			0
$819$	−5.73099e9	+	1.64693e9i	−0.364532	+	0.104757i
$820$		0			0
$821$	−2.88003e9	−	4.98836e9i	−0.181633	−	0.314598i	0.760803	−	0.648982i	$-0.224805\pi$
$821$	−2.88003e9	−	4.98836e9i	−0.181633	−	0.314598i	−0.942437	+	0.334384i	$0.891472\pi$
$822$		0			0
$823$	1.19915e10	−	2.07699e10i	0.749851	−	1.29878i	−0.198042	−	0.980194i	$-0.563458\pi$
$823$	1.19915e10	−	2.07699e10i	0.749851	−	1.29878i	0.947894	−	0.318587i	$-0.103208\pi$
$824$		0			0
$825$	−3.74729e9	+	9.28262e9i	−0.232343	+	0.575548i
$826$		0			0
$827$	−2.24793e10			−1.38202			−0.691010	−	0.722845i	$-0.742834\pi$
$827$	−2.24793e10			−1.38202			−0.691010	+	0.722845i	$0.742834\pi$
$828$		0			0
$829$	1.15292e10			0.702846			0.351423	−	0.936217i	$-0.385698\pi$
$829$	1.15292e10			0.702846			0.351423	+	0.936217i	$0.385698\pi$
$830$		0			0
$831$	−1.46190e10	−	1.87003e10i	−0.883718	−	1.13043i
$832$		0			0
$833$	1.20445e9	−	2.08617e9i	0.0721992	−	0.125053i
$834$		0			0
$835$	−9.32355e8	−	1.61489e9i	−0.0554216	−	0.0959930i
$836$		0			0
$837$	3.02872e9	−	2.90592e10i	0.178534	−	1.71295i
$838$		0			0
$839$	−1.47830e9	−	2.56048e9i	−0.0864160	−	0.149677i	0.819578	−	0.572968i	$-0.194208\pi$
$839$	−1.47830e9	−	2.56048e9i	−0.0864160	−	0.149677i	−0.905994	+	0.423291i	$0.860875\pi$
$840$		0			0
$841$	−1.77173e9	+	3.06873e9i	−0.102710	+	0.177899i
$842$		0			0
$843$	−1.92457e10	−	2.46186e10i	−1.10646	−	1.41536i
$844$		0			0
$845$	4.03390e7			0.00229999
$846$		0			0
$847$	3.44924e9			0.195044
$848$		0			0
$849$	9.57195e9	−	2.37112e10i	0.536814	−	1.32977i
$850$		0			0
$851$	1.06399e10	−	1.84288e10i	0.591811	−	1.02505i
$852$		0			0
$853$	−2.92234e9	−	5.06165e9i	−0.161217	−	0.279235i	0.774089	−	0.633077i	$-0.218208\pi$
$853$	−2.92234e9	−	5.06165e9i	−0.161217	−	0.279235i	−0.935305	+	0.353842i	$0.884875\pi$
$854$		0			0
$855$	−6.76782e8	+	2.72114e9i	−0.0370312	+	0.148891i
$856$		0			0
$857$	4.52864e9	+	7.84383e9i	0.245773	+	0.425692i	0.962349	−	0.271818i	$-0.0876248\pi$
$857$	4.52864e9	+	7.84383e9i	0.245773	+	0.425692i	−0.716575	+	0.697510i	$0.754291\pi$
$858$		0			0
$859$	−1.15273e10	+	1.99658e10i	−0.620513	+	1.07476i	0.368878	+	0.929478i	$0.379742\pi$
$859$	−1.15273e10	+	1.99658e10i	−0.620513	+	1.07476i	−0.989390	+	0.145281i	$0.953591\pi$
$860$		0			0
$861$	2.12824e9	−	2.99734e8i	0.113635	−	0.0160039i
$862$		0			0
$863$	−1.98186e10			−1.04963			−0.524814	−	0.851217i	$-0.675865\pi$
$863$	−1.98186e10			−1.04963			−0.524814	+	0.851217i	$0.675865\pi$
$864$		0			0
$865$	1.09722e10			0.576416
$866$		0			0
$867$	−4.12251e8	+	5.80598e7i	−0.0214830	+	0.00302558i
$868$		0			0
$869$	−2.16449e9	+	3.74901e9i	−0.111889	+	0.193797i
$870$		0			0
$871$	−6.39713e9	−	1.10802e10i	−0.328036	−	0.568175i
$872$		0			0
$873$	−8.21864e9	−	7.92746e9i	−0.418071	−	0.403259i
$874$		0			0
$875$	−2.32669e9	−	4.02994e9i	−0.117411	−	0.203362i
$876$		0			0
$877$	9.39734e9	−	1.62767e10i	0.470442	−	0.814830i	−0.528986	−	0.848630i	$-0.677428\pi$
$877$	9.39734e9	−	1.62767e10i	0.470442	−	0.814830i	0.999429	+	0.0338006i	$0.0107611\pi$
$878$		0			0
$879$	1.46556e10	−	3.63042e10i	0.727851	−	1.80300i
$880$		0			0
$881$	−6.78319e9			−0.334209			−0.167104	−	0.985939i	$-0.553442\pi$
$881$	−6.78319e9			−0.334209			−0.167104	+	0.985939i	$0.553442\pi$
$882$		0			0
$883$	−2.48178e10			−1.21311			−0.606556	−	0.795041i	$-0.707449\pi$
$883$	−2.48178e10			−1.21311			−0.606556	+	0.795041i	$0.707449\pi$
$884$		0			0
$885$	−2.36612e9	−	3.02668e9i	−0.114745	−	0.146780i
$886$		0			0
$887$	−4.96331e9	+	8.59670e9i	−0.238802	+	0.413618i	−0.960371	−	0.278725i	$-0.910088\pi$
$887$	−4.96331e9	+	8.59670e9i	−0.238802	+	0.413618i	0.721569	+	0.692343i	$0.243421\pi$
$888$		0			0
$889$	7.89735e8	+	1.36786e9i	0.0376986	+	0.0652959i
$890$		0			0
$891$	−1.29772e10	−	6.88082e9i	−0.614622	−	0.325888i
$892$		0			0
$893$	6.49317e8	+	1.12465e9i	0.0305124	+	0.0528490i
$894$		0			0
$895$	−5.77699e9	+	1.00060e10i	−0.269352	+	0.466532i
$896$		0			0
$897$	−1.31999e10	−	1.68850e10i	−0.610658	−	0.781140i
$898$		0			0
$899$	−4.11926e10			−1.89086
$900$		0			0
$901$	1.56629e10			0.713403
$902$		0			0
$903$	7.17138e8	−	1.77646e9i	0.0324112	−	0.0802876i
$904$		0			0
$905$	8.26819e8	−	1.43209e9i	0.0370801	−	0.0642245i
$906$		0			0
$907$	−2.68556e9	−	4.65153e9i	−0.119512	−	0.207000i	0.800063	−	0.599916i	$-0.204800\pi$
$907$	−2.68556e9	−	4.65153e9i	−0.119512	−	0.207000i	−0.919574	+	0.392916i	$0.871466\pi$
$908$		0			0
$909$	−1.79356e10	−	1.73001e10i	−0.792030	−	0.763968i
$910$		0			0
$911$	1.88958e10	+	3.27286e10i	0.828041	+	1.43421i	0.899573	+	0.436771i	$0.143878\pi$
$911$	1.88958e10	+	3.27286e10i	0.828041	+	1.43421i	−0.0715316	+	0.997438i	$0.522789\pi$
$912$		0			0
$913$	2.89519e9	−	5.01462e9i	0.125901	−	0.218067i
$914$		0			0
$915$	−9.10433e9	+	1.28222e9i	−0.392893	+	0.0553335i
$916$		0			0
$917$	6.21260e9			0.266061
$918$		0			0
$919$	6.91679e9			0.293968			0.146984	−	0.989139i	$-0.453043\pi$
$919$	6.91679e9			0.293968			0.146984	+	0.989139i	$0.453043\pi$
$920$		0			0
$921$	3.06863e10	−	4.32174e9i	1.29430	−	0.182284i
$922$		0			0
$923$	−9.97929e9	+	1.72846e10i	−0.417728	+	0.723527i
$924$		0			0
$925$	1.28635e10	+	2.22802e10i	0.534395	+	0.925600i
$926$		0			0
$927$	7.28116e9	−	2.92754e10i	0.300208	−	1.20704i
$928$		0			0
$929$	2.00263e10	+	3.46865e10i	0.819493	+	1.41940i	0.906056	+	0.423158i	$0.139078\pi$
$929$	2.00263e10	+	3.46865e10i	0.819493	+	1.41940i	−0.0865629	+	0.996246i	$0.527588\pi$
$930$		0			0
$931$	−8.21816e8	+	1.42343e9i	−0.0333773	+	0.0578111i
$932$		0			0
$933$	−8.24331e9	+	2.04199e10i	−0.332289	+	0.823131i
$934$		0			0
$935$	−5.77073e9			−0.230882
$936$		0			0
$937$	−9.65701e9			−0.383490			−0.191745	−	0.981445i	$-0.561415\pi$
$937$	−9.65701e9			−0.383490			−0.191745	+	0.981445i	$0.561415\pi$
$938$		0			0
$939$	1.51554e10	+	1.93864e10i	0.597361	+	0.764131i
$940$		0			0
$941$	7.95833e9	−	1.37842e10i	0.311357	−	0.539286i	−0.667300	−	0.744789i	$-0.732550\pi$
$941$	7.95833e9	−	1.37842e10i	0.311357	−	0.539286i	0.978656	+	0.205504i	$0.0658833\pi$
$942$		0			0
$943$	3.86246e9	+	6.68998e9i	0.149994	+	0.259797i
$944$		0			0
$945$	2.94000e9	−	1.31203e9i	0.113328	−	0.0505748i
$946$		0			0
$947$	−7.35634e9	−	1.27415e10i	−0.281473	−	0.487525i	0.690275	−	0.723547i	$-0.257490\pi$
$947$	−7.35634e9	−	1.27415e10i	−0.281473	−	0.487525i	−0.971748	+	0.236022i	$0.924156\pi$
$948$		0			0
$949$	1.57108e10	−	2.72119e10i	0.596715	−	1.03354i
$950$		0			0
$951$	1.82176e10	+	2.33036e10i	0.686848	+	0.878600i
$952$		0			0
$953$	−3.95979e10			−1.48200			−0.740998	−	0.671507i	$-0.765647\pi$
$953$	−3.95979e10			−1.48200			−0.740998	+	0.671507i	$0.765647\pi$
$954$		0			0
$955$	7.63335e9			0.283598
$956$		0			0
$957$	−7.75231e9	+	1.92036e10i	−0.285917	+	0.708259i
$958$		0			0
$959$	−1.04744e9	+	1.81422e9i	−0.0383500	+	0.0664241i
$960$		0			0
$961$	−2.70458e10	−	4.68448e10i	−0.983034	−	1.70267i
$962$		0			0
$963$	−2.50542e10	+	7.19987e9i	−0.904040	+	0.259796i
$964$		0			0
$965$	6.24561e9	+	1.08177e10i	0.223733	+	0.387516i
$966$		0			0
$967$	6.55024e9	−	1.13454e10i	0.232951	−	0.403483i	−0.725724	−	0.687986i	$-0.758495\pi$
$967$	6.55024e9	−	1.13454e10i	0.232951	−	0.403483i	0.958675	+	0.284503i	$0.0918285\pi$
$968$		0			0
$969$	1.32467e10	−	1.86561e9i	0.467708	−	0.0658701i
$970$		0			0
$971$	−9.57880e9			−0.335771			−0.167886	−	0.985806i	$-0.553694\pi$
$971$	−9.57880e9			−0.335771			−0.167886	+	0.985806i	$0.553694\pi$
$972$		0			0
$973$	6.13455e9			0.213495
$974$		0			0
$975$	2.56582e10	−	3.61360e9i	0.886563	−	0.124860i
$976$		0			0
$977$	2.68959e10	−	4.65851e10i	0.922689	−	1.59814i	0.127452	−	0.991845i	$-0.459320\pi$
$977$	2.68959e10	−	4.65851e10i	0.922689	−	1.59814i	0.795237	−	0.606299i	$-0.207347\pi$
$978$		0			0
$979$	8.62137e9	+	1.49327e10i	0.293655	+	0.508625i
$980$		0			0
$981$	−3.64277e10	+	1.04683e10i	−1.23194	+	0.354025i
$982$		0			0
$983$	4.40275e9	+	7.62578e9i	0.147838	+	0.256063i	0.930428	−	0.366474i	$-0.119435\pi$
$983$	4.40275e9	+	7.62578e9i	0.147838	+	0.256063i	−0.782590	+	0.622537i	$0.786102\pi$
$984$		0			0
$985$	9.38644e9	−	1.62578e10i	0.312949	−	0.542044i
$986$		0			0
$987$	5.58152e8	−	1.38263e9i	0.0184775	−	0.0457715i
$988$		0			0
$989$	6.88568e9			0.226339
$990$		0			0
$991$	8.12712e9			0.265264			0.132632	−	0.991165i	$-0.457657\pi$
$991$	8.12712e9			0.265264			0.132632	+	0.991165i	$0.457657\pi$
$992$		0			0
$993$	4.65665e9	+	5.95668e9i	0.150921	+	0.193055i
$994$		0			0
$995$	−1.95704e9	+	3.38968e9i	−0.0629822	+	0.109088i
$996$		0			0
$997$	1.12329e10	+	1.94559e10i	0.358970	+	0.621755i	0.987789	−	0.155797i	$-0.0497946\pi$
$997$	1.12329e10	+	1.94559e10i	0.358970	+	0.621755i	−0.628819	+	0.777552i	$0.716461\pi$
$998$		0			0
$999$	−3.44727e10	+	1.53841e10i	−1.09395	+	0.488195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.8.j.b.85.1	✓	42
9.7	even	3	inner	252.8.j.b.169.1	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.8.j.b.85.1	✓	42	1.1	even	1	trivial
252.8.j.b.169.1	yes	42	9.7	even	3	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	252.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-46.3084 + 6.52189i) q^{3} +(-45.8869 + 79.4784i) q^{5} +(171.500 + 297.047i) q^{7} +(2101.93 - 604.036i) q^{9} +(-1535.50 - 2659.57i) q^{11} +(-3974.55 + 6884.12i) q^{13} +(1606.60 - 3979.78i) q^{15} -20475.4 q^{17} +13970.6 q^{19} +(-9879.19 - 12637.2i) q^{21} +(28826.8 - 49929.5i) q^{23} +(34851.3 + 60364.2i) q^{25} +(-93397.5 + 41680.5i) q^{27} +(72099.5 + 124880. i) q^{29} +(-142832. + 247393. i) q^{31} +(88452.0 + 113146. i) q^{33} -31478.4 q^{35} +369096. q^{37} +(139157. - 344714. i) q^{39} +(-66994.3 + 116038. i) q^{41} +(59715.9 + 103431. i) q^{43} +(-48443.1 + 194775. i) q^{45} +(46477.2 + 80500.9i) q^{47} +(-58824.5 + 101887. i) q^{49} +(948181. - 133538. i) q^{51} -764962. q^{53} +281838. q^{55} +(-646958. + 91115.0i) q^{57} +(447569. - 775213. i) q^{59} +(-1.07113e6 - 1.85524e6i) q^{61} +(539908. + 520779. i) q^{63} +(-364759. - 631781. i) q^{65} +(-804762. + 1.39389e6i) q^{67} +(-1.00929e6 + 2.50016e6i) q^{69} +2.51080e6 q^{71} -3.95286e6 q^{73} +(-2.00760e6 - 2.56807e6i) q^{75} +(526677. - 912232. i) q^{77} +(-704815. - 1.22078e6i) q^{79} +(4.05325e6 - 2.53928e6i) q^{81} +(942751. + 1.63289e6i) q^{83} +(939551. - 1.62735e6i) q^{85} +(-4.15326e6 - 5.31276e6i) q^{87} -5.61469e6 q^{89} -2.72654e6 q^{91} +(5.00086e6 - 1.23879e7i) q^{93} +(-641069. + 1.11036e6i) q^{95} +(-2.61063e6 - 4.52174e6i) q^{97} +(-4.83399e6 - 4.66273e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 82 q^{3} + 179 q^{5} + 7203 q^{7} + 890 q^{9} + 3958 q^{11} - 6177 q^{13} + 20077 q^{15} + 22036 q^{17} + 2094 q^{19} + 686 q^{21} + 91390 q^{23} - 284160 q^{25} - 16247 q^{27} + 180179 q^{29} + 99327 q^{31}+ \cdots - 61176680 q^{99}+O(q^{100}) \) 42 * q + 82 * q^3 + 179 * q^5 + 7203 * q^7 + 890 * q^9 + 3958 * q^11 - 6177 * q^13 + 20077 * q^15 + 22036 * q^17 + 2094 * q^19 + 686 * q^21 + 91390 * q^23 - 284160 * q^25 - 16247 * q^27 + 180179 * q^29 + 99327 * q^31 + 175070 * q^33 + 122794 * q^35 - 151782 * q^37 - 8736 * q^39 - 59940 * q^41 + 360321 * q^43 + 357467 * q^45 + 1348899 * q^47 - 2470629 * q^49 - 1657207 * q^51 + 1010028 * q^53 - 1105080 * q^55 - 1937515 * q^57 - 458041 * q^59 - 1085874 * q^61 - 949424 * q^63 - 1175811 * q^65 + 384222 * q^67 + 3999311 * q^69 - 4838366 * q^71 - 1822650 * q^73 - 1387237 * q^75 - 1357594 * q^77 + 238365 * q^79 - 17003890 * q^81 + 1228174 * q^83 + 356127 * q^85 + 33054031 * q^87 + 34786068 * q^89 - 4237422 * q^91 - 1689051 * q^93 - 12321596 * q^95 + 926001 * q^97 - 61176680 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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