LMFDB - Embedded newform 99.8.f.a.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, 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:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Character	$\chi$	$=$	99.91
Dual form			99.8.f.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.83171 + 5.69007i) q^{2} +(-10.5954 + 32.6093i) q^{4} +(-9.68480 - 7.03642i) q^{5} +(520.681 - 1602.49i) q^{7} +(-485.474 - 1494.14i) q^{8} +O(q^{10})$	\(q+(-7.83171 + 5.69007i) q^{2} +(-10.5954 + 32.6093i) q^{4} +(-9.68480 - 7.03642i) q^{5} +(520.681 - 1602.49i) q^{7} +(-485.474 - 1494.14i) q^{8} +115.886 q^{10} +(-1180.96 + 4253.53i) q^{11} +(-1165.28 + 846.624i) q^{13} +(5040.47 + 15513.0i) q^{14} +(8753.22 + 6359.59i) q^{16} +(4288.90 + 3116.07i) q^{17} +(5051.18 + 15545.9i) q^{19} +(332.067 - 241.261i) q^{20} +(-14953.9 - 40032.1i) q^{22} +15294.8 q^{23} +(-24097.7 - 74165.0i) q^{25} +(4308.77 - 13261.0i) q^{26} +(46739.3 + 33958.1i) q^{28} +(-34293.0 + 105543. i) q^{29} +(-103156. + 74946.9i) q^{31} +96352.3 q^{32} -51320.1 q^{34} +(-16318.5 + 11856.1i) q^{35} +(-147498. + 453952. i) q^{37} +(-128017. - 93009.6i) q^{38} +(-5811.65 + 17886.4i) q^{40} +(-30396.4 - 93550.4i) q^{41} -356722. q^{43} +(-126192. - 83578.1i) q^{44} +(-119784. + 87028.3i) q^{46} +(-337944. - 1.04008e6i) q^{47} +(-1.63061e6 - 1.18471e6i) q^{49} +(610730. + 443721. i) q^{50} +(-15261.2 - 46969.2i) q^{52} +(-793185. + 576282. i) q^{53} +(41367.0 - 32884.8i) q^{55} -2.64712e6 q^{56} +(-331974. - 1.02171e6i) q^{58} +(-553410. + 1.70322e6i) q^{59} +(208208. + 151272. i) q^{61} +(381431. - 1.17392e6i) q^{62} +(-1.87502e6 + 1.36228e6i) q^{64} +17242.7 q^{65} +175696. q^{67} +(-147056. + 106842. i) q^{68} +(60339.8 - 185707. i) q^{70} +(-648524. - 471181. i) q^{71} +(875594. - 2.69480e6i) q^{73} +(-1.42786e6 - 4.39449e6i) q^{74} -560461. q^{76} +(6.20134e6 + 4.10721e6i) q^{77} +(-5.16160e6 + 3.75012e6i) q^{79} +(-40024.5 - 123183. i) q^{80} +(770364. + 559702. i) q^{82} +(2.14752e6 + 1.56027e6i) q^{83} +(-19611.2 - 60357.0i) q^{85} +(2.79374e6 - 2.02977e6i) q^{86} +(6.92868e6 - 300465. i) q^{88} -7.10000e6 q^{89} +(749970. + 2.30817e6i) q^{91} +(-162054. + 498752. i) q^{92} +(8.56483e6 + 6.22271e6i) q^{94} +(60468.0 - 186101. i) q^{95} +(3.30212e6 - 2.39913e6i) q^{97} +1.95116e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 505 q^{4} + 72 q^{5} + 68 q^{7} + 4545 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 505 * q^4 + 72 * q^5 + 68 * q^7 + 4545 * q^8	\( 24 q - 3 q^{2} - 505 q^{4} + 72 q^{5} + 68 q^{7} + 4545 q^{8} + 4240 q^{10} - 5952 q^{11} - 16564 q^{13} + 29544 q^{14} + 13279 q^{16} + 65592 q^{17} - 37804 q^{19} - 120702 q^{20} + 246233 q^{22} + 26304 q^{23} - 210646 q^{25} + 336384 q^{26} + 92334 q^{28} + 231048 q^{29} + 141004 q^{31} + 260892 q^{32} + 1512162 q^{34} + 342588 q^{35} - 836112 q^{37} + 2387040 q^{38} - 1906028 q^{40} - 1930344 q^{41} + 2877456 q^{43} - 5822808 q^{44} - 4951876 q^{46} + 2462532 q^{47} - 6581826 q^{49} + 2698797 q^{50} + 1655498 q^{52} - 6157836 q^{53} + 11721612 q^{55} - 11431080 q^{56} - 15150140 q^{58} + 2480268 q^{59} - 4195044 q^{61} + 6436524 q^{62} + 11301151 q^{64} - 11117640 q^{65} + 16682528 q^{67} + 14718306 q^{68} - 16625944 q^{70} + 20942628 q^{71} - 456824 q^{73} - 8747736 q^{74} + 18091206 q^{76} - 13904988 q^{77} - 12976692 q^{79} + 11893596 q^{80} - 32706099 q^{82} + 4471404 q^{83} + 25528128 q^{85} - 20374383 q^{86} + 25246815 q^{88} + 2477316 q^{89} - 18339604 q^{91} - 1026678 q^{92} - 4961738 q^{94} + 25328772 q^{95} - 34034202 q^{97} + 51534036 q^{98}+O(q^{100}) \) 24 * q - 3 * q^2 - 505 * q^4 + 72 * q^5 + 68 * q^7 + 4545 * q^8 + 4240 * q^10 - 5952 * q^11 - 16564 * q^13 + 29544 * q^14 + 13279 * q^16 + 65592 * q^17 - 37804 * q^19 - 120702 * q^20 + 246233 * q^22 + 26304 * q^23 - 210646 * q^25 + 336384 * q^26 + 92334 * q^28 + 231048 * q^29 + 141004 * q^31 + 260892 * q^32 + 1512162 * q^34 + 342588 * q^35 - 836112 * q^37 + 2387040 * q^38 - 1906028 * q^40 - 1930344 * q^41 + 2877456 * q^43 - 5822808 * q^44 - 4951876 * q^46 + 2462532 * q^47 - 6581826 * q^49 + 2698797 * q^50 + 1655498 * q^52 - 6157836 * q^53 + 11721612 * q^55 - 11431080 * q^56 - 15150140 * q^58 + 2480268 * q^59 - 4195044 * q^61 + 6436524 * q^62 + 11301151 * q^64 - 11117640 * q^65 + 16682528 * q^67 + 14718306 * q^68 - 16625944 * q^70 + 20942628 * q^71 - 456824 * q^73 - 8747736 * q^74 + 18091206 * q^76 - 13904988 * q^77 - 12976692 * q^79 + 11893596 * q^80 - 32706099 * q^82 + 4471404 * q^83 + 25528128 * q^85 - 20374383 * q^86 + 25246815 * q^88 + 2477316 * q^89 - 18339604 * q^91 - 1026678 * q^92 - 4961738 * q^94 + 25328772 * q^95 - 34034202 * q^97 + 51534036 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−7.83171	+	5.69007i	−0.692232	+	0.502936i	−0.877393	−	0.479772i	$-0.840719\pi$
$2$	−7.83171	+	5.69007i	−0.692232	+	0.502936i	0.185161	+	0.982708i	$0.440719\pi$
$3$		0			0
$3$		0			0
$4$	−10.5954	+	32.6093i	−0.0827766	+	0.254760i
$5$	−9.68480	−	7.03642i	−0.0346494	−	0.0251743i	0.570326	−	0.821419i	$-0.306817\pi$
$5$	−9.68480	−	7.03642i	−0.0346494	−	0.0251743i	−0.604975	+	0.796244i	$0.706817\pi$
$6$		0			0
$7$	520.681	−	1602.49i	0.573758	−	1.76585i	−0.0666109	−	0.997779i	$-0.521219\pi$
$7$	520.681	−	1602.49i	0.573758	−	1.76585i	0.640369	−	0.768067i	$-0.278781\pi$
$8$	−485.474	−	1494.14i	−0.335236	−	1.03175i
$9$		0			0
$10$	115.886			0.0366464
$11$	−1180.96	+	4253.53i	−0.267523	+	0.963552i
$11$	−1180.96	+	4253.53i	−0.267523	+	0.963552i
$12$		0			0
$13$	−1165.28	+	846.624i	−0.147105	+	0.106878i	−0.658904	−	0.752227i	$-0.728979\pi$
$13$	−1165.28	+	846.624i	−0.147105	+	0.106878i	0.511798	+	0.859106i	$0.328979\pi$
$14$	5040.47	+	15513.0i	0.490934	+	1.51094i
$15$		0			0
$16$	8753.22	+	6359.59i	0.534254	+	0.388159i
$17$	4288.90	+	3116.07i	0.211726	+	0.153828i	0.688594	−	0.725147i	$-0.258228\pi$
$17$	4288.90	+	3116.07i	0.211726	+	0.153828i	−0.476868	+	0.878975i	$0.658228\pi$
$18$		0			0
$19$	5051.18	+	15545.9i	0.168949	+	0.519971i	0.999306	−	0.0372614i	$-0.0118634\pi$
$19$	5051.18	+	15545.9i	0.168949	+	0.519971i	−0.830357	+	0.557232i	$0.811863\pi$
$20$	332.067	−	241.261i	0.00928155	−	0.00674344i
$21$		0			0
$22$	−14953.9	−	40032.1i	−0.299417	−	0.801548i
$23$	15294.8			0.262117			0.131059	−	0.991375i	$-0.458162\pi$
$23$	15294.8			0.262117			0.131059	+	0.991375i	$0.458162\pi$
$24$		0			0
$25$	−24097.7	−	74165.0i	−0.308450	−	0.949312i
$26$	4308.77	−	13261.0i	0.0480780	−	0.147969i
$27$		0			0
$28$	46739.3	+	33958.1i	0.402373	+	0.292341i
$29$	−34293.0	+	105543.i	−0.261103	+	0.803593i	0.731462	+	0.681882i	$0.238838\pi$
$29$	−34293.0	+	105543.i	−0.261103	+	0.803593i	−0.992566	+	0.121711i	$0.961162\pi$
$30$		0			0
$31$	−103156.	+	74946.9i	−0.621909	+	0.451843i	−0.853588	−	0.520949i	$-0.825578\pi$
$31$	−103156.	+	74946.9i	−0.621909	+	0.451843i	0.231679	+	0.972792i	$0.425578\pi$
$32$	96352.3			0.519801
$33$		0			0
$34$	−51320.1			−0.223930
$35$	−16318.5	+	11856.1i	−0.0643342	+	0.0467416i
$36$		0			0
$37$	−147498.	+	453952.i	−0.478718	+	1.47334i	0.362159	+	0.932116i	$0.382040\pi$
$37$	−147498.	+	453952.i	−0.478718	+	1.47334i	−0.840877	+	0.541226i	$0.817960\pi$
$38$	−128017.	−	93009.6i	−0.378464	−	0.274970i
$39$		0			0
$40$	−5811.65	+	17886.4i	−0.0143578	+	0.0441889i
$41$	−30396.4	−	93550.4i	−0.0688777	−	0.211984i	0.910693	−	0.413084i	$-0.135548\pi$
$41$	−30396.4	−	93550.4i	−0.0688777	−	0.211984i	−0.979571	+	0.201100i	$0.935548\pi$
$42$		0			0
$43$	−356722.			−0.684211			−0.342106	−	0.939662i	$-0.611140\pi$
$43$	−356722.			−0.684211			−0.342106	+	0.939662i	$0.611140\pi$
$44$	−126192.	−	83578.1i	−0.223330	−	0.147914i
$45$		0			0
$46$	−119784.	+	87028.3i	−0.181446	+	0.131828i
$47$	−337944.	−	1.04008e6i	−0.474790	−	1.46125i	−0.846240	−	0.532801i	$-0.821139\pi$
$47$	−337944.	−	1.04008e6i	−0.474790	−	1.46125i	0.371450	−	0.928453i	$-0.378861\pi$
$48$		0			0
$49$	−1.63061e6	−	1.18471e6i	−1.98000	−	1.43855i
$50$	610730.	+	443721.i	0.690962	+	0.502013i
$51$		0			0
$52$	−15261.2	−	46969.2i	−0.0150514	−	0.0463235i
$53$	−793185.	+	576282.i	−0.731828	+	0.531704i	−0.890141	−	0.455685i	$-0.849394\pi$
$53$	−793185.	+	576282.i	−0.731828	+	0.531704i	0.158314	+	0.987389i	$0.449394\pi$
$54$		0			0
$55$	41367.0	−	32884.8i	0.0335262	−	0.0266518i
$56$	−2.64712e6			−2.01426
$57$		0			0
$58$	−331974.	−	1.02171e6i	−0.223412	−	0.687591i
$59$	−553410.	+	1.70322e6i	−0.350805	+	1.07967i	0.607598	+	0.794245i	$0.292133\pi$
$59$	−553410.	+	1.70322e6i	−0.350805	+	1.07967i	−0.958402	+	0.285421i	$0.907867\pi$
$60$		0			0
$61$	208208.	+	151272.i	0.117447	+	0.0853306i	0.644958	−	0.764218i	$-0.276875\pi$
$61$	208208.	+	151272.i	0.117447	+	0.0853306i	−0.527511	+	0.849548i	$0.676875\pi$
$62$	381431.	−	1.17392e6i	0.203257	−	0.625561i
$63$		0			0
$64$	−1.87502e6	+	1.36228e6i	−0.894077	+	0.649585i
$65$	17242.7			0.00778768
$66$		0			0
$67$	175696.			0.0713674			0.0356837	−	0.999363i	$-0.488639\pi$
$67$	175696.			0.0713674			0.0356837	+	0.999363i	$0.488639\pi$
$68$	−147056.	+	106842.i	−0.0567153	+	0.0412061i
$69$		0			0
$70$	60339.8	−	185707.i	0.0210262	−	0.0647120i
$71$	−648524.	−	471181.i	−0.215041	−	0.156237i	0.475050	−	0.879959i	$-0.342430\pi$
$71$	−648524.	−	471181.i	−0.215041	−	0.156237i	−0.690092	+	0.723722i	$0.742430\pi$
$72$		0			0
$73$	875594.	−	2.69480e6i	0.263435	−	0.810769i	−0.728615	−	0.684923i	$-0.759836\pi$
$73$	875594.	−	2.69480e6i	0.263435	−	0.810769i	0.992050	−	0.125845i	$-0.0401643\pi$
$74$	−1.42786e6	−	4.39449e6i	−0.409613	−	1.26066i
$75$		0			0
$76$	−560461.			−0.146453
$77$	6.20134e6	+	4.10721e6i	1.54799	+	1.02525i
$78$		0			0
$79$	−5.16160e6	+	3.75012e6i	−1.17785	+	0.855757i	−0.991927	−	0.126808i	$-0.959527\pi$
$79$	−5.16160e6	+	3.75012e6i	−1.17785	+	0.855757i	−0.185921	+	0.982565i	$0.559527\pi$
$80$	−40024.5	−	123183.i	−0.00873999	−	0.0268989i
$81$		0			0
$82$	770364.	+	559702.i	0.154293	+	0.112101i
$83$	2.14752e6	+	1.56027e6i	0.412254	+	0.299520i	0.774514	−	0.632557i	$-0.217995\pi$
$83$	2.14752e6	+	1.56027e6i	0.412254	+	0.299520i	−0.362260	+	0.932077i	$0.617995\pi$
$84$		0			0
$85$	−19611.2	−	60357.0i	−0.00346368	−	0.0106601i
$86$	2.79374e6	−	2.02977e6i	0.473633	−	0.344114i
$87$		0			0
$88$	6.92868e6	−	300465.i	1.08383	−	0.0470007i
$89$	−7.10000e6			−1.06756			−0.533782	−	0.845622i	$-0.679230\pi$
$89$	−7.10000e6			−1.06756			−0.533782	+	0.845622i	$0.679230\pi$
$90$		0			0
$91$	749970.	+	2.30817e6i	0.104328	+	0.321087i
$92$	−162054.	+	498752.i	−0.0216972	+	0.0667770i
$93$		0			0
$94$	8.56483e6	+	6.22271e6i	1.06358	+	0.772738i
$95$	60468.0	−	186101.i	0.00723590	−	0.0222698i
$96$		0			0
$97$	3.30212e6	−	2.39913e6i	0.367360	−	0.266903i	−0.388755	−	0.921341i	$-0.627095\pi$
$97$	3.30212e6	−	2.39913e6i	0.367360	−	0.266903i	0.756115	+	0.654438i	$0.227095\pi$
$98$	1.95116e7			2.09412
$99$		0			0
$100$	2.67379e6			0.267379
$101$	−5.20732e6	+	3.78334e6i	−0.502909	+	0.365385i	−0.810127	−	0.586254i	$-0.800602\pi$
$101$	−5.20732e6	+	3.78334e6i	−0.502909	+	0.365385i	0.307218	+	0.951639i	$0.400602\pi$
$102$		0			0
$103$	−3.67151e6	+	1.12997e7i	−0.331066	+	1.01892i	0.637562	+	0.770399i	$0.279943\pi$
$103$	−3.67151e6	+	1.12997e7i	−0.331066	+	1.01892i	−0.968628	+	0.248516i	$0.920057\pi$
$104$	1.83068e6	+	1.33007e6i	0.159587	+	0.115947i
$105$		0			0
$106$	2.93290e6	−	9.02655e6i	0.239181	−	0.736125i
$107$	3.15155e6	+	9.69948e6i	0.248703	+	0.765430i	0.995005	+	0.0998224i	$0.0318275\pi$
$107$	3.15155e6	+	9.69948e6i	0.248703	+	0.765430i	−0.746302	+	0.665607i	$0.768173\pi$
$108$		0			0
$109$	9.27437e6			0.685949			0.342974	−	0.939345i	$-0.388566\pi$
$109$	9.27437e6			0.685949			0.342974	+	0.939345i	$0.388566\pi$
$110$	−136857.	+	492925.i	−0.00980375	+	0.0353107i
$111$		0			0
$112$	1.47488e7	−	1.07157e7i	0.991961	−	0.720702i
$113$	−3.04904e6	−	9.38399e6i	−0.198787	−	0.611805i	−0.999911	−	0.0133065i	$-0.995764\pi$
$113$	−3.04904e6	−	9.38399e6i	−0.198787	−	0.611805i	0.801124	−	0.598498i	$-0.204236\pi$
$114$		0			0
$115$	−148127.	−	107620.i	−0.00908220	−	0.00659860i
$116$	−3.07833e6	−	2.23654e6i	−0.183110	−	0.133037i
$117$		0			0
$118$	−5.35730e6	−	1.64881e7i	−0.300164	−	0.923811i
$119$	7.22663e6	−	5.25046e6i	0.393117	−	0.285616i
$120$		0			0
$121$	−1.66978e7	−	1.00465e7i	−0.856863	−	0.515544i
$122$	−2.49138e6			−0.124217
$123$		0			0
$124$	−1.35099e6	−	4.15792e6i	−0.0636322	−	0.195840i
$125$	−577480.	+	1.77730e6i	−0.0264455	+	0.0813909i
$126$		0			0
$127$	1.37295e7	+	9.97507e6i	0.594760	+	0.432119i	0.844015	−	0.536319i	$-0.180186\pi$
$127$	1.37295e7	+	9.97507e6i	0.594760	+	0.432119i	−0.249255	+	0.968438i	$0.580186\pi$
$128$	3.12198e6	−	9.60847e6i	0.131582	−	0.404967i
$129$		0			0
$130$	−135040.	+	98112.1i	−0.00539088	+	0.00391670i
$131$	−3.48321e7			−1.35373			−0.676863	−	0.736109i	$-0.736661\pi$
$131$	−3.48321e7			−1.35373			−0.676863	+	0.736109i	$0.736661\pi$
$132$		0			0
$133$	2.75423e7			1.01512
$134$	−1.37600e6	+	999722.i	−0.0494028	+	0.0358932i
$135$		0			0
$136$	2.57368e6	−	7.92098e6i	0.0877342	−	0.270018i
$137$	1.47015e7	+	1.06813e7i	0.488473	+	0.354897i	0.804597	−	0.593821i	$-0.202381\pi$
$137$	1.47015e7	+	1.06813e7i	0.488473	+	0.354897i	−0.316123	+	0.948718i	$0.602381\pi$
$138$		0			0
$139$	−1.47915e7	+	4.55234e7i	−0.467153	+	1.43775i	0.389101	+	0.921195i	$0.372786\pi$
$139$	−1.47915e7	+	4.55234e7i	−0.467153	+	1.43775i	−0.856254	+	0.516554i	$0.827214\pi$
$140$	−213717.	−	657755.i	−0.00658252	−	0.0202589i
$141$		0			0
$142$	7.76010e6			0.227436
$143$	−2.22499e6	−	5.95637e6i	−0.0636286	−	0.170336i
$144$		0			0
$145$	1.07477e6	−	780863.i	0.0292769	−	0.0212709i
$146$	8.47621e6	+	2.60871e7i	0.225407	+	0.693731i
$147$		0			0
$148$	−1.32402e7	−	9.61960e6i	−0.335722	−	0.243916i
$149$	−2.17433e7	−	1.57974e7i	−0.538484	−	0.391231i	0.285038	−	0.958516i	$-0.407994\pi$
$149$	−2.17433e7	−	1.57974e7i	−0.538484	−	0.391231i	−0.823522	+	0.567285i	$0.807994\pi$
$150$		0			0
$151$	1.40308e7	+	4.31822e7i	0.331636	+	1.02067i	0.968355	+	0.249575i	$0.0802910\pi$
$151$	1.40308e7	+	4.31822e7i	0.331636	+	1.02067i	−0.636719	+	0.771096i	$0.719709\pi$
$152$	2.07755e7	−	1.50943e7i	0.479843	−	0.348626i
$153$		0			0
$154$	−7.19375e7	+	3.11959e6i	−1.58720	+	0.0688297i
$155$	1.52640e6			0.0329236
$156$		0			0
$157$	−1.41417e7	−	4.35238e7i	−0.291645	−	0.897590i	−0.984328	−	0.176348i	$-0.943572\pi$
$157$	−1.41417e7	−	4.35238e7i	−0.291645	−	0.897590i	0.692683	−	0.721242i	$-0.256428\pi$
$158$	1.90857e7	−	5.87397e7i	0.384953	−	1.18476i
$159$		0			0
$160$	−933153.	−	677975.i	−0.0180108	−	0.0130856i
$161$	7.96370e6	−	2.45098e7i	0.150392	−	0.462859i
$162$		0			0
$163$	2.66891e7	−	1.93908e7i	0.482701	−	0.350703i	−0.319670	−	0.947529i	$-0.603572\pi$
$163$	2.66891e7	−	1.93908e7i	0.482701	−	0.350703i	0.802370	+	0.596826i	$0.203572\pi$
$164$	3.37268e6			0.0597064
$165$		0			0
$166$	−2.56968e7			−0.436015
$167$	−5.15876e7	+	3.74806e7i	−0.857112	+	0.622729i	−0.927098	−	0.374819i	$-0.877705\pi$
$167$	−5.15876e7	+	3.74806e7i	−0.857112	+	0.622729i	0.0699855	+	0.997548i	$0.477705\pi$
$168$		0			0
$169$	−1.87493e7	+	5.77043e7i	−0.298800	+	0.919612i
$170$	497025.	+	361110.i	0.00775902	+	0.00563726i
$171$		0			0
$172$	3.77961e6	−	1.16324e7i	0.0566367	−	0.174310i
$173$	1.43831e7	+	4.42665e7i	0.211198	+	0.650000i	0.999402	+	0.0345861i	$0.0110113\pi$
$173$	1.43831e7	+	4.42665e7i	0.211198	+	0.650000i	−0.788204	+	0.615414i	$0.788989\pi$
$174$		0			0
$175$	−1.31396e8			−1.85331
$176$	−3.73879e7	+	2.97217e7i	−0.516936	+	0.410940i
$177$		0			0
$178$	5.56052e7	−	4.03995e7i	0.739001	−	0.536916i
$179$	2.95754e7	+	9.10236e7i	0.385429	+	1.18623i	0.936169	+	0.351552i	$0.114346\pi$
$179$	2.95754e7	+	9.10236e7i	0.385429	+	1.18623i	−0.550739	+	0.834677i	$0.685654\pi$
$180$		0			0
$181$	3.42658e7	+	2.48956e7i	0.429523	+	0.312066i	0.781458	−	0.623958i	$-0.214476\pi$
$181$	3.42658e7	+	2.48956e7i	0.429523	+	0.312066i	−0.351935	+	0.936024i	$0.614476\pi$
$182$	−1.90072e7	−	1.38095e7i	−0.233705	−	0.169797i
$183$		0			0
$184$	−7.42522e6	−	2.28525e7i	−0.0878712	−	0.270440i
$185$	4.62268e6	−	3.35857e6i	0.0536776	−	0.0389990i
$186$		0			0
$187$	−1.83193e7	+	1.45630e7i	−0.204863	+	0.162857i
$188$	3.74970e7			0.411571
$189$		0			0
$190$	585362.	+	1.80156e6i	0.00619137	+	0.0190551i
$191$	2.80749e7	−	8.64057e7i	0.291542	−	0.897275i	−0.692819	−	0.721112i	$-0.743631\pi$
$191$	2.80749e7	−	8.64057e7i	0.291542	−	0.897275i	0.984361	−	0.176163i	$-0.0563687\pi$
$192$		0			0
$193$	−1.08150e7	−	7.85757e6i	−0.108287	−	0.0786751i	0.532324	−	0.846541i	$-0.321319\pi$
$193$	−1.08150e7	−	7.85757e6i	−0.108287	−	0.0786751i	−0.640611	+	0.767866i	$0.721319\pi$
$194$	−1.22100e7	+	3.75786e7i	−0.120063	+	0.369517i
$195$		0			0
$196$	5.59096e7	−	4.06207e7i	0.530383	−	0.385346i
$197$	−1.08300e8			−1.00924			−0.504622	−	0.863340i	$-0.668368\pi$
$197$	−1.08300e8			−1.00924			−0.504622	+	0.863340i	$0.668368\pi$
$198$		0			0
$199$	−5.07125e7			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$199$	−5.07125e7			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$200$	−9.91138e7	+	7.20104e7i	−0.876050	+	0.636488i
$201$		0			0
$202$	1.92547e7	−	5.92600e7i	0.164364	−	0.505862i
$203$	1.51276e8	+	1.09909e8i	1.26921	+	0.922137i
$204$		0			0
$205$	−363877.	+	1.11990e6i	−0.00294996	+	0.00907905i
$206$	−3.55421e7	−	1.09387e8i	−0.283275	−	0.871831i
$207$		0			0
$208$	−1.55841e7			−0.120077
$209$	−7.20903e7	+	3.12622e6i	−0.546216	+	0.0236869i
$210$		0			0
$211$	−9.59432e7	+	6.97068e7i	−0.703114	+	0.510842i	−0.880945	−	0.473219i	$-0.843092\pi$
$211$	−9.59432e7	+	6.97068e7i	−0.703114	+	0.510842i	0.177831	+	0.984061i	$0.443092\pi$
$212$	−1.03881e7	−	3.19711e7i	−0.0748787	−	0.230453i
$213$		0			0
$214$	−7.98728e7	−	5.80310e7i	−0.557122	−	0.404773i
$215$	3.45478e6	+	2.51004e6i	0.0237075	+	0.0172245i
$216$		0			0
$217$	6.63907e7	+	2.04330e8i	0.441060	+	1.35744i
$218$	−7.26342e7	+	5.27718e7i	−0.474836	+	0.344988i
$219$		0			0
$220$	634052.	+	1.69738e6i	0.00401463	+	0.0107473i
$221$	−7.63591e6			−0.0475869
$222$		0			0
$223$	−8.06901e7	−	2.48339e8i	−0.487252	−	1.49961i	−0.828693	−	0.559704i	$-0.810915\pi$
$223$	−8.06901e7	−	2.48339e8i	−0.487252	−	1.49961i	0.341441	−	0.939903i	$-0.389085\pi$
$224$	5.01689e7	−	1.54404e8i	0.298240	−	0.917889i
$225$		0			0
$226$	7.72748e7	+	5.61434e7i	0.445306	+	0.323533i
$227$	8.17966e7	−	2.51744e8i	0.464135	−	1.42846i	−0.395932	−	0.918280i	$-0.629578\pi$
$227$	8.17966e7	−	2.51744e8i	0.464135	−	1.42846i	0.860067	−	0.510181i	$-0.170422\pi$
$228$		0			0
$229$	−5.36082e7	+	3.89487e7i	−0.294990	+	0.214323i	−0.725429	−	0.688297i	$-0.758359\pi$
$229$	−5.36082e7	+	3.89487e7i	−0.294990	+	0.214323i	0.430439	+	0.902620i	$0.358359\pi$
$230$	1.77245e6			0.00960566
$231$		0			0
$232$	1.74344e8			0.916640
$233$	−2.40517e7	+	1.74746e7i	−0.124566	+	0.0905024i	−0.648324	−	0.761365i	$-0.724530\pi$
$233$	−2.40517e7	+	1.74746e7i	−0.124566	+	0.0905024i	0.523758	+	0.851867i	$0.324530\pi$
$234$		0			0
$235$	−4.04555e6	+	1.24509e7i	−0.0203348	+	0.0625841i
$236$	−4.96773e7	−	3.60926e7i	−0.246017	−	0.178742i
$237$		0			0
$238$	−2.67214e7	+	8.22401e7i	−0.128481	+	0.395425i
$239$	−3.06689e7	−	9.43892e7i	−0.145313	−	0.447229i	0.851738	−	0.523968i	$-0.175549\pi$
$239$	−3.06689e7	−	9.43892e7i	−0.145313	−	0.447229i	−0.997051	+	0.0767397i	$0.975549\pi$
$240$		0			0
$241$	1.04295e8			0.479959			0.239980	−	0.970778i	$-0.422859\pi$
$241$	1.04295e8			0.479959			0.239980	+	0.970778i	$0.422859\pi$
$242$	1.87938e8	−	1.63307e7i	0.852433	−	0.0740715i
$243$		0			0
$244$	−7.13893e6	+	5.18674e6i	−0.0314607	+	0.0228576i
$245$	7.45605e6	+	2.29474e7i	0.0323912	+	0.0996899i
$246$		0			0
$247$	−1.90476e7	−	1.38389e7i	−0.0804267	−	0.0584334i
$248$	1.62060e8	+	1.17744e8i	0.674677	+	0.490181i
$249$		0			0
$250$	−5.59031e6	−	1.72052e7i	−0.0226280	−	0.0696417i
$251$	1.18286e8	−	8.59399e7i	0.472146	−	0.343034i	−0.326131	−	0.945324i	$-0.605745\pi$
$251$	1.18286e8	−	8.59399e7i	0.472146	−	0.343034i	0.798277	+	0.602291i	$0.205745\pi$
$252$		0			0
$253$	−1.80625e7	+	6.50567e7i	−0.0701223	+	0.252563i
$254$	−1.64284e8			−0.629040
$255$		0			0
$256$	−6.14502e7	−	1.89124e8i	−0.228920	−	0.704543i
$257$	−9.20672e7	+	2.83354e8i	−0.338329	+	1.04127i	0.626730	+	0.779237i	$0.284393\pi$
$257$	−9.20672e7	+	2.83354e8i	−0.338329	+	1.04127i	−0.965059	+	0.262033i	$0.915607\pi$
$258$		0			0
$259$	6.50655e8	+	4.72728e8i	2.32703	+	1.69068i
$260$	−182693.	+	562272.i	−0.000644637	+	0.00198399i
$261$		0			0
$262$	2.72795e8	−	1.98197e8i	0.937092	−	0.680837i
$263$	2.53813e7			0.0860339			0.0430169	−	0.999074i	$-0.486303\pi$
$263$	2.53813e7			0.0860339			0.0430169	+	0.999074i	$0.486303\pi$
$264$		0			0
$265$	1.17368e7			0.0387426
$266$	−2.15703e8	+	1.56717e8i	−0.702701	+	0.510542i
$267$		0			0
$268$	−1.86157e6	+	5.72932e6i	−0.00590755	+	0.0181816i
$269$	1.61958e8	+	1.17669e8i	0.507306	+	0.368579i	0.811800	−	0.583935i	$-0.198488\pi$
$269$	1.61958e8	+	1.17669e8i	0.507306	+	0.368579i	−0.304495	+	0.952514i	$0.598488\pi$
$270$		0			0
$271$	9.64508e7	−	2.96845e8i	0.294384	−	0.906019i	−0.689044	−	0.724719i	$-0.741969\pi$
$271$	9.64508e7	−	2.96845e8i	0.294384	−	0.906019i	0.983428	−	0.181300i	$-0.0580305\pi$
$272$	1.77248e7	+	5.45513e7i	0.0534060	+	0.164367i
$273$		0			0
$274$	−1.75916e8			−0.516627
$275$	3.43921e8	−	1.49143e7i	0.997228	−	0.0432452i
$276$		0			0
$277$	9.45141e7	−	6.86685e7i	0.267188	−	0.194124i	−0.446122	−	0.894972i	$-0.647195\pi$
$277$	9.45141e7	−	6.86685e7i	0.267188	−	0.194124i	0.713310	+	0.700849i	$0.247195\pi$
$278$	−1.43189e8	−	4.40691e8i	−0.399718	−	1.23020i
$279$		0			0
$280$	2.56368e7	+	1.86262e7i	0.0697929	+	0.0507075i
$281$	4.50717e8	+	3.27465e8i	1.21180	+	0.880425i	0.995393	−	0.0958779i	$-0.0305658\pi$
$281$	4.50717e8	+	3.27465e8i	1.21180	+	0.880425i	0.216408	+	0.976303i	$0.430566\pi$
$282$		0			0
$283$	−2.57057e7	−	7.91141e7i	−0.0674182	−	0.207492i	0.911672	−	0.410919i	$-0.134792\pi$
$283$	−2.57057e7	−	7.91141e7i	−0.0674182	−	0.207492i	−0.979090	+	0.203427i	$0.934792\pi$
$284$	2.22362e7	−	1.61556e7i	0.0576033	−	0.0418512i
$285$		0			0
$286$	5.13177e7	+	3.39882e7i	0.129714	+	0.0859107i
$287$	−1.65741e8			−0.413850
$288$		0			0
$289$	−1.18117e8	−	3.63526e8i	−0.287852	−	0.885917i
$290$	−3.97409e6	+	1.22310e7i	−0.00956851	+	0.0294488i
$291$		0			0
$292$	7.85983e7	+	5.71050e7i	0.184745	+	0.134225i
$293$	−1.90101e8	+	5.85072e8i	−0.441518	+	1.35885i	0.444739	+	0.895660i	$0.353296\pi$
$293$	−1.90101e8	+	5.85072e8i	−0.441518	+	1.35885i	−0.886257	+	0.463193i	$0.846704\pi$
$294$		0			0
$295$	1.73442e7	−	1.26013e7i	0.0393349	−	0.0285785i
$296$	7.49872e8			1.68061
$297$		0			0
$298$	2.60175e8			0.569520
$299$	−1.78227e7	+	1.29489e7i	−0.0385588	+	0.0280146i
$300$		0			0
$301$	−1.85738e8	+	5.71644e8i	−0.392572	+	1.20821i
$302$	−3.55595e8	−	2.58355e8i	−0.742901	−	0.539749i
$303$		0			0
$304$	−5.46516e7	+	1.68200e8i	−0.111569	+	0.343375i
$305$	−952041.	−	2.93008e6i	−0.00192135	−	0.00591330i
$306$		0			0
$307$	−3.40406e8			−0.671449			−0.335725	−	0.941960i	$-0.608981\pi$
$307$	−3.40406e8			−0.671449			−0.335725	+	0.941960i	$0.608981\pi$
$308$	−1.99639e8	+	1.58704e8i	−0.389330	+	0.309500i
$309$		0			0
$310$	−1.19543e7	+	8.68532e6i	−0.0227908	+	0.0165585i
$311$	−1.52109e8	−	4.68144e8i	−0.286744	−	0.882507i	−0.985871	−	0.167509i	$-0.946428\pi$
$311$	−1.52109e8	−	4.68144e8i	−0.286744	−	0.882507i	0.699127	−	0.714998i	$-0.253572\pi$
$312$		0			0
$313$	6.30495e8	+	4.58082e8i	1.16219	+	0.844380i	0.990053	−	0.140693i	$-0.0449332\pi$
$313$	6.30495e8	+	4.58082e8i	1.16219	+	0.844380i	0.172136	+	0.985073i	$0.444933\pi$
$314$	3.58407e8	+	2.60398e8i	0.653316	+	0.474662i
$315$		0			0
$316$	−6.75995e7	−	2.08050e8i	−0.120514	−	0.370905i
$317$	5.71510e8	−	4.15226e8i	1.00766	−	0.732111i	0.0439470	−	0.999034i	$-0.486007\pi$
$317$	5.71510e8	−	4.15226e8i	1.00766	−	0.732111i	0.963718	+	0.266922i	$0.0860067\pi$
$318$		0			0
$319$	−4.08431e8	−	2.70508e8i	−0.704453	−	0.466566i
$320$	2.77447e7			0.0473321
$321$		0			0
$322$	7.70928e7	+	2.37267e8i	0.128682	+	0.396043i
$323$	−2.67782e7	+	8.24148e7i	−0.0442153	+	0.136081i
$324$		0			0
$325$	9.08704e7	+	6.60212e7i	0.146835	+	0.106682i
$326$	−9.86866e7	+	3.03726e8i	−0.157760	+	0.485535i
$327$		0			0
$328$	−1.25020e8	+	9.08327e7i	−0.195624	+	0.142129i
$329$	−1.84269e9			−2.85277
$330$		0			0
$331$	−7.01547e8			−1.06331			−0.531653	−	0.846962i	$-0.678429\pi$
$331$	−7.01547e8			−1.06331			−0.531653	+	0.846962i	$0.678429\pi$
$332$	−7.36331e7	+	5.34976e7i	−0.110431	+	0.0802326i
$333$		0			0
$334$	1.90752e8	−	5.87074e8i	0.280128	−	0.862145i
$335$	−1.70158e6	−	1.23627e6i	−0.00247284	−	0.00179662i
$336$		0			0
$337$	2.14132e7	−	6.59029e7i	0.0304773	−	0.0937994i	−0.934661	−	0.355541i	$-0.884297\pi$
$337$	2.14132e7	−	6.59029e7i	0.0304773	−	0.0937994i	0.965138	+	0.261741i	$0.0842967\pi$
$338$	−1.81503e8	−	5.58608e8i	−0.255667	−	0.786862i
$339$		0			0
$340$	2.17599e6			0.00300248
$341$	−1.96966e8	−	5.27285e8i	−0.269000	−	0.720120i
$342$		0			0
$343$	−1.62490e9	+	1.18056e9i	−2.17418	+	1.57964i
$344$	1.73179e8	+	5.32991e8i	0.229373	+	0.705936i
$345$		0			0
$346$	−3.64523e8	−	2.64842e8i	−0.473106	−	0.343732i
$347$	−4.37513e8	−	3.17872e8i	−0.562131	−	0.408412i	0.270107	−	0.962830i	$-0.412941\pi$
$347$	−4.37513e8	−	3.17872e8i	−0.562131	−	0.408412i	−0.832238	+	0.554418i	$0.812941\pi$
$348$		0			0
$349$	−4.34914e8	−	1.33853e9i	−0.547664	−	1.68554i	−0.714571	−	0.699563i	$-0.753378\pi$
$349$	−4.34914e8	−	1.33853e9i	−0.547664	−	1.68554i	0.166907	−	0.985973i	$-0.446622\pi$
$350$	1.02906e9	−	7.47653e8i	1.28292	−	0.932099i
$351$		0			0
$352$	−1.13788e8	+	4.09837e8i	−0.139059	+	0.500855i
$353$	−9.96153e8			−1.20535			−0.602677	−	0.797985i	$-0.705899\pi$
$353$	−9.96153e8			−1.20535			−0.602677	+	0.797985i	$0.705899\pi$
$354$		0			0
$355$	2.96540e6	+	9.12658e6i	0.00351791	+	0.0108270i
$356$	7.52274e7	−	2.31526e8i	0.0883692	−	0.271973i
$357$		0			0
$358$	−7.49556e8	−	5.44585e8i	−0.863403	−	0.627299i
$359$	2.41120e8	−	7.42090e8i	0.275044	−	0.846498i	−0.714164	−	0.699979i	$-0.753193\pi$
$359$	2.41120e8	−	7.42090e8i	0.275044	−	0.846498i	0.989208	−	0.146520i	$-0.0468072\pi$
$360$		0			0
$361$	5.06996e8	−	3.68354e8i	0.567191	−	0.412089i
$362$	−4.10017e8			−0.454279
$363$		0			0
$364$	−8.32141e7			−0.0904361
$365$	−2.74417e7	+	1.99376e7i	−0.0295383	+	0.0214609i
$366$		0			0
$367$	2.16123e8	−	6.65158e8i	0.228229	−	0.702415i	−0.769719	−	0.638382i	$-0.779604\pi$
$367$	2.16123e8	−	6.65158e8i	0.228229	−	0.702415i	0.997948	−	0.0640326i	$-0.0203962\pi$
$368$	1.33879e8	+	9.72684e7i	0.140037	+	0.101743i
$369$		0			0
$370$	−1.70930e7	+	5.26068e7i	−0.0175433	+	0.0539927i
$371$	5.10492e8	+	1.57113e9i	0.519015	+	1.59736i
$372$		0			0
$373$	−3.54424e7			−0.0353625			−0.0176812	−	0.999844i	$-0.505628\pi$
$373$	−3.54424e7			−0.0353625			−0.0176812	+	0.999844i	$0.505628\pi$
$374$	6.06070e7	−	2.18292e8i	0.0599062	−	0.215768i
$375$		0			0
$376$	−1.38996e9	+	1.00987e9i	−1.34848	+	0.979731i
$377$	−4.93944e7	−	1.52020e8i	−0.0474769	−	0.146119i
$378$		0			0
$379$	1.31861e9	+	9.58027e8i	1.24417	+	0.903942i	0.997869	−	0.0652517i	$-0.0207850\pi$
$379$	1.31861e9	+	9.58027e8i	1.24417	+	0.903942i	0.246300	+	0.969194i	$0.420785\pi$
$380$	5.42795e6	+	3.94364e6i	0.00507450	+	0.00368684i
$381$		0			0
$382$	2.71780e8	+	8.36453e8i	0.249457	+	0.767750i
$383$	−1.46606e9	+	1.06515e9i	−1.33339	+	0.968762i	−0.333727	+	0.942670i	$0.608306\pi$
$383$	−1.46606e9	+	1.06515e9i	−1.33339	+	0.968762i	−0.999660	+	0.0260922i	$0.991694\pi$
$384$		0			0
$385$	−3.11587e7	−	8.34128e7i	−0.0278270	−	0.0744938i
$386$	1.29410e8			0.114528
$387$		0			0
$388$	4.32467e7	+	1.33100e8i	0.0375874	+	0.115682i
$389$	4.99750e8	−	1.53807e9i	0.430457	−	1.32481i	−0.467215	−	0.884144i	$-0.654743\pi$
$389$	4.99750e8	−	1.53807e9i	0.430457	−	1.32481i	0.897671	−	0.440665i	$-0.145257\pi$
$390$		0			0
$391$	6.55978e7	+	4.76596e7i	0.0554971	+	0.0403210i
$392$	−9.78497e8	+	3.01150e9i	−0.820462	+	2.52512i
$393$		0			0
$394$	8.48173e8	−	6.16234e8i	0.698631	−	0.507585i
$395$	7.63764e7			0.0623547
$396$		0			0
$397$	2.03453e8			0.163192			0.0815959	−	0.996665i	$-0.473998\pi$
$397$	2.03453e8			0.163192			0.0815959	+	0.996665i	$0.473998\pi$
$398$	3.97165e8	−	2.88557e8i	0.315777	−	0.229425i
$399$		0			0
$400$	2.60727e8	−	8.02434e8i	0.203693	−	0.626902i
$401$	8.68034e8	+	6.30663e8i	0.672251	+	0.488419i	0.870778	−	0.491677i	$-0.163616\pi$
$401$	8.68034e8	+	6.30663e8i	0.672251	+	0.488419i	−0.198527	+	0.980095i	$0.563616\pi$
$402$		0			0
$403$	5.67531e7	−	1.74668e8i	0.0431938	−	0.132937i
$404$	−6.81984e7	−	2.09893e8i	−0.0514564	−	0.158366i
$405$		0			0
$406$	−1.81014e9			−1.34236
$407$	−1.75671e9	−	1.16348e9i	−1.29157	−	0.855422i
$408$		0			0
$409$	1.57975e9	−	1.14776e9i	1.14172	−	0.829505i	0.154358	−	0.988015i	$-0.450669\pi$
$409$	1.57975e9	−	1.14776e9i	1.14172	−	0.829505i	0.987357	+	0.158510i	$0.0506691\pi$
$410$	−3.52252e6	−	1.08412e7i	−0.00252412	−	0.00776845i
$411$		0			0
$412$	−3.29575e8	−	2.39451e8i	−0.232175	−	0.168685i
$413$	2.44125e9	+	1.77367e9i	1.70525	+	1.23893i
$414$		0			0
$415$	−9.81964e6	−	3.02217e7i	−0.00674415	−	0.0207564i
$416$	−1.12277e8	+	8.15742e7i	−0.0764654	+	0.0555554i
$417$		0			0
$418$	5.46801e8	−	4.34682e8i	0.366195	−	0.291108i
$419$	1.02012e9			0.677487			0.338744	−	0.940879i	$-0.389998\pi$
$419$	1.02012e9			0.677487			0.338744	+	0.940879i	$0.389998\pi$
$420$		0			0
$421$	2.09612e8	+	6.45120e8i	0.136908	+	0.421360i	0.995882	−	0.0906596i	$-0.0288975\pi$
$421$	2.09612e8	+	6.45120e8i	0.136908	+	0.421360i	−0.858974	+	0.512020i	$0.828898\pi$
$422$	3.54763e8	−	1.09185e9i	0.229797	−	0.707243i
$423$		0			0
$424$	1.24611e9	+	9.05355e8i	0.793922	+	0.576818i
$425$	1.27751e8	−	3.93177e8i	0.0807240	−	0.248443i
$426$		0			0
$427$	3.50823e8	−	2.54888e8i	0.218067	−	0.158435i
$428$	−3.49685e8			−0.215588
$429$		0			0
$430$	−4.13392e7			−0.0250739
$431$	1.94470e9	−	1.41290e9i	1.16999	−	0.850046i	0.178980	−	0.983853i	$-0.442720\pi$
$431$	1.94470e9	−	1.41290e9i	1.16999	−	0.850046i	0.991007	+	0.133807i	$0.0427202\pi$
$432$		0			0
$433$	3.90162e8	−	1.20080e9i	0.230960	−	0.710823i	−0.766671	−	0.642040i	$-0.778088\pi$
$433$	3.90162e8	−	1.20080e9i	0.230960	−	0.710823i	0.997632	−	0.0687831i	$-0.0219116\pi$
$434$	−1.68260e9	−	1.22248e9i	−0.988024	−	0.717841i
$435$		0			0
$436$	−9.82657e7	+	3.02431e8i	−0.0567805	+	0.174752i
$437$	7.72566e7	+	2.37771e8i	0.0442844	+	0.136293i
$438$		0			0
$439$	−6.54804e8			−0.369390			−0.184695	−	0.982796i	$-0.559130\pi$
$439$	−6.54804e8			−0.369390			−0.184695	+	0.982796i	$0.559130\pi$
$440$	−6.92170e7	−	4.58431e7i	−0.0387372	−	0.0256560i
$441$		0			0
$442$	5.98022e7	−	4.34488e7i	0.0329412	−	0.0239332i
$443$	6.13763e8	+	1.88897e9i	0.335419	+	1.03231i	0.966515	+	0.256609i	$0.0826053\pi$
$443$	6.13763e8	+	1.88897e9i	0.335419	+	1.03231i	−0.631096	+	0.775705i	$0.717395\pi$
$444$		0			0
$445$	6.87621e7	+	4.99586e7i	0.0369904	+	0.0268751i
$446$	2.04501e9	+	1.48578e9i	1.09150	+	0.793019i
$447$		0			0
$448$	1.20676e9	+	3.71401e9i	0.634083	+	1.95151i
$449$	2.68490e9	−	1.95070e9i	1.39980	−	1.01702i	0.405093	−	0.914275i	$-0.367239\pi$
$449$	2.68490e9	−	1.95070e9i	1.39980	−	1.01702i	0.994708	−	0.102740i	$-0.0327609\pi$
$450$		0			0
$451$	4.33816e8	−	1.88126e7i	0.222684	−	0.00965675i
$452$	3.38311e8			0.172318
$453$		0			0
$454$	7.91834e8	+	2.43701e9i	0.397135	+	1.22226i
$455$	8.97794e6	−	2.76313e7i	0.00446825	−	0.0137518i
$456$		0			0
$457$	3.57583e8	+	2.59799e8i	0.175255	+	0.127330i	0.671955	−	0.740592i	$-0.265455\pi$
$457$	3.57583e8	+	2.59799e8i	0.175255	+	0.127330i	−0.496700	+	0.867922i	$0.665455\pi$
$458$	1.98223e8	−	6.10069e8i	0.0964108	−	0.296722i
$459$		0			0
$460$	5.07889e6	−	3.69003e6i	0.00243285	−	0.00176757i
$461$	−2.31636e9			−1.10117			−0.550584	−	0.834780i	$-0.685595\pi$
$461$	−2.31636e9			−1.10117			−0.550584	+	0.834780i	$0.685595\pi$
$462$		0			0
$463$	−8.87002e8			−0.415328			−0.207664	−	0.978200i	$-0.566586\pi$
$463$	−8.87002e8			−0.415328			−0.207664	+	0.978200i	$0.566586\pi$
$464$	−9.71384e8	+	7.05752e8i	−0.451417	+	0.327974i
$465$		0			0
$466$	8.89342e7	−	2.73711e8i	0.0407116	−	0.125297i
$467$	−1.18106e9	−	8.58090e8i	−0.536615	−	0.389874i	0.286211	−	0.958166i	$-0.407604\pi$
$467$	−1.18106e9	−	8.58090e8i	−0.536615	−	0.389874i	−0.822826	+	0.568293i	$0.807604\pi$
$468$		0			0
$469$	9.14816e7	−	2.81551e8i	0.0409476	−	0.126024i
$470$	−3.91630e7	−	1.20531e8i	−0.0173994	−	0.0535498i
$471$		0			0
$472$	2.81351e9			1.23155
$473$	4.21274e8	−	1.51733e9i	0.183042	−	0.659273i
$474$		0			0
$475$	1.03124e9	−	7.49241e8i	0.441502	−	0.320770i
$476$	9.46446e7	+	2.91286e8i	0.0402227	+	0.123793i
$477$		0			0
$478$	7.77271e8	+	5.64720e8i	0.325518	+	0.236503i
$479$	9.39718e8	+	6.82745e8i	0.390682	+	0.283847i	0.765735	−	0.643156i	$-0.222375\pi$
$479$	9.39718e8	+	6.82745e8i	0.390682	+	0.283847i	−0.375053	+	0.927003i	$0.622375\pi$
$480$		0			0
$481$	−2.12450e8	−	6.53855e8i	−0.0870462	−	0.267901i
$482$	−8.16809e8	+	5.93446e8i	−0.332243	+	0.241389i
$483$		0			0
$484$	5.04529e8	−	4.38058e8i	0.202268	−	0.175620i
$485$	−4.88617e7			−0.0194479
$486$		0			0
$487$	−1.18317e9	−	3.64143e9i	−0.464191	−	1.42863i	−0.859997	−	0.510299i	$-0.829535\pi$
$487$	−1.18317e9	−	3.64143e9i	−0.464191	−	1.42863i	0.395806	−	0.918334i	$-0.370465\pi$
$488$	1.24941e8	−	3.84530e8i	0.0486673	−	0.149783i
$489$		0			0
$490$	−1.88966e8	−	1.37292e8i	−0.0725599	−	0.0527178i
$491$	−8.13032e8	+	2.50226e9i	−0.309972	+	0.953996i	0.667803	+	0.744338i	$0.267235\pi$
$491$	−8.13032e8	+	2.50226e9i	−0.309972	+	0.953996i	−0.977775	+	0.209657i	$0.932765\pi$
$492$		0			0
$493$	−4.75959e8	+	3.45804e8i	−0.178898	+	0.129977i
$494$	2.27919e8			0.0850622
$495$		0			0
$496$	−1.37958e9			−0.507644
$497$	−1.09274e9	+	7.93921e8i	−0.399272	+	0.290088i
$498$		0			0
$499$	7.80275e8	−	2.40144e9i	0.281122	−	0.865206i	−0.706412	−	0.707801i	$-0.749687\pi$
$499$	7.80275e8	−	2.40144e9i	0.281122	−	0.865206i	0.987534	−	0.157405i	$-0.0503127\pi$
$500$	−5.18379e7	−	3.76624e7i	−0.0185461	−	0.0134745i
$501$		0			0
$502$	−4.37379e8	+	1.34611e9i	−0.154310	+	0.474918i
$503$	−8.97011e8	−	2.76072e9i	−0.314275	−	0.967239i	−0.976052	−	0.217538i	$-0.930197\pi$
$503$	−8.97011e8	−	2.76072e9i	−0.314275	−	0.967239i	0.661777	−	0.749701i	$-0.269803\pi$
$504$		0			0
$505$	7.70530e7			0.0266238
$506$	−2.28717e8	−	6.12282e8i	−0.0784823	−	0.210099i
$507$		0			0
$508$	−4.70750e8	+	3.42020e8i	−0.159319	+	0.115752i
$509$	1.90430e8	+	5.86083e8i	0.0640063	+	0.196991i	0.977946	−	0.208860i	$-0.0669752\pi$
$509$	1.90430e8	+	5.86083e8i	0.0640063	+	0.196991i	−0.913939	+	0.405851i	$0.866975\pi$
$510$		0			0
$511$	−3.86250e9	−	2.80627e9i	−1.28054	−	0.930370i
$512$	2.60359e9	+	1.89162e9i	0.857291	+	0.622858i
$513$		0			0
$514$	−8.91259e8	−	2.74301e9i	−0.289490	−	0.890958i
$515$	1.15068e8	−	8.36014e7i	0.0371217	−	0.0269705i
$516$		0			0
$517$	4.82312e9	−	2.09157e8i	1.53501	−	0.0665663i
$518$	−7.78560e9			−2.46115
$519$		0			0
$520$	−8.37088e6	−	2.57629e7i	−0.00261071	−	0.00803495i
$521$	3.13424e8	−	9.64621e8i	0.0970958	−	0.298830i	−0.890698	−	0.454595i	$-0.849784\pi$
$521$	3.13424e8	−	9.64621e8i	0.0970958	−	0.298830i	0.987794	+	0.155764i	$0.0497841\pi$
$522$		0			0
$523$	2.67136e9	+	1.94085e9i	0.816537	+	0.593249i	0.915718	−	0.401821i	$-0.131622\pi$
$523$	2.67136e9	+	1.94085e9i	0.816537	+	0.593249i	−0.0991817	+	0.995069i	$0.531622\pi$
$524$	3.69060e8	−	1.13585e9i	0.112057	−	0.344875i
$525$		0			0
$526$	−1.98779e8	+	1.44422e8i	−0.0595554	+	0.0432695i
$527$	−6.75964e8			−0.201181
$528$		0			0
$529$	−3.17090e9			−0.931295
$530$	−9.19192e7	+	6.67832e7i	−0.0268189	+	0.0194851i
$531$		0			0
$532$	−2.91821e8	+	8.98134e8i	−0.0840285	+	0.258613i
$533$	1.14622e8	+	8.32780e7i	0.0327887	+	0.0238224i
$534$		0			0
$535$	3.77275e7	−	1.16113e8i	0.0106517	−	0.0327826i
$536$	−8.52958e7	−	2.62513e8i	−0.0239249	−	0.0736334i
$537$		0			0
$538$	−1.93796e9			−0.536545
$539$	6.96489e9	−	5.53677e9i	1.91581	−	1.52298i
$540$		0			0
$541$	−2.67331e9	+	1.94227e9i	−0.725869	+	0.527375i	−0.888254	−	0.459353i	$-0.848081\pi$
$541$	−2.67331e9	+	1.94227e9i	−0.725869	+	0.527375i	0.162385	+	0.986728i	$0.448081\pi$
$542$	9.33695e8	+	2.87362e9i	0.251888	+	0.775231i
$543$		0			0
$544$	4.13246e8	+	3.00241e8i	0.110056	+	0.0799601i
$545$	−8.98204e7	−	6.52584e7i	−0.0237677	−	0.0172683i
$546$		0			0
$547$	−1.25114e9	−	3.85060e9i	−0.326850	−	1.00594i	−0.970598	−	0.240705i	$-0.922622\pi$
$547$	−1.25114e9	−	3.85060e9i	−0.326850	−	1.00594i	0.643748	−	0.765238i	$-0.277378\pi$
$548$	−5.04078e8	+	3.66234e8i	−0.130848	+	0.0950664i
$549$		0			0
$550$	−2.60863e9	+	2.07374e9i	−0.668564	+	0.531478i
$551$	−1.81398e9			−0.461958
$552$		0			0
$553$	3.32199e9	+	1.02240e10i	0.835335	+	2.57090i
$554$	−3.49478e8	+	1.07558e9i	−0.0873245	+	0.268757i
$555$		0			0
$556$	−1.32777e9	−	9.64678e8i	−0.327612	−	0.238024i
$557$	−7.00508e8	+	2.15594e9i	−0.171759	+	0.528620i	−0.999471	−	0.0325336i	$-0.989642\pi$
$557$	−7.00508e8	+	2.15594e9i	−0.171759	+	0.528620i	0.827712	+	0.561154i	$0.189642\pi$
$558$		0			0
$559$	4.15680e8	−	3.02009e8i	0.100651	−	0.0731272i
$560$	−2.18239e8			−0.0525140
$561$		0			0
$562$	−5.39318e9			−1.28164
$563$	−6.17525e9	+	4.48658e9i	−1.45840	+	1.05959i	−0.474619	+	0.880191i	$0.657414\pi$
$563$	−6.17525e9	+	4.48658e9i	−1.45840	+	1.05959i	−0.983777	+	0.179395i	$0.942586\pi$
$564$		0			0
$565$	−3.65003e7	+	1.12336e8i	−0.00851387	+	0.0262030i
$566$	6.51484e8	+	4.73331e8i	0.151024	+	0.109725i
$567$		0			0
$568$	−3.89166e8	+	1.19773e9i	−0.0891078	+	0.274246i
$569$	9.90011e8	+	3.04694e9i	0.225293	+	0.693379i	0.998262	+	0.0589357i	$0.0187707\pi$
$569$	9.90011e8	+	3.04694e9i	0.225293	+	0.693379i	−0.772969	+	0.634444i	$0.781229\pi$
$570$		0			0
$571$	1.98405e9			0.445992			0.222996	−	0.974819i	$-0.428416\pi$
$571$	1.98405e9			0.445992			0.222996	+	0.974819i	$0.428416\pi$
$572$	2.17808e8	−	9.44532e6i	0.0486617	−	0.00211023i
$573$		0			0
$574$	1.29803e9	−	9.43076e8i	0.286480	−	0.208140i
$575$	−3.68568e8	−	1.13434e9i	−0.0808501	−	0.248831i
$576$		0			0
$577$	−4.17451e7	−	3.03296e7i	−0.00904669	−	0.00657281i	0.583253	−	0.812291i	$-0.301780\pi$
$577$	−4.17451e7	−	3.03296e7i	−0.00904669	−	0.00657281i	−0.592299	+	0.805718i	$0.701780\pi$
$578$	2.99355e9	+	2.17494e9i	0.644820	+	0.468489i
$579$		0			0
$580$	1.40758e7	+	4.33209e7i	0.00299554	+	0.00921933i
$581$	3.61849e9	−	2.62899e9i	0.765440	−	0.556125i
$582$		0			0
$583$	−1.51451e9	−	4.05440e9i	−0.316544	−	0.847396i
$584$	−4.45148e9			−0.924825
$585$		0			0
$586$	−1.84028e9	−	5.66380e9i	−0.377783	−	1.16270i
$587$	1.88628e9	−	5.80536e9i	0.384921	−	1.18467i	−0.551616	−	0.834098i	$-0.685989\pi$
$587$	1.88628e9	−	5.80536e9i	0.384921	−	1.18467i	0.936537	−	0.350568i	$-0.114011\pi$
$588$		0			0
$589$	−1.68618e9	−	1.22508e9i	−0.340016	−	0.247036i
$590$	−6.41326e7	+	1.97380e8i	−0.0128557	+	0.0395659i
$591$		0			0
$592$	−4.17803e9	+	3.03551e9i	−0.827647	+	0.601321i
$593$	8.88268e9			1.74925			0.874626	−	0.484798i	$-0.161107\pi$
$593$	8.88268e9			1.74925			0.874626	+	0.484798i	$0.161107\pi$
$594$		0			0
$595$	−1.06933e8			−0.0208114
$596$	7.45521e8	−	5.41653e8i	0.144244	−	0.104799i
$597$		0			0
$598$	6.59016e7	−	2.02824e8i	0.0126021	−	0.0387852i
$599$	−7.88108e9	−	5.72594e9i	−1.49828	−	1.08856i	−0.971062	−	0.238828i	$-0.923237\pi$
$599$	−7.88108e9	−	5.72594e9i	−1.49828	−	1.08856i	−0.527213	−	0.849733i	$-0.676763\pi$
$600$		0			0
$601$	−1.88840e9	+	5.81189e9i	−0.354840	+	1.09209i	0.601262	+	0.799052i	$0.294665\pi$
$601$	−1.88840e9	+	5.81189e9i	−0.354840	+	1.09209i	−0.956102	+	0.293033i	$0.905335\pi$
$602$	−1.79805e9	−	5.53382e9i	−0.335902	−	1.03380i
$603$		0			0
$604$	−1.55680e9			−0.287478
$605$	9.10239e7	+	2.14791e8i	0.0167114	+	0.0394342i
$606$		0			0
$607$	5.39702e9	−	3.92117e9i	0.979476	−	0.711631i	0.0218849	−	0.999760i	$-0.493033\pi$
$607$	5.39702e9	−	3.92117e9i	0.979476	−	0.711631i	0.957592	+	0.288129i	$0.0930333\pi$
$608$	4.86693e8	+	1.49789e9i	0.0878197	+	0.270281i
$609$		0			0
$610$	2.41285e7	+	1.75304e7i	0.00430403	+	0.00312706i
$611$	1.27436e9	+	9.25875e8i	0.226020	+	0.164213i
$612$		0			0
$613$	9.68711e8	+	2.98139e9i	0.169857	+	0.522765i	0.999361	−	0.0357348i	$-0.0113772\pi$
$613$	9.68711e8	+	2.98139e9i	0.169857	+	0.522765i	−0.829505	+	0.558500i	$0.811377\pi$
$614$	2.66596e9	−	1.93693e9i	0.464798	−	0.337696i
$615$		0			0
$616$	3.12614e9	−	1.12596e10i	0.538860	−	1.94084i
$617$	−3.92783e9			−0.673216			−0.336608	−	0.941645i	$-0.609280\pi$
$617$	−3.92783e9			−0.673216			−0.336608	+	0.941645i	$0.609280\pi$
$618$		0			0
$619$	2.01199e9	+	6.19226e9i	0.340963	+	1.04938i	0.963709	+	0.266953i	$0.0860169\pi$
$619$	2.01199e9	+	6.19226e9i	0.340963	+	1.04938i	−0.622746	+	0.782424i	$0.713983\pi$
$620$	−1.61728e7	+	4.97748e7i	−0.00272530	+	0.00838762i
$621$		0			0
$622$	3.85505e9	+	2.80086e9i	0.642338	+	0.466686i
$623$	−3.69684e9	+	1.13777e10i	−0.612523	+	1.88515i
$624$		0			0
$625$	−4.91069e9	+	3.56783e9i	−0.804568	+	0.584553i
$626$	−7.54437e9			−1.22917
$627$		0			0
$628$	1.56912e9			0.252811
$629$	−2.04715e9	+	1.48734e9i	−0.327999	+	0.238305i
$630$		0			0
$631$	−1.90612e9	+	5.86642e9i	−0.302027	+	0.929545i	0.678742	+	0.734377i	$0.262525\pi$
$631$	−1.90612e9	+	5.86642e9i	−0.302027	+	0.929545i	−0.980770	+	0.195168i	$0.937475\pi$
$632$	8.10901e9	+	5.89154e9i	1.27779	+	0.928366i
$633$		0			0
$634$	−2.11323e9	+	6.50386e9i	−0.329333	+	1.01358i
$635$	−6.27787e7	−	1.93213e8i	−0.00972981	−	0.0299453i
$636$		0			0
$637$	2.90312e9			0.445018
$638$	4.73793e9	−	2.05462e8i	0.722297	−	0.0313227i
$639$		0			0
$640$	−9.78450e7	+	7.10885e7i	−0.0147540	+	0.0107194i
$641$	2.07228e9	+	6.37782e9i	0.310774	+	0.956465i	0.977459	+	0.211125i	$0.0677128\pi$
$641$	2.07228e9	+	6.37782e9i	0.310774	+	0.956465i	−0.666685	+	0.745340i	$0.732287\pi$
$642$		0			0
$643$	−7.50292e9	−	5.45119e9i	−1.11299	−	0.808635i	−0.129859	−	0.991532i	$-0.541452\pi$
$643$	−7.50292e9	−	5.45119e9i	−1.11299	−	0.808635i	−0.983132	+	0.182897i	$0.941452\pi$
$644$	7.14867e8	+	5.19381e8i	0.105469	+	0.0766277i
$645$		0			0
$646$	−2.59227e8	−	7.97818e8i	−0.0378326	−	0.116437i
$647$	2.30426e9	−	1.67414e9i	0.334477	−	0.243011i	−0.407851	−	0.913048i	$-0.633722\pi$
$647$	2.30426e9	−	1.67414e9i	0.334477	−	0.243011i	0.742328	+	0.670037i	$0.233722\pi$
$648$		0			0
$649$	−6.59115e9	−	4.36538e9i	−0.946465	−	0.626853i
$650$	−1.08734e9			−0.155298
$651$		0			0
$652$	3.49538e8	+	1.07577e9i	0.0493887	+	0.152003i
$653$	5.40437e8	−	1.66329e9i	0.0759536	−	0.233761i	−0.905870	−	0.423555i	$-0.860782\pi$
$653$	5.40437e8	−	1.66329e9i	0.0759536	−	0.233761i	0.981824	+	0.189794i	$0.0607820\pi$
$654$		0			0
$655$	3.37342e8	+	2.45093e8i	0.0469058	+	0.0340790i
$656$	3.28876e8	−	1.01218e9i	0.0454851	−	0.139989i
$657$		0			0
$658$	1.44314e10	−	1.04850e10i	1.97477	−	1.43476i
$659$	−1.09640e10			−1.49235			−0.746177	−	0.665748i	$-0.768113\pi$
$659$	−1.09640e10			−1.49235			−0.746177	+	0.665748i	$0.768113\pi$
$660$		0			0
$661$	4.24060e9			0.571113			0.285557	−	0.958362i	$-0.407822\pi$
$661$	4.24060e9			0.571113			0.285557	+	0.958362i	$0.407822\pi$
$662$	5.49431e9	−	3.99185e9i	0.736055	−	0.534775i
$663$		0			0
$664$	1.28868e9	−	3.96616e9i	0.170828	−	0.525754i
$665$	−2.66741e8	−	1.93799e8i	−0.0351734	−	0.0255550i
$666$		0			0
$667$	−5.24503e8	+	1.61426e9i	−0.0684397	+	0.210636i
$668$	−6.75624e8	−	2.07936e9i	−0.0876976	−	0.269905i
$669$		0			0
$670$	2.03607e7			0.00261536
$671$	−8.89326e8	+	7.06974e8i	−0.113640	+	0.0903388i
$672$		0			0
$673$	6.89743e9	−	5.01128e9i	0.872238	−	0.633718i	−0.0589488	−	0.998261i	$-0.518775\pi$
$673$	6.89743e9	−	5.01128e9i	0.872238	−	0.633718i	0.931186	+	0.364543i	$0.118775\pi$
$674$	2.07291e8	+	6.37975e8i	0.0260777	+	0.0802590i
$675$		0			0
$676$	−1.68304e9	−	1.22280e9i	−0.209547	−	0.152245i
$677$	−7.06155e9	−	5.13051e9i	−0.874661	−	0.635478i	0.0571729	−	0.998364i	$-0.481791\pi$
$677$	−7.06155e9	−	5.13051e9i	−0.874661	−	0.635478i	−0.931833	+	0.362886i	$0.881791\pi$
$678$		0			0
$679$	−2.12524e9	−	6.54081e9i	−0.260533	−	0.801839i
$680$	−8.06609e7	+	5.86036e7i	−0.00983744	+	0.00714731i
$681$		0			0
$682$	4.54287e9	+	3.00879e9i	0.548384	+	0.363200i
$683$	−7.49982e9			−0.900696			−0.450348	−	0.892853i	$-0.648700\pi$
$683$	−7.49982e9			−0.900696			−0.450348	+	0.892853i	$0.648700\pi$
$684$		0			0
$685$	−6.72234e7	−	2.06892e8i	−0.00799105	−	0.0245939i
$686$	6.00827e9	−	1.84916e10i	0.710583	−	2.18695i
$687$		0			0
$688$	−3.12247e9	−	2.26860e9i	−0.365543	−	0.265582i
$689$	4.36386e8	−	1.34306e9i	0.0508281	−	0.156433i
$690$		0			0
$691$	−2.51983e9	+	1.83076e9i	−0.290535	+	0.211086i	−0.723499	−	0.690325i	$-0.757467\pi$
$691$	−2.51983e9	+	1.83076e9i	−0.290535	+	0.211086i	0.432965	+	0.901411i	$0.357467\pi$
$692$	−1.59589e9			−0.183076
$693$		0			0
$694$	5.23519e9			0.594530
$695$	4.63574e8	−	3.36806e8i	0.0523808	−	0.0380569i
$696$		0			0
$697$	1.61143e8	−	4.95946e8i	0.0180259	−	0.0554779i
$698$	1.10224e10	+	8.00826e9i	1.22683	+	0.891342i
$699$		0			0
$700$	1.39219e9	−	4.28473e9i	0.153411	−	0.472151i
$701$	2.04345e9	+	6.28910e9i	0.224053	+	0.689565i	0.998386	+	0.0567870i	$0.0180856\pi$
$701$	2.04345e9	+	6.28910e9i	0.224053	+	0.689565i	−0.774333	+	0.632778i	$0.781914\pi$
$702$		0			0
$703$	−7.80213e9			−0.846973
$704$	−3.58017e9	−	9.58423e9i	−0.386723	−	1.03527i
$705$		0			0
$706$	7.80158e9	−	5.66818e9i	0.834385	−	0.606216i
$707$	3.35142e9	+	1.03146e10i	0.356665	+	1.09770i
$708$		0			0
$709$	4.71854e9	+	3.42822e9i	0.497217	+	0.361249i	0.807953	−	0.589247i	$-0.200575\pi$
$709$	4.71854e9	+	3.42822e9i	0.497217	+	0.361249i	−0.310736	+	0.950496i	$0.600575\pi$
$710$	−7.51550e7	−	5.46033e7i	−0.00788050	−	0.00572552i
$711$		0			0
$712$	3.44687e9	+	1.06084e10i	0.357886	+	1.10146i
$713$	−1.57774e9	+	1.14630e9i	−0.163013	+	0.118436i
$714$		0			0
$715$	−2.03629e7	+	7.33422e7i	−0.00208338	+	0.00750383i
$716$	−3.28158e9			−0.334108
$717$		0			0
$718$	2.33417e9	+	7.18382e9i	0.235340	+	0.724303i
$719$	3.10332e9	−	9.55105e9i	0.311369	−	0.958297i	−0.665854	−	0.746082i	$-0.731932\pi$
$719$	3.10332e9	−	9.55105e9i	0.311369	−	0.958297i	0.977223	−	0.212214i	$-0.0680675\pi$
$720$		0			0
$721$	1.61961e10	+	1.17671e10i	1.60930	+	1.16922i
$722$	−1.87468e9	+	5.76969e9i	−0.185374	+	0.570522i
$723$		0			0
$724$	−1.17489e9	+	8.53605e8i	−0.115056	+	0.0835934i
$725$	8.65398e9			0.843398
$726$		0			0
$727$	3.51655e9			0.339427			0.169713	−	0.985493i	$-0.445716\pi$
$727$	3.51655e9			0.339427			0.169713	+	0.985493i	$0.445716\pi$
$728$	3.08463e9	−	2.24111e9i	0.296308	−	0.215280i
$729$		0			0
$730$	1.01469e8	−	3.12290e8i	0.00965394	−	0.0297118i
$731$	−1.52995e9	−	1.11157e9i	−0.144866	−	0.105251i
$732$		0			0
$733$	−6.04072e9	+	1.85914e10i	−0.566533	+	1.74361i	0.0968207	+	0.995302i	$0.469133\pi$
$733$	−6.04072e9	+	1.85914e10i	−0.566533	+	1.74361i	−0.663353	+	0.748306i	$0.730867\pi$
$734$	2.09218e9	+	6.43908e9i	0.195283	+	0.601018i
$735$		0			0
$736$	1.47369e9			0.136249
$737$	−2.07490e8	+	7.47327e8i	−0.0190924	+	0.0687661i
$738$		0			0
$739$	−8.66718e9	+	6.29708e9i	−0.789991	+	0.573962i	−0.907961	−	0.419055i	$-0.862361\pi$
$739$	−8.66718e9	+	6.29708e9i	−0.789991	+	0.573962i	0.117970	+	0.993017i	$0.462361\pi$
$740$	6.05416e7	+	1.86328e8i	0.00549215	+	0.0169031i
$741$		0			0
$742$	−1.29379e10	−	9.39992e9i	−1.16265	−	0.844715i
$743$	1.64821e10	+	1.19749e10i	1.47418	+	1.07106i	0.979375	+	0.202052i	$0.0647610\pi$
$743$	1.64821e10	+	1.19749e10i	1.47418	+	1.07106i	0.494806	+	0.869003i	$0.335239\pi$
$744$		0			0
$745$	9.94220e7	+	3.05989e8i	0.00880918	+	0.0271119i
$746$	2.77575e8	−	2.01670e8i	0.0244790	−	0.0177851i
$747$		0			0
$748$	−2.80789e8	−	7.51681e8i	−0.0245316	−	0.0656717i
$749$	1.71843e10			1.49433
$750$		0			0
$751$	3.88243e9	+	1.19489e10i	0.334475	+	1.02941i	0.966980	+	0.254853i	$0.0820270\pi$
$751$	3.88243e9	+	1.19489e10i	0.334475	+	1.02941i	−0.632505	+	0.774557i	$0.717973\pi$
$752$	3.65641e9	−	1.12533e10i	0.313540	−	0.964975i
$753$		0			0
$754$	1.25185e9	+	9.09521e8i	0.106353	+	0.0772703i
$755$	1.67963e8	−	5.16937e8i	0.0142036	−	0.0437143i
$756$		0			0
$757$	−1.33500e9	+	9.69935e8i	−0.111853	+	0.0812656i	−0.642305	−	0.766449i	$-0.722022\pi$
$757$	−1.33500e9	+	9.69935e8i	−0.111853	+	0.0812656i	0.530453	+	0.847714i	$0.322022\pi$
$758$	−1.57782e10			−1.31588
$759$		0			0
$760$	−3.07416e8			−0.0254027
$761$	−5.95172e9	+	4.32418e9i	−0.489549	+	0.355678i	−0.805011	−	0.593260i	$-0.797841\pi$
$761$	−5.95172e9	+	4.32418e9i	−0.489549	+	0.355678i	0.315462	+	0.948938i	$0.397841\pi$
$762$		0			0
$763$	4.82899e9	−	1.48621e10i	0.393569	−	1.21128i
$764$	2.52016e9	+	1.83101e9i	0.204457	+	0.148547i
$765$		0			0
$766$	5.42095e9	−	1.66840e10i	0.435787	−	1.34122i
$767$	−7.97112e8	−	2.45326e9i	−0.0637875	−	0.196318i
$768$		0			0
$769$	2.63374e9			0.208848			0.104424	−	0.994533i	$-0.466700\pi$
$769$	2.63374e9			0.208848			0.104424	+	0.994533i	$0.466700\pi$
$770$	7.18650e8	+	4.75969e8i	0.0567284	+	0.0375717i
$771$		0			0
$772$	3.70819e8	−	2.69416e8i	0.0290069	−	0.0210748i
$773$	2.57988e9	+	7.94006e9i	0.200896	+	0.618295i	0.999857	+	0.0169118i	$0.00538344\pi$
$773$	2.57988e9	+	7.94006e9i	0.200896	+	0.618295i	−0.798961	+	0.601383i	$0.794617\pi$
$774$		0			0
$775$	8.04425e9	+	5.84449e9i	0.620768	+	0.451014i
$776$	−5.18772e9	−	3.76910e9i	−0.398530	−	0.289549i
$777$		0			0
$778$	4.83784e9	+	1.48894e10i	0.368318	+	1.13357i
$779$	1.30079e9	−	9.45080e8i	0.0985885	−	0.0716287i
$780$		0			0
$781$	2.77006e9	−	2.20207e9i	0.208071	−	0.165407i
$782$	−7.84929e8			−0.0586958
$783$		0			0
$784$	−6.73885e9	−	2.07401e10i	−0.499436	−	1.53711i
$785$	−1.69292e8	+	5.21026e8i	−0.0124908	+	0.0384429i
$786$		0			0
$787$	−1.83103e10	−	1.33032e10i	−1.33901	−	0.972848i	−0.999480	−	0.0322525i	$-0.989732\pi$
$787$	−1.83103e10	−	1.33032e10i	−1.33901	−	0.972848i	−0.339530	−	0.940595i	$-0.610268\pi$
$788$	1.14748e9	−	3.53158e9i	0.0835417	−	0.257115i
$789$		0			0
$790$	−5.98158e8	+	4.34587e8i	−0.0431639	+	0.0313604i
$791$	−1.66254e10			−1.19441
$792$		0			0
$793$	−3.70691e8			−0.0263971
$794$	−1.59339e9	+	1.15766e9i	−0.112967	+	0.0820750i
$795$		0			0
$796$	5.37319e8	−	1.65370e9i	0.0377604	−	0.116215i
$797$	−1.32668e10	−	9.63888e9i	−0.928242	−	0.674407i	0.0173197	−	0.999850i	$-0.494487\pi$
$797$	−1.32668e10	−	9.63888e9i	−0.928242	−	0.674407i	−0.945562	+	0.325443i	$0.894487\pi$
$798$		0			0
$799$	1.79157e9	−	5.51388e9i	0.124257	−	0.382422i
$800$	−2.32187e9	−	7.14597e9i	−0.160333	−	0.493454i
$801$		0			0
$802$	−1.03867e10			−0.710997
$803$	1.04284e10	+	6.90682e9i	0.710743	+	0.470732i
$804$		0			0
$805$	−2.49588e8	+	1.81336e8i	−0.0168631	+	0.0122518i
$806$	5.49400e8	+	1.69088e9i	0.0369586	+	0.113747i
$807$		0			0
$808$	8.18084e9	+	5.94373e9i	0.545580	+	0.396387i
$809$	1.17866e10	+	8.56347e9i	0.782653	+	0.568630i	0.905774	−	0.423761i	$-0.139290\pi$
$809$	1.17866e10	+	8.56347e9i	0.782653	+	0.568630i	−0.123121	+	0.992392i	$0.539290\pi$
$810$		0			0
$811$	−3.10353e9	−	9.55168e9i	−0.204307	−	0.628792i	−0.999741	−	0.0227520i	$-0.992757\pi$
$811$	−3.10353e9	−	9.55168e9i	−0.204307	−	0.628792i	0.795434	−	0.606040i	$-0.207243\pi$
$812$	−5.18687e9	+	3.76848e9i	−0.339985	+	0.247013i
$813$		0			0
$814$	2.03783e10	−	8.83714e8i	1.32429	−	0.0574283i
$815$	−3.94921e8			−0.0255540
$816$		0			0
$817$	−1.80186e9	−	5.54557e9i	−0.115597	−	0.355770i
$818$	−5.84135e9	+	1.79778e10i	−0.373144	+	1.14842i
$819$		0			0
$820$	−3.26637e7	−	2.37316e7i	−0.00206879	−	0.00150306i
$821$	−2.75292e9	+	8.47262e9i	−0.173617	+	0.534339i	−0.999568	−	0.0294039i	$-0.990639\pi$
$821$	−2.75292e9	+	8.47262e9i	−0.173617	+	0.534339i	0.825950	+	0.563743i	$0.190639\pi$
$822$		0			0
$823$	−2.54170e10	+	1.84665e10i	−1.58937	+	1.15475i	−0.684537	+	0.728978i	$0.739996\pi$
$823$	−2.54170e10	+	1.84665e10i	−1.58937	+	1.15475i	−0.904833	+	0.425767i	$0.860004\pi$
$824$	1.86658e10			1.16225
$825$		0			0
$826$	−2.92115e10			−1.80353
$827$	−2.15622e10	+	1.56658e10i	−1.32563	+	0.963129i	−0.325789	+	0.945442i	$0.605630\pi$
$827$	−2.15622e10	+	1.56658e10i	−1.32563	+	0.963129i	−0.999844	+	0.0176861i	$0.994370\pi$
$828$		0			0
$829$	3.58539e9	−	1.10347e10i	0.218573	−	0.672697i	−0.780308	−	0.625395i	$-0.784938\pi$
$829$	3.58539e9	−	1.10347e10i	0.218573	−	0.672697i	0.998881	−	0.0473018i	$-0.0150623\pi$
$830$	2.48868e8	+	1.80813e8i	0.0151076	+	0.0109763i
$831$		0			0
$832$	1.03158e9	−	3.17487e9i	0.0620969	−	0.191115i
$833$	−3.30190e9	−	1.01622e10i	−0.197928	−	0.609159i
$834$		0			0
$835$	7.63345e8			0.0453751
$836$	6.61881e8	−	2.38394e9i	0.0391794	−	0.141115i
$837$		0			0
$838$	−7.98926e9	+	5.80454e9i	−0.468978	+	0.340733i
$839$	−6.69105e9	−	2.05929e10i	−0.391136	−	1.20379i	−0.931930	−	0.362637i	$-0.881876\pi$
$839$	−6.69105e9	−	2.05929e10i	−0.391136	−	1.20379i	0.540795	−	0.841155i	$-0.318124\pi$
$840$		0			0
$841$	3.99213e9	+	2.90045e9i	0.231430	+	0.168143i
$842$	−5.31240e9	−	3.85968e9i	−0.306689	−	0.222823i
$843$		0			0
$844$	−1.25653e9	−	3.86721e9i	−0.0719409	−	0.221411i
$845$	5.87614e8	−	4.26927e8i	0.0335038	−	0.0243419i
$846$		0			0
$847$	−2.47937e10	+	2.15271e10i	−1.40200	+	1.21729i
$848$	−1.06078e10			−0.597367
$849$		0			0
$850$	1.23670e9	+	3.80616e9i	0.0690711	+	0.212579i
$851$	−2.25595e9	+	6.94309e9i	−0.125480	+	0.386188i
$852$		0			0
$853$	1.80900e10	+	1.31432e10i	0.997971	+	0.725069i	0.961652	−	0.274272i	$-0.0884367\pi$
$853$	1.80900e10	+	1.31432e10i	0.997971	+	0.725069i	0.0363191	+	0.999340i	$0.488437\pi$
$854$	−1.29721e9	+	3.99241e9i	−0.0712703	+	0.219348i
$855$		0			0
$856$	1.29624e10	−	9.41770e9i	0.706359	−	0.513200i
$857$	1.04481e10			0.567027			0.283514	−	0.958968i	$-0.408500\pi$
$857$	1.04481e10			0.567027			0.283514	+	0.958968i	$0.408500\pi$
$858$		0			0
$859$	−2.69860e10			−1.45266			−0.726328	−	0.687348i	$-0.758775\pi$
$859$	−2.69860e10			−1.45266			−0.726328	+	0.687348i	$0.758775\pi$
$860$	−1.18456e8	+	8.60630e7i	−0.00635054	+	0.00461394i
$861$		0			0
$862$	−7.19077e9	+	2.21309e10i	−0.382384	+	1.17686i
$863$	−9.73164e9	−	7.07045e9i	−0.515405	−	0.374463i	0.299465	−	0.954107i	$-0.403192\pi$
$863$	−9.73164e9	−	7.07045e9i	−0.515405	−	0.374463i	−0.814870	+	0.579644i	$0.803192\pi$
$864$		0			0
$865$	1.72180e8	−	5.29917e8i	0.00904540	−	0.0278389i
$866$	3.77697e9	+	1.16243e10i	0.197620	+	0.608213i
$867$		0			0
$868$	−7.36648e9			−0.382332
$869$	−9.85560e9	−	2.63837e10i	−0.509465	−	1.36385i
$870$		0			0
$871$	−2.04735e8	+	1.48748e8i	−0.0104985	+	0.00762761i
$872$	−4.50247e9	−	1.38572e10i	−0.229955	−	0.707729i
$873$		0			0
$874$	−1.95799e9	−	1.42256e9i	−0.0992018	−	0.0720743i
$875$	2.54743e9	+	1.85081e9i	0.128550	+	0.0933974i
$876$		0			0
$877$	−5.72076e9	−	1.76067e10i	−0.286388	−	0.881413i	−0.985979	−	0.166869i	$-0.946634\pi$
$877$	−5.72076e9	−	1.76067e10i	−0.286388	−	0.881413i	0.699591	−	0.714544i	$-0.253366\pi$
$878$	5.12823e9	−	3.72588e9i	0.255704	−	0.185780i
$879$		0			0
$880$	5.71228e8	−	2.47715e7i	0.0282566	−	0.00122536i
$881$	−1.27133e10			−0.626386			−0.313193	−	0.949689i	$-0.601399\pi$
$881$	−1.27133e10			−0.626386			−0.313193	+	0.949689i	$0.601399\pi$
$882$		0			0
$883$	−5.82374e9	−	1.79236e10i	−0.284669	−	0.876120i	−0.986498	−	0.163775i	$-0.947633\pi$
$883$	−5.82374e9	−	1.79236e10i	−0.284669	−	0.876120i	0.701829	−	0.712345i	$-0.252367\pi$
$884$	8.09055e7	−	2.49002e8i	0.00393908	−	0.0121233i
$885$		0			0
$886$	−1.55552e10	−	1.13015e10i	−0.751375	−	0.545906i
$887$	9.13082e9	−	2.81018e10i	0.439316	−	1.35208i	−0.449282	−	0.893390i	$-0.648320\pi$
$887$	9.13082e9	−	2.81018e10i	0.439316	−	1.35208i	0.888598	−	0.458686i	$-0.151680\pi$
$888$		0			0
$889$	2.31337e10	−	1.68076e10i	1.10430	−	0.802323i
$890$	−8.22793e8			−0.0391224
$891$		0			0
$892$	8.95309e9			0.422373
$893$	1.44620e10	−	1.05073e10i	0.679594	−	0.493754i
$894$		0			0
$895$	3.54049e8	−	1.08965e9i	0.0165075	−	0.0508050i
$896$	−1.37719e10	−	1.00059e10i	−0.639613	−	0.464706i
$897$		0			0
$898$	−9.92778e9	+	3.05546e10i	−0.457494	+	1.40802i
$899$	−4.37261e9	−	1.34575e10i	−0.200716	−	0.617740i
$900$		0			0
$901$	−5.19763e9			−0.236738
$902$	−3.29048e9	+	2.61578e9i	−0.149292	+	0.118680i
$903$		0			0
$904$	−1.25407e10	+	9.11137e9i	−0.564590	+	0.410199i
$905$	−1.56682e8	−	4.82217e8i	−0.00702665	−	0.0216258i
$906$		0			0
$907$	−1.76874e10	−	1.28506e10i	−0.787114	−	0.571872i	0.119992	−	0.992775i	$-0.461713\pi$
$907$	−1.76874e10	−	1.28506e10i	−0.787114	−	0.571872i	−0.907106	+	0.420903i	$0.861713\pi$
$908$	7.34252e9	+	5.33466e9i	0.325495	+	0.236486i
$909$		0			0
$910$	8.69112e7	+	2.67485e8i	0.00382323	+	0.0117667i
$911$	3.59004e9	−	2.60831e9i	0.157320	−	0.114300i	−0.506340	−	0.862334i	$-0.669002\pi$
$911$	3.59004e9	−	2.60831e9i	0.157320	−	0.114300i	0.663660	+	0.748034i	$0.269002\pi$
$912$		0			0
$913$	−9.17278e9	+	7.29194e9i	−0.398890	+	0.317099i
$914$	−4.27876e9			−0.185356
$915$		0			0
$916$	−7.02087e8	−	2.16080e9i	−0.0301826	−	0.0928926i
$917$	−1.81364e10	+	5.58182e10i	−0.776711	+	2.39047i
$918$		0			0
$919$	2.62202e10	+	1.90501e10i	1.11438	+	0.809641i	0.983347	−	0.181737i	$-0.0581721\pi$
$919$	2.62202e10	+	1.90501e10i	1.11438	+	0.809641i	0.131028	+	0.991379i	$0.458172\pi$
$920$	−8.88878e7	+	2.73568e8i	−0.00376344	+	0.0115827i
$921$		0			0
$922$	1.81411e10	−	1.31803e10i	0.762263	−	0.553816i
$923$	1.15462e9			0.0483320
$924$		0			0
$925$	3.72217e10			1.54632
$926$	6.94674e9	−	5.04710e9i	0.287503	−	0.208883i
$927$		0			0
$928$	−3.30421e9	+	1.01693e10i	−0.135722	+	0.417709i
$929$	1.15817e10	+	8.41463e9i	0.473935	+	0.344334i	0.798973	−	0.601367i	$-0.205377\pi$
$929$	1.15817e10	+	8.41463e9i	0.473935	+	0.344334i	−0.325038	+	0.945701i	$0.605377\pi$
$930$		0			0
$931$	1.01809e10	−	3.13336e10i	0.413487	−	1.27258i
$932$	−3.14996e8	−	9.69457e8i	−0.0127453	−	0.0392259i
$933$		0			0
$934$	1.41323e10			0.567543
$935$	2.79890e8	−	1.21376e7i	0.0111982	−	0.000485613i
$936$		0			0
$937$	−1.62699e10	+	1.18208e10i	−0.646096	+	0.469416i	−0.861939	−	0.507012i	$-0.830750\pi$
$937$	−1.62699e10	+	1.18208e10i	−0.646096	+	0.469416i	0.215843	+	0.976428i	$0.430750\pi$
$938$	8.85590e8	+	2.72556e9i	0.0350366	+	0.107832i
$939$		0			0
$940$	−3.63151e8	−	2.63845e8i	−0.0142607	−	0.0103610i
$941$	−2.01514e9	−	1.46408e9i	−0.0788390	−	0.0572799i	0.547668	−	0.836696i	$-0.315516\pi$
$941$	−2.01514e9	−	1.46408e9i	−0.0788390	−	0.0572799i	−0.626507	+	0.779416i	$0.715516\pi$
$942$		0			0
$943$	−4.64906e8	−	1.43083e9i	−0.0180540	−	0.0555646i
$944$	−1.56759e10	+	1.13892e10i	−0.606500	+	0.440648i
$945$		0			0
$946$	5.33440e9	+	1.42803e10i	0.204864	+	0.548428i
$947$	4.66294e10			1.78417			0.892083	−	0.451872i	$-0.149244\pi$
$947$	4.66294e10			1.78417			0.892083	+	0.451872i	$0.149244\pi$
$948$		0			0
$949$	1.26117e9	+	3.88149e9i	0.0479008	+	0.147424i
$950$	−3.81315e9	+	1.17357e10i	−0.144295	+	0.444094i
$951$		0			0
$952$	−1.13532e10	−	8.24861e9i	−0.426472	−	0.309850i
$953$	−9.76317e9	+	3.00480e10i	−0.365398	+	1.12458i	0.584334	+	0.811513i	$0.301356\pi$
$953$	−9.76317e9	+	3.00480e10i	−0.365398	+	1.12458i	−0.949732	+	0.313065i	$0.898644\pi$
$954$		0			0
$955$	−8.79887e8	+	6.39275e8i	−0.0326900	+	0.0237507i
$956$	3.40291e9			0.125965
$957$		0			0
$958$	−1.12445e10			−0.413199
$959$	2.47715e10	−	1.79976e10i	0.906959	−	0.658944i
$960$		0			0
$961$	−3.47783e9	+	1.07037e10i	−0.126409	+	0.389046i
$962$	5.38433e9	+	3.91195e9i	0.194993	+	0.141671i
$963$		0			0
$964$	−1.10505e9	+	3.40099e9i	−0.0397294	+	0.122274i
$965$	4.94521e7	+	1.52198e8i	0.00177149	+	0.00545209i
$966$		0			0
$967$	3.24264e10			1.15320			0.576602	−	0.817025i	$-0.304378\pi$
$967$	3.24264e10			1.15320			0.576602	+	0.817025i	$0.304378\pi$
$968$	−6.90445e9	+	2.98262e10i	−0.244661	+	1.05690i
$969$		0			0
$970$	3.82670e8	−	2.78026e8i	0.0134624	−	0.00978104i
$971$	−1.23156e10	−	3.79034e10i	−0.431704	−	1.32865i	−0.896426	−	0.443193i	$-0.853846\pi$
$971$	−1.23156e10	−	3.79034e10i	−0.431704	−	1.32865i	0.464722	−	0.885457i	$-0.346154\pi$
$972$		0			0
$973$	6.52493e10	+	4.74064e10i	2.27081	+	1.64984i
$974$	2.99863e10	+	2.17863e10i	1.03984	+	0.755487i
$975$		0			0
$976$	8.60465e8	+	2.64824e9i	0.0296250	+	0.0911764i
$977$	4.44342e10	−	3.22833e10i	1.52436	−	1.10751i	0.565081	−	0.825035i	$-0.308845\pi$
$977$	4.44342e10	−	3.22833e10i	1.52436	−	1.10751i	0.959275	−	0.282474i	$-0.0911552\pi$
$978$		0			0
$979$	8.38482e9	−	3.02001e10i	0.285597	−	1.02865i
$980$	−8.27297e8			−0.0280783
$981$		0			0
$982$	−7.87058e9	−	2.42231e10i	−0.265226	−	0.816282i
$983$	−6.47909e9	+	1.99406e10i	−0.217559	+	0.669577i	0.781403	+	0.624026i	$0.214504\pi$
$983$	−6.47909e9	+	1.99406e10i	−0.217559	+	0.669577i	−0.998962	+	0.0455506i	$0.985496\pi$
$984$		0			0
$985$	1.04886e9	+	7.62043e8i	0.0349697	+	0.0254070i
$986$	1.75992e9	−	5.41648e9i	0.0584687	−	0.179948i
$987$		0			0
$988$	6.53093e8	−	4.74500e8i	0.0215440	−	0.0156526i
$989$	−5.45598e9			−0.179343
$990$		0			0
$991$	1.26660e10			0.413411			0.206706	−	0.978403i	$-0.433726\pi$
$991$	1.26660e10			0.413411			0.206706	+	0.978403i	$0.433726\pi$
$992$	−9.93928e9	+	7.22131e9i	−0.323269	+	0.234869i
$993$		0			0
$994$	4.04054e9	−	1.24355e10i	0.130493	−	0.401616i
$995$	4.91140e8	+	3.56834e8i	0.0158061	+	0.0114838i
$996$		0			0
$997$	1.29787e10	−	3.99442e10i	0.414760	−	1.27650i	−0.497705	−	0.867346i	$-0.665824\pi$
$997$	1.29787e10	−	3.99442e10i	0.414760	−	1.27650i	0.912465	−	0.409154i	$-0.134176\pi$
$998$	7.55347e9	+	2.32472e10i	0.240541	+	0.740310i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.a.91.2		24
3.2	odd	2		11.8.c.a.3.5	✓	24
11.4	even	5	inner	99.8.f.a.37.2		24
33.2	even	10		121.8.a.g.1.9		12
33.20	odd	10		121.8.a.i.1.4		12
33.26	odd	10		11.8.c.a.4.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.8.c.a.3.5	✓	24	3.2	odd	2
11.8.c.a.4.5	yes	24	33.26	odd	10
99.8.f.a.37.2		24	11.4	even	5	inner
99.8.f.a.91.2		24	1.1	even	1	trivial
121.8.a.g.1.9		12	33.2	even	10
121.8.a.i.1.4		12	33.20	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.83171 + 5.69007i) q^{2} +(-10.5954 + 32.6093i) q^{4} +(-9.68480 - 7.03642i) q^{5} +(520.681 - 1602.49i) q^{7} +(-485.474 - 1494.14i) q^{8} +O(q^{10})\)	\(q+(-7.83171 + 5.69007i) q^{2} +(-10.5954 + 32.6093i) q^{4} +(-9.68480 - 7.03642i) q^{5} +(520.681 - 1602.49i) q^{7} +(-485.474 - 1494.14i) q^{8} +115.886 q^{10} +(-1180.96 + 4253.53i) q^{11} +(-1165.28 + 846.624i) q^{13} +(5040.47 + 15513.0i) q^{14} +(8753.22 + 6359.59i) q^{16} +(4288.90 + 3116.07i) q^{17} +(5051.18 + 15545.9i) q^{19} +(332.067 - 241.261i) q^{20} +(-14953.9 - 40032.1i) q^{22} +15294.8 q^{23} +(-24097.7 - 74165.0i) q^{25} +(4308.77 - 13261.0i) q^{26} +(46739.3 + 33958.1i) q^{28} +(-34293.0 + 105543. i) q^{29} +(-103156. + 74946.9i) q^{31} +96352.3 q^{32} -51320.1 q^{34} +(-16318.5 + 11856.1i) q^{35} +(-147498. + 453952. i) q^{37} +(-128017. - 93009.6i) q^{38} +(-5811.65 + 17886.4i) q^{40} +(-30396.4 - 93550.4i) q^{41} -356722. q^{43} +(-126192. - 83578.1i) q^{44} +(-119784. + 87028.3i) q^{46} +(-337944. - 1.04008e6i) q^{47} +(-1.63061e6 - 1.18471e6i) q^{49} +(610730. + 443721. i) q^{50} +(-15261.2 - 46969.2i) q^{52} +(-793185. + 576282. i) q^{53} +(41367.0 - 32884.8i) q^{55} -2.64712e6 q^{56} +(-331974. - 1.02171e6i) q^{58} +(-553410. + 1.70322e6i) q^{59} +(208208. + 151272. i) q^{61} +(381431. - 1.17392e6i) q^{62} +(-1.87502e6 + 1.36228e6i) q^{64} +17242.7 q^{65} +175696. q^{67} +(-147056. + 106842. i) q^{68} +(60339.8 - 185707. i) q^{70} +(-648524. - 471181. i) q^{71} +(875594. - 2.69480e6i) q^{73} +(-1.42786e6 - 4.39449e6i) q^{74} -560461. q^{76} +(6.20134e6 + 4.10721e6i) q^{77} +(-5.16160e6 + 3.75012e6i) q^{79} +(-40024.5 - 123183. i) q^{80} +(770364. + 559702. i) q^{82} +(2.14752e6 + 1.56027e6i) q^{83} +(-19611.2 - 60357.0i) q^{85} +(2.79374e6 - 2.02977e6i) q^{86} +(6.92868e6 - 300465. i) q^{88} -7.10000e6 q^{89} +(749970. + 2.30817e6i) q^{91} +(-162054. + 498752. i) q^{92} +(8.56483e6 + 6.22271e6i) q^{94} +(60468.0 - 186101. i) q^{95} +(3.30212e6 - 2.39913e6i) q^{97} +1.95116e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 505 q^{4} + 72 q^{5} + 68 q^{7} + 4545 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 505 * q^4 + 72 * q^5 + 68 * q^7 + 4545 * q^8	\( 24 q - 3 q^{2} - 505 q^{4} + 72 q^{5} + 68 q^{7} + 4545 q^{8} + 4240 q^{10} - 5952 q^{11} - 16564 q^{13} + 29544 q^{14} + 13279 q^{16} + 65592 q^{17} - 37804 q^{19} - 120702 q^{20} + 246233 q^{22} + 26304 q^{23} - 210646 q^{25} + 336384 q^{26} + 92334 q^{28} + 231048 q^{29} + 141004 q^{31} + 260892 q^{32} + 1512162 q^{34} + 342588 q^{35} - 836112 q^{37} + 2387040 q^{38} - 1906028 q^{40} - 1930344 q^{41} + 2877456 q^{43} - 5822808 q^{44} - 4951876 q^{46} + 2462532 q^{47} - 6581826 q^{49} + 2698797 q^{50} + 1655498 q^{52} - 6157836 q^{53} + 11721612 q^{55} - 11431080 q^{56} - 15150140 q^{58} + 2480268 q^{59} - 4195044 q^{61} + 6436524 q^{62} + 11301151 q^{64} - 11117640 q^{65} + 16682528 q^{67} + 14718306 q^{68} - 16625944 q^{70} + 20942628 q^{71} - 456824 q^{73} - 8747736 q^{74} + 18091206 q^{76} - 13904988 q^{77} - 12976692 q^{79} + 11893596 q^{80} - 32706099 q^{82} + 4471404 q^{83} + 25528128 q^{85} - 20374383 q^{86} + 25246815 q^{88} + 2477316 q^{89} - 18339604 q^{91} - 1026678 q^{92} - 4961738 q^{94} + 25328772 q^{95} - 34034202 q^{97} + 51534036 q^{98}+O(q^{100}) \) 24 * q - 3 * q^2 - 505 * q^4 + 72 * q^5 + 68 * q^7 + 4545 * q^8 + 4240 * q^10 - 5952 * q^11 - 16564 * q^13 + 29544 * q^14 + 13279 * q^16 + 65592 * q^17 - 37804 * q^19 - 120702 * q^20 + 246233 * q^22 + 26304 * q^23 - 210646 * q^25 + 336384 * q^26 + 92334 * q^28 + 231048 * q^29 + 141004 * q^31 + 260892 * q^32 + 1512162 * q^34 + 342588 * q^35 - 836112 * q^37 + 2387040 * q^38 - 1906028 * q^40 - 1930344 * q^41 + 2877456 * q^43 - 5822808 * q^44 - 4951876 * q^46 + 2462532 * q^47 - 6581826 * q^49 + 2698797 * q^50 + 1655498 * q^52 - 6157836 * q^53 + 11721612 * q^55 - 11431080 * q^56 - 15150140 * q^58 + 2480268 * q^59 - 4195044 * q^61 + 6436524 * q^62 + 11301151 * q^64 - 11117640 * q^65 + 16682528 * q^67 + 14718306 * q^68 - 16625944 * q^70 + 20942628 * q^71 - 456824 * q^73 - 8747736 * q^74 + 18091206 * q^76 - 13904988 * q^77 - 12976692 * q^79 + 11893596 * q^80 - 32706099 * q^82 + 4471404 * q^83 + 25528128 * q^85 - 20374383 * q^86 + 25246815 * q^88 + 2477316 * q^89 - 18339604 * q^91 - 1026678 * q^92 - 4961738 * q^94 + 25328772 * q^95 - 34034202 * q^97 + 51534036 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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