LMFDB - Embedded newform 5.8.b.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,8,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, 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:	$1.56192512742$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-29}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 29 $ x^2 + 29
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.2
Root			$5.38516i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.8.b.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.7703i q^{2} +32.3110i q^{3} +12.0000 q^{4} +(75.0000 - 269.258i) q^{5} -348.000 q^{6} -420.043i q^{7} +1507.85i q^{8} +1143.00 q^{9} +O(q^{10})$	\(q+10.7703i q^{2} +32.3110i q^{3} +12.0000 q^{4} +(75.0000 - 269.258i) q^{5} -348.000 q^{6} -420.043i q^{7} +1507.85i q^{8} +1143.00 q^{9} +(2900.00 + 807.775i) q^{10} -6828.00 q^{11} +387.732i q^{12} -10145.7i q^{13} +4524.00 q^{14} +(8700.00 + 2423.32i) q^{15} -14704.0 q^{16} +15681.6i q^{17} +12310.5i q^{18} +6860.00 q^{19} +(900.000 - 3231.10i) q^{20} +13572.0 q^{21} -73539.8i q^{22} +29219.9i q^{23} -48720.0 q^{24} +(-66875.0 - 40388.7i) q^{25} +109272. q^{26} +107596. i q^{27} -5040.51i q^{28} +25590.0 q^{29} +(-26100.0 + 93701.9i) q^{30} +82112.0 q^{31} +34637.4i q^{32} -220619. i q^{33} -168896. q^{34} +(-113100. - 31503.2i) q^{35} +13716.0 q^{36} -223527. i q^{37} +73884.5i q^{38} +327816. q^{39} +(406000. + 113088. i) q^{40} -533118. q^{41} +146175. i q^{42} +708935. i q^{43} -81936.0 q^{44} +(85725.0 - 307762. i) q^{45} -314708. q^{46} +5826.75i q^{47} -475101. i q^{48} +647107. q^{49} +(435000. - 720266. i) q^{50} -506688. q^{51} -121748. i q^{52} -589374. i q^{53} -1.15884e6 q^{54} +(-512100. + 1.83850e6i) q^{55} +633360. q^{56} +221653. i q^{57} +275613. i q^{58} +1.43898e6 q^{59} +(104400. + 29079.9i) q^{60} +1.38102e6 q^{61} +884373. i q^{62} -480109. i q^{63} -2.25517e6 q^{64} +(-2.73180e6 - 760924. i) q^{65} +2.37614e6 q^{66} -2.71487e6i q^{67} +188179. i q^{68} -944124. q^{69} +(339300. - 1.21812e6i) q^{70} -481608. q^{71} +1.72347e6i q^{72} +1.48618e6i q^{73} +2.40746e6 q^{74} +(1.30500e6 - 2.16080e6i) q^{75} +82320.0 q^{76} +2.86805e6i q^{77} +3.53069e6i q^{78} -1.05976e6 q^{79} +(-1.10280e6 + 3.95917e6i) q^{80} -976779. q^{81} -5.74186e6i q^{82} -2.60380e6i q^{83} +162864. q^{84} +(4.22240e6 + 1.17612e6i) q^{85} -7.63547e6 q^{86} +826838. i q^{87} -1.02956e7i q^{88} +5.64417e6 q^{89} +(3.31470e6 + 923287. i) q^{90} -4.26161e6 q^{91} +350639. i q^{92} +2.65312e6i q^{93} -62756.0 q^{94} +(514500. - 1.84711e6i) q^{95} -1.11917e6 q^{96} +1.20091e7i q^{97} +6.96956e6i q^{98} -7.80440e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 24 q^{4} + 150 q^{5} - 696 q^{6} + 2286 q^{9}+O(q^{10}) $ 2 * q + 24 * q^4 + 150 * q^5 - 696 * q^6 + 2286 * q^9	$ 2 q + 24 q^{4} + 150 q^{5} - 696 q^{6} + 2286 q^{9} + 5800 q^{10} - 13656 q^{11} + 9048 q^{14} + 17400 q^{15} - 29408 q^{16} + 13720 q^{19} + 1800 q^{20} + 27144 q^{21} - 97440 q^{24} - 133750 q^{25} + 218544 q^{26} + 51180 q^{29} - 52200 q^{30} + 164224 q^{31} - 337792 q^{34} - 226200 q^{35} + 27432 q^{36} + 655632 q^{39} + 812000 q^{40} - 1066236 q^{41} - 163872 q^{44} + 171450 q^{45} - 629416 q^{46} + 1294214 q^{49} + 870000 q^{50} - 1013376 q^{51} - 2317680 q^{54} - 1024200 q^{55} + 1266720 q^{56} + 2877960 q^{59} + 208800 q^{60} + 2762044 q^{61} - 4510336 q^{64} - 5463600 q^{65} + 4752288 q^{66} - 1888248 q^{69} + 678600 q^{70} - 963216 q^{71} + 4814928 q^{74} + 2610000 q^{75} + 164640 q^{76} - 2119520 q^{79} - 2205600 q^{80} - 1953558 q^{81} + 325728 q^{84} + 8444800 q^{85} - 15270936 q^{86} + 11288340 q^{89} + 6629400 q^{90} - 8523216 q^{91} - 125512 q^{94} + 1029000 q^{95} - 2238336 q^{96} - 15608808 q^{99}+O(q^{100}) $ 2 * q + 24 * q^4 + 150 * q^5 - 696 * q^6 + 2286 * q^9 + 5800 * q^10 - 13656 * q^11 + 9048 * q^14 + 17400 * q^15 - 29408 * q^16 + 13720 * q^19 + 1800 * q^20 + 27144 * q^21 - 97440 * q^24 - 133750 * q^25 + 218544 * q^26 + 51180 * q^29 - 52200 * q^30 + 164224 * q^31 - 337792 * q^34 - 226200 * q^35 + 27432 * q^36 + 655632 * q^39 + 812000 * q^40 - 1066236 * q^41 - 163872 * q^44 + 171450 * q^45 - 629416 * q^46 + 1294214 * q^49 + 870000 * q^50 - 1013376 * q^51 - 2317680 * q^54 - 1024200 * q^55 + 1266720 * q^56 + 2877960 * q^59 + 208800 * q^60 + 2762044 * q^61 - 4510336 * q^64 - 5463600 * q^65 + 4752288 * q^66 - 1888248 * q^69 + 678600 * q^70 - 963216 * q^71 + 4814928 * q^74 + 2610000 * q^75 + 164640 * q^76 - 2119520 * q^79 - 2205600 * q^80 - 1953558 * q^81 + 325728 * q^84 + 8444800 * q^85 - 15270936 * q^86 + 11288340 * q^89 + 6629400 * q^90 - 8523216 * q^91 - 125512 * q^94 + 1029000 * q^95 - 2238336 * q^96 - 15608808 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			10.7703i			0.951972i	0.879453	+	0.475986i	$0.157909\pi$
$2$			10.7703i			0.951972i	−0.879453	+	0.475986i	$0.842091\pi$
$3$			32.3110i			0.690917i	0.938434	+	0.345458i	$0.112277\pi$
$3$			32.3110i			0.690917i	−0.938434	+	0.345458i	$0.887723\pi$
$4$	12.0000			0.0937500
$5$	75.0000	−	269.258i	0.268328	−	0.963328i
$5$	75.0000	−	269.258i	0.268328	−	0.963328i
$6$	−348.000			−0.657733
$7$		−	420.043i		−	0.462861i	−0.972851	−	0.231430i	$-0.925659\pi$
$7$		−	420.043i		−	0.462861i	0.972851	−	0.231430i	$-0.0743406\pi$
$8$			1507.85i			1.04122i
$9$	1143.00			0.522634
$10$	2900.00	+	807.775i	0.917061	+	0.255441i
$11$	−6828.00			−1.54675			−0.773373	−	0.633951i	$-0.781432\pi$
$11$	−6828.00			−1.54675			−0.773373	+	0.633951i	$0.781432\pi$
$12$			387.732i			0.0647735i
$13$		−	10145.7i		−	1.28079i	−0.768045	−	0.640395i	$-0.778771\pi$
$13$		−	10145.7i		−	1.28079i	0.768045	−	0.640395i	$-0.221229\pi$
$14$	4524.00			0.440630
$15$	8700.00	+	2423.32i	0.665579	+	0.185392i
$16$	−14704.0			−0.897461
$17$			15681.6i			0.774139i	0.922050	+	0.387070i	$0.126513\pi$
$17$			15681.6i			0.774139i	−0.922050	+	0.387070i	$0.873487\pi$
$18$			12310.5i			0.497533i
$19$	6860.00			0.229449			0.114725	−	0.993397i	$-0.463401\pi$
$19$	6860.00			0.229449			0.114725	+	0.993397i	$0.463401\pi$
$20$	900.000	−	3231.10i	0.0251558	−	0.0903120i
$21$	13572.0			0.319798
$22$		−	73539.8i		−	1.47246i
$23$			29219.9i			0.500762i	0.968147	+	0.250381i	$0.0805559\pi$
$23$			29219.9i			0.500762i	−0.968147	+	0.250381i	$0.919444\pi$
$24$	−48720.0			−0.719396
$25$	−66875.0	−	40388.7i	−0.856000	−	0.516976i
$26$	109272.			1.21928
$27$			107596.i			1.05201i
$28$		−	5040.51i		−	0.0433932i
$29$	25590.0			0.194840			0.0974198	−	0.995243i	$-0.468941\pi$
$29$	25590.0			0.194840			0.0974198	+	0.995243i	$0.468941\pi$
$30$	−26100.0	+	93701.9i	−0.176488	+	0.633613i
$31$	82112.0			0.495040			0.247520	−	0.968883i	$-0.420384\pi$
$31$	82112.0			0.495040			0.247520	+	0.968883i	$0.420384\pi$
$32$			34637.4i			0.186862i
$33$		−	220619.i		−	1.06867i
$34$	−168896.			−0.736959
$35$	−113100.	−	31503.2i	−0.445887	−	0.124199i
$36$	13716.0			0.0489969
$37$		−	223527.i		−	0.725479i	−0.931891	−	0.362739i	$-0.881842\pi$
$37$		−	223527.i		−	0.725479i	0.931891	−	0.362739i	$-0.118158\pi$
$38$			73884.5i			0.218429i
$39$	327816.			0.884920
$40$	406000.	+	113088.i	1.00303	+	0.279388i
$41$	−533118.			−1.20804			−0.604018	−	0.796971i	$-0.706434\pi$
$41$	−533118.			−1.20804			−0.604018	+	0.796971i	$0.706434\pi$
$42$			146175.i			0.304439i
$43$			708935.i			1.35978i	0.733316	+	0.679888i	$0.237971\pi$
$43$			708935.i			1.35978i	−0.733316	+	0.679888i	$0.762029\pi$
$44$	−81936.0			−0.145007
$45$	85725.0	−	307762.i	0.140237	−	0.503467i
$46$	−314708.			−0.476711
$47$			5826.75i			0.00818623i	0.999992	+	0.00409311i	$0.00130288\pi$
$47$			5826.75i			0.00818623i	−0.999992	+	0.00409311i	$0.998697\pi$
$48$		−	475101.i		−	0.620071i
$49$	647107.			0.785760
$50$	435000.	−	720266.i	0.492146	−	0.814888i
$51$	−506688.			−0.534866
$52$		−	121748.i		−	0.120074i
$53$		−	589374.i		−	0.543783i	−0.962328	−	0.271891i	$-0.912351\pi$
$53$		−	589374.i		−	0.543783i	0.962328	−	0.271891i	$-0.0876491\pi$
$54$	−1.15884e6			−1.00149
$55$	−512100.	+	1.83850e6i	−0.415036	+	1.49002i
$56$	633360.			0.481940
$57$			221653.i			0.158530i
$58$			275613.i			0.185482i
$59$	1.43898e6			0.912164			0.456082	−	0.889938i	$-0.349252\pi$
$59$	1.43898e6			0.912164			0.456082	+	0.889938i	$0.349252\pi$
$60$	104400.	+	29079.9i	0.0623981	+	0.0173805i
$61$	1.38102e6			0.779016			0.389508	−	0.921023i	$-0.372645\pi$
$61$	1.38102e6			0.779016			0.389508	+	0.921023i	$0.372645\pi$
$62$			884373.i			0.471264i
$63$		−	480109.i		−	0.241907i
$64$	−2.25517e6			−1.07535
$65$	−2.73180e6	−	760924.i	−1.23382	−	0.343672i
$66$	2.37614e6			1.01735
$67$		−	2.71487e6i		−	1.10277i	−0.834250	−	0.551387i	$-0.814099\pi$
$67$		−	2.71487e6i		−	1.10277i	0.834250	−	0.551387i	$-0.185901\pi$
$68$			188179.i			0.0725756i
$69$	−944124.			−0.345985
$70$	339300.	−	1.21812e6i	0.118234	−	0.424471i
$71$	−481608.			−0.159694			−0.0798472	−	0.996807i	$-0.525443\pi$
$71$	−481608.			−0.159694			−0.0798472	+	0.996807i	$0.525443\pi$
$72$			1.72347e6i			0.544176i
$73$			1.48618e6i			0.447137i	0.974688	+	0.223568i	$0.0717706\pi$
$73$			1.48618e6i			0.447137i	−0.974688	+	0.223568i	$0.928229\pi$
$74$	2.40746e6			0.690635
$75$	1.30500e6	−	2.16080e6i	0.357187	−	0.591425i
$76$	82320.0			0.0215109
$77$			2.86805e6i			0.715928i
$78$			3.53069e6i			0.842419i
$79$	−1.05976e6			−0.241831			−0.120916	−	0.992663i	$-0.538583\pi$
$79$	−1.05976e6			−0.241831			−0.120916	+	0.992663i	$0.538583\pi$
$80$	−1.10280e6	+	3.95917e6i	−0.240814	+	0.864549i
$81$	−976779.			−0.204220
$82$		−	5.74186e6i		−	1.15002i
$83$		−	2.60380e6i		−	0.499844i	−0.968266	−	0.249922i	$-0.919595\pi$
$83$		−	2.60380e6i		−	0.499844i	0.968266	−	0.249922i	$-0.0804050\pi$
$84$	162864.			0.0299811
$85$	4.22240e6	+	1.17612e6i	0.745750	+	0.207723i
$86$	−7.63547e6			−1.29447
$87$			826838.i			0.134618i
$88$		−	1.02956e7i		−	1.61050i
$89$	5.64417e6			0.848663			0.424331	−	0.905507i	$-0.360509\pi$
$89$	5.64417e6			0.848663			0.424331	+	0.905507i	$0.360509\pi$
$90$	3.31470e6	+	923287.i	0.479287	+	0.133502i
$91$	−4.26161e6			−0.592828
$92$			350639.i			0.0469464i
$93$			2.65312e6i			0.342032i
$94$	−62756.0			−0.00779306
$95$	514500.	−	1.84711e6i	0.0615677	−	0.221035i
$96$	−1.11917e6			−0.129106
$97$			1.20091e7i			1.33601i	0.744158	+	0.668004i	$0.232851\pi$
$97$			1.20091e7i			1.33601i	−0.744158	+	0.668004i	$0.767149\pi$
$98$			6.96956e6i			0.748021i
$99$	−7.80440e6			−0.808382
$100$	−802500.	−	484665.i	−0.0802500	−	0.0484665i
$101$	5.14270e6			0.496668			0.248334	−	0.968674i	$-0.420117\pi$
$101$	5.14270e6			0.496668			0.248334	+	0.968674i	$0.420117\pi$
$102$		−	5.45720e6i		−	0.509177i
$103$			3.48477e6i			0.314227i	0.987581	+	0.157114i	$0.0502189\pi$
$103$			3.48477e6i			0.314227i	−0.987581	+	0.157114i	$0.949781\pi$
$104$	1.52981e7			1.33358
$105$	1.01790e6	−	3.65437e6i	0.0858109	−	0.308071i
$106$	6.34775e6			0.517666
$107$		−	1.48640e7i		−	1.17299i	−0.809954	−	0.586493i	$-0.800508\pi$
$107$		−	1.48640e7i		−	1.17299i	0.809954	−	0.586493i	$-0.199492\pi$
$108$			1.29115e6i			0.0986263i
$109$	−2.01124e7			−1.48755			−0.743773	−	0.668432i	$-0.766966\pi$
$109$	−2.01124e7			−1.48755			−0.743773	+	0.668432i	$0.766966\pi$
$110$	−1.98012e7	−	5.51549e6i	−1.41846	−	0.395102i
$111$	7.22239e6			0.501246
$112$			6.17631e6i			0.415400i
$113$		−	5.62633e6i		−	0.366818i	−0.983037	−	0.183409i	$-0.941287\pi$
$113$		−	5.62633e6i		−	0.366818i	0.983037	−	0.183409i	$-0.0587133\pi$
$114$	−2.38728e6			−0.150916
$115$	7.86770e6	+	2.19149e6i	0.482398	+	0.134369i
$116$	307080.			0.0182662
$117$		−	1.15965e7i		−	0.669384i
$118$			1.54983e7i			0.868354i
$119$	6.58694e6			0.358319
$120$	−3.65400e6	+	1.31183e7i	−0.193034	+	0.693014i
$121$	2.71344e7			1.39242
$122$			1.48741e7i			0.741601i
$123$		−	1.72256e7i		−	0.834653i
$124$	985344.			0.0464100
$125$	−1.58906e7	+	1.49775e7i	−0.727706	+	0.685889i
$126$	5.17093e6			0.230288
$127$			2.85360e7i			1.23618i	0.786109	+	0.618088i	$0.212092\pi$
$127$			2.85360e7i			1.23618i	−0.786109	+	0.618088i	$0.787908\pi$
$128$		−	1.98553e7i		−	0.836839i
$129$	−2.29064e7			−0.939492
$130$	8.19540e6	−	2.94224e7i	0.327166	−	1.17456i
$131$	−3.33132e7			−1.29469			−0.647346	−	0.762196i	$-0.724121\pi$
$131$	−3.33132e7			−1.29469			−0.647346	+	0.762196i	$0.724121\pi$
$132$		−	2.64743e6i		−	0.100188i
$133$		−	2.88149e6i		−	0.106203i
$134$	2.92400e7			1.04981
$135$	2.89710e7	+	8.06967e6i	1.01343	+	0.282285i
$136$	−2.36454e7			−0.806049
$137$		−	4.28099e7i		−	1.42240i	−0.702988	−	0.711202i	$-0.748151\pi$
$137$		−	4.28099e7i		−	1.42240i	0.702988	−	0.711202i	$-0.251849\pi$
$138$		−	1.01685e7i		−	0.329368i
$139$	1.13808e7			0.359436			0.179718	−	0.983718i	$-0.442481\pi$
$139$	1.13808e7			0.359436			0.179718	+	0.983718i	$0.442481\pi$
$140$	−1.35720e6	−	378039.i	−0.0418019	−	0.0116436i
$141$	−188268.			−0.00565600
$142$		−	5.18708e6i		−	0.152024i
$143$			6.92745e7i			1.98106i
$144$	−1.68067e7			−0.469043
$145$	1.91925e6	−	6.89032e6i	0.0522810	−	0.187694i
$146$	−1.60066e7			−0.425661
$147$			2.09087e7i			0.542895i
$148$		−	2.68233e6i		−	0.0680136i
$149$	4.00070e7			0.990794			0.495397	−	0.868667i	$-0.335023\pi$
$149$	4.00070e7			0.990794			0.495397	+	0.868667i	$0.335023\pi$
$150$	2.32725e7	+	1.40553e7i	0.563020	+	0.340032i
$151$	−2.86594e7			−0.677405			−0.338703	−	0.940893i	$-0.609988\pi$
$151$	−2.86594e7			−0.677405			−0.338703	+	0.940893i	$0.609988\pi$
$152$			1.03438e7i			0.238907i
$153$			1.79241e7i			0.404591i
$154$	−3.08899e7			−0.681544
$155$	6.15840e6	−	2.21093e7i	0.132833	−	0.476886i
$156$	3.93379e6			0.0829613
$157$		−	3.01958e7i		−	0.622728i	−0.950291	−	0.311364i	$-0.899214\pi$
$157$		−	3.01958e7i		−	0.622728i	0.950291	−	0.311364i	$-0.100786\pi$
$158$		−	1.14140e7i		−	0.230217i
$159$	1.90433e7			0.375709
$160$	9.32640e6	+	2.59780e6i	0.180009	+	0.0501402i
$161$	1.22736e7			0.231783
$162$		−	1.05202e7i		−	0.194412i
$163$		−	9.35416e7i		−	1.69180i	−0.533345	−	0.845898i	$-0.679065\pi$
$163$		−	9.35416e7i		−	1.69180i	0.533345	−	0.845898i	$-0.320935\pi$
$164$	−6.39742e6			−0.113253
$165$	−5.94036e7	−	1.65465e7i	−1.02948	−	0.286755i
$166$	2.80438e7			0.475838
$167$			5.73507e7i			0.952865i	0.879211	+	0.476432i	$0.158070\pi$
$167$			5.73507e7i			0.952865i	−0.879211	+	0.476432i	$0.841930\pi$
$168$			2.04645e7i			0.332980i
$169$	−4.01857e7			−0.640425
$170$	−1.26672e7	+	4.54766e7i	−0.197747	+	0.709933i
$171$	7.84098e6			0.119918
$172$			8.50722e6i			0.127479i
$173$		−	4.87192e7i		−	0.715383i	−0.933840	−	0.357691i	$-0.883564\pi$
$173$		−	4.87192e7i		−	0.715383i	0.933840	−	0.357691i	$-0.116436\pi$
$174$	−8.90532e6			−0.128153
$175$	−1.69650e7	+	2.80904e7i	−0.239288	+	0.396209i
$176$	1.00399e8			1.38814
$177$			4.64949e7i			0.630229i
$178$			6.07896e7i			0.807903i
$179$	1.93505e7			0.252178			0.126089	−	0.992019i	$-0.459757\pi$
$179$	1.93505e7			0.252178			0.126089	+	0.992019i	$0.459757\pi$
$180$	1.02870e6	−	3.69315e6i	0.0131473	−	0.0472001i
$181$	7.82617e7			0.981011			0.490506	−	0.871438i	$-0.336812\pi$
$181$	7.82617e7			0.981011			0.490506	+	0.871438i	$0.336812\pi$
$182$		−	4.58989e7i		−	0.564355i
$183$			4.46222e7i			0.538235i
$184$	−4.40591e7			−0.521403
$185$	−6.01866e7	−	1.67646e7i	−0.698874	−	0.194666i
$186$	−2.85750e7			−0.325605
$187$		−	1.07074e8i		−	1.19740i
$188$			69921.0i			0.000767459i
$189$	4.51948e7			0.486936
$190$	1.98940e7	+	5.54133e6i	0.210419	+	0.0586107i
$191$	−1.19454e8			−1.24046			−0.620229	−	0.784420i	$-0.712960\pi$
$191$	−1.19454e8			−1.24046			−0.620229	+	0.784420i	$0.712960\pi$
$192$		−	7.28667e7i		−	0.742976i
$193$			5.98469e7i			0.599227i	0.954061	+	0.299613i	$0.0968577\pi$
$193$			5.98469e7i			0.599227i	−0.954061	+	0.299613i	$0.903142\pi$
$194$	−1.29342e8			−1.27184
$195$	2.45862e7	−	8.82672e7i	0.237449	−	0.852468i
$196$	7.76528e6			0.0736650
$197$			1.22964e8i			1.14590i	0.819589	+	0.572952i	$0.194202\pi$
$197$			1.22964e8i			1.14590i	−0.819589	+	0.572952i	$0.805798\pi$
$198$		−	8.40560e7i		−	0.769557i
$199$	1.69053e8			1.52067			0.760337	−	0.649529i	$-0.225034\pi$
$199$	1.69053e8			1.52067			0.760337	+	0.649529i	$0.225034\pi$
$200$	6.09000e7	−	1.00837e8i	0.538285	−	0.891283i
$201$	8.77200e7			0.761925
$202$			5.53886e7i			0.472814i
$203$		−	1.07489e7i		−	0.0901836i
$204$	−6.08026e6			−0.0501437
$205$	−3.99838e7	+	1.43546e8i	−0.324150	+	1.16373i
$206$	−3.75321e7			−0.299136
$207$			3.33984e7i			0.261715i
$208$			1.49182e8i			1.14946i
$209$	−4.68401e7			−0.354900
$210$	3.93588e7	+	1.09631e7i	0.293275	+	0.0816896i
$211$	−2.67605e8			−1.96113			−0.980565	−	0.196195i	$-0.937141\pi$
$211$	−2.67605e8			−1.96113			−0.980565	+	0.196195i	$0.937141\pi$
$212$		−	7.07249e6i		−	0.0509796i
$213$		−	1.55612e7i		−	0.110336i
$214$	1.60090e8			1.11665
$215$	1.90887e8	+	5.31702e7i	1.30991	+	0.364866i
$216$	−1.62238e8			−1.09538
$217$		−	3.44906e7i		−	0.229135i
$218$		−	2.16617e8i		−	1.41610i
$219$	−4.80198e7			−0.308934
$220$	−6.14520e6	+	2.20619e7i	−0.0389096	+	0.139690i
$221$	1.59100e8			0.991510
$222$			7.77875e7i			0.477172i
$223$		−	1.49333e8i		−	0.901753i	−0.892586	−	0.450877i	$-0.851111\pi$
$223$		−	1.49333e8i		−	0.901753i	0.892586	−	0.450877i	$-0.148889\pi$
$224$	1.45492e7			0.0864909
$225$	−7.64381e7	−	4.61643e7i	−0.447374	−	0.270189i
$226$	6.05975e7			0.349201
$227$		−	2.34185e8i		−	1.32883i	−0.747365	−	0.664414i	$-0.768681\pi$
$227$		−	2.34185e8i		−	1.32883i	0.747365	−	0.664414i	$-0.231319\pi$
$228$			2.65984e6i			0.0148622i
$229$	−1.31882e8			−0.725706			−0.362853	−	0.931846i	$-0.618197\pi$
$229$	−1.31882e8			−0.725706			−0.362853	+	0.931846i	$0.618197\pi$
$230$	−2.36031e7	+	8.47377e7i	−0.127915	+	0.459229i
$231$	−9.26696e7			−0.494647
$232$			3.85858e7i			0.202871i
$233$			1.83419e8i			0.949948i	0.880000	+	0.474974i	$0.157542\pi$
$233$			1.83419e8i			0.949948i	−0.880000	+	0.474974i	$0.842458\pi$
$234$	1.24898e8			0.637235
$235$	1.56890e6	+	437006.i	0.00788602	+	0.00219660i
$236$	1.72678e7			0.0855153
$237$		−	3.42419e7i		−	0.167085i
$238$			7.09436e7i			0.341109i
$239$	−1.05117e8			−0.498058			−0.249029	−	0.968496i	$-0.580111\pi$
$239$	−1.05117e8			−0.498058			−0.249029	+	0.968496i	$0.580111\pi$
$240$	−1.27925e8	−	3.56326e7i	−0.597331	−	0.166383i
$241$	1.94216e8			0.893770			0.446885	−	0.894591i	$-0.352533\pi$
$241$	1.94216e8			0.893770			0.446885	+	0.894591i	$0.352533\pi$
$242$			2.92247e8i			1.32555i
$243$			2.03751e8i			0.910914i
$244$	1.65723e7			0.0730327
$245$	4.85330e7	−	1.74239e8i	0.210841	−	0.756944i
$246$	1.85525e8			0.794566
$247$		−	6.95992e7i		−	0.293876i
$248$			1.23812e8i			0.515446i
$249$	8.41314e7			0.345351
$250$	−1.61312e8	−	1.71147e8i	−0.652947	−	0.692755i
$251$	2.02689e8			0.809045			0.404523	−	0.914528i	$-0.367438\pi$
$251$	2.02689e8			0.809045			0.404523	+	0.914528i	$0.367438\pi$
$252$		−	5.76131e6i		−	0.0226788i
$253$		−	1.99514e8i		−	0.774552i
$254$	−3.07342e8			−1.17680
$255$	−3.80016e7	+	1.36430e8i	−0.143520	+	0.515251i
$256$	−7.48132e7			−0.278701
$257$		−	1.34593e7i		−	0.0494603i	−0.999694	−	0.0247301i	$-0.992127\pi$
$257$		−	1.34593e7i		−	0.0494603i	0.999694	−	0.0247301i	$-0.00787265\pi$
$258$		−	2.46710e8i		−	0.894369i
$259$	−9.38911e7			−0.335796
$260$	−3.27816e7	−	9.13109e6i	−0.115671	−	0.0322193i
$261$	2.92494e7			0.101830
$262$		−	3.58794e8i		−	1.23251i
$263$			1.42205e8i			0.482026i	0.970522	+	0.241013i	$0.0774797\pi$
$263$			1.42205e8i			0.482026i	−0.970522	+	0.241013i	$0.922520\pi$
$264$	3.32660e8			1.11272
$265$	−1.58694e8	−	4.42030e7i	−0.523841	−	0.145912i
$266$	3.10346e7			0.101102
$267$			1.82369e8i			0.586355i
$268$		−	3.25784e7i		−	0.103385i
$269$	−5.07548e8			−1.58981			−0.794903	−	0.606737i	$-0.792478\pi$
$269$	−5.07548e8			−1.58981			−0.794903	+	0.606737i	$0.792478\pi$
$270$	−8.69130e7	+	3.12027e8i	−0.268727	+	0.964760i
$271$	1.12836e8			0.344393			0.172197	−	0.985063i	$-0.444914\pi$
$271$	1.12836e8			0.344393			0.172197	+	0.985063i	$0.444914\pi$
$272$		−	2.30582e8i		−	0.694760i
$273$		−	1.37697e8i		−	0.409595i
$274$	4.61077e8			1.35409
$275$	4.56622e8	+	2.75774e8i	1.32401	+	0.799630i
$276$	−1.13295e7			−0.0324361
$277$			5.10728e8i			1.44381i	0.691991	+	0.721906i	$0.256734\pi$
$277$			5.10728e8i			1.44381i	−0.691991	+	0.721906i	$0.743266\pi$
$278$			1.22575e8i			0.342173i
$279$	9.38540e7			0.258725
$280$	4.75020e7	−	1.70537e8i	0.129318	−	0.464266i
$281$	−1.70459e8			−0.458297			−0.229148	−	0.973391i	$-0.573594\pi$
$281$	−1.70459e8			−0.458297			−0.229148	+	0.973391i	$0.573594\pi$
$282$		−	2.02771e6i		−	0.00538435i
$283$		−	1.62144e8i		−	0.425253i	−0.977134	−	0.212626i	$-0.931798\pi$
$283$		−	1.62144e8i		−	0.425253i	0.977134	−	0.212626i	$-0.0682017\pi$
$284$	−5.77930e6			−0.0149713
$285$	5.96820e7	+	1.66240e7i	0.152717	+	0.0425382i
$286$	−7.46109e8			−1.88591
$287$			2.23932e8i			0.559153i
$288$			3.95905e7i			0.0976602i
$289$	1.64426e8			0.400708
$290$	7.42110e7	+	2.06710e7i	0.178680	+	0.0497700i
$291$	−3.88026e8			−0.923071
$292$			1.78341e7i			0.0419191i
$293$		−	3.85845e8i		−	0.896141i	−0.893998	−	0.448070i	$-0.852111\pi$
$293$		−	3.85845e8i		−	0.896141i	0.893998	−	0.448070i	$-0.147889\pi$
$294$	−2.25193e8			−0.516820
$295$	1.07924e8	−	3.87457e8i	0.244759	−	0.878712i
$296$	3.37045e8			0.755382
$297$		−	7.34663e8i		−	1.62720i
$298$			4.30888e8i			0.943208i
$299$	2.96455e8			0.641371
$300$	1.56600e7	−	2.59296e7i	0.0334863	−	0.0554461i
$301$	2.97783e8			0.629387
$302$		−	3.08672e8i		−	0.644871i
$303$			1.66166e8i			0.343157i
$304$	−1.00869e8			−0.205922
$305$	1.03577e8	−	3.71852e8i	0.209032	−	0.750447i
$306$	−1.93048e8			−0.385159
$307$			6.37817e8i			1.25809i	0.777369	+	0.629045i	$0.216554\pi$
$307$			6.37817e8i			1.25809i	−0.777369	+	0.629045i	$0.783446\pi$
$308$			3.44166e7i			0.0671183i
$309$	−1.12596e8			−0.217105
$310$	2.38125e8	+	6.63280e7i	0.453982	+	0.126454i
$311$	−7.27817e8			−1.37202			−0.686010	−	0.727592i	$-0.740640\pi$
$311$	−7.27817e8			−1.37202			−0.686010	+	0.727592i	$0.740640\pi$
$312$			4.94296e8i			0.921396i
$313$			4.46869e8i			0.823711i	0.911249	+	0.411855i	$0.135119\pi$
$313$			4.46869e8i			0.823711i	−0.911249	+	0.411855i	$0.864881\pi$
$314$	3.25219e8			0.592819
$315$	−1.29273e8	−	3.60082e7i	−0.233035	−	0.0649104i
$316$	−1.27171e7			−0.0226717
$317$		−	5.91083e8i		−	1.04218i	−0.853503	−	0.521088i	$-0.825526\pi$
$317$		−	5.91083e8i		−	1.04218i	0.853503	−	0.521088i	$-0.174474\pi$
$318$			2.05102e8i			0.357664i
$319$	−1.74729e8			−0.301367
$320$	−1.69138e8	+	6.07223e8i	−0.288546	+	1.03591i
$321$	4.80271e8			0.810436
$322$			1.32191e8i			0.220651i
$323$			1.07576e8i			0.177626i
$324$	−1.17213e7			−0.0191456
$325$	−4.09770e8	+	6.78490e8i	−0.662138	+	1.09636i
$326$	1.00747e9			1.61054
$327$		−	6.49851e8i		−	1.02777i
$328$		−	8.03860e8i		−	1.25783i
$329$	2.44748e6			0.00378908
$330$	1.78211e8	−	6.39796e8i	0.272983	−	0.980038i
$331$	5.84868e8			0.886462			0.443231	−	0.896407i	$-0.353832\pi$
$331$	5.84868e8			0.886462			0.443231	+	0.896407i	$0.353832\pi$
$332$		−	3.12456e7i		−	0.0468604i
$333$		−	2.55492e8i		−	0.379160i
$334$	−6.17686e8			−0.907100
$335$	−7.31000e8	−	2.03615e8i	−1.06233	−	0.295905i
$336$	−1.99563e8			−0.287007
$337$			7.39373e8i			1.05235i	0.850377	+	0.526174i	$0.176374\pi$
$337$			7.39373e8i			1.05235i	−0.850377	+	0.526174i	$0.823626\pi$
$338$		−	4.32813e8i		−	0.609666i
$339$	1.81792e8			0.253441
$340$	5.06688e7	+	1.41134e7i	0.0699140	+	0.0194741i
$341$	−5.60661e8			−0.765702
$342$			8.44499e7i			0.114158i
$343$		−	6.17736e8i		−	0.826558i
$344$	−1.06897e9			−1.41582
$345$	−7.08093e7	+	2.54213e8i	−0.0928375	+	0.333297i
$346$	5.24722e8			0.681024
$347$			3.70870e8i			0.476506i	0.971203	+	0.238253i	$0.0765747\pi$
$347$			3.70870e8i			0.476506i	−0.971203	+	0.238253i	$0.923425\pi$
$348$			9.92206e6i			0.0126204i
$349$	1.13274e9			1.42640			0.713199	−	0.700962i	$-0.247246\pi$
$349$	1.13274e9			1.42640			0.713199	+	0.700962i	$0.247246\pi$
$350$	−3.02542e8	−	1.82719e8i	−0.377180	−	0.227795i
$351$	1.09163e9			1.34741
$352$		−	2.36504e8i		−	0.289028i
$353$			8.32858e8i			1.00777i	0.863772	+	0.503883i	$0.168096\pi$
$353$			8.32858e8i			1.00777i	−0.863772	+	0.503883i	$0.831904\pi$
$354$	−5.00765e8			−0.599960
$355$	−3.61206e7	+	1.29677e8i	−0.0428505	+	0.153838i
$356$	6.77300e7			0.0795621
$357$			2.12831e8i			0.247569i
$358$			2.08412e8i			0.240066i
$359$	6.75318e8			0.770332			0.385166	−	0.922847i	$-0.374144\pi$
$359$	6.75318e8			0.770332			0.385166	+	0.922847i	$0.374144\pi$
$360$	4.64058e8	+	1.29260e8i	0.524220	+	0.146018i
$361$	−8.46812e8			−0.947353
$362$			8.42904e8i			0.933895i
$363$			8.76740e8i			0.962050i
$364$	−5.11393e7			−0.0555776
$365$	4.00165e8	+	1.11463e8i	0.430739	+	0.119979i
$366$	−4.80596e8			−0.512385
$367$		−	1.80237e9i		−	1.90333i	−0.307141	−	0.951664i	$-0.599372\pi$
$367$		−	1.80237e9i		−	1.90333i	0.307141	−	0.951664i	$-0.400628\pi$
$368$		−	4.29649e8i		−	0.449414i
$369$	−6.09354e8			−0.631360
$370$	1.80560e8	−	6.48230e8i	0.185317	−	0.665308i
$371$	−2.47562e8			−0.251696
$372$			3.18374e7i			0.0320655i
$373$			9.29928e8i			0.927830i	0.885880	+	0.463915i	$0.153556\pi$
$373$			9.29928e8i			0.927830i	−0.885880	+	0.463915i	$0.846444\pi$
$374$	1.15322e9			1.13989
$375$	−4.83938e8	−	5.13442e8i	−0.473893	−	0.502784i
$376$	−8.78584e6			−0.00852365
$377$		−	2.59627e8i		−	0.249549i
$378$			4.86762e8i			0.463549i
$379$	−1.43545e9			−1.35441			−0.677206	−	0.735794i	$-0.736809\pi$
$379$	−1.43545e9			−1.35441			−0.677206	+	0.735794i	$0.736809\pi$
$380$	6.17400e6	−	2.21653e7i	0.00577197	−	0.0207220i
$381$	−9.22026e8			−0.854094
$382$		−	1.28655e9i		−	1.18088i
$383$		−	1.57707e9i		−	1.43435i	−0.696894	−	0.717174i	$-0.745435\pi$
$383$		−	1.57707e9i		−	1.43435i	0.696894	−	0.717174i	$-0.254565\pi$
$384$	6.41545e8			0.578186
$385$	7.72247e8	+	2.15104e8i	0.689674	+	0.192104i
$386$	−6.44571e8			−0.570447
$387$			8.10313e8i			0.710664i
$388$			1.44109e8i			0.125251i
$389$	2.24425e9			1.93307			0.966537	−	0.256528i	$-0.0825785\pi$
$389$	2.24425e9			1.93307			0.966537	+	0.256528i	$0.0825785\pi$
$390$	9.50666e8	+	2.64801e8i	0.811525	+	0.226045i
$391$	−4.58215e8			−0.387660
$392$			9.75738e8i			0.818148i
$393$		−	1.07638e9i		−	0.894525i
$394$	−1.32437e9			−1.09087
$395$	−7.94820e7	+	2.85349e8i	−0.0648902	+	0.232963i
$396$	−9.36528e7			−0.0757858
$397$		−	2.26641e8i		−	0.181791i	−0.995860	−	0.0908956i	$-0.971027\pi$
$397$		−	2.26641e8i		−	0.181791i	0.995860	−	0.0908956i	$-0.0289729\pi$
$398$			1.82075e9i			1.44764i
$399$	9.31039e7			0.0733775
$400$	9.83330e8	+	5.93876e8i	0.768227	+	0.463966i
$401$	−9.11721e8			−0.706085			−0.353042	−	0.935607i	$-0.614853\pi$
$401$	−9.11721e8			−0.706085			−0.353042	+	0.935607i	$0.614853\pi$
$402$			9.44773e8i			0.725331i
$403$		−	8.33080e8i		−	0.634043i
$404$	6.17124e7			0.0465627
$405$	−7.32584e7	+	2.63006e8i	−0.0547980	+	0.196731i
$406$	1.15769e8			0.0858523
$407$			1.52625e9i			1.12213i
$408$		−	7.64008e8i		−	0.556913i
$409$	−2.55215e8			−0.184449			−0.0922243	−	0.995738i	$-0.529398\pi$
$409$	−2.55215e8			−0.184449			−0.0922243	+	0.995738i	$0.529398\pi$
$410$	−1.54604e9	−	4.30639e8i	−1.10784	−	0.308582i
$411$	1.38323e9			0.982763
$412$			4.18173e7i			0.0294588i
$413$		−	6.04433e8i		−	0.422205i
$414$	−3.59711e8			−0.249145
$415$	−7.01095e8	−	1.95285e8i	−0.481514	−	0.134122i
$416$	3.51419e8			0.239331
$417$			3.67726e8i			0.248341i
$418$		−	5.04483e8i		−	0.337854i
$419$	2.96316e8			0.196791			0.0983957	−	0.995147i	$-0.468629\pi$
$419$	2.96316e8			0.196791			0.0983957	+	0.995147i	$0.468629\pi$
$420$	1.22148e7	−	4.38525e7i	0.00804477	−	0.0288816i
$421$	1.06676e9			0.696754			0.348377	−	0.937354i	$-0.386733\pi$
$421$	1.06676e9			0.696754			0.348377	+	0.937354i	$0.386733\pi$
$422$		−	2.88220e9i		−	1.86694i
$423$			6.65997e6i			0.00427840i
$424$	8.88685e8			0.566197
$425$	6.33360e8	−	1.04871e9i	0.400211	−	0.662663i
$426$	1.67600e8			0.105036
$427$		−	5.80088e8i		−	0.360576i
$428$		−	1.78368e8i		−	0.109967i
$429$	−2.23833e9			−1.36875
$430$	−5.72660e8	+	2.05591e9i	−0.347342	+	1.24700i
$431$	9.53169e7			0.0573455			0.0286728	−	0.999589i	$-0.490872\pi$
$431$	9.53169e7			0.0573455			0.0286728	+	0.999589i	$0.490872\pi$
$432$		−	1.58209e9i		−	0.944141i
$433$			1.89973e9i			1.12456i	0.826946	+	0.562281i	$0.190076\pi$
$433$			1.89973e9i			1.12456i	−0.826946	+	0.562281i	$0.809924\pi$
$434$	3.71475e8			0.218130
$435$	2.22633e8	+	6.20129e7i	0.129681	+	0.0361218i
$436$	−2.41348e8			−0.139457
$437$			2.00449e8i			0.114899i
$438$		−	5.17189e8i		−	0.294097i
$439$	−1.11226e9			−0.627450			−0.313725	−	0.949514i	$-0.601577\pi$
$439$	−1.11226e9			−0.627450			−0.313725	+	0.949514i	$0.601577\pi$
$440$	−2.77217e9	−	7.72168e8i	−1.55144	−	0.432143i
$441$	7.39643e8			0.410665
$442$			1.71356e9i			0.943890i
$443$			3.22249e9i			1.76108i	0.473972	+	0.880540i	$0.342820\pi$
$443$			3.22249e9i			1.76108i	−0.473972	+	0.880540i	$0.657180\pi$
$444$	8.66687e7			0.0469918
$445$	4.23313e8	−	1.51974e9i	0.227720	−	0.817540i
$446$	1.60836e9			0.858443
$447$			1.29266e9i			0.684557i
$448$			9.47267e8i			0.497736i
$449$	−7.29482e7			−0.0380323			−0.0190161	−	0.999819i	$-0.506053\pi$
$449$	−7.29482e7			−0.0380323			−0.0190161	+	0.999819i	$0.506053\pi$
$450$	4.97205e8	−	8.23264e8i	0.257212	−	0.425888i
$451$	3.64013e9			1.86853
$452$		−	6.75160e7i		−	0.0343892i
$453$		−	9.26015e8i		−	0.468031i
$454$	2.52225e9			1.26501
$455$	−3.19621e8	+	1.14747e9i	−0.159072	+	0.571087i
$456$	−3.34219e8			−0.165065
$457$			2.45286e8i			0.120217i	0.998192	+	0.0601085i	$0.0191447\pi$
$457$			2.45286e8i			0.120217i	−0.998192	+	0.0601085i	$0.980855\pi$
$458$		−	1.42041e9i		−	0.690852i
$459$	−1.68727e9			−0.814405
$460$	9.44124e7	+	2.62979e7i	0.0452248	+	0.0125971i
$461$	−3.25654e9			−1.54812			−0.774058	−	0.633115i	$-0.781776\pi$
$461$	−3.25654e9			−1.54812			−0.774058	+	0.633115i	$0.781776\pi$
$462$		−	9.98082e8i		−	0.470890i
$463$			5.48463e8i			0.256811i	0.991722	+	0.128406i	$0.0409859\pi$
$463$			5.48463e8i			0.256811i	−0.991722	+	0.128406i	$0.959014\pi$
$464$	−3.76275e8			−0.174861
$465$	7.14374e8	+	1.98984e8i	0.329489	+	0.0917768i
$466$	−1.97549e9			−0.904323
$467$		−	1.31891e9i		−	0.599245i	−0.954058	−	0.299623i	$-0.903139\pi$
$467$		−	1.31891e9i		−	0.599245i	0.954058	−	0.299623i	$-0.0968607\pi$
$468$		−	1.39158e8i		−	0.0627548i
$469$	−1.14036e9			−0.510431
$470$	−4.70670e6	+	1.68976e7i	−0.00209110	+	0.00750727i
$471$	9.75658e8			0.430253
$472$			2.16976e9i			0.949762i
$473$		−	4.84061e9i		−	2.10323i
$474$	3.68796e8			0.159061
$475$	−4.58762e8	−	2.77067e8i	−0.196408	−	0.118620i
$476$	7.90433e7			0.0335924
$477$		−	6.73654e8i		−	0.284199i
$478$		−	1.13214e9i		−	0.474137i
$479$	1.59989e9			0.665144			0.332572	−	0.943078i	$-0.392084\pi$
$479$	1.59989e9			0.665144			0.332572	+	0.943078i	$0.392084\pi$
$480$	−8.39376e7	+	3.01345e8i	−0.0346427	+	0.124371i
$481$	−2.26783e9			−0.929187
$482$			2.09177e9i			0.850844i
$483$			3.96573e8i			0.160143i
$484$	3.25613e8			0.130540
$485$	3.23355e9	+	9.00682e8i	1.28701	+	0.358489i
$486$	−2.19446e9			−0.867165
$487$		−	1.95948e9i		−	0.768759i	−0.923175	−	0.384380i	$-0.874415\pi$
$487$		−	1.95948e9i		−	0.768759i	0.923175	−	0.384380i	$-0.125585\pi$
$488$			2.08237e9i			0.811126i
$489$	3.02242e9			1.16889
$490$	1.87661e9	+	5.22717e8i	0.720589	+	0.200715i
$491$	2.38785e8			0.0910376			0.0455188	−	0.998963i	$-0.485506\pi$
$491$	2.38785e8			0.0910376			0.0455188	+	0.998963i	$0.485506\pi$
$492$		−	2.06707e8i		−	0.0782487i
$493$			4.01292e8i			0.150833i
$494$	7.49606e8			0.279762
$495$	−5.85330e8	+	2.10140e9i	−0.216912	+	0.778737i
$496$	−1.20737e9			−0.444279
$497$			2.02296e8i			0.0739163i
$498$			9.06123e8i			0.328764i
$499$	−3.06642e9			−1.10479			−0.552394	−	0.833583i	$-0.686286\pi$
$499$	−3.06642e9			−1.10479			−0.552394	+	0.833583i	$0.686286\pi$
$500$	−1.90688e8	+	1.79730e8i	−0.0682224	+	0.0643021i
$501$	−1.85306e9			−0.658350
$502$			2.18303e9i			0.770188i
$503$			1.60348e9i			0.561793i	0.959738	+	0.280897i	$0.0906318\pi$
$503$			1.60348e9i			0.561793i	−0.959738	+	0.280897i	$0.909368\pi$
$504$	7.23930e8			0.251878
$505$	3.85703e8	−	1.38471e9i	0.133270	−	0.478454i
$506$	2.14883e9			0.737351
$507$		−	1.29844e9i		−	0.442480i
$508$			3.42432e8i			0.115891i
$509$	−1.21742e9			−0.409192			−0.204596	−	0.978847i	$-0.565588\pi$
$509$	−1.21742e9			−0.409192			−0.204596	+	0.978847i	$0.565588\pi$
$510$	−1.46940e9	−	4.09290e8i	−0.490505	−	0.136627i
$511$	6.24258e8			0.206962
$512$		−	3.34724e9i		−	1.10215i
$513$			7.38106e8i			0.241384i
$514$	1.44961e8			0.0470848
$515$	9.38304e8	+	2.61358e8i	0.302704	+	0.0843161i
$516$	−2.74877e8			−0.0880773
$517$		−	3.97850e7i		−	0.0126620i
$518$		−	1.01124e9i		−	0.319668i
$519$	1.57416e9			0.494270
$520$	1.14736e9	−	4.11913e9i	0.357838	−	1.28468i
$521$	−2.08635e9			−0.646331			−0.323166	−	0.946342i	$-0.604747\pi$
$521$	−2.08635e9			−0.646331			−0.323166	+	0.946342i	$0.604747\pi$
$522$			3.15025e8i			0.0969390i
$523$		−	4.28922e9i		−	1.31106i	−0.755169	−	0.655531i	$-0.772445\pi$
$523$		−	4.28922e9i		−	1.31106i	0.755169	−	0.655531i	$-0.227555\pi$
$524$	−3.99758e8			−0.121377
$525$	−9.07628e8	−	5.48156e8i	−0.273747	−	0.165328i
$526$	−1.53160e9			−0.458875
$527$			1.28765e9i			0.383230i
$528$			3.24399e9i			0.959093i
$529$	2.55102e9			0.749237
$530$	4.76081e8	−	1.70918e9i	0.138904	−	0.498682i
$531$	1.64475e9			0.476727
$532$		−	3.45779e7i		−	0.00995654i
$533$			5.40883e9i			1.54724i
$534$	−1.96417e9			−0.558194
$535$	−4.00226e9	−	1.11480e9i	−1.12997	−	0.314745i
$536$	4.09360e9			1.14823
$537$			6.25235e8i			0.174234i
$538$		−	5.46646e9i		−	1.51345i
$539$	−4.41845e9			−1.21537
$540$	3.47652e8	+	9.68360e7i	0.0950094	+	0.0264642i
$541$	4.91116e9			1.33350			0.666751	−	0.745280i	$-0.267684\pi$
$541$	4.91116e9			1.33350			0.666751	+	0.745280i	$0.267684\pi$
$542$			1.21528e9i			0.327852i
$543$			2.52871e9i			0.677797i
$544$	−5.43170e8			−0.144657
$545$	−1.50843e9	+	5.41542e9i	−0.399151	+	1.43299i
$546$	1.48304e9			0.389923
$547$			1.76451e9i			0.460965i	0.973077	+	0.230482i	$0.0740304\pi$
$547$			1.76451e9i			0.460965i	−0.973077	+	0.230482i	$0.925970\pi$
$548$		−	5.13719e8i		−	0.133350i
$549$	1.57851e9			0.407140
$550$	−2.97018e9	+	4.91797e9i	−0.761226	+	1.26042i
$551$	1.75547e8			0.0447058
$552$		−	1.42359e9i		−	0.360246i
$553$			4.45145e8i			0.111934i
$554$	−5.50071e9			−1.37447
$555$	5.41679e8	−	1.94469e9i	0.134498	−	0.482864i
$556$	1.36570e8			0.0336971
$557$		−	4.13406e8i		−	0.101364i	−0.998715	−	0.0506820i	$-0.983860\pi$
$557$		−	4.13406e8i		−	0.101364i	0.998715	−	0.0506820i	$-0.0161395\pi$
$558$			1.01084e9i			0.246299i
$559$	7.19261e9			1.74159
$560$	1.66302e9	+	4.63223e8i	0.400166	+	0.111463i
$561$	3.45967e9			0.827302
$562$		−	1.83590e9i		−	0.436286i
$563$		−	7.57073e9i		−	1.78796i	−0.448104	−	0.893982i	$-0.647900\pi$
$563$		−	7.57073e9i		−	1.78796i	0.448104	−	0.893982i	$-0.352100\pi$
$564$	−2.25922e6			−0.000530250
$565$	−1.51494e9	−	4.21975e8i	−0.353366	−	0.0984277i
$566$	1.74634e9			0.404829
$567$			4.10289e8i			0.0945255i
$568$		−	7.26191e8i		−	0.166277i
$569$	−8.90287e8			−0.202599			−0.101299	−	0.994856i	$-0.532300\pi$
$569$	−8.90287e8			−0.202599			−0.101299	+	0.994856i	$0.532300\pi$
$570$	−1.79046e8	+	6.42795e8i	−0.0404951	+	0.145382i
$571$	−4.96089e9			−1.11515			−0.557575	−	0.830126i	$-0.688268\pi$
$571$	−4.96089e9			−1.11515			−0.557575	+	0.830126i	$0.688268\pi$
$572$			8.31294e8i			0.185724i
$573$		−	3.85966e9i		−	0.857054i
$574$	−2.41183e9			−0.532297
$575$	1.18016e9	−	1.95408e9i	0.258882	−	0.428652i
$576$	−2.57766e9			−0.562013
$577$			1.53066e9i			0.331713i	0.986150	+	0.165856i	$0.0530388\pi$
$577$			1.53066e9i			0.331713i	−0.986150	+	0.165856i	$0.946961\pi$
$578$			1.77092e9i			0.381463i
$579$	−1.93371e9			−0.414016
$580$	2.30310e7	−	8.26838e7i	0.00490134	−	0.0175963i
$581$	−1.09371e9			−0.231358
$582$		−	4.17916e9i		−	0.878737i
$583$			4.02425e9i			0.841094i
$584$	−2.24093e9			−0.465567
$585$	−3.12245e9	−	8.69736e8i	−0.644836	−	0.179615i
$586$	4.15568e9			0.853100
$587$		−	4.39564e9i		−	0.896992i	−0.893785	−	0.448496i	$-0.851960\pi$
$587$		−	4.39564e9i		−	0.896992i	0.893785	−	0.448496i	$-0.148040\pi$
$588$			2.50904e8i			0.0508964i
$589$	5.63288e8			0.113587
$590$	4.17304e9	+	1.16237e9i	0.836509	+	0.233004i
$591$	−3.97310e9			−0.791724
$592$			3.28675e9i			0.651089i
$593$			3.32990e9i			0.655753i	0.944721	+	0.327877i	$0.106333\pi$
$593$			3.32990e9i			0.655753i	−0.944721	+	0.327877i	$0.893667\pi$
$594$	7.91256e9			1.54905
$595$	4.94021e8	−	1.77359e9i	0.0961470	−	0.345178i
$596$	4.80083e8			0.0928870
$597$			5.46226e9i			1.05066i
$598$			3.19292e9i			0.610567i
$599$	4.53030e9			0.861258			0.430629	−	0.902529i	$-0.358292\pi$
$599$	4.53030e9			0.861258			0.430629	+	0.902529i	$0.358292\pi$
$600$	3.25815e9	+	1.96774e9i	0.615803	+	0.371910i
$601$	−4.70479e9			−0.884056			−0.442028	−	0.897001i	$-0.645741\pi$
$601$	−4.70479e9			−0.884056			−0.442028	+	0.897001i	$0.645741\pi$
$602$			3.20722e9i			0.599158i
$603$		−	3.10309e9i		−	0.576347i
$604$	−3.43913e8			−0.0635067
$605$	2.03508e9	−	7.30616e9i	0.373627	−	1.34136i
$606$	−1.78966e9			−0.326675
$607$			2.24429e9i			0.407303i	0.979043	+	0.203652i	$0.0652810\pi$
$607$			2.24429e9i			0.407303i	−0.979043	+	0.203652i	$0.934719\pi$
$608$			2.37612e8i			0.0428752i
$609$	3.47307e8			0.0623094
$610$	4.00496e9	+	1.11555e9i	0.714404	+	0.198992i
$611$	5.91162e7			0.0104848
$612$			2.15089e8i			0.0379304i
$613$			8.74415e9i			1.53323i	0.642109	+	0.766613i	$0.278059\pi$
$613$			8.74415e9i			1.53323i	−0.642109	+	0.766613i	$0.721941\pi$
$614$	−6.86950e9			−1.19767
$615$	−4.63813e9	−	1.29192e9i	−0.804044	−	0.223961i
$616$	−4.32458e9			−0.745438
$617$		−	4.49031e9i		−	0.769623i	−0.922995	−	0.384812i	$-0.874266\pi$
$617$		−	4.49031e9i		−	0.769623i	0.922995	−	0.384812i	$-0.125734\pi$
$618$		−	1.21270e9i		−	0.206678i
$619$	3.74101e9			0.633974			0.316987	−	0.948430i	$-0.397329\pi$
$619$	3.74101e9			0.633974			0.316987	+	0.948430i	$0.397329\pi$
$620$	7.39008e7	−	2.65312e8i	0.0124531	−	0.0447081i
$621$	−3.14393e9			−0.526808
$622$		−	7.83883e9i		−	1.30612i
$623$		−	2.37079e9i		−	0.392813i
$624$	−4.82021e9			−0.794181
$625$	2.84102e9	+	5.40199e9i	0.465472	+	0.885063i
$626$	−4.81292e9			−0.784149
$627$		−	1.51345e9i		−	0.245206i
$628$		−	3.62350e8i		−	0.0583808i
$629$	3.50527e9			0.561622
$630$	3.87820e8	−	1.39232e9i	0.0617928	−	0.221843i
$631$	1.93545e9			0.306675			0.153337	−	0.988174i	$-0.450998\pi$
$631$	1.93545e9			0.306675			0.153337	+	0.988174i	$0.450998\pi$
$632$		−	1.59796e9i		−	0.251799i
$633$		−	8.64660e9i		−	1.35498i
$634$	6.36616e9			0.992122
$635$	7.68355e9	+	2.14020e9i	1.19084	+	0.331701i
$636$	2.28519e8			0.0352227
$637$		−	6.56532e9i		−	1.00639i
$638$		−	1.88188e9i		−	0.286893i
$639$	−5.50478e8			−0.0834616
$640$	−5.34621e9	−	1.48915e9i	−0.806150	−	0.224547i
$641$	5.89076e9			0.883422			0.441711	−	0.897157i	$-0.354372\pi$
$641$	5.89076e9			0.883422			0.441711	+	0.897157i	$0.354372\pi$
$642$			5.17268e9i			0.771512i
$643$			3.16008e9i			0.468770i	0.972144	+	0.234385i	$0.0753076\pi$
$643$			3.16008e9i			0.468770i	−0.972144	+	0.234385i	$0.924692\pi$
$644$	1.47283e8			0.0217297
$645$	−1.71798e9	+	6.16774e9i	−0.252092	+	0.905038i
$646$	−1.15863e9			−0.169095
$647$			1.27557e10i			1.85157i	0.378054	+	0.925783i	$0.376593\pi$
$647$			1.27557e10i			1.85157i	−0.378054	+	0.925783i	$0.623407\pi$
$648$		−	1.47283e9i		−	0.212638i
$649$	−9.82536e9			−1.41089
$650$	−7.30756e9	−	4.41336e9i	−1.04370	−	0.630336i
$651$	1.11442e9			0.158313
$652$		−	1.12250e9i		−	0.158606i
$653$		−	4.43892e9i		−	0.623852i	−0.950106	−	0.311926i	$-0.899026\pi$
$653$		−	4.43892e9i		−	0.623852i	0.950106	−	0.311926i	$-0.100974\pi$
$654$	6.99910e9			0.978409
$655$	−2.49849e9	+	8.96985e9i	−0.347402	+	1.24721i
$656$	7.83897e9			1.08417
$657$			1.69870e9i			0.233689i
$658$			2.63602e7i			0.00360710i
$659$	−1.08526e10			−1.47719			−0.738595	−	0.674149i	$-0.764511\pi$
$659$	−1.08526e10			−1.47719			−0.738595	+	0.674149i	$0.764511\pi$
$660$	−7.12843e8	−	1.98557e8i	−0.0965140	−	0.0268833i
$661$	8.49307e9			1.14382			0.571912	−	0.820315i	$-0.306202\pi$
$661$	8.49307e9			1.14382			0.571912	+	0.820315i	$0.306202\pi$
$662$			6.29922e9i			0.843887i
$663$			5.14068e9i			0.685051i
$664$	3.92613e9			0.520447
$665$	−7.75866e8	−	2.16112e8i	−0.102308	−	0.0284973i
$666$	2.75173e9			0.360949
$667$			7.47737e8i			0.0975683i
$668$			6.88209e8i			0.0893311i
$669$	4.82509e9			0.623037
$670$	2.19300e9	−	7.87311e9i	0.281694	−	1.01131i
$671$	−9.42962e9			−1.20494
$672$			4.70099e8i			0.0597581i
$673$		−	4.20188e9i		−	0.531362i	−0.964061	−	0.265681i	$-0.914403\pi$
$673$		−	4.20188e9i		−	0.531362i	0.964061	−	0.265681i	$-0.0855969\pi$
$674$	−7.96330e9			−1.00180
$675$	4.34565e9	−	7.19546e9i	0.543866	−	0.900524i
$676$	−4.82228e8			−0.0600398
$677$		−	6.56755e9i		−	0.813472i	−0.913546	−	0.406736i	$-0.866667\pi$
$677$		−	6.56755e9i		−	0.813472i	0.913546	−	0.406736i	$-0.133333\pi$
$678$			1.95796e9i			0.241269i
$679$	5.04433e9			0.618386
$680$	−1.77341e9	+	6.36673e9i	−0.216286	+	0.776489i
$681$	7.56676e9			0.918110
$682$		−	6.03850e9i		−	0.728927i
$683$			6.31484e9i			0.758386i	0.925318	+	0.379193i	$0.123798\pi$
$683$			6.31484e9i			0.758386i	−0.925318	+	0.379193i	$0.876202\pi$
$684$	9.40918e7			0.0112423
$685$	−1.15269e10	−	3.21075e9i	−1.37024	−	0.381671i
$686$	6.65322e9			0.786860
$687$		−	4.26123e9i		−	0.501403i
$688$		−	1.04242e10i		−	1.22035i
$689$	−5.97958e9			−0.696472
$690$	−2.73796e9	−	7.62640e8i	−0.317289	−	0.0883787i
$691$	3.76447e9			0.434041			0.217020	−	0.976167i	$-0.430366\pi$
$691$	3.76447e9			0.434041			0.217020	+	0.976167i	$0.430366\pi$
$692$		−	5.84630e8i		−	0.0670672i
$693$			3.27818e9i			0.374168i
$694$	−3.99439e9			−0.453620
$695$	8.53562e8	−	3.06438e9i	0.0964468	−	0.346255i
$696$	−1.24674e9			−0.140167
$697$		−	8.36014e9i		−	0.935188i
$698$			1.22000e10i			1.35789i
$699$	−5.92646e9			−0.656335
$700$	−2.03580e8	+	3.37084e8i	−0.0224332	+	0.0371446i
$701$	1.97083e9			0.216090			0.108045	−	0.994146i	$-0.465541\pi$
$701$	1.97083e9			0.216090			0.108045	+	0.994146i	$0.465541\pi$
$702$			1.17572e10i			1.28270i
$703$		−	1.53340e9i		−	0.166461i
$704$	1.53983e10			1.66329
$705$	−1.41201e7	+	5.06927e7i	−0.00151766	+	0.00544858i
$706$	−8.97016e9			−0.959364
$707$		−	2.16016e9i		−	0.229888i
$708$			5.57938e8i			0.0590840i
$709$	−9.62853e9			−1.01461			−0.507304	−	0.861767i	$-0.669358\pi$
$709$	−9.62853e9			−1.01461			−0.507304	+	0.861767i	$0.669358\pi$
$710$	−1.39666e9	−	3.89031e8i	−0.146449	−	0.0407924i
$711$	−1.21131e9			−0.126389
$712$			8.51054e9i			0.883644i
$713$			2.39930e9i			0.247897i
$714$	−2.29226e9			−0.235678
$715$	1.86527e10	+	5.19559e9i	1.90841	+	0.531574i
$716$	2.32206e8			0.0236417
$717$		−	3.39643e9i		−	0.344117i
$718$			7.27340e9i			0.733334i
$719$	1.89490e10			1.90123			0.950614	−	0.310376i	$-0.100455\pi$
$719$	1.89490e10			1.90123			0.950614	+	0.310376i	$0.100455\pi$
$720$	−1.26050e9	+	4.52533e9i	−0.125858	+	0.451842i
$721$	1.46375e9			0.145444
$722$		−	9.12045e9i		−	0.901853i
$723$			6.27532e9i			0.617521i
$724$	9.39140e8			0.0919698
$725$	−1.71133e9	−	1.03355e9i	−0.166783	−	0.100727i
$726$	−9.44278e9			−0.915844
$727$		−	1.44446e9i		−	0.139423i	−0.997567	−	0.0697116i	$-0.977792\pi$
$727$		−	1.44446e9i		−	0.139423i	0.997567	−	0.0697116i	$-0.0222079\pi$
$728$		−	6.42585e9i		−	0.617264i
$729$	−8.71961e9			−0.833586
$730$	−1.20050e9	+	4.30991e9i	−0.114217	+	0.410051i
$731$	−1.11172e10			−1.05266
$732$			5.35466e8i			0.0504595i
$733$		−	1.38939e10i		−	1.30305i	−0.758627	−	0.651525i	$-0.774129\pi$
$733$		−	1.38939e10i		−	1.30305i	0.758627	−	0.651525i	$-0.225871\pi$
$734$	1.94122e10			1.81191
$735$	5.62983e9	+	1.56815e9i	0.522986	+	0.145674i
$736$	−1.01210e9			−0.0935732
$737$			1.85371e10i			1.70571i
$738$		−	6.56294e9i		−	0.601037i
$739$	−1.19008e10			−1.08473			−0.542366	−	0.840142i	$-0.682471\pi$
$739$	−1.19008e10			−1.08473			−0.542366	+	0.840142i	$0.682471\pi$
$740$	−7.22239e8	−	2.01175e8i	−0.0655194	−	0.0182500i
$741$	2.24882e9			0.203044
$742$		−	2.66633e9i		−	0.239607i
$743$		−	1.57512e10i		−	1.40882i	−0.709796	−	0.704408i	$-0.751213\pi$
$743$		−	1.57512e10i		−	1.40882i	0.709796	−	0.704408i	$-0.248787\pi$
$744$	−4.00050e9			−0.356130
$745$	3.00052e9	−	1.07722e10i	0.265858	−	0.954459i
$746$	−1.00156e10			−0.883268
$747$		−	2.97615e9i		−	0.261235i
$748$		−	1.28489e9i		−	0.112256i
$749$	−6.24352e9			−0.542929
$750$	5.52994e9	−	5.21217e9i	0.478636	−	0.451132i
$751$	−1.60645e10			−1.38397			−0.691984	−	0.721912i	$-0.743263\pi$
$751$	−1.60645e10			−1.38397			−0.691984	+	0.721912i	$0.743263\pi$
$752$		−	8.56765e7i		−	0.00734682i
$753$			6.54909e9i			0.558983i
$754$	2.79627e9			0.237563
$755$	−2.14946e9	+	7.71679e9i	−0.181767	+	0.652563i
$756$	5.42337e8			0.0456502
$757$			1.88969e10i			1.58327i	0.610993	+	0.791636i	$0.290771\pi$
$757$			1.88969e10i			1.58327i	−0.610993	+	0.791636i	$0.709229\pi$
$758$		−	1.54603e10i		−	1.28936i
$759$	6.44648e9			0.535151
$760$	2.78516e9	+	7.75787e8i	0.230146	+	0.0641054i
$761$	1.01100e10			0.831584			0.415792	−	0.909460i	$-0.363504\pi$
$761$	1.01100e10			0.831584			0.415792	+	0.909460i	$0.363504\pi$
$762$		−	9.93053e9i		−	0.813074i
$763$			8.44806e9i			0.688527i
$764$	−1.43344e9			−0.116293
$765$	4.82620e9	+	1.34431e9i	0.389754	+	0.108563i
$766$	1.69855e10			1.36546
$767$		−	1.45994e10i		−	1.16829i
$768$		−	2.41729e9i		−	0.192559i
$769$	2.00677e10			1.59132			0.795658	−	0.605746i	$-0.207125\pi$
$769$	2.00677e10			1.59132			0.795658	+	0.605746i	$0.207125\pi$
$770$	−2.31674e9	+	8.31735e9i	−0.182877	+	0.656550i
$771$	4.34883e8			0.0341729
$772$			7.18163e8i			0.0561775i
$773$			2.15770e10i			1.68020i	0.542428	+	0.840102i	$0.317505\pi$
$773$			2.15770e10i			1.68020i	−0.542428	+	0.840102i	$0.682495\pi$
$774$	−8.72734e9			−0.676532
$775$	−5.49124e9	−	3.31640e9i	−0.423755	−	0.255924i
$776$	−1.81079e10			−1.39108
$777$		−	3.03371e9i		−	0.232007i
$778$			2.41714e10i			1.84023i
$779$	−3.65719e9			−0.277183
$780$	2.95034e8	−	1.05921e9i	0.0222608	−	0.0799189i
$781$	3.28842e9			0.247007
$782$		−	4.93512e9i		−	0.369041i
$783$			2.75337e9i			0.204974i
$784$	−9.51506e9			−0.705189
$785$	−8.13048e9	−	2.26469e9i	−0.599891	−	0.167095i
$786$	1.15930e10			0.851563
$787$			2.32055e10i			1.69699i	0.529205	+	0.848494i	$0.322490\pi$
$787$			2.32055e10i			1.69699i	−0.529205	+	0.848494i	$0.677510\pi$
$788$			1.47557e9i			0.107428i
$789$	−4.59479e9			−0.333040
$790$	−3.07330e9	−	8.56047e8i	−0.221774	−	0.0617736i
$791$	−2.36330e9			−0.169786
$792$		−	1.17678e10i		−	0.841703i
$793$		−	1.40114e10i		−	0.997756i
$794$	2.44100e9			0.173060
$795$	1.42824e9	−	5.12755e9i	0.100813	−	0.361931i
$796$	2.02863e9			0.142563
$797$		−	6.77123e8i		−	0.0473766i	−0.999719	−	0.0236883i	$-0.992459\pi$
$797$		−	6.77123e8i		−	0.0473766i	0.999719	−	0.0236883i	$-0.00754092\pi$
$798$			1.00276e9i			0.0698533i
$799$	−9.13727e7			−0.00633728
$800$	1.39896e9	−	2.31637e9i	0.0966029	−	0.159954i
$801$	6.45129e9			0.443540
$802$		−	9.81954e9i		−	0.672173i
$803$		−	1.01476e10i		−	0.691607i
$804$	1.05264e9			0.0714305
$805$	9.20521e8	−	3.30477e9i	0.0621939	−	0.223283i
$806$	8.97254e9			0.603591
$807$		−	1.63994e10i		−	1.09842i
$808$			7.75440e9i			0.517141i
$809$	5.84504e9			0.388122			0.194061	−	0.980990i	$-0.437834\pi$
$809$	5.84504e9			0.388122			0.194061	+	0.980990i	$0.437834\pi$
$810$	−2.83266e9	−	7.89017e8i	−0.187282	−	0.0521662i
$811$	1.91491e10			1.26060			0.630299	−	0.776353i	$-0.282932\pi$
$811$	1.91491e10			1.26060			0.630299	+	0.776353i	$0.282932\pi$
$812$		−	1.28987e8i		−	0.00845472i
$813$			3.64584e9i			0.237947i
$814$	−1.64382e10			−1.06824
$815$	−2.51868e10	−	7.01562e9i	−1.62975	−	0.453957i
$816$	7.45034e9			0.480021
$817$			4.86330e9i			0.311999i
$818$		−	2.74875e9i		−	0.175590i
$819$	−4.87102e9			−0.309832
$820$	−4.79806e8	+	1.72256e9i	−0.0303891	+	0.109100i
$821$	6.17006e9			0.389124			0.194562	−	0.980890i	$-0.437671\pi$
$821$	6.17006e9			0.389124			0.194562	+	0.980890i	$0.437671\pi$
$822$			1.48979e10i			0.935562i
$823$		−	2.25285e10i		−	1.40875i	−0.709830	−	0.704373i	$-0.751228\pi$
$823$		−	2.25285e10i		−	1.40875i	0.709830	−	0.704373i	$-0.248772\pi$
$824$	−5.25450e9			−0.327180
$825$	−8.91054e9	+	1.47539e10i	−0.552478	+	0.914784i
$826$	6.50995e9			0.401927
$827$		−	6.08545e9i		−	0.374131i	−0.982347	−	0.187065i	$-0.940102\pi$
$827$		−	6.08545e9i		−	0.374131i	0.982347	−	0.187065i	$-0.0598976\pi$
$828$			4.00780e8i			0.0245358i
$829$	−4.81588e9			−0.293586			−0.146793	−	0.989167i	$-0.546895\pi$
$829$	−4.81588e9			−0.293586			−0.146793	+	0.989167i	$0.546895\pi$
$830$	2.10329e9	−	7.55103e9i	0.127681	−	0.458387i
$831$	−1.65021e10			−0.997554
$832$			2.28801e10i			1.37730i
$833$			1.01477e10i			0.608288i
$834$	−3.96053e9			−0.236413
$835$	1.54422e10	+	4.30130e9i	0.917921	+	0.255680i
$836$	−5.62081e8			−0.0332718
$837$			8.83489e9i			0.520789i
$838$			3.19142e9i			0.187340i
$839$	2.92635e10			1.71064			0.855320	−	0.518100i	$-0.173360\pi$
$839$	2.92635e10			1.71064			0.855320	+	0.518100i	$0.173360\pi$
$840$	5.51023e9	+	1.53484e9i	0.320769	+	0.0893480i
$841$	−1.65950e10			−0.962038
$842$			1.14894e10i			0.663290i
$843$		−	5.50769e9i		−	0.316645i
$844$	−3.21127e9			−0.183856
$845$	−3.01393e9	+	1.08203e10i	−0.171844	+	0.616939i
$846$	−7.17301e7			−0.00407291
$847$		−	1.13976e10i		−	0.644499i
$848$			8.66615e9i			0.488024i
$849$	5.23902e9			0.293814
$850$	1.12949e10	+	6.82150e9i	0.630837	+	0.380990i
$851$	6.53145e9			0.363292
$852$		−	1.86735e8i		−	0.0103440i
$853$		−	2.17155e10i		−	1.19797i	−0.800759	−	0.598987i	$-0.795570\pi$
$853$		−	2.17155e10i		−	1.19797i	0.800759	−	0.598987i	$-0.204430\pi$
$854$	6.24774e9			0.343258
$855$	5.88074e8	−	2.11125e9i	0.0321773	−	0.115520i
$856$	2.24126e10			1.22134
$857$		−	4.01757e9i		−	0.218037i	−0.994040	−	0.109019i	$-0.965229\pi$
$857$		−	4.01757e9i		−	0.218037i	0.994040	−	0.109019i	$-0.0347708\pi$
$858$		−	2.41075e10i		−	1.30301i
$859$	−1.62487e10			−0.874666			−0.437333	−	0.899300i	$-0.644077\pi$
$859$	−1.62487e10			−0.874666			−0.437333	+	0.899300i	$0.644077\pi$
$860$	2.29064e9	+	6.38042e8i	0.122804	+	0.0342062i
$861$	−7.23548e9			−0.386328
$862$			1.02659e9i			0.0545913i
$863$			1.95958e10i			1.03783i	0.854826	+	0.518914i	$0.173664\pi$
$863$			1.95958e10i			1.03783i	−0.854826	+	0.518914i	$0.826336\pi$
$864$	−3.72683e9			−0.196581
$865$	−1.31180e10	−	3.65394e9i	−0.689148	−	0.191957i
$866$	−2.04607e10			−1.07055
$867$			5.31277e9i			0.276856i
$868$		−	4.13887e8i		−	0.0214814i
$869$	7.23604e9			0.374052
$870$	−6.67899e8	+	2.39783e9i	−0.0343869	+	0.123453i
$871$	−2.75441e10			−1.41242
$872$		−	3.03264e10i		−	1.54886i
$873$			1.37264e10i			0.698243i
$874$	−2.15890e9			−0.109381
$875$	6.29119e9	+	6.67474e9i	0.317471	+	0.336827i
$876$	−5.76238e8			−0.0289626
$877$		−	3.67840e10i		−	1.84145i	−0.390207	−	0.920727i	$-0.627597\pi$
$877$		−	3.67840e10i		−	1.84145i	0.390207	−	0.920727i	$-0.372403\pi$
$878$		−	1.19794e10i		−	0.597314i
$879$	1.24670e10			0.619159
$880$	7.52992e9	−	2.70332e10i	0.372478	−	1.33724i
$881$	1.48378e9			0.0731062			0.0365531	−	0.999332i	$-0.488362\pi$
$881$	1.48378e9			0.0731062			0.0365531	+	0.999332i	$0.488362\pi$
$882$			7.96620e9i			0.390941i
$883$			2.36597e10i			1.15650i	0.815859	+	0.578250i	$0.196264\pi$
$883$			2.36597e10i			1.15650i	−0.815859	+	0.578250i	$0.803736\pi$
$884$	1.90920e9			0.0929541
$885$	1.25191e10	+	3.48712e9i	0.607117	+	0.169108i
$886$	−3.47073e10			−1.67650
$887$			4.21269e9i			0.202687i	0.994851	+	0.101344i	$0.0323142\pi$
$887$			4.21269e9i			0.202687i	−0.994851	+	0.101344i	$0.967686\pi$
$888$			1.08903e10i			0.521907i
$889$	1.19863e10			0.572177
$890$	1.63681e10	+	4.55922e9i	0.778275	+	0.216783i
$891$	6.66945e9			0.315877
$892$		−	1.79199e9i		−	0.0845394i
$893$			3.99715e7i			0.00187832i
$894$	−1.39224e10			−0.651678
$895$	1.45129e9	−	5.21029e9i	0.0676665	−	0.242930i
$896$	−8.34008e9			−0.387340
$897$			9.57875e9i			0.443134i
$898$		−	7.85676e8i		−	0.0362056i
$899$	2.10125e9			0.0964535
$900$	−9.17258e8	−	5.53972e8i	−0.0419414	−	0.0253302i
$901$	9.24233e9			0.420964
$902$			3.92054e10i			1.77878i
$903$			9.62167e9i			0.434854i
$904$	8.48365e9			0.381938
$905$	5.86962e9	−	2.10726e10i	0.263233	−	0.945035i
$906$	9.97349e9			0.445552
$907$			1.32662e10i			0.590367i	0.955441	+	0.295184i	$0.0953808\pi$
$907$			1.32662e10i			0.590367i	−0.955441	+	0.295184i	$0.904619\pi$
$908$		−	2.81022e9i		−	0.124578i
$909$	5.87811e9			0.259576
$910$	−1.23587e10	−	3.44242e9i	−0.543659	−	0.151432i
$911$	7.15727e9			0.313641			0.156821	−	0.987627i	$-0.449876\pi$
$911$	7.15727e9			0.313641			0.156821	+	0.987627i	$0.449876\pi$
$912$		−	3.25919e9i		−	0.142275i
$913$			1.77788e10i			0.773132i
$914$	−2.64181e9			−0.114443
$915$	1.20149e10	+	3.34666e9i	0.518497	+	0.144424i
$916$	−1.58258e9			−0.0680349
$917$			1.39930e10i			0.599263i
$918$		−	1.81725e10i		−	0.775291i
$919$	9.78152e9			0.415721			0.207860	−	0.978158i	$-0.433350\pi$
$919$	9.78152e9			0.415721			0.207860	+	0.978158i	$0.433350\pi$
$920$	−3.30443e9	+	1.18633e10i	−0.139907	+	0.502282i
$921$	−2.06085e10			−0.869236
$922$		−	3.50740e10i		−	1.47376i
$923$			4.88623e9i			0.204535i
$924$	−1.11204e9			−0.0463732
$925$	−9.02799e9	+	1.49484e10i	−0.375055	+	0.621010i
$926$	−5.90713e9			−0.244477
$927$			3.98309e9i			0.164226i
$928$			8.86371e8i			0.0364080i
$929$	−2.92073e10			−1.19519			−0.597594	−	0.801799i	$-0.703876\pi$
$929$	−2.92073e10			−1.19519			−0.597594	+	0.801799i	$0.703876\pi$
$930$	−2.14312e9	+	7.69405e9i	−0.0873689	+	0.313664i
$931$	4.43915e9			0.180292
$932$			2.20103e9i			0.0890576i
$933$		−	2.35165e10i		−	0.947952i
$934$	1.42050e10			0.570464
$935$	−2.88305e10	−	8.03055e9i	−1.15349	−	0.321295i
$936$	1.74857e10			0.696976
$937$		−	3.72053e10i		−	1.47746i	−0.674000	−	0.738731i	$-0.735425\pi$
$937$		−	3.72053e10i		−	1.47746i	0.674000	−	0.738731i	$-0.264575\pi$
$938$		−	1.22821e10i		−	0.485916i
$939$	−1.44388e10			−0.569116
$940$	1.88268e7	+	5.24407e6i	0.000739314	+	0.000205931i
$941$	6.20016e9			0.242571			0.121286	−	0.992618i	$-0.461298\pi$
$941$	6.20016e9			0.242571			0.121286	+	0.992618i	$0.461298\pi$
$942$			1.05082e10i			0.409589i
$943$		−	1.55777e10i		−	0.604938i
$944$	−2.11588e10			−0.818631
$945$	3.38961e9	−	1.21691e10i	0.130659	−	0.469079i
$946$	5.21350e10			2.00221
$947$			1.27543e10i			0.488015i	0.969773	+	0.244008i	$0.0784622\pi$
$947$			1.27543e10i			0.488015i	−0.969773	+	0.244008i	$0.921538\pi$
$948$		−	4.10903e8i		−	0.0156643i
$949$	1.50782e10			0.572689
$950$	2.98410e9	−	4.94102e9i	0.112923	−	0.186975i
$951$	1.90985e10			0.720057
$952$			9.93210e9i			0.373088i
$953$		−	3.08638e10i		−	1.15511i	−0.816351	−	0.577556i	$-0.804006\pi$
$953$		−	3.08638e10i		−	1.15511i	0.816351	−	0.577556i	$-0.195994\pi$
$954$	7.25548e9			0.270550
$955$	−8.95902e9	+	3.21639e10i	−0.332850	+	1.19497i
$956$	−1.26140e9			−0.0466929
$957$		−	5.64565e9i		−	0.208220i
$958$			1.72313e10i			0.633198i
$959$	−1.79820e10			−0.658375
$960$	−1.96200e10	−	5.46500e9i	−0.715729	−	0.199361i
$961$	−2.07702e10			−0.754935
$962$		−	2.44253e10i		−	0.884559i
$963$		−	1.69896e10i		−	0.613042i
$964$	2.33060e9			0.0837910
$965$	1.61143e10	+	4.48852e9i	0.577252	+	0.160789i
$966$	−4.27122e9			−0.152451
$967$			3.32539e10i			1.18263i	0.806439	+	0.591317i	$0.201392\pi$
$967$			3.32539e10i			1.18263i	−0.806439	+	0.591317i	$0.798608\pi$
$968$			4.09145e10i			1.44982i
$969$	−3.47588e9			−0.122725
$970$	−9.70064e9	+	3.48264e10i	−0.341271	+	1.22520i
$971$	4.45095e10			1.56022			0.780108	−	0.625644i	$-0.215164\pi$
$971$	4.45095e10			1.56022			0.780108	+	0.625644i	$0.215164\pi$
$972$			2.44501e9i			0.0853982i
$973$		−	4.78043e9i		−	0.166369i
$974$	2.11043e10			0.731837
$975$	−2.19227e10	−	1.32401e10i	−0.757492	−	0.457482i
$976$	−2.03065e10			−0.699136
$977$		−	6.80736e9i		−	0.233533i	−0.993159	−	0.116766i	$-0.962747\pi$
$977$		−	6.80736e9i		−	0.233533i	0.993159	−	0.116766i	$-0.0372529\pi$
$978$			3.25525e10i			1.11275i
$979$	−3.85384e10			−1.31267
$980$	5.82396e8	−	2.09087e9i	0.0197664	−	0.0709635i
$981$	−2.29884e10			−0.777442
$982$			2.57179e9i			0.0866652i
$983$			6.37498e8i			0.0214063i	0.999943	+	0.0107031i	$0.00340698\pi$
$983$			6.37498e8i			0.0214063i	−0.999943	+	0.0107031i	$0.996593\pi$
$984$	2.59735e10			0.869056
$985$	3.31092e10	+	9.22234e9i	1.10388	+	0.307478i
$986$	−4.32205e9			−0.143589
$987$			7.90806e7i			0.00261794i
$988$		−	8.35190e8i		−	0.0275509i
$989$	−2.07150e10			−0.680924
$990$	−2.26328e10	−	6.30420e9i	−0.741335	−	0.206494i
$991$	5.60147e10			1.82828			0.914142	−	0.405393i	$-0.132865\pi$
$991$	5.60147e10			1.82828			0.914142	+	0.405393i	$0.132865\pi$
$992$			2.84414e9i			0.0925041i
$993$			1.88977e10i			0.612472i
$994$	−2.17879e9			−0.0703662
$995$	1.26789e10	−	4.55188e10i	0.408040	−	1.46491i
$996$	1.00958e9			0.0323766
$997$			8.97443e9i			0.286796i	0.989665	+	0.143398i	$0.0458030\pi$
$997$			8.97443e9i			0.286796i	−0.989665	+	0.143398i	$0.954197\pi$
$998$		−	3.30263e10i		−	1.05173i
$999$	2.40506e10			0.763214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.8.b.a.4.2	yes	2
3.2	odd	2		45.8.b.a.19.1		2
4.3	odd	2		80.8.c.a.49.1		2
5.2	odd	4		25.8.a.d.1.1		2
5.3	odd	4		25.8.a.d.1.2		2
5.4	even	2	inner	5.8.b.a.4.1	✓	2
8.3	odd	2		320.8.c.c.129.2		2
8.5	even	2		320.8.c.d.129.1		2
15.2	even	4		225.8.a.n.1.2		2
15.8	even	4		225.8.a.n.1.1		2
15.14	odd	2		45.8.b.a.19.2		2
20.3	even	4		400.8.a.y.1.2		2
20.7	even	4		400.8.a.y.1.1		2
20.19	odd	2		80.8.c.a.49.2		2
40.19	odd	2		320.8.c.c.129.1		2
40.29	even	2		320.8.c.d.129.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.8.b.a.4.1	✓	2	5.4	even	2	inner
5.8.b.a.4.2	yes	2	1.1	even	1	trivial
25.8.a.d.1.1		2	5.2	odd	4
25.8.a.d.1.2		2	5.3	odd	4
45.8.b.a.19.1		2	3.2	odd	2
45.8.b.a.19.2		2	15.14	odd	2
80.8.c.a.49.1		2	4.3	odd	2
80.8.c.a.49.2		2	20.19	odd	2
225.8.a.n.1.1		2	15.8	even	4
225.8.a.n.1.2		2	15.2	even	4
320.8.c.c.129.1		2	40.19	odd	2
320.8.c.c.129.2		2	8.3	odd	2
320.8.c.d.129.1		2	8.5	even	2
320.8.c.d.129.2		2	40.29	even	2
400.8.a.y.1.1		2	20.7	even	4
400.8.a.y.1.2		2	20.3	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+10.7703i q^{2} +32.3110i q^{3} +12.0000 q^{4} +(75.0000 - 269.258i) q^{5} -348.000 q^{6} -420.043i q^{7} +1507.85i q^{8} +1143.00 q^{9} +O(q^{10})\)	\(q+10.7703i q^{2} +32.3110i q^{3} +12.0000 q^{4} +(75.0000 - 269.258i) q^{5} -348.000 q^{6} -420.043i q^{7} +1507.85i q^{8} +1143.00 q^{9} +(2900.00 + 807.775i) q^{10} -6828.00 q^{11} +387.732i q^{12} -10145.7i q^{13} +4524.00 q^{14} +(8700.00 + 2423.32i) q^{15} -14704.0 q^{16} +15681.6i q^{17} +12310.5i q^{18} +6860.00 q^{19} +(900.000 - 3231.10i) q^{20} +13572.0 q^{21} -73539.8i q^{22} +29219.9i q^{23} -48720.0 q^{24} +(-66875.0 - 40388.7i) q^{25} +109272. q^{26} +107596. i q^{27} -5040.51i q^{28} +25590.0 q^{29} +(-26100.0 + 93701.9i) q^{30} +82112.0 q^{31} +34637.4i q^{32} -220619. i q^{33} -168896. q^{34} +(-113100. - 31503.2i) q^{35} +13716.0 q^{36} -223527. i q^{37} +73884.5i q^{38} +327816. q^{39} +(406000. + 113088. i) q^{40} -533118. q^{41} +146175. i q^{42} +708935. i q^{43} -81936.0 q^{44} +(85725.0 - 307762. i) q^{45} -314708. q^{46} +5826.75i q^{47} -475101. i q^{48} +647107. q^{49} +(435000. - 720266. i) q^{50} -506688. q^{51} -121748. i q^{52} -589374. i q^{53} -1.15884e6 q^{54} +(-512100. + 1.83850e6i) q^{55} +633360. q^{56} +221653. i q^{57} +275613. i q^{58} +1.43898e6 q^{59} +(104400. + 29079.9i) q^{60} +1.38102e6 q^{61} +884373. i q^{62} -480109. i q^{63} -2.25517e6 q^{64} +(-2.73180e6 - 760924. i) q^{65} +2.37614e6 q^{66} -2.71487e6i q^{67} +188179. i q^{68} -944124. q^{69} +(339300. - 1.21812e6i) q^{70} -481608. q^{71} +1.72347e6i q^{72} +1.48618e6i q^{73} +2.40746e6 q^{74} +(1.30500e6 - 2.16080e6i) q^{75} +82320.0 q^{76} +2.86805e6i q^{77} +3.53069e6i q^{78} -1.05976e6 q^{79} +(-1.10280e6 + 3.95917e6i) q^{80} -976779. q^{81} -5.74186e6i q^{82} -2.60380e6i q^{83} +162864. q^{84} +(4.22240e6 + 1.17612e6i) q^{85} -7.63547e6 q^{86} +826838. i q^{87} -1.02956e7i q^{88} +5.64417e6 q^{89} +(3.31470e6 + 923287. i) q^{90} -4.26161e6 q^{91} +350639. i q^{92} +2.65312e6i q^{93} -62756.0 q^{94} +(514500. - 1.84711e6i) q^{95} -1.11917e6 q^{96} +1.20091e7i q^{97} +6.96956e6i q^{98} -7.80440e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 24 q^{4} + 150 q^{5} - 696 q^{6} + 2286 q^{9}+O(q^{10}) \) 2 * q + 24 * q^4 + 150 * q^5 - 696 * q^6 + 2286 * q^9	\( 2 q + 24 q^{4} + 150 q^{5} - 696 q^{6} + 2286 q^{9} + 5800 q^{10} - 13656 q^{11} + 9048 q^{14} + 17400 q^{15} - 29408 q^{16} + 13720 q^{19} + 1800 q^{20} + 27144 q^{21} - 97440 q^{24} - 133750 q^{25} + 218544 q^{26} + 51180 q^{29} - 52200 q^{30} + 164224 q^{31} - 337792 q^{34} - 226200 q^{35} + 27432 q^{36} + 655632 q^{39} + 812000 q^{40} - 1066236 q^{41} - 163872 q^{44} + 171450 q^{45} - 629416 q^{46} + 1294214 q^{49} + 870000 q^{50} - 1013376 q^{51} - 2317680 q^{54} - 1024200 q^{55} + 1266720 q^{56} + 2877960 q^{59} + 208800 q^{60} + 2762044 q^{61} - 4510336 q^{64} - 5463600 q^{65} + 4752288 q^{66} - 1888248 q^{69} + 678600 q^{70} - 963216 q^{71} + 4814928 q^{74} + 2610000 q^{75} + 164640 q^{76} - 2119520 q^{79} - 2205600 q^{80} - 1953558 q^{81} + 325728 q^{84} + 8444800 q^{85} - 15270936 q^{86} + 11288340 q^{89} + 6629400 q^{90} - 8523216 q^{91} - 125512 q^{94} + 1029000 q^{95} - 2238336 q^{96} - 15608808 q^{99}+O(q^{100}) \) 2 * q + 24 * q^4 + 150 * q^5 - 696 * q^6 + 2286 * q^9 + 5800 * q^10 - 13656 * q^11 + 9048 * q^14 + 17400 * q^15 - 29408 * q^16 + 13720 * q^19 + 1800 * q^20 + 27144 * q^21 - 97440 * q^24 - 133750 * q^25 + 218544 * q^26 + 51180 * q^29 - 52200 * q^30 + 164224 * q^31 - 337792 * q^34 - 226200 * q^35 + 27432 * q^36 + 655632 * q^39 + 812000 * q^40 - 1066236 * q^41 - 163872 * q^44 + 171450 * q^45 - 629416 * q^46 + 1294214 * q^49 + 870000 * q^50 - 1013376 * q^51 - 2317680 * q^54 - 1024200 * q^55 + 1266720 * q^56 + 2877960 * q^59 + 208800 * q^60 + 2762044 * q^61 - 4510336 * q^64 - 5463600 * q^65 + 4752288 * q^66 - 1888248 * q^69 + 678600 * q^70 - 963216 * q^71 + 4814928 * q^74 + 2610000 * q^75 + 164640 * q^76 - 2119520 * q^79 - 2205600 * q^80 - 1953558 * q^81 + 325728 * q^84 + 8444800 * q^85 - 15270936 * q^86 + 11288340 * q^89 + 6629400 * q^90 - 8523216 * q^91 - 125512 * q^94 + 1029000 * q^95 - 2238336 * q^96 - 15608808 * q^99

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