LMFDB - Embedded newform 27.7.f.a.14.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.17
Character	$\chi$	$=$	27.14
Dual form			27.7.f.a.2.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(14.6025 - 2.57482i) q^{2} +(19.5272 + 18.6464i) q^{3} +(146.463 - 53.3083i) q^{4} +(-47.4564 + 56.5563i) q^{5} +(333.158 + 222.005i) q^{6} +(-559.698 - 203.713i) q^{7} +(1179.64 - 681.064i) q^{8} +(33.6255 + 728.224i) q^{9} +(-547.361 + 948.057i) q^{10} +(-103.550 - 123.406i) q^{11} +(3854.03 + 1690.05i) q^{12} +(611.857 - 3470.01i) q^{13} +(-8697.52 - 1533.61i) q^{14} +(-1981.26 + 219.499i) q^{15} +(7830.57 - 6570.63i) q^{16} +(991.661 + 572.536i) q^{17} +(2366.06 + 10547.3i) q^{18} +(1966.90 + 3406.77i) q^{19} +(-3935.71 + 10813.3i) q^{20} +(-7130.83 - 14414.3i) q^{21} +(-1829.83 - 1535.41i) q^{22} +(2407.96 + 6615.81i) q^{23} +(35734.4 + 8696.66i) q^{24} +(1766.74 + 10019.7i) q^{25} -52246.4i q^{26} +(-12922.1 + 14847.2i) q^{27} -92834.9 q^{28} +(-17217.1 + 3035.84i) q^{29} +(-28366.3 + 8306.63i) q^{30} +(-11762.6 + 4281.22i) q^{31} +(41392.2 - 49329.2i) q^{32} +(279.030 - 4340.60i) q^{33} +(15954.9 + 5807.12i) q^{34} +(38082.5 - 21987.0i) q^{35} +(43745.3 + 104866. i) q^{36} +(2070.19 - 3585.67i) q^{37} +(37493.4 + 44682.9i) q^{38} +(76651.1 - 56350.9i) q^{39} +(-17462.9 + 99036.8i) q^{40} +(87069.7 + 15352.7i) q^{41} +(-141242. - 192124. i) q^{42} +(-31361.3 + 26315.3i) q^{43} +(-21744.8 - 12554.4i) q^{44} +(-42781.4 - 32657.2i) q^{45} +(52196.7 + 90407.4i) q^{46} +(41464.3 - 113922. i) q^{47} +(275428. + 17705.6i) q^{48} +(181638. + 152412. i) q^{49} +(51597.8 + 141764. i) q^{50} +(8688.68 + 29670.9i) q^{51} +(-95366.0 - 540847. i) q^{52} -13899.3i q^{53} +(-150467. + 250079. i) q^{54} +11893.5 q^{55} +(-798982. + 140882. i) q^{56} +(-25115.8 + 103200. i) q^{57} +(-243596. + 88661.9i) q^{58} +(233288. - 278022. i) q^{59} +(-278482. + 137766. i) q^{60} +(-36081.6 - 13132.6i) q^{61} +(-160739. + 92803.0i) q^{62} +(129529. - 414435. i) q^{63} +(150309. - 260343. i) q^{64} +(167215. + 199279. i) q^{65} +(-7101.71 - 64102.1i) q^{66} +(-44093.4 + 250066. i) q^{67} +(175763. + 30991.8i) q^{68} +(-76340.1 + 174088. i) q^{69} +(499488. - 419120. i) q^{70} +(-181755. - 104936. i) q^{71} +(535633. + 836139. i) q^{72} +(-280379. - 485631. i) q^{73} +(20997.5 - 57690.1i) q^{74} +(-152331. + 228600. i) q^{75} +(469688. + 394115. i) q^{76} +(32817.2 + 90164.4i) q^{77} +(974205. - 1.02023e6i) q^{78} +(74801.8 + 424222. i) q^{79} +754687. i q^{80} +(-529180. + 48973.8i) q^{81} +1.31097e6 q^{82} +(-581811. + 102589. i) q^{83} +(-1.81281e6 - 1.73103e6i) q^{84} +(-79441.2 + 28914.2i) q^{85} +(-390197. + 465019. i) q^{86} +(-392810. - 261755. i) q^{87} +(-206198. - 75050.0i) q^{88} +(816149. - 471204. i) q^{89} +(-708803. - 366722. i) q^{90} +(-1.04934e6 + 1.81752e6i) q^{91} +(705356. + 840610. i) q^{92} +(-309519. - 135729. i) q^{93} +(312154. - 1.77032e6i) q^{94} +(-286016. - 50432.3i) q^{95} +(1.72809e6 - 191450. i) q^{96} +(-663894. + 557074. i) q^{97} +(3.04481e6 + 1.75792e6i) q^{98} +(86385.1 - 79557.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18}+ \cdots + 1743822 q^{99}+O(q^{100}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	14.6025	−	2.57482i	1.82531	−	0.321852i	0.847416	−	0.530930i	$-0.178157\pi$
$2$	14.6025	−	2.57482i	1.82531	−	0.321852i	0.977899	+	0.209078i	$0.0670462\pi$
$3$	19.5272	+	18.6464i	0.723231	+	0.690606i
$3$	19.5272	+	18.6464i	0.723231	+	0.690606i
$4$	146.463	−	53.3083i	2.28849	−	0.832943i
$5$	−47.4564	+	56.5563i	−0.379651	+	0.452451i	−0.921704	−	0.387894i	$-0.873203\pi$
$5$	−47.4564	+	56.5563i	−0.379651	+	0.452451i	0.542053	+	0.840344i	$0.317647\pi$
$6$	333.158	+	222.005i	1.54240	+	1.02780i
$7$	−559.698	−	203.713i	−1.63177	−	0.593916i	−0.646199	−	0.763169i	$-0.723643\pi$
$7$	−559.698	−	203.713i	−1.63177	−	0.593916i	−0.985573	+	0.169252i	$0.945865\pi$
$8$	1179.64	−	681.064i	2.30398	−	1.33020i
$9$	33.6255	+	728.224i	0.0461255	+	0.998936i
$10$	−547.361	+	948.057i	−0.547361	+	0.948057i
$11$	−103.550	−	123.406i	−0.0777984	−	0.0927166i	0.725741	−	0.687968i	$-0.241497\pi$
$11$	−103.550	−	123.406i	−0.0777984	−	0.0927166i	−0.803540	+	0.595251i	$0.797053\pi$
$12$	3854.03	+	1690.05i	2.23034	+	0.978037i
$13$	611.857	−	3470.01i	0.278497	−	1.57943i	−0.449134	−	0.893464i	$-0.648268\pi$
$13$	611.857	−	3470.01i	0.278497	−	1.57943i	0.727631	−	0.685969i	$-0.240621\pi$
$14$	−8697.52	−	1533.61i	−3.16965	−	0.558895i
$15$	−1981.26	+	219.499i	−0.587041	+	0.0650367i
$16$	7830.57	−	6570.63i	1.91176	−	1.60416i
$17$	991.661	+	572.536i	0.201844	+	0.116535i	0.597515	−	0.801857i	$-0.296155\pi$
$17$	991.661	+	572.536i	0.201844	+	0.116535i	−0.395671	+	0.918392i	$0.629488\pi$
$18$	2366.06	+	10547.3i	0.405703	+	1.80853i
$19$	1966.90	+	3406.77i	0.286761	+	0.496685i	0.973035	−	0.230658i	$-0.0740880\pi$
$19$	1966.90	+	3406.77i	0.286761	+	0.496685i	−0.686273	+	0.727344i	$0.740755\pi$
$20$	−3935.71	+	10813.3i	−0.491963	+	1.35166i
$21$	−7130.83	−	14414.3i	−0.769985	−	1.55645i
$22$	−1829.83	−	1535.41i	−0.171848	−	0.144197i
$23$	2407.96	+	6615.81i	0.197909	+	0.543750i	0.998458	−	0.0555173i	$-0.0176808\pi$
$23$	2407.96	+	6615.81i	0.197909	+	0.543750i	−0.800549	+	0.599268i	$0.795459\pi$
$24$	35734.4	+	8696.66i	2.58495	+	0.629099i
$25$	1766.74	+	10019.7i	0.113072	+	0.641261i
$26$		−	52246.4i		−	2.97260i
$27$	−12922.1	+	14847.2i	−0.656512	+	0.754316i
$28$	−92834.9			−4.22900
$29$	−17217.1	+	3035.84i	−0.705938	+	0.124476i	−0.515080	−	0.857142i	$-0.672238\pi$
$29$	−17217.1	+	3035.84i	−0.705938	+	0.124476i	−0.190857	+	0.981618i	$0.561127\pi$
$30$	−28366.3	+	8306.63i	−1.05060	+	0.307653i
$31$	−11762.6	+	4281.22i	−0.394836	+	0.143708i	−0.531805	−	0.846867i	$-0.678486\pi$
$31$	−11762.6	+	4281.22i	−0.394836	+	0.143708i	0.136969	+	0.990575i	$0.456264\pi$
$32$	41392.2	−	49329.2i	1.26319	−	1.50541i
$33$	279.030	−	4340.60i	0.00776443	−	0.120784i
$34$	15954.9	+	5807.12i	0.405936	+	0.147749i
$35$	38082.5	−	21987.0i	0.888222	−	0.512815i
$36$	43745.3	+	104866.i	0.937614	+	2.24764i
$37$	2070.19	−	3585.67i	0.0408700	−	0.0707889i	−0.844867	−	0.534977i	$-0.820320\pi$
$37$	2070.19	−	3585.67i	0.0408700	−	0.0707889i	0.885737	+	0.464188i	$0.153654\pi$
$38$	37493.4	+	44682.9i	0.683289	+	0.814312i
$39$	76651.1	−	56350.9i	1.29218	−	0.949963i
$40$	−17462.9	+	99036.8i	−0.272857	+	1.54745i
$41$	87069.7	+	15352.7i	1.26333	+	0.222758i	0.764886	−	0.644166i	$-0.222795\pi$
$41$	87069.7	+	15352.7i	1.26333	+	0.222758i	0.498440	+	0.866924i	$0.333906\pi$
$42$	−141242.	−	192124.i	−1.90641	−	2.59319i
$43$	−31361.3	+	26315.3i	−0.394448	+	0.330981i	−0.818343	−	0.574730i	$-0.805107\pi$
$43$	−31361.3	+	26315.3i	−0.394448	+	0.330981i	0.423895	+	0.905711i	$0.360662\pi$
$44$	−21744.8	−	12554.4i	−0.255269	−	0.147379i
$45$	−42781.4	−	32657.2i	−0.469481	−	0.358378i
$46$	52196.7	+	90407.4i	0.536253	+	0.928818i
$47$	41464.3	−	113922.i	0.399375	−	1.09727i	−0.563214	−	0.826311i	$-0.690435\pi$
$47$	41464.3	−	113922.i	0.399375	−	1.09727i	0.962590	−	0.270964i	$-0.0873424\pi$
$48$	275428.	+	17705.6i	2.49049	+	0.160098i
$49$	181638.	+	152412.i	1.54390	+	1.29548i
$50$	51597.8	+	141764.i	0.412782	+	1.13411i
$51$	8688.68	+	29670.9i	0.0655003	+	0.223677i
$52$	−95366.0	−	540847.i	−0.678240	−	3.84649i
$53$		−	13899.3i		−	0.0933608i	−0.998910	−	0.0466804i	$-0.985136\pi$
$53$		−	13899.3i		−	0.0933608i	0.998910	−	0.0466804i	$-0.0148642\pi$
$54$	−150467.	+	250079.i	−0.955563	+	1.58816i
$55$	11893.5			0.0714860
$56$	−798982.	+	140882.i	−4.54960	+	0.802217i
$57$	−25115.8	+	103200.i	−0.135619	+	0.557257i
$58$	−243596.	+	88661.9i	−1.24850	+	0.454415i
$59$	233288.	−	278022.i	1.13589	−	1.35370i	0.209205	−	0.977872i	$-0.432912\pi$
$59$	233288.	−	278022.i	1.13589	−	1.35370i	0.926688	−	0.375832i	$-0.122643\pi$
$60$	−278482.	+	137766.i	−1.28927	+	0.637807i
$61$	−36081.6	−	13132.6i	−0.158963	−	0.0578578i	0.261313	−	0.965254i	$-0.415845\pi$
$61$	−36081.6	−	13132.6i	−0.158963	−	0.0578578i	−0.420276	+	0.907396i	$0.638067\pi$
$62$	−160739.	+	92803.0i	−0.674446	+	0.389392i
$63$	129529.	−	414435.i	0.518018	−	1.65743i
$64$	150309.	−	260343.i	0.573383	−	0.993129i
$65$	167215.	+	199279.i	0.608884	+	0.725640i
$66$	−7101.71	−	64102.1i	−0.0247019	−	0.222967i
$67$	−44093.4	+	250066.i	−0.146605	+	0.831438i	0.819459	+	0.573137i	$0.194274\pi$
$67$	−44093.4	+	250066.i	−0.146605	+	0.831438i	−0.966064	+	0.258301i	$0.916837\pi$
$68$	175763.	+	30991.8i	0.558986	+	0.0985643i
$69$	−76340.1	+	174088.i	−0.232384	+	0.529934i
$70$	499488.	−	419120.i	1.45623	−	1.22193i
$71$	−181755.	−	104936.i	−0.507821	−	0.293191i	0.224116	−	0.974562i	$-0.428050\pi$
$71$	−181755.	−	104936.i	−0.507821	−	0.293191i	−0.731938	+	0.681372i	$0.761384\pi$
$72$	535633.	+	836139.i	1.43506	+	2.24017i
$73$	−280379.	−	485631.i	−0.720738	−	1.24835i	−0.960705	−	0.277573i	$-0.910470\pi$
$73$	−280379.	−	485631.i	−0.720738	−	1.24835i	0.239967	−	0.970781i	$-0.422863\pi$
$74$	20997.5	−	57690.1i	0.0518170	−	0.142366i
$75$	−152331.	+	228600.i	−0.361082	+	0.541867i
$76$	469688.	+	394115.i	1.06996	+	0.897805i
$77$	32817.2	+	90164.4i	0.0718834	+	0.197498i
$78$	974205.	−	1.02023e6i	2.05289	−	2.14987i
$79$	74801.8	+	424222.i	0.151716	+	0.860423i	0.961727	+	0.274009i	$0.0883498\pi$
$79$	74801.8	+	424222.i	0.151716	+	0.860423i	−0.810011	+	0.586414i	$0.800539\pi$
$80$			754687.i			1.47400i
$81$	−529180.	+	48973.8i	−0.995745	+	0.0921528i
$82$	1.31097e6			2.37766
$83$	−581811.	+	102589.i	−1.01753	+	0.179418i	−0.657446	−	0.753502i	$-0.728363\pi$
$83$	−581811.	+	102589.i	−1.01753	+	0.179418i	−0.360085	+	0.932920i	$0.617252\pi$
$84$	−1.81281e6	−	1.73103e6i	−3.05854	−	2.92057i
$85$	−79441.2	+	28914.2i	−0.129357	+	0.0470820i
$86$	−390197.	+	465019.i	−0.613464	+	0.731098i
$87$	−392810.	−	261755.i	−0.596520	−	0.397500i
$88$	−206198.	−	75050.0i	−0.302578	−	0.110129i
$89$	816149.	−	471204.i	1.15771	−	0.668403i	0.206955	−	0.978350i	$-0.433645\pi$
$89$	816149.	−	471204.i	1.15771	−	0.668403i	0.950754	+	0.309947i	$0.100311\pi$
$90$	−708803.	−	366722.i	−0.972295	−	0.503049i
$91$	−1.04934e6	+	1.81752e6i	−1.39249	+	2.41187i
$92$	705356.	+	840610.i	0.905826	+	1.07952i
$93$	−309519.	−	135729.i	−0.384803	−	0.168742i
$94$	312154.	−	1.77032e6i	0.375825	−	2.13141i
$95$	−286016.	−	50432.3i	−0.333595	−	0.0588218i
$96$	1.72809e6	−	191450.i	1.95322	−	0.216392i
$97$	−663894.	+	557074.i	−0.727418	+	0.610376i	−0.929426	−	0.369008i	$-0.879698\pi$
$97$	−663894.	+	557074.i	−0.727418	+	0.610376i	0.202009	+	0.979384i	$0.435253\pi$
$98$	3.04481e6	+	1.75792e6i	3.23506	+	1.86776i
$99$	86385.1	−	79557.0i	0.0890294	−	0.0819922i
$100$	792897.	+	1.37334e6i	0.792897	+	1.37334i
$101$	368309.	−	1.01192e6i	0.357477	−	0.982160i	−0.622425	−	0.782680i	$-0.713852\pi$
$101$	368309.	−	1.01192e6i	0.357477	−	0.982160i	0.979902	−	0.199481i	$-0.0639255\pi$
$102$	203274.	+	410898.i	0.191549	+	0.387199i
$103$	−795051.	−	667127.i	−0.727585	−	0.610516i	0.201887	−	0.979409i	$-0.435292\pi$
$103$	−795051.	−	667127.i	−0.727585	−	0.610516i	−0.929472	+	0.368893i	$0.879737\pi$
$104$	−1.64153e6	−	4.51007e6i	−1.45932	−	4.00944i
$105$	1.15362e6	+	280757.i	0.996543	+	0.242528i
$106$	−35788.1	−	202964.i	−0.0300484	−	0.170413i
$107$		−	623153.i		−	0.508678i	−0.967115	−	0.254339i	$-0.918142\pi$
$107$		−	623153.i		−	0.508678i	0.967115	−	0.254339i	$-0.0818579\pi$
$108$	−1.10114e6	+	2.86343e6i	−0.874121	+	2.27308i
$109$	1.02596e6			0.792230			0.396115	−	0.918201i	$-0.370358\pi$
$109$	1.02596e6			0.792230			0.396115	+	0.918201i	$0.370358\pi$
$110$	173675.	−	30623.5i	0.130484	−	0.0230079i
$111$	107285.	−	31416.7i	0.0784457	−	0.0229716i
$112$	−5.72128e6	+	2.08238e6i	−4.07229	+	1.48219i
$113$	−303556.	+	361764.i	−0.210380	+	0.250721i	−0.860907	−	0.508762i	$-0.830103\pi$
$113$	−303556.	+	361764.i	−0.210380	+	0.250721i	0.650528	+	0.759483i	$0.274548\pi$
$114$	−101032.	+	1.57165e6i	−0.0681936	+	1.06082i
$115$	−488439.	−	177777.i	−0.321157	−	0.116891i
$116$	−2.35984e6	+	1.36246e6i	−1.51185	+	0.872868i
$117$	2.54752e6	+	328888.i	1.59060	+	0.205348i
$118$	2.69074e6	−	4.66050e6i	1.63767	−	2.83653i
$119$	−438397.	−	522462.i	−0.260152	−	0.310037i
$120$	−2.18768e6	+	1.60830e6i	−1.26602	+	0.930726i
$121$	303122.	−	1.71909e6i	0.171104	−	0.970381i
$122$	−560696.	−	98865.9i	−0.308779	−	0.0544461i
$123$	1.41396e6	+	1.92333e6i	0.759838	+	1.03357i
$124$	−1.49456e6	+	1.25408e6i	−0.783877	+	0.657751i
$125$	−1.64955e6	−	952368.i	−0.844569	−	0.487612i
$126$	824352.	−	6.38531e6i	0.412098	−	3.19206i
$127$	623904.	+	1.08063e6i	0.304584	+	0.527555i	0.977169	−	0.212465i	$-0.0681493\pi$
$127$	623904.	+	1.08063e6i	0.304584	+	0.527555i	−0.672585	+	0.740020i	$0.734816\pi$
$128$	114999.	−	315956.i	0.0548356	−	0.150659i
$129$	−1.10308e6	−	70910.5i	−0.513854	−	0.0330325i
$130$	2.95486e6	+	2.47942e6i	1.34495	+	1.12855i
$131$	909859.	+	2.49982e6i	0.404725	+	1.11197i	0.959925	+	0.280256i	$0.0904194\pi$
$131$	909859.	+	2.49982e6i	0.404725	+	1.11197i	−0.555200	+	0.831717i	$0.687358\pi$
$132$	−190522.	−	650614.i	−0.0828370	−	0.282880i
$133$	−406864.	−	2.30744e6i	−0.172940	−	0.980790i
$134$			3.76512e6i			1.56482i
$135$	−226465.	−	1.43542e6i	−0.0920450	−	0.583416i
$136$	1.55973e6			0.620060
$137$	−1.60194e6	+	282466.i	−0.622997	+	0.109851i	−0.476231	−	0.879320i	$-0.657997\pi$
$137$	−1.60194e6	+	282466.i	−0.622997	+	0.109851i	−0.146766	+	0.989171i	$0.546886\pi$
$138$	−666513.	+	2.73869e6i	−0.253613	+	1.04209i
$139$	145773.	−	53057.1i	0.0542792	−	0.0197560i	−0.314738	−	0.949179i	$-0.601917\pi$
$139$	145773.	−	53057.1i	0.0542792	−	0.0197560i	0.369017	+	0.929423i	$0.379694\pi$
$140$	4.40561e6	−	5.25040e6i	1.60554	−	1.91341i
$141$	2.93392e6	−	1.45143e6i	1.04663	−	0.517772i
$142$	−2.92427e6	−	1.06435e6i	−1.02130	−	0.371722i
$143$	−491577.	+	283812.i	−0.168106	+	0.0970562i
$144$	5.04820e6	+	5.48147e6i	1.69063	+	1.83573i
$145$	645366.	−	1.11781e6i	0.211691	−	0.366659i
$146$	−5.34465e6	−	6.36951e6i	−1.71736	−	2.04667i
$147$	704950.	+	6.36309e6i	0.221925	+	2.00316i
$148$	112061.	−	635528.i	0.0345675	−	0.196042i
$149$	−226549.	−	39946.6i	−0.0684861	−	0.0120760i	0.139300	−	0.990250i	$-0.455515\pi$
$149$	−226549.	−	39946.6i	−0.0684861	−	0.0120760i	−0.207786	+	0.978174i	$0.566626\pi$
$150$	−1.63582e6	+	3.73037e6i	−0.484687	+	1.10529i
$151$	1.03626e6	−	869523.i	0.300979	−	0.252552i	−0.479772	−	0.877393i	$-0.659281\pi$
$151$	1.03626e6	−	869523.i	0.300979	−	0.252552i	0.780752	+	0.624841i	$0.214836\pi$
$152$	4.64045e6	+	2.67916e6i	1.32138	+	0.762902i
$153$	−383589.	+	741403.i	−0.107101	+	0.207005i
$154$	711370.	+	1.23213e6i	0.194775	+	0.337360i
$155$	316078.	−	868418.i	0.0848789	−	0.233203i
$156$	8.22261e6	−	1.23395e7i	2.16589	−	3.25030i
$157$	5.01529e6	+	4.20833e6i	1.29598	+	1.08745i	0.990825	+	0.135150i	$0.0431517\pi$
$157$	5.01529e6	+	4.20833e6i	1.29598	+	1.08745i	0.305152	+	0.952304i	$0.401293\pi$
$158$	2.18459e6	+	6.00211e6i	0.553858	+	1.52171i
$159$	259171.	−	271414.i	0.0644756	−	0.0675214i
$160$	825559.	+	4.68198e6i	0.201552	+	1.14306i
$161$		−	4.19339e6i		−	1.00482i
$162$	−7.60126e6	+	2.07768e6i	−1.78789	+	0.488691i
$163$	−7.97331e6			−1.84109			−0.920547	−	0.390633i	$-0.872256\pi$
$163$	−7.97331e6			−1.84109			−0.920547	+	0.390633i	$0.872256\pi$
$164$	1.35710e7	−	2.39293e6i	3.07666	−	0.542497i
$165$	232247.	+	221770.i	0.0517008	+	0.0493687i
$166$	−8.23175e6	+	2.99611e6i	−1.79957	+	0.654989i
$167$	−1.06294e6	+	1.26676e6i	−0.228222	+	0.271985i	−0.867988	−	0.496585i	$-0.834587\pi$
$167$	−1.06294e6	+	1.26676e6i	−0.228222	+	0.271985i	0.639766	+	0.768570i	$0.279031\pi$
$168$	−1.82288e7	−	1.21471e7i	−3.84442	−	2.56179i
$169$	−7.13091e6	−	2.59544e6i	−1.47736	−	0.537714i
$170$	−1.08559e6	+	626767.i	−0.220963	+	0.127573i
$171$	−2.41475e6	+	1.54690e6i	−0.482930	+	0.309366i
$172$	−3.19047e6	+	5.52605e6i	−0.627002	+	1.08600i
$173$	−1.04297e6	−	1.24296e6i	−0.201434	−	0.240060i	0.655865	−	0.754878i	$-0.272304\pi$
$173$	−1.04297e6	−	1.24296e6i	−0.201434	−	0.240060i	−0.857299	+	0.514818i	$0.827859\pi$
$174$	−6.40999e6	−	2.81087e6i	−1.21677	−	0.533572i
$175$	1.05230e6	−	5.96791e6i	0.196348	−	1.11355i
$176$	−1.62171e6	−	285951.i	−0.297464	−	0.0524509i
$177$	9.73959e6	−	1.07902e6i	1.75639	−	0.194586i
$178$	1.07046e7	−	8.98219e6i	1.89806	−	1.59266i
$179$	−1.60588e6	−	927154.i	−0.279997	−	0.161656i	0.353425	−	0.935463i	$-0.385017\pi$
$179$	−1.60588e6	−	927154.i	−0.279997	−	0.161656i	−0.633422	+	0.773806i	$0.718350\pi$
$180$	−8.00682e6	−	2.50247e6i	−1.37291	−	0.429094i
$181$	1.12919e6	+	1.95581e6i	0.190428	+	0.329831i	0.945392	−	0.325935i	$-0.105679\pi$
$181$	1.12919e6	+	1.95581e6i	0.190428	+	0.329831i	−0.754964	+	0.655766i	$0.772346\pi$
$182$	−1.06433e7	+	2.92422e7i	−1.76547	+	4.85060i
$183$	−459698.	−	929235.i	−0.0750100	−	0.151625i
$184$	7.34630e6	+	6.16428e6i	1.17928	+	0.989530i
$185$	104549.	+	287245.i	0.0165121	+	0.0453667i
$186$	−4.86924e6	−	1.18502e6i	−0.756697	−	0.184157i
$187$	−32032.0	−	181663.i	−0.00489846	−	0.0277805i
$188$		−	1.88959e7i		−	2.84376i
$189$	1.02571e7	−	5.67753e6i	1.51928	−	0.840958i
$190$	−4.30641e6			−0.627848
$191$	−9.40988e6	+	1.65922e6i	−1.35047	+	0.238124i	−0.801637	−	0.597811i	$-0.796037\pi$
$191$	−9.40988e6	+	1.65922e6i	−1.35047	+	0.238124i	−0.548829	+	0.835934i	$0.684926\pi$
$192$	7.78957e6	−	2.28106e6i	1.10055	−	0.322279i
$193$	6.45129e6	−	2.34808e6i	0.897376	−	0.326618i	0.148176	−	0.988961i	$-0.452660\pi$
$193$	6.45129e6	−	2.34808e6i	0.897376	−	0.326618i	0.749201	+	0.662343i	$0.230438\pi$
$194$	−8.26017e6	+	9.84408e6i	−1.13132	+	1.34825i
$195$	−450586.	+	7.00931e6i	−0.0607678	+	0.945304i
$196$	3.47282e7	+	1.26400e7i	4.61226	+	1.67873i
$197$	7.79923e6	−	4.50289e6i	1.02012	−	0.588969i	0.105985	−	0.994368i	$-0.466201\pi$
$197$	7.79923e6	−	4.50289e6i	1.02012	−	0.588969i	0.914140	+	0.405399i	$0.132867\pi$
$198$	1.05660e6	−	1.38416e6i	0.136117	−	0.178316i
$199$	−4.26198e6	+	7.38197e6i	−0.540820	+	0.936727i	0.458038	+	0.888933i	$0.348553\pi$
$199$	−4.26198e6	+	7.38197e6i	−0.540820	+	0.936727i	−0.998857	+	0.0477942i	$0.984781\pi$
$200$	8.90817e6	+	1.06163e7i	1.11352	+	1.32704i
$201$	−5.52384e6	+	4.06091e6i	−0.680226	+	0.500075i
$202$	2.77273e6	−	1.57249e7i	0.336398	−	1.90781i
$203$	1.02548e7	+	1.80820e6i	1.22586	+	0.216152i
$204$	2.85428e6	+	3.88253e6i	0.336207	+	0.457324i
$205$	−5.00031e6	+	4.19576e6i	−0.580410	+	0.487022i
$206$	−1.33275e7	−	7.69462e6i	−1.52457	−	0.880209i
$207$	−4.73682e6	+	1.97599e6i	−0.534043	+	0.222779i
$208$	−1.80090e7	−	3.11925e7i	−2.00124	−	3.46625i
$209$	216743.	−	595496.i	0.0237414	−	0.0652289i
$210$	1.75687e7	+	1.12938e6i	1.89706	+	0.121951i
$211$	3.69743e6	+	3.10251e6i	0.393598	+	0.330268i	0.818013	−	0.575200i	$-0.195076\pi$
$211$	3.69743e6	+	3.10251e6i	0.393598	+	0.330268i	−0.424415	+	0.905468i	$0.639520\pi$
$212$	−740948.	−	2.03574e6i	−0.0777642	−	0.213655i
$213$	−1.59249e6	−	5.43818e6i	−0.164793	−	0.562749i
$214$	−1.60450e6	−	9.09960e6i	−0.163719	−	0.928498i
$215$		−	3.02251e6i		−	0.304125i
$216$	−5.13153e6	+	2.63151e7i	−0.509197	+	2.61122i
$217$	7.45561e6			0.729633
$218$	1.49816e7	−	2.64166e6i	1.44607	−	0.254981i
$219$	3.58023e6	−	1.47111e7i	0.340862	−	1.40059i
$220$	1.74196e6	−	634022.i	0.163595	−	0.0595437i
$221$	2.59346e6	−	3.09077e6i	0.240272	−	0.286345i
$222$	1.48573e6	−	735002.i	0.135795	−	0.0671784i
$223$	−7.09719e6	−	2.58316e6i	−0.639988	−	0.232936i	0.00158493	−	0.999999i	$-0.499496\pi$
$223$	−7.09719e6	−	2.58316e6i	−0.639988	−	0.232936i	−0.641573	+	0.767062i	$0.721718\pi$
$224$	−3.32161e7	+	1.91773e7i	−2.95532	+	1.70626i
$225$	−7.23718e6	+	1.62350e6i	−0.635363	+	0.142530i
$226$	−3.50121e6	+	6.06427e6i	−0.303314	+	0.525356i
$227$	−1.01109e7	−	1.20497e7i	−0.864397	−	1.03015i	−0.999228	−	0.0392798i	$-0.987494\pi$
$227$	−1.01109e7	−	1.20497e7i	−0.864397	−	1.03015i	0.134831	−	0.990869i	$-0.456951\pi$
$228$	1.82289e6	+	1.64539e7i	0.153800	+	1.38824i
$229$	−333632.	+	1.89212e6i	−0.0277818	+	0.157559i	−0.995543	−	0.0943124i	$-0.969935\pi$
$229$	−333632.	+	1.89212e6i	−0.0277818	+	0.157559i	0.967761	+	0.251871i	$0.0810459\pi$
$230$	−7.59018e6	−	1.33835e6i	−0.623833	−	0.109999i
$231$	−1.04041e6	+	2.37258e6i	−0.0844051	+	0.192480i
$232$	−1.82423e7	+	1.53071e7i	−1.46089	+	1.22583i
$233$	1.98898e7	+	1.14834e7i	1.57240	+	0.907824i	0.995874	+	0.0907426i	$0.0289241\pi$
$233$	1.98898e7	+	1.14834e7i	1.57240	+	0.907824i	0.576523	+	0.817081i	$0.304409\pi$
$234$	3.80471e7	−	1.75681e6i	2.96943	−	0.137113i
$235$	4.47528e6	+	7.75142e6i	0.344839	+	0.597279i
$236$	1.93473e7	−	5.31564e7i	1.47192	−	4.04407i
$237$	−6.44953e6	+	9.67867e6i	−0.484488	+	0.727060i
$238$	−7.74695e6	−	6.50046e6i	−0.574645	−	0.482185i
$239$	7.15104e6	+	1.96473e7i	0.523812	+	1.43916i	0.866245	+	0.499619i	$0.166527\pi$
$239$	7.15104e6	+	1.96473e7i	0.523812	+	1.43916i	−0.342433	+	0.939542i	$0.611251\pi$
$240$	−1.40722e7	+	1.47370e7i	−1.01795	+	1.06604i
$241$	311092.	+	1.76429e6i	0.0222248	+	0.126043i	0.993902	−	0.110271i	$-0.0351718\pi$
$241$	311092.	+	1.76429e6i	0.0222248	+	0.126043i	−0.971677	+	0.236314i	$0.924061\pi$
$242$		−	2.58835e7i		−	1.82632i
$243$	−1.12466e7	−	8.91096e6i	−0.783795	−	0.621020i
$244$	−5.98471e6			−0.411978
$245$	−1.72398e7	+	3.03984e6i	−1.17229	+	0.206706i
$246$	2.55996e7	+	2.44448e7i	1.71960	+	1.64203i
$247$	1.30250e7	−	4.74071e6i	0.864343	−	0.314595i
$248$	−1.09598e7	+	1.30613e7i	−0.718532	+	0.856313i
$249$	−1.32741e7	−	8.84538e6i	−0.859817	−	0.572953i
$250$	−2.65398e7	−	9.65968e6i	−1.69854	−	0.618219i
$251$	−8.93419e6	+	5.15816e6i	−0.564981	+	0.326192i	−0.755142	−	0.655561i	$-0.772432\pi$
$251$	−8.93419e6	+	5.15816e6i	−0.564981	+	0.326192i	0.190161	+	0.981753i	$0.439099\pi$
$252$	−3.12162e6	−	6.76046e7i	−0.195065	−	4.22449i
$253$	567086.	−	982221.i	0.0350177	−	0.0606524i
$254$	1.18930e7	+	1.41735e7i	0.725756	+	0.864922i
$255$	−2.09041e6	−	916675.i	−0.126070	−	0.0552834i
$256$	−2.47517e6	+	1.40374e7i	−0.147532	+	0.836694i
$257$	1.81411e7	+	3.19877e6i	1.06872	+	0.188445i	0.680224	−	0.733005i	$-0.261883\pi$
$257$	1.81411e7	+	3.19877e6i	1.06872	+	0.188445i	0.388499	+	0.921449i	$0.372994\pi$
$258$	−1.62904e7	+	1.80477e6i	−0.948577	+	0.105090i
$259$	−1.88913e6	+	1.58517e6i	−0.108733	+	0.0912380i
$260$	3.51141e7	+	2.02731e7i	1.99784	+	1.15346i
$261$	−2.78971e6	−	1.24358e7i	−0.156905	−	0.699445i
$262$	1.97228e7	+	3.41609e7i	1.09664	+	1.89944i
$263$	5.77222e6	−	1.58590e7i	0.317304	−	0.871786i	−0.673826	−	0.738890i	$-0.735350\pi$
$263$	5.77222e6	−	1.58590e7i	0.317304	−	0.871786i	0.991130	−	0.132896i	$-0.0424275\pi$
$264$	−2.62707e6	−	5.31037e6i	−0.142778	−	0.288611i
$265$	786092.	+	659610.i	0.0422412	+	0.0354446i
$266$	−1.18825e7	−	3.26469e7i	−0.631339	−	1.73459i
$267$	2.47234e7	+	6.01691e6i	1.29889	+	0.316111i
$268$	6.87253e6	+	3.89761e7i	0.357036	+	2.02485i
$269$			1.30934e7i			0.672659i	0.941744	+	0.336330i	$0.109186\pi$
$269$			1.30934e7i			0.672659i	−0.941744	+	0.336330i	$0.890814\pi$
$270$	−7.00292e6	−	2.03777e7i	−0.355785	−	1.03529i
$271$	−9.88645e6			−0.496744			−0.248372	−	0.968665i	$-0.579895\pi$
$271$	−9.88645e6			−0.496744			−0.248372	+	0.968665i	$0.579895\pi$
$272$	1.15272e7	−	2.03256e6i	0.572818	−	0.101003i
$273$	−5.43809e7	+	1.59246e7i	−2.67275	+	0.782674i
$274$	−2.26651e7	+	8.24943e6i	−1.10181	+	0.401026i
$275$	1.05354e6	−	1.25556e6i	0.0506587	−	0.0603727i
$276$	−1.90069e6	+	2.95671e7i	−0.0904032	+	1.40631i
$277$	−9.04601e6	−	3.29248e6i	−0.425616	−	0.154912i	0.120326	−	0.992734i	$-0.461606\pi$
$277$	−9.04601e6	−	3.29248e6i	−0.425616	−	0.154912i	−0.545942	+	0.837823i	$0.683828\pi$
$278$	1.99204e6	−	1.15011e6i	0.0927180	−	0.0535308i
$279$	−3.51321e6	−	8.42181e6i	−0.161767	−	0.387787i
$280$	2.99490e7	−	5.18733e7i	1.36430	−	2.36303i
$281$	2.10977e7	+	2.51433e7i	0.950859	+	1.13319i	0.990982	+	0.133995i	$0.0427807\pi$
$281$	2.10977e7	+	2.51433e7i	0.950859	+	1.13319i	−0.0401225	+	0.999195i	$0.512775\pi$
$282$	3.91055e7	−	2.87488e7i	1.74377	−	1.28195i
$283$	−2.76569e6	+	1.56850e7i	−0.122024	+	0.692031i	0.861007	+	0.508593i	$0.169834\pi$
$283$	−2.76569e6	+	1.56850e7i	−0.122024	+	0.692031i	−0.983031	+	0.183439i	$0.941277\pi$
$284$	−3.22144e7	−	5.68027e6i	−1.40636	−	0.247979i
$285$	−4.64472e6	−	6.31797e6i	−0.200643	−	0.272925i
$286$	−6.44750e6	+	5.41010e6i	−0.275609	+	0.231263i
$287$	−4.56052e7	−	2.63301e7i	−1.92916	−	1.11380i
$288$	3.73146e7	+	2.84840e7i	1.56207	+	1.19241i
$289$	−1.14132e7	−	1.97682e7i	−0.472839	−	0.818982i
$290$	6.54582e6	−	1.79845e7i	0.268392	−	0.737402i
$291$	−2.33514e7	−	1.50112e6i	−0.947620	−	0.0609167i
$292$	−6.69535e7	−	5.61807e7i	−2.68921	−	2.25651i
$293$	−6.42966e6	−	1.76654e7i	−0.255614	−	0.702295i	−0.999425	−	0.0339045i	$-0.989206\pi$
$293$	−6.42966e6	−	1.76654e7i	−0.255614	−	0.702295i	0.743811	−	0.668390i	$-0.233016\pi$
$294$	2.66778e7	+	9.11020e7i	1.04980	+	3.58497i
$295$	4.65290e6	+	2.63879e7i	0.181241	+	1.02787i
$296$		−	5.63972e6i		−	0.217461i
$297$	3.17031e6	+	57241.9i	0.121013	+	0.00218497i
$298$	−3.41104e6			−0.128895
$299$	2.44303e7	−	4.30772e6i	0.913934	−	0.161151i
$300$	−1.01247e7	+	4.16021e7i	−0.374988	+	1.54082i
$301$	2.29136e7	−	8.33989e6i	0.840223	−	0.305816i
$302$	1.28931e7	−	1.53654e7i	0.468098	−	0.557857i
$303$	2.60607e7	−	1.28924e7i	0.936825	−	0.463453i
$304$	3.77865e7	+	1.37532e7i	1.34498	+	0.489533i
$305$	2.45504e6	−	1.41742e6i	0.0865283	−	0.0499572i
$306$	−3.69239e6	+	1.18140e7i	−0.128867	+	0.412319i
$307$	−9.94796e6	+	1.72304e7i	−0.343810	+	0.595497i	−0.985137	−	0.171771i	$-0.945051\pi$
$307$	−9.94796e6	+	1.72304e7i	−0.343810	+	0.595497i	0.641327	+	0.767268i	$0.278384\pi$
$308$	9.61303e6	+	1.14564e7i	0.329009	+	0.392098i
$309$	−3.08565e6	−	2.78520e7i	−0.104585	−	0.944018i
$310$	2.37952e6	−	1.34949e7i	0.0798738	−	0.452987i
$311$	5.01806e6	+	884819.i	0.166823	+	0.0294153i	0.256435	−	0.966561i	$-0.417452\pi$
$311$	5.01806e6	+	884819.i	0.166823	+	0.0294153i	−0.0896129	+	0.995977i	$0.528563\pi$
$312$	5.20419e7	−	1.18678e8i	1.71352	−	3.90756i
$313$	2.40732e7	−	2.01999e7i	0.785058	−	0.658742i	−0.159459	−	0.987205i	$-0.550975\pi$
$313$	2.40732e7	−	2.01999e7i	0.785058	−	0.658742i	0.944517	+	0.328463i	$0.106531\pi$
$314$	8.40716e7	+	4.85388e7i	2.71557	+	1.56783i
$315$	1.72920e7	+	2.69933e7i	0.553239	+	0.863623i
$316$	3.35703e7	+	5.81455e7i	1.06388	+	1.84270i
$317$	−3.94498e6	+	1.08388e7i	−0.123842	+	0.340253i	−0.986085	−	0.166242i	$-0.946837\pi$
$317$	−3.94498e6	+	1.08388e7i	−0.123842	+	0.340253i	0.862243	+	0.506495i	$0.169059\pi$
$318$	3.08571e6	−	4.63065e6i	0.0959563	−	0.143999i
$319$	2.15747e6	+	1.81033e6i	0.0664618	+	0.0557681i
$320$	7.59091e6	+	2.08559e7i	0.231656	+	0.636470i
$321$	1.16195e7	−	1.21684e7i	0.351296	−	0.367892i
$322$	−1.07972e7	−	6.12340e7i	−0.323403	−	1.83411i
$323$			4.50447e6i			0.133671i
$324$	−7.48948e7	+	3.53826e7i	−2.20200	+	1.04029i
$325$	3.58495e7			1.04432
$326$	−1.16430e8	+	2.05298e7i	−3.36057	+	0.592560i
$327$	2.00342e7	+	1.91305e7i	0.572965	+	0.547119i
$328$	1.13167e8	−	4.11893e7i	3.20699	−	1.16725i
$329$	−4.64150e7	+	5.53152e7i	−1.30338	+	1.55331i
$330$	3.96240e6	+	2.64041e6i	0.110260	+	0.0734733i
$331$	8.13639e6	+	2.96140e6i	0.224361	+	0.0816608i	0.451755	−	0.892142i	$-0.350798\pi$
$331$	8.13639e6	+	2.96140e6i	0.224361	+	0.0816608i	−0.227394	+	0.973803i	$0.573020\pi$
$332$	−7.97452e7	+	4.60409e7i	−2.17917	+	1.25814i
$333$	2.68078e6	+	1.38699e6i	0.0725987	+	0.0375613i
$334$	−1.22599e7	+	2.12347e7i	−0.329039	+	0.569912i
$335$	−1.20503e7	−	1.43610e7i	−0.320526	−	0.381988i
$336$	−1.50550e8	−	6.60181e7i	−3.96882	−	1.74038i
$337$	9.27535e6	−	5.26031e7i	0.242349	−	1.37443i	−0.584222	−	0.811594i	$-0.698600\pi$
$337$	9.27535e6	−	5.26031e7i	0.242349	−	1.37443i	0.826570	−	0.562833i	$-0.190289\pi$
$338$	−1.10812e8	−	1.95392e7i	−2.86970	−	0.506006i
$339$	−1.26732e7	+	1.40403e6i	−0.325303	+	0.0360394i
$340$	−1.00939e7	+	8.46976e6i	−0.256815	+	0.215494i
$341$	1.74634e6	+	1.00825e6i	0.0440418	+	0.0254275i
$342$	−3.12785e7	+	2.88061e7i	−0.781929	+	0.720122i
$343$	−3.55771e7	−	6.16213e7i	−0.881633	−	1.52703i
$344$	−1.90726e7	+	5.24016e7i	−0.468527	+	1.28727i
$345$	−6.22296e6	−	1.25791e7i	−0.151544	−	0.306332i
$346$	−1.84304e7	−	1.54649e7i	−0.444944	−	0.373353i
$347$	1.79347e7	+	4.92752e7i	0.429246	+	1.17934i	0.946271	+	0.323373i	$0.104817\pi$
$347$	1.79347e7	+	4.92752e7i	0.429246	+	1.17934i	−0.517026	+	0.855970i	$0.672961\pi$
$348$	−7.14861e7	−	1.73975e7i	−1.69623	−	0.412809i
$349$	5.58236e6	+	3.16591e7i	0.131323	+	0.744771i	0.977350	+	0.211630i	$0.0678772\pi$
$349$	5.58236e6	+	3.16591e7i	0.131323	+	0.744771i	−0.846027	+	0.533141i	$0.821012\pi$
$350$		−	8.98560e7i		−	2.09577i
$351$	4.36135e7	+	5.39243e7i	1.00855	+	1.24699i
$352$	−1.03737e7			−0.237850
$353$	3.73627e7	−	6.58805e6i	0.849403	−	0.149773i	0.268031	−	0.963410i	$-0.413627\pi$
$353$	3.73627e7	−	6.58805e6i	0.849403	−	0.149773i	0.581372	+	0.813638i	$0.302516\pi$
$354$	1.39444e8	−	4.08341e7i	3.14334	−	0.920478i
$355$	1.45602e7	−	5.29949e6i	0.325449	−	0.118454i
$356$	9.44169e7	−	1.12522e8i	2.09267	−	2.49394i
$357$	1.18133e6	−	1.83767e7i	0.0259637	−	0.403891i
$358$	−2.58371e7	−	9.40394e6i	−0.563112	−	0.204956i
$359$	1.41170e7	−	8.15045e6i	0.305112	−	0.176156i	−0.339625	−	0.940561i	$-0.610300\pi$
$359$	1.41170e7	−	8.15045e6i	0.305112	−	0.176156i	0.644737	+	0.764405i	$0.276967\pi$
$360$	−7.27082e7	−	9.38671e6i	−1.55839	−	0.201190i
$361$	1.57856e7	−	2.73414e7i	0.335536	−	0.581165i
$362$	2.15248e7	+	2.56523e7i	0.453747	+	0.540755i
$363$	3.79739e7	−	2.79169e7i	0.793900	−	0.583644i
$364$	−5.68017e7	+	3.22138e8i	−1.17776	+	6.67942i
$365$	4.07713e7	+	7.18908e6i	0.838448	+	0.147841i
$366$	−9.10535e6	−	1.23855e7i	−0.185718	−	0.252622i
$367$	1.89496e7	−	1.59006e7i	0.383355	−	0.321673i	−0.430663	−	0.902513i	$-0.641720\pi$
$367$	1.89496e7	−	1.59006e7i	0.383355	−	0.321673i	0.814018	+	0.580840i	$0.197276\pi$
$368$	6.23257e7	+	3.59838e7i	1.25062	+	0.722043i
$369$	−8.25247e6	+	6.39225e7i	−0.164250	+	1.27226i
$370$	2.26628e6	+	3.92531e6i	0.0447412	+	0.0774941i
$371$	−2.83147e6	+	7.77940e6i	−0.0554485	+	0.152344i
$372$	−5.25687e7	−	3.37932e6i	−1.02117	−	0.0656448i
$373$	−1.14620e7	−	9.61778e6i	−0.220869	−	0.185331i	0.525639	−	0.850708i	$-0.323826\pi$
$373$	−1.14620e7	−	9.61778e6i	−0.220869	−	0.185331i	−0.746508	+	0.665377i	$0.768271\pi$
$374$	−935496.	−	2.57025e6i	−0.0178825	−	0.0491316i
$375$	−1.44529e7	−	4.93552e7i	−0.274070	−	0.935921i
$376$	−2.86755e7	−	1.62627e8i	−0.539445	−	3.05935i
$377$			6.16011e7i			1.14965i
$378$	1.35160e8	−	1.09316e8i	2.50250	−	2.02400i
$379$	2.40788e7			0.442300			0.221150	−	0.975240i	$-0.429019\pi$
$379$	2.40788e7			0.442300			0.221150	+	0.975240i	$0.429019\pi$
$380$	−4.45794e7	+	7.86055e6i	−0.812425	+	0.143252i
$381$	−7.96678e6	+	3.27353e7i	−0.144048	+	0.591891i
$382$	−1.33136e8	+	4.84574e7i	−2.38839	+	0.869301i
$383$	5.87013e7	−	6.99574e7i	1.04484	−	1.24520i	0.0761077	−	0.997100i	$-0.475751\pi$
$383$	5.87013e7	−	6.99574e7i	1.04484	−	1.24520i	0.968735	−	0.248096i	$-0.0798049\pi$
$384$	8.13703e6	−	4.02544e6i	0.143705	−	0.0710918i
$385$	−6.65675e6	−	2.42286e6i	−0.116649	−	0.0424567i
$386$	8.81592e7	−	5.08987e7i	1.53287	−	0.885004i
$387$	−2.02180e7	−	2.19532e7i	−0.348823	−	0.378761i
$388$	−6.75396e7	+	1.16982e8i	−1.15628	+	2.00274i
$389$	−5.94954e7	−	7.09038e7i	−1.01073	−	1.20454i	−0.978751	−	0.205050i	$-0.934264\pi$
$389$	−5.94954e7	−	7.09038e7i	−1.01073	−	1.20454i	−0.0319768	−	0.999489i	$-0.510180\pi$
$390$	1.14680e7	+	1.03514e8i	0.193328	+	1.74504i
$391$	−1.39991e6	+	7.93928e6i	−0.0234191	+	0.132816i
$392$	3.18070e8	+	5.60843e7i	5.28037	+	0.931071i
$393$	−2.88455e7	+	6.57800e7i	−0.475226	+	1.08372i
$394$	1.02294e8	−	8.58351e7i	1.67249	−	1.40338i
$395$	−2.75423e7	−	1.59015e7i	−0.446898	−	0.258017i
$396$	8.41122e6	−	1.62572e7i	0.135448	−	0.261795i
$397$	−1.77215e7	−	3.06945e7i	−0.283223	−	0.490556i	0.688954	−	0.724805i	$-0.258070\pi$
$397$	−1.77215e7	−	3.06945e7i	−0.283223	−	0.490556i	−0.972177	+	0.234249i	$0.924737\pi$
$398$	−4.32284e7	+	1.18769e8i	−0.685678	+	1.88389i
$399$	3.50805e7	−	5.26445e7i	0.552264	−	0.828771i
$400$	7.96704e7	+	6.68514e7i	1.24485	+	1.04455i
$401$	−6.34964e6	−	1.74455e7i	−0.0984727	−	0.270552i	0.880668	−	0.473733i	$-0.157094\pi$
$401$	−6.34964e6	−	1.74455e7i	−0.0984727	−	0.270552i	−0.979141	+	0.203182i	$0.934872\pi$
$402$	−7.02059e7	+	7.35224e7i	−1.08068	+	1.13173i
$403$	7.65889e6	+	4.34357e7i	0.117017	+	0.663639i
$404$		−	1.67843e8i		−	2.54542i
$405$	2.23432e7	−	3.22526e7i	0.336341	−	0.485511i
$406$	1.54402e8			2.30714
$407$	−656859.	+	115822.i	−0.00974292	+	0.00171794i
$408$	3.04573e7	+	2.90834e7i	0.448446	+	0.428217i
$409$	−6.73824e6	+	2.45252e6i	−0.0984864	+	0.0358461i	−0.390793	−	0.920478i	$-0.627799\pi$
$409$	−6.73824e6	+	2.45252e6i	−0.0984864	+	0.0358461i	0.292307	+	0.956325i	$0.405577\pi$
$410$	−6.22138e7	+	7.41435e7i	−0.902683	+	1.07578i
$411$	−3.65485e7	−	2.43547e7i	−0.526434	−	0.350798i
$412$	−1.52009e8	−	5.53269e7i	−2.17360	−	0.791124i
$413$	−1.87208e8	+	1.08085e8i	−2.65750	+	1.53431i
$414$	−6.40817e7	+	4.10509e7i	−0.903094	+	0.578525i
$415$	2.18086e7	−	3.77736e7i	0.305129	−	0.528499i
$416$	−1.45847e8	−	1.73814e8i	−2.02590	−	2.41437i
$417$	3.83587e6	+	1.68208e6i	0.0529000	+	0.0231974i
$418$	1.63170e6	−	9.25381e6i	0.0223414	−	0.126704i
$419$	−7.00262e7	−	1.23475e7i	−0.951959	−	0.167856i	−0.323961	−	0.946071i	$-0.605015\pi$
$419$	−7.00262e7	−	1.23475e7i	−0.951959	−	0.167856i	−0.627999	+	0.778215i	$0.716126\pi$
$420$	1.83930e8	−	2.03772e7i	2.48259	−	0.275040i
$421$	−2.60986e6	+	2.18993e6i	−0.0349761	+	0.0293484i	−0.660108	−	0.751171i	$-0.729490\pi$
$421$	−2.60986e6	+	2.18993e6i	−0.0349761	+	0.0293484i	0.625132	+	0.780519i	$0.285045\pi$
$422$	6.19802e7	+	3.57843e7i	0.824737	+	0.476162i
$423$	8.43553e7	+	2.63646e7i	1.11453	+	0.348338i
$424$	−9.46629e6	−	1.63961e7i	−0.124189	−	0.215101i
$425$	−3.98463e6	+	1.09477e7i	−0.0519064	+	0.142612i
$426$	−3.72567e7	−	7.53108e7i	−0.481920	−	0.974156i
$427$	1.75195e7	+	1.47006e7i	0.225029	+	0.188822i
$428$	−3.32192e7	−	9.12691e7i	−0.423700	−	1.16411i
$429$	−1.48912e7	−	3.62407e6i	−0.188607	−	0.0459012i
$430$	−7.78242e6	−	4.41363e7i	−0.0978834	−	0.555124i
$431$			1.01266e8i			1.26483i	0.774631	+	0.632414i	$0.217936\pi$
$431$			1.01266e8i			1.26483i	−0.774631	+	0.632414i	$0.782064\pi$
$432$	−3.63222e6	+	2.01169e8i	−0.0450527	+	2.49522i
$433$	−1.59344e8			−1.96278			−0.981390	−	0.192024i	$-0.938495\pi$
$433$	−1.59344e8			−1.96278			−0.981390	+	0.192024i	$0.938495\pi$
$434$	1.08871e8	−	1.91968e7i	1.33181	−	0.234834i
$435$	3.34453e7	−	9.79394e6i	0.406319	−	0.118984i
$436$	1.50266e8	−	5.46923e7i	1.81301	−	0.659882i
$437$	−1.78023e7	+	2.12160e7i	−0.213320	+	0.254225i
$438$	1.44020e7	−	2.24037e8i	0.171396	−	2.66623i
$439$	−5.27244e7	−	1.91901e7i	−0.623187	−	0.226821i	0.0110763	−	0.999939i	$-0.496474\pi$
$439$	−5.27244e7	−	1.91901e7i	−0.623187	−	0.226821i	−0.634263	+	0.773117i	$0.718696\pi$
$440$	1.40300e7	−	8.10021e6i	0.164702	−	0.0950908i
$441$	−1.04883e8	+	1.37398e8i	−1.22289	+	1.60201i
$442$	2.99129e7	−	5.18107e7i	0.346411	−	0.600002i
$443$	−4.03373e7	−	4.80721e7i	−0.463976	−	0.552945i	0.482426	−	0.875937i	$-0.339756\pi$
$443$	−4.03373e7	−	4.80721e7i	−0.463976	−	0.552945i	−0.946402	+	0.322992i	$0.895311\pi$
$444$	1.40385e7	−	1.03206e7i	0.160388	−	0.117911i
$445$	−1.20819e7	+	6.85200e7i	−0.137106	+	0.777566i
$446$	−1.10288e8	−	1.94467e7i	−1.24315	−	0.219201i
$447$	−3.67901e6	−	5.00436e6i	−0.0411916	−	0.0560307i
$448$	−1.37163e8	+	1.15093e8i	−1.52547	+	1.28002i
$449$	−1.52920e7	−	8.82885e6i	−0.168937	−	0.0975360i	0.413147	−	0.910664i	$-0.364429\pi$
$449$	−1.52920e7	−	8.82885e6i	−0.168937	−	0.0975360i	−0.582085	+	0.813128i	$0.697763\pi$
$450$	−1.01501e8	+	4.23416e7i	−1.11386	+	0.464654i
$451$	−7.12143e6	−	1.23347e7i	−0.0776314	−	0.134461i
$452$	−2.51749e7	+	6.91674e7i	−0.272616	+	0.749007i
$453$	3.64487e7	+	2.34306e6i	0.392092	+	0.0252052i
$454$	−1.78671e8	−	1.49923e8i	−1.90935	−	1.60214i
$455$	−5.29940e7	−	1.45600e8i	−0.562591	−	1.54570i
$456$	4.06584e7	+	1.38844e8i	0.428801	+	1.46431i
$457$	3.04959e7	+	1.72951e8i	0.319517	+	1.81207i	0.545697	+	0.837983i	$0.316265\pi$
$457$	3.04959e7	+	1.72951e8i	0.319517	+	1.81207i	−0.226180	+	0.974085i	$0.572624\pi$
$458$			2.84887e7i			0.296536i
$459$	−2.13149e7	+	7.32500e6i	−0.220417	+	0.0757478i
$460$	−8.10155e7			−0.832328
$461$	1.78928e8	−	3.15498e7i	1.82631	−	0.322028i	0.848133	−	0.529784i	$-0.177727\pi$
$461$	1.78928e8	−	3.15498e7i	1.82631	−	0.322028i	0.978181	+	0.207756i	$0.0666159\pi$
$462$	−9.08365e6	+	3.73245e7i	−0.0921159	+	0.378502i
$463$	−1.34275e7	+	4.88720e6i	−0.135286	+	0.0492399i	−0.408776	−	0.912635i	$-0.634044\pi$
$463$	−1.34275e7	+	4.88720e6i	−0.135286	+	0.0492399i	0.273490	+	0.961875i	$0.411822\pi$
$464$	−1.14872e8	+	1.36900e8i	−1.14991	+	1.37040i
$465$	2.23650e7	−	1.10641e7i	0.222438	−	0.110042i
$466$	3.20008e8	+	1.16474e8i	3.16230	+	1.15098i
$467$	1.13523e8	−	6.55426e7i	1.11464	−	0.643537i	0.174611	−	0.984637i	$-0.444133\pi$
$467$	1.13523e8	−	6.55426e7i	1.11464	−	0.643537i	0.940027	+	0.341101i	$0.110800\pi$
$468$	3.90651e8	−	8.76341e7i	3.81111	−	0.854940i
$469$	7.56207e7	−	1.30979e8i	0.733031	−	1.26965i
$470$	8.53089e7	+	1.01667e8i	0.821676	+	0.979235i
$471$	1.94647e7	+	1.75694e8i	0.186288	+	1.68149i
$472$	8.58448e7	−	4.86850e8i	0.816371	−	4.62987i
$473$	6.49492e6	+	1.14523e6i	0.0613748	+	0.0108220i
$474$	−6.92586e7	+	1.57939e8i	−0.650337	+	1.48305i
$475$	−3.06598e7	+	2.57266e7i	−0.286080	+	0.240050i
$476$	−9.20608e7	−	5.31513e7i	−0.853599	−	0.492825i
$477$	1.01218e7	−	467370.i	0.0932615	−	0.00430632i
$478$	1.55011e8	+	2.68488e8i	1.41932	+	2.45833i
$479$	1.49099e7	−	4.09646e7i	0.135665	−	0.372737i	−0.853194	−	0.521594i	$-0.825337\pi$
$479$	1.49099e7	−	4.09646e7i	0.135665	−	0.372737i	0.988859	+	0.148858i	$0.0475596\pi$
$480$	−7.11810e7	+	1.06820e8i	−0.643636	+	0.965890i
$481$	−1.11757e7	−	9.37750e6i	−0.100424	−	0.0842659i
$482$	9.08545e6	+	2.49621e7i	0.0811345	+	0.222915i
$483$	7.81915e7	−	8.18852e7i	0.693934	−	0.726715i
$484$	−4.72455e7	−	2.67943e8i	−0.416701	−	2.36323i
$485$		−	6.39841e7i		−	0.560851i
$486$	−1.87173e8	−	1.01164e8i	−1.63055	−	0.881291i
$487$	−1.72331e8			−1.49203			−0.746014	−	0.665930i	$-0.768035\pi$
$487$	−1.72331e8			−1.49203			−0.746014	+	0.665930i	$0.768035\pi$
$488$	−5.15073e7	+	9.08213e6i	−0.443210	+	0.0781499i
$489$	−1.55697e8	−	1.48673e8i	−1.33154	−	1.27147i
$490$	−2.43917e8	+	8.87786e7i	−2.07326	+	0.754606i
$491$	1.09688e8	−	1.30721e8i	0.926647	−	1.10433i	−0.0676525	−	0.997709i	$-0.521551\pi$
$491$	1.09688e8	−	1.30721e8i	0.926647	−	1.10433i	0.994299	−	0.106626i	$-0.0340046\pi$
$492$	3.09623e8	+	2.06322e8i	2.59978	+	1.73241i
$493$	−1.88117e7	−	6.84689e6i	−0.156995	−	0.0571416i
$494$	1.77991e8	−	1.02763e8i	1.47645	−	0.852426i
$495$	399924.	+	8.66112e6i	0.00329733	+	0.0714099i
$496$	−6.39772e7	+	1.10812e8i	−0.524300	+	0.908115i
$497$	8.03509e7	+	9.57584e7i	0.654518	+	0.780024i
$498$	−2.16610e8	−	9.49866e7i	−1.75384	−	0.769085i
$499$	−2.25353e7	+	1.27804e8i	−0.181369	+	1.02859i	0.749165	+	0.662384i	$0.230455\pi$
$499$	−2.25353e7	+	1.27804e8i	−0.181369	+	1.02859i	−0.930533	+	0.366208i	$0.880656\pi$
$500$	−2.92368e8	−	5.15524e7i	−2.33894	−	0.412419i
$501$	−4.43767e7	+	4.91638e6i	−0.352892	+	0.0390960i
$502$	−1.17180e8	+	9.83260e7i	−0.926283	+	0.777243i
$503$	3.28835e7	+	1.89853e7i	0.258389	+	0.149181i	0.623599	−	0.781744i	$-0.285670\pi$
$503$	3.28835e7	+	1.89853e7i	0.258389	+	0.149181i	−0.365211	+	0.930925i	$0.619003\pi$
$504$	−1.29460e8	−	5.77101e8i	−1.01122	−	4.50775i
$505$	3.97519e7	+	6.88523e7i	0.308662	+	0.534619i
$506$	5.75184e6	−	1.58030e7i	0.0443971	−	0.121980i
$507$	−9.08515e7	−	1.83647e8i	−0.697121	−	1.40916i
$508$	1.48986e8	+	1.25014e8i	1.13646	+	0.953604i
$509$	5.74105e7	+	1.57734e8i	0.435349	+	1.19611i	0.942486	+	0.334246i	$0.108482\pi$
$509$	5.74105e7	+	1.57734e8i	0.435349	+	1.19611i	−0.507137	+	0.861866i	$0.669296\pi$
$510$	−3.28855e7	−	8.00334e6i	−0.247910	−	0.0603338i
$511$	5.79981e7	+	3.28924e8i	0.434661	+	2.46509i
$512$			2.32873e8i			1.73504i
$513$	−7.59974e7	−	1.48198e7i	−0.562920	−	0.109771i
$514$	2.73142e8			2.01141
$515$	7.54605e7	−	1.33057e7i	0.552457	−	0.0974130i
$516$	−1.65342e8	+	4.84178e7i	−1.20346	+	0.352416i
$517$	−1.83523e7	+	6.67969e6i	−0.132806	+	0.0483375i
$518$	−2.35045e7	+	2.80116e7i	−0.169107	+	0.201534i
$519$	2.81044e6	−	4.37192e7i	0.0201035	−	0.312730i
$520$	3.32974e8	+	1.21193e8i	2.36810	+	0.861919i
$521$	−1.23265e8	+	7.11671e7i	−0.871618	+	0.503229i	−0.867886	−	0.496764i	$-0.834522\pi$
$521$	−1.23265e8	+	7.11671e7i	−0.871618	+	0.503229i	−0.00373275	+	0.999993i	$0.501188\pi$
$522$	−7.27568e7	−	1.74412e8i	−0.511519	−	1.22621i
$523$	5.46812e7	−	9.47107e7i	0.382237	−	0.662055i	−0.609144	−	0.793059i	$-0.708487\pi$
$523$	5.46812e7	−	9.47107e7i	0.382237	−	0.662055i	0.991382	+	0.131005i	$0.0418203\pi$
$524$	2.66522e8	+	3.17629e8i	1.85242	+	2.20763i
$525$	1.31829e8	−	9.69152e7i	0.911027	−	0.669752i
$526$	4.34548e7	−	2.46444e8i	0.298594	−	1.69341i
$527$	−1.41156e7	−	2.48896e6i	−0.0964424	−	0.0170054i
$528$	−2.63355e7	−	3.58228e7i	−0.178912	−	0.243365i
$529$	7.54314e7	−	6.32945e7i	0.509548	−	0.427562i
$530$	1.31773e7	+	7.60792e6i	0.0885113	+	0.0511020i
$531$	2.10307e8	+	1.60538e8i	1.40466	+	1.07224i
$532$	−1.82597e8	−	3.16267e8i	−1.21271	−	2.10048i
$533$	1.06548e8	−	2.92739e8i	0.703664	−	1.93330i
$534$	3.76516e8	+	2.42039e7i	2.47263	+	0.158950i
$535$	3.52432e7	+	2.95726e7i	0.230152	+	0.193120i
$536$	1.18297e8	+	3.25017e8i	0.768207	+	2.11063i
$537$	−1.40703e7	−	4.80485e7i	−0.0908615	−	0.310283i
$538$	3.37131e7	+	1.91196e8i	0.216497	+	1.22781i
$539$		−	3.81975e7i		−	0.243932i
$540$	−1.09689e8	−	1.98164e8i	−0.696597	−	1.25847i
$541$	1.97603e8			1.24796			0.623982	−	0.781438i	$-0.285514\pi$
$541$	1.97603e8			1.24796			0.623982	+	0.781438i	$0.285514\pi$
$542$	−1.44367e8	+	2.54558e7i	−0.906713	+	0.159878i
$543$	−1.44189e7	+	5.92468e7i	−0.0900599	+	0.370054i
$544$	6.92897e7	−	2.52194e7i	0.430400	−	0.156653i
$545$	−4.86884e7	+	5.80246e7i	−0.300771	+	0.358445i
$546$	−7.53094e8	+	3.72560e8i	−4.62670	+	2.28886i
$547$	−2.50338e8	−	9.11156e7i	−1.52955	−	0.556712i	−0.566042	−	0.824376i	$-0.691526\pi$
$547$	−2.50338e8	−	9.11156e7i	−1.52955	−	0.556712i	−0.963512	+	0.267664i	$0.913748\pi$
$548$	−2.19569e8	+	1.26768e8i	−1.33422	+	0.770314i
$549$	8.35023e6	−	2.67171e7i	0.0504640	−	0.161463i
$550$	1.21515e7	−	2.10471e7i	0.0730370	−	0.126504i
$551$	−4.42067e7	−	5.26835e7i	−0.264261	−	0.314934i
$552$	2.85115e7	+	2.57353e8i	0.169513	+	1.53007i
$553$	4.45533e7	−	2.52674e8i	0.263454	−	1.49412i
$554$	−1.40572e8	−	2.47867e7i	−0.826742	−	0.145777i
$555$	−3.31453e6	+	7.55856e6i	−0.0193885	+	0.0442140i
$556$	1.85221e7	−	1.55419e7i	0.107762	−	0.0904229i
$557$	1.96611e8	+	1.13513e8i	1.13774	+	0.656872i	0.945869	−	0.324549i	$-0.105213\pi$
$557$	1.96611e8	+	1.13513e8i	1.13774	+	0.656872i	0.191867	+	0.981421i	$0.438546\pi$
$558$	−7.29863e7	−	1.13934e8i	−0.420087	−	0.655768i
$559$	7.21258e7	+	1.24925e8i	0.412910	+	0.715180i
$560$	1.53740e8	−	4.22397e8i	0.875432	−	2.40523i
$561$	2.76185e6	−	4.14465e6i	0.0156427	−	0.0234746i
$562$	3.72819e8	+	3.12832e8i	2.10034	+	1.76239i
$563$	−1.01505e8	−	2.78883e8i	−0.568804	−	1.56278i	−0.806374	−	0.591406i	$-0.798573\pi$
$563$	−1.01505e8	−	2.78883e8i	−0.568804	−	1.56278i	0.237570	−	0.971370i	$-0.423649\pi$
$564$	3.52339e8	−	3.68984e8i	1.96392	−	2.05670i
$565$	−6.05438e6	−	3.43361e7i	−0.0335679	−	0.190373i
$566$			2.36162e8i			1.30245i
$567$	3.06157e8	+	8.03904e7i	1.67956	+	0.441017i
$568$	−2.85873e8			−1.56001
$569$	−9.21596e7	+	1.62502e7i	−0.500269	+	0.0882110i	−0.418088	−	0.908406i	$-0.637300\pi$
$569$	−9.21596e7	+	1.62502e7i	−0.500269	+	0.0882110i	−0.0821811	+	0.996617i	$0.526189\pi$
$570$	−8.40922e7	−	8.02989e7i	−0.454079	−	0.433596i
$571$	−2.75151e8	+	1.00147e8i	−1.47796	+	0.537934i	−0.950250	−	0.311489i	$-0.899172\pi$
$571$	−2.75151e8	+	1.00147e8i	−1.47796	+	0.537934i	−0.527712	+	0.849423i	$0.676950\pi$
$572$	−5.68686e7	+	6.77733e7i	−0.303867	+	0.362135i
$573$	−2.14687e8	−	1.43060e8i	−1.14115	−	0.760423i
$574$	−7.33745e8	−	2.67061e8i	−3.87980	−	1.41213i
$575$	−6.20342e7	+	3.58154e7i	−0.326308	+	0.188394i
$576$	1.94642e8	+	1.00704e8i	1.01852	+	0.526964i
$577$	−1.42181e8	+	2.46265e8i	−0.740141	+	1.28196i	0.212289	+	0.977207i	$0.431908\pi$
$577$	−1.42181e8	+	2.46265e8i	−0.740141	+	1.28196i	−0.952431	+	0.304755i	$0.901425\pi$
$578$	−2.17561e8	−	2.59279e8i	−1.12667	−	1.34271i
$579$	1.69759e8	+	7.44417e7i	0.874575	+	0.383514i
$580$	3.49341e7	−	1.98121e8i	0.179047	−	1.01542i
$581$	3.46537e8	+	6.11038e7i	1.76694	+	0.311559i
$582$	−3.44855e8	+	3.82055e7i	−1.74931	+	0.193802i
$583$	−1.71525e6	+	1.43927e6i	−0.00865610	+	0.00726333i
$584$	−6.61491e8	−	3.81912e8i	−3.32113	−	1.91745i
$585$	−1.39497e8	+	1.28471e8i	−0.696782	+	0.641706i
$586$	−1.39374e8	−	2.41403e8i	−0.692612	−	1.19964i
$587$	5.40599e7	−	1.48528e8i	0.267277	−	0.734337i	−0.731353	−	0.681999i	$-0.761111\pi$
$587$	5.40599e7	−	1.48528e8i	0.267277	−	0.734337i	0.998629	−	0.0523375i	$-0.0166671\pi$
$588$	4.42455e8	+	8.94380e8i	2.17639	+	4.39937i
$589$	−3.77208e7	−	3.16515e7i	−0.184602	−	0.154899i
$590$	1.35888e8	+	3.73349e8i	0.661645	+	1.81785i
$591$	2.36260e8	+	5.74985e7i	1.14453	+	0.278544i
$592$	−7.34936e6	−	4.16803e7i	−0.0354229	−	0.200893i
$593$		−	2.00427e8i		−	0.961150i	−0.876954	−	0.480575i	$-0.840428\pi$
$593$		−	2.00427e8i		−	0.961150i	0.876954	−	0.480575i	$-0.159572\pi$
$594$	4.64419e7	−	7.32710e6i	0.221590	−	0.0349601i
$595$	5.03533e7			0.239043
$596$	−3.53106e7	+	6.22621e6i	−0.166789	+	0.0294093i
$597$	−2.20872e8	+	6.46789e7i	−1.03805	+	0.303976i
$598$	3.45652e8	−	1.25807e8i	1.61635	−	0.588303i
$599$	−1.50949e8	+	1.79894e8i	−0.702344	+	0.837021i	−0.992790	−	0.119870i	$-0.961752\pi$
$599$	−1.50949e8	+	1.79894e8i	−0.702344	+	0.837021i	0.290445	+	0.956892i	$0.406197\pi$
$600$	−2.40044e7	+	3.73413e8i	−0.111132	+	1.72876i
$601$	1.43185e8	+	5.21153e7i	0.659592	+	0.240072i	0.650060	−	0.759883i	$-0.274744\pi$
$601$	1.43185e8	+	5.21153e7i	0.659592	+	0.240072i	0.00953195	+	0.999955i	$0.496966\pi$
$602$	3.13123e8	−	1.80782e8i	1.43524	−	0.828639i
$603$	−1.83587e8	−	2.37013e7i	−0.837316	−	0.108098i
$604$	1.05421e8	−	1.82595e8i	0.478428	−	0.828661i
$605$	8.28404e7	+	9.87253e7i	0.374090	+	0.445823i
$606$	3.47356e8	−	2.55363e8i	1.56084	−	1.14747i
$607$	−3.34378e7	+	1.89635e8i	−0.149510	+	0.847915i	0.814124	+	0.580691i	$0.197217\pi$
$607$	−3.34378e7	+	1.89635e8i	−0.149510	+	0.847915i	−0.963634	+	0.267224i	$0.913894\pi$
$608$	2.49467e8	+	4.39878e7i	1.10995	+	0.195714i
$609$	1.66532e8	+	2.26524e8i	0.737302	+	1.00291i
$610$	3.22001e7	−	2.70191e7i	0.141863	−	0.119037i
$611$	−3.69942e8	−	2.13586e8i	−1.62185	−	0.936374i
$612$	−1.66588e7	+	1.29037e8i	−0.0726759	+	0.562937i
$613$	−1.99190e8	−	3.45006e8i	−0.864739	−	1.49777i	−0.867306	−	0.497776i	$-0.834150\pi$
$613$	−1.99190e8	−	3.45006e8i	−0.864739	−	1.49777i	0.00256657	−	0.999997i	$-0.499183\pi$
$614$	−1.00900e8	+	2.77221e8i	−0.435900	+	1.19763i
$615$	−1.75878e8	−	1.13061e7i	−0.756111	−	0.0486058i
$616$	1.00120e8	+	8.40107e7i	0.428330	+	0.359412i
$617$	3.73596e7	+	1.02645e8i	0.159055	+	0.436999i	0.993464	−	0.114146i	$-0.0364133\pi$
$617$	3.73596e7	+	1.02645e8i	0.159055	+	0.436999i	−0.834409	+	0.551145i	$0.814191\pi$
$618$	−1.16772e8	−	3.98764e8i	−0.494735	−	1.68947i
$619$	−4.16470e6	−	2.36192e7i	−0.0175595	−	0.0995849i	0.974768	−	0.223219i	$-0.0716563\pi$
$619$	−4.16470e6	−	2.36192e7i	−0.0175595	−	0.0995849i	−0.992328	+	0.123634i	$0.960545\pi$
$620$		−	1.44041e8i		−	0.604382i
$621$	−1.29342e8	−	4.97389e7i	−0.540089	−	0.207693i
$622$	7.55546e7			0.313971
$623$	−5.52787e8	+	9.74713e7i	−2.28609	+	0.403100i
$624$	2.29961e8	−	9.44905e8i	0.946456	−	3.88897i
$625$	−1.72416e7	+	6.27542e6i	−0.0706215	+	0.0257041i
$626$	2.99519e8	−	3.56953e8i	1.22096	−	1.45508i
$627$	1.53362e7	−	7.58692e6i	0.0622180	−	0.0307796i
$628$	9.58896e8	+	3.49010e8i	3.87162	+	1.40915i
$629$	4.10585e6	−	2.37051e6i	0.0164987	−	0.00952555i
$630$	3.22009e8	+	3.49646e8i	1.28779	+	1.39832i
$631$	−6.80754e7	+	1.17910e8i	−0.270958	+	0.469313i	−0.969107	−	0.246639i	$-0.920674\pi$
$631$	−6.80754e7	+	1.17910e8i	−0.270958	+	0.469313i	0.698149	+	0.715952i	$0.254007\pi$
$632$	3.77161e8	+	4.49483e8i	1.49409	+	1.78058i
$633$	1.43500e7	+	1.29527e8i	0.0565770	+	0.510681i
$634$	−2.96989e7	+	1.68431e8i	−0.116539	+	0.660927i
$635$	−9.07250e7	−	1.59973e7i	−0.354328	−	0.0624776i
$636$	2.34905e7	−	5.35683e7i	0.0913104	−	0.208227i
$637$	6.40010e8	−	5.37032e8i	2.47610	−	2.07770i
$638$	3.61657e7	+	2.08803e7i	0.139263	+	0.0804034i
$639$	7.03055e7	−	1.35887e8i	0.269455	−	0.520804i
$640$	1.24119e7	+	2.14980e7i	0.0473476	+	0.0820084i
$641$	−1.43355e8	+	3.93863e8i	−0.544299	+	1.49545i	0.297000	+	0.954878i	$0.404014\pi$
$641$	−1.43355e8	+	3.93863e8i	−0.544299	+	1.49545i	−0.841298	+	0.540571i	$0.818208\pi$
$642$	1.38343e8	−	2.07608e8i	0.522820	−	0.784584i
$643$	1.75722e8	+	1.47448e8i	0.660987	+	0.554634i	0.910382	−	0.413768i	$-0.135787\pi$
$643$	1.75722e8	+	1.47448e8i	0.660987	+	0.554634i	−0.249395	+	0.968402i	$0.580232\pi$
$644$	−2.23543e8	−	6.14178e8i	−0.836956	−	2.29952i
$645$	5.63589e7	−	5.90213e7i	0.210031	−	0.219953i
$646$	1.15982e7	+	6.57767e7i	0.0430222	+	0.243991i
$647$			2.21728e8i			0.818666i	0.912385	+	0.409333i	$0.134239\pi$
$647$			2.21728e8i			0.818666i	−0.912385	+	0.409333i	$0.865761\pi$
$648$	−5.90886e8	+	4.18176e8i	−2.17159	+	1.53686i
$649$	−5.84665e7			−0.213881
$650$	5.23493e8	−	9.23059e7i	1.90621	−	0.336116i
$651$	1.45588e8	+	1.39020e8i	0.527693	+	0.503889i
$652$	−1.16780e9	+	4.25044e8i	−4.21333	+	1.53353i
$653$	1.13406e8	−	1.35152e8i	0.407282	−	0.485380i	−0.522944	−	0.852367i	$-0.675166\pi$
$653$	1.13406e8	−	1.35152e8i	0.407282	−	0.485380i	0.930226	+	0.366987i	$0.119611\pi$
$654$	3.41807e8	+	2.27768e8i	1.22193	+	0.814255i
$655$	−1.84559e8	−	6.71740e7i	−0.656767	−	0.239044i
$656$	7.82683e8	−	4.51882e8i	2.77252	−	1.60071i
$657$	3.44220e8	−	2.20508e8i	1.21378	−	0.777551i
$658$	−5.35349e8	+	9.27252e8i	−1.87914	+	3.25477i
$659$	2.66519e8	+	3.17625e8i	0.931261	+	1.10983i	0.993732	+	0.111787i	$0.0356575\pi$
$659$	2.66519e8	+	3.17625e8i	0.931261	+	1.10983i	−0.0624710	+	0.998047i	$0.519898\pi$
$660$	4.58379e7	+	2.01005e7i	0.159438	+	0.0699159i
$661$	7.45997e7	−	4.23076e8i	0.258305	−	1.46492i	−0.529140	−	0.848535i	$-0.677485\pi$
$661$	7.45997e7	−	4.23076e8i	0.258305	−	1.46492i	0.787445	−	0.616385i	$-0.211404\pi$
$662$	1.26437e8	+	2.22942e7i	0.435812	+	0.0768455i
$663$	1.08275e8	−	1.19955e7i	0.371524	−	0.0411601i
$664$	−6.16456e8	+	5.17268e8i	−2.10571	+	1.76690i
$665$	1.49809e8	+	8.64922e7i	0.509416	+	0.294111i
$666$	4.27174e7	+	1.33510e7i	0.144605	+	0.0451952i
$667$	−6.15426e7	−	1.06595e8i	−0.207395	−	0.359219i
$668$	−8.81527e7	+	2.42197e8i	−0.295737	+	0.812531i
$669$	−9.04218e7	−	1.82779e8i	−0.301991	−	0.610446i
$670$	−2.12942e8	−	1.78679e8i	−0.708005	−	0.594086i
$671$	2.11560e6	+	5.81256e6i	0.00700270	+	0.0192398i
$672$	−1.00621e9	−	2.44880e8i	−3.31573	−	0.806948i
$673$	−6.78340e6	−	3.84706e7i	−0.0222537	−	0.126207i	0.971657	−	0.236395i	$-0.0759659\pi$
$673$	−6.78340e6	−	3.84706e7i	−0.0222537	−	0.126207i	−0.993911	+	0.110188i	$0.964855\pi$
$674$		−	7.92020e8i		−	2.58676i
$675$	−1.71595e8	−	1.03245e8i	−0.557946	−	0.335704i
$676$	−1.18278e9			−3.82880
$677$	−2.61634e7	+	4.61332e6i	−0.0843196	+	0.0148678i	−0.215649	−	0.976471i	$-0.569187\pi$
$677$	−2.61634e7	+	4.61332e6i	−0.0843196	+	0.0148678i	0.131329	+	0.991339i	$0.458076\pi$
$678$	−1.81446e8	+	5.31336e7i	−0.582180	+	0.170483i
$679$	4.85064e8	−	1.76549e8i	1.54949	−	0.563969i
$680$	−7.40193e7	+	8.82128e7i	−0.235406	+	0.280547i
$681$	2.72454e7	−	4.23830e8i	0.0862685	−	1.34199i
$682$	2.80969e7	+	1.02265e7i	0.0885740	+	0.0322383i
$683$	2.48430e8	−	1.43431e8i	0.779727	−	0.450176i	−0.0566065	−	0.998397i	$-0.518028\pi$
$683$	2.48430e8	−	1.43431e8i	0.779727	−	0.450176i	0.836334	+	0.548221i	$0.184695\pi$
$684$	−2.71210e8	+	3.55290e8i	−0.847496	+	1.11023i
$685$	6.00473e7	−	1.04005e8i	0.186819	−	0.323580i
$686$	−6.78179e8	−	8.08222e8i	−2.10074	−	2.50356i
$687$	−4.17961e7	+	3.07268e7i	−0.128904	+	0.0947649i
$688$	−7.26692e7	+	4.12128e8i	−0.223144	+	1.26551i
$689$	−4.82307e7	−	8.50437e6i	−0.147457	−	0.0260007i
$690$	−1.23260e8	−	1.67664e8i	−0.375210	−	0.510378i
$691$	−1.80309e8	+	1.51297e8i	−0.546491	+	0.458560i	−0.873751	−	0.486374i	$-0.838319\pi$
$691$	−1.80309e8	+	1.51297e8i	−0.546491	+	0.458560i	0.327260	+	0.944934i	$0.393875\pi$
$692$	−2.19017e8	−	1.26450e8i	−0.660937	−	0.381592i
$693$	−6.45564e7	+	2.69301e7i	−0.193972	+	0.0809166i
$694$	3.88767e8	+	6.73364e8i	1.16308	+	2.01452i
$695$	−3.91716e6	+	1.07623e7i	−0.0116685	+	0.0320590i
$696$	−6.41645e8	−	4.12474e7i	−1.90312	−	0.122340i
$697$	7.75536e7	+	6.50752e7i	0.229036	+	0.192184i
$698$	1.63033e8	+	4.47929e8i	0.479412	+	1.31717i
$699$	1.74269e8	+	5.95111e8i	0.510257	+	1.74247i
$700$	−1.64015e8	−	9.30178e8i	−0.478179	−	2.71189i
$701$		−	1.04150e8i		−	0.302348i	−0.988507	−	0.151174i	$-0.951695\pi$
$701$		−	1.04150e8i		−	0.302348i	0.988507	−	0.151174i	$-0.0483053\pi$
$702$	7.75712e8	+	6.75134e8i	2.24228	+	1.95155i
$703$	1.62874e7			0.0468797
$704$	−4.76922e7	+	8.40943e6i	−0.136688	+	0.0241017i
$705$	−5.71459e7	+	2.34811e8i	−0.163086	+	0.670119i
$706$	5.28626e8	−	1.92404e8i	1.50222	−	0.546764i
$707$	−4.12283e8	+	4.91340e8i	−1.16664	+	1.39035i
$708$	1.36897e9	−	6.77239e8i	3.85740	−	1.90828i
$709$	−5.75437e8	−	2.09442e8i	−1.61458	−	0.587659i	−0.632240	−	0.774772i	$-0.717864\pi$
$709$	−5.75437e8	−	2.09442e8i	−1.61458	−	0.587659i	−0.982338	+	0.187114i	$0.940087\pi$
$710$	1.98971e8	−	1.14876e8i	0.555923	−	0.320962i
$711$	−3.06414e8	+	6.87372e7i	−0.852509	+	0.191242i
$712$	6.41840e8	−	1.11170e9i	1.77822	−	3.07997i
$713$	−5.66474e7	−	6.75098e7i	−0.156283	−	0.186251i
$714$	−3.00664e7	−	2.71388e8i	−0.0826013	−	0.745584i
$715$	7.27711e6	−	4.12705e7i	0.0199086	−	0.112907i
$716$	−2.84627e8	−	5.01875e7i	−0.775421	−	0.136728i
$717$	−2.26711e8	+	5.16999e8i	−0.615057	+	1.40259i
$718$	1.85158e8	−	1.55366e8i	0.500229	−	0.419742i
$719$	−5.78049e7	−	3.33737e7i	−0.155517	−	0.0897878i	0.420222	−	0.907421i	$-0.361952\pi$
$719$	−5.78049e7	−	3.33737e7i	−0.155517	−	0.0897878i	−0.575739	+	0.817634i	$0.695286\pi$
$720$	−5.49581e8	+	2.53767e7i	−1.47243	+	0.0679889i
$721$	3.09086e8	+	5.35352e8i	0.824657	+	1.42835i
$722$	1.60110e8	−	4.39898e8i	0.425409	−	1.16880i
$723$	−2.68229e7	+	4.02524e7i	−0.0709725	+	0.106507i
$724$	2.69646e8	+	2.26260e8i	0.710522	+	0.596199i
$725$	−6.08365e7	−	1.67147e8i	−0.159643	−	0.438616i
$726$	4.82634e8	−	5.05433e8i	1.26127	−	1.32085i
$727$	2.85836e7	+	1.62106e8i	0.0743898	+	0.421886i	0.999146	+	0.0413249i	$0.0131579\pi$
$727$	2.85836e7	+	1.62106e8i	0.0743898	+	0.421886i	−0.924756	+	0.380561i	$0.875731\pi$
$728$			2.85868e9i			7.40920i
$729$	−5.34578e7	−	3.83715e8i	−0.137984	−	0.990434i
$730$	6.13874e8			1.57801
$731$	−4.61663e7	+	8.14036e6i	−0.118188	+	0.0208397i
$732$	−1.16865e8	−	1.11593e8i	−0.297955	−	0.284515i
$733$	3.78558e8	−	1.37784e8i	0.961216	−	0.349854i	0.186706	−	0.982416i	$-0.440219\pi$
$733$	3.78558e8	−	1.37784e8i	0.961216	−	0.349854i	0.774510	+	0.632562i	$0.217997\pi$
$734$	2.35770e8	−	2.80980e8i	0.596212	−	0.710538i
$735$	−3.93327e8	−	2.62100e8i	−0.990586	−	0.660092i
$736$	4.26023e8	+	1.55060e8i	1.06856	+	0.388925i
$737$	3.54254e7	−	2.04529e7i	0.0884937	−	0.0510919i
$738$	4.40819e7	+	9.54678e8i	0.109671	+	2.37513i
$739$	4.44944e7	−	7.70666e7i	0.110248	−	0.190956i	−0.805622	−	0.592430i	$-0.798169\pi$
$739$	4.44944e7	−	7.70666e7i	0.110248	−	0.190956i	0.915870	+	0.401474i	$0.131502\pi$
$740$	3.06251e7	+	3.64976e7i	0.0755758	+	0.0900677i
$741$	3.42739e8	+	1.50296e8i	0.842381	+	0.369396i
$742$	−2.13160e7	+	1.20889e8i	−0.0521789	+	0.295921i
$743$	7.44404e8	+	1.31258e8i	1.81486	+	0.320008i	0.974899	−	0.222647i	$-0.0714696\pi$
$743$	7.44404e8	+	1.31258e8i	1.81486	+	0.320008i	0.839956	+	0.542655i	$0.182581\pi$
$744$	−4.57560e8	+	5.06919e7i	−1.11104	+	0.123089i
$745$	1.30104e7	−	1.09170e7i	0.0314646	−	0.0264020i
$746$	−1.92138e8	−	1.10931e8i	−0.462805	−	0.267200i
$747$	−9.42714e7	−	4.20239e8i	−0.226161	−	1.00817i
$748$	−1.43757e7	−	2.48994e7i	−0.0343497	−	0.0594954i
$749$	−1.26944e8	+	3.48777e8i	−0.302112	+	0.830047i
$750$	−3.38130e8	−	6.83497e8i	−0.801493	−	1.62014i
$751$	−4.35376e8	−	3.65324e8i	−1.02789	−	0.862499i	−0.0372886	−	0.999305i	$-0.511872\pi$
$751$	−4.35376e8	−	3.65324e8i	−1.02789	−	0.862499i	−0.990598	+	0.136805i	$0.956317\pi$
$752$	−4.23852e8	−	1.16452e9i	−0.996692	−	2.73839i
$753$	−2.70641e8	−	6.58657e7i	−0.633882	−	0.154268i
$754$	1.58612e8	+	8.99532e8i	0.370017	+	2.09847i
$755$			9.98714e7i			0.232060i
$756$	1.19962e9	−	1.37834e9i	2.77639	−	3.19000i
$757$	9.82086e7			0.226392			0.113196	−	0.993573i	$-0.463891\pi$
$757$	9.82086e7			0.226392			0.113196	+	0.993573i	$0.463891\pi$
$758$	3.51611e8	−	6.19985e7i	0.807337	−	0.142355i
$759$	2.93885e7	−	8.60597e6i	0.0672127	−	0.0196822i
$760$	−3.71743e8	+	1.35303e8i	−0.846841	+	0.308225i
$761$	−4.40178e8	+	5.24584e8i	−0.998791	+	1.19031i	−0.0170958	+	0.999854i	$0.505442\pi$
$761$	−4.40178e8	+	5.24584e8i	−0.998791	+	1.19031i	−0.981695	+	0.190459i	$0.939002\pi$
$762$	−3.20475e7	+	4.98531e8i	−0.0724318	+	1.12675i
$763$	−5.74228e8	−	2.09002e8i	−1.29274	−	0.470519i
$764$	−1.28975e9	+	7.44639e8i	−2.89219	+	1.66981i
$765$	−2.37273e7	−	5.68787e7i	−0.0529985	−	0.127047i
$766$	6.77059e8	−	1.17270e9i	1.50640	−	2.60916i
$767$	−8.22003e8	−	9.79624e8i	−1.82174	−	2.17107i
$768$	−3.10080e8	+	2.27959e8i	−0.684526	+	0.503237i
$769$	−9.47827e7	+	5.37539e8i	−0.208425	+	1.18204i	0.683533	+	0.729920i	$0.260443\pi$
$769$	−9.47827e7	+	5.37539e8i	−0.208425	+	1.18204i	−0.891958	+	0.452118i	$0.850669\pi$
$770$	−1.03444e8	−	1.82399e7i	−0.226585	−	0.0399531i
$771$	2.94601e8	+	4.00730e8i	0.642792	+	0.874356i
$772$	8.19706e8	−	6.87815e8i	1.78158	−	1.49493i
$773$	2.77715e8	+	1.60339e8i	0.601258	+	0.347136i	0.769536	−	0.638603i	$-0.220487\pi$
$773$	2.77715e8	+	1.60339e8i	0.601258	+	0.347136i	−0.168278	+	0.985739i	$0.553821\pi$
$774$	−3.51759e8	−	2.68515e8i	−0.758616	−	0.579089i
$775$	−6.36779e7	−	1.10293e8i	−0.136799	−	0.236943i
$776$	−4.03752e8	+	1.10930e9i	−0.864031	+	2.37391i
$777$	−6.64470e7	−	4.27147e6i	−0.141649	−	0.00910572i
$778$	−1.05135e9	−	8.82185e8i	−2.23258	−	1.87336i
$779$	1.18954e8	+	3.26823e8i	0.251632	+	0.691354i
$780$	3.07661e8	+	1.05063e9i	0.648318	+	2.21394i
$781$	5.87093e6	+	3.32957e7i	0.0123241	+	0.0698932i
$782$			1.19538e8i			0.249969i
$783$	1.77408e8	−	2.94855e8i	0.369563	−	0.614220i
$784$	2.42378e9			5.02973
$785$	−4.76016e8	+	8.39344e7i	−0.984039	+	0.173513i
$786$	−2.51845e8	+	1.03483e9i	−0.518640	+	2.13108i
$787$	1.61806e8	−	5.88927e7i	0.331949	−	0.120820i	−0.170668	−	0.985329i	$-0.554593\pi$
$787$	1.61806e8	−	5.88927e7i	0.331949	−	0.120820i	0.502617	+	0.864509i	$0.332370\pi$
$788$	9.02261e8	−	1.07527e9i	1.84397	−	2.19756i
$789$	4.08429e8	−	2.02052e8i	0.831545	−	0.411370i
$790$	−4.43130e8	−	1.61286e8i	−0.898773	−	0.327127i
$791$	2.43596e8	−	1.40640e8i	0.492199	−	0.284171i
$792$	4.77197e7	−	1.52682e8i	0.0960555	−	0.307335i
$793$	−6.76472e7	+	1.17168e8i	−0.135653	+	0.234958i
$794$	−3.37811e8	−	4.02587e8i	−0.674857	−	0.804263i
$795$	3.05088e6	+	2.75381e7i	0.00607188	+	0.0548066i
$796$	−2.30704e8	+	1.30839e9i	−0.457421	+	2.59416i
$797$	−2.92838e8	−	5.16352e7i	−0.578431	−	0.101993i	−0.123225	−	0.992379i	$-0.539324\pi$
$797$	−2.92838e8	−	5.16352e7i	−0.578431	−	0.101993i	−0.455207	+	0.890386i	$0.650435\pi$
$798$	3.76714e8	−	8.59068e8i	0.741315	−	1.69051i
$799$	1.06343e8	−	8.92325e7i	0.208482	−	0.174937i
$800$	5.67394e8	+	3.27585e8i	1.10819	+	0.639814i
$801$	3.70585e8	+	5.78495e8i	0.721092	+	1.12565i
$802$	−1.37640e8	−	2.38399e8i	−0.266821	−	0.462148i
$803$	−3.08965e7	+	8.48874e7i	−0.0596709	+	0.163944i
$804$	−5.92561e8	+	8.89242e8i	−1.14016	+	1.71101i
$805$	2.37163e8	+	1.99003e8i	0.454631	+	0.381480i
$806$	2.23678e8	+	6.14550e8i	0.427187	+	1.17369i
$807$	−2.44144e8	+	2.55678e8i	−0.464543	+	0.486488i
$808$	−2.54712e8	−	1.44454e9i	−0.482853	−	2.73839i
$809$		−	7.09709e8i		−	1.34040i	−0.742180	−	0.670201i	$-0.766208\pi$
$809$		−	7.09709e8i		−	1.34040i	0.742180	−	0.670201i	$-0.233792\pi$
$810$	2.43222e8	−	5.28499e8i	0.457666	−	0.994463i
$811$	5.31041e8			0.995556			0.497778	−	0.867305i	$-0.334149\pi$
$811$	5.31041e8			0.995556			0.497778	+	0.867305i	$0.334149\pi$
$812$	1.59835e9	−	2.81832e8i	2.98541	−	0.526408i
$813$	−1.93055e8	−	1.84346e8i	−0.359260	−	0.343054i
$814$	−9.29358e6	+	3.38259e6i	−0.0172310	+	0.00627156i
$815$	3.78385e8	−	4.50941e8i	0.698973	−	0.833004i
$816$	2.62994e8	+	1.75250e8i	0.484033	+	0.322543i
$817$	−1.51335e8	−	5.50813e7i	−0.277506	−	0.101004i
$818$	−9.20805e7	+	5.31627e7i	−0.168232	+	0.0971286i
$819$	−1.35884e9	−	7.03042e8i	−2.47353	−	1.27976i
$820$	−5.08694e8	+	8.81083e8i	−0.922603	+	1.59800i
$821$	3.61711e8	+	4.31071e8i	0.653631	+	0.778967i	0.986457	−	0.164022i	$-0.0524467\pi$
$821$	3.61711e8	+	4.31071e8i	0.653631	+	0.778967i	−0.332826	+	0.942988i	$0.608002\pi$
$822$	−5.96409e8	−	2.61534e8i	−1.07381	−	0.470882i
$823$	6.00379e7	−	3.40492e8i	0.107702	−	0.610811i	−0.882404	−	0.470493i	$-0.844076\pi$
$823$	6.00379e7	−	3.40492e8i	0.107702	−	0.610811i	0.990106	−	0.140319i	$-0.0448127\pi$
$824$	−1.39223e9	−	2.45487e8i	−2.48845	−	0.438781i
$825$	4.39845e7	−	4.87292e6i	0.0783317	−	0.00867816i
$826$	−2.45541e9	+	2.06033e9i	−4.35696	+	3.65592i
$827$	2.66378e8	+	1.53793e8i	0.470958	+	0.271907i	0.716640	−	0.697443i	$-0.245679\pi$
$827$	2.66378e8	+	1.53793e8i	0.470958	+	0.271907i	−0.245683	+	0.969350i	$0.579012\pi$
$828$	−5.88435e8	+	5.41923e8i	−1.03659	+	0.954655i
$829$	3.02471e8	+	5.23895e8i	0.530909	+	0.919562i	0.999349	+	0.0360664i	$0.0114828\pi$
$829$	3.02471e8	+	5.23895e8i	0.530909	+	0.919562i	−0.468440	+	0.883495i	$0.655184\pi$
$830$	2.21200e8	−	6.07743e8i	0.386858	−	1.06288i
$831$	−1.15251e8	−	2.32968e8i	−0.200836	−	0.405970i
$832$	−8.11425e8	−	6.80867e8i	−1.40890	−	1.18220i
$833$	9.28619e7	+	2.55136e8i	0.160658	+	0.441404i
$834$	6.03444e7	+	1.46860e7i	0.104025	+	0.0253166i
$835$	−2.12001e7	−	1.20232e8i	−0.0364148	−	0.206519i
$836$		−	9.87726e7i		−	0.169051i
$837$	8.84331e7	−	2.29963e8i	0.150813	−	0.392177i
$838$	−1.05435e9			−1.79165
$839$	1.04031e9	−	1.83434e8i	1.76147	−	0.310595i	0.803040	−	0.595925i	$-0.203214\pi$
$839$	1.04031e9	−	1.83434e8i	1.76147	−	0.310595i	0.958429	+	0.285330i	$0.0921032\pi$
$840$	1.55207e9	−	4.54500e8i	2.61863	−	0.766825i
$841$	−2.71738e8	+	9.89047e7i	−0.456839	+	0.166276i
$842$	−3.24718e7	+	3.86984e7i	−0.0543965	+	0.0648272i
$843$	−5.68510e7	+	8.84374e8i	−0.0948976	+	1.47623i
$844$	7.06928e8	+	2.57301e8i	1.17584	+	0.427971i
$845$	4.85196e8	−	2.80128e8i	0.804169	−	0.464287i
$846$	1.29968e9	+	1.67791e8i	2.14648	+	0.277113i
$847$	−5.19858e8	+	9.00421e8i	−0.855529	+	1.48182i
$848$	−9.13270e7	−	1.08839e8i	−0.149766	−	0.178484i
$849$	−3.46475e8	+	2.54715e8i	−0.566173	+	0.416228i
$850$	−2.99973e7	+	1.70123e8i	−0.0488456	+	0.277017i
$851$	2.87070e7	+	5.06182e6i	0.0465800	+	0.00821331i
$852$	−5.23142e8	−	7.11602e8i	−0.845864	−	1.15058i
$853$	3.97149e8	−	3.33248e8i	0.639892	−	0.536933i	−0.264093	−	0.964497i	$-0.585073\pi$
$853$	3.97149e8	−	3.33248e8i	0.639892	−	0.536933i	0.903985	+	0.427564i	$0.140628\pi$
$854$	2.93680e8	+	1.69556e8i	0.471521	+	0.272233i
$855$	2.71086e7	−	2.09980e8i	0.0433720	−	0.335953i
$856$	−4.24407e8	−	7.35094e8i	−0.676645	−	1.17198i
$857$	5.33251e7	−	1.46510e8i	0.0847207	−	0.232768i	−0.890097	−	0.455771i	$-0.849364\pi$
$857$	5.33251e7	−	1.46510e8i	0.0847207	−	0.232768i	0.974818	+	0.223003i	$0.0715859\pi$
$858$	−2.26781e8	−	1.45783e7i	−0.359041	−	0.0230805i
$859$	−1.10632e7	−	9.28314e6i	−0.0174543	−	0.0146459i	0.634019	−	0.773318i	$-0.281404\pi$
$859$	−1.10632e7	−	9.28314e6i	−0.0174543	−	0.0146459i	−0.651473	+	0.758672i	$0.725849\pi$
$860$	−1.61125e8	−	4.42688e8i	−0.253319	−	0.695988i
$861$	−3.99581e8	−	1.36453e9i	−0.626030	−	2.13783i
$862$	2.60741e8	+	1.47874e9i	0.407088	+	2.30871i
$863$			5.67161e8i			0.882418i	0.897404	+	0.441209i	$0.145450\pi$
$863$			5.67161e8i			0.882418i	−0.897404	+	0.441209i	$0.854550\pi$
$864$	1.97526e8	+	1.25200e9i	0.306255	+	1.94116i
$865$	1.19793e8			0.185090
$866$	−2.32682e9	+	4.10282e8i	−3.58269	+	0.631725i
$867$	1.45738e8	−	5.98833e8i	0.223622	−	0.918859i
$868$	1.09198e9	−	3.97446e8i	1.66976	−	0.607742i
$869$	4.46057e7	−	5.31591e7i	0.0679722	−	0.0810061i
$870$	4.63167e8	−	2.29132e8i	0.703364	−	0.347958i
$871$	8.40753e8	+	3.06009e8i	1.27237	+	0.463106i
$872$	1.21026e9	−	6.98745e8i	1.82528	−	1.05383i
$873$	−4.27998e8	−	4.64732e8i	−0.643279	−	0.698489i
$874$	−2.05331e8	+	3.55644e8i	−0.307554	+	0.532698i
$875$	7.29239e8	+	8.69074e8i	1.08854	+	1.29728i
$876$	−2.59851e8	−	2.34549e9i	−0.386556	−	3.48917i
$877$	7.40500e7	−	4.19958e8i	0.109781	−	0.622597i	−0.879422	−	0.476043i	$-0.842071\pi$
$877$	7.40500e7	−	4.19958e8i	0.109781	−	0.622597i	0.989203	−	0.146554i	$-0.0468183\pi$
$878$	−8.19320e8	−	1.44468e8i	−1.21052	−	0.213446i
$879$	2.03841e8	−	4.64845e8i	0.300141	−	0.684450i
$880$	9.31327e7	−	7.81476e7i	0.136664	−	0.114675i
$881$	1.81973e8	+	1.05062e8i	0.266121	+	0.153645i	0.627124	−	0.778920i	$-0.284232\pi$
$881$	1.81973e8	+	1.05062e8i	0.266121	+	0.153645i	−0.361003	+	0.932565i	$0.617565\pi$
$882$	−1.17778e9	+	2.27641e9i	−1.71655	+	3.31776i
$883$	5.60616e8	+	9.71015e8i	0.814297	+	1.41040i	0.909831	+	0.414978i	$0.136211\pi$
$883$	5.60616e8	+	9.71015e8i	0.814297	+	1.41040i	−0.0955339	+	0.995426i	$0.530456\pi$
$884$	2.15084e8	−	5.90938e8i	0.311351	−	0.855431i
$885$	−4.01180e8	+	6.02042e8i	−0.578775	+	0.868554i
$886$	−7.12802e8	−	5.98112e8i	−1.02487	−	0.859967i
$887$	−4.50701e8	−	1.23829e9i	−0.645828	−	1.77440i	−0.632590	−	0.774487i	$-0.718008\pi$
$887$	−4.50701e8	−	1.23829e9i	−0.645828	−	1.77440i	−0.0132385	−	0.999912i	$-0.504214\pi$
$888$	1.05160e8	−	1.10128e8i	0.150180	−	0.157275i
$889$	−1.29058e8	−	7.31926e8i	−0.183688	−	1.04175i
$890$			1.03167e9i			1.46343i
$891$	6.08401e7	+	6.02326e7i	0.0860115	+	0.0851527i
$892$	−1.17718e9			−1.65863
$893$	4.69663e8	−	8.28142e7i	0.659526	−	0.116292i
$894$	−6.66081e7	−	6.36034e7i	−0.0932211	−	0.0890160i
$895$	1.28646e8	−	4.68232e7i	0.179443	−	0.0653118i
$896$	−1.28729e8	+	1.53413e8i	−0.178958	+	0.213274i
$897$	5.57379e8	+	3.71418e8i	0.772277	+	0.514619i
$898$	−2.46035e8	−	8.95493e7i	−0.339756	−	0.123661i
$899$	1.89520e8	−	1.09419e8i	0.260841	−	0.150597i
$900$	−9.73436e8	+	6.23586e8i	−1.33530	+	0.855399i
$901$	7.95783e6	−	1.37834e7i	0.0108798	−	0.0188443i
$902$	−1.35750e8	−	1.61781e8i	−0.184978	−	0.220449i
$903$	6.02949e8	+	2.64402e8i	0.818874	+	0.359088i
$904$	−1.11702e8	+	6.33492e8i	−0.151201	+	0.857503i
$905$	−1.64201e8	−	2.89530e7i	−0.221528	−	0.0390614i
$906$	5.38276e8	−	5.96341e7i	0.723803	−	0.0801882i
$907$	7.91819e8	−	6.64415e8i	1.06122	−	0.890467i	0.0669891	−	0.997754i	$-0.478661\pi$
$907$	7.91819e8	−	6.64415e8i	1.06122	−	0.890467i	0.994228	+	0.107287i	$0.0342163\pi$
$908$	−2.12323e9	−	1.22585e9i	−2.83622	−	1.63749i
$909$	7.49290e8	+	2.34185e8i	0.997604	+	0.311794i
$910$	−1.14874e9	−	1.98967e9i	−1.52439	−	2.64033i
$911$	−2.20682e8	+	6.06319e8i	−0.291885	+	0.801947i	0.703906	+	0.710293i	$0.251438\pi$
$911$	−2.20682e8	+	6.06319e8i	−0.291885	+	0.801947i	−0.995791	+	0.0916542i	$0.970785\pi$
$912$	4.81419e8	+	9.73143e8i	0.634657	+	1.28290i
$913$	7.29064e7	+	6.11757e7i	0.0957973	+	0.0803835i
$914$	8.90635e8	+	2.44700e9i	1.16644	+	3.20476i
$915$	7.43697e7	+	1.80993e7i	0.0970807	+	0.0236265i
$916$	5.20009e7	+	2.94912e8i	0.0676588	+	0.383712i
$917$		−	1.58449e9i		−	2.05486i
$918$	−2.92391e8	+	1.61846e8i	−0.377951	+	0.209205i
$919$	−1.19216e9			−1.53598			−0.767992	−	0.640460i	$-0.778744\pi$
$919$	−1.19216e9			−1.53598			−0.767992	+	0.640460i	$0.778744\pi$
$920$	−6.97258e8	+	1.22945e8i	−0.895427	+	0.157888i
$921$	−5.15540e8	+	1.50968e8i	−0.659908	+	0.193244i
$922$	2.53156e9	−	9.21413e8i	3.22995	−	1.17561i
$923$	−4.75338e8	+	5.66486e8i	−0.604502	+	0.720417i
$924$	−2.59038e7	+	4.02959e8i	−0.0328358	+	0.510793i
$925$	3.95848e7	+	1.44077e7i	0.0500154	+	0.0182041i
$926$	−1.83491e8	+	1.05939e8i	−0.231091	+	0.133420i
$927$	4.59084e8	−	6.01408e8i	0.576306	−	0.754970i
$928$	−5.62898e8	+	9.74967e8i	−0.704345	+	1.21996i
$929$	2.33105e8	+	2.77804e8i	0.290740	+	0.346491i	0.891567	−	0.452888i	$-0.149606\pi$
$929$	2.33105e8	+	2.77804e8i	0.290740	+	0.346491i	−0.600827	+	0.799379i	$0.705162\pi$
$930$	2.98097e8	−	2.19149e8i	0.370603	−	0.272453i
$931$	−1.61970e8	+	9.18578e8i	−0.200718	+	1.13833i
$932$	3.52529e9	+	6.21603e8i	4.35458	+	0.767831i
$933$	8.14902e7	+	1.10847e8i	0.100337	+	0.136483i
$934$	1.48896e9	−	1.24939e9i	1.82744	−	1.53341i
$935$	1.17943e7	+	6.80944e6i	0.0144290	+	0.00833061i
$936$	3.22915e9	−	1.34706e9i	3.93786	−	1.64270i
$937$	−1.51909e8	−	2.63114e8i	−0.184656	−	0.319834i	0.758804	−	0.651319i	$-0.225784\pi$
$937$	−1.51909e8	−	2.63114e8i	−0.184656	−	0.319834i	−0.943461	+	0.331484i	$0.892451\pi$
$938$	7.67006e8	−	2.10733e9i	0.929373	−	2.55343i
$939$	8.46738e8	+	5.44316e7i	1.02271	+	0.0657437i
$940$	1.06868e9	+	8.96730e8i	1.28666	+	1.07964i
$941$	−8.39042e7	−	2.30525e8i	−0.100697	−	0.276662i	0.879107	−	0.476625i	$-0.158140\pi$
$941$	−8.39042e7	−	2.30525e8i	−0.100697	−	0.276662i	−0.979803	+	0.199963i	$0.935918\pi$
$942$	7.36614e8	+	2.51546e9i	0.881225	+	3.00929i
$943$	1.08089e8	+	6.13005e8i	0.128898	+	0.731020i
$944$		−	3.70993e9i		−	4.41011i
$945$	−1.65663e8	+	8.49537e8i	−0.196304	+	1.00667i
$946$	9.77909e7			0.115511
$947$	−1.20777e9	+	2.12962e8i	−1.42211	+	0.250756i	−0.831196	−	0.555980i	$-0.812343\pi$
$947$	−1.20777e9	+	2.12962e8i	−1.42211	+	0.250756i	−0.590912	+	0.806736i	$0.701232\pi$
$948$	−4.28667e8	+	1.76138e9i	−0.503147	+	2.06742i
$949$	−1.85670e9	+	6.75783e8i	−2.17241	+	0.790694i
$950$	−3.81468e8	+	4.54616e8i	−0.444926	+	0.530242i
$951$	−2.79138e8	+	1.38091e8i	−0.324547	+	0.160555i
$952$	−8.72979e8	−	3.17738e8i	−1.01180	−	0.368264i
$953$	−1.25317e8	+	7.23517e7i	−0.144787	+	0.0835930i	−0.570644	−	0.821198i	$-0.693306\pi$
$953$	−1.25317e8	+	7.23517e7i	−0.144787	+	0.0835930i	0.425856	+	0.904791i	$0.359973\pi$
$954$	1.46600e8	−	3.28865e7i	0.168846	−	0.0378768i
$955$	3.52720e8	−	6.10929e8i	0.404967	−	0.701424i
$956$	2.09473e9	+	2.49640e9i	2.39748	+	2.85720i
$957$	8.37327e6	+	7.55797e7i	0.00955343	+	0.0862322i
$958$	1.12246e8	−	6.36577e8i	0.127665	−	0.724026i
$959$	9.54147e8	+	1.68242e8i	1.08183	+	0.190756i
$960$	−2.40657e8	+	5.48800e8i	−0.272010	+	0.620298i
$961$	−5.59839e8	+	4.69760e8i	−0.630801	+	0.529305i
$962$	−1.87338e8	−	1.08160e8i	−0.210427	−	0.121490i
$963$	4.53795e8	−	2.09538e7i	0.508137	−	0.0234630i
$964$	1.39615e8	+	2.41820e8i	0.155848	+	0.269937i
$965$	−1.73356e8	+	4.76293e8i	−0.192911	+	0.530020i
$966$	9.30953e8	−	1.39706e9i	1.03275	−	1.54983i
$967$	−6.85491e8	−	5.75195e8i	−0.758092	−	0.636115i	0.179537	−	0.983751i	$-0.442540\pi$
$967$	−6.85491e8	−	5.75195e8i	−0.758092	−	0.636115i	−0.937629	+	0.347636i	$0.886984\pi$
$968$	−8.13236e8	−	2.23435e9i	−0.896583	−	2.46334i
$969$	−8.39921e7	+	8.79599e7i	−0.0923139	+	0.0966749i
$970$	−1.64747e8	−	9.34329e8i	−0.180511	−	1.02373i
$971$		−	3.69610e8i		−	0.403726i	−0.979414	−	0.201863i	$-0.935300\pi$
$971$		−	3.69610e8i		−	0.403726i	0.979414	−	0.201863i	$-0.0646995\pi$
$972$	−2.12224e9	−	7.05593e8i	−2.31098	−	0.768343i
$973$	−9.23974e7			−0.100305
$974$	−2.51647e9	+	4.43721e8i	−2.72342	+	0.480213i
$975$	7.00041e8	+	6.68463e8i	0.755283	+	0.721213i
$976$	−3.68829e8	+	1.34243e8i	−0.396712	+	0.144392i
$977$	−2.10370e8	+	2.50710e8i	−0.225580	+	0.268836i	−0.866949	−	0.498397i	$-0.833922\pi$
$977$	−2.10370e8	+	2.50710e8i	−0.225580	+	0.268836i	0.641369	+	0.767233i	$0.278367\pi$
$978$	−2.65637e9	−	1.77011e9i	−2.83970	−	1.89228i
$979$	−1.42661e8	−	5.19244e7i	−0.152040	−	0.0553380i
$980$	−2.36295e9	+	1.36425e9i	−2.51059	+	1.44949i
$981$	3.44984e7	+	7.47130e8i	0.0365420	+	0.791387i
$982$	1.26514e9	−	2.19128e9i	1.33599	−	2.31400i
$983$	−9.96825e8	−	1.18797e9i	−1.04944	−	1.25068i	−0.967187	−	0.254065i	$-0.918232\pi$
$983$	−9.96825e8	−	1.18797e9i	−1.04944	−	1.25068i	−0.0822548	−	0.996611i	$-0.526212\pi$
$984$	2.97787e9	+	1.30584e9i	3.12550	+	1.37058i
$985$	−1.15457e8	+	6.54787e8i	−0.120812	+	0.685159i
$986$	−2.92327e8	−	5.15452e7i	−0.304957	−	0.0537721i
$987$	−1.93779e9	+	2.14682e8i	−2.01537	+	0.223277i
$988$	1.65497e9	−	1.38868e9i	1.71600	−	1.43990i
$989$	−2.49614e8	−	1.44115e8i	−0.258036	−	0.148977i
$990$	2.81407e7	+	1.25444e8i	0.0290021	+	0.129284i
$991$	−1.73518e8	−	3.00542e8i	−0.178289	−	0.308805i	0.763006	−	0.646392i	$-0.223723\pi$
$991$	−1.73518e8	−	3.00542e8i	−0.178289	−	0.308805i	−0.941294	+	0.337587i	$0.890389\pi$
$992$	−2.75688e8	+	7.57447e8i	−0.282412	+	0.775920i
$993$	1.03662e8	+	2.09542e8i	0.105869	+	0.214005i
$994$	1.41989e9	+	1.19143e9i	1.44575	+	1.21313i
$995$	−2.15239e8	−	5.91364e8i	−0.218500	−	0.600324i
$996$	−2.41570e9	−	5.87907e8i	−2.44492	−	0.595019i
$997$	−4.35489e6	−	2.46978e7i	−0.00439432	−	0.0249214i	0.982532	−	0.186095i	$-0.0595832\pi$
$997$	−4.35489e6	−	2.46978e7i	−0.00439432	−	0.0249214i	−0.986926	+	0.161174i	$0.948472\pi$
$998$			1.92429e9i			1.93588i
$999$	2.64859e7	+	7.70709e7i	0.0265655	+	0.0773026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.f.a.14.17	yes	102
3.2	odd	2		81.7.f.a.71.1		102
27.2	odd	18	inner	27.7.f.a.2.17	✓	102
27.25	even	9		81.7.f.a.8.1		102

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.f.a.2.17	✓	102	27.2	odd	18	inner
27.7.f.a.14.17	yes	102	1.1	even	1	trivial
81.7.f.a.8.1		102	27.25	even	9
81.7.f.a.71.1		102	3.2	odd	2

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(14.6025 - 2.57482i) q^{2} +(19.5272 + 18.6464i) q^{3} +(146.463 - 53.3083i) q^{4} +(-47.4564 + 56.5563i) q^{5} +(333.158 + 222.005i) q^{6} +(-559.698 - 203.713i) q^{7} +(1179.64 - 681.064i) q^{8} +(33.6255 + 728.224i) q^{9} +(-547.361 + 948.057i) q^{10} +(-103.550 - 123.406i) q^{11} +(3854.03 + 1690.05i) q^{12} +(611.857 - 3470.01i) q^{13} +(-8697.52 - 1533.61i) q^{14} +(-1981.26 + 219.499i) q^{15} +(7830.57 - 6570.63i) q^{16} +(991.661 + 572.536i) q^{17} +(2366.06 + 10547.3i) q^{18} +(1966.90 + 3406.77i) q^{19} +(-3935.71 + 10813.3i) q^{20} +(-7130.83 - 14414.3i) q^{21} +(-1829.83 - 1535.41i) q^{22} +(2407.96 + 6615.81i) q^{23} +(35734.4 + 8696.66i) q^{24} +(1766.74 + 10019.7i) q^{25} -52246.4i q^{26} +(-12922.1 + 14847.2i) q^{27} -92834.9 q^{28} +(-17217.1 + 3035.84i) q^{29} +(-28366.3 + 8306.63i) q^{30} +(-11762.6 + 4281.22i) q^{31} +(41392.2 - 49329.2i) q^{32} +(279.030 - 4340.60i) q^{33} +(15954.9 + 5807.12i) q^{34} +(38082.5 - 21987.0i) q^{35} +(43745.3 + 104866. i) q^{36} +(2070.19 - 3585.67i) q^{37} +(37493.4 + 44682.9i) q^{38} +(76651.1 - 56350.9i) q^{39} +(-17462.9 + 99036.8i) q^{40} +(87069.7 + 15352.7i) q^{41} +(-141242. - 192124. i) q^{42} +(-31361.3 + 26315.3i) q^{43} +(-21744.8 - 12554.4i) q^{44} +(-42781.4 - 32657.2i) q^{45} +(52196.7 + 90407.4i) q^{46} +(41464.3 - 113922. i) q^{47} +(275428. + 17705.6i) q^{48} +(181638. + 152412. i) q^{49} +(51597.8 + 141764. i) q^{50} +(8688.68 + 29670.9i) q^{51} +(-95366.0 - 540847. i) q^{52} -13899.3i q^{53} +(-150467. + 250079. i) q^{54} +11893.5 q^{55} +(-798982. + 140882. i) q^{56} +(-25115.8 + 103200. i) q^{57} +(-243596. + 88661.9i) q^{58} +(233288. - 278022. i) q^{59} +(-278482. + 137766. i) q^{60} +(-36081.6 - 13132.6i) q^{61} +(-160739. + 92803.0i) q^{62} +(129529. - 414435. i) q^{63} +(150309. - 260343. i) q^{64} +(167215. + 199279. i) q^{65} +(-7101.71 - 64102.1i) q^{66} +(-44093.4 + 250066. i) q^{67} +(175763. + 30991.8i) q^{68} +(-76340.1 + 174088. i) q^{69} +(499488. - 419120. i) q^{70} +(-181755. - 104936. i) q^{71} +(535633. + 836139. i) q^{72} +(-280379. - 485631. i) q^{73} +(20997.5 - 57690.1i) q^{74} +(-152331. + 228600. i) q^{75} +(469688. + 394115. i) q^{76} +(32817.2 + 90164.4i) q^{77} +(974205. - 1.02023e6i) q^{78} +(74801.8 + 424222. i) q^{79} +754687. i q^{80} +(-529180. + 48973.8i) q^{81} +1.31097e6 q^{82} +(-581811. + 102589. i) q^{83} +(-1.81281e6 - 1.73103e6i) q^{84} +(-79441.2 + 28914.2i) q^{85} +(-390197. + 465019. i) q^{86} +(-392810. - 261755. i) q^{87} +(-206198. - 75050.0i) q^{88} +(816149. - 471204. i) q^{89} +(-708803. - 366722. i) q^{90} +(-1.04934e6 + 1.81752e6i) q^{91} +(705356. + 840610. i) q^{92} +(-309519. - 135729. i) q^{93} +(312154. - 1.77032e6i) q^{94} +(-286016. - 50432.3i) q^{95} +(1.72809e6 - 191450. i) q^{96} +(-663894. + 557074. i) q^{97} +(3.04481e6 + 1.75792e6i) q^{98} +(86385.1 - 79557.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18}+ \cdots + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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