LMFDB - Embedded newform 7.8.c.a.4.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7,8,Mod(2,7)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7.2"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.18669517839$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 103x^{6} - 378x^{5} + 9744x^{4} - 22680x^{3} + 149400x^{2} + 216000x + 810000 $ x^8 - x^7 + 103x^6 - 378x^5 + 9744x^4 - 22680x^3 + 149400x^2 + 216000x + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.1
Root			$-1.02959 + 1.78331i$ of defining polynomial
Character	$\chi$	$=$	7.4
Dual form			7.8.c.a.2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.50966 - 16.4712i) q^{2} +(-19.7308 + 34.1747i) q^{3} +(-116.867 + 202.420i) q^{4} +(-175.002 - 303.113i) q^{5} +750.531 q^{6} +(-666.505 - 615.885i) q^{7} +2011.00 q^{8} +(314.894 + 545.412i) q^{9} +(-3328.43 + 5765.00i) q^{10} +(3134.64 - 5429.36i) q^{11} +(-4611.76 - 7987.80i) q^{12} -4122.67 q^{13} +(-3806.14 + 16835.0i) q^{14} +13811.7 q^{15} +(-4164.91 - 7213.83i) q^{16} +(-5571.35 + 9649.87i) q^{17} +(5989.07 - 10373.4i) q^{18} +(-8439.78 - 14618.1i) q^{19} +81808.2 q^{20} +(34198.3 - 10625.7i) q^{21} -119238. q^{22} +(-17395.9 - 30130.7i) q^{23} +(-39678.6 + 68725.3i) q^{24} +(-22189.1 + 38432.7i) q^{25} +(39205.2 + 67905.4i) q^{26} -111155. q^{27} +(202560. - 62937.2i) q^{28} +40847.7 q^{29} +(-131345. - 227496. i) q^{30} +(21955.6 - 38028.2i) q^{31} +(49490.2 - 85719.6i) q^{32} +(123698. + 214251. i) q^{33} +211927. q^{34} +(-70042.8 + 309808. i) q^{35} -147203. q^{36} +(-38998.2 - 67546.8i) q^{37} +(-160519. + 278027. i) q^{38} +(81343.5 - 140891. i) q^{39} +(-351930. - 609560. i) q^{40} -41821.6 q^{41} +(-500233. - 462241. i) q^{42} +331256. q^{43} +(732674. + 1.26903e6i) q^{44} +(110214. - 190897. i) q^{45} +(-330859. + 573065. i) q^{46} +(-550427. - 953368. i) q^{47} +328707. q^{48} +(64914.4 + 820981. i) q^{49} +844045. q^{50} +(-219854. - 380799. i) q^{51} +(481805. - 834511. i) q^{52} +(780322. - 1.35156e6i) q^{53} +(1.05704e6 + 1.83085e6i) q^{54} -2.19428e6 q^{55} +(-1.34034e6 - 1.23854e6i) q^{56} +666093. q^{57} +(-388448. - 672812. i) q^{58} +(137167. - 237581. i) q^{59} +(-1.61414e6 + 2.79577e6i) q^{60} +(1.52543e6 + 2.64213e6i) q^{61} -835161. q^{62} +(126033. - 557458. i) q^{63} -2.94876e6 q^{64} +(721477. + 1.24964e6i) q^{65} +(2.35265e6 - 4.07491e6i) q^{66} +(322932. - 559334. i) q^{67} +(-1.30222e6 - 2.25551e6i) q^{68} +1.37294e6 q^{69} +(5.76899e6 - 1.79247e6i) q^{70} +531485. q^{71} +(633251. + 1.09682e6i) q^{72} +(-2.32873e6 + 4.03347e6i) q^{73} +(-741719. + 1.28469e6i) q^{74} +(-875618. - 1.51661e6i) q^{75} +3.94533e6 q^{76} +(-5.43312e6 + 1.68812e6i) q^{77} -3.09419e6 q^{78} +(-1.17506e6 - 2.03526e6i) q^{79} +(-1.45774e6 + 2.52488e6i) q^{80} +(1.50450e6 - 2.60586e6i) q^{81} +(397709. + 688852. i) q^{82} -107925. q^{83} +(-1.84581e6 + 8.16422e6i) q^{84} +3.90000e6 q^{85} +(-3.15013e6 - 5.45619e6i) q^{86} +(-805957. + 1.39596e6i) q^{87} +(6.30376e6 - 1.09184e7i) q^{88} +(-3.98287e6 - 6.89853e6i) q^{89} -4.19240e6 q^{90} +(2.74778e6 + 2.53909e6i) q^{91} +8.13206e6 q^{92} +(866402. + 1.50065e6i) q^{93} +(-1.04688e7 + 1.81324e7i) q^{94} +(-2.95396e6 + 5.11641e6i) q^{95} +(1.95296e6 + 3.38263e6i) q^{96} +1.44749e7 q^{97} +(1.29052e7 - 8.87647e6i) q^{98} +3.94832e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 28 q^{3} - 348 q^{4} - 252 q^{5} + 2044 q^{6} + 672 q^{7} - 1968 q^{8} - 2008 q^{9} - 4774 q^{10} + 3972 q^{11} + 5404 q^{12} - 2352 q^{13} + 47502 q^{14} - 33112 q^{15} - 57264 q^{16} - 56364 q^{17}+ \cdots + 30427952 q^{99}+O(q^{100}) $ 8 * q + 6 * q^2 - 28 * q^3 - 348 * q^4 - 252 * q^5 + 2044 * q^6 + 672 * q^7 - 1968 * q^8 - 2008 * q^9 - 4774 * q^10 + 3972 * q^11 + 5404 * q^12 - 2352 * q^13 + 47502 * q^14 - 33112 * q^15 - 57264 * q^16 - 56364 * q^17 + 35908 * q^18 - 41748 * q^19 + 324744 * q^20 + 188524 * q^21 - 305908 * q^22 - 131748 * q^23 - 389592 * q^24 + 68016 * q^25 - 113652 * q^26 + 378056 * q^27 + 681548 * q^28 + 68112 * q^29 - 605378 * q^30 - 401212 * q^31 + 453408 * q^32 - 24052 * q^33 + 164220 * q^34 + 40404 * q^35 - 720176 * q^36 + 5396 * q^37 - 31794 * q^38 - 364840 * q^39 + 443688 * q^40 + 820848 * q^41 - 240856 * q^42 + 93088 * q^43 + 1465836 * q^44 + 1209656 * q^45 - 1379202 * q^46 - 1470084 * q^47 - 4037600 * q^48 - 2793784 * q^49 + 2791056 * q^50 + 1724796 * q^51 + 5269768 * q^52 + 642372 * q^53 + 4567318 * q^54 - 6126680 * q^55 - 6195168 * q^56 + 6718136 * q^57 + 1972220 * q^58 - 752220 * q^59 - 2123324 * q^60 - 1325772 * q^61 - 6032628 * q^62 - 6412616 * q^63 - 1731712 * q^64 + 4868808 * q^65 + 6013294 * q^66 + 290916 * q^67 - 2453556 * q^68 + 9830520 * q^69 + 11665990 * q^70 + 6755520 * q^71 - 4557744 * q^72 - 6706588 * q^73 - 3616878 * q^74 - 7223888 * q^75 + 5846008 * q^76 - 5310564 * q^77 - 32576264 * q^78 - 3946244 * q^79 - 10695888 * q^80 + 11731292 * q^81 + 17563252 * q^82 + 19084128 * q^83 + 38088092 * q^84 + 14012136 * q^85 - 23237832 * q^86 - 17836840 * q^87 + 8043336 * q^88 - 16165212 * q^89 + 6831496 * q^90 - 2414720 * q^91 - 38885256 * q^92 - 12552852 * q^93 - 5720442 * q^94 + 3268452 * q^95 + 8448608 * q^96 + 3066224 * q^97 + 60255006 * q^98 + 30427952 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−9.50966	−	16.4712i	−0.840543	−	1.45586i	−0.889436	−	0.457059i	$-0.848903\pi$
$2$	−9.50966	−	16.4712i	−0.840543	−	1.45586i	0.0488930	−	0.998804i	$-0.484431\pi$
$3$	−19.7308	+	34.1747i	−0.421910	+	0.730769i	−0.996126	−	0.0879344i	$-0.971973\pi$
$3$	−19.7308	+	34.1747i	−0.421910	+	0.730769i	0.574217	+	0.818703i	$0.305307\pi$
$4$	−116.867	+	202.420i	−0.913026	+	1.58141i
$5$	−175.002	−	303.113i	−0.626107	−	1.08445i	−0.988326	−	0.152357i	$-0.951314\pi$
$5$	−175.002	−	303.113i	−0.626107	−	1.08445i	0.362218	−	0.932093i	$-0.382020\pi$
$6$	750.531			1.41853
$7$	−666.505	−	615.885i	−0.734447	−	0.678667i
$7$	−666.505	−	615.885i	−0.734447	−	0.678667i
$8$	2011.00			1.38866
$9$	314.894	+	545.412i	0.143984	+	0.249388i
$10$	−3328.43	+	5765.00i	−1.05254	+	1.82305i
$11$	3134.64	−	5429.36i	0.710090	−	1.22991i	−0.254732	−	0.967012i	$-0.581987\pi$
$11$	3134.64	−	5429.36i	0.710090	−	1.22991i	0.964823	−	0.262901i	$-0.0846793\pi$
$12$	−4611.76	−	7987.80i	−0.770429	−	1.33442i
$13$	−4122.67			−0.520448			−0.260224	−	0.965548i	$-0.583796\pi$
$13$	−4122.67			−0.520448			−0.260224	+	0.965548i	$0.583796\pi$
$14$	−3806.14	+	16835.0i	−0.370712	+	1.63970i
$15$	13811.7			1.05664
$16$	−4164.91	−	7213.83i	−0.254206	−	0.440297i
$17$	−5571.35	+	9649.87i	−0.275036	+	0.476376i	−0.970144	−	0.242529i	$-0.922023\pi$
$17$	−5571.35	+	9649.87i	−0.275036	+	0.476376i	0.695108	+	0.718905i	$0.255356\pi$
$18$	5989.07	−	10373.4i	0.242050	−	0.419243i
$19$	−8439.78	−	14618.1i	−0.282289	−	0.488938i	0.689659	−	0.724134i	$-0.257760\pi$
$19$	−8439.78	−	14618.1i	−0.282289	−	0.488938i	−0.971948	+	0.235196i	$0.924427\pi$
$20$	81808.2			2.28661
$21$	34198.3	−	10625.7i	0.805819	−	0.250375i
$22$	−119238.			−2.38745
$23$	−17395.9	−	30130.7i	−0.298126	−	0.516370i	0.677581	−	0.735448i	$-0.263028\pi$
$23$	−17395.9	−	30130.7i	−0.298126	−	0.516370i	−0.975707	+	0.219078i	$0.929695\pi$
$24$	−39678.6	+	68725.3i	−0.585891	+	1.01479i
$25$	−22189.1	+	38432.7i	−0.284021	+	0.491939i
$26$	39205.2	+	67905.4i	0.437459	+	0.757701i
$27$	−111155.			−1.08681
$28$	202560.	−	62937.2i	1.74382	−	0.541819i
$29$	40847.7			0.311010			0.155505	−	0.987835i	$-0.450299\pi$
$29$	40847.7			0.311010			0.155505	+	0.987835i	$0.450299\pi$
$30$	−131345.	−	227496.i	−0.888154	−	1.53833i
$31$	21955.6	−	38028.2i	0.132367	−	0.229266i	−0.792222	−	0.610234i	$-0.791076\pi$
$31$	21955.6	−	38028.2i	0.132367	−	0.229266i	0.924589	+	0.380967i	$0.124409\pi$
$32$	49490.2	−	85719.6i	0.266990	−	0.462440i
$33$	123698.	+	214251.i	0.599188	+	1.03782i
$34$	211927.			0.924718
$35$	−70042.8	+	309808.i	−0.276137	+	1.22139i
$36$	−147203.			−0.525846
$37$	−38998.2	−	67546.8i	−0.126572	−	0.219229i	0.795774	−	0.605593i	$-0.207064\pi$
$37$	−38998.2	−	67546.8i	−0.126572	−	0.219229i	−0.922346	+	0.386364i	$0.873731\pi$
$38$	−160519.	+	278027.i	−0.474551	+	0.821947i
$39$	81343.5	−	140891.i	0.219582	−	0.380327i
$40$	−351930.	−	609560.i	−0.869452	−	1.50594i
$41$	−41821.6			−0.0947670			−0.0473835	−	0.998877i	$-0.515088\pi$
$41$	−41821.6			−0.0947670			−0.0473835	+	0.998877i	$0.515088\pi$
$42$	−500233.	−	462241.i	−1.04184	−	0.962711i
$43$	331256.			0.635366			0.317683	−	0.948197i	$-0.397095\pi$
$43$	331256.			0.635366			0.317683	+	0.948197i	$0.397095\pi$
$44$	732674.	+	1.26903e6i	1.29666	+	2.24588i
$45$	110214.	−	190897.i	0.180299	−	0.312288i
$46$	−330859.	+	573065.i	−0.501176	+	0.868063i
$47$	−550427.	−	953368.i	−0.773317	−	1.33942i	−0.935736	−	0.352703i	$-0.885263\pi$
$47$	−550427.	−	953368.i	−0.773317	−	1.33942i	0.162418	−	0.986722i	$-0.448071\pi$
$48$	328707.			0.429008
$49$	64914.4	+	820981.i	0.0788234	+	0.996889i
$50$	844045.			0.954928
$51$	−219854.	−	380799.i	−0.232081	−	0.401976i
$52$	481805.	−	834511.i	0.475182	−	0.823039i
$53$	780322.	−	1.35156e6i	0.719960	−	1.24701i	−0.241055	−	0.970511i	$-0.577493\pi$
$53$	780322.	−	1.35156e6i	0.719960	−	1.24701i	0.961015	−	0.276496i	$-0.0891733\pi$
$54$	1.05704e6	+	1.83085e6i	0.913513	+	1.58225i
$55$	−2.19428e6			−1.77837
$56$	−1.34034e6	−	1.23854e6i	−1.01990	−	0.942439i
$57$	666093.			0.476401
$58$	−388448.	−	672812.i	−0.261418	−	0.452789i
$59$	137167.	−	237581.i	0.0869498	−	0.150602i	−0.819271	−	0.573407i	$-0.805621\pi$
$59$	137167.	−	237581.i	0.0869498	−	0.150602i	0.906220	+	0.422806i	$0.138955\pi$
$60$	−1.61414e6	+	2.79577e6i	−0.964742	+	1.67098i
$61$	1.52543e6	+	2.64213e6i	0.860476	+	1.49039i	0.871470	+	0.490449i	$0.163167\pi$
$61$	1.52543e6	+	2.64213e6i	0.860476	+	1.49039i	−0.0109938	+	0.999940i	$0.503500\pi$
$62$	−835161.			−0.445040
$63$	126033.	−	557458.i	0.0635027	−	0.280880i
$64$	−2.94876e6			−1.40608
$65$	721477.	+	1.24964e6i	0.325856	+	0.564399i
$66$	2.35265e6	−	4.07491e6i	1.00729	−	1.74467i
$67$	322932.	−	559334.i	0.131174	−	0.227201i	−0.792955	−	0.609280i	$-0.791459\pi$
$67$	322932.	−	559334.i	0.131174	−	0.227201i	0.924130	+	0.382079i	$0.124792\pi$
$68$	−1.30222e6	−	2.25551e6i	−0.502230	−	0.869887i
$69$	1.37294e6			0.503130
$70$	5.76899e6	−	1.79247e6i	2.01028	−	0.624611i
$71$	531485.			0.176233			0.0881165	−	0.996110i	$-0.471915\pi$
$71$	531485.			0.176233			0.0881165	+	0.996110i	$0.471915\pi$
$72$	633251.	+	1.09682e6i	0.199946	+	0.346316i
$73$	−2.32873e6	+	4.03347e6i	−0.700630	+	1.21353i	0.267616	+	0.963526i	$0.413764\pi$
$73$	−2.32873e6	+	4.03347e6i	−0.700630	+	1.21353i	−0.968246	+	0.250001i	$0.919569\pi$
$74$	−741719.	+	1.28469e6i	−0.212779	+	0.368544i
$75$	−875618.	−	1.51661e6i	−0.239662	−	0.415108i
$76$	3.94533e6			1.03095
$77$	−5.43312e6	+	1.68812e6i	−1.35622	+	0.421390i
$78$	−3.09419e6			−0.738272
$79$	−1.17506e6	−	2.03526e6i	−0.268141	−	0.464434i	0.700241	−	0.713907i	$-0.253076\pi$
$79$	−1.17506e6	−	2.03526e6i	−0.268141	−	0.464434i	−0.968382	+	0.249473i	$0.919743\pi$
$80$	−1.45774e6	+	2.52488e6i	−0.318320	+	0.551347i
$81$	1.50450e6	−	2.60586e6i	0.314553	−	0.544821i
$82$	397709.	+	688852.i	0.0796557	+	0.137968i
$83$	−107925.			−0.0207181			−0.0103591	−	0.999946i	$-0.503297\pi$
$83$	−107925.			−0.0207181			−0.0103591	+	0.999946i	$0.503297\pi$
$84$	−1.84581e6	+	8.16422e6i	−0.339789	+	1.50293i
$85$	3.90000e6			0.688808
$86$	−3.15013e6	−	5.45619e6i	−0.534053	−	0.925007i
$87$	−805957.	+	1.39596e6i	−0.131218	+	0.227277i
$88$	6.30376e6	−	1.09184e7i	0.986076	−	1.70793i
$89$	−3.98287e6	−	6.89853e6i	−0.598868	−	1.03727i	−0.992989	−	0.118211i	$-0.962284\pi$
$89$	−3.98287e6	−	6.89853e6i	−0.598868	−	1.03727i	0.394121	−	0.919059i	$-0.371049\pi$
$90$	−4.19240e6			−0.606198
$91$	2.74778e6	+	2.53909e6i	0.382241	+	0.353210i
$92$	8.13206e6			1.08879
$93$	866402.	+	1.50065e6i	0.111694	+	0.193459i
$94$	−1.04688e7	+	1.81324e7i	−1.30001	+	2.25169i
$95$	−2.95396e6	+	5.11641e6i	−0.353486	+	0.612256i
$96$	1.95296e6	+	3.38263e6i	0.225291	+	0.390216i
$97$	1.44749e7			1.61033			0.805167	−	0.593048i	$-0.202076\pi$
$97$	1.44749e7			1.61033			0.805167	+	0.593048i	$0.202076\pi$
$98$	1.29052e7	−	8.87647e6i	1.38508	−	0.952684i
$99$	3.94832e6			0.408968
$100$	−5.18637e6	−	8.98306e6i	−0.518637	−	0.898306i
$101$	2.71235e6	−	4.69793e6i	0.261951	−	0.453713i	−0.704809	−	0.709397i	$-0.748967\pi$
$101$	2.71235e6	−	4.69793e6i	0.261951	−	0.453713i	0.966760	+	0.255684i	$0.0823007\pi$
$102$	−4.18148e6	+	7.24253e6i	−0.390148	+	0.675756i
$103$	−8.54197e6	−	1.47951e7i	−0.770243	−	1.33410i	−0.937430	−	0.348175i	$-0.886802\pi$
$103$	−8.54197e6	−	1.47951e7i	−0.770243	−	1.33410i	0.167187	−	0.985925i	$-0.446532\pi$
$104$	−8.29069e6			−0.722726
$105$	−9.20558e6	−	8.50643e6i	−0.776048	−	0.717108i
$106$	−2.96824e7			−2.42063
$107$	1.12457e7	+	1.94781e7i	0.887447	+	1.53710i	0.842884	+	0.538096i	$0.180856\pi$
$107$	1.12457e7	+	1.94781e7i	0.887447	+	1.53710i	0.0445629	+	0.999007i	$0.485810\pi$
$108$	1.29904e7	−	2.25000e7i	0.992288	−	1.71869i
$109$	−554558.	+	960522.i	−0.0410161	+	0.0710419i	−0.885805	−	0.464058i	$-0.846393\pi$
$109$	−554558.	+	960522.i	−0.0410161	+	0.0710419i	0.844789	+	0.535100i	$0.179726\pi$
$110$	2.08669e7	+	3.61424e7i	1.49480	+	2.58907i
$111$	3.07786e6			0.213608
$112$	−1.66696e6	+	7.37316e6i	−0.112115	+	0.495896i
$113$	−1.59055e7			−1.03698			−0.518492	−	0.855082i	$-0.673507\pi$
$113$	−1.59055e7			−1.03698			−0.518492	+	0.855082i	$0.673507\pi$
$114$	−6.33432e6	−	1.09714e7i	−0.400436	−	0.693575i
$115$	−6.08866e6	+	1.05459e7i	−0.373318	+	0.646606i
$116$	−4.77376e6	+	8.26840e6i	−0.283960	+	0.491834i
$117$	−1.29820e6	−	2.24856e6i	−0.0749363	−	0.129794i
$118$	−5.21766e6			−0.292340
$119$	9.65654e6	−	3.00037e6i	0.525300	−	0.163215i
$120$	2.77754e7			1.46732
$121$	−9.90838e6	−	1.71618e7i	−0.508457	−	0.880673i
$122$	2.90127e7	−	5.02515e7i	1.44653	−	2.50547i
$123$	825172.	−	1.42924e6i	0.0399831	−	0.0692528i
$124$	5.13178e6	+	8.88851e6i	0.241709	+	0.418652i
$125$	−1.18115e7			−0.540904
$126$	−1.03805e7	+	3.22532e6i	−0.462299	+	0.143640i
$127$	2.24962e7			0.974532			0.487266	−	0.873254i	$-0.337994\pi$
$127$	2.24962e7			0.974532			0.487266	+	0.873254i	$0.337994\pi$
$128$	2.17069e7	+	3.75975e7i	0.914879	+	1.58462i
$129$	−6.53594e6	+	1.13206e7i	−0.268067	+	0.464306i
$130$	1.37220e7	−	2.37672e7i	0.547792	−	0.948804i
$131$	−9.39089e6	−	1.62655e7i	−0.364970	−	0.632146i	0.623801	−	0.781583i	$-0.285587\pi$
$131$	−9.39089e6	−	1.62655e7i	−0.364970	−	0.632146i	−0.988771	+	0.149436i	$0.952254\pi$
$132$	−5.78249e7			−2.18830
$133$	−3.37793e6	+	1.49410e7i	−0.124500	+	0.550679i
$134$	−1.22839e7			−0.441031
$135$	1.94523e7	+	3.36924e7i	0.680462	+	1.17859i
$136$	−1.12040e7	+	1.94059e7i	−0.381932	+	0.661526i
$137$	−1.96800e7	+	3.40868e7i	−0.653889	+	1.13257i	0.328282	+	0.944580i	$0.393530\pi$
$137$	−1.96800e7	+	3.40868e7i	−0.653889	+	1.13257i	−0.982171	+	0.187989i	$0.939803\pi$
$138$	−1.30562e7	−	2.26140e7i	−0.422902	−	0.732488i
$139$	2.45180e7			0.774343			0.387172	−	0.922008i	$-0.373452\pi$
$139$	2.45180e7			0.774343			0.387172	+	0.922008i	$0.373452\pi$
$140$	−5.45256e7	−	5.03844e7i	−1.67939	−	1.55184i
$141$	4.34414e7			1.30508
$142$	−5.05425e6	−	8.75421e6i	−0.148131	−	0.256571i
$143$	−1.29231e7	+	2.23835e7i	−0.369565	+	0.640105i
$144$	2.62301e6	−	4.54319e6i	0.0732034	−	0.126792i
$145$	−7.14845e6	−	1.23815e7i	−0.194726	−	0.337275i
$146$	8.85816e7			2.35564
$147$	−2.93376e7	−	1.39801e7i	−0.761752	−	0.362995i
$148$	1.82304e7			0.462255
$149$	−2.16986e7	−	3.75832e7i	−0.537379	−	0.930768i	−0.999044	−	0.0437135i	$-0.986081\pi$
$149$	−2.16986e7	−	3.75832e7i	−0.537379	−	0.930768i	0.461665	−	0.887054i	$-0.347252\pi$
$150$	−1.66537e7	+	2.88450e7i	−0.402893	+	0.697832i
$151$	1.68021e7	−	2.91021e7i	0.397140	−	0.687867i	−0.596231	−	0.802813i	$-0.703336\pi$
$151$	1.68021e7	−	2.91021e7i	0.397140	−	0.687867i	0.993372	+	0.114945i	$0.0366693\pi$
$152$	−1.69724e7	−	2.93970e7i	−0.392004	−	0.678970i
$153$	−7.01754e6			−0.158404
$154$	7.94724e7	+	7.34366e7i	1.75345	+	1.62028i
$155$	−1.53691e7			−0.331504
$156$	1.90128e7	+	3.29311e7i	0.400968	+	0.694496i
$157$	3.20924e7	−	5.55857e7i	0.661841	−	1.14634i	−0.318291	−	0.947993i	$-0.603109\pi$
$157$	3.20924e7	−	5.55857e7i	0.661841	−	1.14634i	0.980132	−	0.198349i	$-0.0635578\pi$
$158$	−2.23488e7	+	3.87092e7i	−0.450769	+	0.780754i
$159$	3.07927e7	+	5.33345e7i	0.607516	+	1.05225i
$160$	−3.46436e7			−0.668657
$161$	−6.96254e6	+	3.07961e7i	−0.131485	+	0.581575i
$162$	−5.72289e7			−1.05758
$163$	−2.06179e7	−	3.57113e7i	−0.372897	−	0.645876i	0.617113	−	0.786874i	$-0.288302\pi$
$163$	−2.06179e7	−	3.57113e7i	−0.372897	−	0.645876i	−0.990010	+	0.140999i	$0.954969\pi$
$164$	4.88758e6	−	8.46553e6i	0.0865247	−	0.149865i
$165$	4.32948e7	−	7.49888e7i	0.750312	−	1.29958i
$166$	1.02633e6	+	1.77766e6i	0.0174145	+	0.0301628i
$167$	−5.94520e7			−0.987776			−0.493888	−	0.869526i	$-0.664425\pi$
$167$	−5.94520e7			−0.987776			−0.493888	+	0.869526i	$0.664425\pi$
$168$	6.87728e7	−	2.13683e7i	1.11901	−	0.347686i
$169$	−4.57521e7			−0.729134
$170$	−3.70877e7	−	6.42377e7i	−0.578973	−	1.00281i
$171$	5.31527e6	−	9.20631e6i	0.0812903	−	0.140799i
$172$	−3.87130e7	+	6.70529e7i	−0.580106	+	1.00477i
$173$	2.21908e7	+	3.84356e7i	0.325845	+	0.564381i	0.981683	−	0.190521i	$-0.0610178\pi$
$173$	2.21908e7	+	3.84356e7i	0.325845	+	0.564381i	−0.655838	+	0.754902i	$0.727684\pi$
$174$	3.06575e7			0.441179
$175$	3.84593e7	−	1.19496e7i	0.542461	−	0.168547i
$176$	−5.22220e7			−0.722037
$177$	5.41283e6	+	9.37530e6i	0.0733700	+	0.127080i
$178$	−7.57514e7	+	1.31205e8i	−1.00675	+	1.74374i
$179$	3.18052e7	−	5.50883e7i	0.414489	−	0.717916i	−0.580886	−	0.813985i	$-0.697294\pi$
$179$	3.18052e7	−	5.50883e7i	0.414489	−	0.717916i	0.995375	+	0.0960691i	$0.0306270\pi$
$180$	2.57609e7	+	4.46192e7i	0.329236	+	0.570254i
$181$	−1.52914e6			−0.0191678			−0.00958389	−	0.999954i	$-0.503051\pi$
$181$	−1.52914e6			−0.0191678			−0.00958389	+	0.999954i	$0.503051\pi$
$182$	1.56915e7	−	6.94052e7i	0.192936	−	0.853379i
$183$	−1.20392e8			−1.45217
$184$	−3.49832e7	−	6.05927e7i	−0.413997	−	0.717064i
$185$	−1.36495e7	+	2.36417e7i	−0.158496	+	0.274522i
$186$	1.64784e7	−	2.85414e7i	0.187767	−	0.325222i
$187$	3.49284e7	+	6.04978e7i	0.390601	+	0.676540i
$188$	2.57308e8			2.82423
$189$	7.40852e7	+	6.84585e7i	0.798206	+	0.737584i
$190$	1.12365e8			1.18848
$191$	2.75145e7	+	4.76565e7i	0.285723	+	0.494887i	0.972784	−	0.231713i	$-0.0744330\pi$
$191$	2.75145e7	+	4.76565e7i	0.285723	+	0.494887i	−0.687061	+	0.726599i	$0.741100\pi$
$192$	5.81812e7	−	1.00773e8i	0.593238	−	1.02752i
$193$	−6.79598e7	+	1.17710e8i	−0.680458	+	1.17859i	0.294383	+	0.955687i	$0.404886\pi$
$193$	−6.79598e7	+	1.17710e8i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$194$	−1.37652e8	−	2.38420e8i	−1.35356	−	2.34443i
$195$	−5.69412e7			−0.549927
$196$	−1.73769e8	−	8.28058e7i	−1.64845	−	0.785533i
$197$	1.66347e8			1.55018			0.775091	−	0.631850i	$-0.217704\pi$
$197$	1.66347e8			1.55018			0.775091	+	0.631850i	$0.217704\pi$
$198$	−3.75472e7	−	6.50336e7i	−0.343755	−	0.595401i
$199$	3.19605e7	−	5.53573e7i	0.287494	−	0.497954i	−0.685717	−	0.727868i	$-0.740511\pi$
$199$	3.19605e7	−	5.53573e7i	0.287494	−	0.497954i	0.973211	+	0.229914i	$0.0738446\pi$
$200$	−4.46224e7	+	7.72882e7i	−0.394410	+	0.683138i
$201$	1.27434e7	+	2.20722e7i	0.110688	+	0.191716i
$202$	−1.03174e8			−0.880726
$203$	−2.72252e7	−	2.51575e7i	−0.228420	−	0.211072i
$204$	1.02775e8			0.847582
$205$	7.31888e6	+	1.26767e7i	0.0593343	+	0.102770i
$206$	−1.62462e8	+	2.81393e8i	−1.29484	+	2.24274i
$207$	1.09558e7	−	1.89759e7i	0.0858511	−	0.148699i
$208$	1.71706e7	+	2.97403e7i	0.132301	+	0.229152i
$209$	−1.05823e8			−0.801802
$210$	−5.25693e7	+	2.32520e8i	−0.391710	+	1.73258i
$211$	−6.44393e7			−0.472239			−0.236120	−	0.971724i	$-0.575876\pi$
$211$	−6.44393e7			−0.472239			−0.236120	+	0.971724i	$0.575876\pi$
$212$	1.82388e8	+	3.15906e8i	1.31468	+	2.27710i
$213$	−1.04866e7	+	1.81633e7i	−0.0743544	+	0.128786i
$214$	2.13885e8	−	3.70460e8i	1.49187	−	2.58400i
$215$	−5.79706e7	−	1.00408e8i	−0.397808	−	0.689023i
$216$	−2.23532e8			−1.50922
$217$	−3.80545e7	+	1.18239e7i	−0.252812	+	0.0785508i
$218$	2.10946e7			0.137903
$219$	−9.18952e7	−	1.59167e8i	−0.591205	−	1.02400i
$220$	2.56439e8	−	4.44166e8i	1.62370	−	2.81233i
$221$	2.29689e7	−	3.97832e7i	0.143142	−	0.247929i
$222$	−2.92694e7	−	5.06960e7i	−0.179547	−	0.310984i
$223$	9.27372e7			0.559998			0.279999	−	0.960000i	$-0.409666\pi$
$223$	9.27372e7			0.559998			0.279999	+	0.960000i	$0.409666\pi$
$224$	−8.57789e7	+	2.66522e7i	−0.509932	+	0.158440i
$225$	−2.79489e7			−0.163578
$226$	1.51256e8	+	2.61983e8i	0.871630	+	1.50971i
$227$	1.61267e7	−	2.79322e7i	0.0915070	−	0.158495i	−0.816638	−	0.577150i	$-0.804165\pi$
$227$	1.61267e7	−	2.79322e7i	0.0915070	−	0.158495i	0.908145	+	0.418655i	$0.137498\pi$
$228$	−7.78445e7	+	1.34831e8i	−0.434966	+	0.753384i
$229$	1.42975e8	+	2.47639e8i	0.786746	+	1.36268i	0.927951	+	0.372703i	$0.121569\pi$
$229$	1.42975e8	+	2.47639e8i	0.786746	+	1.36268i	−0.141205	+	0.989980i	$0.545098\pi$
$230$	2.31604e8			1.25516
$231$	4.95087e7	−	2.18983e8i	0.264265	−	1.16888i
$232$	8.21447e7			0.431889
$233$	−3.21833e7	−	5.57432e7i	−0.166681	−	0.288700i	0.770570	−	0.637355i	$-0.219972\pi$
$233$	−3.21833e7	−	5.57432e7i	−0.166681	−	0.288700i	−0.937251	+	0.348656i	$0.886638\pi$
$234$	−2.46910e7	+	4.27660e7i	−0.125974	+	0.218194i
$235$	−1.92652e8	+	3.33683e8i	−0.968359	+	1.67725i
$236$	3.20608e7	+	5.55309e7i	0.158775	+	0.275006i
$237$	9.27390e7			0.452526
$238$	−1.41250e8	−	1.30522e8i	−0.679156	−	0.627575i
$239$	−7.70718e7			−0.365177			−0.182588	−	0.983189i	$-0.558448\pi$
$239$	−7.70718e7			−0.365177			−0.182588	+	0.983189i	$0.558448\pi$
$240$	−5.75246e7	−	9.96354e7i	−0.268605	−	0.465237i
$241$	1.15866e8	−	2.00687e8i	0.533210	−	0.923546i	−0.466038	−	0.884765i	$-0.654319\pi$
$241$	1.15866e8	−	2.00687e8i	0.533210	−	0.923546i	0.999248	−	0.0387817i	$-0.0123477\pi$
$242$	−1.88451e8	+	3.26406e8i	−0.854760	+	1.48049i
$243$	−6.21780e7	−	1.07696e8i	−0.277981	−	0.481477i
$244$	−7.13093e8			−3.14255
$245$	2.37490e8	−	1.63350e8i	1.03172	−	0.709639i
$246$	−3.13884e7			−0.134430
$247$	3.47944e7	+	6.02657e7i	0.146916	+	0.254467i
$248$	4.41527e7	−	7.64747e7i	0.183813	−	0.318374i
$249$	2.12945e6	−	3.68832e6i	0.00874118	−	0.0151402i
$250$	1.12323e8	+	1.94550e8i	0.454653	+	0.787482i
$251$	4.88898e8			1.95146			0.975731	−	0.218975i	$-0.0702712\pi$
$251$	4.88898e8			1.95146			0.975731	+	0.218975i	$0.0702712\pi$
$252$	9.81116e7	+	9.06602e7i	0.386206	+	0.356874i
$253$	−2.18120e8			−0.846787
$254$	−2.13931e8	−	3.70540e8i	−0.819136	−	1.41879i
$255$	−7.69500e7	+	1.33281e8i	−0.290615	+	0.503360i
$256$	2.24131e8	−	3.88206e8i	0.834952	−	1.44618i
$257$	−1.92334e7	−	3.33133e7i	−0.0706791	−	0.122420i	0.828520	−	0.559959i	$-0.189183\pi$
$257$	−1.92334e7	−	3.33133e7i	−0.0706791	−	0.122420i	−0.899199	+	0.437540i	$0.855850\pi$
$258$	2.48618e8			0.901288
$259$	−1.56086e7	+	6.90387e7i	−0.0558232	+	0.246913i
$260$	−3.37268e8			−1.19006
$261$	1.28627e7	+	2.22789e7i	0.0447807	+	0.0775624i
$262$	−1.78608e8	+	3.09359e8i	−0.613546	+	1.06269i
$263$	−1.23784e8	+	2.14401e8i	−0.419585	+	0.726743i	−0.995898	−	0.0904864i	$-0.971158\pi$
$263$	−1.23784e8	+	2.14401e8i	−0.419585	+	0.726743i	0.576312	+	0.817229i	$0.304491\pi$
$264$	2.48756e8	+	4.30858e8i	0.832070	+	1.44119i
$265$	−5.46233e8			−1.80309
$266$	2.78219e8	−	8.64450e7i	0.906361	−	0.281614i
$267$	3.14340e8			1.01067
$268$	7.54803e7	+	1.30736e8i	0.239531	+	0.414880i
$269$	1.24138e7	−	2.15014e7i	0.0388841	−	0.0673493i	−0.845928	−	0.533296i	$-0.820953\pi$
$269$	1.24138e7	−	2.15014e7i	0.0388841	−	0.0673493i	0.884813	+	0.465947i	$0.154286\pi$
$270$	3.69970e8	−	6.40807e8i	1.14391	−	1.98132i
$271$	−9.17581e7	−	1.58930e8i	−0.280061	−	0.485079i	0.691339	−	0.722531i	$-0.257021\pi$
$271$	−9.17581e7	−	1.58930e8i	−0.280061	−	0.485079i	−0.971399	+	0.237452i	$0.923688\pi$
$272$	9.28167e7			0.279663
$273$	−1.40988e8	+	4.38063e7i	−0.419386	+	0.130307i
$274$	7.48602e8			2.19849
$275$	1.39110e8	+	2.40946e8i	0.403361	+	0.698642i
$276$	−1.60452e8	+	2.77911e8i	−0.459370	+	0.795653i
$277$	1.89077e8	−	3.27491e8i	0.534515	−	0.925807i	−0.464672	−	0.885483i	$-0.653828\pi$
$277$	1.89077e8	−	3.27491e8i	0.534515	−	0.925807i	0.999187	−	0.0403238i	$-0.0128390\pi$
$278$	−2.33158e8	−	4.03842e8i	−0.650869	−	1.12734i
$279$	2.76547e7			0.0762351
$280$	−1.40856e8	+	6.23023e8i	−0.383462	+	1.69610i
$281$	−6.03667e8			−1.62302			−0.811512	−	0.584335i	$-0.801355\pi$
$281$	−6.03667e8			−1.62302			−0.811512	+	0.584335i	$0.801355\pi$
$282$	−4.13113e8	−	7.15533e8i	−1.09698	−	1.90002i
$283$	7.79186e7	−	1.34959e8i	0.204356	−	0.353956i	−0.745571	−	0.666426i	$-0.767823\pi$
$283$	7.79186e7	−	1.34959e8i	0.204356	−	0.353956i	0.949928	+	0.312470i	$0.101157\pi$
$284$	−6.21133e7	+	1.07583e8i	−0.160905	+	0.278696i
$285$	−1.16568e8	−	2.01901e8i	−0.298278	−	0.516633i
$286$	4.91577e8			1.24254
$287$	2.78743e7	+	2.57573e7i	0.0696013	+	0.0643152i
$288$	6.23367e7			0.153769
$289$	1.43089e8	+	2.47838e8i	0.348710	+	0.603984i
$290$	−1.35959e8	+	2.35487e8i	−0.327351	+	0.566989i
$291$	−2.85602e8	+	4.94677e8i	−0.679415	+	1.17678i
$292$	−5.44304e8	−	9.42762e8i	−1.27939	−	2.21596i
$293$	4.10409e8			0.953191			0.476596	−	0.879123i	$-0.341871\pi$
$293$	4.10409e8			0.953191			0.476596	+	0.879123i	$0.341871\pi$
$294$	4.87203e7	+	6.16172e8i	0.111814	+	1.41412i
$295$	−9.60185e7			−0.217760
$296$	−7.84253e7	−	1.35837e8i	−0.175766	−	0.304436i
$297$	−3.48430e8	+	6.03499e8i	−0.771736	+	1.33669i
$298$	−4.12694e8	+	7.14806e8i	−0.903381	+	1.56470i
$299$	7.17177e7	+	1.24219e8i	0.155159	+	0.268744i
$300$	4.09324e8			0.875272
$301$	−2.20784e8	−	2.04016e8i	−0.466643	−	0.431202i
$302$	−6.39129e8			−1.33525
$303$	1.07033e8	+	1.85387e8i	0.221040	+	0.382852i
$304$	−7.03018e7	+	1.21766e8i	−0.143519	+	0.248582i
$305$	5.33909e8	−	9.24757e8i	1.07750	−	1.86629i
$306$	6.67344e7	+	1.15587e8i	0.133145	+	0.230614i
$307$	6.12316e8			1.20779			0.603895	−	0.797064i	$-0.293615\pi$
$307$	6.12316e8			1.20779			0.603895	+	0.797064i	$0.293615\pi$
$308$	2.93245e8	−	1.29706e9i	0.571878	−	2.52948i
$309$	6.74158e8			1.29989
$310$	1.46155e8	+	2.53148e8i	0.278643	+	0.482624i
$311$	−4.07432e7	+	7.05694e7i	−0.0768058	+	0.133032i	−0.901870	−	0.432007i	$-0.857805\pi$
$311$	−4.07432e7	+	7.05694e7i	−0.0768058	+	0.133032i	0.825064	+	0.565039i	$0.191139\pi$
$312$	1.63582e8	−	2.83332e8i	0.304925	−	0.528146i
$313$	2.33255e8	+	4.04010e8i	0.429958	+	0.744709i	0.996869	−	0.0790699i	$-0.0251950\pi$
$313$	2.33255e8	+	4.04010e8i	0.429958	+	0.744709i	−0.566911	+	0.823779i	$0.691862\pi$
$314$	−1.22075e9			−2.22522
$315$	−1.91029e8	+	5.93543e7i	−0.344360	+	0.106995i
$316$	5.49302e8			0.979279
$317$	−2.18932e8	−	3.79202e8i	−0.386014	−	0.668595i	0.605896	−	0.795544i	$-0.292815\pi$
$317$	−2.18932e8	−	3.79202e8i	−0.386014	−	0.668595i	−0.991909	+	0.126949i	$0.959482\pi$
$318$	5.85656e8	−	1.01439e9i	1.02129	−	1.76892i
$319$	1.28043e8	−	2.21777e8i	0.220845	−	0.382516i
$320$	5.16039e8	+	8.93807e8i	0.880355	+	1.52482i
$321$	−8.87543e8			−1.49769
$322$	5.73461e8	−	1.78179e8i	0.957212	−	0.297414i
$323$	1.88084e8			0.310558
$324$	3.51652e8	+	6.09080e8i	0.574389	+	0.994871i
$325$	9.14786e7	−	1.58446e8i	0.147818	−	0.256028i
$326$	−3.92139e8	+	6.79204e8i	−0.626871	+	1.08577i
$327$	−2.18837e7	−	3.79037e7i	−0.0346102	−	0.0599466i
$328$	−8.41032e7			−0.131599
$329$	−2.20303e8	+	9.74425e8i	−0.341063	+	1.50856i
$330$	−1.64688e9			−2.52268
$331$	−5.91794e8	−	1.02502e9i	−0.896960	−	1.55358i	−0.831360	−	0.555734i	$-0.812437\pi$
$331$	−5.91794e8	−	1.02502e9i	−0.896960	−	1.55358i	−0.0655992	−	0.997846i	$-0.520896\pi$
$332$	1.26129e7	−	2.18463e7i	0.0189162	−	0.0327638i
$333$	2.45606e7	−	4.25402e7i	0.0364488	−	0.0631313i
$334$	5.65368e8	+	9.79246e8i	0.830268	+	1.43807i
$335$	−2.26055e8			−0.328517
$336$	−2.19085e8	−	2.02446e8i	−0.315083	−	0.291153i
$337$	2.24486e8			0.319510			0.159755	−	0.987157i	$-0.448930\pi$
$337$	2.24486e8			0.319510			0.159755	+	0.987157i	$0.448930\pi$
$338$	4.35087e8	+	7.53593e8i	0.612869	+	1.06152i
$339$	3.13827e8	−	5.43565e8i	0.437514	−	0.757796i
$340$	−4.55782e8	+	7.89438e8i	−0.628900	+	1.08929i
$341$	−1.37646e8	−	2.38410e8i	−0.187985	−	0.325600i
$342$	−2.02186e8			−0.273312
$343$	4.62364e8	−	5.87167e8i	0.618663	−	0.785656i
$344$	6.66156e8			0.882310
$345$	−2.40268e8	−	4.16156e8i	−0.315013	−	0.545619i
$346$	4.22054e8	−	7.31019e8i	0.547774	−	0.948773i
$347$	−2.83498e8	+	4.91033e8i	−0.364248	+	0.630896i	−0.988655	−	0.150203i	$-0.952007\pi$
$347$	−2.83498e8	+	4.91033e8i	−0.364248	+	0.630896i	0.624407	+	0.781099i	$0.285341\pi$
$348$	−1.88380e8	−	3.26284e8i	−0.239611	−	0.415019i
$349$	−1.28642e9			−1.61992			−0.809958	−	0.586487i	$-0.800510\pi$
$349$	−1.28642e9			−1.61992			−0.809958	+	0.586487i	$0.800510\pi$
$350$	−5.62560e8	−	5.19835e8i	−0.701343	−	0.648078i
$351$	4.58255e8			0.565629
$352$	−3.10268e8	−	5.37400e8i	−0.379174	−	0.656748i
$353$	1.56009e8	−	2.70216e8i	0.188773	−	0.326964i	−0.756069	−	0.654492i	$-0.772882\pi$
$353$	1.56009e8	−	2.70216e8i	0.188773	−	0.326964i	0.944841	+	0.327528i	$0.106216\pi$
$354$	1.02948e8	−	1.78312e8i	0.123341	−	0.213633i
$355$	−9.30112e7	−	1.61100e8i	−0.110341	−	0.191116i
$356$	1.86187e9			2.18713
$357$	−8.79942e7	+	3.89209e8i	−0.102357	+	0.452735i
$358$	−1.20983e9			−1.39358
$359$	7.22284e8	+	1.25103e9i	0.823906	+	1.42705i	0.902753	+	0.430160i	$0.141543\pi$
$359$	7.22284e8	+	1.25103e9i	0.823906	+	1.42705i	−0.0788465	+	0.996887i	$0.525124\pi$
$360$	2.21641e8	−	3.83893e8i	0.250375	−	0.433663i
$361$	3.04476e8	−	5.27368e8i	0.340626	−	0.589982i
$362$	1.45416e7	+	2.51868e7i	0.0161113	+	0.0279057i
$363$	7.82000e8			0.858091
$364$	−8.35089e8	+	2.59469e8i	−0.907565	+	0.281988i
$365$	1.63013e9			1.75468
$366$	1.14489e9	+	1.98300e9i	1.22061	+	2.11417i
$367$	−6.44286e8	+	1.11594e9i	−0.680373	+	1.17844i	0.294494	+	0.955653i	$0.404849\pi$
$367$	−6.44286e8	+	1.11594e9i	−0.680373	+	1.17844i	−0.974867	+	0.222788i	$0.928484\pi$
$368$	−1.44905e8	+	2.50983e8i	−0.151571	+	0.262529i
$369$	−1.31694e7	−	2.28100e7i	−0.0136450	−	0.0236338i
$370$	5.19210e8			0.532890
$371$	−1.35249e9	+	4.20231e8i	−1.37507	+	0.427247i
$372$	−4.05016e8			−0.407917
$373$	4.47861e8	+	7.75718e8i	0.446850	+	0.773968i	0.998179	−	0.0603206i	$-0.0192123\pi$
$373$	4.47861e8	+	7.75718e8i	0.446850	+	0.773968i	−0.551329	+	0.834288i	$0.685879\pi$
$374$	6.64315e8	−	1.15063e9i	0.656634	−	1.13732i
$375$	2.33050e8	−	4.03655e8i	0.228213	−	0.395276i
$376$	−1.10691e9	−	1.91722e9i	−1.07388	−	1.86001i
$377$	−1.68402e8			−0.161865
$378$	4.23070e8	−	1.87129e9i	0.402895	−	1.78205i
$379$	−1.52727e9			−1.44105			−0.720527	−	0.693427i	$-0.756100\pi$
$379$	−1.52727e9			−1.44105			−0.720527	+	0.693427i	$0.756100\pi$
$380$	−6.90443e8	−	1.19588e9i	−0.645483	−	1.11801i
$381$	−4.43867e8	+	7.68801e8i	−0.411165	+	0.712158i
$382$	5.23307e8	−	9.06395e8i	0.480325	−	0.831947i
$383$	−8.75621e8	−	1.51662e9i	−0.796380	−	1.37937i	−0.921959	−	0.387287i	$-0.873412\pi$
$383$	−8.75621e8	−	1.51662e9i	−0.796380	−	1.37937i	0.125579	−	0.992084i	$-0.459921\pi$
$384$	−1.71318e9			−1.54398
$385$	1.46250e9	+	1.35142e9i	1.30612	+	1.20692i
$386$	2.58510e9			2.28782
$387$	1.04311e8	+	1.80671e8i	0.0914829	+	0.158453i
$388$	−1.69165e9	+	2.93002e9i	−1.47028	+	2.54659i
$389$	3.10366e8	−	5.37570e8i	0.267332	−	0.463033i	−0.700840	−	0.713319i	$-0.747191\pi$
$389$	3.10366e8	−	5.37570e8i	0.267332	−	0.463033i	0.968172	+	0.250286i	$0.0805246\pi$
$390$	5.41491e8	+	9.37890e8i	0.462238	+	0.800619i
$391$	3.87676e8			0.327982
$392$	1.30543e8	+	1.65099e9i	0.109459	+	1.38434i
$393$	7.41157e8			0.615937
$394$	−1.58190e9	−	2.73993e9i	−1.30299	−	2.25685i
$395$	−4.11275e8	+	7.12349e8i	−0.335771	+	0.581572i
$396$	−4.61429e8	+	7.99219e8i	−0.373398	+	0.646744i
$397$	7.95344e8	+	1.37758e9i	0.637952	+	1.10497i	0.985881	+	0.167445i	$0.0535517\pi$
$397$	7.95344e8	+	1.37758e9i	0.637952	+	1.10497i	−0.347929	+	0.937521i	$0.613115\pi$
$398$	−1.21574e9			−0.966604
$399$	−4.43954e8	−	4.10237e8i	−0.349891	−	0.323318i
$400$	3.69663e8			0.288799
$401$	−2.49459e8	−	4.32075e8i	−0.193194	−	0.334621i	0.753113	−	0.657891i	$-0.228551\pi$
$401$	−2.49459e8	−	4.32075e8i	−0.193194	−	0.334621i	−0.946307	+	0.323270i	$0.895218\pi$
$402$	2.42371e8	−	4.19798e8i	0.186075	−	0.322292i
$403$	−9.05157e7	+	1.56778e8i	−0.0688900	+	0.119321i
$404$	6.33970e8	+	1.09807e9i	0.478337	+	0.828503i
$405$	−1.05316e9			−0.787775
$406$	−1.55472e8	+	6.87672e8i	−0.115295	+	0.509964i
$407$	−4.88981e8			−0.359511
$408$	−4.42126e8	−	7.65786e8i	−0.322282	−	0.558209i
$409$	1.18578e9	−	2.05383e9i	0.856984	−	1.48434i	−0.0178086	−	0.999841i	$-0.505669\pi$
$409$	1.18578e9	−	2.05383e9i	0.856984	−	1.48434i	0.874792	−	0.484498i	$-0.160998\pi$
$410$	1.39200e8	−	2.41102e8i	0.0997461	−	0.172765i
$411$	−7.76605e8	−	1.34512e9i	−0.551764	−	0.955684i
$412$	3.99311e9			2.81301
$413$	−2.37745e8	+	7.38695e7i	−0.166068	+	0.0515988i
$414$	−4.16742e8			−0.288646
$415$	1.88872e7	+	3.27136e7i	0.0129718	+	0.0224678i
$416$	−2.04032e8	+	3.53394e8i	−0.138954	+	0.240676i
$417$	−4.83759e8	+	8.37896e8i	−0.326703	+	0.565866i
$418$	1.00634e9	+	1.74303e9i	0.673949	+	1.16731i
$419$	8.82367e8			0.586003			0.293002	−	0.956112i	$-0.405346\pi$
$419$	8.82367e8			0.586003			0.293002	+	0.956112i	$0.405346\pi$
$420$	2.79770e9	−	8.69270e8i	1.84259	−	0.572509i
$421$	−1.22486e9			−0.800019			−0.400010	−	0.916511i	$-0.630993\pi$
$421$	−1.22486e9			−0.800019			−0.400010	+	0.916511i	$0.630993\pi$
$422$	6.12796e8	+	1.06139e9i	0.396938	+	0.687516i
$423$	3.46653e8	−	6.00420e8i	0.222691	−	0.385713i
$424$	1.56923e9	−	2.71798e9i	0.999782	−	1.73167i
$425$	−2.47247e8	−	4.28245e8i	−0.156232	−	0.270602i
$426$	3.98897e8			0.249992
$427$	6.10538e8	−	2.70048e9i	0.379503	−	1.67859i
$428$	−5.25700e9			−3.24105
$429$	−5.09965e8	−	8.83286e8i	−0.311846	−	0.540133i
$430$	−1.10256e9	+	1.90969e9i	−0.668749	+	1.15831i
$431$	−3.21370e8	+	5.56629e8i	−0.193346	+	0.334885i	−0.946357	−	0.323123i	$-0.895267\pi$
$431$	−3.21370e8	+	5.56629e8i	−0.193346	+	0.334885i	0.753011	+	0.658008i	$0.228601\pi$
$432$	4.62949e8	+	8.01852e8i	0.276274	+	0.478521i
$433$	2.02652e9			1.19962			0.599811	−	0.800142i	$-0.295243\pi$
$433$	2.02652e9			1.19962			0.599811	+	0.800142i	$0.295243\pi$
$434$	5.56639e8	+	5.14363e8i	0.326858	+	0.302034i
$435$	5.64177e8			0.328627
$436$	−1.29619e8	−	2.24507e8i	−0.0748975	−	0.129726i
$437$	−2.93636e8	+	5.08592e8i	−0.168315	+	0.291531i
$438$	−1.74778e9	+	3.02725e9i	−0.993867	+	1.72143i
$439$	6.43251e7	+	1.11414e8i	0.0362873	+	0.0628515i	0.883599	−	0.468245i	$-0.155114\pi$
$439$	6.43251e7	+	1.11414e8i	0.0362873	+	0.0628515i	−0.847311	+	0.531096i	$0.821780\pi$
$440$	−4.41269e9			−2.46956
$441$	−4.27332e8	+	2.93927e8i	−0.237263	+	0.163194i
$442$	−8.73704e8			−0.481267
$443$	−4.27978e7	−	7.41280e7i	−0.0233889	−	0.0405107i	0.854094	−	0.520119i	$-0.174112\pi$
$443$	−4.27978e7	−	7.41280e7i	−0.0233889	−	0.0405107i	−0.877483	+	0.479608i	$0.840779\pi$
$444$	−3.59701e8	+	6.23020e8i	−0.195030	+	0.337801i
$445$	−1.39402e9	+	2.41452e9i	−0.749911	+	1.29888i
$446$	−8.81899e8	−	1.52749e9i	−0.470703	−	0.815281i
$447$	1.71252e9			0.906902
$448$	1.96536e9	+	1.81610e9i	1.03269	+	0.954258i
$449$	4.64175e8			0.242002			0.121001	−	0.992652i	$-0.461390\pi$
$449$	4.64175e8			0.242002			0.121001	+	0.992652i	$0.461390\pi$
$450$	2.65785e8	+	4.60352e8i	0.137495	+	0.238148i
$451$	−1.31096e8	+	2.27064e8i	−0.0672931	+	0.116555i
$452$	1.85883e9	−	3.21959e9i	0.946794	−	1.63989i
$453$	6.63036e8	+	1.14841e9i	0.335115	+	0.580436i
$454$	−6.13437e8			−0.307662
$455$	2.88763e8	−	1.27723e9i	0.143715	−	0.635669i
$456$	1.33951e9			0.661561
$457$	2.72986e8	+	4.72826e8i	0.133793	+	0.231736i	0.925136	−	0.379636i	$-0.123951\pi$
$457$	2.72986e8	+	4.72826e8i	0.133793	+	0.231736i	−0.791343	+	0.611373i	$0.790618\pi$
$458$	2.71928e9	−	4.70993e9i	1.32259	−	2.29079i
$459$	6.19282e8	−	1.07263e9i	0.298913	−	0.517732i
$460$	−1.42313e9	−	2.46493e9i	−0.681698	−	1.18074i
$461$	−1.36175e9			−0.647355			−0.323678	−	0.946167i	$-0.604919\pi$
$461$	−1.36175e9			−0.647355			−0.323678	+	0.946167i	$0.604919\pi$
$462$	−4.07772e9	+	1.26698e9i	−1.92385	+	0.597756i
$463$	−1.76640e9			−0.827097			−0.413549	−	0.910482i	$-0.635711\pi$
$463$	−1.76640e9			−0.827097			−0.413549	+	0.910482i	$0.635711\pi$
$464$	−1.70127e8	−	2.94669e8i	−0.0790607	−	0.136937i
$465$	3.03245e8	−	5.25235e8i	0.139865	−	0.242253i
$466$	−6.12105e8	+	1.06020e9i	−0.280205	+	0.485329i
$467$	8.57060e8	+	1.48447e9i	0.389405	+	0.674470i	0.992370	−	0.123298i	$-0.0393472\pi$
$467$	8.57060e8	+	1.48447e9i	0.389405	+	0.674470i	−0.602964	+	0.797768i	$0.706014\pi$
$468$	6.06870e8			0.273675
$469$	−5.59721e8	+	1.73910e8i	−0.250534	+	0.0778431i
$470$	7.32823e9			3.25579
$471$	1.26642e9	+	2.19350e9i	0.558474	+	0.967305i
$472$	2.75843e8	−	4.77775e8i	0.120744	−	0.209135i
$473$	1.03837e9	−	1.79851e9i	0.451168	−	0.781445i
$474$	−8.81916e8	−	1.52752e9i	−0.380367	−	0.658816i
$475$	7.49086e8			0.320704
$476$	−5.21199e8	+	2.30532e9i	−0.221503	+	0.979732i
$477$	9.82875e8			0.414652
$478$	7.32927e8	+	1.26947e9i	0.306947	+	0.531647i
$479$	−1.79752e9	+	3.11340e9i	−0.747308	+	1.29438i	0.201800	+	0.979427i	$0.435321\pi$
$479$	−1.79752e9	+	3.11340e9i	−0.747308	+	1.29438i	−0.949108	+	0.314949i	$0.898012\pi$
$480$	6.83545e8	−	1.18393e9i	0.282113	−	0.488634i
$481$	1.60777e8	+	2.78473e8i	0.0658742	+	0.114097i
$482$	−4.40740e9			−1.79274
$483$	−9.15072e8	−	8.45574e8i	−0.369522	−	0.341457i
$484$	4.63186e9			1.85694
$485$	−2.53315e9	−	4.38754e9i	−1.00824	−	1.74633i
$486$	−1.18258e9	+	2.04830e9i	−0.467310	+	0.809405i
$487$	−1.05474e9	+	1.82686e9i	−0.413802	+	0.716725i	−0.995302	−	0.0968209i	$-0.969133\pi$
$487$	−1.05474e9	+	1.82686e9i	−0.413802	+	0.716725i	0.581500	+	0.813546i	$0.302466\pi$
$488$	3.06765e9	+	5.31332e9i	1.19491	+	2.06965i
$489$	1.62723e9			0.629315
$490$	−4.94902e9	−	2.35834e9i	−1.90035	−	0.905567i
$491$	−1.92961e9			−0.735671			−0.367835	−	0.929891i	$-0.619901\pi$
$491$	−1.92961e9			−0.735671			−0.367835	+	0.929891i	$0.619901\pi$
$492$	1.92871e8	+	3.34063e8i	0.0730112	+	0.126459i
$493$	−2.27577e8	+	3.94175e8i	−0.0855390	+	0.148158i
$494$	6.61766e8	−	1.14621e9i	0.246979	−	0.427780i
$495$	−6.90965e8	−	1.19679e9i	−0.256058	−	0.443505i
$496$	−3.65772e8			−0.134594
$497$	−3.54238e8	−	3.27334e8i	−0.129434	−	0.119603i
$498$	−8.10014e7			−0.0293893
$499$	1.91072e9	+	3.30946e9i	0.688407	+	1.19236i	0.972353	+	0.233515i	$0.0750229\pi$
$499$	1.91072e9	+	3.30946e9i	0.688407	+	1.19236i	−0.283946	+	0.958840i	$0.591644\pi$
$500$	1.38038e9	−	2.39089e9i	0.493859	−	0.855389i
$501$	1.17303e9	−	2.03175e9i	0.416752	−	0.721836i
$502$	−4.64925e9	−	8.05274e9i	−1.64029	−	2.84106i
$503$	1.26027e8			0.0441547			0.0220773	−	0.999756i	$-0.492972\pi$
$503$	1.26027e8			0.0441547			0.0220773	+	0.999756i	$0.492972\pi$
$504$	2.53452e8	−	1.12105e9i	0.0881838	−	0.390048i
$505$	−1.89867e9			−0.656039
$506$	2.07425e9	+	3.59271e9i	0.711761	+	1.23281i
$507$	9.02724e8	−	1.56356e9i	0.307629	−	0.532829i
$508$	−2.62907e9	+	4.55368e9i	−0.889773	+	1.54113i
$509$	−1.02983e8	−	1.78372e8i	−0.0346142	−	0.0599536i	0.848199	−	0.529677i	$-0.177687\pi$
$509$	−1.02983e8	−	1.78372e8i	−0.0346142	−	0.0599536i	−0.882814	+	0.469724i	$0.844354\pi$
$510$	2.92707e9			0.977097
$511$	4.03626e9	−	1.25410e9i	1.33816	−	0.415776i
$512$	−2.96865e9			−0.977494
$513$	9.38121e8	+	1.62487e9i	0.306795	+	0.531384i
$514$	−3.65807e8	+	6.33596e8i	−0.118818	+	0.205798i
$515$	−2.98973e9	+	5.17836e9i	−0.964510	+	1.67058i
$516$	−1.52767e9	−	2.64601e9i	−0.489505	−	0.847847i
$517$	−6.90157e9			−2.19650
$518$	1.28558e9	−	3.99442e8i	0.406393	−	0.126270i
$519$	−1.75137e9			−0.549909
$520$	1.45089e9	+	2.51302e9i	0.452504	+	0.783761i
$521$	1.26558e9	−	2.19206e9i	0.392066	−	0.679078i	−0.600656	−	0.799507i	$-0.705094\pi$
$521$	1.26558e9	−	2.19206e9i	0.392066	−	0.679078i	0.992722	+	0.120430i	$0.0384273\pi$
$522$	2.44640e8	−	4.23729e8i	0.0752801	−	0.130389i
$523$	1.42408e9	+	2.46658e9i	0.435289	+	0.753943i	0.997319	−	0.0731738i	$-0.0233128\pi$
$523$	1.42408e9	+	2.46658e9i	0.435289	+	0.753943i	−0.562030	+	0.827117i	$0.689979\pi$
$524$	4.38995e9			1.33291
$525$	−3.50456e8	+	1.55011e9i	−0.105700	+	0.467525i
$526$	4.70858e9			1.41072
$527$	2.44645e8	+	4.23737e8i	0.0728113	+	0.126113i
$528$	1.03038e9	−	1.78467e9i	0.304634	−	0.527642i
$529$	1.09718e9	−	1.90036e9i	0.322241	−	0.558138i
$530$	5.19449e9	+	8.99712e9i	1.51557	+	2.62505i
$531$	1.72773e8			0.0500777
$532$	−2.62958e9	−	2.42987e9i	−0.757175	−	0.699669i
$533$	1.72417e8			0.0493212
$534$	−2.98927e9	−	5.17756e9i	−0.849514	−	1.47140i
$535$	3.93604e9	−	6.81742e9i	1.11127	−	1.92478i
$536$	6.49416e8	−	1.12482e9i	0.182157	−	0.315505i
$537$	1.25508e9	+	2.17387e9i	0.349754	+	0.605792i
$538$	−4.72205e8			−0.130735
$539$	4.66088e9	+	2.22104e9i	1.28206	+	0.610935i
$540$	−9.09337e9			−2.48512
$541$	−2.98333e9	−	5.16729e9i	−0.810049	−	1.40305i	−0.912829	−	0.408343i	$-0.866107\pi$
$541$	−2.98333e9	−	5.16729e9i	−0.810049	−	1.40305i	0.102779	−	0.994704i	$-0.467226\pi$
$542$	−1.74518e9	+	3.02273e9i	−0.470806	+	0.815460i
$543$	3.01711e7	−	5.22578e7i	0.00808707	−	0.0140072i
$544$	5.51455e8	+	9.55148e8i	0.146864	+	0.254375i
$545$	3.88196e8			0.102722
$546$	2.06230e9	+	1.90567e9i	0.542221	+	0.501041i
$547$	4.54821e9			1.18819			0.594093	−	0.804396i	$-0.297511\pi$
$547$	4.54821e9			1.18819			0.594093	+	0.804396i	$0.297511\pi$
$548$	−4.59991e9	−	7.96727e9i	−1.19403	−	2.06813i
$549$	−9.60699e8	+	1.66398e9i	−0.247790	+	0.429185i
$550$	2.64578e9	−	4.58262e9i	0.678085	−	1.17448i
$551$	−3.44746e8	−	5.97117e8i	−0.0877947	−	0.152065i
$552$	2.76098e9			0.698678
$553$	−4.70303e8	+	2.08021e9i	−0.118261	+	0.523081i
$554$	−7.19224e9			−1.79713
$555$	−5.38632e8	−	9.32938e8i	−0.133742	−	0.231647i
$556$	−2.86535e9	+	4.96294e9i	−0.706995	+	1.22455i
$557$	2.09487e9	−	3.62843e9i	0.513647	−	0.889662i	−0.486228	−	0.873832i	$-0.661628\pi$
$557$	2.09487e9	−	3.62843e9i	0.513647	−	0.889662i	0.999875	−	0.0158302i	$-0.00503911\pi$
$558$	−2.62987e8	−	4.55507e8i	−0.0640789	−	0.110988i
$559$	−1.36566e9			−0.330675
$560$	2.52662e9	−	7.85043e8i	0.607970	−	0.188902i
$561$	−2.75666e9			−0.659193
$562$	5.74067e9	+	9.94313e9i	1.36422	+	2.36290i
$563$	−8.49590e8	+	1.47153e9i	−0.200646	+	0.347528i	−0.948737	−	0.316068i	$-0.897637\pi$
$563$	−8.49590e8	+	1.47153e9i	−0.200646	+	0.347528i	0.748091	+	0.663596i	$0.230971\pi$
$564$	−5.07688e9	+	8.79341e9i	−1.19157	+	2.06386i
$565$	2.78350e9	+	4.82116e9i	0.649264	+	1.12456i
$566$	−2.96392e9			−0.687082
$567$	−2.60766e9	+	8.10224e8i	−0.600774	+	0.186666i
$568$	1.06882e9			0.244728
$569$	2.24289e8	+	3.88481e8i	0.0510406	+	0.0884049i	0.890417	−	0.455146i	$-0.150413\pi$
$569$	2.24289e8	+	3.88481e8i	0.0510406	+	0.0884049i	−0.839376	+	0.543551i	$0.817080\pi$
$570$	−2.21704e9	+	3.84003e9i	−0.501432	+	0.868505i
$571$	1.54508e8	−	2.67615e8i	0.0347315	−	0.0601567i	−0.848137	−	0.529777i	$-0.822276\pi$
$571$	1.54508e8	−	2.67615e8i	0.0347315	−	0.0601567i	0.882869	+	0.469620i	$0.155609\pi$
$572$	−3.02058e9	−	5.23179e9i	−0.674844	−	1.16886i
$573$	−2.17153e9			−0.482197
$574$	1.59179e8	−	7.04067e8i	0.0351312	−	0.155390i
$575$	1.54400e9			0.338697
$576$	−9.28546e8	−	1.60829e9i	−0.202453	−	0.350659i
$577$	2.84850e9	−	4.93375e9i	0.617307	−	1.06921i	−0.372668	−	0.927965i	$-0.621557\pi$
$577$	2.84850e9	−	4.93375e9i	0.617307	−	1.06921i	0.989975	−	0.141242i	$-0.0451095\pi$
$578$	2.72146e9	−	4.71371e9i	0.586212	−	1.01535i
$579$	−2.68180e9	−	4.64501e9i	−0.574184	−	0.994515i
$580$	3.34168e9			0.711159
$581$	7.19328e7	+	6.64696e7i	0.0152164	+	0.0140607i
$582$	1.08639e10			2.28431
$583$	−4.89206e9	−	8.47330e9i	−1.02247	−	1.77098i
$584$	−4.68307e9	+	8.11131e9i	−0.972939	+	1.68518i
$585$	−4.54378e8	+	7.87005e8i	−0.0938364	+	0.162529i
$586$	−3.90285e9	−	6.75993e9i	−0.801198	−	1.38772i
$587$	−1.74145e8			−0.0355368			−0.0177684	−	0.999842i	$-0.505656\pi$
$587$	−1.74145e8			−0.0355368			−0.0177684	+	0.999842i	$0.505656\pi$
$588$	6.25846e9	−	4.30469e9i	1.26954	−	0.873215i
$589$	−7.41202e8			−0.149463
$590$	9.13103e8	+	1.58154e9i	0.183036	+	0.317028i
$591$	−3.28215e9	+	5.68485e9i	−0.654036	+	1.13282i
$592$	−3.24848e8	+	5.62653e8i	−0.0643508	+	0.111459i
$593$	−1.91825e8	−	3.32251e8i	−0.0377758	−	0.0654297i	0.846519	−	0.532358i	$-0.178694\pi$
$593$	−1.91825e8	−	3.32251e8i	−0.0377758	−	0.0654297i	−0.884295	+	0.466928i	$0.845361\pi$
$594$	1.32538e10			2.59471
$595$	−2.59937e9	−	2.40195e9i	−0.505893	−	0.467471i
$596$	1.01434e10			1.96256
$597$	1.26121e9	+	2.18448e9i	0.242593	+	0.420183i
$598$	1.36402e9	−	2.36256e9i	0.260836	−	0.451781i
$599$	6.34413e8	−	1.09883e9i	0.120609	−	0.208900i	−0.799399	−	0.600800i	$-0.794849\pi$
$599$	6.34413e8	−	1.09883e9i	0.120609	−	0.208900i	0.920008	+	0.391900i	$0.128182\pi$
$600$	−1.76087e9	−	3.04991e9i	−0.332810	−	0.576445i
$601$	2.12270e9			0.398867			0.199434	−	0.979911i	$-0.436090\pi$
$601$	2.12270e9			0.398867			0.199434	+	0.979911i	$0.436090\pi$
$602$	−1.26081e9	+	5.57670e9i	−0.235538	+	1.04181i
$603$	4.06757e8			0.0755483
$604$	3.92723e9	+	6.80216e9i	0.725199	+	1.25608i
$605$	−3.46798e9	+	6.00672e9i	−0.636697	+	1.10279i
$606$	2.03570e9	−	3.52594e9i	0.371587	−	0.643607i
$607$	1.73844e9	+	3.01106e9i	0.315499	+	0.546461i	0.979544	−	0.201232i	$-0.0644946\pi$
$607$	1.73844e9	+	3.01106e9i	0.315499	+	0.546461i	−0.664044	+	0.747693i	$0.731161\pi$
$608$	−1.67075e9			−0.301473
$609$	1.39692e9	−	4.34036e8i	0.250618	−	0.0778691i
$610$	−2.03092e10			−3.62274
$611$	2.26923e9	+	3.93042e9i	0.402471	+	0.697100i
$612$	8.20121e8	−	1.42049e9i	0.144627	−	0.250500i
$613$	−2.28719e9	+	3.96154e9i	−0.401043	+	0.694627i	−0.993852	−	0.110716i	$-0.964686\pi$
$613$	−2.28719e9	+	3.96154e9i	−0.401043	+	0.694627i	0.592809	+	0.805343i	$0.298019\pi$
$614$	−5.82292e9	−	1.00856e10i	−1.01520	−	1.75838i
$615$	−5.77628e8			−0.100135
$616$	−1.09260e10	+	3.39480e9i	−1.88334	+	0.585169i
$617$	4.07855e9			0.699049			0.349525	−	0.936927i	$-0.386343\pi$
$617$	4.07855e9			0.699049			0.349525	+	0.936927i	$0.386343\pi$
$618$	−6.41102e9	−	1.11042e10i	−1.09262	−	1.89246i
$619$	−2.42630e8	+	4.20248e8i	−0.0411176	+	0.0712177i	−0.885852	−	0.463968i	$-0.846425\pi$
$619$	−2.42630e8	+	4.20248e8i	−0.0411176	+	0.0712177i	0.844734	+	0.535186i	$0.179758\pi$
$620$	1.79615e9	−	3.11102e9i	0.302671	−	0.524242i
$621$	1.93364e9	+	3.34917e9i	0.324008	+	0.561198i
$622$	1.54982e9			0.258234
$623$	−1.59410e9	+	7.05089e9i	−0.264124	+	1.16825i
$624$	−1.35515e9			−0.223276
$625$	3.80057e9	+	6.58278e9i	0.622685	+	1.07852i
$626$	4.43635e9	−	7.68399e9i	0.722796	−	1.25192i
$627$	2.08796e9	−	3.61646e9i	0.338288	−	0.585932i
$628$	7.50110e9	+	1.29923e10i	1.20856	+	2.09328i
$629$	8.69091e8			0.139248
$630$	2.79426e9	+	2.58204e9i	0.445220	+	0.411406i
$631$	5.74787e9			0.910760			0.455380	−	0.890297i	$-0.349503\pi$
$631$	5.74787e9			0.910760			0.455380	+	0.890297i	$0.349503\pi$
$632$	−2.36304e9	−	4.09290e9i	−0.372358	−	0.644943i
$633$	1.27144e9	−	2.20219e9i	0.199242	−	0.345098i
$634$	−4.16395e9	+	7.21217e9i	−0.648922	+	1.12397i
$635$	−3.93689e9	−	6.81889e9i	−0.610162	−	1.05683i
$636$	−1.43946e10			−2.21871
$637$	−2.67621e8	−	3.38463e9i	−0.0410234	−	0.518828i
$638$	−4.87058e9			−0.742521
$639$	1.67362e8	+	2.89879e8i	0.0253748	+	0.0439504i
$640$	7.59753e9	−	1.31593e10i	1.14562	−	1.98428i
$641$	2.83872e9	−	4.91682e9i	0.425716	−	0.737362i	−0.570771	−	0.821109i	$-0.693356\pi$
$641$	2.83872e9	−	4.91682e9i	0.425716	−	0.737362i	0.996487	+	0.0837473i	$0.0266889\pi$
$642$	8.44023e9	+	1.46189e10i	1.25887	+	2.18043i
$643$	−9.43725e9			−1.39993			−0.699966	−	0.714176i	$-0.746802\pi$
$643$	−9.43725e9			−1.39993			−0.699966	+	0.714176i	$0.746802\pi$
$644$	−5.42006e9	−	5.00842e9i	−0.799657	−	0.738924i
$645$	4.57522e9			0.671356
$646$	−1.78861e9	−	3.09797e9i	−0.261037	−	0.452130i
$647$	3.30928e8	−	5.73185e8i	0.0480362	−	0.0832012i	−0.841008	−	0.541023i	$-0.818037\pi$
$647$	3.30928e8	−	5.73185e8i	0.0480362	−	0.0832012i	0.889044	+	0.457822i	$0.151370\pi$
$648$	3.02554e9	−	5.24039e9i	0.436808	−	0.756573i
$649$	−8.59941e8	−	1.48946e9i	−0.123484	−	0.213881i
$650$	−3.47972e9			−0.496990
$651$	3.46768e8	−	1.53380e9i	0.0492613	−	0.217888i
$652$	9.63824e9			1.36186
$653$	1.06718e9	+	1.84842e9i	0.149983	+	0.259779i	0.931221	−	0.364455i	$-0.118745\pi$
$653$	1.06718e9	+	1.84842e9i	0.149983	+	0.259779i	−0.781238	+	0.624234i	$0.785411\pi$
$654$	−4.16213e8	+	7.20902e8i	−0.0581827	+	0.100775i
$655$	−3.28685e9	+	5.69300e9i	−0.457021	+	0.791583i
$656$	1.74183e8	+	3.01694e8i	0.0240903	+	0.0417257i
$657$	−2.93321e9			−0.403519
$658$	1.81450e10	−	5.63779e9i	2.48294	−	0.771469i
$659$	−9.15512e9			−1.24613			−0.623067	−	0.782168i	$-0.714114\pi$
$659$	−9.15512e9			−1.24613			−0.623067	+	0.782168i	$0.714114\pi$
$660$	1.01195e10	+	1.75275e10i	1.37011	+	2.37310i
$661$	−1.40726e9	+	2.43745e9i	−0.189527	+	0.328270i	−0.945093	−	0.326803i	$-0.894029\pi$
$661$	−1.40726e9	+	2.43745e9i	−0.189527	+	0.328270i	0.755566	+	0.655073i	$0.227362\pi$
$662$	−1.12555e10	+	1.94951e10i	−1.50787	+	2.61170i
$663$	9.06386e8	+	1.56991e9i	0.120786	+	0.209207i
$664$	−2.17038e8			−0.0287705
$665$	5.11995e9	−	1.59081e9i	0.675134	−	0.209770i
$666$	−9.34251e8			−0.122547
$667$	−7.10585e8	−	1.23077e9i	−0.0927204	−	0.160596i
$668$	6.94799e9	−	1.20343e10i	0.901865	−	1.56208i
$669$	−1.82977e9	+	3.16926e9i	−0.236269	+	0.409229i
$670$	2.14971e9	+	3.72341e9i	0.276133	+	0.478276i
$671$	1.91268e10			2.44406
$672$	7.81651e8	−	3.45733e9i	0.0993620	−	0.439490i
$673$	−1.09650e10			−1.38661			−0.693307	−	0.720643i	$-0.743847\pi$
$673$	−1.09650e10			−1.38661			−0.693307	+	0.720643i	$0.743847\pi$
$674$	−2.13478e9	−	3.69755e9i	−0.268562	−	0.465162i
$675$	2.46643e9	−	4.27198e9i	0.308678	−	0.534646i
$676$	5.34692e9	−	9.26114e9i	0.665718	−	1.15306i
$677$	−5.18004e9	−	8.97209e9i	−0.641612	−	1.11130i	−0.985073	−	0.172138i	$-0.944933\pi$
$677$	−5.18004e9	−	8.97209e9i	−0.641612	−	1.11130i	0.343461	−	0.939167i	$-0.388401\pi$
$678$	−1.19376e10			−1.47100
$679$	−9.64762e9	−	8.91490e9i	−1.18270	−	1.09288i
$680$	7.84290e9			0.956523
$681$	6.36383e8	+	1.10225e9i	0.0772154	+	0.133741i
$682$	−2.61793e9	+	4.53439e9i	−0.316019	+	0.547361i
$683$	4.23940e9	−	7.34286e9i	0.509134	−	0.881846i	−0.490810	−	0.871267i	$-0.663299\pi$
$683$	4.23940e9	−	7.34286e9i	0.509134	−	0.881846i	0.999944	−	0.0105792i	$-0.00336752\pi$
$684$	1.24236e9	+	2.15183e9i	0.148440	+	0.257106i
$685$	1.37762e10			1.63762
$686$	−1.40683e10	−	2.03193e9i	−1.66382	−	0.240312i
$687$	−1.12840e10			−1.32774
$688$	−1.37965e9	−	2.38963e9i	−0.161514	−	0.279750i
$689$	−3.21701e9	+	5.57203e9i	−0.374701	+	0.649002i
$690$	−4.56973e9	+	7.91501e9i	−0.529564	+	0.917233i
$691$	4.97824e8	+	8.62257e8i	0.0573988	+	0.0994176i	0.893297	−	0.449467i	$-0.148386\pi$
$691$	4.97824e8	+	8.62257e8i	0.0573988	+	0.0994176i	−0.835898	+	0.548884i	$0.815053\pi$
$692$	−1.03735e10			−1.19002
$693$	−2.63157e9	−	2.43171e9i	−0.300365	−	0.277553i
$694$	1.07839e10			1.22466
$695$	−4.29071e9	−	7.43173e9i	−0.484822	−	0.839737i
$696$	−1.62078e9	+	2.80727e9i	−0.182218	+	0.315611i
$697$	2.33003e8	−	4.03573e8i	0.0260643	−	0.0451447i
$698$	1.22334e10	+	2.11888e10i	1.36161	+	2.35838i
$699$	2.54001e9			0.281297
$700$	−2.07579e9	+	9.18146e9i	−0.228739	+	1.01174i
$701$	1.18853e10			1.30316			0.651579	−	0.758581i	$-0.274107\pi$
$701$	1.18853e10			1.30316			0.651579	+	0.758581i	$0.274107\pi$
$702$	−4.35784e9	−	7.54801e9i	−0.475436	−	0.823479i
$703$	−6.58272e8	+	1.14016e9i	−0.0714598	+	0.123772i
$704$	−9.24330e9	+	1.60099e10i	−0.998442	+	1.72935i
$705$	−7.60235e9	−	1.31677e10i	−0.817120	−	1.41529i
$706$	−5.93439e9			−0.634687
$707$	−4.70118e9	+	1.46070e9i	−0.500309	+	0.155450i
$708$	−2.53033e9			−0.267955
$709$	6.91626e9	+	1.19793e10i	0.728802	+	1.26232i	0.957390	+	0.288799i	$0.0932558\pi$
$709$	6.91626e9	+	1.19793e10i	0.728802	+	1.26232i	−0.228588	+	0.973523i	$0.573411\pi$
$710$	−1.76901e9	+	3.06401e9i	−0.185492	+	0.321282i
$711$	7.40036e8	−	1.28178e9i	0.0772163	−	0.133743i
$712$	−8.00954e9	−	1.38729e10i	−0.831625	−	1.44042i
$713$	−1.52775e9			−0.157848
$714$	7.24754e9	−	2.25187e9i	0.745155	−	0.231526i
$715$	9.04629e9			0.925549
$716$	7.43398e9	+	1.28760e10i	0.756878	+	1.31095i
$717$	1.52069e9	−	2.63391e9i	0.154072	−	0.266860i
$718$	1.37374e10	−	2.37938e10i	1.38506	−	2.39899i
$719$	2.74302e9	+	4.75106e9i	0.275219	+	0.476693i	0.970190	−	0.242344i	$-0.0779163\pi$
$719$	2.74302e9	+	4.75106e9i	0.275219	+	0.476693i	−0.694971	+	0.719037i	$0.744583\pi$
$720$	−1.83613e9			−0.183333
$721$	−3.41883e9	+	1.51219e10i	−0.339707	+	1.50256i
$722$	−1.15819e10			−1.14524
$723$	4.57227e9	+	7.91940e9i	0.449933	+	0.779306i
$724$	1.78706e8	−	3.09528e8i	0.0175007	−	0.0303121i
$725$	−9.06376e8	+	1.56989e9i	−0.0883335	+	0.152998i
$726$	−7.43655e9	−	1.28805e10i	−0.721263	−	1.24926i
$727$	4.80453e9			0.463746			0.231873	−	0.972746i	$-0.425515\pi$
$727$	4.80453e9			0.463746			0.231873	+	0.972746i	$0.425515\pi$
$728$	5.52578e9	+	5.10611e9i	0.530804	+	0.490490i
$729$	1.14879e10			1.09824
$730$	−1.55020e10	−	2.68502e10i	−1.47488	−	2.55457i
$731$	−1.84554e9	+	3.19658e9i	−0.174749	+	0.302673i
$732$	1.40699e10	−	2.43697e10i	1.32587	−	2.29648i
$733$	−4.98193e9	−	8.62896e9i	−0.467233	−	0.809272i	0.532066	−	0.846703i	$-0.321416\pi$
$733$	−4.98193e9	−	8.62896e9i	−0.467233	−	0.809272i	−0.999299	+	0.0374310i	$0.988083\pi$
$734$	2.45078e10			2.28753
$735$	8.96580e8	+	1.13392e10i	0.0832882	+	1.05336i
$736$	−3.44372e9			−0.318387
$737$	−2.02455e9	−	3.50663e9i	−0.186291	−	0.322666i
$738$	−2.50472e8	+	4.33831e8i	−0.0229384	+	0.0397304i
$739$	−3.44707e9	+	5.97050e9i	−0.314192	+	0.544196i	−0.979265	−	0.202582i	$-0.935067\pi$
$739$	−3.44707e9	+	5.97050e9i	−0.314192	+	0.544196i	0.665074	+	0.746778i	$0.268400\pi$
$740$	−3.19037e9	−	5.52588e9i	−0.289421	−	0.501292i
$741$	−2.74608e9			−0.247942
$742$	1.97835e10	+	1.82809e10i	1.77782	+	1.64280i
$743$	7.75055e9			0.693221			0.346610	−	0.938009i	$-0.387333\pi$
$743$	7.75055e9			0.693221			0.346610	+	0.938009i	$0.387333\pi$
$744$	1.74233e9	+	3.01781e9i	0.155105	+	0.268650i
$745$	−7.59463e9	+	1.31543e10i	−0.672914	+	1.16552i
$746$	8.51801e9	−	1.47536e10i	0.751194	−	1.30111i
$747$	−3.39851e7	−	5.88639e7i	−0.00298309	−	0.00516686i
$748$	−1.63279e10			−1.42651
$749$	4.50096e9	−	1.99083e10i	0.391398	−	1.73120i
$750$	−8.86491e9			−0.767290
$751$	−4.29507e9	−	7.43927e9i	−0.370024	−	0.640900i	0.619545	−	0.784961i	$-0.287317\pi$
$751$	−4.29507e9	−	7.43927e9i	−0.370024	−	0.640900i	−0.989569	+	0.144061i	$0.953984\pi$
$752$	−4.58496e9	+	7.94138e9i	−0.393163	+	0.680979i
$753$	−9.64632e9	+	1.67079e10i	−0.823340	+	1.42607i
$754$	1.60144e9	+	2.77378e9i	0.136054	+	0.235653i
$755$	−1.17616e10			−0.994610
$756$	−2.25155e10	+	6.99576e9i	−1.89520	+	0.588856i
$757$	−3.04455e9			−0.255087			−0.127543	−	0.991833i	$-0.540709\pi$
$757$	−3.04455e9			−0.255087			−0.127543	+	0.991833i	$0.540709\pi$
$758$	1.45239e10	+	2.51561e10i	1.21127	+	2.09798i
$759$	4.30368e9	−	7.45419e9i	0.357268	−	0.618806i
$760$	−5.94041e9	+	1.02891e10i	−0.490873	+	0.850217i
$761$	1.44475e9	+	2.50238e9i	0.118835	+	0.205829i	0.919306	−	0.393542i	$-0.128751\pi$
$761$	1.44475e9	+	2.50238e9i	0.118835	+	0.205829i	−0.800471	+	0.599372i	$0.795417\pi$
$762$	1.68841e10			1.38241
$763$	9.61187e8	−	2.98649e8i	0.0783379	−	0.0243403i
$764$	−1.28622e10			−1.04349
$765$	1.22809e9	+	2.12711e9i	0.0991777	+	0.171781i
$766$	−1.66537e10	+	2.88451e10i	−1.33878	+	2.31884i
$767$	−5.65496e8	+	9.79468e8i	−0.0452528	+	0.0783802i
$768$	8.84454e9	+	1.53192e10i	0.704548	+	1.22031i
$769$	−3.71789e9			−0.294818			−0.147409	−	0.989076i	$-0.547093\pi$
$769$	−3.71789e9			−0.294818			−0.147409	+	0.989076i	$0.547093\pi$
$770$	8.35173e9	−	3.69407e10i	0.659263	−	2.91600i
$771$	1.51796e9			0.119281
$772$	−1.58845e10	−	2.75128e10i	−1.24255	−	2.15216i
$773$	2.28075e9	−	3.95037e9i	0.177602	−	0.307616i	−0.763456	−	0.645859i	$-0.776499\pi$
$773$	2.28075e9	−	3.95037e9i	0.177602	−	0.307616i	0.941059	+	0.338243i	$0.109833\pi$
$774$	1.98392e9	−	3.43624e9i	0.153791	−	0.266373i
$775$	9.74352e8	+	1.68763e9i	0.0751900	+	0.130233i
$776$	2.91091e10			2.23621
$777$	−2.05141e9	−	1.89560e9i	−0.156884	−	0.144969i
$778$	−1.18059e10			−0.898817
$779$	3.52965e8	+	6.11353e8i	0.0267516	+	0.0463352i
$780$	6.65456e9	−	1.15260e10i	0.502098	−	0.869659i
$781$	1.66602e9	−	2.88563e9i	0.125141	−	0.216751i
$782$	−3.68666e9	−	6.38549e9i	−0.275683	−	0.477497i
$783$	−4.54042e9			−0.338010
$784$	5.65205e9	−	3.88759e9i	0.418890	−	0.288121i
$785$	−2.24650e10			−1.65753
$786$	−7.04815e9	−	1.22078e10i	−0.517722	−	0.896721i
$787$	−3.25875e9	+	5.64432e9i	−0.238308	+	0.412762i	−0.960229	−	0.279214i	$-0.909926\pi$
$787$	−3.25875e9	+	5.64432e9i	−0.238308	+	0.412762i	0.721921	+	0.691976i	$0.243260\pi$
$788$	−1.94405e10	+	3.36719e10i	−1.41536	+	2.45147i
$789$	−4.88472e9	−	8.46058e9i	−0.354054	−	0.613240i
$790$	1.56443e10			1.12892
$791$	1.06011e10	+	9.79595e9i	0.761610	+	0.703767i
$792$	7.94007e9			0.567919
$793$	−6.28886e9	−	1.08926e10i	−0.447833	−	0.775669i
$794$	1.51269e10	−	2.62006e10i	1.07245	−	1.85754i
$795$	1.07776e10	−	1.86673e10i	0.760741	−	1.31764i
$796$	7.47028e9	+	1.29389e10i	0.524978	+	0.909289i
$797$	5.00841e9			0.350425			0.175213	−	0.984531i	$-0.443939\pi$
$797$	5.00841e9			0.350425			0.175213	+	0.984531i	$0.443939\pi$
$798$	−2.53524e9	+	1.12137e10i	−0.176608	+	0.781156i
$799$	1.22665e10			0.850760
$800$	2.19629e9	+	3.80409e9i	0.151661	+	0.262685i
$801$	2.50836e9	−	4.34461e9i	0.172455	−	0.298701i
$802$	−4.74453e9	+	8.21777e9i	−0.324775	+	0.562527i
$803$	1.45995e10	+	2.52870e10i	0.995021	+	1.72343i
$804$	−5.95714e9			−0.404242
$805$	1.05532e10	−	3.27896e9i	0.713013	−	0.221539i
$806$	3.44310e9			0.231620
$807$	4.89868e8	+	8.48476e8i	0.0328112	+	0.0568306i
$808$	5.45453e9	−	9.44753e9i	0.363762	−	0.630055i
$809$	−4.49065e8	+	7.77803e8i	−0.0298187	+	0.0516476i	−0.880550	−	0.473954i	$-0.842826\pi$
$809$	−4.49065e8	+	7.77803e8i	−0.0298187	+	0.0516476i	0.850731	+	0.525601i	$0.176160\pi$
$810$	1.00152e10	+	1.73468e10i	0.662159	+	1.14689i
$811$	−1.37233e10			−0.903413			−0.451707	−	0.892167i	$-0.649185\pi$
$811$	−1.37233e10			−0.903413			−0.451707	+	0.892167i	$0.649185\pi$
$812$	8.27412e9	−	2.57084e9i	0.542345	−	0.168511i
$813$	7.24183e9			0.472641
$814$	4.65005e9	+	8.05412e9i	0.302184	+	0.523399i
$815$	−7.21637e9	+	1.24991e10i	−0.466947	+	0.808775i
$816$	−1.83134e9	+	3.17198e9i	−0.117993	+	0.204369i
$817$	−2.79573e9	−	4.84234e9i	−0.179357	−	0.310655i
$818$	−4.51055e10			−2.88133
$819$	−5.19592e8	+	2.29822e9i	−0.0330498	+	0.146183i
$820$	−3.42135e9			−0.216695
$821$	−7.28722e9	−	1.26218e10i	−0.459580	−	0.796015i	0.539359	−	0.842076i	$-0.318667\pi$
$821$	−7.28722e9	−	1.26218e10i	−0.459580	−	0.796015i	−0.998939	+	0.0460606i	$0.985333\pi$
$822$	−1.47705e10	+	2.55832e10i	−0.927563	+	1.60659i
$823$	1.27966e10	−	2.21644e10i	0.800196	−	1.38598i	−0.119290	−	0.992859i	$-0.538062\pi$
$823$	1.27966e10	−	2.21644e10i	0.800196	−	1.38598i	0.919487	−	0.393121i	$-0.128605\pi$
$824$	−1.71779e10	−	2.97530e10i	−1.06961	−	1.85262i
$825$	−1.09790e10			−0.680728
$826$	3.47760e9	+	3.21348e9i	0.214708	+	0.198402i
$827$	5.33790e9			0.328172			0.164086	−	0.986446i	$-0.447533\pi$
$827$	5.33790e9			0.328172			0.164086	+	0.986446i	$0.447533\pi$
$828$	2.56074e9	+	4.43533e9i	0.156769	+	0.271531i
$829$	9.40458e9	−	1.62892e10i	0.573322	−	0.993022i	−0.422900	−	0.906176i	$-0.638988\pi$
$829$	9.40458e9	−	1.62892e10i	0.573322	−	0.993022i	0.996222	−	0.0868459i	$-0.0276788\pi$
$830$	3.59222e8	−	6.22190e8i	0.0218067	−	0.0377703i
$831$	7.46127e9	+	1.29233e10i	0.451034	+	0.781214i
$832$	1.21568e10			0.731789
$833$	−8.28402e9	−	3.94756e9i	−0.496573	−	0.236631i
$834$	1.84015e10			1.09843
$835$	1.04042e10	+	1.80207e10i	0.618454	+	1.07119i
$836$	1.23672e10	−	2.14206e10i	0.732065	−	1.26797i
$837$	−2.44047e9	+	4.22702e9i	−0.143858	+	0.249170i
$838$	−8.39101e9	−	1.45337e10i	−0.492561	−	0.853141i
$839$	−1.81462e10			−1.06077			−0.530383	−	0.847758i	$-0.677952\pi$
$839$	−1.81462e10			−1.06077			−0.530383	+	0.847758i	$0.677952\pi$
$840$	−1.85124e10	−	1.71064e10i	−1.07767	−	0.995822i
$841$	−1.55813e10			−0.903273
$842$	1.16480e10	+	2.01750e10i	0.672451	+	1.16472i
$843$	1.19108e10	−	2.06301e10i	0.684770	−	1.18606i
$844$	7.53084e9	−	1.30438e10i	0.431167	−	0.746802i
$845$	8.00672e9	+	1.38681e10i	0.456516	+	0.790710i
$846$	−1.31862e10			−0.748726
$847$	−3.96572e9	+	1.75409e10i	−0.224249	+	0.991880i
$848$	−1.29999e10			−0.732072
$849$	3.07479e9	+	5.32568e9i	0.172440	+	0.298675i
$850$	−4.70247e9	+	8.14492e9i	−0.262639	+	0.454905i
$851$	−1.35682e9	+	2.35008e9i	−0.0754690	+	0.130716i
$852$	−2.45108e9	−	4.24540e9i	−0.135775	−	0.235169i
$853$	2.76121e10			1.52327			0.761637	−	0.648004i	$-0.224396\pi$
$853$	2.76121e10			1.52327			0.761637	+	0.648004i	$0.224396\pi$
$854$	−5.02862e10	+	1.56244e10i	−2.76278	+	0.858420i
$855$	−3.72074e9			−0.203586
$856$	2.26150e10	+	3.91704e10i	1.23236	+	2.13452i
$857$	1.04002e9	−	1.80136e9i	0.0564427	−	0.0977617i	−0.836423	−	0.548084i	$-0.815357\pi$
$857$	1.04002e9	−	1.80136e9i	0.0564427	−	0.0977617i	0.892866	+	0.450322i	$0.148691\pi$
$858$	−9.69919e9	+	1.67995e10i	−0.524240	+	0.908010i
$859$	−6.02401e9	−	1.04339e10i	−0.324272	−	0.561656i	0.657092	−	0.753810i	$-0.271786\pi$
$859$	−6.02401e9	−	1.04339e10i	−0.324272	−	0.561656i	−0.981365	+	0.192154i	$0.938453\pi$
$860$	2.70995e10			1.45283
$861$	−1.43023e9	+	4.44384e8i	−0.0763650	+	0.0237273i
$862$	1.22245e10			0.650062
$863$	−1.22979e10	−	2.13006e10i	−0.651319	−	1.12812i	−0.982803	−	0.184656i	$-0.940883\pi$
$863$	−1.22979e10	−	2.13006e10i	−0.651319	−	1.12812i	0.331485	−	0.943461i	$-0.392450\pi$
$864$	−5.50107e9	+	9.52814e9i	−0.290168	+	0.502585i
$865$	7.76688e9	−	1.34526e10i	0.408028	−	0.706726i
$866$	−1.92716e10	−	3.33793e10i	−1.00833	−	1.74648i
$867$	−1.12931e10			−0.588497
$868$	2.05394e9	−	9.08482e9i	0.106603	−	0.471517i
$869$	−1.47335e10			−0.761618
$870$	−5.36513e9	−	9.29269e9i	−0.276225	−	0.478436i
$871$	−1.33134e9	+	2.30595e9i	−0.0682694	+	0.118246i
$872$	−1.11522e9	+	1.93161e9i	−0.0569575	+	0.0986533i
$873$	4.55807e9	+	7.89481e9i	0.231863	+	0.401598i
$874$	1.11695e10			0.565905
$875$	7.87243e9	+	7.27453e9i	0.397265	+	0.367094i
$876$	4.29581e10			2.15914
$877$	6.77289e9	+	1.17310e10i	0.339059	+	0.587268i	0.984256	−	0.176749i	$-0.0565580\pi$
$877$	6.77289e9	+	1.17310e10i	0.339059	+	0.587268i	−0.645197	+	0.764016i	$0.723225\pi$
$878$	1.22342e9	−	2.11903e9i	0.0610021	−	0.105659i
$879$	−8.09768e9	+	1.40256e10i	−0.402161	+	0.696562i
$880$	9.13897e9	+	1.58292e10i	0.452072	+	0.783012i
$881$	2.21441e10			1.09105			0.545523	−	0.838096i	$-0.316331\pi$
$881$	2.21441e10			1.09105			0.545523	+	0.838096i	$0.316331\pi$
$882$	8.90511e9	+	4.24353e9i	0.437018	+	0.208251i
$883$	2.02852e10			0.991556			0.495778	−	0.868449i	$-0.334883\pi$
$883$	2.02852e10			0.991556			0.495778	+	0.868449i	$0.334883\pi$
$884$	5.36862e9	+	9.29872e9i	0.261384	+	0.452731i
$885$	1.89452e9	−	3.28140e9i	0.0918750	−	0.159132i
$886$	−8.13986e8	+	1.40987e9i	−0.0393187	+	0.0681019i
$887$	−1.58624e10	−	2.74746e10i	−0.763198	−	1.32190i	−0.941194	−	0.337867i	$-0.890295\pi$
$887$	−1.58624e10	−	2.74746e10i	−0.763198	−	1.32190i	0.177996	−	0.984031i	$-0.443039\pi$
$888$	6.18957e9			0.296630
$889$	−1.49938e10	−	1.38551e10i	−0.715742	−	0.661382i
$890$	5.30267e10			2.52133
$891$	−9.43211e9	−	1.63369e10i	−0.446721	−	0.773744i
$892$	−1.08379e10	+	1.87719e10i	−0.511293	+	0.885585i
$893$	−9.29097e9	+	1.60924e10i	−0.436597	+	0.756208i
$894$	−1.62855e10	−	2.82073e10i	−0.762290	−	1.32033i
$895$	−2.22640e10			−1.03806
$896$	8.68797e9	−	3.84279e10i	0.403497	−	1.78471i
$897$	−5.66018e9			−0.261853
$898$	−4.41415e9	−	7.64552e9i	−0.203413	−	0.352322i
$899$	8.96837e8	−	1.55337e9i	0.0411675	−	0.0713042i
$900$	3.26631e9	−	5.65742e9i	0.149351	−	0.258684i
$901$	8.69490e9	+	1.50600e10i	0.396030	+	0.685944i
$902$	4.98670e9			0.226251
$903$	1.13284e10	−	3.51983e9i	0.511990	−	0.159080i
$904$	−3.19859e10			−1.44002
$905$	2.67603e8	+	4.63502e8i	0.0120011	+	0.0207865i
$906$	1.26105e10	−	2.18420e10i	0.563357	−	0.975762i
$907$	−1.32831e8	+	2.30070e8i	−0.00591117	+	0.0102384i	−0.868966	−	0.494872i	$-0.835215\pi$
$907$	−1.32831e8	+	2.30070e8i	−0.00591117	+	0.0102384i	0.863055	+	0.505110i	$0.168548\pi$
$908$	3.76936e9	+	6.52872e9i	0.167096	+	0.289420i
$909$	3.41641e9			0.150868
$910$	−2.37837e10	+	7.38978e9i	−1.04625	+	0.325077i
$911$	−3.13936e10			−1.37571			−0.687854	−	0.725849i	$-0.741447\pi$
$911$	−3.13936e10			−1.37571			−0.687854	+	0.725849i	$0.741447\pi$
$912$	−2.77422e9	−	4.80508e9i	−0.121104	−	0.209758i
$913$	−3.38308e8	+	5.85966e8i	−0.0147117	+	0.0254815i
$914$	5.19201e9	−	8.99282e9i	0.224918	−	0.389569i
$915$	2.10689e10	+	3.64923e10i	0.909216	+	1.57481i
$916$	−6.68362e10			−2.87328
$917$	−3.75860e9	+	1.66247e10i	−0.160966	+	0.711971i
$918$	−2.35567e10			−1.00500
$919$	−1.67830e9	−	2.90690e9i	−0.0713288	−	0.123545i	0.828155	−	0.560499i	$-0.189391\pi$
$919$	−1.67830e9	−	2.90690e9i	−0.0713288	−	0.123545i	−0.899484	+	0.436954i	$0.856057\pi$
$920$	−1.22443e10	+	2.12077e10i	−0.518414	+	0.897919i
$921$	−1.20815e10	+	2.09257e10i	−0.509578	+	0.882616i
$922$	1.29497e10	+	2.24296e10i	0.544130	+	0.942461i
$923$	−2.19114e9			−0.0917200
$924$	3.85406e10	+	3.56135e10i	1.60719	+	1.48512i
$925$	3.46135e9			0.143797
$926$	1.67979e10	+	2.90948e10i	0.695211	+	1.20414i
$927$	5.37963e9	−	9.31779e9i	0.221806	−	0.384179i
$928$	2.02156e9	−	3.50145e9i	0.0830366	−	0.143824i
$929$	1.54576e10	+	2.67734e10i	0.632539	+	1.09559i	0.987031	+	0.160531i	$0.0513206\pi$
$929$	1.54576e10	+	2.67734e10i	0.632539	+	1.09559i	−0.354492	+	0.935059i	$0.615346\pi$
$930$	−1.15350e10			−0.470249
$931$	1.14533e10	−	7.87782e9i	0.465166	−	0.319950i
$932$	1.50447e10			0.608735
$933$	−1.60779e9	−	2.78477e9i	−0.0648103	−	0.112255i
$934$	1.63007e10	−	2.82336e10i	0.654624	−	1.13384i
$935$	1.22251e10	−	2.11745e10i	0.489116	−	0.847174i
$936$	−2.61069e9	−	4.52184e9i	−0.104061	−	0.180240i
$937$	−5.91421e9			−0.234860			−0.117430	−	0.993081i	$-0.537466\pi$
$937$	−5.91421e9			−0.234860			−0.117430	+	0.993081i	$0.537466\pi$
$938$	8.18727e9	+	7.56546e9i	0.323914	+	0.299313i
$939$	−1.84092e10			−0.725614
$940$	−4.50295e10	−	7.79933e10i	−1.76827	−	3.06274i
$941$	−2.50638e10	+	4.34117e10i	−0.980580	+	1.69841i	−0.320444	+	0.947267i	$0.603832\pi$
$941$	−2.50638e10	+	4.34117e10i	−0.980580	+	1.69841i	−0.660135	+	0.751147i	$0.729501\pi$
$942$	2.40864e10	−	4.17188e10i	0.938843	−	1.62612i
$943$	7.27526e8	+	1.26011e9i	0.0282525	+	0.0489348i
$944$	−2.28516e9			−0.0884126
$945$	7.78559e9	−	3.44366e10i	0.300110	−	1.32742i
$946$	−3.94982e10			−1.51690
$947$	3.23598e9	+	5.60489e9i	0.123817	+	0.214458i	0.921270	−	0.388924i	$-0.127153\pi$
$947$	3.23598e9	+	5.60489e9i	0.123817	+	0.214458i	−0.797453	+	0.603381i	$0.793820\pi$
$948$	−1.08382e10	+	1.87722e10i	−0.413167	+	0.715627i
$949$	9.60058e9	−	1.66287e10i	0.364641	−	0.631577i
$950$	−7.12355e9	−	1.23383e10i	−0.269565	−	0.466901i
$951$	1.72788e10			0.651452
$952$	1.94193e10	−	6.03374e9i	0.729465	−	0.226651i
$953$	1.92800e9			0.0721575			0.0360788	−	0.999349i	$-0.488513\pi$
$953$	1.92800e9			0.0721575			0.0360788	+	0.999349i	$0.488513\pi$
$954$	−9.34681e9	−	1.61891e10i	−0.348533	−	0.603677i
$955$	9.63021e9	−	1.66800e10i	0.357786	−	0.619704i
$956$	9.00718e9	−	1.56009e10i	0.333416	−	0.577493i
$957$	5.05277e9	+	8.75166e9i	0.186354	+	0.322774i
$958$	6.83753e10			2.51258
$959$	3.41104e10	−	1.05984e10i	1.24888	−	0.388039i
$960$	−4.07274e10			−1.48572
$961$	1.27922e10	+	2.21568e10i	0.464958	+	0.805331i
$962$	3.05786e9	−	5.29637e9i	0.110740	−	0.191808i
$963$	−7.08239e9	+	1.22671e10i	−0.255557	+	0.442638i
$964$	2.70820e10	+	4.69074e10i	0.973668	+	1.68644i
$965$	4.75725e10			1.70416
$966$	−5.22560e9	+	2.31135e10i	−0.186516	+	0.824983i
$967$	9.68312e9			0.344368			0.172184	−	0.985065i	$-0.444918\pi$
$967$	9.68312e9			0.344368			0.172184	+	0.985065i	$0.444918\pi$
$968$	−1.99258e10	−	3.45124e10i	−0.706075	−	1.22296i
$969$	−3.71104e9	+	6.42771e9i	−0.131027	+	0.226946i
$970$	−4.81788e10	+	8.34481e10i	−1.69494	+	2.93573i
$971$	−2.12209e10	−	3.67557e10i	−0.743870	−	1.28842i	−0.950721	−	0.310048i	$-0.899655\pi$
$971$	−2.12209e10	−	3.67557e10i	−0.743870	−	1.28842i	0.206851	−	0.978372i	$-0.433678\pi$
$972$	2.90663e10			1.01522
$973$	−1.63414e10	−	1.51003e10i	−0.568714	−	0.525521i
$974$	4.01207e10			1.39127
$975$	3.60988e9	+	6.25250e9i	0.124732	+	0.216042i
$976$	1.27066e10	−	2.20084e10i	0.437476	−	0.757731i
$977$	−2.18835e10	+	3.79034e10i	−0.750734	+	1.30031i	0.196733	+	0.980457i	$0.436967\pi$
$977$	−2.18835e10	+	3.79034e10i	−0.750734	+	1.30031i	−0.947467	+	0.319852i	$0.896367\pi$
$978$	−1.54744e10	−	2.68024e10i	−0.528966	−	0.916196i
$979$	−4.99395e10			−1.70100
$980$	5.31053e9	+	6.71629e10i	0.180238	+	2.27949i
$981$	−6.98508e8			−0.0236227
$982$	1.83499e10	+	3.17830e10i	0.618363	+	1.07104i
$983$	−5.72456e8	+	9.91522e8i	−0.0192223	+	0.0332939i	−0.875477	−	0.483261i	$-0.839452\pi$
$983$	−5.72456e8	+	9.91522e8i	−0.0192223	+	0.0332939i	0.856254	+	0.516555i	$0.172786\pi$
$984$	1.65942e9	−	2.87420e9i	0.0555231	−	0.0961688i
$985$	−2.91111e10	−	5.04218e10i	−0.970580	−	1.68109i
$986$	8.65672e9			0.287597
$987$	−2.89539e10	−	2.67549e10i	−0.958511	−	0.885714i
$988$	−1.62653e10			−0.536554
$989$	−5.76251e9	−	9.98096e9i	−0.189420	−	0.328084i
$990$	−1.31417e10	+	2.27621e10i	−0.430455	+	0.745570i
$991$	−7.50813e9	+	1.30045e10i	−0.245061	+	0.424458i	−0.962149	−	0.272525i	$-0.912141\pi$
$991$	−7.50813e9	+	1.30045e10i	−0.245061	+	0.424458i	0.717088	+	0.696983i	$0.245475\pi$
$992$	−2.17318e9	−	3.76405e9i	−0.0706812	−	0.122423i
$993$	4.67062e10			1.51374
$994$	−2.02291e9	+	8.94756e9i	−0.0653317	+	0.288970i
$995$	−2.23727e10			−0.720008
$996$	4.97726e8	+	8.62087e8i	0.0159618	+	0.0276467i
$997$	2.67183e10	−	4.62775e10i	0.853839	−	1.47889i	−0.0238793	−	0.999715i	$-0.507602\pi$
$997$	2.67183e10	−	4.62775e10i	0.853839	−	1.47889i	0.877718	−	0.479177i	$-0.159065\pi$
$998$	3.63406e10	−	6.29438e10i	1.15727	−	2.00445i
$999$	4.33483e9	+	7.50815e9i	0.137560	+	0.238261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.8.c.a.4.1	yes	8
3.2	odd	2		63.8.e.b.46.4		8
4.3	odd	2		112.8.i.c.81.3		8
7.2	even	3	inner	7.8.c.a.2.1	✓	8
7.3	odd	6		49.8.a.e.1.4		4
7.4	even	3		49.8.a.f.1.4		4
7.5	odd	6		49.8.c.g.30.1		8
7.6	odd	2		49.8.c.g.18.1		8
21.2	odd	6		63.8.e.b.37.4		8
21.11	odd	6		441.8.a.s.1.1		4
21.17	even	6		441.8.a.t.1.1		4
28.23	odd	6		112.8.i.c.65.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.8.c.a.2.1	✓	8	7.2	even	3	inner
7.8.c.a.4.1	yes	8	1.1	even	1	trivial
49.8.a.e.1.4		4	7.3	odd	6
49.8.a.f.1.4		4	7.4	even	3
49.8.c.g.18.1		8	7.6	odd	2
49.8.c.g.30.1		8	7.5	odd	6
63.8.e.b.37.4		8	21.2	odd	6
63.8.e.b.46.4		8	3.2	odd	2
112.8.i.c.65.3		8	28.23	odd	6
112.8.i.c.81.3		8	4.3	odd	2
441.8.a.s.1.1		4	21.11	odd	6
441.8.a.t.1.1		4	21.17	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.50966 - 16.4712i) q^{2} +(-19.7308 + 34.1747i) q^{3} +(-116.867 + 202.420i) q^{4} +(-175.002 - 303.113i) q^{5} +750.531 q^{6} +(-666.505 - 615.885i) q^{7} +2011.00 q^{8} +(314.894 + 545.412i) q^{9} +(-3328.43 + 5765.00i) q^{10} +(3134.64 - 5429.36i) q^{11} +(-4611.76 - 7987.80i) q^{12} -4122.67 q^{13} +(-3806.14 + 16835.0i) q^{14} +13811.7 q^{15} +(-4164.91 - 7213.83i) q^{16} +(-5571.35 + 9649.87i) q^{17} +(5989.07 - 10373.4i) q^{18} +(-8439.78 - 14618.1i) q^{19} +81808.2 q^{20} +(34198.3 - 10625.7i) q^{21} -119238. q^{22} +(-17395.9 - 30130.7i) q^{23} +(-39678.6 + 68725.3i) q^{24} +(-22189.1 + 38432.7i) q^{25} +(39205.2 + 67905.4i) q^{26} -111155. q^{27} +(202560. - 62937.2i) q^{28} +40847.7 q^{29} +(-131345. - 227496. i) q^{30} +(21955.6 - 38028.2i) q^{31} +(49490.2 - 85719.6i) q^{32} +(123698. + 214251. i) q^{33} +211927. q^{34} +(-70042.8 + 309808. i) q^{35} -147203. q^{36} +(-38998.2 - 67546.8i) q^{37} +(-160519. + 278027. i) q^{38} +(81343.5 - 140891. i) q^{39} +(-351930. - 609560. i) q^{40} -41821.6 q^{41} +(-500233. - 462241. i) q^{42} +331256. q^{43} +(732674. + 1.26903e6i) q^{44} +(110214. - 190897. i) q^{45} +(-330859. + 573065. i) q^{46} +(-550427. - 953368. i) q^{47} +328707. q^{48} +(64914.4 + 820981. i) q^{49} +844045. q^{50} +(-219854. - 380799. i) q^{51} +(481805. - 834511. i) q^{52} +(780322. - 1.35156e6i) q^{53} +(1.05704e6 + 1.83085e6i) q^{54} -2.19428e6 q^{55} +(-1.34034e6 - 1.23854e6i) q^{56} +666093. q^{57} +(-388448. - 672812. i) q^{58} +(137167. - 237581. i) q^{59} +(-1.61414e6 + 2.79577e6i) q^{60} +(1.52543e6 + 2.64213e6i) q^{61} -835161. q^{62} +(126033. - 557458. i) q^{63} -2.94876e6 q^{64} +(721477. + 1.24964e6i) q^{65} +(2.35265e6 - 4.07491e6i) q^{66} +(322932. - 559334. i) q^{67} +(-1.30222e6 - 2.25551e6i) q^{68} +1.37294e6 q^{69} +(5.76899e6 - 1.79247e6i) q^{70} +531485. q^{71} +(633251. + 1.09682e6i) q^{72} +(-2.32873e6 + 4.03347e6i) q^{73} +(-741719. + 1.28469e6i) q^{74} +(-875618. - 1.51661e6i) q^{75} +3.94533e6 q^{76} +(-5.43312e6 + 1.68812e6i) q^{77} -3.09419e6 q^{78} +(-1.17506e6 - 2.03526e6i) q^{79} +(-1.45774e6 + 2.52488e6i) q^{80} +(1.50450e6 - 2.60586e6i) q^{81} +(397709. + 688852. i) q^{82} -107925. q^{83} +(-1.84581e6 + 8.16422e6i) q^{84} +3.90000e6 q^{85} +(-3.15013e6 - 5.45619e6i) q^{86} +(-805957. + 1.39596e6i) q^{87} +(6.30376e6 - 1.09184e7i) q^{88} +(-3.98287e6 - 6.89853e6i) q^{89} -4.19240e6 q^{90} +(2.74778e6 + 2.53909e6i) q^{91} +8.13206e6 q^{92} +(866402. + 1.50065e6i) q^{93} +(-1.04688e7 + 1.81324e7i) q^{94} +(-2.95396e6 + 5.11641e6i) q^{95} +(1.95296e6 + 3.38263e6i) q^{96} +1.44749e7 q^{97} +(1.29052e7 - 8.87647e6i) q^{98} +3.94832e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 28 q^{3} - 348 q^{4} - 252 q^{5} + 2044 q^{6} + 672 q^{7} - 1968 q^{8} - 2008 q^{9} - 4774 q^{10} + 3972 q^{11} + 5404 q^{12} - 2352 q^{13} + 47502 q^{14} - 33112 q^{15} - 57264 q^{16} - 56364 q^{17}+ \cdots + 30427952 q^{99}+O(q^{100}) \) 8 * q + 6 * q^2 - 28 * q^3 - 348 * q^4 - 252 * q^5 + 2044 * q^6 + 672 * q^7 - 1968 * q^8 - 2008 * q^9 - 4774 * q^10 + 3972 * q^11 + 5404 * q^12 - 2352 * q^13 + 47502 * q^14 - 33112 * q^15 - 57264 * q^16 - 56364 * q^17 + 35908 * q^18 - 41748 * q^19 + 324744 * q^20 + 188524 * q^21 - 305908 * q^22 - 131748 * q^23 - 389592 * q^24 + 68016 * q^25 - 113652 * q^26 + 378056 * q^27 + 681548 * q^28 + 68112 * q^29 - 605378 * q^30 - 401212 * q^31 + 453408 * q^32 - 24052 * q^33 + 164220 * q^34 + 40404 * q^35 - 720176 * q^36 + 5396 * q^37 - 31794 * q^38 - 364840 * q^39 + 443688 * q^40 + 820848 * q^41 - 240856 * q^42 + 93088 * q^43 + 1465836 * q^44 + 1209656 * q^45 - 1379202 * q^46 - 1470084 * q^47 - 4037600 * q^48 - 2793784 * q^49 + 2791056 * q^50 + 1724796 * q^51 + 5269768 * q^52 + 642372 * q^53 + 4567318 * q^54 - 6126680 * q^55 - 6195168 * q^56 + 6718136 * q^57 + 1972220 * q^58 - 752220 * q^59 - 2123324 * q^60 - 1325772 * q^61 - 6032628 * q^62 - 6412616 * q^63 - 1731712 * q^64 + 4868808 * q^65 + 6013294 * q^66 + 290916 * q^67 - 2453556 * q^68 + 9830520 * q^69 + 11665990 * q^70 + 6755520 * q^71 - 4557744 * q^72 - 6706588 * q^73 - 3616878 * q^74 - 7223888 * q^75 + 5846008 * q^76 - 5310564 * q^77 - 32576264 * q^78 - 3946244 * q^79 - 10695888 * q^80 + 11731292 * q^81 + 17563252 * q^82 + 19084128 * q^83 + 38088092 * q^84 + 14012136 * q^85 - 23237832 * q^86 - 17836840 * q^87 + 8043336 * q^88 - 16165212 * q^89 + 6831496 * q^90 - 2414720 * q^91 - 38885256 * q^92 - 12552852 * q^93 - 5720442 * q^94 + 3268452 * q^95 + 8448608 * q^96 + 3066224 * q^97 + 60255006 * q^98 + 30427952 * q^99

Introduction

L-functions

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