LMFDB - Embedded newform 7.8.c.a.2.4

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			2.4
Root			$-5.15962 - 8.93672i$ of defining polynomial
Character	$\chi$	$=$	7.2
Dual form			7.8.c.a.4.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.4120 - 18.0342i) q^{2} +(22.7504 + 39.4049i) q^{3} +(-152.821 - 264.694i) q^{4} +(-96.7016 + 167.492i) q^{5} +947.513 q^{6} +(612.373 + 669.733i) q^{7} -3699.23 q^{8} +(58.3362 - 101.041i) q^{9} +(2013.72 + 3487.87i) q^{10} +(-151.972 - 263.223i) q^{11} +(6953.49 - 12043.8i) q^{12} -9891.04 q^{13} +(18454.1 - 4070.37i) q^{14} -8800.01 q^{15} +(-18955.5 + 32831.8i) q^{16} +(-6242.26 - 10811.9i) q^{17} +(-1214.80 - 2104.09i) q^{18} +(-561.837 + 973.131i) q^{19} +59112.1 q^{20} +(-12459.0 + 39367.2i) q^{21} -6329.35 q^{22} +(22359.5 - 38727.8i) q^{23} +(-84159.2 - 145768. i) q^{24} +(20360.1 + 35264.8i) q^{25} +(-102986. + 178377. i) q^{26} +104819. q^{27} +(83690.6 - 264441. i) q^{28} +51216.6 q^{29} +(-91626.0 + 158701. i) q^{30} +(-12816.5 - 22198.9i) q^{31} +(157979. + 273628. i) q^{32} +(6914.85 - 11976.9i) q^{33} -259978. q^{34} +(-171392. + 37803.5i) q^{35} -35660.0 q^{36} +(21054.5 - 36467.4i) q^{37} +(11699.7 + 20264.6i) q^{38} +(-225025. - 389755. i) q^{39} +(357722. - 619592. i) q^{40} +787100. q^{41} +(580232. + 634581. i) q^{42} -629737. q^{43} +(-46449.0 + 80452.1i) q^{44} +(11282.4 + 19541.7i) q^{45} +(-465616. - 806470. i) q^{46} +(-313344. + 542727. i) q^{47} -1.72498e6 q^{48} +(-73540.5 + 820253. i) q^{49} +847961. q^{50} +(284028. - 491951. i) q^{51} +(1.51156e6 + 2.61810e6i) q^{52} +(268306. + 464719. i) q^{53} +(1.09138e6 - 1.89033e6i) q^{54} +58783.7 q^{55} +(-2.26531e6 - 2.47750e6i) q^{56} -51128.2 q^{57} +(533269. - 923649. i) q^{58} +(-1.06004e6 - 1.83605e6i) q^{59} +(1.34483e6 + 2.32931e6i) q^{60} +(-1.35734e6 + 2.35098e6i) q^{61} -533785. q^{62} +(103394. - 22805.3i) q^{63} +1.72694e6 q^{64} +(956479. - 1.65667e6i) q^{65} +(-143995. - 249407. i) q^{66} +(-1.88702e6 - 3.26842e6i) q^{67} +(-1.90790e6 + 3.30457e6i) q^{68} +2.03475e6 q^{69} +(-1.10279e6 + 3.48453e6i) q^{70} +4.31646e6 q^{71} +(-215799. + 373775. i) q^{72} +(355018. + 614910. i) q^{73} +(-438440. - 759401. i) q^{74} +(-926403. + 1.60458e6i) q^{75} +343442. q^{76} +(83225.5 - 262971. i) q^{77} -9.37189e6 q^{78} +(-1.39606e6 + 2.41804e6i) q^{79} +(-3.66605e6 - 6.34978e6i) q^{80} +(2.25710e6 + 3.90941e6i) q^{81} +(8.19532e6 - 1.41947e7i) q^{82} +538991. q^{83} +(1.23243e7 - 2.71832e6i) q^{84} +2.41454e6 q^{85} +(-6.55684e6 + 1.13568e7i) q^{86} +(1.16520e6 + 2.01818e6i) q^{87} +(562180. + 973724. i) q^{88} +(1.09927e6 - 1.90400e6i) q^{89} +469891. q^{90} +(-6.05701e6 - 6.62435e6i) q^{91} -1.36680e7 q^{92} +(583163. - 1.01007e6i) q^{93} +(6.52509e6 + 1.13018e7i) q^{94} +(-108661. - 188207. i) q^{95} +(-7.18819e6 + 1.24503e7i) q^{96} -1.16799e7 q^{97} +(1.40269e7 + 9.86675e6i) q^{98} -35461.9 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 $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

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

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 $

$2$	10.4120	−	18.0342i	0.920303	−	1.59401i	0.121357	−	0.992609i	$-0.461276\pi$
$2$	10.4120	−	18.0342i	0.920303	−	1.59401i	0.798946	−	0.601402i	$-0.205391\pi$
$3$	22.7504	+	39.4049i	0.486480	+	0.842608i	0.999879	−	0.0155416i	$-0.00494725\pi$
$3$	22.7504	+	39.4049i	0.486480	+	0.842608i	−0.513399	+	0.858150i	$0.671614\pi$
$4$	−152.821	−	264.694i	−1.19391	−	2.06792i
$5$	−96.7016	+	167.492i	−0.345970	+	0.599238i	−0.985530	−	0.169504i	$-0.945783\pi$
$5$	−96.7016	+	167.492i	−0.345970	+	0.599238i	0.639559	+	0.768742i	$0.279117\pi$
$6$	947.513			1.79084
$7$	612.373	+	669.733i	0.674797	+	0.738003i
$7$	612.373	+	669.733i	0.674797	+	0.738003i
$8$	−3699.23			−2.55445
$9$	58.3362	−	101.041i	0.0266741	−	0.0462009i
$10$	2013.72	+	3487.87i	0.636794	+	1.10296i
$11$	−151.972	−	263.223i	−0.0344262	−	0.0596279i	0.848299	−	0.529518i	$-0.177627\pi$
$11$	−151.972	−	263.223i	−0.0344262	−	0.0596279i	−0.882725	+	0.469890i	$0.844294\pi$
$12$	6953.49	−	12043.8i	1.16163	−	2.01201i
$13$	−9891.04			−1.24865			−0.624324	−	0.781165i	$-0.714626\pi$
$13$	−9891.04			−1.24865			−0.624324	+	0.781165i	$0.714626\pi$
$14$	18454.1	−	4070.37i	1.79740	−	0.396448i
$15$	−8800.01			−0.673230
$16$	−18955.5	+	32831.8i	−1.15695	+	2.00390i
$17$	−6242.26	−	10811.9i	−0.308156	−	0.533742i	0.669803	−	0.742539i	$-0.266378\pi$
$17$	−6242.26	−	10811.9i	−0.308156	−	0.533742i	−0.977959	+	0.208797i	$0.933045\pi$
$18$	−1214.80	−	2104.09i	−0.0490965	−	0.0850376i
$19$	−561.837	+	973.131i	−0.0187920	+	0.0325487i	−0.875268	−	0.483637i	$-0.839315\pi$
$19$	−561.837	+	973.131i	−0.0187920	+	0.0325487i	0.856476	+	0.516186i	$0.172649\pi$
$20$	59112.1			1.65223
$21$	−12459.0	+	39367.2i	−0.293572	+	0.927614i
$22$	−6329.35			−0.126730
$23$	22359.5	−	38727.8i	0.383190	−	0.663705i	−0.608326	−	0.793687i	$-0.708159\pi$
$23$	22359.5	−	38727.8i	0.383190	−	0.663705i	0.991516	+	0.129982i	$0.0414920\pi$
$24$	−84159.2	−	145768.i	−1.24269	−	2.15240i
$25$	20360.1	+	35264.8i	0.260610	+	0.451389i
$26$	−102986.	+	178377.i	−1.14913	+	1.99036i
$27$	104819.			1.02487
$28$	83690.6	−	264441.i	0.720482	−	2.27654i
$29$	51216.6			0.389958			0.194979	−	0.980807i	$-0.437536\pi$
$29$	51216.6			0.389958			0.194979	+	0.980807i	$0.437536\pi$
$30$	−91626.0	+	158701.i	−0.619576	+	1.07314i
$31$	−12816.5	−	22198.9i	−0.0772688	−	0.133834i	0.824802	−	0.565422i	$-0.191287\pi$
$31$	−12816.5	−	22198.9i	−0.0772688	−	0.133834i	−0.902071	+	0.431588i	$0.857953\pi$
$32$	157979.	+	273628.i	0.852266	+	1.47617i
$33$	6914.85	−	11976.9i	0.0334953	−	0.0580156i
$34$	−259978.			−1.13439
$35$	−171392.	+	37803.5i	−0.675699	+	0.149037i
$36$	−35660.0			−0.127386
$37$	21054.5	−	36467.4i	0.0683343	−	0.118358i	−0.829834	−	0.558010i	$-0.811565\pi$
$37$	21054.5	−	36467.4i	0.0683343	−	0.118358i	0.898168	+	0.439652i	$0.144898\pi$
$38$	11699.7	+	20264.6i	0.0345887	+	0.0599093i
$39$	−225025.	−	389755.i	−0.607443	−	1.05212i
$40$	357722.	−	619592.i	0.883762	−	1.53072i
$41$	787100.			1.78356			0.891778	−	0.452474i	$-0.149458\pi$
$41$	787100.			1.78356			0.891778	+	0.452474i	$0.149458\pi$
$42$	580232.	+	634581.i	1.20845	+	1.32164i
$43$	−629737.			−1.20787			−0.603934	−	0.797034i	$-0.706401\pi$
$43$	−629737.			−1.20787			−0.603934	+	0.797034i	$0.706401\pi$
$44$	−46449.0	+	80452.1i	−0.0822039	+	0.142381i
$45$	11282.4	+	19541.7i	0.0184569	+	0.0319682i
$46$	−465616.	−	806470.i	−0.705302	−	1.22162i
$47$	−313344.	+	542727.i	−0.440229	+	0.762498i	−0.997706	−	0.0676937i	$-0.978436\pi$
$47$	−313344.	+	542727.i	−0.440229	+	0.762498i	0.557478	+	0.830192i	$0.311769\pi$
$48$	−1.72498e6			−2.25133
$49$	−73540.5	+	820253.i	−0.0892977	+	0.996005i
$50$	847961.			0.959359
$51$	284028.	−	491951.i	0.299823	−	0.519309i
$52$	1.51156e6	+	2.61810e6i	1.49078	+	2.58211i
$53$	268306.	+	464719.i	0.247551	+	0.428770i	0.962846	−	0.270052i	$-0.0870410\pi$
$53$	268306.	+	464719.i	0.247551	+	0.428770i	−0.715295	+	0.698823i	$0.753708\pi$
$54$	1.09138e6	−	1.89033e6i	0.943187	−	1.63365i
$55$	58783.7			0.0476417
$56$	−2.26531e6	−	2.47750e6i	−1.72373	−	1.88519i
$57$	−51128.2			−0.0365677
$58$	533269.	−	923649.i	0.358879	−	0.621597i
$59$	−1.06004e6	−	1.83605e6i	−0.671958	−	1.16386i	−0.977348	−	0.211638i	$-0.932120\pi$
$59$	−1.06004e6	−	1.83605e6i	−0.671958	−	1.16386i	0.305390	−	0.952227i	$-0.401213\pi$
$60$	1.34483e6	+	2.32931e6i	0.803779	+	1.39219i
$61$	−1.35734e6	+	2.35098e6i	−0.765656	+	1.32616i	0.174242	+	0.984703i	$0.444252\pi$
$61$	−1.35734e6	+	2.35098e6i	−0.765656	+	1.32616i	−0.939899	+	0.341453i	$0.889081\pi$
$62$	−533785.			−0.284443
$63$	103394.	−	22805.3i	0.0520960	−	0.0114906i
$64$	1.72694e6			0.823470
$65$	956479.	−	1.65667e6i	0.431995	−	0.748237i
$66$	−143995.	−	249407.i	−0.0616517	−	0.106784i
$67$	−1.88702e6	−	3.26842e6i	−0.766506	−	1.32763i	−0.939447	−	0.342695i	$-0.888660\pi$
$67$	−1.88702e6	−	3.26842e6i	−0.766506	−	1.32763i	0.172941	−	0.984932i	$-0.444673\pi$
$68$	−1.90790e6	+	3.30457e6i	−0.735824	+	1.27448i
$69$	2.03475e6			0.745658
$70$	−1.10279e6	+	3.48453e6i	−0.384281	+	1.21423i
$71$	4.31646e6			1.43128			0.715638	−	0.698472i	$-0.246136\pi$
$71$	4.31646e6			1.43128			0.715638	+	0.698472i	$0.246136\pi$
$72$	−215799.	+	373775.i	−0.0681375	+	0.118018i
$73$	355018.	+	614910.i	0.106812	+	0.185004i	0.914477	−	0.404638i	$-0.132602\pi$
$73$	355018.	+	614910.i	0.106812	+	0.185004i	−0.807665	+	0.589642i	$0.799269\pi$
$74$	−438440.	−	759401.i	−0.125776	−	0.217851i
$75$	−926403.	+	1.60458e6i	−0.253563	+	0.439184i
$76$	343442.			0.0897442
$77$	83225.5	−	262971.i	0.0207749	−	0.0656434i
$78$	−9.37189e6			−2.23613
$79$	−1.39606e6	+	2.41804e6i	−0.318572	+	0.551783i	−0.980190	−	0.198058i	$-0.936537\pi$
$79$	−1.39606e6	+	2.41804e6i	−0.318572	+	0.551783i	0.661618	+	0.749841i	$0.269870\pi$
$80$	−3.66605e6	−	6.34978e6i	−0.800540	−	1.38658i
$81$	2.25710e6	+	3.90941e6i	0.471903	+	0.817360i
$82$	8.19532e6	−	1.41947e7i	1.64141	−	2.84301i
$83$	538991.			0.103468			0.0517342	−	0.998661i	$-0.483525\pi$
$83$	538991.			0.103468			0.0517342	+	0.998661i	$0.483525\pi$
$84$	1.23243e7	−	2.71832e6i	2.26873	−	0.500407i
$85$	2.41454e6			0.426451
$86$	−6.55684e6	+	1.13568e7i	−1.11160	+	1.92536i
$87$	1.16520e6	+	2.01818e6i	0.189707	+	0.328582i
$88$	562180.	+	973724.i	0.0879399	+	0.152316i
$89$	1.09927e6	−	1.90400e6i	0.165288	−	0.286287i	−0.771470	−	0.636266i	$-0.780478\pi$
$89$	1.09927e6	−	1.90400e6i	0.165288	−	0.286287i	0.936757	+	0.349979i	$0.113811\pi$
$90$	469891.			0.0679436
$91$	−6.05701e6	−	6.62435e6i	−0.842584	−	0.921507i
$92$	−1.36680e7			−1.82999
$93$	583163.	−	1.01007e6i	0.0751795	−	0.130215i
$94$	6.52509e6	+	1.13018e7i	0.810287	+	1.40346i
$95$	−108661.	−	188207.i	−0.0130029	−	0.0225218i
$96$	−7.18819e6	+	1.24503e7i	−0.829221	+	1.43625i
$97$	−1.16799e7			−1.29938			−0.649691	−	0.760198i	$-0.725102\pi$
$97$	−1.16799e7			−1.29938			−0.649691	+	0.760198i	$0.725102\pi$
$98$	1.40269e7	+	9.86675e6i	1.50546	+	1.05897i
$99$	−35461.9			−0.00367315
$100$	6.22291e6	−	1.07784e7i	0.622291	−	1.07784i
$101$	−5.79389e6	−	1.00353e7i	−0.559558	−	0.969184i	−0.997533	−	0.0701964i	$-0.977637\pi$
$101$	−5.79389e6	−	1.00353e7i	−0.559558	−	0.969184i	0.437975	−	0.898987i	$-0.355696\pi$
$102$	−5.91462e6	−	1.02444e7i	−0.551857	−	0.955844i
$103$	−4.20034e6	+	7.27521e6i	−0.378752	+	0.656017i	−0.990881	−	0.134741i	$-0.956980\pi$
$103$	−4.20034e6	+	7.27521e6i	−0.378752	+	0.656017i	0.612129	+	0.790758i	$0.290313\pi$
$104$	3.65893e7			3.18961
$105$	−5.38889e6	−	5.89365e6i	−0.454294	−	0.496846i
$106$	1.11744e7			0.911286
$107$	−1.45109e6	+	2.51336e6i	−0.114512	+	0.198341i	−0.917585	−	0.397541i	$-0.869864\pi$
$107$	−1.45109e6	+	2.51336e6i	−0.114512	+	0.198341i	0.803072	+	0.595881i	$0.203197\pi$
$108$	−1.60186e7	−	2.77450e7i	−1.22360	−	2.11934i
$109$	9.92983e6	+	1.71990e7i	0.734428	+	1.27207i	0.954974	+	0.296690i	$0.0958828\pi$
$109$	9.92983e6	+	1.71990e7i	0.734428	+	1.27207i	−0.220546	+	0.975377i	$0.570784\pi$
$110$	612058.	−	1.06012e6i	0.0438448	−	0.0759414i
$111$	1.91599e6			0.132973
$112$	−3.35964e7	+	7.41025e6i	−2.25959	+	0.498390i
$113$	7.27288e6			0.474167			0.237084	−	0.971489i	$-0.423808\pi$
$113$	7.27288e6			0.474167			0.237084	+	0.971489i	$0.423808\pi$
$114$	−532348.	+	922054.i	−0.0336534	+	0.0582894i
$115$	4.32440e6	+	7.49007e6i	0.265145	+	0.459244i
$116$	−7.82698e6	−	1.35567e7i	−0.465576	−	0.806402i
$117$	−577006.	+	999403.i	−0.0333065	+	0.0576886i
$118$	−4.41489e7			−2.47362
$119$	3.41849e6	−	1.08016e7i	0.185960	−	0.587587i
$120$	3.25533e7			1.71973
$121$	9.69739e6	−	1.67964e7i	0.497630	−	0.861920i
$122$	2.82653e7	+	4.89570e7i	1.40927	+	2.44093i
$123$	1.79069e7	+	3.10156e7i	0.867664	+	1.50284i
$124$	−3.91727e6	+	6.78491e6i	−0.184505	+	0.319572i
$125$	−2.29850e7			−1.05259
$126$	665269.	−	2.10208e6i	0.0296279	−	0.0936164i
$127$	2.81015e7			1.21735			0.608676	−	0.793419i	$-0.291701\pi$
$127$	2.81015e7			1.21735			0.608676	+	0.793419i	$0.291701\pi$
$128$	−2.24036e6	+	3.88042e6i	−0.0944241	+	0.163547i
$129$	−1.43268e7	−	2.48147e7i	−0.587604	−	1.01776i
$130$	−1.99178e7	−	3.44986e7i	−0.795132	−	1.37721i
$131$	9.59472e6	−	1.66185e7i	0.372892	−	0.645867i	−0.617117	−	0.786871i	$-0.711700\pi$
$131$	9.59472e6	−	1.66185e7i	0.372892	−	0.645867i	0.990009	+	0.141004i	$0.0450329\pi$
$132$	−4.22694e6			−0.159962
$133$	−995792.	+	219639.i	−0.0367018	+	0.00809521i
$134$	−7.85910e7			−2.82167
$135$	−1.01362e7	+	1.75564e7i	−0.354573	+	0.614138i
$136$	2.30916e7	+	3.99958e7i	0.787168	+	1.36341i
$137$	−8.60460e6	−	1.49036e7i	−0.285897	−	0.495187i	0.686930	−	0.726724i	$-0.258958\pi$
$137$	−8.60460e6	−	1.49036e7i	−0.285897	−	0.495187i	−0.972826	+	0.231537i	$0.925625\pi$
$138$	2.11859e7	−	3.66951e7i	0.686231	−	1.18859i
$139$	4.17445e7			1.31840			0.659200	−	0.751968i	$-0.270895\pi$
$139$	4.17445e7			1.31840			0.659200	+	0.751968i	$0.270895\pi$
$140$	3.61987e7	+	3.95893e7i	1.11492	+	1.21935i
$141$	−2.85148e7			−0.856650
$142$	4.49431e7	−	7.78438e7i	1.31721	−	2.28147i
$143$	1.50316e6	+	2.60355e6i	0.0429862	+	0.0744543i
$144$	2.21158e6	+	3.83057e6i	0.0617212	+	0.106904i
$145$	−4.95272e6	+	8.57837e6i	−0.134914	+	0.233677i
$146$	1.47859e7			0.393198
$147$	−3.39951e7	+	1.57632e7i	−0.882684	+	0.409294i
$148$	−1.28703e7			−0.326341
$149$	−1.99889e6	+	3.46218e6i	−0.0495036	+	0.0857428i	−0.889715	−	0.456516i	$-0.849097\pi$
$149$	−1.99889e6	+	3.46218e6i	−0.0495036	+	0.0857428i	0.840212	+	0.542258i	$0.182431\pi$
$150$	1.92915e7	+	3.34138e7i	0.466709	+	0.808364i
$151$	−2.86457e7	−	4.96158e7i	−0.677081	−	1.17274i	−0.975856	−	0.218415i	$-0.929911\pi$
$151$	−2.86457e7	−	4.96158e7i	−0.677081	−	1.17274i	0.298775	−	0.954323i	$-0.403422\pi$
$152$	2.07837e6	−	3.59984e6i	0.0480032	−	0.0831439i
$153$	−1.45660e6			−0.0328791
$154$	−3.87593e6	−	4.23897e6i	−0.0855171	−	0.0935272i
$155$	4.95751e6			0.106931
$156$	−6.87772e7	+	1.19126e8i	−1.45047	+	2.51229i
$157$	1.42614e7	+	2.47014e7i	0.294112	+	0.509416i	0.974778	−	0.223177i	$-0.0716429\pi$
$157$	1.42614e7	+	2.47014e7i	0.294112	+	0.509416i	−0.680666	+	0.732594i	$0.738310\pi$
$158$	2.90716e7	+	5.03534e7i	0.586366	+	1.01562i
$159$	−1.22081e7	+	2.11451e7i	−0.240857	+	0.417177i
$160$	−6.11073e7			−1.17943
$161$	3.96296e7	−	8.74098e6i	0.748392	−	0.165071i
$162$	9.40039e7			1.73717
$163$	−1.61353e7	+	2.79472e7i	−0.291824	+	0.505454i	−0.974241	−	0.225509i	$-0.927595\pi$
$163$	−1.61353e7	+	2.79472e7i	−0.291824	+	0.505454i	0.682417	+	0.730963i	$0.260929\pi$
$164$	−1.20286e8	−	2.08341e8i	−2.12941	−	3.68825i
$165$	1.33735e6	+	2.31637e6i	0.0231768	+	0.0401433i
$166$	5.61199e6	−	9.72026e6i	0.0952223	−	0.164930i
$167$	1.88088e7			0.312502			0.156251	−	0.987717i	$-0.450059\pi$
$167$	1.88088e7			0.312502			0.156251	+	0.987717i	$0.450059\pi$
$168$	4.60887e7	−	1.45629e8i	0.749915	−	2.36954i
$169$	3.50841e7			0.559123
$170$	2.51403e7	−	4.35443e7i	0.392464	−	0.679767i
$171$	65550.9	+	113538.i	0.00100252	+	0.00173641i
$172$	9.62371e7	+	1.66687e8i	1.44209	+	2.49778i
$173$	−4.67229e7	+	8.09264e7i	−0.686070	+	1.18831i	0.287029	+	0.957922i	$0.407332\pi$
$173$	−4.67229e7	+	8.09264e7i	−0.686070	+	1.18831i	−0.973099	+	0.230386i	$0.926001\pi$
$174$	4.85284e7			0.698351
$175$	−1.11500e7	+	3.52310e7i	−0.157268	+	0.496927i
$176$	1.15228e7			0.159318
$177$	4.82329e7	−	8.35419e7i	0.653788	−	1.13239i
$178$	−2.28913e7	−	3.96489e7i	−0.304229	−	0.526941i
$179$	−4.41581e7	−	7.64841e7i	−0.575473	−	0.996748i	−0.995990	−	0.0894634i	$-0.971485\pi$
$179$	−4.41581e7	−	7.64841e7i	−0.575473	−	0.996748i	0.420517	−	0.907284i	$-0.361849\pi$
$180$	3.44838e6	−	5.97277e6i	0.0440718	−	0.0763347i
$181$	−1.09260e7			−0.136958			−0.0684789	−	0.997653i	$-0.521815\pi$
$181$	−1.09260e7			−0.136958			−0.0684789	+	0.997653i	$0.521815\pi$
$182$	−1.82531e8	+	4.02602e7i	−2.24432	+	0.495024i
$183$	−1.23520e8			−1.48991
$184$	−8.27130e7	+	1.43263e8i	−0.978840	+	1.69540i
$185$	4.07200e6	+	7.05292e6i	0.0472832	+	0.0818969i
$186$	−1.21438e7	−	2.10337e7i	−0.138376	−	0.239674i
$187$	−1.89730e6	+	3.28621e6i	−0.0212173	+	0.0367494i
$188$	1.91542e8			2.10238
$189$	6.41884e7	+	7.02007e7i	0.691577	+	0.756354i
$190$	−4.52553e6			−0.0478666
$191$	5.24786e7	−	9.08956e7i	0.544961	−	0.943900i	−0.453648	−	0.891181i	$-0.649878\pi$
$191$	5.24786e7	−	9.08956e7i	0.544961	−	0.943900i	0.998609	−	0.0527193i	$-0.0167889\pi$
$192$	3.92886e7	+	6.80499e7i	0.400602	+	0.693862i
$193$	−7.92806e6	−	1.37318e7i	−0.0793809	−	0.137492i	0.823602	−	0.567168i	$-0.191961\pi$
$193$	−7.92806e6	−	1.37318e7i	−0.0793809	−	0.137492i	−0.902983	+	0.429676i	$0.858628\pi$
$194$	−1.21611e8	+	2.10637e8i	−1.19582	+	2.07123i
$195$	8.70412e7			0.840628
$196$	2.28354e8	−	1.05886e8i	2.16627	−	1.00448i
$197$	4.99805e6			0.0465767			0.0232883	−	0.999729i	$-0.492586\pi$
$197$	4.99805e6			0.0465767			0.0232883	+	0.999729i	$0.492586\pi$
$198$	−369230.	+	639526.i	−0.00338041	+	0.00585504i
$199$	−2.75134e7	−	4.76545e7i	−0.247490	−	0.428665i	0.715339	−	0.698778i	$-0.246272\pi$
$199$	−2.75134e7	−	4.76545e7i	−0.247490	−	0.428665i	−0.962829	+	0.270112i	$0.912939\pi$
$200$	−7.53168e7	−	1.30453e8i	−0.665713	−	1.15305i
$201$	8.58612e7	−	1.48716e8i	0.745780	−	1.29173i
$202$	−2.41305e8			−2.05985
$203$	3.13637e7	+	3.43014e7i	0.263142	+	0.287790i
$204$	−1.73622e8			−1.43185
$205$	−7.61138e7	+	1.31833e8i	−0.617057	+	1.06877i
$206$	8.74683e7	+	1.51499e8i	0.697132	+	1.20747i
$207$	−2.60874e6	−	4.51846e6i	−0.0204425	−	0.0354074i
$208$	1.87489e8	−	3.24741e8i	1.44462	−	2.50216i
$209$	341534.			0.00258775
$210$	−1.62397e8	+	3.58193e7i	−1.21007	+	0.266901i
$211$	−5.55200e7			−0.406875			−0.203437	−	0.979088i	$-0.565211\pi$
$211$	−5.55200e7			−0.406875			−0.203437	+	0.979088i	$0.565211\pi$
$212$	8.20055e7	−	1.42038e8i	0.591109	−	1.02383i
$213$	9.82013e7	+	1.70090e8i	0.696287	+	1.20600i
$214$	3.02176e7	+	5.23385e7i	0.210772	+	0.365067i
$215$	6.08965e7	−	1.05476e8i	0.417886	−	0.723800i
$216$	−3.87750e8			−2.61797
$217$	7.01881e6	−	2.21776e7i	0.0466288	−	0.147335i
$218$	4.13559e8			2.70358
$219$	−1.61536e7	+	2.79789e7i	−0.103924	+	0.180002i
$220$	−8.98339e6	−	1.55597e7i	−0.0568802	−	0.0985193i
$221$	6.17424e7	+	1.06941e8i	0.384778	+	0.666456i
$222$	1.99494e7	−	3.45534e7i	0.122376	−	0.211961i
$223$	−3.31811e7			−0.200366			−0.100183	−	0.994969i	$-0.531943\pi$
$223$	−3.31811e7			−0.200366			−0.100183	+	0.994969i	$0.531943\pi$
$224$	−8.65153e7	+	2.73366e8i	−0.514310	+	1.62509i
$225$	4.75093e6			0.0278061
$226$	7.57255e7	−	1.31160e8i	0.436378	−	0.755828i
$227$	4.88085e6	+	8.45388e6i	0.0276952	+	0.0479695i	0.879541	−	0.475823i	$-0.157850\pi$
$227$	4.88085e6	+	8.45388e6i	0.0276952	+	0.0479695i	−0.851846	+	0.523793i	$0.824517\pi$
$228$	7.81346e6	+	1.35333e7i	0.0436588	+	0.0756192i
$229$	6.85558e6	−	1.18742e7i	0.0377242	−	0.0653403i	−0.846547	−	0.532314i	$-0.821322\pi$
$229$	6.85558e6	−	1.18742e7i	0.0377242	−	0.0653403i	0.884271	+	0.466974i	$0.154656\pi$
$230$	1.80103e8			0.976054
$231$	1.22558e7	−	2.70322e6i	0.0654182	−	0.0144291i
$232$	−1.89462e8			−0.996127
$233$	−1.14766e8	+	1.98781e8i	−0.594385	+	1.02950i	0.399249	+	0.916843i	$0.369271\pi$
$233$	−1.14766e8	+	1.98781e8i	−0.594385	+	1.02950i	−0.993633	+	0.112662i	$0.964062\pi$
$234$	1.20156e7	+	2.08116e7i	0.0613042	+	0.106182i
$235$	−6.06016e7	−	1.04965e8i	−0.304612	−	0.527603i
$236$	−3.23994e8	+	5.61174e8i	−1.60452	+	2.77911i
$237$	−1.27043e8			−0.619916
$238$	−1.59204e8	−	1.74116e8i	−0.765481	−	0.837181i
$239$	−1.18140e8			−0.559764			−0.279882	−	0.960034i	$-0.590295\pi$
$239$	−1.18140e8			−0.559764			−0.279882	+	0.960034i	$0.590295\pi$
$240$	1.66808e8	−	2.88920e8i	0.778894	−	1.34908i
$241$	−1.10867e8	−	1.92027e8i	−0.510202	−	0.883695i	−0.999930	−	0.0118201i	$-0.996237\pi$
$241$	−1.10867e8	−	1.92027e8i	−0.510202	−	0.883695i	0.489729	−	0.871875i	$-0.337096\pi$
$242$	−2.01939e8	−	3.49769e8i	−0.915940	−	1.58645i
$243$	1.19198e7	−	2.06457e7i	0.0532902	−	0.0923013i
$244$	8.29720e8			3.65651
$245$	−1.30274e8	−	9.16372e7i	−0.565949	−	0.398098i
$246$	7.45788e8			3.19406
$247$	5.55716e6	−	9.62528e6i	0.0234646	−	0.0406419i
$248$	4.74113e7	+	8.21188e7i	0.197379	+	0.341871i
$249$	1.22623e7	+	2.12389e7i	0.0503354	+	0.0871834i
$250$	−2.39321e8	+	4.14516e8i	−0.968704	+	1.67784i
$251$	−1.95230e8			−0.779273			−0.389636	−	0.920969i	$-0.627399\pi$
$251$	−1.95230e8			−0.779273			−0.389636	+	0.920969i	$0.627399\pi$
$252$	−2.18372e7	−	2.38827e7i	−0.0859599	−	0.0940115i
$253$	−1.35921e7			−0.0527671
$254$	2.92594e8	−	5.06787e8i	1.12033	−	1.94047i
$255$	5.49319e7	+	9.51449e7i	0.207460	+	0.359331i
$256$	1.57178e8	+	2.72240e8i	0.585532	+	1.01417i
$257$	2.59127e8	−	4.48821e8i	0.952240	−	1.64933i	0.211679	−	0.977339i	$-0.432107\pi$
$257$	2.59127e8	−	4.48821e8i	0.952240	−	1.64933i	0.740561	−	0.671989i	$-0.234560\pi$
$258$	−5.96684e8			−2.16309
$259$	3.73166e7	−	8.23082e6i	0.133461	−	0.0294370i
$260$	−5.84681e8			−2.06306
$261$	2.98778e6	−	5.17499e6i	0.0104018	−	0.0180164i
$262$	−1.99801e8	−	3.46066e8i	−0.686347	−	1.18879i
$263$	1.95491e8	+	3.38600e8i	0.662646	+	1.14774i	0.979918	+	0.199402i	$0.0639000\pi$
$263$	1.95491e8	+	3.38600e8i	0.662646	+	1.14774i	−0.317271	+	0.948335i	$0.602767\pi$
$264$	−2.55797e7	+	4.43053e7i	−0.0855620	+	0.148198i
$265$	−1.03782e8			−0.342580
$266$	−6.40722e6	+	2.02452e7i	−0.0208729	+	0.0659532i
$267$	1.00036e8			0.321637
$268$	−5.76754e8	+	9.98967e8i	−1.83028	+	3.17015i
$269$	1.79359e8	+	3.10659e8i	0.561810	+	0.973084i	0.997339	+	0.0729092i	$0.0232283\pi$
$269$	1.79359e8	+	3.10659e8i	0.561810	+	0.973084i	−0.435528	+	0.900175i	$0.643438\pi$
$270$	2.11076e8	+	3.65595e8i	0.652629	+	1.13039i
$271$	−9.85150e7	+	1.70633e8i	−0.300684	+	0.520799i	−0.976291	−	0.216462i	$-0.930548\pi$
$271$	−9.85150e7	+	1.70633e8i	−0.300684	+	0.520799i	0.675607	+	0.737262i	$0.263881\pi$
$272$	4.73300e8			1.42608
$273$	1.23232e8	−	3.89383e8i	0.366569	−	1.15826i
$274$	−3.58366e8			−1.05245
$275$	6.18833e6	−	1.07185e7i	0.0179436	−	0.0310792i
$276$	−3.10953e8	−	5.38587e8i	−0.890252	−	1.54196i
$277$	2.00995e8	+	3.48134e8i	0.568207	+	0.984164i	0.996743	+	0.0806391i	$0.0256961\pi$
$277$	2.00995e8	+	3.48134e8i	0.568207	+	0.984164i	−0.428536	+	0.903525i	$0.640971\pi$
$278$	4.34645e8	−	7.52828e8i	1.21333	−	2.10155i
$279$	−2.99067e6			−0.00824430
$280$	6.34020e8	−	1.39844e8i	1.72604	−	0.380707i
$281$	2.80445e7			0.0754008			0.0377004	−	0.999289i	$-0.487997\pi$
$281$	2.80445e7			0.0754008			0.0377004	+	0.999289i	$0.487997\pi$
$282$	−2.96897e8	+	5.14241e8i	−0.788377	+	1.36551i
$283$	−1.03202e6	−	1.78751e6i	−0.00270667	−	0.00468809i	0.864669	−	0.502342i	$-0.167528\pi$
$283$	−1.03202e6	−	1.78751e6i	−0.00270667	−	0.00468809i	−0.867376	+	0.497654i	$0.834195\pi$
$284$	−6.59646e8	−	1.14254e9i	−1.70882	−	2.95977i
$285$	4.94417e6	−	8.56356e6i	0.0126513	−	0.0219128i
$286$	6.26038e7			0.158241
$287$	4.81999e8	+	5.27147e8i	1.20354	+	1.31627i
$288$	3.68636e7			0.0909336
$289$	1.27238e8	−	2.20382e8i	0.310080	−	0.537074i
$290$	1.03136e8	+	1.78637e8i	0.248323	+	0.430108i
$291$	−2.65722e8	−	4.60244e8i	−0.632123	−	1.09487i
$292$	1.08509e8	−	1.87942e8i	0.255049	−	0.441758i
$293$	−3.77433e8			−0.876604			−0.438302	−	0.898828i	$-0.644420\pi$
$293$	−3.77433e8			−0.876604			−0.438302	+	0.898828i	$0.644420\pi$
$294$	−6.96806e7	+	7.77201e8i	−0.159918	+	1.78368i
$295$	4.10032e8			0.929909
$296$	−7.78855e7	+	1.34902e8i	−0.174556	+	0.302340i
$297$	−1.59296e7	−	2.75908e7i	−0.0352822	−	0.0611106i
$298$	4.16250e7	+	7.20967e7i	0.0911166	+	0.157819i
$299$	−2.21159e8	+	3.83058e8i	−0.478470	+	0.828734i
$300$	5.66295e8			1.21093
$301$	−3.85634e8	−	4.21755e8i	−0.815066	−	0.891411i
$302$	−1.19304e9			−2.49248
$303$	2.63627e8	−	4.56615e8i	0.544428	−	0.942977i
$304$	−2.12998e7	−	3.68923e7i	−0.0434828	−	0.0753145i
$305$	−2.62514e8	−	4.54687e8i	−0.529788	−	0.917620i
$306$	−1.51662e7	+	2.62686e7i	−0.0302587	+	0.0524096i
$307$	5.18232e8			1.02221			0.511105	−	0.859519i	$-0.329236\pi$
$307$	5.18232e8			1.02221			0.511105	+	0.859519i	$0.329236\pi$
$308$	−8.23255e7	+	1.81583e7i	−0.160549	+	0.0354118i
$309$	−3.82238e8			−0.737021
$310$	5.16178e7	−	8.94046e7i	0.0984087	−	0.170449i
$311$	−1.41916e8	−	2.45806e8i	−0.267529	−	0.463374i	0.700694	−	0.713462i	$-0.252874\pi$
$311$	−1.41916e8	−	2.45806e8i	−0.267529	−	0.463374i	−0.968223	+	0.250088i	$0.919540\pi$
$312$	8.32421e8	+	1.44180e9i	1.55168	+	2.68759i
$313$	1.65050e7	−	2.85875e7i	0.0304236	−	0.0526952i	−0.850413	−	0.526116i	$-0.823648\pi$
$313$	1.65050e7	−	2.85875e7i	0.0304236	−	0.0526952i	0.880836	+	0.473421i	$0.156981\pi$
$314$	5.93959e8			1.08269
$315$	−6.17867e6	+	1.95230e7i	−0.0111380	+	0.0351933i
$316$	8.53387e8			1.52139
$317$	−5.46589e8	+	9.46720e8i	−0.963726	+	1.66922i	−0.250727	+	0.968058i	$0.580669\pi$
$317$	−5.46589e8	+	9.46720e8i	−0.963726	+	1.66922i	−0.713000	+	0.701165i	$0.752664\pi$
$318$	2.54223e8	+	4.40327e8i	0.443323	+	0.767858i
$319$	−7.78348e6	−	1.34814e7i	−0.0134248	−	0.0232524i
$320$	−1.66998e8	+	2.89249e8i	−0.284896	+	0.493454i
$321$	−1.32052e8			−0.222832
$322$	2.54989e8	−	8.05699e8i	0.425623	−	1.34486i
$323$	1.40285e7			0.0231635
$324$	6.89864e8	−	1.19488e9i	1.12682	−	1.95172i
$325$	−2.01383e8	−	3.48805e8i	−0.325410	−	0.563626i
$326$	3.36003e8	+	5.81974e8i	0.537133	+	0.930341i
$327$	−4.51816e8	+	7.82568e8i	−0.714569	+	1.23767i
$328$	−2.91167e9			−4.55600
$329$	−5.55365e8	+	1.22495e8i	−0.859791	+	0.189641i
$330$	5.56983e7			0.0853185
$331$	1.60956e8	−	2.78785e8i	0.243955	−	0.422543i	−0.717882	−	0.696165i	$-0.754888\pi$
$331$	1.60956e8	−	2.78785e8i	0.243955	−	0.422543i	0.961837	+	0.273622i	$0.0882216\pi$
$332$	−8.23692e7	−	1.42668e8i	−0.123533	−	0.213965i
$333$	−2.45648e6	−	4.25474e6i	−0.00364551	−	0.00631420i
$334$	1.95838e8	−	3.39201e8i	0.287597	−	0.498132i
$335$	7.29912e8			1.06075
$336$	−1.05633e9	−	1.15528e9i	−1.51919	−	1.66149i
$337$	1.31007e9			1.86461			0.932307	−	0.361668i	$-0.117793\pi$
$337$	1.31007e9			1.86461			0.932307	+	0.361668i	$0.117793\pi$
$338$	3.65297e8	−	6.32713e8i	0.514562	−	0.891248i
$339$	1.65461e8	+	2.86587e8i	0.230673	+	0.399537i
$340$	−3.68993e8	−	6.39115e8i	−0.509146	−	0.881866i
$341$	−3.89550e6	+	6.74721e6i	−0.00532014	+	0.00921476i
$342$	2.73008e6			0.00369048
$343$	−5.94384e8	+	4.53049e8i	−0.795313	+	0.606199i
$344$	2.32954e9			3.08543
$345$	−1.96764e8	+	3.40805e8i	−0.257975	+	0.446826i
$346$	9.72961e8	+	1.68522e9i	1.26278	+	2.18721i
$347$	−8.33411e7	−	1.44351e8i	−0.107079	−	0.185467i	0.807506	−	0.589859i	$-0.200817\pi$
$347$	−8.33411e7	−	1.44351e8i	−0.107079	−	0.185467i	−0.914586	+	0.404392i	$0.867483\pi$
$348$	3.56134e8	−	6.16842e8i	0.452987	−	0.784597i
$349$	7.47430e8			0.941199			0.470599	−	0.882347i	$-0.344038\pi$
$349$	7.47430e8			0.941199			0.470599	+	0.882347i	$0.344038\pi$
$350$	5.19269e8	+	5.67907e8i	0.647372	+	0.708010i
$351$	−1.03677e9			−1.27970
$352$	4.80168e7	−	8.31675e7i	0.0586805	−	0.101638i
$353$	−3.08956e8	−	5.35127e8i	−0.373839	−	0.647509i	0.616313	−	0.787501i	$-0.288625\pi$
$353$	−3.08956e8	−	5.35127e8i	−0.373839	−	0.647509i	−0.990153	+	0.139992i	$0.955292\pi$
$354$	−1.00441e9	−	1.73968e9i	−1.20337	−	2.08429i
$355$	−4.17408e8	+	7.22972e8i	−0.495178	+	0.857674i
$356$	−6.71968e8			−0.789357
$357$	5.03407e8	−	1.11035e8i	0.585572	−	0.129158i
$358$	−1.83910e9			−2.11844
$359$	5.08337e8	−	8.80465e8i	0.579857	−	1.00434i	−0.415638	−	0.909530i	$-0.636442\pi$
$359$	5.08337e8	−	8.80465e8i	0.579857	−	1.00434i	0.995495	−	0.0948120i	$-0.0302250\pi$
$360$	−4.17363e7	−	7.22893e7i	−0.0471471	−	0.0816611i
$361$	4.46305e8	+	7.73022e8i	0.499294	+	0.864802i
$362$	−1.13762e8	+	1.97042e8i	−0.126043	+	0.218312i
$363$	8.82479e8			0.968348
$364$	−8.27786e8	+	2.61559e9i	−0.899629	+	2.84260i
$365$	−1.37323e8			−0.147815
$366$	−1.28610e9	+	2.22759e9i	−1.37117	+	2.37493i
$367$	−7.38499e8	−	1.27912e9i	−0.779864	−	1.35076i	−0.932020	−	0.362407i	$-0.881955\pi$
$367$	−7.38499e8	−	1.27912e9i	−0.779864	−	1.35076i	0.152156	−	0.988356i	$-0.451378\pi$
$368$	8.47670e8	+	1.46821e9i	0.886664	+	1.53575i
$369$	4.59164e7	−	7.95296e7i	0.0475747	−	0.0824018i
$370$	1.69591e8			0.174060
$371$	−1.46934e8	+	4.64274e8i	−0.149387	+	0.472026i
$372$	−3.56478e8			−0.359032
$373$	8.15971e8	−	1.41330e9i	0.814130	−	1.41011i	−0.0958211	−	0.995399i	$-0.530548\pi$
$373$	8.15971e8	−	1.41330e9i	0.814130	−	1.41011i	0.909951	−	0.414716i	$-0.136119\pi$
$374$	3.95094e7	+	6.84323e7i	0.0390526	+	0.0676411i
$375$	−5.22919e8	−	9.05723e8i	−0.512065	−	0.886923i
$376$	1.15913e9	−	2.00767e9i	1.12454	−	1.94776i
$377$	−5.06585e8			−0.486920
$378$	1.93434e9	−	4.26652e8i	1.84210	−	0.406306i
$379$	−3.41392e8			−0.322118			−0.161059	−	0.986945i	$-0.551491\pi$
$379$	−3.41392e8			−0.322118			−0.161059	+	0.986945i	$0.551491\pi$
$380$	−3.32114e7	+	5.75239e7i	−0.0310488	+	0.0537781i
$381$	6.39321e8	+	1.10734e9i	0.592218	+	1.02575i
$382$	−1.09282e9	−	1.89282e9i	−1.00306	−	1.73735i
$383$	1.85545e8	−	3.21374e8i	0.168754	−	0.292290i	−0.769228	−	0.638974i	$-0.779359\pi$
$383$	1.85545e8	−	3.21374e8i	0.168754	−	0.292290i	0.937982	+	0.346684i	$0.112692\pi$
$384$	−2.03877e8			−0.183742
$385$	3.59976e7	+	3.93694e7i	0.0321485	+	0.0351597i
$386$	−3.30189e8			−0.292218
$387$	−3.67365e7	+	6.36294e7i	−0.0322188	+	0.0558045i
$388$	1.78493e9	+	3.09159e9i	1.55135	+	2.68702i
$389$	4.74511e8	+	8.21877e8i	0.408717	+	0.707919i	0.994746	−	0.102371i	$-0.0326430\pi$
$389$	4.74511e8	+	8.21877e8i	0.408717	+	0.707919i	−0.586029	+	0.810290i	$0.699310\pi$
$390$	9.06276e8	−	1.56972e9i	0.773632	−	1.33997i
$391$	−5.58295e8			−0.472329
$392$	2.72044e8	−	3.03431e9i	0.228106	−	2.54424i
$393$	8.73136e8			0.725618
$394$	5.20399e7	−	9.01357e7i	0.0428647	−	0.0742438i
$395$	−2.70001e8	−	4.67656e8i	−0.220433	−	0.381801i
$396$	5.41932e6	+	9.38654e6i	0.00438543	+	0.00759578i
$397$	−3.81892e8	+	6.61456e8i	−0.306319	+	0.530560i	−0.977554	−	0.210685i	$-0.932431\pi$
$397$	−3.81892e8	+	6.61456e8i	−0.306319	+	0.530560i	0.671235	+	0.741244i	$0.265764\pi$
$398$	−1.14588e9			−0.911063
$399$	−3.13095e7	−	3.42422e7i	−0.0246758	−	0.0269871i
$400$	−1.54374e9			−1.20605
$401$	−4.60425e8	+	7.97479e8i	−0.356577	+	0.617610i	−0.987387	−	0.158328i	$-0.949390\pi$
$401$	−4.60425e8	+	7.97479e8i	−0.356577	+	0.617610i	0.630809	+	0.775938i	$0.282723\pi$
$402$	−1.78798e9	−	3.09687e9i	−1.37269	−	2.37756i
$403$	1.26769e8	+	2.19570e8i	0.0964816	+	0.167111i
$404$	−1.77086e9	+	3.06721e9i	−1.33613	+	2.31425i
$405$	−8.73059e8			−0.653057
$406$	9.45158e8	−	2.08471e8i	0.700912	−	0.154598i
$407$	−1.27988e7			−0.00940996
$408$	−1.05069e9	+	1.81984e9i	−0.765883	+	1.32655i
$409$	4.04665e8	+	7.00900e8i	0.292458	+	0.506552i	0.974390	−	0.224863i	$-0.0721935\pi$
$409$	4.04665e8	+	7.00900e8i	0.292458	+	0.506552i	−0.681932	+	0.731415i	$0.738860\pi$
$410$	1.58500e9	+	2.74530e9i	1.13576	+	1.96719i
$411$	3.91517e8	−	6.78127e8i	0.278166	−	0.481798i
$412$	2.56760e9			1.80879
$413$	5.80520e8	−	1.83429e9i	0.405501	−	1.28128i
$414$	−1.08649e8			−0.0752532
$415$	−5.21212e7	+	9.02766e7i	−0.0357970	+	0.0620022i
$416$	−1.56258e9	−	2.70646e9i	−1.06418	−	1.84321i
$417$	9.49705e8	+	1.64494e9i	0.641376	+	1.11090i
$418$	3.55607e6	−	6.15929e6i	0.00238151	−	0.00412490i
$419$	2.33725e9			1.55223			0.776115	−	0.630592i	$-0.217188\pi$
$419$	2.33725e9			1.55223			0.776115	+	0.630592i	$0.217188\pi$
$420$	−7.36477e8	+	2.32708e9i	−0.485050	+	1.53264i
$421$	6.85194e8			0.447534			0.223767	−	0.974643i	$-0.428164\pi$
$421$	6.85194e8			0.447534			0.223767	+	0.974643i	$0.428164\pi$
$422$	−5.78076e8	+	1.00126e9i	−0.374448	+	0.648563i
$423$	3.65585e7	+	6.33213e7i	0.0234854	+	0.0406779i
$424$	−9.92525e8	−	1.71910e9i	−0.632355	−	1.09527i
$425$	2.54186e8	−	4.40263e8i	0.160617	−	0.278196i
$426$	4.08990e9			2.56318
$427$	−2.40573e9	+	5.30624e8i	−1.49537	+	0.329829i
$428$	8.87029e8			0.546871
$429$	−6.83951e7	+	1.18464e8i	−0.0418239	+	0.0724411i
$430$	−1.26811e9	−	2.19644e9i	−0.769164	−	1.33223i
$431$	−7.97694e8	−	1.38165e9i	−0.479917	−	0.831240i	0.519818	−	0.854277i	$-0.326000\pi$
$431$	−7.97694e8	−	1.38165e9i	−0.479917	−	0.831240i	−0.999735	+	0.0230370i	$0.992666\pi$
$432$	−1.98689e9	+	3.44140e9i	−1.18572	+	2.05373i
$433$	−3.20663e9			−1.89820			−0.949098	−	0.314981i	$-0.898002\pi$
$433$	−3.20663e9			−1.89820			−0.949098	+	0.314981i	$0.898002\pi$
$434$	−3.26875e8	−	3.57493e8i	−0.191941	−	0.209920i
$435$	−4.50706e8			−0.262531
$436$	3.03498e9	−	5.25673e9i	1.75369	−	3.03748i
$437$	2.51248e7	+	4.35174e7i	0.0144018	+	0.0249447i
$438$	3.36385e8	+	5.82635e8i	0.191283	+	0.331312i
$439$	−9.31855e8	+	1.61402e9i	−0.525681	+	0.910507i	0.473871	+	0.880594i	$0.342856\pi$
$439$	−9.31855e8	+	1.61402e9i	−0.525681	+	0.910507i	−0.999553	+	0.0299126i	$0.990477\pi$
$440$	−2.17455e8			−0.121698
$441$	7.85893e7	+	5.52811e7i	0.0436343	+	0.0306931i
$442$	2.57146e9			1.41645
$443$	−3.99132e8	+	6.91317e8i	−0.218124	+	0.377802i	−0.954234	−	0.299060i	$-0.903327\pi$
$443$	−3.99132e8	+	6.91317e8i	−0.218124	+	0.377802i	0.736110	+	0.676861i	$0.236660\pi$
$444$	−2.92804e8	−	5.07152e8i	−0.158759	−	0.274978i
$445$	2.12603e8	+	3.68239e8i	0.114369	+	0.198093i
$446$	−3.45483e8	+	5.98394e8i	−0.184397	+	0.319386i
$447$	−1.81902e8			−0.0963301
$448$	1.05753e9	+	1.15659e9i	0.555675	+	0.607723i
$449$	−4.99626e8			−0.260485			−0.130242	−	0.991482i	$-0.541576\pi$
$449$	−4.99626e8			−0.260485			−0.130242	+	0.991482i	$0.541576\pi$
$450$	4.94668e7	−	8.56791e7i	0.0255900	−	0.0443232i
$451$	−1.19617e8	−	2.07183e8i	−0.0614010	−	0.106350i
$452$	−1.11145e9	−	1.92509e9i	−0.566115	−	0.980541i
$453$	1.30340e9	−	2.25756e9i	0.658773	−	1.14103i
$454$	2.03278e8			0.101952
$455$	1.69525e9	−	3.73916e8i	0.843710	−	0.186095i
$456$	1.89135e8			0.0934104
$457$	−1.33706e9	+	2.31585e9i	−0.655305	+	1.13502i	0.326513	+	0.945193i	$0.394126\pi$
$457$	−1.33706e9	+	2.31585e9i	−0.655305	+	1.13502i	−0.981817	+	0.189828i	$0.939207\pi$
$458$	−1.42761e8	−	2.47270e8i	−0.0694354	−	0.120266i
$459$	−6.54308e8	−	1.13329e9i	−0.315818	−	0.547014i
$460$	1.32172e9	−	2.28928e9i	0.633120	−	1.09660i
$461$	−2.67032e9			−1.26943			−0.634716	−	0.772746i	$-0.718883\pi$
$461$	−2.67032e9			−1.26943			−0.634716	+	0.772746i	$0.718883\pi$
$462$	7.88573e7	−	2.49169e8i	0.0372045	−	0.117557i
$463$	1.72345e9			0.806983			0.403492	−	0.914983i	$-0.367796\pi$
$463$	1.72345e9			0.806983			0.403492	+	0.914983i	$0.367796\pi$
$464$	−9.70835e8	+	1.68153e9i	−0.451162	+	0.781435i
$465$	1.12785e8	+	1.95350e8i	0.0520197	+	0.0901008i
$466$	2.38990e9	+	4.13942e9i	1.09403	+	1.89491i
$467$	1.41354e9	−	2.44832e9i	0.642242	−	1.11240i	−0.342689	−	0.939449i	$-0.611338\pi$
$467$	1.41354e9	−	2.44832e9i	0.642242	−	1.11240i	0.984931	−	0.172947i	$-0.0553289\pi$
$468$	3.52715e8			0.159061
$469$	1.03340e9	−	3.26529e9i	0.462557	−	1.46156i
$470$	−2.52395e9			−1.12134
$471$	−6.48904e8	+	1.12393e9i	−0.286159	+	0.495642i
$472$	3.92135e9	+	6.79198e9i	1.71648	+	2.97303i
$473$	9.57023e7	+	1.65761e8i	0.0415823	+	0.0720227i
$474$	−1.32278e9	+	2.29112e9i	−0.570511	+	0.988153i
$475$	−4.57563e7			−0.0195895
$476$	−3.38153e9	+	7.45853e8i	−1.43711	+	0.316978i
$477$	6.26077e7			0.0264127
$478$	−1.23008e9	+	2.13056e9i	−0.515153	+	0.892271i
$479$	1.54711e9	+	2.67967e9i	0.643200	+	1.11405i	0.984714	+	0.174178i	$0.0557268\pi$
$479$	1.54711e9	+	2.67967e9i	0.643200	+	1.11405i	−0.341515	+	0.939876i	$0.610940\pi$
$480$	−1.39022e9	−	2.40793e9i	−0.573771	−	0.993800i
$481$	−2.08251e8	+	3.60701e8i	−0.0853255	+	0.147788i
$482$	−4.61740e9			−1.87816
$483$	1.24603e9	+	1.36274e9i	0.503168	+	0.550298i
$484$	−5.92787e9			−2.37651
$485$	1.12946e9	−	1.95628e9i	0.449547	−	0.778638i
$486$	−2.48219e8	−	4.29928e8i	−0.0980862	−	0.169890i
$487$	2.11545e8	+	3.66407e8i	0.0829949	+	0.143751i	0.904535	−	0.426399i	$-0.140218\pi$
$487$	2.11545e8	+	3.66407e8i	0.0829949	+	0.143751i	−0.821540	+	0.570151i	$0.806885\pi$
$488$	5.02112e9	−	8.69683e9i	1.95583	−	3.38759i
$489$	−1.46834e9			−0.567866
$490$	−3.00902e9	+	1.39526e9i	−1.15542	+	0.535759i
$491$	−9.85934e8			−0.375892			−0.187946	−	0.982179i	$-0.560183\pi$
$491$	−9.85934e8			−0.375892			−0.187946	+	0.982179i	$0.560183\pi$
$492$	5.47309e9	−	9.47968e9i	2.07183	−	3.58852i
$493$	−3.19707e8	−	5.53749e8i	−0.120168	−	0.208137i
$494$	−1.15723e8	−	2.00437e8i	−0.0431891	−	0.0748057i
$495$	3.42922e6	−	5.93958e6i	0.00127080	−	0.00220109i
$496$	9.71773e8			0.357585
$497$	2.64328e9	+	2.89087e9i	0.965821	+	1.05629i
$498$	5.10701e8			0.185295
$499$	2.62370e8	−	4.54437e8i	0.0945282	−	0.163728i	−0.814883	−	0.579625i	$-0.803199\pi$
$499$	2.62370e8	−	4.54437e8i	0.0945282	−	0.163728i	0.909412	+	0.415897i	$0.136532\pi$
$500$	3.51260e9	+	6.08400e9i	1.25671	+	2.17668i
$501$	4.27908e8	+	7.41158e8i	0.152026	+	0.263317i
$502$	−2.03275e9	+	3.52082e9i	−0.717167	+	1.24217i
$503$	4.23277e9			1.48298			0.741492	−	0.670962i	$-0.234119\pi$
$503$	4.23277e9			1.48298			0.741492	+	0.670962i	$0.234119\pi$
$504$	−3.82479e8	+	8.43623e7i	−0.133076	+	0.0293522i
$505$	2.24111e9			0.774362
$506$	−1.41521e8	+	2.45122e8i	−0.0485618	+	0.0841114i
$507$	7.98179e8	+	1.38249e9i	0.272002	+	0.471122i
$508$	−4.29450e9	−	7.43829e9i	−1.45341	−	2.51739i
$509$	1.16011e9	−	2.00938e9i	0.389931	−	0.675381i	−0.602508	−	0.798113i	$-0.705832\pi$
$509$	1.16011e9	−	2.00938e9i	0.389931	−	0.675381i	0.992440	+	0.122731i	$0.0391654\pi$
$510$	2.28781e9			0.763704
$511$	−1.94421e8	+	6.14322e8i	−0.0644571	+	0.203668i
$512$	5.97263e9			1.96662
$513$	−5.88913e7	+	1.02003e8i	−0.0192593	+	0.0333581i
$514$	−5.39608e9	−	9.34628e9i	−1.75270	−	3.03576i
$515$	−8.12359e8	−	1.40705e9i	−0.262073	−	0.453924i
$516$	−4.37887e9	+	7.58442e9i	−1.40310	+	2.43024i
$517$	1.90478e8			0.0606216
$518$	2.40106e8	−	7.58675e8i	0.0759013	−	0.239829i
$519$	−4.25186e9			−1.33504
$520$	−3.53824e9	+	6.12841e9i	−1.10351	+	1.91133i
$521$	−1.37985e9	−	2.38996e9i	−0.427463	−	0.740388i	0.569184	−	0.822210i	$-0.307259\pi$
$521$	−1.37985e9	−	2.38996e9i	−0.427463	−	0.740388i	−0.996647	+	0.0818227i	$0.973926\pi$
$522$	−6.22178e7	−	1.07764e8i	−0.0191456	−	0.0331611i
$523$	−2.22280e9	+	3.85001e9i	−0.679430	+	1.17681i	0.295722	+	0.955274i	$0.404440\pi$
$523$	−2.22280e9	+	3.85001e9i	−0.679430	+	1.17681i	−0.975153	+	0.221534i	$0.928894\pi$
$524$	−5.86510e9			−1.78080
$525$	−1.64194e9	+	3.62158e8i	−0.495222	+	0.109230i
$526$	8.14184e9			2.43934
$527$	−1.60008e8	+	2.77142e8i	−0.0476217	+	0.0824832i
$528$	2.62149e8	+	4.54055e8i	0.0775048	+	0.134242i
$529$	7.02518e8	+	1.21680e9i	0.206330	+	0.357374i
$530$	−1.08058e9	+	1.87163e9i	−0.315278	+	0.546077i
$531$	−2.47356e8			−0.0716954
$532$	2.10315e8	+	2.30015e8i	0.0605591	+	0.0662315i
$533$	−7.78524e9			−2.22703
$534$	1.04158e9	−	1.80406e9i	0.296003	−	0.512692i
$535$	−2.80646e8	−	4.86092e8i	−0.0792355	−	0.137240i
$536$	6.98054e9	+	1.20907e10i	1.95800	+	3.39135i
$537$	2.00923e9	−	3.48009e9i	0.559912	−	0.969796i
$538$	7.46997e9			2.06814
$539$	2.27086e8	−	1.05298e8i	0.0624639	−	0.0289640i
$540$	6.19608e9			1.69332
$541$	2.67831e9	−	4.63897e9i	0.727228	−	1.25960i	−0.230822	−	0.972996i	$-0.574141\pi$
$541$	2.67831e9	−	4.63897e9i	0.727228	−	1.25960i	0.958050	−	0.286601i	$-0.0925253\pi$
$542$	2.05148e9	+	3.55327e9i	0.553440	+	0.958586i
$543$	−2.48572e8	−	4.30539e8i	−0.0666273	−	0.115402i
$544$	1.97229e9	−	3.41611e9i	0.525261	−	0.909779i
$545$	−3.84092e9			−1.01636
$546$	−5.73910e9	−	6.27666e9i	−1.50893	−	1.65027i
$547$	1.36408e9			0.356357			0.178178	−	0.983998i	$-0.442980\pi$
$547$	1.36408e9			0.356357			0.178178	+	0.983998i	$0.442980\pi$
$548$	−2.62993e9	+	4.55517e9i	−0.682672	+	1.18242i
$549$	1.58364e8	+	2.74295e8i	0.0408464	+	0.0707480i
$550$	−1.28866e8	−	2.23203e8i	−0.0330271	−	0.0572046i
$551$	−2.87754e7	+	4.98405e7i	−0.00732809	+	0.0126926i
$552$	−7.52703e9			−1.90474
$553$	−2.47435e9	+	5.45759e8i	−0.622189	+	0.137234i
$554$	8.37108e9			2.09169
$555$	−1.85280e8	+	3.20914e8i	−0.0460047	+	0.0796825i
$556$	−6.37944e9	−	1.10495e10i	−1.57406	−	2.72635i
$557$	−1.54479e9	−	2.67566e9i	−0.378771	−	0.656051i	0.612113	−	0.790770i	$-0.290320\pi$
$557$	−1.54479e9	−	2.67566e9i	−0.378771	−	0.656051i	−0.990884	+	0.134720i	$0.956987\pi$
$558$	−3.11390e7	+	5.39343e7i	−0.00758725	+	0.0131415i
$559$	6.22875e9			1.50820
$560$	2.00766e9	−	6.34371e9i	0.483096	−	1.52646i
$561$	−1.72657e8			−0.0412871
$562$	2.92001e8	−	5.05760e8i	0.0693916	−	0.120190i
$563$	9.48459e8	+	1.64278e9i	0.223995	+	0.387971i	0.956018	−	0.293309i	$-0.0947566\pi$
$563$	9.48459e8	+	1.64278e9i	0.223995	+	0.387971i	−0.732022	+	0.681281i	$0.761423\pi$
$564$	4.35766e9	+	7.54769e9i	1.02277	+	1.77148i
$565$	−7.03299e8	+	1.21815e9i	−0.164048	+	0.284139i
$566$	−4.29817e7			−0.00996383
$567$	−1.23607e9	+	3.90567e9i	−0.284776	+	0.899818i
$568$	−1.59676e10			−3.65612
$569$	−4.17854e9	+	7.23744e9i	−0.950893	+	1.64699i	−0.207393	+	0.978258i	$0.566498\pi$
$569$	−4.17854e9	+	7.23744e9i	−0.950893	+	1.64699i	−0.743499	+	0.668737i	$0.766835\pi$
$570$	−1.02958e8	−	1.78328e8i	−0.0232861	−	0.0403328i
$571$	−2.33771e9	−	4.04904e9i	−0.525491	−	0.910177i	−0.999559	−	0.0296886i	$-0.990548\pi$
$571$	−2.33771e9	−	4.04904e9i	−0.525491	−	0.910177i	0.474069	−	0.880488i	$-0.342785\pi$
$572$	4.59429e8	−	7.95755e8i	0.102644	−	0.177784i
$573$	4.77564e9			1.06045
$574$	1.45253e10	−	3.20379e9i	3.20577	−	0.707086i
$575$	1.82097e9			0.399452
$576$	1.00743e8	−	1.74492e8i	0.0219653	−	0.0380450i
$577$	3.88363e8	+	6.72664e8i	0.0841632	+	0.145775i	0.905034	−	0.425338i	$-0.139845\pi$
$577$	3.88363e8	+	6.72664e8i	0.0841632	+	0.145775i	−0.820871	+	0.571113i	$0.806512\pi$
$578$	−2.64961e9	−	4.58926e9i	−0.570735	−	0.988542i
$579$	3.60733e8	−	6.24808e8i	0.0772345	−	0.133774i
$580$	3.02752e9			0.644302
$581$	3.30064e8	+	3.60980e8i	0.0698202	+	0.0763601i
$582$	−1.10668e10			−2.32698
$583$	8.15498e7	−	1.41248e8i	0.0170445	−	0.0295219i
$584$	−1.31330e9	−	2.27470e9i	−0.272846	−	0.472583i
$585$	−1.11595e8	−	1.93288e8i	−0.0230461	−	0.0399171i
$586$	−3.92985e9	+	6.80670e9i	−0.806741	+	1.39732i
$587$	1.89326e9			0.386347			0.193174	−	0.981165i	$-0.438122\pi$
$587$	1.89326e9			0.386347			0.193174	+	0.981165i	$0.438122\pi$
$588$	9.36760e9	+	6.58933e9i	1.90024	+	1.33666i
$589$	2.88032e7			0.00580814
$590$	4.26927e9	−	7.39459e9i	0.855798	−	1.48229i
$591$	1.13708e8	+	1.96948e8i	0.0226586	+	0.0392459i
$592$	7.98195e8	+	1.38251e9i	0.158119	+	0.273870i
$593$	−2.22153e9	+	3.84780e9i	−0.437483	+	0.757742i	−0.997495	−	0.0707423i	$-0.977463\pi$
$593$	−2.22153e9	+	3.84780e9i	−0.437483	+	0.757742i	0.560012	+	0.828485i	$0.310797\pi$
$594$	−6.63437e8			−0.129881
$595$	1.47860e9	+	1.61710e9i	0.287768	+	0.314722i
$596$	1.22189e9			0.236412
$597$	1.25188e9	−	2.16832e9i	0.240798	−	0.417074i
$598$	4.60542e9	+	7.97683e9i	0.880675	+	1.52537i
$599$	−1.11024e9	−	1.92299e9i	−0.211068	−	0.365581i	0.740981	−	0.671526i	$-0.234361\pi$
$599$	−1.11024e9	−	1.92299e9i	−0.211068	−	0.365581i	−0.952049	+	0.305945i	$0.901028\pi$
$600$	3.42698e9	−	5.93570e9i	0.647713	−	1.12187i
$601$	5.04814e9			0.948574			0.474287	−	0.880370i	$-0.342706\pi$
$601$	5.04814e9			0.948574			0.474287	+	0.880370i	$0.342706\pi$
$602$	−1.16212e10	+	2.56326e9i	−2.17103	+	0.478856i
$603$	−4.40327e8			−0.0817833
$604$	−8.75534e9	+	1.51647e10i	−1.61675	+	2.80030i
$605$	1.87551e9	+	3.24847e9i	0.344330	+	0.596397i
$606$	−5.48979e9	−	9.50859e9i	−1.00208	−	1.73565i
$607$	1.41439e9	−	2.44980e9i	0.256691	−	0.444601i	−0.708663	−	0.705547i	$-0.750701\pi$
$607$	1.41439e9	−	2.44980e9i	0.256691	−	0.444601i	0.965353	+	0.260946i	$0.0840346\pi$
$608$	−3.55034e8			−0.0640631
$609$	−6.38107e8	+	2.01625e9i	−0.114481	+	0.361730i
$610$	−1.09332e10			−1.95026
$611$	3.09929e9	−	5.36813e9i	0.549691	−	0.952092i
$612$	2.22599e8	+	3.85553e8i	0.0392548	+	0.0679914i
$613$	1.60514e9	+	2.78018e9i	0.281450	+	0.487486i	0.971742	−	0.236045i	$-0.0758513\pi$
$613$	1.60514e9	+	2.78018e9i	0.281450	+	0.487486i	−0.690292	+	0.723531i	$0.742518\pi$
$614$	5.39585e9	−	9.34589e9i	0.940742	−	1.62941i
$615$	−6.92649e9			−1.20074
$616$	−3.07871e8	+	9.72793e8i	−0.0530684	+	0.167683i
$617$	2.94679e9			0.505070			0.252535	−	0.967588i	$-0.418736\pi$
$617$	2.94679e9			0.505070			0.252535	+	0.967588i	$0.418736\pi$
$618$	−3.97988e9	+	6.89335e9i	−0.678282	+	1.17482i
$619$	−3.20494e9	−	5.55111e9i	−0.543128	−	0.940725i	−0.998722	−	0.0505376i	$-0.983907\pi$
$619$	−3.20494e9	−	5.55111e9i	−0.543128	−	0.940725i	0.455594	−	0.890188i	$-0.349427\pi$
$620$	−7.57612e8	−	1.31222e9i	−0.127666	−	0.221124i
$621$	2.34370e9	−	4.05941e9i	0.392719	−	0.680209i
$622$	−5.91055e9			−0.984831
$623$	1.94833e9	−	4.29738e8i	0.322816	−	0.0712025i
$624$	1.70618e10			2.81112
$625$	6.32055e8	−	1.09475e9i	0.103556	−	0.179364i
$626$	−3.43702e8	−	5.95309e8i	−0.0559978	−	0.0969911i
$627$	7.77005e6	+	1.34581e7i	0.00125889	+	0.00218046i
$628$	4.35887e9	−	7.54979e9i	0.702288	−	1.21640i
$629$	−5.25710e8			−0.0842304
$630$	2.87749e8	+	3.14702e8i	0.0458482	+	0.0501426i
$631$	−1.37351e9			−0.217636			−0.108818	−	0.994062i	$-0.534707\pi$
$631$	−1.37351e9			−0.217636			−0.108818	+	0.994062i	$0.534707\pi$
$632$	5.16433e9	−	8.94489e9i	0.813776	−	1.40950i
$633$	−1.26310e9	−	2.18776e9i	−0.197936	−	0.342836i
$634$	1.13822e10	+	1.97146e10i	1.77384	+	3.07238i
$635$	−2.71746e9	+	4.70677e9i	−0.421167	+	0.729483i
$636$	7.46264e9			1.15025
$637$	7.27392e8	−	8.11315e9i	0.111501	−	1.24366i
$638$	−3.24168e8			−0.0494194
$639$	2.51806e8	−	4.36140e8i	0.0381780	−	0.0661262i
$640$	−4.33293e8	−	7.50485e8i	−0.0653358	−	0.113165i
$641$	2.39553e9	+	4.14917e9i	0.359251	+	0.622241i	0.987836	−	0.155500i	$-0.0496989\pi$
$641$	2.39553e9	+	4.14917e9i	0.359251	+	0.622241i	−0.628585	+	0.777741i	$0.716366\pi$
$642$	−1.37493e9	+	2.38145e9i	−0.205072	+	0.355196i
$643$	−9.77303e9			−1.44974			−0.724871	−	0.688884i	$-0.758101\pi$
$643$	−9.77303e9			−1.44974			−0.724871	+	0.688884i	$0.758101\pi$
$644$	−8.36993e9	−	9.15391e9i	−1.23487	−	1.35054i
$645$	5.54169e9			0.813173
$646$	1.46066e8	−	2.52993e8i	0.0213174	−	0.0369228i
$647$	−5.49025e9	−	9.50939e9i	−0.796943	−	1.38035i	−0.921598	−	0.388145i	$-0.873116\pi$
$647$	−5.49025e9	−	9.50939e9i	−0.796943	−	1.38035i	0.124656	−	0.992200i	$-0.460217\pi$
$648$	−8.34953e9	−	1.44618e10i	−1.20545	−	2.08790i
$649$	−3.22194e8	+	5.58056e8i	−0.0462659	+	0.0801349i
$650$	−8.38722e9			−1.19790
$651$	1.03359e9	−	2.27975e8i	0.146830	−	0.0323858i
$652$	9.86326e9			1.39365
$653$	−2.11369e9	+	3.66101e9i	−0.297060	+	0.514523i	−0.975462	−	0.220168i	$-0.929340\pi$
$653$	−2.11369e9	+	3.66101e9i	−0.297060	+	0.514523i	0.678402	+	0.734691i	$0.262673\pi$
$654$	9.40865e9	+	1.62963e10i	1.31524	+	2.27806i
$655$	1.85565e9	+	3.21408e9i	0.258019	+	0.446902i
$656$	−1.49199e10	+	2.58420e10i	−2.06348	+	3.57406i
$657$	8.28417e7			0.0113965
$658$	−3.57338e9	+	1.12910e10i	−0.488978	+	1.54504i
$659$	1.09220e9			0.148663			0.0743314	−	0.997234i	$-0.476318\pi$
$659$	1.09220e9			0.148663			0.0743314	+	0.997234i	$0.476318\pi$
$660$	4.08752e8	−	7.07979e8i	0.0553421	−	0.0958554i
$661$	5.74047e9	+	9.94278e9i	0.773111	+	1.33907i	0.935850	+	0.352399i	$0.114634\pi$
$661$	5.74047e9	+	9.94278e9i	0.773111	+	1.33907i	−0.162738	+	0.986669i	$0.552033\pi$
$662$	−3.35177e9	−	5.80543e9i	−0.449026	−	0.777735i
$663$	−2.80933e9	+	4.86591e9i	−0.374374	+	0.648435i
$664$	−1.99385e9			−0.264305
$665$	5.95069e7	−	1.88027e8i	0.00784678	−	0.0247938i
$666$	−1.02308e8			−0.0134199
$667$	1.14518e9	−	1.98351e9i	0.149428	−	0.258817i
$668$	−2.87438e9	−	4.97857e9i	−0.373101	−	0.646230i
$669$	−7.54884e8	−	1.30750e9i	−0.0974741	−	0.168830i
$670$	7.59987e9	−	1.31634e10i	0.976213	−	1.69085i
$671$	8.25110e8			0.105435
$672$	−1.27402e10	+	2.81007e9i	−1.61951	+	0.357211i
$673$	7.00125e9			0.885366			0.442683	−	0.896678i	$-0.354027\pi$
$673$	7.00125e9			0.885366			0.442683	+	0.896678i	$0.354027\pi$
$674$	1.36405e10	−	2.36260e10i	1.71601	−	2.97222i
$675$	2.13413e9	+	3.69642e9i	0.267090	+	0.462613i
$676$	−5.36159e9	−	9.28655e9i	−0.667545	−	1.15622i
$677$	−6.16353e9	+	1.06756e10i	−0.763430	+	1.32230i	0.177642	+	0.984095i	$0.443153\pi$
$677$	−6.16353e9	+	1.06756e10i	−0.763430	+	1.32230i	−0.941072	+	0.338205i	$0.890180\pi$
$678$	6.89115e9			0.849156
$679$	−7.15244e9	−	7.82239e9i	−0.876819	−	0.958948i
$680$	−8.93196e9			−1.08935
$681$	−2.22083e8	+	3.84659e8i	−0.0269464	+	0.0466725i
$682$	8.11203e7	+	1.40504e8i	0.00979229	+	0.0169607i
$683$	6.31879e9	+	1.09445e10i	0.758860	+	1.31438i	0.943432	+	0.331565i	$0.107577\pi$
$683$	6.31879e9	+	1.09445e10i	0.758860	+	1.31438i	−0.184572	+	0.982819i	$0.559090\pi$
$684$	2.00351e7	−	3.47019e7i	0.00239384	−	0.00414626i
$685$	3.32831e9			0.395647
$686$	1.98161e9	+	1.54364e10i	0.234360	+	1.82562i
$687$	6.23870e8			0.0734083
$688$	1.19370e10	−	2.06754e10i	1.39744	−	2.42044i
$689$	−2.65382e9	−	4.59655e9i	−0.309104	−	0.535383i
$690$	4.09742e9	+	7.09694e9i	0.474831	+	0.822431i
$691$	2.44577e8	−	4.23619e8i	0.0281995	−	0.0488430i	−0.851581	−	0.524223i	$-0.824356\pi$
$691$	2.44577e8	−	4.23619e8i	0.0281995	−	0.0488430i	0.879781	+	0.475380i	$0.157689\pi$
$692$	2.85610e10			3.27644
$693$	−2.17159e7	−	2.37500e7i	−0.00247863	−	0.00271080i
$694$	−3.47100e9			−0.394182
$695$	−4.03676e9	+	6.99187e9i	−0.456127	+	0.790035i
$696$	−4.31035e9	−	7.46574e9i	−0.484596	−	0.839345i
$697$	−4.91328e9	−	8.51006e9i	−0.549613	−	0.951958i
$698$	7.78227e9	−	1.34793e10i	0.866188	−	1.50028i
$699$	−1.04439e10			−1.15663
$700$	1.10294e10	−	2.43272e9i	1.21537	−	0.268070i
$701$	−1.30414e9			−0.142992			−0.0714959	−	0.997441i	$-0.522777\pi$
$701$	−1.30414e9			−0.142992			−0.0714959	+	0.997441i	$0.522777\pi$
$702$	−1.07949e10	+	1.86973e10i	−1.17771	+	2.03985i
$703$	2.36584e7	+	4.09775e7i	0.00256828	+	0.00444838i
$704$	−2.62447e8	−	4.54571e8i	−0.0283489	−	0.0491018i
$705$	2.75743e9	−	4.77600e9i	0.296375	−	0.513337i
$706$	−1.28674e10			−1.37618
$707$	3.17295e9	−	1.00257e10i	0.337672	−	1.06696i
$708$	−2.94840e10			−3.12227
$709$	−4.42227e9	+	7.65959e9i	−0.465997	+	0.807131i	−0.999246	−	0.0388278i	$-0.987638\pi$
$709$	−4.42227e9	+	7.65959e9i	−0.465997	+	0.807131i	0.533249	+	0.845958i	$0.320971\pi$
$710$	8.69214e9	+	1.50552e10i	0.911428	+	1.57864i
$711$	1.62881e8	+	2.82118e8i	0.0169952	+	0.0294366i
$712$	−4.06647e9	+	7.04333e9i	−0.422218	+	0.731304i
$713$	−1.14628e9			−0.118435
$714$	3.23907e9	−	1.02346e10i	0.333025	−	1.05227i
$715$	−5.81432e8			−0.0594878
$716$	−1.34966e10	+	2.33768e10i	−1.37413	+	2.38006i
$717$	−2.68774e9	−	4.65530e9i	−0.272314	−	0.471662i
$718$	−1.05856e10	−	1.83349e10i	−1.06729	−	1.84860i
$719$	7.53570e9	−	1.30522e10i	0.756088	−	1.30958i	−0.188743	−	0.982026i	$-0.560441\pi$
$719$	7.53570e9	−	1.30522e10i	0.756088	−	1.30958i	0.944832	−	0.327557i	$-0.106225\pi$
$720$	−8.55453e8			−0.0854147
$721$	−7.44462e9	+	1.64204e9i	−0.739723	+	0.163158i
$722$	1.85878e10			1.83801
$723$	5.04453e9	−	8.73739e9i	0.496406	−	0.859800i
$724$	1.66973e9	+	2.89205e9i	0.163516	+	0.283218i
$725$	1.04278e9	+	1.80614e9i	0.101627	+	0.176023i
$726$	9.18841e9	−	1.59148e10i	0.891173	−	1.54356i
$727$	−4.87633e9			−0.470677			−0.235338	−	0.971914i	$-0.575620\pi$
$727$	−4.87633e9			−0.470677			−0.235338	+	0.971914i	$0.575620\pi$
$728$	2.24063e10	+	2.45050e10i	2.15234	+	2.35394i
$729$	1.09573e10			1.04750
$730$	−1.42982e9	+	2.47651e9i	−0.136035	+	0.235619i
$731$	3.93098e9	+	6.80866e9i	0.372212	+	0.644689i
$732$	1.88765e10	+	3.26950e10i	1.77882	+	3.08101i
$733$	−2.55573e9	+	4.42665e9i	−0.239691	+	0.415156i	−0.960625	−	0.277847i	$-0.910379\pi$
$733$	−2.55573e9	+	4.42665e9i	−0.239691	+	0.415156i	0.720935	+	0.693003i	$0.243713\pi$
$734$	−3.07571e10			−2.87084
$735$	6.47157e8	−	7.21823e9i	0.0601179	−	0.670541i
$736$	1.41293e10			1.30632
$737$	−5.73549e8	+	9.93416e8i	−0.0527757	+	0.0914103i
$738$	−9.56168e8	−	1.65613e9i	−0.0875663	−	0.151669i
$739$	5.73949e9	+	9.94109e9i	0.523140	+	0.906105i	0.999637	+	0.0269293i	$0.00857290\pi$
$739$	5.73949e9	+	9.94109e9i	0.523140	+	0.906105i	−0.476497	+	0.879176i	$0.658094\pi$
$740$	1.24458e9	−	2.15567e9i	0.112904	−	0.195556i
$741$	5.05711e8			0.0456603
$742$	6.84292e9	+	7.48388e9i	0.614933	+	0.672532i
$743$	−3.64003e9			−0.325570			−0.162785	−	0.986662i	$-0.552048\pi$
$743$	−3.64003e9			−0.325570			−0.162785	+	0.986662i	$0.552048\pi$
$744$	−2.15726e9	+	3.73648e9i	−0.192042	+	0.332627i
$745$	−3.86591e8	−	6.69596e8i	−0.0342535	−	0.0593289i
$746$	−1.69918e10	−	2.94307e10i	−1.49849	−	2.59546i
$747$	3.14427e7	−	5.44603e7i	0.00275993	−	0.00478033i
$748$	1.15979e9			0.101326
$749$	−2.57189e9	+	5.67274e8i	−0.223649	+	0.0493295i
$750$	−2.17786e10			−1.88502
$751$	1.86199e9	−	3.22506e9i	0.160412	−	0.277842i	−0.774604	−	0.632446i	$-0.782051\pi$
$751$	1.86199e9	−	3.22506e9i	0.160412	−	0.277842i	0.935017	+	0.354604i	$0.115384\pi$
$752$	−1.18791e10	−	2.05753e10i	−1.01865	−	1.76435i
$753$	−4.44158e9	−	7.69303e9i	−0.379101	−	0.656622i
$754$	−5.27459e9	+	9.13585e9i	−0.448114	+	0.776156i
$755$	1.10803e10			0.936998
$756$	8.77236e9	−	2.77184e10i	0.738398	−	2.33315i
$757$	−1.47428e10			−1.23522			−0.617611	−	0.786484i	$-0.711899\pi$
$757$	−1.47428e10			−1.23522			−0.617611	+	0.786484i	$0.711899\pi$
$758$	−3.55458e9	+	6.15672e9i	−0.296447	+	0.513460i
$759$	−3.09225e8	−	5.35594e8i	−0.0256702	−	0.0444620i
$760$	4.01963e8	+	6.96220e8i	0.0332153	+	0.0575306i
$761$	3.67298e9	−	6.36179e9i	0.302115	−	0.523278i	−0.674500	−	0.738275i	$-0.735641\pi$
$761$	3.67298e9	−	6.36179e9i	0.302115	−	0.523278i	0.976615	+	0.214997i	$0.0689740\pi$
$762$	2.66265e10			2.18008
$763$	−5.43795e9	+	1.71825e10i	−0.443199	+	1.40040i
$764$	−3.20793e10			−2.60255
$765$	1.40855e8	−	2.43969e8i	0.0113752	−	0.0197024i
$766$	−3.86381e9	−	6.69231e9i	−0.310610	−	0.537992i
$767$	1.04849e10	+	1.81604e10i	0.839039	+	1.45326i
$768$	−7.15172e9	+	1.23871e10i	−0.569700	+	0.986749i
$769$	9.27906e9			0.735803			0.367902	−	0.929865i	$-0.380076\pi$
$769$	9.27906e9			0.735803			0.367902	+	0.929865i	$0.380076\pi$
$770$	1.08480e9	−	2.39271e8i	0.0856314	−	0.0188874i
$771$	2.35810e10			1.85298
$772$	−2.42315e9	+	4.19702e9i	−0.189548	+	0.328307i
$773$	−4.84009e9	−	8.38329e9i	−0.376900	−	0.652809i	0.613710	−	0.789532i	$-0.289676\pi$
$773$	−4.84009e9	−	8.38329e9i	−0.376900	−	0.652809i	−0.990609	+	0.136722i	$0.956343\pi$
$774$	7.65003e8	+	1.32502e9i	0.0593020	+	0.102714i
$775$	5.21892e8	−	9.03943e8i	0.0402740	−	0.0697566i
$776$	4.32066e10			3.31920
$777$	1.17330e9	+	1.28320e9i	0.0897298	+	0.0981346i
$778$	1.97625e10			1.50457
$779$	−4.42222e8	+	7.65952e8i	−0.0335166	+	0.0580524i
$780$	−1.33017e10	−	2.30393e10i	−1.00364	−	1.73835i
$781$	−6.55980e8	−	1.13619e9i	−0.0492734	−	0.0853440i
$782$	−5.81299e9	+	1.00684e10i	−0.434686	+	0.752899i
$783$	5.36848e9			0.399655
$784$	−2.55364e10	−	1.79628e10i	−1.89258	−	1.33127i
$785$	−5.51638e9			−0.407015
$786$	9.09112e9	−	1.57463e10i	0.667788	−	1.15664i
$787$	−8.05129e8	−	1.39453e9i	−0.0588781	−	0.101980i	0.835084	−	0.550123i	$-0.185419\pi$
$787$	−8.05129e8	−	1.39453e9i	−0.0588781	−	0.101980i	−0.893962	+	0.448143i	$0.852086\pi$
$788$	−7.63807e8	−	1.32295e9i	−0.0556086	−	0.0963169i
$789$	−8.89501e9	+	1.54066e10i	−0.644729	+	1.11670i
$790$	−1.12451e10			−0.811460
$791$	4.45372e9	+	4.87088e9i	0.319967	+	0.349937i
$792$	1.31182e8			0.00938286
$793$	1.34255e10	−	2.32536e10i	0.956036	−	1.65590i
$794$	7.95254e9	+	1.37742e10i	0.563812	+	0.976551i
$795$	−2.36109e9	−	4.08953e9i	−0.166659	−	0.288661i
$796$	−8.40924e9	+	1.45652e10i	−0.590964	+	1.02358i
$797$	1.04405e10			0.730497			0.365249	−	0.930910i	$-0.380984\pi$
$797$	1.04405e10			0.730497			0.365249	+	0.930910i	$0.380984\pi$
$798$	−9.43526e8	+	2.08111e8i	−0.0657270	+	0.0144972i
$799$	7.82388e9			0.542636
$800$	−6.43295e9	+	1.11422e10i	−0.444217	+	0.769406i
$801$	−1.28255e8	−	2.22144e8i	−0.00881779	−	0.0152729i
$802$	9.58792e9	+	1.66068e10i	0.656318	+	1.13678i
$803$	1.07906e8	−	1.86898e8i	0.00735427	−	0.0127380i
$804$	−5.24856e10			−3.56159
$805$	−2.36820e9	+	7.48291e9i	−0.160005	+	0.505574i
$806$	5.27968e9			0.355169
$807$	−8.16098e9	+	1.41352e10i	−0.546619	+	0.946772i
$808$	2.14330e10	+	3.71230e10i	1.42936	+	2.47573i
$809$	−9.81852e9	−	1.70062e10i	−0.651968	−	1.12924i	−0.982645	−	0.185497i	$-0.940610\pi$
$809$	−9.81852e9	−	1.70062e10i	−0.651968	−	1.12924i	0.330677	−	0.943744i	$-0.392723\pi$
$810$	−9.09033e9	+	1.57449e10i	−0.601010	+	1.04098i
$811$	−2.66078e10			−1.75161			−0.875803	−	0.482669i	$-0.839668\pi$
$811$	−2.66078e10			−1.75161			−0.875803	+	0.482669i	$0.839668\pi$
$812$	4.28634e9	−	1.35438e10i	0.280958	−	0.887755i
$813$	−8.96503e9			−0.585106
$814$	−1.33261e8	+	2.30815e8i	−0.00866001	+	0.0149996i
$815$	−3.12062e9	−	5.40507e9i	−0.201925	−	0.349744i
$816$	1.07678e10	+	1.86503e10i	0.693762	+	1.20163i
$817$	3.53810e8	−	6.12816e8i	0.0226983	−	0.0393145i
$818$	1.68535e10			1.07660
$819$	−1.02268e9	+	2.25568e8i	−0.0650496	+	0.0143478i
$820$	4.65272e10			2.94685
$821$	3.57247e9	−	6.18771e9i	0.225304	−	0.390237i	−0.731107	−	0.682263i	$-0.760996\pi$
$821$	3.57247e9	−	6.18771e9i	0.225304	−	0.390237i	0.956410	+	0.292026i	$0.0943293\pi$
$822$	−8.15298e9	−	1.41214e10i	−0.511994	−	0.886800i
$823$	−4.17193e9	−	7.22600e9i	−0.260878	−	0.451855i	0.705597	−	0.708613i	$-0.250679\pi$
$823$	−4.17193e9	−	7.22600e9i	−0.260878	−	0.451855i	−0.966476	+	0.256759i	$0.917345\pi$
$824$	1.55381e10	−	2.69127e10i	0.967501	−	1.67576i
$825$	5.63149e8			0.0349168
$826$	−2.70356e10	−	2.95679e10i	−1.66919	−	1.82554i
$827$	−2.92874e10			−1.80058			−0.900288	−	0.435295i	$-0.856644\pi$
$827$	−2.92874e10			−1.80058			−0.900288	+	0.435295i	$0.856644\pi$
$828$	−7.97340e8	+	1.38103e9i	−0.0488132	+	0.0845469i
$829$	4.01367e9	+	6.95188e9i	0.244681	+	0.423800i	0.962042	−	0.272902i	$-0.0879834\pi$
$829$	4.01367e9	+	6.95188e9i	0.244681	+	0.423800i	−0.717361	+	0.696702i	$0.754650\pi$
$830$	1.08538e9	+	1.87993e9i	0.0658881	+	0.114122i
$831$	−9.14546e9	+	1.58404e10i	−0.552843	+	0.957552i
$832$	−1.70812e10			−1.02822
$833$	9.32756e9	−	4.32512e9i	0.559127	−	0.259263i
$834$	3.95535e10			2.36104
$835$	−1.81884e9	+	3.15032e9i	−0.108116	+	0.187263i
$836$	−5.21936e7	−	9.04020e7i	−0.00308955	−	0.00535126i
$837$	−1.34342e9	−	2.32686e9i	−0.0791902	−	0.137161i
$838$	2.43355e10	−	4.21504e10i	1.42852	−	2.47427i
$839$	5.19771e9			0.303840			0.151920	−	0.988393i	$-0.451454\pi$
$839$	5.19771e9			0.303840			0.151920	+	0.988393i	$0.451454\pi$
$840$	1.99348e10	+	2.18020e10i	1.16047	+	1.26917i
$841$	−1.46267e10			−0.847933
$842$	7.13427e9	−	1.23569e10i	0.411867	−	0.713375i
$843$	6.38025e8	+	1.10509e9i	0.0366810	+	0.0635334i
$844$	8.48462e9	+	1.46958e10i	0.485774	+	0.841384i
$845$	−3.39269e9	+	5.87631e9i	−0.193440	+	0.335047i
$846$	1.52260e9			0.0864547
$847$	1.71875e10	−	3.79100e9i	0.971899	−	0.214369i
$848$	−2.03434e10			−1.14562
$849$	4.69578e7	−	8.13333e7i	0.00263348	−	0.00456133i
$850$	−5.29319e9	−	9.16808e9i	−0.295632	−	0.512050i
$851$	−9.41535e8	−	1.63079e9i	−0.0523701	−	0.0907076i
$852$	3.00144e10	−	5.19865e10i	1.66262	−	2.87973i
$853$	5.41443e9			0.298697			0.149349	−	0.988785i	$-0.452282\pi$
$853$	5.41443e9			0.298697			0.149349	+	0.988785i	$0.452282\pi$
$854$	−1.54792e10	+	4.89102e10i	−0.850442	+	2.68718i
$855$	−2.53555e7			−0.00138737
$856$	5.36793e9	−	9.29752e9i	0.292515	−	0.506651i
$857$	−9.54181e9	−	1.65269e10i	−0.517843	−	0.896930i	−0.999785	−	0.0207269i	$-0.993402\pi$
$857$	−9.54181e9	−	1.65269e10i	−0.517843	−	0.896930i	0.481943	−	0.876203i	$-0.339931\pi$
$858$	1.42426e9	+	2.46690e9i	0.0769813	+	0.133335i
$859$	1.59722e10	−	2.76646e10i	0.859781	−	1.48918i	−0.0123568	−	0.999924i	$-0.503933\pi$
$859$	1.59722e10	−	2.76646e10i	0.859781	−	1.48918i	0.872138	−	0.489261i	$-0.162733\pi$
$860$	−3.72251e10			−1.99568
$861$	−9.80647e9	+	3.09859e10i	−0.523603	+	1.65445i
$862$	−3.32225e10			−1.76667
$863$	−5.60085e9	+	9.70096e9i	−0.296631	+	0.513780i	−0.975363	−	0.220606i	$-0.929196\pi$
$863$	−5.60085e9	+	9.70096e9i	−0.296631	+	0.513780i	0.678732	+	0.734386i	$0.262530\pi$
$864$	1.65592e10	+	2.86814e10i	0.873458	+	1.51287i
$865$	−9.03635e9	−	1.56514e10i	−0.474719	−	0.822238i
$866$	−3.33875e10	+	5.78289e10i	−1.74692	+	3.02575i
$867$	1.15789e10			0.603391
$868$	−6.94291e9	+	1.53138e9i	−0.360348	+	0.0794809i
$869$	8.48645e8			0.0438689
$870$	−4.69277e9	+	8.12812e9i	−0.241608	+	0.418478i
$871$	1.86646e10	+	3.23281e10i	0.957096	+	1.65774i
$872$	−3.67328e10	−	6.36230e10i	−1.87606	−	3.24943i
$873$	−6.81359e8	+	1.18015e9i	−0.0346598	+	0.0600326i
$874$	1.04640e9			0.0530162
$875$	−1.40754e10	−	1.53938e10i	−0.710286	−	0.776817i
$876$	9.87447e9			0.496306
$877$	−1.36545e9	+	2.36504e9i	−0.0683563	+	0.118397i	−0.898178	−	0.439632i	$-0.855109\pi$
$877$	−1.36545e9	+	2.36504e9i	−0.0683563	+	0.118397i	0.829822	+	0.558029i	$0.188442\pi$
$878$	1.94050e10	+	3.36105e10i	0.967572	+	1.67588i
$879$	−8.58677e9	−	1.48727e10i	−0.426451	−	0.738634i
$880$	−1.11427e9	+	1.92998e9i	−0.0551191	+	0.0954691i
$881$	2.77466e10			1.36708			0.683539	−	0.729914i	$-0.260440\pi$
$881$	2.77466e10			1.36708			0.683539	+	0.729914i	$0.260440\pi$
$882$	1.81522e9	−	8.41705e8i	0.0890820	−	0.0413067i
$883$	1.21160e10			0.592240			0.296120	−	0.955151i	$-0.404307\pi$
$883$	1.21160e10			0.592240			0.296120	+	0.955151i	$0.404307\pi$
$884$	1.88711e10	−	3.26857e10i	0.918785	−	1.59138i
$885$	9.32840e9	+	1.61573e10i	0.452382	+	0.783549i
$886$	8.31156e9	+	1.43960e10i	0.401480	+	0.695384i
$887$	−3.28535e9	+	5.69039e9i	−0.158070	+	0.273785i	−0.934173	−	0.356822i	$-0.883860\pi$
$887$	−3.28535e9	+	5.69039e9i	−0.158070	+	0.273785i	0.776103	+	0.630606i	$0.217194\pi$
$888$	−7.08771e9			−0.339673
$889$	1.72086e10	+	1.88205e10i	0.821466	+	0.898410i
$890$	8.85451e9			0.421017
$891$	6.86031e8	−	1.18824e9i	0.0324916	−	0.0562772i
$892$	5.07077e9	+	8.78284e9i	0.239220	+	0.414341i
$893$	−3.52096e8	−	6.09849e8i	−0.0165456	−	0.0286577i
$894$	−1.89397e9	+	3.28046e9i	−0.0886529	+	0.153551i
$895$	1.70806e10			0.796385
$896$	−3.97078e9	+	8.75823e8i	−0.184416	+	0.0406760i
$897$	−2.01258e10			−0.931065
$898$	−5.20212e9	+	9.01034e9i	−0.239725	+	0.415216i
$899$	−6.56419e8	−	1.13695e9i	−0.0301316	−	0.0521894i
$900$	−7.26042e8	−	1.25754e9i	−0.0331981	−	0.0575008i
$901$	3.34966e9	−	5.80179e9i	0.152568	−	0.264256i
$902$	−4.98183e9			−0.226030
$903$	7.84588e9	−	2.47910e10i	0.354597	−	1.12043i
$904$	−2.69041e10			−1.21124
$905$	1.05656e9	−	1.83002e9i	0.0473833	−	0.0820703i
$906$	−2.71422e10	−	4.70117e10i	−1.21254	−	2.10018i
$907$	−1.21871e9	−	2.11087e9i	−0.0542344	−	0.0939367i	0.837634	−	0.546232i	$-0.183938\pi$
$907$	−1.21871e9	−	2.11087e9i	−0.0542344	−	0.0939367i	−0.891868	+	0.452296i	$0.850605\pi$
$908$	1.49179e9	−	2.58386e9i	0.0661315	−	0.114543i
$909$	−1.35197e9			−0.0597028
$910$	1.09077e10	−	3.44656e10i	0.479832	−	1.51615i
$911$	2.15307e10			0.943502			0.471751	−	0.881732i	$-0.343622\pi$
$911$	2.15307e10			0.943502			0.471751	+	0.881732i	$0.343622\pi$
$912$	9.69158e8	−	1.67863e9i	0.0423071	−	0.0732780i
$913$	−8.19115e7	−	1.41875e8i	−0.00356203	−	0.00616961i
$914$	2.78430e10	+	4.82254e10i	1.20616	+	2.08913i
$915$	1.19446e10	−	2.06886e10i	0.515463	−	0.892808i
$916$	−4.19071e9			−0.180158
$917$	1.70055e10	−	3.75086e9i	0.728279	−	0.160634i
$918$	−2.72507e10			−1.16259
$919$	−1.64198e10	+	2.84400e10i	−0.697853	+	1.20872i	0.271356	+	0.962479i	$0.412528\pi$
$919$	−1.64198e10	+	2.84400e10i	−0.697853	+	1.20872i	−0.969209	+	0.246238i	$0.920806\pi$
$920$	−1.59970e10	−	2.77075e10i	−0.677298	−	1.17311i
$921$	1.17900e10	+	2.04209e10i	0.497285	+	0.861322i
$922$	−2.78034e10	+	4.81570e10i	−1.16826	+	2.02349i
$923$	−4.26943e10			−1.78716
$924$	−2.58847e9	−	2.83092e9i	−0.107942	−	0.118053i
$925$	1.71469e9			0.0712342
$926$	1.79446e10	−	3.10810e10i	0.742669	−	1.28634i
$927$	4.90064e8	+	8.48816e8i	0.0202057	+	0.0349973i
$928$	8.09116e9	+	1.40143e10i	0.332348	+	0.575643i
$929$	−6.42189e9	+	1.11230e10i	−0.262789	+	0.455164i	−0.966982	−	0.254844i	$-0.917976\pi$
$929$	−6.42189e9	+	1.11230e10i	−0.262789	+	0.455164i	0.704193	+	0.710009i	$0.251309\pi$
$930$	4.69731e9			0.191496
$931$	−7.56896e8	−	5.32413e8i	−0.0307406	−	0.0216235i
$932$	7.01547e10			2.83858
$933$	6.45731e9	−	1.11844e10i	0.260295	−	0.450844i
$934$	−2.94356e10	−	5.09840e10i	−1.18211	−	2.04748i
$935$	−3.66943e8	−	6.35564e8i	−0.0146811	−	0.0254284i
$936$	2.13448e9	−	3.69703e9i	0.0850798	−	0.147363i
$937$	−2.05391e10			−0.815628			−0.407814	−	0.913065i	$-0.633709\pi$
$937$	−2.05391e10			−0.815628			−0.407814	+	0.913065i	$0.633709\pi$
$938$	−4.81271e10	−	5.26350e10i	−1.90405	−	2.08240i
$939$	1.50198e9			0.0592019
$940$	−1.85224e10	+	3.20818e10i	−0.727361	+	1.25983i
$941$	−8.06628e9	−	1.39712e10i	−0.315580	−	0.546601i	0.663981	−	0.747750i	$-0.268866\pi$
$941$	−8.06628e9	−	1.39712e10i	−0.315580	−	0.546601i	−0.979561	+	0.201149i	$0.935532\pi$
$942$	1.35128e10	+	2.34049e10i	0.526706	+	0.912281i
$943$	1.75992e10	−	3.04827e10i	0.683441	−	1.18376i
$944$	8.03746e10			3.10969
$945$	−1.79652e10	+	3.96252e9i	−0.692501	+	0.152743i
$946$	3.98583e9			0.153073
$947$	−1.63336e9	+	2.82905e9i	−0.0624965	+	0.108247i	−0.895581	−	0.444899i	$-0.853240\pi$
$947$	−1.63336e9	+	2.82905e9i	−0.0624965	+	0.108247i	0.833084	+	0.553146i	$0.186573\pi$
$948$	1.94149e10	+	3.36276e10i	0.740127	+	1.28194i
$949$	−3.51150e9	−	6.08210e9i	−0.133371	−	0.231005i
$950$	−4.76416e8	+	8.25177e8i	−0.0180283	+	0.0312259i
$951$	−4.97405e10			−1.87533
$952$	−1.26458e10	+	3.99575e10i	−0.475026	+	1.50096i
$953$	2.56668e10			0.960609			0.480304	−	0.877102i	$-0.340526\pi$
$953$	2.56668e10			0.960609			0.480304	+	0.877102i	$0.340526\pi$
$954$	6.51874e8	−	1.12908e9i	0.0243077	−	0.0421022i
$955$	1.01495e10	+	1.75795e10i	0.377080	+	0.653122i
$956$	1.80543e10	+	3.12710e10i	0.668311	+	1.15755i
$957$	3.54155e8	−	6.13415e8i	0.0130618	−	0.0226236i
$958$	6.44341e10			2.36775
$959$	4.71220e9	−	1.48894e10i	0.172528	−	0.545144i
$960$	−1.51971e10			−0.554385
$961$	1.34278e10	−	2.32576e10i	0.488059	−	0.845343i
$962$	4.33663e9	+	7.51126e9i	0.157051	+	0.272020i
$963$	1.69302e8	+	2.93240e8i	0.00610901	+	0.0105811i
$964$	−3.38856e10	+	5.86915e10i	−1.21827	+	2.11011i
$965$	3.06662e9			0.109854
$966$	3.75496e10	−	8.28220e9i	1.34025	−	0.295614i
$967$	−4.14546e10			−1.47428			−0.737141	−	0.675739i	$-0.763825\pi$
$967$	−4.14546e10			−1.47428			−0.737141	+	0.675739i	$0.763825\pi$
$968$	−3.58729e10	+	6.21337e10i	−1.27117	+	2.20173i
$969$	3.19155e8	+	5.52793e8i	0.0112686	+	0.0195177i
$970$	−2.35200e10	−	4.07378e10i	−0.827439	−	1.43317i
$971$	−7.03038e9	+	1.21770e10i	−0.246440	+	0.426847i	−0.962536	−	0.271155i	$-0.912594\pi$
$971$	−7.03038e9	+	1.21770e10i	−0.246440	+	0.426847i	0.716095	+	0.698003i	$0.245928\pi$
$972$	−7.28639e9			−0.254496
$973$	2.55632e10	+	2.79576e10i	0.889653	+	0.972984i
$974$	8.81046e9			0.305522
$975$	9.16308e9	−	1.58709e10i	0.316611	−	0.548386i
$976$	−5.14580e10	−	8.91279e10i	−1.77165	−	3.06859i
$977$	1.22458e10	+	2.12104e10i	0.420104	+	0.727642i	0.995949	−	0.0899169i	$-0.0286601\pi$
$977$	1.22458e10	+	2.12104e10i	0.420104	+	0.727642i	−0.575845	+	0.817559i	$0.695327\pi$
$978$	−1.52884e10	+	2.64803e10i	−0.522609	+	0.905185i
$979$	−6.68234e8			−0.0227609
$980$	−4.34714e9	+	4.84869e10i	−0.147541	+	1.64563i
$981$	2.31707e9			0.0783607
$982$	−1.02656e10	+	1.77805e10i	−0.345934	+	0.599176i
$983$	−2.87162e10	−	4.97379e10i	−0.964249	−	1.67013i	−0.711619	−	0.702566i	$-0.752038\pi$
$983$	−2.87162e10	−	4.97379e10i	−0.964249	−	1.67013i	−0.252630	−	0.967563i	$-0.581296\pi$
$984$	−6.62417e10	−	1.14734e11i	−2.21640	−	3.83892i
$985$	−4.83319e8	+	8.37133e8i	−0.0161141	+	0.0279105i
$986$	−1.33152e10			−0.442363
$987$	−1.74617e10	−	1.90973e10i	−0.578065	−	0.632211i
$988$	−3.39700e9			−0.112059
$989$	−1.40806e10	+	2.43883e10i	−0.462843	+	0.801668i
$990$	−7.14103e7	−	1.23686e8i	−0.00233904	−	0.00405134i
$991$	1.22798e10	+	2.12693e10i	0.400806	+	0.694217i	0.993823	−	0.110973i	$-0.0353967\pi$
$991$	1.22798e10	+	2.12693e10i	0.400806	+	0.694217i	−0.593017	+	0.805190i	$0.702063\pi$
$992$	4.04949e9	−	7.01392e9i	0.131707	−	0.228123i
$993$	1.46473e10			0.474718
$994$	7.96565e10	−	1.75696e10i	2.57258	−	0.567426i
$995$	1.06423e10			0.342497
$996$	3.74787e9	−	6.49150e9i	0.120192	−	0.208179i
$997$	8.29325e9	+	1.43643e10i	0.265028	+	0.459042i	0.967571	−	0.252599i	$-0.0812855\pi$
$997$	8.29325e9	+	1.43643e10i	0.265028	+	0.459042i	−0.702543	+	0.711641i	$0.747952\pi$
$998$	−5.46360e9	−	9.46324e9i	−0.173989	−	0.301358i
$999$	2.20691e9	−	3.82248e9i	0.0700335	−	0.121302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.8.c.a.2.4	✓	8
3.2	odd	2		63.8.e.b.37.1		8
4.3	odd	2		112.8.i.c.65.1		8
7.2	even	3		49.8.a.f.1.1		4
7.3	odd	6		49.8.c.g.18.4		8
7.4	even	3	inner	7.8.c.a.4.4	yes	8
7.5	odd	6		49.8.a.e.1.1		4
7.6	odd	2		49.8.c.g.30.4		8
21.2	odd	6		441.8.a.s.1.4		4
21.5	even	6		441.8.a.t.1.4		4
21.11	odd	6		63.8.e.b.46.1		8
28.11	odd	6		112.8.i.c.81.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.8.c.a.2.4	✓	8	1.1	even	1	trivial
7.8.c.a.4.4	yes	8	7.4	even	3	inner
49.8.a.e.1.1		4	7.5	odd	6
49.8.a.f.1.1		4	7.2	even	3
49.8.c.g.18.4		8	7.3	odd	6
49.8.c.g.30.4		8	7.6	odd	2
63.8.e.b.37.1		8	3.2	odd	2
63.8.e.b.46.1		8	21.11	odd	6
112.8.i.c.65.1		8	4.3	odd	2
112.8.i.c.81.1		8	28.11	odd	6
441.8.a.s.1.4		4	21.2	odd	6
441.8.a.t.1.4		4	21.5	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+(10.4120 - 18.0342i) q^{2} +(22.7504 + 39.4049i) q^{3} +(-152.821 - 264.694i) q^{4} +(-96.7016 + 167.492i) q^{5} +947.513 q^{6} +(612.373 + 669.733i) q^{7} -3699.23 q^{8} +(58.3362 - 101.041i) q^{9} +(2013.72 + 3487.87i) q^{10} +(-151.972 - 263.223i) q^{11} +(6953.49 - 12043.8i) q^{12} -9891.04 q^{13} +(18454.1 - 4070.37i) q^{14} -8800.01 q^{15} +(-18955.5 + 32831.8i) q^{16} +(-6242.26 - 10811.9i) q^{17} +(-1214.80 - 2104.09i) q^{18} +(-561.837 + 973.131i) q^{19} +59112.1 q^{20} +(-12459.0 + 39367.2i) q^{21} -6329.35 q^{22} +(22359.5 - 38727.8i) q^{23} +(-84159.2 - 145768. i) q^{24} +(20360.1 + 35264.8i) q^{25} +(-102986. + 178377. i) q^{26} +104819. q^{27} +(83690.6 - 264441. i) q^{28} +51216.6 q^{29} +(-91626.0 + 158701. i) q^{30} +(-12816.5 - 22198.9i) q^{31} +(157979. + 273628. i) q^{32} +(6914.85 - 11976.9i) q^{33} -259978. q^{34} +(-171392. + 37803.5i) q^{35} -35660.0 q^{36} +(21054.5 - 36467.4i) q^{37} +(11699.7 + 20264.6i) q^{38} +(-225025. - 389755. i) q^{39} +(357722. - 619592. i) q^{40} +787100. q^{41} +(580232. + 634581. i) q^{42} -629737. q^{43} +(-46449.0 + 80452.1i) q^{44} +(11282.4 + 19541.7i) q^{45} +(-465616. - 806470. i) q^{46} +(-313344. + 542727. i) q^{47} -1.72498e6 q^{48} +(-73540.5 + 820253. i) q^{49} +847961. q^{50} +(284028. - 491951. i) q^{51} +(1.51156e6 + 2.61810e6i) q^{52} +(268306. + 464719. i) q^{53} +(1.09138e6 - 1.89033e6i) q^{54} +58783.7 q^{55} +(-2.26531e6 - 2.47750e6i) q^{56} -51128.2 q^{57} +(533269. - 923649. i) q^{58} +(-1.06004e6 - 1.83605e6i) q^{59} +(1.34483e6 + 2.32931e6i) q^{60} +(-1.35734e6 + 2.35098e6i) q^{61} -533785. q^{62} +(103394. - 22805.3i) q^{63} +1.72694e6 q^{64} +(956479. - 1.65667e6i) q^{65} +(-143995. - 249407. i) q^{66} +(-1.88702e6 - 3.26842e6i) q^{67} +(-1.90790e6 + 3.30457e6i) q^{68} +2.03475e6 q^{69} +(-1.10279e6 + 3.48453e6i) q^{70} +4.31646e6 q^{71} +(-215799. + 373775. i) q^{72} +(355018. + 614910. i) q^{73} +(-438440. - 759401. i) q^{74} +(-926403. + 1.60458e6i) q^{75} +343442. q^{76} +(83225.5 - 262971. i) q^{77} -9.37189e6 q^{78} +(-1.39606e6 + 2.41804e6i) q^{79} +(-3.66605e6 - 6.34978e6i) q^{80} +(2.25710e6 + 3.90941e6i) q^{81} +(8.19532e6 - 1.41947e7i) q^{82} +538991. q^{83} +(1.23243e7 - 2.71832e6i) q^{84} +2.41454e6 q^{85} +(-6.55684e6 + 1.13568e7i) q^{86} +(1.16520e6 + 2.01818e6i) q^{87} +(562180. + 973724. i) q^{88} +(1.09927e6 - 1.90400e6i) q^{89} +469891. q^{90} +(-6.05701e6 - 6.62435e6i) q^{91} -1.36680e7 q^{92} +(583163. - 1.01007e6i) q^{93} +(6.52509e6 + 1.13018e7i) q^{94} +(-108661. - 188207. i) q^{95} +(-7.18819e6 + 1.24503e7i) q^{96} -1.16799e7 q^{97} +(1.40269e7 + 9.86675e6i) q^{98} -35461.9 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

Modular forms

Varieties

Fields

Representations

Groups

Database

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