LMFDB - Embedded newform 18.8.c.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,8,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.62293045871$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.14601465675.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 52x^{4} - 99x^{3} + 709x^{2} - 660x + 1872 $ x^6 - 3x^5 + 52x^4 - 99x^3 + 709x^2 - 660*x + 1872
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.2
Root			$0.500000 + 5.21243i$ of defining polynomial
Character	$\chi$	$=$	18.7
Dual form			18.8.c.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 + 6.92820i) q^{2} +(-11.7819 - 45.2569i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(187.789 + 325.261i) q^{5} +(360.677 + 99.4005i) q^{6} +(-528.867 + 916.024i) q^{7} +512.000 q^{8} +(-1909.38 + 1066.42i) q^{9} -3004.63 q^{10} +(-849.965 + 1472.18i) q^{11} +(-2131.37 + 2101.24i) q^{12} +(6256.75 + 10837.0i) q^{13} +(-4230.93 - 7328.19i) q^{14} +(12507.8 - 12330.9i) q^{15} +(-2048.00 + 3547.24i) q^{16} +16879.9 q^{17} +(249.117 - 17494.2i) q^{18} -35281.9 q^{19} +(12018.5 - 20816.7i) q^{20} +(47687.4 + 13142.4i) q^{21} +(-6799.72 - 11777.5i) q^{22} +(-35482.7 - 61457.8i) q^{23} +(-6032.31 - 23171.5i) q^{24} +(-31467.1 + 54502.6i) q^{25} -100108. q^{26} +(70758.9 + 73848.0i) q^{27} +67694.9 q^{28} +(38827.4 - 67251.0i) q^{29} +(35400.1 + 135980. i) q^{30} +(63093.8 + 109282. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(76640.6 + 21121.7i) q^{33} +(-67519.4 + 116947. i) q^{34} -397262. q^{35} +(120207. + 71702.8i) q^{36} -528664. q^{37} +(141128. - 244440. i) q^{38} +(416733. - 410841. i) q^{39} +(96148.1 + 166533. i) q^{40} +(258960. + 448533. i) q^{41} +(-281803. + 277819. i) q^{42} +(135830. - 235264. i) q^{43} +108795. q^{44} +(-705425. - 420782. i) q^{45} +567723. q^{46} +(211814. - 366873. i) q^{47} +(184666. + 50893.0i) q^{48} +(-147628. - 255699. i) q^{49} +(-251737. - 436021. i) q^{50} +(-198876. - 763930. i) q^{51} +(400432. - 693568. i) q^{52} +1.24314e6 q^{53} +(-794670. + 194840. i) q^{54} -638457. q^{55} +(-270780. + 469004. i) q^{56} +(415687. + 1.59675e6i) q^{57} +(310619. + 538008. i) q^{58} +(1.34086e6 + 2.32244e6i) q^{59} +(-1.08370e6 - 298661. i) q^{60} +(377040. - 653052. i) q^{61} -1.00950e6 q^{62} +(32937.4 - 2.31303e6i) q^{63} +262144. q^{64} +(-2.34990e6 + 4.07014e6i) q^{65} +(-452898. + 446495. i) q^{66} +(131285. + 227392. i) q^{67} +(-540156. - 935577. i) q^{68} +(-2.36334e6 + 2.32993e6i) q^{69} +(1.58905e6 - 2.75231e6i) q^{70} +990913. q^{71} +(-977600. + 546008. i) q^{72} -1.04389e6 q^{73} +(2.11466e6 - 3.66269e6i) q^{74} +(2.83736e6 + 781961. i) q^{75} +(1.12902e6 + 1.95552e6i) q^{76} +(-899036. - 1.55718e6i) q^{77} +(1.17946e6 + 4.53058e6i) q^{78} +(3.66860e6 - 6.35419e6i) q^{79} -1.53837e6 q^{80} +(2.50846e6 - 4.07240e6i) q^{81} -4.14337e6 q^{82} +(1.94611e6 - 3.37075e6i) q^{83} +(-797572. - 3.06366e6i) q^{84} +(3.16986e6 + 5.49035e6i) q^{85} +(1.08664e6 + 1.88211e6i) q^{86} +(-3.50103e6 - 964865. i) q^{87} +(-435182. + 753757. i) q^{88} +675681. q^{89} +(5.73696e6 - 3.20420e6i) q^{90} -1.32359e7 q^{91} +(-2.27089e6 + 3.93330e6i) q^{92} +(4.20239e6 - 4.14298e6i) q^{93} +(1.69452e6 + 2.93499e6i) q^{94} +(-6.62556e6 - 1.14758e7i) q^{95} +(-1.09126e6 + 1.07583e6i) q^{96} +(-8.12785e6 + 1.40779e7i) q^{97} +2.36205e6 q^{98} +(52935.2 - 3.71737e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 27 q^{3} - 192 q^{4} + 54 q^{5} + 792 q^{6} + 210 q^{7} + 3072 q^{8} + 2295 q^{9} - 864 q^{10} + 6579 q^{11} - 4608 q^{12} + 10092 q^{13} + 1680 q^{14} + 756 q^{15} - 12288 q^{16} - 29790 q^{17}+ \cdots - 11453238 q^{99}+O(q^{100}) $ 6 * q - 24 * q^2 - 27 * q^3 - 192 * q^4 + 54 * q^5 + 792 * q^6 + 210 * q^7 + 3072 * q^8 + 2295 * q^9 - 864 * q^10 + 6579 * q^11 - 4608 * q^12 + 10092 * q^13 + 1680 * q^14 + 756 * q^15 - 12288 * q^16 - 29790 * q^17 + 19008 * q^18 - 137490 * q^19 + 3456 * q^20 + 85464 * q^21 + 52632 * q^22 - 39654 * q^23 - 13824 * q^24 - 7923 * q^25 - 161472 * q^26 + 87480 * q^27 - 26880 * q^28 + 239832 * q^29 + 283392 * q^30 + 145704 * q^31 - 98304 * q^32 + 175365 * q^33 + 119160 * q^34 - 1087776 * q^35 - 298944 * q^36 - 720384 * q^37 + 549960 * q^38 + 2386548 * q^39 + 27648 * q^40 + 1086993 * q^41 - 752400 * q^42 - 299967 * q^43 - 842112 * q^44 - 2798874 * q^45 + 634464 * q^46 + 131634 * q^47 + 405504 * q^48 + 482175 * q^49 - 63384 * q^50 - 3719223 * q^51 + 645888 * q^52 + 1909152 * q^53 - 1222776 * q^54 - 5494824 * q^55 + 107520 * q^56 + 6076107 * q^57 + 1918656 * q^58 + 2504853 * q^59 - 2315520 * q^60 + 7309038 * q^61 - 2331264 * q^62 - 1254960 * q^63 + 1572864 * q^64 - 1786698 * q^65 + 2211408 * q^66 + 3433035 * q^67 + 953280 * q^68 - 5815206 * q^69 + 4351104 * q^70 + 2269368 * q^71 + 1175040 * q^72 - 15901746 * q^73 + 2881536 * q^74 + 4230945 * q^75 + 4399680 * q^76 - 6147432 * q^77 - 12143088 * q^78 + 7076928 * q^79 - 442368 * q^80 + 4749435 * q^81 - 17391888 * q^82 - 10914444 * q^83 + 549504 * q^84 + 17613396 * q^85 - 2399736 * q^86 - 11533266 * q^87 + 3368448 * q^88 + 23800356 * q^89 + 18592416 * q^90 - 37170552 * q^91 - 2537856 * q^92 + 30872466 * q^93 + 1053072 * q^94 - 17342424 * q^95 - 2359296 * q^96 + 519357 * q^97 - 7714800 * q^98 - 11453238 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$	−11.7819	−	45.2569i	−0.251936	−	0.967744i
$3$	−11.7819	−	45.2569i	−0.251936	−	0.967744i
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	187.789	+	325.261i	0.671855	+	1.16369i	0.977377	+	0.211502i	$0.0678356\pi$
$5$	187.789	+	325.261i	0.671855	+	1.16369i	−0.305522	+	0.952185i	$0.598831\pi$
$6$	360.677	+	99.4005i	0.681692	+	0.187871i
$7$	−528.867	+	916.024i	−0.582778	+	1.00940i	0.412371	+	0.911016i	$0.364701\pi$
$7$	−528.867	+	916.024i	−0.582778	+	1.00940i	−0.995148	+	0.0983845i	$0.968633\pi$
$8$	512.000			0.353553
$9$	−1909.38	+	1066.42i	−0.873057	+	0.487618i
$10$	−3004.63			−0.950147
$11$	−849.965	+	1472.18i	−0.192542	+	0.333493i	−0.946092	−	0.323898i	$-0.895007\pi$
$11$	−849.965	+	1472.18i	−0.192542	+	0.333493i	0.753550	+	0.657391i	$0.228340\pi$
$12$	−2131.37	+	2101.24i	−0.356062	+	0.351027i
$13$	6256.75	+	10837.0i	0.789854	+	1.36807i	0.926056	+	0.377386i	$0.123177\pi$
$13$	6256.75	+	10837.0i	0.789854	+	1.36807i	−0.136202	+	0.990681i	$0.543490\pi$
$14$	−4230.93	−	7328.19i	−0.412086	−	0.713754i
$15$	12507.8	−	12330.9i	0.956887	−	0.943358i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	16879.9			0.833293			0.416646	−	0.909069i	$-0.363205\pi$
$17$	16879.9			0.833293			0.416646	+	0.909069i	$0.363205\pi$
$18$	249.117	−	17494.2i	0.0100682	−	0.707035i
$19$	−35281.9			−1.18009			−0.590044	−	0.807371i	$-0.700890\pi$
$19$	−35281.9			−1.18009			−0.590044	+	0.807371i	$0.700890\pi$
$20$	12018.5	−	20816.7i	0.335928	−	0.581844i
$21$	47687.4	+	13142.4i	1.12366	+	0.309676i
$22$	−6799.72	−	11777.5i	−0.136148	−	0.235815i
$23$	−35482.7	−	61457.8i	−0.608092	−	1.05325i	−0.991555	−	0.129690i	$-0.958602\pi$
$23$	−35482.7	−	61457.8i	−0.608092	−	1.05325i	0.383463	−	0.923556i	$-0.374731\pi$
$24$	−6032.31	−	23171.5i	−0.0890727	−	0.342149i
$25$	−31467.1	+	54502.6i	−0.402779	+	0.697634i
$26$	−100108.			−1.11702
$27$	70758.9	+	73848.0i	0.691844	+	0.722047i
$28$	67694.9			0.582778
$29$	38827.4	−	67251.0i	0.295628	−	0.512042i	−0.679503	−	0.733673i	$-0.737805\pi$
$29$	38827.4	−	67251.0i	0.295628	−	0.512042i	0.975131	+	0.221631i	$0.0711379\pi$
$30$	35400.1	+	135980.i	0.239376	+	0.919499i
$31$	63093.8	+	109282.i	0.380383	+	0.658843i	0.991117	−	0.132993i	$-0.0424588\pi$
$31$	63093.8	+	109282.i	0.380383	+	0.658843i	−0.610734	+	0.791836i	$0.709126\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$	76640.6	+	21121.7i	0.371244	+	0.102313i
$34$	−67519.4	+	116947.i	−0.294614	+	0.510286i
$35$	−397262.			−1.56617
$36$	120207.	+	71702.8i	0.429409	+	0.256140i
$37$	−528664.			−1.71583			−0.857914	−	0.513794i	$-0.828240\pi$
$37$	−528664.			−1.71583			−0.857914	+	0.513794i	$0.828240\pi$
$38$	141128.	−	244440.i	0.417224	−	0.722654i
$39$	416733.	−	410841.i	1.12495	−	1.10904i
$40$	96148.1	+	166533.i	0.237537	+	0.411426i
$41$	258960.	+	448533.i	0.586800	+	1.01637i	0.994648	+	0.103318i	$0.0329458\pi$
$41$	258960.	+	448533.i	0.586800	+	1.01637i	−0.407849	+	0.913050i	$0.633721\pi$
$42$	−281803.	+	277819.i	−0.586912	+	0.578614i
$43$	135830.	−	235264.i	0.260529	−	0.451249i	−0.705854	−	0.708358i	$-0.749436\pi$
$43$	135830.	−	235264.i	0.260529	−	0.451249i	0.966383	+	0.257109i	$0.0827698\pi$
$44$	108795.			0.192542
$45$	−705425.	−	420782.i	−1.15400	−	0.688356i
$46$	567723.			0.859972
$47$	211814.	−	366873.i	0.297586	−	0.515435i	−0.677997	−	0.735065i	$-0.737152\pi$
$47$	211814.	−	366873.i	0.297586	−	0.515435i	0.975583	+	0.219630i	$0.0704850\pi$
$48$	184666.	+	50893.0i	0.241015	+	0.0664223i
$49$	−147628.	−	255699.i	−0.179260	−	0.310487i
$50$	−251737.	−	436021.i	−0.284808	−	0.493301i
$51$	−198876.	−	763930.i	−0.209936	−	0.806414i
$52$	400432.	−	693568.i	0.394927	−	0.684034i
$53$	1.24314e6			1.14698			0.573490	−	0.819213i	$-0.305589\pi$
$53$	1.24314e6			1.14698			0.573490	+	0.819213i	$0.305589\pi$
$54$	−794670.	+	194840.i	−0.686765	+	0.168384i
$55$	−638457.			−0.517443
$56$	−270780.	+	469004.i	−0.206043	+	0.356877i
$57$	415687.	+	1.59675e6i	0.297306	+	1.14202i
$58$	310619.	+	538008.i	0.209040	+	0.362068i
$59$	1.34086e6	+	2.32244e6i	0.849968	+	1.47219i	0.881236	+	0.472677i	$0.156712\pi$
$59$	1.34086e6	+	2.32244e6i	0.849968	+	1.47219i	−0.0312678	+	0.999511i	$0.509954\pi$
$60$	−1.08370e6	−	298661.i	−0.647708	−	0.178505i
$61$	377040.	−	653052.i	0.212683	−	0.368378i	−0.739870	−	0.672750i	$-0.765113\pi$
$61$	377040.	−	653052.i	0.212683	−	0.368378i	0.952553	+	0.304372i	$0.0984465\pi$
$62$	−1.00950e6			−0.537943
$63$	32937.4	−	2.31303e6i	0.0165958	−	1.16544i
$64$	262144.			0.125000
$65$	−2.34990e6	+	4.07014e6i	−1.06133	+	1.83829i
$66$	−452898.	+	446495.i	−0.193908	+	0.191167i
$67$	131285.	+	227392.i	0.0533278	+	0.0923664i	0.891457	−	0.453105i	$-0.149684\pi$
$67$	131285.	+	227392.i	0.0533278	+	0.0923664i	−0.838129	+	0.545472i	$0.816351\pi$
$68$	−540156.	−	935577.i	−0.208323	−	0.360826i
$69$	−2.36334e6	+	2.32993e6i	−0.866073	+	0.853828i
$70$	1.58905e6	−	2.75231e6i	0.553724	−	0.959079i
$71$	990913.			0.328573			0.164286	−	0.986413i	$-0.447468\pi$
$71$	990913.			0.328573			0.164286	+	0.986413i	$0.447468\pi$
$72$	−977600.	+	546008.i	−0.308672	+	0.172399i
$73$	−1.04389e6			−0.314068			−0.157034	−	0.987593i	$-0.550193\pi$
$73$	−1.04389e6			−0.314068			−0.157034	+	0.987593i	$0.550193\pi$
$74$	2.11466e6	−	3.66269e6i	0.606637	−	1.05073i
$75$	2.83736e6	+	781961.i	0.776605	+	0.214028i
$76$	1.12902e6	+	1.95552e6i	0.295022	+	0.510993i
$77$	−899036.	−	1.55718e6i	−0.224419	−	0.388705i
$78$	1.17946e6	+	4.53058e6i	0.281418	+	1.08099i
$79$	3.66860e6	−	6.35419e6i	0.837153	−	1.44999i	−0.0551117	−	0.998480i	$-0.517551\pi$
$79$	3.66860e6	−	6.35419e6i	0.837153	−	1.44999i	0.892265	−	0.451512i	$-0.149115\pi$
$80$	−1.53837e6			−0.335928
$81$	2.50846e6	−	4.07240e6i	0.524457	−	0.851437i
$82$	−4.14337e6			−0.829860
$83$	1.94611e6	−	3.37075e6i	0.373588	−	0.647074i	−0.616526	−	0.787334i	$-0.711461\pi$
$83$	1.94611e6	−	3.37075e6i	0.373588	−	0.647074i	0.990115	+	0.140260i	$0.0447940\pi$
$84$	−797572.	−	3.06366e6i	−0.146822	−	0.563980i
$85$	3.16986e6	+	5.49035e6i	0.559852	+	0.969692i
$86$	1.08664e6	+	1.88211e6i	0.184222	+	0.319081i
$87$	−3.50103e6	−	964865.i	−0.570005	−	0.157090i
$88$	−435182.	+	753757.i	−0.0680740	+	0.117908i
$89$	675681.			0.101596			0.0507980	−	0.998709i	$-0.483824\pi$
$89$	675681.			0.101596			0.0507980	+	0.998709i	$0.483824\pi$
$90$	5.73696e6	−	3.20420e6i	0.829532	−	0.463309i
$91$	−1.32359e7			−1.84124
$92$	−2.27089e6	+	3.93330e6i	−0.304046	+	0.526623i
$93$	4.20239e6	−	4.14298e6i	0.541759	−	0.534099i
$94$	1.69452e6	+	2.93499e6i	0.210425	+	0.364467i
$95$	−6.62556e6	−	1.14758e7i	−0.792849	−	1.37325i
$96$	−1.09126e6	+	1.07583e6i	−0.125887	+	0.124107i
$97$	−8.12785e6	+	1.40779e7i	−0.904221	+	1.56616i	−0.0822619	+	0.996611i	$0.526214\pi$
$97$	−8.12785e6	+	1.40779e7i	−0.904221	+	1.56616i	−0.821959	+	0.569546i	$0.807119\pi$
$98$	2.36205e6			0.253512
$99$	52935.2	−	3.71737e6i	0.00548304	−	0.385046i
$100$	4.02779e6			0.402779
$101$	212270.	−	367662.i	0.0205005	−	0.0355079i	−0.855593	−	0.517649i	$-0.826807\pi$
$101$	212270.	−	367662.i	0.0205005	−	0.0355079i	0.876094	+	0.482141i	$0.160141\pi$
$102$	6.08817e6	+	1.67787e6i	0.568049	+	0.156551i
$103$	2.43167e6	+	4.21178e6i	0.219268	+	0.379783i	0.954584	−	0.297941i	$-0.0962999\pi$
$103$	2.43167e6	+	4.21178e6i	0.219268	+	0.379783i	−0.735317	+	0.677724i	$0.762967\pi$
$104$	3.20345e6	+	5.54854e6i	0.279256	+	0.483685i
$105$	4.68048e6	+	1.79788e7i	0.394574	+	1.51565i
$106$	−4.97257e6	+	8.61275e6i	−0.405519	+	0.702379i
$107$	2.83648e6			0.223839			0.111920	−	0.993717i	$-0.464300\pi$
$107$	2.83648e6			0.223839			0.111920	+	0.993717i	$0.464300\pi$
$108$	1.82879e6	−	6.28499e6i	0.139695	−	0.480089i
$109$	6.31389e6			0.466987			0.233493	−	0.972358i	$-0.424984\pi$
$109$	6.31389e6			0.466987			0.233493	+	0.972358i	$0.424984\pi$
$110$	2.55383e6	−	4.42336e6i	0.182944	−	0.316868i
$111$	6.22865e6	+	2.39257e7i	0.432278	+	1.66048i
$112$	−2.16624e6	−	3.75203e6i	−0.145694	−	0.252350i
$113$	−1.07218e7	−	1.85708e7i	−0.699029	−	1.21075i	−0.968804	−	0.247830i	$-0.920283\pi$
$113$	−1.07218e7	−	1.85708e7i	−0.699029	−	1.21075i	0.269775	−	0.962923i	$-0.413051\pi$
$114$	−1.27254e7	−	3.50704e6i	−0.804457	−	0.221704i
$115$	1.33265e7	−	2.30822e7i	0.817100	−	1.41526i
$116$	−4.96990e6			−0.295628
$117$	−2.35033e7	−	1.40196e7i	−1.35668	−	0.809253i
$118$	−2.14538e7			−1.20204
$119$	−8.92719e6	+	1.54624e7i	−0.485624	+	0.841126i
$120$	6.40398e6	−	6.31344e6i	0.338311	−	0.333527i
$121$	8.29871e6	+	1.43738e7i	0.425855	+	0.737602i
$122$	3.01632e6	+	5.22442e6i	0.150390	+	0.260483i
$123$	1.72482e7	−	1.70043e7i	0.835747	−	0.823931i
$124$	4.03801e6	−	6.99403e6i	0.190191	−	0.329421i
$125$	5.70534e6			0.261274
$126$	1.58934e7	+	9.48031e6i	0.707814	+	0.422207i
$127$	1.35681e7			0.587768			0.293884	−	0.955841i	$-0.405052\pi$
$127$	1.35681e7			0.587768			0.293884	+	0.955841i	$0.405052\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$	−1.22477e7	−	3.37539e6i	−0.502330	−	0.138439i
$130$	−1.87992e7	−	3.25612e7i	−0.750477	−	1.29986i
$131$	1.17657e7	+	2.03788e7i	0.457265	+	0.792005i	0.998815	−	0.0486627i	$-0.0154959\pi$
$131$	1.17657e7	+	2.03788e7i	0.457265	+	0.792005i	−0.541551	+	0.840668i	$0.682163\pi$
$132$	−1.28181e6	−	4.92375e6i	−0.0485083	−	0.186332i
$133$	1.86594e7	−	3.23191e7i	0.687729	−	1.19118i
$134$	−2.10056e6			−0.0754169
$135$	−1.07321e7	+	3.68829e7i	−0.375418	+	1.29020i
$136$	8.64249e6			0.294614
$137$	1.39952e7	−	2.42405e7i	0.465006	−	0.805414i	−0.534196	−	0.845361i	$-0.679385\pi$
$137$	1.39952e7	−	2.42405e7i	0.465006	−	0.805414i	0.999202	+	0.0399467i	$0.0127188\pi$
$138$	−6.68884e6	−	2.56934e7i	−0.216658	−	0.832233i
$139$	4.00094e6	+	6.92982e6i	0.126360	+	0.218862i	0.922264	−	0.386561i	$-0.126337\pi$
$139$	4.00094e6	+	6.92982e6i	0.126360	+	0.218862i	−0.795904	+	0.605423i	$0.793004\pi$
$140$	1.27124e7	+	2.20185e7i	0.391542	+	0.678171i
$141$	−1.90991e7	−	5.26361e6i	−0.573781	−	0.158131i
$142$	−3.96365e6	+	6.86525e6i	−0.116168	+	0.201209i
$143$	−2.12721e7			−0.608322
$144$	127548.	−	8.95704e6i	0.00355963	−	0.249975i
$145$	2.91655e7			0.794476
$146$	4.17555e6	−	7.23226e6i	0.111040	−	0.192327i
$147$	−9.83283e6	+	9.69381e6i	−0.255310	+	0.251700i
$148$	1.69172e7	+	2.93015e7i	0.428957	+	0.742975i
$149$	1.35829e7	+	2.35262e7i	0.336387	+	0.582639i	0.983750	−	0.179542i	$-0.0574617\pi$
$149$	1.35829e7	+	2.35262e7i	0.336387	+	0.582639i	−0.647363	+	0.762182i	$0.724128\pi$
$150$	−1.67670e7	+	1.65300e7i	−0.405636	+	0.399901i
$151$	−2.09932e7	+	3.63612e7i	−0.496202	+	0.859447i	−0.999990	−	0.00438023i	$-0.998606\pi$
$151$	−2.09932e7	+	3.63612e7i	−0.496202	+	0.859447i	0.503789	+	0.863827i	$0.331939\pi$
$152$	−1.80643e7			−0.417224
$153$	−3.22300e7	+	1.80010e7i	−0.727512	+	0.406329i
$154$	1.43846e7			0.317376
$155$	−2.36967e7	+	4.10439e7i	−0.511125	+	0.885294i
$156$	−3.61066e7	−	9.95078e6i	−0.761466	−	0.209856i
$157$	−4.10239e7	−	7.10556e7i	−0.846036	−	1.46538i	−0.884719	−	0.466125i	$-0.845650\pi$
$157$	−4.10239e7	−	7.10556e7i	−0.846036	−	1.46538i	0.0386831	−	0.999252i	$-0.487684\pi$
$158$	2.93488e7	+	5.08336e7i	0.591957	+	1.02530i
$159$	−1.46465e7	−	5.62608e7i	−0.288965	−	1.10998i
$160$	6.15348e6	−	1.06581e7i	0.118768	−	0.205713i
$161$	7.50625e7			1.41753
$162$	1.81806e7	+	3.36687e7i	0.335973	+	0.622191i
$163$	−2.89286e7			−0.523203			−0.261602	−	0.965176i	$-0.584251\pi$
$163$	−2.89286e7			−0.523203			−0.261602	+	0.965176i	$0.584251\pi$
$164$	1.65735e7	−	2.87061e7i	0.293400	−	0.508184i
$165$	7.52221e6	+	2.88946e7i	0.130362	+	0.500752i
$166$	1.55688e7	+	2.69660e7i	0.264167	+	0.457550i
$167$	−1.33585e7	−	2.31376e7i	−0.221947	−	0.384424i	0.733452	−	0.679741i	$-0.237908\pi$
$167$	−1.33585e7	−	2.31376e7i	−0.221947	−	0.384424i	−0.955399	+	0.295318i	$0.904575\pi$
$168$	2.44160e7	+	6.72891e6i	0.397275	+	0.109487i
$169$	−4.69195e7	+	8.12669e7i	−0.747738	+	1.29512i
$170$	−5.07177e7			−0.791751
$171$	6.73664e7	−	3.76254e7i	1.03028	−	0.575433i
$172$	−1.73862e7			−0.260529
$173$	1.31561e7	−	2.27871e7i	0.193182	−	0.334601i	−0.753121	−	0.657882i	$-0.771453\pi$
$173$	1.31561e7	−	2.27871e7i	0.193182	−	0.334601i	0.946303	+	0.323281i	$0.104786\pi$
$174$	2.06889e7	−	2.03964e7i	0.297725	−	0.293515i
$175$	−3.32838e7	−	5.76492e7i	−0.469461	−	0.813131i
$176$	−3.48146e6	−	6.03006e6i	−0.0481356	−	0.0833733i
$177$	8.93088e7	−	8.80461e7i	1.21056	−	1.19345i
$178$	−2.70272e6	+	4.68125e6i	−0.0359196	+	0.0622146i
$179$	−2.19724e7			−0.286347			−0.143174	−	0.989698i	$-0.545731\pi$
$179$	−2.19724e7			−0.286347			−0.143174	+	0.989698i	$0.545731\pi$
$180$	−748504.	+	5.25636e7i	−0.00956623	+	0.671787i
$181$	1.26202e8			1.58195			0.790975	−	0.611849i	$-0.209574\pi$
$181$	1.26202e8			1.58195			0.790975	+	0.611849i	$0.209574\pi$
$182$	5.29437e7	−	9.17012e7i	0.650976	−	1.12752i
$183$	−3.39974e7	−	9.36949e6i	−0.410078	−	0.113015i
$184$	−1.81671e7	−	3.14664e7i	−0.214993	−	0.372379i
$185$	−9.92774e7	−	1.71954e8i	−1.15279	−	1.99669i
$186$	1.18938e7	+	4.56869e7i	0.135527	+	0.520591i
$187$	−1.43473e7	+	2.48502e7i	−0.160444	+	0.277898i
$188$	−2.71122e7			−0.297586
$189$	−1.05069e8	+	2.57611e7i	−1.13203	+	0.277555i
$190$	1.06009e8			1.12126
$191$	−8.97257e7	+	1.55409e8i	−0.931752	+	1.61384i	−0.151425	+	0.988469i	$0.548386\pi$
$191$	−8.97257e7	+	1.55409e8i	−0.931752	+	1.61384i	−0.780326	+	0.625372i	$0.784947\pi$
$192$	−3.08854e6	−	1.18638e7i	−0.0314920	−	0.120968i
$193$	1.49157e7	+	2.58348e7i	0.149346	+	0.258675i	0.930986	−	0.365055i	$-0.118950\pi$
$193$	1.49157e7	+	2.58348e7i	0.149346	+	0.258675i	−0.781640	+	0.623730i	$0.785617\pi$
$194$	−6.50228e7	−	1.12623e8i	−0.639381	−	1.10744i
$195$	2.11888e8	+	5.83953e7i	2.04638	+	0.563971i
$196$	−9.44820e6	+	1.63648e7i	−0.0896299	+	0.155243i
$197$	6.70863e7			0.625176			0.312588	−	0.949889i	$-0.398804\pi$
$197$	6.70863e7			0.625176			0.312588	+	0.949889i	$0.398804\pi$
$198$	2.55429e7	+	1.52362e7i	0.233853	+	0.139492i
$199$	−1.18177e8			−1.06304			−0.531519	−	0.847046i	$-0.678379\pi$
$199$	−1.18177e8			−1.06304			−0.531519	+	0.847046i	$0.678379\pi$
$200$	−1.61112e7	+	2.79053e7i	−0.142404	+	0.246651i
$201$	8.74429e6	−	8.62066e6i	0.0759519	−	0.0748780i
$202$	1.69816e6	+	2.94130e6i	0.0144960	+	0.0251078i
$203$	4.10690e7	+	7.11336e7i	0.344570	+	0.596813i
$204$	−3.59773e7	+	3.54686e7i	−0.296704	+	0.292509i
$205$	−9.72600e7	+	1.68459e8i	−0.788489	+	1.36570i
$206$	−3.89067e7			−0.310091
$207$	1.33290e8	+	7.95066e7i	1.04448	+	0.623027i
$208$	−5.12553e7			−0.394927
$209$	2.99884e7	−	5.19414e7i	0.227217	−	0.393552i
$210$	−1.43283e8	−	3.94880e7i	−1.06765	−	0.294237i
$211$	−5.19927e7	−	9.00540e7i	−0.381025	−	0.659955i	0.610184	−	0.792260i	$-0.291096\pi$
$211$	−5.19927e7	−	9.00540e7i	−0.381025	−	0.659955i	−0.991209	+	0.132305i	$0.957762\pi$
$212$	−3.97806e7	−	6.89020e7i	−0.286745	−	0.496657i
$213$	−1.16748e7	−	4.48457e7i	−0.0827791	−	0.317974i
$214$	−1.13459e7	+	1.96517e7i	−0.0791392	+	0.137073i
$215$	1.02030e8			0.700150
$216$	3.62286e7	+	3.78102e7i	0.244604	+	0.255282i
$217$	−1.33473e8			−0.886715
$218$	−2.52556e7	+	4.37439e7i	−0.165105	+	0.285970i
$219$	1.22989e7	+	4.72431e7i	0.0791249	+	0.303937i
$220$	2.04306e7	+	3.53869e7i	0.129361	+	0.224059i
$221$	1.05613e8	+	1.82927e8i	0.658180	+	1.14000i
$222$	−1.90677e8	−	5.25495e7i	−1.16967	−	0.322354i
$223$	8.07648e7	−	1.39889e8i	0.487703	−	0.844726i	−0.512197	−	0.858868i	$-0.671168\pi$
$223$	8.07648e7	−	1.39889e8i	0.487703	−	0.844726i	0.999900	+	0.0141421i	$0.00450171\pi$
$224$	3.46598e7			0.206043
$225$	1.95975e6	−	1.37623e8i	0.0114700	−	0.805476i
$226$	1.71550e8			0.988576
$227$	−1.90267e7	+	3.29553e7i	−0.107963	+	0.186997i	−0.914945	−	0.403579i	$-0.867766\pi$
$227$	−1.90267e7	+	3.29553e7i	−0.107963	+	0.186997i	0.806982	+	0.590576i	$0.201099\pi$
$228$	7.51989e7	−	7.41357e7i	0.420184	−	0.414243i
$229$	1.44858e8	+	2.50901e8i	0.797110	+	1.38064i	0.921491	+	0.388401i	$0.126972\pi$
$229$	1.44858e8	+	2.50901e8i	0.797110	+	1.38064i	−0.124381	+	0.992235i	$0.539694\pi$
$230$	1.06612e8	+	1.84658e8i	0.577777	+	1.00074i
$231$	−5.98806e7	+	5.90340e7i	−0.319628	+	0.315109i
$232$	1.98796e7	−	3.44325e7i	0.104520	−	0.181034i
$233$	−7.45094e7			−0.385892			−0.192946	−	0.981209i	$-0.561804\pi$
$233$	−7.45094e7			−0.385892			−0.192946	+	0.981209i	$0.561804\pi$
$234$	1.91144e8	−	1.06757e8i	0.975224	−	0.544681i
$235$	1.59106e8			0.799740
$236$	8.58153e7	−	1.48636e8i	0.424984	−	0.736094i
$237$	−3.30794e8	−	9.11650e7i	−1.61413	−	0.444845i
$238$	−7.14175e7	−	1.23699e8i	−0.343388	−	0.594766i
$239$	−8.98328e7	−	1.55595e8i	−0.425640	−	0.737230i	0.570840	−	0.821061i	$-0.306618\pi$
$239$	−8.98328e7	−	1.55595e8i	−0.425640	−	0.737230i	−0.996480	+	0.0838313i	$0.973284\pi$
$240$	1.81249e7	+	6.96218e7i	0.0846321	+	0.325092i
$241$	3.04341e7	−	5.27134e7i	0.140056	−	0.242583i	−0.787462	−	0.616364i	$-0.788605\pi$
$241$	3.04341e7	−	5.27134e7i	0.140056	−	0.242583i	0.927517	+	0.373780i	$0.121939\pi$
$242$	−1.32779e8			−0.602250
$243$	−2.13858e8	−	6.55447e7i	−0.956103	−	0.293032i
$244$	−4.82611e7			−0.212683
$245$	5.54459e7	−	9.60352e7i	0.240873	−	0.417205i
$246$	4.88166e7	+	1.87516e8i	0.209071	+	0.803092i
$247$	−2.20750e8	−	3.82350e8i	−0.932098	−	1.61444i
$248$	3.23041e7	+	5.59523e7i	0.134486	+	0.232936i
$249$	−1.75479e8	−	4.83610e7i	−0.720322	−	0.198517i
$250$	−2.28213e7	+	3.95277e7i	−0.0923743	+	0.159997i
$251$	2.14309e8			0.855426			0.427713	−	0.903915i	$-0.359319\pi$
$251$	2.14309e8			0.855426			0.427713	+	0.903915i	$0.359319\pi$
$252$	−1.29255e8	+	7.21913e7i	−0.508798	+	0.284173i
$253$	1.20636e8			0.468334
$254$	−5.42724e7	+	9.40025e7i	−0.207807	+	0.359933i
$255$	2.11130e8	−	2.08144e8i	0.797367	−	0.786094i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	2.63538e7	+	4.56461e7i	0.0968450	+	0.167740i	0.910377	−	0.413779i	$-0.135792\pi$
$257$	2.63538e7	+	4.56461e7i	0.0968450	+	0.167740i	−0.813532	+	0.581520i	$0.802458\pi$
$258$	7.23760e7	−	7.13527e7i	0.262377	−	0.258667i
$259$	2.79593e8	−	4.84269e8i	0.999946	−	1.73196i
$260$	3.00787e8			1.06133
$261$	−2.41814e6	+	1.69814e8i	−0.00841860	+	0.591195i
$262$	−1.88251e8			−0.646670
$263$	−2.44289e8	+	4.23121e8i	−0.828055	+	1.43423i	0.0715077	+	0.997440i	$0.477219\pi$
$263$	−2.44289e8	+	4.23121e8i	−0.828055	+	1.43423i	−0.899562	+	0.436793i	$0.856114\pi$
$264$	3.92400e7	+	1.08143e7i	0.131255	+	0.0361731i
$265$	2.33449e8	+	4.04346e8i	0.770604	+	1.33473i
$266$	1.49275e8	+	2.58553e8i	0.486298	+	0.842293i
$267$	−7.96078e6	−	3.05792e7i	−0.0255956	−	0.0983189i
$268$	8.40224e6	−	1.45531e7i	0.0266639	−	0.0461832i
$269$	−1.69083e8			−0.529622			−0.264811	−	0.964300i	$-0.585310\pi$
$269$	−1.69083e8			−0.529622			−0.264811	+	0.964300i	$0.585310\pi$
$270$	−2.12604e8	−	2.21886e8i	−0.657353	−	0.686051i
$271$	−1.99531e8			−0.609001			−0.304501	−	0.952512i	$-0.598490\pi$
$271$	−1.99531e8			−0.609001			−0.304501	+	0.952512i	$0.598490\pi$
$272$	−3.45700e7	+	5.98769e7i	−0.104162	+	0.180413i
$273$	1.55944e8	+	5.99017e8i	0.463873	+	1.78185i
$274$	1.11962e8	+	1.93924e8i	0.328809	+	0.569514i
$275$	−5.34919e7	−	9.26506e7i	−0.155104	−	0.268648i
$276$	2.04764e8	+	5.64320e7i	0.586236	+	0.161564i
$277$	1.77438e8	−	3.07331e8i	0.501611	−	0.868816i	−0.498387	−	0.866955i	$-0.666074\pi$
$277$	1.77438e8	−	3.07331e8i	0.501611	−	0.868816i	0.999998	−	0.00186126i	$-0.000592457\pi$
$278$	−6.40150e7			−0.178700
$279$	−2.37010e8	−	1.41375e8i	−0.653360	−	0.389725i
$280$	−2.03398e8			−0.553724
$281$	1.40245e8	−	2.42912e8i	0.377065	−	0.653096i	−0.613569	−	0.789641i	$-0.710267\pi$
$281$	1.40245e8	−	2.42912e8i	0.377065	−	0.653096i	0.990634	+	0.136545i	$0.0436000\pi$
$282$	1.12864e8	−	1.11268e8i	0.299697	−	0.295460i
$283$	7.95244e7	+	1.37740e8i	0.208568	+	0.361251i	0.951264	−	0.308379i	$-0.0997863\pi$
$283$	7.95244e7	+	1.37740e8i	0.208568	+	0.361251i	−0.742696	+	0.669629i	$0.766453\pi$
$284$	−3.17092e7	−	5.49220e7i	−0.0821431	−	0.142276i
$285$	−4.41298e8	+	4.35059e8i	−1.12921	+	1.11325i
$286$	8.50882e7	−	1.47377e8i	0.215074	−	0.372519i
$287$	−5.47822e8			−1.36790
$288$	6.15460e7	+	3.67119e7i	0.151819	+	0.0905592i
$289$	−1.25409e8			−0.305623
$290$	−1.16662e8	+	2.02064e8i	−0.280890	+	0.486515i
$291$	7.32881e8	+	2.01978e8i	1.74344	+	0.480484i
$292$	3.34044e7	+	5.78581e7i	0.0785170	+	0.135995i
$293$	−1.72190e8	−	2.98242e8i	−0.399918	−	0.692679i	0.593797	−	0.804615i	$-0.297628\pi$
$293$	−1.72190e8	−	2.98242e8i	−0.399918	−	0.692679i	−0.993715	+	0.111936i	$0.964295\pi$
$294$	−2.78293e7	−	1.06899e8i	−0.0638686	−	0.245334i
$295$	−5.03600e8	+	8.72260e8i	−1.14211	+	1.97819i
$296$	−2.70676e8			−0.606637
$297$	−1.68860e8	+	4.14019e7i	−0.374007	+	0.0917006i
$298$	−2.17326e8			−0.475723
$299$	4.44013e8	−	7.69052e8i	0.960608	−	1.66382i
$300$	−4.74549e7	−	1.82285e8i	−0.101474	−	0.389787i
$301$	1.43672e8	+	2.48847e8i	0.303661	+	0.525956i
$302$	−1.67945e8	−	2.90890e8i	−0.350868	−	0.607721i
$303$	−1.91402e7	−	5.27494e6i	−0.0395273	−	0.0108935i
$304$	7.22574e7	−	1.25153e8i	0.147511	−	0.255497i
$305$	2.83216e8			0.571569
$306$	4.20506e6	−	2.95300e8i	0.00838972	−	0.589167i
$307$	5.28744e8			1.04294			0.521472	−	0.853269i	$-0.325383\pi$
$307$	5.28744e8			1.04294			0.521472	+	0.853269i	$0.325383\pi$
$308$	−5.75383e7	+	9.96592e7i	−0.112209	+	0.194352i
$309$	1.61962e8	−	1.59673e8i	0.312291	−	0.307876i
$310$	−1.89574e8	−	3.28351e8i	−0.361420	−	0.625997i
$311$	1.43382e8	+	2.48345e8i	0.270292	+	0.468159i	0.968937	−	0.247310i	$-0.0795465\pi$
$311$	1.43382e8	+	2.48345e8i	0.270292	+	0.468159i	−0.698645	+	0.715469i	$0.746213\pi$
$312$	2.13367e8	−	2.10351e8i	0.397729	−	0.392105i
$313$	−1.25124e7	+	2.16722e7i	−0.0230641	+	0.0399482i	−0.877327	−	0.479893i	$-0.840676\pi$
$313$	−1.25124e7	+	2.16722e7i	−0.0230641	+	0.0399482i	0.854263	+	0.519841i	$0.174009\pi$
$314$	6.56383e8			1.19648
$315$	7.58522e8	−	4.23648e8i	1.36735	−	0.763693i
$316$	−4.69580e8			−0.837153
$317$	2.60137e8	−	4.50570e8i	0.458663	−	0.794428i	−0.540227	−	0.841519i	$-0.681662\pi$
$317$	2.60137e8	−	4.50570e8i	0.458663	−	0.794428i	0.998891	+	0.0470910i	$0.0149951\pi$
$318$	4.48373e8	+	1.23569e8i	0.781887	+	0.215484i
$319$	6.60038e7	+	1.14322e8i	0.113842	+	0.197180i
$320$	4.92278e7	+	8.52651e7i	0.0839819	+	0.145461i
$321$	−3.34190e7	−	1.28370e8i	−0.0563931	−	0.216619i
$322$	−3.00250e8	+	5.20048e8i	−0.501172	+	0.868056i
$323$	−5.95554e8			−0.983359
$324$	−3.05986e8	−	8.71622e6i	−0.499797	−	0.0142371i
$325$	−7.87527e8			−1.27255
$326$	1.15714e8	−	2.00423e8i	0.184980	−	0.320395i
$327$	−7.43894e7	−	2.85747e8i	−0.117651	−	0.451924i
$328$	1.32588e8	+	2.29649e8i	0.207465	+	0.359340i
$329$	2.24043e8	+	3.88054e8i	0.346853	+	0.600768i
$330$	−2.30276e8	−	6.34629e7i	−0.352737	−	0.0972123i
$331$	2.52520e8	−	4.37377e8i	0.382734	−	0.662915i	−0.608718	−	0.793387i	$-0.708316\pi$
$331$	2.52520e8	−	4.37377e8i	0.382734	−	0.662915i	0.991452	+	0.130472i	$0.0416492\pi$
$332$	−2.49102e8			−0.373588
$333$	1.00942e9	−	5.63779e8i	1.49802	−	0.836669i
$334$	2.13736e8			0.313881
$335$	−4.93078e7	+	8.54037e7i	−0.0716571	+	0.124114i
$336$	−1.44283e8	+	1.42243e8i	−0.207505	+	0.204571i
$337$	9.18750e7	+	1.59132e8i	0.130765	+	0.226492i	0.923972	−	0.382461i	$-0.124923\pi$
$337$	9.18750e7	+	1.59132e8i	0.130765	+	0.226492i	−0.793206	+	0.608953i	$0.791590\pi$
$338$	−3.75356e8	−	6.50135e8i	−0.528731	−	0.915789i
$339$	−7.14133e8	+	7.04036e8i	−0.995589	+	0.981513i
$340$	2.02871e8	−	3.51383e8i	0.279926	−	0.484846i
$341$	−2.14510e8			−0.292960
$342$	−8.78933e6	+	6.17230e8i	−0.0118813	+	0.834364i
$343$	−5.58786e8			−0.747681
$344$	6.95449e7	−	1.20455e8i	0.0921108	−	0.159541i
$345$	−1.20164e9	−	3.31166e8i	−1.57546	−	0.434189i
$346$	1.05249e8	+	1.82296e8i	0.136600	+	0.236598i
$347$	1.43066e8	+	2.47797e8i	0.183816	+	0.318378i	0.943177	−	0.332291i	$-0.107822\pi$
$347$	1.43066e8	+	2.47797e8i	0.183816	+	0.318378i	−0.759361	+	0.650670i	$0.774488\pi$
$348$	5.85547e7	+	2.24922e8i	0.0744791	+	0.286092i
$349$	1.83182e7	−	3.17281e7i	0.0230672	−	0.0399535i	−0.854261	−	0.519844i	$-0.825990\pi$
$349$	1.83182e7	−	3.17281e7i	0.0230672	−	0.0399535i	0.877329	+	0.479890i	$0.159324\pi$
$350$	5.32541e8			0.663918
$351$	−3.57570e8	+	1.22886e9i	−0.441353	+	1.51680i
$352$	5.57033e7			0.0680740
$353$	−2.38469e8	+	4.13040e8i	−0.288549	+	0.499782i	−0.973464	−	0.228841i	$-0.926506\pi$
$353$	−2.38469e8	+	4.13040e8i	−0.288549	+	0.499782i	0.684914	+	0.728624i	$0.259840\pi$
$354$	2.52766e8	+	9.70934e8i	0.302836	+	1.16326i
$355$	1.86083e8	+	3.22305e8i	0.220753	+	0.382356i
$356$	−2.16218e7	−	3.74500e7i	−0.0253990	−	0.0439923i
$357$	8.04957e8	+	2.21842e8i	0.936341	+	0.258050i
$358$	8.78898e7	−	1.52230e8i	0.101239	−	0.175351i
$359$	−3.73983e8			−0.426600			−0.213300	−	0.976987i	$-0.568421\pi$
$359$	−3.73983e8			−0.426600			−0.213300	+	0.976987i	$0.568421\pi$
$360$	−3.61178e8	−	2.15440e8i	−0.408002	−	0.243371i
$361$	3.50942e8			0.392609
$362$	−5.04809e8	+	8.74356e8i	−0.559303	+	0.968742i
$363$	5.52739e8	−	5.44924e8i	0.606522	−	0.597947i
$364$	4.23550e8	+	7.33610e8i	0.460309	+	0.797279i
$365$	−1.96031e8	−	3.39535e8i	−0.211008	−	0.365477i
$366$	2.00903e8	−	1.98063e8i	0.214192	−	0.211164i
$367$	2.91624e8	−	5.05107e8i	0.307958	−	0.533399i	−0.669957	−	0.742400i	$-0.733688\pi$
$367$	2.91624e8	−	5.05107e8i	0.307958	−	0.533399i	0.977916	+	0.209000i	$0.0670209\pi$
$368$	2.90674e8			0.304046
$369$	−9.72778e8	−	5.80256e8i	−1.00791	−	0.601212i
$370$	1.58844e9			1.63029
$371$	−6.57457e8	+	1.13875e9i	−0.668434	+	1.15776i
$372$	−3.64104e8	−	1.00345e8i	−0.366712	−	0.101064i
$373$	−7.38605e8	−	1.27930e9i	−0.736939	−	1.27642i	−0.953867	−	0.300228i	$-0.902937\pi$
$373$	−7.38605e8	−	1.27930e9i	−0.736939	−	1.27642i	0.216928	−	0.976188i	$-0.430396\pi$
$374$	−1.14778e8	−	1.98802e8i	−0.113451	−	0.196503i
$375$	−6.72195e7	−	2.58206e8i	−0.0658242	−	0.252846i
$376$	1.08449e8	−	1.87839e8i	0.105213	−	0.182234i
$377$	9.71732e8			0.934011
$378$	2.41796e8	−	8.30981e8i	0.230265	−	0.791352i
$379$	−6.08958e8			−0.574580			−0.287290	−	0.957844i	$-0.592754\pi$
$379$	−6.08958e8			−0.574580			−0.287290	+	0.957844i	$0.592754\pi$
$380$	−4.24036e8	+	7.34452e8i	−0.396424	+	0.686627i
$381$	−1.59857e8	−	6.14050e8i	−0.148080	−	0.568809i
$382$	−7.17806e8	−	1.24328e9i	−0.658848	−	1.14116i
$383$	4.24357e8	+	7.35008e8i	0.385954	+	0.668492i	0.991901	−	0.127013i	$-0.0405390\pi$
$383$	4.24357e8	+	7.35008e8i	0.385954	+	0.668492i	−0.605947	+	0.795505i	$0.707206\pi$
$384$	9.45492e7	+	2.60572e7i	0.0852116	+	0.0234838i
$385$	3.37659e8	−	5.84842e8i	0.301554	−	0.522307i
$386$	−2.38651e8			−0.211207
$387$	−8.45939e6	+	5.94060e8i	−0.00741909	+	0.521005i
$388$	1.04036e9			0.904221
$389$	1.26651e8	−	2.19367e8i	0.109090	−	0.188950i	−0.806312	−	0.591491i	$-0.798540\pi$
$389$	1.26651e8	−	2.19367e8i	0.109090	−	0.188950i	0.915402	+	0.402541i	$0.131873\pi$
$390$	−1.25213e9	+	1.23442e9i	−1.06886	+	1.05375i
$391$	−5.98943e8	−	1.03740e9i	−0.506719	−	0.877662i
$392$	−7.55856e7	−	1.30918e8i	−0.0633779	−	0.109774i
$393$	7.83658e8	−	7.72578e8i	0.651257	−	0.642049i
$394$	−2.68345e8	+	4.64788e8i	−0.221033	+	0.382841i
$395$	2.75569e9			2.24978
$396$	−2.07731e8	+	1.16022e8i	−0.168101	+	0.0938872i
$397$	9.92215e8			0.795865			0.397932	−	0.917415i	$-0.369728\pi$
$397$	9.92215e8			0.795865			0.397932	+	0.917415i	$0.369728\pi$
$398$	4.72710e8	−	8.18758e8i	0.375841	−	0.650975i
$399$	−1.68250e9	−	4.63689e8i	−1.32602	−	0.365445i
$400$	−1.28889e8	−	2.23243e8i	−0.100695	−	0.174408i
$401$	4.74376e8	+	8.21644e8i	0.367382	+	0.636324i	0.989155	−	0.146873i	$-0.0469209\pi$
$401$	4.74376e8	+	8.21644e8i	0.367382	+	0.636324i	−0.621774	+	0.783197i	$0.713588\pi$
$402$	2.47485e7	+	9.50649e7i	0.0190002	+	0.0729842i
$403$	−7.89524e8	+	1.36750e9i	−0.600894	+	1.04078i
$404$	−2.71706e7			−0.0205005
$405$	1.79565e9	+	5.11504e7i	1.34317	+	0.0382610i
$406$	−6.57104e8			−0.487296
$407$	4.49346e8	−	7.78290e8i	0.330370	−	0.572217i
$408$	−1.01825e8	−	3.91132e8i	−0.0742236	−	0.285110i
$409$	−3.88383e8	−	6.72699e8i	−0.280691	−	0.486171i	0.690864	−	0.722985i	$-0.257230\pi$
$409$	−3.88383e8	−	6.72699e8i	−0.280691	−	0.486171i	−0.971555	+	0.236813i	$0.923897\pi$
$410$	−7.78080e8	−	1.34767e9i	−0.557546	−	0.965698i
$411$	−1.26194e9	−	3.47784e8i	−0.896586	−	0.247094i
$412$	1.55627e8	−	2.69554e8i	0.109634	−	0.189891i
$413$	−2.83655e9			−1.98137
$414$	−1.08400e9	+	6.05432e8i	−0.750804	+	0.419338i
$415$	1.46183e9			1.00399
$416$	2.05021e8	−	3.55107e8i	0.139628	−	0.241842i
$417$	2.66484e8	−	2.62716e8i	0.179968	−	0.177423i
$418$	2.39907e8	+	4.15531e8i	0.160667	+	0.278283i
$419$	3.14943e8	+	5.45498e8i	0.209162	+	0.362280i	0.951451	−	0.307801i	$-0.0995930\pi$
$419$	3.14943e8	+	5.45498e8i	0.209162	+	0.362280i	−0.742289	+	0.670080i	$0.766260\pi$
$420$	8.46713e8	−	8.34742e8i	0.557653	−	0.549768i
$421$	−5.52425e8	+	9.56829e8i	−0.360816	+	0.624952i	−0.988095	−	0.153842i	$-0.950835\pi$
$421$	−5.52425e8	+	9.56829e8i	−0.360816	+	0.624952i	0.627279	+	0.778795i	$0.284169\pi$
$422$	8.31883e8			0.538851
$423$	−1.31917e7	+	9.26382e8i	−0.00847438	+	0.595112i
$424$	6.36490e8			0.405519
$425$	−5.31160e8	+	9.19997e8i	−0.335633	+	0.581333i
$426$	3.57399e8	+	9.84972e7i	0.223985	+	0.0617292i
$427$	3.98808e8	+	6.90755e8i	0.247894	+	0.429365i
$428$	−9.07674e7	−	1.57214e8i	−0.0559599	−	0.0969253i
$429$	2.50624e8	+	9.62707e8i	0.153258	+	0.588700i
$430$	−4.08118e8	+	7.06881e8i	−0.247541	+	0.428753i
$431$	−2.85661e8			−0.171863			−0.0859313	−	0.996301i	$-0.527387\pi$
$431$	−2.85661e8			−0.171863			−0.0859313	+	0.996301i	$0.527387\pi$
$432$	−4.06871e8	+	9.97582e7i	−0.242808	+	0.0595327i
$433$	4.76788e8			0.282239			0.141120	−	0.989993i	$-0.454930\pi$
$433$	4.76788e8			0.282239			0.141120	+	0.989993i	$0.454930\pi$
$434$	5.33892e8	−	9.24727e8i	0.313501	−	0.543000i
$435$	−3.43623e8	−	1.31994e9i	−0.200157	−	0.768849i
$436$	−2.02045e8	−	3.49952e8i	−0.116747	−	0.202211i
$437$	1.25190e9	+	2.16835e9i	0.717602	+	1.24292i
$438$	−3.76506e8	−	1.03763e8i	−0.214098	−	0.0590042i
$439$	−1.25879e9	+	2.18029e9i	−0.710112	+	1.22995i	0.254703	+	0.967019i	$0.418022\pi$
$439$	−1.25879e9	+	2.18029e9i	−0.710112	+	1.22995i	−0.964815	+	0.262931i	$0.915311\pi$
$440$	−3.26890e8			−0.182944
$441$	5.54561e8	+	3.30792e8i	0.307903	+	0.183662i
$442$	−1.68981e9			−0.930807
$443$	2.29324e8	−	3.97201e8i	0.125325	−	0.217069i	−0.796535	−	0.604592i	$-0.793336\pi$
$443$	2.29324e8	−	3.97201e8i	0.125325	−	0.217069i	0.921860	+	0.387523i	$0.126669\pi$
$444$	1.12678e9	−	1.11085e9i	0.610940	−	0.602302i
$445$	1.26886e8	+	2.19772e8i	0.0682578	+	0.118226i
$446$	6.46118e8	+	1.11911e9i	0.344858	+	0.597311i
$447$	9.04691e8	−	8.91900e8i	0.479098	−	0.472324i
$448$	−1.38639e8	+	2.40130e8i	−0.0728472	+	0.126175i
$449$	−1.46433e9			−0.763444			−0.381722	−	0.924277i	$-0.624669\pi$
$449$	−1.46433e9			−0.763444			−0.381722	+	0.924277i	$0.624669\pi$
$450$	9.45642e8	+	5.64070e8i	0.489196	+	0.291803i
$451$	−8.80429e8			−0.451936
$452$	−6.86198e8	+	1.18853e9i	−0.349514	+	0.605377i
$453$	1.89293e9	+	5.21682e8i	0.956735	+	0.263671i
$454$	−1.52214e8	−	2.63642e8i	−0.0763411	−	0.132227i
$455$	−2.48557e9	−	4.30513e9i	−1.23704	−	2.14262i
$456$	2.12832e8	+	8.17536e8i	0.105114	+	0.403766i
$457$	−6.98299e8	+	1.20949e9i	−0.342243	+	0.592783i	−0.984849	−	0.173414i	$-0.944520\pi$
$457$	−6.98299e8	+	1.20949e9i	−0.342243	+	0.592783i	0.642606	+	0.766197i	$0.277853\pi$
$458$	−2.31773e9			−1.12728
$459$	1.19440e9	+	1.24654e9i	0.576509	+	0.601677i
$460$	−1.70580e9			−0.817100
$461$	1.98110e9	−	3.43137e9i	0.941789	−	1.63123i	0.179733	−	0.983715i	$-0.442476\pi$
$461$	1.98110e9	−	3.43137e9i	0.941789	−	1.63123i	0.762056	−	0.647511i	$-0.224190\pi$
$462$	−1.69477e8	−	6.51001e8i	−0.0799584	−	0.307139i
$463$	9.40813e8	+	1.62954e9i	0.440524	+	0.763010i	0.997728	−	0.0673653i	$-0.0214593\pi$
$463$	9.40813e8	+	1.62954e9i	0.440524	+	0.763010i	−0.557204	+	0.830375i	$0.688126\pi$
$464$	1.59037e8	+	2.75460e8i	0.0739069	+	0.128011i
$465$	2.13671e9	+	5.88866e8i	0.985508	+	0.271601i
$466$	2.98038e8	−	5.16217e8i	0.136433	−	0.236310i
$467$	9.69518e8			0.440501			0.220250	−	0.975443i	$-0.429313\pi$
$467$	9.69518e8			0.440501			0.220250	+	0.975443i	$0.429313\pi$
$468$	−2.49386e7	+	1.75131e9i	−0.0112464	+	0.789774i
$469$	−2.77729e8			−0.124313
$470$	−6.36424e8	+	1.10232e9i	−0.282751	+	0.489739i
$471$	−2.73242e9	+	2.69378e9i	−1.20496	+	1.18793i
$472$	6.86522e8	+	1.18909e9i	0.300509	+	0.520497i
$473$	2.30901e8	+	3.99933e8i	0.100326	+	0.173769i
$474$	1.95479e9	−	1.92715e9i	0.843092	−	0.831172i
$475$	1.11022e9	−	1.92296e9i	0.475315	−	0.823269i
$476$	1.14268e9			0.485624
$477$	−2.37363e9	+	1.32571e9i	−1.00138	+	0.559288i
$478$	1.43733e9			0.601946
$479$	1.00435e9	−	1.73959e9i	0.417552	−	0.723222i	−0.578140	−	0.815937i	$-0.696221\pi$
$479$	1.00435e9	−	1.73959e9i	0.417552	−	0.723222i	0.995693	+	0.0927156i	$0.0295547\pi$
$480$	−5.54854e8	−	1.52915e8i	−0.228999	−	0.0631110i
$481$	−3.30772e9	−	5.72913e9i	−1.35525	−	2.34737i
$482$	2.43473e8	+	4.21707e8i	0.0990343	+	0.171532i
$483$	−8.84376e8	−	3.39709e9i	−0.357126	−	1.37181i
$484$	5.31117e8	−	9.19922e8i	0.212927	−	0.368801i
$485$	−6.10529e9			−2.43002
$486$	1.30954e9	−	1.21948e9i	0.517478	−	0.481888i
$487$	3.02884e9			1.18830			0.594148	−	0.804356i	$-0.297490\pi$
$487$	3.02884e9			1.18830			0.594148	+	0.804356i	$0.297490\pi$
$488$	1.93044e8	−	3.34363e8i	0.0751948	−	0.130241i
$489$	3.40833e8	+	1.30922e9i	0.131814	+	0.506327i
$490$	4.43567e8	+	7.68281e8i	0.170323	+	0.295008i
$491$	−2.25862e9	−	3.91204e9i	−0.861107	−	1.49148i	−0.870861	−	0.491529i	$-0.836438\pi$
$491$	−2.25862e9	−	3.91204e9i	−0.861107	−	1.49148i	0.00975413	−	0.999952i	$-0.496895\pi$
$492$	−1.49442e9	−	4.11853e8i	−0.565709	−	0.155906i
$493$	6.55401e8	−	1.13519e9i	0.246344	−	0.426681i
$494$	3.53200e9			1.31819
$495$	1.21905e9	−	6.80864e8i	0.451757	−	0.252315i
$496$	−5.16865e8			−0.190191
$497$	−5.24061e8	+	9.07700e8i	−0.191485	+	0.331661i
$498$	1.03697e9	−	1.02231e9i	0.376239	−	0.370919i
$499$	2.32832e9	+	4.03277e9i	0.838862	+	1.45295i	0.890846	+	0.454305i	$0.150112\pi$
$499$	2.32832e9	+	4.03277e9i	0.838862	+	1.45295i	−0.0519839	+	0.998648i	$0.516554\pi$
$500$	−1.82571e8	−	3.16222e8i	−0.0653185	−	0.113135i
$501$	−8.89747e8	+	8.77167e8i	−0.316107	+	0.311638i
$502$	−8.57236e8	+	1.48478e9i	−0.302439	+	0.523840i
$503$	2.88413e9			1.01048			0.505239	−	0.862980i	$-0.331404\pi$
$503$	2.88413e9			1.01048			0.505239	+	0.862980i	$0.331404\pi$
$504$	1.68640e7	−	1.18427e9i	0.00586750	−	0.412044i
$505$	1.59448e8			0.0550934
$506$	−4.82545e8	+	8.35792e8i	−0.165581	+	0.286795i
$507$	4.23069e9	+	1.16595e9i	1.44173	+	0.397332i
$508$	−4.34179e8	−	7.52020e8i	−0.146942	−	0.254511i
$509$	6.60362e8	+	1.14378e9i	0.221957	+	0.384442i	0.955402	−	0.295307i	$-0.0954221\pi$
$509$	6.60362e8	+	1.14378e9i	0.221957	+	0.384442i	−0.733445	+	0.679749i	$0.762089\pi$
$510$	5.97549e8	+	2.29533e9i	0.199470	+	0.766212i
$511$	5.52077e8	−	9.56225e8i	0.183032	−	0.317020i
$512$	1.34218e8			0.0441942
$513$	−2.49651e9	−	2.60550e9i	−0.816437	−	0.852079i
$514$	−4.21661e8			−0.136960
$515$	−9.13283e8	+	1.58185e9i	−0.294632	+	0.510318i
$516$	2.04842e8	+	7.86847e8i	0.0656365	+	0.252125i
$517$	3.60070e8	+	6.23659e8i	0.114596	+	0.198486i
$518$	2.23674e9	+	3.87415e9i	0.707069	+	1.22468i
$519$	−1.18628e9	−	3.26931e8i	−0.372477	−	0.102653i
$520$	−1.20315e9	+	2.08391e9i	−0.375239	+	0.649932i
$521$	5.14654e9			1.59435			0.797175	−	0.603749i	$-0.206327\pi$
$521$	5.14654e9			1.59435			0.797175	+	0.603749i	$0.206327\pi$
$522$	−1.16683e9	−	6.96008e8i	−0.359055	−	0.214174i
$523$	−2.17050e9			−0.663444			−0.331722	−	0.943377i	$-0.607630\pi$
$523$	−2.17050e9			−0.663444			−0.331722	+	0.943377i	$0.607630\pi$
$524$	7.53004e8	−	1.30424e9i	0.228632	−	0.396003i
$525$	−2.21688e9	+	2.18554e9i	−0.668628	+	0.659175i
$526$	−1.95431e9	−	3.38497e9i	−0.585523	−	1.01416i
$527$	1.06502e9	+	1.84466e9i	0.316970	+	0.549009i
$528$	−2.31884e8	+	2.28605e8i	−0.0685570	+	0.0675877i
$529$	−8.15632e8	+	1.41272e9i	−0.239552	+	0.414916i
$530$	−3.73518e9			−1.08980
$531$	−5.03692e9	−	3.00449e9i	−1.45994	−	0.870844i
$532$	−2.38841e9			−0.687729
$533$	−3.24050e9	+	5.61271e9i	−0.926972	+	1.60556i
$534$	2.43702e8	+	6.71630e7i	0.0692572	+	0.0190869i
$535$	5.32661e8	+	9.22595e8i	0.150388	+	0.260479i
$536$	6.72180e7	+	1.16425e8i	0.0188542	+	0.0326565i
$537$	2.58876e8	+	9.94405e8i	0.0721410	+	0.277111i
$538$	6.76330e8	−	1.17144e9i	0.187250	−	0.324326i
$539$	5.01915e8			0.138060
$540$	2.38769e9	−	5.85423e8i	0.652528	−	0.159989i
$541$	−9.27955e7			−0.0251963			−0.0125981	−	0.999921i	$-0.504010\pi$
$541$	−9.27955e7			−0.0251963			−0.0125981	+	0.999921i	$0.504010\pi$
$542$	7.98125e8	−	1.38239e9i	0.215314	−	0.372936i
$543$	−1.48690e9	−	5.71153e9i	−0.398549	−	1.53092i
$544$	−2.76560e8	−	4.79015e8i	−0.0736534	−	0.127571i
$545$	1.18568e9	+	2.05366e9i	0.313747	+	0.543427i
$546$	−4.77389e9	−	1.31566e9i	−1.25516	−	0.345915i
$547$	2.73518e9	−	4.73747e9i	0.714547	−	1.23763i	−0.248588	−	0.968609i	$-0.579966\pi$
$547$	2.73518e9	−	4.73747e9i	0.714547	−	1.23763i	0.963134	−	0.269022i	$-0.0867003\pi$
$548$	−1.79139e9			−0.465006
$549$	−2.34818e7	+	1.64901e9i	−0.00605659	+	0.425323i
$550$	8.55870e8			0.219350
$551$	−1.36990e9	+	2.37274e9i	−0.348867	+	0.604255i
$552$	−1.21003e9	+	1.19292e9i	−0.306203	+	0.301874i
$553$	3.88039e9	+	6.72104e9i	0.975749	+	1.69005i
$554$	1.41950e9	+	2.45865e9i	0.354693	+	0.614346i
$555$	−6.61241e9	+	6.51892e9i	−1.64185	+	1.61864i
$556$	2.56060e8	−	4.43509e8i	0.0631800	−	0.109431i
$557$	4.50060e9			1.10351			0.551756	−	0.834006i	$-0.313958\pi$
$557$	4.50060e9			1.10351			0.551756	+	0.834006i	$0.313958\pi$
$558$	1.92752e9	−	1.07655e9i	0.469655	−	0.262311i
$559$	3.39941e9			0.823119
$560$	8.13592e8	−	1.40918e9i	0.195771	−	0.339086i
$561$	1.29368e9	+	3.56532e8i	0.309355	+	0.0852567i
$562$	1.12196e9	+	1.94330e9i	0.266625	+	0.461809i
$563$	−3.06529e9	−	5.30923e9i	−0.723922	−	1.25387i	−0.959416	−	0.281994i	$-0.909004\pi$
$563$	−3.06529e9	−	5.30923e9i	−0.723922	−	1.25387i	0.235494	−	0.971876i	$-0.424329\pi$
$564$	3.19433e8	+	1.22702e9i	0.0749726	+	0.287987i
$565$	4.02690e9	−	6.97479e9i	0.939292	−	1.62690i
$566$	−1.27239e9			−0.294960
$567$	2.40377e9	+	4.45156e9i	0.553800	+	1.02559i
$568$	5.07347e8			0.116168
$569$	1.71059e9	−	2.96282e9i	0.389271	−	0.674238i	−0.603080	−	0.797680i	$-0.706060\pi$
$569$	1.71059e9	−	2.96282e9i	0.389271	−	0.674238i	0.992352	+	0.123443i	$0.0393935\pi$
$570$	−1.24898e9	−	4.79764e9i	−0.282485	−	1.08509i
$571$	−1.14292e9	−	1.97960e9i	−0.256916	−	0.444991i	0.708498	−	0.705712i	$-0.249373\pi$
$571$	−1.14292e9	−	1.97960e9i	−0.256916	−	0.444991i	−0.965414	+	0.260721i	$0.916040\pi$
$572$	6.80706e8	+	1.17902e9i	0.152080	+	0.263411i
$573$	8.09049e9	+	2.22969e9i	1.79653	+	0.495113i
$574$	2.19129e9	−	3.79542e9i	0.483624	−	0.837661i
$575$	4.46615e9			0.979706
$576$	−5.00531e8	+	2.79556e8i	−0.109132	+	0.0609523i
$577$	−7.03121e9			−1.52375			−0.761877	−	0.647722i	$-0.775722\pi$
$577$	−7.03121e9			−1.52375			−0.761877	+	0.647722i	$0.775722\pi$
$578$	5.01636e8	−	8.68859e8i	0.108054	−	0.187155i
$579$	9.93467e8	−	9.79420e8i	0.212705	−	0.209698i
$580$	−9.33295e8	−	1.61651e9i	−0.198619	−	0.344018i
$581$	2.05846e9	+	3.56536e9i	0.435438	+	0.754200i
$582$	−4.33087e9	+	4.26964e9i	−0.910636	+	0.897761i
$583$	−1.05663e9	+	1.83013e9i	−0.220842	+	0.382510i
$584$	−5.34470e8			−0.111040
$585$	1.46350e8	−	1.02774e10i	0.0302237	−	2.12245i
$586$	2.75504e9			0.565570
$587$	4.47158e8	−	7.74500e8i	0.0912488	−	0.158048i	−0.816788	−	0.576938i	$-0.804247\pi$
$587$	4.47158e8	−	7.74500e8i	0.0912488	−	0.158048i	0.908037	+	0.418890i	$0.137581\pi$
$588$	8.51936e8	+	2.34789e8i	0.172817	+	0.0476274i
$589$	−2.22607e9	−	3.85567e9i	−0.448886	−	0.777493i
$590$	−4.02880e9	−	6.97808e9i	−0.807594	−	1.39879i
$591$	−7.90402e8	−	3.03612e9i	−0.157504	−	0.605010i
$592$	1.08270e9	−	1.87530e9i	0.214478	−	0.371488i
$593$	−8.80907e9			−1.73476			−0.867379	−	0.497649i	$-0.834197\pi$
$593$	−8.80907e9			−1.73476			−0.867379	+	0.497649i	$0.834197\pi$
$594$	3.88601e8	−	1.33551e9i	0.0760766	−	0.261453i
$595$	−6.70572e9			−1.30508
$596$	8.69302e8	−	1.50568e9i	0.168193	−	0.291320i
$597$	1.39235e9	+	5.34835e9i	0.267817	+	1.02875i
$598$	3.55210e9	+	6.15242e9i	0.679252	+	1.17650i
$599$	−4.91595e8	−	8.51468e8i	−0.0934574	−	0.161873i	0.815506	−	0.578748i	$-0.196459\pi$
$599$	−4.91595e8	−	8.51468e8i	−0.0934574	−	0.161873i	−0.908964	+	0.416875i	$0.863125\pi$
$600$	1.45273e9	+	4.00364e8i	0.274571	+	0.0756704i
$601$	−1.02236e9	+	1.77078e9i	−0.192107	+	0.332739i	−0.945948	−	0.324317i	$-0.894865\pi$
$601$	−1.02236e9	+	1.77078e9i	−0.192107	+	0.332739i	0.753841	+	0.657056i	$0.228199\pi$
$602$	−2.29875e9			−0.429441
$603$	−4.93169e8	−	2.94172e8i	−0.0915978	−	0.0546375i
$604$	2.68712e9			0.496202
$605$	−3.11682e9	+	5.39848e9i	−0.572226	+	0.991124i
$606$	1.13107e8	−	1.11507e8i	0.0206459	−	0.0203540i
$607$	−1.78806e9	−	3.09701e9i	−0.324505	−	0.562059i	0.656907	−	0.753971i	$-0.271864\pi$
$607$	−1.78806e9	−	3.09701e9i	−0.324505	−	0.562059i	−0.981412	+	0.191913i	$0.938531\pi$
$608$	5.78059e8	+	1.00123e9i	0.104306	+	0.180663i
$609$	2.73542e9	−	2.69674e9i	0.490753	−	0.483815i
$610$	−1.13286e9	+	1.96218e9i	−0.202080	+	0.350013i
$611$	5.30108e9			0.940199
$612$	2.02908e9	+	1.21033e9i	0.357824	+	0.213440i
$613$	1.22567e9			0.214913			0.107457	−	0.994210i	$-0.465729\pi$
$613$	1.22567e9			0.214913			0.107457	+	0.994210i	$0.465729\pi$
$614$	−2.11497e9	+	3.66324e9i	−0.368736	+	0.638670i
$615$	8.76985e9	+	2.41692e9i	1.52030	+	0.418986i
$616$	−4.60306e8	−	7.97274e8i	−0.0793441	−	0.137428i
$617$	−3.80166e9	−	6.58468e9i	−0.651592	−	1.12859i	−0.982737	−	0.185010i	$-0.940768\pi$
$617$	−3.80166e9	−	6.58468e9i	−0.651592	−	1.12859i	0.331145	−	0.943580i	$-0.392565\pi$
$618$	4.58394e8	+	1.76080e9i	0.0781230	+	0.300089i
$619$	−2.87850e9	+	4.98571e9i	−0.487808	+	0.844908i	−0.999902	−	0.0140213i	$-0.995537\pi$
$619$	−2.87850e9	+	4.98571e9i	−0.487808	+	0.844908i	0.512094	+	0.858930i	$0.328870\pi$
$620$	3.03318e9			0.511125
$621$	2.02782e9	−	6.96902e9i	0.339789	−	1.16775i
$622$	−2.29411e9			−0.382250
$623$	−3.57345e8	+	6.18940e8i	−0.0592079	+	0.102551i
$624$	6.03883e8	+	2.31965e9i	0.0994962	+	0.382188i
$625$	3.52977e9	+	6.11374e9i	0.578317	+	1.00167i
$626$	−1.00099e8	−	1.73377e8i	−0.0163088	−	0.0282476i
$627$	−2.70403e9	−	7.45215e8i	−0.438101	−	0.120738i
$628$	−2.62553e9	+	4.54756e9i	−0.423018	+	0.732688i
$629$	−8.92377e9			−1.42979
$630$	−9.89647e7	+	6.94979e9i	−0.0157684	+	1.10734i
$631$	−2.41912e9			−0.383313			−0.191657	−	0.981462i	$-0.561386\pi$
$631$	−2.41912e9			−0.383313			−0.191657	+	0.981462i	$0.561386\pi$
$632$	1.87832e9	−	3.25335e9i	0.295978	−	0.512650i
$633$	−3.46299e9	+	3.41403e9i	−0.542674	+	0.535001i
$634$	2.08109e9	+	3.60456e9i	0.324324	+	0.561746i
$635$	2.54794e9	+	4.41316e9i	0.394895	+	0.683978i
$636$	−2.64960e9	+	2.61214e9i	−0.408395	+	0.402621i
$637$	1.84734e9	−	3.19969e9i	0.283178	−	0.490479i
$638$	−1.05606e9			−0.160997
$639$	−1.89202e9	+	1.05673e9i	−0.286863	+	0.160218i
$640$	−7.87645e8			−0.118768
$641$	3.95891e9	−	6.85703e9i	0.593707	−	1.02833i	−0.400021	−	0.916506i	$-0.630997\pi$
$641$	3.95891e9	−	6.85703e9i	0.593707	−	1.02833i	0.993728	−	0.111825i	$-0.0356696\pi$
$642$	1.02305e9	+	2.81948e8i	0.152590	+	0.0420529i
$643$	5.35854e9	+	9.28126e9i	0.794891	+	1.37679i	0.922908	+	0.385020i	$0.125805\pi$
$643$	5.35854e9	+	9.28126e9i	0.794891	+	1.37679i	−0.128017	+	0.991772i	$0.540861\pi$
$644$	−2.40200e9	−	4.16038e9i	−0.354382	−	0.613808i
$645$	−1.20210e9	−	4.61754e9i	−0.176393	−	0.677566i
$646$	2.38222e9	−	4.12612e9i	0.347670	−	0.602182i
$647$	8.06643e9			1.17089			0.585446	−	0.810712i	$-0.300920\pi$
$647$	8.06643e9			1.17089			0.585446	+	0.810712i	$0.300920\pi$
$648$	1.28433e9	−	2.08507e9i	0.185423	−	0.301029i
$649$	−4.55875e9			−0.654620
$650$	3.15011e9	−	5.45614e9i	0.449913	−	0.779272i
$651$	1.57256e9	+	6.04057e9i	0.223395	+	0.858113i
$652$	9.25715e8	+	1.60338e9i	0.130801	+	0.226554i
$653$	−5.00680e9	−	8.67202e9i	−0.703661	−	1.21878i	−0.967172	−	0.254121i	$-0.918214\pi$
$653$	−5.00680e9	−	8.67202e9i	−0.703661	−	1.21878i	0.263511	−	0.964656i	$-0.415119\pi$
$654$	2.27727e9	+	6.27604e8i	0.318341	+	0.0877331i
$655$	−4.41894e9	+	7.65382e9i	−0.614431	+	1.06423i
$656$	−2.12140e9			−0.293400
$657$	1.99317e9	−	1.11322e9i	0.274199	−	0.153145i
$658$	−3.58469e9			−0.490525
$659$	−7.05570e9	+	1.22208e10i	−0.960376	+	1.66342i	−0.238821	+	0.971064i	$0.576761\pi$
$659$	−7.05570e9	+	1.22208e10i	−0.960376	+	1.66342i	−0.721555	+	0.692357i	$0.756572\pi$
$660$	1.36079e9	−	1.34155e9i	0.184241	−	0.181637i
$661$	−4.81075e9	−	8.33246e9i	−0.647899	−	1.12219i	−0.983624	−	0.180234i	$-0.942315\pi$
$661$	−4.81075e9	−	8.33246e9i	−0.647899	−	1.12219i	0.335725	−	0.941960i	$-0.391019\pi$
$662$	2.02016e9	+	3.49902e9i	0.270634	+	0.468752i
$663$	7.03440e9	−	6.93494e9i	0.937410	−	0.924156i
$664$	9.96406e8	−	1.72583e9i	0.132083	−	0.228775i
$665$	1.40162e10			1.84822
$666$	−1.31699e8	+	9.24857e9i	−0.0172752	+	1.21315i
$667$	−5.51080e9			−0.719075
$668$	−8.54943e8	+	1.48080e9i	−0.110974	+	0.192212i
$669$	−7.28249e9	−	2.00701e9i	−0.940348	−	0.259155i
$670$	−3.94463e8	−	6.83230e8i	−0.0506692	−	0.0877617i
$671$	6.40941e8	+	1.11014e9i	0.0819011	+	0.141857i
$672$	−4.08357e8	−	1.56860e9i	−0.0519096	−	0.199397i
$673$	−5.84290e9	+	1.01202e10i	−0.738884	+	1.27978i	0.214115	+	0.976808i	$0.431313\pi$
$673$	−5.84290e9	+	1.01202e10i	−0.738884	+	1.27978i	−0.952998	+	0.302975i	$0.902020\pi$
$674$	−1.47000e9			−0.184930
$675$	−6.25149e9	+	1.53276e9i	−0.782384	+	0.191828i
$676$	6.00569e9			0.747738
$677$	5.55719e9	−	9.62534e9i	0.688327	−	1.19222i	−0.284051	−	0.958809i	$-0.591679\pi$
$677$	5.55719e9	−	9.62534e9i	0.688327	−	1.19222i	0.972379	−	0.233409i	$-0.0749881\pi$
$678$	−2.02117e9	−	7.76380e9i	−0.249058	−	0.956688i
$679$	−8.59710e9	−	1.48906e10i	−1.05392	−	1.82544i
$680$	1.62297e9	+	2.81106e9i	0.197938	+	0.342838i
$681$	1.71562e9	+	4.72817e8i	0.208165	+	0.0573691i
$682$	8.58041e8	−	1.48617e9i	0.103577	−	0.179400i
$683$	−1.61450e10			−1.93894			−0.969472	−	0.245201i	$-0.921146\pi$
$683$	−1.61450e10			−1.93894			−0.969472	+	0.245201i	$0.921146\pi$
$684$	−4.24114e9	−	2.52981e9i	−0.506741	−	0.302268i
$685$	1.05126e10			1.24967
$686$	2.23515e9	−	3.87139e9i	0.264345	−	0.457859i
$687$	9.64833e9	−	9.51191e9i	1.13528	−	1.11923i
$688$	5.56359e8	+	9.63642e8i	0.0651322	+	0.112812i
$689$	7.77803e9	+	1.34719e10i	0.905946	+	1.56915i
$690$	7.10096e9	−	7.00056e9i	0.822896	−	0.811262i
$691$	6.98902e8	−	1.21053e9i	0.0805829	−	0.139574i	−0.822918	−	0.568161i	$-0.807655\pi$
$691$	6.98902e8	−	1.21053e9i	0.0805829	−	0.139574i	0.903500	+	0.428587i	$0.140988\pi$
$692$	−1.68398e9			−0.193182
$693$	3.37720e9	+	2.01448e9i	0.385470	+	0.229931i
$694$	−2.28905e9			−0.259955
$695$	−1.50267e9	+	2.60269e9i	−0.169791	+	0.294087i
$696$	−1.79253e9	−	4.94011e8i	−0.201527	−	0.0555398i
$697$	4.37122e9	+	7.57117e9i	0.488976	+	0.846931i
$698$	1.46546e8	+	2.53825e8i	0.0163110	+	0.0282514i
$699$	8.77860e8	+	3.37207e9i	0.0972199	+	0.373445i
$700$	−2.13016e9	+	3.68955e9i	−0.234731	+	0.406565i
$701$	−1.34244e9			−0.147191			−0.0735956	−	0.997288i	$-0.523447\pi$
$701$	−1.34244e9			−0.147191			−0.0735956	+	0.997288i	$0.523447\pi$
$702$	−7.08353e9	−	7.39277e9i	−0.772805	−	0.806543i
$703$	1.86523e10			2.02483
$704$	−2.22813e8	+	3.85924e8i	−0.0240678	+	0.0416867i
$705$	−1.87456e9	−	7.20064e9i	−0.201483	−	0.773943i
$706$	−1.90775e9	−	3.30432e9i	−0.204035	−	0.353399i
$707$	2.24525e8	+	3.88889e8i	0.0238944	+	0.0413864i
$708$	−7.73789e9	−	2.13252e9i	−0.819419	−	0.225827i
$709$	7.93153e9	−	1.37378e10i	0.835786	−	1.44762i	−0.0576025	−	0.998340i	$-0.518346\pi$
$709$	7.93153e9	−	1.37378e10i	0.835786	−	1.44762i	0.893389	−	0.449285i	$-0.148321\pi$
$710$	−2.97732e9			−0.312192
$711$	−2.28478e8	+	1.60448e10i	−0.0238397	+	1.67414i
$712$	3.45949e8			0.0359196
$713$	4.47748e9	−	7.75522e9i	0.462616	−	0.801274i
$714$	−4.75679e9	+	4.68954e9i	−0.489070	+	0.482155i
$715$	−3.99466e9	−	6.91896e9i	−0.408704	−	0.707896i
$716$	7.03118e8	+	1.21784e9i	0.0715868	+	0.123992i
$717$	−5.98335e9	+	5.89875e9i	−0.606216	+	0.597645i
$718$	1.49593e9	−	2.59103e9i	0.150826	−	0.261238i
$719$	2.14766e9			0.215483			0.107742	−	0.994179i	$-0.465638\pi$
$719$	2.14766e9			0.215483			0.107742	+	0.994179i	$0.465638\pi$
$720$	2.93732e9	−	1.64055e9i	0.293284	−	0.163804i
$721$	−5.14412e9			−0.511137
$722$	−1.40377e9	+	2.43140e9i	−0.138808	+	0.240423i
$723$	−2.74421e9	−	7.56291e8i	−0.270044	−	0.0744226i
$724$	−4.03848e9	−	6.99485e9i	−0.395487	−	0.685004i
$725$	2.44357e9	+	4.23239e9i	0.238145	+	0.412480i
$726$	1.56439e9	+	6.00918e9i	0.151728	+	0.582823i
$727$	5.14336e9	−	8.90856e9i	0.496451	−	0.859879i	−0.503540	−	0.863972i	$-0.667969\pi$
$727$	5.14336e9	−	8.90856e9i	0.496451	−	0.859879i	0.999992	+	0.00409288i	$0.00130281\pi$
$728$	−6.77680e9			−0.650976
$729$	−4.46699e8	+	1.04508e10i	−0.0427040	+	0.999088i
$730$	3.13649e9			0.298411
$731$	2.29279e9	−	3.97123e9i	0.217097	−	0.376023i
$732$	5.68606e8	+	2.18415e9i	0.0535825	+	0.205823i
$733$	1.60210e9	+	2.77493e9i	0.150254	+	0.260248i	0.931321	−	0.364200i	$-0.118657\pi$
$733$	1.60210e9	+	2.77493e9i	0.150254	+	0.260248i	−0.781067	+	0.624448i	$0.785324\pi$
$734$	2.33299e9	+	4.04086e9i	0.217759	+	0.377170i
$735$	−4.99951e9	−	1.37784e9i	−0.464432	−	0.127995i
$736$	−1.16270e9	+	2.01385e9i	−0.107496	+	0.186189i
$737$	−4.46351e8			−0.0410715
$738$	7.91124e9	−	4.41858e9i	0.724515	−	0.404655i
$739$	1.29766e10			1.18279			0.591394	−	0.806383i	$-0.298578\pi$
$739$	1.29766e10			1.18279			0.591394	+	0.806383i	$0.298578\pi$
$740$	−6.35375e9	+	1.10050e10i	−0.576394	+	0.998343i
$741$	−1.47031e10	+	1.44953e10i	−1.32754	+	1.30877i
$742$	−5.25966e9	−	9.10999e9i	−0.472654	−	0.818661i
$743$	−3.62353e9	−	6.27614e9i	−0.324094	−	0.561348i	0.657234	−	0.753686i	$-0.271726\pi$
$743$	−3.62353e9	−	6.27614e9i	−0.324094	−	0.561348i	−0.981329	+	0.192339i	$0.938393\pi$
$744$	2.15162e9	−	2.12120e9i	0.191541	−	0.188833i
$745$	−5.10143e9	+	8.83593e9i	−0.452007	+	0.782898i
$746$	1.18177e10			1.04219
$747$	−1.21202e8	+	8.51141e9i	−0.0106387	+	0.747101i
$748$	1.83645e9			0.160444
$749$	−1.50012e9	+	2.59828e9i	−0.130449	+	0.225944i
$750$	2.05778e9	+	5.67113e8i	0.178109	+	0.0490857i
$751$	4.47123e9	+	7.74440e9i	0.385201	+	0.667188i	0.991797	−	0.127822i	$-0.0407988\pi$
$751$	4.47123e9	+	7.74440e9i	0.385201	+	0.667188i	−0.606596	+	0.795010i	$0.707465\pi$
$752$	8.67592e8	+	1.50271e9i	0.0743966	+	0.128859i
$753$	−2.52496e9	−	9.69897e9i	−0.215512	−	0.827834i
$754$	−3.88693e9	+	6.73236e9i	−0.330223	+	0.571962i
$755$	−1.57692e10			−1.33350
$756$	4.79002e9	+	4.99913e9i	0.403191	+	0.420793i
$757$	1.36108e10			1.14037			0.570187	−	0.821515i	$-0.306871\pi$
$757$	1.36108e10			1.14037			0.570187	+	0.821515i	$0.306871\pi$
$758$	2.43583e9	−	4.21899e9i	0.203145	−	0.351857i
$759$	−1.42132e9	−	5.45962e9i	−0.117990	−	0.453228i
$760$	−3.39229e9	−	5.87562e9i	−0.280314	−	0.485519i
$761$	1.10122e10	+	1.90738e10i	0.905794	+	1.56888i	0.819848	+	0.572582i	$0.194058\pi$
$761$	1.10122e10	+	1.90738e10i	0.905794	+	1.56888i	0.0859464	+	0.996300i	$0.472609\pi$
$762$	4.89369e9	+	1.34867e9i	0.400677	+	0.110424i
$763$	−3.33921e9	+	5.78368e9i	−0.272149	+	0.471377i
$764$	1.14849e10			0.931752
$765$	−1.19075e10	−	7.10274e9i	−0.961623	−	0.573602i
$766$	−6.78971e9			−0.545821
$767$	−1.67789e10	+	2.90619e10i	−1.34270	+	2.32563i
$768$	−5.58727e8	+	5.50827e8i	−0.0445077	+	0.0438784i
$769$	−5.17112e9	−	8.95663e9i	−0.410055	−	0.710236i	0.584840	−	0.811148i	$-0.301157\pi$
$769$	−5.17112e9	−	8.95663e9i	−0.410055	−	0.710236i	−0.994895	+	0.100912i	$0.967824\pi$
$770$	2.70127e9	+	4.67873e9i	0.213231	+	0.369327i
$771$	1.75531e9	−	1.73049e9i	0.137931	−	0.135981i
$772$	9.54605e8	−	1.65342e9i	0.0746729	−	0.129337i
$773$	3.65169e9			0.284358			0.142179	−	0.989841i	$-0.454589\pi$
$773$	3.65169e9			0.284358			0.142179	+	0.989841i	$0.454589\pi$
$774$	−4.08193e9	−	2.43485e9i	−0.316426	−	0.188746i
$775$	−7.94152e9			−0.612841
$776$	−4.16146e9	+	7.20786e9i	−0.319690	+	0.553720i
$777$	−2.52106e10	−	6.94791e9i	−1.92801	−	0.531350i
$778$	1.01321e9	+	1.75493e9i	0.0771385	+	0.133608i
$779$	−9.13662e9	−	1.58251e10i	−0.692476	−	1.19940i
$780$	−3.54383e9	−	1.36127e10i	−0.267388	−	1.02710i
$781$	−8.42241e8	+	1.45880e9i	−0.0632642	+	0.109577i
$782$	9.58309e9			0.716608
$783$	7.71373e9	−	1.89128e9i	0.574247	−	0.140796i
$784$	1.20937e9			0.0896299
$785$	1.54077e10	−	2.66869e10i	1.13683	−	1.96904i
$786$	2.21795e9	+	8.51965e9i	0.162919	+	0.625811i
$787$	−1.19537e10	−	2.07044e10i	−0.874158	−	1.51409i	−0.857657	−	0.514222i	$-0.828081\pi$
$787$	−1.19537e10	−	2.07044e10i	−0.874158	−	1.51409i	−0.0165008	−	0.999864i	$-0.505253\pi$
$788$	−2.14676e9	−	3.71830e9i	−0.156294	−	0.270709i
$789$	2.20273e10	+	6.07061e9i	1.59659	+	0.440011i
$790$	−1.10228e10	+	1.90920e10i	−0.795419	+	1.37771i
$791$	2.26817e10			1.62951
$792$	2.71028e7	−	1.90329e9i	0.00193855	−	0.136134i
$793$	9.43617e9			0.671954
$794$	−3.96886e9	+	6.87427e9i	−0.281381	+	0.487366i
$795$	1.55490e10	−	1.53291e10i	1.09753	−	1.08201i
$796$	3.78168e9	+	6.55006e9i	0.265760	+	0.460309i
$797$	−1.36082e10	−	2.35700e10i	−0.952128	−	1.64913i	−0.740807	−	0.671718i	$-0.765557\pi$
$797$	−1.36082e10	−	2.35700e10i	−0.952128	−	1.64913i	−0.211321	−	0.977417i	$-0.567777\pi$
$798$	9.94255e9	−	9.80197e9i	0.692608	−	0.682816i
$799$	3.57540e9	−	6.19277e9i	0.247977	−	0.429508i
$800$	2.06223e9			0.142404
$801$	−1.29013e9	+	7.20560e8i	−0.0886991	+	0.0495401i
$802$	−7.59002e9			−0.519556
$803$	8.87267e8	−	1.53679e9i	0.0604714	−	0.104740i
$804$	−7.57623e8	−	2.08797e8i	−0.0514111	−	0.0141686i
$805$	1.40959e10	+	2.44149e10i	0.952375	+	1.64956i
$806$	−6.31619e9	−	1.09400e10i	−0.424896	−	0.735942i
$807$	1.99211e9	+	7.65216e9i	0.133431	+	0.512538i
$808$	1.08682e8	−	1.88243e8i	0.00724801	−	0.0125539i
$809$	−2.09999e10			−1.39443			−0.697216	−	0.716861i	$-0.745578\pi$
$809$	−2.09999e10			−1.39443			−0.697216	+	0.716861i	$0.745578\pi$
$810$	−7.53699e9	+	1.22360e10i	−0.498311	+	0.808990i
$811$	−1.21414e10			−0.799276			−0.399638	−	0.916673i	$-0.630864\pi$
$811$	−1.21414e10			−0.799276			−0.399638	+	0.916673i	$0.630864\pi$
$812$	2.62842e9	−	4.55255e9i	0.172285	−	0.298407i
$813$	2.35085e9	+	9.03016e9i	0.153429	+	0.589357i
$814$	3.59477e9	+	6.22632e9i	0.233607	+	0.404619i
$815$	−5.43248e9	−	9.40933e9i	−0.351517	−	0.608845i
$816$	3.11714e9	+	8.59068e8i	0.200836	+	0.0553493i
$817$	−4.79234e9	+	8.30057e9i	−0.307447	+	0.532514i
$818$	6.21413e9			0.396957
$819$	2.52724e10	−	1.41151e10i	1.60750	−	0.897821i
$820$	1.24493e10			0.788489
$821$	5.66101e9	−	9.80516e9i	0.357020	−	0.618377i	−0.630441	−	0.776237i	$-0.717126\pi$
$821$	5.66101e9	−	9.80516e9i	0.357020	−	0.618377i	0.987462	+	0.157860i	$0.0504593\pi$
$822$	7.45727e9	−	7.35184e9i	0.468305	−	0.461684i
$823$	2.91399e9	+	5.04718e9i	0.182217	+	0.315609i	0.942635	−	0.333825i	$-0.108339\pi$
$823$	2.91399e9	+	5.04718e9i	0.182217	+	0.315609i	−0.760418	+	0.649434i	$0.775006\pi$
$824$	1.24502e9	+	2.15643e9i	0.0775228	+	0.134273i
$825$	−3.56285e9	+	3.51247e9i	−0.220906	+	0.217783i
$826$	1.13462e10	−	1.96522e10i	0.700520	−	1.21334i
$827$	2.11794e10			1.30210			0.651050	−	0.759034i	$-0.274329\pi$
$827$	2.11794e10			1.30210			0.651050	+	0.759034i	$0.274329\pi$
$828$	1.41430e8	−	9.93188e9i	0.00865833	−	0.608030i
$829$	−1.77492e10			−1.08203			−0.541013	−	0.841014i	$-0.681959\pi$
$829$	−1.77492e10			−1.08203			−0.541013	+	0.841014i	$0.681959\pi$
$830$	−5.84733e9	+	1.01279e10i	−0.354964	+	0.614815i
$831$	−1.59994e10	−	4.40935e9i	−0.967165	−	0.266545i
$832$	1.64017e9	+	2.84085e9i	0.0987317	+	0.171008i
$833$	−2.49194e9	−	4.31617e9i	−0.149376	−	0.258727i
$834$	7.54216e8	+	2.89712e9i	0.0450209	+	0.172936i
$835$	5.01716e9	−	8.68997e9i	0.298233	−	0.516554i
$836$	−3.83851e9			−0.227217
$837$	−3.60578e9	+	1.23920e10i	−0.212550	+	0.730471i
$838$	−5.03909e9			−0.295800
$839$	1.31911e10	−	2.28476e10i	0.771104	−	1.33559i	−0.165855	−	0.986150i	$-0.553038\pi$
$839$	1.31911e10	−	2.28476e10i	0.771104	−	1.33559i	0.936959	−	0.349441i	$-0.113628\pi$
$840$	2.39641e9	+	9.20517e9i	0.139503	+	0.535863i
$841$	5.60981e9	+	9.71647e9i	0.325209	+	0.563278i
$842$	−4.41940e9	−	7.65463e9i	−0.255136	−	0.441908i
$843$	−1.26458e10	−	3.48511e9i	−0.727026	−	0.200364i
$844$	−3.32753e9	+	5.76345e9i	−0.190513	+	0.329977i
$845$	−3.52439e10			−2.00949
$846$	−6.36540e9	−	3.79692e9i	−0.361434	−	0.215593i
$847$	−1.75556e10			−0.992715
$848$	−2.54596e9	+	4.40973e9i	−0.143372	+	0.248328i
$849$	5.29676e9	−	5.22187e9i	0.297052	−	0.292853i
$850$	−4.24928e9	−	7.35997e9i	−0.237328	−	0.411065i
$851$	1.87584e10	+	3.24905e10i	1.04338	+	1.80719i
$852$	−2.11200e9	+	2.08214e9i	−0.116992	+	0.115338i
$853$	−1.33903e10	+	2.31927e10i	−0.738701	+	1.27947i	0.214379	+	0.976750i	$0.431227\pi$
$853$	−1.33903e10	+	2.31927e10i	−0.738701	+	1.27947i	−0.953080	+	0.302717i	$0.902106\pi$
$854$	−6.38092e9			−0.350575
$855$	2.48887e10	+	1.48460e10i	1.36183	+	0.812321i
$856$	1.45228e9			0.0791392
$857$	−6.44399e9	+	1.11613e10i	−0.349721	+	0.605735i	−0.986200	−	0.165560i	$-0.947057\pi$
$857$	−6.44399e9	+	1.11613e10i	−0.349721	+	0.605735i	0.636479	+	0.771294i	$0.280390\pi$
$858$	−7.67233e9	−	2.11445e9i	−0.414688	−	0.114286i
$859$	−2.13794e9	−	3.70302e9i	−0.115085	−	0.199333i	0.802729	−	0.596344i	$-0.203381\pi$
$859$	−2.13794e9	−	3.70302e9i	−0.115085	−	0.199333i	−0.917814	+	0.397011i	$0.870047\pi$
$860$	−3.26495e9	−	5.65505e9i	−0.175038	−	0.303174i
$861$	6.45437e9	+	2.47927e10i	0.344622	+	1.32377i
$862$	1.14265e9	−	1.97912e9i	0.0607626	−	0.105244i
$863$	−2.63998e10			−1.39818			−0.699089	−	0.715035i	$-0.746411\pi$
$863$	−2.63998e10			−1.39818			−0.699089	+	0.715035i	$0.746411\pi$
$864$	9.36338e8	−	3.21792e9i	0.0493895	−	0.169737i
$865$	9.88231e9			0.519161
$866$	−1.90715e9	+	3.30328e9i	−0.0997867	+	0.172836i
$867$	1.47755e9	+	5.67562e9i	0.0769973	+	0.295765i
$868$	4.27113e9	+	7.39782e9i	0.221679	+	0.383959i
$869$	6.23635e9	+	1.08017e10i	0.322375	+	0.558370i
$870$	1.05193e10	+	2.89906e9i	0.541588	+	0.149259i
$871$	−1.64283e9	+	2.84547e9i	−0.0842423	+	0.145912i
$872$	3.23271e9			0.165105
$873$	5.06197e8	−	3.55476e10i	0.0257495	−	1.80826i
$874$	−2.00304e10			−1.01484
$875$	−3.01736e9	+	5.22622e9i	−0.152265	+	0.263730i
$876$	2.22491e9	−	2.19346e9i	0.111827	−	0.110246i
$877$	−7.19624e9	−	1.24642e10i	−0.360252	−	0.623975i	0.627750	−	0.778415i	$-0.283976\pi$
$877$	−7.19624e9	−	1.24642e10i	−0.360252	−	0.623975i	−0.988002	+	0.154440i	$0.950643\pi$
$878$	−1.00703e10	−	1.74423e10i	−0.502125	−	0.869706i
$879$	−1.14688e10	+	1.13066e10i	−0.569582	+	0.561529i
$880$	1.30756e9	−	2.26476e9i	0.0646803	−	0.112030i
$881$	2.86878e10			1.41345			0.706727	−	0.707487i	$-0.250171\pi$
$881$	2.86878e10			1.41345			0.706727	+	0.707487i	$0.250171\pi$
$882$	−4.51004e9	+	2.51894e9i	−0.221330	+	0.123617i
$883$	1.10176e10			0.538550			0.269275	−	0.963063i	$-0.413216\pi$
$883$	1.10176e10			0.538550			0.269275	+	0.963063i	$0.413216\pi$
$884$	6.75923e9	−	1.17073e10i	0.329090	−	0.570000i
$885$	4.54091e10	+	1.25145e10i	2.20212	+	0.606893i
$886$	1.83459e9	+	3.17761e9i	0.0886180	+	0.153491i
$887$	−8.77534e9	−	1.51993e10i	−0.422213	−	0.731294i	0.573943	−	0.818895i	$-0.305413\pi$
$887$	−8.77534e9	−	1.51993e10i	−0.422213	−	0.731294i	−0.996156	+	0.0876014i	$0.972080\pi$
$888$	3.18907e9	+	1.22500e10i	0.152833	+	0.587069i
$889$	−7.17571e9	+	1.24287e10i	−0.342538	+	0.593293i
$890$	−2.03017e9			−0.0965311
$891$	3.86321e9	+	7.15430e9i	0.182968	+	0.338841i
$892$	−1.03379e10			−0.487703
$893$	−7.47322e9	+	1.29440e10i	−0.351178	+	0.608259i
$894$	2.56050e9	+	9.83549e9i	0.119852	+	0.460378i
$895$	−4.12619e9	−	7.14677e9i	−0.192384	−	0.333218i
$896$	−1.10911e9	−	1.92104e9i	−0.0515108	−	0.0892193i
$897$	−4.00362e10	−	1.10338e10i	−1.85216	−	0.510446i
$898$	5.85733e9	−	1.01452e10i	0.269918	−	0.467512i
$899$	9.79907e9			0.449807
$900$	−7.69056e9	+	4.29532e9i	−0.351649	+	0.196402i
$901$	2.09841e10			0.955770
$902$	3.52172e9	−	6.09979e9i	0.159783	−	0.276753i
$903$	9.56931e9	−	9.43402e9i	0.432488	−	0.426373i
$904$	−5.48959e9	−	9.50824e9i	−0.247144	−	0.428066i
$905$	2.36994e10	+	4.10486e10i	1.06284	+	1.84089i
$906$	−1.11861e10	+	1.10279e10i	−0.499722	+	0.492657i
$907$	8.42225e9	−	1.45878e10i	0.374803	−	0.649177i	−0.615495	−	0.788141i	$-0.711044\pi$
$907$	8.42225e9	−	1.45878e10i	0.374803	−	0.649177i	0.990297	+	0.138964i	$0.0443771\pi$
$908$	2.43542e9			0.107963
$909$	−1.32200e7	+	9.28375e8i	−0.000583793	+	0.0409968i
$910$	3.97691e10			1.74945
$911$	−7.36357e9	+	1.27541e10i	−0.322682	+	0.558901i	−0.981040	−	0.193803i	$-0.937918\pi$
$911$	−7.36357e9	+	1.27541e10i	−0.322682	+	0.558901i	0.658359	+	0.752704i	$0.271251\pi$
$912$	−6.51538e9	−	1.79560e9i	−0.284419	−	0.0783842i
$913$	3.30824e9	+	5.73005e9i	0.143863	+	0.249178i
$914$	−5.58639e9	−	9.67592e9i	−0.242003	−	0.419161i
$915$	−3.33682e9	−	1.28175e10i	−0.143999	−	0.553133i
$916$	9.27091e9	−	1.60577e10i	0.398555	−	0.690318i
$917$	−2.48899e10			−1.06593
$918$	−1.34139e10	+	3.28888e9i	−0.572277	+	0.140313i
$919$	7.11506e9			0.302395			0.151197	−	0.988504i	$-0.451687\pi$
$919$	7.11506e9			0.302395			0.151197	+	0.988504i	$0.451687\pi$
$920$	6.82319e9	−	1.18181e10i	0.288888	−	0.500369i
$921$	−6.22958e9	−	2.39293e10i	−0.262755	−	1.00930i
$922$	1.58488e10	+	2.74510e10i	0.665946	+	1.15345i
$923$	6.19989e9	+	1.07385e10i	0.259524	+	0.449509i
$924$	5.18818e9	+	1.42983e9i	0.216353	+	0.0596257i
$925$	1.66355e10	−	2.88136e10i	0.691099	−	1.19702i
$926$	−1.50530e10			−0.622995
$927$	−9.13450e9	−	5.44868e9i	−0.376622	−	0.224653i
$928$	−2.54459e9			−0.104520
$929$	1.69702e10	−	2.93933e10i	0.694437	−	1.20280i	−0.275933	−	0.961177i	$-0.588987\pi$
$929$	1.69702e10	−	2.93933e10i	0.694437	−	1.20280i	0.970370	−	0.241624i	$-0.0776799\pi$
$930$	−1.26266e10	+	1.24481e10i	−0.514751	+	0.507473i
$931$	5.20860e9	+	9.02156e9i	0.211542	+	0.366402i
$932$	2.38430e9	+	4.12973e9i	0.0964730	+	0.167096i
$933$	9.55001e9	−	9.41499e9i	0.384962	−	0.379519i
$934$	−3.87807e9	+	6.71702e9i	−0.155741	+	0.269751i
$935$	−1.07771e10			−0.431181
$936$	−1.20337e10	−	7.17802e9i	−0.479660	−	0.286114i
$937$	−3.78364e10			−1.50252			−0.751261	−	0.660005i	$-0.770554\pi$
$937$	−3.78364e10			−1.50252			−0.751261	+	0.660005i	$0.770554\pi$
$938$	1.11092e9	−	1.92416e9i	0.0439513	−	0.0761258i
$939$	1.12823e9	+	3.10935e8i	0.0444703	+	0.0122558i
$940$	−5.09139e9	−	8.81854e9i	−0.199935	−	0.346298i
$941$	−8.44461e9	−	1.46265e10i	−0.330382	−	0.572238i	0.652205	−	0.758043i	$-0.273844\pi$
$941$	−8.44461e9	−	1.46265e10i	−0.330382	−	0.572238i	−0.982587	+	0.185805i	$0.940511\pi$
$942$	−7.73342e9	−	2.97059e10i	−0.301435	−	1.15788i
$943$	1.83772e10	−	3.18303e10i	0.713657	−	1.23609i
$944$	−1.09844e10			−0.424984
$945$	−2.81098e10	−	2.93370e10i	−1.08354	−	1.13085i
$946$	−3.69442e9			−0.141882
$947$	−5.84561e9	+	1.01249e10i	−0.223668	+	0.387405i	−0.955919	−	0.293630i	$-0.905137\pi$
$947$	−5.84561e9	+	1.01249e10i	−0.223668	+	0.387405i	0.732251	+	0.681035i	$0.238470\pi$
$948$	5.53253e9	+	2.12517e10i	0.210909	+	0.810150i
$949$	−6.53134e9	−	1.13126e10i	−0.248068	−	0.429666i
$950$	8.88176e9	+	1.53837e10i	0.336098	+	0.582139i
$951$	−2.34563e10	−	6.46443e9i	−0.884357	−	0.243724i
$952$	−4.57072e9	+	7.91672e9i	−0.171694	+	0.297383i
$953$	5.10551e10			1.91079			0.955397	−	0.295323i	$-0.0954274\pi$
$953$	5.10551e10			1.91079			0.955397	+	0.295323i	$0.0954274\pi$
$954$	3.09688e8	−	2.17478e10i	0.0115480	−	0.810955i
$955$	−6.73981e10			−2.50401
$956$	−5.74930e9	+	9.95808e9i	−0.212820	+	0.368615i
$957$	4.39621e9	−	4.33405e9i	0.162139	−	0.159846i
$958$	8.03480e9	+	1.39167e10i	0.295254	+	0.511395i
$959$	1.48032e10	+	2.56400e10i	0.541990	+	0.938755i
$960$	3.27884e9	−	3.23248e9i	0.119611	−	0.117920i
$961$	5.79464e9	−	1.00366e10i	0.210618	−	0.364800i
$962$	5.29235e10			1.91662
$963$	−5.41591e9	+	3.02488e9i	−0.195425	+	0.109148i
$964$	−3.89556e9			−0.140056
$965$	−5.60202e9	+	9.70298e9i	−0.200678	+	0.347584i
$966$	2.70733e10	+	7.46124e9i	0.966319	+	0.266312i
$967$	4.34365e9	+	7.52343e9i	0.154476	+	0.267561i	0.932868	−	0.360218i	$-0.117298\pi$
$967$	4.34365e9	+	7.52343e9i	0.154476	+	0.267561i	−0.778392	+	0.627779i	$0.783964\pi$
$968$	4.24894e9	+	7.35937e9i	0.150562	+	0.260782i
$969$	7.01673e9	+	2.69529e10i	0.247743	+	0.951640i
$970$	2.44212e10	−	4.22987e10i	0.859143	−	1.48808i
$971$	3.91347e10			1.37181			0.685906	−	0.727690i	$-0.259406\pi$
$971$	3.91347e10			1.37181			0.685906	+	0.727690i	$0.259406\pi$
$972$	3.21061e9	+	1.39507e10i	0.112139	+	0.487263i
$973$	−8.46384e9			−0.294559
$974$	−1.21153e10	+	2.09844e10i	−0.420126	+	0.727679i
$975$	9.27853e9	+	3.56410e10i	0.320600	+	1.23150i
$976$	1.54436e9	+	2.67490e9i	0.0531708	+	0.0920945i
$977$	1.36255e10	+	2.36001e10i	0.467437	+	0.809624i	0.999308	−	0.0372010i	$-0.0118442\pi$
$977$	1.36255e10	+	2.36001e10i	0.467437	+	0.809624i	−0.531871	+	0.846825i	$0.678511\pi$
$978$	−1.04339e10	−	2.87552e9i	−0.356664	−	0.0982946i
$979$	−5.74305e8	+	9.94725e8i	−0.0195615	+	0.0338816i
$980$	−7.09708e9			−0.240873
$981$	−1.20556e10	+	6.73327e9i	−0.407706	+	0.227711i
$982$	3.61379e10			1.21779
$983$	−3.56677e9	+	6.17782e9i	−0.119767	+	0.207443i	−0.919675	−	0.392680i	$-0.871548\pi$
$983$	−3.56677e9	+	6.17782e9i	−0.119767	+	0.207443i	0.799908	+	0.600122i	$0.204881\pi$
$984$	8.83106e9	−	8.70620e9i	0.295481	−	0.291304i
$985$	1.25981e10	+	2.18205e10i	0.420028	+	0.727509i
$986$	5.24321e9	+	9.08150e9i	0.174192	+	0.301709i
$987$	1.49225e10	−	1.47115e10i	0.494005	−	0.487020i
$988$	−1.41280e10	+	2.44704e10i	−0.466049	+	0.807220i
$989$	−1.92784e10			−0.633702
$990$	−1.59051e8	+	1.11693e10i	−0.00520969	+	0.365850i
$991$	−1.99378e10			−0.650760			−0.325380	−	0.945583i	$-0.605492\pi$
$991$	−1.99378e10			−0.650760			−0.325380	+	0.945583i	$0.605492\pi$
$992$	2.06746e9	−	3.58094e9i	0.0672428	−	0.116468i
$993$	−2.27695e10	−	6.27514e9i	−0.737956	−	0.203377i
$994$	−4.19249e9	−	7.26160e9i	−0.135400	−	0.234520i
$995$	−2.21925e10	−	3.84385e10i	−0.714208	−	1.23704i
$996$	2.93488e9	+	1.12736e10i	0.0941202	+	0.361538i
$997$	6.37020e9	−	1.10335e10i	0.203573	−	0.352598i	−0.746104	−	0.665829i	$-0.768078\pi$
$997$	6.37020e9	−	1.10335e10i	0.203573	−	0.352598i	0.949677	+	0.313231i	$0.101411\pi$
$998$	−3.72531e10			−1.18633
$999$	−3.74077e10	−	3.90408e10i	−1.18708	−	1.23891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.8.c.a.7.2	✓	6
3.2	odd	2		54.8.c.a.19.1		6
4.3	odd	2		144.8.i.a.97.2		6
9.2	odd	6		162.8.a.e.1.3		3
9.4	even	3	inner	18.8.c.a.13.2	yes	6
9.5	odd	6		54.8.c.a.37.1		6
9.7	even	3		162.8.a.f.1.1		3
12.11	even	2		432.8.i.a.289.1		6
36.23	even	6		432.8.i.a.145.1		6
36.31	odd	6		144.8.i.a.49.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.8.c.a.7.2	✓	6	1.1	even	1	trivial
18.8.c.a.13.2	yes	6	9.4	even	3	inner
54.8.c.a.19.1		6	3.2	odd	2
54.8.c.a.37.1		6	9.5	odd	6
144.8.i.a.49.2		6	36.31	odd	6
144.8.i.a.97.2		6	4.3	odd	2
162.8.a.e.1.3		3	9.2	odd	6
162.8.a.f.1.1		3	9.7	even	3
432.8.i.a.145.1		6	36.23	even	6
432.8.i.a.289.1		6	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(-11.7819 - 45.2569i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(187.789 + 325.261i) q^{5} +(360.677 + 99.4005i) q^{6} +(-528.867 + 916.024i) q^{7} +512.000 q^{8} +(-1909.38 + 1066.42i) q^{9} -3004.63 q^{10} +(-849.965 + 1472.18i) q^{11} +(-2131.37 + 2101.24i) q^{12} +(6256.75 + 10837.0i) q^{13} +(-4230.93 - 7328.19i) q^{14} +(12507.8 - 12330.9i) q^{15} +(-2048.00 + 3547.24i) q^{16} +16879.9 q^{17} +(249.117 - 17494.2i) q^{18} -35281.9 q^{19} +(12018.5 - 20816.7i) q^{20} +(47687.4 + 13142.4i) q^{21} +(-6799.72 - 11777.5i) q^{22} +(-35482.7 - 61457.8i) q^{23} +(-6032.31 - 23171.5i) q^{24} +(-31467.1 + 54502.6i) q^{25} -100108. q^{26} +(70758.9 + 73848.0i) q^{27} +67694.9 q^{28} +(38827.4 - 67251.0i) q^{29} +(35400.1 + 135980. i) q^{30} +(63093.8 + 109282. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(76640.6 + 21121.7i) q^{33} +(-67519.4 + 116947. i) q^{34} -397262. q^{35} +(120207. + 71702.8i) q^{36} -528664. q^{37} +(141128. - 244440. i) q^{38} +(416733. - 410841. i) q^{39} +(96148.1 + 166533. i) q^{40} +(258960. + 448533. i) q^{41} +(-281803. + 277819. i) q^{42} +(135830. - 235264. i) q^{43} +108795. q^{44} +(-705425. - 420782. i) q^{45} +567723. q^{46} +(211814. - 366873. i) q^{47} +(184666. + 50893.0i) q^{48} +(-147628. - 255699. i) q^{49} +(-251737. - 436021. i) q^{50} +(-198876. - 763930. i) q^{51} +(400432. - 693568. i) q^{52} +1.24314e6 q^{53} +(-794670. + 194840. i) q^{54} -638457. q^{55} +(-270780. + 469004. i) q^{56} +(415687. + 1.59675e6i) q^{57} +(310619. + 538008. i) q^{58} +(1.34086e6 + 2.32244e6i) q^{59} +(-1.08370e6 - 298661. i) q^{60} +(377040. - 653052. i) q^{61} -1.00950e6 q^{62} +(32937.4 - 2.31303e6i) q^{63} +262144. q^{64} +(-2.34990e6 + 4.07014e6i) q^{65} +(-452898. + 446495. i) q^{66} +(131285. + 227392. i) q^{67} +(-540156. - 935577. i) q^{68} +(-2.36334e6 + 2.32993e6i) q^{69} +(1.58905e6 - 2.75231e6i) q^{70} +990913. q^{71} +(-977600. + 546008. i) q^{72} -1.04389e6 q^{73} +(2.11466e6 - 3.66269e6i) q^{74} +(2.83736e6 + 781961. i) q^{75} +(1.12902e6 + 1.95552e6i) q^{76} +(-899036. - 1.55718e6i) q^{77} +(1.17946e6 + 4.53058e6i) q^{78} +(3.66860e6 - 6.35419e6i) q^{79} -1.53837e6 q^{80} +(2.50846e6 - 4.07240e6i) q^{81} -4.14337e6 q^{82} +(1.94611e6 - 3.37075e6i) q^{83} +(-797572. - 3.06366e6i) q^{84} +(3.16986e6 + 5.49035e6i) q^{85} +(1.08664e6 + 1.88211e6i) q^{86} +(-3.50103e6 - 964865. i) q^{87} +(-435182. + 753757. i) q^{88} +675681. q^{89} +(5.73696e6 - 3.20420e6i) q^{90} -1.32359e7 q^{91} +(-2.27089e6 + 3.93330e6i) q^{92} +(4.20239e6 - 4.14298e6i) q^{93} +(1.69452e6 + 2.93499e6i) q^{94} +(-6.62556e6 - 1.14758e7i) q^{95} +(-1.09126e6 + 1.07583e6i) q^{96} +(-8.12785e6 + 1.40779e7i) q^{97} +2.36205e6 q^{98} +(52935.2 - 3.71737e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 27 q^{3} - 192 q^{4} + 54 q^{5} + 792 q^{6} + 210 q^{7} + 3072 q^{8} + 2295 q^{9} - 864 q^{10} + 6579 q^{11} - 4608 q^{12} + 10092 q^{13} + 1680 q^{14} + 756 q^{15} - 12288 q^{16} - 29790 q^{17}+ \cdots - 11453238 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 27 * q^3 - 192 * q^4 + 54 * q^5 + 792 * q^6 + 210 * q^7 + 3072 * q^8 + 2295 * q^9 - 864 * q^10 + 6579 * q^11 - 4608 * q^12 + 10092 * q^13 + 1680 * q^14 + 756 * q^15 - 12288 * q^16 - 29790 * q^17 + 19008 * q^18 - 137490 * q^19 + 3456 * q^20 + 85464 * q^21 + 52632 * q^22 - 39654 * q^23 - 13824 * q^24 - 7923 * q^25 - 161472 * q^26 + 87480 * q^27 - 26880 * q^28 + 239832 * q^29 + 283392 * q^30 + 145704 * q^31 - 98304 * q^32 + 175365 * q^33 + 119160 * q^34 - 1087776 * q^35 - 298944 * q^36 - 720384 * q^37 + 549960 * q^38 + 2386548 * q^39 + 27648 * q^40 + 1086993 * q^41 - 752400 * q^42 - 299967 * q^43 - 842112 * q^44 - 2798874 * q^45 + 634464 * q^46 + 131634 * q^47 + 405504 * q^48 + 482175 * q^49 - 63384 * q^50 - 3719223 * q^51 + 645888 * q^52 + 1909152 * q^53 - 1222776 * q^54 - 5494824 * q^55 + 107520 * q^56 + 6076107 * q^57 + 1918656 * q^58 + 2504853 * q^59 - 2315520 * q^60 + 7309038 * q^61 - 2331264 * q^62 - 1254960 * q^63 + 1572864 * q^64 - 1786698 * q^65 + 2211408 * q^66 + 3433035 * q^67 + 953280 * q^68 - 5815206 * q^69 + 4351104 * q^70 + 2269368 * q^71 + 1175040 * q^72 - 15901746 * q^73 + 2881536 * q^74 + 4230945 * q^75 + 4399680 * q^76 - 6147432 * q^77 - 12143088 * q^78 + 7076928 * q^79 - 442368 * q^80 + 4749435 * q^81 - 17391888 * q^82 - 10914444 * q^83 + 549504 * q^84 + 17613396 * q^85 - 2399736 * q^86 - 11533266 * q^87 + 3368448 * q^88 + 23800356 * q^89 + 18592416 * q^90 - 37170552 * q^91 - 2537856 * q^92 + 30872466 * q^93 + 1053072 * q^94 - 17342424 * q^95 - 2359296 * q^96 + 519357 * q^97 - 7714800 * q^98 - 11453238 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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