LMFDB - Embedded newform 16.28.e.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,28,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, 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:	$73.8968919741$
Analytic rank:	$0$
Dimension:	$106$
Relative dimension:	$53$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	16.13
Dual form			16.28.e.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11441.8 - 1817.09i) q^{2} +(153675. + 153675. i) q^{3} +(1.27614e8 + 4.15818e7i) q^{4} +(2.87142e9 - 2.87142e9i) q^{5} +(-1.47908e9 - 2.03757e9i) q^{6} +4.55239e11i q^{7} +(-1.38458e12 - 7.07660e11i) q^{8} -7.57837e12i q^{9} +(-3.80720e13 + 2.76367e13i) q^{10} +(2.18329e13 - 2.18329e13i) q^{11} +(1.32210e13 + 2.60012e13i) q^{12} +(6.58714e13 + 6.58714e13i) q^{13} +(8.27212e14 - 5.20877e15i) q^{14} +8.82531e14 q^{15} +(1.45563e16 + 1.06129e16i) q^{16} +3.33490e16 q^{17} +(-1.37706e16 + 8.67105e16i) q^{18} +(2.22948e17 + 2.22948e17i) q^{19} +(4.85833e17 - 2.47035e17i) q^{20} +(-6.99588e16 + 6.99588e16i) q^{21} +(-2.89482e17 + 2.10137e17i) q^{22} -4.14853e18i q^{23} +(-1.04026e17 - 3.21525e17i) q^{24} -9.03953e18i q^{25} +(-6.33996e17 - 8.73385e17i) q^{26} +(2.33647e18 - 2.33647e18i) q^{27} +(-1.89297e19 + 5.80949e19i) q^{28} +(1.87317e19 + 1.87317e19i) q^{29} +(-1.00978e19 - 1.60364e18i) q^{30} -5.35086e19 q^{31} +(-1.47266e20 - 1.47881e20i) q^{32} +6.71035e18 q^{33} +(-3.81574e20 - 6.05982e19i) q^{34} +(1.30718e21 + 1.30718e21i) q^{35} +(3.15122e20 - 9.67106e20i) q^{36} +(-1.64430e21 + 1.64430e21i) q^{37} +(-2.14582e21 - 2.95605e21i) q^{38} +2.02456e19i q^{39} +(-6.00771e21 + 1.94373e21i) q^{40} +3.79544e21i q^{41} +(9.27580e20 - 6.73336e20i) q^{42} +(4.06962e21 - 4.06962e21i) q^{43} +(3.69404e21 - 1.87834e21i) q^{44} +(-2.17607e22 - 2.17607e22i) q^{45} +(-7.53827e21 + 4.74668e22i) q^{46} +3.33844e22 q^{47} +(6.06009e20 + 3.86787e21i) q^{48} -1.41530e23 q^{49} +(-1.64257e22 + 1.03429e23i) q^{50} +(5.12490e21 + 5.12490e21i) q^{51} +(5.66706e21 + 1.11452e22i) q^{52} +(-7.44190e22 + 7.44190e22i) q^{53} +(-3.09791e22 + 2.24879e22i) q^{54} -1.25383e23i q^{55} +(3.22154e23 - 6.30316e23i) q^{56} +6.85230e22i q^{57} +(-1.80288e23 - 2.48363e23i) q^{58} +(3.85569e23 - 3.85569e23i) q^{59} +(1.12623e23 + 3.66973e22i) q^{60} +(3.77791e23 + 3.77791e23i) q^{61} +(6.12237e23 + 9.72301e22i) q^{62} +3.44997e24 q^{63} +(1.41629e24 + 1.95963e24i) q^{64} +3.78289e23 q^{65} +(-7.67788e22 - 1.21933e22i) q^{66} +(1.29676e24 + 1.29676e24i) q^{67} +(4.25580e24 + 1.38671e24i) q^{68} +(6.37525e23 - 6.37525e23i) q^{69} +(-1.25813e25 - 1.73318e25i) q^{70} -1.59810e25i q^{71} +(-5.36291e24 + 1.04929e25i) q^{72} +1.45671e25i q^{73} +(2.18017e25 - 1.58260e25i) q^{74} +(1.38915e24 - 1.38915e24i) q^{75} +(1.91807e25 + 3.77219e25i) q^{76} +(9.93919e24 + 9.93919e24i) q^{77} +(3.67881e22 - 2.31647e23i) q^{78} +3.96590e25 q^{79} +(7.22712e25 - 1.13233e25i) q^{80} -5.70715e25 q^{81} +(6.89668e24 - 4.34269e25i) q^{82} +(-2.74260e25 - 2.74260e25i) q^{83} +(-1.18367e25 + 6.01871e24i) q^{84} +(9.57589e25 - 9.57589e25i) q^{85} +(-5.39588e25 + 3.91691e25i) q^{86} +5.75719e24i q^{87} +(-4.56798e25 + 1.47792e25i) q^{88} +1.01566e26i q^{89} +(2.09441e26 + 2.88523e26i) q^{90} +(-2.99872e25 + 2.99872e25i) q^{91} +(1.72503e26 - 5.29411e26i) q^{92} +(-8.22293e24 - 8.22293e24i) q^{93} +(-3.81980e26 - 6.06627e25i) q^{94} +1.28035e27 q^{95} +(9.44244e22 - 4.53567e25i) q^{96} +5.84303e26 q^{97} +(1.61936e27 + 2.57173e26i) q^{98} +(-1.65458e26 - 1.65458e26i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12} - 2 q^{13} - 71\!\cdots\!60 q^{14} - 15\!\cdots\!04 q^{15}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) $ 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−11441.8	−	1817.09i	−0.987623	−	0.156846i
$2$	−11441.8	−	1817.09i	−0.987623	−	0.156846i
$3$	153675.	+	153675.i	0.0556501	+	0.0556501i	0.734384	−	0.678734i	$-0.237471\pi$
$3$	153675.	+	153675.i	0.0556501	+	0.0556501i	−0.678734	+	0.734384i	$0.737471\pi$
$4$	1.27614e8	+	4.15818e7i	0.950799	+	0.309809i
$5$	2.87142e9	−	2.87142e9i	1.05197	−	1.05197i	0.0533923	−	0.998574i	$-0.482997\pi$
$5$	2.87142e9	−	2.87142e9i	1.05197	−	1.05197i	0.998574	−	0.0533923i	$-0.0170034\pi$
$6$	−1.47908e9	−	2.03757e9i	−0.0462329	−	0.0636898i
$7$			4.55239e11i			1.77589i	0.459951	+	0.887944i	$0.347867\pi$
$7$			4.55239e11i			1.77589i	−0.459951	+	0.887944i	$0.652133\pi$
$8$	−1.38458e12	−	7.07660e11i	−0.890439	−	0.455103i
$9$		−	7.57837e12i		−	0.993806i
$10$	−3.80720e13	+	2.76367e13i	−1.20394	+	0.873950i
$11$	2.18329e13	−	2.18329e13i	0.190682	−	0.190682i	−0.605309	−	0.795991i	$-0.706950\pi$
$11$	2.18329e13	−	2.18329e13i	0.190682	−	0.190682i	0.795991	+	0.605309i	$0.206950\pi$
$12$	1.32210e13	+	2.60012e13i	0.0356712	+	0.0701530i
$13$	6.58714e13	+	6.58714e13i	0.0603200	+	0.0603200i	0.736623	−	0.676303i	$-0.236419\pi$
$13$	6.58714e13	+	6.58714e13i	0.0603200	+	0.0603200i	−0.676303	+	0.736623i	$0.736419\pi$
$14$	8.27212e14	−	5.20877e15i	0.278540	−	1.75391i
$15$	8.82531e14			0.117084
$16$	1.45563e16	+	1.06129e16i	0.808037	+	0.589132i
$17$	3.33490e16			0.816623			0.408312	−	0.912843i	$-0.366118\pi$
$17$	3.33490e16			0.816623			0.408312	+	0.912843i	$0.366118\pi$
$18$	−1.37706e16	+	8.67105e16i	−0.155874	+	0.981506i
$19$	2.22948e17	+	2.22948e17i	1.21627	+	1.21627i	0.968929	+	0.247340i	$0.0795566\pi$
$19$	2.22948e17	+	2.22948e17i	1.21627	+	1.21627i	0.247340	+	0.968929i	$0.420443\pi$
$20$	4.85833e17	−	2.47035e17i	1.32612	−	0.674300i
$21$	−6.99588e16	+	6.99588e16i	−0.0988284	+	0.0988284i
$22$	−2.89482e17	+	2.10137e17i	−0.218230	+	0.158415i
$23$		−	4.14853e18i		−	1.71620i	−0.513481	−	0.858101i	$-0.671644\pi$
$23$		−	4.14853e18i		−	1.71620i	0.513481	−	0.858101i	$-0.328356\pi$
$24$	−1.04026e17	−	3.21525e17i	−0.0242265	−	0.0748796i
$25$		−	9.03953e18i		−	1.21326i
$26$	−6.33996e17	−	8.73385e17i	−0.0501125	−	0.0690344i
$27$	2.33647e18	−	2.33647e18i	0.110956	−	0.110956i
$28$	−1.89297e19	+	5.80949e19i	−0.550186	+	1.68851i
$29$	1.87317e19	+	1.87317e19i	0.339004	+	0.339004i	0.855992	−	0.516988i	$-0.172947\pi$
$29$	1.87317e19	+	1.87317e19i	0.339004	+	0.339004i	−0.516988	+	0.855992i	$0.672947\pi$
$30$	−1.00978e19	−	1.60364e18i	−0.115635	−	0.0183641i
$31$	−5.35086e19			−0.393587			−0.196793	−	0.980445i	$-0.563053\pi$
$31$	−5.35086e19			−0.393587			−0.196793	+	0.980445i	$0.563053\pi$
$32$	−1.47266e20	−	1.47881e20i	−0.705633	−	0.708577i
$33$	6.71035e18			0.0212230
$34$	−3.81574e20	−	6.05982e19i	−0.806516	−	0.128084i
$35$	1.30718e21	+	1.30718e21i	1.86817	+	1.86817i
$36$	3.15122e20	−	9.67106e20i	0.307890	−	0.944910i
$37$	−1.64430e21	+	1.64430e21i	−1.10983	+	1.10983i	−0.116663	+	0.993172i	$0.537220\pi$
$37$	−1.64430e21	+	1.64430e21i	−1.10983	+	1.10983i	−0.993172	+	0.116663i	$0.962780\pi$
$38$	−2.14582e21	−	2.95605e21i	−1.01045	−	1.39198i
$39$			2.02456e19i			0.00671364i
$40$	−6.00771e21	+	1.94373e21i	−1.41546	+	0.457958i
$41$			3.79544e21i			0.640738i	0.947293	+	0.320369i	$0.103807\pi$
$41$			3.79544e21i			0.640738i	−0.947293	+	0.320369i	$0.896193\pi$
$42$	9.27580e20	−	6.73336e20i	0.113106	−	0.0821044i
$43$	4.06962e21	−	4.06962e21i	0.361185	−	0.361185i	−0.503064	−	0.864249i	$-0.667794\pi$
$43$	4.06962e21	−	4.06962e21i	0.361185	−	0.361185i	0.864249	+	0.503064i	$0.167794\pi$
$44$	3.69404e21	−	1.87834e21i	0.240376	−	0.122226i
$45$	−2.17607e22	−	2.17607e22i	−1.04545	−	1.04545i
$46$	−7.53827e21	+	4.74668e22i	−0.269179	+	1.69496i
$47$	3.33844e22			0.891709			0.445854	−	0.895105i	$-0.352900\pi$
$47$	3.33844e22			0.891709			0.445854	+	0.895105i	$0.352900\pi$
$48$	6.06009e20	+	3.86787e21i	0.0121821	+	0.0777526i
$49$	−1.41530e23			−2.15378
$50$	−1.64257e22	+	1.03429e23i	−0.190295	+	1.19825i
$51$	5.12490e21	+	5.12490e21i	0.0454452	+	0.0454452i
$52$	5.66706e21	+	1.11452e22i	0.0386645	+	0.0760399i
$53$	−7.44190e22	+	7.44190e22i	−0.392609	+	0.392609i	−0.875616	−	0.483008i	$-0.839544\pi$
$53$	−7.44190e22	+	7.44190e22i	−0.392609	+	0.392609i	0.483008	+	0.875616i	$0.339544\pi$
$54$	−3.09791e22	+	2.24879e22i	−0.126985	+	0.0921794i
$55$		−	1.25383e23i		−	0.401183i
$56$	3.22154e23	−	6.30316e23i	0.808212	−	1.58132i
$57$			6.85230e22i			0.135371i
$58$	−1.80288e23	−	2.48363e23i	−0.281637	−	0.387979i
$59$	3.85569e23	−	3.85569e23i	0.478189	−	0.478189i	−0.426363	−	0.904552i	$-0.640205\pi$
$59$	3.85569e23	−	3.85569e23i	0.478189	−	0.478189i	0.904552	+	0.426363i	$0.140205\pi$
$60$	1.12623e23	+	3.66973e22i	0.111323	+	0.0362737i
$61$	3.77791e23	+	3.77791e23i	0.298744	+	0.298744i	0.840522	−	0.541778i	$-0.182249\pi$
$61$	3.77791e23	+	3.77791e23i	0.298744	+	0.298744i	−0.541778	+	0.840522i	$0.682249\pi$
$62$	6.12237e23	+	9.72301e22i	0.388715	+	0.0617324i
$63$	3.44997e24			1.76489
$64$	1.41629e24	+	1.95963e24i	0.585762	+	0.810483i
$65$	3.78289e23			0.126909
$66$	−7.67788e22	−	1.21933e22i	−0.0209603	−	0.00332874i
$67$	1.29676e24	+	1.29676e24i	0.288967	+	0.288967i	0.836672	−	0.547704i	$-0.184498\pi$
$67$	1.29676e24	+	1.29676e24i	0.288967	+	0.288967i	−0.547704	+	0.836672i	$0.684498\pi$
$68$	4.25580e24	+	1.38671e24i	0.776445	+	0.252997i
$69$	6.37525e23	−	6.37525e23i	0.0955068	−	0.0955068i
$70$	−1.25813e25	−	1.73318e25i	−1.55204	−	2.13807i
$71$		−	1.59810e25i		−	1.62786i	−0.580966	−	0.813928i	$-0.697325\pi$
$71$		−	1.59810e25i		−	1.62786i	0.580966	−	0.813928i	$-0.302675\pi$
$72$	−5.36291e24	+	1.04929e25i	−0.452284	+	0.884923i
$73$			1.45671e25i			1.01980i	0.860235	+	0.509898i	$0.170317\pi$
$73$			1.45671e25i			1.01980i	−0.860235	+	0.509898i	$0.829683\pi$
$74$	2.18017e25	−	1.58260e25i	1.27017	−	0.922026i
$75$	1.38915e24	−	1.38915e24i	0.0675183	−	0.0675183i
$76$	1.91807e25	+	3.77219e25i	0.779616	+	1.53324i
$77$	9.93919e24	+	9.93919e24i	0.338631	+	0.338631i
$78$	3.67881e22	−	2.31647e23i	0.00105300	−	0.00663054i
$79$	3.96590e25			0.955819			0.477910	−	0.878409i	$-0.341395\pi$
$79$	3.96590e25			0.955819			0.477910	+	0.878409i	$0.341395\pi$
$80$	7.22712e25	−	1.13233e25i	1.46977	−	0.230281i
$81$	−5.70715e25			−0.981457
$82$	6.89668e24	−	4.34269e25i	0.100497	−	0.632808i
$83$	−2.74260e25	−	2.74260e25i	−0.339318	−	0.339318i	0.516792	−	0.856111i	$-0.327126\pi$
$83$	−2.74260e25	−	2.74260e25i	−0.339318	−	0.339318i	−0.856111	+	0.516792i	$0.827126\pi$
$84$	−1.18367e25	+	6.01871e24i	−0.124584	+	0.0633480i
$85$	9.57589e25	−	9.57589e25i	0.859060	−	0.859060i
$86$	−5.39588e25	+	3.91691e25i	−0.413365	+	0.300064i
$87$			5.75719e24i			0.0377312i
$88$	−4.56798e25	+	1.47792e25i	−0.256571	+	0.0830109i
$89$			1.01566e26i			0.489762i	0.969553	+	0.244881i	$0.0787489\pi$
$89$			1.01566e26i			0.489762i	−0.969553	+	0.244881i	$0.921251\pi$
$90$	2.09441e26	+	2.88523e26i	0.868536	+	1.19649i
$91$	−2.99872e25	+	2.99872e25i	−0.107122	+	0.107122i
$92$	1.72503e26	−	5.29411e26i	0.531694	−	1.63176i
$93$	−8.22293e24	−	8.22293e24i	−0.0219031	−	0.0219031i
$94$	−3.81980e26	−	6.06627e25i	−0.880672	−	0.139861i
$95$	1.28035e27			2.55895
$96$	9.44244e22	−	4.53567e25i	0.000163841	−	0.0787010i
$97$	5.84303e26			0.881494			0.440747	−	0.897631i	$-0.354714\pi$
$97$	5.84303e26			0.881494			0.440747	+	0.897631i	$0.354714\pi$
$98$	1.61936e27	+	2.57173e26i	2.12712	+	0.337811i
$99$	−1.65458e26	−	1.65458e26i	−0.189501	−	0.189501i
$100$	3.75880e26	−	1.15357e27i	0.375880	−	1.15357i
$101$	1.19384e27	−	1.19384e27i	1.04378	−	1.04378i	0.0447787	−	0.998997i	$-0.485742\pi$
$101$	1.19384e27	−	1.19384e27i	1.04378	−	1.04378i	0.998997	−	0.0447787i	$-0.0142583\pi$
$102$	−4.93259e25	−	6.79507e25i	−0.0377548	−	0.0520106i
$103$			1.35013e27i			0.905882i	0.891540	+	0.452941i	$0.149625\pi$
$103$			1.35013e27i			0.905882i	−0.891540	+	0.452941i	$0.850375\pi$
$104$	−4.45898e25	−	1.37819e26i	−0.0262595	−	0.0811631i
$105$			4.01762e26i			0.207928i
$106$	9.86718e26	−	7.16265e26i	0.449328	−	0.326170i
$107$	−9.58345e26	+	9.58345e26i	−0.384451	+	0.384451i	−0.872703	−	0.488252i	$-0.837635\pi$
$107$	−9.58345e26	+	9.58345e26i	−0.384451	+	0.384451i	0.488252	+	0.872703i	$0.337635\pi$
$108$	3.95321e26	−	2.01012e26i	0.139871	−	0.0711214i
$109$	−2.50641e27	−	2.50641e27i	−0.783059	−	0.783059i	0.197287	−	0.980346i	$-0.436787\pi$
$109$	−2.50641e27	−	2.50641e27i	−0.783059	−	0.783059i	−0.980346	+	0.197287i	$0.936787\pi$
$110$	−2.27833e26	+	1.43461e27i	−0.0629238	+	0.396218i
$111$	−5.05376e26			−0.123525
$112$	−4.83138e27	+	6.62659e27i	−1.04623	+	1.43498i
$113$	5.60122e27			1.07578			0.537891	−	0.843015i	$-0.319221\pi$
$113$	5.60122e27			1.07578			0.537891	+	0.843015i	$0.319221\pi$
$114$	1.24513e26	−	7.84030e26i	0.0212324	−	0.133696i
$115$	−1.19122e28	−	1.19122e28i	−1.80539	−	1.80539i
$116$	1.61153e27	+	3.16933e27i	0.217298	+	0.427351i
$117$	4.99198e26	−	4.99198e26i	0.0599464	−	0.0599464i
$118$	−5.11223e27	+	3.71100e27i	−0.547272	+	0.397269i
$119$			1.51817e28i			1.45023i
$120$	−1.22194e27	−	6.24532e26i	−0.104256	−	0.0532853i
$121$			1.21566e28i			0.927280i
$122$	−3.63614e27	−	5.00911e27i	−0.248190	−	0.341903i
$123$	−5.83265e26	+	5.83265e26i	−0.0356572	+	0.0356572i
$124$	−6.82844e27	−	2.22498e27i	−0.374222	−	0.121937i
$125$	−4.56253e27	−	4.56253e27i	−0.224347	−	0.224347i
$126$	−3.94740e28	−	6.26891e27i	−1.74304	−	0.276815i
$127$	3.17933e28			1.26179			0.630893	−	0.775870i	$-0.282689\pi$
$127$	3.17933e28			1.26179			0.630893	+	0.775870i	$0.282689\pi$
$128$	−1.26441e28	−	2.49953e28i	−0.451392	−	0.892326i
$129$	1.25080e27			0.0402000
$130$	−4.32832e27	−	6.87387e26i	−0.125339	−	0.0199052i
$131$	1.18201e28	+	1.18201e28i	0.308644	+	0.308644i	0.844384	−	0.535739i	$-0.179967\pi$
$131$	1.18201e28	+	1.18201e28i	0.308644	+	0.308644i	−0.535739	+	0.844384i	$0.679967\pi$
$132$	8.56335e26	+	2.79029e26i	0.0201788	+	0.00657508i
$133$	−1.01494e29	+	1.01494e29i	−2.15996	+	2.15996i
$134$	−1.24810e28	−	1.71936e28i	−0.240068	−	0.330714i
$135$		−	1.34180e28i		−	0.233443i
$136$	−4.61744e28	−	2.35997e28i	−0.727153	−	0.371648i
$137$		−	1.29893e29i		−	1.85293i	−0.376383	−	0.926464i	$-0.622832\pi$
$137$		−	1.29893e29i		−	1.85293i	0.376383	−	0.926464i	$-0.377168\pi$
$138$	−8.45291e27	+	6.13602e27i	−0.109305	+	0.0793449i
$139$	1.03822e29	−	1.03822e29i	1.21783	−	1.21783i	0.249446	−	0.968389i	$-0.419752\pi$
$139$	1.03822e29	−	1.03822e29i	1.21783	−	1.21783i	0.968389	−	0.249446i	$-0.0802484\pi$
$140$	1.12460e29	+	2.21170e29i	1.19748	+	2.35503i
$141$	5.13035e27	+	5.13035e27i	0.0496237	+	0.0496237i
$142$	−2.90390e28	+	1.82852e29i	−0.255322	+	1.60771i
$143$	2.87633e27			0.0230039
$144$	8.04281e28	−	1.10313e29i	0.585483	−	0.803032i
$145$	1.07573e29			0.713241
$146$	2.64697e28	−	1.66674e29i	0.159951	−	1.00717i
$147$	−2.17496e28	−	2.17496e28i	−0.119858	−	0.119858i
$148$	−2.78209e29	+	1.41463e29i	−1.39907	+	0.711393i
$149$	5.27481e28	−	5.27481e28i	0.242210	−	0.242210i	−0.575554	−	0.817764i	$-0.695214\pi$
$149$	5.27481e28	−	5.27481e28i	0.242210	−	0.242210i	0.817764	+	0.575554i	$0.195214\pi$
$150$	−1.84186e28	+	1.33702e28i	−0.0772726	+	0.0560927i
$151$			2.37511e29i			0.910950i	0.890249	+	0.455475i	$0.150531\pi$
$151$			2.37511e29i			0.910950i	−0.890249	+	0.455475i	$0.849469\pi$
$152$	−1.50918e29	−	4.66461e29i	−0.529485	−	1.63654i
$153$		−	2.52731e29i		−	0.811565i
$154$	−9.56623e28	−	1.31783e29i	−0.281327	−	0.387552i
$155$	−1.53646e29	+	1.53646e29i	−0.414040	+	0.414040i
$156$	−8.41848e26	+	2.58362e27i	−0.00207994	+	0.00638332i
$157$	5.88693e29	+	5.88693e29i	1.33427	+	1.33427i	0.901508	+	0.432762i	$0.142461\pi$
$157$	5.88693e29	+	5.88693e29i	1.33427	+	1.33427i	0.432762	+	0.901508i	$0.357539\pi$
$158$	−4.53772e29	−	7.20641e28i	−0.943989	−	0.149916i
$159$	−2.28727e28			−0.0436974
$160$	−8.47492e29	−	1.76432e27i	−1.48770	−	0.00309712i
$161$	1.88857e30			3.04778
$162$	6.53003e29	+	1.03704e29i	0.969309	+	0.153937i
$163$	3.31372e28	+	3.31372e28i	0.0452671	+	0.0452671i	0.729378	−	0.684111i	$-0.239810\pi$
$163$	3.31372e28	+	3.31372e28i	0.0452671	+	0.0452671i	−0.684111	+	0.729378i	$0.739810\pi$
$164$	−1.57822e29	+	4.84352e29i	−0.198506	+	0.609213i
$165$	1.92682e28	−	1.92682e28i	0.0223259	−	0.0223259i
$166$	2.63968e29	+	3.63639e29i	0.281898	+	0.388339i
$167$			2.32054e29i			0.228516i	0.993451	+	0.114258i	$0.0364490\pi$
$167$			2.32054e29i			0.228516i	−0.993451	+	0.114258i	$0.963551\pi$
$168$	1.46371e29	−	4.73567e28i	0.132978	−	0.0430235i
$169$		−	1.18386e30i		−	0.992723i
$170$	−1.26966e30	+	9.21655e29i	−0.983167	+	0.713688i
$171$	1.68958e30	−	1.68958e30i	1.20874	−	1.20874i
$172$	6.88562e29	−	3.50118e29i	0.455312	−	0.231516i
$173$	−1.18946e30	−	1.18946e30i	−0.727326	−	0.727326i	0.242760	−	0.970086i	$-0.421947\pi$
$173$	−1.18946e30	−	1.18946e30i	−0.727326	−	0.727326i	−0.970086	+	0.242760i	$0.921947\pi$
$174$	1.04614e28	−	6.58729e28i	0.00591798	−	0.0372642i
$175$	4.11514e30			2.15462
$176$	5.49516e29	−	8.60969e28i	0.266416	−	0.0417414i
$177$	1.18504e29			0.0532225
$178$	1.84556e29	−	1.16211e30i	0.0768171	−	0.483700i
$179$	4.08322e29	+	4.08322e29i	0.157575	+	0.157575i	0.781491	−	0.623916i	$-0.214459\pi$
$179$	4.08322e29	+	4.08322e29i	0.157575	+	0.157575i	−0.623916	+	0.781491i	$0.714459\pi$
$180$	−1.87212e30	−	3.68182e30i	−0.670123	−	1.31790i
$181$	1.71793e30	−	1.71793e30i	0.570618	−	0.570618i	−0.361683	−	0.932301i	$-0.617798\pi$
$181$	1.71793e30	−	1.71793e30i	0.570618	−	0.570618i	0.932301	+	0.361683i	$0.117798\pi$
$182$	3.97599e29	−	2.88619e29i	0.122597	−	0.0889942i
$183$			1.16114e29i			0.0332503i
$184$	−2.93575e30	+	5.74398e30i	−0.781049	+	1.52817i
$185$			9.44296e30i			2.33502i
$186$	7.91436e28	+	1.09027e29i	0.0181966	+	0.0250675i
$187$	7.28105e29	−	7.28105e29i	0.155716	−	0.155716i
$188$	4.26032e30	+	1.38819e30i	0.847836	+	0.276259i
$189$	1.06365e30	+	1.06365e30i	0.197045	+	0.197045i
$190$	−1.46496e31	−	2.32652e30i	−2.52728	−	0.401360i
$191$	6.03283e30			0.969552			0.484776	−	0.874638i	$-0.338901\pi$
$191$	6.03283e30			0.969552			0.484776	+	0.874638i	$0.338901\pi$
$192$	−8.34979e28	+	5.18793e29i	−0.0125057	+	0.0777012i
$193$	−6.79651e30			−0.948992			−0.474496	−	0.880258i	$-0.657370\pi$
$193$	−6.79651e30			−0.948992			−0.474496	+	0.880258i	$0.657370\pi$
$194$	−6.68550e30	−	1.06173e30i	−0.870584	−	0.138259i
$195$	5.81335e28	+	5.81335e28i	0.00706252	+	0.00706252i
$196$	−1.80612e31	−	5.88507e30i	−2.04781	−	0.667260i
$197$	8.40201e30	−	8.40201e30i	0.889384	−	0.889384i	−0.105080	−	0.994464i	$-0.533510\pi$
$197$	8.40201e30	−	8.40201e30i	0.889384	−	0.889384i	0.994464	+	0.105080i	$0.0335099\pi$
$198$	1.59249e30	+	2.19380e30i	0.157433	+	0.216878i
$199$		−	1.08195e31i		−	0.999292i	−0.866230	−	0.499646i	$-0.833463\pi$
$199$		−	1.08195e31i		−	0.999292i	0.866230	−	0.499646i	$-0.166537\pi$
$200$	−6.39691e30	+	1.25160e31i	−0.552161	+	1.08034i
$201$			3.98558e29i			0.0321621i
$202$	−1.58290e31	+	1.14904e31i	−1.19457	+	0.867145i
$203$	−8.52740e30	+	8.52740e30i	−0.602033	+	0.602033i
$204$	4.40906e29	+	8.67112e29i	0.0291299	+	0.0572886i
$205$	1.08983e31	+	1.08983e31i	0.674035	+	0.674035i
$206$	2.45331e30	−	1.54479e31i	0.142084	−	0.894670i
$207$	−3.14391e31			−1.70557
$208$	2.59760e29	+	1.65793e30i	0.0132044	+	0.0842773i
$209$	9.73521e30			0.463842
$210$	7.30040e29	−	4.59690e30i	0.0326126	−	0.205355i
$211$	2.43603e31	+	2.43603e31i	1.02063	+	1.02063i	0.999783	+	0.0208483i	$0.00663670\pi$
$211$	2.43603e31	+	2.43603e31i	1.02063	+	1.02063i	0.0208483	+	0.999783i	$0.493363\pi$
$212$	−1.25914e31	+	6.40243e30i	−0.494925	+	0.251658i
$213$	2.45588e30	−	2.45588e30i	0.0905903	−	0.0905903i
$214$	1.27066e31	−	9.22383e30i	0.439992	−	0.319393i
$215$		−	2.33712e31i		−	0.759908i
$216$	−4.88846e30	+	1.58161e30i	−0.149295	+	0.0483029i
$217$		−	2.43592e31i		−	0.698966i
$218$	2.41236e31	+	3.32324e31i	0.650548	+	0.896187i
$219$	−2.23859e30	+	2.23859e30i	−0.0567518	+	0.0567518i
$220$	5.21366e30	−	1.60006e31i	0.124290	−	0.381444i
$221$	2.19674e30	+	2.19674e30i	0.0492588	+	0.0492588i
$222$	5.78244e30	+	9.18316e29i	0.121996	+	0.0193743i
$223$	2.69870e31			0.535844			0.267922	−	0.963441i	$-0.413663\pi$
$223$	2.69870e31			0.535844			0.267922	+	0.963441i	$0.413663\pi$
$224$	6.73211e31	−	6.70414e31i	1.25835	−	1.25313i
$225$	−6.85048e31			−1.20575
$226$	−6.40884e31	−	1.01780e31i	−1.06247	−	0.168732i
$227$	3.30034e31	+	3.30034e31i	0.515477	+	0.515477i	0.916200	−	0.400722i	$-0.131241\pi$
$227$	3.30034e31	+	3.30034e31i	0.515477	+	0.515477i	−0.400722	+	0.916200i	$0.631241\pi$
$228$	−2.84931e30	+	8.74450e30i	−0.0419392	+	0.128711i
$229$	4.38926e31	−	4.38926e31i	0.608993	−	0.608993i	−0.333690	−	0.942683i	$-0.608294\pi$
$229$	4.38926e31	−	4.38926e31i	0.608993	−	0.608993i	0.942683	+	0.333690i	$0.108294\pi$
$230$	1.14652e32	+	1.57943e32i	1.49987	+	2.06621i
$231$			3.05481e30i			0.0376897i
$232$	−1.26799e31	−	3.91913e31i	−0.147581	−	0.456144i
$233$		−	3.31103e30i		−	0.0363628i	−0.999835	−	0.0181814i	$-0.994212\pi$
$233$		−	3.31103e30i		−	0.0363628i	0.999835	−	0.0181814i	$-0.00578764\pi$
$234$	−6.61883e30	+	4.80465e30i	−0.0686068	+	0.0498021i
$235$	9.58608e31	−	9.58608e31i	0.938047	−	0.938047i
$236$	6.52366e31	−	3.31713e31i	0.602809	−	0.306514i
$237$	6.09459e30	+	6.09459e30i	0.0531915	+	0.0531915i
$238$	2.75866e31	−	1.73707e32i	0.227463	−	1.43228i
$239$	−1.30034e32			−1.01318			−0.506588	−	0.862188i	$-0.669093\pi$
$239$	−1.30034e32			−1.01318			−0.506588	+	0.862188i	$0.669093\pi$
$240$	1.28464e31	+	9.36617e30i	0.0946083	+	0.0689780i
$241$	2.73585e32			1.90485			0.952427	−	0.304768i	$-0.0985788\pi$
$241$	2.73585e32			1.90485			0.952427	+	0.304768i	$0.0985788\pi$
$242$	2.20898e31	−	1.39094e32i	0.145440	−	0.915804i
$243$	−2.65874e31	−	2.65874e31i	−0.165574	−	0.165574i
$244$	3.25022e31	+	6.39207e31i	0.191492	+	0.376599i
$245$	−4.06392e32	+	4.06392e32i	−2.26570	+	2.26570i
$246$	7.73347e30	−	5.61378e30i	0.0408085	−	0.0296232i
$247$			2.93718e31i			0.146731i
$248$	7.40870e31	+	3.78659e31i	0.350465	+	0.179122i
$249$		−	8.42936e30i		−	0.0377662i
$250$	4.39132e31	+	6.04943e31i	0.186383	+	0.256758i
$251$	−1.10138e32	+	1.10138e32i	−0.442939	+	0.442939i	−0.892999	−	0.450060i	$-0.851403\pi$
$251$	−1.10138e32	+	1.10138e32i	−0.442939	+	0.442939i	0.450060	+	0.892999i	$0.351403\pi$
$252$	4.40264e32	+	1.43456e32i	1.67805	+	0.546778i
$253$	−9.05745e31	−	9.05745e31i	−0.327250	−	0.327250i
$254$	−3.63774e32	−	5.77715e31i	−1.24617	−	0.197906i
$255$	2.94315e31			0.0956136
$256$	9.92532e31	+	3.08968e32i	0.305847	+	0.952081i
$257$	−4.78115e32			−1.39777			−0.698885	−	0.715234i	$-0.746320\pi$
$257$	−4.78115e32			−1.39777			−0.698885	+	0.715234i	$0.746320\pi$
$258$	−1.43114e31	−	2.27282e30i	−0.0397024	−	0.00630519i
$259$	−7.48550e32	−	7.48550e32i	−1.97094	−	1.97094i
$260$	4.82750e31	+	1.57299e31i	0.120665	+	0.0393176i
$261$	1.41956e32	−	1.41956e32i	0.336904	−	0.336904i
$262$	−1.13766e32	−	1.56722e32i	−0.256415	−	0.353234i
$263$			7.64350e31i			0.163640i	0.996647	+	0.0818201i	$0.0260733\pi$
$263$			7.64350e31i			0.163640i	−0.996647	+	0.0818201i	$0.973927\pi$
$264$	−9.29103e30	−	4.74865e30i	−0.0188978	−	0.00965866i
$265$			4.27377e32i			0.826022i
$266$	1.34571e33	−	9.76859e32i	2.47200	−	1.79444i
$267$	−1.56082e31	+	1.56082e31i	−0.0272553	+	0.0272553i
$268$	1.11563e32	+	2.19406e32i	0.185225	+	0.364275i
$269$	−3.05722e32	−	3.05722e32i	−0.482693	−	0.482693i	0.423298	−	0.905991i	$-0.360872\pi$
$269$	−3.05722e32	−	3.05722e32i	−0.482693	−	0.482693i	−0.905991	+	0.423298i	$0.860872\pi$
$270$	−2.43817e31	+	1.53526e32i	−0.0366145	+	0.230554i
$271$	7.43075e32			1.06157			0.530783	−	0.847508i	$-0.321898\pi$
$271$	7.43075e32			1.06157			0.530783	+	0.847508i	$0.321898\pi$
$272$	4.85437e32	+	3.53928e32i	0.659862	+	0.481099i
$273$	−9.21657e30			−0.0119227
$274$	−2.36028e32	+	1.48622e33i	−0.290624	+	1.83000i
$275$	−1.97359e32	−	1.97359e32i	−0.231348	−	0.231348i
$276$	1.07867e32	−	5.48477e31i	0.120397	−	0.0612189i
$277$	−5.42675e32	+	5.42675e32i	−0.576850	+	0.576850i	−0.934034	−	0.357184i	$-0.883737\pi$
$277$	−5.42675e32	+	5.42675e32i	−0.576850	+	0.576850i	0.357184	+	0.934034i	$0.383737\pi$
$278$	−1.37657e33	+	9.99258e32i	−1.39377	+	1.01175i
$279$			4.05507e32i			0.391149i
$280$	−8.84861e32	−	2.73494e33i	−0.813283	−	2.51371i
$281$			5.44277e32i			0.476743i	0.971174	+	0.238372i	$0.0766136\pi$
$281$			5.44277e32i			0.476743i	−0.971174	+	0.238372i	$0.923386\pi$
$282$	−4.93784e31	−	6.80231e31i	−0.0412263	−	0.0567928i
$283$	−6.86710e32	+	6.86710e32i	−0.546584	+	0.546584i	−0.925451	−	0.378867i	$-0.876314\pi$
$283$	−6.86710e32	+	6.86710e32i	−0.546584	+	0.546584i	0.378867	+	0.925451i	$0.376314\pi$
$284$	6.64519e32	−	2.03940e33i	0.504324	−	1.54776i
$285$	1.96758e32	+	1.96758e32i	0.142406	+	0.142406i
$286$	−3.29105e31	−	5.22657e30i	−0.0227192	−	0.00360807i
$287$	−1.72783e33			−1.13788
$288$	−1.12070e33	+	1.11604e33i	−0.704188	+	0.701263i
$289$	−5.55559e32			−0.333126
$290$	−1.23084e33	−	1.95471e32i	−0.704414	−	0.111869i
$291$	8.97927e31	+	8.97927e31i	0.0490553	+	0.0490553i
$292$	−6.05725e32	+	1.85896e33i	−0.315942	+	0.969621i
$293$	−8.74372e31	+	8.74372e31i	−0.0435495	+	0.0435495i	−0.728546	−	0.684997i	$-0.759804\pi$
$293$	−8.74372e31	+	8.74372e31i	−0.0435495	+	0.0435495i	0.684997	+	0.728546i	$0.259804\pi$
$294$	2.09335e32	+	2.88377e32i	0.0995754	+	0.137174i
$295$		−	2.21426e33i		−	1.00608i
$296$	3.44028e33	−	1.11307e33i	1.49333	−	0.483151i
$297$		−	1.02024e32i		−	0.0423146i
$298$	−6.99384e32	+	5.07687e32i	−0.277202	+	0.201223i
$299$	2.73269e32	−	2.73269e32i	0.103521	−	0.103521i
$300$	2.35038e32	−	1.19512e32i	0.0851141	−	0.0432786i
$301$	1.85265e33	+	1.85265e33i	0.641424	+	0.641424i
$302$	4.31579e32	−	2.71756e33i	0.142879	−	0.899675i
$303$	3.66926e32			0.116172
$304$	8.79182e32	+	5.61141e33i	0.266248	+	1.69933i
$305$	2.16959e33			0.628536
$306$	−4.59235e32	+	2.89170e33i	−0.127291	+	0.801521i
$307$	4.34162e32	+	4.34162e32i	0.115155	+	0.115155i	0.762336	−	0.647181i	$-0.224052\pi$
$307$	4.34162e32	+	4.34162e32i	0.115155	+	0.115155i	−0.647181	+	0.762336i	$0.724052\pi$
$308$	8.55091e32	+	1.68167e33i	0.217059	+	0.426880i
$309$	−2.07480e32	+	2.07480e32i	−0.0504125	+	0.0504125i
$310$	2.03718e33	−	1.47880e33i	0.473856	−	0.343975i
$311$		−	6.90950e33i		−	1.53880i	−0.638769	−	0.769399i	$-0.720556\pi$
$311$		−	6.90950e33i		−	1.53880i	0.638769	−	0.769399i	$-0.279444\pi$
$312$	1.43270e31	−	2.80317e31i	0.00305540	−	0.00597808i
$313$			1.74170e33i			0.355733i	0.984055	+	0.177866i	$0.0569195\pi$
$313$			1.74170e33i			0.355733i	−0.984055	+	0.177866i	$0.943081\pi$
$314$	−5.66603e33	−	7.80545e33i	−1.10848	−	1.52703i
$315$	9.90630e33	−	9.90630e33i	1.85660	−	1.85660i
$316$	5.06104e33	+	1.64909e33i	0.908792	+	0.296121i
$317$	3.54910e33	+	3.54910e33i	0.610686	+	0.610686i	0.943125	−	0.332439i	$-0.107871\pi$
$317$	3.54910e33	+	3.54910e33i	0.610686	+	0.610686i	−0.332439	+	0.943125i	$0.607871\pi$
$318$	2.61706e32	+	4.15618e31i	0.0431566	+	0.00685375i
$319$	8.17937e32			0.129284
$320$	9.69367e33	+	1.56016e33i	1.46880	+	0.236398i
$321$	−2.94547e32			−0.0427895
$322$	−2.16087e34	−	3.43171e33i	−3.01006	−	0.478031i
$323$	7.43508e33	+	7.43508e33i	0.993234	+	0.993234i
$324$	−7.28312e33	−	2.37314e33i	−0.933168	−	0.304064i
$325$	5.95446e32	−	5.95446e32i	0.0731842	−	0.0731842i
$326$	−3.18937e32	−	4.39364e32i	−0.0376069	−	0.0518068i
$327$		−	7.70345e32i		−	0.0871547i
$328$	2.68588e33	−	5.25510e33i	0.291602	−	0.570538i
$329$			1.51979e34i			1.58358i
$330$	−2.55476e32	+	1.85452e32i	−0.0255513	+	0.0185478i
$331$	9.41812e33	−	9.41812e33i	0.904246	−	0.904246i	−0.0915543	−	0.995800i	$-0.529184\pi$
$331$	9.41812e33	−	9.41812e33i	0.904246	−	0.904246i	0.995800	+	0.0915543i	$0.0291835\pi$
$332$	−2.35952e33	−	4.64036e33i	−0.217500	−	0.427747i
$333$	1.24611e34	+	1.24611e34i	1.10296	+	1.10296i
$334$	4.21664e32	−	2.65513e33i	0.0358417	−	0.225688i
$335$	7.44707e33			0.607968
$336$	−1.76080e33	+	2.75879e32i	−0.138080	+	0.0216340i
$337$	7.50286e32			0.0565227			0.0282614	−	0.999601i	$-0.491003\pi$
$337$	7.50286e32			0.0565227			0.0282614	+	0.999601i	$0.491003\pi$
$338$	−2.15118e33	+	1.35455e34i	−0.155704	+	0.980436i
$339$	8.60768e32	+	8.60768e32i	0.0598674	+	0.0598674i
$340$	1.62020e34	−	8.23835e33i	1.08294	−	0.550649i
$341$	−1.16825e33	+	1.16825e33i	−0.0750501	+	0.0750501i
$342$	−2.24020e34	+	1.62618e34i	−1.38336	+	1.00419i
$343$		−	3.45151e34i		−	2.04898i
$344$	−8.51462e33	+	2.75482e33i	−0.485989	+	0.157237i
$345$		−	3.66120e33i		−	0.200940i
$346$	1.14483e34	+	1.57710e34i	0.604246	+	0.832402i
$347$	−1.83944e34	+	1.83944e34i	−0.933767	+	0.933767i	−0.997939	−	0.0641721i	$-0.979559\pi$
$347$	−1.83944e34	+	1.83944e34i	−0.933767	+	0.933767i	0.0641721	+	0.997939i	$0.479559\pi$
$348$	−2.39395e32	+	7.34699e32i	−0.0116895	+	0.0358748i
$349$	−2.08846e34	−	2.08846e34i	−0.981030	−	0.981030i	0.0187932	−	0.999823i	$-0.494018\pi$
$349$	−2.08846e34	−	2.08846e34i	−0.981030	−	0.981030i	−0.999823	+	0.0187932i	$0.994018\pi$
$350$	−4.70848e34	−	7.47760e33i	−2.12795	−	0.337943i
$351$	3.07813e32			0.0133857
$352$	−6.44393e33	−	1.34151e31i	−0.269665	−	0.000561393i
$353$	−1.93143e34			−0.777892			−0.388946	−	0.921260i	$-0.627161\pi$
$353$	−1.93143e34			−0.777892			−0.388946	+	0.921260i	$0.627161\pi$
$354$	−1.35591e33	−	2.15334e32i	−0.0525638	−	0.00834773i
$355$	−4.58881e34	−	4.58881e34i	−1.71245	−	1.71245i
$356$	−4.22332e33	+	1.29613e34i	−0.151733	+	0.465665i
$357$	−2.33305e33	+	2.33305e33i	−0.0807056	+	0.0807056i
$358$	−3.93000e33	−	5.41391e33i	−0.130910	−	0.180339i
$359$			2.85790e34i			0.916793i	0.888748	+	0.458397i	$0.151576\pi$
$359$			2.85790e34i			0.916793i	−0.888748	+	0.458397i	$0.848424\pi$
$360$	1.47303e34	+	4.55286e34i	0.455122	+	1.40670i
$361$			6.58109e34i			1.95862i
$362$	−2.27780e34	+	1.65347e34i	−0.653055	+	0.474057i
$363$	−1.86817e33	+	1.86817e33i	−0.0516033	+	0.0516033i
$364$	−5.07371e33	+	2.57987e33i	−0.135038	+	0.0686639i
$365$	4.18281e34	+	4.18281e34i	1.07279	+	1.07279i
$366$	2.10990e32	−	1.32856e33i	0.00521516	−	0.0328387i
$367$	2.74472e34			0.653893			0.326947	−	0.945043i	$-0.393980\pi$
$367$	2.74472e34			0.653893			0.326947	+	0.945043i	$0.393980\pi$
$368$	4.40277e34	−	6.03872e34i	1.01107	−	1.38675i
$369$	2.87633e34			0.636769
$370$	1.71588e34	−	1.08045e35i	0.366237	−	2.30612i
$371$	−3.38784e34	−	3.38784e34i	−0.697229	−	0.697229i
$372$	−7.07437e32	−	1.39129e33i	−0.0140397	−	0.0276113i
$373$	−2.09474e34	+	2.09474e34i	−0.400923	+	0.400923i	−0.878558	−	0.477635i	$-0.841494\pi$
$373$	−2.09474e34	+	2.09474e34i	−0.400923	+	0.400923i	0.477635	+	0.878558i	$0.341494\pi$
$374$	−9.65391e33	+	7.00783e33i	−0.178212	+	0.129365i
$375$		−	1.40229e33i		−	0.0249699i
$376$	−4.62235e34	−	2.36248e34i	−0.794012	−	0.405819i
$377$			2.46777e33i			0.0408975i
$378$	−1.02374e34	−	1.41029e34i	−0.163700	−	0.225511i
$379$	5.06575e34	−	5.06575e34i	0.781653	−	0.781653i	−0.198456	−	0.980110i	$-0.563593\pi$
$379$	5.06575e34	−	5.06575e34i	0.781653	−	0.781653i	0.980110	+	0.198456i	$0.0635928\pi$
$380$	1.63391e35	+	5.32395e34i	2.43304	+	0.792784i
$381$	4.88584e33	+	4.88584e33i	0.0702186	+	0.0702186i
$382$	−6.90268e34	−	1.09622e34i	−0.957552	−	0.152070i
$383$	−1.82405e34			−0.244261			−0.122131	−	0.992514i	$-0.538973\pi$
$383$	−1.82405e34			−0.244261			−0.122131	+	0.992514i	$0.538973\pi$
$384$	1.89807e33	−	5.78423e33i	0.0245380	−	0.0747781i
$385$	5.70792e34			0.712456
$386$	7.77647e34	+	1.23499e34i	0.937246	+	0.148845i
$387$	−3.08410e34	−	3.08410e34i	−0.358948	−	0.358948i
$388$	7.45653e34	+	2.42964e34i	0.838124	+	0.273095i
$389$	−1.25284e35	+	1.25284e35i	−1.36011	+	1.36011i	−0.486345	+	0.873767i	$0.661670\pi$
$389$	−1.25284e35	+	1.25284e35i	−1.36011	+	1.36011i	−0.873767	+	0.486345i	$0.838330\pi$
$390$	−5.59521e32	−	7.70789e32i	−0.00586738	−	0.00808283i
$391$		−	1.38349e35i		−	1.40149i
$392$	1.95960e35	+	1.00155e35i	1.91781	+	0.980191i
$393$			3.63291e33i			0.0343522i
$394$	−1.11402e35	+	8.08673e34i	−1.01787	+	0.738880i
$395$	1.13878e35	−	1.13878e35i	1.00549	−	1.00549i
$396$	−1.42347e34	−	2.79948e34i	−0.121468	−	0.238887i
$397$	−9.17948e34	−	9.17948e34i	−0.757088	−	0.757088i	0.218704	−	0.975791i	$-0.429817\pi$
$397$	−9.17948e34	−	9.17948e34i	−0.757088	−	0.757088i	−0.975791	+	0.218704i	$0.929817\pi$
$398$	−1.96601e34	+	1.23796e35i	−0.156735	+	0.986924i
$399$	−3.11943e34			−0.240404
$400$	9.59352e34	−	1.31582e35i	0.714773	−	0.980363i
$401$	−1.65648e35			−1.19326			−0.596632	−	0.802515i	$-0.703495\pi$
$401$	−1.65648e35			−1.19326			−0.596632	+	0.802515i	$0.703495\pi$
$402$	7.24218e32	−	4.56024e33i	0.00504449	−	0.0317641i
$403$	−3.52468e33	−	3.52468e33i	−0.0237412	−	0.0237412i
$404$	2.01993e35	−	1.02709e35i	1.31579	−	0.669050i
$405$	−1.63876e35	+	1.63876e35i	−1.03246	+	1.03246i
$406$	1.13064e35	−	8.20742e34i	0.689008	−	0.500155i
$407$			7.17998e34i			0.423252i
$408$	−3.46916e33	−	1.07225e34i	−0.0197839	−	0.0611484i
$409$			1.06755e35i			0.589013i	0.955650	+	0.294506i	$0.0951552\pi$
$409$			1.06755e35i			0.589013i	−0.955650	+	0.294506i	$0.904845\pi$
$410$	−1.04894e35	−	1.44500e35i	−0.559973	−	0.771411i
$411$	1.99613e34	−	1.99613e34i	0.103116	−	0.103116i
$412$	−5.61407e34	+	1.72295e35i	−0.280650	+	0.861312i
$413$	1.75526e35	+	1.75526e35i	0.849210	+	0.849210i
$414$	3.59721e35	+	5.71278e34i	1.68446	+	0.267512i
$415$	−1.57503e35			−0.713903
$416$	4.04742e31	−	1.94418e34i	0.000177590	−	0.0853052i
$417$	3.19096e34			0.135545
$418$	−1.11389e35	−	1.76898e34i	−0.458101	−	0.0727517i
$419$	1.17918e35	+	1.17918e35i	0.469560	+	0.469560i	0.901772	−	0.432212i	$-0.142267\pi$
$419$	1.17918e35	+	1.17918e35i	0.469560	+	0.469560i	−0.432212	+	0.901772i	$0.642267\pi$
$420$	−1.67060e34	+	5.12705e34i	−0.0644180	+	0.197698i
$421$	−4.51119e33	+	4.51119e33i	−0.0168455	+	0.0168455i	−0.715479	−	0.698634i	$-0.753792\pi$
$421$	−4.51119e33	+	4.51119e33i	−0.0168455	+	0.0168455i	0.698634	+	0.715479i	$0.253792\pi$
$422$	−2.34461e35	−	3.22991e35i	−0.847917	−	1.16808i
$423$		−	2.53000e35i		−	0.886186i
$424$	1.55703e35	−	5.03759e34i	0.528271	−	0.170917i
$425$		−	3.01459e35i		−	0.990780i
$426$	−3.25623e34	+	2.36372e34i	−0.103678	+	0.0752604i
$427$	−1.71985e35	+	1.71985e35i	−0.530535	+	0.530535i
$428$	−1.62148e35	+	8.24485e34i	−0.484642	+	0.246429i
$429$	4.42020e32	+	4.42020e32i	0.00128017	+	0.00128017i
$430$	−4.24676e34	+	2.67409e35i	−0.119188	+	0.750503i
$431$	−3.28518e35			−0.893544			−0.446772	−	0.894648i	$-0.647427\pi$
$431$	−3.28518e35			−0.893544			−0.446772	+	0.894648i	$0.647427\pi$
$432$	5.88069e34	−	9.21373e33i	0.155024	−	0.0242887i
$433$	−1.91557e35			−0.489453			−0.244727	−	0.969592i	$-0.578698\pi$
$433$	−1.91557e35			−0.489453			−0.244727	+	0.969592i	$0.578698\pi$
$434$	−4.42629e34	+	2.78714e35i	−0.109630	+	0.690315i
$435$	1.65313e34	+	1.65313e34i	0.0396920	+	0.0396920i
$436$	−2.15632e35	−	4.24075e35i	−0.501933	−	0.987131i
$437$	9.24905e35	−	9.24905e35i	2.08736	−	2.08736i
$438$	2.96814e34	−	2.15459e34i	0.0649506	−	0.0471481i
$439$		−	3.32065e35i		−	0.704616i	−0.935884	−	0.352308i	$-0.885397\pi$
$439$		−	3.32065e35i		−	0.704616i	0.935884	−	0.352308i	$-0.114603\pi$
$440$	−8.87285e34	+	1.73603e35i	−0.182580	+	0.357229i
$441$			1.07257e36i			2.14044i
$442$	−2.11431e34	−	2.91265e34i	−0.0409231	−	0.0563751i
$443$	−4.50120e35	+	4.50120e35i	−0.845042	+	0.845042i	−0.989510	−	0.144467i	$-0.953853\pi$
$443$	−4.50120e35	+	4.50120e35i	−0.845042	+	0.845042i	0.144467	+	0.989510i	$0.453853\pi$
$444$	−6.44931e34	−	2.10145e34i	−0.117447	−	0.0382691i
$445$	2.91640e35	+	2.91640e35i	0.515213	+	0.515213i
$446$	−3.08781e35	−	4.90379e34i	−0.529212	−	0.0840448i
$447$	1.62121e34			0.0269580
$448$	−8.92098e35	+	6.44748e35i	−1.43933	+	1.04025i
$449$	−1.77106e35			−0.277273			−0.138636	−	0.990343i	$-0.544272\pi$
$449$	−1.77106e35			−0.277273			−0.138636	+	0.990343i	$0.544272\pi$
$450$	7.83822e35	+	1.24480e35i	1.19083	+	0.189117i
$451$	8.28656e34	+	8.28656e34i	0.122177	+	0.122177i
$452$	7.14795e35	+	2.32909e35i	1.02285	+	0.333287i
$453$	−3.64994e34	+	3.64994e34i	−0.0506945	+	0.0506945i
$454$	−3.17650e35	−	4.37590e35i	−0.428247	−	0.589948i
$455$			1.72212e35i			0.225377i
$456$	4.84910e34	−	9.48758e34i	0.0616078	−	0.120540i
$457$		−	2.87408e35i		−	0.354512i	−0.984165	−	0.177256i	$-0.943278\pi$
$457$		−	2.87408e35i		−	0.354512i	0.984165	−	0.177256i	$-0.0567220\pi$
$458$	−5.81969e35	+	4.22455e35i	−0.696973	+	0.505937i
$459$	7.79188e34	−	7.79188e34i	0.0906089	−	0.0906089i
$460$	−1.02483e36	−	2.01549e36i	−1.15723	−	2.27588i
$461$	−1.23052e36	−	1.23052e36i	−1.34935	−	1.34935i	−0.886362	−	0.462992i	$-0.846776\pi$
$461$	−1.23052e36	−	1.23052e36i	−1.34935	−	1.34935i	−0.462992	−	0.886362i	$-0.653224\pi$
$462$	5.55088e33	−	3.49527e34i	0.00591146	−	0.0372232i
$463$	9.13513e35			0.944868			0.472434	−	0.881366i	$-0.343375\pi$
$463$	9.13513e35			0.944868			0.472434	+	0.881366i	$0.343375\pi$
$464$	7.38675e34	+	4.71462e35i	0.0742097	+	0.473646i
$465$	−4.72229e34			−0.0460827
$466$	−6.01645e33	+	3.78842e34i	−0.00570335	+	0.0359128i
$467$	4.82407e35	+	4.82407e35i	0.444258	+	0.444258i	0.893440	−	0.449182i	$-0.148285\pi$
$467$	4.82407e35	+	4.82407e35i	0.444258	+	0.444258i	−0.449182	+	0.893440i	$0.648285\pi$
$468$	8.44622e34	−	4.29471e34i	0.0755689	−	0.0384251i
$469$	−5.90334e35	+	5.90334e35i	−0.513174	+	0.513174i
$470$	−1.27101e36	+	9.22636e35i	−1.07357	+	0.779309i
$471$			1.80935e35i			0.148505i
$472$	−8.06703e35	+	2.61000e35i	−0.643423	+	0.208173i
$473$		−	1.77703e35i		−	0.137743i
$474$	−5.86590e34	−	8.08079e34i	−0.0441903	−	0.0608760i
$475$	2.01534e36	−	2.01534e36i	1.47566	−	1.47566i
$476$	−6.31284e35	+	1.93740e36i	−0.449295	+	1.37888i
$477$	5.63975e35	+	5.63975e35i	0.390177	+	0.390177i
$478$	1.48783e36	+	2.36284e35i	1.00064	+	0.158912i
$479$	1.91939e36			1.25497			0.627485	−	0.778629i	$-0.284085\pi$
$479$	1.91939e36			1.25497			0.627485	+	0.778629i	$0.284085\pi$
$480$	−1.29967e35	−	1.30509e35i	−0.0826184	−	0.0829631i
$481$	−2.16625e35			−0.133891
$482$	−3.13031e36	−	4.97129e35i	−1.88128	−	0.298768i
$483$	2.90226e35	+	2.90226e35i	0.169609	+	0.169609i
$484$	−5.05495e35	+	1.55136e36i	−0.287280	+	0.881657i
$485$	1.67778e36	−	1.67778e36i	0.927302	−	0.927302i
$486$	2.55897e35	+	3.52521e35i	0.137555	+	0.189494i
$487$			2.62926e36i			1.37465i	0.726350	+	0.687325i	$0.241215\pi$
$487$			2.62926e36i			1.37465i	−0.726350	+	0.687325i	$0.758785\pi$
$488$	−2.55735e35	−	7.90430e35i	−0.130054	−	0.401972i
$489$			1.01847e34i			0.00503824i
$490$	5.38833e36	−	3.91142e36i	2.59303	−	1.88229i
$491$	−1.17898e36	+	1.17898e36i	−0.551959	+	0.551959i	−0.927006	−	0.375047i	$-0.877627\pi$
$491$	−1.17898e36	+	1.17898e36i	−0.551959	+	0.551959i	0.375047	+	0.927006i	$0.377627\pi$
$492$	−9.86860e34	+	5.01796e34i	−0.0449497	+	0.0228559i
$493$	6.24683e35	+	6.24683e35i	0.276839	+	0.276839i
$494$	5.33713e34	−	3.36067e35i	0.0230141	−	0.144915i
$495$	−9.50198e35			−0.398698
$496$	−7.78887e35	−	5.67879e35i	−0.318033	−	0.231874i
$497$	7.27516e36			2.89089
$498$	−1.53170e34	+	9.64475e34i	−0.00592347	+	0.0372988i
$499$	−9.61527e33	−	9.61527e33i	−0.00361913	−	0.00361913i	0.705295	−	0.708914i	$-0.250815\pi$
$499$	−9.61527e33	−	9.61527e33i	−0.00361913	−	0.00361913i	−0.708914	+	0.705295i	$0.750815\pi$
$500$	−3.92525e35	−	7.71962e35i	−0.143804	−	0.282814i
$501$	−3.56609e34	+	3.56609e34i	−0.0127169	+	0.0127169i
$502$	1.46032e36	−	1.06006e36i	0.506930	−	0.367984i
$503$			1.91301e36i			0.646472i	0.946318	+	0.323236i	$0.104771\pi$
$503$			1.91301e36i			0.646472i	−0.946318	+	0.323236i	$0.895229\pi$
$504$	−4.77676e36	−	2.44140e36i	−1.57153	−	0.803206i
$505$		−	6.85603e36i		−	2.19603i
$506$	8.71757e35	+	1.20092e36i	0.271872	+	0.374527i
$507$	1.81929e35	−	1.81929e35i	0.0552452	−	0.0552452i
$508$	4.05728e36	+	1.32203e36i	1.19970	+	0.390913i
$509$	−2.47536e36	−	2.47536e36i	−0.712767	−	0.712767i	0.254346	−	0.967113i	$-0.418140\pi$
$509$	−2.47536e36	−	2.47536e36i	−0.712767	−	0.712767i	−0.967113	+	0.254346i	$0.918140\pi$
$510$	−3.36751e35	−	5.34798e34i	−0.0944302	−	0.0149966i
$511$	−6.63149e36			−1.81104
$512$	−5.74216e35	−	3.71552e36i	−0.152732	−	0.988268i
$513$	1.04182e36			0.269904
$514$	5.47052e36	+	8.68781e35i	1.38047	+	0.219234i
$515$	3.87678e36	+	3.87678e36i	0.952957	+	0.952957i
$516$	1.59619e35	+	5.20104e34i	0.0382221	+	0.0124543i
$517$	7.28880e35	−	7.28880e35i	0.170033	−	0.170033i
$518$	7.20461e36	+	9.92498e36i	1.63741	+	2.25568i
$519$		−	3.65582e35i		−	0.0809516i
$520$	−5.23772e35	−	2.67700e35i	−0.113005	−	0.0577568i
$521$		−	2.21889e36i		−	0.466473i	−0.972420	−	0.233237i	$-0.925068\pi$
$521$		−	2.21889e36i		−	0.466473i	0.972420	−	0.233237i	$-0.0749317\pi$
$522$	−1.88218e36	+	1.36629e36i	−0.385576	+	0.279892i
$523$	−3.94162e36	+	3.94162e36i	−0.786869	+	0.786869i	−0.980980	−	0.194111i	$-0.937818\pi$
$523$	−3.94162e36	+	3.94162e36i	−0.786869	+	0.786869i	0.194111	+	0.980980i	$0.437818\pi$
$524$	1.01691e36	+	1.99991e36i	0.197838	+	0.389080i
$525$	6.32394e35	+	6.32394e35i	0.119905	+	0.119905i
$526$	1.38890e35	−	8.74558e35i	0.0256663	−	0.161615i
$527$	−1.78445e36			−0.321412
$528$	9.76778e34	+	7.12160e34i	0.0171490	+	0.0125031i
$529$	−1.13671e37			−1.94535
$530$	7.76584e35	−	4.88998e36i	0.129558	−	0.815798i
$531$	−2.92198e36	−	2.92198e36i	−0.475227	−	0.475227i
$532$	−1.71724e37	+	8.73180e36i	−2.72286	+	1.38451i
$533$	−2.50011e35	+	2.50011e35i	−0.0386493	+	0.0386493i
$534$	2.06949e35	−	1.50225e35i	0.0311929	−	0.0226431i
$535$			5.50362e36i			0.808858i
$536$	−8.77804e35	−	2.71313e36i	−0.125798	−	0.388818i
$537$			1.25498e35i			0.0175381i
$538$	2.94250e36	+	4.05355e36i	0.401010	+	0.552427i
$539$	−3.09001e36	+	3.09001e36i	−0.410688	+	0.410688i
$540$	5.57944e35	−	1.71232e36i	0.0723227	−	0.221957i
$541$	−8.88352e36	−	8.88352e36i	−1.12311	−	1.12311i	−0.991271	−	0.131838i	$-0.957912\pi$
$541$	−8.88352e36	−	8.88352e36i	−1.12311	−	1.12311i	−0.131838	−	0.991271i	$-0.542088\pi$
$542$	−8.50215e36	−	1.35024e36i	−1.04843	−	0.166502i
$543$	5.28007e35			0.0635100
$544$	−4.91118e36	−	4.93167e36i	−0.576237	−	0.578641i
$545$	−1.43939e37			−1.64750
$546$	1.05455e35	+	1.67474e34i	0.0117751	+	0.00187002i
$547$	8.41587e36	+	8.41587e36i	0.916791	+	0.916791i	0.996795	−	0.0800039i	$-0.0254933\pi$
$547$	8.41587e36	+	8.41587e36i	0.916791	+	0.916791i	−0.0800039	+	0.996795i	$0.525493\pi$
$548$	5.40120e36	−	1.65762e37i	0.574054	−	1.76176i
$549$	2.86304e36	−	2.86304e36i	0.296893	−	0.296893i
$550$	1.89953e36	+	2.61678e36i	0.192199	+	0.264771i
$551$			8.35239e36i			0.824640i
$552$	−1.33386e36	+	4.31555e35i	−0.128508	+	0.0415775i
$553$			1.80543e37i			1.69743i
$554$	7.19529e36	−	5.22311e36i	0.660187	−	0.479234i
$555$	−1.45115e36	+	1.45115e36i	−0.129944	+	0.129944i
$556$	1.75662e37	−	8.93201e36i	1.53521	−	0.780620i
$557$	−5.30672e36	−	5.30672e36i	−0.452669	−	0.452669i	0.443570	−	0.896240i	$-0.353712\pi$
$557$	−5.30672e36	−	5.30672e36i	−0.452669	−	0.452669i	−0.896240	+	0.443570i	$0.853712\pi$
$558$	7.36845e35	−	4.63975e36i	0.0613500	−	0.386308i
$559$	5.36143e35			0.0435734
$560$	5.15480e36	+	3.29007e37i	0.408953	+	2.61015i
$561$	2.23783e35			0.0173312
$562$	9.89002e35	−	6.22753e36i	0.0747751	−	0.470842i
$563$	−4.31269e36	−	4.31269e36i	−0.318335	−	0.318335i	0.529792	−	0.848128i	$-0.322270\pi$
$563$	−4.31269e36	−	4.31269e36i	−0.318335	−	0.318335i	−0.848128	+	0.529792i	$0.822270\pi$
$564$	4.41376e35	+	8.68035e35i	0.0318083	+	0.0625560i
$565$	1.60835e37	−	1.60835e37i	1.13169	−	1.13169i
$566$	9.10505e36	−	6.60942e36i	0.625548	−	0.454089i
$567$		−	2.59811e37i		−	1.74296i
$568$	−1.13091e37	+	2.21270e37i	−0.740842	+	1.44951i
$569$			1.64419e37i			1.05181i	0.850543	+	0.525905i	$0.176273\pi$
$569$			1.64419e37i			1.05181i	−0.850543	+	0.525905i	$0.823727\pi$
$570$	−1.89375e36	−	2.60881e36i	−0.118307	−	0.162979i
$571$	2.14249e36	−	2.14249e36i	0.130717	−	0.130717i	−0.638721	−	0.769438i	$-0.720536\pi$
$571$	2.14249e36	−	2.14249e36i	0.130717	−	0.130717i	0.769438	+	0.638721i	$0.220536\pi$
$572$	3.67060e35	+	1.19603e35i	0.0218721	+	0.00712683i
$573$	9.27096e35	+	9.27096e35i	0.0539557	+	0.0539557i
$574$	1.97696e37	+	3.13964e36i	1.12380	+	0.178471i
$575$	−3.75007e37			−2.08221
$576$	1.48508e37	−	1.07331e37i	0.805463	−	0.582134i
$577$	6.01546e36			0.318710			0.159355	−	0.987221i	$-0.449059\pi$
$577$	6.01546e36			0.318710			0.159355	+	0.987221i	$0.449059\pi$
$578$	6.35662e36	+	1.00950e36i	0.329003	+	0.0522494i
$579$	−1.04445e36	−	1.04445e36i	−0.0528115	−	0.0528115i
$580$	1.37279e37	+	4.47310e36i	0.678149	+	0.220968i
$581$	1.24854e37	−	1.24854e37i	0.602592	−	0.602592i
$582$	−8.64233e35	−	1.19056e36i	−0.0407540	−	0.0561422i
$583$			3.24957e36i			0.149727i
$584$	1.03085e37	−	2.01693e37i	0.464112	−	0.908066i
$585$		−	2.86681e36i		−	0.126123i
$586$	1.15933e36	−	8.41562e35i	0.0498411	−	0.0361800i
$587$	7.92351e36	−	7.92351e36i	0.332892	−	0.332892i	−0.520792	−	0.853684i	$-0.674363\pi$
$587$	7.92351e36	−	7.92351e36i	0.332892	−	0.332892i	0.853684	+	0.520792i	$0.174363\pi$
$588$	−1.87117e36	−	3.67994e36i	−0.0768278	−	0.151094i
$589$	−1.19296e37	−	1.19296e37i	−0.478707	−	0.478707i
$590$	−4.02352e36	+	2.53352e37i	−0.157799	+	0.993625i
$591$	2.58236e36			0.0989886
$592$	−4.13857e37	+	6.48421e36i	−1.55063	+	0.242949i
$593$	3.75224e36			0.137421			0.0687103	−	0.997637i	$-0.478112\pi$
$593$	3.75224e36			0.137421			0.0687103	+	0.997637i	$0.478112\pi$
$594$	−1.85387e35	+	1.16734e36i	−0.00663686	+	0.0417908i
$595$	4.35931e37	+	4.35931e37i	1.52559	+	1.52559i
$596$	8.92476e36	−	4.53803e36i	0.305332	−	0.155254i
$597$	1.66269e36	−	1.66269e36i	0.0556108	−	0.0556108i
$598$	−3.62326e36	+	2.63015e36i	−0.118477	+	0.0860032i
$599$		−	2.92712e36i		−	0.0935789i	−0.998905	−	0.0467895i	$-0.985101\pi$
$599$		−	2.92712e36i		−	0.0935789i	0.998905	−	0.0467895i	$-0.0148990\pi$
$600$	−2.90644e36	+	9.40346e35i	−0.0908488	+	0.0293931i
$601$			5.94441e36i			0.181679i	0.995866	+	0.0908393i	$0.0289550\pi$
$601$			5.94441e36i			0.181679i	−0.995866	+	0.0908393i	$0.971045\pi$
$602$	−1.78313e37	−	2.45641e37i	−0.532880	−	0.734089i
$603$	9.82730e36	−	9.82730e36i	0.287178	−	0.287178i
$604$	−9.87613e36	+	3.03097e37i	−0.282220	+	0.866130i
$605$	3.49068e37	+	3.49068e37i	0.975467	+	0.975467i
$606$	−4.19831e36	−	6.66740e35i	−0.114735	−	0.0182212i
$607$	2.73065e37			0.729824			0.364912	−	0.931042i	$-0.381099\pi$
$607$	2.73065e37			0.729824			0.364912	+	0.931042i	$0.381099\pi$
$608$	1.36989e35	−	6.58024e37i	0.00358085	−	1.72006i
$609$	−2.62090e36			−0.0670064
$610$	−2.48242e37	−	3.94236e36i	−0.620757	−	0.0985832i
$611$	2.19908e36	+	2.19908e36i	0.0537879	+	0.0537879i
$612$	1.05090e37	−	3.22520e37i	0.251430	−	0.771635i
$613$	1.84705e37	−	1.84705e37i	0.432276	−	0.432276i	−0.457126	−	0.889402i	$-0.651121\pi$
$613$	1.84705e37	−	1.84705e37i	0.432276	−	0.432276i	0.889402	+	0.457126i	$0.151121\pi$
$614$	−4.17870e36	−	5.75653e36i	−0.0956684	−	0.131792i
$615$			3.34960e36i			0.0750202i
$616$	−6.72807e36	−	2.07952e37i	−0.147418	−	0.455642i
$617$			3.47154e37i			0.744171i	0.928199	+	0.372085i	$0.121357\pi$
$617$			3.47154e37i			0.744171i	−0.928199	+	0.372085i	$0.878643\pi$
$618$	2.75097e36	−	1.99695e36i	0.0576955	−	0.0418815i
$619$	2.44788e37	−	2.44788e37i	0.502304	−	0.502304i	−0.409849	−	0.912153i	$-0.634419\pi$
$619$	2.44788e37	−	2.44788e37i	0.502304	−	0.502304i	0.912153	+	0.409849i	$0.134419\pi$
$620$	−2.59962e37	+	1.32185e37i	−0.521942	+	0.265395i
$621$	−9.69291e36	−	9.69291e36i	−0.190422	−	0.190422i
$622$	−1.25552e37	+	7.90575e37i	−0.241354	+	1.51975i
$623$	−4.62370e37			−0.869763
$624$	−2.14863e35	+	2.94701e35i	−0.00395522	+	0.00542487i
$625$	4.11478e37			0.741253
$626$	3.16483e36	−	1.99282e37i	0.0557951	−	0.351330i
$627$	1.49606e36	+	1.49606e36i	0.0258129	+	0.0258129i
$628$	5.06466e37	+	9.96045e37i	0.855254	+	1.68199i
$629$	−5.48357e37	+	5.48357e37i	−0.906317	+	0.906317i
$630$	−1.31347e38	+	9.53457e37i	−2.12482	+	1.54242i
$631$		−	6.20642e37i		−	0.982753i	−0.870947	−	0.491377i	$-0.836494\pi$
$631$		−	6.20642e37i		−	0.982753i	0.870947	−	0.491377i	$-0.163506\pi$
$632$	−5.49111e37	−	2.80651e37i	−0.851099	−	0.434996i
$633$			7.48712e36i			0.113596i
$634$	−3.41592e37	−	4.70573e37i	−0.507344	−	0.698911i
$635$	9.12920e37	−	9.12920e37i	1.32736	−	1.32736i
$636$	−2.91888e36	−	9.51088e35i	−0.0415475	−	0.0135379i
$637$	−9.32277e36	−	9.32277e36i	−0.129916	−	0.129916i
$638$	−9.35871e36	−	1.48627e36i	−0.127684	−	0.0202777i
$639$	−1.21110e38			−1.61777
$640$	−1.08079e38	−	3.54654e37i	−1.41355	−	0.463848i
$641$	−1.15765e37			−0.148250			−0.0741249	−	0.997249i	$-0.523616\pi$
$641$	−1.15765e37			−0.148250			−0.0741249	+	0.997249i	$0.523616\pi$
$642$	3.37016e36	+	5.35220e35i	0.0422599	+	0.00671134i
$643$	4.93165e37	+	4.93165e37i	0.605541	+	0.605541i	0.941778	−	0.336236i	$-0.109154\pi$
$643$	4.93165e37	+	4.93165e37i	0.605541	+	0.605541i	−0.336236	+	0.941778i	$0.609154\pi$
$644$	2.41008e38	+	7.85302e37i	2.89783	+	0.944230i
$645$	3.59156e36	−	3.59156e36i	0.0422890	−	0.0422890i
$646$	−7.15608e37	−	9.85813e37i	−0.825156	−	1.13672i
$647$		−	9.23628e37i		−	1.04301i	−0.853247	−	0.521506i	$-0.825370\pi$
$647$		−	9.23628e37i		−	1.04301i	0.853247	−	0.521506i	$-0.174630\pi$
$648$	7.90201e37	+	4.03872e37i	0.873927	+	0.446664i
$649$		−	1.68362e37i		−	0.182364i
$650$	−7.89499e36	+	5.73102e36i	−0.0837570	+	0.0607998i
$651$	3.74339e36	−	3.74339e36i	0.0388975	−	0.0388975i
$652$	2.85087e36	+	5.60668e36i	0.0290158	+	0.0570641i
$653$	2.71168e37	+	2.71168e37i	0.270340	+	0.270340i	0.829237	−	0.558897i	$-0.188775\pi$
$653$	2.71168e37	+	2.71168e37i	0.270340	+	0.270340i	−0.558897	+	0.829237i	$0.688775\pi$
$654$	−1.39979e36	+	8.81417e36i	−0.0136698	+	0.0860760i
$655$	6.78809e37			0.649367
$656$	−4.02805e37	+	5.52476e37i	−0.377479	+	0.517740i
$657$	1.10394e38			1.01348
$658$	2.76160e37	−	1.73892e38i	0.248377	−	1.56398i
$659$	−1.00793e38	−	1.00793e38i	−0.888129	−	0.888129i	0.106214	−	0.994343i	$-0.466127\pi$
$659$	−1.00793e38	−	1.00793e38i	−0.888129	−	0.888129i	−0.994343	+	0.106214i	$0.966127\pi$
$660$	3.26011e36	−	1.65769e36i	0.0281442	−	0.0143107i
$661$	1.35144e37	−	1.35144e37i	0.114308	−	0.114308i	−0.647639	−	0.761947i	$-0.724244\pi$
$661$	1.35144e37	−	1.35144e37i	0.114308	−	0.114308i	0.761947	+	0.647639i	$0.224244\pi$
$662$	−1.24874e38	+	9.06471e37i	−1.03488	+	0.751227i
$663$			6.75169e35i			0.00548251i
$664$	1.85652e37	+	5.73817e37i	0.147717	+	0.456567i
$665$			5.82867e38i			4.54440i
$666$	−1.19935e38	−	1.65221e38i	−0.916315	−	1.26230i
$667$	7.77091e37	−	7.77091e37i	0.581799	−	0.581799i
$668$	−9.64923e36	+	2.96133e37i	−0.0707963	+	0.217273i
$669$	4.14722e36	+	4.14722e36i	0.0298198	+	0.0298198i
$670$	−8.52082e37	−	1.35320e37i	−0.600443	−	0.0953571i
$671$	1.64966e37			0.113930
$672$	2.06481e37	+	4.29857e34i	0.139764	+	0.000290963i
$673$	−2.89022e38			−1.91747			−0.958733	−	0.284310i	$-0.908236\pi$
$673$	−2.89022e38			−1.91747			−0.958733	+	0.284310i	$0.908236\pi$
$674$	−8.58466e36	−	1.36334e36i	−0.0558232	−	0.00886535i
$675$	−2.11206e37	−	2.11206e37i	−0.134618	−	0.134618i
$676$	4.92269e37	−	1.51077e38i	0.307554	−	0.943880i
$677$	9.90192e37	−	9.90192e37i	0.606418	−	0.606418i	−0.335590	−	0.942008i	$-0.608936\pi$
$677$	9.90192e37	−	9.90192e37i	0.606418	−	0.606418i	0.942008	+	0.335590i	$0.108936\pi$
$678$	−8.28468e36	−	1.14129e37i	−0.0497365	−	0.0685163i
$679$			2.65997e38i			1.56544i
$680$	−2.00351e38	+	6.48213e37i	−1.15590	+	0.373979i
$681$			1.01436e37i			0.0573728i
$682$	1.54897e37	−	1.12441e37i	0.0858925	−	0.0623499i
$683$	3.59208e37	−	3.59208e37i	0.195284	−	0.195284i	−0.602691	−	0.797975i	$-0.705905\pi$
$683$	3.59208e37	−	3.59208e37i	0.195284	−	0.195284i	0.797975	+	0.602691i	$0.205905\pi$
$684$	2.85870e38	−	1.45358e38i	1.52374	−	0.774787i
$685$	−3.72978e38	−	3.72978e38i	−1.94922	−	1.94922i
$686$	−6.27171e37	+	3.94916e38i	−0.321374	+	2.02362i
$687$	1.34904e37			0.0677810
$688$	1.02429e38	−	1.60483e37i	0.504636	−	0.0790652i
$689$	−9.80417e36			−0.0473643
$690$	−6.65275e36	+	4.18909e37i	−0.0315166	+	0.198453i
$691$	5.41728e37	+	5.41728e37i	0.251668	+	0.251668i	0.821654	−	0.569986i	$-0.193052\pi$
$691$	5.41728e37	+	5.41728e37i	0.251668	+	0.251668i	−0.569986	+	0.821654i	$0.693052\pi$
$692$	−1.02332e38	−	2.01252e38i	−0.466209	−	0.916873i
$693$	7.53228e37	−	7.53228e37i	0.336533	−	0.336533i
$694$	2.43891e38	−	1.77042e38i	1.06867	−	0.775752i
$695$		−	5.96231e38i		−	2.56224i
$696$	4.07414e36	−	7.97131e36i	0.0171716	−	0.0335973i
$697$			1.26574e38i			0.523242i
$698$	2.01009e38	+	2.76907e38i	0.815018	+	1.12276i
$699$	5.08822e35	−	5.08822e35i	0.00202360	−	0.00202360i
$700$	5.25150e38	+	1.71115e38i	2.04861	+	0.667521i
$701$	2.30040e38	+	2.30040e38i	0.880260	+	0.880260i	0.993561	−	0.113301i	$-0.0361424\pi$
$701$	2.30040e38	+	2.30040e38i	0.880260	+	0.880260i	−0.113301	+	0.993561i	$0.536142\pi$
$702$	−3.52195e36	−	5.59325e35i	−0.0132200	−	0.00209949i
$703$	−7.33187e38			−2.69972
$704$	7.37061e37	+	1.18627e37i	0.266239	+	0.0428503i
$705$	2.94628e37			0.104405
$706$	2.20991e38	+	3.50958e37i	0.768264	+	0.122009i
$707$	5.43482e38	+	5.43482e38i	1.85363	+	1.85363i
$708$	1.51228e37	+	4.92763e36i	0.0506039	+	0.0164888i
$709$	3.74383e38	−	3.74383e38i	1.22911	−	1.22911i	0.264815	−	0.964299i	$-0.414689\pi$
$709$	3.74383e38	−	3.74383e38i	1.22911	−	1.22911i	0.964299	−	0.264815i	$-0.0853111\pi$
$710$	4.41662e38	+	6.08428e38i	1.42266	+	1.95984i
$711$		−	3.00550e38i		−	0.949899i
$712$	7.18745e37	−	1.40627e38i	0.222892	−	0.436103i
$713$			2.21982e38i			0.675474i
$714$	3.09338e37	−	2.24551e37i	0.0923650	−	0.0670484i
$715$	8.25915e36	−	8.25915e36i	0.0241994	−	0.0241994i
$716$	3.51288e37	+	6.90864e37i	0.101004	+	0.198640i
$717$	−1.99829e37	−	1.99829e37i	−0.0563834	−	0.0563834i
$718$	5.19307e37	−	3.26996e38i	0.143795	−	0.905446i
$719$	−6.01048e38			−1.63331			−0.816657	−	0.577124i	$-0.804175\pi$
$719$	−6.01048e38			−1.63331			−0.816657	+	0.577124i	$0.804175\pi$
$720$	−8.58120e37	−	5.47698e38i	−0.228854	−	1.46067i
$721$	−6.14629e38			−1.60875
$722$	1.19585e38	−	7.52998e38i	0.307201	−	1.93438i
$723$	4.20431e37	+	4.20431e37i	0.106005	+	0.106005i
$724$	2.90667e38	−	1.47798e38i	0.719326	−	0.365761i
$725$	1.69326e38	−	1.69326e38i	0.411302	−	0.411302i
$726$	2.47700e37	−	1.79807e37i	0.0590583	−	0.0428708i
$727$			9.65612e37i			0.225989i	0.993596	+	0.112995i	$0.0360443\pi$
$727$			9.65612e37i			0.225989i	−0.993596	+	0.112995i	$0.963956\pi$
$728$	6.27405e37	−	2.02990e37i	0.144137	−	0.0466339i
$729$			4.27032e38i			0.963028i
$730$	−4.02586e38	−	5.54597e38i	−0.891250	−	1.22778i
$731$	1.35717e38	−	1.35717e38i	0.294952	−	0.294952i
$732$	−4.82823e36	+	1.48178e37i	−0.0103012	+	0.0316143i
$733$	1.29335e38	+	1.29335e38i	0.270903	+	0.270903i	0.829464	−	0.558561i	$-0.188646\pi$
$733$	1.29335e38	+	1.29335e38i	0.270903	+	0.270903i	−0.558561	+	0.829464i	$0.688646\pi$
$734$	−3.14047e38	−	4.98742e37i	−0.645800	−	0.102560i
$735$	−1.24904e38			−0.252173
$736$	−6.13488e38	+	6.10939e38i	−1.21606	+	1.21101i
$737$	5.66240e37			0.110202
$738$	−3.29105e38	−	5.22656e37i	−0.628888	−	0.0998745i
$739$	1.04049e38	+	1.04049e38i	0.195226	+	0.195226i	0.797950	−	0.602724i	$-0.205918\pi$
$739$	1.04049e38	+	1.04049e38i	0.195226	+	0.195226i	−0.602724	+	0.797950i	$0.705918\pi$
$740$	−3.92656e38	+	1.20505e39i	−0.723409	+	2.22013i
$741$	−4.51371e36	+	4.51371e36i	−0.00816559	+	0.00816559i
$742$	3.26071e38	+	4.49192e38i	0.579242	+	0.797957i
$743$			1.56514e38i			0.273025i	0.990638	+	0.136513i	$0.0435895\pi$
$743$			1.56514e38i			0.273025i	−0.990638	+	0.136513i	$0.956411\pi$
$744$	5.56628e36	+	1.72044e37i	0.00953522	+	0.0294716i
$745$		−	3.02924e38i		−	0.509593i
$746$	2.77741e38	−	2.01614e38i	0.458844	−	0.333078i
$747$	−2.07844e38	+	2.07844e38i	−0.337217	+	0.337217i
$748$	1.23192e38	−	6.26405e37i	0.196296	−	0.0998122i
$749$	−4.36276e38	−	4.36276e38i	−0.682742	−	0.682742i
$750$	−2.54810e36	+	1.60448e37i	−0.00391642	+	0.0246609i
$751$	−8.62284e38			−1.30170			−0.650850	−	0.759206i	$-0.725587\pi$
$751$	−8.62284e38			−1.30170			−0.650850	+	0.759206i	$0.725587\pi$
$752$	4.85954e38	+	3.54304e38i	0.720534	+	0.525334i
$753$	−3.38511e37			−0.0492992
$754$	4.48417e36	−	2.82358e37i	0.00641459	−	0.0403913i
$755$	6.81993e38	+	6.81993e38i	0.958288	+	0.958288i
$756$	9.15082e37	+	1.79965e38i	0.126304	+	0.248396i
$757$	−2.30509e38	+	2.30509e38i	−0.312531	+	0.312531i	−0.845889	−	0.533358i	$-0.820930\pi$
$757$	−2.30509e38	+	2.30509e38i	−0.312531	+	0.312531i	0.533358	+	0.845889i	$0.320930\pi$
$758$	−6.71665e38	+	4.87566e38i	−0.894578	+	0.649380i
$759$		−	2.78381e37i		−	0.0364230i
$760$	−1.77276e39	−	9.06055e38i	−2.27859	−	1.16458i
$761$			6.34201e38i			0.800818i	0.916337	+	0.400409i	$0.131132\pi$
$761$			6.34201e38i			0.800818i	−0.916337	+	0.400409i	$0.868868\pi$
$762$	−4.70250e37	−	6.47811e37i	−0.0583360	−	0.0803630i
$763$	1.14102e39	−	1.14102e39i	1.39063	−	1.39063i
$764$	7.69874e38	+	2.50856e38i	0.921849	+	0.300376i
$765$	−7.25696e38	−	7.25696e38i	−0.853739	−	0.853739i
$766$	2.08706e38	+	3.31448e37i	0.241238	+	0.0383113i
$767$	5.07959e37			0.0576887
$768$	−3.22279e37	+	6.27333e37i	−0.0359630	+	0.0700039i
$769$	−1.41142e39			−1.54758			−0.773788	−	0.633445i	$-0.781640\pi$
$769$	−1.41142e39			−1.54758			−0.773788	+	0.633445i	$0.781640\pi$
$770$	−6.53092e38	−	1.03718e38i	−0.703638	−	0.111746i
$771$	−7.34744e37	−	7.34744e37i	−0.0777860	−	0.0777860i
$772$	−8.67330e38	−	2.82611e38i	−0.902300	−	0.294006i
$773$	3.47235e38	−	3.47235e38i	0.354977	−	0.354977i	−0.506981	−	0.861957i	$-0.669238\pi$
$773$	3.47235e38	−	3.47235e38i	0.354977	−	0.354977i	0.861957	+	0.506981i	$0.169238\pi$
$774$	2.96837e38	+	4.08920e38i	0.298206	+	0.410804i
$775$			4.83692e38i			0.477525i
$776$	−8.09016e38	−	4.13488e38i	−0.784917	−	0.401171i
$777$		−	2.30067e38i		−	0.219366i
$778$	1.66113e39	−	1.20582e39i	1.55661	−	1.12995i
$779$	−8.46186e38	+	8.46186e38i	−0.779310	+	0.779310i
$780$	5.00136e36	+	9.83596e36i	0.00452700	+	0.00890306i
$781$	−3.48912e38	−	3.48912e38i	−0.310403	−	0.310403i
$782$	−2.51393e38	+	1.58297e39i	−0.219818	+	1.38414i
$783$	8.75322e37			0.0752288
$784$	−2.06015e39	−	1.50204e39i	−1.74033	−	1.26886i
$785$	3.38077e39			2.80721
$786$	6.60133e36	−	4.15672e37i	0.00538800	−	0.0339270i
$787$	5.24570e38	+	5.24570e38i	0.420867	+	0.420867i	0.885502	−	0.464635i	$-0.153815\pi$
$787$	5.24570e38	+	5.24570e38i	0.420867	+	0.420867i	−0.464635	+	0.885502i	$0.653815\pi$
$788$	1.42159e39	−	7.22844e38i	1.12116	−	0.570086i
$789$	−1.17462e37	+	1.17462e37i	−0.00910660	+	0.00910660i
$790$	−1.50990e39	+	1.09604e39i	−1.15075	+	0.835338i
$791$			2.54989e39i			1.91047i
$792$	1.12002e38	+	3.46178e38i	0.0824967	+	0.254982i
$793$			4.97712e37i			0.0360405i
$794$	8.83502e38	+	1.21710e39i	0.628971	+	0.866463i
$795$	−6.56771e37	+	6.56771e37i	−0.0459682	+	0.0459682i
$796$	4.49897e38	−	1.38073e39i	0.309590	−	0.950126i
$797$	−1.48169e39	−	1.48169e39i	−1.00247	−	1.00247i	−0.999997	−	0.00247153i	$-0.999213\pi$
$797$	−1.48169e39	−	1.48169e39i	−1.00247	−	1.00247i	−0.00247153	−	0.999997i	$-0.500787\pi$
$798$	3.56921e38	+	5.66830e37i	0.237428	+	0.0377063i
$799$	1.11334e39			0.728190
$800$	−1.33677e39	+	1.33122e39i	−0.859692	+	0.856120i
$801$	7.69708e38			0.486729
$802$	1.89532e39	+	3.00998e38i	1.17849	+	0.187158i
$803$	3.18042e38	+	3.18042e38i	0.194457	+	0.194457i
$804$	−1.65728e37	+	5.08616e37i	−0.00996412	+	0.0305797i
$805$	5.42288e39	−	5.42288e39i	3.20616	−	3.20616i
$806$	3.39242e37	+	4.67336e37i	0.0197236	+	0.0271710i
$807$		−	9.39636e37i		−	0.0537238i
$808$	−2.49780e39	+	8.08137e38i	−1.40444	+	0.454393i
$809$			8.66013e38i			0.478872i	0.970912	+	0.239436i	$0.0769625\pi$
$809$			8.66013e38i			0.478872i	−0.970912	+	0.239436i	$0.923037\pi$
$810$	2.17282e39	−	1.57727e39i	1.18162	−	0.857744i
$811$	1.79675e39	−	1.79675e39i	0.960964	−	0.960964i	−0.0383020	−	0.999266i	$-0.512195\pi$
$811$	1.79675e39	−	1.79675e39i	0.960964	−	0.960964i	0.999266	+	0.0383020i	$0.0121949\pi$
$812$	−1.44280e39	+	7.33632e38i	−0.758928	+	0.385897i
$813$	1.14192e38	+	1.14192e38i	0.0590763	+	0.0590763i
$814$	1.30467e38	−	8.21523e38i	0.0663852	−	0.418013i
$815$	1.90302e38			0.0952390
$816$	2.02098e37	+	1.28989e38i	0.00994819	+	0.0634946i
$817$	1.81462e39			0.878595
$818$	1.93984e38	−	1.22148e39i	0.0923841	−	0.581722i
$819$	2.27254e38	+	2.27254e38i	0.106458	+	0.106458i
$820$	9.37606e38	+	1.84395e39i	0.432049	+	0.849693i
$821$	−9.83041e37	+	9.83041e37i	−0.0445594	+	0.0445594i	−0.729035	−	0.684476i	$-0.760031\pi$
$821$	−9.83041e37	+	9.83041e37i	−0.0445594	+	0.0445594i	0.684476	+	0.729035i	$0.260031\pi$
$822$	−2.64666e38	+	1.92123e38i	−0.118013	+	0.0856662i
$823$			4.74746e38i			0.208240i	0.994565	+	0.104120i	$0.0332025\pi$
$823$			4.74746e38i			0.208240i	−0.994565	+	0.104120i	$0.966797\pi$
$824$	9.55430e38	−	1.86936e39i	0.412270	−	0.806632i
$825$		−	6.06584e37i		−	0.0257491i
$826$	−1.68939e39	−	2.32729e39i	−0.705504	−	0.971894i
$827$	−2.62963e39	+	2.62963e39i	−1.08036	+	1.08036i	−0.0838872	+	0.996475i	$0.526734\pi$
$827$	−2.62963e39	+	2.62963e39i	−1.08036	+	1.08036i	−0.996475	+	0.0838872i	$0.973266\pi$
$828$	−4.01207e39	−	1.30729e39i	−1.62166	−	0.528401i
$829$	3.34566e39	+	3.34566e39i	1.33044	+	1.33044i	0.904973	+	0.425469i	$0.139891\pi$
$829$	3.34566e39	+	3.34566e39i	1.33044	+	1.33044i	0.425469	+	0.904973i	$0.360109\pi$
$830$	1.80212e39	+	2.86198e38i	0.705067	+	0.111973i
$831$	−1.66791e38			−0.0642035
$832$	−3.57906e37	+	2.22376e38i	−0.0135551	+	0.0842216i
$833$	−4.71987e39			−1.75883
$834$	−3.65105e38	−	5.79827e37i	−0.133868	−	0.0212597i
$835$	6.66324e38	+	6.66324e38i	0.240391	+	0.240391i
$836$	1.24235e39	+	4.04808e38i	0.441021	+	0.143702i
$837$	−1.25021e38	+	1.25021e38i	−0.0436706	+	0.0436706i
$838$	−1.13493e39	−	1.56347e39i	−0.390100	−	0.537397i
$839$			4.70090e38i			0.158999i	0.996835	+	0.0794995i	$0.0253322\pi$
$839$			4.70090e38i			0.158999i	−0.996835	+	0.0794995i	$0.974668\pi$
$840$	2.84311e38	−	5.56273e38i	0.0946288	−	0.185147i
$841$		−	2.35138e39i		−	0.770153i
$842$	5.98136e37	−	4.34191e37i	0.0192791	−	0.0139948i
$843$	−8.36417e37	+	8.36417e37i	−0.0265308	+	0.0265308i
$844$	2.09577e39	+	4.12166e39i	0.654214	+	1.28662i
$845$	−3.39935e39	−	3.39935e39i	−1.04431	−	1.04431i
$846$	−4.59724e38	+	2.89478e39i	−0.138994	+	0.875217i
$847$	−5.53417e39			−1.64675
$848$	−1.87306e39	+	2.93467e38i	−0.548540	+	0.0859440i
$849$	−2.11060e38			−0.0608349
$850$	−5.47779e38	+	3.44925e39i	−0.155400	+	0.978518i
$851$	6.82143e39	+	6.82143e39i	1.90470	+	1.90470i
$852$	4.15524e38	−	2.11285e38i	0.114199	−	0.0580675i
$853$	−3.59322e39	+	3.59322e39i	−0.972014	+	0.972014i	−0.999619	−	0.0276050i	$-0.991212\pi$
$853$	−3.59322e39	+	3.59322e39i	−0.972014	+	0.972014i	0.0276050	+	0.999619i	$0.491212\pi$
$854$	2.28034e39	−	1.65531e39i	0.607181	−	0.440757i
$855$		−	9.70299e39i		−	2.54310i
$856$	2.00509e39	−	6.48725e38i	0.517295	−	0.167365i
$857$			3.99267e39i			1.01396i	0.861957	+	0.506982i	$0.169239\pi$
$857$			3.99267e39i			1.01396i	−0.861957	+	0.506982i	$0.830761\pi$
$858$	−4.25433e36	−	5.86072e36i	−0.00106354	−	0.00146512i
$859$	1.87112e39	−	1.87112e39i	0.460461	−	0.460461i	−0.438345	−	0.898807i	$-0.644435\pi$
$859$	1.87112e39	−	1.87112e39i	0.460461	−	0.460461i	0.898807	+	0.438345i	$0.144435\pi$
$860$	9.71816e38	−	2.98249e39i	0.235426	−	0.722520i
$861$	−2.65525e38	−	2.65525e38i	−0.0633231	−	0.0633231i
$862$	3.75885e39	+	5.96948e38i	0.882485	+	0.140149i
$863$	−5.19935e39			−1.20172			−0.600860	−	0.799354i	$-0.705175\pi$
$863$	−5.19935e39			−1.20172			−0.600860	+	0.799354i	$0.705175\pi$
$864$	−6.89602e38	−	1.43563e36i	−0.156915	−	0.000326667i
$865$	−6.83090e39			−1.53024
$866$	2.19177e39	+	3.48077e38i	0.483396	+	0.0767687i
$867$	−8.53754e37	−	8.53754e37i	−0.0185385	−	0.0185385i
$868$	1.01290e39	−	3.10857e39i	0.216546	−	0.664576i
$869$	8.65872e38	−	8.65872e38i	0.182258	−	0.182258i
$870$	−1.59110e38	−	2.19188e38i	−0.0329752	−	0.0454262i
$871$			1.70838e38i			0.0348611i
$872$	1.69665e39	+	5.24402e39i	0.340894	+	1.05364i
$873$		−	4.42806e39i		−	0.876035i
$874$	−1.22633e40	+	8.90199e39i	−2.38892	+	1.73413i
$875$	2.07704e39	−	2.07704e39i	0.398416	−	0.398416i
$876$	−3.78761e38	+	1.92591e38i	−0.0715417	+	0.0363773i
$877$	−2.99599e39	−	2.99599e39i	−0.557245	−	0.557245i	0.371277	−	0.928522i	$-0.378920\pi$
$877$	−2.99599e39	−	2.99599e39i	−0.557245	−	0.557245i	−0.928522	+	0.371277i	$0.878920\pi$
$878$	−6.03394e38	+	3.79944e39i	−0.110516	+	0.695895i
$879$	−2.68738e37			−0.00484708
$880$	1.33067e39	−	1.82511e39i	0.236350	−	0.324171i
$881$	8.15347e38			0.142616			0.0713079	−	0.997454i	$-0.477283\pi$
$881$	8.15347e38			0.142616			0.0713079	+	0.997454i	$0.477283\pi$
$882$	1.94895e39	−	1.22721e40i	0.335719	−	2.11395i
$883$	−5.24483e39	−	5.24483e39i	−0.889737	−	0.889737i	0.104761	−	0.994497i	$-0.466592\pi$
$883$	−5.24483e39	−	5.24483e39i	−0.889737	−	0.889737i	−0.994497	+	0.104761i	$0.966592\pi$
$884$	1.88991e38	+	3.71680e38i	0.0315744	+	0.0620960i
$885$	3.40276e38	−	3.40276e38i	0.0559883	−	0.0559883i
$886$	5.96812e39	−	4.33230e39i	0.967125	−	0.702042i
$887$			7.01133e39i			1.11900i	0.828829	+	0.559502i	$0.189008\pi$
$887$			7.01133e39i			1.11900i	−0.828829	+	0.559502i	$0.810992\pi$
$888$	6.99735e38	+	3.57634e38i	0.109991	+	0.0562166i
$889$			1.44736e40i			2.24079i
$890$	−2.80696e39	−	3.86684e39i	−0.428027	−	0.589645i
$891$	−1.24604e39	+	1.24604e39i	−0.187147	+	0.187147i
$892$	3.44392e39	+	1.12217e39i	0.509480	+	0.166009i
$893$	7.44299e39	+	7.44299e39i	1.08456	+	1.08456i
$894$	−1.85497e38	−	2.94590e37i	−0.0266244	−	0.00422825i
$895$	2.34493e39			0.331526
$896$	1.13788e40	−	5.75609e39i	1.58467	−	0.801621i
$897$	8.39893e37			0.0115220
$898$	2.02642e39	+	3.21818e38i	0.273841	+	0.0434890i
$899$	−1.00231e39	−	1.00231e39i	−0.133427	−	0.133427i
$900$	−8.74218e39	−	2.84856e39i	−1.14643	−	0.373552i
$901$	−2.48180e39	+	2.48180e39i	−0.320613	+	0.320613i
$902$	−7.97561e38	−	1.09871e39i	−0.101502	−	0.139828i
$903$			5.69411e38i			0.0713906i
$904$	−7.75536e39	−	3.96376e39i	−0.957917	−	0.489591i
$905$		−	9.86582e39i		−	1.20054i
$906$	4.83944e38	−	3.51298e38i	0.0580182	−	0.0421158i
$907$	−6.84881e39	+	6.84881e39i	−0.808941	+	0.808941i	−0.984474	−	0.175533i	$-0.943835\pi$
$907$	−6.84881e39	+	6.84881e39i	−0.808941	+	0.808941i	0.175533	+	0.984474i	$0.443835\pi$
$908$	2.83936e39	+	5.58404e39i	0.330416	+	0.649815i
$909$	−9.04735e39	−	9.04735e39i	−1.03731	−	1.03731i
$910$	3.12925e38	−	1.97042e39i	0.0353494	−	0.222587i
$911$	−8.87316e39			−0.987598			−0.493799	−	0.869576i	$-0.664392\pi$
$911$	−8.87316e39			−0.987598			−0.493799	+	0.869576i	$0.664392\pi$
$912$	−7.27225e38	+	9.97441e38i	−0.0797514	+	0.109385i
$913$	−1.19758e39			−0.129404
$914$	−5.22248e38	+	3.28848e39i	−0.0556036	+	0.350124i
$915$	3.33412e38	+	3.33412e38i	0.0349781	+	0.0349781i
$916$	7.42644e39	−	3.77618e39i	0.767701	−	0.390358i
$917$	−5.38096e39	+	5.38096e39i	−0.548118	+	0.548118i
$918$	−1.03312e39	+	7.49949e38i	−0.103699	+	0.0752758i
$919$		−	5.12418e39i		−	0.506833i	−0.967357	−	0.253417i	$-0.918446\pi$
$919$		−	5.12418e39i		−	0.506833i	0.967357	−	0.253417i	$-0.0815543\pi$
$920$	8.06362e39	+	2.49231e40i	0.785949	+	2.42922i
$921$			1.33440e38i			0.0128168i
$922$	1.18434e40	+	1.63154e40i	1.12101	+	1.54429i
$923$	1.05269e39	−	1.05269e39i	0.0981923	−	0.0981923i
$924$	−1.27025e38	+	3.89837e38i	−0.0116766	+	0.0358353i
$925$	1.48637e40	+	1.48637e40i	1.34652	+	1.34652i
$926$	−1.04523e40	−	1.65994e39i	−0.933174	−	0.148199i
$927$	1.02317e40			0.900271
$928$	1.15096e37	−	5.52862e39i	0.000998071	−	0.479423i
$929$	1.46890e40			1.25540			0.627699	−	0.778457i	$-0.283997\pi$
$929$	1.46890e40			1.25540			0.627699	+	0.778457i	$0.283997\pi$
$930$	5.40318e38	+	8.58086e37i	0.0455124	+	0.00722788i
$931$	−3.15538e40	−	3.15538e40i	−2.61957	−	2.61957i
$932$	1.37679e38	−	4.22533e38i	0.0112655	−	0.0345737i
$933$	1.06182e39	−	1.06182e39i	0.0856343	−	0.0856343i
$934$	−4.64305e39	−	6.39620e39i	−0.369080	−	0.508440i
$935$		−	4.18139e39i		−	0.327615i
$936$	−1.04444e39	+	3.37918e38i	−0.0806604	+	0.0260968i
$937$		−	5.56778e38i		−	0.0423836i	−0.999775	−	0.0211918i	$-0.993254\pi$
$937$		−	5.56778e38i		−	0.0423836i	0.999775	−	0.0211918i	$-0.00674606\pi$
$938$	7.82721e39	−	5.68182e39i	0.587311	−	0.426333i
$939$	−2.67655e38	+	2.67655e38i	−0.0197966	+	0.0197966i
$940$	1.62192e40	−	8.24711e39i	1.18251	−	0.601279i
$941$	−8.75326e39	−	8.75326e39i	−0.629086	−	0.629086i	0.318752	−	0.947838i	$-0.396736\pi$
$941$	−8.75326e39	−	8.75326e39i	−0.629086	−	0.629086i	−0.947838	+	0.318752i	$0.896736\pi$
$942$	3.28776e38	−	2.07023e39i	0.0232923	−	0.146667i
$943$	1.57455e40			1.09964
$944$	9.70443e39	−	1.52047e39i	0.668111	−	0.104678i
$945$	6.10838e39			0.414569
$946$	−3.22904e38	+	2.03325e39i	−0.0216044	+	0.136038i
$947$	4.16979e39	+	4.16979e39i	0.275036	+	0.275036i	0.831124	−	0.556088i	$-0.187698\pi$
$947$	4.16979e39	+	4.16979e39i	0.275036	+	0.275036i	−0.556088	+	0.831124i	$0.687698\pi$
$948$	5.24331e38	+	1.03118e39i	0.0340952	+	0.0670536i
$949$	−9.59553e38	+	9.59553e38i	−0.0615141	+	0.0615141i
$950$	−2.67213e40	+	1.93972e40i	−1.68884	+	1.22594i
$951$			1.09082e39i			0.0679695i
$952$	1.07435e40	−	2.10204e40i	0.660005	−	1.29134i
$953$			1.42045e40i			0.860341i	0.902748	+	0.430170i	$0.141547\pi$
$953$			1.42045e40i			0.860341i	−0.902748	+	0.430170i	$0.858453\pi$
$954$	−5.42812e39	−	7.47771e39i	−0.324150	−	0.446545i
$955$	1.73228e40	−	1.73228e40i	1.01994	−	1.01994i
$956$	−1.65941e40	−	5.40705e39i	−0.963326	−	0.313891i
$957$	1.25696e38	+	1.25696e38i	0.00719468	+	0.00719468i
$958$	−2.19613e40	−	3.48771e39i	−1.23944	−	0.196836i
$959$	5.91324e40			3.29059
$960$	1.24992e39	+	1.72943e39i	0.0685834	+	0.0948946i
$961$	−1.56195e40			−0.845090
$962$	2.47859e39	+	3.93628e38i	0.132233	+	0.0210002i
$963$	7.26269e39	+	7.26269e39i	0.382070	+	0.382070i
$964$	3.49132e40	+	1.13762e40i	1.81113	+	0.590140i
$965$	−1.95156e40	+	1.95156e40i	−0.998307	+	0.998307i
$966$	−2.79335e39	−	3.84809e39i	−0.140908	−	0.194113i
$967$			1.62138e40i			0.806545i	0.915080	+	0.403272i	$0.132127\pi$
$967$			1.62138e40i			0.806545i	−0.915080	+	0.403272i	$0.867873\pi$
$968$	8.60277e39	−	1.68319e40i	0.422008	−	0.825686i
$969$			2.28517e39i			0.110547i
$970$	−2.22456e40	+	1.61482e40i	−1.06127	+	0.770382i
$971$	4.18113e39	−	4.18113e39i	0.196714	−	0.196714i	−0.601876	−	0.798590i	$-0.705580\pi$
$971$	4.18113e39	−	4.18113e39i	0.196714	−	0.196714i	0.798590	+	0.601876i	$0.205580\pi$
$972$	−2.28737e39	−	4.49848e39i	−0.106131	−	0.208724i
$973$	4.72636e40	+	4.72636e40i	2.16274	+	2.16274i
$974$	4.77761e39	−	3.00836e40i	0.215608	−	1.35764i
$975$	1.83010e38			0.00814542
$976$	1.48980e39	+	9.50868e39i	0.0653965	+	0.417395i
$977$	1.68679e40			0.730270			0.365135	−	0.930955i	$-0.381023\pi$
$977$	1.68679e40			0.730270			0.365135	+	0.930955i	$0.381023\pi$
$978$	1.85066e37	−	1.16532e38i	0.000790227	−	0.00497589i
$979$	2.21749e39	+	2.21749e39i	0.0933891	+	0.0933891i
$980$	−6.87598e40	+	3.49628e40i	−2.85616	+	1.45229i
$981$	−1.89945e40	+	1.89945e40i	−0.778209	+	0.778209i
$982$	1.56320e40	−	1.13474e40i	0.631699	−	0.458555i
$983$		−	4.74470e40i		−	1.89120i	−0.325338	−	0.945598i	$-0.605478\pi$
$983$		−	4.74470e40i		−	1.89120i	0.325338	−	0.945598i	$-0.394522\pi$
$984$	1.22033e39	−	3.94825e38i	0.0479782	−	0.0155228i
$985$		−	4.82514e40i		−	1.87120i
$986$	−6.01242e39	−	8.28264e39i	−0.229991	−	0.316833i
$987$	−2.33554e39	+	2.33554e39i	−0.0881262	+	0.0881262i
$988$	−1.22133e39	+	3.74825e39i	−0.0454585	+	0.139511i
$989$	−1.68829e40	−	1.68829e40i	−0.619866	−	0.619866i
$990$	1.08720e40	+	1.72660e39i	0.393763	+	0.0625341i
$991$	−8.24450e39			−0.294558			−0.147279	−	0.989095i	$-0.547051\pi$
$991$	−8.24450e39			−0.294558			−0.147279	+	0.989095i	$0.547051\pi$
$992$	7.88001e39	+	7.91289e39i	0.277728	+	0.278887i
$993$	2.89466e39			0.100643
$994$	−8.32413e40	−	1.32197e40i	−2.85511	−	0.453423i
$995$	−3.10675e40	−	3.10675e40i	−1.05122	−	1.05122i
$996$	3.50508e38	−	1.07571e39i	0.0117003	−	0.0359081i
$997$	−5.30882e39	+	5.30882e39i	−0.174829	+	0.174829i	−0.789097	−	0.614268i	$-0.789451\pi$
$997$	−5.30882e39	+	5.30882e39i	−0.174829	+	0.174829i	0.614268	+	0.789097i	$0.289451\pi$
$998$	9.25446e37	+	1.27488e38i	0.00300669	+	0.00414198i
$999$			7.68372e39i			0.246285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.28.e.a.13.4	yes	106
16.5	even	4	inner	16.28.e.a.5.4	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.28.e.a.5.4	✓	106	16.5	even	4	inner
16.28.e.a.13.4	yes	106	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11441.8 - 1817.09i) q^{2} +(153675. + 153675. i) q^{3} +(1.27614e8 + 4.15818e7i) q^{4} +(2.87142e9 - 2.87142e9i) q^{5} +(-1.47908e9 - 2.03757e9i) q^{6} +4.55239e11i q^{7} +(-1.38458e12 - 7.07660e11i) q^{8} -7.57837e12i q^{9} +(-3.80720e13 + 2.76367e13i) q^{10} +(2.18329e13 - 2.18329e13i) q^{11} +(1.32210e13 + 2.60012e13i) q^{12} +(6.58714e13 + 6.58714e13i) q^{13} +(8.27212e14 - 5.20877e15i) q^{14} +8.82531e14 q^{15} +(1.45563e16 + 1.06129e16i) q^{16} +3.33490e16 q^{17} +(-1.37706e16 + 8.67105e16i) q^{18} +(2.22948e17 + 2.22948e17i) q^{19} +(4.85833e17 - 2.47035e17i) q^{20} +(-6.99588e16 + 6.99588e16i) q^{21} +(-2.89482e17 + 2.10137e17i) q^{22} -4.14853e18i q^{23} +(-1.04026e17 - 3.21525e17i) q^{24} -9.03953e18i q^{25} +(-6.33996e17 - 8.73385e17i) q^{26} +(2.33647e18 - 2.33647e18i) q^{27} +(-1.89297e19 + 5.80949e19i) q^{28} +(1.87317e19 + 1.87317e19i) q^{29} +(-1.00978e19 - 1.60364e18i) q^{30} -5.35086e19 q^{31} +(-1.47266e20 - 1.47881e20i) q^{32} +6.71035e18 q^{33} +(-3.81574e20 - 6.05982e19i) q^{34} +(1.30718e21 + 1.30718e21i) q^{35} +(3.15122e20 - 9.67106e20i) q^{36} +(-1.64430e21 + 1.64430e21i) q^{37} +(-2.14582e21 - 2.95605e21i) q^{38} +2.02456e19i q^{39} +(-6.00771e21 + 1.94373e21i) q^{40} +3.79544e21i q^{41} +(9.27580e20 - 6.73336e20i) q^{42} +(4.06962e21 - 4.06962e21i) q^{43} +(3.69404e21 - 1.87834e21i) q^{44} +(-2.17607e22 - 2.17607e22i) q^{45} +(-7.53827e21 + 4.74668e22i) q^{46} +3.33844e22 q^{47} +(6.06009e20 + 3.86787e21i) q^{48} -1.41530e23 q^{49} +(-1.64257e22 + 1.03429e23i) q^{50} +(5.12490e21 + 5.12490e21i) q^{51} +(5.66706e21 + 1.11452e22i) q^{52} +(-7.44190e22 + 7.44190e22i) q^{53} +(-3.09791e22 + 2.24879e22i) q^{54} -1.25383e23i q^{55} +(3.22154e23 - 6.30316e23i) q^{56} +6.85230e22i q^{57} +(-1.80288e23 - 2.48363e23i) q^{58} +(3.85569e23 - 3.85569e23i) q^{59} +(1.12623e23 + 3.66973e22i) q^{60} +(3.77791e23 + 3.77791e23i) q^{61} +(6.12237e23 + 9.72301e22i) q^{62} +3.44997e24 q^{63} +(1.41629e24 + 1.95963e24i) q^{64} +3.78289e23 q^{65} +(-7.67788e22 - 1.21933e22i) q^{66} +(1.29676e24 + 1.29676e24i) q^{67} +(4.25580e24 + 1.38671e24i) q^{68} +(6.37525e23 - 6.37525e23i) q^{69} +(-1.25813e25 - 1.73318e25i) q^{70} -1.59810e25i q^{71} +(-5.36291e24 + 1.04929e25i) q^{72} +1.45671e25i q^{73} +(2.18017e25 - 1.58260e25i) q^{74} +(1.38915e24 - 1.38915e24i) q^{75} +(1.91807e25 + 3.77219e25i) q^{76} +(9.93919e24 + 9.93919e24i) q^{77} +(3.67881e22 - 2.31647e23i) q^{78} +3.96590e25 q^{79} +(7.22712e25 - 1.13233e25i) q^{80} -5.70715e25 q^{81} +(6.89668e24 - 4.34269e25i) q^{82} +(-2.74260e25 - 2.74260e25i) q^{83} +(-1.18367e25 + 6.01871e24i) q^{84} +(9.57589e25 - 9.57589e25i) q^{85} +(-5.39588e25 + 3.91691e25i) q^{86} +5.75719e24i q^{87} +(-4.56798e25 + 1.47792e25i) q^{88} +1.01566e26i q^{89} +(2.09441e26 + 2.88523e26i) q^{90} +(-2.99872e25 + 2.99872e25i) q^{91} +(1.72503e26 - 5.29411e26i) q^{92} +(-8.22293e24 - 8.22293e24i) q^{93} +(-3.81980e26 - 6.06627e25i) q^{94} +1.28035e27 q^{95} +(9.44244e22 - 4.53567e25i) q^{96} +5.84303e26 q^{97} +(1.61936e27 + 2.57173e26i) q^{98} +(-1.65458e26 - 1.65458e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12} - 2 q^{13} - 71\!\cdots\!60 q^{14} - 15\!\cdots\!04 q^{15}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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