LMFDB - Embedded newform 16.28.e.a.5.17

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			5.17
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5798.80 - 10029.5i) q^{2} +(1.92086e6 - 1.92086e6i) q^{3} +(-6.69655e7 + 1.16319e8i) q^{4} +(4.80331e8 + 4.80331e8i) q^{5} +(-3.04040e10 - 8.12664e9i) q^{6} +4.11420e11i q^{7} +(1.55494e12 - 2.87564e9i) q^{8} +2.46204e11i q^{9} +(2.03215e12 - 7.60284e12i) q^{10} +(2.97858e13 + 2.97858e13i) q^{11} +(9.48003e13 + 3.52063e14i) q^{12} +(3.90244e14 - 3.90244e14i) q^{13} +(4.12636e15 - 2.38575e15i) q^{14} +1.84530e15 q^{15} +(-9.04564e15 - 1.55787e16i) q^{16} -1.80150e16 q^{17} +(2.46931e15 - 1.42769e15i) q^{18} +(3.44699e16 - 3.44699e16i) q^{19} +(-8.80370e16 + 2.37058e16i) q^{20} +(7.90280e17 + 7.90280e17i) q^{21} +(1.26016e17 - 4.71460e17i) q^{22} +2.55457e18i q^{23} +(2.98130e18 - 2.99235e18i) q^{24} -6.98915e18i q^{25} +(-6.17692e18 - 1.65102e18i) q^{26} +(1.51206e19 + 1.51206e19i) q^{27} +(-4.78558e19 - 2.75510e19i) q^{28} +(-7.52283e19 + 7.52283e19i) q^{29} +(-1.07005e19 - 1.85075e19i) q^{30} -1.10062e20 q^{31} +(-1.03793e20 + 1.81061e20i) q^{32} +1.14429e20 q^{33} +(1.04466e20 + 1.80682e20i) q^{34} +(-1.97618e20 + 1.97618e20i) q^{35} +(-2.86381e19 - 1.64872e19i) q^{36} +(-1.76426e21 - 1.76426e21i) q^{37} +(-5.45601e20 - 1.45833e20i) q^{38} -1.49921e21i q^{39} +(7.48268e20 + 7.45505e20i) q^{40} -3.54498e21i q^{41} +(3.34347e21 - 1.25088e22i) q^{42} +(5.32060e20 + 5.32060e20i) q^{43} +(-5.45926e21 + 1.47002e21i) q^{44} +(-1.18259e20 + 1.18259e20i) q^{45} +(2.56212e22 - 1.48135e22i) q^{46} +1.45259e22 q^{47} +(-4.72998e22 - 1.25490e22i) q^{48} -1.03554e23 q^{49} +(-7.00979e22 + 4.05287e22i) q^{50} +(-3.46043e22 + 3.46043e22i) q^{51} +(1.92598e22 + 7.15256e22i) q^{52} +(-2.22737e23 - 2.22737e23i) q^{53} +(6.39713e22 - 2.39334e23i) q^{54} +2.86141e22i q^{55} +(1.18310e21 + 6.39735e23i) q^{56} -1.32424e23i q^{57} +(1.19074e24 + 3.18271e23i) q^{58} +(-2.61506e22 - 2.61506e22i) q^{59} +(-1.23571e23 + 2.14642e23i) q^{60} +(-5.21421e23 + 5.21421e23i) q^{61} +(6.38230e23 + 1.10388e24i) q^{62} -1.01293e23 q^{63} +(2.41784e24 - 8.94290e21i) q^{64} +3.74893e23 q^{65} +(-6.63549e23 - 1.14767e24i) q^{66} +(-1.61528e24 + 1.61528e24i) q^{67} +(1.20639e24 - 2.09548e24i) q^{68} +(4.90697e24 + 4.90697e24i) q^{69} +(3.12796e24 + 8.36069e23i) q^{70} +6.23292e23i q^{71} +(7.07993e20 + 3.82833e23i) q^{72} +1.16831e25i q^{73} +(-7.46412e24 + 2.79253e25i) q^{74} +(-1.34252e25 - 1.34252e25i) q^{75} +(1.70120e24 + 6.31778e24i) q^{76} +(-1.22545e25 + 1.22545e25i) q^{77} +(-1.50364e25 + 8.69361e24i) q^{78} -2.79686e25 q^{79} +(3.13802e24 - 1.18278e25i) q^{80} +5.62117e25 q^{81} +(-3.55545e25 + 2.05566e25i) q^{82} +(1.86732e25 - 1.86732e25i) q^{83} +(-1.44846e26 + 3.90028e25i) q^{84} +(-8.65317e24 - 8.65317e24i) q^{85} +(2.25100e24 - 8.42162e24i) q^{86} +2.89006e26i q^{87} +(4.64008e25 + 4.62295e25i) q^{88} +1.37565e26i q^{89} +(1.87185e24 + 5.00324e23i) q^{90} +(1.60554e26 + 1.60554e26i) q^{91} +(-2.97144e26 - 1.71068e26i) q^{92} +(-2.11414e26 + 2.11414e26i) q^{93} +(-8.42326e25 - 1.45688e26i) q^{94} +3.31139e25 q^{95} +(1.48421e26 + 5.47165e26i) q^{96} +8.72016e26 q^{97} +(6.00491e26 + 1.03860e27i) q^{98} +(-7.33338e24 + 7.33338e24i) 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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

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

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 $

$2$	−5798.80	−	10029.5i	−0.500534	−	0.865717i
$2$	−5798.80	−	10029.5i	−0.500534	−	0.865717i
$3$	1.92086e6	−	1.92086e6i	0.695598	−	0.695598i	−0.267860	−	0.963458i	$-0.586316\pi$
$3$	1.92086e6	−	1.92086e6i	0.695598	−	0.695598i	0.963458	+	0.267860i	$0.0863164\pi$
$4$	−6.69655e7	+	1.16319e8i	−0.498932	+	0.866641i
$5$	4.80331e8	+	4.80331e8i	0.175973	+	0.175973i	0.789598	−	0.613625i	$-0.210289\pi$
$5$	4.80331e8	+	4.80331e8i	0.175973	+	0.175973i	−0.613625	+	0.789598i	$0.710289\pi$
$6$	−3.04040e10	−	8.12664e9i	−0.950361	−	0.254021i
$7$			4.11420e11i			1.60495i	0.596684	+	0.802476i	$0.296485\pi$
$7$			4.11420e11i			1.60495i	−0.596684	+	0.802476i	$0.703515\pi$
$8$	1.55494e12	−	2.87564e9i	0.999998	−	0.00184935i
$9$			2.46204e11i			0.0322865i
$10$	2.03215e12	−	7.60284e12i	0.0642623	−	0.240423i
$11$	2.97858e13	+	2.97858e13i	0.260140	+	0.260140i	0.825111	−	0.564971i	$-0.191112\pi$
$11$	2.97858e13	+	2.97858e13i	0.260140	+	0.260140i	−0.564971	+	0.825111i	$0.691112\pi$
$12$	9.48003e13	+	3.52063e14i	0.255778	+	0.949890i
$13$	3.90244e14	−	3.90244e14i	0.357356	−	0.357356i	−0.505481	−	0.862838i	$-0.668685\pi$
$13$	3.90244e14	−	3.90244e14i	0.357356	−	0.357356i	0.862838	+	0.505481i	$0.168685\pi$
$14$	4.12636e15	−	2.38575e15i	1.38943	−	0.803333i
$15$	1.84530e15			0.244813
$16$	−9.04564e15	−	1.55787e16i	−0.502134	−	0.864790i
$17$	−1.80150e16			−0.441138			−0.220569	−	0.975371i	$-0.570791\pi$
$17$	−1.80150e16			−0.441138			−0.220569	+	0.975371i	$0.570791\pi$
$18$	2.46931e15	−	1.42769e15i	0.0279510	−	0.0161605i
$19$	3.44699e16	−	3.44699e16i	0.188047	−	0.188047i	−0.606804	−	0.794851i	$-0.707549\pi$
$19$	3.44699e16	−	3.44699e16i	0.188047	−	0.188047i	0.794851	+	0.606804i	$0.207549\pi$
$20$	−8.80370e16	+	2.37058e16i	−0.240304	+	0.0647068i
$21$	7.90280e17	+	7.90280e17i	1.11640	+	1.11640i
$22$	1.26016e17	−	4.71460e17i	0.0949990	−	0.355417i
$23$			2.55457e18i			1.05680i	0.848996	+	0.528399i	$0.177208\pi$
$23$			2.55457e18i			1.05680i	−0.848996	+	0.528399i	$0.822792\pi$
$24$	2.98130e18	−	2.99235e18i	0.694311	−	0.696883i
$25$		−	6.98915e18i		−	0.938067i
$26$	−6.17692e18	−	1.65102e18i	−0.488238	−	0.130500i
$27$	1.51206e19	+	1.51206e19i	0.718057	+	0.718057i
$28$	−4.78558e19	−	2.75510e19i	−1.39092	−	0.800762i
$29$	−7.52283e19	+	7.52283e19i	−1.36147	+	1.36147i	−0.489424	+	0.872046i	$0.662793\pi$
$29$	−7.52283e19	+	7.52283e19i	−1.36147	+	1.36147i	−0.872046	+	0.489424i	$0.837207\pi$
$30$	−1.07005e19	−	1.85075e19i	−0.122537	−	0.211938i
$31$	−1.10062e20			−0.809573			−0.404787	−	0.914411i	$-0.632654\pi$
$31$	−1.10062e20			−0.809573			−0.404787	+	0.914411i	$0.632654\pi$
$32$	−1.03793e20	+	1.81061e20i	−0.497328	+	0.867562i
$33$	1.14429e20			0.361906
$34$	1.04466e20	+	1.80682e20i	0.220804	+	0.381901i
$35$	−1.97618e20	+	1.97618e20i	−0.282428	+	0.282428i
$36$	−2.86381e19	−	1.64872e19i	−0.0279808	−	0.0161088i
$37$	−1.76426e21	−	1.76426e21i	−1.19080	−	1.19080i	−0.976843	−	0.213959i	$-0.931364\pi$
$37$	−1.76426e21	−	1.76426e21i	−1.19080	−	1.19080i	−0.213959	−	0.976843i	$-0.568636\pi$
$38$	−5.45601e20	−	1.45833e20i	−0.256919	−	0.0686716i
$39$		−	1.49921e21i		−	0.497153i
$40$	7.48268e20	+	7.45505e20i	0.176298	+	0.175647i
$41$		−	3.54498e21i		−	0.598456i	−0.954182	−	0.299228i	$-0.903271\pi$
$41$		−	3.54498e21i		−	0.598456i	0.954182	−	0.299228i	$-0.0967290\pi$
$42$	3.34347e21	−	1.25088e22i	0.407691	−	1.52529i
$43$	5.32060e20	+	5.32060e20i	0.0472211	+	0.0472211i	0.730323	−	0.683102i	$-0.239370\pi$
$43$	5.32060e20	+	5.32060e20i	0.0472211	+	0.0472211i	−0.683102	+	0.730323i	$0.739370\pi$
$44$	−5.45926e21	+	1.47002e21i	−0.355241	+	0.0956561i
$45$	−1.18259e20	+	1.18259e20i	−0.00568155	+	0.00568155i
$46$	2.56212e22	−	1.48135e22i	0.914888	−	0.528963i
$47$	1.45259e22			0.387990			0.193995	−	0.981003i	$-0.437855\pi$
$47$	1.45259e22			0.387990			0.193995	+	0.981003i	$0.437855\pi$
$48$	−4.72998e22	−	1.25490e22i	−0.950830	−	0.252263i
$49$	−1.03554e23			−1.57587
$50$	−7.00979e22	+	4.05287e22i	−0.812101	+	0.469534i
$51$	−3.46043e22	+	3.46043e22i	−0.306855	+	0.306855i
$52$	1.92598e22	+	7.15256e22i	0.131403	+	0.487996i
$53$	−2.22737e23	−	2.22737e23i	−1.17508	−	1.17508i	−0.980982	−	0.194098i	$-0.937822\pi$
$53$	−2.22737e23	−	2.22737e23i	−1.17508	−	1.17508i	−0.194098	−	0.980982i	$-0.562178\pi$
$54$	6.39713e22	−	2.39334e23i	0.262222	−	0.981045i
$55$			2.86141e22i			0.0915553i
$56$	1.18310e21	+	6.39735e23i	0.00296812	+	1.60495i
$57$		−	1.32424e23i		−	0.261610i
$58$	1.19074e24	+	3.18271e23i	1.86011	+	0.497186i
$59$	−2.61506e22	−	2.61506e22i	−0.0324324	−	0.0324324i	0.690705	−	0.723137i	$-0.257300\pi$
$59$	−2.61506e22	−	2.61506e22i	−0.0324324	−	0.0324324i	−0.723137	+	0.690705i	$0.757300\pi$
$60$	−1.23571e23	+	2.14642e23i	−0.122145	+	0.212165i
$61$	−5.21421e23	+	5.21421e23i	−0.412321	+	0.412321i	−0.882546	−	0.470225i	$-0.844173\pi$
$61$	−5.21421e23	+	5.21421e23i	−0.412321	+	0.412321i	0.470225	+	0.882546i	$0.344173\pi$
$62$	6.38230e23	+	1.10388e24i	0.405219	+	0.700861i
$63$	−1.01293e23			−0.0518183
$64$	2.41784e24	−	8.94290e21i	0.999993	−	0.00369870i
$65$	3.74893e23			0.125770
$66$	−6.63549e23	−	1.14767e24i	−0.181146	−	0.313309i
$67$	−1.61528e24	+	1.61528e24i	−0.359946	+	0.359946i	−0.863793	−	0.503847i	$-0.831918\pi$
$67$	−1.61528e24	+	1.61528e24i	−0.359946	+	0.359946i	0.503847	+	0.863793i	$0.331918\pi$
$68$	1.20639e24	−	2.09548e24i	0.220098	−	0.382308i
$69$	4.90697e24	+	4.90697e24i	0.735107	+	0.735107i
$70$	3.12796e24	+	8.36069e23i	0.385867	+	0.103138i
$71$			6.23292e23i			0.0634898i	0.999496	+	0.0317449i	$0.0101064\pi$
$71$			6.23292e23i			0.0634898i	−0.999496	+	0.0317449i	$0.989894\pi$
$72$	7.07993e20	+	3.82833e23i	5.97091e−5	+	0.0322864i
$73$			1.16831e25i			0.817900i	0.912557	+	0.408950i	$0.134105\pi$
$73$			1.16831e25i			0.817900i	−0.912557	+	0.408950i	$0.865895\pi$
$74$	−7.46412e24	+	2.79253e25i	−0.434861	+	1.62693i
$75$	−1.34252e25	−	1.34252e25i	−0.652518	−	0.652518i
$76$	1.70120e24	+	6.31778e24i	0.0691466	+	0.256792i
$77$	−1.22545e25	+	1.22545e25i	−0.417513	+	0.417513i
$78$	−1.50364e25	+	8.69361e24i	−0.430393	+	0.248842i
$79$	−2.79686e25			−0.674069			−0.337035	−	0.941492i	$-0.609424\pi$
$79$	−2.79686e25			−0.674069			−0.337035	+	0.941492i	$0.609424\pi$
$80$	3.13802e24	−	1.18278e25i	0.0638176	−	0.240541i
$81$	5.62117e25			0.966671
$82$	−3.55545e25	+	2.05566e25i	−0.518093	+	0.299547i
$83$	1.86732e25	−	1.86732e25i	0.231028	−	0.231028i	−0.582094	−	0.813122i	$-0.697766\pi$
$83$	1.86732e25	−	1.86732e25i	0.231028	−	0.231028i	0.813122	+	0.582094i	$0.197766\pi$
$84$	−1.44846e26	+	3.90028e25i	−1.52453	+	0.410511i
$85$	−8.65317e24	−	8.65317e24i	−0.0776283	−	0.0776283i
$86$	2.25100e24	−	8.42162e24i	0.0172444	−	0.0645159i
$87$			2.89006e26i			1.89407i
$88$	4.64008e25	+	4.62295e25i	0.260621	+	0.259659i
$89$			1.37565e26i			0.663349i	0.943394	+	0.331674i	$0.107614\pi$
$89$			1.37565e26i			0.663349i	−0.943394	+	0.331674i	$0.892386\pi$
$90$	1.87185e24	+	5.00324e23i	0.00776242	+	0.00207481i
$91$	1.60554e26	+	1.60554e26i	0.573540	+	0.573540i
$92$	−2.97144e26	−	1.71068e26i	−0.915865	−	0.527270i
$93$	−2.11414e26	+	2.11414e26i	−0.563138	+	0.563138i
$94$	−8.42326e25	−	1.45688e26i	−0.194202	−	0.335890i
$95$	3.31139e25			0.0661823
$96$	1.48421e26	+	5.47165e26i	0.257534	+	0.949415i
$97$	8.72016e26			1.31555			0.657773	−	0.753216i	$-0.271499\pi$
$97$	8.72016e26			1.31555			0.657773	+	0.753216i	$0.271499\pi$
$98$	6.00491e26	+	1.03860e27i	0.788778	+	1.36426i
$99$	−7.33338e24	+	7.33338e24i	−0.00839903	+	0.00839903i
$100$	8.12968e26	+	4.68032e26i	0.812968	+	0.468032i
$101$	−6.47267e26	−	6.47267e26i	−0.565907	−	0.565907i	0.365072	−	0.930979i	$-0.381044\pi$
$101$	−6.47267e26	−	6.47267e26i	−0.565907	−	0.565907i	−0.930979	+	0.365072i	$0.881044\pi$
$102$	5.47729e26	+	1.46402e26i	0.419241	+	0.112058i
$103$			2.56301e27i			1.71968i	0.510562	+	0.859841i	$0.329438\pi$
$103$			2.56301e27i			1.71968i	−0.510562	+	0.859841i	$0.670562\pi$
$104$	6.05685e26	−	6.07929e26i	0.356695	−	0.358016i
$105$			7.59192e26i			0.392913i
$106$	−9.42339e26	+	3.52555e27i	−0.429119	+	1.60545i
$107$	−3.01990e27	−	3.01990e27i	−1.21147	−	1.21147i	−0.970544	−	0.240925i	$-0.922549\pi$
$107$	−3.01990e27	−	3.01990e27i	−1.21147	−	1.21147i	−0.240925	−	0.970544i	$-0.577451\pi$
$108$	−2.77137e27	+	7.46249e26i	−0.980559	+	0.264036i
$109$	−7.85340e26	+	7.85340e26i	−0.245358	+	0.245358i	−0.819062	−	0.573704i	$-0.805506\pi$
$109$	−7.85340e26	+	7.85340e26i	−0.245358	+	0.245358i	0.573704	+	0.819062i	$0.305506\pi$
$110$	2.86986e26	−	1.65927e26i	0.0792610	−	0.0458265i
$111$	−6.77779e27			−1.65664
$112$	6.40938e27	−	3.72156e27i	1.38795	−	0.805901i
$113$	7.96150e27			1.52910			0.764550	−	0.644565i	$-0.222961\pi$
$113$	7.96150e27			1.52910			0.764550	+	0.644565i	$0.222961\pi$
$114$	−1.32815e27	+	7.67898e26i	−0.226480	+	0.130945i
$115$	−1.22704e27	+	1.22704e27i	−0.185968	+	0.185968i
$116$	−3.71275e27	−	1.37881e28i	−0.500625	−	1.85919i
$117$	9.60797e25	+	9.60797e25i	0.0115378	+	0.0115378i
$118$	−1.10636e26	+	4.13920e26i	−0.0118438	+	0.0443108i
$119$		−	7.41175e27i		−	0.708006i
$120$	2.86933e27	−	5.30640e24i	0.244812	−	0.000452745i
$121$		−	1.13356e28i		−	0.864654i
$122$	8.25323e27	+	2.20599e27i	0.563334	+	0.150573i
$123$	−6.80941e27	−	6.80941e27i	−0.416285	−	0.416285i
$124$	7.37039e27	−	1.28023e28i	0.403922	−	0.701610i
$125$	6.93585e27	−	6.93585e27i	0.341047	−	0.341047i
$126$	5.87380e26	+	1.01592e27i	0.0259368	+	0.0448600i
$127$	−1.22523e28			−0.486258			−0.243129	−	0.969994i	$-0.578174\pi$
$127$	−1.22523e28			−0.486258			−0.243129	+	0.969994i	$0.578174\pi$
$128$	−1.41102e28	−	2.41979e28i	−0.503732	−	0.863860i
$129$	2.04402e27			0.0656938
$130$	−2.17393e27	−	3.76000e27i	−0.0629521	−	0.108881i
$131$	−2.63310e26	+	2.63310e26i	−0.00687551	+	0.00687551i	−0.710536	−	0.703661i	$-0.751548\pi$
$131$	−2.63310e26	+	2.63310e26i	−0.00687551	+	0.00687551i	0.703661	+	0.710536i	$0.251548\pi$
$132$	−7.66277e27	+	1.33102e28i	−0.180567	+	0.313643i
$133$	1.41816e28	+	1.41816e28i	0.301806	+	0.301806i
$134$	2.55672e28	+	6.83382e27i	0.491777	+	0.131446i
$135$			1.45258e28i			0.252717i
$136$	−2.80123e28	+	5.18047e25i	−0.441137	+	0.000815819i
$137$			1.10648e27i			0.0157839i	0.999969	+	0.00789195i	$0.00251211\pi$
$137$			1.10648e27i			0.0157839i	−0.999969	+	0.00789195i	$0.997488\pi$
$138$	2.07601e28	−	7.76692e28i	0.268449	−	1.00434i
$139$	3.99650e28	+	3.99650e28i	0.468791	+	0.468791i	0.901523	−	0.432732i	$-0.142450\pi$
$139$	3.99650e28	+	3.99650e28i	0.468791	+	0.468791i	−0.432732	+	0.901523i	$0.642450\pi$
$140$	−9.75306e27	−	3.62202e28i	−0.103851	−	0.385676i
$141$	2.79021e28	−	2.79021e28i	0.269885	−	0.269885i
$142$	6.25133e27	−	3.61435e27i	0.0549642	−	0.0317788i
$143$	2.32475e28			0.185926
$144$	3.83553e27	−	2.22707e27i	0.0279210	−	0.0162121i
$145$	−7.22689e28			−0.479163
$146$	1.17176e29	−	6.77481e28i	0.708070	−	0.409386i
$147$	−1.98913e29	+	1.98913e29i	−1.09617	+	1.09617i
$148$	3.23361e29	−	8.70717e28i	1.62613	−	0.437869i
$149$	−3.60656e27	−	3.60656e27i	−0.0165607	−	0.0165607i	0.698778	−	0.715339i	$-0.253728\pi$
$149$	−3.60656e27	−	3.60656e27i	−0.0165607	−	0.0165607i	−0.715339	+	0.698778i	$0.753728\pi$
$150$	−5.67983e28	+	2.12498e29i	−0.238289	+	0.891503i
$151$		−	4.10002e29i		−	1.57252i	−0.617894	−	0.786261i	$-0.712014\pi$
$151$		−	4.10002e29i		−	1.57252i	0.617894	−	0.786261i	$-0.287986\pi$
$152$	5.34995e28	−	5.36978e28i	0.187699	−	0.188394i
$153$		−	4.43537e27i		−	0.0142428i
$154$	1.93968e29	+	5.18455e28i	0.570428	+	0.152469i
$155$	−5.28664e28	−	5.28664e28i	−0.142463	−	0.142463i
$156$	1.74386e29	+	1.00395e29i	0.430853	+	0.248045i
$157$	−4.46652e29	+	4.46652e29i	−1.01233	+	1.01233i	−0.0124115	+	0.999923i	$0.503951\pi$
$157$	−4.46652e29	+	4.46652e29i	−1.01233	+	1.01233i	−0.999923	+	0.0124115i	$0.996049\pi$
$158$	1.62184e29	+	2.80512e29i	0.337394	+	0.583553i
$159$	−8.55691e29			−1.63477
$160$	−1.36824e29	+	3.71143e28i	−0.240184	+	0.0651511i
$161$	−1.05100e30			−1.69611
$162$	−3.25960e29	−	5.63777e29i	−0.483852	−	0.836864i
$163$	−3.19372e29	+	3.19372e29i	−0.436279	+	0.436279i	−0.890758	−	0.454479i	$-0.849826\pi$
$163$	−3.19372e29	+	3.19372e29i	−0.436279	+	0.436279i	0.454479	+	0.890758i	$0.349826\pi$
$164$	4.12347e29	+	2.37391e29i	0.518646	+	0.298589i
$165$	5.49636e28	+	5.49636e28i	0.0636857	+	0.0636857i
$166$	−2.95565e29	−	7.90013e28i	−0.315642	−	0.0843674i
$167$			1.80078e30i			1.77333i	0.462413	+	0.886665i	$0.346984\pi$
$167$			1.80078e30i			1.77333i	−0.462413	+	0.886665i	$0.653016\pi$
$168$	1.23111e30	+	1.22657e30i	1.11846	+	1.11434i
$169$			8.87952e29i			0.744593i
$170$	−3.66093e28	+	1.36965e29i	−0.0283485	+	0.106060i
$171$	8.48662e27	+	8.48662e27i	0.00607138	+	0.00607138i
$172$	−9.75181e28	+	2.62588e28i	−0.0644839	+	0.0173636i
$173$	−1.53158e30	+	1.53158e30i	−0.936522	+	0.936522i	−0.998102	−	0.0615805i	$-0.980386\pi$
$173$	−1.53158e30	+	1.53158e30i	−0.936522	+	0.936522i	0.0615805	+	0.998102i	$0.480386\pi$
$174$	2.89859e30	−	1.67589e30i	1.63973	−	0.948047i
$175$	2.87548e30			1.50555
$176$	1.94591e29	−	7.33455e29i	0.0943415	−	0.355592i
$177$	−1.00463e29			−0.0451198
$178$	1.37971e30	−	7.97710e29i	0.574272	−	0.332028i
$179$	7.77018e29	−	7.77018e29i	0.299858	−	0.299858i	−0.541100	−	0.840958i	$-0.681992\pi$
$179$	7.77018e29	−	7.77018e29i	0.299858	−	0.299858i	0.840958	+	0.541100i	$0.181992\pi$
$180$	−5.83647e27	−	2.16751e28i	−0.00208916	−	0.00775857i
$181$	−2.70650e30	−	2.70650e30i	−0.898974	−	0.898974i	0.0963716	−	0.995345i	$-0.469276\pi$
$181$	−2.70650e30	−	2.70650e30i	−0.898974	−	0.898974i	−0.995345	+	0.0963716i	$0.969276\pi$
$182$	6.79263e29	−	2.54131e30i	0.209447	−	0.783599i
$183$			2.00315e30i			0.573620i
$184$	7.34602e27	+	3.97221e30i	0.00195439	+	1.05680i
$185$		−	1.69486e30i		−	0.419097i
$186$	3.34634e30	+	8.94438e29i	0.769387	+	0.205648i
$187$	−5.36592e29	−	5.36592e29i	−0.114758	−	0.114758i
$188$	−9.72731e29	+	1.68963e30i	−0.193581	+	0.336248i
$189$	−6.22093e30	+	6.22093e30i	−1.15245	+	1.15245i
$190$	−1.92021e29	−	3.32117e29i	−0.0331265	−	0.0572951i
$191$	−6.84092e30			−1.09942			−0.549710	−	0.835355i	$-0.685262\pi$
$191$	−6.84092e30			−1.09942			−0.549710	+	0.835355i	$0.685262\pi$
$192$	4.62714e30	−	4.66150e30i	0.693021	−	0.698166i
$193$	3.61438e30			0.504673			0.252337	−	0.967640i	$-0.418801\pi$
$193$	3.61438e30			0.504673			0.252337	+	0.967640i	$0.418801\pi$
$194$	−5.05665e30	−	8.74592e30i	−0.658475	−	1.13889i
$195$	7.20116e29	−	7.20116e29i	0.0874853	−	0.0874853i
$196$	6.93457e30	−	1.20453e31i	0.786253	−	1.36572i
$197$	−3.90430e30	−	3.90430e30i	−0.413285	−	0.413285i	0.469596	−	0.882881i	$-0.344399\pi$
$197$	−3.90430e30	−	3.90430e30i	−0.413285	−	0.413285i	−0.882881	+	0.469596i	$0.844399\pi$
$198$	1.16075e29	+	3.10256e28i	0.0114752	+	0.00306718i
$199$			7.25369e30i			0.669950i	0.942227	+	0.334975i	$0.108728\pi$
$199$			7.25369e30i			0.669950i	−0.942227	+	0.334975i	$0.891272\pi$
$200$	−2.00983e28	−	1.08677e31i	−0.00173482	−	0.938066i
$201$			6.20544e30i			0.500756i
$202$	−2.73841e30	+	1.02452e31i	−0.206660	+	0.773171i
$203$	−3.09504e31	−	3.09504e31i	−2.18509	−	2.18509i
$204$	−1.70783e30	−	6.34242e30i	−0.112833	−	0.419033i
$205$	1.70276e30	−	1.70276e30i	0.105312	−	0.105312i
$206$	2.57058e31	−	1.48624e31i	1.48876	−	0.860759i
$207$	−6.28945e29			−0.0341203
$208$	−9.60950e30	−	2.54948e30i	−0.488479	−	0.129597i
$209$	2.05343e30			0.0978373
$210$	7.61434e30	−	4.40240e30i	0.340151	−	0.196666i
$211$	−8.25043e30	+	8.25043e30i	−0.345672	+	0.345672i	−0.858494	−	0.512823i	$-0.828600\pi$
$211$	−8.25043e30	+	8.25043e30i	−0.345672	+	0.345672i	0.512823	+	0.858494i	$0.328600\pi$
$212$	4.08241e31	−	1.09927e31i	1.60466	−	0.432088i
$213$	1.19726e30	+	1.19726e30i	0.0441634	+	0.0441634i
$214$	−1.27764e31	+	4.78001e31i	−0.442408	+	1.65517i
$215$			5.11129e29i			0.0166193i
$216$	2.35552e31	+	2.34682e31i	0.719383	+	0.716727i
$217$		−	4.52819e31i		−	1.29933i
$218$	1.24306e31	+	3.32257e30i	0.335221	+	0.0896006i
$219$	2.24416e31	+	2.24416e31i	0.568930	+	0.568930i
$220$	−3.32835e30	−	1.91616e30i	−0.0793456	−	0.0456799i
$221$	−7.03026e30	+	7.03026e30i	−0.157643	+	0.157643i
$222$	3.93031e31	+	6.79781e31i	0.829204	+	1.43418i
$223$	−1.75149e30			−0.0347771			−0.0173885	−	0.999849i	$-0.505535\pi$
$223$	−1.75149e30			−0.0347771			−0.0173885	+	0.999849i	$0.505535\pi$
$224$	−7.44923e31	−	4.27025e31i	−1.39240	−	0.798188i
$225$	1.72075e30			0.0302869
$226$	−4.61671e31	−	7.98501e31i	−0.765366	−	1.32377i
$227$	−2.57645e31	+	2.57645e31i	−0.402414	+	0.402414i	−0.879083	−	0.476669i	$-0.841844\pi$
$227$	−2.57645e31	+	2.57645e31i	−0.402414	+	0.402414i	0.476669	+	0.879083i	$0.341844\pi$
$228$	1.54033e31	+	8.86781e30i	0.226722	+	0.130526i
$229$	7.35315e31	+	7.35315e31i	1.02022	+	1.02022i	0.999791	+	0.0204302i	$0.00650360\pi$
$229$	7.35315e31	+	7.35315e31i	1.02022	+	1.02022i	0.0204302	+	0.999791i	$0.493496\pi$
$230$	1.94220e31	+	5.19128e30i	0.254079	+	0.0679123i
$231$			4.70783e31i			0.580843i
$232$	−1.16759e32	+	1.17192e32i	−1.35895	+	1.36399i
$233$			2.95940e31i			0.325012i	0.986708	+	0.162506i	$0.0519576\pi$
$233$			2.95940e31i			0.325012i	−0.986708	+	0.162506i	$0.948042\pi$
$234$	4.06488e29	−	1.52078e30i	0.00421340	−	0.0157635i
$235$	6.97722e30	+	6.97722e30i	0.0682757	+	0.0682757i
$236$	4.79298e30	−	1.29061e30i	0.0442888	−	0.0119257i
$237$	−5.37236e31	+	5.37236e31i	−0.468881	+	0.468881i
$238$	−7.43364e31	+	4.29793e31i	−0.612932	+	0.354381i
$239$	2.50948e32			1.95529			0.977645	−	0.210262i	$-0.0674316\pi$
$239$	2.50948e32			1.95529			0.977645	+	0.210262i	$0.0674316\pi$
$240$	−1.66919e31	−	2.87472e31i	−0.122929	−	0.211711i
$241$	1.32138e32			0.920019			0.460010	−	0.887914i	$-0.347846\pi$
$241$	1.32138e32			0.920019			0.460010	+	0.887914i	$0.347846\pi$
$242$	−1.13691e32	+	6.57329e31i	−0.748546	+	0.432788i
$243$	−7.32907e30	+	7.32907e30i	−0.0456420	+	0.0456420i
$244$	−2.57337e31	−	9.55681e31i	−0.151614	−	0.563055i
$245$	−4.97403e31	−	4.97403e31i	−0.277311	−	0.277311i
$246$	−2.88088e31	+	1.07782e32i	−0.152020	+	0.568749i
$247$		−	2.69034e31i		−	0.134399i
$248$	−1.71141e32	+	3.16500e29i	−0.809572	+	0.00149719i
$249$		−	7.17371e31i		−	0.321405i
$250$	−1.09783e32	−	2.93437e31i	−0.465956	−	0.124545i
$251$	−2.83073e32	−	2.83073e32i	−1.13842	−	1.13842i	−0.988733	−	0.149690i	$-0.952172\pi$
$251$	−2.83073e32	−	2.83073e32i	−1.13842	−	1.13842i	−0.149690	−	0.988733i	$-0.547828\pi$
$252$	6.78316e30	−	1.17823e31i	0.0258538	−	0.0449079i
$253$	−7.60899e31	+	7.60899e31i	−0.274916	+	0.274916i
$254$	7.10486e31	+	1.22885e32i	0.243389	+	0.420962i
$255$	−3.32430e31			−0.107996
$256$	−1.60871e32	+	2.81838e32i	−0.495723	+	0.868481i
$257$	3.07303e32			0.898401			0.449200	−	0.893431i	$-0.351709\pi$
$257$	3.07303e32			0.898401			0.449200	+	0.893431i	$0.351709\pi$
$258$	−1.18529e31	−	2.05006e31i	−0.0328820	−	0.0568723i
$259$	7.25853e32	−	7.25853e32i	1.91118	−	1.91118i
$260$	−2.51049e31	+	4.36070e31i	−0.0627506	+	0.108997i
$261$	−1.85215e31	−	1.85215e31i	−0.0439571	−	0.0439571i
$262$	4.16776e30	+	1.11400e30i	0.00939367	+	0.00251082i
$263$			9.92943e31i			0.212580i	0.994335	+	0.106290i	$0.0338971\pi$
$263$			9.92943e31i			0.212580i	−0.994335	+	0.106290i	$0.966103\pi$
$264$	1.77930e32	−	3.29055e29i	0.361906	−	0.000669292i
$265$		−	2.13975e32i		−	0.413564i
$266$	5.99986e31	−	2.24471e32i	0.110215	−	0.412343i
$267$	2.64242e32	+	2.64242e32i	0.461424	+	0.461424i
$268$	−7.97190e31	−	2.96055e32i	−0.132356	−	0.491533i
$269$	−6.77329e32	+	6.77329e32i	−1.06941	+	1.06941i	−0.0720049	+	0.997404i	$0.522940\pi$
$269$	−6.77329e32	+	6.77329e32i	−1.06941	+	1.06941i	−0.997404	+	0.0720049i	$0.977060\pi$
$270$	1.45687e32	−	8.42322e31i	0.218781	−	0.126493i
$271$	9.89672e32			1.41386			0.706929	−	0.707285i	$-0.250080\pi$
$271$	9.89672e32			1.41386			0.706929	+	0.707285i	$0.250080\pi$
$272$	1.62957e32	+	2.80650e32i	0.221510	+	0.381492i
$273$	6.16805e32			0.797906
$274$	1.10974e31	−	6.41624e30i	0.0136644	−	0.00790038i
$275$	2.08177e32	−	2.08177e32i	0.244029	−	0.244029i
$276$	−8.99369e32	+	2.42174e32i	−1.00384	+	0.270306i
$277$	−8.93560e32	−	8.93560e32i	−0.949833	−	0.949833i	0.0489678	−	0.998800i	$-0.484407\pi$
$277$	−8.93560e32	−	8.93560e32i	−0.949833	−	0.949833i	−0.998800	+	0.0489678i	$0.984407\pi$
$278$	1.69081e32	−	6.32579e32i	0.171195	−	0.640487i
$279$		−	2.70978e31i		−	0.0261383i
$280$	−3.06716e32	+	3.07853e32i	−0.281905	+	0.282950i
$281$		−	4.24304e32i		−	0.371656i	−0.982582	−	0.185828i	$-0.940503\pi$
$281$		−	4.24304e32i		−	0.371656i	0.982582	−	0.185828i	$-0.0594968\pi$
$282$	−4.41644e32	−	1.18046e32i	−0.368731	−	0.0985575i
$283$	−8.55563e32	−	8.55563e32i	−0.680981	−	0.680981i	0.279240	−	0.960221i	$-0.409918\pi$
$283$	−8.55563e32	−	8.55563e32i	−0.680981	−	0.680981i	−0.960221	+	0.279240i	$0.909918\pi$
$284$	−7.25005e31	−	4.17391e31i	−0.0550229	−	0.0316771i
$285$	6.36071e31	−	6.36071e31i	0.0460363	−	0.0460363i
$286$	−1.34808e32	−	2.33161e32i	−0.0930621	−	0.160959i
$287$	1.45848e33			0.960493
$288$	−4.45780e31	−	2.55542e31i	−0.0280106	−	0.0160570i
$289$	−1.34317e33			−0.805397
$290$	4.19073e32	+	7.24824e32i	0.239837	+	0.414820i
$291$	1.67502e33	−	1.67502e33i	0.915091	−	0.915091i
$292$	−1.35896e33	−	7.82366e32i	−0.708826	−	0.408076i
$293$	7.75799e32	+	7.75799e32i	0.386399	+	0.386399i	0.873401	−	0.487002i	$-0.161909\pi$
$293$	7.75799e32	+	7.75799e32i	0.386399	+	0.386399i	−0.487002	+	0.873401i	$0.661909\pi$
$294$	3.14847e33	+	8.41549e32i	1.49765	+	0.400305i
$295$		−	2.51219e31i		−	0.0114144i
$296$	−2.74840e33	−	2.73825e33i	−1.19300	−	1.18860i
$297$			9.00759e32i			0.373591i
$298$	−1.52584e31	+	5.70858e31i	−0.00604768	+	0.0226260i
$299$	9.96907e32	+	9.96907e32i	0.377653	+	0.377653i
$300$	2.46062e33	−	6.62573e32i	0.891061	−	0.239937i
$301$	−2.18900e32	+	2.18900e32i	−0.0757876	+	0.0757876i
$302$	−4.11213e33	+	2.37752e33i	−1.36136	+	0.787100i
$303$	−2.48662e33			−0.787287
$304$	−8.48797e32	−	2.25193e32i	−0.257046	−	0.0681963i
$305$	−5.00909e32			−0.145115
$306$	−4.44847e31	+	2.57198e31i	−0.0123302	+	0.00712900i
$307$	−4.78646e33	+	4.78646e33i	−1.26954	+	1.26954i	−0.323215	+	0.946326i	$0.604764\pi$
$307$	−4.78646e33	+	4.78646e33i	−1.26954	+	1.26954i	−0.946326	+	0.323215i	$0.895236\pi$
$308$	−6.04797e32	−	2.24605e33i	−0.153523	−	0.570145i
$309$	4.92318e33	+	4.92318e33i	1.19621	+	1.19621i
$310$	−2.23664e32	+	8.36787e32i	−0.0520251	+	0.194640i
$311$		−	8.17994e33i		−	1.82173i	−0.412701	−	0.910867i	$-0.635415\pi$
$311$		−	8.17994e33i		−	1.82173i	0.412701	−	0.910867i	$-0.364585\pi$
$312$	−4.31118e30	−	2.33118e33i	−0.000919410	−	0.497152i
$313$			9.44940e33i			1.92999i	0.262261	+	0.964997i	$0.415532\pi$
$313$			9.44940e33i			1.92999i	−0.262261	+	0.964997i	$0.584468\pi$
$314$	7.06976e33	+	1.88967e33i	1.38310	+	0.369688i
$315$	−4.86543e31	−	4.86543e31i	−0.00911861	−	0.00911861i
$316$	1.87293e33	−	3.25326e33i	0.336315	−	0.584176i
$317$	−2.40108e33	+	2.40108e33i	−0.413150	+	0.413150i	−0.882834	−	0.469685i	$-0.844368\pi$
$317$	−2.40108e33	+	2.40108e33i	−0.413150	+	0.413150i	0.469685	+	0.882834i	$0.344368\pi$
$318$	4.96198e33	+	8.58218e33i	0.818256	+	1.41525i
$319$	−4.48147e33			−0.708347
$320$	1.16566e33	+	1.15707e33i	0.176622	+	0.175321i
$321$	−1.16016e34			−1.68539
$322$	6.09455e33	+	1.05411e34i	0.848961	+	1.46835i
$323$	−6.20976e32	+	6.20976e32i	−0.0829546	+	0.0829546i
$324$	−3.76424e33	+	6.53846e33i	−0.482303	+	0.837757i
$325$	−2.72747e33	−	2.72747e33i	−0.335224	−	0.335224i
$326$	5.05513e33	+	1.35118e33i	0.596066	+	0.159322i
$327$			3.01706e33i			0.341341i
$328$	−1.01941e31	−	5.51224e33i	−0.00110675	−	0.598455i
$329$			5.97623e33i			0.622706i
$330$	2.32536e32	−	8.69982e32i	0.0232569	−	0.0870106i
$331$	−4.34123e32	−	4.34123e32i	−0.0416807	−	0.0416807i	0.685959	−	0.727640i	$-0.259383\pi$
$331$	−4.34123e32	−	4.34123e32i	−0.0416807	−	0.0416807i	−0.727640	+	0.685959i	$0.759383\pi$
$332$	9.21580e32	+	3.42250e33i	0.0849510	+	0.315485i
$333$	4.34368e32	−	4.34368e32i	0.0384468	−	0.0384468i
$334$	1.80610e34	−	1.04424e34i	1.53520	−	0.887611i
$335$	−1.55174e33			−0.126681
$336$	5.16292e33	−	1.94601e34i	0.404870	−	1.52604i
$337$	−2.00111e34			−1.50753			−0.753767	−	0.657142i	$-0.771765\pi$
$337$	−2.00111e34			−1.50753			−0.753767	+	0.657142i	$0.771765\pi$
$338$	8.90575e33	−	5.14906e33i	0.644607	−	0.372694i
$339$	1.52929e34	−	1.52929e34i	1.06364	−	1.06364i
$340$	1.58599e33	−	4.27061e32i	0.106007	−	0.0285446i
$341$	−3.27830e33	−	3.27830e33i	−0.210603	−	0.210603i
$342$	3.59046e31	−	1.34329e32i	0.00221717	−	0.00829503i
$343$		−	1.55690e34i		−	0.924249i
$344$	8.28852e32	+	8.25792e32i	0.0473084	+	0.0471337i
$345$			4.71394e33i			0.258718i
$346$	2.42424e34	+	6.47972e33i	1.27952	+	0.342002i
$347$	1.11424e34	+	1.11424e34i	0.565628	+	0.565628i	0.930901	−	0.365273i	$-0.119024\pi$
$347$	1.11424e34	+	1.11424e34i	0.565628	+	0.565628i	−0.365273	+	0.930901i	$0.619024\pi$
$348$	−3.36167e34	−	1.93534e34i	−1.64148	−	0.945013i
$349$	−1.81949e34	+	1.81949e34i	−0.854683	+	0.854683i	−0.990706	−	0.136022i	$-0.956568\pi$
$349$	−1.81949e34	+	1.81949e34i	−0.854683	+	0.854683i	0.136022	+	0.990706i	$0.456568\pi$
$350$	−1.66743e34	−	2.88397e34i	−0.753580	−	1.30338i
$351$	1.18015e34			0.513204
$352$	−8.48461e33	+	2.30150e33i	−0.355063	+	0.0963129i
$353$	−7.57777e33			−0.305199			−0.152599	−	0.988288i	$-0.548764\pi$
$353$	−7.57777e33			−0.305199			−0.152599	+	0.988288i	$0.548764\pi$
$354$	5.82566e32	+	1.00760e33i	0.0225840	+	0.0390610i
$355$	−2.99386e32	+	2.99386e32i	−0.0111725	+	0.0111725i
$356$	−1.60013e34	−	9.21209e33i	−0.574885	−	0.330966i
$357$	−1.42369e34	−	1.42369e34i	−0.492487	−	0.492487i
$358$	−1.22989e34	−	3.28736e33i	−0.409681	−	0.109503i
$359$		−	3.28159e34i		−	1.05271i	−0.850264	−	0.526356i	$-0.823558\pi$
$359$		−	3.28159e34i		−	1.05271i	0.850264	−	0.526356i	$-0.176442\pi$
$360$	−1.83546e32	+	1.84226e32i	−0.00567103	+	0.00569204i
$361$			3.12243e34i			0.929277i
$362$	−1.14505e34	+	4.28394e34i	−0.328290	+	1.22822i
$363$	−2.17741e34	−	2.17741e34i	−0.601452	−	0.601452i
$364$	−2.94271e34	+	7.92386e33i	−0.783210	+	0.210896i
$365$	−5.61176e33	+	5.61176e33i	−0.143928	+	0.143928i
$366$	2.00907e34	−	1.16159e34i	0.496592	−	0.287116i
$367$	1.71102e34			0.407627			0.203814	−	0.979010i	$-0.434666\pi$
$367$	1.71102e34			0.407627			0.203814	+	0.979010i	$0.434666\pi$
$368$	3.97968e34	−	2.31077e34i	0.913908	−	0.530654i
$369$	8.72788e32			0.0193220
$370$	−1.69986e34	+	9.82814e33i	−0.362820	+	0.209772i
$371$	9.16384e34	−	9.16384e34i	1.88595	−	1.88595i
$372$	−1.04340e34	−	3.87489e34i	−0.207071	−	0.769006i
$373$	1.61906e34	+	1.61906e34i	0.309879	+	0.309879i	0.844863	−	0.534983i	$-0.179682\pi$
$373$	1.61906e34	+	1.61906e34i	0.309879	+	0.309879i	−0.534983	+	0.844863i	$0.679682\pi$
$374$	−2.27018e33	+	8.49336e33i	−0.0419076	+	0.156788i
$375$		−	2.66456e34i		−	0.474463i
$376$	2.25869e34	−	4.17711e31i	0.387989	−	0.000717530i
$377$			5.87148e34i			0.973059i
$378$	9.84670e34	+	2.63191e34i	1.57453	+	0.420854i
$379$	5.85197e34	+	5.85197e34i	0.902969	+	0.902969i	0.995692	−	0.0927227i	$-0.0295570\pi$
$379$	5.85197e34	+	5.85197e34i	0.902969	+	0.902969i	−0.0927227	+	0.995692i	$0.529557\pi$
$380$	−2.21749e33	+	3.85176e33i	−0.0330205	+	0.0573563i
$381$	−2.35349e34	+	2.35349e34i	−0.338240	+	0.338240i
$382$	3.96691e34	+	6.86112e34i	0.550297	+	0.951787i
$383$	6.29135e34			0.842481			0.421241	−	0.906949i	$-0.361595\pi$
$383$	6.29135e34			0.842481			0.421241	+	0.906949i	$0.361595\pi$
$384$	−7.35845e34	−	1.93770e34i	−0.951295	−	0.250504i
$385$	−1.17724e34			−0.146942
$386$	−2.09591e34	−	3.62506e34i	−0.252606	−	0.436904i
$387$	−1.30995e32	+	1.30995e32i	−0.00152460	+	0.00152460i
$388$	−5.83950e34	+	1.01432e35i	−0.656368	+	1.14011i
$389$	2.91144e34	+	2.91144e34i	0.316073	+	0.316073i	0.847257	−	0.531184i	$-0.178253\pi$
$389$	2.91144e34	+	2.91144e34i	0.316073	+	0.316073i	−0.531184	+	0.847257i	$0.678253\pi$
$390$	−1.13982e34	−	3.04662e33i	−0.119527	−	0.0319482i
$391$		−	4.60207e34i		−	0.466194i
$392$	−1.61021e35	+	2.97785e32i	−1.57587	+	0.00291434i
$393$			1.01156e33i			0.00956519i
$394$	−1.65181e34	+	6.17986e34i	−0.150925	+	0.564651i
$395$	−1.34342e34	−	1.34342e34i	−0.118618	−	0.118618i
$396$	−3.61925e32	−	1.34409e33i	−0.00308840	−	0.0114695i
$397$	−3.35154e34	+	3.35154e34i	−0.276422	+	0.276422i	−0.831679	−	0.555257i	$-0.812620\pi$
$397$	−3.35154e34	+	3.35154e34i	−0.276422	+	0.276422i	0.555257	+	0.831679i	$0.312620\pi$
$398$	7.27512e34	−	4.20627e34i	0.579987	−	0.335333i
$399$	5.44817e34			0.419872
$400$	−1.08882e35	+	6.32213e34i	−0.811231	+	0.471035i
$401$	−1.58137e35			−1.13916			−0.569579	−	0.821937i	$-0.692894\pi$
$401$	−1.58137e35			−1.13916			−0.569579	+	0.821937i	$0.692894\pi$
$402$	6.22377e34	−	3.59841e34i	0.433513	−	0.250645i
$403$	−4.29512e34	+	4.29512e34i	−0.289306	+	0.289306i
$404$	1.18634e35	−	3.19446e34i	0.772787	−	0.208089i
$405$	2.70002e34	+	2.70002e34i	0.170108	+	0.170108i
$406$	−1.30943e35	+	4.89894e35i	−0.797960	+	2.98539i
$407$		−	1.05100e35i		−	0.619551i
$408$	−5.37082e34	+	5.39072e34i	−0.306287	+	0.307422i
$409$		−	1.01544e35i		−	0.560262i	−0.959962	−	0.280131i	$-0.909622\pi$
$409$		−	1.01544e35i		−	0.560262i	0.959962	−	0.280131i	$-0.0903778\pi$
$410$	−2.69519e34	−	7.20394e33i	−0.143882	−	0.0384581i
$411$	2.12538e33	+	2.12538e33i	0.0109793	+	0.0109793i
$412$	−2.98126e35	−	1.71633e35i	−1.49035	−	0.858004i
$413$	1.07589e34	−	1.07589e34i	0.0520525	−	0.0520525i
$414$	3.64713e33	+	6.30803e33i	0.0170784	+	0.0295385i
$415$	1.79386e34			0.0813092
$416$	3.01535e34	+	1.11163e35i	0.132305	+	0.487752i
$417$	1.53534e35			0.652181
$418$	−1.19074e34	−	2.05949e34i	−0.0489708	−	0.0846994i
$419$	1.96727e35	−	1.96727e35i	0.783383	−	0.783383i	−0.197017	−	0.980400i	$-0.563125\pi$
$419$	1.96727e35	−	1.96727e35i	0.783383	−	0.783383i	0.980400	+	0.197017i	$0.0631253\pi$
$420$	−8.83082e34	−	5.08397e34i	−0.340514	−	0.196037i
$421$	1.76535e35	+	1.76535e35i	0.659209	+	0.659209i	0.955193	−	0.295984i	$-0.0956474\pi$
$421$	1.76535e35	+	1.76535e35i	0.659209	+	0.659209i	−0.295984	+	0.955193i	$0.595647\pi$
$422$	1.30591e35	+	3.49054e34i	0.472274	+	0.126233i
$423$			3.57632e33i			0.0125268i
$424$	−3.46983e35	−	3.45702e35i	−1.17725	−	1.17290i
$425$			1.25910e35i			0.413817i
$426$	5.06527e33	−	1.89506e34i	0.0161277	−	0.0603382i
$427$	−2.14523e35	−	2.14523e35i	−0.661756	−	0.661756i
$428$	5.53501e35	−	1.49042e35i	1.65435	−	0.445468i
$429$	4.46551e34	−	4.46551e34i	0.129330	−	0.129330i
$430$	5.12639e33	−	2.96394e33i	0.0143876	−	0.00831850i
$431$	3.08951e35			0.840322			0.420161	−	0.907450i	$-0.361974\pi$
$431$	3.08951e35			0.840322			0.420161	+	0.907450i	$0.361974\pi$
$432$	9.87834e34	−	3.72335e35i	0.260407	−	0.981529i
$433$	6.37253e35			1.62827			0.814133	−	0.580678i	$-0.197213\pi$
$433$	6.37253e35			1.62827			0.814133	+	0.580678i	$0.197213\pi$
$434$	−4.54157e35	+	2.62581e35i	−1.12485	+	0.650357i
$435$	−1.38818e35	+	1.38818e35i	−0.333305	+	0.333305i
$436$	−3.87590e34	−	1.43940e35i	−0.0902204	−	0.335054i
$437$	8.80558e34	+	8.80558e34i	0.198728	+	0.198728i
$438$	9.49445e34	−	3.55213e35i	0.207764	−	0.777300i
$439$			5.41749e35i			1.14955i	0.818312	+	0.574774i	$0.194910\pi$
$439$			5.41749e35i			1.14955i	−0.818312	+	0.574774i	$0.805090\pi$
$440$	8.22838e31	+	4.44932e34i	0.000169318	+	0.0915551i
$441$		−	2.54955e34i		−	0.0508794i
$442$	1.11277e35	+	2.97432e34i	0.215380	+	0.0575687i
$443$	−3.88681e35	−	3.88681e35i	−0.729697	−	0.729697i	0.240862	−	0.970559i	$-0.422570\pi$
$443$	−3.88681e35	−	3.88681e35i	−0.729697	−	0.729697i	−0.970559	+	0.240862i	$0.922570\pi$
$444$	4.53878e35	−	7.88383e35i	0.826550	−	1.43571i
$445$	−6.60766e34	+	6.60766e34i	−0.116731	+	0.116731i
$446$	1.01566e34	+	1.75667e34i	0.0174071	+	0.0301071i
$447$	−1.38554e34			−0.0230392
$448$	3.67929e33	+	9.94747e35i	0.00593623	+	1.60494i
$449$	−3.77145e35			−0.590450			−0.295225	−	0.955428i	$-0.595395\pi$
$449$	−3.77145e35			−0.590450			−0.295225	+	0.955428i	$0.595395\pi$
$450$	−9.97832e33	−	1.72584e34i	−0.0151596	−	0.0262199i
$451$	1.05590e35	−	1.05590e35i	0.155683	−	0.155683i
$452$	−5.33146e35	+	9.26070e35i	−0.762916	+	1.32518i
$453$	−7.87555e35	−	7.87555e35i	−1.09384	−	1.09384i
$454$	4.07810e35	+	1.09003e35i	0.549799	+	0.146955i
$455$			1.54239e35i			0.201855i
$456$	−3.80802e32	−	2.05911e35i	−0.000483809	−	0.261610i
$457$		−	9.14618e35i		−	1.12816i	−0.825720	−	0.564080i	$-0.809231\pi$
$457$		−	9.14618e35i		−	1.12816i	0.825720	−	0.564080i	$-0.190769\pi$
$458$	3.11092e35	−	1.16388e36i	0.372568	−	1.39388i
$459$	−2.72398e35	−	2.72398e35i	−0.316762	−	0.316762i
$460$	−6.05582e34	−	2.24897e35i	−0.0683821	−	0.253953i
$461$	−1.11560e36	+	1.11560e36i	−1.22333	+	1.22333i	−0.256894	+	0.966440i	$0.582699\pi$
$461$	−1.11560e36	+	1.11560e36i	−1.22333	+	1.22333i	−0.966440	+	0.256894i	$0.917301\pi$
$462$	4.72173e35	−	2.72997e35i	0.502845	−	0.290731i
$463$	−6.55011e35			−0.677494			−0.338747	−	0.940878i	$-0.610003\pi$
$463$	−6.55011e35			−0.677494			−0.338747	+	0.940878i	$0.610003\pi$
$464$	1.85244e36	+	4.91468e35i	1.86103	+	0.493745i
$465$	−2.03098e35			−0.198194
$466$	2.96814e35	−	1.71610e35i	0.281368	−	0.162679i
$467$	8.69703e35	−	8.69703e35i	0.800927	−	0.800927i	−0.182313	−	0.983240i	$-0.558359\pi$
$467$	8.69703e35	−	8.69703e35i	0.800927	−	0.800927i	0.983240	+	0.182313i	$0.0583585\pi$
$468$	−1.76099e34	+	4.74183e33i	−0.0157557	+	0.00424255i
$469$	−6.64559e35	−	6.64559e35i	−0.577697	−	0.577697i
$470$	2.95188e34	−	1.10438e35i	0.0249331	−	0.0932817i
$471$			1.71591e36i			1.40836i
$472$	−4.07378e34	−	4.05874e34i	−0.0324923	−	0.0323724i
$473$			3.16956e34i			0.0245682i
$474$	8.50356e35	+	2.27290e35i	0.640609	+	0.171228i
$475$	−2.40915e35	−	2.40915e35i	−0.176401	−	0.176401i
$476$	8.62124e35	+	4.96331e35i	0.613587	+	0.353247i
$477$	5.48386e34	−	5.48386e34i	0.0379392	−	0.0379392i
$478$	−1.45520e36	−	2.51689e36i	−0.978689	−	1.69273i
$479$	−5.54869e35			−0.362795			−0.181398	−	0.983410i	$-0.558062\pi$
$479$	−5.54869e35			−0.362795			−0.181398	+	0.983410i	$0.558062\pi$
$480$	−1.91529e35	+	3.34111e35i	−0.121752	+	0.212390i
$481$	−1.37698e36			−0.851081
$482$	−7.66241e35	−	1.32528e36i	−0.460501	−	0.796477i
$483$	−2.01883e36	+	2.01883e36i	−1.17981	+	1.17981i
$484$	1.31854e36	+	7.59095e35i	0.749345	+	0.431403i
$485$	4.18856e35	+	4.18856e35i	0.231500	+	0.231500i
$486$	1.16007e35	+	3.10074e34i	0.0623584	+	0.0166677i
$487$			1.84121e36i			0.962636i	0.876546	+	0.481318i	$0.159842\pi$
$487$			1.84121e36i			0.962636i	−0.876546	+	0.481318i	$0.840158\pi$
$488$	−8.09279e35	+	8.12278e35i	−0.411558	+	0.413083i
$489$			1.22694e36i			0.606949i
$490$	−2.10438e35	+	7.87307e35i	−0.101269	+	0.378876i
$491$	1.12746e36	+	1.12746e36i	0.527836	+	0.527836i	0.919927	−	0.392090i	$-0.128248\pi$
$491$	1.12746e36	+	1.12746e36i	0.527836	+	0.527836i	−0.392090	+	0.919927i	$0.628248\pi$
$492$	1.24806e36	−	3.36065e35i	0.568467	−	0.153072i
$493$	1.35524e36	−	1.35524e36i	0.600596	−	0.600596i
$494$	−2.69828e35	+	1.56007e35i	−0.116352	+	0.0672715i
$495$	−7.04490e33			−0.00295600
$496$	9.95585e35	+	1.71463e36i	0.406514	+	0.700111i
$497$	−2.56435e35			−0.101898
$498$	−7.19490e35	+	4.15989e35i	−0.278246	+	0.160874i
$499$	−2.19578e36	+	2.19578e36i	−0.826479	+	0.826479i	−0.987028	−	0.160549i	$-0.948674\pi$
$499$	−2.19578e36	+	2.19578e36i	−0.826479	+	0.826479i	0.160549	+	0.987028i	$0.448674\pi$
$500$	3.42306e35	+	1.27123e36i	0.125406	+	0.465725i
$501$	3.45905e36	+	3.45905e36i	1.23352	+	1.23352i
$502$	−1.19761e36	+	4.48058e36i	−0.415733	+	1.55537i
$503$		−	4.88288e36i		−	1.65009i	−0.565064	−	0.825047i	$-0.691149\pi$
$503$		−	4.88288e36i		−	1.65009i	0.565064	−	0.825047i	$-0.308851\pi$
$504$	−1.57505e35	+	2.91283e32i	−0.0518182	+	9.58303e-5i
$505$		−	6.21805e35i		−	0.199168i
$506$	1.20438e36	+	3.21916e35i	0.375604	+	0.100395i
$507$	1.70563e36	+	1.70563e36i	0.517938	+	0.517938i
$508$	8.20481e35	−	1.42517e36i	0.242610	−	0.421412i
$509$	3.60237e36	−	3.60237e36i	1.03729	−	1.03729i	0.0380079	−	0.999277i	$-0.487899\pi$
$509$	3.60237e36	−	3.60237e36i	1.03729	−	1.03729i	0.999277	−	0.0380079i	$-0.0121012\pi$
$510$	1.92770e35	+	3.33412e35i	0.0540557	+	0.0934941i
$511$	−4.80667e36			−1.31269
$512$	3.75957e36	−	2.08585e34i	0.999985	−	0.00554803i
$513$	1.04241e36			0.270057
$514$	−1.78199e36	−	3.08211e36i	−0.449680	−	0.777761i
$515$	−1.23109e36	+	1.23109e36i	−0.302617	+	0.302617i
$516$	−1.36879e35	+	2.37758e35i	−0.0327767	+	0.0569330i
$517$	4.32664e35	+	4.32664e35i	0.100932	+	0.100932i
$518$	−1.14890e37	−	3.07089e36i	−2.61115	−	0.697931i
$519$			5.88390e36i			1.30289i
$520$	5.82936e35	−	1.07806e33i	0.125770	−	0.000232593i
$521$		−	4.71541e36i		−	0.991312i	−0.868519	−	0.495656i	$-0.834928\pi$
$521$		−	4.71541e36i		−	0.991312i	0.868519	−	0.495656i	$-0.165072\pi$
$522$	−7.83595e34	+	2.93164e35i	−0.0160524	+	0.0600564i
$523$	1.91592e36	+	1.91592e36i	0.382477	+	0.382477i	0.871994	−	0.489517i	$-0.162827\pi$
$523$	1.91592e36	+	1.91592e36i	0.382477	+	0.382477i	−0.489517	+	0.871994i	$0.662827\pi$
$524$	−1.29952e34	−	4.82606e34i	−0.00252819	−	0.00938901i
$525$	5.52338e36	−	5.52338e36i	1.04726	−	1.04726i
$526$	9.95876e35	−	5.75788e35i	0.184034	−	0.106403i
$527$	1.98278e36			0.357134
$528$	−1.03508e36	−	1.78265e36i	−0.181726	−	0.312973i
$529$	−6.82620e35			−0.116823
$530$	−2.14607e36	+	1.24080e36i	−0.358029	+	0.207003i
$531$	6.43837e33	−	6.43837e33i	0.00104713	−	0.00104713i
$532$	−2.59926e36	+	6.99907e35i	−0.412139	+	0.110977i
$533$	−1.38341e36	−	1.38341e36i	−0.213862	−	0.213862i
$534$	1.11794e36	−	4.18252e36i	0.168504	−	0.630421i
$535$		−	2.90111e36i		−	0.426371i
$536$	−2.50702e36	+	2.51631e36i	−0.359280	+	0.360611i
$537$		−	2.98508e36i		−	0.417161i
$538$	1.07210e37	+	2.86560e36i	1.46108	+	0.390530i
$539$	−3.08445e36	−	3.08445e36i	−0.409948	−	0.409948i
$540$	−1.68962e36	−	9.72727e35i	−0.219015	−	0.126088i
$541$	8.14549e36	−	8.14549e36i	1.02980	−	1.02980i	0.0302608	−	0.999542i	$-0.490366\pi$
$541$	8.14549e36	−	8.14549e36i	1.02980	−	1.02980i	0.999542	−	0.0302608i	$-0.00963378\pi$
$542$	−5.73891e36	−	9.92595e36i	−0.707684	−	1.22400i
$543$	−1.03976e37			−1.25065
$544$	1.86983e36	−	3.26182e36i	0.219390	−	0.382715i
$545$	−7.54447e35			−0.0863527
$546$	−3.57673e36	−	6.18627e36i	−0.399379	−	0.690761i
$547$	5.22456e36	−	5.22456e36i	0.569142	−	0.569142i	−0.362746	−	0.931888i	$-0.618161\pi$
$547$	5.22456e36	−	5.22456e36i	0.569142	−	0.569142i	0.931888	+	0.362746i	$0.118161\pi$
$548$	−1.28704e35	−	7.40957e34i	−0.0136790	−	0.00787509i
$549$	−1.28376e35	−	1.28376e35i	−0.0133124	−	0.0133124i
$550$	−3.29510e36	−	8.80743e35i	−0.333405	−	0.0891154i
$551$			5.18622e36i			0.512041i
$552$	7.64416e36	+	7.61594e36i	0.736465	+	0.733746i
$553$		−	1.15068e37i		−	1.08185i
$554$	−3.78042e36	+	1.41436e37i	−0.346863	+	1.29771i
$555$	−3.25558e36	−	3.25558e36i	−0.291523	−	0.291523i
$556$	−7.32494e36	+	1.97239e36i	−0.640169	+	0.172379i
$557$	1.24729e37	−	1.24729e37i	1.06395	−	1.06395i	0.0661450	−	0.997810i	$-0.478930\pi$
$557$	1.24729e37	−	1.24729e37i	1.06395	−	1.06395i	0.997810	−	0.0661450i	$-0.0210700\pi$
$558$	−2.71778e35	+	1.57135e35i	−0.0226284	+	0.0130831i
$559$	4.15266e35			0.0337495
$560$	4.86620e36	+	1.29104e36i	0.386057	+	0.102424i
$561$	−2.06143e36			−0.159651
$562$	−4.25557e36	+	2.46045e36i	−0.321749	+	0.186027i
$563$	6.46499e36	−	6.46499e36i	0.477204	−	0.477204i	−0.427032	−	0.904236i	$-0.640441\pi$
$563$	6.46499e36	−	6.46499e36i	0.477204	−	0.477204i	0.904236	+	0.427032i	$0.140441\pi$
$564$	1.37706e36	+	5.11401e36i	0.0992393	+	0.368548i
$565$	3.82415e36	+	3.82415e36i	0.269080	+	0.269080i
$566$	−3.61966e36	+	1.35421e37i	−0.248683	+	0.930391i
$567$			2.31266e37i			1.55146i
$568$	1.79236e33	+	9.69183e35i	0.000117415	+	0.0634897i
$569$			2.49481e37i			1.59596i	0.602686	+	0.797978i	$0.294097\pi$
$569$			2.49481e37i			1.59596i	−0.602686	+	0.797978i	$0.705903\pi$
$570$	−1.00680e36	−	2.69105e35i	−0.0628971	−	0.0168117i
$571$	−2.51848e35	−	2.51848e35i	−0.0153656	−	0.0153656i	0.699382	−	0.714748i	$-0.253459\pi$
$571$	−2.51848e35	−	2.51848e35i	−0.0153656	−	0.0153656i	−0.714748	+	0.699382i	$0.753459\pi$
$572$	−1.55678e36	+	2.70411e36i	−0.0927642	+	0.161131i
$573$	−1.31404e37	+	1.31404e37i	−0.764755	+	0.764755i
$574$	−8.45742e36	−	1.46279e37i	−0.480759	−	0.831515i
$575$	1.78543e37			0.991348
$576$	2.20178e33	+	5.95280e35i	0.000119418	+	0.0322863i
$577$	2.93920e37			1.55724			0.778619	−	0.627497i	$-0.215921\pi$
$577$	2.93920e37			1.55724			0.778619	+	0.627497i	$0.215921\pi$
$578$	7.78878e36	+	1.34714e37i	0.403129	+	0.697246i
$579$	6.94271e36	−	6.94271e36i	0.351050	−	0.351050i
$580$	4.83952e36	−	8.40622e36i	0.239070	−	0.415263i
$581$	7.68253e36	+	7.68253e36i	0.370789	+	0.370789i
$582$	−2.65128e37	−	7.08656e36i	−1.25024	−	0.334176i
$583$		−	1.32688e37i		−	0.611372i
$584$	3.35964e34	+	1.81666e37i	0.00151258	+	0.817898i
$585$			9.23000e34i			0.00406067i
$586$	3.28220e36	−	1.22796e37i	0.141107	−	0.527918i
$587$	−1.47989e35	−	1.47989e35i	−0.00621747	−	0.00621747i	0.703991	−	0.710209i	$-0.251399\pi$
$587$	−1.47989e35	−	1.47989e35i	−0.00621747	−	0.00621747i	−0.710209	+	0.703991i	$0.751399\pi$
$588$	−9.81699e36	−	3.64576e37i	−0.403074	−	1.49691i
$589$	−3.79384e36	+	3.79384e36i	−0.152238	+	0.152238i
$590$	−2.51961e35	+	1.45677e35i	−0.00988167	+	0.00571331i
$591$	−1.49992e37			−0.574960
$592$	−1.15260e37	+	4.34437e37i	−0.431851	+	1.62773i
$593$	−4.23155e37			−1.54975			−0.774874	−	0.632116i	$-0.782187\pi$
$593$	−4.23155e37			−1.54975			−0.774874	+	0.632116i	$0.782187\pi$
$594$	9.03420e36	−	5.22332e36i	0.323424	−	0.186995i
$595$	3.56009e36	−	3.56009e36i	0.124590	−	0.124590i
$596$	6.61025e35	−	1.77995e35i	0.0226148	−	0.00608952i
$597$	1.39333e37	+	1.39333e37i	0.466016	+	0.466016i
$598$	4.21765e36	−	1.57794e37i	0.137913	−	0.515969i
$599$			5.49505e37i			1.75675i	0.477974	+	0.878374i	$0.341371\pi$
$599$			5.49505e37i			1.75675i	−0.477974	+	0.878374i	$0.658629\pi$
$600$	−2.09139e37	−	2.08367e37i	−0.653723	−	0.651310i
$601$		−	1.72453e37i		−	0.527066i	−0.964650	−	0.263533i	$-0.915112\pi$
$601$		−	1.72453e37i		−	0.527066i	0.964650	−	0.263533i	$-0.0848877\pi$
$602$	3.46483e36	+	9.26109e35i	0.103545	+	0.0276764i
$603$	−3.97688e35	−	3.97688e35i	−0.0116214	−	0.0116214i
$604$	4.76908e37	+	2.74560e37i	1.36281	+	0.784581i
$605$	5.44484e36	−	5.44484e36i	0.152156	−	0.152156i
$606$	1.44194e37	+	2.49396e37i	0.394064	+	0.681568i
$607$	5.57558e37			1.49019			0.745096	−	0.666957i	$-0.232404\pi$
$607$	5.57558e37			1.49019			0.745096	+	0.666957i	$0.232404\pi$
$608$	2.66343e36	+	9.81889e36i	0.0696214	+	0.256664i
$609$	−1.18903e38			−3.03990
$610$	2.90467e36	+	5.02389e36i	0.0726347	+	0.125628i
$611$	5.66863e36	−	5.66863e36i	0.138651	−	0.138651i
$612$	5.15916e35	+	2.97017e35i	0.0123434	+	0.00710619i
$613$	−4.97190e36	−	4.97190e36i	−0.116361	−	0.116361i	0.646529	−	0.762890i	$-0.276220\pi$
$613$	−4.97190e36	−	4.97190e36i	−0.116361	−	0.116361i	−0.762890	+	0.646529i	$0.776220\pi$
$614$	7.57618e37	+	2.02503e37i	1.73451	+	0.463615i
$615$		−	6.54154e36i		−	0.146509i
$616$	−1.90198e37	+	1.90902e37i	−0.416740	+	0.418285i
$617$		−	1.59253e37i		−	0.341379i	−0.985325	−	0.170689i	$-0.945401\pi$
$617$		−	1.59253e37i		−	0.341379i	0.985325	−	0.170689i	$-0.0545995\pi$
$618$	2.08287e37	−	7.79258e37i	0.436835	−	1.63432i
$619$	−5.19437e37	−	5.19437e37i	−1.06588	−	1.06588i	−0.997671	−	0.0682110i	$-0.978271\pi$
$619$	−5.19437e37	−	5.19437e37i	−1.06588	−	1.06588i	−0.0682110	−	0.997671i	$-0.521729\pi$
$620$	9.68957e36	−	2.60912e36i	0.194543	−	0.0523849i
$621$	−3.86267e37	+	3.86267e37i	−0.758841	+	0.758841i
$622$	−8.20410e37	+	4.74338e37i	−1.57711	+	0.911839i
$623$	−5.65969e37			−1.06464
$624$	−2.33557e37	+	1.35613e37i	−0.429933	+	0.249637i
$625$	−4.54102e37			−0.818037
$626$	9.47732e37	−	5.47952e37i	1.67083	−	0.966027i
$627$	3.94434e36	−	3.94434e36i	0.0680554	−	0.0680554i
$628$	−2.20437e37	−	8.18642e37i	−0.372245	−	1.38242i
$629$	3.17832e37	+	3.17832e37i	0.525308	+	0.525308i
$630$	−2.05843e35	+	7.70117e35i	−0.00332996	+	0.0124583i
$631$			1.50618e37i			0.238496i	0.992865	+	0.119248i	$0.0380483\pi$
$631$			1.50618e37i			0.238496i	−0.992865	+	0.119248i	$0.961952\pi$
$632$	−4.34895e37	+	8.04275e34i	−0.674068	+	0.00124659i
$633$			3.16958e37i			0.480897i
$634$	3.80052e37	+	1.01583e37i	0.564466	+	0.150875i
$635$	−5.88515e36	−	5.88515e36i	−0.0855682	−	0.0855682i
$636$	5.73018e37	−	9.95328e37i	0.815637	−	1.41676i
$637$	−4.04115e37	+	4.04115e37i	−0.563148	+	0.563148i
$638$	2.59871e37	+	4.49470e37i	0.354552	+	0.613228i
$639$	−1.53457e35			−0.00204986
$640$	4.84542e36	−	1.84006e37i	0.0633726	−	0.240659i
$641$	8.00815e37			1.02553			0.512765	−	0.858529i	$-0.328621\pi$
$641$	8.00815e37			1.02553			0.512765	+	0.858529i	$0.328621\pi$
$642$	6.72755e37	+	1.16359e38i	0.843595	+	1.45907i
$643$	7.28689e37	−	7.28689e37i	0.894735	−	0.894735i	−0.100230	−	0.994964i	$-0.531958\pi$
$643$	7.28689e37	−	7.28689e37i	0.894735	−	0.894735i	0.994964	+	0.100230i	$0.0319578\pi$
$644$	7.03809e37	−	1.22251e38i	0.846244	−	1.46992i
$645$	9.81807e35	+	9.81807e35i	0.0115603	+	0.0115603i
$646$	9.82902e36	+	2.62718e36i	0.113337	+	0.0302936i
$647$			8.15309e36i			0.0920692i	0.998940	+	0.0460346i	$0.0146584\pi$
$647$			8.15309e36i			0.0920692i	−0.998940	+	0.0460346i	$0.985342\pi$
$648$	8.74059e37	−	1.61644e35i	0.966669	−	0.00178771i
$649$		−	1.55783e36i		−	0.0168740i
$650$	−1.15392e37	+	4.31714e37i	−0.122418	+	0.458000i
$651$	−8.69802e37	−	8.69802e37i	−0.903809	−	0.903809i
$652$	−1.57620e37	−	5.85358e37i	−0.160424	−	0.595770i
$653$	4.01892e37	−	4.01892e37i	0.400665	−	0.400665i	−0.477802	−	0.878467i	$-0.658566\pi$
$653$	4.01892e37	−	4.01892e37i	0.400665	−	0.400665i	0.878467	+	0.477802i	$0.158566\pi$
$654$	3.02597e37	−	1.74953e37i	0.295505	−	0.170853i
$655$	−2.52952e35			−0.00241981
$656$	−5.52261e37	+	3.20666e37i	−0.517538	+	0.300505i
$657$	−2.87643e36			−0.0264071
$658$	5.99388e37	−	3.46550e37i	0.539087	−	0.311685i
$659$	9.00593e37	−	9.00593e37i	0.793552	−	0.793552i	−0.188518	−	0.982070i	$-0.560368\pi$
$659$	9.00593e37	−	9.00593e37i	0.793552	−	0.793552i	0.982070	+	0.188518i	$0.0603682\pi$
$660$	−1.00740e37	+	2.71262e36i	−0.0869675	+	0.0234178i
$661$	1.26696e38	+	1.26696e38i	1.07163	+	1.07163i	0.997228	+	0.0744009i	$0.0237045\pi$
$661$	1.26696e38	+	1.26696e38i	1.07163	+	1.07163i	0.0744009	+	0.997228i	$0.476296\pi$
$662$	−1.83666e36	+	6.87145e36i	−0.0152211	+	0.0569463i
$663$			2.70083e37i			0.219313i
$664$	2.89820e37	−	2.90894e37i	0.230600	−	0.231455i
$665$			1.36237e37i			0.106219i
$666$	−6.87532e36	−	1.83769e36i	−0.0525280	−	0.0140401i
$667$	−1.92176e38	−	1.92176e38i	−1.43880	−	1.43880i
$668$	−2.09465e38	−	1.20590e38i	−1.53684	−	0.884771i
$669$	−3.36437e36	+	3.36437e36i	−0.0241909	+	0.0241909i
$670$	8.99821e36	+	1.55632e37i	0.0634084	+	0.109670i
$671$	−3.10619e37			−0.214523
$672$	−2.25115e38	+	6.10636e37i	−1.52377	+	0.413330i
$673$	−2.18110e38			−1.44701			−0.723506	−	0.690318i	$-0.757471\pi$
$673$	−2.18110e38			−1.44701			−0.723506	+	0.690318i	$0.757471\pi$
$674$	1.16040e38	+	2.00702e38i	0.754571	+	1.30510i
$675$	1.05680e38	−	1.05680e38i	0.673585	−	0.673585i
$676$	−1.03285e38	−	5.94622e37i	−0.645295	−	0.371501i
$677$	8.33269e36	+	8.33269e36i	0.0510315	+	0.0510315i	0.732162	−	0.681131i	$-0.238511\pi$
$677$	8.33269e36	+	8.33269e36i	0.0510315	+	0.0510315i	−0.681131	+	0.732162i	$0.738511\pi$
$678$	−2.42061e38	−	6.47002e37i	−1.45320	−	0.388423i
$679$			3.58765e38i			2.11139i
$680$	−1.34801e37	−	1.34303e37i	−0.0777717	−	0.0774846i
$681$			9.89801e37i			0.559837i
$682$	−1.38696e37	+	5.18900e37i	−0.0769086	+	0.287736i
$683$	1.18619e38	+	1.18619e38i	0.644876	+	0.644876i	0.951750	−	0.306874i	$-0.0992831\pi$
$683$	1.18619e38	+	1.18619e38i	0.644876	+	0.644876i	−0.306874	+	0.951750i	$0.599283\pi$
$684$	−1.55546e36	+	4.18841e35i	−0.00829091	+	0.00223250i
$685$	−5.31475e35	+	5.31475e35i	−0.00277754	+	0.00277754i
$686$	−1.56149e38	+	9.02813e37i	−0.800138	+	0.462618i
$687$	2.82487e38			1.41933
$688$	3.47596e36	−	1.31016e37i	0.0171250	−	0.0645477i
$689$	−1.73843e38			−0.839844
$690$	4.72786e37	−	2.73352e37i	0.223976	−	0.129497i
$691$	1.42316e38	−	1.42316e38i	0.661151	−	0.661151i	−0.294500	−	0.955651i	$-0.595153\pi$
$691$	1.42316e38	−	1.42316e38i	0.661151	−	0.661151i	0.955651	+	0.294500i	$0.0951531\pi$
$692$	−7.55883e37	−	2.80715e38i	−0.344368	−	1.27889i
$693$	−3.01710e36	−	3.01710e36i	−0.0134800	−	0.0134800i
$694$	4.71406e37	−	1.76366e38i	0.206558	−	0.772790i
$695$			3.83928e37i			0.164989i
$696$	8.31076e35	+	4.49387e38i	0.00350281	+	1.89407i
$697$			6.38629e37i			0.264001i
$698$	2.87994e38	+	7.69776e37i	1.16771	+	0.312116i
$699$	5.68459e37	+	5.68459e37i	0.226077	+	0.226077i
$700$	−1.92558e38	+	3.34471e38i	−0.751169	+	1.30477i
$701$	4.87512e36	−	4.87512e36i	0.0186548	−	0.0186548i	−0.697718	−	0.716373i	$-0.745801\pi$
$701$	4.87512e36	−	4.87512e36i	0.0186548	−	0.0186548i	0.716373	+	0.697718i	$0.245801\pi$
$702$	−6.84344e37	−	1.18363e38i	−0.256876	−	0.444289i
$703$	−1.21628e38			−0.447853
$704$	7.22835e37	+	7.17508e37i	0.261101	+	0.259177i
$705$	2.68045e37			0.0949849
$706$	4.39420e37	+	7.60015e37i	0.152762	+	0.264216i
$707$	2.66299e38	−	2.66299e38i	0.908254	−	0.908254i
$708$	6.72756e36	−	1.16857e37i	0.0225117	−	0.0391027i
$709$	1.72511e38	+	1.72511e38i	0.566362	+	0.566362i	0.931107	−	0.364746i	$-0.118844\pi$
$709$	1.72511e38	+	1.72511e38i	0.566362	+	0.566362i	−0.364746	+	0.931107i	$0.618844\pi$
$710$	4.73879e36	+	1.26662e36i	0.0152644	+	0.00408000i
$711$		−	6.88597e36i		−	0.0217633i
$712$	3.95586e35	+	2.13905e38i	0.00122677	+	0.663348i
$713$		−	2.81162e38i		−	0.855556i
$714$	−6.02326e37	+	2.25347e38i	−0.179848	+	0.672861i
$715$	1.11665e37	+	1.11665e37i	0.0327178	+	0.0327178i
$716$	3.83483e37	+	1.42415e38i	0.110260	+	0.409478i
$717$	4.82035e38	−	4.82035e38i	1.36010	−	1.36010i
$718$	−3.29129e38	+	1.90293e38i	−0.911351	+	0.526918i
$719$	1.03369e38			0.280899			0.140449	−	0.990088i	$-0.455145\pi$
$719$	1.03369e38			0.280899			0.140449	+	0.990088i	$0.455145\pi$
$720$	2.91205e36	+	7.72592e35i	0.00776624	+	0.00206045i
$721$	−1.05448e39			−2.76001
$722$	3.13165e38	−	1.81063e38i	0.804491	−	0.465134i
$723$	2.53818e38	−	2.53818e38i	0.639964	−	0.639964i
$724$	4.96058e38	−	1.33574e38i	1.22761	−	0.330561i
$725$	5.25781e38	+	5.25781e38i	1.27715	+	1.27715i
$726$	−9.21204e37	+	3.44648e38i	−0.219640	+	0.821734i
$727$		−	7.47472e37i		−	0.174936i	−0.996167	−	0.0874682i	$-0.972122\pi$
$727$		−	7.47472e37i		−	0.174936i	0.996167	−	0.0874682i	$-0.0278776\pi$
$728$	2.50114e38	+	2.49191e38i	0.574599	+	0.572478i
$729$			4.56804e38i			1.03017i
$730$	8.88249e37	+	2.37419e37i	0.196642	+	0.0525601i
$731$	−9.58507e36	−	9.58507e36i	−0.0208310	−	0.0208310i
$732$	−2.33004e38	−	1.34142e38i	−0.497122	−	0.286197i
$733$	8.00218e37	−	8.00218e37i	0.167612	−	0.167612i	−0.618317	−	0.785929i	$-0.712185\pi$
$733$	8.00218e37	−	8.00218e37i	0.167612	−	0.167612i	0.785929	+	0.618317i	$0.212185\pi$
$734$	−9.92187e37	−	1.71607e38i	−0.204031	−	0.352890i
$735$	−1.91088e38			−0.385794
$736$	−4.62534e38	−	2.65146e38i	−0.916839	−	0.525576i
$737$	−9.62247e37			−0.187273
$738$	−5.06113e36	−	8.75366e36i	−0.00967133	−	0.0167274i
$739$	−3.01672e38	+	3.01672e38i	−0.566025	+	0.566025i	−0.931012	−	0.364987i	$-0.881073\pi$
$739$	−3.01672e38	+	3.01672e38i	−0.566025	+	0.566025i	0.364987	+	0.931012i	$0.381073\pi$
$740$	1.97143e38	+	1.13497e38i	0.363207	+	0.209101i
$741$	−5.16775e37	−	5.16775e37i	−0.0934880	−	0.0934880i
$742$	−1.45048e39	−	3.87698e38i	−2.57668	−	0.688716i
$743$			1.23804e38i			0.215966i	0.994153	+	0.107983i	$0.0344392\pi$
$743$			1.23804e38i			0.215966i	−0.994153	+	0.107983i	$0.965561\pi$
$744$	−3.28129e38	+	3.29345e38i	−0.562095	+	0.564178i
$745$		−	3.46468e36i		−	0.00582846i
$746$	6.84980e37	−	2.56270e38i	0.113163	−	0.423373i
$747$	4.59741e36	+	4.59741e36i	0.00745908	+	0.00745908i
$748$	9.83488e37	−	2.64825e37i	0.156710	−	0.0421975i
$749$	1.24245e39	−	1.24245e39i	1.94435	−	1.94435i
$750$	−2.67243e38	+	1.54512e38i	−0.410751	+	0.237485i
$751$	−1.23465e38			−0.186383			−0.0931913	−	0.995648i	$-0.529707\pi$
$751$	−1.23465e38			−0.186383			−0.0931913	+	0.995648i	$0.529707\pi$
$752$	−1.31396e38	−	2.26293e38i	−0.194823	−	0.335530i
$753$	−1.08749e39			−1.58377
$754$	5.88882e38	−	3.40476e38i	0.842394	−	0.487049i
$755$	1.96936e38	−	1.96936e38i	0.276721	−	0.276721i
$756$	−3.07022e38	−	1.14020e39i	−0.423765	−	1.57375i
$757$	4.32514e38	+	4.32514e38i	0.586416	+	0.586416i	0.936659	−	0.350243i	$-0.113901\pi$
$757$	4.32514e38	+	4.32514e38i	0.586416	+	0.586416i	−0.350243	+	0.936659i	$0.613901\pi$
$758$	2.47581e38	−	9.26270e38i	0.329749	−	1.23368i
$759$			2.92316e38i			0.382462i
$760$	5.14902e37	−	9.52236e34i	0.0661822	−	0.000122394i
$761$		−	7.49993e37i		−	0.0947031i	−0.998878	−	0.0473516i	$-0.984922\pi$
$761$		−	7.49993e37i		−	0.0947031i	0.998878	−	0.0473516i	$-0.0150781\pi$
$762$	3.72519e38	+	9.95700e37i	0.462121	+	0.123520i
$763$	−3.23105e38	−	3.23105e38i	−0.393788	−	0.393788i
$764$	4.58106e38	−	7.95726e38i	0.548536	−	0.952803i
$765$	2.13044e36	−	2.13044e36i	0.00250635	−	0.00250635i
$766$	−3.64823e38	−	6.30993e38i	−0.421690	−	0.729351i
$767$	−2.04102e37			−0.0231798
$768$	2.32360e38	+	8.50382e38i	0.259290	+	0.948938i
$769$	8.26548e38			0.906280			0.453140	−	0.891439i	$-0.350304\pi$
$769$	8.26548e38			0.906280			0.453140	+	0.891439i	$0.350304\pi$
$770$	6.82659e37	+	1.18072e38i	0.0735494	+	0.127210i
$771$	5.90286e38	−	5.90286e38i	0.624926	−	0.624926i
$772$	−2.42039e38	+	4.20420e38i	−0.251798	+	0.437371i
$773$	2.90047e37	+	2.90047e37i	0.0296514	+	0.0296514i	0.721777	−	0.692126i	$-0.243326\pi$
$773$	2.90047e37	+	2.90047e37i	0.0296514	+	0.0296514i	−0.692126	+	0.721777i	$0.743326\pi$
$774$	2.07344e36	+	5.54206e35i	0.00208299	+	0.000556760i
$775$			7.69242e38i			0.759434i
$776$	1.35593e39	−	2.50760e36i	1.31554	−	0.00243291i
$777$		−	2.78852e39i		−	2.65883i
$778$	1.23175e38	−	4.60832e38i	0.115425	−	0.431835i
$779$	−1.22195e38	−	1.22195e38i	−0.112538	−	0.112538i
$780$	3.55400e37	+	1.31986e38i	0.0321692	+	0.119468i
$781$	−1.85652e37	+	1.85652e37i	−0.0165163	+	0.0165163i
$782$	−4.61566e38	+	2.66865e38i	−0.403592	+	0.233346i
$783$	−2.27500e39			−1.95522
$784$	9.36715e38	+	1.61324e39i	0.791299	+	1.36280i
$785$	−4.29082e38			−0.356287
$786$	1.01455e37	−	5.86585e36i	0.00828074	−	0.00478770i
$787$	−1.08803e39	+	1.08803e39i	−0.872939	+	0.872939i	−0.992792	−	0.119853i	$-0.961758\pi$
$787$	−1.08803e39	+	1.08803e39i	−0.872939	+	0.872939i	0.119853	+	0.992792i	$0.461758\pi$
$788$	7.15597e38	−	1.92690e38i	0.564371	−	0.151969i
$789$	1.90730e38	+	1.90730e38i	0.147870	+	0.147870i
$790$	−5.68364e37	+	2.12640e38i	−0.0433172	+	0.162062i
$791$			3.27552e39i			2.45413i
$792$	−1.13819e37	+	1.14241e37i	−0.00838348	+	0.00841455i
$793$			4.06963e38i			0.294691i
$794$	5.30494e38	+	1.41795e38i	0.377662	+	0.100945i
$795$	−4.11015e38	−	4.11015e38i	−0.287674	−	0.287674i
$796$	−8.43739e38	−	4.85747e38i	−0.580607	−	0.334260i
$797$	−5.06247e38	+	5.06247e38i	−0.342511	+	0.342511i	−0.857311	−	0.514799i	$-0.827866\pi$
$797$	−5.06247e38	+	5.06247e38i	−0.342511	+	0.342511i	0.514799	+	0.857311i	$0.327866\pi$
$798$	−3.15929e38	−	5.46427e38i	−0.210160	−	0.363490i
$799$	−2.61684e38			−0.171157
$800$	1.26546e39	+	7.25424e38i	0.813832	+	0.466527i
$801$	−3.38690e37			−0.0214172
$802$	9.17004e38	+	1.58604e39i	0.570187	+	0.986189i
$803$	−3.47991e38	+	3.47991e38i	−0.212769	+	0.212769i
$804$	−7.21809e38	−	4.15551e38i	−0.433976	−	0.249843i
$805$	−5.04829e38	−	5.04829e38i	−0.298469	−	0.298469i
$806$	6.79847e38	+	1.81715e38i	0.395265	+	0.105650i
$807$			2.60211e39i			1.48776i
$808$	−1.00832e39	−	1.00460e39i	−0.566952	−	0.564859i
$809$			2.79536e39i			1.54572i	0.634574	+	0.772862i	$0.281176\pi$
$809$			2.79536e39i			1.54572i	−0.634574	+	0.772862i	$0.718824\pi$
$810$	1.14231e38	−	4.27368e38i	0.0621205	−	0.232410i
$811$	−2.49140e39	−	2.49140e39i	−1.33248	−	1.33248i	−0.903142	−	0.429342i	$-0.858746\pi$
$811$	−2.49140e39	−	2.49140e39i	−1.33248	−	1.33248i	−0.429342	−	0.903142i	$-0.641254\pi$
$812$	5.67272e39	−	1.52750e39i	2.98391	−	0.803480i
$813$	1.90102e39	−	1.90102e39i	0.983477	−	0.983477i
$814$	−1.05410e39	+	6.09453e38i	−0.536356	+	0.310106i
$815$	−3.06808e38			−0.153546
$816$	8.52107e38	+	2.26071e38i	0.419447	+	0.111283i
$817$	3.66801e37			0.0177596
$818$	−1.01844e39	+	5.88835e38i	−0.485028	+	0.280430i
$819$	−3.95291e37	+	3.95291e37i	−0.0185176	+	0.0185176i
$820$	8.40367e37	+	3.12090e38i	0.0387242	+	0.143811i
$821$	1.69300e39	+	1.69300e39i	0.767405	+	0.767405i	0.977649	−	0.210244i	$-0.0674258\pi$
$821$	1.69300e39	+	1.69300e39i	0.767405	+	0.767405i	−0.210244	+	0.977649i	$0.567426\pi$
$822$	8.99193e36	−	3.36413e37i	0.00400944	−	0.0150004i
$823$			2.69876e39i			1.18377i	0.806023	+	0.591885i	$0.201616\pi$
$823$			2.69876e39i			1.18377i	−0.806023	+	0.591885i	$0.798384\pi$
$824$	7.37030e36	+	3.98534e39i	0.00318030	+	1.71968i
$825$		−	7.99758e38i		−	0.339493i
$826$	−1.70295e38	−	4.55180e37i	−0.0711167	−	0.0190087i
$827$	−2.20032e37	−	2.20032e37i	−0.00903986	−	0.00903986i	0.702572	−	0.711612i	$-0.252035\pi$
$827$	−2.20032e37	−	2.20032e37i	−0.00903986	−	0.00903986i	−0.711612	+	0.702572i	$0.752035\pi$
$828$	4.21176e37	−	7.31580e37i	0.0170237	−	0.0295701i
$829$	−2.14342e39	+	2.14342e39i	−0.852354	+	0.852354i	−0.990423	−	0.138068i	$-0.955911\pi$
$829$	−2.14342e39	+	2.14342e39i	−0.852354	+	0.852354i	0.138068	+	0.990423i	$0.455911\pi$
$830$	−1.04022e38	−	1.79916e38i	−0.0406980	−	0.0703907i
$831$	−3.43281e39			−1.32140
$832$	9.40056e38	−	9.47036e38i	0.356032	−	0.358675i
$833$	1.86553e39			0.695177
$834$	−8.90314e38	−	1.53988e39i	−0.326438	−	0.564604i
$835$	−8.64972e38	+	8.64972e38i	−0.312058	+	0.312058i
$836$	−1.37509e38	+	2.38852e38i	−0.0488141	+	0.0847898i
$837$	−1.66421e39	−	1.66421e39i	−0.581320	−	0.581320i
$838$	−3.11386e39	−	8.32299e38i	−1.07030	−	0.286079i
$839$		−	1.41620e39i		−	0.479001i	−0.970896	−	0.239501i	$-0.923016\pi$
$839$		−	1.41620e39i		−	0.479001i	0.970896	−	0.239501i	$-0.0769837\pi$
$840$	2.18316e36	+	1.18050e39i	0.000726634	+	0.392912i
$841$		−	8.26545e39i		−	2.70720i
$842$	7.46874e38	−	2.79426e39i	0.240732	−	0.900645i
$843$	−8.15027e38	−	8.15027e38i	−0.258523	−	0.258523i
$844$	−4.07185e38	−	1.51217e39i	−0.127107	−	0.472040i
$845$	−4.26511e38	+	4.26511e38i	−0.131028	+	0.131028i
$846$	3.58689e37	−	2.07384e37i	0.0108447	−	0.00627011i
$847$	4.66370e39			1.38773
$848$	−1.45514e39	+	5.48474e39i	−0.426150	+	1.60624i
$849$	−3.28683e39			−0.947379
$850$	1.26282e39	−	7.30125e38i	0.358248	−	0.207129i
$851$	4.50693e39	−	4.50693e39i	1.25844	−	1.25844i
$852$	−2.19438e38	+	5.90883e37i	−0.0603083	+	0.0162393i
$853$	2.69291e39	+	2.69291e39i	0.728467	+	0.728467i	0.970314	−	0.241847i	$-0.0777532\pi$
$853$	2.69291e39	+	2.69291e39i	0.728467	+	0.728467i	−0.241847	+	0.970314i	$0.577753\pi$
$854$	−9.07590e38	+	3.39554e39i	−0.241662	+	0.904124i
$855$			8.15277e36i			0.00213679i
$856$	−4.70446e39	−	4.68709e39i	−1.21371	−	1.20923i
$857$			5.45772e39i			1.38602i	0.720927	+	0.693011i	$0.243716\pi$
$857$			5.45772e39i			1.38602i	−0.720927	+	0.693011i	$0.756284\pi$
$858$	−7.06816e38	−	1.88924e38i	−0.176697	−	0.0472290i
$859$	1.09872e39	+	1.09872e39i	0.270384	+	0.270384i	0.829255	−	0.558871i	$-0.188765\pi$
$859$	1.09872e39	+	1.09872e39i	0.270384	+	0.270384i	−0.558871	+	0.829255i	$0.688765\pi$
$860$	−5.94539e37	−	3.42280e37i	−0.0144029	−	0.00829188i
$861$	2.80153e39	−	2.80153e39i	0.668117	−	0.668117i
$862$	−1.79154e39	−	3.09863e39i	−0.420610	−	0.727481i
$863$	7.47384e39			1.72742			0.863710	−	0.503989i	$-0.168135\pi$
$863$	7.47384e39			1.72742			0.863710	+	0.503989i	$0.168135\pi$
$864$	−4.30717e39	+	1.16834e39i	−0.980069	+	0.265849i
$865$	−1.47133e39			−0.329605
$866$	−3.69531e39	−	6.39135e39i	−0.815002	−	1.40962i
$867$	−2.58004e39	+	2.58004e39i	−0.560233	+	0.560233i
$868$	5.26713e39	+	3.03233e39i	1.12605	+	0.648276i
$869$	−8.33066e38	−	8.33066e38i	−0.175353	−	0.175353i
$870$	2.19726e39	+	5.87304e38i	0.455378	+	0.121717i
$871$			1.26071e39i			0.257258i
$872$	−1.21890e39	+	1.22342e39i	−0.244904	+	0.245811i
$873$			2.14694e38i			0.0424744i
$874$	3.72541e38	−	1.39378e39i	0.0725720	−	0.271512i
$875$	2.85355e39	+	2.85355e39i	0.547364	+	0.547364i
$876$	−4.11319e39	+	1.10756e39i	−0.776915	+	0.209201i
$877$	1.71825e39	−	1.71825e39i	0.319589	−	0.319589i	−0.529020	−	0.848609i	$-0.677440\pi$
$877$	1.71825e39	−	1.71825e39i	0.319589	−	0.319589i	0.848609	+	0.529020i	$0.177440\pi$
$878$	5.43350e39	−	3.14150e39i	0.995184	−	0.575388i
$879$	2.98040e39			0.537557
$880$	4.45769e38	−	2.58833e38i	0.0791761	−	0.0459730i
$881$	−2.73189e39			−0.477846			−0.238923	−	0.971038i	$-0.576794\pi$
$881$	−2.73189e39			−0.477846			−0.238923	+	0.971038i	$0.576794\pi$
$882$	−2.55708e38	+	1.47843e38i	−0.0440472	+	0.0254669i
$883$	1.21446e39	−	1.21446e39i	0.206022	−	0.206022i	−0.596552	−	0.802574i	$-0.703463\pi$
$883$	1.21446e39	−	1.21446e39i	0.206022	−	0.206022i	0.802574	+	0.596552i	$0.203463\pi$
$884$	−3.46965e38	−	1.28854e39i	−0.0579669	−	0.215274i
$885$	−4.82555e37	−	4.82555e37i	−0.00793986	−	0.00793986i
$886$	−1.64440e39	+	6.15217e39i	−0.266473	+	0.996949i
$887$		−	8.63905e39i		−	1.37879i	−0.724387	−	0.689393i	$-0.757877\pi$
$887$		−	8.63905e39i		−	1.37879i	0.724387	−	0.689393i	$-0.242123\pi$
$888$	−1.05391e40	+	1.94905e37i	−1.65664	+	0.00306371i
$889$		−	5.04084e39i		−	0.780422i
$890$	1.04588e39	+	2.79552e38i	0.159484	+	0.0426283i
$891$	1.67431e39	+	1.67431e39i	0.251470	+	0.251470i
$892$	1.17290e38	−	2.03731e38i	0.0173514	−	0.0301392i
$893$	5.00705e38	−	5.00705e38i	0.0729603	−	0.0729603i
$894$	8.03446e37	+	1.38963e38i	0.0115319	+	0.0199454i
$895$	7.46452e38			0.105534
$896$	9.95551e39	−	5.80524e39i	1.38645	−	0.808467i
$897$	3.82983e39			0.525390
$898$	2.18699e39	+	3.78259e39i	0.295540	+	0.511162i
$899$	8.27981e39	−	8.27981e39i	1.10221	−	1.10221i
$900$	−1.15231e38	+	2.00156e38i	−0.0151111	+	0.0262479i
$901$	4.01261e39	+	4.01261e39i	0.518372	+	0.518372i
$902$	−1.67132e39	−	4.46724e38i	−0.212701	−	0.0568526i
$903$			8.40952e38i			0.105435i
$904$	1.23797e40	−	2.28944e37i	1.52910	−	0.00282784i
$905$		−	2.60003e39i		−	0.316390i
$906$	−3.33194e39	+	1.24657e40i	−0.399453	+	1.49446i
$907$	−9.13266e39	−	9.13266e39i	−1.07870	−	1.07870i	−0.996627	−	0.0820691i	$-0.973847\pi$
$907$	−9.13266e39	−	9.13266e39i	−1.07870	−	1.07870i	−0.0820691	−	0.996627i	$-0.526153\pi$
$908$	−1.27156e39	−	4.72223e39i	−0.147971	−	0.549526i
$909$	1.59360e38	−	1.59360e38i	0.0182711	−	0.0182711i
$910$	1.54694e39	−	8.94399e38i	0.174749	−	0.101035i
$911$	−1.31335e40			−1.46178			−0.730890	−	0.682496i	$-0.760895\pi$
$911$	−1.31335e40			−1.46178			−0.730890	+	0.682496i	$0.760895\pi$
$912$	−2.06298e39	+	1.19786e39i	−0.226238	+	0.131363i
$913$	1.11239e39			0.120199
$914$	−9.17320e39	+	5.30369e39i	−0.976668	+	0.564683i
$915$	−9.62175e38	+	9.62175e38i	−0.100941	+	0.100941i
$916$	−1.34772e40	+	3.62901e39i	−1.39319	+	0.375145i
$917$	−1.08331e38	−	1.08331e38i	−0.0110349	−	0.0110349i
$918$	−1.15244e39	+	4.31161e39i	−0.115676	+	0.432776i
$919$		−	1.26537e40i		−	1.25158i	−0.779993	−	0.625788i	$-0.784778\pi$
$919$		−	1.26537e40i		−	1.25158i	0.779993	−	0.625788i	$-0.215222\pi$
$920$	−1.90445e39	+	1.91150e39i	−0.185623	+	0.186311i
$921$			1.83882e40i			1.76618i
$922$	1.76581e40	+	4.71980e39i	1.67138	+	0.446741i
$923$	2.43236e38	+	2.43236e38i	0.0226885	+	0.0226885i
$924$	−5.47608e39	−	3.15262e39i	−0.503382	−	0.289801i
$925$	−1.23307e40	+	1.23307e40i	−1.11705	+	1.11705i
$926$	3.79828e39	+	6.56946e39i	0.339109	+	0.586518i
$927$	−6.31024e38			−0.0555225
$928$	−5.81276e39	−	2.14291e40i	−0.504063	−	1.85826i
$929$	1.71148e40			1.46272			0.731359	−	0.681993i	$-0.238886\pi$
$929$	1.71148e40			1.46272			0.731359	+	0.681993i	$0.238886\pi$
$930$	1.17772e39	+	2.03698e39i	0.0992027	+	0.171580i
$931$	−3.56951e39	+	3.56951e39i	−0.296338	+	0.296338i
$932$	−3.44233e39	−	1.98178e39i	−0.281668	−	0.162159i
$933$	−1.57125e40	−	1.57125e40i	−1.26719	−	1.26719i
$934$	−1.37660e40	−	3.67948e39i	−1.09427	−	0.292485i
$935$		−	5.15483e38i		−	0.0403885i
$936$	1.49675e38	+	1.49122e38i	0.0115591	+	0.0115164i
$937$			8.71604e39i			0.663491i	0.943369	+	0.331745i	$0.107637\pi$
$937$			8.71604e39i			0.663491i	−0.943369	+	0.331745i	$0.892363\pi$
$938$	−2.81157e39	+	1.05189e40i	−0.210965	+	0.789279i
$939$	1.81510e40	+	1.81510e40i	1.34250	+	1.34250i
$940$	−1.27881e39	+	3.44347e38i	−0.0932354	+	0.0251056i
$941$	3.91604e39	−	3.91604e39i	0.281441	−	0.281441i	−0.552243	−	0.833683i	$-0.686228\pi$
$941$	3.91604e39	−	3.91604e39i	0.281441	−	0.281441i	0.833683	+	0.552243i	$0.186228\pi$
$942$	1.72098e40	−	9.95023e39i	1.21924	−	0.704930i
$943$	9.05591e39			0.632447
$944$	−1.70842e38	+	6.43940e38i	−0.0117618	+	0.0443326i
$945$	−5.97621e39			−0.405598
$946$	3.17893e38	−	1.83797e38i	0.0212691	−	0.0122972i
$947$	−4.83693e39	+	4.83693e39i	−0.319040	+	0.319040i	−0.848398	−	0.529358i	$-0.822433\pi$
$947$	−4.83693e39	+	4.83693e39i	−0.319040	+	0.319040i	0.529358	+	0.848398i	$0.322433\pi$
$948$	−2.65143e39	−	9.84669e39i	−0.172412	−	0.640291i
$949$	4.55927e39	+	4.55927e39i	0.292282	+	0.292282i
$950$	−1.01925e39	+	3.81329e39i	−0.0644186	+	0.241008i
$951$			9.22428e39i			0.574772i
$952$	−2.13135e37	−	1.15248e40i	−0.00130935	−	0.708004i
$953$			1.47180e40i			0.891448i	0.895170	+	0.445724i	$0.147054\pi$
$953$			1.47180e40i			0.891448i	−0.895170	+	0.445724i	$0.852946\pi$
$954$	−8.68004e38	−	2.32008e38i	−0.0518345	−	0.0138548i
$955$	−3.28590e39	−	3.28590e39i	−0.193468	−	0.193468i
$956$	−1.68048e40	+	2.91899e40i	−0.975557	+	1.69454i
$957$	−8.60826e39	+	8.60826e39i	−0.492725	+	0.492725i
$958$	3.21758e39	+	5.56508e39i	0.181591	+	0.314078i
$959$	−4.55227e38			−0.0253324
$960$	4.46162e39	−	1.65023e37i	0.244811	−	0.000905488i
$961$	−6.36897e39			−0.344591
$962$	7.98486e39	+	1.38105e40i	0.425995	+	0.736795i
$963$	7.43512e38	−	7.43512e38i	0.0391141	−	0.0391141i
$964$	−8.84868e39	+	1.53701e40i	−0.459027	+	0.797327i
$965$	1.73610e39	+	1.73610e39i	0.0888088	+	0.0888088i
$966$	3.19547e40	+	8.54112e39i	1.61192	+	0.430848i
$967$		−	3.38989e40i		−	1.68627i	−0.537699	−	0.843137i	$-0.680706\pi$
$967$		−	3.38989e40i		−	1.68627i	0.537699	−	0.843137i	$-0.319294\pi$
$968$	−3.25971e37	−	1.76262e40i	−0.00159905	−	0.864652i
$969$			2.38561e39i			0.115406i
$970$	1.77207e39	−	6.62980e39i	0.0845400	−	0.316287i
$971$	1.32150e40	+	1.32150e40i	0.621740	+	0.621740i	0.945976	−	0.324236i	$-0.105107\pi$
$971$	1.32150e40	+	1.32150e40i	0.621740	+	0.621740i	−0.324236	+	0.945976i	$0.605107\pi$
$972$	−3.61713e38	−	1.34330e39i	−0.0167830	−	0.0623274i
$973$	−1.64424e40	+	1.64424e40i	−0.752388	+	0.752388i
$974$	1.84665e40	−	1.06768e40i	0.833371	−	0.481832i
$975$	−1.04782e40			−0.466363
$976$	1.28396e40	+	3.40646e39i	0.563612	+	0.149531i
$977$	−1.70203e40			−0.736870			−0.368435	−	0.929654i	$-0.620106\pi$
$977$	−1.70203e40			−0.736870			−0.368435	+	0.929654i	$0.620106\pi$
$978$	1.23056e40	−	7.11476e39i	0.525446	−	0.303799i
$979$	−4.09747e39	+	4.09747e39i	−0.172564	+	0.172564i
$980$	9.11662e39	−	2.45484e39i	0.378688	−	0.101970i
$981$	−1.93354e38	−	1.93354e38i	−0.00792175	−	0.00792175i
$982$	4.76996e39	−	1.78457e40i	0.192757	−	0.721157i
$983$		−	1.89387e40i		−	0.754878i	−0.926034	−	0.377439i	$-0.876805\pi$
$983$		−	1.89387e40i		−	0.754878i	0.926034	−	0.377439i	$-0.123195\pi$
$984$	−1.06078e40	−	1.05686e40i	−0.417054	−	0.415514i
$985$		−	3.75072e39i		−	0.145454i
$986$	−2.14512e40	−	5.73366e39i	−0.820565	−	0.219328i
$987$	1.14795e40	+	1.14795e40i	0.433153	+	0.433153i
$988$	3.12936e39	+	1.80160e39i	0.116476	+	0.0670562i
$989$	−1.35918e39	+	1.35918e39i	−0.0499032	+	0.0499032i
$990$	4.08520e37	+	7.06570e37i	0.00147958	+	0.00255906i
$991$	1.60655e40			0.573984			0.286992	−	0.957933i	$-0.407345\pi$
$991$	1.60655e40			0.573984			0.286992	+	0.957933i	$0.407345\pi$
$992$	1.14237e40	−	1.99280e40i	0.402624	−	0.702355i
$993$	−1.66778e39			−0.0579860
$994$	1.48702e39	+	2.57192e39i	0.0510034	+	0.0882149i
$995$	−3.48417e39	+	3.48417e39i	−0.117893	+	0.117893i
$996$	8.34436e39	+	4.80391e39i	0.278543	+	0.160359i
$997$	−2.06068e40	−	2.06068e40i	−0.678619	−	0.678619i	0.281069	−	0.959688i	$-0.409311\pi$
$997$	−2.06068e40	−	2.06068e40i	−0.678619	−	0.678619i	−0.959688	+	0.281069i	$0.909311\pi$
$998$	3.47556e40	+	9.28977e39i	1.12918	+	0.301816i
$999$		−	5.33534e40i		−	1.71013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.28.e.a.5.17	✓	106
16.13	even	4	inner	16.28.e.a.13.17	yes	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.28.e.a.5.17	✓	106	1.1	even	1	trivial
16.28.e.a.13.17	yes	106	16.13	even	4	inner

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+(-5798.80 - 10029.5i) q^{2} +(1.92086e6 - 1.92086e6i) q^{3} +(-6.69655e7 + 1.16319e8i) q^{4} +(4.80331e8 + 4.80331e8i) q^{5} +(-3.04040e10 - 8.12664e9i) q^{6} +4.11420e11i q^{7} +(1.55494e12 - 2.87564e9i) q^{8} +2.46204e11i q^{9} +(2.03215e12 - 7.60284e12i) q^{10} +(2.97858e13 + 2.97858e13i) q^{11} +(9.48003e13 + 3.52063e14i) q^{12} +(3.90244e14 - 3.90244e14i) q^{13} +(4.12636e15 - 2.38575e15i) q^{14} +1.84530e15 q^{15} +(-9.04564e15 - 1.55787e16i) q^{16} -1.80150e16 q^{17} +(2.46931e15 - 1.42769e15i) q^{18} +(3.44699e16 - 3.44699e16i) q^{19} +(-8.80370e16 + 2.37058e16i) q^{20} +(7.90280e17 + 7.90280e17i) q^{21} +(1.26016e17 - 4.71460e17i) q^{22} +2.55457e18i q^{23} +(2.98130e18 - 2.99235e18i) q^{24} -6.98915e18i q^{25} +(-6.17692e18 - 1.65102e18i) q^{26} +(1.51206e19 + 1.51206e19i) q^{27} +(-4.78558e19 - 2.75510e19i) q^{28} +(-7.52283e19 + 7.52283e19i) q^{29} +(-1.07005e19 - 1.85075e19i) q^{30} -1.10062e20 q^{31} +(-1.03793e20 + 1.81061e20i) q^{32} +1.14429e20 q^{33} +(1.04466e20 + 1.80682e20i) q^{34} +(-1.97618e20 + 1.97618e20i) q^{35} +(-2.86381e19 - 1.64872e19i) q^{36} +(-1.76426e21 - 1.76426e21i) q^{37} +(-5.45601e20 - 1.45833e20i) q^{38} -1.49921e21i q^{39} +(7.48268e20 + 7.45505e20i) q^{40} -3.54498e21i q^{41} +(3.34347e21 - 1.25088e22i) q^{42} +(5.32060e20 + 5.32060e20i) q^{43} +(-5.45926e21 + 1.47002e21i) q^{44} +(-1.18259e20 + 1.18259e20i) q^{45} +(2.56212e22 - 1.48135e22i) q^{46} +1.45259e22 q^{47} +(-4.72998e22 - 1.25490e22i) q^{48} -1.03554e23 q^{49} +(-7.00979e22 + 4.05287e22i) q^{50} +(-3.46043e22 + 3.46043e22i) q^{51} +(1.92598e22 + 7.15256e22i) q^{52} +(-2.22737e23 - 2.22737e23i) q^{53} +(6.39713e22 - 2.39334e23i) q^{54} +2.86141e22i q^{55} +(1.18310e21 + 6.39735e23i) q^{56} -1.32424e23i q^{57} +(1.19074e24 + 3.18271e23i) q^{58} +(-2.61506e22 - 2.61506e22i) q^{59} +(-1.23571e23 + 2.14642e23i) q^{60} +(-5.21421e23 + 5.21421e23i) q^{61} +(6.38230e23 + 1.10388e24i) q^{62} -1.01293e23 q^{63} +(2.41784e24 - 8.94290e21i) q^{64} +3.74893e23 q^{65} +(-6.63549e23 - 1.14767e24i) q^{66} +(-1.61528e24 + 1.61528e24i) q^{67} +(1.20639e24 - 2.09548e24i) q^{68} +(4.90697e24 + 4.90697e24i) q^{69} +(3.12796e24 + 8.36069e23i) q^{70} +6.23292e23i q^{71} +(7.07993e20 + 3.82833e23i) q^{72} +1.16831e25i q^{73} +(-7.46412e24 + 2.79253e25i) q^{74} +(-1.34252e25 - 1.34252e25i) q^{75} +(1.70120e24 + 6.31778e24i) q^{76} +(-1.22545e25 + 1.22545e25i) q^{77} +(-1.50364e25 + 8.69361e24i) q^{78} -2.79686e25 q^{79} +(3.13802e24 - 1.18278e25i) q^{80} +5.62117e25 q^{81} +(-3.55545e25 + 2.05566e25i) q^{82} +(1.86732e25 - 1.86732e25i) q^{83} +(-1.44846e26 + 3.90028e25i) q^{84} +(-8.65317e24 - 8.65317e24i) q^{85} +(2.25100e24 - 8.42162e24i) q^{86} +2.89006e26i q^{87} +(4.64008e25 + 4.62295e25i) q^{88} +1.37565e26i q^{89} +(1.87185e24 + 5.00324e23i) q^{90} +(1.60554e26 + 1.60554e26i) q^{91} +(-2.97144e26 - 1.71068e26i) q^{92} +(-2.11414e26 + 2.11414e26i) q^{93} +(-8.42326e25 - 1.45688e26i) q^{94} +3.31139e25 q^{95} +(1.48421e26 + 5.47165e26i) q^{96} +8.72016e26 q^{97} +(6.00491e26 + 1.03860e27i) q^{98} +(-7.33338e24 + 7.33338e24i) 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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