LMFDB - Embedded newform 16.28.e.a.13.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [16,28,Mod(5,16)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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

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

Self dual:	no
Analytic conductor:	$73.8968919741$
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			13.18
Character	$\chi$	$=$	16.13
Dual form			16.28.e.a.5.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5041.21 + 10430.9i) q^{2} +(-329571. - 329571. i) q^{3} +(-8.33902e7 - 1.05169e8i) q^{4} +(-2.69387e8 + 2.69387e8i) q^{5} +(5.09916e9 - 1.77629e9i) q^{6} +2.71695e11i q^{7} +(1.51739e12 - 3.39659e11i) q^{8} -7.40836e12i q^{9} +(-1.45192e12 - 4.16799e12i) q^{10} +(2.66489e13 - 2.66489e13i) q^{11} +(-7.17757e12 + 6.21435e13i) q^{12} +(-4.16447e14 - 4.16447e14i) q^{13} +(-2.83402e15 - 1.36967e15i) q^{14} +1.77564e14 q^{15} +(-4.10654e15 + 1.75401e16i) q^{16} +2.48650e16 q^{17} +(7.72760e16 + 3.73471e16i) q^{18} +(3.21749e16 + 3.21749e16i) q^{19} +(5.07954e16 + 5.86686e15i) q^{20} +(8.95425e16 - 8.95425e16i) q^{21} +(1.43630e17 + 4.12316e17i) q^{22} +1.49823e18i q^{23} +(-6.12030e17 - 3.88147e17i) q^{24} +7.30544e18i q^{25} +(6.44332e18 - 2.24453e18i) q^{26} +(-4.95475e18 + 4.95475e18i) q^{27} +(2.85738e19 - 2.26567e19i) q^{28} +(8.47986e18 + 8.47986e18i) q^{29} +(-8.95138e17 + 1.85216e18i) q^{30} -1.32940e20 q^{31} +(-1.62257e20 - 1.31258e20i) q^{32} -1.75654e19 q^{33} +(-1.25350e20 + 2.59365e20i) q^{34} +(-7.31910e19 - 7.31910e19i) q^{35} +(-7.79128e20 + 6.17785e20i) q^{36} +(7.33132e20 - 7.33132e20i) q^{37} +(-4.97815e20 + 1.73414e20i) q^{38} +2.74498e20i q^{39} +(-3.17267e20 + 5.00266e20i) q^{40} -9.82451e20i q^{41} +(4.82608e20 + 1.38541e21i) q^{42} +(-1.30008e22 + 1.30008e22i) q^{43} +(-5.02490e21 - 5.80375e20i) q^{44} +(1.99572e21 + 1.99572e21i) q^{45} +(-1.56279e22 - 7.55286e21i) q^{46} -4.26559e22 q^{47} +(7.13409e21 - 4.42730e21i) q^{48} -8.10557e21 q^{49} +(-7.62024e22 - 3.68282e22i) q^{50} +(-8.19477e21 - 8.19477e21i) q^{51} +(-9.06962e21 + 7.85249e22i) q^{52} +(1.05894e23 - 1.05894e23i) q^{53} +(-2.67047e22 - 7.66605e22i) q^{54} +1.43578e22i q^{55} +(9.22835e22 + 4.12268e23i) q^{56} -2.12078e22i q^{57} +(-1.31201e23 + 4.57040e22i) q^{58} +(2.50600e23 - 2.50600e23i) q^{59} +(-1.48071e22 - 1.86742e22i) q^{60} +(2.69362e23 + 2.69362e23i) q^{61} +(6.70177e23 - 1.38668e24i) q^{62} +2.01281e24 q^{63} +(2.18712e24 - 1.03079e24i) q^{64} +2.24371e23 q^{65} +(8.85509e22 - 1.83223e23i) q^{66} +(-1.96312e24 - 1.96312e24i) q^{67} +(-2.07350e24 - 2.61502e24i) q^{68} +(4.93771e23 - 4.93771e23i) q^{69} +(1.13242e24 - 3.94478e23i) q^{70} -3.69903e24i q^{71} +(-2.51632e24 - 1.12414e25i) q^{72} -1.22287e25i q^{73} +(3.95137e24 + 1.13431e25i) q^{74} +(2.40766e24 - 2.40766e24i) q^{75} +(7.00724e23 - 6.06688e24i) q^{76} +(7.24037e24 + 7.24037e24i) q^{77} +(-2.86326e24 - 1.38380e24i) q^{78} +3.63425e25 q^{79} +(-3.61883e24 - 5.83133e24i) q^{80} -5.32273e25 q^{81} +(1.02479e25 + 4.95274e24i) q^{82} +(-8.16524e25 - 8.16524e25i) q^{83} +(-1.68840e25 - 1.95011e24i) q^{84} +(-6.69831e24 + 6.69831e24i) q^{85} +(-7.00708e25 - 2.01151e26i) q^{86} -5.58942e24i q^{87} +(3.13854e25 - 4.94885e25i) q^{88} -2.68126e26i q^{89} +(-3.08780e25 + 1.07563e25i) q^{90} +(1.13146e26 - 1.13146e26i) q^{91} +(1.57567e26 - 1.24937e26i) q^{92} +(4.38131e25 + 4.38131e25i) q^{93} +(2.15037e26 - 4.44940e26i) q^{94} -1.73350e25 q^{95} +(1.02164e25 + 9.67341e25i) q^{96} +1.84751e25 q^{97} +(4.08618e25 - 8.45485e25i) q^{98} +(-1.97425e26 - 1.97425e26i) 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 $

$2$	−5041.21	+	10430.9i	−0.435140	+	0.900363i
$2$	−5041.21	+	10430.9i	−0.435140	+	0.900363i
$3$	−329571.	−	329571.i	−0.119347	−	0.119347i	0.644911	−	0.764258i	$-0.276894\pi$
$3$	−329571.	−	329571.i	−0.119347	−	0.119347i	−0.764258	+	0.644911i	$0.776894\pi$
$4$	−8.33902e7	−	1.05169e8i	−0.621306	−	0.783568i
$5$	−2.69387e8	+	2.69387e8i	−0.0986920	+	0.0986920i	−0.754729	−	0.656037i	$-0.772232\pi$
$5$	−2.69387e8	+	2.69387e8i	−0.0986920	+	0.0986920i	0.656037	+	0.754729i	$0.272232\pi$
$6$	5.09916e9	−	1.77629e9i	0.159388	−	0.0555229i
$7$			2.71695e11i			1.05988i	0.848035	+	0.529941i	$0.177786\pi$
$7$			2.71695e11i			1.05988i	−0.848035	+	0.529941i	$0.822214\pi$
$8$	1.51739e12	−	3.39659e11i	0.975851	−	0.218438i
$9$		−	7.40836e12i		−	0.971513i
$10$	−1.45192e12	−	4.16799e12i	−0.0459137	−	0.131803i
$11$	2.66489e13	−	2.66489e13i	0.232744	−	0.232744i	−0.581093	−	0.813837i	$-0.697375\pi$
$11$	2.66489e13	−	2.66489e13i	0.232744	−	0.232744i	0.813837	+	0.581093i	$0.197375\pi$
$12$	−7.17757e12	+	6.21435e13i	−0.0193656	+	0.167667i
$13$	−4.16447e14	−	4.16447e14i	−0.381351	−	0.381351i	0.490238	−	0.871589i	$-0.336910\pi$
$13$	−4.16447e14	−	4.16447e14i	−0.381351	−	0.381351i	−0.871589	+	0.490238i	$0.836910\pi$
$14$	−2.83402e15	−	1.36967e15i	−0.954278	−	0.461197i
$15$	1.77564e14			0.0235572
$16$	−4.10654e15	+	1.75401e16i	−0.227959	+	0.973671i
$17$	2.48650e16			0.608875			0.304437	−	0.952532i	$-0.401532\pi$
$17$	2.48650e16			0.608875			0.304437	+	0.952532i	$0.401532\pi$
$18$	7.72760e16	+	3.73471e16i	0.874714	+	0.422744i
$19$	3.21749e16	+	3.21749e16i	0.175527	+	0.175527i	0.789403	−	0.613876i	$-0.210390\pi$
$19$	3.21749e16	+	3.21749e16i	0.175527	+	0.175527i	−0.613876	+	0.789403i	$0.710390\pi$
$20$	5.07954e16	+	5.86686e15i	0.138650	+	0.0160140i
$21$	8.95425e16	−	8.95425e16i	0.126494	−	0.126494i
$22$	1.43630e17	+	4.12316e17i	0.108278	+	0.310830i
$23$			1.49823e18i			0.619800i	0.950769	+	0.309900i	$0.100296\pi$
$23$			1.49823e18i			0.619800i	−0.950769	+	0.309900i	$0.899704\pi$
$24$	−6.12030e17	−	3.88147e17i	−0.142535	−	0.0903949i
$25$			7.30544e18i			0.980520i
$26$	6.44332e18	−	2.24453e18i	0.509295	−	0.177413i
$27$	−4.95475e18	+	4.95475e18i	−0.235294	+	0.235294i
$28$	2.85738e19	−	2.26567e19i	0.830490	−	0.658510i
$29$	8.47986e18	+	8.47986e18i	0.153467	+	0.153467i	0.779665	−	0.626197i	$-0.215390\pi$
$29$	8.47986e18	+	8.47986e18i	0.153467	+	0.153467i	−0.626197	+	0.779665i	$0.715390\pi$
$30$	−8.95138e17	+	1.85216e18i	−0.0102507	+	0.0212100i
$31$	−1.32940e20			−0.977851			−0.488925	−	0.872326i	$-0.662611\pi$
$31$	−1.32940e20			−0.977851			−0.488925	+	0.872326i	$0.662611\pi$
$32$	−1.62257e20	−	1.31258e20i	−0.777463	−	0.628929i
$33$	−1.75654e19			−0.0555546
$34$	−1.25350e20	+	2.59365e20i	−0.264946	+	0.548208i
$35$	−7.31910e19	−	7.31910e19i	−0.104602	−	0.104602i
$36$	−7.79128e20	+	6.17785e20i	−0.761247	+	0.603606i
$37$	7.33132e20	−	7.33132e20i	0.494833	−	0.494833i	−0.414992	−	0.909825i	$-0.636216\pi$
$37$	7.33132e20	−	7.33132e20i	0.494833	−	0.494833i	0.909825	+	0.414992i	$0.136216\pi$
$38$	−4.97815e20	+	1.73414e20i	−0.234417	+	0.0816591i
$39$			2.74498e20i			0.0910262i
$40$	−3.17267e20	+	5.00266e20i	−0.0747506	+	0.117867i
$41$		−	9.82451e20i		−	0.165855i	−0.996556	−	0.0829276i	$-0.973573\pi$
$41$		−	9.82451e20i		−	0.165855i	0.996556	−	0.0829276i	$-0.0264270\pi$
$42$	4.82608e20	+	1.38541e21i	0.0588477	+	0.168933i
$43$	−1.30008e22	+	1.30008e22i	−1.15385	+	1.15385i	−0.168070	+	0.985775i	$0.553753\pi$
$43$	−1.30008e22	+	1.30008e22i	−1.15385	+	1.15385i	−0.985775	+	0.168070i	$0.946247\pi$
$44$	−5.02490e21	−	5.80375e20i	−0.326976	−	0.0377657i
$45$	1.99572e21	+	1.99572e21i	0.0958805	+	0.0958805i
$46$	−1.56279e22	−	7.55286e21i	−0.558044	−	0.269700i
$47$	−4.26559e22			−1.13935			−0.569676	−	0.821869i	$-0.692931\pi$
$47$	−4.26559e22			−1.13935			−0.569676	+	0.821869i	$0.692931\pi$
$48$	7.13409e21	−	4.42730e21i	0.143411	−	0.0889985i
$49$	−8.10557e21			−0.123349
$50$	−7.62024e22	−	3.68282e22i	−0.882823	−	0.426664i
$51$	−8.19477e21	−	8.19477e21i	−0.0726674	−	0.0726674i
$52$	−9.06962e21	+	7.85249e22i	−0.0618791	+	0.535750i
$53$	1.05894e23	−	1.05894e23i	0.558658	−	0.558658i	−0.370267	−	0.928925i	$-0.620734\pi$
$53$	1.05894e23	−	1.05894e23i	0.558658	−	0.558658i	0.928925	+	0.370267i	$0.120734\pi$
$54$	−2.67047e22	−	7.66605e22i	−0.109464	−	0.314236i
$55$			1.43578e22i			0.0459400i
$56$	9.22835e22	+	4.12268e23i	0.231518	+	1.03429i
$57$		−	2.12078e22i		−	0.0418973i
$58$	−1.31201e23	+	4.57040e22i	−0.204956	+	0.0713964i
$59$	2.50600e23	−	2.50600e23i	0.310799	−	0.310799i	−0.534420	−	0.845219i	$-0.679470\pi$
$59$	2.50600e23	−	2.50600e23i	0.310799	−	0.310799i	0.845219	+	0.534420i	$0.179470\pi$
$60$	−1.48071e22	−	1.86742e22i	−0.0146362	−	0.0184587i
$61$	2.69362e23	+	2.69362e23i	0.213002	+	0.213002i	0.805541	−	0.592540i	$-0.201875\pi$
$61$	2.69362e23	+	2.69362e23i	0.213002	+	0.213002i	−0.592540	+	0.805541i	$0.701875\pi$
$62$	6.70177e23	−	1.38668e24i	0.425502	−	0.880420i
$63$	2.01281e24			1.02969
$64$	2.18712e24	−	1.03079e24i	0.904570	−	0.426326i
$65$	2.24371e23			0.0752726
$66$	8.85509e22	−	1.83223e23i	0.0241741	−	0.0500193i
$67$	−1.96312e24	−	1.96312e24i	−0.437458	−	0.437458i	0.453698	−	0.891156i	$-0.350105\pi$
$67$	−1.96312e24	−	1.96312e24i	−0.437458	−	0.437458i	−0.891156	+	0.453698i	$0.850105\pi$
$68$	−2.07350e24	−	2.61502e24i	−0.378297	−	0.477095i
$69$	4.93771e23	−	4.93771e23i	0.0739712	−	0.0739712i
$70$	1.13242e24	−	3.94478e23i	0.139696	−	0.0486631i
$71$		−	3.69903e24i		−	0.376791i	−0.982093	−	0.188395i	$-0.939671\pi$
$71$		−	3.69903e24i		−	0.376791i	0.982093	−	0.188395i	$-0.0603286\pi$
$72$	−2.51632e24	−	1.12414e25i	−0.212215	−	0.948051i
$73$		−	1.22287e25i		−	0.856097i	−0.903756	−	0.428049i	$-0.859201\pi$
$73$		−	1.22287e25i		−	0.856097i	0.903756	−	0.428049i	$-0.140799\pi$
$74$	3.95137e24	+	1.13431e25i	0.230207	+	0.660851i
$75$	2.40766e24	−	2.40766e24i	0.117022	−	0.117022i
$76$	7.00724e23	−	6.06688e24i	0.0284815	−	0.246593i
$77$	7.24037e24	+	7.24037e24i	0.246681	+	0.246681i
$78$	−2.86326e24	−	1.38380e24i	−0.0819566	−	0.0396092i
$79$	3.63425e25			0.875889			0.437944	−	0.899002i	$-0.355707\pi$
$79$	3.63425e25			0.875889			0.437944	+	0.899002i	$0.355707\pi$
$80$	−3.61883e24	−	5.83133e24i	−0.0735958	−	0.118591i
$81$	−5.32273e25			−0.915349
$82$	1.02479e25	+	4.95274e24i	0.149330	+	0.0721703i
$83$	−8.16524e25	−	8.16524e25i	−1.01022	−	1.01022i	−0.999947	−	0.0102696i	$-0.996731\pi$
$83$	−8.16524e25	−	8.16524e25i	−1.01022	−	1.01022i	−0.0102696	−	0.999947i	$-0.503269\pi$
$84$	−1.68840e25	−	1.95011e24i	−0.177708	−	0.0205252i
$85$	−6.69831e24	+	6.69831e24i	−0.0600911	+	0.0600911i
$86$	−7.00708e25	−	2.01151e26i	−0.536794	−	1.54096i
$87$		−	5.58942e24i		−	0.0366317i
$88$	3.13854e25	−	4.94885e25i	0.176283	−	0.277964i
$89$		−	2.68126e26i		−	1.29293i	−0.762945	−	0.646463i	$-0.776247\pi$
$89$		−	2.68126e26i		−	1.29293i	0.762945	−	0.646463i	$-0.223753\pi$
$90$	−3.08780e25	+	1.07563e25i	−0.128049	+	0.0446057i
$91$	1.13146e26	−	1.13146e26i	0.404187	−	0.404187i
$92$	1.57567e26	−	1.24937e26i	0.485655	−	0.385085i
$93$	4.38131e25	+	4.38131e25i	0.116704	+	0.116704i
$94$	2.15037e26	−	4.44940e26i	0.495779	−	1.02583i
$95$	−1.73350e25			−0.0346462
$96$	1.02164e25	+	9.67341e25i	0.0177270	+	0.167849i
$97$	1.84751e25			0.0278721			0.0139360	−	0.999903i	$-0.495564\pi$
$97$	1.84751e25			0.0278721			0.0139360	+	0.999903i	$0.495564\pi$
$98$	4.08618e25	−	8.45485e25i	0.0536742	−	0.111059i
$99$	−1.97425e26	−	1.97425e26i	−0.226114	−	0.226114i
$100$	7.68304e26	−	6.09202e26i	0.768304	−	0.609202i
$101$	1.43550e27	−	1.43550e27i	1.25506	−	1.25506i	0.301637	−	0.953423i	$-0.402467\pi$
$101$	1.43550e27	−	1.43550e27i	1.25506	−	1.25506i	0.953423	−	0.301637i	$-0.0975332\pi$
$102$	1.26791e26	−	4.41674e25i	0.0970475	−	0.0338065i
$103$			4.16136e26i			0.279211i	0.990207	+	0.139606i	$0.0445835\pi$
$103$			4.16136e26i			0.279211i	−0.990207	+	0.139606i	$0.955417\pi$
$104$	−7.73365e26	−	4.90465e26i	−0.455443	−	0.288840i
$105$			4.82432e25i			0.0249678i
$106$	5.70736e26	+	1.63840e27i	0.259900	+	0.746089i
$107$	1.61351e27	−	1.61351e27i	0.647278	−	0.647278i	−0.305056	−	0.952334i	$-0.598675\pi$
$107$	1.61351e27	−	1.61351e27i	0.647278	−	0.647278i	0.952334	+	0.305056i	$0.0986753\pi$
$108$	9.34263e26	+	1.07907e26i	0.330559	+	0.0381795i
$109$	8.78792e25	+	8.78792e25i	0.0274554	+	0.0274554i	0.720701	−	0.693246i	$-0.243820\pi$
$109$	8.78792e25	+	8.78792e25i	0.0274554	+	0.0274554i	−0.693246	+	0.720701i	$0.743820\pi$
$110$	−1.49765e26	−	7.23805e25i	−0.0413626	−	0.0199903i
$111$	−4.83237e26			−0.118114
$112$	−4.76555e27	−	1.11572e27i	−1.03198	−	0.241609i
$113$	−8.03820e27			−1.54383			−0.771916	−	0.635725i	$-0.780701\pi$
$113$	−8.03820e27			−1.54383			−0.771916	+	0.635725i	$0.780701\pi$
$114$	2.21217e26	+	1.06913e26i	0.0377227	+	0.0182312i
$115$	−4.03603e26	−	4.03603e26i	−0.0611693	−	0.0611693i
$116$	1.84679e26	−	1.59895e27i	0.0249020	−	0.215602i
$117$	−3.08519e27	+	3.08519e27i	−0.370487	+	0.370487i
$118$	1.35066e27	+	3.87732e27i	0.144590	+	0.415073i
$119$			6.75569e27i			0.645335i
$120$	2.69435e26	−	6.03113e25i	0.0229883	−	0.00514578i
$121$			1.16897e28i			0.891660i
$122$	−4.16760e27	+	1.45178e27i	−0.284465	+	0.0990931i
$123$	−3.23787e26	+	3.23787e26i	−0.0197943	+	0.0197943i
$124$	1.10859e28	+	1.39811e28i	0.607544	+	0.766213i
$125$	−3.97508e27	−	3.97508e27i	−0.195461	−	0.195461i
$126$	−1.01470e28	+	2.09955e28i	−0.448059	+	0.927093i
$127$	−3.90825e27			−0.155107			−0.0775537	−	0.996988i	$-0.524711\pi$
$127$	−3.90825e27			−0.155107			−0.0775537	+	0.996988i	$0.524711\pi$
$128$	−2.73589e26	+	2.80100e28i	−0.00976706	+	0.999952i
$129$	8.56939e27			0.275416
$130$	−1.13110e27	+	2.34040e27i	−0.0327541	+	0.0677726i
$131$	9.69050e26	+	9.69050e26i	0.0253037	+	0.0253037i	0.719645	−	0.694342i	$-0.244304\pi$
$131$	9.69050e26	+	9.69050e26i	0.0253037	+	0.0253037i	−0.694342	+	0.719645i	$0.744304\pi$
$132$	1.46478e27	+	1.84733e27i	0.0345164	+	0.0435308i
$133$	−8.74176e27	+	8.74176e27i	−0.186038	+	0.186038i
$134$	3.03736e28	−	1.05806e28i	0.584227	−	0.203515i
$135$		−	2.66949e27i		−	0.0464433i
$136$	3.77300e28	−	8.44562e27i	0.594171	−	0.133001i
$137$		−	4.94336e28i		−	0.705172i	−0.935779	−	0.352586i	$-0.885302\pi$
$137$		−	4.94336e28i		−	0.705172i	0.935779	−	0.352586i	$-0.114698\pi$
$138$	2.66128e27	+	7.63968e27i	0.0344131	+	0.0987888i
$139$	−7.67653e28	+	7.67653e28i	−0.900462	+	0.900462i	−0.995476	−	0.0950144i	$-0.969710\pi$
$139$	−7.67653e28	+	7.67653e28i	−0.900462	+	0.900462i	0.0950144	+	0.995476i	$0.469710\pi$
$140$	−1.59399e27	+	1.38008e28i	−0.0169730	+	0.146952i
$141$	1.40581e28	+	1.40581e28i	0.135978	+	0.135978i
$142$	3.85843e28	+	1.86476e28i	0.339248	+	0.163957i
$143$	−2.21958e28			−0.177514
$144$	1.29943e29	+	3.04227e28i	0.945933	+	0.221465i
$145$	−4.56873e27			−0.0302920
$146$	1.27557e29	+	6.16476e28i	0.770798	+	0.372523i
$147$	2.67136e27	+	2.67136e27i	0.0147214	+	0.0147214i
$148$	−1.38239e29	−	1.59665e28i	−0.695178	−	0.0802930i
$149$	−1.10859e29	+	1.10859e29i	−0.509044	+	0.509044i	−0.914233	−	0.405189i	$-0.867206\pi$
$149$	−1.10859e29	+	1.10859e29i	−0.509044	+	0.509044i	0.405189	+	0.914233i	$0.367206\pi$
$150$	1.29766e28	+	3.72516e28i	0.0544413	+	0.156283i
$151$		−	4.24881e29i		−	1.62959i	−0.579750	−	0.814795i	$-0.696850\pi$
$151$		−	4.24881e29i		−	1.62959i	0.579750	−	0.814795i	$-0.303150\pi$
$152$	5.97506e28	+	3.78936e28i	0.209630	+	0.132946i
$153$		−	1.84209e29i		−	0.591530i
$154$	−1.12024e29	+	3.90235e28i	−0.329444	+	0.114762i
$155$	3.58123e28	−	3.58123e28i	0.0965060	−	0.0965060i
$156$	2.88686e28	−	2.28904e28i	0.0713252	−	0.0565551i
$157$	−4.14338e29	−	4.14338e29i	−0.939094	−	0.939094i	0.0591544	−	0.998249i	$-0.481160\pi$
$157$	−4.14338e29	−	4.14338e29i	−0.939094	−	0.939094i	−0.998249	+	0.0591544i	$0.981160\pi$
$158$	−1.83210e29	+	3.79085e29i	−0.381135	+	0.788617i
$159$	−6.97989e28			−0.133348
$160$	7.90693e28	−	8.35077e27i	0.138800	−	0.0146591i
$161$	−4.07060e29			−0.656914
$162$	2.68330e29	−	5.55210e29i	0.398306	−	0.824146i
$163$	−5.13776e29	−	5.13776e29i	−0.701845	−	0.701845i	0.262961	−	0.964806i	$-0.415301\pi$
$163$	−5.13776e29	−	5.13776e29i	−0.701845	−	0.701845i	−0.964806	+	0.262961i	$0.915301\pi$
$164$	−1.03323e29	+	8.19268e28i	−0.129959	+	0.103047i
$165$	4.73190e27	−	4.73190e27i	0.00548280	−	0.00548280i
$166$	1.26334e30	−	4.40083e29i	1.34915	−	0.469975i
$167$		−	8.93544e28i		−	0.0879921i	−0.999032	−	0.0439960i	$-0.985991\pi$
$167$		−	8.93544e28i		−	0.0879921i	0.999032	−	0.0439960i	$-0.0140089\pi$
$168$	1.05457e29	−	1.66285e29i	0.0958079	−	0.151070i
$169$		−	8.45676e29i		−	0.709143i
$170$	−3.61020e28	−	1.03637e29i	−0.0279557	−	0.0802518i
$171$	2.38364e29	−	2.38364e29i	0.170527	−	0.170527i
$172$	2.45143e30	+	2.83139e29i	1.62101	+	0.187226i
$173$	−4.52209e29	−	4.52209e29i	−0.276514	−	0.276514i	0.555202	−	0.831716i	$-0.312641\pi$
$173$	−4.52209e29	−	4.52209e29i	−0.276514	−	0.276514i	−0.831716	+	0.555202i	$0.812641\pi$
$174$	5.83028e28	+	2.81774e28i	0.0329818	+	0.0159399i
$175$	−1.98485e30			−1.03923
$176$	3.57990e29	+	5.76860e29i	0.173560	+	0.279672i
$177$	−1.65181e29			−0.0741858
$178$	2.79680e30	+	1.35168e30i	1.16410	+	0.562605i
$179$	−1.97214e30	−	1.97214e30i	−0.761064	−	0.761064i	0.215451	−	0.976515i	$-0.430878\pi$
$179$	−1.97214e30	−	1.97214e30i	−0.761064	−	0.761064i	−0.976515	+	0.215451i	$0.930878\pi$
$180$	4.34638e28	−	3.76311e29i	0.0155578	−	0.134700i
$181$	3.02766e30	−	3.02766e30i	1.00565	−	1.00565i	0.00566486	−	0.999984i	$-0.498197\pi$
$181$	3.02766e30	−	3.02766e30i	1.00565	−	1.00565i	0.999984	−	0.00566486i	$-0.00180319\pi$
$182$	6.09827e29	+	1.75062e30i	0.188037	+	0.539793i
$183$		−	1.77547e29i		−	0.0508422i
$184$	5.08886e29	+	2.27340e30i	0.135388	+	0.604832i
$185$			3.94993e29i			0.0976722i
$186$	−6.77881e29	+	2.36140e29i	−0.155858	+	0.0542931i
$187$	6.62626e29	−	6.62626e29i	0.141712	−	0.141712i
$188$	3.55709e30	+	4.48607e30i	0.707886	+	0.892761i
$189$	−1.34618e30	−	1.34618e30i	−0.249384	−	0.249384i
$190$	8.73895e28	−	1.80820e29i	0.0150760	−	0.0311942i
$191$	−6.07002e30			−0.975528			−0.487764	−	0.872975i	$-0.662187\pi$
$191$	−6.07002e30			−0.975528			−0.487764	+	0.872975i	$0.662187\pi$
$192$	−1.06053e30	−	3.81090e29i	−0.158838	−	0.0570770i
$193$	−1.28234e31			−1.79053			−0.895263	−	0.445538i	$-0.853012\pi$
$193$	−1.28234e31			−1.79053			−0.895263	+	0.445538i	$0.853012\pi$
$194$	−9.31370e28	+	1.92713e29i	−0.0121283	+	0.0250950i
$195$	−7.39461e28	−	7.39461e28i	−0.00898356	−	0.00898356i
$196$	6.75925e29	+	8.52452e29i	0.0766375	+	0.0966525i
$197$	−9.66074e30	+	9.66074e30i	−1.02262	+	1.02262i	−0.0228865	+	0.999738i	$0.507286\pi$
$197$	−9.66074e30	+	9.66074e30i	−1.02262	+	1.02262i	−0.999738	+	0.0228865i	$0.992714\pi$
$198$	3.05458e30	−	1.06406e30i	0.301976	−	0.105193i
$199$			5.43325e30i			0.501814i	0.968011	+	0.250907i	$0.0807289\pi$
$199$			5.43325e30i			0.501814i	−0.968011	+	0.250907i	$0.919271\pi$
$200$	2.48136e30	+	1.10852e31i	0.214183	+	0.956841i
$201$			1.29397e30i			0.104419i
$202$	7.73692e30	+	2.22102e31i	0.583882	+	1.67614i
$203$	−2.30393e30	+	2.30393e30i	−0.162657	+	0.162657i
$204$	−1.78470e29	+	1.54520e30i	−0.0117912	+	0.102089i
$205$	2.64660e29	+	2.64660e29i	0.0163686	+	0.0163686i
$206$	−4.34068e30	−	2.09783e30i	−0.251391	−	0.121496i
$207$	1.10994e31			0.602143
$208$	9.01468e30	−	5.59437e30i	0.458243	−	0.284378i
$209$	1.71486e30			0.0817058
$210$	−5.03221e29	−	2.43204e29i	−0.0224801	−	0.0108645i
$211$	−1.07638e31	−	1.07638e31i	−0.450976	−	0.450976i	0.444702	−	0.895678i	$-0.353309\pi$
$211$	−1.07638e31	−	1.07638e31i	−0.450976	−	0.450976i	−0.895678	+	0.444702i	$0.853309\pi$
$212$	−1.99672e31	−	2.30621e30i	−0.784844	−	0.0906494i
$213$	−1.21909e30	+	1.21909e30i	−0.0449688	+	0.0449688i
$214$	8.69635e30	+	2.49644e31i	0.301128	+	0.864442i
$215$		−	7.00452e30i		−	0.227751i
$216$	−5.83538e30	+	9.20123e30i	−0.178215	+	0.281009i
$217$		−	3.61191e31i		−	1.03641i
$218$	−1.35968e30	+	4.73643e29i	−0.0366668	+	0.0127729i
$219$	−4.03023e30	+	4.03023e30i	−0.102173	+	0.102173i
$220$	1.50999e30	−	1.19730e30i	0.0359971	−	0.0285428i
$221$	−1.03550e31	−	1.03550e31i	−0.232195	−	0.232195i
$222$	2.43610e30	−	5.04061e30i	0.0513961	−	0.106345i
$223$	−1.55403e31			−0.308563			−0.154281	−	0.988027i	$-0.549306\pi$
$223$	−1.55403e31			−0.308563			−0.154281	+	0.988027i	$0.549306\pi$
$224$	3.56621e31	−	4.40844e31i	0.666590	−	0.824018i
$225$	5.41214e31			0.952587
$226$	4.05222e31	−	8.38458e31i	0.671784	−	1.39001i
$227$	3.81035e31	+	3.81035e31i	0.595135	+	0.595135i	0.939014	−	0.343879i	$-0.111741\pi$
$227$	3.81035e31	+	3.81035e31i	0.595135	+	0.595135i	−0.343879	+	0.939014i	$0.611741\pi$
$228$	−2.23040e30	+	1.76853e30i	−0.0328294	+	0.0260310i
$229$	2.60208e31	−	2.60208e31i	0.361028	−	0.361028i	−0.503163	−	0.864191i	$-0.667831\pi$
$229$	2.60208e31	−	2.60208e31i	0.361028	−	0.361028i	0.864191	+	0.503163i	$0.167831\pi$
$230$	6.24459e30	−	2.17530e30i	0.0816917	−	0.0284573i
$231$		−	4.77243e30i		−	0.0588813i
$232$	1.57475e31	+	9.98703e30i	0.183284	+	0.116238i
$233$			1.75984e31i			0.193272i	0.995320	+	0.0966358i	$0.0308082\pi$
$233$			1.75984e31i			0.193272i	−0.995320	+	0.0966358i	$0.969192\pi$
$234$	−1.66283e31	−	4.77345e31i	−0.172359	−	0.494787i
$235$	1.14910e31	−	1.14910e31i	0.112445	−	0.112445i
$236$	−4.72529e31	−	5.45771e30i	−0.436633	−	0.0504311i
$237$	−1.19774e31	−	1.19774e31i	−0.104535	−	0.104535i
$238$	−7.04680e31	−	3.40568e31i	−0.581036	−	0.280812i
$239$	4.27604e31			0.333173			0.166587	−	0.986027i	$-0.446725\pi$
$239$	4.27604e31			0.333173			0.166587	+	0.986027i	$0.446725\pi$
$240$	−7.29174e29	+	3.11449e30i	−0.00537007	+	0.0229369i
$241$	−7.70917e31			−0.536757			−0.268379	−	0.963314i	$-0.586488\pi$
$241$	−7.70917e31			−0.536757			−0.268379	+	0.963314i	$0.586488\pi$
$242$	−1.21934e32	−	5.89300e31i	−0.802818	−	0.387997i
$243$	5.53251e31	+	5.53251e31i	0.344538	+	0.344538i
$244$	5.86631e30	−	5.07906e31i	0.0345623	−	0.299241i
$245$	2.18354e30	−	2.18354e30i	0.0121736	−	0.0121736i
$246$	−1.74512e30	−	5.00967e30i	−0.00920875	−	0.0264354i
$247$		−	2.67983e31i		−	0.133875i
$248$	−2.01722e32	+	4.51542e31i	−0.954236	+	0.213600i
$249$			5.38204e31i			0.241133i
$250$	6.15030e31	−	2.14245e31i	0.261039	−	0.0909330i
$251$	1.33650e32	−	1.33650e32i	0.537492	−	0.537492i	−0.385299	−	0.922792i	$-0.625902\pi$
$251$	1.33650e32	−	1.33650e32i	0.537492	−	0.537492i	0.922792	+	0.385299i	$0.125902\pi$
$252$	−1.67849e32	−	2.11685e32i	−0.639751	−	0.806831i
$253$	3.99261e31	+	3.99261e31i	0.144255	+	0.144255i
$254$	1.97023e31	−	4.07667e31i	0.0674935	−	0.139653i
$255$	4.41513e30			0.0143434
$256$	−2.90791e32	−	1.44058e32i	−0.896070	−	0.443914i
$257$	1.37592e32			0.402249			0.201125	−	0.979566i	$-0.435540\pi$
$257$	1.37592e32			0.402249			0.201125	+	0.979566i	$0.435540\pi$
$258$	−4.32001e31	+	8.93866e31i	−0.119845	+	0.247974i
$259$	1.99188e32	+	1.99188e32i	0.524465	+	0.524465i
$260$	−1.87104e31	−	2.35968e31i	−0.0467673	−	0.0589812i
$261$	6.28219e31	−	6.28219e31i	0.149095	−	0.149095i
$262$	−1.49933e31	+	5.22290e30i	−0.0337931	+	0.0117718i
$263$			7.01364e32i			1.50155i	0.660556	+	0.750777i	$0.270321\pi$
$263$			7.01364e32i			1.50155i	−0.660556	+	0.750777i	$0.729679\pi$
$264$	−2.66536e31	+	5.96625e30i	−0.0542130	+	0.0121352i
$265$			5.70528e31i			0.110270i
$266$	−4.71155e31	−	1.35254e32i	−0.0865490	−	0.248454i
$267$	−8.83664e31	+	8.83664e31i	−0.154307	+	0.154307i
$268$	−4.27538e31	+	3.70163e32i	−0.0709832	+	0.614573i
$269$	6.36975e32	+	6.36975e32i	1.00570	+	1.00570i	0.999984	+	0.00571206i	$0.00181821\pi$
$269$	6.36975e32	+	6.36975e32i	1.00570	+	1.00570i	0.00571206	+	0.999984i	$0.498182\pi$
$270$	2.78453e31	+	1.34575e31i	0.0418158	+	0.0202094i
$271$	7.56447e32			1.08067			0.540335	−	0.841450i	$-0.318298\pi$
$271$	7.56447e32			1.08067			0.540335	+	0.841450i	$0.318298\pi$
$272$	−1.02109e32	+	4.36135e32i	−0.138798	+	0.592844i
$273$	−7.45795e31			−0.0964770
$274$	5.15638e32	+	2.49205e32i	0.634910	+	0.306849i
$275$	1.94682e32	+	1.94682e32i	0.228210	+	0.228210i
$276$	−9.31050e31	−	1.07536e31i	−0.103920	−	0.0120028i
$277$	1.92129e32	−	1.92129e32i	0.204229	−	0.204229i	−0.597580	−	0.801809i	$-0.703871\pi$
$277$	1.92129e32	−	1.92129e32i	0.204229	−	0.204229i	0.801809	+	0.597580i	$0.203871\pi$
$278$	−4.13743e32	−	1.18772e33i	−0.418915	−	1.20257i
$279$			9.84867e32i			0.949994i
$280$	−1.35920e32	−	8.61996e31i	−0.124925	−	0.0792268i
$281$		−	9.16183e32i		−	0.802503i	−0.915968	−	0.401252i	$-0.868575\pi$
$281$		−	9.16183e32i		−	0.802503i	0.915968	−	0.401252i	$-0.131425\pi$
$282$	−2.17509e32	+	7.57693e31i	−0.181600	+	0.0632601i
$283$	−6.94410e32	+	6.94410e32i	−0.552712	+	0.552712i	−0.927223	−	0.374511i	$-0.877811\pi$
$283$	−6.94410e32	+	6.94410e32i	−0.552712	+	0.552712i	0.374511	+	0.927223i	$0.377811\pi$
$284$	−3.89022e32	+	3.08463e32i	−0.295241	+	0.234102i
$285$	5.71312e30	+	5.71312e30i	0.00413492	+	0.00413492i
$286$	1.11893e32	−	2.31522e32i	0.0772437	−	0.159827i
$287$	2.66927e32			0.175787
$288$	−9.72408e32	+	1.20206e33i	−0.611013	+	0.755315i
$289$	−1.04944e33			−0.629271
$290$	2.30319e31	−	4.76560e31i	0.0131813	−	0.0272738i
$291$	−6.08886e30	−	6.08886e30i	−0.00332645	−	0.00332645i
$292$	−1.28608e33	+	1.01976e33i	−0.670811	+	0.531898i
$293$	−2.36830e32	+	2.36830e32i	−0.117957	+	0.117957i	−0.763621	−	0.645664i	$-0.776581\pi$
$293$	−2.36830e32	+	2.36830e32i	−0.117957	+	0.117957i	0.645664	+	0.763621i	$0.276581\pi$
$294$	−4.13315e31	+	1.43978e31i	−0.0196604	+	0.00684870i
$295$			1.35017e32i			0.0613467i
$296$	8.63435e32	−	1.36146e33i	0.374793	−	0.590974i
$297$			2.64078e32i			0.109527i
$298$	−5.97497e32	−	1.71522e33i	−0.236819	−	0.679830i
$299$	6.23932e32	−	6.23932e32i	0.236361	−	0.236361i
$300$	−4.53986e32	−	5.24353e31i	−0.164401	−	0.0189883i
$301$	−3.53226e33	−	3.53226e33i	−1.22294	−	1.22294i
$302$	4.43189e33	+	2.14191e33i	1.46722	+	0.709100i
$303$	−9.46197e32			−0.299575
$304$	−6.96479e32	+	4.32224e32i	−0.210919	+	0.130893i
$305$	−1.45125e32			−0.0420431
$306$	1.92147e33	+	9.28635e32i	0.532591	+	0.257399i
$307$	2.77134e33	+	2.77134e33i	0.735057	+	0.735057i	0.971617	−	0.236560i	$-0.0760198\pi$
$307$	2.77134e33	+	2.77134e33i	0.735057	+	0.735057i	−0.236560	+	0.971617i	$0.576020\pi$
$308$	1.57685e32	−	1.36524e33i	0.0400272	−	0.346556i
$309$	1.37146e32	−	1.37146e32i	0.0333230	−	0.0333230i
$310$	1.93018e32	+	5.54092e32i	0.0448967	+	0.128884i
$311$		−	2.46792e33i		−	0.549624i	−0.961498	−	0.274812i	$-0.911384\pi$
$311$		−	2.46792e33i		−	0.549624i	0.961498	−	0.274812i	$-0.0886156\pi$
$312$	9.32356e31	+	4.16521e32i	0.0198836	+	0.0888280i
$313$		−	4.53667e33i		−	0.926592i	−0.886204	−	0.463296i	$-0.846667\pi$
$313$		−	4.53667e33i		−	0.926592i	0.886204	−	0.463296i	$-0.153333\pi$
$314$	6.41068e33	−	2.23316e33i	1.25416	−	0.436888i
$315$	−5.42226e32	+	5.42226e32i	−0.101622	+	0.101622i
$316$	−3.03061e33	−	3.82210e33i	−0.544195	−	0.686319i
$317$	−6.57166e33	−	6.57166e33i	−1.13077	−	1.13077i	−0.990049	−	0.140723i	$-0.955057\pi$
$317$	−6.57166e33	−	6.57166e33i	−1.13077	−	1.13077i	−0.140723	−	0.990049i	$-0.544943\pi$
$318$	3.51871e32	−	7.28067e32i	0.0580252	−	0.120062i
$319$	4.51959e32			0.0714372
$320$	−3.11499e32	+	8.66863e32i	−0.0471988	+	0.131349i
$321$	−1.06353e33			−0.154501
$322$	2.05207e33	−	4.24600e33i	0.285850	−	0.591461i
$323$	8.00030e32	+	8.00030e32i	0.106874	+	0.106874i
$324$	4.43864e33	+	5.59785e33i	0.568712	+	0.717239i
$325$	3.04233e33	−	3.04233e33i	0.373922	−	0.373922i
$326$	7.94920e33	−	2.76910e33i	0.937316	−	0.326514i
$327$		−	5.79248e31i		−	0.00655345i
$328$	−3.33698e32	−	1.49076e33i	−0.0362291	−	0.161850i
$329$		−	1.15894e34i		−	1.20758i
$330$	2.55036e31	+	7.32125e31i	0.00255072	+	0.00732229i
$331$	1.65630e33	−	1.65630e33i	0.159023	−	0.159023i	−0.623111	−	0.782134i	$-0.714131\pi$
$331$	1.65630e33	−	1.65630e33i	0.159023	−	0.159023i	0.782134	+	0.623111i	$0.214131\pi$
$332$	−1.77827e33	+	1.53963e34i	−0.163921	+	1.41923i
$333$	−5.43131e33	−	5.43131e33i	−0.480737	−	0.480737i
$334$	9.32048e32	+	4.50454e32i	0.0792248	+	0.0382889i
$335$	1.05768e33			0.0863472
$336$	1.20287e33	+	1.93829e33i	0.0943279	+	0.151999i
$337$	−7.21385e33			−0.543455			−0.271727	−	0.962374i	$-0.587595\pi$
$337$	−7.21385e33			−0.543455			−0.271727	+	0.962374i	$0.587595\pi$
$338$	8.82118e33	+	4.26323e33i	0.638486	+	0.308577i
$339$	2.64915e33	+	2.64915e33i	0.184252	+	0.184252i
$340$	1.26303e33	+	1.45880e32i	0.0844204	+	0.00975055i
$341$	−3.54271e33	+	3.54271e33i	−0.227589	+	0.227589i
$342$	1.28471e33	+	3.68799e33i	0.0793328	+	0.227739i
$343$			1.56515e34i			0.929146i
$344$	−1.53115e34	+	2.41433e34i	−0.873937	+	1.37802i
$345$			2.66031e32i			0.0146007i
$346$	6.99664e33	−	2.43728e33i	0.369285	−	0.128640i
$347$	−2.17247e34	+	2.17247e34i	−1.10282	+	1.10282i	−0.108756	+	0.994068i	$0.534687\pi$
$347$	−2.17247e34	+	2.17247e34i	−1.10282	+	1.10282i	−0.994068	+	0.108756i	$0.965313\pi$
$348$	−5.87833e32	+	4.66103e32i	−0.0287034	+	0.0227595i
$349$	−1.27630e34	−	1.27630e34i	−0.599526	−	0.599526i	0.340660	−	0.940186i	$-0.389349\pi$
$349$	−1.27630e34	−	1.27630e34i	−0.599526	−	0.599526i	−0.940186	+	0.340660i	$0.889349\pi$
$350$	1.00060e34	−	2.07038e34i	0.452213	−	0.935688i
$351$	4.12679e33			0.179459
$352$	−7.82188e33	+	8.26094e32i	−0.327329	+	0.0345703i
$353$	−2.91455e34			−1.17385			−0.586925	−	0.809641i	$-0.699662\pi$
$353$	−2.91455e34			−1.17385			−0.586925	+	0.809641i	$0.699662\pi$
$354$	8.32711e32	−	1.72299e33i	0.0322812	−	0.0667941i
$355$	9.96471e32	+	9.96471e32i	0.0371862	+	0.0371862i
$356$	−2.81985e34	+	2.23591e34i	−1.01310	+	0.803303i
$357$	2.22648e33	−	2.22648e33i	0.0770188	−	0.0770188i
$358$	3.05131e34	−	1.06292e34i	1.01640	−	0.354064i
$359$			4.76762e34i			1.52942i	0.644375	+	0.764710i	$0.277118\pi$
$359$			4.76762e34i			1.52942i	−0.644375	+	0.764710i	$0.722882\pi$
$360$	3.70615e33	+	2.35043e33i	0.114509	+	0.0726211i
$361$		−	3.15302e34i		−	0.938380i
$362$	1.63182e34	+	4.68443e34i	0.467850	+	1.34305i
$363$	3.85257e33	−	3.85257e33i	0.106417	−	0.106417i
$364$	−2.13348e34	−	2.46417e33i	−0.567832	−	0.0655845i
$365$	3.29427e33	+	3.29427e33i	0.0844899	+	0.0844899i
$366$	1.85198e33	+	8.95053e32i	0.0457765	+	0.0221235i
$367$	3.17989e34			0.757566			0.378783	−	0.925486i	$-0.376343\pi$
$367$	3.17989e34			0.757566			0.378783	+	0.925486i	$0.376343\pi$
$368$	−2.62790e34	−	6.15252e33i	−0.603481	−	0.141289i
$369$	−7.27835e33			−0.161130
$370$	−4.12014e33	−	1.99124e33i	−0.0879404	−	0.0425011i
$371$	2.87708e34	+	2.87708e34i	0.592111	+	0.592111i
$372$	9.54185e32	−	8.26135e33i	0.0189366	−	0.163954i
$373$	2.63701e34	−	2.63701e34i	0.504711	−	0.504711i	−0.408187	−	0.912898i	$-0.633839\pi$
$373$	2.63701e34	−	2.63701e34i	0.504711	−	0.504711i	0.912898	+	0.408187i	$0.133839\pi$
$374$	3.57136e33	+	1.02522e34i	0.0659276	+	0.189257i
$375$			2.62014e33i			0.0466555i
$376$	−6.47258e34	+	1.44885e34i	−1.11184	+	0.248878i
$377$		−	7.06283e33i		−	0.117050i
$378$	2.08282e34	−	7.25551e33i	0.333053	−	0.116019i
$379$	1.01154e34	−	1.01154e34i	0.156082	−	0.156082i	−0.624746	−	0.780828i	$-0.714797\pi$
$379$	1.01154e34	−	1.01154e34i	0.156082	−	0.156082i	0.780828	+	0.624746i	$0.214797\pi$
$380$	1.44557e33	+	1.82310e33i	0.0215259	+	0.0271477i
$381$	1.28805e33	+	1.28805e33i	0.0185116	+	0.0185116i
$382$	3.06002e34	−	6.33159e34i	0.424492	−	0.878329i
$383$	5.14162e34			0.688520			0.344260	−	0.938874i	$-0.388130\pi$
$383$	5.14162e34			0.688520			0.344260	+	0.938874i	$0.388130\pi$
$384$	9.32145e33	−	9.14112e33i	0.120507	−	0.118176i
$385$	−3.90093e33			−0.0486909
$386$	6.46456e34	−	1.33760e35i	0.779130	−	1.61212i
$387$	9.63150e34	+	9.63150e34i	1.12097	+	1.12097i
$388$	−1.54065e33	−	1.94301e33i	−0.0173171	−	0.0218397i
$389$	1.04864e34	−	1.04864e34i	0.113843	−	0.113843i	−0.647890	−	0.761734i	$-0.724348\pi$
$389$	1.04864e34	−	1.04864e34i	0.113843	−	0.113843i	0.761734	+	0.647890i	$0.224348\pi$
$390$	1.14410e33	−	3.98548e32i	0.0119976	−	0.00417935i
$391$			3.72534e34i			0.377381i
$392$	−1.22993e34	+	2.75313e33i	−0.120370	+	0.0269441i
$393$		−	6.38741e32i		−	0.00603984i
$394$	−5.20686e34	−	1.49472e35i	−0.475748	−	1.36572i
$395$	−9.79020e33	+	9.79020e33i	−0.0864432	+	0.0864432i
$396$	−4.29963e33	+	3.72263e34i	−0.0366899	+	0.317661i
$397$	−1.24235e35	−	1.24235e35i	−1.02464	−	1.02464i	−0.999689	−	0.0249500i	$-0.992057\pi$
$397$	−1.24235e35	−	1.24235e35i	−1.02464	−	1.02464i	−0.0249500	−	0.999689i	$-0.507943\pi$
$398$	−5.66738e34	−	2.73901e34i	−0.451815	−	0.218360i
$399$	5.76205e33			0.0444061
$400$	−1.28138e35	−	3.00001e34i	−0.954703	−	0.223518i
$401$	1.20822e35			0.870359			0.435180	−	0.900344i	$-0.356685\pi$
$401$	1.20822e35			0.870359			0.435180	+	0.900344i	$0.356685\pi$
$402$	−1.34973e34	−	6.52318e33i	−0.0940146	−	0.0454368i
$403$	5.53625e34	+	5.53625e34i	0.372904	+	0.372904i
$404$	−2.70676e35	−	3.12631e34i	−1.76320	−	0.203650i
$405$	1.43388e34	−	1.43388e34i	0.0903376	−	0.0903376i
$406$	−1.24175e34	−	3.56467e34i	−0.0756717	−	0.217229i
$407$		−	3.90744e34i		−	0.230339i
$408$	−1.52181e34	−	9.65127e33i	−0.0867859	−	0.0550392i
$409$		−	2.18216e35i		−	1.20398i	−0.798502	−	0.601992i	$-0.794374\pi$
$409$		−	2.18216e35i		−	1.20398i	0.798502	−	0.601992i	$-0.205626\pi$
$410$	−4.09485e33	+	1.42644e33i	−0.0218603	+	0.00761502i
$411$	−1.62919e34	+	1.62919e34i	−0.0841601	+	0.0841601i
$412$	4.37645e34	−	3.47017e34i	0.218781	−	0.173476i
$413$	6.80867e34	+	6.80867e34i	0.329410	+	0.329410i
$414$	−5.59543e34	+	1.15777e35i	−0.262017	+	0.542147i
$415$	4.39922e34			0.199401
$416$	1.29095e34	+	1.22234e35i	0.0566434	+	0.536329i
$417$	5.05992e34			0.214935
$418$	−8.64494e33	+	1.78875e34i	−0.0355535	+	0.0735649i
$419$	1.06185e35	+	1.06185e35i	0.422839	+	0.422839i	0.886180	−	0.463341i	$-0.153349\pi$
$419$	1.06185e35	+	1.06185e35i	0.422839	+	0.422839i	−0.463341	+	0.886180i	$0.653349\pi$
$420$	5.07368e33	−	4.02301e33i	0.0195640	−	0.0155127i
$421$	1.59527e34	−	1.59527e34i	0.0595699	−	0.0595699i	−0.676694	−	0.736264i	$-0.736588\pi$
$421$	1.59527e34	−	1.59527e34i	0.0595699	−	0.0595699i	0.736264	+	0.676694i	$0.236588\pi$
$422$	1.66539e35	−	5.80139e34i	0.602280	−	0.209804i
$423$			3.16011e35i			1.10690i
$424$	1.24715e35	−	1.96650e35i	0.423135	−	0.667199i
$425$			1.81650e35i			0.597014i
$426$	−6.57055e33	−	1.88619e34i	−0.0209205	−	0.0600560i
$427$	−7.31841e34	+	7.31841e34i	−0.225757	+	0.225757i
$428$	−3.04242e35	−	3.51399e34i	−0.909344	−	0.105029i
$429$	7.31507e33	+	7.31507e33i	0.0211858	+	0.0211858i
$430$	7.30636e34	+	3.53112e34i	0.205058	+	0.0991035i
$431$	1.75558e35			0.477504			0.238752	−	0.971081i	$-0.423262\pi$
$431$	1.75558e35			0.477504			0.238752	+	0.971081i	$0.423262\pi$
$432$	−6.65599e34	−	1.07254e35i	−0.175462	−	0.282736i
$433$	−5.02623e35			−1.28427			−0.642134	−	0.766592i	$-0.721951\pi$
$433$	−5.02623e35			−1.28427			−0.642134	+	0.766592i	$0.721951\pi$
$434$	3.76755e35	+	1.82084e35i	0.933141	+	0.450982i
$435$	1.50572e33	+	1.50572e33i	0.00361526	+	0.00361526i
$436$	1.91388e33	−	1.65704e34i	0.00445500	−	0.0385714i
$437$	−4.82053e34	+	4.82053e34i	−0.108792	+	0.108792i
$438$	−2.17218e34	−	6.23562e34i	−0.0475330	−	0.136452i
$439$		−	2.07452e35i		−	0.440196i	−0.975478	−	0.220098i	$-0.929362\pi$
$439$		−	2.07452e35i		−	0.440196i	0.975478	−	0.220098i	$-0.0706377\pi$
$440$	4.87674e33	+	2.17864e34i	0.0100350	+	0.0448305i
$441$			6.00490e34i			0.119835i
$442$	1.60213e35	−	5.58103e34i	0.310097	−	0.108022i
$443$	1.45875e35	−	1.45875e35i	0.273861	−	0.273861i	−0.556792	−	0.830652i	$-0.687968\pi$
$443$	1.45875e35	−	1.45875e35i	0.273861	−	0.273861i	0.830652	+	0.556792i	$0.187968\pi$
$444$	4.02973e34	+	5.08215e34i	0.0733847	+	0.0925502i
$445$	7.22297e34	+	7.22297e34i	0.127601	+	0.127601i
$446$	7.83418e34	−	1.62099e35i	0.134268	−	0.277818i
$447$	7.30716e34			0.121506
$448$	2.80061e35	+	5.94227e35i	0.451855	+	0.958737i
$449$	−1.58886e35			−0.248749			−0.124374	−	0.992235i	$-0.539692\pi$
$449$	−1.58886e35			−0.248749			−0.124374	+	0.992235i	$0.539692\pi$
$450$	−2.72837e35	+	5.64535e35i	−0.414509	+	0.857674i
$451$	−2.61813e34	−	2.61813e34i	−0.0386018	−	0.0386018i
$452$	6.70307e35	+	8.45368e35i	0.959191	+	1.20970i
$453$	−1.40028e35	+	1.40028e35i	−0.194487	+	0.194487i
$454$	−5.89542e35	+	2.05367e35i	−0.794805	+	0.276870i
$455$			6.09604e34i			0.0797800i
$456$	−7.20343e33	−	3.21806e34i	−0.00915196	−	0.0408855i
$457$		−	4.37733e35i		−	0.539934i	−0.962870	−	0.269967i	$-0.912987\pi$
$457$		−	4.37733e35i		−	0.539934i	0.962870	−	0.269967i	$-0.0870129\pi$
$458$	1.40244e35	+	4.02597e35i	0.167958	+	0.482154i
$459$	−1.23200e35	+	1.23200e35i	−0.143265	+	0.143265i
$460$	−8.78988e33	+	7.61029e34i	−0.00992550	+	0.0859351i
$461$	5.18659e35	+	5.18659e35i	0.568747	+	0.568747i	0.931777	−	0.363030i	$-0.118258\pi$
$461$	5.18659e35	+	5.18659e35i	0.568747	+	0.568747i	−0.363030	+	0.931777i	$0.618258\pi$
$462$	4.97808e34	+	2.40588e34i	0.0530145	+	0.0256216i
$463$	−1.07568e36			−1.11260			−0.556300	−	0.830982i	$-0.687779\pi$
$463$	−1.07568e36			−1.11260			−0.556300	+	0.830982i	$0.687779\pi$
$464$	−1.83560e35	+	1.13915e35i	−0.184411	+	0.114442i
$465$	−2.36054e34			−0.0230354
$466$	−1.83567e35	−	8.87171e34i	−0.174014	−	0.0841003i
$467$	−1.42282e36	−	1.42282e36i	−1.31030	−	1.31030i	−0.921190	−	0.389113i	$-0.872782\pi$
$467$	−1.42282e36	−	1.42282e36i	−1.31030	−	1.31030i	−0.389113	−	0.921190i	$-0.627218\pi$
$468$	5.81741e35	+	6.71910e34i	0.520488	+	0.0601163i
$469$	5.33368e35	−	5.33368e35i	0.463654	−	0.463654i
$470$	6.19329e34	+	1.77790e35i	0.0523119	+	0.150171i
$471$			2.73107e35i			0.224156i
$472$	2.95140e35	−	4.65378e35i	0.235403	−	0.371183i
$473$			6.92918e35i			0.537101i
$474$	1.85316e35	−	6.45548e34i	0.139606	−	0.0486319i
$475$	−2.35052e35	+	2.35052e35i	−0.172108	+	0.172108i
$476$	7.10487e35	−	5.63358e35i	0.505664	−	0.400951i
$477$	−7.84499e35	−	7.84499e35i	−0.542743	−	0.542743i
$478$	−2.15564e35	+	4.46030e35i	−0.144977	+	0.299977i
$479$	−1.77534e36			−1.16079			−0.580394	−	0.814336i	$-0.697101\pi$
$479$	−1.77534e36			−1.16079			−0.580394	+	0.814336i	$0.697101\pi$
$480$	−2.88111e34	−	2.33068e34i	−0.0183148	−	0.0148158i
$481$	−6.10622e35			−0.377410
$482$	3.88635e35	−	8.04137e35i	0.233565	−	0.483276i
$483$	1.34155e35	+	1.34155e35i	0.0784008	+	0.0784008i
$484$	1.22939e36	−	9.74804e35i	0.698677	−	0.553994i
$485$	−4.97697e33	+	4.97697e33i	−0.00275075	+	0.00275075i
$486$	−8.55997e35	+	2.98186e35i	−0.460132	+	0.160287i
$487$		−	3.44720e36i		−	1.80229i	−0.433515	−	0.901146i	$-0.642727\pi$
$487$		−	3.44720e36i		−	1.80229i	0.433515	−	0.901146i	$-0.357273\pi$
$488$	5.00219e35	+	3.17237e35i	0.254386	+	0.161330i
$489$			3.38651e35i			0.167526i
$490$	1.17686e34	+	3.37839e34i	0.00566342	+	0.0162578i
$491$	1.23849e36	−	1.23849e36i	0.579819	−	0.579819i	−0.355034	−	0.934853i	$-0.615531\pi$
$491$	1.23849e36	−	1.23849e36i	0.579819	−	0.579819i	0.934853	+	0.355034i	$0.115531\pi$
$492$	6.10529e34	+	7.05161e33i	0.0278085	+	0.00321188i
$493$	2.10852e35	+	2.10852e35i	0.0934424	+	0.0934424i
$494$	2.79531e35	+	1.35096e35i	0.120536	+	0.0582544i
$495$	1.06368e35			0.0446313
$496$	5.45923e35	−	2.33178e36i	0.222910	−	0.952105i
$497$	1.00501e36			0.399354
$498$	−5.61396e35	−	2.71320e35i	−0.217107	−	0.104927i
$499$	−1.72024e35	−	1.72024e35i	−0.0647488	−	0.0647488i	0.673991	−	0.738740i	$-0.264579\pi$
$499$	−1.72024e35	−	1.72024e35i	−0.0647488	−	0.0647488i	−0.738740	+	0.673991i	$0.764579\pi$
$500$	−8.65715e34	+	7.49538e35i	−0.0317161	+	0.274599i
$501$	−2.94486e34	+	2.94486e34i	−0.0105016	+	0.0105016i
$502$	7.20332e35	+	2.06784e36i	0.250053	+	0.717823i
$503$		−	5.63157e36i		−	1.90310i	−0.307494	−	0.951550i	$-0.599490\pi$
$503$		−	5.63157e36i		−	1.90310i	0.307494	−	0.951550i	$-0.400510\pi$
$504$	3.05423e36	−	6.83670e35i	1.00482	−	0.224923i
$505$			7.73410e35i			0.247729i
$506$	−6.17742e35	+	2.15190e35i	−0.192653	+	0.0671105i
$507$	−2.78710e35	+	2.78710e35i	−0.0846341	+	0.0846341i
$508$	3.25910e35	+	4.11026e35i	0.0963691	+	0.121537i
$509$	2.78787e36	+	2.78787e36i	0.802754	+	0.802754i	0.983525	−	0.180771i	$-0.0578593\pi$
$509$	2.78787e36	+	2.78787e36i	0.802754	+	0.802754i	−0.180771	+	0.983525i	$0.557859\pi$
$510$	−2.22576e34	+	4.60539e34i	−0.00624138	+	0.0129142i
$511$	3.32248e36			0.907362
$512$	2.96860e36	−	2.30699e36i	0.789599	−	0.613623i
$513$	−3.18838e35			−0.0826010
$514$	−6.93628e35	+	1.43521e36i	−0.175035	+	0.362170i
$515$	−1.12102e35	−	1.12102e35i	−0.0275559	−	0.0275559i
$516$	−7.14604e35	−	9.01232e35i	−0.171117	−	0.215807i
$517$	−1.13674e36	+	1.13674e36i	−0.265178	+	0.265178i
$518$	−3.08186e36	+	1.07357e36i	−0.700424	+	0.243993i
$519$			2.98070e35i			0.0660022i
$520$	3.40459e35	−	7.62097e34i	0.0734548	−	0.0164424i
$521$			3.93661e36i			0.827586i	0.910371	+	0.413793i	$0.135796\pi$
$521$			3.93661e36i			0.827586i	−0.910371	+	0.413793i	$0.864204\pi$
$522$	3.38592e35	+	9.71988e35i	0.0693625	+	0.199117i
$523$	−4.43031e36	+	4.43031e36i	−0.884426	+	0.884426i	−0.993981	−	0.109555i	$-0.965058\pi$
$523$	−4.43031e36	+	4.43031e36i	−0.884426	+	0.884426i	0.109555	+	0.993981i	$0.465058\pi$
$524$	2.11045e34	−	1.82723e35i	0.00410585	−	0.0355485i
$525$	6.54148e35	+	6.54148e35i	0.124030	+	0.124030i
$526$	−7.31587e36	−	3.53572e36i	−1.35194	−	0.653387i
$527$	−3.30555e36			−0.595389
$528$	7.21331e34	−	3.08099e35i	0.0126642	−	0.0540919i
$529$	3.59853e36			0.615848
$530$	−5.95113e35	−	2.87615e35i	−0.0992831	−	0.0479830i
$531$	−1.85654e36	−	1.85654e36i	−0.301945	−	0.301945i
$532$	1.64834e36	+	1.90383e35i	0.261360	+	0.0301870i
$533$	−4.09139e35	+	4.09139e35i	−0.0632490	+	0.0632490i
$534$	−4.76269e35	−	1.36722e36i	−0.0717870	−	0.206077i
$535$			8.69318e35i			0.127762i
$536$	−3.64561e36	−	2.31203e36i	−0.522451	−	0.331336i
$537$			1.29992e36i			0.181661i
$538$	−9.85535e36	+	3.43311e36i	−1.34311	+	0.467872i
$539$	−2.16005e35	+	2.16005e35i	−0.0287088	+	0.0287088i
$540$	−2.80747e35	+	2.22610e35i	−0.0363915	+	0.0288555i
$541$	1.06990e37	+	1.06990e37i	1.35264	+	1.35264i	0.882701	+	0.469936i	$0.155723\pi$
$541$	1.06990e37	+	1.06990e37i	1.35264	+	1.35264i	0.469936	+	0.882701i	$0.344277\pi$
$542$	−3.81340e36	+	7.89043e36i	−0.470243	+	0.972994i
$543$	−1.99566e36			−0.240042
$544$	−4.03453e36	−	3.26374e36i	−0.473378	−	0.382939i
$545$	−4.73471e34			−0.00541926
$546$	3.75971e35	−	7.77932e35i	0.0419810	−	0.0868643i
$547$	3.51189e36	+	3.51189e36i	0.382571	+	0.382571i	0.872028	−	0.489456i	$-0.162805\pi$
$547$	3.51189e36	+	3.51189e36i	0.382571	+	0.382571i	−0.489456	+	0.872028i	$0.662805\pi$
$548$	−5.19888e36	+	4.12228e36i	−0.552550	+	0.438127i
$549$	1.99553e36	−	1.99553e36i	0.206934	−	0.206934i
$550$	−3.01215e36	+	1.04928e36i	−0.304775	+	0.106168i
$551$			5.45678e35i			0.0538753i
$552$	5.81531e35	−	9.16959e35i	0.0560268	−	0.0883430i
$553$			9.87406e36i			0.928338i
$554$	1.03552e36	+	2.97265e36i	0.0950118	+	0.272748i
$555$	1.30178e35	−	1.30178e35i	0.0116569	−	0.0116569i
$556$	1.44748e37	+	1.67184e36i	1.26503	+	0.146111i
$557$	5.37536e36	+	5.37536e36i	0.458525	+	0.458525i	0.898171	−	0.439646i	$-0.144896\pi$
$557$	5.37536e36	+	5.37536e36i	0.458525	+	0.458525i	−0.439646	+	0.898171i	$0.644896\pi$
$558$	−1.02731e37	−	4.96492e36i	−0.855339	−	0.413381i
$559$	1.08283e37			0.880040
$560$	1.58434e36	−	9.83216e35i	0.125693	−	0.0780028i
$561$	−4.36764e35			−0.0338258
$562$	9.55662e36	+	4.61866e36i	0.722544	+	0.349202i
$563$	4.56503e36	+	4.56503e36i	0.336962	+	0.336962i	0.855223	−	0.518261i	$-0.173420\pi$
$563$	4.56503e36	+	4.56503e36i	0.336962	+	0.336962i	−0.518261	+	0.855223i	$0.673420\pi$
$564$	3.06166e35	−	2.65079e36i	0.0220642	−	0.191032i
$565$	2.16539e36	−	2.16539e36i	0.152364	−	0.152364i
$566$	−3.74267e36	−	1.07440e37i	−0.257134	−	0.738149i
$567$		−	1.44616e37i		−	0.970162i
$568$	−1.25641e36	−	5.61289e36i	−0.0823054	−	0.367692i
$569$			9.92659e36i			0.635016i	0.948256	+	0.317508i	$0.102846\pi$
$569$			9.92659e36i			0.635016i	−0.948256	+	0.317508i	$0.897154\pi$
$570$	−8.83941e34	+	3.07920e34i	−0.00552220	+	0.00192366i
$571$	1.08491e37	−	1.08491e37i	0.661921	−	0.661921i	−0.293911	−	0.955833i	$-0.594957\pi$
$571$	1.08491e37	−	1.08491e37i	0.661921	−	0.661921i	0.955833	+	0.293911i	$0.0949570\pi$
$572$	1.85091e36	+	2.33430e36i	0.110291	+	0.139095i
$573$	2.00050e36	+	2.00050e36i	0.116426	+	0.116426i
$574$	−1.34563e36	+	2.78429e36i	−0.0764919	+	0.158272i
$575$	−1.09452e37			−0.607726
$576$	−7.63649e36	−	1.62029e37i	−0.414181	−	0.878801i
$577$	−2.35051e37			−1.24534			−0.622670	−	0.782485i	$-0.713952\pi$
$577$	−2.35051e37			−1.24534			−0.622670	+	0.782485i	$0.713952\pi$
$578$	5.29046e36	−	1.09466e37i	0.273821	−	0.566572i
$579$	4.22623e36	+	4.22623e36i	0.213694	+	0.213694i
$580$	3.80988e35	+	4.80488e35i	0.0188206	+	0.0237358i
$581$	2.21845e37	−	2.21845e37i	1.07071	−	1.07071i
$582$	9.42076e34	−	3.28172e34i	0.00444248	−	0.00154754i
$583$		−	5.64391e36i		−	0.260049i
$584$	−4.15360e36	−	1.85558e37i	−0.187004	−	0.835423i
$585$		−	1.66222e36i		−	0.0731283i
$586$	−1.27645e36	−	3.66426e36i	−0.0548763	−	0.157532i
$587$	−5.43774e36	+	5.43774e36i	−0.228457	+	0.228457i	−0.812048	−	0.583591i	$-0.801647\pi$
$587$	−5.43774e36	+	5.43774e36i	−0.228457	+	0.228457i	0.583591	+	0.812048i	$0.301647\pi$
$588$	5.81782e34	−	5.03708e35i	0.00238873	−	0.0206816i
$589$	−4.27734e36	−	4.27734e36i	−0.171639	−	0.171639i
$590$	−1.40835e36	−	6.80648e35i	−0.0552342	−	0.0266944i
$591$	6.36779e36			0.244094
$592$	9.84857e36	+	1.58698e37i	0.369003	+	0.594606i
$593$	−1.08949e37			−0.399012			−0.199506	−	0.979897i	$-0.563934\pi$
$593$	−1.08949e37			−0.399012			−0.199506	+	0.979897i	$0.563934\pi$
$594$	−2.75457e36	−	1.33127e36i	−0.0986137	−	0.0476595i
$595$	−1.81990e36	−	1.81990e36i	−0.0636894	−	0.0636894i
$596$	2.09034e37	+	2.41434e36i	0.715143	+	0.0825990i
$597$	1.79064e36	−	1.79064e36i	0.0598900	−	0.0598900i
$598$	3.36281e36	+	9.65355e36i	0.109960	+	0.315661i
$599$		−	2.67698e37i		−	0.855820i	−0.903821	−	0.427910i	$-0.859250\pi$
$599$		−	2.67698e37i		−	0.855820i	0.903821	−	0.427910i	$-0.140750\pi$
$600$	2.83558e36	−	4.47115e36i	0.0886340	−	0.139758i
$601$		−	2.29702e37i		−	0.702037i	−0.936368	−	0.351019i	$-0.885835\pi$
$601$		−	2.29702e37i		−	0.702037i	0.936368	−	0.351019i	$-0.114165\pi$
$602$	5.46515e37	−	1.90378e37i	1.63324	−	0.568938i
$603$	−1.45435e37	+	1.45435e37i	−0.424996	+	0.424996i
$604$	−4.46842e37	+	3.54309e37i	−1.27689	+	1.01247i
$605$	−3.14905e36	−	3.14905e36i	−0.0879997	−	0.0879997i
$606$	4.76997e36	−	9.86970e36i	0.130357	−	0.269726i
$607$	−4.92115e37			−1.31528			−0.657642	−	0.753331i	$-0.728446\pi$
$607$	−4.92115e37			−1.31528			−0.657642	+	0.753331i	$0.728446\pi$
$608$	−9.97395e35	−	9.44385e36i	−0.0260717	−	0.246860i
$609$	1.51862e36			0.0388253
$610$	7.31606e35	−	1.51379e36i	0.0182947	−	0.0378541i
$611$	1.77639e37	+	1.77639e37i	0.434493	+	0.434493i
$612$	−1.93730e37	+	1.53612e37i	−0.463504	+	0.367521i
$613$	−4.48554e36	+	4.48554e36i	−0.104978	+	0.104978i	−0.757645	−	0.652667i	$-0.773650\pi$
$613$	−4.48554e36	+	4.48554e36i	−0.104978	+	0.104978i	0.652667	+	0.757645i	$0.273650\pi$
$614$	−4.28785e37	+	1.49367e37i	−0.981671	+	0.341965i
$615$		−	1.74448e35i		−	0.00390708i
$616$	1.34458e37	+	8.52724e36i	0.294609	+	0.186840i
$617$		−	7.12796e37i		−	1.52797i	−0.645232	−	0.763987i	$-0.723239\pi$
$617$		−	7.12796e37i		−	1.52797i	0.645232	−	0.763987i	$-0.276761\pi$
$618$	7.39178e35	+	2.12194e36i	0.0155026	+	0.0445030i
$619$	−6.68210e37	+	6.68210e37i	−1.37116	+	1.37116i	−0.512439	+	0.858723i	$0.671258\pi$
$619$	−6.68210e37	+	6.68210e37i	−1.37116	+	1.37116i	−0.858723	+	0.512439i	$0.828742\pi$
$620$	−6.75273e36	−	7.79940e35i	−0.135579	−	0.0156593i
$621$	−7.42333e36	−	7.42333e36i	−0.145835	−	0.145835i
$622$	2.57426e37	+	1.24413e37i	0.494861	+	0.239164i
$623$	7.28484e37			1.37035
$624$	−4.81471e36	−	1.12724e36i	−0.0886295	−	0.0207502i
$625$	−5.22881e37			−0.941939
$626$	4.73216e37	+	2.28703e37i	0.834269	+	0.403198i
$627$	−5.65166e35	−	5.65166e35i	−0.00975134	−	0.00975134i
$628$	−9.02367e36	+	7.81271e37i	−0.152380	+	1.31931i
$629$	1.82293e37	−	1.82293e37i	0.301292	−	0.301292i
$630$	−2.92244e36	−	8.38938e36i	−0.0472768	−	0.135716i
$631$		−	7.29155e37i		−	1.15458i	−0.816540	−	0.577289i	$-0.804111\pi$
$631$		−	7.29155e37i		−	1.15458i	0.816540	−	0.577289i	$-0.195889\pi$
$632$	5.51459e37	−	1.23441e37i	0.854737	−	0.191327i
$633$			7.09488e36i			0.107645i
$634$	1.01677e38	−	3.54193e37i	1.51015	−	0.526060i
$635$	1.05283e36	−	1.05283e36i	0.0153079	−	0.0153079i
$636$	5.82055e36	+	7.34067e36i	0.0828500	+	0.104488i
$637$	3.37554e36	+	3.37554e36i	0.0470393	+	0.0470393i
$638$	−2.27842e36	+	4.71434e36i	−0.0310852	+	0.0643194i
$639$	−2.74038e37			−0.366057
$640$	−7.47185e36	−	7.61925e36i	−0.0977233	−	0.0996512i
$641$	−1.48409e38			−1.90054			−0.950272	−	0.311422i	$-0.899195\pi$
$641$	−1.48409e38			−1.90054			−0.950272	+	0.311422i	$0.899195\pi$
$642$	5.36148e36	−	1.10936e37i	0.0672298	−	0.139107i
$643$	9.72315e37	+	9.72315e37i	1.19387	+	1.19387i	0.975970	+	0.217905i	$0.0699223\pi$
$643$	9.72315e37	+	9.72315e37i	1.19387	+	1.19387i	0.217905	+	0.975970i	$0.430078\pi$
$644$	3.39448e37	+	4.28100e37i	0.408145	+	0.514737i
$645$	−2.30848e36	+	2.30848e36i	−0.0271813	+	0.0271813i
$646$	−1.23782e37	+	4.31193e36i	−0.142731	+	0.0497202i
$647$			1.26136e37i			0.142439i	0.997461	+	0.0712197i	$0.0226892\pi$
$647$			1.26136e37i			0.142439i	−0.997461	+	0.0712197i	$0.977311\pi$
$648$	−8.07668e37	+	1.80791e37i	−0.893244	+	0.199947i
$649$		−	1.33565e37i		−	0.144673i
$650$	1.63973e37	+	4.70713e37i	0.173957	+	0.499374i
$651$	−1.19038e37	+	1.19038e37i	−0.123692	+	0.123692i
$652$	−1.11893e37	+	9.68771e37i	−0.113883	+	0.986004i
$653$	−3.28457e36	−	3.28457e36i	−0.0327455	−	0.0327455i	0.690544	−	0.723290i	$-0.257371\pi$
$653$	−3.28457e36	−	3.28457e36i	−0.0327455	−	0.0327455i	−0.723290	+	0.690544i	$0.757371\pi$
$654$	6.04209e35	+	2.92011e35i	0.00590048	+	0.00285167i
$655$	−5.22099e35			−0.00499454
$656$	1.72323e37	+	4.03447e36i	0.161488	+	0.0378081i
$657$	−9.05949e37			−0.831709
$658$	1.20888e38	+	5.84245e37i	1.08726	+	0.525467i
$659$	1.21892e38	+	1.21892e38i	1.07404	+	1.07404i	0.997030	+	0.0770134i	$0.0245384\pi$
$659$	1.21892e38	+	1.21892e38i	1.07404	+	1.07404i	0.0770134	+	0.997030i	$0.475462\pi$
$660$	−8.92242e35	−	1.03054e35i	−0.00770264	−	0.000889654i
$661$	7.61509e37	−	7.61509e37i	0.644103	−	0.644103i	−0.307459	−	0.951561i	$-0.599479\pi$
$661$	7.61509e37	−	7.61509e37i	0.644103	−	0.644103i	0.951561	+	0.307459i	$0.0994785\pi$
$662$	8.92696e36	+	2.56264e37i	0.0739811	+	0.212376i
$663$			6.82538e36i			0.0554236i
$664$	−1.51633e38	−	9.61648e37i	−1.20649	−	0.765151i
$665$		−	4.70984e36i		−	0.0367209i
$666$	8.40339e37	−	2.92732e37i	0.642025	−	0.223649i
$667$	−1.27047e37	+	1.27047e37i	−0.0951189	+	0.0951189i
$668$	−9.39729e36	+	7.45128e36i	−0.0689478	+	0.0546700i
$669$	5.12162e36	+	5.12162e36i	0.0368260	+	0.0368260i
$670$	−5.33197e36	+	1.10325e37i	−0.0375732	+	0.0777438i
$671$	1.43564e37			0.0991498
$672$	−2.62821e37	+	2.77574e36i	−0.177900	+	0.0187886i
$673$	−1.93876e38			−1.28624			−0.643118	−	0.765767i	$-0.722360\pi$
$673$	−1.93876e38			−1.28624			−0.643118	+	0.765767i	$0.722360\pi$
$674$	3.63665e37	−	7.52470e37i	0.236479	−	0.489306i
$675$	−3.61966e37	−	3.61966e37i	−0.230711	−	0.230711i
$676$	−8.89387e37	+	7.05211e37i	−0.555662	+	0.440594i
$677$	1.81496e38	−	1.81496e38i	1.11153	−	1.11153i	0.118583	−	0.992944i	$-0.462165\pi$
$677$	1.81496e38	−	1.81496e38i	1.11153	−	1.11153i	0.992944	−	0.118583i	$-0.0378353\pi$
$678$	−4.09880e37	+	1.42782e37i	−0.246069	+	0.0857179i
$679$			5.01959e36i			0.0295411i
$680$	−7.88884e36	+	1.24391e37i	−0.0455138	+	0.0717661i
$681$		−	2.51156e37i		−	0.142055i
$682$	−1.90942e37	−	5.48132e37i	−0.105879	−	0.303946i
$683$	−1.46467e38	+	1.46467e38i	−0.796272	+	0.796272i	−0.982506	−	0.186233i	$-0.940372\pi$
$683$	−1.46467e38	+	1.46467e38i	−0.796272	+	0.796272i	0.186233	+	0.982506i	$0.440372\pi$
$684$	−4.49456e37	−	5.19121e36i	−0.239569	−	0.0276702i
$685$	1.33168e37	+	1.33168e37i	0.0695948	+	0.0695948i
$686$	−1.63259e38	−	7.89022e37i	−0.836568	−	0.404309i
$687$	−1.71514e37			−0.0861753
$688$	−1.74648e38	−	2.81425e38i	−0.860436	−	1.38649i
$689$	−8.81983e37			−0.426090
$690$	−2.77495e36	−	1.34112e36i	−0.0131460	−	0.00635337i
$691$	8.84575e37	+	8.84575e37i	0.410943	+	0.410943i	0.882067	−	0.471124i	$-0.156152\pi$
$691$	8.84575e37	+	8.84575e37i	0.410943	+	0.410943i	−0.471124	+	0.882067i	$0.656152\pi$
$692$	−9.84846e36	+	8.52681e37i	−0.0448679	+	0.388467i
$693$	5.36393e37	−	5.36393e37i	0.239654	−	0.239654i
$694$	−1.17090e38	−	3.36128e38i	−0.513058	−	1.47283i
$695$		−	4.13592e37i		−	0.177737i
$696$	−1.89850e36	−	8.48136e36i	−0.00800176	−	0.0357471i
$697$		−	2.44287e37i		−	0.100985i
$698$	1.97470e38	−	6.87886e37i	0.800669	−	0.278913i
$699$	5.79991e36	−	5.79991e36i	0.0230664	−	0.0230664i
$700$	1.65517e38	+	2.08744e38i	0.645682	+	0.814312i
$701$	2.17436e38	+	2.17436e38i	0.832028	+	0.832028i	0.987794	−	0.155766i	$-0.0497847\pi$
$701$	2.17436e38	+	2.17436e38i	0.832028	+	0.832028i	−0.155766	+	0.987794i	$0.549785\pi$
$702$	−2.08040e37	+	4.30462e37i	−0.0780900	+	0.161578i
$703$	4.71770e37			0.173713
$704$	3.08148e37	−	8.57538e37i	0.111308	−	0.309758i
$705$	−7.57416e36			−0.0268399
$706$	1.46928e38	−	3.04014e38i	0.510790	−	1.05689i
$707$	3.90017e38	+	3.90017e38i	1.33022	+	1.33022i
$708$	1.37745e37	+	1.73719e37i	0.0460920	+	0.0581296i
$709$	2.65902e38	−	2.65902e38i	0.872965	−	0.872965i	−0.119830	−	0.992794i	$-0.538235\pi$
$709$	2.65902e38	−	2.65902e38i	0.872965	−	0.872965i	0.992794	+	0.119830i	$0.0382349\pi$
$710$	−1.54175e37	+	5.37069e36i	−0.0496623	+	0.0172999i
$711$		−	2.69238e38i		−	0.850937i
$712$	−9.10714e37	−	4.06853e38i	−0.282424	−	1.26170i
$713$		−	1.99174e38i		−	0.606072i
$714$	1.20001e37	+	3.44483e37i	0.0358309	+	0.102859i
$715$	5.97926e36	−	5.97926e36i	0.0175193	−	0.0175193i
$716$	−4.29503e37	+	3.71864e38i	−0.123492	+	1.06920i
$717$	−1.40926e37	−	1.40926e37i	−0.0397632	−	0.0397632i
$718$	−4.97306e38	−	2.40346e38i	−1.37703	−	0.665512i
$719$	5.65075e38			1.53556			0.767779	−	0.640715i	$-0.221362\pi$
$719$	5.65075e38			1.53556			0.767779	+	0.640715i	$0.221362\pi$
$720$	−4.32006e37	+	2.68096e37i	−0.115213	+	0.0714992i
$721$	−1.13062e38			−0.295931
$722$	3.28888e38	+	1.58950e38i	0.844883	+	0.408327i
$723$	2.54072e37	+	2.54072e37i	0.0640603	+	0.0640603i
$724$	−5.70893e38	−	6.59380e37i	−1.41281	−	0.163179i
$725$	−6.19491e37	+	6.19491e37i	−0.150478	+	0.150478i
$726$	2.07642e37	+	5.96074e37i	0.0495075	+	0.142120i
$727$		−	6.96433e38i		−	1.62992i	−0.579521	−	0.814958i	$-0.696760\pi$
$727$		−	6.96433e38i		−	1.62992i	0.579521	−	0.814958i	$-0.303240\pi$
$728$	1.33257e38	−	2.10119e38i	0.306136	−	0.482716i
$729$			3.69423e38i			0.833110i
$730$	−5.09693e37	+	1.77551e37i	−0.112837	+	0.0393066i
$731$	−3.23266e38	+	3.23266e38i	−0.702547	+	0.702547i
$732$	−1.86724e37	+	1.48057e37i	−0.0398384	+	0.0315886i
$733$	3.61307e38	+	3.61307e38i	0.756784	+	0.756784i	0.975736	−	0.218951i	$-0.0702636\pi$
$733$	3.61307e38	+	3.61307e38i	0.756784	+	0.756784i	−0.218951	+	0.975736i	$0.570264\pi$
$734$	−1.60305e38	+	3.31692e38i	−0.329648	+	0.682084i
$735$	−1.43926e36			−0.00290576
$736$	1.96654e38	−	2.43098e38i	0.389810	−	0.481871i
$737$	−1.04630e38			−0.203632
$738$	3.66917e37	−	7.59199e37i	0.0701143	−	0.145076i
$739$	3.43885e38	+	3.43885e38i	0.645229	+	0.645229i	0.951836	−	0.306607i	$-0.0991938\pi$
$739$	3.43885e38	+	3.43885e38i	0.645229	+	0.645229i	−0.306607	+	0.951836i	$0.599194\pi$
$740$	4.15409e37	−	3.29385e37i	0.0765328	−	0.0606843i
$741$	−8.83195e36	+	8.83195e36i	−0.0159776	+	0.0159776i
$742$	−4.45145e38	+	1.55066e38i	−0.790767	+	0.275463i
$743$		−	5.06142e38i		−	0.882925i	−0.897280	−	0.441462i	$-0.854460\pi$
$743$		−	5.06142e38i		−	0.882925i	0.897280	−	0.441462i	$-0.145540\pi$
$744$	8.13632e37	+	5.16002e37i	0.139378	+	0.0883928i
$745$		−	5.97279e37i		−	0.100477i
$746$	1.42127e38	+	4.08001e38i	0.234803	+	0.674043i
$747$	−6.04911e38	+	6.04911e38i	−0.981438	+	0.981438i
$748$	−1.24944e38	−	1.44310e37i	−0.199088	−	0.0229946i
$749$	4.38382e38	+	4.38382e38i	0.686038	+	0.686038i
$750$	−2.73305e37	−	1.32087e37i	−0.0420068	−	0.0203017i
$751$	−9.93228e38			−1.49937			−0.749687	−	0.661793i	$-0.769796\pi$
$751$	−9.93228e38			−1.49937			−0.749687	+	0.661793i	$0.769796\pi$
$752$	1.75168e38	−	7.48189e38i	0.259726	−	1.10935i
$753$	−8.80939e37			−0.128296
$754$	7.36718e37	+	3.56052e37i	0.105387	+	0.0509331i
$755$	1.14457e38	+	1.14457e38i	0.160827	+	0.160827i
$756$	−2.93178e37	+	2.53834e38i	−0.0404657	+	0.350353i
$757$	−3.50475e38	+	3.50475e38i	−0.475185	+	0.475185i	−0.903588	−	0.428403i	$-0.859076\pi$
$757$	−3.50475e38	+	3.50475e38i	−0.475185	+	0.475185i	0.428403	+	0.903588i	$0.359076\pi$
$758$	5.45190e37	+	1.56506e38i	0.0726128	+	0.208448i
$759$		−	2.63169e37i		−	0.0344327i
$760$	−2.63041e37	+	5.88800e36i	−0.0338096	+	0.00756806i
$761$			1.23292e39i			1.55684i	0.627746	+	0.778419i	$0.283978\pi$
$761$			1.23292e39i			1.55684i	−0.627746	+	0.778419i	$0.716022\pi$
$762$	−1.99288e37	+	6.94219e36i	−0.0247223	+	0.00861200i
$763$	−2.38763e37	+	2.38763e37i	−0.0290995	+	0.0290995i
$764$	5.06181e38	+	6.38377e38i	0.606101	+	0.764393i
$765$	4.96236e37	+	4.96236e37i	0.0583792	+	0.0583792i
$766$	−2.59200e38	+	5.36318e38i	−0.299603	+	0.619918i
$767$	−2.08724e38			−0.237047
$768$	4.83589e37	+	1.43314e38i	0.0539635	+	0.159923i
$769$	−1.60259e39			−1.75718			−0.878590	−	0.477578i	$-0.841515\pi$
$769$	−1.60259e39			−1.75718			−0.878590	+	0.477578i	$0.841515\pi$
$770$	1.96654e37	−	4.06902e37i	0.0211874	−	0.0438395i
$771$	−4.53462e37	−	4.53462e37i	−0.0480072	−	0.0480072i
$772$	1.06935e39	+	1.34862e39i	1.11246	+	1.40300i
$773$	1.31478e39	−	1.31478e39i	1.34410	−	1.34410i	0.452159	−	0.891937i	$-0.350654\pi$
$773$	1.31478e39	−	1.31478e39i	1.34410	−	1.34410i	0.891937	−	0.452159i	$-0.149346\pi$
$774$	−1.49020e39	+	5.19110e38i	−1.49707	+	0.521502i
$775$		−	9.71185e38i		−	0.958802i
$776$	2.80341e37	−	6.27525e36i	0.0271990	−	0.00608832i
$777$		−	1.31293e38i		−	0.125187i
$778$	5.65188e37	+	1.62247e38i	0.0529625	+	0.152038i
$779$	3.16103e37	−	3.16103e37i	0.0291121	−	0.0291121i
$780$	−1.61044e36	+	1.39432e37i	−0.00145770	+	0.0126208i
$781$	−9.85753e37	−	9.85753e37i	−0.0876958	−	0.0876958i
$782$	−3.88587e38	−	1.87802e38i	−0.339779	−	0.164214i
$783$	−8.40312e37			−0.0722199
$784$	3.32858e37	−	1.42172e38i	0.0281185	−	0.120101i
$785$	2.23235e38			0.185362
$786$	6.66265e36	+	3.22002e36i	0.00543804	+	0.00262818i
$787$	−7.23652e38	−	7.23652e38i	−0.580592	−	0.580592i	0.354474	−	0.935066i	$-0.384660\pi$
$787$	−7.23652e38	−	7.23652e38i	−0.580592	−	0.580592i	−0.935066	+	0.354474i	$0.884660\pi$
$788$	1.82162e39	+	2.10397e38i	1.43666	+	0.165934i
$789$	2.31149e38	−	2.31149e38i	0.179206	−	0.179206i
$790$	−5.27663e37	−	1.51475e38i	−0.0402153	−	0.115445i
$791$		−	2.18394e39i		−	1.63628i
$792$	−3.66629e38	−	2.32514e38i	−0.270045	−	0.171262i
$793$		−	2.24350e38i		−	0.162457i
$794$	1.92217e39	−	6.69588e38i	1.36841	−	0.476685i
$795$	1.88029e37	−	1.88029e37i	0.0131604	−	0.0131604i
$796$	5.71408e38	−	4.53080e38i	0.393206	−	0.311780i
$797$	1.85197e39	+	1.85197e39i	1.25299	+	1.25299i	0.954373	+	0.298616i	$0.0965250\pi$
$797$	1.85197e39	+	1.85197e39i	1.25299	+	1.25299i	0.298616	+	0.954373i	$0.403475\pi$
$798$	−2.90477e37	+	6.01035e37i	−0.0193229	+	0.0399816i
$799$	−1.06064e39			−0.693724
$800$	9.58899e38	−	1.18536e39i	0.616677	−	0.762318i
$801$	−1.98638e39			−1.25609
$802$	−6.09091e38	+	1.26029e39i	−0.378729	+	0.783639i
$803$	−3.25883e38	−	3.25883e38i	−0.199252	−	0.199252i
$804$	1.36085e38	−	1.07905e38i	0.0818191	−	0.0648759i
$805$	1.09657e38	−	1.09657e38i	0.0648322	−	0.0648322i
$806$	−8.56575e38	+	2.98388e38i	−0.498015	+	0.173483i
$807$		−	4.19856e38i		−	0.240054i
$808$	1.69064e39	−	2.66580e39i	0.950599	−	1.49890i
$809$			3.47992e38i			0.192426i	0.995361	+	0.0962131i	$0.0306730\pi$
$809$			3.47992e38i			0.192426i	−0.995361	+	0.0962131i	$0.969327\pi$
$810$	7.72817e37	+	2.21851e38i	0.0420271	+	0.120646i
$811$	2.13612e38	−	2.13612e38i	0.114247	−	0.114247i	−0.647672	−	0.761919i	$-0.724257\pi$
$811$	2.13612e38	−	2.13612e38i	0.114247	−	0.114247i	0.761919	+	0.647672i	$0.224257\pi$
$812$	4.34427e38	+	5.01763e37i	0.228513	+	0.0263932i
$813$	−2.49303e38	−	2.49303e38i	−0.128975	−	0.128975i
$814$	4.07582e38	+	1.96982e38i	0.207389	+	0.100230i
$815$	2.76809e38			0.138533
$816$	1.77389e38	−	1.10085e38i	0.0873193	−	0.0541890i
$817$	−8.36603e38			−0.405062
$818$	2.27619e39	+	1.10007e39i	1.08402	+	0.523902i
$819$	−8.38230e38	−	8.38230e38i	−0.392673	−	0.392673i
$820$	5.76390e36	−	4.99040e37i	0.00265601	−	0.0229958i
$821$	3.87704e38	−	3.87704e38i	0.175739	−	0.175739i	−0.613757	−	0.789495i	$-0.710342\pi$
$821$	3.87704e38	−	3.87704e38i	0.175739	−	0.175739i	0.789495	+	0.613757i	$0.210342\pi$
$822$	−8.78085e37	−	2.52070e38i	−0.0391532	−	0.112396i
$823$		−	1.89883e39i		−	0.832889i	−0.909161	−	0.416445i	$-0.863276\pi$
$823$		−	1.89883e39i		−	0.832889i	0.909161	−	0.416445i	$-0.136724\pi$
$824$	1.41344e38	+	6.31442e38i	0.0609903	+	0.272469i
$825$		−	1.28323e38i		−	0.0544724i
$826$	−1.05345e39	+	3.66967e38i	−0.439928	+	0.153249i
$827$	5.65145e37	−	5.65145e37i	0.0232186	−	0.0232186i	−0.695402	−	0.718621i	$-0.744774\pi$
$827$	5.65145e37	−	5.65145e37i	0.0232186	−	0.0232186i	0.718621	+	0.695402i	$0.244774\pi$
$828$	−9.25581e38	−	1.16731e39i	−0.374115	−	0.471820i
$829$	1.15307e39	+	1.15307e39i	0.458533	+	0.458533i	0.898174	−	0.439641i	$-0.144894\pi$
$829$	1.15307e39	+	1.15307e39i	0.458533	+	0.458533i	−0.439641	+	0.898174i	$0.644894\pi$
$830$	−2.21774e38	+	4.58879e38i	−0.0867673	+	0.179533i
$831$	−1.26640e38			−0.0487482
$832$	−1.34009e39	−	4.81548e38i	−0.507538	−	0.182379i
$833$	−2.01545e38			−0.0751042
$834$	−2.55081e38	+	5.27796e38i	−0.0935268	+	0.193519i
$835$	2.40709e37	+	2.40709e37i	0.00868411	+	0.00868411i
$836$	−1.43002e38	−	1.80349e38i	−0.0507643	−	0.0640221i
$837$	6.58684e38	−	6.58684e38i	0.230083	−	0.230083i
$838$	−1.64291e39	+	5.72308e38i	−0.564703	+	0.196714i
$839$		−	2.52472e39i		−	0.853940i	−0.904266	−	0.426970i	$-0.859581\pi$
$839$		−	2.52472e39i		−	0.853940i	0.904266	−	0.426970i	$-0.140419\pi$
$840$	1.63862e37	+	7.32040e37i	0.00545392	+	0.0243649i
$841$		−	2.90932e39i		−	0.952896i
$842$	8.59806e37	+	2.46823e38i	0.0277132	+	0.0795558i
$843$	−3.01947e38	+	3.01947e38i	−0.0957763	+	0.0957763i
$844$	−2.34420e38	+	2.02962e39i	−0.0731766	+	0.633564i
$845$	2.27814e38	+	2.27814e38i	0.0699867	+	0.0699867i
$846$	−3.29628e39	−	1.59307e39i	−0.996608	−	0.481655i
$847$	−3.17602e39			−0.945054
$848$	1.42253e39	+	2.29224e39i	0.416598	+	0.671300i
$849$	4.57714e38			0.131929
$850$	−1.89477e39	−	9.15734e38i	−0.537529	−	0.259785i
$851$	1.09840e39	+	1.09840e39i	0.306697	+	0.306697i
$852$	2.29871e38	+	2.65500e37i	0.0631756	+	0.00729677i
$853$	−2.25797e39	+	2.25797e39i	−0.610811	+	0.610811i	−0.943157	−	0.332346i	$-0.892160\pi$
$853$	−2.25797e39	+	2.25797e39i	−0.610811	+	0.610811i	0.332346	+	0.943157i	$0.392160\pi$
$854$	−3.94441e38	−	1.13231e39i	−0.105027	−	0.301499i
$855$			1.28424e38i			0.0336593i
$856$	1.90029e39	−	2.99637e39i	0.490257	−	0.773037i
$857$			6.71387e39i			1.70503i	0.522704	+	0.852514i	$0.324923\pi$
$857$			6.71387e39i			1.70503i	−0.522704	+	0.852514i	$0.675077\pi$
$858$	−1.13180e38	+	3.94261e37i	−0.0282937	+	0.00985611i
$859$	−3.20458e39	+	3.20458e39i	−0.788612	+	0.788612i	−0.981267	−	0.192655i	$-0.938290\pi$
$859$	−3.20458e39	+	3.20458e39i	−0.788612	+	0.788612i	0.192655	+	0.981267i	$0.438290\pi$
$860$	−7.36657e38	+	5.84109e38i	−0.178458	+	0.141503i
$861$	−8.79711e37	−	8.79711e37i	−0.0209796	−	0.0209796i
$862$	−8.85023e38	+	1.83123e39i	−0.207781	+	0.429927i
$863$	4.07217e39			0.941196			0.470598	−	0.882348i	$-0.344038\pi$
$863$	4.07217e39			0.941196			0.470598	+	0.882348i	$0.344038\pi$
$864$	1.45430e39	−	1.53593e38i	0.330916	−	0.0349491i
$865$	2.43639e38			0.0545794
$866$	2.53383e39	−	5.24282e39i	0.558837	−	1.15631i
$867$	3.45865e38	+	3.45865e38i	0.0751016	+	0.0751016i
$868$	−3.79860e39	+	3.01198e39i	−0.812095	+	0.643925i
$869$	9.68489e38	−	9.68489e38i	0.203858	−	0.203858i
$870$	−2.32967e37	+	8.11539e36i	−0.00482819	+	0.00168190i
$871$			1.63507e39i			0.333650i
$872$	1.63196e38	+	1.03498e38i	0.0327897	+	0.0207951i
$873$		−	1.36871e38i		−	0.0270781i
$874$	−2.59813e38	−	7.45839e38i	−0.0506123	−	0.145292i
$875$	1.08001e39	−	1.08001e39i	0.207166	−	0.207166i
$876$	7.59937e38	+	8.77726e37i	0.143540	+	0.0165788i
$877$	4.52885e39	+	4.52885e39i	0.842352	+	0.842352i	0.989164	−	0.146812i	$-0.0469014\pi$
$877$	4.52885e39	+	4.52885e39i	0.842352	+	0.842352i	−0.146812	+	0.989164i	$0.546901\pi$
$878$	2.16391e39	+	1.04581e39i	0.396336	+	0.191547i
$879$	1.56105e38			0.0281557
$880$	−2.51837e38	−	5.89608e37i	−0.0447304	−	0.0104724i
$881$	6.97370e39			1.21980			0.609900	−	0.792479i	$-0.291210\pi$
$881$	6.97370e39			1.21980			0.609900	+	0.792479i	$0.291210\pi$
$882$	−6.26366e38	−	3.02719e38i	−0.107895	−	0.0521452i
$883$	7.90137e39	+	7.90137e39i	1.34040	+	1.34040i	0.895663	+	0.444733i	$0.146701\pi$
$883$	7.90137e39	+	7.90137e39i	1.34040	+	1.34040i	0.444733	+	0.895663i	$0.353299\pi$
$884$	−2.25516e38	+	1.95252e39i	−0.0376766	+	0.326205i
$885$	4.44976e37	−	4.44976e37i	0.00732154	−	0.00732154i
$886$	7.86222e38	+	2.25699e39i	0.127406	+	0.365742i
$887$			4.64791e39i			0.741803i	0.928672	+	0.370902i	$0.120951\pi$
$887$			4.64791e39i			0.741803i	−0.928672	+	0.370902i	$0.879049\pi$
$888$	−7.33261e38	+	1.64136e38i	−0.115261	+	0.0258005i
$889$		−	1.06185e39i		−	0.164395i
$890$	−1.11755e39	+	3.89297e38i	−0.170412	+	0.0593630i
$891$	−1.41845e39	+	1.41845e39i	−0.213042	+	0.213042i
$892$	1.29591e39	+	1.63435e39i	0.191712	+	0.241780i
$893$	−1.37245e39	−	1.37245e39i	−0.199987	−	0.199987i
$894$	−3.68369e38	+	7.62204e38i	−0.0528721	+	0.109399i
$895$	1.06254e39			0.150222
$896$	−7.61018e39	−	7.43326e37i	−1.05983	−	0.0103519i
$897$	−4.11259e38			−0.0564180
$898$	8.00978e38	−	1.65733e39i	0.108241	−	0.223964i
$899$	−1.12731e39	−	1.12731e39i	−0.150068	−	0.150068i
$900$	−4.51319e39	−	5.69188e39i	−0.591848	−	0.746417i
$901$	2.63305e39	−	2.63305e39i	0.340153	−	0.340153i
$902$	4.05080e38	−	1.41109e38i	0.0515528	−	0.0179584i
$903$			2.32826e39i			0.291908i
$904$	−1.21971e40	+	2.73025e39i	−1.50655	+	0.337231i
$905$			1.63123e39i			0.198499i
$906$	−7.54711e38	−	2.16653e39i	−0.0904795	−	0.259737i
$907$	7.65326e39	−	7.65326e39i	0.903957	−	0.903957i	−0.0918185	−	0.995776i	$-0.529268\pi$
$907$	7.65326e39	−	7.65326e39i	0.903957	−	0.903957i	0.995776	+	0.0918185i	$0.0292679\pi$
$908$	8.29838e38	−	7.18475e39i	0.0965683	−	0.836090i
$909$	−1.06347e40	−	1.06347e40i	−1.21931	−	1.21931i
$910$	−6.35873e38	−	3.07314e38i	−0.0718310	−	0.0347155i
$911$	3.90883e39			0.435059			0.217530	−	0.976054i	$-0.430200\pi$
$911$	3.90883e39			0.435059			0.217530	+	0.976054i	$0.430200\pi$
$912$	3.71987e38	+	8.70908e37i	0.0407941	+	0.00955085i
$913$	−4.35190e39			−0.470244
$914$	4.56596e39	+	2.20670e39i	0.486137	+	0.234947i
$915$	4.78290e37	+	4.78290e37i	0.00501772	+	0.00501772i
$916$	−4.90645e39	−	5.66695e38i	−0.507199	−	0.0585815i
$917$	−2.63286e38	+	2.63286e38i	−0.0268189	+	0.0268189i
$918$	−6.64012e38	−	1.90616e39i	−0.0666499	−	0.191330i
$919$			1.36872e40i			1.35380i	0.736075	+	0.676900i	$0.236677\pi$
$919$			1.36872e40i			1.35380i	−0.736075	+	0.676900i	$0.763323\pi$
$920$	−7.49511e38	−	4.75337e38i	−0.0730538	−	0.0463304i
$921$		−	1.82670e39i		−	0.175454i
$922$	−8.02475e39	+	2.79542e39i	−0.759564	+	0.264594i
$923$	−1.54045e39	+	1.54045e39i	−0.143690	+	0.143690i
$924$	−5.01910e38	+	3.97974e38i	−0.0461375	+	0.0365833i
$925$	5.35585e39	+	5.35585e39i	0.485194	+	0.485194i
$926$	5.42271e39	−	1.12203e40i	0.484137	−	1.00174i
$927$	3.08289e39			0.271257
$928$	−2.62868e38	−	2.48897e39i	−0.0227950	−	0.215835i
$929$	−4.41905e39			−0.377674			−0.188837	−	0.982008i	$-0.560472\pi$
$929$	−4.41905e39			−0.377674			−0.188837	+	0.982008i	$0.560472\pi$
$930$	1.19000e38	−	2.46226e38i	0.0100236	−	0.0207402i
$931$	−2.60796e38	−	2.60796e38i	−0.0216511	−	0.0216511i
$932$	1.85080e39	−	1.46753e39i	0.151441	−	0.120081i
$933$	−8.13353e38	+	8.13353e38i	−0.0655960	+	0.0655960i
$934$	2.20140e40	−	7.66858e39i	1.74991	−	0.609582i
$935$			3.57006e38i			0.0279717i
$936$	−3.63354e39	+	5.72937e39i	−0.280612	+	0.442469i
$937$		−	1.37894e40i		−	1.04969i	−0.851198	−	0.524845i	$-0.824123\pi$
$937$		−	1.37894e40i		−	1.04969i	0.851198	−	0.524845i	$-0.175877\pi$
$938$	2.87470e39	+	8.25234e39i	0.215702	+	0.619211i
$939$	−1.49515e39	+	1.49515e39i	−0.110586	+	0.110586i
$940$	−2.16672e39	−	2.50256e38i	−0.157971	−	0.0182456i
$941$	−1.27895e40	−	1.27895e40i	−0.919169	−	0.919169i	0.0778002	−	0.996969i	$-0.475210\pi$
$941$	−1.27895e40	−	1.27895e40i	−0.919169	−	0.919169i	−0.996969	+	0.0778002i	$0.975210\pi$
$942$	−2.84876e39	−	1.37679e39i	−0.201822	−	0.0975394i
$943$	1.47193e39			0.102797
$944$	3.36645e39	+	5.42465e39i	0.231766	+	0.373465i
$945$	7.25287e38			0.0492244
$946$	−7.22776e39	−	3.49314e39i	−0.483586	−	0.233715i
$947$	1.46286e38	+	1.46286e38i	0.00964888	+	0.00964888i	0.711915	−	0.702266i	$-0.247828\pi$
$947$	1.46286e38	+	1.46286e38i	0.00964888	+	0.00964888i	−0.702266	+	0.711915i	$0.747828\pi$
$948$	−2.60851e38	+	2.25845e39i	−0.0169621	+	0.146858i
$949$	−5.09263e39	+	5.09263e39i	−0.326474	+	0.326474i
$950$	−1.26686e39	−	3.63676e39i	−0.0800684	−	0.229851i
$951$			4.33165e39i			0.269908i
$952$	2.29463e39	+	1.02510e40i	0.140966	+	0.629751i
$953$		−	2.03392e40i		−	1.23191i	−0.787781	−	0.615955i	$-0.788770\pi$
$953$		−	2.03392e40i		−	1.23191i	0.787781	−	0.615955i	$-0.211230\pi$
$954$	1.21379e40	−	4.22822e39i	0.724835	−	0.252496i
$955$	1.63519e39	−	1.63519e39i	0.0962768	−	0.0962768i
$956$	−3.56580e39	−	4.49706e39i	−0.207002	−	0.261064i
$957$	−1.48952e38	−	1.48952e38i	−0.00852582	−	0.00852582i
$958$	8.94987e39	−	1.85184e40i	0.505106	−	1.04513i
$959$	1.34309e40			0.747399
$960$	3.88353e38	−	1.83032e38i	0.0213091	−	0.0100430i
$961$	−8.09690e38			−0.0438079
$962$	3.07827e39	−	6.36934e39i	0.164226	−	0.339806i
$963$	−1.19535e40	−	1.19535e40i	−0.628839	−	0.628839i
$964$	6.42870e39	+	8.10764e39i	0.333490	+	0.420586i
$965$	3.45447e39	−	3.45447e39i	0.176711	−	0.176711i
$966$	−2.07566e39	+	7.23056e38i	−0.104704	+	0.0364738i
$967$		−	9.35606e38i		−	0.0465410i	−0.999729	−	0.0232705i	$-0.992592\pi$
$967$		−	9.35606e38i		−	0.0465410i	0.999729	−	0.0232705i	$-0.00740790\pi$
$968$	3.97050e39	+	1.77378e40i	0.194772	+	0.870127i
$969$		−	5.27333e38i		−	0.0255102i
$970$	−2.68244e37	−	7.70042e37i	−0.00127971	−	0.00367364i
$971$	2.66123e39	−	2.66123e39i	0.125205	−	0.125205i	−0.641728	−	0.766933i	$-0.721782\pi$
$971$	2.66123e39	−	2.66123e39i	0.125205	−	0.125205i	0.766933	+	0.641728i	$0.221782\pi$
$972$	1.20490e39	−	1.04320e40i	0.0559057	−	0.484033i
$973$	−2.08567e40	−	2.08567e40i	−0.954383	−	0.954383i
$974$	3.59574e40	+	1.73780e40i	1.62272	+	0.784250i
$975$	−2.00533e39			−0.0892530
$976$	−5.83078e39	+	3.61849e39i	−0.255949	+	0.158838i
$977$	2.40406e40			1.04080			0.520401	−	0.853922i	$-0.325782\pi$
$977$	2.40406e40			1.04080			0.520401	+	0.853922i	$0.325782\pi$
$978$	−3.53244e39	−	1.70721e39i	−0.150834	−	0.0728974i
$979$	−7.14528e39	−	7.14528e39i	−0.300921	−	0.300921i
$980$	−4.11725e38	−	4.75542e37i	−0.0171023	−	0.00197532i
$981$	6.51041e38	−	6.51041e38i	0.0266733	−	0.0266733i
$982$	6.67510e39	+	1.91621e40i	0.269745	+	0.774350i
$983$			4.18132e40i			1.66664i	0.552792	+	0.833319i	$0.313562\pi$
$983$			4.18132e40i			1.66664i	−0.552792	+	0.833319i	$0.686438\pi$
$984$	−3.81335e38	+	6.01289e38i	−0.0149925	+	0.0236401i
$985$		−	5.20496e39i		−	0.201850i
$986$	−3.26232e39	+	1.13643e39i	−0.124793	+	0.0434715i
$987$	−3.81952e39	+	3.81952e39i	−0.144121	+	0.144121i
$988$	−2.81835e39	+	2.23472e39i	−0.104900	+	0.0831772i
$989$	−1.94782e40	−	1.94782e40i	−0.715153	−	0.715153i
$990$	−5.36221e38	+	1.10951e39i	−0.0194209	+	0.0401843i
$991$	−2.91867e40			−1.04278			−0.521388	−	0.853320i	$-0.674586\pi$
$991$	−2.91867e40			−1.04278			−0.521388	+	0.853320i	$0.674586\pi$
$992$	2.15705e40	+	1.74495e40i	0.760242	+	0.614999i
$993$	−1.09173e39			−0.0379579
$994$	−5.06644e39	+	1.04831e40i	−0.173775	+	0.359563i
$995$	−1.46365e39	−	1.46365e39i	−0.0495251	−	0.0495251i
$996$	5.66023e39	−	4.48810e39i	0.188944	−	0.149817i
$997$	−3.47730e40	+	3.47730e40i	−1.14514	+	1.14514i	−0.157642	+	0.987496i	$0.550389\pi$
$997$	−3.47730e40	+	3.47730e40i	−1.14514	+	1.14514i	−0.987496	+	0.157642i	$0.949611\pi$
$998$	2.66158e39	−	9.27159e38i	0.0864722	−	0.0301226i
$999$			7.26497e39i			0.232863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.28.e.a.13.18	yes	106
16.5	even	4	inner	16.28.e.a.5.18	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.28.e.a.5.18	✓	106	16.5	even	4	inner
16.28.e.a.13.18	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-5041.21 + 10430.9i) q^{2} +(-329571. - 329571. i) q^{3} +(-8.33902e7 - 1.05169e8i) q^{4} +(-2.69387e8 + 2.69387e8i) q^{5} +(5.09916e9 - 1.77629e9i) q^{6} +2.71695e11i q^{7} +(1.51739e12 - 3.39659e11i) q^{8} -7.40836e12i q^{9} +(-1.45192e12 - 4.16799e12i) q^{10} +(2.66489e13 - 2.66489e13i) q^{11} +(-7.17757e12 + 6.21435e13i) q^{12} +(-4.16447e14 - 4.16447e14i) q^{13} +(-2.83402e15 - 1.36967e15i) q^{14} +1.77564e14 q^{15} +(-4.10654e15 + 1.75401e16i) q^{16} +2.48650e16 q^{17} +(7.72760e16 + 3.73471e16i) q^{18} +(3.21749e16 + 3.21749e16i) q^{19} +(5.07954e16 + 5.86686e15i) q^{20} +(8.95425e16 - 8.95425e16i) q^{21} +(1.43630e17 + 4.12316e17i) q^{22} +1.49823e18i q^{23} +(-6.12030e17 - 3.88147e17i) q^{24} +7.30544e18i q^{25} +(6.44332e18 - 2.24453e18i) q^{26} +(-4.95475e18 + 4.95475e18i) q^{27} +(2.85738e19 - 2.26567e19i) q^{28} +(8.47986e18 + 8.47986e18i) q^{29} +(-8.95138e17 + 1.85216e18i) q^{30} -1.32940e20 q^{31} +(-1.62257e20 - 1.31258e20i) q^{32} -1.75654e19 q^{33} +(-1.25350e20 + 2.59365e20i) q^{34} +(-7.31910e19 - 7.31910e19i) q^{35} +(-7.79128e20 + 6.17785e20i) q^{36} +(7.33132e20 - 7.33132e20i) q^{37} +(-4.97815e20 + 1.73414e20i) q^{38} +2.74498e20i q^{39} +(-3.17267e20 + 5.00266e20i) q^{40} -9.82451e20i q^{41} +(4.82608e20 + 1.38541e21i) q^{42} +(-1.30008e22 + 1.30008e22i) q^{43} +(-5.02490e21 - 5.80375e20i) q^{44} +(1.99572e21 + 1.99572e21i) q^{45} +(-1.56279e22 - 7.55286e21i) q^{46} -4.26559e22 q^{47} +(7.13409e21 - 4.42730e21i) q^{48} -8.10557e21 q^{49} +(-7.62024e22 - 3.68282e22i) q^{50} +(-8.19477e21 - 8.19477e21i) q^{51} +(-9.06962e21 + 7.85249e22i) q^{52} +(1.05894e23 - 1.05894e23i) q^{53} +(-2.67047e22 - 7.66605e22i) q^{54} +1.43578e22i q^{55} +(9.22835e22 + 4.12268e23i) q^{56} -2.12078e22i q^{57} +(-1.31201e23 + 4.57040e22i) q^{58} +(2.50600e23 - 2.50600e23i) q^{59} +(-1.48071e22 - 1.86742e22i) q^{60} +(2.69362e23 + 2.69362e23i) q^{61} +(6.70177e23 - 1.38668e24i) q^{62} +2.01281e24 q^{63} +(2.18712e24 - 1.03079e24i) q^{64} +2.24371e23 q^{65} +(8.85509e22 - 1.83223e23i) q^{66} +(-1.96312e24 - 1.96312e24i) q^{67} +(-2.07350e24 - 2.61502e24i) q^{68} +(4.93771e23 - 4.93771e23i) q^{69} +(1.13242e24 - 3.94478e23i) q^{70} -3.69903e24i q^{71} +(-2.51632e24 - 1.12414e25i) q^{72} -1.22287e25i q^{73} +(3.95137e24 + 1.13431e25i) q^{74} +(2.40766e24 - 2.40766e24i) q^{75} +(7.00724e23 - 6.06688e24i) q^{76} +(7.24037e24 + 7.24037e24i) q^{77} +(-2.86326e24 - 1.38380e24i) q^{78} +3.63425e25 q^{79} +(-3.61883e24 - 5.83133e24i) q^{80} -5.32273e25 q^{81} +(1.02479e25 + 4.95274e24i) q^{82} +(-8.16524e25 - 8.16524e25i) q^{83} +(-1.68840e25 - 1.95011e24i) q^{84} +(-6.69831e24 + 6.69831e24i) q^{85} +(-7.00708e25 - 2.01151e26i) q^{86} -5.58942e24i q^{87} +(3.13854e25 - 4.94885e25i) q^{88} -2.68126e26i q^{89} +(-3.08780e25 + 1.07563e25i) q^{90} +(1.13146e26 - 1.13146e26i) q^{91} +(1.57567e26 - 1.24937e26i) q^{92} +(4.38131e25 + 4.38131e25i) q^{93} +(2.15037e26 - 4.44940e26i) q^{94} -1.73350e25 q^{95} +(1.02164e25 + 9.67341e25i) q^{96} +1.84751e25 q^{97} +(4.08618e25 - 8.45485e25i) q^{98} +(-1.97425e26 - 1.97425e26i) 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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