LMFDB - Embedded newform 8.19.d.b.3.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,19,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	8.d (of order $2$, degree $1$, 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:	$16.4308910168$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 56971 x^{14} - 14457953 x^{13} + 5222713963 x^{12} - 1887111404561 x^{11} + \cdots + 32\!\cdots\!30 $ x^16 - 5x^15 + 56971x^14 - 14457953x^13 + 5222713963x^12 - 1887111404561x^11 + 551417417640415x^10 - 120118761233202509x^9 + 30966377422568512537x^8 - 9791029903061915769567x^7 + 2760409144896820517353041x^6 - 573126276959276881630152915x^5 + 113556201106829558152115445753x^4 - 24602953293990202118839424410059x^3 + 5109186069446462658360003036354309x^2 - 959560421721305781394985245626434751*x + 326887106263049715278881269448539579330
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{13}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.10
Root			$24.2392 + 253.277i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.19.d.b.3.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(74.4785 + 506.554i) q^{2} +19252.8 q^{3} +(-251050. + 75454.8i) q^{4} -901770. i q^{5} +(1.43392e6 + 9.75260e6i) q^{6} -6.41362e7i q^{7} +(-5.69197e7 - 1.21551e8i) q^{8} -1.67489e7 q^{9} +O(q^{10})$	\(q+(74.4785 + 506.554i) q^{2} +19252.8 q^{3} +(-251050. + 75454.8i) q^{4} -901770. i q^{5} +(1.43392e6 + 9.75260e6i) q^{6} -6.41362e7i q^{7} +(-5.69197e7 - 1.21551e8i) q^{8} -1.67489e7 q^{9} +(4.56795e8 - 6.71625e7i) q^{10} -4.00472e9 q^{11} +(-4.83342e9 + 1.45272e9i) q^{12} -6.96512e9i q^{13} +(3.24884e10 - 4.77677e9i) q^{14} -1.73616e10i q^{15} +(5.73326e10 - 3.78858e10i) q^{16} -4.44913e10 q^{17} +(-1.24743e9 - 8.48423e9i) q^{18} +3.48273e11 q^{19} +(6.80429e10 + 2.26389e11i) q^{20} -1.23480e12i q^{21} +(-2.98266e11 - 2.02861e12i) q^{22} +8.34298e10i q^{23} +(-1.09587e12 - 2.34019e12i) q^{24} +3.00151e12 q^{25} +(3.52821e12 - 5.18752e11i) q^{26} -7.78141e12 q^{27} +(4.83938e12 + 1.61014e13i) q^{28} -1.31449e13i q^{29} +(8.79461e12 - 1.29307e12i) q^{30} +3.17699e13i q^{31} +(2.34613e13 + 2.62204e13i) q^{32} -7.71023e13 q^{33} +(-3.31364e12 - 2.25372e13i) q^{34} -5.78361e13 q^{35} +(4.20481e12 - 1.26379e12i) q^{36} +2.75668e13i q^{37} +(2.59389e13 + 1.76419e14i) q^{38} -1.34098e14i q^{39} +(-1.09611e14 + 5.13285e13i) q^{40} -8.15259e13 q^{41} +(6.25494e14 - 9.19663e13i) q^{42} -4.72967e14 q^{43} +(1.00539e15 - 3.02175e14i) q^{44} +1.51037e13i q^{45} +(-4.22617e13 + 6.21373e12i) q^{46} -2.03341e15i q^{47} +(1.10382e15 - 7.29409e14i) q^{48} -2.48503e15 q^{49} +(2.23548e14 + 1.52043e15i) q^{50} -8.56583e14 q^{51} +(5.25552e14 + 1.74859e15i) q^{52} +8.44274e14i q^{53} +(-5.79547e14 - 3.94170e15i) q^{54} +3.61134e15i q^{55} +(-7.79579e15 + 3.65061e15i) q^{56} +6.70525e15 q^{57} +(6.65861e15 - 9.79013e14i) q^{58} +3.72136e15 q^{59} +(1.31002e15 + 4.35864e15i) q^{60} +9.22472e15i q^{61} +(-1.60932e16 + 2.36617e15i) q^{62} +1.07421e15i q^{63} +(-1.15347e16 + 1.38373e16i) q^{64} -6.28094e15 q^{65} +(-5.74246e15 - 3.90565e16i) q^{66} +1.99514e16 q^{67} +(1.11695e16 - 3.35708e15i) q^{68} +1.60626e15i q^{69} +(-4.30755e15 - 2.92971e16i) q^{70} -8.00356e16i q^{71} +(9.53344e14 + 2.03584e15i) q^{72} +7.99804e16 q^{73} +(-1.39640e16 + 2.05313e15i) q^{74} +5.77875e16 q^{75} +(-8.74340e16 + 2.62789e16i) q^{76} +2.56848e17i q^{77} +(6.79281e16 - 9.98745e15i) q^{78} -1.42845e17i q^{79} +(-3.41643e16 - 5.17009e16i) q^{80} -1.43325e17 q^{81} +(-6.07192e15 - 4.12973e16i) q^{82} -4.91298e16 q^{83} +(9.31718e16 + 3.09997e17i) q^{84} +4.01209e16i q^{85} +(-3.52259e16 - 2.39583e17i) q^{86} -2.53077e17i q^{87} +(2.27948e17 + 4.86776e17i) q^{88} -5.98246e17 q^{89} +(-7.65083e15 + 1.12490e15i) q^{90} -4.46716e17 q^{91} +(-6.29518e15 - 2.09450e16i) q^{92} +6.11660e17i q^{93} +(1.03003e18 - 1.51445e17i) q^{94} -3.14063e17i q^{95} +(4.51696e17 + 5.04817e17i) q^{96} +9.77272e17 q^{97} +(-1.85082e17 - 1.25880e18i) q^{98} +6.70748e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9}+O(q^{10}) $ 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9	$ 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9} - 1569837600 q^{10} - 2471571264 q^{11} + 4764364056 q^{12} + 26163923904 q^{14} - 192320075504 q^{16} - 176439301344 q^{17} - 1044291511122 q^{18} - 833365634368 q^{19} + 1256486405760 q^{20} + 59927319356 q^{22} - 1968891910512 q^{24} - 15320509140080 q^{25} + 4184514840864 q^{26} + 11565649473408 q^{27} - 12301604294400 q^{28} - 36336510039360 q^{30} + 141481742931936 q^{32} - 900457491648 q^{33} + 80653465357268 q^{34} + 20487495736320 q^{35} + 277183098847068 q^{36} + 493456694265564 q^{38} - 519930573603840 q^{40} - 594931562445024 q^{41} - 222362598288000 q^{42} - 25\!\cdots\!92 q^{43}+ \cdots - 81\!\cdots\!68 q^{99}+O(q^{100}) $ 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9 - 1569837600 * q^10 - 2471571264 * q^11 + 4764364056 * q^12 + 26163923904 * q^14 - 192320075504 * q^16 - 176439301344 * q^17 - 1044291511122 * q^18 - 833365634368 * q^19 + 1256486405760 * q^20 + 59927319356 * q^22 - 1968891910512 * q^24 - 15320509140080 * q^25 + 4184514840864 * q^26 + 11565649473408 * q^27 - 12301604294400 * q^28 - 36336510039360 * q^30 + 141481742931936 * q^32 - 900457491648 * q^33 + 80653465357268 * q^34 + 20487495736320 * q^35 + 277183098847068 * q^36 + 493456694265564 * q^38 - 519930573603840 * q^40 - 594931562445024 * q^41 - 222362598288000 * q^42 - 2540155017577792 * q^43 + 73781630442072 * q^44 + 153882272211264 * q^46 + 897135071530464 * q^48 - 3186415704132848 * q^49 + 5668141028706330 * q^50 + 2916050119466880 * q^51 - 4594372123628160 * q^52 - 1377307163285640 * q^54 + 8184134137073664 * q^56 + 9540488340840768 * q^57 - 10505700099162720 * q^58 + 556807886314176 * q^59 + 29677718651516160 * q^60 + 6212402633091840 * q^62 - 56432885385732032 * q^64 - 21153177930524160 * q^65 - 23515570511959320 * q^66 + 162428574934613696 * q^67 - 70717864614203736 * q^68 + 4248100663257600 * q^70 - 36801123950767128 * q^72 - 7655712852492256 * q^73 + 9613779604149984 * q^74 - 384388788469704000 * q^75 - 151130166278324584 * q^76 - 93022771634070720 * q^78 + 26870186366192640 * q^80 + 99506910981790800 * q^81 + 329788507250077556 * q^82 + 866357336138514624 * q^83 + 451843591950574080 * q^84 + 1269201398006865468 * q^86 - 758460699051663856 * q^88 - 883646550464284128 * q^89 - 1227675520905095520 * q^90 - 379834560933460992 * q^91 + 1413121475102841600 * q^92 + 671428514272869504 * q^94 - 483149691255826368 * q^96 - 2614894858526780128 * q^97 - 81635840192738166 * q^98 - 816916348833567168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	74.4785	+	506.554i	0.145466	+	0.989363i
$2$	74.4785	+	506.554i	0.145466	+	0.989363i
$3$	19252.8			0.978145			0.489073	−	0.872243i	$-0.337335\pi$
$3$	19252.8			0.978145			0.489073	+	0.872243i	$0.337335\pi$
$4$	−251050.	+	75454.8i	−0.957679	+	0.287837i
$5$		−	901770.i		−	0.461706i	−0.972989	−	0.230853i	$-0.925848\pi$
$5$		−	901770.i		−	0.461706i	0.972989	−	0.230853i	$-0.0741517\pi$
$6$	1.43392e6	+	9.75260e6i	0.142287	+	0.967741i
$7$		−	6.41362e7i		−	1.58935i	−0.607032	−	0.794677i	$-0.707640\pi$
$7$		−	6.41362e7i		−	1.58935i	0.607032	−	0.794677i	$-0.292360\pi$
$8$	−5.69197e7	−	1.21551e8i	−0.424085	−	0.905622i
$9$	−1.67489e7			−0.0432319
$10$	4.56795e8	−	6.71625e7i	0.456795	−	0.0671625i
$11$	−4.00472e9			−1.69839			−0.849197	−	0.528077i	$-0.822913\pi$
$11$	−4.00472e9			−1.69839			−0.849197	+	0.528077i	$0.822913\pi$
$12$	−4.83342e9	+	1.45272e9i	−0.936750	+	0.281546i
$13$		−	6.96512e9i		−	0.656808i	−0.944537	−	0.328404i	$-0.893489\pi$
$13$		−	6.96512e9i		−	0.656808i	0.944537	−	0.328404i	$-0.106511\pi$
$14$	3.24884e10	−	4.77677e9i	1.57245	−	0.231197i
$15$		−	1.73616e10i		−	0.451616i
$16$	5.73326e10	−	3.78858e10i	0.834300	−	0.551311i
$17$	−4.44913e10			−0.375175			−0.187588	−	0.982248i	$-0.560067\pi$
$17$	−4.44913e10			−0.375175			−0.187588	+	0.982248i	$0.560067\pi$
$18$	−1.24743e9	−	8.48423e9i	−0.00628876	−	0.0427720i
$19$	3.48273e11			1.07929			0.539644	−	0.841893i	$-0.318559\pi$
$19$	3.48273e11			1.07929			0.539644	+	0.841893i	$0.318559\pi$
$20$	6.80429e10	+	2.26389e11i	0.132896	+	0.442167i
$21$		−	1.23480e12i		−	1.55462i
$22$	−2.98266e11	−	2.02861e12i	−0.247058	−	1.68033i
$23$			8.34298e10i			0.0463202i	0.999732	+	0.0231601i	$0.00737275\pi$
$23$			8.34298e10i			0.0463202i	−0.999732	+	0.0231601i	$0.992627\pi$
$24$	−1.09587e12	−	2.34019e12i	−0.414817	−	0.885830i
$25$	3.00151e12			0.786827
$26$	3.52821e12	−	5.18752e11i	0.649822	−	0.0955432i
$27$	−7.78141e12			−1.02043
$28$	4.83938e12	+	1.61014e13i	0.457475	+	1.52209i
$29$		−	1.31449e13i		−	0.906099i	−0.891485	−	0.453049i	$-0.850336\pi$
$29$		−	1.31449e13i		−	0.906099i	0.891485	−	0.453049i	$-0.149664\pi$
$30$	8.79461e12	−	1.29307e12i	0.446812	−	0.0656947i
$31$			3.17699e13i			1.20160i	0.799399	+	0.600801i	$0.205152\pi$
$31$			3.17699e13i			1.20160i	−0.799399	+	0.600801i	$0.794848\pi$
$32$	2.34613e13	+	2.62204e13i	0.666809	+	0.745228i
$33$	−7.71023e13			−1.66128
$34$	−3.31364e12	−	2.25372e13i	−0.0545752	−	0.371185i
$35$	−5.78361e13			−0.733815
$36$	4.20481e12	−	1.26379e12i	0.0414023	−	0.0124437i
$37$			2.75668e13i			0.212114i	0.994360	+	0.106057i	$0.0338227\pi$
$37$			2.75668e13i			0.212114i	−0.994360	+	0.106057i	$0.966177\pi$
$38$	2.59389e13	+	1.76419e14i	0.157000	+	1.06781i
$39$		−	1.34098e14i		−	0.642454i
$40$	−1.09611e14	+	5.13285e13i	−0.418132	+	0.195803i
$41$	−8.15259e13			−0.249024			−0.124512	−	0.992218i	$-0.539736\pi$
$41$	−8.15259e13			−0.249024			−0.124512	+	0.992218i	$0.539736\pi$
$42$	6.25494e14	−	9.19663e13i	1.53808	−	0.226144i
$43$	−4.72967e14			−0.941055			−0.470527	−	0.882385i	$-0.655936\pi$
$43$	−4.72967e14			−0.941055			−0.470527	+	0.882385i	$0.655936\pi$
$44$	1.00539e15	−	3.02175e14i	1.62652	−	0.488861i
$45$			1.51037e13i			0.0199604i
$46$	−4.22617e13	+	6.21373e12i	−0.0458275	+	0.00673801i
$47$		−	2.03341e15i		−	1.81695i	−0.417937	−	0.908476i	$-0.637247\pi$
$47$		−	2.03341e15i		−	1.81695i	0.417937	−	0.908476i	$-0.362753\pi$
$48$	1.10382e15	−	7.29409e14i	0.816066	−	0.539262i
$49$	−2.48503e15			−1.52605
$50$	2.23548e14	+	1.52043e15i	0.114456	+	0.778458i
$51$	−8.56583e14			−0.366976
$52$	5.25552e14	+	1.74859e15i	0.189054	+	0.629012i
$53$			8.44274e14i			0.255859i	0.991783	+	0.127930i	$0.0408331\pi$
$53$			8.44274e14i			0.255859i	−0.991783	+	0.127930i	$0.959167\pi$
$54$	−5.79547e14	−	3.94170e15i	−0.148438	−	1.00958i
$55$			3.61134e15i			0.784159i
$56$	−7.79579e15	+	3.65061e15i	−1.43935	+	0.674021i
$57$	6.70525e15			1.05570
$58$	6.65861e15	−	9.79013e14i	0.896461	−	0.131806i
$59$	3.72136e15			0.429570			0.214785	−	0.976661i	$-0.431095\pi$
$59$	3.72136e15			0.429570			0.214785	+	0.976661i	$0.431095\pi$
$60$	1.31002e15	+	4.35864e15i	0.129992	+	0.432503i
$61$			9.22472e15i			0.788833i	0.918932	+	0.394416i	$0.129053\pi$
$61$			9.22472e15i			0.788833i	−0.918932	+	0.394416i	$0.870947\pi$
$62$	−1.60932e16	+	2.36617e15i	−1.18882	+	0.174792i
$63$			1.07421e15i			0.0687108i
$64$	−1.15347e16	+	1.38373e16i	−0.640304	+	0.768122i
$65$	−6.28094e15			−0.303253
$66$	−5.74246e15	−	3.90565e16i	−0.241659	−	1.64360i
$67$	1.99514e16			0.733330			0.366665	−	0.930353i	$-0.380499\pi$
$67$	1.99514e16			0.733330			0.366665	+	0.930353i	$0.380499\pi$
$68$	1.11695e16	−	3.35708e15i	0.359298	−	0.107989i
$69$			1.60626e15i			0.0453079i
$70$	−4.30755e15	−	2.92971e16i	−0.106745	−	0.726010i
$71$		−	8.00356e16i		−	1.74565i	−0.488030	−	0.872827i	$-0.662284\pi$
$71$		−	8.00356e16i		−	1.74565i	0.488030	−	0.872827i	$-0.337716\pi$
$72$	9.53344e14	+	2.03584e15i	0.0183340	+	0.0391518i
$73$	7.99804e16			1.35856			0.679278	−	0.733881i	$-0.262293\pi$
$73$	7.99804e16			1.35856			0.679278	+	0.733881i	$0.262293\pi$
$74$	−1.39640e16	+	2.05313e15i	−0.209858	+	0.0308554i
$75$	5.77875e16			0.769631
$76$	−8.74340e16	+	2.62789e16i	−1.03361	+	0.310659i
$77$			2.56848e17i			2.69935i
$78$	6.79281e16	−	9.98745e15i	0.635620	−	0.0934551i
$79$		−	1.42845e17i		−	1.19185i	−0.803041	−	0.595923i	$-0.796786\pi$
$79$		−	1.42845e17i		−	1.19185i	0.803041	−	0.595923i	$-0.203214\pi$
$80$	−3.41643e16	−	5.17009e16i	−0.254544	−	0.385202i
$81$	−1.43325e17			−0.954899
$82$	−6.07192e15	−	4.12973e16i	−0.0362244	−	0.246375i
$83$	−4.91298e16			−0.262810			−0.131405	−	0.991329i	$-0.541949\pi$
$83$	−4.91298e16			−0.262810			−0.131405	+	0.991329i	$0.541949\pi$
$84$	9.31718e16	+	3.09997e17i	0.447477	+	1.48883i
$85$			4.01209e16i			0.173221i
$86$	−3.52259e16	−	2.39583e17i	−0.136891	−	0.931045i
$87$		−	2.53077e17i		−	0.886296i
$88$	2.27948e17	+	4.86776e17i	0.720263	+	1.53810i
$89$	−5.98246e17			−1.70753			−0.853767	−	0.520655i	$-0.825688\pi$
$89$	−5.98246e17			−1.70753			−0.853767	+	0.520655i	$0.825688\pi$
$90$	−7.65083e15	+	1.12490e15i	−0.0197481	+	0.00290356i
$91$	−4.46716e17			−1.04390
$92$	−6.29518e15	−	2.09450e16i	−0.0133327	−	0.0443599i
$93$			6.11660e17i			1.17534i
$94$	1.03003e18	−	1.51445e17i	1.79763	−	0.264304i
$95$		−	3.14063e17i		−	0.498315i
$96$	4.51696e17	+	5.04817e17i	0.652236	+	0.728942i
$97$	9.77272e17			1.28549			0.642747	−	0.766079i	$-0.277795\pi$
$97$	9.77272e17			1.28549			0.642747	+	0.766079i	$0.277795\pi$
$98$	−1.85082e17	−	1.25880e18i	−0.221988	−	1.50981i
$99$	6.70748e16			0.0734247
$100$	−7.53528e17	+	2.26478e17i	−0.753528	+	0.226478i
$101$		−	1.24108e18i		−	1.13476i	−0.823455	−	0.567382i	$-0.807956\pi$
$101$		−	1.24108e18i		−	1.13476i	0.823455	−	0.567382i	$-0.192044\pi$
$102$	−6.37970e16	−	4.33905e17i	−0.0533825	−	0.363073i
$103$		−	1.20427e18i		−	0.922969i	−0.887148	−	0.461484i	$-0.847317\pi$
$103$		−	1.20427e18i		−	0.922969i	0.887148	−	0.461484i	$-0.152683\pi$
$104$	−8.46615e17	+	3.96453e17i	−0.594820	+	0.278543i
$105$	−1.11351e18			−0.717778
$106$	−4.27671e17	+	6.28803e16i	−0.253138	+	0.0372187i
$107$	1.88107e18			1.02318			0.511590	−	0.859230i	$-0.329057\pi$
$107$	1.88107e18			1.02318			0.511590	+	0.859230i	$0.329057\pi$
$108$	1.95352e18	−	5.87144e17i	0.977247	−	0.293718i
$109$			3.64101e18i			1.67642i	0.545345	+	0.838212i	$0.316399\pi$
$109$			3.64101e18i			1.67642i	−0.545345	+	0.838212i	$0.683601\pi$
$110$	−1.82934e18	+	2.68967e17i	−0.775818	+	0.114068i
$111$			5.30738e17i			0.207479i
$112$	−2.42985e18	−	3.67710e18i	−0.876229	−	1.32600i
$113$	−1.69653e17			−0.0564749			−0.0282375	−	0.999601i	$-0.508989\pi$
$113$	−1.69653e17			−0.0564749			−0.0282375	+	0.999601i	$0.508989\pi$
$114$	4.99397e17	+	3.39657e18i	0.153568	+	1.04447i
$115$	7.52345e16			0.0213863
$116$	9.91846e17	+	3.30003e18i	0.260809	+	0.867752i
$117$			1.16658e17i			0.0283951i
$118$	2.77161e17	+	1.88507e18i	0.0624877	+	0.425000i
$119$			2.85350e18i			0.596287i
$120$	−2.11032e18	+	9.88220e17i	−0.408994	+	0.191524i
$121$	1.04779e19			1.88454
$122$	−4.67282e18	+	6.87044e17i	−0.780442	+	0.114748i
$123$	−1.56960e18			−0.243581
$124$	−2.39719e18	−	7.97583e18i	−0.345866	−	1.15075i
$125$		−	6.14665e18i		−	0.824990i
$126$	−5.44146e17	+	8.00057e16i	−0.0679799	+	0.00999507i
$127$			9.09963e18i			1.05874i	0.848390	+	0.529371i	$0.177572\pi$
$127$			9.09963e18i			1.05874i	−0.848390	+	0.529371i	$0.822428\pi$
$128$	−7.86840e18	−	4.81236e18i	−0.853094	−	0.521758i
$129$	−9.10596e18			−0.920488
$130$	−4.67795e17	−	3.18164e18i	−0.0441129	−	0.300027i
$131$	5.95821e18			0.524414			0.262207	−	0.965012i	$-0.415550\pi$
$131$	5.95821e18			0.524414			0.262207	+	0.965012i	$0.415550\pi$
$132$	1.93565e19	−	5.81773e18i	1.59097	−	0.478177i
$133$		−	2.23369e19i		−	1.71537i
$134$	1.48595e18	+	1.01065e19i	0.106675	+	0.725530i
$135$			7.01704e18i			0.471140i
$136$	2.53243e18	+	5.40794e18i	0.159106	+	0.339767i
$137$	−2.88174e18			−0.169500			−0.0847501	−	0.996402i	$-0.527009\pi$
$137$	−2.88174e18			−0.169500			−0.0847501	+	0.996402i	$0.527009\pi$
$138$	−8.13657e17	+	1.19632e17i	−0.0448260	+	0.00659075i
$139$	−1.42133e19			−0.733772			−0.366886	−	0.930266i	$-0.619576\pi$
$139$	−1.42133e19			−0.733772			−0.366886	+	0.930266i	$0.619576\pi$
$140$	1.45197e19	−	4.36401e18i	0.702760	−	0.211219i
$141$		−	3.91488e19i		−	1.77724i
$142$	4.05424e19	−	5.96093e18i	1.72709	−	0.253933i
$143$			2.78934e19i			1.11552i
$144$	−9.60260e17	+	6.34547e17i	−0.0360683	+	0.0238342i
$145$	−1.18537e19			−0.418352
$146$	5.95682e18	+	4.05144e19i	0.197624	+	1.34411i
$147$	−4.78440e19			−1.49269
$148$	−2.08004e18	−	6.92063e18i	−0.0610544	−	0.203138i
$149$			6.26737e19i			1.73145i	0.500523	+	0.865723i	$0.333141\pi$
$149$			6.26737e19i			1.73145i	−0.500523	+	0.865723i	$0.666859\pi$
$150$	4.30393e18	+	2.92725e19i	0.111955	+	0.761445i
$151$		−	2.98623e19i		−	0.731696i	−0.930675	−	0.365848i	$-0.880779\pi$
$151$		−	2.98623e19i		−	0.731696i	0.930675	−	0.365848i	$-0.119221\pi$
$152$	−1.98236e19	−	4.23328e19i	−0.457710	−	0.977428i
$153$	7.45180e17			0.0162195
$154$	−1.30107e20	+	1.91296e19i	−2.67064	+	0.392663i
$155$	2.86491e19			0.554787
$156$	1.01184e19	+	3.36654e19i	0.184922	+	0.615265i
$157$		−	2.48770e19i		−	0.429241i	−0.976697	−	0.214621i	$-0.931148\pi$
$157$		−	2.48770e19i		−	0.429241i	0.976697	−	0.214621i	$-0.0688515\pi$
$158$	7.23586e19	−	1.06389e19i	1.17917	−	0.173373i
$159$			1.62547e19i			0.250267i
$160$	2.36448e19	−	2.11567e19i	0.344077	−	0.307870i
$161$	5.35087e18			0.0736192
$162$	−1.06746e19	−	7.26020e19i	−0.138905	−	0.944742i
$163$	1.08320e20			1.33359			0.666794	−	0.745242i	$-0.267666\pi$
$163$	1.08320e20			1.33359			0.666794	+	0.745242i	$0.267666\pi$
$164$	2.04671e19	−	6.15151e18i	0.238485	−	0.0716783i
$165$			6.95285e19i			0.767022i
$166$	−3.65912e18	−	2.48869e19i	−0.0382299	−	0.260015i
$167$		−	4.61780e19i		−	0.457074i	−0.973535	−	0.228537i	$-0.926606\pi$
$167$		−	4.61780e19i		−	0.457074i	0.973535	−	0.228537i	$-0.0733943\pi$
$168$	−1.50091e20	+	7.02846e19i	−1.40790	+	0.659291i
$169$	6.39425e19			0.568603
$170$	−2.03234e19	+	2.98814e18i	−0.171378	+	0.0251977i
$171$	−5.83320e18			−0.0466597
$172$	1.18738e20	−	3.56876e19i	0.901229	−	0.270870i
$173$			1.31842e19i			0.0949812i	0.998872	+	0.0474906i	$0.0151224\pi$
$173$			1.31842e19i			0.0949812i	−0.998872	+	0.0474906i	$0.984878\pi$
$174$	1.28197e20	−	1.88488e19i	0.876869	−	0.128926i
$175$		−	1.92505e20i		−	1.25055i
$176$	−2.29601e20	+	1.51722e20i	−1.41697	+	0.936343i
$177$	7.16467e19			0.420182
$178$	−4.45564e19	−	3.03044e20i	−0.248388	−	1.68937i
$179$	−3.72485e19			−0.197439			−0.0987193	−	0.995115i	$-0.531475\pi$
$179$	−3.72485e19			−0.197439			−0.0987193	+	0.995115i	$0.531475\pi$
$180$	−1.13964e18	−	3.79178e18i	−0.00574535	−	0.0191157i
$181$			2.48256e17i			0.00119067i	1.00000		0.000595336i	$0.000189501\pi$
$181$			2.48256e17i			0.00119067i	−1.00000		0.000595336i	$0.999810\pi$
$182$	−3.32708e19	−	2.26286e20i	−0.151852	−	1.03280i
$183$			1.77602e20i			0.771593i
$184$	1.01409e19	−	4.74880e18i	0.0419486	−	0.0196437i
$185$	2.48589e19			0.0979346
$186$	−3.09839e20	+	4.55556e19i	−1.16284	+	0.170972i
$187$	1.78175e20			0.637195
$188$	1.53430e20	+	5.10486e20i	0.522986	+	1.74006i
$189$			4.99070e20i			1.62183i
$190$	1.59090e20	−	2.33909e19i	0.493014	−	0.0724877i
$191$		−	1.59607e20i		−	0.471792i	−0.971778	−	0.235896i	$-0.924198\pi$
$191$		−	1.59607e20i		−	0.471792i	0.971778	−	0.235896i	$-0.0758024\pi$
$192$	−2.22075e20	+	2.66406e20i	−0.626310	+	0.751335i
$193$	−5.79946e20			−1.56089			−0.780444	−	0.625226i	$-0.785007\pi$
$193$	−5.79946e20			−1.56089			−0.780444	+	0.625226i	$0.785007\pi$
$194$	7.27858e19	+	4.95041e20i	0.186995	+	1.27182i
$195$	−1.20926e20			−0.296625
$196$	6.23868e20	−	1.87508e20i	1.46146	−	0.439253i
$197$			1.40475e20i			0.314342i	0.987571	+	0.157171i	$0.0502373\pi$
$197$			1.40475e20i			0.314342i	−0.987571	+	0.157171i	$0.949763\pi$
$198$	4.99563e18	+	3.39770e19i	0.0106808	+	0.0726437i
$199$		−	7.58756e20i		−	1.55033i	−0.631759	−	0.775165i	$-0.717667\pi$
$199$		−	7.58756e20i		−	1.55033i	0.631759	−	0.775165i	$-0.282333\pi$
$200$	−1.70845e20	−	3.64835e20i	−0.333682	−	0.712568i
$201$	3.84121e20			0.717304
$202$	6.28672e20	−	9.24334e19i	1.12269	−	0.165069i
$203$	−8.43064e20			−1.44011
$204$	2.15045e20	−	6.46333e19i	0.351445	−	0.105629i
$205$			7.35176e19i			0.114976i
$206$	6.10025e20	−	8.96919e19i	0.913152	−	0.134260i
$207$		−	1.39736e18i		−	0.00200251i
$208$	−2.63879e20	−	3.99329e20i	−0.362106	−	0.547975i
$209$	−1.39474e21			−1.83306
$210$	−8.29325e19	−	5.64052e20i	−0.104412	−	0.710143i
$211$	7.87850e19			0.0950389			0.0475195	−	0.998870i	$-0.484868\pi$
$211$	7.87850e19			0.0950389			0.0475195	+	0.998870i	$0.484868\pi$
$212$	−6.37045e19	−	2.11955e20i	−0.0736457	−	0.245031i
$213$		−	1.54091e21i		−	1.70750i
$214$	1.40099e20	+	9.52865e20i	0.148838	+	1.01230i
$215$			4.26508e20i			0.434491i
$216$	4.42916e20	+	9.45834e20i	0.432750	+	0.924126i
$217$	2.03760e21			1.90977
$218$	−1.84437e21	+	2.71177e20i	−1.65859	+	0.243862i
$219$	1.53985e21			1.32887
$220$	−2.72493e20	−	9.06627e20i	−0.225710	−	0.750973i
$221$			3.09887e20i			0.246418i
$222$	−2.68848e20	+	3.95286e19i	−0.205272	+	0.0301811i
$223$			1.02870e21i			0.754302i	0.926152	+	0.377151i	$0.123096\pi$
$223$			1.02870e21i			0.754302i	−0.926152	+	0.377151i	$0.876904\pi$
$224$	1.68168e21	−	1.50472e21i	1.18443	−	1.05980i
$225$	−5.02720e19			−0.0340160
$226$	−1.26355e19	−	8.59384e19i	−0.00821517	−	0.0558742i
$227$	−8.88017e19			−0.0554867			−0.0277433	−	0.999615i	$-0.508832\pi$
$227$	−8.88017e19			−0.0554867			−0.0277433	+	0.999615i	$0.508832\pi$
$228$	−1.68335e21	+	5.05943e20i	−1.01102	+	0.303870i
$229$		−	1.10819e21i		−	0.639872i	−0.947439	−	0.319936i	$-0.896339\pi$
$229$		−	1.10819e21i		−	0.639872i	0.947439	−	0.319936i	$-0.103661\pi$
$230$	5.60335e18	+	3.81103e19i	0.00311098	+	0.0211589i
$231$			4.94504e21i			2.64035i
$232$	−1.59777e21	+	7.48205e20i	−0.820583	+	0.384263i
$233$	1.22861e21			0.607029			0.303515	−	0.952827i	$-0.401840\pi$
$233$	1.22861e21			0.607029			0.303515	+	0.952827i	$0.401840\pi$
$234$	−5.90937e19	+	8.68853e18i	−0.0280930	+	0.00413051i
$235$	−1.83367e21			−0.838898
$236$	−9.34247e20	+	2.80794e20i	−0.411390	+	0.123646i
$237$		−	2.75017e21i		−	1.16580i
$238$	−1.44545e21	+	2.12524e20i	−0.589944	+	0.0867393i
$239$		−	5.66737e20i		−	0.222741i	−0.993779	−	0.111370i	$-0.964476\pi$
$239$		−	5.66737e20i		−	0.222741i	0.993779	−	0.111370i	$-0.0355240\pi$
$240$	−6.57760e20	−	9.95388e20i	−0.248981	−	0.376783i
$241$	1.43466e20			0.0523113			0.0261556	−	0.999658i	$-0.491673\pi$
$241$	1.43466e20			0.0523113			0.0261556	+	0.999658i	$0.491673\pi$
$242$	7.80377e20	+	5.30761e21i	0.274136	+	1.86449i
$243$	2.55259e20			0.0864023
$244$	−6.96049e20	−	2.31587e21i	−0.227055	−	0.755449i
$245$			2.24093e21i			0.704585i
$246$	−1.16902e20	−	7.95089e20i	−0.0354328	−	0.240990i
$247$		−	2.42577e21i		−	0.708886i
$248$	3.86165e21	−	1.80833e21i	1.08820	−	0.509581i
$249$	−9.45888e20			−0.257067
$250$	3.11361e21	−	4.57793e20i	0.816214	−	0.120008i
$251$	4.12850e21			1.04407			0.522033	−	0.852925i	$-0.325174\pi$
$251$	4.12850e21			1.04407			0.522033	+	0.852925i	$0.325174\pi$
$252$	−8.10544e19	−	2.69681e20i	−0.0197775	−	0.0658029i
$253$		−	3.34113e20i		−	0.0786700i
$254$	−4.60945e21	+	6.77727e20i	−1.04748	+	0.154011i
$255$			7.72441e20i			0.169435i
$256$	1.85170e21	−	4.34419e21i	0.392112	−	0.919918i
$257$	−9.73451e20			−0.199029			−0.0995144	−	0.995036i	$-0.531729\pi$
$257$	−9.73451e20			−0.199029			−0.0995144	+	0.995036i	$0.531729\pi$
$258$	−6.78198e20	−	4.61266e21i	−0.133900	−	0.910697i
$259$	1.76803e21			0.337125
$260$	1.57683e21	−	4.73927e20i	0.290419	−	0.0872874i
$261$			2.20163e20i			0.0391724i
$262$	4.43759e20	+	3.01816e21i	0.0762843	+	0.518836i
$263$		−	6.63310e21i		−	1.10183i	−0.834561	−	0.550915i	$-0.814279\pi$
$263$		−	6.63310e21i		−	1.10183i	0.834561	−	0.550915i	$-0.185721\pi$
$264$	4.38864e21	+	9.37182e21i	0.704522	+	1.50449i
$265$	7.61342e20			0.118132
$266$	1.13149e22	−	1.66362e21i	1.69713	−	0.249528i
$267$	−1.15179e22			−1.67022
$268$	−5.00879e21	+	1.50543e21i	−0.702295	+	0.211080i
$269$		−	2.27472e21i		−	0.308430i	−0.988037	−	0.154215i	$-0.950715\pi$
$269$		−	2.27472e21i		−	0.308430i	0.988037	−	0.154215i	$-0.0492849\pi$
$270$	−3.55451e21	+	5.22619e20i	−0.466129	+	0.0685348i
$271$		−	3.29856e21i		−	0.418409i	−0.977872	−	0.209205i	$-0.932913\pi$
$271$		−	3.29856e21i		−	0.418409i	0.977872	−	0.209205i	$-0.0670875\pi$
$272$	−2.55080e21	+	1.68559e21i	−0.313009	+	0.206838i
$273$	−8.60056e21			−1.02109
$274$	−2.14628e20	−	1.45976e21i	−0.0246565	−	0.167697i
$275$	−1.20202e22			−1.33634
$276$	−1.21200e20	−	4.03251e20i	−0.0130413	−	0.0433905i
$277$			1.65779e22i			1.72668i	0.504626	+	0.863338i	$0.331630\pi$
$277$			1.65779e22i			1.72668i	−0.504626	+	0.863338i	$0.668370\pi$
$278$	−1.05858e21	−	7.19980e21i	−0.106739	−	0.725967i
$279$		−	5.32111e20i		−	0.0519475i
$280$	3.29202e21	+	7.03001e21i	0.311200	+	0.664559i
$281$	1.01678e21			0.0930834			0.0465417	−	0.998916i	$-0.485180\pi$
$281$	1.01678e21			0.0930834			0.0465417	+	0.998916i	$0.485180\pi$
$282$	1.98310e22	−	2.91575e21i	1.75834	−	0.258528i
$283$	1.48763e22			1.27766			0.638831	−	0.769347i	$-0.279418\pi$
$283$	1.48763e22			1.27766			0.638831	+	0.769347i	$0.279418\pi$
$284$	6.03907e21	+	2.00929e22i	0.502464	+	1.67178i
$285$		−	6.04659e21i		−	0.487424i
$286$	−1.41295e22	+	2.07746e21i	−1.10365	+	0.162270i
$287$			5.22876e21i			0.395787i
$288$	−3.92951e20	−	4.39163e20i	−0.0288274	−	0.0322176i
$289$	−1.20836e22			−0.859243
$290$	−8.82845e20	−	6.00453e21i	−0.0608559	−	0.413902i
$291$	1.88153e22			1.25740
$292$	−2.00791e22	+	6.03490e21i	−1.30106	+	0.391043i
$293$			5.01654e21i			0.315207i	0.987502	+	0.157603i	$0.0503768\pi$
$293$			5.01654e21i			0.315207i	−0.987502	+	0.157603i	$0.949623\pi$
$294$	−3.56335e21	−	2.42355e22i	−0.217136	−	1.47682i
$295$		−	3.35581e21i		−	0.198335i
$296$	3.35075e21	−	1.56909e21i	0.192096	−	0.0899545i
$297$	3.11624e22			1.73310
$298$	−3.17476e22	+	4.66785e21i	−1.71303	+	0.251866i
$299$	5.81099e20			0.0304235
$300$	−1.45076e22	+	4.36034e21i	−0.737060	+	0.221528i
$301$			3.03343e22i			1.49567i
$302$	1.51269e22	−	2.22410e21i	0.723913	−	0.106437i
$303$		−	2.38942e22i		−	1.10996i
$304$	1.99674e22	−	1.31946e22i	0.900450	−	0.595024i
$305$	8.31858e21			0.364209
$306$	5.54999e19	+	3.77474e20i	0.00235939	+	0.0160470i
$307$	7.20961e19			0.00297623			0.00148811	−	0.999999i	$-0.499526\pi$
$307$	7.20961e19			0.00297623			0.00148811	+	0.999999i	$0.499526\pi$
$308$	−1.93804e22	−	6.44816e22i	−0.776972	−	2.58511i
$309$		−	2.31855e22i		−	0.902798i
$310$	2.13375e21	+	1.45123e22i	0.0807026	+	0.548886i
$311$		−	4.12301e22i		−	1.51485i	−0.652920	−	0.757427i	$-0.726456\pi$
$311$		−	4.12301e22i		−	1.51485i	0.652920	−	0.757427i	$-0.273544\pi$
$312$	−1.62997e22	+	7.63284e21i	−0.581821	+	0.272455i
$313$	−5.52191e21			−0.191509			−0.0957547	−	0.995405i	$-0.530526\pi$
$313$	−5.52191e21			−0.191509			−0.0957547	+	0.995405i	$0.530526\pi$
$314$	1.26016e22	−	1.85280e21i	0.424676	−	0.0624400i
$315$	9.68692e20			0.0317242
$316$	1.07783e22	+	3.58612e22i	0.343058	+	1.14141i
$317$			1.33182e22i			0.412015i	0.978550	+	0.206008i	$0.0660472\pi$
$317$			1.33182e22i			0.412015i	−0.978550	+	0.206008i	$0.933953\pi$
$318$	−8.23387e21	+	1.21062e21i	−0.247605	+	0.0364053i
$319$			5.26417e22i			1.53891i
$320$	1.24780e22	+	1.04016e22i	0.354647	+	0.295632i
$321$	3.62160e22			1.00082
$322$	3.98525e20	+	2.71050e21i	0.0107091	+	0.0728362i
$323$	−1.54951e22			−0.404923
$324$	3.59818e22	−	1.08146e22i	0.914487	−	0.274855i
$325$		−	2.09059e22i		−	0.516795i
$326$	8.06754e21	+	5.48701e22i	0.193991	+	1.31940i
$327$			7.00998e22i			1.63979i
$328$	4.64043e21	+	9.90952e21i	0.105607	+	0.225521i
$329$	−1.30415e23			−2.88778
$330$	−3.52200e22	+	5.17838e21i	−0.758863	+	0.111575i
$331$	7.95162e21			0.166726			0.0833631	−	0.996519i	$-0.473434\pi$
$331$	7.95162e21			0.166726			0.0833631	+	0.996519i	$0.473434\pi$
$332$	1.23340e22	−	3.70708e21i	0.251688	−	0.0756465i
$333$		−	4.61713e20i		−	0.00917010i
$334$	2.33917e22	−	3.43927e21i	0.452213	−	0.0664887i
$335$		−	1.79916e22i		−	0.338583i
$336$	−4.67815e22	−	7.07945e22i	−0.857079	−	1.29702i
$337$	6.65602e22			1.18726			0.593629	−	0.804739i	$-0.297695\pi$
$337$	6.65602e22			1.18726			0.593629	+	0.804739i	$0.297695\pi$
$338$	4.76234e21	+	3.23903e22i	0.0827123	+	0.562555i
$339$	−3.26630e21			−0.0552407
$340$	−3.02731e21	−	1.00723e22i	−0.0498594	−	0.165890i
$341$		−	1.27230e23i		−	2.04079i
$342$	−4.34448e20	−	2.95483e21i	−0.00678739	−	0.0461634i
$343$			5.49404e22i			0.836074i
$344$	2.69212e22	+	5.74894e22i	0.399087	+	0.852240i
$345$	1.44848e21			0.0209190
$346$	−6.67849e21	+	9.81936e20i	−0.0939709	+	0.0138165i
$347$	−1.17440e23			−1.61009			−0.805044	−	0.593215i	$-0.797858\pi$
$347$	−1.17440e23			−1.61009			−0.805044	+	0.593215i	$0.797858\pi$
$348$	1.90958e22	+	6.35349e22i	0.255109	+	0.848788i
$349$		−	6.96686e22i		−	0.907002i	−0.891256	−	0.453501i	$-0.850175\pi$
$349$		−	6.96686e22i		−	0.907002i	0.891256	−	0.453501i	$-0.149825\pi$
$350$	9.75143e22	−	1.43375e22i	1.23725	−	0.181912i
$351$			5.41985e22i			0.670228i
$352$	−9.39558e22	−	1.05005e23i	−1.13250	−	1.26569i
$353$	5.24943e21			0.0616793			0.0308397	−	0.999524i	$-0.490182\pi$
$353$	5.24943e21			0.0616793			0.0308397	+	0.999524i	$0.490182\pi$
$354$	5.33614e21	+	3.62929e22i	0.0611220	+	0.415712i
$355$	−7.21737e22			−0.805980
$356$	1.50190e23	−	4.51405e22i	1.63527	−	0.491492i
$357$			5.49379e22i			0.583255i
$358$	−2.77422e21	−	1.88684e22i	−0.0287206	−	0.195338i
$359$			2.69352e22i			0.271938i	0.990713	+	0.135969i	$0.0434148\pi$
$359$			2.69352e22i			0.271938i	−0.990713	+	0.135969i	$0.956585\pi$
$360$	1.83586e21	−	8.59697e20i	0.0180766	−	0.00846492i
$361$	1.71669e22			0.164865
$362$	−1.25755e20	+	1.84897e19i	−0.00117801	+	0.000173202i
$363$	2.01729e23			1.84335
$364$	1.12148e23	−	3.37069e22i	0.999723	−	0.300473i
$365$		−	7.21239e22i		−	0.627254i
$366$	−8.99650e22	+	1.32275e22i	−0.763386	+	0.112240i
$367$		−	1.77388e23i		−	1.46869i	−0.678776	−	0.734346i	$-0.737489\pi$
$367$		−	1.77388e23i		−	1.46869i	0.678776	−	0.734346i	$-0.262511\pi$
$368$	3.16081e21	+	4.78325e21i	0.0255369	+	0.0386449i
$369$	1.36547e21			0.0107658
$370$	1.85145e21	+	1.25924e22i	0.0142461	+	0.0968929i
$371$	5.41485e22			0.406651
$372$	−4.61527e22	−	1.53557e23i	−0.338307	−	1.12560i
$373$			1.33782e23i			0.957233i	0.878024	+	0.478616i	$0.158862\pi$
$373$			1.33782e23i			0.957233i	−0.878024	+	0.478616i	$0.841138\pi$
$374$	1.32702e22	+	9.02553e22i	0.0926902	+	0.630418i
$375$		−	1.18340e23i		−	0.806960i
$376$	−2.47162e23	+	1.15741e23i	−1.64547	+	0.770542i
$377$	−9.15559e22			−0.595133
$378$	−2.52806e23	+	3.71700e22i	−1.60458	+	0.235921i
$379$	5.75609e22			0.356759			0.178379	−	0.983962i	$-0.442915\pi$
$379$	5.75609e22			0.356759			0.178379	+	0.983962i	$0.442915\pi$
$380$	2.36975e22	+	7.88454e22i	0.143433	+	0.477226i
$381$			1.75194e23i			1.03560i
$382$	8.08493e22	−	1.18873e22i	0.466773	−	0.0686296i
$383$			2.65245e23i			1.49575i	0.663842	+	0.747873i	$0.268925\pi$
$383$			2.65245e23i			1.49575i	−0.663842	+	0.747873i	$0.731075\pi$
$384$	−1.51489e23	−	9.26516e22i	−0.834450	−	0.510355i
$385$	2.31618e23			1.24631
$386$	−4.31935e22	−	2.93774e23i	−0.227056	−	1.54429i
$387$	7.92169e21			0.0406836
$388$	−2.45344e23	+	7.37398e22i	−1.23109	+	0.370013i
$389$			2.80395e23i			1.37475i	0.726302	+	0.687375i	$0.241237\pi$
$389$			2.80395e23i			1.37475i	−0.726302	+	0.687375i	$0.758763\pi$
$390$	−9.00638e21	−	6.12555e22i	−0.0431488	−	0.293470i
$391$		−	3.71190e21i		−	0.0173782i
$392$	1.41447e23	+	3.02057e23i	0.647173	+	1.38202i
$393$	1.14712e23			0.512953
$394$	−7.11580e22	+	1.04623e22i	−0.310998	+	0.0457260i
$395$	−1.28813e23			−0.550283
$396$	−1.68391e22	+	5.06111e21i	−0.0703174	+	0.0211344i
$397$		−	1.39840e23i		−	0.570843i	−0.958402	−	0.285422i	$-0.907866\pi$
$397$		−	1.39840e23i		−	0.570843i	0.958402	−	0.285422i	$-0.0921336\pi$
$398$	3.84351e23	−	5.65110e22i	1.53384	−	0.225520i
$399$		−	4.30049e23i		−	1.67788i
$400$	1.72084e23	−	1.13715e23i	0.656450	−	0.433787i
$401$	−1.63795e23			−0.610944			−0.305472	−	0.952201i	$-0.598814\pi$
$401$	−1.63795e23			−0.610944			−0.305472	+	0.952201i	$0.598814\pi$
$402$	2.86087e22	+	1.94578e23i	0.104343	+	0.709674i
$403$	2.21281e23			0.789222
$404$	9.36450e22	+	3.11572e23i	0.326627	+	1.08674i
$405$			1.29246e23i			0.440883i
$406$	−6.27901e22	−	4.27057e23i	−0.209487	−	1.42479i
$407$		−	1.10397e23i		−	0.360254i
$408$	4.87565e22	+	1.04118e23i	0.155629	+	0.332342i
$409$	−1.75290e23			−0.547327			−0.273664	−	0.961825i	$-0.588236\pi$
$409$	−1.75290e23			−0.547327			−0.273664	+	0.961825i	$0.588236\pi$
$410$	−3.72406e22	+	5.47548e21i	−0.113753	+	0.0167251i
$411$	−5.54817e22			−0.165796
$412$	9.08675e22	+	3.02331e23i	0.265665	+	0.883908i
$413$		−	2.38674e23i		−	0.682738i
$414$	7.07838e20	−	1.04073e20i	0.00198121	−	0.000291297i
$415$			4.43038e22i			0.121341i
$416$	1.82628e23	−	1.63411e23i	0.489472	−	0.437966i
$417$	−2.73646e23			−0.717736
$418$	−1.03878e23	−	7.06510e23i	−0.266647	−	1.81356i
$419$	−6.82114e23			−1.71368			−0.856842	−	0.515580i	$-0.827577\pi$
$419$	−6.82114e23			−1.71368			−0.856842	+	0.515580i	$0.827577\pi$
$420$	2.79546e23	−	8.40195e22i	0.687401	−	0.206603i
$421$		−	2.69375e23i		−	0.648364i	−0.945995	−	0.324182i	$-0.894911\pi$
$421$		−	2.69375e23i		−	0.648364i	0.945995	−	0.324182i	$-0.105089\pi$
$422$	5.86779e21	+	3.99089e22i	0.0138249	+	0.0940280i
$423$			3.40574e22i			0.0785503i
$424$	1.02622e23	−	4.80559e22i	0.231712	−	0.108506i
$425$	−1.33541e23			−0.295198
$426$	7.80555e23	−	1.14765e23i	1.68934	−	0.248383i
$427$	5.91638e23			1.25373
$428$	−4.72243e23	+	1.41936e23i	−0.979877	+	0.294509i
$429$			5.37027e23i			1.09114i
$430$	−2.16049e23	+	3.17657e22i	−0.429870	+	0.0632036i
$431$		−	5.78076e23i		−	1.12639i	−0.826324	−	0.563196i	$-0.809572\pi$
$431$		−	5.78076e23i		−	1.12639i	0.826324	−	0.563196i	$-0.190428\pi$
$432$	−4.46129e23	+	2.94805e23i	−0.851346	+	0.562576i
$433$	3.81902e23			0.713774			0.356887	−	0.934147i	$-0.383838\pi$
$433$	3.81902e23			0.713774			0.356887	+	0.934147i	$0.383838\pi$
$434$	1.51757e23	+	1.03215e24i	0.277806	+	1.88946i
$435$	−2.28217e23			−0.409209
$436$	−2.74732e23	−	9.14076e23i	−0.482537	−	1.60548i
$437$			2.90564e22i			0.0499929i
$438$	1.14686e23	+	7.80017e23i	0.193305	+	1.31473i
$439$		−	1.10083e23i		−	0.181777i	−0.995861	−	0.0908885i	$-0.971029\pi$
$439$		−	1.10083e23i		−	0.181777i	0.995861	−	0.0908885i	$-0.0289707\pi$
$440$	4.38960e23	−	2.05557e23i	0.710152	−	0.332550i
$441$	4.16216e22			0.0659739
$442$	−1.56975e23	+	2.30799e22i	−0.243797	+	0.0358455i
$443$	−3.53389e23			−0.537799			−0.268899	−	0.963168i	$-0.586660\pi$
$443$	−3.53389e23			−0.537799			−0.268899	+	0.963168i	$0.586660\pi$
$444$	−4.00467e22	−	1.33242e23i	−0.0597201	−	0.198698i
$445$			5.39480e23i			0.788380i
$446$	−5.21092e23	+	7.66161e22i	−0.746279	+	0.109725i
$447$			1.20665e24i			1.69361i
$448$	8.87468e23	+	7.39791e23i	1.22082	+	1.01767i
$449$	−4.03200e23			−0.543631			−0.271815	−	0.962349i	$-0.587624\pi$
$449$	−4.03200e23			−0.543631			−0.271815	+	0.962349i	$0.587624\pi$
$450$	−3.74418e21	−	2.54655e22i	−0.00494817	−	0.0336542i
$451$	3.26488e23			0.422940
$452$	4.25914e22	−	1.28011e22i	0.0540849	−	0.0162556i
$453$		−	5.74934e23i		−	0.715705i
$454$	−6.61382e21	−	4.49829e22i	−0.00807141	−	0.0548965i
$455$			4.02836e23i			0.481976i
$456$	−3.81661e23	−	8.15027e23i	−0.447707	−	0.956067i
$457$	−1.42418e23			−0.163802			−0.0819008	−	0.996640i	$-0.526099\pi$
$457$	−1.42418e23			−0.163802			−0.0819008	+	0.996640i	$0.526099\pi$
$458$	5.61356e23	−	8.25360e22i	0.633066	−	0.0930795i
$459$	3.46205e23			0.382841
$460$	−1.88876e22	+	5.67680e21i	−0.0204813	+	0.00615578i
$461$		−	1.02010e24i		−	1.08476i	−0.840133	−	0.542380i	$-0.817523\pi$
$461$		−	1.02010e24i		−	1.08476i	0.840133	−	0.542380i	$-0.182477\pi$
$462$	−2.50493e24	+	3.68299e23i	−2.61227	+	0.384081i
$463$			6.28501e23i			0.642802i	0.946943	+	0.321401i	$0.104154\pi$
$463$			6.28501e23i			0.642802i	−0.946943	+	0.321401i	$0.895846\pi$
$464$	−4.98006e23	−	7.53632e23i	−0.499542	−	0.755958i
$465$	5.51577e23			0.542662
$466$	9.15048e22	+	6.22356e23i	0.0883020	+	0.600572i
$467$	−3.13589e23			−0.296831			−0.148416	−	0.988925i	$-0.547417\pi$
$467$	−3.13589e23			−0.296831			−0.148416	+	0.988925i	$0.547417\pi$
$468$	−8.80242e21	−	2.92871e22i	−0.00817315	−	0.0271934i
$469$		−	1.27961e24i		−	1.16552i
$470$	−1.36569e23	−	9.28851e23i	−0.122031	−	0.829975i
$471$		−	4.78953e23i		−	0.419860i
$472$	−2.11819e23	−	4.52333e23i	−0.182174	−	0.389028i
$473$	1.89410e24			1.59828
$474$	1.39311e24	−	2.04828e23i	1.15340	−	0.169584i
$475$	1.04534e24			0.849214
$476$	−2.15310e23	−	7.16371e23i	−0.171633	−	0.571051i
$477$		−	1.41407e22i		−	0.0110613i
$478$	2.87083e23	−	4.22097e22i	0.220372	−	0.0324012i
$479$			1.50901e24i			1.13677i	0.822764	+	0.568383i	$0.192431\pi$
$479$			1.50901e24i			1.13677i	−0.822764	+	0.568383i	$0.807569\pi$
$480$	4.55229e23	−	4.07326e23i	0.336557	−	0.301142i
$481$	1.92006e23			0.139319
$482$	1.06851e22	+	7.26732e22i	0.00760950	+	0.0517548i
$483$	1.03019e23			0.0720103
$484$	−2.63047e24	+	7.90606e23i	−1.80478	+	0.542440i
$485$		−	8.81275e23i		−	0.593521i
$486$	1.90113e22	+	1.29303e23i	0.0125686	+	0.0854832i
$487$			9.60144e23i			0.623126i	0.950226	+	0.311563i	$0.100852\pi$
$487$			9.60144e23i			0.623126i	−0.950226	+	0.311563i	$0.899148\pi$
$488$	1.12127e24	−	5.25069e23i	0.714385	−	0.334532i
$489$	2.08547e24			1.30444
$490$	−1.13515e24	+	1.66901e23i	−0.697091	+	0.102493i
$491$	6.43315e23			0.387874			0.193937	−	0.981014i	$-0.437874\pi$
$491$	6.43315e23			0.387874			0.193937	+	0.981014i	$0.437874\pi$
$492$	3.94049e23	−	1.18434e23i	0.233273	−	0.0701117i
$493$			5.84833e23i			0.339946i
$494$	1.22878e24	−	1.80667e23i	0.701346	−	0.103119i
$495$		−	6.04860e22i		−	0.0339007i
$496$	1.20363e24	+	1.82145e24i	0.662457	+	1.00250i
$497$	−5.13318e24			−2.77446
$498$	−7.04483e22	−	4.79143e23i	−0.0373944	−	0.254332i
$499$	−3.20532e24			−1.67096			−0.835481	−	0.549519i	$-0.814811\pi$
$499$	−3.20532e24			−1.67096			−0.835481	+	0.549519i	$0.814811\pi$
$500$	4.63794e23	+	1.54312e24i	0.237463	+	0.790076i
$501$		−	8.89057e23i		−	0.447085i
$502$	3.07484e23	+	2.09131e24i	0.151876	+	1.03296i
$503$		−	3.87516e23i		−	0.188008i	−0.995572	−	0.0940042i	$-0.970033\pi$
$503$		−	3.87516e23i		−	0.188008i	0.995572	−	0.0940042i	$-0.0299667\pi$
$504$	1.30571e23	−	6.11438e22i	0.0622260	−	0.0291392i
$505$	−1.11916e24			−0.523928
$506$	1.69246e23	−	2.48842e22i	0.0778332	−	0.0114438i
$507$	1.23107e24			0.556176
$508$	−6.86610e23	−	2.28446e24i	−0.304745	−	1.01394i
$509$			1.28844e24i			0.561828i	0.959733	+	0.280914i	$0.0906375\pi$
$509$			1.28844e24i			0.561828i	−0.959733	+	0.280914i	$0.909363\pi$
$510$	−3.91283e23	+	5.75302e22i	−0.167633	+	0.0246470i
$511$		−	5.12963e24i		−	2.15923i
$512$	2.33848e24	+	6.14435e23i	0.967172	+	0.254124i
$513$	−2.71006e24			−1.10134
$514$	−7.25012e22	−	4.93105e23i	−0.0289519	−	0.196912i
$515$	−1.08597e24			−0.426141
$516$	2.28605e24	−	6.87088e23i	0.881533	−	0.264951i
$517$			8.14323e24i			3.08590i
$518$	1.31680e23	+	8.95601e23i	0.0490401	+	0.333539i
$519$			2.53832e23i			0.0929054i
$520$	3.57510e23	+	7.63452e23i	0.128605	+	0.274632i
$521$	2.25884e24			0.798631			0.399315	−	0.916814i	$-0.369248\pi$
$521$	2.25884e24			0.798631			0.399315	+	0.916814i	$0.369248\pi$
$522$	−1.11524e23	+	1.63974e22i	−0.0387557	+	0.00569824i
$523$	−3.36407e24			−1.14908			−0.574540	−	0.818477i	$-0.694819\pi$
$523$	−3.36407e24			−1.14908			−0.574540	+	0.818477i	$0.694819\pi$
$524$	−1.49581e24	+	4.49575e23i	−0.502220	+	0.150946i
$525$		−	3.70627e24i		−	1.22322i
$526$	3.36002e24	−	4.94023e23i	1.09011	−	0.160279i
$527$		−	1.41348e24i		−	0.450811i
$528$	−4.42048e24	+	2.92108e24i	−1.38600	+	0.915880i
$529$	3.23719e24			0.997854
$530$	5.67036e22	+	3.85661e23i	0.0171841	+	0.116875i
$531$	−6.23288e22			−0.0185711
$532$	1.68543e24	+	5.60768e24i	0.493748	+	1.64278i
$533$			5.67838e23i			0.163561i
$534$	−8.57838e23	−	5.83445e24i	−0.242959	−	1.65245i
$535$		−	1.69630e24i		−	0.472408i
$536$	−1.13563e24	−	2.42510e24i	−0.310994	−	0.664120i
$537$	−7.17140e23			−0.193124
$538$	1.15227e24	−	1.69418e23i	0.305150	−	0.0448661i
$539$	9.95187e24			2.59183
$540$	−5.29469e23	−	1.76163e24i	−0.135612	−	0.451201i
$541$			4.51285e23i			0.113678i	0.998383	+	0.0568389i	$0.0181021\pi$
$541$			4.51285e23i			0.113678i	−0.998383	+	0.0568389i	$0.981898\pi$
$542$	1.67090e24	−	2.45672e23i	0.413959	−	0.0608642i
$543$			4.77963e21i			0.00116465i
$544$	−1.04382e24	−	1.16658e24i	−0.250170	−	0.279591i
$545$	3.28336e24			0.774016
$546$	−6.40556e23	−	4.35665e24i	−0.148533	−	1.01023i
$547$	−2.07543e24			−0.473393			−0.236696	−	0.971584i	$-0.576065\pi$
$547$	−2.07543e24			−0.473393			−0.236696	+	0.971584i	$0.576065\pi$
$548$	7.23461e23	−	2.17441e23i	0.162327	−	0.0487884i
$549$		−	1.54504e23i		−	0.0341027i
$550$	−8.95247e23	−	6.08888e24i	−0.194392	−	1.32213i
$551$		−	4.57802e24i		−	0.977942i
$552$	1.95242e23	−	9.14279e22i	0.0410319	−	0.0192144i
$553$	−9.16152e24			−1.89427
$554$	−8.39759e24	+	1.23470e24i	−1.70831	+	0.251172i
$555$	4.78604e23			0.0957942
$556$	3.56824e24	−	1.07246e24i	0.702719	−	0.211207i
$557$			1.02777e24i			0.199158i	0.995030	+	0.0995789i	$0.0317496\pi$
$557$			1.02777e24i			0.199158i	−0.995030	+	0.0995789i	$0.968250\pi$
$558$	2.69543e23	−	3.96309e22i	0.0513950	−	0.00755659i
$559$			3.29428e24i			0.618093i
$560$	−3.31590e24	+	2.19117e24i	−0.612222	+	0.404560i
$561$	3.43038e24			0.623270
$562$	7.57286e22	+	5.15056e23i	0.0135404	+	0.0920933i
$563$	−2.08140e24			−0.366252			−0.183126	−	0.983089i	$-0.558622\pi$
$563$	−2.08140e24			−0.366252			−0.183126	+	0.983089i	$0.558622\pi$
$564$	2.95397e24	+	9.82831e24i	0.511556	+	1.70203i
$565$			1.52988e23i			0.0260748i
$566$	1.10796e24	+	7.53563e24i	0.185856	+	1.26407i
$567$			9.19233e24i			1.51767i
$568$	−9.72837e24	+	4.55560e24i	−1.58090	+	0.740306i
$569$	6.16361e24			0.985881			0.492941	−	0.870063i	$-0.335922\pi$
$569$	6.16361e24			0.985881			0.492941	+	0.870063i	$0.335922\pi$
$570$	3.06293e24	−	4.50341e23i	0.482239	−	0.0709035i
$571$	7.55309e24			1.17058			0.585288	−	0.810825i	$-0.300981\pi$
$571$	7.55309e24			1.17058			0.585288	+	0.810825i	$0.300981\pi$
$572$	−2.10469e24	−	7.00263e24i	−0.321088	−	1.06831i
$573$		−	3.07288e24i		−	0.461481i
$574$	−2.64865e24	+	3.89430e23i	−0.391577	+	0.0575735i
$575$			2.50415e23i			0.0364460i
$576$	1.93194e23	−	2.31759e23i	0.0276815	−	0.0332074i
$577$	4.79719e24			0.676713			0.338356	−	0.941018i	$-0.390129\pi$
$577$	4.79719e24			0.676713			0.338356	+	0.941018i	$0.390129\pi$
$578$	−8.99969e23	−	6.12100e24i	−0.124991	−	0.850104i
$579$	−1.11656e25			−1.52678
$580$	2.97587e24	−	8.94417e23i	0.400647	−	0.120417i
$581$			3.15100e24i			0.417699i
$582$	1.40133e24	+	9.53094e24i	0.182909	+	1.24402i
$583$		−	3.38108e24i		−	0.434549i
$584$	−4.55246e24	−	9.72166e24i	−0.576144	−	1.23034i
$585$	1.05199e23			0.0131102
$586$	−2.54115e24	+	3.73624e23i	−0.311854	+	0.0458518i
$587$	2.40438e24			0.290576			0.145288	−	0.989389i	$-0.453589\pi$
$587$	2.40438e24			0.290576			0.145288	+	0.989389i	$0.453589\pi$
$588$	1.20112e25	−	3.61005e24i	1.42952	−	0.429653i
$589$			1.10646e25i			1.29688i
$590$	1.69990e24	−	2.49936e23i	0.196225	−	0.0288510i
$591$			2.70453e24i			0.307472i
$592$	1.04439e24	+	1.58047e24i	0.116941	+	0.176967i
$593$	1.42297e24			0.156929			0.0784644	−	0.996917i	$-0.474998\pi$
$593$	1.42297e24			0.156929			0.0784644	+	0.996917i	$0.474998\pi$
$594$	2.32093e24	+	1.57854e25i	0.252106	+	1.71466i
$595$	2.57320e24			0.275309
$596$	−4.72903e24	−	1.57342e25i	−0.498375	−	1.65817i
$597$		−	1.46082e25i		−	1.51645i
$598$	4.32794e22	+	2.94358e23i	0.00442558	+	0.0300999i
$599$			7.65150e24i			0.770735i	0.922763	+	0.385367i	$0.125925\pi$
$599$			7.65150e24i			0.770735i	−0.922763	+	0.385367i	$0.874075\pi$
$600$	−3.28925e24	−	7.02411e24i	−0.326389	−	0.696995i
$601$	−1.43021e25			−1.39807			−0.699034	−	0.715088i	$-0.746386\pi$
$601$	−1.43021e25			−1.39807			−0.699034	+	0.715088i	$0.746386\pi$
$602$	−1.53660e25	+	2.25925e24i	−1.47976	+	0.217569i
$603$	−3.34164e23			−0.0317033
$604$	2.25325e24	+	7.49693e24i	0.210609	+	0.700730i
$605$		−	9.44865e24i		−	0.870104i
$606$	1.21037e25	−	1.77960e24i	1.09816	−	0.161462i
$607$		−	1.73076e25i		−	1.54717i	−0.633690	−	0.773587i	$-0.718460\pi$
$607$		−	1.73076e25i		−	1.54717i	0.633690	−	0.773587i	$-0.281540\pi$
$608$	8.17093e24	+	9.13186e24i	0.719680	+	0.804317i
$609$	−1.62314e25			−1.40864
$610$	6.19556e23	+	4.21381e24i	0.0529800	+	0.360335i
$611$	−1.41629e25			−1.19339
$612$	−1.87077e23	+	5.62274e22i	−0.0155331	+	0.00466859i
$613$		−	2.30830e25i		−	1.88864i	−0.329033	−	0.944318i	$-0.606723\pi$
$613$		−	2.30830e25i		−	1.88864i	0.329033	−	0.944318i	$-0.393277\pi$
$614$	5.36961e21	+	3.65205e22i	0.000432939	+	0.00294457i
$615$			1.41542e24i			0.112463i
$616$	3.12200e25	−	1.46197e25i	2.44459	−	1.14475i
$617$	8.84924e24			0.682872			0.341436	−	0.939905i	$-0.389087\pi$
$617$	8.84924e24			0.682872			0.341436	+	0.939905i	$0.389087\pi$
$618$	1.17447e25	−	1.72682e24i	0.893195	−	0.131326i
$619$	1.54376e25			1.15708			0.578542	−	0.815653i	$-0.303622\pi$
$619$	1.54376e25			1.15708			0.578542	+	0.815653i	$0.303622\pi$
$620$	−7.19237e24	+	2.16171e24i	−0.531308	+	0.159688i
$621$		−	6.49201e23i		−	0.0472667i
$622$	2.08853e25	−	3.07076e24i	1.49874	−	0.220360i
$623$			3.83692e25i			2.71388i
$624$	−5.08043e24	−	7.68821e24i	−0.354192	−	0.535999i
$625$	5.90697e24			0.405924
$626$	−4.11263e23	−	2.79714e24i	−0.0278581	−	0.189472i
$627$	−2.68527e25			−1.79300
$628$	1.87709e24	+	6.24538e24i	0.123552	+	0.411076i
$629$		−	1.22648e24i		−	0.0795801i
$630$	7.21467e22	+	4.90695e23i	0.00461479	+	0.0313868i
$631$		−	1.15644e25i		−	0.729224i	−0.931160	−	0.364612i	$-0.881202\pi$
$631$		−	1.15644e25i		−	0.729224i	0.931160	−	0.364612i	$-0.118798\pi$
$632$	−1.73629e25	+	8.13068e24i	−1.07936	+	0.505444i
$633$	1.51683e24			0.0929619
$634$	−6.74641e24	+	9.91923e23i	−0.407633	+	0.0599342i
$635$	8.20578e24			0.488828
$636$	−1.22649e24	−	4.08073e24i	−0.0720362	−	0.239676i
$637$			1.73086e25i			1.00232i
$638$	−2.66659e25	+	3.92067e24i	−1.52254	+	0.223859i
$639$			1.34051e24i			0.0754679i
$640$	−4.33965e24	+	7.09549e24i	−0.240899	+	0.393879i
$641$	2.61107e25			1.42921			0.714605	−	0.699528i	$-0.246606\pi$
$641$	2.61107e25			1.42921			0.714605	+	0.699528i	$0.246606\pi$
$642$	2.69731e24	+	1.83454e25i	0.145585	+	0.990172i
$643$	−2.18361e25			−1.16219			−0.581095	−	0.813836i	$-0.697376\pi$
$643$	−2.18361e25			−1.16219			−0.581095	+	0.813836i	$0.697376\pi$
$644$	−1.34333e24	+	4.03748e23i	−0.0705036	+	0.0211903i
$645$			8.21148e24i			0.424995i
$646$	−1.15405e24	−	7.84911e24i	−0.0589024	−	0.400616i
$647$			8.93428e24i			0.449698i	0.974394	+	0.224849i	$0.0721889\pi$
$647$			8.93428e24i			0.449698i	−0.974394	+	0.224849i	$0.927811\pi$
$648$	8.15803e24	+	1.74213e25i	0.404958	+	0.864778i
$649$	−1.49030e25			−0.729578
$650$	1.05900e25	−	1.55704e24i	0.511298	−	0.0751760i
$651$	3.92296e25			1.86803
$652$	−2.71938e25	+	8.17329e24i	−1.27715	+	0.383856i
$653$		−	2.28994e25i		−	1.06073i	−0.847769	−	0.530365i	$-0.822055\pi$
$653$		−	2.28994e25i		−	1.06073i	0.847769	−	0.530365i	$-0.177945\pi$
$654$	−3.55094e25	+	5.22093e24i	−1.62234	+	0.238533i
$655$		−	5.37294e24i		−	0.242125i
$656$	−4.67409e24	+	3.08867e24i	−0.207760	+	0.137290i
$657$	−1.33958e24			−0.0587330
$658$	−9.71310e24	−	6.60622e25i	−0.420073	−	2.85706i
$659$	2.86787e25			1.22346			0.611731	−	0.791066i	$-0.290474\pi$
$659$	2.86787e25			1.22346			0.611731	+	0.791066i	$0.290474\pi$
$660$	−5.24626e24	−	1.74551e25i	−0.220777	−	0.734561i
$661$			2.83671e25i			1.17761i	0.808274	+	0.588806i	$0.200402\pi$
$661$			2.83671e25i			1.17761i	−0.808274	+	0.588806i	$0.799598\pi$
$662$	5.92225e23	+	4.02793e24i	0.0242530	+	0.164953i
$663$			5.96621e24i			0.241033i
$664$	2.79646e24	+	5.97176e24i	0.111454	+	0.238007i
$665$	−2.01428e25			−0.791998
$666$	2.33883e23	−	3.43877e22i	0.00907256	−	0.00133394i
$667$	1.09668e24			0.0419707
$668$	3.48435e24	+	1.15930e25i	0.131563	+	0.437731i
$669$			1.98054e25i			0.737817i
$670$	9.11370e24	−	1.33998e24i	0.334982	−	0.0492523i
$671$		−	3.69425e25i		−	1.33975i
$672$	3.23770e25	−	2.89700e25i	1.15855	−	1.03663i
$673$	3.17507e25			1.12103			0.560515	−	0.828144i	$-0.310603\pi$
$673$	3.17507e25			1.12103			0.560515	+	0.828144i	$0.310603\pi$
$674$	4.95730e24	+	3.37163e25i	0.172705	+	1.17463i
$675$	−2.33559e25			−0.802904
$676$	−1.60527e25	+	4.82476e24i	−0.544539	+	0.163665i
$677$			4.49927e25i			1.50607i	0.657983	+	0.753033i	$0.271410\pi$
$677$			4.49927e25i			1.50607i	−0.657983	+	0.753033i	$0.728590\pi$
$678$	−2.43269e23	−	1.65456e24i	−0.00803563	−	0.0546531i
$679$		−	6.26785e25i		−	2.04310i
$680$	4.87672e24	−	2.28367e24i	0.156873	−	0.0734604i
$681$	−1.70968e24			−0.0542740
$682$	6.44487e25	−	9.47587e24i	2.01908	−	0.296865i
$683$	4.19294e25			1.29638			0.648190	−	0.761478i	$-0.275526\pi$
$683$	4.19294e25			1.29638			0.648190	+	0.761478i	$0.275526\pi$
$684$	1.46442e24	−	4.40143e23i	0.0446850	−	0.0134304i
$685$			2.59867e24i			0.0782593i
$686$	−2.78303e25	+	4.09188e24i	−0.827181	+	0.121620i
$687$		−	2.13357e25i		−	0.625888i
$688$	−2.71165e25	+	1.79188e25i	−0.785122	+	0.518814i
$689$	5.88048e24			0.168050
$690$	1.07880e23	+	7.33732e23i	0.00304299	+	0.0206964i
$691$	−3.79149e25			−1.05562			−0.527811	−	0.849362i	$-0.676987\pi$
$691$	−3.79149e25			−1.05562			−0.527811	+	0.849362i	$0.676987\pi$
$692$	−9.94808e23	−	3.30988e24i	−0.0273391	−	0.0909615i
$693$		−	4.30192e24i		−	0.116698i
$694$	−8.74673e24	−	5.94895e25i	−0.234213	−	1.59296i
$695$			1.28171e25i			0.338787i
$696$	−3.07616e25	+	1.44051e25i	−0.802650	+	0.375865i
$697$	3.62719e24			0.0934276
$698$	3.52909e25	−	5.18881e24i	0.897355	−	0.131938i
$699$	2.36542e25			0.593763
$700$	1.45254e25	+	4.83284e25i	0.359954	+	1.19762i
$701$		−	2.58354e25i		−	0.632052i	−0.948750	−	0.316026i	$-0.897651\pi$
$701$		−	2.58354e25i		−	0.632052i	0.948750	−	0.316026i	$-0.102349\pi$
$702$	−2.74544e25	+	4.03662e24i	−0.663099	+	0.0974953i
$703$			9.60076e24i			0.228933i
$704$	4.61932e25	−	5.54144e25i	1.08749	−	1.30457i
$705$	−3.53033e25			−0.820564
$706$	3.90969e23	+	2.65912e24i	0.00897223	+	0.0610233i
$707$	−7.95978e25			−1.80354
$708$	−1.79869e25	+	5.40609e24i	−0.402399	+	0.120944i
$709$			2.54021e25i			0.561116i	0.959837	+	0.280558i	$0.0905195\pi$
$709$			2.54021e25i			0.561116i	−0.959837	+	0.280558i	$0.909480\pi$
$710$	−5.37539e24	−	3.65599e25i	−0.117242	−	0.797407i
$711$			2.39249e24i			0.0515258i
$712$	3.40520e25	+	7.27171e25i	0.724140	+	1.54638i
$713$	−2.65056e24			−0.0556585
$714$	−2.78290e25	+	4.09170e24i	−0.577051	+	0.0848437i
$715$	2.51534e25			0.515042
$716$	9.35124e24	−	2.81058e24i	0.189083	−	0.0568301i
$717$		−	1.09113e25i		−	0.217873i
$718$	−1.36441e25	+	2.00609e24i	−0.269046	+	0.0395577i
$719$			4.44020e25i			0.864654i	0.901717	+	0.432327i	$0.142307\pi$
$719$			4.44020e25i			0.864654i	−0.901717	+	0.432327i	$0.857693\pi$
$720$	5.72215e23	+	8.65934e23i	0.0110044	+	0.0166530i
$721$	−7.72369e25			−1.46692
$722$	1.27857e24	+	8.69596e24i	0.0239821	+	0.163111i
$723$	2.76212e24			0.0511680
$724$	−1.87321e22	−	6.23246e22i	−0.000342720	−	0.00114028i
$725$		−	3.94545e25i		−	0.712943i
$726$	1.50245e25	+	1.02187e26i	0.268145	+	1.82375i
$727$		−	9.80580e24i		−	0.172852i	−0.996258	−	0.0864258i	$-0.972455\pi$
$727$		−	9.80580e24i		−	0.172852i	0.996258	−	0.0864258i	$-0.0275445\pi$
$728$	2.54270e25	+	5.42986e25i	0.442703	+	0.945380i
$729$	6.04416e25			1.03941
$730$	3.65347e25	−	5.37168e24i	0.620582	−	0.0912441i
$731$	2.10429e25			0.353061
$732$	−1.34009e25	−	4.45870e25i	−0.222093	−	0.738939i
$733$			3.43904e25i			0.562990i	0.959563	+	0.281495i	$0.0908303\pi$
$733$			3.43904e25i			0.562990i	−0.959563	+	0.281495i	$0.909170\pi$
$734$	8.98568e25	−	1.32116e25i	1.45307	−	0.213644i
$735$			4.31443e25i			0.689187i
$736$	−2.18756e24	+	1.95737e24i	−0.0345192	+	0.0308868i
$737$	−7.98997e25			−1.24548
$738$	1.01698e23	+	6.91684e23i	0.00156605	+	0.0106513i
$739$	−9.72094e25			−1.47880			−0.739398	−	0.673269i	$-0.764890\pi$
$739$	−9.72094e25			−1.47880			−0.739398	+	0.673269i	$0.764890\pi$
$740$	−6.24082e24	+	1.87572e24i	−0.0937899	+	0.0281892i
$741$		−	4.67029e25i		−	0.693393i
$742$	4.03290e24	+	2.74292e25i	0.0591538	+	0.402325i
$743$			1.12699e26i			1.63313i	0.577252	+	0.816566i	$0.304125\pi$
$743$			1.12699e26i			1.63313i	−0.577252	+	0.816566i	$0.695875\pi$
$744$	7.43477e25	−	3.48155e25i	1.06442	−	0.498445i
$745$	5.65173e25			0.799420
$746$	−6.77677e25	+	9.96387e24i	−0.947051	+	0.139245i
$747$	8.22871e23			0.0113618
$748$	−4.47309e25	+	1.34442e25i	−0.610229	+	0.183408i
$749$		−	1.20645e26i		−	1.62619i
$750$	5.99458e25	−	8.81382e24i	0.798376	−	0.117385i
$751$		−	1.13541e26i		−	1.49415i	−0.664740	−	0.747075i	$-0.731458\pi$
$751$		−	1.13541e26i		−	1.49415i	0.664740	−	0.747075i	$-0.268542\pi$
$752$	−7.70373e25	−	1.16581e26i	−1.00171	−	1.51588i
$753$	7.94852e25			1.02125
$754$	−6.81895e24	−	4.63780e25i	−0.0865715	−	0.588803i
$755$	−2.69289e25			−0.337829
$756$	−3.76572e25	−	1.25291e26i	−0.466822	−	1.55319i
$757$			2.68863e25i			0.329358i	0.986347	+	0.164679i	$0.0526589\pi$
$757$			2.68863e25i			0.329358i	−0.986347	+	0.164679i	$0.947341\pi$
$758$	4.28705e24	+	2.91577e25i	0.0518962	+	0.352964i
$759$		−	6.43263e24i		−	0.0769506i
$760$	−3.81745e25	+	1.78764e25i	−0.451285	+	0.211328i
$761$	6.38389e25			0.745802			0.372901	−	0.927871i	$-0.378363\pi$
$761$	6.38389e25			0.745802			0.372901	+	0.927871i	$0.378363\pi$
$762$	−8.87451e25	+	1.30482e25i	−1.02459	+	0.150645i
$763$	2.33521e26			2.66443
$764$	1.20431e25	+	4.00692e25i	0.135799	+	0.451825i
$765$		−	6.71982e23i		−	0.00748867i
$766$	−1.34361e26	+	1.97550e25i	−1.47984	+	0.217580i
$767$		−	2.59197e25i		−	0.282145i
$768$	3.56504e25	−	8.36379e25i	0.383542	−	0.899813i
$769$	−2.82096e25			−0.299957			−0.149979	−	0.988689i	$-0.547921\pi$
$769$	−2.82096e25			−0.299957			−0.149979	+	0.988689i	$0.547921\pi$
$770$	1.72505e25	+	1.17327e26i	0.181295	+	1.23305i
$771$	−1.87417e25			−0.194679
$772$	1.45595e26	−	4.37597e25i	1.49483	−	0.449281i
$773$		−	1.14936e26i		−	1.16638i	−0.812336	−	0.583189i	$-0.801805\pi$
$773$		−	1.14936e26i		−	1.16638i	0.812336	−	0.583189i	$-0.198195\pi$
$774$	5.89996e23	+	4.01276e24i	0.00591807	+	0.0402508i
$775$			9.53576e25i			0.945453i
$776$	−5.56261e25	−	1.18788e26i	−0.545159	−	1.16417i
$777$	3.40395e25			0.329757
$778$	−1.42035e26	+	2.08834e25i	−1.36013	+	0.199979i
$779$	−2.83933e25			−0.268769
$780$	3.03584e25	−	9.12444e24i	0.284072	−	0.0853797i
$781$			3.20520e26i			2.96481i
$782$	1.88028e24	−	2.76457e23i	0.0171934	−	0.00252794i
$783$			1.02286e26i			0.924612i
$784$	−1.42474e26	+	9.41476e25i	−1.27318	+	0.841326i
$785$	−2.24334e25			−0.198184
$786$	8.54361e24	+	5.81081e25i	0.0746171	+	0.507497i
$787$	1.03177e26			0.890861			0.445430	−	0.895317i	$-0.353051\pi$
$787$	1.03177e26			0.890861			0.445430	+	0.895317i	$0.353051\pi$
$788$	−1.05995e25	−	3.52661e25i	−0.0904792	−	0.301038i
$789$		−	1.27706e26i		−	1.07775i
$790$	−9.59381e24	−	6.52508e25i	−0.0800474	−	0.544430i
$791$			1.08809e25i			0.0897587i
$792$	−3.81788e24	−	8.15298e24i	−0.0311383	−	0.0664951i
$793$	6.42514e25			0.518112
$794$	7.08365e25	−	1.04151e25i	0.564771	−	0.0830381i
$795$	1.46580e25			0.115550
$796$	5.72517e25	+	1.90486e26i	0.446243	+	1.48472i
$797$		−	1.59966e26i		−	1.23283i	−0.787423	−	0.616413i	$-0.788585\pi$
$797$		−	1.59966e26i		−	1.23283i	0.787423	−	0.616413i	$-0.211415\pi$
$798$	2.17843e26	−	3.20294e25i	1.66004	−	0.244075i
$799$			9.04688e25i			0.681676i
$800$	7.04192e25	+	7.87007e25i	0.524664	+	0.586366i
$801$	1.00200e25			0.0738199
$802$	−1.21992e25	−	8.29710e25i	−0.0888714	−	0.604445i
$803$	−3.20299e26			−2.30736
$804$	−9.64334e25	+	2.89837e25i	−0.686947	+	0.206467i
$805$		−	4.82525e24i		−	0.0339905i
$806$	1.64807e25	+	1.12091e26i	0.114805	+	0.780827i
$807$		−	4.37948e25i		−	0.301690i
$808$	−1.50853e26	+	7.06417e25i	−1.02767	+	0.481237i
$809$	−4.97682e25			−0.335286			−0.167643	−	0.985848i	$-0.553616\pi$
$809$	−4.97682e25			−0.335286			−0.167643	+	0.985848i	$0.553616\pi$
$810$	−6.54703e25	+	9.62608e24i	−0.436194	+	0.0641334i
$811$	−7.70764e25			−0.507848			−0.253924	−	0.967224i	$-0.581721\pi$
$811$	−7.70764e25			−0.507848			−0.253924	+	0.967224i	$0.581721\pi$
$812$	2.11651e26	−	6.36132e25i	1.37917	−	0.414518i
$813$		−	6.35067e25i		−	0.409265i
$814$	5.59221e25	−	8.22222e24i	0.356422	−	0.0524046i
$815$		−	9.76801e25i		−	0.615726i
$816$	−4.91101e25	+	3.24523e25i	−0.306168	+	0.202318i
$817$	−1.64722e26			−1.01567
$818$	−1.30553e25	−	8.87938e25i	−0.0796174	−	0.541506i
$819$	7.48202e24			0.0451298
$820$	−5.54725e24	−	1.84566e25i	−0.0330943	−	0.110110i
$821$			2.78841e26i			1.64539i	0.568484	+	0.822694i	$0.307530\pi$
$821$			2.78841e26i			1.64539i	−0.568484	+	0.822694i	$0.692470\pi$
$822$	−4.13219e24	−	2.81045e25i	−0.0241176	−	0.164032i
$823$		−	2.38986e26i		−	1.37967i	−0.723967	−	0.689834i	$-0.757683\pi$
$823$		−	2.38986e26i		−	1.37967i	0.723967	−	0.689834i	$-0.242317\pi$
$824$	−1.46379e26	+	6.85464e25i	−0.835861	+	0.391417i
$825$	−2.31423e26			−1.30714
$826$	1.20901e26	−	1.77761e25i	0.675476	−	0.0993151i
$827$	2.28959e26			1.26534			0.632672	−	0.774420i	$-0.281958\pi$
$827$	2.28959e26			1.26534			0.632672	+	0.774420i	$0.281958\pi$
$828$	1.05437e23	+	3.50807e23i	0.000576397	+	0.00191776i
$829$			1.23830e26i			0.669629i	0.942284	+	0.334814i	$0.108674\pi$
$829$			1.23830e26i			0.669629i	−0.942284	+	0.334814i	$0.891326\pi$
$830$	−2.24423e25	+	3.29968e24i	−0.120051	+	0.0176510i
$831$			3.19171e26i			1.68894i
$832$	9.63782e25	+	8.03405e25i	0.504509	+	0.420557i
$833$	1.10562e26			0.572535
$834$	−2.03807e25	−	1.38617e26i	−0.104406	−	0.710102i
$835$	−4.16420e25			−0.211034
$836$	3.50149e26	−	1.05240e26i	1.75548	−	0.527622i
$837$		−	2.47214e26i		−	1.22615i
$838$	−5.08028e25	−	3.45527e26i	−0.249282	−	1.69546i
$839$		−	1.75905e26i		−	0.853927i	−0.904269	−	0.426963i	$-0.859583\pi$
$839$		−	1.75905e26i		−	0.853927i	0.904269	−	0.426963i	$-0.140417\pi$
$840$	6.33806e25	+	1.35348e26i	0.304399	+	0.650035i
$841$	3.76687e25			0.178985
$842$	1.36453e26	−	2.00627e25i	0.641467	−	0.0943148i
$843$	1.95760e25			0.0910491
$844$	−1.97790e25	+	5.94471e24i	−0.0910168	+	0.0273557i
$845$		−	5.76614e25i		−	0.262528i
$846$	−1.72519e25	+	2.53654e24i	−0.0777147	+	0.0114264i
$847$		−	6.72011e26i		−	2.99520i
$848$	3.19860e25	+	4.84045e25i	0.141058	+	0.213463i
$849$	2.86410e26			1.24974
$850$	−9.94592e24	−	6.76457e25i	−0.0429413	−	0.292058i
$851$	−2.29989e24			−0.00982519
$852$	1.16269e26	+	3.86846e26i	0.491483	+	1.63524i
$853$			3.18598e26i			1.33261i	0.745681	+	0.666303i	$0.232124\pi$
$853$			3.18598e26i			1.33261i	−0.745681	+	0.666303i	$0.767876\pi$
$854$	4.40643e25	+	2.99697e26i	0.182375	+	1.24040i
$855$			5.26021e24i			0.0215431i
$856$	−1.07070e26	−	2.28645e26i	−0.433915	−	0.926614i
$857$	−2.87937e26			−1.15470			−0.577352	−	0.816495i	$-0.695914\pi$
$857$	−2.87937e26			−1.15470			−0.577352	+	0.816495i	$0.695914\pi$
$858$	−2.72033e26	+	3.99969e25i	−1.07953	+	0.158724i
$859$	1.17066e26			0.459720			0.229860	−	0.973224i	$-0.426173\pi$
$859$	1.17066e26			0.459720			0.229860	+	0.973224i	$0.426173\pi$
$860$	−3.21820e25	−	1.07075e26i	−0.125063	−	0.416103i
$861$			1.00668e26i			0.387137i
$862$	2.92826e26	−	4.30542e25i	1.11441	−	0.163851i
$863$			7.42559e25i			0.279662i	0.990175	+	0.139831i	$0.0446560\pi$
$863$			7.42559e25i			0.279662i	−0.990175	+	0.139831i	$0.955344\pi$
$864$	−1.82562e26	−	2.04032e26i	−0.680434	−	0.760455i
$865$	1.18891e25			0.0438534
$866$	2.84435e25	+	1.93454e26i	0.103830	+	0.706182i
$867$	−2.32644e26			−0.840465
$868$	−5.11539e26	+	1.53747e26i	−1.82895	+	0.549703i
$869$			5.72054e26i			2.02422i
$870$	−1.69973e25	−	1.15604e26i	−0.0595259	−	0.404856i
$871$		−	1.38964e26i		−	0.481658i
$872$	4.42567e26	−	2.07246e26i	1.51821	−	0.710946i
$873$	−1.63683e25			−0.0555743
$874$	−1.47186e25	+	2.16407e24i	−0.0494611	+	0.00727226i
$875$	−3.94223e26			−1.31120
$876$	−3.86579e26	+	1.16189e26i	−1.27263	+	0.382497i
$877$			8.15436e25i			0.265701i	0.991136	+	0.132851i	$0.0424131\pi$
$877$			8.15436e25i			0.265701i	−0.991136	+	0.132851i	$0.957587\pi$
$878$	5.57629e25	−	8.19881e24i	0.179844	−	0.0264423i
$879$			9.65826e25i			0.308318i
$880$	1.36819e26	+	2.07048e26i	0.432316	+	0.654224i
$881$	−2.40657e26			−0.752688			−0.376344	−	0.926480i	$-0.622819\pi$
$881$	−2.40657e26			−0.752688			−0.376344	+	0.926480i	$0.622819\pi$
$882$	3.09992e24	+	2.10836e25i	0.00959694	+	0.0652721i
$883$	3.18933e26			0.977357			0.488678	−	0.872464i	$-0.337479\pi$
$883$	3.18933e26			0.977357			0.488678	+	0.872464i	$0.337479\pi$
$884$	−2.33825e25	−	7.77971e25i	−0.0709283	−	0.235990i
$885$		−	6.46089e25i		−	0.194001i
$886$	−2.63199e25	−	1.79011e26i	−0.0782313	−	0.532078i
$887$			2.84683e26i			0.837624i	0.908073	+	0.418812i	$0.137553\pi$
$887$			2.84683e26i			0.837624i	−0.908073	+	0.418812i	$0.862447\pi$
$888$	6.45115e25	−	3.02095e25i	0.187897	−	0.0879886i
$889$	5.83615e26			1.68272
$890$	−2.73276e26	+	4.01797e25i	−0.779994	+	0.114682i
$891$	5.73978e26			1.62179
$892$	−7.76204e25	−	2.58255e26i	−0.217116	−	0.722379i
$893$		−	7.08181e26i		−	1.96102i
$894$	−6.11232e26	+	8.98693e25i	−1.67559	+	0.246362i
$895$			3.35896e25i			0.0911586i
$896$	−3.08647e26	+	5.04649e26i	−0.829257	+	1.35587i
$897$	1.11878e25			0.0297586
$898$	−3.00298e25	−	2.04243e26i	−0.0790797	−	0.537848i
$899$	4.17612e26			1.08877
$900$	1.26208e25	−	3.79326e24i	0.0325764	−	0.00979107i
$901$		−	3.75628e25i		−	0.0959920i
$902$	2.43164e25	+	1.65384e26i	0.0615233	+	0.418441i
$903$			5.84021e26i			1.46298i
$904$	9.65661e24	+	2.06214e25i	0.0239502	+	0.0511450i
$905$	2.23870e23			0.000549741
$906$	2.91235e26	−	4.28202e25i	0.708092	−	0.104111i
$907$	−1.48819e26			−0.358255			−0.179127	−	0.983826i	$-0.557327\pi$
$907$	−1.48819e26			−0.358255			−0.179127	+	0.983826i	$0.557327\pi$
$908$	2.22937e25	−	6.70051e24i	0.0531384	−	0.0159711i
$909$			2.07867e25i			0.0490580i
$910$	−2.04058e26	+	3.00026e25i	−0.476849	+	0.0701110i
$911$			5.20898e26i			1.20528i	0.798014	+	0.602639i	$0.205884\pi$
$911$			5.20898e26i			1.20528i	−0.798014	+	0.602639i	$0.794116\pi$
$912$	3.84429e26	−	2.54034e26i	0.880771	−	0.582020i
$913$	1.96751e26			0.446355
$914$	−1.06071e25	−	7.21423e25i	−0.0238275	−	0.162059i
$915$	1.60156e26			0.356249
$916$	8.36179e25	+	2.78210e26i	0.184179	+	0.612792i
$917$		−	3.82137e26i		−	0.833480i
$918$	2.57848e25	+	1.75371e26i	0.0556903	+	0.378769i
$919$		−	3.60132e26i		−	0.770233i	−0.922868	−	0.385116i	$-0.874161\pi$
$919$		−	3.60132e26i		−	0.770233i	0.922868	−	0.385116i	$-0.125839\pi$
$920$	−4.28233e24	−	9.14480e24i	−0.00906963	−	0.0193680i
$921$	1.38805e24			0.00291118
$922$	5.16735e26	−	7.59754e25i	1.07322	−	0.157796i
$923$	−5.57458e26			−1.14656
$924$	−3.73127e26	−	1.24145e27i	−0.759992	−	2.52861i
$925$			8.27418e25i			0.166897i
$926$	−3.18370e26	+	4.68098e25i	−0.635964	+	0.0935057i
$927$			2.01701e25i			0.0399017i
$928$	3.44665e26	−	3.08396e26i	0.675251	−	0.604195i
$929$	4.90802e26			0.952280			0.476140	−	0.879369i	$-0.342036\pi$
$929$	4.90802e26			0.952280			0.476140	+	0.879369i	$0.342036\pi$
$930$	4.10806e25	+	2.79404e26i	0.0789388	+	0.536890i
$931$	−8.65471e26			−1.64704
$932$	−3.08442e26	+	9.27042e25i	−0.581339	+	0.174725i
$933$		−	7.93796e26i		−	1.48175i
$934$	−2.33557e25	−	1.58850e26i	−0.0431788	−	0.293674i
$935$		−	1.60673e26i		−	0.294197i
$936$	1.41799e25	−	6.64016e24i	0.0257152	−	0.0120419i
$937$	−8.57456e26			−1.54012			−0.770062	−	0.637969i	$-0.779775\pi$
$937$	−8.57456e26			−1.54012			−0.770062	+	0.637969i	$0.779775\pi$
$938$	6.48189e26	−	9.53031e25i	1.15312	−	0.169544i
$939$	−1.06312e26			−0.187324
$940$	4.60342e26	−	1.38359e26i	0.803396	−	0.241466i
$941$		−	5.46981e26i		−	0.945510i	−0.881194	−	0.472755i	$-0.843260\pi$
$941$		−	5.46981e26i		−	0.945510i	0.881194	−	0.472755i	$-0.156740\pi$
$942$	2.42616e26	−	3.56717e25i	0.415395	−	0.0610753i
$943$		−	6.80169e24i		−	0.0115348i
$944$	2.13355e26	−	1.40987e26i	0.358390	−	0.236827i
$945$	4.50046e26			0.748809
$946$	1.41070e26	+	9.59465e26i	0.232495	+	1.58128i
$947$	6.96849e25			0.113760			0.0568799	−	0.998381i	$-0.481885\pi$
$947$	6.96849e25			0.113760			0.0568799	+	0.998381i	$0.481885\pi$
$948$	2.07513e26	+	6.90429e26i	0.335560	+	1.11646i
$949$		−	5.57073e26i		−	0.892311i
$950$	7.78557e25	+	5.29524e26i	0.123532	+	0.840181i
$951$			2.56414e26i			0.403011i
$952$	3.46844e26	−	1.62420e26i	0.540011	−	0.252876i
$953$	−1.08360e27			−1.67121			−0.835605	−	0.549330i	$-0.814883\pi$
$953$	−1.08360e27			−1.67121			−0.835605	+	0.549330i	$0.814883\pi$
$954$	7.16302e24	−	1.05318e24i	0.0109436	−	0.00160904i
$955$	−1.43928e26			−0.217829
$956$	4.27630e25	+	1.42279e26i	0.0641131	+	0.213314i
$957$			1.01350e27i			1.50528i
$958$	−7.64393e26	+	1.12389e26i	−1.12468	+	0.165361i
$959$			1.84824e26i			0.269396i
$960$	2.40237e26	+	2.00261e26i	0.346896	+	0.289171i
$961$	−3.10273e26			−0.443847
$962$	1.43003e25	+	9.72613e25i	0.0202661	+	0.137837i
$963$	−3.15059e25			−0.0442340
$964$	−3.60171e25	+	1.08252e25i	−0.0500974	+	0.0150571i
$965$			5.22978e26i			0.720672i
$966$	7.67273e24	+	5.21849e25i	0.0104750	+	0.0712444i
$967$			4.08963e26i			0.553153i	0.960992	+	0.276577i	$0.0891999\pi$
$967$			4.08963e26i			0.553153i	−0.960992	+	0.276577i	$0.910800\pi$
$968$	−5.96398e26	−	1.27359e27i	−0.799205	−	1.70668i
$969$	−2.98325e26			−0.396073
$970$	4.46413e26	−	6.56360e25i	0.587208	−	0.0863370i
$971$	2.93639e26			0.382684			0.191342	−	0.981523i	$-0.438716\pi$
$971$	2.93639e26			0.382684			0.191342	+	0.981523i	$0.438716\pi$
$972$	−6.40828e25	+	1.92605e25i	−0.0827457	+	0.0248698i
$973$			9.11586e26i			1.16622i
$974$	−4.86365e26	+	7.15101e25i	−0.616498	+	0.0906435i
$975$		−	4.02497e26i		−	0.505500i
$976$	3.49486e26	+	5.28878e26i	0.434892	+	0.658123i
$977$	5.13596e26			0.633243			0.316621	−	0.948552i	$-0.397452\pi$
$977$	5.13596e26			0.633243			0.316621	+	0.948552i	$0.397452\pi$
$978$	1.55323e26	+	1.05640e27i	0.189752	+	1.29057i
$979$	2.39581e27			2.90006
$980$	−1.69089e26	−	5.62585e26i	−0.202806	−	0.674767i
$981$		−	6.09830e25i		−	0.0724750i
$982$	4.79132e25	+	3.25874e26i	0.0564224	+	0.383748i
$983$		−	5.83673e25i		−	0.0681064i	−0.999420	−	0.0340532i	$-0.989158\pi$
$983$		−	5.83673e25i		−	0.0681064i	0.999420	−	0.0340532i	$-0.0108416\pi$
$984$	8.93414e25	+	1.90786e26i	0.103299	+	0.220593i
$985$	1.26676e26			0.145134
$986$	−2.96250e26	+	4.35575e25i	−0.336330	+	0.0494505i
$987$	−2.51086e27			−2.82467
$988$	1.83036e26	+	6.08988e26i	0.204044	+	0.678886i
$989$		−	3.94596e25i		−	0.0435899i
$990$	3.06394e25	−	4.50491e24i	0.0335401	−	0.00493139i
$991$		−	6.68451e26i		−	0.725115i	−0.931961	−	0.362557i	$-0.881904\pi$
$991$		−	6.68451e26i		−	0.725115i	0.931961	−	0.362557i	$-0.118096\pi$
$992$	−8.33019e26	+	7.45362e26i	−0.895468	+	0.801239i
$993$	1.53091e26			0.163082
$994$	−3.82311e26	−	2.60023e27i	−0.403589	−	2.74495i
$995$	−6.84223e26			−0.715797
$996$	2.37465e26	−	7.13718e25i	0.246187	−	0.0739933i
$997$		−	1.24786e27i		−	1.28206i	−0.767514	−	0.641032i	$-0.778507\pi$
$997$		−	1.24786e27i		−	1.28206i	0.767514	−	0.641032i	$-0.221493\pi$
$998$	−2.38728e26	−	1.62367e27i	−0.243068	−	1.65319i
$999$		−	2.14508e26i		−	0.216448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.19.d.b.3.10	yes	16
3.2	odd	2		72.19.b.b.19.7		16
4.3	odd	2		32.19.d.b.15.5		16
8.3	odd	2	inner	8.19.d.b.3.9	✓	16
8.5	even	2		32.19.d.b.15.6		16
24.11	even	2		72.19.b.b.19.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.19.d.b.3.9	✓	16	8.3	odd	2	inner
8.19.d.b.3.10	yes	16	1.1	even	1	trivial
32.19.d.b.15.5		16	4.3	odd	2
32.19.d.b.15.6		16	8.5	even	2
72.19.b.b.19.7		16	3.2	odd	2
72.19.b.b.19.8		16	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(74.4785 + 506.554i) q^{2} +19252.8 q^{3} +(-251050. + 75454.8i) q^{4} -901770. i q^{5} +(1.43392e6 + 9.75260e6i) q^{6} -6.41362e7i q^{7} +(-5.69197e7 - 1.21551e8i) q^{8} -1.67489e7 q^{9} +O(q^{10})\)	\(q+(74.4785 + 506.554i) q^{2} +19252.8 q^{3} +(-251050. + 75454.8i) q^{4} -901770. i q^{5} +(1.43392e6 + 9.75260e6i) q^{6} -6.41362e7i q^{7} +(-5.69197e7 - 1.21551e8i) q^{8} -1.67489e7 q^{9} +(4.56795e8 - 6.71625e7i) q^{10} -4.00472e9 q^{11} +(-4.83342e9 + 1.45272e9i) q^{12} -6.96512e9i q^{13} +(3.24884e10 - 4.77677e9i) q^{14} -1.73616e10i q^{15} +(5.73326e10 - 3.78858e10i) q^{16} -4.44913e10 q^{17} +(-1.24743e9 - 8.48423e9i) q^{18} +3.48273e11 q^{19} +(6.80429e10 + 2.26389e11i) q^{20} -1.23480e12i q^{21} +(-2.98266e11 - 2.02861e12i) q^{22} +8.34298e10i q^{23} +(-1.09587e12 - 2.34019e12i) q^{24} +3.00151e12 q^{25} +(3.52821e12 - 5.18752e11i) q^{26} -7.78141e12 q^{27} +(4.83938e12 + 1.61014e13i) q^{28} -1.31449e13i q^{29} +(8.79461e12 - 1.29307e12i) q^{30} +3.17699e13i q^{31} +(2.34613e13 + 2.62204e13i) q^{32} -7.71023e13 q^{33} +(-3.31364e12 - 2.25372e13i) q^{34} -5.78361e13 q^{35} +(4.20481e12 - 1.26379e12i) q^{36} +2.75668e13i q^{37} +(2.59389e13 + 1.76419e14i) q^{38} -1.34098e14i q^{39} +(-1.09611e14 + 5.13285e13i) q^{40} -8.15259e13 q^{41} +(6.25494e14 - 9.19663e13i) q^{42} -4.72967e14 q^{43} +(1.00539e15 - 3.02175e14i) q^{44} +1.51037e13i q^{45} +(-4.22617e13 + 6.21373e12i) q^{46} -2.03341e15i q^{47} +(1.10382e15 - 7.29409e14i) q^{48} -2.48503e15 q^{49} +(2.23548e14 + 1.52043e15i) q^{50} -8.56583e14 q^{51} +(5.25552e14 + 1.74859e15i) q^{52} +8.44274e14i q^{53} +(-5.79547e14 - 3.94170e15i) q^{54} +3.61134e15i q^{55} +(-7.79579e15 + 3.65061e15i) q^{56} +6.70525e15 q^{57} +(6.65861e15 - 9.79013e14i) q^{58} +3.72136e15 q^{59} +(1.31002e15 + 4.35864e15i) q^{60} +9.22472e15i q^{61} +(-1.60932e16 + 2.36617e15i) q^{62} +1.07421e15i q^{63} +(-1.15347e16 + 1.38373e16i) q^{64} -6.28094e15 q^{65} +(-5.74246e15 - 3.90565e16i) q^{66} +1.99514e16 q^{67} +(1.11695e16 - 3.35708e15i) q^{68} +1.60626e15i q^{69} +(-4.30755e15 - 2.92971e16i) q^{70} -8.00356e16i q^{71} +(9.53344e14 + 2.03584e15i) q^{72} +7.99804e16 q^{73} +(-1.39640e16 + 2.05313e15i) q^{74} +5.77875e16 q^{75} +(-8.74340e16 + 2.62789e16i) q^{76} +2.56848e17i q^{77} +(6.79281e16 - 9.98745e15i) q^{78} -1.42845e17i q^{79} +(-3.41643e16 - 5.17009e16i) q^{80} -1.43325e17 q^{81} +(-6.07192e15 - 4.12973e16i) q^{82} -4.91298e16 q^{83} +(9.31718e16 + 3.09997e17i) q^{84} +4.01209e16i q^{85} +(-3.52259e16 - 2.39583e17i) q^{86} -2.53077e17i q^{87} +(2.27948e17 + 4.86776e17i) q^{88} -5.98246e17 q^{89} +(-7.65083e15 + 1.12490e15i) q^{90} -4.46716e17 q^{91} +(-6.29518e15 - 2.09450e16i) q^{92} +6.11660e17i q^{93} +(1.03003e18 - 1.51445e17i) q^{94} -3.14063e17i q^{95} +(4.51696e17 + 5.04817e17i) q^{96} +9.77272e17 q^{97} +(-1.85082e17 - 1.25880e18i) q^{98} +6.70748e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9}+O(q^{10}) \) 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9	\( 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9} - 1569837600 q^{10} - 2471571264 q^{11} + 4764364056 q^{12} + 26163923904 q^{14} - 192320075504 q^{16} - 176439301344 q^{17} - 1044291511122 q^{18} - 833365634368 q^{19} + 1256486405760 q^{20} + 59927319356 q^{22} - 1968891910512 q^{24} - 15320509140080 q^{25} + 4184514840864 q^{26} + 11565649473408 q^{27} - 12301604294400 q^{28} - 36336510039360 q^{30} + 141481742931936 q^{32} - 900457491648 q^{33} + 80653465357268 q^{34} + 20487495736320 q^{35} + 277183098847068 q^{36} + 493456694265564 q^{38} - 519930573603840 q^{40} - 594931562445024 q^{41} - 222362598288000 q^{42} - 25\!\cdots\!92 q^{43}+ \cdots - 81\!\cdots\!68 q^{99}+O(q^{100}) \) 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9 - 1569837600 * q^10 - 2471571264 * q^11 + 4764364056 * q^12 + 26163923904 * q^14 - 192320075504 * q^16 - 176439301344 * q^17 - 1044291511122 * q^18 - 833365634368 * q^19 + 1256486405760 * q^20 + 59927319356 * q^22 - 1968891910512 * q^24 - 15320509140080 * q^25 + 4184514840864 * q^26 + 11565649473408 * q^27 - 12301604294400 * q^28 - 36336510039360 * q^30 + 141481742931936 * q^32 - 900457491648 * q^33 + 80653465357268 * q^34 + 20487495736320 * q^35 + 277183098847068 * q^36 + 493456694265564 * q^38 - 519930573603840 * q^40 - 594931562445024 * q^41 - 222362598288000 * q^42 - 2540155017577792 * q^43 + 73781630442072 * q^44 + 153882272211264 * q^46 + 897135071530464 * q^48 - 3186415704132848 * q^49 + 5668141028706330 * q^50 + 2916050119466880 * q^51 - 4594372123628160 * q^52 - 1377307163285640 * q^54 + 8184134137073664 * q^56 + 9540488340840768 * q^57 - 10505700099162720 * q^58 + 556807886314176 * q^59 + 29677718651516160 * q^60 + 6212402633091840 * q^62 - 56432885385732032 * q^64 - 21153177930524160 * q^65 - 23515570511959320 * q^66 + 162428574934613696 * q^67 - 70717864614203736 * q^68 + 4248100663257600 * q^70 - 36801123950767128 * q^72 - 7655712852492256 * q^73 + 9613779604149984 * q^74 - 384388788469704000 * q^75 - 151130166278324584 * q^76 - 93022771634070720 * q^78 + 26870186366192640 * q^80 + 99506910981790800 * q^81 + 329788507250077556 * q^82 + 866357336138514624 * q^83 + 451843591950574080 * q^84 + 1269201398006865468 * q^86 - 758460699051663856 * q^88 - 883646550464284128 * q^89 - 1227675520905095520 * q^90 - 379834560933460992 * q^91 + 1413121475102841600 * q^92 + 671428514272869504 * q^94 - 483149691255826368 * q^96 - 2614894858526780128 * q^97 - 81635840192738166 * q^98 - 816916348833567168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more