LMFDB - Embedded newform 8.19.d.b.3.13

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			3.13
Root			$202.692 - 137.887i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.19.d.b.3.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(431.385 - 275.773i) q^{2} +22640.1 q^{3} +(110042. - 237929. i) q^{4} -113148. i q^{5} +(9.76661e6 - 6.24355e6i) q^{6} -3.55480e7i q^{7} +(-1.81440e7 - 1.32986e8i) q^{8} +1.25155e8 q^{9} +O(q^{10})$	\(q+(431.385 - 275.773i) q^{2} +22640.1 q^{3} +(110042. - 237929. i) q^{4} -113148. i q^{5} +(9.76661e6 - 6.24355e6i) q^{6} -3.55480e7i q^{7} +(-1.81440e7 - 1.32986e8i) q^{8} +1.25155e8 q^{9} +(-3.12032e7 - 4.88104e7i) q^{10} +2.18476e9 q^{11} +(2.49137e9 - 5.38675e9i) q^{12} +7.03609e9i q^{13} +(-9.80319e9 - 1.53349e10i) q^{14} -2.56169e9i q^{15} +(-4.45010e10 - 5.23644e10i) q^{16} +6.55631e10 q^{17} +(5.39900e10 - 3.45145e10i) q^{18} -1.62851e11 q^{19} +(-2.69212e10 - 1.24510e10i) q^{20} -8.04811e11i q^{21} +(9.42471e11 - 6.02498e11i) q^{22} -3.09603e12i q^{23} +(-4.10784e11 - 3.01081e12i) q^{24} +3.80189e12 q^{25} +(1.94037e12 + 3.03526e12i) q^{26} -5.93772e12 q^{27} +(-8.45790e12 - 3.91177e12i) q^{28} +2.64850e13i q^{29} +(-7.06445e11 - 1.10507e12i) q^{30} +2.98862e13i q^{31} +(-3.36378e13 - 1.03170e13i) q^{32} +4.94632e13 q^{33} +(2.82829e13 - 1.80806e13i) q^{34} -4.02219e12 q^{35} +(1.37723e13 - 2.97780e13i) q^{36} +1.12077e14i q^{37} +(-7.02515e13 + 4.49100e13i) q^{38} +1.59298e14i q^{39} +(-1.50471e13 + 2.05296e12i) q^{40} -1.86561e14 q^{41} +(-2.21946e14 - 3.47184e14i) q^{42} +7.27808e14 q^{43} +(2.40415e14 - 5.19817e14i) q^{44} -1.41611e13i q^{45} +(-8.53803e14 - 1.33558e15i) q^{46} +1.44996e15i q^{47} +(-1.00751e15 - 1.18554e15i) q^{48} +3.64754e14 q^{49} +(1.64008e15 - 1.04846e15i) q^{50} +1.48436e15 q^{51} +(1.67409e15 + 7.74265e14i) q^{52} +6.79100e14i q^{53} +(-2.56144e15 + 1.63747e15i) q^{54} -2.47201e14i q^{55} +(-4.72737e15 + 6.44985e14i) q^{56} -3.68697e15 q^{57} +(7.30385e15 + 1.14252e16i) q^{58} -6.53060e15 q^{59} +(-6.09500e14 - 2.81893e14i) q^{60} +7.84501e14i q^{61} +(8.24182e15 + 1.28925e16i) q^{62} -4.44901e15i q^{63} +(-1.73560e16 + 4.82580e15i) q^{64} +7.96120e14 q^{65} +(2.13377e16 - 1.36406e16i) q^{66} +1.65722e16 q^{67} +(7.21469e15 - 1.55994e16i) q^{68} -7.00945e16i q^{69} +(-1.73511e15 + 1.10921e15i) q^{70} -1.64782e16i q^{71} +(-2.27082e15 - 1.66438e16i) q^{72} -1.15920e17 q^{73} +(3.09077e16 + 4.83481e16i) q^{74} +8.60754e16 q^{75} +(-1.79205e16 + 3.87470e16i) q^{76} -7.76637e16i q^{77} +(4.39301e16 + 6.87187e16i) q^{78} +9.97517e16i q^{79} +(-5.92493e15 + 5.03520e15i) q^{80} -1.82918e17 q^{81} +(-8.04794e16 + 5.14484e16i) q^{82} +2.58659e17 q^{83} +(-1.91488e17 - 8.85630e16i) q^{84} -7.41833e15i q^{85} +(3.13965e17 - 2.00710e17i) q^{86} +5.99623e17i q^{87} +(-3.96403e16 - 2.90541e17i) q^{88} +1.02832e17 q^{89} +(-3.90524e15 - 6.10887e15i) q^{90} +2.50119e17 q^{91} +(-7.36636e17 - 3.40693e17i) q^{92} +6.76627e17i q^{93} +(3.99860e17 + 6.25491e17i) q^{94} +1.84263e16i q^{95} +(-7.61563e17 - 2.33579e17i) q^{96} -4.73017e17 q^{97} +(1.57349e17 - 1.00589e17i) q^{98} +2.73434e17 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 $

$2$	431.385	−	275.773i	0.842549	−	0.538620i
$2$	431.385	−	275.773i	0.842549	−	0.538620i
$3$	22640.1			1.15024			0.575119	−	0.818070i	$-0.304956\pi$
$3$	22640.1			1.15024			0.575119	+	0.818070i	$0.304956\pi$
$4$	110042.	−	237929.i	0.419777	−	0.907627i
$5$		−	113148.i		−	0.0579318i	−0.999580	−	0.0289659i	$-0.990779\pi$
$5$		−	113148.i		−	0.0579318i	0.999580	−	0.0289659i	$-0.00922142\pi$
$6$	9.76661e6	−	6.24355e6i	0.969132	−	0.619541i
$7$		−	3.55480e7i		−	0.880912i	−0.897774	−	0.440456i	$-0.854817\pi$
$7$		−	3.55480e7i		−	0.880912i	0.897774	−	0.440456i	$-0.145183\pi$
$8$	−1.81440e7	−	1.32986e8i	−0.135184	−	0.990821i
$9$	1.25155e8			0.323047
$10$	−3.12032e7	−	4.88104e7i	−0.0312032	−	0.0488104i
$11$	2.18476e9			0.926550			0.463275	−	0.886215i	$-0.346674\pi$
$11$	2.18476e9			0.926550			0.463275	+	0.886215i	$0.346674\pi$
$12$	2.49137e9	−	5.38675e9i	0.482843	−	1.04399i
$13$			7.03609e9i			0.663500i	0.943367	+	0.331750i	$0.107639\pi$
$13$			7.03609e9i			0.663500i	−0.943367	+	0.331750i	$0.892361\pi$
$14$	−9.80319e9	−	1.53349e10i	−0.474477	−	0.742212i
$15$		−	2.56169e9i		−	0.0666354i
$16$	−4.45010e10	−	5.23644e10i	−0.647575	−	0.762002i
$17$	6.55631e10			0.552865			0.276432	−	0.961033i	$-0.410848\pi$
$17$	6.55631e10			0.552865			0.276432	+	0.961033i	$0.410848\pi$
$18$	5.39900e10	−	3.45145e10i	0.272183	−	0.174000i
$19$	−1.62851e11			−0.504671			−0.252336	−	0.967640i	$-0.581199\pi$
$19$	−1.62851e11			−0.504671			−0.252336	+	0.967640i	$0.581199\pi$
$20$	−2.69212e10	−	1.24510e10i	−0.0525805	−	0.0243184i
$21$		−	8.04811e11i		−	1.01326i
$22$	9.42471e11	−	6.02498e11i	0.780664	−	0.499058i
$23$		−	3.09603e12i		−	1.71892i	−0.511206	−	0.859458i	$-0.670801\pi$
$23$		−	3.09603e12i		−	1.71892i	0.511206	−	0.859458i	$-0.329199\pi$
$24$	−4.10784e11	−	3.01081e12i	−0.155493	−	1.13968i
$25$	3.80189e12			0.996644
$26$	1.94037e12	+	3.03526e12i	0.357375	+	0.559031i
$27$	−5.93772e12			−0.778657
$28$	−8.45790e12	−	3.91177e12i	−0.799540	−	0.369787i
$29$			2.64850e13i			1.82565i	0.408352	+	0.912825i	$0.366104\pi$
$29$			2.64850e13i			1.82565i	−0.408352	+	0.912825i	$0.633896\pi$
$30$	−7.06445e11	−	1.10507e12i	−0.0358911	−	0.0561435i
$31$			2.98862e13i			1.13036i	0.824969	+	0.565178i	$0.191193\pi$
$31$			2.98862e13i			1.13036i	−0.824969	+	0.565178i	$0.808807\pi$
$32$	−3.36378e13	−	1.03170e13i	−0.956043	−	0.293227i
$33$	4.94632e13			1.06575
$34$	2.82829e13	−	1.80806e13i	0.465816	−	0.297784i
$35$	−4.02219e12			−0.0510328
$36$	1.37723e13	−	2.97780e13i	0.135608	−	0.293207i
$37$			1.12077e14i			0.862381i	0.902261	+	0.431191i	$0.141906\pi$
$37$			1.12077e14i			0.862381i	−0.902261	+	0.431191i	$0.858094\pi$
$38$	−7.02515e13	+	4.49100e13i	−0.425210	+	0.271826i
$39$			1.59298e14i			0.763183i
$40$	−1.50471e13	+	2.05296e12i	−0.0574000	+	0.00783144i
$41$	−1.86561e14			−0.569856			−0.284928	−	0.958549i	$-0.591970\pi$
$41$	−1.86561e14			−0.569856			−0.284928	+	0.958549i	$0.591970\pi$
$42$	−2.21946e14	−	3.47184e14i	−0.545762	−	0.853720i
$43$	7.27808e14			1.44811			0.724054	−	0.689744i	$-0.242277\pi$
$43$	7.27808e14			1.44811			0.724054	+	0.689744i	$0.242277\pi$
$44$	2.40415e14	−	5.19817e14i	0.388944	−	0.840962i
$45$		−	1.41611e13i		−	0.0187147i
$46$	−8.53803e14	−	1.33558e15i	−0.925843	−	1.44827i
$47$			1.44996e15i			1.29561i	0.761805	+	0.647806i	$0.224313\pi$
$47$			1.44996e15i			1.29561i	−0.761805	+	0.647806i	$0.775687\pi$
$48$	−1.00751e15	−	1.18554e15i	−0.744865	−	0.876484i
$49$	3.64754e14			0.223993
$50$	1.64008e15	−	1.04846e15i	0.839721	−	0.536812i
$51$	1.48436e15			0.635926
$52$	1.67409e15	+	7.74265e14i	0.602211	+	0.278522i
$53$			6.79100e14i			0.205802i	0.994692	+	0.102901i	$0.0328126\pi$
$53$			6.79100e14i			0.205802i	−0.994692	+	0.102901i	$0.967187\pi$
$54$	−2.56144e15	+	1.63747e15i	−0.656056	+	0.419400i
$55$		−	2.47201e14i		−	0.0536767i
$56$	−4.72737e15	+	6.44985e14i	−0.872826	+	0.119085i
$57$	−3.68697e15			−0.580492
$58$	7.30385e15	+	1.14252e16i	0.983331	+	1.53820i
$59$	−6.53060e15			−0.753850			−0.376925	−	0.926244i	$-0.623018\pi$
$59$	−6.53060e15			−0.753850			−0.376925	+	0.926244i	$0.623018\pi$
$60$	−6.09500e14	−	2.81893e14i	−0.0604801	−	0.0279720i
$61$			7.84501e14i			0.0670850i	0.999437	+	0.0335425i	$0.0106789\pi$
$61$			7.84501e14i			0.0670850i	−0.999437	+	0.0335425i	$0.989321\pi$
$62$	8.24182e15	+	1.28925e16i	0.608832	+	0.952380i
$63$		−	4.44901e15i		−	0.284576i
$64$	−1.73560e16	+	4.82580e15i	−0.963451	+	0.267886i
$65$	7.96120e14			0.0384378
$66$	2.13377e16	−	1.36406e16i	0.897949	−	0.574036i
$67$	1.65722e16			0.609127			0.304563	−	0.952492i	$-0.401489\pi$
$67$	1.65722e16			0.609127			0.304563	+	0.952492i	$0.401489\pi$
$68$	7.21469e15	−	1.55994e16i	0.232080	−	0.501795i
$69$		−	7.00945e16i		−	1.97716i
$70$	−1.73511e15	+	1.10921e15i	−0.0429977	+	0.0274873i
$71$		−	1.64782e16i		−	0.359406i	−0.983721	−	0.179703i	$-0.942486\pi$
$71$		−	1.64782e16i		−	0.359406i	0.983721	−	0.179703i	$-0.0575137\pi$
$72$	−2.27082e15	−	1.66438e16i	−0.0436707	−	0.320082i
$73$	−1.15920e17			−1.96903			−0.984516	−	0.175294i	$-0.943912\pi$
$73$	−1.15920e17			−1.96903			−0.984516	+	0.175294i	$0.943912\pi$
$74$	3.09077e16	+	4.83481e16i	0.464496	+	0.726598i
$75$	8.60754e16			1.14638
$76$	−1.79205e16	+	3.87470e16i	−0.211849	+	0.458053i
$77$		−	7.76637e16i		−	0.816210i
$78$	4.39301e16	+	6.87187e16i	0.411066	+	0.643019i
$79$			9.97517e16i			0.832294i	0.909297	+	0.416147i	$0.136620\pi$
$79$			9.97517e16i			0.832294i	−0.909297	+	0.416147i	$0.863380\pi$
$80$	−5.92493e15	+	5.03520e15i	−0.0441442	+	0.0375152i
$81$	−1.82918e17			−1.21869
$82$	−8.04794e16	+	5.14484e16i	−0.480131	+	0.306936i
$83$	2.58659e17			1.38365			0.691824	−	0.722066i	$-0.256807\pi$
$83$	2.58659e17			1.38365			0.691824	+	0.722066i	$0.256807\pi$
$84$	−1.91488e17	−	8.85630e16i	−0.919661	−	0.425343i
$85$		−	7.41833e15i		−	0.0320285i
$86$	3.13965e17	−	2.00710e17i	1.22010	−	0.779980i
$87$			5.99623e17i			2.09993i
$88$	−3.96403e16	−	2.90541e17i	−0.125254	−	0.918045i
$89$	1.02832e17			0.293506			0.146753	−	0.989173i	$-0.453118\pi$
$89$	1.02832e17			0.293506			0.146753	+	0.989173i	$0.453118\pi$
$90$	−3.90524e15	−	6.10887e15i	−0.0100801	−	0.0157681i
$91$	2.50119e17			0.584486
$92$	−7.36636e17	−	3.40693e17i	−1.56014	−	0.721561i
$93$			6.76627e17i			1.30018i
$94$	3.99860e17	+	6.25491e17i	0.697843	+	1.09162i
$95$			1.84263e16i			0.0292365i
$96$	−7.61563e17	−	2.33579e17i	−1.09968	−	0.337281i
$97$	−4.73017e17			−0.622201			−0.311101	−	0.950377i	$-0.600698\pi$
$97$	−4.73017e17			−0.622201			−0.311101	+	0.950377i	$0.600698\pi$
$98$	1.57349e17	−	1.00589e17i	0.188725	−	0.120647i
$99$	2.73434e17			0.299320
$100$	4.18368e17	−	9.04581e17i	0.418368	−	0.904581i
$101$		−	1.84048e18i		−	1.68283i	−0.540392	−	0.841413i	$-0.681724\pi$
$101$		−	1.84048e18i		−	1.68283i	0.540392	−	0.841413i	$-0.318276\pi$
$102$	6.40329e17	−	4.09346e17i	0.535799	−	0.342522i
$103$		−	1.07149e18i		−	0.821209i	−0.911813	−	0.410605i	$-0.865318\pi$
$103$		−	1.07149e18i		−	0.821209i	0.911813	−	0.410605i	$-0.134682\pi$
$104$	9.35699e17	−	1.27663e17i	0.657410	−	0.0896944i
$105$	−9.10628e16			−0.0586999
$106$	1.87278e17	+	2.92953e17i	0.110849	+	0.173399i
$107$	6.29108e17			0.342193			0.171096	−	0.985254i	$-0.445269\pi$
$107$	6.29108e17			0.342193			0.171096	+	0.985254i	$0.445269\pi$
$108$	−6.53399e17	+	1.41276e18i	−0.326862	+	0.706730i
$109$		−	3.93478e17i		−	0.181168i	−0.995889	−	0.0905841i	$-0.971127\pi$
$109$		−	3.93478e17i		−	0.181168i	0.995889	−	0.0905841i	$-0.0288734\pi$
$110$	−6.81715e16	−	1.06639e17i	−0.0289114	−	0.0452253i
$111$			2.53743e18i			0.991944i
$112$	−1.86145e18	+	1.58192e18i	−0.671257	+	0.570457i
$113$	−2.22499e18			−0.740666			−0.370333	−	0.928899i	$-0.620756\pi$
$113$	−2.22499e18			−0.740666			−0.370333	+	0.928899i	$0.620756\pi$
$114$	−1.59050e18	+	1.01677e18i	−0.489093	+	0.312665i
$115$	−3.50310e17			−0.0995799
$116$	6.30154e18	+	2.91446e18i	1.65701	+	0.766366i
$117$			8.80603e17i			0.214342i
$118$	−2.81720e18	+	1.80097e18i	−0.635155	+	0.406039i
$119$		−	2.33064e18i		−	0.487025i
$120$	−3.40668e17	+	4.64794e16i	−0.0660237	+	0.00900801i
$121$	−7.86755e17			−0.141505
$122$	2.16345e17	+	3.38422e17i	0.0361333	+	0.0565223i
$123$	−4.22376e18			−0.655470
$124$	7.11079e18	+	3.28874e18i	1.02594	+	0.474497i
$125$		−	8.61803e17i		−	0.115669i
$126$	−1.22692e18	−	1.91924e18i	−0.153279	−	0.239769i
$127$		−	1.42919e19i		−	1.66286i	−0.555632	−	0.831429i	$-0.687523\pi$
$127$		−	1.42919e19i		−	1.66286i	0.555632	−	0.831429i	$-0.312477\pi$
$128$	−6.15628e18	+	6.86810e18i	−0.667466	+	0.744641i
$129$	1.64777e19			1.66567
$130$	3.43434e17	−	2.19549e17i	0.0323857	−	0.0207034i
$131$	−1.54914e19			−1.36348			−0.681738	−	0.731596i	$-0.738776\pi$
$131$	−1.54914e19			−1.36348			−0.681738	+	0.731596i	$0.738776\pi$
$132$	5.44303e18	−	1.17687e19i	0.447379	−	0.967307i
$133$			5.78903e18i			0.444571i
$134$	7.14901e18	−	4.57018e18i	0.513219	−	0.328088i
$135$			6.71842e17i			0.0451090i
$136$	−1.18958e18	−	8.71895e18i	−0.0747383	−	0.547790i
$137$	2.18638e19			1.28600			0.643000	−	0.765866i	$-0.277689\pi$
$137$	2.18638e19			1.28600			0.643000	+	0.765866i	$0.277689\pi$
$138$	−1.93302e19	−	3.02377e19i	−1.06494	−	1.66586i
$139$	−7.61120e18			−0.392934			−0.196467	−	0.980510i	$-0.562947\pi$
$139$	−7.61120e18			−0.392934			−0.196467	+	0.980510i	$0.562947\pi$
$140$	−4.42609e17	+	9.56995e17i	−0.0214224	+	0.0463188i
$141$			3.28273e19i			1.49026i
$142$	−4.54426e18	−	7.10846e18i	−0.193583	−	0.302817i
$143$			1.53721e19i			0.614766i
$144$	−5.56953e18	−	6.55367e18i	−0.209197	−	0.246163i
$145$	2.99672e18			0.105763
$146$	−5.00062e19	+	3.19677e19i	−1.65901	+	1.06056i
$147$	8.25807e18			0.257646
$148$	2.66663e19	+	1.23331e19i	0.782721	+	0.362008i
$149$			4.22440e19i			1.16705i	0.812096	+	0.583524i	$0.198326\pi$
$149$			4.22440e19i			1.16705i	−0.812096	+	0.583524i	$0.801674\pi$
$150$	3.71316e19	−	2.37373e19i	0.965879	−	0.617462i
$151$			2.44512e18i			0.0599111i	0.999551	+	0.0299555i	$0.00953657\pi$
$151$			2.44512e18i			0.0599111i	−0.999551	+	0.0299555i	$0.990463\pi$
$152$	2.95478e18	+	2.16569e19i	0.0682233	+	0.500039i
$153$	8.20555e18			0.178601
$154$	−2.14176e19	−	3.35030e19i	−0.439627	−	0.687696i
$155$	3.38156e18			0.0654836
$156$	3.79016e19	+	1.75295e19i	0.692686	+	0.320367i
$157$		−	1.10362e20i		−	1.90425i	−0.305711	−	0.952125i	$-0.598894\pi$
$157$		−	1.10362e20i		−	1.90425i	0.305711	−	0.952125i	$-0.401106\pi$
$158$	2.75089e19	+	4.30314e19i	0.448290	+	0.701248i
$159$			1.53749e19i			0.236722i
$160$	−1.16735e18	+	3.80605e18i	−0.0169872	+	0.0553853i
$161$	−1.10058e20			−1.51421
$162$	−7.89083e19	+	5.04441e19i	−1.02680	+	0.656410i
$163$	3.18939e19			0.392663			0.196331	−	0.980538i	$-0.437097\pi$
$163$	3.18939e19			0.392663			0.196331	+	0.980538i	$0.437097\pi$
$164$	−2.05295e19	+	4.43882e19i	−0.239212	+	0.517217i
$165$		−	5.59666e18i		−	0.0617410i
$166$	1.11582e20	−	7.13314e19i	1.16579	−	0.745260i
$167$		−	2.78729e19i		−	0.275889i	−0.990440	−	0.137944i	$-0.955950\pi$
$167$		−	2.78729e19i		−	0.275889i	0.990440	−	0.137944i	$-0.0440495\pi$
$168$	−1.07028e20	+	1.46025e19i	−1.00396	+	0.136976i
$169$	6.29489e19			0.559767
$170$	−2.04578e18	−	3.20016e18i	−0.0172512	−	0.0269855i
$171$	−2.03817e19			−0.163033
$172$	8.00894e19	−	1.73167e20i	0.607882	−	1.31434i
$173$		−	4.59488e19i		−	0.331024i	−0.986208	−	0.165512i	$-0.947072\pi$
$173$		−	4.59488e19i		−	0.331024i	0.986208	−	0.165512i	$-0.0529277\pi$
$174$	1.65360e20	+	2.58668e20i	1.13107	+	1.76929i
$175$		−	1.35150e20i		−	0.877956i
$176$	−9.72238e19	−	1.14403e20i	−0.600010	−	0.706033i
$177$	−1.47854e20			−0.867106
$178$	4.43600e19	−	2.83582e19i	0.247293	−	0.158088i
$179$	7.29815e19			0.386844			0.193422	−	0.981116i	$-0.438041\pi$
$179$	7.29815e19			0.386844			0.193422	+	0.981116i	$0.438041\pi$
$180$	−3.36933e18	−	1.55831e18i	−0.0169860	−	0.00785600i
$181$		−	2.45633e20i		−	1.17810i	−0.808098	−	0.589048i	$-0.799503\pi$
$181$		−	2.45633e20i		−	1.17810i	0.808098	−	0.589048i	$-0.200497\pi$
$182$	1.07897e20	−	6.89761e19i	0.492458	−	0.314816i
$183$			1.77612e19i			0.0771637i
$184$	−4.11728e20	+	5.61745e19i	−1.70314	+	0.232369i
$185$	1.26812e19			0.0499593
$186$	1.86596e20	+	2.91887e20i	0.700302	+	1.09546i
$187$	1.43239e20			0.512257
$188$	3.44988e20	+	1.59556e20i	1.17593	+	0.543868i
$189$			2.11074e20i			0.685928i
$190$	5.08148e18	+	7.94883e18i	0.0157474	+	0.0246332i
$191$			6.07829e20i			1.79672i	0.439257	+	0.898362i	$0.355242\pi$
$191$			6.07829e20i			1.79672i	−0.439257	+	0.898362i	$0.644758\pi$
$192$	−3.92942e20	+	1.09257e20i	−1.10820	+	0.308132i
$193$	−4.79968e20			−1.29180			−0.645902	−	0.763420i	$-0.723519\pi$
$193$	−4.79968e20			−1.29180			−0.645902	+	0.763420i	$0.723519\pi$
$194$	−2.04052e20	+	1.30445e20i	−0.524235	+	0.335130i
$195$	1.80243e19			0.0442126
$196$	4.01382e19	−	8.67855e19i	0.0940272	−	0.203302i
$197$			1.80171e20i			0.403170i	0.979471	+	0.201585i	$0.0646092\pi$
$197$			1.80171e20i			0.403170i	−0.979471	+	0.201585i	$0.935391\pi$
$198$	1.17955e20	−	7.54057e19i	0.252191	−	0.161219i
$199$			4.29390e20i			0.877353i	0.898645	+	0.438677i	$0.144553\pi$
$199$			4.29390e20i			0.877353i	−0.898645	+	0.438677i	$0.855447\pi$
$200$	−6.89818e19	−	5.05598e20i	−0.134730	−	0.987495i
$201$	3.75198e20			0.700641
$202$	−5.07556e20	−	7.93956e20i	−0.906404	−	1.41786i
$203$	9.41487e20			1.60824
$204$	1.63342e20	−	3.53172e20i	0.266947	−	0.577184i
$205$			2.11090e19i			0.0330128i
$206$	−2.95489e20	−	4.62226e20i	−0.442320	−	0.691909i
$207$		−	3.87484e20i		−	0.555291i
$208$	3.68440e20	−	3.13113e20i	0.505589	−	0.429666i
$209$	−3.55790e20			−0.467603
$210$	−3.92831e19	+	2.51127e19i	−0.0494575	+	0.0316170i
$211$	2.28708e20			0.275892			0.137946	−	0.990440i	$-0.455950\pi$
$211$	2.28708e20			0.275892			0.137946	+	0.990440i	$0.455950\pi$
$212$	1.61578e20	+	7.47295e19i	0.186792	+	0.0863911i
$213$		−	3.73069e20i		−	0.413403i
$214$	2.71388e20	−	1.73491e20i	0.288314	−	0.184312i
$215$		−	8.23501e19i		−	0.0838915i
$216$	1.07734e20	+	7.89632e20i	0.105262	+	0.771509i
$217$	1.06239e21			0.995745
$218$	−1.08511e20	−	1.69740e20i	−0.0975808	−	0.152643i
$219$	−2.62445e21			−2.26486
$220$	−5.88163e19	−	2.72025e19i	−0.0487185	−	0.0225323i
$221$			4.61307e20i			0.366826i
$222$	6.99755e20	+	1.09461e21i	0.534281	+	0.835761i
$223$		−	1.63549e21i		−	1.19923i	−0.800288	−	0.599616i	$-0.795320\pi$
$223$		−	1.63549e21i		−	1.19923i	0.800288	−	0.599616i	$-0.204680\pi$
$224$	−3.66749e20	+	1.19576e21i	−0.258307	+	0.842190i
$225$	4.75827e20			0.321963
$226$	−9.59828e20	+	6.13594e20i	−0.624047	+	0.398937i
$227$	−1.59050e21			−0.993807			−0.496904	−	0.867806i	$-0.665530\pi$
$227$	−1.59050e21			−0.993807			−0.496904	+	0.867806i	$0.665530\pi$
$228$	−4.05722e20	+	8.77238e20i	−0.243677	+	0.526870i
$229$			2.79204e20i			0.161214i	0.996746	+	0.0806070i	$0.0256859\pi$
$229$			2.79204e20i			0.161214i	−0.996746	+	0.0806070i	$0.974314\pi$
$230$	−1.51118e20	+	9.66061e19i	−0.0839009	+	0.0536357i
$231$		−	1.75832e21i		−	0.938835i
$232$	3.52212e21	−	4.80544e20i	1.80889	−	0.246798i
$233$	2.76663e21			1.36694			0.683468	−	0.729981i	$-0.260471\pi$
$233$	2.76663e21			1.36694			0.683468	+	0.729981i	$0.260471\pi$
$234$	2.42847e20	+	3.79879e20i	0.115449	+	0.180594i
$235$	1.64060e20			0.0750572
$236$	−7.18640e20	+	1.55382e21i	−0.316449	+	0.684215i
$237$			2.25839e21i			0.957336i
$238$	−6.42727e20	−	1.00540e21i	−0.262322	−	0.410343i
$239$			9.30010e20i			0.365516i	0.983158	+	0.182758i	$0.0585025\pi$
$239$			9.30010e20i			0.365516i	−0.983158	+	0.182758i	$0.941497\pi$
$240$	−1.34141e20	+	1.13998e20i	−0.0507763	+	0.0431514i
$241$	−3.49001e21			−1.27255			−0.636273	−	0.771464i	$-0.719525\pi$
$241$	−3.49001e21			−1.27255			−0.636273	+	0.771464i	$0.719525\pi$
$242$	−3.39394e20	+	2.16966e20i	−0.119225	+	0.0762173i
$243$	−1.84090e21			−0.623124
$244$	1.86656e20	+	8.63281e19i	0.0608881	+	0.0281607i
$245$		−	4.12712e19i		−	0.0129763i
$246$	−1.82206e21	+	1.16480e21i	−0.552265	+	0.353049i
$247$		−	1.14584e21i		−	0.334849i
$248$	3.97444e21	−	5.42256e20i	1.11998	−	0.152806i
$249$	5.85609e21			1.59152
$250$	−2.37662e20	−	3.71769e20i	−0.0623017	−	0.0974569i
$251$	8.66928e20			0.219240			0.109620	−	0.993974i	$-0.465037\pi$
$251$	8.66928e20			0.219240			0.109620	+	0.993974i	$0.465037\pi$
$252$	−1.05855e21	−	4.89578e20i	−0.258289	−	0.119459i
$253$		−	6.76407e21i		−	1.59266i
$254$	−3.94131e21	−	6.16529e21i	−0.895648	−	1.40104i
$255$		−	1.67952e20i		−	0.0368403i
$256$	−7.61690e20	+	4.66053e21i	−0.161294	+	0.986906i
$257$	−8.00388e21			−1.63645			−0.818225	−	0.574898i	$-0.805042\pi$
$257$	−8.00388e21			−1.63645			−0.818225	+	0.574898i	$0.805042\pi$
$258$	7.10822e21	−	4.54410e21i	1.40341	−	0.897162i
$259$	3.98410e21			0.759682
$260$	8.76066e19	−	1.89420e20i	0.0161353	−	0.0348872i
$261$			3.31473e21i			0.589771i
$262$	−6.68274e21	+	4.27210e21i	−1.14880	+	0.734396i
$263$			4.28394e21i			0.711610i	0.934560	+	0.355805i	$0.115793\pi$
$263$			4.28394e21i			0.711610i	−0.934560	+	0.355805i	$0.884207\pi$
$264$	−8.97462e20	−	6.57790e21i	−0.144072	−	1.05597i
$265$	7.68388e19			0.0119225
$266$	1.59646e21	+	2.49730e21i	0.239455	+	0.374573i
$267$	2.32812e21			0.337601
$268$	1.82364e21	−	3.94302e21i	0.255697	−	0.552860i
$269$			2.24980e21i			0.305052i	0.988299	+	0.152526i	$0.0487407\pi$
$269$			2.24980e21i			0.305052i	−0.988299	+	0.152526i	$0.951259\pi$
$270$	1.85276e20	+	2.89822e20i	0.0242966	+	0.0380065i
$271$			5.50680e21i			0.698515i	0.937027	+	0.349258i	$0.113566\pi$
$271$			5.50680e21i			0.698515i	−0.937027	+	0.349258i	$0.886434\pi$
$272$	−2.91762e21	−	3.43317e21i	−0.358021	−	0.421284i
$273$	5.66272e21			0.672297
$274$	9.43173e21	−	6.02946e21i	1.08352	−	0.692666i
$275$	8.30622e21			0.923441
$276$	−1.66775e22	−	7.71334e21i	−1.79453	−	0.829967i
$277$			9.00261e21i			0.937671i	0.883285	+	0.468836i	$0.155326\pi$
$277$			9.00261e21i			0.937671i	−0.883285	+	0.468836i	$0.844674\pi$
$278$	−3.28336e21	+	2.09897e21i	−0.331066	+	0.211642i
$279$			3.74041e21i			0.365158i
$280$	7.29787e19	+	5.34893e20i	0.00689881	+	0.0505644i
$281$	−4.16171e21			−0.380991			−0.190495	−	0.981688i	$-0.561009\pi$
$281$	−4.16171e21			−0.380991			−0.190495	+	0.981688i	$0.561009\pi$
$282$	9.05289e21	+	1.41612e22i	0.802686	+	1.25562i
$283$	−3.09629e21			−0.265928			−0.132964	−	0.991121i	$-0.542449\pi$
$283$	−3.09629e21			−0.265928			−0.132964	+	0.991121i	$0.542449\pi$
$284$	−3.92065e21	−	1.81330e21i	−0.326207	−	0.150870i
$285$			4.17174e20i			0.0336289i
$286$	4.23923e21	+	6.63131e21i	0.331125	+	0.517971i
$287$			6.63185e21i			0.501993i
$288$	−4.20994e21	−	1.29123e21i	−0.308847	−	0.0947262i
$289$	−9.76457e21			−0.694341
$290$	1.29274e21	−	8.26416e20i	0.0891106	−	0.0569662i
$291$	−1.07092e22			−0.715679
$292$	−1.27561e22	+	2.75807e22i	−0.826554	+	1.78715i
$293$		−	2.15579e22i		−	1.35456i	−0.735725	−	0.677281i	$-0.763158\pi$
$293$		−	2.15579e22i		−	1.35456i	0.735725	−	0.677281i	$-0.236842\pi$
$294$	3.56241e21	−	2.27736e21i	0.217079	−	0.138773i
$295$			7.38924e20i			0.0436719i
$296$	1.49046e22	−	2.03352e21i	0.854465	−	0.116580i
$297$	−1.29725e22			−0.721464
$298$	1.16498e22	+	1.82234e22i	0.628595	+	0.983294i
$299$	2.17839e22			1.14050
$300$	9.47191e21	−	2.04798e22i	0.481223	−	1.04048i
$301$		−	2.58721e22i		−	1.27566i
$302$	6.74299e20	+	1.05479e21i	0.0322693	+	0.0504780i
$303$		−	4.16688e22i		−	1.93565i
$304$	7.24704e21	+	8.52760e21i	0.326812	+	0.384560i
$305$	8.87648e19			0.00388635
$306$	3.53975e21	−	2.26287e21i	0.150480	−	0.0961983i
$307$	8.47967e21			0.350053			0.175026	−	0.984564i	$-0.443999\pi$
$307$	8.47967e21			0.350053			0.175026	+	0.984564i	$0.443999\pi$
$308$	−1.84785e22	−	8.54627e21i	−0.740814	−	0.342626i
$309$		−	2.42587e22i		−	0.944586i
$310$	1.45876e21	−	9.32546e20i	0.0551731	−	0.0352708i
$311$		−	4.93345e21i		−	0.181262i	−0.995885	−	0.0906311i	$-0.971112\pi$
$311$		−	4.93345e21i		−	0.181262i	0.995885	−	0.0906311i	$-0.0288884\pi$
$312$	2.11843e22	−	2.89031e21i	0.756178	−	0.103170i
$313$	−2.56237e22			−0.888674			−0.444337	−	0.895860i	$-0.646561\pi$
$313$	−2.56237e22			−0.888674			−0.444337	+	0.895860i	$0.646561\pi$
$314$	−3.04350e22	−	4.76086e22i	−1.02567	−	1.60442i
$315$	−5.03397e20			−0.0164860
$316$	2.37338e22	+	1.09769e22i	0.755412	+	0.349378i
$317$			4.19078e22i			1.29647i	0.761441	+	0.648234i	$0.224492\pi$
$317$			4.19078e22i			1.29647i	−0.761441	+	0.648234i	$0.775508\pi$
$318$	4.23999e21	+	6.63250e21i	0.127503	+	0.199450i
$319$			5.78632e22i			1.69156i
$320$	5.46030e20	+	1.96380e21i	0.0155191	+	0.0558144i
$321$	1.42431e22			0.393603
$322$	−4.74772e22	+	3.03510e22i	−1.27580	+	0.815586i
$323$	−1.06770e22			−0.279015
$324$	−2.01287e22	+	4.35216e22i	−0.511577	+	1.10611i
$325$			2.67505e22i			0.661273i
$326$	1.37586e22	−	8.79550e21i	0.330838	−	0.211496i
$327$		−	8.90839e21i		−	0.208387i
$328$	3.38496e21	+	2.48099e22i	0.0770352	+	0.564625i
$329$	5.15432e22			1.14132
$330$	−1.54341e21	−	2.41432e21i	−0.0332549	−	0.0520198i
$331$	−4.54525e22			−0.953028			−0.476514	−	0.879167i	$-0.658100\pi$
$331$	−4.54525e22			−0.953028			−0.476514	+	0.879167i	$0.658100\pi$
$332$	2.84634e22	−	6.15426e22i	0.580823	−	1.25584i
$333$			1.40270e22i			0.278590i
$334$	−7.68661e21	−	1.20240e22i	−0.148599	−	0.232450i
$335$		−	1.87512e21i		−	0.0352878i
$336$	−4.21434e22	+	3.58149e22i	−0.772105	+	0.656161i
$337$	6.95979e22			1.24144			0.620722	−	0.784031i	$-0.286840\pi$
$337$	6.95979e22			1.24144			0.620722	+	0.784031i	$0.286840\pi$
$338$	2.71552e22	−	1.73596e22i	0.471631	−	0.301502i
$339$	−5.03741e22			−0.851942
$340$	−1.76504e21	−	8.16328e20i	−0.0290699	−	0.0134448i
$341$			6.52941e22i			1.04733i
$342$	−8.79234e21	+	5.62072e21i	−0.137363	+	0.0878126i
$343$		−	7.08531e22i		−	1.07823i
$344$	−1.32054e22	−	9.67880e22i	−0.195760	−	1.43481i
$345$	−7.93106e21			−0.114541
$346$	−1.26715e22	−	1.98216e22i	−0.178296	−	0.278904i
$347$	−2.62695e21			−0.0360153			−0.0180076	−	0.999838i	$-0.505732\pi$
$347$	−2.62695e21			−0.0360153			−0.0180076	+	0.999838i	$0.505732\pi$
$348$	1.42668e23	+	6.59837e22i	1.90595	+	0.881503i
$349$			7.00595e22i			0.912091i	0.889956	+	0.456045i	$0.150735\pi$
$349$			7.00595e22i			0.912091i	−0.889956	+	0.456045i	$0.849265\pi$
$350$	−3.72707e22	−	5.83016e22i	−0.472885	−	0.739721i
$351$		−	4.17783e22i		−	0.516639i
$352$	−7.34903e22	−	2.25402e22i	−0.885822	−	0.271690i
$353$	1.24853e23			1.46698			0.733492	−	0.679699i	$-0.237889\pi$
$353$	1.24853e23			1.46698			0.733492	+	0.679699i	$0.237889\pi$
$354$	−6.37818e22	+	4.07741e22i	−0.730580	+	0.467041i
$355$	−1.86448e21			−0.0208211
$356$	1.13158e22	−	2.44666e22i	0.123207	−	0.266394i
$357$		−	5.27659e22i		−	0.560195i
$358$	3.14831e22	−	2.01264e22i	0.325935	−	0.208362i
$359$			1.48797e23i			1.50226i	0.660156	+	0.751129i	$0.270490\pi$
$359$			1.48797e23i			1.50226i	−0.660156	+	0.751129i	$0.729510\pi$
$360$	−1.88322e21	+	2.56939e20i	−0.0185429	+	0.00252992i
$361$	−7.76068e22			−0.745307
$362$	−6.77392e22	−	1.05963e23i	−0.634546	−	0.992603i
$363$	−1.78122e22			−0.162764
$364$	2.75236e22	−	5.95105e22i	0.245354	−	0.530495i
$365$			1.31161e22i			0.114070i
$366$	4.89807e21	+	7.66192e21i	0.0415619	+	0.0650141i
$367$		−	1.48550e23i		−	1.22992i	−0.788556	−	0.614962i	$-0.789171\pi$
$367$		−	1.48550e23i		−	1.22992i	0.788556	−	0.614962i	$-0.210829\pi$
$368$	−1.62122e23	+	1.37776e23i	−1.30982	+	1.11313i
$369$	−2.33490e22			−0.184090
$370$	5.47050e21	−	3.49715e21i	0.0420932	−	0.0269091i
$371$	2.41406e22			0.181294
$372$	1.60989e23	+	7.44574e22i	1.18008	+	0.545785i
$373$		−	1.47581e23i		−	1.05597i	−0.849253	−	0.527986i	$-0.822947\pi$
$373$		−	1.47581e23i		−	1.05597i	0.849253	−	0.527986i	$-0.177053\pi$
$374$	6.17913e22	−	3.95016e22i	0.431601	−	0.275912i
$375$		−	1.95113e22i		−	0.133047i
$376$	1.92824e23	−	2.63081e22i	1.28372	−	0.175146i
$377$	−1.86351e23			−1.21132
$378$	5.82086e22	+	9.10542e22i	0.369455	+	0.577928i
$379$	8.96290e22			0.555515			0.277757	−	0.960651i	$-0.410409\pi$
$379$	8.96290e22			0.555515			0.277757	+	0.960651i	$0.410409\pi$
$380$	4.38415e21	+	2.02767e21i	0.0265359	+	0.0122728i
$381$		−	3.23569e23i		−	1.91268i
$382$	1.67623e23	+	2.62208e23i	0.967751	+	1.51383i
$383$			1.85064e23i			1.04360i	0.853068	+	0.521799i	$0.174739\pi$
$383$			1.85064e23i			1.04360i	−0.853068	+	0.521799i	$0.825261\pi$
$384$	−1.39379e23	+	1.55495e23i	−0.767744	+	0.856514i
$385$	−8.78750e21			−0.0472845
$386$	−2.07051e23	+	1.32363e23i	−1.08841	+	0.695792i
$387$	9.10889e22			0.467807
$388$	−5.20517e22	+	1.12544e23i	−0.261186	+	0.564727i
$389$			3.35149e23i			1.64321i	0.570061	+	0.821603i	$0.306920\pi$
$389$			3.35149e23i			1.64321i	−0.570061	+	0.821603i	$0.693080\pi$
$390$	7.77539e21	−	4.97061e21i	0.0372513	−	0.0238138i
$391$		−	2.02985e23i		−	0.950328i
$392$	−6.61811e21	−	4.85070e22i	−0.0302802	−	0.221937i
$393$	−3.50726e23			−1.56832
$394$	4.96863e22	+	7.77229e22i	0.217155	+	0.339690i
$395$	1.12867e22			0.0482163
$396$	3.00892e22	−	6.50578e22i	0.125647	−	0.271671i
$397$		−	1.51630e23i		−	0.618970i	−0.950904	−	0.309485i	$-0.899843\pi$
$397$		−	1.51630e23i		−	0.618970i	0.950904	−	0.309485i	$-0.100157\pi$
$398$	1.18414e23	+	1.85232e23i	0.472560	+	0.739213i
$399$			1.31064e23i			0.511362i
$400$	−1.69188e23	−	1.99084e23i	−0.645401	−	0.759445i
$401$	2.40805e23			0.898187			0.449093	−	0.893485i	$-0.351747\pi$
$401$	2.40805e23			0.898187			0.449093	+	0.893485i	$0.351747\pi$
$402$	1.61855e23	−	1.03470e23i	0.590324	−	0.377379i
$403$	−2.10282e23			−0.749992
$404$	−4.37904e23	−	2.02530e23i	−1.52738	−	0.706412i
$405$			2.06969e22i			0.0706008i
$406$	4.06143e23	−	2.59637e23i	1.35502	−	0.866229i
$407$			2.44860e23i			0.799039i
$408$	−2.69322e22	−	1.97398e23i	−0.0859668	−	0.630089i
$409$	1.51761e23			0.473861			0.236930	−	0.971527i	$-0.423859\pi$
$409$	1.51761e23			0.473861			0.236930	+	0.971527i	$0.423859\pi$
$410$	5.82129e21	+	9.10609e21i	0.0177813	+	0.0278149i
$411$	4.95000e23			1.47921
$412$	−2.54939e23	−	1.17909e23i	−0.745352	−	0.344725i
$413$			2.32150e23i			0.664076i
$414$	−1.06858e23	−	1.67155e23i	−0.299091	−	0.467860i
$415$		−	2.92668e22i		−	0.0801572i
$416$	7.25914e22	−	2.36678e23i	0.194556	−	0.634335i
$417$	−1.72319e23			−0.451968
$418$	−1.53483e23	+	9.81175e22i	−0.393978	+	0.251860i
$419$	5.84461e22			0.146835			0.0734175	−	0.997301i	$-0.476609\pi$
$419$	5.84461e22			0.146835			0.0734175	+	0.997301i	$0.476609\pi$
$420$	−1.00207e22	+	2.16665e22i	−0.0246409	+	0.0532776i
$421$		−	6.10981e23i		−	1.47058i	−0.677752	−	0.735291i	$-0.737046\pi$
$421$		−	6.10981e23i		−	1.47058i	0.677752	−	0.735291i	$-0.262954\pi$
$422$	9.86611e22	−	6.30715e22i	0.232452	−	0.148601i
$423$			1.81470e23i			0.418544i
$424$	9.03105e22	−	1.23216e22i	0.203913	−	0.0278211i
$425$	2.49264e23			0.551009
$426$	−1.02883e23	−	1.60937e23i	−0.222667	−	0.348312i
$427$	2.78874e22			0.0590960
$428$	6.92283e22	−	1.49683e23i	0.143645	−	0.310584i
$429$			3.48027e23i			0.707127i
$430$	−2.27100e22	−	3.55246e22i	−0.0451856	−	0.0706827i
$431$		−	1.91603e23i		−	0.373342i	−0.982423	−	0.186671i	$-0.940230\pi$
$431$		−	1.91603e23i		−	0.373342i	0.982423	−	0.186671i	$-0.0597698\pi$
$432$	2.64235e23	+	3.10925e23i	0.504238	+	0.593338i
$433$	−5.30516e23			−0.991534			−0.495767	−	0.868456i	$-0.665113\pi$
$433$	−5.30516e23			−0.991534			−0.495767	+	0.868456i	$0.665113\pi$
$434$	4.58301e23	−	2.92980e23i	0.838963	−	0.536328i
$435$	6.78462e22			0.121653
$436$	−9.36198e22	−	4.32991e22i	−0.164433	−	0.0760502i
$437$			5.04192e23i			0.867487i
$438$	−1.13215e24	+	7.23752e23i	−1.90825	+	1.21990i
$439$			3.48322e21i			0.00575176i	0.999996	+	0.00287588i	$0.000915422\pi$
$439$			3.48322e21i			0.00575176i	−0.999996	+	0.00287588i	$0.999085\pi$
$440$	−3.28742e22	+	4.48523e21i	−0.0531840	+	0.00725622i
$441$	4.56508e22			0.0723604
$442$	1.27216e23	+	1.99001e23i	0.197580	+	0.309069i
$443$	3.92705e22			0.0597631			0.0298816	−	0.999553i	$-0.490487\pi$
$443$	3.92705e22			0.0597631			0.0298816	+	0.999553i	$0.490487\pi$
$444$	6.03728e23	+	2.79224e23i	0.900315	+	0.416395i
$445$		−	1.16352e22i		−	0.0170033i
$446$	−4.51024e23	−	7.05525e23i	−0.645931	−	1.01041i
$447$			9.56409e23i			1.34238i
$448$	1.71547e23	+	6.16970e23i	0.235984	+	0.848716i
$449$	−2.06326e22			−0.0278186			−0.0139093	−	0.999903i	$-0.504428\pi$
$449$	−2.06326e22			−0.0278186			−0.0139093	+	0.999903i	$0.504428\pi$
$450$	2.05264e23	−	1.31220e23i	0.271270	−	0.173416i
$451$	−4.07589e23			−0.528000
$452$	−2.44842e23	+	5.29390e23i	−0.310914	+	0.672249i
$453$			5.53578e22i			0.0689120i
$454$	−6.86120e23	+	4.38619e23i	−0.837331	+	0.535284i
$455$		−	2.83005e22i		−	0.0338603i
$456$	6.68966e22	+	4.90315e23i	0.0784730	+	0.575163i
$457$	8.85559e23			1.01852			0.509262	−	0.860611i	$-0.329918\pi$
$457$	8.85559e23			1.01852			0.509262	+	0.860611i	$0.329918\pi$
$458$	7.69971e22	+	1.20444e23i	0.0868330	+	0.135831i
$459$	−3.89295e23			−0.430492
$460$	−3.85488e22	+	8.33489e22i	−0.0418014	+	0.0903814i
$461$		−	8.74950e22i		−	0.0930412i	−0.998917	−	0.0465206i	$-0.985187\pi$
$461$		−	8.74950e22i		−	0.0930412i	0.998917	−	0.0465206i	$-0.0148133\pi$
$462$	−4.84897e23	−	7.58512e23i	−0.505675	−	0.791014i
$463$		−	1.46379e24i		−	1.49710i	−0.663081	−	0.748548i	$-0.730752\pi$
$463$		−	1.46379e24i		−	1.49710i	0.663081	−	0.748548i	$-0.269248\pi$
$464$	1.38687e24	−	1.17861e24i	1.39115	−	1.18224i
$465$	7.65591e22			0.0753217
$466$	1.19348e24	−	7.62963e23i	1.15171	−	0.736259i
$467$	−9.70941e23			−0.919054			−0.459527	−	0.888164i	$-0.651981\pi$
$467$	−9.70941e23			−0.919054			−0.459527	+	0.888164i	$0.651981\pi$
$468$	2.09521e23	+	9.69033e22i	0.194543	+	0.0899758i
$469$		−	5.89110e23i		−	0.536587i
$470$	7.07731e22	−	4.52434e22i	0.0632394	−	0.0404273i
$471$		−	2.49862e24i		−	2.19034i
$472$	1.18491e23	+	8.68476e23i	0.101908	+	0.746930i
$473$	1.59008e24			1.34174
$474$	6.22805e23	+	9.74236e23i	0.515640	+	0.806602i
$475$	−6.19143e23			−0.502977
$476$	−5.54526e23	−	2.56468e23i	−0.442038	−	0.204442i
$477$			8.49928e22i			0.0664839i
$478$	2.56472e23	+	4.01193e23i	0.196874	+	0.307965i
$479$		−	1.17844e24i		−	0.887743i	−0.896091	−	0.443871i	$-0.853605\pi$
$479$		−	1.17844e24i		−	0.887743i	0.896091	−	0.443871i	$-0.146395\pi$
$480$	−2.64290e22	+	8.61694e22i	−0.0195393	+	0.0637063i
$481$	−7.88581e23			−0.572190
$482$	−1.50554e24	+	9.62452e23i	−1.07218	+	0.685418i
$483$	−2.49172e24			−1.74171
$484$	−8.65761e22	+	1.87192e23i	−0.0594004	+	0.128434i
$485$			5.35209e22i			0.0360452i
$486$	−7.94138e23	+	5.07672e23i	−0.525013	+	0.335627i
$487$			1.57953e24i			1.02510i	0.858657	+	0.512551i	$0.171299\pi$
$487$			1.57953e24i			1.02510i	−0.858657	+	0.512551i	$0.828701\pi$
$488$	1.04327e23	−	1.42340e22i	0.0664692	−	0.00906879i
$489$	7.22083e23			0.451656
$490$	−1.13815e22	−	1.78038e22i	−0.00698932	−	0.0109332i
$491$	1.54781e24			0.933222			0.466611	−	0.884463i	$-0.345475\pi$
$491$	1.54781e24			0.933222			0.466611	+	0.884463i	$0.345475\pi$
$492$	−4.64791e23	+	1.00495e24i	−0.275151	+	0.594922i
$493$			1.73644e24i			1.00934i
$494$	−3.15991e23	−	4.94296e23i	−0.180357	−	0.282127i
$495$		−	3.09385e22i		−	0.0173401i
$496$	1.56497e24	−	1.32996e24i	0.861334	−	0.731990i
$497$	−5.85768e23			−0.316605
$498$	2.52623e24	−	1.61495e24i	1.34094	−	0.857227i
$499$	1.65895e24			0.864826			0.432413	−	0.901676i	$-0.357662\pi$
$499$	1.65895e24			0.864826			0.432413	+	0.901676i	$0.357662\pi$
$500$	−2.05048e23	−	9.48345e22i	−0.104985	−	0.0485553i
$501$		−	6.31047e23i		−	0.317338i
$502$	3.73980e23	−	2.39076e23i	0.184720	−	0.118087i
$503$			2.67912e24i			1.29981i	0.760016	+	0.649905i	$0.225191\pi$
$503$			2.67912e24i			1.29981i	−0.760016	+	0.649905i	$0.774809\pi$
$504$	−5.91655e23	+	8.07231e22i	−0.281964	+	0.0384701i
$505$	−2.08247e23			−0.0974892
$506$	−1.86535e24	−	2.91792e24i	−0.857840	−	1.34190i
$507$	1.42517e24			0.643866
$508$	−3.40045e24	−	1.57270e24i	−1.50925	−	0.698029i
$509$		−	1.48596e23i		−	0.0647957i	−0.999475	−	0.0323979i	$-0.989686\pi$
$509$		−	1.48596e23i		−	0.0647957i	0.999475	−	0.0323979i	$-0.0103144\pi$
$510$	−4.63167e22	−	7.24520e22i	−0.0198429	−	0.0310398i
$511$			4.12073e24i			1.73454i
$512$	9.56670e23	+	2.22054e24i	0.395669	+	0.918393i
$513$	9.66965e23			0.392966
$514$	−3.45276e24	+	2.20726e24i	−1.37879	+	0.881425i
$515$	−1.21237e23			−0.0475741
$516$	1.81324e24	−	3.92052e24i	0.699209	−	1.51181i
$517$			3.16781e24i			1.20045i
$518$	1.71868e24	−	1.09871e24i	0.640069	−	0.409180i
$519$		−	1.04029e24i		−	0.380756i
$520$	−1.44448e22	−	1.05873e23i	−0.00519616	−	0.0380849i
$521$	−2.56332e24			−0.906282			−0.453141	−	0.891439i	$-0.649697\pi$
$521$	−2.56332e24			−0.906282			−0.453141	+	0.891439i	$0.649697\pi$
$522$	9.14114e23	+	1.42992e24i	0.317663	+	0.496911i
$523$	5.30862e24			1.81329			0.906643	−	0.421899i	$-0.138636\pi$
$523$	5.30862e24			1.81329			0.906643	+	0.421899i	$0.138636\pi$
$524$	−1.70470e24	+	3.68584e24i	−0.572356	+	1.23753i
$525$		−	3.05981e24i		−	1.00986i
$526$	1.18140e24	+	1.84803e24i	0.383287	+	0.599566i
$527$			1.95943e24i			0.624934i
$528$	−2.20116e24	−	2.59011e24i	−0.690155	−	0.812106i
$529$	−6.34125e24			−1.95467
$530$	3.31471e22	−	2.11901e22i	0.0100453	−	0.00642170i
$531$	−8.17338e23			−0.243529
$532$	1.37738e24	+	6.37037e23i	0.403505	+	0.186621i
$533$		−	1.31266e24i		−	0.378100i
$534$	1.00432e24	−	6.42034e23i	0.284445	−	0.181839i
$535$		−	7.11823e22i		−	0.0198239i
$536$	−3.00687e23	−	2.20387e24i	−0.0823440	−	0.603535i
$537$	1.65231e24			0.444962
$538$	6.20435e23	+	9.70530e23i	0.164307	+	0.257021i
$539$	7.96898e23			0.207541
$540$	1.59851e23	+	7.39308e22i	0.0409422	+	0.0189357i
$541$		−	5.00294e24i		−	1.26023i	−0.776502	−	0.630115i	$-0.783008\pi$
$541$		−	5.00294e24i		−	1.26023i	0.776502	−	0.630115i	$-0.216992\pi$
$542$	1.51863e24	+	2.37555e24i	0.376234	+	0.588533i
$543$		−	5.56117e24i		−	1.35509i
$544$	−2.20539e24	−	6.76415e23i	−0.528562	−	0.162115i
$545$	−4.45213e22			−0.0104954
$546$	2.44281e24	−	1.56163e24i	0.566443	−	0.362113i
$547$	−1.96669e24			−0.448591			−0.224296	−	0.974521i	$-0.572008\pi$
$547$	−1.96669e24			−0.448591			−0.224296	+	0.974521i	$0.572008\pi$
$548$	2.40594e24	−	5.20204e24i	0.539833	−	1.16721i
$549$			9.81844e22i			0.0216716i
$550$	3.58318e24	−	2.29063e24i	0.778044	−	0.497384i
$551$		−	4.31311e24i		−	0.921353i
$552$	−9.32157e24	+	1.27180e24i	−1.95901	+	0.267280i
$553$	3.54597e24			0.733178
$554$	2.48268e24	+	3.88359e24i	0.505049	+	0.790034i
$555$	2.87105e23			0.0574651
$556$	−8.37552e23	+	1.81093e24i	−0.164945	+	0.356638i
$557$		−	2.32652e24i		−	0.450826i	−0.974263	−	0.225413i	$-0.927627\pi$
$557$		−	2.32652e24i		−	0.450826i	0.974263	−	0.225413i	$-0.0723732\pi$
$558$	1.03151e24	+	1.61356e24i	0.196682	+	0.307664i
$559$			5.12092e24i			0.960819i
$560$	1.78991e23	+	2.10619e23i	0.0330476	+	0.0388871i
$561$	3.24296e24			0.589217
$562$	−1.79530e24	+	1.14769e24i	−0.321003	+	0.205209i
$563$	−6.75142e24			−1.18801			−0.594004	−	0.804462i	$-0.702454\pi$
$563$	−6.75142e24			−1.18801			−0.594004	+	0.804462i	$0.702454\pi$
$564$	7.81056e24	+	3.61238e24i	1.35260	+	0.625578i
$565$			2.51753e23i			0.0429081i
$566$	−1.33569e24	+	8.53874e23i	−0.224057	+	0.143234i
$567$			6.50239e24i			1.07356i
$568$	−2.19137e24	+	2.98982e23i	−0.356107	+	0.0485859i
$569$	−6.03935e24			−0.966005			−0.483003	−	0.875619i	$-0.660454\pi$
$569$	−6.03935e24			−0.966005			−0.483003	+	0.875619i	$0.660454\pi$
$570$	1.15045e23	+	1.79962e23i	0.0181132	+	0.0283340i
$571$	9.32782e24			1.44562			0.722812	−	0.691045i	$-0.242849\pi$
$571$	9.32782e24			1.44562			0.722812	+	0.691045i	$0.242849\pi$
$572$	3.65748e24	+	1.69158e24i	0.557979	+	0.258065i
$573$			1.37613e25i			2.06666i
$574$	1.82889e24	+	2.86088e24i	0.270384	+	0.422954i
$575$		−	1.17708e25i		−	1.71315i
$576$	−2.17219e24	+	6.03973e23i	−0.311240	+	0.0865397i
$577$	−5.83171e24			−0.822647			−0.411324	−	0.911489i	$-0.634933\pi$
$577$	−5.83171e24			−0.822647			−0.411324	+	0.911489i	$0.634933\pi$
$578$	−4.21229e24	+	2.69281e24i	−0.585016	+	0.373986i
$579$	−1.08665e25			−1.48588
$580$	3.29765e23	−	7.13007e23i	0.0443969	−	0.0959935i
$581$		−	9.19483e24i		−	1.21887i
$582$	−4.61977e24	+	2.95330e24i	−0.602995	+	0.385479i
$583$			1.48367e24i			0.190686i
$584$	2.10326e24	+	1.54157e25i	0.266181	+	1.95096i
$585$	9.96385e22			0.0124172
$586$	−5.94511e24	−	9.29977e24i	−0.729594	−	1.14128i
$587$	3.83187e24			0.463093			0.231546	−	0.972824i	$-0.425622\pi$
$587$	3.83187e24			0.463093			0.231546	+	0.972824i	$0.425622\pi$
$588$	9.08735e23	−	1.96484e24i	0.108154	−	0.233846i
$589$		−	4.86700e24i		−	0.570458i
$590$	2.03776e23	+	3.18761e23i	0.0235225	+	0.0367957i
$591$			4.07909e24i			0.463741i
$592$	5.86882e24	−	4.98752e24i	0.657136	−	0.558456i
$593$	1.53612e25			1.69408			0.847038	−	0.531532i	$-0.178384\pi$
$593$	1.53612e25			1.69408			0.847038	+	0.531532i	$0.178384\pi$
$594$	−5.59613e24	+	3.57747e24i	−0.607869	+	0.388595i
$595$	−2.63707e23			−0.0282143
$596$	1.00511e25	+	4.64861e24i	1.05924	+	0.489899i
$597$			9.72145e24i			1.00916i
$598$	9.39726e24	−	6.00743e24i	0.960928	−	0.614297i
$599$		−	6.43360e24i		−	0.648056i	−0.946048	−	0.324028i	$-0.894963\pi$
$599$		−	6.43360e24i		−	0.648056i	0.946048	−	0.324028i	$-0.105037\pi$
$600$	−1.56176e24	−	1.14468e25i	−0.154972	−	1.13585i
$601$	−7.46762e24			−0.729981			−0.364991	−	0.931011i	$-0.618928\pi$
$601$	−7.46762e24			−0.729981			−0.364991	+	0.931011i	$0.618928\pi$
$602$	−7.13484e24	−	1.11608e25i	−0.687094	−	1.07480i
$603$	2.07410e24			0.196777
$604$	5.81765e23	+	2.69066e23i	0.0543769	+	0.0251493i
$605$			8.90198e22i			0.00819763i
$606$	−1.14911e25	−	1.79753e25i	−1.04258	−	1.63088i
$607$			7.43659e24i			0.664777i	0.943143	+	0.332388i	$0.107854\pi$
$607$			7.43659e24i			0.664777i	−0.943143	+	0.332388i	$0.892146\pi$
$608$	5.47795e24	+	1.68014e24i	0.482487	+	0.147983i
$609$	2.13154e25			1.84986
$610$	3.82918e22	−	2.44790e22i	0.00327444	−	0.00209327i
$611$	−1.02020e25			−0.859639
$612$	9.02956e23	−	1.95234e24i	0.0749728	−	0.162104i
$613$			2.69426e23i			0.0220443i	0.999939	+	0.0110221i	$0.00350853\pi$
$613$			2.69426e23i			0.0220443i	−0.999939	+	0.0110221i	$0.996491\pi$
$614$	3.65800e24	−	2.33847e24i	0.294936	−	0.188545i
$615$			4.77910e23i			0.0379726i
$616$	−1.03282e25	+	1.40913e24i	−0.808717	+	0.110338i
$617$	−6.86594e24			−0.529826			−0.264913	−	0.964272i	$-0.585343\pi$
$617$	−6.86594e24			−0.529826			−0.264913	+	0.964272i	$0.585343\pi$
$618$	−6.68991e24	−	1.04648e25i	−0.508773	−	0.795860i
$619$	4.75751e24			0.356586			0.178293	−	0.983977i	$-0.442943\pi$
$619$	4.75751e24			0.356586			0.178293	+	0.983977i	$0.442943\pi$
$620$	3.72114e23	−	8.04572e23i	0.0274885	−	0.0594347i
$621$			1.83834e25i			1.33845i
$622$	−1.36051e24	−	2.12822e24i	−0.0976314	−	0.152722i
$623$		−	3.65545e24i		−	0.258553i
$624$	8.34154e24	−	7.08892e24i	0.581547	−	0.494218i
$625$	1.44056e25			0.989943
$626$	−1.10537e25	+	7.06633e24i	−0.748751	+	0.478658i
$627$	−8.05514e24			−0.537855
$628$	−2.62584e25	−	1.21445e25i	−1.72835	−	0.799360i
$629$			7.34808e24i			0.476780i
$630$	−2.17158e23	+	1.38824e23i	−0.0138903	+	0.00887970i
$631$		−	4.34498e24i		−	0.273983i	−0.990572	−	0.136992i	$-0.956257\pi$
$631$		−	4.34498e24i		−	0.273983i	0.990572	−	0.136992i	$-0.0437433\pi$
$632$	1.32655e25	−	1.80990e24i	0.824654	−	0.112513i
$633$	5.17797e24			0.317341
$634$	1.15571e25	+	1.80784e25i	0.698304	+	1.09234i
$635$	−1.61710e24			−0.0963323
$636$	3.65814e24	+	1.69189e24i	0.214855	+	0.0993704i
$637$			2.56644e24i			0.148620i
$638$	1.59571e25	+	2.49613e25i	0.911106	+	1.42522i
$639$		−	2.06234e24i		−	0.116105i
$640$	7.77112e23	+	6.96572e23i	0.0431384	+	0.0386675i
$641$	−2.78209e24			−0.152282			−0.0761410	−	0.997097i	$-0.524260\pi$
$641$	−2.78209e24			−0.152282			−0.0761410	+	0.997097i	$0.524260\pi$
$642$	6.14425e24	−	3.92786e24i	0.331630	−	0.212003i
$643$	−2.82296e25			−1.50247			−0.751235	−	0.660035i	$-0.770541\pi$
$643$	−2.82296e25			−1.50247			−0.751235	+	0.660035i	$0.770541\pi$
$644$	−1.21110e25	+	2.61859e25i	−0.635632	+	1.37434i
$645$		−	1.86442e24i		−	0.0964951i
$646$	−4.60591e24	+	2.94444e24i	−0.235084	+	0.150283i
$647$		−	1.05429e25i		−	0.530665i	−0.964157	−	0.265333i	$-0.914518\pi$
$647$		−	1.05429e25i		−	0.530665i	0.964157	−	0.265333i	$-0.0854818\pi$
$648$	3.31888e24	+	2.43255e25i	0.164747	+	1.20750i
$649$	−1.42678e25			−0.698480
$650$	7.37707e24	+	1.15397e25i	0.356175	+	0.557155i
$651$	2.40527e25			1.14534
$652$	3.50967e24	−	7.58849e24i	0.164831	−	0.356391i
$653$		−	8.89053e24i		−	0.411821i	−0.978571	−	0.205911i	$-0.933984\pi$
$653$		−	8.89053e24i		−	0.411821i	0.978571	−	0.205911i	$-0.0660156\pi$
$654$	−2.45670e24	−	3.84295e24i	−0.112241	−	0.175576i
$655$			1.75282e24i			0.0789887i
$656$	8.30213e24	+	9.76913e24i	0.369024	+	0.434231i
$657$	−1.45080e25			−0.636090
$658$	2.22349e25	−	1.42142e25i	0.961619	−	0.614739i
$659$	−2.22891e25			−0.950877			−0.475439	−	0.879749i	$-0.657711\pi$
$659$	−2.22891e25			−0.950877			−0.475439	+	0.879749i	$0.657711\pi$
$660$	−1.33161e24	−	6.15868e23i	−0.0560378	−	0.0259175i
$661$		−	4.13676e25i		−	1.71731i	−0.512558	−	0.858653i	$-0.671302\pi$
$661$		−	4.13676e25i		−	1.71731i	0.512558	−	0.858653i	$-0.328698\pi$
$662$	−1.96075e25	+	1.25346e25i	−0.802972	+	0.513320i
$663$			1.04441e25i			0.421937i
$664$	−4.69313e24	−	3.43980e25i	−0.187047	−	1.37095i
$665$	6.55018e23			0.0257548
$666$	3.86826e24	+	6.05102e24i	0.150054	+	0.234726i
$667$	8.19982e25			3.13814
$668$	−6.63178e24	−	3.06719e24i	−0.250404	−	0.115812i
$669$		−	3.70277e25i		−	1.37940i
$670$	−5.17107e23	−	8.08897e23i	−0.0190067	−	0.0297317i
$671$			1.71394e24i			0.0621576i
$672$	−8.30325e24	+	2.70721e25i	−0.297115	+	0.968719i
$673$	−2.74787e25			−0.970198			−0.485099	−	0.874459i	$-0.661216\pi$
$673$	−2.74787e25			−0.970198			−0.485099	+	0.874459i	$0.661216\pi$
$674$	3.00235e25	−	1.91933e25i	1.04598	−	0.668667i
$675$	−2.25746e25			−0.776043
$676$	6.92702e24	−	1.49774e25i	0.234977	−	0.508060i
$677$			2.76232e25i			0.924648i	0.886711	+	0.462324i	$0.152984\pi$
$677$			2.76232e25i			0.924648i	−0.886711	+	0.462324i	$0.847016\pi$
$678$	−2.17306e25	+	1.38918e25i	−0.717803	+	0.458873i
$679$			1.68148e25i			0.548105i
$680$	−9.86532e23	+	1.34599e23i	−0.0317345	+	0.00432973i
$681$	−3.60092e25			−1.14311
$682$	1.80064e25	+	2.81669e25i	0.564114	+	0.882428i
$683$	−1.28178e25			−0.396304			−0.198152	−	0.980171i	$-0.563494\pi$
$683$	−1.28178e25			−0.396304			−0.198152	+	0.980171i	$0.563494\pi$
$684$	−2.24284e24	+	4.84939e24i	−0.0684373	+	0.147973i
$685$		−	2.47385e24i		−	0.0745003i
$686$	−1.95394e25	−	3.05650e25i	−0.580757	−	0.908462i
$687$			6.32122e24i			0.185434i
$688$	−3.23882e25	−	3.81112e25i	−0.937758	−	1.10346i
$689$	−4.77820e24			−0.136550
$690$	−3.42134e24	+	2.18718e24i	−0.0965060	+	0.0616939i
$691$	4.86348e25			1.35408			0.677040	−	0.735946i	$-0.263262\pi$
$691$	4.86348e25			1.35408			0.677040	+	0.735946i	$0.263262\pi$
$692$	−1.09326e25	−	5.05630e24i	−0.300446	−	0.138956i
$693$		−	9.72001e24i		−	0.263674i
$694$	−1.13323e24	+	7.24443e23i	−0.0303446	+	0.0193985i
$695$			8.61192e23i			0.0227634i
$696$	7.97413e25	−	1.08796e25i	2.08065	−	0.283876i
$697$	−1.22315e25			−0.315053
$698$	1.93205e25	+	3.02226e25i	0.491270	+	0.768481i
$699$	6.26369e25			1.57230
$700$	−3.21560e25	−	1.48721e25i	−0.796857	−	0.368546i
$701$		−	2.96961e25i		−	0.726504i	−0.931691	−	0.363252i	$-0.881666\pi$
$701$		−	2.96961e25i		−	0.726504i	0.931691	−	0.363252i	$-0.118334\pi$
$702$	−1.15214e25	−	1.80225e25i	−0.278272	−	0.435293i
$703$		−	1.82518e25i		−	0.435219i
$704$	−3.79186e25	+	1.05432e25i	−0.892685	+	0.248209i
$705$	3.71434e24			0.0863336
$706$	5.38595e25	−	3.44310e25i	1.23600	−	0.790146i
$707$	−6.54254e25			−1.48242
$708$	−1.62701e25	+	3.51787e25i	−0.363991	+	0.787010i
$709$			1.70455e25i			0.376524i	0.982119	+	0.188262i	$0.0602854\pi$
$709$			1.70455e25i			0.376524i	−0.982119	+	0.188262i	$0.939715\pi$
$710$	−8.04309e23	+	5.14174e23i	−0.0175428	+	0.0112146i
$711$			1.24844e25i			0.268870i
$712$	−1.86578e24	−	1.36751e25i	−0.0396772	−	0.290811i
$713$	9.25285e25			1.94299
$714$	−1.45514e25	−	2.27624e25i	−0.301732	−	0.471992i
$715$	1.73933e24			0.0356145
$716$	8.03103e24	−	1.73644e25i	0.162388	−	0.351110i
$717$			2.10556e25i			0.420431i
$718$	4.10343e25	+	6.41888e25i	0.809146	+	1.26573i
$719$			3.68922e25i			0.718414i	0.933258	+	0.359207i	$0.116953\pi$
$719$			3.68922e25i			0.718414i	−0.933258	+	0.359207i	$0.883047\pi$
$720$	−7.41535e23	+	6.30181e23i	−0.0142606	+	0.0121192i
$721$	−3.80894e25			−0.723414
$722$	−3.34784e25	+	2.14019e25i	−0.627958	+	0.401437i
$723$	−7.90143e25			−1.46373
$724$	−5.84433e25	−	2.70300e25i	−1.06927	−	0.494537i
$725$			1.00693e26i			1.81952i
$726$	−7.68393e24	+	4.91214e24i	−0.137137	+	0.0876680i
$727$			7.06957e25i			1.24619i	0.782147	+	0.623094i	$0.214124\pi$
$727$			7.06957e25i			1.24619i	−0.782147	+	0.623094i	$0.785876\pi$
$728$	−4.53817e24	−	3.32622e25i	−0.0790129	−	0.579120i
$729$	2.91881e25			0.501947
$730$	3.61708e24	+	5.65810e24i	0.0614402	+	0.0961092i
$731$	4.77173e25			0.800607
$732$	4.22591e24	+	1.95448e24i	0.0700358	+	0.0323915i
$733$			7.99496e25i			1.30882i	0.756139	+	0.654411i	$0.227083\pi$
$733$			7.99496e25i			1.30882i	−0.756139	+	0.654411i	$0.772917\pi$
$734$	−4.09662e25	−	6.40823e25i	−0.662462	−	1.03627i
$735$		−	9.34385e23i		−	0.0149259i
$736$	−3.19418e25	+	1.04144e26i	−0.504033	+	1.64336i
$737$	3.62063e25			0.564387
$738$	−1.00724e25	+	6.43904e24i	−0.155105	+	0.0991548i
$739$	−5.02297e25			−0.764118			−0.382059	−	0.924138i	$-0.624785\pi$
$739$	−5.02297e25			−0.764118			−0.382059	+	0.924138i	$0.624785\pi$
$740$	1.39547e24	−	3.01724e24i	0.0209718	−	0.0453444i
$741$		−	2.59419e25i		−	0.385156i
$742$	1.04139e25	−	6.65734e24i	0.152749	−	0.0976486i
$743$		−	1.12022e26i		−	1.62332i	−0.584132	−	0.811659i	$-0.698565\pi$
$743$		−	1.12022e26i		−	1.62332i	0.584132	−	0.811659i	$-0.301435\pi$
$744$	8.99817e25	−	1.22768e25i	1.28824	−	0.175763i
$745$	4.77982e24			0.0676091
$746$	−4.06991e25	−	6.36644e25i	−0.568768	−	0.889708i
$747$	3.23726e25			0.446984
$748$	1.57623e25	−	3.40808e25i	0.215034	−	0.464938i
$749$		−	2.23635e25i		−	0.301442i
$750$	−5.38071e24	−	8.41689e24i	−0.0716618	−	0.112099i
$751$			8.47144e24i			0.111480i	0.998445	+	0.0557401i	$0.0177518\pi$
$751$			8.47144e24i			0.111480i	−0.998445	+	0.0557401i	$0.982248\pi$
$752$	7.59263e25	−	6.45247e25i	0.987260	−	0.839006i
$753$	1.96274e25			0.252178
$754$	−8.03888e25	+	5.13905e25i	−1.02060	+	0.652441i
$755$	2.76660e23			0.00347076
$756$	5.02207e25	+	2.32270e25i	0.622567	+	0.287937i
$757$		−	1.52142e26i		−	1.86374i	−0.362790	−	0.931871i	$-0.618176\pi$
$757$		−	1.52142e26i		−	1.86374i	0.362790	−	0.931871i	$-0.381824\pi$
$758$	3.86646e25	−	2.47173e25i	0.468048	−	0.299211i
$759$		−	1.53140e26i		−	1.83194i
$760$	2.45043e24	−	3.34328e23i	0.0289681	−	0.00395230i
$761$	2.22675e25			0.260142			0.130071	−	0.991505i	$-0.458479\pi$
$761$	2.22675e25			0.260142			0.130071	+	0.991505i	$0.458479\pi$
$762$	−8.92318e25	−	1.39583e26i	−1.03021	−	1.61153i
$763$	−1.39874e25			−0.159593
$764$	1.44620e26	+	6.68867e25i	1.63075	+	0.754223i
$765$		−	9.28442e23i		−	0.0103467i
$766$	5.10358e25	+	7.98339e25i	0.562103	+	0.879282i
$767$		−	4.59499e25i		−	0.500179i
$768$	−1.72448e25	+	1.05515e26i	−0.185527	+	1.13518i
$769$	−1.17966e26			−1.25436			−0.627178	−	0.778876i	$-0.715790\pi$
$769$	−1.17966e26			−1.25436			−0.627178	+	0.778876i	$0.715790\pi$
$770$	−3.79080e24	+	2.42336e24i	−0.0398395	+	0.0254684i
$771$	−1.81209e26			−1.88231
$772$	−5.28167e25	+	1.14198e26i	−0.542270	+	1.17248i
$773$		−	3.65457e25i		−	0.370869i	−0.982657	−	0.185435i	$-0.940631\pi$
$773$		−	3.65457e25i		−	0.370869i	0.982657	−	0.185435i	$-0.0593693\pi$
$774$	3.92944e25	−	2.51199e25i	0.394150	−	0.251970i
$775$			1.13624e26i			1.12656i
$776$	8.58244e24	+	6.29044e25i	0.0841115	+	0.616490i
$777$	9.02005e25			0.873815
$778$	9.24253e25	+	1.44578e26i	0.885063	+	1.38448i
$779$	3.03816e25			0.287590
$780$	1.98343e24	−	4.28849e24i	0.0185594	−	0.0401285i
$781$		−	3.60009e25i		−	0.333008i
$782$	−5.59779e25	−	8.75648e25i	−0.511866	−	0.800698i
$783$		−	1.57260e26i		−	1.42155i
$784$	−1.62319e25	−	1.91001e25i	−0.145052	−	0.170683i
$785$	−1.24873e25			−0.110317
$786$	−1.51298e26	+	9.67210e25i	−1.32139	+	0.844730i
$787$	8.18286e25			0.706533			0.353266	−	0.935523i	$-0.385071\pi$
$787$	8.18286e25			0.706533			0.353266	+	0.935523i	$0.385071\pi$
$788$	4.28678e25	+	1.98263e25i	0.365928	+	0.169241i
$789$			9.69890e25i			0.818521i
$790$	4.86892e24	−	3.11258e24i	0.0406246	−	0.0259702i
$791$			7.90940e25i			0.652462i
$792$	−4.96119e24	−	3.63627e25i	−0.0404631	−	0.296572i
$793$	−5.51982e24			−0.0445109
$794$	−4.18154e25	−	6.54108e25i	−0.333390	−	0.521512i
$795$	1.73964e24			0.0137137
$796$	1.02164e26	+	4.72509e25i	0.796310	+	0.368293i
$797$			1.22191e26i			0.941701i	0.882213	+	0.470850i	$0.156053\pi$
$797$			1.22191e26i			0.941701i	−0.882213	+	0.470850i	$0.843947\pi$
$798$	3.61441e25	+	5.65392e25i	0.275430	+	0.430848i
$799$			9.50638e25i			0.716299i
$800$	−1.27887e26	−	3.92242e25i	−0.952834	−	0.292243i
$801$	1.28699e25			0.0948162
$802$	1.03880e26	−	6.64077e25i	0.756766	−	0.483781i
$803$	−2.53257e26			−1.82441
$804$	4.12875e25	−	8.92704e25i	0.294113	−	0.635921i
$805$			1.24528e25i			0.0877212i
$806$	−9.07124e25	+	5.79901e25i	−0.631904	+	0.403960i
$807$			5.09358e25i			0.350882i
$808$	−2.44758e26	+	3.33938e25i	−1.66738	+	0.227491i
$809$	1.23505e26			0.832046			0.416023	−	0.909354i	$-0.363424\pi$
$809$	1.23505e26			0.832046			0.416023	+	0.909354i	$0.363424\pi$
$810$	5.70765e24	+	8.92832e24i	0.0380270	+	0.0594846i
$811$	2.17591e26			1.43368			0.716842	−	0.697236i	$-0.245587\pi$
$811$	2.17591e26			1.43368			0.716842	+	0.697236i	$0.245587\pi$
$812$	1.03603e26	−	2.24007e26i	0.675101	−	1.45968i
$813$			1.24675e26i			0.803459i
$814$	6.75259e25	+	1.05629e26i	0.430379	+	0.673230i
$815$		−	3.60874e24i		−	0.0227477i
$816$	−6.60553e25	−	7.77274e25i	−0.411810	−	0.484577i
$817$	−1.18524e26			−0.730818
$818$	6.54675e25	−	4.18517e25i	0.399251	−	0.255231i
$819$	3.13037e25			0.188816
$820$	5.02244e24	+	2.32287e24i	0.0299633	+	0.0138580i
$821$			1.39500e26i			0.823162i	0.911373	+	0.411581i	$0.135023\pi$
$821$			1.39500e26i			0.823162i	−0.911373	+	0.411581i	$0.864977\pi$
$822$	2.13536e26	−	1.36508e26i	1.24630	−	0.796730i
$823$		−	1.20324e26i		−	0.694632i	−0.937748	−	0.347316i	$-0.887093\pi$
$823$		−	1.20324e26i		−	0.694632i	0.937748	−	0.347316i	$-0.112907\pi$
$824$	−1.42493e26	+	1.94412e25i	−0.813671	+	0.111014i
$825$	1.88054e26			1.06218
$826$	6.40207e25	+	1.00146e26i	0.357684	+	0.559516i
$827$	1.50885e26			0.833869			0.416934	−	0.908937i	$-0.363105\pi$
$827$	1.50885e26			0.833869			0.416934	+	0.908937i	$0.363105\pi$
$828$	−9.21937e25	−	4.26395e25i	−0.503997	−	0.233098i
$829$		−	3.08933e26i		−	1.67061i	−0.549789	−	0.835303i	$-0.685292\pi$
$829$		−	3.08933e26i		−	1.67061i	0.549789	−	0.835303i	$-0.314708\pi$
$830$	−8.07101e24	−	1.26253e25i	−0.0431743	−	0.0675364i
$831$			2.03820e26i			1.07855i
$832$	−3.39547e25	−	1.22118e26i	−0.177742	−	0.639250i
$833$	2.39144e25			0.123838
$834$	−7.43356e25	+	4.75209e25i	−0.380805	+	0.243439i
$835$	−3.15377e24			−0.0159827
$836$	−3.91519e25	+	8.46528e25i	−0.196289	+	0.424409i
$837$		−	1.77456e26i		−	0.880159i
$838$	2.52128e25	−	1.61179e25i	0.123716	−	0.0790882i
$839$			9.77175e25i			0.474367i	0.971465	+	0.237184i	$0.0762243\pi$
$839$			9.77175e25i			0.474367i	−0.971465	+	0.237184i	$0.923776\pi$
$840$	1.65225e24	+	1.21101e25i	0.00793527	+	0.0581611i
$841$	−4.90996e26			−2.33300
$842$	−1.68492e26	−	2.63568e26i	−0.792084	−	1.23904i
$843$	−9.42216e25			−0.438230
$844$	2.51675e25	−	5.44162e25i	0.115813	−	0.250407i
$845$		−	7.12254e24i		−	0.0324283i
$846$	5.00446e25	+	7.82834e25i	0.225436	+	0.352644i
$847$			2.79676e25i			0.124653i
$848$	3.55606e25	−	3.02206e25i	0.156822	−	0.133272i
$849$	−7.01004e25			−0.305880
$850$	1.07529e26	−	6.87404e25i	0.464252	−	0.296785i
$851$	3.46992e26			1.48236
$852$	−8.87641e25	−	4.10533e25i	−0.375216	−	0.173537i
$853$		−	1.94352e26i		−	0.812920i	−0.913669	−	0.406460i	$-0.866763\pi$
$853$		−	1.94352e26i		−	0.812920i	0.913669	−	0.406460i	$-0.133237\pi$
$854$	1.20302e25	−	7.69062e24i	0.0497912	−	0.0318303i
$855$			2.30615e24i			0.00944478i
$856$	−1.14146e25	−	8.36623e25i	−0.0462589	−	0.339052i
$857$	−9.21795e25			−0.369664			−0.184832	−	0.982770i	$-0.559174\pi$
$857$	−9.21795e25			−0.369664			−0.184832	+	0.982770i	$0.559174\pi$
$858$	9.59767e25	+	1.50134e26i	0.380873	+	0.595789i
$859$	3.96463e26			1.55691			0.778456	−	0.627700i	$-0.216003\pi$
$859$	3.96463e26			1.55691			0.778456	+	0.627700i	$0.216003\pi$
$860$	−1.95935e25	−	9.06197e24i	−0.0761422	−	0.0352157i
$861$			1.50146e26i			0.577412i
$862$	−5.28390e25	−	8.26546e25i	−0.201089	−	0.314559i
$863$			2.33974e26i			0.881191i	0.897706	+	0.440596i	$0.145233\pi$
$863$			2.33974e26i			0.881191i	−0.897706	+	0.440596i	$0.854767\pi$
$864$	1.99732e26	+	6.12596e25i	0.744429	+	0.228323i
$865$	−5.19902e24			−0.0191768
$866$	−2.28857e26	+	1.46302e26i	−0.835415	+	0.534060i
$867$	−2.21071e26			−0.798657
$868$	1.16908e26	−	2.52774e26i	0.417991	−	0.903765i
$869$			2.17933e26i			0.771162i
$870$	2.92678e25	−	1.87102e25i	0.102498	−	0.0655246i
$871$			1.16604e26i			0.404156i
$872$	−5.23269e25	+	7.13928e24i	−0.179505	+	0.0244910i
$873$	−5.92005e25			−0.201000
$874$	1.39043e26	+	2.17501e26i	0.467246	+	0.730900i
$875$	−3.06354e25			−0.101894
$876$	−2.88799e26	+	6.24432e26i	−0.950734	+	2.05564i
$877$		−	2.68768e26i		−	0.875752i	−0.899035	−	0.437876i	$-0.855731\pi$
$877$		−	2.68768e26i		−	0.875752i	0.899035	−	0.437876i	$-0.144269\pi$
$878$	9.60581e23	+	1.50261e24i	0.00309801	+	0.00484614i
$879$		−	4.88075e26i		−	1.55807i
$880$	−1.29445e25	+	1.10007e25i	−0.0409018	+	0.0347597i
$881$	1.24868e26			0.390541			0.195271	−	0.980749i	$-0.437441\pi$
$881$	1.24868e26			0.390541			0.195271	+	0.980749i	$0.437441\pi$
$882$	1.96931e25	−	1.25893e25i	0.0609672	−	0.0389748i
$883$	4.01276e26			1.22969			0.614847	−	0.788646i	$-0.289218\pi$
$883$	4.01276e26			1.22969			0.614847	+	0.788646i	$0.289218\pi$
$884$	1.09758e26	+	5.07632e25i	0.332941	+	0.153985i
$885$			1.67293e25i			0.0502330i
$886$	1.69407e25	−	1.08298e25i	0.0503534	−	0.0321896i
$887$			2.82251e26i			0.830468i	0.909715	+	0.415234i	$0.136300\pi$
$887$			2.82251e26i			0.830468i	−0.909715	+	0.415234i	$0.863700\pi$
$888$	3.37442e26	−	4.60392e25i	0.982838	−	0.134095i
$889$	−5.08047e26			−1.46483
$890$	−3.20868e24	−	5.01925e24i	−0.00915832	−	0.0143261i
$891$	−3.99632e26			−1.12918
$892$	−3.89130e26	−	1.79972e26i	−1.08846	−	0.503410i
$893$		−	2.36128e26i		−	0.653858i
$894$	2.63752e26	+	4.12581e26i	0.723034	+	1.13102i
$895$		−	8.25772e24i		−	0.0224106i
$896$	2.44147e26	+	2.18844e26i	0.655963	+	0.587979i
$897$	4.93191e26			1.31185
$898$	−8.90057e24	+	5.68991e24i	−0.0234386	+	0.0149837i
$899$	−7.91535e26			−2.06363
$900$	5.23609e25	−	1.13213e26i	0.135153	−	0.292223i
$901$			4.45238e25i			0.113781i
$902$	−1.75828e26	+	1.12402e26i	−0.444866	+	0.284391i
$903$		−	5.85748e26i		−	1.46731i
$904$	4.03703e25	+	2.95892e26i	0.100126	+	0.733867i
$905$	−2.77929e25			−0.0682492
$906$	1.52662e25	+	2.38805e25i	0.0371174	+	0.0580617i
$907$	−2.96851e26			−0.714615			−0.357308	−	0.933987i	$-0.616305\pi$
$907$	−2.96851e26			−0.714615			−0.357308	+	0.933987i	$0.616305\pi$
$908$	−1.75022e26	+	3.78427e26i	−0.417177	+	0.902007i
$909$		−	2.30346e26i		−	0.543632i
$910$	−7.80451e24	−	1.22084e25i	−0.0182378	−	0.0285290i
$911$			1.03197e25i			0.0238782i	0.999929	+	0.0119391i	$0.00380043\pi$
$911$			1.03197e25i			0.0238782i	−0.999929	+	0.0119391i	$0.996200\pi$
$912$	1.64074e26	+	1.93066e26i	0.375912	+	0.442336i
$913$	5.65108e26			1.28202
$914$	3.82017e26	−	2.44214e26i	0.858157	−	0.548598i
$915$	2.00965e24			0.00447023
$916$	6.64308e25	+	3.07242e25i	0.146322	+	0.0676739i
$917$			5.50687e26i			1.20110i
$918$	−1.67936e26	+	1.07357e26i	−0.362710	+	0.231872i
$919$		−	6.91739e26i		−	1.47946i	−0.672905	−	0.739729i	$-0.734954\pi$
$919$		−	6.91739e26i		−	1.47946i	0.672905	−	0.739729i	$-0.265046\pi$
$920$	6.35604e24	+	4.65862e25i	0.0134616	+	0.0986658i
$921$	1.91981e26			0.402644
$922$	−2.41288e25	−	3.77440e25i	−0.0501138	−	0.0783917i
$923$	1.15942e26			0.238466
$924$	−4.18355e26	−	1.93489e26i	−0.852112	−	0.394101i
$925$			4.26103e26i			0.859487i
$926$	−4.03674e26	−	6.31456e26i	−0.806366	−	1.26138i
$927$		−	1.34103e26i		−	0.265289i
$928$	2.73246e26	−	8.90895e26i	0.535330	−	1.74540i
$929$	3.23600e26			0.627866			0.313933	−	0.949445i	$-0.398353\pi$
$929$	3.23600e26			0.627866			0.313933	+	0.949445i	$0.398353\pi$
$930$	3.30264e25	−	2.11130e25i	0.0634622	−	0.0405698i
$931$	−5.94006e25			−0.113043
$932$	3.04446e26	−	6.58262e26i	0.573808	−	1.24067i
$933$		−	1.11694e26i		−	0.208495i
$934$	−4.18849e26	+	2.67760e26i	−0.774348	+	0.495021i
$935$		−	1.62073e25i		−	0.0296760i
$936$	1.17108e26	−	1.59777e25i	0.212374	−	0.0289755i
$937$	1.90645e26			0.342427			0.171214	−	0.985234i	$-0.445231\pi$
$937$	1.90645e26			0.342427			0.171214	+	0.985234i	$0.445231\pi$
$938$	−1.62461e26	−	2.54133e26i	−0.289017	−	0.452101i
$939$	−5.80123e26			−1.02219
$940$	1.80535e25	−	3.90347e25i	0.0315073	−	0.0681240i
$941$			4.95020e26i			0.855689i	0.903852	+	0.427844i	$0.140727\pi$
$941$			4.95020e26i			0.855689i	−0.903852	+	0.427844i	$0.859273\pi$
$942$	−6.89052e26	−	1.07787e27i	−1.17976	−	1.84547i
$943$			5.77597e26i			0.979535i
$944$	2.90618e26	+	3.41971e26i	0.488174	+	0.574435i
$945$	2.38826e25			0.0397371
$946$	6.85938e26	−	4.38503e26i	1.13048	−	0.722690i
$947$	1.12770e27			1.84096			0.920480	−	0.390789i	$-0.127798\pi$
$947$	1.12770e27			1.84096			0.920480	+	0.390789i	$0.127798\pi$
$948$	5.37337e26	+	2.48518e26i	0.868904	+	0.401867i
$949$		−	8.15624e26i		−	1.30645i
$950$	−2.67089e26	+	1.70743e26i	−0.423783	+	0.270914i
$951$			9.48799e26i			1.49125i
$952$	−3.09941e26	+	4.22872e25i	−0.482555	+	0.0658379i
$953$	4.60259e25			0.0709849			0.0354925	−	0.999370i	$-0.488700\pi$
$953$	4.60259e25			0.0709849			0.0354925	+	0.999370i	$0.488700\pi$
$954$	2.34388e25	+	3.66646e25i	0.0358096	+	0.0560160i
$955$	6.87747e25			0.104087
$956$	2.21276e26	+	1.02340e26i	0.331753	+	0.153435i
$957$			1.31003e27i			1.94569i
$958$	−3.24982e26	−	5.08360e26i	−0.478156	−	0.747966i
$959$		−	7.77215e26i		−	1.13285i
$960$	1.23622e25	+	4.44606e25i	0.0178507	+	0.0641999i
$961$	−1.94131e26			−0.277705
$962$	−3.40182e26	+	2.17470e26i	−0.482098	+	0.308193i
$963$	7.87360e25			0.110544
$964$	−3.84048e26	+	8.30375e26i	−0.534185	+	1.15500i
$965$			5.43075e25i			0.0748366i
$966$	−1.07489e27	+	6.87150e26i	−1.46747	+	0.938118i
$967$			1.23225e27i			1.66672i	0.552732	+	0.833359i	$0.313585\pi$
$967$			1.23225e27i			1.66672i	−0.552732	+	0.833359i	$0.686415\pi$
$968$	1.42749e25	+	1.04627e26i	0.0191291	+	0.140206i
$969$	−2.41729e26			−0.320934
$970$	1.47596e25	+	2.30881e25i	0.0194147	+	0.0303699i
$971$	−1.39039e27			−1.81202			−0.906011	−	0.423255i	$-0.860888\pi$
$971$	−1.39039e27			−1.81202			−0.906011	+	0.423255i	$0.860888\pi$
$972$	−2.02577e26	+	4.38004e26i	−0.261573	+	0.565565i
$973$			2.70563e26i			0.346141i
$974$	4.35592e26	+	6.81385e26i	0.552140	+	0.863698i
$975$			6.05634e26i			0.760622i
$976$	4.10799e25	−	3.49111e25i	0.0511189	−	0.0434425i
$977$	8.32038e25			0.102587			0.0512935	−	0.998684i	$-0.483666\pi$
$977$	8.32038e25			0.102587			0.0512935	+	0.998684i	$0.483666\pi$
$978$	3.11496e26	−	1.99131e26i	0.380542	−	0.243271i
$979$	2.24662e26			0.271948
$980$	−9.81961e24	−	4.54156e24i	−0.0117777	−	0.00544717i
$981$		−	4.92458e25i		−	0.0585259i
$982$	6.67703e26	−	4.26846e26i	0.786285	−	0.502652i
$983$		−	8.05329e26i		−	0.939705i	−0.882745	−	0.469852i	$-0.844307\pi$
$983$		−	8.05329e26i		−	0.939705i	0.882745	−	0.469852i	$-0.155693\pi$
$984$	7.66360e25	+	5.61699e26i	0.0886089	+	0.649453i
$985$	2.03860e25			0.0233564
$986$	4.78863e26	+	7.49072e26i	0.543649	+	0.850416i
$987$	1.16694e27			1.31279
$988$	−2.72627e26	−	1.26090e26i	−0.303918	−	0.140562i
$989$		−	2.25332e27i		−	2.48917i
$990$	−8.53201e24	−	1.33464e25i	−0.00933974	−	0.0146099i
$991$		−	8.98283e26i		−	0.974429i	−0.873282	−	0.487215i	$-0.838013\pi$
$991$		−	8.98283e26i		−	0.974429i	0.873282	−	0.487215i	$-0.161987\pi$
$992$	3.08336e26	−	1.00530e27i	0.331451	−	1.08067i
$993$	−1.02905e27			−1.09621
$994$	−2.52692e26	+	1.61539e26i	−0.266755	+	0.170530i
$995$	4.85847e25			0.0508266
$996$	6.44415e26	−	1.39333e27i	0.668085	−	1.44451i
$997$			7.57501e26i			0.778263i	0.921182	+	0.389132i	$0.127225\pi$
$997$			7.57501e26i			0.778263i	−0.921182	+	0.389132i	$0.872775\pi$
$998$	7.15646e26	−	4.57495e26i	0.728658	−	0.465812i
$999$		−	6.65480e26i		−	0.671499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.19.d.b.3.13	✓	16
3.2	odd	2		72.19.b.b.19.4		16
4.3	odd	2		32.19.d.b.15.3		16
8.3	odd	2	inner	8.19.d.b.3.14	yes	16
8.5	even	2		32.19.d.b.15.4		16
24.11	even	2		72.19.b.b.19.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.19.d.b.3.13	✓	16	1.1	even	1	trivial
8.19.d.b.3.14	yes	16	8.3	odd	2	inner
32.19.d.b.15.3		16	4.3	odd	2
32.19.d.b.15.4		16	8.5	even	2
72.19.b.b.19.3		16	24.11	even	2
72.19.b.b.19.4		16	3.2	odd	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)

\(f(q)\)	\(=\)	\(q+(431.385 - 275.773i) q^{2} +22640.1 q^{3} +(110042. - 237929. i) q^{4} -113148. i q^{5} +(9.76661e6 - 6.24355e6i) q^{6} -3.55480e7i q^{7} +(-1.81440e7 - 1.32986e8i) q^{8} +1.25155e8 q^{9} +O(q^{10})\)	\(q+(431.385 - 275.773i) q^{2} +22640.1 q^{3} +(110042. - 237929. i) q^{4} -113148. i q^{5} +(9.76661e6 - 6.24355e6i) q^{6} -3.55480e7i q^{7} +(-1.81440e7 - 1.32986e8i) q^{8} +1.25155e8 q^{9} +(-3.12032e7 - 4.88104e7i) q^{10} +2.18476e9 q^{11} +(2.49137e9 - 5.38675e9i) q^{12} +7.03609e9i q^{13} +(-9.80319e9 - 1.53349e10i) q^{14} -2.56169e9i q^{15} +(-4.45010e10 - 5.23644e10i) q^{16} +6.55631e10 q^{17} +(5.39900e10 - 3.45145e10i) q^{18} -1.62851e11 q^{19} +(-2.69212e10 - 1.24510e10i) q^{20} -8.04811e11i q^{21} +(9.42471e11 - 6.02498e11i) q^{22} -3.09603e12i q^{23} +(-4.10784e11 - 3.01081e12i) q^{24} +3.80189e12 q^{25} +(1.94037e12 + 3.03526e12i) q^{26} -5.93772e12 q^{27} +(-8.45790e12 - 3.91177e12i) q^{28} +2.64850e13i q^{29} +(-7.06445e11 - 1.10507e12i) q^{30} +2.98862e13i q^{31} +(-3.36378e13 - 1.03170e13i) q^{32} +4.94632e13 q^{33} +(2.82829e13 - 1.80806e13i) q^{34} -4.02219e12 q^{35} +(1.37723e13 - 2.97780e13i) q^{36} +1.12077e14i q^{37} +(-7.02515e13 + 4.49100e13i) q^{38} +1.59298e14i q^{39} +(-1.50471e13 + 2.05296e12i) q^{40} -1.86561e14 q^{41} +(-2.21946e14 - 3.47184e14i) q^{42} +7.27808e14 q^{43} +(2.40415e14 - 5.19817e14i) q^{44} -1.41611e13i q^{45} +(-8.53803e14 - 1.33558e15i) q^{46} +1.44996e15i q^{47} +(-1.00751e15 - 1.18554e15i) q^{48} +3.64754e14 q^{49} +(1.64008e15 - 1.04846e15i) q^{50} +1.48436e15 q^{51} +(1.67409e15 + 7.74265e14i) q^{52} +6.79100e14i q^{53} +(-2.56144e15 + 1.63747e15i) q^{54} -2.47201e14i q^{55} +(-4.72737e15 + 6.44985e14i) q^{56} -3.68697e15 q^{57} +(7.30385e15 + 1.14252e16i) q^{58} -6.53060e15 q^{59} +(-6.09500e14 - 2.81893e14i) q^{60} +7.84501e14i q^{61} +(8.24182e15 + 1.28925e16i) q^{62} -4.44901e15i q^{63} +(-1.73560e16 + 4.82580e15i) q^{64} +7.96120e14 q^{65} +(2.13377e16 - 1.36406e16i) q^{66} +1.65722e16 q^{67} +(7.21469e15 - 1.55994e16i) q^{68} -7.00945e16i q^{69} +(-1.73511e15 + 1.10921e15i) q^{70} -1.64782e16i q^{71} +(-2.27082e15 - 1.66438e16i) q^{72} -1.15920e17 q^{73} +(3.09077e16 + 4.83481e16i) q^{74} +8.60754e16 q^{75} +(-1.79205e16 + 3.87470e16i) q^{76} -7.76637e16i q^{77} +(4.39301e16 + 6.87187e16i) q^{78} +9.97517e16i q^{79} +(-5.92493e15 + 5.03520e15i) q^{80} -1.82918e17 q^{81} +(-8.04794e16 + 5.14484e16i) q^{82} +2.58659e17 q^{83} +(-1.91488e17 - 8.85630e16i) q^{84} -7.41833e15i q^{85} +(3.13965e17 - 2.00710e17i) q^{86} +5.99623e17i q^{87} +(-3.96403e16 - 2.90541e17i) q^{88} +1.02832e17 q^{89} +(-3.90524e15 - 6.10887e15i) q^{90} +2.50119e17 q^{91} +(-7.36636e17 - 3.40693e17i) q^{92} +6.76627e17i q^{93} +(3.99860e17 + 6.25491e17i) q^{94} +1.84263e16i q^{95} +(-7.61563e17 - 2.33579e17i) q^{96} -4.73017e17 q^{97} +(1.57349e17 - 1.00589e17i) q^{98} +2.73434e17 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

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