LMFDB - Embedded newform 8.19.d.b.3.5

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			3.5
Root			$-162.812 - 207.587i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.19.d.b.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-299.623 - 415.174i) q^{2} +5937.76 q^{3} +(-82595.7 + 248792. i) q^{4} +2.28157e6i q^{5} +(-1.77909e6 - 2.46521e6i) q^{6} -3.15838e7i q^{7} +(1.28040e8 - 4.02522e7i) q^{8} -3.52164e8 q^{9} +O(q^{10})$	\(q+(-299.623 - 415.174i) q^{2} +5937.76 q^{3} +(-82595.7 + 248792. i) q^{4} +2.28157e6i q^{5} +(-1.77909e6 - 2.46521e6i) q^{6} -3.15838e7i q^{7} +(1.28040e8 - 4.02522e7i) q^{8} -3.52164e8 q^{9} +(9.47248e8 - 6.83611e8i) q^{10} +2.35396e9 q^{11} +(-4.90433e8 + 1.47727e9i) q^{12} -1.20623e10i q^{13} +(-1.31128e10 + 9.46323e9i) q^{14} +1.35474e10i q^{15} +(-5.50754e10 - 4.10983e10i) q^{16} -1.97418e11 q^{17} +(1.05516e11 + 1.46209e11i) q^{18} -1.48691e11 q^{19} +(-5.67635e11 - 1.88448e11i) q^{20} -1.87537e11i q^{21} +(-7.05302e11 - 9.77305e11i) q^{22} -1.21145e12i q^{23} +(7.60268e11 - 2.39008e11i) q^{24} -1.39085e12 q^{25} +(-5.00794e12 + 3.61413e12i) q^{26} -4.39147e12 q^{27} +(7.85778e12 + 2.60868e12i) q^{28} +1.97751e12i q^{29} +(5.62453e12 - 4.05911e12i) q^{30} -2.27392e13i q^{31} +(-5.61095e11 + 3.51799e13i) q^{32} +1.39773e13 q^{33} +(5.91511e13 + 8.19629e13i) q^{34} +7.20605e13 q^{35} +(2.90872e13 - 8.76154e13i) q^{36} -1.66947e14i q^{37} +(4.45513e13 + 6.17327e13i) q^{38} -7.16227e13i q^{39} +(9.18382e13 + 2.92131e14i) q^{40} -2.66745e14 q^{41} +(-7.78605e13 + 5.61904e13i) q^{42} -7.20962e14 q^{43} +(-1.94427e14 + 5.85647e14i) q^{44} -8.03485e14i q^{45} +(-5.02962e14 + 3.62978e14i) q^{46} -1.62833e15i q^{47} +(-3.27024e14 - 2.44032e14i) q^{48} +6.30880e14 q^{49} +(4.16731e14 + 5.77445e14i) q^{50} -1.17222e15 q^{51} +(3.00099e15 + 9.96290e14i) q^{52} -2.17325e15i q^{53} +(1.31579e15 + 1.82323e15i) q^{54} +5.37072e15i q^{55} +(-1.27132e15 - 4.04397e15i) q^{56} -8.82891e14 q^{57} +(8.21010e14 - 5.92507e14i) q^{58} +1.10087e16 q^{59} +(-3.37048e15 - 1.11896e15i) q^{60} +6.26095e15i q^{61} +(-9.44075e15 + 6.81320e15i) q^{62} +1.11226e16i q^{63} +(1.47739e16 - 1.03078e16i) q^{64} +2.75208e16 q^{65} +(-4.18791e15 - 5.80300e15i) q^{66} -4.55298e16 q^{67} +(1.63059e16 - 4.91160e16i) q^{68} -7.19328e15i q^{69} +(-2.15910e16 - 2.99177e16i) q^{70} +5.40107e16i q^{71} +(-4.50909e16 + 1.41754e16i) q^{72} +4.71784e14 q^{73} +(-6.93122e16 + 5.00213e16i) q^{74} -8.25853e15 q^{75} +(1.22812e16 - 3.69931e16i) q^{76} -7.43470e16i q^{77} +(-2.97359e16 + 2.14598e16i) q^{78} +1.72873e17i q^{79} +(9.37685e16 - 1.25658e17i) q^{80} +1.10360e17 q^{81} +(7.99229e16 + 1.10746e17i) q^{82} -8.17983e16 q^{83} +(4.66576e16 + 1.54897e16i) q^{84} -4.50422e17i q^{85} +(2.16017e17 + 2.99325e17i) q^{86} +1.17420e16i q^{87} +(3.01400e17 - 9.47522e16i) q^{88} +4.18502e17 q^{89} +(-3.33586e17 + 2.40743e17i) q^{90} -3.80971e17 q^{91} +(3.01399e17 + 1.00060e17i) q^{92} -1.35020e17i q^{93} +(-6.76042e17 + 4.87886e17i) q^{94} -3.39248e17i q^{95} +(-3.33165e15 + 2.08890e17i) q^{96} -5.20072e17 q^{97} +(-1.89026e17 - 2.61925e17i) q^{98} -8.28979e17 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 $

$2$	−299.623	−	415.174i	−0.585202	−	0.810888i
$2$	−299.623	−	415.174i	−0.585202	−	0.810888i
$3$	5937.76			0.301669			0.150835	−	0.988559i	$-0.451804\pi$
$3$	5937.76			0.301669			0.150835	+	0.988559i	$0.451804\pi$
$4$	−82595.7	+	248792.i	−0.315078	+	0.949066i
$5$			2.28157e6i			1.16816i	0.811695	+	0.584081i	$0.198545\pi$
$5$			2.28157e6i			1.16816i	−0.811695	+	0.584081i	$0.801455\pi$
$6$	−1.77909e6	−	2.46521e6i	−0.176537	−	0.244620i
$7$		−	3.15838e7i		−	0.782675i	−0.920247	−	0.391337i	$-0.872013\pi$
$7$		−	3.15838e7i		−	0.782675i	0.920247	−	0.391337i	$-0.127987\pi$
$8$	1.28040e8	−	4.02522e7i	0.953970	−	0.299903i
$9$	−3.52164e8			−0.908996
$10$	9.47248e8	−	6.83611e8i	0.947248	−	0.683611i
$11$	2.35396e9			0.998309			0.499155	−	0.866513i	$-0.333644\pi$
$11$	2.35396e9			0.998309			0.499155	+	0.866513i	$0.333644\pi$
$12$	−4.90433e8	+	1.47727e9i	−0.0950493	+	0.286304i
$13$		−	1.20623e10i		−	1.13747i	−0.822522	−	0.568733i	$-0.807434\pi$
$13$		−	1.20623e10i		−	1.13747i	0.822522	−	0.568733i	$-0.192566\pi$
$14$	−1.31128e10	+	9.46323e9i	−0.634661	+	0.458023i
$15$			1.35474e10i			0.352399i
$16$	−5.50754e10	−	4.10983e10i	−0.801452	−	0.598059i
$17$	−1.97418e11			−1.66474			−0.832370	−	0.554220i	$-0.813017\pi$
$17$	−1.97418e11			−1.66474			−0.832370	+	0.554220i	$0.813017\pi$
$18$	1.05516e11	+	1.46209e11i	0.531946	+	0.737093i
$19$	−1.48691e11			−0.460789			−0.230395	−	0.973097i	$-0.574002\pi$
$19$	−1.48691e11			−0.460789			−0.230395	+	0.973097i	$0.574002\pi$
$20$	−5.67635e11	−	1.88448e11i	−1.10866	−	0.368062i
$21$		−	1.87537e11i		−	0.236109i
$22$	−7.05302e11	−	9.77305e11i	−0.584213	−	0.809517i
$23$		−	1.21145e12i		−	0.672596i	−0.941756	−	0.336298i	$-0.890825\pi$
$23$		−	1.21145e12i		−	0.672596i	0.941756	−	0.336298i	$-0.109175\pi$
$24$	7.60268e11	−	2.39008e11i	0.287783	−	0.0904714i
$25$	−1.39085e12			−0.364603
$26$	−5.00794e12	+	3.61413e12i	−0.922357	+	0.665647i
$27$	−4.39147e12			−0.575885
$28$	7.85778e12	+	2.60868e12i	0.742810	+	0.246603i
$29$			1.97751e12i			0.136313i	0.997675	+	0.0681563i	$0.0217117\pi$
$29$			1.97751e12i			0.136313i	−0.997675	+	0.0681563i	$0.978288\pi$
$30$	5.62453e12	−	4.05911e12i	0.285756	−	0.206224i
$31$		−	2.27392e13i		−	0.860044i	−0.902819	−	0.430022i	$-0.858506\pi$
$31$		−	2.27392e13i		−	0.860044i	0.902819	−	0.430022i	$-0.141494\pi$
$32$	−5.61095e11	+	3.51799e13i	−0.0159473	+	0.999873i
$33$	1.39773e13			0.301159
$34$	5.91511e13	+	8.19629e13i	0.974209	+	1.34992i
$35$	7.20605e13			0.914291
$36$	2.90872e13	−	8.76154e13i	0.286404	−	0.862697i
$37$		−	1.66947e14i		−	1.28459i	−0.766459	−	0.642294i	$-0.777983\pi$
$37$		−	1.66947e14i		−	1.28459i	0.766459	−	0.642294i	$-0.222017\pi$
$38$	4.45513e13	+	6.17327e13i	0.269655	+	0.373648i
$39$		−	7.16227e13i		−	0.343138i
$40$	9.18382e13	+	2.92131e14i	0.350335	+	1.11439i
$41$	−2.66745e14			−0.814781			−0.407390	−	0.913254i	$-0.633561\pi$
$41$	−2.66745e14			−0.814781			−0.407390	+	0.913254i	$0.633561\pi$
$42$	−7.78605e13	+	5.61904e13i	−0.191458	+	0.138171i
$43$	−7.20962e14			−1.43449			−0.717243	−	0.696824i	$-0.754596\pi$
$43$	−7.20962e14			−1.43449			−0.717243	+	0.696824i	$0.754596\pi$
$44$	−1.94427e14	+	5.85647e14i	−0.314545	+	0.947461i
$45$		−	8.03485e14i		−	1.06185i
$46$	−5.02962e14	+	3.62978e14i	−0.545400	+	0.393604i
$47$		−	1.62833e15i		−	1.45500i	−0.686109	−	0.727498i	$-0.740683\pi$
$47$		−	1.62833e15i		−	1.45500i	0.686109	−	0.727498i	$-0.259317\pi$
$48$	−3.27024e14	−	2.44032e14i	−0.241774	−	0.180416i
$49$	6.30880e14			0.387420
$50$	4.16731e14	+	5.77445e14i	0.213366	+	0.295652i
$51$	−1.17222e15			−0.502201
$52$	3.00099e15	+	9.96290e14i	1.07953	+	0.358390i
$53$		−	2.17325e15i		−	0.658608i	−0.944224	−	0.329304i	$-0.893186\pi$
$53$		−	2.17325e15i		−	0.658608i	0.944224	−	0.329304i	$-0.106814\pi$
$54$	1.31579e15	+	1.82323e15i	0.337009	+	0.466978i
$55$			5.37072e15i			1.16619i
$56$	−1.27132e15	−	4.04397e15i	−0.234726	−	0.746648i
$57$	−8.82891e14			−0.139006
$58$	8.21010e14	−	5.92507e14i	0.110534	−	0.0797704i
$59$	1.10087e16			1.27077			0.635386	−	0.772195i	$-0.280841\pi$
$59$	1.10087e16			1.27077			0.635386	+	0.772195i	$0.280841\pi$
$60$	−3.37048e15	−	1.11896e15i	−0.334450	−	0.111033i
$61$			6.26095e15i			0.535392i	0.963503	+	0.267696i	$0.0862623\pi$
$61$			6.26095e15i			0.535392i	−0.963503	+	0.267696i	$0.913738\pi$
$62$	−9.44075e15	+	6.81320e15i	−0.697399	+	0.503299i
$63$			1.11226e16i			0.711448i
$64$	1.47739e16	−	1.03078e16i	0.820117	−	0.572196i
$65$	2.75208e16			1.32874
$66$	−4.18791e15	−	5.80300e15i	−0.176239	−	0.244206i
$67$	−4.55298e16			−1.67349			−0.836744	−	0.547595i	$-0.815544\pi$
$67$	−4.55298e16			−1.67349			−0.836744	+	0.547595i	$0.815544\pi$
$68$	1.63059e16	−	4.91160e16i	0.524523	−	1.57995i
$69$		−	7.19328e15i		−	0.202902i
$70$	−2.15910e16	−	2.99177e16i	−0.535045	−	0.741388i
$71$			5.40107e16i			1.17803i	0.808123	+	0.589013i	$0.200483\pi$
$71$			5.40107e16i			1.17803i	−0.808123	+	0.589013i	$0.799517\pi$
$72$	−4.50909e16	+	1.41754e16i	−0.867154	+	0.272610i
$73$	4.71784e14			0.00801378			0.00400689	−	0.999992i	$-0.498725\pi$
$73$	4.71784e14			0.00801378			0.00400689	+	0.999992i	$0.498725\pi$
$74$	−6.93122e16	+	5.00213e16i	−1.04166	+	0.751743i
$75$	−8.25853e15			−0.109989
$76$	1.22812e16	−	3.69931e16i	0.145184	−	0.437319i
$77$		−	7.43470e16i		−	0.781352i
$78$	−2.97359e16	+	2.14598e16i	−0.278247	+	0.200805i
$79$			1.72873e17i			1.44240i	0.692729	+	0.721198i	$0.256408\pi$
$79$			1.72873e17i			1.44240i	−0.692729	+	0.721198i	$0.743592\pi$
$80$	9.37685e16	−	1.25658e17i	0.698630	−	0.936226i
$81$	1.10360e17			0.735269
$82$	7.99229e16	+	1.10746e17i	0.476811	+	0.660696i
$83$	−8.17983e16			−0.437564			−0.218782	−	0.975774i	$-0.570208\pi$
$83$	−8.17983e16			−0.437564			−0.218782	+	0.975774i	$0.570208\pi$
$84$	4.66576e16	+	1.54897e16i	0.224083	+	0.0743927i
$85$		−	4.50422e17i		−	1.94469i
$86$	2.16017e17	+	2.99325e17i	0.839463	+	1.16321i
$87$			1.17420e16i			0.0411213i
$88$	3.01400e17	−	9.47522e16i	0.952357	−	0.299396i
$89$	4.18502e17			1.19450			0.597252	−	0.802053i	$-0.296259\pi$
$89$	4.18502e17			1.19450			0.597252	+	0.802053i	$0.296259\pi$
$90$	−3.33586e17	+	2.40743e17i	−0.861045	+	0.621399i
$91$	−3.80971e17			−0.890266
$92$	3.01399e17	+	1.00060e17i	0.638338	+	0.211920i
$93$		−	1.35020e17i		−	0.259449i
$94$	−6.76042e17	+	4.87886e17i	−1.17984	+	0.851467i
$95$		−	3.39248e17i		−	0.538276i
$96$	−3.33165e15	+	2.08890e17i	−0.00481081	+	0.301631i
$97$	−5.20072e17			−0.684097			−0.342048	−	0.939682i	$-0.611121\pi$
$97$	−5.20072e17			−0.684097			−0.342048	+	0.939682i	$0.611121\pi$
$98$	−1.89026e17	−	2.61925e17i	−0.226719	−	0.314154i
$99$	−8.28979e17			−0.907459
$100$	1.14878e17	−	3.46032e17i	0.114878	−	0.346032i
$101$		−	1.51822e18i		−	1.38817i	−0.719892	−	0.694086i	$-0.755809\pi$
$101$		−	1.51822e18i		−	1.38817i	0.719892	−	0.694086i	$-0.244191\pi$
$102$	3.51225e17	+	4.86676e17i	0.293889	+	0.407229i
$103$			1.83823e18i			1.40885i	0.709776	+	0.704427i	$0.248796\pi$
$103$			1.83823e18i			1.40885i	−0.709776	+	0.704427i	$0.751204\pi$
$104$	−4.85533e17	−	1.54445e18i	−0.341129	−	1.08511i
$105$	4.27877e17			0.275814
$106$	−9.02278e17	+	6.51156e17i	−0.534057	+	0.385418i
$107$	6.17561e17			0.335913			0.167956	−	0.985794i	$-0.446283\pi$
$107$	6.17561e17			0.335913			0.167956	+	0.985794i	$0.446283\pi$
$108$	3.62717e17	−	1.09256e18i	0.181449	−	0.546553i
$109$			1.49091e18i			0.686458i	0.939252	+	0.343229i	$0.111521\pi$
$109$			1.49091e18i			0.686458i	−0.939252	+	0.343229i	$0.888479\pi$
$110$	2.22979e18	−	1.60919e18i	0.945647	−	0.682455i
$111$		−	9.91292e17i		−	0.387521i
$112$	−1.29804e18	+	1.73949e18i	−0.468086	+	0.627277i
$113$	1.52525e18			0.507734			0.253867	−	0.967239i	$-0.418297\pi$
$113$	1.52525e18			0.507734			0.253867	+	0.967239i	$0.418297\pi$
$114$	2.64535e17	+	3.66554e17i	0.0813465	+	0.112718i
$115$	2.76400e18			0.785701
$116$	−4.91988e17	−	1.63334e17i	−0.129370	−	0.0429491i
$117$			4.24789e18i			1.03395i
$118$	−3.29846e18	−	4.57053e18i	−0.743658	−	1.03045i
$119$			6.23520e18i			1.30295i
$120$	5.45313e17	+	1.73460e18i	0.105685	+	0.336178i
$121$	−1.87828e16			−0.00337826
$122$	2.59939e18	−	1.87593e18i	0.434143	−	0.313312i
$123$	−1.58386e18			−0.245794
$124$	5.65734e18	+	1.87816e18i	0.816238	+	0.270980i
$125$			5.53017e18i			0.742247i
$126$	4.61784e18	−	3.33260e18i	0.576905	−	0.416341i
$127$		−	1.57929e19i		−	1.83750i	−0.394836	−	0.918751i	$-0.629199\pi$
$127$		−	1.57929e19i		−	1.83750i	0.394836	−	0.918751i	$-0.370801\pi$
$128$	−8.70613e18	−	3.04530e18i	−0.943921	−	0.330173i
$129$	−4.28090e18			−0.432740
$130$	−8.24588e18	−	1.14259e19i	−0.777583	−	1.07746i
$131$	1.13035e19			0.994884			0.497442	−	0.867497i	$-0.334273\pi$
$131$	1.13035e19			0.994884			0.497442	+	0.867497i	$0.334273\pi$
$132$	−1.15446e18	+	3.47743e18i	−0.0948886	+	0.285820i
$133$			4.69622e18i			0.360648i
$134$	1.36418e19	+	1.89028e19i	0.979328	+	1.35701i
$135$		−	1.00194e19i		−	0.672728i
$136$	−2.52773e19	+	7.94652e18i	−1.58811	+	0.499260i
$137$	−3.18491e19			−1.87332			−0.936661	−	0.350237i	$-0.886101\pi$
$137$	−3.18491e19			−1.87332			−0.936661	+	0.350237i	$0.886101\pi$
$138$	−2.98647e18	+	2.15528e18i	−0.164530	+	0.118738i
$139$	−3.62220e18			−0.186999			−0.0934996	−	0.995619i	$-0.529805\pi$
$139$	−3.62220e18			−0.186999			−0.0934996	+	0.995619i	$0.529805\pi$
$140$	−5.95188e18	+	1.79281e19i	−0.288073	+	0.867723i
$141$		−	9.66864e18i		−	0.438928i
$142$	2.24239e19	−	1.61829e19i	0.955247	−	0.689383i
$143$		−	2.83941e19i		−	1.13554i
$144$	1.93955e19	+	1.44733e19i	0.728517	+	0.543633i
$145$	−4.51181e18			−0.159235
$146$	−1.41357e17	−	1.95873e17i	−0.00468968	−	0.00649827i
$147$	3.74601e18			0.116873
$148$	4.15351e19	+	1.37891e19i	1.21916	+	0.404745i
$149$			1.37566e19i			0.380046i	0.981780	+	0.190023i	$0.0608563\pi$
$149$			1.37566e19i			0.380046i	−0.981780	+	0.190023i	$0.939144\pi$
$150$	2.47445e18	+	3.42873e18i	0.0643660	+	0.0891891i
$151$		−	2.58894e18i		−	0.0634351i	−0.999497	−	0.0317176i	$-0.989902\pi$
$151$		−	2.58894e18i		−	0.0634351i	0.999497	−	0.0317176i	$-0.0100977\pi$
$152$	−1.90383e19	+	5.98514e18i	−0.439579	+	0.138192i
$153$	6.95234e19			1.51324
$154$	−3.08670e19	+	2.22761e19i	−0.633589	+	0.457249i
$155$	5.18811e19			1.00467
$156$	1.78192e19	+	5.91573e18i	0.325661	+	0.108115i
$157$			3.57853e18i			0.0617458i	0.999523	+	0.0308729i	$0.00982871\pi$
$157$			3.57853e18i			0.0617458i	−0.999523	+	0.0308729i	$0.990171\pi$
$158$	7.17726e19	−	5.17969e19i	1.16962	−	0.844092i
$159$		−	1.29042e19i		−	0.198682i
$160$	−8.02653e19	−	1.28018e18i	−1.16801	−	0.0186290i
$161$	−3.82621e19			−0.526424
$162$	−3.30664e19	−	4.58186e19i	−0.430281	−	0.596220i
$163$	−1.25921e20			−1.55028			−0.775142	−	0.631787i	$-0.782322\pi$
$163$	−1.25921e20			−1.55028			−0.775142	+	0.631787i	$0.782322\pi$
$164$	2.20320e19	−	6.63639e19i	0.256719	−	0.773281i
$165$			3.18900e19i			0.351803i
$166$	2.45087e19	+	3.39606e19i	0.256063	+	0.354815i
$167$			2.01076e20i			1.99027i	0.0985377	+	0.995133i	$0.468584\pi$
$167$			2.01076e20i			1.99027i	−0.0985377	+	0.995133i	$0.531416\pi$
$168$	−7.54877e18	−	2.40121e19i	−0.0708097	−	0.225241i
$169$	−3.30425e19			−0.293828
$170$	−1.87004e20	+	1.34957e20i	−1.57692	+	1.13803i
$171$	5.23635e19			0.418855
$172$	5.95483e19	−	1.79369e20i	0.451974	−	1.36142i
$173$		−	1.31482e20i		−	0.947218i	−0.880735	−	0.473609i	$-0.842951\pi$
$173$		−	1.31482e20i		−	0.947218i	0.880735	−	0.473609i	$-0.157049\pi$
$174$	4.87496e18	−	3.51816e18i	0.0333448	−	0.0240643i
$175$			4.39283e19i			0.285366i
$176$	−1.29645e20	−	9.67438e19i	−0.800097	−	0.597048i
$177$	6.53670e19			0.383353
$178$	−1.25393e20	−	1.73751e20i	−0.699026	−	0.968609i
$179$	6.48527e19			0.343756			0.171878	−	0.985118i	$-0.445016\pi$
$179$	6.48527e19			0.343756			0.171878	+	0.985118i	$0.445016\pi$
$180$	1.99900e20	+	6.63644e19i	1.00777	+	0.334567i
$181$		−	2.49257e19i		−	0.119547i	−0.998212	−	0.0597736i	$-0.980962\pi$
$181$		−	2.49257e19i		−	0.119547i	0.998212	−	0.0597736i	$-0.0190379\pi$
$182$	1.14148e20	+	1.58170e20i	0.520985	+	0.721906i
$183$			3.71760e19i			0.161511i
$184$	−4.87635e19	−	1.55113e20i	−0.201713	−	0.641636i
$185$	3.80901e20			1.50061
$186$	−5.60569e19	+	4.04551e19i	−0.210384	+	0.151830i
$187$	−4.64715e20			−1.66193
$188$	4.05116e20	+	1.34493e20i	1.38089	+	0.458437i
$189$			1.38699e20i			0.450731i
$190$	−1.40847e20	+	1.01647e20i	−0.436482	+	0.315000i
$191$			2.45881e20i			0.726817i	0.931630	+	0.363408i	$0.118387\pi$
$191$			2.45881e20i			0.726817i	−0.931630	+	0.363408i	$0.881613\pi$
$192$	8.77239e19	−	6.12050e19i	0.247404	−	0.172614i
$193$	2.94564e19			0.0792800			0.0396400	−	0.999214i	$-0.487379\pi$
$193$	2.94564e19			0.0792800			0.0396400	+	0.999214i	$0.487379\pi$
$194$	1.55826e20	+	2.15920e20i	0.400335	+	0.554726i
$195$	1.63412e20			0.400841
$196$	−5.21080e19	+	1.56958e20i	−0.122067	+	0.367687i
$197$		−	7.48850e20i		−	1.67571i	−0.545892	−	0.837855i	$-0.683809\pi$
$197$		−	7.48850e20i		−	1.67571i	0.545892	−	0.837855i	$-0.316191\pi$
$198$	2.48382e20	+	3.44171e20i	0.531047	+	0.735847i
$199$		−	4.33087e20i		−	0.884906i	−0.896792	−	0.442453i	$-0.854108\pi$
$199$		−	4.33087e20i		−	0.884906i	0.896792	−	0.442453i	$-0.145892\pi$
$200$	−1.78084e20	+	5.59848e19i	−0.347820	+	0.109345i
$201$	−2.70345e20			−0.504840
$202$	−6.30328e20	+	4.54895e20i	−1.12565	+	0.812361i
$203$	6.24571e19			0.106688
$204$	9.68204e19	−	2.91639e20i	0.158232	−	0.476622i
$205$		−	6.08595e20i		−	0.951796i
$206$	7.63188e20	−	5.50778e20i	1.14242	−	0.824464i
$207$			4.26628e20i			0.611387i
$208$	−4.95738e20	+	6.64333e20i	−0.680271	+	0.911624i
$209$	−3.50013e20			−0.460010
$210$	−1.28202e20	−	1.77644e20i	−0.161407	−	0.223654i
$211$	−2.15183e20			−0.259577			−0.129789	−	0.991542i	$-0.541430\pi$
$211$	−2.15183e20			−0.259577			−0.129789	+	0.991542i	$0.541430\pi$
$212$	5.40687e20	+	1.79501e20i	0.625062	+	0.207513i
$213$			3.20703e20i			0.355374i
$214$	−1.85036e20	−	2.56396e20i	−0.196577	−	0.272387i
$215$		−	1.64492e21i		−	1.67571i
$216$	−5.62282e20	+	1.76767e20i	−0.549377	+	0.172710i
$217$	−7.18190e20			−0.673135
$218$	6.18990e20	−	4.46713e20i	0.556641	−	0.401717i
$219$	2.80134e18			0.00241751
$220$	−1.33619e21	−	4.43598e20i	−1.10679	−	0.367440i
$221$			2.38131e21i			1.89359i
$222$	−4.11559e20	+	2.97014e20i	−0.314236	+	0.226778i
$223$			7.77856e20i			0.570369i	0.958473	+	0.285184i	$0.0920548\pi$
$223$			7.77856e20i			0.570369i	−0.958473	+	0.285184i	$0.907945\pi$
$224$	1.11111e21	+	1.77215e19i	0.782575	+	0.0124815i
$225$	4.89806e20			0.331422
$226$	−4.57002e20	−	6.33247e20i	−0.297127	−	0.411715i
$227$	4.74764e20			0.296650			0.148325	−	0.988939i	$-0.452612\pi$
$227$	4.74764e20			0.296650			0.148325	+	0.988939i	$0.452612\pi$
$228$	7.29230e19	−	2.19656e20i	0.0437977	−	0.131926i
$229$			1.42048e21i			0.820192i	0.912042	+	0.410096i	$0.134505\pi$
$229$			1.42048e21i			0.820192i	−0.912042	+	0.410096i	$0.865495\pi$
$230$	−8.28159e20	−	1.14754e21i	−0.459794	−	0.637115i
$231$		−	4.41454e20i		−	0.235710i
$232$	7.95991e19	+	2.53199e20i	0.0408805	+	0.130038i
$233$	1.81736e21			0.897920			0.448960	−	0.893552i	$-0.351795\pi$
$233$	1.81736e21			0.897920			0.448960	+	0.893552i	$0.351795\pi$
$234$	1.76361e21	−	1.27277e21i	0.838418	−	0.605070i
$235$	3.71515e21			1.69967
$236$	−9.09271e20	+	2.73887e21i	−0.400392	+	1.20605i
$237$			1.02648e21i			0.435126i
$238$	2.58870e21	−	1.86821e21i	1.05655	−	0.762489i
$239$		−	8.68263e20i		−	0.341248i	−0.985336	−	0.170624i	$-0.945422\pi$
$239$		−	8.68263e20i		−	0.341248i	0.985336	−	0.170624i	$-0.0545783\pi$
$240$	5.56775e20	−	7.46128e20i	0.210755	−	0.282431i
$241$	−4.45834e21			−1.62562			−0.812811	−	0.582527i	$-0.802064\pi$
$241$	−4.45834e21			−1.62562			−0.812811	+	0.582527i	$0.802064\pi$
$242$	5.62777e18	+	7.79815e18i	0.00197696	+	0.00273939i
$243$	2.35664e21			0.797693
$244$	−1.55767e21	−	5.17128e20i	−0.508122	−	0.168690i
$245$			1.43939e21i			0.452569i
$246$	4.74563e20	+	6.57580e20i	0.143839	+	0.199312i
$247$			1.79355e21i			0.524132i
$248$	−9.15305e20	−	2.91152e21i	−0.257929	−	0.820456i
$249$	−4.85699e20			−0.132000
$250$	2.29599e21	−	1.65697e21i	0.601879	−	0.434364i
$251$	−4.99327e21			−1.26276			−0.631382	−	0.775472i	$-0.717512\pi$
$251$	−4.99327e21			−1.26276			−0.631382	+	0.775472i	$0.717512\pi$
$252$	−2.76723e21	−	9.18683e20i	−0.675211	−	0.224161i
$253$		−	2.85170e21i		−	0.671459i
$254$	−6.55680e21	+	4.73192e21i	−1.49001	+	1.07531i
$255$		−	2.67450e21i		−	0.586652i
$256$	1.34423e21	+	4.52701e21i	0.284651	+	0.958631i
$257$	3.92398e20			0.0802285			0.0401143	−	0.999195i	$-0.487228\pi$
$257$	3.92398e20			0.0802285			0.0401143	+	0.999195i	$0.487228\pi$
$258$	1.28266e21	+	1.77732e21i	0.253240	+	0.350904i
$259$	−5.27282e21			−1.00541
$260$	−2.27310e21	+	6.84696e21i	−0.418658	+	1.26107i
$261$		−	6.96406e20i		−	0.123908i
$262$	−3.38680e21	−	4.69294e21i	−0.582208	−	0.806739i
$263$		−	2.33587e21i		−	0.388014i	−0.981000	−	0.194007i	$-0.937852\pi$
$263$		−	2.33587e21i		−	0.388014i	0.981000	−	0.194007i	$-0.0621485\pi$
$264$	1.78964e21	−	5.62616e20i	0.287297	−	0.0903185i
$265$	4.95841e21			0.769360
$266$	1.94975e21	−	1.40710e21i	0.292445	−	0.211052i
$267$	2.48496e21			0.360345
$268$	3.76057e21	−	1.13274e22i	0.527278	−	1.58825i
$269$		−	9.87480e21i		−	1.33893i	−0.742844	−	0.669465i	$-0.766523\pi$
$269$		−	9.87480e21i		−	1.33893i	0.742844	−	0.669465i	$-0.233477\pi$
$270$	−4.15981e21	+	3.00206e21i	−0.545506	+	0.393681i
$271$		−	2.00043e21i		−	0.253746i	−0.991919	−	0.126873i	$-0.959506\pi$
$271$		−	2.00043e21i		−	0.253746i	0.991919	−	0.126873i	$-0.0404941\pi$
$272$	1.08729e22	+	8.11355e21i	1.33421	+	0.995613i
$273$	−2.26211e21			−0.268566
$274$	9.54274e21	+	1.32229e22i	1.09627	+	1.51905i
$275$	−3.27401e21			−0.363986
$276$	1.78963e21	+	5.94134e20i	0.192567	+	0.0639298i
$277$		−	1.56250e21i		−	0.162743i	−0.996684	−	0.0813713i	$-0.974070\pi$
$277$		−	1.56250e21i		−	0.162743i	0.996684	−	0.0813713i	$-0.0259300\pi$
$278$	1.08530e21	+	1.50385e21i	0.109432	+	0.151635i
$279$			8.00793e21i			0.781776i
$280$	9.22660e21	−	2.90059e21i	0.872206	−	0.274198i
$281$	−1.34574e21			−0.123198			−0.0615991	−	0.998101i	$-0.519620\pi$
$281$	−1.34574e21			−0.123198			−0.0615991	+	0.998101i	$0.519620\pi$
$282$	−4.01417e21	+	2.89695e21i	−0.355921	+	0.256861i
$283$	4.08841e21			0.351137			0.175569	−	0.984467i	$-0.443824\pi$
$283$	4.08841e21			0.351137			0.175569	+	0.984467i	$0.443824\pi$
$284$	−1.34374e22	−	4.46106e21i	−1.11802	−	0.371170i
$285$		−	2.01437e21i		−	0.162381i
$286$	−1.17885e22	+	8.50753e21i	−0.920797	+	0.664522i
$287$			8.42480e21i			0.637709i
$288$	1.97597e20	−	1.23891e22i	0.0144960	−	0.908880i
$289$	2.49108e22			1.77136
$290$	1.35184e21	+	1.87319e21i	0.0931848	+	0.129122i
$291$	−3.08806e21			−0.206371
$292$	−3.89673e19	+	1.17376e20i	−0.00252496	+	0.00760560i
$293$		−	1.32334e22i		−	0.831503i	−0.909478	−	0.415752i	$-0.863519\pi$
$293$		−	1.32334e22i		−	0.831503i	0.909478	−	0.415752i	$-0.136481\pi$
$294$	−1.12239e21	−	1.55525e21i	−0.0683941	−	0.0947706i
$295$			2.51171e22i			1.48447i
$296$	−6.72000e21	−	2.13759e22i	−0.385251	−	1.22546i
$297$	−1.03374e22			−0.574912
$298$	5.71141e21	−	4.12181e21i	0.308175	−	0.222404i
$299$	−1.46128e22			−0.765055
$300$	6.82119e20	−	2.05465e21i	0.0346552	−	0.104387i
$301$			2.27707e22i			1.12274i
$302$	−1.07486e21	+	7.75707e20i	−0.0514387	+	0.0371223i
$303$		−	9.01485e21i		−	0.418769i
$304$	8.18921e21	+	6.11095e21i	0.369300	+	0.275579i
$305$	−1.42848e22			−0.625425
$306$	−2.08308e22	−	2.88644e22i	−0.885552	−	1.22707i
$307$	9.21006e21			0.380204			0.190102	−	0.981764i	$-0.439118\pi$
$307$	9.21006e21			0.380204			0.190102	+	0.981764i	$0.439118\pi$
$308$	1.84969e22	+	6.14074e21i	0.741554	+	0.246186i
$309$			1.09150e22i			0.425008i
$310$	−1.55448e22	−	2.15397e22i	−0.587935	−	0.814675i
$311$		−	2.22406e21i		−	0.0817151i	−0.999165	−	0.0408576i	$-0.986991\pi$
$311$		−	2.22406e21i		−	0.0817151i	0.999165	−	0.0408576i	$-0.0130090\pi$
$312$	−2.88297e21	−	9.17055e21i	−0.102908	−	0.327344i
$313$	3.00302e22			1.04150			0.520751	−	0.853709i	$-0.325652\pi$
$313$	3.00302e22			1.04150			0.520751	+	0.853709i	$0.325652\pi$
$314$	1.48571e21	−	1.07221e21i	0.0500689	−	0.0361338i
$315$	−2.53771e22			−0.831087
$316$	−4.30095e22	−	1.42786e22i	−1.36893	−	0.454466i
$317$		−	2.62622e22i		−	0.812453i	−0.913772	−	0.406227i	$-0.866844\pi$
$317$		−	2.62622e22i		−	0.812453i	0.913772	−	0.406227i	$-0.133156\pi$
$318$	−5.35751e21	+	3.86641e21i	−0.161109	+	0.116269i
$319$			4.65498e21i			0.136082i
$320$	2.35179e22	+	3.37077e22i	0.668418	+	0.958030i
$321$	3.66693e21			0.101335
$322$	1.14642e22	+	1.58854e22i	0.308064	+	0.426871i
$323$	2.93543e22			0.767094
$324$	−9.11525e21	+	2.74566e22i	−0.231667	+	0.697818i
$325$			1.67768e22i			0.414723i
$326$	3.77290e22	+	5.22794e22i	0.907229	+	1.25711i
$327$			8.85269e21i			0.207083i
$328$	−3.41539e22	+	1.07371e22i	−0.777276	+	0.244355i
$329$	−5.14288e22			−1.13879
$330$	1.32399e22	−	9.55500e21i	0.285273	−	0.205876i
$331$	4.90686e22			1.02885			0.514425	−	0.857535i	$-0.328005\pi$
$331$	4.90686e22			1.02885			0.514425	+	0.857535i	$0.328005\pi$
$332$	6.75619e21	−	2.03508e22i	0.137867	−	0.415277i
$333$			5.87927e22i			1.16768i
$334$	8.34815e22	−	6.02470e22i	1.61388	−	1.16471i
$335$		−	1.03879e23i		−	1.95490i
$336$	−7.70744e21	+	1.03287e22i	−0.141207	+	0.189230i
$337$	−3.64989e22			−0.651044			−0.325522	−	0.945535i	$-0.605540\pi$
$337$	−3.64989e22			−0.651044			−0.325522	+	0.945535i	$0.605540\pi$
$338$	9.90031e21	+	1.37184e22i	0.171949	+	0.238261i
$339$	9.05659e21			0.153168
$340$	1.12061e23	+	3.72030e22i	1.84564	+	0.612727i
$341$		−	5.35273e22i		−	0.858590i
$342$	−1.56893e22	−	2.17400e22i	−0.245115	−	0.339645i
$343$		−	7.13570e22i		−	1.08590i
$344$	−9.23117e22	+	2.90203e22i	−1.36846	+	0.430206i
$345$	1.64120e22			0.237022
$346$	−5.45878e22	+	3.93949e22i	−0.768087	+	0.554313i
$347$	5.72256e22			0.784558			0.392279	−	0.919846i	$-0.371687\pi$
$347$	5.72256e22			0.784558			0.392279	+	0.919846i	$0.371687\pi$
$348$	−2.92130e21	−	9.69835e20i	−0.0390269	−	0.0129564i
$349$			1.68448e22i			0.219300i	0.993970	+	0.109650i	$0.0349729\pi$
$349$			1.68448e22i			0.219300i	−0.993970	+	0.109650i	$0.965027\pi$
$350$	1.82379e22	−	1.31619e22i	0.231399	−	0.166996i
$351$			5.29710e22i			0.655050i
$352$	−1.32080e21	+	8.28121e22i	−0.0159203	+	0.998182i
$353$	−3.65726e22			−0.429718			−0.214859	−	0.976645i	$-0.568929\pi$
$353$	−3.65726e22			−0.429718			−0.214859	+	0.976645i	$0.568929\pi$
$354$	−1.95855e22	−	2.71387e22i	−0.224339	−	0.310856i
$355$	−1.23229e23			−1.37613
$356$	−3.45665e22	+	1.04120e23i	−0.376362	+	1.13366i
$357$			3.70231e22i			0.393060i
$358$	−1.94314e22	−	2.69252e22i	−0.201167	−	0.278748i
$359$		−	1.53519e23i		−	1.54993i	−0.632001	−	0.774967i	$-0.717766\pi$
$359$		−	1.53519e23i		−	1.54993i	0.632001	−	0.774967i	$-0.282234\pi$
$360$	−3.23421e22	−	1.02878e23i	−0.318453	−	1.01298i
$361$	−8.20183e22			−0.787673
$362$	−1.03485e22	+	7.46831e21i	−0.0969394	+	0.0699593i
$363$	−1.11528e20			−0.00101912
$364$	3.14666e22	−	9.47826e22i	0.280503	−	0.844921i
$365$			1.07641e21i			0.00936139i
$366$	1.54345e22	−	1.11388e22i	0.130968	−	0.0945167i
$367$			1.28235e23i			1.06172i	0.847458	+	0.530862i	$0.178132\pi$
$367$			1.28235e23i			1.06172i	−0.847458	+	0.530862i	$0.821868\pi$
$368$	−4.97884e22	+	6.67210e22i	−0.402252	+	0.539054i
$369$	9.39377e22			0.740632
$370$	−1.14127e23	−	1.58140e23i	−0.878158	−	1.21682i
$371$	−6.86394e22			−0.515476
$372$	3.35919e22	+	1.11521e22i	0.246234	+	0.0817465i
$373$			1.23697e23i			0.885078i	0.896749	+	0.442539i	$0.145922\pi$
$373$			1.23697e23i			0.885078i	−0.896749	+	0.442539i	$0.854078\pi$
$374$	1.39239e23	+	1.92938e23i	0.972562	+	1.34764i
$375$			3.28368e22i			0.223913i
$376$	−6.55440e22	−	2.08491e23i	−0.436357	−	1.38802i
$377$	2.38532e22			0.155051
$378$	5.75843e22	−	4.15575e22i	0.365492	−	0.263769i
$379$	1.99505e23			1.23652			0.618261	−	0.785973i	$-0.287837\pi$
$379$	1.99505e23			1.23652			0.618261	+	0.785973i	$0.287837\pi$
$380$	8.44023e22	+	2.80205e22i	0.510860	+	0.169599i
$381$		−	9.37743e22i		−	0.554318i
$382$	1.02084e23	−	7.36717e22i	0.589367	−	0.425335i
$383$			2.81741e23i			1.58877i	0.607414	+	0.794385i	$0.292207\pi$
$383$			2.81741e23i			1.58877i	−0.607414	+	0.794385i	$0.707793\pi$
$384$	−5.16949e22	−	1.80823e22i	−0.284752	−	0.0996029i
$385$	1.69628e23			0.912746
$386$	−8.82582e21	−	1.22295e22i	−0.0463948	−	0.0642872i
$387$	2.53896e23			1.30394
$388$	4.29557e22	−	1.29390e23i	0.215544	−	0.649253i
$389$		−	1.39106e23i		−	0.682025i	−0.940059	−	0.341013i	$-0.889230\pi$
$389$		−	1.39106e23i		−	0.682025i	0.940059	−	0.341013i	$-0.110770\pi$
$390$	−4.89621e22	−	6.78445e22i	−0.234573	−	0.325037i
$391$			2.39162e23i			1.11970i
$392$	8.07776e22	−	2.53943e22i	0.369587	−	0.116188i
$393$	6.71176e22			0.300126
$394$	−3.10904e23	+	2.24373e23i	−1.35881	+	0.980629i
$395$	−3.94422e23			−1.68495
$396$	6.84701e22	−	2.06243e23i	0.285920	−	0.861238i
$397$		−	7.33153e22i		−	0.299282i	−0.988740	−	0.149641i	$-0.952188\pi$
$397$		−	7.33153e22i		−	0.299282i	0.988740	−	0.149641i	$-0.0478118\pi$
$398$	−1.79806e23	+	1.29763e23i	−0.717559	+	0.517848i
$399$			2.78850e22i			0.108796i
$400$	7.66015e22	+	5.71615e22i	0.292212	+	0.218054i
$401$	8.73430e22			0.325783			0.162892	−	0.986644i	$-0.447918\pi$
$401$	8.73430e22			0.325783			0.162892	+	0.986644i	$0.447918\pi$
$402$	8.10016e22	+	1.12240e23i	0.295433	+	0.409368i
$403$	−2.74286e23			−0.978270
$404$	3.77722e23	+	1.25399e23i	1.31747	+	0.437382i
$405$			2.51793e23i			0.858913i
$406$	−1.87136e22	−	2.59306e22i	−0.0624343	−	0.0865124i
$407$		−	3.92987e23i		−	1.28242i
$408$	−1.50091e23	+	4.71845e22i	−0.479085	+	0.150611i
$409$	−1.40850e23			−0.439792			−0.219896	−	0.975523i	$-0.570572\pi$
$409$	−1.40850e23			−0.439792			−0.219896	+	0.975523i	$0.570572\pi$
$410$	−2.52673e23	+	1.82349e23i	−0.771800	+	0.556993i
$411$	−1.89112e23			−0.565124
$412$	−4.57338e23	−	1.51830e23i	−1.33710	−	0.443898i
$413$		−	3.47696e23i		−	0.994602i
$414$	1.77125e23	−	1.27828e23i	0.495766	−	0.357785i
$415$		−	1.86628e23i		−	0.511146i
$416$	4.24349e23	+	6.76807e21i	1.13732	+	0.0181395i
$417$	−2.15078e22			−0.0564119
$418$	1.04872e23	+	1.45316e23i	0.269199	+	0.373017i
$419$	−5.27955e22			−0.132639			−0.0663194	−	0.997798i	$-0.521126\pi$
$419$	−5.27955e22			−0.132639			−0.0663194	+	0.997798i	$0.521126\pi$
$420$	−3.53408e22	+	1.06452e23i	−0.0869027	+	0.261765i
$421$		−	6.84254e23i		−	1.64694i	−0.567358	−	0.823471i	$-0.692034\pi$
$421$		−	6.84254e23i		−	1.64694i	0.567358	−	0.823471i	$-0.307966\pi$
$422$	6.44739e22	+	8.93386e22i	0.151905	+	0.210488i
$423$			5.73439e23i			1.32259i
$424$	−8.74781e22	−	2.78262e23i	−0.197518	−	0.628292i
$425$	2.74579e23			0.606969
$426$	1.33148e23	−	9.60900e22i	0.288169	−	0.207966i
$427$	1.97744e23			0.419038
$428$	−5.10079e22	+	1.53644e23i	−0.105839	+	0.318803i
$429$		−	1.68597e23i		−	0.342558i
$430$	−6.82930e23	+	4.92857e23i	−1.35881	+	0.980629i
$431$		−	7.07267e23i		−	1.37812i	−0.724703	−	0.689062i	$-0.758023\pi$
$431$		−	7.07267e23i		−	1.37812i	0.724703	−	0.689062i	$-0.241977\pi$
$432$	2.41862e23	+	1.80482e23i	0.461545	+	0.344413i
$433$	−4.41534e23			−0.825227			−0.412614	−	0.910906i	$-0.635384\pi$
$433$	−4.41534e23			−0.825227			−0.412614	+	0.910906i	$0.635384\pi$
$434$	2.15187e23	+	2.98174e23i	0.393920	+	0.545837i
$435$	−2.67901e22			−0.0480364
$436$	−3.70927e23	−	1.23143e23i	−0.651494	−	0.216288i
$437$			1.80131e23i			0.309925i
$438$	−8.39346e20	−	1.16304e21i	−0.00141473	−	0.00196033i
$439$			5.68846e23i			0.939321i	0.882847	+	0.469660i	$0.155624\pi$
$439$			5.68846e23i			0.939321i	−0.882847	+	0.469660i	$0.844376\pi$
$440$	2.16183e23	+	6.87665e23i	0.349743	+	1.11251i
$441$	−2.22173e23			−0.352163
$442$	9.88658e23	−	7.13495e23i	1.53548	−	1.10813i
$443$	7.74459e23			1.17860			0.589298	−	0.807916i	$-0.299405\pi$
$443$	7.74459e23			1.17860			0.589298	+	0.807916i	$0.299405\pi$
$444$	2.46625e23	+	8.18765e22i	0.367783	+	0.122099i
$445$			9.54841e23i			1.39537i
$446$	3.22946e23	−	2.33064e23i	0.462505	−	0.333781i
$447$			8.16836e22i			0.114648i
$448$	−3.25558e23	−	4.66616e23i	−0.447843	−	0.641885i
$449$	−1.71986e23			−0.231886			−0.115943	−	0.993256i	$-0.536989\pi$
$449$	−1.71986e23			−0.231886			−0.115943	+	0.993256i	$0.536989\pi$
$450$	−1.46757e23	−	2.03355e23i	−0.193949	−	0.268746i
$451$	−6.27906e23			−0.813403
$452$	−1.25979e23	+	3.79471e23i	−0.159976	+	0.481873i
$453$		−	1.53725e22i		−	0.0191364i
$454$	−1.42250e23	−	1.97110e23i	−0.173600	−	0.240550i
$455$		−	8.69211e23i		−	1.03997i
$456$	−1.13045e23	+	3.55383e22i	−0.132607	+	0.0416882i
$457$	1.16332e24			1.33799			0.668994	−	0.743268i	$-0.266725\pi$
$457$	1.16332e24			1.33799			0.668994	+	0.743268i	$0.266725\pi$
$458$	5.89747e23	−	4.25609e23i	0.665084	−	0.479978i
$459$	8.66956e23			0.958700
$460$	−2.28295e23	+	6.87661e23i	−0.247557	+	0.745682i
$461$			7.56568e23i			0.804525i	0.915524	+	0.402262i	$0.131776\pi$
$461$			7.56568e23i			0.804525i	−0.915524	+	0.402262i	$0.868224\pi$
$462$	−1.83281e23	+	1.32270e23i	−0.191134	+	0.137938i
$463$		−	5.36371e23i		−	0.548575i	−0.961648	−	0.274288i	$-0.911558\pi$
$463$		−	5.36371e23i		−	0.548575i	0.961648	−	0.274288i	$-0.0884420\pi$
$464$	8.12722e22	−	1.08912e23i	0.0815230	−	0.109248i
$465$	3.08057e23			0.303078
$466$	−5.44523e23	−	7.54521e23i	−0.525464	−	0.728112i
$467$	6.57507e22			0.0622370			0.0311185	−	0.999516i	$-0.490093\pi$
$467$	6.57507e22			0.0622370			0.0311185	+	0.999516i	$0.490093\pi$
$468$	−1.05684e24	−	3.50857e23i	−0.981288	−	0.325775i
$469$			1.43800e24i			1.30980i
$470$	−1.11314e24	−	1.54243e24i	−0.994651	−	1.37824i
$471$			2.12484e22i			0.0186268i
$472$	1.40955e24	−	4.43125e23i	1.21228	−	0.381108i
$473$	−1.69712e24			−1.43206
$474$	4.26168e23	−	3.07557e23i	0.352839	−	0.254637i
$475$	2.06807e23			0.168005
$476$	−1.55127e24	−	5.15001e23i	−1.23659	−	0.410531i
$477$			7.65339e23i			0.598671i
$478$	−3.60481e23	+	2.60152e23i	−0.276714	+	0.199699i
$479$			5.93035e23i			0.446746i	0.974733	+	0.223373i	$0.0717067\pi$
$479$			5.93035e23i			0.446746i	−0.974733	+	0.223373i	$0.928293\pi$
$480$	−4.76596e23	−	7.60137e21i	−0.352354	−	0.00561980i
$481$	−2.01376e24			−1.46117
$482$	1.33582e24	+	1.85099e24i	0.951317	+	1.31820i
$483$	−2.27191e23			−0.158806
$484$	1.55138e21	−	4.67301e21i	0.00106441	−	0.00320619i
$485$		−	1.18658e24i		−	0.799136i
$486$	−7.06103e23	−	9.78415e23i	−0.466812	−	0.646840i
$487$			7.87024e23i			0.510773i	0.966839	+	0.255386i	$0.0822026\pi$
$487$			7.87024e23i			0.510773i	−0.966839	+	0.255386i	$0.917797\pi$
$488$	2.52017e23	+	8.01650e23i	0.160565	+	0.510748i
$489$	−7.47691e23			−0.467673
$490$	5.97600e23	−	4.31276e23i	0.366983	−	0.264844i
$491$	1.18812e24			0.716352			0.358176	−	0.933654i	$-0.383399\pi$
$491$	1.18812e24			0.716352			0.358176	+	0.933654i	$0.383399\pi$
$492$	1.30820e23	−	3.94053e23i	0.0774443	−	0.233275i
$493$		−	3.90396e23i		−	0.226925i
$494$	7.44635e23	−	5.37389e23i	0.425012	−	0.306723i
$495$		−	1.89137e24i		−	1.06006i
$496$	−9.34543e23	+	1.25237e24i	−0.514357	+	0.689284i
$497$	1.70586e24			0.922012
$498$	1.45527e23	+	2.01650e23i	0.0772464	+	0.107037i
$499$	2.13800e23			0.111456			0.0557280	−	0.998446i	$-0.482252\pi$
$499$	2.13800e23			0.111456			0.0557280	+	0.998446i	$0.482252\pi$
$500$	−1.37586e24	−	4.56768e23i	−0.704441	−	0.233865i
$501$			1.19394e24i			0.600402i
$502$	1.49610e24	+	2.07308e24i	0.738971	+	1.02396i
$503$		−	4.77628e23i		−	0.231728i	−0.993265	−	0.115864i	$-0.963036\pi$
$503$		−	4.77628e23i		−	0.231728i	0.993265	−	0.115864i	$-0.0369637\pi$
$504$	4.47711e23	+	1.42414e24i	0.213365	+	0.678700i
$505$	3.46393e24			1.62161
$506$	−1.18395e24	+	8.54436e23i	−0.544478	+	0.392939i
$507$	−1.96198e23			−0.0886388
$508$	3.92914e24	+	1.30442e24i	1.74391	+	0.578956i
$509$		−	2.94342e24i		−	1.28349i	−0.766918	−	0.641745i	$-0.778211\pi$
$509$		−	2.94342e24i		−	1.28349i	0.766918	−	0.641745i	$-0.221789\pi$
$510$	−1.11038e24	+	8.01342e23i	−0.475709	+	0.343310i
$511$		−	1.49007e22i		−	0.00627218i
$512$	1.47674e24	−	1.91449e24i	0.610764	−	0.791813i
$513$	6.52972e23			0.265362
$514$	−1.17572e23	−	1.62914e23i	−0.0469499	−	0.0650563i
$515$	−4.19406e24			−1.64577
$516$	3.53584e23	−	1.06505e24i	0.136347	−	0.410699i
$517$		−	3.83303e24i		−	1.45254i
$518$	1.57986e24	+	2.18914e24i	0.588370	+	0.815278i
$519$		−	7.80705e23i		−	0.285746i
$520$	3.52376e24	−	1.10778e24i	1.26758	−	0.398494i
$521$	−2.63387e24			−0.931225			−0.465613	−	0.884989i	$-0.654166\pi$
$521$	−2.63387e24			−0.931225			−0.465613	+	0.884989i	$0.654166\pi$
$522$	−2.89130e23	+	2.08659e23i	−0.100475	+	0.0725109i
$523$	1.34682e24			0.460040			0.230020	−	0.973186i	$-0.426121\pi$
$523$	1.34682e24			0.460040			0.230020	+	0.973186i	$0.426121\pi$
$524$	−9.33623e23	+	2.81223e24i	−0.313466	+	0.944211i
$525$			2.60835e23i			0.0860860i
$526$	−9.69795e23	+	6.99882e23i	−0.314636	+	0.227067i
$527$			4.48913e24i			1.43175i
$528$	−7.69802e23	−	5.74441e23i	−0.241365	−	0.180111i
$529$	1.77654e24			0.547615
$530$	−1.48566e24	−	2.05861e24i	−0.450231	−	0.623865i
$531$	−3.87686e24			−1.15513
$532$	−1.16838e24	−	3.87888e23i	−0.342279	−	0.113632i
$533$			3.21754e24i			0.926785i
$534$	−7.44553e23	−	1.03169e24i	−0.210875	−	0.292200i
$535$			1.40901e24i			0.392400i
$536$	−5.82962e24	+	1.83268e24i	−1.59646	+	0.501883i
$537$	3.85079e23			0.103701
$538$	−4.09976e24	+	2.95872e24i	−1.08572	+	0.783544i
$539$	1.48507e24			0.386765
$540$	2.49275e24	+	8.27562e23i	0.638463	+	0.211961i
$541$		−	6.78202e24i		−	1.70838i	−0.519964	−	0.854188i	$-0.674055\pi$
$541$		−	6.78202e24i		−	1.70838i	0.519964	−	0.854188i	$-0.325945\pi$
$542$	−8.30527e23	+	5.99375e23i	−0.205760	+	0.148493i
$543$		−	1.48003e23i		−	0.0360637i
$544$	1.10770e23	−	6.94515e24i	0.0265481	−	1.66453i
$545$	−3.40162e24			−0.801895
$546$	6.77782e23	+	9.39172e23i	0.157165	+	0.217777i
$547$	−7.61034e23			−0.173587			−0.0867937	−	0.996226i	$-0.527662\pi$
$547$	−7.61034e23			−0.173587			−0.0867937	+	0.996226i	$0.527662\pi$
$548$	2.63060e24	−	7.92381e24i	0.590242	−	1.77791i
$549$		−	2.20488e24i		−	0.486669i
$550$	9.80969e23	+	1.35928e24i	0.213006	+	0.295152i
$551$		−	2.94037e23i		−	0.0628114i
$552$	−2.89546e23	−	9.21026e23i	−0.0608507	−	0.193562i
$553$	5.45999e24			1.12893
$554$	−6.48709e23	+	4.68160e23i	−0.131966	+	0.0952373i
$555$	2.26170e24			0.452687
$556$	2.99178e23	−	9.01175e23i	0.0589193	−	0.177475i
$557$			7.01797e24i			1.35993i	0.733247	+	0.679963i	$0.238004\pi$
$557$			7.01797e24i			1.35993i	−0.733247	+	0.679963i	$0.761996\pi$
$558$	3.32469e24	−	2.39936e24i	0.633932	−	0.457497i
$559$			8.69642e24i			1.63168i
$560$	−3.96876e24	−	2.96156e24i	−0.732761	−	0.546800i
$561$	−2.75936e24			−0.501352
$562$	4.03215e23	+	5.58717e23i	0.0720958	+	0.0998999i
$563$	5.94509e23			0.104612			0.0523061	−	0.998631i	$-0.483343\pi$
$563$	5.94509e23			0.104612			0.0523061	+	0.998631i	$0.483343\pi$
$564$	2.40548e24	+	7.98588e23i	0.416572	+	0.138296i
$565$			3.47997e24i			0.593116i
$566$	−1.22498e24	−	1.69740e24i	−0.205486	−	0.284733i
$567$		−	3.48558e24i		−	0.575476i
$568$	2.17405e24	+	6.91552e24i	0.353293	+	1.12380i
$569$	5.55373e24			0.888330			0.444165	−	0.895945i	$-0.353500\pi$
$569$	5.55373e24			0.888330			0.444165	+	0.895945i	$0.353500\pi$
$570$	−8.36317e23	+	6.03554e23i	−0.131673	+	0.0950259i
$571$	−2.47515e24			−0.383598			−0.191799	−	0.981434i	$-0.561432\pi$
$571$	−2.47515e24			−0.383598			−0.191799	+	0.981434i	$0.561432\pi$
$572$	7.06422e24	+	2.34523e24i	1.07770	+	0.357784i
$573$			1.45998e24i			0.219258i
$574$	3.49776e24	−	2.52427e24i	0.517110	−	0.373188i
$575$			1.68494e24i			0.245230i
$576$	−5.20283e24	+	3.63002e24i	−0.745483	+	0.520124i
$577$	4.72502e24			0.666532			0.333266	−	0.942833i	$-0.391849\pi$
$577$	4.72502e24			0.666532			0.333266	+	0.942833i	$0.391849\pi$
$578$	−7.46386e24	−	1.03423e25i	−1.03660	−	1.43638i
$579$	1.74905e23			0.0239163
$580$	3.72656e23	−	1.12250e24i	0.0501715	−	0.151125i
$581$			2.58350e24i			0.342470i
$582$	9.25254e23	+	1.28208e24i	0.120769	+	0.167344i
$583$		−	5.11574e24i		−	0.657494i
$584$	6.04070e22	−	1.89903e22i	0.00764490	−	0.00240335i
$585$	−9.69183e24			−1.20782
$586$	−5.49418e24	+	3.96504e24i	−0.674256	+	0.486597i
$587$	1.57029e25			1.89774			0.948868	−	0.315673i	$-0.102230\pi$
$587$	1.57029e25			1.89774			0.948868	+	0.315673i	$0.102230\pi$
$588$	−3.09404e23	+	9.31977e23i	−0.0368240	+	0.110920i
$589$			3.38112e24i			0.396299i
$590$	1.04280e25	−	7.52566e24i	1.20374	−	0.868713i
$591$		−	4.44649e24i		−	0.505510i
$592$	−6.86124e24	+	9.19468e24i	−0.768259	+	1.02954i
$593$	3.27442e24			0.361112			0.180556	−	0.983565i	$-0.442210\pi$
$593$	3.27442e24			0.361112			0.180556	+	0.983565i	$0.442210\pi$
$594$	3.09731e24	+	4.29180e24i	0.336439	+	0.466189i
$595$	−1.42260e25			−1.52206
$596$	−3.42254e24	−	1.13624e24i	−0.360689	−	0.119744i
$597$		−	2.57156e24i		−	0.266949i
$598$	4.37833e24	+	6.06686e24i	0.447711	+	0.620373i
$599$		−	1.49219e24i		−	0.150308i	−0.997172	−	0.0751539i	$-0.976055\pi$
$599$		−	1.49219e24i		−	0.150308i	0.997172	−	0.0751539i	$-0.0239448\pi$
$600$	−1.05742e24	+	3.32424e23i	−0.104927	+	0.0329861i
$601$	−1.53036e25			−1.49597			−0.747986	−	0.663715i	$-0.768979\pi$
$601$	−1.53036e25			−1.49597			−0.747986	+	0.663715i	$0.768979\pi$
$602$	9.45380e24	−	6.82263e24i	0.910412	−	0.657027i
$603$	1.60339e25			1.52119
$604$	6.44108e23	+	2.13835e23i	0.0602041	+	0.0199870i
$605$		−	4.28543e22i		−	0.00394635i
$606$	−3.74273e24	+	2.70106e24i	−0.339575	+	0.245064i
$607$		−	1.56235e25i		−	1.39663i	−0.715792	−	0.698314i	$-0.753934\pi$
$607$		−	1.56235e25i		−	1.39663i	0.715792	−	0.698314i	$-0.246066\pi$
$608$	8.34298e22	−	5.23093e24i	0.00734833	−	0.460731i
$609$	3.70855e23			0.0321846
$610$	4.28005e24	+	5.93068e24i	0.366000	+	0.507149i
$611$	−1.96413e25			−1.65501
$612$	−5.74234e24	+	1.72969e25i	−0.476789	+	1.43617i
$613$		−	1.88084e25i		−	1.53889i	−0.638712	−	0.769446i	$-0.720533\pi$
$613$		−	1.88084e25i		−	1.53889i	0.638712	−	0.769446i	$-0.279467\pi$
$614$	−2.75955e24	−	3.82378e24i	−0.222496	−	0.308303i
$615$		−	3.61369e24i		−	0.287128i
$616$	−2.99263e24	−	9.51936e24i	−0.234329	−	0.745386i
$617$	−5.11620e24			−0.394804			−0.197402	−	0.980323i	$-0.563250\pi$
$617$	−5.11620e24			−0.394804			−0.197402	+	0.980323i	$0.563250\pi$
$618$	4.53163e24	−	3.27039e24i	0.344634	−	0.248715i
$619$	5.65819e24			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$619$	5.65819e24			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$620$	−4.28515e24	+	1.29076e25i	−0.316549	+	0.953498i
$621$			5.32004e24i			0.387338i
$622$	−9.23372e23	+	6.66380e23i	−0.0662618	+	0.0478199i
$623$		−	1.32179e25i		−	0.934909i
$624$	−2.94357e24	+	3.94465e24i	−0.205217	+	0.275009i
$625$	−1.79231e25			−1.23167
$626$	−8.99776e24	−	1.24678e25i	−0.609489	−	0.844541i
$627$	−2.07829e24			−0.138771
$628$	−8.90309e23	−	2.95571e23i	−0.0586009	−	0.0194547i
$629$			3.29584e25i			2.13850i
$630$	7.60356e24	+	1.05359e25i	0.486354	+	0.673918i
$631$			1.37960e25i			0.869940i	0.900445	+	0.434970i	$0.143241\pi$
$631$			1.37960e25i			0.869940i	−0.900445	+	0.434970i	$0.856759\pi$
$632$	6.95854e24	+	2.21346e25i	0.432578	+	1.37600i
$633$	−1.27771e24			−0.0783064
$634$	−1.09034e25	+	7.86878e24i	−0.658808	+	0.475449i
$635$	3.60325e25			2.14650
$636$	3.21047e24	+	1.06583e24i	0.188562	+	0.0626002i
$637$		−	7.60983e24i		−	0.440677i
$638$	1.93263e24	−	1.39474e24i	0.110347	−	0.0796355i
$639$		−	1.90206e25i		−	1.07082i
$640$	6.94807e24	−	1.98636e25i	0.385695	−	1.10265i
$641$	2.98207e25			1.63228			0.816142	−	0.577852i	$-0.196109\pi$
$641$	2.98207e25			1.63228			0.816142	+	0.577852i	$0.196109\pi$
$642$	−1.09870e24	−	1.52242e24i	−0.0593011	−	0.0821709i
$643$	−2.25277e25			−1.19899			−0.599497	−	0.800377i	$-0.704633\pi$
$643$	−2.25277e25			−1.19899			−0.599497	+	0.800377i	$0.704633\pi$
$644$	3.16028e24	−	9.51930e24i	0.165864	−	0.499611i
$645$		−	9.76715e24i		−	0.505511i
$646$	−8.79523e24	−	1.21871e25i	−0.448905	−	0.622027i
$647$			2.02021e25i			1.01685i	0.861105	+	0.508427i	$0.169773\pi$
$647$			2.02021e25i			1.01685i	−0.861105	+	0.508427i	$0.830227\pi$
$648$	1.41304e25	−	4.44223e24i	0.701424	−	0.220509i
$649$	2.59140e25			1.26862
$650$	6.96529e24	−	5.02671e24i	0.336294	−	0.242697i
$651$	−4.26444e24			−0.203064
$652$	1.04006e25	−	3.13282e25i	0.488460	−	1.47132i
$653$			2.21111e25i			1.02422i	0.858921	+	0.512109i	$0.171135\pi$
$653$			2.21111e25i			1.02422i	−0.858921	+	0.512109i	$0.828865\pi$
$654$	3.67541e24	−	2.65247e24i	0.167921	−	0.121186i
$655$			2.57898e25i			1.16219i
$656$	1.46911e25	+	1.09627e25i	0.653008	+	0.487287i
$657$	−1.66145e23			−0.00728449
$658$	1.54093e25	+	2.13519e25i	0.666422	+	0.923431i
$659$	−6.18455e24			−0.263839			−0.131920	−	0.991260i	$-0.542114\pi$
$659$	−6.18455e24			−0.263839			−0.131920	+	0.991260i	$0.542114\pi$
$660$	−7.93398e24	−	2.63398e24i	−0.333884	−	0.110845i
$661$		−	2.01390e25i		−	0.836035i	−0.908439	−	0.418018i	$-0.862725\pi$
$661$		−	2.01390e25i		−	0.836035i	0.908439	−	0.418018i	$-0.137275\pi$
$662$	−1.47021e25	−	2.03720e25i	−0.602085	−	0.834282i
$663$			1.41396e25i			0.571237i
$664$	−1.04734e25	+	3.29257e24i	−0.417423	+	0.131227i
$665$	−1.07147e25			−0.421295
$666$	2.44092e25	−	1.76157e25i	0.946861	−	0.683331i
$667$	2.39565e24			0.0916833
$668$	−5.00260e25	−	1.66080e25i	−1.88889	−	0.627088i
$669$			4.61872e24i			0.172063i
$670$	−4.31280e25	+	3.11247e25i	−1.58521	+	1.14401i
$671$			1.47380e25i			0.534487i
$672$	6.59752e24	+	1.05226e23i	0.236079	+	0.00376530i
$673$	−3.96508e24			−0.139996			−0.0699980	−	0.997547i	$-0.522299\pi$
$673$	−3.96508e24			−0.139996			−0.0699980	+	0.997547i	$0.522299\pi$
$674$	1.09359e25	+	1.51534e25i	0.380992	+	0.527923i
$675$	6.10787e24			0.209969
$676$	2.72917e24	−	8.22071e24i	0.0925785	−	0.278862i
$677$		−	1.33836e24i		−	0.0447997i	−0.999749	−	0.0223999i	$-0.992869\pi$
$677$		−	1.33836e24i		−	0.0447997i	0.999749	−	0.0223999i	$-0.00713070\pi$
$678$	−2.71357e24	−	3.76006e24i	−0.0896340	−	0.124202i
$679$			1.64258e25i			0.535425i
$680$	−1.81305e25	−	5.76719e25i	−0.583217	−	1.85517i
$681$	2.81903e24			0.0894904
$682$	−2.22232e25	+	1.60380e25i	−0.696220	+	0.502448i
$683$	−5.65250e24			−0.174765			−0.0873825	−	0.996175i	$-0.527850\pi$
$683$	−5.65250e24			−0.174765			−0.0873825	+	0.996175i	$0.527850\pi$
$684$	−4.32500e24	+	1.30276e25i	−0.131972	+	0.397521i
$685$		−	7.26659e25i		−	2.18834i
$686$	−2.96256e25	+	2.13802e25i	−0.880542	+	0.635470i
$687$			8.43446e24i			0.247427i
$688$	3.97072e25	+	2.96303e25i	1.14967	+	0.857907i
$689$	−2.62143e25			−0.749143
$690$	−4.91741e24	−	6.81383e24i	−0.138706	−	0.192198i
$691$	−6.02349e25			−1.67705			−0.838525	−	0.544864i	$-0.816581\pi$
$691$	−6.02349e25			−1.67705			−0.838525	+	0.544864i	$0.816581\pi$
$692$	3.27115e25	+	1.08598e25i	0.898972	+	0.298447i
$693$			2.61823e25i			0.710245i
$694$	−1.71461e25	−	2.37586e25i	−0.459125	−	0.636188i
$695$		−	8.26430e24i		−	0.218445i
$696$	4.72640e23	+	1.50344e24i	0.0123324	+	0.0392285i
$697$	5.26602e25			1.35640
$698$	6.99354e24	−	5.04710e24i	0.177827	−	0.128334i
$699$	1.07910e25			0.270875
$700$	−1.09290e25	−	3.62829e24i	−0.270831	−	0.0899123i
$701$		−	1.73501e25i		−	0.424463i	−0.977219	−	0.212231i	$-0.931927\pi$
$701$		−	1.73501e25i		−	0.424463i	0.977219	−	0.212231i	$-0.0680731\pi$
$702$	2.19922e25	−	1.58714e25i	0.531172	−	0.383336i
$703$			2.48235e25i			0.591924i
$704$	3.47772e25	−	2.42641e25i	0.818730	−	0.571229i
$705$	2.20596e25			0.512739
$706$	1.09580e25	+	1.51840e25i	0.251472	+	0.348453i
$707$	−4.79512e25			−1.08649
$708$	−5.39903e24	+	1.62628e25i	−0.120786	+	0.363827i
$709$		−	8.74520e24i		−	0.193176i	−0.995324	−	0.0965881i	$-0.969207\pi$
$709$		−	8.74520e24i		−	0.193176i	0.995324	−	0.0965881i	$-0.0307930\pi$
$710$	3.69223e25	+	5.11616e25i	0.805311	+	1.11588i
$711$		−	6.08797e25i		−	1.31113i
$712$	5.35849e25	−	1.68457e25i	1.13952	−	0.358235i
$713$	−2.75474e25			−0.578462
$714$	1.53711e25	−	1.10930e25i	0.318728	−	0.230020i
$715$	6.47830e25			1.32650
$716$	−5.35655e24	+	1.61348e25i	−0.108310	+	0.326247i
$717$		−	5.15553e24i		−	0.102944i
$718$	−6.37374e25	+	4.59980e25i	−1.25682	+	0.907025i
$719$		−	3.39963e25i		−	0.662021i	−0.943627	−	0.331011i	$-0.892610\pi$
$719$		−	3.39963e25i		−	0.662021i	0.943627	−	0.331011i	$-0.107390\pi$
$720$	−3.30218e25	+	4.42522e25i	−0.635051	+	0.851025i
$721$	5.80584e25			1.10267
$722$	2.45746e25	+	3.40519e25i	0.460948	+	0.638715i
$723$	−2.64725e25			−0.490401
$724$	6.20130e24	+	2.05875e24i	0.113458	+	0.0376667i
$725$		−	2.75041e24i		−	0.0497000i
$726$	3.34163e22	+	4.63035e22i	0.000596389	+	0.000826389i
$727$		−	2.19781e25i		−	0.387419i	−0.981059	−	0.193710i	$-0.937948\pi$
$727$		−	2.19781e25i		−	0.387419i	0.981059	−	0.193710i	$-0.0620519\pi$
$728$	−4.87794e25	+	1.53349e25i	−0.849287	+	0.266993i
$729$	−2.87625e25			−0.494629
$730$	4.46896e23	−	3.22516e23i	0.00759104	−	0.00547830i
$731$	1.42331e26			2.38805
$732$	−9.24909e24	−	3.07058e24i	−0.153285	−	0.0508886i
$733$			4.81569e25i			0.788357i	0.919034	+	0.394179i	$0.128971\pi$
$733$			4.81569e25i			0.788357i	−0.919034	+	0.394179i	$0.871029\pi$
$734$	5.32398e25	−	3.84222e25i	0.860939	−	0.621323i
$735$			8.54677e24i			0.136526i
$736$	4.26186e25	+	6.79738e23i	0.672510	+	0.0107261i
$737$	−1.07175e26			−1.67066
$738$	−2.81459e25	−	3.90005e25i	−0.433419	−	0.600570i
$739$	−1.08279e26			−1.64719			−0.823596	−	0.567176i	$-0.808036\pi$
$739$	−1.08279e26			−1.64719			−0.823596	+	0.567176i	$0.808036\pi$
$740$	−3.14608e25	+	9.47651e25i	−0.472807	+	1.42417i
$741$			1.06497e25i			0.158114i
$742$	2.05660e25	+	2.84973e25i	0.301657	+	0.417993i
$743$		−	2.25860e25i		−	0.327296i	−0.986519	−	0.163648i	$-0.947674\pi$
$743$		−	2.25860e25i		−	0.327296i	0.986519	−	0.163648i	$-0.0523261\pi$
$744$	−5.43486e24	−	1.72879e25i	−0.0778093	−	0.247506i
$745$	−3.13867e25			−0.443955
$746$	5.13560e25	−	3.70627e25i	0.717699	−	0.517949i
$747$	2.88064e25			0.397744
$748$	3.83834e25	−	1.15617e26i	0.523636	−	1.57728i
$749$		−	1.95049e25i		−	0.262910i
$750$	1.36330e25	−	9.83868e24i	0.181568	−	0.131034i
$751$			7.67021e25i			1.00936i	0.863305	+	0.504682i	$0.168390\pi$
$751$			7.67021e25i			1.00936i	−0.863305	+	0.504682i	$0.831610\pi$
$752$	−6.69216e25	+	8.96810e25i	−0.870174	+	1.16611i
$753$	−2.96488e25			−0.380937
$754$	−7.14697e24	−	9.90323e24i	−0.0907361	−	0.125729i
$755$	5.90684e24			0.0741025
$756$	−3.45072e25	−	1.14560e25i	−0.427774	−	0.142015i
$757$		−	6.00705e25i		−	0.735865i	−0.929852	−	0.367933i	$-0.880066\pi$
$757$		−	6.00705e25i		−	0.735865i	0.929852	−	0.367933i	$-0.119934\pi$
$758$	−5.97765e25	−	8.28296e25i	−0.723615	−	1.00268i
$759$		−	1.69327e25i		−	0.202559i
$760$	−1.36555e25	−	4.34372e25i	−0.161430	−	0.513499i
$761$	2.68948e25			0.314200			0.157100	−	0.987583i	$-0.449785\pi$
$761$	2.68948e25			0.314200			0.157100	+	0.987583i	$0.449785\pi$
$762$	−3.89327e25	+	2.80970e25i	−0.449490	+	0.324388i
$763$	4.70887e25			0.537274
$764$	−6.11732e25	−	2.03087e25i	−0.689797	−	0.229004i
$765$			1.58622e26i			1.76771i
$766$	1.16972e26	−	8.44162e25i	1.28831	−	0.929752i
$767$		−	1.32790e26i		−	1.44546i
$768$	7.98169e24	+	2.68803e25i	0.0858705	+	0.289190i
$769$	7.48604e25			0.796004			0.398002	−	0.917385i	$-0.369704\pi$
$769$	7.48604e25			0.796004			0.398002	+	0.917385i	$0.369704\pi$
$770$	−5.08244e25	−	7.04250e25i	−0.534140	−	0.740134i
$771$	2.32996e24			0.0242025
$772$	−2.43297e24	+	7.32851e24i	−0.0249794	+	0.0752419i
$773$			1.49818e26i			1.52037i	0.649706	+	0.760186i	$0.274892\pi$
$773$			1.49818e26i			1.52037i	−0.649706	+	0.760186i	$0.725108\pi$
$774$	−7.60733e25	−	1.05411e26i	−0.763068	−	1.05735i
$775$			3.16268e25i			0.313574i
$776$	−6.65898e25	+	2.09340e25i	−0.652608	+	0.205162i
$777$	−3.13087e25			−0.303303
$778$	−5.77534e25	+	4.16795e25i	−0.553046	+	0.399122i
$779$	3.96625e25			0.375442
$780$	−1.34971e25	+	4.06556e25i	−0.126296	+	0.380425i
$781$			1.27139e26i			1.17603i
$782$	9.92938e25	−	7.16584e25i	0.907949	−	0.655249i
$783$		−	8.68416e24i		−	0.0785004i
$784$	−3.47459e25	−	2.59281e25i	−0.310498	−	0.231700i
$785$	−8.16465e24			−0.0721291
$786$	−2.01100e25	−	2.78655e25i	−0.175634	−	0.243369i
$787$	−8.02440e25			−0.692851			−0.346426	−	0.938077i	$-0.612605\pi$
$787$	−8.02440e25			−0.692851			−0.346426	+	0.938077i	$0.612605\pi$
$788$	1.86308e26	+	6.18518e25i	1.59036	+	0.527979i
$789$		−	1.38698e25i		−	0.117052i
$790$	1.18178e26	+	1.63754e26i	0.986037	+	1.36631i
$791$		−	4.81733e25i		−	0.397391i
$792$	−1.06142e26	+	3.33683e25i	−0.865688	+	0.272149i
$793$	7.55212e25			0.608990
$794$	−3.04387e25	+	2.19670e25i	−0.242684	+	0.175140i
$795$	2.94419e25			0.232092
$796$	1.07748e26	+	3.57711e25i	0.839834	+	0.278814i
$797$		−	1.67418e26i		−	1.29026i	−0.764073	−	0.645129i	$-0.776803\pi$
$797$		−	1.67418e26i		−	1.29026i	0.764073	−	0.645129i	$-0.223197\pi$
$798$	1.15771e25	−	8.35500e24i	0.0882217	−	0.0636679i
$799$			3.21462e26i			2.42219i
$800$	7.80399e23	−	4.89299e25i	0.00581442	−	0.364556i
$801$	−1.47381e26			−1.08580
$802$	−2.61700e25	−	3.62626e25i	−0.190649	−	0.264174i
$803$	1.11056e24			0.00800023
$804$	2.23293e25	−	6.72596e25i	0.159064	−	0.479126i
$805$		−	8.72975e25i		−	0.614949i
$806$	8.21826e25	+	1.13877e26i	0.572485	+	0.793267i
$807$		−	5.86342e25i		−	0.403914i
$808$	−6.11119e25	−	1.94393e26i	−0.416317	−	1.32427i
$809$	2.62973e25			0.177163			0.0885816	−	0.996069i	$-0.471767\pi$
$809$	2.62973e25			0.177163			0.0885816	+	0.996069i	$0.471767\pi$
$810$	1.04538e26	−	7.54432e25i	0.696482	−	0.502637i
$811$	2.21655e26			1.46046			0.730231	−	0.683201i	$-0.239413\pi$
$811$	2.21655e26			1.46046			0.730231	+	0.683201i	$0.239413\pi$
$812$	−5.15869e24	+	1.55388e25i	−0.0336152	+	0.101254i
$813$		−	1.18781e25i		−	0.0765474i
$814$	−1.63158e26	+	1.17748e26i	−1.03990	+	0.750472i
$815$		−	2.87298e26i		−	1.81098i
$816$	6.45605e25	+	4.81763e25i	0.402490	+	0.300346i
$817$	1.07200e26			0.660995
$818$	4.22020e25	+	5.84773e25i	0.257367	+	0.356622i
$819$	1.34164e26			0.809248
$820$	1.51414e26	+	5.02674e25i	0.903317	+	0.299890i
$821$		−	1.11156e26i		−	0.655912i	−0.944693	−	0.327956i	$-0.893640\pi$
$821$		−	1.11156e26i		−	0.655912i	0.944693	−	0.327956i	$-0.106360\pi$
$822$	5.66625e25	+	7.85146e25i	0.330711	+	0.458252i
$823$			4.27602e25i			0.246854i	0.992354	+	0.123427i	$0.0393885\pi$
$823$			4.27602e25i			0.246854i	−0.992354	+	0.123427i	$0.960611\pi$
$824$	7.39931e25	+	2.35367e26i	0.422519	+	1.34400i
$825$	−1.94403e25			−0.109804
$826$	−1.44354e26	+	1.04178e26i	−0.806510	+	0.582043i
$827$	−2.87229e26			−1.58737			−0.793686	−	0.608328i	$-0.791840\pi$
$827$	−2.87229e26			−1.58737			−0.793686	+	0.608328i	$0.791840\pi$
$828$	−1.06142e26	−	3.52376e25i	−0.580246	−	0.192634i
$829$		−	1.66637e26i		−	0.901114i	−0.892748	−	0.450557i	$-0.851225\pi$
$829$		−	1.66637e26i		−	0.901114i	0.892748	−	0.450557i	$-0.148775\pi$
$830$	−7.74833e25	+	5.59182e25i	−0.414482	+	0.299123i
$831$		−	9.27773e24i		−	0.0490944i
$832$	−1.24335e26	−	1.78207e26i	−0.650853	−	0.932855i
$833$	−1.24547e26			−0.644954
$834$	6.44423e24	+	8.92948e24i	0.0330124	+	0.0457437i
$835$	−4.58768e26			−2.32495
$836$	2.89096e25	−	8.70804e25i	0.144939	−	0.436580i
$837$			9.98586e25i			0.495287i
$838$	1.58188e25	+	2.19194e25i	0.0776205	+	0.107555i
$839$			1.34302e26i			0.651966i	0.945376	+	0.325983i	$0.105695\pi$
$839$			1.34302e26i			0.651966i	−0.945376	+	0.325983i	$0.894305\pi$
$840$	5.47853e25	−	1.72230e25i	0.263118	−	0.0827172i
$841$	2.06547e26			0.981419
$842$	−2.84085e26	+	2.05018e26i	−1.33549	+	0.963794i
$843$	−7.99068e24			−0.0371651
$844$	1.77732e25	−	5.35358e25i	0.0817869	−	0.246356i
$845$		−	7.53887e25i		−	0.343238i
$846$	2.38077e26	−	1.71816e26i	1.07247	−	0.773980i
$847$			5.93232e23i			0.00264408i
$848$	−8.93168e25	+	1.19693e26i	−0.393886	+	0.527842i
$849$	2.42760e25			0.105927
$850$	−8.22702e25	−	1.13998e26i	−0.355199	−	0.492184i
$851$	−2.02248e26			−0.864008
$852$	−7.97882e25	−	2.64887e25i	−0.337274	−	0.111971i
$853$		−	4.35359e26i		−	1.82099i	−0.413525	−	0.910493i	$-0.635702\pi$
$853$		−	4.35359e26i		−	1.82099i	0.413525	−	0.910493i	$-0.364298\pi$
$854$	−5.92488e25	−	8.20984e25i	−0.245222	−	0.339793i
$855$			1.19471e26i			0.489291i
$856$	7.90724e25	−	2.48582e25i	0.320450	−	0.100741i
$857$	−1.71357e26			−0.687184			−0.343592	−	0.939119i	$-0.611644\pi$
$857$	−1.71357e26			−0.687184			−0.343592	+	0.939119i	$0.611644\pi$
$858$	−6.99972e25	+	5.05156e25i	−0.277776	+	0.200466i
$859$	1.21980e25			0.0479016			0.0239508	−	0.999713i	$-0.492375\pi$
$859$	1.21980e25			0.0479016			0.0239508	+	0.999713i	$0.492375\pi$
$860$	4.09243e26	+	1.35863e26i	1.59036	+	0.527979i
$861$			5.00244e25i			0.192377i
$862$	−2.93639e26	+	2.11914e26i	−1.11750	+	0.806480i
$863$		−	1.05114e26i		−	0.395878i	−0.980214	−	0.197939i	$-0.936575\pi$
$863$		−	1.05114e26i		−	0.395878i	0.980214	−	0.197939i	$-0.0634248\pi$
$864$	2.46403e24	−	1.54491e26i	0.00918381	−	0.575812i
$865$	2.99984e26			1.10650
$866$	1.32294e26	+	1.83314e26i	0.482924	+	0.669166i
$867$	1.47914e26			0.534365
$868$	5.93194e25	−	1.78680e26i	0.212090	−	0.638849i
$869$			4.06937e26i			1.43996i
$870$	8.02693e24	+	1.11225e25i	0.0281110	+	0.0389521i
$871$			5.49192e26i			1.90353i
$872$	6.00126e25	+	1.90896e26i	0.205871	+	0.654861i
$873$	1.83150e26			0.621841
$874$	7.47860e25	−	5.39716e25i	0.251314	−	0.181369i
$875$	1.74664e26			0.580938
$876$	−2.31378e23	+	6.96950e23i	−0.000761703	+	0.00229438i
$877$		−	3.91748e26i		−	1.27647i	−0.769841	−	0.638235i	$-0.779665\pi$
$877$		−	3.91748e26i		−	1.27647i	0.769841	−	0.638235i	$-0.220335\pi$
$878$	2.36170e26	−	1.70439e26i	0.761683	−	0.549692i
$879$		−	7.85769e25i		−	0.250839i
$880$	2.20727e26	−	2.95794e26i	0.697449	−	0.934643i
$881$	2.84213e26			0.888917			0.444459	−	0.895799i	$-0.353396\pi$
$881$	2.84213e26			0.888917			0.444459	+	0.895799i	$0.353396\pi$
$882$	6.65682e25	+	9.22405e25i	0.206086	+	0.285565i
$883$	3.72981e26			1.14299			0.571493	−	0.820607i	$-0.306364\pi$
$883$	3.72981e26			1.14299			0.571493	+	0.820607i	$0.306364\pi$
$884$	−5.92450e26	−	1.96686e26i	−1.79714	−	0.596626i
$885$			1.49139e26i			0.447818i
$886$	−2.32046e26	−	3.21535e26i	−0.689716	−	0.955708i
$887$		−	5.42179e25i		−	0.159526i	−0.996814	−	0.0797628i	$-0.974584\pi$
$887$		−	5.42179e25i		−	0.159526i	0.996814	−	0.0797628i	$-0.0254163\pi$
$888$	−3.99017e25	−	1.26925e26i	−0.116218	−	0.369683i
$889$	−4.98799e26			−1.43817
$890$	3.96426e26	−	2.86093e26i	1.13149	−	0.816576i
$891$	2.59783e26			0.734026
$892$	−1.93524e26	−	6.42476e25i	−0.541317	−	0.179710i
$893$			2.42118e26i			0.670447i
$894$	3.39130e25	−	2.44743e25i	0.0929668	−	0.0670924i
$895$			1.47966e26i			0.401563i
$896$	−9.61822e25	+	2.74972e26i	−0.258418	+	0.738783i
$897$	−8.67672e25			−0.230794
$898$	5.15309e25	+	7.14041e25i	0.135700	+	0.188034i
$899$	4.49670e25			0.117235
$900$	−4.04559e25	+	1.21860e26i	−0.104424	+	0.314542i
$901$			4.29039e26i			1.09641i
$902$	1.88135e26	+	2.60691e26i	0.476005	+	0.659579i
$903$			1.35207e26i			0.338695i
$904$	1.95293e26	−	6.13949e25i	0.484363	−	0.152271i
$905$	5.68696e25			0.139651
$906$	−6.38227e24	+	4.60596e24i	−0.0155175	+	0.0111987i
$907$	−7.92341e26			−1.90742			−0.953711	−	0.300726i	$-0.902771\pi$
$907$	−7.92341e26			−1.90742			−0.953711	+	0.300726i	$0.902771\pi$
$908$	−3.92135e25	+	1.18117e26i	−0.0934679	+	0.281541i
$909$			5.34663e26i			1.26184i
$910$	−3.60874e26	+	2.60436e26i	−0.843303	+	0.608595i
$911$		−	6.20038e25i		−	0.143467i	−0.997424	−	0.0717337i	$-0.977147\pi$
$911$		−	6.20038e25i		−	0.143467i	0.997424	−	0.0717337i	$-0.0228532\pi$
$912$	4.86255e25	+	3.62853e25i	0.111407	+	0.0831337i
$913$	−1.92550e26			−0.436824
$914$	−3.48557e26	−	4.82979e26i	−0.782993	−	1.08496i
$915$	−8.48196e25			−0.188671
$916$	−3.53404e26	−	1.17325e26i	−0.778416	−	0.258424i
$917$		−	3.57008e26i		−	0.778671i
$918$	−2.59760e26	−	3.59938e26i	−0.561033	−	0.777398i
$919$		−	4.21982e26i		−	0.902515i	−0.892394	−	0.451257i	$-0.850976\pi$
$919$		−	4.21982e26i		−	0.902515i	0.892394	−	0.451257i	$-0.149024\pi$
$920$	3.53902e26	−	1.11257e26i	0.749535	−	0.235634i
$921$	5.46871e25			0.114696
$922$	3.14108e26	−	2.26685e26i	0.652379	−	0.470809i
$923$	6.51491e26			1.33996
$924$	1.09830e26	+	3.64622e25i	0.223704	+	0.0742669i
$925$			2.32198e26i			0.468364i
$926$	−2.22687e26	+	1.60709e26i	−0.444833	+	0.321027i
$927$		−	6.47359e26i		−	1.28064i
$928$	−6.95685e25	−	1.10957e24i	−0.136295	−	0.00217382i
$929$	−2.05506e25			−0.0398735			−0.0199367	−	0.999801i	$-0.506346\pi$
$929$	−2.05506e25			−0.0398735			−0.0199367	+	0.999801i	$0.506346\pi$
$930$	−9.23011e25	−	1.27897e26i	−0.177362	−	0.245762i
$931$	−9.38061e25			−0.178519
$932$	−1.50106e26	+	4.52144e26i	−0.282914	+	0.852185i
$933$		−	1.32059e25i		−	0.0246510i
$934$	−1.97005e25	−	2.72980e25i	−0.0364212	−	0.0504672i
$935$		−	1.06028e27i		−	1.94140i
$936$	1.70987e26	+	5.43898e26i	0.310085	+	0.986358i
$937$	−6.71887e26			−1.20681			−0.603406	−	0.797434i	$-0.706190\pi$
$937$	−6.71887e26			−1.20681			−0.603406	+	0.797434i	$0.706190\pi$
$938$	5.97022e26	−	4.30859e26i	1.06210	−	0.766495i
$939$	1.78312e26			0.314189
$940$	−3.06855e26	+	9.24299e26i	−0.535529	+	1.61310i
$941$		−	4.67913e26i		−	0.808833i	−0.914575	−	0.404417i	$-0.867475\pi$
$941$		−	4.67913e26i		−	0.808833i	0.914575	−	0.404417i	$-0.132525\pi$
$942$	8.82181e24	−	6.36653e24i	0.0151043	−	0.0109004i
$943$			3.23147e26i			0.548018i
$944$	−6.06308e26	−	4.52439e26i	−1.01846	−	0.759997i
$945$	−3.16451e26			−0.526527
$946$	5.08495e26	+	7.04599e26i	0.838044	+	1.16124i
$947$	4.93745e26			0.806033			0.403017	−	0.915193i	$-0.367962\pi$
$947$	4.93745e26			0.806033			0.403017	+	0.915193i	$0.367962\pi$
$948$	−2.55380e26	−	8.47828e25i	−0.412964	−	0.137099i
$949$		−	5.69077e24i		−	0.00911539i
$950$	−6.19641e25	−	8.58609e25i	−0.0983168	−	0.136233i
$951$		−	1.55939e26i		−	0.245092i
$952$	2.50981e26	+	7.98353e26i	0.390758	+	1.24298i
$953$	5.69412e25			0.0878193			0.0439097	−	0.999036i	$-0.486019\pi$
$953$	5.69412e25			0.0878193			0.0439097	+	0.999036i	$0.486019\pi$
$954$	3.17749e26	−	2.29313e26i	0.485455	−	0.350344i
$955$	−5.60994e26			−0.849040
$956$	2.16017e26	+	7.17148e25i	0.323867	+	0.107520i
$957$			2.76401e25i			0.0410518i
$958$	2.46213e26	−	1.77687e26i	0.362261	−	0.261436i
$959$			1.00592e27i			1.46620i
$960$	1.39643e26	+	2.00148e26i	0.201641	+	0.289008i
$961$	1.81981e26			0.260325
$962$	6.03369e26	+	8.36061e26i	0.855082	+	1.18485i
$963$	−2.17483e26			−0.305343
$964$	3.68240e26	−	1.10920e27i	0.512197	−	1.54282i
$965$			6.72067e25i			0.0926119i
$966$	6.80717e25	+	9.43239e25i	0.0929336	+	0.128774i
$967$		−	1.15434e27i		−	1.56133i	−0.624952	−	0.780663i	$-0.714882\pi$
$967$		−	1.15434e27i		−	1.56133i	0.624952	−	0.780663i	$-0.285118\pi$
$968$	−2.40495e24	+	7.56051e23i	−0.00322275	+	0.00101315i
$969$	1.74299e26			0.231409
$970$	−4.92637e26	+	3.55526e26i	−0.648009	+	0.467656i
$971$	7.22634e25			0.0941772			0.0470886	−	0.998891i	$-0.485006\pi$
$971$	7.22634e25			0.0941772			0.0470886	+	0.998891i	$0.485006\pi$
$972$	−1.94648e26	+	5.86312e26i	−0.251335	+	0.757064i
$973$			1.14403e26i			0.146360i
$974$	3.26752e26	−	2.35811e26i	0.414179	−	0.298905i
$975$			9.96164e25i			0.125109i
$976$	2.57314e26	−	3.44824e26i	0.320196	−	0.429091i
$977$	−7.87011e26			−0.970353			−0.485177	−	0.874416i	$-0.661245\pi$
$977$	−7.87011e26			−0.970353			−0.485177	+	0.874416i	$0.661245\pi$
$978$	2.24026e26	+	3.10422e26i	0.273683	+	0.379230i
$979$	9.85138e26			1.19249
$980$	−3.58110e26	−	1.18888e26i	−0.429518	−	0.142594i
$981$		−	5.25046e26i		−	0.623988i
$982$	−3.55988e26	−	4.93277e26i	−0.419211	−	0.580881i
$983$			7.96537e26i			0.929446i	0.885456	+	0.464723i	$0.153846\pi$
$983$			7.96537e26i			0.929446i	−0.885456	+	0.464723i	$0.846154\pi$
$984$	−2.02797e26	+	6.37541e25i	−0.234480	+	0.0737144i
$985$	1.70855e27			1.95750
$986$	−1.62082e26	+	1.16972e26i	−0.184011	+	0.132797i
$987$	−3.05372e26			−0.343538
$988$	−4.46220e26	−	1.48139e26i	−0.497436	−	0.165142i
$989$			8.73408e26i			0.964829i
$990$	−7.85249e26	+	5.66699e26i	−0.859589	+	0.620349i
$991$		−	9.86827e25i		−	0.107048i	−0.998567	−	0.0535239i	$-0.982955\pi$
$991$		−	9.86827e25i		−	0.107048i	0.998567	−	0.0535239i	$-0.0170453\pi$
$992$	7.99964e26	+	1.27589e25i	0.859934	+	0.0137154i
$993$	2.91358e26			0.310373
$994$	−5.11116e26	−	7.08230e26i	−0.539563	−	0.747648i
$995$	9.88116e26			1.03371
$996$	4.01166e25	−	1.20838e26i	0.0415901	−	0.125276i
$997$		−	1.06974e27i		−	1.09906i	−0.835474	−	0.549530i	$-0.814807\pi$
$997$		−	1.06974e27i		−	1.09906i	0.835474	−	0.549530i	$-0.185193\pi$
$998$	−6.40595e25	−	8.87644e25i	−0.0652242	−	0.0903782i
$999$			7.33144e26i			0.739775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.19.d.b.3.5	✓	16
3.2	odd	2		72.19.b.b.19.12		16
4.3	odd	2		32.19.d.b.15.8		16
8.3	odd	2	inner	8.19.d.b.3.6	yes	16
8.5	even	2		32.19.d.b.15.7		16
24.11	even	2		72.19.b.b.19.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.19.d.b.3.5	✓	16	1.1	even	1	trivial
8.19.d.b.3.6	yes	16	8.3	odd	2	inner
32.19.d.b.15.7		16	8.5	even	2
32.19.d.b.15.8		16	4.3	odd	2
72.19.b.b.19.11		16	24.11	even	2
72.19.b.b.19.12		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)

\(f(q)\)	\(=\)	\(q+(-299.623 - 415.174i) q^{2} +5937.76 q^{3} +(-82595.7 + 248792. i) q^{4} +2.28157e6i q^{5} +(-1.77909e6 - 2.46521e6i) q^{6} -3.15838e7i q^{7} +(1.28040e8 - 4.02522e7i) q^{8} -3.52164e8 q^{9} +O(q^{10})\)	\(q+(-299.623 - 415.174i) q^{2} +5937.76 q^{3} +(-82595.7 + 248792. i) q^{4} +2.28157e6i q^{5} +(-1.77909e6 - 2.46521e6i) q^{6} -3.15838e7i q^{7} +(1.28040e8 - 4.02522e7i) q^{8} -3.52164e8 q^{9} +(9.47248e8 - 6.83611e8i) q^{10} +2.35396e9 q^{11} +(-4.90433e8 + 1.47727e9i) q^{12} -1.20623e10i q^{13} +(-1.31128e10 + 9.46323e9i) q^{14} +1.35474e10i q^{15} +(-5.50754e10 - 4.10983e10i) q^{16} -1.97418e11 q^{17} +(1.05516e11 + 1.46209e11i) q^{18} -1.48691e11 q^{19} +(-5.67635e11 - 1.88448e11i) q^{20} -1.87537e11i q^{21} +(-7.05302e11 - 9.77305e11i) q^{22} -1.21145e12i q^{23} +(7.60268e11 - 2.39008e11i) q^{24} -1.39085e12 q^{25} +(-5.00794e12 + 3.61413e12i) q^{26} -4.39147e12 q^{27} +(7.85778e12 + 2.60868e12i) q^{28} +1.97751e12i q^{29} +(5.62453e12 - 4.05911e12i) q^{30} -2.27392e13i q^{31} +(-5.61095e11 + 3.51799e13i) q^{32} +1.39773e13 q^{33} +(5.91511e13 + 8.19629e13i) q^{34} +7.20605e13 q^{35} +(2.90872e13 - 8.76154e13i) q^{36} -1.66947e14i q^{37} +(4.45513e13 + 6.17327e13i) q^{38} -7.16227e13i q^{39} +(9.18382e13 + 2.92131e14i) q^{40} -2.66745e14 q^{41} +(-7.78605e13 + 5.61904e13i) q^{42} -7.20962e14 q^{43} +(-1.94427e14 + 5.85647e14i) q^{44} -8.03485e14i q^{45} +(-5.02962e14 + 3.62978e14i) q^{46} -1.62833e15i q^{47} +(-3.27024e14 - 2.44032e14i) q^{48} +6.30880e14 q^{49} +(4.16731e14 + 5.77445e14i) q^{50} -1.17222e15 q^{51} +(3.00099e15 + 9.96290e14i) q^{52} -2.17325e15i q^{53} +(1.31579e15 + 1.82323e15i) q^{54} +5.37072e15i q^{55} +(-1.27132e15 - 4.04397e15i) q^{56} -8.82891e14 q^{57} +(8.21010e14 - 5.92507e14i) q^{58} +1.10087e16 q^{59} +(-3.37048e15 - 1.11896e15i) q^{60} +6.26095e15i q^{61} +(-9.44075e15 + 6.81320e15i) q^{62} +1.11226e16i q^{63} +(1.47739e16 - 1.03078e16i) q^{64} +2.75208e16 q^{65} +(-4.18791e15 - 5.80300e15i) q^{66} -4.55298e16 q^{67} +(1.63059e16 - 4.91160e16i) q^{68} -7.19328e15i q^{69} +(-2.15910e16 - 2.99177e16i) q^{70} +5.40107e16i q^{71} +(-4.50909e16 + 1.41754e16i) q^{72} +4.71784e14 q^{73} +(-6.93122e16 + 5.00213e16i) q^{74} -8.25853e15 q^{75} +(1.22812e16 - 3.69931e16i) q^{76} -7.43470e16i q^{77} +(-2.97359e16 + 2.14598e16i) q^{78} +1.72873e17i q^{79} +(9.37685e16 - 1.25658e17i) q^{80} +1.10360e17 q^{81} +(7.99229e16 + 1.10746e17i) q^{82} -8.17983e16 q^{83} +(4.66576e16 + 1.54897e16i) q^{84} -4.50422e17i q^{85} +(2.16017e17 + 2.99325e17i) q^{86} +1.17420e16i q^{87} +(3.01400e17 - 9.47522e16i) q^{88} +4.18502e17 q^{89} +(-3.33586e17 + 2.40743e17i) q^{90} -3.80971e17 q^{91} +(3.01399e17 + 1.00060e17i) q^{92} -1.35020e17i q^{93} +(-6.76042e17 + 4.87886e17i) q^{94} -3.39248e17i q^{95} +(-3.33165e15 + 2.08890e17i) q^{96} -5.20072e17 q^{97} +(-1.89026e17 - 2.61925e17i) q^{98} -8.28979e17 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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