LMFDB - Embedded newform 5.21.c.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,21,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.6756882551$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 7326009 x^{16} + 21914129354136 x^{14} + \cdots + 79\!\cdots\!76 $ x^18 + 7326009x^16 + 21914129354136x^14 + 34716886079362208784x^12 + 31708037646565185778430976x^10 + 17074068956994774485619232997376x^8 + 5289719974975064649188570034899779584x^6 + 860456443567863287787024826102919920091136x^4 + 56032264901085762369236000491606259366923075584x^2 + 797517854172776133766249661927470942176176766976
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{16}\cdot 5^{32} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.4
Root			$439.799i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.21.c.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-439.799 - 439.799i) q^{2} +(-48235.4 + 48235.4i) q^{3} -661730. i q^{4} +(5.04058e6 - 8.36421e6i) q^{5} +4.24277e7 q^{6} +(-2.17438e8 - 2.17438e8i) q^{7} +(-7.52190e8 + 7.52190e8i) q^{8} -1.16652e9i q^{9} +O(q^{10})$	\(q+(-439.799 - 439.799i) q^{2} +(-48235.4 + 48235.4i) q^{3} -661730. i q^{4} +(5.04058e6 - 8.36421e6i) q^{5} +4.24277e7 q^{6} +(-2.17438e8 - 2.17438e8i) q^{7} +(-7.52190e8 + 7.52190e8i) q^{8} -1.16652e9i q^{9} +(-5.89541e9 + 1.46173e9i) q^{10} +2.92465e10 q^{11} +(3.19188e10 + 3.19188e10i) q^{12} +(-1.32797e11 + 1.32797e11i) q^{13} +1.91258e11i q^{14} +(1.60317e11 + 6.46585e11i) q^{15} -3.22498e10 q^{16} +(-1.20974e11 - 1.20974e11i) q^{17} +(-5.13033e11 + 5.13033e11i) q^{18} +1.13733e13i q^{19} +(-5.53485e12 - 3.33550e12i) q^{20} +2.09764e13 q^{21} +(-1.28626e13 - 1.28626e13i) q^{22} +(2.06261e11 - 2.06261e11i) q^{23} -7.25644e13i q^{24} +(-4.45526e13 - 8.43209e13i) q^{25} +1.16808e14 q^{26} +(-1.11919e14 - 1.11919e14i) q^{27} +(-1.43886e14 + 1.43886e14i) q^{28} +3.26999e14i q^{29} +(2.13860e14 - 3.54874e14i) q^{30} +5.37589e14 q^{31} +(8.02912e14 + 8.02912e14i) q^{32} +(-1.41072e15 + 1.41072e15i) q^{33} +1.06409e14i q^{34} +(-2.91471e15 + 7.22685e14i) q^{35} -7.71921e14 q^{36} +(2.32105e15 + 2.32105e15i) q^{37} +(5.00197e15 - 5.00197e15i) q^{38} -1.28110e16i q^{39} +(2.50000e15 + 1.00830e16i) q^{40} +6.93055e14 q^{41} +(-9.22541e15 - 9.22541e15i) q^{42} +(-2.46881e15 + 2.46881e15i) q^{43} -1.93533e16i q^{44} +(-9.75701e15 - 5.87993e15i) q^{45} -1.81426e14 q^{46} +(2.52036e16 + 2.52036e16i) q^{47} +(1.55558e15 - 1.55558e15i) q^{48} +1.47666e16i q^{49} +(-1.74901e16 + 5.66784e16i) q^{50} +1.16705e16 q^{51} +(8.78759e16 + 8.78759e16i) q^{52} +(-2.12298e17 + 2.12298e17i) q^{53} +9.84436e16i q^{54} +(1.47419e17 - 2.44624e17i) q^{55} +3.27110e17 q^{56} +(-5.48596e17 - 5.48596e17i) q^{57} +(1.43814e17 - 1.43814e17i) q^{58} -1.07910e17i q^{59} +(4.27865e17 - 1.06086e17i) q^{60} -4.78276e17 q^{61} +(-2.36431e17 - 2.36431e17i) q^{62} +(-2.53646e17 + 2.53646e17i) q^{63} -6.72423e17i q^{64} +(4.41369e17 + 1.78012e18i) q^{65} +1.24086e18 q^{66} +(-9.30171e16 - 9.30171e16i) q^{67} +(-8.00524e16 + 8.00524e16i) q^{68} +1.98981e16i q^{69} +(1.59972e18 + 9.64052e17i) q^{70} -4.63712e18 q^{71} +(8.77444e17 + 8.77444e17i) q^{72} +(-4.17970e18 + 4.17970e18i) q^{73} -2.04159e18i q^{74} +(6.21626e18 + 1.91824e18i) q^{75} +7.52606e18 q^{76} +(-6.35931e18 - 6.35931e18i) q^{77} +(-5.63428e18 + 5.63428e18i) q^{78} -1.74550e19i q^{79} +(-1.62557e17 + 2.69744e17i) q^{80} +1.48643e19 q^{81} +(-3.04805e17 - 3.04805e17i) q^{82} +(-6.68028e18 + 6.68028e18i) q^{83} -1.38807e19i q^{84} +(-1.62164e18 + 4.02074e17i) q^{85} +2.17156e18 q^{86} +(-1.57729e19 - 1.57729e19i) q^{87} +(-2.19989e19 + 2.19989e19i) q^{88} +2.68948e19i q^{89} +(1.70513e18 + 6.87710e18i) q^{90} +5.77504e19 q^{91} +(-1.36489e17 - 1.36489e17i) q^{92} +(-2.59308e19 + 2.59308e19i) q^{93} -2.21690e19i q^{94} +(9.51288e19 + 5.73281e19i) q^{95} -7.74575e19 q^{96} +(2.43424e18 + 2.43424e18i) q^{97} +(6.49432e18 - 6.49432e18i) q^{98} -3.41166e19i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8	$ 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) $ 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8 - 17138778090 * q^10 - 6506343064 * q^11 + 140311795848 * q^12 - 369354655602 * q^13 + 998626204320 * q^15 - 6345876020232 * q^16 + 6508314764998 * q^17 - 11265991705902 * q^18 + 38356516779780 * q^20 - 97402974719064 * q^21 + 161054386758096 * q^22 - 81655963656152 * q^23 + 33913283845350 * q^25 + 234104101103636 * q^26 - 511935279143400 * q^27 + 772213614545352 * q^28 - 877127470680480 * q^30 + 1742256896900736 * q^31 - 4072699683722552 * q^32 + 1579138514189496 * q^33 - 4817791288113440 * q^35 + 2214548622647868 * q^36 + 6383289895587498 * q^37 - 14134212502378200 * q^38 + 43297629431150700 * q^40 - 30602304597564664 * q^41 + 48810732785962896 * q^42 - 46399469942287752 * q^43 + 67947826451186070 * q^45 + 17467214047538136 * q^46 - 137109249757437752 * q^47 - 103698596104819152 * q^48 - 40012852869983150 * q^50 + 686047946059669536 * q^51 - 745026624616846452 * q^52 - 184102027021671302 * q^53 + 752956242406989720 * q^55 + 685775432394721200 * q^56 - 785021725278622800 * q^57 - 2701246502184220800 * q^58 + 6219197632829342760 * q^60 + 49879194030044136 * q^61 - 1190554579738283704 * q^62 - 7082176979112100152 * q^63 + 6907070599410641170 * q^65 + 11227963704975799872 * q^66 - 5597336519263153752 * q^67 - 25617328014464685148 * q^68 + 31706333959370270760 * q^70 + 10983277495574224736 * q^71 - 41525052650392592700 * q^72 - 19072400700441139902 * q^73 + 36766882672050433200 * q^75 + 75630007803532292400 * q^76 - 47766064678699704904 * q^77 - 109239984515466629304 * q^78 + 134231700802559812960 * q^80 + 74219234884008322518 * q^81 - 83501540658117625104 * q^82 - 119739383617210903952 * q^83 + 169044713294843560110 * q^85 + 33497378050769887736 * q^86 - 28944830404542403200 * q^87 - 337125565675837197600 * q^88 + 396784292056608506070 * q^90 + 86281377644254817136 * q^91 - 206921051460419061752 * q^92 - 285487695991878257304 * q^93 + 118106834336527303800 * q^95 + 377091713708556287136 * q^96 - 318608382222604685502 * q^97 - 27697031317753120498 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−439.799	−	439.799i	−0.429491	−	0.429491i	0.458964	−	0.888455i	$-0.348221\pi$
$2$	−439.799	−	439.799i	−0.429491	−	0.429491i	−0.888455	+	0.458964i	$0.848221\pi$
$3$	−48235.4	+	48235.4i	−0.816870	+	0.816870i	−0.985653	−	0.168783i	$-0.946016\pi$
$3$	−48235.4	+	48235.4i	−0.816870	+	0.816870i	0.168783	+	0.985653i	$0.446016\pi$
$4$		−	661730.i		−	0.631075i
$5$	5.04058e6	−	8.36421e6i	0.516155	−	0.856495i
$5$	5.04058e6	−	8.36421e6i	0.516155	−	0.856495i
$6$	4.24277e7			0.701677
$7$	−2.17438e8	−	2.17438e8i	−0.769761	−	0.769761i	0.208304	−	0.978064i	$-0.433206\pi$
$7$	−2.17438e8	−	2.17438e8i	−0.769761	−	0.769761i	−0.978064	+	0.208304i	$0.933206\pi$
$8$	−7.52190e8	+	7.52190e8i	−0.700532	+	0.700532i
$9$		−	1.16652e9i		−	0.334554i
$10$	−5.89541e9	+	1.46173e9i	−0.589541	+	0.146173i
$11$	2.92465e10			1.12758			0.563790	−	0.825919i	$-0.309343\pi$
$11$	2.92465e10			1.12758			0.563790	+	0.825919i	$0.309343\pi$
$12$	3.19188e10	+	3.19188e10i	0.515507	+	0.515507i
$13$	−1.32797e11	+	1.32797e11i	−0.963286	+	0.963286i	−0.999349	−	0.0360639i	$-0.988518\pi$
$13$	−1.32797e11	+	1.32797e11i	−0.963286	+	0.963286i	0.0360639	+	0.999349i	$0.488518\pi$
$14$			1.91258e11i			0.661210i
$15$	1.60317e11	+	6.46585e11i	0.278014	+	1.12128i
$16$	−3.22498e10			−0.0293310
$17$	−1.20974e11	−	1.20974e11i	−0.0600073	−	0.0600073i	0.676466	−	0.736474i	$-0.263510\pi$
$17$	−1.20974e11	−	1.20974e11i	−0.0600073	−	0.0600073i	−0.736474	+	0.676466i	$0.763510\pi$
$18$	−5.13033e11	+	5.13033e11i	−0.143688	+	0.143688i
$19$			1.13733e13i			1.85503i	0.373786	+	0.927515i	$0.378059\pi$
$19$			1.13733e13i			1.85503i	−0.373786	+	0.927515i	$0.621941\pi$
$20$	−5.53485e12	−	3.33550e12i	−0.540513	−	0.325733i
$21$	2.09764e13			1.25759
$22$	−1.28626e13	−	1.28626e13i	−0.484285	−	0.484285i
$23$	2.06261e11	−	2.06261e11i	0.00497895	−	0.00497895i	−0.704613	−	0.709592i	$-0.748879\pi$
$23$	2.06261e11	−	2.06261e11i	0.00497895	−	0.00497895i	0.709592	+	0.704613i	$0.248879\pi$
$24$		−	7.25644e13i		−	1.14449i
$25$	−4.45526e13	−	8.43209e13i	−0.467168	−	0.884169i
$26$	1.16808e14			0.827445
$27$	−1.11919e14	−	1.11919e14i	−0.543583	−	0.543583i
$28$	−1.43886e14	+	1.43886e14i	−0.485777	+	0.485777i
$29$			3.26999e14i			0.777260i	0.921394	+	0.388630i	$0.127051\pi$
$29$			3.26999e14i			0.777260i	−0.921394	+	0.388630i	$0.872949\pi$
$30$	2.13860e14	−	3.54874e14i	0.362174	−	0.600983i
$31$	5.37589e14			0.655894			0.327947	−	0.944696i	$-0.393643\pi$
$31$	5.37589e14			0.655894			0.327947	+	0.944696i	$0.393643\pi$
$32$	8.02912e14	+	8.02912e14i	0.713129	+	0.713129i
$33$	−1.41072e15	+	1.41072e15i	−0.921086	+	0.921086i
$34$			1.06409e14i			0.0515452i
$35$	−2.91471e15	+	7.22685e14i	−1.05661	+	0.261980i
$36$	−7.71921e14			−0.211129
$37$	2.32105e15	+	2.32105e15i	0.482689	+	0.482689i	0.905990	−	0.423300i	$-0.139128\pi$
$37$	2.32105e15	+	2.32105e15i	0.482689	+	0.482689i	−0.423300	+	0.905990i	$0.639128\pi$
$38$	5.00197e15	−	5.00197e15i	0.796718	−	0.796718i
$39$		−	1.28110e16i		−	1.57376i
$40$	2.50000e15	+	1.00830e16i	0.238419	+	0.961585i
$41$	6.93055e14			0.0516332			0.0258166	−	0.999667i	$-0.491781\pi$
$41$	6.93055e14			0.0516332			0.0258166	+	0.999667i	$0.491781\pi$
$42$	−9.22541e15	−	9.22541e15i	−0.540123	−	0.540123i
$43$	−2.46881e15	+	2.46881e15i	−0.114236	+	0.114236i	−0.761914	−	0.647678i	$-0.775740\pi$
$43$	−2.46881e15	+	2.46881e15i	−0.114236	+	0.114236i	0.647678	+	0.761914i	$0.275740\pi$
$44$		−	1.93533e16i		−	0.711587i
$45$	−9.75701e15	−	5.87993e15i	−0.286544	−	0.172682i
$46$	−1.81426e14			−0.00427683
$47$	2.52036e16	+	2.52036e16i	0.479163	+	0.479163i	0.904864	−	0.425701i	$-0.139972\pi$
$47$	2.52036e16	+	2.52036e16i	0.479163	+	0.479163i	−0.425701	+	0.904864i	$0.639972\pi$
$48$	1.55558e15	−	1.55558e15i	0.0239596	−	0.0239596i
$49$			1.47666e16i			0.185063i
$50$	−1.74901e16	+	5.66784e16i	−0.179098	+	0.580387i
$51$	1.16705e16			0.0980364
$52$	8.78759e16	+	8.78759e16i	0.607906	+	0.607906i
$53$	−2.12298e17	+	2.12298e17i	−1.21391	+	1.21391i	−0.244179	+	0.969730i	$0.578519\pi$
$53$	−2.12298e17	+	2.12298e17i	−1.21391	+	1.21391i	−0.969730	+	0.244179i	$0.921481\pi$
$54$			9.84436e16i			0.466928i
$55$	1.47419e17	−	2.44624e17i	0.582006	−	0.965766i
$56$	3.27110e17			1.07848
$57$	−5.48596e17	−	5.48596e17i	−1.51532	−	1.51532i
$58$	1.43814e17	−	1.43814e17i	0.333826	−	0.333826i
$59$		−	1.07910e17i		−	0.211125i	−0.994413	−	0.105563i	$-0.966336\pi$
$59$		−	1.07910e17i		−	0.211125i	0.994413	−	0.105563i	$-0.0336644\pi$
$60$	4.27865e17	−	1.06086e17i	0.707610	−	0.175447i
$61$	−4.78276e17			−0.670471			−0.335235	−	0.942134i	$-0.608816\pi$
$61$	−4.78276e17			−0.670471			−0.335235	+	0.942134i	$0.608816\pi$
$62$	−2.36431e17	−	2.36431e17i	−0.281701	−	0.281701i
$63$	−2.53646e17	+	2.53646e17i	−0.257527	+	0.257527i
$64$		−	6.72423e17i		−	0.583234i
$65$	4.41369e17	+	1.78012e18i	0.327844	+	1.32225i
$66$	1.24086e18			0.791196
$67$	−9.30171e16	−	9.30171e16i	−0.0510287	−	0.0510287i	0.681132	−	0.732161i	$-0.261488\pi$
$67$	−9.30171e16	−	9.30171e16i	−0.0510287	−	0.0510287i	−0.732161	+	0.681132i	$0.761488\pi$
$68$	−8.00524e16	+	8.00524e16i	−0.0378691	+	0.0378691i
$69$			1.98981e16i			0.00813432i
$70$	1.59972e18	+	9.64052e17i	0.566323	+	0.341287i
$71$	−4.63712e18			−1.42451			−0.712254	−	0.701922i	$-0.752326\pi$
$71$	−4.63712e18			−1.42451			−0.712254	+	0.701922i	$0.752326\pi$
$72$	8.77444e17	+	8.77444e17i	0.234366	+	0.234366i
$73$	−4.17970e18	+	4.17970e18i	−0.972561	+	0.972561i	−0.999633	−	0.0270728i	$-0.991381\pi$
$73$	−4.17970e18	+	4.17970e18i	−0.972561	+	0.972561i	0.0270728	+	0.999633i	$0.491381\pi$
$74$		−	2.04159e18i		−	0.414621i
$75$	6.21626e18	+	1.91824e18i	1.10387	+	0.340636i
$76$	7.52606e18			1.17066
$77$	−6.35931e18	−	6.35931e18i	−0.867966	−	0.867966i
$78$	−5.63428e18	+	5.63428e18i	−0.675915	+	0.675915i
$79$		−	1.74550e19i		−	1.84352i	−0.387759	−	0.921761i	$-0.626751\pi$
$79$		−	1.74550e19i		−	1.84352i	0.387759	−	0.921761i	$-0.373249\pi$
$80$	−1.62557e17	+	2.69744e17i	−0.0151393	+	0.0251218i
$81$	1.48643e19			1.22263
$82$	−3.04805e17	−	3.04805e17i	−0.0221760	−	0.0221760i
$83$	−6.68028e18	+	6.68028e18i	−0.430540	+	0.430540i	−0.888812	−	0.458272i	$-0.848469\pi$
$83$	−6.68028e18	+	6.68028e18i	−0.430540	+	0.430540i	0.458272	+	0.888812i	$0.348469\pi$
$84$		−	1.38807e19i		−	0.793633i
$85$	−1.62164e18	+	4.02074e17i	−0.0823691	+	0.0204229i
$86$	2.17156e18			0.0981266
$87$	−1.57729e19	−	1.57729e19i	−0.634920	−	0.634920i
$88$	−2.19989e19	+	2.19989e19i	−0.789905	+	0.789905i
$89$			2.68948e19i			0.862518i	0.902228	+	0.431259i	$0.141931\pi$
$89$			2.68948e19i			0.862518i	−0.902228	+	0.431259i	$0.858069\pi$
$90$	1.70513e18	+	6.87710e18i	0.0489028	+	0.197233i
$91$	5.77504e19			1.48300
$92$	−1.36489e17	−	1.36489e17i	−0.00314209	−	0.00314209i
$93$	−2.59308e19	+	2.59308e19i	−0.535780	+	0.535780i
$94$		−	2.21690e19i		−	0.411592i
$95$	9.51288e19	+	5.73281e19i	1.58882	+	0.957483i
$96$	−7.74575e19			−1.16507
$97$	2.43424e18	+	2.43424e18i	0.0330101	+	0.0330101i	0.723419	−	0.690409i	$-0.242569\pi$
$97$	2.43424e18	+	2.43424e18i	0.0330101	+	0.0330101i	−0.690409	+	0.723419i	$0.742569\pi$
$98$	6.49432e18	−	6.49432e18i	0.0794827	−	0.0794827i
$99$		−	3.41166e19i		−	0.377236i
$100$	−5.57977e19	+	2.94818e19i	−0.557977	+	0.294818i
$101$	−1.40574e20			−1.27260			−0.636299	−	0.771443i	$-0.719535\pi$
$101$	−1.40574e20			−1.27260			−0.636299	+	0.771443i	$0.719535\pi$
$102$	−5.13267e18	−	5.13267e18i	−0.0421057	−	0.0421057i
$103$	1.17405e20	−	1.17405e20i	0.873606	−	0.873606i	−0.119257	−	0.992863i	$-0.538051\pi$
$103$	1.17405e20	−	1.17405e20i	0.873606	−	0.873606i	0.992863	+	0.119257i	$0.0380513\pi$
$104$		−	1.99777e20i		−	1.34962i
$105$	1.05733e20	−	1.75451e20i	0.649111	−	1.07712i
$106$	1.86736e20			1.04273
$107$	−3.53613e19	−	3.53613e19i	−0.179759	−	0.179759i	0.611492	−	0.791251i	$-0.290570\pi$
$107$	−3.53613e19	−	3.53613e19i	−0.179759	−	0.179759i	−0.791251	+	0.611492i	$0.790570\pi$
$108$	−7.40601e19	+	7.40601e19i	−0.343042	+	0.343042i
$109$			4.11650e20i			1.73886i	0.494060	+	0.869428i	$0.335512\pi$
$109$			4.11650e20i			1.73886i	−0.494060	+	0.869428i	$0.664488\pi$
$110$	−1.72420e20	+	4.27504e19i	−0.664754	+	0.164821i
$111$	−2.23914e20			−0.788589
$112$	7.01233e18	+	7.01233e18i	0.0225778	+	0.0225778i
$113$	2.08038e20	−	2.08038e20i	0.612856	−	0.612856i	−0.330833	−	0.943689i	$-0.607330\pi$
$113$	2.08038e20	−	2.08038e20i	0.612856	−	0.612856i	0.943689	+	0.330833i	$0.107330\pi$
$114$			4.82544e20i			1.30163i
$115$	−6.85535e17	−	2.76488e18i	−0.00169454	−	0.00683436i
$116$	2.16385e20			0.490509
$117$	1.54910e20	+	1.54910e20i	0.322271	+	0.322271i
$118$	−4.74585e19	+	4.74585e19i	−0.0906764	+	0.0906764i
$119$			5.26089e19i			0.0923825i
$120$	−6.06944e20	−	3.65766e20i	−0.980248	−	0.590733i
$121$	1.82608e20			0.271434
$122$	2.10345e20	+	2.10345e20i	0.287961	+	0.287961i
$123$	−3.34298e19	+	3.34298e19i	−0.0421777	+	0.0421777i
$124$		−	3.55739e20i		−	0.413918i
$125$	−9.29848e20	−	5.23790e19i	−0.998417	−	0.0562416i
$126$	2.23106e20			0.221211
$127$	5.35939e20	+	5.35939e20i	0.490996	+	0.490996i	0.908620	−	0.417624i	$-0.137137\pi$
$127$	5.35939e20	+	5.35939e20i	0.490996	+	0.490996i	−0.417624	+	0.908620i	$0.637137\pi$
$128$	5.46184e20	−	5.46184e20i	0.462636	−	0.462636i
$129$		−	2.38168e20i		−	0.186632i
$130$	5.88780e20	−	9.77006e20i	0.427090	−	0.708702i
$131$	−2.38985e21			−1.60568			−0.802839	−	0.596196i	$-0.796678\pi$
$131$	−2.38985e21			−1.60568			−0.802839	+	0.596196i	$0.796678\pi$
$132$	9.33513e20	+	9.33513e20i	0.581274	+	0.581274i
$133$	2.47299e21	−	2.47299e21i	1.42793	−	1.42793i
$134$			8.18176e19i			0.0438327i
$135$	−1.50025e21	+	3.71977e20i	−0.746149	+	0.185003i
$136$	1.81992e20			0.0840741
$137$	−1.13067e21	−	1.13067e21i	−0.485436	−	0.485436i	0.421427	−	0.906863i	$-0.361530\pi$
$137$	−1.13067e21	−	1.13067e21i	−0.485436	−	0.485436i	−0.906863	+	0.421427i	$0.861530\pi$
$138$	8.75117e18	−	8.75117e18i	0.00349362	−	0.00349362i
$139$			1.17195e21i			0.435271i	0.976030	+	0.217635i	$0.0698343\pi$
$139$			1.17195e21i			0.435271i	−0.976030	+	0.217635i	$0.930166\pi$
$140$	4.78222e20	+	1.92875e21i	0.165329	+	0.666802i
$141$	−2.43141e21			−0.782828
$142$	2.03940e21	+	2.03940e21i	0.611813	+	0.611813i
$143$	−3.88385e21	+	3.88385e21i	−1.08618	+	1.08618i
$144$			3.76200e19i			0.00981281i
$145$	2.73509e21	+	1.64826e21i	0.665719	+	0.401187i
$146$	3.67645e21			0.835412
$147$	−7.12271e20	−	7.12271e20i	−0.151172	−	0.151172i
$148$	1.53591e21	−	1.53591e21i	0.304613	−	0.304613i
$149$			3.27221e21i			0.606707i	0.952878	+	0.303354i	$0.0981063\pi$
$149$			3.27221e21i			0.606707i	−0.952878	+	0.303354i	$0.901894\pi$
$150$	−1.89026e21	−	3.57754e21i	−0.327801	−	0.620401i
$151$	8.67493e21			1.40766			0.703828	−	0.710370i	$-0.251472\pi$
$151$	8.67493e21			1.40766			0.703828	+	0.710370i	$0.251472\pi$
$152$	−8.55490e21	−	8.55490e21i	−1.29951	−	1.29951i
$153$	−1.41119e20	+	1.41119e20i	−0.0200757	+	0.0200757i
$154$			5.59363e21i			0.745567i
$155$	2.70976e21	−	4.49651e21i	0.338543	−	0.561770i
$156$	−8.47745e21			−0.993160
$157$	1.35685e21	+	1.35685e21i	0.149119	+	0.149119i	0.777725	−	0.628605i	$-0.216374\pi$
$157$	1.35685e21	+	1.35685e21i	0.149119	+	0.149119i	−0.628605	+	0.777725i	$0.716374\pi$
$158$	−7.67667e21	+	7.67667e21i	−0.791776	+	0.791776i
$159$		−	2.04805e22i		−	1.98321i
$160$	1.07629e22	−	2.66858e21i	0.978877	−	0.242706i
$161$	−8.96980e19			−0.00766521
$162$	−6.53730e21	−	6.53730e21i	−0.525107	−	0.525107i
$163$	4.71825e21	−	4.71825e21i	0.356373	−	0.356373i	−0.506101	−	0.862474i	$-0.668914\pi$
$163$	4.71825e21	−	4.71825e21i	0.356373	−	0.356373i	0.862474	+	0.506101i	$0.168914\pi$
$164$		−	4.58616e20i		−	0.0325844i
$165$	4.68870e21	+	1.89103e22i	0.313482	+	1.26433i
$166$	5.87596e21			0.369826
$167$	8.95766e21	+	8.95766e21i	0.530921	+	0.530921i	0.920846	−	0.389926i	$-0.127499\pi$
$167$	8.95766e21	+	8.95766e21i	0.530921	+	0.530921i	−0.389926	+	0.920846i	$0.627499\pi$
$168$	−1.57783e22	+	1.57783e22i	−0.880981	+	0.880981i
$169$		−	1.62652e22i		−	0.855838i
$170$	8.90025e20	+	5.36362e20i	0.0441482	+	0.0266053i
$171$	1.32672e22			0.620608
$172$	1.63368e21	+	1.63368e21i	0.0720915	+	0.0720915i
$173$	−2.05146e22	+	2.05146e22i	−0.854282	+	0.854282i	−0.990657	−	0.136375i	$-0.956455\pi$
$173$	−2.05146e22	+	2.05146e22i	−0.854282	+	0.854282i	0.136375	+	0.990657i	$0.456455\pi$
$174$			1.38738e22i			0.545385i
$175$	−8.64716e21	+	2.80220e22i	−0.320991	+	1.04021i
$176$	−9.43193e20			−0.0330730
$177$	5.20506e21	+	5.20506e21i	0.172462	+	0.172462i
$178$	1.18283e22	−	1.18283e22i	0.370444	−	0.370444i
$179$		−	4.23376e22i		−	1.25371i	−0.779137	−	0.626854i	$-0.784342\pi$
$179$		−	4.23376e22i		−	1.25371i	0.779137	−	0.626854i	$-0.215658\pi$
$180$	−3.89093e21	+	6.45651e21i	−0.108975	+	0.180831i
$181$	−2.46017e22			−0.651898			−0.325949	−	0.945387i	$-0.605684\pi$
$181$	−2.46017e22			−0.651898			−0.325949	+	0.945387i	$0.605684\pi$
$182$	−2.53985e22	−	2.53985e22i	−0.636934	−	0.636934i
$183$	2.30698e22	−	2.30698e22i	0.547688	−	0.547688i
$184$			3.10295e20i			0.00697583i
$185$	3.11132e22	−	7.71432e21i	0.662564	−	0.164278i
$186$	2.28087e22			0.460226
$187$	−3.53808e21	−	3.53808e21i	−0.0676630	−	0.0676630i
$188$	1.66780e22	−	1.66780e22i	0.302388	−	0.302388i
$189$			4.86709e22i			0.836857i
$190$	−1.66247e22	−	6.70503e22i	−0.271155	−	1.09362i
$191$	1.02010e22			0.157873			0.0789364	−	0.996880i	$-0.474848\pi$
$191$	1.02010e22			0.157873			0.0789364	+	0.996880i	$0.474848\pi$
$192$	3.24346e22	+	3.24346e22i	0.476427	+	0.476427i
$193$	−3.03807e22	+	3.03807e22i	−0.423667	+	0.423667i	−0.886464	−	0.462797i	$-0.846846\pi$
$193$	−3.03807e22	+	3.03807e22i	−0.423667	+	0.423667i	0.462797	+	0.886464i	$0.346846\pi$
$194$		−	2.14115e21i		−	0.0283550i
$195$	−1.07154e23	−	6.45750e22i	−1.34792	−	0.812304i
$196$	9.77149e21			0.116788
$197$	−3.46738e22	−	3.46738e22i	−0.393858	−	0.393858i	0.482202	−	0.876060i	$-0.339837\pi$
$197$	−3.46738e22	−	3.46738e22i	−0.393858	−	0.393858i	−0.876060	+	0.482202i	$0.839837\pi$
$198$	−1.50044e22	+	1.50044e22i	−0.162020	+	0.162020i
$199$			8.14208e22i			0.835997i	0.908448	+	0.417998i	$0.137268\pi$
$199$			8.14208e22i			0.835997i	−0.908448	+	0.417998i	$0.862732\pi$
$200$	9.69374e22	+	2.99134e22i	0.946654	+	0.292123i
$201$	8.97343e21			0.0833677
$202$	6.18242e22	+	6.18242e22i	0.546569	+	0.546569i
$203$	7.11020e22	−	7.11020e22i	0.598304	−	0.598304i
$204$		−	7.72272e21i		−	0.0618683i
$205$	3.49340e21	−	5.79686e21i	0.0266508	−	0.0442236i
$206$	−1.03269e23			−0.750412
$207$	−2.40607e20	−	2.40607e20i	−0.00166573	−	0.00166573i
$208$	4.28267e21	−	4.28267e21i	0.0282541	−	0.0282541i
$209$			3.32630e23i			2.09169i
$210$	−1.23665e23	+	3.06619e22i	−0.741400	+	0.183825i
$211$	−2.99408e23			−1.71175			−0.855873	−	0.517185i	$-0.826980\pi$
$211$	−2.99408e23			−1.71175			−0.855873	+	0.517185i	$0.826980\pi$
$212$	1.40484e23	+	1.40484e23i	0.766068	+	0.766068i
$213$	2.23673e23	−	2.23673e23i	1.16364	−	1.16364i
$214$			3.11037e22i			0.154410i
$215$	8.20541e21	+	3.30938e22i	0.0388790	+	0.156806i
$216$	1.68369e23			0.761594
$217$	−1.16893e23	−	1.16893e23i	−0.504881	−	0.504881i
$218$	1.81043e23	−	1.81043e23i	0.746823	−	0.746823i
$219$		−	4.03219e23i		−	1.58891i
$220$	−1.61875e23	−	9.75518e22i	−0.609471	−	0.367289i
$221$	3.21301e22			0.115608
$222$	9.84770e22	+	9.84770e22i	0.338692	+	0.338692i
$223$	2.93012e22	−	2.93012e22i	0.0963468	−	0.0963468i	−0.657291	−	0.753637i	$-0.728298\pi$
$223$	2.93012e22	−	2.93012e22i	0.0963468	−	0.0963468i	0.753637	+	0.657291i	$0.228298\pi$
$224$		−	3.49168e23i		−	1.09788i
$225$	−9.83619e22	+	5.19714e22i	−0.295802	+	0.156293i
$226$	−1.82990e23			−0.526432
$227$	−6.81571e22	−	6.81571e22i	−0.187609	−	0.187609i	0.607053	−	0.794661i	$-0.292352\pi$
$227$	−6.81571e22	−	6.81571e22i	−0.187609	−	0.187609i	−0.794661	+	0.607053i	$0.792352\pi$
$228$	−3.63023e23	+	3.63023e23i	−0.956280	+	0.956280i
$229$			3.46118e23i			0.872709i	0.899775	+	0.436355i	$0.143731\pi$
$229$			3.46118e23i			0.872709i	−0.899775	+	0.436355i	$0.856269\pi$
$230$	−9.14494e20	+	1.51749e21i	−0.00220751	+	0.00366309i
$231$	6.13487e23			1.41803
$232$	−2.45965e23	−	2.45965e23i	−0.544495	−	0.544495i
$233$	−3.13363e23	+	3.13363e23i	−0.664491	+	0.664491i	−0.956435	−	0.291944i	$-0.905698\pi$
$233$	−3.13363e23	+	3.13363e23i	−0.664491	+	0.664491i	0.291944	+	0.956435i	$0.405698\pi$
$234$		−	1.36259e23i		−	0.276825i
$235$	3.37848e23	−	8.37674e22i	0.657723	−	0.163078i
$236$	−7.14071e22			−0.133236
$237$	8.41947e23	+	8.41947e23i	1.50592	+	1.50592i
$238$	2.31373e22	−	2.31373e22i	0.0396775	−	0.0396775i
$239$			2.33099e23i			0.383320i	0.981461	+	0.191660i	$0.0613871\pi$
$239$			2.33099e23i			0.383320i	−0.981461	+	0.191660i	$0.938613\pi$
$240$	−5.17017e21	−	2.08522e22i	−0.00815441	−	0.0328882i
$241$	−5.21330e22			−0.0788756			−0.0394378	−	0.999222i	$-0.512557\pi$
$241$	−5.21330e22			−0.0788756			−0.0394378	+	0.999222i	$0.512557\pi$
$242$	−8.03106e22	−	8.03106e22i	−0.116579	−	0.116579i
$243$	−3.26748e23	+	3.26748e23i	−0.455146	+	0.455146i
$244$			3.16489e23i			0.423118i
$245$	1.23511e23	+	7.44321e22i	0.158505	+	0.0955211i
$246$	2.94047e22			0.0362298
$247$	−1.51034e24	−	1.51034e24i	−1.78692	−	1.78692i
$248$	−4.04370e23	+	4.04370e23i	−0.459475	+	0.459475i
$249$		−	6.44452e23i		−	0.703391i
$250$	3.85910e23	+	4.31982e23i	0.404656	+	0.452966i
$251$	1.50915e24			1.52054			0.760268	−	0.649610i	$-0.225068\pi$
$251$	1.50915e24			1.52054			0.760268	+	0.649610i	$0.225068\pi$
$252$	1.67845e23	+	1.67845e23i	0.162519	+	0.162519i
$253$	6.03240e21	−	6.03240e21i	0.00561417	−	0.00561417i
$254$		−	4.71410e23i		−	0.421757i
$255$	5.88260e22	−	9.76144e22i	0.0506020	−	0.0839677i
$256$	−1.18551e24			−0.980630
$257$	−7.22221e23	−	7.22221e23i	−0.574564	−	0.574564i	0.358836	−	0.933401i	$-0.383174\pi$
$257$	−7.22221e23	−	7.22221e23i	−0.574564	−	0.574564i	−0.933401	+	0.358836i	$0.883174\pi$
$258$	−1.04746e23	+	1.04746e23i	−0.0801567	+	0.0801567i
$259$		−	1.00937e24i		−	0.743111i
$260$	1.17796e24	−	2.92067e23i	0.834442	−	0.206895i
$261$	3.81450e23			0.260036
$262$	1.05105e24	+	1.05105e24i	0.689624	+	0.689624i
$263$	1.33366e24	−	1.33366e24i	0.842342	−	0.842342i	−0.146821	−	0.989163i	$-0.546904\pi$
$263$	1.33366e24	−	1.33366e24i	0.842342	−	0.842342i	0.989163	+	0.146821i	$0.0469042\pi$
$264$		−	2.12225e24i		−	1.29050i
$265$	7.05599e23	+	2.84580e24i	0.413142	+	1.66627i
$266$	−2.17524e24			−1.22656
$267$	−1.29728e24	−	1.29728e24i	−0.704566	−	0.704566i
$268$	−6.15522e22	+	6.15522e22i	−0.0322030	+	0.0322030i
$269$			3.34326e24i			1.68518i	0.538554	+	0.842591i	$0.318971\pi$
$269$			3.34326e24i			1.68518i	−0.538554	+	0.842591i	$0.681029\pi$
$270$	8.23403e23	+	4.96212e23i	0.399921	+	0.241007i
$271$	7.83272e21			0.00366623			0.00183312	−	0.999998i	$-0.499417\pi$
$271$	7.83272e21			0.00366623			0.00183312	+	0.999998i	$0.499417\pi$
$272$	3.90140e21	+	3.90140e21i	0.00176007	+	0.00176007i
$273$	−2.78561e24	+	2.78561e24i	−1.21142	+	1.21142i
$274$			9.94538e23i			0.416981i
$275$	−1.30301e24	−	2.46609e24i	−0.526768	−	0.996970i
$276$	1.31672e22			0.00513337
$277$	1.75043e24	+	1.75043e24i	0.658185	+	0.658185i	0.954950	−	0.296765i	$-0.0959079\pi$
$277$	1.75043e24	+	1.75043e24i	0.658185	+	0.658185i	−0.296765	+	0.954950i	$0.595908\pi$
$278$	5.15420e23	−	5.15420e23i	0.186945	−	0.186945i
$279$		−	6.27108e23i		−	0.219432i
$280$	1.64882e24	−	2.73602e24i	0.556665	−	0.923716i
$281$	1.50772e24			0.491198			0.245599	−	0.969372i	$-0.421015\pi$
$281$	1.50772e24			0.491198			0.245599	+	0.969372i	$0.421015\pi$
$282$	1.06933e24	+	1.06933e24i	0.336218	+	0.336218i
$283$	8.13508e23	−	8.13508e23i	0.246886	−	0.246886i	−0.572805	−	0.819692i	$-0.694145\pi$
$283$	8.13508e23	−	8.13508e23i	0.246886	−	0.246886i	0.819692	+	0.572805i	$0.194145\pi$
$284$			3.06852e24i			0.898972i
$285$	−7.35381e24	+	1.82333e24i	−2.08000	+	0.515723i
$286$	3.41622e24			0.933009
$287$	−1.50697e23	−	1.50697e23i	−0.0397452	−	0.0397452i
$288$	9.36612e23	−	9.36612e23i	0.238581	−	0.238581i
$289$		−	4.03496e24i		−	0.992798i
$290$	−4.77983e23	−	1.92779e24i	−0.113614	−	0.458226i
$291$	−2.34833e23			−0.0539299
$292$	2.76584e24	+	2.76584e24i	0.613759	+	0.613759i
$293$	5.57634e23	−	5.57634e23i	0.119584	−	0.119584i	−0.644782	−	0.764366i	$-0.723052\pi$
$293$	5.57634e23	−	5.57634e23i	0.119584	−	0.119584i	0.764366	+	0.644782i	$0.223052\pi$
$294$			6.26512e23i			0.129854i
$295$	−9.02579e23	−	5.43927e23i	−0.180828	−	0.108973i
$296$	−3.49175e24			−0.676279
$297$	−3.27324e24	−	3.27324e24i	−0.612933	−	0.612933i
$298$	1.43912e24	−	1.43912e24i	0.260575	−	0.260575i
$299$			5.47817e22i			0.00959231i
$300$	1.26936e24	−	4.11349e24i	0.214967	−	0.696623i
$301$	1.07363e24			0.175869
$302$	−3.81522e24	−	3.81522e24i	−0.604576	−	0.604576i
$303$	6.78063e24	−	6.78063e24i	1.03955	−	1.03955i
$304$		−	3.66787e23i		−	0.0544099i
$305$	−2.41079e24	+	4.00040e24i	−0.346067	+	0.574255i
$306$	1.24128e23			0.0172447
$307$	2.72803e24	+	2.72803e24i	0.366831	+	0.366831i	0.866320	−	0.499489i	$-0.166479\pi$
$307$	2.72803e24	+	2.72803e24i	0.366831	+	0.366831i	−0.499489	+	0.866320i	$0.666479\pi$
$308$	−4.20815e24	+	4.20815e24i	−0.547752	+	0.547752i
$309$			1.13262e25i			1.42725i
$310$	−3.16931e24	+	7.85810e23i	−0.386676	+	0.0958739i
$311$	−6.13785e24			−0.725124			−0.362562	−	0.931960i	$-0.618098\pi$
$311$	−6.13785e24			−0.725124			−0.362562	+	0.931960i	$0.618098\pi$
$312$	9.63634e24	+	9.63634e24i	1.10247	+	1.10247i
$313$	1.07045e25	−	1.07045e25i	1.18610	−	1.18610i	0.207966	−	0.978136i	$-0.433316\pi$
$313$	1.07045e25	−	1.07045e25i	1.18610	−	1.18610i	0.978136	−	0.207966i	$-0.0666843\pi$
$314$		−	1.19348e24i		−	0.128091i
$315$	8.43025e23	+	3.40007e24i	0.0876466	+	0.353494i
$316$	−1.15505e25			−1.16340
$317$	8.07543e24	+	8.07543e24i	0.788085	+	0.788085i	0.981180	−	0.193095i	$-0.0618525\pi$
$317$	8.07543e24	+	8.07543e24i	0.788085	+	0.788085i	−0.193095	+	0.981180i	$0.561852\pi$
$318$	−9.00730e24	+	9.00730e24i	−0.851772	+	0.851772i
$319$			9.56357e24i			0.876422i
$320$	−5.62429e24	−	3.38940e24i	−0.499537	−	0.301039i
$321$	3.41134e24			0.293680
$322$	3.94490e22	+	3.94490e22i	0.00329214	+	0.00329214i
$323$	1.37588e24	−	1.37588e24i	0.111315	−	0.111315i
$324$		−	9.83616e24i		−	0.771570i
$325$	1.71140e25	+	5.28112e24i	1.30172	+	0.401691i
$326$	−4.15016e24			−0.306118
$327$	−1.98561e25	−	1.98561e25i	−1.42042	−	1.42042i
$328$	−5.21310e23	+	5.21310e23i	−0.0361707	+	0.0361707i
$329$		−	1.09604e25i		−	0.737682i
$330$	6.25466e24	−	1.03788e25i	0.408380	−	0.677655i
$331$	1.02880e25			0.651703			0.325852	−	0.945421i	$-0.394349\pi$
$331$	1.02880e25			0.651703			0.325852	+	0.945421i	$0.394349\pi$
$332$	4.42054e24	+	4.42054e24i	0.271703	+	0.271703i
$333$	2.70755e24	−	2.70755e24i	0.161486	−	0.161486i
$334$		−	7.87913e24i		−	0.456051i
$335$	−1.24687e24	+	3.09155e23i	−0.0700446	+	0.0173671i
$336$	−6.76485e23			−0.0368863
$337$	−1.90017e25	−	1.90017e25i	−1.00576	−	1.00576i	−0.999983	−	0.00577643i	$-0.998161\pi$
$337$	−1.90017e25	−	1.90017e25i	−1.00576	−	1.00576i	−0.00577643	−	0.999983i	$-0.501839\pi$
$338$	−7.15340e24	+	7.15340e24i	−0.367575	+	0.367575i
$339$			2.00696e25i			1.00125i
$340$	2.66065e23	+	1.07309e24i	0.0128884	+	0.0519811i
$341$	1.57226e25			0.739572
$342$	−5.83489e24	−	5.83489e24i	−0.266546	−	0.266546i
$343$	−1.41391e25	+	1.41391e25i	−0.627307	+	0.627307i
$344$		−	3.71403e24i		−	0.160052i
$345$	1.66432e23	+	1.00298e23i	0.00696701	+	0.00419857i
$346$	1.80446e25			0.733813
$347$	−6.18237e24	−	6.18237e24i	−0.244264	−	0.244264i	0.574347	−	0.818612i	$-0.305256\pi$
$347$	−6.18237e24	−	6.18237e24i	−0.244264	−	0.244264i	−0.818612	+	0.574347i	$0.805256\pi$
$348$	−1.04374e25	+	1.04374e25i	−0.400682	+	0.400682i
$349$		−	1.41295e25i		−	0.527075i	−0.964649	−	0.263538i	$-0.915111\pi$
$349$		−	1.41295e25i		−	0.527075i	0.964649	−	0.263538i	$-0.0848893\pi$
$350$	1.61271e25	−	8.52104e24i	0.584622	−	0.308896i
$351$	2.97250e25			1.04725
$352$	2.34824e25	+	2.34824e25i	0.804110	+	0.804110i
$353$	−5.62213e24	+	5.62213e24i	−0.187135	+	0.187135i	−0.794456	−	0.607322i	$-0.792244\pi$
$353$	−5.62213e24	+	5.62213e24i	−0.187135	+	0.187135i	0.607322	+	0.794456i	$0.292244\pi$
$354$		−	4.57836e24i		−	0.148142i
$355$	−2.33738e25	+	3.87858e25i	−0.735267	+	1.22008i
$356$	1.77971e25			0.544314
$357$	−2.53761e24	−	2.53761e24i	−0.0754646	−	0.0754646i
$358$	−1.86200e25	+	1.86200e25i	−0.538456	+	0.538456i
$359$		−	1.89467e25i		−	0.532832i	−0.963858	−	0.266416i	$-0.914161\pi$
$359$		−	1.89467e25i		−	0.532832i	0.963858	−	0.266416i	$-0.0858394\pi$
$360$	1.17620e25	−	2.91630e24i	0.321703	−	0.0797641i
$361$	−9.17622e25			−2.44114
$362$	1.08198e25	+	1.08198e25i	0.279984	+	0.279984i
$363$	−8.80814e24	+	8.80814e24i	−0.221727	+	0.221727i
$364$		−	3.82152e25i		−	0.935884i
$365$	1.38918e25	+	5.60280e25i	0.331001	+	1.33499i
$366$	−2.02921e25			−0.470454
$367$	−1.11215e24	−	1.11215e24i	−0.0250901	−	0.0250901i	0.694450	−	0.719541i	$-0.255648\pi$
$367$	−1.11215e24	−	1.11215e24i	−0.0250901	−	0.0250901i	−0.719541	+	0.694450i	$0.755648\pi$
$368$	−6.65186e21	+	6.65186e21i	−0.000146038	+	0.000146038i
$369$		−	8.08462e23i		−	0.0172741i
$370$	−1.70763e25	−	1.02908e25i	−0.355121	−	0.214009i
$371$	9.23232e25			1.86884
$372$	1.71592e25	+	1.71592e25i	0.338118	+	0.338118i
$373$	4.51612e25	−	4.51612e25i	0.866318	−	0.866318i	−0.125745	−	0.992063i	$-0.540132\pi$
$373$	4.51612e25	−	4.51612e25i	0.866318	−	0.866318i	0.992063	+	0.125745i	$0.0401320\pi$
$374$			3.11208e24i			0.0581213i
$375$	4.73781e25	−	4.23251e25i	0.861519	−	0.769635i
$376$	−3.79158e25			−0.671338
$377$	−4.34245e25	−	4.34245e25i	−0.748723	−	0.748723i
$378$	2.14054e25	−	2.14054e25i	0.359423	−	0.359423i
$379$		−	2.27694e25i		−	0.372357i	−0.982516	−	0.186178i	$-0.940390\pi$
$379$		−	2.27694e25i		−	0.372357i	0.982516	−	0.186178i	$-0.0596102\pi$
$380$	3.79357e25	−	6.29496e25i	0.604244	−	1.00267i
$381$	−5.17024e25			−0.802160
$382$	−4.48637e24	−	4.48637e24i	−0.0678049	−	0.0678049i
$383$	−4.76226e25	+	4.76226e25i	−0.701173	+	0.701173i	−0.964662	−	0.263489i	$-0.915127\pi$
$383$	−4.76226e25	+	4.76226e25i	−0.701173	+	0.701173i	0.263489	+	0.964662i	$0.415127\pi$
$384$			5.26908e25i			0.755827i
$385$	−8.52452e25	+	2.11360e25i	−1.19141	+	0.295403i
$386$	2.67228e25			0.363922
$387$	2.87991e24	+	2.87991e24i	0.0382181	+	0.0382181i
$388$	1.61081e24	−	1.61081e24i	0.0208318	−	0.0208318i
$389$		−	1.13634e25i		−	0.143223i	−0.997433	−	0.0716116i	$-0.977186\pi$
$389$		−	1.13634e25i		−	0.143223i	0.997433	−	0.0716116i	$-0.0228142\pi$
$390$	1.87263e25	+	7.55263e25i	0.230041	+	0.927795i
$391$	−4.99045e22			−0.000597548
$392$	−1.11073e25	−	1.11073e25i	−0.129642	−	0.129642i
$393$	1.15276e26	−	1.15276e26i	1.31163	−	1.31163i
$394$			3.04990e25i			0.338316i
$395$	−1.45997e26	−	8.79831e25i	−1.57897	−	0.951543i
$396$	−2.25760e25			−0.238065
$397$	6.78782e25	+	6.78782e25i	0.697951	+	0.697951i	0.963968	−	0.266017i	$-0.0857078\pi$
$397$	6.78782e25	+	6.78782e25i	0.697951	+	0.697951i	−0.266017	+	0.963968i	$0.585708\pi$
$398$	3.58088e25	−	3.58088e25i	0.359053	−	0.359053i
$399$			2.38572e26i			2.33287i
$400$	1.43681e24	+	2.71933e24i	0.0137025	+	0.0259335i
$401$	5.90231e25			0.549007			0.274504	−	0.961586i	$-0.411486\pi$
$401$	5.90231e25			0.549007			0.274504	+	0.961586i	$0.411486\pi$
$402$	−3.94650e24	−	3.94650e24i	−0.0358057	−	0.0358057i
$403$	−7.13903e25	+	7.13903e25i	−0.631813	+	0.631813i
$404$			9.30220e25i			0.803104i
$405$	7.49247e25	−	1.24328e26i	0.631066	−	1.04717i
$406$	−6.25412e25			−0.513932
$407$	6.78827e25	+	6.78827e25i	0.544270	+	0.544270i
$408$	−8.77843e24	+	8.77843e24i	−0.0686776	+	0.0686776i
$409$		−	1.06791e25i		−	0.0815272i	−0.999169	−	0.0407636i	$-0.987021\pi$
$409$		−	1.06791e25i		−	0.0815272i	0.999169	−	0.0407636i	$-0.0129790\pi$
$410$	−4.08584e24	+	1.01306e24i	−0.0304399	+	0.00754738i
$411$	1.09077e26			0.793076
$412$	−7.76907e25	−	7.76907e25i	−0.551311	−	0.551311i
$413$	−2.34637e25	+	2.34637e25i	−0.162516	+	0.162516i
$414$			2.11637e23i			0.00143083i
$415$	2.22028e25	+	8.95478e25i	0.146530	+	0.590981i
$416$	−2.13249e26			−1.37389
$417$	−5.65292e25	−	5.65292e25i	−0.355560	−	0.355560i
$418$	1.46290e26	−	1.46290e26i	0.898363	−	0.898363i
$419$		−	5.03380e25i		−	0.301825i	−0.988547	−	0.150913i	$-0.951779\pi$
$419$		−	5.03380e25i		−	0.301825i	0.988547	−	0.150913i	$-0.0482212\pi$
$420$	−1.16101e26	−	6.99670e25i	−0.679743	−	0.409638i
$421$	4.64309e25			0.265452			0.132726	−	0.991153i	$-0.457627\pi$
$421$	4.64309e25			0.265452			0.132726	+	0.991153i	$0.457627\pi$
$422$	1.31679e26	+	1.31679e26i	0.735180	+	0.735180i
$423$	2.94004e25	−	2.94004e25i	0.160306	−	0.160306i
$424$		−	3.19376e26i		−	1.70076i
$425$	−4.81095e24	+	1.55904e25i	−0.0250231	+	0.0810901i
$426$	−1.96742e26			−0.999544
$427$	1.03995e26	+	1.03995e26i	0.516102	+	0.516102i
$428$	−2.33997e25	+	2.33997e25i	−0.113442	+	0.113442i
$429$		−	3.74678e26i		−	1.77454i
$430$	1.09459e25	−	1.81634e25i	0.0506485	−	0.0840449i
$431$	−1.21487e25			−0.0549235			−0.0274618	−	0.999623i	$-0.508742\pi$
$431$	−1.21487e25			−0.0549235			−0.0274618	+	0.999623i	$0.508742\pi$
$432$	3.60936e24	+	3.60936e24i	0.0159438	+	0.0159438i
$433$	2.04913e26	−	2.04913e26i	0.884486	−	0.884486i	−0.109501	−	0.993987i	$-0.534925\pi$
$433$	2.04913e26	−	2.04913e26i	0.884486	−	0.884486i	0.993987	+	0.109501i	$0.0349252\pi$
$434$			1.02818e26i			0.433684i
$435$	−2.11432e26	+	5.24233e25i	−0.871523	+	0.216089i
$436$	2.72402e26			1.09735
$437$	2.34587e24	+	2.34587e24i	0.00923611	+	0.00923611i
$438$	−1.77335e26	+	1.77335e26i	−0.682423	+	0.682423i
$439$			4.05743e26i			1.52618i	0.646292	+	0.763090i	$0.276319\pi$
$439$			4.05743e26i			1.52618i	−0.646292	+	0.763090i	$0.723681\pi$
$440$	7.31163e25	+	2.94891e26i	0.268836	+	1.08426i
$441$	1.72255e25			0.0619135
$442$	−1.41308e25	−	1.41308e25i	−0.0496527	−	0.0496527i
$443$	−1.35510e26	+	1.35510e26i	−0.465516	+	0.465516i	−0.900458	−	0.434942i	$-0.856769\pi$
$443$	−1.35510e26	+	1.35510e26i	−0.465516	+	0.465516i	0.434942	+	0.900458i	$0.356769\pi$
$444$			1.48170e26i			0.497659i
$445$	2.24954e26	+	1.35565e26i	0.738743	+	0.445193i
$446$	−2.57733e25			−0.0827601
$447$	−1.57836e26	−	1.57836e26i	−0.495601	−	0.495601i
$448$	−1.46211e26	+	1.46211e26i	−0.448951	+	0.448951i
$449$		−	3.31599e26i		−	0.995749i	−0.867249	−	0.497875i	$-0.834114\pi$
$449$		−	3.31599e26i		−	0.995749i	0.867249	−	0.497875i	$-0.165886\pi$
$450$	6.61164e25	+	2.04025e25i	0.194171	+	0.0599181i
$451$	2.02694e25			0.0582205
$452$	−1.37665e26	−	1.37665e26i	−0.386758	−	0.386758i
$453$	−4.18439e26	+	4.18439e26i	−1.14987	+	1.14987i
$454$			5.99508e25i			0.161152i
$455$	2.91095e26	−	4.83036e26i	0.765457	−	1.27018i
$456$	8.25297e26			2.12306
$457$	−2.15736e25	−	2.15736e25i	−0.0542951	−	0.0542951i	0.679438	−	0.733733i	$-0.262224\pi$
$457$	−2.15736e25	−	2.15736e25i	−0.0542951	−	0.0542951i	−0.733733	+	0.679438i	$0.762224\pi$
$458$	1.52222e26	−	1.52222e26i	0.374821	−	0.374821i
$459$			2.70786e25i			0.0652379i
$460$	−1.82961e24	+	4.53639e23i	−0.00431300	+	0.00106938i
$461$	−5.32970e26			−1.22940			−0.614700	−	0.788761i	$-0.710723\pi$
$461$	−5.32970e26			−1.22940			−0.614700	+	0.788761i	$0.710723\pi$
$462$	−2.69811e26	−	2.69811e26i	−0.609031	−	0.609031i
$463$	−2.32531e26	+	2.32531e26i	−0.513654	+	0.513654i	−0.915644	−	0.401990i	$-0.868319\pi$
$463$	−2.32531e26	+	2.32531e26i	−0.513654	+	0.513654i	0.401990	+	0.915644i	$0.368319\pi$
$464$		−	1.05456e25i		−	0.0227978i
$465$	8.61845e25	+	3.47597e26i	0.182347	+	0.735439i
$466$	2.75634e26			0.570785
$467$	−2.28694e26	−	2.28694e26i	−0.463538	−	0.463538i	0.436275	−	0.899813i	$-0.356297\pi$
$467$	−2.28694e26	−	2.28694e26i	−0.463538	−	0.463538i	−0.899813	+	0.436275i	$0.856297\pi$
$468$	1.02509e26	−	1.02509e26i	0.203377	−	0.203377i
$469$			4.04510e25i			0.0785598i
$470$	−1.85426e26	−	1.11745e26i	−0.352527	−	0.212446i
$471$	−1.30896e26			−0.243622
$472$	8.11686e25	+	8.11686e25i	0.147900	+	0.147900i
$473$	−7.22040e25	+	7.22040e25i	−0.128810	+	0.128810i
$474$		−	7.40574e26i		−	1.29356i
$475$	9.59008e26	−	5.06710e26i	1.64016	−	0.866610i
$476$	3.48129e25			0.0583003
$477$	2.47649e26	+	2.47649e26i	0.406119	+	0.406119i
$478$	1.02517e26	−	1.02517e26i	0.164633	−	0.164633i
$479$		−	2.16563e26i		−	0.340588i	−0.985393	−	0.170294i	$-0.945528\pi$
$479$		−	2.16563e26i		−	0.340588i	0.985393	−	0.170294i	$-0.0544717\pi$
$480$	−3.90431e26	+	6.47871e26i	−0.601356	+	0.997875i
$481$	−6.16458e26			−0.929936
$482$	2.29280e25	+	2.29280e25i	0.0338763	+	0.0338763i
$483$	4.32662e24	−	4.32662e24i	0.00626148	−	0.00626148i
$484$		−	1.20837e26i		−	0.171296i
$485$	3.26305e25	−	8.09052e24i	0.0453113	−	0.0112346i
$486$	2.87407e26			0.390962
$487$	−3.30240e26	−	3.30240e26i	−0.440089	−	0.440089i	0.451953	−	0.892042i	$-0.350727\pi$
$487$	−3.30240e26	−	3.30240e26i	−0.440089	−	0.440089i	−0.892042	+	0.451953i	$0.850727\pi$
$488$	3.59754e26	−	3.59754e26i	0.469686	−	0.469686i
$489$			4.55173e26i			0.582221i
$490$	−2.15847e25	−	8.70550e25i	−0.0270511	−	0.109102i
$491$	−3.23997e26			−0.397856			−0.198928	−	0.980014i	$-0.563746\pi$
$491$	−3.23997e26			−0.397856			−0.198928	+	0.980014i	$0.563746\pi$
$492$	2.21215e25	+	2.21215e25i	0.0266173	+	0.0266173i
$493$	3.95585e25	−	3.95585e25i	0.0466413	−	0.0466413i
$494$			1.32849e27i			1.53493i
$495$	−2.85358e26	−	1.71967e26i	−0.323101	−	0.194713i
$496$	−1.73371e25			−0.0192380
$497$	1.00829e27	+	1.00829e27i	1.09653	+	1.09653i
$498$	−2.83429e26	+	2.83429e26i	−0.302100	+	0.302100i
$499$			6.31149e25i			0.0659366i	0.999456	+	0.0329683i	$0.0104960\pi$
$499$			6.31149e25i			0.0659366i	−0.999456	+	0.0329683i	$0.989504\pi$
$500$	−3.46608e25	+	6.15309e26i	−0.0354927	+	0.630076i
$501$	−8.64152e26			−0.867387
$502$	−6.63724e26	−	6.63724e26i	−0.653056	−	0.653056i
$503$	4.15790e25	−	4.15790e25i	0.0401046	−	0.0401046i	−0.686770	−	0.726875i	$-0.740972\pi$
$503$	4.15790e25	−	4.15790e25i	0.0401046	−	0.0401046i	0.726875	+	0.686770i	$0.240972\pi$
$504$		−	3.81580e26i		−	0.360811i
$505$	−7.08574e26	+	1.17579e27i	−0.656858	+	1.08997i
$506$	−5.30609e24			−0.00482247
$507$	7.84557e26	+	7.84557e26i	0.699109	+	0.699109i
$508$	3.54647e26	−	3.54647e26i	0.309855	−	0.309855i
$509$		−	8.23873e26i		−	0.705801i	−0.935661	−	0.352901i	$-0.885195\pi$
$509$		−	8.23873e26i		−	0.705801i	0.935661	−	0.352901i	$-0.114805\pi$
$510$	−6.88023e25	+	1.70591e25i	−0.0577965	+	0.0143303i
$511$	1.81765e27			1.49728
$512$	−5.13300e25	−	5.13300e25i	−0.0414641	−	0.0414641i
$513$	1.27289e27	−	1.27289e27i	1.00836	−	1.00836i
$514$			6.35263e26i			0.493540i
$515$	−3.90212e26	−	1.57379e27i	−0.297323	−	1.19916i
$516$	−1.57603e26			−0.117779
$517$	7.37116e26	+	7.37116e26i	0.540294	+	0.540294i
$518$	−4.43920e26	+	4.43920e26i	−0.319159	+	0.319159i
$519$		−	1.97906e27i		−	1.39567i
$520$	−1.67098e27	−	1.00699e27i	−1.15595	−	0.696616i
$521$	4.11777e26			0.279438			0.139719	−	0.990191i	$-0.455380\pi$
$521$	4.11777e26			0.279438			0.139719	+	0.990191i	$0.455380\pi$
$522$	−1.67761e26	−	1.67761e26i	−0.111683	−	0.111683i
$523$	−1.80993e26	+	1.80993e26i	−0.118208	+	0.118208i	−0.763736	−	0.645529i	$-0.776637\pi$
$523$	−1.80993e26	+	1.80993e26i	−0.118208	+	0.118208i	0.645529	+	0.763736i	$0.276637\pi$
$524$			1.58144e27i			1.01330i
$525$	−9.34554e26	−	1.76875e27i	−0.587505	−	1.11192i
$526$	−1.17309e27			−0.723556
$527$	−6.50345e25	−	6.50345e25i	−0.0393584	−	0.0393584i
$528$	4.54952e25	−	4.54952e25i	0.0270164	−	0.0270164i
$529$			1.71607e27i			0.999950i
$530$	9.41259e26	−	1.56190e27i	0.538208	−	0.893090i
$531$	−1.25879e26			−0.0706329
$532$	−1.63645e27	−	1.63645e27i	−0.901130	−	0.901130i
$533$	−9.20357e25	+	9.20357e25i	−0.0497375	+	0.0497375i
$534$			1.14108e27i			0.605209i
$535$	−4.74011e26	+	1.17528e26i	−0.246746	+	0.0611792i
$536$	1.39933e26			0.0714945
$537$	2.04217e27	+	2.04217e27i	1.02412	+	1.02412i
$538$	1.47036e27	−	1.47036e27i	0.723770	−	0.723770i
$539$			4.31871e26i			0.208673i
$540$	2.46149e26	+	9.92760e26i	0.116751	+	0.470876i
$541$	−1.52715e27			−0.711063			−0.355532	−	0.934664i	$-0.615700\pi$
$541$	−1.52715e27			−0.711063			−0.355532	+	0.934664i	$0.615700\pi$
$542$	−3.44482e24	−	3.44482e24i	−0.00157461	−	0.00157461i
$543$	1.18667e27	−	1.18667e27i	0.532516	−	0.532516i
$544$		−	1.94264e26i		−	0.0855860i
$545$	3.44313e27	+	2.07496e27i	1.48932	+	0.897519i
$546$	2.45022e27			1.04059
$547$	3.90302e25	+	3.90302e25i	0.0162752	+	0.0162752i	0.715198	−	0.698922i	$-0.246337\pi$
$547$	3.90302e25	+	3.90302e25i	0.0162752	+	0.0162752i	−0.698922	+	0.715198i	$0.746337\pi$
$548$	−7.48202e26	+	7.48202e26i	−0.306347	+	0.306347i
$549$			5.57918e26i			0.224309i
$550$	−5.11523e26	+	1.65764e27i	−0.201947	+	0.654432i
$551$	−3.71906e27			−1.44184
$552$	−1.49672e25	−	1.49672e25i	−0.00569835	−	0.00569835i
$553$	−3.79538e27	+	3.79538e27i	−1.41907	+	1.41907i
$554$		−	1.53968e27i		−	0.565369i
$555$	−1.12865e27	+	1.87286e27i	−0.407035	+	0.675423i
$556$	7.75512e26			0.274688
$557$	1.33618e26	+	1.33618e26i	0.0464851	+	0.0464851i	0.729967	−	0.683482i	$-0.239535\pi$
$557$	1.33618e26	+	1.33618e26i	0.0464851	+	0.0464851i	−0.683482	+	0.729967i	$0.739535\pi$
$558$	−2.75801e26	+	2.75801e26i	−0.0942441	+	0.0942441i
$559$		−	6.55701e26i		−	0.220084i
$560$	9.39989e25	−	2.33064e25i	0.0309915	−	0.00768414i
$561$	3.41321e26			0.110544
$562$	−6.63091e26	−	6.63091e26i	−0.210965	−	0.210965i
$563$	2.19838e27	−	2.19838e27i	0.687098	−	0.687098i	−0.274492	−	0.961589i	$-0.588510\pi$
$563$	2.19838e27	−	2.19838e27i	0.687098	−	0.687098i	0.961589	+	0.274492i	$0.0885096\pi$
$564$			1.60894e27i			0.494024i
$565$	−6.91442e26	−	2.78871e27i	−0.208579	−	0.841237i
$566$	−7.15559e26			−0.212071
$567$	−3.23207e27	−	3.23207e27i	−0.941131	−	0.941131i
$568$	3.48800e27	−	3.48800e27i	0.997913	−	0.997913i
$569$		−	3.70599e27i		−	1.04179i	−0.853620	−	0.520897i	$-0.825598\pi$
$569$		−	3.70599e27i		−	1.04179i	0.853620	−	0.520897i	$-0.174402\pi$
$570$	4.03610e27	+	2.43230e27i	1.11484	+	0.671844i
$571$	1.37923e27			0.374348			0.187174	−	0.982327i	$-0.440067\pi$
$571$	1.37923e27			0.374348			0.187174	+	0.982327i	$0.440067\pi$
$572$	2.57006e27	+	2.57006e27i	0.685462	+	0.685462i
$573$	−4.92047e26	+	4.92047e26i	−0.128962	+	0.128962i
$574$			1.32552e26i			0.0341404i
$575$	−2.65815e25	−	8.20265e24i	−0.00672824	−	0.00207623i
$576$	−7.84394e26			−0.195123
$577$	−5.24045e27	−	5.24045e27i	−1.28118	−	1.28118i	−0.939996	−	0.341186i	$-0.889171\pi$
$577$	−5.24045e27	−	5.24045e27i	−1.28118	−	1.28118i	−0.341186	−	0.939996i	$-0.610829\pi$
$578$	−1.77457e27	+	1.77457e27i	−0.426398	+	0.426398i
$579$		−	2.93085e27i		−	0.692162i
$580$	1.09071e27	−	1.80989e27i	0.253179	−	0.420119i
$581$	2.90510e27			0.662826
$582$	1.03279e26	+	1.03279e26i	0.0231624	+	0.0231624i
$583$	−6.20896e27	+	6.20896e27i	−1.36878	+	1.36878i
$584$		−	6.28786e27i		−	1.36262i
$585$	2.07654e27	−	5.14865e26i	0.442366	−	0.109682i
$586$	−4.90493e26			−0.102720
$587$	4.10494e27	+	4.10494e27i	0.845134	+	0.845134i	0.989521	−	0.144387i	$-0.0461210\pi$
$587$	4.10494e27	+	4.10494e27i	0.845134	+	0.845134i	−0.144387	+	0.989521i	$0.546121\pi$
$588$	−4.71331e26	+	4.71331e26i	−0.0954010	+	0.0954010i
$589$			6.11417e27i			1.21670i
$590$	1.57735e26	+	6.36171e26i	0.0308608	+	0.124467i
$591$	3.34501e27			0.643461
$592$	−7.48534e25	−	7.48534e25i	−0.0141578	−	0.0141578i
$593$	−3.20911e27	+	3.20911e27i	−0.596812	+	0.596812i	−0.939463	−	0.342651i	$-0.888675\pi$
$593$	−3.20911e27	+	3.20911e27i	−0.596812	+	0.596812i	0.342651	+	0.939463i	$0.388675\pi$
$594$			2.87913e27i			0.526498i
$595$	4.40032e26	+	2.65179e26i	0.0791252	+	0.0476837i
$596$	2.16532e27			0.382878
$597$	−3.92736e27	−	3.92736e27i	−0.682901	−	0.682901i
$598$	2.40929e25	−	2.40929e25i	0.00411981	−	0.00411981i
$599$		−	5.72543e27i		−	0.962809i	−0.876499	−	0.481404i	$-0.840127\pi$
$599$		−	5.72543e27i		−	0.962809i	0.876499	−	0.481404i	$-0.159873\pi$
$600$	−6.11869e27	+	3.23293e27i	−1.01192	+	0.534667i
$601$	8.66001e27			1.40855			0.704277	−	0.709925i	$-0.251271\pi$
$601$	8.66001e27			1.40855			0.704277	+	0.709925i	$0.251271\pi$
$602$	−4.72180e26	−	4.72180e26i	−0.0755340	−	0.0755340i
$603$	−1.08506e26	+	1.08506e26i	−0.0170719	+	0.0170719i
$604$		−	5.74047e27i		−	0.888337i
$605$	9.20448e26	−	1.52737e27i	0.140102	−	0.232482i
$606$	−5.96423e27			−0.892952
$607$	7.18513e27	+	7.18513e27i	1.05815	+	1.05815i	0.998201	+	0.0599492i	$0.0190939\pi$
$607$	7.18513e27	+	7.18513e27i	1.05815	+	1.05815i	0.0599492	+	0.998201i	$0.480906\pi$
$608$	−9.13177e27	+	9.13177e27i	−1.32288	+	1.32288i
$609$			6.85927e27i			0.977473i
$610$	2.81963e27	−	6.99109e26i	0.395270	−	0.0980047i
$611$	−6.69392e27			−0.923142
$612$	9.33827e25	+	9.33827e25i	0.0126693	+	0.0126693i
$613$	4.07920e27	−	4.07920e27i	0.544465	−	0.544465i	−0.380369	−	0.924835i	$-0.624203\pi$
$613$	4.07920e27	−	4.07920e27i	0.544465	−	0.544465i	0.924835	+	0.380369i	$0.124203\pi$
$614$		−	2.39957e27i		−	0.315101i
$615$	1.11108e26	+	4.48119e26i	0.0143547	+	0.0578952i
$616$	9.56682e27			1.21608
$617$	−1.97241e27	−	1.97241e27i	−0.246687	−	0.246687i	0.572923	−	0.819609i	$-0.305809\pi$
$617$	−1.97241e27	−	1.97241e27i	−0.246687	−	0.246687i	−0.819609	+	0.572923i	$0.805809\pi$
$618$	4.98124e27	−	4.98124e27i	0.612989	−	0.612989i
$619$			8.79821e27i			1.06534i	0.846324	+	0.532669i	$0.178811\pi$
$619$			8.79821e27i			1.06534i	−0.846324	+	0.532669i	$0.821189\pi$
$620$	−2.97548e27	−	1.79313e27i	−0.354519	−	0.213646i
$621$	−4.61689e25			−0.00541295
$622$	2.69942e27	+	2.69942e27i	0.311434	+	0.311434i
$623$	5.84796e27	−	5.84796e27i	0.663933	−	0.663933i
$624$			4.13153e26i			0.0461599i
$625$	−5.12508e27	+	7.51343e27i	−0.563509	+	0.826110i
$626$	−9.41563e27			−1.01884
$627$	−1.60445e28	−	1.60445e28i	−1.70864	−	1.70864i
$628$	8.97866e26	−	8.97866e26i	0.0941055	−	0.0941055i
$629$		−	5.61576e26i		−	0.0579298i
$630$	1.12458e27	−	1.86611e27i	0.114179	−	0.189466i
$631$	1.20808e27			0.120727			0.0603633	−	0.998176i	$-0.480774\pi$
$631$	1.20808e27			0.120727			0.0603633	+	0.998176i	$0.480774\pi$
$632$	1.31295e28	+	1.31295e28i	1.29145	+	1.29145i
$633$	1.44421e28	−	1.44421e28i	1.39828	−	1.39828i
$634$		−	7.10313e27i		−	0.676951i
$635$	7.18415e27	−	1.78126e27i	0.673966	−	0.167106i
$636$	−1.35526e28			−1.25156
$637$	−1.96096e27	−	1.96096e27i	−0.178268	−	0.178268i
$638$	4.20604e27	−	4.20604e27i	0.376415	−	0.376415i
$639$			5.40929e27i			0.476575i
$640$	−1.81531e27	−	7.32148e27i	−0.157453	−	0.635037i
$641$	−1.83851e28			−1.56995			−0.784976	−	0.619526i	$-0.787325\pi$
$641$	−1.83851e28			−1.56995			−0.784976	+	0.619526i	$0.787325\pi$
$642$	−1.50030e27	−	1.50030e27i	−0.126133	−	0.126133i
$643$	1.41917e28	−	1.41917e28i	1.17469	−	1.17469i	0.193616	−	0.981077i	$-0.437979\pi$
$643$	1.41917e28	−	1.41917e28i	1.17469	−	1.17469i	0.981077	−	0.193616i	$-0.0620214\pi$
$644$			5.93559e25i			0.00483732i
$645$	−1.99208e27	−	1.20050e27i	−0.159849	−	0.0963310i
$646$	−1.21022e27			−0.0956179
$647$	1.45935e28	+	1.45935e28i	1.13532	+	1.13532i	0.989279	+	0.146040i	$0.0466528\pi$
$647$	1.45935e28	+	1.45935e28i	1.13532	+	1.13532i	0.146040	+	0.989279i	$0.453347\pi$
$648$	−1.11808e28	+	1.11808e28i	−0.856490	+	0.856490i
$649$		−	3.15598e27i		−	0.238060i
$650$	−5.20410e27	−	9.84935e27i	−0.386555	−	0.731601i
$651$	1.12767e28			0.824845
$652$	−3.12221e27	−	3.12221e27i	−0.224898	−	0.224898i
$653$	−1.71374e28	+	1.71374e28i	−1.21566	+	1.21566i	−0.246524	+	0.969137i	$0.579288\pi$
$653$	−1.71374e28	+	1.71374e28i	−1.21566	+	1.21566i	−0.969137	+	0.246524i	$0.920712\pi$
$654$			1.74654e28i			1.22011i
$655$	−1.20462e28	+	1.99892e28i	−0.828779	+	1.37526i
$656$	−2.23509e25			−0.00151445
$657$	4.87570e27	+	4.87570e27i	0.325374	+	0.325374i
$658$	−4.82039e27	+	4.82039e27i	−0.316828	+	0.316828i
$659$			2.42844e28i			1.57207i	0.618179	+	0.786037i	$0.287871\pi$
$659$			2.42844e28i			1.57207i	−0.618179	+	0.786037i	$0.712129\pi$
$660$	1.25135e28	−	3.10265e27i	0.797886	−	0.197831i
$661$	3.12842e28			1.96476			0.982382	−	0.186884i	$-0.0598389\pi$
$661$	3.12842e28			1.96476			0.982382	+	0.186884i	$0.0598389\pi$
$662$	−4.52464e27	−	4.52464e27i	−0.279901	−	0.279901i
$663$	−1.54981e27	+	1.54981e27i	−0.0944371	+	0.0944371i
$664$		−	1.00497e28i		−	0.603215i
$665$	−8.21932e27	−	3.31500e28i	−0.485981	−	1.96005i
$666$	−2.38156e27			−0.138713
$667$	6.74470e25	+	6.74470e25i	0.00386994	+	0.00386994i
$668$	5.92755e27	−	5.92755e27i	0.335051	−	0.335051i
$669$			2.82671e27i			0.157406i
$670$	6.84339e26	+	4.12408e26i	0.0375425	+	0.0226245i
$671$	−1.39879e28			−0.756009
$672$	1.68422e28	+	1.68422e28i	0.896824	+	0.896824i
$673$	1.38495e28	−	1.38495e28i	0.726581	−	0.726581i	−0.243356	−	0.969937i	$-0.578248\pi$
$673$	1.38495e28	−	1.38495e28i	0.726581	−	0.726581i	0.969937	+	0.243356i	$0.0782484\pi$
$674$			1.67139e28i			0.863929i
$675$	−4.45083e27	+	1.44234e28i	−0.226675	+	0.734563i
$676$	−1.07632e28			−0.540098
$677$	−1.47564e28	−	1.47564e28i	−0.729613	−	0.729613i	0.240930	−	0.970543i	$-0.422548\pi$
$677$	−1.47564e28	−	1.47564e28i	−0.729613	−	0.729613i	−0.970543	+	0.240930i	$0.922548\pi$
$678$	8.82658e27	−	8.82658e27i	0.430027	−	0.430027i
$679$		−	1.05859e27i		−	0.0508197i
$680$	9.17343e26	−	1.52222e27i	0.0433953	−	0.0720090i
$681$	6.57517e27			0.306504
$682$	−6.91478e27	−	6.91478e27i	−0.317640	−	0.317640i
$683$	−5.64316e27	+	5.64316e27i	−0.255456	+	0.255456i	−0.823203	−	0.567747i	$-0.807815\pi$
$683$	−5.64316e27	+	5.64316e27i	−0.255456	+	0.255456i	0.567747	+	0.823203i	$0.307815\pi$
$684$		−	8.77930e27i		−	0.391650i
$685$	−1.51565e28	+	3.75795e27i	−0.666334	+	0.165213i
$686$	1.24367e28			0.538845
$687$	−1.66951e28	−	1.66951e28i	−0.712890	−	0.712890i
$688$	7.96185e25	−	7.96185e25i	0.00335065	−	0.00335065i
$689$		−	5.63850e28i		−	2.33868i
$690$	−2.90857e25	−	1.17308e26i	−0.00118902	−	0.00479551i
$691$	−2.64105e28			−1.06413			−0.532066	−	0.846703i	$-0.678584\pi$
$691$	−2.64105e28			−1.06413			−0.532066	+	0.846703i	$0.678584\pi$
$692$	1.35751e28	+	1.35751e28i	0.539116	+	0.539116i
$693$	−7.41825e27	+	7.41825e27i	−0.290382	+	0.290382i
$694$			5.43800e27i			0.209819i
$695$	9.80240e27	+	5.90728e27i	0.372807	+	0.224667i
$696$	2.37285e28			0.889564
$697$	−8.38419e25	−	8.38419e25i	−0.00309837	−	0.00309837i
$698$	−6.21414e27	+	6.21414e27i	−0.226374	+	0.226374i
$699$		−	3.02304e28i		−	1.08561i
$700$	1.85430e28	+	5.72209e27i	0.656448	+	0.202569i
$701$	4.38378e28			1.52992			0.764960	−	0.644077i	$-0.222758\pi$
$701$	4.38378e28			1.52992			0.764960	+	0.644077i	$0.222758\pi$
$702$	−1.30730e28	−	1.30730e28i	−0.449785	−	0.449785i
$703$	−2.63981e28	+	2.63981e28i	−0.895403	+	0.895403i
$704$		−	1.96660e28i		−	0.657643i
$705$	−1.22557e28	+	2.03368e28i	−0.404061	+	0.670489i
$706$	4.94521e27			0.160745
$707$	3.05661e28	+	3.05661e28i	0.979595	+	0.979595i
$708$	3.44435e27	−	3.44435e27i	0.108836	−	0.108836i
$709$			1.59131e28i			0.495785i	0.968788	+	0.247892i	$0.0797379\pi$
$709$			1.59131e28i			0.495785i	−0.968788	+	0.247892i	$0.920262\pi$
$710$	2.73377e28	−	6.77821e27i	0.839806	−	0.208224i
$711$	−2.03616e28			−0.616758
$712$	−2.02300e28	−	2.02300e28i	−0.604222	−	0.604222i
$713$	1.10884e26	−	1.10884e26i	0.00326567	−	0.00326567i
$714$			2.23208e27i			0.0648227i
$715$	1.29085e28	+	5.20622e28i	0.369671	+	1.49095i
$716$	−2.80161e28			−0.791184
$717$	−1.12436e28	−	1.12436e28i	−0.313123	−	0.313123i
$718$	−8.33275e27	+	8.33275e27i	−0.228846	+	0.228846i
$719$			5.18288e27i			0.140372i	0.997534	+	0.0701862i	$0.0223594\pi$
$719$			5.18288e27i			0.140372i	−0.997534	+	0.0701862i	$0.977641\pi$
$720$	3.14661e26	+	1.89626e26i	0.00840462	+	0.00506493i
$721$	−5.10568e28			−1.34494
$722$	4.03569e28	+	4.03569e28i	1.04845	+	1.04845i
$723$	2.51466e27	−	2.51466e27i	0.0644311	−	0.0644311i
$724$			1.62797e28i			0.411396i
$725$	2.75728e28	−	1.45686e28i	0.687229	−	0.363110i
$726$	7.74762e27			0.190459
$727$	−2.87727e28	−	2.87727e28i	−0.697648	−	0.697648i	0.266255	−	0.963903i	$-0.414214\pi$
$727$	−2.87727e28	−	2.87727e28i	−0.697648	−	0.697648i	−0.963903	+	0.266255i	$0.914214\pi$
$728$	−4.34393e28	+	4.34393e28i	−1.03889	+	1.03889i
$729$			2.03070e28i			0.479038i
$730$	1.85315e28	−	3.07506e28i	0.431202	−	0.715526i
$731$	5.97325e26			0.0137100
$732$	−1.52660e28	−	1.52660e28i	−0.345632	−	0.345632i
$733$	1.20767e28	−	1.20767e28i	0.269718	−	0.269718i	−0.559269	−	0.828986i	$-0.688918\pi$
$733$	1.20767e28	−	1.20767e28i	0.269718	−	0.269718i	0.828986	+	0.559269i	$0.188918\pi$
$734$			9.78245e26i			0.0215520i
$735$	−9.54784e27	+	2.36733e27i	−0.207507	+	0.0514499i
$736$	3.31219e26			0.00710128
$737$	−2.72042e27	−	2.72042e27i	−0.0575389	−	0.0575389i
$738$	−3.55561e26	+	3.55561e26i	−0.00741908	+	0.00741908i
$739$		−	1.01196e28i		−	0.208315i	−0.994561	−	0.104157i	$-0.966785\pi$
$739$		−	1.01196e28i		−	0.208315i	0.994561	−	0.104157i	$-0.0332146\pi$
$740$	−5.10480e27	−	2.05886e28i	−0.103672	−	0.418128i
$741$	1.45704e29			2.91937
$742$	−4.06036e28	−	4.06036e28i	−0.802649	−	0.802649i
$743$	4.70523e28	−	4.70523e28i	0.917682	−	0.917682i	−0.0791781	−	0.996860i	$-0.525230\pi$
$743$	4.70523e28	−	4.70523e28i	0.917682	−	0.917682i	0.996860	+	0.0791781i	$0.0252296\pi$
$744$		−	3.90098e28i		−	0.750663i
$745$	2.73695e28	+	1.64939e28i	0.519642	+	0.313155i
$746$	−3.97237e28			−0.744151
$747$	7.79267e27	+	7.79267e27i	0.144039	+	0.144039i
$748$	−2.34125e27	+	2.34125e27i	−0.0427004	+	0.0427004i
$749$			1.53778e28i			0.276743i
$750$	−3.94513e28	−	2.22232e27i	−0.700566	−	0.0394634i
$751$	3.35385e27			0.0587684			0.0293842	−	0.999568i	$-0.490645\pi$
$751$	3.35385e27			0.0587684			0.0293842	+	0.999568i	$0.490645\pi$
$752$	−8.12809e26	−	8.12809e26i	−0.0140543	−	0.0140543i
$753$	−7.27946e28	+	7.27946e28i	−1.24208	+	1.24208i
$754$			3.81961e28i			0.643139i
$755$	4.37267e28	−	7.25590e28i	0.726569	−	1.20565i
$756$	3.22070e28			0.528120
$757$	−3.89653e28	−	3.89653e28i	−0.630549	−	0.630549i	0.317657	−	0.948206i	$-0.397104\pi$
$757$	−3.89653e28	−	3.89653e28i	−0.630549	−	0.630549i	−0.948206	+	0.317657i	$0.897104\pi$
$758$	−1.00139e28	+	1.00139e28i	−0.159924	+	0.159924i
$759$			5.81951e26i			0.00917209i
$760$	−1.14677e29	+	2.84333e28i	−1.78377	+	0.442274i
$761$	−1.18988e29			−1.82666			−0.913328	−	0.407225i	$-0.866497\pi$
$761$	−1.18988e29			−1.82666			−0.913328	+	0.407225i	$0.866497\pi$
$762$	2.27387e28	+	2.27387e28i	0.344521	+	0.344521i
$763$	8.95086e28	−	8.95086e28i	1.33850	−	1.33850i
$764$		−	6.75028e27i		−	0.0996296i
$765$	4.69027e26	+	1.89167e27i	0.00683256	+	0.0275569i
$766$	4.18887e28			0.602295
$767$	1.43301e28	+	1.43301e28i	0.203374	+	0.203374i
$768$	5.71834e28	−	5.71834e28i	0.801047	−	0.801047i
$769$			1.32466e28i			0.183165i	0.995798	+	0.0915824i	$0.0291925\pi$
$769$			1.32466e28i			0.183165i	−0.995798	+	0.0915824i	$0.970808\pi$
$770$	4.67863e28	+	2.81951e28i	0.638574	+	0.384828i
$771$	6.96732e28			0.938689
$772$	2.01038e28	+	2.01038e28i	0.267366	+	0.267366i
$773$	−4.79068e28	+	4.79068e28i	−0.628930	+	0.628930i	−0.947799	−	0.318869i	$-0.896697\pi$
$773$	−4.79068e28	+	4.79068e28i	−0.628930	+	0.628930i	0.318869	+	0.947799i	$0.396697\pi$
$774$		−	2.53316e27i		−	0.0328287i
$775$	−2.39510e28	−	4.53300e28i	−0.306412	−	0.579921i
$776$	−3.66203e27			−0.0462492
$777$	4.86874e28	+	4.86874e28i	0.607025	+	0.607025i
$778$	−4.99762e27	+	4.99762e27i	−0.0615130	+	0.0615130i
$779$			7.88233e27i			0.0957812i
$780$	−4.27313e28	+	7.09072e28i	−0.512625	+	0.850637i
$781$	−1.35620e29			−1.60625
$782$	2.19480e25	+	2.19480e25i	0.000256641	+	0.000256641i
$783$	3.65973e28	−	3.65973e28i	0.422505	−	0.422505i
$784$		−	4.76218e26i		−	0.00542807i
$785$	1.81882e28	−	4.50966e27i	0.204689	−	0.0507513i
$786$	−1.01396e29			−1.12667
$787$	1.10075e29	+	1.10075e29i	1.20765	+	1.20765i	0.971787	+	0.235860i	$0.0757907\pi$
$787$	1.10075e29	+	1.10075e29i	1.20765	+	1.20765i	0.235860	+	0.971787i	$0.424209\pi$
$788$	−2.29447e28	+	2.29447e28i	−0.248554	+	0.248554i
$789$			1.28659e29i			1.37617i
$790$	2.55144e28	+	1.02904e29i	0.269473	+	1.08683i
$791$	−9.04709e28			−0.943504
$792$	2.56622e28	+	2.56622e28i	0.264266	+	0.264266i
$793$	6.35136e28	−	6.35136e28i	0.645855	−	0.645855i
$794$		−	5.97055e28i		−	0.599527i
$795$	−1.71303e29	−	1.03234e29i	−1.69861	−	1.02365i
$796$	5.38786e28			0.527577
$797$	1.22430e29	+	1.22430e29i	1.18387	+	1.18387i	0.978734	+	0.205133i	$0.0657628\pi$
$797$	1.22430e29	+	1.22430e29i	1.18387	+	1.18387i	0.205133	+	0.978734i	$0.434237\pi$
$798$	1.04923e29	−	1.04923e29i	1.00194	−	1.00194i
$799$		−	6.09797e27i		−	0.0575066i
$800$	3.19305e28	−	1.03474e29i	0.297376	−	0.963678i
$801$	3.13733e28			0.288559
$802$	−2.59583e28	−	2.59583e28i	−0.235794	−	0.235794i
$803$	−1.22242e29	+	1.22242e29i	−1.09664	+	1.09664i
$804$		−	5.93799e27i		−	0.0526113i
$805$	−4.52130e26	+	7.50253e26i	−0.00395644	+	0.00656521i
$806$	6.27947e28			0.542716
$807$	−1.61263e29	−	1.61263e29i	−1.37658	−	1.37658i
$808$	1.05738e29	−	1.05738e29i	0.891495	−	0.891495i
$809$		−	9.07745e28i		−	0.755925i	−0.925821	−	0.377963i	$-0.876625\pi$
$809$		−	9.07745e28i		−	0.755925i	0.925821	−	0.377963i	$-0.123375\pi$
$810$	−8.76311e28	+	2.17276e28i	−0.720789	+	0.178715i
$811$	1.80954e29			1.47014			0.735070	−	0.677991i	$-0.237149\pi$
$811$	1.80954e29			1.47014			0.735070	+	0.677991i	$0.237149\pi$
$812$	−4.70504e28	−	4.70504e28i	−0.377575	−	0.377575i
$813$	−3.77814e26	+	3.77814e26i	−0.00299484	+	0.00299484i
$814$		−	5.97094e28i		−	0.467518i
$815$	−1.56817e28	−	6.32471e28i	−0.121288	−	0.489175i
$816$	−3.76371e26			−0.00287550
$817$	−2.80785e28	−	2.80785e28i	−0.211911	−	0.211911i
$818$	−4.69666e27	+	4.69666e27i	−0.0350152	+	0.0350152i
$819$		−	6.73669e28i		−	0.496144i
$820$	−3.83596e27	−	2.31169e27i	−0.0279084	−	0.0168186i
$821$	−1.29666e29			−0.931952			−0.465976	−	0.884797i	$-0.654297\pi$
$821$	−1.29666e29			−0.931952			−0.465976	+	0.884797i	$0.654297\pi$
$822$	−4.79719e28	−	4.79719e28i	−0.340619	−	0.340619i
$823$	−8.88461e28	+	8.88461e28i	−0.623218	+	0.623218i	−0.946353	−	0.323135i	$-0.895263\pi$
$823$	−8.88461e28	+	8.88461e28i	−0.623218	+	0.623218i	0.323135	+	0.946353i	$0.395263\pi$
$824$			1.76622e29i			1.22398i
$825$	1.81804e29	+	5.61018e28i	1.24470	+	0.384094i
$826$	2.06386e28			0.139598
$827$	−1.55507e28	−	1.55507e28i	−0.103919	−	0.103919i	0.653236	−	0.757155i	$-0.273411\pi$
$827$	−1.55507e28	−	1.55507e28i	−0.103919	−	0.103919i	−0.757155	+	0.653236i	$0.773411\pi$
$828$	−1.59217e26	+	1.59217e26i	−0.00105120	+	0.00105120i
$829$			8.08698e28i			0.527523i	0.964588	+	0.263761i	$0.0849631\pi$
$829$			8.08698e28i			0.527523i	−0.964588	+	0.263761i	$0.915037\pi$
$830$	2.96182e28	−	4.91477e28i	0.190888	−	0.316754i
$831$	−1.68866e29			−1.07530
$832$	8.92958e28	+	8.92958e28i	0.561821	+	0.561821i
$833$	1.78638e27	−	1.78638e27i	0.0111051	−	0.0111051i
$834$			4.97230e28i			0.305419i
$835$	1.20075e29	−	2.97720e28i	0.728769	−	0.180694i
$836$	2.20111e29			1.32002
$837$	−6.01664e28	−	6.01664e28i	−0.356533	−	0.356533i
$838$	−2.21386e28	+	2.21386e28i	−0.129631	+	0.129631i
$839$			5.24742e28i			0.303617i	0.988410	+	0.151809i	$0.0485097\pi$
$839$			5.24742e28i			0.303617i	−0.988410	+	0.151809i	$0.951490\pi$
$840$	5.24412e28	+	2.11504e29i	0.299833	+	1.20928i
$841$	7.00664e28			0.395868
$842$	−2.04202e28	−	2.04202e28i	−0.114009	−	0.114009i
$843$	−7.27252e28	+	7.27252e28i	−0.401245	+	0.401245i
$844$			1.98128e29i			1.08024i
$845$	−1.36045e29	−	8.19859e28i	−0.733021	−	0.441745i
$846$	−2.58605e28			−0.137700
$847$	−3.97059e28	−	3.97059e28i	−0.208940	−	0.208940i
$848$	6.84655e27	−	6.84655e27i	0.0356052	−	0.0356052i
$849$			7.84797e28i			0.403348i
$850$	8.97248e27	−	4.74078e27i	0.0455747	−	0.0240802i
$851$	9.57484e26			0.00480658
$852$	−1.48011e29	−	1.48011e29i	−0.734343	−	0.734343i
$853$	1.80902e28	−	1.80902e28i	0.0887062	−	0.0887062i	−0.661361	−	0.750067i	$-0.730021\pi$
$853$	1.80902e28	−	1.80902e28i	0.0887062	−	0.0887062i	0.750067	+	0.661361i	$0.230021\pi$
$854$		−	9.14741e28i		−	0.443322i
$855$	6.68743e28	−	1.10969e29i	0.320330	−	0.531548i
$856$	5.31969e28			0.251854
$857$	2.27649e29	+	2.27649e29i	1.06526	+	1.06526i	0.997716	+	0.0675477i	$0.0215175\pi$
$857$	2.27649e29	+	2.27649e29i	1.06526	+	1.06526i	0.0675477	+	0.997716i	$0.478483\pi$
$858$	−1.64783e29	+	1.64783e29i	−0.762148	+	0.762148i
$859$		−	3.29341e29i		−	1.50561i	−0.658241	−	0.752807i	$-0.728699\pi$
$859$		−	3.29341e29i		−	1.50561i	0.658241	−	0.752807i	$-0.271301\pi$
$860$	2.18992e28	−	5.42977e27i	0.0989564	−	0.0245356i
$861$	1.45378e28			0.0649334
$862$	5.34300e27	+	5.34300e27i	0.0235892	+	0.0235892i
$863$	−1.37244e29	+	1.37244e29i	−0.598943	+	0.598943i	−0.940031	−	0.341088i	$-0.889205\pi$
$863$	−1.37244e29	+	1.37244e29i	−0.598943	+	0.598943i	0.341088	+	0.940031i	$0.389205\pi$
$864$		−	1.79722e29i		−	0.775290i
$865$	6.81828e28	+	2.74993e29i	0.290746	+	1.17263i
$866$	−1.80241e29			−0.759757
$867$	1.94628e29	+	1.94628e29i	0.810987	+	0.810987i
$868$	−7.73513e28	+	7.73513e28i	−0.318618	+	0.318618i
$869$		−	5.10497e29i		−	2.07872i
$870$	1.16043e29	+	6.99320e28i	0.467120	+	0.281503i
$871$	2.47048e28			0.0983105
$872$	−3.09639e29	−	3.09639e29i	−1.21812	−	1.21812i
$873$	2.83959e27	−	2.83959e27i	0.0110437	−	0.0110437i
$874$		−	2.06342e27i		−	0.00793365i
$875$	1.90795e29	+	2.13574e29i	0.725250	+	0.811835i
$876$	−2.66822e29			−1.00272
$877$	−2.10647e29	−	2.10647e29i	−0.782636	−	0.782636i	0.197639	−	0.980275i	$-0.436673\pi$
$877$	−2.10647e29	−	2.10647e29i	−0.782636	−	0.782636i	−0.980275	+	0.197639i	$0.936673\pi$
$878$	1.78445e29	−	1.78445e29i	0.655481	−	0.655481i
$879$			5.37954e28i			0.195369i
$880$	−4.75424e27	+	7.88906e27i	−0.0170708	+	0.0283269i
$881$	8.01729e28			0.284622			0.142311	−	0.989822i	$-0.454547\pi$
$881$	8.01729e28			0.284622			0.142311	+	0.989822i	$0.454547\pi$
$882$	−7.57575e27	−	7.57575e27i	−0.0265913	−	0.0265913i
$883$	1.82760e29	−	1.82760e29i	0.634271	−	0.634271i	−0.314866	−	0.949136i	$-0.601959\pi$
$883$	1.82760e29	−	1.82760e29i	0.634271	−	0.634271i	0.949136	+	0.314866i	$0.101959\pi$
$884$		−	2.12615e28i		−	0.0729576i
$885$	6.97728e28	−	1.72997e28i	0.236730	−	0.0586957i
$886$	1.19194e29			0.399870
$887$	2.58480e29	+	2.58480e29i	0.857414	+	0.857414i	0.991033	−	0.133618i	$-0.0426597\pi$
$887$	2.58480e29	+	2.58480e29i	0.857414	+	0.857414i	−0.133618	+	0.991033i	$0.542660\pi$
$888$	1.68426e29	−	1.68426e29i	0.552432	−	0.552432i
$889$		−	2.33067e29i		−	0.755899i
$890$	−3.93129e28	−	1.58556e29i	−0.126077	−	0.508490i
$891$	4.34729e29			1.37861
$892$	−1.93895e28	−	1.93895e28i	−0.0608021	−	0.0608021i
$893$	−2.86648e29	+	2.86648e29i	−0.888862	+	0.888862i
$894$			1.38833e29i			0.425712i
$895$	−3.54121e29	−	2.13406e29i	−1.07379	−	0.647108i
$896$	−2.37523e29			−0.712237
$897$	−2.64241e27	−	2.64241e27i	−0.00783567	−	0.00783567i
$898$	−1.45837e29	+	1.45837e29i	−0.427665	+	0.427665i
$899$			1.75791e29i			0.509800i
$900$	3.43911e28	+	6.50891e28i	0.0986326	+	0.186674i
$901$	5.13651e28			0.145687
$902$	−8.91447e27	−	8.91447e27i	−0.0250052	−	0.0250052i
$903$	−5.17868e28	+	5.17868e28i	−0.143662	+	0.143662i
$904$			3.12968e29i			0.858650i
$905$	−1.24007e29	+	2.05774e29i	−0.336480	+	0.558347i
$906$	3.68058e29			0.987720
$907$	−2.93347e29	−	2.93347e29i	−0.778591	−	0.778591i	0.201000	−	0.979591i	$-0.435581\pi$
$907$	−2.93347e29	−	2.93347e29i	−0.778591	−	0.778591i	−0.979591	+	0.201000i	$0.935581\pi$
$908$	−4.51016e28	+	4.51016e28i	−0.118395	+	0.118395i
$909$			1.63982e29i			0.425753i
$910$	−3.40462e29	+	8.44153e28i	−0.874288	+	0.216774i
$911$	−1.50167e29			−0.381408			−0.190704	−	0.981648i	$-0.561077\pi$
$911$	−1.50167e29			−0.381408			−0.190704	+	0.981648i	$0.561077\pi$
$912$	1.76921e28	+	1.76921e28i	0.0444458	+	0.0444458i
$913$	−1.95375e29	+	1.95375e29i	−0.485468	+	0.485468i
$914$			1.89761e28i			0.0466385i
$915$	−7.66755e28	−	3.09246e29i	−0.186400	−	0.751784i
$916$	2.29037e29			0.550745
$917$	5.19646e29	+	5.19646e29i	1.23599	+	1.23599i
$918$	1.19092e28	−	1.19092e28i	0.0280191	−	0.0280191i
$919$			5.72025e29i			1.33125i	0.746286	+	0.665625i	$0.231835\pi$
$919$			5.72025e29i			1.33125i	−0.746286	+	0.665625i	$0.768165\pi$
$920$	2.59537e27	+	1.56406e27i	0.00597477	+	0.00360061i
$921$	−2.63175e29			−0.599306
$922$	2.34400e29	+	2.34400e29i	0.528016	+	0.528016i
$923$	6.15796e29	−	6.15796e29i	1.37221	−	1.37221i
$924$		−	4.05963e29i		−	0.894884i
$925$	9.23044e28	−	2.99122e29i	0.201282	−	0.652276i
$926$	2.04533e29			0.441219
$927$	−1.36956e29	−	1.36956e29i	−0.292269	−	0.292269i
$928$	−2.62551e29	+	2.62551e29i	−0.554287	+	0.554287i
$929$		−	1.88546e29i		−	0.393785i	−0.980425	−	0.196893i	$-0.936915\pi$
$929$		−	1.88546e29i		−	0.393785i	0.980425	−	0.196893i	$-0.0630851\pi$
$930$	1.14969e29	−	1.90777e29i	0.237548	−	0.394181i
$931$	−1.67945e29			−0.343297
$932$	2.07362e29	+	2.07362e29i	0.419344	+	0.419344i
$933$	2.96061e29	−	2.96061e29i	0.592332	−	0.592332i
$934$			2.01158e29i			0.398171i
$935$	−4.74272e28	+	1.17593e28i	−0.0928776	+	0.0230284i
$936$	−2.33044e29			−0.451523
$937$	−2.82646e29	−	2.82646e29i	−0.541809	−	0.541809i	0.382250	−	0.924059i	$-0.375149\pi$
$937$	−2.82646e29	−	2.82646e29i	−0.541809	−	0.541809i	−0.924059	+	0.382250i	$0.875149\pi$
$938$	1.77903e28	−	1.77903e28i	0.0337407	−	0.0337407i
$939$			1.03267e30i			1.93778i
$940$	−5.54314e28	−	2.23565e29i	−0.102915	−	0.415073i
$941$	−6.47757e29			−1.18991			−0.594957	−	0.803757i	$-0.702831\pi$
$941$	−6.47757e29			−1.18991			−0.594957	+	0.803757i	$0.702831\pi$
$942$	5.75679e28	+	5.75679e28i	0.104634	+	0.104634i
$943$	1.42950e26	−	1.42950e26i	0.000257080	−	0.000257080i
$944$			3.48006e27i			0.00619251i
$945$	4.07094e29	+	2.45330e29i	0.716764	+	0.431948i
$946$	6.35104e28			0.110645
$947$	−8.96883e28	−	8.96883e28i	−0.154609	−	0.154609i	0.625564	−	0.780173i	$-0.284869\pi$
$947$	−8.96883e28	−	8.96883e28i	−0.154609	−	0.154609i	−0.780173	+	0.625564i	$0.784869\pi$
$948$	5.57142e29	−	5.57142e29i	0.950347	−	0.950347i
$949$		−	1.11010e30i		−	1.87371i
$950$	−6.44621e29	−	1.98920e29i	−1.07663	−	0.332233i
$951$	−7.79043e29			−1.28753
$952$	−3.95719e28	−	3.95719e28i	−0.0647169	−	0.0647169i
$953$	6.00585e29	−	6.00585e29i	0.971953	−	0.971953i	−0.0276638	−	0.999617i	$-0.508807\pi$
$953$	6.00585e29	−	6.00585e29i	0.971953	−	0.971953i	0.999617	+	0.0276638i	$0.00880679\pi$
$954$		−	2.17831e29i		−	0.348848i
$955$	5.14187e28	−	8.53229e28i	0.0814869	−	0.135217i
$956$	1.54249e29			0.241904
$957$	−4.61302e29	−	4.61302e29i	−0.715923	−	0.715923i
$958$	−9.52441e28	+	9.52441e28i	−0.146279	+	0.146279i
$959$			4.91704e29i			0.747339i
$960$	4.34779e29	−	1.07801e29i	0.653967	−	0.162147i
$961$	−3.82788e29			−0.569803
$962$	2.71117e29	+	2.71117e29i	0.399399	+	0.399399i
$963$	−4.12497e28	+	4.12497e28i	−0.0601392	+	0.0601392i
$964$			3.44980e28i			0.0497764i
$965$	1.00974e29	+	4.07247e29i	0.144191	+	0.581547i
$966$	−3.80568e27			−0.00537850
$967$	6.24268e29	+	6.24268e29i	0.873186	+	0.873186i	0.992818	−	0.119632i	$-0.0381716\pi$
$967$	6.24268e29	+	6.24268e29i	0.873186	+	0.873186i	−0.119632	+	0.992818i	$0.538172\pi$
$968$	−1.37356e29	+	1.37356e29i	−0.190149	+	0.190149i
$969$			1.32732e29i			0.181860i
$970$	−1.79090e28	−	1.07926e28i	−0.0242860	−	0.0146356i
$971$	7.59062e29			1.01879			0.509395	−	0.860533i	$-0.329869\pi$
$971$	7.59062e29			1.01879			0.509395	+	0.860533i	$0.329869\pi$
$972$	2.16219e29	+	2.16219e29i	0.287231	+	0.287231i
$973$	2.54826e29	−	2.54826e29i	0.335054	−	0.335054i
$974$			2.90478e29i			0.378028i
$975$	−1.08024e30	+	5.70765e29i	−1.39147	+	0.735209i
$976$	1.54243e28			0.0196656
$977$	−4.49674e29	−	4.49674e29i	−0.567482	−	0.567482i	0.363940	−	0.931422i	$-0.381431\pi$
$977$	−4.49674e29	−	4.49674e29i	−0.567482	−	0.567482i	−0.931422	+	0.363940i	$0.881431\pi$
$978$	2.00184e29	−	2.00184e29i	0.250059	−	0.250059i
$979$			7.86579e29i			0.972557i
$980$	4.92539e28	−	8.17308e28i	0.0602810	−	0.100029i
$981$	4.80198e29			0.581742
$982$	1.42493e29	+	1.42493e29i	0.170876	+	0.170876i
$983$	−2.38392e29	+	2.38392e29i	−0.282981	+	0.282981i	−0.834297	−	0.551316i	$-0.814126\pi$
$983$	−2.38392e29	+	2.38392e29i	−0.282981	+	0.282981i	0.551316	+	0.834297i	$0.314126\pi$
$984$		−	5.02911e28i		−	0.0590936i
$985$	−4.64795e29	+	1.15243e29i	−0.540629	+	0.134045i
$986$	−3.47955e28			−0.0400640
$987$	5.28681e29	+	5.28681e29i	0.602590	+	0.602590i
$988$	−9.99439e29	+	9.99439e29i	−1.12768	+	1.12768i
$989$			1.01844e27i			0.00113755i
$990$	4.98692e28	+	2.01131e29i	0.0551417	+	0.222396i
$991$	−5.61776e29			−0.614932			−0.307466	−	0.951559i	$-0.599481\pi$
$991$	−5.61776e29			−0.614932			−0.307466	+	0.951559i	$0.599481\pi$
$992$	4.31637e29	+	4.31637e29i	0.467737	+	0.467737i
$993$	−4.96244e29	+	4.96244e29i	−0.532357	+	0.532357i
$994$		−	8.86887e29i		−	0.941899i
$995$	6.81021e29	+	4.10408e29i	0.716027	+	0.431504i
$996$	−4.26453e29			−0.443893
$997$	−6.62572e29	−	6.62572e29i	−0.682781	−	0.682781i	0.277845	−	0.960626i	$-0.410380\pi$
$997$	−6.62572e29	−	6.62572e29i	−0.682781	−	0.682781i	−0.960626	+	0.277845i	$0.910380\pi$
$998$	2.77579e28	−	2.77579e28i	0.0283192	−	0.0283192i
$999$		−	5.19539e29i		−	0.524763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.21.c.a.2.4	✓	18
3.2	odd	2		45.21.g.a.37.6		18
5.2	odd	4		25.21.c.b.18.6		18
5.3	odd	4	inner	5.21.c.a.3.4	yes	18
5.4	even	2		25.21.c.b.7.6		18
15.8	even	4		45.21.g.a.28.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.21.c.a.2.4	✓	18	1.1	even	1	trivial
5.21.c.a.3.4	yes	18	5.3	odd	4	inner
25.21.c.b.7.6		18	5.4	even	2
25.21.c.b.18.6		18	5.2	odd	4
45.21.g.a.28.6		18	15.8	even	4
45.21.g.a.37.6		18	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-439.799 - 439.799i) q^{2} +(-48235.4 + 48235.4i) q^{3} -661730. i q^{4} +(5.04058e6 - 8.36421e6i) q^{5} +4.24277e7 q^{6} +(-2.17438e8 - 2.17438e8i) q^{7} +(-7.52190e8 + 7.52190e8i) q^{8} -1.16652e9i q^{9} +O(q^{10})\)	\(q+(-439.799 - 439.799i) q^{2} +(-48235.4 + 48235.4i) q^{3} -661730. i q^{4} +(5.04058e6 - 8.36421e6i) q^{5} +4.24277e7 q^{6} +(-2.17438e8 - 2.17438e8i) q^{7} +(-7.52190e8 + 7.52190e8i) q^{8} -1.16652e9i q^{9} +(-5.89541e9 + 1.46173e9i) q^{10} +2.92465e10 q^{11} +(3.19188e10 + 3.19188e10i) q^{12} +(-1.32797e11 + 1.32797e11i) q^{13} +1.91258e11i q^{14} +(1.60317e11 + 6.46585e11i) q^{15} -3.22498e10 q^{16} +(-1.20974e11 - 1.20974e11i) q^{17} +(-5.13033e11 + 5.13033e11i) q^{18} +1.13733e13i q^{19} +(-5.53485e12 - 3.33550e12i) q^{20} +2.09764e13 q^{21} +(-1.28626e13 - 1.28626e13i) q^{22} +(2.06261e11 - 2.06261e11i) q^{23} -7.25644e13i q^{24} +(-4.45526e13 - 8.43209e13i) q^{25} +1.16808e14 q^{26} +(-1.11919e14 - 1.11919e14i) q^{27} +(-1.43886e14 + 1.43886e14i) q^{28} +3.26999e14i q^{29} +(2.13860e14 - 3.54874e14i) q^{30} +5.37589e14 q^{31} +(8.02912e14 + 8.02912e14i) q^{32} +(-1.41072e15 + 1.41072e15i) q^{33} +1.06409e14i q^{34} +(-2.91471e15 + 7.22685e14i) q^{35} -7.71921e14 q^{36} +(2.32105e15 + 2.32105e15i) q^{37} +(5.00197e15 - 5.00197e15i) q^{38} -1.28110e16i q^{39} +(2.50000e15 + 1.00830e16i) q^{40} +6.93055e14 q^{41} +(-9.22541e15 - 9.22541e15i) q^{42} +(-2.46881e15 + 2.46881e15i) q^{43} -1.93533e16i q^{44} +(-9.75701e15 - 5.87993e15i) q^{45} -1.81426e14 q^{46} +(2.52036e16 + 2.52036e16i) q^{47} +(1.55558e15 - 1.55558e15i) q^{48} +1.47666e16i q^{49} +(-1.74901e16 + 5.66784e16i) q^{50} +1.16705e16 q^{51} +(8.78759e16 + 8.78759e16i) q^{52} +(-2.12298e17 + 2.12298e17i) q^{53} +9.84436e16i q^{54} +(1.47419e17 - 2.44624e17i) q^{55} +3.27110e17 q^{56} +(-5.48596e17 - 5.48596e17i) q^{57} +(1.43814e17 - 1.43814e17i) q^{58} -1.07910e17i q^{59} +(4.27865e17 - 1.06086e17i) q^{60} -4.78276e17 q^{61} +(-2.36431e17 - 2.36431e17i) q^{62} +(-2.53646e17 + 2.53646e17i) q^{63} -6.72423e17i q^{64} +(4.41369e17 + 1.78012e18i) q^{65} +1.24086e18 q^{66} +(-9.30171e16 - 9.30171e16i) q^{67} +(-8.00524e16 + 8.00524e16i) q^{68} +1.98981e16i q^{69} +(1.59972e18 + 9.64052e17i) q^{70} -4.63712e18 q^{71} +(8.77444e17 + 8.77444e17i) q^{72} +(-4.17970e18 + 4.17970e18i) q^{73} -2.04159e18i q^{74} +(6.21626e18 + 1.91824e18i) q^{75} +7.52606e18 q^{76} +(-6.35931e18 - 6.35931e18i) q^{77} +(-5.63428e18 + 5.63428e18i) q^{78} -1.74550e19i q^{79} +(-1.62557e17 + 2.69744e17i) q^{80} +1.48643e19 q^{81} +(-3.04805e17 - 3.04805e17i) q^{82} +(-6.68028e18 + 6.68028e18i) q^{83} -1.38807e19i q^{84} +(-1.62164e18 + 4.02074e17i) q^{85} +2.17156e18 q^{86} +(-1.57729e19 - 1.57729e19i) q^{87} +(-2.19989e19 + 2.19989e19i) q^{88} +2.68948e19i q^{89} +(1.70513e18 + 6.87710e18i) q^{90} +5.77504e19 q^{91} +(-1.36489e17 - 1.36489e17i) q^{92} +(-2.59308e19 + 2.59308e19i) q^{93} -2.21690e19i q^{94} +(9.51288e19 + 5.73281e19i) q^{95} -7.74575e19 q^{96} +(2.43424e18 + 2.43424e18i) q^{97} +(6.49432e18 - 6.49432e18i) q^{98} -3.41166e19i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8	\( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8 - 17138778090 * q^10 - 6506343064 * q^11 + 140311795848 * q^12 - 369354655602 * q^13 + 998626204320 * q^15 - 6345876020232 * q^16 + 6508314764998 * q^17 - 11265991705902 * q^18 + 38356516779780 * q^20 - 97402974719064 * q^21 + 161054386758096 * q^22 - 81655963656152 * q^23 + 33913283845350 * q^25 + 234104101103636 * q^26 - 511935279143400 * q^27 + 772213614545352 * q^28 - 877127470680480 * q^30 + 1742256896900736 * q^31 - 4072699683722552 * q^32 + 1579138514189496 * q^33 - 4817791288113440 * q^35 + 2214548622647868 * q^36 + 6383289895587498 * q^37 - 14134212502378200 * q^38 + 43297629431150700 * q^40 - 30602304597564664 * q^41 + 48810732785962896 * q^42 - 46399469942287752 * q^43 + 67947826451186070 * q^45 + 17467214047538136 * q^46 - 137109249757437752 * q^47 - 103698596104819152 * q^48 - 40012852869983150 * q^50 + 686047946059669536 * q^51 - 745026624616846452 * q^52 - 184102027021671302 * q^53 + 752956242406989720 * q^55 + 685775432394721200 * q^56 - 785021725278622800 * q^57 - 2701246502184220800 * q^58 + 6219197632829342760 * q^60 + 49879194030044136 * q^61 - 1190554579738283704 * q^62 - 7082176979112100152 * q^63 + 6907070599410641170 * q^65 + 11227963704975799872 * q^66 - 5597336519263153752 * q^67 - 25617328014464685148 * q^68 + 31706333959370270760 * q^70 + 10983277495574224736 * q^71 - 41525052650392592700 * q^72 - 19072400700441139902 * q^73 + 36766882672050433200 * q^75 + 75630007803532292400 * q^76 - 47766064678699704904 * q^77 - 109239984515466629304 * q^78 + 134231700802559812960 * q^80 + 74219234884008322518 * q^81 - 83501540658117625104 * q^82 - 119739383617210903952 * q^83 + 169044713294843560110 * q^85 + 33497378050769887736 * q^86 - 28944830404542403200 * q^87 - 337125565675837197600 * q^88 + 396784292056608506070 * q^90 + 86281377644254817136 * q^91 - 206921051460419061752 * q^92 - 285487695991878257304 * q^93 + 118106834336527303800 * q^95 + 377091713708556287136 * q^96 - 318608382222604685502 * q^97 - 27697031317753120498 * q^98

Introduction

L-functions

Modular forms

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