LMFDB - Embedded newform 5.21.c.a.2.3

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			2.3
Root			$670.386i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.21.c.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-670.386 - 670.386i) q^{2} +(17254.5 - 17254.5i) q^{3} -149742. i q^{4} +(4.96780e6 + 8.40764e6i) q^{5} -2.31343e7 q^{6} +(9.51724e7 + 9.51724e7i) q^{7} +(-8.03335e8 + 8.03335e8i) q^{8} +2.89135e9i q^{9} +O(q^{10})$	\(q+(-670.386 - 670.386i) q^{2} +(17254.5 - 17254.5i) q^{3} -149742. i q^{4} +(4.96780e6 + 8.40764e6i) q^{5} -2.31343e7 q^{6} +(9.51724e7 + 9.51724e7i) q^{7} +(-8.03335e8 + 8.03335e8i) q^{8} +2.89135e9i q^{9} +(2.30602e9 - 8.96670e9i) q^{10} +1.64301e10 q^{11} +(-2.58372e9 - 2.58372e9i) q^{12} +(1.63865e11 - 1.63865e11i) q^{13} -1.27604e11i q^{14} +(2.30786e11 + 5.93527e10i) q^{15} +9.20073e11 q^{16} +(1.01198e12 + 1.01198e12i) q^{17} +(1.93832e12 - 1.93832e12i) q^{18} -3.85220e12i q^{19} +(1.25898e12 - 7.43887e11i) q^{20} +3.28430e12 q^{21} +(-1.10145e13 - 1.10145e13i) q^{22} +(-1.75206e13 + 1.75206e13i) q^{23} +2.77222e13i q^{24} +(-4.60094e13 + 8.35349e13i) q^{25} -2.19705e14 q^{26} +(1.10051e14 + 1.10051e14i) q^{27} +(1.42513e13 - 1.42513e13i) q^{28} -4.19714e14i q^{29} +(-1.14926e14 - 1.94505e14i) q^{30} +1.16378e15 q^{31} +(2.25554e14 + 2.25554e14i) q^{32} +(2.83493e14 - 2.83493e14i) q^{33} -1.35683e15i q^{34} +(-3.27378e14 + 1.27297e15i) q^{35} +4.32956e14 q^{36} +(2.42381e15 + 2.42381e15i) q^{37} +(-2.58246e15 + 2.58246e15i) q^{38} -5.65480e15i q^{39} +(-1.07450e16 - 2.76335e15i) q^{40} +6.21313e15 q^{41} +(-2.20175e15 - 2.20175e15i) q^{42} +(-1.85951e16 + 1.85951e16i) q^{43} -2.46028e15i q^{44} +(-2.43094e16 + 1.43636e16i) q^{45} +2.34911e16 q^{46} +(2.20380e16 + 2.20380e16i) q^{47} +(1.58754e16 - 1.58754e16i) q^{48} -6.16767e16i q^{49} +(8.68447e16 - 2.51565e16i) q^{50} +3.49222e16 q^{51} +(-2.45374e16 - 2.45374e16i) q^{52} +(4.27674e16 - 4.27674e16i) q^{53} -1.47554e17i q^{54} +(8.16215e16 + 1.38139e17i) q^{55} -1.52911e17 q^{56} +(-6.64677e16 - 6.64677e16i) q^{57} +(-2.81370e17 + 2.81370e17i) q^{58} +8.59684e17i q^{59} +(8.88758e15 - 3.45583e16i) q^{60} -2.26704e17 q^{61} +(-7.80179e17 - 7.80179e17i) q^{62} +(-2.75177e17 + 2.75177e17i) q^{63} -1.26718e18i q^{64} +(2.19176e18 + 5.63670e17i) q^{65} -3.80099e17 q^{66} +(-1.90225e17 - 1.90225e17i) q^{67} +(1.51535e17 - 1.51535e17i) q^{68} +6.04616e17i q^{69} +(1.07285e18 - 6.33913e17i) q^{70} +6.18041e18 q^{71} +(-2.32272e18 - 2.32272e18i) q^{72} +(-4.37711e18 + 4.37711e18i) q^{73} -3.24978e18i q^{74} +(6.47482e17 + 2.23522e18i) q^{75} -5.76836e17 q^{76} +(1.56369e18 + 1.56369e18i) q^{77} +(-3.79090e18 + 3.79090e18i) q^{78} -1.66472e19i q^{79} +(4.57074e18 + 7.73565e18i) q^{80} -6.28376e18 q^{81} +(-4.16519e18 - 4.16519e18i) q^{82} +(-1.64730e19 + 1.64730e19i) q^{83} -4.91797e17i q^{84} +(-3.48104e18 + 1.35356e19i) q^{85} +2.49317e19 q^{86} +(-7.24194e18 - 7.24194e18i) q^{87} +(-1.31989e19 + 1.31989e19i) q^{88} -3.70725e19i q^{89} +(2.59259e19 + 6.66752e18i) q^{90} +3.11908e19 q^{91} +(2.62356e18 + 2.62356e18i) q^{92} +(2.00803e19 - 2.00803e19i) q^{93} -2.95480e19i q^{94} +(3.23879e19 - 1.91369e19i) q^{95} +7.78363e18 q^{96} +(-2.73465e19 - 2.73465e19i) q^{97} +(-4.13472e19 + 4.13472e19i) q^{98} +4.75052e19i 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 $

$2$	−670.386	−	670.386i	−0.654674	−	0.654674i	0.299441	−	0.954115i	$-0.403200\pi$
$2$	−670.386	−	670.386i	−0.654674	−	0.654674i	−0.954115	+	0.299441i	$0.903200\pi$
$3$	17254.5	−	17254.5i	0.292206	−	0.292206i	−0.545745	−	0.837951i	$-0.683753\pi$
$3$	17254.5	−	17254.5i	0.292206	−	0.292206i	0.837951	+	0.545745i	$0.183753\pi$
$4$		−	149742.i		−	0.142805i
$5$	4.96780e6	+	8.40764e6i	0.508702	+	0.860942i
$5$	4.96780e6	+	8.40764e6i	0.508702	+	0.860942i
$6$	−2.31343e7			−0.382599
$7$	9.51724e7	+	9.51724e7i	0.336923	+	0.336923i	0.855208	−	0.518285i	$-0.173429\pi$
$7$	9.51724e7	+	9.51724e7i	0.336923	+	0.336923i	−0.518285	+	0.855208i	$0.673429\pi$
$8$	−8.03335e8	+	8.03335e8i	−0.748164	+	0.748164i
$9$			2.89135e9i			0.829231i
$10$	2.30602e9	−	8.96670e9i	0.230602	−	0.896670i
$11$	1.64301e10			0.633452			0.316726	−	0.948517i	$-0.397416\pi$
$11$	1.64301e10			0.633452			0.316726	+	0.948517i	$0.397416\pi$
$12$	−2.58372e9	−	2.58372e9i	−0.0417284	−	0.0417284i
$13$	1.63865e11	−	1.63865e11i	1.18865	−	1.18865i	0.211203	−	0.977442i	$-0.432262\pi$
$13$	1.63865e11	−	1.63865e11i	1.18865	−	1.18865i	0.977442	−	0.211203i	$-0.0677381\pi$
$14$		−	1.27604e11i		−	0.441149i
$15$	2.30786e11	+	5.93527e10i	0.400218	+	0.102927i
$16$	9.20073e11			0.836802
$17$	1.01198e12	+	1.01198e12i	0.501974	+	0.501974i	0.912051	−	0.410077i	$-0.134498\pi$
$17$	1.01198e12	+	1.01198e12i	0.501974	+	0.501974i	−0.410077	+	0.912051i	$0.634498\pi$
$18$	1.93832e12	−	1.93832e12i	0.542876	−	0.542876i
$19$		−	3.85220e12i		−	0.628308i	−0.949372	−	0.314154i	$-0.898279\pi$
$19$		−	3.85220e12i		−	0.628308i	0.949372	−	0.314154i	$-0.101721\pi$
$20$	1.25898e12	−	7.43887e11i	0.122947	−	0.0726452i
$21$	3.28430e12			0.196902
$22$	−1.10145e13	−	1.10145e13i	−0.414704	−	0.414704i
$23$	−1.75206e13	+	1.75206e13i	−0.422931	+	0.422931i	−0.886212	−	0.463281i	$-0.846672\pi$
$23$	−1.75206e13	+	1.75206e13i	−0.422931	+	0.422931i	0.463281	+	0.886212i	$0.346672\pi$
$24$			2.77222e13i			0.437236i
$25$	−4.60094e13	+	8.35349e13i	−0.482444	+	0.875927i
$26$	−2.19705e14			−1.55635
$27$	1.10051e14	+	1.10051e14i	0.534512	+	0.534512i
$28$	1.42513e13	−	1.42513e13i	0.0481142	−	0.0481142i
$29$		−	4.19714e14i		−	0.997639i	−0.866706	−	0.498820i	$-0.833767\pi$
$29$		−	4.19714e14i		−	0.997639i	0.866706	−	0.498820i	$-0.166233\pi$
$30$	−1.14926e14	−	1.94505e14i	−0.194629	−	0.329396i
$31$	1.16378e15			1.41988			0.709941	−	0.704261i	$-0.248722\pi$
$31$	1.16378e15			1.41988			0.709941	+	0.704261i	$0.248722\pi$
$32$	2.25554e14	+	2.25554e14i	0.200332	+	0.200332i
$33$	2.83493e14	−	2.83493e14i	0.185099	−	0.185099i
$34$		−	1.35683e15i		−	0.657258i
$35$	−3.27378e14	+	1.27297e15i	−0.118678	+	0.461465i
$36$	4.32956e14			0.118418
$37$	2.42381e15	+	2.42381e15i	0.504060	+	0.504060i	0.912697	−	0.408637i	$-0.133996\pi$
$37$	2.42381e15	+	2.42381e15i	0.504060	+	0.504060i	−0.408637	+	0.912697i	$0.633996\pi$
$38$	−2.58246e15	+	2.58246e15i	−0.411337	+	0.411337i
$39$		−	5.65480e15i		−	0.694658i
$40$	−1.07450e16	−	2.76335e15i	−1.02472	−	0.263533i
$41$	6.21313e15			0.462883			0.231442	−	0.972849i	$-0.425656\pi$
$41$	6.21313e15			0.462883			0.231442	+	0.972849i	$0.425656\pi$
$42$	−2.20175e15	−	2.20175e15i	−0.128906	−	0.128906i
$43$	−1.85951e16	+	1.85951e16i	−0.860425	+	0.860425i	−0.991387	−	0.130963i	$-0.958193\pi$
$43$	−1.85951e16	+	1.85951e16i	−0.860425	+	0.860425i	0.130963	+	0.991387i	$0.458193\pi$
$44$		−	2.46028e15i		−	0.0904601i
$45$	−2.43094e16	+	1.43636e16i	−0.713921	+	0.421832i
$46$	2.34911e16			0.553764
$47$	2.20380e16	+	2.20380e16i	0.418981	+	0.418981i	0.884852	−	0.465872i	$-0.154259\pi$
$47$	2.20380e16	+	2.20380e16i	0.418981	+	0.418981i	−0.465872	+	0.884852i	$0.654259\pi$
$48$	1.58754e16	−	1.58754e16i	0.244518	−	0.244518i
$49$		−	6.16767e16i		−	0.772966i
$50$	8.68447e16	−	2.51565e16i	0.889289	−	0.257603i
$51$	3.49222e16			0.293359
$52$	−2.45374e16	−	2.45374e16i	−0.169744	−	0.169744i
$53$	4.27674e16	−	4.27674e16i	0.244542	−	0.244542i	−0.574184	−	0.818726i	$-0.694681\pi$
$53$	4.27674e16	−	4.27674e16i	0.244542	−	0.244542i	0.818726	+	0.574184i	$0.194681\pi$
$54$		−	1.47554e17i		−	0.699862i
$55$	8.16215e16	+	1.38139e17i	0.322239	+	0.545366i
$56$	−1.52911e17			−0.504147
$57$	−6.64677e16	−	6.64677e16i	−0.183595	−	0.183595i
$58$	−2.81370e17	+	2.81370e17i	−0.653128	+	0.653128i
$59$			8.59684e17i			1.68197i	0.541058	+	0.840986i	$0.318024\pi$
$59$			8.59684e17i			1.68197i	−0.541058	+	0.840986i	$0.681976\pi$
$60$	8.88758e15	−	3.45583e16i	0.0146984	−	0.0571532i
$61$	−2.26704e17			−0.317804			−0.158902	−	0.987294i	$-0.550795\pi$
$61$	−2.26704e17			−0.317804			−0.158902	+	0.987294i	$0.550795\pi$
$62$	−7.80179e17	−	7.80179e17i	−0.929559	−	0.929559i
$63$	−2.75177e17	+	2.75177e17i	−0.279387	+	0.279387i
$64$		−	1.26718e18i		−	1.09911i
$65$	2.19176e18	+	5.63670e17i	1.62802	+	0.418689i
$66$	−3.80099e17			−0.242358
$67$	−1.90225e17	−	1.90225e17i	−0.104356	−	0.104356i	0.653001	−	0.757357i	$-0.273510\pi$
$67$	−1.90225e17	−	1.90225e17i	−0.104356	−	0.104356i	−0.757357	+	0.653001i	$0.773510\pi$
$68$	1.51535e17	−	1.51535e17i	0.0716843	−	0.0716843i
$69$			6.04616e17i			0.247166i
$70$	1.07285e18	−	6.33913e17i	0.379804	−	0.224414i
$71$	6.18041e18			1.89860			0.949301	−	0.314368i	$-0.101793\pi$
$71$	6.18041e18			1.89860			0.949301	+	0.314368i	$0.101793\pi$
$72$	−2.32272e18	−	2.32272e18i	−0.620401	−	0.620401i
$73$	−4.37711e18	+	4.37711e18i	−1.01850	+	1.01850i	−0.0186701	+	0.999826i	$0.505943\pi$
$73$	−4.37711e18	+	4.37711e18i	−1.01850	+	1.01850i	−0.999826	+	0.0186701i	$0.994057\pi$
$74$		−	3.24978e18i		−	0.659989i
$75$	6.47482e17	+	2.23522e18i	0.114978	+	0.396924i
$76$	−5.76836e17			−0.0897255
$77$	1.56369e18	+	1.56369e18i	0.213425	+	0.213425i
$78$	−3.79090e18	+	3.79090e18i	−0.454775	+	0.454775i
$79$		−	1.66472e19i		−	1.75821i	−0.476629	−	0.879105i	$-0.658141\pi$
$79$		−	1.66472e19i		−	1.75821i	0.476629	−	0.879105i	$-0.341859\pi$
$80$	4.57074e18	+	7.73565e18i	0.425683	+	0.720438i
$81$	−6.28376e18			−0.516856
$82$	−4.16519e18	−	4.16519e18i	−0.303038	−	0.303038i
$83$	−1.64730e19	+	1.64730e19i	−1.06168	+	1.06168i	−0.0637101	+	0.997968i	$0.520293\pi$
$83$	−1.64730e19	+	1.64730e19i	−1.06168	+	1.06168i	−0.997968	+	0.0637101i	$0.979707\pi$
$84$		−	4.91797e17i		−	0.0281185i
$85$	−3.48104e18	+	1.35356e19i	−0.176815	+	0.687526i
$86$	2.49317e19			1.12659
$87$	−7.24194e18	−	7.24194e18i	−0.291516	−	0.291516i
$88$	−1.31989e19	+	1.31989e19i	−0.473926	+	0.473926i
$89$		−	3.70725e19i		−	1.18892i	−0.804126	−	0.594459i	$-0.797366\pi$
$89$		−	3.70725e19i		−	1.18892i	0.804126	−	0.594459i	$-0.202634\pi$
$90$	2.59259e19	+	6.66752e18i	0.743547	+	0.191223i
$91$	3.11908e19			0.800963
$92$	2.62356e18	+	2.62356e18i	0.0603967	+	0.0603967i
$93$	2.00803e19	−	2.00803e19i	0.414898	−	0.414898i
$94$		−	2.95480e19i		−	0.548591i
$95$	3.23879e19	−	1.91369e19i	0.540937	−	0.319622i
$96$	7.78363e18			0.117076
$97$	−2.73465e19	−	2.73465e19i	−0.370838	−	0.370838i	0.496944	−	0.867783i	$-0.334455\pi$
$97$	−2.73465e19	−	2.73465e19i	−0.370838	−	0.370838i	−0.867783	+	0.496944i	$0.834455\pi$
$98$	−4.13472e19	+	4.13472e19i	−0.506040	+	0.506040i
$99$			4.75052e19i			0.525278i
$100$	1.25087e19	+	6.88954e18i	0.125087	+	0.0688954i
$101$	−1.08232e20			−0.979810			−0.489905	−	0.871776i	$-0.662969\pi$
$101$	−1.08232e20			−0.979810			−0.489905	+	0.871776i	$0.662969\pi$
$102$	−2.34114e19	−	2.34114e19i	−0.192055	−	0.192055i
$103$	−1.84893e19	+	1.84893e19i	−0.137578	+	0.137578i	−0.772542	−	0.634964i	$-0.781015\pi$
$103$	−1.84893e19	+	1.84893e19i	−0.137578	+	0.137578i	0.634964	+	0.772542i	$0.281015\pi$
$104$			2.63277e20i			1.77860i
$105$	1.63157e19	+	2.76132e19i	0.100164	+	0.169521i
$106$	−5.73413e19			−0.320191
$107$	−9.57718e19	−	9.57718e19i	−0.486855	−	0.486855i	0.420457	−	0.907312i	$-0.361870\pi$
$107$	−9.57718e19	−	9.57718e19i	−0.486855	−	0.486855i	−0.907312	+	0.420457i	$0.861870\pi$
$108$	1.64793e19	−	1.64793e19i	0.0763310	−	0.0763310i
$109$		−	1.84936e20i		−	0.781188i	−0.920563	−	0.390594i	$-0.872270\pi$
$109$		−	1.84936e20i		−	0.781188i	0.920563	−	0.390594i	$-0.127730\pi$
$110$	3.78882e19	−	1.47324e20i	0.146076	−	0.567998i
$111$	8.36432e19			0.294578
$112$	8.75656e19	+	8.75656e19i	0.281938	+	0.281938i
$113$	2.07227e20	−	2.07227e20i	0.610466	−	0.610466i	−0.332602	−	0.943067i	$-0.607926\pi$
$113$	2.07227e20	−	2.07227e20i	0.610466	−	0.610466i	0.943067	+	0.332602i	$0.107926\pi$
$114$			8.91180e19i			0.240390i
$115$	−2.34345e20	−	6.02680e19i	−0.579265	−	0.148973i
$116$	−6.28487e19			−0.142468
$117$	4.73791e20	+	4.73791e20i	0.985662	+	0.985662i
$118$	5.76320e20	−	5.76320e20i	1.10114	−	1.10114i
$119$			1.92624e20i			0.338253i
$120$	−2.33079e20	+	1.37718e20i	−0.376435	+	0.222423i
$121$	−4.02801e20			−0.598738
$122$	1.51979e20	+	1.51979e20i	0.208058	+	0.208058i
$123$	1.07204e20	−	1.07204e20i	0.135257	−	0.135257i
$124$		−	1.74266e20i		−	0.202766i
$125$	−9.30897e20	+	2.81536e19i	−0.999543	+	0.0302297i
$126$	3.68949e20			0.365815
$127$	1.27942e20	+	1.27942e20i	0.117213	+	0.117213i	0.763280	−	0.646067i	$-0.223588\pi$
$127$	1.27942e20	+	1.27942e20i	0.117213	+	0.117213i	−0.646067	+	0.763280i	$0.723588\pi$
$128$	−6.12991e20	+	6.12991e20i	−0.519224	+	0.519224i
$129$			6.41695e20i			0.502842i
$130$	−1.09145e21	−	1.84720e21i	−0.791719	−	1.33993i
$131$	−8.11019e18			−0.00544901			−0.00272451	−	0.999996i	$-0.500867\pi$
$131$	−8.11019e18			−0.00544901			−0.00272451	+	0.999996i	$0.500867\pi$
$132$	−4.24508e19	−	4.24508e19i	−0.0264330	−	0.0264330i
$133$	3.66623e20	−	3.66623e20i	0.211691	−	0.211691i
$134$			2.55048e20i			0.136639i
$135$	−3.78560e20	+	1.47198e21i	−0.188277	+	0.732092i
$136$	−1.62591e21			−0.751118
$137$	2.98481e21	+	2.98481e21i	1.28148	+	1.28148i	0.939828	+	0.341647i	$0.110985\pi$
$137$	2.98481e21	+	2.98481e21i	1.28148	+	1.28148i	0.341647	+	0.939828i	$0.389015\pi$
$138$	4.05326e20	−	4.05326e20i	0.161813	−	0.161813i
$139$		−	4.52877e20i		−	0.168202i	−0.996457	−	0.0841011i	$-0.973198\pi$
$139$		−	4.52877e20i		−	0.168202i	0.996457	−	0.0841011i	$-0.0268019\pi$
$140$	1.90617e20	+	4.90222e19i	0.0658994	+	0.0169478i
$141$	7.60509e20			0.244857
$142$	−4.14326e21	−	4.14326e21i	−1.24296	−	1.24296i
$143$	2.69232e21	−	2.69232e21i	0.752950	−	0.752950i
$144$			2.66026e21i			0.693902i
$145$	3.52880e21	−	2.08505e21i	0.858910	−	0.507501i
$146$	5.86871e21			1.33356
$147$	−1.06420e21	−	1.06420e21i	−0.225865	−	0.225865i
$148$	3.62946e20	−	3.62946e20i	0.0719822	−	0.0719822i
$149$			1.65648e20i			0.0307131i	0.999882	+	0.0153566i	$0.00488834\pi$
$149$			1.65648e20i			0.0307131i	−0.999882	+	0.0153566i	$0.995112\pi$
$150$	1.06440e21	−	1.93252e21i	0.184583	−	0.335129i
$151$	−1.00574e22			−1.63198			−0.815989	−	0.578068i	$-0.803807\pi$
$151$	−1.00574e22			−1.63198			−0.815989	+	0.578068i	$0.803807\pi$
$152$	3.09461e21	+	3.09461e21i	0.470078	+	0.470078i
$153$	−2.92598e21	+	2.92598e21i	−0.416252	+	0.416252i
$154$		−	2.09656e21i		−	0.279447i
$155$	5.78140e21	+	9.78461e21i	0.722297	+	1.22244i
$156$	−8.46760e20			−0.0992006
$157$	−1.01160e22	−	1.01160e22i	−1.11176	−	1.11176i	−0.992912	−	0.118850i	$-0.962079\pi$
$157$	−1.01160e22	−	1.01160e22i	−1.11176	−	1.11176i	−0.118850	−	0.992912i	$-0.537921\pi$
$158$	−1.11601e22	+	1.11601e22i	−1.15105	+	1.15105i
$159$		−	1.47586e21i		−	0.142913i
$160$	−7.75871e20	+	3.01688e21i	−0.0705650	+	0.274384i
$161$	−3.33495e21			−0.284990
$162$	4.21255e21	+	4.21255e21i	0.338372	+	0.338372i
$163$	−3.08856e20	+	3.08856e20i	−0.0233282	+	0.0233282i	−0.718675	−	0.695346i	$-0.755251\pi$
$163$	−3.08856e20	+	3.08856e20i	−0.0233282	+	0.0233282i	0.695346	+	0.718675i	$0.255251\pi$
$164$		−	9.30365e20i		−	0.0661020i
$165$	3.79184e21	+	9.75172e20i	0.253519	+	0.0651991i
$166$	2.20866e22			1.39011
$167$	−7.80216e21	−	7.80216e21i	−0.462434	−	0.462434i	0.437018	−	0.899453i	$-0.356035\pi$
$167$	−7.80216e21	−	7.80216e21i	−0.462434	−	0.462434i	−0.899453	+	0.437018i	$0.856035\pi$
$168$	−2.63839e21	+	2.63839e21i	−0.147315	+	0.147315i
$169$		−	3.46984e22i		−	1.82575i
$170$	1.14077e22	−	6.74045e21i	0.565861	−	0.334349i
$171$	1.11381e22			0.521013
$172$	2.78446e21	+	2.78446e21i	0.122873	+	0.122873i
$173$	4.62227e20	−	4.62227e20i	0.0192484	−	0.0192484i	−0.697417	−	0.716665i	$-0.745667\pi$
$173$	4.62227e20	−	4.62227e20i	0.0192484	−	0.0192484i	0.716665	+	0.697417i	$0.245667\pi$
$174$			9.70979e21i			0.381696i
$175$	−1.23290e22	+	3.57139e21i	−0.457666	+	0.132573i
$176$	1.51169e22			0.530074
$177$	1.48334e22	+	1.48334e22i	0.491482	+	0.491482i
$178$	−2.48529e22	+	2.48529e22i	−0.778353	+	0.778353i
$179$		−	9.29195e21i		−	0.275154i	−0.990491	−	0.137577i	$-0.956068\pi$
$179$		−	9.29195e21i		−	0.275154i	0.990491	−	0.137577i	$-0.0439315\pi$
$180$	2.15084e21	+	3.64014e21i	0.0602397	+	0.101951i
$181$	1.48883e22			0.394511			0.197255	−	0.980352i	$-0.436797\pi$
$181$	1.48883e22			0.394511			0.197255	+	0.980352i	$0.436797\pi$
$182$	−2.09099e22	−	2.09099e22i	−0.524370	−	0.524370i
$183$	−3.91165e21	+	3.91165e21i	−0.0928643	+	0.0928643i
$184$		−	2.81498e22i		−	0.632844i
$185$	−8.33754e21	+	3.24196e22i	−0.177550	+	0.690383i
$186$	−2.69231e22			−0.543246
$187$	1.66269e22	+	1.66269e22i	0.317976	+	0.317976i
$188$	3.30001e21	−	3.30001e21i	0.0598325	−	0.0598325i
$189$			2.09477e22i			0.360179i
$190$	−3.45415e22	−	8.88326e21i	−0.563386	−	0.144889i
$191$	−7.65756e22			−1.18510			−0.592552	−	0.805532i	$-0.701880\pi$
$191$	−7.65756e22			−1.18510			−0.592552	+	0.805532i	$0.701880\pi$
$192$	−2.18646e22	−	2.18646e22i	−0.321165	−	0.321165i
$193$	4.12834e22	−	4.12834e22i	0.575708	−	0.575708i	−0.358010	−	0.933718i	$-0.616544\pi$
$193$	4.12834e22	−	4.12834e22i	0.575708	−	0.575708i	0.933718	+	0.358010i	$0.116544\pi$
$194$			3.66654e22i			0.485556i
$195$	4.75435e22	−	2.80919e22i	0.598061	−	0.353374i
$196$	−9.23558e21			−0.110383
$197$	1.85485e22	+	1.85485e22i	0.210692	+	0.210692i	0.804561	−	0.593870i	$-0.202401\pi$
$197$	1.85485e22	+	1.85485e22i	0.210692	+	0.210692i	−0.593870	+	0.804561i	$0.702401\pi$
$198$	3.18468e22	−	3.18468e22i	0.343886	−	0.343886i
$199$			1.61230e23i			1.65544i	0.561139	+	0.827721i	$0.310363\pi$
$199$			1.61230e23i			1.65544i	−0.561139	+	0.827721i	$0.689637\pi$
$200$	−3.01455e22	−	1.04068e23i	−0.294390	−	1.01628i
$201$	−6.56445e21			−0.0609871
$202$	7.25572e22	+	7.25572e22i	0.641456	+	0.641456i
$203$	3.99452e22	−	3.99452e22i	0.336127	−	0.336127i
$204$		−	5.22932e21i		−	0.0418932i
$205$	3.08655e22	+	5.22377e22i	0.235470	+	0.398516i
$206$	2.47900e22			0.180138
$207$	−5.06581e22	−	5.06581e22i	−0.350708	−	0.350708i
$208$	1.50768e23	−	1.50768e23i	0.994660	−	0.994660i
$209$		−	6.32921e22i		−	0.398003i
$210$	7.57366e21	−	2.94493e22i	0.0454060	−	0.176556i
$211$	−5.20613e22			−0.297640			−0.148820	−	0.988864i	$-0.547547\pi$
$211$	−5.20613e22			−0.297640			−0.148820	+	0.988864i	$0.547547\pi$
$212$	−6.40406e21	−	6.40406e21i	−0.0349218	−	0.0349218i
$213$	1.06640e23	−	1.06640e23i	0.554783	−	0.554783i
$214$			1.28408e23i			0.637463i
$215$	−2.48717e23	−	6.39641e22i	−1.17848	−	0.303076i
$216$	−1.76816e23			−0.799806
$217$	1.10759e23	+	1.10759e23i	0.478391	+	0.478391i
$218$	−1.23978e23	+	1.23978e23i	−0.511423	+	0.511423i
$219$			1.51050e23i			0.595221i
$220$	2.06851e22	−	1.22222e22i	0.0778809	−	0.0460173i
$221$	3.31655e23			1.19334
$222$	−5.60732e22	−	5.60732e22i	−0.192853	−	0.192853i
$223$	−3.34631e23	+	3.34631e23i	−1.10032	+	1.10032i	−0.105944	+	0.994372i	$0.533786\pi$
$223$	−3.34631e23	+	3.34631e23i	−1.10032	+	1.10032i	−0.994372	+	0.105944i	$0.966214\pi$
$224$			4.29330e22i			0.134993i
$225$	−2.41529e23	−	1.33029e23i	−0.726346	−	0.400058i
$226$	−2.77844e23			−0.799312
$227$	1.22468e22	+	1.22468e22i	0.0337103	+	0.0337103i	0.723761	−	0.690051i	$-0.242412\pi$
$227$	1.22468e22	+	1.22468e22i	0.0337103	+	0.0337103i	−0.690051	+	0.723761i	$0.742412\pi$
$228$	−9.95299e21	+	9.95299e21i	−0.0262183	+	0.0262183i
$229$		−	1.42874e23i		−	0.360245i	−0.983644	−	0.180123i	$-0.942351\pi$
$229$		−	1.42874e23i		−	0.360245i	0.983644	−	0.180123i	$-0.0576495\pi$
$230$	1.16699e23	+	1.97504e23i	0.281701	+	0.476759i
$231$	5.39614e22			0.124728
$232$	3.37171e23	+	3.37171e23i	0.746398	+	0.746398i
$233$	4.68531e23	−	4.68531e23i	0.993526	−	0.993526i	−0.00645362	−	0.999979i	$-0.502054\pi$
$233$	4.68531e23	−	4.68531e23i	0.993526	−	0.993526i	0.999979	+	0.00645362i	$0.00205426\pi$
$234$		−	6.35245e23i		−	1.29057i
$235$	−7.58074e22	+	2.94768e23i	−0.147582	+	0.573855i
$236$	1.28731e23			0.240194
$237$	−2.87239e23	−	2.87239e23i	−0.513759	−	0.513759i
$238$	1.29133e23	−	1.29133e23i	0.221445	−	0.221445i
$239$		−	6.31792e23i		−	1.03895i	−0.854485	−	0.519476i	$-0.826127\pi$
$239$		−	6.31792e23i		−	1.03895i	0.854485	−	0.519476i	$-0.173873\pi$
$240$	2.12340e23	+	5.46088e22i	0.334903	+	0.0861292i
$241$	9.42815e23			1.42645			0.713224	−	0.700936i	$-0.247234\pi$
$241$	9.42815e23			1.42645			0.713224	+	0.700936i	$0.247234\pi$
$242$	2.70032e23	+	2.70032e23i	0.391978	+	0.391978i
$243$	−4.92148e23	+	4.92148e23i	−0.685541	+	0.685541i
$244$			3.39470e22i			0.0453840i
$245$	5.18556e23	−	3.06397e23i	0.665479	−	0.393210i
$246$	−1.43736e23			−0.177099
$247$	−6.31240e23	−	6.31240e23i	−0.746836	−	0.746836i
$248$	−9.34902e23	+	9.34902e23i	−1.06231	+	1.06231i
$249$			5.68467e23i			0.620458i
$250$	6.42934e23	+	6.05186e23i	0.674165	+	0.634584i
$251$	−8.07799e23			−0.813890			−0.406945	−	0.913453i	$-0.633406\pi$
$251$	−8.07799e23			−0.813890			−0.406945	+	0.913453i	$0.633406\pi$
$252$	4.12055e22	+	4.12055e22i	0.0398978	+	0.0398978i
$253$	−2.87865e23	+	2.87865e23i	−0.267907	+	0.267907i
$254$		−	1.71541e23i		−	0.153472i
$255$	1.73486e23	+	2.93614e23i	0.149233	+	0.252566i
$256$	−5.06857e23			−0.419262
$257$	−1.38516e24	−	1.38516e24i	−1.10196	−	1.10196i	−0.994174	−	0.107791i	$-0.965622\pi$
$257$	−1.38516e24	−	1.38516e24i	−1.10196	−	1.10196i	−0.107791	−	0.994174i	$-0.534378\pi$
$258$	4.30184e23	−	4.30184e23i	0.329198	−	0.329198i
$259$			4.61360e23i			0.339658i
$260$	8.44049e22	−	3.28199e23i	0.0597908	−	0.232490i
$261$	1.21354e24			0.827274
$262$	5.43696e21	+	5.43696e21i	0.00356733	+	0.00356733i
$263$	−5.60211e23	+	5.60211e23i	−0.353829	+	0.353829i	−0.861532	−	0.507703i	$-0.830495\pi$
$263$	−5.60211e23	+	5.60211e23i	−0.353829	+	0.353829i	0.507703	+	0.861532i	$0.330495\pi$
$264$			4.55480e23i			0.276968i
$265$	5.72032e23	+	1.47113e23i	0.334936	+	0.0861376i
$266$	−4.91558e23			−0.277178
$267$	−6.39666e23	−	6.39666e23i	−0.347409	−	0.347409i
$268$	−2.84846e22	+	2.84846e22i	−0.0149026	+	0.0149026i
$269$			5.07900e23i			0.256009i	0.991774	+	0.128005i	$0.0408572\pi$
$269$			5.07900e23i			0.256009i	−0.991774	+	0.128005i	$0.959143\pi$
$270$	1.24058e24	−	7.33017e23i	0.602541	−	0.356022i
$271$	4.25757e22			0.0199282			0.00996411	−	0.999950i	$-0.496828\pi$
$271$	4.25757e22			0.0199282			0.00996411	+	0.999950i	$0.496828\pi$
$272$	9.31092e23	+	9.31092e23i	0.420053	+	0.420053i
$273$	5.38181e23	−	5.38181e23i	0.234046	−	0.234046i
$274$		−	4.00194e24i		−	1.67790i
$275$	−7.55940e23	+	1.37249e24i	−0.305605	+	0.554858i
$276$	9.05363e22			0.0352965
$277$	1.59802e24	+	1.59802e24i	0.600875	+	0.600875i	0.940545	−	0.339669i	$-0.110315\pi$
$277$	1.59802e24	+	1.59802e24i	0.600875	+	0.600875i	−0.339669	+	0.940545i	$0.610315\pi$
$278$	−3.03602e23	+	3.03602e23i	−0.110118	+	0.110118i
$279$			3.36488e24i			1.17741i
$280$	−7.59629e23	−	1.28562e24i	−0.256461	−	0.434042i
$281$	3.89651e24			1.26944			0.634721	−	0.772742i	$-0.281115\pi$
$281$	3.89651e24			1.26944			0.634721	+	0.772742i	$0.281115\pi$
$282$	−5.09834e23	−	5.09834e23i	−0.160302	−	0.160302i
$283$	1.67995e24	−	1.67995e24i	0.509839	−	0.509839i	−0.404638	−	0.914477i	$-0.632602\pi$
$283$	1.67995e24	−	1.67995e24i	0.509839	−	0.509839i	0.914477	+	0.404638i	$0.132602\pi$
$284$		−	9.25466e23i		−	0.271130i
$285$	2.28638e23	−	8.89034e23i	0.0646697	−	0.251461i
$286$	−3.60978e24			−0.985873
$287$	5.91318e23	+	5.91318e23i	0.155956	+	0.155956i
$288$	−6.52156e23	+	6.52156e23i	−0.166122	+	0.166122i
$289$		−	2.01604e24i		−	0.496045i
$290$	−3.76345e24	−	9.67870e23i	−0.894553	−	0.230058i
$291$	−9.43699e23			−0.216722
$292$	6.55437e23	+	6.55437e23i	0.145446	+	0.145446i
$293$	2.94969e24	−	2.94969e24i	0.632557	−	0.632557i	−0.316152	−	0.948709i	$-0.602391\pi$
$293$	2.94969e24	−	2.94969e24i	0.632557	−	0.632557i	0.948709	+	0.316152i	$0.102391\pi$
$294$			1.42685e24i			0.295736i
$295$	−7.22791e24	+	4.27073e24i	−1.44808	+	0.855623i
$296$	−3.89427e24			−0.754239
$297$	1.80816e24	+	1.80816e24i	0.338588	+	0.338588i
$298$	1.11048e23	−	1.11048e23i	0.0201071	−	0.0201071i
$299$			5.74201e24i			1.00543i
$300$	3.34706e23	−	9.69551e22i	0.0566827	−	0.0164194i
$301$	−3.53947e24			−0.579793
$302$	6.74231e24	+	6.74231e24i	1.06841	+	1.06841i
$303$	−1.86749e24	+	1.86749e24i	−0.286306	+	0.286306i
$304$		−	3.54431e24i		−	0.525770i
$305$	−1.12622e24	−	1.90604e24i	−0.161668	−	0.273611i
$306$	3.92307e24			0.545019
$307$	−6.08551e24	−	6.08551e24i	−0.818302	−	0.818302i	0.167560	−	0.985862i	$-0.446411\pi$
$307$	−6.08551e24	−	6.08551e24i	−0.818302	−	0.818302i	−0.985862	+	0.167560i	$0.946411\pi$
$308$	2.34150e23	−	2.34150e23i	0.0304781	−	0.0304781i
$309$			6.38048e23i			0.0804023i
$310$	2.68369e24	−	1.04352e25i	0.327428	−	1.27317i
$311$	8.89425e24			1.05076			0.525382	−	0.850866i	$-0.323922\pi$
$311$	8.89425e24			1.05076			0.525382	+	0.850866i	$0.323922\pi$
$312$	4.54270e24	+	4.54270e24i	0.519719	+	0.519719i
$313$	1.11709e25	−	1.11709e25i	1.23778	−	1.23778i	0.276873	−	0.960906i	$-0.410702\pi$
$313$	1.11709e25	−	1.11709e25i	1.23778	−	1.23778i	0.960906	−	0.276873i	$-0.0892982\pi$
$314$			1.35632e25i			1.45568i
$315$	−3.68061e24	−	9.46565e23i	−0.382661	−	0.0984113i
$316$	−2.49278e24			−0.251081
$317$	−8.49770e24	−	8.49770e24i	−0.829294	−	0.829294i	0.158125	−	0.987419i	$-0.449455\pi$
$317$	−8.49770e24	−	8.49770e24i	−0.829294	−	0.829294i	−0.987419	+	0.158125i	$0.949455\pi$
$318$	−9.89393e23	+	9.89393e23i	−0.0935616	+	0.0935616i
$319$		−	6.89595e24i		−	0.631957i
$320$	1.06540e25	−	6.29511e24i	0.946267	−	0.559118i
$321$	−3.30498e24			−0.284524
$322$	2.23570e24	+	2.23570e24i	0.186576	+	0.186576i
$323$	3.89834e24	−	3.89834e24i	0.315394	−	0.315394i
$324$			9.40942e23i			0.0738096i
$325$	6.14910e24	+	2.12278e25i	0.467712	+	1.61462i
$326$	4.14106e23			0.0305447
$327$	−3.19096e24	−	3.19096e24i	−0.228268	−	0.228268i
$328$	−4.99122e24	+	4.99122e24i	−0.346313	+	0.346313i
$329$			4.19482e24i			0.282328i
$330$	−1.88826e24	−	3.19574e24i	−0.123288	−	0.208656i
$331$	−2.57503e25			−1.63118			−0.815590	−	0.578631i	$-0.803587\pi$
$331$	−2.57503e25			−1.63118			−0.815590	+	0.578631i	$0.803587\pi$
$332$	2.46670e24	+	2.46670e24i	0.151613	+	0.151613i
$333$	−7.00810e24	+	7.00810e24i	−0.417982	+	0.417982i
$334$			1.04609e25i			0.605487i
$335$	6.54343e23	−	2.54434e24i	0.0367585	−	0.142931i
$336$	3.02179e24			0.164768
$337$	−4.35992e24	−	4.35992e24i	−0.230770	−	0.230770i	0.582244	−	0.813014i	$-0.302175\pi$
$337$	−4.35992e24	−	4.35992e24i	−0.230770	−	0.230770i	−0.813014	+	0.582244i	$0.802175\pi$
$338$	−2.32613e25	+	2.32613e25i	−1.19527	+	1.19527i
$339$		−	7.15118e24i		−	0.356764i
$340$	2.02685e24	+	5.21257e23i	0.0981821	+	0.0252501i
$341$	1.91210e25			0.899428
$342$	−7.46680e24	−	7.46680e24i	−0.341094	−	0.341094i
$343$	1.34639e25	−	1.34639e25i	0.597353	−	0.597353i
$344$		−	2.98761e25i		−	1.28748i
$345$	−5.08339e24	+	3.00361e24i	−0.212796	+	0.125734i
$346$	−6.19741e23			−0.0252028
$347$	−5.71195e24	−	5.71195e24i	−0.225678	−	0.225678i	0.585206	−	0.810885i	$-0.301014\pi$
$347$	−5.71195e24	−	5.71195e24i	−0.225678	−	0.225678i	−0.810885	+	0.585206i	$0.801014\pi$
$348$	−1.08442e24	+	1.08442e24i	−0.0416299	+	0.0416299i
$349$		−	9.00712e24i		−	0.335994i	−0.985788	−	0.167997i	$-0.946270\pi$
$349$		−	9.00712e24i		−	0.335994i	0.985788	−	0.167997i	$-0.0537299\pi$
$350$	1.06594e25	+	5.87101e24i	0.386414	+	0.212830i
$351$	3.60671e25			1.27069
$352$	3.70588e24	+	3.70588e24i	0.126901	+	0.126901i
$353$	−1.30615e25	+	1.30615e25i	−0.434757	+	0.434757i	−0.890243	−	0.455486i	$-0.849465\pi$
$353$	−1.30615e25	+	1.30615e25i	−0.434757	+	0.434757i	0.455486	+	0.890243i	$0.349465\pi$
$354$		−	1.98882e25i		−	0.643520i
$355$	3.07030e25	+	5.19627e25i	0.965823	+	1.63459i
$356$	−5.55130e24			−0.169783
$357$	3.32363e24	+	3.32363e24i	0.0988395	+	0.0988395i
$358$	−6.22919e24	+	6.22919e24i	−0.180136	+	0.180136i
$359$		−	2.55266e25i		−	0.717876i	−0.933361	−	0.358938i	$-0.883139\pi$
$359$		−	2.55266e25i		−	0.717876i	0.933361	−	0.358938i	$-0.116861\pi$
$360$	7.98981e24	−	3.10675e25i	0.218530	−	0.849729i
$361$	2.27505e25			0.605229
$362$	−9.98090e24	−	9.98090e24i	−0.258276	−	0.258276i
$363$	−6.95012e24	+	6.95012e24i	−0.174955	+	0.174955i
$364$		−	4.67057e24i		−	0.114382i
$365$	−5.85458e25	−	1.50566e25i	−1.39498	−	0.358755i
$366$	5.24463e24			0.121592
$367$	3.81798e25	+	3.81798e25i	0.861336	+	0.861336i	0.991493	−	0.130157i	$-0.0415482\pi$
$367$	3.81798e25	+	3.81798e25i	0.861336	+	0.861336i	−0.130157	+	0.991493i	$0.541548\pi$
$368$	−1.61202e25	+	1.61202e25i	−0.353910	+	0.353910i
$369$			1.79643e25i			0.383837i
$370$	2.73230e25	−	1.61442e25i	0.568213	−	0.335738i
$371$	8.14054e24			0.164784
$372$	−3.00686e24	−	3.00686e24i	−0.0592495	−	0.0592495i
$373$	−1.47663e25	+	1.47663e25i	−0.283259	+	0.283259i	−0.834407	−	0.551148i	$-0.814190\pi$
$373$	−1.47663e25	+	1.47663e25i	−0.283259	+	0.283259i	0.551148	+	0.834407i	$0.314190\pi$
$374$		−	2.22929e25i		−	0.416342i
$375$	−1.55764e25	+	1.65479e25i	−0.283239	+	0.300906i
$376$	−3.54078e25			−0.626933
$377$	−6.87764e25	−	6.87764e25i	−1.18584	−	1.18584i
$378$	1.40430e25	−	1.40430e25i	0.235800	−	0.235800i
$379$			3.49263e25i			0.571164i	0.958354	+	0.285582i	$0.0921868\pi$
$379$			3.49263e25i			0.571164i	−0.958354	+	0.285582i	$0.907813\pi$
$380$	−2.86560e24	−	4.84983e24i	−0.0456436	−	0.0772485i
$381$	4.41513e24			0.0685006
$382$	5.13352e25	+	5.13352e25i	0.775857	+	0.775857i
$383$	2.39273e25	−	2.39273e25i	0.352295	−	0.352295i	−0.508668	−	0.860963i	$-0.669862\pi$
$383$	2.39273e25	−	2.39273e25i	0.352295	−	0.352295i	0.860963	+	0.508668i	$0.169862\pi$
$384$			2.11537e25i			0.303440i
$385$	−5.37886e24	+	2.09151e25i	−0.0751767	+	0.292316i
$386$	−5.53516e25			−0.753802
$387$	−5.37648e25	−	5.37648e25i	−0.713491	−	0.713491i
$388$	−4.09492e24	+	4.09492e24i	−0.0529576	+	0.0529576i
$389$			1.38595e26i			1.74684i	0.486970	+	0.873419i	$0.338102\pi$
$389$			1.38595e26i			1.74684i	−0.486970	+	0.873419i	$0.661898\pi$
$390$	−5.07049e25	−	1.30401e25i	−0.622880	−	0.160190i
$391$	−3.54608e25			−0.424601
$392$	4.95471e25	+	4.95471e25i	0.578306	+	0.578306i
$393$	−1.39937e23	+	1.39937e23i	−0.00159223	+	0.00159223i
$394$		−	2.48694e25i		−	0.275869i
$395$	1.39964e26	−	8.26999e25i	1.51372	−	0.894405i
$396$	7.11352e24			0.0750124
$397$	2.26838e25	+	2.26838e25i	0.233244	+	0.233244i	0.814045	−	0.580801i	$-0.197261\pi$
$397$	2.26838e25	+	2.26838e25i	0.233244	+	0.233244i	−0.580801	+	0.814045i	$0.697261\pi$
$398$	1.08086e26	−	1.08086e26i	1.08377	−	1.08377i
$399$		−	1.26518e25i		−	0.123715i
$400$	−4.23320e25	+	7.68582e25i	−0.403710	+	0.732977i
$401$	−4.76262e25			−0.442998			−0.221499	−	0.975161i	$-0.571095\pi$
$401$	−4.76262e25			−0.442998			−0.221499	+	0.975161i	$0.571095\pi$
$402$	4.40072e24	+	4.40072e24i	0.0399266	+	0.0399266i
$403$	1.90702e26	−	1.90702e26i	1.68774	−	1.68774i
$404$			1.62069e25i			0.139922i
$405$	−3.12165e25	−	5.28316e25i	−0.262926	−	0.444983i
$406$	−5.35574e25			−0.440107
$407$	3.98235e25	+	3.98235e25i	0.319298	+	0.319298i
$408$	−2.80543e25	+	2.80543e25i	−0.219481	+	0.219481i
$409$		−	1.87355e25i		−	0.143031i	−0.997439	−	0.0715157i	$-0.977216\pi$
$409$		−	1.87355e25i		−	0.143031i	0.997439	−	0.0715157i	$-0.0227836\pi$
$410$	1.43276e25	−	5.57113e25i	0.106742	−	0.415054i
$411$	1.03002e26			0.748910
$412$	2.76863e24	+	2.76863e24i	0.0196468	+	0.0196468i
$413$	−8.18181e25	+	8.18181e25i	−0.566694	+	0.566694i
$414$			6.79209e25i			0.459198i
$415$	−2.20334e26	−	5.66647e25i	−1.45412	−	0.373966i
$416$	7.39207e25			0.476248
$417$	−7.81414e24	−	7.81414e24i	−0.0491497	−	0.0491497i
$418$	−4.24301e25	+	4.24301e25i	−0.260562	+	0.260562i
$419$			9.19248e25i			0.551179i	0.961275	+	0.275589i	$0.0888730\pi$
$419$			9.19248e25i			0.551179i	−0.961275	+	0.275589i	$0.911127\pi$
$420$	4.13485e24	−	2.44315e24i	0.0242084	−	0.0143040i
$421$	−1.14138e26			−0.652543			−0.326272	−	0.945276i	$-0.605792\pi$
$421$	−1.14138e26			−0.652543			−0.326272	+	0.945276i	$0.605792\pi$
$422$	3.49012e25	+	3.49012e25i	0.194857	+	0.194857i
$423$	−6.37197e25	+	6.37197e25i	−0.347432	+	0.347432i
$424$			6.87131e25i			0.365915i
$425$	−1.31096e26	+	3.79749e25i	−0.681867	+	0.197518i
$426$	−1.42980e26			−0.726403
$427$	−2.15759e25	−	2.15759e25i	−0.107076	−	0.107076i
$428$	−1.43410e25	+	1.43410e25i	−0.0695253	+	0.0695253i
$429$		−	9.29091e25i		−	0.440033i
$430$	1.23856e26	+	2.09617e26i	0.573101	+	0.969933i
$431$	1.05705e26			0.477885			0.238943	−	0.971034i	$-0.423199\pi$
$431$	1.05705e26			0.477885			0.238943	+	0.971034i	$0.423199\pi$
$432$	1.01255e26	+	1.01255e26i	0.447281	+	0.447281i
$433$	−4.95657e25	+	4.95657e25i	−0.213945	+	0.213945i	−0.805941	−	0.591996i	$-0.798340\pi$
$433$	−4.95657e25	+	4.95657e25i	−0.213945	+	0.213945i	0.591996	+	0.805941i	$0.298340\pi$
$434$		−	1.48503e26i		−	0.626380i
$435$	2.49112e25	−	9.68641e25i	0.102684	−	0.399273i
$436$	−2.76926e25			−0.111557
$437$	6.74927e25	+	6.74927e25i	0.265731	+	0.265731i
$438$	1.01261e26	−	1.01261e26i	0.389675	−	0.389675i
$439$		−	3.95803e26i		−	1.48879i	−0.667738	−	0.744396i	$-0.732737\pi$
$439$		−	3.95803e26i		−	1.48879i	0.667738	−	0.744396i	$-0.267263\pi$
$440$	−1.76541e26	−	4.54021e25i	−0.649111	−	0.166936i
$441$	1.78329e26			0.640968
$442$	−2.22337e26	−	2.22337e26i	−0.781247	−	0.781247i
$443$	−1.89753e26	+	1.89753e26i	−0.651855	+	0.651855i	−0.953440	−	0.301584i	$-0.902485\pi$
$443$	−1.89753e26	+	1.89753e26i	−0.651855	+	0.651855i	0.301584	+	0.953440i	$0.402485\pi$
$444$		−	1.25249e25i		−	0.0420673i
$445$	3.11692e26	−	1.84169e26i	1.02359	−	0.604805i
$446$	4.48664e26			1.44070
$447$	2.85817e24	+	2.85817e24i	0.00897456	+	0.00897456i
$448$	1.20601e26	−	1.20601e26i	0.370314	−	0.370314i
$449$			6.72525e25i			0.201951i	0.994889	+	0.100975i	$0.0321963\pi$
$449$			6.72525e25i			0.201951i	−0.994889	+	0.100975i	$0.967804\pi$
$450$	7.27364e25	+	2.51098e26i	0.213612	+	0.737427i
$451$	1.02082e26			0.293214
$452$	−3.10305e25	−	3.10305e25i	−0.0871775	−	0.0871775i
$453$	−1.73534e26	+	1.73534e26i	−0.476874	+	0.476874i
$454$		−	1.64201e25i		−	0.0441385i
$455$	1.54950e26	+	2.62241e26i	0.407452	+	0.689583i
$456$	1.06792e26			0.274719
$457$	−1.21557e26	−	1.21557e26i	−0.305927	−	0.305927i	0.537400	−	0.843327i	$-0.319406\pi$
$457$	−1.21557e26	−	1.21557e26i	−0.305927	−	0.305927i	−0.843327	+	0.537400i	$0.819406\pi$
$458$	−9.57807e25	+	9.57807e25i	−0.235843	+	0.235843i
$459$			2.22739e26i			0.536622i
$460$	−9.02464e24	+	3.50913e25i	−0.0212741	+	0.0827220i
$461$	−4.10500e26			−0.946901			−0.473450	−	0.880821i	$-0.656992\pi$
$461$	−4.10500e26			−0.946901			−0.473450	+	0.880821i	$0.656992\pi$
$462$	−3.61749e25	−	3.61749e25i	−0.0816560	−	0.0816560i
$463$	5.78115e25	−	5.78115e25i	0.127704	−	0.127704i	−0.640366	−	0.768070i	$-0.721217\pi$
$463$	5.78115e25	−	5.78115e25i	0.127704	−	0.127704i	0.768070	+	0.640366i	$0.221217\pi$
$464$		−	3.86168e26i		−	0.834826i
$465$	2.68583e26	+	6.90732e25i	0.568263	+	0.146144i
$466$	−6.28193e26			−1.30087
$467$	2.16380e26	+	2.16380e26i	0.438579	+	0.438579i	0.891534	−	0.452954i	$-0.149630\pi$
$467$	2.16380e26	+	2.16380e26i	0.438579	+	0.438579i	−0.452954	+	0.891534i	$0.649630\pi$
$468$	7.09463e25	−	7.09463e25i	0.140757	−	0.140757i
$469$		−	3.62083e25i		−	0.0703201i
$470$	2.48429e26	−	1.46788e26i	0.472306	−	0.279070i
$471$	−3.49092e26			−0.649727
$472$	−6.90614e26	−	6.90614e26i	−1.25839	−	1.25839i
$473$	−3.05519e26	+	3.05519e26i	−0.545038	+	0.545038i
$474$			3.85122e26i			0.672689i
$475$	3.21793e26	+	1.77238e26i	0.550352	+	0.303124i
$476$	2.88439e25			0.0483042
$477$	1.23655e26	+	1.23655e26i	0.202782	+	0.202782i
$478$	−4.23545e26	+	4.23545e26i	−0.680174	+	0.680174i
$479$		−	2.84405e25i		−	0.0447283i	−0.999750	−	0.0223642i	$-0.992881\pi$
$479$		−	2.84405e25i		−	0.0447283i	0.999750	−	0.0223642i	$-0.00711933\pi$
$480$	3.86675e25	+	6.54419e25i	0.0595571	+	0.100796i
$481$	7.94356e26			1.19830
$482$	−6.32050e26	−	6.32050e26i	−0.933858	−	0.933858i
$483$	−5.75427e25	+	5.75427e25i	−0.0832759	+	0.0832759i
$484$			6.03162e25i			0.0855028i
$485$	9.40678e25	−	3.65772e26i	0.130624	−	0.507917i
$486$	6.59858e26			0.897611
$487$	5.59949e26	+	5.59949e26i	0.746207	+	0.746207i	0.973765	−	0.227558i	$-0.0730741\pi$
$487$	5.59949e26	+	5.59949e26i	0.746207	+	0.746207i	−0.227558	+	0.973765i	$0.573074\pi$
$488$	1.82119e26	−	1.82119e26i	0.237770	−	0.237770i
$489$			1.06583e25i			0.0136333i
$490$	−5.53037e26	−	1.42228e26i	−0.693096	−	0.178248i
$491$	−9.37396e26			−1.15109			−0.575544	−	0.817771i	$-0.695210\pi$
$491$	−9.37396e26			−1.15109			−0.575544	+	0.817771i	$0.695210\pi$
$492$	−1.60529e25	−	1.60529e25i	−0.0193154	−	0.0193154i
$493$	4.24741e26	−	4.24741e26i	0.500789	−	0.500789i
$494$			8.46349e26i			0.977867i
$495$	−3.99407e26	+	2.35996e26i	−0.452235	+	0.267210i
$496$	1.07076e27			1.18816
$497$	5.88204e26	+	5.88204e26i	0.639682	+	0.639682i
$498$	3.81092e26	−	3.81092e26i	0.406197	−	0.406197i
$499$		−	9.32948e26i		−	0.974658i	−0.873219	−	0.487329i	$-0.837971\pi$
$499$		−	9.32948e26i		−	0.974658i	0.873219	−	0.487329i	$-0.162029\pi$
$500$	4.21577e24	+	1.39394e26i	0.00431695	+	0.142740i
$501$	−2.69244e26			−0.270252
$502$	5.41537e26	+	5.41537e26i	0.532832	+	0.532832i
$503$	3.08486e26	−	3.08486e26i	0.297547	−	0.297547i	−0.542505	−	0.840052i	$-0.682524\pi$
$503$	3.08486e26	−	3.08486e26i	0.297547	−	0.297547i	0.840052	+	0.542505i	$0.182524\pi$
$504$		−	4.42118e26i		−	0.418055i
$505$	−5.37674e26	−	9.09976e26i	−0.498432	−	0.843560i
$506$	3.85961e26			0.350783
$507$	−5.98703e26	−	5.98703e26i	−0.533496	−	0.533496i
$508$	1.91582e25	−	1.91582e25i	0.0167386	−	0.0167386i
$509$		−	9.84939e26i		−	0.843785i	−0.906646	−	0.421892i	$-0.861366\pi$
$509$		−	9.84939e26i		−	0.843785i	0.906646	−	0.421892i	$-0.138634\pi$
$510$	8.05314e25	−	3.13137e26i	0.0676494	−	0.263047i
$511$	−8.33160e26			−0.686309
$512$	9.82557e26	+	9.82557e26i	0.793704	+	0.793704i
$513$	4.23940e26	−	4.23940e26i	0.335839	−	0.335839i
$514$			1.85718e27i			1.44285i
$515$	−2.47303e26	−	6.36005e25i	−0.188433	−	0.0484605i
$516$	9.60886e25			0.0718084
$517$	3.62087e26	+	3.62087e26i	0.265404	+	0.265404i
$518$	3.09289e26	−	3.09289e26i	0.222365	−	0.222365i
$519$		−	1.59510e25i		−	0.0112490i
$520$	−2.21354e27	+	1.30791e27i	−1.53128	+	0.904780i
$521$	−1.52627e27			−1.03575			−0.517873	−	0.855458i	$-0.673276\pi$
$521$	−1.52627e27			−1.03575			−0.517873	+	0.855458i	$0.673276\pi$
$522$	−8.13540e26	−	8.13540e26i	−0.541594	−	0.541594i
$523$	−1.24174e27	+	1.24174e27i	−0.810990	+	0.810990i	−0.984782	−	0.173792i	$-0.944398\pi$
$523$	−1.24174e27	+	1.24174e27i	−0.810990	+	0.810990i	0.173792	+	0.984782i	$0.444398\pi$
$524$			1.21443e24i			0.000778146i
$525$	−1.51109e26	+	2.74353e26i	−0.0949940	+	0.172472i
$526$	7.51115e26			0.463286
$527$	1.17771e27	+	1.17771e27i	0.712744	+	0.712744i
$528$	2.60834e26	−	2.60834e26i	0.154891	−	0.154891i
$529$			1.10222e27i			0.642258i
$530$	−2.84860e26	−	4.82105e26i	−0.162882	−	0.275666i
$531$	−2.48565e27			−1.39474
$532$	−5.48988e25	−	5.48988e25i	−0.0302306	−	0.0302306i
$533$	1.01811e27	−	1.01811e27i	0.550204	−	0.550204i
$534$			8.57646e26i			0.454879i
$535$	3.29440e26	−	1.28099e27i	0.171490	−	0.666819i
$536$	3.05628e26			0.156151
$537$	−1.60328e26	−	1.60328e26i	−0.0804017	−	0.0804017i
$538$	3.40489e26	−	3.40489e26i	0.167603	−	0.167603i
$539$		−	1.01336e27i		−	0.489637i
$540$	2.20418e26	+	5.66862e25i	0.104546	+	0.0268868i
$541$	3.47339e27			1.61726			0.808631	−	0.588316i	$-0.200209\pi$
$541$	3.47339e27			1.61726			0.808631	+	0.588316i	$0.200209\pi$
$542$	−2.85421e25	−	2.85421e25i	−0.0130465	−	0.0130465i
$543$	2.56889e26	−	2.56889e26i	0.115278	−	0.115278i
$544$			4.56510e26i			0.201123i
$545$	1.55487e27	−	9.18722e26i	0.672558	−	0.397392i
$546$	−7.21577e26			−0.306448
$547$	2.65760e25	+	2.65760e25i	0.0110820	+	0.0110820i	0.712626	−	0.701544i	$-0.247506\pi$
$547$	2.65760e25	+	2.65760e25i	0.0110820	+	0.0110820i	−0.701544	+	0.712626i	$0.747506\pi$
$548$	4.46950e26	−	4.46950e26i	0.183001	−	0.183001i
$549$		−	6.55479e26i		−	0.263533i
$550$	1.42687e27	−	4.13325e26i	0.563322	−	0.163179i
$551$	−1.61682e27			−0.626825
$552$	−4.85709e26	−	4.85709e26i	−0.184921	−	0.184921i
$553$	1.58435e27	−	1.58435e27i	0.592381	−	0.592381i
$554$		−	2.14258e27i		−	0.786755i
$555$	4.15523e26	+	7.03242e26i	0.149853	+	0.253615i
$556$	−6.78146e25			−0.0240201
$557$	5.53894e25	+	5.53894e25i	0.0192697	+	0.0192697i	0.716676	−	0.697406i	$-0.245663\pi$
$557$	5.53894e25	+	5.53894e25i	0.0192697	+	0.0192697i	−0.697406	+	0.716676i	$0.745663\pi$
$558$	2.25577e27	−	2.25577e27i	0.770820	−	0.770820i
$559$			6.09415e27i			2.04548i
$560$	−3.01212e26	+	1.17123e27i	−0.0993097	+	0.386154i
$561$	5.73776e26			0.185829
$562$	−2.61217e27	−	2.61217e27i	−0.831070	−	0.831070i
$563$	−3.57265e27	+	3.57265e27i	−1.11662	+	1.11662i	−0.124390	+	0.992233i	$0.539697\pi$
$563$	−3.57265e27	+	3.57265e27i	−1.11662	+	1.11662i	−0.992233	+	0.124390i	$0.960303\pi$
$564$		−	1.13880e26i		−	0.0349668i
$565$	2.77175e27	+	7.12828e26i	0.836121	+	0.215031i
$566$	−2.25244e27			−0.667557
$567$	−5.98041e26	−	5.98041e26i	−0.174141	−	0.174141i
$568$	−4.96494e27	+	4.96494e27i	−1.42047	+	1.42047i
$569$		−	6.72486e26i		−	0.189043i	−0.995523	−	0.0945215i	$-0.969868\pi$
$569$		−	6.72486e26i		−	0.189043i	0.995523	−	0.0945215i	$-0.0301321\pi$
$570$	−7.49272e26	+	4.42720e26i	−0.206962	+	0.122287i
$571$	4.68751e27			1.27228			0.636138	−	0.771575i	$-0.280531\pi$
$571$	4.68751e27			1.27228			0.636138	+	0.771575i	$0.280531\pi$
$572$	−4.03153e26	−	4.03153e26i	−0.107525	−	0.107525i
$573$	−1.32127e27	+	1.32127e27i	−0.346295	+	0.346295i
$574$		−	7.92822e26i		−	0.204201i
$575$	−6.57467e26	−	2.26969e27i	−0.166416	−	0.574497i
$576$	3.66387e27			0.911413
$577$	−1.14107e27	−	1.14107e27i	−0.278968	−	0.278968i	0.553729	−	0.832697i	$-0.313204\pi$
$577$	−1.14107e27	−	1.14107e27i	−0.278968	−	0.278968i	−0.832697	+	0.553729i	$0.813204\pi$
$578$	−1.35152e27	+	1.35152e27i	−0.324747	+	0.324747i
$579$		−	1.42465e27i		−	0.336451i
$580$	−3.12220e26	−	5.28410e26i	−0.0724737	−	0.122657i
$581$	−3.13556e27			−0.715407
$582$	6.32643e26	+	6.32643e26i	0.141882	+	0.141882i
$583$	7.02673e26	−	7.02673e26i	0.154906	−	0.154906i
$584$		−	7.03258e27i		−	1.52400i
$585$	−1.62977e27	+	6.33716e27i	−0.347190	+	1.35001i
$586$	−3.95486e27			−0.828237
$587$	−8.52391e26	−	8.52391e26i	−0.175492	−	0.175492i	0.613895	−	0.789388i	$-0.289602\pi$
$587$	−8.52391e26	−	8.52391e26i	−0.175492	−	0.175492i	−0.789388	+	0.613895i	$0.789602\pi$
$588$	−1.59355e26	+	1.59355e26i	−0.0322547	+	0.0322547i
$589$		−	4.48310e27i		−	0.892124i
$590$	7.70853e27	+	1.98245e27i	1.50817	+	0.387866i
$591$	6.40090e26			0.123131
$592$	2.23009e27	+	2.23009e27i	0.421798	+	0.421798i
$593$	−3.48391e27	+	3.48391e27i	−0.647918	+	0.647918i	−0.952490	−	0.304571i	$-0.901487\pi$
$593$	−3.48391e27	+	3.48391e27i	−0.647918	+	0.647918i	0.304571	+	0.952490i	$0.401487\pi$
$594$		−	2.42432e27i		−	0.443329i
$595$	−1.61952e27	+	9.56918e26i	−0.291216	+	0.172070i
$596$	2.48045e25			0.00438599
$597$	2.78193e27	+	2.78193e27i	0.483730	+	0.483730i
$598$	3.84936e27	−	3.84936e27i	0.658229	−	0.658229i
$599$			4.97440e26i			0.0836512i	0.999125	+	0.0418256i	$0.0133174\pi$
$599$			4.97440e26i			0.0836512i	−0.999125	+	0.0418256i	$0.986683\pi$
$600$	−2.31577e27	−	1.27548e27i	−0.382987	−	0.210942i
$601$	7.41921e27			1.20674			0.603369	−	0.797462i	$-0.293825\pi$
$601$	7.41921e27			1.20674			0.603369	+	0.797462i	$0.293825\pi$
$602$	2.37281e27	+	2.37281e27i	0.379575	+	0.379575i
$603$	5.50006e26	−	5.50006e26i	0.0865356	−	0.0865356i
$604$			1.50601e27i			0.233054i
$605$	−2.00103e27	−	3.38661e27i	−0.304580	−	0.515479i
$606$	2.50387e27			0.374874
$607$	−5.27735e27	−	5.27735e27i	−0.777194	−	0.777194i	0.202159	−	0.979353i	$-0.435204\pi$
$607$	−5.27735e27	−	5.27735e27i	−0.777194	−	0.777194i	−0.979353	+	0.202159i	$0.935204\pi$
$608$	8.68879e26	−	8.68879e26i	0.125870	−	0.125870i
$609$		−	1.37847e27i		−	0.196437i
$610$	−5.22784e26	+	2.03278e27i	−0.0732864	+	0.284966i
$611$	7.22252e27			0.996039
$612$	4.38141e26	+	4.38141e26i	0.0594429	+	0.0594429i
$613$	−2.99915e27	+	2.99915e27i	−0.400307	+	0.400307i	−0.878341	−	0.478034i	$-0.841350\pi$
$613$	−2.99915e27	+	2.99915e27i	−0.400307	+	0.400307i	0.478034	+	0.878341i	$0.341350\pi$
$614$			8.15928e27i			1.07144i
$615$	1.43390e27	+	3.68766e26i	0.185254	+	0.0476430i
$616$	−2.51234e27			−0.319353
$617$	2.50485e27	+	2.50485e27i	0.313278	+	0.313278i	0.846178	−	0.532900i	$-0.178898\pi$
$617$	2.50485e27	+	2.50485e27i	0.313278	+	0.313278i	−0.532900	+	0.846178i	$0.678898\pi$
$618$	4.27738e26	−	4.27738e26i	0.0526372	−	0.0526372i
$619$		−	5.98580e27i		−	0.724796i	−0.932023	−	0.362398i	$-0.881958\pi$
$619$		−	5.98580e27i		−	0.724796i	0.932023	−	0.362398i	$-0.118042\pi$
$620$	1.46516e27	−	8.65717e26i	0.174570	−	0.103148i
$621$	−3.85632e27			−0.452124
$622$	−5.96258e27	−	5.96258e27i	−0.687908	−	0.687908i
$623$	3.52828e27	−	3.52828e27i	0.400573	−	0.400573i
$624$		−	5.20283e27i		−	0.581291i
$625$	−4.86121e27	−	7.68679e27i	−0.534496	−	0.845171i
$626$	−1.49776e28			−1.62068
$627$	−1.09207e27	−	1.09207e27i	−0.116299	−	0.116299i
$628$	−1.51479e27	+	1.51479e27i	−0.158765	+	0.158765i
$629$			4.90568e27i			0.506050i
$630$	1.83286e27	+	3.10199e27i	0.186091	+	0.314945i
$631$	2.63734e27			0.263556			0.131778	−	0.991279i	$-0.457931\pi$
$631$	2.63734e27			0.263556			0.131778	+	0.991279i	$0.457931\pi$
$632$	1.33733e28	+	1.33733e28i	1.31543	+	1.31543i
$633$	−8.98291e26	+	8.98291e26i	−0.0869721	+	0.0869721i
$634$			1.13935e28i			1.08583i
$635$	−4.40100e26	+	1.71128e27i	−0.0412870	+	0.160540i
$636$	−2.20997e26			−0.0204087
$637$	−1.01066e28	−	1.01066e28i	−0.918782	−	0.918782i
$638$	−4.62295e27	+	4.62295e27i	−0.413725	+	0.413725i
$639$			1.78697e28i			1.57438i
$640$	−8.19902e27	−	2.10859e27i	−0.711152	−	0.182891i
$641$	−9.43523e27			−0.805698			−0.402849	−	0.915267i	$-0.631980\pi$
$641$	−9.43523e27			−0.805698			−0.402849	+	0.915267i	$0.631980\pi$
$642$	2.21561e27	+	2.21561e27i	0.186270	+	0.186270i
$643$	1.55313e28	−	1.55313e28i	1.28557	−	1.28557i	0.348126	−	0.937448i	$-0.386818\pi$
$643$	1.55313e28	−	1.55313e28i	1.28557	−	1.28557i	0.937448	−	0.348126i	$-0.113182\pi$
$644$			4.99381e26i			0.0406980i
$645$	−5.39515e27	+	3.18781e27i	−0.432918	+	0.255797i
$646$	−5.22678e27			−0.412961
$647$	3.08834e27	+	3.08834e27i	0.240261	+	0.240261i	0.816958	−	0.576697i	$-0.195659\pi$
$647$	3.08834e27	+	3.08834e27i	0.240261	+	0.240261i	−0.576697	+	0.816958i	$0.695659\pi$
$648$	5.04797e27	−	5.04797e27i	0.386693	−	0.386693i
$649$			1.41247e28i			1.06545i
$650$	1.01085e28	−	1.83531e28i	0.750851	−	1.36325i
$651$	3.82218e27			0.279577
$652$	4.62487e25	+	4.62487e25i	0.00333138	+	0.00333138i
$653$	7.28776e27	−	7.28776e27i	0.516967	−	0.516967i	−0.399686	−	0.916652i	$-0.630881\pi$
$653$	7.28776e27	−	7.28776e27i	0.516967	−	0.516967i	0.916652	+	0.399686i	$0.130881\pi$
$654$			4.27835e27i			0.298882i
$655$	−4.02898e25	−	6.81876e25i	−0.00277193	−	0.00469129i
$656$	5.71653e27			0.387342
$657$	−1.26558e28	−	1.26558e28i	−0.844569	−	0.844569i
$658$	2.81215e27	−	2.81215e27i	0.184833	−	0.184833i
$659$		−	1.29108e28i		−	0.835795i	−0.908494	−	0.417897i	$-0.862767\pi$
$659$		−	1.29108e28i		−	0.835795i	0.908494	−	0.417897i	$-0.137233\pi$
$660$	1.46024e26	−	5.67797e26i	0.00931075	−	0.0362038i
$661$	−3.92118e27			−0.246265			−0.123132	−	0.992390i	$-0.539294\pi$
$661$	−3.92118e27			−0.246265			−0.123132	+	0.992390i	$0.539294\pi$
$662$	1.72626e28	+	1.72626e28i	1.06789	+	1.06789i
$663$	5.72252e27	−	5.72252e27i	0.348700	−	0.348700i
$664$		−	2.64668e28i		−	1.58862i
$665$	4.90374e27	+	1.26113e27i	0.289942	+	0.0745662i
$666$	9.39626e27			0.547284
$667$	7.35362e27	+	7.35362e27i	0.421933	+	0.421933i
$668$	−1.16831e27	+	1.16831e27i	−0.0660379	+	0.0660379i
$669$			1.15478e28i			0.643038i
$670$	−2.14435e27	+	1.26703e27i	−0.117638	+	0.0695084i
$671$	−3.72477e27			−0.201314
$672$	7.40786e26	+	7.40786e26i	0.0394457	+	0.0394457i
$673$	6.79384e27	−	6.79384e27i	0.356422	−	0.356422i	−0.506070	−	0.862492i	$-0.668902\pi$
$673$	6.79384e27	−	6.79384e27i	0.356422	−	0.356422i	0.862492	+	0.506070i	$0.168902\pi$
$674$			5.84566e27i			0.302158i
$675$	−1.42565e28	+	4.12973e27i	−0.726066	+	0.210322i
$676$	−5.19580e27			−0.260727
$677$	9.03091e27	+	9.03091e27i	0.446524	+	0.446524i	0.894197	−	0.447673i	$-0.147747\pi$
$677$	9.03091e27	+	9.03091e27i	0.446524	+	0.446524i	−0.447673	+	0.894197i	$0.647747\pi$
$678$	−4.79405e27	+	4.79405e27i	−0.233564	+	0.233564i
$679$		−	5.20527e27i		−	0.249888i
$680$	−8.07720e27	−	1.36701e28i	−0.382095	−	0.646669i
$681$	4.22622e26			0.0197007
$682$	−1.28184e28	−	1.28184e28i	−0.588831	−	0.588831i
$683$	−1.96925e28	+	1.96925e28i	−0.891446	+	0.891446i	−0.994659	−	0.103214i	$-0.967087\pi$
$683$	−1.96925e28	+	1.96925e28i	−0.891446	+	0.891446i	0.103214	+	0.994659i	$0.467087\pi$
$684$		−	1.66783e27i		−	0.0744032i
$685$	−1.02673e28	+	3.99231e28i	−0.451387	+	1.75517i
$686$	−1.80521e28			−0.782142
$687$	−2.46522e27	−	2.46522e27i	−0.105266	−	0.105266i
$688$	−1.71088e28	+	1.71088e28i	−0.720005	+	0.720005i
$689$		−	1.40161e28i		−	0.581348i
$690$	5.42141e27	+	1.39426e27i	0.221626	+	0.0569970i
$691$	2.45108e28			0.987589			0.493795	−	0.869579i	$-0.335609\pi$
$691$	2.45108e28			0.987589			0.493795	+	0.869579i	$0.335609\pi$
$692$	−6.92147e25	−	6.92147e25i	−0.00274876	−	0.00274876i
$693$	−4.52119e27	+	4.52119e27i	−0.176978	+	0.176978i
$694$			7.65843e27i			0.295491i
$695$	3.80762e27	−	2.24980e27i	0.144812	−	0.0855649i
$696$	1.16354e28			0.436204
$697$	6.28753e27	+	6.28753e27i	0.232355	+	0.232355i
$698$	−6.03824e27	+	6.03824e27i	−0.219966	+	0.219966i
$699$		−	1.61685e28i		−	0.580628i
$700$	5.34786e26	+	1.84617e27i	0.0189321	+	0.0653570i
$701$	−1.70566e28			−0.595269			−0.297635	−	0.954680i	$-0.596198\pi$
$701$	−1.70566e28			−0.595269			−0.297635	+	0.954680i	$0.596198\pi$
$702$	−2.41789e28	−	2.41789e28i	−0.831888	−	0.831888i
$703$	9.33702e27	−	9.33702e27i	0.316705	−	0.316705i
$704$		−	2.08200e28i		−	0.696231i
$705$	3.77805e27	+	6.39409e27i	0.124560	+	0.210808i
$706$	1.75125e28			0.569248
$707$	−1.03007e28	−	1.03007e28i	−0.330120	−	0.330120i
$708$	2.22118e27	−	2.22118e27i	0.0701860	−	0.0701860i
$709$			3.18246e27i			0.0991517i	0.998770	+	0.0495759i	$0.0157870\pi$
$709$			3.18246e27i			0.0991517i	−0.998770	+	0.0495759i	$0.984213\pi$
$710$	1.42522e28	−	5.54179e28i	0.437822	−	1.70242i
$711$	4.81329e28			1.45796
$712$	2.97816e28	+	2.97816e28i	0.889506	+	0.889506i
$713$	−2.03900e28	+	2.03900e28i	−0.600512	+	0.600512i
$714$		−	4.45623e27i		−	0.129415i
$715$	3.60109e28	+	9.26116e27i	1.03127	+	0.265219i
$716$	−1.39139e27			−0.0392934
$717$	−1.09012e28	−	1.09012e28i	−0.303588	−	0.303588i
$718$	−1.71127e28	+	1.71127e28i	−0.469974	+	0.469974i
$719$			7.56616e27i			0.204921i	0.994737	+	0.102461i	$0.0326715\pi$
$719$			7.56616e27i			0.204921i	−0.994737	+	0.102461i	$0.967328\pi$
$720$	−2.23665e28	+	1.32156e28i	−0.597410	+	0.352990i
$721$	−3.51935e27			−0.0927064
$722$	−1.52516e28	−	1.52516e28i	−0.396227	−	0.396227i
$723$	1.62678e28	−	1.62678e28i	0.416817	−	0.416817i
$724$		−	2.22940e27i		−	0.0563381i
$725$	3.50608e28	+	1.93108e28i	0.873859	+	0.481305i
$726$	9.31852e27			0.229077
$727$	−8.50933e27	−	8.50933e27i	−0.206325	−	0.206325i	0.596379	−	0.802703i	$-0.296606\pi$
$727$	−8.50933e27	−	8.50933e27i	−0.206325	−	0.206325i	−0.802703	+	0.596379i	$0.796606\pi$
$728$	−2.50567e28	+	2.50567e28i	−0.599252	+	0.599252i
$729$		−	4.92661e27i		−	0.116218i
$730$	2.91546e28	+	4.93420e28i	0.678387	+	1.14812i
$731$	−3.76355e28			−0.863821
$732$	5.85737e26	+	5.85737e26i	0.0132615	+	0.0132615i
$733$	3.84631e28	−	3.84631e28i	0.859023	−	0.859023i	−0.132200	−	0.991223i	$-0.542204\pi$
$733$	3.84631e28	−	3.84631e28i	0.859023	−	0.859023i	0.991223	+	0.132200i	$0.0422040\pi$
$734$		−	5.11904e28i		−	1.12779i
$735$	3.66068e27	−	1.42341e28i	0.0795588	−	0.309355i
$736$	−7.90366e27			−0.169453
$737$	−3.12541e27	−	3.12541e27i	−0.0661048	−	0.0661048i
$738$	1.20430e28	−	1.20430e28i	0.251288	−	0.251288i
$739$			3.72642e28i			0.767093i	0.923522	+	0.383546i	$0.125297\pi$
$739$			3.72642e28i			0.767093i	−0.923522	+	0.383546i	$0.874703\pi$
$740$	4.85456e27	+	1.24848e27i	0.0985901	+	0.0253550i
$741$	−2.17834e28			−0.436460
$742$	−5.45730e27	−	5.45730e27i	−0.107880	−	0.107880i
$743$	−4.27045e28	+	4.27045e28i	−0.832885	+	0.832885i	−0.987911	−	0.155025i	$-0.950454\pi$
$743$	−4.27045e28	+	4.27045e28i	−0.832885	+	0.832885i	0.155025	+	0.987911i	$0.450454\pi$
$744$			3.22625e28i			0.620824i
$745$	−1.39271e27	+	8.22907e26i	−0.0264423	+	0.0156238i
$746$	1.97982e28			0.370884
$747$	−4.76294e28	−	4.76294e28i	−0.880377	−	0.880377i
$748$	2.48974e27	−	2.48974e27i	0.0454086	−	0.0454086i
$749$		−	1.82297e28i		−	0.328065i
$750$	2.15356e28	−	6.51314e26i	0.382424	−	0.0115659i
$751$	−5.30671e28			−0.929878			−0.464939	−	0.885343i	$-0.653924\pi$
$751$	−5.30671e28			−0.929878			−0.464939	+	0.885343i	$0.653924\pi$
$752$	2.02766e28	+	2.02766e28i	0.350604	+	0.350604i
$753$	−1.39381e28	+	1.39381e28i	−0.237824	+	0.237824i
$754$			9.22134e28i			1.55267i
$755$	−4.99629e28	−	8.45586e28i	−0.830191	−	1.40504i
$756$	3.13675e27			0.0514353
$757$	−3.10184e28	−	3.10184e28i	−0.501951	−	0.501951i	0.410093	−	0.912044i	$-0.365496\pi$
$757$	−3.10184e28	−	3.10184e28i	−0.501951	−	0.501951i	−0.912044	+	0.410093i	$0.865496\pi$
$758$	2.34141e28	−	2.34141e28i	0.373926	−	0.373926i
$759$			9.93391e27i			0.156568i
$760$	−1.06450e28	+	4.13917e28i	−0.165580	+	0.643840i
$761$	2.17890e28			0.334496			0.167248	−	0.985915i	$-0.446512\pi$
$761$	2.17890e28			0.334496			0.167248	+	0.985915i	$0.446512\pi$
$762$	−2.95984e27	−	2.95984e27i	−0.0448455	−	0.0448455i
$763$	1.76007e28	−	1.76007e28i	0.263200	−	0.263200i
$764$			1.14666e28i			0.169239i
$765$	−3.91362e28	−	1.00649e28i	−0.570118	−	0.146621i
$766$	−3.20811e28			−0.461277
$767$	1.40872e29	+	1.40872e29i	1.99927	+	1.99927i
$768$	−8.74554e27	+	8.74554e27i	−0.122511	+	0.122511i
$769$		−	1.15230e29i		−	1.59332i	−0.604426	−	0.796661i	$-0.706597\pi$
$769$		−	1.15230e29i		−	1.59332i	0.604426	−	0.796661i	$-0.293403\pi$
$770$	1.76271e28	−	1.04153e28i	0.240588	−	0.142155i
$771$	−4.78003e28			−0.644001
$772$	−6.18185e27	−	6.18185e27i	−0.0822140	−	0.0822140i
$773$	−2.03319e26	+	2.03319e26i	−0.00266921	+	0.00266921i	−0.708440	−	0.705771i	$-0.750601\pi$
$773$	−2.03319e26	+	2.03319e26i	−0.00266921	+	0.00266921i	0.705771	+	0.708440i	$0.250601\pi$
$774$			7.20863e28i			0.934208i
$775$	−5.35447e28	+	9.72159e28i	−0.685013	+	1.24371i
$776$	4.39369e28			0.554896
$777$	7.96052e27	+	7.96052e27i	0.0992502	+	0.0992502i
$778$	9.29123e28	−	9.29123e28i	1.14361	−	1.14361i
$779$		−	2.39342e28i		−	0.290834i
$780$	−4.20653e27	−	7.11926e27i	−0.0504636	−	0.0854060i
$781$	1.01545e29			1.20267
$782$	2.37724e28	+	2.37724e28i	0.277975	+	0.277975i
$783$	4.61901e28	−	4.61901e28i	0.533250	−	0.533250i
$784$		−	5.67471e28i		−	0.646819i
$785$	3.47974e28	−	1.35306e29i	0.391607	−	1.52272i
$786$	1.87624e26			0.00208479
$787$	−1.82978e28	−	1.82978e28i	−0.200748	−	0.200748i	0.599573	−	0.800320i	$-0.295337\pi$
$787$	−1.82978e28	−	1.82978e28i	−0.200748	−	0.200748i	−0.800320	+	0.599573i	$0.795337\pi$
$788$	2.77749e27	−	2.77749e27i	0.0300878	−	0.0300878i
$789$			1.93323e28i			0.206782i
$790$	−1.49271e29	−	3.83888e28i	−1.57653	−	0.405447i
$791$	3.94445e28			0.411360
$792$	−3.81626e28	−	3.81626e28i	−0.392995	−	0.392995i
$793$	−3.71487e28	+	3.71487e28i	−0.377757	+	0.377757i
$794$		−	3.04138e28i		−	0.305398i
$795$	1.24085e28	−	7.33175e27i	0.123040	−	0.0727004i
$796$	2.41428e28			0.236405
$797$	6.58445e28	+	6.58445e28i	0.636702	+	0.636702i	0.949740	−	0.313038i	$-0.101347\pi$
$797$	6.58445e28	+	6.58445e28i	0.636702	+	0.636702i	−0.313038	+	0.949740i	$0.601347\pi$
$798$	−8.48157e27	+	8.48157e27i	−0.0809929	+	0.0809929i
$799$			4.46039e28i			0.420635i
$800$	−2.92192e28	+	8.46402e27i	−0.272125	+	0.0788273i
$801$	1.07190e29			0.985888
$802$	3.19279e28	+	3.19279e28i	0.290019	+	0.290019i
$803$	−7.19165e28	+	7.19165e28i	−0.645168	+	0.645168i
$804$			9.82973e26i			0.00870926i
$805$	−1.65673e28	−	2.80390e28i	−0.144975	−	0.245360i
$806$	−2.55688e29			−2.20983
$807$	8.76355e27	+	8.76355e27i	0.0748074	+	0.0748074i
$808$	8.69466e28	−	8.69466e28i	0.733059	−	0.733059i
$809$			2.00522e29i			1.66985i	0.550365	+	0.834924i	$0.314489\pi$
$809$			2.00522e29i			1.66985i	−0.550365	+	0.834924i	$0.685511\pi$
$810$	−1.44905e28	+	5.63446e28i	−0.119188	+	0.463449i
$811$	−1.87745e29			−1.52531			−0.762657	−	0.646803i	$-0.776106\pi$
$811$	−1.87745e29			−1.52531			−0.762657	+	0.646803i	$0.776106\pi$
$812$	−5.98146e27	−	5.98146e27i	−0.0480006	−	0.0480006i
$813$	7.34620e26	−	7.34620e26i	0.00582314	−	0.00582314i
$814$		−	5.33943e28i		−	0.418072i
$815$	−4.13109e27	−	1.06242e27i	−0.0319513	−	0.00821711i
$816$	3.21310e28			0.245484
$817$	7.16319e28	+	7.16319e28i	0.540612	+	0.540612i
$818$	−1.25600e28	+	1.25600e28i	−0.0936389	+	0.0936389i
$819$			9.01836e28i			0.664184i
$820$	7.82217e27	−	4.62186e27i	0.0569100	−	0.0336263i
$821$	−4.49409e28			−0.323006			−0.161503	−	0.986872i	$-0.551634\pi$
$821$	−4.49409e28			−0.323006			−0.161503	+	0.986872i	$0.551634\pi$
$822$	−6.90514e28	−	6.90514e28i	−0.490291	−	0.490291i
$823$	−3.71438e28	+	3.71438e28i	−0.260548	+	0.260548i	−0.825277	−	0.564729i	$-0.808981\pi$
$823$	−3.71438e28	+	3.71438e28i	−0.260548	+	0.260548i	0.564729	+	0.825277i	$0.308981\pi$
$824$		−	2.97063e28i		−	0.205862i
$825$	1.06382e28	+	3.67249e28i	0.0728331	+	0.251432i
$826$	1.09699e29			0.742000
$827$	−7.70208e28	−	7.70208e28i	−0.514699	−	0.514699i	0.401264	−	0.915963i	$-0.368571\pi$
$827$	−7.70208e28	−	7.70208e28i	−0.514699	−	0.514699i	−0.915963	+	0.401264i	$0.868571\pi$
$828$	−7.58564e27	+	7.58564e27i	−0.0500828	+	0.0500828i
$829$		−	1.18337e29i		−	0.771923i	−0.922515	−	0.385961i	$-0.873870\pi$
$829$		−	1.18337e29i		−	0.771923i	0.922515	−	0.385961i	$-0.126130\pi$
$830$	1.09722e29	+	1.85696e29i	0.707150	+	1.19680i
$831$	5.51460e28			0.351159
$832$	−2.07647e29	−	2.07647e29i	−1.30645	−	1.30645i
$833$	6.24154e28	−	6.24154e28i	0.388009	−	0.388009i
$834$			1.04770e28i			0.0643540i
$835$	2.68382e28	−	1.04357e29i	0.162888	−	0.633371i
$836$	−9.47748e27			−0.0568368
$837$	1.28075e29	+	1.28075e29i	0.758944	+	0.758944i
$838$	6.16251e28	−	6.16251e28i	0.360842	−	0.360842i
$839$		−	8.84271e28i		−	0.511641i	−0.966724	−	0.255821i	$-0.917654\pi$
$839$		−	8.84271e28i		−	0.511641i	0.966724	−	0.255821i	$-0.0823457\pi$
$840$	−3.52896e28	−	9.07566e27i	−0.201769	−	0.0518902i
$841$	8.34739e26			0.00471619
$842$	7.65165e28	+	7.65165e28i	0.427203	+	0.427203i
$843$	6.72322e28	−	6.72322e28i	0.370938	−	0.370938i
$844$			7.79576e27i			0.0425044i
$845$	2.91732e29	−	1.72375e29i	1.57187	−	0.928766i
$846$	8.54335e28			0.454909
$847$	−3.83355e28	−	3.83355e28i	−0.201729	−	0.201729i
$848$	3.93491e28	−	3.93491e28i	0.204633	−	0.204633i
$849$		−	5.79735e28i		−	0.297956i
$850$	1.13343e29	+	6.24269e28i	0.575710	+	0.317090i
$851$	−8.49331e28			−0.426365
$852$	−1.59684e28	−	1.59684e28i	−0.0792257	−	0.0792257i
$853$	−2.29692e29	+	2.29692e29i	−1.12630	+	1.12630i	−0.135529	+	0.990773i	$0.543274\pi$
$853$	−2.29692e29	+	2.29692e29i	−1.12630	+	1.12630i	−0.990773	+	0.135529i	$0.956726\pi$
$854$			2.89284e28i			0.140199i
$855$	5.53316e28	+	9.36448e28i	0.265041	+	0.448562i
$856$	1.53874e29			0.728495
$857$	−1.15057e29	−	1.15057e29i	−0.538400	−	0.538400i	0.384659	−	0.923059i	$-0.374319\pi$
$857$	−1.15057e29	−	1.15057e29i	−0.538400	−	0.538400i	−0.923059	+	0.384659i	$0.874319\pi$
$858$	−6.22849e28	+	6.22849e28i	−0.288078	+	0.288078i
$859$			1.48441e29i			0.678613i	0.940676	+	0.339307i	$0.110192\pi$
$859$			1.48441e29i			0.678613i	−0.940676	+	0.339307i	$0.889808\pi$
$860$	−9.57810e27	+	3.72433e28i	−0.0432808	+	0.168292i
$861$	2.04057e28			0.0911425
$862$	−7.08633e28	−	7.08633e28i	−0.312859	−	0.312859i
$863$	−2.73242e29	+	2.73242e29i	−1.19245	+	1.19245i	−0.216069	+	0.976378i	$0.569324\pi$
$863$	−2.73242e29	+	2.73242e29i	−1.19245	+	1.19245i	−0.976378	+	0.216069i	$0.930676\pi$
$864$			4.96450e28i			0.214160i
$865$	6.18249e27	+	1.58999e27i	0.0263635	+	0.00678005i
$866$	6.64563e28			0.280129
$867$	−3.47857e28	−	3.47857e28i	−0.144947	−	0.144947i
$868$	1.65853e28	−	1.65853e28i	0.0683166	−	0.0683166i
$869$		−	2.73516e29i		−	1.11374i
$870$	−8.16364e28	+	4.82363e28i	−0.328618	+	0.194170i
$871$	−6.23423e28			−0.248085
$872$	1.48565e29	+	1.48565e29i	0.584457	+	0.584457i
$873$	7.90684e28	−	7.90684e28i	0.307511	−	0.307511i
$874$		−	9.04923e28i		−	0.347934i
$875$	−9.12751e28	−	8.59162e28i	−0.346954	−	0.326584i
$876$	2.26184e28			0.0850005
$877$	−2.38043e29	−	2.38043e29i	−0.884420	−	0.884420i	0.109560	−	0.993980i	$-0.465056\pi$
$877$	−2.38043e29	−	2.38043e29i	−0.884420	−	0.884420i	−0.993980	+	0.109560i	$0.965056\pi$
$878$	−2.65341e29	+	2.65341e29i	−0.974673	+	0.974673i
$879$		−	1.01791e29i		−	0.369674i
$880$	7.50978e28	+	1.27098e29i	0.269650	+	0.456363i
$881$	−8.52246e28			−0.302556			−0.151278	−	0.988491i	$-0.548339\pi$
$881$	−8.52246e28			−0.302556			−0.151278	+	0.988491i	$0.548339\pi$
$882$	−1.19549e29	−	1.19549e29i	−0.419625	−	0.419625i
$883$	1.04292e29	−	1.04292e29i	0.361946	−	0.361946i	−0.502583	−	0.864529i	$-0.667617\pi$
$883$	1.04292e29	−	1.04292e29i	0.361946	−	0.361946i	0.864529	+	0.502583i	$0.167617\pi$
$884$		−	4.96626e28i		−	0.170414i
$885$	−5.10245e28	+	1.98403e29i	−0.173120	+	0.673156i
$886$	2.54415e29			0.853505
$887$	3.37048e29	+	3.37048e29i	1.11804	+	1.11804i	0.992029	+	0.126006i	$0.0402159\pi$
$887$	3.37048e29	+	3.37048e29i	1.11804	+	1.11804i	0.126006	+	0.992029i	$0.459784\pi$
$888$	−6.71936e28	+	6.71936e28i	−0.220393	+	0.220393i
$889$			2.43530e28i			0.0789833i
$890$	−3.32418e29	−	8.54900e28i	−1.06607	−	0.274167i
$891$	−1.03243e29			−0.327404
$892$	5.01082e28	+	5.01082e28i	0.157131	+	0.157131i
$893$	8.48949e28	−	8.48949e28i	0.263249	−	0.263249i
$894$		−	3.83216e27i		−	0.0117508i
$895$	7.81233e28	−	4.61605e28i	0.236892	−	0.139972i
$896$	−1.16680e29			−0.349877
$897$	9.90753e28	+	9.90753e28i	0.293793	+	0.293793i
$898$	4.50851e28	−	4.50851e28i	0.132212	−	0.132212i
$899$		−	4.88453e29i		−	1.41653i
$900$	−1.99201e28	+	3.61669e28i	−0.0571302	+	0.103726i
$901$	8.65591e28			0.245508
$902$	−6.84346e28	−	6.84346e28i	−0.191960	−	0.191960i
$903$	−6.10717e28	+	6.10717e28i	−0.169419	+	0.169419i
$904$			3.32945e29i			0.913458i
$905$	7.39620e28	+	1.25175e29i	0.200689	+	0.339651i
$906$	2.32670e29			0.624393
$907$	7.37309e28	+	7.37309e28i	0.195694	+	0.195694i	0.798151	−	0.602457i	$-0.205812\pi$
$907$	7.37309e28	+	7.37309e28i	0.195694	+	0.195694i	−0.602457	+	0.798151i	$0.705812\pi$
$908$	1.83385e27	−	1.83385e27i	0.00481399	−	0.00481399i
$909$		−	3.12937e29i		−	0.812489i
$910$	7.19267e28	−	2.79679e29i	0.184704	−	0.718200i
$911$	2.79015e29			0.708670			0.354335	−	0.935118i	$-0.384707\pi$
$911$	2.79015e29			0.708670			0.354335	+	0.935118i	$0.384707\pi$
$912$	−6.11551e28	−	6.11551e28i	−0.153633	−	0.153633i
$913$	−2.70654e29	+	2.70654e29i	−0.672523	+	0.672523i
$914$			1.62980e29i			0.400565i
$915$	−5.23200e28	−	1.34555e28i	−0.127191	−	0.0327105i
$916$	−2.13942e28			−0.0514448
$917$	−7.71866e26	−	7.71866e26i	−0.00183590	−	0.00183590i
$918$	1.49321e29	−	1.49321e29i	0.351312	−	0.351312i
$919$			5.61270e29i			1.30622i	0.757263	+	0.653110i	$0.226536\pi$
$919$			5.61270e29i			1.30622i	−0.757263	+	0.653110i	$0.773464\pi$
$920$	2.36673e29	−	1.39842e29i	0.544842	−	0.321929i
$921$	−2.10005e29			−0.478225
$922$	2.75194e29	+	2.75194e29i	0.619911	+	0.619911i
$923$	1.01275e30	−	1.01275e30i	2.25676	−	2.25676i
$924$		−	8.08028e27i		−	0.0178117i
$925$	−3.13991e29	+	9.09547e28i	−0.684700	+	0.198339i
$926$	−7.75120e28			−0.167209
$927$	−5.34592e28	−	5.34592e28i	−0.114084	−	0.114084i
$928$	9.46682e28	−	9.46682e28i	0.199859	−	0.199859i
$929$			2.27402e29i			0.474938i	0.971395	+	0.237469i	$0.0763178\pi$
$929$			2.27402e29i			0.474938i	−0.971395	+	0.237469i	$0.923682\pi$
$930$	−1.33749e29	−	2.26360e29i	−0.276350	−	0.467703i
$931$	−2.37591e29			−0.485661
$932$	−7.01587e28	−	7.01587e28i	−0.141880	−	0.141880i
$933$	1.53466e29	−	1.53466e29i	0.307040	−	0.307040i
$934$		−	2.90116e29i		−	0.574253i
$935$	−5.71939e28	+	2.22392e29i	−0.112004	+	0.435515i
$936$	−7.61226e29			−1.47487
$937$	−1.39803e29	−	1.39803e29i	−0.267991	−	0.267991i	0.560299	−	0.828290i	$-0.310686\pi$
$937$	−1.39803e29	−	1.39803e29i	−0.267991	−	0.267991i	−0.828290	+	0.560299i	$0.810686\pi$
$938$	−2.42735e28	+	2.42735e28i	−0.0460367	+	0.0460367i
$939$		−	3.85495e29i		−	0.723373i
$940$	4.41391e28	+	1.13515e28i	0.0819493	+	0.0210754i
$941$	−6.13810e29			−1.12755			−0.563777	−	0.825927i	$-0.690652\pi$
$941$	−6.13810e29			−1.12755			−0.563777	+	0.825927i	$0.690652\pi$
$942$	2.34026e29	+	2.34026e29i	0.425359	+	0.425359i
$943$	−1.08857e29	+	1.08857e29i	−0.195768	+	0.195768i
$944$			7.90972e29i			1.40748i
$945$	−1.76121e29	+	1.04064e29i	−0.310093	+	0.183224i
$946$	4.09631e29			0.713644
$947$	2.18054e29	+	2.18054e29i	0.375893	+	0.375893i	0.869618	−	0.493725i	$-0.164365\pi$
$947$	2.18054e29	+	2.18054e29i	0.375893	+	0.375893i	−0.493725	+	0.869618i	$0.664365\pi$
$948$	−4.30117e28	+	4.30117e28i	−0.0733673	+	0.0733673i
$949$			1.43451e30i			2.42126i
$950$	−9.69080e28	−	3.34543e29i	−0.161854	−	0.558748i
$951$	−2.93246e29			−0.484649
$952$	−1.54742e29	−	1.54742e29i	−0.253069	−	0.253069i
$953$	−5.58819e29	+	5.58819e29i	−0.904362	+	0.904362i	−0.995810	−	0.0914478i	$-0.970851\pi$
$953$	−5.58819e29	+	5.58819e29i	−0.904362	+	0.904362i	0.0914478	+	0.995810i	$0.470851\pi$
$954$		−	1.65794e29i		−	0.265512i
$955$	−3.80412e29	−	6.43820e29i	−0.602866	−	1.02031i
$956$	−9.46057e28			−0.148367
$957$	−1.18986e29	−	1.18986e29i	−0.184662	−	0.184662i
$958$	−1.90661e28	+	1.90661e28i	−0.0292825	+	0.0292825i
$959$			5.68142e29i			0.863517i
$960$	7.52107e28	−	2.92448e29i	0.113127	−	0.439882i
$961$	6.82583e29			1.01607
$962$	−5.32525e29	−	5.32525e29i	−0.784493	−	0.784493i
$963$	2.76910e29	−	2.76910e29i	0.403716	−	0.403716i
$964$		−	1.41179e29i		−	0.203704i
$965$	5.52184e29	+	1.42009e29i	0.788516	+	0.202788i
$966$	7.71517e28			0.109037
$967$	7.18597e29	+	7.18597e29i	1.00513	+	1.00513i	0.999987	+	0.00513997i	$0.00163611\pi$
$967$	7.18597e29	+	7.18597e29i	1.00513	+	1.00513i	0.00513997	+	0.999987i	$0.498364\pi$
$968$	3.23584e29	−	3.23584e29i	0.447955	−	0.447955i
$969$		−	1.34527e29i		−	0.184320i
$970$	−3.08270e29	+	1.82146e29i	−0.418036	+	0.247004i
$971$	1.83338e29			0.246072			0.123036	−	0.992402i	$-0.460737\pi$
$971$	1.83338e29			0.246072			0.123036	+	0.992402i	$0.460737\pi$
$972$	7.36952e28	+	7.36952e28i	0.0978986	+	0.0978986i
$973$	4.31013e28	−	4.31013e28i	0.0566712	−	0.0566712i
$974$		−	7.50764e29i		−	0.977044i
$975$	4.72373e29	+	2.60174e29i	0.608470	+	0.335134i
$976$	−2.08584e29			−0.265939
$977$	−9.06654e29	−	9.06654e29i	−1.14418	−	1.14418i	−0.987677	−	0.156507i	$-0.949977\pi$
$977$	−9.06654e29	−	9.06654e29i	−1.14418	−	1.14418i	−0.156507	−	0.987677i	$-0.550023\pi$
$978$	7.14517e27	−	7.14517e27i	0.00892533	−	0.00892533i
$979$		−	6.09105e29i		−	0.753122i
$980$	−4.58805e28	−	7.76495e28i	−0.0561523	−	0.0950337i
$981$	5.34713e29			0.647785
$982$	6.28417e29	+	6.28417e29i	0.753587	+	0.753587i
$983$	1.09338e30	−	1.09338e30i	1.29789	−	1.29789i	0.368102	−	0.929785i	$-0.380008\pi$
$983$	1.09338e30	−	1.09338e30i	1.29789	−	1.29789i	0.929785	−	0.368102i	$-0.119992\pi$
$984$			1.72242e29i			0.202389i
$985$	−6.38041e28	+	2.48095e29i	−0.0742141	+	0.288573i
$986$	−5.69480e29			−0.655706
$987$	7.23794e28	+	7.23794e28i	0.0824980	+	0.0824980i
$988$	−9.45231e28	+	9.45231e28i	−0.106652	+	0.106652i
$989$		−	6.51592e29i		−	0.727801i
$990$	4.25965e29	+	1.09548e29i	0.471002	+	0.121130i
$991$	8.90185e29			0.974415			0.487207	−	0.873286i	$-0.338016\pi$
$991$	8.90185e29			0.974415			0.487207	+	0.873286i	$0.338016\pi$
$992$	2.62494e29	+	2.62494e29i	0.284448	+	0.284448i
$993$	−4.44307e29	+	4.44307e29i	−0.476640	+	0.476640i
$994$		−	7.88648e29i		−	0.837566i
$995$	−1.35556e30	+	8.00956e29i	−1.42524	+	0.842128i
$996$	8.51233e28			0.0886044
$997$	−1.72862e29	−	1.72862e29i	−0.178134	−	0.178134i	0.612408	−	0.790542i	$-0.290201\pi$
$997$	−1.72862e29	−	1.72862e29i	−0.178134	−	0.178134i	−0.790542	+	0.612408i	$0.790201\pi$
$998$	−6.25435e29	+	6.25435e29i	−0.638083	+	0.638083i
$999$			5.33488e29i			0.538852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.21.c.a.2.3	✓	18
3.2	odd	2		45.21.g.a.37.7		18
5.2	odd	4		25.21.c.b.18.7		18
5.3	odd	4	inner	5.21.c.a.3.3	yes	18
5.4	even	2		25.21.c.b.7.7		18
15.8	even	4		45.21.g.a.28.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.21.c.a.2.3	✓	18	1.1	even	1	trivial
5.21.c.a.3.3	yes	18	5.3	odd	4	inner
25.21.c.b.7.7		18	5.4	even	2
25.21.c.b.18.7		18	5.2	odd	4
45.21.g.a.28.7		18	15.8	even	4
45.21.g.a.37.7		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)

\(f(q)\)	\(=\)	\(q+(-670.386 - 670.386i) q^{2} +(17254.5 - 17254.5i) q^{3} -149742. i q^{4} +(4.96780e6 + 8.40764e6i) q^{5} -2.31343e7 q^{6} +(9.51724e7 + 9.51724e7i) q^{7} +(-8.03335e8 + 8.03335e8i) q^{8} +2.89135e9i q^{9} +O(q^{10})\)	\(q+(-670.386 - 670.386i) q^{2} +(17254.5 - 17254.5i) q^{3} -149742. i q^{4} +(4.96780e6 + 8.40764e6i) q^{5} -2.31343e7 q^{6} +(9.51724e7 + 9.51724e7i) q^{7} +(-8.03335e8 + 8.03335e8i) q^{8} +2.89135e9i q^{9} +(2.30602e9 - 8.96670e9i) q^{10} +1.64301e10 q^{11} +(-2.58372e9 - 2.58372e9i) q^{12} +(1.63865e11 - 1.63865e11i) q^{13} -1.27604e11i q^{14} +(2.30786e11 + 5.93527e10i) q^{15} +9.20073e11 q^{16} +(1.01198e12 + 1.01198e12i) q^{17} +(1.93832e12 - 1.93832e12i) q^{18} -3.85220e12i q^{19} +(1.25898e12 - 7.43887e11i) q^{20} +3.28430e12 q^{21} +(-1.10145e13 - 1.10145e13i) q^{22} +(-1.75206e13 + 1.75206e13i) q^{23} +2.77222e13i q^{24} +(-4.60094e13 + 8.35349e13i) q^{25} -2.19705e14 q^{26} +(1.10051e14 + 1.10051e14i) q^{27} +(1.42513e13 - 1.42513e13i) q^{28} -4.19714e14i q^{29} +(-1.14926e14 - 1.94505e14i) q^{30} +1.16378e15 q^{31} +(2.25554e14 + 2.25554e14i) q^{32} +(2.83493e14 - 2.83493e14i) q^{33} -1.35683e15i q^{34} +(-3.27378e14 + 1.27297e15i) q^{35} +4.32956e14 q^{36} +(2.42381e15 + 2.42381e15i) q^{37} +(-2.58246e15 + 2.58246e15i) q^{38} -5.65480e15i q^{39} +(-1.07450e16 - 2.76335e15i) q^{40} +6.21313e15 q^{41} +(-2.20175e15 - 2.20175e15i) q^{42} +(-1.85951e16 + 1.85951e16i) q^{43} -2.46028e15i q^{44} +(-2.43094e16 + 1.43636e16i) q^{45} +2.34911e16 q^{46} +(2.20380e16 + 2.20380e16i) q^{47} +(1.58754e16 - 1.58754e16i) q^{48} -6.16767e16i q^{49} +(8.68447e16 - 2.51565e16i) q^{50} +3.49222e16 q^{51} +(-2.45374e16 - 2.45374e16i) q^{52} +(4.27674e16 - 4.27674e16i) q^{53} -1.47554e17i q^{54} +(8.16215e16 + 1.38139e17i) q^{55} -1.52911e17 q^{56} +(-6.64677e16 - 6.64677e16i) q^{57} +(-2.81370e17 + 2.81370e17i) q^{58} +8.59684e17i q^{59} +(8.88758e15 - 3.45583e16i) q^{60} -2.26704e17 q^{61} +(-7.80179e17 - 7.80179e17i) q^{62} +(-2.75177e17 + 2.75177e17i) q^{63} -1.26718e18i q^{64} +(2.19176e18 + 5.63670e17i) q^{65} -3.80099e17 q^{66} +(-1.90225e17 - 1.90225e17i) q^{67} +(1.51535e17 - 1.51535e17i) q^{68} +6.04616e17i q^{69} +(1.07285e18 - 6.33913e17i) q^{70} +6.18041e18 q^{71} +(-2.32272e18 - 2.32272e18i) q^{72} +(-4.37711e18 + 4.37711e18i) q^{73} -3.24978e18i q^{74} +(6.47482e17 + 2.23522e18i) q^{75} -5.76836e17 q^{76} +(1.56369e18 + 1.56369e18i) q^{77} +(-3.79090e18 + 3.79090e18i) q^{78} -1.66472e19i q^{79} +(4.57074e18 + 7.73565e18i) q^{80} -6.28376e18 q^{81} +(-4.16519e18 - 4.16519e18i) q^{82} +(-1.64730e19 + 1.64730e19i) q^{83} -4.91797e17i q^{84} +(-3.48104e18 + 1.35356e19i) q^{85} +2.49317e19 q^{86} +(-7.24194e18 - 7.24194e18i) q^{87} +(-1.31989e19 + 1.31989e19i) q^{88} -3.70725e19i q^{89} +(2.59259e19 + 6.66752e18i) q^{90} +3.11908e19 q^{91} +(2.62356e18 + 2.62356e18i) q^{92} +(2.00803e19 - 2.00803e19i) q^{93} -2.95480e19i q^{94} +(3.23879e19 - 1.91369e19i) q^{95} +7.78363e18 q^{96} +(-2.73465e19 - 2.73465e19i) q^{97} +(-4.13472e19 + 4.13472e19i) q^{98} +4.75052e19i 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more