LMFDB - Embedded newform 10.22.b.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,22,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	10.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$27.9477344287$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 124640735 x^{8} + \cdots + 49\!\cdots\!00 $ x^10 + 124640735x^8 + 4978985708344843x^6 + 72834822986364822545965x^4 + 290426118121262728766390623556x^2 + 4921147175535440508379606707124900
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{61}\cdot 3^{4}\cdot 5^{20}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.6
Root			$130.450i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.22.b.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1024.00i q^{2} -142338. i q^{3} -1.04858e6 q^{4} +(1.55398e7 + 1.53412e7i) q^{5} +1.45754e8 q^{6} +1.78369e8i q^{7} -1.07374e9i q^{8} -9.79977e9 q^{9} +(-1.57093e10 + 1.59128e10i) q^{10} -6.70297e10 q^{11} +1.49252e11i q^{12} +3.80041e11i q^{13} -1.82650e11 q^{14} +(2.18363e12 - 2.21191e12i) q^{15} +1.09951e12 q^{16} -5.49812e12i q^{17} -1.00350e13i q^{18} +4.09605e13 q^{19} +(-1.62947e13 - 1.60864e13i) q^{20} +2.53887e13 q^{21} -6.86384e13i q^{22} +3.64174e14i q^{23} -1.52834e14 q^{24} +(6.13507e12 + 4.76798e14i) q^{25} -3.89162e14 q^{26} -9.40260e13i q^{27} -1.87033e14i q^{28} +2.31200e15 q^{29} +(2.26499e15 + 2.23604e15i) q^{30} +4.60475e15 q^{31} +1.12590e15i q^{32} +9.54088e15i q^{33} +5.63008e15 q^{34} +(-2.73639e15 + 2.77182e15i) q^{35} +1.02758e16 q^{36} +7.46426e15i q^{37} +4.19435e16i q^{38} +5.40943e16 q^{39} +(1.64724e16 - 1.66858e16i) q^{40} +6.15616e16 q^{41} +2.59980e16i q^{42} +8.30442e16i q^{43} +7.02858e16 q^{44} +(-1.52287e17 - 1.50340e17i) q^{45} -3.72914e17 q^{46} +2.46162e17i q^{47} -1.56502e17i q^{48} +5.26730e17 q^{49} +(-4.88241e17 + 6.28231e15i) q^{50} -7.82592e17 q^{51} -3.98502e17i q^{52} -1.24023e18i q^{53} +9.62827e16 q^{54} +(-1.04163e18 - 1.02831e18i) q^{55} +1.91522e17 q^{56} -5.83023e18i q^{57} +2.36748e18i q^{58} +6.57687e18 q^{59} +(-2.28970e18 + 2.31935e18i) q^{60} -7.93046e18 q^{61} +4.71527e18i q^{62} -1.74798e18i q^{63} -1.15292e18 q^{64} +(-5.83026e18 + 5.90577e18i) q^{65} -9.76986e18 q^{66} +1.67617e19i q^{67} +5.76520e18i q^{68} +5.18358e19 q^{69} +(-2.83835e18 - 2.80206e18i) q^{70} +3.45785e19 q^{71} +1.05224e19i q^{72} -4.09328e19i q^{73} -7.64340e18 q^{74} +(6.78665e19 - 8.73254e17i) q^{75} -4.29502e19 q^{76} -1.19560e19i q^{77} +5.53925e19i q^{78} -5.41982e19 q^{79} +(1.70862e19 + 1.68678e19i) q^{80} -1.15893e20 q^{81} +6.30391e19i q^{82} +6.11198e19i q^{83} -2.66220e19 q^{84} +(8.43476e19 - 8.54399e19i) q^{85} -8.50372e19 q^{86} -3.29085e20i q^{87} +7.19726e19i q^{88} -4.72382e20 q^{89} +(1.53948e20 - 1.55942e20i) q^{90} -6.77875e19 q^{91} -3.81864e20i q^{92} -6.55432e20i q^{93} -2.52070e20 q^{94} +(6.36518e20 + 6.28381e20i) q^{95} +1.60258e20 q^{96} +6.31547e20i q^{97} +5.39372e20i q^{98} +6.56876e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10485760 q^{4} + 27722150 q^{5} - 230748160 q^{6} - 12711922730 q^{9} - 22426931200 q^{10} - 199435236680 q^{11} - 104903905280 q^{14} - 1714785566200 q^{15} + 10995116277760 q^{16} + 123436918144200 q^{19}+ \cdots + 21\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q - 10485760 * q^4 + 27722150 * q^5 - 230748160 * q^6 - 12711922730 * q^9 - 22426931200 * q^10 - 199435236680 * q^11 - 104903905280 * q^14 - 1714785566200 * q^15 + 10995116277760 * q^16 + 123436918144200 * q^19 - 29068781158400 * q^20 - 158960071181080 * q^21 + 241956982620160 * q^24 - 753844388658750 * q^25 - 173073038991360 * q^26 + 1774546489874700 * q^29 + 5639638400921600 * q^30 + 10456190999441920 * q^31 - 18958190285946880 * q^34 + 24035281816377400 * q^35 + 13329417088532480 * q^36 + 45468500581785840 * q^39 + 23516341809971200 * q^40 + 93828363171915220 * q^41 + 209123002736967680 * q^44 - 1294878557826950 * q^45 - 453509186534543360 * q^46 - 1584589583512161570 * q^49 + 130953516753920000 * q^50 - 512256548145748480 * q^51 - 3219652987818598400 * q^54 + 8644481518774929800 * q^55 + 109999717382881280 * q^56 - 5722347962825378600 * q^59 + 1798082989863731200 * q^60 - 12650867843198554180 * q^61 - 11529215046068469760 * q^64 + 26346750548743534800 * q^65 - 32504410286103019520 * q^66 + 96951047157018456040 * q^69 + 41090423076705996800 * q^70 - 104781163131643184880 * q^71 + 32904860966761553920 * q^74 + 296606638041153670000 * q^75 - 129432989879972659200 * q^76 + 96531112322635730400 * q^79 + 30480826271950438400 * q^80 - 828031346148584406190 * q^81 + 166681715598772142080 * q^84 + 634500251198792806400 * q^85 - 1012021399291540418560 * q^86 + 1925821863958052788100 * q^89 + 598299873941928857600 * q^90 - 3491972396700191783280 * q^91 + 919679051426714398720 * q^94 + 1154253771449725323000 * q^95 - 253710285007916892160 * q^96 + 2120189706372537680840 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1024.00i			0.707107i
$2$			1024.00i			0.707107i
$3$		−	142338.i		−	1.39171i	−0.718184	−	0.695854i	$-0.755026\pi$
$3$		−	142338.i		−	1.39171i	0.718184	−	0.695854i	$-0.244974\pi$
$4$	−1.04858e6			−0.500000
$5$	1.55398e7	+	1.53412e7i	0.711641	+	0.702543i
$5$	1.55398e7	+	1.53412e7i	0.711641	+	0.702543i
$6$	1.45754e8			0.984086
$7$			1.78369e8i			0.238666i	0.992854	+	0.119333i	$0.0380756\pi$
$7$			1.78369e8i			0.238666i	−0.992854	+	0.119333i	$0.961924\pi$
$8$		−	1.07374e9i		−	0.353553i
$9$	−9.79977e9			−0.936849
$10$	−1.57093e10	+	1.59128e10i	−0.496773	+	0.503206i
$11$	−6.70297e10			−0.779192			−0.389596	−	0.920986i	$-0.627385\pi$
$11$	−6.70297e10			−0.779192			−0.389596	+	0.920986i	$0.627385\pi$
$12$			1.49252e11i			0.695854i
$13$			3.80041e11i			0.764584i	0.924042	+	0.382292i	$0.124865\pi$
$13$			3.80041e11i			0.764584i	−0.924042	+	0.382292i	$0.875135\pi$
$14$	−1.82650e11			−0.168762
$15$	2.18363e12	−	2.21191e12i	0.977734	−	0.990396i
$16$	1.09951e12			0.250000
$17$		−	5.49812e12i		−	0.661456i	−0.943726	−	0.330728i	$-0.892706\pi$
$17$		−	5.49812e12i		−	0.661456i	0.943726	−	0.330728i	$-0.107294\pi$
$18$		−	1.00350e13i		−	0.662452i
$19$	4.09605e13			1.53268			0.766341	−	0.642434i	$-0.222075\pi$
$19$	4.09605e13			1.53268			0.766341	+	0.642434i	$0.222075\pi$
$20$	−1.62947e13	−	1.60864e13i	−0.355821	−	0.351272i
$21$	2.53887e13			0.332153
$22$		−	6.86384e13i		−	0.550972i
$23$			3.64174e14i			1.83302i	0.400014	+	0.916509i	$0.369005\pi$
$23$			3.64174e14i			1.83302i	−0.400014	+	0.916509i	$0.630995\pi$
$24$	−1.52834e14			−0.492043
$25$	6.13507e12	+	4.76798e14i	0.0128662	+	0.999917i
$26$	−3.89162e14			−0.540642
$27$		−	9.40260e13i		−	0.0878878i
$28$		−	1.87033e14i		−	0.119333i
$29$	2.31200e15			1.02049			0.510244	−	0.860030i	$-0.329555\pi$
$29$	2.31200e15			1.02049			0.510244	+	0.860030i	$0.329555\pi$
$30$	2.26499e15	+	2.23604e15i	0.700316	+	0.691363i
$31$	4.60475e15			1.00904			0.504520	−	0.863400i	$-0.331669\pi$
$31$	4.60475e15			1.00904			0.504520	+	0.863400i	$0.331669\pi$
$32$			1.12590e15i			0.176777i
$33$			9.54088e15i			1.08441i
$34$	5.63008e15			0.467720
$35$	−2.73639e15	+	2.77182e15i	−0.167673	+	0.169844i
$36$	1.02758e16			0.468424
$37$			7.46426e15i			0.255193i	0.991826	+	0.127596i	$0.0407262\pi$
$37$			7.46426e15i			0.255193i	−0.991826	+	0.127596i	$0.959274\pi$
$38$			4.19435e16i			1.08377i
$39$	5.40943e16			1.06408
$40$	1.64724e16	−	1.66858e16i	0.248387	−	0.251603i
$41$	6.15616e16			0.716275			0.358137	−	0.933669i	$-0.383412\pi$
$41$	6.15616e16			0.716275			0.358137	+	0.933669i	$0.383412\pi$
$42$			2.59980e16i			0.234867i
$43$			8.30442e16i			0.585990i	0.956114	+	0.292995i	$0.0946520\pi$
$43$			8.30442e16i			0.585990i	−0.956114	+	0.292995i	$0.905348\pi$
$44$	7.02858e16			0.389596
$45$	−1.52287e17	−	1.50340e17i	−0.666700	−	0.658177i
$46$	−3.72914e17			−1.29614
$47$			2.46162e17i			0.682643i	0.939947	+	0.341322i	$0.110875\pi$
$47$			2.46162e17i			0.682643i	−0.939947	+	0.341322i	$0.889125\pi$
$48$		−	1.56502e17i		−	0.347927i
$49$	5.26730e17			0.943039
$50$	−4.88241e17	+	6.28231e15i	−0.707048	+	0.00909776i
$51$	−7.82592e17			−0.920553
$52$		−	3.98502e17i		−	0.382292i
$53$		−	1.24023e18i		−	0.974104i	−0.873373	−	0.487052i	$-0.838072\pi$
$53$		−	1.24023e18i		−	0.974104i	0.873373	−	0.487052i	$-0.161928\pi$
$54$	9.62827e16			0.0621461
$55$	−1.04163e18	−	1.02831e18i	−0.554505	−	0.547416i
$56$	1.91522e17			0.0843810
$57$		−	5.83023e18i		−	2.13304i
$58$			2.36748e18i			0.721594i
$59$	6.57687e18			1.67523			0.837613	−	0.546265i	$-0.183951\pi$
$59$	6.57687e18			1.67523			0.837613	+	0.546265i	$0.183951\pi$
$60$	−2.28970e18	+	2.31935e18i	−0.488867	+	0.495198i
$61$	−7.93046e18			−1.42343			−0.711713	−	0.702470i	$-0.752081\pi$
$61$	−7.93046e18			−1.42343			−0.711713	+	0.702470i	$0.752081\pi$
$62$			4.71527e18i			0.713500i
$63$		−	1.74798e18i		−	0.223594i
$64$	−1.15292e18			−0.125000
$65$	−5.83026e18	+	5.90577e18i	−0.537153	+	0.544109i
$66$	−9.76986e18			−0.766791
$67$			1.67617e19i			1.12340i	0.827342	+	0.561698i	$0.189852\pi$
$67$			1.67617e19i			1.12340i	−0.827342	+	0.561698i	$0.810148\pi$
$68$			5.76520e18i			0.330728i
$69$	5.18358e19			2.55102
$70$	−2.83835e18	−	2.80206e18i	−0.120098	−	0.118563i
$71$	3.45785e19			1.26065			0.630323	−	0.776333i	$-0.282923\pi$
$71$	3.45785e19			1.26065			0.630323	+	0.776333i	$0.282923\pi$
$72$			1.05224e19i			0.331226i
$73$		−	4.09328e19i		−	1.11476i	−0.830257	−	0.557381i	$-0.811806\pi$
$73$		−	4.09328e19i		−	1.11476i	0.830257	−	0.557381i	$-0.188194\pi$
$74$	−7.64340e18			−0.180449
$75$	6.78665e19	−	8.73254e17i	1.39159	−	0.0179059i
$76$	−4.29502e19			−0.766341
$77$		−	1.19560e19i		−	0.185966i
$78$			5.53925e19i			0.752416i
$79$	−5.41982e19			−0.644021			−0.322011	−	0.946736i	$-0.604359\pi$
$79$	−5.41982e19			−0.644021			−0.322011	+	0.946736i	$0.604359\pi$
$80$	1.70862e19	+	1.68678e19i	0.177910	+	0.175636i
$81$	−1.15893e20			−1.05916
$82$			6.30391e19i			0.506483i
$83$			6.11198e19i			0.432377i	0.976352	+	0.216188i	$0.0693625\pi$
$83$			6.11198e19i			0.432377i	−0.976352	+	0.216188i	$0.930637\pi$
$84$	−2.66220e19			−0.166076
$85$	8.43476e19	−	8.54399e19i	0.464701	−	0.470719i
$86$	−8.50372e19			−0.414358
$87$		−	3.29085e20i		−	1.42022i
$88$			7.19726e19i			0.275486i
$89$	−4.72382e20			−1.60582			−0.802912	−	0.596097i	$-0.796717\pi$
$89$	−4.72382e20			−1.60582			−0.802912	+	0.596097i	$0.796717\pi$
$90$	1.53948e20	−	1.55942e20i	0.465401	−	0.471428i
$91$	−6.77875e19			−0.182480
$92$		−	3.81864e20i		−	0.916509i
$93$		−	6.55432e20i		−	1.40429i
$94$	−2.52070e20			−0.482702
$95$	6.36518e20	+	6.28381e20i	1.09072	+	1.07678i
$96$	1.60258e20			0.246021
$97$			6.31547e20i			0.869566i	0.900535	+	0.434783i	$0.143175\pi$
$97$			6.31547e20i			0.869566i	−0.900535	+	0.434783i	$0.856825\pi$
$98$			5.39372e20i			0.666829i
$99$	6.56876e20			0.729985
$100$	−6.43309e18	−	4.99959e20i	−0.00643309	−	0.499959i
$101$	−1.50801e21			−1.35841			−0.679203	−	0.733950i	$-0.737675\pi$
$101$	−1.50801e21			−1.35841			−0.679203	+	0.733950i	$0.737675\pi$
$102$		−	8.01374e20i		−	0.650929i
$103$			9.50255e20i			0.696705i	0.937364	+	0.348353i	$0.113259\pi$
$103$			9.50255e20i			0.696705i	−0.937364	+	0.348353i	$0.886741\pi$
$104$	4.08066e20			0.270321
$105$	3.94536e20	+	3.89492e20i	0.236374	+	0.233352i
$106$	1.26999e21			0.688796
$107$			3.15786e21i			1.55190i	0.630794	+	0.775950i	$0.282729\pi$
$107$			3.15786e21i			1.55190i	−0.630794	+	0.775950i	$0.717271\pi$
$108$			9.85934e19i			0.0439439i
$109$	4.26206e20			0.172441			0.0862207	−	0.996276i	$-0.472521\pi$
$109$	4.26206e20			0.172441			0.0862207	+	0.996276i	$0.472521\pi$
$110$	1.05299e21	−	1.06663e21i	0.387081	−	0.392094i
$111$	1.06245e21			0.355154
$112$			1.96119e20i			0.0596664i
$113$		−	3.04833e21i		−	0.844769i	−0.906417	−	0.422385i	$-0.861193\pi$
$113$		−	3.04833e21i		−	0.844769i	0.906417	−	0.422385i	$-0.138807\pi$
$114$	5.97016e21			1.50829
$115$	−5.58685e21	+	5.65920e21i	−1.28777	+	1.30445i
$116$	−2.42430e21			−0.510244
$117$		−	3.72431e21i		−	0.716299i
$118$			6.73472e21i			1.18456i
$119$	9.80695e20			0.157867
$120$	−2.37502e21	−	2.34466e21i	−0.350158	−	0.345681i
$121$	−2.90727e21			−0.392861
$122$		−	8.12079e21i		−	1.00651i
$123$		−	8.76256e21i		−	0.996845i
$124$	−4.82844e21			−0.504520
$125$	−7.21929e21	+	7.50347e21i	−0.693329	+	0.720621i
$126$	1.78993e21			0.158105
$127$		−	1.51178e22i		−	1.22899i	−0.788920	−	0.614496i	$-0.789359\pi$
$127$		−	1.51178e22i		−	1.22899i	0.788920	−	0.614496i	$-0.210641\pi$
$128$		−	1.18059e21i		−	0.0883883i
$129$	1.18203e22			0.815527
$130$	−6.04750e21	−	5.97019e21i	−0.384743	−	0.379825i
$131$	1.11001e22			0.651597			0.325798	−	0.945439i	$-0.394367\pi$
$131$	1.11001e22			0.651597			0.325798	+	0.945439i	$0.394367\pi$
$132$		−	1.00043e22i		−	0.542203i
$133$			7.30608e21i			0.365799i
$134$	−1.71640e22			−0.794361
$135$	1.44247e21	−	1.46115e21i	0.0617450	−	0.0625446i
$136$	−5.90356e21			−0.233860
$137$			1.34159e21i			0.0492099i	0.999697	+	0.0246050i	$0.00783279\pi$
$137$			1.34159e21i			0.0492099i	−0.999697	+	0.0246050i	$0.992167\pi$
$138$			5.30799e22i			1.80385i
$139$	−5.51062e22			−1.73598			−0.867991	−	0.496580i	$-0.834589\pi$
$139$	−5.51062e22			−1.73598			−0.867991	+	0.496580i	$0.834589\pi$
$140$	2.86931e21	−	2.90647e21i	0.0838365	−	0.0849221i
$141$	3.50382e22			0.950039
$142$			3.54083e22i			0.891411i
$143$		−	2.54740e22i		−	0.595757i
$144$	−1.07750e22			−0.234212
$145$	3.59280e22	+	3.54687e22i	0.726222	+	0.716937i
$146$	4.19152e22			0.788255
$147$		−	7.49738e22i		−	1.31243i
$148$		−	7.82684e21i		−	0.127596i
$149$	6.59576e22			1.00186			0.500932	−	0.865487i	$-0.332991\pi$
$149$	6.59576e22			1.00186			0.500932	+	0.865487i	$0.332991\pi$
$150$	8.94212e20	+	6.94953e22i	0.0126614	+	0.984004i
$151$	8.29720e22			1.09565			0.547827	−	0.836592i	$-0.315455\pi$
$151$	8.29720e22			1.09565			0.547827	+	0.836592i	$0.315455\pi$
$152$		−	4.39810e22i		−	0.541885i
$153$			5.38803e22i			0.619684i
$154$	1.22430e22			0.131498
$155$	7.15571e22	+	7.06423e22i	0.718075	+	0.708895i
$156$	−5.67219e22			−0.532038
$157$		−	1.01202e23i		−	0.887650i	−0.896113	−	0.443825i	$-0.853621\pi$
$157$		−	1.01202e23i		−	0.887650i	0.896113	−	0.443825i	$-0.146379\pi$
$158$		−	5.54989e22i		−	0.455392i
$159$	−1.76532e23			−1.35567
$160$	−1.72726e22	+	1.74963e22i	−0.124193	+	0.125802i
$161$	−6.49574e22			−0.437478
$162$		−	1.18674e23i		−	0.748941i
$163$			2.20609e23i			1.30513i	0.757734	+	0.652564i	$0.226307\pi$
$163$			2.20609e23i			1.30513i	−0.757734	+	0.652564i	$0.773693\pi$
$164$	−6.45520e22			−0.358137
$165$	−1.46368e23	+	1.48264e23i	−0.761842	+	0.771708i
$166$	−6.25867e22			−0.305736
$167$		−	2.57472e23i		−	1.18088i	−0.807080	−	0.590442i	$-0.798954\pi$
$167$		−	2.57472e23i		−	1.18088i	0.807080	−	0.590442i	$-0.201046\pi$
$168$		−	2.72609e22i		−	0.117434i
$169$	1.02634e23			0.415412
$170$	8.74904e22	+	8.63719e22i	0.332849	+	0.328593i
$171$	−4.01403e23			−1.43589
$172$		−	8.70781e22i		−	0.292995i
$173$		−	2.16173e21i		−	0.00684413i	−0.999994	−	0.00342207i	$-0.998911\pi$
$173$		−	2.16173e21i		−	0.00684413i	0.999994	−	0.00342207i	$-0.00108928\pi$
$174$	3.36983e23			1.00425
$175$	−8.50459e22	+	1.09431e21i	−0.238646	+	0.00307071i
$176$	−7.37000e22			−0.194798
$177$		−	9.36139e23i		−	2.33142i
$178$		−	4.83719e23i		−	1.13549i
$179$	5.83289e23			1.29100			0.645501	−	0.763759i	$-0.276648\pi$
$179$	5.83289e23			1.29100			0.645501	+	0.763759i	$0.276648\pi$
$180$	1.59684e23	+	1.57643e23i	0.333350	+	0.329088i
$181$	−6.17348e23			−1.21592			−0.607960	−	0.793967i	$-0.708012\pi$
$181$	−6.17348e23			−1.21592			−0.607960	+	0.793967i	$0.708012\pi$
$182$		−	6.94144e22i		−	0.129033i
$183$			1.12881e24i			1.98099i
$184$	3.91029e23			0.648070
$185$	−1.14510e23	+	1.15993e23i	−0.179284	+	0.181606i
$186$	6.71162e23			0.992982
$187$			3.68538e23i			0.515401i
$188$		−	2.58120e23i		−	0.341322i
$189$	1.67713e22			0.0209758
$190$	−6.43462e23	+	6.51795e23i	−0.761395	+	0.771255i
$191$	−1.21745e23			−0.136332			−0.0681662	−	0.997674i	$-0.521715\pi$
$191$	−1.21745e23			−0.136332			−0.0681662	+	0.997674i	$0.521715\pi$
$192$			1.64105e23i			0.173963i
$193$			1.29605e24i			1.30098i	0.759514	+	0.650491i	$0.225437\pi$
$193$			1.29605e24i			1.30098i	−0.759514	+	0.650491i	$0.774563\pi$
$194$	−6.46704e23			−0.614876
$195$	8.40615e23	+	8.29869e23i	0.757241	+	0.747560i
$196$	−5.52317e23			−0.471519
$197$		−	1.39082e24i		−	1.12557i	−0.826602	−	0.562787i	$-0.809729\pi$
$197$		−	1.39082e24i		−	1.12557i	0.826602	−	0.562787i	$-0.190271\pi$
$198$			6.72641e23i			0.516177i
$199$	4.95954e22			0.0360981			0.0180490	−	0.999837i	$-0.494255\pi$
$199$	4.95954e22			0.0360981			0.0180490	+	0.999837i	$0.494255\pi$
$200$	5.11958e23	−	6.58748e21i	0.353524	−	0.00454888i
$201$	2.38583e24			1.56344
$202$		−	1.54420e24i		−	0.960538i
$203$			4.12388e23i			0.243556i
$204$	8.20607e23			0.460276
$205$	9.56657e23	+	9.44426e23i	0.509731	+	0.503214i
$206$	−9.73061e23			−0.492645
$207$		−	3.56882e24i		−	1.71726i
$208$			4.17859e23i			0.191146i
$209$	−2.74557e24			−1.19425
$210$	−3.98840e23	+	4.04005e23i	−0.165005	+	0.167141i
$211$	1.11013e24			0.436925			0.218463	−	0.975845i	$-0.429896\pi$
$211$	1.11013e24			0.436925			0.218463	+	0.975845i	$0.429896\pi$
$212$			1.30047e24i			0.487052i
$213$		−	4.92183e24i		−	1.75445i
$214$	−3.23365e24			−1.09736
$215$	−1.27399e24	+	1.29049e24i	−0.411684	+	0.417015i
$216$	−1.00960e23			−0.0310730
$217$			8.21345e23i			0.240823i
$218$			4.36435e23i			0.121934i
$219$	−5.82630e24			−1.55142
$220$	1.09223e24	+	1.07826e24i	0.277252	+	0.273708i
$221$	2.08951e24			0.505738
$222$			1.08795e24i			0.251132i
$223$		−	4.06196e24i		−	0.894406i	−0.894432	−	0.447203i	$-0.852420\pi$
$223$		−	4.06196e24i		−	0.894406i	0.894432	−	0.447203i	$-0.147580\pi$
$224$	−2.00826e23			−0.0421905
$225$	−6.01223e22	−	4.67251e24i	−0.0120537	−	0.936771i
$226$	3.12149e24			0.597342
$227$			1.96136e24i			0.358331i	0.983819	+	0.179166i	$0.0573398\pi$
$227$			1.96136e24i			0.358331i	−0.983819	+	0.179166i	$0.942660\pi$
$228$			6.11344e24i			1.06652i
$229$	7.50360e24			1.25025			0.625125	−	0.780525i	$-0.285048\pi$
$229$	7.50360e24			1.25025			0.625125	+	0.780525i	$0.285048\pi$
$230$	−5.79502e24	−	5.72094e24i	−0.922386	−	0.910594i
$231$	−1.70180e24			−0.258811
$232$		−	2.48249e24i		−	0.360797i
$233$		−	1.66202e23i		−	0.0230887i	−0.999933	−	0.0115444i	$-0.996325\pi$
$233$		−	1.66202e23i		−	0.0230887i	0.999933	−	0.0115444i	$-0.00367477\pi$
$234$	3.81370e24			0.506500
$235$	−3.77641e24	+	3.82532e24i	−0.479586	+	0.485797i
$236$	−6.89635e24			−0.837613
$237$			7.71446e24i			0.896289i
$238$			1.00423e24i			0.111629i
$239$	−1.13691e23			−0.0120934			−0.00604669	−	0.999982i	$-0.501925\pi$
$239$	−1.13691e23			−0.0120934			−0.00604669	+	0.999982i	$0.501925\pi$
$240$	2.40093e24	−	2.43202e24i	0.244434	−	0.247599i
$241$	1.20656e25			1.17590			0.587948	−	0.808898i	$-0.299936\pi$
$241$	1.20656e25			1.17590			0.587948	+	0.808898i	$0.299936\pi$
$242$		−	2.97704e24i		−	0.277794i
$243$			1.55124e25i			1.38616i
$244$	8.31569e24			0.711713
$245$	8.18530e24	+	8.08065e24i	0.671105	+	0.662525i
$246$	8.97286e24			0.704876
$247$			1.55666e25i			1.17186i
$248$		−	4.94432e24i		−	0.356750i
$249$	8.69968e24			0.601742
$250$	−7.68355e24	−	7.39255e24i	−0.509556	−	0.490258i
$251$	−2.25612e25			−1.43479			−0.717394	−	0.696667i	$-0.754665\pi$
$251$	−2.25612e25			−1.43479			−0.717394	+	0.696667i	$0.754665\pi$
$252$			1.83288e24i			0.111797i
$253$		−	2.44105e25i		−	1.42827i
$254$	1.54806e25			0.869029
$255$	−1.21613e25	−	1.20059e25i	−0.655103	−	0.646728i
$256$	1.20893e24			0.0625000
$257$		−	5.68486e23i		−	0.0282112i	−0.999901	−	0.0141056i	$-0.995510\pi$
$257$		−	5.68486e23i		−	0.0282112i	0.999901	−	0.0141056i	$-0.00449010\pi$
$258$			1.21040e25i			0.576665i
$259$	−1.33139e24			−0.0609058
$260$	6.11348e24	−	6.19264e24i	0.268577	−	0.272055i
$261$	−2.26570e25			−0.956043
$262$			1.13665e25i			0.460749i
$263$		−	3.01647e25i		−	1.17480i	−0.809297	−	0.587400i	$-0.800151\pi$
$263$		−	3.01647e25i		−	1.17480i	0.809297	−	0.587400i	$-0.199849\pi$
$264$	1.02444e25			0.383396
$265$	1.90265e25	−	1.92729e25i	0.684350	−	0.693213i
$266$	−7.48142e24			−0.258659
$267$			6.72379e25i			2.23484i
$268$		−	1.75759e25i		−	0.561698i
$269$	−5.19995e25			−1.59809			−0.799044	−	0.601273i	$-0.794660\pi$
$269$	−5.19995e25			−1.59809			−0.799044	+	0.601273i	$0.794660\pi$
$270$	1.49622e24	+	1.47709e24i	0.0442257	+	0.0436603i
$271$	−1.02768e25			−0.292201			−0.146101	−	0.989270i	$-0.546672\pi$
$271$	−1.02768e25			−0.292201			−0.146101	+	0.989270i	$0.546672\pi$
$272$		−	6.04525e24i		−	0.165364i
$273$			9.64874e24i			0.253959i
$274$	−1.37378e24			−0.0347967
$275$	−4.11232e23	−	3.19596e25i	−0.0100252	−	0.779127i
$276$	−5.43538e25			−1.27551
$277$		−	4.71844e24i		−	0.106601i	−0.998579	−	0.0533004i	$-0.983026\pi$
$277$		−	4.71844e24i		−	0.106601i	0.998579	−	0.0533004i	$-0.0169741\pi$
$278$		−	5.64288e25i		−	1.22752i
$279$	−4.51255e25			−0.945319
$280$	2.97622e24	+	2.93817e24i	0.0600490	+	0.0592813i
$281$	5.82199e25			1.13150			0.565750	−	0.824577i	$-0.308587\pi$
$281$	5.82199e25			1.13150			0.565750	+	0.824577i	$0.308587\pi$
$282$			3.58792e25i			0.671779i
$283$			4.92992e25i			0.889369i	0.895687	+	0.444684i	$0.146684\pi$
$283$			4.92992e25i			0.889369i	−0.895687	+	0.444684i	$0.853316\pi$
$284$	−3.62581e25			−0.630323
$285$	8.94425e25	−	9.06008e25i	1.49856	−	1.51796i
$286$	2.60854e25			0.421264
$287$			1.09807e25i			0.170950i
$288$		−	1.10336e25i		−	0.165613i
$289$	3.88626e25			0.562476
$290$	−3.63199e25	+	3.67903e25i	−0.506951	+	0.513516i
$291$	8.98932e25			1.21018
$292$			4.29212e25i			0.557381i
$293$		−	1.19516e26i		−	1.49733i	−0.662950	−	0.748664i	$-0.730696\pi$
$293$		−	1.19516e26i		−	1.49733i	0.662950	−	0.748664i	$-0.269304\pi$
$294$	7.67732e25			0.928031
$295$	1.02203e26	+	1.00897e26i	1.19216	+	1.17692i
$296$	8.01468e24			0.0902243
$297$			6.30254e24i			0.0684814i
$298$			6.75405e25i			0.708425i
$299$	−1.38401e26			−1.40150
$300$	−7.11631e25	+	9.15673e23i	−0.695796	+	0.00895297i
$301$	−1.48125e25			−0.139856
$302$			8.49633e25i			0.774745i
$303$			2.14647e26i			1.89050i
$304$	4.50365e25			0.383171
$305$	−1.23238e26	−	1.21662e26i	−1.01297	−	1.00002i
$306$	−5.51735e25			−0.438183
$307$		−	1.43113e24i		−	0.0109831i	−0.999985	−	0.00549155i	$-0.998252\pi$
$307$		−	1.43113e24i		−	0.0109831i	0.999985	−	0.00549155i	$-0.00174802\pi$
$308$			1.25368e25i			0.0929831i
$309$	1.35257e26			0.969610
$310$	−7.23377e25	+	7.32744e25i	−0.501264	+	0.507756i
$311$	−9.90177e25			−0.663328			−0.331664	−	0.943398i	$-0.607610\pi$
$311$	−9.90177e25			−0.663328			−0.331664	+	0.943398i	$0.607610\pi$
$312$		−	5.80833e25i		−	0.376208i
$313$			1.03606e26i			0.648889i	0.945905	+	0.324444i	$0.105177\pi$
$313$			1.03606e26i			0.648889i	−0.945905	+	0.324444i	$0.894823\pi$
$314$	1.03631e26			0.627663
$315$	2.68160e25	−	2.71632e25i	0.157084	−	0.159118i
$316$	5.68309e25			0.322011
$317$		−	2.08733e26i		−	1.14411i	−0.820214	−	0.572057i	$-0.806146\pi$
$317$		−	2.08733e26i		−	1.14411i	0.820214	−	0.572057i	$-0.193854\pi$
$318$		−	1.80769e26i		−	0.958602i
$319$	−1.54972e26			−0.795156
$320$	−1.79162e25	−	1.76871e25i	−0.0889551	−	0.0878179i
$321$	4.49484e26			2.15979
$322$		−	6.65163e25i		−	0.309344i
$323$		−	2.25206e26i		−	1.01380i
$324$	1.21522e26			0.529582
$325$	−1.81203e26	+	2.33158e24i	−0.764520	+	0.00983727i
$326$	−2.25903e26			−0.922865
$327$		−	6.06654e25i		−	0.239988i
$328$		−	6.61013e25i		−	0.253241i
$329$	−4.39077e25			−0.162923
$330$	−1.51822e26	−	1.49881e26i	−0.545680	−	0.538704i
$331$	−1.81420e26			−0.631671			−0.315836	−	0.948814i	$-0.602285\pi$
$331$	−1.81420e26			−0.631671			−0.315836	+	0.948814i	$0.602285\pi$
$332$		−	6.40888e25i		−	0.216188i
$333$		−	7.31480e25i		−	0.239077i
$334$	2.63651e26			0.835011
$335$	−2.57144e26	+	2.60474e26i	−0.789234	+	0.799455i
$336$	2.79152e25			0.0830382
$337$			3.16535e26i			0.912658i	0.889811	+	0.456329i	$0.150836\pi$
$337$			3.16535e26i			0.912658i	−0.889811	+	0.456329i	$0.849164\pi$
$338$			1.05097e26i			0.293741i
$339$	−4.33893e26			−1.17567
$340$	−8.84448e25	+	8.95902e25i	−0.232351	+	0.235360i
$341$	−3.08655e26			−0.786236
$342$		−	4.11037e26i		−	1.01533i
$343$			1.93580e26i			0.463737i
$344$	8.91680e25			0.207179
$345$	8.05520e26	+	7.95222e26i	1.81541	+	1.79220i
$346$	2.21362e24			0.00483953
$347$		−	7.23207e26i		−	1.53392i	−0.641693	−	0.766961i	$-0.721768\pi$
$347$		−	7.23207e26i		−	1.53392i	0.641693	−	0.766961i	$-0.278232\pi$
$348$			3.45071e26i			0.710111i
$349$	−5.37828e26			−1.07393			−0.536966	−	0.843604i	$-0.680430\pi$
$349$	−5.37828e26			−1.07393			−0.536966	+	0.843604i	$0.680430\pi$
$350$	−1.12057e24	−	8.70870e25i	−0.00217132	−	0.168748i
$351$	3.57337e25			0.0671976
$352$		−	7.54688e25i		−	0.137743i
$353$		−	1.49413e25i		−	0.0264700i	−0.999912	−	0.0132350i	$-0.995787\pi$
$353$		−	1.49413e25i		−	0.0264700i	0.999912	−	0.0132350i	$-0.00421296\pi$
$354$	9.58606e26			1.64857
$355$	5.37343e26	+	5.30473e26i	0.897127	+	0.885658i
$356$	4.95328e26			0.802912
$357$		−	1.39590e26i		−	0.219704i
$358$			5.97288e26i			0.912877i
$359$	−4.59034e26			−0.681323			−0.340661	−	0.940186i	$-0.610651\pi$
$359$	−4.59034e26			−0.681323			−0.340661	+	0.940186i	$0.610651\pi$
$360$	−1.61426e26	+	1.63517e26i	−0.232701	+	0.235714i
$361$	9.63550e26			1.34911
$362$		−	6.32165e26i		−	0.859786i
$363$			4.13815e26i			0.546747i
$364$	7.10803e25			0.0912399
$365$	6.27957e26	−	6.36089e26i	0.783168	−	0.793310i
$366$	−1.15590e27			−1.40077
$367$		−	1.01095e27i		−	1.19052i	−0.803532	−	0.595262i	$-0.797048\pi$
$367$		−	1.01095e27i		−	1.19052i	0.803532	−	0.595262i	$-0.202952\pi$
$368$			4.00414e26i			0.458255i
$369$	−6.03290e26			−0.671041
$370$	−1.18777e26	−	1.17259e26i	−0.128415	−	0.126773i
$371$	2.21218e26			0.232485
$372$			6.87270e26i			0.702145i
$373$		−	1.87767e26i		−	0.186499i	−0.995643	−	0.0932496i	$-0.970275\pi$
$373$		−	1.87767e26i		−	0.186499i	0.995643	−	0.0932496i	$-0.0297254\pi$
$374$	−3.77383e26			−0.364443
$375$	1.06803e27	+	1.02758e27i	1.00289	+	0.964911i
$376$	2.64315e26			0.241351
$377$			8.78653e26i			0.780249i
$378$			1.71738e25i			0.0148321i
$379$	6.20634e26			0.521344			0.260672	−	0.965427i	$-0.416056\pi$
$379$	6.20634e26			0.521344			0.260672	+	0.965427i	$0.416056\pi$
$380$	−6.67438e26	−	6.58905e26i	−0.545360	−	0.538388i
$381$	−2.15184e27			−1.71040
$382$		−	1.24666e26i		−	0.0964016i
$383$		−	4.82230e26i		−	0.362800i	−0.983409	−	0.181400i	$-0.941937\pi$
$383$		−	4.82230e26i		−	0.362800i	0.983409	−	0.181400i	$-0.0580629\pi$
$384$	−1.68043e26			−0.123011
$385$	1.83419e26	−	1.85794e26i	0.130649	−	0.132341i
$386$	−1.32716e27			−0.919933
$387$		−	8.13814e26i		−	0.548984i
$388$		−	6.62225e26i		−	0.434783i
$389$	−1.62973e27			−1.04147			−0.520733	−	0.853720i	$-0.674341\pi$
$389$	−1.62973e27			−1.04147			−0.520733	+	0.853720i	$0.674341\pi$
$390$	−8.49785e26	+	8.60790e26i	−0.528605	+	0.535450i
$391$	2.00227e27			1.21246
$392$		−	5.65572e26i		−	0.333415i
$393$		−	1.57997e27i		−	0.906832i
$394$	1.42420e27			0.795901
$395$	−8.42230e26	−	8.31463e26i	−0.458312	−	0.452453i
$396$	−6.88784e26			−0.364992
$397$		−	2.48117e27i		−	1.28043i	−0.768195	−	0.640216i	$-0.778845\pi$
$397$		−	2.48117e27i		−	1.28043i	0.768195	−	0.640216i	$-0.221155\pi$
$398$			5.07857e25i			0.0255252i
$399$	1.03993e27			0.509085
$400$	6.74558e24	+	5.24245e26i	0.00321654	+	0.249979i
$401$	4.11919e25			0.0191336			0.00956679	−	0.999954i	$-0.496955\pi$
$401$	4.11919e25			0.0191336			0.00956679	+	0.999954i	$0.496955\pi$
$402$			2.44309e27i			1.10552i
$403$			1.74999e27i			0.771496i
$404$	1.58126e27			0.679203
$405$	−1.80095e27	−	1.77793e27i	−0.753744	−	0.744108i
$406$	−4.22286e26			−0.172220
$407$		−	5.00327e26i		−	0.198844i
$408$			8.40302e26i			0.325465i
$409$	−1.84199e26			−0.0695334			−0.0347667	−	0.999395i	$-0.511069\pi$
$409$	−1.84199e26			−0.0695334			−0.0347667	+	0.999395i	$0.511069\pi$
$410$	−9.67093e26	+	9.79617e26i	−0.355826	+	0.360434i
$411$	1.90959e26			0.0684858
$412$		−	9.96414e26i		−	0.348353i
$413$			1.17311e27i			0.399819i
$414$	3.65447e27			1.21429
$415$	−9.37649e26	+	9.49792e26i	−0.303763	+	0.307697i
$416$	−4.27888e26			−0.135161
$417$			7.84371e27i			2.41598i
$418$		−	2.81146e27i		−	0.844464i
$419$	1.87171e27			0.548266			0.274133	−	0.961692i	$-0.411609\pi$
$419$	1.87171e27			0.548266			0.274133	+	0.961692i	$0.411609\pi$
$420$	−4.13701e26	−	4.08412e26i	−0.118187	−	0.116676i
$421$	1.76316e27			0.491280			0.245640	−	0.969361i	$-0.421002\pi$
$421$	1.76316e27			0.491280			0.245640	+	0.969361i	$0.421002\pi$
$422$			1.13677e27i			0.308953i
$423$		−	2.41233e27i		−	0.639534i
$424$	−1.33169e27			−0.344398
$425$	2.62149e27	−	3.37314e25i	0.661401	−	0.00851040i
$426$	5.03995e27			1.24058
$427$		−	1.41455e27i		−	0.339723i
$428$		−	3.31126e27i		−	0.775950i
$429$	−3.62592e27			−0.829119
$430$	−1.32146e27	−	1.30457e27i	−0.294874	−	0.291104i
$431$	5.60334e27			1.22021			0.610107	−	0.792319i	$-0.291127\pi$
$431$	5.60334e27			1.22021			0.610107	+	0.792319i	$0.291127\pi$
$432$		−	1.03383e26i		−	0.0219720i
$433$			8.19818e27i			1.70057i	0.526322	+	0.850286i	$0.323571\pi$
$433$			8.19818e27i			1.70057i	−0.526322	+	0.850286i	$0.676429\pi$
$434$	−8.41058e26			−0.170288
$435$	5.04854e27	−	5.11392e27i	0.997767	−	1.01069i
$436$	−4.46910e26			−0.0862207
$437$			1.49167e28i			2.80943i
$438$		−	5.96613e27i		−	1.09702i
$439$	−6.90584e27			−1.23976			−0.619882	−	0.784695i	$-0.712819\pi$
$439$	−6.90584e27			−1.23976			−0.619882	+	0.784695i	$0.712819\pi$
$440$	−1.10414e27	+	1.11844e27i	−0.193541	+	0.196047i
$441$	−5.16184e27			−0.883485
$442$			2.13966e27i			0.357611i
$443$			3.71736e27i			0.606730i	0.952874	+	0.303365i	$0.0981101\pi$
$443$			3.71736e27i			0.606730i	−0.952874	+	0.303365i	$0.901890\pi$
$444$	−1.11406e27			−0.177577
$445$	−7.34073e27	−	7.24688e27i	−1.14277	−	1.12816i
$446$	4.15945e27			0.632441
$447$		−	9.38827e27i		−	1.39430i
$448$		−	2.05645e26i		−	0.0298332i
$449$	−4.05084e27			−0.574062			−0.287031	−	0.957921i	$-0.592668\pi$
$449$	−4.05084e27			−0.574062			−0.287031	+	0.957921i	$0.592668\pi$
$450$	4.78465e27	−	6.15652e25i	0.662397	−	0.00852323i
$451$	−4.12646e27			−0.558115
$452$			3.19640e27i			0.422385i
$453$		−	1.18101e28i		−	1.52483i
$454$	−2.00843e27			−0.253379
$455$	−1.05341e27	−	1.03994e27i	−0.129860	−	0.128200i
$456$	−6.26017e27			−0.754145
$457$			1.13881e28i			1.34070i	0.742046	+	0.670349i	$0.233856\pi$
$457$			1.13881e28i			1.34070i	−0.742046	+	0.670349i	$0.766144\pi$
$458$			7.68368e27i			0.884060i
$459$	−5.16967e26			−0.0581339
$460$	5.85824e27	−	5.93410e27i	0.643887	−	0.652225i
$461$	8.63960e27			0.928183			0.464092	−	0.885787i	$-0.346381\pi$
$461$	8.63960e27			0.928183			0.464092	+	0.885787i	$0.346381\pi$
$462$		−	1.74264e27i		−	0.183007i
$463$		−	1.02368e28i		−	1.05091i	−0.850822	−	0.525454i	$-0.823896\pi$
$463$		−	1.02368e28i		−	1.05091i	0.850822	−	0.525454i	$-0.176104\pi$
$464$	2.54207e27			0.255122
$465$	1.00551e28	−	1.01853e28i	0.986574	−	0.999350i
$466$	1.70191e26			0.0163262
$467$		−	1.49455e28i		−	1.40179i	−0.713264	−	0.700896i	$-0.752784\pi$
$467$		−	1.49455e28i		−	1.40179i	0.713264	−	0.700896i	$-0.247216\pi$
$468$			3.90522e27i			0.358150i
$469$	−2.98977e27			−0.268116
$470$	−3.91712e27	−	3.86705e27i	−0.343510	−	0.339119i
$471$	−1.44049e28			−1.23535
$472$		−	7.06186e27i		−	0.592282i
$473$		−	5.56643e27i		−	0.456599i
$474$	−7.89961e27			−0.633772
$475$	2.51295e26	+	1.95299e28i	0.0197198	+	1.53256i
$476$	−1.02833e27			−0.0789334
$477$			1.21540e28i			0.912588i
$478$		−	1.16419e26i		−	0.00855131i
$479$	1.84470e28			1.32557			0.662786	−	0.748809i	$-0.269374\pi$
$479$	1.84470e28			1.32557			0.662786	+	0.748809i	$0.269374\pi$
$480$	2.49039e27	+	2.45855e27i	0.175079	+	0.172841i
$481$	−2.83672e27			−0.195116
$482$			1.23552e28i			0.831485i
$483$			9.24590e27i			0.608842i
$484$	3.04849e27			0.196430
$485$	−9.68866e27	+	9.81413e27i	−0.610908	+	0.618819i
$486$	−1.58847e28			−0.980161
$487$			4.08637e27i			0.246765i	0.992359	+	0.123382i	$0.0393742\pi$
$487$			4.08637e27i			0.246765i	−0.992359	+	0.123382i	$0.960626\pi$
$488$			8.51527e27i			0.503257i
$489$	3.14010e28			1.81636
$490$	−8.27459e27	+	8.38174e27i	−0.468476	+	0.474543i
$491$	2.06798e28			1.14601			0.573007	−	0.819551i	$-0.305777\pi$
$491$	2.06798e28			1.14601			0.573007	+	0.819551i	$0.305777\pi$
$492$			9.18821e27i			0.498422i
$493$		−	1.27116e28i		−	0.675008i
$494$	−1.59402e28			−0.828633
$495$	1.02077e28	+	1.00772e28i	0.519487	+	0.512846i
$496$	5.06298e27			0.252260
$497$			6.16772e27i			0.300873i
$498$			8.90847e27i			0.425496i
$499$	1.27489e28			0.596235			0.298117	−	0.954529i	$-0.403641\pi$
$499$	1.27489e28			0.596235			0.298117	+	0.954529i	$0.403641\pi$
$500$	7.56997e27	−	7.86796e27i	0.346664	−	0.360311i
$501$	−3.66481e28			−1.64344
$502$		−	2.31027e28i		−	1.01455i
$503$		−	5.90848e27i		−	0.254104i	−0.991896	−	0.127052i	$-0.959448\pi$
$503$		−	5.90848e27i		−	0.254104i	0.991896	−	0.127052i	$-0.0405516\pi$
$504$	−1.87687e27			−0.0790523
$505$	−2.34342e28	−	2.31346e28i	−0.966698	−	0.954339i
$506$	2.49963e28			1.00994
$507$		−	1.46087e28i		−	0.578132i
$508$			1.58522e28i			0.614496i
$509$	4.92856e28			1.87147			0.935736	−	0.352702i	$-0.114737\pi$
$509$	4.92856e28			1.87147			0.935736	+	0.352702i	$0.114737\pi$
$510$	1.22940e28	−	1.24532e28i	0.457306	−	0.463228i
$511$	7.30115e27			0.266055
$512$			1.23794e27i			0.0441942i
$513$		−	3.85135e27i		−	0.134704i
$514$	5.82129e26			0.0199483
$515$	−1.45780e28	+	1.47668e28i	−0.489466	+	0.495804i
$516$	−1.23945e28			−0.407763
$517$		−	1.65002e28i		−	0.531910i
$518$		−	1.36335e27i		−	0.0430669i
$519$	−3.07697e26			−0.00952503
$520$	6.34127e27	+	6.26020e27i	0.192372	+	0.189912i
$521$	−6.81675e27			−0.202666			−0.101333	−	0.994853i	$-0.532311\pi$
$521$	−6.81675e27			−0.202666			−0.101333	+	0.994853i	$0.532311\pi$
$522$		−	2.32008e28i		−	0.676025i
$523$			7.41483e27i			0.211755i	0.994379	+	0.105877i	$0.0337651\pi$
$523$			7.41483e27i			0.211755i	−0.994379	+	0.105877i	$0.966235\pi$
$524$	−1.16393e28			−0.325798
$525$	1.55761e26	+	1.21053e28i	0.00427353	+	0.332125i
$526$	3.08887e28			0.830709
$527$		−	2.53175e28i		−	0.667436i
$528$			1.04903e28i			0.271102i
$529$	−9.31512e28			−2.35996
$530$	1.97355e28	+	1.94832e28i	0.490175	+	0.483909i
$531$	−6.44518e28			−1.56943
$532$		−	7.66098e27i		−	0.182899i
$533$			2.33959e28i			0.547652i
$534$	−6.88516e28			−1.58027
$535$	−4.84453e28	+	4.90727e28i	−1.09028	+	1.10440i
$536$	1.79978e28			0.397181
$537$		−	8.30243e28i		−	1.79670i
$538$		−	5.32475e28i		−	1.13002i
$539$	−3.53066e28			−0.734808
$540$	−1.51254e27	+	1.53212e27i	−0.0308725	+	0.0312723i
$541$	5.59874e28			1.12078			0.560388	−	0.828230i	$-0.310652\pi$
$541$	5.59874e28			1.12078			0.560388	+	0.828230i	$0.310652\pi$
$542$		−	1.05235e28i		−	0.206617i
$543$			8.78722e28i			1.69221i
$544$	6.19034e27			0.116930
$545$	6.62317e27	+	6.53850e27i	0.122716	+	0.121148i
$546$	−9.88031e27			−0.179576
$547$		−	3.53803e28i		−	0.630805i	−0.948958	−	0.315403i	$-0.897860\pi$
$547$		−	3.53803e28i		−	0.630805i	0.948958	−	0.315403i	$-0.102140\pi$
$548$		−	1.40675e27i		−	0.0246050i
$549$	7.77167e28			1.33354
$550$	3.27266e28	−	4.21102e26i	0.550926	−	0.00708890i
$551$	9.47004e28			1.56408
$552$		−	5.56583e28i		−	0.901923i
$553$		−	9.66727e27i		−	0.153706i
$554$	4.83168e27			0.0753782
$555$	1.65102e28	+	1.62992e28i	0.252742	+	0.249511i
$556$	5.77831e28			0.867991
$557$			5.77519e28i			0.851307i	0.904886	+	0.425654i	$0.139956\pi$
$557$			5.77519e28i			0.851307i	−0.904886	+	0.425654i	$0.860044\pi$
$558$		−	4.62086e28i		−	0.668441i
$559$	−3.15602e28			−0.448039
$560$	−3.00869e27	+	3.04765e27i	−0.0419182	+	0.0424611i
$561$	5.24569e28			0.717287
$562$			5.96171e28i			0.800092i
$563$			5.68315e28i			0.748603i	0.927307	+	0.374301i	$0.122117\pi$
$563$			5.68315e28i			0.748603i	−0.927307	+	0.374301i	$0.877883\pi$
$564$	−3.67403e28			−0.475020
$565$	4.67649e28	−	4.73705e28i	0.593487	−	0.601172i
$566$	−5.04823e28			−0.628879
$567$		−	2.06716e28i		−	0.252786i
$568$		−	3.71283e28i		−	0.445705i
$569$	−9.64871e27			−0.113708			−0.0568539	−	0.998383i	$-0.518107\pi$
$569$	−9.64871e27			−0.113708			−0.0568539	+	0.998383i	$0.518107\pi$
$570$	9.27752e28	+	9.15891e28i	1.07336	+	1.05964i
$571$	−1.10452e29			−1.25457			−0.627285	−	0.778790i	$-0.715834\pi$
$571$	−1.10452e29			−1.25457			−0.627285	+	0.778790i	$0.715834\pi$
$572$			2.67115e28i			0.297879i
$573$			1.73289e28i			0.189735i
$574$	−1.12442e28			−0.120880
$575$	−1.73637e29	+	2.23423e27i	−1.83287	+	0.0235839i
$576$	1.12984e28			0.117106
$577$			7.43531e28i			0.756751i	0.925652	+	0.378376i	$0.123517\pi$
$577$			7.43531e28i			0.756751i	−0.925652	+	0.378376i	$0.876483\pi$
$578$			3.97953e28i			0.397731i
$579$	1.84478e29			1.81058
$580$	−3.76732e28	−	3.71916e28i	−0.363111	−	0.358469i
$581$	−1.09019e28			−0.103193
$582$			9.20506e28i			0.855727i
$583$			8.31322e28i			0.759014i
$584$	−4.39513e28			−0.394128
$585$	5.71353e28	−	5.78752e28i	0.503231	−	0.509748i
$586$	1.22385e29			1.05877
$587$		−	1.42507e29i		−	1.21098i	−0.795853	−	0.605490i	$-0.792977\pi$
$587$		−	1.42507e29i		−	1.21098i	0.795853	−	0.605490i	$-0.207023\pi$
$588$			7.86157e28i			0.656217i
$589$	1.88613e29			1.54654
$590$	−1.03318e29	+	1.04656e29i	−0.832207	+	0.842984i
$591$	−1.97966e29			−1.56647
$592$			8.20704e27i			0.0637982i
$593$		−	2.57402e29i		−	1.96579i	−0.184161	−	0.982896i	$-0.558957\pi$
$593$		−	2.57402e29i		−	1.96579i	0.184161	−	0.982896i	$-0.441043\pi$
$594$	−6.45380e27			−0.0484237
$595$	1.52398e28	+	1.50450e28i	0.112344	+	0.110908i
$596$	−6.91615e28			−0.500932
$597$		−	7.05931e27i		−	0.0502380i
$598$		−	1.41723e29i		−	0.991007i
$599$	2.41880e28			0.166195			0.0830974	−	0.996541i	$-0.473519\pi$
$599$	2.41880e28			0.166195			0.0830974	+	0.996541i	$0.473519\pi$
$600$	−9.37649e26	−	7.28711e28i	−0.00633071	−	0.492002i
$601$	2.23610e27			0.0148358			0.00741789	−	0.999972i	$-0.497639\pi$
$601$	2.23610e27			0.0148358			0.00741789	+	0.999972i	$0.497639\pi$
$602$		−	1.51680e28i		−	0.0988930i
$603$		−	1.64261e29i		−	1.05245i
$604$	−8.70024e28			−0.547827
$605$	−4.51784e28	−	4.46008e28i	−0.279576	−	0.276001i
$606$	−2.19799e29			−1.33679
$607$			1.80792e29i			1.08068i	0.841446	+	0.540340i	$0.181705\pi$
$607$			1.80792e29i			1.08068i	−0.841446	+	0.540340i	$0.818295\pi$
$608$			4.61174e28i			0.270942i
$609$	5.86986e28			0.338958
$610$	1.24582e29	−	1.26196e29i	0.707120	−	0.716277i
$611$	−9.35516e28			−0.521938
$612$		−	5.64976e28i		−	0.309842i
$613$			2.24330e29i			1.20935i	0.796472	+	0.604675i	$0.206697\pi$
$613$			2.24330e29i			1.20935i	−0.796472	+	0.604675i	$0.793303\pi$
$614$	1.46547e27			0.00776623
$615$	1.34428e29	−	1.36169e29i	0.700326	−	0.709396i
$616$	−1.28377e28			−0.0657490
$617$		−	1.44425e29i		−	0.727192i	−0.931557	−	0.363596i	$-0.881549\pi$
$617$		−	1.44425e29i		−	0.727192i	0.931557	−	0.363596i	$-0.118451\pi$
$618$			1.38504e29i			0.685618i
$619$	−1.30078e29			−0.633073			−0.316536	−	0.948580i	$-0.602520\pi$
$619$	−1.30078e29			−0.633073			−0.316536	+	0.948580i	$0.602520\pi$
$620$	−7.50330e28	−	7.40738e28i	−0.359037	−	0.354447i
$621$	3.42418e28			0.161100
$622$		−	1.01394e29i		−	0.469044i
$623$		−	8.42583e28i		−	0.383255i
$624$	5.94773e28			0.266019
$625$	−2.27298e29	+	5.85037e27i	−0.999669	+	0.0257302i
$626$	−1.06093e29			−0.458834
$627$			3.90799e29i			1.66205i
$628$			1.06118e29i			0.443825i
$629$	4.10394e28			0.168799
$630$	2.78151e28	+	2.74595e28i	0.112514	+	0.111075i
$631$	3.07906e29			1.22493			0.612463	−	0.790500i	$-0.290179\pi$
$631$	3.07906e29			1.22493			0.612463	+	0.790500i	$0.290179\pi$
$632$			5.81948e28i			0.227696i
$633$		−	1.58013e29i		−	0.608072i
$634$	2.13743e29			0.809011
$635$	2.31924e29	−	2.34928e29i	0.863421	−	0.874602i
$636$	1.85107e29			0.677834
$637$			2.00179e29i			0.721032i
$638$		−	1.58692e29i		−	0.562260i
$639$	−3.38861e29			−1.18103
$640$	1.81116e28	−	1.83462e28i	0.0620966	−	0.0629008i
$641$	−1.27551e29			−0.430204			−0.215102	−	0.976592i	$-0.569008\pi$
$641$	−1.27551e29			−0.430204			−0.215102	+	0.976592i	$0.569008\pi$
$642$			4.60272e29i			1.52720i
$643$		−	8.64461e28i		−	0.282183i	−0.989997	−	0.141091i	$-0.954939\pi$
$643$		−	8.64461e28i		−	0.282183i	0.989997	−	0.141091i	$-0.0450611\pi$
$644$	6.81127e28			0.218739
$645$	1.83686e29	+	1.81338e29i	0.580363	+	0.572943i
$646$	2.30611e29			0.716866
$647$			3.44053e29i			1.05228i	0.850398	+	0.526139i	$0.176361\pi$
$647$			3.44053e29i			1.05228i	−0.850398	+	0.526139i	$0.823639\pi$
$648$			1.24439e29i			0.374471i
$649$	−4.40846e29			−1.30532
$650$	−2.38753e27	−	1.85551e29i	−0.00695600	−	0.540598i
$651$	1.16909e29			0.335156
$652$		−	2.31325e29i		−	0.652564i
$653$		−	1.56065e29i		−	0.433229i	−0.976257	−	0.216614i	$-0.930499\pi$
$653$		−	1.56065e29i		−	0.433229i	0.976257	−	0.216614i	$-0.0695014\pi$
$654$	6.21213e28			0.169697
$655$	1.72494e29	+	1.70289e29i	0.463703	+	0.457775i
$656$	6.76877e28			0.179069
$657$			4.01132e29i			1.04436i
$658$		−	4.49615e28i		−	0.115204i
$659$	7.18336e28			0.181147			0.0905735	−	0.995890i	$-0.471130\pi$
$659$	7.18336e28			0.181147			0.0905735	+	0.995890i	$0.471130\pi$
$660$	1.53478e29	−	1.55466e29i	0.380921	−	0.385854i
$661$	−1.10954e29			−0.271036			−0.135518	−	0.990775i	$-0.543270\pi$
$661$	−1.10954e29			−0.271036			−0.135518	+	0.990775i	$0.543270\pi$
$662$		−	1.85774e29i		−	0.446659i
$663$		−	2.97417e29i		−	0.703840i
$664$	6.56269e28			0.152868
$665$	−1.12084e29	+	1.13535e29i	−0.256989	+	0.260317i
$666$	7.49035e28			0.169053
$667$			8.41969e29i			1.87057i
$668$			2.69979e29i			0.590442i
$669$	−5.78172e29			−1.24475
$670$	−2.66725e29	−	2.63315e29i	−0.565300	−	0.558073i
$671$	5.31577e29			1.10912
$672$			2.85851e28i			0.0587169i
$673$			1.82178e29i			0.368416i	0.982887	+	0.184208i	$0.0589720\pi$
$673$			1.82178e29i			0.368416i	−0.982887	+	0.184208i	$0.941028\pi$
$674$	−3.24132e29			−0.645347
$675$	4.48314e28	−	5.76856e26i	0.0878805	−	0.00113078i
$676$	−1.07619e29			−0.207706
$677$		−	9.48846e29i		−	1.80308i	−0.432698	−	0.901539i	$-0.642438\pi$
$677$		−	9.48846e29i		−	1.80308i	0.432698	−	0.901539i	$-0.357562\pi$
$678$		−	4.44307e29i		−	0.831325i
$679$	−1.12648e29			−0.207536
$680$	−9.17404e28	−	9.05675e28i	−0.166424	−	0.164297i
$681$	2.79176e29			0.498692
$682$		−	3.16063e29i		−	0.555953i
$683$		−	5.03286e28i		−	0.0871761i	−0.999050	−	0.0435880i	$-0.986121\pi$
$683$		−	5.03286e28i		−	0.0871761i	0.999050	−	0.0435880i	$-0.0138789\pi$
$684$	4.20902e29			0.717946
$685$	−2.05815e28	+	2.08480e28i	−0.0345721	+	0.0350198i
$686$	−1.98226e29			−0.327911
$687$		−	1.06805e30i		−	1.73998i
$688$			9.13081e28i			0.146498i
$689$	4.71338e29			0.744784
$690$	−8.14307e29	+	8.24852e29i	−1.26728	+	1.28369i
$691$	−4.86997e28			−0.0746460			−0.0373230	−	0.999303i	$-0.511883\pi$
$691$	−4.86997e28			−0.0746460			−0.0373230	+	0.999303i	$0.511883\pi$
$692$			2.26674e27i			0.00342207i
$693$			1.17166e29i			0.174222i
$694$	7.40564e29			1.08465
$695$	−8.56341e29	−	8.45393e29i	−1.23540	−	1.21960i
$696$	−3.53352e29			−0.502124
$697$		−	3.38473e29i		−	0.473784i
$698$		−	5.50736e29i		−	0.759384i
$699$	−2.36569e28			−0.0321328
$700$	8.91771e28	−	1.14746e27i	0.119323	−	0.00153536i
$701$	−7.75553e29			−1.02229			−0.511143	−	0.859496i	$-0.670778\pi$
$701$	−7.75553e29			−1.02229			−0.511143	+	0.859496i	$0.670778\pi$
$702$			3.65913e28i			0.0475159i
$703$			3.05739e29i			0.391129i
$704$	7.72800e28			0.0973989
$705$	5.44488e29	+	5.37527e29i	0.676087	+	0.667444i
$706$	1.52999e28			0.0187172
$707$		−	2.68982e29i		−	0.324205i
$708$			9.81613e29i			1.16571i
$709$	−1.04667e30			−1.22469			−0.612343	−	0.790593i	$-0.709773\pi$
$709$	−1.04667e30			−1.22469			−0.612343	+	0.790593i	$0.709773\pi$
$710$	−5.43205e29	+	5.50239e29i	−0.626255	+	0.634365i
$711$	5.31130e29			0.603351
$712$			5.07216e29i			0.567745i
$713$			1.67693e30i			1.84959i
$714$	1.42940e29			0.155354
$715$	3.90801e29	−	3.95862e29i	0.418545	−	0.423965i
$716$	−6.11623e29			−0.645501
$717$			1.61825e28i			0.0168304i
$718$		−	4.70050e29i		−	0.481768i
$719$	8.04520e29			0.812613			0.406306	−	0.913737i	$-0.366817\pi$
$719$	8.04520e29			0.812613			0.406306	+	0.913737i	$0.366817\pi$
$720$	−1.67441e29	−	1.65300e29i	−0.166675	−	0.164544i
$721$	−1.69496e29			−0.166280
$722$			9.86676e29i			0.953968i
$723$		−	1.71739e30i		−	1.63650i
$724$	6.47337e29			0.607960
$725$	1.41843e28	+	1.10235e30i	0.0131298	+	1.02040i
$726$	−4.23746e29			−0.386608
$727$		−	4.15760e29i		−	0.373880i	−0.982371	−	0.186940i	$-0.940143\pi$
$727$		−	4.15760e29i		−	0.373880i	0.982371	−	0.186940i	$-0.0598569\pi$
$728$			7.27863e28i			0.0645164i
$729$	9.95724e29			0.869962
$730$	6.51355e29	+	6.43028e29i	0.560955	+	0.553783i
$731$	4.56587e29			0.387607
$732$		−	1.18364e30i		−	0.990497i
$733$			1.12797e30i			0.930478i	0.885185	+	0.465239i	$0.154032\pi$
$733$			1.12797e30i			0.930478i	−0.885185	+	0.465239i	$0.845968\pi$
$734$	1.03522e30			0.841827
$735$	1.15018e30	−	1.16508e30i	0.922041	−	0.933982i
$736$	−4.10024e29			−0.324035
$737$		−	1.12353e30i		−	0.875341i
$738$		−	6.17769e29i		−	0.474498i
$739$	−4.65858e27			−0.00352766			−0.00176383	−	0.999998i	$-0.500561\pi$
$739$	−4.65858e27			−0.00352766			−0.00176383	+	0.999998i	$0.500561\pi$
$740$	1.20073e29	−	1.21628e29i	0.0896420	−	0.0908028i
$741$	2.21573e30			1.63089
$742$			2.26528e29i			0.164392i
$743$			4.62491e29i			0.330918i	0.986217	+	0.165459i	$0.0529105\pi$
$743$			4.62491e29i			0.330918i	−0.986217	+	0.165459i	$0.947089\pi$
$744$	−7.03765e29			−0.496491
$745$	1.02497e30	+	1.01187e30i	0.712968	+	0.703853i
$746$	1.92274e29			0.131875
$747$		−	5.98960e29i		−	0.405072i
$748$		−	3.86440e29i		−	0.257700i
$749$	−5.63265e29			−0.370385
$750$	−1.05224e30	+	1.09366e30i	−0.682295	+	0.709153i
$751$	−1.10345e30			−0.705557			−0.352778	−	0.935707i	$-0.614763\pi$
$751$	−1.10345e30			−0.705557			−0.352778	+	0.935707i	$0.614763\pi$
$752$			2.70658e29i			0.170661i
$753$			3.21132e30i			1.99681i
$754$	−8.99740e29			−0.551719
$755$	1.28937e30	+	1.27289e30i	0.779713	+	0.769745i
$756$	−1.75860e28			−0.0104879
$757$		−	2.72573e30i		−	1.60316i	−0.597888	−	0.801580i	$-0.703993\pi$
$757$		−	2.72573e30i		−	1.60316i	0.597888	−	0.801580i	$-0.296007\pi$
$758$			6.35530e29i			0.368646i
$759$	−3.47454e30			−1.98774
$760$	6.74719e29	−	6.83456e29i	0.380698	−	0.385628i
$761$	−2.62990e30			−1.46353			−0.731764	−	0.681558i	$-0.761303\pi$
$761$	−2.62990e30			−1.46353			−0.731764	+	0.681558i	$0.761303\pi$
$762$		−	2.20348e30i		−	1.20943i
$763$			7.60220e28i			0.0411558i
$764$	1.27658e29			0.0681662
$765$	−8.26587e29	+	8.37291e29i	−0.435355	+	0.440993i
$766$	4.93804e29			0.256538
$767$			2.49948e30i			1.28085i
$768$		−	1.72076e29i		−	0.0869817i
$769$	−2.58791e30			−1.29040			−0.645198	−	0.764015i	$-0.723225\pi$
$769$	−2.58791e30			−1.29040			−0.645198	+	0.764015i	$0.723225\pi$
$770$	1.90254e29	+	1.87821e29i	0.0935794	+	0.0923830i
$771$	−8.09172e28			−0.0392618
$772$		−	1.35901e30i		−	0.650491i
$773$		−	4.10304e30i		−	1.93741i	−0.248222	−	0.968703i	$-0.579846\pi$
$773$		−	4.10304e30i		−	1.93741i	0.248222	−	0.968703i	$-0.420154\pi$
$774$	8.33346e29			0.388191
$775$	2.82505e28	+	2.19554e30i	0.0129825	+	1.00896i
$776$	6.78119e29			0.307438
$777$			1.89508e29i			0.0847630i
$778$		−	1.66884e30i		−	0.736428i
$779$	2.52159e30			1.09782
$780$	−8.81449e29	−	8.70180e29i	−0.378620	−	0.373780i
$781$	−2.31778e30			−0.982284
$782$			2.05033e30i			0.857339i
$783$		−	2.17388e29i		−	0.0896885i
$784$	5.79146e29			0.235760
$785$	1.55255e30	−	1.57266e30i	0.623612	−	0.631688i
$786$	1.61789e30			0.641227
$787$		−	2.93196e30i		−	1.14663i	−0.819334	−	0.573316i	$-0.805657\pi$
$787$		−	2.93196e30i		−	1.14663i	0.819334	−	0.573316i	$-0.194343\pi$
$788$			1.45838e30i			0.562787i
$789$	−4.29359e30			−1.63498
$790$	8.51418e29	−	8.62444e29i	0.319932	−	0.324076i
$791$	5.43727e29			0.201617
$792$		−	7.05315e29i		−	0.258089i
$793$		−	3.01390e30i		−	1.08833i
$794$	2.54072e30			0.905403
$795$	−2.74327e30	−	2.70820e30i	−0.964749	−	0.952415i
$796$	−5.20045e28			−0.0180490
$797$		−	3.70672e29i		−	0.126963i	−0.997983	−	0.0634815i	$-0.979780\pi$
$797$		−	3.70672e29i		−	0.126963i	0.997983	−	0.0634815i	$-0.0202204\pi$
$798$			1.06489e30i			0.359977i
$799$	1.35343e30			0.451538
$800$	−5.36826e29	+	6.90747e27i	−0.176762	+	0.00227444i
$801$	4.62923e30			1.50442
$802$			4.21805e28i			0.0135295i
$803$			2.74372e30i			0.868613i
$804$	−2.50172e30			−0.781719
$805$	−1.00943e30	−	9.96521e29i	−0.311328	−	0.307347i
$806$	−1.79199e30			−0.545530
$807$			7.40151e30i			2.22407i
$808$			1.61921e30i			0.480269i
$809$	5.86450e30			1.71700			0.858502	−	0.512810i	$-0.171396\pi$
$809$	5.86450e30			1.71700			0.858502	+	0.512810i	$0.171396\pi$
$810$	1.82060e30	−	1.84417e30i	0.526164	−	0.532977i
$811$	1.51644e30			0.432621			0.216311	−	0.976325i	$-0.430598\pi$
$811$	1.51644e30			0.432621			0.216311	+	0.976325i	$0.430598\pi$
$812$		−	4.32421e29i		−	0.121778i
$813$			1.46278e30i			0.406658i
$814$	5.12335e29			0.140604
$815$	−3.38440e30	+	3.42822e30i	−0.916909	+	0.928783i
$816$	−8.60469e29			−0.230138
$817$			3.40153e30i			0.898137i
$818$		−	1.88620e29i		−	0.0491675i
$819$	6.64302e29			0.170956
$820$	−1.00313e30	−	9.90303e29i	−0.254865	−	0.251607i
$821$	8.18462e29			0.205303			0.102652	−	0.994717i	$-0.467267\pi$
$821$	8.18462e29			0.205303			0.102652	+	0.994717i	$0.467267\pi$
$822$			1.95542e29i			0.0484268i
$823$			5.90465e28i			0.0144376i	0.999974	+	0.00721881i	$0.00229784\pi$
$823$			5.90465e28i			0.0144376i	−0.999974	+	0.00721881i	$0.997702\pi$
$824$	1.02033e30			0.246323
$825$	−4.54907e30	+	5.85340e28i	−1.08432	+	0.0139522i
$826$	−1.20126e30			−0.282715
$827$			5.06452e30i			1.17688i	0.808542	+	0.588438i	$0.200257\pi$
$827$			5.06452e30i			1.17688i	−0.808542	+	0.588438i	$0.799743\pi$
$828$			3.74218e30i			0.858630i
$829$	4.68090e30			1.06049			0.530246	−	0.847844i	$-0.322100\pi$
$829$	4.68090e30			1.06049			0.530246	+	0.847844i	$0.322100\pi$
$830$	−9.72587e29	−	9.60153e29i	−0.217575	−	0.214793i
$831$	−6.71613e29			−0.148357
$832$		−	4.38157e29i		−	0.0955730i
$833$		−	2.89603e30i		−	0.623778i
$834$	−8.03196e30			−1.70836
$835$	3.94992e30	−	4.00107e30i	0.829622	−	0.840365i
$836$	2.87894e30			0.597126
$837$		−	4.32967e29i		−	0.0886824i
$838$			1.91663e30i			0.387682i
$839$	4.98895e30			0.996572			0.498286	−	0.867013i	$-0.333963\pi$
$839$	4.98895e30			0.996572			0.498286	+	0.867013i	$0.333963\pi$
$840$	4.18214e29	−	4.23630e29i	0.0825023	−	0.0835707i
$841$	2.12482e29			0.0413966
$842$			1.80547e30i			0.347387i
$843$		−	8.28690e30i		−	1.57472i
$844$	−1.16405e30			−0.218463
$845$	1.59491e30	+	1.57452e30i	0.295624	+	0.291845i
$846$	2.47023e30			0.452218
$847$		−	5.18566e29i		−	0.0937623i
$848$		−	1.36365e30i		−	0.243526i
$849$	7.01715e30			1.23774
$850$	3.45409e28	+	2.68441e30i	0.00601776	+	0.467681i
$851$	−2.71829e30			−0.467773
$852$			5.16091e30i			0.877225i
$853$		−	3.89505e30i		−	0.653955i	−0.945032	−	0.326978i	$-0.893970\pi$
$853$		−	3.89505e30i		−	0.653955i	0.945032	−	0.326978i	$-0.106030\pi$
$854$	1.44850e30			0.240220
$855$	−6.23773e30	−	6.15799e30i	−1.02184	−	1.00878i
$856$	3.39073e30			0.548680
$857$		−	2.04364e30i		−	0.326667i	−0.986571	−	0.163334i	$-0.947775\pi$
$857$		−	2.04364e30i		−	0.326667i	0.986571	−	0.163334i	$-0.0522247\pi$
$858$		−	3.71295e30i		−	0.586276i
$859$	−1.02542e31			−1.59946			−0.799728	−	0.600363i	$-0.795023\pi$
$859$	−1.02542e31			−1.59946			−0.799728	+	0.600363i	$0.795023\pi$
$860$	1.33588e30	−	1.35318e30i	0.205842	−	0.208507i
$861$	1.56297e30			0.237913
$862$			5.73782e30i			0.862821i
$863$			1.42301e30i			0.211394i	0.994398	+	0.105697i	$0.0337074\pi$
$863$			1.42301e30i			0.211394i	−0.994398	+	0.105697i	$0.966293\pi$
$864$	1.05864e29			0.0155365
$865$	3.31635e28	−	3.35930e28i	0.00480830	−	0.00487057i
$866$	−8.39494e30			−1.20249
$867$		−	5.53162e30i		−	0.782802i
$868$		−	8.61243e29i		−	0.120412i
$869$	3.63289e30			0.501816
$870$	5.23666e30	+	5.16971e30i	0.714664	+	0.705528i
$871$	−6.37013e30			−0.858930
$872$		−	4.57635e29i		−	0.0609672i
$873$		−	6.18902e30i		−	0.814652i
$874$	−1.52747e31			−1.98657
$875$	−1.33839e30	−	1.28770e30i	−0.171988	−	0.165474i
$876$	6.10932e30			0.775711
$877$			4.25594e30i			0.533950i	0.963704	+	0.266975i	$0.0860240\pi$
$877$			4.25594e30i			0.533950i	−0.963704	+	0.266975i	$0.913976\pi$
$878$		−	7.07158e30i		−	0.876645i
$879$	−1.70117e31			−2.08384
$880$	−1.14528e30	−	1.13064e30i	−0.138626	−	0.136854i
$881$	−6.89134e30			−0.824246			−0.412123	−	0.911128i	$-0.635213\pi$
$881$	−6.89134e30			−0.824246			−0.412123	+	0.911128i	$0.635213\pi$
$882$		−	5.28572e30i		−	0.624718i
$883$			1.22979e31i			1.43629i	0.695891	+	0.718147i	$0.255010\pi$
$883$			1.22979e31i			1.43629i	−0.695891	+	0.718147i	$0.744990\pi$
$884$	−2.19101e30			−0.252869
$885$	1.43615e31	−	1.45474e31i	1.63793	−	1.65914i
$886$	−3.80658e30			−0.429023
$887$			2.77166e30i			0.308704i	0.988016	+	0.154352i	$0.0493290\pi$
$887$			2.77166e30i			0.308704i	−0.988016	+	0.154352i	$0.950671\pi$
$888$		−	1.14079e30i		−	0.125566i
$889$	2.69655e30			0.293318
$890$	7.42081e30	−	7.51691e30i	0.797730	−	0.808061i
$891$	7.76825e30			0.825291
$892$			4.25928e30i			0.447203i
$893$			1.00829e31i			1.04627i
$894$	9.61359e30			0.985920
$895$	9.06421e30	+	8.94833e30i	0.918731	+	0.906985i
$896$	2.10581e29			0.0210953
$897$			1.96997e31i			1.95047i
$898$		−	4.14806e30i		−	0.405923i
$899$	1.06462e31			1.02971
$900$	6.30428e28	+	4.89948e30i	0.00602683	+	0.468386i
$901$	−6.81893e30			−0.644327
$902$		−	4.22549e30i		−	0.394647i
$903$			2.10838e30i			0.194638i
$904$	−3.27312e30			−0.298671
$905$	−9.59349e30	−	9.47084e30i	−0.865299	−	0.854237i
$906$	1.20935e31			1.07822
$907$		−	7.55149e30i		−	0.665512i	−0.943013	−	0.332756i	$-0.892021\pi$
$907$		−	7.55149e30i		−	0.665512i	0.943013	−	0.332756i	$-0.107979\pi$
$908$		−	2.05663e30i		−	0.179166i
$909$	1.47782e31			1.27262
$910$	1.06490e30	−	1.07869e30i	0.0906511	−	0.0918250i
$911$	−1.03608e31			−0.871865			−0.435933	−	0.899979i	$-0.643581\pi$
$911$	−1.03608e31			−0.871865			−0.435933	+	0.899979i	$0.643581\pi$
$912$		−	6.41041e30i		−	0.533261i
$913$		−	4.09685e30i		−	0.336904i
$914$	−1.16614e31			−0.948017
$915$	−1.73172e31	+	1.75415e31i	−1.39173	+	1.40976i
$916$	−7.86809e30			−0.625125
$917$			1.97992e30i			0.155514i
$918$		−	5.29374e29i		−	0.0411069i
$919$	1.05421e31			0.809307			0.404654	−	0.914470i	$-0.367392\pi$
$919$	1.05421e31			0.809307			0.404654	+	0.914470i	$0.367392\pi$
$920$	6.07652e30	+	5.99884e30i	0.461193	+	0.455297i
$921$	−2.03704e29			−0.0152853
$922$			8.84695e30i			0.656325i
$923$			1.31412e31i			0.963869i
$924$	1.78446e30			0.129405
$925$	−3.55894e30	+	4.57937e28i	−0.255172	+	0.00328335i
$926$	1.04825e31			0.743104
$927$		−	9.31228e30i		−	0.652708i
$928$			2.60308e30i			0.180399i
$929$	−1.37272e31			−0.940629			−0.470314	−	0.882499i	$-0.655859\pi$
$929$	−1.37272e31			−0.940629			−0.470314	+	0.882499i	$0.655859\pi$
$930$	1.04297e31	+	1.02964e31i	0.706647	+	0.697613i
$931$	2.15751e31			1.44538
$932$			1.74276e29i			0.0115444i
$933$			1.40940e31i			0.923159i
$934$	1.53042e31			0.991216
$935$	−5.65379e30	+	5.72701e30i	−0.362091	+	0.366780i
$936$	−3.99895e30			−0.253250
$937$		−	2.58544e31i		−	1.61908i	−0.587063	−	0.809541i	$-0.699716\pi$
$937$		−	2.58544e31i		−	1.61908i	0.587063	−	0.809541i	$-0.300284\pi$
$938$		−	3.06152e30i		−	0.189587i
$939$	1.47471e31			0.903063
$940$	3.95985e30	−	4.01113e30i	0.239793	−	0.242898i
$941$	−9.22685e30			−0.552539			−0.276269	−	0.961080i	$-0.589098\pi$
$941$	−9.22685e30			−0.552539			−0.276269	+	0.961080i	$0.589098\pi$
$942$		−	1.47506e31i		−	0.873524i
$943$			2.24191e31i			1.31294i
$944$	7.23135e30			0.418806
$945$	2.60623e29	+	2.57292e29i	0.0149272	+	0.0147364i
$946$	5.70002e30			0.322864
$947$		−	3.49596e31i		−	1.95836i	−0.202999	−	0.979179i	$-0.565069\pi$
$947$		−	3.49596e31i		−	1.95836i	0.202999	−	0.979179i	$-0.434931\pi$
$948$		−	8.08920e30i		−	0.448145i
$949$	1.55561e31			0.852328
$950$	−1.99986e31	+	2.57326e29i	−1.08368	+	0.0139440i
$951$	−2.97107e31			−1.59227
$952$		−	1.05301e30i		−	0.0558143i
$953$		−	2.36357e31i		−	1.23906i	−0.784973	−	0.619530i	$-0.787323\pi$
$953$		−	2.36357e31i		−	1.23906i	0.784973	−	0.619530i	$-0.212677\pi$
$954$	−1.24457e31			−0.645297
$955$	−1.89189e30	−	1.86770e30i	−0.0970198	−	0.0957794i
$956$	1.19214e29			0.00604669
$957$			2.20585e31i			1.10662i
$958$			1.88898e31i			0.937321i
$959$	−2.39297e29			−0.0117447
$960$	−2.51755e30	+	2.55016e30i	−0.122217	+	0.123800i
$961$	3.78258e29			0.0181632
$962$		−	2.90480e30i		−	0.137968i
$963$		−	3.09464e31i		−	1.45390i
$964$	−1.26517e31			−0.587948
$965$	−1.98829e31	+	2.01404e31i	−0.913995	+	0.925832i
$966$	−9.46781e30			−0.430516
$967$		−	8.92653e30i		−	0.401518i	−0.979641	−	0.200759i	$-0.935659\pi$
$967$		−	8.92653e30i		−	0.401518i	0.979641	−	0.200759i	$-0.0643408\pi$
$968$			3.12165e30i			0.138897i
$969$	−3.20553e31			−1.41091
$970$	−1.00497e31	−	9.92119e30i	−0.437571	−	0.431977i
$971$	2.39800e31			1.03287			0.516437	−	0.856325i	$-0.327258\pi$
$971$	2.39800e31			1.03287			0.516437	+	0.856325i	$0.327258\pi$
$972$		−	1.62659e31i		−	0.693078i
$973$		−	9.82924e30i		−	0.414319i
$974$	−4.18444e30			−0.174489
$975$	3.31872e29	+	2.57920e31i	0.0136906	+	1.06399i
$976$	−8.71963e30			−0.355857
$977$		−	7.53247e30i		−	0.304120i	−0.988371	−	0.152060i	$-0.951409\pi$
$977$		−	7.53247e30i		−	0.304120i	0.988371	−	0.152060i	$-0.0485906\pi$
$978$			3.21547e31i			1.28436i
$979$	3.16636e31			1.25125
$980$	−8.58291e30	−	8.47318e30i	−0.335553	−	0.331263i
$981$	−4.17672e30			−0.161552
$982$			2.11761e31i			0.810354i
$983$		−	1.40460e31i		−	0.531790i	−0.964002	−	0.265895i	$-0.914333\pi$
$983$		−	1.40460e31i		−	0.531790i	0.964002	−	0.265895i	$-0.0856675\pi$
$984$	−9.40873e30			−0.352438
$985$	2.13367e31	−	2.16130e31i	0.790765	−	0.801005i
$986$	1.30167e31			0.477303
$987$			6.24974e30i			0.226742i
$988$		−	1.63228e31i		−	0.585932i
$989$	−3.02425e31			−1.07413
$990$	−1.03191e31	+	1.04527e31i	−0.362637	+	0.367333i
$991$	4.11864e31			1.43212			0.716061	−	0.698037i	$-0.245943\pi$
$991$	4.11864e31			1.43212			0.716061	+	0.698037i	$0.245943\pi$
$992$			5.18449e30i			0.178375i
$993$			2.58230e31i			0.879102i
$994$	−6.31575e30			−0.212749
$995$	7.70704e29	+	7.60851e29i	0.0256889	+	0.0253605i
$996$	−9.12228e30			−0.300871
$997$		−	1.93690e30i		−	0.0632132i	−0.999500	−	0.0316066i	$-0.989938\pi$
$997$		−	1.93690e30i		−	0.0632132i	0.999500	−	0.0316066i	$-0.0100624\pi$
$998$			1.30549e31i			0.421602i
$999$	7.01834e29			0.0224283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.22.b.a.9.6	yes	10
4.3	odd	2		80.22.c.c.49.10		10
5.2	odd	4		50.22.a.k.1.1		5
5.3	odd	4		50.22.a.l.1.5		5
5.4	even	2	inner	10.22.b.a.9.5	✓	10
20.19	odd	2		80.22.c.c.49.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.22.b.a.9.5	✓	10	5.4	even	2	inner
10.22.b.a.9.6	yes	10	1.1	even	1	trivial
50.22.a.k.1.1		5	5.2	odd	4
50.22.a.l.1.5		5	5.3	odd	4
80.22.c.c.49.1		10	20.19	odd	2
80.22.c.c.49.10		10	4.3	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1024.00i q^{2} -142338. i q^{3} -1.04858e6 q^{4} +(1.55398e7 + 1.53412e7i) q^{5} +1.45754e8 q^{6} +1.78369e8i q^{7} -1.07374e9i q^{8} -9.79977e9 q^{9} +(-1.57093e10 + 1.59128e10i) q^{10} -6.70297e10 q^{11} +1.49252e11i q^{12} +3.80041e11i q^{13} -1.82650e11 q^{14} +(2.18363e12 - 2.21191e12i) q^{15} +1.09951e12 q^{16} -5.49812e12i q^{17} -1.00350e13i q^{18} +4.09605e13 q^{19} +(-1.62947e13 - 1.60864e13i) q^{20} +2.53887e13 q^{21} -6.86384e13i q^{22} +3.64174e14i q^{23} -1.52834e14 q^{24} +(6.13507e12 + 4.76798e14i) q^{25} -3.89162e14 q^{26} -9.40260e13i q^{27} -1.87033e14i q^{28} +2.31200e15 q^{29} +(2.26499e15 + 2.23604e15i) q^{30} +4.60475e15 q^{31} +1.12590e15i q^{32} +9.54088e15i q^{33} +5.63008e15 q^{34} +(-2.73639e15 + 2.77182e15i) q^{35} +1.02758e16 q^{36} +7.46426e15i q^{37} +4.19435e16i q^{38} +5.40943e16 q^{39} +(1.64724e16 - 1.66858e16i) q^{40} +6.15616e16 q^{41} +2.59980e16i q^{42} +8.30442e16i q^{43} +7.02858e16 q^{44} +(-1.52287e17 - 1.50340e17i) q^{45} -3.72914e17 q^{46} +2.46162e17i q^{47} -1.56502e17i q^{48} +5.26730e17 q^{49} +(-4.88241e17 + 6.28231e15i) q^{50} -7.82592e17 q^{51} -3.98502e17i q^{52} -1.24023e18i q^{53} +9.62827e16 q^{54} +(-1.04163e18 - 1.02831e18i) q^{55} +1.91522e17 q^{56} -5.83023e18i q^{57} +2.36748e18i q^{58} +6.57687e18 q^{59} +(-2.28970e18 + 2.31935e18i) q^{60} -7.93046e18 q^{61} +4.71527e18i q^{62} -1.74798e18i q^{63} -1.15292e18 q^{64} +(-5.83026e18 + 5.90577e18i) q^{65} -9.76986e18 q^{66} +1.67617e19i q^{67} +5.76520e18i q^{68} +5.18358e19 q^{69} +(-2.83835e18 - 2.80206e18i) q^{70} +3.45785e19 q^{71} +1.05224e19i q^{72} -4.09328e19i q^{73} -7.64340e18 q^{74} +(6.78665e19 - 8.73254e17i) q^{75} -4.29502e19 q^{76} -1.19560e19i q^{77} +5.53925e19i q^{78} -5.41982e19 q^{79} +(1.70862e19 + 1.68678e19i) q^{80} -1.15893e20 q^{81} +6.30391e19i q^{82} +6.11198e19i q^{83} -2.66220e19 q^{84} +(8.43476e19 - 8.54399e19i) q^{85} -8.50372e19 q^{86} -3.29085e20i q^{87} +7.19726e19i q^{88} -4.72382e20 q^{89} +(1.53948e20 - 1.55942e20i) q^{90} -6.77875e19 q^{91} -3.81864e20i q^{92} -6.55432e20i q^{93} -2.52070e20 q^{94} +(6.36518e20 + 6.28381e20i) q^{95} +1.60258e20 q^{96} +6.31547e20i q^{97} +5.39372e20i q^{98} +6.56876e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10485760 q^{4} + 27722150 q^{5} - 230748160 q^{6} - 12711922730 q^{9} - 22426931200 q^{10} - 199435236680 q^{11} - 104903905280 q^{14} - 1714785566200 q^{15} + 10995116277760 q^{16} + 123436918144200 q^{19}+ \cdots + 21\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q - 10485760 * q^4 + 27722150 * q^5 - 230748160 * q^6 - 12711922730 * q^9 - 22426931200 * q^10 - 199435236680 * q^11 - 104903905280 * q^14 - 1714785566200 * q^15 + 10995116277760 * q^16 + 123436918144200 * q^19 - 29068781158400 * q^20 - 158960071181080 * q^21 + 241956982620160 * q^24 - 753844388658750 * q^25 - 173073038991360 * q^26 + 1774546489874700 * q^29 + 5639638400921600 * q^30 + 10456190999441920 * q^31 - 18958190285946880 * q^34 + 24035281816377400 * q^35 + 13329417088532480 * q^36 + 45468500581785840 * q^39 + 23516341809971200 * q^40 + 93828363171915220 * q^41 + 209123002736967680 * q^44 - 1294878557826950 * q^45 - 453509186534543360 * q^46 - 1584589583512161570 * q^49 + 130953516753920000 * q^50 - 512256548145748480 * q^51 - 3219652987818598400 * q^54 + 8644481518774929800 * q^55 + 109999717382881280 * q^56 - 5722347962825378600 * q^59 + 1798082989863731200 * q^60 - 12650867843198554180 * q^61 - 11529215046068469760 * q^64 + 26346750548743534800 * q^65 - 32504410286103019520 * q^66 + 96951047157018456040 * q^69 + 41090423076705996800 * q^70 - 104781163131643184880 * q^71 + 32904860966761553920 * q^74 + 296606638041153670000 * q^75 - 129432989879972659200 * q^76 + 96531112322635730400 * q^79 + 30480826271950438400 * q^80 - 828031346148584406190 * q^81 + 166681715598772142080 * q^84 + 634500251198792806400 * q^85 - 1012021399291540418560 * q^86 + 1925821863958052788100 * q^89 + 598299873941928857600 * q^90 - 3491972396700191783280 * q^91 + 919679051426714398720 * q^94 + 1154253771449725323000 * q^95 - 253710285007916892160 * q^96 + 2120189706372537680840 * q^99

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