LMFDB - Embedded newform 10.18.b.a.9.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,18,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, 18, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
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:	$18.3222087345$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 556201x^{6} + 76870744104x^{4} + 1868329791349729x^{2} + 78074963590050625 $ x^8 + 556201x^6 + 76870744104x^4 + 1868329791349729*x^2 + 78074963590050625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{40}\cdot 3^{4}\cdot 5^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.8
Root			$594.906i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.18.b.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+256.000i q^{2} +20214.2i q^{3} -65536.0 q^{4} +(-765001. + 421560. i) q^{5} -5.17482e6 q^{6} -1.76306e7i q^{7} -1.67772e7i q^{8} -2.79472e8 q^{9} +O(q^{10})$	\(q+256.000i q^{2} +20214.2i q^{3} -65536.0 q^{4} +(-765001. + 421560. i) q^{5} -5.17482e6 q^{6} -1.76306e7i q^{7} -1.67772e7i q^{8} -2.79472e8 q^{9} +(-1.07919e8 - 1.95840e8i) q^{10} +4.98950e8 q^{11} -1.32475e9i q^{12} +5.00327e9i q^{13} +4.51344e9 q^{14} +(-8.52148e9 - 1.54638e10i) q^{15} +4.29497e9 q^{16} +1.61697e10i q^{17} -7.15448e10i q^{18} -3.43950e10 q^{19} +(5.01351e10 - 2.76274e10i) q^{20} +3.56388e11 q^{21} +1.27731e11i q^{22} -4.72599e11i q^{23} +3.39137e11 q^{24} +(4.07513e11 - 6.44988e11i) q^{25} -1.28084e12 q^{26} -3.03883e12i q^{27} +1.15544e12i q^{28} -3.30807e12 q^{29} +(3.95874e12 - 2.18150e12i) q^{30} +3.23730e12 q^{31} +1.09951e12i q^{32} +1.00859e13i q^{33} -4.13944e12 q^{34} +(7.43238e12 + 1.34875e13i) q^{35} +1.83155e13 q^{36} -5.76908e11i q^{37} -8.80513e12i q^{38} -1.01137e14 q^{39} +(7.07261e12 + 1.28346e13i) q^{40} -5.68215e13 q^{41} +9.12354e13i q^{42} -5.07446e12i q^{43} -3.26992e13 q^{44} +(2.13796e14 - 1.17814e14i) q^{45} +1.20985e14 q^{46} -3.32325e13i q^{47} +8.68191e13i q^{48} -7.82089e13 q^{49} +(1.65117e14 + 1.04323e14i) q^{50} -3.26857e14 q^{51} -3.27894e14i q^{52} -6.11026e14i q^{53} +7.77940e14 q^{54} +(-3.81697e14 + 2.10338e14i) q^{55} -2.95793e14 q^{56} -6.95266e14i q^{57} -8.46865e14i q^{58} +8.63122e14 q^{59} +(5.58464e14 + 1.01344e15i) q^{60} -8.57703e14 q^{61} +8.28749e14i q^{62} +4.92727e15i q^{63} -2.81475e14 q^{64} +(-2.10918e15 - 3.82751e15i) q^{65} -2.58198e15 q^{66} +4.06389e14i q^{67} -1.05970e15i q^{68} +9.55319e15 q^{69} +(-3.45279e15 + 1.90269e15i) q^{70} -9.53517e15 q^{71} +4.68876e15i q^{72} +6.07142e15i q^{73} +1.47688e14 q^{74} +(1.30379e16 + 8.23754e15i) q^{75} +2.25411e15 q^{76} -8.79681e15i q^{77} -2.58910e16i q^{78} -1.38305e16 q^{79} +(-3.28565e15 + 1.81059e15i) q^{80} +2.53363e16 q^{81} -1.45463e16i q^{82} +1.96416e16i q^{83} -2.33563e16 q^{84} +(-6.81651e15 - 1.23698e16i) q^{85} +1.29906e15 q^{86} -6.68698e16i q^{87} -8.37099e15i q^{88} -2.45918e16 q^{89} +(3.01604e16 + 5.47318e16i) q^{90} +8.82108e16 q^{91} +3.09722e16i q^{92} +6.54393e16i q^{93} +8.50752e15 q^{94} +(2.63122e16 - 1.44996e16i) q^{95} -2.22257e16 q^{96} +3.63292e16i q^{97} -2.00215e16i q^{98} -1.39443e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 524288 q^{4} - 1225560 q^{5} - 974848 q^{6} - 363182504 q^{9}+O(q^{10}) $ 8 * q - 524288 * q^4 - 1225560 * q^5 - 974848 * q^6 - 363182504 * q^9	$ 8 q - 524288 q^{4} - 1225560 q^{5} - 974848 q^{6} - 363182504 q^{9} - 140779520 q^{10} + 146232096 q^{11} + 14260494336 q^{14} - 39815002720 q^{15} + 34359738368 q^{16} - 54264178080 q^{19} + 80318300160 q^{20} + 515442333056 q^{21} + 63887638528 q^{24} + 1013225778600 q^{25} - 2693383569408 q^{26} + 1660243083120 q^{29} + 4536489205760 q^{30} - 6055476993664 q^{31} + 14158246445056 q^{34} - 8725233780960 q^{35} + 23801528582144 q^{36} - 60047234232768 q^{39} + 9226126622720 q^{40} - 219921829971984 q^{41} - 9583466643456 q^{44} + 503517880841080 q^{45} - 136753191067648 q^{46} + 797208944041464 q^{49} + 535409908531200 q^{50} - 26\!\cdots\!24 q^{51}+ \cdots - 23\!\cdots\!48 q^{99}+O(q^{100}) $ 8 * q - 524288 * q^4 - 1225560 * q^5 - 974848 * q^6 - 363182504 * q^9 - 140779520 * q^10 + 146232096 * q^11 + 14260494336 * q^14 - 39815002720 * q^15 + 34359738368 * q^16 - 54264178080 * q^19 + 80318300160 * q^20 + 515442333056 * q^21 + 63887638528 * q^24 + 1013225778600 * q^25 - 2693383569408 * q^26 + 1660243083120 * q^29 + 4536489205760 * q^30 - 6055476993664 * q^31 + 14158246445056 * q^34 - 8725233780960 * q^35 + 23801528582144 * q^36 - 60047234232768 * q^39 + 9226126622720 * q^40 - 219921829971984 * q^41 - 9583466643456 * q^44 + 503517880841080 * q^45 - 136753191067648 * q^46 + 797208944041464 * q^49 + 535409908531200 * q^50 - 2629370351530624 * q^51 + 1870704820633600 * q^54 + 1370380127176480 * q^55 - 934575756804096 * q^56 - 155410557761760 * q^59 + 2609316018257920 * q^60 - 6350444068968944 * q^61 - 2251799813685248 * q^64 + 10508144084782080 * q^65 - 10180424127512576 * q^66 + 20821360231259392 * q^69 - 1051117677240320 * q^70 - 33149026543733184 * q^71 + 6017648345726976 * q^74 + 17427320439323200 * q^75 + 3556257174650880 * q^76 - 19354668791708160 * q^79 - 5263740119285760 * q^80 + 54432374624835848 * q^81 - 33780028739158016 * q^84 - 71530234876895360 * q^85 + 29616028444434432 * q^86 - 43569230299558320 * q^89 - 33153706682736640 * q^90 + 333420307889971776 * q^91 - 11440296922292224 * q^94 - 131478039235197600 * q^95 - 4186940278571008 * q^96 - 236681336419250848 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$			256.000i			0.707107i
$2$			256.000i			0.707107i
$3$			20214.2i			1.77879i	0.457139	+	0.889395i	$0.348874\pi$
$3$			20214.2i			1.77879i	−0.457139	+	0.889395i	$0.651126\pi$
$4$	−65536.0			−0.500000
$5$	−765001.	+	421560.i	−0.875824	+	0.482630i
$5$	−765001.	+	421560.i	−0.875824	+	0.482630i
$6$	−5.17482e6			−1.25780
$7$		−	1.76306e7i		−	1.15594i	−0.816059	−	0.577969i	$-0.803845\pi$
$7$		−	1.76306e7i		−	1.15594i	0.816059	−	0.577969i	$-0.196155\pi$
$8$		−	1.67772e7i		−	0.353553i
$9$	−2.79472e8			−2.16410
$10$	−1.07919e8	−	1.95840e8i	−0.341271	−	0.619301i
$11$	4.98950e8			0.701810			0.350905	−	0.936411i	$-0.385874\pi$
$11$	4.98950e8			0.701810			0.350905	+	0.936411i	$0.385874\pi$
$12$		−	1.32475e9i		−	0.889395i
$13$			5.00327e9i			1.70112i	0.525877	+	0.850561i	$0.323737\pi$
$13$			5.00327e9i			1.70112i	−0.525877	+	0.850561i	$0.676263\pi$
$14$	4.51344e9			0.817372
$15$	−8.52148e9	−	1.54638e10i	−0.858498	−	1.55791i
$16$	4.29497e9			0.250000
$17$			1.61697e10i			0.562194i	0.959679	+	0.281097i	$0.0906983\pi$
$17$			1.61697e10i			0.562194i	−0.959679	+	0.281097i	$0.909302\pi$
$18$		−	7.15448e10i		−	1.53025i
$19$	−3.43950e10			−0.464612			−0.232306	−	0.972643i	$-0.574627\pi$
$19$	−3.43950e10			−0.464612			−0.232306	+	0.972643i	$0.574627\pi$
$20$	5.01351e10	−	2.76274e10i	0.437912	−	0.241315i
$21$	3.56388e11			2.05617
$22$			1.27731e11i			0.496254i
$23$		−	4.72599e11i		−	1.25836i	−0.777258	−	0.629182i	$-0.783390\pi$
$23$		−	4.72599e11i		−	1.25836i	0.777258	−	0.629182i	$-0.216610\pi$
$24$	3.39137e11			0.628898
$25$	4.07513e11	−	6.44988e11i	0.534136	−	0.845399i
$26$	−1.28084e12			−1.20287
$27$		−	3.03883e12i		−	2.07068i
$28$			1.15544e12i			0.577969i
$29$	−3.30807e12			−1.22798			−0.613990	−	0.789314i	$-0.710437\pi$
$29$	−3.30807e12			−1.22798			−0.613990	+	0.789314i	$0.710437\pi$
$30$	3.95874e12	−	2.18150e12i	1.10161	−	0.607050i
$31$	3.23730e12			0.681724			0.340862	−	0.940113i	$-0.389281\pi$
$31$	3.23730e12			0.681724			0.340862	+	0.940113i	$0.389281\pi$
$32$			1.09951e12i			0.176777i
$33$			1.00859e13i			1.24837i
$34$	−4.13944e12			−0.397531
$35$	7.43238e12	+	1.34875e13i	0.557891	+	1.01240i
$36$	1.83155e13			1.08205
$37$		−	5.76908e11i		−	0.0270017i	−0.999909	−	0.0135009i	$-0.995702\pi$
$37$		−	5.76908e11i		−	0.0270017i	0.999909	−	0.0135009i	$-0.00429759\pi$
$38$		−	8.80513e12i		−	0.328530i
$39$	−1.01137e14			−3.02594
$40$	7.07261e12	+	1.28346e13i	0.170636	+	0.309651i
$41$	−5.68215e13			−1.11135			−0.555674	−	0.831400i	$-0.687540\pi$
$41$	−5.68215e13			−1.11135			−0.555674	+	0.831400i	$0.687540\pi$
$42$			9.12354e13i			1.45393i
$43$		−	5.07446e12i		−	0.0662076i	−0.999452	−	0.0331038i	$-0.989461\pi$
$43$		−	5.07446e12i		−	0.0662076i	0.999452	−	0.0331038i	$-0.0105392\pi$
$44$	−3.26992e13			−0.350905
$45$	2.13796e14	−	1.17814e14i	1.89537	−	1.04446i
$46$	1.20985e14			0.889798
$47$		−	3.32325e13i		−	0.203578i	−0.994806	−	0.101789i	$-0.967543\pi$
$47$		−	3.32325e13i		−	0.203578i	0.994806	−	0.101789i	$-0.0324567\pi$
$48$			8.68191e13i			0.444698i
$49$	−7.82089e13			−0.336193
$50$	1.65117e14	+	1.04323e14i	0.597787	+	0.377691i
$51$	−3.26857e14			−1.00003
$52$		−	3.27894e14i		−	0.850561i
$53$		−	6.11026e14i		−	1.34808i	−0.738696	−	0.674039i	$-0.764558\pi$
$53$		−	6.11026e14i		−	1.34808i	0.738696	−	0.674039i	$-0.235442\pi$
$54$	7.77940e14			1.46420
$55$	−3.81697e14	+	2.10338e14i	−0.614662	+	0.338715i
$56$	−2.95793e14			−0.408686
$57$		−	6.95266e14i		−	0.826447i
$58$		−	8.46865e14i		−	0.868313i
$59$	8.63122e14			0.765297			0.382648	−	0.923894i	$-0.375012\pi$
$59$	8.63122e14			0.765297			0.382648	+	0.923894i	$0.375012\pi$
$60$	5.58464e14	+	1.01344e15i	0.429249	+	0.778954i
$61$	−8.57703e14			−0.572840			−0.286420	−	0.958104i	$-0.592465\pi$
$61$	−8.57703e14			−0.572840			−0.286420	+	0.958104i	$0.592465\pi$
$62$			8.28749e14i			0.482051i
$63$			4.92727e15i			2.50156i
$64$	−2.81475e14			−0.125000
$65$	−2.10918e15	−	3.82751e15i	−0.821013	−	1.48988i
$66$	−2.58198e15			−0.882733
$67$			4.06389e14i			0.122266i	0.998130	+	0.0611331i	$0.0194714\pi$
$67$			4.06389e14i			0.122266i	−0.998130	+	0.0611331i	$0.980529\pi$
$68$		−	1.05970e15i		−	0.281097i
$69$	9.55319e15			2.23837
$70$	−3.45279e15	+	1.90269e15i	−0.715874	+	0.394488i
$71$	−9.53517e15			−1.75240			−0.876198	−	0.481951i	$-0.839928\pi$
$71$	−9.53517e15			−1.75240			−0.876198	+	0.481951i	$0.839928\pi$
$72$			4.68876e15i			0.765124i
$73$			6.07142e15i			0.881142i	0.897718	+	0.440571i	$0.145224\pi$
$73$			6.07142e15i			0.881142i	−0.897718	+	0.440571i	$0.854776\pi$
$74$	1.47688e14			0.0190931
$75$	1.30379e16	+	8.23754e15i	1.50379	+	0.950116i
$76$	2.25411e15			0.232306
$77$		−	8.79681e15i		−	0.811249i
$78$		−	2.58910e16i		−	2.13966i
$79$	−1.38305e16			−1.02567			−0.512836	−	0.858486i	$-0.671405\pi$
$79$	−1.38305e16			−1.02567			−0.512836	+	0.858486i	$0.671405\pi$
$80$	−3.28565e15	+	1.81059e15i	−0.218956	+	0.120658i
$81$	2.53363e16			1.51922
$82$		−	1.45463e16i		−	0.785842i
$83$			1.96416e16i			0.957222i	0.878027	+	0.478611i	$0.158860\pi$
$83$			1.96416e16i			0.957222i	−0.878027	+	0.478611i	$0.841140\pi$
$84$	−2.33563e16			−1.02809
$85$	−6.81651e15	−	1.23698e16i	−0.271332	−	0.492383i
$86$	1.29906e15			0.0468158
$87$		−	6.68698e16i		−	2.18432i
$88$		−	8.37099e15i		−	0.248127i
$89$	−2.45918e16			−0.662178			−0.331089	−	0.943600i	$-0.607416\pi$
$89$	−2.45918e16			−0.662178			−0.331089	+	0.943600i	$0.607416\pi$
$90$	3.01604e16	+	5.47318e16i	0.738544	+	1.34023i
$91$	8.82108e16			1.96639
$92$			3.09722e16i			0.629182i
$93$			6.54393e16i			1.21264i
$94$	8.50752e15			0.143951
$95$	2.63122e16	−	1.44996e16i	0.406918	−	0.224236i
$96$	−2.22257e16			−0.314449
$97$			3.63292e16i			0.470647i	0.971917	+	0.235324i	$0.0756150\pi$
$97$			3.63292e16i			0.470647i	−0.971917	+	0.235324i	$0.924385\pi$
$98$		−	2.00215e16i		−	0.237725i
$99$	−1.39443e17			−1.51878
$100$	−2.67068e16	+	4.22699e16i	−0.267068	+	0.422699i
$101$	−1.67053e17			−1.53505			−0.767527	−	0.641017i	$-0.778513\pi$
$101$	−1.67053e17			−1.53505			−0.767527	+	0.641017i	$0.778513\pi$
$102$		−	8.36754e16i		−	0.707125i
$103$		−	1.13488e16i		−	0.0882739i	−0.999025	−	0.0441370i	$-0.985946\pi$
$103$		−	1.13488e16i		−	0.0882739i	0.999025	−	0.0441370i	$-0.0140538\pi$
$104$	8.39409e16			0.601437
$105$	−2.72637e17	+	1.50239e17i	−1.80085	+	0.992371i
$106$	1.56423e17			0.953235
$107$		−	1.72393e17i		−	0.969970i	−0.874522	−	0.484985i	$-0.838825\pi$
$107$		−	1.72393e17i		−	0.969970i	0.874522	−	0.484985i	$-0.161175\pi$
$108$			1.99153e17i			1.03534i
$109$	3.17806e17			1.52770			0.763848	−	0.645396i	$-0.223307\pi$
$109$	3.17806e17			1.52770			0.763848	+	0.645396i	$0.223307\pi$
$110$	−5.38464e16	−	9.77145e16i	−0.239507	−	0.434632i
$111$	1.16617e16			0.0480304
$112$		−	7.57230e16i		−	0.288985i
$113$			3.07271e17i			1.08731i	0.839307	+	0.543657i	$0.182961\pi$
$113$			3.07271e17i			1.08731i	−0.839307	+	0.543657i	$0.817039\pi$
$114$	1.77988e17			0.584386
$115$	1.99229e17	+	3.61539e17i	0.607325	+	1.10211i
$116$	2.16798e17			0.613990
$117$		−	1.39827e18i		−	3.68139i
$118$			2.20959e17i			0.541147i
$119$	2.85082e17			0.649862
$120$	−2.59440e17	+	1.42967e17i	−0.550804	+	0.303525i
$121$	−2.56496e17			−0.507463
$122$		−	2.19572e17i		−	0.405059i
$123$		−	1.14860e18i		−	1.97686i
$124$	−2.12160e17			−0.340862
$125$	−3.98468e16	+	6.65208e17i	−0.0597941	+	0.998211i
$126$	−1.26138e18			−1.76887
$127$			8.22015e17i			1.07782i	0.842362	+	0.538912i	$0.181165\pi$
$127$			8.22015e17i			1.07782i	−0.842362	+	0.538912i	$0.818835\pi$
$128$		−	7.20576e16i		−	0.0883883i
$129$	1.02576e17			0.117769
$130$	9.79841e17	−	5.39950e17i	1.05351	−	0.580544i
$131$	2.64662e17			0.266616			0.133308	−	0.991075i	$-0.457440\pi$
$131$	2.64662e17			0.266616			0.133308	+	0.991075i	$0.457440\pi$
$132$		−	6.60987e17i		−	0.624186i
$133$			6.06406e17i			0.537062i
$134$	−1.04036e17			−0.0864553
$135$	1.28105e18	+	2.32471e18i	0.999375	+	1.81356i
$136$	2.71283e17			0.198766
$137$			1.71830e17i			0.118297i	0.998249	+	0.0591486i	$0.0188386\pi$
$137$			1.71830e17i			0.118297i	−0.998249	+	0.0591486i	$0.981161\pi$
$138$			2.44562e18i			1.58276i
$139$	−2.86799e18			−1.74563			−0.872814	−	0.488053i	$-0.837707\pi$
$139$	−2.86799e18			−1.74563			−0.872814	+	0.488053i	$0.837707\pi$
$140$	−4.87088e17	−	8.83914e17i	−0.278945	−	0.506199i
$141$	6.71767e17			0.362123
$142$		−	2.44100e18i		−	1.23913i
$143$			2.49638e18i			1.19386i
$144$	−1.20032e18			−0.541024
$145$	2.53067e18	−	1.39455e18i	1.07549	−	0.592661i
$146$	−1.55428e18			−0.623061
$147$		−	1.58093e18i		−	0.598018i
$148$			3.78082e16i			0.0135009i
$149$	−2.17323e18			−0.732863			−0.366431	−	0.930445i	$-0.619421\pi$
$149$	−2.17323e18			−0.732863			−0.366431	+	0.930445i	$0.619421\pi$
$150$	−2.10881e18	+	3.33770e18i	−0.671833	+	1.06334i
$151$	1.81870e18			0.547591			0.273796	−	0.961788i	$-0.411721\pi$
$151$	1.81870e18			0.547591			0.273796	+	0.961788i	$0.411721\pi$
$152$			5.77053e17i			0.164265i
$153$		−	4.51898e18i		−	1.21664i
$154$	2.25198e18			0.573639
$155$	−2.47654e18	+	1.36472e18i	−0.597070	+	0.329021i
$156$	6.62810e18			1.51297
$157$		−	6.73380e18i		−	1.45584i	−0.685663	−	0.727919i	$-0.740488\pi$
$157$		−	6.73380e18i		−	1.45584i	0.685663	−	0.727919i	$-0.259512\pi$
$158$		−	3.54062e18i		−	0.725260i
$159$	1.23514e19			2.39795
$160$	−4.63510e17	−	8.41127e17i	−0.0853178	−	0.154825i
$161$	−8.33222e18			−1.45459
$162$			6.48609e18i			1.07425i
$163$			1.37505e18i			0.216134i	0.994144	+	0.108067i	$0.0344661\pi$
$163$			1.37505e18i			0.216134i	−0.994144	+	0.108067i	$0.965534\pi$
$164$	3.72386e18			0.555674
$165$	−4.25180e18	−	7.71569e18i	−0.602502	−	1.09335i
$166$	−5.02825e18			−0.676858
$167$			5.07885e18i			0.649644i	0.945775	+	0.324822i	$0.105304\pi$
$167$			5.07885e18i			0.649644i	−0.945775	+	0.324822i	$0.894696\pi$
$168$		−	5.97921e18i		−	0.726967i
$169$	−1.63823e19			−1.89381
$170$	3.16668e18	−	1.74503e18i	0.348168	−	0.191861i
$171$	9.61244e18			1.00546
$172$			3.32560e17i			0.0331038i
$173$			1.55546e19i			1.47390i	0.675948	+	0.736949i	$0.263734\pi$
$173$			1.55546e19i			1.47390i	−0.675948	+	0.736949i	$0.736266\pi$
$174$	1.71187e19			1.54455
$175$	−1.13715e19	−	7.18472e18i	−0.977229	−	0.617428i
$176$	2.14297e18			0.175452
$177$			1.74473e19i			1.36130i
$178$		−	6.29549e18i		−	0.468230i
$179$	6.70360e18			0.475398			0.237699	−	0.971339i	$-0.423607\pi$
$179$	6.70360e18			0.475398			0.237699	+	0.971339i	$0.423607\pi$
$180$	−1.40113e19	+	7.72107e18i	−0.947684	+	0.522229i
$181$	1.39268e19			0.898637			0.449318	−	0.893372i	$-0.351667\pi$
$181$	1.39268e19			0.898637			0.449318	+	0.893372i	$0.351667\pi$
$182$			2.25820e19i			1.39045i
$183$		−	1.73377e19i		−	1.01896i
$184$	−7.92890e18			−0.444899
$185$	2.43201e17	+	4.41335e17i	0.0130319	+	0.0236488i
$186$	−1.67524e19			−0.857469
$187$			8.06788e18i			0.394553i
$188$			2.17792e18i			0.101789i
$189$	−5.35765e19			−2.39358
$190$	3.71189e18	+	6.73593e18i	0.158559	+	0.287735i
$191$	−1.88045e18			−0.0768205			−0.0384103	−	0.999262i	$-0.512229\pi$
$191$	−1.88045e18			−0.0768205			−0.0384103	+	0.999262i	$0.512229\pi$
$192$		−	5.68978e18i		−	0.222349i
$193$			2.08963e18i			0.0781325i	0.999237	+	0.0390663i	$0.0124383\pi$
$193$			2.08963e18i			0.0781325i	−0.999237	+	0.0390663i	$0.987562\pi$
$194$	−9.30026e18			−0.332798
$195$	7.73698e19	−	4.26353e19i	2.65019	−	1.46041i
$196$	5.12550e18			0.168097
$197$		−	3.11134e18i		−	0.0977202i	−0.998806	−	0.0488601i	$-0.984441\pi$
$197$		−	3.11134e18i		−	0.0977202i	0.998806	−	0.0488601i	$-0.0155588\pi$
$198$		−	3.56973e19i		−	1.07394i
$199$	2.90090e19			0.836144			0.418072	−	0.908414i	$-0.362706\pi$
$199$	2.90090e19			0.836144			0.418072	+	0.908414i	$0.362706\pi$
$200$	−1.08211e19	−	6.83694e18i	−0.298894	−	0.188846i
$201$	−8.21482e18			−0.217486
$202$		−	4.27656e19i		−	1.08545i
$203$			5.83233e19i			1.41947i
$204$	2.14209e19			0.500013
$205$	4.34685e19	−	2.39537e19i	0.973345	−	0.536370i
$206$	2.90529e18			0.0624191
$207$			1.32078e20i			2.72322i
$208$			2.14889e19i			0.425280i
$209$	−1.71614e19			−0.326069
$210$	−3.84612e19	−	6.97952e19i	−0.701712	−	1.27339i
$211$	3.27307e19			0.573528			0.286764	−	0.958001i	$-0.407420\pi$
$211$	3.27307e19			0.573528			0.286764	+	0.958001i	$0.407420\pi$
$212$			4.00442e19i			0.674039i
$213$		−	1.92745e20i		−	3.11715i
$214$	4.41327e19			0.685873
$215$	2.13919e18	+	3.88197e18i	0.0319538	+	0.0579862i
$216$	−5.09831e19			−0.732098
$217$		−	5.70756e19i		−	0.788031i
$218$			8.13584e19i			1.08024i
$219$	−1.22729e20			−1.56737
$220$	2.50149e19	−	1.37847e19i	0.307331	−	0.169357i
$221$	−8.09014e19			−0.956361
$222$			2.98539e18i			0.0339626i
$223$		−	4.94295e19i		−	0.541246i	−0.962685	−	0.270623i	$-0.912770\pi$
$223$		−	4.94295e19i		−	0.541246i	0.962685	−	0.270623i	$-0.0872297\pi$
$224$	1.93851e19			0.204343
$225$	−1.13888e20	+	1.80256e20i	−1.15592	+	1.82952i
$226$	−7.86615e19			−0.768848
$227$			1.02192e20i			0.962052i	0.876706	+	0.481026i	$0.159736\pi$
$227$			1.02192e20i			0.962052i	−0.876706	+	0.481026i	$0.840264\pi$
$228$			4.55650e19i			0.413223i
$229$	1.74856e20			1.52785			0.763923	−	0.645308i	$-0.223271\pi$
$229$	1.74856e20			1.52785			0.763923	+	0.645308i	$0.223271\pi$
$230$	−9.25539e19	+	5.10026e19i	−0.779306	+	0.429443i
$231$	1.77820e20			1.44304
$232$			5.55002e19i			0.434157i
$233$			1.22044e20i			0.920430i	0.887807	+	0.460215i	$0.152228\pi$
$233$			1.22044e20i			0.920430i	−0.887807	+	0.460215i	$0.847772\pi$
$234$	3.57958e20			2.60314
$235$	1.40095e19	+	2.54229e19i	0.0982530	+	0.178299i
$236$	−5.65656e19			−0.382648
$237$		−	2.79573e20i		−	1.82446i
$238$			7.29811e19i			0.459522i
$239$	−2.03446e20			−1.23614			−0.618069	−	0.786124i	$-0.712085\pi$
$239$	−2.03446e20			−1.23614			−0.618069	+	0.786124i	$0.712085\pi$
$240$	−3.65995e19	−	6.64167e19i	−0.214625	−	0.389477i
$241$	−2.15084e20			−1.21749			−0.608743	−	0.793368i	$-0.708326\pi$
$241$	−2.15084e20			−1.21749			−0.608743	+	0.793368i	$0.708326\pi$
$242$		−	6.56629e19i		−	0.358831i
$243$			1.19717e20i			0.631687i
$244$	5.62104e19			0.286420
$245$	5.98298e19	−	3.29697e19i	0.294446	−	0.162257i
$246$	2.94041e20			1.39785
$247$		−	1.72088e20i		−	0.790361i
$248$		−	5.43129e19i		−	0.241026i
$249$	−3.97038e20			−1.70270
$250$	−1.70293e20	−	1.02008e19i	−0.705842	−	0.0422808i
$251$	−1.40847e19			−0.0564315			−0.0282158	−	0.999602i	$-0.508983\pi$
$251$	−1.40847e19			−0.0564315			−0.0282158	+	0.999602i	$0.508983\pi$
$252$		−	3.22913e20i		−	1.25078i
$253$		−	2.35803e20i		−	0.883132i
$254$	−2.10436e20			−0.762137
$255$	2.50046e20	−	1.37790e20i	0.875847	−	0.482643i
$256$	1.84467e19			0.0625000
$257$			1.66925e20i			0.547129i	0.961854	+	0.273564i	$0.0882026\pi$
$257$			1.66925e20i			0.547129i	−0.961854	+	0.273564i	$0.911797\pi$
$258$			2.62594e19i			0.0832756i
$259$	−1.01712e19			−0.0312123
$260$	1.38227e20	+	2.50839e20i	0.410506	+	0.744942i
$261$	9.24512e20			2.65747
$262$			6.77536e19i			0.188526i
$263$		−	2.85711e20i		−	0.769667i	−0.922986	−	0.384834i	$-0.874259\pi$
$263$		−	2.85711e20i		−	0.769667i	0.922986	−	0.384834i	$-0.125741\pi$
$264$	1.69213e20			0.441366
$265$	2.57584e20	+	4.67435e20i	0.650623	+	1.18068i
$266$	−1.55240e20			−0.379760
$267$		−	4.97102e20i		−	1.17788i
$268$		−	2.66331e19i		−	0.0611331i
$269$	−4.15461e20			−0.923923			−0.461962	−	0.886900i	$-0.652854\pi$
$269$	−4.15461e20			−0.923923			−0.461962	+	0.886900i	$0.652854\pi$
$270$	−5.95125e20	+	3.27948e20i	−1.28238	+	0.706665i
$271$	2.65437e20			0.554272			0.277136	−	0.960831i	$-0.410615\pi$
$271$	2.65437e20			0.554272			0.277136	+	0.960831i	$0.410615\pi$
$272$			6.94484e19i			0.140549i
$273$			1.78311e21i			3.49780i
$274$	−4.39885e19			−0.0836487
$275$	2.03329e20	−	3.21817e20i	0.374862	−	0.593309i
$276$	−6.26078e20			−1.11918
$277$		−	1.04764e21i		−	1.81608i	−0.418886	−	0.908039i	$-0.637579\pi$
$277$		−	1.04764e21i		−	1.81608i	0.418886	−	0.908039i	$-0.362421\pi$
$278$		−	7.34205e20i		−	1.23435i
$279$	−9.04734e20			−1.47532
$280$	2.26282e20	−	1.24695e20i	0.357937	−	0.197244i
$281$	−4.31210e20			−0.661736			−0.330868	−	0.943677i	$-0.607342\pi$
$281$	−4.31210e20			−0.661736			−0.330868	+	0.943677i	$0.607342\pi$
$282$			1.71972e20i			0.256060i
$283$			5.09227e20i			0.735745i	0.929876	+	0.367872i	$0.119914\pi$
$283$			5.09227e20i			0.735745i	−0.929876	+	0.367872i	$0.880086\pi$
$284$	6.24897e20			0.876198
$285$	2.93097e20	+	5.31879e20i	0.398868	+	0.723822i
$286$	−6.39074e20			−0.844189
$287$			1.00180e21i			1.28465i
$288$		−	3.07283e20i		−	0.382562i
$289$	5.65781e20			0.683938
$290$	3.57005e20	+	6.47853e20i	0.419074	+	0.760490i
$291$	−7.34363e20			−0.837183
$292$		−	3.97896e20i		−	0.440571i
$293$			6.39057e20i			0.687329i	0.939093	+	0.343664i	$0.111668\pi$
$293$			6.39057e20i			0.687329i	−0.939093	+	0.343664i	$0.888332\pi$
$294$	4.04717e20			0.422862
$295$	−6.60289e20	+	3.63858e20i	−0.670266	+	0.369356i
$296$	−9.67890e18			−0.00954655
$297$		−	1.51622e21i		−	1.45323i
$298$		−	5.56347e20i		−	0.518212i
$299$	2.36454e21			2.14063
$300$	−8.54451e20	−	5.39855e20i	−0.751894	−	0.475058i
$301$	−8.94659e19			−0.0765319
$302$			4.65587e20i			0.387205i
$303$		−	3.37684e21i		−	2.73054i
$304$	−1.47726e20			−0.116153
$305$	6.56144e20	−	3.61574e20i	0.501707	−	0.276470i
$306$	1.15686e21			0.860296
$307$			2.65100e21i			1.91749i	0.284265	+	0.958746i	$0.408251\pi$
$307$			2.65100e21i			1.91749i	−0.284265	+	0.958746i	$0.591749\pi$
$308$			5.76508e20i			0.405624i
$309$	2.29406e20			0.157021
$310$	−3.49367e20	−	6.33993e20i	−0.232653	−	0.422192i
$311$	−2.17669e21			−1.41037			−0.705185	−	0.709023i	$-0.749136\pi$
$311$	−2.17669e21			−1.41037			−0.705185	+	0.709023i	$0.749136\pi$
$312$			1.69679e21i			1.06983i
$313$		−	6.47134e19i		−	0.0397070i	−0.999803	−	0.0198535i	$-0.993680\pi$
$313$		−	6.47134e19i		−	0.0397070i	0.999803	−	0.0198535i	$-0.00631998\pi$
$314$	1.72385e21			1.02943
$315$	−2.07714e21	−	3.76936e21i	−1.20733	−	2.19093i
$316$	9.06398e20			0.512836
$317$		−	3.20908e21i		−	1.76757i	−0.467893	−	0.883785i	$-0.654987\pi$
$317$		−	3.20908e21i		−	1.76757i	0.467893	−	0.883785i	$-0.345013\pi$
$318$			3.16195e21i			1.69561i
$319$	−1.65056e21			−0.861808
$320$	2.15329e20	−	1.18659e20i	0.109478	−	0.0603288i
$321$	3.48479e21			1.72537
$322$		−	2.13305e21i		−	1.02855i
$323$		−	5.56158e20i		−	0.261202i
$324$	−1.66044e21			−0.759609
$325$	3.22705e21	+	2.03890e21i	1.43813	+	0.908630i
$326$	−3.52012e20			−0.152830
$327$			6.42418e21i			2.71745i
$328$			9.53307e20i			0.392921i
$329$	−5.85910e20			−0.235324
$330$	1.97522e21	−	1.08846e21i	0.773119	−	0.426034i
$331$	−4.59189e21			−1.75167			−0.875837	−	0.482608i	$-0.839690\pi$
$331$	−4.59189e21			−1.75167			−0.875837	+	0.482608i	$0.839690\pi$
$332$		−	1.28723e21i		−	0.478611i
$333$			1.61229e20i			0.0584344i
$334$	−1.30019e21			−0.459368
$335$	−1.71318e20	−	3.10888e20i	−0.0590094	−	0.107084i
$336$	1.53068e21			0.514043
$337$			3.38339e21i			1.10789i	0.832552	+	0.553946i	$0.186879\pi$
$337$			3.38339e21i			1.10789i	−0.832552	+	0.553946i	$0.813121\pi$
$338$		−	4.19386e21i		−	1.33913i
$339$	−6.21123e21			−1.93411
$340$	4.46727e20	+	8.10670e20i	0.135666	+	0.246192i
$341$	1.61525e21			0.478440
$342$			2.46078e21i			0.710971i
$343$		−	2.72255e21i		−	0.767319i
$344$	−8.51353e19			−0.0234079
$345$	−7.30820e21	+	4.02724e21i	−1.96041	+	1.08030i
$346$	−3.98198e21			−1.04220
$347$			7.94764e20i			0.202973i	0.994837	+	0.101486i	$0.0323598\pi$
$347$			7.94764e20i			0.202973i	−0.994837	+	0.101486i	$0.967640\pi$
$348$			4.38238e21i			1.09216i
$349$	5.52679e20			0.134418			0.0672089	−	0.997739i	$-0.478591\pi$
$349$	5.52679e20			0.134418			0.0672089	+	0.997739i	$0.478591\pi$
$350$	1.83929e21	−	2.91112e21i	0.436588	−	0.691005i
$351$	1.52041e22			3.52249
$352$			5.48601e20i			0.124064i
$353$		−	4.24483e21i		−	0.937076i	−0.883443	−	0.468538i	$-0.844781\pi$
$353$		−	4.24483e21i		−	0.937076i	0.883443	−	0.468538i	$-0.155219\pi$
$354$	−4.46650e21			−0.962587
$355$	7.29441e21	−	4.01965e21i	1.53479	−	0.845760i
$356$	1.61165e21			0.331089
$357$			5.76270e21i			1.15597i
$358$			1.71612e21i			0.336157i
$359$	6.15257e21			1.17694			0.588469	−	0.808520i	$-0.299731\pi$
$359$	6.15257e21			1.17694			0.588469	+	0.808520i	$0.299731\pi$
$360$	−1.97659e21	−	3.58691e21i	−0.369272	−	0.670114i
$361$	−4.29737e21			−0.784136
$362$			3.56527e21i			0.635432i
$363$		−	5.18484e21i		−	0.902671i
$364$	−5.78098e21			−0.983196
$365$	−2.55947e21	−	4.64464e21i	−0.425266	−	0.771725i
$366$	4.43846e21			0.720516
$367$		−	1.53580e21i		−	0.243598i	−0.992555	−	0.121799i	$-0.961134\pi$
$367$		−	1.53580e21i		−	0.243598i	0.992555	−	0.121799i	$-0.0388664\pi$
$368$		−	2.02980e21i		−	0.314591i
$369$	1.58800e22			2.40506
$370$	−1.12982e20	+	6.22595e19i	−0.0167222	+	0.00921491i
$371$	−1.07728e22			−1.55829
$372$		−	4.28863e21i		−	0.606322i
$373$			1.00414e22i			1.38762i	0.720160	+	0.693808i	$0.244069\pi$
$373$			1.00414e22i			1.38762i	−0.720160	+	0.693808i	$0.755931\pi$
$374$	−2.06538e21			−0.278991
$375$	−1.34466e22	−	8.05469e20i	−1.77561	−	0.106361i
$376$	−5.57549e20			−0.0719757
$377$		−	1.65511e22i		−	2.08894i
$378$		−	1.37156e22i		−	1.69252i
$379$	1.19831e22			1.44589			0.722944	−	0.690907i	$-0.242788\pi$
$379$	1.19831e22			1.44589			0.722944	+	0.690907i	$0.242788\pi$
$380$	−1.72440e21	+	9.50244e20i	−0.203459	+	0.112118i
$381$	−1.66163e22			−1.91722
$382$		−	4.81394e20i		−	0.0543203i
$383$			1.12305e22i			1.23940i	0.784839	+	0.619699i	$0.212745\pi$
$383$			1.12305e22i			1.23940i	−0.784839	+	0.619699i	$0.787255\pi$
$384$	1.45658e21			0.157224
$385$	3.70839e21	+	6.72957e21i	0.391533	+	0.710511i
$386$	−5.34945e20			−0.0552480
$387$			1.41817e21i			0.143280i
$388$		−	2.38087e21i		−	0.235324i
$389$	2.54158e21			0.245772			0.122886	−	0.992421i	$-0.460785\pi$
$389$	2.54158e21			0.245772			0.122886	+	0.992421i	$0.460785\pi$
$390$	1.09146e22	+	1.98067e22i	1.03267	+	1.87397i
$391$	7.64179e21			0.707445
$392$			1.31213e21i			0.118862i
$393$			5.34993e21i			0.474254i
$394$	7.96503e20			0.0690986
$395$	1.05804e22	−	5.83041e21i	0.898309	−	0.495021i
$396$	9.13850e21			0.759392
$397$			3.06633e21i			0.249402i	0.992194	+	0.124701i	$0.0397972\pi$
$397$			3.06633e21i			0.249402i	−0.992194	+	0.124701i	$0.960203\pi$
$398$			7.42630e21i			0.591243i
$399$	−1.22580e22			−0.955322
$400$	1.75026e21	−	2.77020e21i	0.133534	−	0.211350i
$401$	−1.31178e22			−0.979793			−0.489897	−	0.871781i	$-0.662965\pi$
$401$	−1.31178e22			−0.979793			−0.489897	+	0.871781i	$0.662965\pi$
$402$		−	2.10299e21i		−	0.153786i
$403$			1.61971e22i			1.15969i
$404$	1.09480e22			0.767527
$405$	−1.93823e22	+	1.06808e22i	−1.33057	+	0.733221i
$406$	−1.49308e22			−1.00372
$407$		−	2.87848e20i		−	0.0189501i
$408$			5.48375e21i			0.353563i
$409$	−2.29036e21			−0.144629			−0.0723146	−	0.997382i	$-0.523039\pi$
$409$	−2.29036e21			−0.144629			−0.0723146	+	0.997382i	$0.523039\pi$
$410$	6.13215e21	+	1.11279e22i	0.379271	+	0.688259i
$411$	−3.47340e21			−0.210426
$412$			7.43753e20i			0.0441370i
$413$		−	1.52174e22i		−	0.884636i
$414$	−3.38120e22			−1.92561
$415$	−8.28011e21	−	1.50258e22i	−0.461984	−	0.838358i
$416$	−5.50115e21			−0.300719
$417$		−	5.79740e22i		−	3.10511i
$418$		−	4.39332e21i		−	0.230566i
$419$	9.99153e21			0.513822			0.256911	−	0.966435i	$-0.417295\pi$
$419$	9.99153e21			0.513822			0.256911	+	0.966435i	$0.417295\pi$
$420$	1.78676e22	−	9.84608e21i	0.900423	−	0.496186i
$421$	2.42321e22			1.19672			0.598361	−	0.801227i	$-0.295819\pi$
$421$	2.42321e22			1.19672			0.598361	+	0.801227i	$0.295819\pi$
$422$			8.37906e21i			0.405546i
$423$			9.28754e21i			0.440563i
$424$	−1.02513e22			−0.476617
$425$	1.04293e22	+	6.58937e21i	0.475278	+	0.300288i
$426$	4.93428e22			2.20416
$427$			1.51219e22i			0.662168i
$428$			1.12980e22i			0.484985i
$429$	−5.04622e22			−2.12363
$430$	−9.93783e20	+	5.47633e20i	−0.0410024	+	0.0225947i
$431$	−3.74076e21			−0.151322			−0.0756611	−	0.997134i	$-0.524107\pi$
$431$	−3.74076e21			−0.151322			−0.0756611	+	0.997134i	$0.524107\pi$
$432$		−	1.30517e22i		−	0.517671i
$433$		−	3.00276e22i		−	1.16781i	−0.811820	−	0.583907i	$-0.801523\pi$
$433$		−	3.00276e22i		−	1.16781i	0.811820	−	0.583907i	$-0.198477\pi$
$434$	1.46114e22			0.557222
$435$	2.81896e22	+	5.11554e22i	1.05422	+	1.91308i
$436$	−2.08277e22			−0.763848
$437$			1.62551e22i			0.584650i
$438$		−	3.14185e22i		−	1.10830i
$439$	4.88091e22			1.68870			0.844349	−	0.535793i	$-0.179987\pi$
$439$	4.88091e22			1.68870			0.844349	+	0.535793i	$0.179987\pi$
$440$	3.52888e21	+	6.40382e21i	0.119754	+	0.217316i
$441$	2.18572e22			0.727555
$442$		−	2.07108e22i		−	0.676249i
$443$			8.85676e20i			0.0283689i	0.999899	+	0.0141845i	$0.00451521\pi$
$443$			8.85676e20i			0.0283689i	−0.999899	+	0.0141845i	$0.995485\pi$
$444$	−7.64261e20			−0.0240152
$445$	1.88127e22	−	1.03669e22i	0.579951	−	0.319587i
$446$	1.26540e22			0.382719
$447$		−	4.39300e22i		−	1.30361i
$448$			4.96258e21i			0.144492i
$449$	−1.07587e18			−3.07374e−5			−1.53687e−5	−	1.00000i	$-0.500005\pi$
$449$	−1.07587e18			−3.07374e−5			−1.53687e−5		1.00000i	$0.500005\pi$
$450$	−4.61455e22	−	2.91555e22i	−1.29367	−	0.817360i
$451$	−2.83511e22			−0.779955
$452$		−	2.01373e22i		−	0.543657i
$453$			3.67634e22i			0.974050i
$454$	−2.61612e22			−0.680274
$455$	−6.74814e22	+	3.71862e22i	−1.72221	+	0.949040i
$456$	−1.16646e22			−0.292193
$457$		−	4.30315e21i		−	0.105803i	−0.998600	−	0.0529016i	$-0.983153\pi$
$457$		−	4.30315e21i		−	0.105803i	0.998600	−	0.0529016i	$-0.0168470\pi$
$458$			4.47632e22i			1.08035i
$459$	4.91369e22			1.16413
$460$	−1.30567e22	−	2.36938e22i	−0.303662	−	0.551053i
$461$	−3.48054e22			−0.794674			−0.397337	−	0.917673i	$-0.630066\pi$
$461$	−3.48054e22			−0.794674			−0.397337	+	0.917673i	$0.630066\pi$
$462$			4.55219e22i			1.02038i
$463$			2.06561e21i			0.0454579i	0.999742	+	0.0227290i	$0.00723548\pi$
$463$			2.06561e21i			0.0454579i	−0.999742	+	0.0227290i	$0.992765\pi$
$464$	−1.42080e22			−0.306995
$465$	−2.75866e22	−	5.00611e22i	−0.585259	−	1.06206i
$466$	−3.12432e22			−0.650843
$467$			2.27698e22i			0.465763i	0.972505	+	0.232882i	$0.0748154\pi$
$467$			2.27698e22i			0.465763i	−0.972505	+	0.232882i	$0.925185\pi$
$468$			9.16372e22i			1.84070i
$469$	7.16490e21			0.141332
$470$	−6.50826e21	+	3.58643e21i	−0.126076	+	0.0694753i
$471$	1.36118e23			2.58963
$472$		−	1.44808e22i		−	0.270573i
$473$		−	2.53190e21i		−	0.0464651i
$474$	7.15706e22			1.29009
$475$	−1.40164e22	+	2.21844e22i	−0.248166	+	0.392782i
$476$	−1.86831e22			−0.324931
$477$			1.70765e23i			2.91737i
$478$		−	5.20822e22i		−	0.874081i
$479$	−2.90207e22			−0.478471			−0.239236	−	0.970962i	$-0.576897\pi$
$479$	−2.90207e22			−0.478471			−0.239236	+	0.970962i	$0.576897\pi$
$480$	1.70027e22	−	9.36947e21i	0.275402	−	0.151763i
$481$	2.88642e21			0.0459332
$482$		−	5.50616e22i		−	0.860892i
$483$		−	1.68429e23i		−	2.58741i
$484$	1.68097e22			0.253732
$485$	−1.53149e22	−	2.77918e22i	−0.227149	−	0.412204i
$486$	−3.06475e22			−0.446670
$487$			2.68073e22i			0.383934i	0.981401	+	0.191967i	$0.0614866\pi$
$487$			2.68073e22i			0.383934i	−0.981401	+	0.191967i	$0.938513\pi$
$488$			1.43899e22i			0.202530i
$489$	−2.77954e22			−0.384457
$490$	8.44026e21	+	1.53164e22i	0.114733	+	0.208205i
$491$	−9.88548e22			−1.32070			−0.660351	−	0.750957i	$-0.729593\pi$
$491$	−9.88548e22			−1.32070			−0.660351	+	0.750957i	$0.729593\pi$
$492$			7.52746e22i			0.988428i
$493$		−	5.34905e22i		−	0.690363i
$494$	4.40544e22			0.558869
$495$	1.06674e23	−	5.87834e22i	1.33019	−	0.733011i
$496$	1.39041e22			0.170431
$497$			1.68111e23i			2.02566i
$498$		−	1.01642e23i		−	1.20399i
$499$	−1.20742e23			−1.40606			−0.703030	−	0.711160i	$-0.748170\pi$
$499$	−1.20742e23			−1.40606			−0.703030	+	0.711160i	$0.748170\pi$
$500$	2.61140e21	−	4.35951e22i	0.0298970	−	0.499105i
$501$	−1.02665e23			−1.15558
$502$		−	3.60569e21i		−	0.0399031i
$503$			7.15920e22i			0.778998i	0.921027	+	0.389499i	$0.127352\pi$
$503$			7.15920e22i			0.778998i	−0.921027	+	0.389499i	$0.872648\pi$
$504$	8.26658e22			0.884436
$505$	1.27796e23	−	7.04230e22i	1.34444	−	0.740863i
$506$	6.03657e22			0.624469
$507$		−	3.31154e23i		−	3.36870i
$508$		−	5.38716e22i		−	0.538912i
$509$	9.08719e22			0.893981			0.446991	−	0.894539i	$-0.352496\pi$
$509$	9.08719e22			0.893981			0.446991	+	0.894539i	$0.352496\pi$
$510$	3.52742e22	+	6.40117e22i	0.341280	+	0.619317i
$511$	1.07043e23			1.01855
$512$			4.72237e21i			0.0441942i
$513$			1.04521e23i			0.962064i
$514$	−4.27328e22			−0.386878
$515$	4.78419e21	+	8.68182e21i	0.0426037	+	0.0773124i
$516$	−6.72241e21			−0.0588847
$517$		−	1.65814e22i		−	0.142873i
$518$		−	2.60384e21i		−	0.0220705i
$519$	−3.14424e23			−2.62176
$520$	−6.42149e22	+	3.53862e22i	−0.526753	+	0.290272i
$521$	3.85520e22			0.311119			0.155559	−	0.987827i	$-0.450282\pi$
$521$	3.85520e22			0.311119			0.155559	+	0.987827i	$0.450282\pi$
$522$			2.36675e23i			1.87911i
$523$			1.28297e23i			1.00219i	0.865391	+	0.501097i	$0.167070\pi$
$523$			1.28297e23i			1.00219i	−0.865391	+	0.501097i	$0.832930\pi$
$524$	−1.73449e22			−0.133308
$525$	1.45233e23	−	2.29866e23i	1.09828	−	1.73829i
$526$	7.31420e22			0.544237
$527$			5.23462e22i			0.383261i
$528$			4.33184e22i			0.312093i
$529$	−8.22998e22			−0.583479
$530$	−1.19663e23	+	6.59416e22i	−0.834866	+	0.460060i
$531$	−2.41218e23			−1.65618
$532$		−	3.97414e22i		−	0.268531i
$533$		−	2.84293e23i		−	1.89054i
$534$	1.27258e23			0.832884
$535$	7.26742e22	+	1.31881e23i	0.468137	+	0.849523i
$536$	6.81808e21			0.0432276
$537$			1.35508e23i			0.845633i
$538$		−	1.06358e23i		−	0.653312i
$539$	−3.90223e22			−0.235944
$540$	−8.39548e22	−	1.52352e23i	−0.499688	−	0.906778i
$541$	3.40003e23			1.99207			0.996037	−	0.0889412i	$-0.0283483\pi$
$541$	3.40003e23			1.99207			0.996037	+	0.0889412i	$0.0283483\pi$
$542$			6.79519e22i			0.391929i
$543$			2.81519e23i			1.59849i
$544$	−1.77788e22			−0.0993828
$545$	−2.43122e23	+	1.33974e23i	−1.33799	+	0.737313i
$546$	−4.56475e23			−2.47332
$547$			2.66900e23i			1.42383i	0.702268	+	0.711913i	$0.252171\pi$
$547$			2.66900e23i			1.42383i	−0.702268	+	0.711913i	$0.747829\pi$
$548$		−	1.12611e22i		−	0.0591486i
$549$	2.39704e23			1.23968
$550$	8.23851e22	+	5.20522e22i	0.419533	+	0.265067i
$551$	1.13781e23			0.570534
$552$		−	1.60276e23i		−	0.791382i
$553$			2.43841e23i			1.18561i
$554$	2.68196e23			1.28416
$555$	−8.92121e21	+	4.91611e21i	−0.0420662	+	0.0231809i
$556$	1.87957e23			0.872814
$557$		−	2.58262e22i		−	0.118111i	−0.998255	−	0.0590555i	$-0.981191\pi$
$557$		−	2.58262e22i		−	0.118111i	0.998255	−	0.0590555i	$-0.0188089\pi$
$558$		−	2.31612e23i		−	1.04321i
$559$	2.53889e22			0.112627
$560$	3.19218e22	+	5.79282e22i	0.139473	+	0.253100i
$561$	−1.63085e23			−0.701828
$562$		−	1.10390e23i		−	0.467918i
$563$		−	1.41028e22i		−	0.0588822i	−0.999567	−	0.0294411i	$-0.990627\pi$
$563$		−	1.41028e22i		−	0.0588822i	0.999567	−	0.0294411i	$-0.00937275\pi$
$564$	−4.40249e22			−0.181061
$565$	−1.29533e23	−	2.35063e23i	−0.524771	−	0.952297i
$566$	−1.30362e23			−0.520250
$567$		−	4.46695e23i		−	1.75612i
$568$			1.59974e23i			0.619566i
$569$	2.13811e23			0.815785			0.407892	−	0.913030i	$-0.366264\pi$
$569$	2.13811e23			0.815785			0.407892	+	0.913030i	$0.366264\pi$
$570$	−1.36161e23	+	7.50327e22i	−0.511820	+	0.282043i
$571$	1.13718e23			0.421136			0.210568	−	0.977579i	$-0.432469\pi$
$571$	1.13718e23			0.421136			0.210568	+	0.977579i	$0.432469\pi$
$572$		−	1.63603e23i		−	0.596932i
$573$		−	3.80116e22i		−	0.136648i
$574$	−2.56461e23			−0.908385
$575$	−3.04821e23	−	1.92590e23i	−1.06382	−	0.672137i
$576$	7.86643e22			0.270512
$577$		−	2.79237e23i		−	0.946191i	−0.881011	−	0.473096i	$-0.843136\pi$
$577$		−	2.79237e23i		−	0.946191i	0.881011	−	0.473096i	$-0.156864\pi$
$578$			1.44840e23i			0.483617i
$579$	−4.22401e22			−0.138981
$580$	−1.65850e23	+	9.13932e22i	−0.537747	+	0.296330i
$581$	3.46294e23			1.10649
$582$		−	1.87997e23i		−	0.591978i
$583$		−	3.04872e23i		−	0.946094i
$584$	1.01861e23			0.311531
$585$	5.89456e23	+	1.06968e24i	1.77675	+	3.22425i
$586$	−1.63599e23			−0.486015
$587$		−	6.02342e23i		−	1.76368i	−0.471549	−	0.881840i	$-0.656305\pi$
$587$		−	6.02342e23i		−	1.76368i	0.471549	−	0.881840i	$-0.343695\pi$
$588$			1.03608e23i			0.299009i
$589$	−1.11347e23			−0.316737
$590$	−9.31476e22	−	1.69034e23i	−0.261174	−	0.473949i
$591$	6.28931e22			0.173824
$592$		−	2.47780e21i		−	0.00675043i
$593$		−	3.93286e23i		−	1.05619i	−0.849184	−	0.528097i	$-0.822906\pi$
$593$		−	3.93286e23i		−	1.05619i	0.849184	−	0.528097i	$-0.177094\pi$
$594$	3.88153e23			1.02759
$595$	−2.18088e23	+	1.20179e23i	−0.569165	+	0.313643i
$596$	1.42425e23			0.366431
$597$			5.86392e23i			1.48733i
$598$			6.05322e23i			1.51365i
$599$	3.72267e23			0.917754			0.458877	−	0.888500i	$-0.348252\pi$
$599$	3.72267e23			0.917754			0.458877	+	0.888500i	$0.348252\pi$
$600$	1.38203e23	−	2.18739e23i	0.335917	−	0.531669i
$601$	−2.05419e23			−0.492275			−0.246138	−	0.969235i	$-0.579162\pi$
$601$	−2.05419e23			−0.492275			−0.246138	+	0.969235i	$0.579162\pi$
$602$		−	2.29033e22i		−	0.0541162i
$603$		−	1.13574e23i		−	0.264596i
$604$	−1.19190e23			−0.273796
$605$	1.96219e23	−	1.08128e23i	0.444449	−	0.244917i
$606$	8.64471e23			1.93078
$607$			6.45041e22i			0.142064i	0.997474	+	0.0710319i	$0.0226292\pi$
$607$			6.45041e22i			0.142064i	−0.997474	+	0.0710319i	$0.977371\pi$
$608$		−	3.78177e22i		−	0.0821325i
$609$	−1.17896e24			−2.52494
$610$	9.25628e22	+	1.67973e23i	0.195494	+	0.354761i
$611$	1.66271e23			0.346311
$612$			2.96156e23i			0.608321i
$613$			8.33557e22i			0.168858i	0.996430	+	0.0844289i	$0.0269066\pi$
$613$			8.33557e22i			0.168858i	−0.996430	+	0.0844289i	$0.973093\pi$
$614$	−6.78656e23			−1.35587
$615$	4.84204e23	+	8.78679e23i	0.954091	+	1.73138i
$616$	−1.47586e23			−0.286820
$617$		−	1.53109e23i		−	0.293479i	−0.989175	−	0.146739i	$-0.953122\pi$
$617$		−	1.53109e23i		−	0.293479i	0.989175	−	0.146739i	$-0.0468778\pi$
$618$			5.87279e22i			0.111031i
$619$	−9.76593e23			−1.82114			−0.910569	−	0.413356i	$-0.864356\pi$
$619$	−9.76593e23			−1.82114			−0.910569	+	0.413356i	$0.864356\pi$
$620$	1.62302e23	−	8.94381e22i	0.298535	−	0.164510i
$621$	−1.43615e24			−2.60567
$622$		−	5.57233e23i		−	0.997283i
$623$			4.33568e23i			0.765437i
$624$	−4.34379e23			−0.756485
$625$	−2.49942e23	−	5.25682e23i	−0.429398	−	0.903116i
$626$	1.65666e22			0.0280771
$627$		−	3.46903e23i		−	0.580008i
$628$			4.41306e23i			0.727919i
$629$	9.32843e21			0.0151802
$630$	9.64957e23	−	5.31748e23i	1.54922	−	0.853711i
$631$	−6.02040e23			−0.953621			−0.476811	−	0.879006i	$-0.658207\pi$
$631$	−6.02040e23			−0.953621			−0.476811	+	0.879006i	$0.658207\pi$
$632$			2.32038e23i			0.362630i
$633$			6.61624e23i			1.02019i
$634$	8.21524e23			1.24986
$635$	−3.46529e23	−	6.28842e23i	−0.520191	−	0.943985i
$636$	−8.09460e23			−1.19897
$637$		−	3.91300e23i		−	0.571906i
$638$		−	4.22544e23i		−	0.609391i
$639$	2.66481e24			3.79236
$640$	3.03766e22	+	5.51241e22i	0.0426589	+	0.0774126i
$641$	8.13646e23			1.12757			0.563783	−	0.825923i	$-0.309345\pi$
$641$	8.13646e23			1.12757			0.563783	+	0.825923i	$0.309345\pi$
$642$			8.92105e23i			1.22002i
$643$			1.02063e23i			0.137745i	0.997625	+	0.0688726i	$0.0219402\pi$
$643$			1.02063e23i			0.137745i	−0.997625	+	0.0688726i	$0.978060\pi$
$644$	5.46060e23			0.727295
$645$	−7.84706e22	+	4.32419e22i	−0.103145	+	0.0568391i
$646$	1.42376e23			0.184698
$647$			9.71752e23i			1.24414i	0.782962	+	0.622070i	$0.213708\pi$
$647$			9.71752e23i			1.24414i	−0.782962	+	0.622070i	$0.786292\pi$
$648$		−	4.25072e23i		−	0.537125i
$649$	4.30655e23			0.537093
$650$	−5.21958e23	+	8.26124e23i	−0.642498	+	1.01691i
$651$	1.15374e24			1.40174
$652$		−	9.01151e22i		−	0.108067i
$653$		−	5.73338e23i		−	0.678655i	−0.940668	−	0.339327i	$-0.889801\pi$
$653$		−	5.73338e23i		−	0.678655i	0.940668	−	0.339327i	$-0.110199\pi$
$654$	−1.64459e24			−1.92153
$655$	−2.02467e23	+	1.11571e23i	−0.233509	+	0.128677i
$656$	−2.44047e23			−0.277837
$657$		−	1.69679e24i		−	1.90688i
$658$		−	1.49993e23i		−	0.166399i
$659$	−6.64180e22			−0.0727377			−0.0363689	−	0.999338i	$-0.511579\pi$
$659$	−6.64180e22			−0.0727377			−0.0363689	+	0.999338i	$0.511579\pi$
$660$	2.78646e23	+	5.05655e23i	0.301251	+	0.546677i
$661$	−2.25960e23			−0.241168			−0.120584	−	0.992703i	$-0.538477\pi$
$661$	−2.25960e23			−0.241168			−0.120584	+	0.992703i	$0.538477\pi$
$662$		−	1.17552e24i		−	1.23862i
$663$		−	1.63535e24i		−	1.70117i
$664$	3.29531e23			0.338429
$665$	−2.55637e23	−	4.63901e23i	−0.259203	−	0.470372i
$666$	−4.12747e22			−0.0413193
$667$			1.56339e24i			1.54525i
$668$		−	3.32848e23i		−	0.324822i
$669$	9.99176e23			0.962764
$670$	7.95874e22	−	4.38573e22i	0.0757196	−	0.0417259i
$671$	−4.27951e23			−0.402025
$672$			3.91853e23i			0.363483i
$673$		−	2.25201e23i		−	0.206273i	−0.994667	−	0.103136i	$-0.967112\pi$
$673$		−	2.25201e23i		−	0.206273i	0.994667	−	0.103136i	$-0.0328878\pi$
$674$	−8.66147e23			−0.783398
$675$	−1.96001e24	−	1.23836e24i	−1.75055	−	1.10603i
$676$	1.07363e24			0.946907
$677$			6.00722e23i			0.523203i	0.965176	+	0.261601i	$0.0842505\pi$
$677$			6.00722e23i			0.523203i	−0.965176	+	0.261601i	$0.915749\pi$
$678$		−	1.59008e24i		−	1.36762i
$679$	6.40506e23			0.544039
$680$	−2.07531e23	+	1.14362e23i	−0.174084	+	0.0959303i
$681$	−2.06573e24			−1.71129
$682$			4.13504e23i			0.338308i
$683$			2.10638e24i			1.70200i	0.525163	+	0.851002i	$0.324005\pi$
$683$			2.10638e24i			1.70200i	−0.525163	+	0.851002i	$0.675995\pi$
$684$	−6.29961e23			−0.502732
$685$	−7.24367e22	−	1.31450e23i	−0.0570938	−	0.103607i
$686$	6.96973e23			0.542577
$687$			3.53457e24i			2.71772i
$688$		−	2.17946e22i		−	0.0165519i
$689$	3.05713e24			2.29324
$690$	−1.03097e24	−	1.87090e24i	−0.763890	−	1.38622i
$691$	1.47665e24			1.08072			0.540360	−	0.841434i	$-0.318288\pi$
$691$	1.47665e24			1.08072			0.540360	+	0.841434i	$0.318288\pi$
$692$		−	1.01939e24i		−	0.736949i
$693$			2.45846e24i			1.75562i
$694$	−2.03460e23			−0.143523
$695$	2.19401e24	−	1.20903e24i	1.52886	−	0.842493i
$696$	−1.12189e24			−0.772274
$697$		−	9.18787e23i		−	0.624793i
$698$			1.41486e23i			0.0950478i
$699$	−2.46701e24			−1.63725
$700$	7.45246e23	+	4.70858e23i	0.488614	+	0.308714i
$701$	−1.95160e24			−1.26412			−0.632059	−	0.774920i	$-0.717790\pi$
$701$	−1.95160e24			−1.26412			−0.632059	+	0.774920i	$0.717790\pi$
$702$			3.89224e24i			2.49077i
$703$			1.98428e22i			0.0125453i
$704$	−1.40442e23			−0.0877262
$705$	−5.13902e23	+	2.83190e23i	−0.317156	+	0.174771i
$706$	1.08668e24			0.662613
$707$			2.94526e24i			1.77443i
$708$		−	1.14342e24i		−	0.680652i
$709$	−1.53951e24			−0.905505			−0.452752	−	0.891636i	$-0.649558\pi$
$709$	−1.53951e24			−0.905505			−0.452752	+	0.891636i	$0.649558\pi$
$710$	1.02903e24	+	1.86737e24i	0.598042	+	1.08526i
$711$	3.86525e24			2.21966
$712$			4.12581e23i			0.234115i
$713$		−	1.52994e24i		−	0.857856i
$714$	−1.47525e24			−0.817393
$715$	−1.05238e24	−	1.90973e24i	−0.576195	−	1.04561i
$716$	−4.39327e23			−0.237699
$717$		−	4.11249e24i		−	2.19883i
$718$			1.57506e24i			0.832221i
$719$	−2.84029e24			−1.48309			−0.741545	−	0.670903i	$-0.765907\pi$
$719$	−2.84029e24			−1.48309			−0.741545	+	0.670903i	$0.765907\pi$
$720$	9.18248e23	−	5.06008e23i	0.473842	−	0.261115i
$721$	−2.00086e23			−0.102039
$722$		−	1.10013e24i		−	0.554468i
$723$		−	4.34775e24i		−	2.16565i
$724$	−9.12708e23			−0.449318
$725$	−1.34808e24	+	2.13366e24i	−0.655908	+	1.03813i
$726$	1.32732e24			0.638285
$727$		−	6.98622e23i		−	0.332047i	−0.986122	−	0.166024i	$-0.946907\pi$
$727$		−	6.98622e23i		−	0.332047i	0.986122	−	0.166024i	$-0.0530928\pi$
$728$		−	1.47993e24i		−	0.695224i
$729$	8.51957e23			0.395579
$730$	1.18903e24	−	6.55224e23i	0.545692	−	0.300708i
$731$	8.20525e22			0.0372215
$732$			1.13625e24i			0.509481i
$733$			2.64577e24i			1.17265i	0.810075	+	0.586326i	$0.199426\pi$
$733$			2.64577e24i			1.17265i	−0.810075	+	0.586326i	$0.800574\pi$
$734$	3.93166e23			0.172250
$735$	6.66456e23	+	1.20941e24i	0.288622	+	0.523758i
$736$	5.19628e23			0.222449
$737$			2.02768e23i			0.0858076i
$738$			4.06528e24i			1.70064i
$739$	8.69279e22			0.0359486			0.0179743	−	0.999838i	$-0.494278\pi$
$739$	8.69279e22			0.0359486			0.0179743	+	0.999838i	$0.494278\pi$
$740$	−1.59384e22	−	2.89233e22i	−0.00651593	−	0.0118244i
$741$	3.47860e24			1.40589
$742$		−	2.75783e24i		−	1.10188i
$743$		−	5.50364e23i		−	0.217393i	−0.994075	−	0.108696i	$-0.965332\pi$
$743$		−	5.50364e23i		−	0.217393i	0.994075	−	0.108696i	$-0.0346676\pi$
$744$	1.09789e24			0.428734
$745$	1.66252e24	−	9.16148e23i	0.641859	−	0.353702i
$746$	−2.57060e24			−0.981193
$747$		−	5.48927e24i		−	2.07152i
$748$		−	5.28736e23i		−	0.197277i
$749$	−3.03941e24			−1.12123
$750$	2.06200e23	−	3.44233e24i	0.0752087	−	1.25554i
$751$	−2.95235e24			−1.06470			−0.532352	−	0.846523i	$-0.678692\pi$
$751$	−2.95235e24			−1.06470			−0.532352	+	0.846523i	$0.678692\pi$
$752$		−	1.42732e23i		−	0.0508945i
$753$		−	2.84711e23i		−	0.100380i
$754$	4.23709e24			1.47711
$755$	−1.39131e24	+	7.66691e23i	−0.479594	+	0.264284i
$756$	3.51119e24			1.19679
$757$			4.84963e24i			1.63453i	0.576261	+	0.817266i	$0.304511\pi$
$757$			4.84963e24i			1.63453i	−0.576261	+	0.817266i	$0.695489\pi$
$758$			3.06766e24i			1.02240i
$759$	4.76657e24			1.57091
$760$	−2.43263e23	−	4.41446e23i	−0.0792793	−	0.143867i
$761$	−4.97641e24			−1.60379			−0.801893	−	0.597468i	$-0.796173\pi$
$761$	−4.97641e24			−1.60379			−0.801893	+	0.597468i	$0.796173\pi$
$762$		−	4.25378e24i		−	1.35568i
$763$		−	5.60313e24i		−	1.76592i
$764$	1.23237e23			0.0384103
$765$	1.90502e24	+	3.45702e24i	0.587189	+	1.06556i
$766$	−2.87502e24			−0.876387
$767$			4.31843e24i			1.30186i
$768$			3.72885e23i			0.111174i
$769$	4.91902e23			0.145046			0.0725228	−	0.997367i	$-0.476895\pi$
$769$	4.91902e23			0.145046			0.0725228	+	0.997367i	$0.476895\pi$
$770$	−1.72277e24	+	9.49347e23i	−0.502407	+	0.276856i
$771$	−3.37424e24			−0.973227
$772$		−	1.36946e23i		−	0.0390663i
$773$		−	2.61117e24i		−	0.736732i	−0.929681	−	0.368366i	$-0.879917\pi$
$773$		−	2.61117e24i		−	0.736732i	0.929681	−	0.368366i	$-0.120083\pi$
$774$	−3.63051e23			−0.101314
$775$	1.31924e24	−	2.08802e24i	0.364133	−	0.576328i
$776$	6.09502e23			0.166399
$777$		−	2.05603e23i		−	0.0555202i
$778$			6.50645e23i			0.173787i
$779$	1.95438e24			0.516345
$780$	−5.07051e24	+	2.79415e24i	−1.32510	+	0.730205i
$781$	−4.75757e24			−1.22985
$782$			1.95630e24i			0.500239i
$783$			1.00526e25i			2.54276i
$784$	−3.35904e23			−0.0840484
$785$	2.83870e24	+	5.15136e24i	0.702632	+	1.27506i
$786$	−1.36958e24			−0.335348
$787$		−	4.37257e24i		−	1.05914i	−0.848268	−	0.529568i	$-0.822354\pi$
$787$		−	4.37257e24i		−	1.05914i	0.848268	−	0.529568i	$-0.177646\pi$
$788$			2.03905e23i			0.0488601i
$789$	5.77540e24			1.36908
$790$	1.49258e24	+	2.70858e24i	0.350033	+	0.635200i
$791$	5.41739e24			1.25687
$792$			2.33946e24i			0.536971i
$793$		−	4.29132e24i		−	0.974471i
$794$	−7.84981e23			−0.176354
$795$	−9.44881e24	+	5.20685e24i	−2.10018	+	1.15732i
$796$	−1.90113e24			−0.418072
$797$		−	1.47316e24i		−	0.320519i	−0.987075	−	0.160260i	$-0.948767\pi$
$797$		−	1.47316e24i		−	0.320519i	0.987075	−	0.160260i	$-0.0512331\pi$
$798$		−	3.13805e24i		−	0.675514i
$799$	5.37360e23			0.114450
$800$	7.09172e23	+	4.48066e23i	0.149447	+	0.0944228i
$801$	6.87271e24			1.43302
$802$		−	3.35816e24i		−	0.692818i
$803$			3.02934e24i			0.618394i
$804$	5.38366e23			0.108743
$805$	6.37416e24	−	3.51253e24i	1.27397	−	0.702030i
$806$	−4.14645e24			−0.820028
$807$		−	8.39819e24i		−	1.64347i
$808$			2.80269e24i			0.542723i
$809$	1.91465e24			0.366882			0.183441	−	0.983031i	$-0.441276\pi$
$809$	1.91465e24			0.366882			0.183441	+	0.983031i	$0.441276\pi$
$810$	−2.73428e24	−	4.96186e24i	−0.518465	−	0.940854i
$811$	−4.84935e24			−0.909927			−0.454964	−	0.890510i	$-0.650348\pi$
$811$	−4.84935e24			−0.909927			−0.454964	+	0.890510i	$0.650348\pi$
$812$		−	3.82228e24i		−	0.709735i
$813$			5.36559e24i			0.985933i
$814$	7.36891e22			0.0133997
$815$	−5.79665e23	−	1.05191e24i	−0.104313	−	0.189295i
$816$	−1.40384e24			−0.250006
$817$			1.74536e23i			0.0307608i
$818$		−	5.86332e23i		−	0.102268i
$819$	−2.46524e25			−4.25546
$820$	−2.84875e24	+	1.56983e24i	−0.486673	+	0.268185i
$821$	2.84679e24			0.481326			0.240663	−	0.970609i	$-0.422635\pi$
$821$	2.84679e24			0.481326			0.240663	+	0.970609i	$0.422635\pi$
$822$		−	8.89190e23i		−	0.148794i
$823$			9.76200e24i			1.61674i	0.588674	+	0.808370i	$0.299650\pi$
$823$			9.76200e24i			1.61674i	−0.588674	+	0.808370i	$0.700350\pi$
$824$	−1.90401e23			−0.0312095
$825$	6.50526e24	+	4.11012e24i	1.05537	+	0.666801i
$826$	3.89565e24			0.625532
$827$		−	4.92807e24i		−	0.783213i	−0.920133	−	0.391607i	$-0.871919\pi$
$827$		−	4.92807e24i		−	0.783213i	0.920133	−	0.391607i	$-0.128081\pi$
$828$		−	8.65587e24i		−	1.36161i
$829$	−2.49105e24			−0.387854			−0.193927	−	0.981016i	$-0.562123\pi$
$829$	−2.49105e24			−0.387854			−0.193927	+	0.981016i	$0.562123\pi$
$830$	3.84661e24	−	2.11971e24i	0.592809	−	0.326672i
$831$	2.11772e25			3.23042
$832$		−	1.40829e24i		−	0.212640i
$833$		−	1.26461e24i		−	0.189006i
$834$	1.48413e25			2.19564
$835$	−2.14104e24	−	3.88533e24i	−0.313538	−	0.568974i
$836$	1.12469e24			0.163034
$837$		−	9.83759e24i		−	1.41163i
$838$			2.55783e24i			0.363327i
$839$	−9.44495e23			−0.132808			−0.0664038	−	0.997793i	$-0.521153\pi$
$839$	−9.44495e23			−0.132808			−0.0664038	+	0.997793i	$0.521153\pi$
$840$	2.52060e24	+	4.57410e24i	0.350856	+	0.636695i
$841$	3.68616e24			0.507935
$842$			6.20341e24i			0.846210i
$843$		−	8.71654e24i		−	1.17709i
$844$	−2.14504e24			−0.286764
$845$	1.25325e25	−	6.90612e24i	1.65865	−	0.914012i
$846$	−2.37761e24			−0.311525
$847$			4.52218e24i			0.586596i
$848$		−	2.62434e24i		−	0.337019i
$849$	−1.02936e25			−1.30874
$850$	−1.68688e24	+	2.66989e24i	−0.212336	+	0.336072i
$851$	−2.72646e23			−0.0339780
$852$			1.26318e25i			1.55857i
$853$			1.00068e25i			1.22244i	0.791460	+	0.611221i	$0.209321\pi$
$853$			1.00068e25i			1.22244i	−0.791460	+	0.611221i	$0.790679\pi$
$854$	−3.87120e24			−0.468223
$855$	−7.35353e24	+	4.05222e24i	−0.880610	+	0.485268i
$856$	−2.89228e24			−0.342936
$857$			1.02788e25i			1.20671i	0.797472	+	0.603356i	$0.206170\pi$
$857$			1.02788e25i			1.20671i	−0.797472	+	0.603356i	$0.793830\pi$
$858$		−	1.29183e25i		−	1.50164i
$859$	9.78146e24			1.12580			0.562900	−	0.826525i	$-0.309685\pi$
$859$	9.78146e24			1.12580			0.562900	+	0.826525i	$0.309685\pi$
$860$	−1.40194e23	−	2.54409e23i	−0.0159769	−	0.0289931i
$861$	−2.02505e25			−2.28512
$862$		−	9.57634e23i		−	0.107001i
$863$		−	1.30891e25i		−	1.44816i	−0.689715	−	0.724081i	$-0.742264\pi$
$863$		−	1.30891e25i		−	1.44816i	0.689715	−	0.724081i	$-0.257736\pi$
$864$	3.34123e24			0.366049
$865$	−6.55721e24	−	1.18993e25i	−0.711348	−	1.29088i
$866$	7.68707e24			0.825770
$867$			1.14368e25i			1.21658i
$868$			3.74051e24i			0.394015i
$869$	−6.90075e24			−0.719827
$870$	−1.30958e25	+	7.21655e24i	−1.35275	+	0.745445i
$871$	−2.03327e24			−0.207990
$872$		−	5.33190e24i		−	0.540122i
$873$		−	1.01530e25i		−	1.01853i
$874$	−4.16129e24			−0.413410
$875$	1.17280e25	+	7.02524e23i	1.15387	+	0.0691183i
$876$	8.04314e24			0.783684
$877$		−	9.63915e22i		−	0.00930127i	−0.999989	−	0.00465063i	$-0.998520\pi$
$877$		−	9.63915e22i		−	0.00930127i	0.999989	−	0.00465063i	$-0.00148035\pi$
$878$			1.24951e25i			1.19409i
$879$	−1.29180e25			−1.22261
$880$	−1.63938e24	+	9.03393e23i	−0.153665	+	0.0846787i
$881$	−1.24804e25			−1.15859			−0.579297	−	0.815116i	$-0.696673\pi$
$881$	−1.24804e25			−1.15859			−0.579297	+	0.815116i	$0.696673\pi$
$882$			5.59544e24i			0.514459i
$883$			1.82649e25i			1.66322i	0.555359	+	0.831611i	$0.312581\pi$
$883$			1.82649e25i			1.66322i	−0.555359	+	0.831611i	$0.687419\pi$
$884$	5.30195e24			0.478180
$885$	−7.35508e24	−	1.33472e25i	−0.657006	−	1.19226i
$886$	−2.26733e23			−0.0200599
$887$		−	9.15990e24i		−	0.802675i	−0.915930	−	0.401338i	$-0.868545\pi$
$887$		−	9.15990e24i		−	0.802675i	0.915930	−	0.401338i	$-0.131455\pi$
$888$		−	1.95651e23i		−	0.0169813i
$889$	1.44926e25			1.24590
$890$	2.65393e24	+	4.81606e24i	0.225982	+	0.410088i
$891$	1.26415e25			1.06620
$892$			3.23941e24i			0.270623i
$893$			1.14303e24i			0.0945847i
$894$	1.12461e25			0.921791
$895$	−5.12826e24	+	2.82597e24i	−0.416365	+	0.229441i
$896$	−1.27042e24			−0.102171
$897$			4.77972e25i			3.80773i
$898$		−	2.75424e20i		−	2.17346e-5i
$899$	−1.07092e25			−0.837143
$900$	7.46380e24	−	1.18133e25i	0.577961	−	0.914762i
$901$	9.88011e24			0.757881
$902$		−	7.25788e24i		−	0.551511i
$903$		−	1.80848e24i		−	0.136134i
$904$	5.15516e24			0.384424
$905$	−1.06540e25	+	5.87100e24i	−0.787048	+	0.433709i
$906$	−9.41144e24			−0.688758
$907$		−	2.04267e25i		−	1.48093i	−0.672092	−	0.740467i	$-0.734604\pi$
$907$		−	2.04267e25i		−	1.48093i	0.672092	−	0.740467i	$-0.265396\pi$
$908$		−	6.69728e24i		−	0.481026i
$909$	4.66867e25			3.32200
$910$	−9.51966e24	−	1.72752e25i	−0.671073	−	1.21779i
$911$	7.78026e24			0.543360			0.271680	−	0.962388i	$-0.412421\pi$
$911$	7.78026e24			0.543360			0.271680	+	0.962388i	$0.412421\pi$
$912$		−	2.98615e24i		−	0.206612i
$913$			9.80017e24i			0.671788i
$914$	1.10161e24			0.0748141
$915$	7.30890e24	+	1.32634e25i	0.491782	+	0.892432i
$916$	−1.14594e25			−0.763923
$917$		−	4.66617e24i		−	0.308192i
$918$			1.25791e25i			0.823162i
$919$	1.92668e25			1.24919			0.624594	−	0.780949i	$-0.285264\pi$
$919$	1.92668e25			1.24919			0.624594	+	0.780949i	$0.285264\pi$
$920$	6.06561e24	−	3.34251e24i	0.389653	−	0.214722i
$921$	−5.35877e25			−3.41082
$922$		−	8.91018e24i		−	0.561919i
$923$		−	4.77070e25i		−	2.98104i
$924$	−1.16536e25			−0.721521
$925$	−3.72098e23	−	2.35098e23i	−0.0228272	−	0.0144226i
$926$	−5.28796e23			−0.0321436
$927$			3.17166e24i			0.191033i
$928$		−	3.63726e24i		−	0.217078i
$929$	−1.92204e25			−1.13666			−0.568328	−	0.822802i	$-0.692410\pi$
$929$	−1.92204e25			−1.13666			−0.568328	+	0.822802i	$0.692410\pi$
$930$	1.28156e25	−	7.06217e24i	0.750992	−	0.413840i
$931$	2.69000e24			0.156199
$932$		−	7.99827e24i		−	0.460215i
$933$		−	4.39999e25i		−	2.50875i
$934$	−5.82906e24			−0.329344
$935$	−3.40110e24	−	6.17193e24i	−0.190423	−	0.345559i
$936$	−2.34591e25			−1.30157
$937$			2.49742e25i			1.37311i	0.727079	+	0.686554i	$0.240878\pi$
$937$			2.49742e25i			1.37311i	−0.727079	+	0.686554i	$0.759122\pi$
$938$			1.83421e24i			0.0999370i
$939$	1.30813e24			0.0706304
$940$	−9.18126e23	−	1.66611e24i	−0.0491265	−	0.0891493i
$941$	2.13047e25			1.12970			0.564851	−	0.825193i	$-0.308934\pi$
$941$	2.13047e25			1.12970			0.564851	+	0.825193i	$0.308934\pi$
$942$			3.48462e25i			1.83115i
$943$			2.68538e25i			1.39848i
$944$	3.70708e24			0.191324
$945$	4.09860e25	−	2.25857e25i	2.09636	−	1.15522i
$946$	6.48167e23			0.0328558
$947$			1.70570e25i			0.856893i	0.903567	+	0.428447i	$0.140939\pi$
$947$			1.70570e25i			0.856893i	−0.903567	+	0.428447i	$0.859061\pi$
$948$			1.83221e25i			0.912229i
$949$	−3.03769e25			−1.49893
$950$	−5.67920e24	−	3.58821e24i	−0.277739	−	0.175480i
$951$	6.48688e25			3.14414
$952$		−	4.78289e24i		−	0.229761i
$953$		−	6.64867e24i		−	0.316552i	−0.987395	−	0.158276i	$-0.949406\pi$
$953$		−	6.64867e24i		−	0.316552i	0.987395	−	0.158276i	$-0.0505935\pi$
$954$	−4.37157e25			−2.06289
$955$	1.43854e24	−	7.92721e23i	0.0672813	−	0.0370759i
$956$	1.33330e25			0.618069
$957$		−	3.33647e25i		−	1.53298i
$958$		−	7.42929e24i		−	0.338330i
$959$	3.02947e24			0.136744
$960$	2.39858e24	+	4.35269e24i	0.107312	+	0.194738i
$961$	−1.20700e25			−0.535253
$962$			7.38924e23i			0.0324797i
$963$			4.81791e25i			2.09911i
$964$	1.40958e25			0.608743
$965$	−8.80904e23	−	1.59857e24i	−0.0377091	−	0.0684303i
$966$	4.31178e25			1.82958
$967$		−	1.05112e25i		−	0.442105i	−0.975262	−	0.221052i	$-0.929051\pi$
$967$		−	1.05112e25i		−	0.442105i	0.975262	−	0.221052i	$-0.0709492\pi$
$968$			4.30328e24i			0.179415i
$969$	1.12423e25			0.464624
$970$	7.11471e24	−	3.92062e24i	0.291472	−	0.160618i
$971$	−2.13371e25			−0.866507			−0.433254	−	0.901272i	$-0.642635\pi$
$971$	−2.13371e25			−0.866507			−0.433254	+	0.901272i	$0.642635\pi$
$972$		−	7.84576e24i		−	0.315843i
$973$			5.05645e25i			2.01784i
$974$	−6.86266e24			−0.271482
$975$	−4.12146e25	+	6.52320e25i	−1.61626	+	2.55812i
$976$	−3.68381e24			−0.143210
$977$			1.33440e25i			0.514260i	0.966377	+	0.257130i	$0.0827768\pi$
$977$			1.33440e25i			0.514260i	−0.966377	+	0.257130i	$0.917223\pi$
$978$		−	7.11563e24i		−	0.271852i
$979$	−1.22701e25			−0.464723
$980$	−3.92101e24	+	2.16071e24i	−0.147223	+	0.0811286i
$981$	−8.88179e25			−3.30608
$982$		−	2.53068e25i		−	0.933878i
$983$		−	1.31969e25i		−	0.482800i	−0.970426	−	0.241400i	$-0.922393\pi$
$983$		−	1.31969e25i		−	0.482800i	0.970426	−	0.241400i	$-0.0776066\pi$
$984$	−1.92703e25			−0.698924
$985$	1.31162e24	+	2.38018e24i	0.0471627	+	0.0855857i
$986$	1.36936e25			0.488161
$987$		−	1.18437e25i		−	0.418592i
$988$			1.12779e25i			0.395180i
$989$	−2.39818e24			−0.0833132
$990$	1.50486e25	+	2.73085e25i	0.518317	+	0.940585i
$991$	4.80007e25			1.63916			0.819580	−	0.572964i	$-0.194207\pi$
$991$	4.80007e25			1.63916			0.819580	+	0.572964i	$0.194207\pi$
$992$			3.55945e24i			0.120513i
$993$		−	9.28211e25i		−	3.11586i
$994$	−4.30364e25			−1.43236
$995$	−2.21919e25	+	1.22290e25i	−0.732316	+	0.403549i
$996$	2.60203e25			0.851349
$997$		−	1.30477e25i		−	0.423276i	−0.977348	−	0.211638i	$-0.932120\pi$
$997$		−	1.30477e25i		−	0.423276i	0.977348	−	0.211638i	$-0.0678799\pi$
$998$		−	3.09100e25i		−	0.994234i
$999$	−1.75312e24			−0.0559121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.18.b.a.9.8	yes	8
3.2	odd	2		90.18.c.b.19.4		8
4.3	odd	2		80.18.c.a.49.1		8
5.2	odd	4		50.18.a.j.1.4		4
5.3	odd	4		50.18.a.k.1.1		4
5.4	even	2	inner	10.18.b.a.9.1	✓	8
15.14	odd	2		90.18.c.b.19.8		8
20.19	odd	2		80.18.c.a.49.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.b.a.9.1	✓	8	5.4	even	2	inner
10.18.b.a.9.8	yes	8	1.1	even	1	trivial
50.18.a.j.1.4		4	5.2	odd	4
50.18.a.k.1.1		4	5.3	odd	4
80.18.c.a.49.1		8	4.3	odd	2
80.18.c.a.49.8		8	20.19	odd	2
90.18.c.b.19.4		8	3.2	odd	2
90.18.c.b.19.8		8	15.14	odd	2

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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:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+256.000i q^{2} +20214.2i q^{3} -65536.0 q^{4} +(-765001. + 421560. i) q^{5} -5.17482e6 q^{6} -1.76306e7i q^{7} -1.67772e7i q^{8} -2.79472e8 q^{9} +O(q^{10})\)	\(q+256.000i q^{2} +20214.2i q^{3} -65536.0 q^{4} +(-765001. + 421560. i) q^{5} -5.17482e6 q^{6} -1.76306e7i q^{7} -1.67772e7i q^{8} -2.79472e8 q^{9} +(-1.07919e8 - 1.95840e8i) q^{10} +4.98950e8 q^{11} -1.32475e9i q^{12} +5.00327e9i q^{13} +4.51344e9 q^{14} +(-8.52148e9 - 1.54638e10i) q^{15} +4.29497e9 q^{16} +1.61697e10i q^{17} -7.15448e10i q^{18} -3.43950e10 q^{19} +(5.01351e10 - 2.76274e10i) q^{20} +3.56388e11 q^{21} +1.27731e11i q^{22} -4.72599e11i q^{23} +3.39137e11 q^{24} +(4.07513e11 - 6.44988e11i) q^{25} -1.28084e12 q^{26} -3.03883e12i q^{27} +1.15544e12i q^{28} -3.30807e12 q^{29} +(3.95874e12 - 2.18150e12i) q^{30} +3.23730e12 q^{31} +1.09951e12i q^{32} +1.00859e13i q^{33} -4.13944e12 q^{34} +(7.43238e12 + 1.34875e13i) q^{35} +1.83155e13 q^{36} -5.76908e11i q^{37} -8.80513e12i q^{38} -1.01137e14 q^{39} +(7.07261e12 + 1.28346e13i) q^{40} -5.68215e13 q^{41} +9.12354e13i q^{42} -5.07446e12i q^{43} -3.26992e13 q^{44} +(2.13796e14 - 1.17814e14i) q^{45} +1.20985e14 q^{46} -3.32325e13i q^{47} +8.68191e13i q^{48} -7.82089e13 q^{49} +(1.65117e14 + 1.04323e14i) q^{50} -3.26857e14 q^{51} -3.27894e14i q^{52} -6.11026e14i q^{53} +7.77940e14 q^{54} +(-3.81697e14 + 2.10338e14i) q^{55} -2.95793e14 q^{56} -6.95266e14i q^{57} -8.46865e14i q^{58} +8.63122e14 q^{59} +(5.58464e14 + 1.01344e15i) q^{60} -8.57703e14 q^{61} +8.28749e14i q^{62} +4.92727e15i q^{63} -2.81475e14 q^{64} +(-2.10918e15 - 3.82751e15i) q^{65} -2.58198e15 q^{66} +4.06389e14i q^{67} -1.05970e15i q^{68} +9.55319e15 q^{69} +(-3.45279e15 + 1.90269e15i) q^{70} -9.53517e15 q^{71} +4.68876e15i q^{72} +6.07142e15i q^{73} +1.47688e14 q^{74} +(1.30379e16 + 8.23754e15i) q^{75} +2.25411e15 q^{76} -8.79681e15i q^{77} -2.58910e16i q^{78} -1.38305e16 q^{79} +(-3.28565e15 + 1.81059e15i) q^{80} +2.53363e16 q^{81} -1.45463e16i q^{82} +1.96416e16i q^{83} -2.33563e16 q^{84} +(-6.81651e15 - 1.23698e16i) q^{85} +1.29906e15 q^{86} -6.68698e16i q^{87} -8.37099e15i q^{88} -2.45918e16 q^{89} +(3.01604e16 + 5.47318e16i) q^{90} +8.82108e16 q^{91} +3.09722e16i q^{92} +6.54393e16i q^{93} +8.50752e15 q^{94} +(2.63122e16 - 1.44996e16i) q^{95} -2.22257e16 q^{96} +3.63292e16i q^{97} -2.00215e16i q^{98} -1.39443e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 524288 q^{4} - 1225560 q^{5} - 974848 q^{6} - 363182504 q^{9}+O(q^{10}) \) 8 * q - 524288 * q^4 - 1225560 * q^5 - 974848 * q^6 - 363182504 * q^9	\( 8 q - 524288 q^{4} - 1225560 q^{5} - 974848 q^{6} - 363182504 q^{9} - 140779520 q^{10} + 146232096 q^{11} + 14260494336 q^{14} - 39815002720 q^{15} + 34359738368 q^{16} - 54264178080 q^{19} + 80318300160 q^{20} + 515442333056 q^{21} + 63887638528 q^{24} + 1013225778600 q^{25} - 2693383569408 q^{26} + 1660243083120 q^{29} + 4536489205760 q^{30} - 6055476993664 q^{31} + 14158246445056 q^{34} - 8725233780960 q^{35} + 23801528582144 q^{36} - 60047234232768 q^{39} + 9226126622720 q^{40} - 219921829971984 q^{41} - 9583466643456 q^{44} + 503517880841080 q^{45} - 136753191067648 q^{46} + 797208944041464 q^{49} + 535409908531200 q^{50} - 26\!\cdots\!24 q^{51}+ \cdots - 23\!\cdots\!48 q^{99}+O(q^{100}) \) 8 * q - 524288 * q^4 - 1225560 * q^5 - 974848 * q^6 - 363182504 * q^9 - 140779520 * q^10 + 146232096 * q^11 + 14260494336 * q^14 - 39815002720 * q^15 + 34359738368 * q^16 - 54264178080 * q^19 + 80318300160 * q^20 + 515442333056 * q^21 + 63887638528 * q^24 + 1013225778600 * q^25 - 2693383569408 * q^26 + 1660243083120 * q^29 + 4536489205760 * q^30 - 6055476993664 * q^31 + 14158246445056 * q^34 - 8725233780960 * q^35 + 23801528582144 * q^36 - 60047234232768 * q^39 + 9226126622720 * q^40 - 219921829971984 * q^41 - 9583466643456 * q^44 + 503517880841080 * q^45 - 136753191067648 * q^46 + 797208944041464 * q^49 + 535409908531200 * q^50 - 2629370351530624 * q^51 + 1870704820633600 * q^54 + 1370380127176480 * q^55 - 934575756804096 * q^56 - 155410557761760 * q^59 + 2609316018257920 * q^60 - 6350444068968944 * q^61 - 2251799813685248 * q^64 + 10508144084782080 * q^65 - 10180424127512576 * q^66 + 20821360231259392 * q^69 - 1051117677240320 * q^70 - 33149026543733184 * q^71 + 6017648345726976 * q^74 + 17427320439323200 * q^75 + 3556257174650880 * q^76 - 19354668791708160 * q^79 - 5263740119285760 * q^80 + 54432374624835848 * q^81 - 33780028739158016 * q^84 - 71530234876895360 * q^85 + 29616028444434432 * q^86 - 43569230299558320 * q^89 - 33153706682736640 * q^90 + 333420307889971776 * q^91 - 11440296922292224 * q^94 - 131478039235197600 * q^95 - 4186940278571008 * q^96 - 236681336419250848 * q^99

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