LMFDB - Embedded newform 10.18.b.a.9.2

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			9.2
Root			$6.46999i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.18.b.a.9.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-256.000i q^{2} -2973.91i q^{3} -65536.0 q^{4} +(855091. - 178210. i) q^{5} -761320. q^{6} +7.58343e6i q^{7} +1.67772e7i q^{8} +1.20296e8 q^{9} +O(q^{10})$	\(q-256.000i q^{2} -2973.91i q^{3} -65536.0 q^{4} +(855091. - 178210. i) q^{5} -761320. q^{6} +7.58343e6i q^{7} +1.67772e7i q^{8} +1.20296e8 q^{9} +(-4.56218e7 - 2.18903e8i) q^{10} +6.04893e8 q^{11} +1.94898e8i q^{12} +1.32682e9i q^{13} +1.94136e9 q^{14} +(-5.29980e8 - 2.54296e9i) q^{15} +4.29497e9 q^{16} -3.25122e10i q^{17} -3.07958e10i q^{18} -1.67948e10 q^{19} +(-5.60392e10 + 1.16792e10i) q^{20} +2.25524e10 q^{21} -1.54853e11i q^{22} -7.14069e11i q^{23} +4.98939e10 q^{24} +(6.99422e11 - 3.04772e11i) q^{25} +3.39665e11 q^{26} -7.41800e11i q^{27} -4.96988e11i q^{28} +1.25241e12 q^{29} +(-6.50998e11 + 1.35675e11i) q^{30} -1.26092e12 q^{31} -1.09951e12i q^{32} -1.79889e12i q^{33} -8.32313e12 q^{34} +(1.35144e12 + 6.48452e12i) q^{35} -7.88372e12 q^{36} +3.37394e13i q^{37} +4.29946e12i q^{38} +3.94583e12 q^{39} +(2.98987e12 + 1.43460e13i) q^{40} +3.95012e13 q^{41} -5.77342e12i q^{42} +8.15984e13i q^{43} -3.96422e13 q^{44} +(1.02864e14 - 2.14380e13i) q^{45} -1.82802e14 q^{46} -1.28862e14i q^{47} -1.27728e13i q^{48} +1.75122e14 q^{49} +(-7.80216e13 - 1.79052e14i) q^{50} -9.66883e13 q^{51} -8.69542e13i q^{52} -4.11135e14i q^{53} -1.89901e14 q^{54} +(5.17238e14 - 1.07798e14i) q^{55} -1.27229e14 q^{56} +4.99461e13i q^{57} -3.20617e14i q^{58} +1.32582e15 q^{59} +(3.47328e13 + 1.66655e14i) q^{60} -1.20106e15 q^{61} +3.22795e14i q^{62} +9.12257e14i q^{63} -2.81475e14 q^{64} +(2.36452e14 + 1.13455e15i) q^{65} -4.60517e14 q^{66} +2.90250e15i q^{67} +2.13072e15i q^{68} -2.12357e15 q^{69} +(1.66004e15 - 3.45970e14i) q^{70} -7.20936e15 q^{71} +2.01823e15i q^{72} -4.16197e15i q^{73} +8.63730e15 q^{74} +(-9.06362e14 - 2.08001e15i) q^{75} +1.10066e15 q^{76} +4.58716e15i q^{77} -1.01013e15i q^{78} -4.74555e15 q^{79} +(3.67259e15 - 7.65407e14i) q^{80} +1.33290e16 q^{81} -1.01123e16i q^{82} -1.57327e16i q^{83} -1.47799e15 q^{84} +(-5.79401e15 - 2.78009e16i) q^{85} +2.08892e16 q^{86} -3.72455e15i q^{87} +1.01484e16i q^{88} -2.48196e16 q^{89} +(-5.48812e15 - 2.63332e16i) q^{90} -1.00618e16 q^{91} +4.67972e16i q^{92} +3.74985e15i q^{93} -3.29887e16 q^{94} +(-1.43611e16 + 2.99300e15i) q^{95} -3.26984e15 q^{96} +1.31140e17i q^{97} -4.48313e16i q^{98} +7.27662e16 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
$3$		−	2973.91i		−	0.261696i	−0.991402	−	0.130848i	$-0.958230\pi$
$3$		−	2973.91i		−	0.261696i	0.991402	−	0.130848i	$-0.0417699\pi$
$4$	−65536.0			−0.500000
$5$	855091.	−	178210.i	0.978965	−	0.204027i
$5$	855091.	−	178210.i	0.978965	−	0.204027i
$6$	−761320.			−0.185047
$7$			7.58343e6i			0.497201i	0.968606	+	0.248601i	$0.0799707\pi$
$7$			7.58343e6i			0.497201i	−0.968606	+	0.248601i	$0.920029\pi$
$8$			1.67772e7i			0.353553i
$9$	1.20296e8			0.931515
$10$	−4.56218e7	−	2.18903e8i	−0.144269	−	0.692233i
$11$	6.04893e8			0.850825			0.425413	−	0.904999i	$-0.360129\pi$
$11$	6.04893e8			0.850825			0.425413	+	0.904999i	$0.360129\pi$
$12$			1.94898e8i			0.130848i
$13$			1.32682e9i			0.451120i	0.974229	+	0.225560i	$0.0724212\pi$
$13$			1.32682e9i			0.451120i	−0.974229	+	0.225560i	$0.927579\pi$
$14$	1.94136e9			0.351575
$15$	−5.29980e8	−	2.54296e9i	−0.0533929	−	0.256191i
$16$	4.29497e9			0.250000
$17$		−	3.25122e10i		−	1.13040i	−0.824955	−	0.565198i	$-0.808800\pi$
$17$		−	3.25122e10i		−	1.13040i	0.824955	−	0.565198i	$-0.191200\pi$
$18$		−	3.07958e10i		−	0.658681i
$19$	−1.67948e10			−0.226865			−0.113433	−	0.993546i	$-0.536185\pi$
$19$	−1.67948e10			−0.226865			−0.113433	+	0.993546i	$0.536185\pi$
$20$	−5.60392e10	+	1.16792e10i	−0.489483	+	0.102013i
$21$	2.25524e10			0.130115
$22$		−	1.54853e11i		−	0.601624i
$23$		−	7.14069e11i		−	1.90131i	−0.310246	−	0.950656i	$-0.600411\pi$
$23$		−	7.14069e11i		−	1.90131i	0.310246	−	0.950656i	$-0.399589\pi$
$24$	4.98939e10			0.0925234
$25$	6.99422e11	−	3.04772e11i	0.916746	−	0.399470i
$26$	3.39665e11			0.318990
$27$		−	7.41800e11i		−	0.505469i
$28$		−	4.96988e11i		−	0.248601i
$29$	1.25241e12			0.464904			0.232452	−	0.972608i	$-0.425325\pi$
$29$	1.25241e12			0.464904			0.232452	+	0.972608i	$0.425325\pi$
$30$	−6.50998e11	+	1.35675e11i	−0.181154	+	0.0377545i
$31$	−1.26092e12			−0.265529			−0.132764	−	0.991148i	$-0.542385\pi$
$31$	−1.26092e12			−0.265529			−0.132764	+	0.991148i	$0.542385\pi$
$32$		−	1.09951e12i		−	0.176777i
$33$		−	1.79889e12i		−	0.222657i
$34$	−8.32313e12			−0.799311
$35$	1.35144e12	+	6.48452e12i	0.101442	+	0.486743i
$36$	−7.88372e12			−0.465758
$37$			3.37394e13i			1.57915i	0.613655	+	0.789575i	$0.289699\pi$
$37$			3.37394e13i			1.57915i	−0.613655	+	0.789575i	$0.710301\pi$
$38$			4.29946e12i			0.160418i
$39$	3.94583e12			0.118056
$40$	2.98987e12	+	1.43460e13i	0.0721344	+	0.346117i
$41$	3.95012e13			0.772588			0.386294	−	0.922376i	$-0.373755\pi$
$41$	3.95012e13			0.772588			0.386294	+	0.922376i	$0.373755\pi$
$42$		−	5.77342e12i		−	0.0920055i
$43$			8.15984e13i			1.06463i	0.846546	+	0.532316i	$0.178678\pi$
$43$			8.15984e13i			1.06463i	−0.846546	+	0.532316i	$0.821322\pi$
$44$	−3.96422e13			−0.425413
$45$	1.02864e14	−	2.14380e13i	0.911921	−	0.190054i
$46$	−1.82802e14			−1.34443
$47$		−	1.28862e14i		−	0.789392i	−0.918812	−	0.394696i	$-0.870850\pi$
$47$		−	1.28862e14i		−	0.789392i	0.918812	−	0.394696i	$-0.129150\pi$
$48$		−	1.27728e13i		−	0.0654239i
$49$	1.75122e14			0.752791
$50$	−7.80216e13	−	1.79052e14i	−0.282468	−	0.648237i
$51$	−9.66883e13			−0.295820
$52$		−	8.69542e13i		−	0.225560i
$53$		−	4.11135e14i		−	0.907067i	−0.891239	−	0.453533i	$-0.850163\pi$
$53$		−	4.11135e14i		−	0.907067i	0.891239	−	0.453533i	$-0.149837\pi$
$54$	−1.89901e14			−0.357421
$55$	5.17238e14	−	1.07798e14i	0.832929	−	0.173591i
$56$	−1.27229e14			−0.175787
$57$			4.99461e13i			0.0593697i
$58$		−	3.20617e14i		−	0.328737i
$59$	1.32582e15			1.17555			0.587777	−	0.809023i	$-0.300003\pi$
$59$	1.32582e15			1.17555			0.587777	+	0.809023i	$0.300003\pi$
$60$	3.47328e13	+	1.66655e14i	0.0266965	+	0.128096i
$61$	−1.20106e15			−0.802161			−0.401080	−	0.916043i	$-0.631365\pi$
$61$	−1.20106e15			−0.802161			−0.401080	+	0.916043i	$0.631365\pi$
$62$			3.22795e14i			0.187757i
$63$			9.12257e14i			0.463151i
$64$	−2.81475e14			−0.125000
$65$	2.36452e14	+	1.13455e15i	0.0920406	+	0.441631i
$66$	−4.60517e14			−0.157443
$67$			2.90250e15i			0.873246i	0.899645	+	0.436623i	$0.143826\pi$
$67$			2.90250e15i			0.873246i	−0.899645	+	0.436623i	$0.856174\pi$
$68$			2.13072e15i			0.565198i
$69$	−2.12357e15			−0.497565
$70$	1.66004e15	−	3.45970e14i	0.344179	−	0.0717306i
$71$	−7.20936e15			−1.32495			−0.662477	−	0.749082i	$-0.730495\pi$
$71$	−7.20936e15			−1.32495			−0.662477	+	0.749082i	$0.730495\pi$
$72$			2.01823e15i			0.329340i
$73$		−	4.16197e15i		−	0.604024i	−0.953304	−	0.302012i	$-0.902342\pi$
$73$		−	4.16197e15i		−	0.604024i	0.953304	−	0.302012i	$-0.0976583\pi$
$74$	8.63730e15			1.11663
$75$	−9.06362e14	−	2.08001e15i	−0.104540	−	0.239909i
$76$	1.10066e15			0.113433
$77$			4.58716e15i			0.423032i
$78$		−	1.01013e15i		−	0.0834783i
$79$	−4.74555e15			−0.351930			−0.175965	−	0.984396i	$-0.556305\pi$
$79$	−4.74555e15			−0.351930			−0.175965	+	0.984396i	$0.556305\pi$
$80$	3.67259e15	−	7.65407e14i	0.244741	−	0.0510067i
$81$	1.33290e16			0.799236
$82$		−	1.01123e16i		−	0.546302i
$83$		−	1.57327e16i		−	0.766724i	−0.923598	−	0.383362i	$-0.874766\pi$
$83$		−	1.57327e16i		−	0.766724i	0.923598	−	0.383362i	$-0.125234\pi$
$84$	−1.47799e15			−0.0650577
$85$	−5.79401e15	−	2.78009e16i	−0.230631	−	1.10662i
$86$	2.08892e16			0.752809
$87$		−	3.72455e15i		−	0.121663i
$88$			1.01484e16i			0.300812i
$89$	−2.48196e16			−0.668312			−0.334156	−	0.942518i	$-0.608451\pi$
$89$	−2.48196e16			−0.668312			−0.334156	+	0.942518i	$0.608451\pi$
$90$	−5.48812e15	−	2.63332e16i	−0.134389	−	0.644826i
$91$	−1.00618e16			−0.224298
$92$			4.67972e16i			0.950656i
$93$			3.74985e15i			0.0694878i
$94$	−3.29887e16			−0.558185
$95$	−1.43611e16	+	2.99300e15i	−0.222093	+	0.0462866i
$96$	−3.26984e15			−0.0462617
$97$			1.31140e17i			1.69893i	0.527645	+	0.849465i	$0.323075\pi$
$97$			1.31140e17i			1.69893i	−0.527645	+	0.849465i	$0.676925\pi$
$98$		−	4.48313e16i		−	0.532303i
$99$	7.27662e16			0.792557
$100$	−4.58373e16	+	1.99735e16i	−0.458373	+	0.199735i
$101$	1.40289e17			1.28912			0.644560	−	0.764554i	$-0.277041\pi$
$101$	1.40289e17			1.28912			0.644560	+	0.764554i	$0.277041\pi$
$102$			2.47522e16i			0.209176i
$103$		−	2.25271e16i		−	0.175222i	−0.996155	−	0.0876110i	$-0.972077\pi$
$103$		−	2.25271e16i		−	0.175222i	0.996155	−	0.0876110i	$-0.0279233\pi$
$104$	−2.22603e16			−0.159495
$105$	1.92844e16	−	4.01907e15i	0.127379	−	0.0265470i
$106$	−1.05250e17			−0.641393
$107$			2.96635e17i			1.66902i	0.550995	+	0.834509i	$0.314248\pi$
$107$			2.96635e17i			1.66902i	−0.550995	+	0.834509i	$0.685752\pi$
$108$			4.86146e16i			0.252735i
$109$	−1.00693e17			−0.484032			−0.242016	−	0.970272i	$-0.577809\pi$
$109$	−1.00693e17			−0.484032			−0.242016	+	0.970272i	$0.577809\pi$
$110$	−2.75963e16	−	1.32413e17i	−0.122748	−	0.588969i
$111$	1.00338e17			0.413257
$112$			3.25706e16i			0.124300i
$113$		−	2.91587e17i		−	1.03181i	−0.856645	−	0.515906i	$-0.827455\pi$
$113$		−	2.91587e17i		−	1.03181i	0.856645	−	0.515906i	$-0.172545\pi$
$114$	1.27862e16			0.0419807
$115$	−1.27254e17	−	6.10594e17i	−0.387919	−	1.86132i
$116$	−8.20779e16			−0.232452
$117$			1.59611e17i			0.420225i
$118$		−	3.39410e17i		−	0.831242i
$119$	2.46554e17			0.562035
$120$	4.26638e16	−	8.89159e15i	0.0905772	−	0.0188773i
$121$	−1.39552e17			−0.276096
$122$			3.07472e17i			0.567213i
$123$		−	1.17473e17i		−	0.202183i
$124$	8.26354e16			0.132764
$125$	5.43756e17	−	3.85252e17i	0.815960	−	0.578108i
$126$	2.33538e17			0.327497
$127$			6.72025e17i			0.881158i	0.897714	+	0.440579i	$0.145227\pi$
$127$			6.72025e17i			0.881158i	−0.897714	+	0.440579i	$0.854773\pi$
$128$			7.20576e16i			0.0883883i
$129$	2.42666e17			0.278610
$130$	2.90444e17	−	6.05317e16i	0.312280	−	0.0650825i
$131$	−1.65072e18			−1.66290			−0.831452	−	0.555596i	$-0.812490\pi$
$131$	−1.65072e18			−1.66290			−0.831452	+	0.555596i	$0.812490\pi$
$132$			1.17892e17i			0.111329i
$133$		−	1.27362e17i		−	0.112798i
$134$	7.43040e17			0.617478
$135$	−1.32196e17	−	6.34306e17i	−0.103129	−	0.494837i
$136$	5.45465e17			0.399656
$137$			2.53057e18i			1.74218i	0.491123	+	0.871090i	$0.336586\pi$
$137$			2.53057e18i			1.74218i	−0.491123	+	0.871090i	$0.663414\pi$
$138$			5.43635e17i			0.351832i
$139$	−2.77639e18			−1.68987			−0.844937	−	0.534865i	$-0.820362\pi$
$139$	−2.77639e18			−1.68987			−0.844937	+	0.534865i	$0.820362\pi$
$140$	−8.85682e16	−	4.24970e17i	−0.0507212	−	0.243371i
$141$	−3.83223e17			−0.206581
$142$			1.84560e18i			0.936884i
$143$			8.02581e17i			0.383825i
$144$	5.16668e17			0.232879
$145$	1.07092e18	−	2.23192e17i	0.455125	−	0.0948529i
$146$	−1.06546e18			−0.427110
$147$		−	5.20797e17i		−	0.197002i
$148$		−	2.21115e18i		−	0.789575i
$149$	1.48993e18			0.502439			0.251220	−	0.967930i	$-0.419168\pi$
$149$	1.48993e18			0.502439			0.251220	+	0.967930i	$0.419168\pi$
$150$	−5.32484e17	+	2.32029e17i	−0.169641	+	0.0739207i
$151$	2.85975e18			0.861040			0.430520	−	0.902581i	$-0.358330\pi$
$151$	2.85975e18			0.861040			0.430520	+	0.902581i	$0.358330\pi$
$152$		−	2.81769e17i		−	0.0802091i
$153$		−	3.91109e18i		−	1.05298i
$154$	1.17431e18			0.299129
$155$	−1.07820e18	+	2.24708e17i	−0.259944	+	0.0541750i
$156$	−2.58594e17			−0.0590281
$157$		−	1.39051e18i		−	0.300625i	−0.988638	−	0.150313i	$-0.951972\pi$
$157$		−	1.39051e18i		−	0.300625i	0.988638	−	0.150313i	$-0.0480281\pi$
$158$			1.21486e18i			0.248852i
$159$	−1.22268e18			−0.237375
$160$	−1.95944e17	−	9.40182e17i	−0.0360672	−	0.173058i
$161$	5.41509e18			0.945335
$162$		−	3.41223e18i		−	0.565145i
$163$		−	2.67461e18i		−	0.420404i	−0.977658	−	0.210202i	$-0.932588\pi$
$163$		−	2.67461e18i		−	0.420404i	0.977658	−	0.210202i	$-0.0674121\pi$
$164$	−2.58875e18			−0.386294
$165$	−3.20581e17	−	1.53822e18i	−0.0454281	−	0.217974i
$166$	−4.02757e18			−0.542155
$167$		−	2.09954e18i		−	0.268555i	−0.990944	−	0.134278i	$-0.957129\pi$
$167$		−	2.09954e18i		−	0.268555i	0.990944	−	0.134278i	$-0.0428714\pi$
$168$			3.78367e17i			0.0460028i
$169$	6.88997e18			0.796491
$170$	−7.11703e18	+	1.48327e18i	−0.782498	+	0.163081i
$171$	−2.02034e18			−0.211329
$172$		−	5.34763e18i		−	0.532316i
$173$			1.79690e19i			1.70268i	0.524616	+	0.851339i	$0.324209\pi$
$173$			1.79690e19i			1.70268i	−0.524616	+	0.851339i	$0.675791\pi$
$174$	−9.53484e17			−0.0860290
$175$	2.31121e18	+	5.30402e18i	0.198617	+	0.455807i
$176$	2.59799e18			0.212706
$177$		−	3.94287e18i		−	0.307638i
$178$			6.35382e18i			0.472568i
$179$	−2.38231e19			−1.68946			−0.844731	−	0.535191i	$-0.820240\pi$
$179$	−2.38231e19			−1.68946			−0.844731	+	0.535191i	$0.820240\pi$
$180$	−6.74130e18	+	1.40496e18i	−0.455961	+	0.0950271i
$181$	2.36044e19			1.52309			0.761546	−	0.648111i	$-0.224441\pi$
$181$	2.36044e19			1.52309			0.761546	+	0.648111i	$0.224441\pi$
$182$			2.57583e18i			0.158602i
$183$			3.57184e18i			0.209922i
$184$	1.19801e19			0.672216
$185$	6.01271e18	+	2.88503e19i	0.322189	+	1.54593i
$186$	9.59961e17			0.0491353
$187$		−	1.96664e19i		−	0.961770i
$188$			8.44510e18i			0.394696i
$189$	5.62539e18			0.251320
$190$	7.66207e17	+	3.67643e18i	0.0327296	+	0.157044i
$191$	−3.29525e19			−1.34619			−0.673093	−	0.739558i	$-0.735035\pi$
$191$	−3.29525e19			−1.34619			−0.673093	+	0.739558i	$0.735035\pi$
$192$			8.37080e17i			0.0327120i
$193$		−	1.54581e19i		−	0.577989i	−0.957331	−	0.288995i	$-0.906679\pi$
$193$		−	1.54581e19i		−	0.577989i	0.957331	−	0.288995i	$-0.0933210\pi$
$194$	3.35718e19			1.20133
$195$	3.37404e18	−	7.03186e17i	0.115573	−	0.0240866i
$196$	−1.14768e19			−0.376395
$197$		−	2.38607e19i		−	0.749410i	−0.927144	−	0.374705i	$-0.877744\pi$
$197$		−	2.38607e19i		−	0.749410i	0.927144	−	0.374705i	$-0.122256\pi$
$198$		−	1.86281e19i		−	0.560422i
$199$	−5.01370e19			−1.44513			−0.722566	−	0.691302i	$-0.757037\pi$
$199$	−5.01370e19			−1.44513			−0.722566	+	0.691302i	$0.757037\pi$
$200$	5.11322e18	+	1.17344e19i	0.141234	+	0.324119i
$201$	8.63176e18			0.228525
$202$		−	3.59141e19i		−	0.911546i
$203$			9.49756e18i			0.231151i
$204$	6.33656e18			0.147910
$205$	3.37771e19	−	7.03952e18i	0.756336	−	0.157629i
$206$	−5.76694e18			−0.123901
$207$		−	8.58997e19i		−	1.77110i
$208$			5.69863e18i			0.112780i
$209$	−1.01590e19			−0.193023
$210$	−1.02888e18	−	4.93680e18i	−0.0187716	−	0.0900702i
$211$	−3.95410e19			−0.692862			−0.346431	−	0.938075i	$-0.612607\pi$
$211$	−3.95410e19			−0.692862			−0.346431	+	0.938075i	$0.612607\pi$
$212$			2.69441e19i			0.453533i
$213$			2.14400e19i			0.346735i
$214$	7.59387e19			1.18017
$215$	1.45417e19	+	6.97740e19i	0.217214	+	1.04224i
$216$	1.24453e19			0.178710
$217$		−	9.56207e18i		−	0.132021i
$218$			2.57774e19i			0.342263i
$219$	−1.23773e19			−0.158071
$220$	−3.38977e19	+	7.06465e18i	−0.416464	+	0.0867956i
$221$	4.31377e19			0.509945
$222$		−	2.56865e19i		−	0.292217i
$223$		−	1.28208e19i		−	0.140386i	−0.997533	−	0.0701929i	$-0.977639\pi$
$223$		−	1.28208e19i		−	0.140386i	0.997533	−	0.0701929i	$-0.0223615\pi$
$224$	8.33807e18			0.0878936
$225$	8.41377e19	−	3.66628e19i	0.853963	−	0.372113i
$226$	−7.46462e19			−0.729602
$227$			1.74756e20i			1.64517i	0.568639	+	0.822587i	$0.307470\pi$
$227$			1.74756e20i			1.64517i	−0.568639	+	0.822587i	$0.692530\pi$
$228$		−	3.27327e18i		−	0.0296849i
$229$	−5.58613e19			−0.488100			−0.244050	−	0.969763i	$-0.578476\pi$
$229$	−5.58613e19			−0.488100			−0.244050	+	0.969763i	$0.578476\pi$
$230$	−1.56312e20	+	3.25771e19i	−1.31615	+	0.274300i
$231$	1.36418e19			0.110706
$232$			2.10119e19i			0.164368i
$233$			1.93341e20i			1.45814i	0.684440	+	0.729069i	$0.260047\pi$
$233$			1.93341e20i			1.45814i	−0.684440	+	0.729069i	$0.739953\pi$
$234$	4.08603e19			0.297144
$235$	−2.29645e19	−	1.10189e20i	−0.161057	−	0.772788i
$236$	−8.68890e19			−0.587777
$237$			1.41128e19i			0.0920986i
$238$		−	6.31179e19i		−	0.397419i
$239$	−9.14253e19			−0.555500			−0.277750	−	0.960653i	$-0.589589\pi$
$239$	−9.14253e19			−0.555500			−0.277750	+	0.960653i	$0.589589\pi$
$240$	−2.27625e18	−	1.09219e19i	−0.0133482	−	0.0640478i
$241$	1.42371e20			0.805889			0.402945	−	0.915224i	$-0.367987\pi$
$241$	1.42371e20			0.805889			0.402945	+	0.915224i	$0.367987\pi$
$242$			3.57253e19i			0.195229i
$243$		−	1.35435e20i		−	0.714626i
$244$	7.87127e19			0.401080
$245$	1.49745e20	−	3.12085e19i	0.736956	−	0.153589i
$246$	−3.00731e19			−0.142965
$247$		−	2.22836e19i		−	0.102344i
$248$		−	2.11547e19i		−	0.0938786i
$249$	−4.67875e19			−0.200648
$250$	−9.86244e19	−	1.39202e20i	−0.408784	−	0.576971i
$251$	3.37128e20			1.35073			0.675364	−	0.737484i	$-0.263986\pi$
$251$	3.37128e20			1.35073			0.675364	+	0.737484i	$0.263986\pi$
$252$		−	5.97857e19i		−	0.231575i
$253$		−	4.31935e20i		−	1.61769i
$254$	1.72038e20			0.623073
$255$	−8.26773e19	+	1.72308e19i	−0.289597	+	0.0603552i
$256$	1.84467e19			0.0625000
$257$			3.29126e20i			1.07877i	0.842058	+	0.539387i	$0.181344\pi$
$257$			3.29126e20i			1.07877i	−0.842058	+	0.539387i	$0.818656\pi$
$258$		−	6.21225e19i		−	0.197007i
$259$	−2.55861e20			−0.785155
$260$	−1.54961e19	−	7.43538e19i	−0.0460203	−	0.220816i
$261$	1.50660e20			0.433065
$262$			4.22584e20i			1.17585i
$263$		−	1.11758e20i		−	0.301062i	−0.988605	−	0.150531i	$-0.951902\pi$
$263$		−	1.11758e20i		−	0.301062i	0.988605	−	0.150531i	$-0.0480984\pi$
$264$	3.01804e19			0.0787213
$265$	−7.32684e19	−	3.51558e20i	−0.185066	−	0.887987i
$266$	−3.26047e19			−0.0797601
$267$			7.38111e19i			0.174894i
$268$		−	1.90218e20i		−	0.436623i
$269$	−6.46127e20			−1.43689			−0.718445	−	0.695584i	$-0.755146\pi$
$269$	−6.46127e20			−1.43689			−0.718445	+	0.695584i	$0.755146\pi$
$270$	−1.62382e20	+	3.38422e19i	−0.349902	+	0.0729234i
$271$	−1.97364e20			−0.412125			−0.206063	−	0.978539i	$-0.566065\pi$
$271$	−1.97364e20			−0.412125			−0.206063	+	0.978539i	$0.566065\pi$
$272$		−	1.39639e20i		−	0.282599i
$273$			2.99229e19i			0.0586977i
$274$	6.47825e20			1.23191
$275$	4.23075e20	−	1.84354e20i	0.779991	−	0.339880i
$276$	1.39171e20			0.248783
$277$			8.57818e20i			1.48702i	0.668725	+	0.743510i	$0.266840\pi$
$277$			8.57818e20i			1.48702i	−0.668725	+	0.743510i	$0.733160\pi$
$278$			7.10756e20i			1.19492i
$279$	−1.51683e20			−0.247344
$280$	−1.08792e20	+	2.26735e19i	−0.172090	+	0.0358653i
$281$	−8.95650e20			−1.37447			−0.687234	−	0.726436i	$-0.741175\pi$
$281$	−8.95650e20			−1.37447			−0.687234	+	0.726436i	$0.741175\pi$
$282$			9.81052e19i			0.146075i
$283$			7.82868e20i			1.13111i	0.824712	+	0.565553i	$0.191337\pi$
$283$			7.82868e20i			1.13111i	−0.824712	+	0.565553i	$0.808663\pi$
$284$	4.72473e20			0.662477
$285$	8.90089e18	+	4.27084e19i	0.0121130	+	0.0581209i
$286$	2.05461e20			0.271405
$287$			2.99555e20i			0.384132i
$288$		−	1.32267e20i		−	0.164670i
$289$	−2.29804e20			−0.277796
$290$	−5.71371e19	−	2.74157e20i	−0.0670711	−	0.321822i
$291$	3.89998e20			0.444603
$292$			2.72759e20i			0.302012i
$293$		−	7.78207e20i		−	0.836991i	−0.908219	−	0.418495i	$-0.862558\pi$
$293$		−	7.78207e20i		−	0.836991i	0.908219	−	0.418495i	$-0.137442\pi$
$294$	−1.33324e20			−0.139302
$295$	1.13370e21	−	2.36275e20i	1.15083	−	0.239845i
$296$	−5.66054e20			−0.558314
$297$		−	4.48709e20i		−	0.430066i
$298$		−	3.81423e20i		−	0.355278i
$299$	9.47438e20			0.857720
$300$	5.93994e19	+	1.36316e20i	0.0522698	+	0.119954i
$301$	−6.18796e20			−0.529337
$302$		−	7.32095e20i		−	0.608847i
$303$		−	4.17208e20i		−	0.337357i
$304$	−7.21330e19			−0.0567164
$305$	−1.02702e21	+	2.14041e20i	−0.785288	+	0.163662i
$306$	−1.00124e21			−0.744571
$307$		−	6.36763e20i		−	0.460577i	−0.973122	−	0.230288i	$-0.926033\pi$
$307$		−	6.36763e20i		−	0.460577i	0.973122	−	0.230288i	$-0.0739669\pi$
$308$		−	3.00624e20i		−	0.211516i
$309$	−6.69935e19			−0.0458548
$310$	5.75252e19	+	2.76019e20i	0.0383075	+	0.183808i
$311$	1.01872e21			0.660069			0.330035	−	0.943969i	$-0.392940\pi$
$311$	1.01872e21			0.660069			0.330035	+	0.943969i	$0.392940\pi$
$312$			6.62000e19i			0.0417392i
$313$		−	2.74009e20i		−	0.168127i	−0.996460	−	0.0840636i	$-0.973210\pi$
$313$		−	2.74009e20i		−	0.168127i	0.996460	−	0.0840636i	$-0.0267899\pi$
$314$	−3.55970e20			−0.212574
$315$	1.62573e20	+	7.80063e20i	0.0944952	+	0.453409i
$316$	3.11004e20			0.175965
$317$		−	2.82884e21i		−	1.55814i	−0.626939	−	0.779068i	$-0.715693\pi$
$317$		−	2.82884e21i		−	1.55814i	0.626939	−	0.779068i	$-0.284307\pi$
$318$			3.13005e20i			0.167850i
$319$	7.57573e20			0.395552
$320$	−2.40687e20	+	5.01617e19i	−0.122371	+	0.0255034i
$321$	8.82166e20			0.436775
$322$		−	1.38626e21i		−	0.668453i
$323$			5.46035e20i			0.256448i
$324$	−8.73530e20			−0.399618
$325$	4.04376e20	+	9.28004e20i	0.180209	+	0.413563i
$326$	−6.84701e20			−0.297270
$327$			2.99452e20i			0.126669i
$328$			6.62720e20i			0.273151i
$329$	9.77216e20			0.392487
$330$	−3.93784e20	+	8.20687e19i	−0.154131	+	0.0321225i
$331$	4.45083e20			0.169786			0.0848931	−	0.996390i	$-0.472945\pi$
$331$	4.45083e20			0.169786			0.0848931	+	0.996390i	$0.472945\pi$
$332$			1.03106e21i			0.383362i
$333$			4.05872e21i			1.47100i
$334$	−5.37481e20			−0.189897
$335$	5.17255e20	+	2.48190e21i	0.178166	+	0.854877i
$336$	9.68619e19			0.0325289
$337$			8.92853e20i			0.292365i	0.989258	+	0.146183i	$0.0466987\pi$
$337$			8.92853e20i			0.292365i	−0.989258	+	0.146183i	$0.953301\pi$
$338$		−	1.76383e21i		−	0.563204i
$339$	−8.67151e20			−0.270021
$340$	3.79716e20	+	1.82196e21i	0.115316	+	0.553310i
$341$	−7.62719e20			−0.225919
$342$			5.17208e20i			0.149432i
$343$			3.09216e21i			0.871490i
$344$	−1.36899e21			−0.376404
$345$	−1.81585e21	+	3.78442e20i	−0.487099	+	0.101517i
$346$	4.60007e21			1.20397
$347$		−	6.64293e21i		−	1.69652i	−0.529579	−	0.848261i	$-0.677650\pi$
$347$		−	6.64293e21i		−	1.69652i	0.529579	−	0.848261i	$-0.322350\pi$
$348$			2.44092e20i			0.0608317i
$349$	−5.41147e21			−1.31613			−0.658066	−	0.752961i	$-0.728625\pi$
$349$	−5.41147e21			−1.31613			−0.658066	+	0.752961i	$0.728625\pi$
$350$	1.35783e21	−	5.91671e20i	0.322305	−	0.140444i
$351$	9.84232e20			0.228027
$352$		−	6.65086e20i		−	0.150406i
$353$		−	3.84234e21i		−	0.848225i	−0.905609	−	0.424113i	$-0.860586\pi$
$353$		−	3.84234e21i		−	0.848225i	0.905609	−	0.424113i	$-0.139414\pi$
$354$	−1.00937e21			−0.217533
$355$	−6.16466e21	+	1.28478e21i	−1.29708	+	0.270326i
$356$	1.62658e21			0.334156
$357$		−	7.33229e20i		−	0.147082i
$358$			6.09873e21i			1.19463i
$359$	7.97571e21			1.52569			0.762845	−	0.646581i	$-0.223802\pi$
$359$	7.97571e21			1.52569			0.762845	+	0.646581i	$0.223802\pi$
$360$	3.59669e20	+	1.72577e21i	0.0671943	+	0.322413i
$361$	−5.19832e21			−0.948532
$362$		−	6.04274e21i		−	1.07699i
$363$			4.15014e20i			0.0722532i
$364$	6.59411e20			0.112149
$365$	−7.41705e20	−	3.55886e21i	−0.123237	−	0.591319i
$366$	9.14392e20			0.148437
$367$		−	3.93242e21i		−	0.623733i	−0.950126	−	0.311866i	$-0.899046\pi$
$367$		−	3.93242e21i		−	0.623733i	0.950126	−	0.311866i	$-0.100954\pi$
$368$		−	3.06690e21i		−	0.475328i
$369$	4.75184e21			0.719677
$370$	7.38567e21	−	1.53925e21i	1.09314	−	0.227822i
$371$	3.11781e21			0.450995
$372$		−	2.45750e20i		−	0.0347439i
$373$		−	2.14982e21i		−	0.297082i	−0.988906	−	0.148541i	$-0.952542\pi$
$373$		−	2.14982e21i		−	0.297082i	0.988906	−	0.148541i	$-0.0474577\pi$
$374$	−5.03460e21			−0.680074
$375$	−1.14570e21	−	1.61708e21i	−0.151288	−	0.213533i
$376$	2.16194e21			0.279092
$377$			1.66172e21i			0.209728i
$378$		−	1.44010e21i		−	0.177710i
$379$	−2.31293e21			−0.279080			−0.139540	−	0.990216i	$-0.544562\pi$
$379$	−2.31293e21			−0.279080			−0.139540	+	0.990216i	$0.544562\pi$
$380$	9.41166e20	−	1.96149e20i	0.111047	−	0.0231433i
$381$	1.99854e21			0.230595
$382$			8.43585e21i			0.951898i
$383$		−	7.24934e21i		−	0.800034i	−0.916508	−	0.400017i	$-0.869004\pi$
$383$		−	7.24934e21i		−	0.800034i	0.916508	−	0.400017i	$-0.130996\pi$
$384$	2.14293e20			0.0231308
$385$	8.17478e20	+	3.92244e21i	0.0863098	+	0.414133i
$386$	−3.95728e21			−0.408700
$387$			9.81596e21i			0.991721i
$388$		−	8.59439e21i		−	0.849465i
$389$	1.22297e22			1.18261			0.591306	−	0.806447i	$-0.298612\pi$
$389$	1.22297e22			1.18261			0.591306	+	0.806447i	$0.298612\pi$
$390$	−1.80016e20	−	8.63754e20i	−0.0170318	−	0.0817224i
$391$	−2.32160e22			−2.14924
$392$			2.93806e21i			0.266152i
$393$			4.90909e21i			0.435175i
$394$	−6.10833e21			−0.529913
$395$	−4.05788e21	+	8.45705e20i	−0.344527	+	0.0718032i
$396$	−4.76880e21			−0.396278
$397$			7.39980e21i			0.601867i	0.953645	+	0.300934i	$0.0972983\pi$
$397$			7.39980e21i			0.601867i	−0.953645	+	0.300934i	$0.902702\pi$
$398$			1.28351e22i			1.02186i
$399$	−3.78763e20			−0.0295187
$400$	3.00399e21	−	1.30898e21i	0.229187	−	0.0998676i
$401$	2.64241e21			0.197366			0.0986832	−	0.995119i	$-0.468537\pi$
$401$	2.64241e21			0.197366			0.0986832	+	0.995119i	$0.468537\pi$
$402$		−	2.20973e21i		−	0.161591i
$403$		−	1.67300e21i		−	0.119785i
$404$	−9.19401e21			−0.644560
$405$	1.13975e22	−	2.37536e21i	0.782425	−	0.163066i
$406$	2.43138e21			0.163448
$407$			2.04087e22i			1.34358i
$408$		−	1.62216e21i		−	0.104588i
$409$	1.85381e22			1.17063			0.585313	−	0.810808i	$-0.300972\pi$
$409$	1.85381e22			1.17063			0.585313	+	0.810808i	$0.300972\pi$
$410$	−1.80212e21	−	8.64695e21i	−0.111460	−	0.534811i
$411$	7.52567e21			0.455921
$412$			1.47634e21i			0.0876110i
$413$			1.00543e22i			0.584487i
$414$	−2.19903e22			−1.25236
$415$	−2.80372e21	−	1.34529e22i	−0.156432	−	0.750596i
$416$	1.45885e21			0.0797475
$417$			8.25672e21i			0.442233i
$418$			2.60071e21i			0.136488i
$419$	1.33787e22			0.688010			0.344005	−	0.938968i	$-0.388216\pi$
$419$	1.33787e22			0.688010			0.344005	+	0.938968i	$0.388216\pi$
$420$	−1.26382e21	+	2.63394e20i	−0.0636893	+	0.0132735i
$421$	1.34296e22			0.663233			0.331616	−	0.943414i	$-0.392406\pi$
$421$	1.34296e22			0.663233			0.331616	+	0.943414i	$0.392406\pi$
$422$			1.01225e22i			0.489928i
$423$		−	1.55016e22i		−	0.735331i
$424$	6.89770e21			0.320697
$425$	−9.90881e21	−	2.27398e22i	−0.451560	−	1.03629i
$426$	5.48863e21			0.245179
$427$		−	9.10816e21i		−	0.398836i
$428$		−	1.94403e22i		−	0.834509i
$429$	2.38680e21			0.100445
$430$	1.78622e22	−	3.72266e21i	0.736974	−	0.153593i
$431$	−2.93523e22			−1.18737			−0.593685	−	0.804698i	$-0.702327\pi$
$431$	−2.93523e22			−1.18737			−0.593685	+	0.804698i	$0.702327\pi$
$432$		−	3.18601e21i		−	0.126367i
$433$		−	2.26238e22i		−	0.879870i	−0.898030	−	0.439935i	$-0.855002\pi$
$433$		−	2.26238e22i		−	0.879870i	0.898030	−	0.439935i	$-0.144998\pi$
$434$	−2.44789e21			−0.0933532
$435$	−6.63752e20	−	3.18483e21i	−0.0248226	−	0.119104i
$436$	6.59902e21			0.242016
$437$			1.19926e22i			0.431342i
$438$			3.16859e21i			0.111773i
$439$	−4.27977e22			−1.48072			−0.740359	−	0.672211i	$-0.765345\pi$
$439$	−4.27977e22			−1.48072			−0.740359	+	0.672211i	$0.765345\pi$
$440$	1.80855e21	+	8.67782e21i	0.0613738	+	0.294485i
$441$	2.10665e22			0.701236
$442$		−	1.10433e22i		−	0.360585i
$443$			6.70939e20i			0.0214908i	0.999942	+	0.0107454i	$0.00342043\pi$
$443$			6.70939e20i			0.0214908i	−0.999942	+	0.0107454i	$0.996580\pi$
$444$	−6.57575e21			−0.206628
$445$	−2.12230e22	+	4.42310e21i	−0.654255	+	0.136354i
$446$	−3.28212e21			−0.0992678
$447$		−	4.43092e21i		−	0.131486i
$448$		−	2.13455e21i		−	0.0621502i
$449$	1.57543e22			0.450096			0.225048	−	0.974348i	$-0.427746\pi$
$449$	1.57543e22			0.450096			0.225048	+	0.974348i	$0.427746\pi$
$450$	−9.38568e21	−	2.15392e22i	−0.263123	−	0.603843i
$451$	2.38940e22			0.657337
$452$			1.91094e22i			0.515906i
$453$		−	8.50462e21i		−	0.225331i
$454$	4.47375e22			1.16331
$455$	−8.60377e21	+	1.79312e21i	−0.219580	+	0.0457627i
$456$	−8.37956e20			−0.0209904
$457$			7.49413e21i			0.184261i	0.995747	+	0.0921305i	$0.0293677\pi$
$457$			7.49413e21i			0.184261i	−0.995747	+	0.0921305i	$0.970632\pi$
$458$			1.43005e22i			0.345139i
$459$	−2.41176e22			−0.571381
$460$	8.33974e21	+	4.00159e22i	0.193959	+	0.930660i
$461$	−7.56013e21			−0.172612			−0.0863061	−	0.996269i	$-0.527506\pi$
$461$	−7.56013e21			−0.172612			−0.0863061	+	0.996269i	$0.527506\pi$
$462$		−	3.49230e21i		−	0.0782806i
$463$			3.41230e22i			0.750946i	0.926833	+	0.375473i	$0.122520\pi$
$463$			3.41230e22i			0.750946i	−0.926833	+	0.375473i	$0.877480\pi$
$464$	5.37906e21			0.116226
$465$	6.68260e20	+	3.20646e21i	0.0141774	+	0.0680261i
$466$	4.94953e22			1.03106
$467$			4.12036e22i			0.842834i	0.906867	+	0.421417i	$0.138467\pi$
$467$			4.12036e22i			0.842834i	−0.906867	+	0.421417i	$0.861533\pi$
$468$		−	1.04602e22i		−	0.210113i
$469$	−2.20109e22			−0.434179
$470$	−2.82083e22	+	5.87891e21i	−0.546443	+	0.113885i
$471$	−4.13523e21			−0.0786724
$472$			2.22436e22i			0.415621i
$473$			4.93582e22i			0.905816i
$474$	3.61288e21			0.0651235
$475$	−1.17466e22	+	5.11857e21i	−0.207978	+	0.0906260i
$476$	−1.61582e22			−0.281017
$477$		−	4.94579e22i		−	0.844947i
$478$			2.34049e22i			0.392798i
$479$	1.24427e22			0.205146			0.102573	−	0.994725i	$-0.467293\pi$
$479$	1.24427e22			0.205146			0.102573	+	0.994725i	$0.467293\pi$
$480$	−2.79601e21	+	5.82719e20i	−0.0452886	+	0.00943863i
$481$	−4.47660e22			−0.712386
$482$		−	3.64469e22i		−	0.569850i
$483$		−	1.61040e22i		−	0.247390i
$484$	9.14568e21			0.138048
$485$	2.33705e22	+	1.12137e23i	0.346627	+	1.66319i
$486$	−3.46715e22			−0.505317
$487$		−	1.33157e23i		−	1.90707i	−0.301281	−	0.953535i	$-0.597414\pi$
$487$		−	1.33157e23i		−	1.90707i	0.301281	−	0.953535i	$-0.402586\pi$
$488$		−	2.01505e22i		−	0.283607i
$489$	−7.95405e21			−0.110018
$490$	−7.98938e21	−	3.83348e22i	−0.108604	−	0.521107i
$491$	4.18591e22			0.559238			0.279619	−	0.960111i	$-0.409792\pi$
$491$	4.18591e22			0.559238			0.279619	+	0.960111i	$0.409792\pi$
$492$			7.69870e21i			0.101091i
$493$		−	4.07186e22i		−	0.525526i
$494$	−5.70459e21			−0.0723679
$495$	6.22217e22	−	1.29677e22i	0.775886	−	0.161703i
$496$	−5.41559e21			−0.0663822
$497$		−	5.46717e22i		−	0.658769i
$498$			1.19776e22i			0.141880i
$499$	−1.80695e22			−0.210422			−0.105211	−	0.994450i	$-0.533552\pi$
$499$	−1.80695e22			−0.210422			−0.105211	+	0.994450i	$0.533552\pi$
$500$	−3.56356e22	+	2.52478e22i	−0.407980	+	0.289054i
$501$	−6.24383e21			−0.0702797
$502$		−	8.63047e22i		−	0.955109i
$503$			9.01337e22i			0.980752i	0.871511	+	0.490376i	$0.163141\pi$
$503$			9.01337e22i			0.980752i	−0.871511	+	0.490376i	$0.836859\pi$
$504$	−1.53051e22			−0.163749
$505$	1.19960e23	−	2.50010e22i	1.26200	−	0.263015i
$506$	−1.10575e23			−1.14388
$507$		−	2.04901e22i		−	0.208438i
$508$		−	4.40418e22i		−	0.440579i
$509$	4.22002e22			0.415158			0.207579	−	0.978218i	$-0.433442\pi$
$509$	4.22002e22			0.415158			0.207579	+	0.978218i	$0.433442\pi$
$510$	4.41109e21	+	2.11654e22i	0.0426776	+	0.204776i
$511$	3.15620e22			0.300322
$512$		−	4.72237e21i		−	0.0441942i
$513$			1.24584e22i			0.114674i
$514$	8.42563e22			0.762809
$515$	−4.01455e21	−	1.92627e22i	−0.0357500	−	0.171536i
$516$	−1.59034e22			−0.139305
$517$		−	7.79476e22i		−	0.671635i
$518$			6.55003e22i			0.555189i
$519$	5.34382e22			0.445583
$520$	−1.90346e22	+	3.96701e21i	−0.156140	+	0.0325413i
$521$	8.04709e21			0.0649409			0.0324704	−	0.999473i	$-0.489663\pi$
$521$	8.04709e21			0.0649409			0.0324704	+	0.999473i	$0.489663\pi$
$522$		−	3.85689e22i		−	0.306223i
$523$		−	3.43617e22i		−	0.268417i	−0.990953	−	0.134209i	$-0.957151\pi$
$523$		−	3.43617e22i		−	0.268417i	0.990953	−	0.134209i	$-0.0428492\pi$
$524$	1.08182e23			0.831452
$525$	1.57736e22	−	6.87334e21i	0.119283	−	0.0519773i
$526$	−2.86101e22			−0.212883
$527$			4.09952e22i			0.300153i
$528$		−	7.72619e21i		−	0.0556643i
$529$	−3.68844e23			−2.61499
$530$	−8.99987e22	+	1.87567e22i	−0.627902	+	0.130861i
$531$	1.59491e23			1.09505
$532$			8.34679e21i			0.0563989i
$533$			5.24109e22i			0.348530i
$534$	1.88956e22			0.123669
$535$	5.28634e22	+	2.53650e23i	0.340524	+	1.63391i
$536$	−4.86959e22			−0.308739
$537$			7.08478e22i			0.442125i
$538$			1.65408e23i			1.01603i
$539$	1.05930e23			0.640493
$540$	8.66361e21	+	4.15699e22i	0.0515646	+	0.247418i
$541$	−1.71006e23			−1.00192			−0.500961	−	0.865470i	$-0.667020\pi$
$541$	−1.71006e23			−1.00192			−0.500961	+	0.865470i	$0.667020\pi$
$542$			5.05252e22i			0.291417i
$543$		−	7.01974e22i		−	0.398586i
$544$	−3.57476e22			−0.199828
$545$	−8.61017e22	+	1.79445e22i	−0.473851	+	0.0987556i
$546$	7.66026e21			0.0415056
$547$			1.89622e23i			1.01157i	0.862659	+	0.505787i	$0.168798\pi$
$547$			1.89622e23i			1.01157i	−0.862659	+	0.505787i	$0.831202\pi$
$548$		−	1.65843e23i		−	0.871090i
$549$	−1.44483e23			−0.747225
$550$	−4.71947e22	−	1.08307e23i	−0.240331	−	0.551537i
$551$	−2.10339e22			−0.105471
$552$		−	3.56277e22i		−	0.175916i
$553$		−	3.59875e22i		−	0.174980i
$554$	2.19601e23			1.05148
$555$	8.57981e22	−	1.78812e22i	0.404564	−	0.0843154i
$556$	1.81953e23			0.844937
$557$		−	2.07568e23i		−	0.949274i	−0.880182	−	0.474637i	$-0.842579\pi$
$557$		−	2.07568e23i		−	0.949274i	0.880182	−	0.474637i	$-0.157421\pi$
$558$			3.88309e22i			0.174899i
$559$	−1.08266e23			−0.480277
$560$	5.80441e21	+	2.78508e22i	0.0253606	+	0.121686i
$561$	−5.84860e22			−0.251691
$562$			2.29286e23i			0.971895i
$563$		−	2.04881e22i		−	0.0855423i	−0.999085	−	0.0427712i	$-0.986381\pi$
$563$		−	2.04881e22i		−	0.0855423i	0.999085	−	0.0427712i	$-0.0136186\pi$
$564$	2.51149e22			0.103290
$565$	−5.19637e22	−	2.49333e23i	−0.210517	−	1.01011i
$566$	2.00414e23			0.799813
$567$			1.01080e23i			0.397381i
$568$		−	1.20953e23i		−	0.468442i
$569$	9.64035e22			0.367823			0.183911	−	0.982943i	$-0.441124\pi$
$569$	9.64035e22			0.367823			0.183911	+	0.982943i	$0.441124\pi$
$570$	1.09334e22	−	2.27863e21i	0.0410977	−	0.00856520i
$571$	2.17004e23			0.803640			0.401820	−	0.915719i	$-0.368378\pi$
$571$	2.17004e23			0.803640			0.401820	+	0.915719i	$0.368378\pi$
$572$		−	5.25980e22i		−	0.191912i
$573$			9.79978e22i			0.352291i
$574$	7.66860e22			0.271622
$575$	−2.17628e23	−	4.99435e23i	−0.759518	−	1.74302i
$576$	−3.38603e22			−0.116439
$577$			2.31188e23i			0.783376i	0.920098	+	0.391688i	$0.128109\pi$
$577$			2.31188e23i			0.783376i	−0.920098	+	0.391688i	$0.871891\pi$
$578$			5.88299e22i			0.196432i
$579$	−4.59710e22			−0.151257
$580$	−7.01841e22	+	1.46271e22i	−0.227562	+	0.0474264i
$581$	1.19308e23			0.381216
$582$		−	9.98395e22i		−	0.314382i
$583$		−	2.48692e23i		−	0.771755i
$584$	6.98262e22			0.213555
$585$	2.84442e22	+	1.36482e23i	0.0857372	+	0.411386i
$586$	−1.99221e23			−0.591842
$587$		−	1.48857e23i		−	0.435858i	−0.975965	−	0.217929i	$-0.930070\pi$
$587$		−	1.48857e23i		−	0.435858i	0.975965	−	0.217929i	$-0.0699301\pi$
$588$			3.41309e22i			0.0985010i
$589$	2.11768e22			0.0602393
$590$	−6.04863e22	−	2.90227e23i	−0.169596	−	0.813758i
$591$	−7.09593e22			−0.196117
$592$			1.44910e23i			0.394787i
$593$		−	4.31467e23i		−	1.15873i	−0.815068	−	0.579366i	$-0.803300\pi$
$593$		−	4.31467e23i		−	1.15873i	0.815068	−	0.579366i	$-0.196700\pi$
$594$	−1.14870e23			−0.304103
$595$	2.10826e23	−	4.39384e22i	0.550213	−	0.114670i
$596$	−9.76443e22			−0.251220
$597$			1.49103e23i			0.378185i
$598$		−	2.42544e23i		−	0.606500i
$599$	−3.97221e23			−0.979275			−0.489637	−	0.871926i	$-0.662871\pi$
$599$	−3.97221e23			−0.979275			−0.489637	+	0.871926i	$0.662871\pi$
$600$	3.48969e22	−	1.52062e22i	0.0848205	−	0.0369604i
$601$	3.06679e23			0.734938			0.367469	−	0.930036i	$-0.380224\pi$
$601$	3.06679e23			0.734938			0.367469	+	0.930036i	$0.380224\pi$
$602$			1.58412e23i			0.374298i
$603$			3.49159e23i			0.813442i
$604$	−1.87416e23			−0.430520
$605$	−1.19330e23	+	2.48696e22i	−0.270289	+	0.0563310i
$606$	−1.06805e23			−0.238548
$607$			7.44484e23i			1.63965i	0.572614	+	0.819825i	$0.305930\pi$
$607$			7.44484e23i			1.63965i	−0.572614	+	0.819825i	$0.694070\pi$
$608$			1.84660e22i			0.0401045i
$609$	2.82448e22			0.0604912
$610$	5.47946e22	+	2.62916e23i	0.115727	+	0.555282i
$611$	1.70976e23			0.356111
$612$			2.56317e23i			0.526491i
$613$			4.11346e23i			0.833285i	0.909070	+	0.416642i	$0.136793\pi$
$613$			4.11346e23i			0.833285i	−0.909070	+	0.416642i	$0.863207\pi$
$614$	−1.63011e23			−0.325677
$615$	−2.09349e22	−	1.00450e23i	−0.0412507	−	0.197930i
$616$	−7.69598e22			−0.149564
$617$			4.85159e23i			0.929951i	0.885324	+	0.464975i	$0.153937\pi$
$617$			4.85159e23i			0.929951i	−0.885324	+	0.464975i	$0.846063\pi$
$618$			1.71503e22i			0.0324243i
$619$	7.11624e23			1.32703			0.663514	−	0.748164i	$-0.269064\pi$
$619$	7.11624e23			1.32703			0.663514	+	0.748164i	$0.269064\pi$
$620$	7.06608e22	−	1.47265e22i	0.129972	−	0.0270875i
$621$	−5.29696e23			−0.961055
$622$		−	2.60791e23i		−	0.466739i
$623$		−	1.88218e23i		−	0.332286i
$624$	1.69472e22			0.0295141
$625$	3.96305e23	−	4.26328e23i	0.680847	−	0.732426i
$626$	−7.01463e22			−0.118884
$627$			3.02120e22i			0.0505133i
$628$			9.11282e22i			0.150313i
$629$	1.09694e24			1.78506
$630$	1.99696e23	−	4.16188e22i	0.320608	−	0.0668182i
$631$	−1.18116e23			−0.187093			−0.0935467	−	0.995615i	$-0.529820\pi$
$631$	−1.18116e23			−0.187093			−0.0935467	+	0.995615i	$0.529820\pi$
$632$		−	7.96171e22i		−	0.124426i
$633$			1.17591e23i			0.181319i
$634$	−7.24184e23			−1.10177
$635$	1.19762e23	+	5.74642e23i	0.179780	+	0.862623i
$636$	8.01293e22			0.118688
$637$			2.32355e23i			0.339599i
$638$		−	1.93939e23i		−	0.279698i
$639$	−8.67258e23			−1.23422
$640$	1.28414e22	+	6.16158e22i	0.0180336	+	0.0865291i
$641$	−1.00048e24			−1.38648			−0.693240	−	0.720707i	$-0.743817\pi$
$641$	−1.00048e24			−1.38648			−0.693240	+	0.720707i	$0.743817\pi$
$642$		−	2.25834e23i		−	0.308846i
$643$		−	1.69711e23i		−	0.229043i	−0.993421	−	0.114521i	$-0.963467\pi$
$643$		−	1.69711e23i		−	0.229043i	0.993421	−	0.114521i	$-0.0365334\pi$
$644$	−3.54883e23			−0.472668
$645$	2.07501e23	−	4.32455e22i	0.272749	−	0.0568438i
$646$	1.39785e23			0.181336
$647$		−	1.31645e24i		−	1.68546i	−0.538338	−	0.842729i	$-0.680948\pi$
$647$		−	1.31645e24i		−	1.68546i	0.538338	−	0.842729i	$-0.319052\pi$
$648$			2.23624e23i			0.282573i
$649$	8.01979e23			1.00019
$650$	2.37569e23	−	1.03520e23i	0.292433	−	0.127427i
$651$	−2.84367e22			−0.0345494
$652$			1.75284e23i			0.210202i
$653$		−	8.36567e23i		−	0.990236i	−0.868826	−	0.495118i	$-0.835125\pi$
$653$		−	8.36567e23i		−	0.990236i	0.868826	−	0.495118i	$-0.164875\pi$
$654$	7.66596e22			0.0895686
$655$	−1.41152e24	+	2.94175e23i	−1.62793	+	0.339277i
$656$	1.69656e23			0.193147
$657$		−	5.00668e23i		−	0.562658i
$658$		−	2.50167e23i		−	0.277530i
$659$	5.10849e23			0.559457			0.279728	−	0.960079i	$-0.409756\pi$
$659$	5.10849e23			0.559457			0.279728	+	0.960079i	$0.409756\pi$
$660$	2.10096e22	+	1.00809e23i	0.0227140	+	0.108987i
$661$	4.02261e23			0.429334			0.214667	−	0.976687i	$-0.431133\pi$
$661$	4.02261e23			0.429334			0.214667	+	0.976687i	$0.431133\pi$
$662$		−	1.13941e23i		−	0.120057i
$663$		−	1.28288e23i		−	0.133450i
$664$	2.63951e23			0.271078
$665$	−2.26972e22	−	1.08906e23i	−0.0230138	−	0.110425i
$666$	1.03903e24			1.04016
$667$		−	8.94307e23i		−	0.883928i
$668$			1.37595e23i			0.134278i
$669$	−3.81278e22			−0.0367384
$670$	6.35367e23	−	1.32417e23i	0.604489	−	0.125982i
$671$	−7.26513e23			−0.682499
$672$		−	2.47966e22i		−	0.0230014i
$673$			7.03551e23i			0.644418i	0.946669	+	0.322209i	$0.104425\pi$
$673$			7.03551e23i			0.644418i	−0.946669	+	0.322209i	$0.895575\pi$
$674$	2.28570e23			0.206734
$675$	−2.26080e23	−	5.18831e23i	−0.201920	−	0.463387i
$676$	−4.51541e23			−0.398245
$677$		−	6.68647e23i		−	0.582362i	−0.956668	−	0.291181i	$-0.905952\pi$
$677$		−	6.68647e23i		−	0.582362i	0.956668	−	0.291181i	$-0.0940482\pi$
$678$			2.21991e23i			0.190934i
$679$	−9.94491e23			−0.844711
$680$	4.66422e23	−	9.72073e22i	0.391249	−	0.0815404i
$681$	5.19707e23			0.430535
$682$			1.95256e23i			0.159749i
$683$			1.48694e24i			1.20148i	0.799445	+	0.600740i	$0.205127\pi$
$683$			1.48694e24i			1.20148i	−0.799445	+	0.600740i	$0.794873\pi$
$684$	1.32405e23			0.105664
$685$	4.50973e23	+	2.16387e24i	0.355451	+	1.70553i
$686$	7.91594e23			0.616237
$687$			1.66126e23i			0.127734i
$688$			3.50462e23i			0.266158i
$689$	5.45500e23			0.409196
$690$	9.68812e22	+	4.64857e23i	0.0717831	+	0.344431i
$691$	5.53790e23			0.405304			0.202652	−	0.979251i	$-0.435044\pi$
$691$	5.53790e23			0.405304			0.202652	+	0.979251i	$0.435044\pi$
$692$		−	1.17762e24i		−	0.851339i
$693$			5.51817e23i			0.394060i
$694$	−1.70059e24			−1.19962
$695$	−2.37407e24	+	4.94781e23i	−1.65433	+	0.344780i
$696$	6.24875e22			0.0430145
$697$		−	1.28427e24i		−	0.873330i
$698$			1.38534e24i			0.930645i
$699$	5.74978e23			0.381588
$700$	−1.51468e23	−	3.47604e23i	−0.0993086	−	0.227904i
$701$	−3.73720e23			−0.242071			−0.121036	−	0.992648i	$-0.538622\pi$
$701$	−3.73720e23			−0.242071			−0.121036	+	0.992648i	$0.538622\pi$
$702$		−	2.51963e23i		−	0.161240i
$703$		−	5.66646e23i		−	0.358254i
$704$	−1.70262e23			−0.106353
$705$	−3.27691e23	+	6.82943e22i	−0.202235	+	0.0421480i
$706$	−9.83640e23			−0.599786
$707$			1.06388e24i			0.640953i
$708$			2.58400e23i			0.153819i
$709$	4.91345e23			0.288997			0.144499	−	0.989505i	$-0.453843\pi$
$709$	4.91345e23			0.288997			0.144499	+	0.989505i	$0.453843\pi$
$710$	3.28904e23	+	1.57815e24i	0.191150	+	0.917177i
$711$	−5.70871e23			−0.327828
$712$		−	4.16404e23i		−	0.236284i
$713$			9.00381e23i			0.504853i
$714$	−1.87707e23			−0.104003
$715$	1.43028e23	+	6.86280e23i	0.0783105	+	0.375751i
$716$	1.56127e24			0.844731
$717$			2.71890e23i			0.145372i
$718$		−	2.04178e24i		−	1.07883i
$719$	−1.07832e24			−0.563059			−0.281529	−	0.959553i	$-0.590842\pi$
$719$	−1.07832e24			−0.563059			−0.281529	+	0.959553i	$0.590842\pi$
$720$	4.41798e23	−	9.20754e22i	0.227980	−	0.0475135i
$721$	1.70833e23			0.0871206
$722$			1.33077e24i			0.670713i
$723$		−	4.23397e23i		−	0.210898i
$724$	−1.54694e24			−0.761546
$725$	8.75962e23	−	3.81699e23i	0.426199	−	0.185715i
$726$	1.06244e23			0.0510907
$727$		−	2.32801e24i		−	1.10648i	−0.833023	−	0.553239i	$-0.813392\pi$
$727$		−	2.32801e24i		−	1.10648i	0.833023	−	0.553239i	$-0.186608\pi$
$728$		−	1.68809e23i		−	0.0793012i
$729$	1.31854e24			0.612222
$730$	−9.11069e23	+	1.89876e23i	−0.418126	+	0.0871418i
$731$	2.65294e24			1.20346
$732$		−	2.34084e23i		−	0.104961i
$733$		−	2.98796e24i		−	1.32431i	−0.749365	−	0.662157i	$-0.769641\pi$
$733$		−	2.98796e24i		−	1.32431i	0.749365	−	0.662157i	$-0.230359\pi$
$734$	−1.00670e24			−0.441045
$735$	−9.28112e22	−	4.45329e23i	−0.0401937	−	0.192858i
$736$	−7.85127e23			−0.336108
$737$			1.75570e24i			0.742980i
$738$		−	1.21647e24i		−	0.508889i
$739$	3.82346e24			1.58117			0.790585	−	0.612352i	$-0.209777\pi$
$739$	3.82346e24			1.58117			0.790585	+	0.612352i	$0.209777\pi$
$740$	−3.94049e23	−	1.89073e24i	−0.161094	−	0.772966i
$741$	−6.62692e22			−0.0267829
$742$		−	7.98160e23i		−	0.318902i
$743$			1.76990e24i			0.699107i	0.936916	+	0.349553i	$0.113667\pi$
$743$			1.76990e24i			0.699107i	−0.936916	+	0.349553i	$0.886333\pi$
$744$	−6.29120e22			−0.0245676
$745$	1.27403e24	−	2.65521e23i	0.491871	−	0.102511i
$746$	−5.50353e23			−0.210069
$747$		−	1.89258e24i		−	0.714215i
$748$			1.28886e24i			0.480885i
$749$	−2.24951e24			−0.829838
$750$	−4.13972e23	+	2.93300e23i	−0.150991	+	0.106977i
$751$	1.13869e24			0.410645			0.205323	−	0.978694i	$-0.434176\pi$
$751$	1.13869e24			0.410645			0.205323	+	0.978694i	$0.434176\pi$
$752$		−	5.53458e23i		−	0.197348i
$753$		−	1.00259e24i		−	0.353480i
$754$	4.25400e23			0.148300
$755$	2.44534e24	−	5.09636e23i	0.842929	−	0.175675i
$756$	−3.68665e23			−0.125660
$757$			1.41930e24i			0.478365i	0.970975	+	0.239183i	$0.0768795\pi$
$757$			1.41930e24i			0.478365i	−0.970975	+	0.239183i	$0.923121\pi$
$758$			5.92109e23i			0.197339i
$759$	−1.28453e24			−0.423341
$760$	−5.02142e22	−	2.40939e23i	−0.0163648	−	0.0785219i
$761$	−4.87450e24			−1.57094			−0.785471	−	0.618898i	$-0.787579\pi$
$761$	−4.87450e24			−1.57094			−0.785471	+	0.618898i	$0.787579\pi$
$762$		−	5.11626e23i		−	0.163055i
$763$		−	7.63599e23i		−	0.240662i
$764$	2.15958e24			0.673093
$765$	−6.96996e23	−	3.34434e24i	−0.214837	−	1.03083i
$766$	−1.85583e24			−0.565710
$767$			1.75912e24i			0.530316i
$768$		−	5.48589e22i		−	0.0163560i
$769$	3.78215e23			0.111523			0.0557616	−	0.998444i	$-0.482241\pi$
$769$	3.78215e23			0.111523			0.0557616	+	0.998444i	$0.482241\pi$
$770$	1.00414e24	−	2.09274e23i	0.292836	−	0.0610302i
$771$	9.78790e23			0.282311
$772$			1.01306e24i			0.288995i
$773$			4.68953e24i			1.32313i	0.749886	+	0.661567i	$0.230108\pi$
$773$			4.68953e24i			1.32313i	−0.749886	+	0.661567i	$0.769892\pi$
$774$	2.51289e24			0.701253
$775$	−8.81912e23	+	3.84292e23i	−0.243423	+	0.106071i
$776$	−2.20016e24			−0.600663
$777$			7.60906e23i			0.205472i
$778$		−	3.13079e24i		−	0.836233i
$779$	−6.63414e23			−0.175273
$780$	−2.21121e23	+	4.60840e22i	−0.0577865	+	0.0120433i
$781$	−4.36089e24			−1.12731
$782$			5.94329e24i			1.51974i
$783$		−	9.29037e23i		−	0.234995i
$784$	7.52144e23			0.188198
$785$	−2.47802e23	−	1.18901e24i	−0.0613357	−	0.294302i
$786$	1.25673e24			0.307715
$787$			7.53697e24i			1.82563i	0.408379	+	0.912813i	$0.366094\pi$
$787$			7.53697e24i			1.82563i	−0.408379	+	0.912813i	$0.633906\pi$
$788$			1.56373e24i			0.374705i
$789$	−3.32359e23			−0.0787867
$790$	2.16500e23	+	1.03882e24i	0.0507725	+	0.243618i
$791$	2.21123e24			0.513019
$792$			1.22081e24i			0.280211i
$793$		−	1.59359e24i		−	0.361871i
$794$	1.89435e24			0.425585
$795$	−1.04550e24	+	2.17893e23i	−0.232382	+	0.0484310i
$796$	3.28578e24			0.722566
$797$			1.17363e24i			0.255349i	0.991816	+	0.127674i	$0.0407512\pi$
$797$			1.17363e24i			0.255349i	−0.991816	+	0.127674i	$0.959249\pi$
$798$			9.69632e22i			0.0208729i
$799$	−4.18959e24			−0.892326
$800$	−3.35100e23	−	7.69022e23i	−0.0706170	−	0.162059i
$801$	−2.98570e24			−0.622543
$802$		−	6.76457e23i		−	0.139559i
$803$		−	2.51754e24i		−	0.513919i
$804$	−5.65691e23			−0.114262
$805$	4.63040e24	−	9.65024e23i	0.925451	−	0.192874i
$806$	−4.28289e23			−0.0847011
$807$			1.92152e24i			0.376028i
$808$			2.35367e24i			0.455773i
$809$	−1.76470e24			−0.338149			−0.169075	−	0.985603i	$-0.554078\pi$
$809$	−1.76470e24			−0.338149			−0.169075	+	0.985603i	$0.554078\pi$
$810$	−6.08093e23	−	2.91776e24i	−0.115305	−	0.553258i
$811$	8.84401e24			1.65948			0.829740	−	0.558151i	$-0.188489\pi$
$811$	8.84401e24			1.65948			0.829740	+	0.558151i	$0.188489\pi$
$812$		−	6.22432e23i		−	0.115575i
$813$			5.86943e23i			0.107851i
$814$	5.22464e24			0.950055
$815$	−4.76643e23	−	2.28704e24i	−0.0857736	−	0.411561i
$816$	−4.15273e23			−0.0739550
$817$		−	1.37043e24i		−	0.241528i
$818$		−	4.74576e24i		−	0.827757i
$819$	−1.21040e24			−0.208937
$820$	−2.21362e24	+	4.61342e23i	−0.378168	+	0.0788143i
$821$	−4.68909e24			−0.792815			−0.396408	−	0.918075i	$-0.629743\pi$
$821$	−4.68909e24			−0.792815			−0.396408	+	0.918075i	$0.629743\pi$
$822$		−	1.92657e24i		−	0.322385i
$823$		−	5.49318e24i		−	0.909756i	−0.890554	−	0.454878i	$-0.849683\pi$
$823$		−	5.49318e24i		−	0.909756i	0.890554	−	0.454878i	$-0.150317\pi$
$824$	3.77942e23			0.0619503
$825$	−5.48252e23	−	1.25819e24i	−0.0889450	−	0.204120i
$826$	2.57389e24			0.413295
$827$			8.88420e23i			0.141196i	0.997505	+	0.0705978i	$0.0224907\pi$
$827$			8.88420e23i			0.141196i	−0.997505	+	0.0705978i	$0.977509\pi$
$828$			5.62952e24i			0.885551i
$829$	−2.89244e24			−0.450350			−0.225175	−	0.974318i	$-0.572295\pi$
$829$	−2.89244e24			−0.450350			−0.225175	+	0.974318i	$0.572295\pi$
$830$	−3.44394e24	+	7.17753e23i	−0.530751	+	0.110614i
$831$	2.55107e24			0.389147
$832$		−	3.73466e23i		−	0.0563900i
$833$		−	5.69361e24i		−	0.850952i
$834$	2.11372e24			0.312706
$835$	−3.74159e23	−	1.79530e24i	−0.0547925	−	0.262906i
$836$	6.65782e23			0.0965115
$837$			9.35347e23i			0.134217i
$838$		−	3.42495e24i		−	0.486497i
$839$	−1.16441e25			−1.63730			−0.818650	−	0.574293i	$-0.805277\pi$
$839$	−1.16441e25			−1.63730			−0.818650	+	0.574293i	$0.805277\pi$
$840$	6.74288e22	+	3.23538e23i	0.00938580	+	0.0450351i
$841$	−5.68862e24			−0.783864
$842$		−	3.43798e24i		−	0.468976i
$843$			2.66358e24i			0.359692i
$844$	2.59136e24			0.346431
$845$	5.89156e24	−	1.22786e24i	0.779737	−	0.162505i
$846$	−3.96841e24			−0.519958
$847$		−	1.05828e24i		−	0.137275i
$848$		−	1.76581e24i		−	0.226767i
$849$	2.32817e24			0.296006
$850$	−5.82138e24	+	2.53665e24i	−0.732765	+	0.319301i
$851$	2.40923e25			3.00246
$852$		−	1.40509e24i		−	0.173367i
$853$		−	6.33999e24i		−	0.774501i	−0.921975	−	0.387250i	$-0.873425\pi$
$853$		−	6.33999e24i		−	0.774501i	0.921975	−	0.387250i	$-0.126575\pi$
$854$	−2.33169e24			−0.282019
$855$	−1.72758e24	+	3.60046e23i	−0.206883	+	0.0431167i
$856$	−4.97672e24			−0.590087
$857$		−	6.31715e24i		−	0.741625i	−0.928708	−	0.370813i	$-0.879079\pi$
$857$		−	6.31715e24i		−	0.741625i	0.928708	−	0.370813i	$-0.120921\pi$
$858$		−	6.11021e23i		−	0.0710255i
$859$	8.91034e24			1.02554			0.512770	−	0.858526i	$-0.328619\pi$
$859$	8.91034e24			1.02554			0.512770	+	0.858526i	$0.328619\pi$
$860$	−9.53002e23	−	4.57271e24i	−0.108607	−	0.521119i
$861$	8.90848e23			0.100526
$862$			7.51420e24i			0.839597i
$863$			1.00324e25i			1.10997i	0.831861	+	0.554985i	$0.187276\pi$
$863$			1.00324e25i			1.10997i	−0.831861	+	0.554985i	$0.812724\pi$
$864$	−8.15618e23			−0.0893552
$865$	3.20226e24	+	1.53651e25i	0.347392	+	1.66686i
$866$	−5.79169e24			−0.622162
$867$			6.83417e23i			0.0726981i
$868$			6.26660e23i			0.0660107i
$869$	−2.87055e24			−0.299431
$870$	−8.15316e23	+	1.69920e23i	−0.0842194	+	0.0175522i
$871$	−3.85108e24			−0.393939
$872$		−	1.68935e24i		−	0.171131i
$873$			1.57756e25i			1.58258i
$874$	3.07011e24			0.305005
$875$	2.92153e24	+	4.12353e24i	0.287436	+	0.405696i
$876$	8.11159e23			0.0790353
$877$			1.88816e24i			0.182197i	0.995842	+	0.0910986i	$0.0290378\pi$
$877$			1.88816e24i			0.182197i	−0.995842	+	0.0910986i	$0.970962\pi$
$878$			1.09562e25i			1.04703i
$879$	−2.31432e24			−0.219037
$880$	2.22152e24	−	4.62989e23i	0.208232	−	0.0433978i
$881$	1.45784e24			0.135336			0.0676680	−	0.997708i	$-0.478444\pi$
$881$	1.45784e24			0.135336			0.0676680	+	0.997708i	$0.478444\pi$
$882$		−	5.39302e24i		−	0.495849i
$883$			5.53794e24i			0.504292i	0.967689	+	0.252146i	$0.0811363\pi$
$883$			5.53794e24i			0.504292i	−0.967689	+	0.252146i	$0.918864\pi$
$884$	−2.82708e24			−0.254972
$885$	−7.02659e23	−	3.37151e24i	−0.0627663	−	0.301166i
$886$	1.71760e23			0.0151963
$887$		−	1.80604e25i		−	1.58262i	−0.611417	−	0.791309i	$-0.709400\pi$
$887$		−	1.80604e25i		−	1.58262i	0.611417	−	0.791309i	$-0.290600\pi$
$888$			1.68339e24i			0.146108i
$889$	−5.09625e24			−0.438113
$890$	1.13231e24	+	5.43309e24i	0.0964166	+	0.462628i
$891$	8.06262e24			0.680010
$892$			8.40223e23i			0.0701929i
$893$			2.16421e24i			0.179086i
$894$	−1.13432e24			−0.0929748
$895$	−2.03710e25	+	4.24553e24i	−1.65392	+	0.344695i
$896$	−5.46444e23			−0.0439468
$897$		−	2.81759e24i		−	0.224462i
$898$		−	4.03310e24i		−	0.318266i
$899$	−1.57918e24			−0.123445
$900$	−5.51405e24	+	2.40274e24i	−0.426982	+	0.186056i
$901$	−1.33669e25			−1.02535
$902$		−	6.11686e24i		−	0.464808i
$903$			1.84024e24i			0.138525i
$904$	4.89201e24			0.364801
$905$	2.01839e25	−	4.20655e24i	1.49105	−	0.310751i
$906$	−2.17718e24			−0.159333
$907$			1.19863e24i			0.0869010i	0.999056	+	0.0434505i	$0.0138351\pi$
$907$			1.19863e24i			0.0869010i	−0.999056	+	0.0434505i	$0.986165\pi$
$908$		−	1.14528e25i		−	0.822587i
$909$	1.68763e25			1.20084
$910$	4.59038e23	+	2.20257e24i	0.0323591	+	0.155266i
$911$	−2.15950e25			−1.50816			−0.754078	−	0.656785i	$-0.771916\pi$
$911$	−2.15950e25			−1.50816			−0.754078	+	0.656785i	$0.771916\pi$
$912$			2.14517e23i			0.0148424i
$913$		−	9.51658e24i		−	0.652348i
$914$	1.91850e24			0.130292
$915$	6.36538e23	+	3.05425e24i	0.0428297	+	0.205506i
$916$	3.66092e24			0.244050
$917$		−	1.25181e25i		−	0.826799i
$918$			6.17410e24i			0.404027i
$919$	−9.95266e24			−0.645294			−0.322647	−	0.946519i	$-0.604573\pi$
$919$	−9.95266e24			−0.645294			−0.322647	+	0.946519i	$0.604573\pi$
$920$	1.02441e25	−	2.13497e24i	0.658076	−	0.137150i
$921$	−1.89367e24			−0.120531
$922$			1.93539e24i			0.122055i
$923$		−	9.56550e24i		−	0.597714i
$924$	−8.94028e23			−0.0553528
$925$	1.02828e25	+	2.35981e25i	0.630823	+	1.44768i
$926$	8.73548e24			0.530999
$927$		−	2.70992e24i		−	0.163222i
$928$		−	1.37704e24i		−	0.0821842i
$929$	1.13092e25			0.668806			0.334403	−	0.942430i	$-0.391465\pi$
$929$	1.13092e25			0.668806			0.334403	+	0.942430i	$0.391465\pi$
$930$	8.20854e23	−	1.71075e23i	0.0481017	−	0.0100249i
$931$	−2.94114e24			−0.170782
$932$		−	1.26708e25i		−	0.729069i
$933$		−	3.02956e24i		−	0.172737i
$934$	1.05481e25			0.595973
$935$	−3.50475e24	−	1.68166e25i	−0.196227	−	0.941540i
$936$	−2.67782e24			−0.148572
$937$		−	9.71463e24i		−	0.534121i	−0.963680	−	0.267061i	$-0.913948\pi$
$937$		−	9.71463e24i		−	0.534121i	0.963680	−	0.267061i	$-0.0860524\pi$
$938$			5.63479e24i			0.307011i
$939$	−8.14877e23			−0.0439982
$940$	1.50500e24	+	7.22133e24i	0.0805286	+	0.386394i
$941$	7.36745e23			0.0390666			0.0195333	−	0.999809i	$-0.493782\pi$
$941$	7.36745e23			0.0390666			0.0195333	+	0.999809i	$0.493782\pi$
$942$			1.05862e24i			0.0556298i
$943$		−	2.82066e25i		−	1.46893i
$944$	5.69436e24			0.293889
$945$	4.81022e24	−	1.00250e24i	0.246034	−	0.0512760i
$946$	1.26357e25			0.640509
$947$		−	2.10628e25i		−	1.05814i	−0.848579	−	0.529069i	$-0.822541\pi$
$947$		−	2.10628e25i		−	1.05814i	0.848579	−	0.529069i	$-0.177459\pi$
$948$		−	9.24898e23i		−	0.0460493i
$949$	5.52217e24			0.272488
$950$	1.31035e24	+	3.00714e24i	0.0640823	+	0.147063i
$951$	−8.41272e24			−0.407757
$952$			4.13649e24i			0.198709i
$953$			3.64294e25i			1.73445i	0.497915	+	0.867226i	$0.334099\pi$
$953$			3.64294e25i			1.73445i	−0.497915	+	0.867226i	$0.665901\pi$
$954$	−1.26612e25			−0.597468
$955$	−2.81774e25	+	5.87247e24i	−1.31787	+	0.274658i
$956$	5.99165e24			0.277750
$957$		−	2.25295e24i		−	0.103514i
$958$		−	3.18533e24i		−	0.145060i
$959$	−1.91904e25			−0.866214
$960$	1.49176e23	+	7.15780e23i	0.00667412	+	0.0320239i
$961$	−2.09602e25			−0.929494
$962$			1.14601e25i			0.503733i
$963$			3.56841e25i			1.55472i
$964$	−9.33040e24			−0.402945
$965$	−2.75479e24	−	1.32181e25i	−0.117925	−	0.565831i
$966$	−4.12262e24			−0.174931
$967$			4.62502e25i			1.94531i	0.232255	+	0.972655i	$0.425390\pi$
$967$			4.62502e25i			1.94531i	−0.232255	+	0.972655i	$0.574610\pi$
$968$		−	2.34129e24i		−	0.0976147i
$969$	1.62386e24			0.0671113
$970$	2.87070e25	−	5.98284e24i	1.17606	−	0.245103i
$971$	3.90538e25			1.58599			0.792995	−	0.609229i	$-0.208521\pi$
$971$	3.90538e25			1.58599			0.792995	+	0.609229i	$0.208521\pi$
$972$			8.87589e24i			0.357313i
$973$		−	2.10546e25i		−	0.840208i
$974$	−3.40881e25			−1.34850
$975$	2.75980e24	−	1.20258e24i	0.108228	−	0.0471600i
$976$	−5.15852e24			−0.200540
$977$			2.75744e25i			1.06268i	0.847159	+	0.531340i	$0.178311\pi$
$977$			2.75744e25i			1.06268i	−0.847159	+	0.531340i	$0.821689\pi$
$978$			2.03624e24i			0.0777944i
$979$	−1.50132e25			−0.568617
$980$	−9.81371e24	+	2.04528e24i	−0.368478	+	0.0767947i
$981$	−1.21130e25			−0.450884
$982$		−	1.07159e25i		−	0.395441i
$983$			1.24713e25i			0.456253i	0.973631	+	0.228127i	$0.0732601\pi$
$983$			1.24713e25i			0.456253i	−0.973631	+	0.228127i	$0.926740\pi$
$984$	1.97087e24			0.0714824
$985$	−4.25221e24	−	2.04030e25i	−0.152900	−	0.733646i
$986$	−1.04240e25			−0.371603
$987$		−	2.90615e24i		−	0.102712i
$988$			1.46038e24i			0.0511718i
$989$	5.82669e25			2.02420
$990$	−3.31972e24	−	1.59288e25i	−0.114341	−	0.548634i
$991$	4.73657e25			1.61748			0.808738	−	0.588168i	$-0.200151\pi$
$991$	4.73657e25			1.61748			0.808738	+	0.588168i	$0.200151\pi$
$992$			1.38639e24i			0.0469393i
$993$		−	1.32363e24i		−	0.0444323i
$994$	−1.39960e25			−0.465820
$995$	−4.28717e25	+	8.93492e24i	−1.41473	+	0.294846i
$996$	3.06627e24			0.100324
$997$			4.03130e25i			1.30778i	0.756588	+	0.653892i	$0.226865\pi$
$997$			4.03130e25i			1.30778i	−0.756588	+	0.653892i	$0.773135\pi$
$998$			4.62579e24i			0.148791i
$999$	2.50279e25			0.798211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.18.b.a.9.2	✓	8
3.2	odd	2		90.18.c.b.19.5		8
4.3	odd	2		80.18.c.a.49.5		8
5.2	odd	4		50.18.a.k.1.2		4
5.3	odd	4		50.18.a.j.1.3		4
5.4	even	2	inner	10.18.b.a.9.7	yes	8
15.14	odd	2		90.18.c.b.19.1		8
20.19	odd	2		80.18.c.a.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.b.a.9.2	✓	8	1.1	even	1	trivial
10.18.b.a.9.7	yes	8	5.4	even	2	inner
50.18.a.j.1.3		4	5.3	odd	4
50.18.a.k.1.2		4	5.2	odd	4
80.18.c.a.49.4		8	20.19	odd	2
80.18.c.a.49.5		8	4.3	odd	2
90.18.c.b.19.1		8	15.14	odd	2
90.18.c.b.19.5		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-256.000i q^{2} -2973.91i q^{3} -65536.0 q^{4} +(855091. - 178210. i) q^{5} -761320. q^{6} +7.58343e6i q^{7} +1.67772e7i q^{8} +1.20296e8 q^{9} +O(q^{10})\)	\(q-256.000i q^{2} -2973.91i q^{3} -65536.0 q^{4} +(855091. - 178210. i) q^{5} -761320. q^{6} +7.58343e6i q^{7} +1.67772e7i q^{8} +1.20296e8 q^{9} +(-4.56218e7 - 2.18903e8i) q^{10} +6.04893e8 q^{11} +1.94898e8i q^{12} +1.32682e9i q^{13} +1.94136e9 q^{14} +(-5.29980e8 - 2.54296e9i) q^{15} +4.29497e9 q^{16} -3.25122e10i q^{17} -3.07958e10i q^{18} -1.67948e10 q^{19} +(-5.60392e10 + 1.16792e10i) q^{20} +2.25524e10 q^{21} -1.54853e11i q^{22} -7.14069e11i q^{23} +4.98939e10 q^{24} +(6.99422e11 - 3.04772e11i) q^{25} +3.39665e11 q^{26} -7.41800e11i q^{27} -4.96988e11i q^{28} +1.25241e12 q^{29} +(-6.50998e11 + 1.35675e11i) q^{30} -1.26092e12 q^{31} -1.09951e12i q^{32} -1.79889e12i q^{33} -8.32313e12 q^{34} +(1.35144e12 + 6.48452e12i) q^{35} -7.88372e12 q^{36} +3.37394e13i q^{37} +4.29946e12i q^{38} +3.94583e12 q^{39} +(2.98987e12 + 1.43460e13i) q^{40} +3.95012e13 q^{41} -5.77342e12i q^{42} +8.15984e13i q^{43} -3.96422e13 q^{44} +(1.02864e14 - 2.14380e13i) q^{45} -1.82802e14 q^{46} -1.28862e14i q^{47} -1.27728e13i q^{48} +1.75122e14 q^{49} +(-7.80216e13 - 1.79052e14i) q^{50} -9.66883e13 q^{51} -8.69542e13i q^{52} -4.11135e14i q^{53} -1.89901e14 q^{54} +(5.17238e14 - 1.07798e14i) q^{55} -1.27229e14 q^{56} +4.99461e13i q^{57} -3.20617e14i q^{58} +1.32582e15 q^{59} +(3.47328e13 + 1.66655e14i) q^{60} -1.20106e15 q^{61} +3.22795e14i q^{62} +9.12257e14i q^{63} -2.81475e14 q^{64} +(2.36452e14 + 1.13455e15i) q^{65} -4.60517e14 q^{66} +2.90250e15i q^{67} +2.13072e15i q^{68} -2.12357e15 q^{69} +(1.66004e15 - 3.45970e14i) q^{70} -7.20936e15 q^{71} +2.01823e15i q^{72} -4.16197e15i q^{73} +8.63730e15 q^{74} +(-9.06362e14 - 2.08001e15i) q^{75} +1.10066e15 q^{76} +4.58716e15i q^{77} -1.01013e15i q^{78} -4.74555e15 q^{79} +(3.67259e15 - 7.65407e14i) q^{80} +1.33290e16 q^{81} -1.01123e16i q^{82} -1.57327e16i q^{83} -1.47799e15 q^{84} +(-5.79401e15 - 2.78009e16i) q^{85} +2.08892e16 q^{86} -3.72455e15i q^{87} +1.01484e16i q^{88} -2.48196e16 q^{89} +(-5.48812e15 - 2.63332e16i) q^{90} -1.00618e16 q^{91} +4.67972e16i q^{92} +3.74985e15i q^{93} -3.29887e16 q^{94} +(-1.43611e16 + 2.99300e15i) q^{95} -3.26984e15 q^{96} +1.31140e17i q^{97} -4.48313e16i q^{98} +7.27662e16 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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