LMFDB - Embedded newform 14.13.b.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,13,Mod(13,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("14.13");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	14.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:	$12.7959134419$
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} + 154710x^{6} + 8245426887x^{4} + 174724076278260x^{2} + 1264170035276291934 $ x^8 + 154710x^6 + 8245426887x^4 + 174724076278260*x^2 + 1264170035276291934
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.7
Root			$-149.422i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.13.b.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+45.2548 q^{2} +321.888i q^{3} +2048.00 q^{4} -17149.5i q^{5} +14567.0i q^{6} +(-71756.5 - 93232.5i) q^{7} +92681.9 q^{8} +427829. q^{9} +O(q^{10})$	\(q+45.2548 q^{2} +321.888i q^{3} +2048.00 q^{4} -17149.5i q^{5} +14567.0i q^{6} +(-71756.5 - 93232.5i) q^{7} +92681.9 q^{8} +427829. q^{9} -776099. i q^{10} +1.62995e6 q^{11} +659227. i q^{12} -4.55860e6i q^{13} +(-3.24733e6 - 4.21922e6i) q^{14} +5.52023e6 q^{15} +4.19430e6 q^{16} +1.51452e7i q^{17} +1.93613e7 q^{18} -8.19846e7i q^{19} -3.51222e7i q^{20} +(3.00104e7 - 2.30976e7i) q^{21} +7.37629e7 q^{22} +8.57392e7 q^{23} +2.98332e7i q^{24} -4.99658e7 q^{25} -2.06299e8i q^{26} +3.08778e8i q^{27} +(-1.46957e8 - 1.90940e8i) q^{28} -9.60080e8 q^{29} +2.49817e8 q^{30} +1.52654e9i q^{31} +1.89813e8 q^{32} +5.24661e8i q^{33} +6.85395e8i q^{34} +(-1.59889e9 + 1.23059e9i) q^{35} +8.76194e8 q^{36} -1.82147e9 q^{37} -3.71020e9i q^{38} +1.46736e9 q^{39} -1.58945e9i q^{40} +6.08045e8i q^{41} +(1.35812e9 - 1.04528e9i) q^{42} +3.59485e9 q^{43} +3.33813e9 q^{44} -7.33706e9i q^{45} +3.88011e9 q^{46} -6.65675e9i q^{47} +1.35010e9i q^{48} +(-3.54330e9 + 1.33801e10i) q^{49} -2.26119e9 q^{50} -4.87507e9 q^{51} -9.33602e9i q^{52} +1.15079e10 q^{53} +1.39737e10i q^{54} -2.79528e10i q^{55} +(-6.65053e9 - 8.64096e9i) q^{56} +2.63899e10 q^{57} -4.34482e10 q^{58} +5.91993e10i q^{59} +1.13054e10 q^{60} -2.23715e10i q^{61} +6.90831e10i q^{62} +(-3.06995e10 - 3.98875e10i) q^{63} +8.58993e9 q^{64} -7.81779e10 q^{65} +2.37434e10i q^{66} +5.96155e10 q^{67} +3.10174e10i q^{68} +2.75985e10i q^{69} +(-7.23576e10 + 5.56902e10i) q^{70} +6.47737e10 q^{71} +3.96520e10 q^{72} -1.47593e10i q^{73} -8.24305e10 q^{74} -1.60834e10i q^{75} -1.67904e11i q^{76} +(-1.16959e11 - 1.51964e11i) q^{77} +6.64052e10 q^{78} +2.34078e11 q^{79} -7.19303e10i q^{80} +1.27974e11 q^{81} +2.75170e10i q^{82} -1.33751e11i q^{83} +(6.14614e10 - 4.73038e10i) q^{84} +2.59734e11 q^{85} +1.62684e11 q^{86} -3.09038e11i q^{87} +1.51066e11 q^{88} +3.77427e11i q^{89} -3.32038e11i q^{90} +(-4.25010e11 + 3.27109e11i) q^{91} +1.75594e11 q^{92} -4.91374e11 q^{93} -3.01250e11i q^{94} -1.40600e12 q^{95} +6.10984e10i q^{96} +1.35962e12i q^{97} +(-1.60351e11 + 6.05513e11i) q^{98} +6.97338e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9}+O(q^{10}) $ 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9} - 213840 q^{11} - 8418816 q^{14} + 65882304 q^{15} + 33554432 q^{16} + 32547840 q^{18} - 4449984 q^{21} - 221337600 q^{22} + 156731760 q^{23} + 191237000 q^{25} + 399687680 q^{28} + 308853648 q^{29} - 2203567104 q^{30} - 3764734848 q^{35} - 3028795392 q^{36} - 3243600880 q^{37} + 13521315264 q^{39} - 12108579840 q^{42} + 21006302000 q^{43} - 437944320 q^{44} + 9664610304 q^{46} - 19258758904 q^{49} + 26259489792 q^{50} - 80965832832 q^{51} + 180445637520 q^{53} - 17241735168 q^{56} - 63145962240 q^{57} - 94193264640 q^{58} + 134926958592 q^{60} - 402706514280 q^{63} + 68719476736 q^{64} - 424890168192 q^{65} + 369211259440 q^{67} - 137936354304 q^{70} + 574058144304 q^{71} + 66657976320 q^{72} + 450517137408 q^{74} - 73915435440 q^{77} - 251000847360 q^{78} - 607826610128 q^{79} + 919051941384 q^{81} - 9113567232 q^{84} - 247202260608 q^{85} - 413092638720 q^{86} - 453299404800 q^{88} + 144527421696 q^{91} + 320986644480 q^{92} + 2292312458880 q^{93} - 1053641981376 q^{95} - 290797516800 q^{98} - 1800954256464 q^{99}+O(q^{100}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9 - 213840 * q^11 - 8418816 * q^14 + 65882304 * q^15 + 33554432 * q^16 + 32547840 * q^18 - 4449984 * q^21 - 221337600 * q^22 + 156731760 * q^23 + 191237000 * q^25 + 399687680 * q^28 + 308853648 * q^29 - 2203567104 * q^30 - 3764734848 * q^35 - 3028795392 * q^36 - 3243600880 * q^37 + 13521315264 * q^39 - 12108579840 * q^42 + 21006302000 * q^43 - 437944320 * q^44 + 9664610304 * q^46 - 19258758904 * q^49 + 26259489792 * q^50 - 80965832832 * q^51 + 180445637520 * q^53 - 17241735168 * q^56 - 63145962240 * q^57 - 94193264640 * q^58 + 134926958592 * q^60 - 402706514280 * q^63 + 68719476736 * q^64 - 424890168192 * q^65 + 369211259440 * q^67 - 137936354304 * q^70 + 574058144304 * q^71 + 66657976320 * q^72 + 450517137408 * q^74 - 73915435440 * q^77 - 251000847360 * q^78 - 607826610128 * q^79 + 919051941384 * q^81 - 9113567232 * q^84 - 247202260608 * q^85 - 413092638720 * q^86 - 453299404800 * q^88 + 144527421696 * q^91 + 320986644480 * q^92 + 2292312458880 * q^93 - 1053641981376 * q^95 - 290797516800 * q^98 - 1800954256464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	45.2548			0.707107
$2$	45.2548			0.707107
$3$			321.888i			0.441548i	0.975325	+	0.220774i	$0.0708583\pi$
$3$			321.888i			0.441548i	−0.975325	+	0.220774i	$0.929142\pi$
$4$	2048.00			0.500000
$5$		−	17149.5i		−	1.09757i	−0.835964	−	0.548785i	$-0.815091\pi$
$5$		−	17149.5i		−	1.09757i	0.835964	−	0.548785i	$-0.184909\pi$
$6$			14567.0i			0.312221i
$7$	−71756.5	−	93232.5i	−0.609920	−	0.792463i
$7$	−71756.5	−	93232.5i	−0.609920	−	0.792463i
$8$	92681.9			0.353553
$9$	427829.			0.805036
$10$		−	776099.i		−	0.776099i
$11$	1.62995e6			0.920062			0.460031	−	0.887903i	$-0.347838\pi$
$11$	1.62995e6			0.920062			0.460031	+	0.887903i	$0.347838\pi$
$12$			659227.i			0.220774i
$13$		−	4.55860e6i		−	0.944434i	−0.881482	−	0.472217i	$-0.843454\pi$
$13$		−	4.55860e6i		−	0.944434i	0.881482	−	0.472217i	$-0.156546\pi$
$14$	−3.24733e6	−	4.21922e6i	−0.431279	−	0.560356i
$15$	5.52023e6			0.484630
$16$	4.19430e6			0.250000
$17$			1.51452e7i			0.627455i	0.949513	+	0.313727i	$0.101578\pi$
$17$			1.51452e7i			0.627455i	−0.949513	+	0.313727i	$0.898422\pi$
$18$	1.93613e7			0.569246
$19$		−	8.19846e7i		−	1.74265i	−0.490704	−	0.871326i	$-0.663261\pi$
$19$		−	8.19846e7i		−	1.74265i	0.490704	−	0.871326i	$-0.336739\pi$
$20$		−	3.51222e7i		−	0.548785i
$21$	3.00104e7	−	2.30976e7i	0.349910	−	0.269309i
$22$	7.37629e7			0.650582
$23$	8.57392e7			0.579179			0.289589	−	0.957151i	$-0.406481\pi$
$23$	8.57392e7			0.579179			0.289589	+	0.957151i	$0.406481\pi$
$24$			2.98332e7i			0.156111i
$25$	−4.99658e7			−0.204660
$26$		−	2.06299e8i		−	0.667816i
$27$			3.08778e8i			0.797009i
$28$	−1.46957e8	−	1.90940e8i	−0.304960	−	0.396231i
$29$	−9.60080e8			−1.61406			−0.807029	−	0.590512i	$-0.798926\pi$
$29$	−9.60080e8			−1.61406			−0.807029	+	0.590512i	$0.798926\pi$
$30$	2.49817e8			0.342685
$31$			1.52654e9i			1.72003i	0.510267	+	0.860016i	$0.329547\pi$
$31$			1.52654e9i			1.72003i	−0.510267	+	0.860016i	$0.670453\pi$
$32$	1.89813e8			0.176777
$33$			5.24661e8i			0.406251i
$34$			6.85395e8i			0.443677i
$35$	−1.59889e9	+	1.23059e9i	−0.869783	+	0.669430i
$36$	8.76194e8			0.402518
$37$	−1.82147e9			−0.709926			−0.354963	−	0.934880i	$-0.615506\pi$
$37$	−1.82147e9			−0.709926			−0.354963	+	0.934880i	$0.615506\pi$
$38$		−	3.71020e9i		−	1.23224i
$39$	1.46736e9			0.417013
$40$		−	1.58945e9i		−	0.388050i
$41$			6.08045e8i			0.128007i	0.997950	+	0.0640033i	$0.0203868\pi$
$41$			6.08045e8i			0.128007i	−0.997950	+	0.0640033i	$0.979613\pi$
$42$	1.35812e9	−	1.04528e9i	0.247424	−	0.190430i
$43$	3.59485e9			0.568683			0.284341	−	0.958723i	$-0.408225\pi$
$43$	3.59485e9			0.568683			0.284341	+	0.958723i	$0.408225\pi$
$44$	3.33813e9			0.460031
$45$		−	7.33706e9i		−	0.883583i
$46$	3.88011e9			0.409541
$47$		−	6.65675e9i		−	0.617554i	−0.951134	−	0.308777i	$-0.900080\pi$
$47$		−	6.65675e9i		−	0.617554i	0.951134	−	0.308777i	$-0.0999197\pi$
$48$			1.35010e9i			0.110387i
$49$	−3.54330e9	+	1.33801e10i	−0.255995	+	0.966678i
$50$	−2.26119e9			−0.144716
$51$	−4.87507e9			−0.277051
$52$		−	9.33602e9i		−	0.472217i
$53$	1.15079e10			0.519208			0.259604	−	0.965715i	$-0.416408\pi$
$53$	1.15079e10			0.519208			0.259604	+	0.965715i	$0.416408\pi$
$54$			1.39737e10i			0.563571i
$55$		−	2.79528e10i		−	1.00983i
$56$	−6.65053e9	−	8.64096e9i	−0.215639	−	0.280178i
$57$	2.63899e10			0.769464
$58$	−4.34482e10			−1.14131
$59$			5.91993e10i			1.40347i	0.712436	+	0.701737i	$0.247592\pi$
$59$			5.91993e10i			1.40347i	−0.712436	+	0.701737i	$0.752408\pi$
$60$	1.13054e10			0.242315
$61$		−	2.23715e10i		−	0.434226i	−0.976146	−	0.217113i	$-0.930336\pi$
$61$		−	2.23715e10i		−	0.434226i	0.976146	−	0.217113i	$-0.0696641\pi$
$62$			6.90831e10i			1.21625i
$63$	−3.06995e10	−	3.98875e10i	−0.491007	−	0.637961i
$64$	8.58993e9			0.125000
$65$	−7.81779e10			−1.03658
$66$			2.37434e10i			0.287263i
$67$	5.96155e10			0.659037			0.329519	−	0.944149i	$-0.393114\pi$
$67$	5.96155e10			0.659037			0.329519	+	0.944149i	$0.393114\pi$
$68$			3.10174e10i			0.313727i
$69$			2.75985e10i			0.255735i
$70$	−7.23576e10	+	5.56902e10i	−0.615030	+	0.473359i
$71$	6.47737e10			0.505648			0.252824	−	0.967512i	$-0.418641\pi$
$71$	6.47737e10			0.505648			0.252824	+	0.967512i	$0.418641\pi$
$72$	3.96520e10			0.284623
$73$		−	1.47593e10i		−	0.0975278i	−0.998810	−	0.0487639i	$-0.984472\pi$
$73$		−	1.47593e10i		−	0.0975278i	0.998810	−	0.0487639i	$-0.0155282\pi$
$74$	−8.24305e10			−0.501993
$75$		−	1.60834e10i		−	0.0903671i
$76$		−	1.67904e11i		−	0.871326i
$77$	−1.16959e11	−	1.51964e11i	−0.561164	−	0.729115i
$78$	6.64052e10			0.294873
$79$	2.34078e11			0.962936			0.481468	−	0.876464i	$-0.340104\pi$
$79$	2.34078e11			0.962936			0.481468	+	0.876464i	$0.340104\pi$
$80$		−	7.19303e10i		−	0.274392i
$81$	1.27974e11			0.453118
$82$			2.75170e10i			0.0905143i
$83$		−	1.33751e11i		−	0.409098i	−0.978856	−	0.204549i	$-0.934427\pi$
$83$		−	1.33751e11i		−	0.409098i	0.978856	−	0.204549i	$-0.0655727\pi$
$84$	6.14614e10	−	4.73038e10i	0.174955	−	0.134654i
$85$	2.59734e11			0.688675
$86$	1.62684e11			0.402119
$87$		−	3.09038e11i		−	0.712684i
$88$	1.51066e11			0.325291
$89$			3.77427e11i			0.759440i	0.925101	+	0.379720i	$0.123980\pi$
$89$			3.77427e11i			0.759440i	−0.925101	+	0.379720i	$0.876020\pi$
$90$		−	3.32038e11i		−	0.624787i
$91$	−4.25010e11	+	3.27109e11i	−0.748429	+	0.576030i
$92$	1.75594e11			0.289589
$93$	−4.91374e11			−0.759476
$94$		−	3.01250e11i		−	0.436677i
$95$	−1.40600e12			−1.91268
$96$			6.10984e10i			0.0780554i
$97$			1.35962e12i			1.63225i	0.577874	+	0.816126i	$0.303883\pi$
$97$			1.35962e12i			1.63225i	−0.577874	+	0.816126i	$0.696117\pi$
$98$	−1.60351e11	+	6.05513e11i	−0.181016	+	0.683545i
$99$	6.97338e11			0.740683
$100$	−1.02330e11			−0.102330
$101$			1.34633e12i			1.26831i	0.773208	+	0.634153i	$0.218651\pi$
$101$			1.34633e12i			1.26831i	−0.773208	+	0.634153i	$0.781349\pi$
$102$	−2.20621e11			−0.195905
$103$		−	4.74121e11i		−	0.397069i	−0.980094	−	0.198535i	$-0.936382\pi$
$103$		−	4.74121e11i		−	0.397069i	0.980094	−	0.198535i	$-0.0636182\pi$
$104$		−	4.22500e11i		−	0.333908i
$105$	−3.96113e11	−	5.14665e11i	−0.295585	−	0.384051i
$106$	5.20789e11			0.367136
$107$	2.10200e12			1.40065			0.700327	−	0.713822i	$-0.253038\pi$
$107$	2.10200e12			1.40065			0.700327	+	0.713822i	$0.253038\pi$
$108$			6.32377e11i			0.398505i
$109$	−3.32488e12			−1.98252			−0.991258	−	0.131935i	$-0.957881\pi$
$109$	−3.32488e12			−1.98252			−0.991258	+	0.131935i	$0.957881\pi$
$110$		−	1.26500e12i		−	0.714059i
$111$		−	5.86312e11i		−	0.313466i
$112$	−3.00969e11	−	3.91045e11i	−0.152480	−	0.198116i
$113$	3.62455e12			1.74094			0.870470	−	0.492222i	$-0.163815\pi$
$113$	3.62455e12			1.74094			0.870470	+	0.492222i	$0.163815\pi$
$114$	1.19427e12			0.544093
$115$		−	1.47039e12i		−	0.635689i
$116$	−1.96624e12			−0.807029
$117$		−	1.95030e12i		−	0.760303i
$118$			2.67905e12i			0.992406i
$119$	1.41203e12	−	1.08677e12i	0.497234	−	0.382697i
$120$	5.11626e11			0.171342
$121$	−4.81704e11			−0.153486
$122$		−	1.01242e12i		−	0.307044i
$123$	−1.95722e11			−0.0565210
$124$			3.12634e12i			0.860016i
$125$		−	3.33001e12i		−	0.872941i
$126$	−1.38930e12	−	1.80510e12i	−0.347195	−	0.451106i
$127$	6.01653e12			1.43392			0.716958	−	0.697117i	$-0.245534\pi$
$127$	6.01653e12			1.43392			0.716958	+	0.697117i	$0.245534\pi$
$128$	3.88736e11			0.0883883
$129$			1.15714e12i			0.251101i
$130$	−3.53793e12			−0.732975
$131$		−	2.12789e12i		−	0.421038i	−0.977590	−	0.210519i	$-0.932485\pi$
$131$		−	2.12789e12i		−	0.421038i	0.977590	−	0.210519i	$-0.0675154\pi$
$132$			1.07450e12i			0.203126i
$133$	−7.64363e12	+	5.88293e12i	−1.38099	+	1.06288i
$134$	2.69789e12			0.466010
$135$	5.29539e12			0.874774
$136$			1.40369e12i			0.221839i
$137$	−5.40066e12			−0.816814			−0.408407	−	0.912800i	$-0.633916\pi$
$137$	−5.40066e12			−0.816814			−0.408407	+	0.912800i	$0.633916\pi$
$138$			1.24896e12i			0.180832i
$139$		−	3.07261e12i		−	0.426009i	−0.977051	−	0.213005i	$-0.931675\pi$
$139$		−	3.07261e12i		−	0.426009i	0.977051	−	0.213005i	$-0.0683250\pi$
$140$	−3.27453e12	+	2.52025e12i	−0.434892	+	0.334715i
$141$	2.14273e12			0.272680
$142$	2.93132e12			0.357547
$143$		−	7.43028e12i		−	0.868938i
$144$	1.79444e12			0.201259
$145$			1.64649e13i			1.77154i
$146$		−	6.67929e11i		−	0.0689626i
$147$	−4.30689e12	−	1.14055e12i	−0.426835	−	0.113034i
$148$	−3.73038e12			−0.354963
$149$	−4.81326e12			−0.439867			−0.219934	−	0.975515i	$-0.570584\pi$
$149$	−4.81326e12			−0.439867			−0.219934	+	0.975515i	$0.570584\pi$
$150$		−	7.27852e11i		−	0.0638992i
$151$	−1.38146e13			−1.16541			−0.582704	−	0.812684i	$-0.698005\pi$
$151$	−1.38146e13			−1.16541			−0.582704	+	0.812684i	$0.698005\pi$
$152$		−	7.59849e12i		−	0.616121i
$153$			6.47957e12i			0.505123i
$154$	−5.29297e12	−	6.87710e12i	−0.396803	−	0.515562i
$155$	2.61794e13			1.88786
$156$	3.00516e12			0.208506
$157$			2.01680e13i			1.34668i	0.739332	+	0.673341i	$0.235141\pi$
$157$			2.01680e13i			1.34668i	−0.739332	+	0.673341i	$0.764859\pi$
$158$	1.05931e13			0.680899
$159$			3.70426e12i			0.229255i
$160$		−	3.25520e12i		−	0.194025i
$161$	−6.15235e12	−	7.99368e12i	−0.353253	−	0.458978i
$162$	5.79144e12			0.320403
$163$	−2.02503e13			−1.07971			−0.539853	−	0.841759i	$-0.681520\pi$
$163$	−2.02503e13			−1.07971			−0.539853	+	0.841759i	$0.681520\pi$
$164$			1.24528e12i			0.0640033i
$165$	8.99768e12			0.445889
$166$		−	6.05286e12i		−	0.289276i
$167$		−	1.09922e13i		−	0.506741i	−0.967369	−	0.253370i	$-0.918461\pi$
$167$		−	1.09922e13i		−	0.506741i	0.967369	−	0.253370i	$-0.0815391\pi$
$168$	2.78142e12	−	2.14073e12i	0.123712	−	0.0952151i
$169$	2.51721e12			0.108044
$170$	1.17542e13			0.486967
$171$		−	3.50754e13i		−	1.40290i
$172$	7.36225e12			0.284341
$173$		−	3.94980e13i		−	1.47333i	−0.676260	−	0.736663i	$-0.736401\pi$
$173$		−	3.94980e13i		−	1.47333i	0.676260	−	0.736663i	$-0.263599\pi$
$174$		−	1.39855e13i		−	0.503944i
$175$	3.58537e12	+	4.65843e12i	0.124826	+	0.162185i
$176$	6.83649e12			0.230016
$177$	−1.90556e13			−0.619701
$178$			1.70804e13i			0.537005i
$179$	4.48619e13			1.36383			0.681914	−	0.731433i	$-0.261148\pi$
$179$	4.48619e13			1.36383			0.681914	+	0.731433i	$0.261148\pi$
$180$		−	1.50263e13i		−	0.441791i
$181$			6.52144e13i			1.85469i	0.374205	+	0.927346i	$0.377916\pi$
$181$			6.52144e13i			1.85469i	−0.374205	+	0.927346i	$0.622084\pi$
$182$	−1.92338e13	+	1.48033e13i	−0.529219	+	0.407314i
$183$	7.20113e12			0.191732
$184$	7.94647e12			0.204771
$185$			3.12374e13i			0.779193i
$186$	−2.22370e13			−0.537031
$187$			2.46859e13i			0.577297i
$188$		−	1.36330e13i		−	0.308777i
$189$	2.87881e13	−	2.21568e13i	0.631600	−	0.486112i
$190$	−6.36282e13			−1.35247
$191$	−3.95085e13			−0.813749			−0.406874	−	0.913484i	$-0.633381\pi$
$191$	−3.95085e13			−0.813749			−0.406874	+	0.913484i	$0.633381\pi$
$192$			2.76500e12i			0.0551935i
$193$	−5.42202e13			−1.04910			−0.524551	−	0.851379i	$-0.675767\pi$
$193$	−5.42202e13			−1.04910			−0.524551	+	0.851379i	$0.675767\pi$
$194$			6.15294e13i			1.15418i
$195$		−	2.51646e13i		−	0.457701i
$196$	−7.25667e12	+	2.74024e13i	−0.127997	+	0.483339i
$197$	−3.53646e13			−0.605023			−0.302511	−	0.953146i	$-0.597825\pi$
$197$	−3.53646e13			−0.605023			−0.302511	+	0.953146i	$0.597825\pi$
$198$	3.15579e13			0.523742
$199$		−	5.93934e13i		−	0.956357i	−0.878263	−	0.478178i	$-0.841297\pi$
$199$		−	5.93934e13i		−	0.956357i	0.878263	−	0.478178i	$-0.158703\pi$
$200$	−4.63092e12			−0.0723582
$201$			1.91895e13i			0.290997i
$202$			6.09280e13i			0.896827i
$203$	6.88919e13	+	8.95106e13i	0.984447	+	1.27908i
$204$	−9.98415e12			−0.138526
$205$	1.04277e13			0.140496
$206$		−	2.14563e13i		−	0.280770i
$207$	3.66817e13			0.466259
$208$		−	1.91202e13i		−	0.236109i
$209$		−	1.33630e14i		−	1.60335i
$210$	−1.79260e13	−	2.32911e13i	−0.209010	−	0.271565i
$211$	−6.27775e13			−0.711393			−0.355696	−	0.934602i	$-0.615756\pi$
$211$	−6.27775e13			−0.711393			−0.355696	+	0.934602i	$0.615756\pi$
$212$	2.35682e13			0.259604
$213$			2.08499e13i			0.223268i
$214$	9.51258e13			0.990412
$215$		−	6.16500e13i		−	0.624169i
$216$			2.86181e13i			0.281785i
$217$	1.42323e14	−	1.09539e14i	1.36306	−	1.04908i
$218$	−1.50467e14			−1.40185
$219$	4.75084e12			0.0430632
$220$		−	5.72474e13i		−	0.504916i
$221$	6.90411e13			0.592590
$222$		−	2.65334e13i		−	0.221654i
$223$			6.75460e13i			0.549250i	0.961551	+	0.274625i	$0.0885538\pi$
$223$			6.75460e13i			0.549250i	−0.961551	+	0.274625i	$0.911446\pi$
$224$	−1.36203e13	−	1.76967e13i	−0.107820	−	0.140089i
$225$	−2.13768e13			−0.164758
$226$	1.64029e14			1.23103
$227$			1.22559e14i			0.895758i	0.894094	+	0.447879i	$0.147821\pi$
$227$			1.22559e14i			0.895758i	−0.894094	+	0.447879i	$0.852179\pi$
$228$	5.40465e13			0.384732
$229$		−	7.10590e13i		−	0.492727i	−0.969178	−	0.246363i	$-0.920764\pi$
$229$		−	7.10590e13i		−	0.492727i	0.969178	−	0.246363i	$-0.0792357\pi$
$230$		−	6.65421e13i		−	0.449500i
$231$	4.89154e13	−	3.76478e13i	0.321939	−	0.247781i
$232$	−8.89820e13			−0.570656
$233$	−1.45093e14			−0.906798			−0.453399	−	0.891308i	$-0.649789\pi$
$233$	−1.45093e14			−0.906798			−0.453399	+	0.891308i	$0.649789\pi$
$234$		−	8.82606e13i		−	0.537616i
$235$	−1.14160e14			−0.677809
$236$			1.21240e14i			0.701737i
$237$			7.53469e13i			0.425182i
$238$	6.39010e13	−	4.91815e13i	0.351598	−	0.270608i
$239$	−1.73085e14			−0.928692			−0.464346	−	0.885654i	$-0.653711\pi$
$239$	−1.73085e14			−0.928692			−0.464346	+	0.885654i	$0.653711\pi$
$240$	2.31535e13			0.121157
$241$			1.55030e14i			0.791251i	0.918412	+	0.395625i	$0.129472\pi$
$241$			1.55030e14i			0.791251i	−0.918412	+	0.395625i	$0.870528\pi$
$242$	−2.17994e13			−0.108531
$243$			2.05290e14i			0.997083i
$244$		−	4.58168e13i		−	0.217113i
$245$	2.29462e14	+	6.07659e13i	1.06100	+	0.280972i
$246$	−8.85739e12			−0.0399664
$247$	−3.73735e14			−1.64582
$248$			1.41482e14i			0.608123i
$249$	4.30527e13			0.180636
$250$		−	1.50699e14i		−	0.617263i
$251$		−	2.64148e13i		−	0.105634i	−0.998604	−	0.0528171i	$-0.983180\pi$
$251$		−	2.64148e13i		−	0.105634i	0.998604	−	0.0528171i	$-0.0168200\pi$
$252$	−6.28726e13	−	8.16897e13i	−0.245504	−	0.318980i
$253$	1.39750e14			0.532880
$254$	2.72277e14			1.01393
$255$			8.36052e13i			0.304083i
$256$	1.75922e13			0.0625000
$257$		−	3.96591e13i		−	0.137640i	−0.997629	−	0.0688200i	$-0.978077\pi$
$257$		−	3.96591e13i		−	0.137640i	0.997629	−	0.0688200i	$-0.0219234\pi$
$258$			5.23662e13i			0.177555i
$259$	1.30703e14	+	1.69821e14i	0.432998	+	0.562590i
$260$	−1.60108e14			−0.518291
$261$	−4.10750e14			−1.29937
$262$		−	9.62973e13i		−	0.297719i
$263$	1.78810e14			0.540327			0.270164	−	0.962814i	$-0.412922\pi$
$263$	1.78810e14			0.540327			0.270164	+	0.962814i	$0.412922\pi$
$264$			4.86265e13i			0.143632i
$265$		−	1.97355e14i		−	0.569867i
$266$	−3.45911e14	+	2.66231e14i	−0.976505	+	0.751569i
$267$	−1.21489e14			−0.335329
$268$	1.22092e14			0.329519
$269$		−	5.00560e14i		−	1.32112i	−0.750773	−	0.660560i	$-0.770319\pi$
$269$		−	5.00560e14i		−	1.32112i	0.750773	−	0.660560i	$-0.229681\pi$
$270$	2.39642e14			0.618558
$271$			1.94816e14i			0.491822i	0.969292	+	0.245911i	$0.0790872\pi$
$271$			1.94816e14i			0.491822i	−0.969292	+	0.245911i	$0.920913\pi$
$272$			6.35237e13i			0.156864i
$273$	−1.05293e14	−	1.36806e14i	−0.254345	−	0.330467i
$274$	−2.44406e14			−0.577575
$275$	−8.14415e13			−0.188300
$276$			5.65216e13i			0.127868i
$277$	4.77604e14			1.05728			0.528640	−	0.848846i	$-0.322702\pi$
$277$	4.77604e14			1.05728			0.528640	+	0.848846i	$0.322702\pi$
$278$		−	1.39051e14i		−	0.301234i
$279$			6.53096e14i			1.38469i
$280$	−1.48188e14	+	1.14053e14i	−0.307515	+	0.236679i
$281$	6.92339e14			1.40631			0.703155	−	0.711037i	$-0.251774\pi$
$281$	6.92339e14			1.40631			0.703155	+	0.711037i	$0.251774\pi$
$282$	9.69689e13			0.192814
$283$		−	9.19667e14i		−	1.79024i	−0.445823	−	0.895121i	$-0.647089\pi$
$283$		−	9.19667e14i		−	1.79024i	0.445823	−	0.895121i	$-0.352911\pi$
$284$	1.32657e14			0.252824
$285$		−	4.52574e14i		−	0.844541i
$286$		−	3.36256e14i		−	0.614432i
$287$	5.66895e13	−	4.36312e13i	0.101440	−	0.0780738i
$288$	8.12073e13			0.142312
$289$	3.53244e14			0.606301
$290$			7.45117e14i			1.25267i
$291$	−4.37646e14			−0.720717
$292$		−	3.02270e13i		−	0.0487639i
$293$		−	5.68183e14i		−	0.898013i	−0.893528	−	0.449007i	$-0.851778\pi$
$293$		−	5.68183e14i		−	0.898013i	0.893528	−	0.449007i	$-0.148222\pi$
$294$	−1.94908e14	−	5.16152e13i	−0.301818	−	0.0799270i
$295$	1.01524e15			1.54041
$296$	−1.68818e14			−0.250997
$297$			5.03291e14i			0.733298i
$298$	−2.17823e14			−0.311033
$299$		−	3.90851e14i		−	0.546996i
$300$		−	3.29388e13i		−	0.0451835i
$301$	−2.57954e14	−	3.35157e14i	−0.346851	−	0.450660i
$302$	−6.25180e14			−0.824068
$303$	−4.33368e14			−0.560017
$304$		−	3.43868e14i		−	0.435663i
$305$	−3.83661e14			−0.476594
$306$			2.93232e14i			0.357176i
$307$			1.42572e14i			0.170295i	0.996368	+	0.0851477i	$0.0271362\pi$
$307$			1.42572e14i			0.170295i	−0.996368	+	0.0851477i	$0.972864\pi$
$308$	−2.39532e14	−	3.11222e14i	−0.280582	−	0.364558i
$309$	1.52614e14			0.175325
$310$	1.18474e15			1.33492
$311$			9.22041e14i			1.01903i	0.860461	+	0.509516i	$0.170176\pi$
$311$			9.22041e14i			1.01903i	−0.860461	+	0.509516i	$0.829824\pi$
$312$	1.35998e14			0.147436
$313$			1.10750e15i			1.17781i	0.808201	+	0.588907i	$0.200441\pi$
$313$			1.10750e15i			1.17781i	−0.808201	+	0.588907i	$0.799559\pi$
$314$			9.12700e14i			0.952248i
$315$	−6.84053e14	+	5.26482e14i	−0.700207	+	0.538915i
$316$	4.79391e14			0.481468
$317$	−6.06894e14			−0.598077			−0.299038	−	0.954241i	$-0.596666\pi$
$317$	−6.06894e14			−0.598077			−0.299038	+	0.954241i	$0.596666\pi$
$318$			1.67636e14i			0.162108i
$319$	−1.56488e15			−1.48503
$320$		−	1.47313e14i		−	0.137196i
$321$			6.76610e14i			0.618455i
$322$	−2.78423e14	−	3.61753e14i	−0.249787	−	0.324546i
$323$	1.24168e15			1.09344
$324$	2.62090e14			0.226559
$325$			2.27774e14i			0.193288i
$326$	−9.16424e14			−0.763468
$327$		−	1.07024e15i		−	0.875376i
$328$			5.63547e13i			0.0452572i
$329$	−6.20625e14	+	4.77665e14i	−0.489389	+	0.376659i
$330$	4.07189e14			0.315291
$331$	−5.43125e12			−0.00412982			−0.00206491	−	0.999998i	$-0.500657\pi$
$331$	−5.43125e12			−0.00412982			−0.00206491	+	0.999998i	$0.500657\pi$
$332$		−	2.73921e14i		−	0.204549i
$333$	−7.79280e14			−0.571515
$334$		−	4.97450e14i		−	0.358320i
$335$		−	1.02238e15i		−	0.723340i
$336$	1.25873e14	−	9.68783e13i	0.0874776	−	0.0673272i
$337$	5.72107e14			0.390569			0.195284	−	0.980747i	$-0.437437\pi$
$337$	5.72107e14			0.390569			0.195284	+	0.980747i	$0.437437\pi$
$338$	1.13916e14			0.0763984
$339$			1.16670e15i			0.768708i
$340$	5.31934e14			0.344338
$341$			2.48817e15i			1.58254i
$342$		−	1.58733e15i		−	0.991998i
$343$	1.50171e15	−	6.29757e14i	0.922193	−	0.386730i
$344$	3.33178e14			0.201060
$345$	4.73301e14			0.280687
$346$		−	1.78748e15i		−	1.04180i
$347$	2.48442e14			0.142314			0.0711572	−	0.997465i	$-0.477331\pi$
$347$	2.48442e14			0.142314			0.0711572	+	0.997465i	$0.477331\pi$
$348$		−	6.32911e14i		−	0.356342i
$349$		−	1.93344e15i		−	1.06999i	−0.844856	−	0.534994i	$-0.820314\pi$
$349$		−	1.93344e15i		−	1.06999i	0.844856	−	0.534994i	$-0.179686\pi$
$350$	1.62255e14	+	2.10817e14i	0.0882654	+	0.114682i
$351$	1.40760e15			0.752723
$352$	3.09384e14			0.162646
$353$		−	3.51317e15i		−	1.81573i	−0.419261	−	0.907866i	$-0.637711\pi$
$353$		−	3.51317e15i		−	1.81573i	0.419261	−	0.907866i	$-0.362289\pi$
$354$	−8.62356e14			−0.438195
$355$		−	1.11084e15i		−	0.554985i
$356$			7.72971e14i			0.379720i
$357$	3.49818e14	+	4.54515e14i	0.168979	+	0.219553i
$358$	2.03022e15			0.964371
$359$	1.80389e15			0.842644			0.421322	−	0.906911i	$-0.361566\pi$
$359$	1.80389e15			0.842644			0.421322	+	0.906911i	$0.361566\pi$
$360$		−	6.80013e14i		−	0.312394i
$361$	−4.50816e15			−2.03684
$362$			2.95127e15i			1.31147i
$363$		−	1.55055e14i		−	0.0677713i
$364$	−8.70420e14	+	6.69920e14i	−0.374215	+	0.288015i
$365$	−2.53115e14			−0.107044
$366$	3.25886e14			0.135575
$367$			1.98525e15i			0.812491i	0.913764	+	0.406245i	$0.133162\pi$
$367$			1.98525e15i			0.812491i	−0.913764	+	0.406245i	$0.866838\pi$
$368$	3.59616e14			0.144795
$369$			2.60139e14i			0.103050i
$370$			1.41365e15i			0.550973i
$371$	−8.25768e14	−	1.07291e15i	−0.316676	−	0.411453i
$372$	−1.00633e15			−0.379738
$373$	1.67605e15			0.622348			0.311174	−	0.950353i	$-0.399278\pi$
$373$	1.67605e15			0.622348			0.311174	+	0.950353i	$0.399278\pi$
$374$			1.11716e15i			0.408211i
$375$	1.07189e15			0.385445
$376$		−	6.16960e14i		−	0.218338i
$377$			4.37662e15i			1.52437i
$378$	1.30280e15	−	1.00270e15i	0.446609	−	0.343733i
$379$	−2.71186e15			−0.915024			−0.457512	−	0.889204i	$-0.651259\pi$
$379$	−2.71186e15			−0.915024			−0.457512	+	0.889204i	$0.651259\pi$
$380$	−2.87948e15			−0.956341
$381$			1.93665e15i			0.633142i
$382$	−1.78795e15			−0.575407
$383$		−	5.49836e15i		−	1.74197i	−0.491310	−	0.870985i	$-0.663482\pi$
$383$		−	5.49836e15i		−	1.74197i	0.491310	−	0.870985i	$-0.336518\pi$
$384$			1.25130e14i			0.0390277i
$385$	−2.60611e15	+	2.00580e15i	−0.800255	+	0.615917i
$386$	−2.45373e15			−0.741827
$387$	1.53798e15			0.457810
$388$			2.78450e15i			0.816126i
$389$	3.52503e15			1.01734			0.508668	−	0.860963i	$-0.330138\pi$
$389$	3.52503e15			1.01734			0.508668	+	0.860963i	$0.330138\pi$
$390$		−	1.13882e15i		−	0.323643i
$391$			1.29854e15i			0.363408i
$392$	−3.28399e14	+	1.24009e15i	−0.0905078	+	0.341772i
$393$	6.84943e14			0.185908
$394$	−1.60042e15			−0.427816
$395$		−	4.01432e15i		−	1.05689i
$396$	1.42815e15			0.370341
$397$			2.66362e15i			0.680345i	0.940363	+	0.340173i	$0.110486\pi$
$397$			2.66362e15i			0.680345i	−0.940363	+	0.340173i	$0.889514\pi$
$398$		−	2.68784e15i		−	0.676246i
$399$	−1.89365e15	−	2.46039e15i	−0.469312	−	0.609772i
$400$	−2.09572e14			−0.0511650
$401$	−2.18901e15			−0.526480			−0.263240	−	0.964730i	$-0.584791\pi$
$401$	−2.18901e15			−0.526480			−0.263240	+	0.964730i	$0.584791\pi$
$402$			8.68419e14i			0.205766i
$403$	6.95887e15			1.62446
$404$			2.75729e15i			0.634153i
$405$		−	2.19469e15i		−	0.497329i
$406$	3.11769e15	+	4.05079e15i	0.696109	+	0.904447i
$407$	−2.96891e15			−0.653176
$408$	−4.51831e14			−0.0979524
$409$			5.27335e15i			1.12654i	0.826273	+	0.563270i	$0.190457\pi$
$409$			5.27335e15i			1.12654i	−0.826273	+	0.563270i	$0.809543\pi$
$410$	4.71903e14			0.0993458
$411$		−	1.73841e15i		−	0.360662i
$412$		−	9.71001e14i		−	0.198535i
$413$	5.51929e15	−	4.24793e15i	1.11220	−	0.856007i
$414$	1.66003e15			0.329695
$415$	−2.29376e15			−0.449013
$416$		−	8.65280e14i		−	0.166954i
$417$	9.89039e14			0.188103
$418$		−	6.04743e15i		−	1.13374i
$419$			2.34826e15i			0.433973i	0.976175	+	0.216986i	$0.0696227\pi$
$419$			2.34826e15i			0.433973i	−0.976175	+	0.216986i	$0.930377\pi$
$420$	−8.11239e14	−	1.05403e15i	−0.147793	−	0.192025i
$421$	−7.08816e15			−1.27304			−0.636519	−	0.771261i	$-0.719626\pi$
$421$	−7.08816e15			−1.27304			−0.636519	+	0.771261i	$0.719626\pi$
$422$	−2.84099e15			−0.503031
$423$		−	2.84795e15i		−	0.497153i
$424$	1.06658e15			0.183568
$425$		−	7.56743e14i		−	0.128415i
$426$			9.43559e14i			0.157874i
$427$	−2.08575e15	+	1.60530e15i	−0.344108	+	0.264843i
$428$	4.30490e15			0.700327
$429$	2.39172e15			0.383678
$430$		−	2.78996e15i		−	0.441354i
$431$	6.46463e15			1.00851			0.504255	−	0.863555i	$-0.331767\pi$
$431$	6.46463e15			1.00851			0.504255	+	0.863555i	$0.331767\pi$
$432$			1.29511e15i			0.199252i
$433$		−	4.42035e15i		−	0.670701i	−0.942093	−	0.335351i	$-0.891145\pi$
$433$		−	4.42035e15i		−	0.670701i	0.942093	−	0.335351i	$-0.108855\pi$
$434$	6.44079e15	−	4.95716e15i	0.963830	−	0.741813i
$435$	−5.29986e15			−0.782220
$436$	−6.80935e15			−0.991258
$437$		−	7.02930e15i		−	1.00931i
$438$	2.14999e14			0.0304503
$439$			1.32566e16i			1.85202i	0.377501	+	0.926009i	$0.376783\pi$
$439$			1.32566e16i			1.85202i	−0.377501	+	0.926009i	$0.623217\pi$
$440$		−	2.59072e15i		−	0.357030i
$441$	−1.51592e15	+	5.72438e15i	−0.206085	+	0.778210i
$442$	3.12444e15			0.419024
$443$	6.84771e15			0.905989			0.452995	−	0.891513i	$-0.350356\pi$
$443$	6.84771e15			0.905989			0.452995	+	0.891513i	$0.350356\pi$
$444$		−	1.20077e15i		−	0.156733i
$445$	6.47270e15			0.833538
$446$			3.05678e15i			0.388379i
$447$		−	1.54933e15i		−	0.194222i
$448$	−6.16384e14	−	8.00861e14i	−0.0762400	−	0.0990579i
$449$	−1.39377e16			−1.70103			−0.850515	−	0.525950i	$-0.823710\pi$
$449$	−1.39377e16			−1.70103			−0.850515	+	0.525950i	$0.823710\pi$
$450$	−9.67404e14			−0.116502
$451$			9.91080e14i			0.117774i
$452$	7.42308e15			0.870470
$453$		−	4.44677e15i		−	0.514584i
$454$			5.54640e15i			0.633397i
$455$	5.60977e15	+	7.28872e15i	0.632233	+	0.821453i
$456$	2.44587e15			0.272047
$457$	−7.42405e15			−0.814974			−0.407487	−	0.913211i	$-0.633595\pi$
$457$	−7.42405e15			−0.814974			−0.407487	+	0.913211i	$0.633595\pi$
$458$		−	3.21576e15i		−	0.348410i
$459$	−4.67651e15			−0.500087
$460$		−	3.01135e15i		−	0.317845i
$461$			1.49069e15i			0.155304i	0.996981	+	0.0776521i	$0.0247423\pi$
$461$			1.49069e15i			0.155304i	−0.996981	+	0.0776521i	$0.975258\pi$
$462$	2.21366e15	−	1.70375e15i	0.227645	−	0.175208i
$463$	−5.08405e15			−0.516088			−0.258044	−	0.966133i	$-0.583078\pi$
$463$	−5.08405e15			−0.516088			−0.258044	+	0.966133i	$0.583078\pi$
$464$	−4.02687e15			−0.403515
$465$			8.42683e15i			0.833579i
$466$	−6.56615e15			−0.641203
$467$			1.01578e15i			0.0979256i	0.998801	+	0.0489628i	$0.0155916\pi$
$467$			1.01578e15i			0.0979256i	−0.998801	+	0.0489628i	$0.984408\pi$
$468$		−	3.99422e15i		−	0.380152i
$469$	−4.27780e15	−	5.55810e15i	−0.401960	−	0.522263i
$470$	−5.16630e15			−0.479283
$471$	−6.49184e15			−0.594624
$472$			5.48670e15i			0.496203i
$473$	5.85941e15			0.523223
$474$			3.40981e15i			0.300649i
$475$			4.09642e15i			0.356651i
$476$	2.89183e15	−	2.22570e15i	0.248617	−	0.191349i
$477$	4.92342e15			0.417981
$478$	−7.83293e15			−0.656684
$479$			9.98479e15i			0.826658i	0.910582	+	0.413329i	$0.135634\pi$
$479$			9.98479e15i			0.826658i	−0.910582	+	0.413329i	$0.864366\pi$
$480$	1.04781e15			0.0856712
$481$			8.30338e15i			0.670478i
$482$			7.01587e15i			0.559499i
$483$	2.57307e15	−	1.98037e15i	0.202661	−	0.155978i
$484$	−9.86530e14			−0.0767429
$485$	2.33169e16			1.79151
$486$			9.29039e15i			0.705044i
$487$	−6.94006e15			−0.520223			−0.260111	−	0.965579i	$-0.583759\pi$
$487$	−6.94006e15			−0.520223			−0.260111	+	0.965579i	$0.583759\pi$
$488$		−	2.07343e15i		−	0.153522i
$489$		−	6.51834e15i		−	0.476742i
$490$	1.03843e16	+	2.74995e15i	0.750238	+	0.198677i
$491$	−2.58155e16			−1.84244			−0.921218	−	0.389048i	$-0.872804\pi$
$491$	−2.58155e16			−1.84244			−0.921218	+	0.389048i	$0.872804\pi$
$492$	−4.00840e14			−0.0282605
$493$		−	1.45406e16i		−	1.01275i
$494$	−1.69133e16			−1.16377
$495$		−	1.19590e16i		−	0.812951i
$496$			6.40275e15i			0.430008i
$497$	−4.64793e15	−	6.03901e15i	−0.308405	−	0.400708i
$498$	1.94834e15			0.127729
$499$	2.21490e16			1.43467			0.717334	−	0.696730i	$-0.245362\pi$
$499$	2.21490e16			1.43467			0.717334	+	0.696730i	$0.245362\pi$
$500$		−	6.81986e15i		−	0.436471i
$501$	3.53826e15			0.223750
$502$		−	1.19540e15i		−	0.0746947i
$503$		−	1.32694e16i		−	0.819301i	−0.912243	−	0.409651i	$-0.865651\pi$
$503$		−	1.32694e16i		−	0.819301i	0.912243	−	0.409651i	$-0.134349\pi$
$504$	−2.84529e15	−	3.69685e15i	−0.173597	−	0.225553i
$505$	2.30890e16			1.39205
$506$	6.32438e15			0.376803
$507$			8.10261e14i			0.0477065i
$508$	1.23218e16			0.716958
$509$		−	3.04670e16i		−	1.75195i	−0.482352	−	0.875977i	$-0.660218\pi$
$509$		−	3.04670e16i		−	1.75195i	0.482352	−	0.875977i	$-0.339782\pi$
$510$			3.78354e15i			0.215019i
$511$	−1.37604e15	+	1.05908e15i	−0.0772871	+	0.0594842i
$512$	7.96131e14			0.0441942
$513$	2.53150e16			1.38891
$514$		−	1.79477e15i		−	0.0973261i
$515$	−8.13096e15			−0.435811
$516$			2.36982e15i			0.125550i
$517$		−	1.08501e16i		−	0.568188i
$518$	5.91493e15	+	7.68520e15i	0.306176	+	0.397811i
$519$	1.27140e16			0.650544
$520$	−7.24568e15			−0.366487
$521$			8.65982e15i			0.432995i	0.976283	+	0.216497i	$0.0694633\pi$
$521$			8.65982e15i			0.432995i	−0.976283	+	0.216497i	$0.930537\pi$
$522$	−1.85884e16			−0.918796
$523$			1.27985e15i			0.0625388i	0.999511	+	0.0312694i	$0.00995498\pi$
$523$			1.27985e15i			0.0625388i	−0.999511	+	0.0312694i	$0.990045\pi$
$524$		−	4.35792e15i		−	0.210519i
$525$	−1.49950e15	+	1.15409e15i	−0.0716126	+	0.0551167i
$526$	8.09201e15			0.382069
$527$	−2.31197e16			−1.07924
$528$			2.20059e15i			0.101563i
$529$	−1.45634e16			−0.664552
$530$		−	8.93128e15i		−	0.402957i
$531$			2.53272e16i			1.12985i
$532$	−1.56541e16	+	1.20482e16i	−0.690494	+	0.531439i
$533$	2.77183e15			0.120894
$534$	−5.49799e15			−0.237113
$535$		−	3.60484e16i		−	1.53732i
$536$	5.52527e15			0.233005
$537$			1.44405e16i			0.602195i
$538$		−	2.26528e16i		−	0.934173i
$539$	−5.77538e15	+	2.18088e16i	−0.235531	+	0.889404i
$540$	1.08450e16			0.437387
$541$	−6.76645e15			−0.269884			−0.134942	−	0.990854i	$-0.543085\pi$
$541$	−6.76645e15			−0.269884			−0.134942	+	0.990854i	$0.543085\pi$
$542$			8.81636e15i			0.347771i
$543$	−2.09917e16			−0.818935
$544$			2.87475e15i			0.110919i
$545$			5.70201e16i			2.17595i
$546$	−4.76500e15	−	6.19112e15i	−0.179849	−	0.233676i
$547$	3.11128e16			1.16149			0.580745	−	0.814086i	$-0.302761\pi$
$547$	3.11128e16			1.16149			0.580745	+	0.814086i	$0.302761\pi$
$548$	−1.10605e16			−0.408407
$549$		−	9.57117e15i		−	0.349568i
$550$	−3.68562e15			−0.133148
$551$			7.87117e16i			2.81274i
$552$			2.55788e15i			0.0904160i
$553$	−1.67966e16	−	2.18236e16i	−0.587314	−	0.763091i
$554$	2.16139e16			0.747609
$555$	−1.00550e16			−0.344051
$556$		−	6.29271e15i		−	0.213005i
$557$	−1.20078e16			−0.402098			−0.201049	−	0.979581i	$-0.564435\pi$
$557$	−1.20078e16			−0.402098			−0.201049	+	0.979581i	$0.564435\pi$
$558$			2.95557e16i			0.979122i
$559$		−	1.63875e16i		−	0.537084i
$560$	−6.70624e15	+	5.16147e15i	−0.217446	+	0.167358i
$561$	−7.94610e15			−0.254904
$562$	3.13317e16			0.994411
$563$			2.90442e16i			0.912030i	0.889972	+	0.456015i	$0.150724\pi$
$563$			2.90442e16i			0.912030i	−0.889972	+	0.456015i	$0.849276\pi$
$564$	4.38831e15			0.136340
$565$		−	6.21594e16i		−	1.91080i
$566$		−	4.16194e16i		−	1.26589i
$567$	−9.18296e15	−	1.19313e16i	−0.276366	−	0.359079i
$568$	6.00335e15			0.178774
$569$	−3.98456e16			−1.17411			−0.587053	−	0.809549i	$-0.699712\pi$
$569$	−3.98456e16			−1.17411			−0.587053	+	0.809549i	$0.699712\pi$
$570$		−	2.04812e16i		−	0.597181i
$571$	1.06745e16			0.307986			0.153993	−	0.988072i	$-0.450787\pi$
$571$	1.06745e16			0.307986			0.153993	+	0.988072i	$0.450787\pi$
$572$		−	1.52172e16i		−	0.434469i
$573$		−	1.27173e16i		−	0.359309i
$574$	2.56547e15	−	1.97452e15i	0.0717292	−	0.0552065i
$575$	−4.28403e15			−0.118535
$576$	3.67502e15			0.100629
$577$			5.69176e16i			1.54238i	0.636604	+	0.771191i	$0.280339\pi$
$577$			5.69176e16i			1.54238i	−0.636604	+	0.771191i	$0.719661\pi$
$578$	1.59860e16			0.428719
$579$		−	1.74529e16i		−	0.463228i
$580$			3.37201e16i			0.885771i
$581$	−1.24699e16	+	9.59747e15i	−0.324195	+	0.249517i
$582$	−1.98056e16			−0.509624
$583$	1.87573e16			0.477704
$584$		−	1.36792e15i		−	0.0344813i
$585$	−3.34468e16			−0.834486
$586$		−	2.57130e16i		−	0.634991i
$587$		−	4.51143e16i		−	1.10277i	−0.834250	−	0.551386i	$-0.814099\pi$
$587$		−	4.51143e16i		−	1.10277i	0.834250	−	0.551386i	$-0.185901\pi$
$588$	−8.82051e15	−	2.33584e15i	−0.213417	−	0.0565170i
$589$	1.25152e17			2.99742
$590$	4.59445e16			1.08923
$591$		−	1.13835e16i		−	0.267147i
$592$	−7.63982e15			−0.177481
$593$			1.11718e16i			0.256917i	0.991715	+	0.128459i	$0.0410030\pi$
$593$			1.11718e16i			0.256917i	−0.991715	+	0.128459i	$0.958997\pi$
$594$			2.27764e16i			0.518520i
$595$	−1.86376e16	−	2.42156e16i	−0.420037	−	0.545750i
$596$	−9.85756e15			−0.219934
$597$	1.91180e16			0.422277
$598$		−	1.76879e16i		−	0.386785i
$599$	5.04237e16			1.09163			0.545813	−	0.837907i	$-0.316221\pi$
$599$	5.04237e16			1.09163			0.545813	+	0.837907i	$0.316221\pi$
$600$		−	1.49064e15i		−	0.0319496i
$601$		−	6.11133e15i		−	0.129685i	−0.997896	−	0.0648424i	$-0.979346\pi$
$601$		−	6.11133e15i		−	0.129685i	0.997896	−	0.0648424i	$-0.0206545\pi$
$602$	−1.16737e16	−	1.51675e16i	−0.245261	−	0.318665i
$603$	2.55052e16			0.530549
$604$	−2.82924e16			−0.582704
$605$			8.26100e15i			0.168461i
$606$	−1.96120e16			−0.395992
$607$		−	5.40145e15i		−	0.107989i	−0.998541	−	0.0539943i	$-0.982805\pi$
$607$		−	5.40145e15i		−	0.107989i	0.998541	−	0.0539943i	$-0.0171953\pi$
$608$		−	1.55617e16i		−	0.308060i
$609$	−2.88124e16	+	2.21755e16i	−0.564775	+	0.434680i
$610$	−1.73625e16			−0.337003
$611$	−3.03455e16			−0.583240
$612$			1.32702e16i			0.252562i
$613$	−1.04841e16			−0.197592			−0.0987961	−	0.995108i	$-0.531499\pi$
$613$	−1.04841e16			−0.197592			−0.0987961	+	0.995108i	$0.531499\pi$
$614$			6.45206e15i			0.120417i
$615$			3.35655e15i			0.0620358i
$616$	−1.08400e16	−	1.40843e16i	−0.198402	−	0.257781i
$617$	−3.78397e16			−0.685862			−0.342931	−	0.939361i	$-0.611420\pi$
$617$	−3.78397e16			−0.685862			−0.342931	+	0.939361i	$0.611420\pi$
$618$	6.90653e15			0.123974
$619$		−	2.62642e16i		−	0.466896i	−0.972369	−	0.233448i	$-0.924999\pi$
$619$		−	2.62642e16i		−	0.466896i	0.972369	−	0.233448i	$-0.0750008\pi$
$620$	5.36153e16			0.943928
$621$			2.64744e16i			0.461611i
$622$			4.17268e16i			0.720565i
$623$	3.51885e16	−	2.70829e16i	0.601828	−	0.463198i
$624$	6.15456e15			0.104253
$625$	−6.93067e16			−1.16277
$626$			5.01196e16i			0.832840i
$627$	4.30141e16			0.707955
$628$			4.13041e16i			0.673341i
$629$		−	2.75867e16i		−	0.445446i
$630$	−3.09567e16	+	2.38259e16i	−0.495121	+	0.381070i
$631$	−9.67799e15			−0.153324			−0.0766618	−	0.997057i	$-0.524426\pi$
$631$	−9.67799e15			−0.153324			−0.0766618	+	0.997057i	$0.524426\pi$
$632$	2.16948e16			0.340449
$633$		−	2.02073e16i		−	0.314114i
$634$	−2.74649e16			−0.422904
$635$		−	1.03181e17i		−	1.57382i
$636$			7.58633e15i			0.114628i
$637$	6.09944e16	+	1.61525e16i	0.912964	+	0.241770i
$638$	−7.08183e16			−1.05008
$639$	2.77121e16			0.407065
$640$		−	6.66664e15i		−	0.0970124i
$641$	−5.73035e16			−0.826101			−0.413050	−	0.910708i	$-0.635537\pi$
$641$	−5.73035e16			−0.826101			−0.413050	+	0.910708i	$0.635537\pi$
$642$			3.06199e16i			0.437314i
$643$			4.27668e16i			0.605119i	0.953131	+	0.302559i	$0.0978410\pi$
$643$			4.27668e16i			0.605119i	−0.953131	+	0.302559i	$0.902159\pi$
$644$	−1.26000e16	−	1.63711e16i	−0.176626	−	0.229489i
$645$	1.98444e16			0.275601
$646$	5.61918e16			0.773175
$647$			7.05664e15i			0.0961994i	0.998843	+	0.0480997i	$0.0153165\pi$
$647$			7.05664e15i			0.0961994i	−0.998843	+	0.0480997i	$0.984683\pi$
$648$	1.18609e16			0.160201
$649$			9.64916e16i			1.29128i
$650$			1.03079e16i			0.136675i
$651$	3.52593e16	+	4.58120e16i	0.463220	+	0.601857i
$652$	−4.14726e16			−0.539853
$653$	5.13577e15			0.0662410			0.0331205	−	0.999451i	$-0.489455\pi$
$653$	5.13577e15			0.0662410			0.0331205	+	0.999451i	$0.489455\pi$
$654$		−	4.84335e16i		−	0.618984i
$655$	−3.64923e16			−0.462119
$656$			2.55032e15i			0.0320016i
$657$		−	6.31445e15i		−	0.0785133i
$658$	−2.80863e16	+	2.16167e16i	−0.346050	+	0.266338i
$659$	−7.30365e16			−0.891718			−0.445859	−	0.895103i	$-0.647102\pi$
$659$	−7.30365e16			−0.891718			−0.445859	+	0.895103i	$0.647102\pi$
$660$	1.84273e16			0.222945
$661$		−	5.83643e16i		−	0.699743i	−0.936798	−	0.349871i	$-0.886225\pi$
$661$		−	5.83643e16i		−	0.699743i	0.936798	−	0.349871i	$-0.113775\pi$
$662$	−2.45790e14			−0.00292023
$663$			2.22235e16i			0.261657i
$664$		−	1.23963e16i		−	0.144638i
$665$	1.00889e17	+	1.31085e17i	1.16658	+	1.51573i
$666$	−3.52662e16			−0.404122
$667$	−8.23165e16			−0.934828
$668$		−	2.25120e16i		−	0.253370i
$669$	−2.17423e16			−0.242520
$670$		−	4.62675e16i		−	0.511478i
$671$		−	3.64643e16i		−	0.399515i
$672$	5.69636e15	−	4.38421e15i	0.0618560	−	0.0476075i
$673$	−1.02330e17			−1.10131			−0.550656	−	0.834732i	$-0.685623\pi$
$673$	−1.02330e17			−1.10131			−0.550656	+	0.834732i	$0.685623\pi$
$674$	2.58906e16			0.276174
$675$		−	1.54283e16i		−	0.163116i
$676$	5.15525e15			0.0540219
$677$		−	1.61708e16i		−	0.167957i	−0.996468	−	0.0839787i	$-0.973237\pi$
$677$		−	1.61708e16i		−	0.167957i	0.996468	−	0.0839787i	$-0.0267628\pi$
$678$			5.27989e16i			0.543559i
$679$	1.26761e17	−	9.75616e16i	1.29350	−	0.995544i
$680$	2.40726e16			0.243483
$681$	−3.94504e16			−0.395520
$682$			1.12602e17i			1.11902i
$683$	8.92961e16			0.879646			0.439823	−	0.898084i	$-0.355041\pi$
$683$	8.92961e16			0.879646			0.439823	+	0.898084i	$0.355041\pi$
$684$		−	7.18344e16i		−	0.701448i
$685$			9.26187e16i			0.896511i
$686$	6.79597e16	−	2.84995e16i	0.652089	−	0.273460i
$687$	2.28731e16			0.217562
$688$	1.50779e16			0.142171
$689$		−	5.24600e16i		−	0.490358i
$690$	2.14191e16			0.198476
$691$		−	5.19820e16i		−	0.477512i	−0.971080	−	0.238756i	$-0.923260\pi$
$691$		−	5.19820e16i		−	0.477512i	0.971080	−	0.238756i	$-0.0767397\pi$
$692$		−	8.08919e16i		−	0.736663i
$693$	−5.00385e16	−	6.50145e16i	−0.451757	−	0.586964i
$694$	1.12432e16			0.100631
$695$	−5.26939e16			−0.467575
$696$		−	2.86423e16i		−	0.251972i
$697$	−9.20897e15			−0.0803183
$698$		−	8.74977e16i		−	0.756596i
$699$		−	4.67037e16i		−	0.400395i
$700$	7.34284e15	+	9.54047e15i	0.0624131	+	0.0810927i
$701$	5.55849e16			0.468435			0.234217	−	0.972184i	$-0.424747\pi$
$701$	5.55849e16			0.468435			0.234217	+	0.972184i	$0.424747\pi$
$702$	6.37005e16			0.532256
$703$			1.49333e17i			1.23715i
$704$	1.40011e16			0.115008
$705$		−	3.67468e16i		−	0.299285i
$706$		−	1.58988e17i		−	1.28392i
$707$	1.25522e17	−	9.66080e16i	1.00508	−	0.773565i
$708$	−3.90258e16			−0.309850
$709$	−5.06204e16			−0.398518			−0.199259	−	0.979947i	$-0.563854\pi$
$709$	−5.06204e16			−0.398518			−0.199259	+	0.979947i	$0.563854\pi$
$710$		−	5.02708e16i		−	0.392433i
$711$	1.00145e17			0.775198
$712$			3.49807e16i			0.268503i
$713$			1.30884e17i			0.996206i
$714$	1.58310e16	+	2.05690e16i	0.119486	+	0.155247i
$715$	−1.27426e17			−0.953721
$716$	9.18771e16			0.681914
$717$		−	5.57140e16i		−	0.410062i
$718$	8.16349e16			0.595839
$719$			1.49143e17i			1.07951i	0.841821	+	0.539757i	$0.181484\pi$
$719$			1.49143e17i			1.07951i	−0.841821	+	0.539757i	$0.818516\pi$
$720$		−	3.07739e16i		−	0.220896i
$721$	−4.42035e16	+	3.40213e16i	−0.314663	+	0.242181i
$722$	−2.04016e17			−1.44026
$723$	−4.99024e16			−0.349375
$724$			1.33559e17i			0.927346i
$725$	4.79711e16			0.330333
$726$		−	7.01699e15i		−	0.0479216i
$727$		−	4.70655e16i		−	0.318784i	−0.987215	−	0.159392i	$-0.949047\pi$
$727$		−	4.70655e16i		−	0.318784i	0.987215	−	0.159392i	$-0.0509533\pi$
$728$	−3.93907e16	+	3.03171e16i	−0.264610	+	0.203657i
$729$	1.92995e15			0.0128582
$730$	−1.14547e16			−0.0756912
$731$			5.44448e16i			0.356823i
$732$	1.47479e16			0.0958658
$733$			9.08600e16i			0.585799i	0.956143	+	0.292900i	$0.0946202\pi$
$733$			9.08600e16i			0.585799i	−0.956143	+	0.292900i	$0.905380\pi$
$734$			8.98421e16i			0.574518i
$735$	−1.95598e16	+	7.38611e16i	−0.124063	+	0.468481i
$736$	1.62744e16			0.102385
$737$	9.71700e16			0.606355
$738$			1.17726e16i			0.0728672i
$739$	−1.57582e17			−0.967473			−0.483737	−	0.875214i	$-0.660721\pi$
$739$	−1.57582e17			−0.967473			−0.483737	+	0.875214i	$0.660721\pi$
$740$			6.39743e16i			0.389597i
$741$		−	1.20301e17i		−	0.726708i
$742$	−3.73700e16	−	4.85544e16i	−0.223923	−	0.290941i
$743$	−3.29081e17			−1.95600			−0.978002	−	0.208597i	$-0.933110\pi$
$743$	−3.29081e17			−1.95600			−0.978002	+	0.208597i	$0.933110\pi$
$744$	−4.55415e16			−0.268515
$745$			8.25452e16i			0.482785i
$746$	7.58493e16			0.440067
$747$		−	5.72223e16i		−	0.329338i
$748$			5.05567e16i			0.288649i
$749$	−1.50832e17	−	1.95975e17i	−0.854287	−	1.10997i
$750$	4.85082e16			0.272551
$751$	−1.25278e17			−0.698291			−0.349146	−	0.937068i	$-0.613528\pi$
$751$	−1.25278e17			−0.698291			−0.349146	+	0.937068i	$0.613528\pi$
$752$		−	2.79204e16i		−	0.154389i
$753$	8.50261e15			0.0466426
$754$			1.98063e17i			1.07789i
$755$			2.36915e17i			1.27912i
$756$	5.89581e16	−	4.53772e16i	0.315800	−	0.243056i
$757$	2.14020e17			1.13731			0.568655	−	0.822576i	$-0.307464\pi$
$757$	2.14020e17			1.13731			0.568655	+	0.822576i	$0.307464\pi$
$758$	−1.22725e17			−0.647020
$759$			4.49840e16i			0.235292i
$760$	−1.30311e17			−0.676235
$761$		−	9.85642e16i		−	0.507471i	−0.967274	−	0.253736i	$-0.918341\pi$
$761$		−	9.85642e16i		−	0.507471i	0.967274	−	0.253736i	$-0.0816593\pi$
$762$			8.76427e16i			0.447699i
$763$	2.38582e17	+	3.09987e17i	1.20918	+	1.57107i
$764$	−8.09134e16			−0.406874
$765$	1.11122e17			0.554408
$766$		−	2.48827e17i		−	1.23176i
$767$	2.69866e17			1.32549
$768$			5.66272e15i			0.0275967i
$769$		−	5.66365e16i		−	0.273866i	−0.990580	−	0.136933i	$-0.956275\pi$
$769$		−	5.66365e16i		−	0.273866i	0.990580	−	0.136933i	$-0.0437245\pi$
$770$	−1.17939e17	+	9.07720e16i	−0.565866	+	0.435519i
$771$	1.27658e16			0.0607746
$772$	−1.11043e17			−0.524551
$773$		−	2.50006e17i		−	1.17185i	−0.810364	−	0.585927i	$-0.800730\pi$
$773$		−	2.50006e17i		−	1.17185i	0.810364	−	0.585927i	$-0.199270\pi$
$774$	6.96011e16			0.323720
$775$		−	7.62745e16i		−	0.352022i
$776$			1.26012e17i			0.577088i
$777$	−5.46633e16	+	4.20717e16i	−0.248410	+	0.191189i
$778$	1.59524e17			0.719366
$779$	4.98503e16			0.223071
$780$		−	5.15370e16i		−	0.228850i
$781$	1.05578e17			0.465228
$782$			5.87652e16i			0.256968i
$783$		−	2.96451e17i		−	1.28642i
$784$	−1.48617e16	+	5.61201e16i	−0.0639987	+	0.241670i
$785$	3.45872e17			1.47808
$786$	3.09970e16			0.131457
$787$		−	2.38004e17i		−	1.00169i	−0.865536	−	0.500847i	$-0.833022\pi$
$787$		−	2.38004e17i		−	1.00169i	0.865536	−	0.500847i	$-0.166978\pi$
$788$	−7.24268e16			−0.302511
$789$			5.75568e16i			0.238580i
$790$		−	1.81668e17i		−	0.747334i
$791$	−2.60085e17	−	3.37926e17i	−1.06183	−	1.37963i
$792$	6.46306e16			0.261871
$793$	−1.01983e17			−0.410098
$794$			1.20542e17i			0.481077i
$795$	6.35264e16			0.251624
$796$		−	1.21638e17i		−	0.478178i
$797$		−	4.63716e17i		−	1.80926i	−0.426193	−	0.904632i	$-0.640145\pi$
$797$		−	4.63716e17i		−	1.80926i	0.426193	−	0.904632i	$-0.359855\pi$
$798$	−8.56966e16	−	1.11345e17i	−0.331854	−	0.431174i
$799$	1.00818e17			0.387487
$800$	−9.48413e15			−0.0361791
$801$			1.61474e17i			0.611376i
$802$	−9.90634e16			−0.372278
$803$		−	2.40568e16i		−	0.0897316i
$804$			3.93001e16i			0.145498i
$805$	−1.37088e17	+	1.05510e17i	−0.503760	+	0.387720i
$806$	3.14922e17			1.14867
$807$	1.61124e17			0.583338
$808$			1.24781e17i			0.448414i
$809$	6.94137e15			0.0247602			0.0123801	−	0.999923i	$-0.496059\pi$
$809$	6.94137e15			0.0247602			0.0123801	+	0.999923i	$0.496059\pi$
$810$		−	9.93204e16i		−	0.351664i
$811$			3.87199e17i			1.36085i	0.732819	+	0.680424i	$0.238204\pi$
$811$			3.87199e17i			1.36085i	−0.732819	+	0.680424i	$0.761796\pi$
$812$	1.41091e17	+	1.83318e17i	0.492223	+	0.639541i
$813$	−6.27089e16			−0.217163
$814$	−1.34357e17			−0.461865
$815$			3.47283e17i			1.18505i
$816$	−2.04475e16			−0.0692628
$817$		−	2.94722e17i		−	0.991016i
$818$			2.38644e17i			0.796584i
$819$	−1.81832e17	+	1.39947e17i	−0.602512	+	0.463724i
$820$	2.13559e16			0.0702481
$821$	1.91848e17			0.626467			0.313233	−	0.949676i	$-0.398588\pi$
$821$	1.91848e17			0.626467			0.313233	+	0.949676i	$0.398588\pi$
$822$		−	7.86714e16i		−	0.255027i
$823$	−2.54026e17			−0.817485			−0.408742	−	0.912650i	$-0.634033\pi$
$823$	−2.54026e17			−0.817485			−0.408742	+	0.912650i	$0.634033\pi$
$824$		−	4.39425e16i		−	0.140385i
$825$		−	2.62151e16i		−	0.0831433i
$826$	2.49775e17	−	1.92240e17i	0.786445	−	0.605288i
$827$	−2.42292e16			−0.0757367			−0.0378683	−	0.999283i	$-0.512057\pi$
$827$	−2.42292e16			−0.0757367			−0.0378683	+	0.999283i	$0.512057\pi$
$828$	7.51242e16			0.233130
$829$			1.45965e17i			0.449698i	0.974394	+	0.224849i	$0.0721889\pi$
$829$			1.45965e17i			0.449698i	−0.974394	+	0.224849i	$0.927811\pi$
$830$	−1.03804e17			−0.317500
$831$			1.53735e17i			0.466839i
$832$		−	3.91581e16i		−	0.118054i
$833$	−2.02644e17	−	5.36640e16i	−0.606547	−	0.160625i
$834$	4.47588e16			0.133009
$835$	−1.88511e17			−0.556183
$836$		−	2.73675e17i		−	0.801674i
$837$	−4.71360e17			−1.37088
$838$			1.06270e17i			0.306865i
$839$			4.16440e17i			1.19393i	0.802266	+	0.596967i	$0.203628\pi$
$839$			4.16440e17i			1.19393i	−0.802266	+	0.596967i	$0.796372\pi$
$840$	−3.67125e16	−	4.77001e16i	−0.104505	−	0.135783i
$841$	5.67938e17			1.60518
$842$	−3.20774e17			−0.900173
$843$			2.22856e17i			0.620953i
$844$	−1.28568e17			−0.355696
$845$		−	4.31690e16i		−	0.118586i
$846$		−	1.28884e17i		−	0.351540i
$847$	3.45654e16	+	4.49105e16i	0.0936141	+	0.121632i
$848$	4.82677e16			0.129802
$849$	2.96030e17			0.790478
$850$		−	3.42463e16i		−	0.0908029i
$851$	−1.56172e17			−0.411174
$852$			4.27006e16i			0.111634i
$853$			4.06359e17i			1.05491i	0.849583	+	0.527455i	$0.176854\pi$
$853$			4.06359e17i			1.05491i	−0.849583	+	0.527455i	$0.823146\pi$
$854$	−9.43903e16	+	7.26476e16i	−0.243321	+	0.187273i
$855$	−6.01526e17			−1.53978
$856$	1.94818e17			0.495206
$857$		−	1.14470e17i		−	0.288939i	−0.989509	−	0.144470i	$-0.953852\pi$
$857$		−	1.14470e17i		−	0.288939i	0.989509	−	0.144470i	$-0.0461476\pi$
$858$	1.08237e17			0.271301
$859$		−	3.66056e17i		−	0.911148i	−0.890198	−	0.455574i	$-0.849434\pi$
$859$		−	3.66056e17i		−	0.911148i	0.890198	−	0.455574i	$-0.150566\pi$
$860$		−	1.26259e17i		−	0.312085i
$861$	1.40444e16	+	1.82477e16i	0.0344733	+	0.0447908i
$862$	2.92556e17			0.713124
$863$	4.37768e17			1.05969			0.529845	−	0.848095i	$-0.322250\pi$
$863$	4.37768e17			1.05969			0.529845	+	0.848095i	$0.322250\pi$
$864$			5.86099e16i			0.140893i
$865$	−6.77372e17			−1.61708
$866$		−	2.00042e17i		−	0.474257i
$867$			1.13705e17i			0.267711i
$868$	2.91477e17	−	2.24335e17i	0.681531	−	0.524541i
$869$	3.81534e17			0.885961
$870$	−2.39844e17			−0.553113
$871$		−	2.71763e17i		−	0.622418i
$872$	−3.08156e17			−0.700926
$873$			5.81685e17i			1.31402i
$874$		−	3.18110e17i		−	0.713688i
$875$	−3.10465e17	+	2.38950e17i	−0.691774	+	0.532425i
$876$	9.72973e15			0.0215316
$877$	2.71033e17			0.595696			0.297848	−	0.954613i	$-0.403731\pi$
$877$	2.71033e17			0.595696			0.297848	+	0.954613i	$0.403731\pi$
$878$			5.99926e17i			1.30957i
$879$	1.82892e17			0.396516
$880$		−	1.17243e17i		−	0.252458i
$881$		−	2.64245e17i		−	0.565134i	−0.959248	−	0.282567i	$-0.908814\pi$
$881$		−	2.64245e17i		−	0.565134i	0.959248	−	0.282567i	$-0.0911860\pi$
$882$	−6.86029e16	+	2.59056e17i	−0.145724	+	0.550278i
$883$	−1.41964e17			−0.299511			−0.149756	−	0.988723i	$-0.547849\pi$
$883$	−1.41964e17			−0.299511			−0.149756	+	0.988723i	$0.547849\pi$
$884$	1.41396e17			0.296295
$885$			3.26794e17i			0.680165i
$886$	3.09892e17			0.640631
$887$			6.27004e17i			1.28745i	0.765259	+	0.643723i	$0.222611\pi$
$887$			6.27004e17i			1.28745i	−0.765259	+	0.643723i	$0.777389\pi$
$888$		−	5.43405e16i		−	0.110827i
$889$	−4.31725e17	−	5.60935e17i	−0.874574	−	1.13632i
$890$	2.92921e17			0.589401
$891$	2.08590e17			0.416897
$892$			1.38334e17i			0.274625i
$893$	−5.45751e17			−1.07618
$894$		−	7.01148e16i		−	0.137336i
$895$		−	7.69360e17i		−	1.49690i
$896$	−2.78943e16	−	3.62428e16i	−0.0539098	−	0.0700445i
$897$	1.25810e17			0.241525
$898$	−6.30747e17			−1.20281
$899$		−	1.46560e18i		−	2.77623i
$900$	−4.37797e16			−0.0823792
$901$			1.74290e17i			0.325779i
$902$			4.48512e16i			0.0832788i
$903$	1.07883e17	−	8.30323e16i	0.198988	−	0.153151i
$904$	3.35930e17			0.615515
$905$	1.11840e18			2.03565
$906$		−	2.01238e17i		−	0.363866i
$907$	1.03608e18			1.86101			0.930504	−	0.366281i	$-0.119369\pi$
$907$	1.03608e18			1.86101			0.930504	+	0.366281i	$0.119369\pi$
$908$			2.51001e17i			0.447879i
$909$			5.76000e17i			1.02103i
$910$	2.53869e17	+	3.29850e17i	0.447056	+	0.580855i
$911$	−6.25946e17			−1.09503			−0.547516	−	0.836795i	$-0.684426\pi$
$911$	−6.25946e17			−1.09503			−0.547516	+	0.836795i	$0.684426\pi$
$912$	1.10687e17			0.192366
$913$		−	2.18006e17i		−	0.376395i
$914$	−3.35974e17			−0.576274
$915$		−	1.23496e17i		−	0.210439i
$916$		−	1.45529e17i		−	0.246363i
$917$	−1.98388e17	+	1.52690e17i	−0.333657	+	0.256800i
$918$	−2.11635e17			−0.353615
$919$	1.26202e17			0.209495			0.104748	−	0.994499i	$-0.466597\pi$
$919$	1.26202e17			0.209495			0.104748	+	0.994499i	$0.466597\pi$
$920$		−	1.36278e17i		−	0.224750i
$921$	−4.58922e16			−0.0751936
$922$			6.74611e16i			0.109817i
$923$		−	2.95278e17i		−	0.477552i
$924$	1.00179e17	−	7.71027e16i	0.160970	−	0.123890i
$925$	9.10114e16			0.145293
$926$	−2.30078e17			−0.364929
$927$		−	2.02843e17i		−	0.319655i
$928$	−1.82235e17			−0.285328
$929$		−	5.28504e17i		−	0.822155i	−0.911600	−	0.411078i	$-0.865153\pi$
$929$		−	5.28504e17i		−	0.822155i	0.911600	−	0.411078i	$-0.134847\pi$
$930$			3.81355e17i			0.589429i
$931$	1.09696e18	+	2.90496e17i	1.68458	+	0.446110i
$932$	−2.97150e17			−0.453399
$933$	−2.96794e17			−0.449952
$934$			4.59687e16i			0.0692439i
$935$	4.23352e17			0.633624
$936$		−	1.80758e17i		−	0.268808i
$937$		−	7.15104e17i		−	1.05665i	−0.849042	−	0.528325i	$-0.822820\pi$
$937$		−	7.15104e17i		−	1.05665i	0.849042	−	0.528325i	$-0.177180\pi$
$938$	−1.93591e17	−	2.51531e17i	−0.284229	−	0.369295i
$939$	−3.56490e17			−0.520061
$940$	−2.33800e17			−0.338905
$941$			1.08977e18i			1.56963i	0.619727	+	0.784817i	$0.287243\pi$
$941$			1.08977e18i			1.56963i	−0.619727	+	0.784817i	$0.712757\pi$
$942$	−2.93787e17			−0.420463
$943$			5.21333e16i			0.0741387i
$944$			2.48300e17i			0.350868i
$945$	−3.79979e17	−	4.93703e17i	−0.533542	−	0.693226i
$946$	2.65167e17			0.369975
$947$	−3.24790e17			−0.450300			−0.225150	−	0.974324i	$-0.572287\pi$
$947$	−3.24790e17			−0.450300			−0.225150	+	0.974324i	$0.572287\pi$
$948$			1.54310e17i			0.212591i
$949$	−6.72818e16			−0.0921086
$950$			1.85383e17i			0.252190i
$951$		−	1.95352e17i		−	0.264080i
$952$	1.30869e17	−	1.00724e17i	0.175799	−	0.135304i
$953$	9.80184e16			0.130843			0.0654215	−	0.997858i	$-0.479161\pi$
$953$	9.80184e16			0.130843			0.0654215	+	0.997858i	$0.479161\pi$
$954$	2.22809e17			0.295557
$955$			6.77552e17i			0.893146i
$956$	−3.54478e17			−0.464346
$957$		−	5.03716e17i		−	0.655713i
$958$			4.51860e17i			0.584535i
$959$	3.87532e17	+	5.03517e17i	0.498191	+	0.647295i
$960$	4.74184e16			0.0605787
$961$	−1.54265e18			−1.95851
$962$			3.75768e17i			0.474100i
$963$	8.99298e17			1.12758
$964$			3.17502e17i			0.395625i
$965$			9.29851e17i			1.15146i
$966$	1.16444e17	−	8.96213e16i	0.143303	−	0.110293i
$967$	−2.08918e17			−0.255515			−0.127757	−	0.991805i	$-0.540778\pi$
$967$	−2.08918e17			−0.255515			−0.127757	+	0.991805i	$0.540778\pi$
$968$	−4.46453e16			−0.0542654
$969$			3.99681e17i			0.482804i
$970$	1.05520e18			1.26679
$971$		−	2.81318e17i		−	0.335647i	−0.985817	−	0.167824i	$-0.946326\pi$
$971$		−	2.81318e17i		−	0.335647i	0.985817	−	0.167824i	$-0.0536739\pi$
$972$			4.20435e17i			0.498541i
$973$	−2.86467e17	+	2.20480e17i	−0.337597	+	0.259832i
$974$	−3.14071e17			−0.367853
$975$	−7.33179e16			−0.0853458
$976$		−	9.38329e16i		−	0.108557i
$977$	1.86043e17			0.213918			0.106959	−	0.994263i	$-0.465889\pi$
$977$	1.86043e17			0.213918			0.106959	+	0.994263i	$0.465889\pi$
$978$		−	2.94986e17i		−	0.337108i
$979$			6.15186e17i			0.698732i
$980$	4.69938e17	+	1.24449e17i	0.530498	+	0.140486i
$981$	−1.42248e18			−1.59600
$982$	−1.16828e18			−1.30280
$983$			7.20268e16i			0.0798313i	0.999203	+	0.0399156i	$0.0127089\pi$
$983$			7.20268e16i			0.0798313i	−0.999203	+	0.0399156i	$0.987291\pi$
$984$	−1.81399e16			−0.0199832
$985$			6.06487e17i			0.664055i
$986$		−	6.58033e17i		−	0.716121i
$987$	−1.53755e17	−	1.99772e17i	−0.166313	−	0.216089i
$988$	−7.65410e17			−0.822910
$989$	3.08220e17			0.329369
$990$		−	5.41203e17i		−	0.574843i
$991$	8.33698e17			0.880171			0.440085	−	0.897956i	$-0.354948\pi$
$991$	8.33698e17			0.880171			0.440085	+	0.897956i	$0.354948\pi$
$992$			2.89755e17i			0.304062i
$993$		−	1.74825e15i		−	0.00182351i
$994$	−2.10342e17	−	2.73295e17i	−0.218075	−	0.283343i
$995$	−1.01857e18			−1.04967
$996$	8.81720e16			0.0903181
$997$		−	5.85320e17i		−	0.595968i	−0.954571	−	0.297984i	$-0.903686\pi$
$997$		−	5.85320e17i		−	0.595968i	0.954571	−	0.297984i	$-0.0963142\pi$
$998$	1.00235e18			1.01446
$999$		−	5.62431e17i		−	0.565817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.13.b.a.13.7	yes	8
3.2	odd	2		126.13.c.a.55.4		8
4.3	odd	2		112.13.c.c.97.3		8
7.2	even	3		98.13.d.b.31.2		16
7.3	odd	6		98.13.d.b.19.2		16
7.4	even	3		98.13.d.b.19.3		16
7.5	odd	6		98.13.d.b.31.3		16
7.6	odd	2	inner	14.13.b.a.13.6	✓	8
21.20	even	2		126.13.c.a.55.1		8
28.27	even	2		112.13.c.c.97.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.b.a.13.6	✓	8	7.6	odd	2	inner
14.13.b.a.13.7	yes	8	1.1	even	1	trivial
98.13.d.b.19.2		16	7.3	odd	6
98.13.d.b.19.3		16	7.4	even	3
98.13.d.b.31.2		16	7.2	even	3
98.13.d.b.31.3		16	7.5	odd	6
112.13.c.c.97.3		8	4.3	odd	2
112.13.c.c.97.6		8	28.27	even	2
126.13.c.a.55.1		8	21.20	even	2
126.13.c.a.55.4		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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+45.2548 q^{2} +321.888i q^{3} +2048.00 q^{4} -17149.5i q^{5} +14567.0i q^{6} +(-71756.5 - 93232.5i) q^{7} +92681.9 q^{8} +427829. q^{9} +O(q^{10})\)	\(q+45.2548 q^{2} +321.888i q^{3} +2048.00 q^{4} -17149.5i q^{5} +14567.0i q^{6} +(-71756.5 - 93232.5i) q^{7} +92681.9 q^{8} +427829. q^{9} -776099. i q^{10} +1.62995e6 q^{11} +659227. i q^{12} -4.55860e6i q^{13} +(-3.24733e6 - 4.21922e6i) q^{14} +5.52023e6 q^{15} +4.19430e6 q^{16} +1.51452e7i q^{17} +1.93613e7 q^{18} -8.19846e7i q^{19} -3.51222e7i q^{20} +(3.00104e7 - 2.30976e7i) q^{21} +7.37629e7 q^{22} +8.57392e7 q^{23} +2.98332e7i q^{24} -4.99658e7 q^{25} -2.06299e8i q^{26} +3.08778e8i q^{27} +(-1.46957e8 - 1.90940e8i) q^{28} -9.60080e8 q^{29} +2.49817e8 q^{30} +1.52654e9i q^{31} +1.89813e8 q^{32} +5.24661e8i q^{33} +6.85395e8i q^{34} +(-1.59889e9 + 1.23059e9i) q^{35} +8.76194e8 q^{36} -1.82147e9 q^{37} -3.71020e9i q^{38} +1.46736e9 q^{39} -1.58945e9i q^{40} +6.08045e8i q^{41} +(1.35812e9 - 1.04528e9i) q^{42} +3.59485e9 q^{43} +3.33813e9 q^{44} -7.33706e9i q^{45} +3.88011e9 q^{46} -6.65675e9i q^{47} +1.35010e9i q^{48} +(-3.54330e9 + 1.33801e10i) q^{49} -2.26119e9 q^{50} -4.87507e9 q^{51} -9.33602e9i q^{52} +1.15079e10 q^{53} +1.39737e10i q^{54} -2.79528e10i q^{55} +(-6.65053e9 - 8.64096e9i) q^{56} +2.63899e10 q^{57} -4.34482e10 q^{58} +5.91993e10i q^{59} +1.13054e10 q^{60} -2.23715e10i q^{61} +6.90831e10i q^{62} +(-3.06995e10 - 3.98875e10i) q^{63} +8.58993e9 q^{64} -7.81779e10 q^{65} +2.37434e10i q^{66} +5.96155e10 q^{67} +3.10174e10i q^{68} +2.75985e10i q^{69} +(-7.23576e10 + 5.56902e10i) q^{70} +6.47737e10 q^{71} +3.96520e10 q^{72} -1.47593e10i q^{73} -8.24305e10 q^{74} -1.60834e10i q^{75} -1.67904e11i q^{76} +(-1.16959e11 - 1.51964e11i) q^{77} +6.64052e10 q^{78} +2.34078e11 q^{79} -7.19303e10i q^{80} +1.27974e11 q^{81} +2.75170e10i q^{82} -1.33751e11i q^{83} +(6.14614e10 - 4.73038e10i) q^{84} +2.59734e11 q^{85} +1.62684e11 q^{86} -3.09038e11i q^{87} +1.51066e11 q^{88} +3.77427e11i q^{89} -3.32038e11i q^{90} +(-4.25010e11 + 3.27109e11i) q^{91} +1.75594e11 q^{92} -4.91374e11 q^{93} -3.01250e11i q^{94} -1.40600e12 q^{95} +6.10984e10i q^{96} +1.35962e12i q^{97} +(-1.60351e11 + 6.05513e11i) q^{98} +6.97338e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9}+O(q^{10}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9} - 213840 q^{11} - 8418816 q^{14} + 65882304 q^{15} + 33554432 q^{16} + 32547840 q^{18} - 4449984 q^{21} - 221337600 q^{22} + 156731760 q^{23} + 191237000 q^{25} + 399687680 q^{28} + 308853648 q^{29} - 2203567104 q^{30} - 3764734848 q^{35} - 3028795392 q^{36} - 3243600880 q^{37} + 13521315264 q^{39} - 12108579840 q^{42} + 21006302000 q^{43} - 437944320 q^{44} + 9664610304 q^{46} - 19258758904 q^{49} + 26259489792 q^{50} - 80965832832 q^{51} + 180445637520 q^{53} - 17241735168 q^{56} - 63145962240 q^{57} - 94193264640 q^{58} + 134926958592 q^{60} - 402706514280 q^{63} + 68719476736 q^{64} - 424890168192 q^{65} + 369211259440 q^{67} - 137936354304 q^{70} + 574058144304 q^{71} + 66657976320 q^{72} + 450517137408 q^{74} - 73915435440 q^{77} - 251000847360 q^{78} - 607826610128 q^{79} + 919051941384 q^{81} - 9113567232 q^{84} - 247202260608 q^{85} - 413092638720 q^{86} - 453299404800 q^{88} + 144527421696 q^{91} + 320986644480 q^{92} + 2292312458880 q^{93} - 1053641981376 q^{95} - 290797516800 q^{98} - 1800954256464 q^{99}+O(q^{100}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9 - 213840 * q^11 - 8418816 * q^14 + 65882304 * q^15 + 33554432 * q^16 + 32547840 * q^18 - 4449984 * q^21 - 221337600 * q^22 + 156731760 * q^23 + 191237000 * q^25 + 399687680 * q^28 + 308853648 * q^29 - 2203567104 * q^30 - 3764734848 * q^35 - 3028795392 * q^36 - 3243600880 * q^37 + 13521315264 * q^39 - 12108579840 * q^42 + 21006302000 * q^43 - 437944320 * q^44 + 9664610304 * q^46 - 19258758904 * q^49 + 26259489792 * q^50 - 80965832832 * q^51 + 180445637520 * q^53 - 17241735168 * q^56 - 63145962240 * q^57 - 94193264640 * q^58 + 134926958592 * q^60 - 402706514280 * q^63 + 68719476736 * q^64 - 424890168192 * q^65 + 369211259440 * q^67 - 137936354304 * q^70 + 574058144304 * q^71 + 66657976320 * q^72 + 450517137408 * q^74 - 73915435440 * q^77 - 251000847360 * q^78 - 607826610128 * q^79 + 919051941384 * q^81 - 9113567232 * q^84 - 247202260608 * q^85 - 413092638720 * q^86 - 453299404800 * q^88 + 144527421696 * q^91 + 320986644480 * q^92 + 2292312458880 * q^93 - 1053641981376 * q^95 - 290797516800 * q^98 - 1800954256464 * q^99

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