LMFDB - Embedded newform 14.9.b.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,9,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, 9, names="a")

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

chi := DirichletCharacter("14.13");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
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:	$5.70330054086$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.3520512.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 120x^{2} + 3438 $ x^4 + 120*x^2 + 3438
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.3
Root			$-6.87547i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.9.b.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.3137 q^{2} -63.0589i q^{3} +128.000 q^{4} -390.317i q^{5} -713.430i q^{6} +(-687.442 - 2300.48i) q^{7} +1448.15 q^{8} +2584.58 q^{9} +O(q^{10})$	\(q+11.3137 q^{2} -63.0589i q^{3} +128.000 q^{4} -390.317i q^{5} -713.430i q^{6} +(-687.442 - 2300.48i) q^{7} +1448.15 q^{8} +2584.58 q^{9} -4415.94i q^{10} +4009.17 q^{11} -8071.54i q^{12} -350.590i q^{13} +(-7777.52 - 26027.0i) q^{14} -24613.0 q^{15} +16384.0 q^{16} +97022.3i q^{17} +29241.2 q^{18} +209322. i q^{19} -49960.6i q^{20} +(-145066. + 43349.3i) q^{21} +45358.5 q^{22} -155907. q^{23} -91319.0i q^{24} +238277. q^{25} -3966.48i q^{26} -576710. i q^{27} +(-87992.6 - 294462. i) q^{28} +845181. q^{29} -278464. q^{30} -873444. i q^{31} +185364. q^{32} -252813. i q^{33} +1.09768e6i q^{34} +(-897919. + 268321. i) q^{35} +330826. q^{36} -1.13106e6 q^{37} +2.36821e6i q^{38} -22107.8 q^{39} -565240. i q^{40} +1.80188e6i q^{41} +(-1.64123e6 + 490442. i) q^{42} +3.94686e6 q^{43} +513173. q^{44} -1.00881e6i q^{45} -1.76389e6 q^{46} -2.02387e6i q^{47} -1.03316e6i q^{48} +(-4.81965e6 + 3.16290e6i) q^{49} +2.69580e6 q^{50} +6.11812e6 q^{51} -44875.6i q^{52} -1.13828e7 q^{53} -6.52473e6i q^{54} -1.56485e6i q^{55} +(-995523. - 3.33146e6i) q^{56} +1.31996e7 q^{57} +9.56214e6 q^{58} -9.30141e6i q^{59} -3.15046e6 q^{60} +1.87417e7i q^{61} -9.88189e6i q^{62} +(-1.77675e6 - 5.94578e6i) q^{63} +2.09715e6 q^{64} -136841. q^{65} -2.86026e6i q^{66} -3.87489e7 q^{67} +1.24189e7i q^{68} +9.83134e6i q^{69} +(-1.01588e7 + 3.03570e6i) q^{70} +4.45370e7 q^{71} +3.74287e6 q^{72} +4.68614e7i q^{73} -1.27965e7 q^{74} -1.50255e7i q^{75} +2.67933e7i q^{76} +(-2.75607e6 - 9.22302e6i) q^{77} -250122. q^{78} -3.24052e6 q^{79} -6.39496e6i q^{80} -1.94092e7 q^{81} +2.03860e7i q^{82} -7.02713e7i q^{83} +(-1.85684e7 + 5.54872e6i) q^{84} +3.78695e7 q^{85} +4.46536e7 q^{86} -5.32962e7i q^{87} +5.80589e6 q^{88} -8.92209e7i q^{89} -1.14133e7i q^{90} +(-806527. + 241011. i) q^{91} -1.99561e7 q^{92} -5.50784e7 q^{93} -2.28975e7i q^{94} +8.17021e7 q^{95} -1.16888e7i q^{96} +1.27076e8i q^{97} +(-5.45281e7 + 3.57841e7i) q^{98} +1.03620e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 512 q^{4} - 6076 q^{7} - 13692 q^{9}+O(q^{10}) $ 4 * q + 512 * q^4 - 6076 * q^7 - 13692 * q^9	$ 4 q + 512 q^{4} - 6076 q^{7} - 13692 q^{9} - 13560 q^{11} + 37632 q^{14} - 13056 q^{15} + 65536 q^{16} + 271872 q^{18} - 413952 q^{21} + 334848 q^{22} - 894072 q^{23} + 1216900 q^{25} - 777728 q^{28} + 317064 q^{29} - 966144 q^{30} - 1655808 q^{35} - 1752576 q^{36} - 2495096 q^{37} + 10228992 q^{39} - 1881600 q^{42} + 9186568 q^{43} - 1735680 q^{44} + 3059712 q^{46} + 931588 q^{49} - 2984448 q^{50} - 324096 q^{51} - 38727288 q^{53} + 4816896 q^{56} - 30690816 q^{57} + 34661376 q^{58} - 1671168 q^{60} + 40780740 q^{63} + 8388608 q^{64} - 11891712 q^{65} - 12320248 q^{67} - 21901824 q^{70} + 62168712 q^{71} + 34799616 q^{72} - 22957056 q^{74} + 45208968 q^{77} - 116728320 q^{78} + 24889736 q^{79} - 70788348 q^{81} - 52985856 q^{84} + 89943552 q^{85} + 74680320 q^{86} + 42860544 q^{88} + 38158848 q^{91} - 114441216 q^{92} - 408466944 q^{93} + 227967744 q^{95} - 228652032 q^{98} + 224220168 q^{99}+O(q^{100}) $ 4 * q + 512 * q^4 - 6076 * q^7 - 13692 * q^9 - 13560 * q^11 + 37632 * q^14 - 13056 * q^15 + 65536 * q^16 + 271872 * q^18 - 413952 * q^21 + 334848 * q^22 - 894072 * q^23 + 1216900 * q^25 - 777728 * q^28 + 317064 * q^29 - 966144 * q^30 - 1655808 * q^35 - 1752576 * q^36 - 2495096 * q^37 + 10228992 * q^39 - 1881600 * q^42 + 9186568 * q^43 - 1735680 * q^44 + 3059712 * q^46 + 931588 * q^49 - 2984448 * q^50 - 324096 * q^51 - 38727288 * q^53 + 4816896 * q^56 - 30690816 * q^57 + 34661376 * q^58 - 1671168 * q^60 + 40780740 * q^63 + 8388608 * q^64 - 11891712 * q^65 - 12320248 * q^67 - 21901824 * q^70 + 62168712 * q^71 + 34799616 * q^72 - 22957056 * q^74 + 45208968 * q^77 - 116728320 * q^78 + 24889736 * q^79 - 70788348 * q^81 - 52985856 * q^84 + 89943552 * q^85 + 74680320 * q^86 + 42860544 * q^88 + 38158848 * q^91 - 114441216 * q^92 - 408466944 * q^93 + 227967744 * q^95 - 228652032 * q^98 + 224220168 * 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 $

$2$	11.3137			0.707107
$2$	11.3137			0.707107
$3$		−	63.0589i		−	0.778505i	−0.921131	−	0.389252i	$-0.872733\pi$
$3$		−	63.0589i		−	0.778505i	0.921131	−	0.389252i	$-0.127267\pi$
$4$	128.000			0.500000
$5$		−	390.317i		−	0.624508i	−0.949999	−	0.312254i	$-0.898916\pi$
$5$		−	390.317i		−	0.624508i	0.949999	−	0.312254i	$-0.101084\pi$
$6$		−	713.430i		−	0.550486i
$7$	−687.442	−	2300.48i	−0.286315	−	0.958136i
$7$	−687.442	−	2300.48i	−0.286315	−	0.958136i
$8$	1448.15			0.353553
$9$	2584.58			0.393931
$10$		−	4415.94i		−	0.441594i
$11$	4009.17			0.273831			0.136916	−	0.990583i	$-0.456281\pi$
$11$	4009.17			0.273831			0.136916	+	0.990583i	$0.456281\pi$
$12$		−	8071.54i		−	0.389252i
$13$		−	350.590i		−	0.0122751i	−0.999981	−	0.00613757i	$-0.998046\pi$
$13$		−	350.590i		−	0.0122751i	0.999981	−	0.00613757i	$-0.00195366\pi$
$14$	−7777.52	−	26027.0i	−0.202455	−	0.677504i
$15$	−24613.0			−0.486182
$16$	16384.0			0.250000
$17$			97022.3i			1.16165i	0.814028	+	0.580826i	$0.197270\pi$
$17$			97022.3i			1.16165i	−0.814028	+	0.580826i	$0.802730\pi$
$18$	29241.2			0.278551
$19$			209322.i			1.60621i	0.595840	+	0.803103i	$0.296819\pi$
$19$			209322.i			1.60621i	−0.595840	+	0.803103i	$0.703181\pi$
$20$		−	49960.6i		−	0.312254i
$21$	−145066.	+	43349.3i	−0.745913	+	0.222898i
$22$	45358.5			0.193628
$23$	−155907.			−0.557128			−0.278564	−	0.960418i	$-0.589858\pi$
$23$	−155907.			−0.557128			−0.278564	+	0.960418i	$0.589858\pi$
$24$		−	91319.0i		−	0.275243i
$25$	238277.			0.609990
$26$		−	3966.48i		−	0.00867984i
$27$		−	576710.i		−	1.08518i
$28$	−87992.6	−	294462.i	−0.143158	−	0.479068i
$29$	845181.			1.19497			0.597486	−	0.801879i	$-0.296166\pi$
$29$	845181.			1.19497			0.597486	+	0.801879i	$0.296166\pi$
$30$	−278464.			−0.343783
$31$		−	873444.i		−	0.945776i	−0.881122	−	0.472888i	$-0.843211\pi$
$31$		−	873444.i		−	0.945776i	0.881122	−	0.472888i	$-0.156789\pi$
$32$	185364.			0.176777
$33$		−	252813.i		−	0.213179i
$34$			1.09768e6i			0.821412i
$35$	−897919.	+	268321.i	−0.598363	+	0.178806i
$36$	330826.			0.196965
$37$	−1.13106e6			−0.603501			−0.301751	−	0.953387i	$-0.597571\pi$
$37$	−1.13106e6			−0.603501			−0.301751	+	0.953387i	$0.597571\pi$
$38$			2.36821e6i			1.13576i
$39$	−22107.8			−0.00955626
$40$		−	565240.i		−	0.220797i
$41$			1.80188e6i			0.637663i	0.947811	+	0.318831i	$0.103290\pi$
$41$			1.80188e6i			0.637663i	−0.947811	+	0.318831i	$0.896710\pi$
$42$	−1.64123e6	+	490442.i	−0.527440	+	0.157612i
$43$	3.94686e6			1.15446			0.577229	−	0.816583i	$-0.304134\pi$
$43$	3.94686e6			1.15446			0.577229	+	0.816583i	$0.304134\pi$
$44$	513173.			0.136916
$45$		−	1.00881e6i		−	0.246013i
$46$	−1.76389e6			−0.393949
$47$		−	2.02387e6i		−	0.414755i	−0.978261	−	0.207378i	$-0.933507\pi$
$47$		−	2.02387e6i		−	0.414755i	0.978261	−	0.207378i	$-0.0664928\pi$
$48$		−	1.03316e6i		−	0.194626i
$49$	−4.81965e6	+	3.16290e6i	−0.836047	+	0.548657i
$50$	2.69580e6			0.431328
$51$	6.11812e6			0.904351
$52$		−	44875.6i		−	0.00613757i
$53$	−1.13828e7			−1.44260			−0.721300	−	0.692622i	$-0.756455\pi$
$53$	−1.13828e7			−1.44260			−0.721300	+	0.692622i	$0.756455\pi$
$54$		−	6.52473e6i		−	0.767339i
$55$		−	1.56485e6i		−	0.171010i
$56$	−995523.	−	3.33146e6i	−0.101228	−	0.338752i
$57$	1.31996e7			1.25044
$58$	9.56214e6			0.844973
$59$		−	9.30141e6i		−	0.767610i	−0.923414	−	0.383805i	$-0.874613\pi$
$59$		−	9.30141e6i		−	0.767610i	0.923414	−	0.383805i	$-0.125387\pi$
$60$	−3.15046e6			−0.243091
$61$			1.87417e7i			1.35360i	0.736168	+	0.676799i	$0.236633\pi$
$61$			1.87417e7i			1.35360i	−0.736168	+	0.676799i	$0.763367\pi$
$62$		−	9.88189e6i		−	0.668765i
$63$	−1.77675e6	−	5.94578e6i	−0.112788	−	0.377439i
$64$	2.09715e6			0.125000
$65$	−136841.			−0.00766592
$66$		−	2.86026e6i		−	0.150740i
$67$	−3.87489e7			−1.92292			−0.961458	−	0.274951i	$-0.911338\pi$
$67$	−3.87489e7			−1.92292			−0.961458	+	0.274951i	$0.911338\pi$
$68$			1.24189e7i			0.580826i
$69$			9.83134e6i			0.433727i
$70$	−1.01588e7	+	3.03570e6i	−0.423107	+	0.126435i
$71$	4.45370e7			1.75262			0.876310	−	0.481747i	$-0.159998\pi$
$71$	4.45370e7			1.75262			0.876310	+	0.481747i	$0.159998\pi$
$72$	3.74287e6			0.139276
$73$			4.68614e7i			1.65015i	0.565021	+	0.825076i	$0.308868\pi$
$73$			4.68614e7i			1.65015i	−0.565021	+	0.825076i	$0.691132\pi$
$74$	−1.27965e7			−0.426740
$75$		−	1.50255e7i		−	0.474880i
$76$			2.67933e7i			0.803103i
$77$	−2.75607e6	−	9.22302e6i	−0.0784020	−	0.262368i
$78$	−250122.			−0.00675729
$79$	−3.24052e6			−0.0831968			−0.0415984	−	0.999134i	$-0.513245\pi$
$79$	−3.24052e6			−0.0831968			−0.0415984	+	0.999134i	$0.513245\pi$
$80$		−	6.39496e6i		−	0.156127i
$81$	−1.94092e7			−0.450888
$82$			2.03860e7i			0.450896i
$83$		−	7.02713e7i		−	1.48070i	−0.672224	−	0.740348i	$-0.734661\pi$
$83$		−	7.02713e7i		−	1.48070i	0.672224	−	0.740348i	$-0.265339\pi$
$84$	−1.85684e7	+	5.54872e6i	−0.372956	+	0.111449i
$85$	3.78695e7			0.725461
$86$	4.46536e7			0.816325
$87$		−	5.32962e7i		−	0.930292i
$88$	5.80589e6			0.0968140
$89$		−	8.92209e7i		−	1.42202i	−0.703181	−	0.711011i	$-0.748237\pi$
$89$		−	8.92209e7i		−	1.42202i	0.703181	−	0.711011i	$-0.251763\pi$
$90$		−	1.14133e7i		−	0.173957i
$91$	−806527.	+	241011.i	−0.0117613	+	0.00351456i
$92$	−1.99561e7			−0.278564
$93$	−5.50784e7			−0.736291
$94$		−	2.28975e7i		−	0.293276i
$95$	8.17021e7			1.00309
$96$		−	1.16888e7i		−	0.137621i
$97$			1.27076e8i			1.43542i	0.696344	+	0.717708i	$0.254809\pi$
$97$			1.27076e8i			1.43542i	−0.696344	+	0.717708i	$0.745191\pi$
$98$	−5.45281e7	+	3.57841e7i	−0.591175	+	0.387959i
$99$	1.03620e7			0.107871
$100$	3.04995e7			0.304995
$101$			4.94803e7i			0.475496i	0.971327	+	0.237748i	$0.0764092\pi$
$101$			4.94803e7i			0.475496i	−0.971327	+	0.237748i	$0.923591\pi$
$102$	6.92186e7			0.639473
$103$			9.96346e7i			0.885240i	0.896709	+	0.442620i	$0.145951\pi$
$103$			9.96346e7i			0.885240i	−0.896709	+	0.442620i	$0.854049\pi$
$104$		−	507709.i		−	0.00433992i
$105$	1.69200e7	+	5.66217e7i	0.139201	+	0.465828i
$106$	−1.28782e8			−1.02007
$107$	−1.83886e8			−1.40286			−0.701428	−	0.712741i	$-0.747454\pi$
$107$	−1.83886e8			−1.40286			−0.701428	+	0.712741i	$0.747454\pi$
$108$		−	7.38189e7i		−	0.542591i
$109$	1.58004e7			0.111934			0.0559671	−	0.998433i	$-0.482176\pi$
$109$	1.58004e7			0.111934			0.0559671	+	0.998433i	$0.482176\pi$
$110$		−	1.77042e7i		−	0.120922i
$111$			7.13232e7i			0.469828i
$112$	−1.12631e7	−	3.76911e7i	−0.0715788	−	0.239534i
$113$	−4.97912e7			−0.305379			−0.152689	−	0.988274i	$-0.548793\pi$
$113$	−4.97912e7			−0.305379			−0.152689	+	0.988274i	$0.548793\pi$
$114$	1.49337e8			0.884193
$115$			6.08533e7i			0.347931i
$116$	1.08183e8			0.597486
$117$		−	906129.i		−	0.00483556i
$118$		−	1.05233e8i		−	0.542782i
$119$	2.23198e8	−	6.66973e7i	1.11302	−	0.332598i
$120$	−3.56434e7			−0.171891
$121$	−1.98285e8			−0.925016
$122$			2.12038e8i			0.957138i
$123$	1.13625e8			0.496423
$124$		−	1.11801e8i		−	0.472888i
$125$		−	2.45471e8i		−	1.00545i
$126$	−2.01016e7	−	6.72688e7i	−0.0797534	−	0.266890i
$127$	−1.40133e8			−0.538674			−0.269337	−	0.963046i	$-0.586805\pi$
$127$	−1.40133e8			−0.538674			−0.269337	+	0.963046i	$0.586805\pi$
$128$	2.37266e7			0.0883883
$129$		−	2.48884e8i		−	0.898750i
$130$	−1.54818e6			−0.00542063
$131$			2.20973e8i			0.750333i	0.926957	+	0.375166i	$0.122414\pi$
$131$			2.20973e8i			0.750333i	−0.926957	+	0.375166i	$0.877586\pi$
$132$		−	3.23601e7i		−	0.106589i
$133$	4.81543e8	−	1.43897e8i	1.53896	−	0.459881i
$134$	−4.38394e8			−1.35971
$135$	−2.25100e8			−0.677704
$136$			1.40503e8i			0.410706i
$137$	1.67452e8			0.475344			0.237672	−	0.971345i	$-0.423616\pi$
$137$	1.67452e8			0.475344			0.237672	+	0.971345i	$0.423616\pi$
$138$			1.11229e8i			0.306691i
$139$		−	1.60687e8i		−	0.430448i	−0.976565	−	0.215224i	$-0.930952\pi$
$139$		−	1.60687e8i		−	0.430448i	0.976565	−	0.215224i	$-0.0690482\pi$
$140$	−1.14934e8	+	3.43450e7i	−0.299182	+	0.0894030i
$141$	−1.27623e8			−0.322889
$142$	5.03879e8			1.23929
$143$		−	1.40557e6i		−	0.00336132i
$144$	4.23457e7			0.0984827
$145$		−	3.29889e8i		−	0.746270i
$146$			5.30177e8i			1.16683i
$147$	1.99449e8	+	3.03921e8i	0.427132	+	0.650867i
$148$	−1.44775e8			−0.301751
$149$	3.03708e7			0.0616186			0.0308093	−	0.999525i	$-0.490192\pi$
$149$	3.03708e7			0.0616186			0.0308093	+	0.999525i	$0.490192\pi$
$150$		−	1.69994e8i		−	0.335791i
$151$	−4.30673e8			−0.828400			−0.414200	−	0.910186i	$-0.635939\pi$
$151$	−4.30673e8			−0.828400			−0.414200	+	0.910186i	$0.635939\pi$
$152$			3.03131e8i			0.567879i
$153$			2.50762e8i			0.457610i
$154$	−3.11814e7	−	1.04347e8i	−0.0554386	−	0.185522i
$155$	−3.40920e8			−0.590645
$156$	−2.82980e6			−0.00477813
$157$		−	2.54276e8i		−	0.418510i	−0.977861	−	0.209255i	$-0.932896\pi$
$157$		−	2.54276e8i		−	0.418510i	0.977861	−	0.209255i	$-0.0671039\pi$
$158$	−3.66623e7			−0.0588290
$159$			7.17787e8i			1.12307i
$160$		−	7.23507e7i		−	0.110398i
$161$	1.07177e8	+	3.58662e8i	0.159514	+	0.533804i
$162$	−2.19591e8			−0.318826
$163$	1.17790e6			0.00166862			0.000834312	−	1.00000i	$-0.499734\pi$
$163$	1.17790e6			0.00166862			0.000834312		1.00000i	$0.499734\pi$
$164$			2.30641e8i			0.318831i
$165$	−9.86775e7			−0.133132
$166$		−	7.95029e8i		−	1.04701i
$167$			6.76671e7i			0.0869985i	0.999053	+	0.0434993i	$0.0138506\pi$
$167$			6.76671e7i			0.0869985i	−0.999053	+	0.0434993i	$0.986149\pi$
$168$	−2.10078e8	+	6.27766e7i	−0.263720	+	0.0788062i
$169$	8.15608e8			0.999849
$170$	4.28444e8			0.512978
$171$			5.41010e8i			0.632734i
$172$	5.05198e8			0.577229
$173$		−	1.75158e9i		−	1.95544i	−0.209905	−	0.977722i	$-0.567316\pi$
$173$		−	1.75158e9i		−	1.95544i	0.209905	−	0.977722i	$-0.432684\pi$
$174$		−	6.02977e8i		−	0.657816i
$175$	−1.63802e8	−	5.48153e8i	−0.174649	−	0.584453i
$176$	6.56862e7			0.0684578
$177$	−5.86536e8			−0.597588
$178$		−	1.00942e9i		−	1.00552i
$179$	3.22726e8			0.314356			0.157178	−	0.987570i	$-0.449760\pi$
$179$	3.22726e8			0.314356			0.157178	+	0.987570i	$0.449760\pi$
$180$		−	1.29127e8i		−	0.123006i
$181$			2.77541e8i			0.258590i	0.991606	+	0.129295i	$0.0412715\pi$
$181$			2.77541e8i			0.258590i	−0.991606	+	0.129295i	$0.958729\pi$
$182$	−9.12482e6	+	2.72672e6i	−0.00831646	+	0.00248517i
$183$	1.18183e9			1.05378
$184$	−2.25778e8			−0.196975
$185$			4.41472e8i			0.376891i
$186$	−6.23141e8			−0.520636
$187$			3.88979e8i			0.318097i
$188$		−	2.59056e8i		−	0.207378i
$189$	−1.32671e9	+	3.96455e8i	−1.03975	+	0.310704i
$190$	9.24354e8			0.709290
$191$	−6.83273e8			−0.513406			−0.256703	−	0.966490i	$-0.582636\pi$
$191$	−6.83273e8			−0.513406			−0.256703	+	0.966490i	$0.582636\pi$
$192$		−	1.32244e8i		−	0.0973131i
$193$	−8.28870e8			−0.597389			−0.298695	−	0.954349i	$-0.596551\pi$
$193$	−8.28870e8			−0.597389			−0.298695	+	0.954349i	$0.596551\pi$
$194$			1.43770e9i			1.01499i
$195$			8.62907e6i			0.00596795i
$196$	−6.16915e8	+	4.04851e8i	−0.418024	+	0.274329i
$197$	9.93472e8			0.659615			0.329807	−	0.944048i	$-0.393016\pi$
$197$	9.93472e8			0.659615			0.329807	+	0.944048i	$0.393016\pi$
$198$	1.17233e8			0.0762760
$199$			1.21114e9i			0.772293i	0.922437	+	0.386146i	$0.126194\pi$
$199$			1.21114e9i			0.772293i	−0.922437	+	0.386146i	$0.873806\pi$
$200$	3.45063e8			0.215664
$201$			2.44346e9i			1.49700i
$202$			5.59805e8i			0.336226i
$203$	−5.81014e8	−	1.94433e9i	−0.342139	−	1.14495i
$204$	7.83119e8			0.452176
$205$	7.03306e8			0.398225
$206$			1.12724e9i			0.625959i
$207$	−4.02955e8			−0.219470
$208$		−	5.74407e6i		−	0.00306879i
$209$			8.39208e8i			0.439830i
$210$	1.91428e8	+	6.40602e8i	0.0984301	+	0.329390i
$211$	1.23772e9			0.624444			0.312222	−	0.950009i	$-0.398927\pi$
$211$	1.23772e9			0.624444			0.312222	+	0.950009i	$0.398927\pi$
$212$	−1.45700e9			−0.721300
$213$		−	2.80845e9i		−	1.36442i
$214$	−2.08043e9			−0.991968
$215$		−	1.54053e9i		−	0.720967i
$216$		−	8.35165e8i		−	0.383670i
$217$	−2.00934e9	+	6.00443e8i	−0.906182	+	0.270790i
$218$	1.78762e8			0.0791495
$219$	2.95503e9			1.28465
$220$		−	2.00300e8i		−	0.0855049i
$221$	3.40151e7			0.0142594
$222$			8.06930e8i			0.332219i
$223$		−	3.39581e9i		−	1.37317i	−0.727049	−	0.686585i	$-0.759109\pi$
$223$		−	3.39581e9i		−	1.37317i	0.727049	−	0.686585i	$-0.240891\pi$
$224$	−1.27427e8	−	4.26426e8i	−0.0506138	−	0.169376i
$225$	6.15847e8			0.240294
$226$	−5.63323e8			−0.215935
$227$		−	1.25356e9i		−	0.472110i	−0.971740	−	0.236055i	$-0.924145\pi$
$227$		−	1.25356e9i		−	0.472110i	0.971740	−	0.236055i	$-0.0758545\pi$
$228$	1.68955e9			0.625219
$229$		−	7.90350e8i		−	0.287394i	−0.989622	−	0.143697i	$-0.954101\pi$
$229$		−	7.90350e8i		−	0.287394i	0.989622	−	0.143697i	$-0.0458991\pi$
$230$			6.88477e8i			0.246024i
$231$	−5.81593e8	+	1.73795e8i	−0.204254	+	0.0610363i
$232$	1.22395e9			0.422487
$233$	2.89689e9			0.982898			0.491449	−	0.870906i	$-0.336467\pi$
$233$	2.89689e9			0.982898			0.491449	+	0.870906i	$0.336467\pi$
$234$		−	1.02517e7i		−	0.00341925i
$235$	−7.89952e8			−0.259018
$236$		−	1.19058e9i		−	0.383805i
$237$			2.04344e8i			0.0647691i
$238$	2.52520e9	−	7.54594e8i	0.787024	−	0.235183i
$239$	−3.82362e9			−1.17188			−0.585940	−	0.810354i	$-0.699275\pi$
$239$	−3.82362e9			−1.17188			−0.585940	+	0.810354i	$0.699275\pi$
$240$	−4.03259e8			−0.121546
$241$			5.42966e9i			1.60955i	0.593579	+	0.804776i	$0.297714\pi$
$241$			5.42966e9i			1.60955i	−0.593579	+	0.804776i	$0.702286\pi$
$242$	−2.24334e9			−0.654085
$243$		−	2.55987e9i		−	0.734163i
$244$			2.39894e9i			0.676799i
$245$	1.23453e9	+	1.88119e9i	0.342641	+	0.522118i
$246$	1.28552e9			0.351024
$247$	7.33864e7			0.0197164
$248$		−	1.26488e9i		−	0.334382i
$249$	−4.43123e9			−1.15273
$250$		−	2.77719e9i		−	0.710961i
$251$			2.98297e9i			0.751544i	0.926712	+	0.375772i	$0.122622\pi$
$251$			2.98297e9i			0.751544i	−0.926712	+	0.375772i	$0.877378\pi$
$252$	−2.27424e8	−	7.61060e8i	−0.0563941	−	0.188719i
$253$	−6.25058e8			−0.152559
$254$	−1.58542e9			−0.380900
$255$		−	2.38801e9i		−	0.564774i
$256$	2.68435e8			0.0625000
$257$			3.75861e9i			0.861579i	0.902452	+	0.430789i	$0.141765\pi$
$257$			3.75861e9i			0.861579i	−0.902452	+	0.430789i	$0.858235\pi$
$258$		−	2.81581e9i		−	0.635512i
$259$	7.77537e8	+	2.60198e9i	0.172791	+	0.578236i
$260$	−1.75157e7			−0.00383296
$261$	2.18444e9			0.470736
$262$			2.50002e9i			0.530565i
$263$	5.44132e9			1.13732			0.568658	−	0.822574i	$-0.307463\pi$
$263$	5.44132e9			1.13732			0.568658	+	0.822574i	$0.307463\pi$
$264$		−	3.66113e8i		−	0.0753702i
$265$			4.44291e9i			0.900915i
$266$	5.44803e9	−	1.62801e9i	1.08821	−	0.325185i
$267$	−5.62617e9			−1.10705
$268$	−4.95986e9			−0.961458
$269$		−	2.01871e9i		−	0.385536i	−0.981244	−	0.192768i	$-0.938254\pi$
$269$		−	2.01871e9i		−	0.385536i	0.981244	−	0.192768i	$-0.0617465\pi$
$270$	−2.54671e9			−0.479209
$271$			4.63979e9i			0.860243i	0.902771	+	0.430121i	$0.141529\pi$
$271$			4.63979e9i			0.860243i	−0.902771	+	0.430121i	$0.858471\pi$
$272$			1.58961e9i			0.290413i
$273$	1.51979e7	+	5.08587e7i	0.00273610	+	0.00915619i
$274$	1.89450e9			0.336119
$275$	9.55293e8			0.167034
$276$			1.25841e9i			0.216863i
$277$	3.96862e9			0.674094			0.337047	−	0.941488i	$-0.390572\pi$
$277$	3.96862e9			0.674094			0.337047	+	0.941488i	$0.390572\pi$
$278$		−	1.81796e9i		−	0.304373i
$279$		−	2.25749e9i		−	0.372570i
$280$	−1.30032e9	+	3.88570e8i	−0.211553	+	0.0632175i
$281$	−1.06501e10			−1.70817			−0.854083	−	0.520136i	$-0.825881\pi$
$281$	−1.06501e10			−1.70817			−0.854083	+	0.520136i	$0.825881\pi$
$282$	−1.44389e9			−0.228317
$283$		−	3.76400e9i		−	0.586818i	−0.955987	−	0.293409i	$-0.905210\pi$
$283$		−	3.76400e9i		−	0.586818i	0.955987	−	0.293409i	$-0.0947898\pi$
$284$	5.70074e9			0.876310
$285$		−	5.15204e9i		−	0.780908i
$286$		−	1.59023e7i		−	0.00237681i
$287$	4.14520e9	−	1.23869e9i	0.610967	−	0.182572i
$288$	4.79087e8			0.0696378
$289$	−2.43758e9			−0.349435
$290$		−	3.73227e9i		−	0.527692i
$291$	8.01329e9			1.11748
$292$			5.99826e9i			0.825076i
$293$		−	1.33762e10i		−	1.81495i	−0.420111	−	0.907473i	$-0.638009\pi$
$293$		−	1.33762e10i		−	1.81495i	0.420111	−	0.907473i	$-0.361991\pi$
$294$	2.25651e9	+	3.43848e9i	0.302028	+	0.460232i
$295$	−3.63050e9			−0.479378
$296$	−1.63795e9			−0.213370
$297$		−	2.31213e9i		−	0.297157i
$298$	3.43607e8			0.0435709
$299$			5.46596e7i			0.00683883i
$300$		−	1.92326e9i		−	0.237440i
$301$	−2.71324e9	−	9.07968e9i	−0.330538	−	1.10613i
$302$	−4.87251e9			−0.585767
$303$	3.12017e9			0.370176
$304$			3.42954e9i			0.401551i
$305$	7.31521e9			0.845332
$306$			2.83705e9i			0.323579i
$307$			1.63542e9i			0.184110i	0.995754	+	0.0920549i	$0.0293435\pi$
$307$			1.63542e9i			0.184110i	−0.995754	+	0.0920549i	$0.970656\pi$
$308$	−3.52777e8	−	1.18055e9i	−0.0392010	−	0.131184i
$309$	6.28284e9			0.689164
$310$	−3.85707e9			−0.417649
$311$			1.06927e10i			1.14300i	0.820604	+	0.571498i	$0.193637\pi$
$311$			1.06927e10i			1.14300i	−0.820604	+	0.571498i	$0.806363\pi$
$312$	−3.20156e7			−0.00337865
$313$			2.98022e9i			0.310507i	0.987875	+	0.155254i	$0.0496195\pi$
$313$			2.98022e9i			0.310507i	−0.987875	+	0.155254i	$0.950381\pi$
$314$		−	2.87680e9i		−	0.295932i
$315$	−2.32074e9	+	6.93496e8i	−0.235714	+	0.0704372i
$316$	−4.14787e8			−0.0415984
$317$	2.57274e9			0.254776			0.127388	−	0.991853i	$-0.459341\pi$
$317$	2.57274e9			0.254776			0.127388	+	0.991853i	$0.459341\pi$
$318$			8.12084e9i			0.794131i
$319$	3.38847e9			0.327221
$320$		−	8.18555e8i		−	0.0780635i
$321$			1.15956e10i			1.09213i
$322$	1.21257e9	+	4.05780e9i	0.112794	+	0.377457i
$323$	−2.03089e10			−1.86585
$324$	−2.48438e9			−0.225444
$325$		−	8.35378e7i		−	0.00748772i
$326$	1.33264e7			0.00117990
$327$		−	9.96358e8i		−	0.0871414i
$328$			2.60940e9i			0.225448i
$329$	−4.65588e9	+	1.39130e9i	−0.397392	+	0.118751i
$330$	−1.11641e9			−0.0941385
$331$	−1.53695e10			−1.28041			−0.640205	−	0.768204i	$-0.721151\pi$
$331$	−1.53695e10			−1.28041			−0.640205	+	0.768204i	$0.721151\pi$
$332$		−	8.99473e9i		−	0.740348i
$333$	−2.92331e9			−0.237738
$334$			7.65566e8i			0.0615173i
$335$			1.51244e10i			1.20088i
$336$	−2.37676e9	+	7.10236e8i	−0.186478	+	0.0557244i
$337$	2.21413e10			1.71666			0.858329	−	0.513100i	$-0.171503\pi$
$337$	2.21413e10			1.71666			0.858329	+	0.513100i	$0.171503\pi$
$338$	9.22755e9			0.707000
$339$			3.13978e9i			0.237739i
$340$	4.84730e9			0.362730
$341$		−	3.50178e9i		−	0.258983i
$342$			6.12083e9i			0.447410i
$343$	1.05894e10	+	8.91321e9i	0.765061	+	0.643958i
$344$	5.71566e9			0.408162
$345$	3.83734e9			0.270866
$346$		−	1.98169e10i		−	1.38271i
$347$	−2.45446e9			−0.169293			−0.0846465	−	0.996411i	$-0.526976\pi$
$347$	−2.45446e9			−0.169293			−0.0846465	+	0.996411i	$0.526976\pi$
$348$		−	6.82191e9i		−	0.465146i
$349$		−	2.43917e10i		−	1.64415i	−0.569381	−	0.822073i	$-0.692817\pi$
$349$		−	2.43917e10i		−	1.64415i	0.569381	−	0.822073i	$-0.307183\pi$
$350$	−1.85321e9	−	6.20165e9i	−0.123496	−	0.413271i
$351$	−2.02189e8			−0.0133208
$352$	7.43154e8			0.0484070
$353$			9.23681e9i			0.594872i	0.954742	+	0.297436i	$0.0961314\pi$
$353$			9.23681e9i			0.594872i	−0.954742	+	0.297436i	$0.903869\pi$
$354$	−6.63590e9			−0.422558
$355$		−	1.73836e10i		−	1.09452i
$356$		−	1.14203e10i		−	0.711011i
$357$	−4.20585e9	−	1.40746e10i	−0.258929	−	0.866491i
$358$	3.65122e9			0.222283
$359$	−1.47081e9			−0.0885481			−0.0442740	−	0.999019i	$-0.514097\pi$
$359$	−1.47081e9			−0.0885481			−0.0442740	+	0.999019i	$0.514097\pi$
$360$		−	1.46091e9i		−	0.0869786i
$361$	−2.68323e10			−1.57990
$362$			3.14001e9i			0.182851i
$363$			1.25037e10i			0.720129i
$364$	−1.03236e8	+	3.08494e7i	−0.00588063	+	0.00175728i
$365$	1.82908e10			1.03053
$366$	1.33709e10			0.745137
$367$		−	2.03734e10i		−	1.12305i	−0.827460	−	0.561525i	$-0.810215\pi$
$367$		−	2.03734e10i		−	1.12305i	0.827460	−	0.561525i	$-0.189785\pi$
$368$	−2.55438e9			−0.139282
$369$			4.65711e9i			0.251195i
$370$			4.99468e9i			0.266502i
$371$	7.82503e9	+	2.61860e10i	0.413038	+	1.38221i
$372$	−7.05004e9			−0.368146
$373$	5.23051e8			0.0270215			0.0135107	−	0.999909i	$-0.495699\pi$
$373$	5.23051e8			0.0270215			0.0135107	+	0.999909i	$0.495699\pi$
$374$			4.40079e9i			0.224928i
$375$	−1.54792e10			−0.782748
$376$		−	2.93088e9i		−	0.146638i
$377$		−	2.96312e8i		−	0.0146685i
$378$	−1.50100e10	+	4.48537e9i	−0.735215	+	0.219701i
$379$	2.88196e10			1.39679			0.698395	−	0.715712i	$-0.253898\pi$
$379$	2.88196e10			1.39679			0.698395	+	0.715712i	$0.253898\pi$
$380$	1.04579e10			0.501544
$381$			8.83663e9i			0.419360i
$382$	−7.73036e9			−0.363033
$383$			1.93044e10i			0.897141i	0.893747	+	0.448570i	$0.148067\pi$
$383$			1.93044e10i			0.897141i	−0.893747	+	0.448570i	$0.851933\pi$
$384$		−	1.49617e9i		−	0.0688107i
$385$	−3.59990e9	+	1.07574e9i	−0.163851	+	0.0489627i
$386$	−9.37760e9			−0.422418
$387$	1.02010e10			0.454776
$388$			1.62658e10i			0.717708i
$389$	−2.42405e10			−1.05863			−0.529314	−	0.848426i	$-0.677551\pi$
$389$	−2.42405e10			−1.05863			−0.529314	+	0.848426i	$0.677551\pi$
$390$			9.76268e7i			0.00421998i
$391$		−	1.51265e10i		−	0.647189i
$392$	−6.97959e9	+	4.58037e9i	−0.295587	+	0.193980i
$393$	1.39343e10			0.584138
$394$	1.12398e10			0.466418
$395$			1.26483e9i			0.0519570i
$396$	1.32634e9			0.0539353
$397$			5.65338e9i			0.227587i	0.993504	+	0.113793i	$0.0363001\pi$
$397$			5.65338e9i			0.227587i	−0.993504	+	0.113793i	$0.963700\pi$
$398$			1.37025e10i			0.546094i
$399$	−9.07398e9	−	3.03655e10i	−0.358019	−	1.19809i
$400$	3.90394e9			0.152498
$401$	−2.88963e9			−0.111755			−0.0558773	−	0.998438i	$-0.517796\pi$
$401$	−2.88963e9			−0.111755			−0.0558773	+	0.998438i	$0.517796\pi$
$402$			2.76446e10i			1.05854i
$403$	−3.06221e8			−0.0116095
$404$			6.33348e9i			0.237748i
$405$			7.57577e9i			0.281583i
$406$	−6.57342e9	−	2.19975e10i	−0.241929	−	0.809599i
$407$	−4.53460e9			−0.165258
$408$	8.85998e9			0.319737
$409$		−	1.05612e10i		−	0.377416i	−0.982033	−	0.188708i	$-0.939570\pi$
$409$		−	1.05612e10i		−	0.377416i	0.982033	−	0.188708i	$-0.0604300\pi$
$410$	7.95700e9			0.281588
$411$		−	1.05593e10i		−	0.370058i
$412$			1.27532e10i			0.442620i
$413$	−2.13977e10	+	6.39418e9i	−0.735474	+	0.219778i
$414$	−4.55891e9			−0.155189
$415$	−2.74281e10			−0.924706
$416$		−	6.49868e7i		−	0.00216996i
$417$	−1.01327e10			−0.335106
$418$			9.49455e9i			0.311006i
$419$		−	2.55995e10i		−	0.830568i	−0.909692	−	0.415284i	$-0.863682\pi$
$419$		−	2.55995e10i		−	0.830568i	0.909692	−	0.415284i	$-0.136318\pi$
$420$	2.16576e9	+	7.24758e9i	0.0696006	+	0.232914i
$421$	5.42252e10			1.72613			0.863063	−	0.505096i	$-0.168543\pi$
$421$	5.42252e10			1.72613			0.863063	+	0.505096i	$0.168543\pi$
$422$	1.40032e10			0.441549
$423$		−	5.23086e9i		−	0.163385i
$424$	−1.64841e10			−0.510036
$425$			2.31182e10i			0.708596i
$426$		−	3.17740e10i		−	0.964793i
$427$	4.31150e10	−	1.28838e10i	1.29693	−	0.387555i
$428$	−2.35374e10			−0.701428
$429$	−8.86340e7			−0.00261680
$430$		−	1.74291e10i		−	0.509801i
$431$	4.72258e10			1.36858			0.684289	−	0.729211i	$-0.260112\pi$
$431$	4.72258e10			1.36858			0.684289	+	0.729211i	$0.260112\pi$
$432$		−	9.44881e9i		−	0.271295i
$433$			2.47140e10i			0.703058i	0.936177	+	0.351529i	$0.114338\pi$
$433$			2.47140e10i			0.703058i	−0.936177	+	0.351529i	$0.885662\pi$
$434$	−2.27331e10	+	6.79323e9i	−0.640767	+	0.191477i
$435$	−2.08024e10			−0.580974
$436$	2.02246e9			0.0559671
$437$		−	3.26349e10i		−	0.894862i
$438$	3.34323e10			0.908386
$439$		−	1.51087e10i		−	0.406788i	−0.979097	−	0.203394i	$-0.934803\pi$
$439$		−	1.51087e10i		−	0.406788i	0.979097	−	0.203394i	$-0.0651972\pi$
$440$		−	2.26614e9i		−	0.0604611i
$441$	−1.24568e10	+	8.17477e9i	−0.329345	+	0.216133i
$442$	3.84837e8			0.0100830
$443$	−2.25425e10			−0.585312			−0.292656	−	0.956218i	$-0.594539\pi$
$443$	−2.25425e10			−0.585312			−0.292656	+	0.956218i	$0.594539\pi$
$444$			9.12937e9i			0.234914i
$445$	−3.48245e10			−0.888064
$446$		−	3.84192e10i		−	0.970978i
$447$		−	1.91515e9i		−	0.0479704i
$448$	−1.44167e9	−	4.82446e9i	−0.0357894	−	0.119767i
$449$	3.37233e10			0.829744			0.414872	−	0.909880i	$-0.363826\pi$
$449$	3.37233e10			0.829744			0.414872	+	0.909880i	$0.363826\pi$
$450$	6.96751e9			0.169913
$451$			7.22404e9i			0.174612i
$452$	−6.37327e9			−0.152689
$453$			2.71578e10i			0.644913i
$454$		−	1.41825e10i		−	0.333832i
$455$	9.40706e7	+	3.14802e8i	0.00219487	+	0.00734499i
$456$	1.91151e10			0.442097
$457$	−6.87894e10			−1.57709			−0.788545	−	0.614977i	$-0.789165\pi$
$457$	−6.87894e10			−1.57709			−0.788545	+	0.614977i	$0.789165\pi$
$458$		−	8.94179e9i		−	0.203218i
$459$	5.59537e10			1.26060
$460$			7.78922e9i			0.173965i
$461$			4.88554e9i			0.108170i	0.998536	+	0.0540852i	$0.0172243\pi$
$461$			4.88554e9i			0.108170i	−0.998536	+	0.0540852i	$0.982776\pi$
$462$	−6.57997e9	+	1.96626e9i	−0.144430	+	0.0431592i
$463$	−6.59037e10			−1.43412			−0.717061	−	0.697011i	$-0.754513\pi$
$463$	−6.59037e10			−1.43412			−0.717061	+	0.697011i	$0.754513\pi$
$464$	1.38475e10			0.298743
$465$			2.14981e10i			0.459820i
$466$	3.27746e10			0.695014
$467$		−	3.75858e10i		−	0.790234i	−0.918631	−	0.395117i	$-0.870704\pi$
$467$		−	3.75858e10i		−	0.790234i	0.918631	−	0.395117i	$-0.129296\pi$
$468$		−	1.15984e8i		−	0.00241778i
$469$	2.66377e10	+	8.91413e10i	0.550560	+	1.84241i
$470$	−8.93729e9			−0.183153
$471$	−1.60343e10			−0.325812
$472$		−	1.34699e10i		−	0.271391i
$473$	1.58236e10			0.316127
$474$			2.31188e9i			0.0457987i
$475$			4.98768e10i			0.979770i
$476$	2.85694e10	−	8.53725e9i	0.556510	−	0.166299i
$477$	−2.94198e10			−0.568285
$478$	−4.32594e10			−0.828645
$479$			3.43929e10i			0.653322i	0.945142	+	0.326661i	$0.105924\pi$
$479$			3.43929e10i			0.653322i	−0.945142	+	0.326661i	$0.894076\pi$
$480$	−4.56235e9			−0.0859457
$481$			3.96538e8i			0.00740806i
$482$			6.14296e10i			1.13812i
$483$	2.26168e10	−	6.75848e9i	0.415569	−	0.124182i
$484$	−2.53805e10			−0.462508
$485$	4.96001e10			0.896428
$486$		−	2.89616e10i		−	0.519132i
$487$	2.94678e10			0.523879			0.261940	−	0.965084i	$-0.415638\pi$
$487$	2.94678e10			0.523879			0.261940	+	0.965084i	$0.415638\pi$
$488$			2.71409e10i			0.478569i
$489$		−	7.42771e7i		−	0.00129903i
$490$	1.39672e10	+	2.12833e10i	0.242284	+	0.369193i
$491$	−7.21979e10			−1.24222			−0.621110	−	0.783723i	$-0.713318\pi$
$491$	−7.21979e10			−1.24222			−0.621110	+	0.783723i	$0.713318\pi$
$492$	1.45440e10			0.248212
$493$			8.20015e10i			1.38814i
$494$	8.30272e8			0.0139416
$495$		−	4.04447e9i		−	0.0673660i
$496$		−	1.43105e10i		−	0.236444i
$497$	−3.06166e10	−	1.02457e11i	−0.501802	−	1.67925i
$498$	−5.01336e10			−0.815102
$499$	−3.79818e10			−0.612594			−0.306297	−	0.951936i	$-0.599090\pi$
$499$	−3.79818e10			−0.612594			−0.306297	+	0.951936i	$0.599090\pi$
$500$		−	3.14204e10i		−	0.502726i
$501$	4.26701e9			0.0677288
$502$			3.37485e10i			0.531422i
$503$		−	6.53658e10i		−	1.02113i	−0.859841	−	0.510563i	$-0.829437\pi$
$503$		−	6.53658e10i		−	1.02113i	0.859841	−	0.510563i	$-0.170563\pi$
$504$	−2.57301e9	−	8.61041e9i	−0.0398767	−	0.133445i
$505$	1.93130e10			0.296951
$506$	−7.07172e9			−0.107876
$507$		−	5.14313e10i		−	0.778387i
$508$	−1.79370e10			−0.269337
$509$		−	1.00823e11i		−	1.50207i	−0.660264	−	0.751034i	$-0.729555\pi$
$509$		−	1.00823e11i		−	1.50207i	0.660264	−	0.751034i	$-0.270445\pi$
$510$		−	2.70172e10i		−	0.399356i
$511$	1.07804e11	−	3.22145e10i	1.58107	−	0.472464i
$512$	3.03700e9			0.0441942
$513$	1.20718e11			1.74302
$514$			4.25238e10i			0.609228i
$515$	3.88891e10			0.552839
$516$		−	3.18572e10i		−	0.449375i
$517$		−	8.11404e9i		−	0.113573i
$518$	8.79683e9	+	2.94380e10i	0.122182	+	0.408874i
$519$	−1.10453e11			−1.52232
$520$	−1.98168e8			−0.00271031
$521$		−	1.25916e11i		−	1.70895i	−0.519491	−	0.854476i	$-0.673878\pi$
$521$		−	1.25916e11i		−	1.70895i	0.519491	−	0.854476i	$-0.326122\pi$
$522$	2.47141e10			0.332861
$523$			4.72666e10i			0.631753i	0.948800	+	0.315877i	$0.102299\pi$
$523$			4.72666e10i			0.631753i	−0.948800	+	0.315877i	$0.897701\pi$
$524$			2.82845e10i			0.375166i
$525$	−3.45659e10	+	1.03292e10i	−0.454999	+	0.135965i
$526$	6.15615e10			0.804204
$527$	8.47436e10			1.09866
$528$		−	4.14210e9i		−	0.0532947i
$529$	−5.40039e10			−0.689608
$530$			5.02658e10i			0.637043i
$531$		−	2.40402e10i		−	0.302385i
$532$	6.16374e10	−	1.84188e10i	0.769481	−	0.229940i
$533$	6.31723e8			0.00782740
$534$	−6.36528e10			−0.782803
$535$			7.17738e10i			0.876094i
$536$	−5.61144e10			−0.679854
$537$		−	2.03507e10i		−	0.244727i
$538$		−	2.28391e10i		−	0.272615i
$539$	−1.93228e10	+	1.26806e10i	−0.228936	+	0.150240i
$540$	−2.88128e10			−0.338852
$541$	−1.02877e11			−1.20097			−0.600483	−	0.799637i	$-0.705025\pi$
$541$	−1.02877e11			−1.20097			−0.600483	+	0.799637i	$0.705025\pi$
$542$			5.24932e10i			0.608284i
$543$	1.75014e10			0.201314
$544$			1.79844e10i			0.205353i
$545$		−	6.16719e9i		−	0.0699038i
$546$	1.71944e8	+	5.75401e8i	0.00193471	+	0.00647440i
$547$	−4.11293e10			−0.459411			−0.229706	−	0.973260i	$-0.573776\pi$
$547$	−4.11293e10			−0.459411			−0.229706	+	0.973260i	$0.573776\pi$
$548$	2.14339e10			0.237672
$549$			4.84394e10i			0.533224i
$550$	1.08079e10			0.118111
$551$			1.76915e11i			1.91937i
$552$			1.42373e10i			0.153346i
$553$	2.22767e9	+	7.45477e9i	0.0238205	+	0.0797138i
$554$	4.48998e10			0.476656
$555$	2.78387e10			0.293411
$556$		−	2.05679e10i		−	0.215224i
$557$	−4.40191e10			−0.457320			−0.228660	−	0.973506i	$-0.573434\pi$
$557$	−4.40191e10			−0.457320			−0.228660	+	0.973506i	$0.573434\pi$
$558$		−	2.55405e10i		−	0.263447i
$559$		−	1.38373e9i		−	0.0141711i
$560$	−1.47115e10	+	4.39617e9i	−0.149591	+	0.0447015i
$561$	2.45286e10			0.247640
$562$	−1.20493e11			−1.20786
$563$			7.42103e10i			0.738636i	0.929303	+	0.369318i	$0.120409\pi$
$563$			7.42103e10i			0.738636i	−0.929303	+	0.369318i	$0.879591\pi$
$564$	−1.63358e10			−0.161444
$565$			1.94344e10i			0.190711i
$566$		−	4.25848e10i		−	0.414943i
$567$	1.33427e10	+	4.46507e10i	0.129096	+	0.432012i
$568$	6.44965e10			0.619645
$569$	1.35895e11			1.29645			0.648223	−	0.761450i	$-0.275512\pi$
$569$	1.35895e11			1.29645			0.648223	+	0.761450i	$0.275512\pi$
$570$		−	5.82887e10i		−	0.552186i
$571$	−5.09298e9			−0.0479101			−0.0239551	−	0.999713i	$-0.507626\pi$
$571$	−5.09298e9			−0.0479101			−0.0239551	+	0.999713i	$0.507626\pi$
$572$		−	1.79914e8i		−	0.00168066i
$573$			4.30865e10i			0.399689i
$574$	4.68976e10	−	1.40142e10i	0.432019	−	0.129098i
$575$	−3.71492e10			−0.339843
$576$	5.42026e9			0.0492413
$577$		−	1.48143e11i		−	1.33652i	−0.743926	−	0.668262i	$-0.767038\pi$
$577$		−	1.48143e11i		−	1.33652i	0.743926	−	0.668262i	$-0.232962\pi$
$578$	−2.75780e10			−0.247088
$579$			5.22676e10i			0.465070i
$580$		−	4.22258e10i		−	0.373135i
$581$	−1.61658e11	+	4.83075e10i	−1.41871	+	0.423945i
$582$	9.06600e10			0.790176
$583$	−4.56356e10			−0.395029
$584$			6.78626e10i			0.583417i
$585$	−3.53678e8			−0.00301984
$586$		−	1.51335e11i		−	1.28336i
$587$			1.42185e11i			1.19757i	0.800908	+	0.598787i	$0.204350\pi$
$587$			1.42185e11i			1.19757i	−0.800908	+	0.598787i	$0.795650\pi$
$588$	2.55295e10	+	3.89019e10i	0.213566	+	0.325433i
$589$	1.82831e11			1.51911
$590$	−4.10744e10			−0.338972
$591$		−	6.26472e10i		−	0.513513i
$592$	−1.85313e10			−0.150875
$593$		−	2.13933e11i		−	1.73005i	−0.501729	−	0.865025i	$-0.667303\pi$
$593$		−	2.13933e11i		−	1.73005i	0.501729	−	0.865025i	$-0.332697\pi$
$594$		−	2.61587e10i		−	0.210122i
$595$	−2.60331e10	−	8.71182e10i	−0.207710	−	0.695090i
$596$	3.88747e9			0.0308093
$597$	7.63731e10			0.601234
$598$			6.18403e8i			0.00483578i
$599$	3.18702e9			0.0247558			0.0123779	−	0.999923i	$-0.496060\pi$
$599$	3.18702e9			0.0247558			0.0123779	+	0.999923i	$0.496060\pi$
$600$		−	2.17593e10i		−	0.167895i
$601$			1.64772e10i			0.126295i	0.998004	+	0.0631475i	$0.0201139\pi$
$601$			1.64772e10i			0.126295i	−0.998004	+	0.0631475i	$0.979886\pi$
$602$	−3.06968e10	−	1.02725e11i	−0.233726	−	0.782150i
$603$	−1.00150e11			−0.757496
$604$	−5.51261e10			−0.414200
$605$			7.73943e10i			0.577680i
$606$	3.53007e10			0.261754
$607$		−	8.85174e10i		−	0.652040i	−0.945363	−	0.326020i	$-0.894292\pi$
$607$		−	8.85174e10i		−	0.652040i	0.945363	−	0.326020i	$-0.105708\pi$
$608$			3.88008e10i			0.283940i
$609$	−1.22607e11	+	3.66381e10i	−0.891345	+	0.266356i
$610$	8.27622e10			0.597740
$611$	−7.09550e8			−0.00509118
$612$			3.20975e10i			0.228805i
$613$	−2.18305e10			−0.154604			−0.0773021	−	0.997008i	$-0.524631\pi$
$613$	−2.18305e10			−0.154604			−0.0773021	+	0.997008i	$0.524631\pi$
$614$			1.85027e10i			0.130185i
$615$		−	4.43497e10i		−	0.310020i
$616$	−3.99122e9	−	1.33564e10i	−0.0277193	−	0.0927609i
$617$	2.42237e11			1.67148			0.835739	−	0.549127i	$-0.185040\pi$
$617$	2.42237e11			1.67148			0.835739	+	0.549127i	$0.185040\pi$
$618$	7.10823e10			0.487312
$619$		−	6.65872e10i		−	0.453553i	−0.973947	−	0.226777i	$-0.927181\pi$
$619$		−	6.65872e10i		−	0.453553i	0.973947	−	0.226777i	$-0.0728187\pi$
$620$	−4.36378e10			−0.295322
$621$			8.99133e10i			0.604585i
$622$			1.20974e11i			0.808220i
$623$	−2.05251e11	+	6.13342e10i	−1.36249	+	0.407146i
$624$	−3.62215e8			−0.00238906
$625$	−2.73467e9			−0.0179219
$626$			3.37174e10i			0.219562i
$627$	5.29195e10			0.342409
$628$		−	3.25473e10i		−	0.209255i
$629$		−	1.09738e11i		−	0.701058i
$630$	−2.62562e10	+	7.84601e9i	−0.166675	+	0.0498066i
$631$	1.31642e11			0.830379			0.415189	−	0.909735i	$-0.363715\pi$
$631$	1.31642e11			0.830379			0.415189	+	0.909735i	$0.363715\pi$
$632$	−4.69278e9			−0.0294145
$633$		−	7.80494e10i		−	0.486133i
$634$	2.91073e10			0.180154
$635$			5.46964e10i			0.336406i
$636$			9.18768e10i			0.561536i
$637$	1.10888e9	+	1.68972e9i	0.00673485	+	0.0102626i
$638$	3.83362e10			0.231380
$639$	1.15109e11			0.690411
$640$		−	9.26089e9i		−	0.0551992i
$641$	−1.05575e11			−0.625360			−0.312680	−	0.949859i	$-0.601227\pi$
$641$	−1.05575e11			−0.625360			−0.312680	+	0.949859i	$0.601227\pi$
$642$			1.31189e11i			0.772252i
$643$		−	2.06835e11i		−	1.20998i	−0.796232	−	0.604991i	$-0.793177\pi$
$643$		−	2.06835e11i		−	1.20998i	0.796232	−	0.604991i	$-0.206823\pi$
$644$	1.37187e10	+	4.59087e10i	0.0797571	+	0.266902i
$645$	−9.71439e10			−0.561276
$646$	−2.29769e11			−1.31936
$647$			2.50568e10i			0.142991i	0.997441	+	0.0714955i	$0.0227772\pi$
$647$			2.50568e10i			0.142991i	−0.997441	+	0.0714955i	$0.977223\pi$
$648$	−2.81076e10			−0.159413
$649$		−	3.72909e10i		−	0.210196i
$650$		−	9.45122e8i		−	0.00529462i
$651$	3.78632e10	+	1.26707e11i	0.210811	+	0.705467i
$652$	1.50771e8			0.000834312
$653$	1.61819e11			0.889973			0.444986	−	0.895537i	$-0.353209\pi$
$653$	1.61819e11			0.889973			0.444986	+	0.895537i	$0.353209\pi$
$654$		−	1.12725e10i		−	0.0616182i
$655$	8.62496e10			0.468589
$656$			2.95220e10i			0.159416i
$657$			1.21117e11i			0.650046i
$658$	−5.26753e10	+	1.57407e10i	−0.280998	+	0.0839694i
$659$	−1.02652e11			−0.544283			−0.272142	−	0.962257i	$-0.587732\pi$
$659$	−1.02652e11			−0.544283			−0.272142	+	0.962257i	$0.587732\pi$
$660$	−1.26307e10			−0.0665660
$661$			3.00191e11i			1.57250i	0.617907	+	0.786252i	$0.287981\pi$
$661$			3.00191e11i			1.57250i	−0.617907	+	0.786252i	$0.712019\pi$
$662$	−1.73887e11			−0.905387
$663$		−	2.14495e9i		−	0.0111010i
$664$		−	1.01764e11i		−	0.523505i
$665$	−5.61655e10	−	1.87954e11i	−0.287199	−	0.961094i
$666$	−3.30735e10			−0.168106
$667$	−1.31770e11			−0.665753
$668$			8.66139e9i			0.0434993i
$669$	−2.14136e11			−1.06902
$670$			1.71113e11i			0.849148i
$671$			7.51386e10i			0.370658i
$672$	−2.68900e10	+	8.03540e9i	−0.131860	+	0.0394031i
$673$	1.07564e11			0.524333			0.262167	−	0.965023i	$-0.415563\pi$
$673$	1.07564e11			0.524333			0.262167	+	0.965023i	$0.415563\pi$
$674$	2.50500e11			1.21386
$675$		−	1.37417e11i		−	0.661950i
$676$	1.04398e11			0.499925
$677$			2.08464e11i			0.992376i	0.868215	+	0.496188i	$0.165267\pi$
$677$			2.08464e11i			0.992376i	−0.868215	+	0.496188i	$0.834733\pi$
$678$			3.55225e10i			0.168107i
$679$	2.92337e11	−	8.73577e10i	1.37532	−	0.410981i
$680$	5.48409e10			0.256489
$681$	−7.90483e10			−0.367540
$682$		−	3.96181e10i		−	0.183129i
$683$	8.80075e10			0.404424			0.202212	−	0.979342i	$-0.435187\pi$
$683$	8.80075e10			0.404424			0.202212	+	0.979342i	$0.435187\pi$
$684$			6.92493e10i			0.316367i
$685$		−	6.53595e10i		−	0.296856i
$686$	1.19806e11	+	1.00841e11i	0.540980	+	0.455347i
$687$	−4.98386e10			−0.223738
$688$	6.46653e10			0.288614
$689$			3.99071e9i			0.0177081i
$690$	4.34146e10			0.191531
$691$		−	1.24749e11i		−	0.547175i	−0.961847	−	0.273587i	$-0.911790\pi$
$691$		−	1.24749e11i		−	0.547175i	0.961847	−	0.273587i	$-0.0882102\pi$
$692$		−	2.24202e11i		−	0.977722i
$693$	−7.12328e9	−	2.38376e10i	−0.0308850	−	0.103355i
$694$	−2.77691e10			−0.119708
$695$	−6.27188e10			−0.268818
$696$		−	7.71811e10i		−	0.328908i
$697$	−1.74823e11			−0.740742
$698$		−	2.75961e11i		−	1.16259i
$699$		−	1.82675e11i		−	0.765191i
$700$	−2.09667e10	−	7.01636e10i	−0.0873247	−	0.292227i
$701$	6.16985e10			0.255507			0.127753	−	0.991806i	$-0.459223\pi$
$701$	6.16985e10			0.255507			0.127753	+	0.991806i	$0.459223\pi$
$702$	−2.28751e9			−0.00941920
$703$		−	2.36756e11i		−	0.969347i
$704$	8.40783e9			0.0342289
$705$			4.98135e10i			0.201646i
$706$			1.04503e11i			0.420638i
$707$	1.13829e11	−	3.40148e10i	0.455589	−	0.136142i
$708$	−7.50766e10			−0.298794
$709$	−2.62101e11			−1.03725			−0.518626	−	0.855002i	$-0.673556\pi$
$709$	−2.62101e11			−1.03725			−0.518626	+	0.855002i	$0.673556\pi$
$710$		−	1.96673e11i		−	0.773946i
$711$	−8.37538e9			−0.0327738
$712$		−	1.29206e11i		−	0.502761i
$713$			1.36176e11i			0.526919i
$714$	−4.75838e10	−	1.59236e11i	−0.183091	−	0.612702i
$715$	−5.48620e8			−0.00209917
$716$	4.13089e10			0.157178
$717$			2.41113e11i			0.912314i
$718$	−1.66403e10			−0.0626129
$719$		−	2.34993e11i		−	0.879305i	−0.898168	−	0.439652i	$-0.855102\pi$
$719$		−	2.34993e11i		−	0.879305i	0.898168	−	0.439652i	$-0.144898\pi$
$720$		−	1.65283e10i		−	0.0615032i
$721$	2.29208e11	−	6.84930e10i	0.848180	−	0.253458i
$722$	−3.03573e11			−1.11716
$723$	3.42389e11			1.25304
$724$			3.55252e10i			0.129295i
$725$	2.01388e11			0.728922
$726$			1.41463e11i			0.509208i
$727$			4.00180e11i			1.43258i	0.697804	+	0.716288i	$0.254161\pi$
$727$			4.00180e11i			1.43258i	−0.697804	+	0.716288i	$0.745839\pi$
$728$	−1.16798e9	+	3.49021e8i	−0.00415823	+	0.00124258i
$729$	−2.88766e11			−1.02244
$730$	2.06937e11			0.728697
$731$			3.82934e11i			1.34108i
$732$	1.51274e11			0.526891
$733$			1.72841e11i			0.598729i	0.954139	+	0.299364i	$0.0967746\pi$
$733$			1.72841e11i			0.598729i	−0.954139	+	0.299364i	$0.903225\pi$
$734$		−	2.30499e11i		−	0.794116i
$735$	1.18626e11	−	7.78484e10i	0.406471	−	0.266747i
$736$	−2.88996e10			−0.0984873
$737$	−1.55351e11			−0.526555
$738$			5.26892e10i			0.177622i
$739$	8.57210e9			0.0287415			0.0143708	−	0.999897i	$-0.495425\pi$
$739$	8.57210e9			0.0287415			0.0143708	+	0.999897i	$0.495425\pi$
$740$			5.65084e10i			0.188446i
$741$		−	4.62766e9i		−	0.0153493i
$742$	8.85301e10	+	2.96261e11i	0.292062	+	0.977368i
$743$	−3.54812e11			−1.16424			−0.582121	−	0.813102i	$-0.697777\pi$
$743$	−3.54812e11			−1.16424			−0.582121	+	0.813102i	$0.697777\pi$
$744$	−7.97621e10			−0.260318
$745$		−	1.18543e10i		−	0.0384813i
$746$	5.91765e9			0.0191071
$747$		−	1.81622e11i		−	0.583291i
$748$			4.97893e10i			0.159048i
$749$	1.26411e11	+	4.23026e11i	0.401658	+	1.34413i
$750$	−1.75127e11			−0.553487
$751$	−4.80478e11			−1.51047			−0.755237	−	0.655451i	$-0.772478\pi$
$751$	−4.80478e11			−1.51047			−0.755237	+	0.655451i	$0.772478\pi$
$752$		−	3.31591e10i		−	0.103689i
$753$	1.88103e11			0.585080
$754$		−	3.35239e9i		−	0.0103722i
$755$			1.68099e11i			0.517342i
$756$	−1.69819e11	+	5.07462e10i	−0.519875	+	0.155352i
$757$	−1.55185e11			−0.472570			−0.236285	−	0.971684i	$-0.575930\pi$
$757$	−1.55185e11			−0.472570			−0.236285	+	0.971684i	$0.575930\pi$
$758$	3.26057e11			0.987680
$759$			3.94155e10i			0.118768i
$760$	1.18317e11			0.354645
$761$			1.40466e11i			0.418826i	0.977827	+	0.209413i	$0.0671553\pi$
$761$			1.40466e11i			0.418826i	−0.977827	+	0.209413i	$0.932845\pi$
$762$			9.99751e10i			0.296532i
$763$	−1.08619e10	−	3.63486e10i	−0.0320485	−	0.107248i
$764$	−8.74590e10			−0.256703
$765$	9.78767e10			0.285781
$766$			2.18404e11i			0.634374i
$767$	−3.26098e9			−0.00942252
$768$		−	1.69272e10i		−	0.0486565i
$769$			1.78759e11i			0.511168i	0.966787	+	0.255584i	$0.0822677\pi$
$769$			1.78759e11i			0.511168i	−0.966787	+	0.255584i	$0.917732\pi$
$770$	−4.07283e10	+	1.21706e10i	−0.115860	+	0.0346218i
$771$	2.37014e11			0.670743
$772$	−1.06095e11			−0.298695
$773$		−	5.28570e11i		−	1.48042i	−0.672376	−	0.740210i	$-0.734726\pi$
$773$		−	5.28570e11i		−	1.48042i	0.672376	−	0.740210i	$-0.265274\pi$
$774$	1.15411e11			0.321575
$775$		−	2.08122e11i		−	0.576914i
$776$			1.84026e11i			0.507496i
$777$	1.64078e11	−	4.90306e10i	0.450159	−	0.134519i
$778$	−2.74250e11			−0.748563
$779$	−3.77174e11			−1.02422
$780$			1.10452e9i			0.00298398i
$781$	1.78556e11			0.479922
$782$		−	1.71137e11i		−	0.457632i
$783$		−	4.87424e11i		−	1.29676i
$784$	−7.89651e10	+	5.18210e10i	−0.209012	+	0.137164i
$785$	−9.92482e10			−0.261363
$786$	1.57649e11			0.413048
$787$		−	2.40815e11i		−	0.627746i	−0.949465	−	0.313873i	$-0.898373\pi$
$787$		−	2.40815e11i		−	0.627746i	0.949465	−	0.313873i	$-0.101627\pi$
$788$	1.27164e11			0.329807
$789$		−	3.43123e11i		−	0.885406i
$790$			1.43099e10i			0.0367392i
$791$	3.42286e10	+	1.14544e11i	0.0874345	+	0.292594i
$792$	1.50058e10			0.0381380
$793$	6.57066e9			0.0166156
$794$			6.39607e10i			0.160928i
$795$	2.80165e11			0.701367
$796$			1.55026e11i			0.386146i
$797$		−	6.80241e11i		−	1.68589i	−0.537999	−	0.842946i	$-0.680820\pi$
$797$		−	6.80241e11i		−	1.68589i	0.537999	−	0.842946i	$-0.319180\pi$
$798$	−1.02660e11	−	3.43547e11i	−0.253158	−	0.847177i
$799$	1.96361e11			0.481801
$800$	4.41680e10			0.107832
$801$		−	2.30598e11i		−	0.560178i
$802$	−3.26925e10			−0.0790224
$803$			1.87875e11i			0.451864i
$804$			3.12763e11i			0.748500i
$805$	1.39992e11	−	4.18331e10i	0.333365	−	0.0996178i
$806$	−3.46450e9			−0.00820918
$807$	−1.27298e11			−0.300142
$808$			7.16551e10i			0.168113i
$809$	6.57997e11			1.53614			0.768068	−	0.640369i	$-0.221218\pi$
$809$	6.57997e11			1.53614			0.768068	+	0.640369i	$0.221218\pi$
$810$			8.57100e10i			0.199109i
$811$		−	6.43078e10i		−	0.148655i	−0.997234	−	0.0743276i	$-0.976319\pi$
$811$		−	6.43078e10i		−	0.148655i	0.997234	−	0.0743276i	$-0.0236811\pi$
$812$	−7.43697e10	−	2.48874e11i	−0.171069	−	0.572473i
$813$	2.92580e11			0.669703
$814$	−5.13031e10			−0.116855
$815$		−	4.59755e8i		−	0.00104207i
$816$	1.00239e11			0.226088
$817$			8.26166e11i			1.85430i
$818$		−	1.19487e11i		−	0.266874i
$819$	−2.08453e9	+	6.22911e8i	−0.00463312	+	0.00138449i
$820$	9.00232e10			0.199113
$821$	−5.94524e11			−1.30857			−0.654285	−	0.756248i	$-0.727030\pi$
$821$	−5.94524e11			−1.30857			−0.654285	+	0.756248i	$0.727030\pi$
$822$		−	1.19465e11i		−	0.261670i
$823$	−4.42327e11			−0.964149			−0.482075	−	0.876130i	$-0.660117\pi$
$823$	−4.42327e11			−0.964149			−0.482075	+	0.876130i	$0.660117\pi$
$824$			1.44286e11i			0.312980i
$825$		−	6.02397e10i		−	0.130037i
$826$	−2.42088e11	+	7.23419e10i	−0.520059	+	0.155407i
$827$	1.25503e11			0.268307			0.134153	−	0.990961i	$-0.457169\pi$
$827$	1.25503e11			0.268307			0.134153	+	0.990961i	$0.457169\pi$
$828$	−5.15782e10			−0.109735
$829$			8.34051e10i			0.176593i	0.996094	+	0.0882967i	$0.0281424\pi$
$829$			8.34051e10i			0.176593i	−0.996094	+	0.0882967i	$0.971858\pi$
$830$	−3.10314e11			−0.653866
$831$		−	2.50257e11i		−	0.524785i
$832$		−	7.35241e8i		−	0.00153439i
$833$	−3.06872e11	−	4.67613e11i	−0.637349	−	0.971196i
$834$	−1.14639e11			−0.236956
$835$	2.64117e10			0.0543313
$836$			1.07419e11i			0.219915i
$837$	−5.03724e11			−1.02634
$838$		−	2.89625e11i		−	0.587300i
$839$			9.34541e11i			1.88604i	0.332738	+	0.943019i	$0.392028\pi$
$839$			9.34541e11i			1.88604i	−0.332738	+	0.943019i	$0.607972\pi$
$840$	2.45028e10	+	8.19970e10i	0.0492151	+	0.164695i
$841$	2.14085e11			0.427960
$842$	6.13488e11			1.22056
$843$			6.71586e11i			1.32982i
$844$	1.58429e11			0.312222
$845$		−	3.18346e11i		−	0.624414i
$846$		−	5.91804e10i		−	0.115530i
$847$	1.36310e11	+	4.56152e11i	0.264846	+	0.886291i
$848$	−1.86496e11			−0.360650
$849$	−2.37353e11			−0.456841
$850$			2.61553e11i			0.501053i
$851$	1.76340e11			0.336227
$852$		−	3.59482e11i		−	0.682211i
$853$		−	4.03969e11i		−	0.763049i	−0.924359	−	0.381524i	$-0.875399\pi$
$853$		−	4.03969e11i		−	0.763049i	0.924359	−	0.381524i	$-0.124601\pi$
$854$	4.87790e11	−	1.45764e11i	0.917068	−	0.274043i
$855$	2.11166e11			0.395147
$856$	−2.66295e11			−0.495984
$857$			1.51089e11i			0.280097i	0.990145	+	0.140049i	$0.0447259\pi$
$857$			1.51089e11i			0.280097i	−0.990145	+	0.140049i	$0.955274\pi$
$858$	−1.00278e9			−0.00185036
$859$			6.87985e11i			1.26359i	0.775135	+	0.631795i	$0.217682\pi$
$859$			6.87985e11i			1.26359i	−0.775135	+	0.631795i	$0.782318\pi$
$860$		−	1.97188e11i		−	0.360484i
$861$	−7.81104e10	−	2.61392e11i	−0.142133	−	0.475641i
$862$	5.34298e11			0.967731
$863$	5.26400e11			0.949015			0.474507	−	0.880252i	$-0.342626\pi$
$863$	5.26400e11			0.949015			0.474507	+	0.880252i	$0.342626\pi$
$864$		−	1.06901e11i		−	0.191835i
$865$	−6.83672e11			−1.22119
$866$			2.79607e11i			0.497137i
$867$			1.53711e11i			0.272037i
$868$	−2.57196e11	+	7.68567e10i	−0.453091	+	0.135395i
$869$	−1.29918e10			−0.0227819
$870$	−2.35353e11			−0.410811
$871$			1.35850e10i			0.0236041i
$872$	2.28815e10			0.0395747
$873$			3.28439e11i			0.565454i
$874$		−	3.69221e11i		−	0.632763i
$875$	−5.64703e11	+	1.68748e11i	−0.963359	+	0.287876i
$876$	3.78244e11			0.642326
$877$	6.90759e11			1.16769			0.583846	−	0.811865i	$-0.301547\pi$
$877$	6.90759e11			1.16769			0.583846	+	0.811865i	$0.301547\pi$
$878$		−	1.70935e11i		−	0.287642i
$879$	−8.43491e11			−1.41294
$880$		−	2.56384e10i		−	0.0427525i
$881$			6.90270e10i			0.114582i	0.998358	+	0.0572909i	$0.0182462\pi$
$881$			6.90270e10i			0.114582i	−0.998358	+	0.0572909i	$0.981754\pi$
$882$	−1.40932e11	+	9.24869e10i	−0.232882	+	0.152829i
$883$	3.66101e11			0.602224			0.301112	−	0.953589i	$-0.402642\pi$
$883$	3.66101e11			0.602224			0.301112	+	0.953589i	$0.402642\pi$
$884$	4.35393e9			0.00712972
$885$			2.28935e11i			0.373198i
$886$	−2.55039e11			−0.413878
$887$			2.07121e11i			0.334603i	0.985906	+	0.167301i	$0.0535053\pi$
$887$			2.07121e11i			0.334603i	−0.985906	+	0.167301i	$0.946495\pi$
$888$			1.03287e11i			0.166109i
$889$	9.63334e10	+	3.22374e11i	0.154230	+	0.516122i
$890$	−3.93994e11			−0.627956
$891$	−7.78149e10			−0.123467
$892$		−	4.34664e11i		−	0.686585i
$893$	4.23642e11			0.666182
$894$		−	2.16675e10i		−	0.0339202i
$895$		−	1.25965e11i		−	0.196318i
$896$	−1.63106e10	−	5.45826e10i	−0.0253069	−	0.0846880i
$897$	3.44677e9			0.00532406
$898$	3.81535e11			0.586718
$899$		−	7.38219e11i		−	1.13018i
$900$	7.88284e10			0.120147
$901$		−	1.10439e12i		−	1.67580i
$902$			8.17307e10i			0.123469i
$903$	−5.72555e11	+	1.71094e11i	−0.861124	+	0.257326i
$904$	−7.21053e10			−0.107968
$905$	1.08329e11			0.161492
$906$			3.07255e11i			0.456022i
$907$	−9.59162e11			−1.41730			−0.708652	−	0.705558i	$-0.750696\pi$
$907$	−9.59162e11			−1.41730			−0.708652	+	0.705558i	$0.750696\pi$
$908$		−	1.60456e11i		−	0.236055i
$909$			1.27886e11i			0.187312i
$910$	1.06429e9	+	3.56157e9i	0.00155201	+	0.00519369i
$911$	9.11205e11			1.32295			0.661474	−	0.749968i	$-0.269931\pi$
$911$	9.11205e11			1.32295			0.661474	+	0.749968i	$0.269931\pi$
$912$	2.16263e11			0.312610
$913$		−	2.81729e11i		−	0.405461i
$914$	−7.78263e11			−1.11517
$915$		−	4.61289e11i		−	0.658095i
$916$		−	1.01165e11i		−	0.143697i
$917$	5.08345e11	−	1.51906e11i	0.718921	−	0.214832i
$918$	6.33044e11			0.891381
$919$	1.32026e12			1.85096			0.925478	−	0.378802i	$-0.123664\pi$
$919$	1.32026e12			1.85096			0.925478	+	0.378802i	$0.123664\pi$
$920$			8.81250e10i			0.123012i
$921$	1.03128e11			0.143330
$922$			5.52736e10i			0.0764881i
$923$		−	1.56143e10i		−	0.0215137i
$924$	−7.44439e10	+	2.22457e10i	−0.102127	+	0.0305182i
$925$	−2.69506e11			−0.368130
$926$	−7.45615e11			−1.01408
$927$			2.57513e11i			0.348723i
$928$	1.56666e11			0.211243
$929$		−	1.91730e11i		−	0.257411i	−0.991683	−	0.128706i	$-0.958918\pi$
$929$		−	1.91730e11i		−	0.257411i	0.991683	−	0.128706i	$-0.0410823\pi$
$930$			2.43223e11i			0.325141i
$931$	−6.62066e11	−	1.00886e12i	−0.881256	−	1.34286i
$932$	3.70802e11			0.491449
$933$	6.74268e11			0.889827
$934$		−	4.25234e11i		−	0.558780i
$935$	1.51825e11			0.198654
$936$		−	1.31221e9i		−	0.00170963i
$937$			4.83837e11i			0.627684i	0.949475	+	0.313842i	$0.101616\pi$
$937$			4.83837e11i			0.627684i	−0.949475	+	0.313842i	$0.898384\pi$
$938$	3.01371e11	+	1.00852e12i	0.389305	+	1.30278i
$939$	1.87930e11			0.241731
$940$	−1.01114e11			−0.129509
$941$		−	1.03826e12i		−	1.32418i	−0.749424	−	0.662090i	$-0.769669\pi$
$941$		−	1.03826e12i		−	1.32418i	0.749424	−	0.662090i	$-0.230331\pi$
$942$	−1.81408e11			−0.230384
$943$		−	2.80927e11i		−	0.355260i
$944$		−	1.52394e11i		−	0.191902i
$945$	1.54743e11	+	5.17838e11i	0.194037	+	0.649332i
$946$	1.79024e11			0.223535
$947$	−6.77497e11			−0.842379			−0.421190	−	0.906973i	$-0.638387\pi$
$947$	−6.77497e11			−0.842379			−0.421190	+	0.906973i	$0.638387\pi$
$948$			2.61560e10i			0.0323845i
$949$	1.64292e10			0.0202559
$950$			5.64291e11i			0.692802i
$951$		−	1.62234e11i		−	0.198345i
$952$	3.23226e11	−	9.65880e10i	0.393512	−	0.117591i
$953$	−1.22445e12			−1.48446			−0.742231	−	0.670144i	$-0.766232\pi$
$953$	−1.22445e12			−1.48446			−0.742231	+	0.670144i	$0.766232\pi$
$954$	−3.32847e11			−0.401838
$955$			2.66693e11i			0.320626i
$956$	−4.89424e11			−0.585940
$957$		−	2.13673e11i		−	0.254743i
$958$			3.89112e11i			0.461968i
$959$	−1.15114e11	−	3.85221e11i	−0.136098	−	0.455444i
$960$	−5.16171e10			−0.0607728
$961$	8.99861e10			0.105507
$962$			4.48632e9i			0.00523829i
$963$	−4.75267e11			−0.552628
$964$			6.94997e11i			0.804776i
$965$			3.23522e11i			0.373074i
$966$	2.55880e11	−	7.64634e10i	0.293852	−	0.0878103i
$967$	8.83520e10			0.101044			0.0505220	−	0.998723i	$-0.483911\pi$
$967$	8.83520e10			0.101044			0.0505220	+	0.998723i	$0.483911\pi$
$968$	−2.87148e11			−0.327043
$969$			1.28066e12i			1.45257i
$970$	5.61161e11			0.633871
$971$			5.71167e11i			0.642519i	0.946991	+	0.321259i	$0.104106\pi$
$971$			5.71167e11i			0.642519i	−0.946991	+	0.321259i	$0.895894\pi$
$972$		−	3.27663e11i		−	0.367082i
$973$	−3.69657e11	+	1.10463e11i	−0.412428	+	0.123244i
$974$	3.33390e11			0.370439
$975$	−5.26780e9			−0.00582922
$976$			3.07064e11i			0.338400i
$977$	5.59672e11			0.614265			0.307132	−	0.951667i	$-0.400631\pi$
$977$	5.59672e11			0.614265			0.307132	+	0.951667i	$0.400631\pi$
$978$		−	8.40350e8i		−	0.000918554i
$979$		−	3.57701e11i		−	0.389394i
$980$	1.58020e11	+	2.40793e11i	0.171320	+	0.261059i
$981$	4.08375e10			0.0440944
$982$	−8.16826e11			−0.878383
$983$			1.08008e12i			1.15676i	0.815767	+	0.578380i	$0.196315\pi$
$983$			1.08008e12i			1.15676i	−0.815767	+	0.578380i	$0.803685\pi$
$984$	1.64546e11			0.175512
$985$		−	3.87769e11i		−	0.411935i
$986$			9.27741e11i			0.981565i
$987$	8.77335e10	+	2.93595e11i	0.0924479	+	0.309371i
$988$	9.39346e9			0.00985820
$989$	−6.15344e11			−0.643181
$990$		−	4.57580e10i		−	0.0476350i
$991$	9.22739e11			0.956719			0.478360	−	0.878164i	$-0.341232\pi$
$991$	9.22739e11			0.956719			0.478360	+	0.878164i	$0.341232\pi$
$992$		−	1.61905e11i		−	0.167191i
$993$			9.69186e11i			0.996805i
$994$	−3.46388e11	−	1.15917e12i	−0.354827	−	1.18741i
$995$	4.72729e11			0.482303
$996$	−5.67197e11			−0.576364
$997$			7.27213e11i			0.736006i	0.929825	+	0.368003i	$0.119958\pi$
$997$			7.27213e11i			0.736006i	−0.929825	+	0.368003i	$0.880042\pi$
$998$	−4.29714e11			−0.433169
$999$			6.52292e11i			0.654908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.9.b.a.13.3	✓	4
3.2	odd	2		126.9.c.a.55.2		4
4.3	odd	2		112.9.c.c.97.3		4
5.2	odd	4		350.9.d.a.349.6		8
5.3	odd	4		350.9.d.a.349.3		8
5.4	even	2		350.9.b.a.251.2		4
7.2	even	3		98.9.d.a.31.2		8
7.3	odd	6		98.9.d.a.19.2		8
7.4	even	3		98.9.d.a.19.1		8
7.5	odd	6		98.9.d.a.31.1		8
7.6	odd	2	inner	14.9.b.a.13.4	yes	4
21.20	even	2		126.9.c.a.55.1		4
28.27	even	2		112.9.c.c.97.2		4
35.13	even	4		350.9.d.a.349.2		8
35.27	even	4		350.9.d.a.349.7		8
35.34	odd	2		350.9.b.a.251.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.9.b.a.13.3	✓	4	1.1	even	1	trivial
14.9.b.a.13.4	yes	4	7.6	odd	2	inner
98.9.d.a.19.1		8	7.4	even	3
98.9.d.a.19.2		8	7.3	odd	6
98.9.d.a.31.1		8	7.5	odd	6
98.9.d.a.31.2		8	7.2	even	3
112.9.c.c.97.2		4	28.27	even	2
112.9.c.c.97.3		4	4.3	odd	2
126.9.c.a.55.1		4	21.20	even	2
126.9.c.a.55.2		4	3.2	odd	2
350.9.b.a.251.1		4	35.34	odd	2
350.9.b.a.251.2		4	5.4	even	2
350.9.d.a.349.2		8	35.13	even	4
350.9.d.a.349.3		8	5.3	odd	4
350.9.d.a.349.6		8	5.2	odd	4
350.9.d.a.349.7		8	35.27	even	4

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+11.3137 q^{2} -63.0589i q^{3} +128.000 q^{4} -390.317i q^{5} -713.430i q^{6} +(-687.442 - 2300.48i) q^{7} +1448.15 q^{8} +2584.58 q^{9} +O(q^{10})\)	\(q+11.3137 q^{2} -63.0589i q^{3} +128.000 q^{4} -390.317i q^{5} -713.430i q^{6} +(-687.442 - 2300.48i) q^{7} +1448.15 q^{8} +2584.58 q^{9} -4415.94i q^{10} +4009.17 q^{11} -8071.54i q^{12} -350.590i q^{13} +(-7777.52 - 26027.0i) q^{14} -24613.0 q^{15} +16384.0 q^{16} +97022.3i q^{17} +29241.2 q^{18} +209322. i q^{19} -49960.6i q^{20} +(-145066. + 43349.3i) q^{21} +45358.5 q^{22} -155907. q^{23} -91319.0i q^{24} +238277. q^{25} -3966.48i q^{26} -576710. i q^{27} +(-87992.6 - 294462. i) q^{28} +845181. q^{29} -278464. q^{30} -873444. i q^{31} +185364. q^{32} -252813. i q^{33} +1.09768e6i q^{34} +(-897919. + 268321. i) q^{35} +330826. q^{36} -1.13106e6 q^{37} +2.36821e6i q^{38} -22107.8 q^{39} -565240. i q^{40} +1.80188e6i q^{41} +(-1.64123e6 + 490442. i) q^{42} +3.94686e6 q^{43} +513173. q^{44} -1.00881e6i q^{45} -1.76389e6 q^{46} -2.02387e6i q^{47} -1.03316e6i q^{48} +(-4.81965e6 + 3.16290e6i) q^{49} +2.69580e6 q^{50} +6.11812e6 q^{51} -44875.6i q^{52} -1.13828e7 q^{53} -6.52473e6i q^{54} -1.56485e6i q^{55} +(-995523. - 3.33146e6i) q^{56} +1.31996e7 q^{57} +9.56214e6 q^{58} -9.30141e6i q^{59} -3.15046e6 q^{60} +1.87417e7i q^{61} -9.88189e6i q^{62} +(-1.77675e6 - 5.94578e6i) q^{63} +2.09715e6 q^{64} -136841. q^{65} -2.86026e6i q^{66} -3.87489e7 q^{67} +1.24189e7i q^{68} +9.83134e6i q^{69} +(-1.01588e7 + 3.03570e6i) q^{70} +4.45370e7 q^{71} +3.74287e6 q^{72} +4.68614e7i q^{73} -1.27965e7 q^{74} -1.50255e7i q^{75} +2.67933e7i q^{76} +(-2.75607e6 - 9.22302e6i) q^{77} -250122. q^{78} -3.24052e6 q^{79} -6.39496e6i q^{80} -1.94092e7 q^{81} +2.03860e7i q^{82} -7.02713e7i q^{83} +(-1.85684e7 + 5.54872e6i) q^{84} +3.78695e7 q^{85} +4.46536e7 q^{86} -5.32962e7i q^{87} +5.80589e6 q^{88} -8.92209e7i q^{89} -1.14133e7i q^{90} +(-806527. + 241011. i) q^{91} -1.99561e7 q^{92} -5.50784e7 q^{93} -2.28975e7i q^{94} +8.17021e7 q^{95} -1.16888e7i q^{96} +1.27076e8i q^{97} +(-5.45281e7 + 3.57841e7i) q^{98} +1.03620e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 512 q^{4} - 6076 q^{7} - 13692 q^{9}+O(q^{10}) \) 4 * q + 512 * q^4 - 6076 * q^7 - 13692 * q^9	\( 4 q + 512 q^{4} - 6076 q^{7} - 13692 q^{9} - 13560 q^{11} + 37632 q^{14} - 13056 q^{15} + 65536 q^{16} + 271872 q^{18} - 413952 q^{21} + 334848 q^{22} - 894072 q^{23} + 1216900 q^{25} - 777728 q^{28} + 317064 q^{29} - 966144 q^{30} - 1655808 q^{35} - 1752576 q^{36} - 2495096 q^{37} + 10228992 q^{39} - 1881600 q^{42} + 9186568 q^{43} - 1735680 q^{44} + 3059712 q^{46} + 931588 q^{49} - 2984448 q^{50} - 324096 q^{51} - 38727288 q^{53} + 4816896 q^{56} - 30690816 q^{57} + 34661376 q^{58} - 1671168 q^{60} + 40780740 q^{63} + 8388608 q^{64} - 11891712 q^{65} - 12320248 q^{67} - 21901824 q^{70} + 62168712 q^{71} + 34799616 q^{72} - 22957056 q^{74} + 45208968 q^{77} - 116728320 q^{78} + 24889736 q^{79} - 70788348 q^{81} - 52985856 q^{84} + 89943552 q^{85} + 74680320 q^{86} + 42860544 q^{88} + 38158848 q^{91} - 114441216 q^{92} - 408466944 q^{93} + 227967744 q^{95} - 228652032 q^{98} + 224220168 q^{99}+O(q^{100}) \) 4 * q + 512 * q^4 - 6076 * q^7 - 13692 * q^9 - 13560 * q^11 + 37632 * q^14 - 13056 * q^15 + 65536 * q^16 + 271872 * q^18 - 413952 * q^21 + 334848 * q^22 - 894072 * q^23 + 1216900 * q^25 - 777728 * q^28 + 317064 * q^29 - 966144 * q^30 - 1655808 * q^35 - 1752576 * q^36 - 2495096 * q^37 + 10228992 * q^39 - 1881600 * q^42 + 9186568 * q^43 - 1735680 * q^44 + 3059712 * q^46 + 931588 * q^49 - 2984448 * q^50 - 324096 * q^51 - 38727288 * q^53 + 4816896 * q^56 - 30690816 * q^57 + 34661376 * q^58 - 1671168 * q^60 + 40780740 * q^63 + 8388608 * q^64 - 11891712 * q^65 - 12320248 * q^67 - 21901824 * q^70 + 62168712 * q^71 + 34799616 * q^72 - 22957056 * q^74 + 45208968 * q^77 - 116728320 * q^78 + 24889736 * q^79 - 70788348 * q^81 - 52985856 * q^84 + 89943552 * q^85 + 74680320 * q^86 + 42860544 * q^88 + 38158848 * q^91 - 114441216 * q^92 - 408466944 * q^93 + 227967744 * q^95 - 228652032 * q^98 + 224220168 * q^99

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