LMFDB - Embedded newform 14.9.b.a.13.1

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			13.1
Root			$-8.52807i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.9.b.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.3137 q^{2} -126.458i q^{3} +128.000 q^{4} +143.012i q^{5} +1430.71i q^{6} +(-2350.56 - 489.571i) q^{7} -1448.15 q^{8} -9430.58 q^{9} +O(q^{10})$	\(q-11.3137 q^{2} -126.458i q^{3} +128.000 q^{4} +143.012i q^{5} +1430.71i q^{6} +(-2350.56 - 489.571i) q^{7} -1448.15 q^{8} -9430.58 q^{9} -1617.99i q^{10} -10789.2 q^{11} -16186.6i q^{12} +40619.1i q^{13} +(26593.5 + 5538.87i) q^{14} +18085.0 q^{15} +16384.0 q^{16} -49662.1i q^{17} +106695. q^{18} -225728. i q^{19} +18305.5i q^{20} +(-61910.1 + 297246. i) q^{21} +122065. q^{22} -291129. q^{23} +183130. i q^{24} +370173. q^{25} -459553. i q^{26} +362881. i q^{27} +(-300871. - 62665.1i) q^{28} -686649. q^{29} -204608. q^{30} -1.17948e6i q^{31} -185364. q^{32} +1.36437e6i q^{33} +561863. i q^{34} +(70014.5 - 336158. i) q^{35} -1.20711e6 q^{36} -116490. q^{37} +2.55382e6i q^{38} +5.13660e6 q^{39} -207103. i q^{40} -4.08019e6i q^{41} +(700433. - 3.36296e6i) q^{42} +646424. q^{43} -1.38101e6 q^{44} -1.34868e6i q^{45} +3.29375e6 q^{46} +7.85341e6i q^{47} -2.07188e6i q^{48} +(5.28544e6 + 2.30153e6i) q^{49} -4.18802e6 q^{50} -6.28017e6 q^{51} +5.19925e6i q^{52} -7.98083e6 q^{53} -4.10553e6i q^{54} -1.54298e6i q^{55} +(3.40397e6 + 708975. i) q^{56} -2.85450e7 q^{57} +7.76855e6 q^{58} -5.68993e6i q^{59} +2.31488e6 q^{60} -1.04246e7i q^{61} +1.33443e7i q^{62} +(2.21671e7 + 4.61694e6i) q^{63} +2.09715e6 q^{64} -5.80901e6 q^{65} -1.54361e7i q^{66} +3.25888e7 q^{67} -6.35676e6i q^{68} +3.68155e7i q^{69} +(-792124. + 3.80319e6i) q^{70} -1.34527e7 q^{71} +1.36569e7 q^{72} +3.32131e6i q^{73} +1.31793e6 q^{74} -4.68112e7i q^{75} -2.88932e7i q^{76} +(2.53606e7 + 5.28207e6i) q^{77} -5.81140e7 q^{78} +1.56854e7 q^{79} +2.34311e6i q^{80} -1.59849e7 q^{81} +4.61620e7i q^{82} -4.45273e7i q^{83} +(-7.92450e6 + 3.80475e7i) q^{84} +7.10228e6 q^{85} -7.31346e6 q^{86} +8.68322e7i q^{87} +1.56244e7 q^{88} +3.46802e7i q^{89} +1.52586e7i q^{90} +(1.98860e7 - 9.54776e7i) q^{91} -3.72645e7 q^{92} -1.49155e8 q^{93} -8.88511e7i q^{94} +3.22817e7 q^{95} +2.34407e7i q^{96} -1.47049e7i q^{97} +(-5.97979e7 - 2.60389e7i) q^{98} +1.01748e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	126.458i		−	1.56121i	−0.625026	−	0.780604i	$-0.714912\pi$
$3$		−	126.458i		−	1.56121i	0.625026	−	0.780604i	$-0.285088\pi$
$4$	128.000			0.500000
$5$			143.012i			0.228819i	0.993434	+	0.114409i	$0.0364976\pi$
$5$			143.012i			0.228819i	−0.993434	+	0.114409i	$0.963502\pi$
$6$			1430.71i			1.10394i
$7$	−2350.56	−	489.571i	−0.978991	−	0.203903i
$7$	−2350.56	−	489.571i	−0.978991	−	0.203903i
$8$	−1448.15			−0.353553
$9$	−9430.58			−1.43737
$10$		−	1617.99i		−	0.161799i
$11$	−10789.2			−0.736915			−0.368457	−	0.929645i	$-0.620114\pi$
$11$	−10789.2			−0.736915			−0.368457	+	0.929645i	$0.620114\pi$
$12$		−	16186.6i		−	0.780604i
$13$			40619.1i			1.42219i	0.703097	+	0.711094i	$0.251800\pi$
$13$			40619.1i			1.42219i	−0.703097	+	0.711094i	$0.748200\pi$
$14$	26593.5	+	5538.87i	0.692251	+	0.144181i
$15$	18085.0			0.357234
$16$	16384.0			0.250000
$17$		−	49662.1i		−	0.594607i	−0.954783	−	0.297303i	$-0.903913\pi$
$17$		−	49662.1i		−	0.594607i	0.954783	−	0.297303i	$-0.0960873\pi$
$18$	106695.			1.01637
$19$		−	225728.i		−	1.73209i	−0.499966	−	0.866045i	$-0.666654\pi$
$19$		−	225728.i		−	1.73209i	0.499966	−	0.866045i	$-0.333346\pi$
$20$			18305.5i			0.114409i
$21$	−61910.1	+	297246.i	−0.318335	+	1.52841i
$22$	122065.			0.521077
$23$	−291129.			−1.04034			−0.520168	−	0.854064i	$-0.674131\pi$
$23$	−291129.			−1.04034			−0.520168	+	0.854064i	$0.674131\pi$
$24$			183130.i			0.551970i
$25$	370173.			0.947642
$26$		−	459553.i		−	1.00564i
$27$			362881.i			0.682824i
$28$	−300871.	−	62665.1i	−0.489496	−	0.101952i
$29$	−686649.			−0.970830			−0.485415	−	0.874284i	$-0.661331\pi$
$29$	−686649.			−0.970830			−0.485415	+	0.874284i	$0.661331\pi$
$30$	−204608.			−0.252603
$31$		−	1.17948e6i		−	1.27716i	−0.769555	−	0.638580i	$-0.779522\pi$
$31$		−	1.17948e6i		−	1.27716i	0.769555	−	0.638580i	$-0.220478\pi$
$32$	−185364.			−0.176777
$33$			1.36437e6i			1.15048i
$34$			561863.i			0.420450i
$35$	70014.5	−	336158.i	0.0466569	−	0.224012i
$36$	−1.20711e6			−0.718685
$37$	−116490.			−0.0621558			−0.0310779	−	0.999517i	$-0.509894\pi$
$37$	−116490.			−0.0621558			−0.0310779	+	0.999517i	$0.509894\pi$
$38$			2.55382e6i			1.22477i
$39$	5.13660e6			2.22033
$40$		−	207103.i		−	0.0808997i
$41$		−	4.08019e6i		−	1.44392i	−0.691932	−	0.721962i	$-0.743240\pi$
$41$		−	4.08019e6i		−	1.44392i	0.691932	−	0.721962i	$-0.256760\pi$
$42$	700433.	−	3.36296e6i	0.225097	−	1.08075i
$43$	646424.			0.189079			0.0945396	−	0.995521i	$-0.469862\pi$
$43$	646424.			0.189079			0.0945396	+	0.995521i	$0.469862\pi$
$44$	−1.38101e6			−0.368457
$45$		−	1.34868e6i		−	0.328897i
$46$	3.29375e6			0.735629
$47$			7.85341e6i			1.60941i	0.593675	+	0.804705i	$0.297676\pi$
$47$			7.85341e6i			1.60941i	−0.593675	+	0.804705i	$0.702324\pi$
$48$		−	2.07188e6i		−	0.390302i
$49$	5.28544e6	+	2.30153e6i	0.916847	+	0.399239i
$50$	−4.18802e6			−0.670084
$51$	−6.28017e6			−0.928305
$52$			5.19925e6i			0.711094i
$53$	−7.98083e6			−1.01145			−0.505725	−	0.862695i	$-0.668775\pi$
$53$	−7.98083e6			−1.01145			−0.505725	+	0.862695i	$0.668775\pi$
$54$		−	4.10553e6i		−	0.482830i
$55$		−	1.54298e6i		−	0.168620i
$56$	3.40397e6	+	708975.i	0.346126	+	0.0720906i
$57$	−2.85450e7			−2.70415
$58$	7.76855e6			0.686480
$59$		−	5.68993e6i		−	0.469568i	−0.972048	−	0.234784i	$-0.924562\pi$
$59$		−	5.68993e6i		−	0.469568i	0.972048	−	0.234784i	$-0.0754384\pi$
$60$	2.31488e6			0.178617
$61$		−	1.04246e7i		−	0.752903i	−0.926436	−	0.376451i	$-0.877144\pi$
$61$		−	1.04246e7i		−	0.752903i	0.926436	−	0.376451i	$-0.122856\pi$
$62$			1.33443e7i			0.903089i
$63$	2.21671e7	+	4.61694e6i	1.40717	+	0.293084i
$64$	2.09715e6			0.125000
$65$	−5.80901e6			−0.325424
$66$		−	1.54361e7i		−	0.813510i
$67$	3.25888e7			1.61722			0.808610	−	0.588345i	$-0.200220\pi$
$67$	3.25888e7			1.61722			0.808610	+	0.588345i	$0.200220\pi$
$68$		−	6.35676e6i		−	0.297303i
$69$			3.68155e7i			1.62418i
$70$	−792124.	+	3.80319e6i	−0.0329914	+	0.158400i
$71$	−1.34527e7			−0.529389			−0.264695	−	0.964332i	$-0.585271\pi$
$71$	−1.34527e7			−0.529389			−0.264695	+	0.964332i	$0.585271\pi$
$72$	1.36569e7			0.508187
$73$			3.32131e6i			0.116955i	0.998289	+	0.0584773i	$0.0186245\pi$
$73$			3.32131e6i			0.116955i	−0.998289	+	0.0584773i	$0.981375\pi$
$74$	1.31793e6			0.0439508
$75$		−	4.68112e7i		−	1.47947i
$76$		−	2.88932e7i		−	0.866045i
$77$	2.53606e7	+	5.28207e6i	0.721433	+	0.150259i
$78$	−5.81140e7			−1.57001
$79$	1.56854e7			0.402705			0.201352	−	0.979519i	$-0.435466\pi$
$79$	1.56854e7			0.402705			0.201352	+	0.979519i	$0.435466\pi$
$80$			2.34311e6i			0.0572047i
$81$	−1.59849e7			−0.371339
$82$			4.61620e7i			1.02101i
$83$		−	4.45273e7i		−	0.938240i	−0.883134	−	0.469120i	$-0.844571\pi$
$83$		−	4.45273e7i		−	0.938240i	0.883134	−	0.469120i	$-0.155429\pi$
$84$	−7.92450e6	+	3.80475e7i	−0.159168	+	0.764204i
$85$	7.10228e6			0.136057
$86$	−7.31346e6			−0.133699
$87$			8.68322e7i			1.51567i
$88$	1.56244e7			0.260539
$89$			3.46802e7i			0.552742i	0.961051	+	0.276371i	$0.0891318\pi$
$89$			3.46802e7i			0.552742i	−0.961051	+	0.276371i	$0.910868\pi$
$90$			1.52586e7i			0.232566i
$91$	1.98860e7	−	9.54776e7i	0.289989	−	1.39231i
$92$	−3.72645e7			−0.520168
$93$	−1.49155e8			−1.99391
$94$		−	8.88511e7i		−	1.13802i
$95$	3.22817e7			0.396335
$96$			2.34407e7i			0.275985i
$97$		−	1.47049e7i		−	0.166103i	−0.996545	−	0.0830513i	$-0.973533\pi$
$97$		−	1.47049e7i		−	0.166103i	0.996545	−	0.0830513i	$-0.0264665\pi$
$98$	−5.97979e7	−	2.60389e7i	−0.648309	−	0.282304i
$99$	1.01748e8			1.05922
$100$	4.73821e7			0.473821
$101$		−	2.31942e7i		−	0.222892i	−0.993770	−	0.111446i	$-0.964452\pi$
$101$		−	2.31942e7i		−	0.222892i	0.993770	−	0.111446i	$-0.0355482\pi$
$102$	7.10520e7			0.656410
$103$			1.72248e8i			1.53040i	0.643790	+	0.765202i	$0.277361\pi$
$103$			1.72248e8i			1.53040i	−0.643790	+	0.765202i	$0.722639\pi$
$104$		−	5.88228e7i		−	0.502819i
$105$	−4.25098e7	−	8.85388e6i	−0.349729	−	0.0728411i
$106$	9.02928e7			0.715203
$107$	−7.14412e7			−0.545021			−0.272511	−	0.962153i	$-0.587854\pi$
$107$	−7.14412e7			−0.545021			−0.272511	+	0.962153i	$0.587854\pi$
$108$			4.64487e7i			0.341412i
$109$	5.22967e7			0.370483			0.185241	−	0.982693i	$-0.440693\pi$
$109$	5.22967e7			0.370483			0.185241	+	0.982693i	$0.440693\pi$
$110$			1.74568e7i			0.119232i
$111$			1.47311e7i			0.0970381i
$112$	−3.85115e7	−	8.02114e6i	−0.244748	−	0.0509758i
$113$	1.70334e8			1.04469			0.522345	−	0.852734i	$-0.325057\pi$
$113$	1.70334e8			1.04469			0.522345	+	0.852734i	$0.325057\pi$
$114$	3.22950e8			1.91212
$115$		−	4.16349e7i		−	0.238049i
$116$	−8.78911e7			−0.485415
$117$		−	3.83062e8i		−	2.04421i
$118$			6.43742e7i			0.332035i
$119$	−2.43132e7	+	1.16734e8i	−0.121242	+	0.582115i
$120$	−2.61898e7			−0.126301
$121$	−9.79528e7			−0.456957
$122$			1.17941e8i			0.532383i
$123$	−5.15971e8			−2.25427
$124$		−	1.50974e8i		−	0.638580i
$125$			1.08803e8i			0.445657i
$126$	−2.50792e8	−	5.22347e7i	−0.995021	−	0.207242i
$127$	1.98955e8			0.764785			0.382393	−	0.924000i	$-0.375100\pi$
$127$	1.98955e8			0.764785			0.382393	+	0.924000i	$0.375100\pi$
$128$	−2.37266e7			−0.0883883
$129$		−	8.17454e7i		−	0.295192i
$130$	6.57215e7			0.230109
$131$			2.28759e8i			0.776770i	0.921497	+	0.388385i	$0.126967\pi$
$131$			2.28759e8i			0.776770i	−0.921497	+	0.388385i	$0.873033\pi$
$132$			1.74640e8i			0.575238i
$133$	−1.10510e8	+	5.30586e8i	−0.353179	+	1.69570i
$134$	−3.68700e8			−1.14355
$135$	−5.18962e7			−0.156243
$136$			7.19185e7i			0.210225i
$137$	−1.36959e8			−0.388783			−0.194391	−	0.980924i	$-0.562273\pi$
$137$	−1.36959e8			−0.388783			−0.194391	+	0.980924i	$0.562273\pi$
$138$		−	4.16520e8i		−	1.14847i
$139$		−	1.70787e8i		−	0.457505i	−0.973485	−	0.228752i	$-0.926535\pi$
$139$		−	1.70787e8i		−	0.457505i	0.973485	−	0.228752i	$-0.0734646\pi$
$140$	8.96186e6	−	4.30282e7i	0.0233284	−	0.112006i
$141$	9.93125e8			2.51262
$142$	1.52200e8			0.374335
$143$		−	4.38246e8i		−	1.04803i
$144$	−1.54511e8			−0.359342
$145$		−	9.81990e7i		−	0.222144i
$146$		−	3.75763e7i		−	0.0826994i
$147$	2.91047e8	−	6.68385e8i	0.623294	−	1.43139i
$148$	−1.49107e7			−0.0310779
$149$	6.30533e8			1.27927			0.639636	−	0.768678i	$-0.279085\pi$
$149$	6.30533e8			1.27927			0.639636	+	0.768678i	$0.279085\pi$
$150$			5.29608e8i			1.04614i
$151$	−4.37887e8			−0.842276			−0.421138	−	0.906997i	$-0.638369\pi$
$151$	−4.37887e8			−0.842276			−0.421138	+	0.906997i	$0.638369\pi$
$152$			3.26889e8i			0.612386i
$153$			4.68343e8i			0.854669i
$154$	−2.86922e8	−	5.97598e7i	−0.510130	−	0.106249i
$155$	1.68680e8			0.292239
$156$	6.57485e8			1.11017
$157$		−	5.31144e8i		−	0.874205i	−0.899412	−	0.437103i	$-0.856005\pi$
$157$		−	5.31144e8i		−	0.874205i	0.899412	−	0.437103i	$-0.143995\pi$
$158$	−1.77460e8			−0.284755
$159$			1.00924e9i			1.57908i
$160$		−	2.65092e7i		−	0.0404499i
$161$	6.84315e8	+	1.42528e8i	1.01848	+	0.212128i
$162$	1.80849e8			0.262576
$163$	−1.39209e9			−1.97204			−0.986022	−	0.166616i	$-0.946716\pi$
$163$	−1.39209e9			−1.97204			−0.986022	+	0.166616i	$0.946716\pi$
$164$		−	5.22264e8i		−	0.721962i
$165$	−1.95122e8			−0.263251
$166$			5.03769e8i			0.663436i
$167$		−	1.39136e9i		−	1.78885i	−0.447214	−	0.894427i	$-0.647584\pi$
$167$		−	1.39136e9i		−	1.78885i	0.447214	−	0.894427i	$-0.352416\pi$
$168$	8.96554e7	−	4.30459e8i	0.112548	−	0.540374i
$169$	−8.34181e8			−1.02262
$170$	−8.03531e7			−0.0962070
$171$			2.12874e9i			2.48965i
$172$	8.27423e7			0.0945396
$173$		−	5.28638e8i		−	0.590165i	−0.955472	−	0.295083i	$-0.904653\pi$
$173$		−	5.28638e8i		−	0.590165i	0.955472	−	0.295083i	$-0.0953472\pi$
$174$		−	9.82394e8i		−	1.07174i
$175$	−8.70112e8	−	1.81226e8i	−0.927733	−	0.193227i
$176$	−1.76770e8			−0.184229
$177$	−7.19536e8			−0.733094
$178$		−	3.92362e8i		−	0.390847i
$179$	1.56548e9			1.52488			0.762440	−	0.647059i	$-0.224001\pi$
$179$	1.56548e9			1.52488			0.762440	+	0.647059i	$0.224001\pi$
$180$		−	1.72632e8i		−	0.164449i
$181$			5.62709e8i			0.524288i	0.965029	+	0.262144i	$0.0844295\pi$
$181$			5.62709e8i			0.524288i	−0.965029	+	0.262144i	$0.915570\pi$
$182$	−2.24984e8	+	1.08021e9i	−0.205053	+	0.984511i
$183$	−1.31827e9			−1.17544
$184$	4.21599e8			0.367814
$185$		−	1.66594e7i		−	0.0142224i
$186$	1.68750e9			1.40991
$187$			5.35813e8i			0.438174i
$188$			1.00524e9i			0.804705i
$189$	1.77656e8	−	8.52972e8i	0.139230	−	0.668479i
$190$	−3.65226e8			−0.280251
$191$	5.16655e8			0.388210			0.194105	−	0.980981i	$-0.437820\pi$
$191$	5.16655e8			0.388210			0.194105	+	0.980981i	$0.437820\pi$
$192$		−	2.65201e8i		−	0.195151i
$193$	1.67525e6			0.00120740			0.000603700	−	1.00000i	$-0.499808\pi$
$193$	1.67525e6			0.00120740			0.000603700		1.00000i	$0.499808\pi$
$194$			1.66367e8i			0.117452i
$195$			7.34595e8i			0.508054i
$196$	6.76536e8	+	2.94596e8i	0.458424	+	0.199619i
$197$	−2.80539e8			−0.186264			−0.0931320	−	0.995654i	$-0.529688\pi$
$197$	−2.80539e8			−0.186264			−0.0931320	+	0.995654i	$0.529688\pi$
$198$	−1.15115e9			−0.748980
$199$		−	1.08149e9i		−	0.689618i	−0.938673	−	0.344809i	$-0.887944\pi$
$199$		−	1.08149e9i		−	0.689618i	0.938673	−	0.344809i	$-0.112056\pi$
$200$	−5.36067e8			−0.335042
$201$		−	4.12111e9i		−	2.52482i
$202$			2.62413e8i			0.157608i
$203$	1.61401e9	+	3.36164e8i	0.950434	+	0.197955i
$204$	−8.03861e8			−0.464152
$205$	5.83515e8			0.330397
$206$		−	1.94877e9i		−	1.08216i
$207$	2.74551e9			1.49535
$208$			6.65503e8i			0.355547i
$209$			2.43541e9i			1.27640i
$210$	4.80943e8	+	1.00170e8i	0.247296	+	0.0515064i
$211$	2.42390e8			0.122289			0.0611443	−	0.998129i	$-0.480525\pi$
$211$	2.42390e8			0.122289			0.0611443	+	0.998129i	$0.480525\pi$
$212$	−1.02155e9			−0.505725
$213$			1.70120e9i			0.826487i
$214$	8.08265e8			0.385388
$215$			9.24464e7i			0.0432649i
$216$		−	5.25507e8i		−	0.241415i
$217$	−5.77442e8	+	2.77245e9i	−0.260417	+	1.25033i
$218$	−5.91669e8			−0.261971
$219$	4.20005e8			0.182590
$220$		−	1.97501e8i		−	0.0843100i
$221$	2.01723e9			0.845643
$222$		−	1.66663e8i		−	0.0686163i
$223$		−	1.50987e9i		−	0.610547i	−0.952265	−	0.305274i	$-0.901252\pi$
$223$		−	1.50987e9i		−	0.610547i	0.952265	−	0.305274i	$-0.0987479\pi$
$224$	4.35708e8	+	9.07488e7i	0.173063	+	0.0360453i
$225$	−3.49094e9			−1.36211
$226$	−1.92711e9			−0.738707
$227$		−	1.42867e9i		−	0.538059i	−0.963132	−	0.269029i	$-0.913297\pi$
$227$		−	1.42867e9i		−	0.538059i	0.963132	−	0.269029i	$-0.0867028\pi$
$228$	−3.65376e9			−1.35208
$229$			8.39434e8i			0.305242i	0.988285	+	0.152621i	$0.0487714\pi$
$229$			8.39434e8i			0.305242i	−0.988285	+	0.152621i	$0.951229\pi$
$230$			4.71045e8i			0.168326i
$231$	6.67959e8	−	3.20704e9i	0.234586	−	1.12631i
$232$	9.94375e8			0.343240
$233$	−3.28463e9			−1.11446			−0.557229	−	0.830359i	$-0.688135\pi$
$233$	−3.28463e9			−1.11446			−0.557229	+	0.830359i	$0.688135\pi$
$234$			4.33385e9i			1.44547i
$235$	−1.12313e9			−0.368263
$236$		−	7.28311e8i		−	0.234784i
$237$		−	1.98354e9i		−	0.628706i
$238$	2.75072e8	−	1.32069e9i	0.0857311	−	0.411617i
$239$	−5.17982e9			−1.58753			−0.793767	−	0.608222i	$-0.791883\pi$
$239$	−5.17982e9			−1.58753			−0.793767	+	0.608222i	$0.791883\pi$
$240$	2.96304e8			0.0893085
$241$		−	1.51987e8i		−	0.0450546i	−0.999746	−	0.0225273i	$-0.992829\pi$
$241$		−	1.51987e8i		−	0.0450546i	0.999746	−	0.0225273i	$-0.00717127\pi$
$242$	1.10821e9			0.323117
$243$			4.40228e9i			1.26256i
$244$		−	1.33435e9i		−	0.376451i
$245$	−3.29146e8	+	7.55881e8i	−0.0913534	+	0.209792i
$246$	5.83755e9			1.59401
$247$	9.16886e9			2.46336
$248$			1.70808e9i			0.451544i
$249$	−5.63082e9			−1.46479
$250$		−	1.23097e9i		−	0.315127i
$251$		−	3.45949e9i		−	0.871599i	−0.900044	−	0.435800i	$-0.856466\pi$
$251$		−	3.45949e9i		−	0.871599i	0.900044	−	0.435800i	$-0.143534\pi$
$252$	2.83739e9	+	5.90968e8i	0.703586	+	0.146542i
$253$	3.14104e9			0.766639
$254$	−2.25092e9			−0.540785
$255$		−	8.98138e8i		−	0.212414i
$256$	2.68435e8			0.0625000
$257$			7.64866e9i			1.75329i	0.481141	+	0.876643i	$0.340223\pi$
$257$			7.64866e9i			1.75329i	−0.481141	+	0.876643i	$0.659777\pi$
$258$			9.24844e8i			0.208732i
$259$	2.73816e8	+	5.70301e7i	0.0608500	+	0.0126738i
$260$	−7.43554e8			−0.162712
$261$	6.47550e9			1.39544
$262$		−	2.58811e9i		−	0.549260i
$263$	−1.63968e9			−0.342718			−0.171359	−	0.985209i	$-0.554816\pi$
$263$	−1.63968e9			−0.342718			−0.171359	+	0.985209i	$0.554816\pi$
$264$		−	1.97583e9i		−	0.406755i
$265$		−	1.14135e9i		−	0.231439i
$266$	1.25028e9	−	6.00290e9i	0.249735	−	1.19904i
$267$	4.38559e9			0.862944
$268$	4.17137e9			0.808610
$269$		−	3.97442e9i		−	0.759040i	−0.925184	−	0.379520i	$-0.876089\pi$
$269$		−	3.97442e9i		−	0.759040i	0.925184	−	0.379520i	$-0.123911\pi$
$270$	5.87139e8			0.110481
$271$		−	3.06586e9i		−	0.568427i	−0.958761	−	0.284213i	$-0.908268\pi$
$271$		−	3.06586e9i		−	0.568427i	0.958761	−	0.284213i	$-0.0917324\pi$
$272$		−	8.13665e8i		−	0.148652i
$273$	−1.20739e10	−	2.51473e9i	−2.17368	−	0.452732i
$274$	1.54951e9			0.274911
$275$	−3.99385e9			−0.698331
$276$			4.71238e9i			0.812090i
$277$	−7.26768e7			−0.0123446			−0.00617229	−	0.999981i	$-0.501965\pi$
$277$	−7.26768e7			−0.0123446			−0.00617229	+	0.999981i	$0.501965\pi$
$278$			1.93223e9i			0.323505i
$279$			1.11232e10i			1.83575i
$280$	−1.01392e8	+	4.86808e8i	−0.0164957	+	0.0792001i
$281$	3.00263e8			0.0481589			0.0240794	−	0.999710i	$-0.492335\pi$
$281$	3.00263e8			0.0481589			0.0240794	+	0.999710i	$0.492335\pi$
$282$	−1.12359e10			−1.77669
$283$		−	8.72850e8i		−	0.136080i	−0.997683	−	0.0680399i	$-0.978325\pi$
$283$		−	8.72850e8i		−	0.136080i	0.997683	−	0.0680399i	$-0.0216745\pi$
$284$	−1.72194e9			−0.264695
$285$		−	4.08228e9i		−	0.618761i
$286$			4.95819e9i			0.741070i
$287$	−1.99754e9	+	9.59071e9i	−0.294421	+	1.41359i
$288$	1.74809e9			0.254093
$289$	4.50943e9			0.646443
$290$			1.11100e9i			0.157080i
$291$	−1.85956e9			−0.259321
$292$			4.25127e8i			0.0584773i
$293$		−	5.29924e9i		−	0.719024i	−0.933140	−	0.359512i	$-0.882943\pi$
$293$		−	5.29924e9i		−	0.719024i	0.933140	−	0.359512i	$-0.117057\pi$
$294$	−3.29282e9	+	7.56192e9i	−0.440736	+	1.01214i
$295$	8.13728e8			0.107446
$296$	1.68695e8			0.0219754
$297$		−	3.91518e9i		−	0.503183i
$298$	−7.13367e9			−0.904582
$299$		−	1.18254e10i		−	1.47955i
$300$		−	5.99184e9i		−	0.739733i
$301$	−1.51946e9	−	3.16471e8i	−0.185107	−	0.0385539i
$302$	4.95413e9			0.595579
$303$	−2.93309e9			−0.347981
$304$		−	3.69832e9i		−	0.433023i
$305$	1.49084e9			0.172278
$306$		−	5.29869e9i		−	0.604343i
$307$		−	3.75856e9i		−	0.423125i	−0.977364	−	0.211562i	$-0.932145\pi$
$307$		−	3.75856e9i		−	0.423125i	0.977364	−	0.211562i	$-0.0678551\pi$
$308$	3.24615e9	+	6.76104e8i	0.360716	+	0.0751296i
$309$	2.17822e10			2.38928
$310$	−1.90840e9			−0.206644
$311$			1.28128e10i			1.36963i	0.728716	+	0.684816i	$0.240118\pi$
$311$			1.28128e10i			1.36963i	−0.728716	+	0.684816i	$0.759882\pi$
$312$	−7.43860e9			−0.785005
$313$			1.48364e9i			0.154579i	0.997009	+	0.0772895i	$0.0246266\pi$
$313$			1.48364e9i			0.154579i	−0.997009	+	0.0772895i	$0.975373\pi$
$314$			6.00921e9i			0.618157i
$315$	−6.60277e8	+	3.17016e9i	−0.0670632	+	0.321988i
$316$	2.00773e9			0.201352
$317$	5.48387e9			0.543063			0.271531	−	0.962430i	$-0.412470\pi$
$317$	5.48387e9			0.543063			0.271531	+	0.962430i	$0.412470\pi$
$318$		−	1.14182e10i		−	1.11658i
$319$	7.40837e9			0.715419
$320$			2.99918e8i			0.0286024i
$321$			9.03429e9i			0.850891i
$322$	−7.74214e9	−	1.61252e9i	−0.720174	−	0.149997i
$323$	−1.12101e10			−1.02991
$324$	−2.04607e9			−0.185670
$325$			1.50361e10i			1.34772i
$326$	1.57497e10			1.39445
$327$		−	6.61332e9i		−	0.578400i
$328$			5.90874e9i			0.510504i
$329$	3.84480e9	−	1.84599e10i	0.328164	−	1.57560i
$330$	2.20755e9			0.186146
$331$	−2.53902e9			−0.211521			−0.105761	−	0.994392i	$-0.533728\pi$
$331$	−2.53902e9			−0.211521			−0.105761	+	0.994392i	$0.533728\pi$
$332$		−	5.69949e9i		−	0.469120i
$333$	1.09857e9			0.0893408
$334$			1.57415e10i			1.26491i
$335$			4.66059e9i			0.370051i
$336$	−1.01434e9	+	4.87008e9i	−0.0795838	+	0.382102i
$337$	−8.83901e8			−0.0685305			−0.0342653	−	0.999413i	$-0.510909\pi$
$337$	−8.83901e8			−0.0685305			−0.0342653	+	0.999413i	$0.510909\pi$
$338$	9.43768e9			0.723100
$339$		−	2.15401e10i		−	1.63098i
$340$	9.09091e8			0.0680287
$341$			1.27257e10i			0.941158i
$342$		−	2.40840e10i		−	1.76045i
$343$	−1.12970e10	−	7.99748e9i	−0.816179	−	0.577799i
$344$	−9.36123e8			−0.0668496
$345$	−5.26505e9			−0.371643
$346$			5.98085e9i			0.417310i
$347$	1.38716e9			0.0956770			0.0478385	−	0.998855i	$-0.484767\pi$
$347$	1.38716e9			0.0956770			0.0478385	+	0.998855i	$0.484767\pi$
$348$			1.11145e10i			0.757833i
$349$		−	1.67059e10i		−	1.12608i	−0.826431	−	0.563038i	$-0.809633\pi$
$349$		−	1.67059e10i		−	1.12608i	0.826431	−	0.563038i	$-0.190367\pi$
$350$	9.84419e9	+	2.05034e9i	0.656006	+	0.136632i
$351$	−1.47399e10			−0.971104
$352$	1.99992e9			0.130269
$353$			1.37663e10i			0.886579i	0.896378	+	0.443290i	$0.146189\pi$
$353$			1.37663e10i			0.886579i	−0.896378	+	0.443290i	$0.853811\pi$
$354$	8.14062e9			0.518376
$355$		−	1.92389e9i		−	0.121134i
$356$			4.43907e9i			0.276371i
$357$	1.47619e10	+	3.07459e9i	0.908802	+	0.189284i
$358$	−1.77114e10			−1.07825
$359$	−2.36428e10			−1.42338			−0.711692	−	0.702492i	$-0.752071\pi$
$359$	−2.36428e10			−1.42338			−0.711692	+	0.702492i	$0.752071\pi$
$360$			1.95310e9i			0.116283i
$361$	−3.39694e10			−2.00014
$362$		−	6.36633e9i		−	0.370727i
$363$			1.23869e10i			0.713405i
$364$	2.54540e9	−	1.22211e10i	0.144994	−	0.696155i
$365$	−4.74986e8			−0.0267614
$366$	1.49145e10			0.831160
$367$			1.92044e10i			1.05861i	0.848431	+	0.529305i	$0.177547\pi$
$367$			1.92044e10i			1.05861i	−0.848431	+	0.529305i	$0.822453\pi$
$368$	−4.76985e9			−0.260084
$369$			3.84785e10i			2.07545i
$370$			1.88480e8i			0.0100568i
$371$	1.87594e10	+	3.90718e9i	0.990201	+	0.206238i
$372$	−1.90918e10			−0.996957
$373$	2.24040e10			1.15742			0.578709	−	0.815534i	$-0.303557\pi$
$373$	2.24040e10			1.15742			0.578709	+	0.815534i	$0.303557\pi$
$374$		−	6.06203e9i		−	0.309836i
$375$	1.37590e10			0.695764
$376$		−	1.13729e10i		−	0.569012i
$377$		−	2.78911e10i		−	1.38070i
$378$	−2.00995e9	+	9.65028e9i	−0.0984504	+	0.472686i
$379$	−3.19925e10			−1.55057			−0.775284	−	0.631613i	$-0.782393\pi$
$379$	−3.19925e10			−1.55057			−0.775284	+	0.631613i	$0.782393\pi$
$380$	4.13206e9			0.198168
$381$		−	2.51594e10i		−	1.19399i
$382$	−5.84528e9			−0.274506
$383$		−	2.94595e10i		−	1.36908i	−0.728974	−	0.684541i	$-0.760003\pi$
$383$		−	2.94595e10i		−	1.36908i	0.728974	−	0.684541i	$-0.239997\pi$
$384$			3.00041e9i			0.137993i
$385$	−7.55398e8	+	3.62686e9i	−0.0343821	+	0.165078i
$386$	−1.89533e7			−0.000853761
$387$	−6.09616e9			−0.271777
$388$		−	1.88223e9i		−	0.0830513i
$389$	2.00104e10			0.873892			0.436946	−	0.899488i	$-0.356060\pi$
$389$	2.00104e10			0.873892			0.436946	+	0.899488i	$0.356060\pi$
$390$		−	8.31100e9i		−	0.359248i
$391$			1.44581e10i			0.618591i
$392$	−7.65414e9	−	3.33297e9i	−0.324154	−	0.141152i
$393$	2.89283e10			1.21270
$394$	3.17394e9			0.131709
$395$			2.24320e9i			0.0921465i
$396$	1.30238e10			0.529609
$397$		−	2.67284e10i		−	1.07600i	−0.842946	−	0.537998i	$-0.819181\pi$
$397$		−	2.67284e10i		−	1.07600i	0.842946	−	0.537998i	$-0.180819\pi$
$398$			1.22356e10i			0.487634i
$399$	6.70968e10	+	1.39748e10i	2.64734	+	0.551385i
$400$	6.06491e9			0.236910
$401$	−3.64452e10			−1.40949			−0.704747	−	0.709459i	$-0.748939\pi$
$401$	−3.64452e10			−1.40949			−0.704747	+	0.709459i	$0.748939\pi$
$402$			4.66250e10i			1.78531i
$403$	4.79096e10			1.81636
$404$		−	2.96886e9i		−	0.111446i
$405$		−	2.28603e9i		−	0.0849694i
$406$	−1.82604e10	−	3.80326e9i	−0.672058	−	0.139975i
$407$	1.25683e9			0.0458035
$408$	9.09465e9			0.328205
$409$		−	2.68492e10i		−	0.959484i	−0.877410	−	0.479742i	$-0.840730\pi$
$409$		−	2.68492e10i		−	0.959484i	0.877410	−	0.479742i	$-0.159270\pi$
$410$	−6.60172e9			−0.233626
$411$			1.73195e10i			0.606970i
$412$			2.20478e10i			0.765202i
$413$	−2.78563e9	+	1.33745e10i	−0.0957465	+	0.459703i
$414$	−3.10619e10			−1.05737
$415$	6.36793e9			0.214687
$416$		−	7.52931e9i		−	0.251410i
$417$	−2.15973e10			−0.714260
$418$		−	2.75536e10i		−	0.902553i
$419$			3.81047e10i			1.23630i	0.786062	+	0.618148i	$0.212117\pi$
$419$			3.81047e10i			1.23630i	−0.786062	+	0.618148i	$0.787883\pi$
$420$	−5.44125e9	−	1.13330e9i	−0.174864	−	0.0364206i
$421$	−1.86146e10			−0.592551			−0.296275	−	0.955103i	$-0.595745\pi$
$421$	−1.86146e10			−0.592551			−0.296275	+	0.955103i	$0.595745\pi$
$422$	−2.74234e9			−0.0864710
$423$		−	7.40622e10i		−	2.31332i
$424$	1.15575e10			0.357602
$425$		−	1.83836e10i		−	0.563474i
$426$		−	1.92468e10i		−	0.584414i
$427$	−5.10357e9	+	2.45036e10i	−0.153519	+	0.737085i
$428$	−9.14447e9			−0.272511
$429$	−5.54197e10			−1.63619
$430$		−	1.04591e9i		−	0.0305929i
$431$	−2.81734e10			−0.816452			−0.408226	−	0.912881i	$-0.633853\pi$
$431$	−2.81734e10			−0.816452			−0.408226	+	0.912881i	$0.633853\pi$
$432$			5.94544e9i			0.170706i
$433$			4.31257e10i			1.22683i	0.789760	+	0.613416i	$0.210205\pi$
$433$			4.31257e10i			1.22683i	−0.789760	+	0.613416i	$0.789795\pi$
$434$	6.53301e9	−	3.13667e10i	0.184143	−	0.884116i
$435$	−1.24180e10			−0.346813
$436$	6.69397e9			0.185241
$437$			6.57158e10i			1.80196i
$438$	−4.75181e9			−0.129111
$439$			5.77103e9i			0.155380i	0.996978	+	0.0776900i	$0.0247545\pi$
$439$			5.77103e9i			0.155380i	−0.996978	+	0.0776900i	$0.975246\pi$
$440$			2.23447e9i			0.0596162i
$441$	−4.98448e10	−	2.17048e10i	−1.31785	−	0.573853i
$442$	−2.28224e10			−0.597960
$443$	9.16875e9			0.238065			0.119032	−	0.992890i	$-0.462021\pi$
$443$	9.16875e9			0.238065			0.119032	+	0.992890i	$0.462021\pi$
$444$			1.88558e9i			0.0485190i
$445$	−4.95969e9			−0.126478
$446$			1.70822e10i			0.431722i
$447$		−	7.97358e10i		−	1.99721i
$448$	−4.92948e9	−	1.02671e9i	−0.122374	−	0.0254879i
$449$	5.75612e10			1.41627			0.708133	−	0.706079i	$-0.249538\pi$
$449$	5.75612e10			1.41627			0.708133	+	0.706079i	$0.249538\pi$
$450$	3.94955e10			0.963158
$451$			4.40218e10i			1.06405i
$452$	2.18027e10			0.522345
$453$			5.53742e10i			1.31497i
$454$			1.61636e10i			0.380465i
$455$	1.36544e10	+	2.84393e9i	0.318587	+	0.0663549i
$456$	4.13376e10			0.956062
$457$	2.88888e10			0.662315			0.331157	−	0.943576i	$-0.392561\pi$
$457$	2.88888e10			0.662315			0.331157	+	0.943576i	$0.392561\pi$
$458$		−	9.49712e9i		−	0.215839i
$459$	1.80214e10			0.406012
$460$		−	5.32926e9i		−	0.119024i
$461$		−	5.22913e10i		−	1.15778i	−0.815406	−	0.578889i	$-0.803486\pi$
$461$		−	5.22913e10i		−	1.15778i	0.815406	−	0.578889i	$-0.196514\pi$
$462$	−7.55709e9	+	3.62835e10i	−0.165877	+	0.796419i
$463$	1.72267e10			0.374869			0.187434	−	0.982277i	$-0.439983\pi$
$463$	1.72267e10			0.374869			0.187434	+	0.982277i	$0.439983\pi$
$464$	−1.12501e10			−0.242707
$465$		−	2.13309e10i		−	0.456245i
$466$	3.71614e10			0.788040
$467$			1.99045e10i			0.418488i	0.977863	+	0.209244i	$0.0671003\pi$
$467$			1.99045e10i			0.418488i	−0.977863	+	0.209244i	$0.932900\pi$
$468$		−	4.90319e10i		−	1.02210i
$469$	−7.66019e10	−	1.59545e10i	−1.58324	−	0.329756i
$470$	1.27068e10			0.260402
$471$	−6.71673e10			−1.36482
$472$			8.23990e9i			0.166018i
$473$	−6.97438e9			−0.139335
$474$			2.24412e10i			0.444562i
$475$		−	8.35582e10i		−	1.64140i
$476$	−3.11209e9	+	1.49419e10i	−0.0606211	+	0.291057i
$477$	7.52638e10			1.45383
$478$	5.86030e10			1.12256
$479$		−	5.05001e8i		−	0.00959290i	−0.999988	−	0.00479645i	$-0.998473\pi$
$479$		−	5.05001e8i		−	0.00959290i	0.999988	−	0.00479645i	$-0.00152676\pi$
$480$	−3.35230e9			−0.0631506
$481$		−	4.73172e9i		−	0.0883972i
$482$			1.71954e9i			0.0318584i
$483$	1.80238e10	−	8.65370e10i	0.331175	−	1.59006i
$484$	−1.25380e10			−0.228479
$485$	2.10298e9			0.0380074
$486$		−	4.98061e10i		−	0.892766i
$487$	3.73430e10			0.663886			0.331943	−	0.943299i	$-0.392296\pi$
$487$	3.73430e10			0.663886			0.331943	+	0.943299i	$0.392296\pi$
$488$			1.50964e10i			0.266191i
$489$			1.76041e11i			3.07877i
$490$	3.72386e9	−	8.55181e9i	0.0645966	−	0.148345i
$491$	7.30831e9			0.125745			0.0628726	−	0.998022i	$-0.479974\pi$
$491$	7.30831e9			0.125745			0.0628726	+	0.998022i	$0.479974\pi$
$492$	−6.60443e10			−1.12713
$493$			3.41005e10i			0.577262i
$494$	−1.03734e11			−1.74186
$495$			1.45512e10i			0.242369i
$496$		−	1.93247e10i		−	0.319290i
$497$	3.16213e10	+	6.58604e9i	0.518267	+	0.107944i
$498$	6.37055e10			1.03576
$499$	9.61811e10			1.55127			0.775635	−	0.631181i	$-0.217430\pi$
$499$	9.61811e10			1.55127			0.775635	+	0.631181i	$0.217430\pi$
$500$			1.39268e10i			0.222829i
$501$	−1.75949e11			−2.79277
$502$			3.91396e10i			0.616314i
$503$			5.20858e10i			0.813669i	0.913502	+	0.406834i	$0.133367\pi$
$503$			5.20858e10i			0.813669i	−0.913502	+	0.406834i	$0.866633\pi$
$504$	−3.21014e10	−	6.68605e9i	−0.497510	−	0.103621i
$505$	3.31705e9			0.0510019
$506$	−3.55368e10			−0.542096
$507$			1.05489e11i			1.59652i
$508$	2.54662e10			0.382393
$509$		−	1.19801e11i		−	1.78480i	−0.451241	−	0.892402i	$-0.649018\pi$
$509$		−	1.19801e11i		−	1.78480i	0.451241	−	0.892402i	$-0.350982\pi$
$510$			1.01613e10i			0.150199i
$511$	1.62602e9	−	7.80692e9i	0.0238474	−	0.114498i
$512$	−3.03700e9			−0.0441942
$513$	8.19122e10			1.18271
$514$		−	8.65347e10i		−	1.23976i
$515$	−2.46336e10			−0.350186
$516$		−	1.04634e10i		−	0.147596i
$517$		−	8.47317e10i		−	1.18600i
$518$	−3.09788e9	−	6.45222e8i	−0.0430274	−	0.00896170i
$519$	−6.68504e10			−0.921371
$520$	8.41235e9			0.115055
$521$		−	1.22726e11i		−	1.66565i	−0.553535	−	0.832826i	$-0.686722\pi$
$521$		−	1.22726e11i		−	1.66565i	0.553535	−	0.832826i	$-0.313278\pi$
$522$	−7.32619e10			−0.986726
$523$			1.22825e9i			0.0164165i	0.999966	+	0.00820827i	$0.00261280\pi$
$523$			1.22825e9i			0.0164165i	−0.999966	+	0.00820827i	$0.997387\pi$
$524$			2.92811e10i			0.388385i
$525$	−2.29174e10	+	1.10032e11i	−0.301668	+	1.44838i
$526$	1.85509e10			0.242338
$527$	−5.85757e10			−0.759408
$528$			2.23539e10i			0.287619i
$529$	6.44495e9			0.0822994
$530$			1.29129e10i			0.163652i
$531$			5.36593e10i			0.674943i
$532$	−1.41453e10	+	6.79150e10i	−0.176589	+	0.847850i
$533$	1.65734e11			2.05353
$534$	−4.96173e10			−0.610194
$535$		−	1.02169e10i		−	0.124711i
$536$	−4.71936e10			−0.571774
$537$		−	1.97967e11i		−	2.38065i
$538$			4.49654e10i			0.536722i
$539$	−5.70255e10	−	2.48316e10i	−0.675638	−	0.294205i
$540$	−6.64272e9			−0.0781216
$541$	9.53630e10			1.11324			0.556622	−	0.830766i	$-0.312097\pi$
$541$	9.53630e10			1.11324			0.556622	+	0.830766i	$0.312097\pi$
$542$			3.46862e10i			0.401938i
$543$	7.11590e10			0.818522
$544$			9.20556e9i			0.105113i
$545$			7.47904e9i			0.0847735i
$546$	1.36600e11	+	2.84510e10i	1.53703	+	0.320130i
$547$	−1.37958e11			−1.54098			−0.770492	−	0.637450i	$-0.779989\pi$
$547$	−1.37958e11			−1.54098			−0.770492	+	0.637450i	$0.779989\pi$
$548$	−1.75307e10			−0.194391
$549$			9.83097e10i			1.08220i
$550$	4.51853e10			0.493795
$551$			1.54996e11i			1.68156i
$552$		−	5.33145e10i		−	0.574235i
$553$	−3.68694e10	−	7.67912e9i	−0.394245	−	0.0821128i
$554$	8.22244e8			0.00872894
$555$	−2.10672e9			−0.0222042
$556$		−	2.18607e10i		−	0.228752i
$557$	−3.15909e10			−0.328202			−0.164101	−	0.986444i	$-0.552472\pi$
$557$	−3.15909e10			−0.328202			−0.164101	+	0.986444i	$0.552472\pi$
$558$		−	1.25845e11i		−	1.29807i
$559$			2.62572e10i			0.268906i
$560$	1.14712e9	−	5.50761e9i	0.0116642	−	0.0560029i
$561$	6.77578e10			0.684081
$562$	−3.39708e9			−0.0340535
$563$		−	8.09863e10i		−	0.806080i	−0.915182	−	0.403040i	$-0.867954\pi$
$563$		−	8.09863e10i		−	0.806080i	0.915182	−	0.403040i	$-0.132046\pi$
$564$	1.27120e11			1.25631
$565$			2.43598e10i			0.239045i
$566$			9.87517e9i			0.0962230i
$567$	3.75735e10	+	7.82576e9i	0.363538	+	0.0757172i
$568$	1.94816e10			0.187167
$569$	1.21889e11			1.16283			0.581415	−	0.813607i	$-0.302499\pi$
$569$	1.21889e11			1.16283			0.581415	+	0.813607i	$0.302499\pi$
$570$			4.61857e10i			0.437530i
$571$	3.93072e10			0.369767			0.184883	−	0.982760i	$-0.440809\pi$
$571$	3.93072e10			0.369767			0.184883	+	0.982760i	$0.440809\pi$
$572$		−	5.60955e10i		−	0.524015i
$573$		−	6.53351e10i		−	0.606077i
$574$	2.25996e10	−	1.08507e11i	0.208187	−	0.999559i
$575$	−1.07768e11			−0.985866
$576$	−1.97774e10			−0.179671
$577$		−	6.82213e10i		−	0.615484i	−0.951470	−	0.307742i	$-0.900427\pi$
$577$		−	6.82213e10i		−	0.615484i	0.951470	−	0.307742i	$-0.0995734\pi$
$578$	−5.10184e10			−0.457104
$579$		−	2.11849e8i		−	0.00188500i
$580$		−	1.25695e10i		−	0.111072i
$581$	−2.17993e10	+	1.04664e11i	−0.191310	+	0.918529i
$582$	2.10385e10			0.183367
$583$	8.61065e10			0.745352
$584$		−	4.80976e9i		−	0.0413497i
$585$	5.47824e10			0.467754
$586$			5.99541e10i			0.508427i
$587$		−	1.89401e11i		−	1.59525i	−0.603152	−	0.797626i	$-0.706089\pi$
$587$		−	1.89401e11i		−	1.59525i	0.603152	−	0.797626i	$-0.293911\pi$
$588$	3.72540e10	−	8.55533e10i	0.311647	−	0.715694i
$589$	−2.66242e11			−2.21216
$590$	−9.20628e9			−0.0759759
$591$			3.54764e10i			0.290797i
$592$	−1.90857e9			−0.0155389
$593$			2.23276e11i			1.80561i	0.430055	+	0.902803i	$0.358494\pi$
$593$			2.23276e11i			1.80561i	−0.430055	+	0.902803i	$0.641506\pi$
$594$			4.42952e10i			0.355804i
$595$	−1.66943e10	−	3.47707e9i	−0.133199	−	0.0277425i
$596$	8.07082e10			0.639636
$597$	−1.36762e11			−1.07664
$598$			1.33789e11i			1.04620i
$599$	6.72450e10			0.522339			0.261170	−	0.965293i	$-0.415892\pi$
$599$	6.72450e10			0.522339			0.261170	+	0.965293i	$0.415892\pi$
$600$			6.77899e10i			0.523070i
$601$			1.74729e11i			1.33927i	0.742692	+	0.669633i	$0.233548\pi$
$601$			1.74729e11i			1.33927i	−0.742692	+	0.669633i	$0.766452\pi$
$602$	1.71907e10	+	3.58046e9i	0.130890	+	0.0272617i
$603$	−3.07331e11			−2.32454
$604$	−5.60495e10			−0.421138
$605$		−	1.40084e10i		−	0.104560i
$606$	3.31841e10			0.246059
$607$			1.40790e11i			1.03709i	0.855050	+	0.518545i	$0.173526\pi$
$607$			1.40790e11i			1.03709i	−0.855050	+	0.518545i	$0.826474\pi$
$608$			4.18418e10i			0.306193i
$609$	4.25105e10	−	2.04104e11i	0.309049	−	1.48382i
$610$	−1.68669e10			−0.121819
$611$	−3.18998e11			−2.28888
$612$			5.99479e10i			0.427335i
$613$	7.54986e9			0.0534684			0.0267342	−	0.999643i	$-0.491489\pi$
$613$	7.54986e9			0.0534684			0.0267342	+	0.999643i	$0.491489\pi$
$614$			4.25233e10i			0.299194i
$615$		−	7.37900e10i		−	0.515819i
$616$	−3.67260e10	−	7.64925e9i	−0.255065	−	0.0531246i
$617$	2.51744e11			1.73708			0.868538	−	0.495623i	$-0.165060\pi$
$617$	2.51744e11			1.73708			0.868538	+	0.495623i	$0.165060\pi$
$618$	−2.46437e11			−1.68948
$619$		−	1.71138e11i		−	1.16569i	−0.812582	−	0.582847i	$-0.801939\pi$
$619$		−	1.71138e11i		−	1.16569i	0.812582	−	0.582847i	$-0.198061\pi$
$620$	2.15911e10			0.146119
$621$		−	1.05645e11i		−	0.710367i
$622$		−	1.44961e11i		−	0.968476i
$623$	1.69785e10	−	8.15179e10i	0.112706	−	0.541129i
$624$	8.41581e10			0.555083
$625$	1.29039e11			0.845667
$626$		−	1.67854e10i		−	0.109304i
$627$	3.07977e11			1.99273
$628$		−	6.79864e10i		−	0.437103i
$629$			5.78514e9i			0.0369582i
$630$	7.47019e9	−	3.58663e10i	0.0474208	−	0.227680i
$631$	−1.69838e11			−1.07131			−0.535657	−	0.844436i	$-0.679936\pi$
$631$	−1.69838e11			−1.07131			−0.535657	+	0.844436i	$0.679936\pi$
$632$	−2.27149e10			−0.142378
$633$		−	3.06522e10i		−	0.190918i
$634$	−6.20429e10			−0.384003
$635$			2.84529e10i			0.174997i
$636$			1.29182e11i			0.789542i
$637$	−9.34861e10	+	2.14690e11i	−0.567792	+	1.30393i
$638$	−8.38162e10			−0.505877
$639$	1.26867e11			0.760928
$640$		−	3.39318e9i		−	0.0202249i
$641$	2.76886e11			1.64010			0.820048	−	0.572295i	$-0.193947\pi$
$641$	2.76886e11			1.64010			0.820048	+	0.572295i	$0.193947\pi$
$642$		−	1.02211e11i		−	0.601671i
$643$		−	6.05874e10i		−	0.354436i	−0.984172	−	0.177218i	$-0.943290\pi$
$643$		−	6.05874e10i		−	0.354436i	0.984172	−	0.177218i	$-0.0567098\pi$
$644$	8.75923e10	+	1.82436e10i	0.509240	+	0.106064i
$645$	1.16906e10			0.0675455
$646$	1.26828e11			0.728258
$647$			2.20967e11i			1.26099i	0.776194	+	0.630494i	$0.217148\pi$
$647$			2.20967e11i			1.26099i	−0.776194	+	0.630494i	$0.782852\pi$
$648$	2.31486e10			0.131288
$649$			6.13896e10i			0.346032i
$650$		−	1.70114e11i		−	0.952985i
$651$	3.50598e11	+	7.30220e10i	1.95202	+	0.406565i
$652$	−1.78187e11			−0.986022
$653$	3.84633e10			0.211541			0.105770	−	0.994391i	$-0.466269\pi$
$653$	3.84633e10			0.211541			0.105770	+	0.994391i	$0.466269\pi$
$654$			7.48212e10i			0.408991i
$655$	−3.27152e10			−0.177740
$656$		−	6.68498e10i		−	0.360981i
$657$		−	3.13218e10i		−	0.168107i
$658$	−4.34990e10	+	2.08850e11i	−0.232047	+	1.11412i
$659$	2.57573e11			1.36571			0.682856	−	0.730553i	$-0.260738\pi$
$659$	2.57573e11			1.36571			0.682856	+	0.730553i	$0.260738\pi$
$660$	−2.49756e10			−0.131625
$661$		−	2.65141e10i		−	0.138890i	−0.997586	−	0.0694449i	$-0.977877\pi$
$661$		−	2.65141e10i		−	0.138890i	0.997586	−	0.0694449i	$-0.0221228\pi$
$662$	2.87257e10			0.149568
$663$		−	2.55095e11i		−	1.32022i
$664$			6.44824e10i			0.331718i
$665$	−7.58801e10	−	1.58042e10i	−0.388009	−	0.0808140i
$666$	−1.24289e10			−0.0631735
$667$	1.99903e11			1.00999
$668$		−	1.78095e11i		−	0.894427i
$669$	−1.90934e11			−0.953191
$670$		−	5.27285e10i		−	0.261665i
$671$			1.12472e11i			0.554825i
$672$	1.14759e10	−	5.50987e10i	0.0562742	−	0.270187i
$673$	−3.00891e11			−1.46673			−0.733363	−	0.679837i	$-0.762050\pi$
$673$	−3.00891e11			−1.46673			−0.733363	+	0.679837i	$0.762050\pi$
$674$	1.00002e10			0.0484584
$675$			1.34329e11i			0.647073i
$676$	−1.06775e11			−0.511309
$677$		−	2.60587e11i		−	1.24050i	−0.784403	−	0.620252i	$-0.787030\pi$
$677$		−	2.60587e11i		−	1.24050i	0.784403	−	0.620252i	$-0.212970\pi$
$678$			2.43698e11i			1.15328i
$679$	−7.19912e9	+	3.45648e10i	−0.0338688	+	0.162613i
$680$	−1.02852e10			−0.0481035
$681$	−1.80667e11			−0.840021
$682$		−	1.43974e11i		−	0.665499i
$683$	−2.85098e11			−1.31012			−0.655061	−	0.755576i	$-0.727357\pi$
$683$	−2.85098e11			−1.31012			−0.655061	+	0.755576i	$0.727357\pi$
$684$			2.72479e11i			1.24483i
$685$		−	1.95867e10i		−	0.0889608i
$686$	1.27811e11	+	9.04812e10i	0.577126	+	0.408566i
$687$	1.06153e11			0.476547
$688$	1.05910e10			0.0472698
$689$		−	3.24174e11i		−	1.43847i
$690$	5.95673e10			0.262792
$691$		−	2.05251e11i		−	0.900269i	−0.892961	−	0.450135i	$-0.851376\pi$
$691$		−	2.05251e11i		−	0.900269i	0.892961	−	0.450135i	$-0.148624\pi$
$692$		−	6.76656e10i		−	0.295083i
$693$	−2.39165e11	−	4.98129e10i	−1.03697	−	0.215978i
$694$	−1.56939e10			−0.0676539
$695$	2.44246e10			0.104686
$696$		−	1.25746e11i		−	0.535869i
$697$	−2.02631e11			−0.858567
$698$			1.89005e11i			0.796256i
$699$			4.15368e11i			1.73990i
$700$	−1.11374e11	−	2.31969e10i	−0.463866	−	0.0966136i
$701$	4.37725e10			0.181271			0.0906356	−	0.995884i	$-0.471110\pi$
$701$	4.37725e10			0.181271			0.0906356	+	0.995884i	$0.471110\pi$
$702$	1.66763e11			0.686674
$703$			2.62950e10i			0.107659i
$704$	−2.26265e10			−0.0921143
$705$			1.42029e11i			0.574936i
$706$		−	1.55748e11i		−	0.626906i
$707$	−1.13552e10	+	5.45194e10i	−0.0454484	+	0.218209i
$708$	−9.21006e10			−0.366547
$709$	−6.28400e10			−0.248686			−0.124343	−	0.992239i	$-0.539682\pi$
$709$	−6.28400e10			−0.248686			−0.124343	+	0.992239i	$0.539682\pi$
$710$			2.17664e10i			0.0856549i
$711$	−1.47922e11			−0.578836
$712$		−	5.02224e10i		−	0.195424i
$713$			3.43382e11i			1.32868i
$714$	−1.67012e11	−	3.47850e10i	−0.642620	−	0.133844i
$715$	6.26744e10			0.239809
$716$	2.00382e11			0.762440
$717$			6.55029e11i			2.47847i
$718$	2.67488e11			1.00648
$719$		−	3.21811e11i		−	1.20416i	−0.798434	−	0.602082i	$-0.794338\pi$
$719$		−	3.21811e11i		−	1.20416i	0.798434	−	0.602082i	$-0.205662\pi$
$720$		−	2.20969e10i		−	0.0822243i
$721$	8.43279e10	−	4.04880e11i	0.312054	−	1.49825i
$722$	3.84320e11			1.41431
$723$	−1.92200e10			−0.0703396
$724$			7.20268e10i			0.262144i
$725$	−2.54179e11			−0.919999
$726$		−	1.40142e11i		−	0.504453i
$727$		−	1.50767e10i		−	0.0539720i	−0.999636	−	0.0269860i	$-0.991409\pi$
$727$		−	1.50767e10i		−	0.0539720i	0.999636	−	0.0269860i	$-0.00859096\pi$
$728$	−2.87979e10	+	1.38266e11i	−0.102526	+	0.492256i
$729$	4.51826e11			1.59978
$730$	5.37385e9			0.0189232
$731$		−	3.21028e10i		−	0.112428i
$732$	−1.68738e11			−0.587719
$733$			3.80728e11i			1.31886i	0.751766	+	0.659430i	$0.229202\pi$
$733$			3.80728e11i			1.31886i	−0.751766	+	0.659430i	$0.770798\pi$
$734$		−	2.17273e11i		−	0.748551i
$735$	9.55870e10	+	4.16231e10i	0.327529	+	0.142622i
$736$	5.39647e10			0.183907
$737$	−3.51606e11			−1.19175
$738$		−	4.35335e11i		−	1.46757i
$739$	1.87656e11			0.629194			0.314597	−	0.949225i	$-0.398131\pi$
$739$	1.87656e11			0.629194			0.314597	+	0.949225i	$0.398131\pi$
$740$		−	2.13241e9i		−	0.00711121i
$741$		−	1.15947e12i		−	3.84581i
$742$	−2.12238e11	−	4.42048e10i	−0.700178	−	0.145832i
$743$	−3.02086e11			−0.991233			−0.495616	−	0.868542i	$-0.665058\pi$
$743$	−3.02086e11			−0.991233			−0.495616	+	0.868542i	$0.665058\pi$
$744$	2.16000e11			0.704955
$745$			9.01737e10i			0.292722i
$746$	−2.53472e11			−0.818418
$747$			4.19918e11i			1.34860i
$748$			6.85841e10i			0.219087i
$749$	1.67927e11	+	3.49755e10i	0.533571	+	0.111132i
$750$	−1.55665e11			−0.491979
$751$	4.59708e11			1.44518			0.722591	−	0.691275i	$-0.242951\pi$
$751$	4.59708e11			1.44518			0.722591	+	0.691275i	$0.242951\pi$
$752$			1.28670e11i			0.402352i
$753$	−4.37479e11			−1.36075
$754$			3.15552e11i			0.976304i
$755$		−	6.26230e10i		−	0.192729i
$756$	2.27400e10	−	1.09180e11i	0.0696150	−	0.334239i
$757$	4.87501e11			1.48454			0.742270	−	0.670101i	$-0.233749\pi$
$757$	4.87501e11			1.48454			0.742270	+	0.670101i	$0.233749\pi$
$758$	3.61953e11			1.09642
$759$		−	3.97209e11i		−	1.19688i
$760$	−4.67490e10			−0.140126
$761$			3.71594e11i			1.10798i	0.832525	+	0.553988i	$0.186895\pi$
$761$			3.71594e11i			1.10798i	−0.832525	+	0.553988i	$0.813105\pi$
$762$			2.84646e11i			0.844277i
$763$	−1.22926e11	−	2.56029e10i	−0.362699	−	0.0755426i
$764$	6.61318e10			0.194105
$765$	−6.69786e10			−0.195565
$766$			3.33296e11i			0.968088i
$767$	2.31120e11			0.667815
$768$		−	3.39458e10i		−	0.0975755i
$769$			2.03480e11i			0.581856i	0.956745	+	0.290928i	$0.0939641\pi$
$769$			2.03480e11i			0.581856i	−0.956745	+	0.290928i	$0.906036\pi$
$770$	8.54635e9	−	4.10332e10i	0.0243118	−	0.116727i
$771$	9.67233e11			2.73724
$772$	2.14432e8			0.000603700
$773$			4.31921e11i			1.20972i	0.796331	+	0.604861i	$0.206772\pi$
$773$			4.31921e11i			1.20972i	−0.796331	+	0.604861i	$0.793228\pi$
$774$	6.89701e10			0.192175
$775$		−	4.36613e11i		−	1.21029i
$776$			2.12950e10i			0.0587261i
$777$	7.21191e9	−	3.46262e10i	0.0197864	−	0.0949994i
$778$	−2.26392e11			−0.617935
$779$	−9.21011e11			−2.50101
$780$			9.40282e10i			0.254027i
$781$	1.45143e11			0.390115
$782$		−	1.63574e11i		−	0.437410i
$783$		−	2.49172e11i		−	0.662906i
$784$	8.65967e10	+	3.77083e10i	0.229212	+	0.0998097i
$785$	7.59599e10			0.200035
$786$	−3.27287e11			−0.857508
$787$		−	4.11125e11i		−	1.07170i	−0.844312	−	0.535852i	$-0.819991\pi$
$787$		−	4.11125e11i		−	1.07170i	0.844312	−	0.535852i	$-0.180009\pi$
$788$	−3.59091e10			−0.0931320
$789$			2.07351e11i			0.535054i
$790$		−	2.53789e10i		−	0.0651574i
$791$	−4.00380e11	−	8.33906e10i	−1.02274	−	0.213015i
$792$	−1.47347e11			−0.374490
$793$	4.23437e11			1.07077
$794$			3.02397e11i			0.760845i
$795$	−1.44333e11			−0.361324
$796$		−	1.38430e11i		−	0.344809i
$797$			4.63797e10i			0.114946i	0.998347	+	0.0574731i	$0.0183044\pi$
$797$			4.63797e10i			0.114946i	−0.998347	+	0.0574731i	$0.981696\pi$
$798$	−7.59113e11	−	1.58107e11i	−1.87195	−	0.389888i
$799$	3.90017e11			0.956966
$800$	−6.86166e10			−0.167521
$801$		−	3.27055e11i		−	0.794494i
$802$	4.12331e11			0.996663
$803$		−	3.58341e10i		−	0.0861856i
$804$		−	5.27502e11i		−	1.26241i
$805$	−2.03832e10	+	9.78651e10i	−0.0485389	+	0.233048i
$806$	−5.42035e11			−1.28436
$807$	−5.02596e11			−1.18502
$808$			3.35888e10i			0.0788042i
$809$	6.26109e10			0.146169			0.0730846	−	0.997326i	$-0.476716\pi$
$809$	6.26109e10			0.146169			0.0730846	+	0.997326i	$0.476716\pi$
$810$			2.58635e10i			0.0600824i
$811$			7.64797e11i			1.76792i	0.467562	+	0.883960i	$0.345132\pi$
$811$			7.64797e11i			1.76792i	−0.467562	+	0.883960i	$0.654868\pi$
$812$	2.06593e11	+	4.30290e10i	0.475217	+	0.0989776i
$813$	−3.87701e11			−0.887432
$814$	−1.42194e10			−0.0323880
$815$		−	1.99085e11i		−	0.451241i
$816$	−1.02894e11			−0.232076
$817$		−	1.45916e11i		−	0.327502i
$818$			3.03764e11i			0.678458i
$819$	−1.87536e11	+	9.00409e11i	−0.416821	+	2.00126i
$820$	7.46899e10			0.165199
$821$	1.18664e11			0.261184			0.130592	−	0.991436i	$-0.458312\pi$
$821$	1.18664e11			0.261184			0.130592	+	0.991436i	$0.458312\pi$
$822$		−	1.95948e11i		−	0.429193i
$823$	−4.97104e10			−0.108355			−0.0541774	−	0.998531i	$-0.517254\pi$
$823$	−4.97104e10			−0.108355			−0.0541774	+	0.998531i	$0.517254\pi$
$824$		−	2.49442e11i		−	0.541080i
$825$			5.05054e11i			1.09024i
$826$	3.15158e10	−	1.51315e11i	0.0677030	−	0.325059i
$827$	−4.23663e11			−0.905730			−0.452865	−	0.891579i	$-0.649598\pi$
$827$	−4.23663e11			−0.905730			−0.452865	+	0.891579i	$0.649598\pi$
$828$	3.51426e11			0.747674
$829$		−	3.27268e11i		−	0.692925i	−0.938064	−	0.346462i	$-0.887383\pi$
$829$		−	3.27268e11i		−	0.692925i	0.938064	−	0.346462i	$-0.112617\pi$
$830$	−7.20449e10			−0.151807
$831$			9.19054e9i			0.0192725i
$832$			8.51844e10i			0.177773i
$833$	1.14299e11	−	2.62486e11i	0.237390	−	0.545163i
$834$	2.44346e11			0.505058
$835$	1.98982e11			0.409324
$836$			3.11733e11i			0.638201i
$837$	4.28012e11			0.872076
$838$		−	4.31105e11i		−	0.874193i
$839$			2.88363e11i			0.581958i	0.956730	+	0.290979i	$0.0939809\pi$
$839$			2.88363e11i			0.581958i	−0.956730	+	0.290979i	$0.906019\pi$
$840$	6.15607e10	+	1.28218e10i	0.123648	+	0.0257532i
$841$	−2.87590e10			−0.0574896
$842$	2.10600e11			0.418997
$843$		−	3.79706e10i		−	0.0751860i
$844$	3.10260e10			0.0611443
$845$		−	1.19298e11i		−	0.233995i
$846$			8.37918e11i			1.63576i
$847$	2.30244e11	+	4.79549e10i	0.447357	+	0.0931749i
$848$	−1.30758e11			−0.252863
$849$	−1.10379e11			−0.212449
$850$			2.07986e11i			0.398436i
$851$	3.39136e10			0.0646629
$852$			2.17753e11i			0.413243i
$853$		−	8.59016e11i		−	1.62258i	−0.584647	−	0.811288i	$-0.698767\pi$
$853$		−	8.59016e11i		−	1.62258i	0.584647	−	0.811288i	$-0.301233\pi$
$854$	5.77403e10	−	2.77226e11i	0.108554	−	0.521198i
$855$	−3.04436e11			−0.569680
$856$	1.03458e11			0.192694
$857$		−	7.24754e11i		−	1.34359i	−0.740736	−	0.671796i	$-0.765523\pi$
$857$		−	7.24754e11i		−	1.34359i	0.740736	−	0.671796i	$-0.234477\pi$
$858$	6.27002e11			1.15696
$859$		−	8.52093e11i		−	1.56500i	−0.622651	−	0.782500i	$-0.713944\pi$
$859$		−	8.52093e11i		−	1.56500i	0.622651	−	0.782500i	$-0.286056\pi$
$860$			1.18331e10i			0.0216325i
$861$	1.21282e12	+	2.52605e11i	2.20691	+	0.459652i
$862$	3.18746e11			0.577319
$863$	9.96876e10			0.179721			0.0898603	−	0.995954i	$-0.471358\pi$
$863$	9.96876e10			0.179721			0.0898603	+	0.995954i	$0.471358\pi$
$864$		−	6.72649e10i		−	0.120707i
$865$	7.56015e10			0.135041
$866$		−	4.87912e11i		−	0.867501i
$867$		−	5.70252e11i		−	1.00923i
$868$	−7.39126e10	+	3.54873e11i	−0.130209	+	0.625164i
$869$	−1.69232e11			−0.296759
$870$	1.40494e11			0.245234
$871$			1.32373e12i			2.29999i
$872$	−7.57336e10			−0.130985
$873$			1.38676e11i			0.238751i
$874$		−	7.43490e11i		−	1.27418i
$875$	5.32669e10	−	2.55748e11i	0.0908709	−	0.436295i
$876$	5.37606e10			0.0912952
$877$	−6.19031e11			−1.04644			−0.523219	−	0.852198i	$-0.675269\pi$
$877$	−6.19031e11			−1.04644			−0.523219	+	0.852198i	$0.675269\pi$
$878$		−	6.52918e10i		−	0.109870i
$879$	−6.70131e11			−1.12255
$880$		−	2.52802e10i		−	0.0421550i
$881$			5.89739e10i			0.0978940i	0.998801	+	0.0489470i	$0.0155865\pi$
$881$			5.89739e10i			0.0978940i	−0.998801	+	0.0489470i	$0.984413\pi$
$882$	5.63929e11	+	2.45561e11i	0.931859	+	0.405776i
$883$	−5.12329e11			−0.842764			−0.421382	−	0.906883i	$-0.638455\pi$
$883$	−5.12329e11			−0.842764			−0.421382	+	0.906883i	$0.638455\pi$
$884$	2.58206e11			0.422821
$885$		−	1.02902e11i		−	0.167746i
$886$	−1.03733e11			−0.168337
$887$			9.83599e11i			1.58900i	0.607265	+	0.794499i	$0.292267\pi$
$887$			9.83599e11i			1.58900i	−0.607265	+	0.794499i	$0.707733\pi$
$888$		−	2.13329e10i		−	0.0343081i
$889$	−4.67655e11	−	9.74026e10i	−0.748718	−	0.155942i
$890$	5.61125e10			0.0894333
$891$	1.72464e11			0.273645
$892$		−	1.93263e11i		−	0.305274i
$893$	1.77273e12			2.78764
$894$			9.02108e11i			1.41224i
$895$			2.23882e11i			0.348922i
$896$	5.57707e10	+	1.16158e10i	0.0865314	+	0.0180227i
$897$	−1.49541e12			−2.30989
$898$	−6.51231e11			−1.00145
$899$			8.09893e11i			1.23991i
$900$	−4.46841e11			−0.681056
$901$			3.96345e11i			0.601415i
$902$		−	4.98050e11i		−	0.752396i
$903$	−4.00202e10	+	1.92147e11i	−0.0601906	+	0.288990i
$904$	−2.46670e11			−0.369354
$905$	−8.04741e10			−0.119967
$906$		−	6.26488e11i		−	0.929822i
$907$	−6.57609e11			−0.971715			−0.485857	−	0.874038i	$-0.661493\pi$
$907$	−6.57609e11			−0.971715			−0.485857	+	0.874038i	$0.661493\pi$
$908$		−	1.82870e11i		−	0.269029i
$909$			2.18735e11i			0.320378i
$910$	−1.54482e11	−	3.21754e10i	−0.225275	−	0.0469200i
$911$	1.06492e11			0.154612			0.0773058	−	0.997007i	$-0.475368\pi$
$911$	1.06492e11			0.154612			0.0773058	+	0.997007i	$0.475368\pi$
$912$	−4.67682e11			−0.676038
$913$			4.80412e11i			0.691403i
$914$	−3.26839e11			−0.468327
$915$		−	1.88528e11i		−	0.268962i
$916$			1.07448e11i			0.152621i
$917$	1.11994e11	−	5.37711e11i	0.158386	−	0.760451i
$918$	−2.03889e11			−0.287094
$919$	−5.32765e11			−0.746919			−0.373459	−	0.927647i	$-0.621828\pi$
$919$	−5.32765e11			−0.746919			−0.373459	+	0.927647i	$0.621828\pi$
$920$			6.02937e10i			0.0841629i
$921$	−4.75300e11			−0.660586
$922$			5.91608e11i			0.818673i
$923$		−	5.46436e11i		−	0.752891i
$924$	8.54987e10	−	4.10501e11i	0.117293	−	0.563153i
$925$	−4.31214e10			−0.0589014
$926$	−1.94898e11			−0.265072
$927$		−	1.62440e12i		−	2.19976i
$928$	1.27280e11			0.171620
$929$		−	5.11415e11i		−	0.686611i	−0.939224	−	0.343305i	$-0.888453\pi$
$929$		−	5.11415e11i		−	0.686611i	0.939224	−	0.343305i	$-0.111547\pi$
$930$			2.41332e11i			0.322614i
$931$	5.19519e11	−	1.19307e12i	0.691517	−	1.58806i
$932$	−4.20433e11			−0.557229
$933$	1.62028e12			2.13828
$934$		−	2.25193e11i		−	0.295916i
$935$	−7.66276e10			−0.100263
$936$			5.54733e11i			0.722737i
$937$			7.02976e11i			0.911974i	0.889986	+	0.455987i	$0.150714\pi$
$937$			7.02976e11i			0.911974i	−0.889986	+	0.455987i	$0.849286\pi$
$938$	8.66651e11	+	1.80505e11i	1.11952	+	0.233173i
$939$	1.87618e11			0.241330
$940$	−1.43761e11			−0.184132
$941$			8.73030e11i			1.11345i	0.830697	+	0.556725i	$0.187942\pi$
$941$			8.73030e11i			1.11345i	−0.830697	+	0.556725i	$0.812058\pi$
$942$	7.59911e11			0.965071
$943$			1.18786e12i			1.50217i
$944$		−	9.32238e10i		−	0.117392i
$945$	1.21985e11	+	2.54069e10i	0.152961	+	0.0318585i
$946$	7.89061e10			0.0985249
$947$	8.59495e11			1.06867			0.534335	−	0.845273i	$-0.320562\pi$
$947$	8.59495e11			1.06867			0.534335	+	0.845273i	$0.320562\pi$
$948$		−	2.53893e11i		−	0.314353i
$949$	−1.34908e11			−0.166331
$950$			9.45353e11i			1.16065i
$951$		−	6.93478e11i		−	0.847834i
$952$	3.52092e10	−	1.69049e11i	0.0428656	−	0.205809i
$953$	−3.61718e11			−0.438529			−0.219264	−	0.975665i	$-0.570366\pi$
$953$	−3.61718e11			−0.438529			−0.219264	+	0.975665i	$0.570366\pi$
$954$	−8.51513e11			−1.02801
$955$			7.38878e10i			0.0888299i
$956$	−6.63017e11			−0.793767
$957$		−	9.36847e11i		−	1.11692i
$958$			5.71343e9i			0.00678320i
$959$	3.21929e11	+	6.70510e10i	0.380615	+	0.0792740i
$960$	3.79269e10			0.0446542
$961$	−5.38293e11			−0.631139
$962$			5.35333e10i			0.0625063i
$963$	6.73732e11			0.783397
$964$		−	1.94544e10i		−	0.0225273i
$965$			2.39581e8i			0.000276276i
$966$	−2.03916e11	+	9.79054e11i	−0.234176	+	1.12434i
$967$	7.03562e11			0.804631			0.402315	−	0.915501i	$-0.368206\pi$
$967$	7.03562e11			0.804631			0.402315	+	0.915501i	$0.368206\pi$
$968$	1.41851e11			0.161559
$969$			1.41761e12i			1.60791i
$970$	−2.37925e10			−0.0268753
$971$		−	8.72568e11i		−	0.981572i	−0.871280	−	0.490786i	$-0.836710\pi$
$971$		−	8.72568e11i		−	0.981572i	0.871280	−	0.490786i	$-0.163290\pi$
$972$			5.63492e11i			0.631281i
$973$	−8.36124e10	+	4.01445e11i	−0.0932866	+	0.447893i
$974$	−4.22488e11			−0.469439
$975$	1.90143e12			2.10408
$976$		−	1.70796e11i		−	0.188226i
$977$	1.52543e12			1.67422			0.837111	−	0.547033i	$-0.184243\pi$
$977$	1.52543e12			1.67422			0.837111	+	0.547033i	$0.184243\pi$
$978$		−	1.99167e12i		−	2.17702i
$979$		−	3.74171e11i		−	0.407323i
$980$	−4.21307e10	+	9.67527e10i	−0.0456767	+	0.104896i
$981$	−4.93188e11			−0.532520
$982$	−8.26841e10			−0.0889152
$983$			1.55846e10i			0.0166910i	0.999965	+	0.00834548i	$0.00265648\pi$
$983$			1.55846e10i			0.0166910i	−0.999965	+	0.00834548i	$0.997344\pi$
$984$	7.47206e11			0.797003
$985$		−	4.01205e10i		−	0.0426208i
$986$		−	3.85803e11i		−	0.408186i
$987$	−2.33440e12	−	4.86205e11i	−2.45984	−	0.512332i
$988$	1.17361e12			1.23168
$989$	−1.88193e11			−0.196706
$990$		−	1.64628e11i		−	0.171381i
$991$	−1.08092e12			−1.12073			−0.560364	−	0.828246i	$-0.689339\pi$
$991$	−1.08092e12			−1.12073			−0.560364	+	0.828246i	$0.689339\pi$
$992$			2.18634e11i			0.225772i
$993$			3.21079e11i			0.330229i
$994$	−3.57754e11	−	7.45126e10i	−0.366470	−	0.0763280i
$995$	1.54665e11			0.157798
$996$	−7.20746e11			−0.732394
$997$		−	1.06050e12i		−	1.07332i	−0.843799	−	0.536659i	$-0.819686\pi$
$997$		−	1.06050e12i		−	1.07332i	0.843799	−	0.536659i	$-0.180314\pi$
$998$	−1.08816e12			−1.09691
$999$		−	4.22720e10i		−	0.0424415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.9.b.a.13.1	✓	4
3.2	odd	2		126.9.c.a.55.3		4
4.3	odd	2		112.9.c.c.97.4		4
5.2	odd	4		350.9.d.a.349.1		8
5.3	odd	4		350.9.d.a.349.8		8
5.4	even	2		350.9.b.a.251.4		4
7.2	even	3		98.9.d.a.31.4		8
7.3	odd	6		98.9.d.a.19.4		8
7.4	even	3		98.9.d.a.19.3		8
7.5	odd	6		98.9.d.a.31.3		8
7.6	odd	2	inner	14.9.b.a.13.2	yes	4
21.20	even	2		126.9.c.a.55.4		4
28.27	even	2		112.9.c.c.97.1		4
35.13	even	4		350.9.d.a.349.5		8
35.27	even	4		350.9.d.a.349.4		8
35.34	odd	2		350.9.b.a.251.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.9.b.a.13.1	✓	4	1.1	even	1	trivial
14.9.b.a.13.2	yes	4	7.6	odd	2	inner
98.9.d.a.19.3		8	7.4	even	3
98.9.d.a.19.4		8	7.3	odd	6
98.9.d.a.31.3		8	7.5	odd	6
98.9.d.a.31.4		8	7.2	even	3
112.9.c.c.97.1		4	28.27	even	2
112.9.c.c.97.4		4	4.3	odd	2
126.9.c.a.55.3		4	3.2	odd	2
126.9.c.a.55.4		4	21.20	even	2
350.9.b.a.251.3		4	35.34	odd	2
350.9.b.a.251.4		4	5.4	even	2
350.9.d.a.349.1		8	5.2	odd	4
350.9.d.a.349.4		8	35.27	even	4
350.9.d.a.349.5		8	35.13	even	4
350.9.d.a.349.8		8	5.3	odd	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)

\(f(q)\)	\(=\)	\(q-11.3137 q^{2} -126.458i q^{3} +128.000 q^{4} +143.012i q^{5} +1430.71i q^{6} +(-2350.56 - 489.571i) q^{7} -1448.15 q^{8} -9430.58 q^{9} +O(q^{10})\)	\(q-11.3137 q^{2} -126.458i q^{3} +128.000 q^{4} +143.012i q^{5} +1430.71i q^{6} +(-2350.56 - 489.571i) q^{7} -1448.15 q^{8} -9430.58 q^{9} -1617.99i q^{10} -10789.2 q^{11} -16186.6i q^{12} +40619.1i q^{13} +(26593.5 + 5538.87i) q^{14} +18085.0 q^{15} +16384.0 q^{16} -49662.1i q^{17} +106695. q^{18} -225728. i q^{19} +18305.5i q^{20} +(-61910.1 + 297246. i) q^{21} +122065. q^{22} -291129. q^{23} +183130. i q^{24} +370173. q^{25} -459553. i q^{26} +362881. i q^{27} +(-300871. - 62665.1i) q^{28} -686649. q^{29} -204608. q^{30} -1.17948e6i q^{31} -185364. q^{32} +1.36437e6i q^{33} +561863. i q^{34} +(70014.5 - 336158. i) q^{35} -1.20711e6 q^{36} -116490. q^{37} +2.55382e6i q^{38} +5.13660e6 q^{39} -207103. i q^{40} -4.08019e6i q^{41} +(700433. - 3.36296e6i) q^{42} +646424. q^{43} -1.38101e6 q^{44} -1.34868e6i q^{45} +3.29375e6 q^{46} +7.85341e6i q^{47} -2.07188e6i q^{48} +(5.28544e6 + 2.30153e6i) q^{49} -4.18802e6 q^{50} -6.28017e6 q^{51} +5.19925e6i q^{52} -7.98083e6 q^{53} -4.10553e6i q^{54} -1.54298e6i q^{55} +(3.40397e6 + 708975. i) q^{56} -2.85450e7 q^{57} +7.76855e6 q^{58} -5.68993e6i q^{59} +2.31488e6 q^{60} -1.04246e7i q^{61} +1.33443e7i q^{62} +(2.21671e7 + 4.61694e6i) q^{63} +2.09715e6 q^{64} -5.80901e6 q^{65} -1.54361e7i q^{66} +3.25888e7 q^{67} -6.35676e6i q^{68} +3.68155e7i q^{69} +(-792124. + 3.80319e6i) q^{70} -1.34527e7 q^{71} +1.36569e7 q^{72} +3.32131e6i q^{73} +1.31793e6 q^{74} -4.68112e7i q^{75} -2.88932e7i q^{76} +(2.53606e7 + 5.28207e6i) q^{77} -5.81140e7 q^{78} +1.56854e7 q^{79} +2.34311e6i q^{80} -1.59849e7 q^{81} +4.61620e7i q^{82} -4.45273e7i q^{83} +(-7.92450e6 + 3.80475e7i) q^{84} +7.10228e6 q^{85} -7.31346e6 q^{86} +8.68322e7i q^{87} +1.56244e7 q^{88} +3.46802e7i q^{89} +1.52586e7i q^{90} +(1.98860e7 - 9.54776e7i) q^{91} -3.72645e7 q^{92} -1.49155e8 q^{93} -8.88511e7i q^{94} +3.22817e7 q^{95} +2.34407e7i q^{96} -1.47049e7i q^{97} +(-5.97979e7 - 2.60389e7i) q^{98} +1.01748e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 512 q^{4} - 6076 q^{7} - 13692 q^{9}+O(q^{10}) \) 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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