LMFDB - Embedded newform 8.15.d.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,15,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$9.94631745215$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 4349 x^{10} - 33891 x^{9} + 12151288 x^{8} - 474141530 x^{7} + 82897017850 x^{6} + \cdots + 37\!\cdots\!50 $ x^12 - x^11 + 4349x^10 - 33891x^9 + 12151288x^8 - 474141530x^7 + 82897017850x^6 - 1813403462870x^5 + 371618750972305x^4 - 24344904673267125x^3 + 1896685485375873305x^2 - 84437535339775221175x + 3788457560343891547750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{66}\cdot 3^{6}\cdot 5^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.1
Root			$-64.5010 - 31.8690i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.15.d.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-111.002 - 63.7381i) q^{2} -2044.69 q^{3} +(8258.92 + 14150.1i) q^{4} +54892.6i q^{5} +(226964. + 130324. i) q^{6} +432198. i q^{7} +(-14856.1 - 2.09710e6i) q^{8} -602230. q^{9} +(3.49875e6 - 6.09319e6i) q^{10} -5.00217e6 q^{11} +(-1.68869e7 - 2.89325e7i) q^{12} -1.07060e8i q^{13} +(2.75475e7 - 4.79749e7i) q^{14} -1.12238e8i q^{15} +(-1.32016e8 + 2.33729e8i) q^{16} +5.41735e8 q^{17} +(6.68488e7 + 3.83850e7i) q^{18} -5.65329e8 q^{19} +(-7.76736e8 + 4.53353e8i) q^{20} -8.83710e8i q^{21} +(5.55251e8 + 3.18829e8i) q^{22} +2.23131e8i q^{23} +(3.03761e7 + 4.28791e9i) q^{24} +3.09032e9 q^{25} +(-6.82378e9 + 1.18839e10i) q^{26} +1.10110e10 q^{27} +(-6.11566e9 + 3.56949e9i) q^{28} -2.03130e10i q^{29} +(-7.15384e9 + 1.24587e10i) q^{30} -4.80239e10i q^{31} +(2.95515e10 - 1.75300e10i) q^{32} +1.02279e10 q^{33} +(-6.01337e10 - 3.45291e10i) q^{34} -2.37245e10 q^{35} +(-4.97377e9 - 8.52163e9i) q^{36} -2.61073e9i q^{37} +(6.27527e10 + 3.60330e10i) q^{38} +2.18903e11i q^{39} +(1.15115e11 - 8.15491e8i) q^{40} +1.87732e11 q^{41} +(-5.63259e10 + 9.80936e10i) q^{42} -4.54896e11 q^{43} +(-4.13125e10 - 7.07813e10i) q^{44} -3.30580e10i q^{45} +(1.42219e10 - 2.47680e10i) q^{46} +6.78784e11i q^{47} +(2.69931e11 - 4.77903e11i) q^{48} +4.91428e11 q^{49} +(-3.43032e11 - 1.96971e11i) q^{50} -1.10768e12 q^{51} +(1.51491e12 - 8.84197e11i) q^{52} -1.93748e11i q^{53} +(-1.22225e12 - 7.01822e11i) q^{54} -2.74582e11i q^{55} +(9.06363e11 - 6.42079e9i) q^{56} +1.15592e12 q^{57} +(-1.29471e12 + 2.25479e12i) q^{58} -6.14590e10 q^{59} +(1.58818e12 - 9.26965e11i) q^{60} -4.19014e12i q^{61} +(-3.06095e12 + 5.33075e12i) q^{62} -2.60283e11i q^{63} +(-4.39761e12 + 6.23096e10i) q^{64} +5.87679e12 q^{65} +(-1.13531e12 - 6.51904e11i) q^{66} -2.70811e12 q^{67} +(4.47414e12 + 7.66561e12i) q^{68} -4.56233e11i q^{69} +(2.63347e12 + 1.51215e12i) q^{70} +7.21510e12i q^{71} +(8.94681e9 + 1.26294e12i) q^{72} +3.25297e12 q^{73} +(-1.66403e11 + 2.89797e11i) q^{74} -6.31873e12 q^{75} +(-4.66901e12 - 7.99947e12i) q^{76} -2.16193e12i q^{77} +(1.39525e13 - 2.42987e13i) q^{78} -2.62660e13i q^{79} +(-1.28300e13 - 7.24670e12i) q^{80} -1.96337e13 q^{81} +(-2.08386e13 - 1.19657e13i) q^{82} +2.72551e13 q^{83} +(1.25046e13 - 7.29849e12i) q^{84} +2.97372e13i q^{85} +(5.04944e13 + 2.89942e13i) q^{86} +4.15337e13i q^{87} +(7.43129e10 + 1.04900e13i) q^{88} -8.38435e13 q^{89} +(-2.10705e12 + 3.66950e12i) q^{90} +4.62710e13 q^{91} +(-3.15733e12 + 1.84282e12i) q^{92} +9.81938e13i q^{93} +(4.32644e13 - 7.53464e13i) q^{94} -3.10324e13i q^{95} +(-6.04235e13 + 3.58433e13i) q^{96} +9.36819e12 q^{97} +(-5.45495e13 - 3.13226e13i) q^{98} +3.01246e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9} - 14533440 q^{10} - 28256720 q^{11} + 34920024 q^{12} + 191568384 q^{14} - 185822448 q^{16} + 270339544 q^{17}+ \cdots - 223606851712368 q^{99}+O(q^{100}) $ 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9 - 14533440 * q^10 - 28256720 * q^11 + 34920024 * q^12 + 191568384 * q^14 - 185822448 * q^16 + 270339544 * q^17 + 1420811358 * q^18 - 2481505872 * q^19 - 1679371200 * q^20 + 3042383484 * q^22 + 7581335184 * q^24 - 15857276820 * q^25 - 2773507776 * q^26 - 16574868000 * q^27 + 25329333120 * q^28 + 42207767040 * q^30 + 38309251808 * q^32 - 136227597840 * q^33 + 350437044 * q^34 + 149949623040 * q^35 - 150590403492 * q^36 + 102789916636 * q^38 - 66999085440 * q^40 + 264287409880 * q^41 - 110343609600 * q^42 + 32253127344 * q^43 - 585547356392 * q^44 + 864780977664 * q^46 - 2387663418144 * q^48 - 646589230644 * q^49 - 388785556630 * q^50 + 4755867895776 * q^51 + 798005307840 * q^52 + 1305053764344 * q^54 - 1050155264256 * q^56 - 7479401742480 * q^57 + 389204742720 * q^58 + 1223083947184 * q^59 + 4350689397120 * q^60 + 9957296947200 * q^62 - 16809671099328 * q^64 - 8069319822720 * q^65 - 6067132925784 * q^66 - 9309378171216 * q^67 + 32301846360616 * q^68 + 35197935521280 * q^70 - 43695386222808 * q^72 + 3619334364696 * q^73 - 55499920147776 * q^74 + 9079078926000 * q^75 + 33532610502360 * q^76 + 92515055193600 * q^78 - 86826189154560 * q^80 + 56467107312444 * q^81 - 146233962574956 * q^82 - 18774355695824 * q^83 + 186893160787200 * q^84 + 96253393476220 * q^86 - 166888683024624 * q^88 + 54781416936088 * q^89 - 488020221650880 * q^90 + 36699395136768 * q^91 + 413167093560960 * q^92 + 496016398930944 * q^94 - 616114307580864 * q^96 + 73839238696536 * q^97 - 523654870565638 * q^98 - 223606851712368 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−111.002	−	63.7381i	−0.867204	−	0.497954i
$2$	−111.002	−	63.7381i	−0.867204	−	0.497954i
$3$	−2044.69			−0.934927			−0.467464	−	0.884012i	$-0.654832\pi$
$3$	−2044.69			−0.934927			−0.467464	+	0.884012i	$0.654832\pi$
$4$	8258.92	+	14150.1i	0.504084	+	0.863654i
$5$			54892.6i			0.702625i	0.936258	+	0.351313i	$0.114265\pi$
$5$			54892.6i			0.702625i	−0.936258	+	0.351313i	$0.885735\pi$
$6$	226964.	+	130324.i	0.810772	+	0.465550i
$7$			432198.i			0.524804i	0.964959	+	0.262402i	$0.0845146\pi$
$7$			432198.i			0.524804i	−0.964959	+	0.262402i	$0.915485\pi$
$8$	−14856.1	−	2.09710e6i	−0.00708395	−	0.999975i
$9$	−602230.			−0.125911
$10$	3.49875e6	−	6.09319e6i	0.349875	−	0.609319i
$11$	−5.00217e6			−0.256690			−0.128345	−	0.991730i	$-0.540967\pi$
$11$	−5.00217e6			−0.256690			−0.128345	+	0.991730i	$0.540967\pi$
$12$	−1.68869e7	−	2.89325e7i	−0.471282	−	0.807454i
$13$		−	1.07060e8i		−	1.70617i	−0.521771	−	0.853086i	$-0.674728\pi$
$13$		−	1.07060e8i		−	1.70617i	0.521771	−	0.853086i	$-0.325272\pi$
$14$	2.75475e7	−	4.79749e7i	0.261328	−	0.455112i
$15$		−	1.12238e8i		−	0.656903i
$16$	−1.32016e8	+	2.33729e8i	−0.491798	+	0.870709i
$17$	5.41735e8			1.32021			0.660107	−	0.751172i	$-0.270511\pi$
$17$	5.41735e8			1.32021			0.660107	+	0.751172i	$0.270511\pi$
$18$	6.68488e7	+	3.83850e7i	0.109191	+	0.0626980i
$19$	−5.65329e8			−0.632450			−0.316225	−	0.948684i	$-0.602415\pi$
$19$	−5.65329e8			−0.632450			−0.316225	+	0.948684i	$0.602415\pi$
$20$	−7.76736e8	+	4.53353e8i	−0.606825	+	0.354182i
$21$		−	8.83710e8i		−	0.490653i
$22$	5.55251e8	+	3.18829e8i	0.222603	+	0.127820i
$23$			2.23131e8i			0.0655337i	0.999463	+	0.0327669i	$0.0104319\pi$
$23$			2.23131e8i			0.0655337i	−0.999463	+	0.0327669i	$0.989568\pi$
$24$	3.03761e7	+	4.28791e9i	0.00662298	+	0.934904i
$25$	3.09032e9			0.506318
$26$	−6.82378e9	+	1.18839e10i	−0.849594	+	1.47960i
$27$	1.10110e10			1.05265
$28$	−6.11566e9	+	3.56949e9i	−0.453249	+	0.264545i
$29$		−	2.03130e10i		−	1.17757i	−0.808288	−	0.588787i	$-0.799606\pi$
$29$		−	2.03130e10i		−	1.17757i	0.808288	−	0.588787i	$-0.200394\pi$
$30$	−7.15384e9	+	1.24587e10i	−0.327107	+	0.569669i
$31$		−	4.80239e10i		−	1.74552i	−0.488147	−	0.872761i	$-0.662327\pi$
$31$		−	4.80239e10i		−	1.74552i	0.488147	−	0.872761i	$-0.337673\pi$
$32$	2.95515e10	−	1.75300e10i	0.860062	−	0.510190i
$33$	1.02279e10			0.239987
$34$	−6.01337e10	−	3.45291e10i	−1.14489	−	0.657405i
$35$	−2.37245e10			−0.368740
$36$	−4.97377e9	−	8.52163e9i	−0.0634700	−	0.108744i
$37$		−	2.61073e9i		−	0.0275011i	−0.999905	−	0.0137506i	$-0.995623\pi$
$37$		−	2.61073e9i		−	0.0275011i	0.999905	−	0.0137506i	$-0.00437707\pi$
$38$	6.27527e10	+	3.60330e10i	0.548463	+	0.314931i
$39$			2.18903e11i			1.59515i
$40$	1.15115e11	−	8.15491e8i	0.702608	−	0.00497736i
$41$	1.87732e11			0.963942			0.481971	−	0.876187i	$-0.339921\pi$
$41$	1.87732e11			0.963942			0.481971	+	0.876187i	$0.339921\pi$
$42$	−5.63259e10	+	9.80936e10i	−0.244323	+	0.425496i
$43$	−4.54896e11			−1.67353			−0.836763	−	0.547565i	$-0.815555\pi$
$43$	−4.54896e11			−1.67353			−0.836763	+	0.547565i	$0.815555\pi$
$44$	−4.13125e10	−	7.07813e10i	−0.129394	−	0.221692i
$45$		−	3.30580e10i		−	0.0884685i
$46$	1.42219e10	−	2.47680e10i	0.0326328	−	0.0568311i
$47$			6.78784e11i			1.33982i	0.742442	+	0.669910i	$0.233667\pi$
$47$			6.78784e11i			1.33982i	−0.742442	+	0.669910i	$0.766333\pi$
$48$	2.69931e11	−	4.77903e11i	0.459795	−	0.814050i
$49$	4.91428e11			0.724581
$50$	−3.43032e11	−	1.96971e11i	−0.439081	−	0.252123i
$51$	−1.10768e12			−1.23430
$52$	1.51491e12	−	8.84197e11i	1.47354	−	0.860054i
$53$		−	1.93748e11i		−	0.164932i	−0.996594	−	0.0824660i	$-0.973720\pi$
$53$		−	1.93748e11i		−	0.164932i	0.996594	−	0.0824660i	$-0.0262796\pi$
$54$	−1.22225e12	−	7.01822e11i	−0.912858	−	0.524168i
$55$		−	2.74582e11i		−	0.180357i
$56$	9.06363e11	−	6.42079e9i	0.524790	−	0.00371768i
$57$	1.15592e12			0.591294
$58$	−1.29471e12	+	2.25479e12i	−0.586377	+	1.02120i
$59$	−6.14590e10			−0.0246957			−0.0123479	−	0.999924i	$-0.503931\pi$
$59$	−6.14590e10			−0.0246957			−0.0123479	+	0.999924i	$0.503931\pi$
$60$	1.58818e12	−	9.26965e11i	0.567337	−	0.331135i
$61$		−	4.19014e12i		−	1.33328i	−0.745382	−	0.666638i	$-0.767733\pi$
$61$		−	4.19014e12i		−	1.33328i	0.745382	−	0.666638i	$-0.232267\pi$
$62$	−3.06095e12	+	5.33075e12i	−0.869189	+	1.51372i
$63$		−	2.60283e11i		−	0.0660787i
$64$	−4.39761e12	+	6.23096e10i	−0.999900	+	0.0141676i
$65$	5.87679e12			1.19880
$66$	−1.13531e12	−	6.51904e11i	−0.208117	−	0.119502i
$67$	−2.70811e12			−0.446830			−0.223415	−	0.974723i	$-0.571720\pi$
$67$	−2.70811e12			−0.446830			−0.223415	+	0.974723i	$0.571720\pi$
$68$	4.47414e12	+	7.66561e12i	0.665499	+	1.14021i
$69$		−	4.56233e11i		−	0.0612693i
$70$	2.63347e12	+	1.51215e12i	0.319773	+	0.183616i
$71$			7.21510e12i			0.793293i	0.917971	+	0.396647i	$0.129826\pi$
$71$			7.21510e12i			0.793293i	−0.917971	+	0.396647i	$0.870174\pi$
$72$	8.94681e9	+	1.26294e12i	0.000891950	+	0.125908i
$73$	3.25297e12			0.294456			0.147228	−	0.989103i	$-0.452965\pi$
$73$	3.25297e12			0.294456			0.147228	+	0.989103i	$0.452965\pi$
$74$	−1.66403e11	+	2.89797e11i	−0.0136943	+	0.0238491i
$75$	−6.31873e12			−0.473370
$76$	−4.66901e12	−	7.99947e12i	−0.318808	−	0.546218i
$77$		−	2.16193e12i		−	0.134712i
$78$	1.39525e13	−	2.42987e13i	0.794309	−	1.38332i
$79$		−	2.62660e13i		−	1.36774i	−0.729604	−	0.683870i	$-0.760296\pi$
$79$		−	2.62660e13i		−	1.36774i	0.729604	−	0.683870i	$-0.239704\pi$
$80$	−1.28300e13	−	7.24670e12i	−0.611782	−	0.345550i
$81$	−1.96337e13			−0.858235
$82$	−2.08386e13	−	1.19657e13i	−0.835934	−	0.479998i
$83$	2.72551e13			1.00439			0.502194	−	0.864755i	$-0.332526\pi$
$83$	2.72551e13			1.00439			0.502194	+	0.864755i	$0.332526\pi$
$84$	1.25046e13	−	7.29849e12i	0.423755	−	0.247331i
$85$			2.97372e13i			0.927616i
$86$	5.04944e13	+	2.89942e13i	1.45129	+	0.833339i
$87$			4.15337e13i			1.10095i
$88$	7.43129e10	+	1.04900e13i	0.00181838	+	0.256684i
$89$	−8.38435e13			−1.89557			−0.947784	−	0.318913i	$-0.896682\pi$
$89$	−8.38435e13			−1.89557			−0.947784	+	0.318913i	$0.896682\pi$
$90$	−2.10705e12	+	3.66950e12i	−0.0440532	+	0.0767202i
$91$	4.62710e13			0.895405
$92$	−3.15733e12	+	1.84282e12i	−0.0565985	+	0.0330345i
$93$			9.81938e13i			1.63194i
$94$	4.32644e13	−	7.53464e13i	0.667169	−	1.16190i
$95$		−	3.10324e13i		−	0.444375i
$96$	−6.04235e13	+	3.58433e13i	−0.804095	+	0.476990i
$97$	9.36819e12			0.115945			0.0579727	−	0.998318i	$-0.481536\pi$
$97$	9.36819e12			0.115945			0.0579727	+	0.998318i	$0.481536\pi$
$98$	−5.45495e13	−	3.13226e13i	−0.628359	−	0.360808i
$99$	3.01246e12			0.0323202
$100$	2.55227e13	+	4.37284e13i	0.255227	+	0.437284i
$101$		−	9.26946e13i		−	0.864579i	−0.901735	−	0.432290i	$-0.857706\pi$
$101$		−	9.26946e13i		−	0.864579i	0.901735	−	0.432290i	$-0.142294\pi$
$102$	1.22954e14	+	7.06012e13i	1.07039	+	0.614626i
$103$		−	1.53757e14i		−	1.25018i	−0.780551	−	0.625092i	$-0.785062\pi$
$103$		−	1.53757e14i		−	1.25018i	0.780551	−	0.625092i	$-0.214938\pi$
$104$	−2.24515e14	+	1.59049e12i	−1.70613	+	0.0120864i
$105$	4.85091e13			0.344745
$106$	−1.23491e13	+	2.15064e13i	−0.0821285	+	0.143030i
$107$	6.78082e13			0.422275			0.211138	−	0.977456i	$-0.432283\pi$
$107$	6.78082e13			0.422275			0.211138	+	0.977456i	$0.432283\pi$
$108$	9.09393e13	+	1.55807e14i	0.530622	+	0.909122i
$109$		−	2.35599e14i		−	1.28881i	−0.764685	−	0.644404i	$-0.777106\pi$
$109$		−	2.35599e14i		−	1.28881i	0.764685	−	0.644404i	$-0.222894\pi$
$110$	−1.75013e13	+	3.04792e13i	−0.0898095	+	0.156406i
$111$			5.33813e12i			0.0257115i
$112$	−1.01017e14	−	5.70571e13i	−0.456951	−	0.258097i
$113$	1.76933e14			0.752071			0.376035	−	0.926605i	$-0.377287\pi$
$113$	1.76933e14			0.752071			0.376035	+	0.926605i	$0.377287\pi$
$114$	−1.28310e14	−	7.36761e13i	−0.512773	−	0.294437i
$115$	−1.22482e13			−0.0460457
$116$	2.87431e14	−	1.67763e14i	1.01702	−	0.593596i
$117$			6.44746e13i			0.214826i
$118$	6.82208e12	+	3.91728e12i	0.0214162	+	0.0122973i
$119$			2.34137e14i			0.692853i
$120$	−2.35374e14	+	1.66742e12i	−0.656887	+	0.00465347i
$121$	−3.54728e14			−0.934110
$122$	−2.67072e14	+	4.65114e14i	−0.663909	+	1.15622i
$123$	−3.83852e14			−0.901215
$124$	6.79544e14	−	3.96625e14i	1.50753	−	0.879891i
$125$			5.04673e14i			1.05838i
$126$	−1.65899e13	+	2.88919e13i	−0.0329042	+	0.0573037i
$127$			2.11336e14i			0.396595i	0.980142	+	0.198297i	$0.0635412\pi$
$127$			2.11336e14i			0.396595i	−0.980142	+	0.198297i	$0.936459\pi$
$128$	4.92115e14	+	2.73378e14i	0.874171	+	0.485617i
$129$	9.30119e14			1.56463
$130$	−6.52335e14	−	3.74575e14i	−1.03960	−	0.596946i
$131$	−3.61356e14			−0.545803			−0.272902	−	0.962042i	$-0.587983\pi$
$131$	−3.61356e14			−0.545803			−0.272902	+	0.962042i	$0.587983\pi$
$132$	8.44711e13	+	1.44725e14i	0.120974	+	0.207266i
$133$		−	2.44334e14i		−	0.331912i
$134$	3.00605e14	+	1.72609e14i	0.387492	+	0.222500i
$135$			6.04424e14i			0.739615i
$136$	−8.04808e12	−	1.13607e15i	−0.00935233	−	1.32018i
$137$	−3.84439e14			−0.424408			−0.212204	−	0.977225i	$-0.568064\pi$
$137$	−3.84439e14			−0.424408			−0.212204	+	0.977225i	$0.568064\pi$
$138$	−2.90794e13	+	5.06428e13i	−0.0305093	+	0.0531329i
$139$	−6.72406e14			−0.670699			−0.335350	−	0.942094i	$-0.608854\pi$
$139$	−6.72406e14			−0.670699			−0.335350	+	0.942094i	$0.608854\pi$
$140$	−1.95939e14	−	3.35704e14i	−0.185876	−	0.318464i
$141$		−	1.38790e15i		−	1.25263i
$142$	4.59876e14	−	8.00891e14i	0.395023	−	0.687947i
$143$			5.35531e14i			0.437958i
$144$	7.95040e13	−	1.40759e14i	0.0619229	−	0.109632i
$145$	1.11503e15			0.827393
$146$	−3.61087e14	−	2.07338e14i	−0.255353	−	0.146625i
$147$	−1.00481e15			−0.677431
$148$	3.69421e13	−	2.15618e13i	0.0237515	−	0.0138629i
$149$			4.15519e14i			0.254851i	0.991848	+	0.127426i	$0.0406714\pi$
$149$			4.15519e14i			0.254851i	−0.991848	+	0.127426i	$0.959329\pi$
$150$	7.01392e14	+	4.02744e14i	0.410508	+	0.235716i
$151$		−	1.88889e15i		−	1.05528i	−0.849468	−	0.527640i	$-0.823077\pi$
$151$		−	1.88889e15i		−	1.05528i	0.849468	−	0.527640i	$-0.176923\pi$
$152$	8.39860e12	+	1.18555e15i	0.00448025	+	0.632434i
$153$	−3.26249e14			−0.166230
$154$	−1.37797e14	+	2.39979e14i	−0.0670804	+	0.116823i
$155$	2.63616e15			1.22645
$156$	−3.09751e15	+	1.80791e15i	−1.37765	+	0.804088i
$157$			9.50349e14i			0.404190i	0.979366	+	0.202095i	$0.0647750\pi$
$157$			9.50349e14i			0.404190i	−0.979366	+	0.202095i	$0.935225\pi$
$158$	−1.67414e15	+	2.91558e15i	−0.681071	+	1.18611i
$159$			3.96153e14i			0.154199i
$160$	9.62267e14	+	1.62216e15i	0.358472	+	0.604301i
$161$	−9.64368e13			−0.0343923
$162$	2.17938e15	+	1.25141e15i	0.744264	+	0.427361i
$163$	4.21814e15			1.37977			0.689887	−	0.723917i	$-0.257660\pi$
$163$	4.21814e15			1.37977			0.689887	+	0.723917i	$0.257660\pi$
$164$	1.55046e15	+	2.65643e15i	0.485908	+	0.832512i
$165$			5.61434e14i			0.168621i
$166$	−3.02537e15	−	1.73719e15i	−0.871008	−	0.500138i
$167$		−	5.70680e15i		−	1.57535i	−0.616090	−	0.787676i	$-0.711284\pi$
$167$		−	5.70680e15i		−	1.57535i	0.616090	−	0.787676i	$-0.288716\pi$
$168$	−1.85323e15	+	1.31285e13i	−0.490641	+	0.00347576i
$169$	−7.52441e15			−1.91102
$170$	1.89539e15	−	3.30089e15i	0.461910	−	0.804432i
$171$	3.40458e14			0.0796326
$172$	−3.75695e15	−	6.43683e15i	−0.843599	−	1.44535i
$173$		−	9.03712e13i		−	0.0194853i	−0.999953	−	0.00974266i	$-0.996899\pi$
$173$		−	9.03712e13i		−	0.0194853i	0.999953	−	0.00974266i	$-0.00310123\pi$
$174$	2.64728e15	−	4.61033e15i	0.548220	−	0.954744i
$175$			1.33563e15i			0.265717i
$176$	6.60366e14	−	1.16915e15i	0.126240	−	0.223503i
$177$	1.25664e14			0.0230887
$178$	9.30680e15	+	5.34402e15i	1.64384	+	0.943905i
$179$	1.33017e15			0.225911			0.112955	−	0.993600i	$-0.463968\pi$
$179$	1.33017e15			0.225911			0.112955	+	0.993600i	$0.463968\pi$
$180$	4.67774e14	−	2.73023e14i	0.0764062	−	0.0445956i
$181$			4.15398e15i			0.652701i	0.945249	+	0.326351i	$0.105819\pi$
$181$			4.15398e15i			0.652701i	−0.945249	+	0.326351i	$0.894181\pi$
$182$	−5.13618e15	−	2.94923e15i	−0.776498	−	0.445870i
$183$			8.56752e15i			1.24652i
$184$	4.67928e14	−	3.31486e12i	0.0655321	−	0.000464238i
$185$	1.43310e14			0.0193230
$186$	6.25868e15	−	1.08997e16i	0.812629	−	1.41522i
$187$	−2.70985e15			−0.338886
$188$	−9.60487e15	+	5.60602e15i	−1.15714	+	0.675383i
$189$			4.75895e15i			0.552432i
$190$	−1.97794e15	+	3.44466e15i	−0.221278	+	0.385364i
$191$		−	1.03101e16i		−	1.11181i	−0.831246	−	0.555905i	$-0.812372\pi$
$191$		−	1.03101e16i		−	1.11181i	0.831246	−	0.555905i	$-0.187628\pi$
$192$	8.99172e15	−	1.27403e14i	0.934833	−	0.0132456i
$193$	1.85820e15			0.186290			0.0931451	−	0.995653i	$-0.470308\pi$
$193$	1.85820e15			0.186290			0.0931451	+	0.995653i	$0.470308\pi$
$194$	−1.03989e15	−	5.97110e14i	−0.100548	−	0.0577354i
$195$	−1.20162e16			−1.12079
$196$	4.05866e15	+	6.95376e15i	0.365250	+	0.625788i
$197$		−	9.68240e15i		−	0.840852i	−0.907327	−	0.420426i	$-0.861881\pi$
$197$		−	9.68240e15i		−	0.840852i	0.907327	−	0.420426i	$-0.138119\pi$
$198$	−3.34389e14	−	1.92008e14i	−0.0280282	−	0.0160940i
$199$			1.85225e16i			1.49875i	0.662148	+	0.749373i	$0.269645\pi$
$199$			1.85225e16i			1.49875i	−0.662148	+	0.749373i	$0.730355\pi$
$200$	−4.59102e13	−	6.48071e15i	−0.00358673	−	0.506305i
$201$	5.53723e15			0.417753
$202$	−5.90817e15	+	1.02893e16i	−0.430520	+	0.749766i
$203$	8.77925e15			0.617995
$204$	−9.14822e15	−	1.56738e16i	−0.622193	−	1.06601i
$205$			1.03051e16i			0.677290i
$206$	−9.80016e15	+	1.70673e16i	−0.622533	+	1.08416i
$207$		−	1.34376e14i		−	0.00825144i
$208$	2.50230e16	+	1.41336e16i	1.48558	+	0.839091i
$209$	2.82787e15			0.162344
$210$	−5.38461e15	−	3.09188e15i	−0.298964	−	0.171667i
$211$	−3.50670e15			−0.188331			−0.0941655	−	0.995557i	$-0.530018\pi$
$211$	−3.50670e15			−0.188331			−0.0941655	+	0.995557i	$0.530018\pi$
$212$	2.74155e15	−	1.60015e15i	0.142444	−	0.0831397i
$213$		−	1.47526e16i		−	0.741671i
$214$	−7.52685e15	−	4.32196e15i	−0.366199	−	0.210273i
$215$		−	2.49704e16i		−	1.17586i
$216$	−1.63581e14	−	2.30912e16i	−0.00745689	−	1.05262i
$217$	2.07558e16			0.916057
$218$	−1.50166e16	+	2.61520e16i	−0.641767	+	1.11766i
$219$	−6.65131e15			−0.275295
$220$	3.88537e15	−	2.26775e15i	0.155766	−	0.0909152i
$221$		−	5.79980e16i		−	2.25251i
$222$	3.40242e14	−	5.92543e14i	0.0128031	−	0.0222971i
$223$			5.37468e14i			0.0195983i	0.999952	+	0.00979915i	$0.00311922\pi$
$223$			5.37468e14i			0.0195983i	−0.999952	+	0.00979915i	$0.996881\pi$
$224$	7.57643e15	+	1.27721e16i	0.267749	+	0.451364i
$225$	−1.86108e15			−0.0637512
$226$	−1.96399e16	−	1.12773e16i	−0.652199	−	0.374496i
$227$	−3.16450e15			−0.101888			−0.0509441	−	0.998702i	$-0.516223\pi$
$227$	−3.16450e15			−0.101888			−0.0509441	+	0.998702i	$0.516223\pi$
$228$	9.54665e15	+	1.63564e16i	0.298062	+	0.510674i
$229$			1.94913e16i			0.590191i	0.955468	+	0.295096i	$0.0953515\pi$
$229$			1.94913e16i			0.590191i	−0.955468	+	0.295096i	$0.904648\pi$
$230$	1.35958e15	+	7.80679e14i	0.0399310	+	0.0229286i
$231$			4.42047e15i			0.125946i
$232$	−4.25984e16	+	3.01773e14i	−1.17754	+	0.00834188i
$233$	5.19433e16			1.39328			0.696640	−	0.717421i	$-0.254677\pi$
$233$	5.19433e16			1.39328			0.696640	+	0.717421i	$0.254677\pi$
$234$	4.10949e15	−	7.15681e15i	0.106974	−	0.186298i
$235$	−3.72602e16			−0.941392
$236$	−5.07585e14	−	8.69652e14i	−0.0124487	−	0.0213286i
$237$			5.37056e16i			1.27874i
$238$	1.49234e16	−	2.59897e16i	0.345009	−	0.600845i
$239$			4.74874e16i			1.06609i	0.846088	+	0.533044i	$0.178952\pi$
$239$			4.74874e16i			1.06609i	−0.846088	+	0.533044i	$0.821048\pi$
$240$	2.62333e16	+	1.48172e16i	0.571972	+	0.323064i
$241$	−4.58674e16			−0.971371			−0.485686	−	0.874134i	$-0.661430\pi$
$241$	−4.58674e16			−0.971371			−0.485686	+	0.874134i	$0.661430\pi$
$242$	3.93756e16	+	2.26097e16i	0.810064	+	0.465143i
$243$	−1.25208e16			−0.250258
$244$	5.92910e16	−	3.46060e16i	1.15149	−	0.672083i
$245$			2.69757e16i			0.509109i
$246$	4.26084e16	+	2.44660e16i	0.781537	+	0.448763i
$247$			6.05240e16i			1.07907i
$248$	−1.00711e17	+	7.13449e14i	−1.74548	+	0.0123652i
$249$	−5.57281e16			−0.939029
$250$	3.21669e16	−	5.60198e16i	0.527023	−	0.917828i
$251$	7.41689e16			1.18170			0.590848	−	0.806783i	$-0.298793\pi$
$251$	7.41689e16			1.18170			0.590848	+	0.806783i	$0.298793\pi$
$252$	3.68303e15	−	2.14966e15i	0.0570692	−	0.0333093i
$253$		−	1.11614e15i		−	0.0168219i
$254$	1.34701e16	−	2.34587e16i	0.197486	−	0.343928i
$255$		−	6.08033e16i		−	0.867253i
$256$	−3.72011e16	−	6.17120e16i	−0.516270	−	0.856426i
$257$	−7.34304e16			−0.991617			−0.495808	−	0.868432i	$-0.665128\pi$
$257$	−7.34304e16			−0.991617			−0.495808	+	0.868432i	$0.665128\pi$
$258$	−1.03245e17	−	5.92840e16i	−1.35685	−	0.779111i
$259$	1.12835e15			0.0144327
$260$	4.85359e16	+	8.31572e16i	0.604296	+	1.03535i
$261$			1.22331e16i			0.148270i
$262$	4.01113e16	+	2.30321e16i	0.473323	+	0.271785i
$263$		−	1.51496e17i		−	1.74065i	−0.492476	−	0.870326i	$-0.663908\pi$
$263$		−	1.51496e17i		−	1.74065i	0.492476	−	0.870326i	$-0.336092\pi$
$264$	−1.51946e14	−	2.14488e16i	−0.00170006	−	0.239981i
$265$	1.06353e16			0.115885
$266$	−1.55734e16	+	2.71216e16i	−0.165277	+	0.287835i
$267$	1.71434e17			1.77222
$268$	−2.23660e16	−	3.83200e16i	−0.225240	−	0.385906i
$269$		−	4.91049e15i		−	0.0481791i	−0.999710	−	0.0240896i	$-0.992331\pi$
$269$		−	4.91049e15i		−	0.0481791i	0.999710	−	0.0240896i	$-0.00766869\pi$
$270$	3.85248e16	−	6.70924e16i	0.368294	−	0.641397i
$271$		−	4.28208e16i		−	0.398905i	−0.979908	−	0.199452i	$-0.936084\pi$
$271$		−	4.28208e16i		−	0.398905i	0.979908	−	0.199452i	$-0.0639163\pi$
$272$	−7.15177e16	+	1.26619e17i	−0.649278	+	1.14952i
$273$	−9.46097e16			−0.837138
$274$	4.26735e16	+	2.45034e16i	0.368048	+	0.211336i
$275$	−1.54583e16			−0.129967
$276$	6.45574e15	−	3.76799e15i	0.0529155	−	0.0308849i
$277$			2.72806e16i			0.218019i	0.994041	+	0.109010i	$0.0347680\pi$
$277$			2.72806e16i			0.218019i	−0.994041	+	0.109010i	$0.965232\pi$
$278$	7.46384e16	+	4.28578e16i	0.581633	+	0.333977i
$279$			2.89214e16i			0.219781i
$280$	3.52454e14	+	4.97526e16i	0.00261214	+	0.368731i
$281$	9.69888e16			0.701096			0.350548	−	0.936545i	$-0.385995\pi$
$281$	9.69888e16			0.701096			0.350548	+	0.936545i	$0.385995\pi$
$282$	−8.84621e16	+	1.54060e17i	−0.623754	+	1.08629i
$283$	−5.99694e16			−0.412501			−0.206250	−	0.978499i	$-0.566126\pi$
$283$	−5.99694e16			−0.412501			−0.206250	+	0.978499i	$0.566126\pi$
$284$	−1.02094e17	+	5.95889e16i	−0.685131	+	0.399887i
$285$			6.34514e16i			0.415458i
$286$	3.41337e16	−	5.94450e16i	0.218083	−	0.379799i
$287$			8.11374e16i			0.505880i
$288$	−1.77968e16	+	1.05571e16i	−0.108292	+	0.0642387i
$289$	1.25099e17			0.742965
$290$	−1.23771e17	−	7.10701e16i	−0.717518	−	0.412003i
$291$	−1.91550e16			−0.108401
$292$	2.68660e16	+	4.60299e16i	0.148431	+	0.254308i
$293$		−	2.66691e17i		−	1.43859i	−0.694707	−	0.719293i	$-0.744466\pi$
$293$		−	2.66691e17i		−	1.43859i	0.694707	−	0.719293i	$-0.255534\pi$
$294$	1.11537e17	+	6.40450e16i	0.587470	+	0.337329i
$295$		−	3.37364e15i		−	0.0173518i
$296$	−5.47496e15	+	3.87854e13i	−0.0275004	+	0.000194817i
$297$	−5.50791e16			−0.270204
$298$	2.64844e16	−	4.61234e16i	0.126904	−	0.221008i
$299$	2.38883e16			0.111812
$300$	−5.21859e16	−	8.94107e16i	−0.238619	−	0.408828i
$301$		−	1.96605e17i		−	0.878273i
$302$	−1.20394e17	+	2.09670e17i	−0.525480	+	0.915142i
$303$			1.89531e17i			0.808318i
$304$	7.46325e16	−	1.32134e17i	0.311037	−	0.550680i
$305$	2.30008e17			0.936793
$306$	3.62143e16	+	2.07945e16i	0.144155	+	0.0827748i
$307$	−3.86671e17			−1.50443			−0.752216	−	0.658917i	$-0.771015\pi$
$307$	−3.86671e17			−1.50443			−0.752216	+	0.658917i	$0.771015\pi$
$308$	3.05916e16	−	1.78552e16i	0.116345	−	0.0679063i
$309$			3.14384e17i			1.16883i
$310$	−2.92619e17	−	1.68023e17i	−1.06358	−	0.610714i
$311$		−	1.68432e17i		−	0.598553i	−0.954166	−	0.299277i	$-0.903255\pi$
$311$		−	1.68432e17i		−	0.598553i	0.954166	−	0.299277i	$-0.0967453\pi$
$312$	4.59062e17	−	3.25206e15i	1.59511	−	0.0112999i
$313$	6.39488e16			0.217281			0.108641	−	0.994081i	$-0.465350\pi$
$313$	6.39488e16			0.217281			0.108641	+	0.994081i	$0.465350\pi$
$314$	6.05734e16	−	1.05491e17i	0.201268	−	0.350515i
$315$	1.42876e16			0.0464286
$316$	3.71666e17	−	2.16928e17i	1.18125	−	0.689456i
$317$			2.47885e17i			0.770612i	0.922789	+	0.385306i	$0.125904\pi$
$317$			2.47885e17i			0.770612i	−0.922789	+	0.385306i	$0.874096\pi$
$318$	2.52500e16	−	4.39738e16i	0.0767842	−	0.133722i
$319$			1.01609e17i			0.302272i
$320$	−3.42033e15	−	2.41396e17i	−0.00995448	−	0.702555i
$321$	−1.38646e17			−0.394796
$322$	1.07047e16	+	6.14670e15i	0.0298252	+	0.0171258i
$323$	−3.06258e17			−0.834969
$324$	−1.62153e17	−	2.77819e17i	−0.432623	−	0.741218i
$325$		−	3.30849e17i		−	0.863865i
$326$	−4.68222e17	−	2.68856e17i	−1.19655	−	0.687063i
$327$			4.81726e17i			1.20494i
$328$	−2.78897e15	−	3.93692e17i	−0.00682852	−	0.963917i
$329$	−2.93369e17			−0.703143
$330$	3.57847e16	−	6.23203e16i	0.0839653	−	0.146229i
$331$	2.74519e17			0.630633			0.315316	−	0.948987i	$-0.397889\pi$
$331$	2.74519e17			0.630633			0.315316	+	0.948987i	$0.397889\pi$
$332$	2.25098e17	+	3.85663e17i	0.506296	+	0.867444i
$333$			1.57226e15i			0.00346270i
$334$	−3.63740e17	+	6.33467e17i	−0.784452	+	1.36615i
$335$		−	1.48655e17i		−	0.313954i
$336$	2.06549e17	+	1.16664e17i	0.427216	+	0.241302i
$337$	5.64861e17			1.14428			0.572140	−	0.820156i	$-0.306113\pi$
$337$	5.64861e17			1.14428			0.572140	+	0.820156i	$0.306113\pi$
$338$	8.35225e17	+	4.79591e17i	1.65724	+	0.951600i
$339$	−3.61771e17			−0.703131
$340$	−4.20785e17	+	2.45597e17i	−0.801139	+	0.467597i
$341$			2.40224e17i			0.448059i
$342$	−3.77916e16	−	2.17001e16i	−0.0690577	−	0.0396534i
$343$			5.05521e17i			0.905066i
$344$	6.75799e15	+	9.53962e17i	0.0118552	+	1.67348i
$345$	2.50438e16			0.0430493
$346$	−5.76009e15	+	1.00314e16i	−0.00970279	+	0.0168977i
$347$	7.53091e17			1.24320			0.621600	−	0.783335i	$-0.286483\pi$
$347$	7.53091e17			1.24320			0.621600	+	0.783335i	$0.286483\pi$
$348$	−5.87707e17	+	3.43023e17i	−0.950836	+	0.554969i
$349$		−	4.21333e17i		−	0.668109i	−0.942554	−	0.334054i	$-0.891583\pi$
$349$		−	4.21333e17i		−	0.668109i	0.942554	−	0.334054i	$-0.108417\pi$
$350$	8.51305e16	−	1.48258e17i	0.132315	−	0.230431i
$351$		−	1.17884e18i		−	1.79599i
$352$	−1.47822e17	+	8.76880e16i	−0.220770	+	0.130961i
$353$	2.79388e17			0.409058			0.204529	−	0.978861i	$-0.434434\pi$
$353$	2.79388e17			0.409058			0.204529	+	0.978861i	$0.434434\pi$
$354$	−1.39490e16	−	8.00960e15i	−0.0200226	−	0.0114971i
$355$	−3.96055e17			−0.557388
$356$	−6.92457e17	−	1.18640e18i	−0.955526	−	1.63712i
$357$		−	4.78736e17i		−	0.647767i
$358$	−1.47652e17	−	8.47827e16i	−0.195911	−	0.112493i
$359$		−	2.99544e17i		−	0.389762i	−0.980827	−	0.194881i	$-0.937568\pi$
$359$		−	2.99544e17i		−	0.389762i	0.980827	−	0.194881i	$-0.0624321\pi$
$360$	−6.93259e16	+	4.91114e14i	−0.0884663	+	0.000626707i
$361$	−4.79410e17			−0.600007
$362$	2.64767e17	−	4.61101e17i	0.325015	−	0.566025i
$363$	7.25307e17			0.873325
$364$	3.82149e17	+	6.54740e17i	0.451360	+	0.773320i
$365$			1.78564e17i			0.206892i
$366$	5.46077e17	−	9.51013e17i	0.620707	−	1.08098i
$367$		−	4.41188e17i		−	0.491996i	−0.969270	−	0.245998i	$-0.920884\pi$
$367$		−	4.41188e17i		−	0.491996i	0.969270	−	0.245998i	$-0.0791157\pi$
$368$	−5.21522e16	−	2.94569e16i	−0.0570608	−	0.0322294i
$369$	−1.13058e17			−0.121371
$370$	−1.59077e16	−	9.13429e15i	−0.0167570	−	0.00962194i
$371$	8.37374e16			0.0865570
$372$	−1.38945e18	+	8.10974e17i	−1.40943	+	0.822634i
$373$			1.03275e18i			1.02809i	0.857763	+	0.514045i	$0.171854\pi$
$373$			1.03275e18i			1.02809i	−0.857763	+	0.514045i	$0.828146\pi$
$374$	3.00799e17	+	1.72721e17i	0.293883	+	0.168750i
$375$		−	1.03190e18i		−	0.989505i
$376$	1.42348e18	−	1.00841e16i	1.33979	−	0.00949123i
$377$	−2.17470e18			−2.00914
$378$	3.03326e17	−	5.28254e17i	0.275085	−	0.479071i
$379$	1.28866e18			1.14726			0.573631	−	0.819114i	$-0.305534\pi$
$379$	1.28866e18			1.14726			0.573631	+	0.819114i	$0.305534\pi$
$380$	4.39112e17	−	2.56294e17i	0.383787	−	0.224003i
$381$		−	4.32115e17i		−	0.370787i
$382$	−6.57148e17	+	1.14445e18i	−0.553630	+	0.964166i
$383$			1.79643e18i			1.48600i	0.669293	+	0.742999i	$0.266597\pi$
$383$			1.79643e18i			1.48600i	−0.669293	+	0.742999i	$0.733403\pi$
$384$	−1.00622e18	−	5.58973e17i	−0.817287	−	0.454017i
$385$	1.18674e17			0.0946521
$386$	−2.06264e17	−	1.18438e17i	−0.161552	−	0.0927639i
$387$	2.73952e17			0.210716
$388$	7.73711e16	+	1.32561e17i	0.0584463	+	0.100137i
$389$			1.34353e18i			0.996778i	0.866953	+	0.498389i	$0.166075\pi$
$389$			1.34353e18i			0.996778i	−0.866953	+	0.498389i	$0.833925\pi$
$390$	1.33382e18	+	7.65888e17i	0.971953	+	0.558101i
$391$			1.20878e17i			0.0865186i
$392$	−7.30071e15	−	1.03057e18i	−0.00513290	−	0.724563i
$393$	7.38860e17			0.510286
$394$	−6.17138e17	+	1.07477e18i	−0.418705	+	0.729190i
$395$	1.44181e18			0.961009
$396$	2.48796e16	+	4.26266e16i	0.0162921	+	0.0279135i
$397$			1.67844e18i			1.07987i	0.841707	+	0.539934i	$0.181551\pi$
$397$			1.67844e18i			1.07987i	−0.841707	+	0.539934i	$0.818449\pi$
$398$	1.18059e18	−	2.05604e18i	0.746306	−	1.29972i
$399$			4.99587e17i			0.310313i
$400$	−4.07972e17	+	7.22298e17i	−0.249006	+	0.440856i
$401$	−2.25508e18			−1.35254			−0.676272	−	0.736652i	$-0.736406\pi$
$401$	−2.25508e18			−1.35254			−0.676272	+	0.736652i	$0.736406\pi$
$402$	−6.14643e17	−	3.52932e17i	−0.362277	−	0.208022i
$403$	−5.14142e18			−2.97816
$404$	1.31164e18	−	7.65557e17i	0.746698	−	0.435821i
$405$		−	1.07774e18i		−	0.603018i
$406$	−9.74514e17	−	5.59572e17i	−0.535927	−	0.307733i
$407$			1.30593e16i			0.00705927i
$408$	1.64558e16	+	2.32291e18i	0.00874375	+	1.23427i
$409$	2.72084e18			1.42115			0.710575	−	0.703621i	$-0.248435\pi$
$409$	2.72084e18			1.42115			0.710575	+	0.703621i	$0.248435\pi$
$410$	6.56826e17	−	1.14389e18i	0.337259	−	0.587348i
$411$	7.86057e17			0.396791
$412$	2.17568e18	−	1.26986e18i	1.07973	−	0.630198i
$413$		−	2.65625e16i		−	0.0129604i
$414$	−8.56488e15	+	1.49160e16i	−0.00410884	+	0.00715568i
$415$			1.49610e18i			0.705708i
$416$	−1.87676e18	−	3.16378e18i	−0.870471	−	1.46741i
$417$	1.37486e18			0.627055
$418$	−3.13900e17	−	1.80243e17i	−0.140785	−	0.0808397i
$419$	−1.83280e18			−0.808384			−0.404192	−	0.914674i	$-0.632447\pi$
$419$	−1.83280e18			−0.808384			−0.404192	+	0.914674i	$0.632447\pi$
$420$	4.00633e17	+	6.86410e17i	0.173781	+	0.297741i
$421$		−	3.98490e18i		−	1.69998i	−0.526801	−	0.849989i	$-0.676609\pi$
$421$		−	3.98490e18i		−	1.69998i	0.526801	−	0.849989i	$-0.323391\pi$
$422$	3.89251e17	+	2.23510e17i	0.163321	+	0.0937801i
$423$		−	4.08784e17i		−	0.168699i
$424$	−4.06308e17	+	2.87834e15i	−0.164928	+	0.00116837i
$425$	1.67413e18			0.668448
$426$	−9.40302e17	+	1.63757e18i	−0.369318	+	0.643180i
$427$	1.81097e18			0.699708
$428$	5.60022e17	+	9.59493e17i	0.212862	+	0.364700i
$429$		−	1.09499e18i		−	0.409459i
$430$	−1.59157e18	+	2.77177e18i	−0.585525	+	1.01971i
$431$		−	2.22421e18i		−	0.805074i	−0.915404	−	0.402537i	$-0.868128\pi$
$431$		−	2.22421e18i		−	0.805074i	0.915404	−	0.402537i	$-0.131872\pi$
$432$	−1.45363e18	+	2.57360e18i	−0.517689	+	0.916548i
$433$	3.46168e18			1.21303			0.606515	−	0.795072i	$-0.292567\pi$
$433$	3.46168e18			1.21303			0.606515	+	0.795072i	$0.292567\pi$
$434$	−2.30394e18	−	1.32294e18i	−0.794408	−	0.456154i
$435$	−2.27989e18			−0.773552
$436$	3.33375e18	−	1.94579e18i	1.11308	−	0.649668i
$437$		−	1.26142e17i		−	0.0414468i
$438$	7.38309e17	+	4.23941e17i	0.238737	+	0.137084i
$439$			4.20507e17i			0.133820i	0.997759	+	0.0669101i	$0.0213141\pi$
$439$			4.20507e17i			0.133820i	−0.997759	+	0.0669101i	$0.978686\pi$
$440$	−5.75826e17	+	4.07923e15i	−0.180353	+	0.00127764i
$441$	−2.95953e17			−0.0912330
$442$	−3.69668e18	+	6.43790e18i	−1.12165	+	1.95339i
$443$	8.67951e17			0.259220			0.129610	−	0.991565i	$-0.458627\pi$
$443$	8.67951e17			0.259220			0.129610	+	0.991565i	$0.458627\pi$
$444$	−7.55351e16	+	4.40871e16i	−0.0222059	+	0.0129608i
$445$		−	4.60239e18i		−	1.33187i
$446$	3.42571e16	−	5.96600e16i	0.00975904	−	0.0169957i
$447$		−	8.49605e17i		−	0.238267i
$448$	−2.69301e16	−	1.90064e18i	−0.00743518	−	0.524751i
$449$	−4.11513e18			−1.11856			−0.559281	−	0.828978i	$-0.688923\pi$
$449$	−4.11513e18			−1.11856			−0.559281	+	0.828978i	$0.688923\pi$
$450$	2.06584e17	+	1.18622e17i	0.0552852	+	0.0317451i
$451$	−9.39066e17			−0.247435
$452$	1.46127e18	+	2.50362e18i	0.379107	+	0.649529i
$453$			3.86218e18i			0.986609i
$454$	3.51266e17	+	2.01699e17i	0.0883578	+	0.0507356i
$455$			2.53994e18i			0.629134i
$456$	−1.71725e16	−	2.42408e18i	−0.00418870	−	0.591280i
$457$	3.60354e18			0.865599			0.432799	−	0.901490i	$-0.357526\pi$
$457$	3.60354e18			0.865599			0.432799	+	0.901490i	$0.357526\pi$
$458$	1.24234e18	−	2.16358e18i	0.293888	−	0.511816i
$459$	5.96506e18			1.38972
$460$	−1.01157e17	−	1.73314e17i	−0.0232109	−	0.0397675i
$461$			7.63970e18i			1.72651i	0.504766	+	0.863256i	$0.331579\pi$
$461$			7.63970e18i			1.72651i	−0.504766	+	0.863256i	$0.668421\pi$
$462$	2.81752e17	−	4.90681e17i	0.0627153	−	0.109221i
$463$			2.42998e18i			0.532766i	0.963867	+	0.266383i	$0.0858286\pi$
$463$			2.42998e18i			0.532766i	−0.963867	+	0.266383i	$0.914171\pi$
$464$	4.74774e18	+	2.68164e18i	1.02532	+	0.579128i
$465$	−5.39011e18			−1.14664
$466$	−5.76582e18	−	3.31077e18i	−1.20826	−	0.693789i
$467$	−5.15505e18			−1.06418			−0.532089	−	0.846688i	$-0.678593\pi$
$467$	−5.15505e18			−1.06418			−0.532089	+	0.846688i	$0.678593\pi$
$468$	−9.12323e17	+	5.32490e17i	−0.185536	+	0.108291i
$469$		−	1.17044e18i		−	0.234498i
$470$	4.13596e18	+	2.37489e18i	0.816378	+	0.468769i
$471$		−	1.94316e18i		−	0.377888i
$472$	9.13043e14	+	1.28886e17i	0.000174943	+	0.0246951i
$473$	2.27547e18			0.429578
$474$	3.42309e18	−	5.96143e18i	0.636752	−	1.10893i
$475$	−1.74705e18			−0.320221
$476$	−3.31306e18	+	1.93372e18i	−0.598386	+	0.349256i
$477$			1.16681e17i			0.0207668i
$478$	3.02675e18	−	5.27120e18i	0.530862	−	0.924515i
$479$			1.44418e15i			0.000249617i	1.00000		0.000124808i	$3.97278e-5\pi$
$479$			1.44418e15i			0.000249617i	−1.00000		0.000124808i	$0.999960\pi$
$480$	−1.96753e18	−	3.31680e18i	−0.335145	−	0.564977i
$481$	−2.79504e17			−0.0469216
$482$	5.09138e18	+	2.92350e18i	0.842377	+	0.483698i
$483$	1.97183e17			0.0321543
$484$	−2.92967e18	−	5.01944e18i	−0.470870	−	0.806748i
$485$			5.14244e17i			0.0814662i
$486$	1.38983e18	+	7.98051e17i	0.217025	+	0.124617i
$487$		−	5.22680e18i		−	0.804513i	−0.915527	−	0.402256i	$-0.868226\pi$
$487$		−	5.22680e18i		−	0.804513i	0.915527	−	0.402256i	$-0.131774\pi$
$488$	−8.78714e18	+	6.22493e16i	−1.33324	+	0.00944486i
$489$	−8.62477e18			−1.28999
$490$	1.71938e18	−	2.99436e18i	0.253513	−	0.441501i
$491$	1.26871e19			1.84413			0.922066	−	0.387032i	$-0.126500\pi$
$491$	1.26871e19			1.84413			0.922066	+	0.387032i	$0.126500\pi$
$492$	−3.17021e18	−	5.43156e18i	−0.454288	−	0.778338i
$493$		−	1.10043e19i		−	1.55465i
$494$	3.85768e18	−	6.71829e18i	0.537326	−	0.935771i
$495$			1.65362e17i			0.0227090i
$496$	1.12246e19	+	6.33992e18i	1.51984	+	0.858444i
$497$	−3.11835e18			−0.416323
$498$	6.18594e18	+	3.55200e18i	0.814329	+	0.467593i
$499$	−1.51282e19			−1.96374			−0.981870	−	0.189557i	$-0.939295\pi$
$499$	−1.51282e19			−1.96374			−0.981870	+	0.189557i	$0.939295\pi$
$500$	−7.14119e18	+	4.16806e18i	−0.914072	+	0.533511i
$501$			1.16686e19i			1.47284i
$502$	−8.23290e18	−	4.72738e18i	−1.02477	−	0.588430i
$503$			5.59984e18i			0.687385i	0.939082	+	0.343692i	$0.111678\pi$
$503$			5.59984e18i			0.687385i	−0.939082	+	0.343692i	$0.888322\pi$
$504$	−5.45839e17	+	3.86680e15i	−0.0660771	+	0.000468099i
$505$	5.08825e18			0.607475
$506$	−7.11405e16	+	1.23894e17i	−0.00837652	+	0.0145880i
$507$	1.53850e19			1.78666
$508$	−2.99043e18	+	1.74540e18i	−0.342521	+	0.199917i
$509$			1.36938e19i			1.54703i	0.633780	+	0.773514i	$0.281503\pi$
$509$			1.36938e19i			1.54703i	−0.633780	+	0.773514i	$0.718497\pi$
$510$	−3.87548e18	+	6.74929e18i	−0.431852	+	0.752085i
$511$			1.40593e18i			0.154532i
$512$	1.96001e17	+	9.22129e18i	0.0212504	+	0.999774i
$513$	−6.22486e18			−0.665745
$514$	8.15092e18	+	4.68031e18i	0.859934	+	0.493779i
$515$	8.44011e18			0.878410
$516$	7.68177e18	+	1.31613e19i	0.788703	+	1.35130i
$517$		−	3.39539e18i		−	0.343919i
$518$	−1.25250e17	−	7.19191e16i	−0.0125161	−	0.00718681i
$519$			1.84781e17i			0.0182174i
$520$	−8.73063e16	−	1.23242e19i	−0.00849224	−	1.19877i
$521$	−5.60131e18			−0.537559			−0.268779	−	0.963202i	$-0.586620\pi$
$521$	−5.60131e18			−0.537559			−0.268779	+	0.963202i	$0.586620\pi$
$522$	7.79714e17	−	1.35790e18i	0.0738315	−	0.128580i
$523$	−3.65474e18			−0.341464			−0.170732	−	0.985317i	$-0.554613\pi$
$523$	−3.65474e18			−0.341464			−0.170732	+	0.985317i	$0.554613\pi$
$524$	−2.98441e18	−	5.11323e18i	−0.275131	−	0.471386i
$525$		−	2.73094e18i		−	0.248426i
$526$	−9.65608e18	+	1.68164e19i	−0.866764	+	1.50950i
$527$		−	2.60162e19i		−	2.30446i
$528$	−1.35024e18	+	2.39055e18i	−0.118025	+	0.208959i
$529$	1.15430e19			0.995705
$530$	−1.18054e18	−	6.77874e17i	−0.100496	−	0.0577056i
$531$	3.70125e16			0.00310947
$532$	3.45736e18	−	2.01794e18i	0.286657	−	0.167312i
$533$		−	2.00985e19i		−	1.64465i
$534$	−1.90295e19	−	1.09268e19i	−1.53687	−	0.882482i
$535$			3.72217e18i			0.296701i
$536$	4.02320e16	+	5.67917e18i	0.00316532	+	0.446819i
$537$	−2.71979e18			−0.211210
$538$	−3.12985e17	+	5.45075e17i	−0.0239910	+	0.0417811i
$539$	−2.45820e18			−0.185993
$540$	−8.55268e18	+	4.99189e18i	−0.638772	+	0.372828i
$541$			1.83072e18i			0.134971i	0.997720	+	0.0674856i	$0.0214977\pi$
$541$			1.83072e18i			0.134971i	−0.997720	+	0.0674856i	$0.978502\pi$
$542$	−2.72931e18	+	4.75319e18i	−0.198636	+	0.345932i
$543$		−	8.49359e18i		−	0.610228i
$544$	1.60091e19	−	9.49661e18i	1.13547	−	0.673560i
$545$	1.29326e19			0.905549
$546$	1.05019e19	+	6.03024e18i	0.725969	+	0.416856i
$547$	−4.19929e18			−0.286593			−0.143296	−	0.989680i	$-0.545770\pi$
$547$	−4.19929e18			−0.286593			−0.143296	+	0.989680i	$0.545770\pi$
$548$	−3.17505e18	−	5.43986e18i	−0.213937	−	0.366542i
$549$			2.52343e18i			0.167875i
$550$	1.71590e18	+	9.85282e17i	0.112708	+	0.0647175i
$551$			1.14835e19i			0.744756i
$552$	−9.56765e17	+	6.77785e15i	−0.0612677	+	0.000434029i
$553$	1.13521e19			0.717795
$554$	1.73881e18	−	3.02820e18i	0.108564	−	0.189067i
$555$	−2.93024e17			−0.0180656
$556$	−5.55334e18	−	9.51461e18i	−0.338089	−	0.579252i
$557$		−	2.82092e19i		−	1.69592i	−0.530061	−	0.847959i	$-0.677831\pi$
$557$		−	2.82092e19i		−	1.69592i	0.530061	−	0.847959i	$-0.322169\pi$
$558$	1.84340e18	−	3.21034e18i	0.109441	−	0.190595i
$559$			4.87010e19i			2.85532i
$560$	3.13201e18	−	5.54511e18i	0.181346	−	0.321066i
$561$	5.54079e18			0.316834
$562$	−1.07660e19	−	6.18188e18i	−0.607993	−	0.349113i
$563$	−2.92074e19			−1.62905			−0.814526	−	0.580128i	$-0.803003\pi$
$563$	−2.92074e19			−1.62905			−0.814526	+	0.580128i	$0.803003\pi$
$564$	1.96389e19	−	1.14626e19i	1.08184	−	0.631434i
$565$			9.71229e18i			0.528424i
$566$	6.65673e18	+	3.82234e18i	0.357722	+	0.205406i
$567$		−	8.48564e18i		−	0.450405i
$568$	1.51308e19	−	1.07188e17i	0.793273	−	0.00561965i
$569$	−1.47026e19			−0.761390			−0.380695	−	0.924701i	$-0.624315\pi$
$569$	−1.47026e19			−0.761390			−0.380695	+	0.924701i	$0.624315\pi$
$570$	4.04427e18	−	7.04324e18i	0.206879	−	0.360287i
$571$	−3.05394e19			−1.54315			−0.771574	−	0.636140i	$-0.780530\pi$
$571$	−3.05394e19			−1.54315			−0.771574	+	0.636140i	$0.780530\pi$
$572$	−7.57782e18	+	4.42291e18i	−0.378244	+	0.220768i
$573$			2.10810e19i			1.03946i
$574$	5.17154e18	−	9.00641e18i	0.251905	−	0.438701i
$575$			6.89546e17i			0.0331809i
$576$	2.64837e18	−	3.75247e16i	0.125899	−	0.00178386i
$577$	2.42531e19			1.13903			0.569517	−	0.821979i	$-0.307130\pi$
$577$	2.42531e19			1.13903			0.569517	+	0.821979i	$0.307130\pi$
$578$	−1.38862e19	−	7.97356e18i	−0.644302	−	0.369962i
$579$	−3.79942e18			−0.174168
$580$	9.20897e18	+	1.57778e19i	0.417076	+	0.714582i
$581$			1.17796e19i			0.527106i
$582$	2.12624e18	+	1.22090e18i	0.0940053	+	0.0539784i
$583$			9.69158e17i			0.0423365i
$584$	−4.83266e16	−	6.82181e18i	−0.00208591	−	0.294449i
$585$	−3.53918e18			−0.150942
$586$	−1.69984e19	+	2.96033e19i	−0.716349	+	1.24755i
$587$	3.53344e19			1.47140			0.735701	−	0.677307i	$-0.236853\pi$
$587$	3.53344e19			1.47140			0.735701	+	0.677307i	$0.236853\pi$
$588$	−8.29868e18	−	1.42182e19i	−0.341482	−	0.585066i
$589$			2.71493e19i			1.10396i
$590$	−2.15030e17	+	3.74482e17i	−0.00864040	+	0.0150476i
$591$			1.97975e19i			0.786135i
$592$	6.10204e17	+	3.44658e17i	0.0239455	+	0.0135250i
$593$	2.11027e18			0.0818381			0.0409190	−	0.999162i	$-0.486971\pi$
$593$	2.11027e18			0.0818381			0.0409190	+	0.999162i	$0.486971\pi$
$594$	6.11389e18	+	3.51063e18i	0.234322	+	0.134549i
$595$	−1.28524e19			−0.486816
$596$	−5.87964e18	+	3.43173e18i	−0.220103	+	0.128467i
$597$		−	3.78727e19i		−	1.40122i
$598$	−2.65166e18	−	1.52260e18i	−0.0969636	−	0.0556771i
$599$		−	2.78100e19i		−	1.00511i	−0.864545	−	0.502555i	$-0.832393\pi$
$599$		−	2.78100e19i		−	1.00511i	0.864545	−	0.502555i	$-0.167607\pi$
$600$	9.38719e16	+	1.32510e19i	0.00335333	+	0.473358i
$601$	−2.45714e19			−0.867577			−0.433788	−	0.901015i	$-0.642823\pi$
$601$	−2.45714e19			−0.867577			−0.433788	+	0.901015i	$0.642823\pi$
$602$	−1.25312e19	+	2.18236e19i	−0.437339	+	0.761642i
$603$	1.63090e18			0.0562609
$604$	2.67280e19	−	1.56002e19i	0.911397	−	0.531950i
$605$		−	1.94719e19i		−	0.656329i
$606$	1.20804e19	−	2.10384e19i	0.402505	−	0.700977i
$607$		−	1.00281e19i		−	0.330293i	−0.986269	−	0.165147i	$-0.947190\pi$
$607$		−	1.00281e19i		−	0.330293i	0.986269	−	0.165147i	$-0.0528097\pi$
$608$	−1.67063e19	+	9.91021e18i	−0.543946	+	0.322669i
$609$	−1.79508e19			−0.577780
$610$	−2.55313e19	−	1.46602e19i	−0.812390	−	0.466479i
$611$	7.26704e19			2.28596
$612$	−2.69446e18	−	4.61646e18i	−0.0837939	−	0.143565i
$613$			1.48391e19i			0.456232i	0.973634	+	0.228116i	$0.0732565\pi$
$613$			1.48391e19i			0.456232i	−0.973634	+	0.228116i	$0.926744\pi$
$614$	4.29212e19	+	2.46456e19i	1.30465	+	0.749137i
$615$		−	2.10707e19i		−	0.633216i
$616$	−4.53378e18	+	3.21179e16i	−0.134709	+	0.000954294i
$617$	−5.12905e18			−0.150675			−0.0753374	−	0.997158i	$-0.524003\pi$
$617$	−5.12905e18			−0.150675			−0.0753374	+	0.997158i	$0.524003\pi$
$618$	2.00382e19	−	3.48973e19i	0.582023	−	1.01361i
$619$	−4.00661e18			−0.115065			−0.0575325	−	0.998344i	$-0.518323\pi$
$619$	−4.00661e18			−0.115065			−0.0575325	+	0.998344i	$0.518323\pi$
$620$	2.17718e19	+	3.73019e19i	0.618233	+	1.05923i
$621$			2.45690e18i			0.0689838i
$622$	−1.07356e19	+	1.86963e19i	−0.298052	+	0.519068i
$623$		−	3.62370e19i		−	0.994801i
$624$	−5.11641e19	−	2.88988e19i	−1.38891	−	0.784489i
$625$	−8.84102e18			−0.237324
$626$	−7.09845e18	−	4.07597e18i	−0.188427	−	0.108196i
$627$	−5.78211e18			−0.151780
$628$	−1.34475e19	+	7.84885e18i	−0.349080	+	0.203746i
$629$		−	1.41432e18i		−	0.0363073i
$630$	−1.58595e18	−	9.10664e17i	−0.0402630	−	0.0231193i
$631$			8.02278e18i			0.201428i	0.994915	+	0.100714i	$0.0321127\pi$
$631$			8.02278e18i			0.201428i	−0.994915	+	0.100714i	$0.967887\pi$
$632$	−5.50823e19	+	3.90210e17i	−1.36771	+	0.00968901i
$633$	7.17010e18			0.176076
$634$	1.57997e19	−	2.75158e19i	0.383729	−	0.668277i
$635$	−1.16008e19			−0.278657
$636$	−5.60561e18	+	3.27179e18i	−0.133175	+	0.0777295i
$637$		−	5.26121e19i		−	1.23626i
$638$	6.47637e18	−	1.12788e19i	0.150517	−	0.262131i
$639$		−	4.34515e18i		−	0.0998846i
$640$	−1.50064e19	+	2.70135e19i	−0.341207	+	0.614215i
$641$	4.63741e18			0.104296			0.0521482	−	0.998639i	$-0.483393\pi$
$641$	4.63741e18			0.104296			0.0521482	+	0.998639i	$0.483393\pi$
$642$	1.53900e19	+	8.83705e18i	0.342369	+	0.196590i
$643$	6.78542e19			1.49314			0.746569	−	0.665307i	$-0.231700\pi$
$643$	6.78542e19			1.49314			0.746569	+	0.665307i	$0.231700\pi$
$644$	−7.96464e17	−	1.36459e18i	−0.0173366	−	0.0297031i
$645$			5.10566e19i			1.09935i
$646$	3.39953e19	+	1.95203e19i	0.724088	+	0.415776i
$647$		−	2.38418e19i		−	0.502354i	−0.967941	−	0.251177i	$-0.919182\pi$
$647$		−	2.38418e19i		−	0.502354i	0.967941	−	0.251177i	$-0.0808176\pi$
$648$	2.91680e17	+	4.11737e19i	0.00607970	+	0.858213i
$649$	3.07428e17			0.00633915
$650$	−2.10877e19	+	3.67249e19i	−0.430165	+	0.749147i
$651$	−4.24392e19			−0.856446
$652$	3.48373e19	+	5.96872e19i	0.695522	+	1.19165i
$653$			6.18943e19i			1.22253i	0.791427	+	0.611263i	$0.209338\pi$
$653$			6.18943e19i			1.22253i	−0.791427	+	0.611263i	$0.790662\pi$
$654$	3.07043e19	−	5.34726e19i	0.600005	−	1.04493i
$655$		−	1.98358e19i		−	0.383495i
$656$	−2.47836e19	+	4.38784e19i	−0.474064	+	0.839313i
$657$	−1.95904e18			−0.0370754
$658$	3.25646e19	+	1.86988e19i	0.609768	+	0.350132i
$659$	−1.43861e19			−0.266530			−0.133265	−	0.991080i	$-0.542546\pi$
$659$	−1.43861e19			−0.266530			−0.133265	+	0.991080i	$0.542546\pi$
$660$	−7.94436e18	+	4.63684e18i	−0.145630	+	0.0849991i
$661$			3.46867e18i			0.0629149i	0.999505	+	0.0314574i	$0.0100149\pi$
$661$			3.46867e18i			0.0629149i	−0.999505	+	0.0314574i	$0.989985\pi$
$662$	−3.04722e19	−	1.74973e19i	−0.546887	−	0.314026i
$663$			1.18588e20i			2.10593i
$664$	−4.04905e17	−	5.71567e19i	−0.00711503	−	1.00436i
$665$	1.34121e19			0.233210
$666$	1.00213e17	−	1.74524e17i	0.00172426	−	0.00300287i
$667$	4.53246e18			0.0771708
$668$	8.07519e19	−	4.71320e19i	1.36056	−	0.794110i
$669$		−	1.09895e18i		−	0.0183230i
$670$	−9.47498e18	+	1.65010e19i	−0.156334	+	0.272262i
$671$			2.09598e19i			0.342239i
$672$	−1.54914e19	−	2.61149e19i	−0.250326	−	0.421992i
$673$	−1.04446e20			−1.67028			−0.835138	−	0.550040i	$-0.814612\pi$
$673$	−1.04446e20			−1.67028			−0.835138	+	0.550040i	$0.814612\pi$
$674$	−6.27008e19	−	3.60032e19i	−0.992324	−	0.569799i
$675$	3.40276e19			0.532973
$676$	−6.21435e19	−	1.06471e20i	−0.963316	−	1.65046i
$677$		−	7.96942e18i		−	0.122266i	−0.998130	−	0.0611331i	$-0.980529\pi$
$677$		−	7.96942e18i		−	0.122266i	0.998130	−	0.0611331i	$-0.0194714\pi$
$678$	4.01574e19	+	2.30586e19i	0.609758	+	0.350127i
$679$			4.04892e18i			0.0608486i
$680$	6.23619e19	−	4.41780e17i	0.927592	−	0.00657119i
$681$	6.47040e18			0.0952580
$682$	1.53114e19	−	2.66653e19i	0.223113	−	0.388558i
$683$	−4.58574e19			−0.661400			−0.330700	−	0.943736i	$-0.607285\pi$
$683$	−4.58574e19			−0.661400			−0.330700	+	0.943736i	$0.607285\pi$
$684$	2.81182e18	+	4.81752e18i	0.0401416	+	0.0687751i
$685$		−	2.11029e19i		−	0.298200i
$686$	3.22209e19	−	5.61139e19i	0.450681	−	0.784877i
$687$		−	3.98536e19i		−	0.551786i
$688$	6.00535e19	−	1.06322e20i	0.823037	−	1.45716i
$689$	−2.07426e19			−0.281402
$690$	−2.77991e18	−	1.59624e18i	−0.0373325	−	0.0214366i
$691$	−1.16590e19			−0.154995			−0.0774973	−	0.996993i	$-0.524693\pi$
$691$	−1.16590e19			−0.154995			−0.0774973	+	0.996993i	$0.524693\pi$
$692$	1.27876e18	−	7.46369e17i	0.0168286	−	0.00982224i
$693$			1.30198e18i			0.0169618i
$694$	−8.35946e19	−	4.80006e19i	−1.07811	−	0.619056i
$695$		−	3.69101e19i		−	0.471250i
$696$	8.71003e19	−	6.17030e17i	1.10092	−	0.00779905i
$697$	1.01701e20			1.27261
$698$	−2.68549e19	+	4.67688e19i	−0.332687	+	0.579386i
$699$	−1.06208e20			−1.30262
$700$	−1.88993e19	+	1.10309e19i	−0.229488	+	0.133944i
$701$			2.46544e19i			0.296393i	0.988958	+	0.148197i	$0.0473469\pi$
$701$			2.46544e19i			0.296393i	−0.988958	+	0.148197i	$0.952653\pi$
$702$	−7.51369e19	+	1.30854e20i	−0.894321	+	1.55749i
$703$			1.47592e18i			0.0173931i
$704$	2.19976e19	−	3.11683e17i	0.256665	−	0.00363668i
$705$	7.61854e19			0.880133
$706$	−3.10127e19	−	1.78077e19i	−0.354737	−	0.203692i
$707$	4.00624e19			0.453734
$708$	1.03785e18	+	1.77816e18i	0.0116386	+	0.0199406i
$709$		−	4.80228e19i		−	0.533241i	−0.963802	−	0.266620i	$-0.914093\pi$
$709$		−	4.80228e19i		−	0.533241i	0.963802	−	0.266620i	$-0.0859070\pi$
$710$	4.39630e19	+	2.52438e19i	0.483369	+	0.277553i
$711$			1.58182e19i			0.172214i
$712$	1.24559e18	+	1.75828e20i	0.0134281	+	1.89552i
$713$	1.07156e19			0.114391
$714$	−3.05137e19	+	5.31407e19i	−0.322558	+	0.561746i
$715$	−2.93967e19			−0.307720
$716$	1.09858e19	+	1.88221e19i	0.113878	+	0.195109i
$717$		−	9.70967e19i		−	0.996714i
$718$	−1.90924e19	+	3.32500e19i	−0.194083	+	0.338003i
$719$			1.67604e20i			1.68726i	0.536923	+	0.843631i	$0.319587\pi$
$719$			1.67604e20i			1.68726i	−0.536923	+	0.843631i	$0.680413\pi$
$720$	7.72662e18	+	4.36418e18i	0.0770304	+	0.0435086i
$721$	6.64534e19			0.656101
$722$	5.32155e19	+	3.05567e19i	0.520328	+	0.298776i
$723$	9.37845e19			0.908161
$724$	−5.87793e19	+	3.43074e19i	−0.563709	+	0.329017i
$725$		−	6.27736e19i		−	0.596227i
$726$	−8.05106e19	−	4.62297e19i	−0.757350	−	0.434875i
$727$		−	1.18078e20i		−	1.10009i	−0.835136	−	0.550043i	$-0.814611\pi$
$727$		−	1.18078e20i		−	1.10009i	0.835136	−	0.550043i	$-0.185389\pi$
$728$	−6.87408e17	−	9.70350e19i	−0.00634301	−	0.895382i
$729$	1.19508e20			1.09221
$730$	1.13813e19	−	1.98210e19i	0.103023	−	0.179418i
$731$	−2.46433e20			−2.20941
$732$	−1.21231e20	+	7.07585e19i	−1.07656	+	0.628349i
$733$			7.99457e19i			0.703181i	0.936154	+	0.351591i	$0.114359\pi$
$733$			7.99457e19i			0.703181i	−0.936154	+	0.351591i	$0.885641\pi$
$734$	−2.81205e19	+	4.89728e19i	−0.244991	+	0.426661i
$735$		−	5.51569e19i		−	0.475980i
$736$	3.91148e18	+	6.59385e18i	0.0334346	+	0.0563631i
$737$	1.35464e19			0.114697
$738$	1.25496e19	+	7.20608e18i	0.105254	+	0.0604372i
$739$	6.36292e19			0.528622			0.264311	−	0.964438i	$-0.414855\pi$
$739$	6.36292e19			0.528622			0.264311	+	0.964438i	$0.414855\pi$
$740$	1.18358e18	+	2.02785e18i	0.00974041	+	0.0166884i
$741$		−	1.23752e20i		−	1.00885i
$742$	−9.29502e18	−	5.33726e18i	−0.0750625	−	0.0431013i
$743$			1.61963e20i			1.29567i	0.761780	+	0.647835i	$0.224326\pi$
$743$			1.61963e20i			1.29567i	−0.761780	+	0.647835i	$0.775674\pi$
$744$	2.05922e20	−	1.45878e18i	1.63190	−	0.0115606i
$745$	−2.28089e19			−0.179065
$746$	6.58252e19	−	1.14637e20i	0.511942	−	0.891564i
$747$	−1.64138e19			−0.126464
$748$	−2.23804e19	−	3.83447e19i	−0.170827	−	0.292681i
$749$			2.93066e19i			0.221612i
$750$	−6.57712e19	+	1.14543e20i	−0.492728	+	0.858103i
$751$		−	1.25011e20i		−	0.927830i	−0.885880	−	0.463915i	$-0.846444\pi$
$751$		−	1.25011e20i		−	0.927830i	0.885880	−	0.463915i	$-0.153556\pi$
$752$	−1.58652e20	−	8.96104e19i	−1.16659	−	0.658921i
$753$	−1.51652e20			−1.10480
$754$	2.41397e20	+	1.38611e20i	1.74234	+	1.00046i
$755$	1.03686e20			0.741466
$756$	−6.73397e19	+	3.93038e19i	−0.477110	+	0.278472i
$757$			6.26907e19i			0.440080i	0.975491	+	0.220040i	$0.0706189\pi$
$757$			6.26907e19i			0.440080i	−0.975491	+	0.220040i	$0.929381\pi$
$758$	−1.43044e20	−	8.21365e19i	−0.994910	−	0.571283i
$759$			2.28215e18i			0.0157272i
$760$	−6.50780e19	+	4.61021e17i	−0.444364	+	0.00314793i
$761$	−8.42696e18			−0.0570136			−0.0285068	−	0.999594i	$-0.509075\pi$
$761$	−8.42696e18			−0.0570136			−0.0285068	+	0.999594i	$0.509075\pi$
$762$	−2.75422e19	+	4.79657e19i	−0.184635	+	0.321548i
$763$	1.01826e20			0.676371
$764$	1.45890e20	−	8.51505e19i	0.960220	−	0.560446i
$765$		−	1.79087e19i		−	0.116797i
$766$	1.14501e20	−	1.99407e20i	0.739958	−	1.28866i
$767$			6.57978e18i			0.0421351i
$768$	7.60646e19	+	1.26182e20i	0.482674	+	0.800696i
$769$	−1.14811e20			−0.721938			−0.360969	−	0.932578i	$-0.617554\pi$
$769$	−1.14811e20			−0.721938			−0.360969	+	0.932578i	$0.617554\pi$
$770$	−1.31731e19	−	7.56405e18i	−0.0820826	−	0.0471324i
$771$	1.50142e20			0.927089
$772$	1.53467e19	+	2.62937e19i	0.0939060	+	0.160890i
$773$			1.30976e20i			0.794208i	0.917774	+	0.397104i	$0.129985\pi$
$773$			1.30976e20i			0.794208i	−0.917774	+	0.397104i	$0.870015\pi$
$774$	−3.04092e19	−	1.74612e19i	−0.182734	−	0.104927i
$775$		−	1.48409e20i		−	0.883789i
$776$	−1.39175e17	−	1.96460e19i	−0.000821352	−	0.115943i
$777$	−2.30713e18			−0.0134935
$778$	8.56337e19	−	1.49134e20i	0.496349	−	0.864410i
$779$	−1.06130e20			−0.609645
$780$	−9.92406e19	−	1.70030e20i	−0.564973	−	0.967975i
$781$		−	3.60911e19i		−	0.203631i
$782$	7.70452e18	−	1.34177e19i	0.0430822	−	0.0750292i
$783$		−	2.23667e20i		−	1.23957i
$784$	−6.48763e19	+	1.14861e20i	−0.356347	+	0.630900i
$785$	−5.21671e19			−0.283994
$786$	−8.20149e19	−	4.70935e19i	−0.442522	−	0.254099i
$787$	1.50747e20			0.806168			0.403084	−	0.915163i	$-0.367938\pi$
$787$	1.50747e20			0.806168			0.403084	+	0.915163i	$0.367938\pi$
$788$	1.37007e20	−	7.99662e19i	0.726206	−	0.423860i
$789$			3.09762e20i			1.62738i
$790$	−1.60044e20	−	9.18980e19i	−0.833390	−	0.478538i
$791$			7.64700e19i			0.394689i
$792$	−4.47535e16	−	6.31742e18i	−0.000228955	−	0.0323194i
$793$	−4.48595e20			−2.27480
$794$	1.06980e20	−	1.86310e20i	0.537725	−	0.936466i
$795$	−2.17459e19			−0.108344
$796$	−2.62095e20	+	1.52976e20i	−1.29440	+	0.755494i
$797$			9.56805e19i			0.468398i	0.972189	+	0.234199i	$0.0752467\pi$
$797$			9.56805e19i			0.468398i	−0.972189	+	0.234199i	$0.924753\pi$
$798$	3.18427e19	−	5.54552e19i	0.154522	−	0.269105i
$799$			3.67721e20i			1.76885i
$800$	9.13236e19	−	5.41733e19i	0.435465	−	0.258318i
$801$	5.04931e19			0.238674
$802$	2.50319e20	+	1.43734e20i	1.17293	+	0.673504i
$803$	−1.62719e19			−0.0755840
$804$	4.57315e19	+	7.83524e19i	0.210583	+	0.360794i
$805$		−	5.29367e18i		−	0.0241649i
$806$	5.70709e20	+	3.27704e20i	2.58267	+	1.48299i
$807$			1.00404e19i			0.0450440i
$808$	−1.94390e20	+	1.37708e18i	−0.864557	+	0.00612464i
$809$	−3.54225e18			−0.0156185			−0.00780925	−	0.999970i	$-0.502486\pi$
$809$	−3.54225e18			−0.0156185			−0.00780925	+	0.999970i	$0.502486\pi$
$810$	−6.86932e19	+	1.19632e20i	−0.300275	+	0.522939i
$811$	1.21038e19			0.0524534			0.0262267	−	0.999656i	$-0.491651\pi$
$811$	1.21038e19			0.0524534			0.0262267	+	0.999656i	$0.491651\pi$
$812$	7.25071e19	+	1.24227e20i	0.311522	+	0.533734i
$813$			8.75550e19i			0.372947i
$814$	8.32376e17	−	1.44961e18i	0.00351519	−	0.00612183i
$815$			2.31545e20i			0.969464i
$816$	1.46231e20	−	2.58897e20i	0.607028	−	1.07472i
$817$	2.57166e20			1.05842
$818$	−3.02019e20	−	1.73421e20i	−1.23243	−	0.707667i
$819$	−2.78658e19			−0.112742
$820$	−1.45818e20	+	8.51088e19i	−0.584944	+	0.341411i
$821$		−	8.54416e19i		−	0.339834i	−0.985458	−	0.169917i	$-0.945650\pi$
$821$		−	8.54416e19i		−	0.339834i	0.985458	−	0.169917i	$-0.0543500\pi$
$822$	−8.72540e19	−	5.01018e19i	−0.344098	−	0.197583i
$823$		−	3.15191e20i		−	1.23247i	−0.787564	−	0.616233i	$-0.788658\pi$
$823$		−	3.15191e20i		−	1.23247i	0.787564	−	0.616233i	$-0.211342\pi$
$824$	−3.22443e20	+	2.28423e18i	−1.25015	+	0.00885624i
$825$	3.16074e19			0.121510
$826$	−1.69304e18	+	2.94849e18i	−0.00645368	+	0.0112393i
$827$	−1.08530e20			−0.410215			−0.205108	−	0.978739i	$-0.565754\pi$
$827$	−1.08530e20			−0.410215			−0.205108	+	0.978739i	$0.565754\pi$
$828$	1.90144e18	−	1.10980e18i	0.00712640	−	0.00415942i
$829$		−	4.56483e19i		−	0.169646i	−0.996396	−	0.0848229i	$-0.972968\pi$
$829$		−	4.56483e19i		−	0.169646i	0.996396	−	0.0848229i	$-0.0270324\pi$
$830$	9.53588e19	−	1.66071e20i	0.351410	−	0.611993i
$831$		−	5.57802e19i		−	0.203832i
$832$	6.67084e18	+	4.70806e20i	0.0241723	+	1.70600i
$833$	2.66223e20			0.956602
$834$	−1.52612e20	−	8.76308e19i	−0.543784	−	0.312244i
$835$	3.13261e20			1.10688
$836$	2.33552e19	+	4.00147e19i	0.0818350	+	0.140209i
$837$		−	5.28793e20i		−	1.83742i
$838$	2.03445e20	+	1.16819e20i	0.701034	+	0.402538i
$839$		−	1.81154e20i		−	0.619034i	−0.950894	−	0.309517i	$-0.899833\pi$
$839$		−	1.81154e20i		−	0.619034i	0.950894	−	0.309517i	$-0.100167\pi$
$840$	−7.20658e17	−	1.01728e20i	−0.00244216	−	0.344737i
$841$	−1.15060e20			−0.386680
$842$	−2.53990e20	+	4.42333e20i	−0.846510	+	1.47423i
$843$	−1.98312e20			−0.655474
$844$	−2.89616e19	−	4.96202e19i	−0.0949347	−	0.162653i
$845$		−	4.13034e20i		−	1.34273i
$846$	−2.60551e19	+	4.53759e19i	−0.0840041	+	0.146296i
$847$		−	1.53313e20i		−	0.490224i
$848$	4.52845e19	+	2.55778e19i	0.143608	+	0.0811132i
$849$	1.22619e20			0.385658
$850$	−1.85832e20	−	1.06706e20i	−0.579680	−	0.332856i
$851$	5.82535e17			0.00180225
$852$	2.08751e20	−	1.21841e20i	0.640548	−	0.373865i
$853$			1.77945e20i			0.541555i	0.962642	+	0.270777i	$0.0872808\pi$
$853$			1.77945e20i			0.541555i	−0.962642	+	0.270777i	$0.912719\pi$
$854$	−2.01022e20	−	1.15428e20i	−0.606789	−	0.348422i
$855$			1.86886e19i			0.0559519i
$856$	−1.00737e18	−	1.42200e20i	−0.00299138	−	0.422265i
$857$	2.07445e20			0.610996			0.305498	−	0.952193i	$-0.401177\pi$
$857$	2.07445e20			0.610996			0.305498	+	0.952193i	$0.401177\pi$
$858$	−6.97927e19	+	1.21546e20i	−0.203891	+	0.355084i
$859$	−1.22658e20			−0.355423			−0.177711	−	0.984083i	$-0.556869\pi$
$859$	−1.22658e20			−0.355423			−0.177711	+	0.984083i	$0.556869\pi$
$860$	3.53334e20	−	2.06229e20i	1.01554	−	0.592734i
$861$		−	1.65900e20i		−	0.472961i
$862$	−1.41767e20	+	2.46892e20i	−0.400890	+	0.698163i
$863$		−	4.19874e20i		−	1.17772i	−0.808233	−	0.588862i	$-0.799576\pi$
$863$		−	4.19874e20i		−	1.17772i	0.808233	−	0.588862i	$-0.200424\pi$
$864$	3.25393e20	−	1.93023e20i	0.905340	−	0.537049i
$865$	4.96071e18			0.0136909
$866$	−3.84254e20	−	2.20641e20i	−1.05194	−	0.604033i
$867$	−2.55788e20			−0.694618
$868$	1.71421e20	+	2.93698e20i	0.461770	+	0.791156i
$869$			1.31387e20i			0.351086i
$870$	2.53073e20	+	1.45316e20i	0.670827	+	0.385193i
$871$			2.89929e20i			0.762368i
$872$	−4.94075e20	+	3.50009e18i	−1.28878	+	0.00912986i
$873$	−5.64181e18			−0.0145988
$874$	−8.04007e18	+	1.40021e19i	−0.0206386	+	0.0359428i
$875$	−2.18119e20			−0.555440
$876$	−5.49326e19	−	9.41168e19i	−0.138772	−	0.237760i
$877$			7.53595e20i			1.88860i	0.329079	+	0.944302i	$0.393262\pi$
$877$			7.53595e20i			1.88860i	−0.329079	+	0.944302i	$0.606738\pi$
$878$	2.68023e19	−	4.66772e19i	0.0666363	−	0.116049i
$879$			5.45300e20i			1.34497i
$880$	6.41779e19	+	3.62492e19i	0.157039	+	0.0886993i
$881$	2.02779e20			0.492256			0.246128	−	0.969237i	$-0.420842\pi$
$881$	2.02779e20			0.492256			0.246128	+	0.969237i	$0.420842\pi$
$882$	3.28513e19	+	1.88634e19i	0.0791176	+	0.0454298i
$883$	4.40760e20			1.05312			0.526559	−	0.850138i	$-0.323482\pi$
$883$	4.40760e20			1.05312			0.526559	+	0.850138i	$0.323482\pi$
$884$	8.20678e20	−	4.79001e20i	1.94539	−	1.13546i
$885$			6.89804e18i			0.0162227i
$886$	−9.63444e19	−	5.53215e19i	−0.224797	−	0.129080i
$887$			7.34977e20i			1.70141i	0.525645	+	0.850704i	$0.323824\pi$
$887$			7.34977e20i			1.70141i	−0.525645	+	0.850704i	$0.676176\pi$
$888$	1.11946e19	−	7.93039e16i	0.0257109	−	0.000182139i
$889$	−9.13390e19			−0.208134
$890$	−2.93347e20	+	5.10875e20i	−0.663211	+	1.15501i
$891$	9.82109e19			0.220301
$892$	−7.60523e18	+	4.43890e18i	−0.0169262	+	0.00987919i
$893$		−	3.83736e20i		−	0.847369i
$894$	−5.41522e19	+	9.43079e19i	−0.118646	+	0.206626i
$895$			7.30167e19i			0.158731i
$896$	−1.18154e20	+	2.12691e20i	−0.254854	+	0.458768i
$897$	−4.88441e19			−0.104536
$898$	4.56788e20	+	2.62291e20i	0.970020	+	0.556992i
$899$	−9.75509e20			−2.05548
$900$	−1.53705e19	−	2.63345e19i	−0.0321360	−	0.0550590i
$901$		−	1.04960e20i		−	0.217746i
$902$	1.04238e20	+	5.98543e19i	0.214576	+	0.123211i
$903$			4.01996e20i			0.821121i
$904$	−2.62853e18	−	3.71045e20i	−0.00532763	−	0.752052i
$905$	−2.28023e20			−0.458605
$906$	2.46168e20	−	4.28710e20i	0.491286	−	0.855591i
$907$	6.54832e19			0.129682			0.0648409	−	0.997896i	$-0.479346\pi$
$907$	6.54832e19			0.129682			0.0648409	+	0.997896i	$0.479346\pi$
$908$	−2.61353e19	−	4.47780e19i	−0.0513602	−	0.0879962i
$909$			5.58235e19i			0.108860i
$910$	1.61891e20	−	2.81938e20i	0.313280	−	0.545587i
$911$		−	8.46303e20i		−	1.62516i	−0.582847	−	0.812582i	$-0.698061\pi$
$911$		−	8.46303e20i		−	1.62516i	0.582847	−	0.812582i	$-0.301939\pi$
$912$	−1.52600e20	+	2.70172e20i	−0.290797	+	0.514846i
$913$	−1.36335e20			−0.257817
$914$	−4.00001e20	−	2.29683e20i	−0.750650	−	0.431028i
$915$	−4.70293e20			−0.875833
$916$	−2.75804e20	+	1.60977e20i	−0.509721	+	0.297506i
$917$		−	1.56178e20i		−	0.286440i
$918$	−6.62134e20	−	3.80202e20i	−1.20517	−	0.692014i
$919$		−	1.12189e20i		−	0.202647i	−0.994854	−	0.101323i	$-0.967692\pi$
$919$		−	1.12189e20i		−	0.202647i	0.994854	−	0.101323i	$-0.0323077\pi$
$920$	1.81961e17	+	2.56858e19i	0.000326185	+	0.0460445i
$921$	7.90620e20			1.40653
$922$	4.86939e20	−	8.48022e20i	0.859723	−	1.49724i
$923$	7.72446e20			1.35349
$924$	−6.25501e19	+	3.65083e19i	−0.108774	+	0.0634874i
$925$		−	8.06799e18i		−	0.0139243i
$926$	1.54882e20	−	2.69733e20i	0.265293	−	0.462016i
$927$			9.25970e19i			0.157412i
$928$	−3.56087e20	−	6.00280e20i	−0.600786	−	1.01279i
$929$	2.54705e20			0.426508			0.213254	−	0.976997i	$-0.431594\pi$
$929$	2.54705e20			0.426508			0.213254	+	0.976997i	$0.431594\pi$
$930$	5.98313e20	+	3.43555e20i	0.994370	+	0.570973i
$931$	−2.77818e20			−0.458261
$932$	4.28996e20	+	7.35004e20i	0.702331	+	1.20331i
$933$			3.44391e20i			0.559604i
$934$	5.72221e20	+	3.28573e20i	0.922860	+	0.529912i
$935$		−	1.48751e20i		−	0.238110i
$936$	1.35210e20	−	9.57843e17i	0.214821	−	0.00152182i
$937$	−7.48286e20			−1.18002			−0.590011	−	0.807395i	$-0.700877\pi$
$937$	−7.48286e20			−1.18002			−0.590011	+	0.807395i	$0.700877\pi$
$938$	−7.46015e19	+	1.29921e20i	−0.116769	+	0.203357i
$939$	−1.30755e20			−0.203142
$940$	−3.07729e20	−	5.27236e20i	−0.474541	−	0.813037i
$941$			5.53671e20i			0.847470i	0.905786	+	0.423735i	$0.139281\pi$
$941$			5.53671e20i			0.847470i	−0.905786	+	0.423735i	$0.860719\pi$
$942$	−1.23854e20	+	2.15695e20i	−0.188171	+	0.327706i
$943$			4.18888e19i			0.0631707i
$944$	8.11357e18	−	1.43648e19i	0.0121453	−	0.0215028i
$945$	−2.61231e20			−0.388153
$946$	−2.52581e20	−	1.45034e20i	−0.372532	−	0.213910i
$947$	9.98921e20			1.46245			0.731226	−	0.682136i	$-0.238949\pi$
$947$	9.98921e20			1.46245			0.731226	+	0.682136i	$0.238949\pi$
$948$	−7.59941e20	+	4.43550e20i	−1.10439	+	0.644591i
$949$		−	3.48262e20i		−	0.502392i
$950$	1.93926e20	+	1.11353e20i	0.277696	+	0.159455i
$951$		−	5.06847e20i		−	0.720466i
$952$	4.91008e20	−	3.47837e18i	0.692836	−	0.00490814i
$953$	−5.81895e19			−0.0815069			−0.0407534	−	0.999169i	$-0.512976\pi$
$953$	−5.81895e19			−0.0815069			−0.0407534	+	0.999169i	$0.512976\pi$
$954$	7.43700e18	−	1.29518e19i	0.0103409	−	0.0180091i
$955$	5.65950e20			0.781186
$956$	−6.71952e20	+	3.92194e20i	−0.920731	+	0.537398i
$957$		−	2.07759e20i		−	0.282602i
$958$	9.20495e16	−	1.60307e17i	0.000124298	−	0.000216469i
$959$		−	1.66154e20i		−	0.222731i
$960$	6.99351e18	+	4.93579e20i	0.00930671	+	0.656837i
$961$	−1.54935e21			−2.04685
$962$	3.10255e19	+	1.78151e19i	0.0406906	+	0.0233648i
$963$	−4.08361e19			−0.0531692
$964$	−3.78815e20	−	6.49029e20i	−0.489653	−	0.838929i
$965$			1.02001e20i			0.130892i
$966$	−2.18877e19	−	1.25681e19i	−0.0278844	−	0.0160114i
$967$		−	1.46804e21i		−	1.85675i	−0.371648	−	0.928374i	$-0.621207\pi$
$967$		−	1.46804e21i		−	1.85675i	0.371648	−	0.928374i	$-0.378793\pi$
$968$	5.26989e18	+	7.43900e20i	0.00661719	+	0.934087i
$969$	6.26202e20			0.780635
$970$	3.27769e19	−	5.70822e19i	0.0405664	−	0.0706478i
$971$	1.16650e21			1.43334			0.716670	−	0.697413i	$-0.245666\pi$
$971$	1.16650e21			1.43334			0.716670	+	0.697413i	$0.245666\pi$
$972$	−1.03408e20	−	1.77171e20i	−0.126151	−	0.216136i
$973$		−	2.90613e20i		−	0.351985i
$974$	−3.33146e20	+	5.80185e20i	−0.400610	+	0.697677i
$975$			6.76481e20i			0.807651i
$976$	9.79359e20	+	5.53166e20i	1.16090	+	0.655702i
$977$	−2.95486e20			−0.347757			−0.173878	−	0.984767i	$-0.555630\pi$
$977$	−2.95486e20			−0.347757			−0.173878	+	0.984767i	$0.555630\pi$
$978$	9.57368e20	+	5.49726e20i	1.11868	+	0.642354i
$979$	4.19399e20			0.486574
$980$	−3.81710e20	+	2.22790e20i	−0.439694	+	0.256634i
$981$			1.41885e20i			0.162276i
$982$	−1.40829e21	−	8.08651e20i	−1.59924	−	0.918292i
$983$			1.04368e20i			0.117677i	0.998268	+	0.0588387i	$0.0187398\pi$
$983$			1.04368e20i			0.117677i	−0.998268	+	0.0588387i	$0.981260\pi$
$984$	5.70256e18	+	8.04977e20i	0.00638417	+	0.901193i
$985$	5.31492e20			0.590804
$986$	−7.01390e20	+	1.22150e21i	−0.774143	+	1.34820i
$987$	5.99848e20			0.657387
$988$	−8.56421e20	+	4.99862e20i	−0.931942	+	0.543941i
$989$		−	1.01501e20i		−	0.109672i
$990$	1.05398e19	−	1.83555e19i	0.0113080	−	0.0196933i
$991$			8.51352e19i			0.0906972i	0.998971	+	0.0453486i	$0.0144399\pi$
$991$			8.51352e19i			0.0906972i	−0.998971	+	0.0453486i	$0.985560\pi$
$992$	−8.41858e20	−	1.41918e21i	−0.890548	−	1.50126i
$993$	−5.61305e20			−0.589596
$994$	3.46144e20	+	1.98758e20i	0.361037	+	0.207310i
$995$	−1.01675e21			−1.05306
$996$	−4.60254e20	−	7.88559e20i	−0.473350	−	0.810997i
$997$			9.59960e20i			0.980363i	0.871620	+	0.490182i	$0.163070\pi$
$997$			9.59960e20i			0.980363i	−0.871620	+	0.490182i	$0.836930\pi$
$998$	1.67926e21	+	9.64243e20i	1.70296	+	0.977851i
$999$		−	2.87469e19i		−	0.0289489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.15.d.b.3.1	✓	12
3.2	odd	2		72.15.b.b.19.12		12
4.3	odd	2		32.15.d.b.15.10		12
8.3	odd	2	inner	8.15.d.b.3.2	yes	12
8.5	even	2		32.15.d.b.15.9		12
24.11	even	2		72.15.b.b.19.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.15.d.b.3.1	✓	12	1.1	even	1	trivial
8.15.d.b.3.2	yes	12	8.3	odd	2	inner
32.15.d.b.15.9		12	8.5	even	2
32.15.d.b.15.10		12	4.3	odd	2
72.15.b.b.19.11		12	24.11	even	2
72.15.b.b.19.12		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-111.002 - 63.7381i) q^{2} -2044.69 q^{3} +(8258.92 + 14150.1i) q^{4} +54892.6i q^{5} +(226964. + 130324. i) q^{6} +432198. i q^{7} +(-14856.1 - 2.09710e6i) q^{8} -602230. q^{9} +(3.49875e6 - 6.09319e6i) q^{10} -5.00217e6 q^{11} +(-1.68869e7 - 2.89325e7i) q^{12} -1.07060e8i q^{13} +(2.75475e7 - 4.79749e7i) q^{14} -1.12238e8i q^{15} +(-1.32016e8 + 2.33729e8i) q^{16} +5.41735e8 q^{17} +(6.68488e7 + 3.83850e7i) q^{18} -5.65329e8 q^{19} +(-7.76736e8 + 4.53353e8i) q^{20} -8.83710e8i q^{21} +(5.55251e8 + 3.18829e8i) q^{22} +2.23131e8i q^{23} +(3.03761e7 + 4.28791e9i) q^{24} +3.09032e9 q^{25} +(-6.82378e9 + 1.18839e10i) q^{26} +1.10110e10 q^{27} +(-6.11566e9 + 3.56949e9i) q^{28} -2.03130e10i q^{29} +(-7.15384e9 + 1.24587e10i) q^{30} -4.80239e10i q^{31} +(2.95515e10 - 1.75300e10i) q^{32} +1.02279e10 q^{33} +(-6.01337e10 - 3.45291e10i) q^{34} -2.37245e10 q^{35} +(-4.97377e9 - 8.52163e9i) q^{36} -2.61073e9i q^{37} +(6.27527e10 + 3.60330e10i) q^{38} +2.18903e11i q^{39} +(1.15115e11 - 8.15491e8i) q^{40} +1.87732e11 q^{41} +(-5.63259e10 + 9.80936e10i) q^{42} -4.54896e11 q^{43} +(-4.13125e10 - 7.07813e10i) q^{44} -3.30580e10i q^{45} +(1.42219e10 - 2.47680e10i) q^{46} +6.78784e11i q^{47} +(2.69931e11 - 4.77903e11i) q^{48} +4.91428e11 q^{49} +(-3.43032e11 - 1.96971e11i) q^{50} -1.10768e12 q^{51} +(1.51491e12 - 8.84197e11i) q^{52} -1.93748e11i q^{53} +(-1.22225e12 - 7.01822e11i) q^{54} -2.74582e11i q^{55} +(9.06363e11 - 6.42079e9i) q^{56} +1.15592e12 q^{57} +(-1.29471e12 + 2.25479e12i) q^{58} -6.14590e10 q^{59} +(1.58818e12 - 9.26965e11i) q^{60} -4.19014e12i q^{61} +(-3.06095e12 + 5.33075e12i) q^{62} -2.60283e11i q^{63} +(-4.39761e12 + 6.23096e10i) q^{64} +5.87679e12 q^{65} +(-1.13531e12 - 6.51904e11i) q^{66} -2.70811e12 q^{67} +(4.47414e12 + 7.66561e12i) q^{68} -4.56233e11i q^{69} +(2.63347e12 + 1.51215e12i) q^{70} +7.21510e12i q^{71} +(8.94681e9 + 1.26294e12i) q^{72} +3.25297e12 q^{73} +(-1.66403e11 + 2.89797e11i) q^{74} -6.31873e12 q^{75} +(-4.66901e12 - 7.99947e12i) q^{76} -2.16193e12i q^{77} +(1.39525e13 - 2.42987e13i) q^{78} -2.62660e13i q^{79} +(-1.28300e13 - 7.24670e12i) q^{80} -1.96337e13 q^{81} +(-2.08386e13 - 1.19657e13i) q^{82} +2.72551e13 q^{83} +(1.25046e13 - 7.29849e12i) q^{84} +2.97372e13i q^{85} +(5.04944e13 + 2.89942e13i) q^{86} +4.15337e13i q^{87} +(7.43129e10 + 1.04900e13i) q^{88} -8.38435e13 q^{89} +(-2.10705e12 + 3.66950e12i) q^{90} +4.62710e13 q^{91} +(-3.15733e12 + 1.84282e12i) q^{92} +9.81938e13i q^{93} +(4.32644e13 - 7.53464e13i) q^{94} -3.10324e13i q^{95} +(-6.04235e13 + 3.58433e13i) q^{96} +9.36819e12 q^{97} +(-5.45495e13 - 3.13226e13i) q^{98} +3.01246e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9} - 14533440 q^{10} - 28256720 q^{11} + 34920024 q^{12} + 191568384 q^{14} - 185822448 q^{16} + 270339544 q^{17}+ \cdots - 223606851712368 q^{99}+O(q^{100}) \) 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9 - 14533440 * q^10 - 28256720 * q^11 + 34920024 * q^12 + 191568384 * q^14 - 185822448 * q^16 + 270339544 * q^17 + 1420811358 * q^18 - 2481505872 * q^19 - 1679371200 * q^20 + 3042383484 * q^22 + 7581335184 * q^24 - 15857276820 * q^25 - 2773507776 * q^26 - 16574868000 * q^27 + 25329333120 * q^28 + 42207767040 * q^30 + 38309251808 * q^32 - 136227597840 * q^33 + 350437044 * q^34 + 149949623040 * q^35 - 150590403492 * q^36 + 102789916636 * q^38 - 66999085440 * q^40 + 264287409880 * q^41 - 110343609600 * q^42 + 32253127344 * q^43 - 585547356392 * q^44 + 864780977664 * q^46 - 2387663418144 * q^48 - 646589230644 * q^49 - 388785556630 * q^50 + 4755867895776 * q^51 + 798005307840 * q^52 + 1305053764344 * q^54 - 1050155264256 * q^56 - 7479401742480 * q^57 + 389204742720 * q^58 + 1223083947184 * q^59 + 4350689397120 * q^60 + 9957296947200 * q^62 - 16809671099328 * q^64 - 8069319822720 * q^65 - 6067132925784 * q^66 - 9309378171216 * q^67 + 32301846360616 * q^68 + 35197935521280 * q^70 - 43695386222808 * q^72 + 3619334364696 * q^73 - 55499920147776 * q^74 + 9079078926000 * q^75 + 33532610502360 * q^76 + 92515055193600 * q^78 - 86826189154560 * q^80 + 56467107312444 * q^81 - 146233962574956 * q^82 - 18774355695824 * q^83 + 186893160787200 * q^84 + 96253393476220 * q^86 - 166888683024624 * q^88 + 54781416936088 * q^89 - 488020221650880 * q^90 + 36699395136768 * q^91 + 413167093560960 * q^92 + 496016398930944 * q^94 - 616114307580864 * q^96 + 73839238696536 * q^97 - 523654870565638 * q^98 - 223606851712368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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