LMFDB - Embedded newform 10.17.c.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,17,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	10.c (of order $4$, degree $2$, 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:	$16.2324543857$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1418558x^{6} + 548432140705x^{4} + 58849481441870112x^{2} + 514279003991950266624 $ x^8 + 1418558x^6 + 548432140705x^4 + 58849481441870112*x^2 + 514279003991950266624
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{2}\cdot 5^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$926.880i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.17.c.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)

$f(q)$	$=$	$q+(128.000 + 128.000i) q^{2} +(-5464.81 + 5464.81i) q^{3} +32768.0i q^{4} +(187349. + 342765. i) q^{5} -1.39899e6 q^{6} +(6.16251e6 + 6.16251e6i) q^{7} +(-4.19430e6 + 4.19430e6i) q^{8} -1.66815e7i q^{9} +O(q^{10})$	\(q+(128.000 + 128.000i) q^{2} +(-5464.81 + 5464.81i) q^{3} +32768.0i q^{4} +(187349. + 342765. i) q^{5} -1.39899e6 q^{6} +(6.16251e6 + 6.16251e6i) q^{7} +(-4.19430e6 + 4.19430e6i) q^{8} -1.66815e7i q^{9} +(-1.98933e7 + 6.78547e7i) q^{10} -3.83215e8 q^{11} +(-1.79071e8 - 1.79071e8i) q^{12} +(6.97707e8 - 6.97707e8i) q^{13} +1.57760e9i q^{14} +(-2.89697e9 - 8.49320e8i) q^{15} -1.07374e9 q^{16} +(2.15590e9 + 2.15590e9i) q^{17} +(2.13523e9 - 2.13523e9i) q^{18} -2.01031e10i q^{19} +(-1.12317e10 + 6.13906e9i) q^{20} -6.73539e10 q^{21} +(-4.90515e10 - 4.90515e10i) q^{22} +(-3.86849e10 + 3.86849e10i) q^{23} -4.58421e10i q^{24} +(-8.23885e10 + 1.28434e11i) q^{25} +1.78613e11 q^{26} +(-1.44081e11 - 1.44081e11i) q^{27} +(-2.01933e11 + 2.01933e11i) q^{28} +2.47598e11i q^{29} +(-2.62100e11 - 4.79526e11i) q^{30} +1.30464e12 q^{31} +(-1.37439e11 - 1.37439e11i) q^{32} +(2.09420e12 - 2.09420e12i) q^{33} +5.51910e11i q^{34} +(-9.57755e11 + 3.26684e12i) q^{35} +5.46620e11 q^{36} +(2.17819e12 + 2.17819e12i) q^{37} +(2.57320e12 - 2.57320e12i) q^{38} +7.62567e12i q^{39} +(-2.22346e12 - 6.51863e11i) q^{40} +1.11859e12 q^{41} +(-8.62130e12 - 8.62130e12i) q^{42} +(-9.81045e11 + 9.81045e11i) q^{43} -1.25572e13i q^{44} +(5.71785e12 - 3.12527e12i) q^{45} -9.90334e12 q^{46} +(-9.89161e12 - 9.89161e12i) q^{47} +(5.86779e12 - 5.86779e12i) q^{48} +4.27202e13i q^{49} +(-2.69852e13 + 5.89378e12i) q^{50} -2.35632e13 q^{51} +(2.28625e13 + 2.28625e13i) q^{52} +(1.15512e13 - 1.15512e13i) q^{53} -3.68847e13i q^{54} +(-7.17950e13 - 1.31353e14i) q^{55} -5.16949e13 q^{56} +(1.09860e14 + 1.09860e14i) q^{57} +(-3.16926e13 + 3.16926e13i) q^{58} +1.15552e14i q^{59} +(2.78305e13 - 9.49281e13i) q^{60} +1.18190e12 q^{61} +(1.66994e14 + 1.66994e14i) q^{62} +(1.02800e14 - 1.02800e14i) q^{63} -3.51844e13i q^{64} +(3.69865e14 + 1.08435e14i) q^{65} +5.36114e14 q^{66} +(-6.21036e13 - 6.21036e13i) q^{67} +(-7.06445e13 + 7.06445e13i) q^{68} -4.22811e14i q^{69} +(-5.40748e14 + 2.95563e14i) q^{70} -7.46311e14 q^{71} +(6.99674e13 + 6.99674e13i) q^{72} +(-1.01741e14 + 1.01741e14i) q^{73} +5.57618e14i q^{74} +(-2.51628e14 - 1.15210e15i) q^{75} +6.58739e14 q^{76} +(-2.36157e15 - 2.36157e15i) q^{77} +(-9.76086e14 + 9.76086e14i) q^{78} +3.00973e15i q^{79} +(-2.01165e14 - 3.68042e14i) q^{80} +2.29283e15 q^{81} +(1.43180e14 + 1.43180e14i) q^{82} +(-5.42387e13 + 5.42387e13i) q^{83} -2.20705e15i q^{84} +(-3.35062e14 + 1.14287e15i) q^{85} -2.51148e14 q^{86} +(-1.35308e15 - 1.35308e15i) q^{87} +(1.60732e15 - 1.60732e15i) q^{88} +1.91704e14i q^{89} +(1.13192e15 + 3.31850e14i) q^{90} +8.59926e15 q^{91} +(-1.26763e15 - 1.26763e15i) q^{92} +(-7.12961e15 + 7.12961e15i) q^{93} -2.53225e15i q^{94} +(6.89065e15 - 3.76630e15i) q^{95} +1.50215e15 q^{96} +(5.22568e15 + 5.22568e15i) q^{97} +(-5.46819e15 + 5.46819e15i) q^{98} +6.39261e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 1024 q^{2} - 10438 q^{3} - 216450 q^{5} - 2672128 q^{6} + 3127282 q^{7} - 33554432 q^{8}+O(q^{10}) $ 8 * q + 1024 * q^2 - 10438 * q^3 - 216450 * q^5 - 2672128 * q^6 + 3127282 * q^7 - 33554432 * q^8	\( 8 q + 1024 q^{2} - 10438 q^{3} - 216450 q^{5} - 2672128 q^{6} + 3127282 q^{7} - 33554432 q^{8} - 74291200 q^{10} + 503961116 q^{11} - 342032384 q^{12} + 1217503932 q^{13} - 4976914750 q^{15} - 8589934592 q^{16} + 5385990692 q^{17} - 4243396096 q^{18} - 11925913600 q^{20} + 14153198396 q^{21} + 64507022848 q^{22} - 128259921478 q^{23} - 533485437500 q^{25} + 311681006592 q^{26} + 207672953000 q^{27} - 102474776576 q^{28} - 1513467148800 q^{30} + 3125721174596 q^{31} - 1099511627776 q^{32} + 4056976486124 q^{33} - 4345883408350 q^{35} - 1086309400576 q^{36} + 1590466410672 q^{37} + 3851630689280 q^{38} - 618659840000 q^{40} - 19109223712804 q^{41} + 1811609394688 q^{42} + 51727159732362 q^{43} - 21310193383550 q^{45} - 32834539898368 q^{46} - 995920856358 q^{47} + 11207717158912 q^{48} - 101684562880000 q^{50} - 44717760464924 q^{51} + 39895168843776 q^{52} + 141694298313952 q^{53} - 296517352578900 q^{55} - 26233542803456 q^{56} + 529604819758160 q^{57} + 91941293281280 q^{58} - 224364047564800 q^{60} - 275898028788324 q^{61} + 400092310348288 q^{62} + 155565943639322 q^{63} - 771819436467000 q^{65} + 10\!\cdots\!44 q^{66}+ \cdots - 30\!\cdots\!44 q^{98}+O(q^{100}) \) 8 * q + 1024 * q^2 - 10438 * q^3 - 216450 * q^5 - 2672128 * q^6 + 3127282 * q^7 - 33554432 * q^8 - 74291200 * q^10 + 503961116 * q^11 - 342032384 * q^12 + 1217503932 * q^13 - 4976914750 * q^15 - 8589934592 * q^16 + 5385990692 * q^17 - 4243396096 * q^18 - 11925913600 * q^20 + 14153198396 * q^21 + 64507022848 * q^22 - 128259921478 * q^23 - 533485437500 * q^25 + 311681006592 * q^26 + 207672953000 * q^27 - 102474776576 * q^28 - 1513467148800 * q^30 + 3125721174596 * q^31 - 1099511627776 * q^32 + 4056976486124 * q^33 - 4345883408350 * q^35 - 1086309400576 * q^36 + 1590466410672 * q^37 + 3851630689280 * q^38 - 618659840000 * q^40 - 19109223712804 * q^41 + 1811609394688 * q^42 + 51727159732362 * q^43 - 21310193383550 * q^45 - 32834539898368 * q^46 - 995920856358 * q^47 + 11207717158912 * q^48 - 101684562880000 * q^50 - 44717760464924 * q^51 + 39895168843776 * q^52 + 141694298313952 * q^53 - 296517352578900 * q^55 - 26233542803456 * q^56 + 529604819758160 * q^57 + 91941293281280 * q^58 - 224364047564800 * q^60 - 275898028788324 * q^61 + 400092310348288 * q^62 + 155565943639322 * q^63 - 771819436467000 * q^65 + 1038585980447744 * q^66 - 700220959215398 * q^67 - 176488142995456 * q^68 - 511285790540800 * q^70 + 1921969049667556 * q^71 - 139047603273728 * q^72 - 808847266834888 * q^73 + 2482300760271250 * q^75 + 986017456455680 * q^76 - 5345726343508436 * q^77 - 2838754804096512 * q^78 + 232411417804800 * q^80 + 9359115176899828 * q^81 - 2445980635238912 * q^82 - 13177017950509038 * q^83 + 3955352361175900 * q^85 + 13242152891484672 * q^86 - 14123970165519040 * q^87 - 2113766124683264 * q^88 + 621990363392000 * q^90 + 47376751322244756 * q^91 - 4202821106991104 * q^92 - 26154699869031556 * q^93 - 67475453915000 * q^95 + 2869175592681472 * q^96 - 10816659651879048 * q^97 - 30870381725100544 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	128.000	+	128.000i	0.500000	+	0.500000i
$2$	128.000	+	128.000i	0.500000	+	0.500000i
$3$	−5464.81	+	5464.81i	−0.832923	+	0.832923i	−0.987916	−	0.154993i	$-0.950465\pi$
$3$	−5464.81	+	5464.81i	−0.832923	+	0.832923i	0.154993	+	0.987916i	$0.450465\pi$
$4$			32768.0i			0.500000i
$5$	187349.	+	342765.i	0.479614	+	0.877480i
$5$	187349.	+	342765.i	0.479614	+	0.877480i
$6$	−1.39899e6			−0.832923
$7$	6.16251e6	+	6.16251e6i	1.06899	+	1.06899i	0.997437	+	0.0715531i	$0.0227956\pi$
$7$	6.16251e6	+	6.16251e6i	1.06899	+	1.06899i	0.0715531	+	0.997437i	$0.477204\pi$
$8$	−4.19430e6	+	4.19430e6i	−0.250000	+	0.250000i
$9$		−	1.66815e7i		−	0.387521i
$10$	−1.98933e7	+	6.78547e7i	−0.198933	+	0.678547i
$11$	−3.83215e8			−1.78773			−0.893863	−	0.448340i	$-0.852015\pi$
$11$	−3.83215e8			−1.78773			−0.893863	+	0.448340i	$0.852015\pi$
$12$	−1.79071e8	−	1.79071e8i	−0.416461	−	0.416461i
$13$	6.97707e8	−	6.97707e8i	0.855316	−	0.855316i	−0.135466	−	0.990782i	$-0.543253\pi$
$13$	6.97707e8	−	6.97707e8i	0.855316	−	0.855316i	0.990782	+	0.135466i	$0.0432533\pi$
$14$			1.57760e9i			1.06899i
$15$	−2.89697e9	−	8.49320e8i	−1.13035	−	0.331392i
$16$	−1.07374e9			−0.250000
$17$	2.15590e9	+	2.15590e9i	0.309056	+	0.309056i	0.844543	−	0.535487i	$-0.179872\pi$
$17$	2.15590e9	+	2.15590e9i	0.309056	+	0.309056i	−0.535487	+	0.844543i	$0.679872\pi$
$18$	2.13523e9	−	2.13523e9i	0.193761	−	0.193761i
$19$		−	2.01031e10i		−	1.18368i	−0.806055	−	0.591840i	$-0.798402\pi$
$19$		−	2.01031e10i		−	1.18368i	0.806055	−	0.591840i	$-0.201598\pi$
$20$	−1.12317e10	+	6.13906e9i	−0.438740	+	0.239807i
$21$	−6.73539e10			−1.78077
$22$	−4.90515e10	−	4.90515e10i	−0.893863	−	0.893863i
$23$	−3.86849e10	+	3.86849e10i	−0.493991	+	0.493991i	−0.909561	−	0.415570i	$-0.863582\pi$
$23$	−3.86849e10	+	3.86849e10i	−0.493991	+	0.493991i	0.415570	+	0.909561i	$0.363582\pi$
$24$		−	4.58421e10i		−	0.416461i
$25$	−8.23885e10	+	1.28434e11i	−0.539941	+	0.841703i
$26$	1.78613e11			0.855316
$27$	−1.44081e11	−	1.44081e11i	−0.510148	−	0.510148i
$28$	−2.01933e11	+	2.01933e11i	−0.534495	+	0.534495i
$29$			2.47598e11i			0.494952i	0.968894	+	0.247476i	$0.0796012\pi$
$29$			2.47598e11i			0.494952i	−0.968894	+	0.247476i	$0.920399\pi$
$30$	−2.62100e11	−	4.79526e11i	−0.399481	−	0.730873i
$31$	1.30464e12			1.52967			0.764834	−	0.644228i	$-0.222821\pi$
$31$	1.30464e12			1.52967			0.764834	+	0.644228i	$0.222821\pi$
$32$	−1.37439e11	−	1.37439e11i	−0.125000	−	0.125000i
$33$	2.09420e12	−	2.09420e12i	1.48904	−	1.48904i
$34$			5.51910e11i			0.309056i
$35$	−9.57755e11	+	3.26684e12i	−0.425315	+	1.45072i
$36$	5.46620e11			0.193761
$37$	2.17819e12	+	2.17819e12i	0.620130	+	0.620130i	0.945565	−	0.325435i	$-0.105511\pi$
$37$	2.17819e12	+	2.17819e12i	0.620130	+	0.620130i	−0.325435	+	0.945565i	$0.605511\pi$
$38$	2.57320e12	−	2.57320e12i	0.591840	−	0.591840i
$39$			7.62567e12i			1.42482i
$40$	−2.22346e12	−	6.51863e11i	−0.339273	−	0.0994665i
$41$	1.11859e12			0.140088			0.0700439	−	0.997544i	$-0.477686\pi$
$41$	1.11859e12			0.140088			0.0700439	+	0.997544i	$0.477686\pi$
$42$	−8.62130e12	−	8.62130e12i	−0.890386	−	0.890386i
$43$	−9.81045e11	+	9.81045e11i	−0.0839347	+	0.0839347i	−0.747828	−	0.663893i	$-0.768903\pi$
$43$	−9.81045e11	+	9.81045e11i	−0.0839347	+	0.0839347i	0.663893	+	0.747828i	$0.268903\pi$
$44$		−	1.25572e13i		−	0.893863i
$45$	5.71785e12	−	3.12527e12i	0.340042	−	0.185861i
$46$	−9.90334e12			−0.493991
$47$	−9.89161e12	−	9.89161e12i	−0.415417	−	0.415417i	0.468204	−	0.883621i	$-0.344901\pi$
$47$	−9.89161e12	−	9.89161e12i	−0.415417	−	0.415417i	−0.883621	+	0.468204i	$0.844901\pi$
$48$	5.86779e12	−	5.86779e12i	0.208231	−	0.208231i
$49$			4.27202e13i			1.28548i
$50$	−2.69852e13	+	5.89378e12i	−0.690822	+	0.150881i
$51$	−2.35632e13			−0.514840
$52$	2.28625e13	+	2.28625e13i	0.427658	+	0.427658i
$53$	1.15512e13	−	1.15512e13i	0.185533	−	0.185533i	−0.608229	−	0.793762i	$-0.708120\pi$
$53$	1.15512e13	−	1.15512e13i	0.185533	−	0.185533i	0.793762	+	0.608229i	$0.208120\pi$
$54$		−	3.68847e13i		−	0.510148i
$55$	−7.17950e13	−	1.31353e14i	−0.857418	−	1.56869i
$56$	−5.16949e13			−0.534495
$57$	1.09860e14	+	1.09860e14i	0.985914	+	0.985914i
$58$	−3.16926e13	+	3.16926e13i	−0.247476	+	0.247476i
$59$			1.15552e14i			0.786978i	0.919329	+	0.393489i	$0.128732\pi$
$59$			1.15552e14i			0.786978i	−0.919329	+	0.393489i	$0.871268\pi$
$60$	2.78305e13	−	9.49281e13i	0.165696	−	0.565177i
$61$	1.18190e12			0.00616515			0.00308257	−	0.999995i	$-0.499019\pi$
$61$	1.18190e12			0.00616515			0.00308257	+	0.999995i	$0.499019\pi$
$62$	1.66994e14	+	1.66994e14i	0.764834	+	0.764834i
$63$	1.02800e14	−	1.02800e14i	0.414256	−	0.414256i
$64$		−	3.51844e13i		−	0.125000i
$65$	3.69865e14	+	1.08435e14i	1.16074	+	0.340301i
$66$	5.36114e14			1.48904
$67$	−6.21036e13	−	6.21036e13i	−0.152939	−	0.152939i	0.626490	−	0.779429i	$-0.284491\pi$
$67$	−6.21036e13	−	6.21036e13i	−0.152939	−	0.152939i	−0.779429	+	0.626490i	$0.784491\pi$
$68$	−7.06445e13	+	7.06445e13i	−0.154528	+	0.154528i
$69$		−	4.22811e14i		−	0.822913i
$70$	−5.40748e14	+	2.95563e14i	−0.938017	+	0.512702i
$71$	−7.46311e14			−1.15572			−0.577861	−	0.816135i	$-0.696112\pi$
$71$	−7.46311e14			−1.15572			−0.577861	+	0.816135i	$0.696112\pi$
$72$	6.99674e13	+	6.99674e13i	0.0968803	+	0.0968803i
$73$	−1.01741e14	+	1.01741e14i	−0.126158	+	0.126158i	−0.767367	−	0.641209i	$-0.778433\pi$
$73$	−1.01741e14	+	1.01741e14i	−0.126158	+	0.126158i	0.641209	+	0.767367i	$0.278433\pi$
$74$			5.57618e14i			0.620130i
$75$	−2.51628e14	−	1.15210e15i	−0.251344	−	1.15080i
$76$	6.58739e14			0.591840
$77$	−2.36157e15	−	2.36157e15i	−1.91106	−	1.91106i
$78$	−9.76086e14	+	9.76086e14i	−0.712412	+	0.712412i
$79$			3.00973e15i			1.98386i	0.126802	+	0.991928i	$0.459529\pi$
$79$			3.00973e15i			1.98386i	−0.126802	+	0.991928i	$0.540471\pi$
$80$	−2.01165e14	−	3.68042e14i	−0.119903	−	0.219370i
$81$	2.29283e15			1.23735
$82$	1.43180e14	+	1.43180e14i	0.0700439	+	0.0700439i
$83$	−5.42387e13	+	5.42387e13i	−0.0240816	+	0.0240816i	−0.719045	−	0.694963i	$-0.755421\pi$
$83$	−5.42387e13	+	5.42387e13i	−0.0240816	+	0.0240816i	0.694963	+	0.719045i	$0.255421\pi$
$84$		−	2.20705e15i		−	0.890386i
$85$	−3.35062e14	+	1.14287e15i	−0.122963	+	0.419418i
$86$	−2.51148e14			−0.0839347
$87$	−1.35308e15	−	1.35308e15i	−0.412257	−	0.412257i
$88$	1.60732e15	−	1.60732e15i	0.446932	−	0.446932i
$89$			1.91704e14i			0.0486979i	0.999704	+	0.0243490i	$0.00775128\pi$
$89$			1.91704e14i			0.0486979i	−0.999704	+	0.0243490i	$0.992249\pi$
$90$	1.13192e15	+	3.31850e14i	0.262951	+	0.0770907i
$91$	8.59926e15			1.82865
$92$	−1.26763e15	−	1.26763e15i	−0.246996	−	0.246996i
$93$	−7.12961e15	+	7.12961e15i	−1.27410	+	1.27410i
$94$		−	2.53225e15i		−	0.415417i
$95$	6.89065e15	−	3.76630e15i	1.03866	−	0.567709i
$96$	1.50215e15			0.208231
$97$	5.22568e15	+	5.22568e15i	0.666759	+	0.666759i	0.956964	−	0.290205i	$-0.0937235\pi$
$97$	5.22568e15	+	5.22568e15i	0.666759	+	0.666759i	−0.290205	+	0.956964i	$0.593724\pi$
$98$	−5.46819e15	+	5.46819e15i	−0.642739	+	0.642739i
$99$			6.39261e15i			0.692782i
$100$	−4.20851e15	−	2.69971e15i	−0.420851	−	0.269971i
$101$	1.31493e16			1.21432			0.607160	−	0.794580i	$-0.292309\pi$
$101$	1.31493e16			1.21432			0.607160	+	0.794580i	$0.292309\pi$
$102$	−3.01608e15	−	3.01608e15i	−0.257420	−	0.257420i
$103$	−6.60248e15	+	6.60248e15i	−0.521206	+	0.521206i	−0.917936	−	0.396730i	$-0.870145\pi$
$103$	−6.60248e15	+	6.60248e15i	−0.521206	+	0.521206i	0.396730	+	0.917936i	$0.370145\pi$
$104$			5.85279e15i			0.427658i
$105$	−1.26187e16	−	2.30866e16i	−0.854083	−	1.56259i
$106$	2.95712e15			0.185533
$107$	2.03043e15	+	2.03043e15i	0.118173	+	0.118173i	0.763720	−	0.645547i	$-0.223371\pi$
$107$	2.03043e15	+	2.03043e15i	0.118173	+	0.118173i	−0.645547	+	0.763720i	$0.723371\pi$
$108$	4.72124e15	−	4.72124e15i	0.255074	−	0.255074i
$109$		−	3.44229e15i		−	0.172757i	−0.996262	−	0.0863784i	$-0.972471\pi$
$109$		−	3.44229e15i		−	0.172757i	0.996262	−	0.0863784i	$-0.0275294\pi$
$110$	7.62341e15	−	2.60029e16i	0.355638	−	1.21306i
$111$	−2.38068e16			−1.03304
$112$	−6.61695e15	−	6.61695e15i	−0.267247	−	0.267247i
$113$	−8.20735e15	+	8.20735e15i	−0.308728	+	0.308728i	−0.844416	−	0.535688i	$-0.820052\pi$
$113$	−8.20735e15	+	8.20735e15i	−0.308728	+	0.308728i	0.535688	+	0.844416i	$0.320052\pi$
$114$			2.81241e16i			0.985914i
$115$	−2.05075e16	−	6.01227e15i	−0.670392	−	0.196542i
$116$	−8.11329e15			−0.247476
$117$	−1.16388e16	−	1.16388e16i	−0.331453	−	0.331453i
$118$	−1.47907e16	+	1.47907e16i	−0.393489	+	0.393489i
$119$			2.65715e16i			0.660756i
$120$	1.57131e16	−	8.58848e15i	0.365436	−	0.199741i
$121$	1.00904e17			2.19597
$122$	1.51284e14	+	1.51284e14i	0.00308257	+	0.00308257i
$123$	−6.11288e15	+	6.11288e15i	−0.116682	+	0.116682i
$124$			4.27504e16i			0.764834i
$125$	−5.94580e16	−	4.17799e15i	−0.997540	−	0.0700950i
$126$	2.63168e16			0.414256
$127$	−7.91323e16	−	7.91323e16i	−1.16930	−	1.16930i	−0.982375	−	0.186920i	$-0.940149\pi$
$127$	−7.91323e16	−	7.91323e16i	−1.16930	−	1.16930i	−0.186920	−	0.982375i	$-0.559851\pi$
$128$	4.50360e15	−	4.50360e15i	0.0625000	−	0.0625000i
$129$		−	1.07224e16i		−	0.139822i
$130$	3.34630e16	+	6.12224e16i	0.410221	+	0.750522i
$131$	4.25409e16			0.490497			0.245248	−	0.969460i	$-0.421130\pi$
$131$	4.25409e16			0.490497			0.245248	+	0.969460i	$0.421130\pi$
$132$	6.86226e16	+	6.86226e16i	0.744519	+	0.744519i
$133$	1.23886e17	−	1.23886e17i	1.26534	−	1.26534i
$134$		−	1.58985e16i		−	0.152939i
$135$	2.23925e16	−	7.63793e16i	0.202970	−	0.692318i
$136$	−1.80850e16			−0.154528
$137$	1.28462e17	+	1.28462e17i	1.03516	+	1.03516i	0.999359	+	0.0358041i	$0.0113992\pi$
$137$	1.28462e17	+	1.28462e17i	1.03516	+	1.03516i	0.0358041	+	0.999359i	$0.488601\pi$
$138$	5.41199e16	−	5.41199e16i	0.411457	−	0.411457i
$139$			1.48752e17i			1.06744i	0.845660	+	0.533722i	$0.179207\pi$
$139$			1.48752e17i			1.06744i	−0.845660	+	0.533722i	$0.820793\pi$
$140$	−1.07048e17	−	3.13837e16i	−0.725360	−	0.212657i
$141$	1.08112e17			0.692021
$142$	−9.55279e16	−	9.55279e16i	−0.577861	−	0.577861i
$143$	−2.67372e17	+	2.67372e17i	−1.52907	+	1.52907i
$144$			1.79116e16i			0.0968803i
$145$	−8.48681e16	+	4.63873e16i	−0.434310	+	0.237386i
$146$	−2.60458e16			−0.126158
$147$	−2.33458e17	−	2.33458e17i	−1.07070	−	1.07070i
$148$	−7.13751e16	+	7.13751e16i	−0.310065	+	0.310065i
$149$		−	2.30610e17i		−	0.949267i	−0.880184	−	0.474633i	$-0.842581\pi$
$149$		−	2.30610e17i		−	0.949267i	0.880184	−	0.474633i	$-0.157419\pi$
$150$	1.15261e17	−	1.79677e17i	0.449729	−	0.701074i
$151$	−2.41696e17			−0.894238			−0.447119	−	0.894474i	$-0.647550\pi$
$151$	−2.41696e17			−0.894238			−0.447119	+	0.894474i	$0.647550\pi$
$152$	8.43185e16	+	8.43185e16i	0.295920	+	0.295920i
$153$	3.59637e16	−	3.59637e16i	0.119766	−	0.119766i
$154$		−	6.04561e17i		−	1.91106i
$155$	2.44423e17	+	4.47186e17i	0.733650	+	1.34225i
$156$	−2.49878e17			−0.712412
$157$	2.01006e16	+	2.01006e16i	0.0544516	+	0.0544516i	0.733808	−	0.679357i	$-0.237741\pi$
$157$	2.01006e16	+	2.01006e16i	0.0544516	+	0.0544516i	−0.679357	+	0.733808i	$0.737741\pi$
$158$	−3.85245e17	+	3.85245e17i	−0.991928	+	0.991928i
$159$			1.26251e17i			0.309070i
$160$	2.13603e16	−	7.28584e16i	0.0497332	−	0.169637i
$161$	−4.76793e17			−1.05614
$162$	2.93482e17	+	2.93482e17i	0.618674	+	0.618674i
$163$	5.40453e17	−	5.40453e17i	1.08457	−	1.08457i	0.0884929	−	0.996077i	$-0.471795\pi$
$163$	5.40453e17	−	5.40453e17i	1.08457	−	1.08457i	0.996077	−	0.0884929i	$-0.0282050\pi$
$164$			3.66540e16i			0.0700439i
$165$	1.11016e18	+	3.25472e17i	2.02076	+	0.592437i
$166$	−1.38851e16			−0.0240816
$167$	4.73699e17	+	4.73699e17i	0.783016	+	0.783016i	0.980339	−	0.197323i	$-0.0632247\pi$
$167$	4.73699e17	+	4.73699e17i	0.783016	+	0.783016i	−0.197323	+	0.980339i	$0.563225\pi$
$168$	2.82503e17	−	2.82503e17i	0.445193	−	0.445193i
$169$		−	3.08174e17i		−	0.463130i
$170$	−1.89176e17	+	1.03400e17i	−0.271190	+	0.148228i
$171$	−3.35350e17			−0.458701
$172$	−3.21469e16	−	3.21469e16i	−0.0419673	−	0.0419673i
$173$	4.74596e17	−	4.74596e17i	0.591501	−	0.591501i	−0.346536	−	0.938037i	$-0.612642\pi$
$173$	4.74596e17	−	4.74596e17i	0.591501	−	0.591501i	0.938037	+	0.346536i	$0.112642\pi$
$174$		−	3.46387e17i		−	0.412257i
$175$	−1.29919e18	+	2.83754e17i	−1.47696	+	0.322580i
$176$	4.11474e17			0.446932
$177$	−6.31471e17	−	6.31471e17i	−0.655492	−	0.655492i
$178$	−2.45381e16	+	2.45381e16i	−0.0243490	+	0.0243490i
$179$			1.26329e18i			1.19861i	0.800519	+	0.599307i	$0.204557\pi$
$179$			1.26329e18i			1.19861i	−0.800519	+	0.599307i	$0.795443\pi$
$180$	1.02409e17	+	1.87362e17i	0.0929303	+	0.170021i
$181$	8.67769e17			0.753313			0.376657	−	0.926353i	$-0.377074\pi$
$181$	8.67769e17			0.753313			0.376657	+	0.926353i	$0.377074\pi$
$182$	1.10071e18	+	1.10071e18i	0.914324	+	0.914324i
$183$	−6.45887e15	+	6.45887e15i	−0.00513509	+	0.00513509i
$184$		−	3.24513e17i		−	0.246996i
$185$	−3.38527e17	+	1.15469e18i	−0.246729	+	0.841574i
$186$	−1.82518e18			−1.27410
$187$	−8.26173e17	−	8.26173e17i	−0.552508	−	0.552508i
$188$	3.24128e17	−	3.24128e17i	0.207708	−	0.207708i
$189$		−	1.77580e18i		−	1.09069i
$190$	1.36409e18	+	3.99917e17i	0.803182	+	0.235473i
$191$	−9.57789e17			−0.540758			−0.270379	−	0.962754i	$-0.587149\pi$
$191$	−9.57789e17			−0.540758			−0.270379	+	0.962754i	$0.587149\pi$
$192$	1.92276e17	+	1.92276e17i	0.104115	+	0.104115i
$193$	2.60294e18	−	2.60294e18i	1.35209	−	1.35209i	0.468771	−	0.883319i	$-0.344697\pi$
$193$	2.60294e18	−	2.60294e18i	1.35209	−	1.35209i	0.883319	−	0.468771i	$-0.155303\pi$
$194$			1.33777e18i			0.666759i
$195$	−2.61382e18	+	1.42866e18i	−1.25025	+	0.683365i
$196$	−1.39986e18			−0.642739
$197$	−1.90516e18	−	1.90516e18i	−0.839848	−	0.839848i	0.148991	−	0.988839i	$-0.452398\pi$
$197$	−1.90516e18	−	1.90516e18i	−0.839848	−	0.839848i	−0.988839	+	0.148991i	$0.952398\pi$
$198$	−8.18254e17	+	8.18254e17i	−0.346391	+	0.346391i
$199$		−	3.11875e18i		−	1.26811i	−0.773290	−	0.634053i	$-0.781390\pi$
$199$		−	3.11875e18i		−	1.26811i	0.773290	−	0.634053i	$-0.218610\pi$
$200$	−1.93127e17	−	8.84252e17i	−0.0754404	−	0.345411i
$201$	6.78768e17			0.254773
$202$	1.68312e18	+	1.68312e18i	0.607160	+	0.607160i
$203$	−1.52583e18	+	1.52583e18i	−0.529099	+	0.529099i
$204$		−	7.72118e17i		−	0.257420i
$205$	2.09567e17	+	3.83414e17i	0.0671881	+	0.122924i
$206$	−1.69024e18			−0.521206
$207$	6.45324e17	+	6.45324e17i	0.191432	+	0.191432i
$208$	−7.49157e17	+	7.49157e17i	−0.213829	+	0.213829i
$209$			7.70381e18i			2.11610i
$210$	1.33989e18	−	4.57028e18i	0.354254	−	1.20834i
$211$	−7.24028e17			−0.184288			−0.0921438	−	0.995746i	$-0.529372\pi$
$211$	−7.24028e17			−0.184288			−0.0921438	+	0.995746i	$0.529372\pi$
$212$	3.78511e17	+	3.78511e17i	0.0927666	+	0.0927666i
$213$	4.07845e18	−	4.07845e18i	0.962627	−	0.962627i
$214$			5.19789e17i			0.118173i
$215$	−5.20066e17	−	1.52470e17i	−0.113907	−	0.0333947i
$216$	1.20864e18			0.255074
$217$	8.03986e18	+	8.03986e18i	1.63520	+	1.63520i
$218$	4.40613e17	−	4.40613e17i	0.0863784	−	0.0863784i
$219$		−	1.11199e18i		−	0.210160i
$220$	4.30417e18	−	2.35258e18i	0.784347	−	0.428709i
$221$	3.00837e18			0.528681
$222$	−3.04727e18	−	3.04727e18i	−0.516521	−	0.516521i
$223$	−5.64770e18	+	5.64770e18i	−0.923491	+	0.923491i	−0.997274	−	0.0737830i	$-0.976493\pi$
$223$	−5.64770e18	+	5.64770e18i	−0.923491	+	0.923491i	0.0737830	+	0.997274i	$0.476493\pi$
$224$		−	1.69394e18i		−	0.267247i
$225$	2.14247e18	+	1.37436e18i	0.326178	+	0.209239i
$226$	−2.10108e18			−0.308728
$227$	−5.32960e18	−	5.32960e18i	−0.755941	−	0.755941i	0.219640	−	0.975581i	$-0.429512\pi$
$227$	−5.32960e18	−	5.32960e18i	−0.755941	−	0.755941i	−0.975581	+	0.219640i	$0.929512\pi$
$228$	−3.59988e18	+	3.59988e18i	−0.492957	+	0.492957i
$229$		−	5.40795e18i		−	0.715070i	−0.933900	−	0.357535i	$-0.883617\pi$
$229$		−	5.40795e18i		−	0.715070i	0.933900	−	0.357535i	$-0.116383\pi$
$230$	−1.85538e18	−	3.39452e18i	−0.236925	−	0.433467i
$231$	2.58110e19			3.18353
$232$	−1.03850e18	−	1.03850e18i	−0.123738	−	0.123738i
$233$	−6.06190e18	+	6.06190e18i	−0.697849	+	0.697849i	−0.963946	−	0.266097i	$-0.914266\pi$
$233$	−6.06190e18	+	6.06190e18i	−0.697849	+	0.697849i	0.266097	+	0.963946i	$0.414266\pi$
$234$		−	2.97954e18i		−	0.331453i
$235$	1.53732e18	−	5.24369e18i	0.165280	−	0.563760i
$236$	−3.78642e18			−0.393489
$237$	−1.64476e19	−	1.64476e19i	−1.65240	−	1.65240i
$238$	−3.40116e18	+	3.40116e18i	−0.330378	+	0.330378i
$239$			1.65551e19i			1.55506i	0.628844	+	0.777531i	$0.283528\pi$
$239$			1.65551e19i			1.55506i	−0.628844	+	0.777531i	$0.716472\pi$
$240$	3.11060e18	+	9.11951e17i	0.282589	+	0.0828479i
$241$	−9.87061e18			−0.867376			−0.433688	−	0.901063i	$-0.642788\pi$
$241$	−9.87061e18			−0.867376			−0.433688	+	0.901063i	$0.642788\pi$
$242$	1.29157e19	+	1.29157e19i	1.09798	+	1.09798i
$243$	−6.32768e18	+	6.32768e18i	−0.520468	+	0.520468i
$244$			3.87286e16i			0.00308257i
$245$	−1.46430e19	+	8.00360e18i	−1.12798	+	0.616533i
$246$	−1.56490e18			−0.116682
$247$	−1.40261e19	−	1.40261e19i	−1.01242	−	1.01242i
$248$	−5.47206e18	+	5.47206e18i	−0.382417	+	0.382417i
$249$		−	5.92808e17i		−	0.0401162i
$250$	−7.07585e18	−	8.14541e18i	−0.463723	−	0.533818i
$251$	1.74161e19			1.10550			0.552752	−	0.833346i	$-0.313578\pi$
$251$	1.74161e19			1.10550			0.552752	+	0.833346i	$0.313578\pi$
$252$	3.36855e18	+	3.36855e18i	0.207128	+	0.207128i
$253$	1.48246e19	−	1.48246e19i	0.883121	−	0.883121i
$254$		−	2.02579e19i		−	1.16930i
$255$	−4.41454e18	−	8.07664e18i	−0.246924	−	0.451761i
$256$	1.15292e18			0.0625000
$257$	−7.08166e18	−	7.08166e18i	−0.372109	−	0.372109i	0.496136	−	0.868245i	$-0.334752\pi$
$257$	−7.08166e18	−	7.08166e18i	−0.372109	−	0.372109i	−0.868245	+	0.496136i	$0.834752\pi$
$258$	1.37247e18	−	1.37247e18i	0.0699111	−	0.0699111i
$259$			2.68463e19i			1.32583i
$260$	−3.55320e18	+	1.21197e19i	−0.170150	+	0.580372i
$261$	4.13031e18			0.191804
$262$	5.44523e18	+	5.44523e18i	0.245248	+	0.245248i
$263$	2.35737e19	−	2.35737e19i	1.02987	−	1.02987i	0.0303286	−	0.999540i	$-0.490345\pi$
$263$	2.35737e19	−	2.35737e19i	1.02987	−	1.02987i	0.999540	−	0.0303286i	$-0.00965537\pi$
$264$			1.75674e19i			0.744519i
$265$	6.12348e18	+	1.79525e18i	0.251786	+	0.0738173i
$266$	3.17147e19			1.26534
$267$	−1.04762e18	−	1.04762e18i	−0.0405616	−	0.0405616i
$268$	2.03501e18	−	2.03501e18i	0.0764695	−	0.0764695i
$269$			7.30234e18i			0.266345i	0.991093	+	0.133172i	$0.0425164\pi$
$269$			7.30234e18i			0.266345i	−0.991093	+	0.133172i	$0.957484\pi$
$270$	1.26428e19	−	6.91031e18i	0.447644	−	0.244674i
$271$	1.77235e19			0.609248			0.304624	−	0.952473i	$-0.401469\pi$
$271$	1.77235e19			0.609248			0.304624	+	0.952473i	$0.401469\pi$
$272$	−2.31488e18	−	2.31488e18i	−0.0772640	−	0.0772640i
$273$	−4.69933e19	+	4.69933e19i	−1.52312	+	1.52312i
$274$			3.28862e19i			1.03516i
$275$	3.15725e19	−	4.92177e19i	0.965267	−	1.50473i
$276$	1.38547e19			0.411457
$277$	2.14714e19	+	2.14714e19i	0.619472	+	0.619472i	0.945396	−	0.325924i	$-0.105675\pi$
$277$	2.14714e19	+	2.14714e19i	0.619472	+	0.619472i	−0.325924	+	0.945396i	$0.605675\pi$
$278$	−1.90403e19	+	1.90403e19i	−0.533722	+	0.533722i
$279$		−	2.17634e19i		−	0.592779i
$280$	−9.68500e18	−	1.77192e19i	−0.256351	−	0.469008i
$281$	−6.47018e19			−1.66443			−0.832216	−	0.554452i	$-0.812928\pi$
$281$	−6.47018e19			−1.66443			−0.832216	+	0.554452i	$0.812928\pi$
$282$	1.38383e19	+	1.38383e19i	0.346010	+	0.346010i
$283$	4.41578e19	−	4.41578e19i	1.07329	−	1.07329i	0.0761947	−	0.997093i	$-0.475723\pi$
$283$	4.41578e19	−	4.41578e19i	1.07329	−	1.07329i	0.997093	−	0.0761947i	$-0.0242771\pi$
$284$		−	2.44551e19i		−	0.577861i
$285$	−1.70740e19	+	5.82382e19i	−0.392262	+	1.33798i
$286$	−6.84472e19			−1.52907
$287$	6.89333e18	+	6.89333e18i	0.149752	+	0.149752i
$288$	−2.29269e18	+	2.29269e18i	−0.0484402	+	0.0484402i
$289$		−	3.93654e19i		−	0.808969i
$290$	−1.68007e19	−	4.92554e18i	−0.335848	−	0.0984623i
$291$	−5.71147e19			−1.11072
$292$	−3.33386e18	−	3.33386e18i	−0.0630789	−	0.0630789i
$293$	4.41201e19	−	4.41201e19i	0.812262	−	0.812262i	−0.172711	−	0.984973i	$-0.555253\pi$
$293$	4.41201e19	−	4.41201e19i	0.812262	−	0.812262i	0.984973	+	0.172711i	$0.0552526\pi$
$294$		−	5.97652e19i		−	1.07070i
$295$	−3.96074e19	+	2.16486e19i	−0.690557	+	0.377446i
$296$	−1.82720e19			−0.310065
$297$	5.52139e19	+	5.52139e19i	0.912004	+	0.912004i
$298$	2.95181e19	−	2.95181e19i	0.474633	−	0.474633i
$299$			5.39815e19i			0.845037i
$300$	3.77521e19	−	8.24535e18i	0.575401	−	0.125672i
$301$	−1.20914e19			−0.179451
$302$	−3.09370e19	−	3.09370e19i	−0.447119	−	0.447119i
$303$	−7.18586e19	+	7.18586e19i	−1.01143	+	1.01143i
$304$			2.15855e19i			0.295920i
$305$	2.21429e17	+	4.05116e17i	0.00295689	+	0.00540979i
$306$	9.20670e18			0.119766
$307$	1.27310e19	+	1.27310e19i	0.161344	+	0.161344i	0.783162	−	0.621818i	$-0.213606\pi$
$307$	1.27310e19	+	1.27310e19i	0.161344	+	0.161344i	−0.621818	+	0.783162i	$0.713606\pi$
$308$	7.73839e19	−	7.73839e19i	0.955531	−	0.955531i
$309$		−	7.21626e19i		−	0.868249i
$310$	−2.59536e19	+	8.85259e19i	−0.304301	+	1.03795i
$311$	5.94605e19			0.679431			0.339715	−	0.940528i	$-0.389669\pi$
$311$	5.94605e19			0.679431			0.339715	+	0.940528i	$0.389669\pi$
$312$	−3.19844e19	−	3.19844e19i	−0.356206	−	0.356206i
$313$	−3.04243e19	+	3.04243e19i	−0.330267	+	0.330267i	−0.852688	−	0.522421i	$-0.825029\pi$
$313$	−3.04243e19	+	3.04243e19i	−0.330267	+	0.330267i	0.522421	+	0.852688i	$0.325029\pi$
$314$			5.14574e18i			0.0544516i
$315$	5.44958e19	+	1.59768e19i	0.562185	+	0.164818i
$316$	−9.86227e19			−0.991928
$317$	6.14103e17	+	6.14103e17i	0.00602237	+	0.00602237i	0.710112	−	0.704089i	$-0.248644\pi$
$317$	6.14103e17	+	6.14103e17i	0.00602237	+	0.00602237i	−0.704089	+	0.710112i	$0.748644\pi$
$318$	−1.61601e19	+	1.61601e19i	−0.154535	+	0.154535i
$319$		−	9.48833e19i		−	0.884839i
$320$	1.20600e19	−	6.59176e18i	0.109685	−	0.0599517i
$321$	−2.21918e19			−0.196857
$322$	−6.10295e19	−	6.10295e19i	−0.528072	−	0.528072i
$323$	4.33403e19	−	4.33403e19i	0.365824	−	0.365824i
$324$			7.51315e19i			0.618674i
$325$	3.21261e19	+	1.47092e20i	0.258101	+	1.18174i
$326$	1.38356e20			1.08457
$327$	1.88114e19	+	1.88114e19i	0.143893	+	0.143893i
$328$	−4.69171e18	+	4.69171e18i	−0.0350220	+	0.0350220i
$329$		−	1.21914e20i		−	0.888153i
$330$	1.00441e20	+	1.83761e20i	0.714163	+	1.30660i
$331$	1.77630e20			1.23280			0.616400	−	0.787433i	$-0.288590\pi$
$331$	1.77630e20			1.23280			0.616400	+	0.787433i	$0.288590\pi$
$332$	−1.77729e18	−	1.77729e18i	−0.0120408	−	0.0120408i
$333$	3.63356e19	−	3.63356e19i	0.240314	−	0.240314i
$334$			1.21267e20i			0.783016i
$335$	9.65191e18	−	3.29220e19i	0.0608492	−	0.207553i
$336$	7.23207e19			0.445193
$337$	7.33598e19	+	7.33598e19i	0.440980	+	0.440980i	0.892341	−	0.451361i	$-0.149061\pi$
$337$	7.33598e19	+	7.33598e19i	0.440980	+	0.440980i	−0.451361	+	0.892341i	$0.649061\pi$
$338$	3.94463e19	−	3.94463e19i	0.231565	−	0.231565i
$339$		−	8.97032e19i		−	0.514293i
$340$	−3.74497e19	−	1.09793e19i	−0.209709	−	0.0614814i
$341$	−4.99958e20			−2.73463
$342$	−4.29248e19	−	4.29248e19i	−0.229351	−	0.229351i
$343$	−5.84656e19	+	5.84656e19i	−0.305174	+	0.305174i
$344$		−	8.22960e18i		−	0.0419673i
$345$	1.44925e20	−	7.92134e19i	0.722090	−	0.394681i
$346$	1.21497e20			0.591501
$347$	−5.64999e19	−	5.64999e19i	−0.268789	−	0.268789i	0.559823	−	0.828612i	$-0.310869\pi$
$347$	−5.64999e19	−	5.64999e19i	−0.268789	−	0.268789i	−0.828612	+	0.559823i	$0.810869\pi$
$348$	4.43376e19	−	4.43376e19i	0.206129	−	0.206129i
$349$			1.70580e20i			0.775041i	0.921861	+	0.387521i	$0.126668\pi$
$349$			1.70580e20i			0.775041i	−0.921861	+	0.387521i	$0.873332\pi$
$350$	−2.02617e20	−	1.29976e20i	−0.899772	−	0.577192i
$351$	−2.01052e20			−0.872674
$352$	5.26687e19	+	5.26687e19i	0.223466	+	0.223466i
$353$	2.10385e20	−	2.10385e20i	0.872603	−	0.872603i	−0.120152	−	0.992755i	$-0.538338\pi$
$353$	2.10385e20	−	2.10385e20i	0.872603	−	0.872603i	0.992755	+	0.120152i	$0.0383383\pi$
$354$		−	1.61657e20i		−	0.655492i
$355$	−1.39821e20	−	2.55810e20i	−0.554300	−	1.01412i
$356$	−6.28175e18			−0.0243490
$357$	−1.45208e20	−	1.45208e20i	−0.550359	−	0.550359i
$358$	−1.61701e20	+	1.61701e20i	−0.599307	+	0.599307i
$359$		−	1.02349e20i		−	0.370961i	−0.982648	−	0.185480i	$-0.940616\pi$
$359$		−	1.02349e20i		−	0.370961i	0.982648	−	0.185480i	$-0.0593841\pi$
$360$	−1.08741e19	+	3.70907e19i	−0.0385454	+	0.131476i
$361$	−1.15693e20			−0.401099
$362$	1.11074e20	+	1.11074e20i	0.376657	+	0.376657i
$363$	−5.51421e20	+	5.51421e20i	−1.82907	+	1.82907i
$364$			2.81781e20i			0.914324i
$365$	−5.39345e19	−	1.58123e19i	−0.171208	−	0.0501939i
$366$	−1.65347e18			−0.00513509
$367$	3.62508e20	+	3.62508e20i	1.10151	+	1.10151i	0.994229	+	0.107282i	$0.0342147\pi$
$367$	3.62508e20	+	3.62508e20i	1.10151	+	1.10151i	0.107282	+	0.994229i	$0.465785\pi$
$368$	4.15376e19	−	4.15376e19i	0.123498	−	0.123498i
$369$		−	1.86598e19i		−	0.0542870i
$370$	−1.91132e20	+	1.04469e20i	−0.544151	+	0.297423i
$371$	1.42369e20			0.396666
$372$	−2.33623e20	−	2.33623e20i	−0.637048	−	0.637048i
$373$	1.34570e20	−	1.34570e20i	0.359151	−	0.359151i	−0.504349	−	0.863500i	$-0.668267\pi$
$373$	1.34570e20	−	1.34570e20i	0.359151	−	0.359151i	0.863500	+	0.504349i	$0.168267\pi$
$374$		−	2.11500e20i		−	0.552508i
$375$	3.47759e20	−	3.02095e20i	0.889258	−	0.772490i
$376$	8.29769e19			0.207708
$377$	1.72751e20	+	1.72751e20i	0.423340	+	0.423340i
$378$	2.27302e20	−	2.27302e20i	0.545343	−	0.545343i
$379$			1.87978e20i			0.441564i	0.975323	+	0.220782i	$0.0708609\pi$
$379$			1.87978e20i			0.441564i	−0.975323	+	0.220782i	$0.929139\pi$
$380$	1.23414e20	+	2.25793e20i	0.283855	+	0.519328i
$381$	8.64886e20			1.94787
$382$	−1.22597e20	−	1.22597e20i	−0.270379	−	0.270379i
$383$	−2.03335e20	+	2.03335e20i	−0.439158	+	0.439158i	−0.891729	−	0.452570i	$-0.850507\pi$
$383$	−2.03335e20	+	2.03335e20i	−0.439158	+	0.439158i	0.452570	+	0.891729i	$0.350507\pi$
$384$			4.92226e19i			0.104115i
$385$	3.67026e20	−	1.25190e21i	0.760346	−	2.59349i
$386$	6.66353e20			1.35209
$387$	1.63653e19	+	1.63653e19i	0.0325265	+	0.0325265i
$388$	−1.71235e20	+	1.71235e20i	−0.333380	+	0.333380i
$389$			7.56310e20i			1.44246i	0.692697	+	0.721228i	$0.256422\pi$
$389$			7.56310e20i			1.44246i	−0.692697	+	0.721228i	$0.743578\pi$
$390$	−5.17437e20	−	1.51700e20i	−0.966810	−	0.283444i
$391$	−1.66802e20			−0.305342
$392$	−1.79182e20	−	1.79182e20i	−0.321370	−	0.321370i
$393$	−2.32478e20	+	2.32478e20i	−0.408546	+	0.408546i
$394$		−	4.87720e20i		−	0.839848i
$395$	−1.03163e21	+	5.63870e20i	−1.74079	+	0.951485i
$396$	−2.09473e20			−0.346391
$397$	1.88540e20	+	1.88540e20i	0.305549	+	0.305549i	0.843180	−	0.537631i	$-0.180681\pi$
$397$	1.88540e20	+	1.88540e20i	0.305549	+	0.305549i	−0.537631	+	0.843180i	$0.680681\pi$
$398$	3.99200e20	−	3.99200e20i	0.634053	−	0.634053i
$399$			1.35402e21i			2.10787i
$400$	8.84640e19	−	1.37905e20i	0.134985	−	0.210426i
$401$	1.16131e21			1.73697			0.868487	−	0.495713i	$-0.165093\pi$
$401$	1.16131e21			1.73697			0.868487	+	0.495713i	$0.165093\pi$
$402$	8.68824e19	+	8.68824e19i	0.127386	+	0.127386i
$403$	9.10257e20	−	9.10257e20i	1.30835	−	1.30835i
$404$			4.30878e20i			0.607160i
$405$	4.29560e20	+	7.85904e20i	0.593449	+	1.08575i
$406$	−3.90612e20			−0.529099
$407$	−8.34717e20	−	8.34717e20i	−1.10862	−	1.10862i
$408$	9.88311e19	−	9.88311e19i	0.128710	−	0.128710i
$409$		−	5.86136e20i		−	0.748535i	−0.927321	−	0.374268i	$-0.877894\pi$
$409$		−	5.86136e20i		−	0.748535i	0.927321	−	0.374268i	$-0.122106\pi$
$410$	−2.22525e19	+	7.59016e19i	−0.0278681	+	0.0950562i
$411$	−1.40404e21			−1.72442
$412$	−2.16350e20	−	2.16350e20i	−0.260603	−	0.260603i
$413$	−7.12093e20	+	7.12093e20i	−0.841272	+	0.841272i
$414$			1.65203e20i			0.191432i
$415$	−2.87527e19	−	8.42958e18i	−0.0326809	−	0.00958123i
$416$	−1.91784e20			−0.213829
$417$	−8.12903e20	−	8.12903e20i	−0.889099	−	0.889099i
$418$	−9.86088e20	+	9.86088e20i	−1.05805	+	1.05805i
$419$		−	7.14611e20i		−	0.752242i	−0.926570	−	0.376121i	$-0.877258\pi$
$419$		−	7.14611e20i		−	0.752242i	0.926570	−	0.376121i	$-0.122742\pi$
$420$	7.56502e20	−	4.13489e20i	0.781296	−	0.427042i
$421$	2.95408e20			0.299341			0.149670	−	0.988736i	$-0.452179\pi$
$421$	2.95408e20			0.299341			0.149670	+	0.988736i	$0.452179\pi$
$422$	−9.26756e19	−	9.26756e19i	−0.0921438	−	0.0921438i
$423$	−1.65007e20	+	1.65007e20i	−0.160983	+	0.160983i
$424$			9.68988e19i			0.0927666i
$425$	−4.54511e20	+	9.92688e19i	−0.427005	+	0.0932613i
$426$	1.04408e21			0.962627
$427$	7.28350e18	+	7.28350e18i	0.00659048	+	0.00659048i
$428$	−6.65330e19	+	6.65330e19i	−0.0590863	+	0.0590863i
$429$		−	2.92227e21i		−	2.54720i
$430$	−4.70523e19	−	8.60847e19i	−0.0402562	−	0.0736510i
$431$	4.62632e20			0.388524			0.194262	−	0.980950i	$-0.437769\pi$
$431$	4.62632e20			0.388524			0.194262	+	0.980950i	$0.437769\pi$
$432$	1.54706e20	+	1.54706e20i	0.127537	+	0.127537i
$433$	−7.45454e20	+	7.45454e20i	−0.603278	+	0.603278i	−0.941181	−	0.337903i	$-0.890283\pi$
$433$	−7.45454e20	+	7.45454e20i	−0.603278	+	0.603278i	0.337903	+	0.941181i	$0.390283\pi$
$434$			2.05820e21i			1.63520i
$435$	2.10290e20	−	7.17285e20i	0.164023	−	0.559471i
$436$	1.12797e20			0.0863784
$437$	7.77687e20	+	7.77687e20i	0.584728	+	0.584728i
$438$	1.42335e20	−	1.42335e20i	0.105080	−	0.105080i
$439$		−	1.04843e21i		−	0.760014i	−0.924984	−	0.380007i	$-0.875922\pi$
$439$		−	1.04843e21i		−	0.760014i	0.924984	−	0.380007i	$-0.124078\pi$
$440$	8.52064e20	+	2.49804e20i	0.606528	+	0.177819i
$441$	7.12638e20			0.498150
$442$	3.85072e20	+	3.85072e20i	0.264340	+	0.264340i
$443$	−3.35145e20	+	3.35145e20i	−0.225945	+	0.225945i	−0.810996	−	0.585051i	$-0.801074\pi$
$443$	−3.35145e20	+	3.35145e20i	−0.225945	+	0.225945i	0.585051	+	0.810996i	$0.301074\pi$
$444$		−	7.80102e20i		−	0.516521i
$445$	−6.57094e19	+	3.59155e19i	−0.0427314	+	0.0233562i
$446$	−1.44581e21			−0.923491
$447$	1.26024e21	+	1.26024e21i	0.790666	+	0.790666i
$448$	2.16824e20	−	2.16824e20i	0.133624	−	0.133624i
$449$			2.56993e21i			1.55579i	0.628397	+	0.777893i	$0.283712\pi$
$449$			2.56993e21i			1.55579i	−0.628397	+	0.777893i	$0.716288\pi$
$450$	9.83172e19	+	4.50155e20i	0.0584695	+	0.267708i
$451$	−4.28661e20			−0.250439
$452$	−2.68939e20	−	2.68939e20i	−0.154364	−	0.154364i
$453$	1.32082e21	−	1.32082e21i	0.744831	−	0.744831i
$454$		−	1.36438e21i		−	0.755941i
$455$	1.61106e21	+	2.94753e21i	0.877045	+	1.60460i
$456$	−9.21569e20			−0.492957
$457$	−2.39090e20	−	2.39090e20i	−0.125670	−	0.125670i	0.641474	−	0.767144i	$-0.278323\pi$
$457$	−2.39090e20	−	2.39090e20i	−0.125670	−	0.125670i	−0.767144	+	0.641474i	$0.778323\pi$
$458$	6.92217e20	−	6.92217e20i	0.357535	−	0.357535i
$459$		−	6.21247e20i		−	0.315328i
$460$	1.97010e20	−	6.71988e20i	0.0982711	−	0.335196i
$461$	−2.96336e21			−1.45270			−0.726352	−	0.687323i	$-0.758786\pi$
$461$	−2.96336e21			−1.45270			−0.726352	+	0.687323i	$0.758786\pi$
$462$	3.30381e21	+	3.30381e21i	1.59177	+	1.59177i
$463$	1.80865e21	−	1.80865e21i	0.856458	−	0.856458i	−0.134461	−	0.990919i	$-0.542930\pi$
$463$	1.80865e21	−	1.80865e21i	0.856458	−	0.856458i	0.990919	+	0.134461i	$0.0429304\pi$
$464$		−	2.65856e20i		−	0.123738i
$465$	−3.77951e21	−	1.10806e21i	−1.72907	−	0.506919i
$466$	−1.55185e21			−0.697849
$467$	1.43318e20	+	1.43318e20i	0.0633529	+	0.0633529i	0.738073	−	0.674720i	$-0.235736\pi$
$467$	1.43318e20	+	1.43318e20i	0.0633529	+	0.0633529i	−0.674720	+	0.738073i	$0.735736\pi$
$468$	3.81381e20	−	3.81381e20i	0.165726	−	0.165726i
$469$		−	7.65429e20i		−	0.326981i
$470$	8.67969e20	−	4.74415e20i	0.364520	−	0.199240i
$471$	−2.19691e20			−0.0907080
$472$	−4.84662e20	−	4.84662e20i	−0.196745	−	0.196745i
$473$	3.75951e20	−	3.75951e20i	0.150052	−	0.150052i
$474$		−	4.21058e21i		−	1.65240i
$475$	2.58192e21	+	1.65626e21i	0.996307	+	0.639118i
$476$	−8.70696e20			−0.330378
$477$	−1.92692e20	−	1.92692e20i	−0.0718981	−	0.0718981i
$478$	−2.11905e21	+	2.11905e21i	−0.777531	+	0.777531i
$479$			9.78276e20i			0.353002i	0.984300	+	0.176501i	$0.0564779\pi$
$479$			9.78276e20i			0.353002i	−0.984300	+	0.176501i	$0.943522\pi$
$480$	2.81427e20	+	5.14887e20i	0.0998703	+	0.182718i
$481$	3.03948e21			1.06081
$482$	−1.26344e21	−	1.26344e21i	−0.433688	−	0.433688i
$483$	2.60558e21	−	2.60558e21i	0.879686	−	0.879686i
$484$			3.30642e21i			1.09798i
$485$	−8.12156e20	+	2.77021e21i	−0.265281	+	0.904855i
$486$	−1.61989e21			−0.520468
$487$	−2.11699e21	−	2.11699e21i	−0.669093	−	0.669093i	0.288413	−	0.957506i	$-0.406872\pi$
$487$	−2.11699e21	−	2.11699e21i	−0.669093	−	0.669093i	−0.957506	+	0.288413i	$0.906872\pi$
$488$	−4.95726e18	+	4.95726e18i	−0.00154129	+	0.00154129i
$489$			5.90695e21i			1.80673i
$490$	−2.89877e21	−	8.49846e20i	−0.872258	−	0.255724i
$491$	−7.27622e20			−0.215404			−0.107702	−	0.994183i	$-0.534349\pi$
$491$	−7.27622e20			−0.215404			−0.107702	+	0.994183i	$0.534349\pi$
$492$	−2.00307e20	−	2.00307e20i	−0.0583412	−	0.0583412i
$493$	−5.33797e20	+	5.33797e20i	−0.152968	+	0.152968i
$494$		−	3.59068e21i		−	1.01242i
$495$	−2.19117e21	+	1.19765e21i	−0.607902	+	0.332268i
$496$	−1.40085e21			−0.382417
$497$	−4.59915e21	−	4.59915e21i	−1.23545	−	1.23545i
$498$	7.58794e19	−	7.58794e19i	0.0200581	−	0.0200581i
$499$		−	2.10228e21i		−	0.546872i	−0.961890	−	0.273436i	$-0.911840\pi$
$499$		−	2.10228e21i		−	0.546872i	0.961890	−	0.273436i	$-0.0881602\pi$
$500$	1.36904e20	−	1.94832e21i	0.0350475	−	0.498770i
$501$	−5.17735e21			−1.30438
$502$	2.22926e21	+	2.22926e21i	0.552752	+	0.552752i
$503$	3.42489e21	−	3.42489e21i	0.835801	−	0.835801i	−0.152502	−	0.988303i	$-0.548733\pi$
$503$	3.42489e21	−	3.42489e21i	0.835801	−	0.835801i	0.988303	+	0.152502i	$0.0487330\pi$
$504$			8.62350e20i			0.207128i
$505$	2.46352e21	+	4.50714e21i	0.582405	+	1.06554i
$506$	3.79511e21			0.883121
$507$	1.68411e21	+	1.68411e21i	0.385751	+	0.385751i
$508$	2.59301e21	−	2.59301e21i	0.584648	−	0.584648i
$509$		−	8.32023e20i		−	0.184669i	−0.995728	−	0.0923343i	$-0.970567\pi$
$509$		−	8.32023e20i		−	0.184669i	0.995728	−	0.0923343i	$-0.0294329\pi$
$510$	4.68749e20	−	1.59887e21i	0.102419	−	0.349343i
$511$	−1.25396e21			−0.269723
$512$	1.47574e20	+	1.47574e20i	0.0312500	+	0.0312500i
$513$	−2.89647e21	+	2.89647e21i	−0.603852	+	0.603852i
$514$		−	1.81291e21i		−	0.372109i
$515$	−3.50007e21	−	1.02613e21i	−0.707325	−	0.207370i
$516$	3.51353e20			0.0699111
$517$	3.79061e21	+	3.79061e21i	0.742652	+	0.742652i
$518$	−3.43633e21	+	3.43633e21i	−0.662913	+	0.662913i
$519$			5.18715e21i			0.985350i
$520$	−2.00614e21	+	1.09652e21i	−0.375261	+	0.205111i
$521$	1.00689e22			1.85473			0.927364	−	0.374160i	$-0.122069\pi$
$521$	1.00689e22			1.85473			0.927364	+	0.374160i	$0.122069\pi$
$522$	5.28680e20	+	5.28680e20i	0.0959022	+	0.0959022i
$523$	3.20197e21	−	3.20197e21i	0.572011	−	0.572011i	−0.360679	−	0.932690i	$-0.617455\pi$
$523$	3.20197e21	−	3.20197e21i	0.572011	−	0.572011i	0.932690	+	0.360679i	$0.117455\pi$
$524$			1.39398e21i			0.245248i
$525$	5.54919e21	−	8.65051e21i	0.961512	−	1.49888i
$526$	6.03487e21			1.02987
$527$	2.81267e21	+	2.81267e21i	0.472753	+	0.472753i
$528$	−2.24863e21	+	2.24863e21i	−0.372260	+	0.372260i
$529$			3.13956e21i			0.511945i
$530$	5.54014e20	+	1.01360e21i	0.0889843	+	0.162802i
$531$	1.92759e21			0.304971
$532$	4.05949e21	+	4.05949e21i	0.632671	+	0.632671i
$533$	7.80449e20	−	7.80449e20i	0.119819	−	0.119819i
$534$		−	2.68192e20i		−	0.0405616i
$535$	−3.15561e20	+	1.07636e21i	−0.0470169	+	0.160371i
$536$	5.20963e20			0.0764695
$537$	−6.90364e21	−	6.90364e21i	−0.998353	−	0.998353i
$538$	−9.34700e20	+	9.34700e20i	−0.133172	+	0.133172i
$539$		−	1.63710e22i		−	2.29808i
$540$	2.50280e21	+	7.33758e20i	0.346159	+	0.101485i
$541$	−3.16865e21			−0.431814			−0.215907	−	0.976414i	$-0.569271\pi$
$541$	−3.16865e21			−0.431814			−0.215907	+	0.976414i	$0.569271\pi$
$542$	2.26860e21	+	2.26860e21i	0.304624	+	0.304624i
$543$	−4.74219e21	+	4.74219e21i	−0.627452	+	0.627452i
$544$		−	5.92609e20i		−	0.0772640i
$545$	1.17990e21	−	6.44909e20i	0.151590	−	0.0828565i
$546$	−1.20303e22			−1.52312
$547$	−5.67729e21	−	5.67729e21i	−0.708341	−	0.708341i	0.257845	−	0.966186i	$-0.416988\pi$
$547$	−5.67729e21	−	5.67729e21i	−0.708341	−	0.708341i	−0.966186	+	0.257845i	$0.916988\pi$
$548$	−4.20943e21	+	4.20943e21i	−0.517581	+	0.517581i
$549$		−	1.97159e19i		−	0.00238912i
$550$	1.03411e22	−	2.25859e21i	1.23500	−	0.269734i
$551$	4.97749e21			0.585865
$552$	1.77340e21	+	1.77340e21i	0.205728	+	0.205728i
$553$	−1.85475e22	+	1.85475e22i	−2.12072	+	2.12072i
$554$			5.49667e21i			0.619472i
$555$	−4.46019e21	−	8.16016e21i	−0.495461	−	0.906473i
$556$	−4.87432e21			−0.533722
$557$	−1.05049e22	−	1.05049e22i	−1.13384	−	1.13384i	−0.989534	−	0.144303i	$-0.953906\pi$
$557$	−1.05049e22	−	1.05049e22i	−1.13384	−	1.13384i	−0.144303	−	0.989534i	$-0.546094\pi$
$558$	2.78571e21	−	2.78571e21i	0.296389	−	0.296389i
$559$			1.36896e21i			0.143581i
$560$	1.02838e21	−	3.50774e21i	0.106329	−	0.362680i
$561$	9.02976e21			0.920393
$562$	−8.28184e21	−	8.28184e21i	−0.832216	−	0.832216i
$563$	−2.26617e21	+	2.26617e21i	−0.224504	+	0.224504i	−0.810392	−	0.585888i	$-0.800746\pi$
$563$	−2.26617e21	+	2.26617e21i	−0.224504	+	0.224504i	0.585888	+	0.810392i	$0.300746\pi$
$564$			3.54260e21i			0.346010i
$565$	−4.35084e21	−	1.27556e21i	−0.418972	−	0.122832i
$566$	1.13044e22			1.07329
$567$	1.41296e22	+	1.41296e22i	1.32271	+	1.32271i
$568$	3.13026e21	−	3.13026e21i	0.288930	−	0.288930i
$569$			5.59198e21i			0.508941i	0.967081	+	0.254470i	$0.0819012\pi$
$569$			5.59198e21i			0.508941i	−0.967081	+	0.254470i	$0.918099\pi$
$570$	−9.63996e21	+	5.26902e21i	−0.865120	+	0.472858i
$571$	2.66584e20			0.0235910			0.0117955	−	0.999930i	$-0.496245\pi$
$571$	2.66584e20			0.0235910			0.0117955	+	0.999930i	$0.496245\pi$
$572$	−8.76124e21	−	8.76124e21i	−0.764535	−	0.764535i
$573$	5.23413e21	−	5.23413e21i	0.450410	−	0.450410i
$574$			1.76469e21i			0.149752i
$575$	−1.78125e21	−	8.15564e21i	−0.149068	−	0.682520i
$576$	−5.86929e20			−0.0484402
$577$	5.20931e21	+	5.20931e21i	0.424007	+	0.424007i	0.886581	−	0.462574i	$-0.153074\pi$
$577$	5.20931e21	+	5.20931e21i	0.424007	+	0.424007i	−0.462574	+	0.886581i	$0.653074\pi$
$578$	5.03877e21	−	5.03877e21i	0.404484	−	0.404484i
$579$			2.84491e22i			2.25238i
$580$	−1.52002e21	−	2.78096e21i	−0.118693	−	0.217155i
$581$	−6.68493e20			−0.0514859
$582$	−7.31068e21	−	7.31068e21i	−0.555359	−	0.555359i
$583$	−4.42661e21	+	4.42661e21i	−0.331683	+	0.331683i
$584$		−	8.53468e20i		−	0.0630789i
$585$	1.80886e21	−	6.16991e21i	0.131874	−	0.449813i
$586$	1.12948e22			0.812262
$587$	−8.09602e21	−	8.09602e21i	−0.574337	−	0.574337i	0.359001	−	0.933337i	$-0.383118\pi$
$587$	−8.09602e21	−	8.09602e21i	−0.574337	−	0.574337i	−0.933337	+	0.359001i	$0.883118\pi$
$588$	7.64995e21	−	7.64995e21i	0.535352	−	0.535352i
$589$		−	2.62273e22i		−	1.81064i
$590$	−7.84077e21	−	2.29872e21i	−0.534002	−	0.156556i
$591$	2.08226e22			1.39906
$592$	−2.33882e21	−	2.33882e21i	−0.155033	−	0.155033i
$593$	1.93025e22	−	1.93025e22i	1.26234	−	1.26234i	0.312386	−	0.949955i	$-0.398872\pi$
$593$	1.93025e22	−	1.93025e22i	1.26234	−	1.26234i	0.949955	−	0.312386i	$-0.101128\pi$
$594$			1.41348e22i			0.912004i
$595$	−9.10780e21	+	4.97815e21i	−0.579800	+	0.316908i
$596$	7.55663e21			0.474633
$597$	1.70434e22	+	1.70434e22i	1.05623	+	1.05623i
$598$	−6.90963e21	+	6.90963e21i	−0.422518	+	0.422518i
$599$			9.43902e21i			0.569524i	0.958598	+	0.284762i	$0.0919146\pi$
$599$			9.43902e21i			0.569524i	−0.958598	+	0.284762i	$0.908085\pi$
$600$	5.88767e21	+	3.77686e21i	0.350537	+	0.224865i
$601$	−1.94188e22			−1.14084			−0.570422	−	0.821352i	$-0.693220\pi$
$601$	−1.94188e22			−1.14084			−0.570422	+	0.821352i	$0.693220\pi$
$602$	−1.54770e21	−	1.54770e21i	−0.0897253	−	0.0897253i
$603$	−1.03598e21	+	1.03598e21i	−0.0592671	+	0.0592671i
$604$		−	7.91988e21i		−	0.447119i
$605$	1.89043e22	+	3.45864e22i	1.05322	+	1.92691i
$606$	−1.83958e22			−1.01143
$607$	1.96226e22	+	1.96226e22i	1.06475	+	1.06475i	0.997753	+	0.0669931i	$0.0213406\pi$
$607$	1.96226e22	+	1.96226e22i	1.06475	+	1.06475i	0.0669931	+	0.997753i	$0.478659\pi$
$608$	−2.76295e21	+	2.76295e21i	−0.147960	+	0.147960i
$609$		−	1.66767e22i		−	0.881397i
$610$	−2.35119e19	+	8.01977e19i	−0.00122645	+	0.00418334i
$611$	−1.38029e22			−0.710625
$612$	1.17846e21	+	1.17846e21i	0.0598829	+	0.0598829i
$613$	−4.15797e21	+	4.15797e21i	−0.208544	+	0.208544i	−0.803648	−	0.595104i	$-0.797111\pi$
$613$	−4.15797e21	+	4.15797e21i	−0.208544	+	0.208544i	0.595104	+	0.803648i	$0.297111\pi$
$614$			3.25912e21i			0.161344i
$615$	−3.24053e21	−	9.50042e20i	−0.158349	−	0.0464239i
$616$	1.98103e22			0.955531
$617$	4.70913e21	+	4.70913e21i	0.224212	+	0.224212i	0.810270	−	0.586057i	$-0.199321\pi$
$617$	4.70913e21	+	4.70913e21i	0.224212	+	0.224212i	−0.586057	+	0.810270i	$0.699321\pi$
$618$	9.23681e21	−	9.23681e21i	0.434124	−	0.434124i
$619$		−	2.61926e21i		−	0.121521i	−0.998152	−	0.0607607i	$-0.980647\pi$
$619$		−	2.61926e21i		−	0.121521i	0.998152	−	0.0607607i	$-0.0193527\pi$
$620$	−1.46534e22	+	8.00926e21i	−0.671126	+	0.366825i
$621$	1.11475e22			0.504017
$622$	7.61094e21	+	7.61094e21i	0.339715	+	0.339715i
$623$	−1.18138e21	+	1.18138e21i	−0.0520576	+	0.0520576i
$624$		−	8.18800e21i		−	0.356206i
$625$	−9.70734e21	−	2.11629e22i	−0.416927	−	0.908940i
$626$	−7.78862e21			−0.330267
$627$	−4.20998e22	−	4.20998e22i	−1.76255	−	1.76255i
$628$	−6.58655e20	+	6.58655e20i	−0.0272258	+	0.0272258i
$629$			9.39194e21i			0.383310i
$630$	4.93043e21	+	9.02050e21i	0.198683	+	0.363501i
$631$	−3.02555e22			−1.20384			−0.601920	−	0.798556i	$-0.705598\pi$
$631$	−3.02555e22			−1.20384			−0.601920	+	0.798556i	$0.705598\pi$
$632$	−1.26237e22	−	1.26237e22i	−0.495964	−	0.495964i
$633$	3.95668e21	−	3.95668e21i	0.153497	−	0.153497i
$634$			1.57210e20i			0.00602237i
$635$	1.22985e22	−	4.19492e22i	0.465223	−	1.58684i
$636$	−4.13698e21			−0.154535
$637$	2.98062e22	+	2.98062e22i	1.09949	+	1.09949i
$638$	1.21451e22	−	1.21451e22i	0.442420	−	0.442420i
$639$			1.24496e22i			0.447867i
$640$	2.38742e21	+	6.99933e20i	0.0848183	+	0.0248666i
$641$	−2.36348e22			−0.829253			−0.414626	−	0.909992i	$-0.636088\pi$
$641$	−2.36348e22			−0.829253			−0.414626	+	0.909992i	$0.636088\pi$
$642$	−2.84055e21	−	2.84055e21i	−0.0984287	−	0.0984287i
$643$	−3.25577e21	+	3.25577e21i	−0.111421	+	0.111421i	−0.760619	−	0.649198i	$-0.775104\pi$
$643$	−3.25577e21	+	3.25577e21i	−0.111421	+	0.111421i	0.649198	+	0.760619i	$0.275104\pi$
$644$		−	1.56236e22i		−	0.528072i
$645$	3.67528e21	−	2.00884e21i	0.122691	−	0.0670607i
$646$	1.10951e22			0.365824
$647$	1.96903e22	+	1.96903e22i	0.641238	+	0.641238i	0.950860	−	0.309622i	$-0.100202\pi$
$647$	1.96903e22	+	1.96903e22i	0.641238	+	0.641238i	−0.309622	+	0.950860i	$0.600202\pi$
$648$	−9.61683e21	+	9.61683e21i	−0.309337	+	0.309337i
$649$		−	4.42814e22i		−	1.40690i
$650$	−1.47157e22	+	2.29399e22i	−0.461820	+	0.719922i
$651$	−8.78726e22			−2.72399
$652$	1.77096e22	+	1.77096e22i	0.542285	+	0.542285i
$653$	−5.11277e21	+	5.11277e21i	−0.154650	+	0.154650i	−0.780191	−	0.625541i	$-0.784878\pi$
$653$	−5.11277e21	+	5.11277e21i	−0.154650	+	0.154650i	0.625541	+	0.780191i	$0.284878\pi$
$654$			4.81573e21i			0.143893i
$655$	7.97000e21	+	1.45815e22i	0.235249	+	0.430401i
$656$	−1.20108e21			−0.0350220
$657$	1.69720e21	+	1.69720e21i	0.0488889	+	0.0488889i
$658$	1.56050e22	−	1.56050e22i	0.444077	−	0.444077i
$659$		−	7.32565e21i		−	0.205950i	−0.994684	−	0.102975i	$-0.967164\pi$
$659$		−	7.32565e21i		−	0.205950i	0.994684	−	0.102975i	$-0.0328362\pi$
$660$	−1.06651e22	+	3.63779e22i	−0.296219	+	1.01038i
$661$	−9.95362e21			−0.273130			−0.136565	−	0.990631i	$-0.543606\pi$
$661$	−9.95362e21			−0.273130			−0.136565	+	0.990631i	$0.543606\pi$
$662$	2.27367e22	+	2.27367e22i	0.616400	+	0.616400i
$663$	−1.64402e22	+	1.64402e22i	−0.440351	+	0.440351i
$664$		−	4.54987e20i		−	0.0120408i
$665$	6.56736e22	+	1.92539e22i	1.71719	+	0.503436i
$666$	9.30191e21			0.240314
$667$	−9.57832e21	−	9.57832e21i	−0.244502	−	0.244502i
$668$	−1.55222e22	+	1.55222e22i	−0.391508	+	0.391508i
$669$		−	6.17272e22i		−	1.53839i
$670$	5.44946e21	−	2.97857e21i	0.134201	−	0.0733517i
$671$	−4.52923e20			−0.0110216
$672$	9.25705e21	+	9.25705e21i	0.222597	+	0.222597i
$673$	3.25272e22	−	3.25272e22i	0.772906	−	0.772906i	−0.205708	−	0.978613i	$-0.565950\pi$
$673$	3.25272e22	−	3.25272e22i	0.772906	−	0.772906i	0.978613	+	0.205708i	$0.0659496\pi$
$674$			1.87801e22i			0.440980i
$675$	3.03754e22	−	6.63422e21i	0.704842	−	0.153943i
$676$	1.00982e22			0.231565
$677$	−3.79679e22	−	3.79679e22i	−0.860414	−	0.860414i	0.130972	−	0.991386i	$-0.458190\pi$
$677$	−3.79679e22	−	3.79679e22i	−0.860414	−	0.860414i	−0.991386	+	0.130972i	$0.958190\pi$
$678$	1.14820e22	−	1.14820e22i	0.257146	−	0.257146i
$679$			6.44067e22i			1.42552i
$680$	−3.38821e21	−	6.19891e21i	−0.0741138	−	0.135595i
$681$	5.82505e22			1.25928
$682$	−6.39946e22	−	6.39946e22i	−1.36731	−	1.36731i
$683$	2.13281e22	−	2.13281e22i	0.450389	−	0.450389i	−0.445095	−	0.895483i	$-0.646830\pi$
$683$	2.13281e22	−	2.13281e22i	0.450389	−	0.450389i	0.895483	+	0.445095i	$0.146830\pi$
$684$		−	1.09888e22i		−	0.229351i
$685$	−1.99650e22	+	6.80994e22i	−0.411856	+	1.40481i
$686$	−1.49672e22			−0.305174
$687$	2.95534e22	+	2.95534e22i	0.595598	+	0.595598i
$688$	1.05339e21	−	1.05339e21i	0.0209837	−	0.0209837i
$689$		−	1.61188e22i		−	0.317379i
$690$	2.86897e22	+	8.41111e21i	0.558385	+	0.163705i
$691$	7.94223e22			1.52798			0.763991	−	0.645227i	$-0.223237\pi$
$691$	7.94223e22			1.52798			0.763991	+	0.645227i	$0.223237\pi$
$692$	1.55516e22	+	1.55516e22i	0.295751	+	0.295751i
$693$	−3.93945e22	+	3.93945e22i	−0.740577	+	0.740577i
$694$		−	1.44640e22i		−	0.268789i
$695$	−5.09872e22	+	2.78686e22i	−0.936661	+	0.511961i
$696$	1.13504e22			0.206129
$697$	2.41157e21	+	2.41157e21i	0.0432950	+	0.0432950i
$698$	−2.18342e22	+	2.18342e22i	−0.387521	+	0.387521i
$699$		−	6.62542e22i		−	1.16251i
$700$	−9.29805e21	−	4.25720e22i	−0.161290	−	0.738482i
$701$	−2.82128e22			−0.483840			−0.241920	−	0.970296i	$-0.577777\pi$
$701$	−2.82128e22			−0.483840			−0.241920	+	0.970296i	$0.577777\pi$
$702$	−2.57347e22	−	2.57347e22i	−0.436337	−	0.436337i
$703$	4.37885e22	−	4.37885e22i	0.734036	−	0.734036i
$704$			1.34832e22i			0.223466i
$705$	2.02546e22	+	3.70569e22i	0.331903	+	0.607234i
$706$	5.38585e22			0.872603
$707$	8.10330e22	+	8.10330e22i	1.29810	+	1.29810i
$708$	2.06921e22	−	2.06921e22i	0.327746	−	0.327746i
$709$			5.46577e22i			0.856014i	0.903775	+	0.428007i	$0.140784\pi$
$709$			5.46577e22i			0.856014i	−0.903775	+	0.428007i	$0.859216\pi$
$710$	1.48466e22	−	5.06407e22i	0.229911	−	0.784211i
$711$	5.02068e22			0.768786
$712$	−8.04064e20	−	8.04064e20i	−0.0121745	−	0.0121745i
$713$	−5.04699e22	+	5.04699e22i	−0.755642	+	0.755642i
$714$		−	3.71733e22i		−	0.550359i
$715$	−1.41738e23	−	4.15540e22i	−2.07509	−	0.608365i
$716$	−4.13955e22			−0.599307
$717$	−9.04703e22	−	9.04703e22i	−1.29525	−	1.29525i
$718$	1.31007e22	−	1.31007e22i	0.185480	−	0.185480i
$719$			1.15901e23i			1.62276i	0.584519	+	0.811380i	$0.301283\pi$
$719$			1.15901e23i			1.62276i	−0.584519	+	0.811380i	$0.698717\pi$
$720$	−6.13949e21	+	3.35573e21i	−0.0850105	+	0.0464651i
$721$	−8.13758e22			−1.11433
$722$	−1.48088e22	−	1.48088e22i	−0.200549	−	0.200549i
$723$	5.39410e22	−	5.39410e22i	0.722458	−	0.722458i
$724$			2.84351e22i			0.376657i
$725$	−3.17999e22	−	2.03992e22i	−0.416603	−	0.267245i
$726$	−1.41164e23			−1.82907
$727$	−3.45583e22	−	3.45583e22i	−0.442871	−	0.442871i	0.450105	−	0.892976i	$-0.351387\pi$
$727$	−3.45583e22	−	3.45583e22i	−0.442871	−	0.442871i	−0.892976	+	0.450105i	$0.851387\pi$
$728$	−3.60679e22	+	3.60679e22i	−0.457162	+	0.457162i
$729$			2.95398e22i			0.370329i
$730$	−4.87965e21	−	8.92759e21i	−0.0605071	−	0.110701i
$731$	−4.23007e21			−0.0518810
$732$	−2.11644e20	−	2.11644e20i	−0.00256755	−	0.00256755i
$733$	−8.47770e22	+	8.47770e22i	−1.01729	+	1.01729i	−0.0174461	+	0.999848i	$0.505554\pi$
$733$	−8.47770e22	+	8.47770e22i	−1.01729	+	1.01729i	−0.999848	+	0.0174461i	$0.994446\pi$
$734$			9.28019e22i			1.10151i
$735$	3.62832e22	−	1.23759e23i	0.425997	−	1.45305i
$736$	1.06336e22			0.123498
$737$	2.37990e22	+	2.37990e22i	0.273413	+	0.273413i
$738$	2.38845e21	−	2.38845e21i	0.0271435	−	0.0271435i
$739$		−	1.01731e23i		−	1.14366i	−0.820373	−	0.571829i	$-0.806234\pi$
$739$		−	1.01731e23i		−	1.14366i	0.820373	−	0.571829i	$-0.193766\pi$
$740$	−3.78370e22	−	1.10929e22i	−0.420787	−	0.123364i
$741$	1.53300e23			1.68654
$742$	1.82233e22	+	1.82233e22i	0.198333	+	0.198333i
$743$	3.63999e22	−	3.63999e22i	0.391913	−	0.391913i	−0.483456	−	0.875369i	$-0.660619\pi$
$743$	3.63999e22	−	3.63999e22i	0.391913	−	0.391913i	0.875369	+	0.483456i	$0.160619\pi$
$744$		−	5.98075e22i		−	0.637048i
$745$	7.90452e22	−	4.32046e22i	0.832962	−	0.455282i
$746$	3.44499e22			0.359151
$747$	9.04784e20	+	9.04784e20i	0.00933211	+	0.00933211i
$748$	2.70720e22	−	2.70720e22i	0.276254	−	0.276254i
$749$			2.50251e22i			0.252651i
$750$	8.31812e22	+	5.84497e21i	0.830874	+	0.0583838i
$751$	1.69265e23			1.67281			0.836406	−	0.548110i	$-0.184652\pi$
$751$	1.69265e23			1.67281			0.836406	+	0.548110i	$0.184652\pi$
$752$	1.06210e22	+	1.06210e22i	0.103854	+	0.103854i
$753$	−9.51755e22	+	9.51755e22i	−0.920800	+	0.920800i
$754$			4.42242e22i			0.423340i
$755$	−4.52815e22	−	8.28449e22i	−0.428889	−	0.784676i
$756$	5.81894e22			0.545343
$757$	−9.07751e21	−	9.07751e21i	−0.0841782	−	0.0841782i	0.663764	−	0.747942i	$-0.268958\pi$
$757$	−9.07751e21	−	9.07751e21i	−0.0841782	−	0.0841782i	−0.747942	+	0.663764i	$0.768958\pi$
$758$	−2.40612e22	+	2.40612e22i	−0.220782	+	0.220782i
$759$			1.62028e23i			1.47114i
$760$	−1.31045e22	+	4.46985e22i	−0.117736	+	0.401591i
$761$	−2.01129e23			−1.78812			−0.894060	−	0.447948i	$-0.852155\pi$
$761$	−2.01129e23			−1.78812			−0.894060	+	0.447948i	$0.852155\pi$
$762$	1.10705e23	+	1.10705e23i	0.973933	+	0.973933i
$763$	2.12131e22	−	2.12131e22i	0.184675	−	0.184675i
$764$		−	3.13848e22i		−	0.270379i
$765$	1.90649e22	+	5.58934e21i	0.162533	+	0.0476507i
$766$	−5.20536e22			−0.439158
$767$	8.06217e22	+	8.06217e22i	0.673115	+	0.673115i
$768$	−6.30049e21	+	6.30049e21i	−0.0520577	+	0.0520577i
$769$		−	1.38911e23i		−	1.13586i	−0.823075	−	0.567932i	$-0.807744\pi$
$769$		−	1.38911e23i		−	1.13586i	0.823075	−	0.567932i	$-0.192256\pi$
$770$	2.07223e23	−	1.13264e23i	1.67692	−	0.916572i
$771$	7.73998e22			0.619876
$772$	8.52932e22	+	8.52932e22i	0.676045	+	0.676045i
$773$	7.88116e22	−	7.88116e22i	0.618236	−	0.618236i	−0.326843	−	0.945079i	$-0.605985\pi$
$773$	7.88116e22	−	7.88116e22i	0.618236	−	0.618236i	0.945079	+	0.326843i	$0.105985\pi$
$774$			4.18952e21i			0.0325265i
$775$	−1.07487e23	+	1.67560e23i	−0.825930	+	1.28753i
$776$	−4.38362e22			−0.333380
$777$	−1.46710e23	−	1.46710e23i	−1.10431	−	1.10431i
$778$	−9.68076e22	+	9.68076e22i	−0.721228	+	0.721228i
$779$		−	2.24872e22i		−	0.165819i
$780$	−4.68144e22	−	8.56496e22i	−0.341683	−	0.625127i
$781$	2.85998e23			2.06611
$782$	−2.13506e22	−	2.13506e22i	−0.152671	−	0.152671i
$783$	3.56741e22	−	3.56741e22i	0.252499	−	0.252499i
$784$		−	4.58705e22i		−	0.321370i
$785$	−3.12396e21	+	1.06556e22i	−0.0216644	+	0.0738960i
$786$	−5.95143e22			−0.408546
$787$	−1.41954e23	−	1.41954e23i	−0.964607	−	0.964607i	0.0347880	−	0.999395i	$-0.488924\pi$
$787$	−1.41954e23	−	1.41954e23i	−0.964607	−	0.964607i	−0.999395	+	0.0347880i	$0.988924\pi$
$788$	6.24281e22	−	6.24281e22i	0.419924	−	0.419924i
$789$			2.57651e23i			1.71560i
$790$	−2.04224e23	−	5.98733e22i	−1.34614	−	0.394654i
$791$	−1.01156e23			−0.660054
$792$	−2.68125e22	−	2.68125e22i	−0.173195	−	0.173195i
$793$	8.24623e20	−	8.24623e20i	0.00527314	−	0.00527314i
$794$			4.82663e22i			0.305549i
$795$	−4.32744e22	+	2.36529e22i	−0.271202	+	0.148234i
$796$	1.02195e23			0.634053
$797$	−6.40596e22	−	6.40596e22i	−0.393475	−	0.393475i	0.482449	−	0.875924i	$-0.339747\pi$
$797$	−6.40596e22	−	6.40596e22i	−0.393475	−	0.393475i	−0.875924	+	0.482449i	$0.839747\pi$
$798$	−1.73315e23	+	1.73315e23i	−1.05393	+	1.05393i
$799$		−	4.26507e22i		−	0.256774i
$800$	2.89752e22	−	6.32840e21i	0.172705	−	0.0377202i
$801$	3.19791e21			0.0188715
$802$	1.48648e23	+	1.48648e23i	0.868487	+	0.868487i
$803$	3.89888e22	−	3.89888e22i	0.225536	−	0.225536i
$804$			2.22419e22i			0.127386i
$805$	−8.93268e22	−	1.63428e23i	−0.506541	−	0.926744i
$806$	2.33026e23			1.30835
$807$	−3.99059e22	−	3.99059e22i	−0.221845	−	0.221845i
$808$	−5.51523e22	+	5.51523e22i	−0.303580	+	0.303580i
$809$			6.87072e22i			0.374467i	0.982315	+	0.187234i	$0.0599522\pi$
$809$			6.87072e22i			0.374467i	−0.982315	+	0.187234i	$0.940048\pi$
$810$	−4.56120e22	+	1.55579e23i	−0.246149	+	0.839599i
$811$	−3.14286e23			−1.67941			−0.839707	−	0.543039i	$-0.817273\pi$
$811$	−3.14286e23			−1.67941			−0.839707	+	0.543039i	$0.817273\pi$
$812$	−4.99983e22	−	4.99983e22i	−0.264549	−	0.264549i
$813$	−9.68553e22	+	9.68553e22i	−0.507457	+	0.507457i
$814$		−	2.13687e23i		−	1.10862i
$815$	2.86502e23	+	8.39953e22i	1.47186	+	0.431513i
$816$	2.53007e22			0.128710
$817$	1.97221e22	+	1.97221e22i	0.0993518	+	0.0993518i
$818$	7.50255e22	−	7.50255e22i	0.374268	−	0.374268i
$819$		−	1.43449e23i		−	0.708640i
$820$	−1.25637e22	+	6.86709e21i	−0.0614621	+	0.0335940i
$821$	2.45066e23			1.18724			0.593620	−	0.804746i	$-0.297698\pi$
$821$	2.45066e23			1.18724			0.593620	+	0.804746i	$0.297698\pi$
$822$	−1.79717e23	−	1.79717e23i	−0.862211	−	0.862211i
$823$	1.19003e23	−	1.19003e23i	0.565406	−	0.565406i	−0.365432	−	0.930838i	$-0.619079\pi$
$823$	1.19003e23	−	1.19003e23i	0.565406	−	0.565406i	0.930838	+	0.365432i	$0.119079\pi$
$824$		−	5.53856e22i		−	0.260603i
$825$	9.64276e22	+	4.41503e23i	0.449335	+	2.05732i
$826$	−1.82296e23			−0.841272
$827$	−1.30259e23	−	1.30259e23i	−0.595340	−	0.595340i	0.343729	−	0.939069i	$-0.388310\pi$
$827$	−1.30259e23	−	1.30259e23i	−0.595340	−	0.595340i	−0.939069	+	0.343729i	$0.888310\pi$
$828$	−2.11460e22	+	2.11460e22i	−0.0957160	+	0.0957160i
$829$		−	2.66922e23i		−	1.19660i	−0.801273	−	0.598299i	$-0.795843\pi$
$829$		−	2.66922e23i		−	1.19660i	0.801273	−	0.598299i	$-0.204157\pi$
$830$	−2.60136e21	−	4.75933e21i	−0.0115498	−	0.0211311i
$831$	−2.34674e23			−1.03194
$832$	−2.45484e22	−	2.45484e22i	−0.106914	−	0.106914i
$833$	−9.21006e22	+	9.21006e22i	−0.397285	+	0.397285i
$834$		−	2.08103e23i		−	0.889099i
$835$	−7.36205e22	+	2.51115e23i	−0.311535	+	1.06263i
$836$	−2.52439e23			−1.05805
$837$	−1.87973e23	−	1.87973e23i	−0.780356	−	0.780356i
$838$	9.14703e22	−	9.14703e22i	0.376121	−	0.376121i
$839$		−	3.39945e22i		−	0.138456i	−0.997601	−	0.0692281i	$-0.977946\pi$
$839$		−	3.39945e22i		−	0.138456i	0.997601	−	0.0692281i	$-0.0220536\pi$
$840$	1.49759e23	+	4.39055e22i	0.604169	+	0.177127i
$841$	1.88942e23			0.755022
$842$	3.78123e22	+	3.78123e22i	0.149670	+	0.149670i
$843$	3.53583e23	−	3.53583e23i	1.38634	−	1.38634i
$844$		−	2.37250e22i		−	0.0921438i
$845$	1.05631e23	−	5.77362e22i	0.406387	−	0.222123i
$846$	−4.22418e22			−0.160983
$847$	6.21822e23	+	6.21822e23i	2.34746	+	2.34746i
$848$	−1.24031e22	+	1.24031e22i	−0.0463833	+	0.0463833i
$849$			4.82628e23i			1.78793i
$850$	−7.08839e22	−	4.54711e22i	−0.260133	−	0.166872i
$851$	−1.68527e23			−0.612678
$852$	1.33643e23	+	1.33643e23i	0.481314	+	0.481314i
$853$	−3.05073e23	+	3.05073e23i	−1.08846	+	1.08846i	−0.0927713	+	0.995687i	$0.529573\pi$
$853$	−3.05073e23	+	3.05073e23i	−1.08846	+	1.08846i	−0.995687	+	0.0927713i	$0.970427\pi$
$854$			1.86458e21i			0.00659048i
$855$	−6.28276e22	−	1.14947e23i	−0.219999	−	0.402501i
$856$	−1.70325e22			−0.0590863
$857$	−1.53194e22	−	1.53194e22i	−0.0526496	−	0.0526496i	0.680292	−	0.732941i	$-0.261853\pi$
$857$	−1.53194e22	−	1.53194e22i	−0.0526496	−	0.0526496i	−0.732941	+	0.680292i	$0.761853\pi$
$858$	3.74051e23	−	3.74051e23i	1.27360	−	1.27360i
$859$			5.52417e23i			1.86347i	0.363141	+	0.931734i	$0.381704\pi$
$859$			5.52417e23i			1.86347i	−0.363141	+	0.931734i	$0.618296\pi$
$860$	4.99615e21	−	1.70415e22i	0.0166974	−	0.0569536i
$861$	−7.53415e22			−0.249465
$862$	5.92169e22	+	5.92169e22i	0.194262	+	0.194262i
$863$	5.35457e22	−	5.35457e22i	0.174036	−	0.174036i	−0.614714	−	0.788750i	$-0.710729\pi$
$863$	5.35457e22	−	5.35457e22i	0.174036	−	0.174036i	0.788750	+	0.614714i	$0.210729\pi$
$864$			3.96046e22i			0.127537i
$865$	2.51590e23	+	7.37600e22i	0.802722	+	0.235338i
$866$	−1.90836e23			−0.603278
$867$	2.15124e23	+	2.15124e23i	0.673809	+	0.673809i
$868$	−2.63450e23	+	2.63450e23i	−0.817600	+	0.817600i
$869$		−	1.15337e24i		−	3.54659i
$870$	1.18730e23	−	6.48954e22i	0.361747	−	0.197724i
$871$	−8.66603e22			−0.261622
$872$	1.44380e22	+	1.44380e22i	0.0431892	+	0.0431892i
$873$	8.71723e22	−	8.71723e22i	0.258383	−	0.258383i
$874$			1.99088e23i			0.584728i
$875$	−3.40664e23	−	3.92158e23i	−0.991430	−	1.14129i
$876$	3.64378e22			0.105080
$877$	3.28397e23	+	3.28397e23i	0.938432	+	0.938432i	0.998212	−	0.0597793i	$-0.0190397\pi$
$877$	3.28397e23	+	3.28397e23i	0.938432	+	0.938432i	−0.0597793	+	0.998212i	$0.519040\pi$
$878$	1.34199e23	−	1.34199e23i	0.380007	−	0.380007i
$879$			4.82216e23i			1.35310i
$880$	7.70893e22	+	1.41039e23i	0.214355	+	0.392173i
$881$	2.20339e23			0.607134			0.303567	−	0.952810i	$-0.401822\pi$
$881$	2.20339e23			0.607134			0.303567	+	0.952810i	$0.401822\pi$
$882$	9.12177e22	+	9.12177e22i	0.249075	+	0.249075i
$883$	3.24080e23	−	3.24080e23i	0.876934	−	0.876934i	−0.116282	−	0.993216i	$-0.537098\pi$
$883$	3.24080e23	−	3.24080e23i	0.876934	−	0.876934i	0.993216	+	0.116282i	$0.0370978\pi$
$884$			9.85784e22i			0.264340i
$885$	9.81410e22	−	3.34752e23i	0.260798	−	0.889564i
$886$	−8.57971e22			−0.225945
$887$	−1.96343e23	−	1.96343e23i	−0.512419	−	0.512419i	0.402848	−	0.915267i	$-0.368020\pi$
$887$	−1.96343e23	−	1.96343e23i	−0.512419	−	0.512419i	−0.915267	+	0.402848i	$0.868020\pi$
$888$	9.98530e22	−	9.98530e22i	0.258260	−	0.258260i
$889$		−	9.75308e23i		−	2.49993i
$890$	−1.30080e22	−	3.81362e21i	−0.0330438	−	0.00968762i
$891$	−8.78648e23			−2.21204
$892$	−1.85064e23	−	1.85064e23i	−0.461746	−	0.461746i
$893$	−1.98852e23	+	1.98852e23i	−0.491721	+	0.491721i
$894$			3.22622e23i			0.790666i
$895$	−4.33013e23	+	2.36677e23i	−1.05176	+	0.574872i
$896$	5.55070e22			0.133624
$897$	−2.94999e23	−	2.94999e23i	−0.703851	−	0.703851i
$898$	−3.28951e23	+	3.28951e23i	−0.777893	+	0.777893i
$899$			3.23026e23i			0.757112i
$900$	−4.50352e22	+	7.02044e22i	−0.104619	+	0.163089i
$901$	4.98066e22			0.114680
$902$	−5.48686e22	−	5.48686e22i	−0.125219	−	0.125219i
$903$	6.60772e22	−	6.60772e22i	0.149469	−	0.149469i
$904$		−	6.88483e22i		−	0.154364i
$905$	1.62576e23	+	2.97441e23i	0.361300	+	0.661017i
$906$	3.38130e23			0.744831
$907$	1.97010e23	+	1.97010e23i	0.430159	+	0.430159i	0.888682	−	0.458523i	$-0.151621\pi$
$907$	1.97010e23	+	1.97010e23i	0.430159	+	0.430159i	−0.458523	+	0.888682i	$0.651621\pi$
$908$	1.74640e23	−	1.74640e23i	0.377970	−	0.377970i
$909$		−	2.19351e23i		−	0.470575i
$910$	−1.71068e23	+	5.83500e23i	−0.363778	+	1.24082i
$911$	−6.09464e23			−1.28470			−0.642349	−	0.766413i	$-0.722040\pi$
$911$	−6.09464e23			−1.28470			−0.642349	+	0.766413i	$0.722040\pi$
$912$	−1.17961e23	−	1.17961e23i	−0.246479	−	0.246479i
$913$	2.07851e22	−	2.07851e22i	0.0430512	−	0.0430512i
$914$		−	6.12070e22i		−	0.125670i
$915$	−3.42394e21	−	1.00381e21i	−0.00696880	−	0.00204308i
$916$	1.77208e23			0.357535
$917$	2.62159e23	+	2.62159e23i	0.524336	+	0.524336i
$918$	7.95197e22	−	7.95197e22i	0.157664	−	0.157664i
$919$		−	9.81832e23i		−	1.92980i	−0.262612	−	0.964901i	$-0.584584\pi$
$919$		−	9.81832e23i		−	1.92980i	0.262612	−	0.964901i	$-0.415416\pi$
$920$	1.11232e23	−	6.07972e22i	0.216734	−	0.118463i
$921$	−1.39144e23			−0.268775
$922$	−3.79310e23	−	3.79310e23i	−0.726352	−	0.726352i
$923$	−5.20707e23	+	5.20707e23i	−0.988507	+	0.988507i
$924$			8.45776e23i			1.59177i
$925$	−4.59211e23	+	1.00295e23i	−0.856799	+	0.187131i
$926$	4.63014e23			0.856458
$927$	1.10139e23	+	1.10139e23i	0.201978	+	0.201978i
$928$	3.40296e22	−	3.40296e22i	0.0618690	−	0.0618690i
$929$			1.03341e24i			1.86271i	0.364113	+	0.931355i	$0.381372\pi$
$929$			1.03341e24i			1.86271i	−0.364113	+	0.931355i	$0.618628\pi$
$930$	−3.41946e23	−	6.25608e23i	−0.611074	−	1.11799i
$931$	8.58809e23			1.52160
$932$	−1.98636e23	−	1.98636e23i	−0.348924	−	0.348924i
$933$	−3.24940e23	+	3.24940e23i	−0.565913	+	0.565913i
$934$			3.66895e22i			0.0633529i
$935$	1.28401e23	−	4.37967e23i	0.219824	−	0.749805i
$936$	9.76335e22			0.165726
$937$	−4.13125e23	−	4.13125e23i	−0.695288	−	0.695288i	0.268103	−	0.963390i	$-0.413603\pi$
$937$	−4.13125e23	−	4.13125e23i	−0.695288	−	0.695288i	−0.963390	+	0.268103i	$0.913603\pi$
$938$	9.79749e22	−	9.79749e22i	0.163490	−	0.163490i
$939$		−	3.32526e23i		−	0.550174i
$940$	1.71825e23	+	5.03748e22i	0.281880	+	0.0826401i
$941$	5.83135e23			0.948533			0.474266	−	0.880381i	$-0.342713\pi$
$941$	5.83135e23			0.948533			0.474266	+	0.880381i	$0.342713\pi$
$942$	−2.81205e22	−	2.81205e22i	−0.0453540	−	0.0453540i
$943$	−4.32726e22	+	4.32726e22i	−0.0692022	+	0.0692022i
$944$		−	1.24073e23i		−	0.196745i
$945$	6.08683e23	−	3.32695e23i	0.957054	−	0.523108i
$946$	9.62435e22			0.150052
$947$	−2.04076e23	−	2.04076e23i	−0.315494	−	0.315494i	0.531539	−	0.847034i	$-0.321614\pi$
$947$	−2.04076e23	−	2.04076e23i	−0.315494	−	0.315494i	−0.847034	+	0.531539i	$0.821614\pi$
$948$	5.38954e23	−	5.38954e23i	0.826200	−	0.826200i
$949$			1.41971e23i			0.215810i
$950$	1.18483e23	+	5.42487e23i	0.178595	+	0.817712i
$951$	−6.71191e21			−0.0100323
$952$	−1.11449e23	−	1.11449e23i	−0.165189	−	0.165189i
$953$	8.58478e23	−	8.58478e23i	1.26179	−	1.26179i	0.311560	−	0.950226i	$-0.399148\pi$
$953$	8.58478e23	−	8.58478e23i	1.26179	−	1.26179i	0.950226	−	0.311560i	$-0.100852\pi$
$954$		−	4.93292e22i		−	0.0718981i
$955$	−1.79441e23	−	3.28297e23i	−0.259355	−	0.474504i
$956$	−5.42477e23			−0.777531
$957$	5.18519e23	+	5.18519e23i	0.737003	+	0.737003i
$958$	−1.25219e23	+	1.25219e23i	−0.176501	+	0.176501i
$959$			1.58329e24i			2.21316i
$960$	−2.98828e22	+	1.01928e23i	−0.0414239	+	0.141294i
$961$	9.74662e23			1.33988
$962$	3.89054e23	+	3.89054e23i	0.530407	+	0.530407i
$963$	3.38706e22	−	3.38706e22i	0.0457944	−	0.0457944i
$964$		−	3.23440e23i		−	0.433688i
$965$	1.37986e24	+	4.04540e23i	1.83491	+	0.537951i
$966$	6.67029e23			0.879686
$967$	−2.37469e23	−	2.37469e23i	−0.310595	−	0.310595i	0.534545	−	0.845140i	$-0.320483\pi$
$967$	−2.37469e23	−	2.37469e23i	−0.310595	−	0.310595i	−0.845140	+	0.534545i	$0.820483\pi$
$968$	−4.23222e23	+	4.23222e23i	−0.548991	+	0.548991i
$969$			4.73693e23i			0.609406i
$970$	−4.58543e23	+	2.50631e23i	−0.585068	+	0.319787i
$971$	6.21713e23			0.786749			0.393374	−	0.919378i	$-0.371308\pi$
$971$	6.21713e23			0.786749			0.393374	+	0.919378i	$0.371308\pi$
$972$	−2.07345e23	−	2.07345e23i	−0.260234	−	0.260234i
$973$	−9.16688e23	+	9.16688e23i	−1.14109	+	1.14109i
$974$		−	5.41949e23i		−	0.669093i
$975$	−9.79393e23	−	6.28267e23i	−1.19928	−	0.769321i
$976$	−1.26906e21			−0.00154129
$977$	−5.82281e23	−	5.82281e23i	−0.701417	−	0.701417i	0.263298	−	0.964715i	$-0.415190\pi$
$977$	−5.82281e23	−	5.82281e23i	−0.701417	−	0.701417i	−0.964715	+	0.263298i	$0.915190\pi$
$978$	−7.56089e23	+	7.56089e23i	−0.903363	+	0.903363i
$979$		−	7.34638e22i		−	0.0870586i
$980$	−2.62262e23	−	4.79823e23i	−0.308267	−	0.563991i
$981$	−5.74225e22			−0.0669469
$982$	−9.31356e22	−	9.31356e22i	−0.107702	−	0.107702i
$983$	−1.02711e24	+	1.02711e24i	−1.17812	+	1.17812i	−0.197902	+	0.980222i	$0.563413\pi$
$983$	−1.02711e24	+	1.02711e24i	−1.17812	+	1.17812i	−0.980222	+	0.197902i	$0.936587\pi$
$984$		−	5.12786e22i		−	0.0583412i
$985$	2.96092e23	−	1.00995e24i	0.334147	−	1.13975i
$986$	−1.36652e23			−0.152968
$987$	6.66239e23	+	6.66239e23i	0.739763	+	0.739763i
$988$	4.59607e23	−	4.59607e23i	0.506210	−	0.506210i
$989$		−	7.59033e22i		−	0.0829260i
$990$	−4.33768e23	−	1.27170e23i	−0.470085	−	0.137817i
$991$	1.05863e24			1.13804			0.569018	−	0.822325i	$-0.307323\pi$
$991$	1.05863e24			1.13804			0.569018	+	0.822325i	$0.307323\pi$
$992$	−1.79308e23	−	1.79308e23i	−0.191208	−	0.191208i
$993$	−9.70714e23	+	9.70714e23i	−1.02683	+	1.02683i
$994$		−	1.17738e24i		−	1.23545i
$995$	1.06900e24	−	5.84295e23i	1.11274	−	0.608201i
$996$	1.94251e22			0.0200581
$997$	−3.41909e23	−	3.41909e23i	−0.350227	−	0.350227i	0.509967	−	0.860194i	$-0.329658\pi$
$997$	−3.41909e23	−	3.41909e23i	−0.350227	−	0.350227i	−0.860194	+	0.509967i	$0.829658\pi$
$998$	2.69092e23	−	2.69092e23i	0.273436	−	0.273436i
$999$		−	6.27672e23i		−	0.632716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.17.c.b.7.2	yes	8
3.2	odd	2		90.17.g.a.37.1		8
4.3	odd	2		80.17.p.b.17.3		8
5.2	odd	4		50.17.c.c.43.3		8
5.3	odd	4	inner	10.17.c.b.3.2	✓	8
5.4	even	2		50.17.c.c.7.3		8
15.8	even	4		90.17.g.a.73.1		8
20.3	even	4		80.17.p.b.33.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.17.c.b.3.2	✓	8	5.3	odd	4	inner
10.17.c.b.7.2	yes	8	1.1	even	1	trivial
50.17.c.c.7.3		8	5.4	even	2
50.17.c.c.43.3		8	5.2	odd	4
80.17.p.b.17.3		8	4.3	odd	2
80.17.p.b.33.3		8	20.3	even	4
90.17.g.a.37.1		8	3.2	odd	2
90.17.g.a.73.1		8	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(128.000 + 128.000i) q^{2} +(-5464.81 + 5464.81i) q^{3} +32768.0i q^{4} +(187349. + 342765. i) q^{5} -1.39899e6 q^{6} +(6.16251e6 + 6.16251e6i) q^{7} +(-4.19430e6 + 4.19430e6i) q^{8} -1.66815e7i q^{9} +O(q^{10})\)	\(q+(128.000 + 128.000i) q^{2} +(-5464.81 + 5464.81i) q^{3} +32768.0i q^{4} +(187349. + 342765. i) q^{5} -1.39899e6 q^{6} +(6.16251e6 + 6.16251e6i) q^{7} +(-4.19430e6 + 4.19430e6i) q^{8} -1.66815e7i q^{9} +(-1.98933e7 + 6.78547e7i) q^{10} -3.83215e8 q^{11} +(-1.79071e8 - 1.79071e8i) q^{12} +(6.97707e8 - 6.97707e8i) q^{13} +1.57760e9i q^{14} +(-2.89697e9 - 8.49320e8i) q^{15} -1.07374e9 q^{16} +(2.15590e9 + 2.15590e9i) q^{17} +(2.13523e9 - 2.13523e9i) q^{18} -2.01031e10i q^{19} +(-1.12317e10 + 6.13906e9i) q^{20} -6.73539e10 q^{21} +(-4.90515e10 - 4.90515e10i) q^{22} +(-3.86849e10 + 3.86849e10i) q^{23} -4.58421e10i q^{24} +(-8.23885e10 + 1.28434e11i) q^{25} +1.78613e11 q^{26} +(-1.44081e11 - 1.44081e11i) q^{27} +(-2.01933e11 + 2.01933e11i) q^{28} +2.47598e11i q^{29} +(-2.62100e11 - 4.79526e11i) q^{30} +1.30464e12 q^{31} +(-1.37439e11 - 1.37439e11i) q^{32} +(2.09420e12 - 2.09420e12i) q^{33} +5.51910e11i q^{34} +(-9.57755e11 + 3.26684e12i) q^{35} +5.46620e11 q^{36} +(2.17819e12 + 2.17819e12i) q^{37} +(2.57320e12 - 2.57320e12i) q^{38} +7.62567e12i q^{39} +(-2.22346e12 - 6.51863e11i) q^{40} +1.11859e12 q^{41} +(-8.62130e12 - 8.62130e12i) q^{42} +(-9.81045e11 + 9.81045e11i) q^{43} -1.25572e13i q^{44} +(5.71785e12 - 3.12527e12i) q^{45} -9.90334e12 q^{46} +(-9.89161e12 - 9.89161e12i) q^{47} +(5.86779e12 - 5.86779e12i) q^{48} +4.27202e13i q^{49} +(-2.69852e13 + 5.89378e12i) q^{50} -2.35632e13 q^{51} +(2.28625e13 + 2.28625e13i) q^{52} +(1.15512e13 - 1.15512e13i) q^{53} -3.68847e13i q^{54} +(-7.17950e13 - 1.31353e14i) q^{55} -5.16949e13 q^{56} +(1.09860e14 + 1.09860e14i) q^{57} +(-3.16926e13 + 3.16926e13i) q^{58} +1.15552e14i q^{59} +(2.78305e13 - 9.49281e13i) q^{60} +1.18190e12 q^{61} +(1.66994e14 + 1.66994e14i) q^{62} +(1.02800e14 - 1.02800e14i) q^{63} -3.51844e13i q^{64} +(3.69865e14 + 1.08435e14i) q^{65} +5.36114e14 q^{66} +(-6.21036e13 - 6.21036e13i) q^{67} +(-7.06445e13 + 7.06445e13i) q^{68} -4.22811e14i q^{69} +(-5.40748e14 + 2.95563e14i) q^{70} -7.46311e14 q^{71} +(6.99674e13 + 6.99674e13i) q^{72} +(-1.01741e14 + 1.01741e14i) q^{73} +5.57618e14i q^{74} +(-2.51628e14 - 1.15210e15i) q^{75} +6.58739e14 q^{76} +(-2.36157e15 - 2.36157e15i) q^{77} +(-9.76086e14 + 9.76086e14i) q^{78} +3.00973e15i q^{79} +(-2.01165e14 - 3.68042e14i) q^{80} +2.29283e15 q^{81} +(1.43180e14 + 1.43180e14i) q^{82} +(-5.42387e13 + 5.42387e13i) q^{83} -2.20705e15i q^{84} +(-3.35062e14 + 1.14287e15i) q^{85} -2.51148e14 q^{86} +(-1.35308e15 - 1.35308e15i) q^{87} +(1.60732e15 - 1.60732e15i) q^{88} +1.91704e14i q^{89} +(1.13192e15 + 3.31850e14i) q^{90} +8.59926e15 q^{91} +(-1.26763e15 - 1.26763e15i) q^{92} +(-7.12961e15 + 7.12961e15i) q^{93} -2.53225e15i q^{94} +(6.89065e15 - 3.76630e15i) q^{95} +1.50215e15 q^{96} +(5.22568e15 + 5.22568e15i) q^{97} +(-5.46819e15 + 5.46819e15i) q^{98} +6.39261e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 1024 q^{2} - 10438 q^{3} - 216450 q^{5} - 2672128 q^{6} + 3127282 q^{7} - 33554432 q^{8}+O(q^{10}) \) 8 * q + 1024 * q^2 - 10438 * q^3 - 216450 * q^5 - 2672128 * q^6 + 3127282 * q^7 - 33554432 * q^8	\( 8 q + 1024 q^{2} - 10438 q^{3} - 216450 q^{5} - 2672128 q^{6} + 3127282 q^{7} - 33554432 q^{8} - 74291200 q^{10} + 503961116 q^{11} - 342032384 q^{12} + 1217503932 q^{13} - 4976914750 q^{15} - 8589934592 q^{16} + 5385990692 q^{17} - 4243396096 q^{18} - 11925913600 q^{20} + 14153198396 q^{21} + 64507022848 q^{22} - 128259921478 q^{23} - 533485437500 q^{25} + 311681006592 q^{26} + 207672953000 q^{27} - 102474776576 q^{28} - 1513467148800 q^{30} + 3125721174596 q^{31} - 1099511627776 q^{32} + 4056976486124 q^{33} - 4345883408350 q^{35} - 1086309400576 q^{36} + 1590466410672 q^{37} + 3851630689280 q^{38} - 618659840000 q^{40} - 19109223712804 q^{41} + 1811609394688 q^{42} + 51727159732362 q^{43} - 21310193383550 q^{45} - 32834539898368 q^{46} - 995920856358 q^{47} + 11207717158912 q^{48} - 101684562880000 q^{50} - 44717760464924 q^{51} + 39895168843776 q^{52} + 141694298313952 q^{53} - 296517352578900 q^{55} - 26233542803456 q^{56} + 529604819758160 q^{57} + 91941293281280 q^{58} - 224364047564800 q^{60} - 275898028788324 q^{61} + 400092310348288 q^{62} + 155565943639322 q^{63} - 771819436467000 q^{65} + 10\!\cdots\!44 q^{66}+ \cdots - 30\!\cdots\!44 q^{98}+O(q^{100}) \) 8 * q + 1024 * q^2 - 10438 * q^3 - 216450 * q^5 - 2672128 * q^6 + 3127282 * q^7 - 33554432 * q^8 - 74291200 * q^10 + 503961116 * q^11 - 342032384 * q^12 + 1217503932 * q^13 - 4976914750 * q^15 - 8589934592 * q^16 + 5385990692 * q^17 - 4243396096 * q^18 - 11925913600 * q^20 + 14153198396 * q^21 + 64507022848 * q^22 - 128259921478 * q^23 - 533485437500 * q^25 + 311681006592 * q^26 + 207672953000 * q^27 - 102474776576 * q^28 - 1513467148800 * q^30 + 3125721174596 * q^31 - 1099511627776 * q^32 + 4056976486124 * q^33 - 4345883408350 * q^35 - 1086309400576 * q^36 + 1590466410672 * q^37 + 3851630689280 * q^38 - 618659840000 * q^40 - 19109223712804 * q^41 + 1811609394688 * q^42 + 51727159732362 * q^43 - 21310193383550 * q^45 - 32834539898368 * q^46 - 995920856358 * q^47 + 11207717158912 * q^48 - 101684562880000 * q^50 - 44717760464924 * q^51 + 39895168843776 * q^52 + 141694298313952 * q^53 - 296517352578900 * q^55 - 26233542803456 * q^56 + 529604819758160 * q^57 + 91941293281280 * q^58 - 224364047564800 * q^60 - 275898028788324 * q^61 + 400092310348288 * q^62 + 155565943639322 * q^63 - 771819436467000 * q^65 + 1038585980447744 * q^66 - 700220959215398 * q^67 - 176488142995456 * q^68 - 511285790540800 * q^70 + 1921969049667556 * q^71 - 139047603273728 * q^72 - 808847266834888 * q^73 + 2482300760271250 * q^75 + 986017456455680 * q^76 - 5345726343508436 * q^77 - 2838754804096512 * q^78 + 232411417804800 * q^80 + 9359115176899828 * q^81 - 2445980635238912 * q^82 - 13177017950509038 * q^83 + 3955352361175900 * q^85 + 13242152891484672 * q^86 - 14123970165519040 * q^87 - 2113766124683264 * q^88 + 621990363392000 * q^90 + 47376751322244756 * q^91 - 4202821106991104 * q^92 - 26154699869031556 * q^93 - 67475453915000 * q^95 + 2869175592681472 * q^96 - 10816659651879048 * q^97 - 30870381725100544 * q^98

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