LMFDB - Embedded newform 10.17.c.b.3.3

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			3.3
Root			$400.872i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.17.c.b.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(128.000 - 128.000i) q^{2} +(2246.18 + 2246.18i) q^{3} -32768.0i q^{4} +(-50567.5 - 387338. i) q^{5} +575022. q^{6} +(-5.28707e6 + 5.28707e6i) q^{7} +(-4.19430e6 - 4.19430e6i) q^{8} -3.29561e7i q^{9} +O(q^{10})$	\(q+(128.000 - 128.000i) q^{2} +(2246.18 + 2246.18i) q^{3} -32768.0i q^{4} +(-50567.5 - 387338. i) q^{5} +575022. q^{6} +(-5.28707e6 + 5.28707e6i) q^{7} +(-4.19430e6 - 4.19430e6i) q^{8} -3.29561e7i q^{9} +(-5.60519e7 - 4.31066e7i) q^{10} +1.27647e8 q^{11} +(7.36029e7 - 7.36029e7i) q^{12} +(-1.02176e9 - 1.02176e9i) q^{13} +1.35349e9i q^{14} +(7.56448e8 - 9.83615e8i) q^{15} -1.07374e9 q^{16} +(-6.56739e9 + 6.56739e9i) q^{17} +(-4.21838e9 - 4.21838e9i) q^{18} -7.99348e9i q^{19} +(-1.26923e10 + 1.65700e9i) q^{20} -2.37514e10 q^{21} +(1.63388e10 - 1.63388e10i) q^{22} +(-8.23621e10 - 8.23621e10i) q^{23} -1.88423e10i q^{24} +(-1.47474e11 + 3.91734e10i) q^{25} -2.61570e11 q^{26} +(1.70716e11 - 1.70716e11i) q^{27} +(1.73247e11 + 1.73247e11i) q^{28} +1.95302e11i q^{29} +(-2.90774e10 - 2.22728e11i) q^{30} +1.11018e12 q^{31} +(-1.37439e11 + 1.37439e11i) q^{32} +(2.86718e11 + 2.86718e11i) q^{33} +1.68125e12i q^{34} +(2.31524e12 + 1.78053e12i) q^{35} -1.07990e12 q^{36} +(3.13818e12 - 3.13818e12i) q^{37} +(-1.02317e12 - 1.02317e12i) q^{38} -4.59010e12i q^{39} +(-1.41252e12 + 1.83671e12i) q^{40} +9.50017e11 q^{41} +(-3.04018e12 + 3.04018e12i) q^{42} +(8.52333e12 + 8.52333e12i) q^{43} -4.18273e12i q^{44} +(-1.27651e13 + 1.66651e12i) q^{45} -2.10847e13 q^{46} +(1.33950e13 - 1.33950e13i) q^{47} +(-2.41182e12 - 2.41182e12i) q^{48} -2.26732e13i q^{49} +(-1.38624e13 + 2.38908e13i) q^{50} -2.95031e13 q^{51} +(-3.34809e13 + 3.34809e13i) q^{52} +(2.22995e12 + 2.22995e12i) q^{53} -4.37033e13i q^{54} +(-6.45478e12 - 4.94425e13i) q^{55} +4.43511e13 q^{56} +(1.79548e13 - 1.79548e13i) q^{57} +(2.49987e13 + 2.49987e13i) q^{58} +5.45384e13i q^{59} +(-3.22311e13 - 2.47873e13i) q^{60} +2.17070e14 q^{61} +(1.42104e14 - 1.42104e14i) q^{62} +(1.74241e14 + 1.74241e14i) q^{63} +3.51844e13i q^{64} +(-3.44097e14 + 4.47433e14i) q^{65} +7.33998e13 q^{66} +(-7.25973e13 + 7.25973e13i) q^{67} +(2.15200e14 + 2.15200e14i) q^{68} -3.70000e14i q^{69} +(5.24258e14 - 6.84426e13i) q^{70} +3.26843e13 q^{71} +(-1.38228e14 + 1.38228e14i) q^{72} +(-8.08129e14 - 8.08129e14i) q^{73} -8.03373e14i q^{74} +(-4.19243e14 - 2.43262e14i) q^{75} -2.61930e14 q^{76} +(-6.74878e14 + 6.74878e14i) q^{77} +(-5.87533e14 - 5.87533e14i) q^{78} +8.90178e14i q^{79} +(5.42964e13 + 4.15901e14i) q^{80} -6.51732e14 q^{81} +(1.21602e14 - 1.21602e14i) q^{82} +(-2.53010e15 - 2.53010e15i) q^{83} +7.78287e14i q^{84} +(2.87590e15 + 2.21170e15i) q^{85} +2.18197e15 q^{86} +(-4.38684e14 + 4.38684e14i) q^{87} +(-5.35390e14 - 5.35390e14i) q^{88} -1.01496e15i q^{89} +(-1.42063e15 + 1.84725e15i) q^{90} +1.08042e16 q^{91} +(-2.69884e15 + 2.69884e15i) q^{92} +(2.49368e15 + 2.49368e15i) q^{93} -3.42913e15i q^{94} +(-3.09618e15 + 4.04210e14i) q^{95} -6.17426e14 q^{96} +(2.16280e15 - 2.16280e15i) q^{97} +(-2.90217e15 - 2.90217e15i) q^{98} -4.20674e15i 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 $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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
$3$	2246.18	+	2246.18i	0.342353	+	0.342353i	0.857251	−	0.514898i	$-0.172170\pi$
$3$	2246.18	+	2246.18i	0.342353	+	0.342353i	−0.514898	+	0.857251i	$0.672170\pi$
$4$		−	32768.0i		−	0.500000i
$5$	−50567.5	−	387338.i	−0.129453	−	0.991586i
$5$	−50567.5	−	387338.i	−0.129453	−	0.991586i
$6$	575022.			0.342353
$7$	−5.28707e6	+	5.28707e6i	−0.917129	+	0.917129i	−0.996820	−	0.0796905i	$-0.974607\pi$
$7$	−5.28707e6	+	5.28707e6i	−0.917129	+	0.917129i	0.0796905	+	0.996820i	$0.474607\pi$
$8$	−4.19430e6	−	4.19430e6i	−0.250000	−	0.250000i
$9$		−	3.29561e7i		−	0.765588i
$10$	−5.60519e7	−	4.31066e7i	−0.560519	−	0.431066i
$11$	1.27647e8			0.595482			0.297741	−	0.954647i	$-0.403767\pi$
$11$	1.27647e8			0.595482			0.297741	+	0.954647i	$0.403767\pi$
$12$	7.36029e7	−	7.36029e7i	0.171177	−	0.171177i
$13$	−1.02176e9	−	1.02176e9i	−1.25257	−	1.25257i	−0.954566	−	0.297999i	$-0.903681\pi$
$13$	−1.02176e9	−	1.02176e9i	−1.25257	−	1.25257i	−0.297999	−	0.954566i	$-0.596319\pi$
$14$			1.35349e9i			0.917129i
$15$	7.56448e8	−	9.83615e8i	0.295154	−	0.383791i
$16$	−1.07374e9			−0.250000
$17$	−6.56739e9	+	6.56739e9i	−0.941459	+	0.941459i	−0.998379	−	0.0569196i	$-0.981872\pi$
$17$	−6.56739e9	+	6.56739e9i	−0.941459	+	0.941459i	0.0569196	+	0.998379i	$0.481872\pi$
$18$	−4.21838e9	−	4.21838e9i	−0.382794	−	0.382794i
$19$		−	7.99348e9i		−	0.470660i	−0.971916	−	0.235330i	$-0.924383\pi$
$19$		−	7.99348e9i		−	0.470660i	0.971916	−	0.235330i	$-0.0756171\pi$
$20$	−1.26923e10	+	1.65700e9i	−0.495793	+	0.0647264i
$21$	−2.37514e10			−0.627965
$22$	1.63388e10	−	1.63388e10i	0.297741	−	0.297741i
$23$	−8.23621e10	−	8.23621e10i	−1.05173	−	1.05173i	−0.998587	−	0.0531444i	$-0.983076\pi$
$23$	−8.23621e10	−	8.23621e10i	−1.05173	−	1.05173i	−0.0531444	−	0.998587i	$-0.516924\pi$
$24$		−	1.88423e10i		−	0.171177i
$25$	−1.47474e11	+	3.91734e10i	−0.966484	+	0.256727i
$26$	−2.61570e11			−1.25257
$27$	1.70716e11	−	1.70716e11i	0.604455	−	0.604455i
$28$	1.73247e11	+	1.73247e11i	0.458565	+	0.458565i
$29$			1.95302e11i			0.390412i	0.980762	+	0.195206i	$0.0625375\pi$
$29$			1.95302e11i			0.390412i	−0.980762	+	0.195206i	$0.937463\pi$
$30$	−2.90774e10	−	2.22728e11i	−0.0443186	−	0.339473i
$31$	1.11018e12			1.30167			0.650836	−	0.759218i	$-0.274418\pi$
$31$	1.11018e12			1.30167			0.650836	+	0.759218i	$0.274418\pi$
$32$	−1.37439e11	+	1.37439e11i	−0.125000	+	0.125000i
$33$	2.86718e11	+	2.86718e11i	0.203865	+	0.203865i
$34$			1.68125e12i			0.941459i
$35$	2.31524e12	+	1.78053e12i	1.02814	+	0.790687i
$36$	−1.07990e12			−0.382794
$37$	3.13818e12	−	3.13818e12i	0.893436	−	0.893436i	−0.101409	−	0.994845i	$-0.532335\pi$
$37$	3.13818e12	−	3.13818e12i	0.893436	−	0.893436i	0.994845	+	0.101409i	$0.0323351\pi$
$38$	−1.02317e12	−	1.02317e12i	−0.235330	−	0.235330i
$39$		−	4.59010e12i		−	0.857640i
$40$	−1.41252e12	+	1.83671e12i	−0.215533	+	0.280260i
$41$	9.50017e11			0.118976			0.0594882	−	0.998229i	$-0.481053\pi$
$41$	9.50017e11			0.118976			0.0594882	+	0.998229i	$0.481053\pi$
$42$	−3.04018e12	+	3.04018e12i	−0.313982	+	0.313982i
$43$	8.52333e12	+	8.52333e12i	0.729225	+	0.729225i	0.970465	−	0.241240i	$-0.0775541\pi$
$43$	8.52333e12	+	8.52333e12i	0.729225	+	0.729225i	−0.241240	+	0.970465i	$0.577554\pi$
$44$		−	4.18273e12i		−	0.297741i
$45$	−1.27651e13	+	1.66651e12i	−0.759146	+	0.0991075i
$46$	−2.10847e13			−1.05173
$47$	1.33950e13	−	1.33950e13i	0.562549	−	0.562549i	−0.367481	−	0.930031i	$-0.619780\pi$
$47$	1.33950e13	−	1.33950e13i	0.562549	−	0.562549i	0.930031	+	0.367481i	$0.119780\pi$
$48$	−2.41182e12	−	2.41182e12i	−0.0855884	−	0.0855884i
$49$		−	2.26732e13i		−	0.682252i
$50$	−1.38624e13	+	2.38908e13i	−0.354878	+	0.611606i
$51$	−2.95031e13			−0.644624
$52$	−3.34809e13	+	3.34809e13i	−0.626283	+	0.626283i
$53$	2.22995e12	+	2.22995e12i	0.0358168	+	0.0358168i	0.724788	−	0.688972i	$-0.241938\pi$
$53$	2.22995e12	+	2.22995e12i	0.0358168	+	0.0358168i	−0.688972	+	0.724788i	$0.741938\pi$
$54$		−	4.37033e13i		−	0.604455i
$55$	−6.45478e12	−	4.94425e13i	−0.0770868	−	0.590471i
$56$	4.43511e13			0.458565
$57$	1.79548e13	−	1.79548e13i	0.161132	−	0.161132i
$58$	2.49987e13	+	2.49987e13i	0.195206	+	0.195206i
$59$			5.45384e13i			0.371438i	0.982603	+	0.185719i	$0.0594614\pi$
$59$			5.45384e13i			0.371438i	−0.982603	+	0.185719i	$0.940539\pi$
$60$	−3.22311e13	−	2.47873e13i	−0.191896	−	0.147577i
$61$	2.17070e14			1.13230			0.566149	−	0.824303i	$-0.308433\pi$
$61$	2.17070e14			1.13230			0.566149	+	0.824303i	$0.308433\pi$
$62$	1.42104e14	−	1.42104e14i	0.650836	−	0.650836i
$63$	1.74241e14	+	1.74241e14i	0.702143	+	0.702143i
$64$			3.51844e13i			0.125000i
$65$	−3.44097e14	+	4.47433e14i	−1.07988	+	1.40417i
$66$	7.33998e13			0.203865
$67$	−7.25973e13	+	7.25973e13i	−0.178781	+	0.178781i	−0.790824	−	0.612043i	$-0.790348\pi$
$67$	−7.25973e13	+	7.25973e13i	−0.178781	+	0.178781i	0.612043	+	0.790824i	$0.290348\pi$
$68$	2.15200e14	+	2.15200e14i	0.470730	+	0.470730i
$69$		−	3.70000e14i		−	0.720128i
$70$	5.24258e14	−	6.84426e13i	0.909412	−	0.118725i
$71$	3.26843e13			0.0506142			0.0253071	−	0.999680i	$-0.491944\pi$
$71$	3.26843e13			0.0506142			0.0253071	+	0.999680i	$0.491944\pi$
$72$	−1.38228e14	+	1.38228e14i	−0.191397	+	0.191397i
$73$	−8.08129e14	−	8.08129e14i	−1.00207	−	1.00207i	−0.999998	−	0.00207121i	$-0.999341\pi$
$73$	−8.08129e14	−	8.08129e14i	−1.00207	−	1.00207i	−0.00207121	−	0.999998i	$-0.500659\pi$
$74$		−	8.03373e14i		−	0.893436i
$75$	−4.19243e14	−	2.43262e14i	−0.418771	−	0.242988i
$76$	−2.61930e14			−0.235330
$77$	−6.74878e14	+	6.74878e14i	−0.546134	+	0.546134i
$78$	−5.87533e14	−	5.87533e14i	−0.428820	−	0.428820i
$79$			8.90178e14i			0.586760i	0.955996	+	0.293380i	$0.0947801\pi$
$79$			8.90178e14i			0.586760i	−0.955996	+	0.293380i	$0.905220\pi$
$80$	5.42964e13	+	4.15901e14i	0.0323632	+	0.247896i
$81$	−6.51732e14			−0.351713
$82$	1.21602e14	−	1.21602e14i	0.0594882	−	0.0594882i
$83$	−2.53010e15	−	2.53010e15i	−1.12335	−	1.12335i	−0.991235	−	0.132111i	$-0.957825\pi$
$83$	−2.53010e15	−	2.53010e15i	−1.12335	−	1.12335i	−0.132111	−	0.991235i	$-0.542175\pi$
$84$			7.78287e14i			0.313982i
$85$	2.87590e15	+	2.21170e15i	1.05541	+	0.811663i
$86$	2.18197e15			0.729225
$87$	−4.38684e14	+	4.38684e14i	−0.133659	+	0.133659i
$88$	−5.35390e14	−	5.35390e14i	−0.148871	−	0.148871i
$89$		−	1.01496e15i		−	0.257828i	−0.991656	−	0.128914i	$-0.958851\pi$
$89$		−	1.01496e15i		−	0.257828i	0.991656	−	0.128914i	$-0.0411491\pi$
$90$	−1.42063e15	+	1.84725e15i	−0.330019	+	0.429127i
$91$	1.08042e16			2.29753
$92$	−2.69884e15	+	2.69884e15i	−0.525866	+	0.525866i
$93$	2.49368e15	+	2.49368e15i	0.445632	+	0.445632i
$94$		−	3.42913e15i		−	0.562549i
$95$	−3.09618e15	+	4.04210e14i	−0.466699	+	0.0609282i
$96$	−6.17426e14			−0.0855884
$97$	2.16280e15	−	2.16280e15i	0.275958	−	0.275958i	−0.555535	−	0.831493i	$-0.687487\pi$
$97$	2.16280e15	−	2.16280e15i	0.275958	−	0.275958i	0.831493	+	0.555535i	$0.187487\pi$
$98$	−2.90217e15	−	2.90217e15i	−0.341126	−	0.341126i
$99$		−	4.20674e15i		−	0.455894i
$100$	1.28364e15	+	4.83242e15i	0.128364	+	0.483242i
$101$	1.49540e16			1.38097			0.690487	−	0.723345i	$-0.257396\pi$
$101$	1.49540e16			1.38097			0.690487	+	0.723345i	$0.257396\pi$
$102$	−3.77640e15	+	3.77640e15i	−0.322312	+	0.322312i
$103$	−1.07683e16	−	1.07683e16i	−0.850063	−	0.850063i	0.140077	−	0.990141i	$-0.455265\pi$
$103$	−1.07683e16	−	1.07683e16i	−0.850063	−	0.850063i	−0.990141	+	0.140077i	$0.955265\pi$
$104$			8.57111e15i			0.626283i
$105$	1.20105e15	+	9.19983e15i	0.0812918	+	0.622681i
$106$	5.70866e14			0.0358168
$107$	−1.23463e16	+	1.23463e16i	−0.718567	+	0.718567i	−0.968312	−	0.249745i	$-0.919653\pi$
$107$	−1.23463e16	+	1.23463e16i	−0.718567	+	0.718567i	0.249745	+	0.968312i	$0.419653\pi$
$108$	−5.59402e15	−	5.59402e15i	−0.302228	−	0.302228i
$109$		−	2.18941e16i		−	1.09879i	−0.835562	−	0.549396i	$-0.814858\pi$
$109$		−	2.18941e16i		−	1.09879i	0.835562	−	0.549396i	$-0.185142\pi$
$110$	−7.15485e15	−	5.50243e15i	−0.333779	−	0.256692i
$111$	1.40978e16			0.611742
$112$	5.67694e15	−	5.67694e15i	0.229282	−	0.229282i
$113$	−8.67751e15	−	8.67751e15i	−0.326413	−	0.326413i	0.524808	−	0.851221i	$-0.324137\pi$
$113$	−8.67751e15	−	8.67751e15i	−0.326413	−	0.326413i	−0.851221	+	0.524808i	$0.824137\pi$
$114$		−	4.59643e15i		−	0.161132i
$115$	−2.77371e16	+	3.60668e16i	−0.906732	+	1.17903i
$116$	6.39965e15			0.195206
$117$	−3.36731e16	+	3.36731e16i	−0.958949	+	0.958949i
$118$	6.98092e15	+	6.98092e15i	0.185719	+	0.185719i
$119$		−	6.94445e16i		−	1.72688i
$120$	−7.29835e15	+	9.52810e14i	−0.169736	+	0.0221593i
$121$	−2.96560e16			−0.645401
$122$	2.77849e16	−	2.77849e16i	0.566149	−	0.566149i
$123$	2.13391e15	+	2.13391e15i	0.0407320	+	0.0407320i
$124$		−	3.63785e16i		−	0.650836i
$125$	2.26307e16	+	5.51413e16i	0.379681	+	0.925117i
$126$	4.46057e16			0.702143
$127$	4.32761e16	−	4.32761e16i	0.639467	−	0.639467i	−0.310957	−	0.950424i	$-0.600650\pi$
$127$	4.32761e16	−	4.32761e16i	0.639467	−	0.639467i	0.950424	+	0.310957i	$0.100650\pi$
$128$	4.50360e15	+	4.50360e15i	0.0625000	+	0.0625000i
$129$			3.82899e16i			0.499306i
$130$	1.32269e16	+	1.01316e17i	0.162148	+	1.24203i
$131$	8.62478e16			0.994438			0.497219	−	0.867625i	$-0.334355\pi$
$131$	8.62478e16			0.994438			0.497219	+	0.867625i	$0.334355\pi$
$132$	9.39518e15	−	9.39518e15i	0.101933	−	0.101933i
$133$	4.22621e16	+	4.22621e16i	0.431656	+	0.431656i
$134$			1.85849e16i			0.178781i
$135$	−7.47575e16	−	5.74921e16i	−0.677618	−	0.521121i
$136$	5.50913e16			0.470730
$137$	−6.63377e16	+	6.63377e16i	−0.534560	+	0.534560i	−0.921926	−	0.387366i	$-0.873385\pi$
$137$	−6.63377e16	+	6.63377e16i	−0.534560	+	0.534560i	0.387366	+	0.921926i	$0.373385\pi$
$138$	−4.73601e16	−	4.73601e16i	−0.360064	−	0.360064i
$139$			1.32681e17i			0.952117i	0.879414	+	0.476059i	$0.157935\pi$
$139$			1.32681e17i			0.952117i	−0.879414	+	0.476059i	$0.842065\pi$
$140$	5.83444e16	−	7.58657e16i	0.395344	−	0.514068i
$141$	6.01753e16			0.385182
$142$	4.18359e15	−	4.18359e15i	0.0253071	−	0.0253071i
$143$	−1.30424e17	−	1.30424e17i	−0.745880	−	0.745880i
$144$			3.53863e16i			0.191397i
$145$	7.56479e16	−	9.87593e15i	0.387126	−	0.0505399i
$146$	−2.06881e17			−1.00207
$147$	5.09282e16	−	5.09282e16i	0.233571	−	0.233571i
$148$	−1.02832e17	−	1.02832e17i	−0.446718	−	0.446718i
$149$		−	2.97166e17i		−	1.22323i	−0.791154	−	0.611617i	$-0.790519\pi$
$149$		−	2.97166e17i		−	1.22323i	0.791154	−	0.611617i	$-0.209481\pi$
$150$	−8.48007e16	+	2.25256e16i	−0.330879	+	0.0878914i
$151$	−3.35478e17			−1.24122			−0.620610	−	0.784119i	$-0.713115\pi$
$151$	−3.35478e17			−1.24122			−0.620610	+	0.784119i	$0.713115\pi$
$152$	−3.35271e16	+	3.35271e16i	−0.117665	+	0.117665i
$153$	2.16435e17	+	2.16435e17i	0.720770	+	0.720770i
$154$			1.72769e17i			0.546134i
$155$	−5.61393e16	−	4.30017e17i	−0.168505	−	1.29072i
$156$	−1.50408e17			−0.428820
$157$	−2.44979e17	+	2.44979e17i	−0.663638	+	0.663638i	−0.956236	−	0.292597i	$-0.905480\pi$
$157$	−2.44979e17	+	2.44979e17i	−0.663638	+	0.663638i	0.292597	+	0.956236i	$0.405480\pi$
$158$	1.13943e17	+	1.13943e17i	0.293380	+	0.293380i
$159$			1.00177e16i			0.0245240i
$160$	6.01853e16	+	4.62854e16i	0.140130	+	0.107767i
$161$	8.70908e17			1.92915
$162$	−8.34217e16	+	8.34217e16i	−0.175857	+	0.175857i
$163$	−1.25688e17	−	1.25688e17i	−0.252227	−	0.252227i	0.569656	−	0.821883i	$-0.307076\pi$
$163$	−1.25688e17	−	1.25688e17i	−0.252227	−	0.252227i	−0.821883	+	0.569656i	$0.807076\pi$
$164$		−	3.11302e16i		−	0.0594882i
$165$	9.65582e16	−	1.25555e17i	0.175759	−	0.228541i
$166$	−6.47706e17			−1.12335
$167$	3.11480e17	−	3.11480e17i	0.514871	−	0.514871i	−0.401144	−	0.916015i	$-0.631387\pi$
$167$	3.11480e17	−	3.11480e17i	0.514871	−	0.514871i	0.916015	+	0.401144i	$0.131387\pi$
$168$	9.96207e16	+	9.96207e16i	0.156991	+	0.156991i
$169$			1.42255e18i			2.13784i
$170$	6.51213e17	−	8.50167e16i	0.933537	−	0.121875i
$171$	−2.63434e17			−0.360332
$172$	2.79293e17	−	2.79293e17i	0.364613	−	0.364613i
$173$	7.19501e17	+	7.19501e17i	0.896732	+	0.896732i	0.995146	−	0.0984132i	$-0.0313767\pi$
$173$	7.19501e17	+	7.19501e17i	0.896732	+	0.896732i	−0.0984132	+	0.995146i	$0.531377\pi$
$174$			1.12303e17i			0.133659i
$175$	5.72591e17	−	9.86816e17i	0.650939	−	1.12184i
$176$	−1.37060e17			−0.148871
$177$	−1.22503e17	+	1.22503e17i	−0.127163	+	0.127163i
$178$	−1.29915e17	−	1.29915e17i	−0.128914	−	0.128914i
$179$		−	1.23024e18i		−	1.16725i	−0.812022	−	0.583626i	$-0.801633\pi$
$179$		−	1.23024e18i		−	1.16725i	0.812022	−	0.583626i	$-0.198367\pi$
$180$	5.46081e16	+	4.18288e17i	0.0495538	+	0.379573i
$181$	−1.53035e18			−1.32850			−0.664252	−	0.747509i	$-0.731250\pi$
$181$	−1.53035e18			−1.32850			−0.664252	+	0.747509i	$0.731250\pi$
$182$	1.38294e18	−	1.38294e18i	1.14876	−	1.14876i
$183$	4.87578e17	+	4.87578e17i	0.387646	+	0.387646i
$184$			6.90903e17i			0.525866i
$185$	−1.37422e18	−	1.05685e18i	−1.00158	−	0.770260i
$186$	6.38381e17			0.445632
$187$	−8.38307e17	+	8.38307e17i	−0.560622	+	0.560622i
$188$	−4.38928e17	−	4.38928e17i	−0.281275	−	0.281275i
$189$			1.80517e18i			1.10873i
$190$	−3.44572e17	+	4.48050e17i	−0.202886	+	0.263814i
$191$	−2.48074e18			−1.40060			−0.700299	−	0.713850i	$-0.746950\pi$
$191$	−2.48074e18			−1.40060			−0.700299	+	0.713850i	$0.746950\pi$
$192$	−7.90305e16	+	7.90305e16i	−0.0427942	+	0.0427942i
$193$	1.84775e18	+	1.84775e18i	0.959810	+	0.959810i	0.999223	−	0.0394132i	$-0.0125488\pi$
$193$	1.84775e18	+	1.84775e18i	0.959810	+	0.959810i	−0.0394132	+	0.999223i	$0.512549\pi$
$194$		−	5.53678e17i		−	0.275958i
$195$	−1.77792e18	+	2.32110e17i	−0.850424	+	0.111024i
$196$	−7.42956e17			−0.341126
$197$	1.64312e18	−	1.64312e18i	0.724336	−	0.724336i	−0.245149	−	0.969485i	$-0.578837\pi$
$197$	1.64312e18	−	1.64312e18i	0.724336	−	0.724336i	0.969485	+	0.245149i	$0.0788370\pi$
$198$	−5.38462e17	−	5.38462e17i	−0.227947	−	0.227947i
$199$		−	2.74476e18i		−	1.11604i	−0.829828	−	0.558019i	$-0.811562\pi$
$199$		−	2.74476e18i		−	1.11604i	0.829828	−	0.558019i	$-0.188438\pi$
$200$	7.82855e17	+	4.54244e17i	0.305803	+	0.177439i
$201$	−3.26133e17			−0.122413
$202$	1.91411e18	−	1.91411e18i	0.690487	−	0.690487i
$203$	−1.03257e18	−	1.03257e18i	−0.358058	−	0.358058i
$204$			9.66758e17i			0.322312i
$205$	−4.80400e16	−	3.67978e17i	−0.0154018	−	0.117975i
$206$	−2.75670e18			−0.850063
$207$	−2.71433e18	+	2.71433e18i	−0.805193	+	0.805193i
$208$	1.09710e18	+	1.09710e18i	0.313141	+	0.313141i
$209$		−	1.02034e18i		−	0.280269i
$210$	1.33131e18	+	1.02384e18i	0.351986	+	0.270694i
$211$	6.29015e18			1.60104			0.800519	−	0.599308i	$-0.204557\pi$
$211$	6.29015e18			1.60104			0.800519	+	0.599308i	$0.204557\pi$
$212$	7.30709e16	−	7.30709e16i	0.0179084	−	0.0179084i
$213$	7.34148e16	+	7.34148e16i	0.0173279	+	0.0173279i
$214$			3.16066e18i			0.718567i
$215$	2.87041e18	−	3.73242e18i	0.628689	−	0.817490i
$216$	−1.43207e18			−0.302228
$217$	−5.86962e18	+	5.86962e18i	−1.19380	+	1.19380i
$218$	−2.80245e18	−	2.80245e18i	−0.549396	−	0.549396i
$219$		−	3.63041e18i		−	0.686124i
$220$	−1.62013e18	+	2.11510e17i	−0.295236	+	0.0385434i
$221$	1.34205e19			2.35848
$222$	1.80452e18	−	1.80452e18i	0.305871	−	0.305871i
$223$	7.24125e18	+	7.24125e18i	1.18406	+	1.18406i	0.978682	+	0.205380i	$0.0658430\pi$
$223$	7.24125e18	+	7.24125e18i	1.18406	+	1.18406i	0.205380	+	0.978682i	$0.434157\pi$
$224$		−	1.45330e18i		−	0.229282i
$225$	1.29100e18	+	4.86015e18i	0.196547	+	0.739929i
$226$	−2.22144e18			−0.326413
$227$	1.44997e18	−	1.44997e18i	0.205662	−	0.205662i	−0.596759	−	0.802421i	$-0.703545\pi$
$227$	1.44997e18	−	1.44997e18i	0.205662	−	0.205662i	0.802421	+	0.596759i	$0.203545\pi$
$228$	−5.88343e17	−	5.88343e17i	−0.0805660	−	0.0805660i
$229$		−	3.93960e18i		−	0.520917i	−0.965485	−	0.260458i	$-0.916126\pi$
$229$		−	3.93960e18i		−	0.520917i	0.965485	−	0.260458i	$-0.0838737\pi$
$230$	1.06620e18	+	8.16691e18i	0.136150	+	1.04288i
$231$	−3.03179e18			−0.373942
$232$	8.19156e17	−	8.19156e17i	0.0976029	−	0.0976029i
$233$	−8.51200e18	−	8.51200e18i	−0.979905	−	0.979905i	0.0198969	−	0.999802i	$-0.493666\pi$
$233$	−8.51200e18	−	8.51200e18i	−0.979905	−	0.979905i	−0.999802	+	0.0198969i	$0.993666\pi$
$234$			8.62030e18i			0.958949i
$235$	−5.86576e18	−	4.51105e18i	−0.630640	−	0.484992i
$236$	1.78711e18			0.185719
$237$	−1.99950e18	+	1.99950e18i	−0.200879	+	0.200879i
$238$	−8.88889e18	−	8.88889e18i	−0.863440	−	0.863440i
$239$			3.12944e17i			0.0293957i	0.999892	+	0.0146978i	$0.00467864\pi$
$239$			3.12944e17i			0.0293957i	−0.999892	+	0.0146978i	$0.995321\pi$
$240$	−8.12230e17	+	1.05615e18i	−0.0737885	+	0.0959479i
$241$	6.62990e18			0.582601			0.291300	−	0.956632i	$-0.405912\pi$
$241$	6.62990e18			0.582601			0.291300	+	0.956632i	$0.405912\pi$
$242$	−3.79597e18	+	3.79597e18i	−0.322701	+	0.322701i
$243$	−8.81267e18	−	8.81267e18i	−0.724866	−	0.724866i
$244$		−	7.11294e18i		−	0.566149i
$245$	−8.78220e18	+	1.14653e18i	−0.676511	+	0.0883194i
$246$	5.46281e17			0.0407320
$247$	−8.16739e18	+	8.16739e18i	−0.589532	+	0.589532i
$248$	−4.65645e18	−	4.65645e18i	−0.325418	−	0.325418i
$249$		−	1.13661e19i		−	0.769163i
$250$	9.95482e18	+	4.16135e18i	0.652399	+	0.272718i
$251$	1.02447e19			0.650292			0.325146	−	0.945664i	$-0.394586\pi$
$251$	1.02447e19			0.650292			0.325146	+	0.945664i	$0.394586\pi$
$252$	5.70953e18	−	5.70953e18i	0.351072	−	0.351072i
$253$	−1.05133e19	−	1.05133e19i	−0.626287	−	0.626287i
$254$		−	1.10787e19i		−	0.639467i
$255$	1.49190e18	+	1.14277e19i	0.0834483	+	0.639200i
$256$	1.15292e18			0.0625000
$257$	−1.04652e19	+	1.04652e19i	−0.549901	+	0.549901i	−0.926412	−	0.376511i	$-0.877124\pi$
$257$	−1.04652e19	+	1.04652e19i	−0.549901	+	0.549901i	0.376511	+	0.926412i	$0.377124\pi$
$258$	4.90111e18	+	4.90111e18i	0.249653	+	0.249653i
$259$			3.31835e19i			1.63879i
$260$	1.46615e19	+	1.12754e19i	0.702087	+	0.539939i
$261$	6.43638e18			0.298894
$262$	1.10397e19	−	1.10397e19i	0.497219	−	0.497219i
$263$	1.30853e19	+	1.30853e19i	0.571662	+	0.571662i	0.932593	−	0.360931i	$-0.117541\pi$
$263$	1.30853e19	+	1.30853e19i	0.571662	+	0.571662i	−0.360931	+	0.932593i	$0.617541\pi$
$264$		−	2.40516e18i		−	0.101933i
$265$	7.50980e17	−	9.76506e17i	0.0308789	−	0.0401521i
$266$	1.08191e19			0.431656
$267$	2.27979e18	−	2.27979e18i	0.0882683	−	0.0882683i
$268$	2.37887e18	+	2.37887e18i	0.0893906	+	0.0893906i
$269$		−	2.90871e19i		−	1.06092i	−0.847711	−	0.530459i	$-0.822020\pi$
$269$		−	2.90871e19i		−	1.06092i	0.847711	−	0.530459i	$-0.177980\pi$
$270$	−1.69280e19	+	2.20997e18i	−0.599369	+	0.0782484i
$271$	5.54590e18			0.190642			0.0953208	−	0.995447i	$-0.469612\pi$
$271$	5.54590e18			0.190642			0.0953208	+	0.995447i	$0.469612\pi$
$272$	7.05168e18	−	7.05168e18i	0.235365	−	0.235365i
$273$	2.42682e19	+	2.42682e19i	0.786567	+	0.786567i
$274$			1.69825e19i			0.534560i
$275$	−1.88246e19	+	5.00037e18i	−0.575524	+	0.152876i
$276$	−1.21242e19			−0.360064
$277$	4.11341e18	−	4.11341e18i	0.118676	−	0.118676i	−0.645275	−	0.763951i	$-0.723257\pi$
$277$	4.11341e18	−	4.11341e18i	0.118676	−	0.118676i	0.763951	+	0.645275i	$0.223257\pi$
$278$	1.69832e19	+	1.69832e19i	0.476059	+	0.476059i
$279$		−	3.65873e19i		−	0.996545i
$280$	−2.24273e18	−	1.71789e19i	−0.0593625	−	0.454706i
$281$	−1.27001e19			−0.326706			−0.163353	−	0.986568i	$-0.552231\pi$
$281$	−1.27001e19			−0.326706			−0.163353	+	0.986568i	$0.552231\pi$
$282$	7.70244e18	−	7.70244e18i	0.192591	−	0.192591i
$283$	9.99504e18	+	9.99504e18i	0.242937	+	0.242937i	0.818064	−	0.575127i	$-0.195047\pi$
$283$	9.99504e18	+	9.99504e18i	0.242937	+	0.242937i	−0.575127	+	0.818064i	$0.695047\pi$
$284$		−	1.07100e18i		−	0.0253071i
$285$	−7.86251e18	−	6.04665e18i	−0.180635	−	0.138917i
$286$	−3.33885e19			−0.745880
$287$	−5.02280e18	+	5.02280e18i	−0.109117	+	0.109117i
$288$	4.52945e18	+	4.52945e18i	0.0956985	+	0.0956985i
$289$		−	3.76001e19i		−	0.772691i
$290$	8.41881e18	−	1.09471e19i	0.168293	−	0.218833i
$291$	9.71610e18			0.188950
$292$	−2.64808e19	+	2.64808e19i	−0.501035	+	0.501035i
$293$	−3.41802e19	−	3.41802e19i	−0.629266	−	0.629266i	0.318618	−	0.947883i	$-0.396781\pi$
$293$	−3.41802e19	−	3.41802e19i	−0.629266	−	0.629266i	−0.947883	+	0.318618i	$0.896781\pi$
$294$		−	1.30376e19i		−	0.233571i
$295$	2.11248e19	−	2.75787e18i	0.368313	−	0.0480837i
$296$	−2.63249e19			−0.446718
$297$	2.17914e19	−	2.17914e19i	0.359942	−	0.359942i
$298$	−3.80373e19	−	3.80373e19i	−0.611617	−	0.611617i
$299$			1.68308e20i			2.63472i
$300$	−7.97121e18	+	1.37378e19i	−0.121494	+	0.209385i
$301$	−9.01269e19			−1.33759
$302$	−4.29412e19	+	4.29412e19i	−0.620610	+	0.620610i
$303$	3.35893e19	+	3.35893e19i	0.472781	+	0.472781i
$304$			8.58293e18i			0.117665i
$305$	−1.09767e19	−	8.40794e19i	−0.146579	−	1.12277i
$306$	5.54074e19			0.720770
$307$	7.52907e19	−	7.52907e19i	0.954188	−	0.954188i	−0.0448074	−	0.998996i	$-0.514267\pi$
$307$	7.52907e19	−	7.52907e19i	0.954188	−	0.954188i	0.998996	+	0.0448074i	$0.0142674\pi$
$308$	2.21144e19	+	2.21144e19i	0.273067	+	0.273067i
$309$		−	4.83753e19i		−	0.582044i
$310$	−6.22280e19	−	4.78563e19i	−0.729612	−	0.561107i
$311$	−3.90765e19			−0.446511			−0.223256	−	0.974760i	$-0.571668\pi$
$311$	−3.90765e19			−0.446511			−0.223256	+	0.974760i	$0.571668\pi$
$312$	−1.92523e19	+	1.92523e19i	−0.214410	+	0.214410i
$313$	3.30279e19	+	3.30279e19i	0.358531	+	0.358531i	0.863271	−	0.504740i	$-0.168412\pi$
$313$	3.30279e19	+	3.30279e19i	0.358531	+	0.358531i	−0.504740	+	0.863271i	$0.668412\pi$
$314$			6.27146e19i			0.663638i
$315$	5.86792e19	−	7.63011e19i	0.605341	−	0.787130i
$316$	2.91694e19			0.293380
$317$	−3.87267e18	+	3.87267e18i	−0.0379783	+	0.0379783i	−0.725841	−	0.687863i	$-0.758549\pi$
$317$	−3.87267e18	+	3.87267e18i	−0.0379783	+	0.0379783i	0.687863	+	0.725841i	$0.258549\pi$
$318$	1.28227e18	+	1.28227e18i	0.0122620	+	0.0122620i
$319$			2.49297e19i			0.232483i
$320$	1.36282e19	−	1.77919e18i	0.123948	−	0.0161816i
$321$	−5.54641e19			−0.492008
$322$	1.11476e20	−	1.11476e20i	0.964573	−	0.964573i
$323$	5.24963e19	+	5.24963e19i	0.443107	+	0.443107i
$324$			2.13560e19i			0.175857i
$325$	1.90708e20	+	1.10656e20i	1.53215	+	0.889017i
$326$	−3.21761e19			−0.252227
$327$	4.91781e19	−	4.91781e19i	0.376175	−	0.376175i
$328$	−3.98466e18	−	3.98466e18i	−0.0297441	−	0.0297441i
$329$			1.41641e20i			1.03186i
$330$	−3.71165e18	−	2.84305e19i	−0.0263909	−	0.202150i
$331$	−1.50788e20			−1.04651			−0.523254	−	0.852177i	$-0.675282\pi$
$331$	−1.50788e20			−1.04651			−0.523254	+	0.852177i	$0.675282\pi$
$332$	−8.29064e19	+	8.29064e19i	−0.561673	+	0.561673i
$333$	−1.03422e20	−	1.03422e20i	−0.684004	−	0.684004i
$334$		−	7.97389e19i		−	0.514871i
$335$	3.17908e19	+	2.44486e19i	0.200421	+	0.154133i
$336$	2.55029e19			0.156991
$337$	1.92920e19	−	1.92920e19i	0.115968	−	0.115968i	−0.646741	−	0.762709i	$-0.723869\pi$
$337$	1.92920e19	−	1.92920e19i	0.115968	−	0.115968i	0.762709	+	0.646741i	$0.223869\pi$
$338$	1.82087e20	+	1.82087e20i	1.06892	+	1.06892i
$339$		−	3.89825e19i		−	0.223497i
$340$	7.24731e19	−	9.42374e19i	0.405831	−	0.527706i
$341$	1.41712e20			0.775123
$342$	−3.37195e19	+	3.37195e19i	−0.180166	+	0.180166i
$343$	−5.58299e19	−	5.58299e19i	−0.291416	−	0.291416i
$344$		−	7.14989e19i		−	0.364613i
$345$	−1.43315e20	+	1.87100e19i	−0.714068	+	0.0932226i
$346$	1.84192e20			0.896732
$347$	−2.01207e20	+	2.01207e20i	−0.957212	+	0.957212i	−0.999121	−	0.0419099i	$-0.986656\pi$
$347$	−2.01207e20	+	2.01207e20i	−0.957212	+	0.957212i	0.0419099	+	0.999121i	$0.486656\pi$
$348$	1.43748e19	+	1.43748e19i	0.0668294	+	0.0668294i
$349$			3.03991e20i			1.38120i	0.723235	+	0.690602i	$0.242654\pi$
$349$			3.03991e20i			1.38120i	−0.723235	+	0.690602i	$0.757346\pi$
$350$	−5.30208e19	−	1.99604e20i	−0.235452	−	0.886391i
$351$	−3.48860e20			−1.51424
$352$	−1.75437e19	+	1.75437e19i	−0.0744353	+	0.0744353i
$353$	−2.06471e20	−	2.06471e20i	−0.856371	−	0.856371i	0.134537	−	0.990909i	$-0.457045\pi$
$353$	−2.06471e20	−	2.06471e20i	−0.856371	−	0.856371i	−0.990909	+	0.134537i	$0.957045\pi$
$354$			3.13608e19i			0.127163i
$355$	−1.65276e18	−	1.26599e19i	−0.00655215	−	0.0501883i
$356$	−3.32583e19			−0.128914
$357$	1.55985e20	−	1.55985e20i	0.591203	−	0.591203i
$358$	−1.57470e20	−	1.57470e20i	−0.583626	−	0.583626i
$359$		−	4.18242e20i		−	1.51590i	−0.652310	−	0.757952i	$-0.726200\pi$
$359$		−	4.18242e20i		−	1.51590i	0.652310	−	0.757952i	$-0.273800\pi$
$360$	6.05307e19	+	4.65510e19i	0.214563	+	0.165010i
$361$	2.24546e20			0.778479
$362$	−1.95885e20	+	1.95885e20i	−0.664252	+	0.664252i
$363$	−6.66128e19	−	6.66128e19i	−0.220955	−	0.220955i
$364$		−	3.54032e20i		−	1.14876i
$365$	−2.72154e20	+	3.53884e20i	−0.863917	+	1.12336i
$366$	1.24820e20			0.387646
$367$	1.36871e20	−	1.36871e20i	0.415894	−	0.415894i	−0.467891	−	0.883786i	$-0.654986\pi$
$367$	1.36871e20	−	1.36871e20i	0.415894	−	0.415894i	0.883786	+	0.467891i	$0.154986\pi$
$368$	8.84356e19	+	8.84356e19i	0.262933	+	0.262933i
$369$		−	3.13088e19i		−	0.0910869i
$370$	−3.11177e20	+	4.06246e19i	−0.885918	+	0.115658i
$371$	−2.35797e19			−0.0656974
$372$	8.17128e19	−	8.17128e19i	0.222816	−	0.222816i
$373$	2.62499e20	+	2.62499e20i	0.700580	+	0.700580i	0.964535	−	0.263955i	$-0.0850271\pi$
$373$	2.62499e20	+	2.62499e20i	0.700580	+	0.700580i	−0.263955	+	0.964535i	$0.585027\pi$
$374$			2.14607e20i			0.560622i
$375$	−7.30246e19	+	1.74690e20i	−0.186732	+	0.446702i
$376$	−1.12366e20			−0.281275
$377$	1.99551e20	−	1.99551e20i	0.489016	−	0.489016i
$378$	2.31062e20	+	2.31062e20i	0.554364	+	0.554364i
$379$		−	1.31193e20i		−	0.308174i	−0.988057	−	0.154087i	$-0.950756\pi$
$379$		−	1.31193e20i		−	0.308174i	0.988057	−	0.154087i	$-0.0492436\pi$
$380$	1.32452e19	+	1.01456e20i	0.0304641	+	0.233350i
$381$	1.94412e20			0.437847
$382$	−3.17534e20	+	3.17534e20i	−0.700299	+	0.700299i
$383$	7.10802e19	+	7.10802e19i	0.153518	+	0.153518i	0.779687	−	0.626169i	$-0.215378\pi$
$383$	7.10802e19	+	7.10802e19i	0.153518	+	0.153518i	−0.626169	+	0.779687i	$0.715378\pi$
$384$			2.02318e19i			0.0427942i
$385$	2.95533e20	+	2.27279e20i	0.612237	+	0.470840i
$386$	4.73025e20			0.959810
$387$	2.80895e20	−	2.80895e20i	0.558286	−	0.558286i
$388$	−7.08707e19	−	7.08707e19i	−0.137979	−	0.137979i
$389$		−	8.95111e19i		−	0.170718i	−0.996350	−	0.0853592i	$-0.972796\pi$
$389$		−	8.95111e19i		−	0.170718i	0.996350	−	0.0853592i	$-0.0272038\pi$
$390$	−1.97864e20	+	2.57284e20i	−0.369700	+	0.480724i
$391$	1.08181e21			1.98032
$392$	−9.50984e19	+	9.50984e19i	−0.170563	+	0.170563i
$393$	1.93728e20	+	1.93728e20i	0.340449	+	0.340449i
$394$		−	4.20639e20i		−	0.724336i
$395$	3.44800e20	−	4.50141e19i	0.581822	−	0.0759577i
$396$	−1.37846e20			−0.227947
$397$	−4.37439e20	+	4.37439e20i	−0.708913	+	0.708913i	−0.966307	−	0.257393i	$-0.917136\pi$
$397$	−4.37439e20	+	4.37439e20i	−0.708913	+	0.708913i	0.257393	+	0.966307i	$0.417136\pi$
$398$	−3.51329e20	−	3.51329e20i	−0.558019	−	0.558019i
$399$			1.89857e20i			0.295558i
$400$	1.58349e20	−	4.20622e19i	0.241621	−	0.0641818i
$401$	−3.38912e20			−0.506911			−0.253455	−	0.967347i	$-0.581567\pi$
$401$	−3.38912e20			−0.506911			−0.253455	+	0.967347i	$0.581567\pi$
$402$	−4.17451e19	+	4.17451e19i	−0.0612064	+	0.0612064i
$403$	−1.13434e21	−	1.13434e21i	−1.63043	−	1.63043i
$404$		−	4.90011e20i		−	0.690487i
$405$	3.29565e19	+	2.52441e20i	0.0455303	+	0.348754i
$406$	−2.64339e20			−0.358058
$407$	4.00578e20	−	4.00578e20i	0.532025	−	0.532025i
$408$	1.23745e20	+	1.23745e20i	0.161156	+	0.161156i
$409$			5.19146e20i			0.662984i	0.943458	+	0.331492i	$0.107552\pi$
$409$			5.19146e20i			0.662984i	−0.943458	+	0.331492i	$0.892448\pi$
$410$	−5.32503e19	−	4.09520e19i	−0.0666885	−	0.0512867i
$411$	−2.98013e20			−0.366017
$412$	−3.52857e20	+	3.52857e20i	−0.425032	+	0.425032i
$413$	−2.88348e20	−	2.88348e20i	−0.340657	−	0.340657i
$414$			6.94869e20i			0.805193i
$415$	−8.52064e20	+	1.10795e21i	−0.968473	+	1.25931i
$416$	2.80858e20			0.313141
$417$	−2.98026e20	+	2.98026e20i	−0.325961	+	0.325961i
$418$	−1.30604e20	−	1.30604e20i	−0.140135	−	0.140135i
$419$		−	1.67066e21i		−	1.75864i	−0.476231	−	0.879320i	$-0.657997\pi$
$419$		−	1.67066e21i		−	1.75864i	0.476231	−	0.879320i	$-0.342003\pi$
$420$	3.01460e20	−	3.93560e19i	0.311340	−	0.0406459i
$421$	8.16835e19			0.0827709			0.0413854	−	0.999143i	$-0.486823\pi$
$421$	8.16835e19			0.0827709			0.0413854	+	0.999143i	$0.486823\pi$
$422$	8.05139e20	−	8.05139e20i	0.800519	−	0.800519i
$423$	−4.41447e20	−	4.41447e20i	−0.430681	−	0.430681i
$424$		−	1.87061e19i		−	0.0179084i
$425$	7.11250e20	−	1.22579e21i	0.668207	−	1.15160i
$426$	1.87942e19			0.0173279
$427$	−1.14766e21	+	1.14766e21i	−1.03846	+	1.03846i
$428$	4.04564e20	+	4.04564e20i	0.359283	+	0.359283i
$429$		−	5.85912e20i		−	0.510709i
$430$	−1.10337e20	−	8.45161e20i	−0.0944003	−	0.723089i
$431$	−2.13992e20			−0.179713			−0.0898563	−	0.995955i	$-0.528641\pi$
$431$	−2.13992e20			−0.179713			−0.0898563	+	0.995955i	$0.528641\pi$
$432$	−1.83305e20	+	1.83305e20i	−0.151114	+	0.151114i
$433$	1.14666e21	+	1.14666e21i	0.927967	+	0.927967i	0.997574	−	0.0696073i	$-0.0221746\pi$
$433$	1.14666e21	+	1.14666e21i	0.927967	+	0.927967i	−0.0696073	+	0.997574i	$0.522175\pi$
$434$			1.50262e21i			1.19380i
$435$	1.92102e20	+	1.47736e20i	0.149837	+	0.115232i
$436$	−7.17426e20			−0.549396
$437$	−6.58360e20	+	6.58360e20i	−0.495008	+	0.495008i
$438$	−4.64692e20	−	4.64692e20i	−0.343062	−	0.343062i
$439$			2.06586e21i			1.49756i	0.662819	+	0.748780i	$0.269360\pi$
$439$			2.06586e21i			1.49756i	−0.662819	+	0.748780i	$0.730640\pi$
$440$	−1.80304e20	+	2.34450e20i	−0.128346	+	0.166890i
$441$	−7.47220e20			−0.522324
$442$	1.71783e21	−	1.71783e21i	1.17924	−	1.17924i
$443$	6.82987e20	+	6.82987e20i	0.460450	+	0.460450i	0.898803	−	0.438353i	$-0.144438\pi$
$443$	6.82987e20	+	6.82987e20i	0.460450	+	0.460450i	−0.438353	+	0.898803i	$0.644438\pi$
$444$		−	4.61957e20i		−	0.305871i
$445$	−3.93134e20	+	5.13241e19i	−0.255659	+	0.0333766i
$446$	1.85376e21			1.18406
$447$	6.67489e20	−	6.67489e20i	0.418778	−	0.418778i
$448$	−1.86022e20	−	1.86022e20i	−0.114641	−	0.114641i
$449$			3.47850e20i			0.210582i	0.994441	+	0.105291i	$0.0335774\pi$
$449$			3.47850e20i			0.210582i	−0.994441	+	0.105291i	$0.966423\pi$
$450$	7.87348e20	+	4.56851e20i	0.468238	+	0.271691i
$451$	1.21267e20			0.0708483
$452$	−2.84345e20	+	2.84345e20i	−0.163207	+	0.163207i
$453$	−7.53545e20	−	7.53545e20i	−0.424936	−	0.424936i
$454$		−	3.71193e20i		−	0.205662i
$455$	−5.46341e20	−	4.18487e21i	−0.297421	−	2.27820i
$456$	−1.50616e20			−0.0805660
$457$	5.35611e20	−	5.35611e20i	0.281527	−	0.281527i	−0.552191	−	0.833718i	$-0.686208\pi$
$457$	5.35611e20	−	5.35611e20i	0.281527	−	0.281527i	0.833718	+	0.552191i	$0.186208\pi$
$458$	−5.04269e20	−	5.04269e20i	−0.260458	−	0.260458i
$459$			2.24232e21i			1.13814i
$460$	1.18184e21	+	9.08891e20i	0.589516	+	0.453366i
$461$	2.41650e21			1.18462			0.592310	−	0.805710i	$-0.298216\pi$
$461$	2.41650e21			1.18462			0.592310	+	0.805710i	$0.298216\pi$
$462$	−3.88070e20	+	3.88070e20i	−0.186971	+	0.186971i
$463$	2.23990e21	+	2.23990e21i	1.06067	+	1.06067i	0.998037	+	0.0626330i	$0.0199498\pi$
$463$	2.23990e21	+	2.23990e21i	1.06067	+	1.06067i	0.0626330	+	0.998037i	$0.480050\pi$
$464$		−	2.09704e20i		−	0.0976029i
$465$	8.39797e20	−	1.09199e21i	0.384194	−	0.499571i
$466$	−2.17907e21			−0.979905
$467$	−1.16640e21	+	1.16640e21i	−0.515597	+	0.515597i	−0.916236	−	0.400639i	$-0.868788\pi$
$467$	−1.16640e21	+	1.16640e21i	−0.515597	+	0.515597i	0.400639	+	0.916236i	$0.368788\pi$
$468$	1.10340e21	+	1.10340e21i	0.479475	+	0.479475i
$469$		−	7.67653e20i		−	0.327931i
$470$	−1.32823e21	+	1.73402e20i	−0.557816	+	0.0728236i
$471$	−1.10053e21			−0.454398
$472$	2.28751e20	−	2.28751e20i	0.0928595	−	0.0928595i
$473$	1.08798e21	+	1.08798e21i	0.434241	+	0.434241i
$474$			5.11872e20i			0.200879i
$475$	3.13132e20	+	1.17883e21i	0.120831	+	0.454885i
$476$	−2.27556e21			−0.863440
$477$	7.34902e19	−	7.34902e19i	0.0274210	−	0.0274210i
$478$	4.00568e19	+	4.00568e19i	0.0146978	+	0.0146978i
$479$		−	3.59006e21i		−	1.29544i	−0.761879	−	0.647720i	$-0.775723\pi$
$479$		−	3.59006e21i		−	1.29544i	0.761879	−	0.647720i	$-0.224277\pi$
$480$	3.12217e19	+	2.39152e20i	0.0110797	+	0.0848682i
$481$	−6.41290e21			−2.23817
$482$	8.48628e20	−	8.48628e20i	0.291300	−	0.291300i
$483$	1.95622e21	+	1.95622e21i	0.660450	+	0.660450i
$484$			9.71768e20i			0.322701i
$485$	−9.47104e20	−	7.28369e20i	−0.309360	−	0.237913i
$486$	−2.25604e21			−0.724866
$487$	3.54841e21	−	3.54841e21i	1.12151	−	1.12151i	0.129993	−	0.991515i	$-0.458505\pi$
$487$	3.54841e21	−	3.54841e21i	1.12151	−	1.12151i	0.991515	−	0.129993i	$-0.0414954\pi$
$488$	−9.10457e20	−	9.10457e20i	−0.283074	−	0.283074i
$489$		−	5.64635e20i		−	0.172702i
$490$	−9.77366e20	+	1.27088e21i	−0.294096	+	0.382415i
$491$	−3.31994e20			−0.0982830			−0.0491415	−	0.998792i	$-0.515649\pi$
$491$	−3.31994e20			−0.0982830			−0.0491415	+	0.998792i	$0.515649\pi$
$492$	6.99240e19	−	6.99240e19i	0.0203660	−	0.0203660i
$493$	−1.28262e21	−	1.28262e21i	−0.367557	−	0.367557i
$494$			2.09085e21i			0.589532i
$495$	−1.62943e21	+	2.12724e20i	−0.452058	+	0.0590168i
$496$	−1.19205e21			−0.325418
$497$	−1.72804e20	+	1.72804e20i	−0.0464197	+	0.0464197i
$498$	−1.45487e21	−	1.45487e21i	−0.384581	−	0.384581i
$499$			7.95178e20i			0.206852i	0.994637	+	0.103426i	$0.0329805\pi$
$499$			7.95178e20i			0.206852i	−0.994637	+	0.103426i	$0.967020\pi$
$500$	1.80687e21	−	7.41564e20i	0.462559	−	0.189840i
$501$	1.39928e21			0.352536
$502$	1.31132e21	−	1.31132e21i	0.325146	−	0.325146i
$503$	2.66641e21	+	2.66641e21i	0.650703	+	0.650703i	0.953162	−	0.302459i	$-0.0978076\pi$
$503$	2.66641e21	+	2.66641e21i	0.650703	+	0.650703i	−0.302459	+	0.953162i	$0.597808\pi$
$504$		−	1.46164e21i		−	0.351072i
$505$	−7.56185e20	−	5.79224e21i	−0.178771	−	1.36935i
$506$	−2.69140e21			−0.626287
$507$	−3.19531e21	+	3.19531e21i	−0.731897	+	0.731897i
$508$	−1.41807e21	−	1.41807e21i	−0.319733	−	0.319733i
$509$		−	2.10113e21i		−	0.466348i	−0.972435	−	0.233174i	$-0.925089\pi$
$509$		−	2.10113e21i		−	0.466348i	0.972435	−	0.233174i	$-0.0749112\pi$
$510$	1.65371e21	+	1.27178e21i	0.361324	+	0.277876i
$511$	8.54526e21			1.83805
$512$	1.47574e20	−	1.47574e20i	0.0312500	−	0.0312500i
$513$	−1.36462e21	−	1.36462e21i	−0.284493	−	0.284493i
$514$			2.67910e21i			0.549901i
$515$	−3.62646e21	+	4.71552e21i	−0.732867	+	0.952954i
$516$	1.25468e21			0.249653
$517$	1.70983e21	−	1.70983e21i	0.334988	−	0.334988i
$518$	4.24749e21	+	4.24749e21i	0.819396	+	0.819396i
$519$			3.23226e21i			0.613999i
$520$	3.31992e21	−	4.33420e20i	0.621013	−	0.0810740i
$521$	2.40993e21			0.443918			0.221959	−	0.975056i	$-0.428755\pi$
$521$	2.40993e21			0.443918			0.221959	+	0.975056i	$0.428755\pi$
$522$	8.23857e20	−	8.23857e20i	0.149447	−	0.149447i
$523$	−1.24720e21	−	1.24720e21i	−0.222803	−	0.222803i	0.586875	−	0.809678i	$-0.300358\pi$
$523$	−1.24720e21	−	1.24720e21i	−0.222803	−	0.222803i	−0.809678	+	0.586875i	$0.800358\pi$
$524$		−	2.82617e21i		−	0.497219i
$525$	3.50271e21	−	9.30425e20i	0.606918	−	0.161216i
$526$	3.34985e21			0.571662
$527$	−7.29102e21	+	7.29102e21i	−1.22547	+	1.22547i
$528$	−3.07861e20	−	3.07861e20i	−0.0509663	−	0.0509663i
$529$			7.43442e21i			1.21228i
$530$	−2.88673e19	−	2.21118e20i	−0.00463659	−	0.0355155i
$531$	1.79737e21			0.284369
$532$	1.38484e21	−	1.38484e21i	0.215828	−	0.215828i
$533$	−9.70686e20	−	9.70686e20i	−0.149026	−	0.149026i
$534$		−	5.83626e20i		−	0.0882683i
$535$	5.40652e21	+	4.15788e21i	0.805541	+	0.619500i
$536$	6.08990e20			0.0893906
$537$	2.76334e21	−	2.76334e21i	0.399613	−	0.399613i
$538$	−3.72314e21	−	3.72314e21i	−0.530459	−	0.530459i
$539$		−	2.89417e21i		−	0.406269i
$540$	−1.88390e21	+	2.44965e21i	−0.260560	+	0.338809i
$541$	1.15444e21			0.157324			0.0786619	−	0.996901i	$-0.474935\pi$
$541$	1.15444e21			0.157324			0.0786619	+	0.996901i	$0.474935\pi$
$542$	7.09875e20	−	7.09875e20i	0.0953208	−	0.0953208i
$543$	−3.43745e21	−	3.43745e21i	−0.454818	−	0.454818i
$544$		−	1.80523e21i		−	0.235365i
$545$	−8.48042e21	+	1.10713e21i	−1.08955	+	0.142242i
$546$	6.21265e21			0.786567
$547$	−1.54952e21	+	1.54952e21i	−0.193330	+	0.193330i	−0.797133	−	0.603803i	$-0.793651\pi$
$547$	−1.54952e21	+	1.54952e21i	−0.193330	+	0.193330i	0.603803	+	0.797133i	$0.293651\pi$
$548$	2.17376e21	+	2.17376e21i	0.267280	+	0.267280i
$549$		−	7.15376e21i		−	0.866874i
$550$	−1.76950e21	+	3.04959e21i	−0.211324	+	0.364200i
$551$	1.56114e21			0.183751
$552$	−1.55189e21	+	1.55189e21i	−0.180032	+	0.180032i
$553$	−4.70643e21	−	4.70643e21i	−0.538134	−	0.538134i
$554$		−	1.05303e21i		−	0.118676i
$555$	−7.12892e20	−	5.46062e21i	−0.0791917	−	0.606594i
$556$	4.34769e21			0.476059
$557$	−1.27252e22	+	1.27252e22i	−1.37348	+	1.37348i	−0.518255	+	0.855226i	$0.673418\pi$
$557$	−1.27252e22	+	1.27252e22i	−1.37348	+	1.37348i	−0.855226	+	0.518255i	$0.826582\pi$
$558$	−4.68318e21	−	4.68318e21i	−0.498272	−	0.498272i
$559$		−	1.74175e22i		−	1.82680i
$560$	−2.48597e21	−	1.91183e21i	−0.257034	−	0.197672i
$561$	−3.76598e21			−0.383862
$562$	−1.62562e21	+	1.62562e21i	−0.163353	+	0.163353i
$563$	3.94673e20	+	3.94673e20i	0.0390994	+	0.0390994i	0.726386	−	0.687287i	$-0.241198\pi$
$563$	3.94673e20	+	3.94673e20i	0.0390994	+	0.0390994i	−0.687287	+	0.726386i	$0.741198\pi$
$564$		−	1.97182e21i		−	0.192591i
$565$	−2.92233e21	+	3.79993e21i	−0.281411	+	0.365922i
$566$	2.55873e21			0.242937
$567$	3.44575e21	−	3.44575e21i	0.322567	−	0.322567i
$568$	−1.37088e20	−	1.37088e20i	−0.0126535	−	0.0126535i
$569$			1.13144e22i			1.02975i	0.857264	+	0.514877i	$0.172162\pi$
$569$			1.13144e22i			1.02975i	−0.857264	+	0.514877i	$0.827838\pi$
$570$	−1.78037e21	+	2.32430e20i	−0.159776	+	0.0208590i
$571$	−1.70099e22			−1.50527			−0.752634	−	0.658439i	$-0.771217\pi$
$571$	−1.70099e22			−1.50527			−0.752634	+	0.658439i	$0.771217\pi$
$572$	−4.27373e21	+	4.27373e21i	−0.372940	+	0.372940i
$573$	−5.57218e21	−	5.57218e21i	−0.479500	−	0.479500i
$574$			1.28584e21i			0.109117i
$575$	1.53727e22	+	8.91984e21i	1.28649	+	0.746473i
$576$	1.15954e21			0.0956985
$577$	2.10833e21	−	2.10833e21i	0.171606	−	0.171606i	−0.616079	−	0.787684i	$-0.711280\pi$
$577$	2.10833e21	−	2.10833e21i	0.171606	−	0.171606i	0.787684	+	0.616079i	$0.211280\pi$
$578$	−4.81281e21	−	4.81281e21i	−0.386345	−	0.386345i
$579$			8.30077e21i			0.657188i
$580$	−3.23615e20	−	2.47883e21i	−0.0252699	−	0.193563i
$581$	2.67536e22			2.06051
$582$	1.24366e21	−	1.24366e21i	0.0944752	−	0.0944752i
$583$	2.84646e20	+	2.84646e20i	0.0213283	+	0.0213283i
$584$			6.77907e21i			0.501035i
$585$	1.47456e22	+	1.13401e22i	1.07502	+	0.826741i
$586$	−8.75014e21			−0.629266
$587$	8.83363e21	−	8.83363e21i	0.626663	−	0.626663i	−0.320564	−	0.947227i	$-0.603872\pi$
$587$	8.83363e21	−	8.83363e21i	0.626663	−	0.626663i	0.947227	+	0.320564i	$0.103872\pi$
$588$	−1.66881e21	−	1.66881e21i	−0.116786	−	0.116786i
$589$		−	8.87424e21i		−	0.612645i
$590$	2.35097e21	−	3.05698e21i	0.160114	−	0.208198i
$591$	7.38150e21			0.495958
$592$	−3.36959e21	+	3.36959e21i	−0.223359	+	0.223359i
$593$	4.05680e21	+	4.05680e21i	0.265305	+	0.265305i	0.827205	−	0.561900i	$-0.189929\pi$
$593$	4.05680e21	+	4.05680e21i	0.265305	+	0.265305i	−0.561900	+	0.827205i	$0.689929\pi$
$594$		−	5.57859e21i		−	0.359942i
$595$	−2.68985e22	+	3.51163e21i	−1.71235	+	0.223549i
$596$	−9.73755e21			−0.611617
$597$	6.16522e21	−	6.16522e21i	0.382080	−	0.382080i
$598$	2.15434e22	+	2.15434e22i	1.31736	+	1.31736i
$599$		−	1.13417e22i		−	0.684324i	−0.939641	−	0.342162i	$-0.888841\pi$
$599$		−	1.13417e22i		−	0.684324i	0.939641	−	0.342162i	$-0.111159\pi$
$600$	7.38119e20	+	2.77875e21i	0.0439457	+	0.165440i
$601$	1.96072e22			1.15192			0.575958	−	0.817479i	$-0.304629\pi$
$601$	1.96072e22			1.15192			0.575958	+	0.817479i	$0.304629\pi$
$602$	−1.15362e22	+	1.15362e22i	−0.668794	+	0.668794i
$603$	2.39252e21	+	2.39252e21i	0.136873	+	0.136873i
$604$			1.09930e22i			0.620610i
$605$	1.49963e21	+	1.14869e22i	0.0835490	+	0.639970i
$606$	8.59886e21			0.472781
$607$	2.29409e22	−	2.29409e22i	1.24480	−	1.24480i	0.286818	−	0.957985i	$-0.407402\pi$
$607$	2.29409e22	−	2.29409e22i	1.24480	−	1.24480i	0.957985	−	0.286818i	$-0.0925976\pi$
$608$	1.09862e21	+	1.09862e21i	0.0588325	+	0.0588325i
$609$		−	4.63870e21i		−	0.245165i
$610$	−1.21672e22	−	9.35715e21i	−0.634675	−	0.488095i
$611$	−2.73729e22			−1.40926
$612$	7.09215e21	−	7.09215e21i	0.360385	−	0.360385i
$613$	−1.31842e21	−	1.31842e21i	−0.0661256	−	0.0661256i	0.673271	−	0.739396i	$-0.264889\pi$
$613$	−1.31842e21	−	1.31842e21i	−0.0661256	−	0.0661256i	−0.739396	+	0.673271i	$0.764889\pi$
$614$		−	1.92744e22i		−	0.954188i
$615$	7.18638e20	−	9.34451e20i	0.0351164	−	0.0456621i
$616$	5.66128e21			0.273067
$617$	3.43085e21	−	3.43085e21i	0.163351	−	0.163351i	−0.620699	−	0.784049i	$-0.713151\pi$
$617$	3.43085e21	−	3.43085e21i	0.163351	−	0.163351i	0.784049	+	0.620699i	$0.213151\pi$
$618$	−6.19204e21	−	6.19204e21i	−0.291022	−	0.291022i
$619$			1.00920e22i			0.468223i	0.972210	+	0.234112i	$0.0752181\pi$
$619$			1.00920e22i			0.468223i	−0.972210	+	0.234112i	$0.924782\pi$
$620$	−1.40908e22	+	1.83957e21i	−0.645360	+	0.0842526i
$621$	−2.81211e22			−1.27145
$622$	−5.00179e21	+	5.00179e21i	−0.223256	+	0.223256i
$623$	5.36618e21	+	5.36618e21i	0.236462	+	0.236462i
$624$			4.92858e21i			0.214410i
$625$	2.02139e22	−	1.15541e22i	0.868182	−	0.496245i
$626$	8.45515e21			0.358531
$627$	2.29187e21	−	2.29187e21i	0.0959512	−	0.0959512i
$628$	8.02747e21	+	8.02747e21i	0.331819	+	0.331819i
$629$			4.12192e22i			1.68227i
$630$	−2.25560e21	−	1.72775e22i	−0.0908944	−	0.696235i
$631$	−1.38969e22			−0.552946			−0.276473	−	0.961022i	$-0.589166\pi$
$631$	−1.38969e22			−0.552946			−0.276473	+	0.961022i	$0.589166\pi$
$632$	3.73368e21	−	3.73368e21i	0.146690	−	0.146690i
$633$	1.41288e22	+	1.41288e22i	0.548121	+	0.548121i
$634$			9.91403e20i			0.0379783i
$635$	−1.89508e22	−	1.45741e22i	−0.716867	−	0.551305i
$636$	3.28261e20			0.0122620
$637$	−2.31665e22	+	2.31665e22i	−0.854565	+	0.854565i
$638$	3.19100e21	+	3.19100e21i	0.116242	+	0.116242i
$639$		−	1.07714e21i		−	0.0387496i
$640$	1.51668e21	−	1.97215e21i	0.0538833	−	0.0700649i
$641$	−4.05703e22			−1.42346			−0.711728	−	0.702455i	$-0.752087\pi$
$641$	−4.05703e22			−1.42346			−0.711728	+	0.702455i	$0.752087\pi$
$642$	−7.09941e21	+	7.09941e21i	−0.246004	+	0.246004i
$643$	−2.20545e22	−	2.20545e22i	−0.754760	−	0.754760i	0.220603	−	0.975364i	$-0.429197\pi$
$643$	−2.20545e22	−	2.20545e22i	−0.754760	−	0.754760i	−0.975364	+	0.220603i	$0.929197\pi$
$644$		−	2.85379e22i		−	0.964573i
$645$	1.48311e22	−	1.93622e21i	0.495104	−	0.0646365i
$646$	1.34391e22			0.443107
$647$	1.79779e22	−	1.79779e22i	0.585471	−	0.585471i	−0.350931	−	0.936401i	$-0.614135\pi$
$647$	1.79779e22	−	1.79779e22i	0.585471	−	0.585471i	0.936401	+	0.350931i	$0.114135\pi$
$648$	2.73356e21	+	2.73356e21i	0.0879284	+	0.0879284i
$649$			6.96166e21i			0.221185i
$650$	3.85746e22	−	1.02466e22i	1.21058	−	0.321567i
$651$	−2.63685e22			−0.817404
$652$	−4.11854e21	+	4.11854e21i	−0.126114	+	0.126114i
$653$	−1.83049e22	−	1.83049e22i	−0.553684	−	0.553684i	0.373818	−	0.927502i	$-0.378049\pi$
$653$	−1.83049e22	−	1.83049e22i	−0.553684	−	0.553684i	−0.927502	+	0.373818i	$0.878049\pi$
$654$		−	1.25896e22i		−	0.376175i
$655$	−4.36134e21	−	3.34071e22i	−0.128733	−	0.986071i
$656$	−1.02007e21			−0.0297441
$657$	−2.66327e22	+	2.66327e22i	−0.767172	+	0.767172i
$658$	1.81300e22	+	1.81300e22i	0.515931	+	0.515931i
$659$			1.04004e22i			0.292392i	0.989256	+	0.146196i	$0.0467030\pi$
$659$			1.04004e22i			0.292392i	−0.989256	+	0.146196i	$0.953297\pi$
$660$	−4.11420e21	−	3.16402e21i	−0.114270	−	0.0878795i
$661$	−4.08312e21			−0.112042			−0.0560209	−	0.998430i	$-0.517841\pi$
$661$	−4.08312e21			−0.112042			−0.0560209	+	0.998430i	$0.517841\pi$
$662$	−1.93009e22	+	1.93009e22i	−0.523254	+	0.523254i
$663$	3.01450e22	+	3.01450e22i	0.807433	+	0.807433i
$664$			2.12240e22i			0.561673i
$665$	1.42326e22	−	1.85068e22i	0.372145	−	0.483903i
$666$	−2.64760e22			−0.684004
$667$	1.60855e22	−	1.60855e22i	0.410608	−	0.410608i
$668$	−1.02066e22	−	1.02066e22i	−0.257436	−	0.257436i
$669$			3.25303e22i			0.810736i
$670$	7.19864e21	−	9.39792e20i	0.177277	−	0.0231437i
$671$	2.77083e22			0.674263
$672$	3.26437e21	−	3.26437e21i	0.0784956	−	0.0784956i
$673$	−2.13793e22	−	2.13793e22i	−0.508012	−	0.508012i	0.405904	−	0.913916i	$-0.366957\pi$
$673$	−2.13793e22	−	2.13793e22i	−0.508012	−	0.508012i	−0.913916	+	0.405904i	$0.866957\pi$
$674$		−	4.93876e21i		−	0.115968i
$675$	−1.84886e22	+	3.18637e22i	−0.429016	+	0.739376i
$676$	4.66142e22			1.06892
$677$	5.39911e22	−	5.39911e22i	1.22353	−	1.22353i	0.257156	−	0.966370i	$-0.417215\pi$
$677$	5.39911e22	−	5.39911e22i	1.22353	−	1.22353i	0.966370	−	0.257156i	$-0.0827855\pi$
$678$	−4.98976e21	−	4.98976e21i	−0.111749	−	0.111749i
$679$			2.28698e22i			0.506178i
$680$	−2.78583e21	−	2.13389e22i	−0.0609373	−	0.466769i
$681$	6.51381e21			0.140818
$682$	1.81391e22	−	1.81391e22i	0.387561	−	0.387561i
$683$	3.58198e22	+	3.58198e22i	0.756411	+	0.756411i	0.975667	−	0.219256i	$-0.0703631\pi$
$683$	3.58198e22	+	3.58198e22i	0.756411	+	0.756411i	−0.219256	+	0.975667i	$0.570363\pi$
$684$			8.63219e21i			0.180166i
$685$	2.90497e22	+	2.23406e22i	0.599262	+	0.460861i
$686$	−1.42925e22			−0.291416
$687$	8.84905e21	−	8.84905e21i	0.178338	−	0.178338i
$688$	−9.15186e21	−	9.15186e21i	−0.182306	−	0.182306i
$689$		−	4.55692e21i		−	0.0897259i
$690$	−1.59495e22	+	2.07392e22i	−0.310423	+	0.403645i
$691$	−1.87588e22			−0.360894			−0.180447	−	0.983585i	$-0.557754\pi$
$691$	−1.87588e22			−0.360894			−0.180447	+	0.983585i	$0.557754\pi$
$692$	2.35766e22	−	2.35766e22i	0.448366	−	0.448366i
$693$	2.22413e22	+	2.22413e22i	0.418114	+	0.418114i
$694$			5.15091e22i			0.957212i
$695$	5.13924e22	−	6.70935e21i	0.944106	−	0.123254i
$696$	3.67994e21			0.0668294
$697$	−6.23913e21	+	6.23913e21i	−0.112011	+	0.112011i
$698$	3.89109e22	+	3.89109e22i	0.690602	+	0.690602i
$699$		−	3.82390e22i		−	0.670948i
$700$	−3.23360e22	−	1.87627e22i	−0.560921	−	0.325469i
$701$	2.40868e22			0.413081			0.206541	−	0.978438i	$-0.433779\pi$
$701$	2.40868e22			0.413081			0.206541	+	0.978438i	$0.433779\pi$
$702$	−4.46541e22	+	4.46541e22i	−0.757120	+	0.757120i
$703$	−2.50849e22	−	2.50849e22i	−0.420504	−	0.420504i
$704$			4.49118e21i			0.0744353i
$705$	−3.04292e21	−	2.33082e22i	−0.0498628	−	0.381940i
$706$	−5.28567e22			−0.856371
$707$	−7.90626e22	+	7.90626e22i	−1.26653	+	1.26653i
$708$	4.01418e21	+	4.01418e21i	0.0635816	+	0.0635816i
$709$			2.62288e22i			0.410780i	0.978680	+	0.205390i	$0.0658463\pi$
$709$			2.62288e22i			0.410780i	−0.978680	+	0.205390i	$0.934154\pi$
$710$	−1.83202e21	−	1.40891e21i	−0.0283702	−	0.0218181i
$711$	2.93368e22			0.449216
$712$	−4.25706e21	+	4.25706e21i	−0.0644570	+	0.0644570i
$713$	−9.14372e22	−	9.14372e22i	−1.36901	−	1.36901i
$714$		−	3.99321e22i		−	0.591203i
$715$	−4.39230e22	+	5.71134e22i	−0.643048	+	0.836160i
$716$	−4.03124e22			−0.583626
$717$	−7.02929e20	+	7.02929e20i	−0.0100637	+	0.0100637i
$718$	−5.35349e22	−	5.35349e22i	−0.757952	−	0.757952i
$719$		−	1.03803e23i		−	1.45338i	−0.686966	−	0.726689i	$-0.741058\pi$
$719$		−	1.03803e23i		−	1.45338i	0.686966	−	0.726689i	$-0.258942\pi$
$720$	1.37065e22	−	1.78940e21i	0.189787	−	0.0247769i
$721$	1.13866e23			1.55924
$722$	2.87418e22	−	2.87418e22i	0.389240	−	0.389240i
$723$	1.48920e22	+	1.48920e22i	0.199455	+	0.199455i
$724$			5.01466e22i			0.664252i
$725$	−7.65065e21	−	2.88019e22i	−0.100229	−	0.377326i
$726$	−1.70529e22			−0.220955
$727$	7.91985e22	−	7.91985e22i	1.01494	−	1.01494i	0.0150568	−	0.999887i	$-0.495207\pi$
$727$	7.91985e22	−	7.91985e22i	1.01494	−	1.01494i	0.999887	−	0.0150568i	$-0.00479292\pi$
$728$	−4.53160e22	−	4.53160e22i	−0.574382	−	0.574382i
$729$		−	1.15348e22i		−	0.144607i
$730$	1.04615e22	+	8.01329e22i	0.129721	+	0.993637i
$731$	−1.11952e23			−1.37307
$732$	1.59770e22	−	1.59770e22i	0.193823	−	0.193823i
$733$	−2.14418e22	−	2.14418e22i	−0.257294	−	0.257294i	0.566659	−	0.823953i	$-0.308236\pi$
$733$	−2.14418e22	−	2.14418e22i	−0.257294	−	0.257294i	−0.823953	+	0.566659i	$0.808236\pi$
$734$		−	3.50390e22i		−	0.415894i
$735$	−2.23017e22	−	1.71511e22i	−0.261842	−	0.201369i
$736$	2.26395e22			0.262933
$737$	−9.26682e21	+	9.26682e21i	−0.106461	+	0.106461i
$738$	−4.00753e21	−	4.00753e21i	−0.0455434	−	0.0455434i
$739$			4.09339e21i			0.0460180i	0.999735	+	0.0230090i	$0.00732463\pi$
$739$			4.09339e21i			0.0460180i	−0.999735	+	0.0230090i	$0.992675\pi$
$740$	−3.46307e22	+	4.50306e22i	−0.385130	+	0.500788i
$741$	−3.66909e22			−0.403657
$742$	−3.01821e21	+	3.01821e21i	−0.0328487	+	0.0328487i
$743$	1.22033e23	+	1.22033e23i	1.31391	+	1.31391i	0.918509	+	0.395399i	$0.129394\pi$
$743$	1.22033e23	+	1.22033e23i	1.31391	+	1.31391i	0.395399	+	0.918509i	$0.370606\pi$
$744$		−	2.09185e22i		−	0.222816i
$745$	−1.15104e23	+	1.50270e22i	−1.21294	+	0.158351i
$746$	6.71998e22			0.700580
$747$	−8.33822e22	+	8.33822e22i	−0.860020	+	0.860020i
$748$	2.74696e22	+	2.74696e22i	0.280311	+	0.280311i
$749$		−	1.30552e23i		−	1.31804i
$750$	1.30132e22	+	3.17075e22i	0.129985	+	0.316717i
$751$	1.05158e23			1.03926			0.519631	−	0.854391i	$-0.326070\pi$
$751$	1.05158e23			1.03926			0.519631	+	0.854391i	$0.326070\pi$
$752$	−1.43828e22	+	1.43828e22i	−0.140637	+	0.140637i
$753$	2.30114e22	+	2.30114e22i	0.222630	+	0.222630i
$754$		−	5.10850e22i		−	0.489016i
$755$	1.69643e22	+	1.29944e23i	0.160679	+	1.23078i
$756$	5.91519e22			0.554364
$757$	−1.28238e23	+	1.28238e23i	−1.18918	+	1.18918i	−0.211888	+	0.977294i	$0.567961\pi$
$757$	−1.28238e23	+	1.28238e23i	−1.18918	+	1.18918i	−0.977294	+	0.211888i	$0.932039\pi$
$758$	−1.67926e22	−	1.67926e22i	−0.154087	−	0.154087i
$759$		−	4.72294e22i		−	0.428823i
$760$	1.46817e22	+	1.12909e22i	0.131907	+	0.101443i
$761$	1.97835e23			1.75884			0.879418	−	0.476051i	$-0.157932\pi$
$761$	1.97835e23			1.75884			0.879418	+	0.476051i	$0.157932\pi$
$762$	2.48847e22	−	2.48847e22i	0.218924	−	0.218924i
$763$	1.15756e23	+	1.15756e23i	1.00773	+	1.00773i
$764$			8.12887e22i			0.700299i
$765$	7.28891e22	−	9.47782e22i	0.621399	−	0.808011i
$766$	1.81965e22			0.153518
$767$	5.57249e22	−	5.57249e22i	0.465250	−	0.465250i
$768$	2.58967e21	+	2.58967e21i	0.0213971	+	0.0213971i
$769$		−	3.44250e22i		−	0.281490i	−0.990046	−	0.140745i	$-0.955050\pi$
$769$		−	3.44250e22i		−	0.281490i	0.990046	−	0.140745i	$-0.0449498\pi$
$770$	6.69199e22	−	8.73648e21i	0.541539	−	0.0706986i
$771$	−4.70137e22			−0.376521
$772$	6.05471e22	−	6.05471e22i	0.479905	−	0.479905i
$773$	−1.22391e23	−	1.22391e23i	−0.960094	−	0.960094i	0.0391398	−	0.999234i	$-0.487538\pi$
$773$	−1.22391e23	−	1.22391e23i	−0.960094	−	0.960094i	−0.999234	+	0.0391398i	$0.987538\pi$
$774$		−	7.19092e22i		−	0.558286i
$775$	−1.63723e23	+	4.34898e22i	−1.25805	+	0.334175i
$776$	−1.81429e22			−0.137979
$777$	−7.45361e22	+	7.45361e22i	−0.561046	+	0.561046i
$778$	−1.14574e22	−	1.14574e22i	−0.0853592	−	0.0853592i
$779$		−	7.59394e21i		−	0.0559974i
$780$	7.60577e21	+	5.82589e22i	0.0555120	+	0.425212i
$781$	4.17205e21			0.0301398
$782$	1.38471e23	−	1.38471e23i	0.990162	−	0.990162i
$783$	3.33412e22	+	3.33412e22i	0.235986	+	0.235986i
$784$			2.43452e22i			0.170563i
$785$	1.07278e23	+	8.25017e22i	0.743964	+	0.572144i
$786$	4.95944e22			0.340449
$787$	−2.59647e22	+	2.59647e22i	−0.176435	+	0.176435i	−0.789800	−	0.613365i	$-0.789816\pi$
$787$	−2.59647e22	+	2.59647e22i	−0.176435	+	0.176435i	0.613365	+	0.789800i	$0.289816\pi$
$788$	−5.38418e22	−	5.38418e22i	−0.362168	−	0.362168i
$789$			5.87841e22i			0.391421i
$790$	3.83726e22	−	4.98962e22i	0.252932	−	0.328890i
$791$	9.17571e22			0.598726
$792$	−1.76443e22	+	1.76443e22i	−0.113974	+	0.113974i
$793$	−2.21792e23	−	2.21792e23i	−1.41828	−	1.41828i
$794$			1.11984e23i			0.708913i
$795$	3.88025e21	−	5.06571e20i	0.0243177	−	0.00317471i
$796$	−8.99401e22			−0.558019
$797$	−8.29676e22	+	8.29676e22i	−0.509615	+	0.509615i	−0.914408	−	0.404793i	$-0.867343\pi$
$797$	−8.29676e22	+	8.29676e22i	−0.509615	+	0.509615i	0.404793	+	0.914408i	$0.367343\pi$
$798$	2.43016e22	+	2.43016e22i	0.147779	+	0.147779i
$799$			1.75941e23i			1.05923i
$800$	1.48847e22	−	2.56526e22i	0.0887196	−	0.152901i
$801$	−3.34492e22			−0.197390
$802$	−4.33807e22	+	4.33807e22i	−0.253455	+	0.253455i
$803$	−1.03155e23	−	1.03155e23i	−0.596714	−	0.596714i
$804$			1.06867e22i			0.0612064i
$805$	−4.40396e22	−	3.37336e23i	−0.249733	−	1.91291i
$806$	−2.90390e23			−1.63043
$807$	6.53348e22	−	6.53348e22i	0.363209	−	0.363209i
$808$	−6.27215e22	−	6.27215e22i	−0.345243	−	0.345243i
$809$			1.84193e23i			1.00389i	0.864901	+	0.501943i	$0.167381\pi$
$809$			1.84193e23i			1.00389i	−0.864901	+	0.501943i	$0.832619\pi$
$810$	3.65308e22	+	2.80940e22i	0.197142	+	0.151612i
$811$	1.70390e23			0.910495			0.455248	−	0.890365i	$-0.349551\pi$
$811$	1.70390e23			0.910495			0.455248	+	0.890365i	$0.349551\pi$
$812$	−3.38354e22	+	3.38354e22i	−0.179029	+	0.179029i
$813$	1.24571e22	+	1.24571e22i	0.0652668	+	0.0652668i
$814$		−	1.02548e23i		−	0.532025i
$815$	−4.23280e22	+	5.50394e22i	−0.217454	+	0.282757i
$816$	3.16787e22			0.161156
$817$	6.81311e22	−	6.81311e22i	0.343217	−	0.343217i
$818$	6.64507e22	+	6.64507e22i	0.331492	+	0.331492i
$819$		−	3.56063e23i		−	1.75896i
$820$	−1.20579e22	+	1.57417e21i	−0.0589876	+	0.00770091i
$821$	−2.31857e23			−1.12325			−0.561623	−	0.827393i	$-0.689823\pi$
$821$	−2.31857e23			−1.12325			−0.561623	+	0.827393i	$0.689823\pi$
$822$	−3.81457e22	+	3.81457e22i	−0.183008	+	0.183008i
$823$	1.29990e23	+	1.29990e23i	0.617607	+	0.617607i	0.944917	−	0.327310i	$-0.106142\pi$
$823$	1.29990e23	+	1.29990e23i	0.617607	+	0.617607i	−0.327310	+	0.944917i	$0.606142\pi$
$824$			9.03315e22i			0.425032i
$825$	−5.35151e22	−	3.10516e22i	−0.249370	−	0.144695i
$826$	−7.38171e22			−0.340657
$827$	−1.17991e23	+	1.17991e23i	−0.539267	+	0.539267i	−0.923314	−	0.384047i	$-0.874530\pi$
$827$	−1.17991e23	+	1.17991e23i	−0.539267	+	0.539267i	0.384047	+	0.923314i	$0.374530\pi$
$828$	8.89432e22	+	8.89432e22i	0.402596	+	0.402596i
$829$			3.28704e23i			1.47356i	0.676131	+	0.736781i	$0.263655\pi$
$829$			3.28704e23i			1.47356i	−0.676131	+	0.736781i	$0.736345\pi$
$830$	3.27529e22	+	2.50881e23i	0.145420	+	1.11389i
$831$	1.84789e22			0.0812584
$832$	3.59498e22	−	3.59498e22i	0.156571	−	0.156571i
$833$	1.48904e23	+	1.48904e23i	0.642312	+	0.642312i
$834$			7.62945e22i			0.325961i
$835$	−1.36399e23	−	1.04897e23i	−0.577190	−	0.443887i
$836$	−3.34346e22			−0.140135
$837$	1.89526e23	−	1.89526e23i	0.786803	−	0.786803i
$838$	−2.13845e23	−	2.13845e23i	−0.879320	−	0.879320i
$839$		−	2.77637e23i		−	1.13079i	−0.824820	−	0.565395i	$-0.808724\pi$
$839$		−	2.77637e23i		−	1.13079i	0.824820	−	0.565395i	$-0.191276\pi$
$840$	3.35493e22	−	4.36245e22i	0.135347	−	0.175993i
$841$	2.12104e23			0.847579
$842$	1.04555e22	−	1.04555e22i	0.0413854	−	0.0413854i
$843$	−2.85268e22	−	2.85268e22i	−0.111849	−	0.111849i
$844$		−	2.06116e23i		−	0.800519i
$845$	5.51009e23	−	7.19350e22i	2.11985	−	0.276749i
$846$	−1.13011e23			−0.430681
$847$	1.56793e23	−	1.56793e23i	0.591916	−	0.591916i
$848$	−2.39439e21	−	2.39439e21i	−0.00895421	−	0.00895421i
$849$			4.49014e22i			0.166340i
$850$	−6.58604e22	−	2.47941e23i	−0.241698	−	0.909905i
$851$	−5.16933e23			−1.87931
$852$	2.40566e21	−	2.40566e21i	0.00866397	−	0.00866397i
$853$	2.89145e23	+	2.89145e23i	1.03163	+	1.03163i	0.999483	+	0.0321463i	$0.0102343\pi$
$853$	2.89145e23	+	2.89145e23i	1.03163	+	1.03163i	0.0321463	+	0.999483i	$0.489766\pi$
$854$			2.93802e23i			1.03846i
$855$	1.33212e22	+	1.02038e23i	0.0466459	+	0.357300i
$856$	1.03568e23			0.359283
$857$	−1.85309e23	+	1.85309e23i	−0.636870	+	0.636870i	−0.949782	−	0.312912i	$-0.898695\pi$
$857$	−1.85309e23	+	1.85309e23i	−0.636870	+	0.636870i	0.312912	+	0.949782i	$0.398695\pi$
$858$	−7.49967e22	−	7.49967e22i	−0.255355	−	0.255355i
$859$			1.57630e23i			0.531732i	0.964010	+	0.265866i	$0.0856578\pi$
$859$			1.57630e23i			0.531732i	−0.964010	+	0.265866i	$0.914342\pi$
$860$	−1.22304e23	−	9.40575e22i	−0.408745	−	0.314345i
$861$	−2.25643e22			−0.0747129
$862$	−2.73909e22	+	2.73909e22i	−0.0898563	+	0.0898563i
$863$	2.33656e23	+	2.33656e23i	0.759434	+	0.759434i	0.976219	−	0.216785i	$-0.0695571\pi$
$863$	2.33656e23	+	2.33656e23i	0.759434	+	0.759434i	−0.216785	+	0.976219i	$0.569557\pi$
$864$			4.69261e22i			0.151114i
$865$	2.42307e23	−	3.15074e23i	0.773102	−	1.00527i
$866$	2.93546e23			0.927967
$867$	8.44565e22	−	8.44565e22i	0.264533	−	0.264533i
$868$	1.92336e23	+	1.92336e23i	0.596901	+	0.596901i
$869$			1.13628e23i			0.349405i
$870$	4.34992e22	−	5.67888e21i	0.132534	−	0.0173025i
$871$	1.48353e23			0.447870
$872$	−9.18306e22	+	9.18306e22i	−0.274698	+	0.274698i
$873$	−7.12775e22	−	7.12775e22i	−0.211270	−	0.211270i
$874$			1.68540e23i			0.495008i
$875$	−4.11186e23	−	1.71885e23i	−1.19667	−	0.500236i
$876$	−1.18961e23			−0.343062
$877$	7.23086e22	−	7.23086e22i	0.206630	−	0.206630i	−0.596203	−	0.802833i	$-0.703325\pi$
$877$	7.23086e22	−	7.23086e22i	0.206630	−	0.206630i	0.802833	+	0.596203i	$0.203325\pi$
$878$	2.64430e23	+	2.64430e23i	0.748780	+	0.748780i
$879$		−	1.53550e23i		−	0.430862i
$880$	6.93077e21	+	5.30885e22i	0.0192717	+	0.147618i
$881$	−5.10465e23			−1.40656			−0.703281	−	0.710912i	$-0.748283\pi$
$881$	−5.10465e23			−1.40656			−0.703281	+	0.710912i	$0.748283\pi$
$882$	−9.56442e22	+	9.56442e22i	−0.261162	+	0.261162i
$883$	1.14048e23	+	1.14048e23i	0.308604	+	0.308604i	0.844368	−	0.535764i	$-0.179976\pi$
$883$	1.14048e23	+	1.14048e23i	0.308604	+	0.308604i	−0.535764	+	0.844368i	$0.679976\pi$
$884$		−	4.39764e23i		−	1.17924i
$885$	5.36448e22	+	4.12555e22i	0.142555	+	0.109631i
$886$	1.74845e23			0.460450
$887$	3.70255e23	−	3.70255e23i	0.966300	−	0.966300i	−0.0331502	−	0.999450i	$-0.510554\pi$
$887$	3.70255e23	−	3.70255e23i	0.966300	−	0.966300i	0.999450	+	0.0331502i	$0.0105540\pi$
$888$	−5.91305e22	−	5.91305e22i	−0.152935	−	0.152935i
$889$			4.57607e23i			1.17295i
$890$	−4.37516e22	+	5.68906e22i	−0.111141	+	0.144518i
$891$	−8.31916e22			−0.209439
$892$	2.37281e23	−	2.37281e23i	0.592031	−	0.592031i
$893$	−1.07073e23	−	1.07073e23i	−0.264769	−	0.264769i
$894$		−	1.70877e23i		−	0.418778i
$895$	−4.76518e23	+	6.22101e22i	−1.15743	+	0.151104i
$896$	−4.76217e22			−0.114641
$897$	−3.78050e23	+	3.78050e23i	−0.902007	+	0.902007i
$898$	4.45248e22	+	4.45248e22i	0.105291	+	0.105291i
$899$			2.16821e23i			0.508188i
$900$	1.59258e23	−	4.23036e22i	0.369964	−	0.0982736i
$901$	−2.92899e22			−0.0674402
$902$	1.55221e22	−	1.55221e22i	0.0354241	−	0.0354241i
$903$	−2.02441e23	−	2.02441e23i	−0.457928	−	0.457928i
$904$			7.27922e22i			0.163207i
$905$	7.73861e22	+	5.92764e23i	0.171979	+	1.31733i
$906$	−1.92908e23			−0.424936
$907$	3.49436e23	−	3.49436e23i	0.762972	−	0.762972i	−0.213886	−	0.976859i	$-0.568612\pi$
$907$	3.49436e23	−	3.49436e23i	0.762972	−	0.762972i	0.976859	+	0.213886i	$0.0686122\pi$
$908$	−4.75127e22	−	4.75127e22i	−0.102831	−	0.102831i
$909$		−	4.92824e23i		−	1.05726i
$910$	−6.05595e23	−	4.65732e23i	−1.28781	−	0.990387i
$911$	−7.86216e23			−1.65728			−0.828638	−	0.559785i	$-0.810884\pi$
$911$	−7.86216e23			−1.65728			−0.828638	+	0.559785i	$0.810884\pi$
$912$	−1.92788e22	+	1.92788e22i	−0.0402830	+	0.0402830i
$913$	−3.22960e23	−	3.22960e23i	−0.668932	−	0.668932i
$914$		−	1.37117e23i		−	0.281527i
$915$	1.64202e23	−	2.13513e23i	0.334202	−	0.434566i
$916$	−1.29093e23			−0.260458
$917$	−4.55998e23	+	4.55998e23i	−0.912028	+	0.912028i
$918$	2.87017e23	+	2.87017e23i	0.569070	+	0.569070i
$919$		−	6.50023e23i		−	1.27763i	−0.769361	−	0.638814i	$-0.779425\pi$
$919$		−	6.50023e23i		−	1.27763i	0.769361	−	0.638814i	$-0.220575\pi$
$920$	2.67613e23	−	3.49373e22i	0.521441	−	0.0680748i
$921$	3.38233e23			0.653339
$922$	3.09312e23	−	3.09312e23i	0.592310	−	0.592310i
$923$	−3.33954e22	−	3.33954e22i	−0.0633975	−	0.0633975i
$924$			9.93458e22i			0.186971i
$925$	−3.39865e23	+	5.85732e23i	−0.634122	+	1.09286i
$926$	5.73414e23			1.06067
$927$	−3.54882e23	+	3.54882e23i	−0.650798	+	0.650798i
$928$	−2.68421e22	−	2.68421e22i	−0.0488014	−	0.0488014i
$929$		−	1.20831e23i		−	0.217798i	−0.994053	−	0.108899i	$-0.965267\pi$
$929$		−	1.20831e23i		−	0.217798i	0.994053	−	0.108899i	$-0.0347325\pi$
$930$	−3.22813e22	−	2.47269e23i	−0.0576883	−	0.441882i
$931$	−1.81238e23			−0.321108
$932$	−2.78921e23	+	2.78921e23i	−0.489953	+	0.489953i
$933$	−8.77729e22	−	8.77729e22i	−0.152865	−	0.152865i
$934$			2.98597e23i			0.515597i
$935$	3.67099e23	+	2.82317e23i	0.628479	+	0.483331i
$936$	2.82470e23			0.479475
$937$	4.88406e23	−	4.88406e23i	0.821985	−	0.821985i	−0.164407	−	0.986393i	$-0.552571\pi$
$937$	4.88406e23	−	4.88406e23i	0.821985	−	0.821985i	0.986393	+	0.164407i	$0.0525712\pi$
$938$	−9.82596e22	−	9.82596e22i	−0.163965	−	0.163965i
$939$			1.48373e23i			0.245489i
$940$	−1.47818e23	+	1.92209e23i	−0.242496	+	0.315320i
$941$	1.01088e24			1.64430			0.822150	−	0.569271i	$-0.192774\pi$
$941$	1.01088e24			1.64430			0.822150	+	0.569271i	$0.192774\pi$
$942$	−1.40868e23	+	1.40868e23i	−0.227199	+	0.227199i
$943$	−7.82454e22	−	7.82454e22i	−0.125131	−	0.125131i
$944$		−	5.85602e22i		−	0.0928595i
$945$	6.99213e23	−	9.12831e22i	1.09940	−	0.143528i
$946$	2.78522e23			0.434241
$947$	6.67678e23	−	6.67678e23i	1.03221	−	1.03221i	0.0327442	−	0.999464i	$-0.489575\pi$
$947$	6.67678e23	−	6.67678e23i	1.03221	−	1.03221i	0.999464	−	0.0327442i	$-0.0104247\pi$
$948$	6.55197e22	+	6.55197e22i	0.100440	+	0.100440i
$949$			1.65142e24i			2.51031i
$950$	1.90971e23	+	1.10809e23i	0.287858	+	0.167027i
$951$	−1.73974e22			−0.0260040
$952$	−2.91271e23	+	2.91271e23i	−0.431720	+	0.431720i
$953$	−4.96209e23	−	4.96209e23i	−0.729325	−	0.729325i	0.241160	−	0.970485i	$-0.422472\pi$
$953$	−4.96209e23	−	4.96209e23i	−0.729325	−	0.729325i	−0.970485	+	0.241160i	$0.922472\pi$
$954$		−	1.88135e22i		−	0.0274210i
$955$	1.25445e23	+	9.60883e23i	0.181311	+	1.38881i
$956$	1.02546e22			0.0146978
$957$	−5.59966e22	+	5.59966e22i	−0.0795914	+	0.0795914i
$958$	−4.59527e23	−	4.59527e23i	−0.647720	−	0.647720i
$959$		−	7.01464e23i		−	0.980521i
$960$	3.46079e22	+	2.66151e22i	0.0479739	+	0.0368943i
$961$	5.05087e23			0.694351
$962$	−8.20851e23	+	8.20851e23i	−1.11909	+	1.11909i
$963$	4.06886e23	+	4.06886e23i	0.550126	+	0.550126i
$964$		−	2.17249e23i		−	0.291300i
$965$	6.22269e23	−	8.09141e23i	0.827484	−	1.07598i
$966$	5.00792e23			0.660450
$967$	−1.88455e23	+	1.88455e23i	−0.246488	+	0.246488i	−0.819528	−	0.573040i	$-0.805764\pi$
$967$	−1.88455e23	+	1.88455e23i	−0.246488	+	0.246488i	0.573040	+	0.819528i	$0.305764\pi$
$968$	1.24386e23	+	1.24386e23i	0.161350	+	0.161350i
$969$			2.35832e23i			0.303398i
$970$	−2.14460e23	+	2.79981e22i	−0.273636	+	0.0357236i
$971$	8.51556e23			1.07760			0.538802	−	0.842432i	$-0.318877\pi$
$971$	8.51556e23			1.07760			0.538802	+	0.842432i	$0.318877\pi$
$972$	−2.88774e23	+	2.88774e23i	−0.362433	+	0.362433i
$973$	−7.01493e23	−	7.01493e23i	−0.873214	−	0.873214i
$974$		−	9.08393e23i		−	1.12151i
$975$	1.79810e23	+	6.76919e23i	0.220179	+	0.828895i
$976$	−2.33077e23			−0.283074
$977$	3.68077e23	−	3.68077e23i	0.443386	−	0.443386i	−0.449762	−	0.893148i	$-0.648491\pi$
$977$	3.68077e23	−	3.68077e23i	0.443386	−	0.443386i	0.893148	+	0.449762i	$0.148491\pi$
$978$	−7.22733e22	−	7.22733e22i	−0.0863509	−	0.0863509i
$979$		−	1.29557e23i		−	0.153532i
$980$	3.75694e22	+	2.87775e23i	0.0441597	+	0.338255i
$981$	−7.21544e23			−0.841222
$982$	−4.24952e22	+	4.24952e22i	−0.0491415	+	0.0491415i
$983$	3.49192e23	+	3.49192e23i	0.400530	+	0.400530i	0.878420	−	0.477889i	$-0.158598\pi$
$983$	3.49192e23	+	3.49192e23i	0.400530	+	0.400530i	−0.477889	+	0.878420i	$0.658598\pi$
$984$		−	1.79005e22i		−	0.0203660i
$985$	−7.19532e23	−	5.53355e23i	−0.812008	−	0.624474i
$986$	−3.28352e23			−0.367557
$987$	−3.18151e23	+	3.18151e23i	−0.353261	+	0.353261i
$988$	2.67629e23	+	2.67629e23i	0.294766	+	0.294766i
$989$		−	1.40400e24i		−	1.53390i
$990$	−1.81338e23	+	2.35796e23i	−0.196521	+	0.255537i
$991$	−2.73321e23			−0.293822			−0.146911	−	0.989150i	$-0.546933\pi$
$991$	−2.73321e23			−0.293822			−0.146911	+	0.989150i	$0.546933\pi$
$992$	−1.52583e23	+	1.52583e23i	−0.162709	+	0.162709i
$993$	−3.38697e23	−	3.38697e23i	−0.358276	−	0.358276i
$994$			4.42378e22i			0.0464197i
$995$	−1.06315e24	+	1.38795e23i	−1.10665	+	0.144474i
$996$	−3.72446e23			−0.384581
$997$	−2.63191e23	+	2.63191e23i	−0.269593	+	0.269593i	−0.828936	−	0.559343i	$-0.811053\pi$
$997$	−2.63191e23	+	2.63191e23i	−0.269593	+	0.269593i	0.559343	+	0.828936i	$0.311053\pi$
$998$	1.01783e23	+	1.01783e23i	0.103426	+	0.103426i
$999$		−	1.07147e24i		−	1.08008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.17.c.b.3.3	✓	8
3.2	odd	2		90.17.g.a.73.3		8
4.3	odd	2		80.17.p.b.33.2		8
5.2	odd	4	inner	10.17.c.b.7.3	yes	8
5.3	odd	4		50.17.c.c.7.2		8
5.4	even	2		50.17.c.c.43.2		8
15.2	even	4		90.17.g.a.37.3		8
20.7	even	4		80.17.p.b.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.17.c.b.3.3	✓	8	1.1	even	1	trivial
10.17.c.b.7.3	yes	8	5.2	odd	4	inner
50.17.c.c.7.2		8	5.3	odd	4
50.17.c.c.43.2		8	5.4	even	2
80.17.p.b.17.2		8	20.7	even	4
80.17.p.b.33.2		8	4.3	odd	2
90.17.g.a.37.3		8	15.2	even	4
90.17.g.a.73.3		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(128.000 - 128.000i) q^{2} +(2246.18 + 2246.18i) q^{3} -32768.0i q^{4} +(-50567.5 - 387338. i) q^{5} +575022. q^{6} +(-5.28707e6 + 5.28707e6i) q^{7} +(-4.19430e6 - 4.19430e6i) q^{8} -3.29561e7i q^{9} +O(q^{10})\)	\(q+(128.000 - 128.000i) q^{2} +(2246.18 + 2246.18i) q^{3} -32768.0i q^{4} +(-50567.5 - 387338. i) q^{5} +575022. q^{6} +(-5.28707e6 + 5.28707e6i) q^{7} +(-4.19430e6 - 4.19430e6i) q^{8} -3.29561e7i q^{9} +(-5.60519e7 - 4.31066e7i) q^{10} +1.27647e8 q^{11} +(7.36029e7 - 7.36029e7i) q^{12} +(-1.02176e9 - 1.02176e9i) q^{13} +1.35349e9i q^{14} +(7.56448e8 - 9.83615e8i) q^{15} -1.07374e9 q^{16} +(-6.56739e9 + 6.56739e9i) q^{17} +(-4.21838e9 - 4.21838e9i) q^{18} -7.99348e9i q^{19} +(-1.26923e10 + 1.65700e9i) q^{20} -2.37514e10 q^{21} +(1.63388e10 - 1.63388e10i) q^{22} +(-8.23621e10 - 8.23621e10i) q^{23} -1.88423e10i q^{24} +(-1.47474e11 + 3.91734e10i) q^{25} -2.61570e11 q^{26} +(1.70716e11 - 1.70716e11i) q^{27} +(1.73247e11 + 1.73247e11i) q^{28} +1.95302e11i q^{29} +(-2.90774e10 - 2.22728e11i) q^{30} +1.11018e12 q^{31} +(-1.37439e11 + 1.37439e11i) q^{32} +(2.86718e11 + 2.86718e11i) q^{33} +1.68125e12i q^{34} +(2.31524e12 + 1.78053e12i) q^{35} -1.07990e12 q^{36} +(3.13818e12 - 3.13818e12i) q^{37} +(-1.02317e12 - 1.02317e12i) q^{38} -4.59010e12i q^{39} +(-1.41252e12 + 1.83671e12i) q^{40} +9.50017e11 q^{41} +(-3.04018e12 + 3.04018e12i) q^{42} +(8.52333e12 + 8.52333e12i) q^{43} -4.18273e12i q^{44} +(-1.27651e13 + 1.66651e12i) q^{45} -2.10847e13 q^{46} +(1.33950e13 - 1.33950e13i) q^{47} +(-2.41182e12 - 2.41182e12i) q^{48} -2.26732e13i q^{49} +(-1.38624e13 + 2.38908e13i) q^{50} -2.95031e13 q^{51} +(-3.34809e13 + 3.34809e13i) q^{52} +(2.22995e12 + 2.22995e12i) q^{53} -4.37033e13i q^{54} +(-6.45478e12 - 4.94425e13i) q^{55} +4.43511e13 q^{56} +(1.79548e13 - 1.79548e13i) q^{57} +(2.49987e13 + 2.49987e13i) q^{58} +5.45384e13i q^{59} +(-3.22311e13 - 2.47873e13i) q^{60} +2.17070e14 q^{61} +(1.42104e14 - 1.42104e14i) q^{62} +(1.74241e14 + 1.74241e14i) q^{63} +3.51844e13i q^{64} +(-3.44097e14 + 4.47433e14i) q^{65} +7.33998e13 q^{66} +(-7.25973e13 + 7.25973e13i) q^{67} +(2.15200e14 + 2.15200e14i) q^{68} -3.70000e14i q^{69} +(5.24258e14 - 6.84426e13i) q^{70} +3.26843e13 q^{71} +(-1.38228e14 + 1.38228e14i) q^{72} +(-8.08129e14 - 8.08129e14i) q^{73} -8.03373e14i q^{74} +(-4.19243e14 - 2.43262e14i) q^{75} -2.61930e14 q^{76} +(-6.74878e14 + 6.74878e14i) q^{77} +(-5.87533e14 - 5.87533e14i) q^{78} +8.90178e14i q^{79} +(5.42964e13 + 4.15901e14i) q^{80} -6.51732e14 q^{81} +(1.21602e14 - 1.21602e14i) q^{82} +(-2.53010e15 - 2.53010e15i) q^{83} +7.78287e14i q^{84} +(2.87590e15 + 2.21170e15i) q^{85} +2.18197e15 q^{86} +(-4.38684e14 + 4.38684e14i) q^{87} +(-5.35390e14 - 5.35390e14i) q^{88} -1.01496e15i q^{89} +(-1.42063e15 + 1.84725e15i) q^{90} +1.08042e16 q^{91} +(-2.69884e15 + 2.69884e15i) q^{92} +(2.49368e15 + 2.49368e15i) q^{93} -3.42913e15i q^{94} +(-3.09618e15 + 4.04210e14i) q^{95} -6.17426e14 q^{96} +(2.16280e15 - 2.16280e15i) q^{97} +(-2.90217e15 - 2.90217e15i) q^{98} -4.20674e15i 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

Introduction

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