LMFDB - Embedded newform 22.15.b.a.21.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,15,Mod(21,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	22.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$27.3523729934$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 38299509 x^{12} + 1255603312 x^{11} + 548839279225666 x^{10} + \cdots + 61\!\cdots\!00 $ x^14 - 2x^13 - 38299509x^12 + 1255603312x^11 + 548839279225666x^10 - 62614853719962708x^9 - 3647746096331338780406x^8 + 909709401522475794317032x^7 + 11341528896592004854718535645x^6 - 4608641836922062401823748151666x^5 - 14199433672677462467950659880576257x^4 + 7648786246750765008517429480227297240x^3 + 5468207905418692926727112276614665574080x^2 - 3973529610997293170696151713639263984312200*x + 613220922939245616829253347741252697812260300
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{56}\cdot 3^{6}\cdot 11^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.11
Root			$320.191 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.15.b.a.21.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+90.5097i q^{2} -6.19137 q^{3} -8192.00 q^{4} -140247. q^{5} -560.379i q^{6} -1.02360e6i q^{7} -741455. i q^{8} -4.78293e6 q^{9} +O(q^{10})$	\(q+90.5097i q^{2} -6.19137 q^{3} -8192.00 q^{4} -140247. q^{5} -560.379i q^{6} -1.02360e6i q^{7} -741455. i q^{8} -4.78293e6 q^{9} -1.26937e7i q^{10} +(1.50426e7 + 1.23882e7i) q^{11} +50719.7 q^{12} +6.57004e7i q^{13} +9.26454e7 q^{14} +868318. q^{15} +6.71089e7 q^{16} -6.20507e8i q^{17} -4.32901e8i q^{18} +5.75368e8i q^{19} +1.14890e9 q^{20} +6.33747e6i q^{21} +(-1.12126e9 + 1.36150e9i) q^{22} +1.11162e8 q^{23} +4.59062e6i q^{24} +1.35656e10 q^{25} -5.94652e9 q^{26} +5.92260e7 q^{27} +8.38531e9i q^{28} +1.74829e10i q^{29} +7.85912e7i q^{30} -2.49786e10 q^{31} +6.07400e9i q^{32} +(-9.31345e7 - 7.67002e7i) q^{33} +5.61619e10 q^{34} +1.43556e11i q^{35} +3.91818e10 q^{36} +1.40576e11 q^{37} -5.20763e10 q^{38} -4.06775e8i q^{39} +1.03987e11i q^{40} +8.64115e10i q^{41} -5.73602e8 q^{42} -1.26825e11i q^{43} +(-1.23229e11 - 1.01485e11i) q^{44} +6.70790e11 q^{45} +1.00613e10i q^{46} +3.18992e11 q^{47} -4.15496e8 q^{48} -3.69528e11 q^{49} +1.22782e12i q^{50} +3.84179e9i q^{51} -5.38218e11i q^{52} +1.37130e12 q^{53} +5.36053e9i q^{54} +(-2.10968e12 - 1.73741e12i) q^{55} -7.58951e11 q^{56} -3.56231e9i q^{57} -1.58237e12 q^{58} -3.22811e12 q^{59} -7.11326e9 q^{60} -1.96411e12i q^{61} -2.26081e12i q^{62} +4.89579e12i q^{63} -5.49756e11 q^{64} -9.21426e12i q^{65} +(6.94211e9 - 8.42958e9i) q^{66} +6.50801e12 q^{67} +5.08320e12i q^{68} -6.88247e8 q^{69} -1.29932e13 q^{70} +2.49479e12 q^{71} +3.54633e12i q^{72} -1.88866e13i q^{73} +1.27235e13i q^{74} -8.39895e10 q^{75} -4.71341e12i q^{76} +(1.26806e13 - 1.53976e13i) q^{77} +3.68171e10 q^{78} -2.28648e13i q^{79} -9.41179e12 q^{80} +2.28762e13 q^{81} -7.82107e12 q^{82} +4.23928e13i q^{83} -5.19165e10i q^{84} +8.70240e13i q^{85} +1.14788e13 q^{86} -1.08243e11i q^{87} +(9.18533e12 - 1.11534e13i) q^{88} -1.04167e13 q^{89} +6.07129e13i q^{90} +6.72507e13 q^{91} -9.10642e11 q^{92} +1.54652e11 q^{93} +2.88718e13i q^{94} -8.06933e13i q^{95} -3.76064e10i q^{96} -3.99411e13 q^{97} -3.34459e13i q^{98} +(-7.19479e13 - 5.92521e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9}+O(q^{10}) $ 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9} + 20143042 q^{11} - 35995648 q^{12} + 62814720 q^{14} - 1359602 q^{15} + 939524096 q^{16} - 571457536 q^{20} - 2107666944 q^{22} - 7305755542 q^{23} + 19291879452 q^{25} - 6388480512 q^{26} + 34093422830 q^{27} - 33569873942 q^{31} + 2885838062 q^{33} + 167764701696 q^{34} - 90247757824 q^{36} + 73167823966 q^{37} + 71236111872 q^{38} - 222695314944 q^{42} - 165011800064 q^{44} + 2000205168616 q^{45} - 1612717386124 q^{47} + 294876348416 q^{48} + 3424602524990 q^{49} - 3530064068164 q^{53} - 3715439610854 q^{55} - 514578186240 q^{56} - 1374208002048 q^{58} - 818496564070 q^{59} + 11137859584 q^{60} - 7696581394432 q^{64} - 5938395621888 q^{66} + 16485465276922 q^{67} - 11394452631206 q^{69} - 392146020864 q^{70} - 19380879179878 q^{71} + 23016770893992 q^{75} + 60534793808304 q^{77} + 17335823992320 q^{78} + 4681380134912 q^{80} - 10394309810662 q^{81} - 79417078012416 q^{82} + 6375532305408 q^{86} + 17266007605248 q^{88} - 117770741987650 q^{89} + 150621364097712 q^{91} + 59848749400064 q^{92} + 27345122803162 q^{93} + 123398138843566 q^{97} + 118861332531788 q^{99}+O(q^{100}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9 + 20143042 * q^11 - 35995648 * q^12 + 62814720 * q^14 - 1359602 * q^15 + 939524096 * q^16 - 571457536 * q^20 - 2107666944 * q^22 - 7305755542 * q^23 + 19291879452 * q^25 - 6388480512 * q^26 + 34093422830 * q^27 - 33569873942 * q^31 + 2885838062 * q^33 + 167764701696 * q^34 - 90247757824 * q^36 + 73167823966 * q^37 + 71236111872 * q^38 - 222695314944 * q^42 - 165011800064 * q^44 + 2000205168616 * q^45 - 1612717386124 * q^47 + 294876348416 * q^48 + 3424602524990 * q^49 - 3530064068164 * q^53 - 3715439610854 * q^55 - 514578186240 * q^56 - 1374208002048 * q^58 - 818496564070 * q^59 + 11137859584 * q^60 - 7696581394432 * q^64 - 5938395621888 * q^66 + 16485465276922 * q^67 - 11394452631206 * q^69 - 392146020864 * q^70 - 19380879179878 * q^71 + 23016770893992 * q^75 + 60534793808304 * q^77 + 17335823992320 * q^78 + 4681380134912 * q^80 - 10394309810662 * q^81 - 79417078012416 * q^82 + 6375532305408 * q^86 + 17266007605248 * q^88 - 117770741987650 * q^89 + 150621364097712 * q^91 + 59848749400064 * q^92 + 27345122803162 * q^93 + 123398138843566 * q^97 + 118861332531788 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			90.5097i			0.707107i
$2$			90.5097i			0.707107i
$3$	−6.19137			−0.00283099			−0.00141549	−	0.999999i	$-0.500451\pi$
$3$	−6.19137			−0.00283099			−0.00141549	+	0.999999i	$0.500451\pi$
$4$	−8192.00			−0.500000
$5$	−140247.			−1.79516			−0.897578	−	0.440856i	$-0.854675\pi$
$5$	−140247.			−1.79516			−0.897578	+	0.440856i	$0.854675\pi$
$6$		−	560.379i		−	0.00200181i
$7$		−	1.02360e6i		−	1.24292i	−0.783446	−	0.621459i	$-0.786540\pi$
$7$		−	1.02360e6i		−	1.24292i	0.783446	−	0.621459i	$-0.213460\pi$
$8$		−	741455.i		−	0.353553i
$9$	−4.78293e6			−0.999992
$10$		−	1.26937e7i		−	1.26937i
$11$	1.50426e7	+	1.23882e7i	0.771926	+	0.635713i
$11$	1.50426e7	+	1.23882e7i	0.771926	+	0.635713i
$12$	50719.7			0.00141549
$13$			6.57004e7i			1.04704i	0.852012	+	0.523522i	$0.175382\pi$
$13$			6.57004e7i			1.04704i	−0.852012	+	0.523522i	$0.824618\pi$
$14$	9.26454e7			0.878876
$15$	868318.			0.00508206
$16$	6.71089e7			0.250000
$17$		−	6.20507e8i		−	1.51218i	−0.654466	−	0.756092i	$-0.727106\pi$
$17$		−	6.20507e8i		−	1.51218i	0.654466	−	0.756092i	$-0.272894\pi$
$18$		−	4.32901e8i		−	0.707101i
$19$			5.75368e8i			0.643680i	0.946794	+	0.321840i	$0.104301\pi$
$19$			5.75368e8i			0.643680i	−0.946794	+	0.321840i	$0.895699\pi$
$20$	1.14890e9			0.897578
$21$			6.33747e6i			0.00351869i
$22$	−1.12126e9	+	1.36150e9i	−0.449517	+	0.545834i
$23$	1.11162e8			0.0326485			0.0163242	−	0.999867i	$-0.494804\pi$
$23$	1.11162e8			0.0326485			0.0163242	+	0.999867i	$0.494804\pi$
$24$			4.59062e6i			0.00100090i
$25$	1.35656e10			2.22259
$26$	−5.94652e9			−0.740371
$27$	5.92260e7			0.00566195
$28$			8.38531e9i			0.621459i
$29$			1.74829e10i			1.01351i	0.862091	+	0.506754i	$0.169155\pi$
$29$			1.74829e10i			1.01351i	−0.862091	+	0.506754i	$0.830845\pi$
$30$			7.85912e7i			0.00359356i
$31$	−2.49786e10			−0.907897			−0.453949	−	0.891028i	$-0.649985\pi$
$31$	−2.49786e10			−0.907897			−0.453949	+	0.891028i	$0.649985\pi$
$32$			6.07400e9i			0.176777i
$33$	−9.31345e7	−	7.67002e7i	−0.00218531	−	0.00179969i
$34$	5.61619e10			1.06928
$35$			1.43556e11i			2.23123i
$36$	3.91818e10			0.499996
$37$	1.40576e11			1.48081			0.740405	−	0.672161i	$-0.234634\pi$
$37$	1.40576e11			1.48081			0.740405	+	0.672161i	$0.234634\pi$
$38$	−5.20763e10			−0.455151
$39$		−	4.06775e8i		−	0.00296416i
$40$			1.03987e11i			0.634684i
$41$			8.64115e10i			0.443695i	0.975081	+	0.221847i	$0.0712087\pi$
$41$			8.64115e10i			0.443695i	−0.975081	+	0.221847i	$0.928791\pi$
$42$	−5.73602e8			−0.00248809
$43$		−	1.26825e11i		−	0.466578i	−0.972407	−	0.233289i	$-0.925051\pi$
$43$		−	1.26825e11i		−	0.466578i	0.972407	−	0.233289i	$-0.0749488\pi$
$44$	−1.23229e11	−	1.01485e11i	−0.385963	−	0.317856i
$45$	6.70790e11			1.79514
$46$			1.00613e10i			0.0230860i
$47$	3.18992e11			0.629643			0.314821	−	0.949151i	$-0.398055\pi$
$47$	3.18992e11			0.629643			0.314821	+	0.949151i	$0.398055\pi$
$48$	−4.15496e8			−0.000707747
$49$	−3.69528e11			−0.544848
$50$			1.22782e12i			1.57161i
$51$			3.84179e9i			0.00428097i
$52$		−	5.38218e11i		−	0.523522i
$53$	1.37130e12			1.16735			0.583677	−	0.811986i	$-0.301613\pi$
$53$	1.37130e12			1.16735			0.583677	+	0.811986i	$0.301613\pi$
$54$			5.36053e9i			0.00400360i
$55$	−2.10968e12	−	1.73741e12i	−1.38573	−	1.14120i
$56$	−7.58951e11			−0.439438
$57$		−	3.56231e9i		−	0.00182225i
$58$	−1.58237e12			−0.716658
$59$	−3.22811e12			−1.29713			−0.648565	−	0.761159i	$-0.724631\pi$
$59$	−3.22811e12			−1.29713			−0.648565	+	0.761159i	$0.724631\pi$
$60$	−7.11326e9			−0.00254103
$61$		−	1.96411e12i		−	0.624967i	−0.949923	−	0.312484i	$-0.898839\pi$
$61$		−	1.96411e12i		−	0.624967i	0.949923	−	0.312484i	$-0.101161\pi$
$62$		−	2.26081e12i		−	0.641980i
$63$			4.89579e12i			1.24291i
$64$	−5.49756e11			−0.125000
$65$		−	9.21426e12i		−	1.87961i
$66$	6.94211e9	−	8.42958e9i	0.00127258	−	0.00154525i
$67$	6.50801e12			1.07380			0.536902	−	0.843645i	$-0.319595\pi$
$67$	6.50801e12			1.07380			0.536902	+	0.843645i	$0.319595\pi$
$68$			5.08320e12i			0.756092i
$69$	−6.88247e8			−9.24274e−5
$70$	−1.29932e13			−1.57772
$71$	2.49479e12			0.274300			0.137150	−	0.990550i	$-0.456206\pi$
$71$	2.49479e12			0.274300			0.137150	+	0.990550i	$0.456206\pi$
$72$			3.54633e12i			0.353551i
$73$		−	1.88866e13i		−	1.70960i	−0.518957	−	0.854800i	$-0.673680\pi$
$73$		−	1.88866e13i		−	1.70960i	0.518957	−	0.854800i	$-0.326320\pi$
$74$			1.27235e13i			1.04709i
$75$	−8.39895e10			−0.00629211
$76$		−	4.71341e12i		−	0.321840i
$77$	1.26806e13	−	1.53976e13i	0.790140	−	0.959441i
$78$	3.68171e10			0.00209598
$79$		−	2.28648e13i		−	1.19063i	−0.803491	−	0.595317i	$-0.797026\pi$
$79$		−	2.28648e13i		−	1.19063i	0.803491	−	0.595317i	$-0.202974\pi$
$80$	−9.41179e12			−0.448789
$81$	2.28762e13			0.999976
$82$	−7.82107e12			−0.313740
$83$			4.23928e13i			1.56223i	0.624387	+	0.781115i	$0.285349\pi$
$83$			4.23928e13i			1.56223i	−0.624387	+	0.781115i	$0.714651\pi$
$84$		−	5.19165e10i		−	0.00175934i
$85$			8.70240e13i			2.71461i
$86$	1.14788e13			0.329920
$87$		−	1.08243e11i		−	0.00286923i
$88$	9.18533e12	−	1.11534e13i	0.224758	−	0.272917i
$89$	−1.04167e13			−0.235504			−0.117752	−	0.993043i	$-0.537569\pi$
$89$	−1.04167e13			−0.235504			−0.117752	+	0.993043i	$0.537569\pi$
$90$			6.07129e13i			1.26936i
$91$	6.72507e13			1.30139
$92$	−9.10642e11			−0.0163242
$93$	1.54652e11			0.00257024
$94$			2.88718e13i			0.445225i
$95$		−	8.06933e13i		−	1.15551i
$96$		−	3.76064e10i		−	0.000500452i
$97$	−3.99411e13			−0.494331			−0.247165	−	0.968973i	$-0.579499\pi$
$97$	−3.99411e13			−0.494331			−0.247165	+	0.968973i	$0.579499\pi$
$98$		−	3.34459e13i		−	0.385265i
$99$	−7.19479e13	−	5.92521e13i	−0.771919	−	0.635708i
$100$	−1.11129e14			−1.11129
$101$			9.32804e13i			0.870043i	0.900420	+	0.435021i	$0.143259\pi$
$101$			9.32804e13i			0.870043i	−0.900420	+	0.435021i	$0.856741\pi$
$102$	−3.47719e11			−0.00302710
$103$	2.19326e14			1.78332			0.891662	−	0.452702i	$-0.149540\pi$
$103$	2.19326e14			1.78332			0.891662	+	0.452702i	$0.149540\pi$
$104$	4.87139e13			0.370186
$105$		−	8.88808e11i		−	0.00631659i
$106$			1.24116e14i			0.825444i
$107$		−	3.33533e13i		−	0.207708i	−0.994593	−	0.103854i	$-0.966883\pi$
$107$		−	3.33533e13i		−	0.207708i	0.994593	−	0.103854i	$-0.0331174\pi$
$108$	−4.85179e11			−0.00283097
$109$		−	1.92543e13i		−	0.105328i	−0.998612	−	0.0526639i	$-0.983229\pi$
$109$		−	1.92543e13i		−	0.105328i	0.998612	−	0.0526639i	$-0.0167712\pi$
$110$	1.57252e14	−	1.90946e14i	0.806953	−	0.979857i
$111$	−8.70358e11			−0.00419215
$112$		−	6.86924e13i		−	0.310730i
$113$	−2.25881e14			−0.960131			−0.480065	−	0.877233i	$-0.659387\pi$
$113$	−2.25881e14			−0.960131			−0.480065	+	0.877233i	$0.659387\pi$
$114$	3.22424e11			0.00128853
$115$	−1.55901e13			−0.0586091
$116$		−	1.43220e14i		−	0.506754i
$117$		−	3.14240e14i		−	1.04703i
$118$		−	2.92175e14i		−	0.917210i
$119$	−6.35150e14			−1.87952
$120$		−	6.43819e11i		−	0.00179678i
$121$	7.28125e13	+	3.72704e14i	0.191738	+	0.981446i
$122$	1.77771e14			0.441918
$123$		−	5.35005e11i		−	0.00125609i
$124$	2.04625e14			0.453949
$125$	−1.04653e15			−2.19473
$126$	−4.43117e14			−0.878869
$127$		−	6.96740e14i		−	1.30751i	−0.756707	−	0.653755i	$-0.773193\pi$
$127$		−	6.96740e14i		−	1.30751i	0.756707	−	0.653755i	$-0.226807\pi$
$128$		−	4.97582e13i		−	0.0883883i
$129$			7.85217e11i			0.00132088i
$130$	8.33979e14			1.32908
$131$			1.14010e15i			1.72205i	0.508566	+	0.861023i	$0.330176\pi$
$131$			1.14010e15i			1.72205i	−0.508566	+	0.861023i	$0.669824\pi$
$132$	7.62958e11	+	6.28328e11i	0.00109266	+	0.000899847i
$133$	5.88945e14			0.800043
$134$			5.89038e14i			0.759294i
$135$	−8.30624e12			−0.0101641
$136$	−4.60078e14			−0.534638
$137$	1.39699e15			1.54224			0.771118	−	0.636693i	$-0.219698\pi$
$137$	1.39699e15			1.54224			0.771118	+	0.636693i	$0.219698\pi$
$138$		−	6.22930e10i		−	6.53560e-5i
$139$			1.29804e15i			1.29475i	0.762173	+	0.647374i	$0.224133\pi$
$139$			1.29804e15i			1.29475i	−0.762173	+	0.647374i	$0.775867\pi$
$140$		−	1.17601e15i		−	1.11562i
$141$	−1.97499e12			−0.00178251
$142$			2.25803e14i			0.193959i
$143$	−8.13913e14	+	9.88308e14i	−0.665619	+	0.808239i
$144$	−3.20977e14			−0.249998
$145$		−	2.45191e15i		−	1.81940i
$146$	1.70942e15			1.20887
$147$	2.28788e12			0.00154246
$148$	−1.15160e15			−0.740405
$149$			6.79049e14i			0.416483i	0.978077	+	0.208241i	$0.0667740\pi$
$149$			6.79049e14i			0.416483i	−0.978077	+	0.208241i	$0.933226\pi$
$150$		−	7.60186e12i		−	0.00444919i
$151$		−	1.05477e15i		−	0.589277i	−0.955609	−	0.294639i	$-0.904801\pi$
$151$		−	1.05477e15i		−	0.589277i	0.955609	−	0.294639i	$-0.0951993\pi$
$152$	4.26609e14			0.227575
$153$			2.96784e15i			1.51217i
$154$	1.39363e15	+	1.14771e15i	0.678427	+	0.558713i
$155$	3.50317e15			1.62982
$156$			3.33230e12i			0.00148208i
$157$	9.34964e13			0.0397647			0.0198823	−	0.999802i	$-0.493671\pi$
$157$	9.34964e13			0.0397647			0.0198823	+	0.999802i	$0.493671\pi$
$158$	2.06949e15			0.841906
$159$	−8.49025e12			−0.00330476
$160$		−	8.51858e14i		−	0.317342i
$161$		−	1.13785e14i		−	0.0405794i
$162$			2.07052e15i			0.707090i
$163$	−2.94755e15			−0.964156			−0.482078	−	0.876128i	$-0.660118\pi$
$163$	−2.94755e15			−0.964156			−0.482078	+	0.876128i	$0.660118\pi$
$164$		−	7.07883e14i		−	0.221847i
$165$	1.30618e13	+	1.07569e13i	0.00392297	+	0.00323073i
$166$	−3.83695e15			−1.10466
$167$			3.56447e15i			0.983966i	0.870605	+	0.491983i	$0.163728\pi$
$167$			3.56447e15i			0.983966i	−0.870605	+	0.491983i	$0.836272\pi$
$168$	4.69895e12			0.00124404
$169$	−3.79166e14			−0.0962992
$170$	−7.87652e15			−1.91952
$171$		−	2.75194e15i		−	0.643675i
$172$			1.03895e15i			0.233289i
$173$		−	1.29150e15i		−	0.278466i	−0.990260	−	0.139233i	$-0.955536\pi$
$173$		−	1.29150e15i		−	0.278466i	0.990260	−	0.139233i	$-0.0444637\pi$
$174$	9.79703e12			0.00202885
$175$		−	1.38857e16i		−	2.76249i
$176$	1.00949e15	+	8.31361e14i	0.192981	+	0.158928i
$177$	1.99864e13			0.00367216
$178$		−	9.42809e14i		−	0.166527i
$179$	3.91080e15			0.664192			0.332096	−	0.943246i	$-0.392244\pi$
$179$	3.91080e15			0.664192			0.332096	+	0.943246i	$0.392244\pi$
$180$	−5.49511e15			−0.897571
$181$	8.28150e15			1.30125			0.650623	−	0.759401i	$-0.274508\pi$
$181$	8.28150e15			1.30125			0.650623	+	0.759401i	$0.274508\pi$
$182$			6.08684e15i			0.920221i
$183$			1.21605e13i			0.00176927i
$184$		−	8.24219e13i		−	0.0115430i
$185$	−1.97153e16			−2.65829
$186$			1.39975e13i			0.00181744i
$187$	7.68700e15	−	9.33407e15i	0.961315	−	1.16729i
$188$	−2.61318e15			−0.314821
$189$		−	6.06236e13i		−	0.00703735i
$190$	7.30353e15			0.817067
$191$	−1.89679e15			−0.204544			−0.102272	−	0.994756i	$-0.532611\pi$
$191$	−1.89679e15			−0.204544			−0.102272	+	0.994756i	$0.532611\pi$
$192$	3.40374e12			0.000353873
$193$			1.43375e16i			1.43738i	0.695330	+	0.718690i	$0.255258\pi$
$193$			1.43375e16i			1.43738i	−0.695330	+	0.718690i	$0.744742\pi$
$194$		−	3.61505e15i		−	0.349545i
$195$			5.70488e13i			0.00532114i
$196$	3.02718e15			0.272424
$197$		−	9.49470e15i		−	0.824551i	−0.911059	−	0.412276i	$-0.864734\pi$
$197$		−	9.49470e15i		−	0.824551i	0.911059	−	0.412276i	$-0.135266\pi$
$198$	5.36289e15	−	6.51198e15i	0.449513	−	0.545829i
$199$	1.18215e15			0.0956535			0.0478267	−	0.998856i	$-0.484770\pi$
$199$	1.18215e15			0.0956535			0.0478267	+	0.998856i	$0.484770\pi$
$200$		−	1.00583e16i		−	0.785803i
$201$	−4.02935e13			−0.00303992
$202$	−8.44278e15			−0.615213
$203$	1.78954e16			1.25971
$204$		−	3.14719e13i		−	0.00214049i
$205$		−	1.21189e16i		−	0.796501i
$206$			1.98512e16i			1.26100i
$207$	−5.31682e14			−0.0326482
$208$			4.40908e15i			0.261761i
$209$	−7.12780e15	+	8.65505e15i	−0.409196	+	0.496873i
$210$	8.04457e13			0.00446650
$211$			2.01589e16i			1.08265i	0.840813	+	0.541326i	$0.182077\pi$
$211$			2.01589e16i			1.08265i	−0.840813	+	0.541326i	$0.817923\pi$
$212$	−1.12337e16			−0.583677
$213$	−1.54462e13			−0.000776539
$214$	3.01880e15			0.146872
$215$			1.77867e16i			0.837580i
$216$		−	4.39134e13i		−	0.00200180i
$217$			2.55680e16i			1.12844i
$218$	1.74270e15			0.0744779
$219$			1.16934e14i			0.00483986i
$220$	1.72825e16	+	1.42329e16i	0.692863	+	0.570602i
$221$	4.07676e16			1.58332
$222$		−	7.87759e13i		−	0.00296430i
$223$	2.53275e16			0.923545			0.461772	−	0.886999i	$-0.347214\pi$
$223$	2.53275e16			0.923545			0.461772	+	0.886999i	$0.347214\pi$
$224$	6.21733e15			0.219719
$225$	−6.48832e16			−2.22257
$226$		−	2.04444e16i		−	0.678915i
$227$			5.22912e15i			0.168363i	0.996450	+	0.0841817i	$0.0268276\pi$
$227$			5.22912e15i			0.168363i	−0.996450	+	0.0841817i	$0.973172\pi$
$228$			2.91825e13i			0.000911125i
$229$	−1.59457e16			−0.482832			−0.241416	−	0.970422i	$-0.577612\pi$
$229$	−1.59457e16			−0.482832			−0.241416	+	0.970422i	$0.577612\pi$
$230$		−	1.41106e15i		−	0.0414429i
$231$	−7.85101e13	+	9.53323e13i	−0.00223687	+	0.00271616i
$232$	1.29628e16			0.358329
$233$		−	7.51530e15i		−	0.201583i	−0.994908	−	0.100792i	$-0.967862\pi$
$233$		−	7.51530e15i		−	0.201583i	0.994908	−	0.100792i	$-0.0321376\pi$
$234$	2.84418e16			0.740365
$235$	−4.47375e16			−1.13031
$236$	2.64447e16			0.648565
$237$			1.41565e14i			0.00337067i
$238$		−	5.74872e16i		−	1.32902i
$239$		−	5.88675e16i		−	1.32157i	−0.750575	−	0.660786i	$-0.770223\pi$
$239$		−	5.88675e16i		−	1.32157i	0.750575	−	0.660786i	$-0.229777\pi$
$240$	5.82718e13			0.00127052
$241$			8.01899e16i			1.69824i	0.528196	+	0.849122i	$0.322869\pi$
$241$			8.01899e16i			1.69824i	−0.528196	+	0.849122i	$0.677131\pi$
$242$	−3.37333e16	+	6.59024e15i	−0.693987	+	0.135579i
$243$	−4.24911e14			−0.00849287
$244$			1.60900e16i			0.312484i
$245$	5.18251e16			0.978087
$246$	4.84231e13			0.000888193
$247$	−3.78019e16			−0.673961
$248$			1.85205e16i			0.320990i
$249$		−	2.62469e14i		−	0.00442265i
$250$		−	9.47210e16i		−	1.55191i
$251$	−8.72292e15			−0.138978			−0.0694889	−	0.997583i	$-0.522137\pi$
$251$	−8.72292e15			−0.138978			−0.0694889	+	0.997583i	$0.522137\pi$
$252$		−	4.01063e16i		−	0.621455i
$253$	1.67218e15	+	1.37711e15i	0.0252022	+	0.0207551i
$254$	6.30617e16			0.924549
$255$		−	5.38798e14i		−	0.00768501i
$256$	4.50360e15			0.0625000
$257$	−3.93472e16			−0.531352			−0.265676	−	0.964062i	$-0.585595\pi$
$257$	−3.93472e16			−0.531352			−0.265676	+	0.964062i	$0.585595\pi$
$258$	−7.10698e13			−0.000934000
$259$		−	1.43893e17i		−	1.84053i
$260$			7.54832e16i			0.939803i
$261$		−	8.36194e16i		−	1.01350i
$262$	−1.03190e17			−1.21767
$263$			4.28104e16i			0.491880i	0.969285	+	0.245940i	$0.0790966\pi$
$263$			4.28104e16i			0.491880i	−0.969285	+	0.245940i	$0.920903\pi$
$264$	−5.68697e13	+	6.90551e13i	−0.000636288	+	0.000772624i
$265$	−1.92321e17			−2.09558
$266$			5.33052e16i			0.565715i
$267$	6.44934e13			0.000666709
$268$	−5.33136e16			−0.536902
$269$	1.74537e16			0.171246			0.0856231	−	0.996328i	$-0.472712\pi$
$269$	1.74537e16			0.171246			0.0856231	+	0.996328i	$0.472712\pi$
$270$		−	7.51795e14i		−	0.00718709i
$271$		−	1.28554e17i		−	1.19757i	−0.800908	−	0.598787i	$-0.795650\pi$
$271$		−	1.28554e17i		−	1.19757i	0.800908	−	0.598787i	$-0.204350\pi$
$272$		−	4.16415e16i		−	0.378046i
$273$	−4.16374e14			−0.00368422
$274$			1.26442e17i			1.09053i
$275$	2.04062e17	+	1.68054e17i	1.71567	+	1.41293i
$276$	5.63812e12			4.62137e−5
$277$			2.19932e16i			0.175764i	0.996131	+	0.0878821i	$0.0280099\pi$
$277$			2.19932e16i			0.175764i	−0.996131	+	0.0878821i	$0.971990\pi$
$278$	−1.17485e17			−0.915524
$279$	1.19471e17			0.907890
$280$	1.06440e17			0.788860
$281$			2.42855e17i			1.75551i	0.479111	+	0.877754i	$0.340959\pi$
$281$			2.42855e17i			1.75551i	−0.479111	+	0.877754i	$0.659041\pi$
$282$		−	1.78756e14i		−	0.00126043i
$283$		−	1.02752e17i		−	0.706782i	−0.935476	−	0.353391i	$-0.885029\pi$
$283$		−	1.02752e17i		−	0.706782i	0.935476	−	0.353391i	$-0.114971\pi$
$284$	−2.04373e16			−0.137150
$285$			4.99602e14i			0.00327122i
$286$	−8.94514e16	−	7.36670e16i	−0.571512	−	0.470664i
$287$	8.84505e16			0.551477
$288$		−	2.90515e16i		−	0.176775i
$289$	−2.16652e17			−1.28670
$290$	2.21922e17			1.28651
$291$	2.47290e14			0.00139944
$292$			1.54719e17i			0.854800i
$293$		−	8.86884e15i		−	0.0478403i	−0.999714	−	0.0239201i	$-0.992385\pi$
$293$		−	8.86884e15i		−	0.0478403i	0.999714	−	0.0239201i	$-0.00761474\pi$
$294$			2.07076e14i			0.00109068i
$295$	4.52731e17			2.32855
$296$		−	1.04231e17i		−	0.523546i
$297$	8.90916e14	+	7.33706e14i	0.00437060	+	0.00359937i
$298$	−6.14605e16			−0.294498
$299$			7.30341e15i			0.0341844i
$300$	6.88042e14			0.00314605
$301$	−1.29817e17			−0.579919
$302$	9.54670e16			0.416682
$303$		−	5.77533e14i		−	0.00246308i
$304$			3.86123e16i			0.160920i
$305$			2.75460e17i			1.12191i
$306$	−2.68619e17			−1.06927
$307$		−	3.64134e17i		−	1.41675i	−0.705838	−	0.708374i	$-0.749429\pi$
$307$		−	3.64134e17i		−	1.41675i	0.705838	−	0.708374i	$-0.250571\pi$
$308$	−1.03879e17	+	1.26137e17i	−0.395070	+	0.479720i
$309$	−1.35793e15			−0.00504857
$310$			3.17070e17i			1.15245i
$311$	5.02416e17			1.78542			0.892710	−	0.450631i	$-0.148801\pi$
$311$	5.02416e17			1.78542			0.892710	+	0.450631i	$0.148801\pi$
$312$	−3.01606e14			−0.00104799
$313$	2.26040e17			0.768024			0.384012	−	0.923328i	$-0.374542\pi$
$313$	2.26040e17			0.768024			0.384012	+	0.923328i	$0.374542\pi$
$314$			8.46233e15i			0.0281179i
$315$		−	6.86618e17i		−	2.23122i
$316$			1.87309e17i			0.595317i
$317$	−9.50564e16			−0.295506			−0.147753	−	0.989024i	$-0.547204\pi$
$317$	−9.50564e16			−0.295506			−0.147753	+	0.989024i	$0.547204\pi$
$318$		−	7.68450e14i		−	0.00233682i
$319$	−2.16582e17	+	2.62989e17i	−0.644300	+	0.782352i
$320$	7.71014e16			0.224395
$321$			2.06503e14i			0.000588018i
$322$	1.02987e16			0.0286940
$323$	3.57020e17			0.973363
$324$	−1.87402e17			−0.499988
$325$			8.91264e17i			2.32714i
$326$		−	2.66781e17i		−	0.681761i
$327$			1.19211e14i			0.000298181i
$328$	6.40702e16			0.156870
$329$		−	3.26519e17i		−	0.782595i
$330$	−9.73607e14	+	1.18222e15i	−0.00228447	+	0.00277396i
$331$	−3.76099e17			−0.863986			−0.431993	−	0.901877i	$-0.642189\pi$
$331$	−3.76099e17			−0.863986			−0.431993	+	0.901877i	$0.642189\pi$
$332$		−	3.47281e17i		−	0.781115i
$333$	−6.72366e17			−1.48080
$334$	−3.22619e17			−0.695769
$335$	−9.12726e17			−1.92764
$336$			4.25300e14i			0.000879672i
$337$		−	3.82968e17i		−	0.775806i	−0.921700	−	0.387903i	$-0.873200\pi$
$337$		−	3.82968e17i		−	0.775806i	0.921700	−	0.387903i	$-0.126800\pi$
$338$		−	3.43182e16i		−	0.0680938i
$339$	1.39851e15			0.00271812
$340$		−	7.12901e17i		−	1.35730i
$341$	−3.75745e17	−	3.09441e17i	−0.700829	−	0.577162i
$342$	2.49078e17			0.455147
$343$		−	3.15979e17i		−	0.565718i
$344$	−9.40347e16			−0.164960
$345$	9.65242e13			0.000165922
$346$	1.16893e17			0.196905
$347$			9.92625e17i			1.63862i	0.573349	+	0.819311i	$0.305644\pi$
$347$			9.92625e17i			1.63862i	−0.573349	+	0.819311i	$0.694356\pi$
$348$			8.86726e14i			0.00143461i
$349$		−	8.70181e17i		−	1.37985i	−0.723882	−	0.689924i	$-0.757644\pi$
$349$		−	8.70181e17i		−	1.37985i	0.723882	−	0.689924i	$-0.242356\pi$
$350$	1.25679e18			1.95338
$351$			3.89117e15i			0.00592831i
$352$	−7.52462e16	+	9.13690e16i	−0.112379	+	0.136458i
$353$	6.19745e17			0.907382			0.453691	−	0.891159i	$-0.350107\pi$
$353$	6.19745e17			0.907382			0.453691	+	0.891159i	$0.350107\pi$
$354$			1.80896e15i			0.00259661i
$355$	−3.49886e17			−0.492411
$356$	8.53333e16			0.117752
$357$	3.93244e15			0.00532090
$358$			3.53965e17i			0.469655i
$359$		−	2.11459e14i		−	0.000275147i	−1.00000		0.000137573i	$-0.999956\pi$
$359$		−	2.11459e14i		−	0.000275147i	1.00000		0.000137573i	$-4.37910e-5\pi$
$360$		−	4.97360e17i		−	0.634678i
$361$	4.67959e17			0.585676
$362$			7.49556e17i			0.920119i
$363$	−4.50809e14	−	2.30755e15i	−0.000542808	−	0.00277846i
$364$	−5.50918e17			−0.650695
$365$			2.64879e18i			3.06900i
$366$	−1.10065e15			−0.00125107
$367$	−1.15764e17			−0.129096			−0.0645478	−	0.997915i	$-0.520561\pi$
$367$	−1.15764e17			−0.129096			−0.0645478	+	0.997915i	$0.520561\pi$
$368$	7.45998e15			0.00816212
$369$		−	4.13300e17i		−	0.443691i
$370$		−	1.78443e18i		−	1.87969i
$371$		−	1.40366e18i		−	1.45093i
$372$	−1.26691e15			−0.00128512
$373$		−	8.28323e17i		−	0.824590i	−0.911050	−	0.412295i	$-0.864727\pi$
$373$		−	8.28323e17i		−	0.824590i	0.911050	−	0.412295i	$-0.135273\pi$
$374$	8.44824e17	+	6.95748e17i	0.825401	+	0.679752i
$375$	6.47945e15			0.00621325
$376$		−	2.36518e17i		−	0.222612i
$377$	−1.14863e18			−1.06119
$378$	5.48702e15			0.00497615
$379$	2.14377e18			1.90855			0.954273	−	0.298935i	$-0.0966314\pi$
$379$	2.14377e18			1.90855			0.954273	+	0.298935i	$0.0966314\pi$
$380$			6.61040e17i			0.577753i
$381$			4.31377e15i			0.00370154i
$382$		−	1.71678e17i		−	0.144634i
$383$	4.77226e17			0.394759			0.197380	−	0.980327i	$-0.436757\pi$
$383$	4.77226e17			0.394759			0.197380	+	0.980327i	$0.436757\pi$
$384$			3.08071e14i			0.000250226i
$385$	−1.77841e18	+	2.15946e18i	−1.41842	+	1.72235i
$386$	−1.29768e18			−1.01638
$387$			6.06593e17i			0.466574i
$388$	3.27197e17			0.247165
$389$	1.36394e18			1.01192			0.505960	−	0.862557i	$-0.331138\pi$
$389$	1.36394e18			1.01192			0.505960	+	0.862557i	$0.331138\pi$
$390$	−5.16347e15			−0.00376261
$391$		−	6.89770e16i		−	0.0493705i
$392$			2.73989e17i			0.192633i
$393$		−	7.05879e15i		−	0.00487509i
$394$	8.59362e17			0.583046
$395$			3.20672e18i			2.13738i
$396$	5.89397e17	+	4.85393e17i	0.385960	+	0.317854i
$397$	−8.81694e17			−0.567263			−0.283632	−	0.958933i	$-0.591539\pi$
$397$	−8.81694e17			−0.567263			−0.283632	+	0.958933i	$0.591539\pi$
$398$			1.06996e17i			0.0676372i
$399$	−3.64637e15			−0.00226491
$400$	9.10371e17			0.555646
$401$	1.19545e18			0.717001			0.358501	−	0.933529i	$-0.383288\pi$
$401$	1.19545e18			0.717001			0.358501	+	0.933529i	$0.383288\pi$
$402$		−	3.64695e15i		−	0.00214955i
$403$		−	1.64111e18i		−	0.950607i
$404$		−	7.64153e17i		−	0.435021i
$405$	−3.20831e18			−1.79511
$406$			1.61971e18i			0.890748i
$407$	2.11464e18	+	1.74149e18i	1.14308	+	0.941371i
$408$	2.84851e15			0.00151355
$409$		−	7.10803e17i		−	0.371267i	−0.982619	−	0.185634i	$-0.940566\pi$
$409$		−	7.10803e17i		−	0.371267i	0.982619	−	0.185634i	$-0.0594337\pi$
$410$	1.09688e18			0.563212
$411$	−8.64931e15			−0.00436605
$412$	−1.79672e18			−0.891662
$413$			3.30428e18i			1.61223i
$414$		−	4.81223e16i		−	0.0230858i
$415$		−	5.94544e18i		−	2.80445i
$416$	−3.99064e17			−0.185093
$417$		−	8.03665e15i		−	0.00366541i
$418$	−7.83366e17	−	6.45134e17i	−0.351342	−	0.289345i
$419$	2.10618e18			0.928960			0.464480	−	0.885584i	$-0.346241\pi$
$419$	2.10618e18			0.928960			0.464480	+	0.885584i	$0.346241\pi$
$420$			7.28111e15i			0.00315830i
$421$	3.91041e17			0.166820			0.0834099	−	0.996515i	$-0.473419\pi$
$421$	3.91041e17			0.166820			0.0834099	+	0.996515i	$0.473419\pi$
$422$	−1.82457e18			−0.765550
$423$	−1.52572e18			−0.629638
$424$		−	1.01676e18i		−	0.412722i
$425$		−	8.41755e18i		−	3.36096i
$426$		−	1.39803e15i		−	0.000549096i
$427$	−2.01046e18			−0.776783
$428$			2.73231e17i			0.103854i
$429$	5.03923e15	−	6.11898e15i	0.00188436	−	0.00228811i
$430$	−1.60987e18			−0.592259
$431$		−	5.26408e17i		−	0.190538i	−0.995452	−	0.0952689i	$-0.969629\pi$
$431$		−	5.26408e17i		−	0.190538i	0.995452	−	0.0952689i	$-0.0303711\pi$
$432$	3.97459e15			0.00141549
$433$	4.20656e18			1.47405			0.737024	−	0.675866i	$-0.236230\pi$
$433$	4.20656e18			1.47405			0.737024	+	0.675866i	$0.236230\pi$
$434$	−2.31416e18			−0.797929
$435$			1.51807e16i			0.00515071i
$436$			1.57731e17i			0.0526639i
$437$			6.39592e16i			0.0210152i
$438$	−1.05837e16			−0.00342229
$439$		−	1.00723e18i		−	0.320535i	−0.987074	−	0.160267i	$-0.948764\pi$
$439$		−	1.00723e18i		−	0.320535i	0.987074	−	0.160267i	$-0.0512357\pi$
$440$	−1.28821e18	+	1.56423e18i	−0.403477	+	0.489928i
$441$	1.76743e18			0.544843
$442$			3.68986e18i			1.11958i
$443$	−5.95687e17			−0.177907			−0.0889533	−	0.996036i	$-0.528352\pi$
$443$	−5.95687e17			−0.177907			−0.0889533	+	0.996036i	$0.528352\pi$
$444$	7.12998e15			0.00209608
$445$	1.46090e18			0.422767
$446$			2.29238e18i			0.653045i
$447$		−	4.20424e15i		−	0.00117906i
$448$			5.62729e17i			0.155365i
$449$	3.81287e18			1.03640			0.518200	−	0.855259i	$-0.326602\pi$
$449$	3.81287e18			1.03640			0.518200	+	0.855259i	$0.326602\pi$
$450$		−	5.87256e18i		−	1.57159i
$451$	−1.07049e18	+	1.29986e18i	−0.282063	+	0.342499i
$452$	1.85042e18			0.480065
$453$			6.53048e15i			0.00166824i
$454$	−4.73286e17			−0.119051
$455$	−9.43169e18			−2.33620
$456$	−2.64129e15			−0.000644263
$457$			5.43729e18i			1.30608i	0.757324	+	0.653039i	$0.226506\pi$
$457$			5.43729e18i			1.30608i	−0.757324	+	0.653039i	$0.773494\pi$
$458$		−	1.44324e18i		−	0.341414i
$459$		−	3.67502e16i		−	0.00856191i
$460$	1.27714e17			0.0293045
$461$		−	5.85799e18i		−	1.32386i	−0.749566	−	0.661930i	$-0.769738\pi$
$461$		−	5.85799e18i		−	1.32386i	0.749566	−	0.661930i	$-0.230262\pi$
$462$	−8.62849e15	−	7.10592e15i	−0.00192062	−	0.00158171i
$463$	−9.37770e17			−0.205603			−0.102801	−	0.994702i	$-0.532781\pi$
$463$	−9.37770e17			−0.205603			−0.102801	+	0.994702i	$0.532781\pi$
$464$			1.17326e18i			0.253377i
$465$	−2.16894e16			−0.00461399
$466$	6.80207e17			0.142541
$467$	−2.51221e18			−0.518605			−0.259303	−	0.965796i	$-0.583493\pi$
$467$	−2.51221e18			−0.518605			−0.259303	+	0.965796i	$0.583493\pi$
$468$			2.57426e18i			0.523517i
$469$		−	6.66158e18i		−	1.33465i
$470$		−	4.04918e18i		−	0.799248i
$471$	−5.78871e14			−0.000112573
$472$			2.39350e18i			0.458605i
$473$	1.57113e18	−	1.90778e18i	0.296610	−	0.360163i
$474$	−1.28130e16			−0.00238342
$475$			7.80520e18i			1.43063i
$476$	5.20315e18			0.939761
$477$	−6.55885e18			−1.16735
$478$	5.32808e18			0.934492
$479$			1.11409e19i			1.92563i	0.270157	+	0.962816i	$0.412924\pi$
$479$			1.11409e19i			1.92563i	−0.270157	+	0.962816i	$0.587076\pi$
$480$			5.27416e15i			0.000898390i
$481$			9.23591e18i			1.55047i
$482$	−7.25796e18			−1.20084
$483$			7.04487e14i			0.000114880i
$484$	−5.96480e17	−	3.05319e18i	−0.0958691	−	0.490723i
$485$	5.60160e18			0.887401
$486$		−	3.84586e16i		−	0.00600536i
$487$	6.90285e18			1.06249			0.531246	−	0.847218i	$-0.321724\pi$
$487$	6.90285e18			1.06249			0.531246	+	0.847218i	$0.321724\pi$
$488$	−1.45630e18			−0.220959
$489$	1.82493e16			0.00272951
$490$			4.69067e18i			0.691612i
$491$		−	6.74613e17i		−	0.0980583i	−0.998797	−	0.0490291i	$-0.984387\pi$
$491$		−	6.74613e17i		−	0.0980583i	0.998797	−	0.0490291i	$-0.0156127\pi$
$492$			4.38276e15i			0.000628047i
$493$	1.08483e19			1.53261
$494$		−	3.42144e18i		−	0.476562i
$495$	1.00905e19	+	8.30991e18i	1.38572	+	1.14119i
$496$	−1.67629e18			−0.226974
$497$		−	2.55366e18i		−	0.340933i
$498$	2.37560e16			0.00312729
$499$	4.08215e18			0.529889			0.264944	−	0.964264i	$-0.414646\pi$
$499$	4.08215e18			0.529889			0.264944	+	0.964264i	$0.414646\pi$
$500$	8.57317e18			1.09737
$501$		−	2.20690e16i		−	0.00278559i
$502$		−	7.89508e17i		−	0.0982722i
$503$		−	4.25871e18i		−	0.522760i	−0.965236	−	0.261380i	$-0.915822\pi$
$503$		−	4.25871e18i		−	0.522760i	0.965236	−	0.261380i	$-0.0841776\pi$
$504$	3.63001e18			0.439435
$505$		−	1.30823e19i		−	1.56186i
$506$	−1.24641e17	+	1.51348e17i	−0.0146760	+	0.0178206i
$507$	2.34756e15			0.000272622
$508$			5.70770e18i			0.653755i
$509$	−3.10960e18			−0.351301			−0.175651	−	0.984453i	$-0.556203\pi$
$509$	−3.10960e18			−0.351301			−0.175651	+	0.984453i	$0.556203\pi$
$510$	4.87664e16			0.00543412
$511$	−1.93323e19			−2.12489
$512$			4.07619e17i			0.0441942i
$513$			3.40767e16i			0.00364449i
$514$		−	3.56130e18i		−	0.375722i
$515$	−3.07598e19			−3.20134
$516$		−	6.43250e15i		−	0.000660438i
$517$	4.79848e18	+	3.95175e18i	0.486037	+	0.400272i
$518$	1.30237e19			1.30145
$519$			7.99615e15i			0.000788333i
$520$	−6.83196e18			−0.664541
$521$	6.47563e18			0.621466			0.310733	−	0.950497i	$-0.399425\pi$
$521$	6.47563e18			0.621466			0.310733	+	0.950497i	$0.399425\pi$
$522$	7.56836e18			0.716652
$523$		−	1.65910e18i		−	0.155010i	−0.996992	−	0.0775050i	$-0.975305\pi$
$523$		−	1.65910e18i		−	0.155010i	0.996992	−	0.0775050i	$-0.0246954\pi$
$524$		−	9.33972e18i		−	0.861023i
$525$			8.59714e16i			0.00782058i
$526$	−3.87476e18			−0.347812
$527$			1.54994e19i			1.37291i
$528$	−6.25015e15	−	5.14726e15i	−0.000546328	−	0.000449924i
$529$	−1.15805e19			−0.998934
$530$		−	1.74069e19i		−	1.48180i
$531$	1.54398e19			1.29712
$532$	−4.82464e18			−0.400021
$533$	−5.67727e18			−0.464568
$534$			5.83728e15i			0.000471435i
$535$			4.67769e18i			0.372868i
$536$		−	4.82540e18i		−	0.379647i
$537$	−2.42132e16			−0.00188032
$538$			1.57973e18i			0.121089i
$539$	−5.55868e18	−	4.57781e18i	−0.420582	−	0.346367i
$540$	6.80447e16			0.00508204
$541$		−	5.01328e18i		−	0.369608i	−0.982775	−	0.184804i	$-0.940835\pi$
$541$		−	5.01328e18i		−	0.369608i	0.982775	−	0.184804i	$-0.0591650\pi$
$542$	1.16354e19			0.846812
$543$	−5.12738e16			−0.00368381
$544$	3.76896e18			0.267319
$545$			2.70035e18i			0.189080i
$546$		−	3.76859e16i		−	0.00260513i
$547$		−	1.70318e19i		−	1.16238i	−0.813767	−	0.581191i	$-0.802587\pi$
$547$		−	1.70318e19i		−	1.16238i	0.813767	−	0.581191i	$-0.197413\pi$
$548$	−1.14442e19			−0.771118
$549$			9.39421e18i			0.624962i
$550$	−1.52105e19	+	1.84696e19i	−0.999090	+	1.21316i
$551$	−1.00591e19			−0.652375
$552$			5.10304e14i			3.26780e-5i
$553$	−2.34044e19			−1.47986
$554$	−1.99060e18			−0.124284
$555$	1.22065e17			0.00752557
$556$		−	1.06336e19i		−	0.647374i
$557$		−	4.28571e18i		−	0.257654i	−0.991667	−	0.128827i	$-0.958879\pi$
$557$		−	4.28571e18i		−	0.257654i	0.991667	−	0.128827i	$-0.0411211\pi$
$558$			1.08133e19i			0.641975i
$559$	8.33242e18			0.488527
$560$			9.63388e18i			0.557808i
$561$	−4.75930e16	+	5.77907e16i	−0.00272147	+	0.00330459i
$562$	−2.19807e19			−1.24133
$563$		−	9.47779e18i		−	0.528626i	−0.964437	−	0.264313i	$-0.914855\pi$
$563$		−	9.47779e18i		−	0.528626i	0.964437	−	0.264313i	$-0.0851451\pi$
$564$	1.61792e16			0.000891255
$565$	3.16790e19			1.72358
$566$	9.30005e18			0.499770
$567$		−	2.34161e19i		−	1.24289i
$568$		−	1.84978e18i		−	0.0969797i
$569$		−	3.40436e19i		−	1.76299i	−0.472192	−	0.881496i	$-0.656537\pi$
$569$		−	3.40436e19i		−	1.76299i	0.472192	−	0.881496i	$-0.343463\pi$
$570$	−4.52188e16			−0.00231310
$571$			4.30046e18i			0.217301i	0.994080	+	0.108651i	$0.0346530\pi$
$571$			4.30046e18i			0.217301i	−0.994080	+	0.108651i	$0.965347\pi$
$572$	6.66757e18	−	8.09622e18i	0.332809	−	0.404120i
$573$	1.17437e16			0.000579061
$574$			8.00563e18i			0.389953i
$575$	1.50798e18			0.0725640
$576$	2.62944e18			0.124999
$577$	−1.09117e18			−0.0512460			−0.0256230	−	0.999672i	$-0.508157\pi$
$577$	−1.09117e18			−0.0512460			−0.0256230	+	0.999672i	$0.508157\pi$
$578$		−	1.96091e19i		−	0.909834i
$579$		−	8.87686e16i		−	0.00406920i
$580$			2.00861e19i			0.909702i
$581$	4.33931e19			1.94173
$582$			2.23821e16i			0.000989556i
$583$	2.06280e19	+	1.69881e19i	0.901111	+	0.742102i
$584$	−1.40036e19			−0.604435
$585$			4.40711e19i			1.87959i
$586$	8.02716e17			0.0338282
$587$	−4.48356e19			−1.86705			−0.933525	−	0.358513i	$-0.883284\pi$
$587$	−4.48356e19			−1.86705			−0.933525	+	0.358513i	$0.883284\pi$
$588$	−1.87424e16			−0.000771228
$589$		−	1.43719e19i		−	0.584395i
$590$			4.09765e19i			1.64654i
$591$			5.87852e16i			0.00233429i
$592$	9.43391e18			0.370203
$593$			9.35070e18i			0.362628i	0.983425	+	0.181314i	$0.0580350\pi$
$593$			9.35070e18i			0.362628i	−0.983425	+	0.181314i	$0.941965\pi$
$594$	−6.64075e16	+	8.06365e16i	−0.00254514	+	0.00309048i
$595$	8.90776e19			3.37403
$596$		−	5.56277e18i		−	0.208241i
$597$	−7.31912e15			−0.000270794
$598$	−6.61029e17			−0.0241720
$599$	7.44750e18			0.269168			0.134584	−	0.990902i	$-0.457030\pi$
$599$	7.44750e18			0.269168			0.134584	+	0.990902i	$0.457030\pi$
$600$			6.22745e16i			0.00222460i
$601$			3.77235e19i			1.33196i	0.745970	+	0.665980i	$0.231986\pi$
$601$			3.77235e19i			1.33196i	−0.745970	+	0.665980i	$0.768014\pi$
$602$		−	1.17497e19i		−	0.410064i
$603$	−3.11274e19			−1.07379
$604$			8.64069e18i			0.294639i
$605$	−1.02117e19	−	5.22705e19i	−0.344200	−	1.76185i
$606$	5.22723e16			0.00174166
$607$			1.65517e19i			0.545157i	0.962134	+	0.272579i	$0.0878765\pi$
$607$			1.65517e19i			0.545157i	−0.962134	+	0.272579i	$0.912124\pi$
$608$	−3.49478e18			−0.113788
$609$	−1.10797e17			−0.00356622
$610$	−2.49318e19			−0.793313
$611$			2.09579e19i			0.659263i
$612$		−	2.43126e19i		−	0.756086i
$613$			1.82203e19i			0.560187i	0.959973	+	0.280093i	$0.0903655\pi$
$613$			1.82203e19i			0.560187i	−0.959973	+	0.280093i	$0.909635\pi$
$614$	3.29576e19			1.00179
$615$			7.50326e16i			0.00225488i
$616$	−1.14166e19	−	9.40208e18i	−0.339214	−	0.279357i
$617$	−1.22988e19			−0.361298			−0.180649	−	0.983548i	$-0.557820\pi$
$617$	−1.22988e19			−0.361298			−0.180649	+	0.983548i	$0.557820\pi$
$618$		−	1.22906e17i		−	0.00356988i
$619$	−5.38341e19			−1.54605			−0.773025	−	0.634376i	$-0.781257\pi$
$619$	−5.38341e19			−1.54605			−0.773025	+	0.634376i	$0.781257\pi$
$620$	−2.86979e19			−0.814908
$621$	6.58370e15			0.000184854
$622$			4.54735e19i			1.26248i
$623$			1.06625e19i			0.292713i
$624$		−	2.72982e16i		−	0.000741041i
$625$	6.39744e19			1.71730
$626$			2.04588e19i			0.543075i
$627$	4.41308e16	−	5.35866e16i	0.00115843	−	0.00140664i
$628$	−7.65923e17			−0.0198823
$629$		−	8.72285e19i		−	2.23926i
$630$	6.21456e19			1.57771
$631$	2.28025e19			0.572502			0.286251	−	0.958155i	$-0.407591\pi$
$631$	2.28025e19			0.572502			0.286251	+	0.958155i	$0.407591\pi$
$632$	−1.69533e19			−0.420953
$633$		−	1.24811e17i		−	0.00306497i
$634$		−	8.60353e18i		−	0.208954i
$635$			9.77154e19i			2.34718i
$636$	6.95521e16			0.00165238
$637$		−	2.42782e19i		−	0.570479i
$638$	−2.38030e19	−	1.96028e19i	−0.553207	−	0.455589i
$639$	−1.19324e19			−0.274298
$640$			6.97842e18i			0.158671i
$641$	−5.76223e19			−1.29594			−0.647969	−	0.761667i	$-0.724381\pi$
$641$	−5.76223e19			−1.29594			−0.647969	+	0.761667i	$0.724381\pi$
$642$	−1.86905e16			−0.000415792
$643$	7.35305e19			1.61805			0.809023	−	0.587777i	$-0.199997\pi$
$643$	7.35305e19			1.61805			0.809023	+	0.587777i	$0.199997\pi$
$644$			9.32130e17i			0.0202897i
$645$		−	1.10124e17i		−	0.00237118i
$646$			3.23137e19i			0.688271i
$647$	−8.97802e19			−1.89169			−0.945846	−	0.324615i	$-0.894765\pi$
$647$	−8.97802e19			−1.89169			−0.945846	+	0.324615i	$0.894765\pi$
$648$		−	1.69617e19i		−	0.353545i
$649$	−4.85593e19	−	3.99906e19i	−1.00129	−	0.824603i
$650$	−8.06680e19			−1.64554
$651$		−	1.58301e17i		−	0.00319461i
$652$	2.41463e19			0.482078
$653$	8.44362e19			1.66777			0.833886	−	0.551937i	$-0.186111\pi$
$653$	8.44362e19			1.66777			0.833886	+	0.551937i	$0.186111\pi$
$654$	−1.07897e16			−0.000210846
$655$		−	1.59895e20i		−	3.09134i
$656$			5.79898e18i			0.110924i
$657$			9.03335e19i			1.70959i
$658$	2.95531e19			0.553378
$659$		−	6.10282e19i		−	1.13066i	−0.824864	−	0.565331i	$-0.808748\pi$
$659$		−	6.10282e19i		−	1.13066i	0.824864	−	0.565331i	$-0.191252\pi$
$660$	−1.07002e17	−	8.81208e16i	−0.00196149	−	0.00161537i
$661$	−2.05061e19			−0.371939			−0.185970	−	0.982555i	$-0.559543\pi$
$661$	−2.05061e19			−0.371939			−0.185970	+	0.982555i	$0.559543\pi$
$662$		−	3.40406e19i		−	0.610930i
$663$	−2.52407e17			−0.00448236
$664$	3.14323e19			0.552332
$665$	−8.25975e19			−1.43620
$666$		−	6.08556e19i		−	1.04708i
$667$			1.94344e18i			0.0330895i
$668$		−	2.92002e19i		−	0.491983i
$669$	−1.56812e17			−0.00261454
$670$		−	8.26106e19i		−	1.36305i
$671$	2.43319e19	−	2.95454e19i	0.397300	−	0.482428i
$672$	−3.84938e16			−0.000622022
$673$			2.08739e19i			0.333810i	0.985973	+	0.166905i	$0.0533773\pi$
$673$			2.08739e19i			0.333810i	−0.985973	+	0.166905i	$0.946623\pi$
$674$	3.46623e19			0.548577
$675$	8.03435e17			0.0125842
$676$	3.10613e18			0.0481496
$677$			1.09156e20i			1.67467i	0.546691	+	0.837334i	$0.315887\pi$
$677$			1.09156e20i			1.67467i	−0.546691	+	0.837334i	$0.684113\pi$
$678$			1.26579e17i			0.00192200i
$679$			4.08836e19i			0.614413i
$680$	6.45244e19			0.959758
$681$		−	3.23754e16i		−	0.000476635i
$682$	2.80074e19	−	3.40085e19i	0.408115	−	0.495561i
$683$	5.50592e19			0.794118			0.397059	−	0.917793i	$-0.370031\pi$
$683$	5.50592e19			0.794118			0.397059	+	0.917793i	$0.370031\pi$
$684$			2.25439e19i			0.321838i
$685$	−1.95924e20			−2.76855
$686$	2.85992e19			0.400023
$687$	9.87259e16			0.00136689
$688$		−	8.51105e18i		−	0.116644i
$689$			9.00953e19i			1.22227i
$690$			8.73638e15i			0.000117324i
$691$	−3.15374e19			−0.419256			−0.209628	−	0.977781i	$-0.567225\pi$
$691$	−3.15374e19			−0.419256			−0.209628	+	0.977781i	$0.567225\pi$
$692$			1.05800e19i			0.139233i
$693$	−6.06503e19	+	7.36457e19i	−0.790133	+	0.959433i
$694$	−8.98421e19			−1.15868
$695$		−	1.82046e20i		−	2.32427i
$696$	−8.02573e16			−0.00101442
$697$	5.36189e19			0.670948
$698$	7.87598e19			0.975700
$699$			4.65300e16i			0.000570680i
$700$			1.13752e20i			1.38125i
$701$			3.24746e19i			0.390407i	0.980763	+	0.195204i	$0.0625368\pi$
$701$			3.24746e19i			0.390407i	−0.980763	+	0.195204i	$0.937463\pi$
$702$	−3.52189e17			−0.00419194
$703$			8.08830e19i			0.953169i
$704$	−8.26978e18	−	6.81051e18i	−0.0964907	−	0.0794641i
$705$	2.76986e17			0.00319988
$706$			5.60929e19i			0.641616i
$707$	9.54815e19			1.08139
$708$	−1.63729e17			−0.00183608
$709$	4.78036e18			0.0530808			0.0265404	−	0.999648i	$-0.491551\pi$
$709$	4.78036e18			0.0530808			0.0265404	+	0.999648i	$0.491551\pi$
$710$		−	3.16681e19i		−	0.348187i
$711$			1.09361e20i			1.19063i
$712$			7.72349e18i			0.0832633i
$713$	−2.77668e18			−0.0296414
$714$			3.55924e17i			0.00376244i
$715$	1.14148e20	−	1.38607e20i	1.19489	−	1.45092i
$716$	−3.20372e19			−0.332096
$717$			3.64471e17i			0.00374135i
$718$	1.91391e16			0.000194558
$719$	−4.85384e18			−0.0488633			−0.0244317	−	0.999702i	$-0.507778\pi$
$719$	−4.85384e18			−0.0488633			−0.0244317	+	0.999702i	$0.507778\pi$
$720$	4.50159e19			0.448785
$721$		−	2.24502e20i		−	2.21653i
$722$			4.23548e19i			0.414135i
$723$		−	4.96485e17i		−	0.00480771i
$724$	−6.78421e19			−0.650623
$725$			2.37165e20i			2.25261i
$726$	2.08855e17	−	4.08026e16i	0.00196467	−	0.000383823i
$727$	1.72840e20			1.61029			0.805144	−	0.593079i	$-0.202088\pi$
$727$	1.72840e20			1.61029			0.805144	+	0.593079i	$0.202088\pi$
$728$		−	4.98634e19i		−	0.460111i
$729$	−1.09414e20			−0.999952
$730$	−2.39741e20			−2.17011
$731$	−7.86956e19			−0.705551
$732$		−	9.96191e16i		−	0.000884637i
$733$			1.28441e20i			1.12973i	0.825183	+	0.564866i	$0.191072\pi$
$733$			1.28441e20i			1.12973i	−0.825183	+	0.564866i	$0.808928\pi$
$734$		−	1.04778e19i		−	0.0912844i
$735$	−3.20868e17			−0.00276895
$736$			6.75200e17i			0.00577149i
$737$	9.78977e19	+	8.06228e19i	0.828896	+	0.682631i
$738$	3.74076e19			0.313737
$739$			8.41404e19i			0.699026i	0.936931	+	0.349513i	$0.113653\pi$
$739$			8.41404e19i			0.699026i	−0.936931	+	0.349513i	$0.886347\pi$
$740$	1.61508e20			1.32914
$741$	2.34045e17			0.00190797
$742$	1.27045e20			1.02596
$743$			1.48627e20i			1.18899i	0.804101	+	0.594493i	$0.202647\pi$
$743$			1.48627e20i			1.18899i	−0.804101	+	0.594493i	$0.797353\pi$
$744$		−	1.14667e17i		−	0.000908719i
$745$		−	9.52342e19i		−	0.747652i
$746$	7.49713e19			0.583073
$747$		−	2.02762e20i		−	1.56222i
$748$	−6.29719e19	+	7.64647e19i	−0.480657	+	0.583647i
$749$	−3.41404e19			−0.258164
$750$			5.86453e17i			0.00439343i
$751$	2.03222e20			1.50831			0.754156	−	0.656696i	$-0.228046\pi$
$751$	2.03222e20			1.50831			0.754156	+	0.656696i	$0.228046\pi$
$752$	2.14072e19			0.157411
$753$	5.40068e16			0.000393444
$754$		−	1.03962e20i		−	0.750372i
$755$			1.47928e20i			1.05785i
$756$			4.96628e17i			0.00351867i
$757$	1.55760e20			1.09342			0.546709	−	0.837323i	$-0.315881\pi$
$757$	1.55760e20			1.09342			0.546709	+	0.837323i	$0.315881\pi$
$758$			1.94032e20i			1.34955i
$759$	−1.03531e16	−	8.52617e15i	−7.13470e−5	−	5.87573e-5i
$760$	−5.98305e19			−0.408533
$761$		−	5.08678e19i		−	0.344152i	−0.985084	−	0.172076i	$-0.944952\pi$
$761$		−	5.08678e19i		−	0.344152i	0.985084	−	0.172076i	$-0.0550475\pi$
$762$	−3.90438e17			−0.00261738
$763$	−1.97087e19			−0.130914
$764$	1.55385e19			0.102272
$765$		−	4.16230e20i		−	2.71458i
$766$			4.31935e19i			0.279137i
$767$		−	2.12088e20i		−	1.35815i
$768$	−2.78834e16			−0.000176937
$769$		−	7.57297e19i		−	0.476192i	−0.971242	−	0.238096i	$-0.923477\pi$
$769$		−	7.57297e19i		−	0.476192i	0.971242	−	0.238096i	$-0.0765232\pi$
$770$	−1.95452e20	−	1.60963e20i	−1.21788	−	1.00298i
$771$	2.43613e17			0.00150425
$772$		−	1.17453e20i		−	0.718690i
$773$	−1.53500e20			−0.930793			−0.465397	−	0.885102i	$-0.654088\pi$
$773$	−1.53500e20			−0.930793			−0.465397	+	0.885102i	$0.654088\pi$
$774$	−5.49025e19			−0.329918
$775$	−3.38850e20			−2.01788
$776$			2.96145e19i			0.174772i
$777$			8.90897e17i			0.00521051i
$778$			1.23449e20i			0.715536i
$779$	−4.97184e19			−0.285598
$780$		−	4.67344e17i		−	0.00266057i
$781$	3.75283e19	+	3.09061e19i	0.211739	+	0.174376i
$782$	6.24309e18			0.0349102
$783$			1.03544e18i			0.00573843i
$784$	−2.47986e19			−0.136212
$785$	−1.31126e19			−0.0713838
$786$	6.38889e17			0.00344721
$787$		−	1.04441e20i		−	0.558531i	−0.960214	−	0.279266i	$-0.909909\pi$
$787$		−	1.04441e20i		−	0.558531i	0.960214	−	0.279266i	$-0.0900910\pi$
$788$			7.77806e19i			0.412276i
$789$		−	2.65055e17i		−	0.00139251i
$790$	−2.90239e20			−1.51135
$791$			2.31211e20i			1.19336i
$792$	−4.39328e19	+	5.33462e19i	−0.224757	+	0.272915i
$793$	1.29043e20			0.654367
$794$		−	7.98019e19i		−	0.401116i
$795$	1.19073e18			0.00593257
$796$	−9.68416e18			−0.0478267
$797$	−1.12925e20			−0.552818			−0.276409	−	0.961040i	$-0.589144\pi$
$797$	−1.12925e20			−0.552818			−0.276409	+	0.961040i	$0.589144\pi$
$798$		−	3.30032e17i		−	0.00160153i
$799$		−	1.97937e20i		−	0.952136i
$800$			8.23974e19i			0.392901i
$801$	4.98222e19			0.235502
$802$			1.08200e20i			0.506996i
$803$	2.33972e20	−	2.84105e20i	1.08682	−	1.31968i
$804$	3.30084e17			0.00151996
$805$			1.59580e19i			0.0728464i
$806$	1.48536e20			0.672181
$807$	−1.08062e17			−0.000484796
$808$	6.91632e19			0.307607
$809$			8.41856e19i			0.371192i	0.982626	+	0.185596i	$0.0594215\pi$
$809$			8.41856e19i			0.371192i	−0.982626	+	0.185596i	$0.940578\pi$
$810$		−	2.90383e20i		−	1.26934i
$811$			3.43628e20i			1.48917i	0.667530	+	0.744583i	$0.267352\pi$
$811$			3.43628e20i			1.48917i	−0.667530	+	0.744583i	$0.732648\pi$
$812$	−1.46599e20			−0.629854
$813$			7.95928e17i			0.00339031i
$814$	−1.57622e20	+	1.91395e20i	−0.665649	+	0.808277i
$815$	4.13383e20			1.73081
$816$			2.57818e17i			0.00107024i
$817$	7.29708e19			0.300327
$818$	6.43346e19			0.262525
$819$	−3.21656e20			−1.30138
$820$			9.92781e19i			0.398251i
$821$			5.38083e18i			0.0214017i	0.999943	+	0.0107008i	$0.00340624\pi$
$821$			5.38083e18i			0.0214017i	−0.999943	+	0.0107008i	$0.996594\pi$
$822$		−	7.82846e17i		−	0.00308726i
$823$	−3.25916e20			−1.27440			−0.637202	−	0.770697i	$-0.719908\pi$
$823$	−3.25916e20			−1.27440			−0.637202	+	0.770697i	$0.719908\pi$
$824$		−	1.62621e20i		−	0.630500i
$825$	−1.26342e18	−	1.04048e18i	−0.00485704	−	0.00399997i
$826$	−2.99069e20			−1.14002
$827$			2.89840e17i			0.00109552i	1.00000		0.000547759i	$0.000174357\pi$
$827$			2.89840e17i			0.00109552i	−1.00000		0.000547759i	$0.999826\pi$
$828$	4.35554e18			0.0163241
$829$	−8.65860e19			−0.321785			−0.160893	−	0.986972i	$-0.551437\pi$
$829$	−8.65860e19			−0.321785			−0.160893	+	0.986972i	$0.551437\pi$
$830$	5.38120e20			1.98304
$831$		−	1.36168e17i		−	0.000497586i
$832$		−	3.61192e19i		−	0.130880i
$833$			2.29295e20i			0.823910i
$834$	7.27395e17			0.00259184
$835$		−	4.99905e20i		−	1.76637i
$836$	5.83909e19	−	7.09022e19i	0.204598	−	0.248437i
$837$	−1.47938e18			−0.00514047
$838$			1.90629e20i			0.656874i
$839$	−3.29986e20			−1.12762			−0.563808	−	0.825906i	$-0.690664\pi$
$839$	−3.29986e20			−1.12762			−0.563808	+	0.825906i	$0.690664\pi$
$840$	−6.59011e17			−0.00223325
$841$	−8.09288e18			−0.0271976
$842$			3.53930e19i			0.117959i
$843$		−	1.50361e18i		−	0.00496982i
$844$		−	1.65141e20i		−	0.541326i
$845$	5.31768e19			0.172872
$846$		−	1.38092e20i		−	0.445221i
$847$	3.81499e20	−	7.45307e19i	1.21986	−	0.238315i
$848$	9.20267e19			0.291839
$849$			6.36176e17i			0.00200089i
$850$	7.61869e20			2.37656
$851$	1.56268e19			0.0483462
$852$	1.26535e17			0.000388270
$853$			3.37389e20i			1.02681i	0.858148	+	0.513403i	$0.171615\pi$
$853$			3.37389e20i			1.02681i	−0.858148	+	0.513403i	$0.828385\pi$
$854$		−	1.81966e20i		−	0.549269i
$855$			3.85951e20i			1.15550i
$856$	−2.47300e19			−0.0734358
$857$			4.79566e20i			1.41248i	0.707972	+	0.706240i	$0.249610\pi$
$857$			4.79566e20i			1.41248i	−0.707972	+	0.706240i	$0.750390\pi$
$858$	5.53827e17	+	4.56099e17i	0.00161794	+	0.00133244i
$859$	−4.35174e20			−1.26099			−0.630493	−	0.776195i	$-0.717147\pi$
$859$	−4.35174e20			−1.26099			−0.630493	+	0.776195i	$0.717147\pi$
$860$		−	1.45709e20i		−	0.418790i
$861$	−5.47630e17			−0.00156122
$862$	4.76450e19			0.134731
$863$	6.37261e20			1.78748			0.893741	−	0.448583i	$-0.148071\pi$
$863$	6.37261e20			1.78748			0.893741	+	0.448583i	$0.148071\pi$
$864$			3.59739e17i			0.00100090i
$865$			1.81128e20i			0.499889i
$866$			3.80734e20i			1.04231i
$867$	1.34137e18			0.00364263
$868$		−	2.09453e20i		−	0.564221i
$869$	2.83255e20	−	3.43948e20i	0.756902	−	0.919082i
$870$	−1.37400e18			−0.00364210
$871$			4.27579e20i			1.12432i
$872$	−1.42762e19			−0.0372390
$873$	1.91035e20			0.494327
$874$	−5.78893e18			−0.0148600
$875$			1.07122e21i			2.72787i
$876$		−	9.57924e17i		−	0.00241993i
$877$		−	5.28557e20i		−	1.32463i	−0.749225	−	0.662315i	$-0.769574\pi$
$877$		−	5.28557e20i		−	1.32463i	0.749225	−	0.662315i	$-0.230426\pi$
$878$	9.11637e19			0.226652
$879$			5.49103e16i			0.000135435i
$880$	−1.41578e20	−	1.16596e20i	−0.346432	−	0.285301i
$881$	6.44389e18			0.0156429			0.00782144	−	0.999969i	$-0.497510\pi$
$881$	6.44389e18			0.0156429			0.00782144	+	0.999969i	$0.497510\pi$
$882$			1.59969e20i			0.385262i
$883$	2.19065e20			0.523418			0.261709	−	0.965147i	$-0.415714\pi$
$883$	2.19065e20			0.523418			0.261709	+	0.965147i	$0.415714\pi$
$884$	−3.33968e20			−0.791661
$885$	−2.80302e18			−0.00659210
$886$		−	5.39154e19i		−	0.125799i
$887$		−	4.53853e20i		−	1.05063i	−0.850908	−	0.525315i	$-0.823947\pi$
$887$		−	4.53853e20i		−	1.05063i	0.850908	−	0.525315i	$-0.176053\pi$
$888$			6.45332e17i			0.00148215i
$889$	−7.13181e20			−1.62513
$890$			1.32226e20i			0.298941i
$891$	3.44119e20	+	2.83397e20i	0.771907	+	0.635698i
$892$	−2.07483e20			−0.461772
$893$			1.83537e20i			0.405289i
$894$	3.80524e17			0.000833719
$895$	−5.48476e20			−1.19233
$896$	−5.09324e19			−0.109860
$897$		−	4.52181e16i		−	9.67754e-5i
$898$			3.45102e20i			0.732846i
$899$		−	4.36698e20i		−	0.920161i
$900$	5.31524e20			1.11128
$901$		−	8.50905e20i		−	1.76525i
$902$	−1.17650e20	−	9.68894e19i	−0.242184	−	0.199448i
$903$	8.03746e17			0.00164174
$904$			1.67481e20i			0.339457i
$905$	−1.16145e21			−2.33594
$906$	−5.91071e17			−0.00117962
$907$	−9.17499e20			−1.81700			−0.908499	−	0.417886i	$-0.862771\pi$
$907$	−9.17499e20			−1.81700			−0.908499	+	0.417886i	$0.862771\pi$
$908$		−	4.28370e19i		−	0.0841817i
$909$		−	4.46154e20i		−	0.870036i
$910$		−	8.53659e20i		−	1.65194i
$911$	4.23528e20			0.813305			0.406653	−	0.913583i	$-0.366696\pi$
$911$	4.23528e20			0.813305			0.406653	+	0.913583i	$0.366696\pi$
$912$		−	2.39063e17i		−	0.000455563i
$913$	−5.25172e20	+	6.37699e20i	−0.993130	+	1.20593i
$914$	−4.92127e20			−0.923537
$915$		−	1.70547e18i		−	0.00317612i
$916$	1.30627e20			0.241416
$917$	1.16701e21			2.14036
$918$	3.32625e18			0.00605418
$919$		−	6.33613e20i		−	1.14450i	−0.820079	−	0.572250i	$-0.806071\pi$
$919$		−	6.33613e20i		−	1.14450i	0.820079	−	0.572250i	$-0.193929\pi$
$920$			1.15594e19i			0.0207214i
$921$			2.25449e18i			0.00401079i
$922$	5.30205e20			0.936111
$923$			1.63909e20i			0.287204i
$924$	6.43155e17	−	7.80962e17i	0.00111844	−	0.00135808i
$925$	1.90700e21			3.29123
$926$		−	8.48773e19i		−	0.145383i
$927$	−1.04902e21			−1.78331
$928$	−1.06191e20			−0.179165
$929$	−5.34578e20			−0.895161			−0.447580	−	0.894244i	$-0.647714\pi$
$929$	−5.34578e20			−0.895161			−0.447580	+	0.894244i	$0.647714\pi$
$930$		−	1.96310e18i		−	0.00326258i
$931$		−	2.12615e20i		−	0.350708i
$932$			6.15653e19i			0.100792i
$933$	−3.11064e18			−0.00505450
$934$		−	2.27379e20i		−	0.366709i
$935$	−1.07808e21	+	1.30907e21i	−1.72571	+	2.09547i
$936$	−2.32995e20			−0.370183
$937$		−	2.21764e20i		−	0.349715i	−0.984594	−	0.174857i	$-0.944054\pi$
$937$		−	2.21764e20i		−	0.349715i	0.984594	−	0.174857i	$-0.0559465\pi$
$938$	6.02938e20			0.943740
$939$	−1.39950e18			−0.00217427
$940$	3.66489e20			0.565154
$941$		−	2.53556e20i		−	0.388102i	−0.980991	−	0.194051i	$-0.937837\pi$
$941$		−	2.53556e20i		−	0.388102i	0.980991	−	0.194051i	$-0.0621628\pi$
$942$		−	5.23934e16i		−	7.96013e-5i
$943$			9.60570e18i			0.0144860i
$944$	−2.16635e20			−0.324283
$945$			8.50225e18i			0.0126331i
$946$	1.72672e20	+	1.42203e20i	0.254674	+	0.209735i
$947$	1.37825e20			0.201780			0.100890	−	0.994898i	$-0.467831\pi$
$947$	1.37825e20			0.201780			0.100890	+	0.994898i	$0.467831\pi$
$948$		−	1.15970e18i		−	0.00168534i
$949$	1.24086e21			1.79003
$950$	−7.06446e20			−1.01161
$951$	5.88529e17			0.000836574
$952$			4.70935e20i			0.664511i
$953$		−	9.38386e20i		−	1.31441i	−0.753711	−	0.657206i	$-0.771738\pi$
$953$		−	9.38386e20i		−	1.31441i	0.753711	−	0.657206i	$-0.228262\pi$
$954$		−	5.93640e20i		−	0.825438i
$955$	2.66019e20			0.367188
$956$			4.82243e20i			0.660786i
$957$	1.34094e18	−	1.62826e18i	0.00182400	−	0.00221483i
$958$	−1.00836e21			−1.36163
$959$		−	1.42996e21i		−	1.91687i
$960$	−4.77363e17			−0.000635258
$961$	−1.33012e20			−0.175723
$962$	−8.35939e20			−1.09635
$963$			1.59527e20i			0.207706i
$964$		−	6.56916e20i		−	0.849122i
$965$		−	2.01078e21i		−	2.58032i
$966$	−6.37629e16			−8.12322e−5
$967$			1.21304e21i			1.53423i	0.641511	+	0.767114i	$0.278308\pi$
$967$			1.21304e21i			1.53423i	−0.641511	+	0.767114i	$0.721692\pi$
$968$	2.76343e20	−	5.39872e19i	0.346994	−	0.0677897i
$969$	−2.21044e18			−0.00275558
$970$			5.06999e20i			0.627487i
$971$	−2.90380e20			−0.356806			−0.178403	−	0.983957i	$-0.557093\pi$
$971$	−2.90380e20			−0.356806			−0.178403	+	0.983957i	$0.557093\pi$
$972$	3.48087e18			0.00424643
$973$	1.32867e21			1.60927
$974$			6.24774e20i			0.751295i
$975$		−	5.51814e18i		−	0.00658811i
$976$		−	1.31809e20i		−	0.156242i
$977$	−2.10367e20			−0.247580			−0.123790	−	0.992308i	$-0.539505\pi$
$977$	−2.10367e20			−0.247580			−0.123790	+	0.992308i	$0.539505\pi$
$978$			1.65174e18i			0.00193006i
$979$	−1.56694e20	−	1.29044e20i	−0.181792	−	0.149713i
$980$	−4.24551e20			−0.489043
$981$			9.20921e19i			0.105327i
$982$	6.10590e19			0.0693377
$983$	1.03646e21			1.16864			0.584318	−	0.811525i	$-0.301362\pi$
$983$	1.03646e21			1.16864			0.584318	+	0.811525i	$0.301362\pi$
$984$	−3.96682e17			−0.000444096
$985$			1.33160e21i			1.48020i
$986$			9.81872e20i			1.08372i
$987$			2.02160e18i			0.00221552i
$988$	3.09673e20			0.336981
$989$		−	1.40981e19i		−	0.0152331i
$990$	−7.52127e20	+	9.13283e20i	−0.806947	+	0.979849i
$991$	3.47514e20			0.370217			0.185109	−	0.982718i	$-0.440736\pi$
$991$	3.47514e20			0.370217			0.185109	+	0.982718i	$0.440736\pi$
$992$		−	1.51720e20i		−	0.160495i
$993$	2.32857e18			0.00244593
$994$	2.31131e20			0.241076
$995$	−1.65792e20			−0.171713
$996$			2.15015e18i			0.00221133i
$997$		−	2.31343e20i		−	0.236260i	−0.992998	−	0.118130i	$-0.962310\pi$
$997$		−	2.31343e20i		−	0.236260i	0.992998	−	0.118130i	$-0.0376899\pi$
$998$			3.69474e20i			0.374688i
$999$	8.32576e18			0.00838428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.15.b.a.21.11	yes	14
4.3	odd	2		176.15.h.e.65.8		14
11.10	odd	2	inner	22.15.b.a.21.4	✓	14
44.43	even	2		176.15.h.e.65.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.15.b.a.21.4	✓	14	11.10	odd	2	inner
22.15.b.a.21.11	yes	14	1.1	even	1	trivial
176.15.h.e.65.7		14	44.43	even	2
176.15.h.e.65.8		14	4.3	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+90.5097i q^{2} -6.19137 q^{3} -8192.00 q^{4} -140247. q^{5} -560.379i q^{6} -1.02360e6i q^{7} -741455. i q^{8} -4.78293e6 q^{9} +O(q^{10})\)	\(q+90.5097i q^{2} -6.19137 q^{3} -8192.00 q^{4} -140247. q^{5} -560.379i q^{6} -1.02360e6i q^{7} -741455. i q^{8} -4.78293e6 q^{9} -1.26937e7i q^{10} +(1.50426e7 + 1.23882e7i) q^{11} +50719.7 q^{12} +6.57004e7i q^{13} +9.26454e7 q^{14} +868318. q^{15} +6.71089e7 q^{16} -6.20507e8i q^{17} -4.32901e8i q^{18} +5.75368e8i q^{19} +1.14890e9 q^{20} +6.33747e6i q^{21} +(-1.12126e9 + 1.36150e9i) q^{22} +1.11162e8 q^{23} +4.59062e6i q^{24} +1.35656e10 q^{25} -5.94652e9 q^{26} +5.92260e7 q^{27} +8.38531e9i q^{28} +1.74829e10i q^{29} +7.85912e7i q^{30} -2.49786e10 q^{31} +6.07400e9i q^{32} +(-9.31345e7 - 7.67002e7i) q^{33} +5.61619e10 q^{34} +1.43556e11i q^{35} +3.91818e10 q^{36} +1.40576e11 q^{37} -5.20763e10 q^{38} -4.06775e8i q^{39} +1.03987e11i q^{40} +8.64115e10i q^{41} -5.73602e8 q^{42} -1.26825e11i q^{43} +(-1.23229e11 - 1.01485e11i) q^{44} +6.70790e11 q^{45} +1.00613e10i q^{46} +3.18992e11 q^{47} -4.15496e8 q^{48} -3.69528e11 q^{49} +1.22782e12i q^{50} +3.84179e9i q^{51} -5.38218e11i q^{52} +1.37130e12 q^{53} +5.36053e9i q^{54} +(-2.10968e12 - 1.73741e12i) q^{55} -7.58951e11 q^{56} -3.56231e9i q^{57} -1.58237e12 q^{58} -3.22811e12 q^{59} -7.11326e9 q^{60} -1.96411e12i q^{61} -2.26081e12i q^{62} +4.89579e12i q^{63} -5.49756e11 q^{64} -9.21426e12i q^{65} +(6.94211e9 - 8.42958e9i) q^{66} +6.50801e12 q^{67} +5.08320e12i q^{68} -6.88247e8 q^{69} -1.29932e13 q^{70} +2.49479e12 q^{71} +3.54633e12i q^{72} -1.88866e13i q^{73} +1.27235e13i q^{74} -8.39895e10 q^{75} -4.71341e12i q^{76} +(1.26806e13 - 1.53976e13i) q^{77} +3.68171e10 q^{78} -2.28648e13i q^{79} -9.41179e12 q^{80} +2.28762e13 q^{81} -7.82107e12 q^{82} +4.23928e13i q^{83} -5.19165e10i q^{84} +8.70240e13i q^{85} +1.14788e13 q^{86} -1.08243e11i q^{87} +(9.18533e12 - 1.11534e13i) q^{88} -1.04167e13 q^{89} +6.07129e13i q^{90} +6.72507e13 q^{91} -9.10642e11 q^{92} +1.54652e11 q^{93} +2.88718e13i q^{94} -8.06933e13i q^{95} -3.76064e10i q^{96} -3.99411e13 q^{97} -3.34459e13i q^{98} +(-7.19479e13 - 5.92521e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9}+O(q^{10}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9} + 20143042 q^{11} - 35995648 q^{12} + 62814720 q^{14} - 1359602 q^{15} + 939524096 q^{16} - 571457536 q^{20} - 2107666944 q^{22} - 7305755542 q^{23} + 19291879452 q^{25} - 6388480512 q^{26} + 34093422830 q^{27} - 33569873942 q^{31} + 2885838062 q^{33} + 167764701696 q^{34} - 90247757824 q^{36} + 73167823966 q^{37} + 71236111872 q^{38} - 222695314944 q^{42} - 165011800064 q^{44} + 2000205168616 q^{45} - 1612717386124 q^{47} + 294876348416 q^{48} + 3424602524990 q^{49} - 3530064068164 q^{53} - 3715439610854 q^{55} - 514578186240 q^{56} - 1374208002048 q^{58} - 818496564070 q^{59} + 11137859584 q^{60} - 7696581394432 q^{64} - 5938395621888 q^{66} + 16485465276922 q^{67} - 11394452631206 q^{69} - 392146020864 q^{70} - 19380879179878 q^{71} + 23016770893992 q^{75} + 60534793808304 q^{77} + 17335823992320 q^{78} + 4681380134912 q^{80} - 10394309810662 q^{81} - 79417078012416 q^{82} + 6375532305408 q^{86} + 17266007605248 q^{88} - 117770741987650 q^{89} + 150621364097712 q^{91} + 59848749400064 q^{92} + 27345122803162 q^{93} + 123398138843566 q^{97} + 118861332531788 q^{99}+O(q^{100}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9 + 20143042 * q^11 - 35995648 * q^12 + 62814720 * q^14 - 1359602 * q^15 + 939524096 * q^16 - 571457536 * q^20 - 2107666944 * q^22 - 7305755542 * q^23 + 19291879452 * q^25 - 6388480512 * q^26 + 34093422830 * q^27 - 33569873942 * q^31 + 2885838062 * q^33 + 167764701696 * q^34 - 90247757824 * q^36 + 73167823966 * q^37 + 71236111872 * q^38 - 222695314944 * q^42 - 165011800064 * q^44 + 2000205168616 * q^45 - 1612717386124 * q^47 + 294876348416 * q^48 + 3424602524990 * q^49 - 3530064068164 * q^53 - 3715439610854 * q^55 - 514578186240 * q^56 - 1374208002048 * q^58 - 818496564070 * q^59 + 11137859584 * q^60 - 7696581394432 * q^64 - 5938395621888 * q^66 + 16485465276922 * q^67 - 11394452631206 * q^69 - 392146020864 * q^70 - 19380879179878 * q^71 + 23016770893992 * q^75 + 60534793808304 * q^77 + 17335823992320 * q^78 + 4681380134912 * q^80 - 10394309810662 * q^81 - 79417078012416 * q^82 + 6375532305408 * q^86 + 17266007605248 * q^88 - 117770741987650 * q^89 + 150621364097712 * q^91 + 59848749400064 * q^92 + 27345122803162 * q^93 + 123398138843566 * q^97 + 118861332531788 * q^99

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