LMFDB - Embedded newform 11.15.b.b.10.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,15,Mod(10,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, 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("11.10");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	11.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:	$13.6761864967$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 163566 x^{10} + 10224581640 x^{8} + 305915789698560 x^{6} + \cdots + 66\!\cdots\!00 $ x^12 + 163566x^10 + 10224581640x^8 + 305915789698560x^6 + 4498726586018734080x^4 + 29831480122342818447360*x^2 + 66185787904796350690099200
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{6}\cdot 11^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.11
Root			$216.434i$ of defining polynomial
Character	$\chi$	$=$	11.10
Dual form			11.15.b.b.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+216.434i q^{2} -3231.82 q^{3} -30459.8 q^{4} -114987. q^{5} -699477. i q^{6} +1.23221e6i q^{7} -3.04649e6i q^{8} +5.66171e6 q^{9} +O(q^{10})$	\(q+216.434i q^{2} -3231.82 q^{3} -30459.8 q^{4} -114987. q^{5} -699477. i q^{6} +1.23221e6i q^{7} -3.04649e6i q^{8} +5.66171e6 q^{9} -2.48871e7i q^{10} +(-1.93612e7 + 2.21216e6i) q^{11} +9.84407e7 q^{12} +8.61879e7i q^{13} -2.66692e8 q^{14} +3.71617e8 q^{15} +1.60311e8 q^{16} +1.45522e8i q^{17} +1.22539e9i q^{18} +9.45428e7i q^{19} +3.50248e9 q^{20} -3.98228e9i q^{21} +(-4.78788e8 - 4.19043e9i) q^{22} +1.00361e9 q^{23} +9.84572e9i q^{24} +7.11848e9 q^{25} -1.86540e10 q^{26} -2.83994e9 q^{27} -3.75329e10i q^{28} +1.50920e10i q^{29} +8.04308e10i q^{30} -2.53876e10 q^{31} -1.52168e10i q^{32} +(6.25720e10 - 7.14932e9i) q^{33} -3.14960e10 q^{34} -1.41688e11i q^{35} -1.72455e11 q^{36} -3.26382e10 q^{37} -2.04623e10 q^{38} -2.78544e11i q^{39} +3.50307e11i q^{40} +8.68163e9i q^{41} +8.61903e11 q^{42} +2.89158e11i q^{43} +(5.89739e11 - 6.73821e10i) q^{44} -6.51023e11 q^{45} +2.17216e11i q^{46} +3.08548e11 q^{47} -5.18098e11 q^{48} -8.40117e11 q^{49} +1.54068e12i q^{50} -4.70302e11i q^{51} -2.62527e12i q^{52} -3.04987e11 q^{53} -6.14661e11i q^{54} +(2.22629e12 - 2.54370e11i) q^{55} +3.75391e12 q^{56} -3.05546e11i q^{57} -3.26643e12 q^{58} -6.88450e11 q^{59} -1.13194e13 q^{60} +5.98713e12i q^{61} -5.49476e12i q^{62} +6.97642e12i q^{63} +5.91998e12 q^{64} -9.91048e12i q^{65} +(1.54736e12 + 1.35427e13i) q^{66} -7.55309e12 q^{67} -4.43258e12i q^{68} -3.24349e12 q^{69} +3.06661e13 q^{70} +1.98269e12 q^{71} -1.72483e13i q^{72} +1.83297e13i q^{73} -7.06403e12i q^{74} -2.30057e13 q^{75} -2.87976e12i q^{76} +(-2.72585e12 - 2.38571e13i) q^{77} +6.02865e13 q^{78} +1.71598e12i q^{79} -1.84337e13 q^{80} -1.79016e13 q^{81} -1.87900e12 q^{82} +2.42539e12i q^{83} +1.21300e14i q^{84} -1.67331e13i q^{85} -6.25838e13 q^{86} -4.87748e13i q^{87} +(6.73934e12 + 5.89837e13i) q^{88} +3.96719e13 q^{89} -1.40904e14i q^{90} -1.06202e14 q^{91} -3.05698e13 q^{92} +8.20484e13 q^{93} +6.67803e13i q^{94} -1.08712e13i q^{95} +4.91780e13i q^{96} +1.34426e14 q^{97} -1.81830e14i q^{98} +(-1.09618e14 + 1.25246e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 5832 q^{3} - 130524 q^{4} - 135680 q^{5} + 13200780 q^{9}+O(q^{10}) $ 12 * q - 5832 * q^3 - 130524 * q^4 - 135680 * q^5 + 13200780 * q^9	\( 12 q - 5832 q^{3} - 130524 q^{4} - 135680 q^{5} + 13200780 q^{9} - 2225212 q^{11} + 40811892 q^{12} - 104225352 q^{14} - 135328320 q^{15} - 248620440 q^{16} + 3077616220 q^{20} - 2263930680 q^{22} + 5617677688 q^{23} + 4534941420 q^{25} - 22421106552 q^{26} - 16619859936 q^{27} + 73906813656 q^{31} + 154503019968 q^{33} - 189661264872 q^{34} - 15998386272 q^{36} - 32170218528 q^{37} - 450190787160 q^{38} + 1387253675640 q^{42} + 1658278243820 q^{44} - 1829643576360 q^{45} + 637903655272 q^{47} - 1287941662872 q^{48} - 5577020124564 q^{49} + 8629370688088 q^{53} + 6705223275960 q^{55} - 759657326064 q^{56} + 1308649899360 q^{58} - 319057951208 q^{59} - 23502810498420 q^{60} + 5684019519024 q^{64} + 7079527990920 q^{66} - 689205931848 q^{67} - 20471225254152 q^{69} + 41009932132680 q^{70} + 7251314650744 q^{71} - 50761855847880 q^{75} - 14619293932320 q^{77} + 81513511801800 q^{78} - 77504933615720 q^{80} + 6526391210604 q^{81} + 75766956787080 q^{82} - 124764637159152 q^{86} - 161556660706320 q^{88} + 227512316886784 q^{89} - 215922115692192 q^{91} + 60239663314612 q^{92} + 381197540672856 q^{93} + 23746610676192 q^{97} - 142689964303524 q^{99}+O(q^{100}) \) 12 * q - 5832 * q^3 - 130524 * q^4 - 135680 * q^5 + 13200780 * q^9 - 2225212 * q^11 + 40811892 * q^12 - 104225352 * q^14 - 135328320 * q^15 - 248620440 * q^16 + 3077616220 * q^20 - 2263930680 * q^22 + 5617677688 * q^23 + 4534941420 * q^25 - 22421106552 * q^26 - 16619859936 * q^27 + 73906813656 * q^31 + 154503019968 * q^33 - 189661264872 * q^34 - 15998386272 * q^36 - 32170218528 * q^37 - 450190787160 * q^38 + 1387253675640 * q^42 + 1658278243820 * q^44 - 1829643576360 * q^45 + 637903655272 * q^47 - 1287941662872 * q^48 - 5577020124564 * q^49 + 8629370688088 * q^53 + 6705223275960 * q^55 - 759657326064 * q^56 + 1308649899360 * q^58 - 319057951208 * q^59 - 23502810498420 * q^60 + 5684019519024 * q^64 + 7079527990920 * q^66 - 689205931848 * q^67 - 20471225254152 * q^69 + 41009932132680 * q^70 + 7251314650744 * q^71 - 50761855847880 * q^75 - 14619293932320 * q^77 + 81513511801800 * q^78 - 77504933615720 * q^80 + 6526391210604 * q^81 + 75766956787080 * q^82 - 124764637159152 * q^86 - 161556660706320 * q^88 + 227512316886784 * q^89 - 215922115692192 * q^91 + 60239663314612 * q^92 + 381197540672856 * q^93 + 23746610676192 * q^97 - 142689964303524 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			216.434i			1.69089i	0.534060	+	0.845447i	$0.320666\pi$
$2$			216.434i			1.69089i	−0.534060	+	0.845447i	$0.679334\pi$
$3$	−3231.82			−1.47774			−0.738871	−	0.673847i	$-0.764641\pi$
$3$	−3231.82			−1.47774			−0.738871	+	0.673847i	$0.764641\pi$
$4$	−30459.8			−1.85912
$5$	−114987.			−1.47183			−0.735916	−	0.677073i	$-0.763248\pi$
$5$	−114987.			−1.47183			−0.735916	+	0.677073i	$0.763248\pi$
$6$		−	699477.i		−	2.49870i
$7$			1.23221e6i			1.49623i	0.663569	+	0.748115i	$0.269041\pi$
$7$			1.23221e6i			1.49623i	−0.663569	+	0.748115i	$0.730959\pi$
$8$		−	3.04649e6i		−	1.45268i
$9$	5.66171e6			1.18372
$10$		−	2.48871e7i		−	2.48871i
$11$	−1.93612e7	+	2.21216e6i	−0.993536	+	0.113519i
$11$	−1.93612e7	+	2.21216e6i	−0.993536	+	0.113519i
$12$	9.84407e7			2.74730
$13$			8.61879e7i			1.37354i	0.726873	+	0.686772i	$0.240973\pi$
$13$			8.61879e7i			1.37354i	−0.726873	+	0.686772i	$0.759027\pi$
$14$	−2.66692e8			−2.52996
$15$	3.71617e8			2.17499
$16$	1.60311e8			0.597206
$17$			1.45522e8i			0.354639i	0.984153	+	0.177320i	$0.0567426\pi$
$17$			1.45522e8i			0.354639i	−0.984153	+	0.177320i	$0.943257\pi$
$18$			1.22539e9i			2.00155i
$19$			9.45428e7i			0.105768i	0.998601	+	0.0528839i	$0.0168413\pi$
$19$			9.45428e7i			0.105768i	−0.998601	+	0.0528839i	$0.983159\pi$
$20$	3.50248e9			2.73631
$21$		−	3.98228e9i		−	2.21104i
$22$	−4.78788e8	−	4.19043e9i	−0.191949	−	1.67996i
$23$	1.00361e9			0.294761			0.147381	−	0.989080i	$-0.452916\pi$
$23$	1.00361e9			0.294761			0.147381	+	0.989080i	$0.452916\pi$
$24$			9.84572e9i			2.14669i
$25$	7.11848e9			1.16629
$26$	−1.86540e10			−2.32252
$27$	−2.83994e9			−0.271496
$28$		−	3.75329e10i		−	2.78167i
$29$			1.50920e10i			0.874906i	0.899241	+	0.437453i	$0.144119\pi$
$29$			1.50920e10i			0.874906i	−0.899241	+	0.437453i	$0.855881\pi$
$30$			8.04308e10i			3.67768i
$31$	−2.53876e10			−0.922763			−0.461382	−	0.887202i	$-0.652646\pi$
$31$	−2.53876e10			−0.922763			−0.461382	+	0.887202i	$0.652646\pi$
$32$		−	1.52168e10i		−	0.442867i
$33$	6.25720e10	−	7.14932e9i	1.46819	−	0.167752i
$34$	−3.14960e10			−0.599657
$35$		−	1.41688e11i		−	2.20220i
$36$	−1.72455e11			−2.20068
$37$	−3.26382e10			−0.343807			−0.171903	−	0.985114i	$-0.554992\pi$
$37$	−3.26382e10			−0.343807			−0.171903	+	0.985114i	$0.554992\pi$
$38$	−2.04623e10			−0.178842
$39$		−	2.78544e11i		−	2.02974i
$40$			3.50307e11i			2.13810i
$41$			8.68163e9i			0.0445773i	0.999752	+	0.0222887i	$0.00709529\pi$
$41$			8.68163e9i			0.0445773i	−0.999752	+	0.0222887i	$0.992905\pi$
$42$	8.61903e11			3.73864
$43$			2.89158e11i			1.06379i	0.846810	+	0.531896i	$0.178520\pi$
$43$			2.89158e11i			1.06379i	−0.846810	+	0.531896i	$0.821480\pi$
$44$	5.89739e11	−	6.73821e10i	1.84710	−	0.211045i
$45$	−6.51023e11			−1.74224
$46$			2.17216e11i			0.498410i
$47$	3.08548e11			0.609028			0.304514	−	0.952508i	$-0.401506\pi$
$47$	3.08548e11			0.609028			0.304514	+	0.952508i	$0.401506\pi$
$48$	−5.18098e11			−0.882517
$49$	−8.40117e11			−1.23870
$50$			1.54068e12i			1.97207i
$51$		−	4.70302e11i		−	0.524065i
$52$		−	2.62527e12i		−	2.55358i
$53$	−3.04987e11			−0.259627			−0.129814	−	0.991538i	$-0.541438\pi$
$53$	−3.04987e11			−0.259627			−0.129814	+	0.991538i	$0.541438\pi$
$54$		−	6.14661e11i		−	0.459070i
$55$	2.22629e12	−	2.54370e11i	1.46232	−	0.167081i
$56$	3.75391e12			2.17354
$57$		−	3.05546e11i		−	0.156298i
$58$	−3.26643e12			−1.47937
$59$	−6.88450e11			−0.276636			−0.138318	−	0.990388i	$-0.544170\pi$
$59$	−6.88450e11			−0.276636			−0.138318	+	0.990388i	$0.544170\pi$
$60$	−1.13194e13			−4.04357
$61$			5.98713e12i			1.90506i	0.304439	+	0.952532i	$0.401531\pi$
$61$			5.98713e12i			1.90506i	−0.304439	+	0.952532i	$0.598469\pi$
$62$		−	5.49476e12i		−	1.56029i
$63$			6.97642e12i			1.77112i
$64$	5.91998e12			1.34605
$65$		−	9.91048e12i		−	2.02163i
$66$	1.54736e12	+	1.35427e13i	0.283651	+	2.48255i
$67$	−7.55309e12			−1.24624			−0.623119	−	0.782127i	$-0.714135\pi$
$67$	−7.55309e12			−1.24624			−0.623119	+	0.782127i	$0.714135\pi$
$68$		−	4.43258e12i		−	0.659316i
$69$	−3.24349e12			−0.435581
$70$	3.06661e13			3.72368
$71$	1.98269e12			0.217995			0.108998	−	0.994042i	$-0.465236\pi$
$71$	1.98269e12			0.217995			0.108998	+	0.994042i	$0.465236\pi$
$72$		−	1.72483e13i		−	1.71957i
$73$			1.83297e13i			1.65919i	0.558368	+	0.829594i	$0.311428\pi$
$73$			1.83297e13i			1.65919i	−0.558368	+	0.829594i	$0.688572\pi$
$74$		−	7.06403e12i		−	0.581340i
$75$	−2.30057e13			−1.72348
$76$		−	2.87976e12i		−	0.196635i
$77$	−2.72585e12	−	2.38571e13i	−0.169851	−	1.48656i
$78$	6.02865e13			3.43208
$79$			1.71598e12i			0.0893560i	0.999001	+	0.0446780i	$0.0142262\pi$
$79$			1.71598e12i			0.0893560i	−0.999001	+	0.0446780i	$0.985774\pi$
$80$	−1.84337e13			−0.878988
$81$	−1.79016e13			−0.782522
$82$	−1.87900e12			−0.0753755
$83$			2.42539e12i			0.0893787i	0.999001	+	0.0446894i	$0.0142298\pi$
$83$			2.42539e12i			0.0893787i	−0.999001	+	0.0446894i	$0.985770\pi$
$84$			1.21300e14i			4.11059i
$85$		−	1.67331e13i		−	0.521969i
$86$	−6.25838e13			−1.79876
$87$		−	4.87748e13i		−	1.29289i
$88$	6.73934e12	+	5.89837e13i	0.164907	+	1.44329i
$89$	3.96719e13			0.896919			0.448459	−	0.893803i	$-0.351973\pi$
$89$	3.96719e13			0.896919			0.448459	+	0.893803i	$0.351973\pi$
$90$		−	1.40904e14i		−	2.94595i
$91$	−1.06202e14			−2.05514
$92$	−3.05698e13			−0.547997
$93$	8.20484e13			1.36361
$94$			6.67803e13i			1.02980i
$95$		−	1.08712e13i		−	0.155672i
$96$			4.91780e13i			0.654444i
$97$	1.34426e14			1.66372			0.831861	−	0.554984i	$-0.187275\pi$
$97$	1.34426e14			1.66372			0.831861	+	0.554984i	$0.187275\pi$
$98$		−	1.81830e14i		−	2.09452i
$99$	−1.09618e14	+	1.25246e13i	−1.17607	+	0.134375i
$100$	−2.16827e14			−2.16827
$101$		−	1.26402e14i		−	1.17897i	−0.807779	−	0.589486i	$-0.799330\pi$
$101$		−	1.26402e14i		−	1.17897i	0.807779	−	0.589486i	$-0.200670\pi$
$102$	1.01789e14			0.886138
$103$	−6.34090e13			−0.515573			−0.257787	−	0.966202i	$-0.582993\pi$
$103$	−6.34090e13			−0.515573			−0.257787	+	0.966202i	$0.582993\pi$
$104$	2.62570e14			1.99532
$105$			4.57911e14i			3.25428i
$106$		−	6.60097e13i		−	0.439002i
$107$		−	1.39166e14i		−	0.866653i	−0.901237	−	0.433327i	$-0.857340\pi$
$107$		−	1.39166e14i		−	0.866653i	0.901237	−	0.433327i	$-0.142660\pi$
$108$	8.65041e13			0.504743
$109$		−	1.67916e14i		−	0.918557i	−0.888292	−	0.459279i	$-0.848108\pi$
$109$		−	1.67916e14i		−	0.918557i	0.888292	−	0.459279i	$-0.151892\pi$
$110$	5.50544e13	+	4.81845e14i	0.282516	+	2.47262i
$111$	1.05481e14			0.508058
$112$			1.97537e14i			0.893558i
$113$	2.28383e14			0.970766			0.485383	−	0.874302i	$-0.338680\pi$
$113$	2.28383e14			0.970766			0.485383	+	0.874302i	$0.338680\pi$
$114$	6.61306e13			0.264282
$115$	−1.15402e14			−0.433839
$116$		−	4.59700e14i		−	1.62656i
$117$			4.87971e14i			1.62590i
$118$		−	1.49004e14i		−	0.467762i
$119$	−1.79314e14			−0.530621
$120$		−	1.13213e15i		−	3.15956i
$121$	3.69962e14	−	8.56603e13i	0.974227	−	0.225570i
$122$	−1.29582e15			−3.22126
$123$		−	2.80575e13i		−	0.0658738i
$124$	7.73303e14			1.71553
$125$	−1.16707e14			−0.244753
$126$	−1.50994e15			−2.99478
$127$			2.17352e14i			0.407884i	0.978983	+	0.203942i	$0.0653755\pi$
$127$			2.17352e14i			0.407884i	−0.978983	+	0.203942i	$0.934625\pi$
$128$			1.03197e15i			1.83316i
$129$		−	9.34508e14i		−	1.57201i
$130$	2.14497e15			3.41836
$131$			1.24242e15i			1.87660i	0.345826	+	0.938299i	$0.387599\pi$
$131$			1.24242e15i			1.87660i	−0.345826	+	0.938299i	$0.612401\pi$
$132$	−1.90593e15	+	2.17767e14i	−2.72954	+	0.311871i
$133$	−1.16497e14			−0.158253
$134$		−	1.63475e15i		−	2.10726i
$135$	3.26556e14			0.399596
$136$	4.43332e14			0.515177
$137$	1.06234e15			1.17279			0.586396	−	0.810025i	$-0.300546\pi$
$137$	1.06234e15			1.17279			0.586396	+	0.810025i	$0.300546\pi$
$138$		−	7.02003e14i		−	0.736522i
$139$			8.01502e14i			0.799468i	0.916631	+	0.399734i	$0.130898\pi$
$139$			8.01502e14i			0.799468i	−0.916631	+	0.399734i	$0.869102\pi$
$140$			4.31579e15i			4.09415i
$141$	−9.97172e14			−0.899987
$142$			4.29123e14i			0.368607i
$143$	−1.90662e14	−	1.66870e15i	−0.155923	−	1.36467i
$144$	9.07637e14			0.706927
$145$		−	1.73539e15i		−	1.28772i
$146$	−3.96718e15			−2.80551
$147$	2.71511e15			1.83049
$148$	9.94154e14			0.639178
$149$			2.73497e14i			0.167745i	0.996477	+	0.0838724i	$0.0267288\pi$
$149$			2.73497e14i			0.167745i	−0.996477	+	0.0838724i	$0.973271\pi$
$150$		−	4.97921e15i		−	2.91422i
$151$		−	2.74725e15i		−	1.53483i	−0.641151	−	0.767415i	$-0.721543\pi$
$151$		−	2.74725e15i		−	1.53483i	0.641151	−	0.767415i	$-0.278457\pi$
$152$	2.88024e14			0.153647
$153$			8.23904e14i			0.419794i
$154$	5.16349e15	−	5.89968e14i	2.51361	−	0.287199i
$155$	2.91925e15			1.35815
$156$			8.48440e15i			3.77354i
$157$	−1.53780e15			−0.654036			−0.327018	−	0.945018i	$-0.606044\pi$
$157$	−1.53780e15			−0.654036			−0.327018	+	0.945018i	$0.606044\pi$
$158$	−3.71398e14			−0.151091
$159$	9.85664e14			0.383662
$160$			1.74973e15i			0.651827i
$161$			1.23666e15i			0.441031i
$162$		−	3.87452e15i		−	1.32316i
$163$	−2.78984e15			−0.912569			−0.456285	−	0.889834i	$-0.650820\pi$
$163$	−2.78984e15			−0.912569			−0.456285	+	0.889834i	$0.650820\pi$
$164$		−	2.64441e14i		−	0.0828746i
$165$	−7.19496e15	+	8.22079e14i	−2.16093	+	0.246903i
$166$	−5.24937e14			−0.151130
$167$			1.12259e15i			0.309889i	0.987923	+	0.154945i	$0.0495199\pi$
$167$			1.12259e15i			0.309889i	−0.987923	+	0.154945i	$0.950480\pi$
$168$	−1.21320e16			−3.21194
$169$	−3.49097e15			−0.886624
$170$	3.62163e15			0.882594
$171$			5.35274e14i			0.125200i
$172$		−	8.80771e15i		−	1.97772i
$173$			1.82532e15i			0.393564i	0.980447	+	0.196782i	$0.0630491\pi$
$173$			1.82532e15i			0.393564i	−0.980447	+	0.196782i	$0.936951\pi$
$174$	1.05565e16			2.18613
$175$			8.77145e15i			1.74504i
$176$	−3.10382e15	+	3.54635e14i	−0.593346	+	0.0677943i
$177$	2.22495e15			0.408797
$178$			8.58637e15i			1.51659i
$179$	−9.28031e15			−1.57613			−0.788063	−	0.615594i	$-0.788916\pi$
$179$	−9.28031e15			−1.57613			−0.788063	+	0.615594i	$0.788916\pi$
$180$	1.98300e16			3.23904
$181$	2.83585e15			0.445588			0.222794	−	0.974866i	$-0.428482\pi$
$181$	2.83585e15			0.445588			0.222794	+	0.974866i	$0.428482\pi$
$182$		−	2.29857e16i		−	3.47502i
$183$		−	1.93493e16i		−	2.81519i
$184$		−	3.05749e15i		−	0.428194i
$185$	3.75297e15			0.506026
$186$			1.77581e16i			2.30571i
$187$	−3.21919e14	−	2.81748e15i	−0.0402583	−	0.352347i
$188$	−9.39831e15			−1.13226
$189$		−	3.49940e15i		−	0.406220i
$190$	2.35290e15			0.263226
$191$	−8.36971e15			−0.902562			−0.451281	−	0.892382i	$-0.649033\pi$
$191$	−8.36971e15			−0.902562			−0.451281	+	0.892382i	$0.649033\pi$
$192$	−1.91323e16			−1.98911
$193$			1.21305e16i			1.21612i	0.793889	+	0.608062i	$0.208053\pi$
$193$			1.21305e16i			1.21612i	−0.793889	+	0.608062i	$0.791947\pi$
$194$			2.90944e16i			2.81318i
$195$			3.20289e16i			2.98744i
$196$	2.55898e16			2.30290
$197$		−	8.50358e15i		−	0.738479i	−0.929334	−	0.369240i	$-0.879618\pi$
$197$		−	8.50358e15i		−	0.738479i	0.929334	−	0.369240i	$-0.120382\pi$
$198$	−2.71076e15	−	2.37250e16i	−0.227214	−	1.98861i
$199$	1.38258e16			1.11871			0.559356	−	0.828927i	$-0.311048\pi$
$199$	1.38258e16			1.11871			0.559356	+	0.828927i	$0.311048\pi$
$200$		−	2.16864e16i		−	1.69425i
$201$	2.44103e16			1.84162
$202$	2.73577e16			1.99351
$203$	−1.85965e16			−1.30906
$204$			1.43253e16i			0.974300i
$205$		−	9.98274e14i		−	0.0656104i
$206$		−	1.37239e16i		−	0.871780i
$207$	5.68216e15			0.348916
$208$			1.38169e16i			0.820289i
$209$	−2.09144e14	−	1.83046e15i	−0.0120067	−	0.105084i
$210$	−9.91076e16			−5.50265
$211$			1.24848e16i			0.670507i	0.942128	+	0.335254i	$0.108822\pi$
$211$			1.24848e16i			0.670507i	−0.942128	+	0.335254i	$0.891178\pi$
$212$	9.28985e15			0.482678
$213$	−6.40772e15			−0.322141
$214$	3.01202e16			1.46542
$215$		−	3.32494e16i		−	1.56572i
$216$			8.65185e15i			0.394396i
$217$		−	3.12829e16i		−	1.38067i
$218$	3.63428e16			1.55318
$219$		−	5.92384e16i		−	2.45185i
$220$	−6.78122e16	+	7.74806e15i	−2.71862	+	0.310624i
$221$	−1.25422e16			−0.487112
$222$			2.28297e16i			0.859071i
$223$	−4.45219e16			−1.62345			−0.811726	−	0.584038i	$-0.801472\pi$
$223$	−4.45219e16			−1.62345			−0.811726	+	0.584038i	$0.801472\pi$
$224$	1.87503e16			0.662631
$225$	4.03028e16			1.38057
$226$			4.94299e16i			1.64146i
$227$			9.63888e15i			0.310346i	0.987887	+	0.155173i	$0.0495934\pi$
$227$			9.63888e15i			0.310346i	−0.987887	+	0.155173i	$0.950407\pi$
$228$			9.30687e15i			0.290576i
$229$	3.26013e16			0.987158			0.493579	−	0.869701i	$-0.335688\pi$
$229$	3.26013e16			0.987158			0.493579	+	0.869701i	$0.335688\pi$
$230$		−	2.49770e16i		−	0.733576i
$231$	8.80947e15	+	7.71018e16i	0.250995	+	2.19675i
$232$	4.59777e16			1.27096
$233$			1.53285e16i			0.411157i	0.978641	+	0.205579i	$0.0659076\pi$
$233$			1.53285e16i			0.411157i	−0.978641	+	0.205579i	$0.934092\pi$
$234$	−1.05614e17			−2.74922
$235$	−3.54790e16			−0.896387
$236$	2.09701e16			0.514299
$237$		−	5.54576e15i		−	0.132045i
$238$		−	3.88096e16i		−	0.897224i
$239$		−	2.69062e16i		−	0.604042i	−0.953301	−	0.302021i	$-0.902339\pi$
$239$		−	2.69062e16i		−	0.604042i	0.953301	−	0.302021i	$-0.0976612\pi$
$240$	5.95745e16			1.29892
$241$			7.37881e16i			1.56267i	0.624112	+	0.781335i	$0.285461\pi$
$241$			7.37881e16i			1.56267i	−0.624112	+	0.781335i	$0.714539\pi$
$242$	1.85398e16	+	8.00726e16i	0.381415	+	1.64731i
$243$	7.14382e16			1.42786
$244$		−	1.82367e17i		−	3.54174i
$245$	9.66025e16			1.82316
$246$	6.07260e15			0.111386
$247$	−8.14844e15			−0.145277
$248$			7.73432e16i			1.34048i
$249$		−	7.83842e15i		−	0.132079i
$250$		−	2.52594e16i		−	0.413851i
$251$	−5.43505e16			−0.865940			−0.432970	−	0.901408i	$-0.642534\pi$
$251$	−5.43505e16			−0.865940			−0.432970	+	0.901408i	$0.642534\pi$
$252$		−	2.12500e17i		−	3.29273i
$253$	−1.94311e16	+	2.22015e15i	−0.292856	+	0.0334610i
$254$	−4.70424e16			−0.689689
$255$			5.40785e16i			0.771336i
$256$	−1.26362e17			−1.75362
$257$	4.36745e16			0.589788			0.294894	−	0.955530i	$-0.404716\pi$
$257$	4.36745e16			0.589788			0.294894	+	0.955530i	$0.404716\pi$
$258$	2.02260e17			2.65810
$259$		−	4.02171e16i		−	0.514414i
$260$			3.01871e17i			3.75845i
$261$			8.54467e16i			1.03565i
$262$	−2.68903e17			−3.17313
$263$		−	1.38926e17i		−	1.59622i	−0.602510	−	0.798111i	$-0.705833\pi$
$263$		−	1.38926e17i		−	1.59622i	0.602510	−	0.798111i	$-0.294167\pi$
$264$	−2.17803e16	−	1.90625e17i	−0.243690	−	2.13281i
$265$	3.50695e16			0.382128
$266$		−	2.52139e16i		−	0.267589i
$267$	−1.28213e17			−1.32542
$268$	2.30066e17			2.31691
$269$	−1.18765e17			−1.16526			−0.582630	−	0.812737i	$-0.697976\pi$
$269$	−1.18765e17			−1.16526			−0.582630	+	0.812737i	$0.697976\pi$
$270$			7.06780e16i			0.675675i
$271$			1.46728e17i			1.36688i	0.730009	+	0.683438i	$0.239516\pi$
$271$			1.46728e17i			1.36688i	−0.730009	+	0.683438i	$0.760484\pi$
$272$			2.33288e16i			0.211793i
$273$	3.43224e17			3.03696
$274$			2.29927e17i			1.98306i
$275$	−1.37822e17	+	1.57472e16i	−1.15875	+	0.132396i
$276$	9.87962e16			0.809798
$277$		−	4.78088e16i		−	0.382075i	−0.981583	−	0.191038i	$-0.938815\pi$
$277$		−	4.78088e16i		−	0.382075i	0.981583	−	0.191038i	$-0.0611853\pi$
$278$	−1.73473e17			−1.35182
$279$	−1.43737e17			−1.09230
$280$	−4.31651e17			−3.19909
$281$			5.07327e16i			0.366728i	0.983045	+	0.183364i	$0.0586987\pi$
$281$			5.07327e16i			0.366728i	−0.983045	+	0.183364i	$0.941301\pi$
$282$		−	2.15822e17i		−	1.52178i
$283$		−	1.97808e17i		−	1.36062i	−0.732923	−	0.680312i	$-0.761844\pi$
$283$		−	1.97808e17i		−	1.36062i	0.732923	−	0.680312i	$-0.238156\pi$
$284$	−6.03925e16			−0.405279
$285$			3.51338e16i			0.230044i
$286$	3.61164e17	−	4.12657e16i	2.30750	−	0.263650i
$287$	−1.06976e16			−0.0666979
$288$		−	8.61532e16i		−	0.524232i
$289$	1.47201e17			0.874231
$290$	3.75597e17			2.17739
$291$	−4.34441e17			−2.45855
$292$		−	5.58319e17i		−	3.08463i
$293$		−	2.07336e17i		−	1.11841i	−0.829029	−	0.559206i	$-0.811106\pi$
$293$		−	2.07336e17i		−	1.11841i	0.829029	−	0.559206i	$-0.188894\pi$
$294$			5.87643e17i			3.09515i
$295$	7.91628e16			0.407162
$296$			9.94320e16i			0.499441i
$297$	5.49847e16	−	6.28242e15i	0.269741	−	0.0308199i
$298$	−5.91942e16			−0.283639
$299$			8.64991e16i			0.404868i
$300$	7.00748e17			3.20415
$301$	−3.56304e17			−1.59168
$302$	5.94600e17			2.59523
$303$			4.08508e17i			1.74222i
$304$			1.51563e16i			0.0631652i
$305$		−	6.88441e17i		−	2.80393i
$306$	−1.78321e17			−0.709828
$307$			1.13606e17i			0.442010i	0.975273	+	0.221005i	$0.0709338\pi$
$307$			1.13606e17i			0.442010i	−0.975273	+	0.221005i	$0.929066\pi$
$308$	8.30289e16	+	7.26682e17i	0.315772	+	2.76369i
$309$	2.04927e17			0.761885
$310$			6.31825e17i			2.29649i
$311$	3.10253e17			1.10254			0.551268	−	0.834328i	$-0.314144\pi$
$311$	3.10253e17			1.10254			0.551268	+	0.834328i	$0.314144\pi$
$312$	−8.48581e17			−2.94857
$313$	−2.93282e17			−0.996496			−0.498248	−	0.867035i	$-0.666023\pi$
$313$	−2.93282e17			−0.996496			−0.498248	+	0.867035i	$0.666023\pi$
$314$		−	3.32832e17i		−	1.10591i
$315$		−	8.02197e17i		−	2.60680i
$316$		−	5.22686e16i		−	0.166123i
$317$	−5.88826e14			−0.00183051			−0.000915255	−	1.00000i	$-0.500291\pi$
$317$	−5.88826e14			−0.00183051			−0.000915255		1.00000i	$0.500291\pi$
$318$			2.13332e17i			0.648732i
$319$	−3.33860e16	−	2.92200e17i	−0.0993185	−	0.869251i
$320$	−6.80720e17			−1.98116
$321$			4.49759e17i			1.28069i
$322$	−2.67655e17			−0.745736
$323$	−1.37581e16			−0.0375094
$324$	5.45280e17			1.45480
$325$			6.13526e17i			1.60195i
$326$		−	6.03817e17i		−	1.54306i
$327$			5.42674e17i			1.35739i
$328$	2.64485e16			0.0647566
$329$			3.80195e17i			0.911246i
$330$	−1.77926e17	−	1.55724e18i	−0.417486	−	3.65390i
$331$	1.96885e16			0.0452290			0.0226145	−	0.999744i	$-0.492801\pi$
$331$	1.96885e16			0.0452290			0.0226145	+	0.999744i	$0.492801\pi$
$332$		−	7.38768e16i		−	0.166166i
$333$	−1.84788e17			−0.406972
$334$	−2.42967e17			−0.523989
$335$	8.68507e17			1.83425
$336$		−	6.38405e17i		−	1.32045i
$337$			7.81714e16i			0.158357i	0.996860	+	0.0791787i	$0.0252298\pi$
$337$			7.81714e16i			0.158357i	−0.996860	+	0.0791787i	$0.974770\pi$
$338$		−	7.55566e17i		−	1.49919i
$339$	−7.38093e17			−1.43454
$340$			5.09688e17i			0.970403i
$341$	4.91535e17	−	5.61616e16i	0.916799	−	0.104751i
$342$	−1.15852e17			−0.211699
$343$		−	1.99488e17i		−	0.357155i
$344$	8.80918e17			1.54535
$345$	3.72959e17			0.641103
$346$	−3.95061e17			−0.665475
$347$			7.55434e17i			1.24707i	0.781796	+	0.623534i	$0.214304\pi$
$347$			7.55434e17i			1.24707i	−0.781796	+	0.623534i	$0.785696\pi$
$348$			1.48567e18i			2.40363i
$349$			5.54478e17i			0.879239i	0.898184	+	0.439619i	$0.144887\pi$
$349$			5.54478e17i			0.879239i	−0.898184	+	0.439619i	$0.855113\pi$
$350$	−1.89844e18			−2.95068
$351$		−	2.44769e17i		−	0.372911i
$352$	3.36621e16	+	2.94616e17i	0.0502739	+	0.440005i
$353$	2.09705e17			0.307034			0.153517	−	0.988146i	$-0.450940\pi$
$353$	2.09705e17			0.307034			0.153517	+	0.988146i	$0.450940\pi$
$354$			4.81556e17i			0.691232i
$355$	−2.27984e17			−0.320853
$356$	−1.20840e18			−1.66748
$357$	5.79510e17			0.784122
$358$		−	2.00858e18i		−	2.66506i
$359$		−	7.16006e17i		−	0.931656i	−0.884875	−	0.465828i	$-0.845757\pi$
$359$		−	7.16006e17i		−	0.931656i	0.884875	−	0.465828i	$-0.154243\pi$
$360$			1.98333e18i			2.53092i
$361$	7.90068e17			0.988813
$362$			6.13776e17i			0.753442i
$363$	−1.19565e18	+	2.76839e17i	−1.43966	+	0.333335i
$364$	3.23488e18			3.82075
$365$		−	2.10768e18i		−	2.44205i
$366$	4.18786e18			4.76019
$367$	−6.10608e17			−0.680927			−0.340463	−	0.940258i	$-0.610584\pi$
$367$	−6.10608e17			−0.680927			−0.340463	+	0.940258i	$0.610584\pi$
$368$	1.60890e17			0.176033
$369$			4.91529e16i			0.0527672i
$370$			8.12271e17i			0.855635i
$371$		−	3.75808e17i		−	0.388462i
$372$	−2.49918e18			−2.53511
$373$			5.55797e17i			0.553292i	0.960972	+	0.276646i	$0.0892229\pi$
$373$			5.55797e17i			0.553292i	−0.960972	+	0.276646i	$0.910777\pi$
$374$	6.09800e17	−	6.96743e16i	0.595780	−	0.0680724i
$375$	3.77177e17			0.361682
$376$		−	9.39988e17i		−	0.884723i
$377$	−1.30075e18			−1.20172
$378$	7.57391e17			0.686875
$379$	8.01136e17			0.713234			0.356617	−	0.934251i	$-0.383930\pi$
$379$	8.01136e17			0.713234			0.356617	+	0.934251i	$0.383930\pi$
$380$			3.31134e17i			0.289414i
$381$		−	7.02443e17i		−	0.602748i
$382$		−	1.81149e18i		−	1.52614i
$383$	−3.48384e17			−0.288182			−0.144091	−	0.989564i	$-0.546026\pi$
$383$	−3.48384e17			−0.288182			−0.144091	+	0.989564i	$0.546026\pi$
$384$		−	3.33516e18i		−	2.70893i
$385$	3.13437e17	+	2.74325e18i	0.249992	+	2.18796i
$386$	−2.62546e18			−2.05634
$387$			1.63713e18i			1.25923i
$388$	−4.09459e18			−3.09306
$389$	2.17885e18			1.61651			0.808257	−	0.588830i	$-0.200411\pi$
$389$	2.17885e18			1.61651			0.808257	+	0.588830i	$0.200411\pi$
$390$	−6.93215e18			−5.05145
$391$			1.46048e17i			0.104534i
$392$			2.55941e18i			1.79944i
$393$		−	4.01530e18i		−	2.77313i
$394$	1.84047e18			1.24869
$395$		−	1.97316e17i		−	0.131517i
$396$	3.33893e18	−	3.81498e17i	2.18646	−	0.249819i
$397$	1.78143e18			1.14613			0.573066	−	0.819509i	$-0.305754\pi$
$397$	1.78143e18			1.14613			0.573066	+	0.819509i	$0.305754\pi$
$398$			2.99238e18i			1.89162i
$399$	3.76496e17			0.233857
$400$	1.14117e18			0.696517
$401$	−1.73057e18			−1.03795			−0.518977	−	0.854788i	$-0.673687\pi$
$401$	−1.73057e18			−1.03795			−0.518977	+	0.854788i	$0.673687\pi$
$402$			5.28322e18i			3.11398i
$403$		−	2.18811e18i		−	1.26746i
$404$			3.85017e18i			2.19185i
$405$	2.05845e18			1.15174
$406$		−	4.02493e18i		−	2.21348i
$407$	6.31915e17	−	7.22011e16i	0.341584	−	0.0390286i
$408$	−1.43277e18			−0.761299
$409$			2.77448e18i			1.44917i	0.689186	+	0.724585i	$0.257968\pi$
$409$			2.77448e18i			1.44917i	−0.689186	+	0.724585i	$0.742032\pi$
$410$	2.16061e17			0.110940
$411$	−3.43330e18			−1.73308
$412$	1.93143e18			0.958513
$413$		−	8.48315e17i		−	0.413911i
$414$			1.22981e18i			0.589980i
$415$		−	2.78888e17i		−	0.131551i
$416$	1.31150e18			0.608298
$417$		−	2.59031e18i		−	1.18141i
$418$	3.96175e17	−	4.52660e16i	0.177686	−	0.0203020i
$419$	−2.14535e18			−0.946238			−0.473119	−	0.880999i	$-0.656872\pi$
$419$	−2.14535e18			−0.946238			−0.473119	+	0.880999i	$0.656872\pi$
$420$		−	1.39479e19i		−	6.05010i
$421$	2.13232e18			0.909656			0.454828	−	0.890579i	$-0.349701\pi$
$421$	2.13232e18			0.909656			0.454828	+	0.890579i	$0.349701\pi$
$422$	−2.70213e18			−1.13376
$423$	1.74691e18			0.720921
$424$			9.29140e17i			0.377155i
$425$			1.03590e18i			0.413612i
$426$		−	1.38685e18i		−	0.544706i
$427$	−7.37739e18			−2.85041
$428$			4.23896e18i			1.61121i
$429$	6.16185e17	+	5.39295e18i	0.230415	+	2.01662i
$430$	7.19632e18			2.64747
$431$		−	2.36238e17i		−	0.0855083i	−0.999086	−	0.0427542i	$-0.986387\pi$
$431$		−	2.36238e17i		−	0.0855083i	0.999086	−	0.0427542i	$-0.0136132\pi$
$432$	−4.55275e17			−0.162139
$433$	7.57535e17			0.265453			0.132726	−	0.991153i	$-0.457627\pi$
$433$	7.57535e17			0.265453			0.132726	+	0.991153i	$0.457627\pi$
$434$	6.77069e18			2.33456
$435$			5.60846e18i			1.90291i
$436$			5.11469e18i			1.70771i
$437$			9.48842e16i			0.0311763i
$438$	1.28212e19			4.14582
$439$		−	3.62582e18i		−	1.15386i	−0.816792	−	0.576932i	$-0.804250\pi$
$439$		−	3.62582e18i		−	1.15386i	0.816792	−	0.576932i	$-0.195750\pi$
$440$	−7.74936e17	−	6.78236e18i	−0.242715	−	2.12428i
$441$	−4.75650e18			−1.46628
$442$		−	2.71457e18i		−	0.823655i
$443$	−1.35736e18			−0.405386			−0.202693	−	0.979242i	$-0.564969\pi$
$443$	−1.35736e18			−0.405386			−0.202693	+	0.979242i	$0.564969\pi$
$444$	−3.21293e18			−0.944540
$445$	−4.56175e18			−1.32011
$446$		−	9.63607e18i		−	2.74508i
$447$		−	8.83895e17i		−	0.247884i
$448$			7.29466e18i			2.01400i
$449$	−4.69344e18			−1.27575			−0.637877	−	0.770138i	$-0.720187\pi$
$449$	−4.69344e18			−1.27575			−0.637877	+	0.770138i	$0.720187\pi$
$450$			8.72290e18i			2.33439i
$451$	−1.92052e16	−	1.68087e17i	−0.00506038	−	0.0442892i
$452$	−6.95650e18			−1.80477
$453$			8.87864e18i			2.26808i
$454$	−2.08618e18			−0.524761
$455$	1.22118e19			3.02482
$456$	−9.30842e17			−0.227050
$457$		−	4.44013e18i		−	1.06655i	−0.845941	−	0.533276i	$-0.820961\pi$
$457$		−	4.44013e18i		−	1.06655i	0.845941	−	0.533276i	$-0.179039\pi$
$458$			7.05604e18i			1.66918i
$459$		−	4.13274e17i		−	0.0962830i
$460$	3.51513e18			0.806559
$461$		−	1.09365e18i		−	0.247157i	−0.992335	−	0.123579i	$-0.960563\pi$
$461$		−	1.09365e18i		−	0.247157i	0.992335	−	0.123579i	$-0.0394371\pi$
$462$	−1.66875e19	+	1.90667e18i	−3.71447	+	0.424406i
$463$	5.29701e18			1.16135			0.580676	−	0.814135i	$-0.302788\pi$
$463$	5.29701e18			1.16135			0.580676	+	0.814135i	$0.302788\pi$
$464$			2.41942e18i			0.522500i
$465$	−9.43449e18			−2.00700
$466$	−3.31761e18			−0.695223
$467$	6.80615e18			1.40502			0.702511	−	0.711673i	$-0.252062\pi$
$467$	6.80615e18			1.40502			0.702511	+	0.711673i	$0.252062\pi$
$468$		−	1.48635e19i		−	3.02274i
$469$		−	9.30699e18i		−	1.86466i
$470$		−	7.67886e18i		−	1.51570i
$471$	4.96989e18			0.966497
$472$			2.09736e18i			0.401863i
$473$	−6.39666e17	−	5.59845e18i	−0.120761	−	1.05691i
$474$	1.20029e18			0.223274
$475$			6.73001e17i			0.123356i
$476$	5.46186e18			0.986489
$477$	−1.72675e18			−0.307327
$478$	5.82342e18			1.02137
$479$			9.93370e18i			1.71697i	0.512840	+	0.858484i	$0.328593\pi$
$479$			9.93370e18i			1.71697i	−0.512840	+	0.858484i	$0.671407\pi$
$480$		−	5.65483e18i		−	0.963232i
$481$		−	2.81302e18i		−	0.472234i
$482$	−1.59703e19			−2.64231
$483$		−	3.99666e18i		−	0.651730i
$484$	−1.12690e19	+	2.60920e18i	−1.81120	+	0.419362i
$485$	−1.54572e19			−2.44872
$486$			1.54617e19i			2.41436i
$487$	9.72150e18			1.49634			0.748171	−	0.663506i	$-0.230932\pi$
$487$	9.72150e18			1.49634			0.748171	+	0.663506i	$0.230932\pi$
$488$	1.82397e19			2.76745
$489$	9.01626e18			1.34854
$490$			2.09081e19i			3.08278i
$491$		−	9.89496e18i		−	1.43828i	−0.694865	−	0.719140i	$-0.744536\pi$
$491$		−	9.89496e18i		−	1.43828i	0.694865	−	0.719140i	$-0.255464\pi$
$492$			8.54626e17i			0.122467i
$493$	−2.19622e18			−0.310276
$494$		−	1.76360e18i		−	0.245647i
$495$	1.26046e19	−	1.44017e18i	1.73098	−	0.197778i
$496$	−4.06993e18			−0.551080
$497$			2.44309e18i			0.326171i
$498$	1.69650e18			0.223331
$499$	2.29902e18			0.298427			0.149214	−	0.988805i	$-0.452326\pi$
$499$	2.29902e18			0.298427			0.149214	+	0.988805i	$0.452326\pi$
$500$	3.55488e18			0.455025
$501$		−	3.62801e18i		−	0.457936i
$502$		−	1.17633e19i		−	1.46421i
$503$			1.08258e19i			1.32888i	0.747342	+	0.664440i	$0.231330\pi$
$503$			1.08258e19i			1.32888i	−0.747342	+	0.664440i	$0.768670\pi$
$504$	2.12536e19			2.57287
$505$			1.45345e19i			1.73525i
$506$	−4.80517e17	−	4.20556e18i	−0.0565790	−	0.495188i
$507$	1.12822e19			1.31020
$508$		−	6.62050e18i		−	0.758306i
$509$	−3.80972e18			−0.430397			−0.215198	−	0.976570i	$-0.569040\pi$
$509$	−3.80972e18			−0.430397			−0.215198	+	0.976570i	$0.569040\pi$
$510$	−1.17045e19			−1.30425
$511$	−2.25860e19			−2.48253
$512$		−	1.04412e19i		−	1.13203i
$513$		−	2.68496e17i		−	0.0287155i
$514$			9.45266e18i			0.997268i
$515$	7.29121e18			0.758838
$516$			2.84650e19i			2.92255i
$517$	−5.97385e18	+	6.82558e17i	−0.605091	+	0.0691363i
$518$	8.70436e18			0.869819
$519$		−	5.89910e18i		−	0.581586i
$520$	−3.01922e19			−2.93678
$521$	5.80755e18			0.557352			0.278676	−	0.960385i	$-0.410105\pi$
$521$	5.80755e18			0.557352			0.278676	+	0.960385i	$0.410105\pi$
$522$	−1.84936e19			−1.75117
$523$			9.72444e18i			0.908558i	0.890859	+	0.454279i	$0.150103\pi$
$523$			9.72444e18i			0.908558i	−0.890859	+	0.454279i	$0.849897\pi$
$524$		−	3.78440e19i		−	3.48882i
$525$		−	2.83478e19i		−	2.57872i
$526$	3.00684e19			2.69904
$527$		−	3.69446e18i		−	0.327248i
$528$	1.00310e19	−	1.14612e18i	0.876813	−	0.100183i
$529$	−1.05856e19			−0.913116
$530$			7.59025e18i			0.646138i
$531$	−3.89781e18			−0.327460
$532$	3.54846e18			0.294211
$533$	−7.48251e17			−0.0612289
$534$		−	2.77496e19i		−	2.24114i
$535$			1.60022e19i			1.27557i
$536$			2.30104e19i			1.81038i
$537$	2.99923e19			2.32911
$538$		−	2.57049e19i		−	1.97033i
$539$	1.62657e19	−	1.85848e18i	1.23070	−	0.140616i
$540$	−9.94684e18			−0.742897
$541$		−	1.53769e19i		−	1.13367i	−0.823831	−	0.566835i	$-0.808168\pi$
$541$		−	1.53769e19i		−	1.13367i	0.823831	−	0.566835i	$-0.191832\pi$
$542$	−3.17570e19			−2.31124
$543$	−9.16498e18			−0.658465
$544$	2.21438e18			0.157058
$545$			1.93081e19i			1.35196i
$546$			7.42856e19i			5.13518i
$547$		−	4.65258e18i		−	0.317529i	−0.987317	−	0.158764i	$-0.949249\pi$
$547$		−	4.65258e18i		−	0.317529i	0.987317	−	0.158764i	$-0.0507510\pi$
$548$	−3.23588e19			−2.18036
$549$			3.38974e19i			2.25507i
$550$	−3.40824e18	−	2.98295e19i	−0.223868	−	1.95933i
$551$	−1.42684e18			−0.0925369
$552$			9.88127e18i			0.632760i
$553$	−2.11445e18			−0.133697
$554$	1.03475e19			0.646049
$555$	−1.21289e19			−0.747776
$556$		−	2.44136e19i		−	1.48631i
$557$			1.75369e19i			1.05430i	0.849771	+	0.527152i	$0.176740\pi$
$557$			1.75369e19i			1.05430i	−0.849771	+	0.527152i	$0.823260\pi$
$558$		−	3.11097e19i		−	1.84696i
$559$	−2.49219e19			−1.46116
$560$		−	2.27142e19i		−	1.31517i
$561$	1.04038e18	+	9.10561e18i	0.0594914	+	0.520678i
$562$	−1.09803e19			−0.620098
$563$			1.49013e19i			0.831126i	0.909564	+	0.415563i	$0.136415\pi$
$563$			1.49013e19i			0.831126i	−0.909564	+	0.415563i	$0.863585\pi$
$564$	3.03737e19			1.67318
$565$	−2.62610e19			−1.42880
$566$	4.28124e19			2.30067
$567$		−	2.20585e19i		−	1.17083i
$568$		−	6.04026e18i		−	0.316677i
$569$			1.20137e19i			0.622146i	0.950386	+	0.311073i	$0.100688\pi$
$569$			1.20137e19i			0.622146i	−0.950386	+	0.311073i	$0.899312\pi$
$570$	−7.60415e18			−0.388980
$571$		−	1.28829e19i		−	0.650968i	−0.945547	−	0.325484i	$-0.894473\pi$
$571$		−	1.28829e19i		−	0.650968i	0.945547	−	0.325484i	$-0.105527\pi$
$572$	5.80752e18	+	5.08283e19i	0.289880	+	2.53708i
$573$	2.70494e19			1.33375
$574$		−	2.31532e18i		−	0.112779i
$575$	7.14418e18			0.343778
$576$	3.35172e19			1.59335
$577$	1.16330e19			0.546339			0.273169	−	0.961966i	$-0.411928\pi$
$577$	1.16330e19			0.546339			0.273169	+	0.961966i	$0.411928\pi$
$578$			3.18594e19i			1.47823i
$579$		−	3.92037e19i		−	1.79712i
$580$			5.28595e19i			2.39402i
$581$	−2.98858e18			−0.133731
$582$		−	9.40279e19i		−	4.15715i
$583$	5.90492e18	−	6.74682e17i	0.257949	−	0.0294726i
$584$	5.58413e19			2.41027
$585$		−	5.61103e19i		−	2.39305i
$586$	4.48747e19			1.89112
$587$	1.38054e19			0.574888			0.287444	−	0.957797i	$-0.407194\pi$
$587$	1.38054e19			0.574888			0.287444	+	0.957797i	$0.407194\pi$
$588$	−8.27018e19			−3.40309
$589$		−	2.40022e18i		−	0.0975986i
$590$			1.71335e19i			0.688467i
$591$			2.74821e19i			1.09128i
$592$	−5.23228e18			−0.205324
$593$		−	1.47001e19i		−	0.570082i	−0.958515	−	0.285041i	$-0.907993\pi$
$593$		−	1.47001e19i		−	0.570082i	0.958515	−	0.285041i	$-0.0920072\pi$
$594$	1.35973e18	+	1.19006e19i	0.0521132	+	0.456103i
$595$	2.06187e19			0.780986
$596$		−	8.33068e18i		−	0.311858i
$597$	−4.46825e19			−1.65317
$598$	−1.87214e19			−0.684588
$599$	−1.18031e19			−0.426586			−0.213293	−	0.976988i	$-0.568419\pi$
$599$	−1.18031e19			−0.426586			−0.213293	+	0.976988i	$0.568419\pi$
$600$			7.00865e19i			2.50366i
$601$		−	8.42786e18i		−	0.297575i	−0.988869	−	0.148787i	$-0.952463\pi$
$601$		−	8.42786e18i		−	0.297575i	0.988869	−	0.148787i	$-0.0475370\pi$
$602$		−	7.71163e19i		−	2.69135i
$603$	−4.27634e19			−1.47520
$604$			8.36809e19i			2.85343i
$605$	−4.25408e19	+	9.84982e18i	−1.43390	+	0.332002i
$606$	−8.84151e19			−2.94590
$607$		−	1.81895e19i		−	0.599102i	−0.954080	−	0.299551i	$-0.903163\pi$
$607$		−	1.81895e19i		−	0.599102i	0.954080	−	0.299551i	$-0.0968368\pi$
$608$	1.43864e18			0.0468411
$609$	6.01007e19			1.93446
$610$	1.49002e20			4.74115
$611$			2.65931e19i			0.836527i
$612$		−	2.50960e19i		−	0.780448i
$613$		−	1.36236e19i		−	0.418860i	−0.977824	−	0.209430i	$-0.932839\pi$
$613$		−	1.36236e19i		−	0.418860i	0.977824	−	0.209430i	$-0.0671608\pi$
$614$	−2.45882e19			−0.747392
$615$			3.22624e18i			0.0969553i
$616$	−7.26803e19	+	8.30428e18i	−2.15949	+	0.246738i
$617$	7.46053e18			0.219166			0.109583	−	0.993978i	$-0.465048\pi$
$617$	7.46053e18			0.219166			0.109583	+	0.993978i	$0.465048\pi$
$618$			4.43532e19i			1.28827i
$619$	2.23738e19			0.642547			0.321273	−	0.946986i	$-0.395889\pi$
$619$	2.23738e19			0.642547			0.321273	+	0.946986i	$0.395889\pi$
$620$	−8.89197e19			−2.52497
$621$	−2.85020e18			−0.0800265
$622$			6.71493e19i			1.86427i
$623$			4.88841e19i			1.34200i
$624$		−	4.46538e19i		−	1.21218i
$625$	−3.00279e19			−0.806056
$626$		−	6.34764e19i		−	1.68497i
$627$	6.75917e17	+	5.91573e18i	0.0177427	+	0.155287i
$628$	4.68410e19			1.21593
$629$		−	4.74958e18i		−	0.121927i
$630$	1.73623e20			4.40781
$631$	−6.37441e19			−1.60042			−0.800211	−	0.599718i	$-0.795279\pi$
$631$	−6.37441e19			−1.60042			−0.800211	+	0.599718i	$0.795279\pi$
$632$	5.22773e18			0.129806
$633$		−	4.03486e19i		−	0.990837i
$634$		−	1.27442e17i		−	0.00309520i
$635$		−	2.49926e19i		−	0.600338i
$636$	−3.00232e19			−0.713274
$637$		−	7.24079e19i		−	1.70141i
$638$	6.32421e19	−	7.22589e18i	1.46981	−	0.167937i
$639$	1.12254e19			0.258046
$640$		−	1.18664e20i		−	2.69810i
$641$	−6.41750e19			−1.44331			−0.721655	−	0.692253i	$-0.756618\pi$
$641$	−6.41750e19			−1.44331			−0.721655	+	0.692253i	$0.756618\pi$
$642$	−9.73432e19			−2.16551
$643$	−1.44680e19			−0.318370			−0.159185	−	0.987249i	$-0.550887\pi$
$643$	−1.44680e19			−0.318370			−0.159185	+	0.987249i	$0.550887\pi$
$644$		−	3.76684e19i		−	0.819929i
$645$			1.07456e20i			2.31374i
$646$		−	2.97772e18i		−	0.0634244i
$647$	4.42005e19			0.931316			0.465658	−	0.884965i	$-0.345818\pi$
$647$	4.42005e19			0.931316			0.465658	+	0.884965i	$0.345818\pi$
$648$			5.45371e19i			1.13675i
$649$	1.33292e19	−	1.52297e18i	0.274848	−	0.0314034i
$650$	−1.32788e20			−2.70873
$651$			1.01101e20i			2.04027i
$652$	8.49780e19			1.69658
$653$	3.15590e19			0.623348			0.311674	−	0.950189i	$-0.399110\pi$
$653$	3.15590e19			0.623348			0.311674	+	0.950189i	$0.399110\pi$
$654$	−1.17453e20			−2.29520
$655$		−	1.42863e20i		−	2.76204i
$656$			1.39176e18i			0.0266219i
$657$			1.03777e20i			1.96402i
$658$	−8.22873e19			−1.54082
$659$			2.70091e19i			0.500395i	0.968195	+	0.250197i	$0.0804955\pi$
$659$			2.70091e19i			0.500395i	−0.968195	+	0.250197i	$0.919505\pi$
$660$	2.19157e20	−	2.50404e19i	4.01743	−	0.459022i
$661$	8.52911e19			1.54701			0.773506	−	0.633789i	$-0.218501\pi$
$661$	8.52911e19			1.54701			0.773506	+	0.633789i	$0.218501\pi$
$662$			4.26127e18i			0.0764773i
$663$	4.05343e19			0.719827
$664$	7.38891e18			0.129839
$665$	1.33956e19			0.232922
$666$		−	3.99945e19i		−	0.688146i
$667$			1.51465e19i			0.257889i
$668$		−	3.41939e19i		−	0.576121i
$669$	1.43887e20			2.39904
$670$			1.87975e20i			3.10153i
$671$	−1.32445e19	−	1.15918e20i	−0.216261	−	1.89275i
$672$	−6.05976e19			−0.979199
$673$			1.09560e20i			1.75204i	0.482271	+	0.876022i	$0.339812\pi$
$673$			1.09560e20i			1.75204i	−0.482271	+	0.876022i	$0.660188\pi$
$674$	−1.69190e19			−0.267765
$675$	−2.02161e19			−0.316643
$676$	1.06334e20			1.64834
$677$			1.27029e19i			0.194886i	0.995241	+	0.0974430i	$0.0310664\pi$
$677$			1.27029e19i			0.194886i	−0.995241	+	0.0974430i	$0.968934\pi$
$678$		−	1.59749e20i		−	2.42566i
$679$			1.65641e20i			2.48931i
$680$	−5.09773e19			−0.758254
$681$		−	3.11512e19i		−	0.458611i
$682$	1.21553e19	+	1.06385e20i	0.177123	+	1.55021i
$683$	1.31512e20			1.89680			0.948400	−	0.317078i	$-0.102702\pi$
$683$	1.31512e20			1.89680			0.948400	+	0.317078i	$0.102702\pi$
$684$		−	1.63044e19i		−	0.232761i
$685$	−1.22156e20			−1.72615
$686$	4.31760e19			0.603912
$687$	−1.05362e20			−1.45877
$688$			4.63554e19i			0.635303i
$689$		−	2.62862e19i		−	0.356610i
$690$			8.07212e19i			1.08404i
$691$	−1.88302e19			−0.250328			−0.125164	−	0.992136i	$-0.539946\pi$
$691$	−1.88302e19			−0.250328			−0.125164	+	0.992136i	$0.539946\pi$
$692$		−	5.55988e19i		−	0.731683i
$693$	−1.54330e19	−	1.35072e20i	−0.201056	−	1.75967i
$694$	−1.63502e20			−2.10866
$695$		−	9.21623e19i		−	1.17668i
$696$	−1.48592e20			−1.87815
$697$	−1.26337e18			−0.0158089
$698$	−1.20008e20			−1.48670
$699$		−	4.95389e19i		−	0.607584i
$700$		−	2.67177e20i		−	3.24424i
$701$			5.64050e18i			0.0678097i	0.999425	+	0.0339048i	$0.0107943\pi$
$701$			5.64050e18i			0.0678097i	−0.999425	+	0.0339048i	$0.989206\pi$
$702$	5.29763e19			0.630553
$703$		−	3.08571e18i		−	0.0363637i
$704$	−1.14618e20	+	1.30960e19i	−1.33735	+	0.152802i
$705$	1.14662e20			1.32463
$706$			4.53875e19i			0.519162i
$707$	1.55753e20			1.76401
$708$	−6.77716e19			−0.760002
$709$	1.33847e18			0.0148622			0.00743112	−	0.999972i	$-0.497635\pi$
$709$	1.33847e18			0.0148622			0.00743112	+	0.999972i	$0.497635\pi$
$710$		−	4.93435e19i		−	0.542527i
$711$			9.71541e18i			0.105773i
$712$		−	1.20860e20i		−	1.30294i
$713$	−2.54793e19			−0.271995
$714$			1.25426e20i			1.32587i
$715$	2.19236e19	+	1.91879e20i	0.229493	+	2.00856i
$716$	2.82676e20			2.93021
$717$			8.69560e19i			0.892618i
$718$	1.54968e20			1.57533
$719$	−1.66315e20			−1.67428			−0.837141	−	0.546987i	$-0.815775\pi$
$719$	−1.66315e20			−1.67428			−0.837141	+	0.546987i	$0.815775\pi$
$720$	−1.04366e20			−1.04048
$721$		−	7.81332e19i		−	0.771416i
$722$			1.70998e20i			1.67198i
$723$		−	2.38470e20i		−	2.30922i
$724$	−8.63796e19			−0.828402
$725$			1.07432e20i			1.02040i
$726$	−5.99175e19	−	2.58780e20i	−0.563634	−	2.43431i
$727$	−7.37840e19			−0.687419			−0.343709	−	0.939076i	$-0.611683\pi$
$727$	−7.37840e19			−0.687419			−0.343709	+	0.939076i	$0.611683\pi$
$728$			3.23542e20i			2.98546i
$729$	−1.45253e20			−1.32749
$730$	4.56173e20			4.12924
$731$	−4.20789e19			−0.377262
$732$			5.89377e20i			5.23378i
$733$		−	1.19221e20i		−	1.04864i	−0.851522	−	0.524320i	$-0.824320\pi$
$733$		−	1.19221e20i		−	1.04864i	0.851522	−	0.524320i	$-0.175680\pi$
$734$		−	1.32157e20i		−	1.15137i
$735$	−3.12202e20			−2.69417
$736$		−	1.52718e19i		−	0.130540i
$737$	1.46237e20	−	1.67087e19i	1.23818	−	0.141472i
$738$	−1.06384e19			−0.0892238
$739$		−	1.16659e20i		−	0.969185i	−0.874740	−	0.484593i	$-0.838968\pi$
$739$		−	1.16659e20i		−	0.969185i	0.874740	−	0.484593i	$-0.161032\pi$
$740$	−1.14315e20			−0.940762
$741$	2.63343e19			0.214682
$742$	8.13378e19			0.656848
$743$		−	4.74265e19i		−	0.379402i	−0.981842	−	0.189701i	$-0.939248\pi$
$743$		−	4.74265e19i		−	0.379402i	0.981842	−	0.189701i	$-0.0607519\pi$
$744$		−	2.49959e20i		−	1.98088i
$745$		−	3.14486e19i		−	0.246892i
$746$	−1.20293e20			−0.935557
$747$			1.37318e19i			0.105800i
$748$	9.80559e18	+	8.58200e19i	0.0748449	+	0.655054i
$749$	1.71481e20			1.29671
$750$			8.16341e19i			0.611565i
$751$	−1.39712e20			−1.03694			−0.518470	−	0.855096i	$-0.673498\pi$
$751$	−1.39712e20			−1.03694			−0.518470	+	0.855096i	$0.673498\pi$
$752$	4.94637e19			0.363715
$753$	1.75651e20			1.27964
$754$		−	2.81527e20i		−	2.03198i
$755$			3.15898e20i			2.25901i
$756$			1.06591e20i			0.755212i
$757$	2.02949e20			1.42468			0.712338	−	0.701836i	$-0.247636\pi$
$757$	2.02949e20			1.42468			0.712338	+	0.701836i	$0.247636\pi$
$758$			1.73393e20i			1.20600i
$759$	6.27979e19	−	7.17514e18i	0.432766	−	0.0494468i
$760$	−3.31190e19			−0.226142
$761$		−	2.75741e20i		−	1.86556i	−0.360445	−	0.932780i	$-0.617375\pi$
$761$		−	2.75741e20i		−	1.86556i	0.360445	−	0.932780i	$-0.382625\pi$
$762$	1.52033e20			1.01918
$763$	2.06908e20			1.37437
$764$	2.54940e20			1.67797
$765$		−	9.47382e19i		−	0.617867i
$766$		−	7.54023e19i		−	0.487285i
$767$		−	5.93361e19i		−	0.379972i
$768$	4.08379e20			2.59140
$769$			2.42529e20i			1.52503i	0.646968	+	0.762517i	$0.276037\pi$
$769$			2.42529e20i			1.52503i	−0.646968	+	0.762517i	$0.723963\pi$
$770$	−5.93733e20	+	6.78386e19i	−3.69961	+	0.422709i
$771$	−1.41148e20			−0.871555
$772$		−	3.69493e20i		−	2.26092i
$773$	−1.91938e20			−1.16387			−0.581936	−	0.813235i	$-0.697705\pi$
$773$	−1.91938e20			−1.16387			−0.581936	+	0.813235i	$0.697705\pi$
$774$	−3.54331e20			−2.12923
$775$	−1.80721e20			−1.07621
$776$		−	4.09527e20i		−	2.41686i
$777$			1.29975e20i			0.760171i
$778$			4.71577e20i			2.73335i
$779$	−8.20786e17			−0.00471485
$780$		−	9.75595e20i		−	5.55402i
$781$	−3.83873e19	+	4.38604e18i	−0.216586	+	0.0247466i
$782$	−3.16097e19			−0.176756
$783$		−	4.28605e19i		−	0.237533i
$784$	−1.34680e20			−0.739762
$785$	1.76827e20			0.962632
$786$	8.69048e20			4.68906
$787$			1.51465e20i			0.810010i	0.914315	+	0.405005i	$0.132730\pi$
$787$			1.51465e20i			0.810010i	−0.914315	+	0.405005i	$0.867270\pi$
$788$			2.59017e20i			1.37292i
$789$			4.48985e20i			2.35881i
$790$	4.27059e19			0.222381
$791$			2.81416e20i			1.45249i
$792$	3.81562e19	+	3.33949e20i	0.195204	+	1.70846i
$793$	−5.16017e20			−2.61669
$794$			3.85562e20i			1.93799i
$795$	−1.13339e20			−0.564687
$796$	−4.21131e20			−2.07982
$797$	−2.00337e20			−0.980740			−0.490370	−	0.871514i	$-0.663138\pi$
$797$	−2.00337e20			−0.980740			−0.490370	+	0.871514i	$0.663138\pi$
$798$			8.14867e19i			0.395427i
$799$			4.49005e19i			0.215985i
$800$		−	1.08320e20i		−	0.516512i
$801$	2.24611e20			1.06170
$802$		−	3.74554e20i		−	1.75507i
$803$	−4.05483e19	−	3.54885e20i	−0.188349	−	1.64846i
$804$	−7.43532e20			−3.42379
$805$		−	1.42200e20i		−	0.649123i
$806$	4.73581e20			2.14313
$807$	3.83828e20			1.72196
$808$	−3.85081e20			−1.71267
$809$			2.41860e20i			1.06641i	0.845986	+	0.533206i	$0.179013\pi$
$809$			2.41860e20i			1.06641i	−0.845986	+	0.533206i	$0.820987\pi$
$810$			4.45519e20i			1.94747i
$811$		−	2.45142e19i		−	0.106236i	−0.998588	−	0.0531180i	$-0.983084\pi$
$811$		−	2.45142e19i		−	0.106236i	0.998588	−	0.0531180i	$-0.0169159\pi$
$812$	5.66447e20			2.43370
$813$		−	4.74200e20i		−	2.01989i
$814$	1.56268e19	+	1.36768e20i	0.0659932	+	0.577582i
$815$	3.20795e20			1.34315
$816$		−	7.53947e19i		−	0.312975i
$817$	−2.73378e19			−0.112515
$818$	−6.00494e20			−2.45039
$819$	−6.01282e20			−2.43271
$820$			3.04072e19i			0.121978i
$821$			6.51367e19i			0.259074i	0.991575	+	0.129537i	$0.0413491\pi$
$821$			6.51367e19i			0.259074i	−0.991575	+	0.129537i	$0.958651\pi$
$822$		−	7.43085e20i		−	2.93046i
$823$	−2.36937e20			−0.926475			−0.463238	−	0.886234i	$-0.653312\pi$
$823$	−2.36937e20			−0.926475			−0.463238	+	0.886234i	$0.653312\pi$
$824$			1.93175e20i			0.748963i
$825$	4.45417e20	−	5.08923e19i	1.71234	−	0.195648i
$826$	1.83605e20			0.699879
$827$		−	4.16806e20i		−	1.57542i	−0.616048	−	0.787708i	$-0.711267\pi$
$827$		−	4.16806e20i		−	1.57542i	0.616048	−	0.787708i	$-0.288733\pi$
$828$	−1.73077e20			−0.648676
$829$	−4.42781e20			−1.64554			−0.822768	−	0.568378i	$-0.807571\pi$
$829$	−4.42781e20			−1.64554			−0.822768	+	0.568378i	$0.807571\pi$
$830$	6.03609e19			0.222438
$831$			1.54509e20i			0.564609i
$832$			5.10231e20i			1.84886i
$833$		−	1.22256e20i		−	0.439293i
$834$	5.60633e20			1.99764
$835$		−	1.29083e20i		−	0.456105i
$836$	6.37050e18	+	5.57556e19i	0.0223218	+	0.195364i
$837$	7.20994e19			0.250526
$838$		−	4.64328e20i		−	1.59999i
$839$	1.56856e20			0.536003			0.268001	−	0.963419i	$-0.413637\pi$
$839$	1.56856e20			0.536003			0.268001	+	0.963419i	$0.413637\pi$
$840$	1.39502e21			4.72743
$841$	6.97889e19			0.234539
$842$			4.61507e20i			1.53813i
$843$		−	1.63959e20i		−	0.541930i
$844$		−	3.80284e20i		−	1.24655i
$845$	4.01416e20			1.30496
$846$			3.78091e20i			1.21900i
$847$	1.05551e20	+	4.55871e20i	0.337505	+	1.45767i
$848$	−4.88929e19			−0.155051
$849$			6.39279e20i			2.01065i
$850$	−2.24203e20			−0.699374
$851$	−3.27561e19			−0.101341
$852$	1.95178e20			0.598899
$853$			2.19475e20i			0.667946i	0.942583	+	0.333973i	$0.108389\pi$
$853$			2.19475e20i			0.667946i	−0.942583	+	0.333973i	$0.891611\pi$
$854$		−	1.59672e21i		−	4.81974i
$855$		−	6.15495e19i		−	0.184273i
$856$	−4.23967e20			−1.25897
$857$		−	6.69119e20i		−	1.97078i	−0.170321	−	0.985389i	$-0.554480\pi$
$857$		−	6.69119e20i		−	1.97078i	0.170321	−	0.985389i	$-0.445520\pi$
$858$	−1.16722e21	+	1.33364e20i	−3.40990	+	0.389607i
$859$	4.64209e20			1.34512			0.672560	−	0.740043i	$-0.265195\pi$
$859$	4.64209e20			1.34512			0.672560	+	0.740043i	$0.265195\pi$
$860$			1.01277e21i			2.91087i
$861$	3.45727e19			0.0985624
$862$	5.11300e19			0.144585
$863$	1.87949e20			0.527187			0.263594	−	0.964634i	$-0.415092\pi$
$863$	1.87949e20			0.527187			0.263594	+	0.964634i	$0.415092\pi$
$864$			4.32149e19i			0.120237i
$865$		−	2.09887e20i		−	0.579260i
$866$			1.63956e20i			0.448852i
$867$	−4.75728e20			−1.29189
$868$			9.52871e20i			2.56682i
$869$	−3.79604e18	−	3.32235e19i	−0.0101436	−	0.0887784i
$870$	−1.21386e21			−3.21762
$871$		−	6.50985e20i		−	1.71176i
$872$	−5.11554e20			−1.33437
$873$	7.61081e20			1.96939
$874$	−2.05362e19			−0.0527157
$875$		−	1.43808e20i		−	0.366206i
$876$			1.80439e21i			4.55829i
$877$			4.20602e20i			1.05408i	0.849840	+	0.527040i	$0.176698\pi$
$877$			4.20602e20i			1.05408i	−0.849840	+	0.527040i	$0.823302\pi$
$878$	7.84752e20			1.95106
$879$			6.70074e20i			1.65273i
$880$	3.56899e20	−	4.07784e19i	0.873306	−	0.0997818i
$881$	−4.99677e20			−1.21299			−0.606496	−	0.795086i	$-0.707425\pi$
$881$	−4.99677e20			−1.21299			−0.606496	+	0.795086i	$0.707425\pi$
$882$		−	1.02947e21i		−	2.47933i
$883$	−3.21622e20			−0.768459			−0.384230	−	0.923238i	$-0.625533\pi$
$883$	−3.21622e20			−0.768459			−0.384230	+	0.923238i	$0.625533\pi$
$884$	3.82034e20			0.905600
$885$	−2.55840e20			−0.601680
$886$		−	2.93779e20i		−	0.685465i
$887$		−	1.92311e20i		−	0.445184i	−0.974912	−	0.222592i	$-0.928548\pi$
$887$		−	1.92311e20i		−	0.445184i	0.974912	−	0.222592i	$-0.0714517\pi$
$888$		−	3.21347e20i		−	0.738045i
$889$	−2.67823e20			−0.610289
$890$		−	9.87320e20i		−	2.23217i
$891$	3.46597e20	−	3.96013e19i	0.777464	−	0.0888312i
$892$	1.35613e21			3.01819
$893$			2.91710e19i			0.0644155i
$894$	1.91305e20			0.419145
$895$	1.06711e21			2.31979
$896$	−1.27161e21			−2.74282
$897$		−	2.79550e20i		−	0.598290i
$898$		−	1.01582e21i		−	2.15716i
$899$		−	3.83151e20i		−	0.807332i
$900$	−1.22761e21			−2.56664
$901$		−	4.43824e19i		−	0.0920740i
$902$	3.63797e19	−	4.15666e18i	0.0748883	−	0.00855655i
$903$	1.15151e21			2.35209
$904$		−	6.95766e20i		−	1.41021i
$905$	−3.26086e20			−0.655831
$906$	−1.92164e21			−3.83509
$907$	5.64819e20			1.11856			0.559279	−	0.828980i	$-0.311078\pi$
$907$	5.64819e20			1.11856			0.559279	+	0.828980i	$0.311078\pi$
$908$		−	2.93599e20i		−	0.576970i
$909$		−	7.15650e20i		−	1.39558i
$910$			2.64305e21i			5.11465i
$911$	−4.16746e20			−0.800281			−0.400140	−	0.916454i	$-0.631039\pi$
$911$	−4.16746e20			−0.800281			−0.400140	+	0.916454i	$0.631039\pi$
$912$		−	4.89825e19i		−	0.0933419i
$913$	−5.36535e18	−	4.69584e19i	−0.0101462	−	0.0888010i
$914$	9.60997e20			1.80343
$915$			2.22492e21i			4.14349i
$916$	−9.93030e20			−1.83524
$917$	−1.53093e21			−2.80782
$918$	8.94467e19			0.162804
$919$		−	9.31302e19i		−	0.168222i	−0.996456	−	0.0841109i	$-0.973195\pi$
$919$		−	9.31302e19i		−	0.168222i	0.996456	−	0.0841109i	$-0.0268050\pi$
$920$			3.51571e20i			0.630230i
$921$		−	3.67154e20i		−	0.653178i
$922$	2.36704e20			0.417916
$923$			1.70884e20i			0.299426i
$924$	−2.68335e20	−	2.34851e21i	−0.466630	−	4.08402i
$925$	−2.32334e20			−0.400979
$926$			1.14645e21i			1.96372i
$927$	−3.59004e20			−0.610296
$928$	2.29653e20			0.387468
$929$	9.51470e20			1.59326			0.796628	−	0.604470i	$-0.206615\pi$
$929$	9.51470e20			1.59326			0.796628	+	0.604470i	$0.206615\pi$
$930$		−	2.04195e21i		−	3.39362i
$931$		−	7.94271e19i		−	0.131015i
$932$		−	4.66903e20i		−	0.764390i
$933$	−1.00268e21			−1.62927
$934$			1.47308e21i			2.37574i
$935$	3.70165e19	+	3.23974e20i	0.0592534	+	0.518595i
$936$	1.48660e21			2.36191
$937$			1.53538e20i			0.242124i	0.992645	+	0.121062i	$0.0386300\pi$
$937$			1.53538e20i			0.242124i	−0.992645	+	0.121062i	$0.961370\pi$
$938$	2.01435e21			3.15294
$939$	9.47837e20			1.47256
$940$	1.08068e21			1.66649
$941$			3.21174e20i			0.491601i	0.969320	+	0.245801i	$0.0790509\pi$
$941$			3.21174e20i			0.491601i	−0.969320	+	0.245801i	$0.920949\pi$
$942$			1.07565e21i			1.63424i
$943$			8.71298e18i			0.0131397i
$944$	−1.10366e20			−0.165209
$945$			4.02386e20i			0.597888i
$946$	1.21170e21	−	1.38446e20i	1.78713	−	0.204193i
$947$	−6.74092e20			−0.986891			−0.493446	−	0.869777i	$-0.664263\pi$
$947$	−6.74092e20			−0.986891			−0.493446	+	0.869777i	$0.664263\pi$
$948$			1.68923e20i			0.245488i
$949$	−1.57980e21			−2.27897
$950$	−1.45660e20			−0.208582
$951$	1.90298e18			0.00270502
$952$			5.46277e20i			0.770823i
$953$			9.00434e20i			1.26125i	0.776087	+	0.630625i	$0.217201\pi$
$953$			9.00434e20i			1.26125i	−0.776087	+	0.630625i	$0.782799\pi$
$954$		−	3.73728e20i		−	0.519657i
$955$	9.62408e20			1.32842
$956$			8.19557e20i			1.12299i
$957$	1.07898e20	+	9.44338e20i	0.146767	+	1.28453i
$958$	−2.14999e21			−2.90321
$959$			1.30903e21i			1.75477i
$960$	2.19997e21			2.92764
$961$	−1.12412e20			−0.148508
$962$	6.08833e20			0.798496
$963$		−	7.87915e20i		−	1.02588i
$964$		−	2.24757e21i		−	2.90519i
$965$		−	1.39485e21i		−	1.78993i
$966$	8.65015e20			1.10201
$967$		−	1.29693e21i		−	1.64033i	−0.572125	−	0.820167i	$-0.693881\pi$
$967$		−	1.29693e21i		−	1.64033i	0.572125	−	0.820167i	$-0.306119\pi$
$968$	−2.60963e20	−	1.12709e21i	−0.327682	−	1.41524i
$969$	4.44637e19			0.0554292
$970$		−	3.34547e21i		−	4.14053i
$971$	−3.17425e20			−0.390038			−0.195019	−	0.980799i	$-0.562477\pi$
$971$	−3.17425e20			−0.390038			−0.195019	+	0.980799i	$0.562477\pi$
$972$	−2.17599e21			−2.65457
$973$	−9.87619e20			−1.19619
$974$			2.10407e21i			2.53015i
$975$		−	1.98281e21i		−	2.36727i
$976$			9.59804e20i			1.13772i
$977$	−5.51892e20			−0.649520			−0.324760	−	0.945797i	$-0.605283\pi$
$977$	−5.51892e20			−0.649520			−0.324760	+	0.945797i	$0.605283\pi$
$978$			1.95143e21i			2.28024i
$979$	−7.68096e20	+	8.77608e19i	−0.891121	+	0.101817i
$980$	−2.94249e21			−3.38948
$981$		−	9.50691e20i		−	1.08732i
$982$	2.14161e21			2.43198
$983$	1.41902e21			1.59997			0.799987	−	0.600018i	$-0.204840\pi$
$983$	1.41902e21			1.59997			0.799987	+	0.600018i	$0.204840\pi$
$984$	−8.54768e19			−0.0956936
$985$			9.77800e20i			1.08692i
$986$		−	4.75338e20i		−	0.524644i
$987$		−	1.22872e21i		−	1.34659i
$988$	2.48200e20			0.270087
$989$			2.90202e20i			0.313565i
$990$	3.11702e20	+	2.72806e21i	0.334421	+	2.92690i
$991$	7.06438e20			0.752590			0.376295	−	0.926500i	$-0.377198\pi$
$991$	7.06438e20			0.752590			0.376295	+	0.926500i	$0.377198\pi$
$992$			3.86319e20i			0.408662i
$993$	−6.36297e19			−0.0668368
$994$	−5.28769e20			−0.551520
$995$	−1.58979e21			−1.64656
$996$			2.38757e20i			0.245550i
$997$		−	9.15951e20i		−	0.935419i	−0.883882	−	0.467709i	$-0.845079\pi$
$997$		−	9.15951e20i		−	0.935419i	0.883882	−	0.467709i	$-0.154921\pi$
$998$			4.97586e20i			0.504609i
$999$	9.26906e19			0.0933420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.15.b.b.10.11	yes	12
3.2	odd	2		99.15.c.b.10.2		12
4.3	odd	2		176.15.h.d.65.9		12
11.10	odd	2	inner	11.15.b.b.10.2	✓	12
33.32	even	2		99.15.c.b.10.11		12
44.43	even	2		176.15.h.d.65.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.15.b.b.10.2	✓	12	11.10	odd	2	inner
11.15.b.b.10.11	yes	12	1.1	even	1	trivial
99.15.c.b.10.2		12	3.2	odd	2
99.15.c.b.10.11		12	33.32	even	2
176.15.h.d.65.9		12	4.3	odd	2
176.15.h.d.65.10		12	44.43	even	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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+216.434i q^{2} -3231.82 q^{3} -30459.8 q^{4} -114987. q^{5} -699477. i q^{6} +1.23221e6i q^{7} -3.04649e6i q^{8} +5.66171e6 q^{9} +O(q^{10})\)	\(q+216.434i q^{2} -3231.82 q^{3} -30459.8 q^{4} -114987. q^{5} -699477. i q^{6} +1.23221e6i q^{7} -3.04649e6i q^{8} +5.66171e6 q^{9} -2.48871e7i q^{10} +(-1.93612e7 + 2.21216e6i) q^{11} +9.84407e7 q^{12} +8.61879e7i q^{13} -2.66692e8 q^{14} +3.71617e8 q^{15} +1.60311e8 q^{16} +1.45522e8i q^{17} +1.22539e9i q^{18} +9.45428e7i q^{19} +3.50248e9 q^{20} -3.98228e9i q^{21} +(-4.78788e8 - 4.19043e9i) q^{22} +1.00361e9 q^{23} +9.84572e9i q^{24} +7.11848e9 q^{25} -1.86540e10 q^{26} -2.83994e9 q^{27} -3.75329e10i q^{28} +1.50920e10i q^{29} +8.04308e10i q^{30} -2.53876e10 q^{31} -1.52168e10i q^{32} +(6.25720e10 - 7.14932e9i) q^{33} -3.14960e10 q^{34} -1.41688e11i q^{35} -1.72455e11 q^{36} -3.26382e10 q^{37} -2.04623e10 q^{38} -2.78544e11i q^{39} +3.50307e11i q^{40} +8.68163e9i q^{41} +8.61903e11 q^{42} +2.89158e11i q^{43} +(5.89739e11 - 6.73821e10i) q^{44} -6.51023e11 q^{45} +2.17216e11i q^{46} +3.08548e11 q^{47} -5.18098e11 q^{48} -8.40117e11 q^{49} +1.54068e12i q^{50} -4.70302e11i q^{51} -2.62527e12i q^{52} -3.04987e11 q^{53} -6.14661e11i q^{54} +(2.22629e12 - 2.54370e11i) q^{55} +3.75391e12 q^{56} -3.05546e11i q^{57} -3.26643e12 q^{58} -6.88450e11 q^{59} -1.13194e13 q^{60} +5.98713e12i q^{61} -5.49476e12i q^{62} +6.97642e12i q^{63} +5.91998e12 q^{64} -9.91048e12i q^{65} +(1.54736e12 + 1.35427e13i) q^{66} -7.55309e12 q^{67} -4.43258e12i q^{68} -3.24349e12 q^{69} +3.06661e13 q^{70} +1.98269e12 q^{71} -1.72483e13i q^{72} +1.83297e13i q^{73} -7.06403e12i q^{74} -2.30057e13 q^{75} -2.87976e12i q^{76} +(-2.72585e12 - 2.38571e13i) q^{77} +6.02865e13 q^{78} +1.71598e12i q^{79} -1.84337e13 q^{80} -1.79016e13 q^{81} -1.87900e12 q^{82} +2.42539e12i q^{83} +1.21300e14i q^{84} -1.67331e13i q^{85} -6.25838e13 q^{86} -4.87748e13i q^{87} +(6.73934e12 + 5.89837e13i) q^{88} +3.96719e13 q^{89} -1.40904e14i q^{90} -1.06202e14 q^{91} -3.05698e13 q^{92} +8.20484e13 q^{93} +6.67803e13i q^{94} -1.08712e13i q^{95} +4.91780e13i q^{96} +1.34426e14 q^{97} -1.81830e14i q^{98} +(-1.09618e14 + 1.25246e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 5832 q^{3} - 130524 q^{4} - 135680 q^{5} + 13200780 q^{9}+O(q^{10}) \) 12 * q - 5832 * q^3 - 130524 * q^4 - 135680 * q^5 + 13200780 * q^9	\( 12 q - 5832 q^{3} - 130524 q^{4} - 135680 q^{5} + 13200780 q^{9} - 2225212 q^{11} + 40811892 q^{12} - 104225352 q^{14} - 135328320 q^{15} - 248620440 q^{16} + 3077616220 q^{20} - 2263930680 q^{22} + 5617677688 q^{23} + 4534941420 q^{25} - 22421106552 q^{26} - 16619859936 q^{27} + 73906813656 q^{31} + 154503019968 q^{33} - 189661264872 q^{34} - 15998386272 q^{36} - 32170218528 q^{37} - 450190787160 q^{38} + 1387253675640 q^{42} + 1658278243820 q^{44} - 1829643576360 q^{45} + 637903655272 q^{47} - 1287941662872 q^{48} - 5577020124564 q^{49} + 8629370688088 q^{53} + 6705223275960 q^{55} - 759657326064 q^{56} + 1308649899360 q^{58} - 319057951208 q^{59} - 23502810498420 q^{60} + 5684019519024 q^{64} + 7079527990920 q^{66} - 689205931848 q^{67} - 20471225254152 q^{69} + 41009932132680 q^{70} + 7251314650744 q^{71} - 50761855847880 q^{75} - 14619293932320 q^{77} + 81513511801800 q^{78} - 77504933615720 q^{80} + 6526391210604 q^{81} + 75766956787080 q^{82} - 124764637159152 q^{86} - 161556660706320 q^{88} + 227512316886784 q^{89} - 215922115692192 q^{91} + 60239663314612 q^{92} + 381197540672856 q^{93} + 23746610676192 q^{97} - 142689964303524 q^{99}+O(q^{100}) \) 12 * q - 5832 * q^3 - 130524 * q^4 - 135680 * q^5 + 13200780 * q^9 - 2225212 * q^11 + 40811892 * q^12 - 104225352 * q^14 - 135328320 * q^15 - 248620440 * q^16 + 3077616220 * q^20 - 2263930680 * q^22 + 5617677688 * q^23 + 4534941420 * q^25 - 22421106552 * q^26 - 16619859936 * q^27 + 73906813656 * q^31 + 154503019968 * q^33 - 189661264872 * q^34 - 15998386272 * q^36 - 32170218528 * q^37 - 450190787160 * q^38 + 1387253675640 * q^42 + 1658278243820 * q^44 - 1829643576360 * q^45 + 637903655272 * q^47 - 1287941662872 * q^48 - 5577020124564 * q^49 + 8629370688088 * q^53 + 6705223275960 * q^55 - 759657326064 * q^56 + 1308649899360 * q^58 - 319057951208 * q^59 - 23502810498420 * q^60 + 5684019519024 * q^64 + 7079527990920 * q^66 - 689205931848 * q^67 - 20471225254152 * q^69 + 41009932132680 * q^70 + 7251314650744 * q^71 - 50761855847880 * q^75 - 14619293932320 * q^77 + 81513511801800 * q^78 - 77504933615720 * q^80 + 6526391210604 * q^81 + 75766956787080 * q^82 - 124764637159152 * q^86 - 161556660706320 * q^88 + 227512316886784 * q^89 - 215922115692192 * q^91 + 60239663314612 * q^92 + 381197540672856 * q^93 + 23746610676192 * q^97 - 142689964303524 * q^99

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