LMFDB - Embedded newform 11.13.b.b.10.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,13,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, 13, names="a")

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

chi := DirichletCharacter("11.10");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 13 $
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:	$10.0539319900$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 30654x^{8} + 318945120x^{6} + 1305642637440x^{4} + 2049564619929600x^{2} + 957721368231936000 $ x^10 + 30654x^8 + 318945120x^6 + 1305642637440x^4 + 2049564619929600x^2 + 957721368231936000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 11^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.3
Root			$-64.4927i$ of defining polynomial
Character	$\chi$	$=$	11.10
Dual form			11.13.b.b.10.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-64.4927i q^{2} +344.091 q^{3} -63.3083 q^{4} -22798.6 q^{5} -22191.4i q^{6} -28764.7i q^{7} -260079. i q^{8} -413042. q^{9} +O(q^{10})$	\(q-64.4927i q^{2} +344.091 q^{3} -63.3083 q^{4} -22798.6 q^{5} -22191.4i q^{6} -28764.7i q^{7} -260079. i q^{8} -413042. q^{9} +1.47035e6i q^{10} +(-1.53934e6 - 876847. i) q^{11} -21783.8 q^{12} +9.36222e6i q^{13} -1.85512e6 q^{14} -7.84481e6 q^{15} -1.70325e7 q^{16} -5.13009e6i q^{17} +2.66382e7i q^{18} -6.74464e7i q^{19} +1.44334e6 q^{20} -9.89769e6i q^{21} +(-5.65502e7 + 9.92762e7i) q^{22} +9.96048e7 q^{23} -8.94909e7i q^{24} +2.75638e8 q^{25} +6.03795e8 q^{26} -3.24988e8 q^{27} +1.82105e6i q^{28} -7.79485e8i q^{29} +5.05933e8i q^{30} -8.54169e8 q^{31} +3.31888e7i q^{32} +(-5.29673e8 - 3.01715e8i) q^{33} -3.30853e8 q^{34} +6.55797e8i q^{35} +2.61490e7 q^{36} +1.99533e9 q^{37} -4.34980e9 q^{38} +3.22146e9i q^{39} +5.92945e9i q^{40} -1.86643e9i q^{41} -6.38329e8 q^{42} -6.60198e9i q^{43} +(9.74530e7 + 5.55117e7i) q^{44} +9.41681e9 q^{45} -6.42378e9i q^{46} -4.88403e9 q^{47} -5.86074e9 q^{48} +1.30139e10 q^{49} -1.77766e10i q^{50} -1.76522e9i q^{51} -5.92707e8i q^{52} +1.76347e10 q^{53} +2.09594e10i q^{54} +(3.50949e10 + 1.99909e10i) q^{55} -7.48111e9 q^{56} -2.32077e10i q^{57} -5.02711e10 q^{58} -2.99924e10 q^{59} +4.96642e8 q^{60} +6.58151e10i q^{61} +5.50877e10i q^{62} +1.18811e10i q^{63} -6.76248e10 q^{64} -2.13446e11i q^{65} +(-1.94584e10 + 3.41600e10i) q^{66} -1.21532e9 q^{67} +3.24777e8i q^{68} +3.42731e10 q^{69} +4.22941e10 q^{70} -4.69156e10 q^{71} +1.07424e11i q^{72} +1.49839e11i q^{73} -1.28684e11i q^{74} +9.48445e10 q^{75} +4.26992e9i q^{76} +(-2.52223e10 + 4.42787e10i) q^{77} +2.07760e11 q^{78} -2.60624e11i q^{79} +3.88318e11 q^{80} +1.07682e11 q^{81} -1.20371e11 q^{82} -1.29825e11i q^{83} +6.26606e8i q^{84} +1.16959e11i q^{85} -4.25780e11 q^{86} -2.68214e11i q^{87} +(-2.28050e11 + 4.00350e11i) q^{88} -4.33123e11 q^{89} -6.07315e11i q^{90} +2.69302e11 q^{91} -6.30581e9 q^{92} -2.93912e11 q^{93} +3.14985e11i q^{94} +1.53769e12i q^{95} +1.14200e10i q^{96} -4.99153e11 q^{97} -8.39300e11i q^{98} +(6.35813e11 + 3.62175e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9}+O(q^{10}) $ 10 * q + 2436 * q^3 - 20348 * q^4 + 26492 * q^5 + 756294 * q^9	\( 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9} - 1716374 q^{11} - 8491644 q^{12} - 15139368 q^{14} + 9632184 q^{15} + 17974408 q^{16} - 125399668 q^{20} + 83533560 q^{22} + 330297476 q^{23} - 438477018 q^{25} - 372191832 q^{26} + 1665774072 q^{27} - 1921955548 q^{31} - 2301728484 q^{33} + 7677299352 q^{34} - 14333366928 q^{36} + 1788323996 q^{37} + 11254769640 q^{38} - 32091748680 q^{42} + 6124969708 q^{44} + 43304121996 q^{45} - 24975510124 q^{47} + 32578826856 q^{48} - 6325710998 q^{49} - 16325502124 q^{53} + 14298843812 q^{55} + 82892128176 q^{56} - 84518430720 q^{58} + 62339390564 q^{59} - 286034518116 q^{60} + 95192926864 q^{64} + 322939363560 q^{66} - 90035301244 q^{67} + 346118875824 q^{69} - 382808641560 q^{70} - 359910119740 q^{71} + 14209300764 q^{75} + 425991883680 q^{77} - 483427126680 q^{78} + 1147768798712 q^{80} - 515542099806 q^{81} + 625030365960 q^{82} - 1219447545552 q^{86} + 134692485840 q^{88} + 670996780412 q^{89} + 1356772643808 q^{91} - 3181666532764 q^{92} + 1928296959312 q^{93} - 6250704684964 q^{97} - 1402418596722 q^{99}+O(q^{100}) \) 10 * q + 2436 * q^3 - 20348 * q^4 + 26492 * q^5 + 756294 * q^9 - 1716374 * q^11 - 8491644 * q^12 - 15139368 * q^14 + 9632184 * q^15 + 17974408 * q^16 - 125399668 * q^20 + 83533560 * q^22 + 330297476 * q^23 - 438477018 * q^25 - 372191832 * q^26 + 1665774072 * q^27 - 1921955548 * q^31 - 2301728484 * q^33 + 7677299352 * q^34 - 14333366928 * q^36 + 1788323996 * q^37 + 11254769640 * q^38 - 32091748680 * q^42 + 6124969708 * q^44 + 43304121996 * q^45 - 24975510124 * q^47 + 32578826856 * q^48 - 6325710998 * q^49 - 16325502124 * q^53 + 14298843812 * q^55 + 82892128176 * q^56 - 84518430720 * q^58 + 62339390564 * q^59 - 286034518116 * q^60 + 95192926864 * q^64 + 322939363560 * q^66 - 90035301244 * q^67 + 346118875824 * q^69 - 382808641560 * q^70 - 359910119740 * q^71 + 14209300764 * q^75 + 425991883680 * q^77 - 483427126680 * q^78 + 1147768798712 * q^80 - 515542099806 * q^81 + 625030365960 * q^82 - 1219447545552 * q^86 + 134692485840 * q^88 + 670996780412 * q^89 + 1356772643808 * q^91 - 3181666532764 * q^92 + 1928296959312 * q^93 - 6250704684964 * q^97 - 1402418596722 * 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 $

$2$		−	64.4927i		−	1.00770i	−0.863792	−	0.503849i	$-0.831917\pi$
$2$		−	64.4927i		−	1.00770i	0.863792	−	0.503849i	$-0.168083\pi$
$3$	344.091			0.472004			0.236002	−	0.971753i	$-0.424163\pi$
$3$	344.091			0.472004			0.236002	+	0.971753i	$0.424163\pi$
$4$	−63.3083			−0.0154561
$5$	−22798.6			−1.45911			−0.729557	−	0.683920i	$-0.760274\pi$
$5$	−22798.6			−1.45911			−0.729557	+	0.683920i	$0.760274\pi$
$6$		−	22191.4i		−	0.475638i
$7$		−	28764.7i		−	0.244496i	−0.992500	−	0.122248i	$-0.960990\pi$
$7$		−	28764.7i		−	0.244496i	0.992500	−	0.122248i	$-0.0390104\pi$
$8$		−	260079.i		−	0.992123i
$9$	−413042.			−0.777212
$10$			1.47035e6i			1.47035i
$11$	−1.53934e6	−	876847.i	−0.868917	−	0.494957i
$11$	−1.53934e6	−	876847.i	−0.868917	−	0.494957i
$12$	−21783.8			−0.00729536
$13$			9.36222e6i			1.93963i	0.243841	+	0.969815i	$0.421592\pi$
$13$			9.36222e6i			1.93963i	−0.243841	+	0.969815i	$0.578408\pi$
$14$	−1.85512e6			−0.246379
$15$	−7.84481e6			−0.688708
$16$	−1.70325e7			−1.01522
$17$		−	5.13009e6i		−	0.212536i	−0.994338	−	0.106268i	$-0.966110\pi$
$17$		−	5.13009e6i		−	0.212536i	0.994338	−	0.106268i	$-0.0338901\pi$
$18$			2.66382e7i			0.783195i
$19$		−	6.74464e7i		−	1.43363i	−0.697263	−	0.716815i	$-0.745599\pi$
$19$		−	6.74464e7i		−	1.43363i	0.697263	−	0.716815i	$-0.254401\pi$
$20$	1.44334e6			0.0225522
$21$		−	9.89769e6i		−	0.115403i
$22$	−5.65502e7	+	9.92762e7i	−0.498768	+	0.875607i
$23$	9.96048e7			0.672842			0.336421	−	0.941712i	$-0.390783\pi$
$23$	9.96048e7			0.672842			0.336421	+	0.941712i	$0.390783\pi$
$24$		−	8.94909e7i		−	0.468286i
$25$	2.75638e8			1.12901
$26$	6.03795e8			1.95456
$27$	−3.24988e8			−0.838851
$28$			1.82105e6i			0.00377897i
$29$		−	7.79485e8i		−	1.31045i	−0.755435	−	0.655224i	$-0.772574\pi$
$29$		−	7.79485e8i		−	1.31045i	0.755435	−	0.655224i	$-0.227426\pi$
$30$			5.05933e8i			0.694010i
$31$	−8.54169e8			−0.962440			−0.481220	−	0.876600i	$-0.659806\pi$
$31$	−8.54169e8			−0.962440			−0.481220	+	0.876600i	$0.659806\pi$
$32$			3.31888e7i			0.0309095i
$33$	−5.29673e8	−	3.01715e8i	−0.410133	−	0.233622i
$34$	−3.30853e8			−0.214172
$35$			6.55797e8i			0.356748i
$36$	2.61490e7			0.0120127
$37$	1.99533e9			0.777685			0.388843	−	0.921304i	$-0.372875\pi$
$37$	1.99533e9			0.777685			0.388843	+	0.921304i	$0.372875\pi$
$38$	−4.34980e9			−1.44467
$39$			3.22146e9i			0.915514i
$40$			5.92945e9i			1.44762i
$41$		−	1.86643e9i		−	0.392924i	−0.980511	−	0.196462i	$-0.937055\pi$
$41$		−	1.86643e9i		−	0.392924i	0.980511	−	0.196462i	$-0.0629453\pi$
$42$	−6.38329e8			−0.116292
$43$		−	6.60198e9i		−	1.04439i	−0.852825	−	0.522196i	$-0.825113\pi$
$43$		−	6.60198e9i		−	1.04439i	0.852825	−	0.522196i	$-0.174887\pi$
$44$	9.74530e7	+	5.55117e7i	0.0134301	+	0.00765013i
$45$	9.41681e9			1.13404
$46$		−	6.42378e9i		−	0.678022i
$47$	−4.88403e9			−0.453097			−0.226549	−	0.974000i	$-0.572744\pi$
$47$	−4.88403e9			−0.453097			−0.226549	+	0.974000i	$0.572744\pi$
$48$	−5.86074e9			−0.479187
$49$	1.30139e10			0.940222
$50$		−	1.77766e10i		−	1.13770i
$51$		−	1.76522e9i		−	0.100318i
$52$		−	5.92707e8i		−	0.0299792i
$53$	1.76347e10			0.795631			0.397816	−	0.917465i	$-0.369768\pi$
$53$	1.76347e10			0.795631			0.397816	+	0.917465i	$0.369768\pi$
$54$			2.09594e10i			0.845309i
$55$	3.50949e10	+	1.99909e10i	1.26785	+	0.722199i
$56$	−7.48111e9			−0.242571
$57$		−	2.32077e10i		−	0.676680i
$58$	−5.02711e10			−1.32054
$59$	−2.99924e10			−0.711048			−0.355524	−	0.934667i	$-0.615698\pi$
$59$	−2.99924e10			−0.711048			−0.355524	+	0.934667i	$0.615698\pi$
$60$	4.96642e8			0.0106448
$61$			6.58151e10i			1.27746i	0.769432	+	0.638729i	$0.220539\pi$
$61$			6.58151e10i			1.27746i	−0.769432	+	0.638729i	$0.779461\pi$
$62$			5.50877e10i			0.969849i
$63$			1.18811e10i			0.190026i
$64$	−6.76248e10			−0.984070
$65$		−	2.13446e11i		−	2.83014i
$66$	−1.94584e10	+	3.41600e10i	−0.235420	+	0.413290i
$67$	−1.21532e9			−0.0134352			−0.00671758	−	0.999977i	$-0.502138\pi$
$67$	−1.21532e9			−0.0134352			−0.00671758	+	0.999977i	$0.502138\pi$
$68$			3.24777e8i			0.00328498i
$69$	3.42731e10			0.317584
$70$	4.22941e10			0.359494
$71$	−4.69156e10			−0.366241			−0.183120	−	0.983090i	$-0.558620\pi$
$71$	−4.69156e10			−0.366241			−0.183120	+	0.983090i	$0.558620\pi$
$72$			1.07424e11i			0.771090i
$73$			1.49839e11i			0.990117i	0.868860	+	0.495059i	$0.164853\pi$
$73$			1.49839e11i			0.990117i	−0.868860	+	0.495059i	$0.835147\pi$
$74$		−	1.28684e11i		−	0.783672i
$75$	9.48445e10			0.532898
$76$			4.26992e9i			0.0221584i
$77$	−2.52223e10	+	4.42787e10i	−0.121015	+	0.212447i
$78$	2.07760e11			0.922562
$79$		−	2.60624e11i		−	1.07214i	−0.844173	−	0.536071i	$-0.819908\pi$
$79$		−	2.60624e11i		−	1.07214i	0.844173	−	0.536071i	$-0.180092\pi$
$80$	3.88318e11			1.48132
$81$	1.07682e11			0.381271
$82$	−1.20371e11			−0.395949
$83$		−	1.29825e11i		−	0.397092i	−0.980092	−	0.198546i	$-0.936378\pi$
$83$		−	1.29825e11i		−	0.397092i	0.980092	−	0.198546i	$-0.0636219\pi$
$84$			6.26606e8i			0.00178369i
$85$			1.16959e11i			0.310113i
$86$	−4.25780e11			−1.05243
$87$		−	2.68214e11i		−	0.618537i
$88$	−2.28050e11	+	4.00350e11i	−0.491059	+	0.862073i
$89$	−4.33123e11			−0.871507			−0.435753	−	0.900066i	$-0.643518\pi$
$89$	−4.33123e11			−0.871507			−0.435753	+	0.900066i	$0.643518\pi$
$90$		−	6.07315e11i		−	1.14277i
$91$	2.69302e11			0.474232
$92$	−6.30581e9			−0.0103995
$93$	−2.93912e11			−0.454276
$94$			3.14985e11i			0.456585i
$95$			1.53769e12i			2.09183i
$96$			1.14200e10i			0.0145894i
$97$	−4.99153e11			−0.599243			−0.299622	−	0.954058i	$-0.596860\pi$
$97$	−4.99153e11			−0.599243			−0.299622	+	0.954058i	$0.596860\pi$
$98$		−	8.39300e11i		−	0.947460i
$99$	6.35813e11	+	3.62175e11i	0.675333	+	0.384687i
$100$	−1.74502e10			−0.0174502
$101$			7.51261e11i			0.707722i	0.935298	+	0.353861i	$0.115131\pi$
$101$			7.51261e11i			0.707722i	−0.935298	+	0.353861i	$0.884869\pi$
$102$	−1.13844e11			−0.101090
$103$	−2.12622e12			−1.78067			−0.890336	−	0.455303i	$-0.849531\pi$
$103$	−2.12622e12			−1.78067			−0.890336	+	0.455303i	$0.849531\pi$
$104$	2.43492e12			1.92435
$105$			2.25654e11i			0.168386i
$106$		−	1.13731e12i		−	0.801756i
$107$		−	6.81724e11i		−	0.454261i	−0.973864	−	0.227131i	$-0.927066\pi$
$107$		−	6.81724e11i		−	0.454261i	0.973864	−	0.227131i	$-0.0729344\pi$
$108$	2.05745e10			0.0129654
$109$		−	2.92043e10i		−	0.0174136i	−0.999962	−	0.00870680i	$-0.997229\pi$
$109$		−	2.92043e10i		−	0.0174136i	0.999962	−	0.00870680i	$-0.00277149\pi$
$110$	1.28927e12	−	2.26336e12i	0.727759	−	1.27761i
$111$	6.86574e11			0.367071
$112$			4.89936e11i			0.248217i
$113$	2.13318e12			1.02460			0.512302	−	0.858805i	$-0.328793\pi$
$113$	2.13318e12			1.02460			0.512302	+	0.858805i	$0.328793\pi$
$114$	−1.49673e12			−0.681889
$115$	−2.27085e12			−0.981753
$116$			4.93479e10i			0.0202544i
$117$		−	3.86700e12i		−	1.50750i
$118$			1.93429e12i			0.716522i
$119$	−1.47566e11			−0.0519642
$120$			2.04027e12i			0.683283i
$121$	1.60071e12	+	2.69953e12i	0.510035	+	0.860154i
$122$	4.24459e12			1.28729
$123$		−	6.42222e11i		−	0.185462i
$124$	5.40760e10			0.0148756
$125$	−7.18091e11			−0.188243
$126$	7.66242e11			0.191488
$127$		−	1.82396e12i		−	0.434704i	−0.976093	−	0.217352i	$-0.930258\pi$
$127$		−	1.82396e12i		−	0.434704i	0.976093	−	0.217352i	$-0.0697420\pi$
$128$			4.49724e12i			1.02256i
$129$		−	2.27168e12i		−	0.492957i
$130$	−1.37657e13			−2.85193
$131$			6.40652e12i			1.26763i	0.773483	+	0.633817i	$0.218513\pi$
$131$			6.40652e12i			1.26763i	−0.773483	+	0.633817i	$0.781487\pi$
$132$	3.35327e10	+	1.91011e10i	0.00633906	+	0.00361089i
$133$	−1.94008e12			−0.350517
$134$			7.83795e10i			0.0135386i
$135$	7.40929e12			1.22398
$136$	−1.33423e12			−0.210861
$137$	−1.15119e13			−1.74109			−0.870547	−	0.492084i	$-0.836235\pi$
$137$	−1.15119e13			−1.74109			−0.870547	+	0.492084i	$0.836235\pi$
$138$		−	2.21037e12i		−	0.320029i
$139$		−	8.43509e12i		−	1.16950i	−0.811213	−	0.584751i	$-0.801192\pi$
$139$		−	8.43509e12i		−	1.16950i	0.811213	−	0.584751i	$-0.198808\pi$
$140$		−	4.15174e10i		−	0.00551394i
$141$	−1.68055e12			−0.213864
$142$			3.02571e12i			0.369060i
$143$	8.20924e12	−	1.44116e13i	0.960034	−	1.68538i
$144$	7.03515e12			0.789039
$145$			1.77712e13i			1.91209i
$146$	9.66350e12			0.997740
$147$	4.47796e12			0.443788
$148$	−1.26321e11			−0.0120200
$149$		−	7.25688e12i		−	0.663182i	−0.943423	−	0.331591i	$-0.892415\pi$
$149$		−	7.25688e12i		−	0.663182i	0.943423	−	0.331591i	$-0.107585\pi$
$150$		−	6.11678e12i		−	0.537001i
$151$			9.32708e12i			0.786836i	0.919360	+	0.393418i	$0.128707\pi$
$151$			9.32708e12i			0.786836i	−0.919360	+	0.393418i	$0.871293\pi$
$152$	−1.75414e13			−1.42234
$153$			2.11895e12i			0.165185i
$154$	2.85565e12	+	1.62665e12i	0.214083	+	0.121947i
$155$	1.94739e13			1.40431
$156$		−	2.03945e11i		−	0.0141503i
$157$	2.05515e13			1.37229			0.686144	−	0.727466i	$-0.259302\pi$
$157$	2.05515e13			1.37229			0.686144	+	0.727466i	$0.259302\pi$
$158$	−1.68084e13			−1.08040
$159$	6.06793e12			0.375541
$160$		−	7.56660e11i		−	0.0451005i
$161$		−	2.86511e12i		−	0.164507i
$162$		−	6.94471e12i		−	0.384206i
$163$	−7.09826e12			−0.378465			−0.189233	−	0.981932i	$-0.560600\pi$
$163$	−7.09826e12			−0.378465			−0.189233	+	0.981932i	$0.560600\pi$
$164$			1.18161e11i			0.00607309i
$165$	1.20758e13	+	6.87870e12i	0.598430	+	0.340881i
$166$	−8.37278e12			−0.400149
$167$		−	3.51470e13i		−	1.62028i	−0.586240	−	0.810138i	$-0.699392\pi$
$167$		−	3.51470e13i		−	1.62028i	0.586240	−	0.810138i	$-0.300608\pi$
$168$	−2.57418e12			−0.114494
$169$	−6.43532e13			−2.76217
$170$	7.54301e12			0.312501
$171$			2.78582e13i			1.11424i
$172$			4.17960e11i			0.0161423i
$173$			1.24605e13i			0.464793i	0.972621	+	0.232396i	$0.0746566\pi$
$173$			1.24605e13i			0.464793i	−0.972621	+	0.232396i	$0.925343\pi$
$174$	−1.72978e13			−0.623298
$175$		−	7.92865e12i		−	0.276039i
$176$	2.62188e13	+	1.49349e13i	0.882140	+	0.502489i
$177$	−1.03201e13			−0.335618
$178$			2.79332e13i			0.878216i
$179$	5.11263e12			0.155427			0.0777135	−	0.996976i	$-0.475238\pi$
$179$	5.11263e12			0.155427			0.0777135	+	0.996976i	$0.475238\pi$
$180$	−5.96162e11			−0.0175279
$181$	2.20666e13			0.627574			0.313787	−	0.949493i	$-0.398402\pi$
$181$	2.20666e13			0.627574			0.313787	+	0.949493i	$0.398402\pi$
$182$		−	1.73680e13i		−	0.477883i
$183$			2.26464e13i			0.602965i
$184$		−	2.59051e13i		−	0.667542i
$185$	−4.54908e13			−1.13473
$186$			1.89552e13i			0.457773i
$187$	−4.49831e12	+	7.89695e12i	−0.105196	+	0.184676i
$188$	3.09200e11			0.00700313
$189$			9.34821e12i			0.205096i
$190$	9.91696e13			2.10793
$191$	−3.80755e10			−0.000784234			−0.000392117	−	1.00000i	$-0.500125\pi$
$191$	−3.80755e10			−0.000784234			−0.000392117		1.00000i	$0.500125\pi$
$192$	−2.32691e13			−0.464485
$193$			7.27636e11i			0.0140789i	0.999975	+	0.00703947i	$0.00224075\pi$
$193$			7.27636e11i			0.0140789i	−0.999975	+	0.00703947i	$0.997759\pi$
$194$			3.21917e13i			0.603857i
$195$		−	7.34449e13i		−	1.33584i
$196$	−8.23887e11			−0.0145322
$197$		−	6.80714e13i		−	1.16458i	−0.812983	−	0.582288i	$-0.802158\pi$
$197$		−	6.80714e13i		−	1.16458i	0.812983	−	0.582288i	$-0.197842\pi$
$198$	2.33576e13	−	4.10053e13i	0.387648	−	0.680532i
$199$	4.85799e13			0.782237			0.391118	−	0.920340i	$-0.372088\pi$
$199$	4.85799e13			0.782237			0.391118	+	0.920340i	$0.372088\pi$
$200$		−	7.16876e13i		−	1.12012i
$201$	−4.18182e11			−0.00634145
$202$	4.84509e13			0.713171
$203$	−2.24217e13			−0.320400
$204$			1.11753e11i			0.00155052i
$205$			4.25521e13i			0.573321i
$206$			1.37125e14i			1.79438i
$207$	−4.11410e13			−0.522941
$208$		−	1.59462e14i		−	1.96915i
$209$	−5.91402e13	+	1.03823e14i	−0.709586	+	1.24571i
$210$	1.45530e13			0.169683
$211$		−	5.93114e13i		−	0.672115i	−0.941842	−	0.336057i	$-0.890906\pi$
$211$		−	5.93114e13i		−	0.672115i	0.941842	−	0.336057i	$-0.109094\pi$
$212$	−1.11642e12			−0.0122974
$213$	−1.61432e13			−0.172867
$214$	−4.39662e13			−0.457758
$215$			1.50516e14i			1.52389i
$216$			8.45227e13i			0.832244i
$217$			2.45700e13i			0.235313i
$218$	−1.88347e12			−0.0175477
$219$			5.15581e13i			0.467339i
$220$	−2.22180e12	−	1.26559e12i	−0.0195960	−	0.0111624i
$221$	4.80291e13			0.412240
$222$		−	4.42790e13i		−	0.369896i
$223$	3.67521e13			0.298850			0.149425	−	0.988773i	$-0.452258\pi$
$223$	3.67521e13			0.298850			0.149425	+	0.988773i	$0.452258\pi$
$224$	9.54668e11			0.00755726
$225$	−1.13850e14			−0.877482
$226$		−	1.37574e14i		−	1.03249i
$227$		−	1.20219e14i		−	0.878655i	−0.898327	−	0.439327i	$-0.855217\pi$
$227$		−	1.20219e14i		−	0.878655i	0.898327	−	0.439327i	$-0.144783\pi$
$228$			1.46924e12i			0.0104588i
$229$	2.46682e13			0.171051			0.0855253	−	0.996336i	$-0.472743\pi$
$229$	2.46682e13			0.171051			0.0855253	+	0.996336i	$0.472743\pi$
$230$			1.46454e14i			0.989311i
$231$	−8.67876e12	+	1.52359e13i	−0.0571197	+	0.100276i
$232$	−2.02728e14			−1.30013
$233$			1.68921e14i			1.05572i	0.849332	+	0.527859i	$0.177005\pi$
$233$			1.68921e14i			1.05572i	−0.849332	+	0.527859i	$0.822995\pi$
$234$	−2.49393e14			−1.51911
$235$	1.11349e14			0.661120
$236$	1.89877e12			0.0109901
$237$		−	8.96785e13i		−	0.506056i
$238$			9.51692e12i			0.0523642i
$239$		−	3.39728e14i		−	1.82282i	−0.411497	−	0.911411i	$-0.634994\pi$
$239$		−	3.39728e14i		−	1.82282i	0.411497	−	0.911411i	$-0.365006\pi$
$240$	1.33617e14			0.699188
$241$			2.44296e13i			0.124685i	0.998055	+	0.0623424i	$0.0198571\pi$
$241$			2.44296e13i			0.124685i	−0.998055	+	0.0623424i	$0.980143\pi$
$242$	1.74100e14	−	1.03234e14i	0.866776	−	0.513961i
$243$	2.09765e14			1.01881
$244$		−	4.16664e12i		−	0.0197446i
$245$	−2.96699e14			−1.37189
$246$	−4.14187e13			−0.186890
$247$	6.31448e14			2.78071
$248$			2.22152e14i			0.954859i
$249$		−	4.46717e13i		−	0.187429i
$250$			4.63116e13i			0.189692i
$251$	2.56372e14			1.02525			0.512623	−	0.858614i	$-0.328674\pi$
$251$	2.56372e14			1.02525			0.512623	+	0.858614i	$0.328674\pi$
$252$		−	7.52170e11i		−	0.00293706i
$253$	−1.53326e14	−	8.73381e13i	−0.584644	−	0.333028i
$254$	−1.17632e14			−0.438051
$255$			4.02446e13i			0.146375i
$256$	1.30484e13			0.0463574
$257$	6.72227e13			0.233301			0.116651	−	0.993173i	$-0.462784\pi$
$257$	6.72227e13			0.233301			0.116651	+	0.993173i	$0.462784\pi$
$258$	−1.46507e14			−0.496752
$259$		−	5.73951e13i		−	0.190141i
$260$			1.35129e13i			0.0437430i
$261$			3.21960e14i			1.01850i
$262$	4.13174e14			1.27739
$263$		−	1.43764e14i		−	0.434426i	−0.976124	−	0.217213i	$-0.930303\pi$
$263$		−	1.43764e14i		−	0.434426i	0.976124	−	0.217213i	$-0.0696966\pi$
$264$	−7.84698e13	+	1.37757e14i	−0.231782	+	0.406902i
$265$	−4.02046e14			−1.16092
$266$			1.25121e14i			0.353216i
$267$	−1.49034e14			−0.411355
$268$	7.69401e10			0.000207656
$269$	−4.47244e14			−1.18040			−0.590202	−	0.807256i	$-0.700952\pi$
$269$	−4.47244e14			−1.18040			−0.590202	+	0.807256i	$0.700952\pi$
$270$		−	4.77845e14i		−	1.23340i
$271$		−	6.67508e14i		−	1.68516i	−0.538572	−	0.842580i	$-0.681036\pi$
$271$		−	6.67508e14i		−	1.68516i	0.538572	−	0.842580i	$-0.318964\pi$
$272$			8.73784e13i			0.215770i
$273$	9.26644e13			0.223840
$274$			7.42432e14i			1.75450i
$275$	−4.24300e14	−	2.41692e14i	−0.981018	−	0.558813i
$276$	−2.16977e12			−0.00490862
$277$			1.36711e14i			0.302638i	0.988485	+	0.151319i	$0.0483521\pi$
$277$			1.36711e14i			0.302638i	−0.988485	+	0.151319i	$0.951648\pi$
$278$	−5.44002e14			−1.17851
$279$	3.52808e14			0.748020
$280$	1.70559e14			0.353938
$281$			7.58227e13i			0.154014i	0.997031	+	0.0770072i	$0.0245364\pi$
$281$			7.58227e13i			0.154014i	−0.997031	+	0.0770072i	$0.975464\pi$
$282$			1.08383e14i			0.215510i
$283$			5.79125e14i			1.12734i	0.826001	+	0.563669i	$0.190611\pi$
$283$			5.79125e14i			1.12734i	−0.826001	+	0.563669i	$0.809389\pi$
$284$	2.97015e12			0.00566067
$285$			5.29104e14i			0.987352i
$286$	−9.29446e14	−	5.29436e14i	−1.69835	−	0.967425i
$287$	−5.36874e13			−0.0960686
$288$		−	1.37084e13i		−	0.0240232i
$289$	5.56304e14			0.954829
$290$	1.14611e15			1.92681
$291$	−1.71754e14			−0.282845
$292$		−	9.48603e12i		−	0.0153034i
$293$		−	4.58558e14i		−	0.724751i	−0.932032	−	0.362376i	$-0.881966\pi$
$293$		−	4.58558e14i		−	0.724751i	0.932032	−	0.362376i	$-0.118034\pi$
$294$		−	2.88796e14i		−	0.447205i
$295$	6.83786e14			1.03750
$296$		−	5.18943e14i		−	0.771560i
$297$	5.00267e14	+	2.84965e14i	0.728893	+	0.415196i
$298$	−4.68016e14			−0.668287
$299$			9.32522e14i			1.30506i
$300$	−6.00444e12			−0.00823655
$301$	−1.89904e14			−0.255350
$302$	6.01529e14			0.792893
$303$			2.58502e14i			0.334048i
$304$			1.14878e15i			1.45545i
$305$		−	1.50050e15i		−	1.86396i
$306$	1.36656e14			0.166457
$307$		−	2.92608e14i		−	0.349507i	−0.984612	−	0.174753i	$-0.944087\pi$
$307$		−	2.92608e14i		−	0.349507i	0.984612	−	0.174753i	$-0.0559128\pi$
$308$	1.59678e12	−	2.80321e12i	0.00187043	−	0.00328361i
$309$	−7.31612e14			−0.840485
$310$		−	1.25592e15i		−	1.41512i
$311$	−8.66192e14			−0.957309			−0.478654	−	0.878003i	$-0.658875\pi$
$311$	−8.66192e14			−0.957309			−0.478654	+	0.878003i	$0.658875\pi$
$312$	8.37834e14			0.908302
$313$	−1.05730e14			−0.112443			−0.0562213	−	0.998418i	$-0.517905\pi$
$313$	−1.05730e14			−0.112443			−0.0562213	+	0.998418i	$0.517905\pi$
$314$		−	1.32542e15i		−	1.38285i
$315$		−	2.70872e14i		−	0.277269i
$316$			1.64997e13i			0.0165712i
$317$	8.45915e14			0.833626			0.416813	−	0.908992i	$-0.363147\pi$
$317$	8.45915e14			0.833626			0.416813	+	0.908992i	$0.363147\pi$
$318$		−	3.91337e14i		−	0.378432i
$319$	−6.83489e14	+	1.19989e15i	−0.648616	+	1.13867i
$320$	1.54175e15			1.43587
$321$		−	2.34575e14i		−	0.214413i
$322$	−1.84778e14			−0.165774
$323$	−3.46006e14			−0.304697
$324$	−6.81717e12			−0.00589297
$325$			2.58058e15i			2.18987i
$326$			4.57786e14i			0.381379i
$327$		−	1.00490e13i		−	0.00821929i
$328$	−4.85420e14			−0.389829
$329$			1.40488e14i			0.110781i
$330$	4.43626e14	−	7.78803e14i	0.343505	−	0.603037i
$331$	−2.02215e15			−1.53761			−0.768803	−	0.639486i	$-0.779147\pi$
$331$	−2.02215e15			−1.53761			−0.768803	+	0.639486i	$0.779147\pi$
$332$			8.21902e12i			0.00613750i
$333$	−8.24155e14			−0.604426
$334$	−2.26672e15			−1.63275
$335$	2.77077e13			0.0196034
$336$			1.68583e14i			0.117159i
$337$		−	6.97497e14i		−	0.476171i	−0.971244	−	0.238085i	$-0.923480\pi$
$337$		−	6.97497e14i		−	0.476171i	0.971244	−	0.238085i	$-0.0765198\pi$
$338$			4.15031e15i			2.78343i
$339$	7.34007e14			0.483617
$340$		−	7.40449e12i		−	0.00479315i
$341$	1.31486e15	+	7.48975e14i	0.836281	+	0.476367i
$342$	1.79665e15			1.12281
$343$		−	7.72482e14i		−	0.474377i
$344$	−1.71704e15			−1.03617
$345$	−7.81381e14			−0.463391
$346$	8.03612e14			0.468371
$347$		−	7.86193e14i		−	0.450352i	−0.974318	−	0.225176i	$-0.927704\pi$
$347$		−	7.86193e14i		−	0.450352i	0.974318	−	0.225176i	$-0.0722958\pi$
$348$			1.69802e13i			0.00956018i
$349$		−	2.23741e15i		−	1.23821i	−0.785309	−	0.619104i	$-0.787496\pi$
$349$		−	2.23741e15i		−	1.23821i	0.785309	−	0.619104i	$-0.212504\pi$
$350$	−5.11340e14			−0.278164
$351$		−	3.04261e15i		−	1.62706i
$352$	2.91015e13	−	5.10889e13i	0.0152989	−	0.0268578i
$353$	1.34264e15			0.693921			0.346961	−	0.937880i	$-0.387214\pi$
$353$	1.34264e15			0.693921			0.346961	+	0.937880i	$0.387214\pi$
$354$			6.65572e14i			0.338202i
$355$	1.06961e15			0.534387
$356$	2.74203e13			0.0134701
$357$	−5.07761e13			−0.0245273
$358$		−	3.29728e14i		−	0.156624i
$359$			3.43419e15i			1.60420i	0.597191	+	0.802099i	$0.296283\pi$
$359$			3.43419e15i			1.60420i	−0.597191	+	0.802099i	$0.703717\pi$
$360$		−	2.44912e15i		−	1.12511i
$361$	−2.33570e15			−1.05530
$362$		−	1.42314e15i		−	0.632405i
$363$	5.50789e14	+	9.28885e14i	0.240738	+	0.405996i
$364$	−1.70491e13			−0.00732980
$365$		−	3.41612e15i		−	1.44469i
$366$	1.46053e15			0.607607
$367$	3.15081e15			1.28951			0.644757	−	0.764387i	$-0.276958\pi$
$367$	3.15081e15			1.28951			0.644757	+	0.764387i	$0.276958\pi$
$368$	−1.69652e15			−0.683081
$369$			7.70915e14i			0.305386i
$370$			2.93382e15i			1.14347i
$371$		−	5.07256e14i		−	0.194529i
$372$	1.86071e13			0.00702134
$373$		−	3.37956e14i		−	0.125490i	−0.998030	−	0.0627448i	$-0.980015\pi$
$373$		−	3.37956e14i		−	0.125490i	0.998030	−	0.0627448i	$-0.0199854\pi$
$374$	5.09296e14	+	2.90108e14i	0.186098	+	0.106006i
$375$	−2.47088e14			−0.0888515
$376$			1.27024e15i			0.449528i
$377$	7.29771e15			2.54178
$378$	6.02891e14			0.206675
$379$	−6.02139e14			−0.203171			−0.101585	−	0.994827i	$-0.532392\pi$
$379$	−6.02139e14			−0.203171			−0.101585	+	0.994827i	$0.532392\pi$
$380$		−	9.73484e13i		−	0.0323316i
$381$		−	6.27610e14i		−	0.205182i
$382$			2.45559e12i			0.000790272i
$383$	−4.12926e15			−1.30822			−0.654108	−	0.756401i	$-0.726956\pi$
$383$	−4.12926e15			−1.30822			−0.654108	+	0.756401i	$0.726956\pi$
$384$			1.54746e15i			0.482650i
$385$	5.75034e14	−	1.00950e15i	0.176575	−	0.309984i
$386$	4.69272e13			0.0141873
$387$			2.72690e15i			0.811714i
$388$	3.16005e13			0.00926199
$389$	−2.15519e15			−0.621995			−0.310998	−	0.950411i	$-0.600663\pi$
$389$	−2.15519e15			−0.621995			−0.310998	+	0.950411i	$0.600663\pi$
$390$	−4.73666e15			−1.34612
$391$		−	5.10982e14i		−	0.143003i
$392$		−	3.38464e15i		−	0.932816i
$393$			2.20442e15i			0.598329i
$394$	−4.39011e15			−1.17354
$395$			5.94188e15i			1.56438i
$396$	−4.02522e13	−	2.29287e13i	−0.0104380	−	0.00594577i
$397$	3.91210e15			0.999234			0.499617	−	0.866246i	$-0.333474\pi$
$397$	3.91210e15			0.999234			0.499617	+	0.866246i	$0.333474\pi$
$398$		−	3.13305e15i		−	0.788259i
$399$	−6.67564e14			−0.165446
$400$	−4.69480e15			−1.14619
$401$	3.51122e15			0.844486			0.422243	−	0.906483i	$-0.361243\pi$
$401$	3.51122e15			0.844486			0.422243	+	0.906483i	$0.361243\pi$
$402$			2.69697e13i			0.00639027i
$403$		−	7.99692e15i		−	1.86678i
$404$		−	4.75611e13i		−	0.0109386i
$405$	−2.45501e15			−0.556317
$406$			1.44603e15i			0.322866i
$407$	−3.07149e15	−	1.74960e15i	−0.675744	−	0.384921i
$408$	−4.59097e14			−0.0995275
$409$			3.93083e15i			0.839739i	0.907584	+	0.419870i	$0.137924\pi$
$409$			3.93083e15i			0.839739i	−0.907584	+	0.419870i	$0.862076\pi$
$410$	2.74430e15			0.577735
$411$	−3.96113e15			−0.821804
$412$	1.34607e14			0.0275223
$413$			8.62724e14i			0.173849i
$414$			2.65329e15i			0.526967i
$415$			2.95984e15i			0.579402i
$416$	−3.10721e14			−0.0599530
$417$		−	2.90244e15i		−	0.552010i
$418$	6.69582e15	+	3.81411e15i	1.25530	+	0.715049i
$419$	−4.95102e15			−0.914977			−0.457489	−	0.889216i	$-0.651251\pi$
$419$	−4.95102e15			−0.914977			−0.457489	+	0.889216i	$0.651251\pi$
$420$		−	1.42858e13i		−	0.00260260i
$421$	7.59100e15			1.36335			0.681674	−	0.731656i	$-0.261252\pi$
$421$	7.59100e15			1.36335			0.681674	+	0.731656i	$0.261252\pi$
$422$	−3.82515e15			−0.677289
$423$	2.01731e15			0.352153
$424$		−	4.58641e15i		−	0.789364i
$425$		−	1.41405e15i		−	0.239955i
$426$			1.04112e15i			0.174198i
$427$	1.89315e15			0.312334
$428$			4.31588e13i			0.00702112i
$429$	2.82473e15	−	4.95892e15i	0.453140	−	0.795506i
$430$	9.70720e15			1.53562
$431$			6.52422e15i			1.01781i	0.860824	+	0.508903i	$0.169949\pi$
$431$			6.52422e15i			1.01781i	−0.860824	+	0.508903i	$0.830051\pi$
$432$	5.53537e15			0.851616
$433$	−2.47984e15			−0.376267			−0.188134	−	0.982143i	$-0.560244\pi$
$433$	−2.47984e15			−0.376267			−0.188134	+	0.982143i	$0.560244\pi$
$434$	1.58458e15			0.237125
$435$			6.11491e15i			0.902515i
$436$			1.84888e12i			0.000269147i
$437$		−	6.71798e15i		−	0.964607i
$438$	3.32512e15			0.470937
$439$		−	1.14223e15i		−	0.159576i	−0.996812	−	0.0797880i	$-0.974576\pi$
$439$		−	1.14223e15i		−	0.159576i	0.996812	−	0.0797880i	$-0.0254243\pi$
$440$	5.19922e15	−	9.12744e15i	0.716510	−	1.25786i
$441$	−5.37528e15			−0.730752
$442$		−	3.09752e15i		−	0.415414i
$443$	−8.48409e15			−1.12249			−0.561245	−	0.827649i	$-0.689678\pi$
$443$	−8.48409e15			−1.12249			−0.561245	+	0.827649i	$0.689678\pi$
$444$	−4.34659e13			−0.00567349
$445$	9.87461e15			1.27163
$446$		−	2.37024e15i		−	0.301151i
$447$		−	2.49703e15i		−	0.313024i
$448$			1.94521e15i			0.240601i
$449$	−1.45892e16			−1.78055			−0.890275	−	0.455422i	$-0.849488\pi$
$449$	−1.45892e16			−1.78055			−0.890275	+	0.455422i	$0.849488\pi$
$450$			7.34250e15i			0.884237i
$451$	−1.63657e15	+	2.87307e15i	−0.194481	+	0.341419i
$452$	−1.35048e14			−0.0158364
$453$			3.20936e15i			0.371390i
$454$	−7.75325e15			−0.885419
$455$	−6.13972e15			−0.691959
$456$	−6.03584e15			−0.671350
$457$		−	1.81945e16i		−	1.99729i	−0.0520125	−	0.998646i	$-0.516564\pi$
$457$		−	1.81945e16i		−	1.99729i	0.0520125	−	0.998646i	$-0.483436\pi$
$458$		−	1.59092e15i		−	0.172367i
$459$			1.66722e15i			0.178286i
$460$	1.43764e14			0.0151741
$461$			1.10490e16i			1.15111i	0.817763	+	0.575555i	$0.195214\pi$
$461$			1.10490e16i			1.15111i	−0.817763	+	0.575555i	$0.804786\pi$
$462$	9.82605e14	+	5.59717e14i	0.101048	+	0.0575594i
$463$	2.27373e15			0.230809			0.115405	−	0.993319i	$-0.463184\pi$
$463$	2.27373e15			0.230809			0.115405	+	0.993319i	$0.463184\pi$
$464$			1.32766e16i			1.33039i
$465$	6.70079e15			0.662840
$466$	1.08942e16			1.06384
$467$	−4.39759e14			−0.0423949			−0.0211975	−	0.999775i	$-0.506748\pi$
$467$	−4.39759e14			−0.0423949			−0.0211975	+	0.999775i	$0.506748\pi$
$468$			2.44813e14i			0.0233002i
$469$			3.49585e13i			0.00328485i
$470$		−	7.18122e15i		−	0.666210i
$471$	7.07158e15			0.647726
$472$			7.80040e15i			0.705448i
$473$	−5.78893e15	+	1.01627e16i	−0.516929	+	0.907490i
$474$	−5.78361e15			−0.509951
$475$		−	1.85908e16i		−	1.61859i
$476$	9.34214e12			0.000803165
$477$	−7.28386e15			−0.618374
$478$	−2.19100e16			−1.83686
$479$			1.33845e16i			1.10812i	0.832476	+	0.554061i	$0.186923\pi$
$479$			1.33845e16i			1.10812i	−0.832476	+	0.554061i	$0.813077\pi$
$480$		−	2.60360e14i		−	0.0212876i
$481$			1.86807e16i			1.50842i
$482$	1.57553e15			0.125645
$483$		−	9.85857e14i		−	0.0776482i
$484$	−1.01338e14	−	1.70903e14i	−0.00788316	−	0.0132947i
$485$	1.13800e16			0.874364
$486$		−	1.35283e16i		−	1.02666i
$487$	−5.28570e15			−0.396213			−0.198106	−	0.980181i	$-0.563479\pi$
$487$	−5.28570e15			−0.396213			−0.198106	+	0.980181i	$0.563479\pi$
$488$	1.71171e16			1.26740
$489$	−2.44245e15			−0.178637
$490$			1.91349e16i			1.38245i
$491$			1.71255e16i			1.22223i	0.791541	+	0.611116i	$0.209279\pi$
$491$			1.71255e16i			1.22223i	−0.791541	+	0.611116i	$0.790721\pi$
$492$			4.06580e13i			0.00286652i
$493$	−3.99883e15			−0.278517
$494$		−	4.07238e16i		−	2.80212i
$495$	−1.44957e16	−	8.25710e15i	−0.985387	−	0.561302i
$496$	1.45486e16			0.977086
$497$			1.34951e15i			0.0895446i
$498$	−2.88100e15			−0.188872
$499$	2.75588e16			1.78508			0.892540	−	0.450968i	$-0.148921\pi$
$499$	2.75588e16			1.78508			0.892540	+	0.450968i	$0.148921\pi$
$500$	4.54611e13			0.00290951
$501$		−	1.20938e16i		−	0.764777i
$502$		−	1.65341e16i		−	1.03314i
$503$		−	1.88042e16i		−	1.16104i	−0.814246	−	0.580520i	$-0.802849\pi$
$503$		−	1.88042e16i		−	1.16104i	0.814246	−	0.580520i	$-0.197151\pi$
$504$	3.09002e15			0.188529
$505$		−	1.71277e16i		−	1.03265i
$506$	−5.63267e15	+	9.88838e15i	−0.335592	+	0.589145i
$507$	−2.21433e16			−1.30375
$508$			1.15472e14i			0.00671885i
$509$	1.75797e16			1.01089			0.505445	−	0.862859i	$-0.331328\pi$
$509$	1.75797e16			1.01089			0.505445	+	0.862859i	$0.331328\pi$
$510$	2.59548e15			0.147502
$511$	4.31007e15			0.242080
$512$			1.75792e16i			0.975841i
$513$			2.19193e16i			1.20260i
$514$		−	4.33537e15i		−	0.235097i
$515$	4.84749e16			2.59820
$516$			1.43816e14i			0.00761921i
$517$	7.51819e15	+	4.28255e15i	0.393704	+	0.224264i
$518$	−3.70156e15			−0.191605
$519$			4.28755e15i			0.219384i
$520$	−5.55129e16			−2.80785
$521$	−1.38296e16			−0.691488			−0.345744	−	0.938329i	$-0.612373\pi$
$521$	−1.38296e16			−0.691488			−0.345744	+	0.938329i	$0.612373\pi$
$522$	2.07641e16			1.02634
$523$		−	1.88929e16i		−	0.923182i	−0.887093	−	0.461591i	$-0.847279\pi$
$523$		−	1.88929e16i		−	0.923182i	0.887093	−	0.461591i	$-0.152721\pi$
$524$		−	4.05586e14i		−	0.0195927i
$525$		−	2.72818e15i		−	0.130292i
$526$	−9.27173e15			−0.437770
$527$			4.38196e15i			0.204553i
$528$	9.02167e15	+	5.13897e15i	0.416374	+	0.237177i
$529$	−1.19935e16			−0.547284
$530$			2.59291e16i			1.16985i
$531$	1.23881e16			0.552635
$532$	1.22823e14			0.00541764
$533$	1.74740e16			0.762128
$534$			9.61158e15i			0.414522i
$535$			1.55424e16i			0.662819i
$536$			3.16080e14i			0.0133293i
$537$	1.75921e15			0.0733622
$538$			2.88439e16i			1.18949i
$539$	−2.00328e16	−	1.14112e16i	−0.816975	−	0.465369i
$540$	−4.69070e14			−0.0189180
$541$		−	3.49615e16i		−	1.39446i	−0.716847	−	0.697230i	$-0.754416\pi$
$541$		−	3.49615e16i		−	1.39446i	0.716847	−	0.697230i	$-0.245584\pi$
$542$	−4.30494e16			−1.69813
$543$	7.59293e15			0.296217
$544$	1.70262e14			0.00656937
$545$			6.65819e14i			0.0254084i
$546$		−	5.97618e15i		−	0.225563i
$547$			2.75496e16i			1.02847i	0.857649	+	0.514235i	$0.171924\pi$
$547$			2.75496e16i			1.02847i	−0.857649	+	0.514235i	$0.828076\pi$
$548$	7.28797e14			0.0269106
$549$		−	2.71844e16i		−	0.992855i
$550$	−1.55874e16	+	2.73643e16i	−0.563115	+	0.988570i
$551$	−5.25735e16			−1.87870
$552$		−	8.91372e15i		−	0.315083i
$553$	−7.49679e15			−0.262135
$554$	8.81684e15			0.304968
$555$	−1.56530e16			−0.535598
$556$			5.34012e14i			0.0180760i
$557$			1.46378e16i			0.490168i	0.969502	+	0.245084i	$0.0788155\pi$
$557$			1.46378e16i			0.490168i	−0.969502	+	0.245084i	$0.921184\pi$
$558$		−	2.27535e16i		−	0.753778i
$559$	6.18092e16			2.02573
$560$		−	1.11699e16i		−	0.362177i
$561$	−1.54783e15	+	2.71727e15i	−0.0496530	+	0.0871678i
$562$	4.89001e15			0.155200
$563$		−	5.18884e16i		−	1.62937i	−0.579904	−	0.814685i	$-0.696910\pi$
$563$		−	5.18884e16i		−	1.62937i	0.579904	−	0.814685i	$-0.303090\pi$
$564$	1.06393e14			0.00330551
$565$	−4.86335e16			−1.49501
$566$	3.73494e16			1.13602
$567$		−	3.09745e15i		−	0.0932193i
$568$			1.22018e16i			0.363356i
$569$			1.38033e16i			0.406732i	0.979103	+	0.203366i	$0.0651882\pi$
$569$			1.38033e16i			0.406732i	−0.979103	+	0.203366i	$0.934812\pi$
$570$	3.41234e16			0.994953
$571$			6.15365e15i			0.177548i	0.996052	+	0.0887741i	$0.0282949\pi$
$571$			6.15365e15i			0.177548i	−0.996052	+	0.0887741i	$0.971705\pi$
$572$	−5.19713e14	+	9.12377e14i	−0.0148384	+	0.0260494i
$573$	−1.31014e13			−0.000370162
$574$			3.46245e15i			0.0968081i
$575$	2.74548e16			0.759647
$576$	2.79319e16			0.764831
$577$	−6.00797e15			−0.162807			−0.0814035	−	0.996681i	$-0.525940\pi$
$577$	−6.00797e15			−0.162807			−0.0814035	+	0.996681i	$0.525940\pi$
$578$		−	3.58776e16i		−	0.962179i
$579$			2.50373e14i			0.00664532i
$580$		−	1.12506e15i		−	0.0295535i
$581$	−3.73439e15			−0.0970875
$582$			1.10769e16i			0.285023i
$583$	−2.71457e16	−	1.54629e16i	−0.691338	−	0.393803i
$584$	3.89699e16			0.982318
$585$			8.81623e16i			2.19962i
$586$	−2.95737e16			−0.730331
$587$	4.09287e16			1.00046			0.500230	−	0.865893i	$-0.333249\pi$
$587$	4.09287e16			1.00046			0.500230	+	0.865893i	$0.333249\pi$
$588$	−2.83492e14			−0.00685925
$589$			5.76106e16i			1.37978i
$590$		−	4.40992e16i		−	1.04549i
$591$		−	2.34228e16i		−	0.549684i
$592$	−3.39855e16			−0.789519
$593$			3.15867e16i			0.726400i	0.931711	+	0.363200i	$0.118316\pi$
$593$			3.15867e16i			0.726400i	−0.931711	+	0.363200i	$0.881684\pi$
$594$	1.83782e16	−	3.22636e16i	0.418392	−	0.734504i
$595$	3.36430e15			0.0758216
$596$			4.59421e14i			0.0102502i
$597$	1.67159e16			0.369219
$598$	6.01409e16			1.31511
$599$	2.43537e16			0.527236			0.263618	−	0.964627i	$-0.415084\pi$
$599$	2.43537e16			0.527236			0.263618	+	0.964627i	$0.415084\pi$
$600$		−	2.46671e16i		−	0.528701i
$601$		−	7.07185e16i		−	1.50067i	−0.661055	−	0.750337i	$-0.729891\pi$
$601$		−	7.07185e16i		−	1.50067i	0.661055	−	0.750337i	$-0.270109\pi$
$602$			1.22474e16i			0.257316i
$603$	5.01980e14			0.0104420
$604$		−	5.90482e14i		−	0.0121614i
$605$	−3.64940e16	−	6.15457e16i	−0.744198	−	1.25506i
$606$	1.66715e16			0.336619
$607$			3.79538e16i			0.758793i	0.925234	+	0.379396i	$0.123868\pi$
$607$			3.79538e16i			0.758793i	−0.925234	+	0.379396i	$0.876132\pi$
$608$	2.23847e15			0.0443128
$609$	−7.71510e15			−0.151230
$610$	−9.67710e16			−1.87830
$611$		−	4.57254e16i		−	0.878841i
$612$		−	1.34147e14i		−	0.00255312i
$613$			4.28383e16i			0.807363i	0.914900	+	0.403682i	$0.132270\pi$
$613$			4.28383e16i			0.807363i	−0.914900	+	0.403682i	$0.867730\pi$
$614$	−1.88711e16			−0.352197
$615$			1.46418e16i			0.270610i
$616$	1.15160e16	+	6.55979e15i	0.210774	+	0.120062i
$617$	−7.93651e16			−1.43853			−0.719264	−	0.694737i	$-0.755521\pi$
$617$	−7.93651e16			−1.43853			−0.719264	+	0.694737i	$0.755521\pi$
$618$			4.71836e16i			0.846955i
$619$	3.29337e16			0.585460			0.292730	−	0.956195i	$-0.405436\pi$
$619$	3.29337e16			0.585460			0.292730	+	0.956195i	$0.405436\pi$
$620$	−1.23286e15			−0.0217052
$621$	−3.23704e16			−0.564415
$622$			5.58631e16i			0.964678i
$623$			1.24587e16i			0.213080i
$624$		−	5.48695e16i		−	0.929445i
$625$	−5.09229e16			−0.854344
$626$			6.81879e15i			0.113308i
$627$	−2.03496e16	+	3.57246e16i	−0.334927	+	0.587979i
$628$	−1.30108e15			−0.0212103
$629$		−	1.02362e16i		−	0.165286i
$630$	−1.74693e16			−0.279403
$631$	3.07743e15			0.0487542			0.0243771	−	0.999703i	$-0.492240\pi$
$631$	3.07743e15			0.0487542			0.0243771	+	0.999703i	$0.492240\pi$
$632$	−6.77830e16			−1.06370
$633$		−	2.04085e16i		−	0.317241i
$634$		−	5.45554e16i		−	0.840044i
$635$			4.15839e16i			0.634283i
$636$	−3.84150e14			−0.00580441
$637$			1.21839e17i			1.82368i
$638$	7.73843e16	+	4.40800e16i	1.14744	+	0.653609i
$639$	1.93781e16			0.284647
$640$		−	1.02531e17i		−	1.49202i
$641$	−3.54732e15			−0.0511390			−0.0255695	−	0.999673i	$-0.508140\pi$
$641$	−3.54732e15			−0.0511390			−0.0255695	+	0.999673i	$0.508140\pi$
$642$	−1.51284e16			−0.216064
$643$	1.38382e17			1.95800			0.979001	−	0.203854i	$-0.0653469\pi$
$643$	1.38382e17			1.95800			0.979001	+	0.203854i	$0.0653469\pi$
$644$			1.81385e14i			0.00254265i
$645$			5.17913e16i			0.719281i
$646$			2.23149e16i			0.307043i
$647$	−5.52971e16			−0.753836			−0.376918	−	0.926247i	$-0.623016\pi$
$647$	−5.52971e16			−0.753836			−0.376918	+	0.926247i	$0.623016\pi$
$648$		−	2.80059e16i		−	0.378268i
$649$	4.61685e16	+	2.62987e16i	0.617842	+	0.351939i
$650$	1.66429e17			2.20672
$651$			8.45430e15i			0.111069i
$652$	4.49379e14			0.00584961
$653$	−1.28495e17			−1.65733			−0.828664	−	0.559746i	$-0.810899\pi$
$653$	−1.28495e17			−1.65733			−0.828664	+	0.559746i	$0.810899\pi$
$654$	−6.48084e14			−0.00828256
$655$		−	1.46060e17i		−	1.84962i
$656$			3.17900e16i			0.398904i
$657$		−	6.18897e16i		−	0.769531i
$658$	9.06045e15			0.111633
$659$		−	2.56885e16i		−	0.313636i	−0.987628	−	0.156818i	$-0.949876\pi$
$659$		−	2.56885e16i		−	0.313636i	0.987628	−	0.156818i	$-0.0501236\pi$
$660$	−7.64500e14	−	4.35479e14i	−0.00924941	−	0.00526870i
$661$	−7.96229e15			−0.0954617			−0.0477308	−	0.998860i	$-0.515199\pi$
$661$	−7.96229e15			−0.0954617			−0.0477308	+	0.998860i	$0.515199\pi$
$662$			1.30414e17i			1.54944i
$663$	1.65264e16			0.194579
$664$	−3.37649e16			−0.393964
$665$	4.42312e16			0.511445
$666$			5.31520e16i			0.609079i
$667$		−	7.76404e16i		−	0.881724i
$668$			2.22509e15i			0.0250432i
$669$	1.26461e16			0.141058
$670$		−	1.78695e15i		−	0.0197543i
$671$	5.77098e16	−	1.01312e17i	0.632287	−	1.11000i
$672$	3.28493e14			0.00356706
$673$		−	1.61921e17i		−	1.74266i	−0.490697	−	0.871331i	$-0.663258\pi$
$673$		−	1.61921e17i		−	1.74266i	0.490697	−	0.871331i	$-0.336742\pi$
$674$	−4.49835e16			−0.479837
$675$	−8.95790e16			−0.947073
$676$	4.07409e15			0.0426924
$677$			1.23850e16i			0.128636i	0.997929	+	0.0643182i	$0.0204873\pi$
$677$			1.23850e16i			0.128636i	−0.997929	+	0.0643182i	$0.979513\pi$
$678$		−	4.73381e16i		−	0.487340i
$679$			1.43580e16i			0.146513i
$680$	3.04186e16			0.307671
$681$		−	4.13663e16i		−	0.414729i
$682$	4.83035e16	−	8.47986e16i	0.480034	−	0.842719i
$683$	1.76410e16			0.173780			0.0868899	−	0.996218i	$-0.472307\pi$
$683$	1.76410e16			0.173780			0.0868899	+	0.996218i	$0.472307\pi$
$684$		−	1.76366e15i		−	0.0172218i
$685$	2.62455e17			2.54045
$686$	−4.98195e16			−0.478029
$687$	8.48810e15			0.0807366
$688$			1.12448e17i			1.06028i
$689$			1.65100e17i			1.54323i
$690$			5.03933e16i			0.466959i
$691$	−1.09178e17			−1.00292			−0.501462	−	0.865180i	$-0.667204\pi$
$691$	−1.09178e17			−1.00292			−0.501462	+	0.865180i	$0.667204\pi$
$692$		−	7.88854e14i		−	0.00718389i
$693$	1.04179e16	−	1.82890e16i	0.0940545	−	0.165116i
$694$	−5.07037e16			−0.453819
$695$			1.92309e17i			1.70644i
$696$	−6.97568e16			−0.613665
$697$	−9.57496e15			−0.0835104
$698$	−1.44297e17			−1.24774
$699$			5.81242e16i			0.498303i
$700$			5.01949e14i			0.00426650i
$701$		−	1.02531e17i		−	0.864069i	−0.901857	−	0.432035i	$-0.857796\pi$
$701$		−	1.02531e17i		−	0.864069i	0.901857	−	0.432035i	$-0.142204\pi$
$702$	−1.96226e17			−1.63959
$703$		−	1.34578e17i		−	1.11491i
$704$	1.04097e17	+	5.92966e16i	0.855075	+	0.487073i
$705$	3.83143e16			0.312052
$706$		−	8.65903e16i		−	0.699263i
$707$	2.16098e16			0.173035
$708$	6.53349e14			0.00518735
$709$	1.71448e17			1.34975			0.674877	−	0.737931i	$-0.264197\pi$
$709$	1.71448e17			1.34975			0.674877	+	0.737931i	$0.264197\pi$
$710$		−	6.89821e16i		−	0.538501i
$711$			1.07649e17i			0.833282i
$712$			1.12646e17i			0.864642i
$713$	−8.50793e16			−0.647570
$714$			3.27469e15i			0.0247161i
$715$	−1.87160e17	+	3.28566e17i	−1.40080	+	2.45916i
$716$	−3.23672e14			−0.00240230
$717$		−	1.16897e17i		−	0.860380i
$718$	2.21480e17			1.61655
$719$	5.70456e16			0.412904			0.206452	−	0.978457i	$-0.433808\pi$
$719$	5.70456e16			0.412904			0.206452	+	0.978457i	$0.433808\pi$
$720$	−1.60392e17			−1.15130
$721$			6.11601e16i			0.435368i
$722$			1.50636e17i			1.06342i
$723$			8.40599e15i			0.0588517i
$724$	−1.39700e15			−0.00969986
$725$		−	2.14855e17i		−	1.47951i
$726$	5.99063e16	−	3.55219e16i	0.409122	−	0.242592i
$727$	−1.31016e17			−0.887395			−0.443698	−	0.896177i	$-0.646334\pi$
$727$	−1.31016e17			−0.887395			−0.443698	+	0.896177i	$0.646334\pi$
$728$		−	7.00399e16i		−	0.470497i
$729$	1.49514e16			0.0996132
$730$	−2.20315e17			−1.45582
$731$	−3.38688e16			−0.221970
$732$		−	1.43370e15i		−	0.00931951i
$733$		−	1.84063e17i		−	1.18670i	−0.804943	−	0.593352i	$-0.797804\pi$
$733$		−	1.84063e17i		−	1.18670i	0.804943	−	0.593352i	$-0.202196\pi$
$734$		−	2.03204e17i		−	1.29944i
$735$	−1.02091e17			−0.647538
$736$			3.30577e15i			0.0207972i
$737$	1.87080e15	+	1.06565e15i	0.0116740	+	0.00664983i
$738$	4.97184e16			0.307737
$739$		−	2.48065e17i		−	1.52300i	−0.648166	−	0.761499i	$-0.724464\pi$
$739$		−	2.48065e17i		−	1.52300i	0.648166	−	0.761499i	$-0.275536\pi$
$740$	2.87994e15			0.0175385
$741$	2.17276e17			1.31251
$742$	−3.27143e16			−0.196026
$743$			3.27268e17i			1.94523i	0.232425	+	0.972614i	$0.425334\pi$
$743$			3.27268e17i			1.94523i	−0.232425	+	0.972614i	$0.574666\pi$
$744$			7.64404e16i			0.450697i
$745$			1.65447e17i			0.967657i
$746$	−2.17957e16			−0.126456
$747$			5.36234e16i			0.308624i
$748$	2.84780e14	−	4.99943e14i	0.00162592	−	0.00285437i
$749$	−1.96096e16			−0.111065
$750$			1.59354e16i			0.0895356i
$751$	2.78712e17			1.55352			0.776758	−	0.629799i	$-0.216863\pi$
$751$	2.78712e17			1.55352			0.776758	+	0.629799i	$0.216863\pi$
$752$	8.31874e16			0.459992
$753$	8.82152e16			0.483920
$754$		−	4.70649e17i		−	2.56135i
$755$		−	2.12645e17i		−	1.14808i
$756$		−	5.91819e14i		−	0.00316999i
$757$	1.34441e17			0.714426			0.357213	−	0.934023i	$-0.383727\pi$
$757$	1.34441e17			0.714426			0.357213	+	0.934023i	$0.383727\pi$
$758$			3.88336e16i			0.204735i
$759$	−5.27580e16	−	3.00523e16i	−0.275954	−	0.157191i
$760$	3.99920e17			2.07535
$761$			2.51165e17i			1.29316i	0.762847	+	0.646579i	$0.223801\pi$
$761$			2.51165e17i			1.29316i	−0.762847	+	0.646579i	$0.776199\pi$
$762$	−4.04762e16			−0.206762
$763$	−8.40056e14			−0.00425756
$764$	2.41050e12			1.21212e−5
$765$		−	4.83091e16i		−	0.241024i
$766$			2.66307e17i			1.31829i
$767$		−	2.80796e17i		−	1.37917i
$768$	4.48985e15			0.0218809
$769$			1.54166e17i			0.745471i	0.927938	+	0.372735i	$0.121580\pi$
$769$			1.54166e17i			0.745471i	−0.927938	+	0.372735i	$0.878420\pi$
$770$	−6.51051e16	−	3.70855e16i	−0.312371	−	0.177934i
$771$	2.31307e16			0.110119
$772$		−	4.60654e13i		−	0.000217606i
$773$	−1.86312e16			−0.0873299			−0.0436649	−	0.999046i	$-0.513903\pi$
$773$	−1.86312e16			−0.0873299			−0.0436649	+	0.999046i	$0.513903\pi$
$774$	1.75865e17			0.817963
$775$	−2.35441e17			−1.08661
$776$			1.29819e17i			0.594523i
$777$		−	1.97491e16i		−	0.0897474i
$778$			1.38994e17i			0.626784i
$779$	−1.25884e17			−0.563308
$780$			4.64967e15i			0.0206469i
$781$	7.22190e16	+	4.11378e16i	0.318233	+	0.181274i
$782$	−3.29546e16			−0.144104
$783$			2.53323e17i			1.09927i
$784$	−2.21659e17			−0.954529
$785$	−4.68546e17			−2.00232
$786$	1.42169e17			0.602935
$787$			1.67643e16i			0.0705563i	0.999378	+	0.0352782i	$0.0112317\pi$
$787$			1.67643e16i			0.0705563i	−0.999378	+	0.0352782i	$0.988768\pi$
$788$			4.30949e15i			0.0179998i
$789$		−	4.94679e16i		−	0.205051i
$790$	3.83208e17			1.57642
$791$		−	6.13603e16i		−	0.250512i
$792$	9.41942e16	−	1.65362e17i	0.381657	−	0.670014i
$793$	−6.16176e17			−2.47780
$794$		−	2.52302e17i		−	1.00693i
$795$	−1.38341e17			−0.547957
$796$	−3.07551e15			−0.0120904
$797$	2.05788e17			0.802915			0.401457	−	0.915878i	$-0.368504\pi$
$797$	2.05788e17			0.802915			0.401457	+	0.915878i	$0.368504\pi$
$798$			4.30530e16i			0.166719i
$799$			2.50555e16i			0.0962993i
$800$			9.14809e15i			0.0348972i
$801$	1.78898e17			0.677346
$802$		−	2.26448e17i		−	0.850987i
$803$	1.31386e17	−	2.30653e17i	0.490066	−	0.860330i
$804$	2.64744e13			9.80143e−5
$805$			6.53205e16i			0.240035i
$806$	−5.15743e17			−1.88115
$807$	−1.53892e17			−0.557155
$808$	1.95387e17			0.702148
$809$			9.32696e16i			0.332697i	0.986067	+	0.166349i	$0.0531977\pi$
$809$			9.32696e16i			0.332697i	−0.986067	+	0.166349i	$0.946802\pi$
$810$			1.58330e17i			0.560600i
$811$			3.32746e17i			1.16947i	0.811226	+	0.584733i	$0.198801\pi$
$811$			3.32746e17i			1.16947i	−0.811226	+	0.584733i	$0.801199\pi$
$812$	1.41948e15			0.00495214
$813$		−	2.29684e17i		−	0.795402i
$814$	−1.12836e17	+	1.98089e17i	−0.387884	+	0.680946i
$815$	1.61831e17			0.552224
$816$			3.00661e16i			0.101844i
$817$	−4.45280e17			−1.49727
$818$	2.53510e17			0.846204
$819$	−1.11233e17			−0.368579
$820$		−	2.69390e15i		−	0.00886133i
$821$		−	3.16822e17i		−	1.03456i	−0.855815	−	0.517282i	$-0.826944\pi$
$821$		−	3.16822e17i		−	1.03456i	0.855815	−	0.517282i	$-0.173056\pi$
$822$			2.55464e17i			0.828131i
$823$	−2.57312e17			−0.828060			−0.414030	−	0.910263i	$-0.635879\pi$
$823$	−2.57312e17			−0.828060			−0.414030	+	0.910263i	$0.635879\pi$
$824$			5.52985e17i			1.76665i
$825$	−1.45998e17	−	8.31641e16i	−0.463045	−	0.263762i
$826$	5.56394e16			0.175187
$827$		−	1.40798e17i		−	0.440113i	−0.975487	−	0.220056i	$-0.929376\pi$
$827$		−	1.40798e17i		−	0.440113i	0.975487	−	0.220056i	$-0.0706242\pi$
$828$	2.60457e15			0.00808264
$829$	4.32730e17			1.33318			0.666591	−	0.745424i	$-0.267753\pi$
$829$	4.32730e17			1.33318			0.666591	+	0.745424i	$0.267753\pi$
$830$	1.90888e17			0.583862
$831$			4.70409e16i			0.142846i
$832$		−	6.33118e17i		−	1.90873i
$833$		−	6.67624e16i		−	0.199830i
$834$	−1.87186e17			−0.556260
$835$			8.01303e17i			2.36417i
$836$	3.74407e15	−	6.57286e15i	0.0109675	−	0.0192538i
$837$	2.77595e17			0.807344
$838$			3.19304e17i			0.922021i
$839$	2.37272e17			0.680260			0.340130	−	0.940378i	$-0.389529\pi$
$839$	2.37272e17			0.680260			0.340130	+	0.940378i	$0.389529\pi$
$840$	5.86879e16			0.167060
$841$	−2.53782e17			−0.717273
$842$		−	4.89564e17i		−	1.37384i
$843$			2.60899e16i			0.0726954i
$844$			3.75491e15i			0.0103883i
$845$	1.46717e18			4.03031
$846$		−	1.30102e17i		−	0.354864i
$847$	7.76513e16	−	4.60439e16i	0.210304	−	0.124702i
$848$	−3.00363e17			−0.807738
$849$			1.99272e17i			0.532108i
$850$	−9.11957e16			−0.241802
$851$	1.98744e17			0.523259
$852$	1.02200e15			0.00267186
$853$		−	3.85868e17i		−	1.00172i	−0.865530	−	0.500858i	$-0.833018\pi$
$853$		−	3.85868e17i		−	1.00172i	0.865530	−	0.500858i	$-0.166982\pi$
$854$		−	1.22095e17i		−	0.314738i
$855$		−	6.35130e17i		−	1.62580i
$856$	−1.77302e17			−0.450683
$857$			2.08819e17i			0.527090i	0.964647	+	0.263545i	$0.0848918\pi$
$857$			2.08819e17i			0.527090i	−0.964647	+	0.263545i	$0.915108\pi$
$858$	−3.19814e17	−	1.82174e17i	−0.801630	−	0.456629i
$859$	−5.06753e17			−1.26135			−0.630677	−	0.776045i	$-0.717223\pi$
$859$	−5.06753e17			−1.26135			−0.630677	+	0.776045i	$0.717223\pi$
$860$		−	9.52893e15i		−	0.0235534i
$861$	−1.84734e16			−0.0453448
$862$	4.20764e17			1.02564
$863$	−5.75730e16			−0.139365			−0.0696826	−	0.997569i	$-0.522199\pi$
$863$	−5.75730e16			−0.139365			−0.0696826	+	0.997569i	$0.522199\pi$
$864$		−	1.07860e16i		−	0.0259285i
$865$		−	2.84083e17i		−	0.678185i
$866$			1.59932e17i			0.379164i
$867$	1.91419e17			0.450683
$868$		−	1.55548e15i		−	0.00363703i
$869$	−2.28528e17	+	4.01189e17i	−0.530665	+	0.931603i
$870$	3.94367e17			0.909463
$871$		−	1.13781e16i		−	0.0260592i
$872$	−7.59544e15			−0.0172764
$873$	2.06171e17			0.465739
$874$	−4.33261e17			−0.972033
$875$			2.06557e16i			0.0460248i
$876$		−	3.26406e15i		−	0.00722326i
$877$		−	3.34513e17i		−	0.735216i	−0.929981	−	0.367608i	$-0.880177\pi$
$877$		−	3.34513e17i		−	0.735216i	0.929981	−	0.367608i	$-0.119823\pi$
$878$	−7.36657e16			−0.160804
$879$		−	1.57786e17i		−	0.342086i
$880$	−5.97754e17	−	3.40496e17i	−1.28714	−	0.733189i
$881$	−5.04791e16			−0.107958			−0.0539791	−	0.998542i	$-0.517190\pi$
$881$	−5.04791e16			−0.107958			−0.0539791	+	0.998542i	$0.517190\pi$
$882$			3.46666e17i			0.736377i
$883$	4.75375e15			0.0100293			0.00501467	−	0.999987i	$-0.498404\pi$
$883$	4.75375e15			0.0100293			0.00501467	+	0.999987i	$0.498404\pi$
$884$	−3.04064e15			−0.00637164
$885$	2.35285e17			0.489704
$886$			5.47162e17i			1.13113i
$887$			3.85227e17i			0.790998i	0.918466	+	0.395499i	$0.129428\pi$
$887$			3.85227e17i			0.790998i	−0.918466	+	0.395499i	$0.870572\pi$
$888$		−	1.78564e17i		−	0.364179i
$889$	−5.24659e16			−0.106284
$890$		−	6.36840e17i		−	1.28142i
$891$	−1.65759e17	−	9.44207e16i	−0.331293	−	0.188713i
$892$	−2.32672e15			−0.00461907
$893$			3.29411e17i			0.649574i
$894$	−1.61040e17			−0.315434
$895$	−1.16561e17			−0.226786
$896$	1.29362e17			0.250011
$897$			3.20873e17i			0.615996i
$898$			9.40899e17i			1.79426i
$899$			6.65812e17i			1.26123i
$900$	7.20765e15			0.0135625
$901$		−	9.04674e16i		−	0.169100i
$902$	1.85292e17	+	1.05547e17i	0.344047	+	0.195978i
$903$	−6.53444e16			−0.120526
$904$		−	5.54795e17i		−	1.01653i
$905$	−5.03089e17			−0.915701
$906$	2.06981e17			0.374249
$907$	−1.37016e17			−0.246110			−0.123055	−	0.992400i	$-0.539269\pi$
$907$	−1.37016e17			−0.246110			−0.123055	+	0.992400i	$0.539269\pi$
$908$			7.61087e15i			0.0135806i
$909$		−	3.10303e17i		−	0.550050i
$910$			3.95967e17i			0.697286i
$911$	−2.32726e17			−0.407132			−0.203566	−	0.979061i	$-0.565253\pi$
$911$	−2.32726e17			−0.407132			−0.203566	+	0.979061i	$0.565253\pi$
$912$			3.95286e17i			0.686977i
$913$	−1.13837e17	+	1.99845e17i	−0.196543	+	0.345040i
$914$	−1.17341e18			−2.01267
$915$		−	5.16307e17i		−	0.879795i
$916$	−1.56170e15			−0.00264378
$917$	1.84282e17			0.309932
$918$	1.07523e17			0.179658
$919$			4.40183e17i			0.730702i	0.930870	+	0.365351i	$0.119051\pi$
$919$			4.40183e17i			0.730702i	−0.930870	+	0.365351i	$0.880949\pi$
$920$			5.90602e17i			0.974020i
$921$		−	1.00684e17i		−	0.164969i
$922$	7.12578e17			1.15997
$923$		−	4.39234e17i		−	0.710372i
$924$	5.49438e14	−	9.64560e14i	0.000882850	−	0.00154988i
$925$	5.49987e17			0.878016
$926$		−	1.46639e17i		−	0.232586i
$927$	8.78217e17			1.38396
$928$	2.58702e16			0.0405053
$929$	3.96528e17			0.616850			0.308425	−	0.951249i	$-0.400198\pi$
$929$	3.96528e17			0.616850			0.308425	+	0.951249i	$0.400198\pi$
$930$		−	4.32152e17i		−	0.667942i
$931$		−	8.77739e17i		−	1.34793i
$932$		−	1.06941e16i		−	0.0163173i
$933$	−2.98049e17			−0.451854
$934$			2.83613e16i			0.0427213i
$935$	1.02555e17	−	1.80040e17i	0.153493	−	0.269463i
$936$	−1.00572e18			−1.49563
$937$		−	4.94137e17i		−	0.730147i	−0.930979	−	0.365073i	$-0.881044\pi$
$937$		−	4.94137e17i		−	0.730147i	0.930979	−	0.365073i	$-0.118956\pi$
$938$	2.25457e15			0.00331014
$939$	−3.63806e16			−0.0530733
$940$	−7.04934e15			−0.0102184
$941$		−	7.75019e17i		−	1.11628i	−0.829745	−	0.558142i	$-0.811514\pi$
$941$		−	7.75019e17i		−	1.11628i	0.829745	−	0.558142i	$-0.188486\pi$
$942$		−	4.56065e17i		−	0.652712i
$943$		−	1.85905e17i		−	0.264376i
$944$	5.10846e17			0.721869
$945$		−	2.13126e17i		−	0.299258i
$946$	6.55420e17	+	3.73344e17i	0.914477	+	0.520909i
$947$	8.20559e17			1.13765			0.568826	−	0.822458i	$-0.307398\pi$
$947$	8.20559e17			1.13765			0.568826	+	0.822458i	$0.307398\pi$
$948$			5.67739e15i			0.00782166i
$949$	−1.40282e18			−1.92046
$950$	−1.19897e18			−1.63105
$951$	2.91072e17			0.393475
$952$			3.83788e16i			0.0515549i
$953$			8.58526e17i			1.14603i	0.819545	+	0.573015i	$0.194226\pi$
$953$			8.58526e17i			1.14603i	−0.819545	+	0.573015i	$0.805774\pi$
$954$			4.69756e17i			0.623135i
$955$	8.68071e14			0.00114429
$956$			2.15076e16i			0.0281738i
$957$	−2.35182e17	+	4.12872e17i	−0.306149	+	0.537457i
$958$	8.63200e17			1.11665
$959$			3.31136e17i			0.425691i
$960$	5.30503e17			0.677736
$961$	−5.80582e16			−0.0737095
$962$	1.20477e18			1.52003
$963$			2.81581e17i			0.353057i
$964$		−	1.54659e15i		−	0.00192714i
$965$		−	1.65891e16i		−	0.0205428i
$966$	−6.35806e16			−0.0782460
$967$		−	1.02055e18i		−	1.24817i	−0.781356	−	0.624086i	$-0.785472\pi$
$967$		−	1.02055e18i		−	1.24817i	0.781356	−	0.624086i	$-0.214528\pi$
$968$	7.02092e17	−	4.16311e17i	0.853379	−	0.506017i
$969$	−1.19058e17			−0.143818
$970$		−	7.33928e17i		−	0.881095i
$971$	1.49424e17			0.178281			0.0891403	−	0.996019i	$-0.471588\pi$
$971$	1.49424e17			0.178281			0.0891403	+	0.996019i	$0.471588\pi$
$972$	−1.32798e16			−0.0157469
$973$	−2.42633e17			−0.285939
$974$			3.40889e17i			0.399263i
$975$			8.87955e17i			1.03363i
$976$		−	1.12100e18i		−	1.29690i
$977$	−5.10977e17			−0.587535			−0.293767	−	0.955877i	$-0.594909\pi$
$977$	−5.10977e17			−0.587535			−0.293767	+	0.955877i	$0.594909\pi$
$978$			1.57520e17i			0.180013i
$979$	6.66723e17	+	3.79782e17i	0.757267	+	0.431359i
$980$	1.87835e16			0.0212041
$981$			1.20626e16i			0.0135341i
$982$	1.10447e18			1.23164
$983$	−1.13420e18			−1.25710			−0.628550	−	0.777769i	$-0.716351\pi$
$983$	−1.13420e18			−1.25710			−0.628550	+	0.777769i	$0.716351\pi$
$984$	−1.67029e17			−0.184001
$985$			1.55194e18i			1.69925i
$986$			2.57895e17i			0.280661i
$987$			4.83407e16i			0.0522889i
$988$	−3.99759e16			−0.0429791
$989$		−	6.57589e17i		−	0.702711i
$990$	−5.32523e17	+	9.34865e17i	−0.565623	+	0.992973i
$991$	9.51779e17			1.00483			0.502417	−	0.864626i	$-0.332444\pi$
$991$	9.51779e17			1.00483			0.502417	+	0.864626i	$0.332444\pi$
$992$		−	2.83489e16i		−	0.0297485i
$993$	−6.95803e17			−0.725756
$994$	8.70338e16			0.0902339
$995$	−1.10756e18			−1.14137
$996$			2.82809e15i			0.00289693i
$997$			1.69895e18i			1.72986i	0.501895	+	0.864929i	$0.332636\pi$
$997$			1.69895e18i			1.72986i	−0.501895	+	0.864929i	$0.667364\pi$
$998$		−	1.77734e18i		−	1.79882i
$999$	−6.48458e17			−0.652362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.13.b.b.10.3	✓	10
3.2	odd	2		99.13.c.b.10.8		10
4.3	odd	2		176.13.h.c.65.6		10
11.10	odd	2	inner	11.13.b.b.10.8	yes	10
33.32	even	2		99.13.c.b.10.3		10
44.43	even	2		176.13.h.c.65.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.13.b.b.10.3	✓	10	1.1	even	1	trivial
11.13.b.b.10.8	yes	10	11.10	odd	2	inner
99.13.c.b.10.3		10	33.32	even	2
99.13.c.b.10.8		10	3.2	odd	2
176.13.h.c.65.5		10	44.43	even	2
176.13.h.c.65.6		10	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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-64.4927i q^{2} +344.091 q^{3} -63.3083 q^{4} -22798.6 q^{5} -22191.4i q^{6} -28764.7i q^{7} -260079. i q^{8} -413042. q^{9} +O(q^{10})\)	\(q-64.4927i q^{2} +344.091 q^{3} -63.3083 q^{4} -22798.6 q^{5} -22191.4i q^{6} -28764.7i q^{7} -260079. i q^{8} -413042. q^{9} +1.47035e6i q^{10} +(-1.53934e6 - 876847. i) q^{11} -21783.8 q^{12} +9.36222e6i q^{13} -1.85512e6 q^{14} -7.84481e6 q^{15} -1.70325e7 q^{16} -5.13009e6i q^{17} +2.66382e7i q^{18} -6.74464e7i q^{19} +1.44334e6 q^{20} -9.89769e6i q^{21} +(-5.65502e7 + 9.92762e7i) q^{22} +9.96048e7 q^{23} -8.94909e7i q^{24} +2.75638e8 q^{25} +6.03795e8 q^{26} -3.24988e8 q^{27} +1.82105e6i q^{28} -7.79485e8i q^{29} +5.05933e8i q^{30} -8.54169e8 q^{31} +3.31888e7i q^{32} +(-5.29673e8 - 3.01715e8i) q^{33} -3.30853e8 q^{34} +6.55797e8i q^{35} +2.61490e7 q^{36} +1.99533e9 q^{37} -4.34980e9 q^{38} +3.22146e9i q^{39} +5.92945e9i q^{40} -1.86643e9i q^{41} -6.38329e8 q^{42} -6.60198e9i q^{43} +(9.74530e7 + 5.55117e7i) q^{44} +9.41681e9 q^{45} -6.42378e9i q^{46} -4.88403e9 q^{47} -5.86074e9 q^{48} +1.30139e10 q^{49} -1.77766e10i q^{50} -1.76522e9i q^{51} -5.92707e8i q^{52} +1.76347e10 q^{53} +2.09594e10i q^{54} +(3.50949e10 + 1.99909e10i) q^{55} -7.48111e9 q^{56} -2.32077e10i q^{57} -5.02711e10 q^{58} -2.99924e10 q^{59} +4.96642e8 q^{60} +6.58151e10i q^{61} +5.50877e10i q^{62} +1.18811e10i q^{63} -6.76248e10 q^{64} -2.13446e11i q^{65} +(-1.94584e10 + 3.41600e10i) q^{66} -1.21532e9 q^{67} +3.24777e8i q^{68} +3.42731e10 q^{69} +4.22941e10 q^{70} -4.69156e10 q^{71} +1.07424e11i q^{72} +1.49839e11i q^{73} -1.28684e11i q^{74} +9.48445e10 q^{75} +4.26992e9i q^{76} +(-2.52223e10 + 4.42787e10i) q^{77} +2.07760e11 q^{78} -2.60624e11i q^{79} +3.88318e11 q^{80} +1.07682e11 q^{81} -1.20371e11 q^{82} -1.29825e11i q^{83} +6.26606e8i q^{84} +1.16959e11i q^{85} -4.25780e11 q^{86} -2.68214e11i q^{87} +(-2.28050e11 + 4.00350e11i) q^{88} -4.33123e11 q^{89} -6.07315e11i q^{90} +2.69302e11 q^{91} -6.30581e9 q^{92} -2.93912e11 q^{93} +3.14985e11i q^{94} +1.53769e12i q^{95} +1.14200e10i q^{96} -4.99153e11 q^{97} -8.39300e11i q^{98} +(6.35813e11 + 3.62175e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9}+O(q^{10}) \) 10 * q + 2436 * q^3 - 20348 * q^4 + 26492 * q^5 + 756294 * q^9	\( 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9} - 1716374 q^{11} - 8491644 q^{12} - 15139368 q^{14} + 9632184 q^{15} + 17974408 q^{16} - 125399668 q^{20} + 83533560 q^{22} + 330297476 q^{23} - 438477018 q^{25} - 372191832 q^{26} + 1665774072 q^{27} - 1921955548 q^{31} - 2301728484 q^{33} + 7677299352 q^{34} - 14333366928 q^{36} + 1788323996 q^{37} + 11254769640 q^{38} - 32091748680 q^{42} + 6124969708 q^{44} + 43304121996 q^{45} - 24975510124 q^{47} + 32578826856 q^{48} - 6325710998 q^{49} - 16325502124 q^{53} + 14298843812 q^{55} + 82892128176 q^{56} - 84518430720 q^{58} + 62339390564 q^{59} - 286034518116 q^{60} + 95192926864 q^{64} + 322939363560 q^{66} - 90035301244 q^{67} + 346118875824 q^{69} - 382808641560 q^{70} - 359910119740 q^{71} + 14209300764 q^{75} + 425991883680 q^{77} - 483427126680 q^{78} + 1147768798712 q^{80} - 515542099806 q^{81} + 625030365960 q^{82} - 1219447545552 q^{86} + 134692485840 q^{88} + 670996780412 q^{89} + 1356772643808 q^{91} - 3181666532764 q^{92} + 1928296959312 q^{93} - 6250704684964 q^{97} - 1402418596722 q^{99}+O(q^{100}) \) 10 * q + 2436 * q^3 - 20348 * q^4 + 26492 * q^5 + 756294 * q^9 - 1716374 * q^11 - 8491644 * q^12 - 15139368 * q^14 + 9632184 * q^15 + 17974408 * q^16 - 125399668 * q^20 + 83533560 * q^22 + 330297476 * q^23 - 438477018 * q^25 - 372191832 * q^26 + 1665774072 * q^27 - 1921955548 * q^31 - 2301728484 * q^33 + 7677299352 * q^34 - 14333366928 * q^36 + 1788323996 * q^37 + 11254769640 * q^38 - 32091748680 * q^42 + 6124969708 * q^44 + 43304121996 * q^45 - 24975510124 * q^47 + 32578826856 * q^48 - 6325710998 * q^49 - 16325502124 * q^53 + 14298843812 * q^55 + 82892128176 * q^56 - 84518430720 * q^58 + 62339390564 * q^59 - 286034518116 * q^60 + 95192926864 * q^64 + 322939363560 * q^66 - 90035301244 * q^67 + 346118875824 * q^69 - 382808641560 * q^70 - 359910119740 * q^71 + 14209300764 * q^75 + 425991883680 * q^77 - 483427126680 * q^78 + 1147768798712 * q^80 - 515542099806 * q^81 + 625030365960 * q^82 - 1219447545552 * q^86 + 134692485840 * q^88 + 670996780412 * q^89 + 1356772643808 * q^91 - 3181666532764 * q^92 + 1928296959312 * q^93 - 6250704684964 * q^97 - 1402418596722 * q^99

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