LMFDB - Embedded newform 11.13.b.b.10.10

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			10.10
Root			$110.069i$ of defining polynomial
Character	$\chi$	$=$	11.10
Dual form			11.13.b.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+110.069i q^{2} +1258.46 q^{3} -8019.20 q^{4} +14011.2 q^{5} +138518. i q^{6} +131085. i q^{7} -431823. i q^{8} +1.05229e6 q^{9} +O(q^{10})$	\(q+110.069i q^{2} +1258.46 q^{3} -8019.20 q^{4} +14011.2 q^{5} +138518. i q^{6} +131085. i q^{7} -431823. i q^{8} +1.05229e6 q^{9} +1.54220e6i q^{10} +(-1.39887e6 - 1.08701e6i) q^{11} -1.00919e7 q^{12} +3.22288e6i q^{13} -1.44284e7 q^{14} +1.76326e7 q^{15} +1.46837e7 q^{16} -3.44290e7i q^{17} +1.15824e8i q^{18} -3.46006e7i q^{19} -1.12359e8 q^{20} +1.64965e8i q^{21} +(1.19646e8 - 1.53973e8i) q^{22} +1.65999e8 q^{23} -5.43433e8i q^{24} -4.78263e7 q^{25} -3.54740e8 q^{26} +6.55465e8 q^{27} -1.05120e9i q^{28} +9.11924e8i q^{29} +1.94080e9i q^{30} +2.56746e8 q^{31} -1.52526e8i q^{32} +(-1.76043e9 - 1.36796e9i) q^{33} +3.78957e9 q^{34} +1.83666e9i q^{35} -8.43850e9 q^{36} +1.07127e9 q^{37} +3.80846e9 q^{38} +4.05588e9i q^{39} -6.05036e9i q^{40} -5.70065e9i q^{41} -1.81576e10 q^{42} -3.44514e9i q^{43} +(1.12178e10 + 8.71692e9i) q^{44} +1.47438e10 q^{45} +1.82714e10i q^{46} -2.28345e9 q^{47} +1.84789e10 q^{48} -3.34197e9 q^{49} -5.26420e9i q^{50} -4.33276e10i q^{51} -2.58449e10i q^{52} +6.37380e9 q^{53} +7.21465e10i q^{54} +(-1.95999e10 - 1.52303e10i) q^{55} +5.66054e10 q^{56} -4.35436e10i q^{57} -1.00375e11 q^{58} +4.47524e10 q^{59} -1.41399e11 q^{60} +2.20652e9i q^{61} +2.82598e10i q^{62} +1.37939e11i q^{63} +7.69328e10 q^{64} +4.51565e10i q^{65} +(1.50570e11 - 1.93769e11i) q^{66} -3.46978e10 q^{67} +2.76093e11i q^{68} +2.08904e11 q^{69} -2.02159e11 q^{70} -1.37060e11 q^{71} -4.54402e11i q^{72} -6.76442e10i q^{73} +1.17914e11i q^{74} -6.01877e10 q^{75} +2.77469e11i q^{76} +(1.42490e11 - 1.83371e11i) q^{77} -4.46426e11 q^{78} -9.62506e10i q^{79} +2.05736e11 q^{80} +2.65650e11 q^{81} +6.27465e11 q^{82} +3.17921e11i q^{83} -1.32289e12i q^{84} -4.82392e11i q^{85} +3.79203e11 q^{86} +1.14762e12i q^{87} +(-4.69394e11 + 6.04065e11i) q^{88} +1.40561e11 q^{89} +1.62284e12i q^{90} -4.22471e11 q^{91} -1.33118e12 q^{92} +3.23105e11 q^{93} -2.51338e11i q^{94} -4.84797e11i q^{95} -1.91948e11i q^{96} -1.24384e12 q^{97} -3.67847e11i q^{98} +(-1.47202e12 - 1.14384e12i) 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 $

$2$			110.069i			1.71983i	0.510438	+	0.859915i	$0.329483\pi$
$2$			110.069i			1.71983i	−0.510438	+	0.859915i	$0.670517\pi$
$3$	1258.46			1.72629			0.863143	−	0.504959i	$-0.168493\pi$
$3$	1258.46			1.72629			0.863143	+	0.504959i	$0.168493\pi$
$4$	−8019.20			−1.95781
$5$	14011.2			0.896718			0.448359	−	0.893854i	$-0.352009\pi$
$5$	14011.2			0.896718			0.448359	+	0.893854i	$0.352009\pi$
$6$			138518.i			2.96892i
$7$			131085.i			1.11420i	0.830444	+	0.557102i	$0.188087\pi$
$7$			131085.i			1.11420i	−0.830444	+	0.557102i	$0.811913\pi$
$8$		−	431823.i		−	1.64727i
$9$	1.05229e6			1.98006
$10$			1.54220e6i			1.54220i
$11$	−1.39887e6	−	1.08701e6i	−0.789627	−	0.613587i
$11$	−1.39887e6	−	1.08701e6i	−0.789627	−	0.613587i
$12$	−1.00919e7			−3.37974
$13$			3.22288e6i			0.667704i	0.942625	+	0.333852i	$0.108349\pi$
$13$			3.22288e6i			0.667704i	−0.942625	+	0.333852i	$0.891651\pi$
$14$	−1.44284e7			−1.91624
$15$	1.76326e7			1.54799
$16$	1.46837e7			0.875216
$17$		−	3.44290e7i		−	1.42637i	−0.700978	−	0.713183i	$-0.747253\pi$
$17$		−	3.44290e7i		−	1.42637i	0.700978	−	0.713183i	$-0.252747\pi$
$18$			1.15824e8i			3.40537i
$19$		−	3.46006e7i		−	0.735465i	−0.929932	−	0.367733i	$-0.880134\pi$
$19$		−	3.46006e7i		−	0.735465i	0.929932	−	0.367733i	$-0.119866\pi$
$20$	−1.12359e8			−1.75561
$21$			1.64965e8i			1.92343i
$22$	1.19646e8	−	1.53973e8i	1.05526	−	1.35802i
$23$	1.65999e8			1.12134			0.560672	−	0.828038i	$-0.310543\pi$
$23$	1.65999e8			1.12134			0.560672	+	0.828038i	$0.310543\pi$
$24$		−	5.43433e8i		−	2.84366i
$25$	−4.78263e7			−0.195897
$26$	−3.54740e8			−1.14834
$27$	6.55465e8			1.69187
$28$		−	1.05120e9i		−	2.18140i
$29$			9.11924e8i			1.53310i	0.642184	+	0.766551i	$0.278029\pi$
$29$			9.11924e8i			1.53310i	−0.642184	+	0.766551i	$0.721971\pi$
$30$			1.94080e9i			2.66228i
$31$	2.56746e8			0.289290			0.144645	−	0.989484i	$-0.453796\pi$
$31$	2.56746e8			0.289290			0.144645	+	0.989484i	$0.453796\pi$
$32$		−	1.52526e8i		−	0.142051i
$33$	−1.76043e9	−	1.36796e9i	−1.36312	−	1.05923i
$34$	3.78957e9			2.45311
$35$			1.83666e9i			0.999126i
$36$	−8.43850e9			−3.87659
$37$	1.07127e9			0.417532			0.208766	−	0.977966i	$-0.433055\pi$
$37$	1.07127e9			0.417532			0.208766	+	0.977966i	$0.433055\pi$
$38$	3.80846e9			1.26487
$39$			4.05588e9i			1.15265i
$40$		−	6.05036e9i		−	1.47714i
$41$		−	5.70065e9i		−	1.20011i	−0.799959	−	0.600055i	$-0.795145\pi$
$41$		−	5.70065e9i		−	1.20011i	0.799959	−	0.600055i	$-0.204855\pi$
$42$	−1.81576e10			−3.30798
$43$		−	3.44514e9i		−	0.544999i	−0.962156	−	0.272500i	$-0.912150\pi$
$43$		−	3.44514e9i		−	0.544999i	0.962156	−	0.272500i	$-0.0878504\pi$
$44$	1.12178e10	+	8.71692e9i	1.54594	+	1.20129i
$45$	1.47438e10			1.77556
$46$			1.82714e10i			1.92852i
$47$	−2.28345e9			−0.211839			−0.105919	−	0.994375i	$-0.533779\pi$
$47$	−2.28345e9			−0.211839			−0.105919	+	0.994375i	$0.533779\pi$
$48$	1.84789e10			1.51087
$49$	−3.34197e9			−0.241449
$50$		−	5.26420e9i		−	0.336909i
$51$		−	4.33276e10i		−	2.46232i
$52$		−	2.58449e10i		−	1.30724i
$53$	6.37380e9			0.287570			0.143785	−	0.989609i	$-0.454073\pi$
$53$	6.37380e9			0.287570			0.143785	+	0.989609i	$0.454073\pi$
$54$			7.21465e10i			2.90973i
$55$	−1.95999e10	−	1.52303e10i	−0.708073	−	0.550215i
$56$	5.66054e10			1.83540
$57$		−	4.35436e10i		−	1.26962i
$58$	−1.00375e11			−2.63667
$59$	4.47524e10			1.06097			0.530487	−	0.847693i	$-0.322009\pi$
$59$	4.47524e10			1.06097			0.530487	+	0.847693i	$0.322009\pi$
$60$	−1.41399e11			−3.03068
$61$			2.20652e9i			0.0428281i	0.999771	+	0.0214141i	$0.00681683\pi$
$61$			2.20652e9i			0.0428281i	−0.999771	+	0.0214141i	$0.993183\pi$
$62$			2.82598e10i			0.497530i
$63$			1.37939e11i			2.20619i
$64$	7.69328e10			1.11952
$65$			4.51565e10i			0.598743i
$66$	1.50570e11	−	1.93769e11i	1.82169	−	2.34434i
$67$	−3.46978e10			−0.383578			−0.191789	−	0.981436i	$-0.561429\pi$
$67$	−3.46978e10			−0.383578			−0.191789	+	0.981436i	$0.561429\pi$
$68$			2.76093e11i			2.79256i
$69$	2.08904e11			1.93576
$70$	−2.02159e11			−1.71833
$71$	−1.37060e11			−1.06995			−0.534973	−	0.844869i	$-0.679678\pi$
$71$	−1.37060e11			−1.06995			−0.534973	+	0.844869i	$0.679678\pi$
$72$		−	4.54402e11i		−	3.26171i
$73$		−	6.76442e10i		−	0.446986i	−0.974706	−	0.223493i	$-0.928254\pi$
$73$		−	6.76442e10i		−	0.446986i	0.974706	−	0.223493i	$-0.0717459\pi$
$74$			1.17914e11i			0.718083i
$75$	−6.01877e10			−0.338174
$76$			2.77469e11i			1.43990i
$77$	1.42490e11	−	1.83371e11i	0.683661	−	0.879805i
$78$	−4.46426e11			−1.98236
$79$		−	9.62506e10i		−	0.395951i	−0.980207	−	0.197975i	$-0.936563\pi$
$79$		−	9.62506e10i		−	0.395951i	0.980207	−	0.197975i	$-0.0634366\pi$
$80$	2.05736e11			0.784822
$81$	2.65650e11			0.940589
$82$	6.27465e11			2.06398
$83$			3.17921e11i			0.972413i	0.873844	+	0.486207i	$0.161620\pi$
$83$			3.17921e11i			0.972413i	−0.873844	+	0.486207i	$0.838380\pi$
$84$		−	1.32289e12i		−	3.76572i
$85$		−	4.82392e11i		−	1.27905i
$86$	3.79203e11			0.937306
$87$			1.14762e12i			2.64657i
$88$	−4.69394e11	+	6.04065e11i	−1.01075	+	1.30073i
$89$	1.40561e11			0.282829			0.141415	−	0.989950i	$-0.454835\pi$
$89$	1.40561e11			0.282829			0.141415	+	0.989950i	$0.454835\pi$
$90$			1.62284e12i			3.05366i
$91$	−4.22471e11			−0.743958
$92$	−1.33118e12			−2.19538
$93$	3.23105e11			0.499398
$94$		−	2.51338e11i		−	0.364326i
$95$		−	4.84797e11i		−	0.659505i
$96$		−	1.91948e11i		−	0.245221i
$97$	−1.24384e12			−1.49326			−0.746630	−	0.665239i	$-0.768329\pi$
$97$	−1.24384e12			−1.49326			−0.746630	+	0.665239i	$0.768329\pi$
$98$		−	3.67847e11i		−	0.415251i
$99$	−1.47202e12	−	1.14384e12i	−1.56351	−	1.21494i
$100$	3.83529e11			0.383529
$101$		−	1.66474e12i		−	1.56826i	−0.620597	−	0.784129i	$-0.713110\pi$
$101$		−	1.66474e12i		−	1.56826i	0.620597	−	0.784129i	$-0.286890\pi$
$102$	4.76903e12			4.23476
$103$	−1.06069e12			−0.888310			−0.444155	−	0.895950i	$-0.646496\pi$
$103$	−1.06069e12			−0.888310			−0.444155	+	0.895950i	$0.646496\pi$
$104$	1.39171e12			1.09989
$105$			2.31137e12i			1.72478i
$106$			7.01558e11i			0.494570i
$107$			5.47656e11i			0.364926i	0.983213	+	0.182463i	$0.0584070\pi$
$107$			5.47656e11i			0.364926i	−0.983213	+	0.182463i	$0.941593\pi$
$108$	−5.25631e12			−3.31237
$109$			1.30910e12i			0.780572i	0.920694	+	0.390286i	$0.127624\pi$
$109$			1.30910e12i			0.780572i	−0.920694	+	0.390286i	$0.872376\pi$
$110$	1.67638e12	−	2.15734e12i	0.946275	−	1.21776i
$111$	1.34816e12			0.720779
$112$			1.92481e12i			0.975169i
$113$	−2.96485e12			−1.42407			−0.712036	−	0.702143i	$-0.752227\pi$
$113$	−2.96485e12			−1.42407			−0.712036	+	0.702143i	$0.752227\pi$
$114$	4.79280e12			2.18354
$115$	2.32585e12			1.00553
$116$		−	7.31290e12i		−	3.00152i
$117$			3.39140e12i			1.32210i
$118$			4.92586e12i			1.82469i
$119$	4.51312e12			1.58926
$120$		−	7.61416e12i		−	2.54997i
$121$	7.75260e11	+	3.04117e12i	0.247022	+	0.969010i
$122$	−2.42870e11			−0.0736571
$123$		−	7.17405e12i		−	2.07173i
$124$	−2.05890e12			−0.566376
$125$	−4.09081e12			−1.07238
$126$	−1.51828e13			−3.79428
$127$		−	3.01347e11i		−	0.0718198i	−0.999355	−	0.0359099i	$-0.988567\pi$
$127$		−	3.01347e11i		−	0.0718198i	0.999355	−	0.0359099i	$-0.0114329\pi$
$128$			7.84317e12i			1.78333i
$129$		−	4.33558e12i		−	0.940825i
$130$	−4.97033e12			−1.02973
$131$			4.66258e12i			0.922568i	0.887253	+	0.461284i	$0.152611\pi$
$131$			4.66258e12i			0.922568i	−0.887253	+	0.461284i	$0.847389\pi$
$132$	1.41172e13	+	1.09699e13i	2.66874	+	2.07377i
$133$	4.53562e12			0.819458
$134$		−	3.81916e12i		−	0.659688i
$135$	9.18387e12			1.51713
$136$	−1.48672e13			−2.34961
$137$	−1.97840e12			−0.299220			−0.149610	−	0.988745i	$-0.547802\pi$
$137$	−1.97840e12			−0.299220			−0.149610	+	0.988745i	$0.547802\pi$
$138$			2.29938e13i			3.32918i
$139$		−	2.42384e12i		−	0.336058i	−0.985782	−	0.168029i	$-0.946260\pi$
$139$		−	2.42384e12i		−	0.336058i	0.985782	−	0.168029i	$-0.0537403\pi$
$140$		−	1.47285e13i		−	1.95610i
$141$	−2.87364e12			−0.365694
$142$		−	1.50861e13i		−	1.84012i
$143$	3.50329e12	−	4.50840e12i	0.409695	−	0.527237i
$144$	1.54515e13			1.73298
$145$			1.27772e13i			1.37476i
$146$	7.44554e12			0.768739
$147$	−4.20574e12			−0.416810
$148$	−8.59074e12			−0.817448
$149$			8.27011e12i			0.755777i	0.925851	+	0.377888i	$0.123350\pi$
$149$			8.27011e12i			0.755777i	−0.925851	+	0.377888i	$0.876650\pi$
$150$		−	6.62480e12i		−	0.581601i
$151$		−	4.62597e12i		−	0.390248i	−0.980779	−	0.195124i	$-0.937489\pi$
$151$		−	4.62597e12i		−	0.390248i	0.980779	−	0.195124i	$-0.0625110\pi$
$152$	−1.49413e13			−1.21151
$153$		−	3.62292e13i		−	2.82430i
$154$	2.01835e13	+	1.56838e13i	1.51311	+	1.17578i
$155$	3.59733e12			0.259412
$156$		−	3.25249e13i		−	2.25667i
$157$	−2.00659e13			−1.33987			−0.669933	−	0.742421i	$-0.733677\pi$
$157$	−2.00659e13			−1.33987			−0.669933	+	0.742421i	$0.733677\pi$
$158$	1.05942e13			0.680967
$159$	8.02118e12			0.496427
$160$		−	2.13708e12i		−	0.127380i
$161$			2.17600e13i			1.24940i
$162$			2.92399e13i			1.61765i
$163$	−2.42763e12			−0.129437			−0.0647184	−	0.997904i	$-0.520615\pi$
$163$	−2.42763e12			−0.129437			−0.0647184	+	0.997904i	$0.520615\pi$
$164$			4.57146e13i			2.34959i
$165$	−2.46658e13	−	1.91668e13i	−1.22234	−	0.949828i
$166$	−3.49933e13			−1.67238
$167$		−	4.96523e12i		−	0.228897i	−0.993429	−	0.114449i	$-0.963490\pi$
$167$		−	4.96523e12i		−	0.228897i	0.993429	−	0.114449i	$-0.0365102\pi$
$168$	7.12358e13			3.16842
$169$	1.29111e13			0.554171
$170$	5.30965e13			2.19974
$171$		−	3.64098e13i		−	1.45627i
$172$			2.76273e13i			1.06701i
$173$			3.59785e13i			1.34204i	0.741438	+	0.671022i	$0.234144\pi$
$173$			3.59785e13i			1.34204i	−0.741438	+	0.671022i	$0.765856\pi$
$174$	−1.26318e14			−4.55165
$175$		−	6.26931e12i		−	0.218269i
$176$	−2.05406e13	−	1.59613e13i	−0.691094	−	0.537021i
$177$	5.63193e13			1.83154
$178$			1.54714e13i			0.486418i
$179$	5.45793e13			1.65924			0.829621	−	0.558326i	$-0.188556\pi$
$179$	5.45793e13			1.65924			0.829621	+	0.558326i	$0.188556\pi$
$180$	−1.18234e14			−3.47621
$181$	−2.92102e13			−0.830736			−0.415368	−	0.909653i	$-0.636347\pi$
$181$	−2.92102e13			−0.830736			−0.415368	+	0.909653i	$0.636347\pi$
$182$		−	4.65010e13i		−	1.27948i
$183$			2.77682e12i			0.0739336i
$184$		−	7.16822e13i		−	1.84716i
$185$	1.50098e13			0.374408
$186$			3.55639e13i			0.858879i
$187$	−3.74246e13	+	4.81618e13i	−0.875200	+	1.12630i
$188$	1.83115e13			0.414740
$189$			8.59216e13i			1.88509i
$190$	5.33611e13			1.13424
$191$	−4.78497e13			−0.985550			−0.492775	−	0.870157i	$-0.664017\pi$
$191$	−4.78497e13			−0.985550			−0.492775	+	0.870157i	$0.664017\pi$
$192$	9.68170e13			1.93261
$193$		−	1.00158e14i		−	1.93794i	−0.247170	−	0.968972i	$-0.579501\pi$
$193$		−	1.00158e14i		−	1.93794i	0.247170	−	0.968972i	$-0.420499\pi$
$194$		−	1.36909e14i		−	2.56815i
$195$			5.68278e13i			1.03360i
$196$	2.67999e13			0.472712
$197$			9.24406e13i			1.58149i	0.612148	+	0.790743i	$0.290306\pi$
$197$			9.24406e13i			1.58149i	−0.612148	+	0.790743i	$0.709694\pi$
$198$	1.25902e14	−	1.62023e14i	2.08949	−	2.68897i
$199$	−7.64734e12			−0.123138			−0.0615690	−	0.998103i	$-0.519610\pi$
$199$	−7.64734e12			−0.123138			−0.0615690	+	0.998103i	$0.519610\pi$
$200$			2.06525e13i			0.322695i
$201$	−4.36659e13			−0.662165
$202$	1.83236e14			2.69714
$203$	−1.19540e14			−1.70819
$204$			3.47453e14i			4.82075i
$205$		−	7.98730e13i		−	1.07616i
$206$		−	1.16749e14i		−	1.52774i
$207$	1.74679e14			2.22033
$208$			4.73238e13i			0.584386i
$209$	−3.76111e13	+	4.84019e13i	−0.451272	+	0.580743i
$210$	−2.54410e14			−2.96632
$211$		−	7.34913e12i		−	0.0832801i	−0.999133	−	0.0416400i	$-0.986742\pi$
$211$		−	7.34913e12i		−	0.0832801i	0.999133	−	0.0416400i	$-0.0132583\pi$
$212$	−5.11127e13			−0.563007
$213$	−1.72485e14			−1.84703
$214$	−6.02799e13			−0.627610
$215$		−	4.82706e13i		−	0.488711i
$216$		−	2.83045e14i		−	2.78697i
$217$			3.36555e13i			0.322328i
$218$	−1.44091e14			−1.34245
$219$		−	8.51277e13i		−	0.771625i
$220$	1.57176e14	+	1.22135e14i	1.38627	+	1.07722i
$221$	1.10961e14			0.952391
$222$			1.48390e14i			1.23962i
$223$	8.59256e13			0.698704			0.349352	−	0.936992i	$-0.386402\pi$
$223$	8.59256e13			0.698704			0.349352	+	0.936992i	$0.386402\pi$
$224$	1.99939e13			0.158274
$225$	−5.03271e13			−0.387888
$226$		−	3.26338e14i		−	2.44916i
$227$			1.51492e14i			1.10722i	0.832775	+	0.553611i	$0.186750\pi$
$227$			1.51492e14i			1.10722i	−0.832775	+	0.553611i	$0.813250\pi$
$228$			3.49185e14i			2.48568i
$229$	−9.76230e13			−0.676923			−0.338462	−	0.940980i	$-0.609907\pi$
$229$	−9.76230e13			−0.676923			−0.338462	+	0.940980i	$0.609907\pi$
$230$			2.56004e14i			1.72934i
$231$	1.79319e14	−	2.30766e14i	1.18019	−	1.51880i
$232$	3.93790e14			2.52544
$233$		−	9.85499e13i		−	0.615915i	−0.951400	−	0.307957i	$-0.900355\pi$
$233$		−	9.85499e13i		−	0.615915i	0.951400	−	0.307957i	$-0.0996454\pi$
$234$	−3.73288e14			−2.27378
$235$	−3.19940e13			−0.189960
$236$	−3.58879e14			−2.07719
$237$		−	1.21128e14i		−	0.683524i
$238$			4.96755e14i			2.73326i
$239$		−	2.59108e14i		−	1.39025i	−0.718887	−	0.695127i	$-0.755348\pi$
$239$		−	2.59108e14i		−	1.39025i	0.718887	−	0.695127i	$-0.244652\pi$
$240$	2.58912e14			1.35483
$241$			1.61570e14i			0.824630i	0.911041	+	0.412315i	$0.135280\pi$
$241$			1.61570e14i			0.824630i	−0.911041	+	0.412315i	$0.864720\pi$
$242$	−3.34739e14	+	8.53321e13i	−1.66653	+	0.424835i
$243$	−1.40303e13			−0.0681444
$244$		−	1.76945e13i		−	0.0838494i
$245$	−4.68250e13			−0.216512
$246$	7.89641e14			3.56303
$247$	1.11514e14			0.491073
$248$		−	1.10869e14i		−	0.476540i
$249$			4.00092e14i			1.67866i
$250$		−	4.50272e14i		−	1.84431i
$251$	4.78963e14			1.91540			0.957701	−	0.287765i	$-0.0929123\pi$
$251$	4.78963e14			1.91540			0.957701	+	0.287765i	$0.0929123\pi$
$252$		−	1.10616e15i		−	4.31931i
$253$	−2.32212e14	−	1.80442e14i	−0.885443	−	0.688042i
$254$	3.31689e13			0.123518
$255$		−	6.07073e14i		−	2.20800i
$256$	−5.48174e14			−1.94751
$257$	−2.46569e14			−0.855735			−0.427868	−	0.903841i	$-0.640735\pi$
$257$	−2.46569e14			−0.855735			−0.427868	+	0.903841i	$0.640735\pi$
$258$	4.77213e14			1.61806
$259$			1.40428e14i			0.465215i
$260$		−	3.62119e14i		−	1.17223i
$261$			9.59606e14i			3.03564i
$262$	−5.13205e14			−1.58666
$263$			2.34055e14i			0.707267i	0.935384	+	0.353633i	$0.115054\pi$
$263$			2.34055e14i			0.707267i	−0.935384	+	0.353633i	$0.884946\pi$
$264$	−5.90715e14	+	7.60193e14i	−1.74484	+	2.24543i
$265$	8.93046e13			0.257869
$266$			4.99231e14i			1.40933i
$267$	1.76891e14			0.488245
$268$	2.78249e14			0.750973
$269$	6.99111e14			1.84515			0.922577	−	0.385813i	$-0.126079\pi$
$269$	6.99111e14			1.84515			0.922577	+	0.385813i	$0.126079\pi$
$270$			1.01086e15i			2.60921i
$271$			9.74724e13i			0.246074i	0.992402	+	0.123037i	$0.0392634\pi$
$271$			9.74724e13i			0.246074i	−0.992402	+	0.123037i	$0.960737\pi$
$272$		−	5.05545e14i		−	1.24838i
$273$	−5.31664e14			−1.28429
$274$		−	2.17760e14i		−	0.514607i
$275$	6.69030e13	+	5.19876e13i	0.154685	+	0.120200i
$276$	−1.67524e15			−3.78985
$277$		−	8.35950e14i		−	1.85055i	−0.379293	−	0.925277i	$-0.623833\pi$
$277$		−	8.35950e14i		−	1.85055i	0.379293	−	0.925277i	$-0.376167\pi$
$278$	2.66790e14			0.577963
$279$	2.70171e14			0.572813
$280$	7.93111e14			1.64583
$281$			8.06155e14i			1.63750i	0.574152	+	0.818749i	$0.305332\pi$
$281$			8.06155e14i			1.63750i	−0.574152	+	0.818749i	$0.694668\pi$
$282$		−	3.16299e14i		−	0.628931i
$283$		−	5.16133e14i		−	1.00472i	−0.864660	−	0.502358i	$-0.832466\pi$
$283$		−	5.16133e14i		−	1.00472i	0.864660	−	0.502358i	$-0.167534\pi$
$284$	1.09911e15			2.09475
$285$		−	6.10099e14i		−	1.13849i
$286$	4.96235e14	+	3.85604e14i	0.906758	+	0.704605i
$287$	7.47269e14			1.33717
$288$		−	1.60501e14i		−	0.281270i
$289$	−6.02734e14			−1.03452
$290$	−1.40637e15			−2.36435
$291$	−1.56533e15			−2.57779
$292$			5.42453e14i			0.875114i
$293$			7.70227e14i			1.21734i	0.793422	+	0.608671i	$0.208297\pi$
$293$			7.70227e14i			1.21734i	−0.793422	+	0.608671i	$0.791703\pi$
$294$		−	4.62922e14i		−	0.716842i
$295$	6.27036e14			0.951394
$296$		−	4.62599e14i		−	0.687788i
$297$	−9.16913e14	−	7.12496e14i	−1.33595	−	1.03811i
$298$	−9.10283e14			−1.29981
$299$			5.34995e14i			0.748726i
$300$	4.82657e14			0.662081
$301$	4.51606e14			0.607240
$302$	5.09176e14			0.671160
$303$		−	2.09501e15i		−	2.70726i
$304$		−	5.08065e14i		−	0.643691i
$305$			3.09161e13i			0.0384048i
$306$	3.98771e15			4.85731
$307$			7.09071e14i			0.846954i	0.905907	+	0.423477i	$0.139190\pi$
$307$			7.09071e14i			0.846954i	−0.905907	+	0.423477i	$0.860810\pi$
$308$	−1.14266e15	+	1.47049e15i	−1.33848	+	1.72249i
$309$	−1.33484e15			−1.53348
$310$			3.95954e14i			0.446144i
$311$	9.38277e14			1.03698			0.518488	−	0.855085i	$-0.326495\pi$
$311$	9.38277e14			1.03698			0.518488	+	0.855085i	$0.326495\pi$
$312$	1.75142e15			1.89873
$313$	6.13649e14			0.652611			0.326305	−	0.945264i	$-0.394196\pi$
$313$	6.13649e14			0.652611			0.326305	+	0.945264i	$0.394196\pi$
$314$		−	2.20864e15i		−	2.30434i
$315$			1.93269e15i			1.97833i
$316$			7.71853e14i			0.775197i
$317$	−4.79474e14			−0.472509			−0.236254	−	0.971691i	$-0.575920\pi$
$317$	−4.79474e14			−0.472509			−0.236254	+	0.971691i	$0.575920\pi$
$318$			8.82884e14i			0.853770i
$319$	9.91268e14	−	1.27567e15i	0.940691	−	1.21058i
$320$	1.07792e15			1.00389
$321$			6.89204e14i			0.629967i
$322$	−2.39510e15			−2.14876
$323$	−1.19126e15			−1.04904
$324$	−2.13030e15			−1.84150
$325$		−	1.54139e14i		−	0.130801i
$326$		−	2.67207e14i		−	0.222609i
$327$			1.64745e15i			1.34749i
$328$	−2.46167e15			−1.97691
$329$		−	2.99326e14i		−	0.236031i
$330$	2.10967e15	−	2.71494e15i	1.63354	−	2.10221i
$331$	−1.69210e15			−1.28665			−0.643323	−	0.765595i	$-0.722445\pi$
$331$	−1.69210e15			−1.28665			−0.643323	+	0.765595i	$0.722445\pi$
$332$		−	2.54947e15i		−	1.90380i
$333$	1.12729e15			0.826739
$334$	5.46519e14			0.393664
$335$	−4.86159e14			−0.343961
$336$			2.42230e15i			1.68342i
$337$		−	2.53387e14i		−	0.172983i	−0.996253	−	0.0864917i	$-0.972434\pi$
$337$		−	2.53387e14i		−	0.172983i	0.996253	−	0.0864917i	$-0.0275656\pi$
$338$			1.42112e15i			0.953079i
$339$	−3.73115e15			−2.45835
$340$			3.86840e15i			2.50414i
$341$	−3.59155e14	−	2.79085e14i	−0.228431	−	0.177505i
$342$	4.00759e15			2.50453
$343$			1.37630e15i			0.845180i
$344$	−1.48769e15			−0.897763
$345$	2.92700e15			1.73583
$346$	−3.96012e15			−2.30808
$347$		−	2.04744e15i		−	1.17283i	−0.810012	−	0.586413i	$-0.800540\pi$
$347$		−	2.04744e15i		−	1.17283i	0.810012	−	0.586413i	$-0.199460\pi$
$348$		−	9.20301e15i		−	5.18149i
$349$			2.25596e14i			0.124847i	0.998050	+	0.0624235i	$0.0198830\pi$
$349$			2.25596e14i			0.124847i	−0.998050	+	0.0624235i	$0.980117\pi$
$350$	6.90057e14			0.375385
$351$			2.11249e15i			1.12967i
$352$	−1.65797e14	+	2.13364e14i	−0.0871606	+	0.112167i
$353$	2.52674e15			1.30591			0.652953	−	0.757398i	$-0.273530\pi$
$353$	2.52674e15			1.30591			0.652953	+	0.757398i	$0.273530\pi$
$354$			6.19901e15i			3.14994i
$355$	−1.92038e15			−0.959439
$356$	−1.12719e15			−0.553727
$357$	5.67960e15			2.74352
$358$			6.00749e15i			2.85361i
$359$			5.71819e14i			0.267111i	0.991041	+	0.133556i	$0.0426395\pi$
$359$			5.71819e14i			0.267111i	−0.991041	+	0.133556i	$0.957361\pi$
$360$		−	6.36672e15i		−	2.92483i
$361$	1.01611e15			0.459091
$362$		−	3.21514e15i		−	1.42872i
$363$	9.75636e14	+	3.82720e15i	0.426430	+	1.67279i
$364$	3.38788e15			1.45653
$365$		−	9.47778e14i		−	0.400820i
$366$	−3.05642e14			−0.127153
$367$	2.80841e15			1.14938			0.574692	−	0.818370i	$-0.305122\pi$
$367$	2.80841e15			1.14938			0.574692	+	0.818370i	$0.305122\pi$
$368$	2.43748e15			0.981418
$369$		−	5.99872e15i		−	2.37630i
$370$			1.65212e15i			0.643918i
$371$			8.35508e14i			0.320411i
$372$	−2.59105e15			−0.977727
$373$		−	2.07457e15i		−	0.770327i	−0.922848	−	0.385163i	$-0.874145\pi$
$373$		−	2.07457e15i		−	0.770327i	0.922848	−	0.385163i	$-0.125855\pi$
$374$	−5.30112e15	−	4.11929e15i	−1.93704	−	1.50519i
$375$	−5.14814e15			−1.85124
$376$			9.86048e14i			0.348956i
$377$	−2.93902e15			−1.02366
$378$	−9.45731e15			−3.24203
$379$	4.00294e15			1.35065			0.675326	−	0.737519i	$-0.264003\pi$
$379$	4.00294e15			1.35065			0.675326	+	0.737519i	$0.264003\pi$
$380$			3.88768e15i			1.29119i
$381$		−	3.79233e14i		−	0.123981i
$382$		−	5.26677e15i		−	1.69498i
$383$	2.55436e13			0.00809261			0.00404631	−	0.999992i	$-0.498712\pi$
$383$	2.55436e13			0.00809261			0.00404631	+	0.999992i	$0.498712\pi$
$384$			9.87034e15i			3.07854i
$385$	1.99646e15	−	2.56925e15i	0.613051	−	0.788937i
$386$	1.10243e16			3.33293
$387$		−	3.62528e15i		−	1.07913i
$388$	9.97463e15			2.92352
$389$	−3.61597e15			−1.04358			−0.521792	−	0.853073i	$-0.674736\pi$
$389$	−3.61597e15			−1.04358			−0.521792	+	0.853073i	$0.674736\pi$
$390$	−6.25498e15			−1.77762
$391$		−	5.71518e15i		−	1.59945i
$392$			1.44314e15i			0.397732i
$393$			5.86768e15i			1.59262i
$394$	−1.01749e16			−2.71989
$395$		−	1.34859e15i		−	0.355056i
$396$	1.18044e16	+	9.17271e15i	3.06106	+	2.37863i
$397$	−4.69951e15			−1.20035			−0.600177	−	0.799867i	$-0.704903\pi$
$397$	−4.69951e15			−1.20035			−0.600177	+	0.799867i	$0.704903\pi$
$398$		−	8.41736e14i		−	0.211776i
$399$	5.70791e15			1.41462
$400$	−7.02267e14			−0.171452
$401$	−6.15145e15			−1.47949			−0.739744	−	0.672889i	$-0.765053\pi$
$401$	−6.15145e15			−1.47949			−0.739744	+	0.672889i	$0.765053\pi$
$402$		−	4.80627e15i		−	1.13881i
$403$			8.27462e14i			0.193160i
$404$			1.33499e16i			3.07036i
$405$	3.72208e15			0.843444
$406$		−	1.31576e16i		−	2.93779i
$407$	−1.49857e15	−	1.16448e15i	−0.329694	−	0.256192i
$408$	−1.87099e16			−4.05611
$409$			4.23567e15i			0.904861i	0.891800	+	0.452431i	$0.149443\pi$
$409$			4.23567e15i			0.904861i	−0.891800	+	0.452431i	$0.850557\pi$
$410$	8.79155e15			1.85081
$411$	−2.48974e15			−0.516539
$412$	8.50587e15			1.73914
$413$			5.86637e15i			1.18214i
$414$			1.92267e16i			3.81859i
$415$			4.45446e15i			0.871981i
$416$	4.91573e14			0.0948480
$417$		−	3.05031e15i		−	0.580133i
$418$	−5.32755e15	−	4.13982e15i	−0.998779	−	0.776111i
$419$	−1.99763e15			−0.369174			−0.184587	−	0.982816i	$-0.559095\pi$
$419$	−1.99763e15			−0.369174			−0.184587	+	0.982816i	$0.559095\pi$
$420$		−	1.85353e16i		−	3.37679i
$421$	7.56290e14			0.135830			0.0679150	−	0.997691i	$-0.478365\pi$
$421$	7.56290e14			0.135830			0.0679150	+	0.997691i	$0.478365\pi$
$422$	8.08912e14			0.143227
$423$	−2.40285e15			−0.419454
$424$		−	2.75235e15i		−	0.473706i
$425$			1.64661e15i			0.279420i
$426$		−	1.89853e16i		−	3.17658i
$427$	−2.89242e14			−0.0477192
$428$		−	4.39176e15i		−	0.714457i
$429$	4.40877e15	−	5.67365e15i	0.707250	−	0.910163i
$430$	5.31310e15			0.840499
$431$		−	6.40123e15i		−	0.998618i	−0.866424	−	0.499309i	$-0.833587\pi$
$431$		−	6.40123e15i		−	0.998618i	0.866424	−	0.499309i	$-0.166413\pi$
$432$	9.62465e15			1.48075
$433$	4.99072e15			0.757244			0.378622	−	0.925551i	$-0.376398\pi$
$433$	4.99072e15			0.757244			0.378622	+	0.925551i	$0.376398\pi$
$434$	−3.70443e15			−0.554349
$435$			1.60796e16i			2.37323i
$436$		−	1.04979e16i		−	1.52821i
$437$		−	5.74367e15i		−	0.824710i
$438$	9.36993e15			1.32706
$439$		−	3.14598e15i		−	0.439511i	−0.975555	−	0.219755i	$-0.929474\pi$
$439$		−	3.14598e15i		−	0.439511i	0.975555	−	0.219755i	$-0.0705259\pi$
$440$	−6.57679e15	+	8.46369e15i	−0.906354	+	1.16639i
$441$	−3.51671e15			−0.478084
$442$			1.22133e16i			1.63795i
$443$	9.12607e15			1.20743			0.603715	−	0.797201i	$-0.293687\pi$
$443$	9.12607e15			1.20743			0.603715	+	0.797201i	$0.293687\pi$
$444$	−1.08111e16			−1.41115
$445$	1.96943e15			0.253618
$446$			9.45775e15i			1.20165i
$447$			1.04076e16i			1.30469i
$448$			1.00847e16i			1.24737i
$449$	2.52097e15			0.307673			0.153836	−	0.988096i	$-0.450837\pi$
$449$	2.52097e15			0.307673			0.153836	+	0.988096i	$0.450837\pi$
$450$		−	5.53945e15i		−	0.667101i
$451$	−6.19665e15	+	7.97448e15i	−0.736372	+	0.947640i
$452$	2.37757e16			2.78806
$453$		−	5.82161e15i		−	0.673680i
$454$	−1.66746e16			−1.90423
$455$	−5.91934e15			−0.667121
$456$	−1.88031e16			−2.09142
$457$			7.50373e15i			0.823721i	0.911247	+	0.411861i	$0.135121\pi$
$457$			7.50373e15i			0.823721i	−0.911247	+	0.411861i	$0.864879\pi$
$458$		−	1.07453e16i		−	1.16419i
$459$		−	2.25670e16i		−	2.41323i
$460$	−1.86515e16			−1.96864
$461$			1.10124e16i			1.14730i	0.819099	+	0.573651i	$0.194474\pi$
$461$			1.10124e16i			1.14730i	−0.819099	+	0.573651i	$0.805526\pi$
$462$	2.54002e16	+	1.97374e16i	2.61207	+	2.02973i
$463$	4.64255e15			0.471271			0.235635	−	0.971842i	$-0.424283\pi$
$463$	4.64255e15			0.471271			0.235635	+	0.971842i	$0.424283\pi$
$464$			1.33904e16i			1.34179i
$465$	4.52710e15			0.447819
$466$	1.08473e16			1.05927
$467$	2.10486e15			0.202918			0.101459	−	0.994840i	$-0.467649\pi$
$467$	2.10486e15			0.202918			0.101459	+	0.994840i	$0.467649\pi$
$468$		−	2.71963e16i		−	2.58842i
$469$		−	4.54836e15i		−	0.427384i
$470$		−	3.52155e15i		−	0.326698i
$471$	−2.52522e16			−2.31299
$472$		−	1.93251e16i		−	1.74771i
$473$	−3.74489e15	+	4.81931e15i	−0.334405	+	0.430346i
$474$	1.33324e16			1.17554
$475$			1.65482e15i			0.144075i
$476$	−3.61916e16			−3.11148
$477$	6.70706e15			0.569406
$478$	2.85198e16			2.39100
$479$			6.36757e15i			0.527182i	0.964635	+	0.263591i	$0.0849069\pi$
$479$			6.36757e15i			0.527182i	−0.964635	+	0.263591i	$0.915093\pi$
$480$		−	2.68943e15i		−	0.219894i
$481$			3.45258e15i			0.278788i
$482$	−1.77839e16			−1.41822
$483$			2.73841e16i			2.15683i
$484$	−6.21696e15	−	2.43877e16i	−0.483622	−	1.89714i
$485$	−1.74278e16			−1.33903
$486$		−	1.54431e15i		−	0.117197i
$487$	1.41180e15			0.105828			0.0529140	−	0.998599i	$-0.483149\pi$
$487$	1.41180e15			0.105828			0.0529140	+	0.998599i	$0.483149\pi$
$488$	9.52826e14			0.0705496
$489$	−3.05509e15			−0.223445
$490$		−	5.15398e15i		−	0.372363i
$491$		−	1.81589e16i		−	1.29599i	−0.761645	−	0.647995i	$-0.775608\pi$
$491$		−	1.81589e16i		−	1.29599i	0.761645	−	0.647995i	$-0.224392\pi$
$492$			5.75302e16i			4.05607i
$493$	3.13966e16			2.18676
$494$			1.22742e16i			0.844562i
$495$	−2.06247e16	−	1.60266e16i	−1.40203	−	1.08946i
$496$	3.76998e15			0.253191
$497$		−	1.79665e16i		−	1.19214i
$498$	−4.40377e16			−2.88701
$499$	−8.80426e11			−5.70282e−5			−2.85141e−5	−	1.00000i	$-0.500009\pi$
$499$	−8.80426e11			−5.70282e−5			−2.85141e−5		1.00000i	$0.500009\pi$
$500$	3.28050e16			2.09952
$501$		−	6.24856e15i		−	0.395142i
$502$			5.27190e16i			3.29416i
$503$			2.23972e15i			0.138289i	0.997607	+	0.0691443i	$0.0220269\pi$
$503$			2.23972e15i			0.138289i	−0.997607	+	0.0691443i	$0.977973\pi$
$504$	5.95652e16			3.63420
$505$		−	2.33250e16i		−	1.40629i
$506$	1.98611e16	−	2.55593e16i	1.18331	−	1.52281i
$507$	1.62482e16			0.956658
$508$			2.41656e15i			0.140610i
$509$	−1.11422e16			−0.640715			−0.320358	−	0.947297i	$-0.603803\pi$
$509$	−1.11422e16			−0.640715			−0.320358	+	0.947297i	$0.603803\pi$
$510$	6.68199e16			3.79739
$511$	8.86714e15			0.498033
$512$		−	2.82114e16i		−	1.56605i
$513$		−	2.26795e16i		−	1.24431i
$514$		−	2.71396e16i		−	1.47172i
$515$	−1.48615e16			−0.796563
$516$			3.47679e16i			1.84196i
$517$	3.19426e15	+	2.48213e15i	0.167274	+	0.129981i
$518$	−1.54567e16			−0.800090
$519$			4.52776e16i			2.31675i
$520$	1.94996e16			0.986292
$521$	−3.10384e16			−1.55193			−0.775966	−	0.630775i	$-0.782737\pi$
$521$	−3.10384e16			−1.55193			−0.775966	+	0.630775i	$0.782737\pi$
$522$	−1.05623e17			−5.22078
$523$		−	1.49526e16i		−	0.730648i	−0.930881	−	0.365324i	$-0.880958\pi$
$523$		−	1.49526e16i		−	0.730648i	0.930881	−	0.365324i	$-0.119042\pi$
$524$		−	3.73901e16i		−	1.80621i
$525$		−	7.88969e15i		−	0.376794i
$526$	−2.57622e16			−1.21638
$527$		−	8.83951e15i		−	0.412634i
$528$	−2.58496e16	−	2.00867e16i	−1.19303	−	0.927053i
$529$	5.64108e15			0.257412
$530$			9.82968e15i			0.443490i
$531$	4.70924e16			2.10080
$532$	−3.63720e16			−1.60434
$533$	1.83725e16			0.801319
$534$			1.94702e16i			0.839697i
$535$			7.67332e15i			0.327236i
$536$			1.49833e16i			0.631858i
$537$	6.86860e16			2.86433
$538$			7.69505e16i			3.17335i
$539$	4.67498e15	+	3.63274e15i	0.190655	+	0.148150i
$540$	−7.36473e16			−2.97026
$541$			3.60531e16i			1.43800i	0.695009	+	0.719001i	$0.255400\pi$
$541$			3.60531e16i			1.43800i	−0.695009	+	0.719001i	$0.744600\pi$
$542$	−1.07287e16			−0.423205
$543$	−3.67599e16			−1.43409
$544$	−5.25132e15			−0.202617
$545$			1.83421e16i			0.699953i
$546$		−	5.85198e16i		−	2.20875i
$547$		−	4.36538e16i		−	1.62966i	−0.579698	−	0.814831i	$-0.696830\pi$
$547$		−	4.36538e16i		−	1.62966i	0.579698	−	0.814831i	$-0.303170\pi$
$548$	1.58652e16			0.585816
$549$			2.32189e15i			0.0848024i
$550$	−5.72222e15	+	7.36395e15i	−0.206723	+	0.266032i
$551$	3.15531e16			1.12754
$552$		−	9.02094e16i		−	3.18873i
$553$	1.26170e16			0.441170
$554$	9.20122e16			3.18264
$555$	1.88893e16			0.646335
$556$			1.94372e16i			0.657939i
$557$		−	5.46434e15i		−	0.182981i	−0.995806	−	0.0914906i	$-0.970837\pi$
$557$		−	5.46434e15i		−	0.182981i	0.995806	−	0.0914906i	$-0.0291631\pi$
$558$			2.97374e16i			0.985141i
$559$	1.11033e16			0.363898
$560$			2.69689e16i			0.874451i
$561$	−4.70974e16	+	6.06098e16i	−1.51085	+	1.94431i
$562$	−8.87327e16			−2.81622
$563$			2.85169e15i			0.0895470i	0.998997	+	0.0447735i	$0.0142566\pi$
$563$			2.85169e15i			0.0895470i	−0.998997	+	0.0447735i	$0.985743\pi$
$564$	2.30443e16			0.715960
$565$	−4.15411e16			−1.27699
$566$	5.68103e16			1.72794
$567$			3.48227e16i			1.04801i
$568$			5.91858e16i			1.76249i
$569$		−	6.30617e15i		−	0.185820i	−0.995675	−	0.0929099i	$-0.970383\pi$
$569$		−	6.30617e15i		−	0.185820i	0.995675	−	0.0929099i	$-0.0296168\pi$
$570$	6.71530e16			1.95802
$571$		−	4.94247e16i		−	1.42602i	−0.701151	−	0.713012i	$-0.747330\pi$
$571$		−	4.94247e16i		−	1.42602i	0.701151	−	0.713012i	$-0.252670\pi$
$572$	−2.80936e16	+	3.61538e16i	−0.802105	+	1.03223i
$573$	−6.02170e16			−1.70134
$574$			8.22512e16i			2.29970i
$575$	−7.93913e15			−0.219668
$576$	8.09554e16			2.21672
$577$	−5.31904e15			−0.144138			−0.0720690	−	0.997400i	$-0.522960\pi$
$577$	−5.31904e15			−0.144138			−0.0720690	+	0.997400i	$0.522960\pi$
$578$		−	6.63424e16i		−	1.77920i
$579$		−	1.26045e17i		−	3.34545i
$580$		−	1.02463e17i		−	2.69152i
$581$	−4.16747e16			−1.08347
$582$		−	1.72295e17i		−	4.43337i
$583$	−8.91613e15	−	6.92836e15i	−0.227073	−	0.176449i
$584$	−2.92103e16			−0.736308
$585$			4.75176e16i			1.18555i
$586$	−8.47781e16			−2.09362
$587$	6.06158e16			1.48169			0.740845	−	0.671676i	$-0.234425\pi$
$587$	6.06158e16			1.48169			0.740845	+	0.671676i	$0.234425\pi$
$588$	3.37266e16			0.816036
$589$		−	8.88357e15i		−	0.212763i
$590$			6.90173e16i			1.63624i
$591$			1.16333e17i			2.73010i
$592$	1.57302e16			0.365430
$593$			4.23064e16i			0.972923i	0.873702	+	0.486461i	$0.161713\pi$
$593$			4.23064e16i			0.972923i	−0.873702	+	0.486461i	$0.838287\pi$
$594$	7.84237e16	−	1.00924e17i	1.78537	−	2.29760i
$595$	6.32344e16			1.42512
$596$		−	6.63196e16i		−	1.47967i
$597$	−9.62390e15			−0.212571
$598$	−5.88864e16			−1.28768
$599$	−6.95451e15			−0.150559			−0.0752793	−	0.997162i	$-0.523985\pi$
$599$	−6.95451e15			−0.150559			−0.0752793	+	0.997162i	$0.523985\pi$
$600$			2.59904e16i			0.557065i
$601$			4.23344e16i			0.898352i	0.893443	+	0.449176i	$0.148282\pi$
$601$			4.23344e16i			0.898352i	−0.893443	+	0.449176i	$0.851718\pi$
$602$			4.97078e16i			1.04435i
$603$	−3.65121e16			−0.759509
$604$			3.70966e16i			0.764033i
$605$	1.08623e16	+	4.26105e16i	0.221509	+	0.868929i
$606$	2.30596e17			4.65603
$607$		−	8.57554e16i		−	1.71447i	−0.514927	−	0.857234i	$-0.672181\pi$
$607$		−	8.57554e16i		−	1.71447i	0.514927	−	0.857234i	$-0.327819\pi$
$608$	−5.27749e15			−0.104474
$609$	−1.50436e17			−2.94882
$610$	−3.40290e15			−0.0660496
$611$		−	7.35930e15i		−	0.141446i
$612$			2.90529e17i			5.52944i
$613$		−	4.03048e16i		−	0.759616i	−0.925065	−	0.379808i	$-0.875990\pi$
$613$		−	4.03048e16i		−	0.759616i	0.925065	−	0.379808i	$-0.124010\pi$
$614$	−7.80468e16			−1.45662
$615$		−	1.00517e17i		−	1.85776i
$616$	−7.91838e16	−	6.15305e16i	−1.44928	−	1.12618i
$617$	−5.94762e16			−1.07803			−0.539017	−	0.842295i	$-0.681204\pi$
$617$	−5.94762e16			−1.07803			−0.539017	+	0.842295i	$0.681204\pi$
$618$		−	1.46924e17i		−	2.63732i
$619$	8.45967e16			1.50387			0.751934	−	0.659238i	$-0.229121\pi$
$619$	8.45967e16			1.50387			0.751934	+	0.659238i	$0.229121\pi$
$620$	−2.88477e16			−0.507879
$621$	1.08807e17			1.89717
$622$			1.03275e17i			1.78342i
$623$			1.84254e16i			0.315129i
$624$			5.95552e16i			1.00882i
$625$	−4.56409e16			−0.765728
$626$			6.75438e16i			1.12238i
$627$	−4.73322e16	+	6.09119e16i	−0.779025	+	1.00253i
$628$	1.60913e17			2.62321
$629$		−	3.68828e16i		−	0.595553i
$630$	−2.12730e17			−3.40240
$631$	1.21224e17			1.92050			0.960248	−	0.279147i	$-0.0900517\pi$
$631$	1.21224e17			1.92050			0.960248	+	0.279147i	$0.0900517\pi$
$632$	−4.15632e16			−0.652239
$633$		−	9.24860e15i		−	0.143765i
$634$		−	5.27753e16i		−	0.812634i
$635$		−	4.22223e15i		−	0.0644021i
$636$	−6.43235e16			−0.971911
$637$		−	1.07708e16i		−	0.161217i
$638$	1.40411e17	+	1.09108e17i	2.08199	+	1.61783i
$639$	−1.44227e17			−2.11856
$640$			1.09892e17i			1.59915i
$641$	−6.98489e15			−0.100696			−0.0503479	−	0.998732i	$-0.516033\pi$
$641$	−6.98489e15			−0.100696			−0.0503479	+	0.998732i	$0.516033\pi$
$642$	−7.58601e16			−1.08344
$643$	−8.50297e16			−1.20311			−0.601554	−	0.798832i	$-0.705452\pi$
$643$	−8.50297e16			−1.20311			−0.601554	+	0.798832i	$0.705452\pi$
$644$		−	1.74498e17i		−	2.44610i
$645$		−	6.07467e16i		−	0.843655i
$646$		−	1.31121e17i		−	1.80417i
$647$	4.92373e16			0.671225			0.335613	−	0.942000i	$-0.391057\pi$
$647$	4.92373e16			0.671225			0.335613	+	0.942000i	$0.391057\pi$
$648$		−	1.14714e17i		−	1.54941i
$649$	−6.26029e16	−	4.86462e16i	−0.837773	−	0.651000i
$650$	1.69659e16			0.224956
$651$			4.23542e16i			0.556431i
$652$	1.94677e16			0.253413
$653$	1.39199e17			1.79539			0.897693	−	0.440622i	$-0.145242\pi$
$653$	1.39199e17			1.79539			0.897693	+	0.440622i	$0.145242\pi$
$654$	−1.81333e17			−2.31745
$655$			6.53284e16i			0.827283i
$656$		−	8.37066e16i		−	1.05036i
$657$		−	7.11812e16i		−	0.885060i
$658$	3.29466e16			0.405934
$659$			6.73104e16i			0.821807i	0.911679	+	0.410904i	$0.134787\pi$
$659$			6.73104e16i			0.821807i	−0.911679	+	0.410904i	$0.865213\pi$
$660$	1.97800e17	+	1.53702e17i	2.39310	+	1.85958i
$661$	2.71222e16			0.325175			0.162587	−	0.986694i	$-0.448016\pi$
$661$	2.71222e16			0.325175			0.162587	+	0.986694i	$0.448016\pi$
$662$		−	1.86248e17i		−	2.21281i
$663$	1.39640e17			1.64410
$664$	1.37286e17			1.60183
$665$	6.35496e16			0.734823
$666$			1.24079e17i			1.42185i
$667$			1.51379e17i			1.71913i
$668$			3.98172e16i			0.448138i
$669$	1.08134e17			1.20616
$670$		−	5.35111e16i		−	0.591555i
$671$	2.39850e15	−	3.08664e15i	0.0262788	−	0.0338182i
$672$	2.51615e16			0.273226
$673$			1.09308e17i			1.17641i	0.808710	+	0.588207i	$0.200166\pi$
$673$			1.09308e17i			1.17641i	−0.808710	+	0.588207i	$0.799834\pi$
$674$	2.78900e16			0.297502
$675$	−3.13485e16			−0.331432
$676$	−1.03537e17			−1.08496
$677$			1.79269e17i			1.86198i	0.365048	+	0.930989i	$0.381052\pi$
$677$			1.79269e17i			1.86198i	−0.365048	+	0.930989i	$0.618948\pi$
$678$		−	4.10684e17i		−	4.22795i
$679$		−	1.63049e17i		−	1.66380i
$680$	−2.08308e17			−2.10694
$681$			1.90647e17i			1.91138i
$682$	3.07186e16	−	3.95319e16i	0.305278	−	0.392863i
$683$	−1.51337e17			−1.49080			−0.745401	−	0.666616i	$-0.767742\pi$
$683$	−1.51337e17			−1.49080			−0.745401	+	0.666616i	$0.767742\pi$
$684$			2.91977e17i			2.85110i
$685$	−2.77198e16			−0.268316
$686$	−1.51488e17			−1.45357
$687$	−1.22855e17			−1.16856
$688$		−	5.05874e16i		−	0.476992i
$689$			2.05420e16i			0.192011i
$690$			3.22172e17i			2.98533i
$691$	−1.63937e16			−0.150594			−0.0752971	−	0.997161i	$-0.523991\pi$
$691$	−1.63937e16			−0.150594			−0.0752971	+	0.997161i	$0.523991\pi$
$692$		−	2.88519e17i		−	2.62747i
$693$	1.49941e17	−	1.92959e17i	1.35369	−	1.74207i
$694$	2.25359e17			2.01706
$695$		−	3.39609e16i		−	0.301350i
$696$	4.95570e17			4.35963
$697$	−1.96268e17			−1.71180
$698$	−2.48311e16			−0.214716
$699$		−	1.24021e17i		−	1.06324i
$700$			5.02749e16i			0.427329i
$701$		−	1.01123e17i		−	0.852201i	−0.904676	−	0.426100i	$-0.859887\pi$
$701$		−	1.01123e17i		−	0.852201i	0.904676	−	0.426100i	$-0.140113\pi$
$702$	−2.32520e17			−1.94284
$703$		−	3.70667e16i		−	0.307080i
$704$	−1.07619e17	−	8.36265e16i	−0.884003	−	0.686923i
$705$	−4.02632e16			−0.327925
$706$			2.78116e17i			2.24594i
$707$	2.18222e17			1.74736
$708$	−4.51635e17			−3.58582
$709$	1.91717e17			1.50933			0.754664	−	0.656111i	$-0.227800\pi$
$709$	1.91717e17			1.50933			0.754664	+	0.656111i	$0.227800\pi$
$710$		−	2.11375e17i		−	1.65007i
$711$		−	1.01283e17i		−	0.784008i
$712$		−	6.06974e16i		−	0.465897i
$713$	4.26196e16			0.324394
$714$			6.25148e17i			4.71839i
$715$	4.90854e16	−	6.31682e16i	0.367381	−	0.472783i
$716$	−4.37682e17			−3.24849
$717$		−	3.26078e17i		−	2.39998i
$718$	−6.29396e16			−0.459386
$719$	7.63742e16			0.552807			0.276403	−	0.961042i	$-0.410857\pi$
$719$	7.63742e16			0.552807			0.276403	+	0.961042i	$0.410857\pi$
$720$	2.16494e17			1.55400
$721$		−	1.39040e17i		−	0.989757i
$722$			1.11842e17i			0.789557i
$723$			2.03330e17i			1.42355i
$724$	2.34242e17			1.62642
$725$		−	4.36140e16i		−	0.300329i
$726$	−4.21256e17	+	1.07387e17i	−2.87691	+	0.733387i
$727$	−1.02417e17			−0.693692			−0.346846	−	0.937922i	$-0.612747\pi$
$727$	−1.02417e17			−0.693692			−0.346846	+	0.937922i	$0.612747\pi$
$728$			1.82433e17i			1.22550i
$729$	−1.58834e17			−1.05823
$730$	1.04321e17			0.689342
$731$	−1.18613e17			−0.777368
$732$		−	2.22679e16i		−	0.144748i
$733$			1.22040e17i			0.786827i	0.919362	+	0.393414i	$0.128706\pi$
$733$			1.22040e17i			0.786827i	−0.919362	+	0.393414i	$0.871294\pi$
$734$			3.09120e17i			1.97674i
$735$	−5.89275e16			−0.373761
$736$		−	2.53192e16i		−	0.159288i
$737$	4.85378e16	+	3.77168e16i	0.302883	+	0.235358i
$738$	6.60273e17			4.08682
$739$		−	8.82050e16i		−	0.541535i	−0.962645	−	0.270768i	$-0.912722\pi$
$739$		−	8.82050e16i		−	0.541535i	0.962645	−	0.270768i	$-0.0872775\pi$
$740$	−1.20367e17			−0.733021
$741$	1.40336e17			0.847733
$742$	−9.19636e16			−0.551052
$743$			2.60043e17i			1.54566i	0.634615	+	0.772828i	$0.281159\pi$
$743$			2.60043e17i			1.54566i	−0.634615	+	0.772828i	$0.718841\pi$
$744$		−	1.39524e17i		−	0.822644i
$745$			1.15874e17i			0.677719i
$746$	2.28346e17			1.32483
$747$			3.34544e17i			1.92544i
$748$	3.00115e17	−	3.86219e17i	1.71348	−	2.20508i
$749$	−7.17894e16			−0.406602
$750$		−	5.66650e17i		−	3.18381i
$751$	1.35924e17			0.757631			0.378816	−	0.925472i	$-0.376331\pi$
$751$	1.35924e17			0.757631			0.378816	+	0.925472i	$0.376331\pi$
$752$	−3.35295e16			−0.185405
$753$	6.02757e17			3.30653
$754$		−	3.23496e17i		−	1.76052i
$755$		−	6.48155e16i		−	0.349943i
$756$		−	6.89023e17i		−	3.69065i
$757$	−3.20247e17			−1.70181			−0.850904	−	0.525322i	$-0.823945\pi$
$757$	−3.20247e17			−1.70181			−0.850904	+	0.525322i	$0.823945\pi$
$758$			4.40600e17i			2.32289i
$759$	−2.92230e17	−	2.27080e17i	−1.52853	−	1.18776i
$760$	−2.09346e17			−1.08639
$761$		−	1.46435e16i		−	0.0753940i	−0.999289	−	0.0376970i	$-0.987998\pi$
$761$		−	1.46435e16i		−	0.0753940i	0.999289	−	0.0376970i	$-0.0120022\pi$
$762$	4.17419e16			0.213227
$763$	−1.71603e17			−0.869716
$764$	3.83716e17			1.92952
$765$		−	5.07615e17i		−	2.53260i
$766$			2.81156e15i			0.0139179i
$767$			1.44232e17i			0.708417i
$768$	−6.89857e17			−3.36195
$769$		−	2.35445e17i		−	1.13850i	−0.822165	−	0.569249i	$-0.807234\pi$
$769$		−	2.35445e17i		−	1.13850i	0.822165	−	0.569249i	$-0.192766\pi$
$770$	2.82795e17	+	2.19749e17i	1.35684	+	1.05434i
$771$	−3.10298e17			−1.47724
$772$			8.03186e17i			3.79413i
$773$	−2.15485e17			−1.01004			−0.505022	−	0.863106i	$-0.668516\pi$
$773$	−2.15485e17			−1.01004			−0.505022	+	0.863106i	$0.668516\pi$
$774$	3.99031e17			1.85593
$775$	−1.22792e16			−0.0566710
$776$			5.37120e17i			2.45981i
$777$			1.76723e17i			0.803094i
$778$		−	3.98007e17i		−	1.79479i
$779$	−1.97246e17			−0.882640
$780$		−	4.55713e17i		−	2.02360i
$781$	1.91730e17	+	1.48985e17i	0.844858	+	0.656505i
$782$	6.29065e17			2.75077
$783$			5.97735e17i			2.59381i
$784$	−4.90724e16			−0.211320
$785$	−2.81148e17			−1.20148
$786$	−6.45850e17			−2.73903
$787$			8.63168e16i			0.363285i	0.983365	+	0.181642i	$0.0581413\pi$
$787$			8.63168e16i			0.363285i	−0.983365	+	0.181642i	$0.941859\pi$
$788$		−	7.41300e17i		−	3.09625i
$789$			2.94549e17i			1.22095i
$790$	1.48438e17			0.610636
$791$		−	3.88647e17i		−	1.58670i
$792$	−4.93938e17	+	6.35650e17i	−2.00134	+	2.57553i
$793$	−7.11136e15			−0.0285965
$794$		−	5.17270e17i		−	2.06440i
$795$	1.12387e17			0.445155
$796$	6.13256e16			0.241081
$797$	2.00705e17			0.783082			0.391541	−	0.920161i	$-0.371942\pi$
$797$	2.00705e17			0.783082			0.391541	+	0.920161i	$0.371942\pi$
$798$			6.28264e17i			2.43290i
$799$			7.86171e16i			0.302159i
$800$			7.29476e15i			0.0278273i
$801$	1.47910e17			0.560020
$802$		−	6.77084e17i		−	2.54446i
$803$	−7.35298e16	+	9.46257e16i	−0.274265	+	0.352952i
$804$	3.50166e17			1.29640
$805$			3.04884e17i			1.12036i
$806$	−9.10780e16			−0.332203
$807$	8.79805e17			3.18526
$808$	−7.18872e17			−2.58335
$809$			1.72479e17i			0.615242i	0.951509	+	0.307621i	$0.0995328\pi$
$809$			1.72479e17i			0.615242i	−0.951509	+	0.307621i	$0.900467\pi$
$810$			4.09686e17i			1.45058i
$811$			2.80349e17i			0.985311i	0.870224	+	0.492655i	$0.163974\pi$
$811$			2.80349e17i			0.985311i	−0.870224	+	0.492655i	$0.836026\pi$
$812$	9.58611e17			3.34431
$813$			1.22665e17i			0.424794i
$814$	1.28173e17	−	1.64946e17i	0.440606	−	0.567018i
$815$	−3.40141e16			−0.116068
$816$		−	6.36209e17i		−	2.15506i
$817$	−1.19204e17			−0.400828
$818$	−4.66216e17			−1.55621
$819$	−4.44561e17			−1.47309
$820$			6.40518e17i			2.10692i
$821$		−	6.55715e16i		−	0.214119i	−0.994253	−	0.107060i	$-0.965856\pi$
$821$		−	6.55715e16i		−	0.214119i	0.994253	−	0.107060i	$-0.0341436\pi$
$822$		−	2.74043e17i		−	0.888358i
$823$	4.93737e17			1.58890			0.794450	−	0.607329i	$-0.207759\pi$
$823$	4.93737e17			1.58890			0.794450	+	0.607329i	$0.207759\pi$
$824$			4.58029e17i			1.46329i
$825$	8.41949e16	+	6.54244e16i	0.267031	+	0.207499i
$826$	−6.45706e17			−2.03308
$827$		−	5.20125e17i		−	1.62583i	−0.582384	−	0.812914i	$-0.697880\pi$
$827$		−	5.20125e17i		−	1.62583i	0.582384	−	0.812914i	$-0.302120\pi$
$828$	−1.40078e18			−4.34699
$829$	−2.96441e17			−0.913295			−0.456648	−	0.889648i	$-0.650950\pi$
$829$	−2.96441e17			−0.913295			−0.456648	+	0.889648i	$0.650950\pi$
$830$	−4.90299e17			−1.49966
$831$		−	1.05201e18i		−	3.19458i
$832$			2.47945e17i			0.747508i
$833$			1.15061e17i			0.344395i
$834$	3.35745e17			0.997729
$835$		−	6.95690e16i		−	0.205256i
$836$	3.01611e17	−	3.88144e17i	0.883506	−	1.13699i
$837$	1.68288e17			0.489442
$838$		−	2.19877e17i		−	0.634916i
$839$	−7.21178e16			−0.206762			−0.103381	−	0.994642i	$-0.532966\pi$
$839$	−7.21178e16			−0.206762			−0.103381	+	0.994642i	$0.532966\pi$
$840$	9.98101e17			2.84118
$841$	−4.77791e17			−1.35040
$842$			8.32441e16i			0.233604i
$843$			1.01452e18i			2.82679i
$844$			5.89341e16i			0.163047i
$845$	1.80901e17			0.496935
$846$		−	2.64479e17i		−	0.721389i
$847$	−3.98651e17	+	1.01625e17i	−1.07967	+	0.275232i
$848$	9.35908e16			0.251686
$849$		−	6.49534e17i		−	1.73443i
$850$	−1.81241e17			−0.480555
$851$	1.77830e17			0.468196
$852$	1.38319e18			3.61614
$853$		−	4.12454e17i		−	1.07073i	−0.844619	−	0.535367i	$-0.820173\pi$
$853$		−	4.12454e17i		−	1.07073i	0.844619	−	0.535367i	$-0.179827\pi$
$854$		−	3.18366e16i		−	0.0820689i
$855$		−	5.10146e17i		−	1.30586i
$856$	2.36490e17			0.601133
$857$		−	5.72289e17i		−	1.44454i	−0.691609	−	0.722272i	$-0.743098\pi$
$857$		−	5.72289e17i		−	1.44454i	0.691609	−	0.722272i	$-0.256902\pi$
$858$	6.24494e17	+	4.85269e17i	1.56532	+	1.21635i
$859$	2.16481e17			0.538840			0.269420	−	0.963023i	$-0.413168\pi$
$859$	2.16481e17			0.538840			0.269420	+	0.963023i	$0.413168\pi$
$860$			3.87091e17i			0.956804i
$861$	9.40410e17			2.30833
$862$	7.04577e17			1.71745
$863$	−1.36449e17			−0.330298			−0.165149	−	0.986269i	$-0.552810\pi$
$863$	−1.36449e17			−0.330298			−0.165149	+	0.986269i	$0.552810\pi$
$864$		−	9.99755e16i		−	0.240332i
$865$			5.04103e17i			1.20343i
$866$			5.49324e17i			1.30233i
$867$	−7.58518e17			−1.78588
$868$		−	2.69890e17i		−	0.631058i
$869$	−1.04625e17	+	1.34642e17i	−0.242950	+	0.312653i
$870$	−1.76987e18			−4.08155
$871$		−	1.11827e17i		−	0.256117i
$872$	5.65298e17			1.28582
$873$	−1.30888e18			−2.95675
$874$	6.32201e17			1.41836
$875$		−	5.36244e17i		−	1.19485i
$876$			6.82656e17i			1.51070i
$877$			1.40385e17i			0.308548i	0.988028	+	0.154274i	$0.0493039\pi$
$877$			1.40385e17i			0.308548i	−0.988028	+	0.154274i	$0.950696\pi$
$878$	3.46276e17			0.755883
$879$			9.69302e17i			2.10148i
$880$	−2.87799e17	−	2.23637e17i	−0.619717	−	0.481557i
$881$	5.87967e17			1.25747			0.628735	−	0.777620i	$-0.283573\pi$
$881$	5.87967e17			1.25747			0.628735	+	0.777620i	$0.283573\pi$
$882$		−	3.87081e17i		−	0.822224i
$883$	9.10590e16			0.192114			0.0960569	−	0.995376i	$-0.469377\pi$
$883$	9.10590e16			0.192114			0.0960569	+	0.995376i	$0.469377\pi$
$884$	−8.89815e17			−1.86460
$885$	7.89101e17			1.64238
$886$			1.00450e18i			2.07657i
$887$		−	2.02712e17i		−	0.416234i	−0.978104	−	0.208117i	$-0.933266\pi$
$887$		−	2.02712e17i		−	0.416234i	0.978104	−	0.208117i	$-0.0667336\pi$
$888$		−	5.82164e17i		−	1.18732i
$889$	3.95020e16			0.0800218
$890$			2.16773e17i			0.436180i
$891$	−3.71611e17	−	2.88764e17i	−0.742715	−	0.577134i
$892$	−6.89054e17			−1.36793
$893$			7.90089e16i			0.155800i
$894$	−1.14556e18			−2.24384
$895$	7.64723e17			1.48787
$896$	−1.02812e18			−1.98699
$897$			6.73272e17i			1.29252i
$898$			2.77480e17i			0.529145i
$899$			2.34133e17i			0.443511i
$900$	4.03583e17			0.759412
$901$		−	2.19443e17i		−	0.410179i
$902$	−8.77744e17	−	6.82059e17i	−1.62978	−	1.26643i
$903$	5.68329e17			1.04827
$904$			1.28029e18i			2.34583i
$905$	−4.09270e17			−0.744936
$906$	6.40779e17			1.15861
$907$	−2.28556e17			−0.410534			−0.205267	−	0.978706i	$-0.565806\pi$
$907$	−2.28556e17			−0.410534			−0.205267	+	0.978706i	$0.565806\pi$
$908$		−	1.21484e18i		−	2.16773i
$909$		−	1.75178e18i		−	3.10525i
$910$		−	6.51536e17i		−	1.14733i
$911$	2.86406e17			0.501040			0.250520	−	0.968111i	$-0.419398\pi$
$911$	2.86406e17			0.501040			0.250520	+	0.968111i	$0.419398\pi$
$912$		−	6.39381e17i		−	1.11120i
$913$	3.45583e17	−	4.44731e17i	0.596660	−	0.767844i
$914$	−8.25929e17			−1.41666
$915$			3.89067e16i			0.0662976i
$916$	7.82858e17			1.32529
$917$	−6.11193e17			−1.02793
$918$	2.48393e18			4.15034
$919$			1.17692e18i			1.95368i	0.213981	+	0.976838i	$0.431357\pi$
$919$			1.17692e18i			1.95368i	−0.213981	+	0.976838i	$0.568643\pi$
$920$		−	1.00435e18i		−	1.65638i
$921$			8.92340e17i			1.46208i
$922$	−1.21213e18			−1.97316
$923$		−	4.41729e17i		−	0.714407i
$924$	−1.43799e18	+	1.85056e18i	−2.31060	+	2.97352i
$925$	−5.12350e16			−0.0817931
$926$			5.11001e17i			0.810505i
$927$	−1.11615e18			−1.75891
$928$	1.39092e17			0.217778
$929$	4.49755e16			0.0699651			0.0349826	−	0.999388i	$-0.488862\pi$
$929$	4.49755e16			0.0699651			0.0349826	+	0.999388i	$0.488862\pi$
$930$			4.98294e17i			0.770172i
$931$			1.15634e17i			0.177577i
$932$			7.90291e17i			1.20585i
$933$	1.18079e18			1.79012
$934$			2.31680e17i			0.348985i
$935$	−5.24364e17	+	6.74805e17i	−0.784807	+	1.00997i
$936$	1.46448e18			2.17786
$937$			5.04699e17i			0.745753i	0.927881	+	0.372877i	$0.121629\pi$
$937$			5.04699e17i			0.745753i	−0.927881	+	0.372877i	$0.878371\pi$
$938$	5.00634e17			0.735027
$939$	7.72255e17			1.12659
$940$	2.56566e17			0.371905
$941$		−	5.22795e17i		−	0.752997i	−0.926417	−	0.376499i	$-0.877128\pi$
$941$		−	5.22795e17i		−	0.752997i	0.926417	−	0.376499i	$-0.122872\pi$
$942$		−	2.77949e18i		−	3.97795i
$943$		−	9.46303e17i		−	1.34574i
$944$	6.57131e17			0.928581
$945$			1.20387e18i			1.69039i
$946$	−5.30457e17	−	4.12197e17i	−0.740122	−	0.575119i
$947$	1.34472e18			1.86437			0.932183	−	0.361987i	$-0.117902\pi$
$947$	1.34472e18			1.86437			0.932183	+	0.361987i	$0.117902\pi$
$948$			9.71348e17i			1.33821i
$949$	2.18009e17			0.298454
$950$	−1.82145e17			−0.247785
$951$	−6.03401e17			−0.815685
$952$		−	1.94887e18i		−	2.61795i
$953$			8.71924e17i			1.16392i	0.813219	+	0.581958i	$0.197713\pi$
$953$			8.71924e17i			1.16392i	−0.813219	+	0.581958i	$0.802287\pi$
$954$			7.38240e17i			0.979281i
$955$	−6.70432e17			−0.883760
$956$			2.07784e18i			2.72185i
$957$	1.24747e18	−	1.60538e18i	1.62390	−	2.08980i
$958$	−7.00872e17			−0.906663
$959$		−	2.59338e17i		−	0.333391i
$960$	1.35652e18			1.73301
$961$	−7.21744e17			−0.916311
$962$	−3.80022e17			−0.479467
$963$			5.76291e17i			0.722577i
$964$		−	1.29566e18i		−	1.61447i
$965$		−	1.40333e18i		−	1.73779i
$966$	−3.01414e18			−3.70938
$967$			6.81634e17i			0.833667i	0.908983	+	0.416833i	$0.136860\pi$
$967$			6.81634e17i			0.833667i	−0.908983	+	0.416833i	$0.863140\pi$
$968$	1.31325e18	−	3.34775e17i	1.59622	−	0.406912i
$969$	−1.49916e18			−1.81095
$970$		−	1.91826e18i		−	2.30291i
$971$	1.35264e18			1.61387			0.806934	−	0.590642i	$-0.201125\pi$
$971$	1.35264e18			1.61387			0.806934	+	0.590642i	$0.201125\pi$
$972$	1.12512e17			0.133414
$973$	3.17729e17			0.374437
$974$			1.55396e17i			0.182006i
$975$		−	1.93978e17i		−	0.225800i
$976$			3.23999e16i			0.0374839i
$977$	2.68381e17			0.308592			0.154296	−	0.988025i	$-0.450689\pi$
$977$	2.68381e17			0.308592			0.154296	+	0.988025i	$0.450689\pi$
$978$		−	3.36271e17i		−	0.384287i
$979$	−1.96627e17	−	1.52791e17i	−0.223330	−	0.173540i
$980$	3.75499e17			0.423889
$981$			1.37755e18i			1.54558i
$982$	1.99874e18			2.22888
$983$	−7.48803e17			−0.829940			−0.414970	−	0.909835i	$-0.636208\pi$
$983$	−7.48803e17			−0.829940			−0.414970	+	0.909835i	$0.636208\pi$
$984$	−3.09792e18			−3.41271
$985$			1.29521e18i			1.41815i
$986$			3.45580e18i			3.76086i
$987$		−	3.76691e17i		−	0.407458i
$988$	−8.94250e17			−0.961430
$989$		−	5.71890e17i		−	0.611132i
$990$	1.76404e18	−	2.27015e18i	1.87369	−	2.41125i
$991$	−2.19759e17			−0.232009			−0.116004	−	0.993249i	$-0.537009\pi$
$991$	−2.19759e17			−0.232009			−0.116004	+	0.993249i	$0.537009\pi$
$992$		−	3.91605e16i		−	0.0410939i
$993$	−2.12945e18			−2.22112
$994$	1.97756e18			2.05027
$995$	−1.07149e17			−0.110420
$996$		−	3.20842e18i		−	3.28651i
$997$			1.43003e18i			1.45604i	0.685554	+	0.728022i	$0.259560\pi$
$997$			1.43003e18i			1.45604i	−0.685554	+	0.728022i	$0.740440\pi$
$998$		−	9.69076e13i		−	9.80787e-5i
$999$	7.02182e17			0.706409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.13.b.b.10.10	yes	10
3.2	odd	2		99.13.c.b.10.1		10
4.3	odd	2		176.13.h.c.65.1		10
11.10	odd	2	inner	11.13.b.b.10.1	✓	10
33.32	even	2		99.13.c.b.10.10		10
44.43	even	2		176.13.h.c.65.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.13.b.b.10.1	✓	10	11.10	odd	2	inner
11.13.b.b.10.10	yes	10	1.1	even	1	trivial
99.13.c.b.10.1		10	3.2	odd	2
99.13.c.b.10.10		10	33.32	even	2
176.13.h.c.65.1		10	4.3	odd	2
176.13.h.c.65.2		10	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:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+110.069i q^{2} +1258.46 q^{3} -8019.20 q^{4} +14011.2 q^{5} +138518. i q^{6} +131085. i q^{7} -431823. i q^{8} +1.05229e6 q^{9} +O(q^{10})\)	\(q+110.069i q^{2} +1258.46 q^{3} -8019.20 q^{4} +14011.2 q^{5} +138518. i q^{6} +131085. i q^{7} -431823. i q^{8} +1.05229e6 q^{9} +1.54220e6i q^{10} +(-1.39887e6 - 1.08701e6i) q^{11} -1.00919e7 q^{12} +3.22288e6i q^{13} -1.44284e7 q^{14} +1.76326e7 q^{15} +1.46837e7 q^{16} -3.44290e7i q^{17} +1.15824e8i q^{18} -3.46006e7i q^{19} -1.12359e8 q^{20} +1.64965e8i q^{21} +(1.19646e8 - 1.53973e8i) q^{22} +1.65999e8 q^{23} -5.43433e8i q^{24} -4.78263e7 q^{25} -3.54740e8 q^{26} +6.55465e8 q^{27} -1.05120e9i q^{28} +9.11924e8i q^{29} +1.94080e9i q^{30} +2.56746e8 q^{31} -1.52526e8i q^{32} +(-1.76043e9 - 1.36796e9i) q^{33} +3.78957e9 q^{34} +1.83666e9i q^{35} -8.43850e9 q^{36} +1.07127e9 q^{37} +3.80846e9 q^{38} +4.05588e9i q^{39} -6.05036e9i q^{40} -5.70065e9i q^{41} -1.81576e10 q^{42} -3.44514e9i q^{43} +(1.12178e10 + 8.71692e9i) q^{44} +1.47438e10 q^{45} +1.82714e10i q^{46} -2.28345e9 q^{47} +1.84789e10 q^{48} -3.34197e9 q^{49} -5.26420e9i q^{50} -4.33276e10i q^{51} -2.58449e10i q^{52} +6.37380e9 q^{53} +7.21465e10i q^{54} +(-1.95999e10 - 1.52303e10i) q^{55} +5.66054e10 q^{56} -4.35436e10i q^{57} -1.00375e11 q^{58} +4.47524e10 q^{59} -1.41399e11 q^{60} +2.20652e9i q^{61} +2.82598e10i q^{62} +1.37939e11i q^{63} +7.69328e10 q^{64} +4.51565e10i q^{65} +(1.50570e11 - 1.93769e11i) q^{66} -3.46978e10 q^{67} +2.76093e11i q^{68} +2.08904e11 q^{69} -2.02159e11 q^{70} -1.37060e11 q^{71} -4.54402e11i q^{72} -6.76442e10i q^{73} +1.17914e11i q^{74} -6.01877e10 q^{75} +2.77469e11i q^{76} +(1.42490e11 - 1.83371e11i) q^{77} -4.46426e11 q^{78} -9.62506e10i q^{79} +2.05736e11 q^{80} +2.65650e11 q^{81} +6.27465e11 q^{82} +3.17921e11i q^{83} -1.32289e12i q^{84} -4.82392e11i q^{85} +3.79203e11 q^{86} +1.14762e12i q^{87} +(-4.69394e11 + 6.04065e11i) q^{88} +1.40561e11 q^{89} +1.62284e12i q^{90} -4.22471e11 q^{91} -1.33118e12 q^{92} +3.23105e11 q^{93} -2.51338e11i q^{94} -4.84797e11i q^{95} -1.91948e11i q^{96} -1.24384e12 q^{97} -3.67847e11i q^{98} +(-1.47202e12 - 1.14384e12i) 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

Introduction

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