LMFDB - Embedded newform 75.10.e.g.32.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.9
Character	$\chi$	$=$	75.32
Dual form			75.10.e.g.68.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0913 + 11.0913i) q^{2} +(-138.195 - 24.1892i) q^{3} +265.967i q^{4} +(1801.05 - 1264.47i) q^{6} +(7391.28 + 7391.28i) q^{7} +(-8628.65 - 8628.65i) q^{8} +(18512.8 + 6685.66i) q^{9} +O(q^{10})$	\(q+(-11.0913 + 11.0913i) q^{2} +(-138.195 - 24.1892i) q^{3} +265.967i q^{4} +(1801.05 - 1264.47i) q^{6} +(7391.28 + 7391.28i) q^{7} +(-8628.65 - 8628.65i) q^{8} +(18512.8 + 6685.66i) q^{9} -51315.4i q^{11} +(6433.53 - 36755.3i) q^{12} +(-19292.1 + 19292.1i) q^{13} -163958. q^{14} +55230.6 q^{16} +(-265928. + 265928. i) q^{17} +(-279483. + 131178. i) q^{18} -839953. i q^{19} +(-842650. - 1.20023e6i) q^{21} +(569153. + 569153. i) q^{22} +(-1.09790e6 - 1.09790e6i) q^{23} +(983717. + 1.40116e6i) q^{24} -427949. i q^{26} +(-2.39665e6 - 1.37173e6i) q^{27} +(-1.96584e6 + 1.96584e6i) q^{28} +3.71113e6 q^{29} +4.98830e6 q^{31} +(3.80529e6 - 3.80529e6i) q^{32} +(-1.24128e6 + 7.09153e6i) q^{33} -5.89896e6i q^{34} +(-1.77816e6 + 4.92378e6i) q^{36} +(-6.94044e6 - 6.94044e6i) q^{37} +(9.31616e6 + 9.31616e6i) q^{38} +(3.13274e6 - 2.19942e6i) q^{39} -1.82732e7i q^{41} +(2.26581e7 + 3.96601e6i) q^{42} +(-2.43988e6 + 2.43988e6i) q^{43} +1.36482e7 q^{44} +2.43544e7 q^{46} +(1.65340e7 - 1.65340e7i) q^{47} +(-7.63260e6 - 1.33599e6i) q^{48} +6.89085e7i q^{49} +(4.31825e7 - 3.03173e7i) q^{51} +(-5.13107e6 - 5.13107e6i) q^{52} +(7.36089e7 + 7.36089e7i) q^{53} +(4.17962e7 - 1.13677e7i) q^{54} -1.27554e8i q^{56} +(-2.03178e7 + 1.16077e8i) q^{57} +(-4.11612e7 + 4.11612e7i) q^{58} -4.08308e7 q^{59} +7.68949e7 q^{61} +(-5.53266e7 + 5.53266e7i) q^{62} +(8.74175e7 + 1.86249e8i) q^{63} +1.12689e8i q^{64} +(-6.48868e7 - 9.24215e7i) q^{66} +(9.16819e7 + 9.16819e7i) q^{67} +(-7.07280e7 - 7.07280e7i) q^{68} +(1.25168e8 + 1.78283e8i) q^{69} -1.51302e8i q^{71} +(-1.02052e8 - 2.17428e8i) q^{72} +(6.17833e7 - 6.17833e7i) q^{73} +1.53957e8 q^{74} +2.23400e8 q^{76} +(3.79286e8 - 3.79286e8i) q^{77} +(-1.03518e7 + 5.91405e7i) q^{78} -3.41727e8i q^{79} +(2.98024e8 + 2.47540e8i) q^{81} +(2.02673e8 + 2.02673e8i) q^{82} +(3.79608e8 + 3.79608e8i) q^{83} +(3.19221e8 - 2.24117e8i) q^{84} -5.41229e7i q^{86} +(-5.12860e8 - 8.97694e7i) q^{87} +(-4.42782e8 + 4.42782e8i) q^{88} -6.96227e8 q^{89} -2.85187e8 q^{91} +(2.92006e8 - 2.92006e8i) q^{92} +(-6.89358e8 - 1.20663e8i) q^{93} +3.66767e8i q^{94} +(-6.17919e8 + 4.33826e8i) q^{96} +(-4.49583e8 - 4.49583e8i) q^{97} +(-7.64284e8 - 7.64284e8i) q^{98} +(3.43077e8 - 9.49989e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10788 q^{6}+O(q^{10}) $ 48 * q + 10788 * q^6	$ 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) $ 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−11.0913	+	11.0913i	−0.490170	+	0.490170i	−0.908360	−	0.418190i	$-0.862665\pi$
$2$	−11.0913	+	11.0913i	−0.490170	+	0.490170i	0.418190	+	0.908360i	$0.362665\pi$
$3$	−138.195	−	24.1892i	−0.985024	−	0.172415i
$3$	−138.195	−	24.1892i	−0.985024	−	0.172415i
$4$			265.967i			0.519466i
$5$		0			0
$5$		0			0
$6$	1801.05	−	1264.47i	0.567342	−	0.398317i
$7$	7391.28	+	7391.28i	1.16353	+	1.16353i	0.983697	+	0.179836i	$0.0575567\pi$
$7$	7391.28	+	7391.28i	1.16353	+	1.16353i	0.179836	+	0.983697i	$0.442443\pi$
$8$	−8628.65	−	8628.65i	−0.744797	−	0.744797i
$9$	18512.8	+	6685.66i	0.940546	+	0.339667i
$10$		0			0
$11$		−	51315.4i		−	1.05677i	−0.849005	−	0.528385i	$-0.822798\pi$
$11$		−	51315.4i		−	1.05677i	0.849005	−	0.528385i	$-0.177202\pi$
$12$	6433.53	−	36755.3i	0.0895640	−	0.511687i
$13$	−19292.1	+	19292.1i	−0.187342	+	0.187342i	−0.794546	−	0.607204i	$-0.792291\pi$
$13$	−19292.1	+	19292.1i	−0.187342	+	0.187342i	0.607204	+	0.794546i	$0.292291\pi$
$14$	−163958.			−1.14066
$15$		0			0
$16$	55230.6			0.210688
$17$	−265928.	+	265928.i	−0.772225	+	0.772225i	−0.978495	−	0.206270i	$-0.933867\pi$
$17$	−265928.	+	265928.i	−0.772225	+	0.772225i	0.206270	+	0.978495i	$0.433867\pi$
$18$	−279483.	+	131178.i	−0.627522	+	0.294533i
$19$		−	839953.i		−	1.47865i	−0.673351	−	0.739323i	$-0.735146\pi$
$19$		−	839953.i		−	1.47865i	0.673351	−	0.739323i	$-0.264854\pi$
$20$		0			0
$21$	−842650.	−	1.20023e6i	−0.945497	−	1.34672i
$22$	569153.	+	569153.i	0.517997	+	0.517997i
$23$	−1.09790e6	−	1.09790e6i	−0.818068	−	0.818068i	0.167760	−	0.985828i	$-0.446347\pi$
$23$	−1.09790e6	−	1.09790e6i	−0.818068	−	0.818068i	−0.985828	+	0.167760i	$0.946347\pi$
$24$	983717.	+	1.40116e6i	0.605229	+	0.862058i
$25$		0			0
$26$		−	427949.i		−	0.183659i
$27$	−2.39665e6	−	1.37173e6i	−0.867897	−	0.496745i
$28$	−1.96584e6	+	1.96584e6i	−0.604416	+	0.604416i
$29$	3.71113e6			0.974351			0.487176	−	0.873304i	$-0.338027\pi$
$29$	3.71113e6			0.974351			0.487176	+	0.873304i	$0.338027\pi$
$30$		0			0
$31$	4.98830e6			0.970119			0.485059	−	0.874481i	$-0.338798\pi$
$31$	4.98830e6			0.970119			0.485059	+	0.874481i	$0.338798\pi$
$32$	3.80529e6	−	3.80529e6i	0.641524	−	0.641524i
$33$	−1.24128e6	+	7.09153e6i	−0.182203	+	1.04094i
$34$		−	5.89896e6i		−	0.757043i
$35$		0			0
$36$	−1.77816e6	+	4.92378e6i	−0.176445	+	0.488582i
$37$	−6.94044e6	−	6.94044e6i	−0.608807	−	0.608807i	0.333828	−	0.942634i	$-0.391660\pi$
$37$	−6.94044e6	−	6.94044e6i	−0.608807	−	0.608807i	−0.942634	+	0.333828i	$0.891660\pi$
$38$	9.31616e6	+	9.31616e6i	0.724788	+	0.724788i
$39$	3.13274e6	−	2.19942e6i	0.216837	−	0.152236i
$40$		0			0
$41$		−	1.82732e7i		−	1.00992i	−0.863143	−	0.504960i	$-0.831507\pi$
$41$		−	1.82732e7i		−	1.00992i	0.863143	−	0.504960i	$-0.168493\pi$
$42$	2.26581e7	+	3.96601e6i	1.12358	+	0.196667i
$43$	−2.43988e6	+	2.43988e6i	−0.108833	+	0.108833i	−0.759426	−	0.650593i	$-0.774520\pi$
$43$	−2.43988e6	+	2.43988e6i	−0.108833	+	0.108833i	0.650593	+	0.759426i	$0.274520\pi$
$44$	1.36482e7			0.548956
$45$		0			0
$46$	2.43544e7			0.801985
$47$	1.65340e7	−	1.65340e7i	0.494241	−	0.494241i	−0.415399	−	0.909639i	$-0.636358\pi$
$47$	1.65340e7	−	1.65340e7i	0.494241	−	0.494241i	0.909639	+	0.415399i	$0.136358\pi$
$48$	−7.63260e6	−	1.33599e6i	−0.207533	−	0.0363259i
$49$			6.89085e7i			1.70762i
$50$		0			0
$51$	4.31825e7	−	3.03173e7i	0.893804	−	0.627517i
$52$	−5.13107e6	−	5.13107e6i	−0.0973179	−	0.0973179i
$53$	7.36089e7	+	7.36089e7i	1.28141	+	1.28141i	0.939864	+	0.341549i	$0.110952\pi$
$53$	7.36089e7	+	7.36089e7i	1.28141	+	1.28141i	0.341549	+	0.939864i	$0.389048\pi$
$54$	4.17962e7	−	1.13677e7i	0.668906	−	0.181928i
$55$		0			0
$56$		−	1.27554e8i		−	1.73319i
$57$	−2.03178e7	+	1.16077e8i	−0.254941	+	1.45650i
$58$	−4.11612e7	+	4.11612e7i	−0.477598	+	0.477598i
$59$	−4.08308e7			−0.438686			−0.219343	−	0.975648i	$-0.570391\pi$
$59$	−4.08308e7			−0.438686			−0.219343	+	0.975648i	$0.570391\pi$
$60$		0			0
$61$	7.68949e7			0.711072			0.355536	−	0.934663i	$-0.384298\pi$
$61$	7.68949e7			0.711072			0.355536	+	0.934663i	$0.384298\pi$
$62$	−5.53266e7	+	5.53266e7i	−0.475523	+	0.475523i
$63$	8.74175e7	+	1.86249e8i	0.699142	+	1.48957i
$64$			1.12689e8i			0.839600i
$65$		0			0
$66$	−6.48868e7	−	9.24215e7i	−0.420929	−	0.599550i
$67$	9.16819e7	+	9.16819e7i	0.555836	+	0.555836i	0.928119	−	0.372283i	$-0.121425\pi$
$67$	9.16819e7	+	9.16819e7i	0.555836	+	0.555836i	−0.372283	+	0.928119i	$0.621425\pi$
$68$	−7.07280e7	−	7.07280e7i	−0.401145	−	0.401145i
$69$	1.25168e8	+	1.78283e8i	0.664769	+	0.946865i
$70$		0			0
$71$		−	1.51302e8i		−	0.706611i	−0.935508	−	0.353306i	$-0.885058\pi$
$71$		−	1.51302e8i		−	0.706611i	0.935508	−	0.353306i	$-0.114942\pi$
$72$	−1.02052e8	−	2.17428e8i	−0.447533	−	0.953499i
$73$	6.17833e7	−	6.17833e7i	0.254635	−	0.254635i	−0.568233	−	0.822868i	$-0.692373\pi$
$73$	6.17833e7	−	6.17833e7i	0.254635	−	0.254635i	0.822868	+	0.568233i	$0.192373\pi$
$74$	1.53957e8			0.596838
$75$		0			0
$76$	2.23400e8			0.768107
$77$	3.79286e8	−	3.79286e8i	1.22959	−	1.22959i
$78$	−1.03518e7	+	5.91405e7i	−0.0316656	+	0.180909i
$79$		−	3.41727e8i		−	0.987093i	−0.869720	−	0.493546i	$-0.835700\pi$
$79$		−	3.41727e8i		−	0.987093i	0.869720	−	0.493546i	$-0.164300\pi$
$80$		0			0
$81$	2.98024e8	+	2.47540e8i	0.769253	+	0.638944i
$82$	2.02673e8	+	2.02673e8i	0.495032	+	0.495032i
$83$	3.79608e8	+	3.79608e8i	0.877979	+	0.877979i	0.993325	−	0.115346i	$-0.0367977\pi$
$83$	3.79608e8	+	3.79608e8i	0.877979	+	0.877979i	−0.115346	+	0.993325i	$0.536798\pi$
$84$	3.19221e8	−	2.24117e8i	0.699575	−	0.491154i
$85$		0			0
$86$		−	5.41229e7i		−	0.106694i
$87$	−5.12860e8	−	8.97694e7i	−0.959760	−	0.167993i
$88$	−4.42782e8	+	4.42782e8i	−0.787079	+	0.787079i
$89$	−6.96227e8			−1.17624			−0.588120	−	0.808774i	$-0.700132\pi$
$89$	−6.96227e8			−1.17624			−0.588120	+	0.808774i	$0.700132\pi$
$90$		0			0
$91$	−2.85187e8			−0.435957
$92$	2.92006e8	−	2.92006e8i	0.424959	−	0.424959i
$93$	−6.89358e8	−	1.20663e8i	−0.955590	−	0.167263i
$94$			3.66767e8i			0.484524i
$95$		0			0
$96$	−6.17919e8	+	4.33826e8i	−0.742525	+	0.521308i
$97$	−4.49583e8	−	4.49583e8i	−0.515629	−	0.515629i	0.400617	−	0.916246i	$-0.368796\pi$
$97$	−4.49583e8	−	4.49583e8i	−0.515629	−	0.515629i	−0.916246	+	0.400617i	$0.868796\pi$
$98$	−7.64284e8	−	7.64284e8i	−0.837023	−	0.837023i
$99$	3.43077e8	−	9.49989e8i	0.358949	−	0.993940i
$100$		0			0
$101$		−	2.95567e7i		−	0.0282624i	−0.999900	−	0.0141312i	$-0.995502\pi$
$101$		−	2.95567e7i		−	0.0282624i	0.999900	−	0.0141312i	$-0.00449826\pi$
$102$	−1.42691e8	+	8.15208e8i	−0.130526	+	0.745706i
$103$	1.46219e9	−	1.46219e9i	1.28007	−	1.28007i	0.339450	−	0.940624i	$-0.389759\pi$
$103$	1.46219e9	−	1.46219e9i	1.28007	−	1.28007i	0.940624	−	0.339450i	$-0.110241\pi$
$104$	3.32930e8			0.279064
$105$		0			0
$106$	−1.63284e9			−1.25622
$107$	−7.06154e8	+	7.06154e8i	−0.520801	+	0.520801i	−0.917813	−	0.397012i	$-0.870047\pi$
$107$	−7.06154e8	+	7.06154e8i	−0.520801	+	0.520801i	0.397012	+	0.917813i	$0.370047\pi$
$108$	3.64836e8	−	6.37430e8i	0.258042	−	0.450843i
$109$			1.11195e9i			0.754513i	0.926109	+	0.377257i	$0.123133\pi$
$109$			1.11195e9i			0.754513i	−0.926109	+	0.377257i	$0.876867\pi$
$110$		0			0
$111$	7.91251e8	+	1.12702e9i	0.494722	+	0.704657i
$112$	4.08225e8	+	4.08225e8i	0.245143	+	0.245143i
$113$	−1.89557e9	−	1.89557e9i	−1.09367	−	1.09367i	−0.995134	−	0.0985353i	$-0.968584\pi$
$113$	−1.89557e9	−	1.89557e9i	−1.09367	−	1.09367i	−0.0985353	−	0.995134i	$-0.531416\pi$
$114$	−1.06210e9	−	1.51280e9i	−0.588969	−	0.838898i
$115$		0			0
$116$			9.87039e8i			0.506143i
$117$	−4.86132e8	+	2.28170e8i	−0.239838	+	0.112570i
$118$	4.52866e8	−	4.52866e8i	0.215031	−	0.215031i
$119$	−3.93110e9			−1.79702
$120$		0			0
$121$	−2.75318e8			−0.116762
$122$	−8.52864e8	+	8.52864e8i	−0.348546	+	0.348546i
$123$	−4.42014e8	+	2.52526e9i	−0.174126	+	0.994795i
$124$			1.32672e9i			0.503944i
$125$		0			0
$126$	−3.03531e9	−	1.09617e9i	−1.07284	−	0.387444i
$127$	9.95086e8	+	9.95086e8i	0.339425	+	0.339425i	0.856151	−	0.516726i	$-0.172849\pi$
$127$	9.95086e8	+	9.95086e8i	0.339425	+	0.339425i	−0.516726	+	0.856151i	$0.672849\pi$
$128$	6.98441e8	+	6.98441e8i	0.229977	+	0.229977i
$129$	3.96199e8	−	2.78161e8i	0.125968	−	0.0884388i
$130$		0			0
$131$			4.74131e9i			1.40662i	0.710881	+	0.703312i	$0.248296\pi$
$131$			4.74131e9i			1.40662i	−0.710881	+	0.703312i	$0.751704\pi$
$132$	−1.88611e9	−	3.30139e8i	−0.540735	−	0.0946485i
$133$	6.20833e9	−	6.20833e9i	1.72045	−	1.72045i
$134$	−2.03374e9			−0.544909
$135$		0			0
$136$	4.58920e9			1.15030
$137$	4.38786e9	−	4.38786e9i	1.06417	−	1.06417i	0.0663731	−	0.997795i	$-0.478857\pi$
$137$	4.38786e9	−	4.38786e9i	1.06417	−	1.06417i	0.997795	−	0.0663731i	$-0.0211428\pi$
$138$	−3.36565e9	−	5.89113e8i	−0.789975	−	0.138275i
$139$		−	2.47768e9i		−	0.562961i	−0.959567	−	0.281480i	$-0.909175\pi$
$139$		−	2.47768e9i		−	0.562961i	0.959567	−	0.281480i	$-0.0908254\pi$
$140$		0			0
$141$	−2.68487e9	+	1.88498e9i	−0.572054	+	0.401624i
$142$	1.67813e9	+	1.67813e9i	0.346360	+	0.346360i
$143$	9.89983e8	+	9.89983e8i	0.197977	+	0.197977i
$144$	1.02247e9	+	3.69253e8i	0.198162	+	0.0715637i
$145$		0			0
$146$			1.37051e9i			0.249629i
$147$	1.66684e9	−	9.52281e9i	0.294419	−	1.68204i
$148$	1.84593e9	−	1.84593e9i	0.316255	−	0.316255i
$149$	1.06917e10			1.77708			0.888542	−	0.458796i	$-0.151719\pi$
$149$	1.06917e10			1.77708			0.888542	+	0.458796i	$0.151719\pi$
$150$		0			0
$151$	2.90139e9			0.454162			0.227081	−	0.973876i	$-0.427082\pi$
$151$	2.90139e9			0.454162			0.227081	+	0.973876i	$0.427082\pi$
$152$	−7.24766e9	+	7.24766e9i	−1.10129	+	1.10129i
$153$	−6.70096e9	+	3.14516e9i	−0.988612	+	0.464014i
$154$			8.41354e9i			1.20541i
$155$		0			0
$156$	5.84972e8	+	8.33205e8i	0.0790814	+	0.112640i
$157$	2.48148e9	+	2.48148e9i	0.325959	+	0.325959i	0.851047	−	0.525089i	$-0.175968\pi$
$157$	2.48148e9	+	2.48148e9i	0.325959	+	0.325959i	−0.525089	+	0.851047i	$0.675968\pi$
$158$	3.79020e9	+	3.79020e9i	0.483843	+	0.483843i
$159$	−8.39185e9	−	1.19529e10i	−1.04129	−	1.48316i
$160$		0			0
$161$		−	1.62298e10i		−	1.90370i
$162$	−6.05101e9	+	5.59935e8i	−0.690256	+	0.0638734i
$163$	−8.81005e9	+	8.81005e9i	−0.977539	+	0.977539i	−0.999753	−	0.0222140i	$-0.992928\pi$
$163$	−8.81005e9	+	8.81005e9i	−0.977539	+	0.977539i	0.0222140	+	0.999753i	$0.492928\pi$
$164$	4.86006e9			0.524619
$165$		0			0
$166$	−8.42069e9			−0.860718
$167$	8.08183e7	−	8.08183e7i	0.00804054	−	0.00804054i	−0.703075	−	0.711116i	$-0.748190\pi$
$167$	8.08183e7	−	8.08183e7i	0.00804054	−	0.00804054i	0.711116	+	0.703075i	$0.248190\pi$
$168$	−3.08542e9	+	1.76273e10i	−0.298829	+	1.70724i
$169$			9.86013e9i			0.929806i
$170$		0			0
$171$	5.61564e9	−	1.55499e10i	0.502247	−	1.39073i
$172$	−6.48928e8	−	6.48928e8i	−0.0565352	−	0.0565352i
$173$	−2.06082e9	−	2.06082e9i	−0.174917	−	0.174917i	0.614219	−	0.789136i	$-0.289471\pi$
$173$	−2.06082e9	−	2.06082e9i	−0.174917	−	0.174917i	−0.789136	+	0.614219i	$0.789471\pi$
$174$	6.68394e9	−	4.69262e9i	0.552791	−	0.388100i
$175$		0			0
$176$		−	2.83418e9i		−	0.222649i
$177$	5.64261e9	+	9.87665e8i	0.432116	+	0.0756362i
$178$	7.72205e9	−	7.72205e9i	0.576558	−	0.576558i
$179$	1.04722e10			0.762430			0.381215	−	0.924486i	$-0.375506\pi$
$179$	1.04722e10			0.762430			0.381215	+	0.924486i	$0.375506\pi$
$180$		0			0
$181$	2.43231e10			1.68448			0.842239	−	0.539104i	$-0.181237\pi$
$181$	2.43231e10			1.68448			0.842239	+	0.539104i	$0.181237\pi$
$182$	3.16309e9	−	3.16309e9i	0.213693	−	0.213693i
$183$	−1.06265e10	−	1.86003e9i	−0.700423	−	0.122600i
$184$			1.89469e10i			1.21859i
$185$		0			0
$186$	8.98418e9	−	6.30756e9i	0.550389	−	0.386414i
$187$	1.36462e10	+	1.36462e10i	0.816064	+	0.816064i
$188$	4.39750e9	+	4.39750e9i	0.256741	+	0.256741i
$189$	−7.57545e9	−	2.78532e10i	−0.431848	−	1.58780i
$190$		0			0
$191$		−	1.49663e9i		−	0.0813699i	−0.999172	−	0.0406849i	$-0.987046\pi$
$191$		−	1.49663e9i		−	0.0813699i	0.999172	−	0.0406849i	$-0.0129540\pi$
$192$	2.72586e9	−	1.55731e10i	0.144760	−	0.827026i
$193$	1.17685e10	−	1.17685e10i	0.610541	−	0.610541i	−0.332546	−	0.943087i	$-0.607908\pi$
$193$	1.17685e10	−	1.17685e10i	0.610541	−	0.610541i	0.943087	+	0.332546i	$0.107908\pi$
$194$	9.97290e9			0.505491
$195$		0			0
$196$	−1.83274e10			−0.887050
$197$	−2.18756e9	+	2.18756e9i	−0.103482	+	0.103482i	−0.756952	−	0.653470i	$-0.773312\pi$
$197$	−2.18756e9	+	2.18756e9i	−0.103482	+	0.103482i	0.653470	+	0.756952i	$0.273312\pi$
$198$	6.73143e9	+	1.43418e10i	0.311253	+	0.663146i
$199$			3.23211e10i			1.46099i	0.682918	+	0.730495i	$0.260711\pi$
$199$			3.23211e10i			1.46099i	−0.682918	+	0.730495i	$0.739289\pi$
$200$		0			0
$201$	−1.04523e10	−	1.48877e10i	−0.451677	−	0.643347i
$202$	3.27822e8	+	3.27822e8i	0.0138534	+	0.0138534i
$203$	2.74300e10	+	2.74300e10i	1.13369	+	1.13369i
$204$	8.06341e9	+	1.14851e10i	0.325974	+	0.464301i
$205$		0			0
$206$			3.24350e10i			1.25491i
$207$	−1.29850e10	−	2.76655e10i	−0.491560	−	1.04730i
$208$	−1.06552e9	+	1.06552e9i	−0.0394708	+	0.0394708i
$209$	−4.31025e10			−1.56259
$210$		0			0
$211$	2.05426e10			0.713484			0.356742	−	0.934203i	$-0.383887\pi$
$211$	2.05426e10			0.713484			0.356742	+	0.934203i	$0.383887\pi$
$212$	−1.95775e10	+	1.95775e10i	−0.665651	+	0.665651i
$213$	−3.65986e9	+	2.09091e10i	−0.121831	+	0.696029i
$214$		−	1.56643e10i		−	0.510563i
$215$		0			0
$216$	8.84366e9	+	3.25161e10i	0.276433	+	1.01638i
$217$	3.68699e10	+	3.68699e10i	1.12876	+	1.12876i
$218$	−1.23330e10	−	1.23330e10i	−0.369840	−	0.369840i
$219$	−1.00326e10	+	7.04366e9i	−0.294725	+	0.206919i
$220$		0			0
$221$		−	1.02606e10i		−	0.289340i
$222$	−2.12761e10	−	3.72409e9i	−0.587900	−	0.102904i
$223$	4.22677e10	−	4.22677e10i	1.14456	−	1.14456i	0.156948	−	0.987607i	$-0.449834\pi$
$223$	4.22677e10	−	4.22677e10i	1.14456	−	1.14456i	0.987607	−	0.156948i	$-0.0501656\pi$
$224$	5.62520e10			1.49287
$225$		0			0
$226$	4.20485e10			1.07217
$227$	2.92790e10	−	2.92790e10i	0.731879	−	0.731879i	−0.239113	−	0.970992i	$-0.576857\pi$
$227$	2.92790e10	−	2.92790e10i	0.731879	−	0.731879i	0.970992	+	0.239113i	$0.0768565\pi$
$228$	−3.08727e10	−	5.40386e9i	−0.756604	−	0.132433i
$229$		−	1.17533e10i		−	0.282424i	−0.989979	−	0.141212i	$-0.954900\pi$
$229$		−	1.17533e10i		−	0.282424i	0.989979	−	0.141212i	$-0.0450999\pi$
$230$		0			0
$231$	−6.15901e10	+	4.32409e10i	−1.42317	+	0.999172i
$232$	−3.20221e10	−	3.20221e10i	−0.725694	−	0.725694i
$233$	−3.37400e10	−	3.37400e10i	−0.749970	−	0.749970i	0.224503	−	0.974473i	$-0.427924\pi$
$233$	−3.37400e10	−	3.37400e10i	−0.749970	−	0.749970i	−0.974473	+	0.224503i	$0.927924\pi$
$234$	2.86112e9	−	7.92252e9i	0.0623829	−	0.172740i
$235$		0			0
$236$		−	1.08596e10i		−	0.227883i
$237$	−8.26612e9	+	4.72250e10i	−0.170190	+	0.972310i
$238$	4.36009e10	−	4.36009e10i	0.880844	−	0.880844i
$239$	−7.03178e10			−1.39404			−0.697020	−	0.717052i	$-0.745491\pi$
$239$	−7.03178e10			−1.39404			−0.697020	+	0.717052i	$0.745491\pi$
$240$		0			0
$241$	−8.31891e10			−1.58851			−0.794255	−	0.607585i	$-0.792139\pi$
$241$	−8.31891e10			−1.58851			−0.794255	+	0.607585i	$0.792139\pi$
$242$	3.05363e9	−	3.05363e9i	0.0572330	−	0.0572330i
$243$	−3.51977e10	−	4.14178e10i	−0.647569	−	0.762007i
$244$			2.04515e10i			0.369378i
$245$		0			0
$246$	−2.31059e10	−	3.29109e10i	−0.402268	−	0.572970i
$247$	1.62045e10	+	1.62045e10i	0.277013	+	0.277013i
$248$	−4.30423e10	−	4.30423e10i	−0.722541	−	0.722541i
$249$	−4.32776e10	−	6.16424e10i	−0.713454	−	1.01621i
$250$		0			0
$251$		−	1.10886e10i		−	0.176338i	−0.996106	−	0.0881690i	$-0.971898\pi$
$251$		−	1.10886e10i		−	0.176338i	0.996106	−	0.0881690i	$-0.0281016\pi$
$252$	−4.95360e10	+	2.32501e10i	−0.773781	+	0.363181i
$253$	−5.63394e10	+	5.63394e10i	−0.864509	+	0.864509i
$254$	−2.20736e10			−0.332752
$255$		0			0
$256$	−7.31901e10			−1.06506
$257$	−1.66782e10	+	1.66782e10i	−0.238479	+	0.238479i	−0.816220	−	0.577741i	$-0.803934\pi$
$257$	−1.66782e10	+	1.66782e10i	−0.238479	+	0.238479i	0.577741	+	0.816220i	$0.303934\pi$
$258$	−1.30919e9	+	7.47952e9i	−0.0183956	+	0.105096i
$259$		−	1.02598e11i		−	1.41673i
$260$		0			0
$261$	6.87033e10	+	2.48114e10i	0.916422	+	0.330955i
$262$	−5.25873e10	−	5.25873e10i	−0.689485	−	0.689485i
$263$	−3.58552e10	−	3.58552e10i	−0.462116	−	0.462116i	0.437233	−	0.899348i	$-0.355959\pi$
$263$	−3.58552e10	−	3.58552e10i	−0.462116	−	0.462116i	−0.899348	+	0.437233i	$0.855959\pi$
$264$	7.19009e10	−	5.04798e10i	0.910996	−	0.639587i
$265$		0			0
$266$			1.37717e11i			1.68663i
$267$	9.62152e10	+	1.68412e10i	1.15863	+	0.202802i
$268$	−2.43843e10	+	2.43843e10i	−0.288738	+	0.288738i
$269$	−9.53390e10			−1.11016			−0.555080	−	0.831797i	$-0.687312\pi$
$269$	−9.53390e10			−1.11016			−0.555080	+	0.831797i	$0.687312\pi$
$270$		0			0
$271$	7.68051e10			0.865024			0.432512	−	0.901628i	$-0.357627\pi$
$271$	7.68051e10			0.865024			0.432512	+	0.901628i	$0.357627\pi$
$272$	−1.46874e10	+	1.46874e10i	−0.162699	+	0.162699i
$273$	3.94115e10	+	6.89846e9i	0.429429	+	0.0751658i
$274$			9.73340e10i			1.04325i
$275$		0			0
$276$	−4.74172e10	+	3.32904e10i	−0.491864	+	0.345325i
$277$	−6.14389e10	−	6.14389e10i	−0.627025	−	0.627025i	0.320294	−	0.947318i	$-0.396218\pi$
$277$	−6.14389e10	−	6.14389e10i	−0.627025	−	0.627025i	−0.947318	+	0.320294i	$0.896218\pi$
$278$	2.74806e10	+	2.74806e10i	0.275947	+	0.275947i
$279$	9.23472e10	+	3.33501e10i	0.912441	+	0.329517i
$280$		0			0
$281$		−	1.16686e11i		−	1.11645i	−0.829690	−	0.558225i	$-0.811483\pi$
$281$		−	1.16686e11i		−	1.11645i	0.829690	−	0.558225i	$-0.188517\pi$
$282$	8.87181e9	−	5.06854e10i	0.0835394	−	0.477268i
$283$	7.99516e10	−	7.99516e10i	0.740949	−	0.740949i	−0.231812	−	0.972761i	$-0.574465\pi$
$283$	7.99516e10	−	7.99516e10i	0.740949	−	0.740949i	0.972761	+	0.231812i	$0.0744653\pi$
$284$	4.02412e10			0.367061
$285$		0			0
$286$	−2.19604e10			−0.194085
$287$	1.35062e11	−	1.35062e11i	1.17507	−	1.17507i
$288$	9.58873e10	−	4.50056e10i	0.821287	−	0.385478i
$289$		−	2.28474e10i		−	0.192662i
$290$		0			0
$291$	5.12551e10	+	7.30052e10i	0.419004	+	0.596809i
$292$	1.64323e10	+	1.64323e10i	0.132274	+	0.132274i
$293$	−6.46728e9	−	6.46728e9i	−0.0512646	−	0.0512646i	0.681010	−	0.732274i	$-0.261541\pi$
$293$	−6.46728e9	−	6.46728e9i	−0.0512646	−	0.0512646i	−0.732274	+	0.681010i	$0.761541\pi$
$294$	8.71328e10	+	1.24108e11i	0.680172	+	0.968803i
$295$		0			0
$296$			1.19773e11i			0.906875i
$297$	−7.03910e10	+	1.22985e11i	−0.524945	+	0.917167i
$298$	−1.18584e11	+	1.18584e11i	−0.871073	+	0.871073i
$299$	4.23619e10			0.306517
$300$		0			0
$301$	−3.60677e10			−0.253262
$302$	−3.21802e10	+	3.21802e10i	−0.222616	+	0.222616i
$303$	−7.14953e8	+	4.08459e9i	−0.00487288	+	0.0278392i
$304$		−	4.63911e10i		−	0.311533i
$305$		0			0
$306$	3.94385e10	−	1.09206e11i	0.257142	−	0.712034i
$307$	6.47836e10	+	6.47836e10i	0.416239	+	0.416239i	0.883905	−	0.467666i	$-0.154905\pi$
$307$	6.47836e10	+	6.47836e10i	0.416239	+	0.416239i	−0.467666	+	0.883905i	$0.654905\pi$
$308$	1.00878e11	+	1.00878e11i	0.638729	+	0.638729i
$309$	−2.37436e11	+	1.66698e11i	−1.48161	+	1.04020i
$310$		0			0
$311$		−	2.01388e11i		−	1.22071i	−0.792129	−	0.610354i	$-0.791027\pi$
$311$		−	2.01388e11i		−	1.22071i	0.792129	−	0.610354i	$-0.208973\pi$
$312$	−4.60093e10	−	8.05332e9i	−0.274885	−	0.0481149i
$313$	−4.77001e10	+	4.77001e10i	−0.280912	+	0.280912i	−0.833473	−	0.552561i	$-0.813651\pi$
$313$	−4.77001e10	+	4.77001e10i	−0.280912	+	0.280912i	0.552561	+	0.833473i	$0.313651\pi$
$314$	−5.50456e10			−0.319551
$315$		0			0
$316$	9.08881e10			0.512761
$317$	−2.20743e10	+	2.20743e10i	−0.122778	+	0.122778i	−0.765826	−	0.643048i	$-0.777670\pi$
$317$	−2.20743e10	+	2.20743e10i	−0.122778	+	0.122778i	0.643048	+	0.765826i	$0.277670\pi$
$318$	2.25650e11	+	3.94970e10i	1.23741	+	0.216592i
$319$		−	1.90438e11i		−	1.02966i
$320$		0			0
$321$	1.14668e11	−	8.05056e10i	0.602796	−	0.423208i
$322$	1.80010e11	+	1.80010e11i	0.933136	+	0.933136i
$323$	2.23367e11	+	2.23367e11i	1.14185	+	1.14185i
$324$	−6.58375e10	+	7.92646e10i	−0.331910	+	0.399601i
$325$		0			0
$326$		−	1.95430e11i		−	0.958321i
$327$	2.68973e10	−	1.53666e11i	0.130090	−	0.743214i
$328$	−1.57673e11	+	1.57673e11i	−0.752185	+	0.752185i
$329$	2.44415e11			1.15013
$330$		0			0
$331$	1.85509e11			0.849452			0.424726	−	0.905322i	$-0.360370\pi$
$331$	1.85509e11			0.849452			0.424726	+	0.905322i	$0.360370\pi$
$332$	−1.00963e11	+	1.00963e11i	−0.456081	+	0.456081i
$333$	−8.20853e10	−	1.74888e11i	−0.365819	−	0.779402i
$334$			1.79276e9i			0.00788247i
$335$		0			0
$336$	−4.65401e10	−	6.62893e10i	−0.199205	−	0.283738i
$337$	−1.15910e11	−	1.15910e11i	−0.489536	−	0.489536i	0.418624	−	0.908160i	$-0.362513\pi$
$337$	−1.15910e11	−	1.15910e11i	−0.489536	−	0.489536i	−0.908160	+	0.418624i	$0.862513\pi$
$338$	−1.09361e11	−	1.09361e11i	−0.455763	−	0.455763i
$339$	2.16106e11	+	3.07810e11i	0.888725	+	1.26586i
$340$		0			0
$341$		−	2.55976e11i		−	1.02519i
$342$	1.10183e11	+	2.34753e11i	0.435510	+	0.927882i
$343$	−2.11057e11	+	2.11057e11i	−0.823335	+	0.823335i
$344$	4.21058e10			0.162117
$345$		0			0
$346$	4.57143e10			0.171478
$347$	1.13348e11	−	1.13348e11i	0.419691	−	0.419691i	−0.465406	−	0.885097i	$-0.654092\pi$
$347$	1.13348e11	−	1.13348e11i	0.419691	−	0.419691i	0.885097	+	0.465406i	$0.154092\pi$
$348$	2.38757e10	−	1.36404e11i	0.0872668	−	0.498563i
$349$			5.19614e10i			0.187485i	0.995596	+	0.0937424i	$0.0298830\pi$
$349$			5.19614e10i			0.187485i	−0.995596	+	0.0937424i	$0.970117\pi$
$350$		0			0
$351$	7.27003e10	−	1.97729e10i	0.255655	−	0.0695324i
$352$	−1.95270e11	−	1.95270e11i	−0.677943	−	0.677943i
$353$	1.96245e10	+	1.96245e10i	0.0672686	+	0.0672686i	0.739941	−	0.672672i	$-0.234854\pi$
$353$	1.96245e10	+	1.96245e10i	0.0672686	+	0.0672686i	−0.672672	+	0.739941i	$0.734854\pi$
$354$	−7.35383e10	+	5.16294e10i	−0.248885	+	0.174736i
$355$		0			0
$356$		−	1.85173e11i		−	0.611017i
$357$	5.43258e11	+	9.50901e10i	1.77011	+	0.309834i
$358$	−1.16150e11	+	1.16150e11i	−0.373721	+	0.373721i
$359$	2.29075e11			0.727867			0.363934	−	0.931425i	$-0.381433\pi$
$359$	2.29075e11			0.727867			0.363934	+	0.931425i	$0.381433\pi$
$360$		0			0
$361$	−3.82834e11			−1.18639
$362$	−2.69774e11	+	2.69774e11i	−0.825681	+	0.825681i
$363$	3.80476e10	+	6.65972e9i	0.115013	+	0.0201315i
$364$		−	7.58504e10i		−	0.226465i
$365$		0			0
$366$	1.38492e11	−	9.72315e10i	0.403421	−	0.283232i
$367$	−4.18216e11	−	4.18216e11i	−1.20338	−	1.20338i	−0.973131	−	0.230251i	$-0.926045\pi$
$367$	−4.18216e11	−	4.18216e11i	−1.20338	−	1.20338i	−0.230251	−	0.973131i	$-0.573955\pi$
$368$	−6.06380e10	−	6.06380e10i	−0.172357	−	0.172357i
$369$	1.22168e11	−	3.38287e11i	0.343036	−	0.949875i
$370$		0			0
$371$			1.08813e12i			2.98193i
$372$	3.20924e10	−	1.83346e11i	0.0868877	−	0.496397i
$373$	−1.61719e11	+	1.61719e11i	−0.432585	+	0.432585i	−0.889507	−	0.456922i	$-0.848952\pi$
$373$	−1.61719e11	+	1.61719e11i	−0.432585	+	0.432585i	0.456922	+	0.889507i	$0.348952\pi$
$374$	−3.02707e11			−0.800020
$375$		0			0
$376$	−2.85333e11			−0.736218
$377$	−7.15957e10	+	7.15957e10i	−0.182537	+	0.182537i
$378$	3.92949e11	+	2.24906e11i	0.989973	+	0.566616i
$379$		−	6.61048e11i		−	1.64572i	−0.568243	−	0.822861i	$-0.692377\pi$
$379$		−	6.61048e11i		−	1.64572i	0.568243	−	0.822861i	$-0.307623\pi$
$380$		0			0
$381$	−1.13446e11	−	1.61586e11i	−0.275820	−	0.392864i
$382$	1.65995e10	+	1.65995e10i	0.0398851	+	0.0398851i
$383$	1.13485e11	+	1.13485e11i	0.269490	+	0.269490i	0.828895	−	0.559404i	$-0.188970\pi$
$383$	1.13485e11	+	1.13485e11i	0.269490	+	0.269490i	−0.559404	+	0.828895i	$0.688970\pi$
$384$	−7.96264e10	−	1.13416e11i	−0.186882	−	0.266185i
$385$		0			0
$386$			2.61056e11i			0.598538i
$387$	−6.14812e10	+	2.88568e10i	−0.139330	+	0.0653956i
$388$	1.19574e11	−	1.19574e11i	0.267852	−	0.267852i
$389$	5.03848e11			1.11565			0.557823	−	0.829960i	$-0.311637\pi$
$389$	5.03848e11			1.11565			0.557823	+	0.829960i	$0.311637\pi$
$390$		0			0
$391$	5.83927e11			1.26346
$392$	5.94587e11	−	5.94587e11i	1.27183	−	1.27183i
$393$	1.14689e11	−	6.55226e11i	0.242524	−	1.38556i
$394$		−	4.85258e10i		−	0.101447i
$395$		0			0
$396$	2.52666e11	+	9.12471e10i	0.516319	+	0.186462i
$397$	−3.84774e11	−	3.84774e11i	−0.777406	−	0.777406i	0.201983	−	0.979389i	$-0.435262\pi$
$397$	−3.84774e11	−	3.84774e11i	−0.777406	−	0.777406i	−0.979389	+	0.201983i	$0.935262\pi$
$398$	−3.58483e11	−	3.58483e11i	−0.716134	−	0.716134i
$399$	−1.00814e12	+	7.07786e11i	−1.99132	+	1.39805i
$400$		0			0
$401$			2.62222e10i			0.0506430i	0.999679	+	0.0253215i	$0.00806094\pi$
$401$			2.62222e10i			0.0506430i	−0.999679	+	0.0253215i	$0.991939\pi$
$402$	2.81053e11	+	4.91946e10i	0.536748	+	0.0939507i
$403$	−9.62350e10	+	9.62350e10i	−0.181744	+	0.181744i
$404$	7.86110e9			0.0146814
$405$		0			0
$406$	−6.08469e11			−1.11140
$407$	−3.56151e11	+	3.56151e11i	−0.643368	+	0.643368i
$408$	−6.34205e11	−	1.11009e11i	−1.13308	−	0.198330i
$409$			4.71608e11i			0.833347i	0.909056	+	0.416674i	$0.136804\pi$
$409$			4.71608e11i			0.833347i	−0.909056	+	0.416674i	$0.863196\pi$
$410$		0			0
$411$	−7.12520e11	+	5.00242e11i	−1.23171	+	0.864752i
$412$	3.88893e11	+	3.88893e11i	0.664956	+	0.664956i
$413$	−3.01792e11	−	3.01792e11i	−0.510425	−	0.510425i
$414$	4.50866e11	+	1.62825e11i	0.754304	+	0.272408i
$415$		0			0
$416$			1.46824e11i			0.240369i
$417$	−5.99331e10	+	3.42403e11i	−0.0970631	+	0.554530i
$418$	4.78062e11	−	4.78062e11i	0.765933	−	0.765933i
$419$	−6.07339e11			−0.962649			−0.481324	−	0.876543i	$-0.659844\pi$
$419$	−6.07339e11			−0.962649			−0.481324	+	0.876543i	$0.659844\pi$
$420$		0			0
$421$	3.13033e11			0.485647			0.242824	−	0.970070i	$-0.421926\pi$
$421$	3.13033e11			0.485647			0.242824	+	0.970070i	$0.421926\pi$
$422$	−2.27844e11	+	2.27844e11i	−0.349729	+	0.349729i
$423$	4.16632e11	−	1.95550e11i	0.632733	−	0.296979i
$424$		−	1.27029e12i		−	1.90879i
$425$		0			0
$426$	−1.91316e11	−	2.72502e11i	−0.281455	−	0.400891i
$427$	5.68352e11	+	5.68352e11i	0.827355	+	0.827355i
$428$	−1.87813e11	−	1.87813e11i	−0.270539	−	0.270539i
$429$	−1.12864e11	−	1.60758e11i	−0.160878	−	0.229147i
$430$		0			0
$431$		−	1.07493e12i		−	1.50049i	−0.661158	−	0.750246i	$-0.729935\pi$
$431$		−	1.07493e12i		−	1.50049i	0.661158	−	0.750246i	$-0.270065\pi$
$432$	−1.32369e11	−	7.57618e10i	−0.182856	−	0.104658i
$433$	7.71086e11	−	7.71086e11i	1.05416	−	1.05416i	0.0557147	−	0.998447i	$-0.482256\pi$
$433$	7.71086e11	−	7.71086e11i	1.05416	−	1.05416i	0.998447	−	0.0557147i	$-0.0177437\pi$
$434$	−8.17869e11			−1.10657
$435$		0			0
$436$	−2.95742e11			−0.391944
$437$	−9.22189e11	+	9.22189e11i	−1.20963	+	1.20963i
$438$	3.31516e10	−	1.89398e11i	0.0430399	−	0.245891i
$439$			1.40023e11i			0.179932i	0.995945	+	0.0899661i	$0.0286759\pi$
$439$			1.40023e11i			0.179932i	−0.995945	+	0.0899661i	$0.971324\pi$
$440$		0			0
$441$	−4.60699e11	+	1.27569e12i	−0.580021	+	1.60609i
$442$	1.13804e11	+	1.13804e11i	0.141826	+	0.141826i
$443$	4.32120e11	+	4.32120e11i	0.533074	+	0.533074i	0.921486	−	0.388412i	$-0.126976\pi$
$443$	4.32120e11	+	4.32120e11i	0.533074	+	0.533074i	−0.388412	+	0.921486i	$0.626976\pi$
$444$	−2.99750e11	+	2.10447e11i	−0.366046	+	0.256991i
$445$		0			0
$446$			9.37606e11i			1.12205i
$447$	−1.47754e12	−	2.58623e11i	−1.75047	−	0.306397i
$448$	−8.32918e11	+	8.32918e11i	−0.976902	+	0.976902i
$449$	−3.89979e11			−0.452827			−0.226414	−	0.974031i	$-0.572700\pi$
$449$	−3.89979e11			−0.452827			−0.226414	+	0.974031i	$0.572700\pi$
$450$		0			0
$451$	−9.37694e11			−1.06725
$452$	5.04158e11	−	5.04158e11i	0.568124	−	0.568124i
$453$	−4.00958e11	−	7.01824e10i	−0.447360	−	0.0783045i
$454$			6.49483e11i			0.717491i
$455$		0			0
$456$	1.17691e12	−	8.26276e11i	1.27468	−	0.894919i
$457$	−2.56249e11	−	2.56249e11i	−0.274814	−	0.274814i	0.556221	−	0.831035i	$-0.312251\pi$
$457$	−2.56249e11	−	2.56249e11i	−0.274814	−	0.274814i	−0.831035	+	0.556221i	$0.812251\pi$
$458$	1.30359e11	+	1.30359e11i	0.138436	+	0.138436i
$459$	1.00212e12	−	2.72554e11i	1.05381	−	0.286613i
$460$		0			0
$461$			7.35986e11i			0.758954i	0.925201	+	0.379477i	$0.123896\pi$
$461$			7.35986e11i			0.758954i	−0.925201	+	0.379477i	$0.876104\pi$
$462$	2.03517e11	−	1.16271e12i	0.207832	−	1.18736i
$463$	2.11885e11	−	2.11885e11i	0.214282	−	0.214282i	−0.591802	−	0.806084i	$-0.701583\pi$
$463$	2.11885e11	−	2.11885e11i	0.214282	−	0.214282i	0.806084	+	0.591802i	$0.201583\pi$
$464$	2.04968e11			0.205284
$465$		0			0
$466$	7.48441e11			0.735226
$467$	4.25271e11	−	4.25271e11i	0.413751	−	0.413751i	−0.469292	−	0.883043i	$-0.655491\pi$
$467$	4.25271e11	−	4.25271e11i	0.413751	−	0.413751i	0.883043	+	0.469292i	$0.155491\pi$
$468$	−6.06857e10	−	1.29295e11i	−0.0584763	−	0.124588i
$469$			1.35529e12i			1.29347i
$470$		0			0
$471$	−2.82904e11	−	4.02954e11i	−0.264877	−	0.377278i
$472$	3.52315e11	+	3.52315e11i	0.326732	+	0.326732i
$473$	1.25204e11	+	1.25204e11i	0.115012	+	0.115012i
$474$	−4.32105e11	−	6.15468e11i	−0.393175	−	0.560019i
$475$		0			0
$476$		−	1.04554e12i		−	0.933490i
$477$	8.70580e11	+	1.85483e12i	0.769974	+	1.64048i
$478$	7.79915e11	−	7.79915e11i	0.683316	−	0.683316i
$479$	1.66755e12			1.44734			0.723670	−	0.690147i	$-0.242454\pi$
$479$	1.66755e12			1.44734			0.723670	+	0.690147i	$0.242454\pi$
$480$		0			0
$481$	2.67792e11			0.228110
$482$	9.22674e11	−	9.22674e11i	0.778640	−	0.778640i
$483$	−3.92587e11	+	2.24289e12i	−0.328227	+	1.87519i
$484$		−	7.32254e10i		−	0.0606537i
$485$		0			0
$486$	8.49764e11	+	6.89889e10i	0.690932	+	0.0560940i
$487$	−2.99832e11	−	2.99832e11i	−0.241545	−	0.241545i	0.575944	−	0.817489i	$-0.304635\pi$
$487$	−2.99832e11	−	2.99832e11i	−0.241545	−	0.241545i	−0.817489	+	0.575944i	$0.804635\pi$
$488$	−6.63500e11	−	6.63500e11i	−0.529604	−	0.529604i
$489$	1.43061e12	−	1.00440e12i	1.13144	−	0.794357i
$490$		0			0
$491$		−	2.57444e11i		−	0.199902i	−0.994992	−	0.0999509i	$-0.968131\pi$
$491$		−	2.57444e11i		−	0.199902i	0.994992	−	0.0999509i	$-0.0318686\pi$
$492$	−6.71636e11	−	1.17561e11i	−0.516763	−	0.0904524i
$493$	−9.86894e11	+	9.86894e11i	−0.752418	+	0.752418i
$494$	−3.59457e11			−0.271567
$495$		0			0
$496$	2.75507e11			0.204392
$497$	1.11831e12	−	1.11831e12i	0.822166	−	0.822166i
$498$	1.16370e12	+	2.03690e11i	0.847829	+	0.148401i
$499$			1.55852e12i			1.12528i	0.826703	+	0.562639i	$0.190214\pi$
$499$			1.55852e12i			1.12528i	−0.826703	+	0.562639i	$0.809786\pi$
$500$		0			0
$501$	−1.31236e10	+	9.21376e9i	−0.00930645	+	0.00653382i
$502$	1.22987e11	+	1.22987e11i	0.0864356	+	0.0864356i
$503$	1.07287e11	+	1.07287e11i	0.0747293	+	0.0747293i	0.743484	−	0.668754i	$-0.233172\pi$
$503$	1.07287e11	+	1.07287e11i	0.0747293	+	0.0747293i	−0.668754	+	0.743484i	$0.733172\pi$
$504$	8.52780e11	−	2.36137e12i	0.588708	−	1.63015i
$505$		0			0
$506$		−	1.24975e12i		−	0.847513i
$507$	2.38509e11	−	1.36262e12i	0.160313	−	0.915881i
$508$	−2.64660e11	+	2.64660e11i	−0.176320	+	0.176320i
$509$	−1.01551e12			−0.670583			−0.335292	−	0.942114i	$-0.608835\pi$
$509$	−1.01551e12			−0.670583			−0.335292	+	0.942114i	$0.608835\pi$
$510$		0			0
$511$	9.13316e11			0.592552
$512$	4.54170e11	−	4.54170e11i	0.292081	−	0.292081i
$513$	−1.15219e12	+	2.01308e12i	−0.734509	+	1.28331i
$514$		−	3.69965e11i		−	0.233790i
$515$		0			0
$516$	7.39816e10	+	1.05376e11i	0.0459410	+	0.0654361i
$517$	−8.48450e11	−	8.48450e11i	−0.522298	−	0.522298i
$518$	1.13794e12	+	1.13794e12i	0.694440	+	0.694440i
$519$	2.34945e11	+	3.34645e11i	0.142139	+	0.202456i
$520$		0			0
$521$		−	7.76260e11i		−	0.461570i	−0.973005	−	0.230785i	$-0.925871\pi$
$521$		−	7.76260e11i		−	0.461570i	0.973005	−	0.230785i	$-0.0741293\pi$
$522$	−1.03720e12	+	4.86818e11i	−0.611427	+	0.286979i
$523$	6.97215e10	−	6.97215e10i	0.0407483	−	0.0407483i	−0.686439	−	0.727187i	$-0.740827\pi$
$523$	6.97215e10	−	6.97215e10i	0.0407483	−	0.0407483i	0.727187	+	0.686439i	$0.240827\pi$
$524$	−1.26103e12			−0.730694
$525$		0			0
$526$	7.95359e11			0.453031
$527$	−1.32653e12	+	1.32653e12i	−0.749150	+	0.749150i
$528$	−6.85566e10	+	3.91670e11i	−0.0383881	+	0.219314i
$529$			6.09638e11i			0.338471i
$530$		0			0
$531$	−7.55891e11	−	2.72981e11i	−0.412604	−	0.149007i
$532$	1.65121e12	+	1.65121e12i	0.893717	+	0.893717i
$533$	3.52529e11	+	3.52529e11i	0.189200	+	0.189200i
$534$	−1.25394e12	+	8.80360e11i	−0.667331	+	0.468516i
$535$		0			0
$536$		−	1.58218e12i		−	0.827970i
$537$	−1.44721e12	−	2.53315e11i	−0.751013	−	0.131455i
$538$	1.05743e12	−	1.05743e12i	0.544167	−	0.544167i
$539$	3.53606e12			1.80456
$540$		0			0
$541$	1.99899e10			0.0100328			0.00501640	−	0.999987i	$-0.498403\pi$
$541$	1.99899e10			0.0100328			0.00501640	+	0.999987i	$0.498403\pi$
$542$	−8.51867e11	+	8.51867e11i	−0.424009	+	0.424009i
$543$	−3.36133e12	−	5.88357e11i	−1.65925	−	0.290430i
$544$			2.02387e12i			0.990802i
$545$		0			0
$546$	−5.13637e11	+	3.60611e11i	−0.247337	+	0.173649i
$547$	1.98891e12	+	1.98891e12i	0.949888	+	0.949888i	0.998803	−	0.0489153i	$-0.0155764\pi$
$547$	1.98891e12	+	1.98891e12i	0.949888	+	0.949888i	−0.0489153	+	0.998803i	$0.515576\pi$
$548$	1.16703e12	+	1.16703e12i	0.552800	+	0.552800i
$549$	1.42354e12	+	5.14093e11i	0.668796	+	0.241527i
$550$		0			0
$551$		−	3.11718e12i		−	1.44072i
$552$	4.58310e11	−	2.61837e12i	0.210104	−	1.20034i
$553$	2.52580e12	−	2.52580e12i	1.14851	−	1.14851i
$554$	1.36287e12			0.614698
$555$		0			0
$556$	6.58980e11			0.292439
$557$	−2.46853e11	+	2.46853e11i	−0.108665	+	0.108665i	−0.759349	−	0.650684i	$-0.774482\pi$
$557$	−2.46853e11	+	2.46853e11i	−0.108665	+	0.108665i	0.650684	+	0.759349i	$0.274482\pi$
$558$	−1.39414e12	+	6.54354e11i	−0.608771	+	0.285732i
$559$		−	9.41412e10i		−	0.0407781i
$560$		0			0
$561$	−1.55575e12	−	2.21593e12i	−0.663140	−	0.944544i
$562$	1.29419e12	+	1.29419e12i	0.547251	+	0.547251i
$563$	−1.00153e12	−	1.00153e12i	−0.420121	−	0.420121i	0.465124	−	0.885245i	$-0.346010\pi$
$563$	−1.00153e12	−	1.00153e12i	−0.420121	−	0.420121i	−0.885245	+	0.465124i	$0.846010\pi$
$564$	−5.01341e11	−	7.14086e11i	−0.208630	−	0.297163i
$565$		0			0
$566$			1.77353e12i			0.726382i
$567$	3.73143e11	+	4.03242e12i	0.151618	+	1.63848i
$568$	−1.30553e12	+	1.30553e12i	−0.526282	+	0.526282i
$569$	−3.20924e12			−1.28350			−0.641751	−	0.766913i	$-0.721792\pi$
$569$	−3.20924e12			−1.28350			−0.641751	+	0.766913i	$0.721792\pi$
$570$		0			0
$571$	2.99356e12			1.17849			0.589244	−	0.807955i	$-0.299426\pi$
$571$	2.99356e12			1.17849			0.589244	+	0.807955i	$0.299426\pi$
$572$	−2.63303e11	+	2.63303e11i	−0.102843	+	0.102843i
$573$	−3.62023e10	+	2.06827e11i	−0.0140294	+	0.0801513i
$574$			2.99603e12i			1.15197i
$575$		0			0
$576$	−7.53402e11	+	2.08619e12i	−0.285184	+	0.789682i
$577$	−1.77586e12	−	1.77586e12i	−0.666988	−	0.666988i	0.290030	−	0.957018i	$-0.406335\pi$
$577$	−1.77586e12	−	1.77586e12i	−0.666988	−	0.666988i	−0.957018	+	0.290030i	$0.906335\pi$
$578$	2.53407e11	+	2.53407e11i	0.0944373	+	0.0944373i
$579$	−1.91103e12	+	1.34168e12i	−0.706664	+	0.496131i
$580$		0			0
$581$			5.61158e12i			2.04312i
$582$	−1.37821e12	−	2.41237e11i	−0.497921	−	0.0871545i
$583$	3.77727e12	−	3.77727e12i	1.35416	−	1.35416i
$584$	−1.06621e12			−0.379303
$585$		0			0
$586$	1.43461e11			0.0502567
$587$	5.84314e11	−	5.84314e11i	0.203130	−	0.203130i	−0.598209	−	0.801340i	$-0.704121\pi$
$587$	5.84314e11	−	5.84314e11i	0.203130	−	0.203130i	0.801340	+	0.598209i	$0.204121\pi$
$588$	2.53275e12	+	4.43325e11i	0.873765	+	0.152941i
$589$		−	4.18994e12i		−	1.43446i
$590$		0			0
$591$	3.55226e11	−	2.49395e11i	0.119774	−	0.0840900i
$592$	−3.83325e11	−	3.83325e11i	−0.128268	−	0.128268i
$593$	1.31975e12	+	1.31975e12i	0.438273	+	0.438273i	0.891430	−	0.453158i	$-0.149703\pi$
$593$	1.31975e12	+	1.31975e12i	0.438273	+	0.438273i	−0.453158	+	0.891430i	$0.649703\pi$
$594$	−5.83335e11	−	2.14479e12i	−0.192256	−	0.706880i
$595$		0			0
$596$			2.84363e12i			0.923135i
$597$	7.81822e11	−	4.46662e12i	0.251897	−	1.43911i
$598$	−4.69848e11	+	4.69848e11i	−0.150246	+	0.150246i
$599$	−1.89131e11			−0.0600264			−0.0300132	−	0.999550i	$-0.509555\pi$
$599$	−1.89131e11			−0.0600264			−0.0300132	+	0.999550i	$0.509555\pi$
$600$		0			0
$601$	−3.90111e12			−1.21970			−0.609849	−	0.792517i	$-0.708770\pi$
$601$	−3.90111e12			−1.21970			−0.609849	+	0.792517i	$0.708770\pi$
$602$	4.00038e11	−	4.00038e11i	0.124141	−	0.124141i
$603$	1.08433e12	+	2.31024e12i	0.333990	+	0.711589i
$604$			7.71674e11i			0.235922i
$605$		0			0
$606$	−3.73736e10	−	5.32331e10i	−0.0112574	−	0.0160345i
$607$	−1.15605e12	−	1.15605e12i	−0.345642	−	0.345642i	0.512842	−	0.858483i	$-0.328593\pi$
$607$	−1.15605e12	−	1.15605e12i	−0.345642	−	0.345642i	−0.858483	+	0.512842i	$0.828593\pi$
$608$	−3.19627e12	−	3.19627e12i	−0.948586	−	0.948586i
$609$	−3.12719e12	−	4.45421e12i	−0.921246	−	1.31218i
$610$		0			0
$611$			6.37954e11i			0.185184i
$612$	−8.36507e11	−	1.78223e12i	−0.241040	−	0.513551i
$613$	1.83362e12	−	1.83362e12i	0.524490	−	0.524490i	−0.394434	−	0.918924i	$-0.629059\pi$
$613$	1.83362e12	−	1.83362e12i	0.524490	−	0.524490i	0.918924	+	0.394434i	$0.129059\pi$
$614$	−1.43707e12			−0.408056
$615$		0			0
$616$	−6.54546e12			−1.83158
$617$	2.02959e11	−	2.02959e11i	0.0563801	−	0.0563801i	−0.678355	−	0.734735i	$-0.737307\pi$
$617$	2.02959e11	−	2.02959e11i	0.0563801	−	0.0563801i	0.734735	+	0.678355i	$0.237307\pi$
$618$	7.84578e11	−	4.48236e12i	0.216366	−	1.23612i
$619$			1.60672e12i			0.439877i	0.975514	+	0.219939i	$0.0705857\pi$
$619$			1.60672e12i			0.439877i	−0.975514	+	0.219939i	$0.929414\pi$
$620$		0			0
$621$	1.12526e12	+	4.13733e12i	0.303628	+	1.11637i
$622$	2.23365e12	+	2.23365e12i	0.598354	+	0.598354i
$623$	−5.14601e12	−	5.14601e12i	−1.36859	−	1.36859i
$624$	1.73023e11	−	1.21475e11i	0.0456850	−	0.0320743i
$625$		0			0
$626$		−	1.05811e12i		−	0.275389i
$627$	5.95655e12	+	1.04262e12i	1.53919	+	0.269414i
$628$	−6.59992e11	+	6.59992e11i	−0.169325	+	0.169325i
$629$	3.69131e12			0.940271
$630$		0			0
$631$	4.48133e12			1.12532			0.562658	−	0.826690i	$-0.309779\pi$
$631$	4.48133e12			1.12532			0.562658	+	0.826690i	$0.309779\pi$
$632$	−2.94865e12	+	2.94865e12i	−0.735184	+	0.735184i
$633$	−2.83889e12	−	4.96909e11i	−0.702799	−	0.123016i
$634$		−	4.89665e11i		−	0.120364i
$635$		0			0
$636$	3.17908e12	−	2.23195e12i	0.770451	−	0.540914i
$637$	−1.32939e12	−	1.32939e12i	−0.319908	−	0.319908i
$638$	2.11220e12	+	2.11220e12i	0.504711	+	0.504711i
$639$	1.01155e12	−	2.80101e12i	0.240012	−	0.664600i
$640$		0			0
$641$			8.27911e12i			1.93697i	0.249075	+	0.968484i	$0.419873\pi$
$641$			8.27911e12i			1.93697i	−0.249075	+	0.968484i	$0.580127\pi$
$642$	−3.78907e11	+	2.16473e12i	−0.0880289	+	0.502917i
$643$	−2.88560e12	+	2.88560e12i	−0.665712	+	0.665712i	−0.956721	−	0.291008i	$-0.906009\pi$
$643$	−2.88560e12	+	2.88560e12i	−0.665712	+	0.665712i	0.291008	+	0.956721i	$0.406009\pi$
$644$	4.31660e12			0.988907
$645$		0			0
$646$	−4.95485e12			−1.11940
$647$	−6.61105e11	+	6.61105e11i	−0.148320	+	0.148320i	−0.777367	−	0.629047i	$-0.783445\pi$
$647$	−6.61105e11	+	6.61105e11i	−0.148320	+	0.148320i	0.629047	+	0.777367i	$0.283445\pi$
$648$	−4.35611e11	−	4.70749e12i	−0.0970535	−	1.04882i
$649$			2.09525e12i			0.463590i
$650$		0			0
$651$	−4.20339e12	−	5.98710e12i	−0.917244	−	1.30648i
$652$	−2.34318e12	−	2.34318e12i	−0.507799	−	0.507799i
$653$	−1.59454e12	−	1.59454e12i	−0.343184	−	0.343184i	0.514379	−	0.857563i	$-0.328022\pi$
$653$	−1.59454e12	−	1.59454e12i	−0.343184	−	0.343184i	−0.857563	+	0.514379i	$0.828022\pi$
$654$	1.40603e12	+	2.00268e12i	0.300535	+	0.428067i
$655$		0			0
$656$		−	1.00924e12i		−	0.212778i
$657$	1.55684e12	−	7.30717e11i	0.325987	−	0.153005i
$658$	−2.71088e12	+	2.71088e12i	−0.563760	+	0.563760i
$659$	−5.97837e12			−1.23481			−0.617403	−	0.786647i	$-0.711815\pi$
$659$	−5.97837e12			−1.23481			−0.617403	+	0.786647i	$0.711815\pi$
$660$		0			0
$661$	4.26544e11			0.0869076			0.0434538	−	0.999055i	$-0.486164\pi$
$661$	4.26544e11			0.0869076			0.0434538	+	0.999055i	$0.486164\pi$
$662$	−2.05753e12	+	2.05753e12i	−0.416376	+	0.416376i
$663$	−2.48197e11	+	1.41797e12i	−0.0498868	+	0.285007i
$664$		−	6.55102e12i		−	1.30783i
$665$		0			0
$666$	2.85017e12	+	1.02930e12i	0.561353	+	0.202726i
$667$	−4.07447e12	−	4.07447e12i	−0.797086	−	0.797086i
$668$	2.14950e10	+	2.14950e10i	0.00417679	+	0.00417679i
$669$	−6.86361e12	+	4.81877e12i	−1.32475	+	0.930076i
$670$		0			0
$671$		−	3.94589e12i		−	0.751439i
$672$	−7.77374e12	−	1.36069e12i	−1.47051	−	0.257394i
$673$	7.35750e11	−	7.35750e11i	0.138249	−	0.138249i	−0.634595	−	0.772845i	$-0.718833\pi$
$673$	7.35750e11	−	7.35750e11i	0.138249	−	0.138249i	0.772845	+	0.634595i	$0.218833\pi$
$674$	2.57117e12			0.479912
$675$		0			0
$676$	−2.62247e12			−0.483003
$677$	6.83695e11	−	6.83695e11i	0.125087	−	0.125087i	−0.641792	−	0.766879i	$-0.721809\pi$
$677$	6.83695e11	−	6.83695e11i	0.125087	−	0.125087i	0.766879	+	0.641792i	$0.221809\pi$
$678$	−5.81090e12	−	1.01712e12i	−1.05611	−	0.184858i
$679$		−	6.64599e12i		−	1.19990i
$680$		0			0
$681$	−4.75444e12	+	3.33797e12i	−0.847106	+	0.594731i
$682$	2.83911e12	+	2.83911e12i	0.502518	+	0.502518i
$683$	7.51185e12	+	7.51185e12i	1.32085	+	1.32085i	0.913088	+	0.407763i	$0.133691\pi$
$683$	7.51185e12	+	7.51185e12i	1.32085	+	1.32085i	0.407763	+	0.913088i	$0.366309\pi$
$684$	4.13575e12	+	1.49357e12i	0.722439	+	0.260900i
$685$		0			0
$686$		−	4.68179e12i		−	0.807148i
$687$	−2.84304e11	+	1.62425e12i	−0.0486942	+	0.278194i
$688$	−1.34756e11	+	1.34756e11i	−0.0229299	+	0.0229299i
$689$	−2.84015e12			−0.480125
$690$		0			0
$691$	9.66155e11			0.161211			0.0806057	−	0.996746i	$-0.474315\pi$
$691$	9.66155e11			0.161211			0.0806057	+	0.996746i	$0.474315\pi$
$692$	5.48109e11	−	5.48109e11i	0.0908636	−	0.0908636i
$693$	9.55742e12	−	4.48586e12i	1.57413	−	0.738832i
$694$			2.51434e12i			0.411440i
$695$		0			0
$696$	3.65071e12	+	5.19988e12i	0.589706	+	0.839947i
$697$	4.85935e12	+	4.85935e12i	0.779885	+	0.779885i
$698$	−5.76318e11	−	5.76318e11i	−0.0918994	−	0.0918994i
$699$	3.84656e12	+	5.47885e12i	0.609433	+	0.868045i
$700$		0			0
$701$		−	8.04948e12i		−	1.25903i	−0.776988	−	0.629516i	$-0.783253\pi$
$701$		−	8.04948e12i		−	1.25903i	0.776988	−	0.629516i	$-0.216747\pi$
$702$	−5.87033e11	+	1.02565e12i	−0.0912316	+	0.159397i
$703$	−5.82965e12	+	5.82965e12i	−0.900209	+	0.900209i
$704$	5.78269e12			0.887264
$705$		0			0
$706$	−4.35322e11			−0.0659461
$707$	2.18462e11	−	2.18462e11i	0.0328843	−	0.0328843i
$708$	−2.62686e11	+	1.50075e12i	−0.0392905	+	0.224470i
$709$		−	9.68040e12i		−	1.43875i	−0.694622	−	0.719375i	$-0.744428\pi$
$709$		−	9.68040e12i		−	1.43875i	0.694622	−	0.719375i	$-0.255572\pi$
$710$		0			0
$711$	2.28467e12	−	6.32632e12i	0.335283	−	0.928406i
$712$	6.00750e12	+	6.00750e12i	0.876060	+	0.876060i
$713$	−5.47668e12	−	5.47668e12i	−0.793623	−	0.793623i
$714$	−7.08010e12	+	4.97076e12i	−1.01952	+	0.715782i
$715$		0			0
$716$			2.78526e12i			0.396057i
$717$	9.71758e12	+	1.70093e12i	1.37316	+	0.240354i
$718$	−2.54073e12	+	2.54073e12i	−0.356779	+	0.356779i
$719$	−2.71442e12			−0.378789			−0.189394	−	0.981901i	$-0.560652\pi$
$719$	−2.71442e12			−0.378789			−0.189394	+	0.981901i	$0.560652\pi$
$720$		0			0
$721$	2.16149e13			2.97882
$722$	4.24612e12	−	4.24612e12i	0.581534	−	0.581534i
$723$	1.14963e13	+	2.01228e12i	1.56472	+	0.273884i
$724$			6.46914e12i			0.875030i
$725$		0			0
$726$	−4.95861e11	+	3.48131e11i	−0.0662438	+	0.0465081i
$727$	−4.65032e12	−	4.65032e12i	−0.617416	−	0.617416i	0.327452	−	0.944868i	$-0.393810\pi$
$727$	−4.65032e12	−	4.65032e12i	−0.617416	−	0.617416i	−0.944868	+	0.327452i	$0.893810\pi$
$728$	2.46078e12	+	2.46078e12i	0.324700	+	0.324700i
$729$	3.86229e12	+	6.57514e12i	0.506490	+	0.862246i
$730$		0			0
$731$		−	1.29767e12i		−	0.168087i
$732$	4.94706e11	−	2.82630e12i	0.0636865	−	0.363846i
$733$	4.99937e12	−	4.99937e12i	0.639657	−	0.639657i	−0.310814	−	0.950471i	$-0.600602\pi$
$733$	4.99937e12	−	4.99937e12i	0.639657	−	0.639657i	0.950471	+	0.310814i	$0.100602\pi$
$734$	9.27711e12			1.17972
$735$		0			0
$736$	−8.35570e12			−1.04962
$737$	4.70469e12	−	4.70469e12i	0.587391	−	0.587391i
$738$	2.39703e12	+	5.10704e12i	0.297455	+	0.633746i
$739$			7.80753e12i			0.962973i	0.876454	+	0.481486i	$0.159903\pi$
$739$			7.80753e12i			0.962973i	−0.876454	+	0.481486i	$0.840097\pi$
$740$		0			0
$741$	−1.84741e12	−	2.63136e12i	−0.225103	−	0.320625i
$742$	−1.20687e13	−	1.20687e13i	−1.46165	−	1.46165i
$743$	1.02968e13	+	1.02968e13i	1.23952	+	1.23952i	0.960199	+	0.279318i	$0.0901083\pi$
$743$	1.02968e13	+	1.02968e13i	1.23952	+	1.23952i	0.279318	+	0.960199i	$0.409892\pi$
$744$	4.90707e12	+	6.98939e12i	0.587144	+	0.836298i
$745$		0			0
$746$		−	3.58734e12i		−	0.424080i
$747$	4.48967e12	+	9.56553e12i	0.527559	+	1.12400i
$748$	−3.62943e12	+	3.62943e12i	−0.423918	+	0.423918i
$749$	−1.04388e13			−1.21194
$750$		0			0
$751$	8.15558e12			0.935567			0.467784	−	0.883843i	$-0.345053\pi$
$751$	8.15558e12			0.935567			0.467784	+	0.883843i	$0.345053\pi$
$752$	9.13185e11	−	9.13185e11i	0.104131	−	0.104131i
$753$	−2.68225e11	+	1.53239e12i	−0.0304034	+	0.173697i
$754$		−	1.58818e12i		−	0.178948i
$755$		0			0
$756$	7.40803e12	−	2.01482e12i	0.824811	−	0.224330i
$757$	−4.78606e12	−	4.78606e12i	−0.529720	−	0.529720i	0.390769	−	0.920489i	$-0.372209\pi$
$757$	−4.78606e12	−	4.78606e12i	−0.529720	−	0.529720i	−0.920489	+	0.390769i	$0.872209\pi$
$758$	7.33187e12	+	7.33187e12i	0.806684	+	0.806684i
$759$	9.14863e12	−	6.42302e12i	1.00062	−	0.702508i
$760$		0			0
$761$			5.30063e12i			0.572923i	0.958092	+	0.286462i	$0.0924791\pi$
$761$			5.30063e12i			0.572923i	−0.958092	+	0.286462i	$0.907521\pi$
$762$	3.05046e12	+	5.33942e11i	0.327769	+	0.0573716i
$763$	−8.21875e12	+	8.21875e12i	−0.877901	+	0.877901i
$764$	3.98053e11			0.0422689
$765$		0			0
$766$	−2.51738e12			−0.264192
$767$	7.87713e11	−	7.87713e11i	0.0821844	−	0.0821844i
$768$	1.01145e13	+	1.77041e12i	1.04911	+	0.183632i
$769$		−	1.44301e13i		−	1.48799i	−0.668186	−	0.743994i	$-0.732929\pi$
$769$		−	1.44301e13i		−	1.48799i	0.668186	−	0.743994i	$-0.267071\pi$
$770$		0			0
$771$	2.70827e12	−	1.90141e12i	0.276025	−	0.193790i
$772$	3.13004e12	+	3.13004e12i	0.317155	+	0.317155i
$773$	−7.89816e12	−	7.89816e12i	−0.795643	−	0.795643i	0.186762	−	0.982405i	$-0.440201\pi$
$773$	−7.89816e12	−	7.89816e12i	−0.795643	−	0.795643i	−0.982405	+	0.186762i	$0.940201\pi$
$774$	3.61847e11	−	1.00196e12i	0.0362402	−	0.100350i
$775$		0			0
$776$			7.75859e12i			0.768077i
$777$	−2.48175e12	+	1.41785e13i	−0.244267	+	1.39552i
$778$	−5.58832e12	+	5.58832e12i	−0.546856	+	0.546856i
$779$	−1.53486e13			−1.49331
$780$		0			0
$781$	−7.76409e12			−0.746725
$782$	−6.47650e12	+	6.47650e12i	−0.619313	+	0.619313i
$783$	−8.89430e12	−	5.09069e12i	−0.845636	−	0.484004i
$784$			3.80586e12i			0.359775i
$785$		0			0
$786$	5.99526e12	+	8.53935e12i	0.560282	+	0.798037i
$787$	−4.02593e12	−	4.02593e12i	−0.374094	−	0.374094i	0.494872	−	0.868966i	$-0.335215\pi$
$787$	−4.02593e12	−	4.02593e12i	−0.374094	−	0.374094i	−0.868966	+	0.494872i	$0.835215\pi$
$788$	−5.81819e11	−	5.81819e11i	−0.0537552	−	0.0537552i
$789$	4.08770e12	+	5.82231e12i	0.375519	+	0.534871i
$790$		0			0
$791$		−	2.80213e13i		−	2.54504i
$792$	−1.11574e13	+	5.23683e12i	−1.00763	+	0.472939i
$793$	−1.48347e12	+	1.48347e12i	−0.133214	+	0.133214i
$794$	8.53527e12			0.762123
$795$		0			0
$796$	−8.59634e12			−0.758936
$797$	6.43191e12	−	6.43191e12i	0.564647	−	0.564647i	−0.365977	−	0.930624i	$-0.619265\pi$
$797$	6.43191e12	−	6.43191e12i	0.564647	−	0.564647i	0.930624	+	0.365977i	$0.119265\pi$
$798$	3.33126e12	−	1.90318e13i	0.290801	−	1.66137i
$799$			8.79372e12i			0.763330i
$800$		0			0
$801$	−1.28891e13	−	4.65474e12i	−1.10631	−	0.399530i
$802$	−2.90838e11	−	2.90838e11i	−0.0248237	−	0.0248237i
$803$	−3.17043e12	−	3.17043e12i	−0.269091	−	0.269091i
$804$	3.95963e12	−	2.77996e12i	0.334197	−	0.234631i
$805$		0			0
$806$		−	2.13474e12i		−	0.178171i
$807$	1.31754e13	+	2.30617e12i	1.09353	+	0.191409i
$808$	−2.55034e11	+	2.55034e11i	−0.0210498	+	0.0210498i
$809$	1.63332e13			1.34061			0.670306	−	0.742085i	$-0.266163\pi$
$809$	1.63332e13			1.34061			0.670306	+	0.742085i	$0.266163\pi$
$810$		0			0
$811$	−1.18475e13			−0.961689			−0.480844	−	0.876806i	$-0.659670\pi$
$811$	−1.18475e13			−0.961689			−0.480844	+	0.876806i	$0.659670\pi$
$812$	−7.29548e12	+	7.29548e12i	−0.588914	+	0.588914i
$813$	−1.06141e13	−	1.85786e12i	−0.852070	−	0.149144i
$814$		−	7.90035e12i		−	0.630720i
$815$		0			0
$816$	2.38500e12	−	1.67445e12i	0.188314	−	0.132210i
$817$	2.04939e12	+	2.04939e12i	0.160926	+	0.160926i
$818$	−5.23073e12	−	5.23073e12i	−0.408482	−	0.408482i
$819$	−5.27961e12	−	1.90667e12i	−0.410038	−	0.148080i
$820$		0			0
$821$			1.23623e13i			0.949632i	0.880085	+	0.474816i	$0.157485\pi$
$821$			1.23623e13i			0.949632i	−0.880085	+	0.474816i	$0.842515\pi$
$822$	2.35443e12	−	1.34511e13i	0.179872	−	1.02762i
$823$	−5.60256e12	+	5.60256e12i	−0.425684	+	0.425684i	−0.887155	−	0.461471i	$-0.847322\pi$
$823$	−5.60256e12	+	5.60256e12i	−0.425684	+	0.425684i	0.461471	+	0.887155i	$0.347322\pi$
$824$	−2.52334e13			−1.90679
$825$		0			0
$826$	6.69452e12			0.500391
$827$	9.47032e12	−	9.47032e12i	0.704028	−	0.704028i	−0.261244	−	0.965273i	$-0.584133\pi$
$827$	9.47032e12	−	9.47032e12i	0.704028	−	0.704028i	0.965273	+	0.261244i	$0.0841329\pi$
$828$	7.35810e12	−	3.45359e12i	0.544038	−	0.255349i
$829$		−	1.94392e13i		−	1.42950i	−0.699381	−	0.714749i	$-0.746541\pi$
$829$		−	1.94392e13i		−	1.42950i	0.699381	−	0.714749i	$-0.253459\pi$
$830$		0			0
$831$	7.00440e12	+	9.97672e12i	0.509526	+	0.725743i
$832$	−2.17402e12	−	2.17402e12i	−0.157292	−	0.157292i
$833$	−1.83247e13	−	1.83247e13i	−1.31866	−	1.31866i
$834$	−3.13295e12	−	4.46242e12i	−0.224237	−	0.319392i
$835$		0			0
$836$		−	1.14638e13i		−	0.811712i
$837$	−1.19552e13	−	6.84262e12i	−0.841963	−	0.481901i
$838$	6.73617e12	−	6.73617e12i	0.471862	−	0.471862i
$839$	2.14724e13			1.49607			0.748034	−	0.663661i	$-0.230998\pi$
$839$	2.14724e13			1.49607			0.748034	+	0.663661i	$0.230998\pi$
$840$		0			0
$841$	−7.34630e11			−0.0506392
$842$	−3.47194e12	+	3.47194e12i	−0.238050	+	0.238050i
$843$	−2.82254e12	+	1.61254e13i	−0.192493	+	1.09973i
$844$			5.46365e12i			0.370631i
$845$		0			0
$846$	−2.45208e12	+	6.78988e12i	−0.164577	+	0.455717i
$847$	−2.03495e12	−	2.03495e12i	−0.135856	−	0.135856i
$848$	4.06547e12	+	4.06547e12i	0.269978	+	0.269978i
$849$	−1.29829e13	+	9.11495e12i	−0.857604	+	0.602102i
$850$		0			0
$851$			1.52399e13i			0.996091i
$852$	−5.56113e12	−	9.73403e11i	−0.361564	−	0.0632870i
$853$	8.47899e12	−	8.47899e12i	0.548370	−	0.548370i	−0.377599	−	0.925969i	$-0.623250\pi$
$853$	8.47899e12	−	8.47899e12i	0.548370	−	0.548370i	0.925969	+	0.377599i	$0.123250\pi$
$854$	−1.26075e13			−0.811090
$855$		0			0
$856$	1.21863e13			0.775783
$857$	−8.21448e12	+	8.21448e12i	−0.520195	+	0.520195i	−0.917630	−	0.397435i	$-0.869900\pi$
$857$	−8.21448e12	+	8.21448e12i	−0.520195	+	0.520195i	0.397435	+	0.917630i	$0.369900\pi$
$858$	3.03482e12	+	5.31204e11i	0.191179	+	0.0334633i
$859$		−	1.56474e13i		−	0.980556i	−0.871566	−	0.490278i	$-0.836895\pi$
$859$		−	1.56474e13i		−	0.980556i	0.871566	−	0.490278i	$-0.163105\pi$
$860$		0			0
$861$	−2.19320e13	+	1.53979e13i	−1.36008	+	0.954876i
$862$	1.19224e13	+	1.19224e13i	0.735497	+	0.735497i
$863$	1.18220e13	+	1.18220e13i	0.725510	+	0.725510i	0.969722	−	0.244212i	$-0.0785291\pi$
$863$	1.18220e13	+	1.18220e13i	0.725510	+	0.725510i	−0.244212	+	0.969722i	$0.578529\pi$
$864$	−1.43398e13	+	3.90011e12i	−0.875450	+	0.238103i
$865$		0			0
$866$			1.71047e13i			1.03344i
$867$	−5.52661e11	+	3.15740e12i	−0.0332179	+	0.189777i
$868$	−9.80618e12	+	9.80618e12i	−0.586355	+	0.586355i
$869$	−1.75359e13			−1.04313
$870$		0			0
$871$	−3.53748e12			−0.208263
$872$	9.59465e12	−	9.59465e12i	0.561959	−	0.561959i
$873$	−5.31726e12	−	1.13288e13i	−0.309830	−	0.660114i
$874$		−	2.04565e13i		−	1.18585i
$875$		0			0
$876$	−1.87338e12	−	2.66835e12i	−0.107487	−	0.153100i
$877$	2.83259e12	+	2.83259e12i	0.161691	+	0.161691i	0.783315	−	0.621625i	$-0.213527\pi$
$877$	2.83259e12	+	2.83259e12i	0.161691	+	0.161691i	−0.621625	+	0.783315i	$0.713527\pi$
$878$	−1.55303e12	−	1.55303e12i	−0.0881974	−	0.0881974i
$879$	7.37308e11	+	1.05019e12i	0.0416581	+	0.0593357i
$880$		0			0
$881$			2.29618e13i			1.28414i	0.766644	+	0.642072i	$0.221925\pi$
$881$			2.29618e13i			1.28414i	−0.766644	+	0.642072i	$0.778075\pi$
$882$	−9.03926e12	−	1.92587e13i	−0.502949	−	1.07157i
$883$	2.26739e13	−	2.26739e13i	1.25517	−	1.25517i	0.301803	−	0.953370i	$-0.402412\pi$
$883$	2.26739e13	−	2.26739e13i	1.25517	−	1.25517i	0.953370	−	0.301803i	$-0.0975883\pi$
$884$	2.72899e12			0.150303
$885$		0			0
$886$	−9.58552e12			−0.522594
$887$	−1.18253e12	+	1.18253e12i	−0.0641438	+	0.0641438i	−0.738451	−	0.674307i	$-0.764442\pi$
$887$	−1.18253e12	+	1.18253e12i	−0.0641438	+	0.0641438i	0.674307	+	0.738451i	$0.264442\pi$
$888$	2.89722e12	−	1.65521e13i	0.156359	−	0.893294i
$889$			1.47099e13i			0.789864i
$890$		0			0
$891$	1.27026e13	−	1.52932e13i	0.675217	−	0.812923i
$892$	1.12418e13	+	1.12418e13i	0.594558	+	0.594558i
$893$	−1.38878e13	−	1.38878e13i	−0.730807	−	0.730807i
$894$	1.92563e13	−	1.35193e13i	1.00821	−	0.707842i
$895$		0			0
$896$			1.03247e13i			0.535172i
$897$	−5.85420e12	−	1.02470e12i	−0.301927	−	0.0528483i
$898$	4.32537e12	−	4.32537e12i	0.221962	−	0.221962i
$899$	1.85122e13			0.945236
$900$		0			0
$901$	−3.91493e13			−1.97908
$902$	1.04002e13	−	1.04002e13i	0.523135	−	0.523135i
$903$	4.98439e12	+	8.72450e11i	0.249469	+	0.0436663i
$904$			3.27124e13i			1.62912i
$905$		0			0
$906$	5.22556e12	−	3.66873e12i	0.257665	−	0.180900i
$907$	6.28802e10	+	6.28802e10i	0.00308518	+	0.00308518i	0.708648	−	0.705563i	$-0.249306\pi$
$907$	6.28802e10	+	6.28802e10i	0.00308518	+	0.00308518i	−0.705563	+	0.708648i	$0.749306\pi$
$908$	7.78723e12	+	7.78723e12i	0.380187	+	0.380187i
$909$	1.97606e11	−	5.47176e11i	0.00959981	−	0.0265821i
$910$		0			0
$911$			1.67516e13i			0.805792i	0.915246	+	0.402896i	$0.131996\pi$
$911$			1.67516e13i			0.805792i	−0.915246	+	0.402896i	$0.868004\pi$
$912$	−1.12217e12	+	6.41103e12i	−0.0537131	+	0.306868i
$913$	1.94797e13	−	1.94797e13i	0.927822	−	0.927822i
$914$	5.68426e12			0.269411
$915$		0			0
$916$	3.12599e12			0.146710
$917$	−3.50444e13	+	3.50444e13i	−1.63665	+	1.63665i
$918$	−8.09181e12	+	1.41378e13i	−0.376057	+	0.657035i
$919$			3.65254e13i			1.68918i	0.535415	+	0.844589i	$0.320155\pi$
$919$			3.65254e13i			1.68918i	−0.535415	+	0.844589i	$0.679845\pi$
$920$		0			0
$921$	−7.38571e12	−	1.05198e13i	−0.338239	−	0.481771i
$922$	−8.16303e12	−	8.16303e12i	−0.372017	−	0.372017i
$923$	2.91893e12	+	2.91893e12i	0.132378	+	0.132378i
$924$	−1.15006e13	−	1.63809e13i	−0.519037	−	0.739290i
$925$		0			0
$926$			4.70016e12i			0.210069i
$927$	3.68448e13	−	1.72934e13i	1.63877	−	0.769170i
$928$	1.41219e13	−	1.41219e13i	0.625070	−	0.625070i
$929$	−3.87799e13			−1.70819			−0.854095	−	0.520117i	$-0.825888\pi$
$929$	−3.87799e13			−1.70819			−0.854095	+	0.520117i	$0.825888\pi$
$930$		0			0
$931$	5.78799e13			2.52496
$932$	8.97373e12	−	8.97373e12i	0.389584	−	0.389584i
$933$	−4.87142e12	+	2.78308e13i	−0.210469	+	1.20243i
$934$			9.43359e12i			0.405617i
$935$		0			0
$936$	6.16346e12	+	2.22586e12i	0.262472	+	0.0947887i
$937$	−2.37818e13	−	2.37818e13i	−1.00790	−	1.00790i	−0.999969	−	0.00792835i	$-0.997476\pi$
$937$	−2.37818e13	−	2.37818e13i	−1.00790	−	1.00790i	−0.00792835	−	0.999969i	$-0.502524\pi$
$938$	−1.50319e13	−	1.50319e13i	−0.634019	−	0.634019i
$939$	7.74575e12	−	5.43809e12i	0.325138	−	0.228271i
$940$		0			0
$941$		−	2.83845e13i		−	1.18012i	−0.807358	−	0.590062i	$-0.799103\pi$
$941$		−	2.83845e13i		−	1.18012i	0.807358	−	0.590062i	$-0.200897\pi$
$942$	7.60704e12	+	1.33151e12i	0.314765	+	0.0550954i
$943$	−2.00622e13	+	2.00622e13i	−0.826183	+	0.826183i
$944$	−2.25511e12			−0.0924259
$945$		0			0
$946$	−2.77734e12			−0.112750
$947$	−2.76953e13	+	2.76953e13i	−1.11900	+	1.11900i	−0.127116	+	0.991888i	$0.540572\pi$
$947$	−2.76953e13	+	2.76953e13i	−1.11900	+	1.11900i	−0.991888	+	0.127116i	$0.959428\pi$
$948$	−1.25603e13	−	2.19851e12i	−0.505083	−	0.0884080i
$949$			2.38386e12i			0.0954078i
$950$		0			0
$951$	3.58452e12	−	2.51660e12i	0.142108	−	0.0997705i
$952$	3.39201e13	+	3.39201e13i	1.33841	+	1.33841i
$953$	3.02779e13	+	3.02779e13i	1.18907	+	1.18907i	0.977324	+	0.211748i	$0.0679157\pi$
$953$	3.02779e13	+	3.02779e13i	1.18907	+	1.18907i	0.211748	+	0.977324i	$0.432084\pi$
$954$	−3.02283e13	−	1.09166e13i	−1.18153	−	0.426696i
$955$		0			0
$956$		−	1.87022e13i		−	0.724157i
$957$	−4.60655e12	+	2.63176e13i	−0.177530	+	1.01424i
$958$	−1.84953e13	+	1.84953e13i	−0.709442	+	0.709442i
$959$	6.48638e13			2.47639
$960$		0			0
$961$	−1.55650e12			−0.0588700
$962$	−2.97016e12	+	2.97016e12i	−0.111813	+	0.111813i
$963$	−1.77940e13	+	8.35175e12i	−0.666737	+	0.312939i
$964$		−	2.21256e13i		−	0.825178i
$965$		0			0
$966$	−2.05222e13	−	2.92308e13i	−0.758275	−	1.08005i
$967$	−6.02009e12	−	6.02009e12i	−0.221403	−	0.221403i	0.587686	−	0.809089i	$-0.300039\pi$
$967$	−6.02009e12	−	6.02009e12i	−0.221403	−	0.221403i	−0.809089	+	0.587686i	$0.800039\pi$
$968$	2.37562e12	+	2.37562e12i	0.0869637	+	0.0869637i
$969$	−2.54652e13	−	3.62713e13i	−0.927875	−	1.32162i
$970$		0			0
$971$		−	4.71362e13i		−	1.70164i	−0.525456	−	0.850820i	$-0.676105\pi$
$971$		−	4.71362e13i		−	1.70164i	0.525456	−	0.850820i	$-0.323895\pi$
$972$	1.10158e13	−	9.36142e12i	0.395837	−	0.336390i
$973$	1.83132e13	−	1.83132e13i	0.655023	−	0.655023i
$974$	6.65105e12			0.236796
$975$		0			0
$976$	4.24696e12			0.149814
$977$	1.14585e12	−	1.14585e12i	0.0402349	−	0.0402349i	−0.686703	−	0.726938i	$-0.740943\pi$
$977$	1.14585e12	−	1.14585e12i	0.0402349	−	0.0402349i	0.726938	+	0.686703i	$0.240943\pi$
$978$	−4.72729e12	+	2.70074e13i	−0.165229	+	0.943970i
$979$			3.57271e13i			1.24301i
$980$		0			0
$981$	−7.43414e12	+	2.05853e13i	−0.256283	+	0.709655i
$982$	2.85539e12	+	2.85539e12i	0.0979859	+	0.0979859i
$983$	1.01556e13	+	1.01556e13i	0.346910	+	0.346910i	0.858957	−	0.512047i	$-0.171113\pi$
$983$	1.01556e13	+	1.01556e13i	0.346910	+	0.346910i	−0.512047	+	0.858957i	$0.671113\pi$
$984$	2.56036e13	−	1.79756e13i	0.870609	−	0.611232i
$985$		0			0
$986$		−	2.18918e13i		−	0.737626i
$987$	−3.37770e13	−	5.91222e12i	−1.13291	−	0.198300i
$988$	−4.30986e12	+	4.30986e12i	−0.143899	+	0.143899i
$989$	5.35752e12			0.178066
$990$		0			0
$991$	2.39185e12			0.0787776			0.0393888	−	0.999224i	$-0.487459\pi$
$991$	2.39185e12			0.0787776			0.0393888	+	0.999224i	$0.487459\pi$
$992$	1.89819e13	−	1.89819e13i	0.622354	−	0.622354i
$993$	−2.56364e13	−	4.48732e12i	−0.836731	−	0.146459i
$994$			2.48070e13i			0.806002i
$995$		0			0
$996$	1.63948e13	−	1.15104e13i	0.527886	−	0.370615i
$997$	1.68977e13	+	1.68977e13i	0.541627	+	0.541627i	0.924006	−	0.382378i	$-0.124895\pi$
$997$	1.68977e13	+	1.68977e13i	0.541627	+	0.541627i	−0.382378	+	0.924006i	$0.624895\pi$
$998$	−1.72860e13	−	1.72860e13i	−0.551577	−	0.551577i
$999$	7.11338e12	+	2.61543e13i	0.225960	+	0.830803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.g.32.9	✓	48
3.2	odd	2	inner	75.10.e.g.32.15	yes	48
5.2	odd	4	inner	75.10.e.g.68.10	yes	48
5.3	odd	4	inner	75.10.e.g.68.15	yes	48
5.4	even	2	inner	75.10.e.g.32.16	yes	48
15.2	even	4	inner	75.10.e.g.68.16	yes	48
15.8	even	4	inner	75.10.e.g.68.9	yes	48
15.14	odd	2	inner	75.10.e.g.32.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.10.e.g.32.9	✓	48	1.1	even	1	trivial
75.10.e.g.32.10	yes	48	15.14	odd	2	inner
75.10.e.g.32.15	yes	48	3.2	odd	2	inner
75.10.e.g.32.16	yes	48	5.4	even	2	inner
75.10.e.g.68.9	yes	48	15.8	even	4	inner
75.10.e.g.68.10	yes	48	5.2	odd	4	inner
75.10.e.g.68.15	yes	48	5.3	odd	4	inner
75.10.e.g.68.16	yes	48	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.0913 + 11.0913i) q^{2} +(-138.195 - 24.1892i) q^{3} +265.967i q^{4} +(1801.05 - 1264.47i) q^{6} +(7391.28 + 7391.28i) q^{7} +(-8628.65 - 8628.65i) q^{8} +(18512.8 + 6685.66i) q^{9} +O(q^{10})\)	\(q+(-11.0913 + 11.0913i) q^{2} +(-138.195 - 24.1892i) q^{3} +265.967i q^{4} +(1801.05 - 1264.47i) q^{6} +(7391.28 + 7391.28i) q^{7} +(-8628.65 - 8628.65i) q^{8} +(18512.8 + 6685.66i) q^{9} -51315.4i q^{11} +(6433.53 - 36755.3i) q^{12} +(-19292.1 + 19292.1i) q^{13} -163958. q^{14} +55230.6 q^{16} +(-265928. + 265928. i) q^{17} +(-279483. + 131178. i) q^{18} -839953. i q^{19} +(-842650. - 1.20023e6i) q^{21} +(569153. + 569153. i) q^{22} +(-1.09790e6 - 1.09790e6i) q^{23} +(983717. + 1.40116e6i) q^{24} -427949. i q^{26} +(-2.39665e6 - 1.37173e6i) q^{27} +(-1.96584e6 + 1.96584e6i) q^{28} +3.71113e6 q^{29} +4.98830e6 q^{31} +(3.80529e6 - 3.80529e6i) q^{32} +(-1.24128e6 + 7.09153e6i) q^{33} -5.89896e6i q^{34} +(-1.77816e6 + 4.92378e6i) q^{36} +(-6.94044e6 - 6.94044e6i) q^{37} +(9.31616e6 + 9.31616e6i) q^{38} +(3.13274e6 - 2.19942e6i) q^{39} -1.82732e7i q^{41} +(2.26581e7 + 3.96601e6i) q^{42} +(-2.43988e6 + 2.43988e6i) q^{43} +1.36482e7 q^{44} +2.43544e7 q^{46} +(1.65340e7 - 1.65340e7i) q^{47} +(-7.63260e6 - 1.33599e6i) q^{48} +6.89085e7i q^{49} +(4.31825e7 - 3.03173e7i) q^{51} +(-5.13107e6 - 5.13107e6i) q^{52} +(7.36089e7 + 7.36089e7i) q^{53} +(4.17962e7 - 1.13677e7i) q^{54} -1.27554e8i q^{56} +(-2.03178e7 + 1.16077e8i) q^{57} +(-4.11612e7 + 4.11612e7i) q^{58} -4.08308e7 q^{59} +7.68949e7 q^{61} +(-5.53266e7 + 5.53266e7i) q^{62} +(8.74175e7 + 1.86249e8i) q^{63} +1.12689e8i q^{64} +(-6.48868e7 - 9.24215e7i) q^{66} +(9.16819e7 + 9.16819e7i) q^{67} +(-7.07280e7 - 7.07280e7i) q^{68} +(1.25168e8 + 1.78283e8i) q^{69} -1.51302e8i q^{71} +(-1.02052e8 - 2.17428e8i) q^{72} +(6.17833e7 - 6.17833e7i) q^{73} +1.53957e8 q^{74} +2.23400e8 q^{76} +(3.79286e8 - 3.79286e8i) q^{77} +(-1.03518e7 + 5.91405e7i) q^{78} -3.41727e8i q^{79} +(2.98024e8 + 2.47540e8i) q^{81} +(2.02673e8 + 2.02673e8i) q^{82} +(3.79608e8 + 3.79608e8i) q^{83} +(3.19221e8 - 2.24117e8i) q^{84} -5.41229e7i q^{86} +(-5.12860e8 - 8.97694e7i) q^{87} +(-4.42782e8 + 4.42782e8i) q^{88} -6.96227e8 q^{89} -2.85187e8 q^{91} +(2.92006e8 - 2.92006e8i) q^{92} +(-6.89358e8 - 1.20663e8i) q^{93} +3.66767e8i q^{94} +(-6.17919e8 + 4.33826e8i) q^{96} +(-4.49583e8 - 4.49583e8i) q^{97} +(-7.64284e8 - 7.64284e8i) q^{98} +(3.43077e8 - 9.49989e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10788 q^{6}+O(q^{10}) \) 48 * q + 10788 * q^6	\( 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) \) 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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