LMFDB - Embedded newform 100.11.b.h.51.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,11,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	100.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:	$63.5357252674$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.23
Character	$\chi$	$=$	100.51
Dual form			100.11.b.h.51.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(31.9986 - 0.302723i) q^{2} +375.794i q^{3} +(1023.82 - 19.3734i) q^{4} +(113.762 + 12024.9i) q^{6} -19635.7i q^{7} +(32754.8 - 929.854i) q^{8} -82172.5 q^{9} +O(q^{10})$	\(q+(31.9986 - 0.302723i) q^{2} +375.794i q^{3} +(1023.82 - 19.3734i) q^{4} +(113.762 + 12024.9i) q^{6} -19635.7i q^{7} +(32754.8 - 929.854i) q^{8} -82172.5 q^{9} -163868. i q^{11} +(7280.42 + 384745. i) q^{12} +86535.9 q^{13} +(-5944.18 - 628314. i) q^{14} +(1.04783e6 - 39669.6i) q^{16} +2.09541e6 q^{17} +(-2.62940e6 + 24875.5i) q^{18} -3.13936e6i q^{19} +7.37899e6 q^{21} +(-49606.6 - 5.24354e6i) q^{22} -1.05386e7i q^{23} +(349434. + 1.23091e7i) q^{24} +(2.76902e6 - 26196.4i) q^{26} -8.68968e6i q^{27} +(-380410. - 2.01034e7i) q^{28} -1.13219e7 q^{29} +1.21645e7i q^{31} +(3.35169e7 - 1.58657e6i) q^{32} +6.15807e7 q^{33} +(6.70503e7 - 634330. i) q^{34} +(-8.41296e7 + 1.59196e6i) q^{36} -4.87589e7 q^{37} +(-950356. - 1.00455e8i) q^{38} +3.25197e7i q^{39} +4.55341e7 q^{41} +(2.36117e8 - 2.23379e6i) q^{42} -7.47838e7i q^{43} +(-3.17468e6 - 1.67771e8i) q^{44} +(-3.19029e6 - 3.37222e8i) q^{46} +9.62539e6i q^{47} +(1.49076e7 + 3.93767e8i) q^{48} -1.03086e8 q^{49} +7.87445e8i q^{51} +(8.85969e7 - 1.67649e6i) q^{52} +1.27224e8 q^{53} +(-2.63056e6 - 2.78057e8i) q^{54} +(-1.82583e7 - 6.43164e8i) q^{56} +1.17975e9 q^{57} +(-3.62283e8 + 3.42739e6i) q^{58} +1.18280e9i q^{59} +2.97404e8 q^{61} +(3.68246e6 + 3.89246e8i) q^{62} +1.61351e9i q^{63} +(1.07201e9 - 6.09144e7i) q^{64} +(1.97049e9 - 1.86419e7i) q^{66} +7.15670e8i q^{67} +(2.14532e9 - 4.05953e7i) q^{68} +3.96036e9 q^{69} +2.56419e9i q^{71} +(-2.69154e9 + 7.64084e7i) q^{72} -2.10771e9 q^{73} +(-1.56022e9 + 1.47604e7i) q^{74} +(-6.08201e7 - 3.21413e9i) q^{76} -3.21766e9 q^{77} +(9.84446e6 + 1.04058e9i) q^{78} -3.44771e9i q^{79} -1.58667e9 q^{81} +(1.45702e9 - 1.37842e7i) q^{82} -7.09842e9i q^{83} +(7.55473e9 - 1.42956e8i) q^{84} +(-2.26388e7 - 2.39297e9i) q^{86} -4.25469e9i q^{87} +(-1.52373e8 - 5.36747e9i) q^{88} +3.39502e9 q^{89} -1.69919e9i q^{91} +(-2.04169e8 - 1.07896e10i) q^{92} -4.57134e9 q^{93} +(2.91383e6 + 3.07999e8i) q^{94} +(5.96225e8 + 1.25955e10i) q^{96} -5.71771e9 q^{97} +(-3.29859e9 + 3.12064e7i) q^{98} +1.34654e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9}+O(q^{10}) $ 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9	$ 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9} + 1706016 q^{14} - 4733376 q^{16} - 13030368 q^{21} - 10190784 q^{24} - 9454368 q^{26} - 121656816 q^{29} + 335231168 q^{34} - 276632160 q^{36} + 892843248 q^{41} - 766329600 q^{44} + 433181216 q^{46} + 738102008 q^{49} - 139387968 q^{54} - 2629032384 q^{56} + 228563248 q^{61} + 1875284992 q^{64} - 1440259200 q^{66} + 943422432 q^{69} - 21045467232 q^{74} + 828422400 q^{76} - 5619065544 q^{81} + 28069573632 q^{84} + 8163556416 q^{86} - 4631088816 q^{89} - 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) $ 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9 + 1706016 * q^14 - 4733376 * q^16 - 13030368 * q^21 - 10190784 * q^24 - 9454368 * q^26 - 121656816 * q^29 + 335231168 * q^34 - 276632160 * q^36 + 892843248 * q^41 - 766329600 * q^44 + 433181216 * q^46 + 738102008 * q^49 - 139387968 * q^54 - 2629032384 * q^56 + 228563248 * q^61 + 1875284992 * q^64 - 1440259200 * q^66 + 943422432 * q^69 - 21045467232 * q^74 + 828422400 * q^76 - 5619065544 * q^81 + 28069573632 * q^84 + 8163556416 * q^86 - 4631088816 * q^89 - 63404384 * q^94 - 5617046784 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	31.9986	−	0.302723i	0.999955	−	0.00946009i
$2$	31.9986	−	0.302723i	0.999955	−	0.00946009i
$3$			375.794i			1.54648i	0.634114	+	0.773240i	$0.281365\pi$
$3$			375.794i			1.54648i	−0.634114	+	0.773240i	$0.718635\pi$
$4$	1023.82	−	19.3734i	0.999821	−	0.0189193i
$5$		0			0
$5$		0			0
$6$	113.762	+	12024.9i	0.0146298	+	1.54641i
$7$		−	19635.7i		−	1.16831i	−0.811644	−	0.584153i	$-0.801427\pi$
$7$		−	19635.7i		−	1.16831i	0.811644	−	0.584153i	$-0.198573\pi$
$8$	32754.8	−	929.854i	0.999597	−	0.0283769i
$9$	−82172.5			−1.39160
$10$		0			0
$11$		−	163868.i		−	1.01749i	−0.860917	−	0.508746i	$-0.830109\pi$
$11$		−	163868.i		−	1.01749i	0.860917	−	0.508746i	$-0.169891\pi$
$12$	7280.42	+	384745.i	0.0292584	+	1.54620i
$13$	86535.9			0.233066			0.116533	−	0.993187i	$-0.462822\pi$
$13$	86535.9			0.233066			0.116533	+	0.993187i	$0.462822\pi$
$14$	−5944.18	−	628314.i	−0.0110523	−	1.16825i
$15$		0			0
$16$	1.04783e6	−	39669.6i	0.999284	−	0.0378319i
$17$	2.09541e6			1.47579			0.737896	−	0.674914i	$-0.235819\pi$
$17$	2.09541e6			1.47579			0.737896	+	0.674914i	$0.235819\pi$
$18$	−2.62940e6	+	24875.5i	−1.39154	+	0.0131646i
$19$		−	3.13936e6i		−	1.26787i	−0.773388	−	0.633933i	$-0.781440\pi$
$19$		−	3.13936e6i		−	1.26787i	0.773388	−	0.633933i	$-0.218560\pi$
$20$		0			0
$21$	7.37899e6			1.80676
$22$	−49606.6	−	5.24354e6i	−0.00962557	−	1.01745i
$23$		−	1.05386e7i		−	1.63737i	−0.574246	−	0.818683i	$-0.694705\pi$
$23$		−	1.05386e7i		−	1.63737i	0.574246	−	0.818683i	$-0.305295\pi$
$24$	349434.	+	1.23091e7i	0.0438843	+	1.54586i
$25$		0			0
$26$	2.76902e6	−	26196.4i	0.233056	−	0.00220483i
$27$		−	8.68968e6i		−	0.605598i
$28$	−380410.	−	2.01034e7i	−0.0221036	−	1.16810i
$29$	−1.13219e7			−0.551986			−0.275993	−	0.961160i	$-0.589007\pi$
$29$	−1.13219e7			−0.551986			−0.275993	+	0.961160i	$0.589007\pi$
$30$		0			0
$31$			1.21645e7i			0.424898i	0.977172	+	0.212449i	$0.0681439\pi$
$31$			1.21645e7i			0.424898i	−0.977172	+	0.212449i	$0.931856\pi$
$32$	3.35169e7	−	1.58657e6i	0.998882	−	0.0472835i
$33$	6.15807e7			1.57353
$34$	6.70503e7	−	634330.i	1.47573	−	0.0139611i
$35$		0			0
$36$	−8.41296e7	+	1.59196e6i	−1.39135	+	0.0263281i
$37$	−4.87589e7			−0.703146			−0.351573	−	0.936160i	$-0.614353\pi$
$37$	−4.87589e7			−0.703146			−0.351573	+	0.936160i	$0.614353\pi$
$38$	−950356.	−	1.00455e8i	−0.0119941	−	1.26781i
$39$			3.25197e7i			0.360432i
$40$		0			0
$41$	4.55341e7			0.393022			0.196511	−	0.980502i	$-0.437039\pi$
$41$	4.55341e7			0.393022			0.196511	+	0.980502i	$0.437039\pi$
$42$	2.36117e8	−	2.23379e6i	1.80668	−	0.0170921i
$43$		−	7.47838e7i		−	0.508704i	−0.967112	−	0.254352i	$-0.918138\pi$
$43$		−	7.47838e7i		−	0.508704i	0.967112	−	0.254352i	$-0.0818621\pi$
$44$	−3.17468e6	−	1.67771e8i	−0.0192503	−	1.01731i
$45$		0			0
$46$	−3.19029e6	−	3.37222e8i	−0.0154896	−	1.63729i
$47$			9.62539e6i			0.0419690i	0.999780	+	0.0209845i	$0.00668007\pi$
$47$			9.62539e6i			0.0419690i	−0.999780	+	0.0209845i	$0.993320\pi$
$48$	1.49076e7	+	3.93767e8i	0.0585062	+	1.54537i
$49$	−1.03086e8			−0.364937
$50$		0			0
$51$			7.87445e8i			2.28228i
$52$	8.85969e7	−	1.67649e6i	0.233025	−	0.00440946i
$53$	1.27224e8			0.304222			0.152111	−	0.988363i	$-0.451393\pi$
$53$	1.27224e8			0.304222			0.152111	+	0.988363i	$0.451393\pi$
$54$	−2.63056e6	−	2.78057e8i	−0.00572902	−	0.605571i
$55$		0			0
$56$	−1.82583e7	−	6.43164e8i	−0.0331529	−	1.16783i
$57$	1.17975e9			1.96073
$58$	−3.62283e8	+	3.42739e6i	−0.551961	+	0.00522184i
$59$			1.18280e9i			1.65444i	0.561881	+	0.827218i	$0.310078\pi$
$59$			1.18280e9i			1.65444i	−0.561881	+	0.827218i	$0.689922\pi$
$60$		0			0
$61$	2.97404e8			0.352126			0.176063	−	0.984379i	$-0.443664\pi$
$61$	2.97404e8			0.352126			0.176063	+	0.984379i	$0.443664\pi$
$62$	3.68246e6	+	3.89246e8i	0.00401957	+	0.424879i
$63$			1.61351e9i			1.62581i
$64$	1.07201e9	−	6.09144e7i	0.998390	−	0.0567309i
$65$		0			0
$66$	1.97049e9	−	1.86419e7i	1.57346	−	0.0148857i
$67$			7.15670e8i			0.530077i	0.964238	+	0.265039i	$0.0853847\pi$
$67$			7.15670e8i			0.530077i	−0.964238	+	0.265039i	$0.914615\pi$
$68$	2.14532e9	−	4.05953e7i	1.47553	−	0.0279210i
$69$	3.96036e9			2.53215
$70$		0			0
$71$			2.56419e9i			1.42121i	0.703589	+	0.710607i	$0.251579\pi$
$71$			2.56419e9i			1.42121i	−0.703589	+	0.710607i	$0.748421\pi$
$72$	−2.69154e9	+	7.64084e7i	−1.39104	+	0.0394892i
$73$	−2.10771e9			−1.01671			−0.508355	−	0.861148i	$-0.669746\pi$
$73$	−2.10771e9			−1.01671			−0.508355	+	0.861148i	$0.669746\pi$
$74$	−1.56022e9	+	1.47604e7i	−0.703115	+	0.00665183i
$75$		0			0
$76$	−6.08201e7	−	3.21413e9i	−0.0239872	−	1.26764i
$77$	−3.21766e9			−1.18874
$78$	9.84446e6	+	1.04058e9i	0.00340972	+	0.360416i
$79$		−	3.44771e9i		−	1.12046i	−0.828338	−	0.560229i	$-0.810713\pi$
$79$		−	3.44771e9i		−	1.12046i	0.828338	−	0.560229i	$-0.189287\pi$
$80$		0			0
$81$	−1.58667e9			−0.455053
$82$	1.45702e9	−	1.37842e7i	0.393005	−	0.00371803i
$83$		−	7.09842e9i		−	1.80207i	−0.433748	−	0.901034i	$-0.642809\pi$
$83$		−	7.09842e9i		−	1.80207i	0.433748	−	0.901034i	$-0.357191\pi$
$84$	7.55473e9	−	1.42956e8i	1.80644	−	0.0341827i
$85$		0			0
$86$	−2.26388e7	−	2.39297e9i	−0.00481238	−	0.508681i
$87$		−	4.25469e9i		−	0.853634i
$88$	−1.52373e8	−	5.36747e9i	−0.0288733	−	1.01708i
$89$	3.39502e9			0.607984			0.303992	−	0.952675i	$-0.401680\pi$
$89$	3.39502e9			0.607984			0.303992	+	0.952675i	$0.401680\pi$
$90$		0			0
$91$		−	1.69919e9i		−	0.272292i
$92$	−2.04169e8	−	1.07896e10i	−0.0309779	−	1.63707i
$93$	−4.57134e9			−0.657096
$94$	2.91383e6	+	3.07999e8i	0.000397031	+	0.0419671i
$95$		0			0
$96$	5.96225e8	+	1.25955e10i	0.0731230	+	1.54475i
$97$	−5.71771e9			−0.665830			−0.332915	−	0.942957i	$-0.608032\pi$
$97$	−5.71771e9			−0.665830			−0.332915	+	0.942957i	$0.608032\pi$
$98$	−3.29859e9	+	3.12064e7i	−0.364920	+	0.00345233i
$99$			1.34654e10i			1.41594i
$100$		0			0
$101$	1.71412e10			1.63093			0.815465	−	0.578807i	$-0.196481\pi$
$101$	1.71412e10			1.63093			0.815465	+	0.578807i	$0.196481\pi$
$102$	2.38378e8	+	2.51971e10i	0.0215906	+	2.28218i
$103$			7.45366e9i			0.642960i	0.946916	+	0.321480i	$0.104180\pi$
$103$			7.45366e9i			0.642960i	−0.946916	+	0.321480i	$0.895820\pi$
$104$	2.83447e9	−	8.04657e7i	0.232972	−	0.00661370i
$105$		0			0
$106$	4.07099e9	−	3.85137e7i	0.304208	−	0.00287797i
$107$			7.26790e9i			0.518191i	0.965852	+	0.259096i	$0.0834245\pi$
$107$			7.26790e9i			0.518191i	−0.965852	+	0.259096i	$0.916576\pi$
$108$	−1.68349e8	−	8.89664e9i	−0.0114575	−	0.605490i
$109$	9.09372e9			0.591029			0.295515	−	0.955338i	$-0.404509\pi$
$109$	9.09372e9			0.591029			0.295515	+	0.955338i	$0.404509\pi$
$110$		0			0
$111$		−	1.83233e10i		−	1.08740i
$112$	−7.78941e8	−	2.05748e10i	−0.0441992	−	1.16747i
$113$	7.57770e9			0.411287			0.205644	−	0.978627i	$-0.434071\pi$
$113$	7.57770e9			0.411287			0.205644	+	0.978627i	$0.434071\pi$
$114$	3.77504e10	−	3.57139e8i	1.96064	−	0.0185487i
$115$		0			0
$116$	−1.15915e10	+	2.19343e8i	−0.551887	+	0.0104432i
$117$	−7.11087e9			−0.324335
$118$	3.58060e8	+	3.78478e10i	0.0156511	+	1.65436i
$119$		−	4.11449e10i		−	1.72418i
$120$		0			0
$121$	−9.15322e8			−0.0352896
$122$	9.51652e9	−	9.00312e7i	0.352110	−	0.00333115i
$123$			1.71115e10i			0.607801i
$124$	2.35667e8	+	1.24542e10i	0.00803879	+	0.424822i
$125$		0			0
$126$	4.88448e8	+	5.16302e10i	0.0153803	+	1.62574i
$127$			6.24479e9i			0.189016i	0.995524	+	0.0945081i	$0.0301278\pi$
$127$			6.24479e9i			0.189016i	−0.995524	+	0.0945081i	$0.969872\pi$
$128$	3.42844e10	−	2.27370e9i	0.997808	−	0.0661732i
$129$	2.81033e10			0.786700
$130$		0			0
$131$		−	5.72133e10i		−	1.48300i	−0.670953	−	0.741499i	$-0.734115\pi$
$131$		−	5.72133e10i		−	1.48300i	0.670953	−	0.741499i	$-0.265885\pi$
$132$	6.30474e10	−	1.19303e9i	1.57325	−	0.0297701i
$133$	−6.16435e10			−1.48125
$134$	2.16650e8	+	2.29004e10i	0.00501458	+	0.530053i
$135$		0			0
$136$	6.86349e10	−	1.94843e9i	1.47520	−	0.0418784i
$137$	1.24420e10			0.257803			0.128902	−	0.991657i	$-0.458855\pi$
$137$	1.24420e10			0.257803			0.128902	+	0.991657i	$0.458855\pi$
$138$	1.26726e11	−	1.19889e9i	2.53204	−	0.0239544i
$139$			3.88376e9i			0.0748477i	0.999299	+	0.0374239i	$0.0119152\pi$
$139$			3.88376e9i			0.0748477i	−0.999299	+	0.0374239i	$0.988085\pi$
$140$		0			0
$141$	−3.61717e9			−0.0649042
$142$	7.76241e8	+	8.20506e10i	0.0134448	+	1.42115i
$143$		−	1.41805e10i		−	0.237143i
$144$	−8.61024e10	+	3.25975e9i	−1.39060	+	0.0526468i
$145$		0			0
$146$	−6.74438e10	+	6.38053e8i	−1.01666	+	0.00961817i
$147$		−	3.87390e10i		−	0.564367i
$148$	−4.99202e10	+	9.44626e8i	−0.703020	+	0.0133031i
$149$	−5.05127e10			−0.687811			−0.343905	−	0.939004i	$-0.611750\pi$
$149$	−5.05127e10			−0.687811			−0.343905	+	0.939004i	$0.611750\pi$
$150$		0			0
$151$			5.51200e10i			0.702141i	0.936349	+	0.351070i	$0.114182\pi$
$151$			5.51200e10i			0.702141i	−0.936349	+	0.351070i	$0.885818\pi$
$152$	−2.91915e9	−	1.02829e11i	−0.0359781	−	1.26735i
$153$	−1.72185e11			−2.05371
$154$	−1.02961e11	+	9.74061e8i	−1.18869	+	0.0112456i
$155$		0			0
$156$	6.30017e8	+	3.32942e10i	0.00681914	+	0.360368i
$157$	8.96109e10			0.939426			0.469713	−	0.882819i	$-0.344357\pi$
$157$	8.96109e10			0.939426			0.469713	+	0.882819i	$0.344357\pi$
$158$	−1.04370e9	−	1.10322e11i	−0.0105996	−	1.12041i
$159$			4.78101e10i			0.470473i
$160$		0			0
$161$	−2.06934e11			−1.91294
$162$	−5.07712e10	+	4.80322e8i	−0.455032	+	0.00430484i
$163$		−	1.16440e11i		−	1.01197i	−0.862543	−	0.505983i	$-0.831130\pi$
$163$		−	1.16440e11i		−	1.01197i	0.862543	−	0.505983i	$-0.168870\pi$
$164$	4.66185e10	−	8.82150e8i	0.392952	−	0.00743572i
$165$		0			0
$166$	−2.14885e9	−	2.27139e11i	−0.0170477	−	1.80199i
$167$			9.33076e10i			0.718348i	0.933271	+	0.359174i	$0.116942\pi$
$167$			9.33076e10i			0.718348i	−0.933271	+	0.359174i	$0.883058\pi$
$168$	2.41697e11	−	6.86138e9i	1.80603	−	0.0512702i
$169$	−1.30370e11			−0.945680
$170$		0			0
$171$			2.57969e11i			1.76436i
$172$	−1.44882e9	−	7.65649e10i	−0.00962434	−	0.508613i
$173$	−9.17264e10			−0.591921			−0.295961	−	0.955200i	$-0.595640\pi$
$173$	−9.17264e10			−0.591921			−0.295961	+	0.955200i	$0.595640\pi$
$174$	−1.28799e9	−	1.36144e11i	−0.00807546	−	0.853596i
$175$		0			0
$176$	−6.50058e9	−	1.71705e11i	−0.0384936	−	1.01676i
$177$	−4.44488e11			−2.55855
$178$	1.08636e11	−	1.02775e9i	0.607957	−	0.00575159i
$179$			1.07881e11i			0.587059i	0.955950	+	0.293529i	$0.0948298\pi$
$179$			1.07881e11i			0.587059i	−0.955950	+	0.293529i	$0.905170\pi$
$180$		0			0
$181$	3.43268e11			1.76702			0.883508	−	0.468417i	$-0.155175\pi$
$181$	3.43268e11			1.76702			0.883508	+	0.468417i	$0.155175\pi$
$182$	−5.14385e8	−	5.43717e10i	−0.00257591	−	0.272280i
$183$			1.11763e11i			0.544556i
$184$	−9.79940e9	−	3.45191e11i	−0.0464633	−	1.63671i
$185$		0			0
$186$	−1.46276e11	+	1.38385e9i	−0.657066	+	0.00621619i
$187$		−	3.43372e11i		−	1.50161i
$188$	1.86476e8	+	9.85463e9i	0.000794026	+	0.0419615i
$189$	−1.70628e11			−0.707524
$190$		0			0
$191$			2.33817e10i			0.0919832i	0.998942	+	0.0459916i	$0.0146447\pi$
$191$			2.33817e10i			0.0919832i	−0.998942	+	0.0459916i	$0.985355\pi$
$192$	2.28913e10	+	4.02856e11i	0.0877332	+	1.54399i
$193$	−2.97973e11			−1.11273			−0.556366	−	0.830937i	$-0.687805\pi$
$193$	−2.97973e11			−1.11273			−0.556366	+	0.830937i	$0.687805\pi$
$194$	−1.82958e11	+	1.73088e9i	−0.665800	+	0.00629881i
$195$		0			0
$196$	−1.05541e11	+	1.99712e9i	−0.364871	+	0.00690436i
$197$	−4.56567e11			−1.53877			−0.769385	−	0.638785i	$-0.779437\pi$
$197$	−4.56567e11			−1.53877			−0.769385	+	0.638785i	$0.779437\pi$
$198$	4.07630e9	+	4.30875e11i	0.0133949	+	1.41588i
$199$			1.61572e11i			0.517728i	0.965914	+	0.258864i	$0.0833481\pi$
$199$			1.61572e11i			0.517728i	−0.965914	+	0.258864i	$0.916652\pi$
$200$		0			0
$201$	−2.68945e11			−0.819753
$202$	5.48495e11	−	5.18904e9i	1.63086	−	0.0154287i
$203$			2.22313e11i			0.644888i
$204$	1.52555e10	+	8.06200e11i	0.0431793	+	2.28187i
$205$		0			0
$206$	2.25640e9	+	2.38507e11i	0.00608246	+	0.642931i
$207$			8.65987e11i			2.27855i
$208$	9.06745e10	−	3.43285e9i	0.232899	−	0.00881734i
$209$	−5.14441e11			−1.29004
$210$		0			0
$211$			1.81757e11i			0.434588i	0.976106	+	0.217294i	$0.0697231\pi$
$211$			1.81757e11i			0.434588i	−0.976106	+	0.217294i	$0.930277\pi$
$212$	1.30254e11	−	2.46476e9i	0.304167	−	0.00575567i
$213$	−9.63610e11			−2.19788
$214$	2.20016e9	+	2.32562e11i	0.00490214	+	0.518168i
$215$		0			0
$216$	−8.08013e9	−	2.84629e11i	−0.0171850	−	0.605355i
$217$	2.38858e11			0.496410
$218$	2.90986e11	−	2.75288e9i	0.591003	−	0.00559119i
$219$		−	7.92067e11i		−	1.57232i
$220$		0			0
$221$	1.81329e11			0.343957
$222$	−5.54689e9	−	5.86321e11i	−0.0102869	−	1.08735i
$223$			1.11110e11i			0.201479i	0.994913	+	0.100740i	$0.0321209\pi$
$223$			1.11110e11i			0.201479i	−0.994913	+	0.100740i	$0.967879\pi$
$224$	−3.11535e10	−	6.58128e11i	−0.0552416	−	1.16700i
$225$		0			0
$226$	2.42476e11	−	2.29394e9i	0.411269	−	0.00389082i
$227$		−	9.00145e11i		−	1.49343i	−0.665147	−	0.746713i	$-0.731631\pi$
$227$		−	9.00145e11i		−	1.49343i	0.665147	−	0.746713i	$-0.268369\pi$
$228$	1.20785e12	−	2.28559e10i	1.96038	−	0.0370957i
$229$	5.43837e11			0.863558			0.431779	−	0.901979i	$-0.357886\pi$
$229$	5.43837e11			0.863558			0.431779	+	0.901979i	$0.357886\pi$
$230$		0			0
$231$		−	1.20918e12i		−	1.83836i
$232$	−3.70845e11	+	1.05277e10i	−0.551763	+	0.0156636i
$233$	6.34760e11			0.924336			0.462168	−	0.886792i	$-0.347072\pi$
$233$	6.34760e11			0.924336			0.462168	+	0.886792i	$0.347072\pi$
$234$	−2.27538e11	+	2.15262e9i	−0.324320	+	0.00306823i
$235$		0			0
$236$	2.29148e10	+	1.21097e12i	0.0313008	+	1.65414i
$237$	1.29563e12			1.73277
$238$	−1.24555e10	−	1.31658e12i	−0.0163109	−	1.72410i
$239$			9.24284e10i			0.118527i	0.998242	+	0.0592633i	$0.0188752\pi$
$239$			9.24284e10i			0.118527i	−0.998242	+	0.0592633i	$0.981125\pi$
$240$		0			0
$241$	−9.05993e11			−1.11440			−0.557198	−	0.830379i	$-0.688124\pi$
$241$	−9.05993e11			−1.11440			−0.557198	+	0.830379i	$0.688124\pi$
$242$	−2.92890e10	+	2.77089e8i	−0.0352880	+	0.000333843i
$243$		−	1.10938e12i		−	1.30933i
$244$	3.04488e11	−	5.76174e9i	0.352063	−	0.00666199i
$245$		0			0
$246$	5.18003e9	+	5.47542e11i	0.00574985	+	0.607774i
$247$		−	2.71667e11i		−	0.295497i
$248$	1.13112e10	+	3.98445e11i	0.0120573	+	0.424727i
$249$	2.66755e12			2.78686
$250$		0			0
$251$		−	1.13681e12i		−	1.14109i	−0.821266	−	0.570546i	$-0.806732\pi$
$251$		−	1.13681e12i		−	1.14109i	0.821266	−	0.570546i	$-0.193268\pi$
$252$	3.12593e10	+	1.65194e12i	0.0307593	+	1.62552i
$253$	−1.72695e12			−1.66601
$254$	1.89044e9	+	1.99824e11i	0.00178811	+	0.189008i
$255$		0			0
$256$	1.09636e12	−	8.31337e10i	0.997137	−	0.0756096i
$257$	−6.98643e11			−0.623146			−0.311573	−	0.950222i	$-0.600856\pi$
$257$	−6.98643e11			−0.623146			−0.311573	+	0.950222i	$0.600856\pi$
$258$	8.99266e11	−	8.50752e9i	0.786665	−	0.00744225i
$259$			9.57416e11i			0.821489i
$260$		0			0
$261$	9.30345e11			0.768142
$262$	−1.73198e10	−	1.83075e12i	−0.0140293	−	1.48293i
$263$			4.94717e10i			0.0393168i	0.999807	+	0.0196584i	$0.00625787\pi$
$263$			4.94717e10i			0.0393168i	−0.999807	+	0.0196584i	$0.993742\pi$
$264$	2.01706e12	−	5.72611e10i	1.57290	−	0.0446519i
$265$		0			0
$266$	−1.97251e12	+	1.86609e10i	−1.48119	+	0.0140128i
$267$			1.27583e12i			0.940235i
$268$	1.38650e10	+	7.32715e11i	0.0100287	+	0.529982i
$269$	−1.80389e12			−1.28070			−0.640351	−	0.768083i	$-0.721211\pi$
$269$	−1.80389e12			−1.28070			−0.640351	+	0.768083i	$0.721211\pi$
$270$		0			0
$271$			2.03271e12i			1.39069i	0.718677	+	0.695344i	$0.244748\pi$
$271$			2.03271e12i			1.39069i	−0.718677	+	0.695344i	$0.755252\pi$
$272$	2.19563e12	−	8.31243e10i	1.47474	−	0.0558320i
$273$	6.38547e11			0.421095
$274$	3.98127e11	−	3.76649e9i	0.257792	−	0.00243884i
$275$		0			0
$276$	4.05469e12	−	7.67257e10i	2.53170	−	0.0479066i
$277$	−9.87952e11			−0.605811			−0.302905	−	0.953021i	$-0.597957\pi$
$277$	−9.87952e11			−0.605811			−0.302905	+	0.953021i	$0.597957\pi$
$278$	1.17570e9	+	1.24275e11i	0.000708066	+	0.0748444i
$279$		−	9.99584e11i		−	0.591287i
$280$		0			0
$281$	2.84398e12			1.62328			0.811642	−	0.584155i	$-0.198574\pi$
$281$	2.84398e12			1.62328			0.811642	+	0.584155i	$0.198574\pi$
$282$	−1.15744e11	+	1.09500e9i	−0.0649013	+	0.000614000i
$283$		−	9.25646e10i		−	0.0509932i	−0.999675	−	0.0254966i	$-0.991883\pi$
$283$		−	9.25646e10i		−	0.0509932i	0.999675	−	0.0254966i	$-0.00811671\pi$
$284$	4.96772e10	+	2.62527e12i	0.0268884	+	1.42096i
$285$		0			0
$286$	−4.29275e9	−	4.53755e11i	−0.00224339	−	0.237132i
$287$		−	8.94093e11i		−	0.459170i
$288$	−2.75417e12	+	1.30373e11i	−1.39004	+	0.0657997i
$289$	2.37477e12			1.17796
$290$		0			0
$291$		−	2.14868e12i		−	1.02969i
$292$	−2.15791e12	+	4.08336e10i	−1.01653	+	0.0192355i
$293$	2.24927e12			1.04161			0.520803	−	0.853677i	$-0.325633\pi$
$293$	2.24927e12			1.04161			0.520803	+	0.853677i	$0.325633\pi$
$294$	−1.17272e10	−	1.23959e12i	−0.00533896	−	0.564342i
$295$		0			0
$296$	−1.59709e12	+	4.53387e10i	−0.702863	+	0.0199531i
$297$	−1.42396e12			−0.616192
$298$	−1.61633e12	+	1.52913e10i	−0.687780	+	0.00650675i
$299$		−	9.11971e11i		−	0.381615i
$300$		0			0
$301$	−1.46843e12			−0.594321
$302$	1.66861e10	+	1.76376e12i	0.00664232	+	0.702110i
$303$			6.44158e12i			2.52220i
$304$	−1.24537e11	−	3.28950e12i	−0.0479658	−	1.26696i
$305$		0			0
$306$	−5.50969e12	+	5.21245e10i	−2.05362	+	0.0194283i
$307$		−	2.31537e11i		−	0.0849040i	−0.999099	−	0.0424520i	$-0.986483\pi$
$307$		−	2.31537e11i		−	0.0849040i	0.999099	−	0.0424520i	$-0.0135170\pi$
$308$	−3.29430e12	+	6.23371e10i	−1.18853	+	0.0224902i
$309$	−2.80105e12			−0.994324
$310$		0			0
$311$			3.78881e12i			1.30227i	0.758962	+	0.651135i	$0.225707\pi$
$311$			3.78881e12i			1.30227i	−0.758962	+	0.651135i	$0.774293\pi$
$312$	3.02386e10	+	1.06518e12i	0.0102279	+	0.360287i
$313$	2.24116e12			0.746022			0.373011	−	0.927827i	$-0.378325\pi$
$313$	2.24116e12			0.746022			0.373011	+	0.927827i	$0.378325\pi$
$314$	2.86742e12	−	2.71273e10i	0.939384	−	0.00888705i
$315$		0			0
$316$	−6.67939e10	−	3.52983e12i	−0.0211983	−	1.12026i
$317$	1.42968e12			0.446623			0.223312	−	0.974747i	$-0.428313\pi$
$317$	1.42968e12			0.446623			0.223312	+	0.974747i	$0.428313\pi$
$318$	1.44732e10	+	1.52986e12i	0.00445071	+	0.470452i
$319$			1.85529e12i			0.561641i
$320$		0			0
$321$	−2.73124e12			−0.801372
$322$	−6.62158e12	+	6.26436e10i	−1.91286	+	0.0180966i
$323$		−	6.57826e12i		−	1.87111i
$324$	−1.62446e12	+	3.07392e10i	−0.454971	+	0.00860929i
$325$		0			0
$326$	−3.52492e10	−	3.72593e12i	−0.00957329	−	1.01192i
$327$			3.41737e12i			0.914015i
$328$	1.49146e12	−	4.23400e10i	0.392864	−	0.0111527i
$329$	1.89001e11			0.0490326
$330$		0			0
$331$			6.11524e12i			1.53912i	0.638572	+	0.769562i	$0.279526\pi$
$331$			6.11524e12i			1.53912i	−0.638572	+	0.769562i	$0.720474\pi$
$332$	−1.37521e11	−	7.26748e12i	−0.0340939	−	1.80175i
$333$	4.00664e12			0.978497
$334$	2.82464e10	+	2.98571e12i	0.00679564	+	0.718316i
$335$		0			0
$336$	7.73189e12	−	2.92722e11i	1.80547	−	0.0683531i
$337$	−9.97821e11			−0.229564			−0.114782	−	0.993391i	$-0.536617\pi$
$337$	−9.97821e11			−0.229564			−0.114782	+	0.993391i	$0.536617\pi$
$338$	−4.17165e12	+	3.94660e10i	−0.945638	+	0.00894622i
$339$			2.84766e12i			0.636047i
$340$		0			0
$341$	1.99337e12			0.432330
$342$	7.80931e10	+	8.25464e12i	0.0166910	+	1.76428i
$343$		−	3.52244e12i		−	0.741948i
$344$	−6.95380e10	−	2.44953e12i	−0.0144354	−	0.508499i
$345$		0			0
$346$	−2.93511e12	+	2.77677e10i	−0.591895	+	0.00559963i
$347$		−	5.29192e12i		−	1.05188i	−0.850522	−	0.525940i	$-0.823714\pi$
$347$		−	5.29192e12i		−	1.05188i	0.850522	−	0.525940i	$-0.176286\pi$
$348$	−8.24279e10	−	4.35603e12i	−0.0161502	−	0.853482i
$349$	−3.21483e11			−0.0620912			−0.0310456	−	0.999518i	$-0.509884\pi$
$349$	−3.21483e11			−0.0620912			−0.0310456	+	0.999518i	$0.509884\pi$
$350$		0			0
$351$		−	7.51969e11i		−	0.141145i
$352$	−2.59988e11	−	5.49235e12i	−0.0481106	−	1.01635i
$353$	6.41611e12			1.17057			0.585286	−	0.810827i	$-0.300982\pi$
$353$	6.41611e12			1.17057			0.585286	+	0.810827i	$0.300982\pi$
$354$	−1.42230e13	+	1.34557e11i	−2.55844	+	0.0242041i
$355$		0			0
$356$	3.47588e12	−	6.57731e10i	0.607876	−	0.0115027i
$357$	1.54620e13			2.66640
$358$	3.26582e10	+	3.45205e12i	0.00555363	+	0.587032i
$359$			4.19883e12i			0.704136i	0.935975	+	0.352068i	$0.114521\pi$
$359$			4.19883e12i			0.704136i	−0.935975	+	0.352068i	$0.885479\pi$
$360$		0			0
$361$	−3.72452e12			−0.607483
$362$	1.09841e13	−	1.03915e11i	1.76694	−	0.0167161i
$363$		−	3.43973e11i		−	0.0545747i
$364$	−3.29191e10	−	1.73966e12i	−0.00515159	−	0.272244i
$365$		0			0
$366$	3.38332e10	+	3.57625e12i	0.00515155	+	0.544532i
$367$		−	2.48261e12i		−	0.372888i	−0.982466	−	0.186444i	$-0.940304\pi$
$367$		−	2.48261e12i		−	0.372888i	0.982466	−	0.186444i	$-0.0596963\pi$
$368$	−4.18064e11	−	1.10427e13i	−0.0619446	−	1.63619i
$369$	−3.74165e12			−0.546929
$370$		0			0
$371$		−	2.49814e12i		−	0.355424i
$372$	−4.68021e12	+	8.85624e10i	−0.656978	+	0.0124318i
$373$	−8.44089e12			−1.16908			−0.584539	−	0.811365i	$-0.698725\pi$
$373$	−8.44089e12			−1.16908			−0.584539	+	0.811365i	$0.698725\pi$
$374$	−1.03946e11	−	1.09874e13i	−0.0142053	−	1.50154i
$375$		0			0
$376$	8.95020e9	+	3.15278e11i	0.00119095	+	0.0419521i
$377$	−9.79747e11			−0.128649
$378$	−5.45985e12	+	5.16530e10i	−0.707492	+	0.00669324i
$379$		−	5.11317e12i		−	0.653874i	−0.945046	−	0.326937i	$-0.893984\pi$
$379$		−	5.11317e12i		−	0.653874i	0.945046	−	0.326937i	$-0.106016\pi$
$380$		0			0
$381$	−2.34676e12			−0.292310
$382$	7.07816e9	+	7.48180e11i	0.000870169	+	0.0919791i
$383$			8.87564e12i			1.07698i	0.842633	+	0.538488i	$0.181004\pi$
$383$			8.87564e12i			1.07698i	−0.842633	+	0.538488i	$0.818996\pi$
$384$	8.54442e11	+	1.28839e13i	0.102336	+	1.54309i
$385$		0			0
$386$	−9.53472e12	+	9.02033e10i	−1.11268	+	0.0105266i
$387$			6.14517e12i			0.707911i
$388$	−5.85388e12	+	1.10771e11i	−0.665710	+	0.0125971i
$389$	−1.08604e13			−1.21927			−0.609635	−	0.792683i	$-0.708684\pi$
$389$	−1.08604e13			−1.21927			−0.609635	+	0.792683i	$0.708684\pi$
$390$		0			0
$391$		−	2.20828e13i		−	2.41641i
$392$	−3.37655e12	+	9.58545e10i	−0.364790	+	0.0103558i
$393$	2.15005e13			2.29343
$394$	−1.46095e13	+	1.38213e11i	−1.53870	+	0.0145569i
$395$		0			0
$396$	2.60871e11	+	1.37861e13i	0.0267886	+	1.41569i
$397$	4.51332e12			0.457660			0.228830	−	0.973466i	$-0.426510\pi$
$397$	4.51332e12			0.457660			0.228830	+	0.973466i	$0.426510\pi$
$398$	4.89116e10	+	5.17008e12i	0.00489775	+	0.517705i
$399$		−	2.31653e13i		−	2.29073i
$400$		0			0
$401$	−4.32327e12			−0.416956			−0.208478	−	0.978027i	$-0.566851\pi$
$401$	−4.32327e12			−0.416956			−0.208478	+	0.978027i	$0.566851\pi$
$402$	−8.60585e12	+	8.14158e10i	−0.819717	+	0.00775494i
$403$			1.05266e12i			0.0990294i
$404$	1.75495e13	−	3.32084e11i	1.63064	−	0.0308561i
$405$		0			0
$406$	6.72991e10	+	7.11369e12i	0.00610070	+	0.644859i
$407$			7.99003e12i			0.715446i
$408$	7.32209e11	+	2.57926e13i	0.0647641	+	2.28136i
$409$	−6.11557e11			−0.0534343			−0.0267172	−	0.999643i	$-0.508505\pi$
$409$	−6.11557e11			−0.0534343			−0.0267172	+	0.999643i	$0.508505\pi$
$410$		0			0
$411$			4.67564e12i			0.398687i
$412$	1.44403e11	+	7.63119e12i	0.0121644	+	0.642845i
$413$	2.32250e13			1.93289
$414$	2.62154e11	+	2.77103e13i	0.0215553	+	2.27845i
$415$		0			0
$416$	2.90041e12	−	1.37295e11i	0.232806	−	0.0110202i
$417$	−1.45950e12			−0.115750
$418$	−1.64614e13	+	1.55733e11i	−1.28999	+	0.0122039i
$419$			1.05743e13i			0.818808i	0.912353	+	0.409404i	$0.134263\pi$
$419$			1.05743e13i			0.818808i	−0.912353	+	0.409404i	$0.865737\pi$
$420$		0			0
$421$	6.20493e12			0.469166			0.234583	−	0.972096i	$-0.424628\pi$
$421$	6.20493e12			0.469166			0.234583	+	0.972096i	$0.424628\pi$
$422$	5.50219e10	+	5.81595e12i	0.00411124	+	0.434569i
$423$		−	7.90942e11i		−	0.0584040i
$424$	4.16720e12	−	1.18300e11i	0.304099	−	0.00863287i
$425$		0			0
$426$	−3.08341e13	+	2.91707e11i	−2.19778	+	0.0207921i
$427$		−	5.83975e12i		−	0.411391i
$428$	1.40804e11	+	7.44100e12i	0.00980383	+	0.518098i
$429$	5.32894e12			0.366737
$430$		0			0
$431$		−	3.75598e12i		−	0.252544i	−0.991996	−	0.126272i	$-0.959699\pi$
$431$		−	3.75598e12i		−	0.252544i	0.991996	−	0.126272i	$-0.0403011\pi$
$432$	−3.44716e11	−	9.10526e12i	−0.0229109	−	0.605165i
$433$	−2.25078e13			−1.47874			−0.739372	−	0.673297i	$-0.764878\pi$
$433$	−2.25078e13			−1.47874			−0.739372	+	0.673297i	$0.764878\pi$
$434$	7.64311e12	−	7.23078e10i	0.496388	−	0.00469609i
$435$		0			0
$436$	9.31030e12	−	1.76176e11i	0.590924	−	0.0111819i
$437$	−3.30846e13			−2.07596
$438$	−2.39777e11	−	2.53450e13i	−0.0148743	−	1.57225i
$439$			1.93911e13i			1.18927i	0.803997	+	0.594633i	$0.202703\pi$
$439$			1.93911e13i			1.18927i	−0.803997	+	0.594633i	$0.797297\pi$
$440$		0			0
$441$	8.47080e12			0.507845
$442$	5.80225e12	−	5.48923e10i	0.343942	−	0.00325387i
$443$		−	3.53441e12i		−	0.207157i	−0.994621	−	0.103578i	$-0.966971\pi$
$443$		−	3.53441e12i		−	0.207157i	0.994621	−	0.103578i	$-0.0330292\pi$
$444$	−3.54985e11	−	1.87597e13i	−0.0205729	−	1.08721i
$445$		0			0
$446$	3.36357e10	+	3.55537e12i	0.00190601	+	0.201470i
$447$		−	1.89824e13i		−	1.06369i
$448$	−1.19610e12	−	2.10497e13i	−0.0662790	−	1.16642i
$449$	3.48899e12			0.191192			0.0955958	−	0.995420i	$-0.469524\pi$
$449$	3.48899e12			0.191192			0.0955958	+	0.995420i	$0.469524\pi$
$450$		0			0
$451$		−	7.46158e12i		−	0.399897i
$452$	7.75818e12	−	1.46806e11i	0.411214	−	0.00778128i
$453$	−2.07138e13			−1.08585
$454$	−2.72495e11	−	2.88034e13i	−0.0141279	−	1.49336i
$455$		0			0
$456$	3.86426e13	−	1.09700e12i	1.95994	−	0.0556394i
$457$	3.56649e12			0.178921			0.0894603	−	0.995990i	$-0.471486\pi$
$457$	3.56649e12			0.178921			0.0894603	+	0.995990i	$0.471486\pi$
$458$	1.74020e13	−	1.64632e11i	0.863519	−	0.00816934i
$459$		−	1.82085e13i		−	0.893738i
$460$		0			0
$461$	2.11360e13			1.01512			0.507562	−	0.861615i	$-0.330547\pi$
$461$	2.11360e13			1.01512			0.507562	+	0.861615i	$0.330547\pi$
$462$	−3.66047e11	−	3.86920e13i	−0.0173911	−	1.83828i
$463$			2.00573e13i			0.942686i	0.881950	+	0.471343i	$0.156231\pi$
$463$			2.00573e13i			0.942686i	−0.881950	+	0.471343i	$0.843769\pi$
$464$	−1.18633e13	+	4.49134e11i	−0.551591	+	0.0208827i
$465$		0			0
$466$	2.03114e13	−	1.92156e11i	0.924295	−	0.00874431i
$467$			1.63231e13i			0.734884i	0.930046	+	0.367442i	$0.119766\pi$
$467$			1.63231e13i			0.734884i	−0.930046	+	0.367442i	$0.880234\pi$
$468$	−7.28022e12	+	1.37762e11i	−0.324277	+	0.00613620i
$469$	1.40527e13			0.619292
$470$		0			0
$471$			3.36753e13i			1.45280i
$472$	1.09983e12	+	3.87423e13i	0.0469478	+	1.65377i
$473$	−1.22547e13			−0.517602
$474$	4.14584e13	−	3.92217e11i	1.73269	−	0.0163921i
$475$		0			0
$476$	−7.97117e11	−	4.21249e13i	−0.0326203	−	1.72387i
$477$	−1.04543e13			−0.423354
$478$	2.79802e10	+	2.95758e12i	0.00112127	+	0.118521i
$479$			1.92868e13i			0.764863i	0.923984	+	0.382431i	$0.124913\pi$
$479$			1.92868e13i			0.764863i	−0.923984	+	0.382431i	$0.875087\pi$
$480$		0			0
$481$	−4.21940e12			−0.163880
$482$	−2.89905e13	+	2.74265e11i	−1.11435	+	0.0105423i
$483$		−	7.77645e13i		−	2.95833i
$484$	−9.37122e11	+	1.77329e10i	−0.0352833	+	0.000667656i
$485$		0			0
$486$	−3.35834e11	−	3.54985e13i	−0.0123864	−	1.30927i
$487$			1.78624e13i			0.652071i	0.945358	+	0.326035i	$0.105713\pi$
$487$			1.78624e13i			0.652071i	−0.945358	+	0.326035i	$0.894287\pi$
$488$	9.74143e12	−	2.76543e11i	0.351984	−	0.00999225i
$489$	4.37577e13			1.56498
$490$		0			0
$491$			3.49899e13i			1.22613i	0.790034	+	0.613063i	$0.210063\pi$
$491$			3.49899e13i			1.22613i	−0.790034	+	0.613063i	$0.789937\pi$
$492$	3.31507e11	+	1.75190e13i	0.0114992	+	0.607692i
$493$	−2.37240e13			−0.814616
$494$	−8.22399e10	−	8.69296e12i	−0.00279543	−	0.295483i
$495$		0			0
$496$	4.82560e11	+	1.27462e13i	0.0160747	+	0.424594i
$497$	5.03498e13			1.66041
$498$	8.53577e13	−	8.07528e11i	2.78674	−	0.0263640i
$499$			2.40650e13i			0.777828i	0.921274	+	0.388914i	$0.127150\pi$
$499$			2.40650e13i			0.777828i	−0.921274	+	0.388914i	$0.872850\pi$
$500$		0			0
$501$	−3.50645e13			−1.11091
$502$	−3.44139e11	−	3.63764e13i	−0.0107948	−	1.14104i
$503$			5.61224e13i			1.74299i	0.490401	+	0.871497i	$0.336850\pi$
$503$			5.61224e13i			1.74299i	−0.490401	+	0.871497i	$0.663150\pi$
$504$	1.50033e12	+	5.28503e13i	0.0461355	+	1.62516i
$505$		0			0
$506$	−5.52598e13	+	5.22787e11i	−1.66593	+	0.0157606i
$507$		−	4.89923e13i		−	1.46247i
$508$	1.20983e11	+	6.39352e12i	0.00357606	+	0.188982i
$509$	5.17336e13			1.51420			0.757100	−	0.653298i	$-0.226615\pi$
$509$	5.17336e13			1.51420			0.757100	+	0.653298i	$0.226615\pi$
$510$		0			0
$511$			4.13864e13i			1.18783i
$512$	3.50569e13	−	2.99205e12i	0.996378	−	0.0850393i
$513$	−2.72800e13			−0.767817
$514$	−2.23556e13	+	2.11495e11i	−0.623118	+	0.00589502i
$515$		0			0
$516$	2.87727e13	−	5.44457e11i	0.786559	−	0.0148838i
$517$	1.57729e12			0.0427031
$518$	2.89832e11	+	3.06359e13i	0.00777136	+	0.821452i
$519$		−	3.44703e13i		−	0.915394i
$520$		0			0
$521$	−4.68852e13			−1.22137			−0.610684	−	0.791874i	$-0.709106\pi$
$521$	−4.68852e13			−1.22137			−0.610684	+	0.791874i	$0.709106\pi$
$522$	2.97697e13	−	2.81637e11i	0.768108	−	0.00726670i
$523$		−	2.65731e13i		−	0.679100i	−0.940588	−	0.339550i	$-0.889725\pi$
$523$		−	2.65731e13i		−	0.679100i	0.940588	−	0.339550i	$-0.110275\pi$
$524$	−1.10842e12	−	5.85760e13i	−0.0280574	−	1.48273i
$525$		0			0
$526$	1.49762e10	+	1.58302e12i	0.000371941	+	0.0393151i
$527$			2.54896e13i			0.627061i
$528$	6.45258e13	−	2.44288e12i	1.57240	−	0.0595296i
$529$	−6.96365e13			−1.68097
$530$		0			0
$531$		−	9.71933e13i		−	2.30231i
$532$	−6.31117e13	+	1.19425e12i	−1.48099	+	0.0280243i
$533$	3.94033e12			0.0916002
$534$	3.86223e11	+	4.08247e13i	0.00889471	+	0.940193i
$535$		0			0
$536$	6.65469e11	+	2.34416e13i	0.0150419	+	0.529864i
$537$	−4.05412e13			−0.907874
$538$	−5.77218e13	+	5.46078e11i	−1.28064	+	0.0121156i
$539$			1.68924e13i			0.371320i
$540$		0			0
$541$	6.66188e13			1.43751			0.718755	−	0.695264i	$-0.244712\pi$
$541$	6.66188e13			1.43751			0.718755	+	0.695264i	$0.244712\pi$
$542$	6.15349e11	+	6.50440e13i	0.0131560	+	1.39063i
$543$			1.28998e14i			2.73265i
$544$	7.02318e13	−	3.32453e12i	1.47414	−	0.0697807i
$545$		0			0
$546$	2.04326e13	−	1.93303e11i	0.421076	−	0.00398359i
$547$			2.28605e13i			0.466819i	0.972378	+	0.233410i	$0.0749883\pi$
$547$			2.28605e13i			0.466819i	−0.972378	+	0.233410i	$0.925012\pi$
$548$	1.27384e13	−	2.41044e11i	0.257757	−	0.00487746i
$549$	−2.44385e13			−0.490018
$550$		0			0
$551$			3.55434e13i			0.699844i
$552$	1.29721e14	−	3.68256e12i	2.53113	−	0.0718546i
$553$	−6.76983e13			−1.30904
$554$	−3.16130e13	+	2.99076e11i	−0.605784	+	0.00573103i
$555$		0			0
$556$	7.52417e10	+	3.97626e12i	0.00141607	+	0.0748343i
$557$	−1.22463e12			−0.0228417			−0.0114208	−	0.999935i	$-0.503635\pi$
$557$	−1.22463e12			−0.0228417			−0.0114208	+	0.999935i	$0.503635\pi$
$558$	−3.02597e11	−	3.19853e13i	−0.00559363	−	0.591261i
$559$		−	6.47148e12i		−	0.118562i
$560$		0			0
$561$	1.29037e14			2.32220
$562$	9.10032e13	−	8.60937e11i	1.62321	−	0.0153564i
$563$		−	7.79602e13i		−	1.37826i	−0.724638	−	0.689130i	$-0.757993\pi$
$563$		−	7.79602e13i		−	1.37826i	0.724638	−	0.689130i	$-0.242007\pi$
$564$	−3.70332e12	+	7.00768e10i	−0.0648926	+	0.00122794i
$565$		0			0
$566$	−2.80214e10	−	2.96193e12i	−0.000482401	−	0.0509910i
$567$			3.11554e13i			0.531640i
$568$	2.38433e12	+	8.39897e13i	0.0403296	+	1.42064i
$569$	−7.32445e13			−1.22804			−0.614021	−	0.789290i	$-0.710449\pi$
$569$	−7.32445e13			−1.22804			−0.614021	+	0.789290i	$0.710449\pi$
$570$		0			0
$571$			2.41704e13i			0.398202i	0.979979	+	0.199101i	$0.0638021\pi$
$571$			2.41704e13i			0.398202i	−0.979979	+	0.199101i	$0.936198\pi$
$572$	−2.74724e11	−	1.45182e13i	−0.00448659	−	0.237101i
$573$	−8.78670e12			−0.142250
$574$	−2.70663e11	−	2.86097e13i	−0.00434379	−	0.459149i
$575$		0			0
$576$	−8.80899e13	+	5.00548e12i	−1.38936	+	0.0789466i
$577$	−8.99224e13			−1.40601			−0.703006	−	0.711184i	$-0.748159\pi$
$577$	−8.99224e13			−1.40601			−0.703006	+	0.711184i	$0.748159\pi$
$578$	7.59892e13	−	7.18897e11i	1.17791	−	0.0111436i
$579$		−	1.11977e14i		−	1.72082i
$580$		0			0
$581$	−1.39382e14			−2.10537
$582$	−6.50455e11	−	6.87547e13i	−0.00974098	−	1.02965i
$583$		−	2.08480e13i		−	0.309543i
$584$	−6.90377e13	+	1.95987e12i	−1.01630	+	0.0288511i
$585$		0			0
$586$	7.19734e13	−	6.80906e11i	1.04156	−	0.00985369i
$587$		−	6.12391e13i		−	0.878695i	−0.898317	−	0.439347i	$-0.855210\pi$
$587$		−	6.12391e13i		−	0.878695i	0.898317	−	0.439347i	$-0.144790\pi$
$588$	−7.50506e11	−	3.96616e13i	−0.0106774	−	0.564266i
$589$	3.81886e13			0.538713
$590$		0			0
$591$		−	1.71576e14i		−	2.37968i
$592$	−5.10909e13	+	1.93425e12i	−0.702643	+	0.0266014i
$593$	−6.82796e13			−0.931145			−0.465573	−	0.885010i	$-0.654152\pi$
$593$	−6.82796e13			−0.931145			−0.465573	+	0.885010i	$0.654152\pi$
$594$	−4.55647e13	+	4.31065e11i	−0.616164	+	0.00582923i
$595$		0			0
$596$	−5.17157e13	+	9.78602e11i	−0.687688	+	0.0130129i
$597$	−6.07180e13			−0.800655
$598$	−2.76074e11	−	2.91818e13i	−0.00361011	−	0.381598i
$599$			1.28055e14i			1.66059i	0.557320	+	0.830297i	$0.311829\pi$
$599$			1.28055e14i			1.66059i	−0.557320	+	0.830297i	$0.688171\pi$
$600$		0			0
$601$	2.79462e13			0.356410			0.178205	−	0.983993i	$-0.442971\pi$
$601$	2.79462e13			0.356410			0.178205	+	0.983993i	$0.442971\pi$
$602$	−4.69877e13	+	4.44528e11i	−0.594295	+	0.00562233i
$603$		−	5.88084e13i		−	0.737654i
$604$	1.06786e12	+	5.64328e13i	0.0132840	+	0.702015i
$605$		0			0
$606$	1.95001e12	+	2.06121e14i	0.0238602	+	2.52209i
$607$			3.52260e13i			0.427484i	0.976890	+	0.213742i	$0.0685653\pi$
$607$			3.52260e13i			0.427484i	−0.976890	+	0.213742i	$0.931435\pi$
$608$	−4.98082e12	−	1.05222e14i	−0.0599492	−	1.26645i
$609$	−8.35439e13			−0.997305
$610$		0			0
$611$			8.32941e11i			0.00978156i
$612$	−1.76286e14	+	3.33582e12i	−2.05334	+	0.0388548i
$613$	1.16497e14			1.34590			0.672950	−	0.739688i	$-0.265027\pi$
$613$	1.16497e14			1.34590			0.672950	+	0.739688i	$0.265027\pi$
$614$	−7.00915e10	−	7.40885e12i	−0.000803200	−	0.0849002i
$615$		0			0
$616$	−1.05394e14	+	2.99196e12i	−1.18826	+	0.0337328i
$617$	6.43868e13			0.720064			0.360032	−	0.932940i	$-0.382766\pi$
$617$	6.43868e13			0.720064			0.360032	+	0.932940i	$0.382766\pi$
$618$	−8.96295e13	+	8.47941e11i	−0.994279	+	0.00940639i
$619$			9.70473e13i			1.06790i	0.845516	+	0.533950i	$0.179293\pi$
$619$			9.70473e13i			1.06790i	−0.845516	+	0.533950i	$0.820707\pi$
$620$		0			0
$621$	−9.15774e13			−0.991586
$622$	1.14696e12	+	1.21237e14i	0.0123196	+	1.30221i
$623$		−	6.66636e13i		−	0.710311i
$624$	1.29004e12	+	3.40750e13i	0.0136358	+	0.360174i
$625$		0			0
$626$	7.17140e13	−	6.78451e11i	0.745989	−	0.00705744i
$627$		−	1.93324e14i		−	1.99502i
$628$	9.17451e13	−	1.73607e12i	0.939257	−	0.0177733i
$629$	−1.02170e14			−1.03770
$630$		0			0
$631$		−	3.20145e13i		−	0.320037i	−0.987114	−	0.160019i	$-0.948845\pi$
$631$		−	3.20145e13i		−	0.320037i	0.987114	−	0.160019i	$-0.0511554\pi$
$632$	−3.20587e12	−	1.12929e14i	−0.0317951	−	1.12001i
$633$	−6.83031e13			−0.672082
$634$	4.57476e13	−	4.32796e11i	0.446603	−	0.00422510i
$635$		0			0
$636$	9.26245e11	+	4.89488e13i	0.00890103	+	0.470388i
$637$	−8.92060e12			−0.0850544
$638$	5.61639e11	+	5.93667e13i	0.00531317	+	0.561616i
$639$		−	2.10706e14i		−	1.97776i
$640$		0			0
$641$	−1.25436e14			−1.15913			−0.579566	−	0.814926i	$-0.696778\pi$
$641$	−1.25436e14			−1.15913			−0.579566	+	0.814926i	$0.696778\pi$
$642$	−8.73957e13	+	8.26808e11i	−0.801336	+	0.00758105i
$643$			6.91453e13i			0.629083i	0.949244	+	0.314542i	$0.101851\pi$
$643$			6.91453e13i			0.629083i	−0.949244	+	0.314542i	$0.898149\pi$
$644$	−2.11862e14	+	4.00901e12i	−1.91260	+	0.0361916i
$645$		0			0
$646$	−1.99139e12	−	2.10495e14i	−0.0177008	−	1.87102i
$647$			1.38085e14i			1.21794i	0.793193	+	0.608971i	$0.208417\pi$
$647$			1.38085e14i			1.21794i	−0.793193	+	0.608971i	$0.791583\pi$
$648$	−5.19711e13	+	1.47537e12i	−0.454869	+	0.0129130i
$649$	1.93823e14			1.68338
$650$		0			0
$651$			8.97615e13i			0.767688i
$652$	−2.25585e12	−	1.19214e14i	−0.0191457	−	1.01179i
$653$	−1.70786e14			−1.43842			−0.719211	−	0.694792i	$-0.755497\pi$
$653$	−1.70786e14			−1.43842			−0.719211	+	0.694792i	$0.755497\pi$
$654$	1.03452e12	+	1.09351e14i	0.00864666	+	0.913974i
$655$		0			0
$656$	4.77118e13	−	1.80632e12i	0.392741	−	0.0148688i
$657$	1.73196e14			1.41485
$658$	6.04777e12	−	5.72150e10i	0.0490304	−	0.000463853i
$659$		−	1.58743e14i		−	1.27722i	−0.769530	−	0.638611i	$-0.779509\pi$
$659$		−	1.58743e14i		−	1.27722i	0.769530	−	0.638611i	$-0.220491\pi$
$660$		0			0
$661$	−4.27414e13			−0.338720			−0.169360	−	0.985554i	$-0.554170\pi$
$661$	−4.27414e13			−0.338720			−0.169360	+	0.985554i	$0.554170\pi$
$662$	1.85122e12	+	1.95679e14i	0.0145603	+	1.53906i
$663$			6.81423e13i			0.531923i
$664$	−6.60049e12	−	2.32507e14i	−0.0511371	−	1.80134i
$665$		0			0
$666$	1.28207e14	−	1.21290e12i	0.978453	−	0.00925667i
$667$			1.19317e14i			0.903802i
$668$	1.80769e12	+	9.55299e13i	0.0135907	+	0.718219i
$669$	−4.17547e13			−0.311584
$670$		0			0
$671$		−	4.87351e13i		−	0.358286i
$672$	2.47321e14	−	1.17073e13i	1.80474	−	0.0854300i
$673$	1.88489e14			1.36525			0.682623	−	0.730770i	$-0.260839\pi$
$673$	1.88489e14			1.36525			0.682623	+	0.730770i	$0.260839\pi$
$674$	−3.19289e13	+	3.02063e11i	−0.229553	+	0.00217169i
$675$		0			0
$676$	−1.33475e14	+	2.52571e12i	−0.945511	+	0.0178916i
$677$	−4.14436e13			−0.291417			−0.145708	−	0.989328i	$-0.546546\pi$
$677$	−4.14436e13			−0.291417			−0.145708	+	0.989328i	$0.546546\pi$
$678$	8.62052e11	+	9.11210e13i	0.00601707	+	0.636019i
$679$			1.12271e14i			0.777892i
$680$		0			0
$681$	3.38270e14			2.30955
$682$	6.37849e13	−	6.03438e11i	0.432311	−	0.00408988i
$683$			1.25711e14i			0.845801i	0.906176	+	0.422901i	$0.138988\pi$
$683$			1.25711e14i			0.845801i	−0.906176	+	0.422901i	$0.861012\pi$
$684$	4.99774e12	+	2.64113e14i	0.0333805	+	1.76404i
$685$		0			0
$686$	−1.06632e12	−	1.12713e14i	−0.00701889	−	0.741915i
$687$			2.04371e14i			1.33547i
$688$	−2.96664e12	−	7.83603e13i	−0.0192452	−	0.508340i
$689$	1.10095e13			0.0709038
$690$		0			0
$691$			2.51924e14i			1.59911i	0.600592	+	0.799556i	$0.294932\pi$
$691$			2.51924e14i			1.59911i	−0.600592	+	0.799556i	$0.705068\pi$
$692$	−9.39110e13	+	1.77705e12i	−0.591815	+	0.0111988i
$693$	2.64403e14			1.65425
$694$	−1.60199e12	−	1.69334e14i	−0.00995087	−	1.05183i
$695$		0			0
$696$	−3.95624e12	−	1.39362e14i	−0.0242235	−	0.853291i
$697$	9.54128e13			0.580019
$698$	−1.02870e13	+	9.73202e10i	−0.0620885	+	0.000587389i
$699$			2.38539e14i			1.42947i
$700$		0			0
$701$	−9.22547e13			−0.545002			−0.272501	−	0.962155i	$-0.587851\pi$
$701$	−9.22547e13			−0.545002			−0.272501	+	0.962155i	$0.587851\pi$
$702$	−2.27638e11	−	2.40619e13i	−0.00133524	−	0.141138i
$703$			1.53072e14i			0.891495i
$704$	−9.98192e12	−	1.75669e14i	−0.0577232	−	1.01585i
$705$		0			0
$706$	2.05306e14	−	1.94230e12i	1.17052	−	0.0110737i
$707$		−	3.36580e14i		−	1.90542i
$708$	−4.55075e14	+	8.61125e12i	−2.55809	+	0.0484061i
$709$	−5.98699e13			−0.334177			−0.167089	−	0.985942i	$-0.553437\pi$
$709$	−5.98699e13			−0.334177			−0.167089	+	0.985942i	$0.553437\pi$
$710$		0			0
$711$			2.83307e14i			1.55923i
$712$	1.11203e14	−	3.15687e12i	0.607740	−	0.0172527i
$713$	1.28197e14			0.695713
$714$	4.94763e14	−	4.68071e12i	2.66628	−	0.0252244i
$715$		0			0
$716$	2.09003e12	+	1.10451e14i	0.0111068	+	0.586954i
$717$	−3.47341e13			−0.183299
$718$	1.27108e12	+	1.34357e14i	0.00666119	+	0.704104i
$719$			2.79087e14i			1.45243i	0.687469	+	0.726214i	$0.258722\pi$
$719$			2.79087e14i			1.45243i	−0.687469	+	0.726214i	$0.741278\pi$
$720$		0			0
$721$	1.46358e14			0.751173
$722$	−1.19179e14	+	1.12750e12i	−0.607456	+	0.00574684i
$723$		−	3.40467e14i		−	1.72339i
$724$	3.51443e14	−	6.65027e12i	1.76670	−	0.0334308i
$725$		0			0
$726$	−1.04128e11	−	1.10066e13i	−0.000516281	−	0.0545722i
$727$		−	3.87651e14i		−	1.90883i	−0.298476	−	0.954417i	$-0.596478\pi$
$727$		−	3.87651e14i		−	1.90883i	0.298476	−	0.954417i	$-0.403522\pi$
$728$	−1.58000e12	−	5.56567e13i	−0.00772681	−	0.272183i
$729$	3.23207e14			1.56980
$730$		0			0
$731$		−	1.56703e14i		−	0.750741i
$732$	2.16523e12	+	1.14425e14i	0.0103026	+	0.544458i
$733$	2.86598e14			1.35442			0.677210	−	0.735790i	$-0.263189\pi$
$733$	2.86598e14			1.35442			0.677210	+	0.735790i	$0.263189\pi$
$734$	−7.51543e11	−	7.94400e13i	−0.00352755	−	0.372871i
$735$		0			0
$736$	−1.67203e13	−	3.53223e14i	−0.0774204	−	1.63553i
$737$	1.17276e14			0.539349
$738$	−1.19727e14	+	1.13268e12i	−0.546905	+	0.00517400i
$739$			1.44810e14i			0.657017i	0.944501	+	0.328508i	$0.106546\pi$
$739$			1.44810e14i			0.657017i	−0.944501	+	0.328508i	$0.893454\pi$
$740$		0			0
$741$	1.02091e14			0.456979
$742$	−7.56243e11	−	7.99368e13i	−0.00336234	−	0.355408i
$743$		−	4.64148e13i		−	0.204980i	−0.994734	−	0.102490i	$-0.967319\pi$
$743$		−	4.64148e13i		−	0.204980i	0.994734	−	0.102490i	$-0.0326810\pi$
$744$	−1.49733e14	+	4.25068e12i	−0.656831	+	0.0186463i
$745$		0			0
$746$	−2.70096e14	+	2.55525e12i	−1.16903	+	0.0110596i
$747$			5.83295e14i			2.50776i
$748$	−6.65227e12	−	3.51550e14i	−0.0284094	−	1.50134i
$749$	1.42710e14			0.605405
$750$		0			0
$751$			1.55194e14i			0.649642i	0.945775	+	0.324821i	$0.105304\pi$
$751$			1.55194e14i			0.649642i	−0.945775	+	0.324821i	$0.894696\pi$
$752$	3.81835e11	+	1.00857e13i	0.00158777	+	0.0419390i
$753$	4.27208e14			1.76467
$754$	−3.13505e13	+	2.96592e11i	−0.128643	+	0.00121703i
$755$		0			0
$756$	−1.74692e14	+	3.30564e12i	−0.707397	+	0.0133859i
$757$	2.71076e14			1.09046			0.545232	−	0.838285i	$-0.316442\pi$
$757$	2.71076e14			1.09046			0.545232	+	0.838285i	$0.316442\pi$
$758$	−1.54787e12	−	1.63614e14i	−0.00618571	−	0.653845i
$759$		−	6.48977e14i		−	2.57644i
$760$		0			0
$761$	−3.23023e14			−1.26564			−0.632819	−	0.774300i	$-0.718102\pi$
$761$	−3.23023e14			−1.26564			−0.632819	+	0.774300i	$0.718102\pi$
$762$	−7.50928e13	+	7.10417e11i	−0.292297	+	0.00276528i
$763$		−	1.78562e14i		−	0.690503i
$764$	4.52982e11	+	2.39385e13i	0.00174026	+	0.0919667i
$765$		0			0
$766$	2.68686e12	+	2.84008e14i	0.0101883	+	1.07693i
$767$			1.02354e14i			0.385593i
$768$	3.12412e13	+	4.12008e14i	0.116929	+	1.54205i
$769$	−1.81547e14			−0.675085			−0.337542	−	0.941310i	$-0.609596\pi$
$769$	−1.81547e14			−0.675085			−0.337542	+	0.941310i	$0.609596\pi$
$770$		0			0
$771$		−	2.62546e14i		−	0.963683i
$772$	−3.05070e14	+	5.77276e12i	−1.11253	+	0.0210522i
$773$	−7.48801e13			−0.271312			−0.135656	−	0.990756i	$-0.543314\pi$
$773$	−7.48801e13			−0.271312			−0.135656	+	0.990756i	$0.543314\pi$
$774$	1.86028e12	+	1.96637e14i	0.00669691	+	0.707880i
$775$		0			0
$776$	−1.87282e14	+	5.31663e12i	−0.665561	+	0.0188942i
$777$	−3.59792e14			−1.27042
$778$	−3.47519e14	+	3.28771e12i	−1.21921	+	0.0115344i
$779$		−	1.42948e14i		−	0.498299i
$780$		0			0
$781$	4.20190e14			1.44607
$782$	−6.68498e12	−	7.06619e14i	−0.0228595	−	2.41630i
$783$			9.83833e13i			0.334282i
$784$	−1.08016e14	+	4.08937e12i	−0.364675	+	0.0138062i
$785$		0			0
$786$	6.87984e14	−	6.50868e12i	2.29332	−	0.0216960i
$787$		−	1.15967e14i		−	0.384116i	−0.981384	−	0.192058i	$-0.938484\pi$
$787$		−	1.15967e14i		−	0.384116i	0.981384	−	0.192058i	$-0.0615161\pi$
$788$	−4.67441e14	+	8.84526e12i	−1.53849	+	0.0291125i
$789$	−1.85912e13			−0.0608026
$790$		0			0
$791$		−	1.48794e14i		−	0.480509i
$792$	1.25209e13	+	4.41058e14i	0.0401800	+	1.41537i
$793$	2.57362e13			0.0820687
$794$	1.44420e14	−	1.36628e12i	0.457640	−	0.00432951i
$795$		0			0
$796$	3.13021e12	+	1.65420e14i	0.00979507	+	0.517635i
$797$	1.98139e14			0.616140			0.308070	−	0.951364i	$-0.400317\pi$
$797$	1.98139e14			0.616140			0.308070	+	0.951364i	$0.400317\pi$
$798$	−7.01267e12	−	7.41257e14i	−0.0216705	−	2.29063i
$799$			2.01692e13i			0.0619376i
$800$		0			0
$801$	−2.78977e14			−0.846070
$802$	−1.38338e14	+	1.30875e12i	−0.416938	+	0.00394444i
$803$			3.45387e14i			1.03449i
$804$	−2.75350e14	+	5.21038e12i	−0.819607	+	0.0155092i
$805$		0			0
$806$	3.18665e11	+	3.36837e13i	0.000936827	+	0.0990249i
$807$		−	6.77891e14i		−	1.98058i
$808$	5.61458e14	−	1.59388e13i	1.63027	−	0.0462807i
$809$	3.55439e14			1.02570			0.512852	−	0.858477i	$-0.328589\pi$
$809$	3.55439e14			1.02570			0.512852	+	0.858477i	$0.328589\pi$
$810$		0			0
$811$		−	6.30302e14i		−	1.79657i	−0.439413	−	0.898285i	$-0.644813\pi$
$811$		−	6.30302e14i		−	1.79657i	0.439413	−	0.898285i	$-0.355187\pi$
$812$	4.30695e12	+	2.27607e14i	0.0122008	+	0.644772i
$813$	−7.63883e14			−2.15067
$814$	2.41877e12	+	2.55670e14i	0.00676818	+	0.715413i
$815$		0			0
$816$	3.12377e13	+	8.25105e14i	0.0863431	+	2.28065i
$817$	−2.34773e14			−0.644968
$818$	−1.95689e13	+	1.85132e11i	−0.0534319	+	0.000505494i
$819$			1.39627e14i			0.378922i
$820$		0			0
$821$	−4.02625e13			−0.107941			−0.0539703	−	0.998543i	$-0.517188\pi$
$821$	−4.02625e13			−0.107941			−0.0539703	+	0.998543i	$0.517188\pi$
$822$	1.41542e12	+	1.49614e14i	0.00377162	+	0.398669i
$823$		−	5.78856e14i		−	1.53310i	−0.642183	−	0.766551i	$-0.721971\pi$
$823$		−	5.78856e14i		−	1.53310i	0.642183	−	0.766551i	$-0.278029\pi$
$824$	6.93082e12	+	2.44143e14i	0.0182452	+	0.642701i
$825$		0			0
$826$	7.43168e14	−	7.03075e12i	1.93280	−	0.0182853i
$827$			4.26504e14i			1.10254i	0.834326	+	0.551271i	$0.185857\pi$
$827$			4.26504e14i			1.10254i	−0.834326	+	0.551271i	$0.814143\pi$
$828$	1.67771e13	+	8.86612e14i	0.0431087	+	2.27815i
$829$	−8.67325e13			−0.221518			−0.110759	−	0.993847i	$-0.535328\pi$
$829$	−8.67325e13			−0.221518			−0.110759	+	0.993847i	$0.535328\pi$
$830$		0			0
$831$		−	3.71267e14i		−	0.936874i
$832$	9.27675e13	−	5.27128e12i	0.232691	−	0.0132221i
$833$	−2.16007e14			−0.538571
$834$	−4.67018e13	+	4.41823e11i	−0.115745	+	0.00109501i
$835$		0			0
$836$	−5.26693e14	+	9.96647e12i	−1.28981	+	0.0244068i
$837$	1.05705e14			0.257318
$838$	3.20109e12	+	3.38363e14i	0.00774600	+	0.818771i
$839$			6.16766e13i			0.148358i	0.997245	+	0.0741790i	$0.0236336\pi$
$839$			6.16766e13i			0.148358i	−0.997245	+	0.0741790i	$0.976366\pi$
$840$		0			0
$841$	−2.92523e14			−0.695312
$842$	1.98549e14	−	1.87837e12i	0.469145	−	0.00443835i
$843$			1.06875e15i			2.51037i
$844$	3.52124e12	+	1.86085e14i	0.00822212	+	0.434510i
$845$		0			0
$846$	−2.39436e11	−	2.53090e13i	−0.000552507	−	0.0584014i
$847$			1.79730e13i			0.0412290i
$848$	1.33309e14	−	5.04693e12i	0.304004	−	0.0115093i
$849$	3.47853e13			0.0788600
$850$		0			0
$851$			5.13853e14i			1.15131i
$852$	−9.86560e14	+	1.86684e13i	−2.19748	+	0.0415824i
$853$	5.00937e14			1.10927			0.554636	−	0.832093i	$-0.312857\pi$
$853$	5.00937e14			1.10927			0.554636	+	0.832093i	$0.312857\pi$
$854$	−1.76782e12	−	1.86864e14i	−0.00389179	−	0.411372i
$855$		0			0
$856$	6.75808e12	+	2.38059e14i	0.0147047	+	0.517982i
$857$	−5.92500e14			−1.28169			−0.640847	−	0.767668i	$-0.721417\pi$
$857$	−5.92500e14			−1.28169			−0.640847	+	0.767668i	$0.721417\pi$
$858$	1.70518e14	−	1.61319e12i	0.366720	−	0.00346936i
$859$		−	6.13470e14i		−	1.31168i	−0.754901	−	0.655839i	$-0.772315\pi$
$859$		−	6.13470e14i		−	1.31168i	0.754901	−	0.655839i	$-0.227685\pi$
$860$		0			0
$861$	3.35995e14			0.710097
$862$	−1.13702e12	−	1.20186e14i	−0.00238909	−	0.252532i
$863$		−	6.03721e14i		−	1.26119i	−0.776110	−	0.630597i	$-0.782810\pi$
$863$		−	6.03721e14i		−	1.26119i	0.776110	−	0.630597i	$-0.217190\pi$
$864$	−1.37868e13	−	2.91251e14i	−0.0286348	−	0.604921i
$865$		0			0
$866$	−7.20217e14	+	6.81362e12i	−1.47868	+	0.0139891i
$867$			8.92425e14i			1.82170i
$868$	2.44547e14	−	4.62749e12i	0.496322	−	0.00939176i
$869$	−5.64970e14			−1.14006
$870$		0			0
$871$			6.19312e13i			0.123543i
$872$	2.97863e14	−	8.45583e12i	0.590791	−	0.0167716i
$873$	4.69838e14			0.926567
$874$	−1.05866e15	+	1.00155e13i	−2.07587	+	0.0196388i
$875$		0			0
$876$	−1.53450e13	−	8.10931e14i	−0.0297473	−	1.57204i
$877$	9.12906e14			1.75966			0.879828	−	0.475292i	$-0.157657\pi$
$877$	9.12906e14			1.75966			0.879828	+	0.475292i	$0.157657\pi$
$878$	5.87012e12	+	6.20486e14i	0.0112506	+	1.18921i
$879$			8.45263e14i			1.61082i
$880$		0			0
$881$	−5.56277e14			−1.04812			−0.524060	−	0.851681i	$-0.675583\pi$
$881$	−5.56277e14			−1.04812			−0.524060	+	0.851681i	$0.675583\pi$
$882$	2.71053e14	−	2.56430e12i	0.507822	−	0.00480426i
$883$			4.22428e14i			0.786954i	0.919334	+	0.393477i	$0.128728\pi$
$883$			4.22428e14i			0.786954i	−0.919334	+	0.393477i	$0.871272\pi$
$884$	1.85647e14	−	3.51295e12i	0.343896	−	0.00650745i
$885$		0			0
$886$	−1.06995e12	−	1.13096e14i	−0.00195972	−	0.207147i
$887$		−	4.26239e14i		−	0.776310i	−0.921594	−	0.388155i	$-0.873112\pi$
$887$		−	4.26239e14i		−	0.776310i	0.921594	−	0.388155i	$-0.126888\pi$
$888$	−1.70380e13	−	6.00177e14i	−0.0308571	−	1.08696i
$889$	1.22621e14			0.220829
$890$		0			0
$891$			2.60005e14i			0.463012i
$892$	2.15259e12	+	1.13757e14i	0.00381186	+	0.201443i
$893$	3.02176e13			0.0532111
$894$	−5.74640e12	−	6.07409e14i	−0.0100626	−	1.06364i
$895$		0			0
$896$	−4.46456e13	−	6.73199e14i	−0.0773105	−	1.16574i
$897$	3.42714e14			0.590159
$898$	1.11643e14	−	1.05620e12i	0.191183	−	0.00180869i
$899$		−	1.37724e14i		−	0.234538i
$900$		0			0
$901$	2.66587e14			0.448968
$902$	−2.25879e12	−	2.38760e14i	−0.00378306	−	0.399879i
$903$		−	5.51828e14i		−	0.919105i
$904$	2.48206e14	−	7.04616e12i	0.411122	−	0.0116711i
$905$		0			0
$906$	−6.62811e14	+	6.27054e12i	−1.08580	+	0.0102722i
$907$		−	3.83030e14i		−	0.624017i	−0.950079	−	0.312008i	$-0.898998\pi$
$907$		−	3.83030e14i		−	0.624017i	0.950079	−	0.312008i	$-0.101002\pi$
$908$	−1.74389e13	−	9.21584e14i	−0.0282546	−	1.49316i
$909$	−1.40854e15			−2.26960
$910$		0			0
$911$			1.36122e14i			0.216939i	0.994100	+	0.108470i	$0.0345950\pi$
$911$			1.36122e14i			0.216939i	−0.994100	+	0.108470i	$0.965405\pi$
$912$	1.23618e15	−	4.68004e13i	1.95932	−	0.0741781i
$913$	−1.16320e15			−1.83359
$914$	1.14123e14	−	1.07966e12i	0.178913	−	0.00169261i
$915$		0			0
$916$	5.56789e14	−	1.05360e13i	0.863403	−	0.0163379i
$917$	−1.12342e15			−1.73260
$918$	−5.51212e12	−	5.82645e14i	−0.00845484	−	0.893698i
$919$		−	1.45106e14i		−	0.221365i	−0.993856	−	0.110682i	$-0.964696\pi$
$919$		−	1.45106e14i		−	0.221365i	0.993856	−	0.110682i	$-0.0353036\pi$
$920$		0			0
$921$	8.70103e13			0.131302
$922$	6.76323e14	−	6.39836e12i	1.01508	−	0.00960316i
$923$			2.21895e14i			0.331237i
$924$	−2.34259e13	−	1.23798e15i	−0.0347806	−	1.83803i
$925$		0			0
$926$	6.07180e12	+	6.41804e14i	0.00891789	+	0.942643i
$927$		−	6.12486e14i		−	0.894742i
$928$	−3.79474e14	+	1.79629e13i	−0.551368	+	0.0260998i
$929$	−8.80611e14			−1.27264			−0.636320	−	0.771425i	$-0.719544\pi$
$929$	−8.80611e14			−1.27264			−0.636320	+	0.771425i	$0.719544\pi$
$930$		0			0
$931$			3.23623e14i			0.462691i
$932$	6.49878e14	−	1.22975e13i	0.924171	−	0.0174878i
$933$	−1.42382e15			−2.01394
$934$	4.94139e12	+	5.22317e14i	0.00695207	+	0.734851i
$935$		0			0
$936$	−2.32915e14	+	6.61207e12i	−0.324204	+	0.00920361i
$937$	4.17114e14			0.577506			0.288753	−	0.957404i	$-0.406759\pi$
$937$	4.17114e14			0.577506			0.288753	+	0.957404i	$0.406759\pi$
$938$	4.49666e14	−	4.25407e12i	0.619264	−	0.00585856i
$939$			8.42216e14i			1.15371i
$940$		0			0
$941$	−1.11785e14			−0.151507			−0.0757537	−	0.997127i	$-0.524136\pi$
$941$	−1.11785e14			−0.151507			−0.0757537	+	0.997127i	$0.524136\pi$
$942$	1.01943e13	+	1.07756e15i	0.0137436	+	1.45274i
$943$		−	4.79867e14i		−	0.643521i
$944$	4.69211e13	+	1.23936e15i	0.0625905	+	1.65325i
$945$		0			0
$946$	−3.92132e14	+	3.70977e12i	−0.517579	+	0.00489656i
$947$		−	5.17902e14i		−	0.679982i	−0.940429	−	0.339991i	$-0.889576\pi$
$947$		−	5.17902e14i		−	0.679982i	0.940429	−	0.339991i	$-0.110424\pi$
$948$	1.32649e15	−	2.51008e13i	1.73246	−	0.0327828i
$949$	−1.82393e14			−0.236961
$950$		0			0
$951$			5.37264e14i			0.690694i
$952$	−3.82588e13	−	1.34769e15i	−0.0489267	−	1.72348i
$953$	1.16104e15			1.47701			0.738504	−	0.674249i	$-0.235532\pi$
$953$	1.16104e15			1.47701			0.738504	+	0.674249i	$0.235532\pi$
$954$	−3.34523e14	+	3.16476e12i	−0.423335	+	0.00400497i
$955$		0			0
$956$	1.79065e12	+	9.46298e13i	0.00224245	+	0.118505i
$957$	−6.97208e14			−0.868566
$958$	5.83857e12	+	6.17151e14i	0.00723567	+	0.764828i
$959$		−	2.44308e14i		−	0.301193i
$960$		0			0
$961$	6.71654e14			0.819462
$962$	−1.35015e14	+	1.27731e12i	−0.163872	+	0.00155032i
$963$		−	5.97221e14i		−	0.721114i
$964$	−9.27571e14	+	1.75522e13i	−1.11420	+	0.0210836i
$965$		0			0
$966$	−2.35411e13	−	2.48835e15i	−0.0279860	−	2.95819i
$967$			1.64367e15i			1.94394i	0.235098	+	0.971972i	$0.424459\pi$
$967$			1.64367e15i			1.94394i	−0.235098	+	0.971972i	$0.575541\pi$
$968$	−2.99812e13	+	8.51116e11i	−0.0352754	+	0.00100141i
$969$	2.47207e15			2.89363
$970$		0			0
$971$			1.09038e15i			1.26323i	0.775284	+	0.631613i	$0.217607\pi$
$971$			1.09038e15i			1.26323i	−0.775284	+	0.631613i	$0.782393\pi$
$972$	−2.14924e13	−	1.13580e15i	−0.0247716	−	1.30909i
$973$	7.62604e13			0.0874450
$974$	5.40735e12	+	5.71571e14i	0.00616865	+	0.652042i
$975$		0			0
$976$	3.11628e14	−	1.17979e13i	0.351874	−	0.0133216i
$977$	−8.20193e14			−0.921389			−0.460695	−	0.887559i	$-0.652400\pi$
$977$	−8.20193e14			−0.921389			−0.460695	+	0.887559i	$0.652400\pi$
$978$	1.40018e15	−	1.32465e13i	1.56491	−	0.0148049i
$979$		−	5.56336e14i		−	0.618619i
$980$		0			0
$981$	−7.47254e14			−0.822475
$982$	1.05922e13	+	1.11963e15i	0.0115993	+	1.22607i
$983$		−	1.04826e15i		−	1.14209i	−0.820917	−	0.571047i	$-0.806537\pi$
$983$		−	1.04826e15i		−	1.14209i	0.820917	−	0.571047i	$-0.193463\pi$
$984$	1.59111e13	+	5.60482e14i	0.0172475	+	0.607556i
$985$		0			0
$986$	−7.59134e14	+	7.18180e12i	−0.814580	+	0.00770635i
$987$			7.10256e13i			0.0758279i
$988$	−5.26312e12	−	2.78138e14i	−0.00559060	−	0.295444i
$989$	−7.88119e14			−0.832934
$990$		0			0
$991$		−	3.12148e13i		−	0.0326582i	−0.999867	−	0.0163291i	$-0.994802\pi$
$991$		−	3.12148e13i		−	0.0326582i	0.999867	−	0.0163291i	$-0.00519794\pi$
$992$	1.92998e13	+	4.07715e14i	0.0200907	+	0.424423i
$993$	−2.29807e15			−2.38022
$994$	1.61112e15	−	1.52420e13i	1.66034	−	0.0157076i
$995$		0			0
$996$	2.73108e15	−	5.16795e13i	2.78636	−	0.0527256i
$997$	4.10229e14			0.416438			0.208219	−	0.978082i	$-0.433233\pi$
$997$	4.10229e14			0.416438			0.208219	+	0.978082i	$0.433233\pi$
$998$	7.28503e12	+	7.70046e14i	0.00735832	+	0.777793i
$999$			4.23699e14i			0.425824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.h.51.23		24
4.3	odd	2	inner	100.11.b.h.51.24		24
5.2	odd	4		20.11.d.d.19.14	yes	24
5.3	odd	4		20.11.d.d.19.11	✓	24
5.4	even	2	inner	100.11.b.h.51.2		24
20.3	even	4		20.11.d.d.19.13	yes	24
20.7	even	4		20.11.d.d.19.12	yes	24
20.19	odd	2	inner	100.11.b.h.51.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.11	✓	24	5.3	odd	4
20.11.d.d.19.12	yes	24	20.7	even	4
20.11.d.d.19.13	yes	24	20.3	even	4
20.11.d.d.19.14	yes	24	5.2	odd	4
100.11.b.h.51.1		24	20.19	odd	2	inner
100.11.b.h.51.2		24	5.4	even	2	inner
100.11.b.h.51.23		24	1.1	even	1	trivial
100.11.b.h.51.24		24	4.3	odd	2	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(31.9986 - 0.302723i) q^{2} +375.794i q^{3} +(1023.82 - 19.3734i) q^{4} +(113.762 + 12024.9i) q^{6} -19635.7i q^{7} +(32754.8 - 929.854i) q^{8} -82172.5 q^{9} +O(q^{10})\)	\(q+(31.9986 - 0.302723i) q^{2} +375.794i q^{3} +(1023.82 - 19.3734i) q^{4} +(113.762 + 12024.9i) q^{6} -19635.7i q^{7} +(32754.8 - 929.854i) q^{8} -82172.5 q^{9} -163868. i q^{11} +(7280.42 + 384745. i) q^{12} +86535.9 q^{13} +(-5944.18 - 628314. i) q^{14} +(1.04783e6 - 39669.6i) q^{16} +2.09541e6 q^{17} +(-2.62940e6 + 24875.5i) q^{18} -3.13936e6i q^{19} +7.37899e6 q^{21} +(-49606.6 - 5.24354e6i) q^{22} -1.05386e7i q^{23} +(349434. + 1.23091e7i) q^{24} +(2.76902e6 - 26196.4i) q^{26} -8.68968e6i q^{27} +(-380410. - 2.01034e7i) q^{28} -1.13219e7 q^{29} +1.21645e7i q^{31} +(3.35169e7 - 1.58657e6i) q^{32} +6.15807e7 q^{33} +(6.70503e7 - 634330. i) q^{34} +(-8.41296e7 + 1.59196e6i) q^{36} -4.87589e7 q^{37} +(-950356. - 1.00455e8i) q^{38} +3.25197e7i q^{39} +4.55341e7 q^{41} +(2.36117e8 - 2.23379e6i) q^{42} -7.47838e7i q^{43} +(-3.17468e6 - 1.67771e8i) q^{44} +(-3.19029e6 - 3.37222e8i) q^{46} +9.62539e6i q^{47} +(1.49076e7 + 3.93767e8i) q^{48} -1.03086e8 q^{49} +7.87445e8i q^{51} +(8.85969e7 - 1.67649e6i) q^{52} +1.27224e8 q^{53} +(-2.63056e6 - 2.78057e8i) q^{54} +(-1.82583e7 - 6.43164e8i) q^{56} +1.17975e9 q^{57} +(-3.62283e8 + 3.42739e6i) q^{58} +1.18280e9i q^{59} +2.97404e8 q^{61} +(3.68246e6 + 3.89246e8i) q^{62} +1.61351e9i q^{63} +(1.07201e9 - 6.09144e7i) q^{64} +(1.97049e9 - 1.86419e7i) q^{66} +7.15670e8i q^{67} +(2.14532e9 - 4.05953e7i) q^{68} +3.96036e9 q^{69} +2.56419e9i q^{71} +(-2.69154e9 + 7.64084e7i) q^{72} -2.10771e9 q^{73} +(-1.56022e9 + 1.47604e7i) q^{74} +(-6.08201e7 - 3.21413e9i) q^{76} -3.21766e9 q^{77} +(9.84446e6 + 1.04058e9i) q^{78} -3.44771e9i q^{79} -1.58667e9 q^{81} +(1.45702e9 - 1.37842e7i) q^{82} -7.09842e9i q^{83} +(7.55473e9 - 1.42956e8i) q^{84} +(-2.26388e7 - 2.39297e9i) q^{86} -4.25469e9i q^{87} +(-1.52373e8 - 5.36747e9i) q^{88} +3.39502e9 q^{89} -1.69919e9i q^{91} +(-2.04169e8 - 1.07896e10i) q^{92} -4.57134e9 q^{93} +(2.91383e6 + 3.07999e8i) q^{94} +(5.96225e8 + 1.25955e10i) q^{96} -5.71771e9 q^{97} +(-3.29859e9 + 3.12064e7i) q^{98} +1.34654e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9}+O(q^{10}) \) 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9	\( 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9} + 1706016 q^{14} - 4733376 q^{16} - 13030368 q^{21} - 10190784 q^{24} - 9454368 q^{26} - 121656816 q^{29} + 335231168 q^{34} - 276632160 q^{36} + 892843248 q^{41} - 766329600 q^{44} + 433181216 q^{46} + 738102008 q^{49} - 139387968 q^{54} - 2629032384 q^{56} + 228563248 q^{61} + 1875284992 q^{64} - 1440259200 q^{66} + 943422432 q^{69} - 21045467232 q^{74} + 828422400 q^{76} - 5619065544 q^{81} + 28069573632 q^{84} + 8163556416 q^{86} - 4631088816 q^{89} - 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) \) 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9 + 1706016 * q^14 - 4733376 * q^16 - 13030368 * q^21 - 10190784 * q^24 - 9454368 * q^26 - 121656816 * q^29 + 335231168 * q^34 - 276632160 * q^36 + 892843248 * q^41 - 766329600 * q^44 + 433181216 * q^46 + 738102008 * q^49 - 139387968 * q^54 - 2629032384 * q^56 + 228563248 * q^61 + 1875284992 * q^64 - 1440259200 * q^66 + 943422432 * q^69 - 21045467232 * q^74 + 828422400 * q^76 - 5619065544 * q^81 + 28069573632 * q^84 + 8163556416 * q^86 - 4631088816 * q^89 - 63404384 * q^94 - 5617046784 * q^96

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