LMFDB - Embedded newform 100.9.d.c.99.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,9,Mod(99,100)]

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, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("100.99");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, not 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:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.12
Character	$\chi$	$=$	100.99
Dual form			100.9.d.c.99.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.70489 + 14.5274i) q^{2} +150.211 q^{3} +(-166.089 - 194.809i) q^{4} +(-1007.15 + 2182.17i) q^{6} +2626.96 q^{7} +(3943.67 - 1106.66i) q^{8} +16002.3 q^{9} +O(q^{10})$	\(q+(-6.70489 + 14.5274i) q^{2} +150.211 q^{3} +(-166.089 - 194.809i) q^{4} +(-1007.15 + 2182.17i) q^{6} +2626.96 q^{7} +(3943.67 - 1106.66i) q^{8} +16002.3 q^{9} -2300.68i q^{11} +(-24948.4 - 29262.4i) q^{12} -47058.2i q^{13} +(-17613.5 + 38162.8i) q^{14} +(-10365.0 + 64711.2i) q^{16} -51967.0i q^{17} +(-107294. + 232472. i) q^{18} -59554.7i q^{19} +394598. q^{21} +(33422.9 + 15425.8i) q^{22} -77570.5 q^{23} +(592382. - 166233. i) q^{24} +(683632. + 315520. i) q^{26} +1.41819e6 q^{27} +(-436308. - 511754. i) q^{28} -902211. q^{29} -340014. i q^{31} +(-870587. - 584457. i) q^{32} -345588. i q^{33} +(754943. + 348433. i) q^{34} +(-2.65781e6 - 3.11740e6i) q^{36} -584324. i q^{37} +(865173. + 399308. i) q^{38} -7.06866e6i q^{39} +293985. q^{41} +(-2.64573e6 + 5.73247e6i) q^{42} +2.95292e6 q^{43} +(-448194. + 382118. i) q^{44} +(520102. - 1.12689e6i) q^{46} +5.03746e6 q^{47} +(-1.55693e6 + 9.72033e6i) q^{48} +1.13610e6 q^{49} -7.80601e6i q^{51} +(-9.16736e6 + 7.81585e6i) q^{52} +7.54985e6i q^{53} +(-9.50883e6 + 2.06026e7i) q^{54} +(1.03598e7 - 2.90715e6i) q^{56} -8.94577e6i q^{57} +(6.04923e6 - 1.31068e7i) q^{58} +8.82594e6i q^{59} +1.08173e7 q^{61} +(4.93951e6 + 2.27976e6i) q^{62} +4.20375e7 q^{63} +(1.43278e7 - 8.72861e6i) q^{64} +(5.02049e6 + 2.31713e6i) q^{66} +1.44347e7 q^{67} +(-1.01236e7 + 8.63113e6i) q^{68} -1.16519e7 q^{69} +3.71149e6i q^{71} +(6.31079e7 - 1.77092e7i) q^{72} +3.62775e7i q^{73} +(8.48869e6 + 3.91783e6i) q^{74} +(-1.16018e7 + 9.89137e6i) q^{76} -6.04380e6i q^{77} +(1.02689e8 + 4.73946e7i) q^{78} +4.88562e7i q^{79} +1.08037e8 q^{81} +(-1.97114e6 + 4.27083e6i) q^{82} -6.93862e7 q^{83} +(-6.55383e7 - 7.68711e7i) q^{84} +(-1.97990e7 + 4.28982e7i) q^{86} -1.35522e8 q^{87} +(-2.54608e6 - 9.07314e6i) q^{88} +1.05906e8 q^{89} -1.23620e8i q^{91} +(1.28836e7 + 1.51114e7i) q^{92} -5.10738e7i q^{93} +(-3.37756e7 + 7.31810e7i) q^{94} +(-1.30772e8 - 8.77919e7i) q^{96} +1.33519e8i q^{97} +(-7.61742e6 + 1.65045e7i) q^{98} -3.68163e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9}+O(q^{10}) $ 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9	$ 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44} - 15948304 q^{46} + 65607200 q^{49} - 17797408 q^{54} + 68269536 q^{56} + 16743424 q^{61} + 95087744 q^{64} + 38716000 q^{66} - 15054528 q^{69} + 276421752 q^{74} + 5140800 q^{76} + 281173344 q^{81} - 139523648 q^{84} - 203449344 q^{86} - 213294912 q^{89} - 110529264 q^{94} - 906779904 q^{96}+O(q^{100}) $ 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * 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 $

$2$	−6.70489	+	14.5274i	−0.419056	+	0.907961i
$2$	−6.70489	+	14.5274i	−0.419056	+	0.907961i
$3$	150.211			1.85446			0.927228	−	0.374496i	$-0.122184\pi$
$3$	150.211			1.85446			0.927228	+	0.374496i	$0.122184\pi$
$4$	−166.089	−	194.809i	−0.648785	−	0.760972i
$5$		0			0
$5$		0			0
$6$	−1007.15	+	2182.17i	−0.777121	+	1.68377i
$7$	2626.96			1.09411			0.547055	−	0.837097i	$-0.315749\pi$
$7$	2626.96			1.09411			0.547055	+	0.837097i	$0.315749\pi$
$8$	3943.67	−	1106.66i	0.962810	−	0.270181i
$9$	16002.3			2.43901
$10$		0			0
$11$		−	2300.68i		−	0.157140i	−0.996909	−	0.0785699i	$-0.974965\pi$
$11$		−	2300.68i		−	0.157140i	0.996909	−	0.0785699i	$-0.0250354\pi$
$12$	−24948.4	−	29262.4i	−1.20314	−	1.41119i
$13$		−	47058.2i		−	1.64764i	−0.566852	−	0.823820i	$-0.691839\pi$
$13$		−	47058.2i		−	1.64764i	0.566852	−	0.823820i	$-0.308161\pi$
$14$	−17613.5	+	38162.8i	−0.458493	+	0.993408i
$15$		0			0
$16$	−10365.0	+	64711.2i	−0.158157	+	0.987414i
$17$		−	51967.0i		−	0.622202i	−0.950377	−	0.311101i	$-0.899302\pi$
$17$		−	51967.0i		−	0.622202i	0.950377	−	0.311101i	$-0.100698\pi$
$18$	−107294.	+	232472.i	−1.02208	+	2.21452i
$19$		−	59554.7i		−	0.456985i	−0.973546	−	0.228492i	$-0.926620\pi$
$19$		−	59554.7i		−	0.456985i	0.973546	−	0.228492i	$-0.0733796\pi$
$20$		0			0
$21$	394598.			2.02898
$22$	33422.9	+	15425.8i	0.142677	+	0.0658503i
$23$	−77570.5			−0.277195			−0.138597	−	0.990349i	$-0.544259\pi$
$23$	−77570.5			−0.277195			−0.138597	+	0.990349i	$0.544259\pi$
$24$	592382.	−	166233.i	1.78549	−	0.501039i
$25$		0			0
$26$	683632.	+	315520.i	1.49599	+	0.690453i
$27$	1.41819e6			2.66858
$28$	−436308.	−	511754.i	−0.709841	−	0.832587i
$29$	−902211.			−1.27561			−0.637803	−	0.770200i	$-0.720156\pi$
$29$	−902211.			−1.27561			−0.637803	+	0.770200i	$0.720156\pi$
$30$		0			0
$31$		−	340014.i		−	0.368171i	−0.982910	−	0.184086i	$-0.941068\pi$
$31$		−	340014.i		−	0.368171i	0.982910	−	0.184086i	$-0.0589324\pi$
$32$	−870587.	−	584457.i	−0.830256	−	0.557382i
$33$		−	345588.i		−	0.291409i
$34$	754943.	+	348433.i	0.564935	+	0.260737i
$35$		0			0
$36$	−2.65781e6	−	3.11740e6i	−1.58239	−	1.85602i
$37$		−	584324.i		−	0.311779i	−0.987774	−	0.155890i	$-0.950176\pi$
$37$		−	584324.i		−	0.311779i	0.987774	−	0.155890i	$-0.0498244\pi$
$38$	865173.	+	399308.i	0.414924	+	0.191502i
$39$		−	7.06866e6i		−	3.05548i
$40$		0			0
$41$	293985.			0.104037			0.0520187	−	0.998646i	$-0.483434\pi$
$41$	293985.			0.104037			0.0520187	+	0.998646i	$0.483434\pi$
$42$	−2.64573e6	+	5.73247e6i	−0.850255	+	1.84223i
$43$	2.95292e6			0.863731			0.431866	−	0.901938i	$-0.357856\pi$
$43$	2.95292e6			0.863731			0.431866	+	0.901938i	$0.357856\pi$
$44$	−448194.	+	382118.i	−0.119579	+	0.101950i
$45$		0			0
$46$	520102.	−	1.12689e6i	0.116160	−	0.251682i
$47$	5.03746e6			1.03233			0.516167	−	0.856488i	$-0.327358\pi$
$47$	5.03746e6			1.03233			0.516167	+	0.856488i	$0.327358\pi$
$48$	−1.55693e6	+	9.72033e6i	−0.293295	+	1.83112i
$49$	1.13610e6			0.197075
$50$		0			0
$51$		−	7.80601e6i		−	1.15385i
$52$	−9.16736e6	+	7.81585e6i	−1.25381	+	1.06896i
$53$			7.54985e6i			0.956830i	0.878134	+	0.478415i	$0.158789\pi$
$53$			7.54985e6i			0.956830i	−0.878134	+	0.478415i	$0.841211\pi$
$54$	−9.50883e6	+	2.06026e7i	−1.11828	+	2.42297i
$55$		0			0
$56$	1.03598e7	−	2.90715e6i	1.05342	−	0.295608i
$57$		−	8.94577e6i		−	0.847458i
$58$	6.04923e6	−	1.31068e7i	0.534550	−	1.15820i
$59$			8.82594e6i			0.728372i	0.931326	+	0.364186i	$0.118653\pi$
$59$			8.82594e6i			0.728372i	−0.931326	+	0.364186i	$0.881347\pi$
$60$		0			0
$61$	1.08173e7			0.781269			0.390634	−	0.920546i	$-0.372256\pi$
$61$	1.08173e7			0.781269			0.390634	+	0.920546i	$0.372256\pi$
$62$	4.93951e6	+	2.27976e6i	0.334285	+	0.154284i
$63$	4.20375e7			2.66854
$64$	1.43278e7	−	8.72861e6i	0.854004	−	0.520266i
$65$		0			0
$66$	5.02049e6	+	2.31713e6i	0.264588	+	0.122117i
$67$	1.44347e7			0.716324			0.358162	−	0.933659i	$-0.383404\pi$
$67$	1.44347e7			0.716324			0.358162	+	0.933659i	$0.383404\pi$
$68$	−1.01236e7	+	8.63113e6i	−0.473479	+	0.403675i
$69$	−1.16519e7			−0.514046
$70$		0			0
$71$			3.71149e6i			0.146054i	0.997330	+	0.0730272i	$0.0232660\pi$
$71$			3.71149e6i			0.146054i	−0.997330	+	0.0730272i	$0.976734\pi$
$72$	6.31079e7	−	1.77092e7i	2.34830	−	0.658975i
$73$			3.62775e7i			1.27746i	0.769433	+	0.638728i	$0.220539\pi$
$73$			3.62775e7i			1.27746i	−0.769433	+	0.638728i	$0.779461\pi$
$74$	8.48869e6	+	3.91783e6i	0.283083	+	0.130653i
$75$		0			0
$76$	−1.16018e7	+	9.89137e6i	−0.347752	+	0.296485i
$77$		−	6.04380e6i		−	0.171928i
$78$	1.02689e8	+	4.73946e7i	2.77425	+	1.28041i
$79$			4.88562e7i			1.25433i	0.778887	+	0.627164i	$0.215785\pi$
$79$			4.88562e7i			1.25433i	−0.778887	+	0.627164i	$0.784215\pi$
$80$		0			0
$81$	1.08037e8			2.50976
$82$	−1.97114e6	+	4.27083e6i	−0.0435975	+	0.0944619i
$83$	−6.93862e7			−1.46205			−0.731023	−	0.682353i	$-0.760957\pi$
$83$	−6.93862e7			−1.46205			−0.731023	+	0.682353i	$0.760957\pi$
$84$	−6.55383e7	−	7.68711e7i	−1.31637	−	1.54400i
$85$		0			0
$86$	−1.97990e7	+	4.28982e7i	−0.361951	+	0.784234i
$87$	−1.35522e8			−2.36555
$88$	−2.54608e6	−	9.07314e6i	−0.0424562	−	0.151296i
$89$	1.05906e8			1.68796			0.843979	−	0.536377i	$-0.180207\pi$
$89$	1.05906e8			1.68796			0.843979	+	0.536377i	$0.180207\pi$
$90$		0			0
$91$		−	1.23620e8i		−	1.80270i
$92$	1.28836e7	+	1.51114e7i	0.179840	+	0.210938i
$93$		−	5.10738e7i		−	0.682758i
$94$	−3.37756e7	+	7.31810e7i	−0.432605	+	0.937319i
$95$		0			0
$96$	−1.30772e8	−	8.77919e7i	−1.53967	−	1.03364i
$97$			1.33519e8i			1.50819i	0.656768	+	0.754093i	$0.271923\pi$
$97$			1.33519e8i			1.50819i	−0.656768	+	0.754093i	$0.728077\pi$
$98$	−7.61742e6	+	1.65045e7i	−0.0825854	+	0.178936i
$99$		−	3.68163e7i		−	0.383266i
$100$		0			0
$101$	−6.08853e7			−0.585096			−0.292548	−	0.956251i	$-0.594503\pi$
$101$	−6.08853e7			−0.585096			−0.292548	+	0.956251i	$0.594503\pi$
$102$	1.13401e8	+	5.23384e7i	1.04765	+	0.483526i
$103$	−2.63324e7			−0.233960			−0.116980	−	0.993134i	$-0.537321\pi$
$103$	−2.63324e7			−0.233960			−0.116980	+	0.993134i	$0.537321\pi$
$104$	−5.20776e7	−	1.85582e8i	−0.445161	−	1.58636i
$105$		0			0
$106$	−1.09679e8	−	5.06209e7i	−0.868764	−	0.400965i
$107$	−1.26375e8			−0.964108			−0.482054	−	0.876141i	$-0.660109\pi$
$107$	−1.26375e8			−0.964108			−0.482054	+	0.876141i	$0.660109\pi$
$108$	−2.35546e8	−	2.76277e8i	−1.73133	−	2.03072i
$109$	−7.75869e7			−0.549645			−0.274822	−	0.961495i	$-0.588619\pi$
$109$	−7.75869e7			−0.549645			−0.274822	+	0.961495i	$0.588619\pi$
$110$		0			0
$111$		−	8.77719e7i		−	0.578181i
$112$	−2.72283e7	+	1.69993e8i	−0.173041	+	1.08034i
$113$			9.07281e7i			0.556453i	0.960516	+	0.278226i	$0.0897465\pi$
$113$			9.07281e7i			0.556453i	−0.960516	+	0.278226i	$0.910253\pi$
$114$	1.29958e8	+	5.99804e7i	0.769459	+	0.355132i
$115$		0			0
$116$	1.49847e8	+	1.75759e8i	0.827593	+	0.970700i
$117$		−	7.53042e8i		−	4.01861i
$118$	−1.28218e8	−	5.91770e7i	−0.661333	−	0.305228i
$119$		−	1.36515e8i		−	0.680757i
$120$		0			0
$121$	2.09066e8			0.975307
$122$	−7.25290e7	+	1.57147e8i	−0.327395	+	0.709361i
$123$	4.41598e7			0.192933
$124$	−6.62377e7	+	5.64725e7i	−0.280168	+	0.238864i
$125$		0			0
$126$	−2.81857e8	+	6.10694e8i	−1.11827	+	2.42293i
$127$	3.10844e8			1.19489			0.597445	−	0.801910i	$-0.296183\pi$
$127$	3.10844e8			1.19489			0.597445	+	0.801910i	$0.296183\pi$
$128$	3.07374e7	+	2.66670e8i	0.114506	+	0.993423i
$129$	4.43562e8			1.60175
$130$		0			0
$131$			5.44781e8i			1.84985i	0.380150	+	0.924925i	$0.375872\pi$
$131$			5.44781e8i			1.84985i	−0.380150	+	0.924925i	$0.624128\pi$
$132$	−6.73236e7	+	5.73983e7i	−0.221754	+	0.189062i
$133$		−	1.56448e8i		−	0.499991i
$134$	−9.67833e7	+	2.09699e8i	−0.300180	+	0.650394i
$135$		0			0
$136$	−5.75099e7	−	2.04940e8i	−0.168107	−	0.599062i
$137$		−	1.23319e8i		−	0.350065i	−0.984563	−	0.175033i	$-0.943997\pi$
$137$		−	1.23319e8i		−	0.350065i	0.984563	−	0.175033i	$-0.0560031\pi$
$138$	7.81250e7	−	1.69272e8i	0.215414	−	0.466733i
$139$		−	6.72621e8i		−	1.80182i	−0.434008	−	0.900909i	$-0.642901\pi$
$139$		−	6.72621e8i		−	1.80182i	0.434008	−	0.900909i	$-0.357099\pi$
$140$		0			0
$141$	7.56682e8			1.91442
$142$	−5.39181e7	−	2.48851e7i	−0.132612	−	0.0612049i
$143$	−1.08266e8			−0.258910
$144$	−1.65864e8	+	1.03553e9i	−0.385746	+	2.40831i
$145$		0			0
$146$	−5.27017e8	−	2.43237e8i	−1.15988	−	0.535325i
$147$	1.70655e8			0.365467
$148$	−1.13832e8	+	9.70497e7i	−0.237255	+	0.202277i
$149$	−2.47048e8			−0.501229			−0.250615	−	0.968087i	$-0.580633\pi$
$149$	−2.47048e8			−0.501229			−0.250615	+	0.968087i	$0.580633\pi$
$150$		0			0
$151$		−	4.00056e8i		−	0.769508i	−0.923019	−	0.384754i	$-0.874286\pi$
$151$		−	4.00056e8i		−	0.769508i	0.923019	−	0.384754i	$-0.125714\pi$
$152$	−6.59069e7	−	2.34864e8i	−0.123469	−	0.439989i
$153$		−	8.31593e8i		−	1.51756i
$154$	8.78005e7	+	4.05230e7i	0.156104	+	0.0720475i
$155$		0			0
$156$	−1.37704e9	+	1.17403e9i	−2.32513	+	1.98235i
$157$		−	7.00538e8i		−	1.15301i	−0.817094	−	0.576505i	$-0.804416\pi$
$157$		−	7.00538e8i		−	1.15301i	0.817094	−	0.576505i	$-0.195584\pi$
$158$	−7.09752e8	−	3.27575e8i	−1.13888	−	0.525634i
$159$			1.13407e9i			1.77440i
$160$		0			0
$161$	−2.03774e8			−0.303281
$162$	−7.24376e8	+	1.56949e9i	−1.05173	+	2.27876i
$163$	−2.24412e8			−0.317903			−0.158952	−	0.987286i	$-0.550811\pi$
$163$	−2.24412e8			−0.317903			−0.158952	+	0.987286i	$0.550811\pi$
$164$	−4.88277e7	−	5.72709e7i	−0.0674979	−	0.0791696i
$165$		0			0
$166$	4.65227e8	−	1.00800e9i	0.612678	−	1.32748i
$167$	−1.11919e9			−1.43893			−0.719464	−	0.694530i	$-0.755613\pi$
$167$	−1.11919e9			−1.43893			−0.719464	+	0.694530i	$0.755613\pi$
$168$	1.55616e9	−	4.36686e8i	1.95352	−	0.548192i
$169$	−1.39875e9			−1.71472
$170$		0			0
$171$		−	9.53015e8i		−	1.11459i
$172$	−4.90448e8	−	5.75256e8i	−0.560375	−	0.657275i
$173$			1.58033e9i			1.76426i	0.471005	+	0.882130i	$0.343891\pi$
$173$			1.58033e9i			1.76426i	−0.471005	+	0.882130i	$0.656109\pi$
$174$	9.08661e8	−	1.96878e9i	0.991299	−	2.14783i
$175$		0			0
$176$	1.48880e8	+	2.38465e7i	0.155162	+	0.0248528i
$177$			1.32575e9i			1.35073i
$178$	−7.10090e8	+	1.53854e9i	−0.707348	+	1.53260i
$179$		−	4.43340e8i		−	0.431841i	−0.976411	−	0.215921i	$-0.930725\pi$
$179$		−	4.43340e8i		−	0.431841i	0.976411	−	0.215921i	$-0.0692753\pi$
$180$		0			0
$181$	−1.87230e8			−0.174446			−0.0872232	−	0.996189i	$-0.527799\pi$
$181$	−1.87230e8			−0.174446			−0.0872232	+	0.996189i	$0.527799\pi$
$182$	1.79587e9	+	8.28858e8i	1.63678	+	0.755431i
$183$	1.62488e9			1.44883
$184$	−3.05912e8	+	8.58443e7i	−0.266886	+	0.0748928i
$185$		0			0
$186$	7.41968e8	+	3.42444e8i	0.619917	+	0.286114i
$187$	−1.19560e8			−0.0977728
$188$	−8.36666e8	−	9.81342e8i	−0.669762	−	0.785577i
$189$	3.72553e9			2.91972
$190$		0			0
$191$		−	5.22344e8i		−	0.392485i	−0.980555	−	0.196242i	$-0.937126\pi$
$191$		−	5.22344e8i		−	0.392485i	0.980555	−	0.196242i	$-0.0628740\pi$
$192$	2.15220e9	−	1.31113e9i	1.58371	−	0.964811i
$193$		−	5.01793e7i		−	0.0361655i	−0.999836	−	0.0180828i	$-0.994244\pi$
$193$		−	5.01793e7i		−	0.0361655i	0.999836	−	0.0180828i	$-0.00575624\pi$
$194$	−1.93967e9	−	8.95227e8i	−1.36937	−	0.632014i
$195$		0			0
$196$	−1.88693e8	−	2.21322e8i	−0.127859	−	0.149969i
$197$		−	2.63629e8i		−	0.175036i	−0.996163	−	0.0875181i	$-0.972106\pi$
$197$		−	2.63629e8i		−	0.175036i	0.996163	−	0.0875181i	$-0.0278936\pi$
$198$	5.34845e8	+	2.46850e8i	0.347990	+	0.160610i
$199$		−	1.26573e9i		−	0.807105i	−0.914956	−	0.403553i	$-0.867775\pi$
$199$		−	1.26573e9i		−	0.807105i	0.914956	−	0.403553i	$-0.132225\pi$
$200$		0			0
$201$	2.16826e9			1.32839
$202$	4.08229e8	−	8.84503e8i	0.245188	−	0.531244i
$203$	−2.37007e9			−1.39565
$204$	−1.52068e9	+	1.29649e9i	−0.878046	+	0.748598i
$205$		0			0
$206$	1.76556e8	−	3.82541e8i	0.0980423	−	0.212427i
$207$	−1.24131e9			−0.676081
$208$	3.04519e9	+	4.87757e8i	1.62690	+	0.260586i
$209$	−1.37017e8			−0.0718105
$210$		0			0
$211$			9.34053e8i			0.471240i	0.971845	+	0.235620i	$0.0757120\pi$
$211$			9.34053e8i			0.471240i	−0.971845	+	0.235620i	$0.924288\pi$
$212$	1.47078e9	−	1.25395e9i	0.728121	−	0.620777i
$213$			5.57506e8i			0.270852i
$214$	8.47330e8	−	1.83590e9i	0.404015	−	0.875372i
$215$		0			0
$216$	5.59288e9	−	1.56946e9i	2.56934	−	0.721000i
$217$		−	8.93202e8i		−	0.402820i
$218$	5.20212e8	−	1.12713e9i	0.230332	−	0.499056i
$219$			5.44928e9i			2.36899i
$220$		0			0
$221$	−2.44547e9			−1.02517
$222$	1.27509e9	+	5.88501e8i	0.524965	+	0.242290i
$223$	−5.22225e8			−0.211173			−0.105586	−	0.994410i	$-0.533672\pi$
$223$	−5.22225e8			−0.211173			−0.105586	+	0.994410i	$0.533672\pi$
$224$	−2.28699e9	−	1.53534e9i	−0.908391	−	0.609837i
$225$		0			0
$226$	−1.31804e9	−	6.08322e8i	−0.505237	−	0.233185i
$227$	3.46698e9			1.30571			0.652856	−	0.757482i	$-0.273570\pi$
$227$	3.46698e9			1.30571			0.652856	+	0.757482i	$0.273570\pi$
$228$	−1.74271e9	+	1.48579e9i	−0.644892	+	0.549818i
$229$	−1.31243e9			−0.477239			−0.238619	−	0.971113i	$-0.576695\pi$
$229$	−1.31243e9			−0.477239			−0.238619	+	0.971113i	$0.576695\pi$
$230$		0			0
$231$		−	9.07845e8i		−	0.318833i
$232$	−3.55802e9	+	9.98443e8i	−1.22816	+	0.344644i
$233$			2.43802e9i			0.827207i	0.910457	+	0.413604i	$0.135730\pi$
$233$			2.43802e9i			0.827207i	−0.910457	+	0.413604i	$0.864270\pi$
$234$	1.09397e10	+	5.04906e9i	3.64874	+	1.68402i
$235$		0			0
$236$	1.71937e9	−	1.46589e9i	0.554271	−	0.472556i
$237$			7.33874e9i			2.32610i
$238$	1.98320e9	+	9.15318e8i	0.618101	+	0.285275i
$239$		−	2.78783e9i		−	0.854427i	−0.904151	−	0.427214i	$-0.859495\pi$
$239$		−	2.78783e9i		−	0.854427i	0.904151	−	0.427214i	$-0.140505\pi$
$240$		0			0
$241$	1.16299e9			0.344753			0.172376	−	0.985031i	$-0.444856\pi$
$241$	1.16299e9			0.344753			0.172376	+	0.985031i	$0.444856\pi$
$242$	−1.40176e9	+	3.03717e9i	−0.408708	+	0.885540i
$243$	6.92356e9			1.98566
$244$	−1.79664e9	−	2.10731e9i	−0.506875	−	0.594524i
$245$		0			0
$246$	−2.96087e8	+	6.41526e8i	−0.0808497	+	0.175176i
$247$	−2.80254e9			−0.752946
$248$	−3.76281e8	−	1.34090e9i	−0.0994729	−	0.354479i
$249$	−1.04226e10			−2.71130
$250$		0			0
$251$			6.20014e9i			1.56209i	0.624474	+	0.781046i	$0.285313\pi$
$251$			6.20014e9i			1.56209i	−0.624474	+	0.781046i	$0.714687\pi$
$252$	−6.98195e9	−	8.18927e9i	−1.73131	−	2.03069i
$253$			1.78465e8i			0.0435584i
$254$	−2.08418e9	+	4.51575e9i	−0.500725	+	1.08491i
$255$		0			0
$256$	−4.08010e9	−	1.34146e9i	−0.949973	−	0.312333i
$257$		−	1.12108e9i		−	0.256983i	−0.991711	−	0.128491i	$-0.958987\pi$
$257$		−	1.12108e9i		−	0.256983i	0.991711	−	0.128491i	$-0.0410135\pi$
$258$	−2.97403e9	+	6.44378e9i	−0.671223	+	1.45433i
$259$		−	1.53499e9i		−	0.341120i
$260$		0			0
$261$	−1.44375e10			−3.11121
$262$	−7.91423e9	−	3.65269e9i	−1.67959	−	0.775190i
$263$	1.51480e9			0.316616			0.158308	−	0.987390i	$-0.449396\pi$
$263$	1.51480e9			0.316616			0.158308	+	0.987390i	$0.449396\pi$
$264$	−3.82449e8	−	1.36288e9i	−0.0787332	−	0.280571i
$265$		0			0
$266$	2.27277e9	+	1.04896e9i	0.453972	+	0.209524i
$267$	1.59083e10			3.13024
$268$	−2.39745e9	−	2.81201e9i	−0.464740	−	0.545102i
$269$	2.73389e9			0.522121			0.261060	−	0.965322i	$-0.415928\pi$
$269$	2.73389e9			0.522121			0.261060	+	0.965322i	$0.415928\pi$
$270$		0			0
$271$		−	9.38092e9i		−	1.73927i	−0.493691	−	0.869637i	$-0.664353\pi$
$271$		−	9.38092e9i		−	1.73927i	0.493691	−	0.869637i	$-0.335647\pi$
$272$	3.36284e9	+	5.38636e8i	0.614371	+	0.0984056i
$273$		−	1.85691e10i		−	3.34302i
$274$	1.79151e9	+	8.26843e8i	0.317845	+	0.146697i
$275$		0			0
$276$	1.93526e9	+	2.26990e9i	0.333505	+	0.391174i
$277$			1.88891e9i			0.320842i	0.987049	+	0.160421i	$0.0512852\pi$
$277$			1.88891e9i			0.320842i	−0.987049	+	0.160421i	$0.948715\pi$
$278$	9.77141e9	+	4.50985e9i	1.63598	+	0.755062i
$279$		−	5.44102e9i		−	0.897973i
$280$		0			0
$281$	−1.65526e9			−0.265485			−0.132743	−	0.991151i	$-0.542378\pi$
$281$	−1.65526e9			−0.265485			−0.132743	+	0.991151i	$0.542378\pi$
$282$	−5.07347e9	+	1.09926e10i	−0.802248	+	1.73822i
$283$	−8.61833e9			−1.34362			−0.671811	−	0.740722i	$-0.734483\pi$
$283$	−8.61833e9			−1.34362			−0.671811	+	0.740722i	$0.734483\pi$
$284$	7.23031e8	−	6.16437e8i	0.111143	−	0.0947578i
$285$		0			0
$286$	7.25913e8	−	1.57282e9i	0.108498	−	0.235080i
$287$	7.72286e8			0.113828
$288$	−1.39314e10	−	9.35268e9i	−2.02500	−	1.35946i
$289$	4.27519e9			0.612864
$290$		0			0
$291$			2.00560e10i			2.79686i
$292$	7.06718e9	−	6.02529e9i	0.972108	−	0.828794i
$293$			5.51315e9i			0.748048i	0.927419	+	0.374024i	$0.122022\pi$
$293$			5.51315e9i			0.748048i	−0.927419	+	0.374024i	$0.877978\pi$
$294$	−1.14422e9	+	2.47916e9i	−0.153151	+	0.331830i
$295$		0			0
$296$	−6.46649e8	−	2.30438e9i	−0.0842368	−	0.300184i
$297$		−	3.26282e9i		−	0.419341i
$298$	1.65643e9	−	3.58896e9i	0.210043	−	0.455096i
$299$			3.65033e9i			0.456717i
$300$		0			0
$301$	7.75720e9			0.945016
$302$	5.81177e9	+	2.68233e9i	0.698683	+	0.322467i
$303$	−9.14564e9			−1.08504
$304$	3.85385e9	+	6.17283e8i	0.451233	+	0.0722753i
$305$		0			0
$306$	1.20809e10	+	5.57574e9i	1.37788	+	0.635941i
$307$	−1.53502e10			−1.72806			−0.864032	−	0.503437i	$-0.832069\pi$
$307$	−1.53502e10			−1.72806			−0.864032	+	0.503437i	$0.832069\pi$
$308$	−1.17739e9	+	1.00381e9i	−0.130833	+	0.111544i
$309$	−3.95542e9			−0.433869
$310$		0			0
$311$			5.55831e9i			0.594157i	0.954853	+	0.297079i	$0.0960123\pi$
$311$			5.55831e9i			0.594157i	−0.954853	+	0.297079i	$0.903988\pi$
$312$	−7.82262e9	−	2.78765e10i	−0.825532	−	2.94184i
$313$			1.76829e10i			1.84237i	0.389131	+	0.921183i	$0.372775\pi$
$313$			1.76829e10i			1.84237i	−0.389131	+	0.921183i	$0.627225\pi$
$314$	1.01770e10	+	4.69703e9i	1.04689	+	0.483176i
$315$		0			0
$316$	9.51762e9	−	8.11447e9i	0.954509	−	0.813789i
$317$		−	2.84291e9i		−	0.281531i	−0.990043	−	0.140766i	$-0.955044\pi$
$317$		−	2.84291e9i		−	0.281531i	0.990043	−	0.140766i	$-0.0449564\pi$
$318$	−1.64751e10	−	7.60382e9i	−1.61109	−	0.743572i
$319$			2.07570e9i			0.200448i
$320$		0			0
$321$	−1.89829e10			−1.78790
$322$	1.36628e9	−	2.96030e9i	0.127092	−	0.275368i
$323$	−3.09488e9			−0.284337
$324$	−1.79437e10	−	2.10465e10i	−1.62829	−	1.90986i
$325$		0			0
$326$	1.50466e9	−	3.26011e9i	0.133219	−	0.288643i
$327$	−1.16544e10			−1.01929
$328$	1.15938e9	−	3.25342e8i	0.100168	−	0.0281090i
$329$	1.32332e10			1.12949
$330$		0			0
$331$			1.16323e10i			0.969068i	0.874773	+	0.484534i	$0.161011\pi$
$331$			1.16323e10i			0.969068i	−0.874773	+	0.484534i	$0.838989\pi$
$332$	1.15243e10	+	1.35171e10i	0.948553	+	1.11258i
$333$		−	9.35056e9i		−	0.760432i
$334$	7.50407e9	−	1.62589e10i	0.602991	−	1.30649i
$335$		0			0
$336$	−4.09000e9	+	2.55349e10i	−0.320897	+	2.00344i
$337$			2.09960e10i			1.62786i	0.580963	+	0.813930i	$0.302676\pi$
$337$			2.09960e10i			1.62786i	−0.580963	+	0.813930i	$0.697324\pi$
$338$	9.37844e9	−	2.03201e10i	0.718561	−	1.55689i
$339$			1.36284e10i			1.03192i
$340$		0			0
$341$	−7.82265e8			−0.0578544
$342$	1.38448e10	+	6.38986e9i	1.01200	+	0.467075i
$343$	−1.21594e10			−0.878488
$344$	1.16454e10	−	3.26789e9i	0.831608	−	0.233364i
$345$		0			0
$346$	−2.29580e10	−	1.05959e10i	−1.60188	−	0.739324i
$347$	7.43114e9			0.512552			0.256276	−	0.966604i	$-0.417504\pi$
$347$	7.43114e9			0.512552			0.256276	+	0.966604i	$0.417504\pi$
$348$	2.25087e10	+	2.64009e10i	1.53474	+	1.80012i
$349$	−5.43305e9			−0.366220			−0.183110	−	0.983092i	$-0.558616\pi$
$349$	−5.43305e9			−0.366220			−0.183110	+	0.983092i	$0.558616\pi$
$350$		0			0
$351$		−	6.67377e10i		−	4.39686i
$352$	−1.34465e9	+	2.00295e9i	−0.0875869	+	0.130466i
$353$		−	7.17687e9i		−	0.462207i	−0.972929	−	0.231103i	$-0.925766\pi$
$353$		−	7.17687e9i		−	0.462207i	0.972929	−	0.231103i	$-0.0742336\pi$
$354$	−1.92597e10	−	8.88904e9i	−1.22641	−	0.566033i
$355$		0			0
$356$	−1.75898e10	−	2.06315e10i	−1.09512	−	1.28449i
$357$		−	2.05060e10i		−	1.26244i
$358$	6.44056e9	+	2.97254e9i	0.392095	+	0.180966i
$359$		−	1.10278e10i		−	0.663913i	−0.943295	−	0.331957i	$-0.892291\pi$
$359$		−	1.10278e10i		−	0.663913i	0.943295	−	0.331957i	$-0.107709\pi$
$360$		0			0
$361$	1.34368e10			0.791165
$362$	1.25536e9	−	2.71996e9i	0.0731027	−	0.158390i
$363$	3.14040e10			1.80866
$364$	−2.40823e10	+	2.05319e10i	−1.37180	+	1.16956i
$365$		0			0
$366$	−1.08947e10	+	2.36052e10i	−0.607140	+	1.31548i
$367$	−3.39042e10			−1.86891			−0.934457	−	0.356076i	$-0.884114\pi$
$367$	−3.39042e10			−1.86891			−0.934457	+	0.356076i	$0.884114\pi$
$368$	8.04016e8	−	5.01968e9i	0.0438403	−	0.273706i
$369$	4.70445e9			0.253748
$370$		0			0
$371$			1.98331e10i			1.04688i
$372$	−9.94963e9	+	8.48279e9i	−0.519560	+	0.442963i
$373$		−	3.19254e10i		−	1.64930i	−0.565641	−	0.824651i	$-0.691371\pi$
$373$		−	3.19254e10i		−	1.64930i	0.565641	−	0.824651i	$-0.308629\pi$
$374$	8.01634e8	−	1.73689e9i	0.0409722	−	0.0887738i
$375$		0			0
$376$	1.98661e10	−	5.57477e9i	0.993941	−	0.278917i
$377$			4.24565e10i			2.10174i
$378$	−2.49793e10	+	5.41222e10i	−1.22353	+	2.65099i
$379$			2.66340e10i			1.29086i	0.763819	+	0.645430i	$0.223322\pi$
$379$			2.66340e10i			1.29086i	−0.763819	+	0.645430i	$0.776678\pi$
$380$		0			0
$381$	4.66922e10			2.21587
$382$	7.58828e9	+	3.50226e9i	0.356361	+	0.164473i
$383$	1.61064e10			0.748518			0.374259	−	0.927324i	$-0.377897\pi$
$383$	1.61064e10			0.748518			0.374259	+	0.927324i	$0.377897\pi$
$384$	4.61709e9	+	4.00567e10i	0.212346	+	1.84226i
$385$		0			0
$386$	7.28973e8	+	3.36446e8i	0.0328369	+	0.0151554i
$387$	4.72537e10			2.10665
$388$	2.60106e10	−	2.21759e10i	1.14769	−	0.978487i
$389$	−1.81674e10			−0.793405			−0.396702	−	0.917947i	$-0.629846\pi$
$389$	−1.81674e10			−0.793405			−0.396702	+	0.917947i	$0.629846\pi$
$390$		0			0
$391$			4.03110e9i			0.172471i
$392$	4.48040e9	−	1.25728e9i	0.189746	−	0.0532460i
$393$			8.18320e10i			3.43047i
$394$	3.82983e9	+	1.76760e9i	0.158926	+	0.0733499i
$395$		0			0
$396$	−7.17215e9	+	6.11479e9i	−0.291654	+	0.248657i
$397$		−	4.03325e10i		−	1.62365i	−0.583898	−	0.811827i	$-0.698473\pi$
$397$		−	4.03325e10i		−	1.62365i	0.583898	−	0.811827i	$-0.301527\pi$
$398$	1.83878e10	+	8.48661e9i	0.732820	+	0.338222i
$399$		−	2.35001e10i		−	0.927212i
$400$		0			0
$401$	1.86384e10			0.720826			0.360413	−	0.932793i	$-0.382636\pi$
$401$	1.86384e10			0.720826			0.360413	+	0.932793i	$0.382636\pi$
$402$	−1.45379e10	+	3.14990e10i	−0.556670	+	1.20613i
$403$	−1.60005e10			−0.606614
$404$	1.01124e10	+	1.18610e10i	0.379601	+	0.445242i
$405$		0			0
$406$	1.58911e10	−	3.44309e10i	0.584856	−	1.26720i
$407$	−1.34435e9			−0.0489929
$408$	−8.63861e9	−	3.07843e10i	−0.311748	−	1.11094i
$409$	1.95383e10			0.698222			0.349111	−	0.937081i	$-0.386484\pi$
$409$	1.95383e10			0.698222			0.349111	+	0.937081i	$0.386484\pi$
$410$		0			0
$411$		−	1.85239e10i		−	0.649181i
$412$	4.37352e9	+	5.12979e9i	0.151790	+	0.178037i
$413$			2.31854e10i			0.796918i
$414$	8.32284e9	−	1.80330e10i	0.283316	−	0.613855i
$415$		0			0
$416$	−2.75035e10	+	4.09683e10i	−0.918364	+	1.36796i
$417$		−	1.01035e11i		−	3.34139i
$418$	9.18681e8	−	1.99049e9i	0.0300926	−	0.0652011i
$419$		−	1.60399e10i		−	0.520410i	−0.965553	−	0.260205i	$-0.916210\pi$
$419$		−	1.60399e10i		−	0.520410i	0.965553	−	0.260205i	$-0.0837901\pi$
$420$		0			0
$421$	8.80074e9			0.280150			0.140075	−	0.990141i	$-0.455266\pi$
$421$	8.80074e9			0.280150			0.140075	+	0.990141i	$0.455266\pi$
$422$	−1.35693e10	−	6.26273e9i	−0.427867	−	0.197476i
$423$	8.06112e10			2.51787
$424$	8.35513e9	+	2.97741e10i	0.258517	+	0.921245i
$425$		0			0
$426$	−8.09910e9	−	3.73802e9i	−0.245922	−	0.113502i
$427$	2.84166e10			0.854794
$428$	2.09895e10	+	2.46190e10i	0.625499	+	0.733659i
$429$	−1.62628e10			−0.480137
$430$		0			0
$431$			2.17255e10i			0.629593i	0.949159	+	0.314797i	$0.101936\pi$
$431$			2.17255e10i			0.629593i	−0.949159	+	0.314797i	$0.898064\pi$
$432$	−1.46995e10	+	9.17730e10i	−0.422055	+	2.63499i
$433$		−	2.50658e10i		−	0.713066i	−0.934283	−	0.356533i	$-0.883959\pi$
$433$		−	2.50658e10i		−	0.713066i	0.934283	−	0.356533i	$-0.116041\pi$
$434$	1.29759e10	+	5.98882e9i	0.365744	+	0.168804i
$435$		0			0
$436$	1.28863e10	+	1.51146e10i	0.356601	+	0.418264i
$437$			4.61969e9i			0.126674i
$438$	−7.91637e10	−	3.65368e10i	−2.15095	−	0.992738i
$439$		−	2.69059e10i		−	0.724419i	−0.932097	−	0.362210i	$-0.882022\pi$
$439$		−	2.69059e10i		−	0.724419i	0.932097	−	0.362210i	$-0.117978\pi$
$440$		0			0
$441$	1.81802e10			0.480668
$442$	1.63966e10	−	3.55263e10i	0.429601	−	0.930809i
$443$	−5.16514e10			−1.34112			−0.670560	−	0.741856i	$-0.733946\pi$
$443$	−5.16514e10			−1.34112			−0.670560	+	0.741856i	$0.733946\pi$
$444$	−1.70987e10	+	1.45779e10i	−0.439979	+	0.375115i
$445$		0			0
$446$	3.50146e9	−	7.58655e9i	0.0884932	−	0.191737i
$447$	−3.71093e10			−0.929508
$448$	3.76385e10	−	2.29297e10i	0.934374	−	0.569228i
$449$	4.61561e10			1.13565			0.567825	−	0.823150i	$-0.307785\pi$
$449$	4.61561e10			1.13565			0.567825	+	0.823150i	$0.307785\pi$
$450$		0			0
$451$		−	6.76367e8i		−	0.0163484i
$452$	1.76746e10	−	1.50689e10i	0.423445	−	0.361018i
$453$		−	6.00929e10i		−	1.42702i
$454$	−2.32457e10	+	5.03661e10i	−0.547166	+	1.18554i
$455$		0			0
$456$	−9.89994e9	−	3.52791e10i	−0.228967	−	0.815941i
$457$		−	3.11288e10i		−	0.713669i	−0.934168	−	0.356835i	$-0.883856\pi$
$457$		−	3.11288e10i		−	0.713669i	0.934168	−	0.356835i	$-0.116144\pi$
$458$	8.79973e9	−	1.90662e10i	0.199990	−	0.433314i
$459$		−	7.36992e10i		−	1.66040i
$460$		0			0
$461$	4.68016e10			1.03623			0.518116	−	0.855310i	$-0.326634\pi$
$461$	4.68016e10			1.03623			0.518116	+	0.855310i	$0.326634\pi$
$462$	1.31886e10	+	6.08700e9i	0.289488	+	0.133609i
$463$	−2.03332e10			−0.442468			−0.221234	−	0.975221i	$-0.571008\pi$
$463$	−2.03332e10			−0.442468			−0.221234	+	0.975221i	$0.571008\pi$
$464$	9.35140e9	−	5.83831e10i	0.201746	−	1.25955i
$465$		0			0
$466$	−3.54181e10	−	1.63467e10i	−0.751072	−	0.346646i
$467$	5.89675e10			1.23978			0.619891	−	0.784688i	$-0.287177\pi$
$467$	5.89675e10			1.23978			0.619891	+	0.784688i	$0.287177\pi$
$468$	−1.46699e11	+	1.25072e11i	−3.05805	+	2.60721i
$469$	3.79194e10			0.783737
$470$		0			0
$471$		−	1.05229e11i		−	2.13821i
$472$	9.76734e9	+	3.48066e10i	0.196792	+	0.701283i
$473$		−	6.79375e9i		−	0.135727i
$474$	−1.06613e11	−	4.92054e10i	−2.11201	−	0.974765i
$475$		0			0
$476$	−2.65943e10	+	2.26736e10i	−0.518037	+	0.441665i
$477$			1.20815e11i			2.33372i
$478$	4.04999e10	+	1.86921e10i	0.775786	+	0.358053i
$479$			1.20229e10i			0.228384i	0.993459	+	0.114192i	$0.0364279\pi$
$479$			1.20229e10i			0.228384i	−0.993459	+	0.114192i	$0.963572\pi$
$480$		0			0
$481$	−2.74973e10			−0.513699
$482$	−7.79772e9	+	1.68952e10i	−0.144471	+	0.313022i
$483$	−3.06091e10			−0.562422
$484$	−3.47235e10	−	4.07279e10i	−0.632764	−	0.742181i
$485$		0			0
$486$	−4.64217e10	+	1.00581e11i	−0.832102	+	1.80290i
$487$	−4.85939e10			−0.863905			−0.431953	−	0.901896i	$-0.642175\pi$
$487$	−4.85939e10			−0.863905			−0.431953	+	0.901896i	$0.642175\pi$
$488$	4.26599e10	−	1.19711e10i	0.752213	−	0.211084i
$489$	−3.37091e10			−0.589538
$490$		0			0
$491$			1.71586e9i			0.0295226i	0.999891	+	0.0147613i	$0.00469884\pi$
$491$			1.71586e9i			0.0295226i	−0.999891	+	0.0147613i	$0.995301\pi$
$492$	−7.33445e9	−	8.60272e9i	−0.125172	−	0.146817i
$493$			4.68852e10i			0.793685i
$494$	1.87907e10	−	4.07135e10i	0.315526	−	0.683645i
$495$		0			0
$496$	2.20027e10	+	3.52424e9i	0.363537	+	0.0582289i
$497$			9.74991e9i			0.159799i
$498$	6.98822e10	−	1.51413e11i	1.13619	−	2.46175i
$499$			6.25565e10i			1.00895i	0.863426	+	0.504476i	$0.168314\pi$
$499$			6.25565e10i			1.00895i	−0.863426	+	0.504476i	$0.831686\pi$
$500$		0			0
$501$	−1.68115e11			−2.66843
$502$	−9.00717e10	−	4.15712e10i	−1.41832	−	0.654603i
$503$	−8.60985e10			−1.34500			−0.672502	−	0.740095i	$-0.734780\pi$
$503$	−8.60985e10			−1.34500			−0.672502	+	0.740095i	$0.734780\pi$
$504$	1.65782e11	−	4.65213e10i	2.56930	−	0.720990i
$505$		0			0
$506$	−2.59263e9	−	1.19659e9i	−0.0395493	−	0.0182534i
$507$	−2.10107e11			−3.17987
$508$	−5.16277e10	−	6.05552e10i	−0.775226	−	0.909278i
$509$	−5.17187e10			−0.770506			−0.385253	−	0.922811i	$-0.625886\pi$
$509$	−5.17187e10			−0.770506			−0.385253	+	0.922811i	$0.625886\pi$
$510$		0			0
$511$			9.52994e10i			1.39768i
$512$	4.68445e10	−	5.02788e10i	0.681677	−	0.731653i
$513$		−	8.44601e10i		−	1.21950i
$514$	1.62863e10	+	7.51672e9i	0.233330	+	0.107690i
$515$		0			0
$516$	−7.36707e10	−	8.64098e10i	−1.03919	−	1.21889i
$517$		−	1.15896e10i		−	0.162221i
$518$	2.22994e10	+	1.02920e10i	0.309724	+	0.142948i
$519$			2.37383e11i			3.27175i
$520$		0			0
$521$	6.36828e10			0.864313			0.432157	−	0.901799i	$-0.357753\pi$
$521$	6.36828e10			0.864313			0.432157	+	0.901799i	$0.357753\pi$
$522$	9.68018e10	−	2.09739e11i	1.30377	−	2.82486i
$523$	3.05582e10			0.408434			0.204217	−	0.978926i	$-0.434535\pi$
$523$	3.05582e10			0.408434			0.204217	+	0.978926i	$0.434535\pi$
$524$	1.06128e11	−	9.04820e10i	1.40768	−	1.20015i
$525$		0			0
$526$	−1.01566e10	+	2.20061e10i	−0.132680	+	0.287474i
$527$	−1.76695e10			−0.229077
$528$	2.23634e10	+	3.58201e9i	0.287741	+	0.0460884i
$529$	−7.22938e10			−0.923163
$530$		0			0
$531$			1.41236e11i			1.77651i
$532$	−3.04774e10	+	2.59842e10i	−0.380479	+	0.324387i
$533$		−	1.38344e10i		−	0.171416i
$534$	−1.06663e11	+	2.31105e11i	−1.31175	+	2.84214i
$535$		0			0
$536$	5.69258e10	−	1.59744e10i	0.689683	−	0.193537i
$537$		−	6.65945e10i		−	0.800831i
$538$	−1.83304e10	+	3.97162e10i	−0.218798	+	0.474065i
$539$		−	2.61380e9i		−	0.0309683i
$540$		0			0
$541$	2.53545e10			0.295982			0.147991	−	0.988989i	$-0.452719\pi$
$541$	2.53545e10			0.295982			0.147991	+	0.988989i	$0.452719\pi$
$542$	1.36280e11	+	6.28980e10i	1.57919	+	0.728853i
$543$	−2.81240e10			−0.323503
$544$	−3.03725e10	+	4.52418e10i	−0.346804	+	0.516587i
$545$		0			0
$546$	2.69760e11	+	1.24504e11i	3.03533	+	1.40091i
$547$	5.79915e10			0.647762			0.323881	−	0.946098i	$-0.395012\pi$
$547$	5.79915e10			0.647762			0.323881	+	0.946098i	$0.395012\pi$
$548$	−2.40237e10	+	2.04820e10i	−0.266390	+	0.227117i
$549$	1.73103e11			1.90552
$550$		0			0
$551$			5.37309e10i			0.582932i
$552$	−4.59514e10	+	1.28948e10i	−0.494928	+	0.138885i
$553$			1.28343e11i			1.37237i
$554$	−2.74408e10	−	1.26649e10i	−0.291312	−	0.134451i
$555$		0			0
$556$	−1.31032e11	+	1.11715e11i	−1.37113	+	1.16899i
$557$			1.71554e11i			1.78230i	0.453710	+	0.891149i	$0.350100\pi$
$557$			1.71554e11i			1.78230i	−0.453710	+	0.891149i	$0.649900\pi$
$558$	7.90437e10	+	3.64814e10i	0.815324	+	0.376301i
$559$		−	1.38959e11i		−	1.42312i
$560$		0			0
$561$	−1.79592e10			−0.181315
$562$	1.10983e10	−	2.40465e10i	0.111253	−	0.241050i
$563$	−5.49966e8			−0.00547397			−0.00273698	−	0.999996i	$-0.500871\pi$
$563$	−5.49966e8			−0.00547397			−0.00273698	+	0.999996i	$0.500871\pi$
$564$	−1.25676e11	−	1.47408e11i	−1.24205	−	1.45682i
$565$		0			0
$566$	5.77850e10	−	1.25202e11i	0.563053	−	1.21996i
$567$	2.83808e11			2.74595
$568$	4.10736e9	+	1.46369e10i	0.0394611	+	0.140623i
$569$	1.48683e10			0.141845			0.0709223	−	0.997482i	$-0.477406\pi$
$569$	1.48683e10			0.141845			0.0709223	+	0.997482i	$0.477406\pi$
$570$		0			0
$571$		−	3.55169e10i		−	0.334111i	−0.985947	−	0.167056i	$-0.946574\pi$
$571$		−	3.55169e10i		−	0.334111i	0.985947	−	0.167056i	$-0.0534259\pi$
$572$	1.79818e10	+	2.10912e10i	0.167977	+	0.197023i
$573$		−	7.84618e10i		−	0.727846i
$574$	−5.17809e9	+	1.12193e10i	−0.0477004	+	0.103352i
$575$		0			0
$576$	2.29279e11	−	1.39678e11i	2.08292	−	1.26893i
$577$			4.14670e10i			0.374110i	0.982349	+	0.187055i	$0.0598942\pi$
$577$			4.14670e10i			0.374110i	−0.982349	+	0.187055i	$0.940106\pi$
$578$	−2.86647e10	+	6.21073e10i	−0.256824	+	0.556457i
$579$		−	7.53748e9i		−	0.0670674i
$580$		0			0
$581$	−1.82275e11			−1.59964
$582$	−2.91360e11	−	1.34473e11i	−2.53944	−	1.17204i
$583$	1.73698e10			0.150356
$584$	4.01469e10	+	1.43066e11i	0.345145	+	1.22995i
$585$		0			0
$586$	−8.00916e10	−	3.69651e10i	−0.679198	−	0.313474i
$587$	2.88322e10			0.242843			0.121421	−	0.992601i	$-0.461255\pi$
$587$	2.88322e10			0.242843			0.121421	+	0.992601i	$0.461255\pi$
$588$	−2.83438e10	−	3.32450e10i	−0.237110	−	0.278110i
$589$	−2.02494e10			−0.168249
$590$		0			0
$591$		−	3.95999e10i		−	0.324597i
$592$	3.78123e10	+	6.05651e9i	0.307855	+	0.0493100i
$593$			4.33851e10i			0.350850i	0.984493	+	0.175425i	$0.0561299\pi$
$593$			4.33851e10i			0.350850i	−0.984493	+	0.175425i	$0.943870\pi$
$594$	4.74001e10	+	2.18768e10i	0.380745	+	0.175727i
$595$		0			0
$596$	4.10319e10	+	4.81272e10i	0.325190	+	0.381422i
$597$		−	1.90127e11i		−	1.49674i
$598$	−5.30297e10	−	2.44751e10i	−0.414681	−	0.191390i
$599$		−	1.41612e11i		−	1.10000i	−0.835164	−	0.550000i	$-0.814628\pi$
$599$		−	1.41612e11i		−	1.10000i	0.835164	−	0.550000i	$-0.185372\pi$
$600$		0			0
$601$	−1.16789e11			−0.895170			−0.447585	−	0.894241i	$-0.647716\pi$
$601$	−1.16789e11			−0.895170			−0.447585	+	0.894241i	$0.647716\pi$
$602$	−5.20112e10	+	1.12692e11i	−0.396014	+	0.858037i
$603$	2.30989e11			1.74712
$604$	−7.79345e10	+	6.64449e10i	−0.585574	+	0.499245i
$605$		0			0
$606$	6.13205e10	−	1.32862e11i	0.454690	−	0.985169i
$607$	4.19809e10			0.309241			0.154620	−	0.987974i	$-0.450585\pi$
$607$	4.19809e10			0.309241			0.154620	+	0.987974i	$0.450585\pi$
$608$	−3.48072e10	+	5.18475e10i	−0.254715	+	0.379414i
$609$	−3.56011e11			−2.58818
$610$		0			0
$611$		−	2.37054e11i		−	1.70091i
$612$	−1.62002e11	+	1.38118e11i	−1.15482	+	0.984568i
$613$		−	1.73299e11i		−	1.22731i	−0.789575	−	0.613655i	$-0.789699\pi$
$613$		−	1.73299e11i		−	1.22731i	0.789575	−	0.613655i	$-0.210301\pi$
$614$	1.02921e11	−	2.22998e11i	0.724155	−	1.56901i
$615$		0			0
$616$	−6.68844e9	−	2.38347e10i	−0.0464518	−	0.165534i
$617$			2.09205e11i			1.44355i	0.692130	+	0.721773i	$0.256672\pi$
$617$			2.09205e11i			1.44355i	−0.692130	+	0.721773i	$0.743328\pi$
$618$	2.65206e10	−	5.74618e10i	0.181815	−	0.393936i
$619$		−	1.25079e11i		−	0.851965i	−0.904731	−	0.425983i	$-0.859928\pi$
$619$		−	1.25079e11i		−	0.851965i	0.904731	−	0.425983i	$-0.140072\pi$
$620$		0			0
$621$	−1.10010e11			−0.739717
$622$	−8.07476e10	−	3.72679e10i	−0.539471	−	0.248985i
$623$	2.78211e11			1.84681
$624$	4.57421e11	+	7.32665e10i	3.01702	+	0.483245i
$625$		0			0
$626$	−2.56886e11	−	1.18562e11i	−1.67279	−	0.772054i
$627$	−2.05814e10			−0.133169
$628$	−1.36471e11	+	1.16352e11i	−0.877409	+	0.748055i
$629$	−3.03656e10			−0.193990
$630$		0			0
$631$			2.63720e11i			1.66351i	0.555143	+	0.831755i	$0.312663\pi$
$631$			2.63720e11i			1.66351i	−0.555143	+	0.831755i	$0.687337\pi$
$632$	5.40673e10	+	1.92673e11i	0.338896	+	1.20768i
$633$			1.40305e11i			0.873894i
$634$	4.13001e10	+	1.90614e10i	0.255619	+	0.117977i
$635$		0			0
$636$	2.20927e11	−	1.88356e11i	1.35027	−	1.15120i
$637$		−	5.34628e10i		−	0.324709i
$638$	−3.01545e10	−	1.39174e10i	−0.181999	−	0.0839990i
$639$			5.93925e10i			0.356228i
$640$		0			0
$641$	1.68400e10			0.0997495			0.0498748	−	0.998755i	$-0.484118\pi$
$641$	1.68400e10			0.0997495			0.0498748	+	0.998755i	$0.484118\pi$
$642$	1.27278e11	−	2.75772e11i	0.749228	−	1.62334i
$643$	−2.84422e11			−1.66387			−0.831936	−	0.554871i	$-0.812767\pi$
$643$	−2.84422e11			−1.66387			−0.831936	+	0.554871i	$0.812767\pi$
$644$	3.38446e10	+	3.96970e10i	0.196764	+	0.230789i
$645$		0			0
$646$	2.07508e10	−	4.49604e10i	0.119153	−	0.258167i
$647$	2.11657e11			1.20785			0.603927	−	0.797040i	$-0.293602\pi$
$647$	2.11657e11			1.20785			0.603927	+	0.797040i	$0.293602\pi$
$648$	4.26062e11	−	1.19560e11i	2.41642	−	0.678090i
$649$	2.03057e10			0.114456
$650$		0			0
$651$		−	1.34169e11i		−	0.747012i
$652$	3.72723e10	+	4.37174e10i	0.206251	+	0.241915i
$653$			2.94426e11i			1.61929i	0.586922	+	0.809644i	$0.300340\pi$
$653$			2.94426e11i			1.61929i	−0.586922	+	0.809644i	$0.699660\pi$
$654$	7.81415e10	−	1.69308e11i	0.427140	−	0.925478i
$655$		0			0
$656$	−3.04715e9	+	1.90241e10i	−0.0164543	+	0.102728i
$657$			5.80525e11i			3.11573i
$658$	−8.87271e10	+	1.92243e11i	−0.473318	+	1.02553i
$659$		−	1.18352e11i		−	0.627529i	−0.949501	−	0.313765i	$-0.898410\pi$
$659$		−	1.18352e11i		−	0.627529i	0.949501	−	0.313765i	$-0.101590\pi$
$660$		0			0
$661$	2.01300e11			1.05448			0.527239	−	0.849717i	$-0.323227\pi$
$661$	2.01300e11			1.05448			0.527239	+	0.849717i	$0.323227\pi$
$662$	−1.68987e11	−	7.79934e10i	−0.879875	−	0.406093i
$663$	−3.67337e11			−1.90112
$664$	−2.73636e11	+	7.67871e10i	−1.40767	+	0.395017i
$665$		0			0
$666$	1.35839e11	+	6.26945e10i	0.690442	+	0.318663i
$667$	6.99850e10			0.353591
$668$	1.85886e11	+	2.18029e11i	0.933555	+	1.09498i
$669$	−7.84439e10			−0.391611
$670$		0			0
$671$		−	2.48873e10i		−	0.122768i
$672$	−3.43532e11	−	2.30625e11i	−1.68457	−	1.13092i
$673$		−	2.21745e11i		−	1.08092i	−0.841369	−	0.540461i	$-0.818250\pi$
$673$		−	2.21745e11i		−	1.08092i	0.841369	−	0.540461i	$-0.181750\pi$
$674$	−3.05017e11	−	1.40776e11i	−1.47803	−	0.682164i
$675$		0			0
$676$	2.32316e11	+	2.72488e11i	1.11248	+	1.30485i
$677$		−	3.56145e11i		−	1.69540i	−0.530475	−	0.847701i	$-0.677986\pi$
$677$		−	3.56145e11i		−	1.69540i	0.530475	−	0.847701i	$-0.322014\pi$
$678$	−1.97984e11	−	9.13767e10i	−0.936940	−	0.432431i
$679$			3.50747e11i			1.65012i
$680$		0			0
$681$	5.20778e11			2.42139
$682$	5.24500e9	−	1.13642e10i	0.0242442	−	0.0525295i
$683$	2.15409e11			0.989878			0.494939	−	0.868928i	$-0.335190\pi$
$683$	2.15409e11			0.989878			0.494939	+	0.868928i	$0.335190\pi$
$684$	−1.85656e11	+	1.58285e11i	−0.848172	+	0.723129i
$685$		0			0
$686$	8.15274e10	−	1.76644e11i	0.368135	−	0.797632i
$687$	−1.97142e11			−0.885018
$688$	−3.06070e10	+	1.91087e11i	−0.136605	+	0.852860i
$689$	3.55283e11			1.57651
$690$		0			0
$691$		−	2.64031e11i		−	1.15809i	−0.815296	−	0.579045i	$-0.803426\pi$
$691$		−	2.64031e11i		−	1.15809i	0.815296	−	0.579045i	$-0.196574\pi$
$692$	3.07862e11	−	2.62475e11i	1.34255	−	1.14463i
$693$		−	9.67149e10i		−	0.419334i
$694$	−4.98250e10	+	1.07955e11i	−0.214788	+	0.465377i
$695$		0			0
$696$	−5.34454e11	+	1.49977e11i	−2.27758	+	0.639128i
$697$		−	1.52775e10i		−	0.0647324i
$698$	3.64280e10	−	7.89280e10i	0.153467	−	0.332514i
$699$			3.66218e11i			1.53402i
$700$		0			0
$701$	−1.98676e11			−0.822758			−0.411379	−	0.911464i	$-0.634953\pi$
$701$	−1.98676e11			−0.822758			−0.411379	+	0.911464i	$0.634953\pi$
$702$	9.69523e11	+	4.47469e11i	3.99218	+	1.84253i
$703$	−3.47992e10			−0.142478
$704$	−2.00818e10	−	3.29638e10i	−0.0817545	−	0.134198i
$705$		0			0
$706$	1.04261e11	+	4.81201e10i	0.419666	+	0.193690i
$707$	−1.59943e11			−0.640159
$708$	2.58269e11	−	2.20193e11i	1.02787	−	0.876335i
$709$	1.08511e11			0.429427			0.214713	−	0.976677i	$-0.431118\pi$
$709$	1.08511e11			0.429427			0.214713	+	0.976677i	$0.431118\pi$
$710$		0			0
$711$			7.81814e11i			3.05932i
$712$	4.17659e11	−	1.17202e11i	1.62518	−	0.456054i
$713$			2.63750e10i			0.102055i
$714$	2.97899e11	+	1.37491e11i	1.14624	+	0.529031i
$715$		0			0
$716$	−8.63665e10	+	7.36338e10i	−0.328619	+	0.280172i
$717$		−	4.18763e11i		−	1.58450i
$718$	1.60205e11	+	7.39403e10i	0.602807	+	0.278217i
$719$		−	3.56644e11i		−	1.33450i	−0.744832	−	0.667252i	$-0.767471\pi$
$719$		−	3.56644e11i		−	1.33450i	0.744832	−	0.667252i	$-0.232529\pi$
$720$		0			0
$721$	−6.91741e10			−0.255978
$722$	−9.00923e10	+	1.95201e11i	−0.331542	+	0.718347i
$723$	1.74694e11			0.639329
$724$	3.10969e10	+	3.64741e10i	0.113178	+	0.132749i
$725$		0			0
$726$	−2.10560e11	+	4.56217e11i	−0.757931	+	1.64220i
$727$	−8.05781e10			−0.288456			−0.144228	−	0.989544i	$-0.546070\pi$
$727$	−8.05781e10			−0.288456			−0.144228	+	0.989544i	$0.546070\pi$
$728$	−1.36805e11	−	4.87516e11i	−0.487055	−	1.73565i
$729$	3.31165e11			1.17256
$730$		0			0
$731$		−	1.53455e11i		−	0.537415i
$732$	−2.69875e11	−	3.16541e11i	−0.939978	−	1.10252i
$733$		−	3.80343e11i		−	1.31753i	−0.752351	−	0.658763i	$-0.771080\pi$
$733$		−	3.80343e11i		−	1.31753i	0.752351	−	0.658763i	$-0.228920\pi$
$734$	2.27324e11	−	4.92539e11i	0.783179	−	1.69690i
$735$		0			0
$736$	6.75318e10	+	4.53366e10i	0.230143	+	0.154503i
$737$		−	3.32098e10i		−	0.112563i
$738$	−3.15428e10	+	6.83433e10i	−0.106335	+	0.230394i
$739$			4.01614e11i			1.34658i	0.739381	+	0.673288i	$0.235118\pi$
$739$			4.01614e11i			1.34658i	−0.739381	+	0.673288i	$0.764882\pi$
$740$		0			0
$741$	−4.20972e11			−1.39631
$742$	−2.88123e11	−	1.32979e11i	−0.950523	−	0.438700i
$743$	3.54474e11			1.16313			0.581566	−	0.813499i	$-0.302440\pi$
$743$	3.54474e11			1.16313			0.581566	+	0.813499i	$0.302440\pi$
$744$	−5.65215e10	−	2.01418e11i	−0.184468	−	0.657366i
$745$		0			0
$746$	4.63791e11	+	2.14056e11i	1.49750	+	0.691150i
$747$	−1.11034e12			−3.56594
$748$	1.98575e10	+	2.32913e10i	0.0634335	+	0.0744024i
$749$	−3.31981e11			−1.05484
$750$		0			0
$751$		−	4.84888e11i		−	1.52434i	−0.647378	−	0.762169i	$-0.724134\pi$
$751$		−	4.84888e11i		−	1.52434i	0.647378	−	0.762169i	$-0.275866\pi$
$752$	−5.22132e10	+	3.25980e11i	−0.163271	+	1.01934i
$753$			9.31329e11i			2.89683i
$754$	−6.16781e11	−	2.84666e11i	−1.90829	−	0.880745i
$755$		0			0
$756$	−6.18770e11	−	7.25767e11i	−1.89427	−	2.22183i
$757$			1.22819e11i			0.374009i	0.982359	+	0.187004i	$0.0598779\pi$
$757$			1.22819e11i			0.374009i	−0.982359	+	0.187004i	$0.940122\pi$
$758$	−3.86922e11	−	1.78578e11i	−1.17205	−	0.540942i
$759$			2.68074e10i			0.0807771i
$760$		0			0
$761$	−1.93019e11			−0.575521			−0.287761	−	0.957702i	$-0.592911\pi$
$761$	−1.93019e11			−0.575521			−0.287761	+	0.957702i	$0.592911\pi$
$762$	−3.13066e11	+	6.78315e11i	−0.928573	+	2.01192i
$763$	−2.03817e11			−0.601372
$764$	−1.01757e11	+	8.67555e10i	−0.298670	+	0.254638i
$765$		0			0
$766$	−1.07991e11	+	2.33983e11i	−0.313671	+	0.679625i
$767$	4.15333e11			1.20009
$768$	−6.12876e11	−	2.01502e11i	−1.76168	−	0.579208i
$769$	−1.34359e11			−0.384202			−0.192101	−	0.981375i	$-0.561530\pi$
$769$	−1.34359e11			−0.384202			−0.192101	+	0.981375i	$0.561530\pi$
$770$		0			0
$771$		−	1.68399e11i		−	0.476564i
$772$	−9.77536e9	+	8.33422e9i	−0.0275210	+	0.0234636i
$773$			1.97017e11i			0.551804i	0.961186	+	0.275902i	$0.0889765\pi$
$773$			1.97017e11i			0.551804i	−0.961186	+	0.275902i	$0.911024\pi$
$774$	−3.16831e11	+	6.86472e11i	−0.882803	+	1.91275i
$775$		0			0
$776$	1.47760e11	+	5.26553e11i	0.407483	+	1.45210i
$777$		−	2.30573e11i		−	0.632593i
$778$	1.21811e11	−	2.63925e11i	0.332481	−	0.720380i
$779$		−	1.75082e10i		−	0.0475435i
$780$		0			0
$781$	8.53896e9			0.0229510
$782$	−5.85613e10	−	2.70281e10i	−0.156597	−	0.0722751i
$783$	−1.27951e12			−3.40406
$784$	−1.17756e10	+	7.35183e10i	−0.0311688	+	0.194595i
$785$		0			0
$786$	−1.18880e12	−	5.48675e11i	−3.11473	−	1.43756i
$787$	−3.63175e11			−0.946711			−0.473356	−	0.880871i	$-0.656957\pi$
$787$	−3.63175e11			−0.946711			−0.473356	+	0.880871i	$0.656957\pi$
$788$	−5.13572e10	+	4.37858e10i	−0.133198	+	0.113561i
$789$	2.27540e11			0.587150
$790$		0			0
$791$			2.38339e11i			0.608820i
$792$	−4.07433e10	−	1.45191e11i	−0.103551	−	0.369012i
$793$		−	5.09044e11i		−	1.28725i
$794$	5.85926e11	+	2.70425e11i	1.47421	+	0.680402i
$795$		0			0
$796$	−2.46576e11	+	2.10224e11i	−0.614184	+	0.523637i
$797$		−	5.78264e10i		−	0.143316i	−0.997429	−	0.0716578i	$-0.977171\pi$
$797$		−	5.78264e10i		−	0.143316i	0.997429	−	0.0716578i	$-0.0228289\pi$
$798$	3.41395e11	+	1.57566e11i	0.841872	+	0.388553i
$799$		−	2.61782e11i		−	0.642321i
$800$		0			0
$801$	1.69475e12			4.11694
$802$	−1.24968e11	+	2.70766e11i	−0.302066	+	0.654481i
$803$	8.34631e10			0.200739
$804$	−3.60123e11	−	4.22395e11i	−0.861840	−	1.01087i
$805$		0			0
$806$	1.07281e11	−	2.32444e11i	0.254205	−	0.550781i
$807$	4.10660e11			0.968251
$808$	−2.40111e11	+	6.73795e10i	−0.563336	+	0.158082i
$809$	1.75206e11			0.409031			0.204515	−	0.978863i	$-0.434438\pi$
$809$	1.75206e11			0.409031			0.204515	+	0.978863i	$0.434438\pi$
$810$		0			0
$811$		−	1.53398e11i		−	0.354599i	−0.984157	−	0.177299i	$-0.943264\pi$
$811$		−	1.53398e11i		−	0.354599i	0.984157	−	0.177299i	$-0.0567361\pi$
$812$	3.93642e11	+	4.61711e11i	0.905477	+	1.06205i
$813$		−	1.40912e12i		−	3.22541i
$814$	9.01369e9	−	1.95298e10i	0.0205308	−	0.0444836i
$815$		0			0
$816$	5.05136e11	+	8.09091e10i	1.13932	+	0.182489i
$817$		−	1.75860e11i		−	0.394712i
$818$	−1.31002e11	+	2.83840e11i	−0.292594	+	0.633958i
$819$		−	1.97821e12i		−	4.39680i
$820$		0			0
$821$	−3.12544e11			−0.687922			−0.343961	−	0.938984i	$-0.611769\pi$
$821$	−3.12544e11			−0.687922			−0.343961	+	0.938984i	$0.611769\pi$
$822$	2.69104e11	+	1.24201e11i	0.589431	+	0.272043i
$823$	6.75905e11			1.47328			0.736641	−	0.676283i	$-0.236411\pi$
$823$	6.75905e11			1.47328			0.736641	+	0.676283i	$0.236411\pi$
$824$	−1.03846e11	+	2.91411e10i	−0.225259	+	0.0632116i
$825$		0			0
$826$	−3.36822e11	−	1.55455e11i	−0.723570	−	0.333953i
$827$	7.49212e11			1.60171			0.800853	−	0.598861i	$-0.204380\pi$
$827$	7.49212e11			1.60171			0.800853	+	0.598861i	$0.204380\pi$
$828$	2.06168e11	+	2.41818e11i	0.438631	+	0.514479i
$829$	6.27639e11			1.32890			0.664449	−	0.747333i	$-0.268666\pi$
$829$	6.27639e11			1.32890			0.664449	+	0.747333i	$0.268666\pi$
$830$		0			0
$831$			2.83735e11i			0.594988i
$832$	−4.10753e11	−	6.74242e11i	−0.857211	−	1.40709i
$833$		−	5.90396e10i		−	0.122621i
$834$	1.46777e12	+	6.77429e11i	3.03385	+	1.40023i
$835$		0			0
$836$	2.27569e10	+	2.66920e10i	0.0465895	+	0.0546458i
$837$		−	4.82206e11i		−	0.982495i
$838$	2.33018e11	+	1.07546e11i	0.472512	+	0.218081i
$839$			8.86257e11i			1.78860i	0.447473	+	0.894298i	$0.352324\pi$
$839$			8.86257e11i			1.78860i	−0.447473	+	0.894298i	$0.647676\pi$
$840$		0			0
$841$	3.13739e11			0.627168
$842$	−5.90080e10	+	1.27852e11i	−0.117398	+	0.254365i
$843$	−2.48638e11			−0.492331
$844$	1.81962e11	−	1.55136e11i	0.358600	−	0.305733i
$845$		0			0
$846$	−5.40489e11	+	1.17107e12i	−1.05513	+	2.28613i
$847$	5.49207e11			1.06709
$848$	−4.88560e11	−	7.82540e10i	−0.944787	−	0.151329i
$849$	−1.29457e12			−2.49169
$850$		0			0
$851$			4.53263e10i			0.0864235i
$852$	1.08607e11	−	9.25956e10i	0.206110	−	0.175724i
$853$			4.42385e10i			0.0835611i	0.999127	+	0.0417805i	$0.0133030\pi$
$853$			4.42385e10i			0.0835611i	−0.999127	+	0.0417805i	$0.986697\pi$
$854$	−1.90530e11	+	4.12819e11i	−0.358206	+	0.776119i
$855$		0			0
$856$	−4.98381e11	+	1.39854e11i	−0.928253	+	0.260484i
$857$		−	1.03847e12i		−	1.92517i	−0.270976	−	0.962586i	$-0.587346\pi$
$857$		−	1.03847e12i		−	1.92517i	0.270976	−	0.962586i	$-0.412654\pi$
$858$	1.09040e11	−	2.36255e11i	0.201204	−	0.435945i
$859$		−	5.28066e11i		−	0.969874i	−0.874549	−	0.484937i	$-0.838842\pi$
$859$		−	5.28066e11i		−	0.969874i	0.874549	−	0.484937i	$-0.161158\pi$
$860$		0			0
$861$	1.16006e11			0.211090
$862$	−3.15614e11	−	1.45667e11i	−0.571646	−	0.263835i
$863$	1.90850e11			0.344072			0.172036	−	0.985091i	$-0.444965\pi$
$863$	1.90850e11			0.344072			0.172036	+	0.985091i	$0.444965\pi$
$864$	−1.23466e12	−	8.28873e11i	−2.21561	−	1.48742i
$865$		0			0
$866$	3.64140e11	+	1.68063e11i	0.647436	+	0.298814i
$867$	6.42181e11			1.13653
$868$	−1.74004e11	+	1.48351e11i	−0.306534	+	0.261343i
$869$	1.12403e11			0.197105
$870$		0			0
$871$		−	6.79273e11i		−	1.18024i
$872$	−3.05977e11	+	8.58624e10i	−0.529203	+	0.148504i
$873$			2.13661e12i			3.67848i
$874$	−6.71119e10	−	3.09745e10i	−0.115015	−	0.0530834i
$875$		0			0
$876$	1.06157e12	−	9.05065e11i	1.80273	−	1.53696i
$877$			2.36707e11i			0.400140i	0.979782	+	0.200070i	$0.0641170\pi$
$877$			2.36707e11i			0.400140i	−0.979782	+	0.200070i	$0.935883\pi$
$878$	3.90872e11	+	1.80401e11i	0.657744	+	0.303572i
$879$			8.28136e11i			1.38722i
$880$		0			0
$881$	3.49205e11			0.579665			0.289832	−	0.957077i	$-0.406400\pi$
$881$	3.49205e11			0.579665			0.289832	+	0.957077i	$0.406400\pi$
$882$	−1.21897e11	+	2.64111e11i	−0.201427	+	0.436428i
$883$	5.98818e11			0.985035			0.492518	−	0.870302i	$-0.336077\pi$
$883$	5.98818e11			0.985035			0.492518	+	0.870302i	$0.336077\pi$
$884$	4.06166e11	+	4.76400e11i	0.665111	+	0.780122i
$885$		0			0
$886$	3.46317e11	−	7.50359e11i	0.562004	−	1.21768i
$887$	−5.75931e11			−0.930413			−0.465207	−	0.885202i	$-0.654020\pi$
$887$	−5.75931e11			−0.930413			−0.465207	+	0.885202i	$0.654020\pi$
$888$	−9.71338e10	−	3.46143e11i	−0.156214	−	0.556678i
$889$	8.16574e11			1.30734
$890$		0			0
$891$		−	2.48559e11i		−	0.394383i
$892$	8.67357e10	+	1.01734e11i	0.137006	+	0.160697i
$893$		−	3.00004e11i		−	0.471761i
$894$	2.48814e11	−	5.39101e11i	0.389516	−	0.843957i
$895$		0			0
$896$	8.07457e10	+	7.00530e11i	0.125282	+	1.08691i
$897$			5.48320e11i			0.846962i
$898$	−3.09472e11	+	6.70527e11i	−0.475900	+	1.03112i
$899$			3.06764e11i			0.469641i
$900$		0			0
$901$	3.92343e11			0.595342
$902$	9.82583e9	+	4.53497e9i	0.0148437	+	0.00685091i
$903$	1.16522e12			1.75249
$904$	1.00405e11	+	3.57802e11i	0.150343	+	0.535758i
$905$		0			0
$906$	8.72991e11	+	4.02916e11i	1.29568	+	0.598001i
$907$	−4.04494e11			−0.597699			−0.298849	−	0.954300i	$-0.596603\pi$
$907$	−4.04494e11			−0.597699			−0.298849	+	0.954300i	$0.596603\pi$
$908$	−5.75827e11	−	6.75398e11i	−0.847126	−	0.993611i
$909$	−9.74308e11			−1.42705
$910$		0			0
$911$			6.18016e11i			0.897276i	0.893714	+	0.448638i	$0.148091\pi$
$911$			6.18016e11i			0.897276i	−0.893714	+	0.448638i	$0.851909\pi$
$912$	5.78891e11	+	9.27227e10i	0.836792	+	0.134031i
$913$			1.59636e11i			0.229746i
$914$	4.52219e11	+	2.08715e11i	0.647984	+	0.299067i
$915$		0			0
$916$	2.17981e11	+	2.55674e11i	0.309625	+	0.363165i
$917$			1.43111e12i			2.02394i
$918$	1.07066e12	+	4.94145e11i	1.50758	+	0.695799i
$919$		−	5.11050e11i		−	0.716476i	−0.933630	−	0.358238i	$-0.883378\pi$
$919$		−	5.11050e11i		−	0.716476i	0.933630	−	0.358238i	$-0.116622\pi$
$920$		0			0
$921$	−2.30577e12			−3.20462
$922$	−3.13800e11	+	6.79904e11i	−0.434239	+	0.940858i
$923$	1.74656e11			0.240645
$924$	−1.76856e11	+	1.50783e11i	−0.242623	+	0.206854i
$925$		0			0
$926$	1.36332e11	−	2.95388e11i	0.185419	−	0.401744i
$927$	−4.21380e11			−0.570631
$928$	7.85453e11	+	5.27304e11i	1.05908	+	0.710999i
$929$	−3.49578e11			−0.469333			−0.234666	−	0.972076i	$-0.575400\pi$
$929$	−3.49578e11			−0.469333			−0.234666	+	0.972076i	$0.575400\pi$
$930$		0			0
$931$		−	6.76600e10i		−	0.0900603i
$932$	4.74949e11	−	4.04929e11i	0.629482	−	0.536680i
$933$			8.34919e11i			1.10184i
$934$	−3.95371e11	+	8.56642e11i	−0.519537	+	1.12567i
$935$		0			0
$936$	−8.33363e11	−	2.96975e12i	−1.08575	−	3.86915i
$937$		−	1.37124e11i		−	0.177891i	−0.996036	−	0.0889457i	$-0.971650\pi$
$937$		−	1.37124e11i		−	0.177891i	0.996036	−	0.0889457i	$-0.0283498\pi$
$938$	−2.54245e11	+	5.50869e11i	−0.328429	+	0.711602i
$939$			2.65616e12i			3.41659i
$940$		0			0
$941$	−4.32170e10			−0.0551183			−0.0275592	−	0.999620i	$-0.508773\pi$
$941$	−4.32170e10			−0.0551183			−0.0275592	+	0.999620i	$0.508773\pi$
$942$	1.52869e12	+	7.05546e11i	1.94141	+	0.896028i
$943$	−2.28046e10			−0.0288387
$944$	−5.71137e11	−	9.14807e10i	−0.719204	−	0.115197i
$945$		0			0
$946$	9.86953e10	+	4.55513e10i	0.123234	+	0.0568770i
$947$	−1.24527e12			−1.54832			−0.774162	−	0.632987i	$-0.781829\pi$
$947$	−1.24527e12			−1.54832			−0.774162	+	0.632987i	$0.781829\pi$
$948$	1.42965e12	−	1.21888e12i	1.77010	−	1.50914i
$949$	1.70716e12			2.10479
$950$		0			0
$951$		−	4.27037e11i		−	0.522088i
$952$	−1.51076e11	−	5.38370e11i	−0.183928	−	0.655440i
$953$		−	9.35275e11i		−	1.13388i	−0.823759	−	0.566941i	$-0.808127\pi$
$953$		−	9.35275e11i		−	1.13388i	0.823759	−	0.566941i	$-0.191873\pi$
$954$	−1.75513e12	−	8.10053e11i	−2.11892	−	0.977958i
$955$		0			0
$956$	−5.43095e11	+	4.63028e11i	−0.650195	+	0.554339i
$957$			3.11793e11i			0.371723i
$958$	−1.74661e11	−	8.06120e10i	−0.207364	−	0.0957057i
$959$		−	3.23955e11i		−	0.383010i
$960$		0			0
$961$	7.37282e11			0.864450
$962$	1.84366e11	−	3.99463e11i	0.215269	−	0.466419i
$963$	−2.02229e12			−2.35147
$964$	−1.93160e11	−	2.26561e11i	−0.223670	−	0.262347i
$965$		0			0
$966$	2.05231e11	−	4.44670e11i	0.235686	−	0.510657i
$967$	−1.52906e12			−1.74871			−0.874355	−	0.485286i	$-0.838715\pi$
$967$	−1.52906e12			−1.74871			−0.874355	+	0.485286i	$0.838715\pi$
$968$	8.24486e11	−	2.31365e11i	0.939035	−	0.263510i
$969$	−4.64884e11			−0.527290
$970$		0			0
$971$		−	5.95468e11i		−	0.669856i	−0.942244	−	0.334928i	$-0.891288\pi$
$971$		−	5.95468e11i		−	0.669856i	0.942244	−	0.334928i	$-0.108712\pi$
$972$	−1.14993e12	−	1.34877e12i	−1.28826	−	1.51103i
$973$		−	1.76694e12i		−	1.97139i
$974$	3.25817e11	−	7.05942e11i	0.362024	−	0.784392i
$975$		0			0
$976$	−1.12121e11	+	7.00002e11i	−0.123563	+	0.771436i
$977$			1.10548e12i			1.21332i	0.794962	+	0.606659i	$0.207491\pi$
$977$			1.10548e12i			1.21332i	−0.794962	+	0.606659i	$0.792509\pi$
$978$	2.26016e11	−	4.89704e11i	0.247049	−	0.535277i
$979$		−	2.43657e11i		−	0.265245i
$980$		0			0
$981$	−1.24157e12			−1.34059
$982$	−2.49269e10	−	1.15046e10i	−0.0268054	−	0.0123716i
$983$	−1.26644e10			−0.0135634			−0.00678172	−	0.999977i	$-0.502159\pi$
$983$	−1.26644e10			−0.0135634			−0.00678172	+	0.999977i	$0.502159\pi$
$984$	1.74152e11	−	4.88700e10i	0.185758	−	0.0521269i
$985$		0			0
$986$	−6.81118e11	−	3.14360e11i	−0.720634	−	0.332598i
$987$	1.98777e12			2.09458
$988$	4.65470e11	+	5.45959e11i	0.488500	+	0.572971i
$989$	−2.29060e11			−0.239422
$990$		0			0
$991$		−	7.11883e11i		−	0.738098i	−0.929410	−	0.369049i	$-0.879683\pi$
$991$		−	7.11883e11i		−	0.738098i	0.929410	−	0.369049i	$-0.120317\pi$
$992$	−1.98724e11	+	2.96012e11i	−0.205212	+	0.305677i
$993$			1.74730e12i			1.79709i
$994$	−1.41641e11	−	6.53721e10i	−0.145092	−	0.0669649i
$995$		0			0
$996$	1.73107e12	+	2.03041e12i	1.75905	+	2.06322i
$997$			2.60515e11i			0.263665i	0.991272	+	0.131832i	$0.0420860\pi$
$997$			2.60515e11i			0.263665i	−0.991272	+	0.131832i	$0.957914\pi$
$998$	−9.08782e11	−	4.19435e11i	−0.916089	−	0.422807i
$999$		−	8.28685e11i		−	0.832008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.d.c.99.12		32
4.3	odd	2	inner	100.9.d.c.99.22		32
5.2	odd	4		100.9.b.d.51.1		16
5.3	odd	4		20.9.b.a.11.16	yes	16
5.4	even	2	inner	100.9.d.c.99.21		32
15.8	even	4		180.9.c.a.91.1		16
20.3	even	4		20.9.b.a.11.15	✓	16
20.7	even	4		100.9.b.d.51.2		16
20.19	odd	2	inner	100.9.d.c.99.11		32
40.3	even	4		320.9.b.d.191.16		16
40.13	odd	4		320.9.b.d.191.1		16
60.23	odd	4		180.9.c.a.91.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.15	✓	16	20.3	even	4
20.9.b.a.11.16	yes	16	5.3	odd	4
100.9.b.d.51.1		16	5.2	odd	4
100.9.b.d.51.2		16	20.7	even	4
100.9.d.c.99.11		32	20.19	odd	2	inner
100.9.d.c.99.12		32	1.1	even	1	trivial
100.9.d.c.99.21		32	5.4	even	2	inner
100.9.d.c.99.22		32	4.3	odd	2	inner
180.9.c.a.91.1		16	15.8	even	4
180.9.c.a.91.2		16	60.23	odd	4
320.9.b.d.191.1		16	40.13	odd	4
320.9.b.d.191.16		16	40.3	even	4

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.70489 + 14.5274i) q^{2} +150.211 q^{3} +(-166.089 - 194.809i) q^{4} +(-1007.15 + 2182.17i) q^{6} +2626.96 q^{7} +(3943.67 - 1106.66i) q^{8} +16002.3 q^{9} +O(q^{10})\)	\(q+(-6.70489 + 14.5274i) q^{2} +150.211 q^{3} +(-166.089 - 194.809i) q^{4} +(-1007.15 + 2182.17i) q^{6} +2626.96 q^{7} +(3943.67 - 1106.66i) q^{8} +16002.3 q^{9} -2300.68i q^{11} +(-24948.4 - 29262.4i) q^{12} -47058.2i q^{13} +(-17613.5 + 38162.8i) q^{14} +(-10365.0 + 64711.2i) q^{16} -51967.0i q^{17} +(-107294. + 232472. i) q^{18} -59554.7i q^{19} +394598. q^{21} +(33422.9 + 15425.8i) q^{22} -77570.5 q^{23} +(592382. - 166233. i) q^{24} +(683632. + 315520. i) q^{26} +1.41819e6 q^{27} +(-436308. - 511754. i) q^{28} -902211. q^{29} -340014. i q^{31} +(-870587. - 584457. i) q^{32} -345588. i q^{33} +(754943. + 348433. i) q^{34} +(-2.65781e6 - 3.11740e6i) q^{36} -584324. i q^{37} +(865173. + 399308. i) q^{38} -7.06866e6i q^{39} +293985. q^{41} +(-2.64573e6 + 5.73247e6i) q^{42} +2.95292e6 q^{43} +(-448194. + 382118. i) q^{44} +(520102. - 1.12689e6i) q^{46} +5.03746e6 q^{47} +(-1.55693e6 + 9.72033e6i) q^{48} +1.13610e6 q^{49} -7.80601e6i q^{51} +(-9.16736e6 + 7.81585e6i) q^{52} +7.54985e6i q^{53} +(-9.50883e6 + 2.06026e7i) q^{54} +(1.03598e7 - 2.90715e6i) q^{56} -8.94577e6i q^{57} +(6.04923e6 - 1.31068e7i) q^{58} +8.82594e6i q^{59} +1.08173e7 q^{61} +(4.93951e6 + 2.27976e6i) q^{62} +4.20375e7 q^{63} +(1.43278e7 - 8.72861e6i) q^{64} +(5.02049e6 + 2.31713e6i) q^{66} +1.44347e7 q^{67} +(-1.01236e7 + 8.63113e6i) q^{68} -1.16519e7 q^{69} +3.71149e6i q^{71} +(6.31079e7 - 1.77092e7i) q^{72} +3.62775e7i q^{73} +(8.48869e6 + 3.91783e6i) q^{74} +(-1.16018e7 + 9.89137e6i) q^{76} -6.04380e6i q^{77} +(1.02689e8 + 4.73946e7i) q^{78} +4.88562e7i q^{79} +1.08037e8 q^{81} +(-1.97114e6 + 4.27083e6i) q^{82} -6.93862e7 q^{83} +(-6.55383e7 - 7.68711e7i) q^{84} +(-1.97990e7 + 4.28982e7i) q^{86} -1.35522e8 q^{87} +(-2.54608e6 - 9.07314e6i) q^{88} +1.05906e8 q^{89} -1.23620e8i q^{91} +(1.28836e7 + 1.51114e7i) q^{92} -5.10738e7i q^{93} +(-3.37756e7 + 7.31810e7i) q^{94} +(-1.30772e8 - 8.77919e7i) q^{96} +1.33519e8i q^{97} +(-7.61742e6 + 1.65045e7i) q^{98} -3.68163e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9}+O(q^{10}) \) 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9	\( 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44} - 15948304 q^{46} + 65607200 q^{49} - 17797408 q^{54} + 68269536 q^{56} + 16743424 q^{61} + 95087744 q^{64} + 38716000 q^{66} - 15054528 q^{69} + 276421752 q^{74} + 5140800 q^{76} + 281173344 q^{81} - 139523648 q^{84} - 203449344 q^{86} - 213294912 q^{89} - 110529264 q^{94} - 906779904 q^{96}+O(q^{100}) \) 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

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