LMFDB - Embedded newform 100.9.d.b.99.4

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:	$4$
Coefficient field:	$\Q(i, \sqrt{39})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 19x^{2} + 100 $ x^4 - 19*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$3.12250 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	100.99
Dual form			100.9.d.b.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.4900 + 10.0000i) q^{2} -99.9200 q^{3} +(56.0000 + 249.800i) q^{4} +(-1248.00 - 999.200i) q^{6} +1398.88 q^{7} +(-1798.56 + 3680.00i) q^{8} +3423.00 q^{9} -18485.2i q^{11} +(-5595.52 - 24960.0i) q^{12} -5470.00i q^{13} +(17472.0 + 13988.8i) q^{14} +(-59264.0 + 27977.6i) q^{16} -73090.0i q^{17} +(42753.3 + 34230.0i) q^{18} +19484.4i q^{19} -139776. q^{21} +(184852. - 230880. i) q^{22} +237210. q^{23} +(179712. - 367705. i) q^{24} +(54700.0 - 68320.3i) q^{26} +313549. q^{27} +(78337.3 + 349440. i) q^{28} +128222. q^{29} -67945.6i q^{31} +(-1.01998e6 - 243200. i) q^{32} +1.84704e6i q^{33} +(730900. - 912894. i) q^{34} +(191688. + 855065. i) q^{36} +3.47203e6i q^{37} +(-194844. + 243360. i) q^{38} +546562. i q^{39} +2.14688e6 q^{41} +(-1.74580e6 - 1.39776e6i) q^{42} +5.92815e6 q^{43} +(4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 + 2.37210e6i) q^{46} +7.62629e6 q^{47} +(5.92166e6 - 2.79552e6i) q^{48} -3.80794e6 q^{49} +7.30315e6i q^{51} +(1.36641e6 - 306320. i) q^{52} +824290. i q^{53} +(3.91622e6 + 3.13549e6i) q^{54} +(-2.51597e6 + 5.14788e6i) q^{56} -1.94688e6i q^{57} +(1.60149e6 + 1.28222e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(679456. - 848640. i) q^{62} +4.78836e6 q^{63} +(-1.03076e7 - 1.32374e7i) q^{64} +(-1.84704e7 + 2.30695e7i) q^{66} +1.52567e7 q^{67} +(1.82579e7 - 4.09304e6i) q^{68} -2.37020e7 q^{69} -1.19604e6i q^{71} +(-6.15647e6 + 1.25966e7i) q^{72} -5.72563e6i q^{73} +(-3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 + 1.09113e6i) q^{76} -2.58586e7i q^{77} +(-5.46562e6 + 6.82656e6i) q^{78} -3.59132e7i q^{79} -5.37881e7 q^{81} +(2.68145e7 + 2.14688e7i) q^{82} +5.19603e7 q^{83} +(-7.82746e6 - 3.49160e7i) q^{84} +(7.40426e7 + 5.92815e7i) q^{86} -1.28119e7 q^{87} +(6.80255e7 + 3.32467e7i) q^{88} +8.33242e7 q^{89} -7.65187e6i q^{91} +(1.32838e7 + 5.92550e7i) q^{92} +6.78912e6i q^{93} +(9.52524e7 + 7.62629e7i) q^{94} +(1.01917e8 + 2.43005e7i) q^{96} -1.20619e8i q^{97} +(-4.75611e7 - 3.80794e7i) q^{98} -6.32748e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 224 q^{4} - 4992 q^{6} + 13692 q^{9} + 69888 q^{14} - 237056 q^{16} - 559104 q^{21} + 718848 q^{24} + 218800 q^{26} + 512888 q^{29} + 2923600 q^{34} + 766752 q^{36} + 8587528 q^{41} + 18470400 q^{44}+ \cdots + 407666688 q^{96}+O(q^{100}) $ 4 * q + 224 * q^4 - 4992 * q^6 + 13692 * q^9 + 69888 * q^14 - 237056 * q^16 - 559104 * q^21 + 718848 * q^24 + 218800 * q^26 + 512888 * q^29 + 2923600 * q^34 + 766752 * q^36 + 8587528 * q^41 + 18470400 * q^44 + 11851008 * q^46 - 15231748 * q^49 + 15664896 * q^54 - 10063872 * q^56 - 58984312 * q^61 - 41230336 * q^64 - 73881600 * q^66 - 94808064 * q^69 - 138881200 * q^74 - 19468800 * q^76 - 215152380 * q^81 - 31309824 * q^84 + 296170368 * q^86 + 333296888 * q^89 + 381009408 * q^94 + 407666688 * q^96

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 $

$2$	12.4900	+	10.0000i	0.780625	+	0.625000i
$2$	12.4900	+	10.0000i	0.780625	+	0.625000i
$3$	−99.9200			−1.23358			−0.616790	−	0.787128i	$-0.711567\pi$
$3$	−99.9200			−1.23358			−0.616790	+	0.787128i	$0.711567\pi$
$4$	56.0000	+	249.800i	0.218750	+	0.975781i
$5$		0			0
$5$		0			0
$6$	−1248.00	−	999.200i	−0.962963	−	0.770987i
$7$	1398.88			0.582624			0.291312	−	0.956628i	$-0.405908\pi$
$7$	1398.88			0.582624			0.291312	+	0.956628i	$0.405908\pi$
$8$	−1798.56	+	3680.00i	−0.439101	+	0.898438i
$9$	3423.00			0.521719
$10$		0			0
$11$		−	18485.2i		−	1.26256i	−0.775554	−	0.631282i	$-0.782529\pi$
$11$		−	18485.2i		−	1.26256i	0.775554	−	0.631282i	$-0.217471\pi$
$12$	−5595.52	−	24960.0i	−0.269846	−	1.20370i
$13$		−	5470.00i		−	0.191520i	−0.995404	−	0.0957600i	$-0.969472\pi$
$13$		−	5470.00i		−	0.191520i	0.995404	−	0.0957600i	$-0.0305281\pi$
$14$	17472.0	+	13988.8i	0.454810	+	0.364140i
$15$		0			0
$16$	−59264.0	+	27977.6i	−0.904297	+	0.426904i
$17$		−	73090.0i		−	0.875109i	−0.899192	−	0.437555i	$-0.855845\pi$
$17$		−	73090.0i		−	0.875109i	0.899192	−	0.437555i	$-0.144155\pi$
$18$	42753.3	+	34230.0i	0.407267	+	0.326075i
$19$			19484.4i			0.149511i	0.997202	+	0.0747554i	$0.0238176\pi$
$19$			19484.4i			0.149511i	−0.997202	+	0.0747554i	$0.976182\pi$
$20$		0			0
$21$	−139776.			−0.718713
$22$	184852.	−	230880.i	0.789102	−	0.985588i
$23$	237210.			0.847660			0.423830	−	0.905742i	$-0.360685\pi$
$23$	237210.			0.847660			0.423830	+	0.905742i	$0.360685\pi$
$24$	179712.	−	367705.i	0.541667	−	1.10829i
$25$		0			0
$26$	54700.0	−	68320.3i	0.119700	−	0.149505i
$27$	313549.			0.589997
$28$	78337.3	+	349440.i	0.127449	+	0.568513i
$29$	128222.			0.181289			0.0906443	−	0.995883i	$-0.471107\pi$
$29$	128222.			0.181289			0.0906443	+	0.995883i	$0.471107\pi$
$30$		0			0
$31$		−	67945.6i		−	0.0735723i	−0.999323	−	0.0367862i	$-0.988288\pi$
$31$		−	67945.6i		−	0.0735723i	0.999323	−	0.0367862i	$-0.0117120\pi$
$32$	−1.01998e6	−	243200.i	−0.972732	−	0.231934i
$33$			1.84704e6i			1.55747i
$34$	730900.	−	912894.i	0.546943	−	0.683132i
$35$		0			0
$36$	191688.	+	855065.i	0.114126	+	0.509084i
$37$			3.47203e6i			1.85258i	0.376813	+	0.926289i	$0.377020\pi$
$37$			3.47203e6i			1.85258i	−0.376813	+	0.926289i	$0.622980\pi$
$38$	−194844.	+	243360.i	−0.0934442	+	0.116712i
$39$			546562.i			0.236255i
$40$		0			0
$41$	2.14688e6			0.759754			0.379877	−	0.925037i	$-0.375966\pi$
$41$	2.14688e6			0.759754			0.379877	+	0.925037i	$0.375966\pi$
$42$	−1.74580e6	−	1.39776e6i	−0.561045	−	0.449196i
$43$	5.92815e6			1.73399			0.866993	−	0.498321i	$-0.166050\pi$
$43$	5.92815e6			1.73399			0.866993	+	0.498321i	$0.166050\pi$
$44$	4.61760e6	−	1.03517e6i	1.23199	−	0.276186i
$45$		0			0
$46$	2.96275e6	+	2.37210e6i	0.661704	+	0.529787i
$47$	7.62629e6			1.56287			0.781433	−	0.623989i	$-0.214489\pi$
$47$	7.62629e6			1.56287			0.781433	+	0.623989i	$0.214489\pi$
$48$	5.92166e6	−	2.79552e6i	1.11552	−	0.526620i
$49$	−3.80794e6			−0.660550
$50$		0			0
$51$			7.30315e6i			1.07952i
$52$	1.36641e6	−	306320.i	0.186881	−	0.0418950i
$53$			824290.i			0.104466i	0.998635	+	0.0522332i	$0.0166339\pi$
$53$			824290.i			0.104466i	−0.998635	+	0.0522332i	$0.983366\pi$
$54$	3.91622e6	+	3.13549e6i	0.460567	+	0.368748i
$55$		0			0
$56$	−2.51597e6	+	5.14788e6i	−0.255831	+	0.523451i
$57$		−	1.94688e6i		−	0.184433i
$58$	1.60149e6	+	1.28222e6i	0.141518	+	0.113305i
$59$			3.72552e6i			0.307453i	0.988113	+	0.153726i	$0.0491274\pi$
$59$			3.72552e6i			0.307453i	−0.988113	+	0.153726i	$0.950873\pi$
$60$		0			0
$61$	−1.47461e7			−1.06502			−0.532509	−	0.846424i	$-0.678751\pi$
$61$	−1.47461e7			−1.06502			−0.532509	+	0.846424i	$0.678751\pi$
$62$	679456.	−	848640.i	0.0459827	−	0.0574324i
$63$	4.78836e6			0.303966
$64$	−1.03076e7	−	1.32374e7i	−0.614380	−	0.789010i
$65$		0			0
$66$	−1.84704e7	+	2.30695e7i	−0.973421	+	1.21580i
$67$	1.52567e7			0.757113			0.378557	−	0.925578i	$-0.376421\pi$
$67$	1.52567e7			0.757113			0.378557	+	0.925578i	$0.376421\pi$
$68$	1.82579e7	−	4.09304e6i	0.853915	−	0.191430i
$69$	−2.37020e7			−1.04566
$70$		0			0
$71$		−	1.19604e6i		−	0.0470666i	−0.999723	−	0.0235333i	$-0.992508\pi$
$71$		−	1.19604e6i		−	0.0470666i	0.999723	−	0.0235333i	$-0.00749158\pi$
$72$	−6.15647e6	+	1.25966e7i	−0.229088	+	0.468732i
$73$		−	5.72563e6i		−	0.201619i	−0.994906	−	0.100810i	$-0.967857\pi$
$73$		−	5.72563e6i		−	0.201619i	0.994906	−	0.100810i	$-0.0321433\pi$
$74$	−3.47203e7	+	4.33656e7i	−1.15786	+	1.44617i
$75$		0			0
$76$	−4.86720e6	+	1.09113e6i	−0.145890	+	0.0327055i
$77$		−	2.58586e7i		−	0.735600i
$78$	−5.46562e6	+	6.82656e6i	−0.147659	+	0.184427i
$79$		−	3.59132e7i		−	0.922032i	−0.887392	−	0.461016i	$-0.847485\pi$
$79$		−	3.59132e7i		−	0.922032i	0.887392	−	0.461016i	$-0.152515\pi$
$80$		0			0
$81$	−5.37881e7			−1.24953
$82$	2.68145e7	+	2.14688e7i	0.593082	+	0.474846i
$83$	5.19603e7			1.09486			0.547431	−	0.836851i	$-0.315606\pi$
$83$	5.19603e7			1.09486			0.547431	+	0.836851i	$0.315606\pi$
$84$	−7.82746e6	−	3.49160e7i	−0.157218	−	0.701306i
$85$		0			0
$86$	7.40426e7	+	5.92815e7i	1.35359	+	1.08374i
$87$	−1.28119e7			−0.223634
$88$	6.80255e7	+	3.32467e7i	1.13433	+	0.554393i
$89$	8.33242e7			1.32804			0.664020	−	0.747715i	$-0.268849\pi$
$89$	8.33242e7			1.32804			0.664020	+	0.747715i	$0.268849\pi$
$90$		0			0
$91$		−	7.65187e6i		−	0.111584i
$92$	1.32838e7	+	5.92550e7i	0.185426	+	0.827130i
$93$			6.78912e6i			0.0907573i
$94$	9.52524e7	+	7.62629e7i	1.22001	+	0.976792i
$95$		0			0
$96$	1.01917e8	+	2.43005e7i	1.19994	+	0.286109i
$97$		−	1.20619e8i		−	1.36248i	−0.732062	−	0.681238i	$-0.761442\pi$
$97$		−	1.20619e8i		−	1.36248i	0.732062	−	0.681238i	$-0.238558\pi$
$98$	−4.75611e7	−	3.80794e7i	−0.515641	−	0.412844i
$99$		−	6.32748e7i		−	0.658704i
$100$		0			0
$101$	2.77246e7			0.266428			0.133214	−	0.991087i	$-0.457470\pi$
$101$	2.77246e7			0.266428			0.133214	+	0.991087i	$0.457470\pi$
$102$	−7.30315e7	+	9.12163e7i	−0.674698	+	0.842698i
$103$	−1.04501e8			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$103$	−1.04501e8			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$104$	2.01296e7	+	9.83812e6i	0.172069	+	0.0840967i
$105$		0			0
$106$	−8.24290e6	+	1.02954e7i	−0.0652915	+	0.0815490i
$107$	1.00328e8			0.765394			0.382697	−	0.923874i	$-0.374995\pi$
$107$	1.00328e8			0.765394			0.382697	+	0.923874i	$0.374995\pi$
$108$	1.75587e7	+	7.83245e7i	0.129062	+	0.575708i
$109$	5.90716e7			0.418478			0.209239	−	0.977865i	$-0.432901\pi$
$109$	5.90716e7			0.418478			0.209239	+	0.977865i	$0.432901\pi$
$110$		0			0
$111$		−	3.46925e8i		−	2.28530i
$112$	−8.29032e7	+	3.91373e7i	−0.526865	+	0.248724i
$113$			5.50849e7i			0.337846i	0.985629	+	0.168923i	$0.0540290\pi$
$113$			5.50849e7i			0.337846i	−0.985629	+	0.168923i	$0.945971\pi$
$114$	1.94688e7	−	2.43165e7i	0.115271	−	0.143973i
$115$		0			0
$116$	7.18043e6	+	3.20298e7i	0.0396569	+	0.176898i
$117$		−	1.87238e7i		−	0.0999196i
$118$	−3.72552e7	+	4.65317e7i	−0.192158	+	0.240005i
$119$		−	1.02244e8i		−	0.509859i
$120$		0			0
$121$	−1.27344e8			−0.594067
$122$	−1.84178e8	−	1.47461e8i	−0.831380	−	0.665637i
$123$	−2.14516e8			−0.937217
$124$	1.69728e7	−	3.80495e6i	0.0717905	−	0.0160939i
$125$		0			0
$126$	5.98067e7	+	4.78836e7i	0.237283	+	0.189979i
$127$	2.57160e8			0.988529			0.494264	−	0.869312i	$-0.335438\pi$
$127$	2.57160e8			0.988529			0.494264	+	0.869312i	$0.335438\pi$
$128$	3.63229e6	−	2.68411e8i	0.0135313	−	0.999908i
$129$	−5.92341e8			−2.13901
$130$		0			0
$131$		−	3.12175e8i		−	1.06002i	−0.847992	−	0.530009i	$-0.822188\pi$
$131$		−	3.12175e8i		−	1.06002i	0.847992	−	0.530009i	$-0.177812\pi$
$132$	−4.61390e8	+	1.03434e8i	−1.51975	+	0.340697i
$133$			2.72563e7i			0.0871085i
$134$	1.90556e8	+	1.52567e8i	0.591021	+	0.473196i
$135$		0			0
$136$	2.68971e8	+	1.31457e8i	0.786231	+	0.384262i
$137$		−	2.21980e8i		−	0.630132i	−0.949070	−	0.315066i	$-0.897973\pi$
$137$		−	2.21980e8i		−	0.630132i	0.949070	−	0.315066i	$-0.102027\pi$
$138$	−2.96038e8	−	2.37020e8i	−0.816265	−	0.653535i
$139$			2.95030e8i			0.790328i	0.918611	+	0.395164i	$0.129312\pi$
$139$			2.95030e8i			0.790328i	−0.918611	+	0.395164i	$0.870688\pi$
$140$		0			0
$141$	−7.62019e8			−1.92792
$142$	1.19604e7	−	1.49386e7i	0.0294166	−	0.0367414i
$143$	−1.01114e8			−0.241806
$144$	−2.02861e8	+	9.57673e7i	−0.471789	+	0.222724i
$145$		0			0
$146$	5.72563e7	−	7.15131e7i	0.126012	−	0.157389i
$147$	3.80489e8			0.814841
$148$	−8.67313e8	+	1.94434e8i	−1.80771	+	0.405252i
$149$	−4.03603e8			−0.818859			−0.409429	−	0.912342i	$-0.634272\pi$
$149$	−4.03603e8			−0.818859			−0.409429	+	0.912342i	$0.634272\pi$
$150$		0			0
$151$		−	8.36985e8i		−	1.60994i	−0.593316	−	0.804970i	$-0.702181\pi$
$151$		−	8.36985e8i		−	1.60994i	0.593316	−	0.804970i	$-0.297819\pi$
$152$	−7.17026e7	−	3.50438e7i	−0.134326	−	0.0656504i
$153$		−	2.50187e8i		−	0.456561i
$154$	2.58586e8	−	3.22973e8i	0.459750	−	0.574227i
$155$		0			0
$156$	−1.36531e8	+	3.06075e7i	−0.230533	+	0.0516808i
$157$			2.71319e8i			0.446561i	0.974754	+	0.223281i	$0.0716767\pi$
$157$			2.71319e8i			0.446561i	−0.974754	+	0.223281i	$0.928323\pi$
$158$	3.59132e8	−	4.48556e8i	0.576270	−	0.719761i
$159$		−	8.23630e7i		−	0.128868i
$160$		0			0
$161$	3.31828e8			0.493867
$162$	−6.71813e8	−	5.37881e8i	−0.975413	−	0.780955i
$163$	−5.78509e8			−0.819520			−0.409760	−	0.912193i	$-0.634388\pi$
$163$	−5.78509e8			−0.819520			−0.409760	+	0.912193i	$0.634388\pi$
$164$	1.20225e8	+	5.36291e8i	0.166196	+	0.741353i
$165$		0			0
$166$	6.48984e8	+	5.19603e8i	0.854676	+	0.684288i
$167$	4.68118e8			0.601852			0.300926	−	0.953647i	$-0.402704\pi$
$167$	4.68118e8			0.601852			0.300926	+	0.953647i	$0.402704\pi$
$168$	2.51395e8	−	5.14376e8i	0.315588	−	0.645719i
$169$	7.85810e8			0.963320
$170$		0			0
$171$			6.66951e7i			0.0780026i
$172$	3.31976e8	+	1.48085e9i	0.379309	+	1.69199i
$173$		−	2.06197e8i		−	0.230196i	−0.993354	−	0.115098i	$-0.963282\pi$
$173$		−	2.06197e8i		−	0.230196i	0.993354	−	0.115098i	$-0.0367182\pi$
$174$	−1.60021e8	−	1.28119e8i	−0.174574	−	0.139771i
$175$		0			0
$176$	5.17171e8	+	1.09551e9i	0.538994	+	1.14173i
$177$		−	3.72253e8i		−	0.379268i
$178$	1.04072e9	+	8.33242e8i	1.03670	+	0.830025i
$179$		−	1.41911e8i		−	0.138230i	−0.997609	−	0.0691152i	$-0.977982\pi$
$179$		−	1.41911e8i		−	0.138230i	0.997609	−	0.0691152i	$-0.0220176\pi$
$180$		0			0
$181$	4.82566e8			0.449616			0.224808	−	0.974403i	$-0.427824\pi$
$181$	4.82566e8			0.449616			0.224808	+	0.974403i	$0.427824\pi$
$182$	7.65187e7	−	9.55718e7i	0.0697400	−	0.0871053i
$183$	1.47343e9			1.31379
$184$	−4.26636e8	+	8.72933e8i	−0.372209	+	0.761569i
$185$		0			0
$186$	−6.78912e7	+	8.47961e7i	−0.0567233	+	0.0708474i
$187$	−1.35108e9			−1.10488
$188$	4.27072e8	+	1.90505e9i	0.341877	+	1.52502i
$189$	4.38617e8			0.343747
$190$		0			0
$191$			9.92461e8i			0.745727i	0.927886	+	0.372864i	$0.121624\pi$
$191$			9.92461e8i			0.745727i	−0.927886	+	0.372864i	$0.878376\pi$
$192$	1.02993e9	+	1.32268e9i	0.757887	+	0.973307i
$193$			1.17593e9i			0.847526i	0.905773	+	0.423763i	$0.139291\pi$
$193$			1.17593e9i			0.847526i	−0.905773	+	0.423763i	$0.860709\pi$
$194$	1.20619e9	−	1.50653e9i	0.851547	−	1.06358i
$195$		0			0
$196$	−2.13244e8	−	9.51222e8i	−0.144495	−	0.644552i
$197$		−	1.70538e9i		−	1.13229i	−0.824306	−	0.566144i	$-0.808435\pi$
$197$		−	1.70538e9i		−	1.13229i	0.824306	−	0.566144i	$-0.191565\pi$
$198$	6.32748e8	−	7.90302e8i	0.411690	−	0.514200i
$199$		−	2.49036e9i		−	1.58800i	−0.607919	−	0.793999i	$-0.707996\pi$
$199$		−	2.49036e9i		−	1.58800i	0.607919	−	0.793999i	$-0.292004\pi$
$200$		0			0
$201$	−1.52445e9			−0.933960
$202$	3.46281e8	+	2.77246e8i	0.207981	+	0.166518i
$203$	1.79367e8			0.105623
$204$	−1.82433e9	+	4.08976e8i	−1.05337	+	0.236144i
$205$		0			0
$206$	−1.30522e9	−	1.04501e9i	−0.724792	−	0.580298i
$207$	8.11970e8			0.442241
$208$	1.53037e8	+	3.24174e8i	0.0817606	+	0.173191i
$209$	3.60173e8			0.188767
$210$		0			0
$211$			1.46774e9i			0.740491i	0.928934	+	0.370245i	$0.120726\pi$
$211$			1.46774e9i			0.740491i	−0.928934	+	0.370245i	$0.879274\pi$
$212$	−2.05908e8	+	4.61602e7i	−0.101936	+	0.0228520i
$213$			1.19508e8i			0.0580604i
$214$	1.25309e9	+	1.00328e9i	0.597486	+	0.478371i
$215$		0			0
$216$	−5.63936e8	+	1.15386e9i	−0.259069	+	0.530076i
$217$		−	9.50477e7i		−	0.0428650i
$218$	7.37804e8	+	5.90716e8i	0.326674	+	0.261549i
$219$			5.72105e8i			0.248713i
$220$		0			0
$221$	−3.99802e8			−0.167601
$222$	3.46925e9	−	4.33309e9i	1.42831	−	1.78396i
$223$	1.47920e9			0.598147			0.299073	−	0.954230i	$-0.403322\pi$
$223$	1.47920e9			0.598147			0.299073	+	0.954230i	$0.403322\pi$
$224$	−1.42683e9	−	3.40208e8i	−0.566737	−	0.135130i
$225$		0			0
$226$	−5.50849e8	+	6.88011e8i	−0.211154	+	0.263731i
$227$	−7.50054e8			−0.282481			−0.141241	−	0.989975i	$-0.545109\pi$
$227$	−7.50054e8			−0.282481			−0.141241	+	0.989975i	$0.545109\pi$
$228$	4.86330e8	−	1.09025e8i	0.179967	−	0.0403448i
$229$	2.84784e9			1.03556			0.517778	−	0.855515i	$-0.326759\pi$
$229$	2.84784e9			1.03556			0.517778	+	0.855515i	$0.326759\pi$
$230$		0			0
$231$			2.58379e9i			0.907421i
$232$	−2.30615e8	+	4.71857e8i	−0.0796041	+	0.162876i
$233$			2.20621e8i			0.0748553i	0.999299	+	0.0374276i	$0.0119164\pi$
$233$			2.20621e8i			0.0748553i	−0.999299	+	0.0374276i	$0.988084\pi$
$234$	1.87238e8	−	2.33860e8i	0.0624498	−	0.0779997i
$235$		0			0
$236$	−9.30634e8	+	2.08629e8i	−0.300007	+	0.0672553i
$237$			3.58845e9i			1.13740i
$238$	1.02244e9	−	1.27703e9i	0.318662	−	0.398009i
$239$			4.04493e9i			1.23971i	0.784717	+	0.619855i	$0.212808\pi$
$239$			4.04493e9i			1.23971i	−0.784717	+	0.619855i	$0.787192\pi$
$240$		0			0
$241$	6.17983e9			1.83193			0.915964	−	0.401260i	$-0.131427\pi$
$241$	6.17983e9			1.83193			0.915964	+	0.401260i	$0.131427\pi$
$242$	−1.59052e9	−	1.27344e9i	−0.463743	−	0.371292i
$243$	3.31731e9			0.951395
$244$	−8.25780e8	−	3.68357e9i	−0.232973	−	1.03922i
$245$		0			0
$246$	−2.67931e9	−	2.14516e9i	−0.731615	−	0.585760i
$247$	1.06580e8			0.0286343
$248$	2.50040e8	+	1.22204e8i	0.0661001	+	0.0323057i
$249$	−5.19187e9			−1.35060
$250$		0			0
$251$			5.21367e9i			1.31356i	0.754084	+	0.656778i	$0.228081\pi$
$251$			5.21367e9i			1.31356i	−0.754084	+	0.656778i	$0.771919\pi$
$252$	2.68148e8	+	1.19613e9i	0.0664926	+	0.296604i
$253$		−	4.38487e9i		−	1.07022i
$254$	3.21193e9	+	2.57160e9i	0.771670	+	0.617830i
$255$		0			0
$256$	2.72948e9	−	3.31613e9i	0.635506	−	0.772096i
$257$			6.13693e9i			1.40676i	0.710816	+	0.703378i	$0.248326\pi$
$257$			6.13693e9i			1.40676i	−0.710816	+	0.703378i	$0.751674\pi$
$258$	−7.39833e9	−	5.92341e9i	−1.66976	−	1.33688i
$259$			4.85695e9i			1.07936i
$260$		0			0
$261$	4.38904e8			0.0945818
$262$	3.12175e9	−	3.89907e9i	0.662512	−	0.827477i
$263$	−6.96916e9			−1.45666			−0.728329	−	0.685228i	$-0.759703\pi$
$263$	−6.96916e9			−1.45666			−0.728329	+	0.685228i	$0.759703\pi$
$264$	−6.79711e9	−	3.32201e9i	−1.39929	−	0.683889i
$265$		0			0
$266$	−2.72563e8	+	3.40431e8i	−0.0544428	+	0.0679991i
$267$	−8.32575e9			−1.63824
$268$	8.54374e8	+	3.81112e9i	0.165619	+	0.738777i
$269$	−2.70720e9			−0.517025			−0.258513	−	0.966008i	$-0.583232\pi$
$269$	−2.70720e9			−0.517025			−0.258513	+	0.966008i	$0.583232\pi$
$270$		0			0
$271$		−	7.99032e9i		−	1.48145i	−0.671808	−	0.740725i	$-0.734482\pi$
$271$		−	7.99032e9i		−	1.48145i	0.671808	−	0.740725i	$-0.265518\pi$
$272$	2.04488e9	+	4.33161e9i	0.373588	+	0.791359i
$273$			7.64575e8i			0.137648i
$274$	2.21980e9	−	2.77253e9i	0.393832	−	0.491897i
$275$		0			0
$276$	−1.32731e9	−	5.92076e9i	−0.228737	−	1.02033i
$277$			8.22965e9i			1.39786i	0.715192	+	0.698928i	$0.246339\pi$
$277$			8.22965e9i			1.39786i	−0.715192	+	0.698928i	$0.753661\pi$
$278$	−2.95030e9	+	3.68493e9i	−0.493955	+	0.616949i
$279$		−	2.32578e8i		−	0.0383841i
$280$		0			0
$281$	3.08105e9			0.494167			0.247083	−	0.968994i	$-0.420528\pi$
$281$	3.08105e9			0.494167			0.247083	+	0.968994i	$0.420528\pi$
$282$	−9.51761e9	−	7.62019e9i	−1.50498	−	1.20495i
$283$	−1.17112e9			−0.182582			−0.0912908	−	0.995824i	$-0.529099\pi$
$283$	−1.17112e9			−0.182582			−0.0912908	+	0.995824i	$0.529099\pi$
$284$	2.98771e8	−	6.69784e7i	0.0459267	−	0.0102958i
$285$		0			0
$286$	−1.26291e9	−	1.01114e9i	−0.188760	−	0.151129i
$287$	3.00323e9			0.442650
$288$	−3.49140e9	−	8.32474e8i	−0.507493	−	0.121004i
$289$	1.63361e9			0.234184
$290$		0			0
$291$			1.20522e10i			1.68072i
$292$	1.43026e9	−	3.20635e8i	0.196736	−	0.0441042i
$293$			4.80980e9i			0.652614i	0.945264	+	0.326307i	$0.105804\pi$
$293$			4.80980e9i			0.652614i	−0.945264	+	0.326307i	$0.894196\pi$
$294$	4.75231e9	+	3.80489e9i	0.636085	+	0.509275i
$295$		0			0
$296$	−1.27771e10	−	6.24465e9i	−1.66443	−	0.813470i
$297$		−	5.79601e9i		−	0.744909i
$298$	−5.04100e9	−	4.03603e9i	−0.639221	−	0.511787i
$299$		−	1.29754e9i		−	0.162344i
$300$		0			0
$301$	8.29277e9			1.01026
$302$	8.36985e9	−	1.04539e10i	1.00621	−	1.25676i
$303$	−2.77025e9			−0.328661
$304$	−5.45126e8	−	1.15472e9i	−0.0638268	−	0.135202i
$305$		0			0
$306$	2.50187e9	−	3.12484e9i	0.285351	−	0.356403i
$307$	−3.49176e9			−0.393089			−0.196545	−	0.980495i	$-0.562972\pi$
$307$	−3.49176e9			−0.393089			−0.196545	+	0.980495i	$0.562972\pi$
$308$	6.45947e9	−	1.44808e9i	0.717784	−	0.160912i
$309$	1.04417e10			1.14535
$310$		0			0
$311$		−	1.29807e10i		−	1.38757i	−0.720182	−	0.693785i	$-0.755942\pi$
$311$		−	1.29807e10i		−	1.38757i	0.720182	−	0.693785i	$-0.244058\pi$
$312$	−2.01135e9	−	9.83025e8i	−0.212260	−	0.103740i
$313$		−	6.31165e9i		−	0.657606i	−0.944399	−	0.328803i	$-0.893355\pi$
$313$		−	6.31165e9i		−	0.657606i	0.944399	−	0.328803i	$-0.106645\pi$
$314$	−2.71319e9	+	3.38877e9i	−0.279101	+	0.348597i
$315$		0			0
$316$	8.97112e9	−	2.01114e9i	0.899702	−	0.201695i
$317$		−	1.65902e10i		−	1.64291i	−0.570273	−	0.821455i	$-0.693163\pi$
$317$		−	1.65902e10i		−	1.64291i	0.570273	−	0.821455i	$-0.306837\pi$
$318$	8.23630e8	−	1.02871e9i	0.0805423	−	0.100597i
$319$		−	2.37021e9i		−	0.228888i
$320$		0			0
$321$	−1.00247e10			−0.944175
$322$	4.14453e9	+	3.31828e9i	0.385525	+	0.308667i
$323$	1.42411e9			0.130838
$324$	−3.01213e9	−	1.34363e10i	−0.273334	−	1.21927i
$325$		0			0
$326$	−7.22557e9	−	5.78509e9i	−0.639738	−	0.512200i
$327$	−5.90243e9			−0.516226
$328$	−3.86129e9	+	7.90053e9i	−0.333609	+	0.682591i
$329$	1.06683e10			0.910563
$330$		0			0
$331$			5.48640e9i			0.457062i	0.973537	+	0.228531i	$0.0733922\pi$
$331$			5.48640e9i			0.457062i	−0.973537	+	0.228531i	$0.926608\pi$
$332$	2.90978e9	+	1.29797e10i	0.239501	+	1.06834i
$333$			1.18848e10i			0.966526i
$334$	5.84680e9	+	4.68118e9i	0.469821	+	0.376158i
$335$		0			0
$336$	8.28368e9	−	3.91060e9i	0.649930	−	0.306822i
$337$			3.56226e8i			0.0276189i	0.999905	+	0.0138095i	$0.00439583\pi$
$337$			3.56226e8i			0.0276189i	−0.999905	+	0.0138095i	$0.995604\pi$
$338$	9.81476e9	+	7.85810e9i	0.751992	+	0.602075i
$339$		−	5.50408e9i		−	0.416760i
$340$		0			0
$341$	−1.25599e9			−0.0928897
$342$	−6.66951e8	+	8.33021e8i	−0.0487517	+	0.0608908i
$343$	−1.33911e10			−0.967476
$344$	−1.06621e10	+	2.18156e10i	−0.761396	+	1.55788i
$345$		0			0
$346$	2.06197e9	−	2.57540e9i	0.143872	−	0.179697i
$347$	−1.59731e10			−1.10172			−0.550859	−	0.834599i	$-0.685700\pi$
$347$	−1.59731e10			−1.10172			−0.550859	+	0.834599i	$0.685700\pi$
$348$	−7.17469e8	−	3.20042e9i	−0.0489199	−	0.218218i
$349$	−1.03634e10			−0.698553			−0.349277	−	0.937020i	$-0.613573\pi$
$349$	−1.03634e10			−0.698553			−0.349277	+	0.937020i	$0.613573\pi$
$350$		0			0
$351$		−	1.71511e9i		−	0.112996i
$352$	−4.49560e9	+	1.88546e10i	−0.292831	+	1.22814i
$353$		−	1.30979e10i		−	0.843536i	−0.906704	−	0.421768i	$-0.861410\pi$
$353$		−	1.30979e10i		−	0.843536i	0.906704	−	0.421768i	$-0.138590\pi$
$354$	3.72253e9	−	4.64944e9i	0.237042	−	0.296066i
$355$		0			0
$356$	4.66616e9	+	2.08144e10i	0.290509	+	1.29588i
$357$			1.02162e10i			0.628952i
$358$	1.41911e9	−	1.77247e9i	0.0863940	−	0.107906i
$359$		−	3.31454e9i		−	0.199547i	−0.995010	−	0.0997737i	$-0.968188\pi$
$359$		−	3.31454e9i		−	0.199547i	0.995010	−	0.0997737i	$-0.0318119\pi$
$360$		0			0
$361$	1.66039e10			0.977647
$362$	6.02724e9	+	4.82566e9i	0.350982	+	0.281010i
$363$	1.27242e10			0.732829
$364$	1.91144e9	−	4.28505e8i	0.108882	−	0.0244090i
$365$		0			0
$366$	1.84031e10	+	1.47343e10i	1.02557	+	0.821116i
$367$	1.96628e10			1.08388			0.541939	−	0.840418i	$-0.317691\pi$
$367$	1.96628e10			1.08388			0.541939	+	0.840418i	$0.317691\pi$
$368$	−1.40580e10	+	6.63656e9i	−0.766536	+	0.361870i
$369$	7.34878e9			0.396378
$370$		0			0
$371$			1.15308e9i			0.0608646i
$372$	−1.69592e9	+	3.80191e8i	−0.0885593	+	0.0198532i
$373$		−	2.10063e10i		−	1.08521i	−0.839987	−	0.542606i	$-0.817438\pi$
$373$		−	2.10063e10i		−	1.08521i	0.839987	−	0.542606i	$-0.182562\pi$
$374$	−1.68750e10	−	1.35108e10i	−0.862498	−	0.690551i
$375$		0			0
$376$	−1.37163e10	+	2.80648e10i	−0.686257	+	1.40414i
$377$		−	7.01374e8i		−	0.0347204i
$378$	5.47833e9	+	4.38617e9i	0.268337	+	0.214842i
$379$		−	3.04816e9i		−	0.147734i	−0.997268	−	0.0738670i	$-0.976466\pi$
$379$		−	3.04816e9i		−	0.147734i	0.997268	−	0.0738670i	$-0.0235340\pi$
$380$		0			0
$381$	−2.56955e10			−1.21943
$382$	−9.92461e9	+	1.23958e10i	−0.466080	+	0.582133i
$383$	2.23357e10			1.03802			0.519008	−	0.854770i	$-0.326302\pi$
$383$	2.23357e10			1.03802			0.519008	+	0.854770i	$0.326302\pi$
$384$	−3.62938e8	+	2.68196e10i	−0.0166920	+	1.23347i
$385$		0			0
$386$	−1.17593e10	+	1.46874e10i	−0.529704	+	0.661599i
$387$	2.02921e10			0.904654
$388$	3.01306e10	−	6.75466e9i	1.32948	−	0.298042i
$389$	−3.13680e10			−1.36990			−0.684948	−	0.728592i	$-0.740175\pi$
$389$	−3.13680e10			−1.36990			−0.684948	+	0.728592i	$0.740175\pi$
$390$		0			0
$391$		−	1.73377e10i		−	0.741795i
$392$	6.84880e9	−	1.40132e10i	0.290048	−	0.593463i
$393$			3.11926e10i			1.30762i
$394$	1.70538e10	−	2.13002e10i	0.707680	−	0.883892i
$395$		0			0
$396$	1.58060e10	−	3.54339e9i	0.642751	−	0.144091i
$397$		−	7.65788e9i		−	0.308281i	−0.988049	−	0.154140i	$-0.950739\pi$
$397$		−	7.65788e9i		−	0.308281i	0.988049	−	0.154140i	$-0.0492608\pi$
$398$	2.49036e10	−	3.11046e10i	0.992499	−	1.23963i
$399$		−	2.72345e9i		−	0.107455i
$400$		0			0
$401$	−3.26120e10			−1.26125			−0.630623	−	0.776089i	$-0.717201\pi$
$401$	−3.26120e10			−1.26125			−0.630623	+	0.776089i	$0.717201\pi$
$402$	−1.90403e10	−	1.52445e10i	−0.729072	−	0.583725i
$403$	−3.71662e8			−0.0140906
$404$	1.55258e9	+	6.92561e9i	0.0582812	+	0.259976i
$405$		0			0
$406$	2.24029e9	+	1.79367e9i	0.0824520	+	0.0660144i
$407$	6.41811e10			2.33900
$408$	−2.68756e10	−	1.31352e10i	−0.969879	−	0.474018i
$409$	−2.26168e10			−0.808236			−0.404118	−	0.914707i	$-0.632422\pi$
$409$	−2.26168e10			−0.808236			−0.404118	+	0.914707i	$0.632422\pi$
$410$		0			0
$411$			2.21802e10i			0.777318i
$412$	−5.85205e9	−	2.61043e10i	−0.203104	−	0.905990i
$413$			5.21155e9i			0.179129i
$414$	1.01415e10	+	8.11970e9i	0.345224	+	0.276400i
$415$		0			0
$416$	−1.33030e9	+	5.57931e9i	−0.0444199	+	0.186297i
$417$		−	2.94794e10i		−	0.974932i
$418$	4.49856e9	+	3.60173e9i	0.147356	+	0.117979i
$419$			4.94503e10i			1.60440i	0.597054	+	0.802201i	$0.296338\pi$
$419$			4.94503e10i			1.60440i	−0.597054	+	0.802201i	$0.703662\pi$
$420$		0			0
$421$	−3.34077e10			−1.06345			−0.531726	−	0.846916i	$-0.678457\pi$
$421$	−3.34077e10			−1.06345			−0.531726	+	0.846916i	$0.678457\pi$
$422$	−1.46774e10	+	1.83321e10i	−0.462807	+	0.578045i
$423$	2.61048e10			0.815378
$424$	−3.03339e9	−	1.48253e9i	−0.0938565	−	0.0458713i
$425$		0			0
$426$	−1.19508e9	+	1.49266e9i	−0.0362878	+	0.0453234i
$427$	−2.06280e10			−0.620505
$428$	5.61834e9	+	2.50618e10i	0.167430	+	0.746857i
$429$	1.01033e10			0.298287
$430$		0			0
$431$		−	3.06956e10i		−	0.889544i	−0.895644	−	0.444772i	$-0.853285\pi$
$431$		−	3.06956e10i		−	0.889544i	0.895644	−	0.444772i	$-0.146715\pi$
$432$	−1.85822e10	+	8.77234e9i	−0.533533	+	0.251872i
$433$			2.88433e9i			0.0820529i	0.999158	+	0.0410265i	$0.0130628\pi$
$433$			2.88433e9i			0.0820529i	−0.999158	+	0.0410265i	$0.986937\pi$
$434$	9.50477e8	−	1.18715e9i	0.0267906	−	0.0334615i
$435$		0			0
$436$	3.30801e9	+	1.47561e10i	0.0915421	+	0.408343i
$437$			4.62189e9i			0.126734i
$438$	−5.72105e9	+	7.14559e9i	−0.155446	+	0.194152i
$439$		−	6.92422e10i		−	1.86429i	−0.362088	−	0.932144i	$-0.617936\pi$
$439$		−	6.92422e10i		−	1.86429i	0.362088	−	0.932144i	$-0.382064\pi$
$440$		0			0
$441$	−1.30346e10			−0.344621
$442$	−4.99353e9	−	3.99802e9i	−0.130833	−	0.104751i
$443$	−2.06609e10			−0.536455			−0.268228	−	0.963356i	$-0.586438\pi$
$443$	−2.06609e10			−0.536455			−0.268228	+	0.963356i	$0.586438\pi$
$444$	8.66619e10	−	1.94278e10i	2.22996	−	0.499910i
$445$		0			0
$446$	1.84752e10	+	1.47920e10i	0.466928	+	0.373842i
$447$	4.03280e10			1.01013
$448$	−1.44191e10	−	1.85175e10i	−0.357952	−	0.459696i
$449$	−2.11092e10			−0.519382			−0.259691	−	0.965692i	$-0.583621\pi$
$449$	−2.11092e10			−0.519382			−0.259691	+	0.965692i	$0.583621\pi$
$450$		0			0
$451$		−	3.96855e10i		−	0.959237i
$452$	−1.37602e10	+	3.08476e9i	−0.329664	+	0.0739039i
$453$			8.36315e10i			1.98599i
$454$	−9.36818e9	−	7.50054e9i	−0.220512	−	0.176551i
$455$		0			0
$456$	7.16452e9	+	3.50158e9i	0.165702	+	0.0809850i
$457$			2.06831e10i			0.474188i	0.971487	+	0.237094i	$0.0761950\pi$
$457$			2.06831e10i			0.474188i	−0.971487	+	0.237094i	$0.923805\pi$
$458$	3.55695e10	+	2.84784e10i	0.808381	+	0.647223i
$459$		−	2.29173e10i		−	0.516312i
$460$		0			0
$461$	7.65072e10			1.69394			0.846971	−	0.531640i	$-0.178424\pi$
$461$	7.65072e10			1.69394			0.846971	+	0.531640i	$0.178424\pi$
$462$	−2.58379e10	+	3.22715e10i	−0.567138	+	0.708355i
$463$	−3.41303e9			−0.0742704			−0.0371352	−	0.999310i	$-0.511823\pi$
$463$	−3.41303e9			−0.0742704			−0.0371352	+	0.999310i	$0.511823\pi$
$464$	−7.59895e9	+	3.58734e9i	−0.163939	+	0.0773929i
$465$		0			0
$466$	−2.20621e9	+	2.75555e9i	−0.0467845	+	0.0584339i
$467$	1.92903e10			0.405576			0.202788	−	0.979223i	$-0.435000\pi$
$467$	1.92903e10			0.405576			0.202788	+	0.979223i	$0.435000\pi$
$468$	4.67721e9	−	1.04853e9i	0.0974997	−	0.0218574i
$469$	2.13423e10			0.441112
$470$		0			0
$471$		−	2.71102e10i		−	0.550869i
$472$	−1.37099e10	−	6.70056e9i	−0.276227	−	0.135003i
$473$		−	1.09583e11i		−	2.18927i
$474$	−3.58845e10	+	4.48197e10i	−0.710875	+	0.887883i
$475$		0			0
$476$	2.55406e10	−	5.72567e9i	0.497511	−	0.111532i
$477$			2.82154e9i			0.0545021i
$478$	−4.04493e10	+	5.05212e10i	−0.774818	+	0.967748i
$479$			2.43887e10i			0.463282i	0.972801	+	0.231641i	$0.0744095\pi$
$479$			2.43887e10i			0.463282i	−0.972801	+	0.231641i	$0.925590\pi$
$480$		0			0
$481$	1.89920e10			0.354806
$482$	7.71861e10	+	6.17983e10i	1.43005	+	1.14496i
$483$	−3.31563e10			−0.609224
$484$	−7.13124e9	−	3.18104e10i	−0.129952	−	0.579679i
$485$		0			0
$486$	4.14332e10	+	3.31731e10i	0.742683	+	0.594622i
$487$	−9.30801e10			−1.65478			−0.827391	−	0.561626i	$-0.810176\pi$
$487$	−9.30801e10			−1.65478			−0.827391	+	0.561626i	$0.810176\pi$
$488$	2.65217e10	−	5.42656e10i	0.467651	−	0.956853i
$489$	5.78046e10			1.01094
$490$		0			0
$491$		−	2.12850e9i		−	0.0366225i	−0.999832	−	0.0183113i	$-0.994171\pi$
$491$		−	2.12850e9i		−	0.0366225i	0.999832	−	0.0183113i	$-0.00582898\pi$
$492$	−1.20129e10	−	5.35862e10i	−0.205016	−	0.914518i
$493$		−	9.37175e9i		−	0.158647i
$494$	1.33118e9	+	1.06580e9i	0.0223526	+	0.0178964i
$495$		0			0
$496$	1.90095e9	+	4.02673e9i	0.0314083	+	0.0665312i
$497$		−	1.67312e9i		−	0.0274221i
$498$	−6.48464e10	−	5.19187e10i	−1.05431	−	0.844124i
$499$		−	1.04101e10i		−	0.167901i	−0.996470	−	0.0839503i	$-0.973246\pi$
$499$		−	1.04101e10i		−	0.167901i	0.996470	−	0.0839503i	$-0.0267537\pi$
$500$		0			0
$501$	−4.67744e10			−0.742433
$502$	−5.21367e10	+	6.51187e10i	−0.820973	+	1.02539i
$503$	−3.93019e10			−0.613962			−0.306981	−	0.951716i	$-0.599319\pi$
$503$	−3.93019e10			−0.613962			−0.306981	+	0.951716i	$0.599319\pi$
$504$	−8.61216e9	+	1.76212e10i	−0.133472	+	0.273094i
$505$		0			0
$506$	4.38487e10	−	5.47670e10i	0.668890	−	0.835444i
$507$	−7.85181e10			−1.18833
$508$	1.44010e10	+	6.42387e10i	0.216241	+	0.964587i
$509$	3.25113e10			0.484354			0.242177	−	0.970232i	$-0.422139\pi$
$509$	3.25113e10			0.484354			0.242177	+	0.970232i	$0.422139\pi$
$510$		0			0
$511$		−	8.00947e9i		−	0.117468i
$512$	6.72524e10	−	1.41237e10i	0.978652	−	0.205526i
$513$			6.10931e9i			0.0882110i
$514$	−6.13693e10	+	7.66503e10i	−0.879223	+	1.09815i
$515$		0			0
$516$	−3.31711e10	−	1.47967e11i	−0.467908	−	2.08720i
$517$		−	1.40973e11i		−	1.97322i
$518$	−4.85695e10	+	6.06633e10i	−0.674598	+	0.842572i
$519$			2.06032e10i			0.283965i
$520$		0			0
$521$	1.84550e9			0.0250475			0.0125237	−	0.999922i	$-0.496013\pi$
$521$	1.84550e9			0.0250475			0.0125237	+	0.999922i	$0.496013\pi$
$522$	5.48191e9	+	4.38904e9i	0.0738329	+	0.0591136i
$523$	−6.23770e10			−0.833715			−0.416858	−	0.908972i	$-0.636869\pi$
$523$	−6.23770e10			−0.833715			−0.416858	+	0.908972i	$0.636869\pi$
$524$	7.79814e10	−	1.74818e10i	1.03435	−	0.231879i
$525$		0			0
$526$	−8.70448e10	−	6.96916e10i	−1.13710	−	0.910411i
$527$	−4.96614e9			−0.0643838
$528$	−5.16757e10	−	1.09463e11i	−0.664892	−	1.40842i
$529$	−2.20424e10			−0.281473
$530$		0			0
$531$			1.27524e10i			0.160404i
$532$	−6.80863e9	+	1.52635e9i	−0.0849988	+	0.0190550i
$533$		−	1.17434e10i		−	0.145508i
$534$	−1.03989e11	−	8.32575e10i	−1.27885	−	1.02390i
$535$		0			0
$536$	−2.74400e10	+	5.61446e10i	−0.332449	+	0.680219i
$537$			1.41797e10i			0.170518i
$538$	−3.38130e10	−	2.70720e10i	−0.403603	−	0.323141i
$539$			7.03905e10i			0.833986i
$540$		0			0
$541$	−7.45917e10			−0.870766			−0.435383	−	0.900245i	$-0.643387\pi$
$541$	−7.45917e10			−0.870766			−0.435383	+	0.900245i	$0.643387\pi$
$542$	7.99032e10	−	9.97991e10i	0.925907	−	1.15646i
$543$	−4.82179e10			−0.554638
$544$	−1.77755e10	+	7.45506e10i	−0.202967	+	0.851246i
$545$		0			0
$546$	−7.64575e9	+	9.54954e9i	−0.0860299	+	0.107451i
$547$	1.41531e9			0.0158089			0.00790445	−	0.999969i	$-0.497484\pi$
$547$	1.41531e9			0.0158089			0.00790445	+	0.999969i	$0.497484\pi$
$548$	5.54506e10	−	1.24309e10i	0.614871	−	0.137841i
$549$	−5.04758e10			−0.555641
$550$		0			0
$551$			2.49833e9i			0.0271046i
$552$	4.26295e10	−	8.72234e10i	0.459149	−	0.939457i
$553$		−	5.02383e10i		−	0.537198i
$554$	−8.22965e10	+	1.02788e11i	−0.873660	+	1.09120i
$555$		0			0
$556$	−7.36985e10	+	1.65217e10i	−0.771187	+	0.172884i
$557$			1.37543e11i			1.42895i	0.699661	+	0.714475i	$0.253334\pi$
$557$			1.37543e11i			1.42895i	−0.699661	+	0.714475i	$0.746666\pi$
$558$	2.32578e9	−	2.90489e9i	0.0239901	−	0.0299636i
$559$		−	3.24270e10i		−	0.332093i
$560$		0			0
$561$	1.35000e11			1.36296
$562$	3.84823e10	+	3.08105e10i	0.385759	+	0.308854i
$563$	1.06415e11			1.05918			0.529589	−	0.848255i	$-0.322346\pi$
$563$	1.06415e11			1.05918			0.529589	+	0.848255i	$0.322346\pi$
$564$	−4.26731e10	−	1.90352e11i	−0.421733	−	1.88123i
$565$		0			0
$566$	−1.46273e10	−	1.17112e10i	−0.142528	−	0.114113i
$567$	−7.52431e10			−0.728005
$568$	4.40143e9	+	2.15115e9i	0.0422864	+	0.0206670i
$569$	−4.02429e10			−0.383919			−0.191960	−	0.981403i	$-0.561484\pi$
$569$	−4.02429e10			−0.383919			−0.191960	+	0.981403i	$0.561484\pi$
$570$		0			0
$571$			1.50341e11i			1.41427i	0.707077	+	0.707137i	$0.250014\pi$
$571$			1.50341e11i			1.41427i	−0.707077	+	0.707137i	$0.749986\pi$
$572$	−5.66238e9	−	2.52583e10i	−0.0528951	−	0.235950i
$573$		−	9.91667e10i		−	0.919914i
$574$	3.75103e10	+	3.00323e10i	0.345544	+	0.276657i
$575$		0			0
$576$	−3.52829e10	−	4.53116e10i	−0.320534	−	0.411642i
$577$		−	4.96477e9i		−	0.0447915i	−0.999749	−	0.0223958i	$-0.992871\pi$
$577$		−	4.96477e9i		−	0.0447915i	0.999749	−	0.0223958i	$-0.00712939\pi$
$578$	2.04038e10	+	1.63361e10i	0.182810	+	0.146365i
$579$		−	1.17499e11i		−	1.04549i
$580$		0			0
$581$	7.26862e10			0.637892
$582$	−1.20522e11	+	1.50533e11i	−1.05045	+	1.31201i
$583$	1.52372e10			0.131895
$584$	2.10703e10	+	1.02979e10i	0.181142	+	0.0885313i
$585$		0			0
$586$	−4.80980e10	+	6.00743e10i	−0.407884	+	0.509446i
$587$	1.53440e11			1.29237			0.646185	−	0.763181i	$-0.276363\pi$
$587$	1.53440e11			1.29237			0.646185	+	0.763181i	$0.276363\pi$
$588$	2.13074e10	+	9.50461e10i	0.178246	+	0.795106i
$589$	1.32388e9			0.0109999
$590$		0			0
$591$			1.70402e11i			1.39677i
$592$	−9.71390e10	−	2.05766e11i	−0.790873	−	1.67528i
$593$			2.06036e11i			1.66619i	0.553131	+	0.833094i	$0.313433\pi$
$593$			2.06036e11i			1.66619i	−0.553131	+	0.833094i	$0.686567\pi$
$594$	5.79601e10	−	7.23922e10i	0.465568	−	0.581495i
$595$		0			0
$596$	−2.26017e10	−	1.00820e11i	−0.179125	−	0.799027i
$597$			2.48837e11i			1.95892i
$598$	1.29754e10	−	1.62063e10i	0.101465	−	0.126730i
$599$			2.30634e11i			1.79150i	0.444558	+	0.895750i	$0.353361\pi$
$599$			2.30634e11i			1.79150i	−0.444558	+	0.895750i	$0.646639\pi$
$600$		0			0
$601$	1.01422e11			0.777382			0.388691	−	0.921368i	$-0.372927\pi$
$601$	1.01422e11			0.777382			0.388691	+	0.921368i	$0.372927\pi$
$602$	1.03577e11	+	8.29277e10i	0.788635	+	0.631413i
$603$	5.22236e10			0.395001
$604$	2.09079e11	−	4.68711e10i	1.57095	−	0.352174i
$605$		0			0
$606$	−3.46004e10	−	2.77025e10i	−0.256561	−	0.205413i
$607$	−1.97883e11			−1.45765			−0.728825	−	0.684700i	$-0.759933\pi$
$607$	−1.97883e11			−1.45765			−0.728825	+	0.684700i	$0.759933\pi$
$608$	4.73860e9	−	1.98738e10i	0.0346766	−	0.145434i
$609$	−1.79224e10			−0.130294
$610$		0			0
$611$		−	4.17158e10i		−	0.299320i
$612$	6.24967e10	−	1.40105e10i	0.445504	−	0.0998728i
$613$			1.27158e11i			0.900538i	0.892893	+	0.450269i	$0.148672\pi$
$613$			1.27158e11i			0.900538i	−0.892893	+	0.450269i	$0.851328\pi$
$614$	−4.36121e10	−	3.49176e10i	−0.306855	−	0.245681i
$615$		0			0
$616$	9.51595e10	+	4.65082e10i	0.660890	+	0.323003i
$617$			5.06702e10i			0.349632i	0.984601	+	0.174816i	$0.0559331\pi$
$617$			5.06702e10i			0.349632i	−0.984601	+	0.174816i	$0.944067\pi$
$618$	1.30417e11	+	1.04417e11i	0.894089	+	0.715844i
$619$			7.06748e10i			0.481395i	0.970600	+	0.240698i	$0.0773762\pi$
$619$			7.06748e10i			0.481395i	−0.970600	+	0.240698i	$0.922624\pi$
$620$		0			0
$621$	7.43769e10			0.500117
$622$	1.29807e11	−	1.62128e11i	0.867231	−	1.08317i
$623$	1.16561e11			0.773748
$624$	−1.52915e10	−	3.23915e10i	−0.100858	−	0.213645i
$625$		0			0
$626$	6.31165e10	−	7.88325e10i	0.411004	−	0.513343i
$627$	−3.59885e10			−0.232859
$628$	−6.77754e10	+	1.51938e10i	−0.435746	+	0.0976853i
$629$	2.53771e11			1.62121
$630$		0			0
$631$			1.65273e11i			1.04252i	0.853399	+	0.521259i	$0.174537\pi$
$631$			1.65273e11i			1.04252i	−0.853399	+	0.521259i	$0.825463\pi$
$632$	1.32161e11	+	6.45921e10i	0.828388	+	0.404866i
$633$		−	1.46657e11i		−	0.913454i
$634$	1.65902e11	−	2.07211e11i	1.02682	−	1.28250i
$635$		0			0
$636$	2.05743e10	−	4.61233e9i	0.125747	−	0.0281898i
$637$			2.08294e10i			0.126508i
$638$	2.37021e10	−	2.96039e10i	0.143055	−	0.178676i
$639$		−	4.09405e9i		−	0.0245556i
$640$		0			0
$641$	1.12013e11			0.663490			0.331745	−	0.943369i	$-0.392363\pi$
$641$	1.12013e11			0.663490			0.331745	+	0.943369i	$0.392363\pi$
$642$	−1.25209e11	−	1.00247e11i	−0.737046	−	0.590109i
$643$	2.65913e11			1.55559			0.777795	−	0.628518i	$-0.216338\pi$
$643$	2.65913e11			1.55559			0.777795	+	0.628518i	$0.216338\pi$
$644$	1.85824e10	+	8.28907e10i	0.108033	+	0.481906i
$645$		0			0
$646$	1.77872e10	+	1.42411e10i	0.102136	+	0.0817739i
$647$	2.71996e11			1.55219			0.776097	−	0.630614i	$-0.217197\pi$
$647$	2.71996e11			1.55219			0.776097	+	0.630614i	$0.217197\pi$
$648$	9.67411e10	−	1.97940e11i	0.548670	−	1.12262i
$649$	6.88669e10			0.388179
$650$		0			0
$651$			9.49716e9i			0.0528774i
$652$	−3.23965e10	−	1.44511e11i	−0.179270	−	0.799672i
$653$			3.03789e11i			1.67078i	0.549656	+	0.835391i	$0.314759\pi$
$653$			3.03789e11i			1.67078i	−0.549656	+	0.835391i	$0.685241\pi$
$654$	−7.37213e10	−	5.90243e10i	−0.402979	−	0.322641i
$655$		0			0
$656$	−1.27233e11	+	6.00646e10i	−0.687043	+	0.324342i
$657$		−	1.95988e10i		−	0.105189i
$658$	1.33247e11	+	1.06683e11i	0.710808	+	0.569102i
$659$		−	4.18575e10i		−	0.221938i	−0.993824	−	0.110969i	$-0.964605\pi$
$659$		−	4.18575e10i		−	0.221938i	0.993824	−	0.110969i	$-0.0353954\pi$
$660$		0			0
$661$	−2.46529e11			−1.29141			−0.645703	−	0.763589i	$-0.723435\pi$
$661$	−2.46529e11			−1.29141			−0.645703	+	0.763589i	$0.723435\pi$
$662$	−5.48640e10	+	6.85251e10i	−0.285664	+	0.356794i
$663$	3.99482e10			0.206749
$664$	−9.34537e10	+	1.91214e11i	−0.480755	+	0.983665i
$665$		0			0
$666$	−1.18848e11	+	1.48441e11i	−0.604079	+	0.754494i
$667$	3.04155e10			0.153671
$668$	2.62146e10	+	1.16936e11i	0.131655	+	0.587276i
$669$	−1.47802e11			−0.737862
$670$		0			0
$671$			2.72584e11i			1.34465i
$672$	1.42569e11	+	3.39935e10i	0.699115	+	0.166694i
$673$		−	3.15336e11i		−	1.53714i	−0.639767	−	0.768569i	$-0.720969\pi$
$673$		−	3.15336e11i		−	1.53714i	0.639767	−	0.768569i	$-0.279031\pi$
$674$	−3.56226e9	+	4.44927e9i	−0.0172618	+	0.0215600i
$675$		0			0
$676$	4.40053e10	+	1.96295e11i	0.210726	+	0.939989i
$677$			2.47236e10i			0.117695i	0.998267	+	0.0588475i	$0.0187426\pi$
$677$			2.47236e10i			0.117695i	−0.998267	+	0.0588475i	$0.981257\pi$
$678$	5.50408e10	−	6.87460e10i	0.260475	−	0.325333i
$679$		−	1.68731e11i		−	0.793811i
$680$		0			0
$681$	7.49454e10			0.348463
$682$	−1.56873e10	−	1.25599e10i	−0.0725120	−	0.0580561i
$683$	−7.20843e10			−0.331251			−0.165626	−	0.986189i	$-0.552964\pi$
$683$	−7.20843e10			−0.331251			−0.165626	+	0.986189i	$0.552964\pi$
$684$	−1.66604e10	+	3.73492e9i	−0.0761135	+	0.0170631i
$685$		0			0
$686$	−1.67255e11	−	1.33911e11i	−0.755235	−	0.604672i
$687$	−2.84556e11			−1.27744
$688$	−3.51326e11	+	1.65855e11i	−1.56804	+	0.740246i
$689$	4.50887e9			0.0200074
$690$		0			0
$691$		−	2.95424e11i		−	1.29578i	−0.761732	−	0.647892i	$-0.775651\pi$
$691$		−	2.95424e11i		−	1.29578i	0.761732	−	0.647892i	$-0.224349\pi$
$692$	5.15080e10	−	1.15470e10i	0.224621	−	0.0503554i
$693$		−	8.85139e10i		−	0.383776i
$694$	−1.99503e11	−	1.59731e11i	−0.860028	−	0.688573i
$695$		0			0
$696$	2.30430e10	−	4.71479e10i	0.0981980	−	0.200921i
$697$		−	1.56916e11i		−	0.664867i
$698$	−1.29438e11	−	1.03634e11i	−0.545308	−	0.436596i
$699$		−	2.20444e10i		−	0.0923400i
$700$		0			0
$701$	−2.87925e11			−1.19236			−0.596180	−	0.802851i	$-0.703315\pi$
$701$	−2.87925e11			−1.19236			−0.596180	+	0.802851i	$0.703315\pi$
$702$	1.71511e10	−	2.14217e10i	0.0706227	−	0.0882077i
$703$	−6.76504e10			−0.276980
$704$	−2.44696e11	+	1.90538e11i	−0.996176	+	0.775694i
$705$		0			0
$706$	1.30979e11	−	1.63593e11i	0.527210	−	0.658485i
$707$	3.87834e10			0.155227
$708$	9.29889e10	−	2.08462e10i	0.370082	−	0.0829648i
$709$	−2.51685e11			−0.996030			−0.498015	−	0.867168i	$-0.665938\pi$
$709$	−2.51685e11			−0.996030			−0.498015	+	0.867168i	$0.665938\pi$
$710$		0			0
$711$		−	1.22931e11i		−	0.481042i
$712$	−1.49864e11	+	3.06633e11i	−0.583144	+	1.19316i
$713$		−	1.61174e10i		−	0.0623643i
$714$	−1.02162e11	+	1.27601e11i	−0.393095	+	0.490976i
$715$		0			0
$716$	3.54493e10	−	7.94701e9i	0.134883	−	0.0302379i
$717$		−	4.04170e11i		−	1.52928i
$718$	3.31454e10	−	4.13986e10i	0.124717	−	0.155772i
$719$			1.38856e11i			0.519574i	0.965666	+	0.259787i	$0.0836524\pi$
$719$			1.38856e11i			0.519574i	−0.965666	+	0.259787i	$0.916348\pi$
$720$		0			0
$721$	−1.46184e11			−0.540953
$722$	2.07383e11	+	1.66039e11i	0.763175	+	0.611029i
$723$	−6.17489e11			−2.25983
$724$	2.70237e10	+	1.20545e11i	0.0983536	+	0.438727i
$725$		0			0
$726$	1.58925e11	+	1.27242e11i	0.572064	+	0.458018i
$727$	−1.79083e11			−0.641088			−0.320544	−	0.947234i	$-0.603866\pi$
$727$	−1.79083e11			−0.641088			−0.320544	+	0.947234i	$0.603866\pi$
$728$	2.81589e10	+	1.37623e10i	0.100251	+	0.0489967i
$729$	2.14381e10			0.0759061
$730$		0			0
$731$		−	4.33289e11i		−	1.51743i
$732$	8.25119e10	+	3.68062e11i	0.287391	+	1.28197i
$733$			2.17618e11i			0.753839i	0.926246	+	0.376920i	$0.123017\pi$
$733$			2.17618e11i			0.753839i	−0.926246	+	0.376920i	$0.876983\pi$
$734$	2.45588e11	+	1.96628e11i	0.846101	+	0.677423i
$735$		0			0
$736$	−2.41950e11	−	5.76895e10i	−0.824546	−	0.196601i
$737$		−	2.82023e11i		−	0.955904i
$738$	9.17862e10	+	7.34878e10i	0.309423	+	0.247736i
$739$		−	4.84950e11i		−	1.62599i	−0.582268	−	0.812997i	$-0.697834\pi$
$739$		−	4.84950e11i		−	1.62599i	0.582268	−	0.812997i	$-0.302166\pi$
$740$		0			0
$741$	−1.06494e10			−0.0353227
$742$	−1.15308e10	+	1.44020e10i	−0.0380404	+	0.0475124i
$743$	−2.03509e11			−0.667771			−0.333886	−	0.942614i	$-0.608360\pi$
$743$	−2.03509e11			−0.667771			−0.333886	+	0.942614i	$0.608360\pi$
$744$	−2.49840e10	−	1.22106e10i	−0.0815398	−	0.0398517i
$745$		0			0
$746$	2.10063e11	−	2.62369e11i	0.678258	−	0.847144i
$747$	1.77860e11			0.571210
$748$	−7.56606e10	−	3.37500e11i	−0.241693	−	1.07812i
$749$	1.40346e11			0.445937
$750$		0			0
$751$			2.34693e11i			0.737804i	0.929468	+	0.368902i	$0.120266\pi$
$751$			2.34693e11i			0.737804i	−0.929468	+	0.368902i	$0.879734\pi$
$752$	−4.51965e11	+	2.13365e11i	−1.41330	+	0.667194i
$753$		−	5.20950e11i		−	1.62038i
$754$	7.01374e9	−	8.76016e9i	0.0217002	−	0.0271036i
$755$		0			0
$756$	2.45626e10	+	1.09567e11i	0.0751946	+	0.335421i
$757$			3.84882e11i			1.17204i	0.810295	+	0.586022i	$0.199307\pi$
$757$			3.84882e11i			1.17204i	−0.810295	+	0.586022i	$0.800693\pi$
$758$	3.04816e10	−	3.80715e10i	0.0923338	−	0.115325i
$759$			4.38136e11i			1.32021i
$760$		0			0
$761$	2.39209e11			0.713244			0.356622	−	0.934249i	$-0.383928\pi$
$761$	2.39209e11			0.713244			0.356622	+	0.934249i	$0.383928\pi$
$762$	−3.20936e11	−	2.56955e11i	−0.951916	−	0.762143i
$763$	8.26340e10			0.243815
$764$	−2.47917e11	+	5.55778e10i	−0.727666	+	0.163128i
$765$		0			0
$766$	2.78972e11	+	2.23357e11i	0.810301	+	0.648760i
$767$	2.03786e10			0.0588833
$768$	−2.72729e11	+	3.31347e11i	−0.783947	+	0.952442i
$769$	−2.08457e11			−0.596089			−0.298045	−	0.954552i	$-0.596334\pi$
$769$	−2.08457e11			−0.596089			−0.298045	+	0.954552i	$0.596334\pi$
$770$		0			0
$771$		−	6.13202e11i		−	1.73535i
$772$	−2.93748e11	+	6.58522e10i	−0.826999	+	0.185396i
$773$		−	5.54469e10i		−	0.155296i	−0.996981	−	0.0776478i	$-0.975259\pi$
$773$		−	5.54469e10i		−	0.155296i	0.996981	−	0.0776478i	$-0.0247410\pi$
$774$	2.53448e11	+	2.02921e11i	0.706195	+	0.565409i
$775$		0			0
$776$	4.43878e11	+	2.16940e11i	1.22410	+	0.598265i
$777$		−	4.85306e11i		−	1.33147i
$778$	−3.91786e11	−	3.13680e11i	−1.06938	−	0.856185i
$779$			4.18307e10i			0.113591i
$780$		0			0
$781$	−2.21091e10			−0.0594246
$782$	1.73377e11	−	2.16548e11i	0.463622	−	0.579064i
$783$	4.02039e10			0.106960
$784$	2.25674e11	−	1.06537e11i	0.597333	−	0.281991i
$785$		0			0
$786$	−3.11926e11	+	3.89595e11i	−0.817261	+	1.02076i
$787$	4.05908e11			1.05811			0.529053	−	0.848589i	$-0.322547\pi$
$787$	4.05908e11			1.05811			0.529053	+	0.848589i	$0.322547\pi$
$788$	4.26005e11	−	9.55014e10i	1.10487	−	0.247688i
$789$	6.96358e11			1.79690
$790$		0			0
$791$			7.70572e10i			0.196837i
$792$	2.32851e11	+	1.13804e11i	0.591804	+	0.289238i
$793$			8.06610e10i			0.203972i
$794$	7.65788e10	−	9.56469e10i	0.192676	−	0.240652i
$795$		0			0
$796$	6.22092e11	−	1.39460e11i	1.54954	−	0.347375i
$797$			3.09015e11i			0.765855i	0.923778	+	0.382927i	$0.125084\pi$
$797$			3.09015e11i			0.765855i	−0.923778	+	0.382927i	$0.874916\pi$
$798$	2.72345e10	−	3.40159e10i	0.0671596	−	0.0838823i
$799$		−	5.57406e11i		−	1.36768i
$800$		0			0
$801$	2.85219e11			0.692864
$802$	−4.07324e11	−	3.26120e11i	−0.984560	−	0.788279i
$803$	−1.05839e11			−0.254557
$804$	−8.53690e10	−	3.80807e11i	−0.204304	−	0.911340i
$805$		0			0
$806$	−4.64206e9	−	3.71662e9i	−0.0109994	−	0.00880660i
$807$	2.70504e11			0.637792
$808$	−4.98644e10	+	1.02027e11i	−0.116989	+	0.239369i
$809$	−4.77958e11			−1.11582			−0.557912	−	0.829900i	$-0.688397\pi$
$809$	−4.77958e11			−1.11582			−0.557912	+	0.829900i	$0.688397\pi$
$810$		0			0
$811$		−	6.37503e11i		−	1.47366i	−0.676075	−	0.736832i	$-0.736321\pi$
$811$		−	6.37503e11i		−	1.47366i	0.676075	−	0.736832i	$-0.263679\pi$
$812$	1.00446e10	+	4.48059e10i	0.0231050	+	0.103065i
$813$			7.98393e11i			1.82749i
$814$	8.01622e11	+	6.41811e11i	1.82588	+	1.46187i
$815$		0			0
$816$	−2.04325e11	−	4.32814e11i	−0.460850	−	0.976204i
$817$			1.15506e11i			0.259250i
$818$	−2.82484e11	−	2.26168e11i	−0.630929	−	0.505148i
$819$		−	2.61924e10i		−	0.0582155i
$820$		0			0
$821$	−8.43824e11			−1.85729			−0.928644	−	0.370973i	$-0.879024\pi$
$821$	−8.43824e11			−1.85729			−0.928644	+	0.370973i	$0.879024\pi$
$822$	−2.21802e11	+	2.77031e11i	−0.485824	+	0.606794i
$823$	2.60916e11			0.568723			0.284362	−	0.958717i	$-0.408218\pi$
$823$	2.60916e11			0.568723			0.284362	+	0.958717i	$0.408218\pi$
$824$	1.87951e11	−	3.84563e11i	0.407696	−	0.834179i
$825$		0			0
$826$	−5.21155e10	+	6.50922e10i	−0.111956	+	0.139833i
$827$	2.78675e11			0.595765			0.297883	−	0.954602i	$-0.403720\pi$
$827$	2.78675e11			0.595765			0.297883	+	0.954602i	$0.403720\pi$
$828$	4.54703e10	+	2.02830e11i	0.0967401	+	0.431530i
$829$	−4.75156e11			−1.00605			−0.503023	−	0.864273i	$-0.667779\pi$
$829$	−4.75156e11			−1.00605			−0.503023	+	0.864273i	$0.667779\pi$
$830$		0			0
$831$		−	8.22306e11i		−	1.72437i
$832$	−7.24086e10	+	5.63825e10i	−0.151111	+	0.117666i
$833$			2.78322e11i			0.578053i
$834$	2.94794e11	−	3.68198e11i	0.609333	−	0.761056i
$835$		0			0
$836$	2.01697e10	+	8.99711e10i	0.0412928	+	0.184195i
$837$		−	2.13043e10i		−	0.0434075i
$838$	−4.94503e11	+	6.17635e11i	−1.00275	+	1.25244i
$839$			3.35440e11i			0.676966i	0.940973	+	0.338483i	$0.109914\pi$
$839$			3.35440e11i			0.676966i	−0.940973	+	0.338483i	$0.890086\pi$
$840$		0			0
$841$	−4.83806e11			−0.967134
$842$	−4.17262e11	−	3.34077e11i	−0.830157	−	0.664658i
$843$	−3.07858e11			−0.609594
$844$	−3.66642e11	+	8.21935e10i	−0.722557	+	0.161982i
$845$		0			0
$846$	3.26049e11	+	2.61048e11i	0.636504	+	0.509611i
$847$	−1.78138e11			−0.346117
$848$	−2.30616e10	−	4.88507e10i	−0.0445971	−	0.0944686i
$849$	1.17019e11			0.225229
$850$		0			0
$851$			8.23600e11i			1.57036i
$852$	−2.98532e10	+	6.69247e9i	−0.0566543	+	0.0127007i
$853$		−	9.75408e10i		−	0.184243i	−0.995748	−	0.0921213i	$-0.970635\pi$
$853$		−	9.75408e10i		−	0.184243i	0.995748	−	0.0921213i	$-0.0293648\pi$
$854$	−2.57643e11	−	2.06280e11i	−0.484382	−	0.387816i
$855$		0			0
$856$	−1.80445e11	+	3.69205e11i	−0.336086	+	0.687659i
$857$			7.94769e10i			0.147339i	0.997283	+	0.0736695i	$0.0234710\pi$
$857$			7.94769e10i			0.147339i	−0.997283	+	0.0736695i	$0.976529\pi$
$858$	1.26190e11	+	1.01033e11i	0.232850	+	0.186429i
$859$			4.15618e11i			0.763347i	0.924297	+	0.381673i	$0.124652\pi$
$859$			4.15618e11i			0.763347i	−0.924297	+	0.381673i	$0.875348\pi$
$860$		0			0
$861$	−3.00083e11			−0.546045
$862$	3.06956e11	−	3.83388e11i	0.555965	−	0.694400i
$863$	4.80012e11			0.865383			0.432692	−	0.901542i	$-0.357564\pi$
$863$	4.80012e11			0.865383			0.432692	+	0.901542i	$0.357564\pi$
$864$	−3.19815e11	−	7.62551e10i	−0.573909	−	0.136840i
$865$		0			0
$866$	−2.88433e10	+	3.60253e10i	−0.0512831	+	0.0640525i
$867$	−1.63230e11			−0.288884
$868$	2.37429e10	−	5.32267e9i	0.0418268	−	0.00937671i
$869$	−6.63863e11			−1.16412
$870$		0			0
$871$		−	8.34540e10i		−	0.145002i
$872$	−1.06244e11	+	2.17383e11i	−0.183754	+	0.375976i
$873$		−	4.12879e11i		−	0.710830i
$874$	−4.62189e10	+	5.77274e10i	−0.0792089	+	0.0989319i
$875$		0			0
$876$	−1.42912e11	+	3.20379e10i	−0.242690	+	0.0544060i
$877$		−	2.74155e11i		−	0.463444i	−0.972782	−	0.231722i	$-0.925564\pi$
$877$		−	2.74155e11i		−	0.463444i	0.972782	−	0.231722i	$-0.0744360\pi$
$878$	6.92422e11	−	8.64835e11i	1.16518	−	1.45531i
$879$		−	4.80595e11i		−	0.805051i
$880$		0			0
$881$	8.01838e11			1.33101			0.665507	−	0.746391i	$-0.268215\pi$
$881$	8.01838e11			1.33101			0.665507	+	0.746391i	$0.268215\pi$
$882$	−1.62802e11	−	1.30346e11i	−0.269020	−	0.215388i
$883$	9.95008e11			1.63676			0.818378	−	0.574681i	$-0.194874\pi$
$883$	9.95008e11			1.63676			0.818378	+	0.574681i	$0.194874\pi$
$884$	−2.23889e10	−	9.98706e10i	−0.0366627	−	0.163542i
$885$		0			0
$886$	−2.58054e11	−	2.06609e11i	−0.418770	−	0.335284i
$887$	5.46038e11			0.882122			0.441061	−	0.897477i	$-0.354602\pi$
$887$	5.46038e11			0.882122			0.441061	+	0.897477i	$0.354602\pi$
$888$	1.27668e12	+	6.23965e11i	2.05320	+	1.00348i
$889$	3.59736e11			0.575940
$890$		0			0
$891$			9.94283e11i			1.57761i
$892$	8.28353e10	+	3.69504e11i	0.130845	+	0.583660i
$893$			1.48594e11i			0.233665i
$894$	5.03696e11	+	4.03280e11i	0.788531	+	0.631330i
$895$		0			0
$896$	5.08114e9	−	3.75474e11i	0.00788368	−	0.582570i
$897$			1.29650e11i			0.200264i
$898$	−2.63654e11	−	2.11092e11i	−0.405442	−	0.324614i
$899$		−	8.71212e9i		−	0.0133378i
$900$		0			0
$901$	6.02474e10			0.0914195
$902$	3.96855e11	−	4.95672e11i	0.599523	−	0.748804i
$903$	−8.28613e11			−1.24624
$904$	−2.02713e11	−	9.90735e10i	−0.303534	−	0.148349i
$905$		0			0
$906$	−8.36315e11	+	1.04456e12i	−1.24124	+	1.55031i
$907$	6.55018e11			0.967886			0.483943	−	0.875100i	$-0.339204\pi$
$907$	6.55018e11			0.967886			0.483943	+	0.875100i	$0.339204\pi$
$908$	−4.20030e10	−	1.87364e11i	−0.0617927	−	0.275640i
$909$	9.49014e10			0.139001
$910$		0			0
$911$		−	1.19425e11i		−	0.173389i	−0.996235	−	0.0866943i	$-0.972370\pi$
$911$		−	1.19425e11i		−	0.173389i	0.996235	−	0.0866943i	$-0.0276304\pi$
$912$	5.44690e10	+	1.15380e11i	0.0787354	+	0.166783i
$913$		−	9.60496e11i		−	1.38233i
$914$	−2.06831e11	+	2.58332e11i	−0.296368	+	0.370163i
$915$		0			0
$916$	1.59479e11	+	7.11390e11i	0.226528	+	1.01048i
$917$		−	4.36696e11i		−	0.617592i
$918$	2.29173e11	−	2.86237e11i	0.322695	−	0.403046i
$919$		−	5.33989e10i		−	0.0748635i	−0.999299	−	0.0374318i	$-0.988082\pi$
$919$		−	5.33989e10i		−	0.0748635i	0.999299	−	0.0374318i	$-0.0119177\pi$
$920$		0			0
$921$	3.48897e11			0.484907
$922$	9.55574e11	+	7.65072e11i	1.32233	+	1.05871i
$923$	−6.54235e9			−0.00901420
$924$	−6.45430e11	+	1.44692e11i	−0.885444	+	0.198498i
$925$		0			0
$926$	−4.26287e10	−	3.41303e10i	−0.0579773	−	0.0464190i
$927$	−3.57707e11			−0.484404
$928$	−1.30784e11	−	3.11836e10i	−0.176345	−	0.0420469i
$929$	6.30991e11			0.847150			0.423575	−	0.905861i	$-0.360775\pi$
$929$	6.30991e11			0.847150			0.423575	+	0.905861i	$0.360775\pi$
$930$		0			0
$931$		−	7.41953e10i		−	0.0987593i
$932$	−5.51110e10	+	1.23548e10i	−0.0730423	+	0.0163746i
$933$			1.29703e12i			1.71168i
$934$	2.40936e11	+	1.92903e11i	0.316603	+	0.253485i
$935$		0			0
$936$	6.89036e10	+	3.36759e10i	0.0897715	+	0.0438748i
$937$			8.41436e11i			1.09160i	0.837916	+	0.545799i	$0.183774\pi$
$937$			8.41436e11i			1.09160i	−0.837916	+	0.545799i	$0.816226\pi$
$938$	2.66565e11	+	2.13423e11i	0.344343	+	0.275695i
$939$			6.30660e11i			0.811209i
$940$		0			0
$941$	−4.52935e11			−0.577666			−0.288833	−	0.957379i	$-0.593267\pi$
$941$	−4.52935e11			−0.577666			−0.288833	+	0.957379i	$0.593267\pi$
$942$	2.71102e11	−	3.38606e11i	0.344293	−	0.430022i
$943$	5.09262e11			0.644013
$944$	−1.04231e11	−	2.20789e11i	−0.131253	−	0.278029i
$945$		0			0
$946$	1.09583e12	−	1.36869e12i	1.36829	−	1.70900i
$947$	−1.00309e12			−1.24721			−0.623605	−	0.781739i	$-0.714333\pi$
$947$	−1.00309e12			−1.24721			−0.623605	+	0.781739i	$0.714333\pi$
$948$	−8.96394e11	+	2.00953e11i	−1.10985	+	0.248806i
$949$	−3.13192e10			−0.0386141
$950$		0			0
$951$			1.65769e12i			2.02666i
$952$	3.76258e11	+	1.83892e11i	0.458077	+	0.223880i
$953$		−	1.39040e12i		−	1.68565i	−0.538186	−	0.842826i	$-0.680890\pi$
$953$		−	1.39040e12i		−	1.68565i	0.538186	−	0.842826i	$-0.319110\pi$
$954$	−2.82154e10	+	3.52411e10i	−0.0340638	+	0.0425457i
$955$		0			0
$956$	−1.01042e12	+	2.26516e11i	−1.20968	+	0.271186i
$957$			2.36831e11i			0.282352i
$958$	−2.43887e11	+	3.04614e11i	−0.289551	+	0.361650i
$959$		−	3.10523e11i		−	0.367130i
$960$		0			0
$961$	8.48274e11			0.994587
$962$	2.37210e11	+	1.89920e11i	0.276970	+	0.221754i
$963$	3.43421e11			0.399321
$964$	3.46071e11	+	1.54372e12i	0.400734	+	1.78756i
$965$		0			0
$966$	−4.14122e11	−	3.31563e11i	−0.475575	−	0.380765i
$967$	−9.01843e11			−1.03140			−0.515698	−	0.856771i	$-0.672467\pi$
$967$	−9.01843e11			−1.03140			−0.515698	+	0.856771i	$0.672467\pi$
$968$	2.29035e11	−	4.68624e11i	0.260856	−	0.533732i
$969$	−1.42297e11			−0.161399
$970$		0			0
$971$			1.28411e12i			1.44452i	0.691621	+	0.722261i	$0.256897\pi$
$971$			1.28411e12i			1.44452i	−0.691621	+	0.722261i	$0.743103\pi$
$972$	1.85769e11	+	8.28664e11i	0.208118	+	0.928354i
$973$			4.12712e11i			0.460464i
$974$	−1.16257e12	−	9.30801e11i	−1.29176	−	1.03424i
$975$		0			0
$976$	8.73912e11	−	4.12560e11i	0.963093	−	0.454661i
$977$		−	1.20120e12i		−	1.31837i	−0.751983	−	0.659183i	$-0.770902\pi$
$977$		−	1.20120e12i		−	1.31837i	0.751983	−	0.659183i	$-0.229098\pi$
$978$	7.21979e11	+	5.78046e11i	0.789167	+	0.631840i
$979$		−	1.54026e12i		−	1.67674i
$980$		0			0
$981$	2.02202e11			0.218328
$982$	2.12850e10	−	2.65850e10i	0.0228891	−	0.0285884i
$983$	−3.77388e11			−0.404179			−0.202090	−	0.979367i	$-0.564773\pi$
$983$	−3.77388e11			−0.404179			−0.202090	+	0.979367i	$0.564773\pi$
$984$	3.85820e11	−	7.89420e11i	0.411533	−	0.842031i
$985$		0			0
$986$	9.37175e10	−	1.17053e11i	0.0991546	−	0.123844i
$987$	−1.06597e12			−1.12325
$988$	5.96846e9	+	2.66236e10i	0.00626375	+	0.0279408i
$989$	1.40622e12			1.46983
$990$		0			0
$991$		−	3.35563e11i		−	0.347920i	−0.984753	−	0.173960i	$-0.944344\pi$
$991$		−	3.35563e11i		−	0.347920i	0.984753	−	0.173960i	$-0.0556563\pi$
$992$	−1.65244e10	+	6.93033e10i	−0.0170639	+	0.0715661i
$993$		−	5.48200e11i		−	0.563822i
$994$	1.67312e10	−	2.08972e10i	0.0171388	−	0.0214064i
$995$		0			0
$996$	−2.90745e11	−	1.29693e12i	−0.295444	−	1.31789i
$997$			1.03163e12i			1.04410i	0.852915	+	0.522050i	$0.174833\pi$
$997$			1.03163e12i			1.04410i	−0.852915	+	0.522050i	$0.825167\pi$
$998$	1.04101e11	−	1.30022e11i	0.104938	−	0.131067i
$999$			1.08865e12i			1.09302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.d.b.99.4		4
4.3	odd	2	inner	100.9.d.b.99.2		4
5.2	odd	4		4.9.b.b.3.2	yes	2
5.3	odd	4		100.9.b.c.51.1		2
5.4	even	2	inner	100.9.d.b.99.1		4
15.2	even	4		36.9.d.b.19.1		2
20.3	even	4		100.9.b.c.51.2		2
20.7	even	4		4.9.b.b.3.1	✓	2
20.19	odd	2	inner	100.9.d.b.99.3		4
40.27	even	4		64.9.c.b.63.2		2
40.37	odd	4		64.9.c.b.63.1		2
60.47	odd	4		36.9.d.b.19.2		2
80.27	even	4		256.9.d.e.127.2		4
80.37	odd	4		256.9.d.e.127.4		4
80.67	even	4		256.9.d.e.127.3		4
80.77	odd	4		256.9.d.e.127.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.9.b.b.3.1	✓	2	20.7	even	4
4.9.b.b.3.2	yes	2	5.2	odd	4
36.9.d.b.19.1		2	15.2	even	4
36.9.d.b.19.2		2	60.47	odd	4
64.9.c.b.63.1		2	40.37	odd	4
64.9.c.b.63.2		2	40.27	even	4
100.9.b.c.51.1		2	5.3	odd	4
100.9.b.c.51.2		2	20.3	even	4
100.9.d.b.99.1		4	5.4	even	2	inner
100.9.d.b.99.2		4	4.3	odd	2	inner
100.9.d.b.99.3		4	20.19	odd	2	inner
100.9.d.b.99.4		4	1.1	even	1	trivial
256.9.d.e.127.1		4	80.77	odd	4
256.9.d.e.127.2		4	80.27	even	4
256.9.d.e.127.3		4	80.67	even	4
256.9.d.e.127.4		4	80.37	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.4900 + 10.0000i) q^{2} -99.9200 q^{3} +(56.0000 + 249.800i) q^{4} +(-1248.00 - 999.200i) q^{6} +1398.88 q^{7} +(-1798.56 + 3680.00i) q^{8} +3423.00 q^{9} -18485.2i q^{11} +(-5595.52 - 24960.0i) q^{12} -5470.00i q^{13} +(17472.0 + 13988.8i) q^{14} +(-59264.0 + 27977.6i) q^{16} -73090.0i q^{17} +(42753.3 + 34230.0i) q^{18} +19484.4i q^{19} -139776. q^{21} +(184852. - 230880. i) q^{22} +237210. q^{23} +(179712. - 367705. i) q^{24} +(54700.0 - 68320.3i) q^{26} +313549. q^{27} +(78337.3 + 349440. i) q^{28} +128222. q^{29} -67945.6i q^{31} +(-1.01998e6 - 243200. i) q^{32} +1.84704e6i q^{33} +(730900. - 912894. i) q^{34} +(191688. + 855065. i) q^{36} +3.47203e6i q^{37} +(-194844. + 243360. i) q^{38} +546562. i q^{39} +2.14688e6 q^{41} +(-1.74580e6 - 1.39776e6i) q^{42} +5.92815e6 q^{43} +(4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 + 2.37210e6i) q^{46} +7.62629e6 q^{47} +(5.92166e6 - 2.79552e6i) q^{48} -3.80794e6 q^{49} +7.30315e6i q^{51} +(1.36641e6 - 306320. i) q^{52} +824290. i q^{53} +(3.91622e6 + 3.13549e6i) q^{54} +(-2.51597e6 + 5.14788e6i) q^{56} -1.94688e6i q^{57} +(1.60149e6 + 1.28222e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(679456. - 848640. i) q^{62} +4.78836e6 q^{63} +(-1.03076e7 - 1.32374e7i) q^{64} +(-1.84704e7 + 2.30695e7i) q^{66} +1.52567e7 q^{67} +(1.82579e7 - 4.09304e6i) q^{68} -2.37020e7 q^{69} -1.19604e6i q^{71} +(-6.15647e6 + 1.25966e7i) q^{72} -5.72563e6i q^{73} +(-3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 + 1.09113e6i) q^{76} -2.58586e7i q^{77} +(-5.46562e6 + 6.82656e6i) q^{78} -3.59132e7i q^{79} -5.37881e7 q^{81} +(2.68145e7 + 2.14688e7i) q^{82} +5.19603e7 q^{83} +(-7.82746e6 - 3.49160e7i) q^{84} +(7.40426e7 + 5.92815e7i) q^{86} -1.28119e7 q^{87} +(6.80255e7 + 3.32467e7i) q^{88} +8.33242e7 q^{89} -7.65187e6i q^{91} +(1.32838e7 + 5.92550e7i) q^{92} +6.78912e6i q^{93} +(9.52524e7 + 7.62629e7i) q^{94} +(1.01917e8 + 2.43005e7i) q^{96} -1.20619e8i q^{97} +(-4.75611e7 - 3.80794e7i) q^{98} -6.32748e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 224 q^{4} - 4992 q^{6} + 13692 q^{9} + 69888 q^{14} - 237056 q^{16} - 559104 q^{21} + 718848 q^{24} + 218800 q^{26} + 512888 q^{29} + 2923600 q^{34} + 766752 q^{36} + 8587528 q^{41} + 18470400 q^{44}+ \cdots + 407666688 q^{96}+O(q^{100}) \) 4 * q + 224 * q^4 - 4992 * q^6 + 13692 * q^9 + 69888 * q^14 - 237056 * q^16 - 559104 * q^21 + 718848 * q^24 + 218800 * q^26 + 512888 * q^29 + 2923600 * q^34 + 766752 * q^36 + 8587528 * q^41 + 18470400 * q^44 + 11851008 * q^46 - 15231748 * q^49 + 15664896 * q^54 - 10063872 * q^56 - 58984312 * q^61 - 41230336 * q^64 - 73881600 * q^66 - 94808064 * q^69 - 138881200 * q^74 - 19468800 * q^76 - 215152380 * q^81 - 31309824 * q^84 + 296170368 * q^86 + 333296888 * q^89 + 381009408 * q^94 + 407666688 * q^96

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