LMFDB - Embedded newform 90.11.g.b.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [90,11,Mod(37,90)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("90.37"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(90, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	90.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-32,0,0,3750] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$57.1821527406$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	90.73
Dual form			90.11.g.b.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-16.0000 + 16.0000i) q^{2} -512.000i q^{4} +(1875.00 - 2500.00i) q^{5} +(-8407.00 + 8407.00i) q^{7} +(8192.00 + 8192.00i) q^{8} +(10000.0 + 70000.0i) q^{10} +173398. q^{11} +(-232623. - 232623. i) q^{13} -269024. i q^{14} -262144. q^{16} +(-1.88003e6 + 1.88003e6i) q^{17} +1.10156e6i q^{19} +(-1.28000e6 - 960000. i) q^{20} +(-2.77437e6 + 2.77437e6i) q^{22} +(5.22826e6 + 5.22826e6i) q^{23} +(-2.73438e6 - 9.37500e6i) q^{25} +7.44394e6 q^{26} +(4.30438e6 + 4.30438e6i) q^{28} -2.47908e7i q^{29} -1.00660e7 q^{31} +(4.19430e6 - 4.19430e6i) q^{32} -6.01611e7i q^{34} +(5.25438e6 + 3.67806e7i) q^{35} +(5.63879e7 - 5.63879e7i) q^{37} +(-1.76250e7 - 1.76250e7i) q^{38} +(3.58400e7 - 5.12000e6i) q^{40} +1.53004e8 q^{41} +(5.93725e7 + 5.93725e7i) q^{43} -8.87798e7i q^{44} -1.67304e8 q^{46} +(-1.72339e8 + 1.72339e8i) q^{47} +1.41120e8i q^{49} +(1.93750e8 + 1.06250e8i) q^{50} +(-1.19103e8 + 1.19103e8i) q^{52} +(-1.96386e8 - 1.96386e8i) q^{53} +(3.25121e8 - 4.33495e8i) q^{55} -1.37740e8 q^{56} +(3.96653e8 + 3.96653e8i) q^{58} +6.94069e8i q^{59} +9.06186e8 q^{61} +(1.61056e8 - 1.61056e8i) q^{62} +1.34218e8i q^{64} +(-1.01773e9 + 1.45389e8i) q^{65} +(-9.62074e8 + 9.62074e8i) q^{67} +(9.62577e8 + 9.62577e8i) q^{68} +(-6.72560e8 - 5.04420e8i) q^{70} +3.12088e9 q^{71} +(-6.36339e8 - 6.36339e8i) q^{73} +1.80441e9i q^{74} +5.63999e8 q^{76} +(-1.45776e9 + 1.45776e9i) q^{77} +1.96800e9i q^{79} +(-4.91520e8 + 6.55360e8i) q^{80} +(-2.44806e9 + 2.44806e9i) q^{82} +(5.18382e9 + 5.18382e9i) q^{83} +(1.17502e9 + 8.22514e9i) q^{85} -1.89992e9 q^{86} +(1.42048e9 + 1.42048e9i) q^{88} +7.77138e9i q^{89} +3.91132e9 q^{91} +(2.67687e9 - 2.67687e9i) q^{92} -5.51486e9i q^{94} +(2.75390e9 + 2.06542e9i) q^{95} +(-6.40361e8 + 6.40361e8i) q^{97} +(-2.25792e9 - 2.25792e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} + 3750 q^{5} - 16814 q^{7} + 16384 q^{8} + 20000 q^{10} + 346796 q^{11} - 465246 q^{13} - 524288 q^{16} - 3760066 q^{17} - 2560000 q^{20} - 5548736 q^{22} + 10456526 q^{23} - 5468750 q^{25}+ \cdots - 4515838432 q^{98}+O(q^{100}) $ 2 * q - 32 * q^2 + 3750 * q^5 - 16814 * q^7 + 16384 * q^8 + 20000 * q^10 + 346796 * q^11 - 465246 * q^13 - 524288 * q^16 - 3760066 * q^17 - 2560000 * q^20 - 5548736 * q^22 + 10456526 * q^23 - 5468750 * q^25 + 14887872 * q^26 + 8608768 * q^28 - 20131996 * q^31 + 8388608 * q^32 + 10508750 * q^35 + 112775826 * q^37 - 35249920 * q^38 + 71680000 * q^40 + 306007196 * q^41 + 118744914 * q^43 - 334608832 * q^46 - 344678706 * q^47 + 387500000 * q^50 - 238205952 * q^52 - 392771234 * q^53 + 650242500 * q^55 - 275480576 * q^56 + 793306880 * q^58 + 1812371604 * q^61 + 322111936 * q^62 - 2035451250 * q^65 - 1924147934 * q^67 + 1925153792 * q^68 - 1345120000 * q^70 + 6241755196 * q^71 - 1272678526 * q^73 + 1127997440 * q^76 - 2915513972 * q^77 - 983040000 * q^80 - 4896115136 * q^82 + 10367644206 * q^83 + 2350041250 * q^85 - 3799837248 * q^86 + 2840952832 * q^88 + 7822646244 * q^91 + 5353741312 * q^92 + 5507800000 * q^95 - 1280722494 * q^97 - 4515838432 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−16.0000	+	16.0000i	−0.500000	+	0.500000i
$2$	−16.0000	+	16.0000i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	512.000i		−	0.500000i
$5$	1875.00	−	2500.00i	0.600000	−	0.800000i
$5$	1875.00	−	2500.00i	0.600000	−	0.800000i
$6$		0			0
$7$	−8407.00	+	8407.00i	−0.500208	+	0.500208i	−0.911503	−	0.411294i	$-0.865077\pi$
$7$	−8407.00	+	8407.00i	−0.500208	+	0.500208i	0.411294	+	0.911503i	$0.365077\pi$
$8$	8192.00	+	8192.00i	0.250000	+	0.250000i
$9$		0			0
$10$	10000.0	+	70000.0i	0.100000	+	0.700000i
$11$	173398.			1.07667			0.538333	−	0.842732i	$-0.319054\pi$
$11$	173398.			1.07667			0.538333	+	0.842732i	$0.319054\pi$
$12$		0			0
$13$	−232623.	−	232623.i	−0.626521	−	0.626521i	0.320670	−	0.947191i	$-0.396092\pi$
$13$	−232623.	−	232623.i	−0.626521	−	0.626521i	−0.947191	+	0.320670i	$0.896092\pi$
$14$		−	269024.i		−	0.500208i
$15$		0			0
$16$	−262144.			−0.250000
$17$	−1.88003e6	+	1.88003e6i	−1.32410	+	1.32410i	−0.413676	+	0.910424i	$0.635755\pi$
$17$	−1.88003e6	+	1.88003e6i	−1.32410	+	1.32410i	−0.910424	+	0.413676i	$0.864245\pi$
$18$		0			0
$19$			1.10156e6i			0.444877i	0.974947	+	0.222439i	$0.0714017\pi$
$19$			1.10156e6i			0.444877i	−0.974947	+	0.222439i	$0.928598\pi$
$20$	−1.28000e6	−	960000.i	−0.400000	−	0.300000i
$21$		0			0
$22$	−2.77437e6	+	2.77437e6i	−0.538333	+	0.538333i
$23$	5.22826e6	+	5.22826e6i	0.812303	+	0.812303i	0.984979	−	0.172675i	$-0.0552412\pi$
$23$	5.22826e6	+	5.22826e6i	0.812303	+	0.812303i	−0.172675	+	0.984979i	$0.555241\pi$
$24$		0			0
$25$	−2.73438e6	−	9.37500e6i	−0.280000	−	0.960000i
$26$	7.44394e6			0.626521
$27$		0			0
$28$	4.30438e6	+	4.30438e6i	0.250104	+	0.250104i
$29$		−	2.47908e7i		−	1.20865i	−0.796737	−	0.604326i	$-0.793442\pi$
$29$		−	2.47908e7i		−	1.20865i	0.796737	−	0.604326i	$-0.206558\pi$
$30$		0			0
$31$	−1.00660e7			−0.351600			−0.175800	−	0.984426i	$-0.556251\pi$
$31$	−1.00660e7			−0.351600			−0.175800	+	0.984426i	$0.556251\pi$
$32$	4.19430e6	−	4.19430e6i	0.125000	−	0.125000i
$33$		0			0
$34$		−	6.01611e7i		−	1.32410i
$35$	5.25438e6	+	3.67806e7i	0.100042	+	0.700292i
$36$		0			0
$37$	5.63879e7	−	5.63879e7i	0.813163	−	0.813163i	−0.171944	−	0.985107i	$-0.555005\pi$
$37$	5.63879e7	−	5.63879e7i	0.813163	−	0.813163i	0.985107	+	0.171944i	$0.0550048\pi$
$38$	−1.76250e7	−	1.76250e7i	−0.222439	−	0.222439i
$39$		0			0
$40$	3.58400e7	−	5.12000e6i	0.350000	−	0.0500000i
$41$	1.53004e8			1.32063			0.660317	−	0.750987i	$-0.270422\pi$
$41$	1.53004e8			1.32063			0.660317	+	0.750987i	$0.270422\pi$
$42$		0			0
$43$	5.93725e7	+	5.93725e7i	0.403871	+	0.403871i	0.879595	−	0.475724i	$-0.157814\pi$
$43$	5.93725e7	+	5.93725e7i	0.403871	+	0.403871i	−0.475724	+	0.879595i	$0.657814\pi$
$44$		−	8.87798e7i		−	0.538333i
$45$		0			0
$46$	−1.67304e8			−0.812303
$47$	−1.72339e8	+	1.72339e8i	−0.751441	+	0.751441i	−0.974748	−	0.223307i	$-0.928315\pi$
$47$	−1.72339e8	+	1.72339e8i	−0.751441	+	0.751441i	0.223307	+	0.974748i	$0.428315\pi$
$48$		0			0
$49$			1.41120e8i			0.499583i
$50$	1.93750e8	+	1.06250e8i	0.620000	+	0.340000i
$51$		0			0
$52$	−1.19103e8	+	1.19103e8i	−0.313261	+	0.313261i
$53$	−1.96386e8	−	1.96386e8i	−0.469602	−	0.469602i	0.432183	−	0.901786i	$-0.357743\pi$
$53$	−1.96386e8	−	1.96386e8i	−0.469602	−	0.469602i	−0.901786	+	0.432183i	$0.857743\pi$
$54$		0			0
$55$	3.25121e8	−	4.33495e8i	0.645999	−	0.861332i
$56$	−1.37740e8			−0.250104
$57$		0			0
$58$	3.96653e8	+	3.96653e8i	0.604326	+	0.604326i
$59$			6.94069e8i			0.970829i	0.874284	+	0.485414i	$0.161331\pi$
$59$			6.94069e8i			0.970829i	−0.874284	+	0.485414i	$0.838669\pi$
$60$		0			0
$61$	9.06186e8			1.07292			0.536461	−	0.843925i	$-0.319761\pi$
$61$	9.06186e8			1.07292			0.536461	+	0.843925i	$0.319761\pi$
$62$	1.61056e8	−	1.61056e8i	0.175800	−	0.175800i
$63$		0			0
$64$			1.34218e8i			0.125000i
$65$	−1.01773e9	+	1.45389e8i	−0.877130	+	0.125304i
$66$		0			0
$67$	−9.62074e8	+	9.62074e8i	−0.712581	+	0.712581i	−0.967075	−	0.254493i	$-0.918091\pi$
$67$	−9.62074e8	+	9.62074e8i	−0.712581	+	0.712581i	0.254493	+	0.967075i	$0.418091\pi$
$68$	9.62577e8	+	9.62577e8i	0.662050	+	0.662050i
$69$		0			0
$70$	−6.72560e8	−	5.04420e8i	−0.400167	−	0.300125i
$71$	3.12088e9			1.72976			0.864878	−	0.501982i	$-0.167395\pi$
$71$	3.12088e9			1.72976			0.864878	+	0.501982i	$0.167395\pi$
$72$		0			0
$73$	−6.36339e8	−	6.36339e8i	−0.306955	−	0.306955i	0.536772	−	0.843727i	$-0.319643\pi$
$73$	−6.36339e8	−	6.36339e8i	−0.306955	−	0.306955i	−0.843727	+	0.536772i	$0.819643\pi$
$74$			1.80441e9i			0.813163i
$75$		0			0
$76$	5.63999e8			0.222439
$77$	−1.45776e9	+	1.45776e9i	−0.538557	+	0.538557i
$78$		0			0
$79$			1.96800e9i			0.639571i	0.947490	+	0.319786i	$0.103611\pi$
$79$			1.96800e9i			0.639571i	−0.947490	+	0.319786i	$0.896389\pi$
$80$	−4.91520e8	+	6.55360e8i	−0.150000	+	0.200000i
$81$		0			0
$82$	−2.44806e9	+	2.44806e9i	−0.660317	+	0.660317i
$83$	5.18382e9	+	5.18382e9i	1.31601	+	1.31601i	0.916904	+	0.399107i	$0.130680\pi$
$83$	5.18382e9	+	5.18382e9i	1.31601	+	1.31601i	0.399107	+	0.916904i	$0.369320\pi$
$84$		0			0
$85$	1.17502e9	+	8.22514e9i	0.264820	+	1.85374i
$86$	−1.89992e9			−0.403871
$87$		0			0
$88$	1.42048e9	+	1.42048e9i	0.269166	+	0.269166i
$89$			7.77138e9i			1.39171i	0.718183	+	0.695854i	$0.244974\pi$
$89$			7.77138e9i			1.39171i	−0.718183	+	0.695854i	$0.755026\pi$
$90$		0			0
$91$	3.91132e9			0.626782
$92$	2.67687e9	−	2.67687e9i	0.406152	−	0.406152i
$93$		0			0
$94$		−	5.51486e9i		−	0.751441i
$95$	2.75390e9	+	2.06542e9i	0.355902	+	0.266926i
$96$		0			0
$97$	−6.40361e8	+	6.40361e8i	−0.0745704	+	0.0745704i	−0.743408	−	0.668838i	$-0.766792\pi$
$97$	−6.40361e8	+	6.40361e8i	−0.0745704	+	0.0745704i	0.668838	+	0.743408i	$0.266792\pi$
$98$	−2.25792e9	−	2.25792e9i	−0.249792	−	0.249792i
$99$		0			0
$100$	−4.80000e9	+	1.40000e9i	−0.480000	+	0.140000i
$101$	−2.02434e9			−0.192609			−0.0963047	−	0.995352i	$-0.530702\pi$
$101$	−2.02434e9			−0.192609			−0.0963047	+	0.995352i	$0.530702\pi$
$102$		0			0
$103$	−1.50252e9	−	1.50252e9i	−0.129609	−	0.129609i	0.639326	−	0.768935i	$-0.279213\pi$
$103$	−1.50252e9	−	1.50252e9i	−0.129609	−	0.129609i	−0.768935	+	0.639326i	$0.779213\pi$
$104$		−	3.81130e9i		−	0.313261i
$105$		0			0
$106$	6.28434e9			0.469602
$107$	−1.41812e9	+	1.41812e9i	−0.101110	+	0.101110i	−0.755852	−	0.654742i	$-0.772777\pi$
$107$	−1.41812e9	+	1.41812e9i	−0.101110	+	0.101110i	0.654742	+	0.755852i	$0.272777\pi$
$108$		0			0
$109$			6.21296e9i			0.403800i	0.979406	+	0.201900i	$0.0647116\pi$
$109$			6.21296e9i			0.403800i	−0.979406	+	0.201900i	$0.935288\pi$
$110$	1.73398e9	+	1.21379e10i	0.107667	+	0.753666i
$111$		0			0
$112$	2.20384e9	−	2.20384e9i	0.125052	−	0.125052i
$113$	1.79511e10	+	1.79511e10i	0.974313	+	0.974313i	0.999678	−	0.0253650i	$-0.00807480\pi$
$113$	1.79511e10	+	1.79511e10i	0.974313	+	0.974313i	−0.0253650	+	0.999678i	$0.508075\pi$
$114$		0			0
$115$	2.28737e10	−	3.26766e9i	1.13722	−	0.162461i
$116$	−1.26929e10			−0.604326
$117$		0			0
$118$	−1.11051e10	−	1.11051e10i	−0.485414	−	0.485414i
$119$		−	3.16109e10i		−	1.32465i
$120$		0			0
$121$	4.12944e9			0.159208
$122$	−1.44990e10	+	1.44990e10i	−0.536461	+	0.536461i
$123$		0			0
$124$			5.15379e9i			0.175800i
$125$	−2.85645e10	−	1.07422e10i	−0.936000	−	0.352000i
$126$		0			0
$127$	1.30621e10	−	1.30621e10i	0.395362	−	0.395362i	−0.481232	−	0.876593i	$-0.659810\pi$
$127$	1.30621e10	−	1.30621e10i	0.395362	−	0.395362i	0.876593	+	0.481232i	$0.159810\pi$
$128$	−2.14748e9	−	2.14748e9i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	1.39574e10	−	1.86098e10i	0.375913	−	0.501217i
$131$	5.20222e10			1.34844			0.674221	−	0.738530i	$-0.264480\pi$
$131$	5.20222e10			1.34844			0.674221	+	0.738530i	$0.264480\pi$
$132$		0			0
$133$	−9.26081e9	−	9.26081e9i	−0.222531	−	0.222531i
$134$		−	3.07864e10i		−	0.712581i
$135$		0			0
$136$	−3.08025e10			−0.662050
$137$	1.63815e10	−	1.63815e10i	0.339429	−	0.339429i	−0.516723	−	0.856153i	$-0.672848\pi$
$137$	1.63815e10	−	1.63815e10i	0.339429	−	0.339429i	0.856153	+	0.516723i	$0.172848\pi$
$138$		0			0
$139$			2.61490e10i			0.503942i	0.967735	+	0.251971i	$0.0810787\pi$
$139$			2.61490e10i			0.503942i	−0.967735	+	0.251971i	$0.918921\pi$
$140$	1.88317e10	−	2.69024e9i	0.350146	−	0.0500208i
$141$		0			0
$142$	−4.99340e10	+	4.99340e10i	−0.864878	+	0.864878i
$143$	−4.03364e10	−	4.03364e10i	−0.674554	−	0.674554i
$144$		0			0
$145$	−6.19771e10	−	4.64828e10i	−0.966922	−	0.725191i
$146$	2.03629e10			0.306955
$147$		0			0
$148$	−2.88706e10	−	2.88706e10i	−0.406581	−	0.406581i
$149$			4.31363e9i			0.0587369i	0.999569	+	0.0293685i	$0.00934962\pi$
$149$			4.31363e9i			0.0587369i	−0.999569	+	0.0293685i	$0.990650\pi$
$150$		0			0
$151$	1.13868e11			1.45050			0.725251	−	0.688484i	$-0.241724\pi$
$151$	1.13868e11			1.45050			0.725251	+	0.688484i	$0.241724\pi$
$152$	−9.02398e9	+	9.02398e9i	−0.111219	+	0.111219i
$153$		0			0
$154$		−	4.66482e10i		−	0.538557i
$155$	−1.88737e10	+	2.51650e10i	−0.210960	+	0.281280i
$156$		0			0
$157$	1.04428e10	−	1.04428e10i	0.109476	−	0.109476i	−0.650247	−	0.759723i	$-0.725335\pi$
$157$	1.04428e10	−	1.04428e10i	0.109476	−	0.109476i	0.759723	+	0.650247i	$0.225335\pi$
$158$	−3.14879e10	−	3.14879e10i	−0.319786	−	0.319786i
$159$		0			0
$160$	−2.62144e9	−	1.83501e10i	−0.0250000	−	0.175000i
$161$	−8.79080e10			−0.812642
$162$		0			0
$163$	4.78305e10	+	4.78305e10i	0.415688	+	0.415688i	0.883714	−	0.468027i	$-0.155035\pi$
$163$	4.78305e10	+	4.78305e10i	0.415688	+	0.415688i	−0.468027	+	0.883714i	$0.655035\pi$
$164$		−	7.83378e10i		−	0.660317i
$165$		0			0
$166$	−1.65882e11			−1.31601
$167$	1.18281e10	−	1.18281e10i	0.0910613	−	0.0910613i	−0.660109	−	0.751170i	$-0.729490\pi$
$167$	1.18281e10	−	1.18281e10i	0.0910613	−	0.0910613i	0.751170	+	0.660109i	$0.229490\pi$
$168$		0			0
$169$		−	2.96316e10i		−	0.214942i
$170$	−1.50403e11	−	1.12802e11i	−1.05928	−	0.794460i
$171$		0			0
$172$	3.03987e10	−	3.03987e10i	0.201936	−	0.201936i
$173$	1.16377e11	+	1.16377e11i	0.750997	+	0.750997i	0.974665	−	0.223669i	$-0.0718033\pi$
$173$	1.16377e11	+	1.16377e11i	0.750997	+	0.750997i	−0.223669	+	0.974665i	$0.571803\pi$
$174$		0			0
$175$	1.01804e11	+	5.58277e10i	0.620258	+	0.340142i
$176$	−4.54552e10			−0.269166
$177$		0			0
$178$	−1.24342e11	−	1.24342e11i	−0.695854	−	0.695854i
$179$		−	1.81011e11i		−	0.985008i	−0.870310	−	0.492504i	$-0.836082\pi$
$179$		−	1.81011e11i		−	0.985008i	0.870310	−	0.492504i	$-0.163918\pi$
$180$		0			0
$181$	1.33000e11			0.684636			0.342318	−	0.939584i	$-0.388788\pi$
$181$	1.33000e11			0.684636			0.342318	+	0.939584i	$0.388788\pi$
$182$	−6.25812e10	+	6.25812e10i	−0.313391	+	0.313391i
$183$		0			0
$184$			8.56599e10i			0.406152i
$185$	−3.52424e10	−	2.46697e11i	−0.162633	−	1.13843i
$186$		0			0
$187$	−3.25994e11	+	3.25994e11i	−1.42561	+	1.42561i
$188$	8.82377e10	+	8.82377e10i	0.375721	+	0.375721i
$189$		0			0
$190$	−7.71092e10	+	1.10156e10i	−0.311414	+	0.0444877i
$191$	−1.31044e11			−0.515525			−0.257762	−	0.966208i	$-0.582985\pi$
$191$	−1.31044e11			−0.515525			−0.257762	+	0.966208i	$0.582985\pi$
$192$		0			0
$193$	2.12792e11	+	2.12792e11i	0.794639	+	0.794639i	0.982244	−	0.187606i	$-0.0600727\pi$
$193$	2.12792e11	+	2.12792e11i	0.794639	+	0.794639i	−0.187606	+	0.982244i	$0.560073\pi$
$194$		−	2.04916e10i		−	0.0745704i
$195$		0			0
$196$	7.22534e10			0.249792
$197$	−7.90246e10	+	7.90246e10i	−0.266337	+	0.266337i	−0.827622	−	0.561285i	$-0.810307\pi$
$197$	−7.90246e10	+	7.90246e10i	−0.266337	+	0.266337i	0.561285	+	0.827622i	$0.310307\pi$
$198$		0			0
$199$		−	4.52657e11i		−	1.45045i	−0.688510	−	0.725227i	$-0.741735\pi$
$199$		−	4.52657e11i		−	1.45045i	0.688510	−	0.725227i	$-0.258265\pi$
$200$	5.44000e10	−	9.92000e10i	0.170000	−	0.310000i
$201$		0			0
$202$	3.23895e10	−	3.23895e10i	0.0963047	−	0.0963047i
$203$	2.08417e11	+	2.08417e11i	0.604578	+	0.604578i
$204$		0			0
$205$	2.86882e11	−	3.82509e11i	0.792380	−	1.05651i
$206$	4.80808e10			0.129609
$207$		0			0
$208$	6.09807e10	+	6.09807e10i	0.156630	+	0.156630i
$209$			1.91008e11i			0.478984i
$210$		0			0
$211$	1.37995e11			0.329951			0.164976	−	0.986298i	$-0.447245\pi$
$211$	1.37995e11			0.329951			0.164976	+	0.986298i	$0.447245\pi$
$212$	−1.00549e11	+	1.00549e11i	−0.234801	+	0.234801i
$213$		0			0
$214$		−	4.53797e10i		−	0.101110i
$215$	2.59754e11	−	3.71078e10i	0.565419	−	0.0807742i
$216$		0			0
$217$	8.46248e10	−	8.46248e10i	0.175873	−	0.175873i
$218$	−9.94074e10	−	9.94074e10i	−0.201900	−	0.201900i
$219$		0			0
$220$	−2.21949e11	−	1.66462e11i	−0.430666	−	0.323000i
$221$	8.74678e11			1.65915
$222$		0			0
$223$	−1.26054e11	−	1.26054e11i	−0.228576	−	0.228576i	0.583521	−	0.812098i	$-0.301674\pi$
$223$	−1.26054e11	−	1.26054e11i	−0.228576	−	0.228576i	−0.812098	+	0.583521i	$0.801674\pi$
$224$			7.05230e10i			0.125052i
$225$		0			0
$226$	−5.74435e11			−0.974313
$227$	−1.15268e11	+	1.15268e11i	−0.191241	+	0.191241i	−0.796232	−	0.604991i	$-0.793177\pi$
$227$	−1.15268e11	+	1.15268e11i	−0.191241	+	0.191241i	0.604991	+	0.796232i	$0.293177\pi$
$228$		0			0
$229$			3.29124e11i			0.522615i	0.965256	+	0.261308i	$0.0841537\pi$
$229$			3.29124e11i			0.522615i	−0.965256	+	0.261308i	$0.915846\pi$
$230$	−3.13696e11	+	4.18261e11i	−0.487382	+	0.649843i
$231$		0			0
$232$	2.03087e11	−	2.03087e11i	0.302163	−	0.302163i
$233$	9.97948e10	+	9.97948e10i	0.145321	+	0.145321i	0.776024	−	0.630703i	$-0.217233\pi$
$233$	9.97948e10	+	9.97948e10i	0.145321	+	0.145321i	−0.630703	+	0.776024i	$0.717233\pi$
$234$		0			0
$235$	1.07712e11	+	7.53985e11i	0.150288	+	1.05202i
$236$	3.55363e11			0.485414
$237$		0			0
$238$	5.05774e11	+	5.05774e11i	0.662326	+	0.662326i
$239$		−	3.95622e10i		−	0.0507331i	−0.999678	−	0.0253665i	$-0.991925\pi$
$239$		−	3.95622e10i		−	0.0507331i	0.999678	−	0.0253665i	$-0.00807529\pi$
$240$		0			0
$241$	−8.14271e11			−1.00158			−0.500788	−	0.865570i	$-0.666956\pi$
$241$	−8.14271e11			−1.00158			−0.500788	+	0.865570i	$0.666956\pi$
$242$	−6.60711e10	+	6.60711e10i	−0.0796039	+	0.0796039i
$243$		0			0
$244$		−	4.63967e11i		−	0.536461i
$245$	3.52800e11	+	2.64600e11i	0.399667	+	0.299750i
$246$		0			0
$247$	2.56248e11	−	2.56248e11i	0.278725	−	0.278725i
$248$	−8.24607e10	−	8.24607e10i	−0.0878999	−	0.0878999i
$249$		0			0
$250$	6.28906e11	−	2.85156e11i	0.644000	−	0.292000i
$251$	−4.53171e11			−0.454877			−0.227438	−	0.973793i	$-0.573035\pi$
$251$	−4.53171e11			−0.454877			−0.227438	+	0.973793i	$0.573035\pi$
$252$		0			0
$253$	9.06570e11	+	9.06570e11i	0.874579	+	0.874579i
$254$			4.17987e11i			0.395362i
$255$		0			0
$256$	6.87195e10			0.0625000
$257$	−1.33579e12	+	1.33579e12i	−1.19144	+	1.19144i	−0.214777	+	0.976663i	$0.568902\pi$
$257$	−1.33579e12	+	1.33579e12i	−1.19144	+	1.19144i	−0.976663	+	0.214777i	$0.931098\pi$
$258$		0			0
$259$			9.48106e11i			0.813501i
$260$	7.44394e10	+	5.21076e11i	0.0626521	+	0.438565i
$261$		0			0
$262$	−8.32355e11	+	8.32355e11i	−0.674221	+	0.674221i
$263$	9.12065e11	+	9.12065e11i	0.724848	+	0.724848i	0.969589	−	0.244740i	$-0.0787027\pi$
$263$	9.12065e11	+	9.12065e11i	0.724848	+	0.724848i	−0.244740	+	0.969589i	$0.578703\pi$
$264$		0			0
$265$	−8.59187e11	+	1.22741e11i	−0.657443	+	0.0939205i
$266$	2.96346e11			0.222531
$267$		0			0
$268$	4.92582e11	+	4.92582e11i	0.356291	+	0.356291i
$269$			1.04348e12i			0.740835i	0.928865	+	0.370417i	$0.120785\pi$
$269$			1.04348e12i			0.740835i	−0.928865	+	0.370417i	$0.879215\pi$
$270$		0			0
$271$	7.19445e11			0.492211			0.246105	−	0.969243i	$-0.420849\pi$
$271$	7.19445e11			0.492211			0.246105	+	0.969243i	$0.420849\pi$
$272$	4.92839e11	−	4.92839e11i	0.331025	−	0.331025i
$273$		0			0
$274$			5.24206e11i			0.339429i
$275$	−4.74135e11	−	1.62561e12i	−0.301466	−	1.03360i
$276$		0			0
$277$	−8.62576e11	+	8.62576e11i	−0.528931	+	0.528931i	−0.920253	−	0.391323i	$-0.872018\pi$
$277$	−8.62576e11	+	8.62576e11i	−0.528931	+	0.528931i	0.391323	+	0.920253i	$0.372018\pi$
$278$	−4.18383e11	−	4.18383e11i	−0.251971	−	0.251971i
$279$		0			0
$280$	−2.58263e11	+	3.44351e11i	−0.150062	+	0.200083i
$281$	7.89300e11			0.450516			0.225258	−	0.974299i	$-0.427677\pi$
$281$	7.89300e11			0.450516			0.225258	+	0.974299i	$0.427677\pi$
$282$		0			0
$283$	−6.60245e11	−	6.60245e11i	−0.363725	−	0.363725i	0.501457	−	0.865182i	$-0.332797\pi$
$283$	−6.60245e11	−	6.60245e11i	−0.363725	−	0.363725i	−0.865182	+	0.501457i	$0.832797\pi$
$284$		−	1.59789e12i		−	0.864878i
$285$		0			0
$286$	1.29076e12			0.674554
$287$	−1.28630e12	+	1.28630e12i	−0.660592	+	0.660592i
$288$		0			0
$289$		−	5.05305e12i		−	2.50648i
$290$	1.73536e12	−	2.47908e11i	0.846056	−	0.120865i
$291$		0			0
$292$	−3.25806e11	+	3.25806e11i	−0.153477	+	0.153477i
$293$	−1.79236e11	−	1.79236e11i	−0.0830019	−	0.0830019i	0.664387	−	0.747389i	$-0.268693\pi$
$293$	−1.79236e11	−	1.79236e11i	−0.0830019	−	0.0830019i	−0.747389	+	0.664387i	$0.768693\pi$
$294$		0			0
$295$	1.73517e12	+	1.30138e12i	0.776663	+	0.582497i
$296$	9.23860e11			0.406581
$297$		0			0
$298$	−6.90180e10	−	6.90180e10i	−0.0293685	−	0.0293685i
$299$		−	2.43243e12i		−	1.01785i
$300$		0			0
$301$	−9.98288e11			−0.404039
$302$	−1.82189e12	+	1.82189e12i	−0.725251	+	0.725251i
$303$		0			0
$304$		−	2.88767e11i		−	0.111219i
$305$	1.69910e12	−	2.26546e12i	0.643753	−	0.858337i
$306$		0			0
$307$	−1.10155e12	+	1.10155e12i	−0.403937	+	0.403937i	−0.879618	−	0.475681i	$-0.842202\pi$
$307$	−1.10155e12	+	1.10155e12i	−0.403937	+	0.403937i	0.475681	+	0.879618i	$0.342202\pi$
$308$	7.46372e11	+	7.46372e11i	0.269278	+	0.269278i
$309$		0			0
$310$	−1.00660e11	−	7.04620e11i	−0.0351600	−	0.246120i
$311$	−5.31138e12			−1.82560			−0.912800	−	0.408406i	$-0.866085\pi$
$311$	−5.31138e12			−1.82560			−0.912800	+	0.408406i	$0.866085\pi$
$312$		0			0
$313$	−8.40078e11	−	8.40078e11i	−0.279639	−	0.279639i	0.553326	−	0.832965i	$-0.313358\pi$
$313$	−8.40078e11	−	8.40078e11i	−0.279639	−	0.279639i	−0.832965	+	0.553326i	$0.813358\pi$
$314$			3.34169e11i			0.109476i
$315$		0			0
$316$	1.00761e12			0.319786
$317$	1.16635e12	−	1.16635e12i	0.364361	−	0.364361i	−0.501055	−	0.865416i	$-0.667054\pi$
$317$	1.16635e12	−	1.16635e12i	0.364361	−	0.364361i	0.865416	+	0.501055i	$0.167054\pi$
$318$		0			0
$319$		−	4.29868e12i		−	1.30131i
$320$	3.35544e11	+	2.51658e11i	0.100000	+	0.0750000i
$321$		0			0
$322$	1.40653e12	−	1.40653e12i	0.406321	−	0.406321i
$323$	−2.07097e12	−	2.07097e12i	−0.589062	−	0.589062i
$324$		0			0
$325$	−1.54476e12	+	2.81692e12i	−0.426035	+	0.776887i
$326$	−1.53058e12			−0.415688
$327$		0			0
$328$	1.25341e12	+	1.25341e12i	0.330158	+	0.330158i
$329$		−	2.89771e12i		−	0.751754i
$330$		0			0
$331$	−4.82042e12			−1.21324			−0.606618	−	0.794994i	$-0.707474\pi$
$331$	−4.82042e12			−1.21324			−0.606618	+	0.794994i	$0.707474\pi$
$332$	2.65412e12	−	2.65412e12i	0.658006	−	0.658006i
$333$		0			0
$334$			3.78500e11i			0.0910613i
$335$	6.01296e11	+	4.20907e12i	0.142516	+	0.997614i
$336$		0			0
$337$	−3.68550e12	+	3.68550e12i	−0.847904	+	0.847904i	−0.989871	−	0.141967i	$-0.954657\pi$
$337$	−3.68550e12	+	3.68550e12i	−0.847904	+	0.847904i	0.141967	+	0.989871i	$0.454657\pi$
$338$	4.74105e11	+	4.74105e11i	0.107471	+	0.107471i
$339$		0			0
$340$	4.21127e12	−	6.01611e11i	0.926870	−	0.132410i
$341$	−1.74542e12			−0.378555
$342$		0			0
$343$	−3.56116e12	−	3.56116e12i	−0.750104	−	0.750104i
$344$			9.72758e11i			0.201936i
$345$		0			0
$346$	−3.72408e12			−0.750997
$347$	5.38450e12	−	5.38450e12i	1.07028	−	1.07028i	0.0729452	−	0.997336i	$-0.476760\pi$
$347$	5.38450e12	−	5.38450e12i	1.07028	−	1.07028i	0.997336	−	0.0729452i	$-0.0232398\pi$
$348$		0			0
$349$		−	8.12658e12i		−	1.56957i	−0.619768	−	0.784785i	$-0.712773\pi$
$349$		−	8.12658e12i		−	1.56957i	0.619768	−	0.784785i	$-0.287227\pi$
$350$	−2.52210e12	+	7.35612e11i	−0.480200	+	0.140058i
$351$		0			0
$352$	7.27284e11	−	7.27284e11i	0.134583	−	0.134583i
$353$	−5.49274e12	−	5.49274e12i	−1.00211	−	1.00211i	−0.999998	−	0.00211203i	$-0.999328\pi$
$353$	−5.49274e12	−	5.49274e12i	−1.00211	−	1.00211i	−0.00211203	−	0.999998i	$-0.500672\pi$
$354$		0			0
$355$	5.85165e12	−	7.80219e12i	1.03785	−	1.38381i
$356$	3.97895e12			0.695854
$357$		0			0
$358$	2.89617e12	+	2.89617e12i	0.492504	+	0.492504i
$359$		−	5.91305e12i		−	0.991606i	−0.868435	−	0.495803i	$-0.834874\pi$
$359$		−	5.91305e12i		−	0.991606i	0.868435	−	0.495803i	$-0.165126\pi$
$360$		0			0
$361$	4.91763e12			0.802084
$362$	−2.12801e12	+	2.12801e12i	−0.342318	+	0.342318i
$363$		0			0
$364$		−	2.00260e12i		−	0.313391i
$365$	−2.78398e12	+	3.97712e11i	−0.429737	+	0.0613910i
$366$		0			0
$367$	1.75360e12	−	1.75360e12i	0.263390	−	0.263390i	−0.563040	−	0.826430i	$-0.690368\pi$
$367$	1.75360e12	−	1.75360e12i	0.263390	−	0.263390i	0.826430	+	0.563040i	$0.190368\pi$
$368$	−1.37056e12	−	1.37056e12i	−0.203076	−	0.203076i
$369$		0			0
$370$	4.51103e12	+	3.38327e12i	0.650530	+	0.487898i
$371$	3.30203e12			0.469798
$372$		0			0
$373$	4.25717e12	+	4.25717e12i	0.589627	+	0.589627i	0.937530	−	0.347904i	$-0.113106\pi$
$373$	4.25717e12	+	4.25717e12i	0.589627	+	0.589627i	−0.347904	+	0.937530i	$0.613106\pi$
$374$		−	1.04318e13i		−	1.42561i
$375$		0			0
$376$	−2.82361e12			−0.375721
$377$	−5.76692e12	+	5.76692e12i	−0.757246	+	0.757246i
$378$		0			0
$379$			7.20999e12i			0.922016i	0.887396	+	0.461008i	$0.152512\pi$
$379$			7.20999e12i			0.922016i	−0.887396	+	0.461008i	$0.847488\pi$
$380$	1.05750e12	−	1.41000e12i	0.133463	−	0.177951i
$381$		0			0
$382$	2.09670e12	−	2.09670e12i	0.257762	−	0.257762i
$383$	6.93832e12	+	6.93832e12i	0.841900	+	0.841900i	0.989106	−	0.147206i	$-0.0470281\pi$
$383$	6.93832e12	+	6.93832e12i	0.841900	+	0.841900i	−0.147206	+	0.989106i	$0.547028\pi$
$384$		0			0
$385$	9.11098e11	+	6.37769e12i	0.107711	+	0.753980i
$386$	−6.80936e12			−0.794639
$387$		0			0
$388$	3.27865e11	+	3.27865e11i	0.0372852	+	0.0372852i
$389$			1.12518e13i			1.26320i	0.775293	+	0.631601i	$0.217602\pi$
$389$			1.12518e13i			1.26320i	−0.775293	+	0.631601i	$0.782398\pi$
$390$		0			0
$391$	−1.96586e13			−2.15114
$392$	−1.15605e12	+	1.15605e12i	−0.124896	+	0.124896i
$393$		0			0
$394$		−	2.52879e12i		−	0.266337i
$395$	4.91999e12	+	3.68999e12i	0.511657	+	0.383743i
$396$		0			0
$397$	−7.94628e12	+	7.94628e12i	−0.805770	+	0.805770i	−0.983991	−	0.178221i	$-0.942966\pi$
$397$	−7.94628e12	+	7.94628e12i	−0.805770	+	0.805770i	0.178221	+	0.983991i	$0.442966\pi$
$398$	7.24252e12	+	7.24252e12i	0.725227	+	0.725227i
$399$		0			0
$400$	7.16800e11	+	2.45760e12i	0.0700000	+	0.240000i
$401$	−8.81072e12			−0.849747			−0.424874	−	0.905253i	$-0.639681\pi$
$401$	−8.81072e12			−0.849747			−0.424874	+	0.905253i	$0.639681\pi$
$402$		0			0
$403$	2.34158e12	+	2.34158e12i	0.220285	+	0.220285i
$404$			1.03646e12i			0.0963047i
$405$		0			0
$406$	−6.66933e12			−0.604578
$407$	9.77755e12	−	9.77755e12i	0.875504	−	0.875504i
$408$		0			0
$409$			1.00160e13i			0.875141i	0.899184	+	0.437571i	$0.144161\pi$
$409$			1.00160e13i			0.875141i	−0.899184	+	0.437571i	$0.855839\pi$
$410$	1.53004e12	+	1.07103e13i	0.132063	+	0.924444i
$411$		0			0
$412$	−7.69293e11	+	7.69293e11i	−0.0648045	+	0.0648045i
$413$	−5.83504e12	−	5.83504e12i	−0.485616	−	0.485616i
$414$		0			0
$415$	2.26792e13	−	3.23989e12i	1.84242	−	0.263202i
$416$	−1.95138e12			−0.156630
$417$		0			0
$418$	−3.05613e12	−	3.05613e12i	−0.239492	−	0.239492i
$419$			1.48244e13i			1.14791i	0.818888	+	0.573954i	$0.194591\pi$
$419$			1.48244e13i			1.14791i	−0.818888	+	0.573954i	$0.805409\pi$
$420$		0			0
$421$	−4.68500e12			−0.354241			−0.177121	−	0.984189i	$-0.556678\pi$
$421$	−4.68500e12			−0.354241			−0.177121	+	0.984189i	$0.556678\pi$
$422$	−2.20791e12	+	2.20791e12i	−0.164976	+	0.164976i
$423$		0			0
$424$		−	3.21758e12i		−	0.234801i
$425$	2.27660e13	+	1.24846e13i	1.64188	+	0.900388i
$426$		0			0
$427$	−7.61830e12	+	7.61830e12i	−0.536684	+	0.536684i
$428$	7.26075e11	+	7.26075e11i	0.0505549	+	0.0505549i
$429$		0			0
$430$	−3.56235e12	+	4.74980e12i	−0.242323	+	0.323097i
$431$	−2.39126e13			−1.60783			−0.803917	−	0.594741i	$-0.797254\pi$
$431$	−2.39126e13			−1.60783			−0.803917	+	0.594741i	$0.797254\pi$
$432$		0			0
$433$	−7.41823e11	−	7.41823e11i	−0.0487372	−	0.0487372i	0.682318	−	0.731055i	$-0.260972\pi$
$433$	−7.41823e11	−	7.41823e11i	−0.0487372	−	0.0487372i	−0.731055	+	0.682318i	$0.760972\pi$
$434$			2.70800e12i			0.175873i
$435$		0			0
$436$	3.18104e12			0.201900
$437$	−5.75925e12	+	5.75925e12i	−0.361375	+	0.361375i
$438$		0			0
$439$		−	2.09704e13i		−	1.28613i	−0.765811	−	0.643065i	$-0.777662\pi$
$439$		−	2.09704e13i		−	1.28613i	0.765811	−	0.643065i	$-0.222338\pi$
$440$	6.21458e12	−	8.87798e11i	0.376833	−	0.0538333i
$441$		0			0
$442$	−1.39948e13	+	1.39948e13i	−0.829577	+	0.829577i
$443$	2.38909e13	+	2.38909e13i	1.40028	+	1.40028i	0.799160	+	0.601118i	$0.205278\pi$
$443$	2.38909e13	+	2.38909e13i	1.40028	+	1.40028i	0.601118	+	0.799160i	$0.294722\pi$
$444$		0			0
$445$	1.94285e13	+	1.45713e13i	1.11337	+	0.835025i
$446$	4.03372e12			0.228576
$447$		0			0
$448$	−1.12837e12	−	1.12837e12i	−0.0625260	−	0.0625260i
$449$		−	2.04535e13i		−	1.12082i	−0.828215	−	0.560411i	$-0.810643\pi$
$449$		−	2.04535e13i		−	1.12082i	0.828215	−	0.560411i	$-0.189357\pi$
$450$		0			0
$451$	2.65305e13			1.42188
$452$	9.19096e12	−	9.19096e12i	0.487157	−	0.487157i
$453$		0			0
$454$		−	3.68858e12i		−	0.191241i
$455$	7.33373e12	−	9.77831e12i	0.376069	−	0.501426i
$456$		0			0
$457$	6.88521e12	−	6.88521e12i	0.345411	−	0.345411i	−0.512986	−	0.858397i	$-0.671461\pi$
$457$	6.88521e12	−	6.88521e12i	0.345411	−	0.345411i	0.858397	+	0.512986i	$0.171461\pi$
$458$	−5.26598e12	−	5.26598e12i	−0.261308	−	0.261308i
$459$		0			0
$460$	−1.67304e12	−	1.17113e13i	−0.0812303	−	0.568612i
$461$	1.72039e13			0.826268			0.413134	−	0.910670i	$-0.364434\pi$
$461$	1.72039e13			0.826268			0.413134	+	0.910670i	$0.364434\pi$
$462$		0			0
$463$	−4.67192e11	−	4.67192e11i	−0.0219579	−	0.0219579i	0.696043	−	0.718000i	$-0.254942\pi$
$463$	−4.67192e11	−	4.67192e11i	−0.0219579	−	0.0219579i	−0.718000	+	0.696043i	$0.754942\pi$
$464$			6.49877e12i			0.302163i
$465$		0			0
$466$	−3.19343e12			−0.145321
$467$	−1.62768e13	+	1.62768e13i	−0.732799	+	0.732799i	−0.971173	−	0.238374i	$-0.923385\pi$
$467$	−1.62768e13	+	1.62768e13i	−0.732799	+	0.732799i	0.238374	+	0.971173i	$0.423385\pi$
$468$		0			0
$469$		−	1.61763e13i		−	0.712878i
$470$	−1.37871e13	−	1.03404e13i	−0.601153	−	0.450865i
$471$		0			0
$472$	−5.68581e12	+	5.68581e12i	−0.242707	+	0.242707i
$473$	1.02951e13	+	1.02951e13i	0.434834	+	0.434834i
$474$		0			0
$475$	1.03271e13	−	3.01208e12i	0.427082	−	0.124566i
$476$	−1.61848e13			−0.662326
$477$		0			0
$478$	6.32996e11	+	6.32996e11i	0.0253665	+	0.0253665i
$479$		−	3.26759e13i		−	1.29584i	−0.761710	−	0.647918i	$-0.775640\pi$
$479$		−	3.26759e13i		−	1.29584i	0.761710	−	0.647918i	$-0.224360\pi$
$480$		0			0
$481$	−2.62343e13			−1.01893
$482$	1.30283e13	−	1.30283e13i	0.500788	−	0.500788i
$483$		0			0
$484$		−	2.11427e12i		−	0.0796039i
$485$	4.00226e11	+	2.80158e12i	0.0149141	+	0.104399i
$486$		0			0
$487$	3.91617e12	−	3.91617e12i	0.142961	−	0.142961i	−0.632004	−	0.774965i	$-0.717768\pi$
$487$	3.91617e12	−	3.91617e12i	0.142961	−	0.142961i	0.774965	+	0.632004i	$0.217768\pi$
$488$	7.42347e12	+	7.42347e12i	0.268230	+	0.268230i
$489$		0			0
$490$	−9.87840e12	+	1.41120e12i	−0.349708	+	0.0499583i
$491$	1.66945e12			0.0585015			0.0292508	−	0.999572i	$-0.490688\pi$
$491$	1.66945e12			0.0585015			0.0292508	+	0.999572i	$0.490688\pi$
$492$		0			0
$493$	4.66076e13	+	4.66076e13i	1.60038	+	1.60038i
$494$			8.19994e12i			0.278725i
$495$		0			0
$496$	2.63874e12			0.0878999
$497$	−2.62372e13	+	2.62372e13i	−0.865239	+	0.865239i
$498$		0			0
$499$		−	2.69113e13i		−	0.869824i	−0.900473	−	0.434912i	$-0.856779\pi$
$499$		−	2.69113e13i		−	0.869824i	0.900473	−	0.434912i	$-0.143221\pi$
$500$	−5.50000e12	+	1.46250e13i	−0.176000	+	0.468000i
$501$		0			0
$502$	7.25074e12	−	7.25074e12i	0.227438	−	0.227438i
$503$	−2.35501e13	−	2.35501e13i	−0.731397	−	0.731397i	0.239499	−	0.970897i	$-0.423017\pi$
$503$	−2.35501e13	−	2.35501e13i	−0.731397	−	0.731397i	−0.970897	+	0.239499i	$0.923017\pi$
$504$		0			0
$505$	−3.79564e12	+	5.06086e12i	−0.115566	+	0.154087i
$506$	−2.90103e13			−0.874579
$507$		0			0
$508$	−6.68780e12	−	6.68780e12i	−0.197681	−	0.197681i
$509$		−	8.63621e12i		−	0.252775i	−0.991981	−	0.126388i	$-0.959662\pi$
$509$		−	8.63621e12i		−	0.252775i	0.991981	−	0.126388i	$-0.0403383\pi$
$510$		0			0
$511$	1.06994e13			0.307083
$512$	−1.09951e12	+	1.09951e12i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	4.27452e13i		−	1.19144i
$515$	−6.57355e12	+	9.39078e11i	−0.181453	+	0.0259218i
$516$		0			0
$517$	−2.98833e13	+	2.98833e13i	−0.809051	+	0.809051i
$518$	−1.51697e13	−	1.51697e13i	−0.406751	−	0.406751i
$519$		0			0
$520$	−9.52824e12	−	7.14618e12i	−0.250609	−	0.187956i
$521$	6.27326e13			1.63420			0.817099	−	0.576497i	$-0.195581\pi$
$521$	6.27326e13			1.63420			0.817099	+	0.576497i	$0.195581\pi$
$522$		0			0
$523$	1.48951e12	+	1.48951e12i	0.0380659	+	0.0380659i	0.725884	−	0.687818i	$-0.241431\pi$
$523$	1.48951e12	+	1.48951e12i	0.0380659	+	0.0380659i	−0.687818	+	0.725884i	$0.741431\pi$
$524$		−	2.66354e13i		−	0.674221i
$525$		0			0
$526$	−2.91861e13			−0.724848
$527$	1.89244e13	−	1.89244e13i	0.465553	−	0.465553i
$528$		0			0
$529$			1.32430e13i			0.319673i
$530$	1.17831e13	−	1.57108e13i	0.281761	−	0.375682i
$531$		0			0
$532$	−4.74154e12	+	4.74154e12i	−0.111266	+	0.111266i
$533$	−3.55922e13	−	3.55922e13i	−0.827405	−	0.827405i
$534$		0			0
$535$	8.86323e11	+	6.20426e12i	0.0202219	+	0.141554i
$536$	−1.57626e13			−0.356291
$537$		0			0
$538$	−1.66956e13	−	1.66956e13i	−0.370417	−	0.370417i
$539$			2.44699e13i			0.537884i
$540$		0			0
$541$	−8.97115e13			−1.93581			−0.967903	−	0.251324i	$-0.919134\pi$
$541$	−8.97115e13			−1.93581			−0.967903	+	0.251324i	$0.919134\pi$
$542$	−1.15111e13	+	1.15111e13i	−0.246105	+	0.246105i
$543$		0			0
$544$			1.57709e13i			0.331025i
$545$	1.55324e13	+	1.16493e13i	0.323040	+	0.242280i
$546$		0			0
$547$	3.39955e13	−	3.39955e13i	0.694200	−	0.694200i	−0.268953	−	0.963153i	$-0.586678\pi$
$547$	3.39955e13	−	3.39955e13i	0.694200	−	0.694200i	0.963153	+	0.268953i	$0.0866777\pi$
$548$	−8.38730e12	−	8.38730e12i	−0.169715	−	0.169715i
$549$		0			0
$550$	3.35959e13	+	1.84235e13i	0.667532	+	0.366066i
$551$	2.73086e13			0.537702
$552$		0			0
$553$	−1.65449e13	−	1.65449e13i	−0.319919	−	0.319919i
$554$		−	2.76024e13i		−	0.528931i
$555$		0			0
$556$	1.33883e13			0.251971
$557$	−9.51915e12	+	9.51915e12i	−0.177551	+	0.177551i	−0.790287	−	0.612737i	$-0.790069\pi$
$557$	−9.51915e12	+	9.51915e12i	−0.177551	+	0.177551i	0.612737	+	0.790287i	$0.290069\pi$
$558$		0			0
$559$		−	2.76228e13i		−	0.506068i
$560$	−1.37740e12	−	9.64182e12i	−0.0250104	−	0.175073i
$561$		0			0
$562$	−1.26288e13	+	1.26288e13i	−0.225258	+	0.225258i
$563$	−3.63651e13	−	3.63651e13i	−0.642900	−	0.642900i	0.308367	−	0.951267i	$-0.400217\pi$
$563$	−3.63651e13	−	3.63651e13i	−0.642900	−	0.642900i	−0.951267	+	0.308367i	$0.900217\pi$
$564$		0			0
$565$	7.85360e13	−	1.12194e13i	1.36404	−	0.194863i
$566$	2.11278e13			0.363725
$567$		0			0
$568$	2.55662e13	+	2.55662e13i	0.432439	+	0.432439i
$569$		−	2.82859e13i		−	0.474252i	−0.971479	−	0.237126i	$-0.923795\pi$
$569$		−	2.82859e13i		−	0.474252i	0.971479	−	0.237126i	$-0.0762054\pi$
$570$		0			0
$571$	2.19201e12			0.0361129			0.0180564	−	0.999837i	$-0.494252\pi$
$571$	2.19201e12			0.0361129			0.0180564	+	0.999837i	$0.494252\pi$
$572$	−2.06522e13	+	2.06522e13i	−0.337277	+	0.337277i
$573$		0			0
$574$		−	4.11616e13i		−	0.660592i
$575$	3.47189e13	−	6.33110e13i	0.552366	−	1.00726i
$576$		0			0
$577$	−2.97579e13	+	2.97579e13i	−0.465289	+	0.465289i	−0.900384	−	0.435095i	$-0.856715\pi$
$577$	−2.97579e13	+	2.97579e13i	−0.465289	+	0.465289i	0.435095	+	0.900384i	$0.356715\pi$
$578$	8.08489e13	+	8.08489e13i	1.25324	+	1.25324i
$579$		0			0
$580$	−2.37992e13	+	3.17323e13i	−0.362596	+	0.483461i
$581$	−8.71608e13			−1.31656
$582$		0			0
$583$	−3.40529e13	−	3.40529e13i	−0.505605	−	0.505605i
$584$		−	1.04258e13i		−	0.153477i
$585$		0			0
$586$	5.73556e12			0.0830019
$587$	−4.60333e13	+	4.60333e13i	−0.660513	+	0.660513i	−0.955501	−	0.294988i	$-0.904684\pi$
$587$	−4.60333e13	+	4.60333e13i	−0.660513	+	0.660513i	0.294988	+	0.955501i	$0.404684\pi$
$588$		0			0
$589$		−	1.10883e13i		−	0.156419i
$590$	−4.85848e13	+	6.94069e12i	−0.679580	+	0.0970829i
$591$		0			0
$592$	−1.47818e13	+	1.47818e13i	−0.203291	+	0.203291i
$593$	6.17714e12	+	6.17714e12i	0.0842391	+	0.0842391i	0.747971	−	0.663732i	$-0.231028\pi$
$593$	6.17714e12	+	6.17714e12i	0.0842391	+	0.0842391i	−0.663732	+	0.747971i	$0.731028\pi$
$594$		0			0
$595$	−7.90272e13	−	5.92704e13i	−1.05972	−	0.794791i
$596$	2.20858e12			0.0293685
$597$		0			0
$598$	3.89189e13	+	3.89189e13i	0.508925	+	0.508925i
$599$		−	5.80310e13i		−	0.752534i	−0.926511	−	0.376267i	$-0.877208\pi$
$599$		−	5.80310e13i		−	0.752534i	0.926511	−	0.376267i	$-0.122792\pi$
$600$		0			0
$601$	1.24750e14			1.59100			0.795499	−	0.605955i	$-0.207209\pi$
$601$	1.24750e14			1.59100			0.795499	+	0.605955i	$0.207209\pi$
$602$	1.59726e13	−	1.59726e13i	0.202020	−	0.202020i
$603$		0			0
$604$		−	5.83006e13i		−	0.725251i
$605$	7.74270e12	−	1.03236e13i	0.0955247	−	0.127366i
$606$		0			0
$607$	−9.34184e13	+	9.34184e13i	−1.13368	+	1.13368i	−0.144115	+	0.989561i	$0.546033\pi$
$607$	−9.34184e13	+	9.34184e13i	−1.13368	+	1.13368i	−0.989561	+	0.144115i	$0.953967\pi$
$608$	4.62028e12	+	4.62028e12i	0.0556097	+	0.0556097i
$609$		0			0
$610$	9.06186e12	+	6.34330e13i	0.107292	+	0.751045i
$611$	8.01802e13			0.941588
$612$		0			0
$613$	1.42802e13	+	1.42802e13i	0.164980	+	0.164980i	0.784769	−	0.619789i	$-0.212782\pi$
$613$	1.42802e13	+	1.42802e13i	0.164980	+	0.164980i	−0.619789	+	0.784769i	$0.712782\pi$
$614$		−	3.52497e13i		−	0.403937i
$615$		0			0
$616$	−2.38839e13			−0.269278
$617$	4.17740e12	−	4.17740e12i	0.0467176	−	0.0467176i	−0.683362	−	0.730080i	$-0.739483\pi$
$617$	4.17740e12	−	4.17740e12i	0.0467176	−	0.0467176i	0.730080	+	0.683362i	$0.239483\pi$
$618$		0			0
$619$		−	4.07977e13i		−	0.448934i	−0.974482	−	0.224467i	$-0.927936\pi$
$619$		−	4.07977e13i		−	0.448934i	0.974482	−	0.224467i	$-0.0720642\pi$
$620$	1.28845e13	+	9.66336e12i	0.140640	+	0.105480i
$621$		0			0
$622$	8.49822e13	−	8.49822e13i	0.912800	−	0.912800i
$623$	−6.53340e13	−	6.53340e13i	−0.696144	−	0.696144i
$624$		0			0
$625$	−8.04138e13	+	5.12695e13i	−0.843200	+	0.537600i
$626$	2.68825e13			0.279639
$627$		0			0
$628$	−5.34670e12	−	5.34670e12i	−0.0547379	−	0.0547379i
$629$			2.12022e14i			2.15342i
$630$		0			0
$631$	8.03556e13			0.803284			0.401642	−	0.915797i	$-0.368440\pi$
$631$	8.03556e13			0.803284			0.401642	+	0.915797i	$0.368440\pi$
$632$	−1.61218e13	+	1.61218e13i	−0.159893	+	0.159893i
$633$		0			0
$634$			3.73231e13i			0.364361i
$635$	−8.16382e12	−	5.71467e13i	−0.0790723	−	0.553506i
$636$		0			0
$637$	3.28277e13	−	3.28277e13i	0.313000	−	0.313000i
$638$	6.87789e13	+	6.87789e13i	0.650657	+	0.650657i
$639$		0			0
$640$	−9.39524e12	+	1.34218e12i	−0.0875000	+	0.0125000i
$641$	−9.43477e13			−0.871849			−0.435924	−	0.899983i	$-0.643579\pi$
$641$	−9.43477e13			−0.871849			−0.435924	+	0.899983i	$0.643579\pi$
$642$		0			0
$643$	1.98925e13	+	1.98925e13i	0.180981	+	0.180981i	0.791783	−	0.610802i	$-0.209153\pi$
$643$	1.98925e13	+	1.98925e13i	0.180981	+	0.180981i	−0.610802	+	0.791783i	$0.709153\pi$
$644$			4.50089e13i			0.406321i
$645$		0			0
$646$	6.62710e13			0.589062
$647$	−5.97289e13	+	5.97289e13i	−0.526821	+	0.526821i	−0.919623	−	0.392802i	$-0.871506\pi$
$647$	−5.97289e13	+	5.97289e13i	−0.526821	+	0.526821i	0.392802	+	0.919623i	$0.371506\pi$
$648$		0			0
$649$			1.20350e14i			1.04526i
$650$	−2.03545e13	−	6.97869e13i	−0.175426	−	0.601461i
$651$		0			0
$652$	2.44892e13	−	2.44892e13i	0.207844	−	0.207844i
$653$	9.87072e13	+	9.87072e13i	0.831349	+	0.831349i	0.987701	−	0.156353i	$-0.0499737\pi$
$653$	9.87072e13	+	9.87072e13i	0.831349	+	0.831349i	−0.156353	+	0.987701i	$0.549974\pi$
$654$		0			0
$655$	9.75416e13	−	1.30055e14i	0.809065	−	1.07875i
$656$	−4.01090e13			−0.330158
$657$		0			0
$658$	4.63634e13	+	4.63634e13i	0.375877	+	0.375877i
$659$			5.80689e13i			0.467215i	0.972331	+	0.233607i	$0.0750530\pi$
$659$			5.80689e13i			0.467215i	−0.972331	+	0.233607i	$0.924947\pi$
$660$		0			0
$661$	−1.53137e14			−1.21360			−0.606798	−	0.794856i	$-0.707546\pi$
$661$	−1.53137e14			−1.21360			−0.606798	+	0.794856i	$0.707546\pi$
$662$	7.71268e13	−	7.71268e13i	0.606618	−	0.606618i
$663$		0			0
$664$			8.49317e13i			0.658006i
$665$	−4.05161e13	+	5.78801e12i	−0.311544	+	0.0445062i
$666$		0			0
$667$	1.29613e14	−	1.29613e14i	0.981792	−	0.981792i
$668$	−6.05600e12	−	6.05600e12i	−0.0455306	−	0.0455306i
$669$		0			0
$670$	−7.69659e13	−	5.77244e13i	−0.570065	−	0.427549i
$671$	1.57131e14			1.15518
$672$		0			0
$673$	−8.75360e13	−	8.75360e13i	−0.634032	−	0.634032i	0.315045	−	0.949077i	$-0.397980\pi$
$673$	−8.75360e13	−	8.75360e13i	−0.634032	−	0.634032i	−0.949077	+	0.315045i	$0.897980\pi$
$674$		−	1.17936e14i		−	0.847904i
$675$		0			0
$676$	−1.51714e13			−0.107471
$677$	−1.59452e12	+	1.59452e12i	−0.0112121	+	0.0112121i	−0.712691	−	0.701478i	$-0.752524\pi$
$677$	−1.59452e12	+	1.59452e12i	−0.0112121	+	0.0112121i	0.701478	+	0.712691i	$0.252524\pi$
$678$		0			0
$679$		−	1.07670e13i		−	0.0746014i
$680$	−5.77546e13	+	7.70062e13i	−0.397230	+	0.529640i
$681$		0			0
$682$	2.79268e13	−	2.79268e13i	0.189278	−	0.189278i
$683$	5.65796e13	+	5.65796e13i	0.380677	+	0.380677i	0.871346	−	0.490669i	$-0.163248\pi$
$683$	5.65796e13	+	5.65796e13i	0.380677	+	0.380677i	−0.490669	+	0.871346i	$0.663248\pi$
$684$		0			0
$685$	−1.02384e13	−	7.16689e13i	−0.0678859	−	0.475201i
$686$	1.13957e14			0.750104
$687$		0			0
$688$	−1.55641e13	−	1.55641e13i	−0.100968	−	0.100968i
$689$			9.13676e13i			0.588432i
$690$		0			0
$691$	4.98558e12			0.0316465			0.0158232	−	0.999875i	$-0.494963\pi$
$691$	4.98558e12			0.0316465			0.0158232	+	0.999875i	$0.494963\pi$
$692$	5.95852e13	−	5.95852e13i	0.375498	−	0.375498i
$693$		0			0
$694$			1.72304e14i			1.07028i
$695$	6.53724e13	+	4.90293e13i	0.403153	+	0.302365i
$696$		0			0
$697$	−2.87652e14	+	2.87652e14i	−1.74865	+	1.74865i
$698$	1.30025e14	+	1.30025e14i	0.784785	+	0.784785i
$699$		0			0
$700$	2.85838e13	−	5.21234e13i	0.170071	−	0.310129i
$701$	1.80303e14			1.06516			0.532578	−	0.846381i	$-0.321223\pi$
$701$	1.80303e14			1.06516			0.532578	+	0.846381i	$0.321223\pi$
$702$		0			0
$703$	6.21147e13	+	6.21147e13i	0.361758	+	0.361758i
$704$			2.32731e13i			0.134583i
$705$		0			0
$706$	1.75768e14			1.00211
$707$	1.70187e13	−	1.70187e13i	0.0963448	−	0.0963448i
$708$		0			0
$709$			3.11543e14i			1.73895i	0.493979	+	0.869474i	$0.335542\pi$
$709$			3.11543e14i			1.73895i	−0.493979	+	0.869474i	$0.664458\pi$
$710$	3.12088e13	+	2.18461e14i	0.172976	+	1.21083i
$711$		0			0
$712$	−6.36632e13	+	6.36632e13i	−0.347927	+	0.347927i
$713$	−5.26277e13	−	5.26277e13i	−0.285606	−	0.285606i
$714$		0			0
$715$	−1.76472e14	+	2.52102e13i	−0.944375	+	0.134911i
$716$	−9.26776e13			−0.492504
$717$		0			0
$718$	9.46087e13	+	9.46087e13i	0.495803	+	0.495803i
$719$		−	1.65068e14i		−	0.859051i	−0.903055	−	0.429525i	$-0.858681\pi$
$719$		−	1.65068e14i		−	0.859051i	0.903055	−	0.429525i	$-0.141319\pi$
$720$		0			0
$721$	2.52634e13			0.129663
$722$	−7.86821e13	+	7.86821e13i	−0.401042	+	0.401042i
$723$		0			0
$724$		−	6.80962e13i		−	0.342318i
$725$	−2.32414e14	+	6.77875e13i	−1.16031	+	0.338423i
$726$		0			0
$727$	2.15314e14	−	2.15314e14i	1.06023	−	1.06023i	0.0621642	−	0.998066i	$-0.480200\pi$
$727$	2.15314e14	−	2.15314e14i	1.06023	−	1.06023i	0.998066	−	0.0621642i	$-0.0198002\pi$
$728$	3.20416e13	+	3.20416e13i	0.156696	+	0.156696i
$729$		0			0
$730$	3.81804e13	−	5.09071e13i	0.184173	−	0.245564i
$731$	−2.23244e14			−1.06953
$732$		0			0
$733$	−2.78787e14	−	2.78787e14i	−1.31750	−	1.31750i	−0.915746	−	0.401759i	$-0.868399\pi$
$733$	−2.78787e14	−	2.78787e14i	−1.31750	−	1.31750i	−0.401759	−	0.915746i	$-0.631601\pi$
$734$			5.61152e13i			0.263390i
$735$		0			0
$736$	4.38578e13			0.203076
$737$	−1.66822e14	+	1.66822e14i	−0.767212	+	0.767212i
$738$		0			0
$739$			2.05171e14i			0.930879i	0.885080	+	0.465440i	$0.154104\pi$
$739$			2.05171e14i			0.930879i	−0.885080	+	0.465440i	$0.845896\pi$
$740$	−1.26309e14	+	1.80441e13i	−0.569214	+	0.0813163i
$741$		0			0
$742$	−5.28324e13	+	5.28324e13i	−0.234899	+	0.234899i
$743$	−1.59047e14	−	1.59047e14i	−0.702396	−	0.702396i	0.262528	−	0.964924i	$-0.415444\pi$
$743$	−1.59047e14	−	1.59047e14i	−0.702396	−	0.702396i	−0.964924	+	0.262528i	$0.915444\pi$
$744$		0			0
$745$	1.07841e13	+	8.08805e12i	0.0469895	+	0.0352422i
$746$	−1.36230e14			−0.589627
$747$		0			0
$748$	1.66909e14	+	1.66909e14i	0.712806	+	0.712806i
$749$		−	2.38442e13i		−	0.101152i
$750$		0			0
$751$	−1.40008e14			−0.586074			−0.293037	−	0.956101i	$-0.594666\pi$
$751$	−1.40008e14			−0.586074			−0.293037	+	0.956101i	$0.594666\pi$
$752$	4.51777e13	−	4.51777e13i	0.187860	−	0.187860i
$753$		0			0
$754$		−	1.84541e14i		−	0.757246i
$755$	2.13503e14	−	2.84671e14i	0.870302	−	1.16040i
$756$		0			0
$757$	7.07881e13	−	7.07881e13i	0.284761	−	0.284761i	−0.550243	−	0.835004i	$-0.685465\pi$
$757$	7.07881e13	−	7.07881e13i	0.284761	−	0.284761i	0.835004	+	0.550243i	$0.185465\pi$
$758$	−1.15360e14	−	1.15360e14i	−0.461008	−	0.461008i
$759$		0			0
$760$	5.63999e12	+	3.94799e13i	0.0222439	+	0.155707i
$761$	2.84953e14			1.11648			0.558238	−	0.829681i	$-0.311477\pi$
$761$	2.84953e14			1.11648			0.558238	+	0.829681i	$0.311477\pi$
$762$		0			0
$763$	−5.22324e13	−	5.22324e13i	−0.201984	−	0.201984i
$764$			6.70944e13i			0.257762i
$765$		0			0
$766$	−2.22026e14			−0.841900
$767$	1.61456e14	−	1.61456e14i	0.608245	−	0.608245i
$768$		0			0
$769$			3.59991e14i			1.33863i	0.742980	+	0.669314i	$0.233412\pi$
$769$			3.59991e14i			1.33863i	−0.742980	+	0.669314i	$0.766588\pi$
$770$	−1.16621e14	−	8.74654e13i	−0.430845	−	0.323134i
$771$		0			0
$772$	1.08950e14	−	1.08950e14i	0.397319	−	0.397319i
$773$	−1.40032e14	−	1.40032e14i	−0.507375	−	0.507375i	0.406345	−	0.913720i	$-0.366803\pi$
$773$	−1.40032e14	−	1.40032e14i	−0.507375	−	0.507375i	−0.913720	+	0.406345i	$0.866803\pi$
$774$		0			0
$775$	2.75242e13	+	9.43687e13i	0.0984479	+	0.337536i
$776$	−1.04917e13			−0.0372852
$777$		0			0
$778$	−1.80028e14	−	1.80028e14i	−0.631601	−	0.631601i
$779$			1.68543e14i			0.587520i
$780$		0			0
$781$	5.41154e14			1.86237
$782$	3.14538e14	−	3.14538e14i	1.07557	−	1.07557i
$783$		0			0
$784$		−	3.69937e13i		−	0.124896i
$785$	−6.52674e12	−	4.56872e13i	−0.0218951	−	0.153266i
$786$		0			0
$787$	2.99888e14	−	2.99888e14i	0.993312	−	0.993312i	−0.00666595	−	0.999978i	$-0.502122\pi$
$787$	2.99888e14	−	2.99888e14i	0.993312	−	0.993312i	0.999978	+	0.00666595i	$0.00212185\pi$
$788$	4.04606e13	+	4.04606e13i	0.133168	+	0.133168i
$789$		0			0
$790$	−1.37760e14	+	1.96800e13i	−0.447700	+	0.0639571i
$791$	−3.01830e14			−0.974719
$792$		0			0
$793$	−2.10800e14	−	2.10800e14i	−0.672208	−	0.672208i
$794$		−	2.54281e14i		−	0.805770i
$795$		0			0
$796$	−2.31761e14			−0.725227
$797$	2.14433e14	−	2.14433e14i	0.666807	−	0.666807i	−0.290169	−	0.956976i	$-0.593711\pi$
$797$	2.14433e14	−	2.14433e14i	0.666807	−	0.666807i	0.956976	+	0.290169i	$0.0937114\pi$
$798$		0			0
$799$		−	6.48007e14i		−	1.98997i
$800$	−5.07904e13	−	2.78528e13i	−0.155000	−	0.0850000i
$801$		0			0
$802$	1.40972e14	−	1.40972e14i	0.424874	−	0.424874i
$803$	−1.10340e14	−	1.10340e14i	−0.330488	−	0.330488i
$804$		0			0
$805$	−1.64828e14	+	2.19770e14i	−0.487585	+	0.650113i
$806$	−7.49306e13			−0.220285
$807$		0			0
$808$	−1.65834e13	−	1.65834e13i	−0.0481523	−	0.0481523i
$809$			3.71569e14i			1.07225i	0.844138	+	0.536126i	$0.180113\pi$
$809$			3.71569e14i			1.07225i	−0.844138	+	0.536126i	$0.819887\pi$
$810$		0			0
$811$	4.25889e14			1.21393			0.606963	−	0.794730i	$-0.292388\pi$
$811$	4.25889e14			1.21393			0.606963	+	0.794730i	$0.292388\pi$
$812$	1.06709e14	−	1.06709e14i	0.302289	−	0.302289i
$813$		0			0
$814$			3.12882e14i			0.875504i
$815$	2.09259e14	−	2.98941e13i	0.581963	−	0.0831376i
$816$		0			0
$817$	−6.54023e13	+	6.54023e13i	−0.179673	+	0.179673i
$818$	−1.60256e14	−	1.60256e14i	−0.437571	−	0.437571i
$819$		0			0
$820$	−1.95845e14	−	1.46883e14i	−0.528253	−	0.396190i
$821$	−4.73944e14			−1.27061			−0.635304	−	0.772262i	$-0.719125\pi$
$821$	−4.73944e14			−1.27061			−0.635304	+	0.772262i	$0.719125\pi$
$822$		0			0
$823$	−3.93378e14	−	3.93378e14i	−1.04186	−	1.04186i	−0.999085	−	0.0427794i	$-0.986379\pi$
$823$	−3.93378e14	−	3.93378e14i	−1.04186	−	1.04186i	−0.0427794	−	0.999085i	$-0.513621\pi$
$824$		−	2.46174e13i		−	0.0648045i
$825$		0			0
$826$	1.86721e14			0.485616
$827$	2.32822e14	−	2.32822e14i	0.601861	−	0.601861i	−0.338945	−	0.940806i	$-0.610070\pi$
$827$	2.32822e14	−	2.32822e14i	0.601861	−	0.601861i	0.940806	+	0.338945i	$0.110070\pi$
$828$		0			0
$829$			9.73337e13i			0.248594i	0.992245	+	0.124297i	$0.0396675\pi$
$829$			9.73337e13i			0.248594i	−0.992245	+	0.124297i	$0.960332\pi$
$830$	−3.11029e14	+	4.14706e14i	−0.789607	+	1.05281i
$831$		0			0
$832$	3.12221e13	−	3.12221e13i	0.0783152	−	0.0783152i
$833$	−2.65310e14	−	2.65310e14i	−0.661499	−	0.661499i
$834$		0			0
$835$	−7.39258e12	−	5.17481e13i	−0.0182123	−	0.127486i
$836$	9.77963e13			0.239492
$837$		0			0
$838$	−2.37190e14	−	2.37190e14i	−0.573954	−	0.573954i
$839$			3.82848e14i			0.920910i	0.887683	+	0.460455i	$0.152314\pi$
$839$			3.82848e14i			0.920910i	−0.887683	+	0.460455i	$0.847686\pi$
$840$		0			0
$841$	−1.93879e14			−0.460840
$842$	7.49601e13	−	7.49601e13i	0.177121	−	0.177121i
$843$		0			0
$844$		−	7.06533e13i		−	0.164976i
$845$	−7.40789e13	−	5.55592e13i	−0.171954	−	0.128965i
$846$		0			0
$847$	−3.47162e13	+	3.47162e13i	−0.0796371	+	0.0796371i
$848$	5.14813e13	+	5.14813e13i	0.117401	+	0.117401i
$849$		0			0
$850$	−5.64010e14	+	1.64503e14i	−1.27114	+	0.370748i
$851$	5.89622e14			1.32107
$852$		0			0
$853$	4.25918e14	+	4.25918e14i	0.943149	+	0.943149i	0.998469	−	0.0553196i	$-0.0176178\pi$
$853$	4.25918e14	+	4.25918e14i	0.943149	+	0.943149i	−0.0553196	+	0.998469i	$0.517618\pi$
$854$		−	2.43786e14i		−	0.536684i
$855$		0			0
$856$	−2.32344e13			−0.0505549
$857$	3.58497e14	−	3.58497e14i	0.775498	−	0.775498i	−0.203563	−	0.979062i	$-0.565252\pi$
$857$	3.58497e14	−	3.58497e14i	0.775498	−	0.775498i	0.979062	+	0.203563i	$0.0652523\pi$
$858$		0			0
$859$			7.30888e14i			1.56273i	0.624071	+	0.781367i	$0.285477\pi$
$859$			7.30888e14i			1.56273i	−0.624071	+	0.781367i	$0.714523\pi$
$860$	−1.89992e13	−	1.32994e14i	−0.0403871	−	0.282710i
$861$		0			0
$862$	3.82602e14	−	3.82602e14i	0.803917	−	0.803917i
$863$	−1.48513e14	−	1.48513e14i	−0.310249	−	0.310249i	0.534757	−	0.845006i	$-0.320403\pi$
$863$	−1.48513e14	−	1.48513e14i	−0.310249	−	0.310249i	−0.845006	+	0.534757i	$0.820403\pi$
$864$		0			0
$865$	5.09151e14	−	7.27359e13i	1.05140	−	0.150199i
$866$	2.37383e13			0.0487372
$867$		0			0
$868$	−4.33279e13	−	4.33279e13i	−0.0879365	−	0.0879365i
$869$			3.41247e14i			0.688604i
$870$		0			0
$871$	4.47601e14			0.892895
$872$	−5.08966e13	+	5.08966e13i	−0.100950	+	0.100950i
$873$		0			0
$874$		−	1.84296e14i		−	0.361375i
$875$	3.30451e14	−	1.49832e14i	0.644268	−	0.292122i
$876$		0			0
$877$	−3.85609e13	+	3.85609e13i	−0.0743274	+	0.0743274i	−0.743293	−	0.668966i	$-0.766737\pi$
$877$	−3.85609e13	+	3.85609e13i	−0.0743274	+	0.0743274i	0.668966	+	0.743293i	$0.266737\pi$
$878$	3.35527e14	+	3.35527e14i	0.643065	+	0.643065i
$879$		0			0
$880$	−8.52286e13	+	1.13638e14i	−0.161500	+	0.215333i
$881$	4.11264e14			0.774892			0.387446	−	0.921892i	$-0.373357\pi$
$881$	4.11264e14			0.774892			0.387446	+	0.921892i	$0.373357\pi$
$882$		0			0
$883$	−6.34116e14	−	6.34116e14i	−1.18131	−	1.18131i	−0.979404	−	0.201908i	$-0.935286\pi$
$883$	−6.34116e14	−	6.34116e14i	−1.18131	−	1.18131i	−0.201908	−	0.979404i	$-0.564714\pi$
$884$		−	4.47835e14i		−	0.829577i
$885$		0			0
$886$	−7.64510e14			−1.40028
$887$	−7.15241e14	+	7.15241e14i	−1.30267	+	1.30267i	−0.376083	+	0.926586i	$0.622729\pi$
$887$	−7.15241e14	+	7.15241e14i	−1.30267	+	1.30267i	−0.926586	+	0.376083i	$0.877271\pi$
$888$		0			0
$889$			2.19626e14i			0.395526i
$890$	−5.43997e14	+	7.77138e13i	−0.974196	+	0.139171i
$891$		0			0
$892$	−6.45395e13	+	6.45395e13i	−0.114288	+	0.114288i
$893$	−1.89842e14	−	1.89842e14i	−0.334299	−	0.334299i
$894$		0			0
$895$	−4.52527e14	−	3.39395e14i	−0.788006	−	0.591005i
$896$	3.61078e13			0.0625260
$897$		0			0
$898$	3.27257e14	+	3.27257e14i	0.560411	+	0.560411i
$899$			2.49545e14i			0.424962i
$900$		0			0
$901$	7.38423e14			1.24360
$902$	−4.24488e14	+	4.24488e14i	−0.710940	+	0.710940i
$903$		0			0
$904$			2.94111e14i			0.487157i
$905$	2.49376e14	−	3.32501e14i	0.410782	−	0.547709i
$906$		0			0
$907$	4.62743e14	−	4.62743e14i	0.753882	−	0.753882i	−0.221320	−	0.975201i	$-0.571036\pi$
$907$	4.62743e14	−	4.62743e14i	0.753882	−	0.753882i	0.975201	+	0.221320i	$0.0710364\pi$
$908$	5.90173e13	+	5.90173e13i	0.0956203	+	0.0956203i
$909$		0			0
$910$	3.91132e13	+	2.73793e14i	0.0626782	+	0.438748i
$911$	2.41312e14			0.384580			0.192290	−	0.981338i	$-0.438409\pi$
$911$	2.41312e14			0.384580			0.192290	+	0.981338i	$0.438409\pi$
$912$		0			0
$913$	8.98864e14	+	8.98864e14i	1.41690	+	1.41690i
$914$			2.20327e14i			0.345411i
$915$		0			0
$916$	1.68512e14			0.261308
$917$	−4.37351e14	+	4.37351e14i	−0.674502	+	0.674502i
$918$		0			0
$919$			3.74682e14i			0.571591i	0.958291	+	0.285795i	$0.0922577\pi$
$919$			3.74682e14i			0.571591i	−0.958291	+	0.285795i	$0.907742\pi$
$920$	2.14150e14	+	1.60612e14i	0.324921	+	0.243691i
$921$		0			0
$922$	−2.75262e14	+	2.75262e14i	−0.413134	+	0.413134i
$923$	−7.25988e14	−	7.25988e14i	−1.08373	−	1.08373i
$924$		0			0
$925$	−6.82822e14	−	3.74451e14i	−1.00832	−	0.552951i
$926$	1.49501e13			0.0219579
$927$		0			0
$928$	−1.03980e14	−	1.03980e14i	−0.151081	−	0.151081i
$929$			4.47351e14i			0.646501i	0.946313	+	0.323251i	$0.104776\pi$
$929$			4.47351e14i			0.646501i	−0.946313	+	0.323251i	$0.895224\pi$
$930$		0			0
$931$	−1.55452e14			−0.222253
$932$	5.10949e13	−	5.10949e13i	0.0726605	−	0.0726605i
$933$		0			0
$934$		−	5.20858e14i		−	0.732799i
$935$	2.03746e14	+	1.42622e15i	0.285123	+	1.99586i
$936$		0			0
$937$	−2.34215e14	+	2.34215e14i	−0.324278	+	0.324278i	−0.850405	−	0.526128i	$-0.823643\pi$
$937$	−2.34215e14	+	2.34215e14i	−0.324278	+	0.324278i	0.526128	+	0.850405i	$0.323643\pi$
$938$	2.58821e14	+	2.58821e14i	0.356439	+	0.356439i
$939$		0			0
$940$	3.86040e14	−	5.51486e13i	0.526009	−	0.0751441i
$941$	3.80526e13			0.0515746			0.0257873	−	0.999667i	$-0.491791\pi$
$941$	3.80526e13			0.0515746			0.0257873	+	0.999667i	$0.491791\pi$
$942$		0			0
$943$	7.99943e14	+	7.99943e14i	1.07276	+	1.07276i
$944$		−	1.81946e14i		−	0.242707i
$945$		0			0
$946$	−3.29442e14			−0.434834
$947$	−1.26567e13	+	1.26567e13i	−0.0166176	+	0.0166176i	−0.715367	−	0.698749i	$-0.753740\pi$
$947$	−1.26567e13	+	1.26567e13i	−0.0166176	+	0.0166176i	0.698749	+	0.715367i	$0.253740\pi$
$948$		0			0
$949$			2.96054e14i			0.384627i
$950$	−1.17041e14	+	2.13427e14i	−0.151258	+	0.275824i
$951$		0			0
$952$	2.58956e14	−	2.58956e14i	0.331163	−	0.331163i
$953$	7.73544e14	+	7.73544e14i	0.984057	+	0.984057i	0.999875	−	0.0158178i	$-0.00503519\pi$
$953$	7.73544e14	+	7.73544e14i	0.984057	+	0.984057i	−0.0158178	+	0.999875i	$0.505035\pi$
$954$		0			0
$955$	−2.45707e14	+	3.27610e14i	−0.309315	+	0.412420i
$956$	−2.02559e13			−0.0253665
$957$		0			0
$958$	5.22815e14	+	5.22815e14i	0.647918	+	0.647918i
$959$			2.75438e14i			0.339571i
$960$		0			0
$961$	−7.18304e14			−0.876378
$962$	4.19748e14	−	4.19748e14i	0.509464	−	0.509464i
$963$		0			0
$964$			4.16907e14i			0.500788i
$965$	9.30967e14	−	1.32995e14i	1.11249	−	0.158928i
$966$		0			0
$967$	−5.57904e14	+	5.57904e14i	−0.659822	+	0.659822i	−0.955338	−	0.295516i	$-0.904508\pi$
$967$	−5.57904e14	+	5.57904e14i	−0.659822	+	0.659822i	0.295516	+	0.955338i	$0.404508\pi$
$968$	3.38284e13	+	3.38284e13i	0.0398020	+	0.0398020i
$969$		0			0
$970$	−5.12289e13	−	3.84217e13i	−0.0596563	−	0.0447422i
$971$	−1.01087e14			−0.117112			−0.0585559	−	0.998284i	$-0.518650\pi$
$971$	−1.01087e14			−0.117112			−0.0585559	+	0.998284i	$0.518650\pi$
$972$		0			0
$973$	−2.19834e14	−	2.19834e14i	−0.252076	−	0.252076i
$974$			1.25317e14i			0.142961i
$975$		0			0
$976$	−2.37551e14			−0.268230
$977$	7.13366e14	−	7.13366e14i	0.801382	−	0.801382i	−0.181929	−	0.983312i	$-0.558234\pi$
$977$	7.13366e14	−	7.13366e14i	0.801382	−	0.801382i	0.983312	+	0.181929i	$0.0582342\pi$
$978$		0			0
$979$			1.34754e15i			1.49840i
$980$	1.35475e14	−	1.80634e14i	0.149875	−	0.199833i
$981$		0			0
$982$	−2.67113e13	+	2.67113e13i	−0.0292508	+	0.0292508i
$983$	5.14731e14	+	5.14731e14i	0.560806	+	0.560806i	0.929536	−	0.368731i	$-0.120208\pi$
$983$	5.14731e14	+	5.14731e14i	0.560806	+	0.560806i	−0.368731	+	0.929536i	$0.620208\pi$
$984$		0			0
$985$	4.93904e13	+	3.45733e14i	0.0532674	+	0.372872i
$986$	−1.49144e15			−1.60038
$987$		0			0
$988$	−1.31199e14	−	1.31199e14i	−0.139363	−	0.139363i
$989$			6.20830e14i			0.656132i
$990$		0			0
$991$	1.13356e15			1.18598			0.592990	−	0.805210i	$-0.297947\pi$
$991$	1.13356e15			1.18598			0.592990	+	0.805210i	$0.297947\pi$
$992$	−4.22199e13	+	4.22199e13i	−0.0439499	+	0.0439499i
$993$		0			0
$994$		−	8.39591e14i		−	0.865239i
$995$	−1.13164e15	−	8.48732e14i	−1.16036	−	0.870273i
$996$		0			0
$997$	6.55685e14	−	6.55685e14i	0.665609	−	0.665609i	−0.291087	−	0.956696i	$-0.594017\pi$
$997$	6.55685e14	−	6.55685e14i	0.665609	−	0.665609i	0.956696	+	0.291087i	$0.0940171\pi$
$998$	4.30580e14	+	4.30580e14i	0.434912	+	0.434912i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.11.g.b.73.1		2
3.2	odd	2		10.11.c.a.3.1	✓	2
5.2	odd	4	inner	90.11.g.b.37.1		2
12.11	even	2		80.11.p.b.33.1		2
15.2	even	4		10.11.c.a.7.1	yes	2
15.8	even	4		50.11.c.c.7.1		2
15.14	odd	2		50.11.c.c.43.1		2
60.47	odd	4		80.11.p.b.17.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.11.c.a.3.1	✓	2	3.2	odd	2
10.11.c.a.7.1	yes	2	15.2	even	4
50.11.c.c.7.1		2	15.8	even	4
50.11.c.c.43.1		2	15.14	odd	2
80.11.p.b.17.1		2	60.47	odd	4
80.11.p.b.33.1		2	12.11	even	2
90.11.g.b.37.1		2	5.2	odd	4	inner
90.11.g.b.73.1		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	90.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.0000 + 16.0000i) q^{2} -512.000i q^{4} +(1875.00 - 2500.00i) q^{5} +(-8407.00 + 8407.00i) q^{7} +(8192.00 + 8192.00i) q^{8} +(10000.0 + 70000.0i) q^{10} +173398. q^{11} +(-232623. - 232623. i) q^{13} -269024. i q^{14} -262144. q^{16} +(-1.88003e6 + 1.88003e6i) q^{17} +1.10156e6i q^{19} +(-1.28000e6 - 960000. i) q^{20} +(-2.77437e6 + 2.77437e6i) q^{22} +(5.22826e6 + 5.22826e6i) q^{23} +(-2.73438e6 - 9.37500e6i) q^{25} +7.44394e6 q^{26} +(4.30438e6 + 4.30438e6i) q^{28} -2.47908e7i q^{29} -1.00660e7 q^{31} +(4.19430e6 - 4.19430e6i) q^{32} -6.01611e7i q^{34} +(5.25438e6 + 3.67806e7i) q^{35} +(5.63879e7 - 5.63879e7i) q^{37} +(-1.76250e7 - 1.76250e7i) q^{38} +(3.58400e7 - 5.12000e6i) q^{40} +1.53004e8 q^{41} +(5.93725e7 + 5.93725e7i) q^{43} -8.87798e7i q^{44} -1.67304e8 q^{46} +(-1.72339e8 + 1.72339e8i) q^{47} +1.41120e8i q^{49} +(1.93750e8 + 1.06250e8i) q^{50} +(-1.19103e8 + 1.19103e8i) q^{52} +(-1.96386e8 - 1.96386e8i) q^{53} +(3.25121e8 - 4.33495e8i) q^{55} -1.37740e8 q^{56} +(3.96653e8 + 3.96653e8i) q^{58} +6.94069e8i q^{59} +9.06186e8 q^{61} +(1.61056e8 - 1.61056e8i) q^{62} +1.34218e8i q^{64} +(-1.01773e9 + 1.45389e8i) q^{65} +(-9.62074e8 + 9.62074e8i) q^{67} +(9.62577e8 + 9.62577e8i) q^{68} +(-6.72560e8 - 5.04420e8i) q^{70} +3.12088e9 q^{71} +(-6.36339e8 - 6.36339e8i) q^{73} +1.80441e9i q^{74} +5.63999e8 q^{76} +(-1.45776e9 + 1.45776e9i) q^{77} +1.96800e9i q^{79} +(-4.91520e8 + 6.55360e8i) q^{80} +(-2.44806e9 + 2.44806e9i) q^{82} +(5.18382e9 + 5.18382e9i) q^{83} +(1.17502e9 + 8.22514e9i) q^{85} -1.89992e9 q^{86} +(1.42048e9 + 1.42048e9i) q^{88} +7.77138e9i q^{89} +3.91132e9 q^{91} +(2.67687e9 - 2.67687e9i) q^{92} -5.51486e9i q^{94} +(2.75390e9 + 2.06542e9i) q^{95} +(-6.40361e8 + 6.40361e8i) q^{97} +(-2.25792e9 - 2.25792e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} + 3750 q^{5} - 16814 q^{7} + 16384 q^{8} + 20000 q^{10} + 346796 q^{11} - 465246 q^{13} - 524288 q^{16} - 3760066 q^{17} - 2560000 q^{20} - 5548736 q^{22} + 10456526 q^{23} - 5468750 q^{25}+ \cdots - 4515838432 q^{98}+O(q^{100}) \) 2 * q - 32 * q^2 + 3750 * q^5 - 16814 * q^7 + 16384 * q^8 + 20000 * q^10 + 346796 * q^11 - 465246 * q^13 - 524288 * q^16 - 3760066 * q^17 - 2560000 * q^20 - 5548736 * q^22 + 10456526 * q^23 - 5468750 * q^25 + 14887872 * q^26 + 8608768 * q^28 - 20131996 * q^31 + 8388608 * q^32 + 10508750 * q^35 + 112775826 * q^37 - 35249920 * q^38 + 71680000 * q^40 + 306007196 * q^41 + 118744914 * q^43 - 334608832 * q^46 - 344678706 * q^47 + 387500000 * q^50 - 238205952 * q^52 - 392771234 * q^53 + 650242500 * q^55 - 275480576 * q^56 + 793306880 * q^58 + 1812371604 * q^61 + 322111936 * q^62 - 2035451250 * q^65 - 1924147934 * q^67 + 1925153792 * q^68 - 1345120000 * q^70 + 6241755196 * q^71 - 1272678526 * q^73 + 1127997440 * q^76 - 2915513972 * q^77 - 983040000 * q^80 - 4896115136 * q^82 + 10367644206 * q^83 + 2350041250 * q^85 - 3799837248 * q^86 + 2840952832 * q^88 + 7822646244 * q^91 + 5353741312 * q^92 + 5507800000 * q^95 - 1280722494 * q^97 - 4515838432 * q^98

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