LMFDB - Embedded newform 150.8.e.a.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,8,Mod(107,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("150.107");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	150.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$46.8577538226$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 64 x^{14} - 308 x^{13} + 1346 x^{12} - 4436 x^{11} + 12996 x^{10} - 30704 x^{9} + \cdots + 6793 $ x^16 - 8x^15 + 64x^14 - 308x^13 + 1346x^12 - 4436x^11 + 12996x^10 - 30704x^9 + 63689x^8 - 108460x^7 + 159264x^6 - 189736x^5 + 188072x^4 - 143692x^3 + 83932x^2 - 32020*x + 6793
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{52}\cdot 3^{16}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.2
Root			$0.500000 + 0.415846i$ of defining polynomial
Character	$\chi$	$=$	150.143
Dual form			150.8.e.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.65685 - 5.65685i) q^{2} +(-26.9398 - 38.2263i) q^{3} +64.0000i q^{4} +(-63.8461 + 368.635i) q^{6} +(-6.12631 + 6.12631i) q^{7} +(362.039 - 362.039i) q^{8} +(-735.497 + 2059.61i) q^{9} +2862.04i q^{11} +(2446.48 - 1724.15i) q^{12} +(-2016.24 - 2016.24i) q^{13} +69.3113 q^{14} -4096.00 q^{16} +(8719.44 + 8719.44i) q^{17} +(15811.5 - 7490.34i) q^{18} +1408.92i q^{19} +(399.228 + 69.1446i) q^{21} +(16190.1 - 16190.1i) q^{22} +(52424.7 - 52424.7i) q^{23} +(-23592.6 - 4086.15i) q^{24} +22811.2i q^{26} +(98545.5 - 27370.3i) q^{27} +(-392.084 - 392.084i) q^{28} -95838.3 q^{29} +125580. q^{31} +(23170.5 + 23170.5i) q^{32} +(109405. - 77102.7i) q^{33} -98649.2i q^{34} +(-131815. - 47071.8i) q^{36} +(305427. - 305427. i) q^{37} +(7970.05 - 7970.05i) q^{38} +(-22756.4 + 131391. i) q^{39} -609628. i q^{41} +(-1867.23 - 2649.51i) q^{42} +(317725. + 317725. i) q^{43} -183170. q^{44} -593118. q^{46} +(-435458. - 435458. i) q^{47} +(110345. + 156575. i) q^{48} +823468. i q^{49} +(98412.0 - 568212. i) q^{51} +(129040. - 129040. i) q^{52} +(-1.07335e6 + 1.07335e6i) q^{53} +(-712287. - 402628. i) q^{54} +4435.92i q^{56} +(53857.7 - 37956.0i) q^{57} +(542143. + 542143. i) q^{58} -3.09673e6 q^{59} +1.62355e6 q^{61} +(-710389. - 710389. i) q^{62} +(-8111.96 - 17123.7i) q^{63} -262144. i q^{64} +(-1.05505e6 - 182730. i) q^{66} +(-907865. + 907865. i) q^{67} +(-558044. + 558044. i) q^{68} +(-3.41631e6 - 591692. i) q^{69} -3.60524e6i q^{71} +(479382. + 1.01194e6i) q^{72} +(-2.84276e6 - 2.84276e6i) q^{73} -3.45551e6 q^{74} -90170.8 q^{76} +(-17533.7 - 17533.7i) q^{77} +(871988. - 614529. i) q^{78} +4.14998e6i q^{79} +(-3.70106e6 - 3.02968e6i) q^{81} +(-3.44858e6 + 3.44858e6i) q^{82} +(2.77023e6 - 2.77023e6i) q^{83} +(-4425.26 + 25550.6i) q^{84} -3.59464e6i q^{86} +(2.58186e6 + 3.66354e6i) q^{87} +(1.03617e6 + 1.03617e6i) q^{88} -1.02628e7 q^{89} +24704.3 q^{91} +(3.35518e6 + 3.35518e6i) q^{92} +(-3.38311e6 - 4.80047e6i) q^{93} +4.92664e6i q^{94} +(261514. - 1.50993e6i) q^{96} +(2.22241e6 - 2.22241e6i) q^{97} +(4.65824e6 - 4.65824e6i) q^{98} +(-5.89470e6 - 2.10502e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2304 q^{6} - 65536 q^{16} - 183168 q^{21} + 1410688 q^{31} - 193536 q^{36} + 2302464 q^{46} + 1055808 q^{51} + 21247904 q^{61} - 4589568 q^{66} + 13881344 q^{76} - 36589968 q^{81} + 160819200 q^{91}+ \cdots - 9437184 q^{96}+O(q^{100}) $ 16 * q + 2304 * q^6 - 65536 * q^16 - 183168 * q^21 + 1410688 * q^31 - 193536 * q^36 + 2302464 * q^46 + 1055808 * q^51 + 21247904 * q^61 - 4589568 * q^66 + 13881344 * q^76 - 36589968 * q^81 + 160819200 * q^91 - 9437184 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−5.65685	−	5.65685i	−0.500000	−	0.500000i
$2$	−5.65685	−	5.65685i	−0.500000	−	0.500000i
$3$	−26.9398	−	38.2263i	−0.576063	−	0.817406i
$3$	−26.9398	−	38.2263i	−0.576063	−	0.817406i
$4$			64.0000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−63.8461	+	368.635i	−0.120672	+	0.696734i
$7$	−6.12631	+	6.12631i	−0.00675081	+	0.00675081i	−0.710474	−	0.703723i	$-0.751519\pi$
$7$	−6.12631	+	6.12631i	−0.00675081	+	0.00675081i	0.703723	+	0.710474i	$0.251519\pi$
$8$	362.039	−	362.039i	0.250000	−	0.250000i
$9$	−735.497	+	2059.61i	−0.336304	+	0.941753i
$10$		0			0
$11$			2862.04i			0.648337i	0.945999	+	0.324169i	$0.105085\pi$
$11$			2862.04i			0.648337i	−0.945999	+	0.324169i	$0.894915\pi$
$12$	2446.48	−	1724.15i	0.408703	−	0.288031i
$13$	−2016.24	−	2016.24i	−0.254531	−	0.254531i	0.568294	−	0.822826i	$-0.307604\pi$
$13$	−2016.24	−	2016.24i	−0.254531	−	0.254531i	−0.822826	+	0.568294i	$0.807604\pi$
$14$	69.3113			0.00675081
$15$		0			0
$16$	−4096.00			−0.250000
$17$	8719.44	+	8719.44i	0.430445	+	0.430445i	0.888780	−	0.458335i	$-0.151554\pi$
$17$	8719.44	+	8719.44i	0.430445	+	0.430445i	−0.458335	+	0.888780i	$0.651554\pi$
$18$	15811.5	−	7490.34i	0.639029	−	0.302725i
$19$			1408.92i			0.0471247i	0.999722	+	0.0235623i	$0.00750082\pi$
$19$			1408.92i			0.0471247i	−0.999722	+	0.0235623i	$0.992499\pi$
$20$		0			0
$21$	399.228	+	69.1446i	0.00940704	+	0.00162926i
$22$	16190.1	−	16190.1i	0.324169	−	0.324169i
$23$	52424.7	−	52424.7i	0.898440	−	0.898440i	−0.0968586	−	0.995298i	$-0.530879\pi$
$23$	52424.7	−	52424.7i	0.898440	−	0.898440i	0.995298	+	0.0968586i	$0.0308794\pi$
$24$	−23592.6	−	4086.15i	−0.348367	−	0.0603358i
$25$		0			0
$26$			22811.2i			0.254531i
$27$	98545.5	−	27370.3i	0.963527	−	0.267612i
$28$	−392.084	−	392.084i	−0.00337541	−	0.00337541i
$29$	−95838.3			−0.729703			−0.364852	−	0.931066i	$-0.618880\pi$
$29$	−95838.3			−0.729703			−0.364852	+	0.931066i	$0.618880\pi$
$30$		0			0
$31$	125580.			0.757104			0.378552	−	0.925580i	$-0.376422\pi$
$31$	125580.			0.757104			0.378552	+	0.925580i	$0.376422\pi$
$32$	23170.5	+	23170.5i	0.125000	+	0.125000i
$33$	109405.	−	77102.7i	0.529955	−	0.373483i
$34$		−	98649.2i		−	0.430445i
$35$		0			0
$36$	−131815.	−	47071.8i	−0.470877	−	0.168152i
$37$	305427.	−	305427.i	0.991292	−	0.991292i	−0.00867015	−	0.999962i	$-0.502760\pi$
$37$	305427.	−	305427.i	0.991292	−	0.991292i	0.999962	+	0.00867015i	$0.00275983\pi$
$38$	7970.05	−	7970.05i	0.0235623	−	0.0235623i
$39$	−22756.4	+	131391.i	−0.0614294	+	0.354682i
$40$		0			0
$41$		−	609628.i		−	1.38141i	−0.723138	−	0.690703i	$-0.757301\pi$
$41$		−	609628.i		−	1.38141i	0.723138	−	0.690703i	$-0.242699\pi$
$42$	−1867.23	−	2649.51i	−0.00388889	−	0.00551815i
$43$	317725.	+	317725.i	0.609412	+	0.609412i	0.942792	−	0.333380i	$-0.108189\pi$
$43$	317725.	+	317725.i	0.609412	+	0.609412i	−0.333380	+	0.942792i	$0.608189\pi$
$44$	−183170.			−0.324169
$45$		0			0
$46$	−593118.			−0.898440
$47$	−435458.	−	435458.i	−0.611791	−	0.611791i	0.331621	−	0.943413i	$-0.392404\pi$
$47$	−435458.	−	435458.i	−0.611791	−	0.611791i	−0.943413	+	0.331621i	$0.892404\pi$
$48$	110345.	+	156575.i	0.144016	+	0.204351i
$49$			823468.i			0.999909i
$50$		0			0
$51$	98412.0	−	568212.i	0.103885	−	0.599811i
$52$	129040.	−	129040.i	0.127266	−	0.127266i
$53$	−1.07335e6	+	1.07335e6i	−0.990318	+	0.990318i	−0.999954	−	0.00963560i	$-0.996933\pi$
$53$	−1.07335e6	+	1.07335e6i	−0.990318	+	0.990318i	0.00963560	+	0.999954i	$0.496933\pi$
$54$	−712287.	−	402628.i	−0.615569	−	0.347957i
$55$		0			0
$56$			4435.92i			0.00337541i
$57$	53857.7	−	37956.0i	0.0385200	−	0.0271468i
$58$	542143.	+	542143.i	0.364852	+	0.364852i
$59$	−3.09673e6			−1.96300			−0.981501	−	0.191455i	$-0.938679\pi$
$59$	−3.09673e6			−1.96300			−0.981501	+	0.191455i	$0.938679\pi$
$60$		0			0
$61$	1.62355e6			0.915823			0.457912	−	0.888998i	$-0.348598\pi$
$61$	1.62355e6			0.915823			0.457912	+	0.888998i	$0.348598\pi$
$62$	−710389.	−	710389.i	−0.378552	−	0.378552i
$63$	−8111.96	−	17123.7i	−0.00408727	−	0.00862792i
$64$		−	262144.i		−	0.125000i
$65$		0			0
$66$	−1.05505e6	−	182730.i	−0.451719	−	0.0782359i
$67$	−907865.	+	907865.i	−0.368773	+	0.368773i	−0.867030	−	0.498256i	$-0.833974\pi$
$67$	−907865.	+	907865.i	−0.368773	+	0.368773i	0.498256	+	0.867030i	$0.333974\pi$
$68$	−558044.	+	558044.i	−0.215222	+	0.215222i
$69$	−3.41631e6	−	591692.i	−1.25195	−	0.216832i
$70$		0			0
$71$		−	3.60524e6i		−	1.19545i	−0.801703	−	0.597723i	$-0.796072\pi$
$71$		−	3.60524e6i		−	1.19545i	0.801703	−	0.597723i	$-0.203928\pi$
$72$	479382.	+	1.01194e6i	0.151362	+	0.319514i
$73$	−2.84276e6	−	2.84276e6i	−0.855284	−	0.855284i	0.135494	−	0.990778i	$-0.456738\pi$
$73$	−2.84276e6	−	2.84276e6i	−0.855284	−	0.855284i	−0.990778	+	0.135494i	$0.956738\pi$
$74$	−3.45551e6			−0.991292
$75$		0			0
$76$	−90170.8			−0.0235623
$77$	−17533.7	−	17533.7i	−0.00437680	−	0.00437680i
$78$	871988.	−	614529.i	0.208055	−	0.146626i
$79$			4.14998e6i			0.947002i	0.880793	+	0.473501i	$0.157010\pi$
$79$			4.14998e6i			0.947002i	−0.880793	+	0.473501i	$0.842990\pi$
$80$		0			0
$81$	−3.70106e6	−	3.02968e6i	−0.773799	−	0.633431i
$82$	−3.44858e6	+	3.44858e6i	−0.690703	+	0.690703i
$83$	2.77023e6	−	2.77023e6i	0.531794	−	0.531794i	−0.389312	−	0.921106i	$-0.627287\pi$
$83$	2.77023e6	−	2.77023e6i	0.531794	−	0.531794i	0.921106	+	0.389312i	$0.127287\pi$
$84$	−4425.26	+	25550.6i	−0.000814631	+	0.00470352i
$85$		0			0
$86$		−	3.59464e6i		−	0.609412i
$87$	2.58186e6	+	3.66354e6i	0.420355	+	0.596463i
$88$	1.03617e6	+	1.03617e6i	0.162084	+	0.162084i
$89$	−1.02628e7			−1.54312			−0.771559	−	0.636158i	$-0.780523\pi$
$89$	−1.02628e7			−1.54312			−0.771559	+	0.636158i	$0.780523\pi$
$90$		0			0
$91$	24704.3			0.00343659
$92$	3.35518e6	+	3.35518e6i	0.449220	+	0.449220i
$93$	−3.38311e6	−	4.80047e6i	−0.436139	−	0.618861i
$94$			4.92664e6i			0.611791i
$95$		0			0
$96$	261514.	−	1.50993e6i	0.0301679	−	0.174184i
$97$	2.22241e6	−	2.22241e6i	0.247242	−	0.247242i	−0.572596	−	0.819838i	$-0.694064\pi$
$97$	2.22241e6	−	2.22241e6i	0.247242	−	0.247242i	0.819838	+	0.572596i	$0.194064\pi$
$98$	4.65824e6	−	4.65824e6i	0.499954	−	0.499954i
$99$	−5.89470e6	−	2.10502e6i	−0.610574	−	0.218038i
$100$		0			0
$101$		−	6.99729e6i		−	0.675780i	−0.941186	−	0.337890i	$-0.890287\pi$
$101$		−	6.99729e6i		−	0.675780i	0.941186	−	0.337890i	$-0.109713\pi$
$102$	−3.77099e6	+	2.65759e6i	−0.351848	+	0.247963i
$103$	−7.72957e6	−	7.72957e6i	−0.696988	−	0.696988i	0.266772	−	0.963760i	$-0.414043\pi$
$103$	−7.72957e6	−	7.72957e6i	−0.696988	−	0.696988i	−0.963760	+	0.266772i	$0.914043\pi$
$104$	−1.45992e6			−0.127266
$105$		0			0
$106$	1.21435e7			0.990318
$107$	−3.51399e6	−	3.51399e6i	−0.277304	−	0.277304i	0.554728	−	0.832032i	$-0.312822\pi$
$107$	−3.51399e6	−	3.51399e6i	−0.277304	−	0.277304i	−0.832032	+	0.554728i	$0.812822\pi$
$108$	1.75170e6	+	6.30691e6i	0.133806	+	0.481763i
$109$		−	5.96074e6i		−	0.440867i	−0.975402	−	0.220434i	$-0.929253\pi$
$109$		−	5.96074e6i		−	0.440867i	0.975402	−	0.220434i	$-0.0707472\pi$
$110$		0			0
$111$	−1.99035e7	−	3.44721e6i	−1.38133	−	0.239242i
$112$	25093.4	−	25093.4i	0.00168770	−	0.00168770i
$113$	936497.	−	936497.i	0.0610565	−	0.0610565i	−0.675919	−	0.736976i	$-0.736253\pi$
$113$	936497.	−	936497.i	0.0610565	−	0.0610565i	0.736976	+	0.675919i	$0.236253\pi$
$114$	−519377.	−	89954.0i	−0.0328334	−	0.00568661i
$115$		0			0
$116$		−	6.13365e6i		−	0.364852i
$117$	5.63563e6	−	2.66975e6i	0.325306	−	0.154106i
$118$	1.75177e7	+	1.75177e7i	0.981501	+	0.981501i
$119$	−106836.			−0.00581170
$120$		0			0
$121$	1.12959e7			0.579659
$122$	−9.18419e6	−	9.18419e6i	−0.457912	−	0.457912i
$123$	−2.33038e7	+	1.64232e7i	−1.12917	+	0.795776i
$124$			8.03714e6i			0.378552i
$125$		0			0
$126$	−50978.2	+	142755.i	−0.00227032	+	0.00635760i
$127$	1.66782e7	−	1.66782e7i	0.722497	−	0.722497i	−0.246616	−	0.969113i	$-0.579319\pi$
$127$	1.66782e7	−	1.66782e7i	0.722497	−	0.722497i	0.969113	+	0.246616i	$0.0793187\pi$
$128$	−1.48291e6	+	1.48291e6i	−0.0625000	+	0.0625000i
$129$	3.58600e6	−	2.07049e7i	0.147077	−	0.849197i
$130$		0			0
$131$			2.82268e7i			1.09701i	0.836146	+	0.548506i	$0.184803\pi$
$131$			2.82268e7i			1.09701i	−0.836146	+	0.548506i	$0.815197\pi$
$132$	4.93457e6	+	7.00192e6i	0.186741	+	0.264977i
$133$	−8631.48	−	8631.48i	−0.000318130	−	0.000318130i
$134$	1.02713e7			0.368773
$135$		0			0
$136$	6.31355e6			0.215222
$137$	−2.43514e7	−	2.43514e7i	−0.809098	−	0.809098i	0.175399	−	0.984497i	$-0.443878\pi$
$137$	−2.43514e7	−	2.43514e7i	−0.809098	−	0.809098i	−0.984497	+	0.175399i	$0.943878\pi$
$138$	1.59785e7	+	2.26727e7i	0.517557	+	0.734390i
$139$			2.79446e7i			0.882563i	0.897369	+	0.441281i	$0.145476\pi$
$139$			2.79446e7i			0.882563i	−0.897369	+	0.441281i	$0.854524\pi$
$140$		0			0
$141$	−4.91479e6	+	2.83771e7i	−0.147652	+	0.852512i
$142$	−2.03943e7	+	2.03943e7i	−0.597723	+	0.597723i
$143$	5.77057e6	−	5.77057e6i	0.165022	−	0.165022i
$144$	3.01259e6	−	8.43618e6i	0.0840760	−	0.235438i
$145$		0			0
$146$			3.21622e7i			0.855284i
$147$	3.14781e7	−	2.21840e7i	0.817331	−	0.576010i
$148$	1.95473e7	+	1.95473e7i	0.495646	+	0.495646i
$149$	4.77169e7			1.18174			0.590868	−	0.806768i	$-0.298785\pi$
$149$	4.77169e7			1.18174			0.590868	+	0.806768i	$0.298785\pi$
$150$		0			0
$151$	1.50380e7			0.355443			0.177722	−	0.984081i	$-0.443127\pi$
$151$	1.50380e7			0.355443			0.177722	+	0.984081i	$0.443127\pi$
$152$	510083.	+	510083.i	0.0117812	+	0.0117812i
$153$	−2.43718e7	+	1.15456e7i	−0.550133	+	0.260613i
$154$			198372.i			0.00437680i
$155$		0			0
$156$	−8.40901e6	−	1.45641e6i	−0.177341	−	0.0307147i
$157$	3.59845e7	−	3.59845e7i	0.742107	−	0.742107i	−0.230876	−	0.972983i	$-0.574159\pi$
$157$	3.59845e7	−	3.59845e7i	0.742107	−	0.742107i	0.972983	+	0.230876i	$0.0741591\pi$
$158$	2.34758e7	−	2.34758e7i	0.473501	−	0.473501i
$159$	6.99458e7	+	1.21143e7i	1.37998	+	0.239006i
$160$		0			0
$161$			642341.i			0.0121304i
$162$	3.79788e6	+	3.80748e7i	0.0701842	+	0.703615i
$163$	−5.78634e7	−	5.78634e7i	−1.04652	−	1.04652i	−0.998864	−	0.0476564i	$-0.984825\pi$
$163$	−5.78634e7	−	5.78634e7i	−1.04652	−	1.04652i	−0.0476564	−	0.998864i	$-0.515175\pi$
$164$	3.90162e7			0.690703
$165$		0			0
$166$	−3.13416e7			−0.531794
$167$	−2.91589e7	−	2.91589e7i	−0.484465	−	0.484465i	0.422089	−	0.906554i	$-0.361297\pi$
$167$	−2.91589e7	−	2.91589e7i	−0.484465	−	0.484465i	−0.906554	+	0.422089i	$0.861297\pi$
$168$	169569.	−	119503.i	0.00275908	−	0.00194444i
$169$		−	5.46180e7i		−	0.870427i
$170$		0			0
$171$	−2.90183e6	−	1.03626e6i	−0.0443798	−	0.0158482i
$172$	−2.03344e7	+	2.03344e7i	−0.304706	+	0.304706i
$173$	5.12770e7	−	5.12770e7i	0.752941	−	0.752941i	−0.222086	−	0.975027i	$-0.571286\pi$
$173$	5.12770e7	−	5.12770e7i	0.752941	−	0.752941i	0.975027	+	0.222086i	$0.0712865\pi$
$174$	6.11890e6	−	3.53293e7i	0.0880544	−	0.508409i
$175$		0			0
$176$		−	1.17229e7i		−	0.162084i
$177$	8.34251e7	+	1.18376e8i	1.13081	+	1.60457i
$178$	5.80549e7	+	5.80549e7i	0.771559	+	0.771559i
$179$	1.27198e8			1.65766			0.828828	−	0.559503i	$-0.189008\pi$
$179$	1.27198e8			1.65766			0.828828	+	0.559503i	$0.189008\pi$
$180$		0			0
$181$	1.10662e8			1.38715			0.693576	−	0.720383i	$-0.256034\pi$
$181$	1.10662e8			1.38715			0.693576	+	0.720383i	$0.256034\pi$
$182$	−139749.	−	139749.i	−0.00171829	−	0.00171829i
$183$	−4.37381e7	−	6.20623e7i	−0.527571	−	0.748599i
$184$		−	3.79596e7i		−	0.449220i
$185$		0			0
$186$	−8.01781e6	+	4.62933e7i	−0.0913609	+	0.527500i
$187$	−2.49554e7	+	2.49554e7i	−0.279073	+	0.279073i
$188$	2.78693e7	−	2.78693e7i	0.305896	−	0.305896i
$189$	−436042.	+	771399.i	−0.00469799	+	0.00831118i
$190$		0			0
$191$			8.53658e7i			0.886477i	0.896404	+	0.443238i	$0.146170\pi$
$191$			8.53658e7i			0.886477i	−0.896404	+	0.443238i	$0.853830\pi$
$192$	−1.00208e7	+	7.06210e6i	−0.102176	+	0.0720078i
$193$	−8.56363e7	−	8.56363e7i	−0.857447	−	0.857447i	0.133590	−	0.991037i	$-0.457349\pi$
$193$	−8.56363e7	−	8.56363e7i	−0.857447	−	0.857447i	−0.991037	+	0.133590i	$0.957349\pi$
$194$	−2.51436e7			−0.247242
$195$		0			0
$196$	−5.27019e7			−0.499954
$197$	−9.18117e7	−	9.18117e7i	−0.855591	−	0.855591i	0.135224	−	0.990815i	$-0.456824\pi$
$197$	−9.18117e7	−	9.18117e7i	−0.855591	−	0.855591i	−0.990815	+	0.135224i	$0.956824\pi$
$198$	2.14376e7	+	4.52532e7i	0.196268	+	0.414306i
$199$			6.40625e7i			0.576259i	0.957591	+	0.288130i	$0.0930334\pi$
$199$			6.40625e7i			0.576259i	−0.957591	+	0.288130i	$0.906967\pi$
$200$		0			0
$201$	5.91620e7	+	1.02466e7i	0.513874	+	0.0890009i
$202$	−3.95827e7	+	3.95827e7i	−0.337890	+	0.337890i
$203$	587135.	−	587135.i	0.00492609	−	0.00492609i
$204$	3.63655e7	+	6.29837e6i	0.299906	+	0.0519424i
$205$		0			0
$206$			8.74501e7i			0.696988i
$207$	6.94165e7	+	1.46533e8i	0.543960	+	1.14826i
$208$	8.25854e6	+	8.25854e6i	0.0636329	+	0.0636329i
$209$	−4.03238e6			−0.0305527
$210$		0			0
$211$	−1.27578e8			−0.934949			−0.467475	−	0.884007i	$-0.654836\pi$
$211$	−1.27578e8			−0.934949			−0.467475	+	0.884007i	$0.654836\pi$
$212$	−6.86942e7	−	6.86942e7i	−0.495159	−	0.495159i
$213$	−1.37815e8	+	9.71243e7i	−0.977164	+	0.688651i
$214$			3.97562e7i			0.277304i
$215$		0			0
$216$	2.57682e7	−	4.55864e7i	0.173979	−	0.307785i
$217$	−769344.	+	769344.i	−0.00511107	+	0.00511107i
$218$	−3.37191e7	+	3.37191e7i	−0.220434	+	0.220434i
$219$	−3.20848e7	+	1.85251e8i	−0.206417	+	1.19181i
$220$		0			0
$221$		−	3.51611e7i		−	0.219123i
$222$	9.30908e7	+	1.32091e8i	0.571046	+	0.810288i
$223$	2.45541e7	+	2.45541e7i	0.148271	+	0.148271i	0.777345	−	0.629074i	$-0.216566\pi$
$223$	2.45541e7	+	2.45541e7i	0.148271	+	0.148271i	−0.629074	+	0.777345i	$0.716566\pi$
$224$	−283899.			−0.00168770
$225$		0			0
$226$	−1.05953e7			−0.0610565
$227$	−2.09701e8	−	2.09701e8i	−1.18990	−	1.18990i	−0.977095	−	0.212805i	$-0.931740\pi$
$227$	−2.09701e8	−	2.09701e8i	−1.18990	−	1.18990i	−0.212805	−	0.977095i	$-0.568260\pi$
$228$	2.42918e6	+	3.44689e6i	0.0135734	+	0.0192600i
$229$		−	2.78948e8i		−	1.53497i	−0.641070	−	0.767483i	$-0.721509\pi$
$229$		−	2.78948e8i		−	1.53497i	0.641070	−	0.767483i	$-0.278491\pi$
$230$		0			0
$231$	−197895.	+	1.14260e6i	−0.00105631	+	0.00609893i
$232$	−3.46972e7	+	3.46972e7i	−0.182426	+	0.182426i
$233$	−2.11914e7	+	2.11914e7i	−0.109752	+	0.109752i	−0.759850	−	0.650098i	$-0.774728\pi$
$233$	−2.11914e7	+	2.11914e7i	−0.109752	+	0.109752i	0.650098	+	0.759850i	$0.274728\pi$
$234$	−4.69823e7	−	1.67776e7i	−0.239706	−	0.0856000i
$235$		0			0
$236$		−	1.98191e8i		−	0.981501i
$237$	1.58638e8	−	1.11799e8i	0.774084	−	0.545532i
$238$	604356.	+	604356.i	0.00290585	+	0.00290585i
$239$	−2.40754e8			−1.14073			−0.570363	−	0.821393i	$-0.693197\pi$
$239$	−2.40754e8			−1.14073			−0.570363	+	0.821393i	$0.693197\pi$
$240$		0			0
$241$	−1.04259e8			−0.479792			−0.239896	−	0.970799i	$-0.577113\pi$
$241$	−1.04259e8			−0.479792			−0.239896	+	0.970799i	$0.577113\pi$
$242$	−6.38993e7	−	6.38993e7i	−0.289829	−	0.289829i
$243$	−1.61077e7	+	2.23097e8i	−0.0720133	+	0.997404i
$244$			1.03907e8i			0.457912i
$245$		0			0
$246$	2.24730e8	+	3.89224e7i	0.962473	+	0.166696i
$247$	2.84073e6	−	2.84073e6i	0.0119947	−	0.0119947i
$248$	4.54649e7	−	4.54649e7i	0.189276	−	0.189276i
$249$	−1.80525e8	−	3.12663e7i	−0.741038	−	0.128345i
$250$		0			0
$251$		−	1.88430e8i		−	0.752130i	−0.926593	−	0.376065i	$-0.877277\pi$
$251$		−	1.88430e8i		−	0.752130i	0.926593	−	0.376065i	$-0.122723\pi$
$252$	1.09592e6	−	519165.i	0.00431396	−	0.00204364i
$253$	1.50042e8	+	1.50042e8i	0.582492	+	0.582492i
$254$	−1.88692e8			−0.722497
$255$		0			0
$256$	1.67772e7			0.0625000
$257$	−1.45638e8	−	1.45638e8i	−0.535189	−	0.535189i	0.386923	−	0.922112i	$-0.373538\pi$
$257$	−1.45638e8	−	1.45638e8i	−0.535189	−	0.535189i	−0.922112	+	0.386923i	$0.873538\pi$
$258$	−1.37410e8	+	9.68389e7i	−0.498137	+	0.351060i
$259$			3.74228e6i			0.0133841i
$260$		0			0
$261$	7.04888e7	−	1.97390e8i	0.245402	−	0.687200i
$262$	1.59675e8	−	1.59675e8i	0.548506	−	0.548506i
$263$	2.68726e8	−	2.68726e8i	0.910886	−	0.910886i	−0.0854562	−	0.996342i	$-0.527235\pi$
$263$	2.68726e8	−	2.68726e8i	0.910886	−	0.910886i	0.996342	+	0.0854562i	$0.0272348\pi$
$264$	1.16947e7	−	6.75230e7i	0.0391179	−	0.225859i
$265$		0			0
$266$			97654.0i			0.000318130i
$267$	2.76476e8	+	3.92307e8i	0.888932	+	1.26135i
$268$	−5.81034e7	−	5.81034e7i	−0.184387	−	0.184387i
$269$	−4.82898e8			−1.51259			−0.756297	−	0.654228i	$-0.772994\pi$
$269$	−4.82898e8			−1.51259			−0.756297	+	0.654228i	$0.772994\pi$
$270$		0			0
$271$	−3.56999e8			−1.08962			−0.544810	−	0.838560i	$-0.683398\pi$
$271$	−3.56999e8			−1.08962			−0.544810	+	0.838560i	$0.683398\pi$
$272$	−3.57148e7	−	3.57148e7i	−0.107611	−	0.107611i
$273$	−665528.	−	944353.i	−0.00197969	−	0.00280909i
$274$			2.75504e8i			0.809098i
$275$		0			0
$276$	3.78683e7	−	2.18644e8i	0.108416	−	0.625973i
$277$	2.10083e8	−	2.10083e8i	0.593897	−	0.593897i	−0.344785	−	0.938682i	$-0.612048\pi$
$277$	2.10083e8	−	2.10083e8i	0.593897	−	0.593897i	0.938682	+	0.344785i	$0.112048\pi$
$278$	1.58078e8	−	1.58078e8i	0.441281	−	0.441281i
$279$	−9.23639e7	+	2.58647e8i	−0.254617	+	0.713005i
$280$		0			0
$281$		−	3.10671e8i		−	0.835272i	−0.908614	−	0.417636i	$-0.862859\pi$
$281$		−	3.10671e8i		−	0.835272i	0.908614	−	0.417636i	$-0.137141\pi$
$282$	1.88327e8	−	1.32723e8i	0.500082	−	0.352430i
$283$	9.09536e7	+	9.09536e7i	0.238543	+	0.238543i	0.816247	−	0.577703i	$-0.196051\pi$
$283$	9.09536e7	+	9.09536e7i	0.238543	+	0.238543i	−0.577703	+	0.816247i	$0.696051\pi$
$284$	2.30735e8			0.597723
$285$		0			0
$286$	−6.52865e7			−0.165022
$287$	3.73477e6	+	3.73477e6i	0.00932561	+	0.00932561i
$288$	−6.47641e7	+	3.06804e7i	−0.159757	+	0.0756812i
$289$		−	2.58281e8i		−	0.629435i
$290$		0			0
$291$	−1.44825e8	−	2.50832e7i	−0.344524	−	0.0596701i
$292$	1.81937e8	−	1.81937e8i	0.427642	−	0.427642i
$293$	4.86060e8	−	4.86060e8i	1.12889	−	1.12889i	0.138536	−	0.990357i	$-0.455760\pi$
$293$	4.86060e8	−	4.86060e8i	1.12889	−	1.12889i	0.990357	−	0.138536i	$-0.0442396\pi$
$294$	−3.03559e8	−	5.25752e7i	−0.696671	−	0.120661i
$295$		0			0
$296$		−	2.21153e8i		−	0.495646i
$297$	7.83347e7	+	2.82041e8i	0.173503	+	0.624690i
$298$	−2.69928e8	−	2.69928e8i	−0.590868	−	0.590868i
$299$	−2.11402e8			−0.457362
$300$		0			0
$301$	−3.89296e6			−0.00822805
$302$	−8.50677e7	−	8.50677e7i	−0.177722	−	0.177722i
$303$	−2.67480e8	+	1.88505e8i	−0.552386	+	0.389291i
$304$		−	5.77093e6i		−	0.0117812i
$305$		0			0
$306$	2.03179e8	+	7.25562e7i	0.405373	+	0.144760i
$307$	−3.34862e8	+	3.34862e8i	−0.660514	+	0.660514i	−0.955501	−	0.294987i	$-0.904685\pi$
$307$	−3.34862e8	+	3.34862e8i	−0.660514	+	0.660514i	0.294987	+	0.955501i	$0.404685\pi$
$308$	1.12216e6	−	1.12216e6i	0.00218840	−	0.00218840i
$309$	−8.72398e7	+	5.03706e8i	−0.168213	+	0.971230i
$310$		0			0
$311$			2.15028e7i			0.0405353i	0.999795	+	0.0202676i	$0.00645183\pi$
$311$			2.15028e7i			0.0405353i	−0.999795	+	0.0202676i	$0.993548\pi$
$312$	3.93298e7	+	5.58072e7i	0.0733130	+	0.104028i
$313$	2.82789e8	+	2.82789e8i	0.521263	+	0.521263i	0.917953	−	0.396690i	$-0.129841\pi$
$313$	2.82789e8	+	2.82789e8i	0.521263	+	0.521263i	−0.396690	+	0.917953i	$0.629841\pi$
$314$	−4.07118e8			−0.742107
$315$		0			0
$316$	−2.65598e8			−0.473501
$317$	−1.32636e8	−	1.32636e8i	−0.233860	−	0.233860i	0.580442	−	0.814302i	$-0.302880\pi$
$317$	−1.32636e8	−	1.32636e8i	−0.233860	−	0.233860i	−0.814302	+	0.580442i	$0.802880\pi$
$318$	−3.27144e8	−	4.64202e8i	−0.570485	−	0.809492i
$319$		−	2.74293e8i		−	0.473094i
$320$		0			0
$321$	−3.96606e7	+	2.28993e8i	−0.0669255	+	0.386415i
$322$	3.63363e6	−	3.63363e6i	0.00606520	−	0.00606520i
$323$	−1.22850e7	+	1.22850e7i	−0.0202846	+	0.0202846i
$324$	1.93900e8	−	2.36868e8i	0.316715	−	0.386900i
$325$		0			0
$326$			6.54650e8i			1.04652i
$327$	−2.27857e8	+	1.60581e8i	−0.360367	+	0.253967i
$328$	−2.20709e8	−	2.20709e8i	−0.345352	−	0.345352i
$329$	5.33550e6			0.00826017
$330$		0			0
$331$	9.99204e8			1.51445			0.757227	−	0.653152i	$-0.226554\pi$
$331$	9.99204e8			1.51445			0.757227	+	0.653152i	$0.226554\pi$
$332$	1.77295e8	+	1.77295e8i	0.265897	+	0.265897i
$333$	4.04422e8	+	8.53703e8i	0.600177	+	1.26693i
$334$			3.29895e8i			0.484465i
$335$		0			0
$336$	−1.63524e6	−	283216.i	−0.00235176	−	0.000407315i
$337$	−5.14283e8	+	5.14283e8i	−0.731977	+	0.731977i	−0.971011	−	0.239034i	$-0.923169\pi$
$337$	−5.14283e8	+	5.14283e8i	−0.731977	+	0.731977i	0.239034	+	0.971011i	$0.423169\pi$
$338$	−3.08966e8	+	3.08966e8i	−0.435214	+	0.435214i
$339$	−6.10278e7	−	1.05698e7i	−0.0850803	−	0.0147356i
$340$		0			0
$341$			3.59416e8i			0.490859i
$342$	1.05533e7	+	2.22772e7i	0.0142658	+	0.0301140i
$343$	−1.00901e7	−	1.00901e7i	−0.0135010	−	0.0135010i
$344$	2.30057e8			0.304706
$345$		0			0
$346$	−5.80133e8			−0.752941
$347$	−2.23304e8	−	2.23304e8i	−0.286908	−	0.286908i	0.548948	−	0.835856i	$-0.315028\pi$
$347$	−2.23304e8	−	2.23304e8i	−0.286908	−	0.286908i	−0.835856	+	0.548948i	$0.815028\pi$
$348$	−2.34467e8	+	1.65239e8i	−0.298232	+	0.210177i
$349$		−	6.32133e6i		−	0.00796012i	−0.999992	−	0.00398006i	$-0.998733\pi$
$349$		−	6.32133e6i		−	0.00796012i	0.999992	−	0.00398006i	$-0.00126690\pi$
$350$		0			0
$351$	−2.53877e8	−	1.43507e8i	−0.313364	−	0.177132i
$352$	−6.63148e7	+	6.63148e7i	−0.0810422	+	0.0810422i
$353$	−4.03328e8	+	4.03328e8i	−0.488030	+	0.488030i	−0.907684	−	0.419654i	$-0.862151\pi$
$353$	−4.03328e8	+	4.03328e8i	−0.488030	+	0.488030i	0.419654	+	0.907684i	$0.362151\pi$
$354$	1.97714e8	−	1.14156e9i	0.236879	−	1.36769i
$355$		0			0
$356$		−	6.56816e8i		−	0.771559i
$357$	2.87814e6	+	4.08394e6i	0.00334790	+	0.00475052i
$358$	−7.19540e8	−	7.19540e8i	−0.828828	−	0.828828i
$359$	1.25329e9			1.42962			0.714810	−	0.699319i	$-0.246513\pi$
$359$	1.25329e9			1.42962			0.714810	+	0.699319i	$0.246513\pi$
$360$		0			0
$361$	8.91887e8			0.997779
$362$	−6.26000e8	−	6.26000e8i	−0.693576	−	0.693576i
$363$	−3.04309e8	−	4.31801e8i	−0.333920	−	0.473816i
$364$			1.58107e6i			0.00171829i
$365$		0			0
$366$	−1.03657e8	+	5.98498e8i	−0.110514	+	0.638085i
$367$	−8.33720e8	+	8.33720e8i	−0.880419	+	0.880419i	−0.993577	−	0.113158i	$-0.963903\pi$
$367$	−8.33720e8	+	8.33720e8i	−0.880419	+	0.880419i	0.113158	+	0.993577i	$0.463903\pi$
$368$	−2.14732e8	+	2.14732e8i	−0.224610	+	0.224610i
$369$	1.25560e9	+	4.48379e8i	1.30094	+	0.464572i
$370$		0			0
$371$		−	1.31513e7i		−	0.0133709i
$372$	3.07230e8	−	2.16519e8i	0.309431	−	0.218070i
$373$	7.65695e8	+	7.65695e8i	0.763968	+	0.763968i	0.977037	−	0.213069i	$-0.0683460\pi$
$373$	7.65695e8	+	7.65695e8i	0.763968	+	0.763968i	−0.213069	+	0.977037i	$0.568346\pi$
$374$	2.82338e8			0.279073
$375$		0			0
$376$	−3.15305e8			−0.305896
$377$	1.93233e8	+	1.93233e8i	0.185732	+	0.185732i
$378$	6.83032e6	−	1.89707e6i	0.00650459	−	0.00180660i
$379$		−	4.88370e8i		−	0.460799i	−0.973096	−	0.230400i	$-0.925997\pi$
$379$		−	4.88370e8i		−	0.460799i	0.973096	−	0.230400i	$-0.0740033\pi$
$380$		0			0
$381$	−1.08685e9	−	1.88238e8i	−1.00678	−	0.174370i
$382$	4.82902e8	−	4.82902e8i	0.443238	−	0.443238i
$383$	−4.76741e8	+	4.76741e8i	−0.433597	+	0.433597i	−0.889850	−	0.456253i	$-0.849191\pi$
$383$	−4.76741e8	+	4.76741e8i	−0.433597	+	0.433597i	0.456253	+	0.889850i	$0.349191\pi$
$384$	9.66354e7	+	1.67369e7i	0.0870918	+	0.0150839i
$385$		0			0
$386$			9.68864e8i			0.857447i
$387$	−8.88076e8	+	4.20705e8i	−0.778864	+	0.368968i
$388$	1.42234e8	+	1.42234e8i	0.123621	+	0.123621i
$389$	1.98819e9			1.71251			0.856257	−	0.516550i	$-0.172784\pi$
$389$	1.98819e9			1.71251			0.856257	+	0.516550i	$0.172784\pi$
$390$		0			0
$391$	9.14229e8			0.773457
$392$	2.98127e8	+	2.98127e8i	0.249977	+	0.249977i
$393$	1.07900e9	−	7.60423e8i	0.896704	−	0.631948i
$394$			1.03873e9i			0.855591i
$395$		0			0
$396$	1.34721e8	−	3.77261e8i	0.109019	−	0.305287i
$397$	9.69093e8	−	9.69093e8i	0.777318	−	0.777318i	−0.202056	−	0.979374i	$-0.564762\pi$
$397$	9.69093e8	−	9.69093e8i	0.777318	−	0.777318i	0.979374	+	0.202056i	$0.0647623\pi$
$398$	3.62392e8	−	3.62392e8i	0.288130	−	0.288130i
$399$	−97419.2	+	562479.i	−7.67784e−5	+	0.000443304i
$400$		0			0
$401$			1.62528e9i			1.25871i	0.777120	+	0.629353i	$0.216680\pi$
$401$			1.62528e9i			1.25871i	−0.777120	+	0.629353i	$0.783320\pi$
$402$	−2.76707e8	−	3.92635e8i	−0.212437	−	0.301438i
$403$	−2.53201e8	−	2.53201e8i	−0.192707	−	0.192707i
$404$	4.47827e8			0.337890
$405$		0			0
$406$	−6.64268e6			−0.00492609
$407$	8.74144e8	+	8.74144e8i	0.642692	+	0.642692i
$408$	−1.70086e8	−	2.41344e8i	−0.123982	−	0.175924i
$409$			5.83288e8i			0.421553i	0.977534	+	0.210776i	$0.0675992\pi$
$409$			5.83288e8i			0.421553i	−0.977534	+	0.210776i	$0.932401\pi$
$410$		0			0
$411$	−2.74842e8	+	1.58688e9i	−0.195270	+	1.12745i
$412$	4.94692e8	−	4.94692e8i	0.348494	−	0.348494i
$413$	1.89715e7	−	1.89715e7i	0.0132519	−	0.0132519i
$414$	4.36237e8	−	1.22160e9i	0.302149	−	0.846109i
$415$		0			0
$416$		−	9.34347e7i		−	0.0636329i
$417$	1.06822e9	−	7.52821e8i	0.721412	−	0.508411i
$418$	2.28106e7	+	2.28106e7i	0.0152763	+	0.0152763i
$419$	2.63830e8			0.175217			0.0876083	−	0.996155i	$-0.472078\pi$
$419$	2.63830e8			0.175217			0.0876083	+	0.996155i	$0.472078\pi$
$420$		0			0
$421$	2.33804e8			0.152709			0.0763545	−	0.997081i	$-0.475672\pi$
$421$	2.33804e8			0.152709			0.0763545	+	0.997081i	$0.475672\pi$
$422$	7.21691e8	+	7.21691e8i	0.467475	+	0.467475i
$423$	1.21715e9	−	5.76597e8i	0.781905	−	0.370409i
$424$			7.77186e8i			0.495159i
$425$		0			0
$426$	1.32902e9	+	2.30180e8i	0.832907	+	0.144256i
$427$	−9.94638e6	+	9.94638e6i	−0.00618255	+	0.00618255i
$428$	2.24895e8	−	2.24895e8i	0.138652	−	0.138652i
$429$	−3.76045e8	−	6.51295e7i	−0.229953	−	0.0398270i
$430$		0			0
$431$			2.44883e8i			0.147329i	0.997283	+	0.0736645i	$0.0234694\pi$
$431$			2.44883e8i			0.147329i	−0.997283	+	0.0736645i	$0.976531\pi$
$432$	−4.03643e8	+	1.12109e8i	−0.240882	+	0.0669030i
$433$	7.71156e8	+	7.71156e8i	0.456493	+	0.456493i	0.897503	−	0.441009i	$-0.145379\pi$
$433$	7.71156e8	+	7.71156e8i	0.456493	+	0.456493i	−0.441009	+	0.897503i	$0.645379\pi$
$434$	8.70413e6			0.00511107
$435$		0			0
$436$	3.81488e8			0.220434
$437$	7.38622e7	+	7.38622e7i	0.0423387	+	0.0423387i
$438$	1.22944e9	−	8.66442e8i	0.699114	−	0.492697i
$439$		−	3.41238e9i		−	1.92501i	−0.271272	−	0.962503i	$-0.587444\pi$
$439$		−	3.41238e9i		−	1.92501i	0.271272	−	0.962503i	$-0.412556\pi$
$440$		0			0
$441$	−1.69603e9	−	6.05658e8i	−0.941668	−	0.336273i
$442$	−1.98901e8	+	1.98901e8i	−0.109562	+	0.109562i
$443$	4.85626e8	−	4.85626e8i	0.265393	−	0.265393i	−0.561848	−	0.827241i	$-0.689909\pi$
$443$	4.85626e8	−	4.85626e8i	0.265393	−	0.265393i	0.827241	+	0.561848i	$0.189909\pi$
$444$	2.20621e8	−	1.27382e9i	0.119621	−	0.690667i
$445$		0			0
$446$		−	2.77798e8i		−	0.148271i
$447$	−1.28548e9	−	1.82404e9i	−0.680754	−	0.965958i
$448$	1.60598e6	+	1.60598e6i	0.000843851	+	0.000843851i
$449$	−5.78436e8			−0.301573			−0.150787	−	0.988566i	$-0.548181\pi$
$449$	−5.78436e8			−0.301573			−0.150787	+	0.988566i	$0.548181\pi$
$450$		0			0
$451$	1.74478e9			0.895617
$452$	5.99358e7	+	5.99358e7i	0.0305282	+	0.0305282i
$453$	−4.05120e8	−	5.74846e8i	−0.204757	−	0.290541i
$454$			2.37250e9i			1.18990i
$455$		0			0
$456$	5.75705e6	−	3.32401e7i	0.00284330	−	0.0164167i
$457$	2.70022e9	−	2.70022e9i	1.32340	−	1.32340i	0.412402	−	0.911002i	$-0.364690\pi$
$457$	2.70022e9	−	2.70022e9i	1.32340	−	1.32340i	0.911002	−	0.412402i	$-0.135310\pi$
$458$	−1.57797e9	+	1.57797e9i	−0.767483	+	0.767483i
$459$	1.09792e9	+	6.20609e8i	0.529937	+	0.299553i
$460$		0			0
$461$			8.51165e7i			0.0404632i	0.999795	+	0.0202316i	$0.00644036\pi$
$461$			8.51165e7i			0.0404632i	−0.999795	+	0.0202316i	$0.993560\pi$
$462$	7.58301e6	−	5.34409e6i	0.00357762	−	0.00252131i
$463$	−1.02911e9	−	1.02911e9i	−0.481868	−	0.481868i	0.423860	−	0.905728i	$-0.360675\pi$
$463$	−1.02911e9	−	1.02911e9i	−0.481868	−	0.481868i	−0.905728	+	0.423860i	$0.860675\pi$
$464$	3.92554e8			0.182426
$465$		0			0
$466$	2.39753e8			0.109752
$467$	2.36415e9	+	2.36415e9i	1.07415	+	1.07415i	0.997021	+	0.0771326i	$0.0245765\pi$
$467$	2.36415e9	+	2.36415e9i	1.07415	+	1.07415i	0.0771326	+	0.997021i	$0.475424\pi$
$468$	1.70864e8	+	3.60680e8i	0.0770530	+	0.162653i
$469$		−	1.11237e7i		−	0.00497904i
$470$		0			0
$471$	−2.34497e9	−	4.06139e8i	−1.03410	−	0.179103i
$472$	−1.12113e9	+	1.12113e9i	−0.490751	+	0.490751i
$473$	−9.09340e8	+	9.09340e8i	−0.395105	+	0.395105i
$474$	−1.52983e9	−	2.64960e8i	−0.659808	−	0.114276i
$475$		0			0
$476$		−	6.83751e6i		−	0.00290585i
$477$	−1.42124e9	−	3.00013e9i	−0.599588	−	1.26568i
$478$	1.36191e9	+	1.36191e9i	0.570363	+	0.570363i
$479$	−3.12651e9			−1.29983			−0.649914	−	0.760008i	$-0.725195\pi$
$479$	−3.12651e9			−1.29983			−0.649914	+	0.760008i	$0.725195\pi$
$480$		0			0
$481$	−1.23163e9			−0.504630
$482$	5.89776e8	+	5.89776e8i	0.239896	+	0.239896i
$483$	2.45543e7	−	1.73045e7i	0.00991545	−	0.00698786i
$484$			7.22938e8i			0.289829i
$485$		0			0
$486$	1.35314e9	−	1.17091e9i	0.534708	−	0.462695i
$487$	−2.97686e9	+	2.97686e9i	−1.16790	+	1.16790i	−0.185204	+	0.982700i	$0.559294\pi$
$487$	−2.97686e9	+	2.97686e9i	−1.16790	+	1.16790i	−0.982700	+	0.185204i	$0.940706\pi$
$488$	5.87788e8	−	5.87788e8i	0.228956	−	0.228956i
$489$	−6.53076e8	+	3.77073e9i	−0.252570	+	1.45829i
$490$		0			0
$491$		−	1.72819e9i		−	0.658880i	−0.944177	−	0.329440i	$-0.893140\pi$
$491$		−	1.72819e9i		−	0.658880i	0.944177	−	0.329440i	$-0.106860\pi$
$492$	−1.05109e9	−	1.49144e9i	−0.397888	−	0.564585i
$493$	−8.35657e8	−	8.35657e8i	−0.314097	−	0.314097i
$494$	−3.21391e7			−0.0119947
$495$		0			0
$496$	−5.14377e8			−0.189276
$497$	2.20868e7	+	2.20868e7i	0.00807022	+	0.00807022i
$498$	8.44336e8	+	1.19807e9i	0.306346	+	0.434691i
$499$		−	7.15257e8i		−	0.257698i	−0.991664	−	0.128849i	$-0.958872\pi$
$499$		−	7.15257e8i		−	0.257698i	0.991664	−	0.128849i	$-0.0411282\pi$
$500$		0			0
$501$	−3.29101e8	+	1.90017e9i	−0.116922	+	0.675087i
$502$	−1.06592e9	+	1.06592e9i	−0.376065	+	0.376065i
$503$	−3.37593e9	+	3.37593e9i	−1.18279	+	1.18279i	−0.203765	+	0.979020i	$0.565318\pi$
$503$	−3.37593e9	+	3.37593e9i	−1.18279	+	1.18279i	−0.979020	+	0.203765i	$0.934682\pi$
$504$	−9.13629e6	−	3.26261e6i	−0.00317880	−	0.00113516i
$505$		0			0
$506$		−	1.69753e9i		−	0.582492i
$507$	−2.08784e9	+	1.47140e9i	−0.711492	+	0.501421i
$508$	1.06740e9	+	1.06740e9i	0.361248	+	0.361248i
$509$	−1.54439e9			−0.519094			−0.259547	−	0.965730i	$-0.583573\pi$
$509$	−1.54439e9			−0.519094			−0.259547	+	0.965730i	$0.583573\pi$
$510$		0			0
$511$	3.48313e7			0.0115477
$512$	−9.49063e7	−	9.49063e7i	−0.0312500	−	0.0312500i
$513$	3.85625e7	+	1.38843e8i	0.0126111	+	0.0454059i
$514$			1.64770e9i			0.535189i
$515$		0			0
$516$	1.32511e9	+	2.29504e8i	0.424598	+	0.0735387i
$517$	1.24630e9	−	1.24630e9i	0.396647	−	0.396647i
$518$	2.11696e7	−	2.11696e7i	0.00669203	−	0.00669203i
$519$	−3.34152e9	−	5.78738e8i	−1.04920	−	0.181717i
$520$		0			0
$521$		−	4.27492e9i		−	1.32433i	−0.749358	−	0.662165i	$-0.769638\pi$
$521$		−	4.27492e9i		−	1.32433i	0.749358	−	0.662165i	$-0.230362\pi$
$522$	−1.51535e9	+	7.17862e8i	−0.466301	+	0.220899i
$523$	−3.59310e9	−	3.59310e9i	−1.09828	−	1.09828i	−0.994612	−	0.103670i	$-0.966941\pi$
$523$	−3.59310e9	−	3.59310e9i	−1.09828	−	1.09828i	−0.103670	−	0.994612i	$-0.533059\pi$
$524$	−1.80651e9			−0.548506
$525$		0			0
$526$	−3.04028e9			−0.910886
$527$	1.09499e9	+	1.09499e9i	0.325891	+	0.325891i
$528$	−4.48123e8	+	3.15813e8i	−0.132489	+	0.0933707i
$529$		−	2.09188e9i		−	0.614387i
$530$		0			0
$531$	2.27763e9	−	6.37806e9i	0.660166	−	1.84866i
$532$	552414.	−	552414.i	0.000159065	−	0.000159065i
$533$	−1.22916e9	+	1.22916e9i	−0.351611	+	0.351611i
$534$	6.55237e8	−	3.78321e9i	0.186210	−	1.07514i
$535$		0			0
$536$			6.57365e8i			0.184387i
$537$	−3.42668e9	−	4.86230e9i	−0.954914	−	1.35498i
$538$	2.73168e9	+	2.73168e9i	0.756297	+	0.756297i
$539$	−2.35680e9			−0.648278
$540$		0			0
$541$	−1.34240e9			−0.364495			−0.182247	−	0.983253i	$-0.558337\pi$
$541$	−1.34240e9			−0.364495			−0.182247	+	0.983253i	$0.558337\pi$
$542$	2.01949e9	+	2.01949e9i	0.544810	+	0.544810i
$543$	−2.98122e9	−	4.23020e9i	−0.799087	−	1.13387i
$544$			4.04067e8i			0.107611i
$545$		0			0
$546$	−1.57727e6	+	9.10686e6i	−0.000414698	+	0.00239439i
$547$	−2.35698e9	+	2.35698e9i	−0.615745	+	0.615745i	−0.944437	−	0.328692i	$-0.893392\pi$
$547$	−2.35698e9	+	2.35698e9i	−0.615745	+	0.615745i	0.328692	+	0.944437i	$0.393392\pi$
$548$	1.55849e9	−	1.55849e9i	0.404549	−	0.404549i
$549$	−1.19412e9	+	3.34389e9i	−0.307995	+	0.862480i
$550$		0			0
$551$		−	1.35028e8i		−	0.0343870i
$552$	−1.45105e9	+	1.02262e9i	−0.367195	+	0.258779i
$553$	−2.54240e7	−	2.54240e7i	−0.00639303	−	0.00639303i
$554$	−2.37681e9			−0.593897
$555$		0			0
$556$	−1.78845e9			−0.441281
$557$	5.24979e9	+	5.24979e9i	1.28721	+	1.28721i	0.936476	+	0.350732i	$0.114067\pi$
$557$	5.24979e9	+	5.24979e9i	1.28721	+	1.28721i	0.350732	+	0.936476i	$0.385933\pi$
$558$	1.98562e9	−	9.40639e8i	0.483811	−	0.229194i
$559$		−	1.28122e9i		−	0.310229i
$560$		0			0
$561$	1.62624e9	+	2.81659e8i	0.388880	+	0.0673525i
$562$	−1.75742e9	+	1.75742e9i	−0.417636	+	0.417636i
$563$	3.18694e8	−	3.18694e8i	0.0752654	−	0.0752654i	−0.668472	−	0.743737i	$-0.733051\pi$
$563$	3.18694e8	−	3.18694e8i	0.0752654	−	0.0752654i	0.743737	+	0.668472i	$0.233051\pi$
$564$	−1.81613e9	−	3.14547e8i	−0.426256	−	0.0738258i
$565$		0			0
$566$		−	1.02902e9i		−	0.238543i
$567$	4.12346e7	−	4.11307e6i	0.00949994	−	0.000947600i
$568$	−1.30524e9	−	1.30524e9i	−0.298861	−	0.298861i
$569$	−2.87684e9			−0.654671			−0.327336	−	0.944908i	$-0.606151\pi$
$569$	−2.87684e9			−0.654671			−0.327336	+	0.944908i	$0.606151\pi$
$570$		0			0
$571$	3.80780e9			0.855948			0.427974	−	0.903791i	$-0.359227\pi$
$571$	3.80780e9			0.855948			0.427974	+	0.903791i	$0.359227\pi$
$572$	3.69316e8	+	3.69316e8i	0.0825111	+	0.0825111i
$573$	3.26322e9	−	2.29974e9i	0.724611	−	0.510666i
$574$		−	4.22541e7i		−	0.00932561i
$575$		0			0
$576$	5.39916e8	+	1.92806e8i	0.117719	+	0.0420380i
$577$	6.47107e9	−	6.47107e9i	1.40236	−	1.40236i	0.609839	−	0.792525i	$-0.291234\pi$
$577$	6.47107e9	−	6.47107e9i	1.40236	−	1.40236i	0.792525	−	0.609839i	$-0.208766\pi$
$578$	−1.46106e9	+	1.46106e9i	−0.314717	+	0.314717i
$579$	−9.66534e8	+	5.58058e9i	−0.206939	+	1.19482i
$580$		0			0
$581$			3.39426e7i			0.00718008i
$582$	6.77364e8	+	9.61148e8i	0.142427	+	0.202097i
$583$	−3.07196e9	−	3.07196e9i	−0.642060	−	0.642060i
$584$	−2.05838e9			−0.427642
$585$		0			0
$586$	−5.49914e9			−1.12889
$587$	−1.02779e9	−	1.02779e9i	−0.209734	−	0.209734i	0.594420	−	0.804155i	$-0.297382\pi$
$587$	−1.02779e9	−	1.02779e9i	−0.209734	−	0.209734i	−0.804155	+	0.594420i	$0.797382\pi$
$588$	1.41978e9	+	2.01460e9i	0.288005	+	0.408666i
$589$			1.76932e8i			0.0356783i
$590$		0			0
$591$	−1.03623e9	+	5.98300e9i	−0.206491	+	1.19224i
$592$	−1.25103e9	+	1.25103e9i	−0.247823	+	0.247823i
$593$	3.31531e9	−	3.31531e9i	0.652880	−	0.652880i	−0.300806	−	0.953685i	$-0.597256\pi$
$593$	3.31531e9	−	3.31531e9i	0.652880	−	0.652880i	0.953685	+	0.300806i	$0.0972556\pi$
$594$	1.15234e9	−	2.03859e9i	0.225594	−	0.399097i
$595$		0			0
$596$			3.05388e9i			0.590868i
$597$	2.44887e9	−	1.72583e9i	0.471038	−	0.331961i
$598$	1.19587e9	+	1.19587e9i	0.228681	+	0.228681i
$599$	4.59959e8			0.0874430			0.0437215	−	0.999044i	$-0.486079\pi$
$599$	4.59959e8			0.0874430			0.0437215	+	0.999044i	$0.486079\pi$
$600$		0			0
$601$	2.14425e9			0.402917			0.201458	−	0.979497i	$-0.435432\pi$
$601$	2.14425e9			0.402917			0.201458	+	0.979497i	$0.435432\pi$
$602$	2.20219e7	+	2.20219e7i	0.00411403	+	0.00411403i
$603$	−1.20212e9	−	2.53759e9i	−0.223274	−	0.471314i
$604$			9.62431e8i			0.177722i
$605$		0			0
$606$	2.57945e9	+	4.46750e8i	0.470839	+	0.0815474i
$607$	−1.08733e8	+	1.08733e8i	−0.0197333	+	0.0197333i	−0.716905	−	0.697171i	$-0.754442\pi$
$607$	−1.08733e8	+	1.08733e8i	−0.0197333	+	0.0197333i	0.697171	+	0.716905i	$0.254442\pi$
$608$	−3.26453e7	+	3.26453e7i	−0.00589059	+	0.00589059i
$609$	−3.82613e7	−	6.62670e6i	−0.00686434	−	0.00118888i
$610$		0			0
$611$			1.75598e9i			0.311440i
$612$	−7.38916e8	−	1.55980e9i	−0.130306	−	0.275067i
$613$	3.55732e9	+	3.55732e9i	0.623751	+	0.623751i	0.946488	−	0.322738i	$-0.104603\pi$
$613$	3.55732e9	+	3.55732e9i	0.623751	+	0.623751i	−0.322738	+	0.946488i	$0.604603\pi$
$614$	3.78853e9			0.660514
$615$		0			0
$616$	−1.26958e7			−0.00218840
$617$	−8.21616e8	−	8.21616e8i	−0.140822	−	0.140822i	0.633181	−	0.774003i	$-0.281749\pi$
$617$	−8.21616e8	−	8.21616e8i	−0.140822	−	0.140822i	−0.774003	+	0.633181i	$0.781749\pi$
$618$	3.34289e9	−	2.35589e9i	0.569722	−	0.401508i
$619$		−	7.57610e8i		−	0.128389i	−0.997937	−	0.0641946i	$-0.979552\pi$
$619$		−	7.57610e8i		−	0.128389i	0.997937	−	0.0641946i	$-0.0204478\pi$
$620$		0			0
$621$	3.73135e9	−	6.60110e9i	0.625237	−	1.10610i
$622$	1.21638e8	−	1.21638e8i	0.0202676	−	0.0202676i
$623$	6.28728e7	−	6.28728e7i	0.0104173	−	0.0104173i
$624$	9.32100e7	−	5.38176e8i	0.0153574	−	0.0886704i
$625$		0			0
$626$		−	3.19939e9i		−	0.521263i
$627$	1.08631e8	+	1.54143e8i	0.0176003	+	0.0249739i
$628$	2.30301e9	+	2.30301e9i	0.371054	+	0.371054i
$629$	5.32631e9			0.853393
$630$		0			0
$631$	−8.92366e9			−1.41397			−0.706985	−	0.707228i	$-0.749945\pi$
$631$	−8.92366e9			−1.41397			−0.706985	+	0.707228i	$0.749945\pi$
$632$	1.50245e9	+	1.50245e9i	0.236750	+	0.236750i
$633$	3.43693e9	+	4.87684e9i	0.538589	+	0.764233i
$634$			1.50061e9i			0.233860i
$635$		0			0
$636$	−7.75317e8	+	4.47653e9i	−0.119503	+	0.689988i
$637$	1.66031e9	−	1.66031e9i	0.254508	−	0.254508i
$638$	−1.55164e9	+	1.55164e9i	−0.236547	+	0.236547i
$639$	7.42540e9	+	2.65164e9i	1.12581	+	0.402033i
$640$		0			0
$641$			2.03499e8i			0.0305182i	0.999884	+	0.0152591i	$0.00485731\pi$
$641$			2.03499e8i			0.0305182i	−0.999884	+	0.0152591i	$0.995143\pi$
$642$	1.51973e9	−	1.07102e9i	0.226670	−	0.159745i
$643$	−3.94941e9	−	3.94941e9i	−0.585859	−	0.585859i	0.350648	−	0.936507i	$-0.385961\pi$
$643$	−3.94941e9	−	3.94941e9i	−0.585859	−	0.585859i	−0.936507	+	0.350648i	$0.885961\pi$
$644$	−4.11098e7			−0.00606520
$645$		0			0
$646$	1.38989e8			0.0202846
$647$	7.82378e7	+	7.82378e7i	0.0113567	+	0.0113567i	0.712762	−	0.701406i	$-0.247444\pi$
$647$	7.82378e7	+	7.82378e7i	0.0113567	+	0.0113567i	−0.701406	+	0.712762i	$0.747444\pi$
$648$	−2.43679e9	+	2.43065e8i	−0.351808	+	0.0350921i
$649$		−	8.86295e9i		−	1.27269i
$650$		0			0
$651$	5.01351e7	+	8.68320e6i	0.00712211	+	0.00123352i
$652$	3.70326e9	−	3.70326e9i	0.523260	−	0.523260i
$653$	−6.05012e9	+	6.05012e9i	−0.850292	+	0.850292i	−0.990169	−	0.139877i	$-0.955329\pi$
$653$	−6.05012e9	+	6.05012e9i	−0.850292	+	0.850292i	0.139877	+	0.990169i	$0.455329\pi$
$654$	2.19734e9	+	3.80570e8i	0.307167	+	0.0532001i
$655$		0			0
$656$			2.49704e9i			0.345352i
$657$	7.94583e9	−	3.76415e9i	1.09310	−	0.517831i
$658$	−3.01821e7	−	3.01821e7i	−0.00413009	−	0.00413009i
$659$	1.01449e10			1.38085			0.690427	−	0.723402i	$-0.257423\pi$
$659$	1.01449e10			1.38085			0.690427	+	0.723402i	$0.257423\pi$
$660$		0			0
$661$	1.59862e9			0.215298			0.107649	−	0.994189i	$-0.465668\pi$
$661$	1.59862e9			0.215298			0.107649	+	0.994189i	$0.465668\pi$
$662$	−5.65235e9	−	5.65235e9i	−0.757227	−	0.757227i
$663$	−1.34408e9	+	9.47231e8i	−0.179113	+	0.126229i
$664$		−	2.00586e9i		−	0.265897i
$665$		0			0
$666$	2.54152e9	−	7.11703e9i	0.333376	−	0.933553i
$667$	−5.02430e9	+	5.02430e9i	−0.655594	+	0.655594i
$668$	1.86617e9	−	1.86617e9i	0.242233	−	0.242233i
$669$	2.77130e8	−	1.60010e9i	0.0357843	−	0.206612i
$670$		0			0
$671$			4.64667e9i			0.593762i
$672$	7.64818e6	+	1.08524e7i	0.000972222	+	0.00137954i
$673$	7.66102e9	+	7.66102e9i	0.968799	+	0.968799i	0.999528	−	0.0307286i	$-0.00978276\pi$
$673$	7.66102e9	+	7.66102e9i	0.968799	+	0.968799i	−0.0307286	+	0.999528i	$0.509783\pi$
$674$	5.81845e9			0.731977
$675$		0			0
$676$	3.49555e9			0.435214
$677$	−9.34134e9	−	9.34134e9i	−1.15704	−	1.15704i	−0.985109	−	0.171932i	$-0.944999\pi$
$677$	−9.34134e9	−	9.34134e9i	−1.15704	−	1.15704i	−0.171932	−	0.985109i	$-0.555001\pi$
$678$	2.85434e8	+	4.05017e8i	0.0351724	+	0.0499079i
$679$			2.72303e7i			0.00333817i
$680$		0			0
$681$	−2.36679e9	+	1.36654e10i	−0.287174	+	1.65809i
$682$	2.03316e9	−	2.03316e9i	0.245429	−	0.245429i
$683$	−6.10846e9	+	6.10846e9i	−0.733600	+	0.733600i	−0.971331	−	0.237731i	$-0.923596\pi$
$683$	−6.10846e9	+	6.10846e9i	−0.733600	+	0.733600i	0.237731	+	0.971331i	$0.423596\pi$
$684$	6.63203e7	−	1.85717e8i	0.00792411	−	0.0221899i
$685$		0			0
$686$			1.14156e8i			0.0135010i
$687$	−1.06631e10	+	7.51479e9i	−1.25469	+	0.884236i
$688$	−1.30140e9	−	1.30140e9i	−0.152353	−	0.152353i
$689$	4.32826e9			0.504134
$690$		0			0
$691$	7.53547e9			0.868835			0.434417	−	0.900712i	$-0.356954\pi$
$691$	7.53547e9			0.868835			0.434417	+	0.900712i	$0.356954\pi$
$692$	3.28173e9	+	3.28173e9i	0.376471	+	0.376471i
$693$	4.90088e7	−	2.32167e7i	0.00559381	−	0.00264993i
$694$			2.52639e9i			0.286908i
$695$		0			0
$696$	2.26108e9	+	3.91610e8i	0.254204	+	0.0440272i
$697$	5.31562e9	−	5.31562e9i	0.594619	−	0.594619i
$698$	−3.57588e7	+	3.57588e7i	−0.00398006	+	0.00398006i
$699$	1.38096e9	+	2.39176e8i	0.152936	+	0.0264879i
$700$		0			0
$701$			7.80912e9i			0.856228i	0.903725	+	0.428114i	$0.140822\pi$
$701$			7.80912e9i			0.856228i	−0.903725	+	0.428114i	$0.859178\pi$
$702$	6.24349e8	+	2.24794e9i	0.0681157	+	0.245248i
$703$	4.30322e8	+	4.30322e8i	0.0467143	+	0.0467143i
$704$	7.50266e8			0.0810422
$705$		0			0
$706$	4.56314e9			0.488030
$707$	4.28676e7	+	4.28676e7i	0.00456206	+	0.00456206i
$708$	−7.57609e9	+	5.33921e9i	−0.802285	+	0.565406i
$709$		−	1.35196e10i		−	1.42463i	−0.701859	−	0.712316i	$-0.747647\pi$
$709$		−	1.35196e10i		−	1.42463i	0.701859	−	0.712316i	$-0.252353\pi$
$710$		0			0
$711$	−8.54735e9	−	3.05229e9i	−0.891842	−	0.318480i
$712$	−3.71551e9	+	3.71551e9i	−0.385779	+	0.385779i
$713$	6.58351e9	−	6.58351e9i	0.680212	−	0.680212i
$714$	6.82106e6	−	3.93835e7i	0.000701307	−	0.00404921i
$715$		0			0
$716$			8.14067e9i			0.828828i
$717$	6.48586e9	+	9.20314e9i	0.657129	+	0.932435i
$718$	−7.08967e9	−	7.08967e9i	−0.714810	−	0.714810i
$719$	1.42659e9			0.143136			0.0715679	−	0.997436i	$-0.477200\pi$
$719$	1.42659e9			0.143136			0.0715679	+	0.997436i	$0.477200\pi$
$720$		0			0
$721$	9.47075e7			0.00941046
$722$	−5.04527e9	−	5.04527e9i	−0.498890	−	0.498890i
$723$	2.80871e9	+	3.98542e9i	0.276390	+	0.392184i
$724$			7.08238e9i			0.693576i
$725$		0			0
$726$	−7.21200e8	+	4.16407e9i	−0.0699483	+	0.403868i
$727$	−9.45672e9	+	9.45672e9i	−0.912789	+	0.912789i	−0.996491	−	0.0837022i	$-0.973326\pi$
$727$	−9.45672e9	+	9.45672e9i	−0.912789	+	0.912789i	0.0837022	+	0.996491i	$0.473326\pi$
$728$	8.94391e6	−	8.94391e6i	0.000859147	−	0.000859147i
$729$	8.96209e9	−	5.39443e9i	0.856768	−	0.515703i
$730$		0			0
$731$			5.54076e9i			0.524637i
$732$	3.97199e9	−	2.79924e9i	0.374299	−	0.263786i
$733$	3.48961e9	+	3.48961e9i	0.327275	+	0.327275i	0.851549	−	0.524274i	$-0.175663\pi$
$733$	3.48961e9	+	3.48961e9i	0.327275	+	0.327275i	−0.524274	+	0.851549i	$0.675663\pi$
$734$	9.43247e9			0.880419
$735$		0			0
$736$	2.42941e9			0.224610
$737$	−2.59835e9	−	2.59835e9i	−0.239090	−	0.239090i
$738$	−4.56632e9	−	9.63916e9i	−0.418186	−	0.882758i
$739$			2.10615e10i			1.91970i	0.280512	+	0.959850i	$0.409496\pi$
$739$			2.10615e10i			1.91970i	−0.280512	+	0.959850i	$0.590504\pi$
$740$		0			0
$741$	−1.85119e8	−	3.20619e7i	−0.0167143	−	0.00289484i
$742$	−7.43951e7	+	7.43951e7i	−0.00668545	+	0.00668545i
$743$	1.14614e10	−	1.14614e10i	1.02512	−	1.02512i	0.0254470	−	0.999676i	$-0.491899\pi$
$743$	1.14614e10	−	1.14614e10i	1.02512	−	1.02512i	0.999676	−	0.0254470i	$-0.00810090\pi$
$744$	−2.96277e9	−	5.13140e8i	−0.263750	−	0.0456805i
$745$		0			0
$746$		−	8.66285e9i		−	0.763968i
$747$	3.66812e9	+	7.74311e9i	0.321974	+	0.679663i
$748$	−1.59714e9	−	1.59714e9i	−0.139537	−	0.139537i
$749$	4.30555e7			0.00374406
$750$		0			0
$751$	−1.54716e10			−1.33289			−0.666447	−	0.745553i	$-0.732186\pi$
$751$	−1.54716e10			−1.33289			−0.666447	+	0.745553i	$0.732186\pi$
$752$	1.78363e9	+	1.78363e9i	0.152948	+	0.152948i
$753$	−7.20299e9	+	5.07627e9i	−0.614795	+	0.433274i
$754$		−	2.18619e9i		−	0.185732i
$755$		0			0
$756$	−4.93696e7	−	2.79067e7i	−0.00415559	−	0.00234899i
$757$	1.08146e9	−	1.08146e9i	0.0906096	−	0.0906096i	−0.660349	−	0.750959i	$-0.729592\pi$
$757$	1.08146e9	−	1.08146e9i	0.0906096	−	0.0906096i	0.750959	+	0.660349i	$0.229592\pi$
$758$	−2.76264e9	+	2.76264e9i	−0.230400	+	0.230400i
$759$	1.69345e9	−	9.77762e9i	0.140580	−	0.811684i
$760$		0			0
$761$		−	2.19606e9i		−	0.180633i	−0.995913	−	0.0903166i	$-0.971212\pi$
$761$		−	2.19606e9i		−	0.180633i	0.995913	−	0.0903166i	$-0.0287879\pi$
$762$	5.08333e9	+	7.21300e9i	0.416203	+	0.590573i
$763$	3.65174e7	+	3.65174e7i	0.00297621	+	0.00297621i
$764$	−5.46341e9			−0.443238
$765$		0			0
$766$	5.39370e9			0.433597
$767$	6.24376e9	+	6.24376e9i	0.499646	+	0.499646i
$768$	−4.51974e8	−	6.41331e8i	−0.0360039	−	0.0510879i
$769$			8.38646e9i			0.665023i	0.943099	+	0.332511i	$0.107896\pi$
$769$			8.38646e9i			0.665023i	−0.943099	+	0.332511i	$0.892104\pi$
$770$		0			0
$771$	−1.64374e9	+	9.49062e9i	−0.129164	+	0.745769i
$772$	5.48072e9	−	5.48072e9i	0.428723	−	0.428723i
$773$	1.32895e10	−	1.32895e10i	1.03486	−	1.03486i	0.0354850	−	0.999370i	$-0.488702\pi$
$773$	1.32895e10	−	1.32895e10i	1.03486	−	1.03486i	0.999370	−	0.0354850i	$-0.0112976\pi$
$774$	7.40358e9	+	2.64385e9i	0.573916	+	0.204948i
$775$		0			0
$776$		−	1.60919e9i		−	0.123621i
$777$	1.43054e8	−	1.00816e8i	0.0109402	−	0.00771005i
$778$	−1.12469e10	−	1.12469e10i	−0.856257	−	0.856257i
$779$	8.58916e8			0.0650983
$780$		0			0
$781$	1.03183e10			0.775052
$782$	−5.17166e9	−	5.17166e9i	−0.386729	−	0.386729i
$783$	−9.44444e9	+	2.62312e9i	−0.703088	+	0.195277i
$784$		−	3.37292e9i		−	0.249977i
$785$		0			0
$786$	−1.04054e10	−	1.80217e9i	−0.764326	−	0.132378i
$787$	−1.62056e10	+	1.62056e10i	−1.18510	+	1.18510i	−0.206691	+	0.978406i	$0.566269\pi$
$787$	−1.62056e10	+	1.62056e10i	−1.18510	+	1.18510i	−0.978406	+	0.206691i	$0.933731\pi$
$788$	5.87595e9	−	5.87595e9i	0.427795	−	0.427795i
$789$	−1.75118e10	−	3.03297e9i	−1.26929	−	0.219836i
$790$		0			0
$791$			1.14745e7i			0.000824361i
$792$	−2.89621e9	+	1.37201e9i	−0.207153	+	0.0981339i
$793$	−3.27348e9	−	3.27348e9i	−0.233106	−	0.233106i
$794$	−1.09640e10			−0.777318
$795$		0			0
$796$	−4.10000e9			−0.288130
$797$	−9.60911e9	−	9.60911e9i	−0.672325	−	0.672325i	0.285927	−	0.958251i	$-0.407699\pi$
$797$	−9.60911e9	−	9.60911e9i	−0.672325	−	0.672325i	−0.958251	+	0.285927i	$0.907699\pi$
$798$	3.73295e6	−	2.63078e6i	0.000260041	−	0.000183263i
$799$		−	7.59389e9i		−	0.526685i
$800$		0			0
$801$	7.54823e9	−	2.11373e10i	0.518957	−	1.45324i
$802$	9.19400e9	−	9.19400e9i	0.629353	−	0.629353i
$803$	8.13609e9	−	8.13609e9i	0.554512	−	0.554512i
$804$	−6.55784e8	+	3.78637e9i	−0.0445005	+	0.256937i
$805$		0			0
$806$			2.86464e9i			0.192707i
$807$	1.30092e10	+	1.84594e10i	0.871349	+	1.23640i
$808$	−2.53329e9	−	2.53329e9i	−0.168945	−	0.168945i
$809$	−1.28712e10			−0.854670			−0.427335	−	0.904093i	$-0.640547\pi$
$809$	−1.28712e10			−0.854670			−0.427335	+	0.904093i	$0.640547\pi$
$810$		0			0
$811$	2.57707e10			1.69650			0.848250	−	0.529597i	$-0.177657\pi$
$811$	2.57707e10			1.69650			0.848250	+	0.529597i	$0.177657\pi$
$812$	3.75767e7	+	3.75767e7i	0.00246304	+	0.00246304i
$813$	9.61749e9	+	1.36468e10i	0.627689	+	0.890662i
$814$		−	9.88982e9i		−	0.642692i
$815$		0			0
$816$	−4.03096e8	+	2.32739e9i	−0.0259712	+	0.149953i
$817$	−4.47648e8	+	4.47648e8i	−0.0287184	+	0.0287184i
$818$	3.29958e9	−	3.29958e9i	0.210776	−	0.210776i
$819$	−1.81699e7	+	5.08813e7i	−0.00115574	+	0.00323642i
$820$		0			0
$821$		−	1.40840e10i		−	0.888231i	−0.895970	−	0.444115i	$-0.853518\pi$
$821$		−	1.40840e10i		−	0.888231i	0.895970	−	0.444115i	$-0.146482\pi$
$822$	1.05315e10	−	7.42202e9i	0.661362	−	0.466091i
$823$	1.00043e10	+	1.00043e10i	0.625585	+	0.625585i	0.946954	−	0.321369i	$-0.104143\pi$
$823$	1.00043e10	+	1.00043e10i	0.625585	+	0.625585i	−0.321369	+	0.946954i	$0.604143\pi$
$824$	−5.59681e9			−0.348494
$825$		0			0
$826$	−2.14638e8			−0.0132519
$827$	−9.81003e9	−	9.81003e9i	−0.603116	−	0.603116i	0.338022	−	0.941138i	$-0.390242\pi$
$827$	−9.81003e9	−	9.81003e9i	−0.603116	−	0.603116i	−0.941138	+	0.338022i	$0.890242\pi$
$828$	−9.37811e9	+	4.44266e9i	−0.574129	+	0.271980i
$829$			1.01779e10i			0.620465i	0.950661	+	0.310232i	$0.100407\pi$
$829$			1.01779e10i			0.620465i	−0.950661	+	0.310232i	$0.899593\pi$
$830$		0			0
$831$	−1.36903e10	−	2.37110e9i	−0.827577	−	0.143333i
$832$	−5.28546e8	+	5.28546e8i	−0.0318164	+	0.0318164i
$833$	−7.18018e9	+	7.18018e9i	−0.430406	+	0.430406i
$834$	−1.03013e10	−	1.78415e9i	−0.614912	−	0.106500i
$835$		0			0
$836$		−	2.58072e8i		−	0.0152763i
$837$	1.23754e10	−	3.43717e9i	0.729490	−	0.202610i
$838$	−1.49245e9	−	1.49245e9i	−0.0876083	−	0.0876083i
$839$	−8.79408e9			−0.514071			−0.257036	−	0.966402i	$-0.582746\pi$
$839$	−8.79408e9			−0.514071			−0.257036	+	0.966402i	$0.582746\pi$
$840$		0			0
$841$	−8.06489e9			−0.467533
$842$	−1.32259e9	−	1.32259e9i	−0.0763545	−	0.0763545i
$843$	−1.18758e10	+	8.36940e9i	−0.682756	+	0.481169i
$844$		−	8.16501e9i		−	0.467475i
$845$		0			0
$846$	−1.01470e10	−	3.62353e9i	−0.576157	−	0.205748i
$847$	−6.92022e7	+	6.92022e7i	−0.00391317	+	0.00391317i
$848$	4.39643e9	−	4.39643e9i	0.247579	−	0.247579i
$849$	1.02655e9	−	5.92709e9i	0.0575708	−	0.332403i
$850$		0			0
$851$		−	3.20239e10i		−	1.78123i
$852$	−6.21595e9	−	8.82015e9i	−0.344326	−	0.488582i
$853$	1.44455e10	+	1.44455e10i	0.796914	+	0.796914i	0.982608	−	0.185694i	$-0.0594533\pi$
$853$	1.44455e10	+	1.44455e10i	0.796914	+	0.796914i	−0.185694	+	0.982608i	$0.559453\pi$
$854$	1.12530e8			0.00618255
$855$		0			0
$856$	−2.54440e9			−0.138652
$857$	−3.96978e9	−	3.96978e9i	−0.215443	−	0.215443i	0.591132	−	0.806575i	$-0.298681\pi$
$857$	−3.96978e9	−	3.96978e9i	−0.215443	−	0.215443i	−0.806575	+	0.591132i	$0.798681\pi$
$858$	1.75881e9	+	2.49566e9i	0.0950631	+	0.134890i
$859$			3.68048e10i			1.98120i	0.136791	+	0.990600i	$0.456321\pi$
$859$			3.68048e10i			1.98120i	−0.136791	+	0.990600i	$0.543679\pi$
$860$		0			0
$861$	4.21525e7	−	2.43380e8i	0.00225067	−	0.0129949i
$862$	1.38527e9	−	1.38527e9i	0.0736645	−	0.0736645i
$863$	1.52667e9	−	1.52667e9i	0.0808550	−	0.0808550i	−0.665523	−	0.746378i	$-0.731791\pi$
$863$	1.52667e9	−	1.52667e9i	0.0808550	−	0.0808550i	0.746378	+	0.665523i	$0.231791\pi$
$864$	2.91753e9	+	1.64916e9i	0.153892	+	0.0869893i
$865$		0			0
$866$		−	8.72463e9i		−	0.456493i
$867$	−9.87314e9	+	6.95804e9i	−0.514503	+	0.362594i
$868$	−4.92380e7	−	4.92380e7i	−0.00255553	−	0.00255553i
$869$	−1.18774e10			−0.613977
$870$		0			0
$871$	3.66096e9			0.187729
$872$	−2.15802e9	−	2.15802e9i	−0.110217	−	0.110217i
$873$	2.94273e9	+	6.21187e9i	0.149693	+	0.315989i
$874$		−	8.35656e8i		−	0.0423387i
$875$		0			0
$876$	−1.18561e10	−	2.05343e9i	−0.595905	−	0.103208i
$877$	1.62907e10	−	1.62907e10i	0.815535	−	0.815535i	−0.169923	−	0.985457i	$-0.554352\pi$
$877$	1.62907e10	−	1.62907e10i	0.815535	−	0.815535i	0.985457	+	0.169923i	$0.0543519\pi$
$878$	−1.93034e10	+	1.93034e10i	−0.962503	+	0.962503i
$879$	−3.16746e10	−	5.48591e9i	−1.57308	−	0.272451i
$880$		0			0
$881$			4.54066e9i			0.223719i	0.993724	+	0.111860i	$0.0356807\pi$
$881$			4.54066e9i			0.223719i	−0.993724	+	0.111860i	$0.964319\pi$
$882$	6.16806e9	+	1.30203e10i	0.302697	+	0.638970i
$883$	6.30625e9	+	6.30625e9i	0.308254	+	0.308254i	0.844232	−	0.535978i	$-0.180057\pi$
$883$	6.30625e9	+	6.30625e9i	0.308254	+	0.308254i	−0.535978	+	0.844232i	$0.680057\pi$
$884$	2.25031e9			0.109562
$885$		0			0
$886$	−5.49423e9			−0.265393
$887$	−2.62069e10	−	2.62069e10i	−1.26091	−	1.26091i	−0.950654	−	0.310253i	$-0.899586\pi$
$887$	−2.62069e10	−	2.62069e10i	−1.26091	−	1.26091i	−0.310253	−	0.950654i	$-0.600414\pi$
$888$	−8.45385e9	+	5.95781e9i	−0.405144	+	0.285523i
$889$			2.04352e8i			0.00975488i
$890$		0			0
$891$	8.67106e9	−	1.05926e10i	0.410677	−	0.501683i
$892$	−1.57146e9	+	1.57146e9i	−0.0741357	+	0.0741357i
$893$	6.13524e8	−	6.13524e8i	0.0288305	−	0.0288305i
$894$	−3.04654e9	+	1.75901e10i	−0.142602	+	0.823356i
$895$		0			0
$896$		−	1.81695e7i		−	0.000843851i
$897$	5.69513e9	+	8.08112e9i	0.263469	+	0.373851i
$898$	3.27213e9	+	3.27213e9i	0.150787	+	0.150787i
$899$	−1.20354e10			−0.552461
$900$		0			0
$901$	−1.87180e10			−0.852554
$902$	−9.86996e9	−	9.86996e9i	−0.447809	−	0.447809i
$903$	1.04875e8	+	1.48813e8i	0.00473987	+	0.00672566i
$904$		−	6.78096e8i		−	0.0305282i
$905$		0			0
$906$	−9.60116e8	+	5.54352e9i	−0.0428919	+	0.247649i
$907$	1.46368e10	−	1.46368e10i	0.651359	−	0.651359i	−0.301962	−	0.953320i	$-0.597641\pi$
$907$	1.46368e10	−	1.46368e10i	0.651359	−	0.651359i	0.953320	+	0.301962i	$0.0976414\pi$
$908$	1.34209e10	−	1.34209e10i	0.594950	−	0.594950i
$909$	1.44117e10	+	5.14649e9i	0.636418	+	0.227267i
$910$		0			0
$911$			1.17472e10i			0.514779i	0.966308	+	0.257389i	$0.0828623\pi$
$911$			1.17472e10i			0.514779i	−0.966308	+	0.257389i	$0.917138\pi$
$912$	−2.20601e8	+	1.55468e8i	−0.00962999	+	0.00678669i
$913$	7.92852e9	+	7.92852e9i	0.344782	+	0.344782i
$914$	−3.05495e10			−1.32340
$915$		0			0
$916$	1.78527e10			0.767483
$917$	−1.72926e8	−	1.72926e8i	−0.00740572	−	0.00740572i
$918$	−2.70005e9	−	9.72144e9i	−0.115192	−	0.414745i
$919$		−	6.14798e8i		−	0.0261293i	−0.999915	−	0.0130647i	$-0.995841\pi$
$919$		−	6.14798e8i		−	0.0261293i	0.999915	−	0.0130647i	$-0.00415873\pi$
$920$		0			0
$921$	2.18217e10	+	3.77942e9i	0.920405	+	0.159410i
$922$	4.81491e8	−	4.81491e8i	0.0202316	−	0.0202316i
$923$	−7.26904e9	+	7.26904e9i	−0.304278	+	0.304278i
$924$	−7.31267e7	−	1.26653e7i	−0.00304947	−	0.000528156i
$925$		0			0
$926$			1.16430e10i			0.481868i
$927$	2.16050e10	−	1.02349e10i	0.890790	−	0.421991i
$928$	−2.22062e9	−	2.22062e9i	−0.0912129	−	0.0912129i
$929$	−2.52842e10			−1.03465			−0.517325	−	0.855789i	$-0.673072\pi$
$929$	−2.52842e10			−1.03465			−0.517325	+	0.855789i	$0.673072\pi$
$930$		0			0
$931$	−1.16020e9			−0.0471204
$932$	−1.35625e9	−	1.35625e9i	−0.0548761	−	0.0548761i
$933$	8.21971e8	−	5.79280e8i	0.0331338	−	0.0233509i
$934$		−	2.67473e10i		−	1.07415i
$935$		0			0
$936$	1.07376e9	−	3.00687e9i	0.0428000	−	0.119853i
$937$	−7.18729e9	+	7.18729e9i	−0.285415	+	0.285415i	−0.835264	−	0.549849i	$-0.814685\pi$
$937$	−7.18729e9	+	7.18729e9i	−0.285415	+	0.285415i	0.549849	+	0.835264i	$0.314685\pi$
$938$	−6.29253e7	+	6.29253e7i	−0.00248952	+	0.00248952i
$939$	3.19170e9	−	1.84282e10i	0.125803	−	0.726364i
$940$		0			0
$941$			6.79467e9i			0.265830i	0.991127	+	0.132915i	$0.0424338\pi$
$941$			6.79467e9i			0.265830i	−0.991127	+	0.132915i	$0.957566\pi$
$942$	1.09677e10	+	1.55626e10i	0.427500	+	0.606603i
$943$	−3.19596e10	−	3.19596e10i	−1.24111	−	1.24111i
$944$	1.26842e10			0.490751
$945$		0			0
$946$	1.02880e10			0.395105
$947$	1.06210e10	+	1.06210e10i	0.406387	+	0.406387i	0.880476	−	0.474090i	$-0.157223\pi$
$947$	1.06210e10	+	1.06210e10i	0.406387	+	0.406387i	−0.474090	+	0.880476i	$0.657223\pi$
$948$	7.15516e9	+	1.01528e10i	0.272766	+	0.387042i
$949$			1.14634e10i			0.435393i
$950$		0			0
$951$	−1.49700e9	+	8.64339e9i	−0.0564404	+	0.325876i
$952$	−3.86788e7	+	3.86788e7i	−0.00145293	+	0.00145293i
$953$	1.21090e10	−	1.21090e10i	0.453195	−	0.453195i	−0.443219	−	0.896413i	$-0.646164\pi$
$953$	1.21090e10	−	1.21090e10i	0.453195	−	0.453195i	0.896413	+	0.443219i	$0.146164\pi$
$954$	−8.93153e9	+	2.50110e10i	−0.333048	+	0.932635i
$955$		0			0
$956$		−	1.54083e10i		−	0.570363i
$957$	−1.04852e10	+	7.38939e9i	−0.386710	+	0.272532i
$958$	1.76862e10	+	1.76862e10i	0.649914	+	0.649914i
$959$	2.98368e8			0.0109241
$960$		0			0
$961$	−1.17422e10			−0.426793
$962$	6.96716e9	+	6.96716e9i	0.252315	+	0.252315i
$963$	9.82198e9	−	4.65293e9i	0.354411	−	0.167894i
$964$		−	6.67256e9i		−	0.239896i
$965$		0			0
$966$	−2.36789e8	−	4.10109e7i	−0.00845166	−	0.00146379i
$967$	−1.11474e10	+	1.11474e10i	−0.396443	+	0.396443i	−0.876977	−	0.480533i	$-0.840443\pi$
$967$	−1.11474e10	+	1.11474e10i	−0.396443	+	0.396443i	0.480533	+	0.876977i	$0.340443\pi$
$968$	4.08956e9	−	4.08956e9i	0.144915	−	0.144915i
$969$	8.00564e8	+	1.38655e8i	0.0282659	+	0.00489554i
$970$		0			0
$971$		−	2.00122e10i		−	0.701501i	−0.936469	−	0.350750i	$-0.885927\pi$
$971$		−	2.00122e10i		−	0.701501i	0.936469	−	0.350750i	$-0.114073\pi$
$972$	−1.42782e10	−	1.03090e9i	−0.498702	−	0.0360066i
$973$	−1.71197e8	−	1.71197e8i	−0.00595801	−	0.00595801i
$974$	3.36793e10			1.16790
$975$		0			0
$976$	−6.65007e9			−0.228956
$977$	1.36208e10	+	1.36208e10i	0.467273	+	0.467273i	0.901030	−	0.433757i	$-0.142812\pi$
$977$	1.36208e10	+	1.36208e10i	0.467273	+	0.467273i	−0.433757	+	0.901030i	$0.642812\pi$
$978$	2.50248e10	−	1.76361e10i	0.855431	−	0.602861i
$979$		−	2.93724e10i		−	1.00046i
$980$		0			0
$981$	1.22768e10	+	4.38411e9i	0.415188	+	0.148265i
$982$	−9.77612e9	+	9.77612e9i	−0.329440	+	0.329440i
$983$	−1.66058e9	+	1.66058e9i	−0.0557598	+	0.0557598i	−0.734437	−	0.678677i	$-0.762554\pi$
$983$	−1.66058e9	+	1.66058e9i	−0.0557598	+	0.0557598i	0.678677	+	0.734437i	$0.262554\pi$
$984$	−2.49103e9	+	1.43827e10i	−0.0833482	+	0.481236i
$985$		0			0
$986$			9.45437e9i			0.314097i
$987$	−1.43737e8	−	2.03956e8i	−0.00475838	−	0.00675191i
$988$	1.81806e8	+	1.81806e8i	0.00599736	+	0.00599736i
$989$	3.33133e10			1.09504
$990$		0			0
$991$	−4.37565e10			−1.42819			−0.714093	−	0.700050i	$-0.753161\pi$
$991$	−4.37565e10			−1.42819			−0.714093	+	0.700050i	$0.753161\pi$
$992$	2.90976e9	+	2.90976e9i	0.0946380	+	0.0946380i
$993$	−2.69183e10	−	3.81958e10i	−0.872420	−	1.23792i
$994$		−	2.49884e8i		−	0.00807022i
$995$		0			0
$996$	2.00104e9	−	1.15536e10i	0.0641724	−	0.370519i
$997$	−6.81579e9	+	6.81579e9i	−0.217813	+	0.217813i	−0.807576	−	0.589763i	$-0.799221\pi$
$997$	−6.81579e9	+	6.81579e9i	−0.217813	+	0.217813i	0.589763	+	0.807576i	$0.299221\pi$
$998$	−4.04611e9	+	4.04611e9i	−0.128849	+	0.128849i
$999$	2.17389e10	−	3.84581e10i	0.689855	−	1.22042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.8.e.a.143.2	yes	16
3.2	odd	2	inner	150.8.e.a.143.5	yes	16
5.2	odd	4	inner	150.8.e.a.107.5	yes	16
5.3	odd	4	inner	150.8.e.a.107.4	yes	16
5.4	even	2	inner	150.8.e.a.143.7	yes	16
15.2	even	4	inner	150.8.e.a.107.2	✓	16
15.8	even	4	inner	150.8.e.a.107.7	yes	16
15.14	odd	2	inner	150.8.e.a.143.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.8.e.a.107.2	✓	16	15.2	even	4	inner
150.8.e.a.107.4	yes	16	5.3	odd	4	inner
150.8.e.a.107.5	yes	16	5.2	odd	4	inner
150.8.e.a.107.7	yes	16	15.8	even	4	inner
150.8.e.a.143.2	yes	16	1.1	even	1	trivial
150.8.e.a.143.4	yes	16	15.14	odd	2	inner
150.8.e.a.143.5	yes	16	3.2	odd	2	inner
150.8.e.a.143.7	yes	16	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 5.65685i) q^{2} +(-26.9398 - 38.2263i) q^{3} +64.0000i q^{4} +(-63.8461 + 368.635i) q^{6} +(-6.12631 + 6.12631i) q^{7} +(362.039 - 362.039i) q^{8} +(-735.497 + 2059.61i) q^{9} +2862.04i q^{11} +(2446.48 - 1724.15i) q^{12} +(-2016.24 - 2016.24i) q^{13} +69.3113 q^{14} -4096.00 q^{16} +(8719.44 + 8719.44i) q^{17} +(15811.5 - 7490.34i) q^{18} +1408.92i q^{19} +(399.228 + 69.1446i) q^{21} +(16190.1 - 16190.1i) q^{22} +(52424.7 - 52424.7i) q^{23} +(-23592.6 - 4086.15i) q^{24} +22811.2i q^{26} +(98545.5 - 27370.3i) q^{27} +(-392.084 - 392.084i) q^{28} -95838.3 q^{29} +125580. q^{31} +(23170.5 + 23170.5i) q^{32} +(109405. - 77102.7i) q^{33} -98649.2i q^{34} +(-131815. - 47071.8i) q^{36} +(305427. - 305427. i) q^{37} +(7970.05 - 7970.05i) q^{38} +(-22756.4 + 131391. i) q^{39} -609628. i q^{41} +(-1867.23 - 2649.51i) q^{42} +(317725. + 317725. i) q^{43} -183170. q^{44} -593118. q^{46} +(-435458. - 435458. i) q^{47} +(110345. + 156575. i) q^{48} +823468. i q^{49} +(98412.0 - 568212. i) q^{51} +(129040. - 129040. i) q^{52} +(-1.07335e6 + 1.07335e6i) q^{53} +(-712287. - 402628. i) q^{54} +4435.92i q^{56} +(53857.7 - 37956.0i) q^{57} +(542143. + 542143. i) q^{58} -3.09673e6 q^{59} +1.62355e6 q^{61} +(-710389. - 710389. i) q^{62} +(-8111.96 - 17123.7i) q^{63} -262144. i q^{64} +(-1.05505e6 - 182730. i) q^{66} +(-907865. + 907865. i) q^{67} +(-558044. + 558044. i) q^{68} +(-3.41631e6 - 591692. i) q^{69} -3.60524e6i q^{71} +(479382. + 1.01194e6i) q^{72} +(-2.84276e6 - 2.84276e6i) q^{73} -3.45551e6 q^{74} -90170.8 q^{76} +(-17533.7 - 17533.7i) q^{77} +(871988. - 614529. i) q^{78} +4.14998e6i q^{79} +(-3.70106e6 - 3.02968e6i) q^{81} +(-3.44858e6 + 3.44858e6i) q^{82} +(2.77023e6 - 2.77023e6i) q^{83} +(-4425.26 + 25550.6i) q^{84} -3.59464e6i q^{86} +(2.58186e6 + 3.66354e6i) q^{87} +(1.03617e6 + 1.03617e6i) q^{88} -1.02628e7 q^{89} +24704.3 q^{91} +(3.35518e6 + 3.35518e6i) q^{92} +(-3.38311e6 - 4.80047e6i) q^{93} +4.92664e6i q^{94} +(261514. - 1.50993e6i) q^{96} +(2.22241e6 - 2.22241e6i) q^{97} +(4.65824e6 - 4.65824e6i) q^{98} +(-5.89470e6 - 2.10502e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2304 q^{6} - 65536 q^{16} - 183168 q^{21} + 1410688 q^{31} - 193536 q^{36} + 2302464 q^{46} + 1055808 q^{51} + 21247904 q^{61} - 4589568 q^{66} + 13881344 q^{76} - 36589968 q^{81} + 160819200 q^{91}+ \cdots - 9437184 q^{96}+O(q^{100}) \) 16 * q + 2304 * q^6 - 65536 * q^16 - 183168 * q^21 + 1410688 * q^31 - 193536 * q^36 + 2302464 * q^46 + 1055808 * q^51 + 21247904 * q^61 - 4589568 * q^66 + 13881344 * q^76 - 36589968 * q^81 + 160819200 * q^91 - 9437184 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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