LMFDB - Embedded newform 150.8.e.a.107.5

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			107.5
Root			$0.500000 + 1.41585i$ of defining polynomial
Character	$\chi$	$=$	150.107
Dual form			150.8.e.a.143.5

$q$-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} +(-38.2263 + 26.9398i) 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} +(1724.15 + 2446.48i) q^{12} +(-2016.24 + 2016.24i) q^{13} -69.3113 q^{14} -4096.00 q^{16} +(-8719.44 + 8719.44i) q^{17} +(-7490.34 - 15811.5i) 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} +(27370.3 + 98545.5i) q^{27} +(-392.084 + 392.084i) q^{28} +95838.3 q^{29} +125580. q^{31} +(-23170.5 + 23170.5i) q^{32} +(-77102.7 - 109405. i) 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} +(2649.51 - 1867.23i) q^{42} +(317725. - 317725. i) q^{43} +183170. q^{44} -593118. q^{46} +(435458. - 435458. i) q^{47} +(156575. - 110345. 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} +(37956.0 + 53857.7i) q^{57} +(542143. - 542143. i) q^{58} +3.09673e6 q^{59} +1.62355e6 q^{61} +(710389. - 710389. i) q^{62} +(-17123.7 + 8111.96i) 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} +(-1.01194e6 + 479382. i) q^{72} +(-2.84276e6 + 2.84276e6i) q^{73} +3.45551e6 q^{74} -90170.8 q^{76} +(17533.7 - 17533.7i) q^{77} +(-614529. - 871988. 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} +(-3.66354e6 + 2.58186e6i) q^{87} +(1.03617e6 - 1.03617e6i) q^{88} +1.02628e7 q^{89} +24704.3 q^{91} +(-3.35518e6 + 3.35518e6i) q^{92} +(-4.80047e6 + 3.38311e6i) 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

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
$3$	−38.2263	+	26.9398i	−0.817406	+	0.576063i
$3$	−38.2263	+	26.9398i	−0.817406	+	0.576063i
$4$		−	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	0.703723	−	0.710474i	$-0.251519\pi$
$7$	−6.12631	−	6.12631i	−0.00675081	−	0.00675081i	−0.710474	+	0.703723i	$0.751519\pi$
$8$	−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	$0.894915\pi$
$12$	1724.15	+	2446.48i	0.288031	+	0.408703i
$13$	−2016.24	+	2016.24i	−0.254531	+	0.254531i	−0.822826	−	0.568294i	$-0.807604\pi$
$13$	−2016.24	+	2016.24i	−0.254531	+	0.254531i	0.568294	+	0.822826i	$0.307604\pi$
$14$	−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	$-0.848446\pi$
$17$	−8719.44	+	8719.44i	−0.430445	+	0.430445i	0.458335	+	0.888780i	$0.348446\pi$
$18$	−7490.34	−	15811.5i	−0.302725	−	0.639029i
$19$		−	1408.92i		−	0.0471247i	−0.999722	−	0.0235623i	$-0.992499\pi$
$19$		−	1408.92i		−	0.0471247i	0.999722	−	0.0235623i	$-0.00750082\pi$
$20$		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	$-0.469121\pi$
$23$	−52424.7	−	52424.7i	−0.898440	−	0.898440i	−0.995298	+	0.0968586i	$0.969121\pi$
$24$	23592.6	+	4086.15i	0.348367	+	0.0603358i
$25$		0			0
$26$			22811.2i			0.254531i
$27$	27370.3	+	98545.5i	0.267612	+	0.963527i
$28$	−392.084	+	392.084i	−0.00337541	+	0.00337541i
$29$	95838.3			0.729703			0.364852	−	0.931066i	$-0.381120\pi$
$29$	95838.3			0.729703			0.364852	+	0.931066i	$0.381120\pi$
$30$		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
$33$	−77102.7	−	109405.i	−0.373483	−	0.529955i
$34$			98649.2i			0.430445i
$35$		0			0
$36$	−131815.	−	47071.8i	−0.470877	−	0.168152i
$37$	305427.	+	305427.i	0.991292	+	0.991292i	0.999962	−	0.00867015i	$-0.00275983\pi$
$37$	305427.	+	305427.i	0.991292	+	0.991292i	−0.00867015	+	0.999962i	$0.502760\pi$
$38$	−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	$-0.242699\pi$
$42$	2649.51	−	1867.23i	0.00551815	−	0.00388889i
$43$	317725.	−	317725.i	0.609412	−	0.609412i	−0.333380	−	0.942792i	$-0.608189\pi$
$43$	317725.	−	317725.i	0.609412	−	0.609412i	0.942792	+	0.333380i	$0.108189\pi$
$44$	183170.			0.324169
$45$		0			0
$46$	−593118.			−0.898440
$47$	435458.	−	435458.i	0.611791	−	0.611791i	−0.331621	−	0.943413i	$-0.607596\pi$
$47$	435458.	−	435458.i	0.611791	−	0.611791i	0.943413	+	0.331621i	$0.107596\pi$
$48$	156575.	−	110345.i	0.204351	−	0.144016i
$49$		−	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	$-0.00306715\pi$
$53$	1.07335e6	+	1.07335e6i	0.990318	+	0.990318i	−0.00963560	+	0.999954i	$0.503067\pi$
$54$	712287.	+	402628.i	0.615569	+	0.347957i
$55$		0			0
$56$			4435.92i			0.00337541i
$57$	37956.0	+	53857.7i	0.0271468	+	0.0385200i
$58$	542143.	−	542143.i	0.364852	−	0.364852i
$59$	3.09673e6			1.96300			0.981501	−	0.191455i	$-0.0613208\pi$
$59$	3.09673e6			1.96300			0.981501	+	0.191455i	$0.0613208\pi$
$60$		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
$63$	−17123.7	+	8111.96i	−0.00862792	+	0.00408727i
$64$			262144.i			0.125000i
$65$		0			0
$66$	−1.05505e6	−	182730.i	−0.451719	−	0.0782359i
$67$	−907865.	−	907865.i	−0.368773	−	0.368773i	0.498256	−	0.867030i	$-0.333974\pi$
$67$	−907865.	−	907865.i	−0.368773	−	0.368773i	−0.867030	+	0.498256i	$0.833974\pi$
$68$	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	$-0.203928\pi$
$72$	−1.01194e6	+	479382.i	−0.319514	+	0.151362i
$73$	−2.84276e6	+	2.84276e6i	−0.855284	+	0.855284i	−0.990778	−	0.135494i	$-0.956738\pi$
$73$	−2.84276e6	+	2.84276e6i	−0.855284	+	0.855284i	0.135494	+	0.990778i	$0.456738\pi$
$74$	3.45551e6			0.991292
$75$		0			0
$76$	−90170.8			−0.0235623
$77$	17533.7	−	17533.7i	0.00437680	−	0.00437680i
$78$	−614529.	−	871988.i	−0.146626	−	0.208055i
$79$		−	4.14998e6i		−	0.947002i	−0.880793	−	0.473501i	$-0.842990\pi$
$79$		−	4.14998e6i		−	0.947002i	0.880793	−	0.473501i	$-0.157010\pi$
$80$		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	$-0.372713\pi$
$83$	−2.77023e6	−	2.77023e6i	−0.531794	−	0.531794i	−0.921106	+	0.389312i	$0.872713\pi$
$84$	4425.26	−	25550.6i	0.000814631	−	0.00470352i
$85$		0			0
$86$		−	3.59464e6i		−	0.609412i
$87$	−3.66354e6	+	2.58186e6i	−0.596463	+	0.420355i
$88$	1.03617e6	−	1.03617e6i	0.162084	−	0.162084i
$89$	1.02628e7			1.54312			0.771559	−	0.636158i	$-0.219477\pi$
$89$	1.02628e7			1.54312			0.771559	+	0.636158i	$0.219477\pi$
$90$		0			0
$91$	24704.3			0.00343659
$92$	−3.35518e6	+	3.35518e6i	−0.449220	+	0.449220i
$93$	−4.80047e6	+	3.38311e6i	−0.618861	+	0.436139i
$94$		−	4.92664e6i		−	0.611791i
$95$		0			0
$96$	261514.	−	1.50993e6i	0.0301679	−	0.174184i
$97$	2.22241e6	+	2.22241e6i	0.247242	+	0.247242i	0.819838	−	0.572596i	$-0.194064\pi$
$97$	2.22241e6	+	2.22241e6i	0.247242	+	0.247242i	−0.572596	+	0.819838i	$0.694064\pi$
$98$	−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	$-0.109713\pi$
$102$	−2.65759e6	−	3.77099e6i	−0.247963	−	0.351848i
$103$	−7.72957e6	+	7.72957e6i	−0.696988	+	0.696988i	−0.963760	−	0.266772i	$-0.914043\pi$
$103$	−7.72957e6	+	7.72957e6i	−0.696988	+	0.696988i	0.266772	+	0.963760i	$0.414043\pi$
$104$	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	$-0.687178\pi$
$107$	3.51399e6	−	3.51399e6i	0.277304	−	0.277304i	0.832032	+	0.554728i	$0.187178\pi$
$108$	6.30691e6	−	1.75170e6i	0.481763	−	0.133806i
$109$			5.96074e6i			0.440867i	0.975402	+	0.220434i	$0.0707472\pi$
$109$			5.96074e6i			0.440867i	−0.975402	+	0.220434i	$0.929253\pi$
$110$		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	$-0.263747\pi$
$113$	−936497.	−	936497.i	−0.0610565	−	0.0610565i	−0.736976	+	0.675919i	$0.763747\pi$
$114$	519377.	+	89954.0i	0.0328334	+	0.00568661i
$115$		0			0
$116$		−	6.13365e6i		−	0.364852i
$117$	2.66975e6	+	5.63563e6i	0.154106	+	0.325306i
$118$	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
$123$	1.64232e7	+	2.33038e7i	0.795776	+	1.12917i
$124$		−	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	0.969113	−	0.246616i	$-0.0793187\pi$
$127$	1.66782e7	+	1.66782e7i	0.722497	+	0.722497i	−0.246616	+	0.969113i	$0.579319\pi$
$128$	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	$0.815197\pi$
$132$	−7.00192e6	+	4.93457e6i	−0.264977	+	0.186741i
$133$	−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	$-0.556122\pi$
$137$	2.43514e7	−	2.43514e7i	0.809098	−	0.809098i	0.984497	+	0.175399i	$0.0561216\pi$
$138$	2.26727e7	−	1.59785e7i	0.734390	−	0.517557i
$139$		−	2.79446e7i		−	0.882563i	−0.897369	−	0.441281i	$-0.854524\pi$
$139$		−	2.79446e7i		−	0.882563i	0.897369	−	0.441281i	$-0.145476\pi$
$140$		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
$147$	2.21840e7	+	3.14781e7i	0.576010	+	0.817331i
$148$	1.95473e7	−	1.95473e7i	0.495646	−	0.495646i
$149$	−4.77169e7			−1.18174			−0.590868	−	0.806768i	$-0.701215\pi$
$149$	−4.77169e7			−1.18174			−0.590868	+	0.806768i	$0.701215\pi$
$150$		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
$153$	1.15456e7	+	2.43718e7i	0.260613	+	0.550133i
$154$		−	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	0.972983	−	0.230876i	$-0.0741591\pi$
$157$	3.59845e7	+	3.59845e7i	0.742107	+	0.742107i	−0.230876	+	0.972983i	$0.574159\pi$
$158$	−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
$162$	−3.80748e7	+	3.79788e6i	−0.703615	+	0.0701842i
$163$	−5.78634e7	+	5.78634e7i	−1.04652	+	1.04652i	−0.0476564	+	0.998864i	$0.515175\pi$
$163$	−5.78634e7	+	5.78634e7i	−1.04652	+	1.04652i	−0.998864	+	0.0476564i	$0.984825\pi$
$164$	−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	$-0.638703\pi$
$167$	2.91589e7	−	2.91589e7i	0.484465	−	0.484465i	0.906554	+	0.422089i	$0.138703\pi$
$168$	−119503.	−	169569.i	−0.00194444	−	0.00275908i
$169$			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	$-0.428714\pi$
$173$	−5.12770e7	−	5.12770e7i	−0.752941	−	0.752941i	−0.975027	+	0.222086i	$0.928714\pi$
$174$	−6.11890e6	+	3.53293e7i	−0.0880544	+	0.508409i
$175$		0			0
$176$		−	1.17229e7i		−	0.162084i
$177$	−1.18376e8	+	8.34251e7i	−1.60457	+	1.13081i
$178$	5.80549e7	−	5.80549e7i	0.771559	−	0.771559i
$179$	−1.27198e8			−1.65766			−0.828828	−	0.559503i	$-0.810992\pi$
$179$	−1.27198e8			−1.65766			−0.828828	+	0.559503i	$0.810992\pi$
$180$		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
$183$	−6.20623e7	+	4.37381e7i	−0.748599	+	0.527571i
$184$			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	$0.853830\pi$
$192$	−7.06210e6	−	1.00208e7i	−0.0720078	−	0.102176i
$193$	−8.56363e7	+	8.56363e7i	−0.857447	+	0.857447i	−0.991037	−	0.133590i	$-0.957349\pi$
$193$	−8.56363e7	+	8.56363e7i	−0.857447	+	0.857447i	0.133590	+	0.991037i	$0.457349\pi$
$194$	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	$-0.543176\pi$
$197$	9.18117e7	−	9.18117e7i	0.855591	−	0.855591i	0.990815	+	0.135224i	$0.0431755\pi$
$198$	4.52532e7	−	2.14376e7i	0.414306	−	0.196268i
$199$		−	6.40625e7i		−	0.576259i	−0.957591	−	0.288130i	$-0.906967\pi$
$199$		−	6.40625e7i		−	0.576259i	0.957591	−	0.288130i	$-0.0930334\pi$
$200$		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
$207$	−1.46533e8	+	6.94165e7i	−1.14826	+	0.543960i
$208$	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
$213$	9.71243e7	+	1.37815e8i	0.688651	+	0.977164i
$214$		−	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
$222$	−1.32091e8	+	9.30908e7i	−0.810288	+	0.571046i
$223$	2.45541e7	−	2.45541e7i	0.148271	−	0.148271i	−0.629074	−	0.777345i	$-0.716566\pi$
$223$	2.45541e7	−	2.45541e7i	0.148271	−	0.148271i	0.777345	+	0.629074i	$0.216566\pi$
$224$	283899.			0.00168770
$225$		0			0
$226$	−1.05953e7			−0.0610565
$227$	2.09701e8	−	2.09701e8i	1.18990	−	1.18990i	0.212805	−	0.977095i	$-0.431740\pi$
$227$	2.09701e8	−	2.09701e8i	1.18990	−	1.18990i	0.977095	−	0.212805i	$-0.0682598\pi$
$228$	3.44689e6	−	2.42918e6i	0.0192600	−	0.0135734i
$229$			2.78948e8i			1.53497i	0.641070	+	0.767483i	$0.278491\pi$
$229$			2.78948e8i			1.53497i	−0.641070	+	0.767483i	$0.721509\pi$
$230$		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	$-0.225272\pi$
$233$	2.11914e7	+	2.11914e7i	0.109752	+	0.109752i	−0.650098	+	0.759850i	$0.725272\pi$
$234$	4.69823e7	+	1.67776e7i	0.239706	+	0.0856000i
$235$		0			0
$236$		−	1.98191e8i		−	0.981501i
$237$	1.11799e8	+	1.58638e8i	0.545532	+	0.774084i
$238$	604356.	−	604356.i	0.00290585	−	0.00290585i
$239$	2.40754e8			1.14073			0.570363	−	0.821393i	$-0.306803\pi$
$239$	2.40754e8			1.14073			0.570363	+	0.821393i	$0.306803\pi$
$240$		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
$243$	2.23097e8	+	1.61077e7i	0.997404	+	0.0720133i
$244$		−	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	$-0.122723\pi$
$252$	519165.	+	1.09592e6i	0.00204364	+	0.00431396i
$253$	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	$-0.626462\pi$
$257$	1.45638e8	−	1.45638e8i	0.535189	−	0.535189i	0.922112	+	0.386923i	$0.126462\pi$
$258$	9.68389e7	+	1.37410e8i	0.351060	+	0.498137i
$259$		−	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	$-0.472765\pi$
$263$	−2.68726e8	−	2.68726e8i	−0.910886	−	0.910886i	−0.996342	+	0.0854562i	$0.972765\pi$
$264$	−1.16947e7	+	6.75230e7i	−0.0391179	+	0.225859i
$265$		0			0
$266$			97654.0i			0.000318130i
$267$	−3.92307e8	+	2.76476e8i	−1.26135	+	0.888932i
$268$	−5.81034e7	+	5.81034e7i	−0.184387	+	0.184387i
$269$	4.82898e8			1.51259			0.756297	−	0.654228i	$-0.227006\pi$
$269$	4.82898e8			1.51259			0.756297	+	0.654228i	$0.227006\pi$
$270$		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
$273$	−944353.	+	665528.i	−0.00280909	+	0.00197969i
$274$		−	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	0.938682	−	0.344785i	$-0.112048\pi$
$277$	2.10083e8	+	2.10083e8i	0.593897	+	0.593897i	−0.344785	+	0.938682i	$0.612048\pi$
$278$	−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	$-0.137141\pi$
$282$	1.32723e8	+	1.88327e8i	0.352430	+	0.500082i
$283$	9.09536e7	−	9.09536e7i	0.238543	−	0.238543i	−0.577703	−	0.816247i	$-0.696051\pi$
$283$	9.09536e7	−	9.09536e7i	0.238543	−	0.238543i	0.816247	+	0.577703i	$0.196051\pi$
$284$	−2.30735e8			−0.597723
$285$		0			0
$286$	−6.52865e7			−0.165022
$287$	−3.73477e6	+	3.73477e6i	−0.00932561	+	0.00932561i
$288$	3.06804e7	+	6.47641e7i	0.0756812	+	0.159757i
$289$			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	−0.990357	−	0.138536i	$-0.955760\pi$
$293$	−4.86060e8	−	4.86060e8i	−1.12889	−	1.12889i	−0.138536	−	0.990357i	$-0.544240\pi$
$294$	3.03559e8	+	5.25752e7i	0.696671	+	0.120661i
$295$		0			0
$296$		−	2.21153e8i		−	0.495646i
$297$	−2.82041e8	+	7.83347e7i	−0.624690	+	0.173503i
$298$	−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
$303$	1.88505e8	+	2.67480e8i	0.389291	+	0.552386i
$304$			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	0.294987	−	0.955501i	$-0.404685\pi$
$307$	−3.34862e8	−	3.34862e8i	−0.660514	−	0.660514i	−0.955501	+	0.294987i	$0.904685\pi$
$308$	−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	$0.993548\pi$
$312$	−5.58072e7	+	3.93298e7i	−0.104028	+	0.0733130i
$313$	2.82789e8	−	2.82789e8i	0.521263	−	0.521263i	−0.396690	−	0.917953i	$-0.629841\pi$
$313$	2.82789e8	−	2.82789e8i	0.521263	−	0.521263i	0.917953	+	0.396690i	$0.129841\pi$
$314$	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	$-0.697120\pi$
$317$	1.32636e8	−	1.32636e8i	0.233860	−	0.233860i	0.814302	+	0.580442i	$0.197120\pi$
$318$	−4.64202e8	+	3.27144e8i	−0.809492	+	0.570485i
$319$			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
$327$	−1.60581e8	−	2.27857e8i	−0.253967	−	0.360367i
$328$	−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
$333$	8.53703e8	−	4.04422e8i	1.26693	−	0.600177i
$334$		−	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	0.239034	−	0.971011i	$-0.423169\pi$
$337$	−5.14283e8	−	5.14283e8i	−0.731977	−	0.731977i	−0.971011	+	0.239034i	$0.923169\pi$
$338$	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
$342$	−2.22772e7	+	1.05533e7i	−0.0301140	+	0.0142658i
$343$	−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	$-0.684972\pi$
$347$	2.23304e8	−	2.23304e8i	0.286908	−	0.286908i	0.835856	+	0.548948i	$0.184972\pi$
$348$	1.65239e8	+	2.34467e8i	0.210177	+	0.298232i
$349$			6.32133e6i			0.00796012i	0.999992	+	0.00398006i	$0.00126690\pi$
$349$			6.32133e6i			0.00796012i	−0.999992	+	0.00398006i	$0.998733\pi$
$350$		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	$-0.137849\pi$
$353$	4.03328e8	+	4.03328e8i	0.488030	+	0.488030i	−0.419654	+	0.907684i	$0.637849\pi$
$354$	−1.97714e8	+	1.14156e9i	−0.236879	+	1.36769i
$355$		0			0
$356$		−	6.56816e8i		−	0.771559i
$357$	−4.08394e6	+	2.87814e6i	−0.00475052	+	0.00334790i
$358$	−7.19540e8	+	7.19540e8i	−0.828828	+	0.828828i
$359$	−1.25329e9			−1.42962			−0.714810	−	0.699319i	$-0.753487\pi$
$359$	−1.25329e9			−1.42962			−0.714810	+	0.699319i	$0.753487\pi$
$360$		0			0
$361$	8.91887e8			0.997779
$362$	6.26000e8	−	6.26000e8i	0.693576	−	0.693576i
$363$	−4.31801e8	+	3.04309e8i	−0.473816	+	0.333920i
$364$		−	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	0.113158	−	0.993577i	$-0.463903\pi$
$367$	−8.33720e8	−	8.33720e8i	−0.880419	−	0.880419i	−0.993577	+	0.113158i	$0.963903\pi$
$368$	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
$372$	2.16519e8	+	3.07230e8i	0.218070	+	0.309431i
$373$	7.65695e8	−	7.65695e8i	0.763968	−	0.763968i	−0.213069	−	0.977037i	$-0.568346\pi$
$373$	7.65695e8	−	7.65695e8i	0.763968	−	0.763968i	0.977037	+	0.213069i	$0.0683460\pi$
$374$	−2.82338e8			−0.279073
$375$		0			0
$376$	−3.15305e8			−0.305896
$377$	−1.93233e8	+	1.93233e8i	−0.185732	+	0.185732i
$378$	−1.89707e6	−	6.83032e6i	−0.00180660	−	0.00650459i
$379$			4.88370e8i			0.460799i	0.973096	+	0.230400i	$0.0740033\pi$
$379$			4.88370e8i			0.460799i	−0.973096	+	0.230400i	$0.925997\pi$
$380$		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	$-0.150809\pi$
$383$	4.76741e8	+	4.76741e8i	0.433597	+	0.433597i	−0.456253	+	0.889850i	$0.650809\pi$
$384$	−9.66354e7	−	1.67369e7i	−0.0870918	−	0.0150839i
$385$		0			0
$386$			9.68864e8i			0.857447i
$387$	−4.20705e8	−	8.88076e8i	−0.368968	−	0.778864i
$388$	1.42234e8	−	1.42234e8i	0.123621	−	0.123621i
$389$	−1.98819e9			−1.71251			−0.856257	−	0.516550i	$-0.827216\pi$
$389$	−1.98819e9			−1.71251			−0.856257	+	0.516550i	$0.827216\pi$
$390$		0			0
$391$	9.14229e8			0.773457
$392$	−2.98127e8	+	2.98127e8i	−0.249977	+	0.249977i
$393$	−7.60423e8	−	1.07900e9i	−0.631948	−	0.896704i
$394$		−	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	0.979374	−	0.202056i	$-0.0647623\pi$
$397$	9.69093e8	+	9.69093e8i	0.777318	+	0.777318i	−0.202056	+	0.979374i	$0.564762\pi$
$398$	−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	$0.783320\pi$
$402$	3.92635e8	−	2.76707e8i	0.301438	−	0.212437i
$403$	−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
$408$	−2.41344e8	+	1.70086e8i	−0.175924	+	0.123982i
$409$		−	5.83288e8i		−	0.421553i	−0.977534	−	0.210776i	$-0.932401\pi$
$409$		−	5.83288e8i		−	0.421553i	0.977534	−	0.210776i	$-0.0675992\pi$
$410$		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
$417$	7.52821e8	+	1.06822e9i	0.508411	+	0.721412i
$418$	2.28106e7	−	2.28106e7i	0.0152763	−	0.0152763i
$419$	−2.63830e8			−0.175217			−0.0876083	−	0.996155i	$-0.527922\pi$
$419$	−2.63830e8			−0.175217			−0.0876083	+	0.996155i	$0.527922\pi$
$420$		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
$423$	−5.76597e8	−	1.21715e9i	−0.370409	−	0.781905i
$424$		−	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	$0.976531\pi$
$432$	−1.12109e8	−	4.03643e8i	−0.0669030	−	0.240882i
$433$	7.71156e8	−	7.71156e8i	0.456493	−	0.456493i	−0.441009	−	0.897503i	$-0.645379\pi$
$433$	7.71156e8	−	7.71156e8i	0.456493	−	0.456493i	0.897503	+	0.441009i	$0.145379\pi$
$434$	−8.70413e6			−0.00511107
$435$		0			0
$436$	3.81488e8			0.220434
$437$	−7.38622e7	+	7.38622e7i	−0.0423387	+	0.0423387i
$438$	−8.66442e8	−	1.22944e9i	−0.492697	−	0.699114i
$439$			3.41238e9i			1.92501i	0.271272	+	0.962503i	$0.412556\pi$
$439$			3.41238e9i			1.92501i	−0.271272	+	0.962503i	$0.587444\pi$
$440$		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	$-0.310091\pi$
$443$	−4.85626e8	−	4.85626e8i	−0.265393	−	0.265393i	−0.827241	+	0.561848i	$0.810091\pi$
$444$	−2.20621e8	+	1.27382e9i	−0.119621	+	0.690667i
$445$		0			0
$446$		−	2.77798e8i		−	0.148271i
$447$	1.82404e9	−	1.28548e9i	0.965958	−	0.680754i
$448$	1.60598e6	−	1.60598e6i	0.000843851	−	0.000843851i
$449$	5.78436e8			0.301573			0.150787	−	0.988566i	$-0.451819\pi$
$449$	5.78436e8			0.301573			0.150787	+	0.988566i	$0.451819\pi$
$450$		0			0
$451$	1.74478e9			0.895617
$452$	−5.99358e7	+	5.99358e7i	−0.0305282	+	0.0305282i
$453$	−5.74846e8	+	4.05120e8i	−0.290541	+	0.204757i
$454$		−	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	0.911002	+	0.412402i	$0.135310\pi$
$457$	2.70022e9	+	2.70022e9i	1.32340	+	1.32340i	0.412402	+	0.911002i	$0.364690\pi$
$458$	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	$0.993560\pi$
$462$	5.34409e6	+	7.58301e6i	0.00252131	+	0.00357762i
$463$	−1.02911e9	+	1.02911e9i	−0.481868	+	0.481868i	−0.905728	−	0.423860i	$-0.860675\pi$
$463$	−1.02911e9	+	1.02911e9i	−0.481868	+	0.481868i	0.423860	+	0.905728i	$0.360675\pi$
$464$	−3.92554e8			−0.182426
$465$		0			0
$466$	2.39753e8			0.109752
$467$	−2.36415e9	+	2.36415e9i	−1.07415	+	1.07415i	−0.0771326	+	0.997021i	$0.524576\pi$
$467$	−2.36415e9	+	2.36415e9i	−1.07415	+	1.07415i	−0.997021	+	0.0771326i	$0.975424\pi$
$468$	3.60680e8	−	1.70864e8i	0.162653	−	0.0770530i
$469$			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
$477$	3.00013e9	−	1.42124e9i	1.26568	−	0.599588i
$478$	1.36191e9	−	1.36191e9i	0.570363	−	0.570363i
$479$	3.12651e9			1.29983			0.649914	−	0.760008i	$-0.274805\pi$
$479$	3.12651e9			1.29983			0.649914	+	0.760008i	$0.274805\pi$
$480$		0			0
$481$	−1.23163e9			−0.504630
$482$	−5.89776e8	+	5.89776e8i	−0.239896	+	0.239896i
$483$	−1.73045e7	−	2.45543e7i	−0.00698786	−	0.00991545i
$484$		−	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	−0.982700	−	0.185204i	$-0.940706\pi$
$487$	−2.97686e9	−	2.97686e9i	−1.16790	−	1.16790i	−0.185204	−	0.982700i	$-0.559294\pi$
$488$	−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	$-0.106860\pi$
$492$	1.49144e9	−	1.05109e9i	0.564585	−	0.397888i
$493$	−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
$498$	1.19807e9	−	8.44336e8i	0.434691	−	0.306346i
$499$			7.15257e8i			0.257698i	0.991664	+	0.128849i	$0.0411282\pi$
$499$			7.15257e8i			0.257698i	−0.991664	+	0.128849i	$0.958872\pi$
$500$		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	0.979020	+	0.203765i	$0.0653180\pi$
$503$	3.37593e9	+	3.37593e9i	1.18279	+	1.18279i	0.203765	+	0.979020i	$0.434682\pi$
$504$	9.13629e6	+	3.26261e6i	0.00317880	+	0.00113516i
$505$		0			0
$506$		−	1.69753e9i		−	0.582492i
$507$	−1.47140e9	−	2.08784e9i	−0.501421	−	0.711492i
$508$	1.06740e9	−	1.06740e9i	0.361248	−	0.361248i
$509$	1.54439e9			0.519094			0.259547	−	0.965730i	$-0.416427\pi$
$509$	1.54439e9			0.519094			0.259547	+	0.965730i	$0.416427\pi$
$510$		0			0
$511$	3.48313e7			0.0115477
$512$	9.49063e7	−	9.49063e7i	0.0312500	−	0.0312500i
$513$	1.38843e8	−	3.85625e7i	0.0454059	−	0.0126111i
$514$		−	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	$-0.230362\pi$
$522$	−7.17862e8	−	1.51535e9i	−0.220899	−	0.466301i
$523$	−3.59310e9	+	3.59310e9i	−1.09828	+	1.09828i	−0.103670	+	0.994612i	$0.533059\pi$
$523$	−3.59310e9	+	3.59310e9i	−1.09828	+	1.09828i	−0.994612	+	0.103670i	$0.966941\pi$
$524$	1.80651e9			0.548506
$525$		0			0
$526$	−3.04028e9			−0.910886
$527$	−1.09499e9	+	1.09499e9i	−0.325891	+	0.325891i
$528$	3.15813e8	+	4.48123e8i	0.0933707	+	0.132489i
$529$			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
$537$	4.86230e9	−	3.42668e9i	1.35498	−	0.954914i
$538$	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
$543$	−4.23020e9	+	2.98122e9i	−1.13387	+	0.799087i
$544$		−	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	0.328692	−	0.944437i	$-0.393392\pi$
$547$	−2.35698e9	−	2.35698e9i	−0.615745	−	0.615745i	−0.944437	+	0.328692i	$0.893392\pi$
$548$	−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
$552$	−1.02262e9	−	1.45105e9i	−0.258779	−	0.367195i
$553$	−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	−0.350732	+	0.936476i	$0.614067\pi$
$557$	−5.24979e9	+	5.24979e9i	−1.28721	+	1.28721i	−0.936476	+	0.350732i	$0.885933\pi$
$558$	−9.40639e8	−	1.98562e9i	−0.229194	−	0.483811i
$559$			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	$-0.266949\pi$
$563$	−3.18694e8	−	3.18694e8i	−0.0752654	−	0.0752654i	−0.743737	+	0.668472i	$0.766949\pi$
$564$	1.81613e9	+	3.14547e8i	0.426256	+	0.0738258i
$565$		0			0
$566$		−	1.02902e9i		−	0.238543i
$567$	4.11307e6	+	4.12346e7i	0.000947600	+	0.00949994i
$568$	−1.30524e9	+	1.30524e9i	−0.298861	+	0.298861i
$569$	2.87684e9			0.654671			0.327336	−	0.944908i	$-0.393849\pi$
$569$	2.87684e9			0.654671			0.327336	+	0.944908i	$0.393849\pi$
$570$		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
$573$	−2.29974e9	−	3.26322e9i	−0.510666	−	0.724611i
$574$			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	0.792525	+	0.609839i	$0.208766\pi$
$577$	6.47107e9	+	6.47107e9i	1.40236	+	1.40236i	0.609839	+	0.792525i	$0.291234\pi$
$578$	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
$582$	−9.61148e8	+	6.77364e8i	−0.202097	+	0.142427i
$583$	−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	$-0.702618\pi$
$587$	1.02779e9	−	1.02779e9i	0.209734	−	0.209734i	0.804155	+	0.594420i	$0.202618\pi$
$588$	2.01460e9	−	1.41978e9i	0.408666	−	0.288005i
$589$		−	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	$-0.402744\pi$
$593$	−3.31531e9	−	3.31531e9i	−0.652880	−	0.652880i	−0.953685	+	0.300806i	$0.902744\pi$
$594$	−1.15234e9	+	2.03859e9i	−0.225594	+	0.399097i
$595$		0			0
$596$			3.05388e9i			0.590868i
$597$	1.72583e9	+	2.44887e9i	0.331961	+	0.471038i
$598$	1.19587e9	−	1.19587e9i	0.228681	−	0.228681i
$599$	−4.59959e8			−0.0874430			−0.0437215	−	0.999044i	$-0.513921\pi$
$599$	−4.59959e8			−0.0874430			−0.0437215	+	0.999044i	$0.513921\pi$
$600$		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
$603$	−2.53759e9	+	1.20212e9i	−0.471314	+	0.223274i
$604$		−	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	0.697171	−	0.716905i	$-0.254442\pi$
$607$	−1.08733e8	−	1.08733e8i	−0.0197333	−	0.0197333i	−0.716905	+	0.697171i	$0.754442\pi$
$608$	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
$612$	1.55980e9	−	7.38916e8i	0.275067	−	0.130306i
$613$	3.55732e9	−	3.55732e9i	0.623751	−	0.623751i	−0.322738	−	0.946488i	$-0.604603\pi$
$613$	3.55732e9	−	3.55732e9i	0.623751	−	0.623751i	0.946488	+	0.322738i	$0.104603\pi$
$614$	−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	$-0.718251\pi$
$617$	8.21616e8	−	8.21616e8i	0.140822	−	0.140822i	0.774003	+	0.633181i	$0.218251\pi$
$618$	−2.35589e9	−	3.34289e9i	−0.401508	−	0.569722i
$619$			7.57610e8i			0.128389i	0.997937	+	0.0641946i	$0.0204478\pi$
$619$			7.57610e8i			0.128389i	−0.997937	+	0.0641946i	$0.979552\pi$
$620$		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
$627$	−1.54143e8	+	1.08631e8i	−0.0249739	+	0.0176003i
$628$	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
$633$	4.87684e9	−	3.43693e9i	0.764233	−	0.538589i
$634$		−	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	$0.995143\pi$
$642$	1.07102e9	+	1.51973e9i	0.159745	+	0.226670i
$643$	−3.94941e9	+	3.94941e9i	−0.585859	+	0.585859i	−0.936507	−	0.350648i	$-0.885961\pi$
$643$	−3.94941e9	+	3.94941e9i	−0.585859	+	0.585859i	0.350648	+	0.936507i	$0.385961\pi$
$644$	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	$-0.752556\pi$
$647$	−7.82378e7	+	7.82378e7i	−0.0113567	+	0.0113567i	0.701406	+	0.712762i	$0.252556\pi$
$648$	2.43065e8	+	2.43679e9i	0.0350921	+	0.351808i
$649$			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	$-0.0446707\pi$
$653$	6.05012e9	+	6.05012e9i	0.850292	+	0.850292i	−0.139877	+	0.990169i	$0.544671\pi$
$654$	−2.19734e9	−	3.80570e8i	−0.307167	−	0.0532001i
$655$		0			0
$656$			2.49704e9i			0.345352i
$657$	3.76415e9	+	7.94583e9i	0.517831	+	1.09310i
$658$	−3.01821e7	+	3.01821e7i	−0.00413009	+	0.00413009i
$659$	−1.01449e10			−1.38085			−0.690427	−	0.723402i	$-0.742577\pi$
$659$	−1.01449e10			−1.38085			−0.690427	+	0.723402i	$0.742577\pi$
$660$		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
$663$	9.47231e8	+	1.34408e9i	0.126229	+	0.179113i
$664$			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
$672$	−1.08524e7	+	7.64818e6i	−0.00137954	+	0.000972222i
$673$	7.66102e9	−	7.66102e9i	0.968799	−	0.968799i	−0.0307286	−	0.999528i	$-0.509783\pi$
$673$	7.66102e9	−	7.66102e9i	0.968799	−	0.968799i	0.999528	+	0.0307286i	$0.00978276\pi$
$674$	−5.81845e9			−0.731977
$675$		0			0
$676$	3.49555e9			0.435214
$677$	9.34134e9	−	9.34134e9i	1.15704	−	1.15704i	0.171932	−	0.985109i	$-0.444999\pi$
$677$	9.34134e9	−	9.34134e9i	1.15704	−	1.15704i	0.985109	−	0.171932i	$-0.0550009\pi$
$678$	4.05017e8	−	2.85434e8i	0.0499079	−	0.0351724i
$679$		−	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	$-0.0764038\pi$
$683$	6.10846e9	+	6.10846e9i	0.733600	+	0.733600i	−0.237731	+	0.971331i	$0.576404\pi$
$684$	−6.63203e7	+	1.85717e8i	−0.00792411	+	0.0221899i
$685$		0			0
$686$			1.14156e8i			0.0135010i
$687$	−7.51479e9	−	1.06631e10i	−0.884236	−	1.25469i
$688$	−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
$693$	−2.32167e7	−	4.90088e7i	−0.00264993	−	0.00559381i
$694$		−	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	$0.859178\pi$
$702$	−2.24794e9	+	6.24349e8i	−0.245248	+	0.0681157i
$703$	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
$708$	5.33921e9	+	7.57609e9i	0.565406	+	0.802285i
$709$			1.35196e10i			1.42463i	0.701859	+	0.712316i	$0.252353\pi$
$709$			1.35196e10i			1.42463i	−0.701859	+	0.712316i	$0.747647\pi$
$710$		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
$717$	−9.20314e9	+	6.48586e9i	−0.932435	+	0.657129i
$718$	−7.08967e9	+	7.08967e9i	−0.714810	+	0.714810i
$719$	−1.42659e9			−0.143136			−0.0715679	−	0.997436i	$-0.522800\pi$
$719$	−1.42659e9			−0.143136			−0.0715679	+	0.997436i	$0.522800\pi$
$720$		0			0
$721$	9.47075e7			0.00941046
$722$	5.04527e9	−	5.04527e9i	0.498890	−	0.498890i
$723$	3.98542e9	−	2.80871e9i	0.392184	−	0.276390i
$724$		−	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	0.0837022	−	0.996491i	$-0.473326\pi$
$727$	−9.45672e9	−	9.45672e9i	−0.912789	−	0.912789i	−0.996491	+	0.0837022i	$0.973326\pi$
$728$	−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
$732$	2.79924e9	+	3.97199e9i	0.263786	+	0.374299i
$733$	3.48961e9	−	3.48961e9i	0.327275	−	0.327275i	−0.524274	−	0.851549i	$-0.675663\pi$
$733$	3.48961e9	−	3.48961e9i	0.327275	−	0.327275i	0.851549	+	0.524274i	$0.175663\pi$
$734$	−9.43247e9			−0.880419
$735$		0			0
$736$	2.42941e9			0.224610
$737$	2.59835e9	−	2.59835e9i	0.239090	−	0.239090i
$738$	−9.63916e9	+	4.56632e9i	−0.882758	+	0.418186i
$739$		−	2.10615e10i		−	1.91970i	−0.280512	−	0.959850i	$-0.590504\pi$
$739$		−	2.10615e10i		−	1.91970i	0.280512	−	0.959850i	$-0.409496\pi$
$740$		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	−0.999676	−	0.0254470i	$-0.991899\pi$
$743$	−1.14614e10	−	1.14614e10i	−1.02512	−	1.02512i	−0.0254470	−	0.999676i	$-0.508101\pi$
$744$	2.96277e9	+	5.13140e8i	0.263750	+	0.0456805i
$745$		0			0
$746$		−	8.66285e9i		−	0.763968i
$747$	−7.74311e9	+	3.66812e9i	−0.679663	+	0.321974i
$748$	−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
$753$	5.07627e9	+	7.20299e9i	0.433274	+	0.614795i
$754$			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	0.750959	−	0.660349i	$-0.229592\pi$
$757$	1.08146e9	+	1.08146e9i	0.0906096	+	0.0906096i	−0.660349	+	0.750959i	$0.729592\pi$
$758$	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	$-0.0287879\pi$
$762$	−7.21300e9	+	5.08333e9i	−0.590573	+	0.416203i
$763$	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
$768$	−6.41331e8	+	4.51974e8i	−0.0510879	+	0.0360039i
$769$		−	8.38646e9i		−	0.665023i	−0.943099	−	0.332511i	$-0.892104\pi$
$769$		−	8.38646e9i		−	0.665023i	0.943099	−	0.332511i	$-0.107896\pi$
$770$		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	−0.999370	−	0.0354850i	$-0.988702\pi$
$773$	−1.32895e10	−	1.32895e10i	−1.03486	−	1.03486i	−0.0354850	−	0.999370i	$-0.511298\pi$
$774$	−7.40358e9	−	2.64385e9i	−0.573916	−	0.204948i
$775$		0			0
$776$		−	1.60919e9i		−	0.123621i
$777$	1.00816e8	+	1.43054e8i	0.00771005	+	0.0109402i
$778$	−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
$783$	2.62312e9	+	9.44444e9i	0.195277	+	0.703088i
$784$			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	−0.978406	−	0.206691i	$-0.933731\pi$
$787$	−1.62056e10	−	1.62056e10i	−1.18510	−	1.18510i	−0.206691	−	0.978406i	$-0.566269\pi$
$788$	−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
$792$	−1.37201e9	−	2.89621e9i	−0.0981339	−	0.207153i
$793$	−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	$-0.592301\pi$
$797$	9.60911e9	−	9.60911e9i	0.672325	−	0.672325i	0.958251	+	0.285927i	$0.0923014\pi$
$798$	−2.63078e6	−	3.73295e6i	−0.000183263	−	0.000260041i
$799$			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
$807$	−1.84594e10	+	1.30092e10i	−1.23640	+	0.871349i
$808$	−2.53329e9	+	2.53329e9i	−0.168945	+	0.168945i
$809$	1.28712e10			0.854670			0.427335	−	0.904093i	$-0.359453\pi$
$809$	1.28712e10			0.854670			0.427335	+	0.904093i	$0.359453\pi$
$810$		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
$813$	1.36468e10	−	9.61749e9i	0.890662	−	0.627689i
$814$			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	$-0.146482\pi$
$822$	7.42202e9	+	1.05315e10i	0.466091	+	0.661362i
$823$	1.00043e10	−	1.00043e10i	0.625585	−	0.625585i	−0.321369	−	0.946954i	$-0.604143\pi$
$823$	1.00043e10	−	1.00043e10i	0.625585	−	0.625585i	0.946954	+	0.321369i	$0.104143\pi$
$824$	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	$-0.609758\pi$
$827$	9.81003e9	−	9.81003e9i	0.603116	−	0.603116i	0.941138	+	0.338022i	$0.109758\pi$
$828$	4.44266e9	+	9.37811e9i	0.271980	+	0.574129i
$829$		−	1.01779e10i		−	0.620465i	−0.950661	−	0.310232i	$-0.899593\pi$
$829$		−	1.01779e10i		−	0.620465i	0.950661	−	0.310232i	$-0.100407\pi$
$830$		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
$837$	3.43717e9	+	1.23754e10i	0.202610	+	0.729490i
$838$	−1.49245e9	+	1.49245e9i	−0.0876083	+	0.0876083i
$839$	8.79408e9			0.514071			0.257036	−	0.966402i	$-0.417254\pi$
$839$	8.79408e9			0.514071			0.257036	+	0.966402i	$0.417254\pi$
$840$		0			0
$841$	−8.06489e9			−0.467533
$842$	1.32259e9	−	1.32259e9i	0.0763545	−	0.0763545i
$843$	8.36940e9	+	1.18758e10i	0.481169	+	0.682756i
$844$			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
$852$	8.82015e9	−	6.21595e9i	0.488582	−	0.344326i
$853$	1.44455e10	−	1.44455e10i	0.796914	−	0.796914i	−0.185694	−	0.982608i	$-0.559453\pi$
$853$	1.44455e10	−	1.44455e10i	0.796914	−	0.796914i	0.982608	+	0.185694i	$0.0594533\pi$
$854$	−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	$-0.701319\pi$
$857$	3.96978e9	−	3.96978e9i	0.215443	−	0.215443i	0.806575	+	0.591132i	$0.201319\pi$
$858$	2.49566e9	−	1.75881e9i	0.134890	−	0.0950631i
$859$		−	3.68048e10i		−	1.98120i	−0.136791	−	0.990600i	$-0.543679\pi$
$859$		−	3.68048e10i		−	1.98120i	0.136791	−	0.990600i	$-0.456321\pi$
$860$		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	$-0.268209\pi$
$863$	−1.52667e9	−	1.52667e9i	−0.0808550	−	0.0808550i	−0.746378	+	0.665523i	$0.768209\pi$
$864$	−2.91753e9	−	1.64916e9i	−0.153892	−	0.0869893i
$865$		0			0
$866$		−	8.72463e9i		−	0.456493i
$867$	−6.95804e9	−	9.87314e9i	−0.362594	−	0.514503i
$868$	−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
$873$	6.21187e9	−	2.94273e9i	0.315989	−	0.149693i
$874$			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	0.985457	−	0.169923i	$-0.0543519\pi$
$877$	1.62907e10	+	1.62907e10i	0.815535	+	0.815535i	−0.169923	+	0.985457i	$0.554352\pi$
$878$	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	$0.964319\pi$
$882$	−1.30203e10	+	6.16806e9i	−0.638970	+	0.302697i
$883$	6.30625e9	−	6.30625e9i	0.308254	−	0.308254i	−0.535978	−	0.844232i	$-0.680057\pi$
$883$	6.30625e9	−	6.30625e9i	0.308254	−	0.308254i	0.844232	+	0.535978i	$0.180057\pi$
$884$	−2.25031e9			−0.109562
$885$		0			0
$886$	−5.49423e9			−0.265393
$887$	2.62069e10	−	2.62069e10i	1.26091	−	1.26091i	0.310253	−	0.950654i	$-0.399586\pi$
$887$	2.62069e10	−	2.62069e10i	1.26091	−	1.26091i	0.950654	−	0.310253i	$-0.100414\pi$
$888$	5.95781e9	+	8.45385e9i	0.285523	+	0.405144i
$889$		−	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
$897$	−8.08112e9	+	5.69513e9i	−0.373851	+	0.263469i
$898$	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
$903$	1.48813e8	−	1.04875e8i	0.00672566	−	0.00473987i
$904$			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	0.953320	−	0.301962i	$-0.0976414\pi$
$907$	1.46368e10	+	1.46368e10i	0.651359	+	0.651359i	−0.301962	+	0.953320i	$0.597641\pi$
$908$	−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	$0.917138\pi$
$912$	−1.55468e8	−	2.20601e8i	−0.00678669	−	0.00962999i
$913$	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
$918$	−9.72144e9	+	2.70005e9i	−0.414745	+	0.115192i
$919$			6.14798e8i			0.0261293i	0.999915	+	0.0130647i	$0.00415873\pi$
$919$			6.14798e8i			0.0261293i	−0.999915	+	0.0130647i	$0.995841\pi$
$920$		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
$927$	1.02349e10	+	2.16050e10i	0.421991	+	0.890790i
$928$	−2.22062e9	+	2.22062e9i	−0.0912129	+	0.0912129i
$929$	2.52842e10			1.03465			0.517325	−	0.855789i	$-0.326928\pi$
$929$	2.52842e10			1.03465			0.517325	+	0.855789i	$0.326928\pi$
$930$		0			0
$931$	−1.16020e9			−0.0471204
$932$	1.35625e9	−	1.35625e9i	0.0548761	−	0.0548761i
$933$	−5.79280e8	−	8.21971e8i	−0.0233509	−	0.0331338i
$934$			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	0.549849	−	0.835264i	$-0.314685\pi$
$937$	−7.18729e9	−	7.18729e9i	−0.285415	−	0.285415i	−0.835264	+	0.549849i	$0.814685\pi$
$938$	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	$0.957566\pi$
$942$	−1.55626e10	+	1.09677e10i	−0.606603	+	0.427500i
$943$	−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	$-0.842777\pi$
$947$	−1.06210e10	+	1.06210e10i	−0.406387	+	0.406387i	0.474090	+	0.880476i	$0.342777\pi$
$948$	1.01528e10	−	7.15516e9i	0.387042	−	0.272766i
$949$		−	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	$-0.353836\pi$
$953$	−1.21090e10	−	1.21090e10i	−0.453195	−	0.453195i	−0.896413	+	0.443219i	$0.853836\pi$
$954$	8.93153e9	−	2.50110e10i	0.333048	−	0.932635i
$955$		0			0
$956$		−	1.54083e10i		−	0.570363i
$957$	−7.38939e9	−	1.04852e10i	−0.272532	−	0.386710i
$958$	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
$963$	−4.65293e9	−	9.82198e9i	−0.167894	−	0.354411i
$964$			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	0.480533	−	0.876977i	$-0.340443\pi$
$967$	−1.11474e10	−	1.11474e10i	−0.396443	−	0.396443i	−0.876977	+	0.480533i	$0.840443\pi$
$968$	−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	$-0.114073\pi$
$972$	1.03090e9	−	1.42782e10i	0.0360066	−	0.498702i
$973$	−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	$-0.857188\pi$
$977$	−1.36208e10	+	1.36208e10i	−0.467273	+	0.467273i	0.433757	+	0.901030i	$0.357188\pi$
$978$	−1.76361e10	−	2.50248e10i	−0.602861	−	0.855431i
$979$			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	$-0.237446\pi$
$983$	1.66058e9	+	1.66058e9i	0.0557598	+	0.0557598i	−0.678677	+	0.734437i	$0.737446\pi$
$984$	2.49103e9	−	1.43827e10i	0.0833482	−	0.481236i
$985$		0			0
$986$			9.45437e9i			0.314097i
$987$	2.03956e8	−	1.43737e8i	0.00675191	−	0.00475838i
$988$	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
$993$	−3.81958e10	+	2.69183e10i	−1.23792	+	0.872420i
$994$			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	0.589763	−	0.807576i	$-0.299221\pi$
$997$	−6.81579e9	−	6.81579e9i	−0.217813	−	0.217813i	−0.807576	+	0.589763i	$0.799221\pi$
$998$	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.107.5	yes	16
3.2	odd	2	inner	150.8.e.a.107.2	✓	16
5.2	odd	4	inner	150.8.e.a.143.7	yes	16
5.3	odd	4	inner	150.8.e.a.143.2	yes	16
5.4	even	2	inner	150.8.e.a.107.4	yes	16
15.2	even	4	inner	150.8.e.a.143.4	yes	16
15.8	even	4	inner	150.8.e.a.143.5	yes	16
15.14	odd	2	inner	150.8.e.a.107.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.8.e.a.107.2	✓	16	3.2	odd	2	inner
150.8.e.a.107.4	yes	16	5.4	even	2	inner
150.8.e.a.107.5	yes	16	1.1	even	1	trivial
150.8.e.a.107.7	yes	16	15.14	odd	2	inner
150.8.e.a.143.2	yes	16	5.3	odd	4	inner
150.8.e.a.143.4	yes	16	15.2	even	4	inner
150.8.e.a.143.5	yes	16	15.8	even	4	inner
150.8.e.a.143.7	yes	16	5.2	odd	4	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} +(-38.2263 + 26.9398i) 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} +(1724.15 + 2446.48i) q^{12} +(-2016.24 + 2016.24i) q^{13} -69.3113 q^{14} -4096.00 q^{16} +(-8719.44 + 8719.44i) q^{17} +(-7490.34 - 15811.5i) 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} +(27370.3 + 98545.5i) q^{27} +(-392.084 + 392.084i) q^{28} +95838.3 q^{29} +125580. q^{31} +(-23170.5 + 23170.5i) q^{32} +(-77102.7 - 109405. i) 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} +(2649.51 - 1867.23i) q^{42} +(317725. - 317725. i) q^{43} +183170. q^{44} -593118. q^{46} +(435458. - 435458. i) q^{47} +(156575. - 110345. 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} +(37956.0 + 53857.7i) q^{57} +(542143. - 542143. i) q^{58} +3.09673e6 q^{59} +1.62355e6 q^{61} +(710389. - 710389. i) q^{62} +(-17123.7 + 8111.96i) 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} +(-1.01194e6 + 479382. i) q^{72} +(-2.84276e6 + 2.84276e6i) q^{73} +3.45551e6 q^{74} -90170.8 q^{76} +(17533.7 - 17533.7i) q^{77} +(-614529. - 871988. 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} +(-3.66354e6 + 2.58186e6i) q^{87} +(1.03617e6 - 1.03617e6i) q^{88} +1.02628e7 q^{89} +24704.3 q^{91} +(-3.35518e6 + 3.35518e6i) q^{92} +(-4.80047e6 + 3.38311e6i) 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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