LMFDB - Embedded newform 126.8.g.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,8,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$N$	$=$	$126 = 2 \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	126.g (of order $3$ , 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:	$39.3605132110$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.8.g.a.109.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-145.000 + 251.147i) q^{5} +(738.500 - 527.409i) q^{7} +512.000 q^{8} +(-1160.00 - 2009.18i) q^{10} +(565.000 + 978.609i) q^{11} -7563.00 q^{13} +(700.000 + 7226.12i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(7252.00 + 12560.8i) q^{17} +(-12521.5 + 21687.9i) q^{19} +18560.0 q^{20} -9040.00 q^{22} +(-3332.00 + 5771.19i) q^{23} +(-2987.50 - 5174.50i) q^{25} +(30252.0 - 52398.0i) q^{26} +(-52864.0 - 24054.7i) q^{28} -6820.00 q^{29} +(-88039.5 - 152489. i) q^{31} +(-16384.0 - 28377.9i) q^{32} -116032. q^{34} +(25375.0 + 261947. i) q^{35} +(66492.5 - 115168. i) q^{37} +(-100172. - 173503. i) q^{38} +(-74240.0 + 128587. i) q^{40} -661206. q^{41} +147095. q^{43} +(36160.0 - 62631.0i) q^{44} +(-26656.0 - 46169.5i) q^{46} +(-449817. + 779106. i) q^{47} +(267222. - 778984. i) q^{49} +47800.0 q^{50} +(242016. + 419184. i) q^{52} +(-652566. - 1.13028e6i) q^{53} -327700. q^{55} +(378112. - 270034. i) q^{56} +(27280.0 - 47250.3i) q^{58} +(-1.19078e6 - 2.06249e6i) q^{59} +(1.31255e6 - 2.27341e6i) q^{61} +1.40863e6 q^{62} +262144. q^{64} +(1.09664e6 - 1.89943e6i) q^{65} +(-1.98670e6 - 3.44106e6i) q^{67} +(464128. - 803893. i) q^{68} +(-1.91632e6 - 871984. i) q^{70} +4.29176e6 q^{71} +(-2.96515e6 - 5.13578e6i) q^{73} +(531940. + 921347. i) q^{74} +1.60275e6 q^{76} +(933380. + 424716. i) q^{77} +(-3.14184e6 + 5.44183e6i) q^{79} +(-593920. - 1.02870e6i) q^{80} +(2.64482e6 - 4.58097e6i) q^{82} -4.25225e6 q^{83} -4.20616e6 q^{85} +(-588380. + 1.01910e6i) q^{86} +(289280. + 501048. i) q^{88} +(-740400. + 1.28241e6i) q^{89} +(-5.58528e6 + 3.98880e6i) q^{91} +426496. q^{92} +(-3.59854e6 - 6.23285e6i) q^{94} +(-3.63124e6 - 6.28948e6i) q^{95} +9.40743e6 q^{97} +(4.32807e6 + 4.96730e6i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 8 q^{2} - 64 q^{4} - 290 q^{5} + 1477 q^{7} + 1024 q^{8} - 2320 q^{10} + 1130 q^{11} - 15126 q^{13} + 1400 q^{14} - 4096 q^{16} + 14504 q^{17} - 25043 q^{19} + 37120 q^{20} - 18080 q^{22} - 6664 q^{23}+ \cdots + 8656144 q^{98}+O(q^{100})$ 2 * q - 8 * q^2 - 64 * q^4 - 290 * q^5 + 1477 * q^7 + 1024 * q^8 - 2320 * q^10 + 1130 * q^11 - 15126 * q^13 + 1400 * q^14 - 4096 * q^16 + 14504 * q^17 - 25043 * q^19 + 37120 * q^20 - 18080 * q^22 - 6664 * q^23 - 5975 * q^25 + 60504 * q^26 - 105728 * q^28 - 13640 * q^29 - 176079 * q^31 - 32768 * q^32 - 232064 * q^34 + 50750 * q^35 + 132985 * q^37 - 200344 * q^38 - 148480 * q^40 - 1322412 * q^41 + 294190 * q^43 + 72320 * q^44 - 53312 * q^46 - 899634 * q^47 + 534443 * q^49 + 95600 * q^50 + 484032 * q^52 - 1305132 * q^53 - 655400 * q^55 + 756224 * q^56 + 54560 * q^58 - 2381564 * q^59 + 2625102 * q^61 + 2817264 * q^62 + 524288 * q^64 + 2193270 * q^65 - 3973393 * q^67 + 928256 * q^68 - 3832640 * q^70 + 8583524 * q^71 - 5930293 * q^73 + 1063880 * q^74 + 3205504 * q^76 + 1866760 * q^77 - 6283689 * q^79 - 1187840 * q^80 + 5289648 * q^82 - 8504500 * q^83 - 8412320 * q^85 - 1176760 * q^86 + 578560 * q^88 - 1480800 * q^89 - 11170551 * q^91 + 852992 * q^92 - 7197072 * q^94 - 7262470 * q^95 + 18814868 * q^97 + 8656144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$ .

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−145.000	+	251.147i	−0.518768	+	0.898532i	0.480994	+	0.876724i	$0.340276\pi$
$5$	−145.000	+	251.147i	−0.518768	+	0.898532i	−0.999762	+	0.0218085i	$0.993058\pi$
$6$		0			0
$7$	738.500	−	527.409i	0.813781	−	0.581172i
$7$	738.500	−	527.409i	0.813781	−	0.581172i
$8$	512.000			0.353553
$9$		0			0
$10$	−1160.00	−	2009.18i	−0.366824	−	0.635358i
$11$	565.000	+	978.609i	0.127989	+	0.221684i	0.922898	−	0.385046i	$-0.125814\pi$
$11$	565.000	+	978.609i	0.127989	+	0.221684i	−0.794908	+	0.606730i	$0.792481\pi$
$12$		0			0
$13$	−7563.00			−0.954756			−0.477378	−	0.878698i	$-0.658413\pi$
$13$	−7563.00			−0.954756			−0.477378	+	0.878698i	$0.658413\pi$
$14$	700.000	+	7226.12i	0.0681789	+	0.703812i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	7252.00	+	12560.8i	0.358003	+	0.620079i	0.987627	−	0.156821i	$-0.0501244\pi$
$17$	7252.00	+	12560.8i	0.358003	+	0.620079i	−0.629624	+	0.776900i	$0.716791\pi$
$18$		0			0
$19$	−12521.5	+	21687.9i	−0.418812	+	0.725403i	−0.995820	−	0.0913350i	$-0.970887\pi$
$19$	−12521.5	+	21687.9i	−0.418812	+	0.725403i	0.577009	+	0.816738i	$0.304220\pi$
$20$	18560.0			0.518768
$21$		0			0
$22$	−9040.00			−0.181004
$23$	−3332.00	+	5771.19i	−0.0571028	+	0.0989050i	−0.893164	−	0.449732i	$-0.851520\pi$
$23$	−3332.00	+	5771.19i	−0.0571028	+	0.0989050i	0.836061	+	0.548637i	$0.184853\pi$
$24$		0			0
$25$	−2987.50	−	5174.50i	−0.0382400	−	0.0662336i
$26$	30252.0	−	52398.0i	0.337557	−	0.584666i
$27$		0			0
$28$	−52864.0	−	24054.7i	−0.455100	−	0.207084i
$29$	−6820.00			−0.0519268			−0.0259634	−	0.999663i	$-0.508265\pi$
$29$	−6820.00			−0.0519268			−0.0259634	+	0.999663i	$0.508265\pi$
$30$		0			0
$31$	−88039.5	−	152489.i	−0.530776	−	0.919332i	−0.999355	−	0.0359099i	$-0.988567\pi$
$31$	−88039.5	−	152489.i	−0.530776	−	0.919332i	0.468579	−	0.883422i	$-0.344766\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−116032.			−0.506293
$35$	25375.0	+	261947.i	0.100039	+	1.03270i
$36$		0			0
$37$	66492.5	−	115168.i	0.215808	−	0.373790i	−0.737715	−	0.675113i	$-0.764095\pi$
$37$	66492.5	−	115168.i	0.215808	−	0.373790i	0.953522	+	0.301323i	$0.0974283\pi$
$38$	−100172.	−	173503.i	−0.296145	−	0.512937i
$39$		0			0
$40$	−74240.0	+	128587.i	−0.183412	+	0.317679i
$41$	−661206.			−1.49828			−0.749141	−	0.662411i	$-0.769533\pi$
$41$	−661206.			−1.49828			−0.749141	+	0.662411i	$0.769533\pi$
$42$		0			0
$43$	147095.			0.282136			0.141068	−	0.990000i	$-0.454946\pi$
$43$	147095.			0.282136			0.141068	+	0.990000i	$0.454946\pi$
$44$	36160.0	−	62631.0i	0.0639947	−	0.110842i
$45$		0			0
$46$	−26656.0	−	46169.5i	−0.0403778	−	0.0699364i
$47$	−449817.	+	779106.i	−0.631965	+	1.09460i	0.355184	+	0.934796i	$0.384418\pi$
$47$	−449817.	+	779106.i	−0.631965	+	1.09460i	−0.987149	+	0.159800i	$0.948915\pi$
$48$		0			0
$49$	267222.	−	778984.i	0.324478	−	0.945893i
$50$	47800.0			0.0540795
$51$		0			0
$52$	242016.	+	419184.i	0.238689	+	0.413421i
$53$	−652566.	−	1.13028e6i	−0.602087	−	1.04284i	−0.992505	−	0.122207i	$-0.961003\pi$
$53$	−652566.	−	1.13028e6i	−0.602087	−	1.04284i	0.390418	−	0.920638i	$-0.372330\pi$
$54$		0			0
$55$	−327700.			−0.265587
$56$	378112.	−	270034.i	0.287715	−	0.205475i
$57$		0			0
$58$	27280.0	−	47250.3i	0.0183589	−	0.0317985i
$59$	−1.19078e6	−	2.06249e6i	−0.754832	−	1.30741i	−0.945458	−	0.325744i	$-0.894385\pi$
$59$	−1.19078e6	−	2.06249e6i	−0.754832	−	1.30741i	0.190626	−	0.981663i	$-0.438948\pi$
$60$		0			0
$61$	1.31255e6	−	2.27341e6i	0.740392	−	1.28240i	−0.211925	−	0.977286i	$-0.567973\pi$
$61$	1.31255e6	−	2.27341e6i	0.740392	−	1.28240i	0.952317	−	0.305111i	$-0.0986935\pi$
$62$	1.40863e6			0.750631
$63$		0			0
$64$	262144.			0.125000
$65$	1.09664e6	−	1.89943e6i	0.495297	−	0.857879i
$66$		0			0
$67$	−1.98670e6	−	3.44106e6i	−0.806993	−	1.39775i	−0.914937	−	0.403596i	$-0.867760\pi$
$67$	−1.98670e6	−	3.44106e6i	−0.806993	−	1.39775i	0.107944	−	0.994157i	$-0.465573\pi$
$68$	464128.	−	803893.i	0.179001	−	0.310040i
$69$		0			0
$70$	−1.91632e6	−	871984.i	−0.667767	−	0.303854i
$71$	4.29176e6			1.42309			0.711543	−	0.702642i	$-0.247996\pi$
$71$	4.29176e6			1.42309			0.711543	+	0.702642i	$0.247996\pi$
$72$		0			0
$73$	−2.96515e6	−	5.13578e6i	−0.892105	−	1.54517i	−0.837347	−	0.546672i	$-0.815894\pi$
$73$	−2.96515e6	−	5.13578e6i	−0.892105	−	1.54517i	−0.0547586	−	0.998500i	$-0.517439\pi$
$74$	531940.	+	921347.i	0.152599	+	0.264309i
$75$		0			0
$76$	1.60275e6			0.418812
$77$	933380.	+	424716.i	0.232992	+	0.106018i
$78$		0			0
$79$	−3.14184e6	+	5.44183e6i	−0.716952	+	1.24180i	0.245250	+	0.969460i	$0.421130\pi$
$79$	−3.14184e6	+	5.44183e6i	−0.716952	+	1.24180i	−0.962202	+	0.272337i	$0.912203\pi$
$80$	−593920.	−	1.02870e6i	−0.129692	−	0.224633i
$81$		0			0
$82$	2.64482e6	−	4.58097e6i	0.529722	−	0.917506i
$83$	−4.25225e6			−0.816292			−0.408146	−	0.912917i	$-0.633825\pi$
$83$	−4.25225e6			−0.816292			−0.408146	+	0.912917i	$0.633825\pi$
$84$		0			0
$85$	−4.20616e6			−0.742882
$86$	−588380.	+	1.01910e6i	−0.0997501	+	0.172772i
$87$		0			0
$88$	289280.	+	501048.i	0.0452511	+	0.0783772i
$89$	−740400.	+	1.28241e6i	−0.111327	+	0.192824i	−0.916306	−	0.400480i	$-0.868843\pi$
$89$	−740400.	+	1.28241e6i	−0.111327	+	0.192824i	0.804978	+	0.593304i	$0.202177\pi$
$90$		0			0
$91$	−5.58528e6	+	3.98880e6i	−0.776962	+	0.554878i
$92$	426496.			0.0571028
$93$		0			0
$94$	−3.59854e6	−	6.23285e6i	−0.446867	−	0.773996i
$95$	−3.63124e6	−	6.28948e6i	−0.434532	−	0.752631i
$96$		0			0
$97$	9.40743e6			1.04657			0.523287	−	0.852156i	$-0.324705\pi$
$97$	9.40743e6			1.04657			0.523287	+	0.852156i	$0.324705\pi$
$98$	4.32807e6	+	4.96730e6i	0.464519	+	0.533125i
$99$		0			0
$100$	−191200.	+	331168.i	−0.0191200	+	0.0331168i
$101$	−5.42373e6	−	9.39418e6i	−0.523809	−	0.907265i	−0.999616	−	0.0277146i	$-0.991177\pi$
$101$	−5.42373e6	−	9.39418e6i	−0.523809	−	0.907265i	0.475806	−	0.879550i	$-0.342156\pi$
$102$		0			0
$103$	101052.	−	175028.i	0.00911206	−	0.0157826i	−0.861433	−	0.507871i	$-0.830433\pi$
$103$	101052.	−	175028.i	0.00911206	−	0.0157826i	0.870545	+	0.492088i	$0.163766\pi$
$104$	−3.87226e6			−0.337557
$105$		0			0
$106$	1.04411e7			0.851479
$107$	−6.43483e6	+	1.11455e7i	−0.507802	+	0.879538i	0.492158	+	0.870506i	$0.336208\pi$
$107$	−6.43483e6	+	1.11455e7i	−0.507802	+	0.879538i	−0.999959	+	0.00903196i	$0.997125\pi$
$108$		0			0
$109$	1.09254e7	+	1.89233e7i	0.808061	+	1.39960i	0.914205	+	0.405253i	$0.132816\pi$
$109$	1.09254e7	+	1.89233e7i	0.808061	+	1.39960i	−0.106143	+	0.994351i	$0.533850\pi$
$110$	1.31080e6	−	2.27037e6i	0.0938992	−	0.162638i
$111$		0			0
$112$	358400.	+	3.69977e6i	0.0241049	+	0.248835i
$113$	−4.61360e6			−0.300792			−0.150396	−	0.988626i	$-0.548055\pi$
$113$	−4.61360e6			−0.300792			−0.150396	+	0.988626i	$0.548055\pi$
$114$		0			0
$115$	−966280.	−	1.67365e6i	−0.0592462	−	0.102617i
$116$	218240.	+	378003.i	0.0129817	+	0.0224850i
$117$		0			0
$118$	1.90525e7			1.06749
$119$	1.19803e7	+	5.45140e6i	0.651709	+	0.296547i
$120$		0			0
$121$	9.10514e6	−	1.57706e7i	0.467237	−	0.809279i
$122$	1.05004e7	+	1.81872e7i	0.523536	+	0.906791i
$123$		0			0
$124$	−5.63453e6	+	9.75929e6i	−0.265388	+	0.459666i
$125$	−2.09235e7			−0.958185
$126$		0			0
$127$	−3.70924e7			−1.60684			−0.803419	−	0.595415i	$-0.796988\pi$
$127$	−3.70924e7			−1.60684			−0.803419	+	0.595415i	$0.796988\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	8.77308e6	+	1.51954e7i	0.350228	+	0.606612i
$131$	−1.99174e7	+	3.44980e7i	−0.774076	+	1.34074i	0.161236	+	0.986916i	$0.448452\pi$
$131$	−1.99174e7	+	3.44980e7i	−0.774076	+	1.34074i	−0.935312	+	0.353823i	$0.884882\pi$
$132$		0			0
$133$	2.19126e6	+	2.26205e7i	0.0807632	+	0.833721i
$134$	3.17871e7			1.14126
$135$		0			0
$136$	3.71302e6	+	6.43115e6i	0.126573	+	0.219231i
$137$	−1.28723e7	−	2.22955e7i	−0.427696	−	0.740791i	0.568972	−	0.822357i	$-0.307341\pi$
$137$	−1.28723e7	−	2.22955e7i	−0.427696	−	0.740791i	−0.996668	+	0.0815659i	$0.974008\pi$
$138$		0			0
$139$	−1.29485e7			−0.408948			−0.204474	−	0.978872i	$-0.565548\pi$
$139$	−1.29485e7			−0.408948			−0.204474	+	0.978872i	$0.565548\pi$
$140$	1.37066e7	−	9.78872e6i	0.422163	−	0.301493i
$141$		0			0
$142$	−1.71670e7	+	2.97342e7i	−0.503137	+	0.871459i
$143$	−4.27310e6	−	7.40122e6i	−0.122199	−	0.211654i
$144$		0			0
$145$	988900.	−	1.71283e6i	0.0269379	−	0.0466579i
$146$	4.74423e7			1.26163
$147$		0			0
$148$	−8.51104e6			−0.215808
$149$	−1.56578e7	+	2.71201e7i	−0.387775	+	0.671645i	−0.992150	−	0.125054i	$-0.960089\pi$
$149$	−1.56578e7	+	2.71201e7i	−0.387775	+	0.671645i	0.604375	+	0.796700i	$0.293423\pi$
$150$		0			0
$151$	2.06164e7	+	3.57086e7i	0.487296	+	0.844022i	0.999893	−	0.0146075i	$-0.00464988\pi$
$151$	2.06164e7	+	3.57086e7i	0.487296	+	0.844022i	−0.512597	+	0.858629i	$0.671317\pi$
$152$	−6.41101e6	+	1.11042e7i	−0.148072	+	0.256469i
$153$		0			0
$154$	−6.67604e6	+	4.76778e6i	−0.147298	+	0.105195i
$155$	5.10629e7			1.10140
$156$		0			0
$157$	−2.76616e6	−	4.79112e6i	−0.0570464	−	0.0988072i	0.836092	−	0.548589i	$-0.184835\pi$
$157$	−2.76616e6	−	4.79112e6i	−0.0570464	−	0.0988072i	−0.893138	+	0.449782i	$0.851502\pi$
$158$	−2.51348e7	−	4.35347e7i	−0.506961	−	0.878083i
$159$		0			0
$160$	9.50272e6			0.183412
$161$	583100.	+	6.01935e6i	0.0110117	+	0.113674i
$162$		0			0
$163$	1.67654e7	−	2.90386e7i	0.303220	−	0.525193i	−0.673643	−	0.739057i	$-0.735272\pi$
$163$	1.67654e7	−	2.90386e7i	0.303220	−	0.525193i	0.976864	+	0.213864i	$0.0686048\pi$
$164$	2.11586e7	+	3.66478e7i	0.374570	+	0.648775i
$165$		0			0
$166$	1.70090e7	−	2.94605e7i	0.288603	−	0.499875i
$167$	5.23132e7			0.869167			0.434584	−	0.900632i	$-0.356896\pi$
$167$	5.23132e7			0.869167			0.434584	+	0.900632i	$0.356896\pi$
$168$		0			0
$169$	−5.54955e6			−0.0884411
$170$	1.68246e7	−	2.91411e7i	0.262648	−	0.454920i
$171$		0			0
$172$	−4.70704e6	−	8.15283e6i	−0.0705340	−	0.122168i
$173$	−4.10212e7	+	7.10509e7i	−0.602348	+	1.04330i	0.390117	+	0.920765i	$0.372435\pi$
$173$	−4.10212e7	+	7.10509e7i	−0.602348	+	1.04330i	−0.992465	+	0.122532i	$0.960899\pi$
$174$		0			0
$175$	−4.93535e6	−	2.24573e6i	−0.0696121	−	0.0316756i
$176$	−4.62848e6			−0.0639947
$177$		0			0
$178$	−5.92320e6	−	1.02593e7i	−0.0787202	−	0.136347i
$179$	−5.73149e7	−	9.92724e7i	−0.746934	−	1.29373i	−0.949286	−	0.314415i	$-0.898192\pi$
$179$	−5.73149e7	−	9.92724e7i	−0.746934	−	1.29373i	0.202352	−	0.979313i	$-0.435142\pi$
$180$		0			0
$181$	5.29000e7			0.663102			0.331551	−	0.943437i	$-0.392428\pi$
$181$	5.29000e7			0.663102			0.331551	+	0.943437i	$0.392428\pi$
$182$	−5.29410e6	−	5.46511e7i	−0.0650942	−	0.671969i
$183$		0			0
$184$	−1.70598e6	+	2.95485e6i	−0.0201889	+	0.0349682i
$185$	1.92828e7	+	3.33988e7i	0.223908	+	0.387820i
$186$		0			0
$187$	−8.19476e6	+	1.41937e7i	−0.0916412	+	0.158727i
$188$	5.75766e7			0.631965
$189$		0			0
$190$	5.80998e7			0.614521
$191$	5.14237e7	−	8.90684e7i	0.534006	−	0.924926i	−0.465204	−	0.885203i	$-0.654019\pi$
$191$	5.14237e7	−	8.90684e7i	0.534006	−	0.924926i	0.999211	−	0.0397228i	$-0.0126475\pi$
$192$		0			0
$193$	8.76209e7	+	1.51764e8i	0.877318	+	1.51956i	0.854273	+	0.519824i	$0.174003\pi$
$193$	8.76209e7	+	1.51764e8i	0.877318	+	1.51956i	0.0230445	+	0.999734i	$0.492664\pi$
$194$	−3.76297e7	+	6.51766e7i	−0.370020	+	0.640893i
$195$		0			0
$196$	−5.17268e7	+	1.01166e7i	−0.490703	+	0.0959703i
$197$	−1.57220e8			−1.46513			−0.732563	−	0.680700i	$-0.761676\pi$
$197$	−1.57220e8			−1.46513			−0.732563	+	0.680700i	$0.761676\pi$
$198$		0			0
$199$	−5.53742e7	−	9.59110e7i	−0.498106	−	0.862745i	0.501891	−	0.864931i	$-0.332638\pi$
$199$	−5.53742e7	−	9.59110e7i	−0.498106	−	0.862745i	−0.999998	+	0.00218539i	$0.999304\pi$
$200$	−1.52960e6	−	2.64934e6i	−0.0135199	−	0.0234171i
$201$		0			0
$202$	8.67797e7			0.740778
$203$	−5.03657e6	+	3.59693e6i	−0.0422570	+	0.0301784i
$204$		0			0
$205$	9.58749e7	−	1.66060e8i	0.777260	−	1.34625i
$206$	808420.	+	1.40022e6i	0.00644320	+	0.0111600i
$207$		0			0
$208$	1.54890e7	−	2.68278e7i	0.119344	−	0.206711i
$209$	−2.82986e7			−0.214414
$210$		0			0
$211$	−1.46673e8			−1.07488			−0.537440	−	0.843302i	$-0.680609\pi$
$211$	−1.46673e8			−1.07488			−0.537440	+	0.843302i	$0.680609\pi$
$212$	−4.17642e7	+	7.23378e7i	−0.301043	+	0.521422i
$213$		0			0
$214$	−5.14787e7	−	8.91636e7i	−0.359070	−	0.621927i
$215$	−2.13288e7	+	3.69425e7i	−0.146363	+	0.253508i
$216$		0			0
$217$	−1.45441e8	−	6.61802e7i	−0.966226	−	0.439662i
$218$	−1.74806e8			−1.14277
$219$		0			0
$220$	1.04864e7	+	1.81630e7i	0.0663968	+	0.115003i
$221$	−5.48469e7	−	9.49976e7i	−0.341805	−	0.592024i
$222$		0			0
$223$	−5.90964e7			−0.356857			−0.178428	−	0.983953i	$-0.557101\pi$
$223$	−5.90964e7			−0.356857			−0.178428	+	0.983953i	$0.557101\pi$
$224$	−2.70664e7	−	1.23160e7i	−0.160902	−	0.0732154i
$225$		0			0
$226$	1.84544e7	−	3.19640e7i	0.106346	−	0.184196i
$227$	−2.14526e7	−	3.71570e7i	−0.121728	−	0.210838i	0.798721	−	0.601701i	$-0.205510\pi$
$227$	−2.14526e7	−	3.71570e7i	−0.121728	−	0.210838i	−0.920449	+	0.390863i	$0.872177\pi$
$228$		0			0
$229$	−1.38126e8	+	2.39241e8i	−0.760066	+	1.31647i	0.182749	+	0.983160i	$0.441500\pi$
$229$	−1.38126e8	+	2.39241e8i	−0.760066	+	1.31647i	−0.942816	+	0.333314i	$0.891833\pi$
$230$	1.54605e7			0.0837868
$231$		0			0
$232$	−3.49184e6			−0.0183589
$233$	7.66706e7	−	1.32797e8i	0.397085	−	0.687771i	−0.596280	−	0.802776i	$-0.703355\pi$
$233$	7.66706e7	−	1.32797e8i	0.397085	−	0.687771i	0.993365	+	0.115006i	$0.0366886\pi$
$234$		0			0
$235$	−1.30447e8	−	2.25941e8i	−0.655687	−	1.13568i
$236$	−7.62100e7	+	1.32000e8i	−0.377416	+	0.653704i
$237$		0			0
$238$	−8.56896e7	+	6.11964e7i	−0.412011	+	0.294243i
$239$	3.45622e8			1.63760			0.818801	−	0.574078i	$-0.194639\pi$
$239$	3.45622e8			1.63760			0.818801	+	0.574078i	$0.194639\pi$
$240$		0			0
$241$	−2.70334e7	−	4.68232e7i	−0.124406	−	0.215477i	0.797095	−	0.603854i	$-0.206369\pi$
$241$	−2.70334e7	−	4.68232e7i	−0.124406	−	0.215477i	−0.921501	+	0.388377i	$0.873036\pi$
$242$	7.28411e7	+	1.26164e8i	0.330387	+	0.572247i
$243$		0			0
$244$	−1.68007e8			−0.740392
$245$	1.56893e8	+	1.80065e8i	0.681587	+	0.782253i
$246$		0			0
$247$	9.47001e7	−	1.64025e8i	0.399863	−	0.692583i
$248$	−4.50762e7	−	7.80743e7i	−0.187658	−	0.325033i
$249$		0			0
$250$	8.36940e7	−	1.44962e8i	0.338769	−	0.586766i
$251$	9.40011e7			0.375210			0.187605	−	0.982245i	$-0.439927\pi$
$251$	9.40011e7			0.375210			0.187605	+	0.982245i	$0.439927\pi$
$252$		0			0
$253$	−7.53032e6			−0.0292342
$254$	1.48370e8	−	2.56984e8i	0.568103	−	0.983983i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	3.49001e7	−	6.04487e7i	0.128251	−	0.222137i	−0.794748	−	0.606939i	$-0.792397\pi$
$257$	3.49001e7	−	6.04487e7i	0.128251	−	0.222137i	0.922999	+	0.384802i	$0.125730\pi$
$258$		0			0
$259$	−1.16362e7	−	1.20121e8i	−0.0416161	−	0.429604i
$260$	−1.40369e8			−0.495297
$261$		0			0
$262$	−1.59339e8	−	2.75984e8i	−0.547354	−	0.948046i
$263$	3.56605e7	+	6.17657e7i	0.120876	+	0.209364i	0.920114	−	0.391652i	$-0.128096\pi$
$263$	3.56605e7	+	6.17657e7i	0.120876	+	0.209364i	−0.799237	+	0.601016i	$0.794763\pi$
$264$		0			0
$265$	3.78488e8			1.24937
$266$	−1.65484e8	−	7.53003e7i	−0.539102	−	0.245308i
$267$		0			0
$268$	−1.27149e8	+	2.20228e8i	−0.403496	+	0.698876i
$269$	−1.08752e8	−	1.88365e8i	−0.340648	−	0.590020i	0.643905	−	0.765105i	$-0.277313\pi$
$269$	−1.08752e8	−	1.88365e8i	−0.340648	−	0.590020i	−0.984553	+	0.175085i	$0.943980\pi$
$270$		0			0
$271$	−7.55186e6	+	1.30802e7i	−0.0230495	+	0.0399229i	−0.877320	−	0.479906i	$-0.840671\pi$
$271$	−7.55186e6	+	1.30802e7i	−0.0230495	+	0.0399229i	0.854271	+	0.519829i	$0.174004\pi$
$272$	−5.94084e7			−0.179001
$273$		0			0
$274$	2.05957e8			0.604853
$275$	3.37587e6	−	5.84719e6i	0.00978863	−	0.0169544i
$276$		0			0
$277$	−8.19027e7	−	1.41860e8i	−0.231536	−	0.401032i	0.726724	−	0.686929i	$-0.241042\pi$
$277$	−8.19027e7	−	1.41860e8i	−0.231536	−	0.401032i	−0.958260	+	0.285897i	$0.907708\pi$
$278$	5.17940e7	−	8.97098e7i	0.144585	−	0.250428i
$279$		0			0
$280$	1.29920e7	+	1.34117e8i	0.0353690	+	0.365115i
$281$	4.21200e8			1.13244			0.566221	−	0.824253i	$-0.308405\pi$
$281$	4.21200e8			1.13244			0.566221	+	0.824253i	$0.308405\pi$
$282$		0			0
$283$	3.36002e8	+	5.81972e8i	0.881229	+	1.52633i	0.849975	+	0.526822i	$0.176617\pi$
$283$	3.36002e8	+	5.81972e8i	0.881229	+	1.52633i	0.0312539	+	0.999511i	$0.490050\pi$
$284$	−1.37336e8	−	2.37874e8i	−0.355772	−	0.616215i
$285$		0			0
$286$	6.83695e7			0.172815
$287$	−4.88301e8	+	3.48726e8i	−1.21927	+	0.870759i
$288$		0			0
$289$	9.99863e7	−	1.73181e8i	0.243668	−	0.422045i
$290$	7.91120e6	+	1.37026e7i	0.0190480	+	0.0329921i
$291$		0			0
$292$	−1.89769e8	+	3.28690e8i	−0.446053	+	0.772586i
$293$	−771192.			−0.00179112			−0.000895562	−	1.00000i	$-0.500285\pi$
$293$	−771192.			−0.00179112			−0.000895562		1.00000i	$0.500285\pi$
$294$		0			0
$295$	6.90654e8			1.56633
$296$	3.40442e7	−	5.89662e7i	0.0762995	−	0.132155i
$297$		0			0
$298$	−1.25263e8	−	2.16961e8i	−0.274198	−	0.474925i
$299$	2.51999e7	−	4.36475e7i	0.0545193	−	0.0944301i
$300$		0			0
$301$	1.08630e8	−	7.75793e7i	0.229597	−	0.163970i
$302$	−3.29862e8			−0.689141
$303$		0			0
$304$	−5.12881e7	−	8.88335e7i	−0.104703	−	0.181351i
$305$	3.80640e8	+	6.59287e8i	0.768183	+	1.33053i
$306$		0			0
$307$	2.79387e8			0.551089			0.275544	−	0.961288i	$-0.411142\pi$
$307$	2.79387e8			0.551089			0.275544	+	0.961288i	$0.411142\pi$
$308$	−6.32800e6	−	6.53241e7i	−0.0123407	−	0.127393i
$309$		0			0
$310$	−2.04252e8	+	3.53774e8i	−0.389403	+	0.674466i
$311$	−3.60775e8	−	6.24880e8i	−0.680103	−	1.17797i	−0.974949	−	0.222429i	$-0.928602\pi$
$311$	−3.60775e8	−	6.24880e8i	−0.680103	−	1.17797i	0.294846	−	0.955545i	$-0.404732\pi$
$312$		0			0
$313$	−4.95703e8	+	8.58582e8i	−0.913726	+	1.58262i	−0.104971	+	0.994475i	$0.533475\pi$
$313$	−4.95703e8	+	8.58582e8i	−0.913726	+	1.58262i	−0.808755	+	0.588145i	$0.799858\pi$
$314$	4.42585e7			0.0806758
$315$		0			0
$316$	4.02156e8			0.716952
$317$	−6.02071e7	+	1.04282e8i	−0.106155	+	0.183866i	−0.914210	−	0.405242i	$-0.867187\pi$
$317$	−6.02071e7	+	1.04282e8i	−0.106155	+	0.183866i	0.808054	+	0.589108i	$0.200521\pi$
$318$		0			0
$319$	−3.85330e6	−	6.67411e6i	−0.00664608	−	0.0115113i
$320$	−3.80109e7	+	6.58368e7i	−0.0648460	+	0.112317i
$321$		0			0
$322$	−4.40357e7	−	2.00376e7i	−0.0735037	−	0.0334464i
$323$	−3.63224e8			−0.599743
$324$		0			0
$325$	2.25945e7	+	3.91348e7i	0.0365099	+	0.0632369i
$326$	1.34124e8	+	2.32309e8i	0.214409	+	0.371368i
$327$		0			0
$328$	−3.38537e8			−0.529722
$329$	7.87180e7	+	8.12607e8i	0.121868	+	1.25804i
$330$		0			0
$331$	−9.47655e7	+	1.64139e8i	−0.143632	+	0.248779i	−0.928862	−	0.370426i	$-0.879212\pi$
$331$	−9.47655e7	+	1.64139e8i	−0.143632	+	0.248779i	0.785230	+	0.619205i	$0.212545\pi$
$332$	1.36072e8	+	2.35684e8i	0.204073	+	0.353465i
$333$		0			0
$334$	−2.09253e8	+	3.62436e8i	−0.307297	+	0.532254i
$335$	1.15228e9			1.67457
$336$		0			0
$337$	9.06750e8			1.29057			0.645287	−	0.763940i	$-0.276738\pi$
$337$	9.06750e8			1.29057			0.645287	+	0.763940i	$0.276738\pi$
$338$	2.21982e7	−	3.84484e7i	0.0312687	−	0.0541589i
$339$		0			0
$340$	1.34597e8	+	2.33129e8i	0.185720	+	0.321677i
$341$	9.94846e7	−	1.72312e8i	0.135868	−	0.235329i
$342$		0			0
$343$	−2.13500e8	−	7.16215e8i	−0.285673	−	0.958327i
$344$	7.53126e7			0.0997501
$345$		0			0
$346$	−3.28170e8	−	5.68407e8i	−0.425924	−	0.737723i
$347$	−1.72561e8	−	2.98884e8i	−0.221712	−	0.384016i	0.733616	−	0.679564i	$-0.237831\pi$
$347$	−1.72561e8	−	2.98884e8i	−0.221712	−	0.384016i	−0.955328	+	0.295548i	$0.904498\pi$
$348$		0			0
$349$	−6.01221e8			−0.757086			−0.378543	−	0.925584i	$-0.623575\pi$
$349$	−6.01221e8			−0.757086			−0.378543	+	0.925584i	$0.623575\pi$
$350$	3.53003e7	−	2.52102e7i	0.0440089	−	0.0314295i
$351$		0			0
$352$	1.85139e7	−	3.20671e7i	0.0226255	−	0.0391886i
$353$	1.45774e8	+	2.52487e8i	0.176387	+	0.305512i	0.940640	−	0.339405i	$-0.110226\pi$
$353$	1.45774e8	+	2.52487e8i	0.176387	+	0.305512i	−0.764253	+	0.644916i	$0.776892\pi$
$354$		0			0
$355$	−6.22305e8	+	1.07786e9i	−0.738252	+	1.27869i
$356$	9.47712e7			0.111327
$357$		0			0
$358$	9.17039e8			1.05632
$359$	−2.37795e8	+	4.11872e8i	−0.271251	+	0.469821i	−0.969182	−	0.246344i	$-0.920771\pi$
$359$	−2.37795e8	+	4.11872e8i	−0.271251	+	0.469821i	0.697931	+	0.716165i	$0.254104\pi$
$360$		0			0
$361$	1.33360e8	+	2.30986e8i	0.149194	+	0.258411i
$362$	−2.11600e8	+	3.66502e8i	−0.234442	+	0.406066i
$363$		0			0
$364$	3.99810e8	+	1.81926e8i	0.434510	+	0.197715i
$365$	1.71978e9			1.85118
$366$		0			0
$367$	−8.25397e7	−	1.42963e8i	−0.0871629	−	0.150971i	0.819148	−	0.573582i	$-0.194447\pi$
$367$	−8.25397e7	−	1.42963e8i	−0.0871629	−	0.150971i	−0.906311	+	0.422612i	$0.861113\pi$
$368$	−1.36479e7	−	2.36388e7i	−0.0142757	−	0.0247262i
$369$		0			0
$370$	−3.08525e8			−0.316654
$371$	−1.07804e9	−	4.90540e8i	−1.09604	−	0.498731i
$372$		0			0
$373$	−2.33424e8	+	4.04302e8i	−0.232897	+	0.403390i	−0.958660	−	0.284556i	$-0.908154\pi$
$373$	−2.33424e8	+	4.04302e8i	−0.232897	+	0.403390i	0.725762	+	0.687946i	$0.241487\pi$
$374$	−6.55581e7	−	1.13550e8i	−0.0648001	−	0.112237i
$375$		0			0
$376$	−2.30306e8	+	3.98902e8i	−0.223434	+	0.386998i
$377$	5.15797e7			0.0495774
$378$		0			0
$379$	−2.77160e8			−0.261513			−0.130756	−	0.991415i	$-0.541741\pi$
$379$	−2.77160e8			−0.261513			−0.130756	+	0.991415i	$0.541741\pi$
$380$	−2.32399e8	+	4.02527e8i	−0.217266	+	0.376316i
$381$		0			0
$382$	4.11389e8	+	7.12548e8i	0.377600	+	0.654022i
$383$	−3.98941e6	+	6.90987e6i	−0.00362839	+	0.00628455i	−0.867834	−	0.496854i	$-0.834488\pi$
$383$	−3.98941e6	+	6.90987e6i	−0.00362839	+	0.00628455i	0.864206	+	0.503139i	$0.167822\pi$
$384$		0			0
$385$	−2.42006e8	+	1.72832e8i	−0.216130	+	0.154352i
$386$	−1.40193e9			−1.24071
$387$		0			0
$388$	−3.01038e8	−	5.21413e8i	−0.261644	−	0.453180i
$389$	8.63868e8	+	1.49626e9i	0.744087	+	1.28880i	0.950620	+	0.310357i	$0.100449\pi$
$389$	8.63868e8	+	1.49626e9i	0.744087	+	1.28880i	−0.206533	+	0.978440i	$0.566218\pi$
$390$		0			0
$391$	−9.66547e7			−0.0817719
$392$	1.36817e8	−	3.98840e8i	0.114720	−	0.334424i
$393$		0			0
$394$	6.28878e8	−	1.08925e9i	0.518000	−	0.897202i
$395$	−9.11135e8	−	1.57813e9i	−0.743863	−	1.28841i
$396$		0			0
$397$	−3.96249e8	+	6.86323e8i	−0.317835	+	0.550506i	−0.980036	−	0.198820i	$-0.936289\pi$
$397$	−3.96249e8	+	6.86323e8i	−0.317835	+	0.550506i	0.662201	+	0.749326i	$0.269622\pi$
$398$	8.85988e8			0.704429
$399$		0			0
$400$	2.44736e7			0.0191200
$401$	−3.47592e8	+	6.02048e8i	−0.269194	+	0.466257i	−0.968654	−	0.248414i	$-0.920091\pi$
$401$	−3.47592e8	+	6.02048e8i	−0.269194	+	0.466257i	0.699460	+	0.714672i	$0.253424\pi$
$402$		0			0
$403$	6.65843e8	+	1.15327e9i	0.506762	+	0.877737i
$404$	−3.47119e8	+	6.01227e8i	−0.261905	+	0.453632i
$405$		0			0
$406$	−4.77400e6	−	4.92821e7i	−0.00354031	−	0.0365467i
$407$	1.50273e8			0.110484
$408$		0			0
$409$	−9.83035e8	−	1.70267e9i	−0.710456	−	1.23055i	−0.964686	−	0.263403i	$-0.915155\pi$
$409$	−9.83035e8	−	1.70267e9i	−0.710456	−	1.23055i	0.254229	−	0.967144i	$-0.418178\pi$
$410$	7.66999e8	+	1.32848e9i	0.549606	+	0.951945i
$411$		0			0
$412$	−1.29347e7			−0.00911206
$413$	−1.96717e9	−	8.95123e8i	−1.37410	−	0.625255i
$414$		0			0
$415$	6.16576e8	−	1.06794e9i	0.423466	−	0.733464i
$416$	1.23912e8	+	2.14622e8i	0.0843893	+	0.146167i
$417$		0			0
$418$	1.13194e8	−	1.96058e8i	0.0758067	−	0.131301i
$419$	−2.20900e9			−1.46706			−0.733529	−	0.679658i	$-0.762128\pi$
$419$	−2.20900e9			−1.46706			−0.733529	+	0.679658i	$0.762128\pi$
$420$		0			0
$421$	−4.59955e8			−0.300419			−0.150210	−	0.988654i	$-0.547995\pi$
$421$	−4.59955e8			−0.300419			−0.150210	+	0.988654i	$0.547995\pi$
$422$	5.86690e8	−	1.01618e9i	0.380028	−	0.658227i
$423$		0			0
$424$	−3.34114e8	−	5.78702e8i	−0.212870	−	0.368701i
$425$	4.33307e7	−	7.50510e7i	0.0273801	−	0.0474237i
$426$		0			0
$427$	−2.29696e8	−	2.37116e9i	−0.142776	−	1.47388i
$428$	8.23658e8			0.507802
$429$		0			0
$430$	−1.70630e8	−	2.95540e8i	−0.103494	−	0.179257i
$431$	−1.07759e9	−	1.86643e9i	−0.648308	−	1.12290i	−0.983527	−	0.180763i	$-0.942143\pi$
$431$	−1.07759e9	−	1.86643e9i	−0.648308	−	1.12290i	0.335218	−	0.942140i	$-0.391190\pi$
$432$		0			0
$433$	1.78833e9			1.05862			0.529311	−	0.848428i	$-0.322450\pi$
$433$	1.78833e9			1.05862			0.529311	+	0.848428i	$0.322450\pi$
$434$	1.04027e9	−	7.42926e8i	0.610849	−	0.436246i
$435$		0			0
$436$	6.99225e8	−	1.21109e9i	0.404031	−	0.699802i
$437$	−8.34433e7	−	1.44528e8i	−0.0478307	−	0.0828451i
$438$		0			0
$439$	−7.60502e7	+	1.31723e8i	−0.0429017	+	0.0743080i	−0.886679	−	0.462386i	$-0.846994\pi$
$439$	−7.60502e7	+	1.31723e8i	−0.0429017	+	0.0743080i	0.843777	+	0.536694i	$0.180327\pi$
$440$	−1.67782e8			−0.0938992
$441$		0			0
$442$	8.77550e8			0.483386
$443$	1.34809e9	−	2.33496e9i	0.736727	−	1.27605i	−0.217234	−	0.976119i	$-0.569704\pi$
$443$	1.34809e9	−	2.33496e9i	0.736727	−	1.27605i	0.953961	−	0.299929i	$-0.0969631\pi$
$444$		0			0
$445$	−2.14716e8	−	3.71899e8i	−0.115506	−	0.200062i
$446$	2.36385e8	−	4.09432e8i	0.126168	−	0.218529i
$447$		0			0
$448$	1.93593e8	−	1.38257e8i	0.101723	−	0.0726465i
$449$	5.37859e8			0.280418			0.140209	−	0.990122i	$-0.455223\pi$
$449$	5.37859e8			0.280418			0.140209	+	0.990122i	$0.455223\pi$
$450$		0			0
$451$	−3.73581e8	−	6.47062e8i	−0.191764	−	0.332145i
$452$	1.47635e8	+	2.55712e8i	0.0751979	+	0.130247i
$453$		0			0
$454$	3.43241e8			0.172149
$455$	−1.91911e8	−	1.98110e9i	−0.0955125	−	0.985978i
$456$		0			0
$457$	2.69397e8	−	4.66609e8i	0.132034	−	0.228690i	−0.792427	−	0.609967i	$-0.791183\pi$
$457$	2.69397e8	−	4.66609e8i	0.132034	−	0.228690i	0.924460	+	0.381278i	$0.124516\pi$
$458$	−1.10501e9	−	1.91393e9i	−0.537448	−	0.930887i
$459$		0			0
$460$	−6.18419e7	+	1.07113e8i	−0.0296231	+	0.0513087i
$461$	−5.24391e6			−0.00249288			−0.00124644	−	0.999999i	$-0.500397\pi$
$461$	−5.24391e6			−0.00249288			−0.00124644	+	0.999999i	$0.500397\pi$
$462$		0			0
$463$	2.18426e8			0.102275			0.0511376	−	0.998692i	$-0.483715\pi$
$463$	2.18426e8			0.102275			0.0511376	+	0.998692i	$0.483715\pi$
$464$	1.39674e7	−	2.41922e7i	0.00649085	−	0.0112425i
$465$		0			0
$466$	6.13365e8	+	1.06238e9i	0.280781	+	0.486327i
$467$	−1.74721e8	+	3.02625e8i	−0.0793845	+	0.137498i	−0.902985	−	0.429673i	$-0.858629\pi$
$467$	−1.74721e8	+	3.02625e8i	−0.0793845	+	0.137498i	0.823600	+	0.567171i	$0.191962\pi$
$468$		0			0
$469$	−3.28202e9	−	1.49342e9i	−1.46905	−	0.668462i
$470$	2.08715e9			0.927281
$471$		0			0
$472$	−6.09680e8	−	1.05600e9i	−0.266873	−	0.462238i
$473$	8.31087e7	+	1.43948e8i	0.0361104	+	0.0625451i
$474$		0			0
$475$	1.49632e8			0.0640614
$476$	−8.12224e7	−	8.38461e8i	−0.0345185	−	0.356335i
$477$		0			0
$478$	−1.38249e9	+	2.39454e9i	−0.578979	+	1.00282i
$479$	2.02511e9	+	3.50759e9i	0.841927	+	1.45826i	0.888263	+	0.459335i	$0.151912\pi$
$479$	2.02511e9	+	3.50759e9i	0.841927	+	1.45826i	−0.0463361	+	0.998926i	$0.514755\pi$
$480$		0			0
$481$	−5.02883e8	+	8.71019e8i	−0.206044	+	0.356878i
$482$	4.32534e8			0.175936
$483$		0			0
$484$	−1.16546e9			−0.467237
$485$	−1.36408e9	+	2.36265e9i	−0.542929	+	0.940381i
$486$		0			0
$487$	−4.63317e8	−	8.02488e8i	−0.181772	−	0.314838i	0.760712	−	0.649089i	$-0.224850\pi$
$487$	−4.63317e8	−	8.02488e8i	−0.181772	−	0.314838i	−0.942484	+	0.334251i	$0.891517\pi$
$488$	6.72026e8	−	1.16398e9i	0.261768	−	0.453396i
$489$		0			0
$490$	−1.87509e9	+	3.66725e8i	−0.720007	+	0.140817i
$491$	−2.65906e9			−1.01378			−0.506889	−	0.862011i	$-0.669205\pi$
$491$	−2.65906e9			−1.01378			−0.506889	+	0.862011i	$0.669205\pi$
$492$		0			0
$493$	−4.94586e7	−	8.56649e7i	−0.0185899	−	0.0321987i
$494$	7.57601e8	+	1.31220e9i	0.282746	+	0.489730i
$495$		0			0
$496$	7.21220e8			0.265388
$497$	3.16947e9	−	2.26352e9i	1.15808	−	0.827058i
$498$		0			0
$499$	1.58248e9	−	2.74094e9i	0.570147	−	0.987523i	−0.426404	−	0.904533i	$-0.640220\pi$
$499$	1.58248e9	−	2.74094e9i	0.570147	−	0.987523i	0.996550	−	0.0829901i	$-0.0264470\pi$
$500$	6.69552e8	+	1.15970e9i	0.239546	+	0.414906i
$501$		0			0
$502$	−3.76004e8	+	6.51259e8i	−0.132657	+	0.229768i
$503$	−4.12431e9			−1.44499			−0.722493	−	0.691379i	$-0.757004\pi$
$503$	−4.12431e9			−1.44499			−0.722493	+	0.691379i	$0.757004\pi$
$504$		0			0
$505$	3.14576e9			1.08694
$506$	3.01213e7	−	5.21716e7i	0.0103359	−	0.0179022i
$507$		0			0
$508$	1.18696e9	+	2.05587e9i	0.401709	+	0.695781i
$509$	−2.77566e9	+	4.80758e9i	−0.932940	+	1.61590i	−0.154674	+	0.987966i	$0.549433\pi$
$509$	−2.77566e9	+	4.80758e9i	−0.932940	+	1.61590i	−0.778266	+	0.627935i	$0.783901\pi$
$510$		0			0
$511$	−4.89842e9	−	2.22893e9i	−1.62399	−	0.738964i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	2.79201e8	+	4.83589e8i	0.0906871	+	0.157075i
$515$	2.93052e7	+	5.07581e7i	0.00945409	+	0.0163750i
$516$		0			0
$517$	−1.01659e9			−0.323540
$518$	8.78765e8	+	3.99865e8i	0.277791	+	0.126403i
$519$		0			0
$520$	5.61477e8	−	9.72507e8i	0.175114	−	0.303306i
$521$	1.07072e9	+	1.85455e9i	0.331700	+	0.574522i	0.982845	−	0.184432i	$-0.0590444\pi$
$521$	1.07072e9	+	1.85455e9i	0.331700	+	0.574522i	−0.651145	+	0.758953i	$0.725711\pi$
$522$		0			0
$523$	−9.80200e8	+	1.69776e9i	−0.299612	+	0.518943i	−0.976047	−	0.217559i	$-0.930191\pi$
$523$	−9.80200e8	+	1.69776e9i	−0.299612	+	0.518943i	0.676435	+	0.736502i	$0.263524\pi$
$524$	2.54943e9			0.774076
$525$		0			0
$526$	−5.70567e8			−0.170945
$527$	1.27692e9	−	2.21170e9i	0.380039	−	0.658247i
$528$		0			0
$529$	1.68021e9	+	2.91021e9i	0.493479	+	0.854730i
$530$	−1.51395e9	+	2.62224e9i	−0.441720	+	0.765081i
$531$		0			0
$532$	1.18363e9	−	8.45307e8i	0.340821	−	0.243402i
$533$	5.00070e9			1.43049
$534$		0			0
$535$	−1.86610e9	−	3.23218e9i	−0.526862	−	0.912552i
$536$	−1.01719e9	−	1.76182e9i	−0.285315	−	0.494180i
$537$		0			0
$538$	1.74004e9			0.481749
$539$	9.13300e8	−	1.78621e8i	0.251219	−	0.0491327i
$540$		0			0
$541$	−2.01622e9	+	3.49220e9i	−0.547455	+	0.948219i	0.450993	+	0.892527i	$0.351070\pi$
$541$	−2.01622e9	+	3.49220e9i	−0.547455	+	0.948219i	−0.998448	+	0.0556919i	$0.982264\pi$
$542$	−6.04149e7	−	1.04642e8i	−0.0162985	−	0.0282298i
$543$		0			0
$544$	2.37634e8	−	4.11593e8i	0.0632866	−	0.109616i
$545$	−6.33673e9			−1.67678
$546$		0			0
$547$	4.81827e9			1.25874			0.629369	−	0.777107i	$-0.283313\pi$
$547$	4.81827e9			1.25874			0.629369	+	0.777107i	$0.283313\pi$
$548$	−8.23829e8	+	1.42691e9i	−0.213848	+	0.370395i
$549$		0			0
$550$	2.70070e7	+	4.67775e7i	0.00692161	+	0.0119886i
$551$	8.53966e7	−	1.47911e8i	0.0217475	−	0.0376678i
$552$		0			0
$553$	5.49823e8	+	5.67583e9i	0.138256	+	1.42722i
$554$	1.31044e9			0.327442
$555$		0			0
$556$	4.14352e8	+	7.17679e8i	0.102237	+	0.177079i
$557$	−1.23993e9	−	2.14762e9i	−0.304022	−	0.526581i	0.673021	−	0.739623i	$-0.264996\pi$
$557$	−1.23993e9	−	2.14762e9i	−0.304022	−	0.526581i	−0.977043	+	0.213042i	$0.931663\pi$
$558$		0			0
$559$	−1.11248e9			−0.269371
$560$	−9.81156e8	−	4.46456e8i	−0.236091	−	0.107429i
$561$		0			0
$562$	−1.68480e9	+	2.91816e9i	−0.400379	+	0.693476i
$563$	−2.35080e9	−	4.07171e9i	−0.555184	−	0.961607i	−0.997889	−	0.0649396i	$-0.979315\pi$
$563$	−2.35080e9	−	4.07171e9i	−0.555184	−	0.961607i	0.442705	−	0.896667i	$-0.354019\pi$
$564$		0			0
$565$	6.68972e8	−	1.15869e9i	0.156041	−	0.270271i
$566$	−5.37603e9			−1.24625
$567$		0			0
$568$	2.19738e9			0.503137
$569$	7.08999e8	−	1.22802e9i	0.161344	−	0.279456i	−0.774007	−	0.633177i	$-0.781750\pi$
$569$	7.08999e8	−	1.22802e9i	0.161344	−	0.279456i	0.935351	+	0.353721i	$0.115084\pi$
$570$		0			0
$571$	4.24907e9	+	7.35960e9i	0.955141	+	1.65435i	0.734046	+	0.679100i	$0.237630\pi$
$571$	4.24907e9	+	7.35960e9i	0.955141	+	1.65435i	0.221095	+	0.975252i	$0.429037\pi$
$572$	−2.73478e8	+	4.73678e8i	−0.0610993	+	0.105827i
$573$		0			0
$574$	−4.62844e8	−	4.77795e9i	−0.102151	−	1.05451i
$575$	3.98174e7			0.00873445
$576$		0			0
$577$	2.65730e9	+	4.60258e9i	0.575871	+	0.997438i	0.995946	+	0.0899487i	$0.0286703\pi$
$577$	2.65730e9	+	4.60258e9i	0.575871	+	0.997438i	−0.420075	+	0.907489i	$0.637996\pi$
$578$	7.99891e8	+	1.38545e9i	0.172299	+	0.298431i
$579$		0			0
$580$	−1.26579e8			−0.0269379
$581$	−3.14029e9	+	2.24268e9i	−0.664283	+	0.474406i
$582$		0			0
$583$	7.37400e8	−	1.27721e9i	0.154121	−	0.266946i
$584$	−1.51816e9	−	2.62952e9i	−0.315407	−	0.546301i
$585$		0			0
$586$	3.08477e6	−	5.34297e6i	0.000633258	−	0.00109684i
$587$	6.24032e9			1.27343			0.636713	−	0.771101i	$-0.280294\pi$
$587$	6.24032e9			1.27343			0.636713	+	0.771101i	$0.280294\pi$
$588$		0			0
$589$	4.40955e9			0.889181
$590$	−2.76261e9	+	4.78499e9i	−0.553781	+	0.959177i
$591$		0			0
$592$	2.72353e8	+	4.71730e8i	0.0539519	+	0.0934474i
$593$	−3.35563e9	+	5.81212e9i	−0.660820	+	1.14457i	0.319581	+	0.947559i	$0.396458\pi$
$593$	−3.35563e9	+	5.81212e9i	−0.660820	+	1.14457i	−0.980401	+	0.197014i	$0.936876\pi$
$594$		0			0
$595$	−3.10625e9	+	2.21837e9i	−0.604543	+	0.431742i
$596$	2.00420e9			0.387775
$597$		0			0
$598$	2.01599e8	+	3.49180e8i	0.0385509	+	0.0667722i
$599$	2.92510e9	+	5.06641e9i	0.556091	+	0.963179i	0.997818	+	0.0660287i	$0.0210329\pi$
$599$	2.92510e9	+	5.06641e9i	0.556091	+	0.963179i	−0.441726	+	0.897150i	$0.645634\pi$
$600$		0			0
$601$	−1.23472e9			−0.232010			−0.116005	−	0.993249i	$-0.537009\pi$
$601$	−1.23472e9			−0.232010			−0.116005	+	0.993249i	$0.537009\pi$
$602$	1.02966e8	+	1.06293e9i	0.0192357	+	0.198571i
$603$		0			0
$604$	1.31945e9	−	2.28535e9i	0.243648	−	0.422011i
$605$	2.64049e9	+	4.57346e9i	0.484775	+	0.839656i
$606$		0			0
$607$	−3.74398e8	+	6.48477e8i	−0.0679475	+	0.117689i	−0.897998	−	0.440000i	$-0.854978\pi$
$607$	−3.74398e8	+	6.48477e8i	−0.0679475	+	0.117689i	0.830050	+	0.557689i	$0.188312\pi$
$608$	8.20609e8			0.148072
$609$		0			0
$610$	−6.09024e9			−1.08637
$611$	3.40197e9	−	5.89238e9i	0.603373	−	1.04507i
$612$		0			0
$613$	4.86634e9	+	8.42875e9i	0.853279	+	1.47792i	0.878233	+	0.478234i	$0.158723\pi$
$613$	4.86634e9	+	8.42875e9i	0.853279	+	1.47792i	−0.0249539	+	0.999689i	$0.507944\pi$
$614$	−1.11755e9	+	1.93565e9i	−0.194839	+	0.337471i
$615$		0			0
$616$	4.77891e8	+	2.17455e8i	0.0823751	+	0.0374832i
$617$	9.09192e9			1.55832			0.779161	−	0.626823i	$-0.215645\pi$
$617$	9.09192e9			1.55832			0.779161	+	0.626823i	$0.215645\pi$
$618$		0			0
$619$	−1.27380e9	−	2.20629e9i	−0.215866	−	0.373892i	0.737674	−	0.675157i	$-0.235924\pi$
$619$	−1.27380e9	−	2.20629e9i	−0.215866	−	0.373892i	−0.953540	+	0.301266i	$0.902591\pi$
$620$	−1.63401e9	−	2.83019e9i	−0.275350	−	0.476920i
$621$		0			0
$622$	5.77240e9			0.961811
$623$	1.29570e8	+	1.33755e9i	0.0214682	+	0.221617i
$624$		0			0
$625$	3.26731e9	−	5.65914e9i	0.535315	−	0.927193i
$626$	−3.96562e9	−	6.86866e9i	−0.646102	−	1.11908i
$627$		0			0
$628$	−1.77034e8	+	3.06632e8i	−0.0285232	+	0.0494036i
$629$	1.92881e9			0.309039
$630$		0			0
$631$	−3.43067e9			−0.543595			−0.271798	−	0.962354i	$-0.587618\pi$
$631$	−3.43067e9			−0.543595			−0.271798	+	0.962354i	$0.587618\pi$
$632$	−1.60862e9	+	2.78622e9i	−0.253481	+	0.439041i
$633$		0			0
$634$	−4.81657e8	−	8.34254e8i	−0.0750629	−	0.130013i
$635$	5.37840e9	−	9.31566e9i	0.833575	−	1.44379i
$636$		0			0
$637$	−2.02100e9	+	5.89145e9i	−0.309797	+	0.903097i
$638$	6.16528e7			0.00939897
$639$		0			0
$640$	−3.04087e8	−	5.26694e8i	−0.0458530	−	0.0794198i
$641$	2.20563e9	+	3.82027e9i	0.330773	+	0.572916i	0.982664	−	0.185397i	$-0.0593572\pi$
$641$	2.20563e9	+	3.82027e9i	0.330773	+	0.572916i	−0.651891	+	0.758313i	$0.726024\pi$
$642$		0			0
$643$	−5.39024e9			−0.799595			−0.399797	−	0.916604i	$-0.630919\pi$
$643$	−5.39024e9			−0.799595			−0.399797	+	0.916604i	$0.630919\pi$
$644$	3.14967e8	−	2.24938e8i	0.0464692	−	0.0331866i
$645$		0			0
$646$	1.45289e9	−	2.51649e9i	0.212041	−	0.367266i
$647$	1.26244e9	+	2.18661e9i	0.183251	+	0.317399i	0.942986	−	0.332833i	$-0.108005\pi$
$647$	1.26244e9	+	2.18661e9i	0.183251	+	0.317399i	−0.759735	+	0.650233i	$0.774671\pi$
$648$		0			0
$649$	1.34558e9	−	2.33062e9i	0.193221	−	0.334669i
$650$	−3.61511e8			−0.0516327
$651$		0			0
$652$	−2.14598e9			−0.303220
$653$	−2.95678e8	+	5.12129e8i	−0.0415550	+	0.0719753i	−0.886055	−	0.463580i	$-0.846564\pi$
$653$	−2.95678e8	+	5.12129e8i	−0.0415550	+	0.0719753i	0.844500	+	0.535556i	$0.179898\pi$
$654$		0			0
$655$	−5.77605e9	−	1.00044e10i	−0.803131	−	1.39106i
$656$	1.35415e9	−	2.34546e9i	0.187285	−	0.324387i
$657$		0			0
$658$	−5.94478e9	−	2.70506e9i	−0.813477	−	0.370157i
$659$	7.80244e9			1.06202			0.531009	−	0.847366i	$-0.321813\pi$
$659$	7.80244e9			1.06202			0.531009	+	0.847366i	$0.321813\pi$
$660$		0			0
$661$	−5.60662e9	−	9.71095e9i	−0.755086	−	1.30785i	−0.945332	−	0.326110i	$-0.894262\pi$
$661$	−5.60662e9	−	9.71095e9i	−0.755086	−	1.30785i	0.190246	−	0.981736i	$-0.439071\pi$
$662$	−7.58124e8	−	1.31311e9i	−0.101563	−	0.175913i
$663$		0			0
$664$	−2.17715e9			−0.288603
$665$	−5.99880e9	−	2.72964e9i	−0.791022	−	0.359939i
$666$		0			0
$667$	2.27242e7	−	3.93595e7i	0.00296517	−	0.00513582i
$668$	−1.67402e9	−	2.89949e9i	−0.217292	−	0.376360i
$669$		0			0
$670$	−4.60914e9	+	7.98326e9i	−0.592049	+	1.02546i
$671$	2.96637e9			0.379049
$672$		0			0
$673$	1.09343e10			1.38273			0.691365	−	0.722506i	$-0.257010\pi$
$673$	1.09343e10			1.38273			0.691365	+	0.722506i	$0.257010\pi$
$674$	−3.62700e9	+	6.28215e9i	−0.456287	+	0.790312i
$675$		0			0
$676$	1.77586e8	+	3.07587e8i	0.0221103	+	0.0382961i
$677$	3.08956e9	−	5.35128e9i	0.382681	−	0.662823i	−0.608764	−	0.793352i	$-0.708334\pi$
$677$	3.08956e9	−	5.35128e9i	0.382681	−	0.662823i	0.991444	+	0.130529i	$0.0416676\pi$
$678$		0			0
$679$	6.94739e9	−	4.96157e9i	0.851682	−	0.608240i
$680$	−2.15355e9			−0.262648
$681$		0			0
$682$	7.95877e8	+	1.37850e9i	0.0960729	+	0.166403i
$683$	−5.55747e9	−	9.62582e9i	−0.667428	−	1.15602i	−0.978621	−	0.205673i	$-0.934062\pi$
$683$	−5.55747e9	−	9.62582e9i	−0.667428	−	1.15602i	0.311192	−	0.950347i	$-0.399272\pi$
$684$		0			0
$685$	7.46595e9			0.887499
$686$	5.81608e9	+	1.38568e9i	0.687854	+	0.163882i
$687$		0			0
$688$	−3.01251e8	+	5.21781e8i	−0.0352670	+	0.0610842i
$689$	4.93536e9	+	8.54829e9i	0.574846	+	0.995662i
$690$		0			0
$691$	−5.48065e9	+	9.49277e9i	−0.631916	+	1.09451i	0.355244	+	0.934774i	$0.384398\pi$
$691$	−5.48065e9	+	9.49277e9i	−0.631916	+	1.09451i	−0.987160	+	0.159737i	$0.948935\pi$
$692$	5.25072e9			0.602348
$693$		0			0
$694$	2.76097e9			0.313548
$695$	1.87753e9	−	3.25198e9i	0.212149	−	0.367452i
$696$		0			0
$697$	−4.79507e9	−	8.30530e9i	−0.536389	−	0.929053i
$698$	2.40488e9	−	4.16538e9i	0.267670	−	0.463619i
$699$		0			0
$700$	3.34600e7	+	3.45408e8i	0.00368708	+	0.0380618i
$701$	−1.27383e10			−1.39669			−0.698344	−	0.715762i	$-0.746080\pi$
$701$	−1.27383e10			−1.39669			−0.698344	+	0.715762i	$0.746080\pi$
$702$		0			0
$703$	1.66517e9	+	2.88416e9i	0.180765	+	0.313095i
$704$	1.48111e8	+	2.56536e8i	0.0159987	+	0.0277105i
$705$		0			0
$706$	−2.33238e9			−0.249449
$707$	−8.96000e9	−	4.07707e9i	−0.953543	−	0.433891i
$708$		0			0
$709$	−4.54095e8	+	7.86516e8i	−0.0478504	+	0.0828793i	−0.888959	−	0.457988i	$-0.848570\pi$
$709$	−4.54095e8	+	7.86516e8i	−0.0478504	+	0.0828793i	0.841108	+	0.540867i	$0.181904\pi$
$710$	−4.97844e9	−	8.62292e9i	−0.522023	−	0.904170i
$711$		0			0
$712$	−3.79085e8	+	6.56594e8i	−0.0393601	+	0.0681737i
$713$	1.17339e9			0.121235
$714$		0			0
$715$	2.47840e9			0.253571
$716$	−3.66816e9	+	6.35343e9i	−0.373467	+	0.646864i
$717$		0			0
$718$	−1.90236e9	−	3.29498e9i	−0.191803	−	0.332213i
$719$	−5.93012e9	+	1.02713e10i	−0.594994	+	1.03056i	0.398554	+	0.917145i	$0.369512\pi$
$719$	−5.93012e9	+	1.02713e10i	−0.594994	+	1.03056i	−0.993548	+	0.113414i	$0.963821\pi$
$720$		0			0
$721$	−1.76842e7	−	1.82554e8i	−0.00175716	−	0.0181392i
$722$	−2.13376e9			−0.210992
$723$		0			0
$724$	−1.69280e9	−	2.93202e9i	−0.165776	−	0.287132i
$725$	2.03748e7	+	3.52901e7i	0.00198568	+	0.00343930i
$726$		0			0
$727$	−8.01213e9			−0.773352			−0.386676	−	0.922216i	$-0.626377\pi$
$727$	−8.01213e9			−0.773352			−0.386676	+	0.922216i	$0.626377\pi$
$728$	−2.85966e9	+	2.04226e9i	−0.274698	+	0.196179i
$729$		0			0
$730$	−6.87914e9	+	1.19150e10i	−0.654492	+	1.13361i
$731$	1.06673e9	+	1.84764e9i	0.101005	+	0.174947i
$732$		0			0
$733$	4.90483e9	−	8.49542e9i	0.460003	−	0.796748i	−0.538958	−	0.842333i	$-0.681182\pi$
$733$	4.90483e9	−	8.49542e9i	0.460003	−	0.796748i	0.998960	+	0.0455848i	$0.0145151\pi$
$734$	1.32064e9			0.123267
$735$		0			0
$736$	2.18366e8			0.0201889
$737$	2.24497e9	−	3.88840e9i	0.206573	−	0.357795i
$738$		0			0
$739$	−7.96251e9	−	1.37915e10i	−0.725762	−	1.25706i	−0.958659	−	0.284556i	$-0.908154\pi$
$739$	−7.96251e9	−	1.37915e10i	−0.725762	−	1.25706i	0.232897	−	0.972501i	$-0.425179\pi$
$740$	1.23410e9	−	2.13753e9i	0.111954	−	0.193910i
$741$		0			0
$742$	7.71072e9	−	5.50671e9i	0.692917	−	0.494856i
$743$	−1.85101e10			−1.65558			−0.827788	−	0.561042i	$-0.810401\pi$
$743$	−1.85101e10			−1.65558			−0.827788	+	0.561042i	$0.810401\pi$
$744$		0			0
$745$	−4.54077e9	−	7.86484e9i	−0.402330	−	0.696856i
$746$	−1.86739e9	−	3.23442e9i	−0.164683	−	0.285240i
$747$		0			0
$748$	1.04893e9			0.0916412
$749$	1.12610e9	+	1.16247e10i	0.0979239	+	1.01087i
$750$		0			0
$751$	7.69757e9	−	1.33326e10i	0.663154	−	1.14862i	−0.316629	−	0.948549i	$-0.602551\pi$
$751$	7.69757e9	−	1.33326e10i	0.663154	−	1.14862i	0.979782	−	0.200066i	$-0.0641157\pi$
$752$	−1.84245e9	−	3.19122e9i	−0.157991	−	0.273649i
$753$		0			0
$754$	−2.06319e8	+	3.57354e8i	−0.0175283	+	0.0303598i
$755$	−1.19575e10			−1.01117
$756$		0			0
$757$	5.14693e9			0.431233			0.215617	−	0.976478i	$-0.430824\pi$
$757$	5.14693e9			0.431233			0.215617	+	0.976478i	$0.430824\pi$
$758$	1.10864e9	−	1.92022e9i	0.0924587	−	0.160143i
$759$		0			0
$760$	−1.85919e9	−	3.22022e9i	−0.153630	−	0.266095i
$761$	−1.00114e9	+	1.73402e9i	−0.0823469	+	0.142629i	−0.904258	−	0.426987i	$-0.859575\pi$
$761$	−1.00114e9	+	1.73402e9i	−0.0823469	+	0.142629i	0.821911	+	0.569616i	$0.192908\pi$
$762$		0			0
$763$	1.80488e10	+	8.21273e9i	1.47100	+	0.669347i
$764$	−6.58223e9			−0.534006
$765$		0			0
$766$	−3.19153e7	−	5.52789e7i	−0.00256566	−	0.00444385i
$767$	9.00588e9	+	1.55986e10i	0.720680	+	1.24825i
$768$		0			0
$769$	−9.62216e9			−0.763010			−0.381505	−	0.924367i	$-0.624594\pi$
$769$	−9.62216e9			−0.763010			−0.381505	+	0.924367i	$0.624594\pi$
$770$	−2.29390e8	−	2.36800e9i	−0.0181074	−	0.186923i
$771$		0			0
$772$	5.60773e9	−	9.71288e9i	0.438659	−	0.759779i
$773$	−4.56517e8	−	7.90711e8i	−0.0355491	−	0.0615729i	0.847703	−	0.530470i	$-0.177985\pi$
$773$	−4.56517e8	−	7.90711e8i	−0.0355491	−	0.0615729i	−0.883253	+	0.468898i	$0.844651\pi$
$774$		0			0
$775$	−5.26036e8	+	9.11121e8i	−0.0405938	+	0.0703105i
$776$	4.81661e9			0.370020
$777$		0			0
$778$	−1.38219e10			−1.05230
$779$	8.27929e9	−	1.43402e10i	0.627498	−	1.08686i
$780$		0			0
$781$	2.42485e9	+	4.19996e9i	0.182140	+	0.315476i
$782$	3.86619e8	−	6.69643e8i	0.0289107	−	0.0500749i
$783$		0			0
$784$	2.21597e9	+	2.54326e9i	0.164232	+	0.188488i
$785$	1.60437e9			0.118375
$786$		0			0
$787$	8.12525e9	+	1.40733e10i	0.594189	+	1.02917i	0.993661	+	0.112421i	$0.0358604\pi$
$787$	8.12525e9	+	1.40733e10i	0.594189	+	1.02917i	−0.399471	+	0.916746i	$0.630806\pi$
$788$	5.03103e9	+	8.71399e9i	0.366281	+	0.634418i
$789$		0			0
$790$	1.45782e10			1.05198
$791$	−3.40715e9	+	2.43326e9i	−0.244778	+	0.174812i
$792$		0			0
$793$	−9.92682e9	+	1.71938e10i	−0.706894	+	1.22438i
$794$	−3.16999e9	−	5.49058e9i	−0.224743	−	0.389266i
$795$		0			0
$796$	−3.54395e9	+	6.13830e9i	−0.249053	+	0.431373i
$797$	2.00600e10			1.40355			0.701774	−	0.712400i	$-0.252392\pi$
$797$	2.00600e10			1.40355			0.701774	+	0.712400i	$0.252392\pi$
$798$		0			0
$799$	−1.30483e10			−0.904982
$800$	−9.78944e7	+	1.69558e8i	−0.00675994	+	0.0117086i
$801$		0			0
$802$	−2.78074e9	−	4.81638e9i	−0.190349	−	0.329694i
$803$	3.35062e9	−	5.80344e9i	0.228360	−	0.395531i
$804$		0			0
$805$	−1.59629e9	−	7.26362e8i	−0.107852	−	0.0490758i
$806$	−1.06535e10			−0.716670
$807$		0			0
$808$	−2.77695e9	−	4.80982e9i	−0.185195	−	0.320766i
$809$	−8.90985e9	−	1.54323e10i	−0.591630	−	1.02473i	−0.994013	−	0.109262i	$-0.965151\pi$
$809$	−8.90985e9	−	1.54323e10i	−0.591630	−	1.02473i	0.402383	−	0.915472i	$-0.368182\pi$
$810$		0			0
$811$	4.72659e9			0.311154			0.155577	−	0.987824i	$-0.450276\pi$
$811$	4.72659e9			0.311154			0.155577	+	0.987824i	$0.450276\pi$
$812$	3.60532e8	+	1.64053e8i	0.0236319	+	0.0107532i
$813$		0			0
$814$	−6.01092e8	+	1.04112e9i	−0.0390621	+	0.0676576i
$815$	4.86198e9	+	8.42119e9i	0.314602	+	0.544907i
$816$		0			0
$817$	−1.84185e9	+	3.19018e9i	−0.118162	+	0.204662i
$818$	1.57286e10			1.00474
$819$		0			0
$820$	−1.22720e10			−0.777260
$821$	1.00016e10	−	1.73232e10i	0.630764	−	1.09251i	−0.356632	−	0.934245i	$-0.616075\pi$
$821$	1.00016e10	−	1.73232e10i	0.630764	−	1.09251i	0.987396	−	0.158270i	$-0.0505915\pi$
$822$		0			0
$823$	−7.69179e9	−	1.33226e10i	−0.480981	−	0.833084i	0.518781	−	0.854907i	$-0.326386\pi$
$823$	−7.69179e9	−	1.33226e10i	−0.480981	−	0.833084i	−0.999762	+	0.0218237i	$0.993053\pi$
$824$	5.17389e7	−	8.96144e7i	0.00322160	−	0.00557998i
$825$		0			0
$826$	1.40703e10	−	1.00485e10i	0.868706	−	0.620397i
$827$	−1.42246e10			−0.874520			−0.437260	−	0.899335i	$-0.644051\pi$
$827$	−1.42246e10			−0.874520			−0.437260	+	0.899335i	$0.644051\pi$
$828$		0			0
$829$	1.08624e10	+	1.88143e10i	0.662194	+	1.14695i	0.980038	+	0.198811i	$0.0637080\pi$
$829$	1.08624e10	+	1.88143e10i	0.662194	+	1.14695i	−0.317843	+	0.948143i	$0.602959\pi$
$830$	4.93261e9	+	8.54353e9i	0.299436	+	0.518638i
$831$		0			0
$832$	−1.98260e9			−0.119344
$833$	1.17226e10	−	2.29267e9i	0.702693	−	0.137431i
$834$		0			0
$835$	−7.58541e9	+	1.31383e10i	−0.450896	+	0.780975i
$836$	9.05555e8	+	1.56847e9i	0.0536035	+	0.0928439i
$837$		0			0
$838$	8.83601e9	−	1.53044e10i	0.518683	−	0.898386i
$839$	1.54623e10			0.903871			0.451935	−	0.892051i	$-0.350734\pi$
$839$	1.54623e10			0.903871			0.451935	+	0.892051i	$0.350734\pi$
$840$		0			0
$841$	−1.72034e10			−0.997304
$842$	1.83982e9	−	3.18666e9i	0.106214	−	0.183969i
$843$		0			0
$844$	4.69352e9	+	8.12942e9i	0.268720	+	0.465437i
$845$	8.04684e8	−	1.39375e9i	0.0458804	−	0.0794672i
$846$		0			0
$847$	−1.59340e9	−	1.64487e10i	−0.0901016	−	0.930121i
$848$	5.34582e9			0.301043
$849$		0			0
$850$	3.46646e8	+	6.00408e8i	0.0193606	+	0.0335336i
$851$	4.43106e8	+	7.67482e8i	0.0246464	+	0.0426889i
$852$		0			0
$853$	−1.80110e10			−0.993608			−0.496804	−	0.867863i	$-0.665493\pi$
$853$	−1.80110e10			−0.993608			−0.496804	+	0.867863i	$0.665493\pi$
$854$	1.73467e10	+	7.89326e9i	0.953046	+	0.433665i
$855$		0			0
$856$	−3.29463e9	+	5.70647e9i	−0.179535	+	0.310964i
$857$	−8.58577e7	−	1.48710e8i	−0.00465958	−	0.00807063i	0.863686	−	0.504030i	$-0.168150\pi$
$857$	−8.58577e7	−	1.48710e8i	−0.00465958	−	0.00807063i	−0.868346	+	0.495959i	$0.834817\pi$
$858$		0			0
$859$	−6.88929e8	+	1.19326e9i	−0.0370850	+	0.0642331i	−0.883972	−	0.467540i	$-0.845141\pi$
$859$	−6.88929e8	+	1.19326e9i	−0.0370850	+	0.0642331i	0.846887	+	0.531773i	$0.178474\pi$
$860$	2.73008e9			0.146363
$861$		0			0
$862$	1.72414e10			0.916847
$863$	4.72302e7	−	8.18052e7i	0.00250140	−	0.00433254i	−0.864772	−	0.502165i	$-0.832537\pi$
$863$	4.72302e7	−	8.18052e7i	0.00250140	−	0.00433254i	0.867273	+	0.497832i	$0.165870\pi$
$864$		0			0
$865$	−1.18962e10	−	2.06048e10i	−0.624958	−	1.08246i
$866$	−7.15334e9	+	1.23899e10i	−0.374280	+	0.648271i
$867$		0			0
$868$	9.86042e8	+	1.01789e10i	0.0511772	+	0.528303i
$869$	−7.10057e9			−0.367049
$870$		0			0
$871$	1.50254e10	+	2.60247e10i	0.770481	+	1.33451i
$872$	5.59380e9	+	9.68875e9i	0.285693	+	0.494835i
$873$		0			0
$874$	1.33509e9			0.0676428
$875$	−1.54520e10	+	1.10353e10i	−0.779752	+	0.556870i
$876$		0			0
$877$	6.86881e9	−	1.18971e10i	0.343861	−	0.595585i	−0.641285	−	0.767303i	$-0.721598\pi$
$877$	6.86881e9	−	1.18971e10i	0.343861	−	0.595585i	0.985146	+	0.171718i	$0.0549317\pi$
$878$	−6.08402e8	−	1.05378e9i	−0.0303361	−	0.0525437i
$879$		0			0
$880$	6.71130e8	−	1.16243e9i	0.0331984	−	0.0575013i
$881$	−1.09605e10			−0.540026			−0.270013	−	0.962857i	$-0.587028\pi$
$881$	−1.09605e10			−0.540026			−0.270013	+	0.962857i	$0.587028\pi$
$882$		0			0
$883$	7.24742e9			0.354259			0.177129	−	0.984188i	$-0.443319\pi$
$883$	7.24742e9			0.354259			0.177129	+	0.984188i	$0.443319\pi$
$884$	−3.51020e9	+	6.07984e9i	−0.170903	+	0.296012i
$885$		0			0
$886$	1.07847e10	+	1.86797e10i	0.520945	+	0.902303i
$887$	5.60771e9	−	9.71283e9i	0.269807	−	0.467319i	−0.699005	−	0.715117i	$-0.746374\pi$
$887$	5.60771e9	−	9.71283e9i	0.269807	−	0.467319i	0.968812	+	0.247798i	$0.0797069\pi$
$888$		0			0
$889$	−2.73927e10	+	1.95629e10i	−1.30761	+	0.933849i
$890$	3.43546e9			0.163350
$891$		0			0
$892$	1.89108e9	+	3.27545e9i	0.0892142	+	0.154523i
$893$	−1.12648e10	−	1.95111e10i	−0.529349	−	0.916859i
$894$		0			0
$895$	3.32427e10			1.54994
$896$	1.83501e8	+	1.89428e9i	0.00852236	+	0.0879765i
$897$		0			0
$898$	−2.15143e9	+	3.72639e9i	−0.0991427	+	0.171720i
$899$	6.00429e8	+	1.03997e9i	0.0275615	+	0.0477379i
$900$		0			0
$901$	9.46482e9	−	1.63935e10i	0.431097	−	0.746683i
$902$	5.97730e9			0.271195
$903$		0			0
$904$	−2.36216e9			−0.106346
$905$	−7.67050e9	+	1.32857e10i	−0.343996	+	0.595819i
$906$		0			0
$907$	3.06125e9	+	5.30224e9i	0.136230	+	0.235957i	0.926067	−	0.377360i	$-0.123168\pi$
$907$	3.06125e9	+	5.30224e9i	0.136230	+	0.235957i	−0.789837	+	0.613317i	$0.789835\pi$
$908$	−1.37297e9	+	2.37805e9i	−0.0608638	+	0.105419i
$909$		0			0
$910$	1.44931e10	+	6.59481e9i	0.637554	+	0.290107i
$911$	−1.72053e10			−0.753960			−0.376980	−	0.926221i	$-0.623037\pi$
$911$	−1.72053e10			−0.753960			−0.376980	+	0.926221i	$0.623037\pi$
$912$		0			0
$913$	−2.40252e9	−	4.16129e9i	−0.104477	−	0.180959i
$914$	2.15517e9	+	3.73287e9i	0.0933621	+	0.161708i
$915$		0			0
$916$	1.76801e10			0.760066
$917$	3.48555e9	+	3.59814e10i	0.149272	+	1.54094i
$918$		0			0
$919$	−1.24295e10	+	2.15285e10i	−0.528261	+	0.914976i	0.471196	+	0.882029i	$0.343823\pi$
$919$	−1.24295e10	+	2.15285e10i	−0.528261	+	0.914976i	−0.999457	+	0.0329469i	$0.989511\pi$
$920$	−4.94735e8	−	8.56907e8i	−0.0209467	−	0.0362807i
$921$		0			0
$922$	2.09756e7	−	3.63309e7i	0.000881367	−	0.00152657i
$923$	−3.24586e10			−1.35870
$924$		0			0
$925$	−7.94585e8			−0.0330099
$926$	−8.73703e8	+	1.51330e9i	−0.0361597	+	0.0626305i
$927$		0			0
$928$	1.11739e8	+	1.93537e8i	0.00458972	+	0.00794963i
$929$	8.79888e9	−	1.52401e10i	0.360058	−	0.623638i	−0.627912	−	0.778284i	$-0.716090\pi$
$929$	8.79888e9	−	1.52401e10i	0.360058	−	0.623638i	0.987970	+	0.154646i	$0.0494237\pi$
$930$		0			0
$931$	1.35485e10	+	1.55495e10i	0.550259	+	0.631528i
$932$	−9.81383e9			−0.397085
$933$		0			0
$934$	−1.39777e9	−	2.42100e9i	−0.0561333	−	0.0972258i
$935$	−2.37648e9	−	4.11618e9i	−0.0950810	−	0.164685i
$936$		0			0
$937$	1.80228e10			0.715703			0.357852	−	0.933778i	$-0.383509\pi$
$937$	1.80228e10			0.715703			0.357852	+	0.933778i	$0.383509\pi$
$938$	2.34748e10	−	1.67648e10i	0.928736	−	0.663269i
$939$		0			0
$940$	−8.34860e9	+	1.44602e10i	−0.327843	+	0.567841i
$941$	1.48058e10	+	2.56444e10i	0.579252	+	1.00329i	0.995565	+	0.0940726i	$0.0299886\pi$
$941$	1.48058e10	+	2.56444e10i	0.579252	+	1.00329i	−0.416313	+	0.909221i	$0.636678\pi$
$942$		0			0
$943$	2.20314e9	−	3.81595e9i	0.0855561	−	0.148187i
$944$	9.75489e9			0.377416
$945$		0			0
$946$	−1.32974e9			−0.0510678
$947$	−1.22262e10	+	2.11764e10i	−0.467806	+	0.810264i	−0.999323	−	0.0367838i	$-0.988289\pi$
$947$	−1.22262e10	+	2.11764e10i	−0.467806	+	0.810264i	0.531517	+	0.847047i	$0.321622\pi$
$948$		0			0
$949$	2.24254e10	+	3.88419e10i	0.851743	+	1.47526i
$950$	−5.98528e8	+	1.03668e9i	−0.0226491	+	0.0392295i
$951$		0			0
$952$	6.13392e9	+	2.79112e9i	0.230414	+	0.104845i
$953$	3.27114e10			1.22426			0.612130	−	0.790757i	$-0.290313\pi$
$953$	3.27114e10			1.22426			0.612130	+	0.790757i	$0.290313\pi$
$954$		0			0
$955$	1.49129e10	+	2.58298e10i	0.554051	+	0.959644i
$956$	−1.10599e10	−	1.91563e10i	−0.409400	−	0.709102i
$957$		0			0
$958$	−3.24018e10			−1.19066
$959$	−2.12651e10	−	9.67626e9i	−0.778578	−	0.354276i
$960$		0			0
$961$	−1.74560e9	+	3.02347e9i	−0.0634473	+	0.109894i
$962$	−4.02306e9	−	6.96815e9i	−0.145695	−	0.252351i
$963$		0			0
$964$	−1.73014e9	+	2.99668e9i	−0.0622029	+	0.107739i
$965$	−5.08201e10			−1.82050
$966$		0			0
$967$	−5.41923e9			−0.192728			−0.0963640	−	0.995346i	$-0.530721\pi$
$967$	−5.41923e9			−0.192728			−0.0963640	+	0.995346i	$0.530721\pi$
$968$	4.66183e9	−	8.07453e9i	0.165193	−	0.286123i
$969$		0			0
$970$	−1.09126e10	−	1.89012e10i	−0.383909	−	0.664950i
$971$	4.41271e9	−	7.64304e9i	0.154681	−	0.267916i	−0.778262	−	0.627940i	$-0.783898\pi$
$971$	4.41271e9	−	7.64304e9i	0.154681	−	0.267916i	0.932943	+	0.360024i	$0.117232\pi$
$972$		0			0
$973$	−9.56247e9	+	6.82916e9i	−0.332794	+	0.237669i
$974$	7.41307e9			0.257064
$975$		0			0
$976$	5.37621e9	+	9.31187e9i	0.185098	+	0.320599i
$977$	−1.63411e10	−	2.83037e10i	−0.560597	−	0.970983i	−0.997444	−	0.0714471i	$-0.977238\pi$
$977$	−1.63411e10	−	2.83037e10i	−0.560597	−	0.970983i	0.436847	−	0.899536i	$-0.356095\pi$
$978$		0			0
$979$	−1.67330e9			−0.0569948
$980$	4.95963e9	−	1.44579e10i	0.168329	−	0.490699i
$981$		0			0
$982$	1.06362e10	−	1.84225e10i	0.358425	−	0.620810i
$983$	1.78173e10	+	3.08604e10i	0.598279	+	1.03625i	0.993075	+	0.117481i	$0.0374818\pi$
$983$	1.78173e10	+	3.08604e10i	0.598279	+	1.03625i	−0.394796	+	0.918769i	$0.629185\pi$
$984$		0			0
$985$	2.27968e10	−	3.94853e10i	0.760060	−	1.31646i
$986$	7.91338e8			0.0262901
$987$		0			0
$988$	−1.21216e10			−0.399863
$989$	−4.90121e8	+	8.48914e8i	−0.0161108	+	0.0279046i
$990$		0			0
$991$	−2.56157e10	−	4.43677e10i	−0.836080	−	1.44813i	−0.893148	−	0.449763i	$-0.851508\pi$
$991$	−2.56157e10	−	4.43677e10i	−0.836080	−	1.44813i	0.0570673	−	0.998370i	$-0.481825\pi$
$992$	−2.88488e9	+	4.99676e9i	−0.0938289	+	0.162516i
$993$		0			0
$994$	3.00423e9	+	3.10128e10i	0.0970245	+	1.00159i
$995$	3.21171e10			1.03361
$996$		0			0
$997$	−1.02337e10	−	1.77252e10i	−0.327038	−	0.566447i	0.654885	−	0.755729i	$-0.272717\pi$
$997$	−1.02337e10	−	1.77252e10i	−0.327038	−	0.566447i	−0.981923	+	0.189282i	$0.939384\pi$
$998$	1.26598e10	+	2.19275e10i	0.403155	+	0.698284i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.a.37.1		2
3.2	odd	2		42.8.e.b.37.1	yes	2
7.4	even	3	inner	126.8.g.a.109.1		2
21.2	odd	6		294.8.a.f.1.1		1
21.5	even	6		294.8.a.e.1.1		1
21.11	odd	6		42.8.e.b.25.1	✓	2
21.17	even	6		294.8.e.l.67.1		2
21.20	even	2		294.8.e.l.79.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.b.25.1	✓	2	21.11	odd	6
42.8.e.b.37.1	yes	2	3.2	odd	2
126.8.g.a.37.1		2	1.1	even	1	trivial
126.8.g.a.109.1		2	7.4	even	3	inner
294.8.a.e.1.1		1	21.5	even	6
294.8.a.f.1.1		1	21.2	odd	6
294.8.e.l.67.1		2	21.17	even	6
294.8.e.l.79.1		2	21.20	even	2

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Elliptic curves over $\Q$
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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	126.8.g.a.37.1

Level	$126$
Weight	$8$
Character	126.37
Analytic conductor	$39.361$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$