LMFDB - Embedded newform 126.6.g.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,6,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, 6, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
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:	$20.2083612964$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.6.g.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-6.00000 - 10.3923i) q^{5} +(59.5000 - 115.181i) q^{7} +64.0000 q^{8} +(-24.0000 + 41.5692i) q^{10} +(-144.000 + 249.415i) q^{11} +737.000 q^{13} +(-518.000 + 24.2487i) q^{14} +(-128.000 - 221.703i) q^{16} +(78.0000 - 135.100i) q^{17} +(-308.500 - 534.338i) q^{19} +192.000 q^{20} +1152.00 q^{22} +(-2298.00 - 3980.25i) q^{23} +(1490.50 - 2581.62i) q^{25} +(-1474.00 - 2553.04i) q^{26} +(1120.00 + 1745.91i) q^{28} -5304.00 q^{29} +(-1256.50 + 2176.32i) q^{31} +(-512.000 + 886.810i) q^{32} -624.000 q^{34} +(-1554.00 + 72.7461i) q^{35} +(-1187.50 - 2056.81i) q^{37} +(-1234.00 + 2137.35i) q^{38} +(-384.000 - 665.108i) q^{40} -14280.0 q^{41} -1579.00 q^{43} +(-2304.00 - 3990.65i) q^{44} +(-9192.00 + 15921.0i) q^{46} +(-8634.00 - 14954.5i) q^{47} +(-9726.50 - 13706.6i) q^{49} -11924.0 q^{50} +(-5896.00 + 10212.2i) q^{52} +(9306.00 - 16118.5i) q^{53} +3456.00 q^{55} +(3808.00 - 7371.61i) q^{56} +(10608.0 + 18373.6i) q^{58} +(-14214.0 + 24619.4i) q^{59} +(-7783.00 - 13480.6i) q^{61} +10052.0 q^{62} +4096.00 q^{64} +(-4422.00 - 7659.13i) q^{65} +(4026.50 - 6974.10i) q^{67} +(1248.00 + 2161.60i) q^{68} +(3360.00 + 5237.72i) q^{70} +13020.0 q^{71} +(25131.5 - 43529.0i) q^{73} +(-4750.00 + 8227.24i) q^{74} +9872.00 q^{76} +(20160.0 + 31426.3i) q^{77} +(-15077.5 - 26115.0i) q^{79} +(-1536.00 + 2660.43i) q^{80} +(28560.0 + 49467.4i) q^{82} +99276.0 q^{83} -1872.00 q^{85} +(3158.00 + 5469.82i) q^{86} +(-9216.00 + 15962.6i) q^{88} +(26052.0 + 45123.4i) q^{89} +(43851.5 - 84888.7i) q^{91} +73536.0 q^{92} +(-34536.0 + 59818.1i) q^{94} +(-3702.00 + 6412.05i) q^{95} +116222. q^{97} +(-28028.0 + 61106.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 16 q^{4} - 12 q^{5} + 119 q^{7} + 128 q^{8} - 48 q^{10} - 288 q^{11} + 1474 q^{13} - 1036 q^{14} - 256 q^{16} + 156 q^{17} - 617 q^{19} + 384 q^{20} + 2304 q^{22} - 4596 q^{23} + 2981 q^{25}+ \cdots - 56056 q^{98}+O(q^{100}) $ 2 * q - 4 * q^2 - 16 * q^4 - 12 * q^5 + 119 * q^7 + 128 * q^8 - 48 * q^10 - 288 * q^11 + 1474 * q^13 - 1036 * q^14 - 256 * q^16 + 156 * q^17 - 617 * q^19 + 384 * q^20 + 2304 * q^22 - 4596 * q^23 + 2981 * q^25 - 2948 * q^26 + 2240 * q^28 - 10608 * q^29 - 2513 * q^31 - 1024 * q^32 - 1248 * q^34 - 3108 * q^35 - 2375 * q^37 - 2468 * q^38 - 768 * q^40 - 28560 * q^41 - 3158 * q^43 - 4608 * q^44 - 18384 * q^46 - 17268 * q^47 - 19453 * q^49 - 23848 * q^50 - 11792 * q^52 + 18612 * q^53 + 6912 * q^55 + 7616 * q^56 + 21216 * q^58 - 28428 * q^59 - 15566 * q^61 + 20104 * q^62 + 8192 * q^64 - 8844 * q^65 + 8053 * q^67 + 2496 * q^68 + 6720 * q^70 + 26040 * q^71 + 50263 * q^73 - 9500 * q^74 + 19744 * q^76 + 40320 * q^77 - 30155 * q^79 - 3072 * q^80 + 57120 * q^82 + 198552 * q^83 - 3744 * q^85 + 6316 * q^86 - 18432 * q^88 + 52104 * q^89 + 87703 * q^91 + 147072 * q^92 - 69072 * q^94 - 7404 * q^95 + 232444 * q^97 - 56056 * q^98

Character values

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

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−6.00000	−	10.3923i	−0.107331	−	0.185903i	0.807357	−	0.590063i	$-0.200897\pi$
$5$	−6.00000	−	10.3923i	−0.107331	−	0.185903i	−0.914688	+	0.404160i	$0.867564\pi$
$6$		0			0
$7$	59.5000	−	115.181i	0.458957	−	0.888459i
$7$	59.5000	−	115.181i	0.458957	−	0.888459i
$8$	64.0000			0.353553
$9$		0			0
$10$	−24.0000	+	41.5692i	−0.0758947	+	0.131453i
$11$	−144.000	+	249.415i	−0.358823	+	0.621500i	−0.987765	−	0.155953i	$-0.950155\pi$
$11$	−144.000	+	249.415i	−0.358823	+	0.621500i	0.628941	+	0.777453i	$0.283489\pi$
$12$		0			0
$13$	737.000			1.20951			0.604755	−	0.796412i	$-0.293271\pi$
$13$	737.000			1.20951			0.604755	+	0.796412i	$0.293271\pi$
$14$	−518.000	+	24.2487i	−0.706333	+	0.0330650i
$15$		0			0
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	78.0000	−	135.100i	0.0654594	−	0.113379i	−0.831438	−	0.555617i	$-0.812482\pi$
$17$	78.0000	−	135.100i	0.0654594	−	0.113379i	0.896898	+	0.442238i	$0.145815\pi$
$18$		0			0
$19$	−308.500	−	534.338i	−0.196052	−	0.339572i	0.751193	−	0.660083i	$-0.229479\pi$
$19$	−308.500	−	534.338i	−0.196052	−	0.339572i	−0.947245	+	0.320511i	$0.896145\pi$
$20$	192.000			0.107331
$21$		0			0
$22$	1152.00			0.507453
$23$	−2298.00	−	3980.25i	−0.905796	−	1.56888i	−0.819845	−	0.572585i	$-0.805940\pi$
$23$	−2298.00	−	3980.25i	−0.905796	−	1.56888i	−0.0859510	−	0.996299i	$-0.527393\pi$
$24$		0			0
$25$	1490.50	−	2581.62i	0.476960	−	0.826119i
$26$	−1474.00	−	2553.04i	−0.427626	−	0.740670i
$27$		0			0
$28$	1120.00	+	1745.91i	0.269975	+	0.420849i
$29$	−5304.00			−1.17114			−0.585570	−	0.810622i	$-0.699129\pi$
$29$	−5304.00			−1.17114			−0.585570	+	0.810622i	$0.699129\pi$
$30$		0			0
$31$	−1256.50	+	2176.32i	−0.234833	+	0.406742i	−0.959224	−	0.282647i	$-0.908788\pi$
$31$	−1256.50	+	2176.32i	−0.234833	+	0.406742i	0.724391	+	0.689389i	$0.242121\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−624.000			−0.0925736
$35$	−1554.00	+	72.7461i	−0.214428	+	0.0100378i
$36$		0			0
$37$	−1187.50	−	2056.81i	−0.142603	−	0.246996i	0.785873	−	0.618388i	$-0.212214\pi$
$37$	−1187.50	−	2056.81i	−0.142603	−	0.246996i	−0.928476	+	0.371392i	$0.878881\pi$
$38$	−1234.00	+	2137.35i	−0.138630	+	0.240114i
$39$		0			0
$40$	−384.000	−	665.108i	−0.0379473	−	0.0657267i
$41$	−14280.0			−1.32669			−0.663344	−	0.748315i	$-0.730863\pi$
$41$	−14280.0			−1.32669			−0.663344	+	0.748315i	$0.730863\pi$
$42$		0			0
$43$	−1579.00			−0.130230			−0.0651150	−	0.997878i	$-0.520741\pi$
$43$	−1579.00			−0.130230			−0.0651150	+	0.997878i	$0.520741\pi$
$44$	−2304.00	−	3990.65i	−0.179412	−	0.310750i
$45$		0			0
$46$	−9192.00	+	15921.0i	−0.640495	+	1.10937i
$47$	−8634.00	−	14954.5i	−0.570121	−	0.987479i	−0.996553	−	0.0829595i	$-0.973563\pi$
$47$	−8634.00	−	14954.5i	−0.570121	−	0.987479i	0.426431	−	0.904520i	$-0.359771\pi$
$48$		0			0
$49$	−9726.50	−	13706.6i	−0.578717	−	0.815528i
$50$	−11924.0			−0.674523
$51$		0			0
$52$	−5896.00	+	10212.2i	−0.302377	+	0.523733i
$53$	9306.00	−	16118.5i	0.455065	−	0.788196i	−0.543627	−	0.839327i	$-0.682949\pi$
$53$	9306.00	−	16118.5i	0.455065	−	0.788196i	0.998692	+	0.0511313i	$0.0162827\pi$
$54$		0			0
$55$	3456.00			0.154052
$56$	3808.00	−	7371.61i	0.162266	−	0.314118i
$57$		0			0
$58$	10608.0	+	18373.6i	0.414060	+	0.717173i
$59$	−14214.0	+	24619.4i	−0.531602	+	0.920761i	0.467718	+	0.883878i	$0.345076\pi$
$59$	−14214.0	+	24619.4i	−0.531602	+	0.920761i	−0.999320	+	0.0368832i	$0.988257\pi$
$60$		0			0
$61$	−7783.00	−	13480.6i	−0.267807	−	0.463856i	0.700488	−	0.713664i	$-0.252966\pi$
$61$	−7783.00	−	13480.6i	−0.267807	−	0.463856i	−0.968295	+	0.249808i	$0.919632\pi$
$62$	10052.0			0.332103
$63$		0			0
$64$	4096.00			0.125000
$65$	−4422.00	−	7659.13i	−0.129818	−	0.224852i
$66$		0			0
$67$	4026.50	−	6974.10i	0.109582	−	0.189802i	−0.806019	−	0.591890i	$-0.798382\pi$
$67$	4026.50	−	6974.10i	0.109582	−	0.189802i	0.915601	+	0.402088i	$0.131715\pi$
$68$	1248.00	+	2161.60i	0.0327297	+	0.0566895i
$69$		0			0
$70$	3360.00	+	5237.72i	0.0819585	+	0.127761i
$71$	13020.0			0.306524			0.153262	−	0.988186i	$-0.451022\pi$
$71$	13020.0			0.306524			0.153262	+	0.988186i	$0.451022\pi$
$72$		0			0
$73$	25131.5	−	43529.0i	0.551965	−	0.956031i	−0.446168	−	0.894949i	$-0.647212\pi$
$73$	25131.5	−	43529.0i	0.551965	−	0.956031i	0.998133	−	0.0610816i	$-0.0194550\pi$
$74$	−4750.00	+	8227.24i	−0.100836	+	0.174653i
$75$		0			0
$76$	9872.00			0.196052
$77$	20160.0	+	31426.3i	0.387493	+	0.604042i
$78$		0			0
$79$	−15077.5	−	26115.0i	−0.271808	−	0.470785i	0.697517	−	0.716568i	$-0.254288\pi$
$79$	−15077.5	−	26115.0i	−0.271808	−	0.470785i	−0.969325	+	0.245784i	$0.920955\pi$
$80$	−1536.00	+	2660.43i	−0.0268328	+	0.0464758i
$81$		0			0
$82$	28560.0	+	49467.4i	0.469055	+	0.812427i
$83$	99276.0			1.58179			0.790895	−	0.611951i	$-0.209615\pi$
$83$	99276.0			1.58179			0.790895	+	0.611951i	$0.209615\pi$
$84$		0			0
$85$	−1872.00			−0.0281034
$86$	3158.00	+	5469.82i	0.0460433	+	0.0797493i
$87$		0			0
$88$	−9216.00	+	15962.6i	−0.126863	+	0.219734i
$89$	26052.0	+	45123.4i	0.348631	+	0.603847i	0.986007	−	0.166707i	$-0.0533133\pi$
$89$	26052.0	+	45123.4i	0.348631	+	0.603847i	−0.637375	+	0.770553i	$0.719980\pi$
$90$		0			0
$91$	43851.5	−	84888.7i	0.555112	−	1.07460i
$92$	73536.0			0.905796
$93$		0			0
$94$	−34536.0	+	59818.1i	−0.403137	+	0.698253i
$95$	−3702.00	+	6412.05i	−0.0420850	+	0.0728934i
$96$		0			0
$97$	116222.			1.25418			0.627089	−	0.778948i	$-0.284246\pi$
$97$	116222.			1.25418			0.627089	+	0.778948i	$0.284246\pi$
$98$	−28028.0	+	61106.8i	−0.294800	+	0.642723i
$99$		0			0
$100$	23848.0	+	41305.9i	0.238480	+	0.413059i
$101$	−6432.00	+	11140.6i	−0.0627397	+	0.108668i	−0.895689	−	0.444681i	$-0.853317\pi$
$101$	−6432.00	+	11140.6i	−0.0627397	+	0.108668i	0.832949	+	0.553349i	$0.186650\pi$
$102$		0			0
$103$	−90824.5	−	157313.i	−0.843548	−	1.46107i	−0.886876	−	0.462008i	$-0.847129\pi$
$103$	−90824.5	−	157313.i	−0.843548	−	1.46107i	0.0433277	−	0.999061i	$-0.486204\pi$
$104$	47168.0			0.427626
$105$		0			0
$106$	−74448.0			−0.643559
$107$	60054.0	+	104017.i	0.507087	+	0.878300i	0.999966	+	0.00820281i	$0.00261107\pi$
$107$	60054.0	+	104017.i	0.507087	+	0.878300i	−0.492879	+	0.870098i	$0.664056\pi$
$108$		0			0
$109$	−68852.5	+	119256.i	−0.555077	+	0.961422i	0.442820	+	0.896610i	$0.353978\pi$
$109$	−68852.5	+	119256.i	−0.555077	+	0.961422i	−0.997898	+	0.0648117i	$0.979355\pi$
$110$	−6912.00	−	11971.9i	−0.0544656	−	0.0943371i
$111$		0			0
$112$	−33152.0	+	1551.92i	−0.249727	+	0.0116902i
$113$	145740.			1.07370			0.536850	−	0.843678i	$-0.319614\pi$
$113$	145740.			1.07370			0.536850	+	0.843678i	$0.319614\pi$
$114$		0			0
$115$	−27576.0	+	47763.0i	−0.194440	+	0.336781i
$116$	42432.0	−	73494.4i	0.292785	−	0.507118i
$117$		0			0
$118$	113712.			0.751798
$119$	−10920.0	−	17022.6i	−0.0706896	−	0.110194i
$120$		0			0
$121$	39053.5	+	67642.6i	0.242492	+	0.420008i
$122$	−31132.0	+	53922.2i	−0.189368	+	0.327996i
$123$		0			0
$124$	−20104.0	−	34821.1i	−0.117416	−	0.203371i
$125$	−73272.0			−0.419433
$126$		0			0
$127$	−128731.			−0.708229			−0.354115	−	0.935202i	$-0.615218\pi$
$127$	−128731.			−0.708229			−0.354115	+	0.935202i	$0.615218\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−17688.0	+	30636.5i	−0.0917953	+	0.158994i
$131$	−162300.	−	281112.i	−0.826305	−	1.43120i	−0.900918	−	0.433989i	$-0.857106\pi$
$131$	−162300.	−	281112.i	−0.826305	−	1.43120i	0.0746132	−	0.997213i	$-0.476228\pi$
$132$		0			0
$133$	−79901.5	+	3740.36i	−0.391675	+	0.0183352i
$134$	−32212.0			−0.154973
$135$		0			0
$136$	4992.00	−	8646.40i	0.0231434	−	0.0400856i
$137$	51528.0	−	89249.1i	0.234553	−	0.406259i	−0.724589	−	0.689181i	$-0.757971\pi$
$137$	51528.0	−	89249.1i	0.234553	−	0.406259i	0.959143	+	0.282922i	$0.0913039\pi$
$138$		0			0
$139$	−20263.0			−0.0889543			−0.0444771	−	0.999010i	$-0.514162\pi$
$139$	−20263.0			−0.0889543			−0.0444771	+	0.999010i	$0.514162\pi$
$140$	11424.0	−	22114.8i	0.0492604	−	0.0953594i
$141$		0			0
$142$	−26040.0	−	45102.6i	−0.108373	−	0.187707i
$143$	−106128.	+	183819.i	−0.434000	+	0.751710i
$144$		0			0
$145$	31824.0	+	55120.8i	0.125700	+	0.217719i
$146$	−201052.			−0.780596
$147$		0			0
$148$	38000.0			0.142603
$149$	75192.0	+	130236.i	0.277464	+	0.480581i	0.970754	−	0.240078i	$-0.0771729\pi$
$149$	75192.0	+	130236.i	0.277464	+	0.480581i	−0.693290	+	0.720659i	$0.743840\pi$
$150$		0			0
$151$	−49390.0	+	85546.0i	−0.176277	+	0.305321i	−0.940603	−	0.339510i	$-0.889739\pi$
$151$	−49390.0	+	85546.0i	−0.176277	+	0.305321i	0.764325	+	0.644831i	$0.223072\pi$
$152$	−19744.0	−	34197.6i	−0.0693148	−	0.120057i
$153$		0			0
$154$	68544.0	−	132689.i	0.232899	−	0.450851i
$155$	30156.0			0.100819
$156$		0			0
$157$	26177.0	−	45339.9i	0.0847561	−	0.146802i	−0.820531	−	0.571602i	$-0.806322\pi$
$157$	26177.0	−	45339.9i	0.0847561	−	0.146802i	0.905287	+	0.424800i	$0.139656\pi$
$158$	−60310.0	+	104460.i	−0.192197	+	0.332895i
$159$		0			0
$160$	12288.0			0.0379473
$161$	−595182.	+	27861.8i	−1.80961	+	0.0847118i
$162$		0			0
$163$	243620.	+	421962.i	0.718198	+	1.24395i	0.961713	+	0.274058i	$0.0883659\pi$
$163$	243620.	+	421962.i	0.718198	+	1.24395i	−0.243516	+	0.969897i	$0.578301\pi$
$164$	114240.	−	197869.i	0.331672	−	0.574472i
$165$		0			0
$166$	−198552.	−	343902.i	−0.559247	−	0.968645i
$167$	−199812.			−0.554409			−0.277205	−	0.960811i	$-0.589408\pi$
$167$	−199812.			−0.554409			−0.277205	+	0.960811i	$0.589408\pi$
$168$		0			0
$169$	171876.			0.462912
$170$	3744.00	+	6484.80i	0.00993604	+	0.0172097i
$171$		0			0
$172$	12632.0	−	21879.3i	0.0325575	−	0.0563912i
$173$	−368118.	−	637599.i	−0.935130	−	1.61969i	−0.774403	−	0.632693i	$-0.781949\pi$
$173$	−368118.	−	637599.i	−0.935130	−	1.61969i	−0.160727	−	0.986999i	$-0.551384\pi$
$174$		0			0
$175$	−208670.	−	325284.i	−0.515068	−	0.802912i
$176$	73728.0			0.179412
$177$		0			0
$178$	104208.	−	180494.i	0.246519	−	0.426984i
$179$	123114.	−	213240.i	0.287194	−	0.497434i	−0.685945	−	0.727653i	$-0.740611\pi$
$179$	123114.	−	213240.i	0.287194	−	0.497434i	0.973139	+	0.230219i	$0.0739443\pi$
$180$		0			0
$181$	800225.			1.81558			0.907791	−	0.419424i	$-0.137768\pi$
$181$	800225.			1.81558			0.907791	+	0.419424i	$0.137768\pi$
$182$	−381766.	+	17871.3i	−0.854316	+	0.0399924i
$183$		0			0
$184$	−147072.	−	254736.i	−0.320247	−	0.554685i
$185$	−14250.0	+	24681.7i	−0.0306116	+	0.0530208i
$186$		0			0
$187$	22464.0	+	38908.8i	0.0469768	+	0.0813661i
$188$	276288.			0.570121
$189$		0			0
$190$	29616.0			0.0595172
$191$	−193014.	−	334310.i	−0.382829	−	0.663080i	0.608636	−	0.793450i	$-0.291717\pi$
$191$	−193014.	−	334310.i	−0.382829	−	0.663080i	−0.991465	+	0.130369i	$0.958384\pi$
$192$		0			0
$193$	−248532.	+	430469.i	−0.480273	+	0.831857i	−0.999744	−	0.0226309i	$-0.992796\pi$
$193$	−248532.	+	430469.i	−0.480273	+	0.831857i	0.519471	+	0.854488i	$0.326129\pi$
$194$	−232444.	−	402605.i	−0.443419	−	0.768024i
$195$		0			0
$196$	267736.	−	25121.7i	0.497813	−	0.0467098i
$197$	641028.			1.17682			0.588412	−	0.808561i	$-0.299753\pi$
$197$	641028.			1.17682			0.588412	+	0.808561i	$0.299753\pi$
$198$		0			0
$199$	−158194.	+	274000.i	−0.283177	+	0.490476i	−0.972165	−	0.234296i	$-0.924722\pi$
$199$	−158194.	+	274000.i	−0.283177	+	0.490476i	0.688989	+	0.724772i	$0.258055\pi$
$200$	95392.0	−	165224.i	0.168631	−	0.292077i
$201$		0			0
$202$	51456.0			0.0887274
$203$	−315588.	+	610922.i	−0.537502	+	1.04051i
$204$		0			0
$205$	85680.0	+	148402.i	0.142395	+	0.246635i
$206$	−363298.	+	629251.i	−0.596479	+	1.03313i
$207$		0			0
$208$	−94336.0	−	163395.i	−0.151189	−	0.261866i
$209$	177696.			0.281392
$210$		0			0
$211$	−557776.			−0.862489			−0.431245	−	0.902235i	$-0.641925\pi$
$211$	−557776.			−0.862489			−0.431245	+	0.902235i	$0.641925\pi$
$212$	148896.	+	257895.i	0.227532	+	0.394098i
$213$		0			0
$214$	240216.	−	416066.i	0.358565	−	0.621052i
$215$	9474.00	+	16409.4i	0.0139777	+	0.0242102i
$216$		0			0
$217$	175910.	+	274217.i	0.253595	+	0.395316i
$218$	550820.			0.784998
$219$		0			0
$220$	−27648.0	+	47887.7i	−0.0385130	+	0.0667064i
$221$	57486.0	−	99568.7i	0.0791738	−	0.137133i
$222$		0			0
$223$	−1.26368e6			−1.70166			−0.850832	−	0.525439i	$-0.823901\pi$
$223$	−1.26368e6			−1.70166			−0.850832	+	0.525439i	$0.823901\pi$
$224$	71680.0	+	111738.i	0.0954504	+	0.148793i
$225$		0			0
$226$	−291480.	−	504858.i	−0.379610	−	0.657504i
$227$	−274380.	+	475240.i	−0.353417	+	0.612137i	−0.986846	−	0.161665i	$-0.948314\pi$
$227$	−274380.	+	475240.i	−0.353417	+	0.612137i	0.633428	+	0.773801i	$0.281647\pi$
$228$		0			0
$229$	500968.	+	867701.i	0.631278	+	1.09341i	0.987291	+	0.158925i	$0.0508027\pi$
$229$	500968.	+	867701.i	0.631278	+	1.09341i	−0.356012	+	0.934481i	$0.615864\pi$
$230$	220608.			0.274980
$231$		0			0
$232$	−339456.			−0.414060
$233$	754542.	+	1.30691e6i	0.910529	+	1.57708i	0.813319	+	0.581818i	$0.197658\pi$
$233$	754542.	+	1.30691e6i	0.910529	+	1.57708i	0.0972096	+	0.995264i	$0.469008\pi$
$234$		0			0
$235$	−103608.	+	179454.i	−0.122384	+	0.211975i
$236$	−227424.	−	393910.i	−0.265801	−	0.460380i
$237$		0			0
$238$	−37128.0	+	71873.2i	−0.0424873	+	0.0822478i
$239$	1.50559e6			1.70495			0.852477	−	0.522765i	$-0.175100\pi$
$239$	1.50559e6			1.70495			0.852477	+	0.522765i	$0.175100\pi$
$240$		0			0
$241$	−75679.0	+	131080.i	−0.0839330	+	0.145376i	−0.904936	−	0.425548i	$-0.860082\pi$
$241$	−75679.0	+	131080.i	−0.0839330	+	0.145376i	0.821003	+	0.570924i	$0.193415\pi$
$242$	156214.	−	270571.i	0.171467	−	0.296990i
$243$		0			0
$244$	249056.			0.267807
$245$	−84084.0	+	183320.i	−0.0894949	+	0.195117i
$246$		0			0
$247$	−227364.	−	393807.i	−0.237127	−	0.410715i
$248$	−80416.0	+	139285.i	−0.0830258	+	0.143805i
$249$		0			0
$250$	146544.	+	253822.i	0.148292	+	0.256849i
$251$	936756.			0.938517			0.469259	−	0.883061i	$-0.344521\pi$
$251$	936756.			0.938517			0.469259	+	0.883061i	$0.344521\pi$
$252$		0			0
$253$	1.32365e6			1.30008
$254$	257462.	+	445937.i	0.250397	+	0.433700i
$255$		0			0
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−639018.	−	1.10681e6i	−0.603504	−	1.04530i	−0.992286	−	0.123970i	$-0.960437\pi$
$257$	−639018.	−	1.10681e6i	−0.603504	−	1.04530i	0.388782	−	0.921330i	$-0.372896\pi$
$258$		0			0
$259$	−307562.	+	14397.7i	−0.284894	+	0.0133365i
$260$	141504.			0.129818
$261$		0			0
$262$	−649200.	+	1.12445e6i	−0.584286	+	1.01201i
$263$	856692.	−	1.48383e6i	0.763722	−	1.32281i	−0.177198	−	0.984175i	$-0.556703\pi$
$263$	856692.	−	1.48383e6i	0.763722	−	1.32281i	0.940920	−	0.338630i	$-0.109964\pi$
$264$		0			0
$265$	−223344.			−0.195371
$266$	172760.	+	269306.i	0.149706	+	0.233369i
$267$		0			0
$268$	64424.0	+	111586.i	0.0547912	+	0.0949011i
$269$	−1.00982e6	+	1.74907e6i	−0.850873	+	1.47376i	0.0295476	+	0.999563i	$0.490593\pi$
$269$	−1.00982e6	+	1.74907e6i	−0.850873	+	1.47376i	−0.880421	+	0.474193i	$0.842740\pi$
$270$		0			0
$271$	−743698.	−	1.28812e6i	−0.615139	−	1.06545i	−0.990360	−	0.138517i	$-0.955766\pi$
$271$	−743698.	−	1.28812e6i	−0.615139	−	1.06545i	0.375221	−	0.926935i	$-0.377567\pi$
$272$	−39936.0			−0.0327297
$273$		0			0
$274$	−412224.			−0.331709
$275$	429264.	+	743507.i	0.342289	+	0.592862i
$276$		0			0
$277$	320020.	−	554290.i	0.250598	−	0.434048i	−0.713093	−	0.701070i	$-0.752706\pi$
$277$	320020.	−	554290.i	0.250598	−	0.434048i	0.963691	+	0.267022i	$0.0860395\pi$
$278$	40526.0	+	70193.1i	0.0314501	+	0.0544731i
$279$		0			0
$280$	−99456.0	+	4655.75i	−0.0758116	+	0.00354891i
$281$	1.64063e6			1.23949			0.619747	−	0.784802i	$-0.287235\pi$
$281$	1.64063e6			1.23949			0.619747	+	0.784802i	$0.287235\pi$
$282$		0			0
$283$	1.25895e6	−	2.18056e6i	0.934419	−	1.61846i	0.158752	−	0.987319i	$-0.449253\pi$
$283$	1.25895e6	−	2.18056e6i	0.934419	−	1.61846i	0.775667	−	0.631142i	$-0.217414\pi$
$284$	−104160.	+	180410.i	−0.0766311	+	0.132729i
$285$		0			0
$286$	849024.			0.613769
$287$	−849660.	+	1.64479e6i	−0.608892	+	1.17871i
$288$		0			0
$289$	697760.	+	1.20856e6i	0.491430	+	0.851182i
$290$	127296.	−	220483.i	0.0888832	−	0.153950i
$291$		0			0
$292$	402104.	+	696465.i	0.275982	+	0.478015i
$293$	1.53190e6			1.04246			0.521231	−	0.853416i	$-0.325473\pi$
$293$	1.53190e6			1.04246			0.521231	+	0.853416i	$0.325473\pi$
$294$		0			0
$295$	341136.			0.228230
$296$	−76000.0	−	131636.i	−0.0504178	−	0.0873263i
$297$		0			0
$298$	300768.	−	520945.i	0.196196	−	0.339822i
$299$	−1.69363e6	−	2.93345e6i	−1.09557	−	1.89758i
$300$		0			0
$301$	−93950.5	+	181871.i	−0.0597699	+	0.115704i
$302$	395120.			0.249294
$303$		0			0
$304$	−78976.0	+	136790.i	−0.0490130	+	0.0848930i
$305$	−93396.0	+	161767.i	−0.0574882	+	0.0995725i
$306$		0			0
$307$	−2.23931e6			−1.35603			−0.678013	−	0.735050i	$-0.737159\pi$
$307$	−2.23931e6			−1.35603			−0.678013	+	0.735050i	$0.737159\pi$
$308$	−596736.	+	27934.5i	−0.358431	+	0.0167789i
$309$		0			0
$310$	−60312.0	−	104463.i	−0.0356451	−	0.0617391i
$311$	−968676.	+	1.67780e6i	−0.567907	+	0.983645i	0.428865	+	0.903368i	$0.358914\pi$
$311$	−968676.	+	1.67780e6i	−0.567907	+	0.983645i	−0.996773	+	0.0802761i	$0.974420\pi$
$312$		0			0
$313$	658326.	+	1.14025e6i	0.379822	+	0.657872i	0.991036	−	0.133594i	$-0.0426518\pi$
$313$	658326.	+	1.14025e6i	0.379822	+	0.657872i	−0.611214	+	0.791466i	$0.709318\pi$
$314$	−209416.			−0.119863
$315$		0			0
$316$	482480.			0.271808
$317$	−1.37869e6	−	2.38796e6i	−0.770582	−	1.33469i	−0.937244	−	0.348674i	$-0.886632\pi$
$317$	−1.37869e6	−	2.38796e6i	−0.770582	−	1.33469i	0.166662	−	0.986014i	$-0.446701\pi$
$318$		0			0
$319$	763776.	−	1.32290e6i	0.420232	−	0.727863i
$320$	−24576.0	−	42566.9i	−0.0134164	−	0.0232379i
$321$		0			0
$322$	1.28688e6	+	2.00605e6i	0.691669	+	1.07821i
$323$	−96252.0			−0.0513338
$324$		0			0
$325$	1.09850e6	−	1.90266e6i	0.576887	−	0.999198i
$326$	974480.	−	1.68785e6i	0.507842	−	0.879609i
$327$		0			0
$328$	−913920.			−0.469055
$329$	−2.23621e6	+	104682.i	−1.13900	+	0.0533189i
$330$		0			0
$331$	−1.49407e6	−	2.58781e6i	−0.749551	−	1.29826i	−0.948038	−	0.318157i	$-0.896936\pi$
$331$	−1.49407e6	−	2.58781e6i	−0.749551	−	1.29826i	0.198487	−	0.980104i	$-0.436397\pi$
$332$	−794208.	+	1.37561e6i	−0.395448	+	0.684935i
$333$		0			0
$334$	399624.	+	692169.i	0.196013	+	0.339505i
$335$	−96636.0			−0.0470465
$336$		0			0
$337$	2.34865e6			1.12653			0.563265	−	0.826276i	$-0.309545\pi$
$337$	2.34865e6			1.12653			0.563265	+	0.826276i	$0.309545\pi$
$338$	−343752.	−	595396.i	−0.163664	−	0.283475i
$339$		0			0
$340$	14976.0	−	25939.2i	0.00702584	−	0.0121691i
$341$	−361872.	−	626781.i	−0.168527	−	0.291897i
$342$		0			0
$343$	−2.15747e6	+	304770.i	−0.990169	+	0.139874i
$344$	−101056.			−0.0460433
$345$		0			0
$346$	−1.47247e6	+	2.55040e6i	−0.661236	+	1.14530i
$347$	−255306.	+	442203.i	−0.113825	+	0.197151i	−0.917309	−	0.398175i	$-0.869644\pi$
$347$	−255306.	+	442203.i	−0.113825	+	0.197151i	0.803484	+	0.595326i	$0.202977\pi$
$348$		0			0
$349$	−1.30031e6			−0.571455			−0.285727	−	0.958311i	$-0.592235\pi$
$349$	−1.30031e6			−0.571455			−0.285727	+	0.958311i	$0.592235\pi$
$350$	−709478.	+	1.37342e6i	−0.309577	+	0.599286i
$351$		0			0
$352$	−147456.	−	255401.i	−0.0634316	−	0.109867i
$353$	532662.	−	922598.i	0.227518	−	0.394072i	−0.729554	−	0.683923i	$-0.760272\pi$
$353$	532662.	−	922598.i	0.227518	−	0.394072i	0.957072	+	0.289851i	$0.0936058\pi$
$354$		0			0
$355$	−78120.0	−	135308.i	−0.0328997	−	0.0569839i
$356$	−833664.			−0.348631
$357$		0			0
$358$	−984912.			−0.406153
$359$	563580.	+	976149.i	0.230791	+	0.399742i	0.958041	−	0.286631i	$-0.0925352\pi$
$359$	563580.	+	976149.i	0.230791	+	0.399742i	−0.727250	+	0.686373i	$0.759202\pi$
$360$		0			0
$361$	1.04770e6	−	1.81468e6i	0.423127	−	0.732878i
$362$	−1.60045e6	−	2.77206e6i	−0.641905	−	1.11181i
$363$		0			0
$364$	825440.	+	1.28673e6i	0.326537	+	0.509020i
$365$	−603156.			−0.236972
$366$		0			0
$367$	−34301.5	+	59411.9i	−0.0132938	+	0.0230255i	−0.872596	−	0.488443i	$-0.837565\pi$
$367$	−34301.5	+	59411.9i	−0.0132938	+	0.0230255i	0.859302	+	0.511469i	$0.170898\pi$
$368$	−588288.	+	1.01894e6i	−0.226449	+	0.392221i
$369$		0			0
$370$	114000.			0.0432913
$371$	−1.30284e6	−	2.03093e6i	−0.491424	−	0.766054i
$372$		0			0
$373$	1.65095e6	+	2.85954e6i	0.614417	+	1.06420i	0.990487	+	0.137610i	$0.0439419\pi$
$373$	1.65095e6	+	2.85954e6i	0.614417	+	1.06420i	−0.376070	+	0.926591i	$0.622725\pi$
$374$	89856.0	−	155635.i	0.0332176	−	0.0575345i
$375$		0			0
$376$	−552576.	−	957090.i	−0.201568	−	0.349127i
$377$	−3.90905e6			−1.41650
$378$		0			0
$379$	−3.98509e6			−1.42508			−0.712542	−	0.701630i	$-0.752456\pi$
$379$	−3.98509e6			−1.42508			−0.712542	+	0.701630i	$0.752456\pi$
$380$	−59232.0	−	102593.i	−0.0210425	−	0.0364467i
$381$		0			0
$382$	−772056.	+	1.33724e6i	−0.270701	+	0.468868i
$383$	−1.44003e6	−	2.49421e6i	−0.501620	−	0.868831i	−0.999998	−	0.00187131i	$-0.999404\pi$
$383$	−1.44003e6	−	2.49421e6i	−0.501620	−	0.868831i	0.498379	−	0.866960i	$-0.333929\pi$
$384$		0			0
$385$	205632.	−	398067.i	0.0707032	−	0.136869i
$386$	1.98825e6			0.679209
$387$		0			0
$388$	−929776.	+	1.61042e6i	−0.313544	+	0.543075i
$389$	1.63719e6	−	2.83570e6i	0.548561	−	0.950136i	−0.449812	−	0.893123i	$-0.648509\pi$
$389$	1.63719e6	−	2.83570e6i	0.548561	−	0.950136i	0.998373	−	0.0570127i	$-0.0181576\pi$
$390$		0			0
$391$	−716976.			−0.237172
$392$	−622496.	−	877221.i	−0.204607	−	0.288333i
$393$		0			0
$394$	−1.28206e6	−	2.22059e6i	−0.416070	−	0.720654i
$395$	−180930.	+	313380.i	−0.0583469	+	0.101060i
$396$		0			0
$397$	843018.	+	1.46015e6i	0.268448	+	0.464966i	0.968461	−	0.249164i	$-0.0801558\pi$
$397$	843018.	+	1.46015e6i	0.268448	+	0.464966i	−0.700013	+	0.714130i	$0.746822\pi$
$398$	1.26555e6			0.400472
$399$		0			0
$400$	−763136.			−0.238480
$401$	1.38584e6	+	2.40034e6i	0.430379	+	0.745439i	0.996906	−	0.0786045i	$-0.0250464\pi$
$401$	1.38584e6	+	2.40034e6i	0.430379	+	0.745439i	−0.566526	+	0.824044i	$0.691713\pi$
$402$		0			0
$403$	−926041.	+	1.60395e6i	−0.284032	+	0.491958i
$404$	−102912.	−	178249.i	−0.0313699	−	0.0543342i
$405$		0			0
$406$	2.74747e6	−	128615.i	0.827215	−	0.0387237i
$407$	684000.			0.204677
$408$		0			0
$409$	1.31110e6	−	2.27089e6i	0.387550	−	0.671256i	−0.604570	−	0.796552i	$-0.706655\pi$
$409$	1.31110e6	−	2.27089e6i	0.387550	−	0.671256i	0.992119	+	0.125297i	$0.0399882\pi$
$410$	342720.	−	593608.i	0.100688	−	0.174398i
$411$		0			0
$412$	2.90638e6			0.843548
$413$	1.98996e6	+	3.10204e6i	0.574076	+	0.894896i
$414$		0			0
$415$	−595656.	−	1.03171e6i	−0.169776	−	0.294060i
$416$	−377344.	+	653579.i	−0.106907	+	0.185167i
$417$		0			0
$418$	−355392.	−	615557.i	−0.0994871	−	0.172317i
$419$	1.50802e6			0.419634			0.209817	−	0.977741i	$-0.432713\pi$
$419$	1.50802e6			0.419634			0.209817	+	0.977741i	$0.432713\pi$
$420$		0			0
$421$	1.93085e6			0.530938			0.265469	−	0.964119i	$-0.414473\pi$
$421$	1.93085e6			0.530938			0.265469	+	0.964119i	$0.414473\pi$
$422$	1.11555e6	+	1.93219e6i	0.304936	+	0.528165i
$423$		0			0
$424$	595584.	−	1.03158e6i	0.160890	−	0.278669i
$425$	−232518.	−	402733.i	−0.0624431	−	0.108155i
$426$		0			0
$427$	−2.01580e6	+	94363.9i	−0.535029	+	0.0250459i
$428$	−1.92173e6			−0.507087
$429$		0			0
$430$	37896.0	−	65637.8i	0.00988376	−	0.0171192i
$431$	−844098.	+	1.46202e6i	−0.218877	+	0.379106i	−0.954465	−	0.298323i	$-0.903573\pi$
$431$	−844098.	+	1.46202e6i	−0.218877	+	0.379106i	0.735588	+	0.677429i	$0.236906\pi$
$432$		0			0
$433$	−3.70763e6			−0.950335			−0.475167	−	0.879895i	$-0.657612\pi$
$433$	−3.70763e6			−0.950335			−0.475167	+	0.879895i	$0.657612\pi$
$434$	598094.	−	1.15780e6i	0.152421	−	0.295060i
$435$		0			0
$436$	−1.10164e6	−	1.90810e6i	−0.277539	−	0.480711i
$437$	−1.41787e6	+	2.45582e6i	−0.355166	+	0.615166i
$438$		0			0
$439$	1.86534e6	+	3.23087e6i	0.461952	+	0.800125i	0.999058	−	0.0433899i	$-0.0138158\pi$
$439$	1.86534e6	+	3.23087e6i	0.461952	+	0.800125i	−0.537106	+	0.843515i	$0.680482\pi$
$440$	221184.			0.0544656
$441$		0			0
$442$	−459888.			−0.111969
$443$	1.36419e6	+	2.36285e6i	0.330267	+	0.572040i	0.982564	−	0.185924i	$-0.0595278\pi$
$443$	1.36419e6	+	2.36285e6i	0.330267	+	0.572040i	−0.652297	+	0.757964i	$0.726194\pi$
$444$		0			0
$445$	312624.	−	541481.i	0.0748380	−	0.129623i
$446$	2.52735e6	+	4.37750e6i	0.601629	+	1.04205i
$447$		0			0
$448$	243712.	−	471783.i	0.0573696	−	0.111057i
$449$	6.67201e6			1.56186			0.780928	−	0.624621i	$-0.214747\pi$
$449$	6.67201e6			1.56186			0.780928	+	0.624621i	$0.214747\pi$
$450$		0			0
$451$	2.05632e6	−	3.56165e6i	0.476046	−	0.824537i
$452$	−1.16592e6	+	2.01943e6i	−0.268425	+	0.464925i
$453$		0			0
$454$	2.19504e6			0.499808
$455$	−1.14530e6	+	53613.9i	−0.259352	+	0.0121408i
$456$		0			0
$457$	3.37001e6	+	5.83703e6i	0.754816	+	1.30738i	0.945466	+	0.325721i	$0.105607\pi$
$457$	3.37001e6	+	5.83703e6i	0.754816	+	1.30738i	−0.190650	+	0.981658i	$0.561060\pi$
$458$	2.00387e6	−	3.47080e6i	0.446381	−	0.773155i
$459$		0			0
$460$	−441216.	−	764209.i	−0.0972202	−	0.168390i
$461$	2.22211e6			0.486983			0.243491	−	0.969903i	$-0.421707\pi$
$461$	2.22211e6			0.486983			0.243491	+	0.969903i	$0.421707\pi$
$462$		0			0
$463$	7.74595e6			1.67928			0.839638	−	0.543146i	$-0.182767\pi$
$463$	7.74595e6			1.67928			0.839638	+	0.543146i	$0.182767\pi$
$464$	678912.	+	1.17591e6i	0.146392	+	0.253559i
$465$		0			0
$466$	3.01817e6	−	5.22762e6i	0.643841	−	1.11517i
$467$	3.71761e6	+	6.43908e6i	0.788808	+	1.36626i	0.926698	+	0.375808i	$0.122635\pi$
$467$	3.71761e6	+	6.43908e6i	0.788808	+	1.36626i	−0.137890	+	0.990448i	$0.544032\pi$
$468$		0			0
$469$	−563710.	−	878737.i	−0.118338	−	0.184470i
$470$	828864.			0.173077
$471$		0			0
$472$	−909696.	+	1.57564e6i	−0.187950	+	0.325538i
$473$	227376.	−	393827.i	0.0467296	−	0.0809380i
$474$		0			0
$475$	−1.83928e6			−0.374036
$476$	323232.	−	15131.2i	0.0653878	−	0.00306095i
$477$		0			0
$478$	−3.01118e6	−	5.21552e6i	−0.602792	−	1.04407i
$479$	4.11652e6	−	7.13003e6i	0.819769	−	1.41988i	−0.0860828	−	0.996288i	$-0.527435\pi$
$479$	4.11652e6	−	7.13003e6i	0.819769	−	1.41988i	0.905852	−	0.423594i	$-0.139232\pi$
$480$		0			0
$481$	−875187.	−	1.51587e6i	−0.172480	−	0.298744i
$482$	605432.			0.118699
$483$		0			0
$484$	−1.24971e6			−0.242492
$485$	−697332.	−	1.20781e6i	−0.134612	−	0.233156i
$486$		0			0
$487$	−3.68638e6	+	6.38499e6i	−0.704332	+	1.21994i	0.262601	+	0.964905i	$0.415420\pi$
$487$	−3.68638e6	+	6.38499e6i	−0.704332	+	1.21994i	−0.966932	+	0.255033i	$0.917914\pi$
$488$	−498112.	−	862755.i	−0.0946842	−	0.163998i
$489$		0			0
$490$	803208.	−	75365.0i	0.151126	−	0.0141801i
$491$	960696.			0.179838			0.0899192	−	0.995949i	$-0.471339\pi$
$491$	960696.			0.179838			0.0899192	+	0.995949i	$0.471339\pi$
$492$		0			0
$493$	−413712.	+	716570.i	−0.0766621	+	0.132783i
$494$	−909458.	+	1.57523e6i	−0.167674	+	0.290420i
$495$		0			0
$496$	643328.			0.117416
$497$	774690.	−	1.49966e6i	0.140681	−	0.272334i
$498$		0			0
$499$	3.16713e6	+	5.48564e6i	0.569397	+	0.986224i	0.996626	+	0.0820807i	$0.0261565\pi$
$499$	3.16713e6	+	5.48564e6i	0.569397	+	0.986224i	−0.427229	+	0.904143i	$0.640510\pi$
$500$	586176.	−	1.01529e6i	0.104858	−	0.181620i
$501$		0			0
$502$	−1.87351e6	−	3.24502e6i	−0.331816	−	0.574722i
$503$	−1.04129e6			−0.183506			−0.0917531	−	0.995782i	$-0.529247\pi$
$503$	−1.04129e6			−0.183506			−0.0917531	+	0.995782i	$0.529247\pi$
$504$		0			0
$505$	154368.			0.0269357
$506$	−2.64730e6	−	4.58525e6i	−0.459649	−	0.796135i
$507$		0			0
$508$	1.02985e6	−	1.78375e6i	0.177057	−	0.306672i
$509$	2.49525e6	+	4.32190e6i	0.426894	+	0.739401i	0.996595	−	0.0824503i	$-0.0262746\pi$
$509$	2.49525e6	+	4.32190e6i	0.426894	+	0.739401i	−0.569702	+	0.821852i	$0.692941\pi$
$510$		0			0
$511$	−3.51841e6	−	5.48466e6i	−0.596066	−	0.929175i
$512$	262144.			0.0441942
$513$		0			0
$514$	−2.55607e6	+	4.42725e6i	−0.426742	+	0.739139i
$515$	−1.08989e6	+	1.88775e6i	−0.181078	+	0.313637i
$516$		0			0
$517$	4.97318e6			0.818292
$518$	665000.	+	1.03663e6i	0.108892	+	0.169746i
$519$		0			0
$520$	−283008.	−	490184.i	−0.0458976	−	0.0794970i
$521$	−487308.	+	844042.i	−0.0786519	+	0.136229i	−0.902669	−	0.430337i	$-0.858395\pi$
$521$	−487308.	+	844042.i	−0.0786519	+	0.136229i	0.824017	+	0.566566i	$0.191728\pi$
$522$		0			0
$523$	−1.27483e6	−	2.20806e6i	−0.203796	−	0.352986i	0.745952	−	0.666000i	$-0.231995\pi$
$523$	−1.27483e6	−	2.20806e6i	−0.203796	−	0.352986i	−0.949749	+	0.313014i	$0.898661\pi$
$524$	5.19360e6			0.826305
$525$		0			0
$526$	−6.85354e6			−1.08007
$527$	196014.	+	339506.i	0.0307440	+	0.0532502i
$528$		0			0
$529$	−7.34344e6	+	1.27192e7i	−1.14093	+	1.97615i
$530$	446688.	+	773686.i	0.0690740	+	0.119640i
$531$		0			0
$532$	587384.	−	1.13707e6i	0.0899794	−	0.174184i
$533$	−1.05244e7			−1.60464
$534$		0			0
$535$	720648.	−	1.24820e6i	0.108853	−	0.188538i
$536$	257696.	−	446343.i	0.0387432	−	0.0671052i
$537$		0			0
$538$	8.07859e6			1.20332
$539$	4.81925e6	−	452190.i	0.714508	−	0.0670423i
$540$		0			0
$541$	2.60033e6	+	4.50390e6i	0.381975	+	0.661600i	0.991344	−	0.131287i	$-0.0419108\pi$
$541$	2.60033e6	+	4.50390e6i	0.381975	+	0.661600i	−0.609370	+	0.792886i	$0.708577\pi$
$542$	−2.97479e6	+	5.15249e6i	−0.434969	+	0.753389i
$543$		0			0
$544$	79872.0	+	138342.i	0.0115717	+	0.0200428i
$545$	1.65246e6			0.238309
$546$		0			0
$547$	−5.24222e6			−0.749112			−0.374556	−	0.927204i	$-0.622205\pi$
$547$	−5.24222e6			−0.749112			−0.374556	+	0.927204i	$0.622205\pi$
$548$	824448.	+	1.42799e6i	0.117277	+	0.203129i
$549$		0			0
$550$	1.71706e6	−	2.97403e6i	0.242035	−	0.419216i
$551$	1.63628e6	+	2.83413e6i	0.229604	+	0.397686i
$552$		0			0
$553$	−3.90507e6	+	182805.i	−0.543021	+	0.0254200i
$554$	−2.56016e6			−0.354399
$555$		0			0
$556$	162104.	−	280772.i	0.0222386	−	0.0385183i
$557$	−2.11398e6	+	3.66152e6i	−0.288711	+	0.500062i	−0.973502	−	0.228677i	$-0.926560\pi$
$557$	−2.11398e6	+	3.66152e6i	−0.288711	+	0.500062i	0.684792	+	0.728739i	$0.259893\pi$
$558$		0			0
$559$	−1.16372e6			−0.157514
$560$	215040.	+	335214.i	0.0289767	+	0.0451702i
$561$		0			0
$562$	−3.28126e6	−	5.68330e6i	−0.438227	−	0.759032i
$563$	1.78129e6	−	3.08528e6i	0.236844	−	0.410226i	−0.722963	−	0.690887i	$-0.757220\pi$
$563$	1.78129e6	−	3.08528e6i	0.236844	−	0.410226i	0.959807	+	0.280661i	$0.0905536\pi$
$564$		0			0
$565$	−874440.	−	1.51457e6i	−0.115241	−	0.199604i
$566$	−1.00716e7			−1.32147
$567$		0			0
$568$	833280.			0.108373
$569$	−3.16098e6	−	5.47498e6i	−0.409299	−	0.708927i	0.585512	−	0.810664i	$-0.300894\pi$
$569$	−3.16098e6	−	5.47498e6i	−0.409299	−	0.708927i	−0.994811	+	0.101736i	$0.967560\pi$
$570$		0			0
$571$	−97328.5	+	168578.i	−0.0124925	+	0.0216377i	−0.872204	−	0.489142i	$-0.837310\pi$
$571$	−97328.5	+	168578.i	−0.0124925	+	0.0216377i	0.859712	+	0.510780i	$0.170643\pi$
$572$	−1.69805e6	−	2.94111e6i	−0.217000	−	0.375855i
$573$		0			0
$574$	7.39704e6	−	346272.i	0.937083	−	0.0438669i
$575$	−1.37007e7			−1.72811
$576$		0			0
$577$	−2.05437e6	+	3.55827e6i	−0.256885	+	0.444938i	−0.965406	−	0.260752i	$-0.916030\pi$
$577$	−2.05437e6	+	3.55827e6i	−0.256885	+	0.444938i	0.708521	+	0.705690i	$0.249363\pi$
$578$	2.79104e6	−	4.83423e6i	0.347494	−	0.601877i
$579$		0			0
$580$	−1.01837e6			−0.125700
$581$	5.90692e6	−	1.14347e7i	0.725974	−	1.40536i
$582$		0			0
$583$	2.68013e6	+	4.64212e6i	0.326576	+	0.565646i
$584$	1.60842e6	−	2.78586e6i	0.195149	−	0.338008i
$585$		0			0
$586$	−3.06379e6	−	5.30664e6i	−0.368566	−	0.638375i
$587$	−1.10174e7			−1.31973			−0.659863	−	0.751386i	$-0.729386\pi$
$587$	−1.10174e7			−1.31973			−0.659863	+	0.751386i	$0.729386\pi$
$588$		0			0
$589$	1.55052e6			0.184158
$590$	−682272.	−	1.18173e6i	−0.0806914	−	0.139762i
$591$		0			0
$592$	−304000.	+	526543.i	−0.0356508	+	0.0617490i
$593$	−1.02738e6	−	1.77947e6i	−0.119976	−	0.207805i	0.799782	−	0.600291i	$-0.204948\pi$
$593$	−1.02738e6	−	1.77947e6i	−0.119976	−	0.207805i	−0.919758	+	0.392486i	$0.871615\pi$
$594$		0			0
$595$	−111384.	+	215620.i	−0.0128982	+	0.0249687i
$596$	−2.40614e6			−0.277464
$597$		0			0
$598$	−6.77450e6	+	1.17338e7i	−0.774684	+	1.34179i
$599$	−412200.	+	713951.i	−0.0469398	+	0.0813021i	−0.888541	−	0.458798i	$-0.848280\pi$
$599$	−412200.	+	713951.i	−0.0469398	+	0.0813021i	0.841601	+	0.540100i	$0.181614\pi$
$600$		0			0
$601$	−2.88706e6			−0.326039			−0.163019	−	0.986623i	$-0.552123\pi$
$601$	−2.88706e6			−0.326039			−0.163019	+	0.986623i	$0.552123\pi$
$602$	817922.	−	38288.7i	0.0919858	−	0.00430605i
$603$		0			0
$604$	−790240.	−	1.36874e6i	−0.0881387	−	0.152661i
$605$	468642.	−	811712.i	0.0520538	−	0.0901599i
$606$		0			0
$607$	2.55448e6	+	4.42448e6i	0.281404	+	0.487406i	0.971731	−	0.236092i	$-0.0758666\pi$
$607$	2.55448e6	+	4.42448e6i	0.281404	+	0.487406i	−0.690327	+	0.723498i	$0.742533\pi$
$608$	631808.			0.0693148
$609$		0			0
$610$	747168.			0.0813006
$611$	−6.36326e6	−	1.10215e7i	−0.689567	−	1.19437i
$612$		0			0
$613$	4.92860e6	−	8.53658e6i	0.529751	−	0.917556i	−0.469646	−	0.882855i	$-0.655619\pi$
$613$	4.92860e6	−	8.53658e6i	0.529751	−	0.917556i	0.999398	−	0.0347017i	$-0.0110481\pi$
$614$	4.47862e6	+	7.75719e6i	0.479428	+	0.830393i
$615$		0			0
$616$	1.29024e6	+	2.01129e6i	0.136999	+	0.213561i
$617$	−1.26078e7			−1.33329			−0.666646	−	0.745374i	$-0.732271\pi$
$617$	−1.26078e7			−1.33329			−0.666646	+	0.745374i	$0.732271\pi$
$618$		0			0
$619$	6.14174e6	−	1.06378e7i	0.644266	−	1.11590i	−0.340205	−	0.940351i	$-0.610496\pi$
$619$	6.14174e6	−	1.06378e7i	0.644266	−	1.11590i	0.984471	−	0.175550i	$-0.0561703\pi$
$620$	−241248.	+	417854.i	−0.0252049	+	0.0436561i
$621$		0			0
$622$	7.74941e6			0.803142
$623$	6.74747e6	−	315864.i	0.696499	−	0.0326047i
$624$		0			0
$625$	−4.21818e6	−	7.30610e6i	−0.431942	−	0.748145i
$626$	2.63331e6	−	4.56102e6i	0.268575	−	0.465185i
$627$		0			0
$628$	418832.	+	725438.i	0.0423780	+	0.0734009i
$629$	−370500.			−0.0373389
$630$		0			0
$631$	8.53195e6			0.853051			0.426525	−	0.904476i	$-0.359738\pi$
$631$	8.53195e6			0.853051			0.426525	+	0.904476i	$0.359738\pi$
$632$	−964960.	−	1.67136e6i	−0.0960985	−	0.166447i
$633$		0			0
$634$	−5.51477e6	+	9.55186e6i	−0.544884	+	0.943767i
$635$	772386.	+	1.33781e6i	0.0760151	+	0.131662i
$636$		0			0
$637$	−7.16843e6	−	1.01018e7i	−0.699964	−	0.986389i
$638$	−6.11021e6			−0.594298
$639$		0			0
$640$	−98304.0	+	170268.i	−0.00948683	+	0.0164317i
$641$	−5.41501e6	+	9.37907e6i	−0.520540	+	0.901601i	0.479175	+	0.877719i	$0.340936\pi$
$641$	−5.41501e6	+	9.37907e6i	−0.520540	+	0.901601i	−0.999715	+	0.0238819i	$0.992397\pi$
$642$		0			0
$643$	9.84431e6			0.938984			0.469492	−	0.882937i	$-0.344437\pi$
$643$	9.84431e6			0.938984			0.469492	+	0.882937i	$0.344437\pi$
$644$	4.37539e6	−	8.46998e6i	0.415721	−	0.804762i
$645$		0			0
$646$	192504.	+	333427.i	0.0181492	+	0.0314354i
$647$	270744.	−	468942.i	0.0254272	−	0.0440412i	−0.853032	−	0.521859i	$-0.825239\pi$
$647$	270744.	−	468942.i	0.0254272	−	0.0440412i	0.878459	+	0.477818i	$0.158572\pi$
$648$		0			0
$649$	−4.09363e6	−	7.09038e6i	−0.381502	−	0.660781i
$650$	−8.78799e6			−0.815842
$651$		0			0
$652$	−7.79584e6			−0.718198
$653$	−2.76137e6	−	4.78283e6i	−0.253420	−	0.438937i	0.711045	−	0.703147i	$-0.248222\pi$
$653$	−2.76137e6	−	4.78283e6i	−0.253420	−	0.438937i	−0.964465	+	0.264210i	$0.914889\pi$
$654$		0			0
$655$	−1.94760e6	+	3.37334e6i	−0.177377	+	0.307225i
$656$	1.82784e6	+	3.16591e6i	0.165836	+	0.287236i
$657$		0			0
$658$	4.83504e6	+	7.53708e6i	0.435347	+	0.678638i
$659$	−1.63820e6			−0.146945			−0.0734724	−	0.997297i	$-0.523408\pi$
$659$	−1.63820e6			−0.146945			−0.0734724	+	0.997297i	$0.523408\pi$
$660$		0			0
$661$	1.09590e7	−	1.89816e7i	0.975591	−	1.68977i	0.297620	−	0.954684i	$-0.403807\pi$
$661$	1.09590e7	−	1.89816e7i	0.975591	−	1.68977i	0.677971	−	0.735089i	$-0.262860\pi$
$662$	−5.97629e6	+	1.03512e7i	−0.530013	+	0.918009i
$663$		0			0
$664$	6.35366e6			0.559247
$665$	518280.	+	807919.i	0.0454475	+	0.0708457i
$666$		0			0
$667$	1.21886e7	+	2.11113e7i	1.06081	+	1.83738i
$668$	1.59850e6	−	2.76868e6i	0.138602	−	0.240066i
$669$		0			0
$670$	193272.	+	334757.i	0.0166334	+	0.0288100i
$671$	4.48301e6			0.384382
$672$		0			0
$673$	−1.56750e7			−1.33404			−0.667022	−	0.745038i	$-0.732431\pi$
$673$	−1.56750e7			−1.33404			−0.667022	+	0.745038i	$0.732431\pi$
$674$	−4.69729e6	−	8.13594e6i	−0.398288	−	0.689856i
$675$		0			0
$676$	−1.37501e6	+	2.38158e6i	−0.115728	+	0.200447i
$677$	9.87490e6	+	1.71038e7i	0.828058	+	1.43424i	0.899559	+	0.436798i	$0.143888\pi$
$677$	9.87490e6	+	1.71038e7i	0.828058	+	1.43424i	−0.0715013	+	0.997441i	$0.522779\pi$
$678$		0			0
$679$	6.91521e6	−	1.33866e7i	0.575613	−	1.11428i
$680$	−119808.			−0.00993604
$681$		0			0
$682$	−1.44749e6	+	2.50712e6i	−0.119166	+	0.206402i
$683$	4.90322e6	−	8.49262e6i	0.402188	−	0.696611i	−0.591801	−	0.806084i	$-0.701583\pi$
$683$	4.90322e6	−	8.49262e6i	0.402188	−	0.696611i	0.993990	+	0.109473i	$0.0349164\pi$
$684$		0			0
$685$	−1.23667e6			−0.100700
$686$	5.37069e6	+	6.86416e6i	0.435733	+	0.556899i
$687$		0			0
$688$	202112.	+	350068.i	0.0162787	+	0.0281956i
$689$	6.85852e6	−	1.18793e7i	0.550405	−	0.953330i
$690$		0			0
$691$	2.60038e6	+	4.50398e6i	0.207177	+	0.358841i	0.950824	−	0.309731i	$-0.100239\pi$
$691$	2.60038e6	+	4.50398e6i	0.207177	+	0.358841i	−0.743647	+	0.668572i	$0.766906\pi$
$692$	1.17798e7			0.935130
$693$		0			0
$694$	2.04245e6			0.160973
$695$	121578.	+	210579.i	0.00954757	+	0.0165369i
$696$		0			0
$697$	−1.11384e6	+	1.92923e6i	−0.0868442	+	0.150419i
$698$	2.60061e6	+	4.50439e6i	0.202040	+	0.349943i
$699$		0			0
$700$	6.17663e6	−	289142.i	0.476438	−	0.0223031i
$701$	−1.62944e6			−0.125240			−0.0626202	−	0.998037i	$-0.519946\pi$
$701$	−1.62944e6			−0.125240			−0.0626202	+	0.998037i	$0.519946\pi$
$702$		0			0
$703$	−732688.	+	1.26905e6i	−0.0559153	+	0.0968481i
$704$	−589824.	+	1.02161e6i	−0.0448529	+	0.0776875i
$705$		0			0
$706$	−4.26130e6			−0.321758
$707$	900480.	+	1.40371e6i	0.0677525	+	0.105616i
$708$		0			0
$709$	−5.05324e6	−	8.75246e6i	−0.377532	−	0.653905i	0.613170	−	0.789951i	$-0.289894\pi$
$709$	−5.05324e6	−	8.75246e6i	−0.377532	−	0.653905i	−0.990703	+	0.136046i	$0.956561\pi$
$710$	−312480.	+	541231.i	−0.0232636	+	0.0402937i
$711$		0			0
$712$	1.66733e6	+	2.88790e6i	0.123260	+	0.213492i
$713$	1.15497e7			0.850842
$714$		0			0
$715$	2.54707e6			0.186327
$716$	1.96982e6	+	3.41184e6i	0.143597	+	0.248717i
$717$		0			0
$718$	2.25432e6	−	3.90460e6i	0.163194	−	0.282660i
$719$	1.00360e7	+	1.73828e7i	0.723999	+	1.25400i	0.959385	+	0.282100i	$0.0910312\pi$
$719$	1.00360e7	+	1.73828e7i	0.723999	+	1.25400i	−0.235386	+	0.971902i	$0.575636\pi$
$720$		0			0
$721$	−2.35235e7	+	1.10119e6i	−1.68525	+	0.0788903i
$722$	−8.38164e6			−0.598392
$723$		0			0
$724$	−6.40180e6	+	1.10882e7i	−0.453895	+	0.786170i
$725$	−7.90561e6	+	1.36929e7i	−0.558587	+	0.967500i
$726$		0			0
$727$	−1.52689e7			−1.07145			−0.535726	−	0.844392i	$-0.679962\pi$
$727$	−1.52689e7			−1.07145			−0.535726	+	0.844392i	$0.679962\pi$
$728$	2.80650e6	−	5.43288e6i	0.196262	−	0.379928i
$729$		0			0
$730$	1.20631e6	+	2.08939e6i	0.0837823	+	0.145115i
$731$	−123162.	+	213323.i	−0.00852478	+	0.0147654i
$732$		0			0
$733$	−6.87423e6	−	1.19065e7i	−0.472568	−	0.818512i	0.526939	−	0.849903i	$-0.323340\pi$
$733$	−6.87423e6	−	1.19065e7i	−0.472568	−	0.818512i	−0.999507	+	0.0313912i	$0.990006\pi$
$734$	274412.			0.0188002
$735$		0			0
$736$	4.70630e6			0.320247
$737$	1.15963e6	+	2.00854e6i	0.0786414	+	0.136211i
$738$		0			0
$739$	2.78035e6	−	4.81571e6i	0.187279	−	0.324376i	−0.757063	−	0.653341i	$-0.773367\pi$
$739$	2.78035e6	−	4.81571e6i	0.187279	−	0.324376i	0.944342	+	0.328965i	$0.106700\pi$
$740$	−228000.	−	394908.i	−0.0153058	−	0.0265104i
$741$		0			0
$742$	−4.42966e6	+	8.57502e6i	−0.295366	+	0.571776i
$743$	4.87442e6			0.323930			0.161965	−	0.986796i	$-0.448217\pi$
$743$	4.87442e6			0.323930			0.161965	+	0.986796i	$0.448217\pi$
$744$		0			0
$745$	902304.	−	1.56284e6i	0.0595610	−	0.103163i
$746$	6.60382e6	−	1.14381e7i	0.434458	−	0.752504i
$747$		0			0
$748$	−718848.			−0.0469768
$749$	1.55540e7	−	728116.i	1.01306	−	0.0474238i
$750$		0			0
$751$	−1.40118e6	−	2.42691e6i	−0.0906553	−	0.157020i	0.817132	−	0.576451i	$-0.195563\pi$
$751$	−1.40118e6	−	2.42691e6i	−0.0906553	−	0.157020i	−0.907787	+	0.419431i	$0.862229\pi$
$752$	−2.21030e6	+	3.82836e6i	−0.142530	+	0.246870i
$753$		0			0
$754$	7.81810e6	+	1.35413e7i	0.500810	+	0.867428i
$755$	1.18536e6			0.0756803
$756$		0			0
$757$	2.13836e7			1.35626			0.678128	−	0.734943i	$-0.262791\pi$
$757$	2.13836e7			1.35626			0.678128	+	0.734943i	$0.262791\pi$
$758$	7.97019e6	+	1.38048e7i	0.503843	+	0.872682i
$759$		0			0
$760$	−236928.	+	410371.i	−0.0148793	+	0.0257717i
$761$	8.62037e6	+	1.49309e7i	0.539591	+	0.934599i	0.998926	+	0.0463355i	$0.0147543\pi$
$761$	8.62037e6	+	1.49309e7i	0.539591	+	0.934599i	−0.459335	+	0.888263i	$0.651912\pi$
$762$		0			0
$763$	9.63935e6	+	1.50263e7i	0.599427	+	0.934414i
$764$	6.17645e6			0.382829
$765$		0			0
$766$	−5.76012e6	+	9.97682e6i	−0.354699	+	0.614356i
$767$	−1.04757e7	+	1.81445e7i	−0.642977	+	1.11367i
$768$		0			0
$769$	−2.10762e7			−1.28522			−0.642609	−	0.766194i	$-0.722148\pi$
$769$	−2.10762e7			−1.28522			−0.642609	+	0.766194i	$0.722148\pi$
$770$	−1.79021e6	+	83803.5i	−0.108812	+	0.00509373i
$771$		0			0
$772$	−3.97650e6	−	6.88751e6i	−0.240136	−	0.415929i
$773$	1.58549e7	−	2.74614e7i	0.954364	−	1.65301i	0.218546	−	0.975827i	$-0.429869\pi$
$773$	1.58549e7	−	2.74614e7i	0.954364	−	1.65301i	0.735818	−	0.677180i	$-0.236798\pi$
$774$		0			0
$775$	3.74563e6	+	6.48762e6i	0.224011	+	0.387999i
$776$	7.43821e6			0.443419
$777$		0			0
$778$	−1.30975e7			−0.775783
$779$	4.40538e6	+	7.63034e6i	0.260100	+	0.450506i
$780$		0			0
$781$	−1.87488e6	+	3.24739e6i	−0.109988	+	0.190505i
$782$	1.43395e6	+	2.48368e6i	0.0838528	+	0.145237i
$783$		0			0
$784$	−1.79379e6	+	3.91083e6i	−0.104227	+	0.227237i
$785$	−628248.			−0.0363879
$786$		0			0
$787$	3.34123e6	−	5.78718e6i	0.192296	−	0.333066i	−0.753715	−	0.657201i	$-0.771740\pi$
$787$	3.34123e6	−	5.78718e6i	0.192296	−	0.333066i	0.946011	+	0.324136i	$0.105073\pi$
$788$	−5.12822e6	+	8.88234e6i	−0.294206	+	0.509580i
$789$		0			0
$790$	1.44744e6			0.0825150
$791$	8.67153e6	−	1.67865e7i	0.492782	−	0.953937i
$792$		0			0
$793$	−5.73607e6	−	9.93517e6i	−0.323915	−	0.561038i
$794$	3.37207e6	−	5.84060e6i	0.189822	−	0.328781i
$795$		0			0
$796$	−2.53110e6	−	4.38400e6i	−0.141588	−	0.245238i
$797$	−3.26739e7			−1.82203			−0.911013	−	0.412378i	$-0.864698\pi$
$797$	−3.26739e7			−1.82203			−0.911013	+	0.412378i	$0.864698\pi$
$798$		0			0
$799$	−2.69381e6			−0.149279
$800$	1.52627e6	+	2.64358e6i	0.0843154	+	0.146039i
$801$		0			0
$802$	5.54335e6	−	9.60137e6i	0.304324	−	0.527105i
$803$	7.23787e6	+	1.25364e7i	0.396116	+	0.686092i
$804$		0			0
$805$	3.86064e6	+	6.01814e6i	0.209976	+	0.327320i
$806$	7.40832e6			0.401682
$807$		0			0
$808$	−411648.	+	712995.i	−0.0221818	+	0.0384201i
$809$	1.77627e7	−	3.07659e7i	0.954196	−	1.65272i	0.217998	−	0.975949i	$-0.430047\pi$
$809$	1.77627e7	−	3.07659e7i	0.954196	−	1.65272i	0.736198	−	0.676767i	$-0.236619\pi$
$810$		0			0
$811$	1.09878e7			0.586624			0.293312	−	0.956017i	$-0.405243\pi$
$811$	1.09878e7			0.586624			0.293312	+	0.956017i	$0.405243\pi$
$812$	−5.94048e6	−	9.26029e6i	−0.316178	−	0.492873i
$813$		0			0
$814$	−1.36800e6	−	2.36945e6i	−0.0723644	−	0.125339i
$815$	2.92344e6	−	5.06355e6i	0.154170	−	0.267030i
$816$		0			0
$817$	487122.	+	843719.i	0.0255318	+	0.0442224i
$818$	−1.04888e7			−0.548078
$819$		0			0
$820$	−2.74176e6			−0.142395
$821$	6.97791e6	+	1.20861e7i	0.361300	+	0.625789i	0.988175	−	0.153330i	$-0.0489998\pi$
$821$	6.97791e6	+	1.20861e7i	0.361300	+	0.625789i	−0.626875	+	0.779120i	$0.715667\pi$
$822$		0			0
$823$	8.28862e6	−	1.43563e7i	0.426562	−	0.738828i	−0.570003	−	0.821643i	$-0.693058\pi$
$823$	8.28862e6	−	1.43563e7i	0.426562	−	0.738828i	0.996565	+	0.0828152i	$0.0263911\pi$
$824$	−5.81277e6	−	1.00680e7i	−0.298239	−	0.516566i
$825$		0			0
$826$	6.76586e6	−	1.30975e7i	0.345043	−	0.667942i
$827$	−2.09083e7			−1.06305			−0.531526	−	0.847042i	$-0.678381\pi$
$827$	−2.09083e7			−1.06305			−0.531526	+	0.847042i	$0.678381\pi$
$828$		0			0
$829$	−975728.	+	1.69001e6i	−0.0493109	+	0.0854089i	−0.889627	−	0.456687i	$-0.849036\pi$
$829$	−975728.	+	1.69001e6i	−0.0493109	+	0.0854089i	0.840316	+	0.542096i	$0.182369\pi$
$830$	−2.38262e6	+	4.12683e6i	−0.120049	+	0.207932i
$831$		0			0
$832$	3.01875e6			0.151189
$833$	−2.61043e6	+	244936.i	−0.130346	+	0.0122304i
$834$		0			0
$835$	1.19887e6	+	2.07651e6i	0.0595054	+	0.103066i
$836$	−1.42157e6	+	2.46223e6i	−0.0703480	+	0.121846i
$837$		0			0
$838$	−3.01603e6	−	5.22392e6i	−0.148363	−	0.256972i
$839$	1.18540e7			0.581379			0.290690	−	0.956817i	$-0.406115\pi$
$839$	1.18540e7			0.581379			0.290690	+	0.956817i	$0.406115\pi$
$840$		0			0
$841$	7.62127e6			0.371567
$842$	−3.86171e6	−	6.68867e6i	−0.187715	−	0.325132i
$843$		0			0
$844$	4.46221e6	−	7.72877e6i	0.215622	−	0.373469i
$845$	−1.03126e6	−	1.78619e6i	−0.0496849	−	0.0860568i
$846$		0			0
$847$	1.01149e7	−	473499.i	0.484452	−	0.0226783i
$848$	−4.76467e6			−0.227532
$849$		0			0
$850$	−930072.	+	1.61093e6i	−0.0441539	+	0.0764768i
$851$	−5.45775e6	+	9.45310e6i	−0.258339	+	0.447456i
$852$		0			0
$853$	−1.20052e7			−0.564934			−0.282467	−	0.959277i	$-0.591153\pi$
$853$	−1.20052e7			−0.564934			−0.282467	+	0.959277i	$0.591153\pi$
$854$	4.35848e6	+	6.79420e6i	0.204499	+	0.318782i
$855$		0			0
$856$	3.84346e6	+	6.65706e6i	0.179282	+	0.310526i
$857$	−2.04907e7	+	3.54909e7i	−0.953026	+	1.65069i	−0.214203	+	0.976789i	$0.568715\pi$
$857$	−2.04907e7	+	3.54909e7i	−0.953026	+	1.65069i	−0.738823	+	0.673900i	$0.764618\pi$
$858$		0			0
$859$	8.32687e6	+	1.44226e7i	0.385034	+	0.666898i	0.991774	−	0.128002i	$-0.0408565\pi$
$859$	8.32687e6	+	1.44226e7i	0.385034	+	0.666898i	−0.606740	+	0.794900i	$0.707523\pi$
$860$	−303168.			−0.0139777
$861$		0			0
$862$	6.75278e6			0.309539
$863$	−1.09410e7	−	1.89503e7i	−0.500069	−	0.866144i	−1.00000		7.91703e-5i	$-0.999975\pi$
$863$	−1.09410e7	−	1.89503e7i	−0.500069	−	0.866144i	0.499931	−	0.866065i	$-0.333359\pi$
$864$		0			0
$865$	−4.41742e6	+	7.65119e6i	−0.200737	+	0.347687i
$866$	7.41526e6	+	1.28436e7i	0.335994	+	0.581959i
$867$		0			0
$868$	−5.20694e6	+	243748.i	−0.234576	+	0.0109810i
$869$	8.68464e6			0.390124
$870$		0			0
$871$	2.96753e6	−	5.13991e6i	0.132541	−	0.229568i
$872$	−4.40656e6	+	7.63239e6i	−0.196249	+	0.339914i
$873$		0			0
$874$	1.13429e7			0.502281
$875$	−4.35968e6	+	8.43957e6i	−0.192502	+	0.372649i
$876$		0			0
$877$	1.22354e6	+	2.11923e6i	0.0537178	+	0.0930419i	0.891634	−	0.452757i	$-0.149560\pi$
$877$	1.22354e6	+	2.11923e6i	0.0537178	+	0.0930419i	−0.837916	+	0.545799i	$0.816226\pi$
$878$	7.46137e6	−	1.29235e7i	0.326650	−	0.565774i
$879$		0			0
$880$	−442368.	−	766204.i	−0.0192565	−	0.0333532i
$881$	−1.53097e7			−0.664550			−0.332275	−	0.943183i	$-0.607816\pi$
$881$	−1.53097e7			−0.664550			−0.332275	+	0.943183i	$0.607816\pi$
$882$		0			0
$883$	1.82787e7			0.788941			0.394470	−	0.918909i	$-0.370928\pi$
$883$	1.82787e7			0.788941			0.394470	+	0.918909i	$0.370928\pi$
$884$	919776.	+	1.59310e6i	0.0395869	+	0.0685665i
$885$		0			0
$886$	5.45676e6	−	9.45139e6i	0.233534	−	0.404493i
$887$	−1.79877e7	−	3.11557e7i	−0.767658	−	1.32962i	−0.938830	−	0.344381i	$-0.888089\pi$
$887$	−1.79877e7	−	3.11557e7i	−0.767658	−	1.32962i	0.171172	−	0.985241i	$-0.445245\pi$
$888$		0			0
$889$	−7.65949e6	+	1.48274e7i	−0.325047	+	0.629232i
$890$	−2.50099e6			−0.105837
$891$		0			0
$892$	1.01094e7	−	1.75100e7i	0.425416	−	0.736842i
$893$	−5.32718e6	+	9.22694e6i	−0.223547	+	0.387195i
$894$		0			0
$895$	−2.95474e6			−0.123299
$896$	−2.12173e6	+	99322.7i	−0.0882917	+	0.00413313i
$897$		0			0
$898$	−1.33440e7	−	2.31125e7i	−0.552199	−	0.956438i
$899$	6.66448e6	−	1.15432e7i	0.275022	−	0.476351i
$900$		0			0
$901$	−1.45174e6	−	2.51448e6i	−0.0595766	−	0.103190i
$902$	−1.64506e7			−0.673231
$903$		0			0
$904$	9.32736e6			0.379610
$905$	−4.80135e6	−	8.31618e6i	−0.194869	−	0.337522i
$906$		0			0
$907$	−782598.	+	1.35550e6i	−0.0315879	+	0.0547118i	−0.881387	−	0.472395i	$-0.843390\pi$
$907$	−782598.	+	1.35550e6i	−0.0315879	+	0.0547118i	0.849799	+	0.527106i	$0.176723\pi$
$908$	−4.39008e6	−	7.60384e6i	−0.176709	−	0.306068i
$909$		0			0
$910$	2.47632e6	+	3.86020e6i	0.0991296	+	0.154528i
$911$	−5.87538e6			−0.234552			−0.117276	−	0.993099i	$-0.537416\pi$
$911$	−5.87538e6			−0.234552			−0.117276	+	0.993099i	$0.537416\pi$
$912$		0			0
$913$	−1.42957e7	+	2.47610e7i	−0.567584	+	0.983084i
$914$	1.34800e7	−	2.33481e7i	0.533735	−	0.924457i
$915$		0			0
$916$	−1.60310e7			−0.631278
$917$	−4.20357e7	+	1.96778e6i	−1.65080	+	0.0772776i
$918$		0			0
$919$	−3.12620e6	−	5.41474e6i	−0.122104	−	0.211490i	0.798493	−	0.602003i	$-0.205631\pi$
$919$	−3.12620e6	−	5.41474e6i	−0.122104	−	0.211490i	−0.920597	+	0.390514i	$0.872297\pi$
$920$	−1.76486e6	+	3.05683e6i	−0.0687451	+	0.119070i
$921$		0			0
$922$	−4.44422e6	−	7.69762e6i	−0.172174	−	0.298215i
$923$	9.59574e6			0.370744
$924$		0			0
$925$	−7.07988e6			−0.272064
$926$	−1.54919e7	−	2.68328e7i	−0.593714	−	1.02834i
$927$		0			0
$928$	2.71565e6	−	4.70364e6i	0.103515	−	0.179293i
$929$	−1.89249e7	−	3.27790e7i	−0.719441	−	1.24611i	−0.961221	−	0.275778i	$-0.911065\pi$
$929$	−1.89249e7	−	3.27790e7i	−0.719441	−	1.24611i	0.241780	−	0.970331i	$-0.422269\pi$
$930$		0			0
$931$	−4.32332e6	+	9.42572e6i	−0.163472	+	0.356402i
$932$	−2.41453e7			−0.910529
$933$		0			0
$934$	1.48704e7	−	2.57563e7i	0.557771	−	0.966088i
$935$	269568.	−	466905.i	0.0100842	−	0.0174663i
$936$		0			0
$937$	−3.03736e7			−1.13018			−0.565090	−	0.825030i	$-0.691158\pi$
$937$	−3.03736e7			−1.13018			−0.565090	+	0.825030i	$0.691158\pi$
$938$	−1.91661e6	+	3.71022e6i	−0.0711259	+	0.137687i
$939$		0			0
$940$	−1.65773e6	−	2.87127e6i	−0.0611919	−	0.105987i
$941$	1.90979e7	−	3.30786e7i	0.703091	−	1.21779i	−0.264285	−	0.964445i	$-0.585136\pi$
$941$	1.90979e7	−	3.30786e7i	0.703091	−	1.21779i	0.967376	−	0.253345i	$-0.0815309\pi$
$942$		0			0
$943$	3.28154e7	+	5.68380e7i	1.20171	+	2.08142i
$944$	7.27757e6			0.265801
$945$		0			0
$946$	−1.81901e6			−0.0660856
$947$	−1.56200e6	−	2.70547e6i	−0.0565988	−	0.0980320i	0.836338	−	0.548214i	$-0.184692\pi$
$947$	−1.56200e6	−	2.70547e6i	−0.0565988	−	0.0980320i	−0.892937	+	0.450183i	$0.851359\pi$
$948$		0			0
$949$	1.85219e7	−	3.20809e7i	0.667606	−	1.15633i
$950$	3.67855e6	+	6.37144e6i	0.132242	+	0.229049i
$951$		0			0
$952$	−698880.	−	1.08945e6i	−0.0249925	−	0.0389595i
$953$	1.52870e7			0.545241			0.272621	−	0.962122i	$-0.412110\pi$
$953$	1.52870e7			0.545241			0.272621	+	0.962122i	$0.412110\pi$
$954$		0			0
$955$	−2.31617e6	+	4.01172e6i	−0.0821791	+	0.142338i
$956$	−1.20447e7	+	2.08621e7i	−0.426238	+	0.738267i
$957$		0			0
$958$	−3.29322e7			−1.15933
$959$	−7.21392e6	−	1.12454e7i	−0.253294	−	0.394846i
$960$		0			0
$961$	1.11570e7	+	1.93245e7i	0.389707	+	0.674993i
$962$	−3.50075e6	+	6.06348e6i	−0.121962	+	0.211244i
$963$		0			0
$964$	−1.21086e6	−	2.09728e6i	−0.0419665	−	0.0726881i
$965$	5.96476e6			0.206193
$966$		0			0
$967$	−4.87050e6			−0.167497			−0.0837486	−	0.996487i	$-0.526689\pi$
$967$	−4.87050e6			−0.167497			−0.0837486	+	0.996487i	$0.526689\pi$
$968$	2.49942e6	+	4.32913e6i	0.0857337	+	0.148495i
$969$		0			0
$970$	−2.78933e6	+	4.83126e6i	−0.0951854	+	0.164866i
$971$	−9.37238e6	−	1.62334e7i	−0.319008	−	0.552538i	0.661273	−	0.750145i	$-0.270016\pi$
$971$	−9.37238e6	−	1.62334e7i	−0.319008	−	0.552538i	−0.980281	+	0.197607i	$0.936683\pi$
$972$		0			0
$973$	−1.20565e6	+	2.33392e6i	−0.0408262	+	0.0790322i
$974$	2.94910e7			0.996075
$975$		0			0
$976$	−1.99245e6	+	3.45102e6i	−0.0669518	+	0.115964i
$977$	−4.00150e6	+	6.93079e6i	−0.134118	+	0.232299i	−0.925260	−	0.379333i	$-0.876153\pi$
$977$	−4.00150e6	+	6.93079e6i	−0.134118	+	0.232299i	0.791142	+	0.611632i	$0.209487\pi$
$978$		0			0
$979$	−1.50060e7			−0.500388
$980$	−1.86749e6	−	2.63166e6i	−0.0621144	−	0.0875317i
$981$		0			0
$982$	−1.92139e6	−	3.32795e6i	−0.0635825	−	0.110128i
$983$	−2.70634e7	+	4.68752e7i	−0.893304	+	1.54725i	−0.0574138	+	0.998350i	$0.518285\pi$
$983$	−2.70634e7	+	4.68752e7i	−0.893304	+	1.54725i	−0.835890	+	0.548897i	$0.815048\pi$
$984$		0			0
$985$	−3.84617e6	−	6.66176e6i	−0.126310	−	0.218775i
$986$	3.30970e6			0.108417
$987$		0			0
$988$	7.27566e6			0.237127
$989$	3.62854e6	+	6.28482e6i	0.117962	+	0.204316i
$990$		0			0
$991$	−2.03145e7	+	3.51857e7i	−0.657084	+	1.13810i	0.324282	+	0.945960i	$0.394877\pi$
$991$	−2.03145e7	+	3.51857e7i	−0.657084	+	1.13810i	−0.981367	+	0.192143i	$0.938456\pi$
$992$	−1.28666e6	−	2.22855e6i	−0.0415129	−	0.0719025i
$993$		0			0
$994$	−6.74436e6	+	315718.i	−0.216508	+	0.0101352i
$995$	3.79666e6			0.121575
$996$		0			0
$997$	4.54883e6	−	7.87880e6i	0.144931	−	0.251028i	−0.784416	−	0.620235i	$-0.787037\pi$
$997$	4.54883e6	−	7.87880e6i	0.144931	−	0.251028i	0.929347	+	0.369207i	$0.120371\pi$
$998$	1.26685e7	−	2.19425e7i	0.402624	−	0.697366i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.6.g.a.109.1	yes	2
3.2	odd	2		126.6.g.d.109.1	yes	2
7.2	even	3	inner	126.6.g.a.37.1	✓	2
7.3	odd	6		882.6.a.q.1.1		1
7.4	even	3		882.6.a.r.1.1		1
21.2	odd	6		126.6.g.d.37.1	yes	2
21.11	odd	6		882.6.a.d.1.1		1
21.17	even	6		882.6.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.6.g.a.37.1	✓	2	7.2	even	3	inner
126.6.g.a.109.1	yes	2	1.1	even	1	trivial
126.6.g.d.37.1	yes	2	21.2	odd	6
126.6.g.d.109.1	yes	2	3.2	odd	2
882.6.a.d.1.1		1	21.11	odd	6
882.6.a.h.1.1		1	21.17	even	6
882.6.a.q.1.1		1	7.3	odd	6
882.6.a.r.1.1		1	7.4	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-6.00000 - 10.3923i) q^{5} +(59.5000 - 115.181i) q^{7} +64.0000 q^{8} +(-24.0000 + 41.5692i) q^{10} +(-144.000 + 249.415i) q^{11} +737.000 q^{13} +(-518.000 + 24.2487i) q^{14} +(-128.000 - 221.703i) q^{16} +(78.0000 - 135.100i) q^{17} +(-308.500 - 534.338i) q^{19} +192.000 q^{20} +1152.00 q^{22} +(-2298.00 - 3980.25i) q^{23} +(1490.50 - 2581.62i) q^{25} +(-1474.00 - 2553.04i) q^{26} +(1120.00 + 1745.91i) q^{28} -5304.00 q^{29} +(-1256.50 + 2176.32i) q^{31} +(-512.000 + 886.810i) q^{32} -624.000 q^{34} +(-1554.00 + 72.7461i) q^{35} +(-1187.50 - 2056.81i) q^{37} +(-1234.00 + 2137.35i) q^{38} +(-384.000 - 665.108i) q^{40} -14280.0 q^{41} -1579.00 q^{43} +(-2304.00 - 3990.65i) q^{44} +(-9192.00 + 15921.0i) q^{46} +(-8634.00 - 14954.5i) q^{47} +(-9726.50 - 13706.6i) q^{49} -11924.0 q^{50} +(-5896.00 + 10212.2i) q^{52} +(9306.00 - 16118.5i) q^{53} +3456.00 q^{55} +(3808.00 - 7371.61i) q^{56} +(10608.0 + 18373.6i) q^{58} +(-14214.0 + 24619.4i) q^{59} +(-7783.00 - 13480.6i) q^{61} +10052.0 q^{62} +4096.00 q^{64} +(-4422.00 - 7659.13i) q^{65} +(4026.50 - 6974.10i) q^{67} +(1248.00 + 2161.60i) q^{68} +(3360.00 + 5237.72i) q^{70} +13020.0 q^{71} +(25131.5 - 43529.0i) q^{73} +(-4750.00 + 8227.24i) q^{74} +9872.00 q^{76} +(20160.0 + 31426.3i) q^{77} +(-15077.5 - 26115.0i) q^{79} +(-1536.00 + 2660.43i) q^{80} +(28560.0 + 49467.4i) q^{82} +99276.0 q^{83} -1872.00 q^{85} +(3158.00 + 5469.82i) q^{86} +(-9216.00 + 15962.6i) q^{88} +(26052.0 + 45123.4i) q^{89} +(43851.5 - 84888.7i) q^{91} +73536.0 q^{92} +(-34536.0 + 59818.1i) q^{94} +(-3702.00 + 6412.05i) q^{95} +116222. q^{97} +(-28028.0 + 61106.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 16 q^{4} - 12 q^{5} + 119 q^{7} + 128 q^{8} - 48 q^{10} - 288 q^{11} + 1474 q^{13} - 1036 q^{14} - 256 q^{16} + 156 q^{17} - 617 q^{19} + 384 q^{20} + 2304 q^{22} - 4596 q^{23} + 2981 q^{25}+ \cdots - 56056 q^{98}+O(q^{100}) \) 2 * q - 4 * q^2 - 16 * q^4 - 12 * q^5 + 119 * q^7 + 128 * q^8 - 48 * q^10 - 288 * q^11 + 1474 * q^13 - 1036 * q^14 - 256 * q^16 + 156 * q^17 - 617 * q^19 + 384 * q^20 + 2304 * q^22 - 4596 * q^23 + 2981 * q^25 - 2948 * q^26 + 2240 * q^28 - 10608 * q^29 - 2513 * q^31 - 1024 * q^32 - 1248 * q^34 - 3108 * q^35 - 2375 * q^37 - 2468 * q^38 - 768 * q^40 - 28560 * q^41 - 3158 * q^43 - 4608 * q^44 - 18384 * q^46 - 17268 * q^47 - 19453 * q^49 - 23848 * q^50 - 11792 * q^52 + 18612 * q^53 + 6912 * q^55 + 7616 * q^56 + 21216 * q^58 - 28428 * q^59 - 15566 * q^61 + 20104 * q^62 + 8192 * q^64 - 8844 * q^65 + 8053 * q^67 + 2496 * q^68 + 6720 * q^70 + 26040 * q^71 + 50263 * q^73 - 9500 * q^74 + 19744 * q^76 + 40320 * q^77 - 30155 * q^79 - 3072 * q^80 + 57120 * q^82 + 198552 * q^83 - 3744 * q^85 + 6316 * q^86 - 18432 * q^88 + 52104 * q^89 + 87703 * q^91 + 147072 * q^92 - 69072 * q^94 - 7404 * q^95 + 232444 * q^97 - 56056 * q^98

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