LMFDB - Embedded newform 162.7.d.a.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, not 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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.7.d.a.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-36.7423 + 21.2132i) q^{5} +(-194.500 + 336.884i) q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-36.7423 + 21.2132i) q^{5} +(-194.500 + 336.884i) q^{7} -181.019i q^{8} +240.000 q^{10} +(-1800.37 - 1039.45i) q^{11} +(-707.500 - 1225.43i) q^{13} +(1905.70 - 1100.26i) q^{14} +(-512.000 + 886.810i) q^{16} +2367.39i q^{17} -3067.00 q^{19} +(-1175.76 - 678.823i) q^{20} +(5880.00 + 10184.5i) q^{22} +(18128.7 - 10466.6i) q^{23} +(-6912.50 + 11972.8i) q^{25} +8004.45i q^{26} -12448.0 q^{28} +(-11213.8 - 6474.27i) q^{29} +(5669.00 + 9819.00i) q^{31} +(5016.55 - 2896.31i) q^{32} +(6696.00 - 11597.8i) q^{34} -16503.9i q^{35} +47135.0 q^{37} +(15025.2 + 8674.79i) q^{38} +(3840.00 + 6651.08i) q^{40} +(5364.38 - 3097.13i) q^{41} +(-72559.0 + 125676. i) q^{43} -66524.6i q^{44} -118416. q^{46} +(156045. + 90092.5i) q^{47} +(-16836.0 - 29160.8i) q^{49} +(67728.4 - 39103.0i) q^{50} +(22640.0 - 39213.6i) q^{52} -265810. i q^{53} +88200.0 q^{55} +(60982.5 + 35208.3i) q^{56} +(36624.0 + 63434.6i) q^{58} +(313273. - 180868. i) q^{59} +(175152. - 303373. i) q^{61} -64137.4i q^{62} -32768.0 q^{64} +(51990.4 + 30016.7i) q^{65} +(-60170.5 - 104218. i) q^{67} +(-65607.1 + 37878.3i) q^{68} +(-46680.0 + 80852.1i) q^{70} -335101. i q^{71} +175151. q^{73} +(-230913. - 133318. i) q^{74} +(-49072.0 - 84995.2i) q^{76} +(700346. - 404345. i) q^{77} +(126130. - 218463. i) q^{79} -43444.6i q^{80} -35040.0 q^{82} +(-293660. - 169544. i) q^{83} +(-50220.0 - 86983.6i) q^{85} +(710930. - 410456. i) q^{86} +(-188160. + 325903. i) q^{88} +789971. i q^{89} +550435. q^{91} +(580118. + 334931. i) q^{92} +(-509640. - 882722. i) q^{94} +(112689. - 65060.9i) q^{95} +(648552. - 1.12333e6i) q^{97} +190478. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{4} - 778 q^{7}+O(q^{10}) $ 4 * q + 64 * q^4 - 778 * q^7	$ 4 q + 64 q^{4} - 778 q^{7} + 960 q^{10} - 2830 q^{13} - 2048 q^{16} - 12268 q^{19} + 23520 q^{22} - 27650 q^{25} - 49792 q^{28} + 22676 q^{31} + 26784 q^{34} + 188540 q^{37} + 15360 q^{40} - 290236 q^{43} - 473664 q^{46} - 67344 q^{49} + 90560 q^{52} + 352800 q^{55} + 146496 q^{58} + 700610 q^{61} - 131072 q^{64} - 240682 q^{67} - 186720 q^{70} + 700604 q^{73} - 196288 q^{76} + 504518 q^{79} - 140160 q^{82} - 200880 q^{85} - 752640 q^{88} + 2201740 q^{91} - 2038560 q^{94} + 2594210 q^{97}+O(q^{100}) $ 4 * q + 64 * q^4 - 778 * q^7 + 960 * q^10 - 2830 * q^13 - 2048 * q^16 - 12268 * q^19 + 23520 * q^22 - 27650 * q^25 - 49792 * q^28 + 22676 * q^31 + 26784 * q^34 + 188540 * q^37 + 15360 * q^40 - 290236 * q^43 - 473664 * q^46 - 67344 * q^49 + 90560 * q^52 + 352800 * q^55 + 146496 * q^58 + 700610 * q^61 - 131072 * q^64 - 240682 * q^67 - 186720 * q^70 + 700604 * q^73 - 196288 * q^76 + 504518 * q^79 - 140160 * q^82 - 200880 * q^85 - 752640 * q^88 + 2201740 * q^91 - 2038560 * q^94 + 2594210 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−4.89898	−	2.82843i	−0.612372	−	0.353553i
$2$	−4.89898	−	2.82843i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	−36.7423	+	21.2132i	−0.293939	+	0.169706i	−0.639717	−	0.768611i	$-0.720948\pi$
$5$	−36.7423	+	21.2132i	−0.293939	+	0.169706i	0.345778	+	0.938316i	$0.387615\pi$
$6$		0			0
$7$	−194.500	+	336.884i	−0.567055	+	0.982169i	0.429800	+	0.902924i	$0.358584\pi$
$7$	−194.500	+	336.884i	−0.567055	+	0.982169i	−0.996855	+	0.0792445i	$0.974749\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$	240.000			0.240000
$11$	−1800.37	−	1039.45i	−1.35265	−	0.780952i	−0.364029	−	0.931388i	$-0.618599\pi$
$11$	−1800.37	−	1039.45i	−1.35265	−	0.780952i	−0.988620	+	0.150436i	$0.951932\pi$
$12$		0			0
$13$	−707.500	−	1225.43i	−0.322030	−	0.557772i	0.658877	−	0.752251i	$-0.271032\pi$
$13$	−707.500	−	1225.43i	−0.322030	−	0.557772i	−0.980907	+	0.194479i	$0.937699\pi$
$14$	1905.70	−	1100.26i	0.694498	−	0.400969i
$15$		0			0
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$			2367.39i			0.481863i	0.970542	+	0.240932i	$0.0774529\pi$
$17$			2367.39i			0.481863i	−0.970542	+	0.240932i	$0.922547\pi$
$18$		0			0
$19$	−3067.00			−0.447150			−0.223575	−	0.974687i	$-0.571773\pi$
$19$	−3067.00			−0.447150			−0.223575	+	0.974687i	$0.571773\pi$
$20$	−1175.76	−	678.823i	−0.146969	−	0.0848528i
$21$		0			0
$22$	5880.00	+	10184.5i	0.552216	+	0.956467i
$23$	18128.7	−	10466.6i	1.48999	−	0.860244i	0.490053	−	0.871693i	$-0.336978\pi$
$23$	18128.7	−	10466.6i	1.48999	−	0.860244i	0.999934	+	0.0114483i	$0.00364420\pi$
$24$		0			0
$25$	−6912.50	+	11972.8i	−0.442400	+	0.766259i
$26$			8004.45i			0.455419i
$27$		0			0
$28$	−12448.0			−0.567055
$29$	−11213.8	−	6474.27i	−0.459788	−	0.265459i	0.252167	−	0.967684i	$-0.418857\pi$
$29$	−11213.8	−	6474.27i	−0.459788	−	0.265459i	−0.711955	+	0.702225i	$0.752190\pi$
$30$		0			0
$31$	5669.00	+	9819.00i	0.190292	+	0.329596i	0.945347	−	0.326066i	$-0.105723\pi$
$31$	5669.00	+	9819.00i	0.190292	+	0.329596i	−0.755055	+	0.655662i	$0.772390\pi$
$32$	5016.55	−	2896.31i	0.153093	−	0.0883883i
$33$		0			0
$34$	6696.00	−	11597.8i	0.170364	−	0.295080i
$35$		−	16503.9i		−	0.384930i
$36$		0			0
$37$	47135.0			0.930547			0.465274	−	0.885167i	$-0.345956\pi$
$37$	47135.0			0.930547			0.465274	+	0.885167i	$0.345956\pi$
$38$	15025.2	+	8674.79i	0.273822	+	0.158091i
$39$		0			0
$40$	3840.00	+	6651.08i	0.0600000	+	0.103923i
$41$	5364.38	−	3097.13i	0.0778338	−	0.0449374i	−0.460578	−	0.887619i	$-0.652358\pi$
$41$	5364.38	−	3097.13i	0.0778338	−	0.0449374i	0.538412	+	0.842682i	$0.319025\pi$
$42$		0			0
$43$	−72559.0	+	125676.i	−0.912611	+	1.58069i	−0.102250	+	0.994759i	$0.532604\pi$
$43$	−72559.0	+	125676.i	−0.912611	+	1.58069i	−0.810361	+	0.585931i	$0.800729\pi$
$44$		−	66524.6i		−	0.780952i
$45$		0			0
$46$	−118416.			−1.21657
$47$	156045.	+	90092.5i	1.50299	+	0.867751i	0.999994	+	0.00346085i	$0.00110163\pi$
$47$	156045.	+	90092.5i	1.50299	+	0.867751i	0.502994	+	0.864290i	$0.332232\pi$
$48$		0			0
$49$	−16836.0	−	29160.8i	−0.143104	−	0.247863i
$50$	67728.4	−	39103.0i	0.541827	−	0.312824i
$51$		0			0
$52$	22640.0	−	39213.6i	0.161015	−	0.278886i
$53$		−	265810.i		−	1.78543i	−0.450619	−	0.892717i	$-0.648797\pi$
$53$		−	265810.i		−	1.78543i	0.450619	−	0.892717i	$-0.351203\pi$
$54$		0			0
$55$	88200.0			0.530128
$56$	60982.5	+	35208.3i	0.347249	+	0.200484i
$57$		0			0
$58$	36624.0	+	63434.6i	0.187708	+	0.325119i
$59$	313273.	−	180868.i	1.52534	−	0.880655i	0.525790	−	0.850614i	$-0.323770\pi$
$59$	313273.	−	180868.i	1.52534	−	0.880655i	0.999549	−	0.0300406i	$-0.00956367\pi$
$60$		0			0
$61$	175152.	−	303373.i	0.771662	−	1.33656i	−0.164990	−	0.986295i	$-0.552759\pi$
$61$	175152.	−	303373.i	0.771662	−	1.33656i	0.936652	−	0.350262i	$-0.113907\pi$
$62$		−	64137.4i		−	0.269114i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	51990.4	+	30016.7i	0.189314	+	0.109301i
$66$		0			0
$67$	−60170.5	−	104218.i	−0.200060	−	0.346513i	0.748488	−	0.663148i	$-0.230780\pi$
$67$	−60170.5	−	104218.i	−0.200060	−	0.346513i	−0.948547	+	0.316635i	$0.897447\pi$
$68$	−65607.1	+	37878.3i	−0.208653	+	0.120466i
$69$		0			0
$70$	−46680.0	+	80852.1i	−0.136093	+	0.235721i
$71$		−	335101.i		−	0.936268i	−0.883657	−	0.468134i	$-0.844926\pi$
$71$		−	335101.i		−	0.936268i	0.883657	−	0.468134i	$-0.155074\pi$
$72$		0			0
$73$	175151.			0.450240			0.225120	−	0.974331i	$-0.427723\pi$
$73$	175151.			0.450240			0.225120	+	0.974331i	$0.427723\pi$
$74$	−230913.	−	133318.i	−0.569841	−	0.328998i
$75$		0			0
$76$	−49072.0	−	84995.2i	−0.111787	−	0.193622i
$77$	700346.	−	404345.i	1.53405	−	0.885686i
$78$		0			0
$79$	126130.	−	218463.i	0.255821	−	0.443094i	−0.709298	−	0.704909i	$-0.750988\pi$
$79$	126130.	−	218463.i	0.255821	−	0.443094i	0.965118	+	0.261815i	$0.0843210\pi$
$80$		−	43444.6i		−	0.0848528i
$81$		0			0
$82$	−35040.0			−0.0635510
$83$	−293660.	−	169544.i	−0.513582	−	0.296517i	0.220723	−	0.975337i	$-0.429158\pi$
$83$	−293660.	−	169544.i	−0.513582	−	0.296517i	−0.734305	+	0.678820i	$0.762492\pi$
$84$		0			0
$85$	−50220.0	−	86983.6i	−0.0817749	−	0.141638i
$86$	710930.	−	410456.i	1.11772	−	0.645314i
$87$		0			0
$88$	−188160.	+	325903.i	−0.276108	+	0.478233i
$89$			789971.i			1.12058i	0.828298	+	0.560288i	$0.189310\pi$
$89$			789971.i			1.12058i	−0.828298	+	0.560288i	$0.810690\pi$
$90$		0			0
$91$	550435.			0.730435
$92$	580118.	+	334931.i	0.744994	+	0.430122i
$93$		0			0
$94$	−509640.	−	882722.i	−0.613592	−	1.06277i
$95$	112689.	−	65060.9i	0.131435	−	0.0758838i
$96$		0			0
$97$	648552.	−	1.12333e6i	0.710608	−	1.23081i	−0.254022	−	0.967199i	$-0.581753\pi$
$97$	648552.	−	1.12333e6i	0.710608	−	1.23081i	0.964629	−	0.263610i	$-0.0849132\pi$
$98$			190478.i			0.202379i
$99$		0			0
$100$	−442400.			−0.442400
$101$	651956.	+	376407.i	0.632782	+	0.365337i	0.781829	−	0.623493i	$-0.214287\pi$
$101$	651956.	+	376407.i	0.632782	+	0.365337i	−0.149047	+	0.988830i	$0.547620\pi$
$102$		0			0
$103$	786658.	+	1.36253e6i	0.719903	+	1.24691i	0.961038	+	0.276417i	$0.0891471\pi$
$103$	786658.	+	1.36253e6i	0.719903	+	1.24691i	−0.241135	+	0.970492i	$0.577520\pi$
$104$	−221826.	+	128071.i	−0.197202	+	0.113855i
$105$		0			0
$106$	−751824.	+	1.30220e6i	−0.631246	+	1.09335i
$107$		−	733408.i		−	0.598680i	−0.954147	−	0.299340i	$-0.903234\pi$
$107$		−	733408.i		−	0.598680i	0.954147	−	0.299340i	$-0.0967664\pi$
$108$		0			0
$109$	−485998.			−0.375280			−0.187640	−	0.982238i	$-0.560084\pi$
$109$	−485998.			−0.375280			−0.187640	+	0.982238i	$0.560084\pi$
$110$	−432090.	−	249467.i	−0.324636	−	0.187428i
$111$		0			0
$112$	−199168.	−	344969.i	−0.141764	−	0.245542i
$113$	−1.07365e6	+	619871.i	−0.744092	+	0.429602i	−0.823555	−	0.567236i	$-0.808013\pi$
$113$	−1.07365e6	+	619871.i	−0.744092	+	0.429602i	0.0794632	+	0.996838i	$0.474679\pi$
$114$		0			0
$115$	−444060.	+	769134.i	−0.291977	+	0.505718i
$116$		−	414353.i		−	0.265459i
$117$		0			0
$118$	−2.04629e6			−1.24543
$119$	−797537.	−	460458.i	−0.473271	−	0.273243i
$120$		0			0
$121$	1.27512e6	+	2.20857e6i	0.719772	+	1.24668i
$122$	−1.71614e6	+	990812.i	−0.945088	+	0.545647i
$123$		0			0
$124$	−181408.	+	314208.i	−0.0951462	+	0.164798i
$125$		−	1.24946e6i		−	0.639722i
$126$		0			0
$127$	2.53077e6			1.23549			0.617747	−	0.786377i	$-0.288045\pi$
$127$	2.53077e6			1.23549			0.617747	+	0.786377i	$0.288045\pi$
$128$	160530.	+	92681.9i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−169800.	−	294102.i	−0.0772872	−	0.133865i
$131$	−2.62589e6	+	1.51606e6i	−1.16805	+	0.674375i	−0.953220	−	0.302276i	$-0.902254\pi$
$131$	−2.62589e6	+	1.51606e6i	−1.16805	+	0.674375i	−0.214832	+	0.976651i	$0.568920\pi$
$132$		0			0
$133$	596532.	−	1.03322e6i	0.253559	−	0.439176i
$134$			680751.i			0.282927i
$135$		0			0
$136$	428544.			0.170364
$137$	585401.	+	337981.i	0.227663	+	0.131441i	0.609493	−	0.792791i	$-0.291373\pi$
$137$	585401.	+	337981.i	0.227663	+	0.131441i	−0.381831	+	0.924232i	$0.624706\pi$
$138$		0			0
$139$	−2.00518e6	−	3.47307e6i	−0.746636	−	1.29321i	−0.949427	−	0.313989i	$-0.898335\pi$
$139$	−2.00518e6	−	3.47307e6i	−0.746636	−	1.29321i	0.202791	−	0.979222i	$-0.434999\pi$
$140$	457369.	−	264062.i	0.166680	−	0.0962325i
$141$		0			0
$142$	−947808.	+	1.64165e6i	−0.331021	+	0.573345i
$143$			2.94163e6i			1.00596i
$144$		0			0
$145$	549360.			0.180199
$146$	−858061.	−	495402.i	−0.275715	−	0.159184i
$147$		0			0
$148$	754160.	+	1.30624e6i	0.232637	+	0.402939i
$149$	−2.43325e6	+	1.40484e6i	−0.735578	+	0.424686i	−0.820459	−	0.571705i	$-0.806282\pi$
$149$	−2.43325e6	+	1.40484e6i	−0.735578	+	0.424686i	0.0848813	+	0.996391i	$0.472949\pi$
$150$		0			0
$151$	−608522.	+	1.05399e6i	−0.176744	+	0.306130i	−0.940764	−	0.339063i	$-0.889890\pi$
$151$	−608522.	+	1.05399e6i	−0.176744	+	0.306130i	0.764019	+	0.645194i	$0.223223\pi$
$152$			555186.i			0.158091i
$153$		0			0
$154$	−4.57464e6			−1.25255
$155$	−416585.	−	240515.i	−0.111869	−	0.0645874i
$156$		0			0
$157$	1.40746e6	+	2.43778e6i	0.363694	+	0.629936i	0.988566	−	0.150792i	$-0.0481822\pi$
$157$	1.40746e6	+	2.43778e6i	0.363694	+	0.629936i	−0.624872	+	0.780727i	$0.714849\pi$
$158$	−1.23581e6	+	713496.i	−0.313315	+	0.180892i
$159$		0			0
$160$	−122880.	+	212834.i	−0.0300000	+	0.0519615i
$161$			8.14301e6i			1.95123i
$162$		0			0
$163$	6.92549e6			1.59915			0.799573	−	0.600569i	$-0.205059\pi$
$163$	6.92549e6			1.59915			0.799573	+	0.600569i	$0.205059\pi$
$164$	171660.	+	99108.1i	0.0389169	+	0.0224687i
$165$		0			0
$166$	959088.	+	1.66119e6i	0.209669	+	0.363157i
$167$	−115731.	+	66817.3i	−0.0248485	+	0.0143463i	−0.512373	−	0.858763i	$-0.671233\pi$
$167$	−115731.	+	66817.3i	−0.0248485	+	0.0143463i	0.487524	+	0.873109i	$0.337900\pi$
$168$		0			0
$169$	1.41229e6	−	2.44616e6i	0.292593	−	0.506786i
$170$			568174.i			0.115647i
$171$		0			0
$172$	−4.64378e6			−0.912611
$173$	−7.34449e6	−	4.24034e6i	−1.41848	−	0.818960i	−0.422314	−	0.906449i	$-0.638782\pi$
$173$	−7.34449e6	−	4.24034e6i	−1.41848	−	0.818960i	−0.996165	+	0.0874899i	$0.972115\pi$
$174$		0			0
$175$	−2.68896e6	−	4.65742e6i	−0.501731	−	0.869023i
$176$	1.84358e6	−	1.06439e6i	0.338162	−	0.195238i
$177$		0			0
$178$	2.23438e6	−	3.87005e6i	0.396183	−	0.686210i
$179$			2.64832e6i			0.461755i	0.972983	+	0.230878i	$0.0741597\pi$
$179$			2.64832e6i			0.461755i	−0.972983	+	0.230878i	$0.925840\pi$
$180$		0			0
$181$	−2.07226e6			−0.349468			−0.174734	−	0.984616i	$-0.555907\pi$
$181$	−2.07226e6			−0.349468			−0.174734	+	0.984616i	$0.555907\pi$
$182$	−2.69657e6	−	1.55687e6i	−0.447299	−	0.258248i
$183$		0			0
$184$	−1.89466e6	−	3.28164e6i	−0.304142	−	0.526790i
$185$	−1.73185e6	+	999884.i	−0.273524	+	0.157919i
$186$		0			0
$187$	2.46078e6	−	4.26220e6i	0.376312	−	0.651791i
$188$			5.76592e6i			0.867751i
$189$		0			0
$190$	−736080.			−0.107316
$191$	2.14150e6	+	1.23639e6i	0.307339	+	0.177442i	0.645735	−	0.763562i	$-0.276551\pi$
$191$	2.14150e6	+	1.23639e6i	0.307339	+	0.177442i	−0.338396	+	0.941004i	$0.609884\pi$
$192$		0			0
$193$	493788.	+	855267.i	0.0686861	+	0.118968i	0.898323	−	0.439335i	$-0.144786\pi$
$193$	493788.	+	855267.i	0.0686861	+	0.118968i	−0.829637	+	0.558303i	$0.811453\pi$
$194$	−6.35449e6	+	3.66877e6i	−0.870313	+	0.502476i
$195$		0			0
$196$	538752.	−	933146.i	0.0715518	−	0.123931i
$197$		−	9.86666e6i		−	1.29054i	−0.763955	−	0.645270i	$-0.776745\pi$
$197$		−	9.86666e6i		−	1.29054i	0.763955	−	0.645270i	$-0.223255\pi$
$198$		0			0
$199$	9.55688e6			1.21271			0.606355	−	0.795194i	$-0.292631\pi$
$199$	9.55688e6			1.21271			0.606355	+	0.795194i	$0.292631\pi$
$200$	2.16731e6	+	1.25130e6i	0.270914	+	0.156412i
$201$		0			0
$202$	−2.12928e6	−	3.68802e6i	−0.258332	−	0.447445i
$203$	4.36215e6	−	2.51849e6i	0.521450	−	0.301059i
$204$		0			0
$205$	−131400.	+	227591.i	−0.0152522	+	0.0264177i
$206$		−	8.90001e6i		−	1.01810i
$207$		0			0
$208$	1.44896e6			0.161015
$209$	5.52175e6	+	3.18798e6i	0.604836	+	0.349202i
$210$		0			0
$211$	2.12341e6	+	3.67785e6i	0.226041	+	0.391514i	0.956631	−	0.291302i	$-0.0940885\pi$
$211$	2.12341e6	+	3.67785e6i	0.226041	+	0.391514i	−0.730591	+	0.682816i	$0.760755\pi$
$212$	7.36634e6	−	4.25296e6i	0.773115	−	0.446358i
$213$		0			0
$214$	−2.07439e6	+	3.59295e6i	−0.211665	+	0.366615i
$215$		−	6.15684e6i		−	0.619501i
$216$		0			0
$217$	−4.41048e6			−0.431625
$218$	2.38089e6	+	1.37461e6i	0.229811	+	0.132681i
$219$		0			0
$220$	1.41120e6	+	2.44427e6i	0.132532	+	0.229552i
$221$	2.90107e6	−	1.67493e6i	0.268770	−	0.155174i
$222$		0			0
$223$	−5.70919e6	+	9.88860e6i	−0.514825	+	0.891703i	0.485027	+	0.874499i	$0.338810\pi$
$223$	−5.70919e6	+	9.88860e6i	−0.514825	+	0.891703i	−0.999852	+	0.0172040i	$0.994524\pi$
$224$			2.25333e6i			0.200484i
$225$		0			0
$226$	7.01304e6			0.607549
$227$	7.65428e6	+	4.41920e6i	0.654375	+	0.377804i	0.790131	−	0.612939i	$-0.210013\pi$
$227$	7.65428e6	+	4.41920e6i	0.654375	+	0.377804i	−0.135755	+	0.990742i	$0.543346\pi$
$228$		0			0
$229$	−1.88600e6	−	3.26666e6i	−0.157049	−	0.272018i	0.776754	−	0.629804i	$-0.216865\pi$
$229$	−1.88600e6	−	3.26666e6i	−0.157049	−	0.272018i	−0.933803	+	0.357787i	$0.883532\pi$
$230$	4.35088e6	−	2.51198e6i	0.357597	−	0.206459i
$231$		0			0
$232$	−1.17197e6	+	2.02991e6i	−0.0938538	+	0.162560i
$233$		−	1.11388e7i		−	0.880581i	−0.897855	−	0.440290i	$-0.854875\pi$
$233$		−	1.11388e7i		−	0.880581i	0.897855	−	0.440290i	$-0.145125\pi$
$234$		0			0
$235$	−7.64460e6			−0.589049
$236$	1.00247e7	+	5.78778e6i	0.762669	+	0.440327i
$237$		0			0
$238$	2.60474e6	+	4.51155e6i	0.193212	+	0.334653i
$239$	−3.68667e6	+	2.12850e6i	−0.270048	+	0.155912i	−0.628909	−	0.777479i	$-0.716498\pi$
$239$	−3.68667e6	+	2.12850e6i	−0.270048	+	0.155912i	0.358862	+	0.933391i	$0.383165\pi$
$240$		0			0
$241$	9.90116e6	−	1.71493e7i	0.707351	−	1.22517i	−0.258485	−	0.966015i	$-0.583223\pi$
$241$	9.90116e6	−	1.71493e7i	0.707351	−	1.22517i	0.965836	−	0.259153i	$-0.0834434\pi$
$242$		−	1.44263e7i		−	1.01791i
$243$		0			0
$244$	1.12098e7			0.771662
$245$	1.23719e6	+	714291.i	0.0841274	+	0.0485710i
$246$		0			0
$247$	2.16990e6	+	3.75838e6i	0.143996	+	0.249408i
$248$	1.77743e6	−	1.02620e6i	0.116530	−	0.0672785i
$249$		0			0
$250$	−3.53400e6	+	6.12107e6i	−0.226176	+	0.391748i
$251$		−	5.46165e6i		−	0.345385i	−0.984976	−	0.172692i	$-0.944753\pi$
$251$		−	5.46165e6i		−	0.345385i	0.984976	−	0.172692i	$-0.0552466\pi$
$252$		0			0
$253$	−4.35179e7			−2.68724
$254$	−1.23982e7	−	7.15809e6i	−0.756583	−	0.436813i
$255$		0			0
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	2.33498e7	−	1.34810e7i	1.37557	−	0.794187i	0.383949	−	0.923354i	$-0.374564\pi$
$257$	2.33498e7	−	1.34810e7i	1.37557	−	0.794187i	0.991623	+	0.129167i	$0.0412304\pi$
$258$		0			0
$259$	−9.16776e6	+	1.58790e7i	−0.527672	+	0.913954i
$260$			1.92107e6i			0.109301i
$261$		0			0
$262$	1.71522e7			0.953711
$263$	−3.10961e6	−	1.79533e6i	−0.170938	−	0.0986910i	0.412090	−	0.911143i	$-0.364799\pi$
$263$	−3.10961e6	−	1.79533e6i	−0.170938	−	0.0986910i	−0.583028	+	0.812452i	$0.698132\pi$
$264$		0			0
$265$	5.63868e6	+	9.76648e6i	0.302998	+	0.524808i
$266$	−5.84479e6	+	3.37449e6i	−0.310545	+	0.179293i
$267$		0			0
$268$	1.92546e6	−	3.33499e6i	0.100030	−	0.173257i
$269$			4.44584e6i			0.228400i	0.993458	+	0.114200i	$0.0364305\pi$
$269$			4.44584e6i			0.228400i	−0.993458	+	0.114200i	$0.963569\pi$
$270$		0			0
$271$	−1.61349e6			−0.0810697			−0.0405349	−	0.999178i	$-0.512906\pi$
$271$	−1.61349e6			−0.0810697			−0.0405349	+	0.999178i	$0.512906\pi$
$272$	−2.09943e6	−	1.21211e6i	−0.104326	−	0.0602329i
$273$		0			0
$274$	−1.91191e6	−	3.31153e6i	−0.0929429	−	0.160982i
$275$	2.48902e7	−	1.43704e7i	1.19682	−	0.690986i
$276$		0			0
$277$	−1.22489e7	+	2.12156e7i	−0.576310	+	0.998198i	0.419588	+	0.907715i	$0.362175\pi$
$277$	−1.22489e7	+	2.12156e7i	−0.576310	+	0.998198i	−0.995898	+	0.0904837i	$0.971159\pi$
$278$			2.26860e7i			1.05590i
$279$		0			0
$280$	−2.98752e6			−0.136093
$281$	1.56962e7	+	9.06222e6i	0.707418	+	0.408428i	0.810104	−	0.586286i	$-0.199410\pi$
$281$	1.56962e7	+	9.06222e6i	0.707418	+	0.408428i	−0.102686	+	0.994714i	$0.532744\pi$
$282$		0			0
$283$	7.97942e6	+	1.38208e7i	0.352056	+	0.609779i	0.986610	−	0.163100i	$-0.0521493\pi$
$283$	7.97942e6	+	1.38208e7i	0.352056	+	0.609779i	−0.634553	+	0.772879i	$0.718816\pi$
$284$	9.28658e6	−	5.36161e6i	0.405416	−	0.234067i
$285$		0			0
$286$	8.32020e6	−	1.44110e7i	0.355661	−	0.616022i
$287$			2.40957e6i			0.101928i
$288$		0			0
$289$	1.85330e7			0.767808
$290$	−2.69130e6	−	1.55382e6i	−0.110349	−	0.0637101i
$291$		0			0
$292$	2.80242e6	+	4.85393e6i	0.112560	+	0.194960i
$293$	1.56265e7	−	9.02199e6i	0.621241	−	0.358674i	−0.156111	−	0.987740i	$-0.549896\pi$
$293$	1.56265e7	−	9.02199e6i	0.621241	−	0.358674i	0.777352	+	0.629066i	$0.216562\pi$
$294$		0			0
$295$	−7.67358e6	+	1.32910e7i	−0.298904	+	0.517717i
$296$		−	8.53235e6i		−	0.328998i
$297$		0			0
$298$	1.58940e7			0.600597
$299$	−2.56521e7	−	1.48102e7i	−0.959641	−	0.554049i
$300$		0			0
$301$	−2.82255e7	−	4.88879e7i	−1.03500	−	1.79268i
$302$	5.96228e6	−	3.44232e6i	0.216467	−	0.124977i
$303$		0			0
$304$	1.57030e6	−	2.71985e6i	0.0558937	−	0.0968108i
$305$			1.48622e7i			0.523821i
$306$		0			0
$307$	−1.54024e7			−0.532321			−0.266161	−	0.963929i	$-0.585755\pi$
$307$	−1.54024e7			−0.532321			−0.266161	+	0.963929i	$0.585755\pi$
$308$	2.24111e7	+	1.29390e7i	0.767027	+	0.442843i
$309$		0			0
$310$	1.36056e6	+	2.35656e6i	0.0456702	+	0.0791031i
$311$	−7.98793e6	+	4.61183e6i	−0.265554	+	0.153318i	−0.626865	−	0.779128i	$-0.715662\pi$
$311$	−7.98793e6	+	4.61183e6i	−0.265554	+	0.153318i	0.361311	+	0.932445i	$0.382329\pi$
$312$		0			0
$313$	1.63906e7	−	2.83893e7i	0.534516	−	0.925809i	−0.464670	−	0.885484i	$-0.653827\pi$
$313$	1.63906e7	−	2.83893e7i	0.534516	−	0.925809i	0.999187	−	0.0403254i	$-0.0128394\pi$
$314$		−	1.59235e7i		−	0.514340i
$315$		0			0
$316$	8.07229e6			0.255821
$317$	1.06107e6	+	612612.i	0.0333095	+	0.0192313i	0.516562	−	0.856250i	$-0.327211\pi$
$317$	1.06107e6	+	612612.i	0.0333095	+	0.0192313i	−0.483253	+	0.875481i	$0.660545\pi$
$318$		0			0
$319$	1.34593e7	+	2.33122e7i	0.414621	+	0.718144i
$320$	1.20397e6	−	695114.i	0.0367423	−	0.0212132i
$321$		0			0
$322$	2.30319e7	−	3.98924e7i	0.689862	−	1.19488i
$323$		−	7.26080e6i		−	0.215465i
$324$		0			0
$325$	1.95624e7			0.569864
$326$	−3.39278e7	−	1.95883e7i	−0.979272	−	0.565383i
$327$		0			0
$328$	−560640.	−	971057.i	−0.0158878	−	0.0275184i
$329$	−6.07014e7	+	3.50460e7i	−1.70456	+	0.984125i
$330$		0			0
$331$	−6.80434e6	+	1.17855e7i	−0.187630	+	0.324984i	−0.944460	−	0.328628i	$-0.893414\pi$
$331$	−6.80434e6	+	1.17855e7i	−0.187630	+	0.324984i	0.756830	+	0.653612i	$0.226747\pi$
$332$		−	1.08508e7i		−	0.296517i
$333$		0			0
$334$	755952.			0.0202887
$335$	4.42161e6	+	2.55282e6i	0.117610	+	0.0679025i
$336$		0			0
$337$	−3.00560e7	−	5.20585e7i	−0.785310	−	1.36020i	−0.928813	−	0.370548i	$-0.879170\pi$
$337$	−3.00560e7	−	5.20585e7i	−0.785310	−	1.36020i	0.143503	−	0.989650i	$-0.454163\pi$
$338$	−1.38376e7	+	7.98913e6i	−0.358352	+	0.206895i
$339$		0			0
$340$	1.60704e6	−	2.78347e6i	0.0408874	−	0.0708191i
$341$		−	2.35705e7i		−	0.594437i
$342$		0			0
$343$	−3.26671e7			−0.809520
$344$	2.27498e7	+	1.31346e7i	0.558858	+	0.322657i
$345$		0			0
$346$	2.39870e7	+	4.15467e7i	0.579092	+	1.00302i
$347$	−6.14342e7	+	3.54690e7i	−1.47035	+	0.848909i	−0.999446	−	0.0332744i	$-0.989406\pi$
$347$	−6.14342e7	+	3.54690e7i	−1.47035	+	0.848909i	−0.470907	+	0.882183i	$0.656073\pi$
$348$		0			0
$349$	−1.61557e7	+	2.79824e7i	−0.380057	+	0.658278i	−0.991070	−	0.133343i	$-0.957429\pi$
$349$	−1.61557e7	+	2.79824e7i	−0.380057	+	0.658278i	0.611013	+	0.791621i	$0.290762\pi$
$350$			3.04221e7i			0.709554i
$351$		0			0
$352$	−1.20422e7			−0.276108
$353$	−5.17645e7	−	2.98863e7i	−1.17681	−	0.679434i	−0.221539	−	0.975151i	$-0.571108\pi$
$353$	−5.17645e7	−	2.98863e7i	−1.17681	−	0.679434i	−0.955276	+	0.295717i	$0.904441\pi$
$354$		0			0
$355$	7.10856e6	+	1.23124e7i	0.158890	+	0.275206i
$356$	−2.18923e7	+	1.26395e7i	−0.485224	+	0.280144i
$357$		0			0
$358$	7.49059e6	−	1.29741e7i	0.163255	−	0.282766i
$359$			3.89679e7i			0.842216i	0.907011	+	0.421108i	$0.138359\pi$
$359$			3.89679e7i			0.842216i	−0.907011	+	0.421108i	$0.861641\pi$
$360$		0			0
$361$	−3.76394e7			−0.800057
$362$	1.01519e7	+	5.86123e6i	0.214005	+	0.123556i
$363$		0			0
$364$	8.80696e6	+	1.52541e7i	0.182609	+	0.316288i
$365$	−6.43546e6	+	3.71551e6i	−0.132343	+	0.0764083i
$366$		0			0
$367$	1.69443e7	−	2.93484e7i	0.342788	−	0.593725i	−0.642162	−	0.766569i	$-0.721962\pi$
$367$	1.69443e7	−	2.93484e7i	0.342788	−	0.593725i	0.984949	+	0.172844i	$0.0552956\pi$
$368$			2.14356e7i			0.430122i
$369$		0			0
$370$	1.13124e7			0.223331
$371$	8.95471e7	+	5.17000e7i	1.75360	+	1.01244i
$372$		0			0
$373$	−4.03321e7	−	6.98573e7i	−0.777185	−	1.34612i	−0.933558	−	0.358426i	$-0.883313\pi$
$373$	−4.03321e7	−	6.98573e7i	−0.777185	−	1.34612i	0.156373	−	0.987698i	$-0.450020\pi$
$374$	−2.41106e7	+	1.39203e7i	−0.460886	+	0.266093i
$375$		0			0
$376$	1.63085e7	−	2.82471e7i	0.306796	−	0.531387i
$377$			1.83222e7i			0.341943i
$378$		0			0
$379$	7.63889e7			1.40318			0.701589	−	0.712582i	$-0.252474\pi$
$379$	7.63889e7			1.40318			0.701589	+	0.712582i	$0.252474\pi$
$380$	3.60604e6	+	2.08195e6i	0.0657173	+	0.0379419i
$381$		0			0
$382$	−6.99410e6	−	1.21141e7i	−0.125471	−	0.217321i
$383$	−8.12176e6	+	4.68910e6i	−0.144562	+	0.0834629i	−0.570536	−	0.821272i	$-0.693265\pi$
$383$	−8.12176e6	+	4.68910e6i	−0.144562	+	0.0834629i	0.425974	+	0.904735i	$0.359931\pi$
$384$		0			0
$385$	−1.71549e7	+	2.97132e7i	−0.300612	+	0.520675i
$386$		−	5.58658e6i		−	0.0971369i
$387$		0			0
$388$	4.15074e7			0.710608
$389$	2.16182e6	+	1.24813e6i	0.0367258	+	0.0212037i	0.518251	−	0.855229i	$-0.326583\pi$
$389$	2.16182e6	+	1.24813e6i	0.0367258	+	0.0212037i	−0.481525	+	0.876433i	$0.659917\pi$
$390$		0			0
$391$	2.47785e7	+	4.29177e7i	0.414520	+	0.717970i
$392$	−5.27867e6	+	3.04764e6i	−0.0876327	+	0.0505948i
$393$		0			0
$394$	−2.79071e7	+	4.83366e7i	−0.456275	+	0.790291i
$395$			1.07024e7i			0.173657i
$396$		0			0
$397$	−3.12297e7			−0.499110			−0.249555	−	0.968361i	$-0.580284\pi$
$397$	−3.12297e7			−0.499110			−0.249555	+	0.968361i	$0.580284\pi$
$398$	−4.68189e7	−	2.70309e7i	−0.742630	−	0.428758i
$399$		0			0
$400$	−7.07840e6	−	1.22601e7i	−0.110600	−	0.191565i
$401$	−4.13594e7	+	2.38788e7i	−0.641417	+	0.370322i	−0.785160	−	0.619293i	$-0.787419\pi$
$401$	−4.13594e7	+	2.38788e7i	−0.641417	+	0.370322i	0.143743	+	0.989615i	$0.454086\pi$
$402$		0			0
$403$	8.02164e6	−	1.38939e7i	0.122560	−	0.212280i
$404$			2.40901e7i			0.365337i
$405$		0			0
$406$	−2.84935e7			−0.425762
$407$	−8.48607e7	−	4.89943e7i	−1.25870	−	0.726712i
$408$		0			0
$409$	2.08516e7	+	3.61161e7i	0.304769	+	0.527875i	0.977210	−	0.212276i	$-0.0680875\pi$
$409$	2.08516e7	+	3.61161e7i	0.304769	+	0.527875i	−0.672441	+	0.740151i	$0.734754\pi$
$410$	1.28745e6	−	743311.i	0.0186801	−	0.0107850i
$411$		0			0
$412$	−2.51730e7	+	4.36010e7i	−0.359952	+	0.623454i
$413$			1.40715e8i			1.99752i
$414$		0			0
$415$	1.43863e7			0.201282
$416$	−7.09843e6	−	4.09828e6i	−0.0986012	−	0.0569274i
$417$		0			0
$418$	−1.80340e7	−	3.12357e7i	−0.246923	−	0.427684i
$419$	8.69927e7	−	5.02253e7i	1.18261	−	0.682779i	0.225992	−	0.974129i	$-0.427438\pi$
$419$	8.69927e7	−	5.02253e7i	1.18261	−	0.682779i	0.956617	+	0.291350i	$0.0941044\pi$
$420$		0			0
$421$	−3.73572e7	+	6.47045e7i	−0.500642	+	0.867138i	0.499358	+	0.866396i	$0.333569\pi$
$421$	−3.73572e7	+	6.47045e7i	−0.500642	+	0.867138i	−1.00000		0.000741723i	$0.999764\pi$
$422$		−	2.40236e7i		−	0.319670i
$423$		0			0
$424$	−4.81167e7			−0.631246
$425$	−2.83443e7	−	1.63646e7i	−0.369232	−	0.213176i
$426$		0			0
$427$	6.81343e7	+	1.18012e8i	0.875150	+	1.51580i
$428$	2.03248e7	−	1.17345e7i	0.259236	−	0.149670i
$429$		0			0
$430$	−1.74142e7	+	3.01622e7i	−0.219027	+	0.379365i
$431$			8.67349e6i			0.108333i	0.998532	+	0.0541667i	$0.0172502\pi$
$431$			8.67349e6i			0.108333i	−0.998532	+	0.0541667i	$0.982750\pi$
$432$		0			0
$433$	−1.74353e7			−0.214766			−0.107383	−	0.994218i	$-0.534247\pi$
$433$	−1.74353e7			−0.214766			−0.107383	+	0.994218i	$0.534247\pi$
$434$	2.16069e7	+	1.24747e7i	0.264315	+	0.152603i
$435$		0			0
$436$	−7.77597e6	−	1.34684e7i	−0.0938199	−	0.162501i
$437$	−5.56006e7	+	3.21010e7i	−0.666247	+	0.384658i
$438$		0			0
$439$	4.43814e7	−	7.68709e7i	0.524575	−	0.908591i	−0.475015	−	0.879977i	$-0.657558\pi$
$439$	4.43814e7	−	7.68709e7i	0.524575	−	0.908591i	0.999591	−	0.0286133i	$-0.00910915\pi$
$440$		−	1.59659e7i		−	0.187428i
$441$		0			0
$442$	−1.89497e7			−0.219450
$443$	−1.10137e8	−	6.35878e7i	−1.26685	−	0.731413i	−0.292455	−	0.956279i	$-0.594472\pi$
$443$	−1.10137e8	−	6.35878e7i	−1.26685	−	0.731413i	−0.974390	+	0.224866i	$0.927806\pi$
$444$		0			0
$445$	−1.67578e7	−	2.90254e7i	−0.190168	−	0.329381i
$446$	5.59384e7	−	3.22960e7i	0.630529	−	0.364036i
$447$		0			0
$448$	6.37338e6	−	1.10390e7i	0.0708819	−	0.122771i
$449$		−	1.56764e8i		−	1.73184i	−0.500182	−	0.865920i	$-0.666734\pi$
$449$		−	1.56764e8i		−	1.73184i	0.500182	−	0.865920i	$-0.333266\pi$
$450$		0			0
$451$	−1.28772e7			−0.140376
$452$	−3.43567e7	−	1.98359e7i	−0.372046	−	0.214801i
$453$		0			0
$454$	−2.49988e7	−	4.32992e7i	−0.267148	−	0.462713i
$455$	−2.02243e7	+	1.16765e7i	−0.214703	+	0.123959i
$456$		0			0
$457$	3.15481e7	−	5.46428e7i	0.330540	−	0.572512i	−0.652078	−	0.758152i	$-0.726102\pi$
$457$	3.15481e7	−	5.46428e7i	0.330540	−	0.572512i	0.982618	+	0.185640i	$0.0594358\pi$
$458$			2.13377e7i			0.222101i
$459$		0			0
$460$	−2.84198e7			−0.291977
$461$	1.00461e8	+	5.80014e7i	1.02541	+	0.592019i	0.915666	−	0.401941i	$-0.131664\pi$
$461$	1.00461e8	+	5.80014e7i	1.02541	+	0.592019i	0.109742	+	0.993960i	$0.464998\pi$
$462$		0			0
$463$	6.67204e7	+	1.15563e8i	0.672226	+	1.16433i	0.977271	+	0.211992i	$0.0679951\pi$
$463$	6.67204e7	+	1.15563e8i	0.672226	+	1.16433i	−0.305045	+	0.952338i	$0.598672\pi$
$464$	1.14829e7	−	6.62965e6i	0.114947	−	0.0663646i
$465$		0			0
$466$	−3.15052e7	+	5.45686e7i	−0.311332	+	0.539243i
$467$		−	6.57602e7i		−	0.645672i	−0.946455	−	0.322836i	$-0.895364\pi$
$467$		−	6.57602e7i		−	0.645672i	0.946455	−	0.322836i	$-0.104636\pi$
$468$		0			0
$469$	4.68126e7			0.453779
$470$	3.74507e7	+	2.16222e7i	0.360717	+	0.208260i
$471$		0			0
$472$	−3.27406e7	−	5.67084e7i	−0.311359	−	0.539289i
$473$	2.61267e8	−	1.50842e8i	2.46888	−	1.42541i
$474$		0			0
$475$	2.12006e7	−	3.67206e7i	0.197819	−	0.342633i
$476$		−	2.94693e7i		−	0.273243i
$477$		0			0
$478$	2.40812e7			0.220493
$479$	1.52335e8	+	8.79506e7i	1.38609	+	0.800262i	0.992872	−	0.119181i	$-0.0380270\pi$
$479$	1.52335e8	+	8.79506e7i	1.38609	+	0.800262i	0.393222	+	0.919444i	$0.371360\pi$
$480$		0			0
$481$	−3.33480e7	−	5.77605e7i	−0.299664	−	0.519033i
$482$	−9.70112e7	+	5.60094e7i	−0.866325	+	0.500173i
$483$		0			0
$484$	−4.08038e7	+	7.06743e7i	−0.359886	+	0.623341i
$485$			5.50315e7i			0.482377i
$486$		0			0
$487$	5.72207e7			0.495412			0.247706	−	0.968835i	$-0.420323\pi$
$487$	5.72207e7			0.495412			0.247706	+	0.968835i	$0.420323\pi$
$488$	−5.49164e7	−	3.17060e7i	−0.472544	−	0.272824i
$489$		0			0
$490$	−4.04064e6	−	6.99859e6i	−0.0343449	−	0.0594871i
$491$	−1.10938e7	+	6.40499e6i	−0.0937205	+	0.0541096i	−0.546128	−	0.837702i	$-0.683899\pi$
$491$	−1.10938e7	+	6.40499e6i	−0.0937205	+	0.0541096i	0.452407	+	0.891811i	$0.350565\pi$
$492$		0			0
$493$	1.53271e7	−	2.65474e7i	0.127915	−	0.221555i
$494$		−	2.45496e7i		−	0.203641i
$495$		0			0
$496$	−1.16101e7			−0.0951462
$497$	1.12890e8	+	6.51771e7i	0.919573	+	0.530916i
$498$		0			0
$499$	3.49942e7	+	6.06118e7i	0.281640	+	0.487815i	0.971789	−	0.235853i	$-0.0757882\pi$
$499$	3.49942e7	+	6.06118e7i	0.281640	+	0.487815i	−0.690149	+	0.723668i	$0.742455\pi$
$500$	3.46260e7	−	1.99913e7i	0.277008	−	0.159931i
$501$		0			0
$502$	−1.54479e7	+	2.67565e7i	−0.122112	+	0.211504i
$503$		−	1.81356e8i		−	1.42504i	−0.701652	−	0.712520i	$-0.747554\pi$
$503$		−	1.81356e8i		−	1.42504i	0.701652	−	0.712520i	$-0.252446\pi$
$504$		0			0
$505$	−3.19392e7			−0.247999
$506$	2.13193e8	+	1.23087e8i	1.64559	+	0.950082i
$507$		0			0
$508$	4.04923e7	+	7.01346e7i	0.308874	+	0.534985i
$509$	−3.22576e7	+	1.86239e7i	−0.244613	+	0.141227i	−0.617295	−	0.786732i	$-0.711771\pi$
$509$	−3.22576e7	+	1.86239e7i	−0.244613	+	0.141227i	0.372682	+	0.927959i	$0.378438\pi$
$510$		0			0
$511$	−3.40669e7	+	5.90055e7i	−0.255311	+	0.442212i
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	−1.52520e8			−1.12315
$515$	−5.78073e7	−	3.33751e7i	−0.423215	−	0.244343i
$516$		0			0
$517$	−1.87293e8	−	3.24400e8i	−1.35534	−	2.34752i
$518$	8.98253e7	−	5.18607e7i	0.646263	−	0.373120i
$519$		0			0
$520$	5.43360e6	−	9.41127e6i	0.0386436	−	0.0669327i
$521$		−	1.20022e8i		−	0.848688i	−0.905501	−	0.424344i	$-0.860505\pi$
$521$		−	1.20022e8i		−	0.848688i	0.905501	−	0.424344i	$-0.139495\pi$
$522$		0			0
$523$	2.02395e8			1.41480			0.707398	−	0.706815i	$-0.249869\pi$
$523$	2.02395e8			1.41480			0.707398	+	0.706815i	$0.249869\pi$
$524$	−8.40284e7	−	4.85138e7i	−0.584026	−	0.337188i
$525$		0			0
$526$	1.01559e7	+	1.75906e7i	0.0697851	+	0.120871i
$527$	−2.32454e7	+	1.34208e7i	−0.158820	+	0.0916949i
$528$		0			0
$529$	1.45081e8	−	2.51288e8i	0.980041	−	1.69748i
$530$		−	6.37944e7i		−	0.428504i
$531$		0			0
$532$	3.81780e7			0.253559
$533$	−7.59060e6	−	4.38244e6i	−0.0501296	−	0.0289424i
$534$		0			0
$535$	1.55579e7	+	2.69471e7i	0.101599	+	0.175975i
$536$	−1.88655e7	+	1.08920e7i	−0.122511	+	0.0707317i
$537$		0			0
$538$	1.25747e7	−	2.17801e7i	0.0807517	−	0.139866i
$539$			7.00005e7i			0.447028i
$540$		0			0
$541$	1.68172e8			1.06209			0.531047	−	0.847342i	$-0.321799\pi$
$541$	1.68172e8			1.06209			0.531047	+	0.847342i	$0.321799\pi$
$542$	7.90446e6	+	4.56364e6i	0.0496449	+	0.0286625i
$543$		0			0
$544$	6.85670e6	+	1.18762e7i	0.0425911	+	0.0737699i
$545$	1.78567e7	−	1.03096e7i	0.110309	−	0.0636871i
$546$		0			0
$547$	4.85445e7	−	8.40816e7i	0.296605	−	0.513735i	−0.678752	−	0.734368i	$-0.737479\pi$
$547$	4.85445e7	−	8.40816e7i	0.296605	−	0.513735i	0.975357	+	0.220633i	$0.0708122\pi$
$548$			2.16308e7i			0.131441i
$549$		0			0
$550$	−1.62582e8			−0.977202
$551$	3.43926e7	+	1.98566e7i	0.205594	+	0.118700i
$552$		0			0
$553$	4.90644e7	+	8.49820e7i	0.290129	+	0.502518i
$554$	1.20014e8	−	6.92900e7i	0.705833	−	0.407513i
$555$		0			0
$556$	6.41657e7	−	1.11138e8i	0.373318	−	0.646605i
$557$		−	2.16017e8i		−	1.25004i	−0.780610	−	0.625018i	$-0.785091\pi$
$557$		−	2.16017e8i		−	1.25004i	0.780610	−	0.625018i	$-0.214909\pi$
$558$		0			0
$559$	2.05342e8			1.17555
$560$	1.46358e7	+	8.44998e6i	0.0833398	+	0.0481162i
$561$		0			0
$562$	−5.12637e7	−	8.87913e7i	−0.288802	−	0.500220i
$563$	1.05245e8	−	6.07634e7i	0.589763	−	0.340500i	−0.175241	−	0.984526i	$-0.556070\pi$
$563$	1.05245e8	−	6.07634e7i	0.589763	−	0.340500i	0.765004	+	0.644026i	$0.222737\pi$
$564$		0			0
$565$	2.62989e7	−	4.55510e7i	0.145812	−	0.252553i
$566$		−	9.02768e7i		−	0.497882i
$567$		0			0
$568$	−6.06597e7			−0.331021
$569$	−2.08189e8	−	1.20198e8i	−1.13011	−	0.652469i	−0.186147	−	0.982522i	$-0.559600\pi$
$569$	−2.08189e8	−	1.20198e8i	−1.13011	−	0.652469i	−0.943962	+	0.330053i	$0.892933\pi$
$570$		0			0
$571$	6.73537e7	+	1.16660e8i	0.361787	+	0.626634i	0.988255	−	0.152813i	$-0.0488333\pi$
$571$	6.73537e7	+	1.16660e8i	0.361787	+	0.626634i	−0.626468	+	0.779447i	$0.715500\pi$
$572$	−8.15210e7	+	4.70662e7i	−0.435593	+	0.251490i
$573$		0			0
$574$	6.81528e6	−	1.18044e7i	0.0360369	−	0.0624178i
$575$			2.89401e8i			1.52229i
$576$		0			0
$577$	−3.36318e8			−1.75074			−0.875372	−	0.483450i	$-0.839384\pi$
$577$	−3.36318e8			−1.75074			−0.875372	+	0.483450i	$0.839384\pi$
$578$	−9.07929e7	−	5.24193e7i	−0.470184	−	0.271461i
$579$		0			0
$580$	8.78976e6	+	1.52243e7i	0.0450498	+	0.0780286i
$581$	1.14234e8	−	6.59528e7i	0.582459	−	0.336283i
$582$		0			0
$583$	−2.76295e8	+	4.78558e8i	−1.39434	+	2.41506i
$584$		−	3.17057e7i		−	0.159184i
$585$		0			0
$586$	−1.02072e8			−0.507241
$587$	1.81990e8	+	1.05072e8i	0.899772	+	0.519484i	0.877126	−	0.480260i	$-0.159458\pi$
$587$	1.81990e8	+	1.05072e8i	0.899772	+	0.519484i	0.0226460	+	0.999744i	$0.492791\pi$
$588$		0			0
$589$	−1.73868e7	−	3.01149e7i	−0.0850892	−	0.147379i
$590$	7.51854e7	−	4.34083e7i	0.366081	−	0.211357i
$591$		0			0
$592$	−2.41331e7	+	4.17998e7i	−0.116318	+	0.201469i
$593$			2.99185e8i			1.43475i	0.696689	+	0.717373i	$0.254656\pi$
$593$			2.99185e8i			1.43475i	−0.696689	+	0.717373i	$0.745344\pi$
$594$		0			0
$595$	3.90712e7			0.185484
$596$	−7.78641e7	−	4.49549e7i	−0.367789	−	0.212343i
$597$		0			0
$598$	8.37793e7	+	1.45110e8i	0.391772	+	0.678569i
$599$	2.16171e8	−	1.24807e8i	1.00581	−	0.580707i	0.0958504	−	0.995396i	$-0.469443\pi$
$599$	2.16171e8	−	1.24807e8i	1.00581	−	0.580707i	0.909963	+	0.414689i	$0.136110\pi$
$600$		0			0
$601$	7.32808e7	−	1.26926e8i	0.337572	−	0.584692i	−0.646403	−	0.762996i	$-0.723728\pi$
$601$	7.32808e7	−	1.26926e8i	0.337572	−	0.584692i	0.983975	+	0.178304i	$0.0570610\pi$
$602$			3.19335e8i			1.46371i
$603$		0			0
$604$	−3.89454e7			−0.176744
$605$	−9.37018e7	−	5.40987e7i	−0.423138	−	0.244299i
$606$		0			0
$607$	5.17095e7	+	8.95635e7i	0.231209	+	0.400465i	0.958164	−	0.286219i	$-0.0923987\pi$
$607$	5.17095e7	+	8.95635e7i	0.231209	+	0.400465i	−0.726955	+	0.686685i	$0.759065\pi$
$608$	−1.53858e7	+	8.88298e6i	−0.0684555	+	0.0395228i
$609$		0			0
$610$	4.20366e7	−	7.28095e7i	0.185199	−	0.320774i
$611$		−	2.54962e8i		−	1.11777i
$612$		0			0
$613$	1.44725e8			0.628294			0.314147	−	0.949374i	$-0.398282\pi$
$613$	1.44725e8			0.628294			0.314147	+	0.949374i	$0.398282\pi$
$614$	7.54561e7	+	4.35646e7i	0.325979	+	0.188204i
$615$		0			0
$616$	−7.31942e7	−	1.26776e8i	−0.313137	−	0.542370i
$617$	−2.44531e8	+	1.41180e8i	−1.04107	+	0.601060i	−0.920135	−	0.391601i	$-0.871921\pi$
$617$	−2.44531e8	+	1.41180e8i	−1.04107	+	0.601060i	−0.120931	+	0.992661i	$0.538588\pi$
$618$		0			0
$619$	−1.20304e8	+	2.08373e8i	−0.507234	+	0.878554i	0.492731	+	0.870181i	$0.335999\pi$
$619$	−1.20304e8	+	2.08373e8i	−0.507234	+	0.878554i	−0.999965	+	0.00837278i	$0.997335\pi$
$620$		−	1.53930e7i		−	0.0645874i
$621$		0			0
$622$	5.21769e7			0.216824
$623$	−2.66129e8	−	1.53649e8i	−1.10059	−	0.635429i
$624$		0			0
$625$	−8.15028e7	−	1.41167e8i	−0.333836	−	0.578220i
$626$	−1.60594e8	+	9.27190e7i	−0.654646	+	0.377960i
$627$		0			0
$628$	−4.50386e7	+	7.80091e7i	−0.181847	+	0.314968i
$629$			1.11587e8i			0.448396i
$630$		0			0
$631$	3.67661e8			1.46339			0.731694	−	0.681633i	$-0.238730\pi$
$631$	3.67661e8			1.46339			0.731694	+	0.681633i	$0.238730\pi$
$632$	−3.95460e7	−	2.28319e7i	−0.156657	−	0.0904462i
$633$		0			0
$634$	−3.46546e6	−	6.00235e6i	−0.0135986	−	0.0235534i
$635$	−9.29863e7	+	5.36857e7i	−0.363160	+	0.209670i
$636$		0			0
$637$	−2.38229e7	+	4.12625e7i	−0.0921673	+	0.159639i
$638$		−	1.52275e8i		−	0.586362i
$639$		0			0
$640$	−7.86432e6			−0.0300000
$641$	1.05262e8	+	6.07731e7i	0.399667	+	0.230748i	0.686340	−	0.727281i	$-0.259216\pi$
$641$	1.05262e8	+	6.07731e7i	0.399667	+	0.230748i	−0.286673	+	0.958028i	$0.592549\pi$
$642$		0			0
$643$	−6.76022e7	−	1.17090e8i	−0.254289	−	0.440442i	0.710413	−	0.703785i	$-0.248508\pi$
$643$	−6.76022e7	−	1.17090e8i	−0.254289	−	0.440442i	−0.964702	+	0.263343i	$0.915175\pi$
$644$	−2.25666e8	+	1.30288e8i	−0.844905	+	0.487806i
$645$		0			0
$646$	−2.05366e7	+	3.55705e7i	−0.0761784	+	0.131945i
$647$			9.39417e7i			0.346853i	0.984847	+	0.173427i	$0.0554839\pi$
$647$			9.39417e7i			0.346853i	−0.984847	+	0.173427i	$0.944516\pi$
$648$		0			0
$649$	−7.52011e8			−2.75100
$650$	−9.58357e7	−	5.53308e7i	−0.348969	−	0.201477i
$651$		0			0
$652$	1.10808e8	+	1.91925e8i	0.399786	+	0.692450i
$653$	−1.95674e8	+	1.12973e8i	−0.702739	+	0.405727i	−0.808367	−	0.588679i	$-0.799648\pi$
$653$	−1.95674e8	+	1.12973e8i	−0.702739	+	0.405727i	0.105627	+	0.994406i	$0.466315\pi$
$654$		0			0
$655$	6.43208e7	−	1.11407e8i	0.228891	−	0.396450i
$656$			6.34292e6i			0.0224687i
$657$		0			0
$658$	3.96500e8			1.39176
$659$	1.87102e8	+	1.08023e8i	0.653765	+	0.377452i	0.789897	−	0.613239i	$-0.210134\pi$
$659$	1.87102e8	+	1.08023e8i	0.653765	+	0.377452i	−0.136132	+	0.990691i	$0.543467\pi$
$660$		0			0
$661$	5.18876e6	+	8.98720e6i	0.0179663	+	0.0311186i	0.874869	−	0.484360i	$-0.160947\pi$
$661$	5.18876e6	+	8.98720e6i	0.0179663	+	0.0311186i	−0.856902	+	0.515479i	$0.827614\pi$
$662$	6.66686e7	−	3.84912e7i	0.229799	−	0.132674i
$663$		0			0
$664$	−3.06908e7	+	5.31581e7i	−0.104834	+	0.181579i
$665$			5.06174e7i			0.172121i
$666$		0			0
$667$	−2.71054e8			−0.913437
$668$	−3.70339e6	−	2.13816e6i	−0.0124243	−	0.00717315i
$669$		0			0
$670$	−1.44409e7	−	2.50124e7i	−0.0480143	−	0.0831632i
$671$	−6.30680e8	+	3.64123e8i	−2.08757	+	1.20526i
$672$		0			0
$673$	3.05890e7	−	5.29816e7i	0.100350	−	0.173812i	−0.811479	−	0.584382i	$-0.801337\pi$
$673$	3.05890e7	−	5.29816e7i	0.100350	−	0.173812i	0.911829	+	0.410570i	$0.134670\pi$
$674$			3.40045e8i			1.11060i
$675$		0			0
$676$	9.03867e7			0.292593
$677$	−2.58580e8	−	1.49291e8i	−0.833354	−	0.481137i	0.0216457	−	0.999766i	$-0.493109\pi$
$677$	−2.58580e8	−	1.49291e8i	−0.833354	−	0.481137i	−0.855000	+	0.518629i	$0.826443\pi$
$678$		0			0
$679$	2.52287e8	+	4.36974e8i	0.805908	+	1.39587i
$680$	−1.57457e7	+	9.09079e6i	−0.0500767	+	0.0289118i
$681$		0			0
$682$	−6.66674e7	+	1.15471e8i	−0.210165	+	0.364017i
$683$			4.80446e8i			1.50794i	0.656911	+	0.753968i	$0.271863\pi$
$683$			4.80446e8i			1.50794i	−0.656911	+	0.753968i	$0.728137\pi$
$684$		0			0
$685$	−2.86787e7			−0.0892252
$686$	1.60035e8	+	9.23964e7i	0.495728	+	0.286209i
$687$		0			0
$688$	−7.43004e7	−	1.28692e8i	−0.228153	−	0.395172i
$689$	−3.25730e8	+	1.88061e8i	−0.995865	+	0.574963i
$690$		0			0
$691$	−1.32481e8	+	2.29465e8i	−0.401533	+	0.695475i	−0.993911	−	0.110185i	$-0.964856\pi$
$691$	−1.32481e8	+	2.29465e8i	−0.401533	+	0.695475i	0.592378	+	0.805660i	$0.298189\pi$
$692$		−	2.71382e8i		−	0.818960i
$693$		0			0
$694$	4.01286e8			1.20054
$695$	1.47350e8	+	8.50725e7i	0.438930	+	0.253416i
$696$		0			0
$697$	7.33212e6	+	1.26996e7i	0.0216537	+	0.0375052i
$698$	1.58293e8	−	9.13903e7i	0.465473	−	0.268741i
$699$		0			0
$700$	8.60468e7	−	1.49037e8i	0.250865	−	0.434511i
$701$		−	3.56417e8i		−	1.03468i	−0.855781	−	0.517338i	$-0.826923\pi$
$701$		−	3.56417e8i		−	1.03468i	0.855781	−	0.517338i	$-0.173077\pi$
$702$		0			0
$703$	−1.44563e8			−0.416094
$704$	5.89947e7	+	3.40606e7i	0.169081	+	0.0976190i
$705$		0			0
$706$	1.69062e8	+	2.92824e8i	0.480433	+	0.832134i
$707$	−2.53611e8	+	1.46422e8i	−0.717645	+	0.414333i
$708$		0			0
$709$	1.09900e8	−	1.90353e8i	0.308362	−	0.534098i	−0.669642	−	0.742684i	$-0.733553\pi$
$709$	1.09900e8	−	1.90353e8i	0.308362	−	0.534098i	0.978004	+	0.208585i	$0.0668859\pi$
$710$		−	8.04242e7i		−	0.224704i
$711$		0			0
$712$	1.43000e8			0.396183
$713$	2.05543e8	+	1.18670e8i	0.567066	+	0.327396i
$714$		0			0
$715$	−6.24015e7	−	1.08083e8i	−0.170717	−	0.295691i
$716$	−7.33925e7	+	4.23732e7i	−0.199946	+	0.115439i
$717$		0			0
$718$	1.10218e8	−	1.90903e8i	0.297768	−	0.515750i
$719$		−	9.72141e7i		−	0.261543i	−0.991413	−	0.130771i	$-0.958255\pi$
$719$		−	9.72141e7i		−	0.261543i	0.991413	−	0.130771i	$-0.0417454\pi$
$720$		0			0
$721$	−6.12020e8			−1.63290
$722$	1.84395e8	+	1.06460e8i	0.489933	+	0.282863i
$723$		0			0
$724$	−3.31561e7	−	5.74281e7i	−0.0873671	−	0.151324i
$725$	1.55030e8	−	8.95068e7i	0.406820	−	0.234878i
$726$		0			0
$727$	7.50353e7	−	1.29965e8i	0.195282	−	0.338238i	−0.751711	−	0.659493i	$-0.770771\pi$
$727$	7.50353e7	−	1.29965e8i	0.195282	−	0.338238i	0.946993	+	0.321254i	$0.104104\pi$
$728$		−	9.96394e7i		−	0.258248i
$729$		0			0
$730$	4.20362e7			0.108058
$731$	−2.97524e8	−	1.71776e8i	−0.761676	−	0.439754i
$732$		0			0
$733$	−1.43511e8	−	2.48568e8i	−0.364395	−	0.631150i	0.624284	−	0.781197i	$-0.285391\pi$
$733$	−1.43511e8	−	2.48568e8i	−0.364395	−	0.631150i	−0.988679	+	0.150047i	$0.952057\pi$
$734$	−1.66019e8	+	9.58514e7i	−0.419827	+	0.242387i
$735$		0			0
$736$	6.06290e7	−	1.05012e8i	0.152071	−	0.263395i
$737$			2.50176e8i			0.624947i
$738$		0			0
$739$	4.19241e8			1.03880			0.519398	−	0.854532i	$-0.326156\pi$
$739$	4.19241e8			1.03880			0.519398	+	0.854532i	$0.326156\pi$
$740$	−5.54192e7	−	3.19963e7i	−0.136762	−	0.0789595i
$741$		0			0
$742$	−2.92460e8	−	5.06555e8i	−0.715903	−	1.23998i
$743$	6.09657e8	−	3.51986e8i	1.48634	−	0.858141i	0.486465	−	0.873700i	$-0.338286\pi$
$743$	6.09657e8	−	3.51986e8i	1.48634	−	0.858141i	0.999879	+	0.0155594i	$0.00495292\pi$
$744$		0			0
$745$	5.96023e7	−	1.03234e8i	0.144143	−	0.249663i
$746$			4.56306e8i			1.09911i
$747$		0			0
$748$	1.57490e8			0.376312
$749$	2.47073e8	+	1.42648e8i	0.588004	+	0.339485i
$750$		0			0
$751$	−3.10951e8	−	5.38583e8i	−0.734129	−	1.27155i	−0.955104	−	0.296270i	$-0.904257\pi$
$751$	−3.10951e8	−	5.38583e8i	−0.734129	−	1.27155i	0.220975	−	0.975279i	$-0.429076\pi$
$752$	−1.59790e8	+	9.22547e7i	−0.375747	+	0.216938i
$753$		0			0
$754$	5.18230e7	−	8.97600e7i	0.120895	−	0.209396i
$755$		−	5.16348e7i		−	0.119978i
$756$		0			0
$757$	4.62050e7			0.106513			0.0532563	−	0.998581i	$-0.483040\pi$
$757$	4.62050e7			0.106513			0.0532563	+	0.998581i	$0.483040\pi$
$758$	−3.74228e8	−	2.16061e8i	−0.859268	−	0.496098i
$759$		0			0
$760$	−1.17773e7	−	2.03988e7i	−0.0268290	−	0.0464692i
$761$	1.33797e8	−	7.72478e7i	0.303594	−	0.175280i	−0.340462	−	0.940258i	$-0.610584\pi$
$761$	1.33797e8	−	7.72478e7i	0.303594	−	0.175280i	0.644056	+	0.764978i	$0.277250\pi$
$762$		0			0
$763$	9.45266e7	−	1.63725e8i	0.212804	−	0.368588i
$764$			7.91293e7i			0.177442i
$765$		0			0
$766$	5.30511e7			0.118034
$767$	−4.43281e8	−	2.55928e8i	−0.982410	−	0.567195i
$768$		0			0
$769$	4.08934e8	+	7.08295e8i	0.899237	+	1.55752i	0.828471	+	0.560032i	$0.189211\pi$
$769$	4.08934e8	+	7.08295e8i	0.899237	+	1.55752i	0.0707659	+	0.997493i	$0.477456\pi$
$770$	1.68083e8	−	9.70428e7i	0.368173	−	0.212565i
$771$		0			0
$772$	−1.58012e7	+	2.73685e7i	−0.0343431	+	0.0594839i
$773$		−	1.37465e8i		−	0.297615i	−0.988866	−	0.148807i	$-0.952457\pi$
$773$		−	1.37465e8i		−	0.297615i	0.988866	−	0.148807i	$-0.0475434\pi$
$774$		0			0
$775$	−1.56748e8			−0.336741
$776$	−2.03344e8	−	1.17401e8i	−0.435157	−	0.251238i
$777$		0			0
$778$	−7.06049e6	−	1.22291e7i	−0.0149933	−	0.0259691i
$779$	−1.64526e7	+	9.49889e6i	−0.0348034	+	0.0200937i
$780$		0			0
$781$	−3.48319e8	+	6.03307e8i	−0.731181	+	1.26644i
$782$		−	2.80337e8i		−	0.586220i
$783$		0			0
$784$	3.44801e7			0.0715518
$785$	−1.03426e8	−	5.97133e7i	−0.213807	−	0.123442i
$786$		0			0
$787$	−2.42589e8	−	4.20177e8i	−0.497676	−	0.862001i	0.502320	−	0.864682i	$-0.332480\pi$
$787$	−2.42589e8	−	4.20177e8i	−0.497676	−	0.862001i	−0.999996	+	0.00268100i	$0.999147\pi$
$788$	2.73433e8	−	1.57867e8i	0.558820	−	0.322635i
$789$		0			0
$790$	3.02711e7	−	5.24310e7i	0.0613969	−	0.106343i
$791$		−	4.82260e8i		−	0.974432i
$792$		0			0
$793$	−4.95682e8			−0.993993
$794$	1.52994e8	+	8.83310e7i	0.305641	+	0.176462i
$795$		0			0
$796$	1.52910e8	+	2.64848e8i	0.303177	+	0.525119i
$797$	8.58768e8	−	4.95810e8i	1.69629	−	0.979355i	0.747072	−	0.664743i	$-0.231459\pi$
$797$	8.58768e8	−	4.95810e8i	1.69629	−	0.979355i	0.949221	−	0.314611i	$-0.101874\pi$
$798$		0			0
$799$	−2.13284e8	+	3.69419e8i	−0.418137	+	0.724235i
$800$			8.00830e7i			0.156412i
$801$		0			0
$802$	2.70158e8			0.523715
$803$	−3.15337e8	−	1.82060e8i	−0.609016	−	0.351616i
$804$		0			0
$805$	−1.72739e8	−	2.99193e8i	−0.331134	−	0.573541i
$806$	−7.85957e7	+	4.53772e7i	−0.150104	+	0.0866628i
$807$		0			0
$808$	6.81370e7	−	1.18017e8i	0.129166	−	0.223722i
$809$			7.33707e8i			1.38573i	0.721069	+	0.692863i	$0.243651\pi$
$809$			7.33707e8i			1.38573i	−0.721069	+	0.692863i	$0.756349\pi$
$810$		0			0
$811$	6.35499e8			1.19139			0.595693	−	0.803212i	$-0.296878\pi$
$811$	6.35499e8			1.19139			0.595693	+	0.803212i	$0.296878\pi$
$812$	1.39589e8	+	8.05917e7i	0.260725	+	0.150530i
$813$		0			0
$814$	2.77154e8	+	4.80044e8i	0.513863	+	0.890037i
$815$	−2.54459e8	+	1.46912e8i	−0.470051	+	0.271384i
$816$		0			0
$817$	2.22538e8	−	3.85448e8i	0.408074	−	0.706805i
$818$		−	2.35909e8i		−	0.431008i
$819$		0			0
$820$	−8.40960e6			−0.0152522
$821$	−4.04150e7	−	2.33336e7i	−0.0730319	−	0.0421650i	0.463039	−	0.886338i	$-0.346759\pi$
$821$	−4.04150e7	−	2.33336e7i	−0.0730319	−	0.0421650i	−0.536071	+	0.844173i	$0.680092\pi$
$822$		0			0
$823$	1.81293e8	+	3.14009e8i	0.325224	+	0.563305i	0.981558	−	0.191166i	$-0.0612269\pi$
$823$	1.81293e8	+	3.14009e8i	0.325224	+	0.563305i	−0.656334	+	0.754471i	$0.727894\pi$
$824$	2.46644e8	−	1.42400e8i	0.440849	−	0.254524i
$825$		0			0
$826$	3.98003e8	−	6.89361e8i	0.706230	−	1.22323i
$827$		−	3.89027e8i		−	0.687801i	−0.939006	−	0.343901i	$-0.888252\pi$
$827$		−	3.89027e8i		−	0.687801i	0.939006	−	0.343901i	$-0.111748\pi$
$828$		0			0
$829$	4.96963e8			0.872288			0.436144	−	0.899877i	$-0.356344\pi$
$829$	4.96963e8			0.872288			0.436144	+	0.899877i	$0.356344\pi$
$830$	−7.04783e7	−	4.06907e7i	−0.123260	−	0.0711640i
$831$		0			0
$832$	2.31834e7	+	4.01548e7i	0.0402538	+	0.0697215i
$833$	6.90351e7	−	3.98574e7i	0.119436	−	0.0689564i
$834$		0			0
$835$	2.83482e6	−	4.91005e6i	0.00486929	−	0.00843387i
$836$			2.04031e8i			0.349202i
$837$		0			0
$838$	−5.68234e8			−0.965596
$839$	8.58126e8	+	4.95439e8i	1.45300	+	0.838889i	0.998650	−	0.0519352i	$-0.0165389\pi$
$839$	8.58126e8	+	4.95439e8i	1.45300	+	0.838889i	0.454348	+	0.890824i	$0.349872\pi$
$840$		0			0
$841$	−2.13579e8	−	3.69930e8i	−0.359063	−	0.621916i
$842$	3.66024e8	−	2.11324e8i	0.613159	−	0.354008i
$843$		0			0
$844$	−6.79491e7	+	1.17691e8i	−0.113020	+	0.195757i
$845$			1.19837e8i			0.198619i
$846$		0			0
$847$	−9.92043e8			−1.63260
$848$	2.35723e8	+	1.36095e8i	0.386558	+	0.223179i
$849$		0			0
$850$	9.25722e7	+	1.60340e8i	0.150738	+	0.261087i
$851$	8.54495e8	−	4.93343e8i	1.38650	−	0.800498i
$852$		0			0
$853$	−1.31697e8	+	2.28106e8i	−0.212192	+	0.367527i	−0.952400	−	0.304850i	$-0.901394\pi$
$853$	−1.31697e8	+	2.28106e8i	−0.212192	+	0.367527i	0.740208	+	0.672378i	$0.234727\pi$
$854$		−	7.70852e8i		−	1.23765i
$855$		0			0
$856$	−1.32761e8			−0.211665
$857$	9.16239e8	+	5.28991e8i	1.45568	+	0.840438i	0.998795	−	0.0490862i	$-0.0156309\pi$
$857$	9.16239e8	+	5.28991e8i	1.45568	+	0.840438i	0.456887	+	0.889525i	$0.348964\pi$
$858$		0			0
$859$	2.00544e8	+	3.47352e8i	0.316395	+	0.548013i	0.979733	−	0.200307i	$-0.0641941\pi$
$859$	2.00544e8	+	3.47352e8i	0.316395	+	0.548013i	−0.663338	+	0.748320i	$0.730861\pi$
$860$	1.70623e8	−	9.85094e7i	0.268252	−	0.154875i
$861$		0			0
$862$	2.45323e7	−	4.24913e7i	0.0383016	−	0.0663404i
$863$		−	2.81286e8i		−	0.437638i	−0.975765	−	0.218819i	$-0.929780\pi$
$863$		−	2.81286e8i		−	0.437638i	0.975765	−	0.218819i	$-0.0702205\pi$
$864$		0			0
$865$	3.59805e8			0.555928
$866$	8.54152e7	+	4.93145e7i	0.131517	+	0.0759313i
$867$		0			0
$868$	−7.05677e7	−	1.22227e8i	−0.107906	−	0.186899i
$869$	−4.54161e8	+	2.62210e8i	−0.692070	+	0.399567i
$870$		0			0
$871$	−8.51413e7	+	1.47469e8i	−0.128850	+	0.223175i
$872$			8.79750e7i			0.132681i
$873$		0			0
$874$	3.63182e8			0.543989
$875$	4.20922e8	+	2.43020e8i	0.628315	+	0.362758i
$876$		0			0
$877$	−2.78268e8	−	4.81974e8i	−0.412538	−	0.714537i	0.582628	−	0.812739i	$-0.302024\pi$
$877$	−2.78268e8	−	4.81974e8i	−0.412538	−	0.714537i	−0.995167	+	0.0982017i	$0.968691\pi$
$878$	−4.34847e8	+	2.51059e8i	−0.642471	+	0.370931i
$879$		0			0
$880$	−4.51584e7	+	7.82166e7i	−0.0662660	+	0.114776i
$881$		−	8.25870e8i		−	1.20777i	−0.797072	−	0.603884i	$-0.793619\pi$
$881$		−	8.25870e8i		−	1.20777i	0.797072	−	0.603884i	$-0.206381\pi$
$882$		0			0
$883$	−5.38395e8			−0.782022			−0.391011	−	0.920386i	$-0.627875\pi$
$883$	−5.38395e8			−0.782022			−0.391011	+	0.920386i	$0.627875\pi$
$884$	9.28341e7	+	5.35978e7i	0.134385	+	0.0775872i
$885$		0			0
$886$	3.59707e8	+	6.23031e8i	0.517187	+	0.895795i
$887$	6.31201e8	−	3.64424e8i	0.904476	−	0.522199i	0.0258262	−	0.999666i	$-0.491778\pi$
$887$	6.31201e8	−	3.64424e8i	0.904476	−	0.522199i	0.878650	+	0.477467i	$0.158445\pi$
$888$		0			0
$889$	−4.92234e8	+	8.52574e8i	−0.700594	+	1.21346i
$890$			1.89593e8i			0.268938i
$891$		0			0
$892$	−3.65388e8			−0.514825
$893$	−4.78589e8	−	2.76314e8i	−0.672061	−	0.388014i
$894$		0			0
$895$	−5.61794e7	−	9.73056e7i	−0.0783625	−	0.135728i
$896$	−6.24461e7	+	3.60533e7i	−0.0868123	+	0.0501211i
$897$		0			0
$898$	−4.43396e8	+	7.67985e8i	−0.612298	+	1.06053i
$899$		−	1.46811e8i		−	0.202059i
$900$		0			0
$901$	6.29277e8			0.860334
$902$	6.30851e7	+	3.64222e7i	0.0859622	+	0.0496303i
$903$		0			0
$904$	1.12209e8	+	1.94351e8i	0.151887	+	0.263076i
$905$	7.61396e7	−	4.39592e7i	0.102722	−	0.0593068i
$906$		0			0
$907$	2.17495e8	−	3.76713e8i	0.291493	−	0.504880i	−0.682670	−	0.730727i	$-0.739181\pi$
$907$	2.17495e8	−	3.76713e8i	0.291493	−	0.504880i	0.974163	+	0.225846i	$0.0725148\pi$
$908$			2.82829e8i			0.377804i
$909$		0			0
$910$	1.32104e8			0.175305
$911$	−3.82628e7	−	2.20910e7i	−0.0506083	−	0.0292187i	0.474482	−	0.880265i	$-0.342635\pi$
$911$	−3.82628e7	−	2.20910e7i	−0.0506083	−	0.0292187i	−0.525091	+	0.851046i	$0.675969\pi$
$912$		0			0
$913$	3.52465e8	+	6.10487e8i	0.463131	+	0.802166i
$914$	−3.09107e8	+	1.78463e8i	−0.404827	+	0.233727i
$915$		0			0
$916$	6.03522e7	−	1.04533e8i	0.0785247	−	0.136009i
$917$		−	1.17949e9i		−	1.52963i
$918$		0			0
$919$	4.28966e8			0.552683			0.276342	−	0.961059i	$-0.410878\pi$
$919$	4.28966e8			0.552683			0.276342	+	0.961059i	$0.410878\pi$
$920$	1.39228e8	+	8.03834e7i	0.178798	+	0.103229i
$921$		0			0
$922$	−3.28106e8	−	5.68296e8i	−0.418621	−	0.725073i
$923$	−4.10641e8	+	2.37084e8i	−0.522225	+	0.301507i
$924$		0			0
$925$	−3.25821e8	+	5.64338e8i	−0.411674	+	0.713040i
$926$		−	7.54855e8i		−	0.950671i
$927$		0			0
$928$	−7.50060e7			−0.0938538
$929$	−5.51657e8	−	3.18499e8i	−0.688053	−	0.397247i	0.114829	−	0.993385i	$-0.463368\pi$
$929$	−5.51657e8	−	3.18499e8i	−0.688053	−	0.397247i	−0.802882	+	0.596138i	$0.796701\pi$
$930$		0			0
$931$	5.16360e7	+	8.94362e7i	0.0639888	+	0.110832i
$932$	3.08687e8	−	1.78220e8i	0.381303	−	0.220145i
$933$		0			0
$934$	−1.85998e8	+	3.22158e8i	−0.228280	+	0.395392i
$935$			2.08804e8i			0.255449i
$936$		0			0
$937$	1.11236e7			0.0135216			0.00676079	−	0.999977i	$-0.497848\pi$
$937$	1.11236e7			0.0135216			0.00676079	+	0.999977i	$0.497848\pi$
$938$	−2.29334e8	−	1.32406e8i	−0.277882	−	0.160435i
$939$		0			0
$940$	−1.22314e8	−	2.11853e8i	−0.147262	−	0.255066i
$941$	−6.81926e8	+	3.93710e8i	−0.818405	+	0.472506i	−0.849866	−	0.526999i	$-0.823317\pi$
$941$	−6.81926e8	+	3.93710e8i	−0.818405	+	0.472506i	0.0314611	+	0.999505i	$0.489984\pi$
$942$		0			0
$943$	6.48328e7	−	1.12294e8i	0.0773142	−	0.133912i
$944$			3.70418e8i			0.440327i
$945$		0			0
$946$	−1.70659e9			−2.01584
$947$	1.82193e8	+	1.05189e8i	0.214527	+	0.123857i	0.603413	−	0.797429i	$-0.293807\pi$
$947$	1.82193e8	+	1.05189e8i	0.214527	+	0.123857i	−0.388887	+	0.921286i	$0.627140\pi$
$948$		0			0
$949$	−1.23919e8	−	2.14635e8i	−0.144991	−	0.251131i
$950$	−2.07723e8	+	1.19929e8i	−0.242278	+	0.139879i
$951$		0			0
$952$	−8.33518e7	+	1.44370e8i	−0.0966060	+	0.167327i
$953$		−	1.25814e9i		−	1.45362i	−0.686838	−	0.726811i	$-0.741002\pi$
$953$		−	1.25814e9i		−	1.45362i	0.686838	−	0.726811i	$-0.258998\pi$
$954$		0			0
$955$	−1.04912e8			−0.120452
$956$	−1.17973e8	−	6.81120e7i	−0.135024	−	0.0779560i
$957$		0			0
$958$	−4.97524e8	−	8.61736e8i	−0.565871	−	0.980117i
$959$	−2.27721e8	+	1.31475e8i	−0.258195	+	0.149069i
$960$		0			0
$961$	3.79477e8	−	6.57273e8i	0.427578	−	0.740586i
$962$			3.77290e8i			0.423789i
$963$		0			0
$964$	6.33675e8			0.707351
$965$	−3.62859e7	−	2.09497e7i	−0.0403790	−	0.0233128i
$966$		0			0
$967$	4.06334e8	+	7.03792e8i	0.449370	+	0.778332i	0.998345	−	0.0575069i	$-0.0183151\pi$
$967$	4.06334e8	+	7.03792e8i	0.449370	+	0.778332i	−0.548975	+	0.835839i	$0.684982\pi$
$968$	3.99794e8	−	2.30821e8i	0.440768	−	0.254478i
$969$		0			0
$970$	1.55653e8	−	2.69598e8i	0.170546	−	0.295394i
$971$			1.32700e9i			1.44949i	0.689020	+	0.724743i	$0.258041\pi$
$971$			1.32700e9i			1.44949i	−0.689020	+	0.724743i	$0.741959\pi$
$972$		0			0
$973$	1.56003e9			1.69353
$974$	−2.80323e8	−	1.61845e8i	−0.303377	−	0.175155i
$975$		0			0
$976$	1.79356e8	+	3.10654e8i	0.192915	+	0.334139i
$977$	1.10299e9	−	6.36814e8i	1.18274	−	0.682856i	0.226094	−	0.974106i	$-0.427404\pi$
$977$	1.10299e9	−	6.36814e8i	1.18274	−	0.682856i	0.956647	+	0.291250i	$0.0940710\pi$
$978$		0			0
$979$	8.21133e8	−	1.42224e9i	0.875116	−	1.51575i
$980$			4.57146e7i			0.0485710i
$981$		0			0
$982$	7.24642e7			0.0765225
$983$	−1.16649e8	−	6.73474e7i	−0.122806	−	0.0709023i	0.437338	−	0.899297i	$-0.355921\pi$
$983$	−1.16649e8	−	6.73474e7i	−0.122806	−	0.0709023i	−0.560145	+	0.828395i	$0.689255\pi$
$984$		0			0
$985$	2.09303e8	+	3.62524e8i	0.219012	+	0.379340i
$986$	−1.50175e8	+	8.67034e7i	−0.156663	+	0.0904494i
$987$		0			0
$988$	−6.94369e7	+	1.20268e8i	−0.0719978	+	0.124704i
$989$			3.03778e9i			3.14028i
$990$		0			0
$991$	−6.29070e8			−0.646365			−0.323182	−	0.946337i	$-0.604753\pi$
$991$	−6.29070e8			−0.646365			−0.323182	+	0.946337i	$0.604753\pi$
$992$	5.68777e7	+	3.28384e7i	0.0582649	+	0.0336393i
$993$		0			0
$994$	−3.68697e8	−	6.38602e8i	−0.375414	−	0.650237i
$995$	−3.51142e8	+	2.02732e8i	−0.356462	+	0.205804i
$996$		0			0
$997$	4.96581e8	−	8.60103e8i	0.501077	−	0.867890i	−0.498922	−	0.866647i	$-0.666271\pi$
$997$	4.96581e8	−	8.60103e8i	0.501077	−	0.867890i	0.999999	−	0.00124382i	$-0.000395919\pi$
$998$		−	3.95914e8i		−	0.398299i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.a.107.1		4
3.2	odd	2	inner	162.7.d.a.107.2		4
9.2	odd	6		54.7.b.b.53.1	✓	2
9.4	even	3	inner	162.7.d.a.53.2		4
9.5	odd	6	inner	162.7.d.a.53.1		4
9.7	even	3		54.7.b.b.53.2	yes	2
36.7	odd	6		432.7.e.c.161.1		2
36.11	even	6		432.7.e.c.161.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.7.b.b.53.1	✓	2	9.2	odd	6
54.7.b.b.53.2	yes	2	9.7	even	3
162.7.d.a.53.1		4	9.5	odd	6	inner
162.7.d.a.53.2		4	9.4	even	3	inner
162.7.d.a.107.1		4	1.1	even	1	trivial
162.7.d.a.107.2		4	3.2	odd	2	inner
432.7.e.c.161.1		2	36.7	odd	6
432.7.e.c.161.2		2	36.11	even	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-36.7423 + 21.2132i) q^{5} +(-194.500 + 336.884i) q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-36.7423 + 21.2132i) q^{5} +(-194.500 + 336.884i) q^{7} -181.019i q^{8} +240.000 q^{10} +(-1800.37 - 1039.45i) q^{11} +(-707.500 - 1225.43i) q^{13} +(1905.70 - 1100.26i) q^{14} +(-512.000 + 886.810i) q^{16} +2367.39i q^{17} -3067.00 q^{19} +(-1175.76 - 678.823i) q^{20} +(5880.00 + 10184.5i) q^{22} +(18128.7 - 10466.6i) q^{23} +(-6912.50 + 11972.8i) q^{25} +8004.45i q^{26} -12448.0 q^{28} +(-11213.8 - 6474.27i) q^{29} +(5669.00 + 9819.00i) q^{31} +(5016.55 - 2896.31i) q^{32} +(6696.00 - 11597.8i) q^{34} -16503.9i q^{35} +47135.0 q^{37} +(15025.2 + 8674.79i) q^{38} +(3840.00 + 6651.08i) q^{40} +(5364.38 - 3097.13i) q^{41} +(-72559.0 + 125676. i) q^{43} -66524.6i q^{44} -118416. q^{46} +(156045. + 90092.5i) q^{47} +(-16836.0 - 29160.8i) q^{49} +(67728.4 - 39103.0i) q^{50} +(22640.0 - 39213.6i) q^{52} -265810. i q^{53} +88200.0 q^{55} +(60982.5 + 35208.3i) q^{56} +(36624.0 + 63434.6i) q^{58} +(313273. - 180868. i) q^{59} +(175152. - 303373. i) q^{61} -64137.4i q^{62} -32768.0 q^{64} +(51990.4 + 30016.7i) q^{65} +(-60170.5 - 104218. i) q^{67} +(-65607.1 + 37878.3i) q^{68} +(-46680.0 + 80852.1i) q^{70} -335101. i q^{71} +175151. q^{73} +(-230913. - 133318. i) q^{74} +(-49072.0 - 84995.2i) q^{76} +(700346. - 404345. i) q^{77} +(126130. - 218463. i) q^{79} -43444.6i q^{80} -35040.0 q^{82} +(-293660. - 169544. i) q^{83} +(-50220.0 - 86983.6i) q^{85} +(710930. - 410456. i) q^{86} +(-188160. + 325903. i) q^{88} +789971. i q^{89} +550435. q^{91} +(580118. + 334931. i) q^{92} +(-509640. - 882722. i) q^{94} +(112689. - 65060.9i) q^{95} +(648552. - 1.12333e6i) q^{97} +190478. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{4} - 778 q^{7}+O(q^{10}) \) 4 * q + 64 * q^4 - 778 * q^7	\( 4 q + 64 q^{4} - 778 q^{7} + 960 q^{10} - 2830 q^{13} - 2048 q^{16} - 12268 q^{19} + 23520 q^{22} - 27650 q^{25} - 49792 q^{28} + 22676 q^{31} + 26784 q^{34} + 188540 q^{37} + 15360 q^{40} - 290236 q^{43} - 473664 q^{46} - 67344 q^{49} + 90560 q^{52} + 352800 q^{55} + 146496 q^{58} + 700610 q^{61} - 131072 q^{64} - 240682 q^{67} - 186720 q^{70} + 700604 q^{73} - 196288 q^{76} + 504518 q^{79} - 140160 q^{82} - 200880 q^{85} - 752640 q^{88} + 2201740 q^{91} - 2038560 q^{94} + 2594210 q^{97}+O(q^{100}) \) 4 * q + 64 * q^4 - 778 * q^7 + 960 * q^10 - 2830 * q^13 - 2048 * q^16 - 12268 * q^19 + 23520 * q^22 - 27650 * q^25 - 49792 * q^28 + 22676 * q^31 + 26784 * q^34 + 188540 * q^37 + 15360 * q^40 - 290236 * q^43 - 473664 * q^46 - 67344 * q^49 + 90560 * q^52 + 352800 * q^55 + 146496 * q^58 + 700610 * q^61 - 131072 * q^64 - 240682 * q^67 - 186720 * q^70 + 700604 * q^73 - 196288 * q^76 + 504518 * q^79 - 140160 * q^82 - 200880 * q^85 - 752640 * q^88 + 2201740 * q^91 - 2038560 * q^94 + 2594210 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more