LMFDB - Embedded newform 147.6.c.d.146.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.1
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.23628i q^{2} +(13.6946 + 7.44699i) q^{3} -35.8363 q^{4} -95.6857 q^{5} +(61.3355 - 112.793i) q^{6} +31.5969i q^{8} +(132.085 + 203.967i) q^{9} +O(q^{10})$	\(q-8.23628i q^{2} +(13.6946 + 7.44699i) q^{3} -35.8363 q^{4} -95.6857 q^{5} +(61.3355 - 112.793i) q^{6} +31.5969i q^{8} +(132.085 + 203.967i) q^{9} +788.094i q^{10} -61.6155i q^{11} +(-490.764 - 266.873i) q^{12} +701.342i q^{13} +(-1310.38 - 712.570i) q^{15} -886.521 q^{16} +2099.12 q^{17} +(1679.93 - 1087.89i) q^{18} +766.864i q^{19} +3429.02 q^{20} -507.483 q^{22} -1169.68i q^{23} +(-235.302 + 432.707i) q^{24} +6030.75 q^{25} +5776.45 q^{26} +(289.907 + 3776.89i) q^{27} +3798.83i q^{29} +(-5868.93 + 10792.6i) q^{30} +7898.41i q^{31} +8312.74i q^{32} +(458.850 - 843.801i) q^{33} -17288.9i q^{34} +(-4733.43 - 7309.43i) q^{36} +4072.69 q^{37} +6316.10 q^{38} +(-5222.89 + 9604.60i) q^{39} -3023.37i q^{40} +17850.8 q^{41} -4914.53 q^{43} +2208.07i q^{44} +(-12638.6 - 19516.7i) q^{45} -9633.83 q^{46} -13652.0 q^{47} +(-12140.6 - 6601.91i) q^{48} -49670.9i q^{50} +(28746.6 + 15632.1i) q^{51} -25133.5i q^{52} +7168.22i q^{53} +(31107.5 - 2387.76i) q^{54} +5895.73i q^{55} +(-5710.82 + 10501.9i) q^{57} +31288.2 q^{58} -7816.93 q^{59} +(46959.1 + 25535.9i) q^{60} -4037.59i q^{61} +65053.5 q^{62} +40097.3 q^{64} -67108.4i q^{65} +(-6949.78 - 3779.22i) q^{66} -35769.0 q^{67} -75224.7 q^{68} +(8710.61 - 16018.3i) q^{69} +6743.05i q^{71} +(-6444.73 + 4173.47i) q^{72} +16912.1i q^{73} -33543.8i q^{74} +(82588.8 + 44910.9i) q^{75} -27481.6i q^{76} +(79106.2 + 43017.1i) q^{78} -37459.0 q^{79} +84827.4 q^{80} +(-24156.3 + 53881.9i) q^{81} -147025. i q^{82} -40594.5 q^{83} -200856. q^{85} +40477.4i q^{86} +(-28289.9 + 52023.5i) q^{87} +1946.86 q^{88} +7488.04 q^{89} +(-160745. + 104095. i) q^{90} +41917.1i q^{92} +(-58819.4 + 108166. i) q^{93} +112442. i q^{94} -73377.9i q^{95} +(-61904.8 + 113840. i) q^{96} +35026.7i q^{97} +(12567.6 - 8138.47i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) $ 40 * q - 640 * q^4 + 440 * q^9	$ 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) $ 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	8.23628i		−	1.45598i	−0.685586	−	0.727991i	$-0.740454\pi$
$2$		−	8.23628i		−	1.45598i	0.685586	−	0.727991i	$-0.259546\pi$
$3$	13.6946	+	7.44699i	0.878510	+	0.477725i
$3$	13.6946	+	7.44699i	0.878510	+	0.477725i
$4$	−35.8363			−1.11988
$5$	−95.6857			−1.71168			−0.855839	−	0.517243i	$-0.826958\pi$
$5$	−95.6857			−1.71168			−0.855839	+	0.517243i	$0.826958\pi$
$6$	61.3355	−	112.793i	0.695559	−	1.27909i
$7$		0			0
$7$		0			0
$8$			31.5969i			0.174550i
$9$	132.085	+	203.967i	0.543559	+	0.839371i
$10$			788.094i			2.49217i
$11$		−	61.6155i		−	0.153535i	−0.997049	−	0.0767677i	$-0.975540\pi$
$11$		−	61.6155i		−	0.153535i	0.997049	−	0.0767677i	$-0.0244600\pi$
$12$	−490.764	−	266.873i	−0.983829	−	0.534996i
$13$			701.342i			1.15099i	0.817805	+	0.575495i	$0.195191\pi$
$13$			701.342i			1.15099i	−0.817805	+	0.575495i	$0.804809\pi$
$14$		0			0
$15$	−1310.38	−	712.570i	−1.50373	−	0.817710i
$16$	−886.521			−0.865743
$17$	2099.12			1.76163			0.880815	−	0.473460i	$-0.156995\pi$
$17$	2099.12			1.76163			0.880815	+	0.473460i	$0.156995\pi$
$18$	1679.93	−	1087.89i	1.22211	−	0.791412i
$19$			766.864i			0.487342i	0.969858	+	0.243671i	$0.0783518\pi$
$19$			766.864i			0.487342i	−0.969858	+	0.243671i	$0.921648\pi$
$20$	3429.02			1.91688
$21$		0			0
$22$	−507.483			−0.223545
$23$		−	1169.68i		−	0.461050i	−0.973066	−	0.230525i	$-0.925956\pi$
$23$		−	1169.68i		−	0.461050i	0.973066	−	0.230525i	$-0.0740444\pi$
$24$	−235.302	+	432.707i	−0.0833868	+	0.153344i
$25$	6030.75			1.92984
$26$	5776.45			1.67582
$27$	289.907	+	3776.89i	0.0765331	+	0.997067i
$28$		0			0
$29$			3798.83i			0.838793i	0.907803	+	0.419397i	$0.137758\pi$
$29$			3798.83i			0.838793i	−0.907803	+	0.419397i	$0.862242\pi$
$30$	−5868.93	+	10792.6i	−1.19057	+	2.18940i
$31$			7898.41i			1.47617i	0.674710	+	0.738083i	$0.264269\pi$
$31$			7898.41i			1.47617i	−0.674710	+	0.738083i	$0.735731\pi$
$32$			8312.74i			1.43506i
$33$	458.850	−	843.801i	0.0733476	−	0.134882i
$34$		−	17288.9i		−	2.56490i
$35$		0			0
$36$	−4733.43	−	7309.43i	−0.608723	−	0.939999i
$37$	4072.69			0.489077			0.244538	−	0.969640i	$-0.421364\pi$
$37$	4072.69			0.489077			0.244538	+	0.969640i	$0.421364\pi$
$38$	6316.10			0.709562
$39$	−5222.89	+	9604.60i	−0.549856	+	1.01116i
$40$		−	3023.37i		−	0.298773i
$41$	17850.8			1.65844			0.829219	−	0.558924i	$-0.188786\pi$
$41$	17850.8			1.65844			0.829219	+	0.558924i	$0.188786\pi$
$42$		0			0
$43$	−4914.53			−0.405332			−0.202666	−	0.979248i	$-0.564961\pi$
$43$	−4914.53			−0.405332			−0.202666	+	0.979248i	$0.564961\pi$
$44$			2208.07i			0.171942i
$45$	−12638.6	−	19516.7i	−0.930397	−	1.43673i
$46$	−9633.83			−0.671281
$47$	−13652.0			−0.901473			−0.450737	−	0.892657i	$-0.648839\pi$
$47$	−13652.0			−0.901473			−0.450737	+	0.892657i	$0.648839\pi$
$48$	−12140.6	−	6601.91i	−0.760564	−	0.413587i
$49$		0			0
$50$		−	49670.9i		−	2.80981i
$51$	28746.6	+	15632.1i	1.54761	+	0.841574i
$52$		−	25133.5i		−	1.28898i
$53$			7168.22i			0.350527i	0.984522	+	0.175264i	$0.0560778\pi$
$53$			7168.22i			0.350527i	−0.984522	+	0.175264i	$0.943922\pi$
$54$	31107.5	−	2387.76i	1.45171	−	0.111431i
$55$			5895.73i			0.262803i
$56$		0			0
$57$	−5710.82	+	10501.9i	−0.232815	+	0.428135i
$58$	31288.2			1.22127
$59$	−7816.93			−0.292352			−0.146176	−	0.989259i	$-0.546697\pi$
$59$	−7816.93			−0.292352			−0.146176	+	0.989259i	$0.546697\pi$
$60$	46959.1	+	25535.9i	1.68400	+	0.915741i
$61$		−	4037.59i		−	0.138931i	−0.997584	−	0.0694653i	$-0.977871\pi$
$61$		−	4037.59i		−	0.138931i	0.997584	−	0.0694653i	$-0.0221293\pi$
$62$	65053.5			2.14927
$63$		0			0
$64$	40097.3			1.22367
$65$		−	67108.4i		−	1.97012i
$66$	−6949.78	−	3779.22i	−0.196386	−	0.106793i
$67$	−35769.0			−0.973464			−0.486732	−	0.873551i	$-0.661811\pi$
$67$	−35769.0			−0.973464			−0.486732	+	0.873551i	$0.661811\pi$
$68$	−75224.7			−1.97282
$69$	8710.61	−	16018.3i	0.220255	−	0.405037i
$70$		0			0
$71$			6743.05i			0.158749i	0.996845	+	0.0793744i	$0.0252923\pi$
$71$			6743.05i			0.158749i	−0.996845	+	0.0793744i	$0.974708\pi$
$72$	−6444.73	+	4173.47i	−0.146512	+	0.0948781i
$73$			16912.1i			0.371441i	0.982603	+	0.185721i	$0.0594620\pi$
$73$			16912.1i			0.371441i	−0.982603	+	0.185721i	$0.940538\pi$
$74$		−	33543.8i		−	0.712087i
$75$	82588.8	+	44910.9i	1.69538	+	0.921932i
$76$		−	27481.6i		−	0.545767i
$77$		0			0
$78$	79106.2	+	43017.1i	1.47222	+	0.800581i
$79$	−37459.0			−0.675288			−0.337644	−	0.941274i	$-0.609630\pi$
$79$	−37459.0			−0.675288			−0.337644	+	0.941274i	$0.609630\pi$
$80$	84827.4			1.48187
$81$	−24156.3	+	53881.9i	−0.409088	+	0.912495i
$82$		−	147025.i		−	2.41466i
$83$	−40594.5			−0.646803			−0.323401	−	0.946262i	$-0.604826\pi$
$83$	−40594.5			−0.646803			−0.323401	+	0.946262i	$0.604826\pi$
$84$		0			0
$85$	−200856.			−3.01534
$86$			40477.4i			0.590156i
$87$	−28289.9	+	52023.5i	−0.400712	+	0.736888i
$88$	1946.86			0.0267996
$89$	7488.04			0.100206			0.0501029	−	0.998744i	$-0.484045\pi$
$89$	7488.04			0.100206			0.0501029	+	0.998744i	$0.484045\pi$
$90$	−160745.	+	104095.i	−2.09186	+	1.35464i
$91$		0			0
$92$			41917.1i			0.516323i
$93$	−58819.4	+	108166.i	−0.705201	+	1.29683i
$94$			112442.i			1.31253i
$95$		−	73377.9i		−	0.834173i
$96$	−61904.8	+	113840.i	−0.685562	+	1.26071i
$97$			35026.7i			0.377980i	0.981979	+	0.188990i	$0.0605215\pi$
$97$			35026.7i			0.377980i	−0.981979	+	0.188990i	$0.939479\pi$
$98$		0			0
$99$	12567.6	−	8138.47i	0.128873	−	0.0834555i
$100$	−216120.			−2.16120
$101$	−36980.1			−0.360715			−0.180357	−	0.983601i	$-0.557725\pi$
$101$	−36980.1			−0.360715			−0.180357	+	0.983601i	$0.557725\pi$
$102$	128751.	−	236765.i	1.22532	−	2.25329i
$103$			205100.i			1.90490i	0.304694	+	0.952450i	$0.401446\pi$
$103$			205100.i			1.90490i	−0.304694	+	0.952450i	$0.598554\pi$
$104$	−22160.2			−0.200905
$105$		0			0
$106$	59039.5			0.510361
$107$		−	132093.i		−	1.11537i	−0.830052	−	0.557686i	$-0.811689\pi$
$107$		−	132093.i		−	1.11537i	0.830052	−	0.557686i	$-0.188311\pi$
$108$	−10389.2	−	135350.i	−0.0857083	−	1.11660i
$109$	−87338.7			−0.704110			−0.352055	−	0.935979i	$-0.614517\pi$
$109$	−87338.7			−0.704110			−0.352055	+	0.935979i	$0.614517\pi$
$110$	48558.8			0.382637
$111$	55773.9	+	30329.3i	0.429659	+	0.233644i
$112$		0			0
$113$			166220.i			1.22458i	0.790634	+	0.612289i	$0.209751\pi$
$113$			166220.i			1.22458i	−0.790634	+	0.612289i	$0.790249\pi$
$114$	86496.6	+	47036.0i	0.623357	+	0.338975i
$115$			111922.i			0.789169i
$116$		−	136136.i		−	0.939352i
$117$	−143051.	+	92636.5i	−0.966108	+	0.625630i
$118$			64382.4i			0.425659i
$119$		0			0
$120$	22515.0	−	41403.9i	0.142731	−	0.262475i
$121$	157255.			0.976427
$122$	−33254.8			−0.202281
$123$	244460.	+	132935.i	1.45695	+	0.792277i
$124$		−	283050.i		−	1.65314i
$125$	−278039.			−1.59159
$126$		0			0
$127$	339698.			1.86889			0.934445	−	0.356109i	$-0.115897\pi$
$127$	339698.			1.86889			0.934445	+	0.356109i	$0.115897\pi$
$128$		−	64245.5i		−	0.346591i
$129$	−67302.5	−	36598.4i	−0.356088	−	0.193637i
$130$	−552723.			−2.86846
$131$	119364.			0.607709			0.303854	−	0.952718i	$-0.401726\pi$
$131$	119364.			0.607709			0.303854	+	0.952718i	$0.401726\pi$
$132$	−16443.5	+	30238.7i	−0.0821409	+	0.151053i
$133$		0			0
$134$			294603.i			1.41735i
$135$	−27740.0	−	361394.i	−0.131000	−	1.70666i
$136$			66325.7i			0.307492i
$137$			247347.i			1.12591i	0.826486	+	0.562957i	$0.190336\pi$
$137$			247347.i			1.12591i	−0.826486	+	0.562957i	$0.809664\pi$
$138$	−131932.	−	71743.0i	−0.589727	−	0.320687i
$139$		−	138617.i		−	0.608528i	−0.952588	−	0.304264i	$-0.901589\pi$
$139$		−	138617.i		−	0.608528i	0.952588	−	0.304264i	$-0.0984105\pi$
$140$		0			0
$141$	−186959.	−	101667.i	−0.791953	−	0.430656i
$142$	55537.7			0.231136
$143$	43213.6			0.176718
$144$	−117096.	−	180821.i	−0.470582	−	0.726680i
$145$		−	363494.i		−	1.43574i
$146$	139293.			0.540812
$147$		0			0
$148$	−145950.			−0.547710
$149$		−	221959.i		−	0.819044i	−0.912300	−	0.409522i	$-0.865696\pi$
$149$		−	221959.i		−	0.819044i	0.912300	−	0.409522i	$-0.134304\pi$
$150$	369899.	−	680224.i	1.34232	−	2.46845i
$151$	−7767.65			−0.0277234			−0.0138617	−	0.999904i	$-0.504412\pi$
$151$	−7767.65			−0.0277234			−0.0138617	+	0.999904i	$0.504412\pi$
$152$	−24230.5			−0.0850656
$153$	277262.	+	428152.i	0.957549	+	1.47866i
$154$		0			0
$155$		−	755765.i		−	2.52672i
$156$	187169.	−	344194.i	0.615775	−	1.13238i
$157$			53748.5i			0.174027i	0.996207	+	0.0870136i	$0.0277324\pi$
$157$			53748.5i			0.174027i	−0.996207	+	0.0870136i	$0.972268\pi$
$158$			308523.i			0.983207i
$159$	−53381.7	+	98166.0i	−0.167455	+	0.307942i
$160$		−	795410.i		−	2.45635i
$161$		0			0
$162$	443786.	+	198958.i	1.32858	+	0.595625i
$163$	301739.			0.889534			0.444767	−	0.895646i	$-0.353287\pi$
$163$	301739.			0.889534			0.444767	+	0.895646i	$0.353287\pi$
$164$	−639709.			−1.85726
$165$	−43905.4	+	80739.7i	−0.125547	+	0.230875i
$166$			334348.i			0.941734i
$167$	−499994.			−1.38731			−0.693655	−	0.720307i	$-0.744001\pi$
$167$	−499994.			−1.38731			−0.693655	+	0.720307i	$0.744001\pi$
$168$		0			0
$169$	−120587.			−0.324777
$170$			1.65430e6i			4.39029i
$171$	−156415.	+	101291.i	−0.409061	+	0.264899i
$172$	176119.			0.453925
$173$	59764.2			0.151819			0.0759094	−	0.997115i	$-0.475814\pi$
$173$	59764.2			0.151819			0.0759094	+	0.997115i	$0.475814\pi$
$174$	428480.	+	233003.i	1.07290	+	0.583430i
$175$		0			0
$176$			54623.5i			0.132922i
$177$	−107050.	−	58212.6i	−0.256834	−	0.139664i
$178$		−	61673.6i		−	0.145898i
$179$		−	341307.i		−	0.796182i	−0.917346	−	0.398091i	$-0.869673\pi$
$179$		−	341307.i		−	0.796182i	0.917346	−	0.398091i	$-0.130327\pi$
$180$	452921.	+	699408.i	1.04194	+	1.60898i
$181$			31140.0i			0.0706516i	0.999376	+	0.0353258i	$0.0112469\pi$
$181$			31140.0i			0.0706516i	−0.999376	+	0.0353258i	$0.988753\pi$
$182$		0			0
$183$	30067.9	−	55293.3i	0.0663706	−	0.122052i
$184$	36958.3			0.0804763
$185$	−389698.			−0.837142
$186$	890882.	+	484453.i	1.88816	+	1.02676i
$187$		−	129338.i		−	0.270473i
$188$	489239.			1.00955
$189$		0			0
$190$	−604361.			−1.21454
$191$			381684.i			0.757043i	0.925593	+	0.378521i	$0.123567\pi$
$191$			381684.i			0.757043i	−0.925593	+	0.378521i	$0.876433\pi$
$192$	549118.	+	298604.i	1.07501	+	0.584579i
$193$	363670.			0.702771			0.351386	−	0.936231i	$-0.385711\pi$
$193$	363670.			0.702771			0.351386	+	0.936231i	$0.385711\pi$
$194$	288489.			0.550333
$195$	499755.	−	919023.i	0.941176	−	1.73077i
$196$		0			0
$197$		−	423574.i		−	0.777614i	−0.921319	−	0.388807i	$-0.872887\pi$
$197$		−	423574.i		−	0.777614i	0.921319	−	0.388807i	$-0.127113\pi$
$198$	−67030.7	−	103510.i	−0.121510	−	0.187637i
$199$			789967.i			1.41409i	0.707170	+	0.707043i	$0.249971\pi$
$199$			789967.i			1.41409i	−0.707170	+	0.707043i	$0.750029\pi$
$200$			190553.i			0.336853i
$201$	−489843.	−	266371.i	−0.855197	−	0.465048i
$202$			304578.i			0.525195i
$203$		0			0
$204$	−1.03017e6	−	560197.i	−1.73314	−	0.942466i
$205$	−1.70807e6			−2.83871
$206$	1.68926e6			2.77350
$207$	238577.	−	154497.i	0.386992	−	0.250608i
$208$		−	621754.i		−	0.996461i
$209$	47250.7			0.0748243
$210$		0			0
$211$	−317944.			−0.491638			−0.245819	−	0.969316i	$-0.579057\pi$
$211$	−317944.			−0.491638			−0.245819	+	0.969316i	$0.579057\pi$
$212$		−	256883.i		−	0.392550i
$213$	−50215.4	+	92343.5i	−0.0758382	+	0.139462i
$214$	−1.08795e6			−1.62396
$215$	470250.			0.693797
$216$	−119338.	+	9160.17i	−0.174038	+	0.0133589i
$217$		0			0
$218$			719346.i			1.02517i
$219$	−125944.	+	231605.i	−0.177447	+	0.326315i
$220$		−	211281.i		−	0.294309i
$221$			1.47220e6i			2.02762i
$222$	249800.	−	459370.i	0.340182	−	0.625576i
$223$			626494.i			0.843635i	0.906681	+	0.421818i	$0.138608\pi$
$223$			626494.i			0.843635i	−0.906681	+	0.421818i	$0.861392\pi$
$224$		0			0
$225$	796570.	+	1.23008e6i	1.04898	+	1.61985i
$226$	1.36903e6			1.78296
$227$	−570494.			−0.734830			−0.367415	−	0.930057i	$-0.619757\pi$
$227$	−570494.			−0.734830			−0.367415	+	0.930057i	$0.619757\pi$
$228$	204655.	−	376349.i	0.260726	−	0.479462i
$229$		−	941253.i		−	1.18609i	−0.805169	−	0.593045i	$-0.797926\pi$
$229$		−	941253.i		−	1.18609i	0.805169	−	0.593045i	$-0.202074\pi$
$230$	921819.			1.14902
$231$		0			0
$232$	−120031.			−0.146411
$233$		−	385599.i		−	0.465314i	−0.972559	−	0.232657i	$-0.925258\pi$
$233$		−	385599.i		−	0.465314i	0.972559	−	0.232657i	$-0.0747420\pi$
$234$	762981.	+	1.17821e6i	0.910907	+	1.40664i
$235$	1.30630e6			1.54303
$236$	280130.			0.327400
$237$	−512987.	−	278957.i	−0.593247	−	0.322602i
$238$		0			0
$239$		−	705084.i		−	0.798447i	−0.916854	−	0.399223i	$-0.869280\pi$
$239$		−	705084.i		−	0.798447i	0.916854	−	0.399223i	$-0.130720\pi$
$240$	1.16168e6	+	631708.i	1.30184	+	0.707927i
$241$		−	402646.i		−	0.446561i	−0.974754	−	0.223280i	$-0.928323\pi$
$241$		−	402646.i		−	0.446561i	0.974754	−	0.223280i	$-0.0716765\pi$
$242$		−	1.29519e6i		−	1.42166i
$243$	−732068.	+	558000.i	−0.795309	+	0.606204i
$244$			144692.i			0.155586i
$245$		0			0
$246$	1.09489e6	−	2.01344e6i	1.15354	−	2.12130i
$247$	−537834.			−0.560926
$248$	−249565.			−0.257665
$249$	−555926.	−	302307.i	−0.568223	−	0.308994i
$250$			2.29000e6i			2.31732i
$251$	748914.			0.750322			0.375161	−	0.926960i	$-0.377587\pi$
$251$	748914.			0.750322			0.375161	+	0.926960i	$0.377587\pi$
$252$		0			0
$253$	−72070.6			−0.0707875
$254$		−	2.79785e6i		−	2.72107i
$255$	−2.75064e6	−	1.49577e6i	−2.64901	−	1.44050i
$256$	753972.			0.719043
$257$	−1.25040e6			−1.18091			−0.590456	−	0.807070i	$-0.701052\pi$
$257$	−1.25040e6			−1.18091			−0.590456	+	0.807070i	$0.701052\pi$
$258$	−301435.	+	554323.i	−0.281932	+	0.518458i
$259$		0			0
$260$			2.40492e6i			2.20631i
$261$	−774837.	+	501768.i	−0.704059	+	0.455933i
$262$		−	983116.i		−	0.884814i
$263$		−	823410.i		−	0.734052i	−0.930211	−	0.367026i	$-0.880376\pi$
$263$		−	823410.i		−	0.734052i	0.930211	−	0.367026i	$-0.119624\pi$
$264$	26661.5	+	14498.3i	0.0235437	+	0.0128028i
$265$		−	685896.i		−	0.599990i
$266$		0			0
$267$	102546.	+	55763.4i	0.0880318	+	0.0478708i
$268$	1.28183e6			1.09017
$269$	1.43914e6			1.21261			0.606305	−	0.795232i	$-0.292651\pi$
$269$	1.43914e6			1.21261			0.606305	+	0.795232i	$0.292651\pi$
$270$	−2.97654e6	+	228474.i	−2.48486	+	0.190734i
$271$			168444.i			0.139326i	0.997571	+	0.0696629i	$0.0221924\pi$
$271$			168444.i			0.139326i	−0.997571	+	0.0696629i	$0.977808\pi$
$272$	−1.86091e6			−1.52512
$273$		0			0
$274$	2.03722e6			1.63931
$275$		−	371588.i		−	0.296299i
$276$	−312156.	+	574038.i	−0.246660	+	0.453595i
$277$	−946591.			−0.741247			−0.370624	−	0.928783i	$-0.620856\pi$
$277$	−946591.			−0.741247			−0.370624	+	0.928783i	$0.620856\pi$
$278$	−1.14169e6			−0.886006
$279$	−1.61102e6	+	1.04326e6i	−1.23905	+	0.802383i
$280$		0			0
$281$		−	2.01496e6i		−	1.52230i	−0.648573	−	0.761152i	$-0.724634\pi$
$281$		−	2.01496e6i		−	1.52230i	0.648573	−	0.761152i	$-0.275366\pi$
$282$	−837355.	+	1.53985e6i	−0.627028	+	1.15307i
$283$		−	1.78370e6i		−	1.32390i	−0.749548	−	0.661950i	$-0.769729\pi$
$283$		−	1.78370e6i		−	1.32390i	0.749548	−	0.661950i	$-0.230271\pi$
$284$		−	241646.i		−	0.177780i
$285$	546444.	−	1.00488e6i	0.398505	−	0.732829i
$286$		−	355919.i		−	0.257298i
$287$		0			0
$288$	−1.69553e6	+	1.09799e6i	−1.20455	+	0.780037i
$289$	2.98645e6			2.10334
$290$	−2.99384e6			−2.09042
$291$	−260843.	+	479676.i	−0.180571	+	0.332059i
$292$		−	606067.i		−	0.415972i
$293$	−1.43373e6			−0.975661			−0.487830	−	0.872938i	$-0.662212\pi$
$293$	−1.43373e6			−0.975661			−0.487830	+	0.872938i	$0.662212\pi$
$294$		0			0
$295$	747968.			0.500412
$296$			128684.i			0.0853683i
$297$	232715.	−	17862.8i	0.153085	−	0.0117505i
$298$	−1.82812e6			−1.19251
$299$	820347.			0.530664
$300$	−2.95968e6	−	1.60944e6i	−1.89863	−	1.03246i
$301$		0			0
$302$			63976.5i			0.0403648i
$303$	−506427.	−	275390.i	−0.316892	−	0.172322i
$304$		−	679841.i		−	0.421913i
$305$			386340.i			0.237804i
$306$	3.52638e6	−	2.28360e6i	2.15291	−	1.39417i
$307$			2.69105e6i			1.62958i	0.579754	+	0.814791i	$0.303149\pi$
$307$			2.69105e6i			1.62958i	−0.579754	+	0.814791i	$0.696851\pi$
$308$		0			0
$309$	−1.52738e6	+	2.80876e6i	−0.910018	+	1.67347i
$310$	−6.22469e6			−3.67886
$311$	2.28926e6			1.34213			0.671063	−	0.741400i	$-0.265838\pi$
$311$	2.28926e6			1.34213			0.671063	+	0.741400i	$0.265838\pi$
$312$	−303476.	−	165027.i	−0.176497	−	0.0959773i
$313$			1.81990e6i			1.05000i	0.851104	+	0.524998i	$0.175934\pi$
$313$			1.81990e6i			1.05000i	−0.851104	+	0.524998i	$0.824066\pi$
$314$	442688.			0.253381
$315$		0			0
$316$	1.34239e6			0.756244
$317$		−	2.34265e6i		−	1.30936i	−0.755906	−	0.654681i	$-0.772803\pi$
$317$		−	2.34265e6i		−	1.30936i	0.755906	−	0.654681i	$-0.227197\pi$
$318$	808523.	+	439666.i	0.448357	+	0.243812i
$319$	234067.			0.128784
$320$	−3.83674e6			−2.09454
$321$	983693.	−	1.80896e6i	0.532840	−	0.979864i
$322$		0			0
$323$			1.60974e6i			0.858517i
$324$	865671.	−	1.93093e6i	0.458132	−	1.02189i
$325$			4.22962e6i			2.22123i
$326$		−	2.48521e6i		−	1.29515i
$327$	−1.19607e6	−	650410.i	−0.618567	−	0.336370i
$328$			564032.i			0.289480i
$329$		0			0
$330$	664994.	+	361617.i	0.336150	+	0.182795i
$331$	923839.			0.463475			0.231737	−	0.972778i	$-0.425559\pi$
$331$	923839.			0.463475			0.231737	+	0.972778i	$0.425559\pi$
$332$	1.45476e6			0.724345
$333$	537940.	+	830695.i	0.265842	+	0.410517i
$334$			4.11809e6i			2.01990i
$335$	3.42258e6			1.66626
$336$		0			0
$337$	2.45241e6			1.17630			0.588151	−	0.808751i	$-0.299856\pi$
$337$	2.45241e6			1.17630			0.588151	+	0.808751i	$0.299856\pi$
$338$			993192.i			0.472870i
$339$	−1.23784e6	+	2.27631e6i	−0.585011	+	1.07580i
$340$	7.19793e6			3.37684
$341$	486665.			0.226644
$342$	834261.	+	1.28828e6i	0.385688	+	0.595586i
$343$		0			0
$344$		−	155284.i		−	0.0707506i
$345$	−833480.	+	1.53273e6i	−0.377005	+	0.693293i
$346$		−	492234.i		−	0.221046i
$347$		−	3.03882e6i		−	1.35482i	−0.735606	−	0.677410i	$-0.763102\pi$
$347$		−	3.03882e6i		−	1.35482i	0.735606	−	0.677410i	$-0.236898\pi$
$348$	1.01380e6	−	1.86433e6i	0.448751	−	0.825230i
$349$			563611.i			0.247694i	0.992301	+	0.123847i	$0.0395232\pi$
$349$			563611.i			0.247694i	−0.992301	+	0.123847i	$0.960477\pi$
$350$		0			0
$351$	−2.64889e6	+	203324.i	−1.14761	+	0.0880888i
$352$	512194.			0.220332
$353$	−447733.			−0.191242			−0.0956208	−	0.995418i	$-0.530484\pi$
$353$	−447733.			−0.191242			−0.0956208	+	0.995418i	$0.530484\pi$
$354$	−479455.	+	881692.i	−0.203348	+	0.373946i
$355$		−	645214.i		−	0.271727i
$356$	−268344.			−0.112219
$357$		0			0
$358$	−2.81110e6			−1.15923
$359$			2.40888e6i			0.986457i	0.869900	+	0.493229i	$0.164183\pi$
$359$			2.40888e6i			0.986457i	−0.869900	+	0.493229i	$0.835817\pi$
$360$	616669.	−	399341.i	0.250782	−	0.162401i
$361$	1.88802e6			0.762497
$362$	256478.			0.102867
$363$	2.15354e6	+	1.17107e6i	0.857800	+	0.466463i
$364$		0			0
$365$		−	1.61825e6i		−	0.635788i
$366$	−455411.	−	247648.i	−0.177705	−	0.0966344i
$367$		−	1.21534e6i		−	0.471013i	−0.971873	−	0.235507i	$-0.924325\pi$
$367$		−	1.21534e6i		−	0.471013i	0.971873	−	0.235507i	$-0.0756750\pi$
$368$			1.03695e6i			0.399151i
$369$	2.35782e6	+	3.64099e6i	0.901458	+	1.39205i
$370$			3.20966e6i			1.21886i
$371$		0			0
$372$	2.10787e6	−	3.87626e6i	0.789744	−	1.45230i
$373$	3.39853e6			1.26479			0.632396	−	0.774645i	$-0.282071\pi$
$373$	3.39853e6			1.26479			0.632396	+	0.774645i	$0.282071\pi$
$374$	−1.06527e6			−0.393803
$375$	−3.80763e6	−	2.07055e6i	−1.39822	−	0.760340i
$376$		−	431362.i		−	0.157352i
$377$	−2.66428e6			−0.965442
$378$		0			0
$379$	−4.54643e6			−1.62582			−0.812909	−	0.582390i	$-0.802117\pi$
$379$	−4.54643e6			−1.62582			−0.812909	+	0.582390i	$0.802117\pi$
$380$			2.62959e6i			0.934177i
$381$	4.65203e6	+	2.52973e6i	1.64184	+	0.892814i
$382$	3.14366e6			1.10224
$383$	491317.			0.171145			0.0855726	−	0.996332i	$-0.472728\pi$
$383$	491317.			0.171145			0.0855726	+	0.996332i	$0.472728\pi$
$384$	478435.	−	879817.i	0.165575	−	0.304484i
$385$		0			0
$386$		−	2.99529e6i		−	1.02322i
$387$	−649134.	−	1.00240e6i	−0.220322	−	0.340224i
$388$		−	1.25523e6i		−	0.423295i
$389$			1.46135e6i			0.489644i	0.969568	+	0.244822i	$0.0787294\pi$
$389$			1.46135e6i			0.489644i	−0.969568	+	0.244822i	$0.921271\pi$
$390$	−7.56933e6	−	4.11612e6i	−2.51997	−	1.37034i
$391$		−	2.45530e6i		−	0.812200i
$392$		0			0
$393$	1.63465e6	+	888903.i	0.533878	+	0.290317i
$394$	−3.48868e6			−1.13219
$395$	3.58429e6			1.15588
$396$	−450375.	+	291653.i	−0.144323	+	0.0934605i
$397$		−	3.72908e6i		−	1.18748i	−0.804658	−	0.593739i	$-0.797651\pi$
$397$		−	3.72908e6i		−	1.18748i	0.804658	−	0.593739i	$-0.202349\pi$
$398$	6.50639e6			2.05889
$399$		0			0
$400$	−5.34639e6			−1.67075
$401$		−	739154.i		−	0.229548i	−0.993392	−	0.114774i	$-0.963386\pi$
$401$		−	739154.i		−	0.229548i	0.993392	−	0.114774i	$-0.0366144\pi$
$402$	−2.19391e6	+	4.03448e6i	−0.677101	+	1.24515i
$403$	−5.53948e6			−1.69905
$404$	1.32523e6			0.403959
$405$	2.31141e6	−	5.15573e6i	0.700227	−	1.56190i
$406$		0			0
$407$		−	250941.i		−	0.0750906i
$408$	−493927.	+	908305.i	−0.146897	+	0.270135i
$409$		−	4.67448e6i		−	1.38174i	−0.722981	−	0.690868i	$-0.757229\pi$
$409$		−	4.67448e6i		−	1.38174i	0.722981	−	0.690868i	$-0.242771\pi$
$410$			1.40681e7i			4.13311i
$411$	−1.84199e6	+	3.38732e6i	−0.537877	+	0.989127i
$412$		−	7.35002e6i		−	2.13327i
$413$		0			0
$414$	−1.27248e6	−	1.96498e6i	−0.364880	−	0.563454i
$415$	3.88431e6			1.10712
$416$	−5.83007e6			−1.65174
$417$	1.03228e6	−	1.89831e6i	0.290709	−	0.534598i
$418$		−	389170.i		−	0.108943i
$419$	−5.84468e6			−1.62639			−0.813197	−	0.581989i	$-0.802275\pi$
$419$	−5.84468e6			−1.62639			−0.813197	+	0.581989i	$0.802275\pi$
$420$		0			0
$421$	4.11576e6			1.13173			0.565867	−	0.824497i	$-0.308542\pi$
$421$	4.11576e6			1.13173			0.565867	+	0.824497i	$0.308542\pi$
$422$			2.61868e6i			0.715816i
$423$	−1.80323e6	−	2.78457e6i	−0.490004	−	0.756671i
$424$	−226494.			−0.0611845
$425$	1.26593e7			3.39966
$426$	760567.	+	413588.i	0.203055	+	0.110419i
$427$		0			0
$428$			4.73372e6i			1.24909i
$429$	591793.	+	321811.i	0.155248	+	0.0844224i
$430$		−	3.87311e6i		−	1.01016i
$431$			1.68466e6i			0.436838i	0.975855	+	0.218419i	$0.0700899\pi$
$431$			1.68466e6i			0.436838i	−0.975855	+	0.218419i	$0.929910\pi$
$432$	−257009.	−	3.34829e6i	−0.0662580	−	0.863204i
$433$			1.64848e6i			0.422536i	0.977428	+	0.211268i	$0.0677593\pi$
$433$			1.64848e6i			0.422536i	−0.977428	+	0.211268i	$0.932241\pi$
$434$		0			0
$435$	2.70693e6	−	4.97791e6i	0.685890	−	1.26131i
$436$	3.12989e6			0.788521
$437$	896986.			0.224689
$438$	1.90756e6	+	1.03731e6i	0.475109	+	0.258359i
$439$			4.92043e6i			1.21855i	0.792961	+	0.609273i	$0.208539\pi$
$439$			4.92043e6i			1.21855i	−0.792961	+	0.609273i	$0.791461\pi$
$440$	−186287.			−0.0458723
$441$		0			0
$442$	1.21255e7			2.95218
$443$			5.68024e6i			1.37517i	0.726102	+	0.687587i	$0.241330\pi$
$443$			5.68024e6i			1.37517i	−0.726102	+	0.687587i	$0.758670\pi$
$444$	−1.99873e6	−	1.08689e6i	−0.481168	−	0.261654i
$445$	−716498.			−0.171520
$446$	5.15998e6			1.22832
$447$	1.65293e6	−	3.03964e6i	0.391277	−	0.719538i
$448$		0			0
$449$			4.87600e6i			1.14143i	0.821150	+	0.570713i	$0.193333\pi$
$449$			4.87600e6i			1.14143i	−0.821150	+	0.570713i	$0.806667\pi$
$450$	1.01312e7	−	6.56077e6i	2.35848	−	1.52730i
$451$		−	1.09989e6i		−	0.254629i
$452$		−	5.95670e6i		−	1.37139i
$453$	−106375.	−	57845.6i	−0.0243553	−	0.0132442i
$454$			4.69875e6i			1.06990i
$455$		0			0
$456$	−331828.	−	180444.i	−0.0747309	−	0.0406379i
$457$	−3.57267e6			−0.800208			−0.400104	−	0.916470i	$-0.631026\pi$
$457$	−3.57267e6			−0.800208			−0.400104	+	0.916470i	$0.631026\pi$
$458$	−7.75242e6			−1.72693
$459$	608550.	+	7.92813e6i	0.134823	+	1.75646i
$460$		−	4.01086e6i		−	0.883778i
$461$	250640.			0.0549284			0.0274642	−	0.999623i	$-0.491257\pi$
$461$	250640.			0.0549284			0.0274642	+	0.999623i	$0.491257\pi$
$462$		0			0
$463$	−6.59265e6			−1.42925			−0.714624	−	0.699509i	$-0.753402\pi$
$463$	−6.59265e6			−1.42925			−0.714624	+	0.699509i	$0.753402\pi$
$464$		−	3.36774e6i		−	0.726179i
$465$	5.62817e6	−	1.03499e7i	1.20708	−	2.21975i
$466$	−3.17590e6			−0.677489
$467$	−8.22554e6			−1.74531			−0.872654	−	0.488339i	$-0.837603\pi$
$467$	−8.22554e6			−1.74531			−0.872654	+	0.488339i	$0.837603\pi$
$468$	5.12641e6	−	3.31975e6i	1.08193	−	0.700634i
$469$		0			0
$470$		−	1.07591e7i		−	2.24663i
$471$	−400265.	+	736065.i	−0.0831371	+	0.152885i
$472$		−	246991.i		−	0.0510300i
$473$			302811.i			0.0622328i
$474$	−2.29757e6	+	4.22510e6i	−0.469702	+	0.863757i
$475$			4.62476e6i			0.940493i
$476$		0			0
$477$	−1.46208e6	+	946812.i	−0.294222	+	0.190532i
$478$	−5.80727e6			−1.16252
$479$	−271187.			−0.0540045			−0.0270022	−	0.999635i	$-0.508596\pi$
$479$	−271187.			−0.0540045			−0.0270022	+	0.999635i	$0.508596\pi$
$480$	5.92341e6	−	1.08928e7i	1.17346	−	2.15793i
$481$			2.85635e6i			0.562922i
$482$	−3.31630e6			−0.650184
$483$		0			0
$484$	−5.63542e6			−1.09349
$485$		−	3.35155e6i		−	0.646981i
$486$	4.59585e6	+	6.02952e6i	0.882622	+	1.15796i
$487$	6.25929e6			1.19592			0.597961	−	0.801525i	$-0.295978\pi$
$487$	6.25929e6			1.19592			0.597961	+	0.801525i	$0.295978\pi$
$488$	127576.			0.0242503
$489$	4.13220e6	+	2.24705e6i	0.781464	+	0.424952i
$490$		0			0
$491$			3.62324e6i			0.678255i	0.940740	+	0.339128i	$0.110132\pi$
$491$			3.62324e6i			0.678255i	−0.940740	+	0.339128i	$0.889868\pi$
$492$	−8.76056e6	−	4.76390e6i	−1.63162	−	0.887258i
$493$			7.97420e6i			1.47764i
$494$			4.42975e6i			0.816698i
$495$	−1.20253e6	+	778735.i	−0.220589	+	0.142849i
$496$		−	7.00210e6i		−	1.27798i
$497$		0			0
$498$	−2.48988e6	+	4.57876e6i	−0.449889	+	0.827322i
$499$	8.76412e6			1.57564			0.787820	−	0.615905i	$-0.211210\pi$
$499$	8.76412e6			1.57564			0.787820	+	0.615905i	$0.211210\pi$
$500$	9.96388e6			1.78239
$501$	−6.84722e6	−	3.72345e6i	−1.21877	−	0.662752i
$502$		−	6.16826e6i		−	1.09246i
$503$	−1.64958e6			−0.290705			−0.145353	−	0.989380i	$-0.546432\pi$
$503$	−1.64958e6			−0.290705			−0.145353	+	0.989380i	$0.546432\pi$
$504$		0			0
$505$	3.53846e6			0.617428
$506$			593593.i			0.103065i
$507$	−1.65140e6	−	898014.i	−0.285320	−	0.155154i
$508$	−1.21735e7			−2.09294
$509$	−9.00198e6			−1.54008			−0.770041	−	0.637995i	$-0.779764\pi$
$509$	−9.00198e6			−1.54008			−0.770041	+	0.637995i	$0.779764\pi$
$510$	−1.23196e7	+	2.26550e7i	−2.09735	+	3.85691i
$511$		0			0
$512$		−	8.26578e6i		−	1.39351i
$513$	−2.89636e6	+	222319.i	−0.485913	+	0.0372978i
$514$			1.02987e7i			1.71939i
$515$		−	1.96251e7i		−	3.26058i
$516$	2.41187e6	+	1.31155e6i	0.398777	+	0.216851i
$517$			841178.i			0.138408i
$518$		0			0
$519$	818447.	+	445063.i	0.133374	+	0.0725276i
$520$	2.12042e6			0.343885
$521$	−5.17333e6			−0.834980			−0.417490	−	0.908681i	$-0.637090\pi$
$521$	−5.17333e6			−0.834980			−0.417490	+	0.908681i	$0.637090\pi$
$522$	4.13270e6	+	6.38177e6i	0.663831	+	1.02510i
$523$		−	7.89508e6i		−	1.26212i	−0.775732	−	0.631062i	$-0.782619\pi$
$523$		−	7.89508e6i		−	1.26212i	0.775732	−	0.631062i	$-0.217381\pi$
$524$	−4.27757e6			−0.680564
$525$		0			0
$526$	−6.78183e6			−1.06877
$527$			1.65797e7i			2.60046i
$528$	−406780.	+	748047.i	−0.0635002	+	0.116773i
$529$	5.06819e6			0.787433
$530$	−5.64923e6			−0.873574
$531$	−1.03250e6	−	1.59440e6i	−0.158910	−	0.245392i
$532$		0			0
$533$			1.25195e7i			1.90885i
$534$	459283.	−	844596.i	0.0696991	−	0.128173i
$535$			1.26394e7i			1.90916i
$536$		−	1.13019e6i		−	0.169918i
$537$	2.54171e6	−	4.67406e6i	0.380356	−	0.699454i
$538$		−	1.18531e7i		−	1.76554i
$539$		0			0
$540$	994098.	+	1.29510e7i	0.146705	+	1.91126i
$541$	−6.61608e6			−0.971869			−0.485935	−	0.873995i	$-0.661521\pi$
$541$	−6.61608e6			−0.971869			−0.485935	+	0.873995i	$0.661521\pi$
$542$	1.38735e6			0.202856
$543$	−231899.	+	426450.i	−0.0337520	+	0.0620681i
$544$			1.74494e7i			2.52804i
$545$	8.35706e6			1.20521
$546$		0			0
$547$	1.17393e7			1.67754			0.838770	−	0.544487i	$-0.183275\pi$
$547$	1.17393e7			1.67754			0.838770	+	0.544487i	$0.183275\pi$
$548$		−	8.86401e6i		−	1.26089i
$549$	823537.	−	533304.i	0.116614	−	0.0755169i
$550$	−3.06050e6			−0.431406
$551$	−2.91319e6			−0.408780
$552$	506130.	+	275228.i	0.0706992	+	0.0384455i
$553$		0			0
$554$			7.79639e6i			1.07924i
$555$	−5.33676e6	−	2.90208e6i	−0.735437	−	0.399923i
$556$			4.96754e6i			0.681481i
$557$			6.26910e6i			0.856184i	0.903735	+	0.428092i	$0.140814\pi$
$557$			6.26910e6i			0.856184i	−0.903735	+	0.428092i	$0.859186\pi$
$558$	8.59257e6	+	1.32688e7i	1.16826	+	1.80404i
$559$		−	3.44676e6i		−	0.466533i
$560$		0			0
$561$	963181.	−	1.77124e6i	0.129211	−	0.237613i
$562$	−1.65958e7			−2.21645
$563$	8.03207e6			1.06796			0.533982	−	0.845496i	$-0.320695\pi$
$563$	8.03207e6			1.06796			0.533982	+	0.845496i	$0.320695\pi$
$564$	6.69993e6	+	3.64336e6i	0.886896	+	0.482285i
$565$		−	1.59048e7i		−	2.09608i
$566$	−1.46910e7			−1.92757
$567$		0			0
$568$	−213060.			−0.0277096
$569$		−	1.44118e7i		−	1.86611i	−0.359732	−	0.933056i	$-0.617132\pi$
$569$		−	1.44118e7i		−	1.86611i	0.359732	−	0.933056i	$-0.382868\pi$
$570$	−8.27648e6	−	4.50067e6i	−1.06699	−	0.580216i
$571$	−3.45795e6			−0.443842			−0.221921	−	0.975065i	$-0.571233\pi$
$571$	−3.45795e6			−0.443842			−0.221921	+	0.975065i	$0.571233\pi$
$572$	−1.54861e6			−0.197903
$573$	−2.84240e6	+	5.22701e6i	−0.361658	+	0.665069i
$574$		0			0
$575$		−	7.05406e6i		−	0.889753i
$576$	5.29625e6	+	8.17854e6i	0.665138	+	1.02712i
$577$		−	1.09980e7i		−	1.37523i	−0.726078	−	0.687613i	$-0.758659\pi$
$577$		−	1.09980e7i		−	1.37523i	0.726078	−	0.687613i	$-0.241341\pi$
$578$		−	2.45972e7i		−	3.06243i
$579$	4.98032e6	+	2.70825e6i	0.617392	+	0.335731i
$580$			1.30263e7i			1.60787i
$581$		0			0
$582$	3.95075e6	+	2.14838e6i	0.483473	+	0.262908i
$583$	441674.			0.0538183
$584$	−534370.			−0.0648351
$585$	1.36879e7	−	8.86399e6i	1.65366	−	1.07088i
$586$			1.18086e7i			1.42054i
$587$	7.06815e6			0.846663			0.423331	−	0.905975i	$-0.360861\pi$
$587$	7.06815e6			0.846663			0.423331	+	0.905975i	$0.360861\pi$
$588$		0			0
$589$	−6.05700e6			−0.719398
$590$		−	6.16047e6i		−	0.728591i
$591$	3.15435e6	−	5.80068e6i	0.371485	−	0.683141i
$592$	−3.61053e6			−0.423415
$593$	7.28420e6			0.850639			0.425320	−	0.905043i	$-0.360162\pi$
$593$	7.28420e6			0.850639			0.425320	+	0.905043i	$0.360162\pi$
$594$	−147123.	−	1.91670e6i	−0.0171086	−	0.222889i
$595$		0			0
$596$			7.95419e6i			0.917235i
$597$	−5.88287e6	+	1.08183e7i	−0.675544	+	1.24229i
$598$		−	6.75661e6i		−	0.772637i
$599$			8.87796e6i			1.01099i	0.862830	+	0.505494i	$0.168690\pi$
$599$			8.87796e6i			1.01099i	−0.862830	+	0.505494i	$0.831310\pi$
$600$	−1.41905e6	+	2.60955e6i	−0.160923	+	0.295929i
$601$			1.70395e7i			1.92429i	0.272539	+	0.962145i	$0.412137\pi$
$601$			1.70395e7i			1.92429i	−0.272539	+	0.962145i	$0.587863\pi$
$602$		0			0
$603$	−4.72454e6	−	7.29570e6i	−0.529135	−	0.817098i
$604$	278364.			0.0310471
$605$	−1.50470e7			−1.67133
$606$	−2.26819e6	+	4.17108e6i	−0.250898	+	0.461388i
$607$		−	1.55702e7i		−	1.71524i	−0.514288	−	0.857618i	$-0.671944\pi$
$607$		−	1.55702e7i		−	1.71524i	0.514288	−	0.857618i	$-0.328056\pi$
$608$	−6.37473e6			−0.699364
$609$		0			0
$610$	3.18200e6			0.346239
$611$		−	9.57475e6i		−	1.03759i
$612$	−9.93603e6	−	1.53434e7i	−1.07234	−	1.65593i
$613$	−9.37456e6			−1.00763			−0.503814	−	0.863812i	$-0.668070\pi$
$613$	−9.37456e6			−1.00763			−0.503814	+	0.863812i	$0.668070\pi$
$614$	2.21643e7			2.37264
$615$	−2.33914e7	−	1.27200e7i	−2.49384	−	1.35612i
$616$		0			0
$617$		−	4.65972e6i		−	0.492772i	−0.969172	−	0.246386i	$-0.920757\pi$
$617$		−	4.65972e6i		−	0.492772i	0.969172	−	0.246386i	$-0.0792432\pi$
$618$	2.31338e7	+	1.25799e7i	2.43655	+	1.32497i
$619$			3.92355e6i			0.411579i	0.978596	+	0.205789i	$0.0659762\pi$
$619$			3.92355e6i			0.411579i	−0.978596	+	0.205789i	$0.934024\pi$
$620$			2.70838e7i			2.82964i
$621$	4.41775e6	−	339099.i	0.459698	−	0.0352856i
$622$		−	1.88550e7i		−	1.95411i
$623$		0			0
$624$	4.63020e6	−	8.51468e6i	0.476034	−	0.875401i
$625$	7.75822e6			0.794442
$626$	1.49892e7			1.52877
$627$	647080.	+	351876.i	0.0657339	+	0.0357454i
$628$		−	1.92615e6i		−	0.194890i
$629$	8.54906e6			0.861573
$630$		0			0
$631$	3.69853e6			0.369791			0.184895	−	0.982758i	$-0.440805\pi$
$631$	3.69853e6			0.369791			0.184895	+	0.982758i	$0.440805\pi$
$632$		−	1.18359e6i		−	0.117871i
$633$	−4.35412e6	−	2.36773e6i	−0.431908	−	0.234867i
$634$	−1.92947e7			−1.90641
$635$	−3.25042e7			−3.19894
$636$	1.91300e6	−	3.51791e6i	0.187531	−	0.344859i
$637$		0			0
$638$		−	1.92784e6i		−	0.187508i
$639$	−1.37536e6	+	890654.i	−0.133249	+	0.0862893i
$640$			6.14737e6i			0.593252i
$641$		−	5.46577e6i		−	0.525420i	−0.964875	−	0.262710i	$-0.915384\pi$
$641$		−	5.46577e6i		−	0.525420i	0.964875	−	0.262710i	$-0.0846162\pi$
$642$	−1.48991e7	−	8.10197e6i	−1.42667	−	0.775806i
$643$		−	5.03029e6i		−	0.479806i	−0.970797	−	0.239903i	$-0.922884\pi$
$643$		−	5.03029e6i		−	0.479806i	0.970797	−	0.239903i	$-0.0771157\pi$
$644$		0			0
$645$	6.43989e6	+	3.50195e6i	0.609508	+	0.331444i
$646$	1.32583e7			1.24999
$647$	−2.69180e6			−0.252803			−0.126402	−	0.991979i	$-0.540343\pi$
$647$	−2.69180e6			−0.252803			−0.126402	+	0.991979i	$0.540343\pi$
$648$	−1.70250e6	−	763263.i	−0.159276	−	0.0714063i
$649$			481644.i			0.0448864i
$650$	3.48363e7			3.23407
$651$		0			0
$652$	−1.08132e7			−0.996175
$653$		−	62071.7i		−	0.00569653i	−0.999996	−	0.00284827i	$-0.999093\pi$
$653$		−	62071.7i		−	0.00569653i	0.999996	−	0.00284827i	$-0.000906633\pi$
$654$	−5.35696e6	+	9.85116e6i	−0.489749	+	0.900623i
$655$	−1.14214e7			−1.04020
$656$	−1.58252e7			−1.43578
$657$	−3.44951e6	+	2.23383e6i	−0.311777	+	0.201900i
$658$		0			0
$659$		−	1.25655e7i		−	1.12711i	−0.826078	−	0.563555i	$-0.809433\pi$
$659$		−	1.25655e7i		−	1.12711i	0.826078	−	0.563555i	$-0.190567\pi$
$660$	1.57341e6	−	2.89341e6i	0.140599	−	0.258553i
$661$		−	1.79034e7i		−	1.59379i	−0.604115	−	0.796897i	$-0.706473\pi$
$661$		−	1.79034e7i		−	1.59379i	0.604115	−	0.796897i	$-0.293527\pi$
$662$		−	7.60900e6i		−	0.674811i
$663$	−1.09635e7	+	2.01612e7i	−0.968643	+	1.78128i
$664$		−	1.28266e6i		−	0.112899i
$665$		0			0
$666$	6.84184e6	−	4.43063e6i	0.597706	−	0.387061i
$667$	4.44342e6			0.386726
$668$	1.79179e7			1.55363
$669$	−4.66549e6	+	8.57959e6i	−0.403025	+	0.741142i
$670$		−	2.81893e7i		−	2.42604i
$671$	−248779.			−0.0213308
$672$		0			0
$673$	1.76780e6			0.150451			0.0752257	−	0.997167i	$-0.476032\pi$
$673$	1.76780e6			0.150451			0.0752257	+	0.997167i	$0.476032\pi$
$674$		−	2.01988e7i		−	1.71267i
$675$	1.74836e6	+	2.27774e7i	0.147697	+	1.92418i
$676$	4.32141e6			0.363713
$677$	1.96758e7			1.64991			0.824955	−	0.565199i	$-0.191201\pi$
$677$	1.96758e7			1.64991			0.824955	+	0.565199i	$0.191201\pi$
$678$	1.87484e7	+	1.01952e7i	1.56635	+	0.851766i
$679$		0			0
$680$		−	6.34642e6i		−	0.526328i
$681$	−7.81270e6	−	4.24846e6i	−0.645555	−	0.351046i
$682$		−	4.00831e6i		−	0.329989i
$683$			1.32790e7i			1.08922i	0.838691	+	0.544608i	$0.183321\pi$
$683$			1.32790e7i			1.08922i	−0.838691	+	0.544608i	$0.816679\pi$
$684$	5.60534e6	−	3.62989e6i	0.458101	−	0.296656i
$685$		−	2.36676e7i		−	1.92720i
$686$		0			0
$687$	7.00950e6	−	1.28901e7i	0.566624	−	1.04199i
$688$	4.35683e6			0.350913
$689$	−5.02737e6			−0.403453
$690$	1.26240e7	+	6.86478e6i	1.00942	+	0.548913i
$691$			1.57082e7i			1.25150i	0.780022	+	0.625752i	$0.215208\pi$
$691$			1.57082e7i			1.25150i	−0.780022	+	0.625752i	$0.784792\pi$
$692$	−2.14173e6			−0.170020
$693$		0			0
$694$	−2.50286e7			−1.97259
$695$			1.32637e7i			1.04160i
$696$	−1.64378e6	−	893872.i	−0.128624	−	0.0699443i
$697$	3.74711e7			2.92156
$698$	4.64206e6			0.360639
$699$	2.87155e6	−	5.28063e6i	0.222292	−	0.408783i
$700$		0			0
$701$			1.83549e7i			1.41078i	0.708822	+	0.705388i	$0.249227\pi$
$701$			1.83549e7i			1.41078i	−0.708822	+	0.705388i	$0.750773\pi$
$702$	1.67463e6	+	2.18170e7i	0.128256	+	1.67091i
$703$			3.12320e6i			0.238348i
$704$		−	2.47062e6i		−	0.187877i
$705$	1.78893e7	+	9.72804e6i	1.35557	+	0.737144i
$706$			3.68766e6i			0.278445i
$707$		0			0
$708$	3.83627e6	+	2.08612e6i	0.287624	+	0.156407i
$709$	3.85229e6			0.287808			0.143904	−	0.989592i	$-0.454034\pi$
$709$	3.85229e6			0.287808			0.143904	+	0.989592i	$0.454034\pi$
$710$	−5.31416e6			−0.395630
$711$	−4.94777e6	−	7.64042e6i	−0.367058	−	0.566817i
$712$			236599.i			0.0174909i
$713$	9.23862e6			0.680587
$714$		0			0
$715$	−4.13492e6			−0.302484
$716$			1.22312e7i			0.891632i
$717$	5.25075e6	−	9.65585e6i	0.381438	−	0.701443i
$718$	1.98402e7			1.43626
$719$	6.88826e6			0.496921			0.248461	−	0.968642i	$-0.420075\pi$
$719$	6.88826e6			0.496921			0.248461	+	0.968642i	$0.420075\pi$
$720$	1.12044e7	+	1.73020e7i	0.805485	+	1.24384i
$721$		0			0
$722$		−	1.55503e7i		−	1.11018i
$723$	2.99850e6	−	5.51408e6i	0.213333	−	0.392308i
$724$		−	1.11594e6i		−	0.0791216i
$725$			2.29098e7i			1.61874i
$726$	9.64528e6	−	1.77372e7i	0.679162	−	1.24894i
$727$			1.84898e7i			1.29747i	0.761016	+	0.648734i	$0.224701\pi$
$727$			1.84898e7i			1.29747i	−0.761016	+	0.648734i	$0.775299\pi$
$728$		0			0
$729$	−1.41808e7	+	2.18989e6i	−0.988285	+	0.152617i
$730$	−1.33283e7			−0.925696
$731$	−1.03162e7			−0.714045
$732$	−1.07752e6	+	1.98151e6i	−0.0743274	+	0.136684i
$733$		−	1.29842e7i		−	0.892595i	−0.894885	−	0.446297i	$-0.852742\pi$
$733$		−	1.29842e7i		−	0.892595i	0.894885	−	0.446297i	$-0.147258\pi$
$734$	−1.00099e7			−0.685787
$735$		0			0
$736$	9.72325e6			0.661633
$737$			2.20393e6i			0.149461i
$738$	2.99882e7	−	1.94197e7i	2.02679	−	1.31251i
$739$	−1.20749e6			−0.0813338			−0.0406669	−	0.999173i	$-0.512948\pi$
$739$	−1.20749e6			−0.0813338			−0.0406669	+	0.999173i	$0.512948\pi$
$740$	1.39653e7			0.937502
$741$	−7.36542e6	−	4.00524e6i	−0.492779	−	0.267968i
$742$		0			0
$743$		−	4.25530e6i		−	0.282786i	−0.989954	−	0.141393i	$-0.954842\pi$
$743$		−	4.25530e6i		−	0.282786i	0.989954	−	0.141393i	$-0.0451581\pi$
$744$	−3.41770e6	−	1.85851e6i	−0.226361	−	0.123093i
$745$			2.12383e7i			1.40194i
$746$		−	2.79913e7i		−	1.84152i
$747$	−5.36191e6	−	8.27995e6i	−0.351575	−	0.542908i
$748$			4.63501e6i			0.302898i
$749$		0			0
$750$	−1.70536e7	+	3.13607e7i	−1.10704	+	2.03579i
$751$	−2.15530e7			−1.39447			−0.697233	−	0.716844i	$-0.745586\pi$
$751$	−2.15530e7			−1.39447			−0.697233	+	0.716844i	$0.745586\pi$
$752$	1.21028e7			0.780444
$753$	1.02561e7	+	5.57715e6i	0.659165	+	0.358447i
$754$			2.19438e7i			1.40567i
$755$	743253.			0.0474536
$756$		0			0
$757$	6.79325e6			0.430861			0.215431	−	0.976519i	$-0.430884\pi$
$757$	6.79325e6			0.430861			0.215431	+	0.976519i	$0.430884\pi$
$758$			3.74456e7i			2.36716i
$759$	−986979.	−	536709.i	−0.0621875	−	0.0338169i
$760$	2.31851e6			0.145605
$761$	−137361.			−0.00859806			−0.00429903	−	0.999991i	$-0.501368\pi$
$761$	−137361.			−0.00859806			−0.00429903	+	0.999991i	$0.501368\pi$
$762$	2.08355e7	−	3.83154e7i	1.29992	−	2.39049i
$763$		0			0
$764$		−	1.36781e7i		−	0.847801i
$765$	−2.65300e7	−	4.09680e7i	−1.63902	−	2.53099i
$766$		−	4.04662e6i		−	0.249184i
$767$		−	5.48234e6i		−	0.336494i
$768$	1.03253e7	+	5.61482e6i	0.631687	+	0.343505i
$769$			1.25864e7i			0.767512i	0.923435	+	0.383756i	$0.125370\pi$
$769$			1.25864e7i			0.767512i	−0.923435	+	0.383756i	$0.874630\pi$
$770$		0			0
$771$	−1.71238e7	−	9.31175e6i	−1.03744	−	0.564151i
$772$	−1.30326e7			−0.787023
$773$	2.14904e7			1.29359			0.646793	−	0.762666i	$-0.276110\pi$
$773$	2.14904e7			1.29359			0.646793	+	0.762666i	$0.276110\pi$
$774$	−8.25607e6	+	5.34645e6i	−0.495360	+	0.320784i
$775$			4.76333e7i			2.84876i
$776$	−1.10673e6			−0.0659765
$777$		0			0
$778$	1.20361e7			0.712912
$779$			1.36892e7i			0.808227i
$780$	−1.79094e7	+	3.29344e7i	−1.05401	+	1.93827i
$781$	415477.			0.0243736
$782$	−2.02226e7			−1.18255
$783$	−1.43477e7	+	1.10131e6i	−0.836333	+	0.0641955i
$784$		0			0
$785$		−	5.14296e6i		−	0.297879i
$786$	7.32126e6	−	1.34634e7i	0.422697	−	0.777317i
$787$			2.01019e7i			1.15691i	0.815714	+	0.578456i	$0.196344\pi$
$787$			2.01019e7i			1.15691i	−0.815714	+	0.578456i	$0.803656\pi$
$788$			1.51793e7i			0.870838i
$789$	6.13192e6	−	1.12763e7i	0.350675	−	0.644872i
$790$		−	2.95212e7i		−	1.68293i
$791$		0			0
$792$	257151.	+	397096.i	0.0145671	+	0.0224948i
$793$	2.83173e6			0.159908
$794$	−3.07138e7			−1.72895
$795$	5.10786e6	−	9.39308e6i	0.286630	−	0.527097i
$796$		−	2.83095e7i		−	1.58361i
$797$	−1.57921e7			−0.880633			−0.440316	−	0.897843i	$-0.645134\pi$
$797$	−1.57921e7			−0.880633			−0.440316	+	0.897843i	$0.645134\pi$
$798$		0			0
$799$	−2.86573e7			−1.58806
$800$			5.01320e7i			2.76943i
$801$	989056.	+	1.52732e6i	0.0544678	+	0.0841099i
$802$	−6.08788e6			−0.334218
$803$	1.04205e6			0.0570294
$804$	1.75541e7	+	9.54577e6i	0.957722	+	0.520800i
$805$		0			0
$806$			4.56247e7i			2.47379i
$807$	1.97084e7	+	1.07172e7i	1.06529	+	0.579294i
$808$		−	1.16846e6i		−	0.0629628i
$809$			1.47811e7i			0.794028i	0.917812	+	0.397014i	$0.129954\pi$
$809$			1.47811e7i			0.794028i	−0.917812	+	0.397014i	$0.870046\pi$
$810$	−4.24640e7	−	1.90374e7i	−2.27409	−	1.01952i
$811$			1.02755e7i			0.548594i	0.961645	+	0.274297i	$0.0884451\pi$
$811$			1.02755e7i			0.548594i	−0.961645	+	0.274297i	$0.911555\pi$
$812$		0			0
$813$	−1.25440e6	+	2.30677e6i	−0.0665594	+	0.122399i
$814$	−2.06682e6			−0.109331
$815$	−2.88721e7			−1.52260
$816$	−2.54845e7	−	1.38582e7i	−1.33983	−	0.728587i
$817$		−	3.76877e6i		−	0.197535i
$818$	−3.85003e7			−2.01178
$819$		0			0
$820$	6.12109e7			3.17903
$821$		−	1.64276e7i		−	0.850581i	−0.905057	−	0.425290i	$-0.860172\pi$
$821$		−	1.64276e7i		−	0.850581i	0.905057	−	0.425290i	$-0.139828\pi$
$822$	2.78989e7	+	1.51712e7i	1.44015	+	0.783140i
$823$	−1.43758e7			−0.739831			−0.369916	−	0.929065i	$-0.620613\pi$
$823$	−1.43758e7			−0.739831			−0.369916	+	0.929065i	$0.620613\pi$
$824$	−6.48052e6			−0.332500
$825$	2.76721e6	−	5.08875e6i	0.141549	−	0.260301i
$826$		0			0
$827$		−	7.99009e6i		−	0.406245i	−0.979153	−	0.203122i	$-0.934891\pi$
$827$		−	7.99009e6i		−	0.406245i	0.979153	−	0.203122i	$-0.0651089\pi$
$828$	−8.54971e6	+	5.53661e6i	−0.433387	+	0.280652i
$829$			3.70433e7i			1.87207i	0.351903	+	0.936036i	$0.385535\pi$
$829$			3.70433e7i			1.87207i	−0.351903	+	0.936036i	$0.614465\pi$
$830$		−	3.19923e7i		−	1.61194i
$831$	−1.29632e7	−	7.04925e6i	−0.651193	−	0.354112i
$832$			2.81220e7i			1.40844i
$833$		0			0
$834$	−1.56350e7	−	8.50217e6i	−0.778365	−	0.423267i
$835$	4.78423e7			2.37463
$836$	−1.69329e6			−0.0837946
$837$	−2.98314e7	+	2.28981e6i	−1.47184	+	0.112976i
$838$			4.81384e7i			2.36800i
$839$	−1.69102e7			−0.829361			−0.414680	−	0.909967i	$-0.636107\pi$
$839$	−1.69102e7			−0.829361			−0.414680	+	0.909967i	$0.636107\pi$
$840$		0			0
$841$	6.08003e6			0.296426
$842$		−	3.38985e7i		−	1.64778i
$843$	1.50054e7	−	2.75942e7i	0.727242	−	1.33736i
$844$	1.13940e7			0.550577
$845$	1.15385e7			0.555914
$846$	−2.29345e7	+	1.48519e7i	−1.10170	+	0.713437i
$847$		0			0
$848$		−	6.35478e6i		−	0.303466i
$849$	1.32832e7	−	2.44270e7i	0.632459	−	1.16306i
$850$		−	1.04265e8i		−	4.94985i
$851$		−	4.76375e6i		−	0.225489i
$852$	1.79954e6	−	3.30925e6i	0.0849301	−	0.156182i
$853$		−	1.29148e7i		−	0.607734i	−0.952714	−	0.303867i	$-0.901722\pi$
$853$		−	1.29148e7i		−	0.607734i	0.952714	−	0.303867i	$-0.0982779\pi$
$854$		0			0
$855$	1.49667e7	−	9.69209e6i	0.700181	−	0.453422i
$856$	4.17372e6			0.194688
$857$	−1.91374e7			−0.890086			−0.445043	−	0.895509i	$-0.646812\pi$
$857$	−1.91374e7			−0.890086			−0.445043	+	0.895509i	$0.646812\pi$
$858$	2.65052e6	−	4.87417e6i	0.122917	−	0.226039i
$859$		−	1.79322e7i		−	0.829185i	−0.910007	−	0.414593i	$-0.863924\pi$
$859$		−	1.79322e7i		−	0.829185i	0.910007	−	0.414593i	$-0.136076\pi$
$860$	−1.68520e7			−0.776973
$861$		0			0
$862$	1.38754e7			0.636028
$863$		−	3.14438e7i		−	1.43717i	−0.695440	−	0.718584i	$-0.744791\pi$
$863$		−	3.14438e7i		−	1.43717i	0.695440	−	0.718584i	$-0.255209\pi$
$864$	−3.13962e7	+	2.40992e6i	−1.43085	+	0.109829i
$865$	−5.71858e6			−0.259865
$866$	1.35773e7			0.615205
$867$	4.08982e7	+	2.22400e7i	1.84781	+	1.00482i
$868$		0			0
$869$			2.30806e6i			0.103681i
$870$	−4.09994e7	−	2.22951e7i	−1.83645	−	0.998644i
$871$		−	2.50863e7i		−	1.12045i
$872$		−	2.75963e6i		−	0.122902i
$873$	−7.14429e6	+	4.62649e6i	−0.317266	+	0.205454i
$874$		−	7.38783e6i		−	0.327144i
$875$		0			0
$876$	4.51337e6	−	8.29985e6i	0.198720	−	0.365435i
$877$	5.15527e6			0.226335			0.113168	−	0.993576i	$-0.463900\pi$
$877$	5.15527e6			0.226335			0.113168	+	0.993576i	$0.463900\pi$
$878$	4.05260e7			1.77418
$879$	−1.96344e7	−	1.06770e7i	−0.857128	−	0.466097i
$880$		−	5.22668e6i		−	0.227520i
$881$	1.97715e7			0.858220			0.429110	−	0.903252i	$-0.358827\pi$
$881$	1.97715e7			0.858220			0.429110	+	0.903252i	$0.358827\pi$
$882$		0			0
$883$	−2.10100e7			−0.906825			−0.453412	−	0.891301i	$-0.649793\pi$
$883$	−2.10100e7			−0.906825			−0.453412	+	0.891301i	$0.649793\pi$
$884$		−	5.27582e7i		−	2.27070i
$885$	1.02431e7	+	5.57011e6i	0.439617	+	0.239059i
$886$	4.67841e7			2.00223
$887$	7.50178e6			0.320151			0.160076	−	0.987105i	$-0.448826\pi$
$887$	7.50178e6			0.320151			0.160076	+	0.987105i	$0.448826\pi$
$888$	−958312.	+	1.76228e6i	−0.0407825	+	0.0749969i
$889$		0			0
$890$			5.90128e6i			0.249730i
$891$	3.31996e6	+	1.48840e6i	0.140100	+	0.0628095i
$892$		−	2.24512e7i		−	0.944774i
$893$		−	1.04693e7i		−	0.439326i
$894$	−2.50353e7	−	1.36140e7i	−1.04763	−	0.569693i
$895$			3.26582e7i			1.36281i
$896$		0			0
$897$	1.12343e7	+	6.10911e6i	0.466193	+	0.253511i
$898$	4.01601e7			1.66189
$899$	−3.00047e7			−1.23820
$900$	−2.85461e7	−	4.40814e7i	−1.17474	−	1.81405i
$901$			1.50470e7i			0.617499i
$902$	−9.05900e6			−0.370735
$903$		0			0
$904$	−5.25203e6			−0.213750
$905$		−	2.97965e6i		−	0.120933i
$906$	−476432.	+	876134.i	−0.0192833	+	0.0354609i
$907$	2.36915e7			0.956258			0.478129	−	0.878290i	$-0.341315\pi$
$907$	2.36915e7			0.956258			0.478129	+	0.878290i	$0.341315\pi$
$908$	2.04444e7			0.822924
$909$	−4.88450e6	−	7.54272e6i	−0.196070	−	0.302774i
$910$		0			0
$911$			4.17441e7i			1.66648i	0.552915	+	0.833238i	$0.313516\pi$
$911$			4.17441e7i			1.66648i	−0.552915	+	0.833238i	$0.686484\pi$
$912$	5.06277e6	−	9.31015e6i	0.201558	−	0.370655i
$913$			2.50125e6i			0.0993071i
$914$			2.94255e7i			1.16509i
$915$	−2.87707e6	+	5.29078e6i	−0.113605	+	0.208914i
$916$			3.37310e7i			1.32828i
$917$		0			0
$918$	6.52983e7	−	5.01219e6i	2.55738	−	0.196300i
$919$	−2.81167e7			−1.09819			−0.549093	−	0.835761i	$-0.685027\pi$
$919$	−2.81167e7			−1.09819			−0.549093	+	0.835761i	$0.685027\pi$
$920$	−3.53638e6			−0.137749
$921$	−2.00402e7	+	3.68529e7i	−0.778492	+	1.43160i
$922$		−	2.06434e6i		−	0.0799748i
$923$	−4.72919e6			−0.182718
$924$		0			0
$925$	2.45614e7			0.943840
$926$			5.42989e7i			2.08096i
$927$	−4.18337e7	+	2.70906e7i	−1.59892	+	1.03543i
$928$	−3.15787e7			−1.20372
$929$	2.31372e6			0.0879571			0.0439785	−	0.999032i	$-0.485997\pi$
$929$	2.31372e6			0.0879571			0.0439785	+	0.999032i	$0.485997\pi$
$930$	−8.52447e7	−	4.63552e7i	−3.23192	−	1.75748i
$931$		0			0
$932$			1.38184e7i			0.521098i
$933$	3.13505e7	+	1.70481e7i	1.17907	+	0.641167i
$934$			6.77478e7i			2.54114i
$935$			1.23758e7i			0.462962i
$936$	−2.92703e6	−	4.51996e6i	−0.109204	−	0.168634i
$937$		−	1.00379e7i		−	0.373505i	−0.982407	−	0.186752i	$-0.940204\pi$
$937$		−	1.00379e7i		−	0.373505i	0.982407	−	0.186752i	$-0.0597962\pi$
$938$		0			0
$939$	−1.35528e7	+	2.49229e7i	−0.501609	+	0.922431i
$940$	−4.68131e7			−1.72802
$941$	1.80198e7			0.663400			0.331700	−	0.943385i	$-0.392378\pi$
$941$	1.80198e7			0.663400			0.331700	+	0.943385i	$0.392378\pi$
$942$	6.06244e6	+	3.29669e6i	0.222597	+	0.121046i
$943$		−	2.08798e7i		−	0.764623i
$944$	6.92987e6			0.253102
$945$		0			0
$946$	2.49404e6			0.0906098
$947$		−	1.00293e7i		−	0.363410i	−0.983353	−	0.181705i	$-0.941838\pi$
$947$		−	1.00293e7i		−	0.363410i	0.983353	−	0.181705i	$-0.0581616\pi$
$948$	1.83836e7	+	9.99679e6i	0.664368	+	0.361277i
$949$	−1.18612e7			−0.427525
$950$	3.80908e7			1.36934
$951$	1.74457e7	−	3.20817e7i	0.625514	−	1.15029i
$952$		0			0
$953$			4.78408e7i			1.70634i	0.521630	+	0.853172i	$0.325324\pi$
$953$			4.78408e7i			1.70634i	−0.521630	+	0.853172i	$0.674676\pi$
$954$	7.79821e6	+	1.20421e7i	0.277411	+	0.428383i
$955$		−	3.65217e7i		−	1.29581i
$956$			2.52676e7i			0.894168i
$957$	3.20546e6	+	1.74309e6i	0.113138	+	0.0615235i
$958$			2.23357e6i			0.0786295i
$959$		0			0
$960$	−5.25427e7	−	2.85722e7i	−1.84007	−	1.00061i
$961$	−3.37557e7			−1.17907
$962$	2.35257e7			0.819605
$963$	2.69426e7	−	1.74474e7i	0.936211	−	0.606269i
$964$			1.44293e7i			0.500096i
$965$	−3.47980e7			−1.20292
$966$		0			0
$967$	−4.94295e7			−1.69989			−0.849943	−	0.526874i	$-0.823364\pi$
$967$	−4.94295e7			−1.69989			−0.849943	+	0.526874i	$0.823364\pi$
$968$			4.96876e6i			0.170435i
$969$	−1.19877e7	+	2.20447e7i	−0.410135	+	0.754216i
$970$	−2.76043e7			−0.941992
$971$	−4.77468e7			−1.62516			−0.812579	−	0.582850i	$-0.801937\pi$
$971$	−4.77468e7			−1.62516			−0.812579	+	0.582850i	$0.801937\pi$
$972$	2.62346e7	−	1.99967e7i	0.890655	−	0.678879i
$973$		0			0
$974$		−	5.15533e7i		−	1.74124i
$975$	−3.14979e7	+	5.79230e7i	−1.06113	+	1.95137i
$976$			3.57941e6i			0.120278i
$977$		−	2.05090e7i		−	0.687397i	−0.939080	−	0.343698i	$-0.888320\pi$
$977$		−	2.05090e7i		−	0.687397i	0.939080	−	0.343698i	$-0.111680\pi$
$978$	1.85073e7	−	3.40339e7i	0.618723	−	1.13780i
$979$		−	461380.i		−	0.0153852i
$980$		0			0
$981$	−1.15361e7	−	1.78142e7i	−0.382725	−	0.591009i
$982$	2.98420e7			0.987528
$983$	−7.75238e6			−0.255889			−0.127944	−	0.991781i	$-0.540838\pi$
$983$	−7.75238e6			−0.255889			−0.127944	+	0.991781i	$0.540838\pi$
$984$	−4.20034e6	+	7.72420e6i	−0.138292	+	0.254311i
$985$			4.05300e7i			1.33102i
$986$	6.56777e7			2.15142
$987$		0			0
$988$	1.92740e7			0.628172
$989$			5.74843e6i			0.186878i
$990$	6.41388e6	+	9.90441e6i	0.207985	+	0.321174i
$991$	2.45298e7			0.793434			0.396717	−	0.917941i	$-0.370149\pi$
$991$	2.45298e7			0.793434			0.396717	+	0.917941i	$0.370149\pi$
$992$	−6.56574e7			−2.11838
$993$	1.26516e7	+	6.87982e6i	0.407167	+	0.221413i
$994$		0			0
$995$		−	7.55885e7i		−	2.42046i
$996$	1.99223e7	+	1.08336e7i	0.636344	+	0.346037i
$997$		−	3.22082e7i		−	1.02619i	−0.858331	−	0.513096i	$-0.828499\pi$
$997$		−	3.22082e7i		−	1.02619i	0.858331	−	0.513096i	$-0.171501\pi$
$998$		−	7.21838e7i		−	2.29410i
$999$	1.18070e6	+	1.53821e7i	0.0374306	+	0.487642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.1	✓	40
3.2	odd	2	inner	147.6.c.d.146.40	yes	40
7.6	odd	2	inner	147.6.c.d.146.39	yes	40
21.20	even	2	inner	147.6.c.d.146.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.1	✓	40	1.1	even	1	trivial
147.6.c.d.146.2	yes	40	21.20	even	2	inner
147.6.c.d.146.39	yes	40	7.6	odd	2	inner
147.6.c.d.146.40	yes	40	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.23628i q^{2} +(13.6946 + 7.44699i) q^{3} -35.8363 q^{4} -95.6857 q^{5} +(61.3355 - 112.793i) q^{6} +31.5969i q^{8} +(132.085 + 203.967i) q^{9} +O(q^{10})\)	\(q-8.23628i q^{2} +(13.6946 + 7.44699i) q^{3} -35.8363 q^{4} -95.6857 q^{5} +(61.3355 - 112.793i) q^{6} +31.5969i q^{8} +(132.085 + 203.967i) q^{9} +788.094i q^{10} -61.6155i q^{11} +(-490.764 - 266.873i) q^{12} +701.342i q^{13} +(-1310.38 - 712.570i) q^{15} -886.521 q^{16} +2099.12 q^{17} +(1679.93 - 1087.89i) q^{18} +766.864i q^{19} +3429.02 q^{20} -507.483 q^{22} -1169.68i q^{23} +(-235.302 + 432.707i) q^{24} +6030.75 q^{25} +5776.45 q^{26} +(289.907 + 3776.89i) q^{27} +3798.83i q^{29} +(-5868.93 + 10792.6i) q^{30} +7898.41i q^{31} +8312.74i q^{32} +(458.850 - 843.801i) q^{33} -17288.9i q^{34} +(-4733.43 - 7309.43i) q^{36} +4072.69 q^{37} +6316.10 q^{38} +(-5222.89 + 9604.60i) q^{39} -3023.37i q^{40} +17850.8 q^{41} -4914.53 q^{43} +2208.07i q^{44} +(-12638.6 - 19516.7i) q^{45} -9633.83 q^{46} -13652.0 q^{47} +(-12140.6 - 6601.91i) q^{48} -49670.9i q^{50} +(28746.6 + 15632.1i) q^{51} -25133.5i q^{52} +7168.22i q^{53} +(31107.5 - 2387.76i) q^{54} +5895.73i q^{55} +(-5710.82 + 10501.9i) q^{57} +31288.2 q^{58} -7816.93 q^{59} +(46959.1 + 25535.9i) q^{60} -4037.59i q^{61} +65053.5 q^{62} +40097.3 q^{64} -67108.4i q^{65} +(-6949.78 - 3779.22i) q^{66} -35769.0 q^{67} -75224.7 q^{68} +(8710.61 - 16018.3i) q^{69} +6743.05i q^{71} +(-6444.73 + 4173.47i) q^{72} +16912.1i q^{73} -33543.8i q^{74} +(82588.8 + 44910.9i) q^{75} -27481.6i q^{76} +(79106.2 + 43017.1i) q^{78} -37459.0 q^{79} +84827.4 q^{80} +(-24156.3 + 53881.9i) q^{81} -147025. i q^{82} -40594.5 q^{83} -200856. q^{85} +40477.4i q^{86} +(-28289.9 + 52023.5i) q^{87} +1946.86 q^{88} +7488.04 q^{89} +(-160745. + 104095. i) q^{90} +41917.1i q^{92} +(-58819.4 + 108166. i) q^{93} +112442. i q^{94} -73377.9i q^{95} +(-61904.8 + 113840. i) q^{96} +35026.7i q^{97} +(12567.6 - 8138.47i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) \) 40 * q - 640 * q^4 + 440 * q^9	\( 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) \) 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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