LMFDB - Embedded newform 147.6.c.d.146.19

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			146.19
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50172i q^{2} +(-11.3889 - 10.6440i) q^{3} +29.7448 q^{4} +9.66598 q^{5} +(-15.9842 + 17.1029i) q^{6} -92.7234i q^{8} +(16.4124 + 242.445i) q^{9} +O(q^{10})$	\(q-1.50172i q^{2} +(-11.3889 - 10.6440i) q^{3} +29.7448 q^{4} +9.66598 q^{5} +(-15.9842 + 17.1029i) q^{6} -92.7234i q^{8} +(16.4124 + 242.445i) q^{9} -14.5156i q^{10} +628.236i q^{11} +(-338.760 - 316.603i) q^{12} +282.813i q^{13} +(-110.085 - 102.884i) q^{15} +812.590 q^{16} -1378.69 q^{17} +(364.084 - 24.6468i) q^{18} -158.896i q^{19} +287.513 q^{20} +943.433 q^{22} +2036.83i q^{23} +(-986.944 + 1056.01i) q^{24} -3031.57 q^{25} +424.705 q^{26} +(2393.66 - 2935.87i) q^{27} +4904.16i q^{29} +(-154.503 + 165.316i) q^{30} +5786.98i q^{31} -4187.43i q^{32} +(6686.91 - 7154.89i) q^{33} +2070.41i q^{34} +(488.184 + 7211.49i) q^{36} +12398.7 q^{37} -238.617 q^{38} +(3010.25 - 3220.91i) q^{39} -896.262i q^{40} +3660.98 q^{41} +15461.4 q^{43} +18686.8i q^{44} +(158.642 + 2343.47i) q^{45} +3058.75 q^{46} +23463.0 q^{47} +(-9254.48 - 8649.18i) q^{48} +4552.56i q^{50} +(15701.8 + 14674.8i) q^{51} +8412.22i q^{52} +15574.0i q^{53} +(-4408.85 - 3594.60i) q^{54} +6072.51i q^{55} +(-1691.28 + 1809.64i) q^{57} +7364.67 q^{58} -47288.9 q^{59} +(-3274.45 - 3060.28i) q^{60} -22363.0i q^{61} +8690.41 q^{62} +19714.6 q^{64} +2733.66i q^{65} +(-10744.6 - 10041.9i) q^{66} +1418.77 q^{67} -41009.0 q^{68} +(21680.0 - 23197.2i) q^{69} -26993.2i q^{71} +(22480.3 - 1521.81i) q^{72} +45010.1i q^{73} -18619.4i q^{74} +(34526.1 + 32267.9i) q^{75} -4726.33i q^{76} +(-4836.91 - 4520.54i) q^{78} -86753.6 q^{79} +7854.48 q^{80} +(-58510.3 + 7958.20i) q^{81} -5497.76i q^{82} -30372.1 q^{83} -13326.4 q^{85} -23218.6i q^{86} +(52199.7 - 55852.8i) q^{87} +58252.1 q^{88} -8169.45 q^{89} +(3519.23 - 238.235i) q^{90} +60585.3i q^{92} +(61596.3 - 65907.1i) q^{93} -35234.9i q^{94} -1535.88i q^{95} +(-44570.8 + 47690.1i) q^{96} +154625. i q^{97} +(-152313. + 10310.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.50172i		−	0.265469i	−0.991152	−	0.132734i	$-0.957624\pi$
$2$		−	1.50172i		−	0.265469i	0.991152	−	0.132734i	$-0.0423757\pi$
$3$	−11.3889	−	10.6440i	−0.730596	−	0.682810i
$3$	−11.3889	−	10.6440i	−0.730596	−	0.682810i
$4$	29.7448			0.929526
$5$	9.66598			0.172910			0.0864551	−	0.996256i	$-0.472446\pi$
$5$	9.66598			0.172910			0.0864551	+	0.996256i	$0.472446\pi$
$6$	−15.9842	+	17.1029i	−0.181265	+	0.193950i
$7$		0			0
$7$		0			0
$8$		−	92.7234i		−	0.512229i
$9$	16.4124	+	242.445i	0.0675406	+	0.997717i
$10$		−	14.5156i		−	0.0459023i
$11$			628.236i			1.56546i	0.622364	+	0.782728i	$0.286172\pi$
$11$			628.236i			1.56546i	−0.622364	+	0.782728i	$0.713828\pi$
$12$	−338.760	−	316.603i	−0.679108	−	0.634690i
$13$			282.813i			0.464131i	0.972700	+	0.232065i	$0.0745483\pi$
$13$			282.813i			0.464131i	−0.972700	+	0.232065i	$0.925452\pi$
$14$		0			0
$15$	−110.085	−	102.884i	−0.126328	−	0.118065i
$16$	812.590			0.793545
$17$	−1378.69			−1.15703			−0.578516	−	0.815671i	$-0.696368\pi$
$17$	−1378.69			−1.15703			−0.578516	+	0.815671i	$0.696368\pi$
$18$	364.084	−	24.6468i	0.264863	−	0.0179299i
$19$		−	158.896i		−	0.100978i	−0.998725	−	0.0504892i	$-0.983922\pi$
$19$		−	158.896i		−	0.100978i	0.998725	−	0.0504892i	$-0.0160781\pi$
$20$	287.513			0.160725
$21$		0			0
$22$	943.433			0.415580
$23$			2036.83i			0.802853i	0.915891	+	0.401427i	$0.131486\pi$
$23$			2036.83i			0.802853i	−0.915891	+	0.401427i	$0.868514\pi$
$24$	−986.944	+	1056.01i	−0.349755	+	0.374233i
$25$	−3031.57			−0.970102
$26$	424.705			0.123212
$27$	2393.66	−	2935.87i	0.631906	−	0.775045i
$28$		0			0
$29$			4904.16i			1.08285i	0.840748	+	0.541427i	$0.182116\pi$
$29$			4904.16i			1.08285i	−0.840748	+	0.541427i	$0.817884\pi$
$30$	−154.503	+	165.316i	−0.0313426	+	0.0335360i
$31$			5786.98i			1.08155i	0.841167	+	0.540776i	$0.181869\pi$
$31$			5786.98i			1.08155i	−0.841167	+	0.540776i	$0.818131\pi$
$32$		−	4187.43i		−	0.722891i
$33$	6686.91	−	7154.89i	1.06891	−	1.14372i
$34$			2070.41i			0.307156i
$35$		0			0
$36$	488.184	+	7211.49i	0.0627808	+	0.927404i
$37$	12398.7			1.48893			0.744463	−	0.667664i	$-0.232705\pi$
$37$	12398.7			1.48893			0.744463	+	0.667664i	$0.232705\pi$
$38$	−238.617			−0.0268066
$39$	3010.25	−	3220.91i	0.316913	−	0.339092i
$40$		−	896.262i		−	0.0885697i
$41$	3660.98			0.340124			0.170062	−	0.985433i	$-0.445603\pi$
$41$	3660.98			0.340124			0.170062	+	0.985433i	$0.445603\pi$
$42$		0			0
$43$	15461.4			1.27520			0.637598	−	0.770369i	$-0.279928\pi$
$43$	15461.4			1.27520			0.637598	+	0.770369i	$0.279928\pi$
$44$			18686.8i			1.45513i
$45$	158.642	+	2343.47i	0.0116785	+	0.172515i
$46$	3058.75			0.213133
$47$	23463.0			1.54931			0.774657	−	0.632381i	$-0.217922\pi$
$47$	23463.0			1.54931			0.774657	+	0.632381i	$0.217922\pi$
$48$	−9254.48	−	8649.18i	−0.579761	−	0.541841i
$49$		0			0
$50$			4552.56i			0.257532i
$51$	15701.8	+	14674.8i	0.845323	+	0.790033i
$52$			8412.22i			0.431422i
$53$			15574.0i			0.761573i	0.924663	+	0.380786i	$0.124347\pi$
$53$			15574.0i			0.761573i	−0.924663	+	0.380786i	$0.875653\pi$
$54$	−4408.85	−	3594.60i	−0.205750	−	0.167751i
$55$			6072.51i			0.270683i
$56$		0			0
$57$	−1691.28	+	1809.64i	−0.0689491	+	0.0737744i
$58$	7364.67			0.287464
$59$	−47288.9			−1.76860			−0.884298	−	0.466922i	$-0.845363\pi$
$59$	−47288.9			−1.76860			−0.884298	+	0.466922i	$0.845363\pi$
$60$	−3274.45	−	3060.28i	−0.117425	−	0.109744i
$61$		−	22363.0i		−	0.769493i	−0.923022	−	0.384746i	$-0.874289\pi$
$61$		−	22363.0i		−	0.769493i	0.923022	−	0.384746i	$-0.125711\pi$
$62$	8690.41			0.287118
$63$		0			0
$64$	19714.6			0.601640
$65$			2733.66i			0.0802530i
$66$	−10744.6	−	10041.9i	−0.303621	−	0.283762i
$67$	1418.77			0.0386122			0.0193061	−	0.999814i	$-0.493854\pi$
$67$	1418.77			0.0386122			0.0193061	+	0.999814i	$0.493854\pi$
$68$	−41009.0			−1.07549
$69$	21680.0	−	23197.2i	0.548196	−	0.586561i
$70$		0			0
$71$		−	26993.2i		−	0.635491i	−0.948176	−	0.317745i	$-0.897074\pi$
$71$		−	26993.2i		−	0.635491i	0.948176	−	0.317745i	$-0.102926\pi$
$72$	22480.3	−	1521.81i	0.511060	−	0.0345963i
$73$			45010.1i			0.988559i	0.869303	+	0.494279i	$0.164568\pi$
$73$			45010.1i			0.988559i	−0.869303	+	0.494279i	$0.835432\pi$
$74$		−	18619.4i		−	0.395264i
$75$	34526.1	+	32267.9i	0.708753	+	0.662395i
$76$		−	4726.33i		−	0.0938621i
$77$		0			0
$78$	−4836.91	−	4520.54i	−0.0900184	−	0.0841306i
$79$	−86753.6			−1.56394			−0.781969	−	0.623317i	$-0.785785\pi$
$79$	−86753.6			−1.56394			−0.781969	+	0.623317i	$0.785785\pi$
$80$	7854.48			0.137212
$81$	−58510.3	+	7958.20i	−0.990877	+	0.134773i
$82$		−	5497.76i		−	0.0902923i
$83$	−30372.1			−0.483926			−0.241963	−	0.970285i	$-0.577791\pi$
$83$	−30372.1			−0.483926			−0.241963	+	0.970285i	$0.577791\pi$
$84$		0			0
$85$	−13326.4			−0.200063
$86$		−	23218.6i		−	0.338525i
$87$	52199.7	−	55852.8i	0.739383	−	0.791128i
$88$	58252.1			0.801872
$89$	−8169.45			−0.109325			−0.0546623	−	0.998505i	$-0.517408\pi$
$89$	−8169.45			−0.109325			−0.0546623	+	0.998505i	$0.517408\pi$
$90$	3519.23	−	238.235i	0.0457975	−	0.00310027i
$91$		0			0
$92$			60585.3i			0.746273i
$93$	61596.3	−	65907.1i	0.738495	−	0.790178i
$94$		−	35234.9i		−	0.411295i
$95$		−	1535.88i		−	0.0174602i
$96$	−44570.8	+	47690.1i	−0.493597	+	0.528141i
$97$			154625.i			1.66859i	0.551320	+	0.834294i	$0.314124\pi$
$97$			154625.i			1.66859i	−0.551320	+	0.834294i	$0.685876\pi$
$98$		0			0
$99$	−152313.	+	10310.8i	−1.56188	+	0.105732i
$100$	−90173.5			−0.901735
$101$	185785.			1.81220			0.906101	−	0.423061i	$-0.139044\pi$
$101$	185785.			1.81220			0.906101	+	0.423061i	$0.139044\pi$
$102$	22037.4	−	23579.6i	0.209729	−	0.224407i
$103$		−	4352.95i		−	0.0404288i	−0.999796	−	0.0202144i	$-0.993565\pi$
$103$		−	4352.95i		−	0.0404288i	0.999796	−	0.0202144i	$-0.00643487\pi$
$104$	26223.3			0.237741
$105$		0			0
$106$	23387.8			0.202174
$107$		−	98047.0i		−	0.827894i	−0.910301	−	0.413947i	$-0.864150\pi$
$107$		−	98047.0i		−	0.827894i	0.910301	−	0.413947i	$-0.135850\pi$
$108$	71198.9	−	87326.9i	0.587373	−	0.720425i
$109$	24818.0			0.200078			0.100039	−	0.994983i	$-0.468103\pi$
$109$	24818.0			0.200078			0.100039	+	0.994983i	$0.468103\pi$
$110$	9119.20			0.0718580
$111$	−141208.	−	131972.i	−1.08780	−	1.01665i
$112$		0			0
$113$		−	203103.i		−	1.49631i	−0.663525	−	0.748154i	$-0.730941\pi$
$113$		−	203103.i		−	1.49631i	0.663525	−	0.748154i	$-0.269059\pi$
$114$	2717.58	+	2539.83i	0.0195848	+	0.0183038i
$115$			19688.0i			0.138822i
$116$			145873.i			1.00654i
$117$	−68566.5	+	4641.63i	−0.463071	+	0.0313477i
$118$			71014.6i			0.469507i
$119$		0			0
$120$	−9539.78	+	10207.4i	−0.0604763	+	0.0647087i
$121$	−233629.			−1.45065
$122$	−33582.9			−0.204276
$123$	−41694.3	−	38967.3i	−0.248493	−	0.232240i
$124$			172133.i			1.00533i
$125$	−59509.3			−0.340651
$126$		0			0
$127$	3081.32			0.0169522			0.00847612	−	0.999964i	$-0.497302\pi$
$127$	3081.32			0.0169522			0.00847612	+	0.999964i	$0.497302\pi$
$128$		−	163603.i		−	0.882608i
$129$	−176087.	−	164570.i	−0.931653	−	0.870717i
$130$	4105.19			0.0213047
$131$	−197787.			−1.00697			−0.503487	−	0.864003i	$-0.667950\pi$
$131$	−197787.			−1.00697			−0.503487	+	0.864003i	$0.667950\pi$
$132$	198901.	−	212821.i	0.993579	−	1.06311i
$133$		0			0
$134$		−	2130.59i		−	0.0102503i
$135$	23137.0	−	28378.0i	0.109263	−	0.134013i
$136$			127837.i			0.592666i
$137$		−	235624.i		−	1.07255i	−0.844042	−	0.536277i	$-0.819830\pi$
$137$		−	235624.i		−	1.07255i	0.844042	−	0.536277i	$-0.180170\pi$
$138$	−34835.7	−	32557.2i	−0.155714	−	0.145529i
$139$			374901.i			1.64581i	0.568178	+	0.822906i	$0.307648\pi$
$139$			374901.i			1.64581i	−0.568178	+	0.822906i	$0.692352\pi$
$140$		0			0
$141$	−267217.	−	249740.i	−1.13192	−	1.05789i
$142$	−40536.3			−0.168703
$143$	−177673.			−0.726576
$144$	13336.5	+	197009.i	0.0535966	+	0.791733i
$145$			47403.5i			0.187236i
$146$	67592.5			0.262432
$147$		0			0
$148$	368799.			1.38400
$149$			286096.i			1.05571i	0.849334	+	0.527856i	$0.177004\pi$
$149$			286096.i			1.05571i	−0.849334	+	0.527856i	$0.822996\pi$
$150$	48457.3	−	51848.5i	0.175845	−	0.188152i
$151$	−183870.			−0.656250			−0.328125	−	0.944634i	$-0.606417\pi$
$151$	−183870.			−0.656250			−0.328125	+	0.944634i	$0.606417\pi$
$152$	−14733.4			−0.0517241
$153$	−22627.6	−	334258.i	−0.0781467	−	1.15439i
$154$		0			0
$155$			55936.8i			0.187012i
$156$	89539.3	−	95805.6i	0.294579	−	0.315195i
$157$			203083.i			0.657543i	0.944409	+	0.328772i	$0.106635\pi$
$157$			203083.i			0.657543i	−0.944409	+	0.328772i	$0.893365\pi$
$158$			130279.i			0.415177i
$159$	165769.	−	177370.i	0.520009	−	0.556402i
$160$		−	40475.6i		−	0.124995i
$161$		0			0
$162$	11951.0	+	87866.0i	0.0357780	+	0.263047i
$163$	102245.			0.301421			0.150711	−	0.988578i	$-0.451844\pi$
$163$	102245.			0.301421			0.150711	+	0.988578i	$0.451844\pi$
$164$	108895.			0.316154
$165$	64635.5	−	69159.0i	0.184825	−	0.197760i
$166$			45610.3i			0.128467i
$167$	−370493.			−1.02799			−0.513995	−	0.857793i	$-0.671835\pi$
$167$	−370493.			−1.02799			−0.513995	+	0.857793i	$0.671835\pi$
$168$		0			0
$169$	291310.			0.784583
$170$			20012.5i			0.0531104i
$171$	38523.5	−	2607.86i	0.100748	−	0.00682015i
$172$	459896.			1.18533
$173$	653132.			1.65915			0.829575	−	0.558395i	$-0.188583\pi$
$173$	653132.			1.65915			0.829575	+	0.558395i	$0.188583\pi$
$174$	−83875.2	−	78389.2i	−0.210020	−	0.196283i
$175$		0			0
$176$			510498.i			1.24226i
$177$	538566.	+	503341.i	1.29213	+	1.20762i
$178$			12268.2i			0.0290223i
$179$		−	307188.i		−	0.716592i	−0.933608	−	0.358296i	$-0.883358\pi$
$179$		−	307188.i		−	0.716592i	0.933608	−	0.358296i	$-0.116642\pi$
$180$	4718.77	+	69706.1i	0.0108554	+	0.160358i
$181$			392784.i			0.891163i	0.895241	+	0.445582i	$0.147003\pi$
$181$			392784.i			0.891163i	−0.895241	+	0.445582i	$0.852997\pi$
$182$		0			0
$183$	−238030.	+	254689.i	−0.525417	+	0.562188i
$184$	188862.			0.411245
$185$	119846.			0.257451
$186$	−98973.9	−	92500.4i	−0.209768	−	0.196047i
$187$		−	866144.i		−	1.81128i
$188$	697904.			1.44013
$189$		0			0
$190$	−2306.47			−0.00463514
$191$			127242.i			0.252376i	0.992006	+	0.126188i	$0.0402742\pi$
$191$			127242.i			0.252376i	−0.992006	+	0.126188i	$0.959726\pi$
$192$	−224526.	−	209841.i	−0.439556	−	0.410806i
$193$	−166317.			−0.321398			−0.160699	−	0.987003i	$-0.551375\pi$
$193$	−166317.			−0.321398			−0.160699	+	0.987003i	$0.551375\pi$
$194$	232203.			0.442958
$195$	29097.0	−	31133.3i	0.0547976	−	0.0586325i
$196$		0			0
$197$			187298.i			0.343849i	0.985110	+	0.171924i	$0.0549984\pi$
$197$			187298.i			0.343849i	−0.985110	+	0.171924i	$0.945002\pi$
$198$	15484.0	+	228731.i	0.0280685	+	0.414631i
$199$			872267.i			1.56141i	0.624900	+	0.780705i	$0.285140\pi$
$199$			872267.i			1.56141i	−0.624900	+	0.780705i	$0.714860\pi$
$200$			281097.i			0.496915i
$201$	−16158.1	−	15101.3i	−0.0282099	−	0.0263648i
$202$		−	278997.i		−	0.481083i
$203$		0			0
$204$	467046.	+	436498.i	0.785750	+	0.734357i
$205$	35386.9			0.0588109
$206$	−6536.90			−0.0107326
$207$	−493821.	+	33429.3i	−0.801020	+	0.0542252i
$208$			229811.i			0.368309i
$209$	99824.0			0.158077
$210$		0			0
$211$	38809.1			0.0600105			0.0300053	−	0.999550i	$-0.490448\pi$
$211$	38809.1			0.0600105			0.0300053	+	0.999550i	$0.490448\pi$
$212$			463247.i			0.707902i
$213$	−287315.	+	307422.i	−0.433919	+	0.464287i
$214$	−147239.			−0.219780
$215$	149449.			0.220494
$216$	−272224.	−	221948.i	−0.397001	−	0.323681i
$217$		0			0
$218$		−	37269.6i		−	0.0531146i
$219$	479085.	−	512614.i	0.674998	−	0.722237i
$220$			180626.i			0.251607i
$221$		−	389912.i		−	0.537014i
$222$	−198184.	+	212054.i	−0.269890	+	0.288778i
$223$		−	222598.i		−	0.299751i	−0.988705	−	0.149875i	$-0.952113\pi$
$223$		−	222598.i		−	0.299751i	0.988705	−	0.149875i	$-0.0478872\pi$
$224$		0			0
$225$	−49755.3	−	734989.i	−0.0655213	−	0.967887i
$226$	−305004.			−0.397223
$227$	−1.46936e6			−1.89263			−0.946313	−	0.323251i	$-0.895224\pi$
$227$	−1.46936e6			−1.89263			−0.946313	+	0.323251i	$0.895224\pi$
$228$	−50306.9	+	53827.6i	−0.0640900	+	0.0685753i
$229$		−	724065.i		−	0.912408i	−0.889875	−	0.456204i	$-0.849209\pi$
$229$		−	724065.i		−	0.912408i	0.889875	−	0.456204i	$-0.150791\pi$
$230$	29565.8			0.0368528
$231$		0			0
$232$	454730.			0.554669
$233$			234187.i			0.282601i	0.989967	+	0.141301i	$0.0451284\pi$
$233$			234187.i			0.282601i	−0.989967	+	0.141301i	$0.954872\pi$
$234$	6970.42	+	102968.i	0.00832184	+	0.122931i
$235$	226793.			0.267892
$236$	−1.40660e6			−1.64396
$237$	988025.	+	923401.i	1.14261	+	1.06787i
$238$		0			0
$239$		−	494066.i		−	0.559487i	−0.960075	−	0.279743i	$-0.909751\pi$
$239$		−	494066.i		−	0.559487i	0.960075	−	0.279743i	$-0.0902494\pi$
$240$	−89453.6	−	83602.8i	−0.100247	−	0.0936898i
$241$		−	1.27583e6i		−	1.41498i	−0.706722	−	0.707491i	$-0.749827\pi$
$241$		−	1.27583e6i		−	1.41498i	0.706722	−	0.707491i	$-0.250173\pi$
$242$			350845.i			0.385103i
$243$	751072.	+	532146.i	0.815955	+	0.578116i
$244$		−	665182.i		−	0.715264i
$245$		0			0
$246$	−58517.9	+	62613.2i	−0.0616525	+	0.0659672i
$247$	44937.8			0.0468672
$248$	536588.			0.554003
$249$	345903.	+	323279.i	0.353554	+	0.330430i
$250$			89366.2i			0.0904322i
$251$	−704571.			−0.705896			−0.352948	−	0.935643i	$-0.614821\pi$
$251$	−704571.			−0.705896			−0.352948	+	0.935643i	$0.614821\pi$
$252$		0			0
$253$	−1.27961e6			−1.25683
$254$		−	4627.27i		−	0.00450029i
$255$	151773.	+	141846.i	0.146165	+	0.136605i
$256$	385179.			0.367336
$257$	233813.			0.220819			0.110410	−	0.993886i	$-0.464784\pi$
$257$	233813.			0.220819			0.110410	+	0.993886i	$0.464784\pi$
$258$	−247138.	+	264434.i	−0.231148	+	0.247325i
$259$		0			0
$260$			81312.3i			0.0745973i
$261$	−1.18899e6	+	80488.9i	−1.08038	+	0.0731366i
$262$			297020.i			0.267320i
$263$			959147.i			0.855058i	0.904002	+	0.427529i	$0.140616\pi$
$263$			959147.i			0.855058i	−0.904002	+	0.427529i	$0.859384\pi$
$264$	−663425.	−	620033.i	−0.585844	−	0.547526i
$265$			150538.i			0.131684i
$266$		0			0
$267$	93040.7	+	86955.3i	0.0798721	+	0.0746479i
$268$	42201.0			0.0358910
$269$	1.65800e6			1.39702			0.698512	−	0.715598i	$-0.253846\pi$
$269$	1.65800e6			1.39702			0.698512	+	0.715598i	$0.253846\pi$
$270$	−42615.8	−	34745.3i	−0.0355763	−	0.0290059i
$271$			1.53929e6i			1.27320i	0.771194	+	0.636600i	$0.219660\pi$
$271$			1.53929e6i			1.27320i	−0.771194	+	0.636600i	$0.780340\pi$
$272$	−1.12031e6			−0.918158
$273$		0			0
$274$	−353842.			−0.284729
$275$		−	1.90454e6i		−	1.51865i
$276$	644867.	−	689998.i	0.509563	−	0.545224i
$277$	−542814.			−0.425061			−0.212531	−	0.977154i	$-0.568171\pi$
$277$	−542814.			−0.425061			−0.212531	+	0.977154i	$0.568171\pi$
$278$	562996.			0.436912
$279$	−1.40302e6	+	94978.0i	−1.07908	+	0.0730487i
$280$		0			0
$281$		−	1.40974e6i		−	1.06506i	−0.846412	−	0.532528i	$-0.821242\pi$
$281$		−	1.40974e6i		−	1.06506i	0.846412	−	0.532528i	$-0.178758\pi$
$282$	−375039.	+	401285.i	−0.280836	+	0.300490i
$283$		−	2.23070e6i		−	1.65567i	−0.560968	−	0.827837i	$-0.689571\pi$
$283$		−	2.23070e6i		−	1.65567i	0.560968	−	0.827837i	$-0.310429\pi$
$284$		−	802910.i		−	0.590705i
$285$	−16347.9	+	17492.0i	−0.0119220	+	0.0127564i
$286$			266815.i			0.192883i
$287$		0			0
$288$	1.01522e6	−	68725.7i	0.721240	−	0.0488245i
$289$	480940.			0.338724
$290$	71186.7			0.0497054
$291$	1.64582e6	−	1.76100e6i	1.13933	−	1.21906i
$292$			1.33882e6i			0.918891i
$293$	1.30976e6			0.891296			0.445648	−	0.895208i	$-0.352973\pi$
$293$	1.30976e6			0.891296			0.445648	+	0.895208i	$0.352973\pi$
$294$		0			0
$295$	−457093.			−0.305809
$296$		−	1.14965e6i		−	0.762672i
$297$	1.84442e6	+	1.50378e6i	1.21330	+	0.989221i
$298$	429635.			0.280259
$299$	−576043.			−0.372629
$300$	1.02697e6	+	959803.i	0.658804	+	0.615714i
$301$		0			0
$302$			276121.i			0.174214i
$303$	−2.11588e6	−	1.97749e6i	−1.32399	−	1.23739i
$304$		−	129117.i		−	0.0801310i
$305$		−	216160.i		−	0.133053i
$306$	−501961.	+	33980.4i	−0.306455	+	0.0207455i
$307$		−	1.57544e6i		−	0.954019i	−0.878898	−	0.477009i	$-0.841721\pi$
$307$		−	1.57544e6i		−	0.954019i	0.878898	−	0.477009i	$-0.158279\pi$
$308$		0			0
$309$	−46332.6	+	49575.1i	−0.0276052	+	0.0295371i
$310$	84001.3			0.0496457
$311$	513865.			0.301265			0.150632	−	0.988590i	$-0.451869\pi$
$311$	513865.			0.301265			0.150632	+	0.988590i	$0.451869\pi$
$312$	−298654.	−	279120.i	−0.173693	−	0.162332i
$313$			255691.i			0.147521i	0.997276	+	0.0737605i	$0.0235000\pi$
$313$			255691.i			0.147521i	−0.997276	+	0.0737605i	$0.976500\pi$
$314$	304973.			0.174557
$315$		0			0
$316$	−2.58047e6			−1.45372
$317$			468180.i			0.261677i	0.991404	+	0.130838i	$0.0417669\pi$
$317$			468180.i			0.261677i	−0.991404	+	0.130838i	$0.958233\pi$
$318$	−266361.	−	248939.i	−0.147707	−	0.138046i
$319$	−3.08097e6			−1.69516
$320$	190560.			0.104030
$321$	−1.04361e6	+	1.11664e6i	−0.565295	+	0.604856i
$322$		0			0
$323$			219069.i			0.116835i
$324$	−1.74038e6	+	236715.i	−0.921046	+	0.125275i
$325$		−	857366.i		−	0.450254i
$326$		−	153543.i		−	0.0800179i
$327$	−282649.	−	264162.i	−0.146177	−	0.136616i
$328$		−	339458.i		−	0.174221i
$329$		0			0
$330$	−103857.	−	97064.4i	−0.0524992	−	0.0490654i
$331$	−595797.			−0.298902			−0.149451	−	0.988769i	$-0.547751\pi$
$331$	−595797.			−0.298902			−0.149451	+	0.988769i	$0.547751\pi$
$332$	−903412.			−0.449822
$333$	203493.	+	3.00601e6i	0.100563	+	1.48553i
$334$			556376.i			0.272899i
$335$	13713.8			0.00667644
$336$		0			0
$337$	549255.			0.263451			0.131725	−	0.991286i	$-0.457948\pi$
$337$	549255.			0.263451			0.131725	+	0.991286i	$0.457948\pi$
$338$		−	437466.i		−	0.208282i
$339$	−2.16182e6	+	2.31312e6i	−1.02169	+	1.09320i
$340$	−396392.			−0.185964
$341$	−3.63558e6			−1.69312
$342$	−3916.27	−	57851.5i	−0.00181054	−	0.0267454i
$343$		0			0
$344$		−	1.43363e6i		−	0.653192i
$345$	209558.	−	224224.i	0.0947888	−	0.101422i
$346$		−	980821.i		−	0.440453i
$347$		−	38291.1i		−	0.0170716i	−0.999964	−	0.00853580i	$-0.997283\pi$
$347$		−	38291.1i		−	0.0170716i	0.999964	−	0.00853580i	$-0.00271706\pi$
$348$	1.55267e6	−	1.66133e6i	0.687276	−	0.735374i
$349$		−	1.61275e6i		−	0.708767i	−0.935100	−	0.354383i	$-0.884691\pi$
$349$		−	1.61275e6i		−	0.708767i	0.935100	−	0.354383i	$-0.115309\pi$
$350$		0			0
$351$	830300.	+	676956.i	0.359722	+	0.293287i
$352$	2.63069e6			1.13165
$353$	−575868.			−0.245972			−0.122986	−	0.992408i	$-0.539247\pi$
$353$	−575868.			−0.245972			−0.122986	+	0.992408i	$0.539247\pi$
$354$	755876.	−	808775.i	0.320584	−	0.343020i
$355$		−	260916.i		−	0.109883i
$356$	−242999.			−0.101620
$357$		0			0
$358$	−461310.			−0.190233
$359$			2.58197e6i			1.05734i	0.848827	+	0.528670i	$0.177309\pi$
$359$			2.58197e6i			1.05734i	−0.848827	+	0.528670i	$0.822691\pi$
$360$	217294.	−	14709.8i	0.0883674	−	0.00598205i
$361$	2.45085e6			0.989803
$362$	589851.			0.236576
$363$	2.66077e6	+	2.48674e6i	1.05984	+	0.990520i
$364$		0			0
$365$			435066.i			0.170932i
$366$	382471.	+	357455.i	0.149243	+	0.139482i
$367$		−	1.84805e6i		−	0.716224i	−0.933679	−	0.358112i	$-0.883421\pi$
$367$		−	1.84805e6i		−	0.716224i	0.933679	−	0.358112i	$-0.116579\pi$
$368$			1.65511e6i			0.637100i
$369$	60085.3	+	887586.i	0.0229722	+	0.339347i
$370$		−	179975.i		−	0.0683451i
$371$		0			0
$372$	1.83217e6	−	1.96040e6i	0.686450	−	0.734491i
$373$	3.20102e6			1.19129			0.595644	−	0.803249i	$-0.296897\pi$
$373$	3.20102e6			1.19129			0.595644	+	0.803249i	$0.296897\pi$
$374$	−1.30071e6			−0.480839
$375$	677743.	+	633414.i	0.248878	+	0.232600i
$376$		−	2.17557e6i		−	0.793604i
$377$	−1.38696e6			−0.502585
$378$		0			0
$379$	71359.3			0.0255183			0.0127592	−	0.999919i	$-0.495939\pi$
$379$	71359.3			0.0255183			0.0127592	+	0.999919i	$0.495939\pi$
$380$		−	45684.6i		−	0.0162297i
$381$	−35092.7	−	32797.4i	−0.0123852	−	0.0115752i
$382$	191082.			0.0669979
$383$	1.51160e6			0.526550			0.263275	−	0.964721i	$-0.415197\pi$
$383$	1.51160e6			0.526550			0.263275	+	0.964721i	$0.415197\pi$
$384$	−1.74139e6	+	1.86326e6i	−0.602653	+	0.644829i
$385$		0			0
$386$			249761.i			0.0853213i
$387$	253758.	+	3.74853e6i	0.0861276	+	1.27228i
$388$			4.59928e6i			1.55100i
$389$			760781.i			0.254909i	0.991844	+	0.127455i	$0.0406807\pi$
$389$			760781.i			0.254909i	−0.991844	+	0.127455i	$0.959319\pi$
$390$	−46753.4	−	43695.5i	−0.0155651	−	0.0145470i
$391$		−	2.80817e6i		−	0.928927i
$392$		0			0
$393$	2.25256e6	+	2.10523e6i	0.735692	+	0.687573i
$394$	281269.			0.0912811
$395$	−838558.			−0.270421
$396$	−4.53052e6	+	306694.i	−1.45181	+	0.0982806i
$397$		−	3.19019e6i		−	1.01588i	−0.861394	−	0.507938i	$-0.830408\pi$
$397$		−	3.19019e6i		−	1.01588i	0.861394	−	0.507938i	$-0.169592\pi$
$398$	1.30990e6			0.414506
$399$		0			0
$400$	−2.46342e6			−0.769820
$401$			3.18337e6i			0.988613i	0.869288	+	0.494307i	$0.164578\pi$
$401$			3.18337e6i			0.988613i	−0.869288	+	0.494307i	$0.835422\pi$
$402$	−22677.9	+	24265.0i	−0.00699903	+	0.00748884i
$403$	−1.63663e6			−0.501982
$404$	5.52614e6			1.68449
$405$	−565559.	+	76923.8i	−0.171333	+	0.0233036i
$406$		0			0
$407$			7.78933e6i			2.33085i
$408$	1.36069e6	−	1.45592e6i	0.404678	−	0.432999i
$409$		−	933011.i		−	0.275790i	−0.990447	−	0.137895i	$-0.955966\pi$
$409$		−	933011.i		−	0.275790i	0.990447	−	0.137895i	$-0.0440337\pi$
$410$		−	53141.2i		−	0.0156125i
$411$	−2.50798e6	+	2.68349e6i	−0.732350	+	0.783603i
$412$		−	129478.i		−	0.0375796i
$413$		0			0
$414$	50201.4	+	741580.i	0.0143951	+	0.212646i
$415$	−293576.			−0.0836758
$416$	1.18426e6			0.335516
$417$	3.99043e6	−	4.26970e6i	1.12378	−	1.20242i
$418$		−	149908.i		−	0.0419646i
$419$	2.33809e6			0.650619			0.325310	−	0.945608i	$-0.394531\pi$
$419$	2.33809e6			0.650619			0.325310	+	0.945608i	$0.394531\pi$
$420$		0			0
$421$	4.77324e6			1.31253			0.656263	−	0.754532i	$-0.272136\pi$
$421$	4.77324e6			1.31253			0.656263	+	0.754532i	$0.272136\pi$
$422$		−	58280.4i		−	0.0159309i
$423$	385084.	+	5.68850e6i	0.104642	+	1.54578i
$424$	1.44408e6			0.390100
$425$	4.17961e6			1.12244
$426$	461662.	+	431466.i	0.123254	+	0.115192i
$427$		0			0
$428$		−	2.91639e6i		−	0.769549i
$429$	2.02349e6	+	1.89114e6i	0.530834	+	0.496114i
$430$		−	224431.i		−	0.0585344i
$431$		−	4.99520e6i		−	1.29527i	−0.761951	−	0.647635i	$-0.775758\pi$
$431$		−	4.99520e6i		−	1.29527i	0.761951	−	0.647635i	$-0.224242\pi$
$432$	1.94506e6	−	2.38566e6i	0.501446	−	0.615033i
$433$		−	4.18202e6i		−	1.07193i	−0.844240	−	0.535965i	$-0.819948\pi$
$433$		−	4.18202e6i		−	1.07193i	0.844240	−	0.535965i	$-0.180052\pi$
$434$		0			0
$435$	504561.	−	539872.i	0.127847	−	0.136794i
$436$	738207.			0.185978
$437$	323645.			0.0810709
$438$	−769801.	−	719451.i	−0.191731	−	0.179191i
$439$		−	1.79632e6i		−	0.444860i	−0.974949	−	0.222430i	$-0.928601\pi$
$439$		−	1.79632e6i		−	0.444860i	0.974949	−	0.222430i	$-0.0713988\pi$
$440$	563064.			0.138652
$441$		0			0
$442$	−585538.			−0.142561
$443$		−	3.87717e6i		−	0.938653i	−0.883025	−	0.469327i	$-0.844497\pi$
$443$		−	3.87717e6i		−	0.938653i	0.883025	−	0.469327i	$-0.155503\pi$
$444$	−4.20020e6	−	3.92548e6i	−1.01114	−	0.945007i
$445$	−78965.7			−0.0189033
$446$	−334280.			−0.0795744
$447$	3.04519e6	−	3.25830e6i	0.720851	−	0.771299i
$448$		0			0
$449$			1.00281e6i			0.234748i	0.993088	+	0.117374i	$0.0374477\pi$
$449$			1.00281e6i			0.234748i	−0.993088	+	0.117374i	$0.962552\pi$
$450$	−1.10375e6	+	74718.4i	−0.256944	+	0.0173939i
$451$			2.29996e6i			0.532449i
$452$		−	6.04128e6i		−	1.39086i
$453$	2.09407e6	+	1.95711e6i	0.479453	+	0.448094i
$454$			2.20657e6i			0.502433i
$455$		0			0
$456$	167796.	+	156821.i	0.0377894	+	0.0353177i
$457$	−288772.			−0.0646791			−0.0323395	−	0.999477i	$-0.510296\pi$
$457$	−288772.			−0.0646791			−0.0323395	+	0.999477i	$0.510296\pi$
$458$	−1.08734e6			−0.242216
$459$	−3.30012e6	+	4.04766e6i	−0.731136	+	0.896752i
$460$			585616.i			0.129038i
$461$	−4.27620e6			−0.937142			−0.468571	−	0.883426i	$-0.655231\pi$
$461$	−4.27620e6			−0.937142			−0.468571	+	0.883426i	$0.655231\pi$
$462$		0			0
$463$	5.84178e6			1.26646			0.633232	−	0.773962i	$-0.281728\pi$
$463$	5.84178e6			1.26646			0.633232	+	0.773962i	$0.281728\pi$
$464$			3.98507e6i			0.859293i
$465$	595389.	−	637056.i	0.127693	−	0.136630i
$466$	351684.			0.0750218
$467$	−6.08163e6			−1.29041			−0.645205	−	0.764009i	$-0.723228\pi$
$467$	−6.08163e6			−1.29041			−0.645205	+	0.764009i	$0.723228\pi$
$468$	−2.03950e6	+	138064.i	−0.430437	+	0.0291385i
$469$		0			0
$470$		−	340580.i		−	0.0711171i
$471$	2.16161e6	−	2.31288e6i	0.448977	−	0.480398i
$472$			4.38478e6i			0.905927i
$473$			9.71338e6i			1.99626i
$474$	1.38669e6	−	1.48374e6i	0.283487	−	0.303327i
$475$			481704.i			0.0979594i
$476$		0			0
$477$	−3.77585e6	+	255607.i	−0.759833	+	0.0514371i
$478$	−741948.			−0.148526
$479$	2.39419e6			0.476782			0.238391	−	0.971169i	$-0.423380\pi$
$479$	2.39419e6			0.476782			0.238391	+	0.971169i	$0.423380\pi$
$480$	−430821.	+	460971.i	−0.0853480	+	0.0913210i
$481$			3.50652e6i			0.691057i
$482$	−1.91594e6			−0.375634
$483$		0			0
$484$	−6.94925e6			−1.34842
$485$			1.49460e6i			0.288516i
$486$	799133.	−	1.12790e6i	0.153472	−	0.216611i
$487$	67243.9			0.0128479			0.00642393	−	0.999979i	$-0.497955\pi$
$487$	67243.9			0.0128479			0.00642393	+	0.999979i	$0.497955\pi$
$488$	−2.07357e6			−0.394157
$489$	−1.16446e6	−	1.08829e6i	−0.220217	−	0.205813i
$490$		0			0
$491$		−	2.21012e6i		−	0.413726i	−0.978370	−	0.206863i	$-0.933675\pi$
$491$		−	2.21012e6i		−	0.413726i	0.978370	−	0.206863i	$-0.0663254\pi$
$492$	−1.24019e6	−	1.15908e6i	−0.230981	−	0.215873i
$493$		−	6.76133e6i		−	1.25290i
$494$		−	67483.9i		−	0.0124418i
$495$	−1.47225e6	+	99664.4i	−0.270065	+	0.0182821i
$496$			4.70244e6i			0.858261i
$497$		0			0
$498$	485474.	−	519449.i	0.0877188	−	0.0938577i
$499$	−3.39305e6			−0.610013			−0.305006	−	0.952350i	$-0.598659\pi$
$499$	−3.39305e6			−0.610013			−0.305006	+	0.952350i	$0.598659\pi$
$500$	−1.77009e6			−0.316644
$501$	4.21949e6	+	3.94351e6i	0.751045	+	0.701921i
$502$			1.05807e6i			0.187393i
$503$	8.06225e6			1.42081			0.710405	−	0.703793i	$-0.248512\pi$
$503$	8.06225e6			1.42081			0.710405	+	0.703793i	$0.248512\pi$
$504$		0			0
$505$	1.79579e6			0.313348
$506$			1.92162e6i			0.333650i
$507$	−3.31769e6	−	3.10069e6i	−0.573213	−	0.535721i
$508$	91653.3			0.0157575
$509$	−2.29572e6			−0.392758			−0.196379	−	0.980528i	$-0.562918\pi$
$509$	−2.29572e6			−0.392758			−0.196379	+	0.980528i	$0.562918\pi$
$510$	213013.	−	227920.i	0.0362644	−	0.0388023i
$511$		0			0
$512$		−	5.81374e6i		−	0.980124i
$513$	−466497.	−	380342.i	−0.0782628	−	0.0638089i
$514$		−	351122.i		−	0.0586206i
$515$		−	42075.5i		−	0.00699055i
$516$	−5.23769e6	−	4.89511e6i	−0.865996	−	0.809354i
$517$			1.47403e7i			2.42538i
$518$		0			0
$519$	−7.43843e6	−	6.95191e6i	−1.21217	−	1.13288i
$520$	253474.			0.0411079
$521$	718776.			0.116011			0.0580055	−	0.998316i	$-0.481526\pi$
$521$	718776.			0.116011			0.0580055	+	0.998316i	$0.481526\pi$
$522$	120872.	+	1.78553e6i	0.0194155	+	0.286807i
$523$			2.13963e6i			0.342045i	0.985267	+	0.171023i	$0.0547071\pi$
$523$			2.13963e6i			0.342045i	−0.985267	+	0.171023i	$0.945293\pi$
$524$	−5.88313e6			−0.936010
$525$		0			0
$526$	1.44037e6			0.226991
$527$		−	7.97847e6i		−	1.25139i
$528$	5.43372e6	−	5.81399e6i	0.848228	−	0.907590i
$529$	2.28765e6			0.355427
$530$	226066.			0.0349579
$531$	−776123.	−	1.14650e7i	−0.119452	−	1.76456i
$532$		0			0
$533$			1.03537e6i			0.157862i
$534$	130582.	−	139721.i	0.0198167	−	0.0212035i
$535$		−	947720.i		−	0.143151i
$536$		−	131553.i		−	0.0197783i
$537$	−3.26970e6	+	3.49852e6i	−0.489296	+	0.523539i
$538$		−	2.48985e6i		−	0.370866i
$539$		0			0
$540$	688207.	−	844100.i	0.101563	−	0.124569i
$541$	−9.80342e6			−1.44007			−0.720036	−	0.693936i	$-0.755875\pi$
$541$	−9.80342e6			−1.44007			−0.720036	+	0.693936i	$0.755875\pi$
$542$	2.31158e6			0.337995
$543$	4.18078e6	−	4.47336e6i	0.608495	−	0.651080i
$544$			5.77318e6i			0.836408i
$545$	239890.			0.0345956
$546$		0			0
$547$	3.06860e6			0.438502			0.219251	−	0.975668i	$-0.429639\pi$
$547$	3.06860e6			0.438502			0.219251	+	0.975668i	$0.429639\pi$
$548$		−	7.00861e6i		−	0.996966i
$549$	5.42179e6	−	367029.i	0.767736	−	0.0519720i
$550$	−2.86008e6			−0.403155
$551$	779251.			0.109345
$552$	−2.15093e6	−	2.01024e6i	−0.300454	−	0.280802i
$553$		0			0
$554$			815154.i			0.112841i
$555$	−1.36491e6	−	1.27564e6i	−0.188092	−	0.175790i
$556$			1.11514e7i			1.52982i
$557$			5.90998e6i			0.807139i	0.914949	+	0.403569i	$0.132231\pi$
$557$			5.90998e6i			0.807139i	−0.914949	+	0.403569i	$0.867769\pi$
$558$	142630.	+	2.10695e6i	0.0193922	+	0.286463i
$559$			4.37267e6i			0.591858i
$560$		0			0
$561$	−9.21920e6	+	9.86440e6i	−1.23676	+	1.32332i
$562$	−2.11703e6			−0.282739
$563$	4.05311e6			0.538912			0.269456	−	0.963013i	$-0.413156\pi$
$563$	4.05311e6			0.538912			0.269456	+	0.963013i	$0.413156\pi$
$564$	−7.94834e6	−	7.42846e6i	−1.05215	−	0.983334i
$565$		−	1.96319e6i		−	0.258727i
$566$	−3.34988e6			−0.439530
$567$		0			0
$568$	−2.50290e6			−0.325517
$569$		−	1.07534e7i		−	1.39240i	−0.717849	−	0.696199i	$-0.754873\pi$
$569$		−	1.07534e7i		−	1.39240i	0.717849	−	0.696199i	$-0.245127\pi$
$570$	26268.0	+	24549.9i	0.00338642	+	0.00316492i
$571$	−8.83017e6			−1.13339			−0.566694	−	0.823928i	$-0.691778\pi$
$571$	−8.83017e6			−1.13339			−0.566694	+	0.823928i	$0.691778\pi$
$572$	−5.28485e6			−0.675372
$573$	1.35436e6	−	1.44914e6i	0.172325	−	0.184385i
$574$		0			0
$575$		−	6.17480e6i		−	0.778850i
$576$	323563.	+	4.77970e6i	0.0406352	+	0.600267i
$577$		−	8.51635e6i		−	1.06491i	−0.846458	−	0.532456i	$-0.821269\pi$
$577$		−	8.51635e6i		−	1.06491i	0.846458	−	0.532456i	$-0.178731\pi$
$578$		−	722236.i		−	0.0899207i
$579$	1.89416e6	+	1.77027e6i	0.234812	+	0.219454i
$580$			1.41001e6i			0.174041i
$581$		0			0
$582$	−2.64452e6	−	2.47155e6i	−0.323623	−	0.302456i
$583$	−9.78416e6			−1.19221
$584$	4.17349e6			0.506369
$585$	−662763.	+	44865.9i	−0.0800697	+	0.00542034i
$586$		−	1.96689e6i		−	0.236611i
$587$	8.78002e6			1.05172			0.525860	−	0.850571i	$-0.323744\pi$
$587$	8.78002e6			1.05172			0.525860	+	0.850571i	$0.323744\pi$
$588$		0			0
$589$	919527.			0.109213
$590$			686425.i			0.0811827i
$591$	1.99359e6	−	2.13311e6i	0.234783	−	0.251214i
$592$	1.00751e7			1.18153
$593$	3.08130e6			0.359830			0.179915	−	0.983682i	$-0.442418\pi$
$593$	3.08130e6			0.359830			0.179915	+	0.983682i	$0.442418\pi$
$594$	2.25826e6	−	2.76979e6i	0.262607	−	0.322093i
$595$		0			0
$596$			8.50987e6i			0.981312i
$597$	9.28438e6	−	9.93413e6i	1.06615	−	1.14076i
$598$			865054.i			0.0989214i
$599$		−	1.73626e7i		−	1.97719i	−0.150597	−	0.988595i	$-0.548120\pi$
$599$		−	1.73626e7i		−	1.97719i	0.150597	−	0.988595i	$-0.451880\pi$
$600$	2.99199e6	−	3.20138e6i	0.339298	−	0.363044i
$601$			6.08000e6i			0.686621i	0.939222	+	0.343310i	$0.111548\pi$
$601$			6.08000e6i			0.686621i	−0.939222	+	0.343310i	$0.888452\pi$
$602$		0			0
$603$	23285.3	+	343973.i	0.00260789	+	0.0385240i
$604$	−5.46919e6			−0.610001
$605$	−2.25825e6			−0.250833
$606$	−2.96963e6	+	3.17745e6i	−0.328489	+	0.351478i
$607$			6.83425e6i			0.752868i	0.926443	+	0.376434i	$0.122850\pi$
$607$			6.83425e6i			0.752868i	−0.926443	+	0.376434i	$0.877150\pi$
$608$	−665365.			−0.0729964
$609$		0			0
$610$	−324611.			−0.0353215
$611$			6.63564e6i			0.719085i
$612$	−673056.	−	9.94244e6i	−0.0726394	−	1.07304i
$613$	9.50093e6			1.02121			0.510605	−	0.859815i	$-0.329421\pi$
$613$	9.50093e6			1.02121			0.510605	+	0.859815i	$0.329421\pi$
$614$	−2.36587e6			−0.253262
$615$	−403017.	−	376657.i	−0.0429670	−	0.0401567i
$616$		0			0
$617$		−	3.11884e6i		−	0.329822i	−0.986308	−	0.164911i	$-0.947266\pi$
$617$		−	3.11884e6i		−	0.329822i	0.986308	−	0.164911i	$-0.0527338\pi$
$618$	74447.9	+	69578.5i	0.00784118	+	0.00732831i
$619$			1.26056e7i			1.32232i	0.750243	+	0.661162i	$0.229936\pi$
$619$			1.26056e7i			1.32232i	−0.750243	+	0.661162i	$0.770064\pi$
$620$			1.66383e6i			0.173832i
$621$	5.97987e6	+	4.87548e6i	0.622247	+	0.507328i
$622$		−	771681.i		−	0.0799764i
$623$		0			0
$624$	2.44610e6	−	2.61728e6i	0.251485	−	0.269085i
$625$	8.89844e6			0.911200
$626$	383975.			0.0391622
$627$	−1.13688e6	−	1.06252e6i	−0.115491	−	0.107937i
$628$			6.04067e6i			0.611204i
$629$	−1.70941e7			−1.72274
$630$		0			0
$631$	1.33814e7			1.33792			0.668958	−	0.743301i	$-0.266741\pi$
$631$	1.33814e7			1.33792			0.668958	+	0.743301i	$0.266741\pi$
$632$			8.04409e6i			0.801095i
$633$	−441992.	−	413083.i	−0.0438435	−	0.0409758i
$634$	703075.			0.0694670
$635$	29783.9			0.00293122
$636$	4.93078e6	−	5.27586e6i	0.483362	−	0.517190i
$637$		0			0
$638$			4.62675e6i			0.450012i
$639$	6.54438e6	−	443023.i	0.634040	−	0.0429215i
$640$		−	1.58139e6i		−	0.152612i
$641$			1.70599e7i			1.63995i	0.572399	+	0.819976i	$0.306013\pi$
$641$			1.70599e7i			1.63995i	−0.572399	+	0.819976i	$0.693987\pi$
$642$	1.67689e6	+	1.56721e6i	0.160570	+	0.150068i
$643$		−	2.90090e6i		−	0.276698i	−0.990384	−	0.138349i	$-0.955820\pi$
$643$		−	2.90090e6i		−	0.276698i	0.990384	−	0.138349i	$-0.0441796\pi$
$644$		0			0
$645$	−1.70206e6	−	1.59073e6i	−0.161092	−	0.150556i
$646$	328980.			0.0310161
$647$	−6.45367e6			−0.606102			−0.303051	−	0.952974i	$-0.598005\pi$
$647$	−6.45367e6			−0.606102			−0.303051	+	0.952974i	$0.598005\pi$
$648$	737911.	+	5.42527e6i	0.0690346	+	0.507556i
$649$		−	2.97085e7i		−	2.76866i
$650$	−1.28752e6			−0.119528
$651$		0			0
$652$	3.04127e6			0.280179
$653$			1.77442e7i			1.62845i	0.580551	+	0.814224i	$0.302837\pi$
$653$			1.77442e7i			1.62845i	−0.580551	+	0.814224i	$0.697163\pi$
$654$	−396696.	+	424459.i	−0.0362672	+	0.0388053i
$655$	−1.91180e6			−0.174116
$656$	2.97487e6			0.269904
$657$	−1.09125e7	+	738722.i	−0.986302	+	0.0667679i
$658$		0			0
$659$		−	1.47708e7i		−	1.32492i	−0.749096	−	0.662461i	$-0.769512\pi$
$659$		−	1.47708e7i		−	1.32492i	0.749096	−	0.662461i	$-0.230488\pi$
$660$	1.92257e6	−	2.05712e6i	0.171800	−	0.183823i
$661$			1.76103e6i			0.156770i	0.996923	+	0.0783851i	$0.0249764\pi$
$661$			1.76103e6i			0.156770i	−0.996923	+	0.0783851i	$0.975024\pi$
$662$			894720.i			0.0793492i
$663$	−4.15021e6	+	4.44065e6i	−0.366679	+	0.392341i
$664$			2.81620e6i			0.247881i
$665$		0			0
$666$	4.51419e6	−	305589.i	0.394361	−	0.0266964i
$667$	−9.98896e6			−0.869372
$668$	−1.10202e7			−0.955543
$669$	−2.36933e6	+	2.53514e6i	−0.204673	+	0.218996i
$670$		−	20594.2i		−	0.00177239i
$671$	1.40492e7			1.20461
$672$		0			0
$673$	829541.			0.0705993			0.0352997	−	0.999377i	$-0.488761\pi$
$673$	829541.			0.0705993			0.0352997	+	0.999377i	$0.488761\pi$
$674$		−	824827.i		−	0.0699380i
$675$	−7.25654e6	+	8.90028e6i	−0.613013	+	0.751873i
$676$	8.66497e6			0.729290
$677$	1.93528e6			0.162283			0.0811414	−	0.996703i	$-0.474143\pi$
$677$	1.93528e6			0.162283			0.0811414	+	0.996703i	$0.474143\pi$
$678$	3.47365e6	+	3.24645e6i	0.290210	+	0.271228i
$679$		0			0
$680$			1.23567e6i			0.102478i
$681$	1.67344e7	+	1.56399e7i	1.38275	+	1.29230i
$682$			5.45963e6i			0.449471i
$683$		−	3.13153e6i		−	0.256865i	−0.991718	−	0.128432i	$-0.959006\pi$
$683$		−	3.13153e6i		−	0.256865i	0.991718	−	0.128432i	$-0.0409945\pi$
$684$	1.14588e6	−	77570.4i	0.0936478	−	0.00633951i
$685$		−	2.27754e6i		−	0.185455i
$686$		0			0
$687$	−7.70692e6	+	8.24628e6i	−0.623001	+	0.666601i
$688$	1.25638e7			1.01193
$689$	−4.40453e6			−0.353469
$690$	−336721.	−	314697.i	−0.0269245	−	0.0251635i
$691$		−	1.19257e7i		−	0.950139i	−0.879948	−	0.475070i	$-0.842423\pi$
$691$		−	1.19257e7i		−	0.950139i	0.879948	−	0.475070i	$-0.157577\pi$
$692$	1.94273e7			1.54222
$693$		0			0
$694$	−57502.5			−0.00453198
$695$			3.62379e6i			0.284578i
$696$	−5.17886e6	−	4.84013e6i	−0.405239	−	0.378734i
$697$	−5.04736e6			−0.393534
$698$	−2.42190e6			−0.188155
$699$	2.49268e6	−	2.66713e6i	0.192963	−	0.206467i
$700$		0			0
$701$			1.13239e7i			0.870362i	0.900343	+	0.435181i	$0.143316\pi$
$701$			1.13239e7i			0.870362i	−0.900343	+	0.435181i	$0.856684\pi$
$702$	1.01660e6	−	1.24688e6i	0.0778586	−	0.0954951i
$703$		−	1.97011e6i		−	0.150349i
$704$			1.23854e7i			0.941841i
$705$	−2.58292e6	−	2.41398e6i	−0.195721	−	0.182920i
$706$			864792.i			0.0652980i
$707$		0			0
$708$	1.60196e7	+	1.49718e7i	1.20107	+	1.12251i
$709$	7.31730e6			0.546682			0.273341	−	0.961917i	$-0.411871\pi$
$709$	7.31730e6			0.546682			0.273341	+	0.961917i	$0.411871\pi$
$710$	−391823.			−0.0291705
$711$	−1.42383e6	−	2.10330e7i	−0.105629	−	1.56037i
$712$			757499.i			0.0559992i
$713$	−1.17871e7			−0.868328
$714$		0			0
$715$	−1.71738e6			−0.125633
$716$		−	9.13727e6i		−	0.666091i
$717$	−5.25881e6	+	5.62684e6i	−0.382023	+	0.408759i
$718$	3.87739e6			0.280691
$719$	1.46880e7			1.05959			0.529797	−	0.848124i	$-0.322268\pi$
$719$	1.46880e7			1.05959			0.529797	+	0.848124i	$0.322268\pi$
$720$	128911.	+	1.90428e6i	0.00926740	+	0.136899i
$721$		0			0
$722$		−	3.68049e6i		−	0.262762i
$723$	−1.35799e7	+	1.45303e7i	−0.966165	+	1.03378i
$724$			1.16833e7i			0.828360i
$725$		−	1.48673e7i		−	1.05048i
$726$	3.73438e6	−	3.99572e6i	0.262952	−	0.281355i
$727$		−	6.68528e6i		−	0.469120i	−0.972102	−	0.234560i	$-0.924635\pi$
$727$		−	6.68528e6i		−	0.469120i	0.972102	−	0.234560i	$-0.0753649\pi$
$728$		0			0
$729$	−2.88972e6	−	1.40549e7i	−0.201390	−	0.979511i
$730$	653347.			0.0453771
$731$	−2.13165e7			−1.47544
$732$	−7.08017e6	+	7.57567e6i	−0.488389	+	0.522569i
$733$			1.68777e7i			1.16025i	0.814526	+	0.580127i	$0.196997\pi$
$733$			1.68777e7i			1.16025i	−0.814526	+	0.580127i	$0.803003\pi$
$734$	−2.77525e6			−0.190135
$735$		0			0
$736$	8.52910e6			0.580375
$737$			891320.i			0.0604456i
$738$	1.33290e6	−	90231.2i	0.0900861	−	0.00609840i
$739$	−2.85846e7			−1.92540			−0.962702	−	0.270565i	$-0.912790\pi$
$739$	−2.85846e7			−1.92540			−0.962702	+	0.270565i	$0.912790\pi$
$740$	3.56480e6			0.239307
$741$	−511790.	−	478316.i	−0.0342410	−	0.0320014i
$742$		0			0
$743$			2.60214e7i			1.72925i	0.502416	+	0.864626i	$0.332445\pi$
$743$			2.60214e7i			1.72925i	−0.502416	+	0.864626i	$0.667555\pi$
$744$	−6.11113e6	−	5.71142e6i	−0.404752	−	0.378279i
$745$			2.76539e6i			0.182543i
$746$		−	4.80703e6i		−	0.316250i
$747$	−498478.	−	7.36356e6i	−0.0326847	−	0.482821i
$748$		−	2.57633e7i		−	1.68364i
$749$		0			0
$750$	951210.	−	1.01778e6i	0.0617480	−	0.0660694i
$751$	1.78093e7			1.15225			0.576127	−	0.817360i	$-0.304563\pi$
$751$	1.78093e7			1.15225			0.576127	+	0.817360i	$0.304563\pi$
$752$	1.90658e7			1.22945
$753$	8.02426e6	+	7.49942e6i	0.515725	+	0.481993i
$754$			2.08282e6i			0.133421i
$755$	−1.77729e6			−0.113472
$756$		0			0
$757$	−2.98404e6			−0.189262			−0.0946312	−	0.995512i	$-0.530167\pi$
$757$	−2.98404e6			−0.189262			−0.0946312	+	0.995512i	$0.530167\pi$
$758$		−	107162.i		−	0.00677433i
$759$	1.45733e7	+	1.36201e7i	0.918236	+	0.858177i
$760$	−142412.			−0.00894363
$761$	1.32473e7			0.829213			0.414606	−	0.910001i	$-0.363919\pi$
$761$	1.32473e7			0.829213			0.414606	+	0.910001i	$0.363919\pi$
$762$	−49252.5	+	52699.3i	−0.00307284	+	0.00328789i
$763$		0			0
$764$			3.78480e6i			0.234590i
$765$	−218718.	−	3.23093e6i	−0.0135124	−	0.199606i
$766$		−	2.27000e6i		−	0.139783i
$767$		−	1.33739e7i		−	0.820860i
$768$	−4.38675e6	−	4.09983e6i	−0.268374	−	0.250820i
$769$			2.37349e7i			1.44734i	0.690146	+	0.723670i	$0.257546\pi$
$769$			2.37349e7i			1.44734i	−0.690146	+	0.723670i	$0.742454\pi$
$770$		0			0
$771$	−2.66287e6	−	2.48870e6i	−0.161330	−	0.150778i
$772$	−4.94708e6			−0.298748
$773$	2.24492e7			1.35130			0.675650	−	0.737222i	$-0.263863\pi$
$773$	2.24492e7			1.35130			0.675650	+	0.737222i	$0.263863\pi$
$774$	5.62924e6	−	381073.i	0.337752	−	0.0228642i
$775$		−	1.75436e7i		−	1.04922i
$776$	1.43373e7			0.854699
$777$		0			0
$778$	1.14248e6			0.0676705
$779$		−	581714.i		−	0.0343452i
$780$	865485.	−	926055.i	0.0509358	−	0.0545005i
$781$	1.69581e7			0.994833
$782$	−4.21708e6			−0.246601
$783$	1.43980e7	+	1.17389e7i	0.839260	+	0.684261i
$784$		0			0
$785$			1.96300e6i			0.113696i
$786$	3.16147e6	−	3.38272e6i	0.182529	−	0.195303i
$787$		−	8.77309e6i		−	0.504912i	−0.967608	−	0.252456i	$-0.918762\pi$
$787$		−	8.77309e6i		−	0.504912i	0.967608	−	0.252456i	$-0.0812383\pi$
$788$			5.57115e6i			0.319616i
$789$	1.02091e7	−	1.09236e7i	0.583843	−	0.624702i
$790$			1.25928e6i			0.0717884i
$791$		0			0
$792$	956056.	+	1.41229e7i	0.0541590	+	0.800041i
$793$	6.32453e6			0.357145
$794$	−4.79077e6			−0.269683
$795$	1.60232e6	−	1.71446e6i	0.0899150	−	0.0962076i
$796$			2.59455e7i			1.45137i
$797$	−1.59987e7			−0.892151			−0.446075	−	0.894995i	$-0.647179\pi$
$797$	−1.59987e7			−0.892151			−0.446075	+	0.894995i	$0.647179\pi$
$798$		0			0
$799$	−3.23483e7			−1.79261
$800$			1.26945e7i			0.701278i
$801$	−134080.	−	1.98064e6i	−0.00738385	−	0.109075i
$802$	4.78053e6			0.262446
$803$	−2.82769e7			−1.54755
$804$	−480621.	−	449186.i	−0.0262218	−	0.0245067i
$805$		0			0
$806$			2.45776e6i			0.133261i
$807$	−1.88827e7	−	1.76477e7i	−1.02066	−	0.953902i
$808$		−	1.72266e7i		−	0.928263i
$809$		−	3.03159e6i		−	0.162854i	−0.996679	−	0.0814272i	$-0.974052\pi$
$809$		−	3.03159e6i		−	0.162854i	0.996679	−	0.0814272i	$-0.0259478\pi$
$810$	115518.	+	849311.i	0.00618638	+	0.0454835i
$811$		−	5.36634e6i		−	0.286501i	−0.989686	−	0.143250i	$-0.954245\pi$
$811$		−	5.36634e6i		−	0.286501i	0.989686	−	0.143250i	$-0.0457554\pi$
$812$		0			0
$813$	1.63841e7	−	1.75307e7i	0.869354	−	0.930195i
$814$	1.16974e7			0.618768
$815$	988300.			0.0521188
$816$	1.27591e7	+	1.19246e7i	0.670802	+	0.626927i
$817$		−	2.45675e6i		−	0.128767i
$818$	−1.40112e6			−0.0732137
$819$		0			0
$820$	1.05258e6			0.0546663
$821$		−	8.14158e6i		−	0.421552i	−0.977534	−	0.210776i	$-0.932401\pi$
$821$		−	8.14158e6i		−	0.421552i	0.977534	−	0.210776i	$-0.0675990\pi$
$822$	4.02985e6	+	3.76627e6i	0.208022	+	0.194416i
$823$	−2.78197e7			−1.43170			−0.715852	−	0.698252i	$-0.753962\pi$
$823$	−2.78197e7			−1.43170			−0.715852	+	0.698252i	$0.753962\pi$
$824$	−403620.			−0.0207088
$825$	−2.02718e7	+	2.16905e7i	−1.03695	+	1.10952i
$826$		0			0
$827$		−	2.99686e7i		−	1.52371i	−0.647747	−	0.761856i	$-0.724288\pi$
$827$		−	2.99686e7i		−	1.52371i	0.647747	−	0.761856i	$-0.275712\pi$
$828$	−1.46886e7	+	994349.i	−0.744569	+	0.0504038i
$829$		−	2.96634e7i		−	1.49911i	−0.661941	−	0.749556i	$-0.730267\pi$
$829$		−	2.96634e7i		−	1.49911i	0.661941	−	0.749556i	$-0.269733\pi$
$830$			440868.i			0.0222133i
$831$	6.18203e6	+	5.77769e6i	0.310548	+	0.290236i
$832$			5.57552e6i			0.279240i
$833$		0			0
$834$	−6.41189e6	−	5.99251e6i	−0.319206	−	0.298328i
$835$	−3.58117e6			−0.177750
$836$	2.96925e6			0.146937
$837$	1.69898e7	+	1.38520e7i	0.838252	+	0.683439i
$838$		−	3.51116e6i		−	0.172719i
$839$	−2.45373e7			−1.20343			−0.601716	−	0.798710i	$-0.705516\pi$
$839$	−2.45373e7			−1.20343			−0.601716	+	0.798710i	$0.705516\pi$
$840$		0			0
$841$	−3.53962e6			−0.172571
$842$		−	7.16806e6i		−	0.348435i
$843$	−1.50052e7	+	1.60553e7i	−0.727231	+	0.778126i
$844$	1.15437e6			0.0557814
$845$	2.81580e6			0.135662
$846$	8.54253e6	−	578288.i	0.410356	−	0.0277791i
$847$		0			0
$848$			1.26553e7i			0.604342i
$849$	−2.37435e7	+	2.54051e7i	−1.13051	+	1.20963i
$850$		−	6.27659e6i		−	0.297973i
$851$			2.52542e7i			1.19539i
$852$	−8.54614e6	+	9.14423e6i	−0.403340	+	0.431567i
$853$		−	3.38019e7i		−	1.59063i	−0.606197	−	0.795314i	$-0.707306\pi$
$853$		−	3.38019e7i		−	1.59063i	0.606197	−	0.795314i	$-0.292694\pi$
$854$		0			0
$855$	372368.	−	25207.5i	0.0174203	−	0.00117927i
$856$	−9.09125e6			−0.424072
$857$	2.41304e7			1.12231			0.561155	−	0.827711i	$-0.310357\pi$
$857$	2.41304e7			1.12231			0.561155	+	0.827711i	$0.310357\pi$
$858$	2.83997e6	−	3.03872e6i	0.131703	−	0.140920i
$859$			4.19833e7i			1.94130i	0.240490	+	0.970651i	$0.422692\pi$
$859$			4.19833e7i			1.94130i	−0.240490	+	0.970651i	$0.577308\pi$
$860$	4.44535e6			0.204955
$861$		0			0
$862$	−7.50139e6			−0.343854
$863$		−	2.87410e7i		−	1.31364i	−0.754049	−	0.656818i	$-0.771902\pi$
$863$		−	2.87410e7i		−	1.31364i	0.754049	−	0.656818i	$-0.228098\pi$
$864$	−1.22937e7	−	1.00233e7i	−0.560273	−	0.456799i
$865$	6.31316e6			0.286884
$866$	−6.28021e6			−0.284564
$867$	−5.47735e6	−	5.11910e6i	−0.247470	−	0.231284i
$868$		0			0
$869$		−	5.45017e7i		−	2.44828i
$870$	−810736.	−	757708.i	−0.0363146	−	0.0339394i
$871$			401245.i			0.0179211i
$872$		−	2.30121e6i		−	0.102486i
$873$	−3.74880e7	+	2.53776e6i	−1.66478	+	0.112697i
$874$		−	486023.i		−	0.0215218i
$875$		0			0
$876$	1.42503e7	−	1.52476e7i	0.627428	−	0.671338i
$877$	2.69599e6			0.118364			0.0591820	−	0.998247i	$-0.481151\pi$
$877$	2.69599e6			0.118364			0.0591820	+	0.998247i	$0.481151\pi$
$878$	−2.69757e6			−0.118096
$879$	−1.49166e7	−	1.39410e7i	−0.651177	−	0.608586i
$880$			4.93446e6i			0.214800i
$881$	3.00447e7			1.30415			0.652075	−	0.758154i	$-0.273899\pi$
$881$	3.00447e7			1.30415			0.652075	+	0.758154i	$0.273899\pi$
$882$		0			0
$883$	−6.83651e6			−0.295075			−0.147537	−	0.989056i	$-0.547135\pi$
$883$	−6.83651e6			−0.295075			−0.147537	+	0.989056i	$0.547135\pi$
$884$		−	1.15979e7i		−	0.499169i
$885$	5.20577e6	+	4.86528e6i	0.223422	+	0.208809i
$886$	−5.82241e6			−0.249183
$887$	6.59700e6			0.281538			0.140769	−	0.990042i	$-0.455042\pi$
$887$	6.59700e6			0.281538			0.140769	+	0.990042i	$0.455042\pi$
$888$	−1.22369e7	+	1.30932e7i	−0.520760	+	0.557205i
$889$		0			0
$890$			118584.i			0.00501825i
$891$	−4.99963e6	−	3.67582e7i	−0.210981	−	1.55117i
$892$		−	6.62115e6i		−	0.278626i
$893$		−	3.72818e6i		−	0.156447i
$894$	−4.89305e6	−	4.57302e6i	−0.204756	−	0.191363i
$895$		−	2.96928e6i		−	0.123906i
$896$		0			0
$897$	6.56047e6	+	6.13137e6i	0.272241	+	0.254435i
$898$	1.50594e6			0.0623184
$899$	−2.83803e7			−1.17116
$900$	−1.47996e6	−	2.18621e7i	−0.0609038	−	0.899676i
$901$		−	2.14718e7i		−	0.881164i
$902$	3.45389e6			0.141349
$903$		0			0
$904$	−1.88324e7			−0.766452
$905$			3.79664e6i			0.154091i
$906$	2.93902e6	−	3.14471e6i	0.118955	−	0.127280i
$907$	−2.24039e6			−0.0904284			−0.0452142	−	0.998977i	$-0.514397\pi$
$907$	−2.24039e6			−0.0904284			−0.0452142	+	0.998977i	$0.514397\pi$
$908$	−4.37060e7			−1.75925
$909$	3.04917e6	+	4.50426e7i	0.122397	+	1.80806i
$910$		0			0
$911$			5.18919e6i			0.207159i	0.994621	+	0.103579i	$0.0330296\pi$
$911$			5.18919e6i			0.207159i	−0.994621	+	0.103579i	$0.966970\pi$
$912$	−1.37432e6	+	1.47050e6i	−0.0547142	+	0.0585434i
$913$		−	1.90808e7i		−	0.757565i
$914$			433654.i			0.0171703i
$915$	−2.30080e6	+	2.46181e6i	−0.0908501	+	0.0972081i
$916$		−	2.15372e7i		−	0.848107i
$917$		0			0
$918$	6.07845e6	+	4.95585e6i	0.238060	+	0.194094i
$919$	−2.59662e7			−1.01419			−0.507096	−	0.861890i	$-0.669281\pi$
$919$	−2.59662e7			−1.01419			−0.507096	+	0.861890i	$0.669281\pi$
$920$	1.82554e6			0.0711085
$921$	−1.67690e7	+	1.79425e7i	−0.651414	+	0.697002i
$922$			6.42165e6i			0.248782i
$923$	7.63403e6			0.294951
$924$		0			0
$925$	−3.75876e7			−1.44441
$926$		−	8.77271e6i		−	0.336207i
$927$	1.05535e6	−	71442.2i	0.0403364	−	0.00273058i
$928$	2.05358e7			0.782784
$929$	3.98740e7			1.51583			0.757914	−	0.652354i	$-0.226219\pi$
$929$	3.98740e7			1.51583			0.757914	+	0.652354i	$0.226219\pi$
$930$	−956680.	−	894107.i	−0.0362710	−	0.0338986i
$931$		0			0
$932$			6.96587e6i			0.262685i
$933$	−5.85234e6	−	5.46956e6i	−0.220103	−	0.205707i
$934$			9.13290e6i			0.342564i
$935$		−	8.37213e6i		−	0.313189i
$936$	430387.	+	6.35772e6i	0.0160572	+	0.237198i
$937$		−	2.38938e7i		−	0.889072i	−0.895761	−	0.444536i	$-0.853369\pi$
$937$		−	2.38938e7i		−	0.889072i	0.895761	−	0.444536i	$-0.146631\pi$
$938$		0			0
$939$	2.72156e6	−	2.91203e6i	0.100729	−	0.107778i
$940$	6.74593e6			0.249013
$941$	2.24631e7			0.826981			0.413490	−	0.910509i	$-0.364310\pi$
$941$	2.24631e7			0.826981			0.413490	+	0.910509i	$0.364310\pi$
$942$	−3.47330e6	−	3.24612e6i	−0.127531	−	0.119189i
$943$			7.45680e6i			0.273070i
$944$	−3.84265e7			−1.40346
$945$		0			0
$946$	1.45868e7			0.529946
$947$		−	9.35059e6i		−	0.338816i	−0.985546	−	0.169408i	$-0.945814\pi$
$947$		−	9.35059e6i		−	0.338816i	0.985546	−	0.169408i	$-0.0541856\pi$
$948$	2.93886e7	+	2.74664e7i	1.06208	+	0.992616i
$949$	−1.27294e7			−0.458821
$950$	723384.			0.0260052
$951$	4.98329e6	−	5.33204e6i	0.178675	−	0.191180i
$952$		0			0
$953$			2.95343e7i			1.05340i	0.850050	+	0.526702i	$0.176572\pi$
$953$			2.95343e7i			1.05340i	−0.850050	+	0.526702i	$0.823428\pi$
$954$	383850.	+	5.67026e6i	0.0136550	+	0.201712i
$955$			1.22992e6i			0.0436383i
$956$		−	1.46959e7i		−	0.520058i
$957$	3.50887e7	+	3.27937e7i	1.23848	+	1.15747i
$958$		−	3.59540e6i		−	0.126571i
$959$		0			0
$960$	−2.17027e6	−	2.02832e6i	−0.0760037	−	0.0710326i
$961$	−4.85995e6			−0.169755
$962$	5.26581e6			0.183454
$963$	2.37710e7	−	1.60918e6i	0.826004	−	0.0559165i
$964$		−	3.79494e7i		−	1.31526i
$965$	−1.60762e6			−0.0555731
$966$		0			0
$967$	2.42238e7			0.833059			0.416529	−	0.909122i	$-0.363246\pi$
$967$	2.42238e7			0.833059			0.416529	+	0.909122i	$0.363246\pi$
$968$			2.16629e7i			0.743066i
$969$	2.33176e6	−	2.49494e6i	0.0797763	−	0.0853594i
$970$	2.24446e6			0.0765920
$971$	−2.72108e6			−0.0926175			−0.0463087	−	0.998927i	$-0.514746\pi$
$971$	−2.72108e6			−0.0926175			−0.0463087	+	0.998927i	$0.514746\pi$
$972$	2.23405e7	+	1.58286e7i	0.758451	+	0.537374i
$973$		0			0
$974$		−	100981.i		−	0.00341071i
$975$	−9.12577e6	+	9.76442e6i	−0.307438	+	0.328954i
$976$		−	1.81719e7i		−	0.610627i
$977$			1.37909e7i			0.462229i	0.972927	+	0.231115i	$0.0742372\pi$
$977$			1.37909e7i			0.462229i	−0.972927	+	0.231115i	$0.925763\pi$
$978$	−1.63431e6	+	1.74869e6i	−0.0546371	+	0.0584608i
$979$		−	5.13234e6i		−	0.171143i
$980$		0			0
$981$	407322.	+	6.01700e6i	0.0135134	+	0.199622i
$982$	−3.31898e6			−0.109831
$983$	2.80278e7			0.925135			0.462567	−	0.886584i	$-0.346928\pi$
$983$	2.80278e7			0.925135			0.462567	+	0.886584i	$0.346928\pi$
$984$	−3.61318e6	+	3.86604e6i	−0.118960	+	0.127285i
$985$			1.81042e6i			0.0594550i
$986$	−1.01536e7			−0.332605
$987$		0			0
$988$	1.33667e6			0.0435643
$989$			3.14923e7i			1.02380i
$990$	149668.	+	2.21091e6i	0.00485334	+	0.0716939i
$991$	2.75377e7			0.890723			0.445362	−	0.895351i	$-0.353075\pi$
$991$	2.75377e7			0.890723			0.445362	+	0.895351i	$0.353075\pi$
$992$	2.42326e7			0.781844
$993$	6.78546e6	+	6.34164e6i	0.218376	+	0.204093i
$994$		0			0
$995$			8.43132e6i			0.269984i
$996$	1.02888e7	+	9.61588e6i	0.328638	+	0.307143i
$997$		−	1.26349e6i		−	0.0402562i	−0.999797	−	0.0201281i	$-0.993593\pi$
$997$		−	1.26349e6i		−	0.0402562i	0.999797	−	0.0201281i	$-0.00640740\pi$
$998$			5.09541e6i			0.161939i
$999$	2.96783e7	−	3.64010e7i	0.940862	−	1.15398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.19	✓	40
3.2	odd	2	inner	147.6.c.d.146.22	yes	40
7.6	odd	2	inner	147.6.c.d.146.21	yes	40
21.20	even	2	inner	147.6.c.d.146.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.19	✓	40	1.1	even	1	trivial
147.6.c.d.146.20	yes	40	21.20	even	2	inner
147.6.c.d.146.21	yes	40	7.6	odd	2	inner
147.6.c.d.146.22	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)

\(f(q)\)	\(=\)	\(q-1.50172i q^{2} +(-11.3889 - 10.6440i) q^{3} +29.7448 q^{4} +9.66598 q^{5} +(-15.9842 + 17.1029i) q^{6} -92.7234i q^{8} +(16.4124 + 242.445i) q^{9} +O(q^{10})\)	\(q-1.50172i q^{2} +(-11.3889 - 10.6440i) q^{3} +29.7448 q^{4} +9.66598 q^{5} +(-15.9842 + 17.1029i) q^{6} -92.7234i q^{8} +(16.4124 + 242.445i) q^{9} -14.5156i q^{10} +628.236i q^{11} +(-338.760 - 316.603i) q^{12} +282.813i q^{13} +(-110.085 - 102.884i) q^{15} +812.590 q^{16} -1378.69 q^{17} +(364.084 - 24.6468i) q^{18} -158.896i q^{19} +287.513 q^{20} +943.433 q^{22} +2036.83i q^{23} +(-986.944 + 1056.01i) q^{24} -3031.57 q^{25} +424.705 q^{26} +(2393.66 - 2935.87i) q^{27} +4904.16i q^{29} +(-154.503 + 165.316i) q^{30} +5786.98i q^{31} -4187.43i q^{32} +(6686.91 - 7154.89i) q^{33} +2070.41i q^{34} +(488.184 + 7211.49i) q^{36} +12398.7 q^{37} -238.617 q^{38} +(3010.25 - 3220.91i) q^{39} -896.262i q^{40} +3660.98 q^{41} +15461.4 q^{43} +18686.8i q^{44} +(158.642 + 2343.47i) q^{45} +3058.75 q^{46} +23463.0 q^{47} +(-9254.48 - 8649.18i) q^{48} +4552.56i q^{50} +(15701.8 + 14674.8i) q^{51} +8412.22i q^{52} +15574.0i q^{53} +(-4408.85 - 3594.60i) q^{54} +6072.51i q^{55} +(-1691.28 + 1809.64i) q^{57} +7364.67 q^{58} -47288.9 q^{59} +(-3274.45 - 3060.28i) q^{60} -22363.0i q^{61} +8690.41 q^{62} +19714.6 q^{64} +2733.66i q^{65} +(-10744.6 - 10041.9i) q^{66} +1418.77 q^{67} -41009.0 q^{68} +(21680.0 - 23197.2i) q^{69} -26993.2i q^{71} +(22480.3 - 1521.81i) q^{72} +45010.1i q^{73} -18619.4i q^{74} +(34526.1 + 32267.9i) q^{75} -4726.33i q^{76} +(-4836.91 - 4520.54i) q^{78} -86753.6 q^{79} +7854.48 q^{80} +(-58510.3 + 7958.20i) q^{81} -5497.76i q^{82} -30372.1 q^{83} -13326.4 q^{85} -23218.6i q^{86} +(52199.7 - 55852.8i) q^{87} +58252.1 q^{88} -8169.45 q^{89} +(3519.23 - 238.235i) q^{90} +60585.3i q^{92} +(61596.3 - 65907.1i) q^{93} -35234.9i q^{94} -1535.88i q^{95} +(-44570.8 + 47690.1i) q^{96} +154625. i q^{97} +(-152313. + 10310.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) \) 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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