LMFDB - Embedded newform 147.4.e.l.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$2.13746 - 0.656712i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.l.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.63746 - 4.56821i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-9.91238 - 17.1687i) q^{4} +(-5.27492 + 9.13642i) q^{5} -15.8248 q^{6} -62.3746 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(2.63746 - 4.56821i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-9.91238 - 17.1687i) q^{4} +(-5.27492 + 9.13642i) q^{5} -15.8248 q^{6} -62.3746 q^{8} +(-4.50000 + 7.79423i) q^{9} +(27.8248 + 48.1939i) q^{10} +(-17.3746 - 30.0937i) q^{11} +(-29.7371 + 51.5062i) q^{12} -37.2990 q^{13} +31.6495 q^{15} +(-85.2114 + 147.590i) q^{16} +(5.27492 + 9.13642i) q^{17} +(23.7371 + 41.1139i) q^{18} +(29.2990 - 50.7474i) q^{19} +209.148 q^{20} -183.299 q^{22} +(62.6736 - 108.554i) q^{23} +(93.5619 + 162.054i) q^{24} +(6.85050 + 11.8654i) q^{25} +(-98.3746 + 170.390i) q^{26} +27.0000 q^{27} -35.4020 q^{29} +(83.4743 - 144.582i) q^{30} +(-145.897 - 252.701i) q^{31} +(199.985 + 346.384i) q^{32} +(-52.1238 + 90.2810i) q^{33} +55.6495 q^{34} +178.423 q^{36} +(129.949 - 225.077i) q^{37} +(-154.550 - 267.688i) q^{38} +(55.9485 + 96.9057i) q^{39} +(329.021 - 569.881i) q^{40} -338.248 q^{41} +6.80397 q^{43} +(-344.447 + 596.599i) q^{44} +(-47.4743 - 82.2278i) q^{45} +(-330.598 - 572.613i) q^{46} +(-125.347 + 217.108i) q^{47} +511.268 q^{48} +72.2716 q^{50} +(15.8248 - 27.4093i) q^{51} +(369.722 + 640.377i) q^{52} +(268.450 + 464.969i) q^{53} +(71.2114 - 123.342i) q^{54} +366.598 q^{55} -175.794 q^{57} +(-93.3713 + 161.724i) q^{58} +(17.9452 + 31.0820i) q^{59} +(-313.722 - 543.382i) q^{60} +(-28.8970 + 50.0511i) q^{61} -1539.19 q^{62} +746.423 q^{64} +(196.749 - 340.780i) q^{65} +(274.949 + 476.225i) q^{66} +(-240.846 - 417.157i) q^{67} +(104.574 - 181.127i) q^{68} -376.042 q^{69} +363.752 q^{71} +(280.686 - 486.162i) q^{72} +(-290.650 - 503.420i) q^{73} +(-685.468 - 1187.26i) q^{74} +(20.5515 - 35.5962i) q^{75} -1161.69 q^{76} +590.248 q^{78} +(346.846 - 600.754i) q^{79} +(-898.966 - 1557.05i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-892.114 + 1545.19i) q^{82} +1334.39 q^{83} -111.299 q^{85} +(17.9452 - 31.0820i) q^{86} +(53.1030 + 91.9771i) q^{87} +(1083.73 + 1877.08i) q^{88} +(176.519 - 305.740i) q^{89} -500.846 q^{90} -2484.98 q^{92} +(-437.691 + 758.103i) q^{93} +(661.196 + 1145.23i) q^{94} +(309.100 + 535.376i) q^{95} +(599.954 - 1039.15i) q^{96} +1445.88 q^{97} +312.743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 18 * q^6 - 174 * q^8 - 18 * q^9	\( 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9} + 66 q^{10} + 6 q^{11} - 51 q^{12} + 32 q^{13} + 36 q^{15} - 137 q^{16} + 6 q^{17} + 27 q^{18} - 64 q^{19} + 444 q^{20} - 552 q^{22} - 6 q^{23} + 261 q^{24} + 118 q^{25} - 318 q^{26} + 108 q^{27} - 504 q^{29} + 198 q^{30} - 40 q^{31} + 279 q^{32} + 18 q^{33} + 132 q^{34} + 306 q^{36} + 248 q^{37} - 588 q^{38} - 48 q^{39} + 546 q^{40} - 900 q^{41} + 752 q^{43} - 804 q^{44} - 54 q^{45} - 960 q^{46} + 12 q^{47} + 822 q^{48} - 330 q^{50} + 18 q^{51} + 890 q^{52} + 1104 q^{53} + 81 q^{54} + 1104 q^{55} + 384 q^{57} + 306 q^{58} - 804 q^{59} - 666 q^{60} + 428 q^{61} - 4224 q^{62} + 2578 q^{64} + 636 q^{65} + 828 q^{66} - 148 q^{67} + 222 q^{68} + 36 q^{69} + 1908 q^{71} + 783 q^{72} - 1072 q^{73} - 1398 q^{74} + 354 q^{75} - 3016 q^{76} + 1908 q^{78} + 572 q^{79} - 1950 q^{80} - 162 q^{81} - 1530 q^{82} + 3888 q^{83} - 264 q^{85} - 804 q^{86} + 756 q^{87} + 1164 q^{88} - 366 q^{89} - 1188 q^{90} - 5712 q^{92} - 120 q^{93} + 1920 q^{94} + 1176 q^{95} + 837 q^{96} + 1616 q^{97} - 108 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 18 * q^6 - 174 * q^8 - 18 * q^9 + 66 * q^10 + 6 * q^11 - 51 * q^12 + 32 * q^13 + 36 * q^15 - 137 * q^16 + 6 * q^17 + 27 * q^18 - 64 * q^19 + 444 * q^20 - 552 * q^22 - 6 * q^23 + 261 * q^24 + 118 * q^25 - 318 * q^26 + 108 * q^27 - 504 * q^29 + 198 * q^30 - 40 * q^31 + 279 * q^32 + 18 * q^33 + 132 * q^34 + 306 * q^36 + 248 * q^37 - 588 * q^38 - 48 * q^39 + 546 * q^40 - 900 * q^41 + 752 * q^43 - 804 * q^44 - 54 * q^45 - 960 * q^46 + 12 * q^47 + 822 * q^48 - 330 * q^50 + 18 * q^51 + 890 * q^52 + 1104 * q^53 + 81 * q^54 + 1104 * q^55 + 384 * q^57 + 306 * q^58 - 804 * q^59 - 666 * q^60 + 428 * q^61 - 4224 * q^62 + 2578 * q^64 + 636 * q^65 + 828 * q^66 - 148 * q^67 + 222 * q^68 + 36 * q^69 + 1908 * q^71 + 783 * q^72 - 1072 * q^73 - 1398 * q^74 + 354 * q^75 - 3016 * q^76 + 1908 * q^78 + 572 * q^79 - 1950 * q^80 - 162 * q^81 - 1530 * q^82 + 3888 * q^83 - 264 * q^85 - 804 * q^86 + 756 * q^87 + 1164 * q^88 - 366 * q^89 - 1188 * q^90 - 5712 * q^92 - 120 * q^93 + 1920 * q^94 + 1176 * q^95 + 837 * q^96 + 1616 * q^97 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	2.63746	−	4.56821i	0.932482	−	1.61511i	0.153420	−	0.988161i	$-0.450971\pi$
$2$	2.63746	−	4.56821i	0.932482	−	1.61511i	0.779063	−	0.626946i	$-0.215695\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−9.91238	−	17.1687i	−1.23905	−	2.14609i
$5$	−5.27492	+	9.13642i	−0.471803	+	0.817187i	−0.999480	−	0.0322587i	$-0.989730\pi$
$5$	−5.27492	+	9.13642i	−0.471803	+	0.817187i	0.527677	+	0.849445i	$0.323063\pi$
$6$	−15.8248			−1.07674
$7$		0			0
$7$		0			0
$8$	−62.3746			−2.75659
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	27.8248	+	48.1939i	0.879896	+	1.52402i
$11$	−17.3746	−	30.0937i	−0.476240	−	0.824871i	0.523390	−	0.852093i	$-0.324667\pi$
$11$	−17.3746	−	30.0937i	−0.476240	−	0.824871i	−0.999629	+	0.0272223i	$0.991334\pi$
$12$	−29.7371	+	51.5062i	−0.715364	+	1.23905i
$13$	−37.2990			−0.795760			−0.397880	−	0.917437i	$-0.630254\pi$
$13$	−37.2990			−0.795760			−0.397880	+	0.917437i	$0.630254\pi$
$14$		0			0
$15$	31.6495			0.544791
$16$	−85.2114	+	147.590i	−1.33143	+	2.30610i
$17$	5.27492	+	9.13642i	0.0752562	+	0.130348i	0.901198	−	0.433408i	$-0.142689\pi$
$17$	5.27492	+	9.13642i	0.0752562	+	0.130348i	−0.825941	+	0.563756i	$0.809356\pi$
$18$	23.7371	+	41.1139i	0.310827	+	0.538369i
$19$	29.2990	−	50.7474i	0.353771	−	0.612750i	−0.633136	−	0.774041i	$-0.718232\pi$
$19$	29.2990	−	50.7474i	0.353771	−	0.612750i	0.986907	+	0.161291i	$0.0515658\pi$
$20$	209.148			2.33834
$21$		0			0
$22$	−183.299			−1.77634
$23$	62.6736	−	108.554i	0.568189	−	0.984132i	−0.428556	−	0.903515i	$-0.640978\pi$
$23$	62.6736	−	108.554i	0.568189	−	0.984132i	0.996745	−	0.0806171i	$-0.0256891\pi$
$24$	93.5619	+	162.054i	0.795760	+	1.37830i
$25$	6.85050	+	11.8654i	0.0548040	+	0.0949233i
$26$	−98.3746	+	170.390i	−0.742032	+	1.28524i
$27$	27.0000			0.192450
$28$		0			0
$29$	−35.4020			−0.226689			−0.113345	−	0.993556i	$-0.536156\pi$
$29$	−35.4020			−0.226689			−0.113345	+	0.993556i	$0.536156\pi$
$30$	83.4743	−	144.582i	0.508008	−	0.879896i
$31$	−145.897	−	252.701i	−0.845286	−	1.46408i	−0.885372	−	0.464883i	$-0.846096\pi$
$31$	−145.897	−	252.701i	−0.845286	−	1.46408i	0.0400859	−	0.999196i	$-0.487237\pi$
$32$	199.985	+	346.384i	1.10477	+	1.91352i
$33$	−52.1238	+	90.2810i	−0.274957	+	0.476240i
$34$	55.6495			0.280700
$35$		0			0
$36$	178.423			0.826031
$37$	129.949	−	225.077i	0.577389	−	1.00007i	−0.418388	−	0.908268i	$-0.637405\pi$
$37$	129.949	−	225.077i	0.577389	−	1.00007i	0.995778	−	0.0917993i	$-0.0292618\pi$
$38$	−154.550	−	267.688i	−0.659771	−	1.14276i
$39$	55.9485	+	96.9057i	0.229716	+	0.397880i
$40$	329.021	−	569.881i	1.30057	−	2.25265i
$41$	−338.248			−1.28842			−0.644212	−	0.764847i	$-0.722815\pi$
$41$	−338.248			−1.28842			−0.644212	+	0.764847i	$0.722815\pi$
$42$		0			0
$43$	6.80397			0.0241301			0.0120651	−	0.999927i	$-0.496159\pi$
$43$	6.80397			0.0241301			0.0120651	+	0.999927i	$0.496159\pi$
$44$	−344.447	+	596.599i	−1.18017	+	2.04411i
$45$	−47.4743	−	82.2278i	−0.157268	−	0.272396i
$46$	−330.598	−	572.613i	−1.05965	−	1.83537i
$47$	−125.347	+	217.108i	−0.389016	+	0.673796i	−0.992317	−	0.123717i	$-0.960518\pi$
$47$	−125.347	+	217.108i	−0.389016	+	0.673796i	0.603301	+	0.797513i	$0.293852\pi$
$48$	511.268			1.53740
$49$		0			0
$50$	72.2716			0.204415
$51$	15.8248	−	27.4093i	0.0434492	−	0.0752562i
$52$	369.722	+	640.377i	0.985984	+	1.70777i
$53$	268.450	+	464.969i	0.695745	+	1.20507i	0.969929	+	0.243388i	$0.0782588\pi$
$53$	268.450	+	464.969i	0.695745	+	1.20507i	−0.274184	+	0.961677i	$0.588408\pi$
$54$	71.2114	−	123.342i	0.179456	−	0.310827i
$55$	366.598			0.898765
$56$		0			0
$57$	−175.794			−0.408500
$58$	−93.3713	+	161.724i	−0.211384	+	0.366127i
$59$	17.9452	+	31.0820i	0.0395977	+	0.0685853i	0.885145	−	0.465315i	$-0.154059\pi$
$59$	17.9452	+	31.0820i	0.0395977	+	0.0685853i	−0.845547	+	0.533900i	$0.820726\pi$
$60$	−313.722	−	543.382i	−0.675022	−	1.16917i
$61$	−28.8970	+	50.0511i	−0.0606538	+	0.105056i	−0.894758	−	0.446552i	$-0.852652\pi$
$61$	−28.8970	+	50.0511i	−0.0606538	+	0.105056i	0.834104	+	0.551607i	$0.185985\pi$
$62$	−1539.19			−3.15286
$63$		0			0
$64$	746.423			1.45786
$65$	196.749	−	340.780i	0.375442	−	0.650285i
$66$	274.949	+	476.225i	0.512785	+	0.888170i
$67$	−240.846	−	417.157i	−0.439164	−	0.760654i	0.558462	−	0.829530i	$-0.311392\pi$
$67$	−240.846	−	417.157i	−0.439164	−	0.760654i	−0.997625	+	0.0688767i	$0.978059\pi$
$68$	104.574	−	181.127i	0.186492	−	0.323013i
$69$	−376.042			−0.656088
$70$		0			0
$71$	363.752			0.608021			0.304010	−	0.952669i	$-0.401674\pi$
$71$	363.752			0.608021			0.304010	+	0.952669i	$0.401674\pi$
$72$	280.686	−	486.162i	0.459432	−	0.795760i
$73$	−290.650	−	503.420i	−0.465999	−	0.807135i	0.533247	−	0.845960i	$-0.320972\pi$
$73$	−290.650	−	503.420i	−0.465999	−	0.807135i	−0.999246	+	0.0388253i	$0.987638\pi$
$74$	−685.468	−	1187.26i	−1.07681	−	1.86509i
$75$	20.5515	−	35.5962i	0.0316411	−	0.0548040i
$76$	−1161.69			−1.75336
$77$		0			0
$78$	590.248			0.856825
$79$	346.846	−	600.754i	0.493964	−	0.855571i	−0.506012	−	0.862527i	$-0.668881\pi$
$79$	346.846	−	600.754i	0.493964	−	0.855571i	0.999976	+	0.00695559i	$0.00221405\pi$
$80$	−898.966	−	1557.05i	−1.25634	−	2.17605i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−892.114	+	1545.19i	−1.20143	+	2.08094i
$83$	1334.39			1.76468			0.882341	−	0.470611i	$-0.155967\pi$
$83$	1334.39			1.76468			0.882341	+	0.470611i	$0.155967\pi$
$84$		0			0
$85$	−111.299			−0.142024
$86$	17.9452	−	31.0820i	0.0225009	−	0.0389728i
$87$	53.1030	+	91.9771i	0.0654395	+	0.113345i
$88$	1083.73	+	1877.08i	1.31280	+	2.27383i
$89$	176.519	−	305.740i	0.210236	−	0.364139i	−0.741552	−	0.670895i	$-0.765910\pi$
$89$	176.519	−	305.740i	0.210236	−	0.364139i	0.951788	+	0.306756i	$0.0992435\pi$
$90$	−500.846			−0.586597
$91$		0			0
$92$	−2484.98			−2.81605
$93$	−437.691	+	758.103i	−0.488026	+	0.845286i
$94$	661.196	+	1145.23i	0.725502	+	1.25661i
$95$	309.100	+	535.376i	0.333821	+	0.578194i
$96$	599.954	−	1039.15i	0.637839	−	1.10477i
$97$	1445.88			1.51347			0.756735	−	0.653722i	$-0.226793\pi$
$97$	1445.88			1.51347			0.756735	+	0.653722i	$0.226793\pi$
$98$		0			0
$99$	312.743			0.317493
$100$	135.809	−	235.229i	0.135809	−	0.235229i
$101$	−237.426	−	411.234i	−0.233909	−	0.405142i	0.725046	−	0.688700i	$-0.241818\pi$
$101$	−237.426	−	411.234i	−0.233909	−	0.405142i	−0.958955	+	0.283558i	$0.908485\pi$
$102$	−83.4743	−	144.582i	−0.0810312	−	0.140350i
$103$	999.794	−	1731.69i	0.956433	−	1.65659i	0.225380	−	0.974271i	$-0.427638\pi$
$103$	999.794	−	1731.69i	0.956433	−	1.65659i	0.731053	−	0.682320i	$-0.239029\pi$
$104$	2326.51			2.19359
$105$		0			0
$106$	2832.10			2.59508
$107$	−583.368	+	1010.42i	−0.527068	+	0.912909i	0.472434	+	0.881366i	$0.343375\pi$
$107$	−583.368	+	1010.42i	−0.527068	+	0.912909i	−0.999502	+	0.0315431i	$0.989958\pi$
$108$	−267.634	−	463.556i	−0.238455	−	0.413016i
$109$	668.588	+	1158.03i	0.587515	+	1.01761i	0.994557	+	0.104196i	$0.0332270\pi$
$109$	668.588	+	1158.03i	0.587515	+	1.01761i	−0.407042	+	0.913410i	$0.633440\pi$
$110$	966.887	−	1674.70i	0.838082	−	1.45160i
$111$	−779.691			−0.666712
$112$		0			0
$113$	906.578			0.754723			0.377361	−	0.926066i	$-0.376831\pi$
$113$	906.578			0.754723			0.377361	+	0.926066i	$0.376831\pi$
$114$	−463.650	+	803.064i	−0.380919	+	0.659771i
$115$	661.196	+	1145.23i	0.536146	+	0.928633i
$116$	350.918	+	607.807i	0.280878	+	0.486496i
$117$	167.846	−	290.717i	0.132627	−	0.229716i
$118$	189.319			0.147697
$119$		0			0
$120$	−1974.12			−1.50177
$121$	61.7475	−	106.950i	0.0463918	−	0.0803530i
$122$	152.429	+	264.015i	0.113117	+	0.195925i
$123$	507.371	+	878.793i	0.371936	+	0.644212i
$124$	−2892.37	+	5009.74i	−2.09470	+	3.62813i
$125$	−1463.27			−1.04703
$126$		0			0
$127$	−1714.89			−1.19820			−0.599101	−	0.800674i	$-0.704475\pi$
$127$	−1714.89			−1.19820			−0.599101	+	0.800674i	$0.704475\pi$
$128$	368.782	−	638.749i	0.254656	−	0.441078i
$129$	−10.2060	−	17.6772i	−0.00696577	−	0.0120651i
$130$	−1037.84	−	1797.58i	−0.700186	−	1.21276i
$131$	−235.306	+	407.561i	−0.156937	+	0.271823i	−0.933763	−	0.357893i	$-0.883495\pi$
$131$	−235.306	+	407.561i	−0.156937	+	0.271823i	0.776826	+	0.629716i	$0.216829\pi$
$132$	2066.68			1.36274
$133$		0			0
$134$	−2540.88			−1.63805
$135$	−142.423	+	246.683i	−0.0907985	+	0.157268i
$136$	−329.021	−	569.881i	−0.207451	−	0.359315i
$137$	221.955	+	384.438i	0.138415	+	0.239742i	0.926897	−	0.375316i	$-0.122466\pi$
$137$	221.955	+	384.438i	0.138415	+	0.239742i	−0.788482	+	0.615058i	$0.789132\pi$
$138$	−991.794	+	1717.84i	−0.611791	+	1.05965i
$139$	1669.98			1.01904			0.509518	−	0.860460i	$-0.329824\pi$
$139$	1669.98			1.01904			0.509518	+	0.860460i	$0.329824\pi$
$140$		0			0
$141$	752.083			0.449197
$142$	959.382	−	1661.70i	0.566969	−	0.982019i
$143$	648.055	+	1122.46i	0.378972	+	0.656400i
$144$	−766.902	−	1328.31i	−0.443809	−	0.768700i
$145$	186.743	−	323.448i	0.106953	−	0.185247i
$146$	−3066.30			−1.73814
$147$		0			0
$148$	−5152.39			−2.86165
$149$	−371.935	+	644.211i	−0.204497	+	0.354200i	−0.949973	−	0.312334i	$-0.898889\pi$
$149$	−371.935	+	644.211i	−0.204497	+	0.354200i	0.745475	+	0.666534i	$0.232223\pi$
$150$	−108.407	−	187.767i	−0.0590095	−	0.102207i
$151$	−303.382	−	525.473i	−0.163503	−	0.283195i	0.772620	−	0.634869i	$-0.218946\pi$
$151$	−303.382	−	525.473i	−0.163503	−	0.283195i	−0.936123	+	0.351674i	$0.885613\pi$
$152$	−1827.51	+	3165.35i	−0.975203	+	1.68910i
$153$	−94.9485			−0.0501708
$154$		0			0
$155$	3078.38			1.59523
$156$	1109.17	−	1921.13i	0.569258	−	0.985984i
$157$	−1557.39	−	2697.48i	−0.791678	−	1.37123i	−0.924927	−	0.380144i	$-0.875875\pi$
$157$	−1557.39	−	2697.48i	−0.791678	−	1.37123i	0.133250	−	0.991083i	$-0.457459\pi$
$158$	−1829.58	−	3168.93i	−0.921226	−	1.59561i
$159$	805.350	−	1394.91i	0.401688	−	0.695745i
$160$	−4219.61			−2.08493
$161$		0			0
$162$	−427.268			−0.207218
$163$	−1206.54	+	2089.78i	−0.579774	+	1.00420i	0.415730	+	0.909488i	$0.363526\pi$
$163$	−1206.54	+	2089.78i	−0.579774	+	1.00420i	−0.995505	+	0.0947109i	$0.969807\pi$
$164$	3352.84	+	5807.28i	1.59642	+	2.76508i
$165$	−549.897	−	952.450i	−0.259451	−	0.449382i
$166$	3519.40	−	6095.79i	1.64553	−	2.85015i
$167$	−610.475			−0.282874			−0.141437	−	0.989947i	$-0.545172\pi$
$167$	−610.475			−0.282874			−0.141437	+	0.989947i	$0.545172\pi$
$168$		0			0
$169$	−805.784			−0.366766
$170$	−293.547	+	508.437i	−0.132435	+	0.229385i
$171$	263.691	+	456.726i	0.117924	+	0.204250i
$172$	−67.4435	−	116.816i	−0.0298984	−	0.0517855i
$173$	−1896.90	+	3285.54i	−0.833636	+	1.44390i	0.0615006	+	0.998107i	$0.480411\pi$
$173$	−1896.90	+	3285.54i	−0.833636	+	1.44390i	−0.895136	+	0.445792i	$0.852922\pi$
$174$	560.228			0.244085
$175$		0			0
$176$	5922.05			2.53631
$177$	53.8356	−	93.2460i	0.0228618	−	0.0395977i
$178$	−931.124	−	1612.75i	−0.392082	−	0.679107i
$179$	1402.34	+	2428.92i	0.585562	+	1.01422i	0.994805	+	0.101798i	$0.0324596\pi$
$179$	1402.34	+	2428.92i	0.585562	+	1.01422i	−0.409243	+	0.912426i	$0.634207\pi$
$180$	−941.165	+	1630.15i	−0.389724	+	0.675022i
$181$	3106.04			1.27553			0.637763	−	0.770232i	$-0.279860\pi$
$181$	3106.04			1.27553			0.637763	+	0.770232i	$0.279860\pi$
$182$		0			0
$183$	173.382			0.0700370
$184$	−3909.24	+	6771.00i	−1.56627	+	2.71285i
$185$	1370.94	+	2374.53i	0.544828	+	0.943670i
$186$	2308.78	+	3998.93i	0.910152	+	1.57643i
$187$	183.299	−	317.483i	0.0716800	−	0.124153i
$188$	4969.95			1.92804
$189$		0			0
$190$	3260.95			1.24513
$191$	−130.976	+	226.857i	−0.0496182	+	0.0859413i	−0.889768	−	0.456413i	$-0.849134\pi$
$191$	−130.976	+	226.857i	−0.0496182	+	0.0859413i	0.840150	+	0.542355i	$0.182467\pi$
$192$	−1119.63	−	1939.26i	−0.420847	−	0.728928i
$193$	−2025.54	−	3508.33i	−0.755447	−	1.30847i	−0.945152	−	0.326632i	$-0.894086\pi$
$193$	−2025.54	−	3508.33i	−0.755447	−	1.30847i	0.189704	−	0.981841i	$-0.439247\pi$
$194$	3813.44	−	6605.07i	1.41128	−	2.44442i
$195$	−1180.50			−0.433523
$196$		0			0
$197$	−2874.83			−1.03971			−0.519855	−	0.854254i	$-0.674014\pi$
$197$	−2874.83			−1.03971			−0.519855	+	0.854254i	$0.674014\pi$
$198$	824.846	−	1428.67i	0.296057	−	0.512785i
$199$	1533.49	+	2656.07i	0.546261	+	0.946151i	0.998526	+	0.0542680i	$0.0172825\pi$
$199$	1533.49	+	2656.07i	0.546261	+	0.946151i	−0.452266	+	0.891883i	$0.649384\pi$
$200$	−427.297	−	740.100i	−0.151072	−	0.261665i
$201$	−722.537	+	1251.47i	−0.253551	+	0.439164i
$202$	−2504.81			−0.872463
$203$		0			0
$204$	−627.444			−0.215342
$205$	1784.23	−	3090.37i	0.607882	−	1.05288i
$206$	−5273.83	−	9134.54i	−1.78371	−	3.08948i
$207$	564.062	+	976.985i	0.189396	+	0.328044i
$208$	3178.30	−	5504.98i	1.05950	−	1.83510i
$209$	−2036.23			−0.673919
$210$		0			0
$211$	595.422			0.194268			0.0971340	−	0.995271i	$-0.469032\pi$
$211$	595.422			0.194268			0.0971340	+	0.995271i	$0.469032\pi$
$212$	5321.96	−	9217.90i	1.72412	−	2.98626i
$213$	−545.629	−	945.057i	−0.175520	−	0.304010i
$214$	3077.22	+	5329.90i	0.982964	+	1.70254i
$215$	−35.8904	+	62.1640i	−0.0113847	+	0.0197188i
$216$	−1684.11			−0.530507
$217$		0			0
$218$	7053.49			2.19139
$219$	−871.949	+	1510.26i	−0.269045	+	0.465999i
$220$	−3633.86	−	6294.03i	−1.11361	−	1.92883i
$221$	−196.749	−	340.780i	−0.0598859	−	0.103725i
$222$	−2056.40	+	3561.79i	−0.621697	+	1.07681i
$223$	−3779.79			−1.13504			−0.567520	−	0.823360i	$-0.692097\pi$
$223$	−3779.79			−1.13504			−0.567520	+	0.823360i	$0.692097\pi$
$224$		0			0
$225$	−123.309			−0.0365360
$226$	2391.06	−	4141.44i	0.703766	−	1.21896i
$227$	−913.809	−	1582.76i	−0.267188	−	0.462783i	0.700947	−	0.713214i	$-0.252761\pi$
$227$	−913.809	−	1582.76i	−0.267188	−	0.462783i	−0.968135	+	0.250431i	$0.919428\pi$
$228$	1742.54	+	3018.16i	0.506150	+	0.876678i
$229$	425.125	−	736.338i	0.122677	−	0.212483i	−0.798146	−	0.602465i	$-0.794185\pi$
$229$	425.125	−	736.338i	0.122677	−	0.212483i	0.920823	+	0.389982i	$0.127519\pi$
$230$	6975.51			1.99979
$231$		0			0
$232$	2208.18			0.624890
$233$	3295.55	−	5708.06i	0.926604	−	1.60492i	0.137642	−	0.990482i	$-0.456048\pi$
$233$	3295.55	−	5708.06i	0.926604	−	1.60492i	0.788962	−	0.614443i	$-0.210619\pi$
$234$	−885.371	−	1533.51i	−0.247344	−	0.428413i
$235$	−1322.39	−	2290.45i	−0.367078	−	0.635798i
$236$	355.759	−	616.193i	0.0981269	−	0.169961i
$237$	−2081.07			−0.570381
$238$		0			0
$239$	−182.556			−0.0494083			−0.0247042	−	0.999695i	$-0.507864\pi$
$239$	−182.556			−0.0494083			−0.0247042	+	0.999695i	$0.507864\pi$
$240$	−2696.90	+	4671.16i	−0.725350	+	1.25634i
$241$	−761.949	−	1319.73i	−0.203657	−	0.352745i	0.746047	−	0.665894i	$-0.231950\pi$
$241$	−761.949	−	1319.73i	−0.203657	−	0.352745i	−0.949704	+	0.313149i	$0.898616\pi$
$242$	−325.713	−	564.152i	−0.0865191	−	0.149856i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	1145.75			0.300612
$245$		0			0
$246$	5352.68			1.38730
$247$	−1092.82	+	1892.83i	−0.281517	+	0.487602i
$248$	9100.27	+	15762.1i	2.33011	+	4.03587i
$249$	−2001.59	−	3466.85i	−0.509420	−	0.882341i
$250$	−3859.32	+	6684.54i	−0.976339	+	1.69107i
$251$	2357.73			0.592903			0.296451	−	0.955048i	$-0.404197\pi$
$251$	2357.73			0.592903			0.296451	+	0.955048i	$0.404197\pi$
$252$		0			0
$253$	−4355.71			−1.08238
$254$	−4522.94	+	7833.97i	−1.11730	+	1.93522i
$255$	166.949	+	289.163i	0.0409989	+	0.0710122i
$256$	1040.40	+	1802.02i	0.254003	+	0.439946i
$257$	−1391.27	+	2409.76i	−0.337686	+	0.584890i	−0.983997	−	0.178185i	$-0.942978\pi$
$257$	−1391.27	+	2409.76i	−0.337686	+	0.584890i	0.646311	+	0.763074i	$0.276311\pi$
$258$	−107.671			−0.0259818
$259$		0			0
$260$	−7801.01			−1.86076
$261$	159.309	−	275.931i	0.0377815	−	0.0654395i
$262$	1241.22	+	2149.85i	0.292682	+	0.506940i
$263$	−1021.89	−	1769.97i	−0.239591	−	0.414984i	0.721006	−	0.692929i	$-0.243680\pi$
$263$	−1021.89	−	1769.97i	−0.239591	−	0.414984i	−0.960597	+	0.277945i	$0.910347\pi$
$264$	3251.20	−	5631.24i	0.757945	−	1.31280i
$265$	−5664.21			−1.31302
$266$		0			0
$267$	−1059.11			−0.242759
$268$	−4774.70	+	8270.03i	−1.08829	+	1.88497i
$269$	−1726.42	−	2990.24i	−0.391307	−	0.677763i	0.601315	−	0.799012i	$-0.294644\pi$
$269$	−1726.42	−	2990.24i	−0.391307	−	0.677763i	−0.992622	+	0.121248i	$0.961310\pi$
$270$	751.268	+	1301.23i	0.169336	+	0.293299i
$271$	−1322.15	+	2290.02i	−0.296364	+	0.513318i	−0.975301	−	0.220879i	$-0.929108\pi$
$271$	−1322.15	+	2290.02i	−0.296364	+	0.513318i	0.678937	+	0.734196i	$0.262441\pi$
$272$	−1797.93			−0.400793
$273$		0			0
$274$	2341.59			0.516280
$275$	238.049	−	412.313i	0.0521996	−	0.0904124i
$276$	3727.47	+	6456.16i	0.812924	+	1.40803i
$277$	−1339.74	−	2320.50i	−0.290604	−	0.503341i	0.683349	−	0.730092i	$-0.260523\pi$
$277$	−1339.74	−	2320.50i	−0.290604	−	0.503341i	−0.973953	+	0.226751i	$0.927190\pi$
$278$	4404.50	−	7628.82i	0.950232	−	1.64585i
$279$	2626.15			0.563524
$280$		0			0
$281$	−1019.69			−0.216476			−0.108238	−	0.994125i	$-0.534521\pi$
$281$	−1019.69			−0.216476			−0.108238	+	0.994125i	$0.534521\pi$
$282$	1983.59	−	3435.68i	0.418869	−	0.725502i
$283$	−216.103	−	374.301i	−0.0453922	−	0.0786216i	0.842437	−	0.538795i	$-0.181120\pi$
$283$	−216.103	−	374.301i	−0.0453922	−	0.0786216i	−0.887829	+	0.460174i	$0.847787\pi$
$284$	−3605.65	−	6245.17i	−0.753366	−	1.30487i
$285$	927.299	−	1606.13i	0.192731	−	0.333821i
$286$	6836.87			1.41354
$287$		0			0
$288$	−3599.72			−0.736513
$289$	2400.85	−	4158.40i	0.488673	−	0.846406i
$290$	−985.051	−	1706.16i	−0.199463	−	0.345480i
$291$	−2168.82	−	3756.50i	−0.436901	−	0.756735i
$292$	−5762.05	+	9980.17i	−1.15479	+	2.00016i
$293$	−2245.92			−0.447809			−0.223904	−	0.974611i	$-0.571880\pi$
$293$	−2245.92			−0.447809			−0.223904	+	0.974611i	$0.571880\pi$
$294$		0			0
$295$	−378.638			−0.0747293
$296$	−8105.48	+	14039.1i	−1.59163	+	2.75678i
$297$	−469.114	−	812.529i	−0.0916523	−	0.158747i
$298$	1961.93	+	3398.16i	0.381381	+	0.660571i
$299$	−2337.66	+	4048.95i	−0.452142	+	0.783133i
$300$	−814.856			−0.156819
$301$		0			0
$302$	−3200.63			−0.609853
$303$	−712.278	+	1233.70i	−0.135047	+	0.233909i
$304$	4993.22	+	8648.51i	0.942042	+	1.63166i
$305$	−304.859	−	528.031i	−0.0572333	−	0.0991310i
$306$	−250.423	+	433.745i	−0.0467834	+	0.0810312i
$307$	−3197.08			−0.594354			−0.297177	−	0.954822i	$-0.596045\pi$
$307$	−3197.08			−0.594354			−0.297177	+	0.954822i	$0.596045\pi$
$308$		0			0
$309$	−5998.76			−1.10439
$310$	8119.10	−	14062.7i	1.48753	−	2.57647i
$311$	1677.80	+	2906.04i	0.305915	+	0.529860i	0.977465	−	0.211100i	$-0.0677045\pi$
$311$	1677.80	+	2906.04i	0.305915	+	0.529860i	−0.671550	+	0.740959i	$0.734371\pi$
$312$	−3489.77	−	6044.45i	−0.633234	−	1.09679i
$313$	1128.20	−	1954.09i	0.203736	−	0.352881i	−0.745993	−	0.665954i	$-0.768025\pi$
$313$	1128.20	−	1954.09i	0.203736	−	0.352881i	0.949729	+	0.313072i	$0.101358\pi$
$314$	−16430.2			−2.95290
$315$		0			0
$316$	−13752.3			−2.44818
$317$	3069.59	−	5316.69i	0.543866	−	0.942004i	−0.454811	−	0.890588i	$-0.650293\pi$
$317$	3069.59	−	5316.69i	0.543866	−	0.942004i	0.998677	−	0.0514158i	$-0.0163734\pi$
$318$	−4248.16	−	7358.02i	−0.749135	−	1.29754i
$319$	615.095	+	1065.38i	0.107958	+	0.186989i
$320$	−3937.32	+	6819.64i	−0.687821	+	1.19134i
$321$	3500.21			0.608606
$322$		0			0
$323$	618.199			0.106494
$324$	−802.902	+	1390.67i	−0.137672	+	0.238455i
$325$	−255.517	−	442.568i	−0.0436108	−	0.0755362i
$326$	6364.38	+	11023.4i	1.08126	+	1.87280i
$327$	2005.76	−	3474.09i	0.339202	−	0.587515i
$328$	21098.0			3.55166
$329$		0			0
$330$	−5801.32			−0.967734
$331$	−3514.91	+	6088.00i	−0.583676	+	1.01096i	0.411363	+	0.911472i	$0.365053\pi$
$331$	−3514.91	+	6088.00i	−0.583676	+	1.01096i	−0.995039	+	0.0994849i	$0.968280\pi$
$332$	−13227.0	−	22909.8i	−2.18652	−	3.78717i
$333$	1169.54	+	2025.70i	0.192463	+	0.333356i
$334$	−1610.10	+	2788.78i	−0.263775	+	0.456872i
$335$	5081.76			0.828795
$336$		0			0
$337$	10328.4			1.66951			0.834757	−	0.550619i	$-0.185608\pi$
$337$	10328.4			1.66951			0.834757	+	0.550619i	$0.185608\pi$
$338$	−2125.22	+	3680.99i	−0.342003	+	0.592366i
$339$	−1359.87	−	2355.36i	−0.217870	−	0.377361i
$340$	1103.24	+	1910.86i	0.175975	+	0.304797i
$341$	−5069.80	+	8781.15i	−0.805118	+	1.39450i
$342$	2781.90			0.439847
$343$		0			0
$344$	−424.395			−0.0665170
$345$	1983.59	−	3435.68i	0.309544	−	0.536146i
$346$	10006.0	+	17330.9i	1.55470	+	2.69282i
$347$	−983.768	−	1703.94i	−0.152194	−	0.263608i	0.779840	−	0.625980i	$-0.215301\pi$
$347$	−983.768	−	1703.94i	−0.152194	−	0.263608i	−0.932034	+	0.362371i	$0.881967\pi$
$348$	1052.75	−	1823.42i	0.162165	−	0.280878i
$349$	−4365.46			−0.669564			−0.334782	−	0.942296i	$-0.608663\pi$
$349$	−4365.46			−0.669564			−0.334782	+	0.942296i	$0.608663\pi$
$350$		0			0
$351$	−1007.07			−0.153144
$352$	6949.30	−	12036.5i	1.05227	−	1.82258i
$353$	3035.79	+	5258.15i	0.457731	+	0.792813i	0.998841	−	0.0481389i	$-0.0153290\pi$
$353$	3035.79	+	5258.15i	0.457731	+	0.792813i	−0.541110	+	0.840952i	$0.681996\pi$
$354$	−283.978	−	491.865i	−0.0426364	−	0.0738484i
$355$	−1918.76	+	3323.40i	−0.286866	+	0.496866i
$356$	−6998.90			−1.04197
$357$		0			0
$358$	14794.4			2.18411
$359$	−4819.02	+	8346.79i	−0.708463	+	1.22709i	0.256965	+	0.966421i	$0.417278\pi$
$359$	−4819.02	+	8346.79i	−0.708463	+	1.22709i	−0.965427	+	0.260673i	$0.916056\pi$
$360$	2961.19	+	5128.93i	0.433523	+	0.750884i
$361$	1712.64	+	2966.37i	0.249692	+	0.432479i
$362$	8192.06	−	14189.1i	1.18941	−	2.06011i
$363$	−370.485			−0.0535687
$364$		0			0
$365$	6132.61			0.879439
$366$	457.288	−	792.046i	0.0653083	−	0.113117i
$367$	−261.362	−	452.693i	−0.0371744	−	0.0643879i	0.846840	−	0.531848i	$-0.178502\pi$
$367$	−261.362	−	452.693i	−0.0371744	−	0.0643879i	−0.884014	+	0.467460i	$0.845169\pi$
$368$	10681.0	+	18500.0i	1.51301	+	2.62060i
$369$	1522.11	−	2636.38i	0.214737	−	0.371936i
$370$	14463.1			2.03217
$371$		0			0
$372$	17354.2			2.41875
$373$	−1614.92	+	2797.12i	−0.224175	+	0.388283i	−0.956072	−	0.293133i	$-0.905302\pi$
$373$	−1614.92	+	2797.12i	−0.224175	+	0.388283i	0.731896	+	0.681416i	$0.238636\pi$
$374$	−966.887	−	1674.70i	−0.133681	−	0.231542i
$375$	2194.91	+	3801.69i	0.302252	+	0.523516i
$376$	7818.48	−	13542.0i	1.07236	−	1.85738i
$377$	1320.46			0.180390
$378$		0			0
$379$	6639.71			0.899892			0.449946	−	0.893056i	$-0.351443\pi$
$379$	6639.71			0.899892			0.449946	+	0.893056i	$0.351443\pi$
$380$	6127.82	−	10613.7i	0.827239	−	1.43282i
$381$	2572.33	+	4455.41i	0.345891	+	0.599101i
$382$	690.887	+	1196.65i	0.0925363	+	0.160278i
$383$	7112.22	−	12318.7i	0.948871	−	1.64349i	0.201063	−	0.979578i	$-0.435561\pi$
$383$	7112.22	−	12318.7i	0.948871	−	1.64349i	0.747809	−	0.663914i	$-0.231106\pi$
$384$	−2212.69			−0.294052
$385$		0			0
$386$	−21369.1			−2.81777
$387$	−30.6179	+	53.0317i	−0.00402169	+	0.00696577i
$388$	−14332.1	−	24823.9i	−1.87526	−	3.24805i
$389$	−1460.91	−	2530.37i	−0.190414	−	0.329807i	0.754973	−	0.655755i	$-0.227650\pi$
$389$	−1460.91	−	2530.37i	−0.190414	−	0.329807i	−0.945388	+	0.325948i	$0.894316\pi$
$390$	−3113.51	+	5392.75i	−0.404253	+	0.700186i
$391$	1322.39			0.171039
$392$		0			0
$393$	1411.83			0.181215
$394$	−7582.24	+	13132.8i	−0.969512	+	1.67924i
$395$	3659.16	+	6337.86i	0.466108	+	0.807322i
$396$	−3100.02	−	5369.40i	−0.393389	−	0.681369i
$397$	−405.970	+	703.161i	−0.0513226	+	0.0888933i	−0.890545	−	0.454894i	$-0.849677\pi$
$397$	−405.970	+	703.161i	−0.0513226	+	0.0888933i	0.839223	+	0.543788i	$0.183010\pi$
$398$	16178.0			2.03751
$399$		0			0
$400$	−2334.96			−0.291870
$401$	−1169.32	+	2025.32i	−0.145618	+	0.252218i	−0.929603	−	0.368561i	$-0.879850\pi$
$401$	−1169.32	+	2025.32i	−0.145618	+	0.252218i	0.783985	+	0.620780i	$0.213184\pi$
$402$	3811.32	+	6601.40i	0.472864	+	0.819025i
$403$	5441.81	+	9425.50i	0.672645	+	1.16506i
$404$	−4706.91	+	8152.61i	−0.579648	+	1.00398i
$405$	854.537			0.104845
$406$		0			0
$407$	−9031.21			−1.09990
$408$	−987.062	+	1709.64i	−0.119772	+	0.207451i
$409$	1363.79	+	2362.15i	0.164877	+	0.285576i	0.936612	−	0.350369i	$-0.113944\pi$
$409$	1363.79	+	2362.15i	0.164877	+	0.285576i	−0.771734	+	0.635945i	$0.780610\pi$
$410$	−9411.65	−	16301.5i	−1.13368	−	1.96359i
$411$	665.865	−	1153.31i	0.0799142	−	0.138415i
$412$	−39641.3			−4.74026
$413$		0			0
$414$	5950.76			0.706435
$415$	−7038.81	+	12191.6i	−0.832582	+	1.44207i
$416$	−7459.23	−	12919.8i	−0.879132	−	1.52270i
$417$	−2504.97	−	4338.74i	−0.294170	−	0.509518i
$418$	−5370.48	+	9301.94i	−0.628418	+	1.08845i
$419$	13306.3			1.55144			0.775721	−	0.631076i	$-0.217386\pi$
$419$	13306.3			1.55144			0.775721	+	0.631076i	$0.217386\pi$
$420$		0			0
$421$	−11007.5			−1.27428			−0.637138	−	0.770750i	$-0.719882\pi$
$421$	−11007.5			−1.27428			−0.637138	+	0.770750i	$0.719882\pi$
$422$	1570.40	−	2720.01i	0.181151	−	0.313763i
$423$	−1128.12	−	1953.97i	−0.129672	−	0.224599i
$424$	−16744.5	−	29002.3i	−1.91789	−	3.32187i
$425$	−72.2716	+	125.178i	−0.00824868	+	0.0142871i
$426$	−5756.29			−0.654679
$427$		0			0
$428$	23130.2			2.61225
$429$	1944.16	−	3367.39i	0.218800	−	0.378972i
$430$	189.319	+	327.910i	0.0212320	+	0.0367749i
$431$	3262.81	+	5651.36i	0.364650	+	0.631592i	0.988720	−	0.149776i	$-0.0478553\pi$
$431$	3262.81	+	5651.36i	0.364650	+	0.631592i	−0.624070	+	0.781368i	$0.714522\pi$
$432$	−2300.71	+	3984.94i	−0.256233	+	0.443809i
$433$	−11716.3			−1.30034			−0.650171	−	0.759788i	$-0.725303\pi$
$433$	−11716.3			−1.30034			−0.650171	+	0.759788i	$0.725303\pi$
$434$		0			0
$435$	−1120.46			−0.123498
$436$	13254.6	−	22957.6i	1.45592	−	2.52172i
$437$	−3672.55	−	6361.04i	−0.402018	−	0.696315i
$438$	4599.46	+	7966.49i	0.501759	+	0.869072i
$439$	7305.69	−	12653.8i	0.794264	−	1.37571i	−0.129042	−	0.991639i	$-0.541190\pi$
$439$	7305.69	−	12653.8i	0.794264	−	1.37571i	0.923306	−	0.384066i	$-0.125476\pi$
$440$	−22866.4			−2.47753
$441$		0			0
$442$	−2075.67			−0.223370
$443$	7619.89	−	13198.0i	0.817228	−	1.41548i	−0.0904888	−	0.995897i	$-0.528843\pi$
$443$	7619.89	−	13198.0i	0.817228	−	1.41548i	0.907717	−	0.419583i	$-0.137824\pi$
$444$	7728.59	+	13386.3i	0.826087	+	1.43082i
$445$	1862.25	+	3225.51i	0.198380	+	0.343604i
$446$	−9969.05	+	17266.9i	−1.05840	+	1.83321i
$447$	2231.61			0.236133
$448$		0			0
$449$	10678.8			1.12241			0.561206	−	0.827676i	$-0.310338\pi$
$449$	10678.8			1.12241			0.561206	+	0.827676i	$0.310338\pi$
$450$	−325.222	+	563.301i	−0.0340692	+	0.0590095i
$451$	5876.91	+	10179.1i	0.613598	+	1.06278i
$452$	−8986.34	−	15564.8i	−0.935137	−	1.61971i
$453$	−910.146	+	1576.42i	−0.0943982	+	0.163503i
$454$	−9640.53			−0.996592
$455$		0			0
$456$	10965.1			1.12607
$457$	−2114.12	+	3661.76i	−0.216399	+	0.374814i	−0.953704	−	0.300746i	$-0.902764\pi$
$457$	−2114.12	+	3661.76i	−0.216399	+	0.374814i	0.737306	+	0.675559i	$0.236098\pi$
$458$	−2242.50	−	3884.12i	−0.228788	−	0.396273i
$459$	142.423	+	246.683i	0.0144831	+	0.0250854i
$460$	13108.0	−	22703.8i	1.32862	−	2.30124i
$461$	910.121			0.0919492			0.0459746	−	0.998943i	$-0.485361\pi$
$461$	910.121			0.0919492			0.0459746	+	0.998943i	$0.485361\pi$
$462$		0			0
$463$	4456.16			0.447290			0.223645	−	0.974671i	$-0.428204\pi$
$463$	4456.16			0.447290			0.223645	+	0.974671i	$0.428204\pi$
$464$	3016.65	−	5224.99i	0.301820	−	0.522768i
$465$	−4617.57	−	7997.86i	−0.460505	−	0.797617i
$466$	−17383.8	−	30109.5i	−1.72808	−	2.99313i
$467$	2214.71	−	3835.99i	0.219453	−	0.380104i	−0.735188	−	0.677864i	$-0.762906\pi$
$467$	2214.71	−	3835.99i	0.219453	−	0.380104i	0.954641	+	0.297759i	$0.0962393\pi$
$468$	−6654.99			−0.657323
$469$		0			0
$470$	−13951.0			−1.36918
$471$	−4672.18	+	8092.45i	−0.457075	+	0.791678i
$472$	−1119.32	−	1938.73i	−0.109155	−	0.189062i
$473$	−118.216	−	204.757i	−0.0114917	−	0.0199043i
$474$	−5488.74	+	9506.78i	−0.531870	+	0.921226i
$475$	802.851			0.0775523
$476$		0			0
$477$	−4832.10			−0.463830
$478$	−481.485	+	833.957i	−0.0460724	+	0.0797998i
$479$	−1376.43	−	2384.04i	−0.131296	−	0.227411i	0.792881	−	0.609377i	$-0.208580\pi$
$479$	−1376.43	−	2384.04i	−0.131296	−	0.227411i	−0.924176	+	0.381966i	$0.875247\pi$
$480$	6329.41	+	10962.9i	0.601869	+	1.04247i
$481$	−4846.95	+	8395.16i	−0.459463	+	0.795814i
$482$	−8038.43			−0.759628
$483$		0			0
$484$	−2448.26			−0.229927
$485$	−7626.88	+	13210.1i	−0.714060	+	1.23679i
$486$	640.902	+	1110.08i	0.0598188	+	0.103609i
$487$	335.299	+	580.755i	0.0311989	+	0.0540380i	0.881203	−	0.472738i	$-0.156734\pi$
$487$	335.299	+	580.755i	0.0311989	+	0.0540380i	−0.850004	+	0.526776i	$0.823401\pi$
$488$	1802.44	−	3121.92i	0.167198	−	0.289595i
$489$	7239.22			0.669466
$490$		0			0
$491$	−8244.70			−0.757797			−0.378898	−	0.925438i	$-0.623697\pi$
$491$	−8244.70			−0.757797			−0.378898	+	0.925438i	$0.623697\pi$
$492$	10058.5	−	17421.8i	0.921692	−	1.59642i
$493$	−186.743	−	323.448i	−0.0170598	−	0.0295484i
$494$	5764.56	+	9984.50i	0.525019	+	0.909360i
$495$	−1649.69	+	2857.35i	−0.149794	+	0.259451i
$496$	49728.3			4.50175
$497$		0			0
$498$	−21116.4			−1.90010
$499$	−4082.46	+	7071.02i	−0.366244	+	0.634353i	−0.988975	−	0.148083i	$-0.952690\pi$
$499$	−4082.46	+	7071.02i	−0.366244	+	0.634353i	0.622731	+	0.782436i	$0.286023\pi$
$500$	14504.5	+	25122.5i	1.29732	+	2.24703i
$501$	915.713	+	1586.06i	0.0816587	+	0.141437i
$502$	6218.42	−	10770.6i	0.552872	−	0.957602i
$503$	8175.59			0.724715			0.362357	−	0.932039i	$-0.381972\pi$
$503$	8175.59			0.724715			0.362357	+	0.932039i	$0.381972\pi$
$504$		0			0
$505$	5009.61			0.441435
$506$	−11488.0	+	19897.8i	−1.00930	+	1.74815i
$507$	1208.68	+	2093.49i	0.105876	+	0.183383i
$508$	16998.6	+	29442.4i	1.48463	+	2.57145i
$509$	439.224	−	760.758i	0.0382480	−	0.0662475i	−0.846268	−	0.532758i	$-0.821156\pi$
$509$	439.224	−	760.758i	0.0382480	−	0.0662475i	0.884516	+	0.466510i	$0.154489\pi$
$510$	1761.28			0.152923
$511$		0			0
$512$	16876.5			1.45673
$513$	791.073	−	1370.18i	0.0680833	−	0.117924i
$514$	7338.86	+	12711.3i	0.629773	+	1.09080i
$515$	10547.7	+	18269.1i	0.902496	+	1.56317i
$516$	−202.331	+	350.447i	−0.0172618	+	0.0298984i
$517$	8711.42			0.741060
$518$		0			0
$519$	11381.4			0.962600
$520$	−12272.1	+	21256.0i	−1.03494	+	1.79257i
$521$	−5856.30	−	10143.4i	−0.492455	−	0.852957i	0.507507	−	0.861647i	$-0.330567\pi$
$521$	−5856.30	−	10143.4i	−0.492455	−	0.852957i	−0.999962	+	0.00869048i	$0.997234\pi$
$522$	−840.341	−	1455.51i	−0.0704612	−	0.122042i
$523$	3670.91	−	6358.20i	0.306917	−	0.531596i	−0.670769	−	0.741666i	$-0.734036\pi$
$523$	3670.91	−	6358.20i	0.306917	−	0.531596i	0.977686	+	0.210070i	$0.0673692\pi$
$524$	9329.75			0.777809
$525$		0			0
$526$	−10780.8			−0.893659
$527$	1539.19	−	2665.95i	0.127226	−	0.220362i
$528$	−8883.07	−	15385.9i	−0.732171	−	1.26816i
$529$	−1772.46	−	3069.99i	−0.145678	−	0.252321i
$530$	−14939.1	+	25875.3i	−1.22437	+	2.12066i
$531$	−323.014			−0.0263985
$532$		0			0
$533$	12616.3			1.02528
$534$	−2793.37	+	4838.26i	−0.226369	+	0.392082i
$535$	−6154.44	−	10659.8i	−0.497345	−	0.861426i
$536$	15022.6	+	26020.0i	1.21060	+	2.09681i
$537$	4207.01	−	7286.76i	0.338075	−	0.585562i
$538$	−18213.4			−1.45955
$539$		0			0
$540$	5646.99			0.450015
$541$	7934.36	−	13742.7i	0.630545	−	1.09214i	−0.356895	−	0.934144i	$-0.616165\pi$
$541$	7934.36	−	13742.7i	0.630545	−	1.09214i	0.987440	−	0.157992i	$-0.0505020\pi$
$542$	6974.21	+	12079.7i	0.552709	+	0.957319i
$543$	−4659.07	−	8069.74i	−0.368213	−	0.637763i
$544$	−2109.80	+	3654.29i	−0.166282	+	0.288008i
$545$	−14107.0			−1.10877
$546$		0			0
$547$	2315.26			0.180975			0.0904875	−	0.995898i	$-0.471157\pi$
$547$	2315.26			0.180975			0.0904875	+	0.995898i	$0.471157\pi$
$548$	4400.21	−	7621.38i	0.343006	−	0.594104i
$549$	−260.073	−	450.460i	−0.0202179	−	0.0350185i
$550$	−1255.69	−	2174.92i	−0.0973505	−	0.168616i
$551$	−1037.24	+	1796.56i	−0.0801961	+	0.138904i
$552$	23455.4			1.80857
$553$		0			0
$554$	−14134.1			−1.08393
$555$	4112.81	−	7123.59i	0.314557	−	0.544828i
$556$	−16553.5	−	28671.5i	−1.26263	−	2.18694i
$557$	2409.52	+	4173.42i	0.183294	+	0.317475i	0.943000	−	0.332792i	$-0.107991\pi$
$557$	2409.52	+	4173.42i	0.183294	+	0.317475i	−0.759706	+	0.650266i	$0.774657\pi$
$558$	6926.35	−	11996.8i	0.525476	−	0.910152i
$559$	−253.781			−0.0192018
$560$		0			0
$561$	−1099.79			−0.0827689
$562$	−2689.39	+	4658.17i	−0.201860	+	0.349631i
$563$	−1270.43	−	2200.45i	−0.0951017	−	0.164721i	0.814549	−	0.580094i	$-0.196984\pi$
$563$	−1270.43	−	2200.45i	−0.0951017	−	0.164721i	−0.909651	+	0.415373i	$0.863651\pi$
$564$	−7454.93	−	12912.3i	−0.556577	−	0.964019i
$565$	−4782.12	+	8282.88i	−0.356081	+	0.616750i
$566$	−2279.85			−0.169310
$567$		0			0
$568$	−22688.9			−1.67607
$569$	12110.0	−	20975.1i	0.892227	−	1.54538i	0.0550275	−	0.998485i	$-0.482475\pi$
$569$	12110.0	−	20975.1i	0.892227	−	1.54538i	0.837200	−	0.546898i	$-0.184191\pi$
$570$	−4891.43	−	8472.20i	−0.359437	−	0.622564i
$571$	5886.04	+	10194.9i	0.431389	+	0.747188i	0.996993	−	0.0774891i	$-0.0246903\pi$
$571$	5886.04	+	10194.9i	0.431389	+	0.747188i	−0.565604	+	0.824677i	$0.691357\pi$
$572$	12847.5	−	22252.6i	0.939129	−	1.62662i
$573$	785.855			0.0572942
$574$		0			0
$575$	1717.38			0.124556
$576$	−3358.90	+	5817.79i	−0.242976	+	0.420847i
$577$	−5292.13	−	9166.24i	−0.381827	−	0.661344i	0.609496	−	0.792789i	$-0.291372\pi$
$577$	−5292.13	−	9166.24i	−0.381827	−	0.661344i	−0.991324	+	0.131445i	$0.958038\pi$
$578$	−12664.3	−	21935.2i	−0.911358	−	1.57852i
$579$	−6076.61	+	10525.0i	−0.436158	+	0.755447i
$580$	−7404.25			−0.530077
$581$		0			0
$582$	−22880.6			−1.62961
$583$	9328.42	−	16157.3i	0.662682	−	1.14780i
$584$	18129.1	+	31400.6i	1.28457	+	2.22494i
$585$	1770.74	+	3067.02i	0.125147	+	0.216762i
$586$	−5923.52	+	10259.8i	−0.417574	+	0.723259i
$587$	−8712.63			−0.612621			−0.306311	−	0.951932i	$-0.599095\pi$
$587$	−8712.63			−0.612621			−0.306311	+	0.951932i	$0.599095\pi$
$588$		0			0
$589$	−17098.6			−1.19615
$590$	−998.641	+	1729.70i	−0.0696838	+	0.120696i
$591$	4312.24	+	7469.02i	0.300139	+	0.519855i
$592$	22146.2	+	38358.3i	1.53750	+	2.66304i
$593$	7681.43	−	13304.6i	0.531937	−	0.921341i	−0.467368	−	0.884063i	$-0.654798\pi$
$593$	7681.43	−	13304.6i	0.531937	−	0.921341i	0.999305	−	0.0372786i	$-0.0118689\pi$
$594$	−4949.07			−0.341857
$595$		0			0
$596$	14747.0			1.01353
$597$	4600.46	−	7968.22i	0.315384	−	0.546261i
$598$	12331.0	+	21357.9i	0.843229	+	1.46052i
$599$	−13001.9	−	22519.9i	−0.886883	−	1.53613i	−0.843540	−	0.537066i	$-0.819533\pi$
$599$	−13001.9	−	22519.9i	−0.886883	−	1.53613i	−0.0433430	−	0.999060i	$-0.513801\pi$
$600$	−1281.89	+	2220.30i	−0.0872216	+	0.151072i
$601$	20567.7			1.39596			0.697982	−	0.716115i	$-0.254082\pi$
$601$	20567.7			1.39596			0.697982	+	0.716115i	$0.254082\pi$
$602$		0			0
$603$	4335.22			0.292776
$604$	−6014.48	+	10417.4i	−0.405175	+	0.701783i
$605$	651.426	+	1128.30i	0.0437756	+	0.0758216i
$606$	3757.21	+	6507.68i	0.251858	+	0.436231i
$607$	−9821.04	+	17010.5i	−0.656711	+	1.13746i	0.324751	+	0.945800i	$0.394720\pi$
$607$	−9821.04	+	17010.5i	−0.656711	+	1.13746i	−0.981462	+	0.191657i	$0.938614\pi$
$608$	23437.4			1.56334
$609$		0			0
$610$	−3216.21			−0.213476
$611$	4675.33	−	8097.90i	0.309564	−	0.536180i
$612$	941.165	+	1630.15i	0.0621640	+	0.107671i
$613$	−4227.29	−	7321.89i	−0.278530	−	0.482428i	0.692490	−	0.721428i	$-0.256514\pi$
$613$	−4227.29	−	7321.89i	−0.278530	−	0.482428i	−0.971020	+	0.239000i	$0.923180\pi$
$614$	−8432.16	+	14604.9i	−0.554225	+	0.959946i
$615$	−10705.4			−0.701922
$616$		0			0
$617$	−24168.4			−1.57696			−0.788479	−	0.615061i	$-0.789131\pi$
$617$	−24168.4			−1.57696			−0.788479	+	0.615061i	$0.789131\pi$
$618$	−15821.5	+	27403.6i	−1.02983	+	1.78371i
$619$	1018.78	+	1764.58i	0.0661523	+	0.114579i	0.897205	−	0.441615i	$-0.145594\pi$
$619$	1018.78	+	1764.58i	0.0661523	+	0.114579i	−0.831052	+	0.556194i	$0.812261\pi$
$620$	−30514.0	−	52851.9i	−1.97657	−	3.42352i
$621$	1692.19	−	2930.95i	0.109348	−	0.189396i
$622$	17700.5			1.14104
$623$		0			0
$624$	−19069.8			−1.22340
$625$	6862.33	−	11885.9i	0.439189	−	0.760698i
$626$	−5951.14	−	10307.7i	−0.379961	−	0.658111i
$627$	3054.35	+	5290.29i	0.194544	+	0.336960i
$628$	−30874.9	+	53476.9i	−1.96185	+	3.39803i
$629$	2741.87			0.173808
$630$		0			0
$631$	12339.5			0.778489			0.389244	−	0.921135i	$-0.372736\pi$
$631$	12339.5			0.778489			0.389244	+	0.921135i	$0.372736\pi$
$632$	−21634.3	+	37471.8i	−1.36166	+	2.35846i
$633$	−893.133	−	1546.95i	−0.0560803	−	0.0971340i
$634$	−16191.9	−	28045.1i	−1.01429	−	1.75680i
$635$	9045.89	−	15667.9i	0.565315	−	0.979154i
$636$	−31931.7			−1.99084
$637$		0			0
$638$	6489.15			0.402677
$639$	−1636.89	+	2835.17i	−0.101337	+	0.175520i
$640$	3890.59	+	6738.70i	0.240295	+	0.416204i
$641$	5111.32	+	8853.06i	0.314953	+	0.545515i	0.979428	−	0.201796i	$-0.0646779\pi$
$641$	5111.32	+	8853.06i	0.314953	+	0.545515i	−0.664474	+	0.747311i	$0.731345\pi$
$642$	9231.65	−	15989.7i	0.567514	−	0.982964i
$643$	−1211.75			−0.0743187			−0.0371594	−	0.999309i	$-0.511831\pi$
$643$	−1211.75			−0.0743187			−0.0371594	+	0.999309i	$0.511831\pi$
$644$		0			0
$645$	215.342			0.0131459
$646$	1630.48	−	2824.07i	0.0993037	−	0.171999i
$647$	1408.61	+	2439.78i	0.0855922	+	0.148250i	0.905643	−	0.424040i	$-0.139388\pi$
$647$	1408.61	+	2439.78i	0.0855922	+	0.148250i	−0.820051	+	0.572290i	$0.806055\pi$
$648$	2526.17	+	4375.46i	0.153144	+	0.265253i
$649$	623.581	−	1080.07i	0.0377160	−	0.0653260i
$650$	−2695.66			−0.162665
$651$		0			0
$652$	47838.6			2.87347
$653$	−10493.1	+	18174.6i	−0.628831	+	1.08917i	0.358956	+	0.933355i	$0.383133\pi$
$653$	−10493.1	+	18174.6i	−0.628831	+	1.08917i	−0.987787	+	0.155812i	$0.950201\pi$
$654$	−10580.2	−	18325.5i	−0.632600	−	1.09569i
$655$	−2482.44	−	4299.70i	−0.148087	−	0.256494i
$656$	28822.5	−	49922.1i	1.71544	−	2.97124i
$657$	5231.69			0.310666
$658$		0			0
$659$	−2384.09			−0.140927			−0.0704635	−	0.997514i	$-0.522448\pi$
$659$	−2384.09			−0.140927			−0.0704635	+	0.997514i	$0.522448\pi$
$660$	−10901.6	+	18882.1i	−0.642944	+	1.11361i
$661$	3788.55	+	6561.96i	0.222931	+	0.386128i	0.955697	−	0.294353i	$-0.0951042\pi$
$661$	3788.55	+	6561.96i	0.222931	+	0.386128i	−0.732766	+	0.680481i	$0.761771\pi$
$662$	18540.8	+	32113.7i	1.08854	+	1.88540i
$663$	−590.248	+	1022.34i	−0.0345751	+	0.0598859i
$664$	−83232.2			−4.86451
$665$		0			0
$666$	12338.4			0.717874
$667$	−2218.77	+	3843.02i	−0.128802	+	0.223092i
$668$	6051.26	+	10481.1i	0.350494	+	0.607074i
$669$	5669.69	+	9820.19i	0.327658	+	0.567520i
$670$	13402.9	−	23214.6i	0.772837	−	1.33859i
$671$	2008.30			0.115543
$672$		0			0
$673$	11724.6			0.671547			0.335774	−	0.941943i	$-0.391002\pi$
$673$	11724.6			0.671547			0.335774	+	0.941943i	$0.391002\pi$
$674$	27240.8	−	47182.5i	1.55679	−	2.69644i
$675$	184.963	+	320.366i	0.0105470	+	0.0182680i
$676$	7987.23	+	13834.3i	0.454440	+	0.787113i
$677$	−16152.1	+	27976.3i	−0.916952	+	1.58821i	−0.112935	+	0.993602i	$0.536025\pi$
$677$	−16152.1	+	27976.3i	−0.916952	+	1.58821i	−0.804018	+	0.594606i	$0.797308\pi$
$678$	−14346.4			−0.812639
$679$		0			0
$680$	6942.23			0.391503
$681$	−2741.43	+	4748.29i	−0.154261	+	0.267188i
$682$	26742.8	+	46319.9i	1.50152	+	2.60070i
$683$	−16683.6	−	28896.8i	−0.934669	−	1.61889i	−0.775223	−	0.631687i	$-0.782363\pi$
$683$	−16683.6	−	28896.8i	−0.934669	−	1.61889i	−0.159446	−	0.987207i	$-0.550971\pi$
$684$	5227.61	−	9054.49i	0.292226	−	0.506150i
$685$	−4683.18			−0.261219
$686$		0			0
$687$	−2550.75			−0.141655
$688$	−579.776	+	1004.20i	−0.0321275	+	0.0556465i
$689$	−10012.9	−	17342.9i	−0.553646	−	0.958943i
$690$	−10463.3	−	18122.9i	−0.577289	−	0.999894i
$691$	521.837	−	903.849i	0.0287288	−	0.0497598i	−0.851304	−	0.524674i	$-0.824187\pi$
$691$	521.837	−	903.849i	0.0287288	−	0.0497598i	0.880032	+	0.474914i	$0.157521\pi$
$692$	75211.3			4.13166
$693$		0			0
$694$	−10378.6			−0.567674
$695$	−8809.01	+	15257.6i	−0.480784	+	0.832742i
$696$	−3312.28	−	5737.03i	−0.180390	−	0.312445i
$697$	−1784.23	−	3090.37i	−0.0969619	−	0.167943i
$698$	−11513.7	+	19942.4i	−0.624357	+	1.08142i
$699$	−19773.3			−1.06995
$700$		0			0
$701$	−11305.7			−0.609143			−0.304572	−	0.952489i	$-0.598513\pi$
$701$	−11305.7			−0.609143			−0.304572	+	0.952489i	$0.598513\pi$
$702$	−2656.11	+	4600.52i	−0.142804	+	0.247344i
$703$	−7614.72	−	13189.1i	−0.408527	−	0.707590i
$704$	−12968.8	−	22462.6i	−0.694289	−	1.20254i
$705$	−3967.18	+	6871.35i	−0.211933	+	0.367078i
$706$	32027.1			1.70730
$707$		0			0
$708$	−2134.55			−0.113307
$709$	6653.38	−	11524.0i	0.352430	−	0.610427i	−0.634245	−	0.773132i	$-0.718689\pi$
$709$	6653.38	−	11524.0i	0.352430	−	0.610427i	0.986675	+	0.162706i	$0.0520221\pi$
$710$	10121.3	+	17530.6i	0.534995	+	0.926639i
$711$	3121.61	+	5406.79i	0.164655	+	0.285190i
$712$	−11010.3	+	19070.4i	−0.579535	+	1.00378i
$713$	−36575.6			−1.92113
$714$		0			0
$715$	−13673.7			−0.715201
$716$	27801.0	−	48152.8i	1.45108	−	2.51334i
$717$	273.835	+	474.296i	0.0142630	+	0.0247042i
$718$	25419.9	+	44028.6i	1.32126	+	2.28849i
$719$	−5350.62	+	9267.55i	−0.277531	+	0.480697i	−0.970770	−	0.240010i	$-0.922849\pi$
$719$	−5350.62	+	9267.55i	−0.277531	+	0.480697i	0.693240	+	0.720707i	$0.256183\pi$
$720$	16181.4			0.837562
$721$		0			0
$722$	18068.0			0.931333
$723$	−2285.85	+	3959.20i	−0.117582	+	0.203657i
$724$	−30788.3	−	53326.8i	−1.58044	−	2.73740i
$725$	−242.521	−	420.059i	−0.0124235	−	0.0215181i
$726$	−977.139	+	1692.45i	−0.0499518	+	0.0865191i
$727$	−2121.14			−0.108210			−0.0541051	−	0.998535i	$-0.517231\pi$
$727$	−2121.14			−0.108210			−0.0541051	+	0.998535i	$0.517231\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	16174.5	−	28015.1i	0.820062	−	1.42039i
$731$	35.8904	+	62.1640i	0.00181594	+	0.00314531i
$732$	−1718.63	−	2976.75i	−0.0867792	−	0.150306i
$733$	10792.0	−	18692.3i	0.543809	−	0.941906i	−0.454871	−	0.890557i	$-0.650315\pi$
$733$	10792.0	−	18692.3i	0.543809	−	0.941906i	0.998681	−	0.0513484i	$-0.0163519\pi$
$734$	−2757.33			−0.138658
$735$		0			0
$736$	50135.0			2.51087
$737$	−8369.18	+	14495.8i	−0.418294	+	0.724507i
$738$	−8029.02	−	13906.7i	−0.400478	−	0.693648i
$739$	4972.61	+	8612.81i	0.247524	+	0.428724i	0.962838	−	0.270079i	$-0.0870497\pi$
$739$	4972.61	+	8612.81i	0.247524	+	0.428724i	−0.715314	+	0.698803i	$0.753716\pi$
$740$	27178.5	−	47074.5i	1.35013	−	2.33850i
$741$	6556.94			0.325068
$742$		0			0
$743$	2867.01			0.141562			0.0707808	−	0.997492i	$-0.477451\pi$
$743$	2867.01			0.141562			0.0707808	+	0.997492i	$0.477451\pi$
$744$	27300.8	−	47286.4i	1.34529	−	2.33011i
$745$	−3923.86	−	6796.32i	−0.192965	−	0.334225i
$746$	8518.57	+	14754.6i	0.418079	+	0.724134i
$747$	−6004.76	+	10400.6i	−0.294114	+	0.509420i
$748$	−7267.71			−0.355259
$749$		0			0
$750$	23155.9			1.12738
$751$	5412.05	−	9373.94i	0.262967	−	0.455473i	−0.704062	−	0.710139i	$-0.748632\pi$
$751$	5412.05	−	9373.94i	0.262967	−	0.455473i	0.967029	+	0.254666i	$0.0819655\pi$
$752$	−21362.0	−	37000.1i	−1.03589	−	1.79422i
$753$	−3536.60	−	6125.56i	−0.171156	−	0.296451i
$754$	3482.66	−	6032.14i	0.168211	−	0.291349i
$755$	6401.26			0.308564
$756$		0			0
$757$	−14512.0			−0.696761			−0.348381	−	0.937353i	$-0.613268\pi$
$757$	−14512.0			−0.696761			−0.348381	+	0.937353i	$0.613268\pi$
$758$	17512.0	−	30331.6i	0.839134	−	1.45342i
$759$	6533.57	+	11316.5i	0.312455	+	0.541188i
$760$	−19280.0	−	33393.9i	−0.920208	−	1.59385i
$761$	16537.9	−	28644.5i	0.787778	−	1.36447i	−0.139547	−	0.990215i	$-0.544565\pi$
$761$	16537.9	−	28644.5i	0.787778	−	1.36447i	0.927325	−	0.374256i	$-0.122102\pi$
$762$	27137.7			1.29015
$763$		0			0
$764$	5193.13			0.245917
$765$	500.846	−	867.490i	0.0236707	−	0.0409989i
$766$	−37516.4	−	64980.3i	−1.76961	−	3.06506i
$767$	−669.338	−	1159.33i	−0.0315103	−	0.0545774i
$768$	3121.19	−	5406.06i	0.146649	−	0.254003i
$769$	6728.44			0.315518			0.157759	−	0.987478i	$-0.449573\pi$
$769$	6728.44			0.315518			0.157759	+	0.987478i	$0.449573\pi$
$770$		0			0
$771$	8347.65			0.389926
$772$	−40155.8	+	69551.8i

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.63746 - 4.56821i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-9.91238 - 17.1687i) q^{4} +(-5.27492 + 9.13642i) q^{5} -15.8248 q^{6} -62.3746 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(2.63746 - 4.56821i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-9.91238 - 17.1687i) q^{4} +(-5.27492 + 9.13642i) q^{5} -15.8248 q^{6} -62.3746 q^{8} +(-4.50000 + 7.79423i) q^{9} +(27.8248 + 48.1939i) q^{10} +(-17.3746 - 30.0937i) q^{11} +(-29.7371 + 51.5062i) q^{12} -37.2990 q^{13} +31.6495 q^{15} +(-85.2114 + 147.590i) q^{16} +(5.27492 + 9.13642i) q^{17} +(23.7371 + 41.1139i) q^{18} +(29.2990 - 50.7474i) q^{19} +209.148 q^{20} -183.299 q^{22} +(62.6736 - 108.554i) q^{23} +(93.5619 + 162.054i) q^{24} +(6.85050 + 11.8654i) q^{25} +(-98.3746 + 170.390i) q^{26} +27.0000 q^{27} -35.4020 q^{29} +(83.4743 - 144.582i) q^{30} +(-145.897 - 252.701i) q^{31} +(199.985 + 346.384i) q^{32} +(-52.1238 + 90.2810i) q^{33} +55.6495 q^{34} +178.423 q^{36} +(129.949 - 225.077i) q^{37} +(-154.550 - 267.688i) q^{38} +(55.9485 + 96.9057i) q^{39} +(329.021 - 569.881i) q^{40} -338.248 q^{41} +6.80397 q^{43} +(-344.447 + 596.599i) q^{44} +(-47.4743 - 82.2278i) q^{45} +(-330.598 - 572.613i) q^{46} +(-125.347 + 217.108i) q^{47} +511.268 q^{48} +72.2716 q^{50} +(15.8248 - 27.4093i) q^{51} +(369.722 + 640.377i) q^{52} +(268.450 + 464.969i) q^{53} +(71.2114 - 123.342i) q^{54} +366.598 q^{55} -175.794 q^{57} +(-93.3713 + 161.724i) q^{58} +(17.9452 + 31.0820i) q^{59} +(-313.722 - 543.382i) q^{60} +(-28.8970 + 50.0511i) q^{61} -1539.19 q^{62} +746.423 q^{64} +(196.749 - 340.780i) q^{65} +(274.949 + 476.225i) q^{66} +(-240.846 - 417.157i) q^{67} +(104.574 - 181.127i) q^{68} -376.042 q^{69} +363.752 q^{71} +(280.686 - 486.162i) q^{72} +(-290.650 - 503.420i) q^{73} +(-685.468 - 1187.26i) q^{74} +(20.5515 - 35.5962i) q^{75} -1161.69 q^{76} +590.248 q^{78} +(346.846 - 600.754i) q^{79} +(-898.966 - 1557.05i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-892.114 + 1545.19i) q^{82} +1334.39 q^{83} -111.299 q^{85} +(17.9452 - 31.0820i) q^{86} +(53.1030 + 91.9771i) q^{87} +(1083.73 + 1877.08i) q^{88} +(176.519 - 305.740i) q^{89} -500.846 q^{90} -2484.98 q^{92} +(-437.691 + 758.103i) q^{93} +(661.196 + 1145.23i) q^{94} +(309.100 + 535.376i) q^{95} +(599.954 - 1039.15i) q^{96} +1445.88 q^{97} +312.743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 18 * q^6 - 174 * q^8 - 18 * q^9	\( 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9} + 66 q^{10} + 6 q^{11} - 51 q^{12} + 32 q^{13} + 36 q^{15} - 137 q^{16} + 6 q^{17} + 27 q^{18} - 64 q^{19} + 444 q^{20} - 552 q^{22} - 6 q^{23} + 261 q^{24} + 118 q^{25} - 318 q^{26} + 108 q^{27} - 504 q^{29} + 198 q^{30} - 40 q^{31} + 279 q^{32} + 18 q^{33} + 132 q^{34} + 306 q^{36} + 248 q^{37} - 588 q^{38} - 48 q^{39} + 546 q^{40} - 900 q^{41} + 752 q^{43} - 804 q^{44} - 54 q^{45} - 960 q^{46} + 12 q^{47} + 822 q^{48} - 330 q^{50} + 18 q^{51} + 890 q^{52} + 1104 q^{53} + 81 q^{54} + 1104 q^{55} + 384 q^{57} + 306 q^{58} - 804 q^{59} - 666 q^{60} + 428 q^{61} - 4224 q^{62} + 2578 q^{64} + 636 q^{65} + 828 q^{66} - 148 q^{67} + 222 q^{68} + 36 q^{69} + 1908 q^{71} + 783 q^{72} - 1072 q^{73} - 1398 q^{74} + 354 q^{75} - 3016 q^{76} + 1908 q^{78} + 572 q^{79} - 1950 q^{80} - 162 q^{81} - 1530 q^{82} + 3888 q^{83} - 264 q^{85} - 804 q^{86} + 756 q^{87} + 1164 q^{88} - 366 q^{89} - 1188 q^{90} - 5712 q^{92} - 120 q^{93} + 1920 q^{94} + 1176 q^{95} + 837 q^{96} + 1616 q^{97} - 108 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 18 * q^6 - 174 * q^8 - 18 * q^9 + 66 * q^10 + 6 * q^11 - 51 * q^12 + 32 * q^13 + 36 * q^15 - 137 * q^16 + 6 * q^17 + 27 * q^18 - 64 * q^19 + 444 * q^20 - 552 * q^22 - 6 * q^23 + 261 * q^24 + 118 * q^25 - 318 * q^26 + 108 * q^27 - 504 * q^29 + 198 * q^30 - 40 * q^31 + 279 * q^32 + 18 * q^33 + 132 * q^34 + 306 * q^36 + 248 * q^37 - 588 * q^38 - 48 * q^39 + 546 * q^40 - 900 * q^41 + 752 * q^43 - 804 * q^44 - 54 * q^45 - 960 * q^46 + 12 * q^47 + 822 * q^48 - 330 * q^50 + 18 * q^51 + 890 * q^52 + 1104 * q^53 + 81 * q^54 + 1104 * q^55 + 384 * q^57 + 306 * q^58 - 804 * q^59 - 666 * q^60 + 428 * q^61 - 4224 * q^62 + 2578 * q^64 + 636 * q^65 + 828 * q^66 - 148 * q^67 + 222 * q^68 + 36 * q^69 + 1908 * q^71 + 783 * q^72 - 1072 * q^73 - 1398 * q^74 + 354 * q^75 - 3016 * q^76 + 1908 * q^78 + 572 * q^79 - 1950 * q^80 - 162 * q^81 - 1530 * q^82 + 3888 * q^83 - 264 * q^85 - 804 * q^86 + 756 * q^87 + 1164 * q^88 - 366 * q^89 - 1188 * q^90 - 5712 * q^92 - 120 * q^93 + 1920 * q^94 + 1176 * q^95 + 837 * q^96 + 1616 * q^97 - 108 * q^99

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