LMFDB - Embedded newform 147.4.e.m.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.m.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	−0.527677	−	0.849445i	$-0.676937\pi$
$5$	5.27492	−	9.13642i	0.471803	−	0.817187i	0.999480	+	0.0322587i	$0.0102700\pi$
$6$	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	$-0.369746\pi$
$13$	37.2990			0.795760			0.397880	+	0.917437i	$0.369746\pi$
$14$		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	0.825941	−	0.563756i	$-0.190644\pi$
$17$	−5.27492	−	9.13642i	−0.0752562	−	0.130348i	−0.901198	+	0.433408i	$0.857311\pi$
$18$	23.7371	+	41.1139i	0.310827	+	0.538369i
$19$	−29.2990	+	50.7474i	−0.353771	+	0.612750i	−0.986907	−	0.161291i	$-0.948434\pi$
$19$	−29.2990	+	50.7474i	−0.353771	+	0.612750i	0.633136	+	0.774041i	$0.281768\pi$
$20$	−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	$0.153904\pi$
$31$	145.897	+	252.701i	0.845286	+	1.46408i	−0.0400859	+	0.999196i	$0.512763\pi$
$32$	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	$-0.277185\pi$
$41$	338.248			1.28842			0.644212	+	0.764847i	$0.277185\pi$
$42$		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	−0.603301	−	0.797513i	$-0.706148\pi$
$47$	125.347	−	217.108i	0.389016	−	0.673796i	0.992317	+	0.123717i	$0.0394816\pi$
$48$	−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	0.845547	−	0.533900i	$-0.179274\pi$
$59$	−17.9452	−	31.0820i	−0.0395977	−	0.0685853i	−0.885145	+	0.465315i	$0.845941\pi$
$60$	−313.722	−	543.382i	−0.675022	−	1.16917i
$61$	28.8970	−	50.0511i	0.0606538	−	0.105056i	−0.834104	−	0.551607i	$-0.814015\pi$
$61$	28.8970	−	50.0511i	0.0606538	−	0.105056i	0.894758	+	0.446552i	$0.147348\pi$
$62$	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	0.999246	−	0.0388253i	$-0.0123616\pi$
$73$	290.650	+	503.420i	0.465999	+	0.807135i	−0.533247	+	0.845960i	$0.679028\pi$
$74$	−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	$-0.844033\pi$
$83$	−1334.39			−1.76468			−0.882341	+	0.470611i	$0.844033\pi$
$84$		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	−0.951788	−	0.306756i	$-0.900757\pi$
$89$	−176.519	+	305.740i	−0.210236	+	0.364139i	0.741552	+	0.670895i	$0.234090\pi$
$90$	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	$-0.773207\pi$
$97$	−1445.88			−1.51347			−0.756735	+	0.653722i	$0.773207\pi$
$98$		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	0.958955	−	0.283558i	$-0.0915150\pi$
$101$	237.426	+	411.234i	0.233909	+	0.405142i	−0.725046	+	0.688700i	$0.758182\pi$
$102$	−83.4743	−	144.582i	−0.0810312	−	0.140350i
$103$	−999.794	+	1731.69i	−0.956433	+	1.65659i	−0.225380	+	0.974271i	$0.572362\pi$
$103$	−999.794	+	1731.69i	−0.956433	+	1.65659i	−0.731053	+	0.682320i	$0.760971\pi$
$104$	−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	−0.776826	−	0.629716i	$-0.783171\pi$
$131$	235.306	−	407.561i	0.156937	−	0.271823i	0.933763	+	0.357893i	$0.116505\pi$
$132$	−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	$-0.670176\pi$
$139$	−1669.98			−1.01904			−0.509518	+	0.860460i	$0.670176\pi$
$140$		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	$0.124125\pi$
$157$	1557.39	+	2697.48i	0.791678	+	1.37123i	−0.133250	+	0.991083i	$0.542541\pi$
$158$	−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	$-0.454828\pi$
$167$	610.475			0.282874			0.141437	+	0.989947i	$0.454828\pi$
$168$		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	$-0.519589\pi$
$173$	1896.90	−	3285.54i	0.833636	−	1.44390i	0.895136	−	0.445792i	$-0.147078\pi$
$174$	−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	$-0.720140\pi$
$181$	−3106.04			−1.27553			−0.637763	+	0.770232i	$0.720140\pi$
$182$		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	$-0.982717\pi$
$199$	−1533.49	−	2656.07i	−0.546261	−	0.946151i	0.452266	−	0.891883i	$-0.350616\pi$
$200$	−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	$-0.307903\pi$
$223$	3779.79			1.13504			0.567520	+	0.823360i	$0.307903\pi$
$224$		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	0.968135	−	0.250431i	$-0.0805722\pi$
$227$	913.809	+	1582.76i	0.267188	+	0.462783i	−0.700947	+	0.713214i	$0.747239\pi$
$228$	1742.54	+	3018.16i	0.506150	+	0.876678i
$229$	−425.125	+	736.338i	−0.122677	+	0.212483i	−0.920823	−	0.389982i	$-0.872481\pi$
$229$	−425.125	+	736.338i	−0.122677	+	0.212483i	0.798146	+	0.602465i	$0.205815\pi$
$230$	−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	0.949704	−	0.313149i	$-0.101384\pi$
$241$	761.949	+	1319.73i	0.203657	+	0.352745i	−0.746047	+	0.665894i	$0.768050\pi$
$242$	−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	$-0.595803\pi$
$251$	−2357.73			−0.592903			−0.296451	+	0.955048i	$0.595803\pi$
$252$		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	−0.646311	−	0.763074i	$-0.723689\pi$
$257$	1391.27	−	2409.76i	0.337686	−	0.584890i	0.983997	+	0.178185i	$0.0570224\pi$
$258$	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	0.992622	−	0.121248i	$-0.0386898\pi$
$269$	1726.42	+	2990.24i	0.391307	+	0.677763i	−0.601315	+	0.799012i	$0.705356\pi$
$270$	751.268	+	1301.23i	0.169336	+	0.293299i
$271$	1322.15	−	2290.02i	0.296364	−	0.513318i	−0.678937	−	0.734196i	$-0.737559\pi$
$271$	1322.15	−	2290.02i	0.296364	−	0.513318i	0.975301	+	0.220879i	$0.0708925\pi$
$272$	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	0.887829	−	0.460174i	$-0.152213\pi$
$283$	216.103	+	374.301i	0.0453922	+	0.0786216i	−0.842437	+	0.538795i	$0.818880\pi$
$284$	−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	$-0.428120\pi$
$293$	2245.92			0.447809			0.223904	+	0.974611i	$0.428120\pi$
$294$		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	$-0.403955\pi$
$307$	3197.08			0.594354			0.297177	+	0.954822i	$0.403955\pi$
$308$		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	0.671550	−	0.740959i	$-0.265629\pi$
$311$	−1677.80	−	2906.04i	−0.305915	−	0.529860i	−0.977465	+	0.211100i	$0.932296\pi$
$312$	−3489.77	−	6044.45i	−0.633234	−	1.09679i
$313$	−1128.20	+	1954.09i	−0.203736	+	0.352881i	−0.949729	−	0.313072i	$-0.898642\pi$
$313$	−1128.20	+	1954.09i	−0.203736	+	0.352881i	0.745993	+	0.665954i	$0.231975\pi$
$314$	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	$-0.391337\pi$
$349$	4365.46			0.669564			0.334782	+	0.942296i	$0.391337\pi$
$350$		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	0.541110	−	0.840952i	$-0.318004\pi$
$353$	−3035.79	−	5258.15i	−0.457731	−	0.792813i	−0.998841	+	0.0481389i	$0.984671\pi$
$354$	−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	0.884014	−	0.467460i	$-0.154831\pi$
$367$	261.362	+	452.693i	0.0371744	+	0.0643879i	−0.846840	+	0.531848i	$0.821498\pi$
$368$	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	$0.564439\pi$
$383$	−7112.22	+	12318.7i	−0.948871	+	1.64349i	−0.747809	+	0.663914i	$0.768894\pi$
$384$	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	−0.839223	−	0.543788i	$-0.816990\pi$
$397$	405.970	−	703.161i	0.0513226	−	0.0888933i	0.890545	+	0.454894i	$0.150323\pi$
$398$	−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	0.771734	−	0.635945i	$-0.219390\pi$
$409$	−1363.79	−	2362.15i	−0.164877	−	0.285576i	−0.936612	+	0.350369i	$0.886056\pi$
$410$	−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	$-0.782614\pi$
$419$	−13306.3			−1.55144			−0.775721	+	0.631076i	$0.782614\pi$
$420$		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	$-0.274697\pi$
$433$	11716.3			1.30034			0.650171	+	0.759788i	$0.274697\pi$
$434$		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	$0.458810\pi$
$439$	−7305.69	+	12653.8i	−0.794264	+	1.37571i	−0.923306	+	0.384066i	$0.874524\pi$
$440$	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	$-0.514639\pi$
$461$	−910.121			−0.0919492			−0.0459746	+	0.998943i	$0.514639\pi$
$462$		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	−0.954641	−	0.297759i	$-0.903761\pi$
$467$	−2214.71	+	3835.99i	−0.219453	+	0.380104i	0.735188	+	0.677864i	$0.237094\pi$
$468$	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	0.924176	−	0.381966i	$-0.124753\pi$
$479$	1376.43	+	2384.04i	0.131296	+	0.227411i	−0.792881	+	0.609377i	$0.791420\pi$
$480$	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	$-0.618028\pi$
$503$	−8175.59			−0.724715			−0.362357	+	0.932039i	$0.618028\pi$
$504$		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	−0.884516	−	0.466510i	$-0.845511\pi$
$509$	−439.224	+	760.758i	−0.0382480	+	0.0662475i	0.846268	+	0.532758i	$0.178844\pi$
$510$	−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	0.999962	−	0.00869048i	$-0.00276630\pi$
$521$	5856.30	+	10143.4i	0.492455	+	0.852957i	−0.507507	+	0.861647i	$0.669433\pi$
$522$	−840.341	−	1455.51i	−0.0704612	−	0.122042i
$523$	−3670.91	+	6358.20i	−0.306917	+	0.531596i	−0.977686	−	0.210070i	$-0.932631\pi$
$523$	−3670.91	+	6358.20i	−0.306917	+	0.531596i	0.670769	+	0.741666i	$0.265964\pi$
$524$	−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	0.909651	−	0.415373i	$-0.136349\pi$
$563$	1270.43	+	2200.45i	0.0951017	+	0.164721i	−0.814549	+	0.580094i	$0.803016\pi$
$564$	−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	0.991324	−	0.131445i	$-0.0419616\pi$
$577$	5292.13	+	9166.24i	0.381827	+	0.661344i	−0.609496	+	0.792789i	$0.708628\pi$
$578$	−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	$-0.400905\pi$
$587$	8712.63			0.612621			0.306311	+	0.951932i	$0.400905\pi$
$588$		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	$0.345202\pi$
$593$	−7681.43	+	13304.6i	−0.531937	+	0.921341i	−0.999305	+	0.0372786i	$0.988131\pi$
$594$	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	$-0.745918\pi$
$601$	−20567.7			−1.39596			−0.697982	+	0.716115i	$0.745918\pi$
$602$		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	$-0.605280\pi$
$607$	9821.04	−	17010.5i	0.656711	−	1.13746i	0.981462	−	0.191657i	$-0.0613862\pi$
$608$	−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	0.831052	−	0.556194i	$-0.187739\pi$
$619$	−1018.78	−	1764.58i	−0.0661523	−	0.114579i	−0.897205	+	0.441615i	$0.854406\pi$
$620$	−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	$-0.488169\pi$
$643$	1211.75			0.0743187			0.0371594	+	0.999309i	$0.488169\pi$
$644$		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	0.820051	−	0.572290i	$-0.193945\pi$
$647$	−1408.61	−	2439.78i	−0.0855922	−	0.148250i	−0.905643	+	0.424040i	$0.860612\pi$
$648$	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	0.732766	−	0.680481i	$-0.238229\pi$
$661$	−3788.55	−	6561.96i	−0.222931	−	0.386128i	−0.955697	+	0.294353i	$0.904896\pi$
$662$	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	$-0.463975\pi$
$677$	16152.1	−	27976.3i	0.916952	−	1.58821i	0.804018	−	0.594606i	$-0.202692\pi$
$678$	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	−0.880032	−	0.474914i	$-0.842479\pi$
$691$	−521.837	+	903.849i	−0.0287288	+	0.0497598i	0.851304	+	0.524674i	$0.175813\pi$
$692$	−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	−0.693240	−	0.720707i	$-0.743817\pi$
$719$	5350.62	−	9267.55i	0.277531	−	0.480697i	0.970770	+	0.240010i	$0.0771506\pi$
$720$	−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	$-0.482769\pi$
$727$	2121.14			0.108210			0.0541051	+	0.998535i	$0.482769\pi$
$728$		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	$0.349685\pi$
$733$	−10792.0	+	18692.3i	−0.543809	+	0.941906i	−0.998681	+	0.0513484i	$0.983648\pi$
$734$	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	$0.455435\pi$
$761$	−16537.9	+	28644.5i	−0.787778	+	1.36447i	−0.927325	+	0.374256i	$0.877898\pi$
$762$	−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	$-0.550427\pi$
$769$	−6728.44			−0.315518			−0.157759	+	0.987478i	$0.550427\pi$
$770$		0			0
$771$	8347.65			0.389926
$772$	−40155.8	+	69551.8i	−1.87207	+	3.24252i

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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