LMFDB - Embedded newform 147.4.e.l.67.2

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			67.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.4.e.l.79.2

$q$-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 $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	0.779063	+	0.626946i	$0.215695\pi$
$2$	2.63746	+	4.56821i	0.932482	+	1.61511i	0.153420	+	0.988161i	$0.450971\pi$
$3$	−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	$-0.323063\pi$
$5$	−5.27492	−	9.13642i	−0.471803	−	0.817187i	−0.999480	+	0.0322587i	$0.989730\pi$
$6$	−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	−0.999629	−	0.0272223i	$-0.991334\pi$
$11$	−17.3746	+	30.0937i	−0.476240	+	0.824871i	0.523390	+	0.852093i	$0.324667\pi$
$12$	−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	−0.825941	−	0.563756i	$-0.809356\pi$
$17$	5.27492	−	9.13642i	0.0752562	−	0.130348i	0.901198	+	0.433408i	$0.142689\pi$
$18$	23.7371	−	41.1139i	0.310827	−	0.538369i
$19$	29.2990	+	50.7474i	0.353771	+	0.612750i	0.986907	−	0.161291i	$-0.0515658\pi$
$19$	29.2990	+	50.7474i	0.353771	+	0.612750i	−0.633136	+	0.774041i	$0.718232\pi$
$20$	209.148			2.33834
$21$		0			0
$22$	−183.299			−1.77634
$23$	62.6736	+	108.554i	0.568189	+	0.984132i	0.996745	+	0.0806171i	$0.0256891\pi$
$23$	62.6736	+	108.554i	0.568189	+	0.984132i	−0.428556	+	0.903515i	$0.640978\pi$
$24$	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	0.0400859	+	0.999196i	$0.487237\pi$
$31$	−145.897	+	252.701i	−0.845286	+	1.46408i	−0.885372	+	0.464883i	$0.846096\pi$
$32$	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	0.995778	+	0.0917993i	$0.0292618\pi$
$37$	129.949	+	225.077i	0.577389	+	1.00007i	−0.418388	+	0.908268i	$0.637405\pi$
$38$	−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	0.603301	−	0.797513i	$-0.293852\pi$
$47$	−125.347	−	217.108i	−0.389016	−	0.673796i	−0.992317	+	0.123717i	$0.960518\pi$
$48$	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	−0.274184	−	0.961677i	$-0.588408\pi$
$53$	268.450	−	464.969i	0.695745	−	1.20507i	0.969929	−	0.243388i	$-0.0782588\pi$
$54$	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	$-0.820726\pi$
$59$	17.9452	−	31.0820i	0.0395977	−	0.0685853i	0.885145	+	0.465315i	$0.154059\pi$
$60$	−313.722	+	543.382i	−0.675022	+	1.16917i
$61$	−28.8970	−	50.0511i	−0.0606538	−	0.105056i	0.834104	−	0.551607i	$-0.185985\pi$
$61$	−28.8970	−	50.0511i	−0.0606538	−	0.105056i	−0.894758	+	0.446552i	$0.852652\pi$
$62$	−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	−0.997625	−	0.0688767i	$-0.978059\pi$
$67$	−240.846	+	417.157i	−0.439164	+	0.760654i	0.558462	+	0.829530i	$0.311392\pi$
$68$	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	$-0.987638\pi$
$73$	−290.650	+	503.420i	−0.465999	+	0.807135i	0.533247	+	0.845960i	$0.320972\pi$
$74$	−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	0.999976	−	0.00695559i	$-0.00221405\pi$
$79$	346.846	+	600.754i	0.493964	+	0.855571i	−0.506012	+	0.862527i	$0.668881\pi$
$80$	−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	0.951788	−	0.306756i	$-0.0992435\pi$
$89$	176.519	+	305.740i	0.210236	+	0.364139i	−0.741552	+	0.670895i	$0.765910\pi$
$90$	−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	−0.958955	−	0.283558i	$-0.908485\pi$
$101$	−237.426	+	411.234i	−0.233909	+	0.405142i	0.725046	+	0.688700i	$0.241818\pi$
$102$	−83.4743	+	144.582i	−0.0810312	+	0.140350i
$103$	999.794	+	1731.69i	0.956433	+	1.65659i	0.731053	+	0.682320i	$0.239029\pi$
$103$	999.794	+	1731.69i	0.956433	+	1.65659i	0.225380	+	0.974271i	$0.427638\pi$
$104$	2326.51			2.19359
$105$		0			0
$106$	2832.10			2.59508
$107$	−583.368	−	1010.42i	−0.527068	−	0.912909i	−0.999502	−	0.0315431i	$-0.989958\pi$
$107$	−583.368	−	1010.42i	−0.527068	−	0.912909i	0.472434	−	0.881366i	$-0.343375\pi$
$108$	−267.634	+	463.556i	−0.238455	+	0.413016i
$109$	668.588	−	1158.03i	0.587515	−	1.01761i	−0.407042	−	0.913410i	$-0.633440\pi$
$109$	668.588	−	1158.03i	0.587515	−	1.01761i	0.994557	−	0.104196i	$-0.0332270\pi$
$110$	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	$-0.216829\pi$
$131$	−235.306	−	407.561i	−0.156937	−	0.271823i	−0.933763	+	0.357893i	$0.883495\pi$
$132$	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	−0.788482	−	0.615058i	$-0.789132\pi$
$137$	221.955	−	384.438i	0.138415	−	0.239742i	0.926897	+	0.375316i	$0.122466\pi$
$138$	−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	0.745475	−	0.666534i	$-0.232223\pi$
$149$	−371.935	−	644.211i	−0.204497	−	0.354200i	−0.949973	+	0.312334i	$0.898889\pi$
$150$	−108.407	+	187.767i	−0.0590095	+	0.102207i
$151$	−303.382	+	525.473i	−0.163503	+	0.283195i	−0.936123	−	0.351674i	$-0.885613\pi$
$151$	−303.382	+	525.473i	−0.163503	+	0.283195i	0.772620	+	0.634869i	$0.218946\pi$
$152$	−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	0.133250	+	0.991083i	$0.457459\pi$
$157$	−1557.39	+	2697.48i	−0.791678	+	1.37123i	−0.924927	+	0.380144i	$0.875875\pi$
$158$	−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	−0.995505	−	0.0947109i	$-0.969807\pi$
$163$	−1206.54	−	2089.78i	−0.579774	−	1.00420i	0.415730	−	0.909488i	$-0.363526\pi$
$164$	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	−0.895136	−	0.445792i	$-0.852922\pi$
$173$	−1896.90	−	3285.54i	−0.833636	−	1.44390i	0.0615006	−	0.998107i	$-0.480411\pi$
$174$	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	−0.409243	−	0.912426i	$-0.634207\pi$
$179$	1402.34	−	2428.92i	0.585562	−	1.01422i	0.994805	−	0.101798i	$-0.0324596\pi$
$180$	−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	0.840150	−	0.542355i	$-0.182467\pi$
$191$	−130.976	−	226.857i	−0.0496182	−	0.0859413i	−0.889768	+	0.456413i	$0.849134\pi$
$192$	−1119.63	+	1939.26i	−0.420847	+	0.728928i
$193$	−2025.54	+	3508.33i	−0.755447	+	1.30847i	0.189704	+	0.981841i	$0.439247\pi$
$193$	−2025.54	+	3508.33i	−0.755447	+	1.30847i	−0.945152	+	0.326632i	$0.894086\pi$
$194$	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	−0.452266	−	0.891883i	$-0.649384\pi$
$199$	1533.49	−	2656.07i	0.546261	−	0.946151i	0.998526	−	0.0542680i	$-0.0172825\pi$
$200$	−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	−0.968135	−	0.250431i	$-0.919428\pi$
$227$	−913.809	+	1582.76i	−0.267188	+	0.462783i	0.700947	+	0.713214i	$0.252761\pi$
$228$	1742.54	−	3018.16i	0.506150	−	0.876678i
$229$	425.125	+	736.338i	0.122677	+	0.212483i	0.920823	−	0.389982i	$-0.127519\pi$
$229$	425.125	+	736.338i	0.122677	+	0.212483i	−0.798146	+	0.602465i	$0.794185\pi$
$230$	6975.51			1.99979
$231$		0			0
$232$	2208.18			0.624890
$233$	3295.55	+	5708.06i	0.926604	+	1.60492i	0.788962	+	0.614443i	$0.210619\pi$
$233$	3295.55	+	5708.06i	0.926604	+	1.60492i	0.137642	+	0.990482i	$0.456048\pi$
$234$	−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	$-0.898616\pi$
$241$	−761.949	+	1319.73i	−0.203657	+	0.352745i	0.746047	+	0.665894i	$0.231950\pi$
$242$	−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	0.646311	−	0.763074i	$-0.276311\pi$
$257$	−1391.27	−	2409.76i	−0.337686	−	0.584890i	−0.983997	+	0.178185i	$0.942978\pi$
$258$	−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	−0.960597	−	0.277945i	$-0.910347\pi$
$263$	−1021.89	+	1769.97i	−0.239591	+	0.414984i	0.721006	+	0.692929i	$0.243680\pi$
$264$	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	$-0.961310\pi$
$269$	−1726.42	+	2990.24i	−0.391307	+	0.677763i	0.601315	+	0.799012i	$0.294644\pi$
$270$	751.268	−	1301.23i	0.169336	−	0.293299i
$271$	−1322.15	−	2290.02i	−0.296364	−	0.513318i	0.678937	−	0.734196i	$-0.262441\pi$
$271$	−1322.15	−	2290.02i	−0.296364	−	0.513318i	−0.975301	+	0.220879i	$0.929108\pi$
$272$	−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	−0.973953	−	0.226751i	$-0.927190\pi$
$277$	−1339.74	+	2320.50i	−0.290604	+	0.503341i	0.683349	+	0.730092i	$0.260523\pi$
$278$	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	$-0.847787\pi$
$283$	−216.103	+	374.301i	−0.0453922	+	0.0786216i	0.842437	+	0.538795i	$0.181120\pi$
$284$	−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	−0.671550	−	0.740959i	$-0.734371\pi$
$311$	1677.80	−	2906.04i	0.305915	−	0.529860i	0.977465	+	0.211100i	$0.0677045\pi$
$312$	−3489.77	+	6044.45i	−0.633234	+	1.09679i
$313$	1128.20	+	1954.09i	0.203736	+	0.352881i	0.949729	−	0.313072i	$-0.101358\pi$
$313$	1128.20	+	1954.09i	0.203736	+	0.352881i	−0.745993	+	0.665954i	$0.768025\pi$
$314$	−16430.2			−2.95290
$315$		0			0
$316$	−13752.3			−2.44818
$317$	3069.59	+	5316.69i	0.543866	+	0.942004i	0.998677	+	0.0514158i	$0.0163734\pi$
$317$	3069.59	+	5316.69i	0.543866	+	0.942004i	−0.454811	+	0.890588i	$0.650293\pi$
$318$	−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	−0.995039	−	0.0994849i	$-0.968280\pi$
$331$	−3514.91	−	6088.00i	−0.583676	−	1.01096i	0.411363	−	0.911472i	$-0.365053\pi$
$332$	−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	−0.932034	−	0.362371i	$-0.881967\pi$
$347$	−983.768	+	1703.94i	−0.152194	+	0.263608i	0.779840	+	0.625980i	$0.215301\pi$
$348$	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	−0.541110	−	0.840952i	$-0.681996\pi$
$353$	3035.79	−	5258.15i	0.457731	−	0.792813i	0.998841	+	0.0481389i	$0.0153290\pi$
$354$	−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	−0.965427	−	0.260673i	$-0.916056\pi$
$359$	−4819.02	−	8346.79i	−0.708463	−	1.22709i	0.256965	−	0.966421i	$-0.417278\pi$
$360$	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	$-0.845169\pi$
$367$	−261.362	+	452.693i	−0.0371744	+	0.0643879i	0.846840	+	0.531848i	$0.178502\pi$
$368$	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	0.731896	−	0.681416i	$-0.238636\pi$
$373$	−1614.92	−	2797.12i	−0.224175	−	0.388283i	−0.956072	+	0.293133i	$0.905302\pi$
$374$	−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	0.747809	+	0.663914i	$0.231106\pi$
$383$	7112.22	+	12318.7i	0.948871	+	1.64349i	0.201063	+	0.979578i	$0.435561\pi$
$384$	−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	−0.945388	−	0.325948i	$-0.894316\pi$
$389$	−1460.91	+	2530.37i	−0.190414	+	0.329807i	0.754973	+	0.655755i	$0.227650\pi$
$390$	−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	$-0.183010\pi$
$397$	−405.970	−	703.161i	−0.0513226	−	0.0888933i	−0.890545	+	0.454894i	$0.849677\pi$
$398$	16178.0			2.03751
$399$		0			0
$400$	−2334.96			−0.291870
$401$	−1169.32	−	2025.32i	−0.145618	−	0.252218i	0.783985	−	0.620780i	$-0.213184\pi$
$401$	−1169.32	−	2025.32i	−0.145618	−	0.252218i	−0.929603	+	0.368561i	$0.879850\pi$
$402$	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	$-0.780610\pi$
$409$	1363.79	−	2362.15i	0.164877	−	0.285576i	0.936612	+	0.350369i	$0.113944\pi$
$410$	−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	−0.624070	−	0.781368i	$-0.714522\pi$
$431$	3262.81	−	5651.36i	0.364650	−	0.631592i	0.988720	+	0.149776i	$0.0478553\pi$
$432$	−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	0.923306	+	0.384066i	$0.125476\pi$
$439$	7305.69	+	12653.8i	0.794264	+	1.37571i	−0.129042	+	0.991639i	$0.541190\pi$
$440$	−22866.4			−2.47753
$441$		0			0
$442$	−2075.67			−0.223370
$443$	7619.89	+	13198.0i	0.817228	+	1.41548i	0.907717	+	0.419583i	$0.137824\pi$
$443$	7619.89	+	13198.0i	0.817228	+	1.41548i	−0.0904888	+	0.995897i	$0.528843\pi$
$444$	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	0.737306	−	0.675559i	$-0.236098\pi$
$457$	−2114.12	−	3661.76i	−0.216399	−	0.374814i	−0.953704	+	0.300746i	$0.902764\pi$
$458$	−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	0.954641	−	0.297759i	$-0.0962393\pi$
$467$	2214.71	+	3835.99i	0.219453	+	0.380104i	−0.735188	+	0.677864i	$0.762906\pi$
$468$	−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	$-0.875247\pi$
$479$	−1376.43	+	2384.04i	−0.131296	+	0.227411i	0.792881	+	0.609377i	$0.208580\pi$
$480$	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	−0.850004	−	0.526776i	$-0.823401\pi$
$487$	335.299	−	580.755i	0.0311989	−	0.0540380i	0.881203	+	0.472738i	$0.156734\pi$
$488$	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	0.622731	−	0.782436i	$-0.286023\pi$
$499$	−4082.46	−	7071.02i	−0.366244	−	0.634353i	−0.988975	+	0.148083i	$0.952690\pi$
$500$	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	0.884516	−	0.466510i	$-0.154489\pi$
$509$	439.224	+	760.758i	0.0382480	+	0.0662475i	−0.846268	+	0.532758i	$0.821156\pi$
$510$	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	$-0.997234\pi$
$521$	−5856.30	+	10143.4i	−0.492455	+	0.852957i	0.507507	+	0.861647i	$0.330567\pi$
$522$	−840.341	+	1455.51i	−0.0704612	+	0.122042i
$523$	3670.91	+	6358.20i	0.306917	+	0.531596i	0.977686	−	0.210070i	$-0.0673692\pi$
$523$	3670.91	+	6358.20i	0.306917	+	0.531596i	−0.670769	+	0.741666i	$0.734036\pi$
$524$	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	0.987440	+	0.157992i	$0.0505020\pi$
$541$	7934.36	+	13742.7i	0.630545	+	1.09214i	−0.356895	+	0.934144i	$0.616165\pi$
$542$	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	−0.759706	−	0.650266i	$-0.774657\pi$
$557$	2409.52	−	4173.42i	0.183294	−	0.317475i	0.943000	+	0.332792i	$0.107991\pi$
$558$	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	$-0.863651\pi$
$563$	−1270.43	+	2200.45i	−0.0951017	+	0.164721i	0.814549	+	0.580094i	$0.196984\pi$
$564$	−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	0.837200	+	0.546898i	$0.184191\pi$
$569$	12110.0	+	20975.1i	0.892227	+	1.54538i	0.0550275	+	0.998485i	$0.482475\pi$
$570$	−4891.43	+	8472.20i	−0.359437	+	0.622564i
$571$	5886.04	−	10194.9i	0.431389	−	0.747188i	−0.565604	−	0.824677i	$-0.691357\pi$
$571$	5886.04	−	10194.9i	0.431389	−	0.747188i	0.996993	+	0.0774891i	$0.0246903\pi$
$572$	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	$-0.958038\pi$
$577$	−5292.13	+	9166.24i	−0.381827	+	0.661344i	0.609496	+	0.792789i	$0.291372\pi$
$578$	−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	0.999305	+	0.0372786i	$0.0118689\pi$
$593$	7681.43	+	13304.6i	0.531937	+	0.921341i	−0.467368	+	0.884063i	$0.654798\pi$
$594$	−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	−0.0433430	+	0.999060i	$0.513801\pi$
$599$	−13001.9	+	22519.9i	−0.886883	+	1.53613i	−0.843540	+	0.537066i	$0.819533\pi$
$600$	−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	−0.981462	−	0.191657i	$-0.938614\pi$
$607$	−9821.04	−	17010.5i	−0.656711	−	1.13746i	0.324751	−	0.945800i	$-0.394720\pi$
$608$	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	−0.971020	−	0.239000i	$-0.923180\pi$
$613$	−4227.29	+	7321.89i	−0.278530	+	0.482428i	0.692490	+	0.721428i	$0.256514\pi$
$614$	−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	$-0.812261\pi$
$619$	1018.78	−	1764.58i	0.0661523	−	0.114579i	0.897205	+	0.441615i	$0.145594\pi$
$620$	−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	−0.664474	−	0.747311i	$-0.731345\pi$
$641$	5111.32	−	8853.06i	0.314953	−	0.545515i	0.979428	+	0.201796i	$0.0646779\pi$
$642$	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	−0.820051	−	0.572290i	$-0.806055\pi$
$647$	1408.61	−	2439.78i	0.0855922	−	0.148250i	0.905643	+	0.424040i	$0.139388\pi$
$648$	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	−0.987787	−	0.155812i	$-0.950201\pi$
$653$	−10493.1	−	18174.6i	−0.628831	−	1.08917i	0.358956	−	0.933355i	$-0.383133\pi$
$654$	−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	$-0.761771\pi$
$661$	3788.55	−	6561.96i	0.222931	−	0.386128i	0.955697	+	0.294353i	$0.0951042\pi$
$662$	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	−0.804018	−	0.594606i	$-0.797308\pi$
$677$	−16152.1	−	27976.3i	−0.916952	−	1.58821i	−0.112935	−	0.993602i	$-0.536025\pi$
$678$	−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	−0.159446	+	0.987207i	$0.550971\pi$
$683$	−16683.6	+	28896.8i	−0.934669	+	1.61889i	−0.775223	+	0.631687i	$0.782363\pi$
$684$	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	$-0.157521\pi$
$691$	521.837	+	903.849i	0.0287288	+	0.0497598i	−0.851304	+	0.524674i	$0.824187\pi$
$692$	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	0.986675	−	0.162706i	$-0.0520221\pi$
$709$	6653.38	+	11524.0i	0.352430	+	0.610427i	−0.634245	+	0.773132i	$0.718689\pi$
$710$	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	$-0.256183\pi$
$719$	−5350.62	−	9267.55i	−0.277531	−	0.480697i	−0.970770	+	0.240010i	$0.922849\pi$
$720$	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	0.998681	+	0.0513484i	$0.0163519\pi$
$733$	10792.0	+	18692.3i	0.543809	+	0.941906i	−0.454871	+	0.890557i	$0.650315\pi$
$734$	−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	−0.715314	−	0.698803i	$-0.753716\pi$
$739$	4972.61	−	8612.81i	0.247524	−	0.428724i	0.962838	+	0.270079i	$0.0870497\pi$
$740$	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	0.967029	−	0.254666i	$-0.0819655\pi$
$751$	5412.05	+	9373.94i	0.262967	+	0.455473i	−0.704062	+	0.710139i	$0.748632\pi$
$752$	−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	0.927325	+	0.374256i	$0.122102\pi$
$761$	16537.9	+	28644.5i	0.787778	+	1.36447i	−0.139547	+	0.990215i	$0.544565\pi$
$762$	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	−1.87207	−	3.24252i
$773$	12116.6	−	20986.6i	0.563784	−	0.976503i	−0.433377	−	0.901213i	$-0.642678\pi$
$773$	12116.6	−	20986.6i	0.563784	−	0.976503i	0.997162	−	0.0752907i	$-0.0239885\pi$
$774$	161.507	−	279.738i	0.00750031	−	0.0129909i
$775$	1998.93	+	3462.26i	0.0926501	+	0.160475i
$776$	−90186.0			−4.17202
$777$		0			0
$778$	−15412.4			−0.710231
$779$	−9910.32	−	17165.2i	−0.455807	−	0.789481i
$780$	11701.5	−	20267.6i	0.537155	−	0.930381i
$781$	−6320.05	+	10946.6i	−0.289564	+	0.501539i
$782$	3487.75	+	6040.97i	0.159491	+	0.276246i
$783$	−955.854			−0.0436263
$784$		0			0
$785$	32860.5			1.49406
$786$	3723.65	+	6449.56i	0.168980	+	0.292682i
$787$	8600.19	−	14896.0i	0.389535	−	0.674694i	−0.602852	−	0.797853i	$-0.705969\pi$
$787$	8600.19	−	14896.0i	0.389535	−	0.674694i	0.992387	+	0.123159i	$0.0393026\pi$
$788$	28496.4	−	49357.2i	1.28825	−	2.23131i
$789$	−3065.67	−	5309.90i	−0.138328	−	0.239591i
$790$	38603.6			1.73855
$791$		0			0
$792$	−19507.2			−0.875199
$793$	1077.83	+	1866.86i	0.0482659	+	0.0835990i
$794$	2141.46	−	3709.12i	0.0957148	−	0.165783i
$795$	8496.31	−	14716.0i	0.379035	−	0.656509i
$796$	30401.0	+	52656.0i	1.35369	+	2.34465i
$797$	−4208.87			−0.187059			−0.0935295	−	0.995617i	$-0.529815\pi$
$797$	−4208.87			−0.187059			−0.0935295	+	0.995617i	$0.529815\pi$
$798$		0			0
$799$	−2644.78			−0.117104
$800$	−2739.99	−	4745.80i	−0.121092	−	0.209737i
$801$	1588.67	−	2751.66i	0.0700786	−	0.121380i
$802$	6168.05	−	10683.4i	0.271573	−	0.470378i
$803$	−10099.8	−	17493.4i	−0.443855	−	0.768779i
$804$	28648.2			1.25665
$805$		0			0
$806$	57410.2			2.50892
$807$	−5179.25	−	8970.73i	−0.225921	−	0.391307i
$808$	14809.4	−	25650.6i	0.644791	−	1.11681i
$809$	11816.1	−	20466.0i	0.513511	−	0.889428i	−0.486366	−	0.873755i	$-0.661678\pi$
$809$	11816.1	−	20466.0i	0.513511	−	0.889428i	0.999877	−	0.0156725i	$-0.00498890\pi$
$810$	2253.80	+	3903.70i	0.0977662	+	0.169336i
$811$	28425.1			1.23075			0.615377	−	0.788233i	$-0.289004\pi$
$811$	28425.1			1.23075			0.615377	+	0.788233i	$0.289004\pi$
$812$		0			0
$813$	7932.88			0.342212
$814$	−23819.4	−	41256.5i	−1.02564	−	1.77646i
$815$	−12728.8	+	22046.9i	−0.547079	+	0.947568i
$816$	2696.90	−	4671.16i	0.115699	−	0.200396i
$817$	199.350	+	345.284i	0.00853655	+	0.0147857i
$818$	14387.7			0.614981
$819$		0			0
$820$	−70743.7			−3.01278
$821$	−19704.8	−	34129.7i	−0.837640	−	1.45083i	−0.891863	−	0.452306i	$-0.850601\pi$
$821$	−19704.8	−	34129.7i	−0.837640	−	1.45083i	0.0542229	−	0.998529i	$-0.482732\pi$
$822$	−3512.38	+	6083.63i	−0.149037	+	0.258140i
$823$	−8173.28	+	14156.5i	−0.346176	+	0.599594i	−0.985567	−	0.169288i	$-0.945853\pi$
$823$	−8173.28	+	14156.5i	−0.346176	+	0.599594i	0.639391	+	0.768882i	$0.279187\pi$
$824$	−62361.7	−	108014.i	−2.63650	−	4.56655i
$825$	−1428.29			−0.0602749
$826$		0			0
$827$	−3738.87			−0.157211			−0.0786054	−	0.996906i	$-0.525047\pi$
$827$	−3738.87			−0.157211			−0.0786054	+	0.996906i	$0.525047\pi$
$828$	11182.4	+	19368.5i	0.469342	+	0.812924i
$829$	22598.1	−	39141.1i	0.946761	−	1.63984i	0.194575	−	0.980888i	$-0.437667\pi$
$829$	22598.1	−	39141.1i	0.946761	−	1.63984i	0.752186	−	0.658951i	$-0.228999\pi$
$830$	37129.1	−	64309.5i	1.55274	−	2.68942i
$831$	−4019.23	−	6961.51i	−0.167780	−	0.290604i
$832$	−27840.8			−1.16010
$833$		0			0
$834$	−26427.0			−1.09723
$835$	3220.21	+	5577.56i	0.133461	+	0.231161i
$836$	20183.9	−	34959.5i	0.835018	−	1.44629i
$837$	−3939.22	+	6822.93i	−0.162675	+	0.281762i
$838$	35094.8	+	60785.9i	1.44669	+	2.50574i
$839$	15899.7			0.654254			0.327127	−	0.944980i	$-0.393920\pi$
$839$	15899.7			0.654254			0.327127	+	0.944980i	$0.393920\pi$
$840$		0			0
$841$	−23135.7			−0.948612
$842$	−29031.7	−	50284.4i	−1.18824	−	2.05809i
$843$	1529.54	−	2649.24i	0.0624911	−	0.108238i
$844$	−5902.05	+	10222.6i	−0.240707	+	0.416917i
$845$	4250.44	+	7361.99i	0.173041	+	0.299716i
$846$	−11901.5			−0.483668
$847$		0			0
$848$	−91500.0			−3.70534
$849$	−648.309	−	1122.90i	−0.0262072	−	0.0453922i
$850$	381.227	−	660.304i	0.0153835	−	0.0266450i
$851$	−16288.7	+	28212.8i	−0.656133	+	1.13645i
$852$	−10817.0	−	18735.5i	−0.434956	−	0.753366i
$853$	33926.7			1.36182			0.680908	−	0.732369i	$-0.261585\pi$
$853$	33926.7			1.36182			0.680908	+	0.732369i	$0.261585\pi$
$854$		0			0
$855$	−5563.79			−0.222547
$856$	36387.3	+	63024.7i	1.45291	+	2.51652i
$857$	17716.2	−	30685.4i	0.706154	−	1.22310i	−0.260119	−	0.965577i	$-0.583762\pi$
$857$	17716.2	−	30685.4i	0.706154	−	1.22310i	0.966273	−	0.257519i	$-0.0829049\pi$
$858$	−10255.3	+	17762.7i	−0.408054	+	0.706770i
$859$	3390.09	+	5871.80i	0.134655	+	0.233229i	0.925465	−	0.378832i	$-0.123674\pi$
$859$	3390.09	+	5871.80i	0.134655	+	0.233229i	−0.790811	+	0.612061i	$0.790341\pi$
$860$	1423.04			0.0564246
$861$		0			0
$862$	34422.1			1.36012
$863$	15337.5	+	26565.4i	0.604977	+	1.04785i	0.992055	+	0.125805i	$0.0401512\pi$
$863$	15337.5	+	26565.4i	0.604977	+	1.04785i	−0.387078	+	0.922047i	$0.626515\pi$
$864$	5399.59	−	9352.36i	0.212613	−	0.368257i
$865$	−20012.0	+	34661.9i	−0.786624	+	1.36247i
$866$	−30901.2	−	53522.5i	−1.21255	−	2.10019i
$867$	−14405.1			−0.564271
$868$		0			0
$869$	−24105.2			−0.940981
$870$	−2955.15	−	5118.48i	−0.115160	−	0.199463i
$871$	8983.30	−	15559.5i	0.349469	−	0.605298i
$872$	−41702.9	+	72231.5i	−1.61954	+	2.80512i
$873$	−6506.45	−	11269.5i	−0.252245	−	0.436901i
$874$	−38744.8			−1.49950
$875$		0			0
$876$	34572.3			1.33344
$877$	−20430.6	−	35386.9i	−0.786652	−	1.36252i	−0.928007	−	0.372562i	$-0.878479\pi$
$877$	−20430.6	−	35386.9i	−0.786652	−	1.36252i	0.141355	−	0.989959i	$-0.454854\pi$
$878$	−38536.9	+	66747.9i	−1.48127	+	2.56564i
$879$	3368.88	−	5835.07i	0.129271	−	0.223904i
$880$	−31238.3	−	54106.4i	−1.19664	−	2.07264i
$881$	−43839.0			−1.67647			−0.838236	−	0.545308i	$-0.816413\pi$
$881$	−43839.0			−1.67647			−0.838236	+	0.545308i	$0.816413\pi$
$882$		0			0
$883$	44625.1			1.70074			0.850371	−	0.526183i	$-0.176377\pi$
$883$	44625.1			1.70074			0.850371	+	0.526183i	$0.176377\pi$
$884$	−3900.50	−	6755.87i	−0.148403	−	0.257041i
$885$	567.957	−	983.730i	0.0215725	−	0.0373646i
$886$	−40194.3	+	69618.6i	−1.52410	+	2.63982i
$887$	21983.7	+	38076.9i	0.832178	+	1.44137i	0.896308	+	0.443433i	$0.146239\pi$
$887$	21983.7	+	38076.9i	0.832178	+	1.44137i	−0.0641300	+	0.997942i	$0.520427\pi$
$888$	48632.9			1.83785
$889$		0			0
$890$	19646.4			0.739943
$891$	−1407.34	−	2437.59i	−0.0529155	−	0.0916523i
$892$	37466.7	−	64894.3i	1.40637	−	2.43590i
$893$	7345.10	−	12722.1i	0.275246	−	0.476739i
$894$	5885.78	+	10194.5i	0.220190	+	0.381381i
$895$	−29588.9			−1.10508
$896$		0			0
$897$	14026.0			0.522089
$898$	28164.9	+	48783.0i	1.04663	+	1.81282i
$899$	5165.04	−	8946.12i	0.191617	−	0.331891i
$900$	1222.28	−	2117.06i	0.0452698	−	0.0784096i
$901$	−2832.10	−	4905.35i	−0.104718	−	0.181377i
$902$	62000.4			2.28868
$903$		0			0
$904$	−56547.4			−2.08046
$905$	−16384.1	−	28378.1i	−0.601797	−	1.04234i
$906$	4800.95	−	8315.48i	0.176049	−	0.304927i
$907$	6792.15	−	11764.3i	0.248654	−	0.430682i	−0.714498	−	0.699637i	$-0.753345\pi$
$907$	6792.15	−	11764.3i	0.248654	−	0.430682i	0.963153	+	0.268955i	$0.0866783\pi$
$908$	−18116.0	−	31377.9i	−0.662117	−	1.14682i
$909$	4273.67			0.155939
$910$		0			0
$911$	−16421.6			−0.597226			−0.298613	−	0.954374i	$-0.596524\pi$
$911$	−16421.6			−0.597226			−0.298613	+	0.954374i	$0.596524\pi$
$912$	14979.7	+	25945.5i	0.543888	+	0.942042i
$913$	−23184.5	+	40156.7i	−0.840411	+	1.45563i
$914$	11151.8	−	19315.5i	0.403576	−	0.699014i
$915$	−914.576	−	1584.09i	−0.0330437	−	0.0572333i
$916$	−16856.0			−0.608010
$917$		0			0
$918$	1502.54			0.0540208
$919$	14743.6	+	25536.7i	0.529214	+	0.916625i	0.999420	+	0.0340684i	$0.0108464\pi$
$919$	14743.6	+	25536.7i	0.529214	+	0.916625i	−0.470206	+	0.882557i	$0.655820\pi$
$920$	−41241.8	+	71432.9i	−1.47794	+	2.55986i
$921$	4795.62	−	8306.25i	0.171575	−	0.297177i
$922$	2400.41	+	4157.63i	0.0857410	+	0.148508i
$923$	−13567.6			−0.483839
$924$		0			0
$925$	3560.85			0.126573
$926$	11752.9	+	20356.7i	0.417090	+	0.722422i
$927$	8998.15	−	15585.2i	0.318811	−	0.552197i
$928$	−7079.85	+	12262.7i	−0.250439	+	0.433773i
$929$	−1720.93	−	2980.73i	−0.0607769	−	0.105269i	0.834036	−	0.551710i	$-0.186024\pi$
$929$	−1720.93	−	2980.73i	−0.0607769	−	0.105269i	−0.894813	+	0.446441i	$0.852691\pi$
$930$	−48714.6			−1.71765
$931$		0			0
$932$	−130667.			−4.59242
$933$	5033.41	+	8718.12i	0.176620	+	0.305915i
$934$	−11682.4	+	20234.6i	−0.409273	+	0.708881i
$935$	1933.77	−	3349.40i	0.0676376	−	0.117152i
$936$	−10469.3	−	18133.4i	−0.365598	−	0.633234i
$937$	5646.60			0.196869			0.0984346	−	0.995144i	$-0.468616\pi$
$937$	5646.60			0.196869			0.0984346	+	0.995144i	$0.468616\pi$
$938$		0			0
$939$	−6769.18			−0.235254
$940$	−26216.1	−	45407.6i	−0.909654	−	1.57557i
$941$	22340.1	−	38694.1i	0.773927	−	1.34048i	−0.161469	−	0.986878i	$-0.551623\pi$
$941$	22340.1	−	38694.1i	0.773927	−	1.34048i	0.935396	−	0.353603i	$-0.115044\pi$
$942$	24645.3	−	42687.0i	0.852430	−	1.47645i
$943$	−21199.2	−	36718.1i	−0.732068	−	1.26798i
$944$	−6116.54			−0.210886
$945$		0			0
$946$	−1247.16			−0.0428633
$947$	24462.3	+	42369.9i	0.839406	+	1.45389i	0.890392	+	0.455195i	$0.150430\pi$
$947$	24462.3	+	42369.9i	0.839406	+	1.45389i	−0.0509860	+	0.998699i	$0.516236\pi$
$948$	20628.4	−	35729.4i	0.706729	−	1.22409i
$949$	10840.9	−	18777.1i	0.370824	−	0.642286i
$950$	2117.49	+	3667.59i	0.0723161	+	0.125255i
$951$	−18417.6			−0.628002
$952$		0			0
$953$	52014.3			1.76801			0.884003	−	0.467482i	$-0.154839\pi$
$953$	52014.3			1.76801			0.884003	+	0.467482i	$0.154839\pi$
$954$	−12744.5	−	22074.1i	−0.432513	−	0.749135i
$955$	−1381.77	+	2393.30i	−0.0468201	+	0.0810947i
$956$	1809.57	−	3134.26i	0.0612193	−	0.106035i
$957$	1845.28	+	3196.13i	0.0623298	+	0.107958i
$958$	−14521.1			−0.489723
$959$		0			0
$960$	23623.9			0.794228
$961$	−27676.4	−	47936.9i	−0.929018	−	1.60911i
$962$	25567.3	−	44283.8i	0.856883	−	1.48417i
$963$	−5250.31	+	9093.81i	−0.175689	+	0.304303i
$964$	−15105.4	−	26163.4i	−0.504682	−	0.874135i
$965$	42738.2			1.42569
$966$		0			0
$967$	−47117.7			−1.56691			−0.783456	−	0.621448i	$-0.786545\pi$
$967$	−47117.7			−1.56691			−0.783456	+	0.621448i	$0.786545\pi$
$968$	−3851.48	−	6670.95i	−0.127883	−	0.221501i
$969$	−927.299	+	1606.13i	−0.0307421	+	0.0532470i
$970$	40231.2	−	69682.4i	1.33170	−	2.30657i
$971$	4097.52	+	7097.12i	0.135423	+	0.234560i	0.925759	−	0.378114i	$-0.123427\pi$
$971$	4097.52	+	7097.12i	0.135423	+	0.234560i	−0.790336	+	0.612674i	$0.790094\pi$
$972$	4817.41			0.158970
$973$		0			0
$974$	3537.35			0.116370
$975$	−766.550	−	1327.70i	−0.0251787	−	0.0436108i
$976$	−4924.71	+	8529.85i	−0.161512	+	0.279748i
$977$	−2321.76	+	4021.40i	−0.0760282	+	0.131685i	−0.901533	−	0.432710i	$-0.857557\pi$
$977$	−2321.76	+	4021.40i	−0.0760282	+	0.131685i	0.825505	+	0.564395i	$0.190891\pi$
$978$	19093.1	+	33070.3i	0.624265	+	1.08126i
$979$	−12267.8			−0.400490
$980$		0			0
$981$	−12034.6			−0.391677
$982$	−21745.1	−	37663.6i	−0.706632	−	1.22392i
$983$	−21993.3	+	38093.4i	−0.713607	+	1.23600i	0.249887	+	0.968275i	$0.419607\pi$
$983$	−21993.3	+	38093.4i	−0.713607	+	1.23600i	−0.963494	+	0.267729i	$0.913727\pi$
$984$	−31647.1	+	54814.3i	−1.02528	+	1.77583i
$985$	15164.5	+	26265.6i	0.490538	+	0.849638i
$986$	−1970.10			−0.0636317
$987$		0			0
$988$	43329.9			1.39525
$989$	426.429	+	738.598i	0.0137105	+	0.0237473i
$990$	8701.98	−	15072.3i	0.279361	−	0.483867i
$991$	−797.604	+	1381.49i	−0.0255668	+	0.0442831i	−0.878526	−	0.477695i	$-0.841472\pi$
$991$	−797.604	+	1381.49i	−0.0255668	+	0.0442831i	0.852959	+	0.521978i	$0.174806\pi$
$992$	58354.3	+	101073.i	1.86769	+	3.23494i
$993$	21089.4			0.673971
$994$		0			0
$995$	−32356.0			−1.03091
$996$	−39681.0	−	68729.5i	−1.26239	−	2.18652i
$997$	−10750.6	+	18620.6i	−0.341499	+	0.591494i	−0.984711	−	0.174194i	$-0.944268\pi$
$997$	−10750.6	+	18620.6i	−0.341499	+	0.591494i	0.643212	+	0.765688i	$0.277601\pi$
$998$	21534.6	−	37299.0i	0.683032	−	1.18305i
$999$	3508.61	+	6077.09i	0.111119	+	0.192463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.l.67.2		4
3.2	odd	2		441.4.e.q.361.1		4
7.2	even	3	inner	147.4.e.l.79.2		4
7.3	odd	6		147.4.a.i.1.1		2
7.4	even	3		21.4.a.c.1.1	✓	2
7.5	odd	6		147.4.e.m.79.2		4
7.6	odd	2		147.4.e.m.67.2		4
21.2	odd	6		441.4.e.q.226.1		4
21.5	even	6		441.4.e.p.226.1		4
21.11	odd	6		63.4.a.e.1.2		2
21.17	even	6		441.4.a.r.1.2		2
21.20	even	2		441.4.e.p.361.1		4
28.3	even	6		2352.4.a.bz.1.1		2
28.11	odd	6		336.4.a.m.1.2		2
35.4	even	6		525.4.a.n.1.2		2
35.18	odd	12		525.4.d.g.274.4		4
35.32	odd	12		525.4.d.g.274.1		4
56.11	odd	6		1344.4.a.bo.1.1		2
56.53	even	6		1344.4.a.bg.1.1		2
84.11	even	6		1008.4.a.ba.1.1		2
105.74	odd	6		1575.4.a.p.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.c.1.1	✓	2	7.4	even	3
63.4.a.e.1.2		2	21.11	odd	6
147.4.a.i.1.1		2	7.3	odd	6
147.4.e.l.67.2		4	1.1	even	1	trivial
147.4.e.l.79.2		4	7.2	even	3	inner
147.4.e.m.67.2		4	7.6	odd	2
147.4.e.m.79.2		4	7.5	odd	6
336.4.a.m.1.2		2	28.11	odd	6
441.4.a.r.1.2		2	21.17	even	6
441.4.e.p.226.1		4	21.5	even	6
441.4.e.p.361.1		4	21.20	even	2
441.4.e.q.226.1		4	21.2	odd	6
441.4.e.q.361.1		4	3.2	odd	2
525.4.a.n.1.2		2	35.4	even	6
525.4.d.g.274.1		4	35.32	odd	12
525.4.d.g.274.4		4	35.18	odd	12
1008.4.a.ba.1.1		2	84.11	even	6
1344.4.a.bg.1.1		2	56.53	even	6
1344.4.a.bo.1.1		2	56.11	odd	6
1575.4.a.p.1.1		2	105.74	odd	6
2352.4.a.bz.1.1		2	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
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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