LMFDB - Embedded newform 147.4.e.m.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.m.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	0.999480	−	0.0322587i	$-0.0102700\pi$
$5$	5.27492	+	9.13642i	0.471803	+	0.817187i	−0.527677	+	0.849445i	$0.676937\pi$
$6$	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	$-0.369746\pi$
$13$	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	−0.901198	−	0.433408i	$-0.857311\pi$
$17$	−5.27492	+	9.13642i	−0.0752562	+	0.130348i	0.825941	+	0.563756i	$0.190644\pi$
$18$	23.7371	−	41.1139i	0.310827	−	0.538369i
$19$	−29.2990	−	50.7474i	−0.353771	−	0.612750i	0.633136	−	0.774041i	$-0.281768\pi$
$19$	−29.2990	−	50.7474i	−0.353771	−	0.612750i	−0.986907	+	0.161291i	$0.948434\pi$
$20$	−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	$-0.512763\pi$
$31$	145.897	−	252.701i	0.845286	−	1.46408i	0.885372	−	0.464883i	$-0.153904\pi$
$32$	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	$-0.277185\pi$
$41$	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	0.992317	−	0.123717i	$-0.0394816\pi$
$47$	125.347	+	217.108i	0.389016	+	0.673796i	−0.603301	+	0.797513i	$0.706148\pi$
$48$	−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	−0.885145	−	0.465315i	$-0.845941\pi$
$59$	−17.9452	+	31.0820i	−0.0395977	+	0.0685853i	0.845547	+	0.533900i	$0.179274\pi$
$60$	−313.722	+	543.382i	−0.675022	+	1.16917i
$61$	28.8970	+	50.0511i	0.0606538	+	0.105056i	0.894758	−	0.446552i	$-0.147348\pi$
$61$	28.8970	+	50.0511i	0.0606538	+	0.105056i	−0.834104	+	0.551607i	$0.814015\pi$
$62$	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	−0.533247	−	0.845960i	$-0.679028\pi$
$73$	290.650	−	503.420i	0.465999	−	0.807135i	0.999246	+	0.0388253i	$0.0123616\pi$
$74$	−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	$-0.844033\pi$
$83$	−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	0.741552	−	0.670895i	$-0.234090\pi$
$89$	−176.519	−	305.740i	−0.210236	−	0.364139i	−0.951788	+	0.306756i	$0.900757\pi$
$90$	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	−0.725046	−	0.688700i	$-0.758182\pi$
$101$	237.426	−	411.234i	0.233909	−	0.405142i	0.958955	+	0.283558i	$0.0915150\pi$
$102$	−83.4743	+	144.582i	−0.0810312	+	0.140350i
$103$	−999.794	−	1731.69i	−0.956433	−	1.65659i	−0.731053	−	0.682320i	$-0.760971\pi$
$103$	−999.794	−	1731.69i	−0.956433	−	1.65659i	−0.225380	−	0.974271i	$-0.572362\pi$
$104$	−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	0.933763	−	0.357893i	$-0.116505\pi$
$131$	235.306	+	407.561i	0.156937	+	0.271823i	−0.776826	+	0.629716i	$0.783171\pi$
$132$	−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	$-0.670176\pi$
$139$	−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	0.745475	−	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	$-0.542541\pi$
$157$	1557.39	−	2697.48i	0.791678	−	1.37123i	0.924927	−	0.380144i	$-0.124125\pi$
$158$	−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	$-0.454828\pi$
$167$	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	0.895136	+	0.445792i	$0.147078\pi$
$173$	1896.90	+	3285.54i	0.833636	+	1.44390i	−0.0615006	+	0.998107i	$0.519589\pi$
$174$	−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	$-0.720140\pi$
$181$	−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	0.840150	−	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	$0.350616\pi$
$199$	−1533.49	+	2656.07i	−0.546261	+	0.946151i	−0.998526	+	0.0542680i	$0.982717\pi$
$200$	−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	−0.700947	−	0.713214i	$-0.747239\pi$
$227$	913.809	−	1582.76i	0.267188	−	0.462783i	0.968135	+	0.250431i	$0.0805722\pi$
$228$	1742.54	−	3018.16i	0.506150	−	0.876678i
$229$	−425.125	−	736.338i	−0.122677	−	0.212483i	0.798146	−	0.602465i	$-0.205815\pi$
$229$	−425.125	−	736.338i	−0.122677	−	0.212483i	−0.920823	+	0.389982i	$0.872481\pi$
$230$	−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	−0.746047	−	0.665894i	$-0.768050\pi$
$241$	761.949	−	1319.73i	0.203657	−	0.352745i	0.949704	+	0.313149i	$0.101384\pi$
$242$	−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	0.983997	−	0.178185i	$-0.0570224\pi$
$257$	1391.27	+	2409.76i	0.337686	+	0.584890i	−0.646311	+	0.763074i	$0.723689\pi$
$258$	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	−0.601315	−	0.799012i	$-0.705356\pi$
$269$	1726.42	−	2990.24i	0.391307	−	0.677763i	0.992622	+	0.121248i	$0.0386898\pi$
$270$	751.268	−	1301.23i	0.169336	−	0.293299i
$271$	1322.15	+	2290.02i	0.296364	+	0.513318i	0.975301	−	0.220879i	$-0.0708925\pi$
$271$	1322.15	+	2290.02i	0.296364	+	0.513318i	−0.678937	+	0.734196i	$0.737559\pi$
$272$	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	−0.842437	−	0.538795i	$-0.818880\pi$
$283$	216.103	−	374.301i	0.0453922	−	0.0786216i	0.887829	+	0.460174i	$0.152213\pi$
$284$	−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	−0.977465	−	0.211100i	$-0.932296\pi$
$311$	−1677.80	+	2906.04i	−0.305915	+	0.529860i	0.671550	+	0.740959i	$0.265629\pi$
$312$	−3489.77	+	6044.45i	−0.633234	+	1.09679i
$313$	−1128.20	−	1954.09i	−0.203736	−	0.352881i	0.745993	−	0.665954i	$-0.231975\pi$
$313$	−1128.20	−	1954.09i	−0.203736	−	0.352881i	−0.949729	+	0.313072i	$0.898642\pi$
$314$	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	$-0.391337\pi$
$349$	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	−0.998841	−	0.0481389i	$-0.984671\pi$
$353$	−3035.79	+	5258.15i	−0.457731	+	0.792813i	0.541110	+	0.840952i	$0.318004\pi$
$354$	−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	−0.846840	−	0.531848i	$-0.821498\pi$
$367$	261.362	−	452.693i	0.0371744	−	0.0643879i	0.884014	+	0.467460i	$0.154831\pi$
$368$	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	$-0.768894\pi$
$383$	−7112.22	−	12318.7i	−0.948871	−	1.64349i	−0.201063	−	0.979578i	$-0.564439\pi$
$384$	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	0.890545	−	0.454894i	$-0.150323\pi$
$397$	405.970	+	703.161i	0.0513226	+	0.0888933i	−0.839223	+	0.543788i	$0.816990\pi$
$398$	−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	−0.936612	−	0.350369i	$-0.886056\pi$
$409$	−1363.79	+	2362.15i	−0.164877	+	0.285576i	0.771734	+	0.635945i	$0.219390\pi$
$410$	−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	−0.624070	−	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	$-0.274697\pi$
$433$	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	−0.923306	−	0.384066i	$-0.874524\pi$
$439$	−7305.69	−	12653.8i	−0.794264	−	1.37571i	0.129042	−	0.991639i	$-0.458810\pi$
$440$	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	$-0.514639\pi$
$461$	−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	0.735188	−	0.677864i	$-0.237094\pi$
$467$	−2214.71	−	3835.99i	−0.219453	−	0.380104i	−0.954641	+	0.297759i	$0.903761\pi$
$468$	6654.99			0.657323
$469$		0			0
$470$	−13951.0			−1.36918
$471$	−4672.18	−	8092.45i	−0.457075	−	0.791678i
$472$	1119.32	−	1938.73i	0.109155	−	0.189062i
$473$	−118.216	+	204.757i	−0.0114917	+	0.0199043i
$474$	5488.74	+	9506.78i	0.531870	+	0.921226i
$475$	−802.851			−0.0775523
$476$		0			0
$477$	−4832.10			−0.463830
$478$	−481.485	−	833.957i	−0.0460724	−	0.0797998i
$479$	1376.43	−	2384.04i	0.131296	−	0.227411i	−0.792881	−	0.609377i	$-0.791420\pi$
$479$	1376.43	−	2384.04i	0.131296	−	0.227411i	0.924176	+	0.381966i	$0.124753\pi$
$480$	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	$-0.618028\pi$
$503$	−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	0.846268	−	0.532758i	$-0.178844\pi$
$509$	−439.224	−	760.758i	−0.0382480	−	0.0662475i	−0.884516	+	0.466510i	$0.845511\pi$
$510$	−1761.28			−0.152923
$511$		0			0
$512$	16876.5			1.45673
$513$	791.073	+	1370.18i	0.0680833	+	0.117924i
$514$	−7338.86	+	12711.3i	−0.629773	+	1.09080i
$515$	10547.7	−	18269.1i	0.902496	−	1.56317i
$516$	202.331	+	350.447i	0.0172618	+	0.0298984i
$517$	−8711.42			−0.741060
$518$		0			0
$519$	11381.4			0.962600
$520$	−12272.1	−	21256.0i	−1.03494	−	1.79257i
$521$	5856.30	−	10143.4i	0.492455	−	0.852957i	−0.507507	−	0.861647i	$-0.669433\pi$
$521$	5856.30	−	10143.4i	0.492455	−	0.852957i	0.999962	+	0.00869048i	$0.00276630\pi$
$522$	−840.341	+	1455.51i	−0.0704612	+	0.122042i
$523$	−3670.91	−	6358.20i	−0.306917	−	0.531596i	0.670769	−	0.741666i	$-0.265964\pi$
$523$	−3670.91	−	6358.20i	−0.306917	−	0.531596i	−0.977686	+	0.210070i	$0.932631\pi$
$524$	−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	−0.814549	−	0.580094i	$-0.803016\pi$
$563$	1270.43	−	2200.45i	0.0951017	−	0.164721i	0.909651	+	0.415373i	$0.136349\pi$
$564$	−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	−0.609496	−	0.792789i	$-0.708628\pi$
$577$	5292.13	−	9166.24i	0.381827	−	0.661344i	0.991324	+	0.131445i	$0.0419616\pi$
$578$	−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	−0.999305	−	0.0372786i	$-0.988131\pi$
$593$	−7681.43	−	13304.6i	−0.531937	−	0.921341i	0.467368	−	0.884063i	$-0.345202\pi$
$594$	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	$-0.745918\pi$
$601$	−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	0.981462	+	0.191657i	$0.0613862\pi$
$607$	9821.04	+	17010.5i	0.656711	+	1.13746i	−0.324751	+	0.945800i	$0.605280\pi$
$608$	−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	−0.897205	−	0.441615i	$-0.854406\pi$
$619$	−1018.78	+	1764.58i	−0.0661523	+	0.114579i	0.831052	+	0.556194i	$0.187739\pi$
$620$	−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	$-0.488169\pi$
$643$	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	−0.905643	−	0.424040i	$-0.860612\pi$
$647$	−1408.61	+	2439.78i	−0.0855922	+	0.148250i	0.820051	+	0.572290i	$0.193945\pi$
$648$	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	−0.955697	−	0.294353i	$-0.904896\pi$
$661$	−3788.55	+	6561.96i	−0.222931	+	0.386128i	0.732766	+	0.680481i	$0.238229\pi$
$662$	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	$0.202692\pi$
$677$	16152.1	+	27976.3i	0.916952	+	1.58821i	0.112935	+	0.993602i	$0.463975\pi$
$678$	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	0.851304	−	0.524674i	$-0.175813\pi$
$691$	−521.837	−	903.849i	−0.0287288	−	0.0497598i	−0.880032	+	0.474914i	$0.842479\pi$
$692$	−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	0.970770	−	0.240010i	$-0.0771506\pi$
$719$	5350.62	+	9267.55i	0.277531	+	0.480697i	−0.693240	+	0.720707i	$0.743817\pi$
$720$	−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	−0.998681	−	0.0513484i	$-0.983648\pi$
$733$	−10792.0	−	18692.3i	−0.543809	−	0.941906i	0.454871	−	0.890557i	$-0.349685\pi$
$734$	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	$-0.877898\pi$
$761$	−16537.9	−	28644.5i	−0.787778	−	1.36447i	0.139547	−	0.990215i	$-0.455435\pi$
$762$	−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
$773$	−12116.6	+	20986.6i	−0.563784	+	0.976503i	0.433377	+	0.901213i	$0.357322\pi$
$773$	−12116.6	+	20986.6i	−0.563784	+	0.976503i	−0.997162	+	0.0752907i	$0.976012\pi$
$774$	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	−0.992387	−	0.123159i	$-0.960697\pi$
$787$	−8600.19	+	14896.0i	−0.389535	+	0.674694i	0.602852	+	0.797853i	$0.294031\pi$
$788$	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	$-0.470185\pi$
$797$	4208.87			0.187059			0.0935295	+	0.995617i	$0.470185\pi$
$798$		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	$-0.710996\pi$
$811$	−28425.1			−1.23075			−0.615377	+	0.788233i	$0.710996\pi$
$812$		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	$0.562333\pi$
$829$	−22598.1	+	39141.1i	−0.946761	+	1.63984i	−0.752186	+	0.658951i	$0.771001\pi$
$830$	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	$-0.606080\pi$
$839$	−15899.7			−0.654254			−0.327127	+	0.944980i	$0.606080\pi$
$840$		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	$-0.738415\pi$
$853$	−33926.7			−1.36182			−0.680908	+	0.732369i	$0.738415\pi$
$854$		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	$0.416238\pi$
$857$	−17716.2	+	30685.4i	−0.706154	+	1.22310i	−0.966273	+	0.257519i	$0.917095\pi$
$858$	−10255.3	+	17762.7i	−0.408054	+	0.706770i
$859$	−3390.09	−	5871.80i	−0.134655	−	0.233229i	0.790811	−	0.612061i	$-0.209659\pi$
$859$	−3390.09	−	5871.80i	−0.134655	−	0.233229i	−0.925465	+	0.378832i	$0.876326\pi$
$860$	−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	$-0.183587\pi$
$881$	43839.0			1.67647			0.838236	+	0.545308i	$0.183587\pi$
$882$		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	$-0.853761\pi$
$887$	−21983.7	−	38076.9i	−0.832178	−	1.44137i	0.0641300	−	0.997942i	$-0.479573\pi$
$888$	−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	0.894813	−	0.446441i	$-0.147309\pi$
$929$	1720.93	+	2980.73i	0.0607769	+	0.105269i	−0.834036	+	0.551710i	$0.813976\pi$
$930$	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	$-0.531384\pi$
$937$	−5646.60			−0.196869			−0.0984346	+	0.995144i	$0.531384\pi$
$938$		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	$0.448377\pi$
$941$	−22340.1	+	38694.1i	−0.773927	+	1.34048i	−0.935396	+	0.353603i	$0.884956\pi$
$942$	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	0.790336	−	0.612674i	$-0.209906\pi$
$971$	−4097.52	−	7097.12i	−0.135423	−	0.234560i	−0.925759	+	0.378114i	$0.876573\pi$
$972$	−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	$-0.580393\pi$
$983$	21993.3	−	38093.4i	0.713607	−	1.23600i	0.963494	−	0.267729i	$-0.0862732\pi$
$984$	−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	−0.643212	−	0.765688i	$-0.722399\pi$
$997$	10750.6	−	18620.6i	0.341499	−	0.591494i	0.984711	+	0.174194i	$0.0557321\pi$
$998$	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.m.67.2		4
3.2	odd	2		441.4.e.p.361.1		4
7.2	even	3	inner	147.4.e.m.79.2		4
7.3	odd	6		21.4.a.c.1.1	✓	2
7.4	even	3		147.4.a.i.1.1		2
7.5	odd	6		147.4.e.l.79.2		4
7.6	odd	2		147.4.e.l.67.2		4
21.2	odd	6		441.4.e.p.226.1		4
21.5	even	6		441.4.e.q.226.1		4
21.11	odd	6		441.4.a.r.1.2		2
21.17	even	6		63.4.a.e.1.2		2
21.20	even	2		441.4.e.q.361.1		4
28.3	even	6		336.4.a.m.1.2		2
28.11	odd	6		2352.4.a.bz.1.1		2
35.3	even	12		525.4.d.g.274.4		4
35.17	even	12		525.4.d.g.274.1		4
35.24	odd	6		525.4.a.n.1.2		2
56.3	even	6		1344.4.a.bo.1.1		2
56.45	odd	6		1344.4.a.bg.1.1		2
84.59	odd	6		1008.4.a.ba.1.1		2
105.59	even	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	7.3	odd	6
63.4.a.e.1.2		2	21.17	even	6
147.4.a.i.1.1		2	7.4	even	3
147.4.e.l.67.2		4	7.6	odd	2
147.4.e.l.79.2		4	7.5	odd	6
147.4.e.m.67.2		4	1.1	even	1	trivial
147.4.e.m.79.2		4	7.2	even	3	inner
336.4.a.m.1.2		2	28.3	even	6
441.4.a.r.1.2		2	21.11	odd	6
441.4.e.p.226.1		4	21.2	odd	6
441.4.e.p.361.1		4	3.2	odd	2
441.4.e.q.226.1		4	21.5	even	6
441.4.e.q.361.1		4	21.20	even	2
525.4.a.n.1.2		2	35.24	odd	6
525.4.d.g.274.1		4	35.17	even	12
525.4.d.g.274.4		4	35.3	even	12
1008.4.a.ba.1.1		2	84.59	odd	6
1344.4.a.bg.1.1		2	56.45	odd	6
1344.4.a.bo.1.1		2	56.3	even	6
1575.4.a.p.1.1		2	105.59	even	6
2352.4.a.bz.1.1		2	28.11	odd	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more