LMFDB - Embedded newform 147.4.e.n.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 $ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.124036 - 0.214837i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.n.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.124036 + 0.214837i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(-6.21730 + 10.7687i) q^{5} +0.744216 q^{6} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-0.124036 + 0.214837i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(-6.21730 + 10.7687i) q^{5} +0.744216 q^{6} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-1.54234 - 2.67141i) q^{10} +(-30.1558 - 52.2313i) q^{11} +(11.9077 - 20.6247i) q^{12} -36.4269 q^{13} +37.3038 q^{15} +(-31.2634 + 54.1498i) q^{16} +(-24.3731 - 42.2154i) q^{17} +(-1.11632 - 1.93353i) q^{18} +(-25.2750 + 43.7776i) q^{19} -98.7116 q^{20} +14.9616 q^{22} +(-69.3962 + 120.198i) q^{23} +(5.93083 + 10.2725i) q^{24} +(-14.8097 - 25.6511i) q^{25} +(4.51824 - 7.82583i) q^{26} +27.0000 q^{27} -61.1345 q^{29} +(-4.62701 + 8.01422i) q^{30} +(-0.584676 - 1.01269i) q^{31} +(-23.5711 - 40.8264i) q^{32} +(-90.4673 + 156.694i) q^{33} +12.0925 q^{34} -71.4461 q^{36} +(-34.7634 + 60.2120i) q^{37} +(-6.27001 - 10.8600i) q^{38} +(54.6403 + 94.6398i) q^{39} +(24.5825 - 42.5781i) q^{40} -308.115 q^{41} +174.443 q^{43} +(239.390 - 414.636i) q^{44} +(-55.9557 - 96.9181i) q^{45} +(-17.2153 - 29.8177i) q^{46} +(194.681 - 337.197i) q^{47} +187.581 q^{48} +7.34774 q^{50} +(-73.1192 + 126.646i) q^{51} +(-144.587 - 250.432i) q^{52} +(-157.467 - 272.742i) q^{53} +(-3.34897 + 5.80059i) q^{54} +749.950 q^{55} +151.650 q^{57} +(7.58287 - 13.1339i) q^{58} +(422.263 + 731.381i) q^{59} +(148.067 + 256.460i) q^{60} +(-169.269 + 293.182i) q^{61} +0.290084 q^{62} -488.520 q^{64} +(226.477 - 392.270i) q^{65} +(-22.4424 - 38.8714i) q^{66} +(485.775 + 841.387i) q^{67} +(193.485 - 335.125i) q^{68} +416.377 q^{69} -98.4698 q^{71} +(17.7925 - 30.8175i) q^{72} +(355.117 + 615.082i) q^{73} +(-8.62383 - 14.9369i) q^{74} +(-44.4291 + 76.9534i) q^{75} -401.289 q^{76} -27.1095 q^{78} +(243.442 - 421.654i) q^{79} +(-388.748 - 673.332i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(38.2174 - 66.1944i) q^{82} -605.688 q^{83} +606.139 q^{85} +(-21.6372 + 37.4767i) q^{86} +(91.7017 + 158.832i) q^{87} +(119.232 + 206.517i) q^{88} +(109.034 - 188.853i) q^{89} +27.7621 q^{90} -1101.80 q^{92} +(-1.75403 + 3.03807i) q^{93} +(48.2949 + 83.6491i) q^{94} +(-314.284 - 544.357i) q^{95} +(-70.7133 + 122.479i) q^{96} +782.288 q^{97} +542.804 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 9 q^{3} - 25 q^{4} + 11 q^{5} + 6 q^{6} + 78 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q - q^2 - 9 * q^3 - 25 * q^4 + 11 * q^5 + 6 * q^6 + 78 * q^8 - 27 * q^9	\( 6 q - q^{2} - 9 q^{3} - 25 q^{4} + 11 q^{5} + 6 q^{6} + 78 q^{8} - 27 q^{9} - 55 q^{10} - 35 q^{11} - 75 q^{12} - 124 q^{13} - 66 q^{15} - 241 q^{16} + 48 q^{17} - 9 q^{18} - 202 q^{19} - 878 q^{20} - 14 q^{22} - 216 q^{23} - 117 q^{24} - 130 q^{25} + 274 q^{26} + 162 q^{27} + 106 q^{29} - 165 q^{30} - 95 q^{31} - 683 q^{32} - 105 q^{33} + 48 q^{34} + 450 q^{36} - 262 q^{37} - 398 q^{38} + 186 q^{39} + 21 q^{40} - 488 q^{41} + 720 q^{43} + 905 q^{44} + 99 q^{45} + 1056 q^{46} - 210 q^{47} + 1446 q^{48} - 2756 q^{50} + 144 q^{51} + 324 q^{52} - 393 q^{53} - 27 q^{54} + 2062 q^{55} + 1212 q^{57} + 1249 q^{58} + 1143 q^{59} + 1317 q^{60} - 70 q^{61} - 2118 q^{62} - 798 q^{64} + 472 q^{65} + 21 q^{66} + 628 q^{67} + 1944 q^{68} + 1296 q^{69} + 636 q^{71} - 351 q^{72} + 988 q^{73} - 1002 q^{74} - 390 q^{75} + 4680 q^{76} - 1644 q^{78} - 861 q^{79} + 175 q^{80} - 243 q^{81} + 124 q^{82} - 1038 q^{83} + 3600 q^{85} + 3208 q^{86} - 159 q^{87} + 891 q^{88} + 1766 q^{89} + 990 q^{90} - 1344 q^{92} - 285 q^{93} - 3294 q^{94} + 736 q^{95} - 2049 q^{96} - 38 q^{97} + 630 q^{99}+O(q^{100}) \) 6 * q - q^2 - 9 * q^3 - 25 * q^4 + 11 * q^5 + 6 * q^6 + 78 * q^8 - 27 * q^9 - 55 * q^10 - 35 * q^11 - 75 * q^12 - 124 * q^13 - 66 * q^15 - 241 * q^16 + 48 * q^17 - 9 * q^18 - 202 * q^19 - 878 * q^20 - 14 * q^22 - 216 * q^23 - 117 * q^24 - 130 * q^25 + 274 * q^26 + 162 * q^27 + 106 * q^29 - 165 * q^30 - 95 * q^31 - 683 * q^32 - 105 * q^33 + 48 * q^34 + 450 * q^36 - 262 * q^37 - 398 * q^38 + 186 * q^39 + 21 * q^40 - 488 * q^41 + 720 * q^43 + 905 * q^44 + 99 * q^45 + 1056 * q^46 - 210 * q^47 + 1446 * q^48 - 2756 * q^50 + 144 * q^51 + 324 * q^52 - 393 * q^53 - 27 * q^54 + 2062 * q^55 + 1212 * q^57 + 1249 * q^58 + 1143 * q^59 + 1317 * q^60 - 70 * q^61 - 2118 * q^62 - 798 * q^64 + 472 * q^65 + 21 * q^66 + 628 * q^67 + 1944 * q^68 + 1296 * q^69 + 636 * q^71 - 351 * q^72 + 988 * q^73 - 1002 * q^74 - 390 * q^75 + 4680 * q^76 - 1644 * q^78 - 861 * q^79 + 175 * q^80 - 243 * q^81 + 124 * q^82 - 1038 * q^83 + 3600 * q^85 + 3208 * q^86 - 159 * q^87 + 891 * q^88 + 1766 * q^89 + 990 * q^90 - 1344 * q^92 - 285 * q^93 - 3294 * q^94 + 736 * q^95 - 2049 * q^96 - 38 * q^97 + 630 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.124036	+	0.214837i	−0.0438533	+	0.0759562i	−0.887119	−	0.461541i	$-0.847297\pi$
$2$	−0.124036	+	0.214837i	−0.0438533	+	0.0759562i	0.843266	+	0.537497i	$0.180630\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	3.96923	+	6.87491i	0.496154	+	0.859364i
$5$	−6.21730	+	10.7687i	−0.556092	+	0.963180i	0.441725	+	0.897150i	$0.354367\pi$
$5$	−6.21730	+	10.7687i	−0.556092	+	0.963180i	−0.997818	+	0.0660299i	$0.978967\pi$
$6$	0.744216			0.0506375
$7$		0			0
$7$		0			0
$8$	−3.95388			−0.174739
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−1.54234	−	2.67141i	−0.0487730	−	0.0844773i
$11$	−30.1558	−	52.2313i	−0.826573	−	1.43167i	−0.900711	−	0.434419i	$-0.856954\pi$
$11$	−30.1558	−	52.2313i	−0.826573	−	1.43167i	0.0741379	−	0.997248i	$-0.476379\pi$
$12$	11.9077	−	20.6247i	0.286455	−	0.496154i
$13$	−36.4269			−0.777154			−0.388577	−	0.921416i	$-0.627033\pi$
$13$	−36.4269			−0.777154			−0.388577	+	0.921416i	$0.627033\pi$
$14$		0			0
$15$	37.3038			0.642120
$16$	−31.2634	+	54.1498i	−0.488491	+	0.846091i
$17$	−24.3731	−	42.2154i	−0.347726	−	0.602279i	0.638119	−	0.769937i	$-0.279713\pi$
$17$	−24.3731	−	42.2154i	−0.347726	−	0.602279i	−0.985845	+	0.167659i	$0.946379\pi$
$18$	−1.11632	−	1.93353i	−0.0146178	−	0.0253187i
$19$	−25.2750	+	43.7776i	−0.305183	+	0.528593i	−0.977302	−	0.211851i	$-0.932051\pi$
$19$	−25.2750	+	43.7776i	−0.305183	+	0.528593i	0.672119	+	0.740443i	$0.265384\pi$
$20$	−98.7116			−1.10363
$21$		0			0
$22$	14.9616			0.144992
$23$	−69.3962	+	120.198i	−0.629135	+	1.08969i	0.358590	+	0.933495i	$0.383257\pi$
$23$	−69.3962	+	120.198i	−0.629135	+	1.08969i	−0.987726	+	0.156199i	$0.950076\pi$
$24$	5.93083	+	10.2725i	0.0504427	+	0.0873693i
$25$	−14.8097	−	25.6511i	−0.118478	−	0.205209i
$26$	4.51824	−	7.82583i	0.0340808	−	0.0590297i
$27$	27.0000			0.192450
$28$		0			0
$29$	−61.1345			−0.391462			−0.195731	−	0.980658i	$-0.562708\pi$
$29$	−61.1345			−0.391462			−0.195731	+	0.980658i	$0.562708\pi$
$30$	−4.62701	+	8.01422i	−0.0281591	+	0.0487730i
$31$	−0.584676	−	1.01269i	−0.00338745	−	0.00586724i	0.864327	−	0.502931i	$-0.167745\pi$
$31$	−0.584676	−	1.01269i	−0.00338745	−	0.00586724i	−0.867714	+	0.497064i	$0.834412\pi$
$32$	−23.5711	−	40.8264i	−0.130213	−	0.225536i
$33$	−90.4673	+	156.694i	−0.477222	+	0.826573i
$34$	12.0925			0.0609957
$35$		0			0
$36$	−71.4461			−0.330769
$37$	−34.7634	+	60.2120i	−0.154461	+	0.267535i	−0.932863	−	0.360232i	$-0.882698\pi$
$37$	−34.7634	+	60.2120i	−0.154461	+	0.267535i	0.778401	+	0.627767i	$0.216031\pi$
$38$	−6.27001	−	10.8600i	−0.0267666	−	0.0463611i
$39$	54.6403	+	94.6398i	0.224345	+	0.388577i
$40$	24.5825	−	42.5781i	0.0971708	−	0.168305i
$41$	−308.115			−1.17365			−0.586823	−	0.809715i	$-0.699622\pi$
$41$	−308.115			−1.17365			−0.586823	+	0.809715i	$0.699622\pi$
$42$		0			0
$43$	174.443			0.618657			0.309329	−	0.950955i	$-0.399896\pi$
$43$	174.443			0.618657			0.309329	+	0.950955i	$0.399896\pi$
$44$	239.390	−	414.636i	0.820215	−	1.42065i
$45$	−55.9557	−	96.9181i	−0.185364	−	0.321060i
$46$	−17.2153	−	29.8177i	−0.0551794	−	0.0955734i
$47$	194.681	−	337.197i	0.604194	−	1.04649i	−0.387984	−	0.921666i	$-0.626828\pi$
$47$	194.681	−	337.197i	0.604194	−	1.04649i	0.992178	−	0.124829i	$-0.0398382\pi$
$48$	187.581			0.564061
$49$		0			0
$50$	7.34774			0.0207825
$51$	−73.1192	+	126.646i	−0.200760	+	0.347726i
$52$	−144.587	−	250.432i	−0.385588	−	0.667858i
$53$	−157.467	−	272.742i	−0.408110	−	0.706867i	0.586568	−	0.809900i	$-0.300479\pi$
$53$	−157.467	−	272.742i	−0.408110	−	0.706867i	−0.994678	+	0.103033i	$0.967145\pi$
$54$	−3.34897	+	5.80059i	−0.00843958	+	0.0146178i
$55$	749.950			1.83860
$56$		0			0
$57$	151.650			0.352395
$58$	7.58287	−	13.1339i	0.0171669	−	0.0297339i
$59$	422.263	+	731.381i	0.931762	+	1.61386i	0.780308	+	0.625396i	$0.215062\pi$
$59$	422.263	+	731.381i	0.931762	+	1.61386i	0.151455	+	0.988464i	$0.451604\pi$
$60$	148.067	+	256.460i	0.318590	+	0.551815i
$61$	−169.269	+	293.182i	−0.355290	+	0.615380i	−0.987167	−	0.159688i	$-0.948951\pi$
$61$	−169.269	+	293.182i	−0.355290	+	0.615380i	0.631878	+	0.775068i	$0.282284\pi$
$62$	0.290084			0.000594204
$63$		0			0
$64$	−488.520			−0.954141
$65$	226.477	−	392.270i	0.432169	−	0.748539i
$66$	−22.4424	−	38.8714i	−0.0418556	−	0.0724960i
$67$	485.775	+	841.387i	0.885774	+	1.53421i	0.844824	+	0.535044i	$0.179705\pi$
$67$	485.775	+	841.387i	0.885774	+	1.53421i	0.0409498	+	0.999161i	$0.486962\pi$
$68$	193.485	−	335.125i	0.345051	−	0.597646i
$69$	416.377			0.726463
$70$		0			0
$71$	−98.4698			−0.164595			−0.0822973	−	0.996608i	$-0.526226\pi$
$71$	−98.4698			−0.164595			−0.0822973	+	0.996608i	$0.526226\pi$
$72$	17.7925	−	30.8175i	0.0291231	−	0.0504427i
$73$	355.117	+	615.082i	0.569361	+	0.986162i	0.996629	+	0.0820374i	$0.0261427\pi$
$73$	355.117	+	615.082i	0.569361	+	0.986162i	−0.427268	+	0.904125i	$0.640524\pi$
$74$	−8.62383	−	14.9369i	−0.0135473	−	0.0234646i
$75$	−44.4291	+	76.9534i	−0.0684030	+	0.118478i
$76$	−401.289			−0.605671
$77$		0			0
$78$	−27.1095			−0.0393531
$79$	243.442	−	421.654i	0.346701	−	0.600504i	−0.638960	−	0.769240i	$-0.720635\pi$
$79$	243.442	−	421.654i	0.346701	−	0.600504i	0.985661	+	0.168736i	$0.0539686\pi$
$80$	−388.748	−	673.332i	−0.543292	−	0.941010i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	38.2174	−	66.1944i	0.0514683	−	0.0891458i
$83$	−605.688			−0.800999			−0.400499	−	0.916297i	$-0.631163\pi$
$83$	−605.688			−0.800999			−0.400499	+	0.916297i	$0.631163\pi$
$84$		0			0
$85$	606.139			0.773470
$86$	−21.6372	+	37.4767i	−0.0271302	+	0.0469908i
$87$	91.7017	+	158.832i	0.113005	+	0.195731i
$88$	119.232	+	206.517i	0.144434	+	0.250168i
$89$	109.034	−	188.853i	0.129861	−	0.224925i	−0.793762	−	0.608229i	$-0.791880\pi$
$89$	109.034	−	188.853i	0.129861	−	0.224925i	0.923622	+	0.383303i	$0.125214\pi$
$90$	27.7621			0.0325153
$91$		0			0
$92$	−1101.80			−1.24859
$93$	−1.75403	+	3.03807i	−0.00195575	+	0.00338745i
$94$	48.2949	+	83.6491i	0.0529919	+	0.0917846i
$95$	−314.284	−	544.357i	−0.339420	−	0.587893i
$96$	−70.7133	+	122.479i	−0.0751787	+	0.130213i
$97$	782.288			0.818859			0.409429	−	0.912342i	$-0.365728\pi$
$97$	782.288			0.818859			0.409429	+	0.912342i	$0.365728\pi$
$98$		0			0
$99$	542.804			0.551049
$100$	117.566	−	203.631i	0.117566	−	0.203631i
$101$	−155.823	−	269.893i	−0.153514	−	0.265895i	0.779003	−	0.627021i	$-0.215726\pi$
$101$	−155.823	−	269.893i	−0.153514	−	0.265895i	−0.932517	+	0.361126i	$0.882392\pi$
$102$	−18.1388	−	31.4174i	−0.0176079	−	0.0304979i
$103$	−74.6289	+	129.261i	−0.0713922	+	0.123655i	−0.899512	−	0.436897i	$-0.856078\pi$
$103$	−74.6289	+	129.261i	−0.0713922	+	0.123655i	0.828119	+	0.560552i	$0.189411\pi$
$104$	144.028			0.135799
$105$		0			0
$106$	78.1265			0.0715879
$107$	−425.760	+	737.437i	−0.384670	+	0.666269i	−0.991723	−	0.128393i	$-0.959018\pi$
$107$	−425.760	+	737.437i	−0.384670	+	0.666269i	0.607053	+	0.794661i	$0.292352\pi$
$108$	107.169	+	185.623i	0.0954848	+	0.165385i
$109$	−680.939	−	1179.42i	−0.598369	−	1.03640i	−0.993062	−	0.117592i	$-0.962483\pi$
$109$	−680.939	−	1179.42i	−0.598369	−	1.03640i	0.394694	−	0.918813i	$-0.370851\pi$
$110$	−93.0208	+	161.117i	−0.0806289	+	0.139653i
$111$	208.581			0.178357
$112$		0			0
$113$	1048.55			0.872917			0.436459	−	0.899724i	$-0.356233\pi$
$113$	1048.55			0.872917			0.436459	+	0.899724i	$0.356233\pi$
$114$	−18.8100	+	32.5800i	−0.0154537	+	0.0267666i
$115$	−862.914	−	1494.61i	−0.699715	−	1.21194i
$116$	−242.657	−	420.294i	−0.194225	−	0.336408i
$117$	163.921	−	283.920i	0.129526	−	0.224345i
$118$	−209.503			−0.163444
$119$		0			0
$120$	−147.495			−0.112203
$121$	−1153.24	+	1997.47i	−0.866446	+	1.50073i
$122$	−41.9909	−	72.7303i	−0.0311613	−	0.0539729i
$123$	462.173	+	800.507i	0.338803	+	0.586823i
$124$	4.64143	−	8.03919i	0.00336139	−	0.00582210i
$125$	−1186.02			−0.848647
$126$		0			0
$127$	488.408			0.341254			0.170627	−	0.985336i	$-0.445421\pi$
$127$	488.408			0.341254			0.170627	+	0.985336i	$0.445421\pi$
$128$	249.163	−	431.563i	0.172056	−	0.298009i
$129$	−261.664	−	453.215i	−0.178591	−	0.309329i
$130$	56.1826	+	97.3111i	0.0379041	+	0.0656519i
$131$	−927.114	+	1605.81i	−0.618338	+	1.07099i	0.371451	+	0.928453i	$0.378861\pi$
$131$	−927.114	+	1605.81i	−0.618338	+	1.07099i	−0.989789	+	0.142541i	$0.954473\pi$
$132$	−1436.34			−0.947102
$133$		0			0
$134$	−241.014			−0.155377
$135$	−167.867	+	290.754i	−0.107020	+	0.185364i
$136$	96.3683	+	166.915i	0.0607611	+	0.105241i
$137$	255.558	+	442.639i	0.159370	+	0.276038i	0.934642	−	0.355591i	$-0.115720\pi$
$137$	255.558	+	442.639i	0.159370	+	0.276038i	−0.775271	+	0.631628i	$0.782387\pi$
$138$	−51.6458	+	89.4531i	−0.0318578	+	0.0551794i
$139$	−2266.10			−1.38279			−0.691397	−	0.722475i	$-0.743005\pi$
$139$	−2266.10			−1.38279			−0.691397	+	0.722475i	$0.743005\pi$
$140$		0			0
$141$	−1168.09			−0.697663
$142$	12.2138	−	21.1549i	0.00721802	−	0.0125020i
$143$	1098.48	+	1902.62i	0.642375	+	1.11263i
$144$	−281.371	−	487.348i	−0.162830	−	0.282030i
$145$	380.091	−	658.338i	0.217689	−	0.377048i
$146$	−176.189			−0.0998735
$147$		0			0
$148$	−551.936			−0.306546
$149$	−753.950	+	1305.88i	−0.414537	+	0.717999i	−0.995380	−	0.0960168i	$-0.969390\pi$
$149$	−753.950	+	1305.88i	−0.414537	+	0.717999i	0.580843	+	0.814016i	$0.302723\pi$
$150$	−11.0216	−	19.0900i	−0.00599940	−	0.0103913i
$151$	−795.913	−	1378.56i	−0.428943	−	0.742952i	0.567836	−	0.823142i	$-0.307781\pi$
$151$	−795.913	−	1378.56i	−0.428943	−	0.742952i	−0.996780	+	0.0801897i	$0.974447\pi$
$152$	99.9344	−	173.091i	0.0533273	−	0.0923656i
$153$	438.715			0.231817
$154$		0			0
$155$	14.5404			0.00753494
$156$	−433.760	+	751.295i	−0.222619	+	0.385588i
$157$	582.080	+	1008.19i	0.295892	+	0.512500i	0.975192	−	0.221361i	$-0.0710498\pi$
$157$	582.080	+	1008.19i	0.295892	+	0.512500i	−0.679300	+	0.733861i	$0.737717\pi$
$158$	60.3911	+	104.601i	0.0304080	+	0.0526682i
$159$	−472.402	+	818.225i	−0.235622	+	0.408110i
$160$	586.195			0.289642
$161$		0			0
$162$	20.0938			0.00974519
$163$	577.940	−	1001.02i	0.277716	−	0.481019i	−0.693101	−	0.720841i	$-0.743756\pi$
$163$	577.940	−	1001.02i	0.277716	−	0.481019i	0.970817	+	0.239822i	$0.0770892\pi$
$164$	−1222.98	−	2118.26i	−0.582309	−	1.00859i
$165$	−1124.92	−	1948.43i	−0.530759	−	0.919302i
$166$	75.1271	−	130.124i	0.0351265	−	0.0608408i
$167$	2890.61			1.33941			0.669707	−	0.742626i	$-0.266420\pi$
$167$	2890.61			1.33941			0.669707	+	0.742626i	$0.266420\pi$
$168$		0			0
$169$	−870.082			−0.396032
$170$	−75.1830	+	130.221i	−0.0339193	+	0.0587499i
$171$	−227.475	−	393.998i	−0.101728	−	0.176198i
$172$	692.403	+	1199.28i	0.306949	+	0.531651i
$173$	947.468	−	1641.06i	0.416385	−	0.721200i	−0.579188	−	0.815194i	$-0.696630\pi$
$173$	947.468	−	1641.06i	0.416385	−	0.721200i	0.995573	+	0.0939940i	$0.0299635\pi$
$174$	−45.4972			−0.0198226
$175$		0			0
$176$	3771.09			1.61509
$177$	1266.79	−	2194.14i	0.537953	−	0.931762i
$178$	27.0483	+	46.8491i	0.0113897	+	0.0197275i
$179$	2144.25	+	3713.94i	0.895355	+	1.55080i	0.833365	+	0.552723i	$0.186411\pi$
$179$	2144.25	+	3713.94i	0.895355	+	1.55080i	0.0619893	+	0.998077i	$0.480256\pi$
$180$	444.202	−	769.381i	0.183938	−	0.318590i
$181$	−383.732			−0.157583			−0.0787917	−	0.996891i	$-0.525106\pi$
$181$	−383.732			−0.157583			−0.0787917	+	0.996891i	$0.525106\pi$
$182$		0			0
$183$	1015.61			0.410253
$184$	274.385	−	475.248i	0.109934	−	0.190412i
$185$	−432.269	−	748.712i	−0.171790	−	0.297548i
$186$	−0.435125	−	0.753659i	−0.000171532	−	0.000297102i
$187$	−1469.98	+	2546.07i	−0.574841	+	0.995655i
$188$	3090.93			1.19909
$189$		0			0
$190$	155.930			0.0595388
$191$	−192.655	+	333.689i	−0.0729845	+	0.126413i	−0.900208	−	0.435460i	$-0.856586\pi$
$191$	−192.655	+	333.689i	−0.0729845	+	0.126413i	0.827224	+	0.561873i	$0.189919\pi$
$192$	732.780	+	1269.21i	0.275437	+	0.477070i
$193$	−315.112	−	545.790i	−0.117525	−	0.203559i	0.801262	−	0.598314i	$-0.204163\pi$
$193$	−315.112	−	545.790i	−0.117525	−	0.203559i	−0.918786	+	0.394756i	$0.870829\pi$
$194$	−97.0318	+	168.064i	−0.0359097	+	0.0621974i
$195$	−1358.86			−0.499026
$196$		0			0
$197$	−1250.23			−0.452158			−0.226079	−	0.974109i	$-0.572591\pi$
$197$	−1250.23			−0.452158			−0.226079	+	0.974109i	$0.572591\pi$
$198$	−67.3272	+	116.614i	−0.0241653	+	0.0418556i
$199$	−546.122	−	945.912i	−0.194541	−	0.336954i	0.752209	−	0.658924i	$-0.228988\pi$
$199$	−546.122	−	945.912i	−0.194541	−	0.336954i	−0.946750	+	0.321970i	$0.895655\pi$
$200$	58.5558	+	101.422i	0.0207026	+	0.0358580i
$201$	1457.32	−	2524.16i	0.511402	−	0.885774i
$202$	77.3105			0.0269285
$203$		0			0
$204$	−1160.91			−0.398430
$205$	1915.65	−	3318.00i	0.652656	−	1.13043i
$206$	−18.5133	−	32.0660i	−0.00626158	−	0.0108454i
$207$	−624.566	−	1081.78i	−0.209712	−	0.363231i
$208$	1138.83	−	1972.51i	0.379633	−	0.657543i
$209$	3048.75			1.00902
$210$		0			0
$211$	−3620.05			−1.18111			−0.590556	−	0.806997i	$-0.701091\pi$
$211$	−3620.05			−1.18111			−0.590556	+	0.806997i	$0.701091\pi$
$212$	1250.05	−	2165.15i	0.404970	−	0.701429i
$213$	147.705	+	255.832i	0.0475143	+	0.0822973i
$214$	−105.619	−	182.937i	−0.0337382	−	0.0584362i
$215$	−1084.56	+	1878.52i	−0.344030	+	0.595878i
$216$	−106.755			−0.0336285
$217$		0			0
$218$	337.844			0.104962
$219$	1065.35	−	1845.24i	0.328721	−	0.569361i
$220$	2976.72	+	5155.84i	0.912230	+	1.58003i
$221$	887.835	+	1537.78i	0.270236	+	0.468063i
$222$	−25.8715	+	44.8107i	−0.00782153	+	0.0135473i
$223$	183.844			0.0552069			0.0276034	−	0.999619i	$-0.491212\pi$
$223$	183.844			0.0552069			0.0276034	+	0.999619i	$0.491212\pi$
$224$		0			0
$225$	266.574			0.0789850
$226$	−130.058	+	225.268i	−0.0382803	+	0.0663035i
$227$	1139.76	+	1974.12i	0.333253	+	0.577211i	0.983148	−	0.182813i	$-0.0585203\pi$
$227$	1139.76	+	1974.12i	0.333253	+	0.577211i	−0.649895	+	0.760024i	$0.725187\pi$
$228$	601.933	+	1042.58i	0.174842	+	0.302836i
$229$	2706.34	−	4687.51i	0.780960	−	1.35266i	−0.150424	−	0.988622i	$-0.548064\pi$
$229$	2706.34	−	4687.51i	0.780960	−	1.35266i	0.931383	−	0.364040i	$-0.118603\pi$
$230$	428.130			0.122739
$231$		0			0
$232$	241.719			0.0684035
$233$	−569.184	+	985.856i	−0.160036	+	0.277191i	−0.934882	−	0.354960i	$-0.884494\pi$
$233$	−569.184	+	985.856i	−0.160036	+	0.277191i	0.774845	+	0.632151i	$0.217828\pi$
$234$	40.6642	+	70.4325i	0.0113603	+	0.0196766i
$235$	2420.78	+	4192.91i	0.671975	+	1.16390i
$236$	−3352.12	+	5806.04i	−0.924595	+	1.60145i
$237$	−1460.65			−0.400336
$238$		0			0
$239$	−6226.36			−1.68515			−0.842573	−	0.538583i	$-0.818960\pi$
$239$	−6226.36			−1.68515			−0.842573	+	0.538583i	$0.818960\pi$
$240$	−1166.24	+	2020.00i	−0.313670	+	0.543292i
$241$	−1598.10	−	2767.99i	−0.427147	−	0.739841i	0.569471	−	0.822012i	$-0.307148\pi$
$241$	−1598.10	−	2767.99i	−0.427147	−	0.739841i	−0.996618	+	0.0821704i	$0.973815\pi$
$242$	−286.086	−	495.516i	−0.0759931	−	0.131624i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−2687.47			−0.705113
$245$		0			0
$246$	−229.304			−0.0594305
$247$	920.689	−	1594.68i	0.237174	−	0.410798i
$248$	2.31174	+	4.00406i	0.000591919	+	0.00102523i
$249$	908.532	+	1573.62i	0.231228	+	0.400499i
$250$	147.109	−	254.801i	0.0372160	−	0.0644600i
$251$	−239.608			−0.0602546			−0.0301273	−	0.999546i	$-0.509591\pi$
$251$	−239.608			−0.0602546			−0.0301273	+	0.999546i	$0.509591\pi$
$252$		0			0
$253$	8370.78			2.08010
$254$	−60.5802	+	104.928i	−0.0149651	+	0.0259203i
$255$	−909.208	−	1574.79i	−0.223282	−	0.386735i
$256$	−1892.27	−	3277.51i	−0.461980	−	0.800173i
$257$	349.559	−	605.453i	0.0848439	−	0.146954i	−0.820481	−	0.571674i	$-0.806294\pi$
$257$	349.559	−	605.453i	0.0848439	−	0.146954i	0.905325	+	0.424720i	$0.139628\pi$
$258$	129.823			0.0313272
$259$		0			0
$260$	3595.76			0.857690
$261$	275.105	−	476.496i	0.0652436	−	0.113005i
$262$	−229.991	−	398.356i	−0.0542324	−	0.0939333i
$263$	459.520	+	795.912i	0.107738	+	0.186609i	0.914854	−	0.403785i	$-0.132306\pi$
$263$	459.520	+	795.912i	0.107738	+	0.186609i	−0.807115	+	0.590394i	$0.798972\pi$
$264$	357.697	−	619.550i	0.0833892	−	0.144434i
$265$	3916.09			0.907787
$266$		0			0
$267$	−654.206			−0.149950
$268$	−3856.30	+	6679.32i	−0.878960	+	1.52240i
$269$	−1389.59	−	2406.84i	−0.314961	−	0.545529i	0.664468	−	0.747317i	$-0.268658\pi$
$269$	−1389.59	−	2406.84i	−0.314961	−	0.545529i	−0.979429	+	0.201788i	$0.935325\pi$
$270$	−41.6431	−	72.1280i	−0.00938637	−	0.0162577i
$271$	1113.49	−	1928.62i	0.249593	−	0.432308i	−0.713820	−	0.700329i	$-0.753036\pi$
$271$	1113.49	−	1928.62i	0.249593	−	0.432308i	0.963413	+	0.268021i	$0.0863698\pi$
$272$	3047.94			0.679443
$273$		0			0
$274$	−126.793			−0.0279557
$275$	−893.195	+	1547.06i	−0.195861	+	0.339241i
$276$	1652.70	+	2862.56i	0.360437	+	0.624296i
$277$	−3653.85	−	6328.65i	−0.792557	−	1.37275i	−0.924379	−	0.381476i	$-0.875416\pi$
$277$	−3653.85	−	6328.65i	−0.792557	−	1.37275i	0.131821	−	0.991273i	$-0.457917\pi$
$278$	281.078	−	486.842i	0.0606402	−	0.105032i
$279$	10.5242			0.00225830
$280$		0			0
$281$	2730.61			0.579696			0.289848	−	0.957073i	$-0.406395\pi$
$281$	2730.61			0.579696			0.289848	+	0.957073i	$0.406395\pi$
$282$	144.885	−	250.947i	0.0305949	−	0.0529919i
$283$	−884.926	−	1532.74i	−0.185878	−	0.321950i	0.757994	−	0.652261i	$-0.226179\pi$
$283$	−884.926	−	1532.74i	−0.185878	−	0.321950i	−0.943872	+	0.330312i	$0.892846\pi$
$284$	−390.849	−	676.971i	−0.0816642	−	0.141447i
$285$	−942.853	+	1633.07i	−0.195964	+	0.339420i
$286$	−545.004			−0.112681
$287$		0			0
$288$	424.280			0.0868088
$289$	1268.41	−	2196.95i	0.258174	−	0.447170i
$290$	94.2900	+	163.315i	0.0190928	+	0.0330696i
$291$	−1173.43	−	2032.44i	−0.236384	−	0.409429i
$292$	−2819.09	+	4882.80i	−0.564981	+	0.978576i
$293$	−8228.81			−1.64072			−0.820362	−	0.571844i	$-0.806228\pi$
$293$	−8228.81			−1.64072			−0.820362	+	0.571844i	$0.806228\pi$
$294$		0			0
$295$	−10501.4			−2.07258
$296$	137.451	−	238.071i	0.0269904	−	0.0467487i
$297$	−814.206	−	1410.25i	−0.159074	−	0.275524i
$298$	−187.034	−	323.952i	−0.0363577	−	0.0629733i
$299$	2527.89	−	4378.43i	0.488935	−	0.846860i
$300$	−705.397			−0.135754
$301$		0			0
$302$	394.887			0.0752424
$303$	−467.468	+	809.679i	−0.0886316	+	0.153514i
$304$	−1580.36	−	2737.27i	−0.298158	−	0.516425i
$305$	−2104.79	−	3645.61i	−0.395148	−	0.684416i
$306$	−54.4165	+	94.2521i	−0.0101660	+	0.0176079i
$307$	−6019.62			−1.11908			−0.559541	−	0.828803i	$-0.689023\pi$
$307$	−6019.62			−1.11908			−0.559541	+	0.828803i	$0.689023\pi$
$308$		0			0
$309$	447.773			0.0824366
$310$	−1.80354	+	3.12382i	−0.000330432	+	0.000572326i
$311$	596.857	+	1033.79i	0.108825	+	0.188491i	0.915295	−	0.402785i	$-0.131958\pi$
$311$	596.857	+	1033.79i	0.108825	+	0.188491i	−0.806469	+	0.591276i	$0.798624\pi$
$312$	−216.042	−	374.195i	−0.0392018	−	0.0678994i
$313$	−4423.02	+	7660.89i	−0.798734	+	1.38345i	0.121707	+	0.992566i	$0.461163\pi$
$313$	−4423.02	+	7660.89i	−0.798734	+	1.38345i	−0.920441	+	0.390882i	$0.872170\pi$
$314$	−288.795			−0.0519034
$315$		0			0
$316$	3865.11			0.688068
$317$	−3040.72	+	5266.68i	−0.538750	+	0.933142i	0.460222	+	0.887804i	$0.347770\pi$
$317$	−3040.72	+	5266.68i	−0.538750	+	0.933142i	−0.998972	+	0.0453380i	$0.985564\pi$
$318$	−117.190	−	202.979i	−0.0206656	−	0.0357940i
$319$	1843.56	+	3193.13i	0.323572	+	0.560442i
$320$	3037.28	−	5260.72i	0.530590	−	0.919009i
$321$	2554.56			0.444179
$322$		0			0
$323$	2464.12			0.424480
$324$	321.508	−	556.868i	0.0551282	−	0.0954848i
$325$	539.471	+	934.391i	0.0920753	+	0.159479i
$326$	143.371	+	248.325i	0.0243576	+	0.0421885i
$327$	−2042.82	+	3538.26i	−0.345468	+	0.598369i
$328$	1218.25			0.205082
$329$		0			0
$330$	558.125			0.0931023
$331$	−1526.65	+	2644.23i	−0.253511	+	0.439094i	−0.964490	−	0.264119i	$-0.914919\pi$
$331$	−1526.65	+	2644.23i	−0.253511	+	0.439094i	0.710979	+	0.703213i	$0.248252\pi$
$332$	−2404.12	−	4164.05i	−0.397419	−	0.688349i
$333$	−312.871	−	541.908i	−0.0514871	−	0.0891783i
$334$	−358.539	+	621.009i	−0.0587377	+	0.101737i
$335$	−12080.8			−1.97029
$336$		0			0
$337$	3865.80			0.624877			0.312438	−	0.949938i	$-0.398854\pi$
$337$	3865.80			0.624877			0.312438	+	0.949938i	$0.398854\pi$
$338$	107.921	−	186.925i	0.0173673	−	0.0300811i
$339$	−1572.83	−	2724.22i	−0.251989	−	0.436459i
$340$	2405.90	+	4167.15i	0.383760	+	0.664692i
$341$	−35.2627	+	61.0768i	−0.00559995	+	0.00969940i
$342$	112.860			0.0178444
$343$		0			0
$344$	−689.726			−0.108103
$345$	−2588.74	+	4483.83i	−0.403980	+	0.699715i
$346$	235.040	+	407.101i	0.0365198	+	0.0632541i
$347$	49.7965	+	86.2501i	0.00770380	+	0.0133434i	0.869852	−	0.493313i	$-0.164214\pi$
$347$	49.7965	+	86.2501i	0.00770380	+	0.0133434i	−0.862148	+	0.506657i	$0.830881\pi$
$348$	−727.970	+	1260.88i	−0.112136	+	0.194225i
$349$	3607.34			0.553285			0.276643	−	0.960973i	$-0.410778\pi$
$349$	3607.34			0.553285			0.276643	+	0.960973i	$0.410778\pi$
$350$		0			0
$351$	−983.526			−0.149563
$352$	−1421.61	+	2462.30i	−0.215262	+	0.372844i
$353$	3565.37	+	6175.40i	0.537579	+	0.931114i	0.999034	+	0.0439501i	$0.0139942\pi$
$353$	3565.37	+	6175.40i	0.537579	+	0.931114i	−0.461455	+	0.887164i	$0.652672\pi$
$354$	314.255	+	544.306i	0.0471821	+	0.0817218i
$355$	612.216	−	1060.39i	0.0915298	−	0.158534i
$356$	1731.13			0.257724
$357$		0			0
$358$	−1063.85			−0.157057
$359$	3250.14	−	5629.41i	0.477816	−	0.827602i	−0.521860	−	0.853031i	$-0.674762\pi$
$359$	3250.14	−	5629.41i	0.477816	−	0.827602i	0.999677	+	0.0254289i	$0.00809514\pi$
$360$	221.242	+	383.203i	0.0323903	+	0.0561016i
$361$	2151.85	+	3727.11i	0.313727	+	0.543390i
$362$	47.5966	−	82.4398i	0.00691056	−	0.0119694i
$363$	6919.44			1.00049
$364$		0			0
$365$	−8831.49			−1.26647
$366$	−125.973	+	218.191i	−0.0179910	+	0.0311613i
$367$	412.443	+	714.372i	0.0586631	+	0.101607i	0.893866	−	0.448335i	$-0.147983\pi$
$367$	412.443	+	714.372i	0.0586631	+	0.101607i	−0.835202	+	0.549943i	$0.814650\pi$
$368$	−4339.12	−	7515.58i	−0.614654	−	1.06461i
$369$	1386.52	−	2401.52i	0.195608	−	0.338803i
$370$	214.468			0.0301342
$371$		0			0
$372$	−27.8486			−0.00388140
$373$	−666.925	+	1155.15i	−0.0925793	+	0.160352i	−0.908596	−	0.417677i	$-0.862845\pi$
$373$	−666.925	+	1155.15i	−0.0925793	+	0.160352i	0.816016	+	0.578029i	$0.196178\pi$
$374$	−364.660	−	631.610i	−0.0504174	−	0.0873255i
$375$	1779.03	+	3081.37i	0.244983	+	0.424324i
$376$	−769.746	+	1333.24i	−0.105576	+	0.182863i
$377$	2226.94			0.304226
$378$		0			0
$379$	−1338.29			−0.181380			−0.0906902	−	0.995879i	$-0.528907\pi$
$379$	−1338.29			−0.181380			−0.0906902	+	0.995879i	$0.528907\pi$
$380$	2494.93	−	4321.35i	0.336809	−	0.583370i
$381$	−732.612	−	1268.92i	−0.0985114	−	0.170627i
$382$	−47.7924	−	82.7788i	−0.00640123	−	0.0110873i
$383$	176.688	−	306.032i	0.0235727	−	0.0408290i	−0.853998	−	0.520276i	$-0.825829\pi$
$383$	176.688	−	306.032i	0.0235727	−	0.0408290i	0.877571	+	0.479447i	$0.159163\pi$
$384$	−1494.98			−0.198673
$385$		0			0
$386$	156.341			0.0206154
$387$	−784.992	+	1359.65i	−0.103110	+	0.178591i
$388$	3105.08	+	5378.16i	0.406280	+	0.703697i
$389$	−5868.59	−	10164.7i	−0.764908	−	1.32486i	−0.940295	−	0.340360i	$-0.889451\pi$
$389$	−5868.59	−	10164.7i	−0.764908	−	1.32486i	0.175387	−	0.984500i	$-0.443882\pi$
$390$	168.548	−	291.933i	0.0218840	−	0.0379041i
$391$	6765.59			0.875066
$392$		0			0
$393$	5562.68			0.713996
$394$	155.073	−	268.595i	0.0198286	−	0.0343442i
$395$	3027.11	+	5243.10i	0.385595	+	0.667871i
$396$	2154.51	+	3731.73i	0.273405	+	0.473551i
$397$	6640.71	−	11502.1i	0.839516	−	1.45408i	−0.0507841	−	0.998710i	$-0.516172\pi$
$397$	6640.71	−	11502.1i	0.839516	−	1.45408i	0.890300	−	0.455374i	$-0.150495\pi$
$398$	270.955			0.0341250
$399$		0			0
$400$	1852.01			0.231501
$401$	3741.18	−	6479.91i	0.465899	−	0.806961i	−0.533343	−	0.845899i	$-0.679064\pi$
$401$	3741.18	−	6479.91i	0.465899	−	0.806961i	0.999242	+	0.0389385i	$0.0123976\pi$
$402$	361.521	+	626.173i	0.0448534	+	0.0776883i
$403$	21.2979	+	36.8891i	0.00263257	+	0.00455975i
$404$	1236.99	−	2142.54i	0.152333	−	0.263849i
$405$	1007.20			0.123576
$406$		0			0
$407$	4193.27			0.510694
$408$	289.105	−	500.744i	0.0350805	−	0.0607611i
$409$	−6898.30	−	11948.2i	−0.833983	−	1.44450i	−0.894856	−	0.446355i	$-0.852722\pi$
$409$	−6898.30	−	11948.2i	−0.833983	−	1.44450i	0.0608735	−	0.998145i	$-0.480611\pi$
$410$	475.218	+	823.102i	0.0572423	+	0.0991466i
$411$	766.673	−	1327.92i	0.0920126	−	0.159370i
$412$	−1184.88			−0.141686
$413$		0			0
$414$	309.875			0.0367862
$415$	3765.75	−	6522.46i	0.445429	−	0.771506i
$416$	858.622	+	1487.18i	0.101196	+	0.175276i
$417$	3399.16	+	5887.51i	0.399179	+	0.691397i
$418$	−378.154	+	654.982i	−0.0442491	+	0.0766417i
$419$	−9497.56			−1.10737			−0.553683	−	0.832728i	$-0.686778\pi$
$419$	−9497.56			−1.10737			−0.553683	+	0.832728i	$0.686778\pi$
$420$		0			0
$421$	624.367			0.0722797			0.0361399	−	0.999347i	$-0.488494\pi$
$421$	624.367			0.0722797			0.0361399	+	0.999347i	$0.488494\pi$
$422$	449.016	−	777.719i	0.0517957	−	0.0897127i
$423$	1752.13	+	3034.77i	0.201398	+	0.348832i
$424$	622.608	+	1078.39i	0.0713126	+	0.123517i
$425$	−721.915	+	1250.39i	−0.0823954	+	0.142713i
$426$	−73.2827			−0.00833465
$427$		0			0
$428$	−6759.75			−0.763423
$429$	3295.44	−	5707.87i	0.370875	−	0.642375i
$430$	−269.050	−	466.007i	−0.0301738	−	0.0522625i
$431$	6698.64	+	11602.4i	0.748636	+	1.29668i	0.948476	+	0.316848i	$0.102624\pi$
$431$	6698.64	+	11602.4i	0.748636	+	1.29668i	−0.199840	+	0.979829i	$0.564042\pi$
$432$	−844.112	+	1462.05i	−0.0940101	+	0.162830i
$433$	14057.3			1.56016			0.780079	−	0.625681i	$-0.215179\pi$
$433$	14057.3			1.56016			0.780079	+	0.625681i	$0.215179\pi$
$434$		0			0
$435$	−2280.55			−0.251365
$436$	5405.61	−	9362.79i	0.593766	−	1.02843i
$437$	−3507.98	−	6075.99i	−0.384003	−	0.665112i
$438$	264.284	+	457.753i	0.0288310	+	0.0499368i
$439$	−8184.42	+	14175.8i	−0.889798	+	1.54117i	−0.0496832	+	0.998765i	$0.515821\pi$
$439$	−8184.42	+	14175.8i	−0.889798	+	1.54117i	−0.840114	+	0.542409i	$0.817512\pi$
$440$	−2965.22			−0.321275
$441$		0			0
$442$	−440.494			−0.0474031
$443$	589.354	−	1020.79i	0.0632078	−	0.109479i	−0.832690	−	0.553740i	$-0.813200\pi$
$443$	589.354	−	1020.79i	0.0632078	−	0.109479i	0.895898	+	0.444261i	$0.146534\pi$
$444$	827.904	+	1433.97i	0.0884923	+	0.153273i
$445$	1355.80	+	2348.31i	0.144429	+	0.250159i
$446$	−22.8033	+	39.4965i	−0.00242101	+	0.00419331i
$447$	4523.70			0.478666
$448$		0			0
$449$	−12400.9			−1.30342			−0.651709	−	0.758469i	$-0.725948\pi$
$449$	−12400.9			−1.30342			−0.651709	+	0.758469i	$0.725948\pi$
$450$	−33.0648	+	57.2699i	−0.00346376	+	0.00599940i
$451$	9291.45	+	16093.3i	0.970105	+	1.68027i
$452$	4161.95	+	7208.71i	0.433101	+	0.750153i
$453$	−2387.74	+	4135.68i	−0.247651	+	0.428943i
$454$	−565.484			−0.0584570
$455$		0			0
$456$	−599.606			−0.0615771
$457$	−4962.79	+	8595.81i	−0.507986	+	0.879858i	0.491971	+	0.870611i	$0.336277\pi$
$457$	−4962.79	+	8595.81i	−0.507986	+	0.879858i	−0.999957	+	0.00924618i	$0.997057\pi$
$458$	671.366	+	1162.84i	0.0684954	+	0.118637i
$459$	−658.073	−	1139.82i	−0.0669198	−	0.115909i
$460$	6850.21	−	11864.9i	0.694332	−	1.20262i
$461$	16010.3			1.61751			0.808755	−	0.588146i	$-0.200142\pi$
$461$	16010.3			1.61751			0.808755	+	0.588146i	$0.200142\pi$
$462$		0			0
$463$	17372.4			1.74377			0.871883	−	0.489714i	$-0.162899\pi$
$463$	17372.4			1.74377			0.871883	+	0.489714i	$0.162899\pi$
$464$	1911.27	−	3310.42i	0.191225	−	0.331212i
$465$	−21.8107	−	37.7772i	−0.00217515	−	0.00376747i
$466$	−141.199	−	244.563i	−0.0140363	−	0.0243115i
$467$	1054.03	−	1825.64i	0.104443	−	0.180900i	−0.809068	−	0.587716i	$-0.800027\pi$
$467$	1054.03	−	1825.64i	0.104443	−	0.180900i	0.913510	+	0.406815i	$0.133361\pi$
$468$	2602.56			0.257059
$469$		0			0
$470$	−1201.05			−0.117873
$471$	1746.24	−	3024.58i	0.170833	−	0.295892i
$472$	−1669.58	−	2891.80i	−0.162815	−	0.282004i
$473$	−5260.45	−	9111.37i	−0.511365	−	0.885711i
$474$	181.173	−	313.802i	0.0175561	−	0.0304080i
$475$	1497.26			0.144629
$476$		0			0
$477$	2834.41			0.272073
$478$	772.293	−	1337.65i	0.0738992	−	0.127997i
$479$	−1225.02	−	2121.80i	−0.116853	−	0.202395i	0.801666	−	0.597772i	$-0.203947\pi$
$479$	−1225.02	−	2121.80i	−0.116853	−	0.202395i	−0.918519	+	0.395377i	$0.870614\pi$
$480$	−879.292	−	1522.98i	−0.0836126	−	0.144821i
$481$	1266.32	−	2193.34i	0.120040	−	0.207916i
$482$	792.887			0.0749274
$483$		0			0
$484$	−18309.9			−1.71956
$485$	−4863.72	+	8424.21i	−0.455361	+	0.788709i
$486$	−30.1407	−	52.2053i	−0.00281319	−	0.00487259i
$487$	−322.618	−	558.791i	−0.0300189	−	0.0519943i	0.850626	−	0.525772i	$-0.176223\pi$
$487$	−322.618	−	558.791i	−0.0300189	−	0.0519943i	−0.880645	+	0.473778i	$0.842890\pi$
$488$	669.270	−	1159.21i	0.0620828	−	0.107531i
$489$	−3467.64			−0.320679
$490$		0			0
$491$	11766.1			1.08146			0.540731	−	0.841196i	$-0.318148\pi$
$491$	11766.1			1.08146			0.540731	+	0.841196i	$0.318148\pi$
$492$	−3668.94	+	6354.79i	−0.336196	+	0.582309i
$493$	1490.03	+	2580.81i	0.136121	+	0.235769i
$494$	228.397	+	395.595i	0.0208018	+	0.0360297i
$495$	−3374.77	+	5845.28i	−0.306434	+	0.530759i
$496$	73.1159			0.00661896
$497$		0			0
$498$	−450.763			−0.0405606
$499$	22.0104	−	38.1232i	0.00197459	−	0.00342010i	−0.865036	−	0.501709i	$-0.832705\pi$
$499$	22.0104	−	38.1232i	0.00197459	−	0.00342010i	0.867011	+	0.498289i	$0.166038\pi$
$500$	−4707.59	−	8153.78i	−0.421059	−	0.729296i
$501$	−4335.91	−	7510.02i	−0.386655	−	0.669707i
$502$	29.7200	−	51.4765i	0.00264236	−	0.00457671i
$503$	−8290.27			−0.734880			−0.367440	−	0.930047i	$-0.619766\pi$
$503$	−8290.27			−0.734880			−0.367440	+	0.930047i	$0.619766\pi$
$504$		0			0
$505$	3875.19			0.341473
$506$	−1038.28	+	1798.35i	−0.0912195	+	0.157997i
$507$	1305.12	+	2260.54i	0.114324	+	0.198016i
$508$	1938.60	+	3357.76i	0.169314	+	0.293261i
$509$	3457.52	−	5988.60i	0.301084	−	0.521493i	−0.675298	−	0.737545i	$-0.735985\pi$
$509$	3457.52	−	5988.60i	0.301084	−	0.521493i	0.976382	+	0.216052i	$0.0693181\pi$
$510$	451.098			0.0391666
$511$		0			0
$512$	4925.45			0.425148
$513$	−682.425	+	1181.99i	−0.0587325	+	0.101728i
$514$	86.7157	+	150.196i	0.00744137	+	0.0128888i
$515$	−927.980	−	1607.31i	−0.0794014	−	0.137527i
$516$	2077.21	−	3597.83i	0.177217	−	0.306949i
$517$	−23483.0			−1.99764
$518$		0			0
$519$	−5684.81			−0.480800
$520$	−895.464	+	1550.99i	−0.0755167	+	0.130799i
$521$	6699.64	+	11604.1i	0.563371	+	0.975788i	0.997199	+	0.0747919i	$0.0238293\pi$
$521$	6699.64	+	11604.1i	0.563371	+	0.975788i	−0.433828	+	0.900996i	$0.642837\pi$
$522$	68.2458	+	118.205i	0.00572230	+	0.00991131i
$523$	−4968.50	+	8605.69i	−0.415406	+	0.719504i	−0.995471	−	0.0950662i	$-0.969694\pi$
$523$	−4968.50	+	8605.69i	−0.415406	+	0.719504i	0.580065	+	0.814570i	$0.303027\pi$
$524$	−14719.7			−1.22716
$525$		0			0
$526$	−227.988			−0.0188988
$527$	−28.5007	+	49.3647i	−0.00235581	+	0.00408038i
$528$	−5656.63	−	9797.58i	−0.466237	−	0.807547i
$529$	−3548.17	−	6145.60i	−0.291622	−	0.505104i
$530$	−485.736	+	841.320i	−0.0398095	+	0.0689521i
$531$	−7600.74			−0.621175
$532$		0			0
$533$	11223.7			0.912104
$534$	81.1450	−	140.547i	0.00657582	−	0.0113897i
$535$	−5294.15	−	9169.74i	−0.427825	−	0.741014i
$536$	−1920.70	−	3326.75i	−0.154779	−	0.268085i
$537$	6432.74	−	11141.8i	0.516933	−	0.895355i
$538$	689.435			0.0552484
$539$		0			0
$540$	−2665.21			−0.212394
$541$	−4643.08	+	8042.06i	−0.368987	+	0.639103i	−0.989407	−	0.145166i	$-0.953628\pi$
$541$	−4643.08	+	8042.06i	−0.368987	+	0.639103i	0.620421	+	0.784269i	$0.286962\pi$
$542$	276.226	+	478.437i	0.0218910	+	0.0379163i
$543$	575.599	+	996.966i	0.0454904	+	0.0787917i
$544$	−1149.00	+	1990.13i	−0.0905570	+	0.156849i
$545$	16934.4			1.33099
$546$		0			0
$547$	−16821.6			−1.31488			−0.657438	−	0.753508i	$-0.728360\pi$
$547$	−16821.6			−1.31488			−0.657438	+	0.753508i	$0.728360\pi$
$548$	−2028.73	+	3513.87i	−0.158144	+	0.273914i
$549$	−1523.42	−	2638.64i	−0.118430	−	0.205127i
$550$	−221.577	−	383.782i	−0.0171783	−	0.0297537i
$551$	1545.17	−	2676.32i	0.119467	−	0.206924i
$552$	−1646.31			−0.126941
$553$		0			0
$554$	1812.83			0.139025
$555$	−1296.81	+	2246.14i	−0.0991828	+	0.171790i
$556$	−8994.69	−	15579.3i	−0.686079	−	1.18832i
$557$	−902.972	−	1563.99i	−0.0686897	−	0.118974i	0.829635	−	0.558306i	$-0.188549\pi$
$557$	−902.972	−	1563.99i	−0.0686897	−	0.118974i	−0.898325	+	0.439332i	$0.855215\pi$
$558$	−1.30538	+	2.26098i	−9.90340e−5	+	0.000171532i
$559$	−6354.40			−0.480792
$560$		0			0
$561$	8819.86			0.663770
$562$	−338.694	+	586.635i	−0.0254216	+	0.0440315i
$563$	6107.45	+	10578.4i	0.457190	+	0.791877i	0.998811	−	0.0487460i	$-0.0155225\pi$
$563$	6107.45	+	10578.4i	0.457190	+	0.791877i	−0.541621	+	0.840623i	$0.682189\pi$
$564$	−4636.40	−	8030.48i	−0.346148	−	0.599546i
$565$	−6519.17	+	11291.5i	−0.485423	+	0.840776i
$566$	439.050			0.0326054
$567$		0			0
$568$	389.338			0.0287610
$569$	−2141.89	+	3709.86i	−0.157808	+	0.273331i	−0.934078	−	0.357070i	$-0.883776\pi$
$569$	−2141.89	+	3709.86i	−0.157808	+	0.273331i	0.776270	+	0.630400i	$0.217109\pi$
$570$	−233.895	−	405.119i	−0.0171874	−	0.0297694i
$571$	−3179.97	−	5507.87i	−0.233060	−	0.403673i	0.725647	−	0.688067i	$-0.241541\pi$
$571$	−3179.97	−	5507.87i	−0.233060	−	0.403673i	−0.958707	+	0.284395i	$0.908207\pi$
$572$	−8720.25	+	15103.9i	−0.637433	+	1.10407i
$573$	1155.93			0.0842753
$574$		0			0
$575$	4110.95			0.298153
$576$	2198.34	−	3807.64i	0.159023	−	0.275437i
$577$	7234.36	+	12530.3i	0.521959	+	0.904059i	0.999674	+	0.0255444i	$0.00813192\pi$
$577$	7234.36	+	12530.3i	0.521959	+	0.904059i	−0.477715	+	0.878515i	$0.658535\pi$
$578$	314.656	+	545.001i	0.0226436	+	0.0392198i
$579$	−945.335	+	1637.37i	−0.0678528	+	0.117525i
$580$	6034.68			0.432028
$581$		0			0
$582$	582.191			0.0414649
$583$	−9497.10	+	16449.5i	−0.674665	+	1.16855i
$584$	−1404.09	−	2431.96i	−0.0994894	−	0.172321i
$585$	2038.29	+	3530.43i	0.144056	+	0.249513i
$586$	1020.67	−	1767.85i	0.0719513	−	0.124623i
$587$	11132.6			0.782777			0.391388	−	0.920226i	$-0.371995\pi$
$587$	11132.6			0.782777			0.391388	+	0.920226i	$0.371995\pi$
$588$		0			0
$589$	59.1108			0.00413517
$590$	1302.55	−	2256.07i	0.0908897	−	0.157426i
$591$	1875.34	+	3248.19i	0.130527	+	0.226079i
$592$	−2173.65	−	3764.87i	−0.150906	−	0.261377i
$593$	−9887.81	+	17126.2i	−0.684728	+	1.18598i	0.288794	+	0.957391i	$0.406746\pi$
$593$	−9887.81	+	17126.2i	−0.684728	+	1.18598i	−0.973522	+	0.228592i	$0.926588\pi$
$594$	403.963			0.0279037
$595$		0			0
$596$	−11970.4			−0.822696
$597$	−1638.37	+	2837.73i	−0.112318	+	0.194541i
$598$	627.098	+	1086.17i	0.0428829	+	0.0742753i
$599$	11945.5	+	20690.2i	0.814825	+	1.41132i	0.909453	+	0.415806i	$0.136500\pi$
$599$	11945.5	+	20690.2i	0.814825	+	1.41132i	−0.0946282	+	0.995513i	$0.530166\pi$
$600$	175.667	−	304.265i	0.0119527	−	0.0207026i
$601$	−19395.5			−1.31641			−0.658204	−	0.752840i	$-0.728683\pi$
$601$	−19395.5			−1.31641			−0.658204	+	0.752840i	$0.728683\pi$
$602$		0			0
$603$	−8743.95			−0.590516
$604$	6318.32	−	10943.7i	0.425644	−	0.737237i
$605$	−14340.1	−	24837.8i	−0.963648	−	1.66909i
$606$	−115.966	−	200.859i	−0.00777358	−	0.0134642i
$607$	7298.36	−	12641.1i	0.488025	−	0.845285i	−0.511880	−	0.859057i	$-0.671051\pi$
$607$	7298.36	−	12641.1i	0.488025	−	0.845285i	0.999905	+	0.0137724i	$0.00438402\pi$
$608$	2383.04			0.158956
$609$		0			0
$610$	1044.28			0.0693142
$611$	−7091.62	+	12283.0i	−0.469552	+	0.813288i
$612$	1741.36	+	3016.13i	0.115017	+	0.199215i
$613$	−989.898	−	1714.55i	−0.0652229	−	0.112969i	0.831570	−	0.555420i	$-0.187442\pi$
$613$	−989.898	−	1714.55i	−0.0652229	−	0.112969i	−0.896793	+	0.442451i	$0.854109\pi$
$614$	746.650	−	1293.24i	0.0490755	−	0.0850012i
$615$	−11493.9			−0.753622
$616$		0			0
$617$	16262.4			1.06110			0.530551	−	0.847653i	$-0.321985\pi$
$617$	16262.4			1.06110			0.530551	+	0.847653i	$0.321985\pi$
$618$	−55.5400	+	96.1981i	−0.00361512	+	0.00626158i
$619$	−6010.49	−	10410.5i	−0.390278	−	0.675981i	0.602208	−	0.798339i	$-0.294288\pi$
$619$	−6010.49	−	10410.5i	−0.390278	−	0.675981i	−0.992486	+	0.122358i	$0.960954\pi$
$620$	57.7143	+	99.9642i	0.00373849	+	0.00647526i
$621$	−1873.70	+	3245.34i	−0.121077	+	0.209712i
$622$	−296.127			−0.0190894
$623$		0			0
$624$	−6832.97			−0.438362
$625$	9225.06	−	15978.3i	0.590404	−	1.02261i
$626$	−1097.23	−	1900.45i	−0.0700543	−	0.121338i
$627$	−4573.12	−	7920.87i	−0.291280	−	0.504512i
$628$	−4620.82	+	8003.49i	−0.293616	+	0.508557i
$629$	3389.16			0.214841
$630$		0			0
$631$	25347.6			1.59916			0.799582	−	0.600557i	$-0.205055\pi$
$631$	25347.6			1.59916			0.799582	+	0.600557i	$0.205055\pi$
$632$	−962.542	+	1667.17i	−0.0605821	+	0.104931i
$633$	5430.07	+	9405.16i	0.340957	+	0.590556i
$634$	−754.317	−	1306.51i	−0.0472519	−	0.0818428i
$635$	−3036.58	+	5259.51i	−0.189769	+	0.328689i
$636$	−7500.29			−0.467620
$637$		0			0
$638$	−914.669			−0.0567588
$639$	443.114	−	767.496i	0.0274324	−	0.0475143i
$640$	3098.24	+	5366.31i	0.191358	+	0.331441i
$641$	2555.80	+	4426.78i	0.157485	+	0.272772i	0.933961	−	0.357374i	$-0.116328\pi$
$641$	2555.80	+	4426.78i	0.157485	+	0.272772i	−0.776476	+	0.630147i	$0.782995\pi$
$642$	−316.857	+	548.812i	−0.0194787	+	0.0337382i
$643$	10931.3			0.670435			0.335217	−	0.942141i	$-0.391190\pi$
$643$	10931.3			0.670435			0.335217	+	0.942141i	$0.391190\pi$
$644$		0			0
$645$	6507.38			0.397252
$646$	−305.639	+	529.382i	−0.0186149	+	0.0322419i
$647$	−9203.06	−	15940.2i	−0.559211	−	0.968582i	−0.997563	−	0.0697783i	$-0.977771\pi$
$647$	−9203.06	−	15940.2i	−0.559211	−	0.968582i	0.438352	−	0.898804i	$-0.355563\pi$
$648$	160.132	+	277.357i	0.00970770	+	0.0168142i
$649$	25467.3	−	44110.7i	1.54034	−	2.66795i
$650$	−267.655			−0.0161512
$651$		0			0
$652$	9175.91			0.551160
$653$	−9960.71	+	17252.5i	−0.596926	+	1.03391i	0.396346	+	0.918101i	$0.370278\pi$
$653$	−9960.71	+	17252.5i	−0.596926	+	1.03391i	−0.993272	+	0.115805i	$0.963055\pi$
$654$	−506.766	−	877.744i	−0.0302999	−	0.0524809i
$655$	−11528.3	−	19967.6i	−0.687707	−	1.19114i
$656$	9632.74	−	16684.4i	0.573316	−	0.993012i
$657$	−6392.11			−0.379574
$658$		0			0
$659$	−18858.8			−1.11477			−0.557385	−	0.830254i	$-0.688195\pi$
$659$	−18858.8			−1.11477			−0.557385	+	0.830254i	$0.688195\pi$
$660$	8930.17	−	15467.5i	0.526676	−	0.912230i
$661$	12916.0	+	22371.2i	0.760023	+	1.31640i	0.942838	+	0.333251i	$0.108146\pi$
$661$	12916.0	+	22371.2i	0.760023	+	1.31640i	−0.182815	+	0.983147i	$0.558521\pi$
$662$	−378.718	−	655.960i	−0.0222346	−	0.0385115i
$663$	2663.50	−	4613.33i	0.156021	−	0.270236i
$664$	2394.82			0.139965
$665$		0			0
$666$	155.229			0.00903153
$667$	4242.50	−	7348.22i	0.246282	−	0.426573i
$668$	11473.5	+	19872.7i	0.664555	+	1.15104i
$669$	−275.767	−	477.642i	−0.0159369	−	0.0276034i
$670$	1498.46	−	2595.41i	0.0864037	−	0.149656i
$671$	20417.7			1.17469
$672$		0			0
$673$	−16275.0			−0.932178			−0.466089	−	0.884738i	$-0.654337\pi$
$673$	−16275.0			−0.932178			−0.466089	+	0.884738i	$0.654337\pi$
$674$	−479.498	+	830.515i	−0.0274029	+	0.0474633i
$675$	−399.862	−	692.581i	−0.0228010	−	0.0394925i
$676$	−3453.55	−	5981.73i	−0.196493	−	0.340335i
$677$	−13135.9	+	22752.0i	−0.745720	+	1.29163i	0.204137	+	0.978942i	$0.434561\pi$
$677$	−13135.9	+	22752.0i	−0.745720	+	1.29163i	−0.949857	+	0.312683i	$0.898772\pi$
$678$	780.350			0.0442023
$679$		0			0
$680$	−2396.60			−0.135155
$681$	3419.28	−	5922.36i	0.192404	−	0.333253i
$682$	−8.74769	−	15.1514i	−0.000491153	−	0.000850702i
$683$	4036.14	+	6990.81i	0.226118	+	0.391648i	0.956654	−	0.291226i	$-0.0940631\pi$
$683$	4036.14	+	6990.81i	0.226118	+	0.391648i	−0.730536	+	0.682874i	$0.760730\pi$
$684$	1805.80	−	3127.74i	0.100945	−	0.174842i
$685$	−6355.51			−0.354499
$686$		0			0
$687$	−16238.0			−0.901774
$688$	−5453.67	+	9446.04i	−0.302208	+	0.523440i
$689$	5736.05	+	9935.13i	0.317164	+	0.549344i
$690$	−642.194	−	1112.31i	−0.0354318	−	0.0613696i
$691$	−12242.6	+	21204.9i	−0.673997	+	1.16740i	0.302763	+	0.953066i	$0.402091\pi$
$691$	−12242.6	+	21204.9i	−0.673997	+	1.16740i	−0.976761	+	0.214332i	$0.931243\pi$
$692$	15042.9			0.826364
$693$		0			0
$694$	−24.7062			−0.00135135
$695$	14089.1	−	24403.0i	0.768962	−	1.33188i
$696$	−362.578	−	628.003i	−0.0197464	−	0.0342017i
$697$	7509.71	+	13007.2i	0.408107	+	0.706862i
$698$	−447.440	+	774.989i	−0.0242634	+	0.0420254i
$699$	3415.10			0.184794
$700$		0			0
$701$	778.448			0.0419423			0.0209712	−	0.999780i	$-0.493324\pi$
$701$	778.448			0.0419423			0.0209712	+	0.999780i	$0.493324\pi$
$702$	121.993	−	211.297i	0.00655885	−	0.0113603i
$703$	−1757.29	−	3043.72i	−0.0942780	−	0.163294i
$704$	14731.7	+	25516.0i	0.788667	+	1.36601i
$705$	7262.34	−	12578.7i	0.387965	−	0.671975i
$706$	−1768.93			−0.0942985
$707$		0			0
$708$	20112.7			1.06763
$709$	12086.0	−	20933.6i	0.640197	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$709$	12086.0	−	20933.6i	0.640197	−	1.10885i	0.985389	−	0.170322i	$-0.0544806\pi$
$710$	151.874	+	263.053i	0.00802777	+	0.0139045i
$711$	2190.98	+	3794.89i	0.115567	+	0.200168i
$712$	−431.109	+	746.703i	−0.0226917	+	0.0393032i
$713$	162.297			0.00852466
$714$		0			0
$715$	−27318.3			−1.42888
$716$	−17022.0	+	29483.0i	−0.888467	+	1.53887i
$717$	9339.54	+	16176.6i	0.486460	+	0.842573i
$718$	806.269	+	1396.50i	0.0419077	+	0.0725862i
$719$	−40.9418	+	70.9132i	−0.00212360	+	0.00367819i	−0.867085	−	0.498160i	$-0.834009\pi$
$719$	−40.9418	+	70.9132i	−0.00212360	+	0.00367819i	0.864962	+	0.501838i	$0.167343\pi$
$720$	6997.47			0.362195
$721$		0			0
$722$	−1067.63			−0.0550318
$723$	−4794.29	+	8303.96i	−0.246614	+	0.427147i
$724$	−1523.12	−	2638.13i	−0.0781856	−	0.135421i
$725$	905.382	+	1568.17i	0.0463794	+	0.0803315i
$726$	−858.259	+	1486.55i	−0.0438747	+	0.0759931i
$727$	32542.9			1.66018			0.830088	−	0.557632i	$-0.188290\pi$
$727$	32542.9			1.66018			0.830088	+	0.557632i	$0.188290\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	1095.42	−	1897.33i	0.0555389	−	0.0961962i
$731$	−4251.70	−	7364.16i	−0.215123	−	0.372604i
$732$	4031.20	+	6982.25i	0.203549	+	0.352557i
$733$	−2534.47	+	4389.83i	−0.127712	+	0.221203i	−0.922790	−	0.385304i	$-0.874097\pi$
$733$	−2534.47	+	4389.83i	−0.127712	+	0.221203i	0.795078	+	0.606507i	$0.207430\pi$
$734$	−204.631			−0.0102903
$735$		0			0
$736$	6542.98			0.327687
$737$	29297.8	−	50745.3i	1.46431	−	2.53627i
$738$	343.956	+	595.750i	0.0171561	+	0.0297153i
$739$	19214.2	+	33280.0i	0.956437	+	1.65660i	0.731045	+	0.682329i	$0.239033\pi$
$739$	19214.2	+	33280.0i	0.956437	+	1.65660i	0.225392	+	0.974268i	$0.427634\pi$
$740$	3431.55	−	5943.62i	0.170468	−	0.295259i
$741$	−5524.14			−0.273865
$742$		0			0
$743$	21592.9			1.06617			0.533086	−	0.846061i	$-0.321032\pi$
$743$	21592.9			1.06617			0.533086	+	0.846061i	$0.321032\pi$
$744$	6.93523	−	12.0122i	0.000341744	−	0.000591919i
$745$	−9375.07	−	16238.1i	−0.461042	−	0.798548i
$746$	−165.445	−	286.560i	−0.00811982	−	0.0140639i
$747$	2725.60	−	4720.87i	0.133500	−	0.231228i
$748$	−23338.7			−1.14084
$749$		0			0
$750$	−882.655			−0.0429733
$751$	−4056.30	+	7025.72i	−0.197093	+	0.341374i	−0.947585	−	0.319505i	$-0.896483\pi$
$751$	−4056.30	+	7025.72i	−0.197093	+	0.341374i	0.750492	+	0.660880i	$0.229817\pi$
$752$	12172.8	+	21083.9i	0.590287	+	1.02241i
$753$	359.411	+	622.519i	0.0173940	+	0.0301273i
$754$	−276.220	+	478.428i	−0.0133413	+	0.0231078i
$755$	19793.7			0.954129
$756$		0			0
$757$	3108.01			0.149224			0.0746120	−	0.997213i	$-0.476228\pi$
$757$	3108.01			0.149224			0.0746120	+	0.997213i	$0.476228\pi$
$758$	165.996	−	287.513i	0.00795414	−	0.0137770i
$759$	−12556.2	−	21747.9i	−0.600475	−	1.04005i
$760$	1242.64	+	2152.32i	0.0593098	+	0.102728i
$761$	−3605.96	+	6245.71i	−0.171769	+	0.297512i	−0.939038	−	0.343812i	$-0.888282\pi$
$761$	−3605.96	+	6245.71i	−0.171769	+	0.297512i	0.767269	+	0.641325i	$0.221615\pi$
$762$	363.481			0.0172802
$763$		0			0
$764$	−3058.77			−0.144846
$765$	−2727.62	+	4724.38i	−0.128912	+	0.223282i
$766$	43.8313	+	75.9181i	0.00206748	+	0.00358098i
$767$	−15381.7	−	26641.9i	−0.724123	−	1.25422i
$768$	−5676.81	+	9832.52i	−0.266724	+	0.461980i
$769$	7533.07			0.353250			0.176625	−	0.984278i	$-0.443482\pi$
$769$	7533.07			0.353250			0.176625	+	0.984278i	$0.443482\pi$
$770$		0			0
$771$	−2097.35			−0.0979693
$772$	2501.50	−	4332.73i	0.116621	−	0.201993i
$773$	−12416.3	−	21505.7i	−0.577728	−	1.00065i	−0.995739	−	0.0922122i	$-0.970606\pi$
$773$	−12416.3	−	21505.7i	−0.577728	−	1.00065i	0.418012	−	0.908442i	$-0.362727\pi$
$774$	−194.734	−	337.290i	−0.00904339	−	0.0156636i
$775$	−17.3178	+	29.9952i	−0.000802674	+	0.00139027i
$776$	−3093.08			−0.143086
$777$		0			0
$778$	2911.66			0.134175
$779$	7787.61	−	13488.5i	0.358177	−	0.620381i
$780$	−5393.64	−	9342.05i	−0.247594	−	0.428845i
$781$	2969.43	+	5143.20i	0.136049	+	0.235644i
$782$	−839.177	+	1453.50i	−0.0383746	+	0.0664667i
$783$	−1650.63			−0.0753368
$784$		0			0
$785$	−14475.9			−0.658173
$786$	−689.973	+	1195.07i	−0.0313111	+	0.0542324i
$787$	18156.6	+	31448.1i	0.822378	+	1.42440i	0.903907	+	0.427730i	$0.140686\pi$
$787$	18156.6	+	31448.1i	0.822378	+	1.42440i	−0.0815287	+	0.996671i	$0.525980\pi$
$788$	−4962.45	−	8595.21i	−0.224340	−	0.388568i
$789$	1378.56	−	2387.74i	0.0622028	−	0.107738i
$790$	−1501.88			−0.0676386
$791$		0			0
$792$	−2146.18			−0.0962895
$793$	6165.94	−	10679.7i	0.276115	−	0.478245i
$794$	1647.37	+	2853.34i	0.0736311	+	0.127533i
$795$	−5874.14	−	10174.3i	−0.262056	−	0.453893i
$796$	4335.37	−	7509.08i	0.193044	−	0.334362i
$797$	−31665.7			−1.40735			−0.703675	−	0.710522i	$-0.748459\pi$
$797$	−31665.7			−1.40735			−0.703675	+	0.710522i	$0.748459\pi$
$798$		0			0
$799$	−18979.9			−0.840375
$800$	−698.162	+	1209.25i	−0.0308547	+	0.0534419i
$801$	981.308	+	1699.68i	0.0432869	+	0.0749752i
$802$	928.081	+	1607.48i	0.0408625	+	0.0707759i
$803$	21417.7	−	37096.5i	0.941237	−	1.63027i
$804$	23137.8			1.01494
$805$		0			0
$806$	−10.5668			−0.000461788
$807$	−4168.76	+	7220.51i	−0.181843	+	0.314961i
$808$	616.105	+	1067.13i	0.0268249	+	0.0464621i
$809$	−6192.30	−	10725.4i	−0.269110	−	0.466111i	0.699523	−	0.714610i	$-0.253396\pi$
$809$	−6192.30	−	10725.4i	−0.269110	−	0.466111i	−0.968632	+	0.248499i	$0.920063\pi$
$810$	−124.929	+	216.384i	−0.00541922	+	0.00938637i
$811$	−16742.4			−0.724914			−0.362457	−	0.932000i	$-0.618062\pi$
$811$	−16742.4			−0.724914			−0.362457	+	0.932000i	$0.618062\pi$
$812$		0			0
$813$	−6680.94			−0.288205
$814$	−520.116	+	900.868i	−0.0223957	+	0.0387904i
$815$	7186.45	+	12447.3i	0.308872	+	0.534982i
$816$	−4571.91	−	7918.78i	−0.196138	−	0.339722i
$817$	−4409.04	+	7636.67i	−0.188804	+	0.327018i
$818$	3422.55			0.146292
$819$		0			0
$820$	30414.6			1.29527
$821$	−13228.2	+	22911.9i	−0.562322	+	0.973970i	0.434971	+	0.900444i	$0.356759\pi$
$821$	−13228.2	+	22911.9i	−0.562322	+	0.973970i	−0.997293	+	0.0735259i	$0.976575\pi$
$822$	190.190	+	329.419i	0.00807012	+	0.0139779i
$823$	−11549.3	−	20003.9i	−0.489164	−	0.847257i	0.510758	−	0.859724i	$-0.329365\pi$
$823$	−11549.3	−	20003.9i	−0.489164	−	0.847257i	−0.999922	+	0.0124673i	$0.996031\pi$
$824$	295.074	−	511.083i	0.0124750	−	0.0216073i
$825$	5359.17			0.226160
$826$		0			0
$827$	20647.6			0.868183			0.434092	−	0.900869i	$-0.357069\pi$
$827$	20647.6			0.868183			0.434092	+	0.900869i	$0.357069\pi$
$828$	4958.09	−	8587.67i	0.208099	−	0.360437i
$829$	−11684.3	−	20237.7i	−0.489519	−	0.847871i	0.510409	−	0.859932i	$-0.329494\pi$
$829$	−11684.3	−	20237.7i	−0.489519	−	0.847871i	−0.999927	+	0.0120609i	$0.996161\pi$
$830$	934.176	+	1618.04i	0.0390671	+	0.0676662i
$831$	−10961.5	+	18985.9i	−0.457583	+	0.792557i
$832$	17795.3			0.741514
$833$		0			0
$834$	−1686.47			−0.0700212
$835$	−17971.8	+	31128.0i	−0.744838	+	1.29010i
$836$	12101.2	+	20959.8i	0.500631	+	0.867119i
$837$	−15.7863	−	27.3426i	−0.000651915	−	0.00112915i
$838$	1178.04	−	2040.42i	0.0485617	−	0.0841113i
$839$	−16735.5			−0.688645			−0.344322	−	0.938851i	$-0.611891\pi$
$839$	−16735.5			−0.688645			−0.344322	+	0.938851i	$0.611891\pi$
$840$		0			0
$841$	−20651.6			−0.846758
$842$	−77.4439	+	134.137i	−0.00316971	+	0.00549009i
$843$	−4095.92	−	7094.34i	−0.167344	−	0.289848i
$844$	−14368.8	−	24887.5i	−0.586013	−	1.01500i
$845$	5409.56	−	9369.63i	0.220230	−	0.381450i
$846$	−869.307			−0.0353279
$847$		0			0
$848$	19691.9			0.797432
$849$	−2654.78	+	4598.21i	−0.107317	+	0.185878i
$850$	−179.087	−	310.188i	−0.00722662	−	0.0125169i
$851$	−4824.90	−	8356.97i	−0.194354	−	0.336631i
$852$	−1172.55	+	2030.91i	−0.0471488	+	0.0816642i
$853$	10294.5			0.413219			0.206609	−	0.978424i	$-0.433757\pi$
$853$	10294.5			0.413219			0.206609	+	0.978424i	$0.433757\pi$
$854$		0			0
$855$	5657.12			0.226280
$856$	1683.40	−	2915.74i	0.0672168	−	0.116423i
$857$	−16394.3	−	28395.7i	−0.653463	−	1.13183i	−0.982277	−	0.187437i	$-0.939982\pi$
$857$	−16394.3	−	28395.7i	−0.653463	−	1.13183i	0.328813	−	0.944395i	$-0.393351\pi$
$858$	817.507	+	1415.96i	0.0325282	+	0.0563405i
$859$	−2454.88	+	4251.98i	−0.0975081	+	0.168889i	−0.910653	−	0.413173i	$-0.864421\pi$
$859$	−2454.88	+	4251.98i	−0.0975081	+	0.168889i	0.813145	+	0.582062i	$0.197754\pi$
$860$	−17219.5			−0.682768
$861$		0			0
$862$	−3323.49			−0.131321
$863$	−8897.48	+	15410.9i	−0.350954	+	0.607871i	−0.986417	−	0.164261i	$-0.947476\pi$
$863$	−8897.48	+	15410.9i	−0.350954	+	0.607871i	0.635463	+	0.772132i	$0.280809\pi$
$864$	−636.420	−	1102.31i	−0.0250596	−	0.0434044i
$865$	11781.4	+	20406.0i	0.463097	+	0.802108i
$866$	−1743.60	+	3020.01i	−0.0684181	+	0.118504i
$867$	−7610.44			−0.298113
$868$		0			0
$869$	−29364.7			−1.14629
$870$	282.870	−	489.945i	0.0110232	−	0.0190928i
$871$	−17695.3	−	30649.1i	−0.688383	−	1.19231i
$872$	2692.36	+	4663.30i	0.104558	+	0.181100i
$873$	−3520.30	+	6097.33i	−0.136476	+	0.236384i
$874$	1740.46			0.0673592
$875$		0			0
$876$	16914.5			0.652384
$877$	−17336.1	+	30027.0i	−0.667501	+	1.15615i	0.311099	+	0.950377i	$0.399303\pi$
$877$	−17336.1	+	30027.0i	−0.667501	+	1.15615i	−0.978601	+	0.205769i	$0.934030\pi$
$878$	−2030.33	−	3516.63i	−0.0780412	−	0.135171i
$879$	12343.2	+	21379.1i	0.473636	+	0.820362i
$880$	−23446.0	+	40609.7i	−0.898141	+	1.55563i
$881$	−40848.2			−1.56210			−0.781051	−	0.624467i	$-0.785316\pi$
$881$	−40848.2			−1.56210			−0.781051	+	0.624467i	$0.785316\pi$
$882$		0			0
$883$	30035.1			1.14469			0.572345	−	0.820013i	$-0.306034\pi$
$883$	30035.1			1.14469			0.572345	+	0.820013i	$0.306034\pi$
$884$	−7048.04	+	12207.6i	−0.268158	+	0.464463i
$885$	15752.0	+	27283.3i	0.598304	+	1.03629i
$886$	146.202	+	253.230i	0.00554375	+	0.00960205i
$887$	16605.4	−	28761.3i	0.628583	−	1.08874i	−0.359253	−	0.933240i	$-0.616968\pi$
$887$	16605.4	−	28761.3i	0.628583	−	1.08874i	0.987836	−	0.155498i	$-0.0496983\pi$
$888$	−824.703			−0.0311658
$889$		0			0
$890$	−672.671			−0.0253348
$891$	−2442.62	+	4230.74i	−0.0918415	+	0.159074i
$892$	729.721	+	1263.91i	0.0273911	+	0.0474428i
$893$	9841.11	+	17045.3i	0.368780	+	0.638745i
$894$	−561.102	+	971.856i	−0.0209911	+	0.0363577i
$895$	−53325.7			−1.99160
$896$		0			0
$897$	−15167.3			−0.564573
$898$	1538.16	−	2664.17i	0.0571592	−	0.0990027i
$899$	35.7439	+	61.9102i	0.00132606	+	0.00229680i
$900$	1058.10	+	1832.67i	0.0391887	+	0.0678768i
$901$	−7675.93	+	13295.1i	−0.283820	+	0.491591i
$902$	−4609.90			−0.170169
$903$		0			0
$904$	−4145.86			−0.152532
$905$	2385.78	−	4132.29i	0.0876310	−	0.151781i
$906$	−592.331	−	1025.95i	−0.0217206	−	0.0376212i
$907$	−1248.92	−	2163.18i	−0.0457217	−	0.0791923i	0.842259	−	0.539073i	$-0.181225\pi$
$907$	−1248.92	−	2163.18i	−0.0457217	−	0.0791923i	−0.887981	+	0.459881i	$0.847892\pi$
$908$	−9047.93	+	15671.5i	−0.330690	+	0.572771i
$909$	2804.81			0.102343
$910$		0			0
$911$	−1895.00			−0.0689180			−0.0344590	−	0.999406i	$-0.510971\pi$
$911$	−1895.00			−0.0689180			−0.0344590	+	0.999406i	$0.510971\pi$
$912$	−4741.09	+	8211.82i	−0.172142	+	0.298158i
$913$	18265.0	+	31635.9i	0.662084	+	1.14676i
$914$	−1231.13	−	2132.38i	−0.0445538	−	0.0771694i
$915$	−6314.38	+	10936.8i	−0.228139	+	0.395148i
$916$	42968.3			1.54990
$917$		0			0
$918$	326.499			0.0117386
$919$	−3135.36	+	5430.59i	−0.112542	+	0.194928i	−0.916794	−	0.399360i	$-0.869233\pi$
$919$	−3135.36	+	5430.59i	−0.112542	+	0.194928i	0.804253	+	0.594287i	$0.202566\pi$
$920$	3411.86	+	5909.52i	0.122267	+	0.211773i
$921$	9029.44	+	15639.4i	0.323051	+	0.559541i
$922$	−1985.85	+	3439.59i	−0.0709332	+	0.122860i
$923$	3586.95			0.127915
$924$		0			0
$925$	2059.34			0.0732008
$926$	−2154.80	+	3732.23i	−0.0764700	+	0.132450i
$927$	−671.660	−	1163.35i	−0.0237974	−	0.0412183i
$928$	1441.01	+	2495.90i	0.0509735	+	0.0882887i
$929$	−15776.3	+	27325.3i	−0.557161	+	0.965032i	0.440570	+	0.897718i	$0.354776\pi$
$929$	−15776.3	+	27325.3i	−0.557161	+	0.965032i	−0.997732	+	0.0673138i	$0.978557\pi$
$930$	10.8212			0.000381550
$931$		0			0
$932$	−9036.89			−0.317611
$933$	1790.57	−	3101.36i	0.0628303	−	0.108825i
$934$	261.476	+	452.889i	0.00916033	+	0.0158662i
$935$	−18278.6	−	31659.4i	−0.639330	−	1.10735i
$936$	−648.125	+	1122.59i	−0.0226331	+	0.0392018i
$937$	22030.2			0.768084			0.384042	−	0.923316i	$-0.374532\pi$
$937$	22030.2			0.768084			0.384042	+	0.923316i	$0.374532\pi$
$938$		0			0
$939$	26538.1			0.922299
$940$	−19217.3	+	33285.3i	−0.666806	+	1.15494i
$941$	−16269.3	−	28179.3i	−0.563618	−	0.976214i	−0.997177	−	0.0750892i	$-0.976076\pi$
$941$	−16269.3	−	28179.3i	−0.563618	−	0.976214i	0.433559	−	0.901125i	$-0.357258\pi$
$942$	433.193	+	750.312i	0.0149832	+	0.0259517i
$943$	21382.0	−	37034.8i	0.738383	−	1.27892i
$944$	−52805.6			−1.82063
$945$		0			0
$946$	2609.94			0.0897003
$947$	20355.5	−	35256.8i	0.698485	−	1.20981i	−0.270507	−	0.962718i	$-0.587191\pi$
$947$	20355.5	−	35256.8i	0.698485	−	1.20981i	0.968992	−	0.247093i	$-0.0794753\pi$
$948$	−5797.67	−	10041.9i	−0.198628	−	0.344034i
$949$	−12935.8	−	22405.5i	−0.442481	−	0.766400i
$950$	−185.714	+	321.666i	−0.00634248	+	0.0109855i
$951$	18244.3			0.622095
$952$		0			0
$953$	−52516.4			−1.78507			−0.892536	−	0.450976i	$-0.851076\pi$
$953$	−52516.4			−1.78507			−0.892536	+	0.450976i	$0.851076\pi$
$954$	−351.569	+	608.936i	−0.0119313	+	0.0206656i
$955$	−2395.59	−	4149.29i	−0.0811723	−	0.140595i
$956$	−24713.9	−	42805.7i	−0.836091	−	1.44815i
$957$	5530.67	−	9579.40i	0.186814	−	0.323572i
$958$	607.786			0.0204976
$959$		0			0
$960$	−18223.7			−0.612673
$961$	14894.8	−	25798.6i	0.499977	−	0.865986i
$962$	314.139	+	544.105i	0.0105283	+	0.0182356i
$963$	−3831.84	−	6636.93i	−0.128223	−	0.222090i
$964$	12686.4	−	21973.6i	0.423862	−	0.734150i
$965$	7836.58			0.261418
$966$		0			0
$967$	14721.6			0.489570			0.244785	−	0.969577i	$-0.421283\pi$
$967$	14721.6			0.489570			0.244785	+	0.969577i	$0.421283\pi$
$968$	4559.78	−	7897.77i	0.151402	−	0.262235i
$969$	−3696.17	−	6401.96i	−0.122537	−	0.212240i
$970$	−1206.55	−	2089.81i	−0.0399382	−	0.0691750i
$971$	6886.25	−	11927.3i	0.227590	−	0.394198i	−0.729503	−	0.683978i	$-0.760249\pi$
$971$	6886.25	−	11927.3i	0.227590	−	0.394198i	0.957093	+	0.289779i	$0.0935819\pi$
$972$	−1929.05			−0.0636566
$973$		0			0
$974$	160.065			0.00526572
$975$	1618.41	−	2803.17i	0.0531597	−	0.0920753i
$976$	−10583.8	−	18331.8i	−0.347111	−	0.601215i
$977$	−12391.0	−	21461.9i	−0.405757	−	0.702791i	0.588653	−	0.808386i	$-0.299659\pi$
$977$	−12391.0	−	21461.9i	−0.405757	−	0.702791i	−0.994409	+	0.105595i	$0.966325\pi$
$978$	430.112	−	744.976i	0.0140628	−	0.0243576i
$979$	−13152.0			−0.429358
$980$		0			0
$981$	12256.9			0.398912
$982$	−1459.42	+	2527.79i	−0.0474257	+	0.0821437i
$983$	21402.4	+	37070.0i	0.694435	+	1.20280i	0.970371	+	0.241620i	$0.0776788\pi$
$983$	21402.4	+	37070.0i	0.694435	+	1.20280i	−0.275936	+	0.961176i	$0.588988\pi$
$984$	−1827.38	−	3165.11i	−0.0592019	−	0.102541i
$985$	7773.05	−	13463.3i	0.251442	−	0.435510i
$986$	−739.271			−0.0238775
$987$		0			0
$988$	14617.7			0.470700
$989$	−12105.7	+	20967.6i	−0.389219	+	0.674147i
$990$	−837.187	−	1450.05i	−0.0268763	−	0.0465511i
$991$	−224.931	−	389.592i	−0.00721006	−	0.0124882i	0.862398	−	0.506231i	$-0.168962\pi$
$991$	−224.931	−	389.592i	−0.00721006	−	0.0124882i	−0.869608	+	0.493743i	$0.835628\pi$
$992$	−27.5630	+	47.7404i	−0.000882182	+	0.00152798i
$993$	9159.89			0.292729
$994$		0			0
$995$	13581.6			0.432730
$996$	−7212.35	+	12492.1i	−0.229450	+	0.397419i
$997$	−10736.9	−	18596.8i	−0.341063	−	0.590739i	0.643567	−	0.765390i	$-0.277454\pi$
$997$	−10736.9	−	18596.8i	−0.341063	−	0.590739i	−0.984630	+	0.174651i	$0.944120\pi$
$998$	5.46017	+	9.45729i	0.000173185	+	0.000299965i
$999$	−938.612	+	1625.72i	−0.0297261	+	0.0514871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.n.79.2		6
3.2	odd	2		441.4.e.w.226.2		6
7.2	even	3		147.4.a.m.1.2		3
7.3	odd	6		21.4.e.b.4.2	✓	6
7.4	even	3	inner	147.4.e.n.67.2		6
7.5	odd	6		147.4.a.l.1.2		3
7.6	odd	2		21.4.e.b.16.2	yes	6
21.2	odd	6		441.4.a.t.1.2		3
21.5	even	6		441.4.a.s.1.2		3
21.11	odd	6		441.4.e.w.361.2		6
21.17	even	6		63.4.e.c.46.2		6
21.20	even	2		63.4.e.c.37.2		6
28.3	even	6		336.4.q.k.193.3		6
28.19	even	6		2352.4.a.ci.1.1		3
28.23	odd	6		2352.4.a.cg.1.3		3
28.27	even	2		336.4.q.k.289.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.2	✓	6	7.3	odd	6
21.4.e.b.16.2	yes	6	7.6	odd	2
63.4.e.c.37.2		6	21.20	even	2
63.4.e.c.46.2		6	21.17	even	6
147.4.a.l.1.2		3	7.5	odd	6
147.4.a.m.1.2		3	7.2	even	3
147.4.e.n.67.2		6	7.4	even	3	inner
147.4.e.n.79.2		6	1.1	even	1	trivial
336.4.q.k.193.3		6	28.3	even	6
336.4.q.k.289.3		6	28.27	even	2
441.4.a.s.1.2		3	21.5	even	6
441.4.a.t.1.2		3	21.2	odd	6
441.4.e.w.226.2		6	3.2	odd	2
441.4.e.w.361.2		6	21.11	odd	6
2352.4.a.cg.1.3		3	28.23	odd	6
2352.4.a.ci.1.1		3	28.19	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)

\(f(q)\)	\(=\)	\(q+(-0.124036 + 0.214837i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(-6.21730 + 10.7687i) q^{5} +0.744216 q^{6} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-0.124036 + 0.214837i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(-6.21730 + 10.7687i) q^{5} +0.744216 q^{6} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-1.54234 - 2.67141i) q^{10} +(-30.1558 - 52.2313i) q^{11} +(11.9077 - 20.6247i) q^{12} -36.4269 q^{13} +37.3038 q^{15} +(-31.2634 + 54.1498i) q^{16} +(-24.3731 - 42.2154i) q^{17} +(-1.11632 - 1.93353i) q^{18} +(-25.2750 + 43.7776i) q^{19} -98.7116 q^{20} +14.9616 q^{22} +(-69.3962 + 120.198i) q^{23} +(5.93083 + 10.2725i) q^{24} +(-14.8097 - 25.6511i) q^{25} +(4.51824 - 7.82583i) q^{26} +27.0000 q^{27} -61.1345 q^{29} +(-4.62701 + 8.01422i) q^{30} +(-0.584676 - 1.01269i) q^{31} +(-23.5711 - 40.8264i) q^{32} +(-90.4673 + 156.694i) q^{33} +12.0925 q^{34} -71.4461 q^{36} +(-34.7634 + 60.2120i) q^{37} +(-6.27001 - 10.8600i) q^{38} +(54.6403 + 94.6398i) q^{39} +(24.5825 - 42.5781i) q^{40} -308.115 q^{41} +174.443 q^{43} +(239.390 - 414.636i) q^{44} +(-55.9557 - 96.9181i) q^{45} +(-17.2153 - 29.8177i) q^{46} +(194.681 - 337.197i) q^{47} +187.581 q^{48} +7.34774 q^{50} +(-73.1192 + 126.646i) q^{51} +(-144.587 - 250.432i) q^{52} +(-157.467 - 272.742i) q^{53} +(-3.34897 + 5.80059i) q^{54} +749.950 q^{55} +151.650 q^{57} +(7.58287 - 13.1339i) q^{58} +(422.263 + 731.381i) q^{59} +(148.067 + 256.460i) q^{60} +(-169.269 + 293.182i) q^{61} +0.290084 q^{62} -488.520 q^{64} +(226.477 - 392.270i) q^{65} +(-22.4424 - 38.8714i) q^{66} +(485.775 + 841.387i) q^{67} +(193.485 - 335.125i) q^{68} +416.377 q^{69} -98.4698 q^{71} +(17.7925 - 30.8175i) q^{72} +(355.117 + 615.082i) q^{73} +(-8.62383 - 14.9369i) q^{74} +(-44.4291 + 76.9534i) q^{75} -401.289 q^{76} -27.1095 q^{78} +(243.442 - 421.654i) q^{79} +(-388.748 - 673.332i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(38.2174 - 66.1944i) q^{82} -605.688 q^{83} +606.139 q^{85} +(-21.6372 + 37.4767i) q^{86} +(91.7017 + 158.832i) q^{87} +(119.232 + 206.517i) q^{88} +(109.034 - 188.853i) q^{89} +27.7621 q^{90} -1101.80 q^{92} +(-1.75403 + 3.03807i) q^{93} +(48.2949 + 83.6491i) q^{94} +(-314.284 - 544.357i) q^{95} +(-70.7133 + 122.479i) q^{96} +782.288 q^{97} +542.804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 9 q^{3} - 25 q^{4} + 11 q^{5} + 6 q^{6} + 78 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q - q^2 - 9 * q^3 - 25 * q^4 + 11 * q^5 + 6 * q^6 + 78 * q^8 - 27 * q^9	\( 6 q - q^{2} - 9 q^{3} - 25 q^{4} + 11 q^{5} + 6 q^{6} + 78 q^{8} - 27 q^{9} - 55 q^{10} - 35 q^{11} - 75 q^{12} - 124 q^{13} - 66 q^{15} - 241 q^{16} + 48 q^{17} - 9 q^{18} - 202 q^{19} - 878 q^{20} - 14 q^{22} - 216 q^{23} - 117 q^{24} - 130 q^{25} + 274 q^{26} + 162 q^{27} + 106 q^{29} - 165 q^{30} - 95 q^{31} - 683 q^{32} - 105 q^{33} + 48 q^{34} + 450 q^{36} - 262 q^{37} - 398 q^{38} + 186 q^{39} + 21 q^{40} - 488 q^{41} + 720 q^{43} + 905 q^{44} + 99 q^{45} + 1056 q^{46} - 210 q^{47} + 1446 q^{48} - 2756 q^{50} + 144 q^{51} + 324 q^{52} - 393 q^{53} - 27 q^{54} + 2062 q^{55} + 1212 q^{57} + 1249 q^{58} + 1143 q^{59} + 1317 q^{60} - 70 q^{61} - 2118 q^{62} - 798 q^{64} + 472 q^{65} + 21 q^{66} + 628 q^{67} + 1944 q^{68} + 1296 q^{69} + 636 q^{71} - 351 q^{72} + 988 q^{73} - 1002 q^{74} - 390 q^{75} + 4680 q^{76} - 1644 q^{78} - 861 q^{79} + 175 q^{80} - 243 q^{81} + 124 q^{82} - 1038 q^{83} + 3600 q^{85} + 3208 q^{86} - 159 q^{87} + 891 q^{88} + 1766 q^{89} + 990 q^{90} - 1344 q^{92} - 285 q^{93} - 3294 q^{94} + 736 q^{95} - 2049 q^{96} - 38 q^{97} + 630 q^{99}+O(q^{100}) \) 6 * q - q^2 - 9 * q^3 - 25 * q^4 + 11 * q^5 + 6 * q^6 + 78 * q^8 - 27 * q^9 - 55 * q^10 - 35 * q^11 - 75 * q^12 - 124 * q^13 - 66 * q^15 - 241 * q^16 + 48 * q^17 - 9 * q^18 - 202 * q^19 - 878 * q^20 - 14 * q^22 - 216 * q^23 - 117 * q^24 - 130 * q^25 + 274 * q^26 + 162 * q^27 + 106 * q^29 - 165 * q^30 - 95 * q^31 - 683 * q^32 - 105 * q^33 + 48 * q^34 + 450 * q^36 - 262 * q^37 - 398 * q^38 + 186 * q^39 + 21 * q^40 - 488 * q^41 + 720 * q^43 + 905 * q^44 + 99 * q^45 + 1056 * q^46 - 210 * q^47 + 1446 * q^48 - 2756 * q^50 + 144 * q^51 + 324 * q^52 - 393 * q^53 - 27 * q^54 + 2062 * q^55 + 1212 * q^57 + 1249 * q^58 + 1143 * q^59 + 1317 * q^60 - 70 * q^61 - 2118 * q^62 - 798 * q^64 + 472 * q^65 + 21 * q^66 + 628 * q^67 + 1944 * q^68 + 1296 * q^69 + 636 * q^71 - 351 * q^72 + 988 * q^73 - 1002 * q^74 - 390 * q^75 + 4680 * q^76 - 1644 * q^78 - 861 * q^79 + 175 * q^80 - 243 * q^81 + 124 * q^82 - 1038 * q^83 + 3600 * q^85 + 3208 * q^86 - 159 * q^87 + 891 * q^88 + 1766 * q^89 + 990 * q^90 - 1344 * q^92 - 285 * q^93 - 3294 * q^94 + 736 * q^95 - 2049 * q^96 - 38 * q^97 + 630 * q^99

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