LMFDB - Embedded newform 147.4.e.n.79.1

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			79.1
Root			$2.65415 - 4.59712i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.n.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65415 + 4.59712i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-10.0890 - 17.4746i) q^{4} +(2.78070 - 4.81631i) q^{5} +15.9249 q^{6} +64.6443 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-2.65415 + 4.59712i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-10.0890 - 17.4746i) q^{4} +(2.78070 - 4.81631i) q^{5} +15.9249 q^{6} +64.6443 q^{8} +(-4.50000 + 7.79423i) q^{9} +(14.7608 + 25.5664i) q^{10} +(6.95869 + 12.0528i) q^{11} +(-30.2670 + 52.4239i) q^{12} -38.6718 q^{13} -16.6842 q^{15} +(-90.8636 + 157.380i) q^{16} +(21.7394 + 37.6537i) q^{17} +(-23.8873 - 41.3741i) q^{18} +(-54.5139 + 94.4208i) q^{19} -112.218 q^{20} -73.8775 q^{22} +(37.4389 - 64.8461i) q^{23} +(-96.9665 - 167.951i) q^{24} +(47.0354 + 81.4677i) q^{25} +(102.641 - 177.779i) q^{26} +27.0000 q^{27} -72.3589 q^{29} +(44.2823 - 76.6992i) q^{30} +(32.0215 + 55.4629i) q^{31} +(-223.754 - 387.553i) q^{32} +(20.8761 - 36.1584i) q^{33} -230.798 q^{34} +181.602 q^{36} +(-94.3636 + 163.443i) q^{37} +(-289.376 - 501.213i) q^{38} +(58.0077 + 100.472i) q^{39} +(179.756 - 311.347i) q^{40} +24.7923 q^{41} -243.881 q^{43} +(140.412 - 243.201i) q^{44} +(25.0263 + 43.3468i) q^{45} +(198.737 + 344.222i) q^{46} +(-310.274 + 537.411i) q^{47} +545.182 q^{48} -499.356 q^{50} +(65.2182 - 112.961i) q^{51} +(390.159 + 675.776i) q^{52} +(143.919 + 249.276i) q^{53} +(-71.6620 + 124.122i) q^{54} +77.4001 q^{55} +327.083 q^{57} +(192.051 - 332.642i) q^{58} +(262.526 + 454.708i) q^{59} +(168.327 + 291.551i) q^{60} +(-191.718 + 332.065i) q^{61} -339.960 q^{62} +921.681 q^{64} +(-107.535 + 186.255i) q^{65} +(110.816 + 191.939i) q^{66} +(-99.0583 - 171.574i) q^{67} +(438.657 - 759.776i) q^{68} -224.634 q^{69} +785.432 q^{71} +(-290.900 + 503.853i) q^{72} +(-165.570 - 286.776i) q^{73} +(-500.910 - 867.602i) q^{74} +(141.106 - 244.403i) q^{75} +2199.96 q^{76} -615.844 q^{78} +(-218.823 + 379.013i) q^{79} +(505.329 + 875.255i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-65.8024 + 113.973i) q^{82} -241.241 q^{83} +241.803 q^{85} +(647.297 - 1121.15i) q^{86} +(108.538 + 187.994i) q^{87} +(449.840 + 779.145i) q^{88} +(792.772 - 1373.12i) q^{89} -265.694 q^{90} -1510.88 q^{92} +(96.0646 - 166.389i) q^{93} +(-1647.03 - 2852.73i) q^{94} +(303.173 + 525.112i) q^{95} +(-671.261 + 1162.66i) q^{96} -79.2754 q^{97} -125.256 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 $

$2$	−2.65415	+	4.59712i	−0.938383	+	1.62533i	−0.169895	+	0.985462i	$0.554343\pi$
$2$	−2.65415	+	4.59712i	−0.938383	+	1.62533i	−0.768488	+	0.639864i	$0.778991\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−10.0890	−	17.4746i	−1.26112	−	2.18433i
$5$	2.78070	−	4.81631i	0.248713	−	0.430784i	−0.714456	−	0.699681i	$-0.753326\pi$
$5$	2.78070	−	4.81631i	0.248713	−	0.430784i	0.963169	+	0.268897i	$0.0866590\pi$
$6$	15.9249			1.08355
$7$		0			0
$7$		0			0
$8$	64.6443			2.85690
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	14.7608	+	25.5664i	0.466777	+	0.808481i
$11$	6.95869	+	12.0528i	0.190738	+	0.330369i	0.945495	−	0.325636i	$-0.105578\pi$
$11$	6.95869	+	12.0528i	0.190738	+	0.330369i	−0.754757	+	0.656005i	$0.772245\pi$
$12$	−30.2670	+	52.4239i	−0.728110	+	1.26112i
$13$	−38.6718			−0.825048			−0.412524	−	0.910947i	$-0.635353\pi$
$13$	−38.6718			−0.825048			−0.412524	+	0.910947i	$0.635353\pi$
$14$		0			0
$15$	−16.6842			−0.287189
$16$	−90.8636	+	157.380i	−1.41974	+	2.45907i
$17$	21.7394	+	37.6537i	0.310152	+	0.537198i	0.978395	−	0.206744i	$-0.0662869\pi$
$17$	21.7394	+	37.6537i	0.310152	+	0.537198i	−0.668243	+	0.743943i	$0.732954\pi$
$18$	−23.8873	−	41.3741i	−0.312794	−	0.541776i
$19$	−54.5139	+	94.4208i	−0.658228	+	1.14009i	0.322845	+	0.946452i	$0.395361\pi$
$19$	−54.5139	+	94.4208i	−0.658228	+	1.14009i	−0.981074	+	0.193633i	$0.937973\pi$
$20$	−112.218			−1.25463
$21$		0			0
$22$	−73.8775			−0.715943
$23$	37.4389	−	64.8461i	0.339415	−	0.587885i	−0.644907	−	0.764261i	$-0.723104\pi$
$23$	37.4389	−	64.8461i	0.339415	−	0.587885i	0.984323	+	0.176376i	$0.0564374\pi$
$24$	−96.9665	−	167.951i	−0.824717	−	1.42845i
$25$	47.0354	+	81.4677i	0.376283	+	0.651742i
$26$	102.641	−	177.779i	0.774211	−	1.34097i
$27$	27.0000			0.192450
$28$		0			0
$29$	−72.3589			−0.463335			−0.231667	−	0.972795i	$-0.574418\pi$
$29$	−72.3589			−0.463335			−0.231667	+	0.972795i	$0.574418\pi$
$30$	44.2823	−	76.6992i	0.269494	−	0.466777i
$31$	32.0215	+	55.4629i	0.185524	+	0.321337i	0.943753	−	0.330652i	$-0.107268\pi$
$31$	32.0215	+	55.4629i	0.185524	+	0.321337i	−0.758229	+	0.651988i	$0.773935\pi$
$32$	−223.754	−	387.553i	−1.23608	−	2.14095i
$33$	20.8761	−	36.1584i	0.110123	−	0.190738i
$34$	−230.798			−1.16416
$35$		0			0
$36$	181.602			0.840749
$37$	−94.3636	+	163.443i	−0.419278	+	0.726211i	−0.995867	−	0.0908235i	$-0.971050\pi$
$37$	−94.3636	+	163.443i	−0.419278	+	0.726211i	0.576589	+	0.817034i	$0.304383\pi$
$38$	−289.376	−	501.213i	−1.23534	−	2.13967i
$39$	58.0077	+	100.472i	0.238171	+	0.412524i
$40$	179.756	−	311.347i	0.710550	−	1.23071i
$41$	24.7923			0.0944367			0.0472184	−	0.998885i	$-0.484964\pi$
$41$	24.7923			0.0944367			0.0472184	+	0.998885i	$0.484964\pi$
$42$		0			0
$43$	−243.881			−0.864920			−0.432460	−	0.901653i	$-0.642354\pi$
$43$	−243.881			−0.864920			−0.432460	+	0.901653i	$0.642354\pi$
$44$	140.412	−	243.201i	0.481090	−	0.833272i
$45$	25.0263	+	43.3468i	0.0829044	+	0.143595i
$46$	198.737	+	344.222i	0.637003	+	1.10332i
$47$	−310.274	+	537.411i	−0.962940	+	1.66786i	−0.247888	+	0.968789i	$0.579736\pi$
$47$	−310.274	+	537.411i	−0.962940	+	1.66786i	−0.715052	+	0.699071i	$0.753597\pi$
$48$	545.182			1.63938
$49$		0			0
$50$	−499.356			−1.41239
$51$	65.2182	−	112.961i	0.179066	−	0.310152i
$52$	390.159	+	675.776i	1.04049	+	1.80218i
$53$	143.919	+	249.276i	0.372997	+	0.646050i	0.990025	−	0.140891i	$-0.0449967\pi$
$53$	143.919	+	249.276i	0.372997	+	0.646050i	−0.617028	+	0.786941i	$0.711663\pi$
$54$	−71.6620	+	124.122i	−0.180592	+	0.312794i
$55$	77.4001			0.189757
$56$		0			0
$57$	327.083			0.760057
$58$	192.051	−	332.642i	0.434785	−	0.753070i
$59$	262.526	+	454.708i	0.579287	+	1.00335i	0.995561	+	0.0941152i	$0.0300022\pi$
$59$	262.526	+	454.708i	0.579287	+	1.00335i	−0.416275	+	0.909239i	$0.636664\pi$
$60$	168.327	+	291.551i	0.362182	+	0.627317i
$61$	−191.718	+	332.065i	−0.402409	+	0.696993i	−0.994016	−	0.109234i	$-0.965160\pi$
$61$	−191.718	+	332.065i	−0.402409	+	0.696993i	0.591607	+	0.806226i	$0.298494\pi$
$62$	−339.960			−0.696369
$63$		0			0
$64$	921.681			1.80016
$65$	−107.535	+	186.255i	−0.205200	+	0.355417i
$66$	110.816	+	191.939i	0.206675	+	0.357971i
$67$	−99.0583	−	171.574i	−0.180625	−	0.312852i	0.761468	−	0.648202i	$-0.224479\pi$
$67$	−99.0583	−	171.574i	−0.180625	−	0.312852i	−0.942094	+	0.335350i	$0.891145\pi$
$68$	438.657	−	759.776i	0.782279	−	1.35495i
$69$	−224.634			−0.391923
$70$		0			0
$71$	785.432			1.31287			0.656434	−	0.754384i	$-0.272064\pi$
$71$	785.432			1.31287			0.656434	+	0.754384i	$0.272064\pi$
$72$	−290.900	+	503.853i	−0.476151	+	0.824717i
$73$	−165.570	−	286.776i	−0.265459	−	0.459789i	0.702224	−	0.711956i	$-0.252190\pi$
$73$	−165.570	−	286.776i	−0.265459	−	0.459789i	−0.967684	+	0.252166i	$0.918857\pi$
$74$	−500.910	−	867.602i	−0.786887	−	1.36293i
$75$	141.106	−	244.403i	0.217247	−	0.376283i
$76$	2199.96			3.32043
$77$		0			0
$78$	−615.844			−0.893981
$79$	−218.823	+	379.013i	−0.311640	+	0.539776i	−0.978718	−	0.205212i	$-0.934212\pi$
$79$	−218.823	+	379.013i	−0.311640	+	0.539776i	0.667078	+	0.744988i	$0.267545\pi$
$80$	505.329	+	875.255i	0.706219	+	1.22321i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−65.8024	+	113.973i	−0.0886178	+	0.153491i
$83$	−241.241			−0.319032			−0.159516	−	0.987195i	$-0.550993\pi$
$83$	−241.241			−0.319032			−0.159516	+	0.987195i	$0.550993\pi$
$84$		0			0
$85$	241.803			0.308555
$86$	647.297	−	1121.15i	0.811626	−	1.40578i
$87$	108.538	+	187.994i	0.133753	+	0.231667i
$88$	449.840	+	779.145i	0.544921	+	0.943831i
$89$	792.772	−	1373.12i	0.944198	−	1.63540i	0.186849	−	0.982389i	$-0.440172\pi$
$89$	792.772	−	1373.12i	0.944198	−	1.63540i	0.757349	−	0.653010i	$-0.226494\pi$
$90$	−265.694			−0.311184
$91$		0			0
$92$	−1510.88			−1.71218
$93$	96.0646	−	166.389i	0.107112	−	0.185524i
$94$	−1647.03	−	2852.73i	−1.80721	−	3.13018i
$95$	303.173	+	525.112i	0.327420	+	0.567109i
$96$	−671.261	+	1162.66i	−0.713649	+	1.23608i
$97$	−79.2754			−0.0829814			−0.0414907	−	0.999139i	$-0.513211\pi$
$97$	−79.2754			−0.0829814			−0.0414907	+	0.999139i	$0.513211\pi$
$98$		0			0
$99$	−125.256			−0.127159
$100$	949.080	−	1643.85i	0.949080	−	1.64385i
$101$	577.487	+	1000.24i	0.568931	+	0.985418i	0.996672	+	0.0815165i	$0.0259763\pi$
$101$	577.487	+	1000.24i	0.568931	+	0.985418i	−0.427741	+	0.903902i	$0.640690\pi$
$102$	346.197	+	599.631i	0.336065	+	0.582082i
$103$	−722.430	+	1251.28i	−0.691098	+	1.19702i	0.280380	+	0.959889i	$0.409539\pi$
$103$	−722.430	+	1251.28i	−0.691098	+	1.19702i	−0.971478	+	0.237128i	$0.923794\pi$
$104$	−2499.91			−2.35708
$105$		0			0
$106$	−1527.93			−1.40006
$107$	−495.480	+	858.197i	−0.447662	+	0.775374i	−0.998233	−	0.0594143i	$-0.981077\pi$
$107$	−495.480	+	858.197i	−0.447662	+	0.775374i	0.550571	+	0.834788i	$0.314410\pi$
$108$	−272.403	−	471.816i	−0.242703	−	0.420375i
$109$	−976.585	−	1691.49i	−0.858164	−	1.48638i	−0.873678	−	0.486504i	$-0.838272\pi$
$109$	−976.585	−	1691.49i	−0.858164	−	1.48638i	0.0155145	−	0.999880i	$-0.495061\pi$
$110$	−205.431	+	355.817i	−0.178064	+	0.308417i
$111$	566.182			0.484141
$112$		0			0
$113$	672.882			0.560172			0.280086	−	0.959975i	$-0.409637\pi$
$113$	672.882			0.560172			0.280086	+	0.959975i	$0.409637\pi$
$114$	−868.127	+	1503.64i	−0.713224	+	1.23534i
$115$	−208.213	−	360.635i	−0.168834	−	0.292430i
$116$	730.028	+	1264.45i	0.584323	+	1.01208i
$117$	174.023	−	301.417i	0.137508	−	0.238171i
$118$	−2787.13			−2.17437
$119$		0			0
$120$	−1078.54			−0.820472
$121$	568.653	−	984.936i	0.427238	−	0.739997i
$122$	−1017.69	−	1762.70i	−0.755227	−	1.30809i
$123$	−37.1884	−	64.4123i	−0.0272615	−	0.0472184i
$124$	646.130	−	1119.13i	0.467937	−	0.810491i
$125$	1218.34			0.871773
$126$		0			0
$127$	175.815			0.122843			0.0614216	−	0.998112i	$-0.480437\pi$
$127$	175.815			0.122843			0.0614216	+	0.998112i	$0.480437\pi$
$128$	−656.249	+	1136.66i	−0.453163	+	0.784900i
$129$	365.822	+	633.622i	0.249681	+	0.432460i
$130$	−570.825	−	988.698i	−0.385113	−	0.667035i
$131$	562.965	−	975.085i	0.375470	−	0.650332i	−0.614928	−	0.788584i	$-0.710815\pi$
$131$	562.965	−	975.085i	0.375470	−	0.650332i	0.990397	+	0.138251i	$0.0441481\pi$
$132$	−842.474			−0.555515
$133$		0			0
$134$	1051.66			0.677983
$135$	75.0789	−	130.040i	0.0478649	−	0.0829044i
$136$	1405.33	+	2434.10i	0.886073	+	1.53472i
$137$	−934.350	−	1618.34i	−0.582678	−	1.00923i	−0.995161	−	0.0982624i	$-0.968672\pi$
$137$	−934.350	−	1618.34i	−0.582678	−	1.00923i	0.412483	−	0.910966i	$-0.364662\pi$
$138$	596.210	−	1032.67i	0.367774	−	0.637003i
$139$	2817.19			1.71907			0.859537	−	0.511074i	$-0.170752\pi$
$139$	2817.19			1.71907			0.859537	+	0.511074i	$0.170752\pi$
$140$		0			0
$141$	1861.65			1.11191
$142$	−2084.65	+	3610.72i	−1.23197	+	2.13384i
$143$	−269.105	−	466.103i	−0.157368	−	0.272570i
$144$	−817.773	−	1416.42i	−0.473248	−	0.819690i
$145$	−201.208	+	348.503i	−0.115238	+	0.199597i
$146$	1757.79			0.996410
$147$		0			0
$148$	3808.14			2.11505
$149$	−900.163	+	1559.13i	−0.494928	+	0.857240i	−0.999983	−	0.00584714i	$-0.998139\pi$
$149$	−900.163	+	1559.13i	−0.494928	+	0.857240i	0.505055	+	0.863087i	$0.331472\pi$
$150$	749.034	+	1297.36i	0.407722	+	0.706196i
$151$	226.492	+	392.296i	0.122064	+	0.211421i	0.920581	−	0.390551i	$-0.127715\pi$
$151$	226.492	+	392.296i	0.122064	+	0.211421i	−0.798517	+	0.601972i	$0.794382\pi$
$152$	−3524.01	+	6103.77i	−1.88050	+	3.25711i
$153$	−391.309			−0.206768
$154$		0			0
$155$	356.169			0.184569
$156$	1170.48	−	2027.33i	0.600726	−	1.04049i
$157$	−931.829	−	1613.98i	−0.473682	−	0.820441i	0.525864	−	0.850569i	$-0.323742\pi$
$157$	−931.829	−	1613.98i	−0.473682	−	0.820441i	−0.999546	+	0.0301273i	$0.990409\pi$
$158$	−1161.58	−	2011.91i	−0.584875	−	1.01303i
$159$	431.758	−	747.827i	0.215350	−	0.372997i
$160$	−2488.77			−1.22971
$161$		0			0
$162$	429.972			0.208529
$163$	−1160.57	+	2010.16i	−0.557686	+	0.965940i	0.440004	+	0.897996i	$0.354977\pi$
$163$	−1160.57	+	2010.16i	−0.557686	+	0.965940i	−0.997689	+	0.0679437i	$0.978356\pi$
$164$	−250.129	−	433.237i	−0.119096	−	0.206281i
$165$	−116.100	−	201.091i	−0.0547781	−	0.0948784i
$166$	640.290	−	1109.01i	0.299374	−	0.518531i
$167$	−3211.62			−1.48816			−0.744079	−	0.668092i	$-0.767111\pi$
$167$	−3211.62			−1.48816			−0.744079	+	0.668092i	$0.767111\pi$
$168$		0			0
$169$	−701.494			−0.319296
$170$	−641.780	+	1111.60i	−0.289543	+	0.501503i
$171$	−490.625	−	849.787i	−0.219409	−	0.380028i
$172$	2460.52	+	4261.74i	1.09077	+	1.88927i
$173$	107.139	−	185.569i	0.0470844	−	0.0815525i	−0.841523	−	0.540222i	$-0.818340\pi$
$173$	107.139	−	185.569i	0.0470844	−	0.0815525i	0.888607	+	0.458669i	$0.151674\pi$
$174$	−1152.31			−0.502047
$175$		0			0
$176$	−2529.17			−1.08320
$177$	787.577	−	1364.12i	0.334451	−	0.579287i
$178$	4208.27	+	7288.93i	1.77204	+	3.06926i
$179$	1218.61	+	2110.70i	0.508845	+	0.881345i	0.999948	+	0.0102437i	$0.00326072\pi$
$179$	1218.61	+	2110.70i	0.508845	+	0.881345i	−0.491102	+	0.871102i	$0.663406\pi$
$180$	504.980	−	874.652i	0.209106	−	0.362182i
$181$	248.631			0.102103			0.0510514	−	0.998696i	$-0.483743\pi$
$181$	248.631			0.102103			0.0510514	+	0.998696i	$0.483743\pi$
$182$		0			0
$183$	1150.31			0.464662
$184$	2420.21	−	4191.93i	0.969677	−	1.67953i
$185$	524.794	+	908.970i	0.208560	+	0.361237i
$186$	509.939	+	883.241i	0.201025	+	0.348185i
$187$	−302.555	+	524.041i	−0.118316	+	0.204929i
$188$	12521.4			4.85755
$189$		0			0
$190$	−3218.67			−1.22898
$191$	2156.54	−	3735.24i	0.816972	−	1.41504i	−0.0909306	−	0.995857i	$-0.528984\pi$
$191$	2156.54	−	3735.24i	0.816972	−	1.41504i	0.907903	−	0.419180i	$-0.137683\pi$
$192$	−1382.52	−	2394.60i	−0.519661	−	0.900079i
$193$	−1030.43	−	1784.75i	−0.384309	−	0.665643i	0.607364	−	0.794424i	$-0.292227\pi$
$193$	−1030.43	−	1784.75i	−0.384309	−	0.665643i	−0.991673	+	0.128781i	$0.958894\pi$
$194$	210.409	−	364.438i	0.0778683	−	0.134872i
$195$	645.208			0.236945
$196$		0			0
$197$	−1666.09			−0.602557			−0.301279	−	0.953536i	$-0.597413\pi$
$197$	−1666.09			−0.602557			−0.301279	+	0.953536i	$0.597413\pi$
$198$	332.449	−	575.818i	0.119324	−	0.206675i
$199$	−543.767	−	941.832i	−0.193702	−	0.335501i	0.752773	−	0.658281i	$-0.228716\pi$
$199$	−543.767	−	941.832i	−0.193702	−	0.335501i	−0.946474	+	0.322780i	$0.895383\pi$
$200$	3040.57	+	5266.43i	1.07501	+	1.86196i
$201$	−297.175	+	514.722i	−0.104284	+	0.180625i
$202$	−6130.94			−2.13550
$203$		0			0
$204$	−2631.94			−0.903298
$205$	68.9399	−	119.407i	0.0234877	−	0.0406818i
$206$	−3834.87	−	6642.19i	−1.29703	−	2.24652i
$207$	336.950	+	583.615i	0.113138	+	0.195962i
$208$	3513.86	−	6086.18i	1.17136	−	2.02885i
$209$	−1517.38			−0.502198
$210$		0			0
$211$	−4676.47			−1.52579			−0.762895	−	0.646522i	$-0.776223\pi$
$211$	−4676.47			−1.52579			−0.762895	+	0.646522i	$0.776223\pi$
$212$	2904.01	−	5029.88i	0.940792	−	1.62950i
$213$	−1178.15	−	2040.61i	−0.378992	−	0.656434i
$214$	−2630.15	−	4555.56i	−0.840157	−	1.45520i
$215$	−678.161	+	1174.61i	−0.215117	+	0.372594i
$216$	1745.40			0.549811
$217$		0			0
$218$	10368.0			3.22114
$219$	−496.711	+	860.329i	−0.153263	+	0.265459i
$220$	−780.889	−	1352.54i	−0.239307	−	0.414492i
$221$	−840.701	−	1456.14i	−0.255890	−	0.443214i
$222$	−1502.73	+	2602.80i	−0.454309	+	0.786887i
$223$	−3246.03			−0.974754			−0.487377	−	0.873192i	$-0.662046\pi$
$223$	−3246.03			−0.974754			−0.487377	+	0.873192i	$0.662046\pi$
$224$		0			0
$225$	−846.638			−0.250856
$226$	−1785.93	+	3093.32i	−0.525656	+	0.910463i
$227$	2569.08	+	4449.77i	0.751171	+	1.30107i	0.947256	+	0.320479i	$0.103844\pi$
$227$	2569.08	+	4449.77i	0.751171	+	1.30107i	−0.196085	+	0.980587i	$0.562823\pi$
$228$	−3299.94	−	5715.67i	−0.958526	−	1.66022i
$229$	307.403	−	532.438i	0.0887064	−	0.153644i	−0.818258	−	0.574851i	$-0.805060\pi$
$229$	307.403	−	532.438i	0.0887064	−	0.153644i	0.906965	+	0.421207i	$0.138393\pi$
$230$	2210.51			0.633725
$231$		0			0
$232$	−4677.59			−1.32370
$233$	−1413.71	+	2448.61i	−0.397490	+	0.688472i	−0.993415	−	0.114567i	$-0.963452\pi$
$233$	−1413.71	+	2448.61i	−0.397490	+	0.688472i	0.595926	+	0.803039i	$0.296785\pi$
$234$	923.765	+	1600.01i	0.258070	+	0.446991i
$235$	1725.56	+	2988.76i	0.478992	+	0.829638i
$236$	5297.24	−	9175.09i	1.46111	−	2.53071i
$237$	1312.94			0.359851
$238$		0			0
$239$	−3432.45			−0.928983			−0.464491	−	0.885578i	$-0.653763\pi$
$239$	−3432.45			−0.928983			−0.464491	+	0.885578i	$0.653763\pi$
$240$	1515.99	−	2625.77i	0.407736	−	0.706219i
$241$	−1318.06	−	2282.94i	−0.352296	−	0.610195i	0.634355	−	0.773042i	$-0.281266\pi$
$241$	−1318.06	−	2282.94i	−0.352296	−	0.610195i	−0.986651	+	0.162847i	$0.947932\pi$
$242$	3018.58	+	5228.33i	0.801825	+	1.38880i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	7736.96			2.02995
$245$		0			0
$246$	394.814			0.102327
$247$	2108.15	−	3651.42i	0.543070	−	0.940625i
$248$	2070.01	+	3585.37i	0.530024	+	0.918028i
$249$	361.862	+	626.763i	0.0920967	+	0.159516i
$250$	−3233.65	+	5600.85i	−0.818057	+	1.41692i
$251$	−2057.57			−0.517422			−0.258711	−	0.965955i	$-0.583298\pi$
$251$	−2057.57			−0.517422			−0.258711	+	0.965955i	$0.583298\pi$
$252$		0			0
$253$	1042.10			0.258958
$254$	−466.639	+	808.243i	−0.115274	+	0.199660i
$255$	−362.704	−	628.222i	−0.0890722	−	0.154278i
$256$	203.161	+	351.885i	0.0495998	+	0.0859093i
$257$	1075.10	−	1862.13i	0.260946	−	0.451972i	−0.705548	−	0.708663i	$-0.749299\pi$
$257$	1075.10	−	1862.13i	0.260946	−	0.451972i	0.966494	+	0.256691i	$0.0826322\pi$
$258$	−3883.78			−0.937185
$259$		0			0
$260$	4339.66			1.03513
$261$	325.615	−	563.982i	0.0772225	−	0.133753i
$262$	2988.39	+	5176.04i	0.704668	+	1.22052i
$263$	2295.08	+	3975.19i	0.538100	+	0.932017i	0.999006	+	0.0445683i	$0.0141912\pi$
$263$	2295.08	+	3975.19i	0.538100	+	0.932017i	−0.460906	+	0.887449i	$0.652475\pi$
$264$	1349.52	−	2337.44i	0.314610	−	0.544921i
$265$	1600.79			0.371078
$266$		0			0
$267$	−4756.63			−1.09027
$268$	−1998.80	+	3462.02i	−0.455582	+	0.789091i
$269$	−189.689	−	328.551i	−0.0429945	−	0.0744687i	0.843727	−	0.536772i	$-0.180356\pi$
$269$	−189.689	−	328.551i	−0.0429945	−	0.0744687i	−0.886722	+	0.462303i	$0.847023\pi$
$270$	398.541	+	690.293i	0.0898312	+	0.155592i
$271$	−2684.42	+	4649.55i	−0.601723	+	1.04221i	0.390837	+	0.920460i	$0.372185\pi$
$271$	−2684.42	+	4649.55i	−0.601723	+	1.04221i	−0.992560	+	0.121755i	$0.961148\pi$
$272$	−7901.28			−1.76134
$273$		0			0
$274$	9919.61			2.18710
$275$	−654.610	+	1133.82i	−0.143543	+	0.248624i
$276$	2266.33	+	3925.39i	0.494264	+	0.856090i
$277$	2390.80	+	4140.99i	0.518590	+	0.898224i	0.999767	+	0.0216003i	$0.00687613\pi$
$277$	2390.80	+	4140.99i	0.518590	+	0.898224i	−0.481177	+	0.876624i	$0.659791\pi$
$278$	−7477.25	+	12951.0i	−1.61315	+	2.79406i
$279$	−576.388			−0.123683
$280$		0			0
$281$	−2076.57			−0.440845			−0.220423	−	0.975404i	$-0.570744\pi$
$281$	−2076.57			−0.440845			−0.220423	+	0.975404i	$0.570744\pi$
$282$	−4941.08	+	8558.20i	−1.04339	+	1.80721i
$283$	1278.81	+	2214.96i	0.268612	+	0.465250i	0.968504	−	0.248999i	$-0.0801017\pi$
$283$	1278.81	+	2214.96i	0.268612	+	0.465250i	−0.699892	+	0.714249i	$0.746768\pi$
$284$	−7924.21	−	13725.1i	−1.65569	−	2.86774i
$285$	909.520	−	1575.34i	0.189036	−	0.327420i
$286$	2856.97			0.590687
$287$		0			0
$288$	4027.56			0.824050
$289$	1511.30	−	2617.65i	0.307612	−	0.532800i
$290$	−1068.07	−	1849.96i	−0.216274	−	0.374597i
$291$	118.913	+	205.963i	0.0239547	+	0.0414907i
$292$	−3340.88	+	5786.57i	−0.669555	+	1.15970i
$293$	−560.049			−0.111667			−0.0558335	−	0.998440i	$-0.517782\pi$
$293$	−560.049			−0.111667			−0.0558335	+	0.998440i	$0.517782\pi$
$294$		0			0
$295$	2920.02			0.576305
$296$	−6100.08	+	10565.6i	−1.19784	+	2.07471i
$297$	187.885	+	325.426i	0.0367076	+	0.0635795i
$298$	−4778.33	−	8276.31i	−0.928863	−	1.60884i
$299$	−1447.83	+	2507.71i	−0.280034	+	0.485033i
$300$	−5694.48			−1.09590
$301$		0			0
$302$	−2404.57			−0.458171
$303$	1732.46	−	3000.71i	0.328473	−	0.568931i
$304$	−9906.66	−	17158.8i	−1.86903	−	3.23726i
$305$	1066.22	+	1846.75i	0.200169	+	0.346703i
$306$	1038.59	−	1798.89i	0.194027	−	0.336065i
$307$	−3653.02			−0.679117			−0.339558	−	0.940585i	$-0.610278\pi$
$307$	−3653.02			−0.679117			−0.339558	+	0.940585i	$0.610278\pi$
$308$		0			0
$309$	4334.58			0.798011
$310$	−945.325	+	1637.35i	−0.173196	+	0.299985i
$311$	1746.13	+	3024.39i	0.318374	+	0.551439i	0.980149	−	0.198263i	$-0.0635300\pi$
$311$	1746.13	+	3024.39i	0.318374	+	0.551439i	−0.661775	+	0.749702i	$0.730197\pi$
$312$	3749.87	+	6494.96i	0.680431	+	1.17854i
$313$	4356.05	−	7544.90i	0.786640	−	1.36250i	−0.141374	−	0.989956i	$-0.545152\pi$
$313$	4356.05	−	7544.90i	0.786640	−	1.36250i	0.928014	−	0.372544i	$-0.121515\pi$
$314$	9892.85			1.77798
$315$		0			0
$316$	8830.83			1.57207
$317$	−970.165	+	1680.37i	−0.171892	+	0.297726i	−0.939081	−	0.343695i	$-0.888321\pi$
$317$	−970.165	+	1680.37i	−0.171892	+	0.297726i	0.767189	+	0.641421i	$0.221655\pi$
$318$	2291.90	+	3969.69i	0.404162	+	0.700029i
$319$	−503.523	−	872.127i	−0.0883758	−	0.153071i
$320$	2562.92	−	4439.11i	0.447724	−	0.775480i
$321$	2972.88			0.516916
$322$		0			0
$323$	−4740.39			−0.816602
$324$	−817.208	+	1415.45i	−0.140125	+	0.242703i
$325$	−1818.94	−	3150.50i	−0.310452	−	0.537718i
$326$	−6160.64	−	10670.5i	−1.04665	−	1.81284i
$327$	−2929.75	+	5074.48i	−0.495461	+	0.858164i
$328$	1602.68			0.269797
$329$		0			0
$330$	1232.59			0.205611
$331$	2865.75	−	4963.63i	0.475879	−	0.824247i	−0.523739	−	0.851879i	$-0.675463\pi$
$331$	2865.75	−	4963.63i	0.475879	−	0.824247i	0.999618	+	0.0276315i	$0.00879650\pi$
$332$	2433.88	+	4215.61i	0.402339	+	0.696872i
$333$	−849.273	−	1470.98i	−0.139759	−	0.242070i
$334$	8524.10	−	14764.2i	1.39646	−	2.41874i
$335$	−1101.81			−0.179696
$336$		0			0
$337$	2403.74			0.388547			0.194273	−	0.980947i	$-0.437765\pi$
$337$	2403.74			0.388547			0.194273	+	0.980947i	$0.437765\pi$
$338$	1861.87	−	3224.85i	0.299622	−	0.518960i
$339$	−1009.32	−	1748.20i	−0.161708	−	0.280086i
$340$	−2439.55	−	4225.42i	−0.389127	−	0.673987i
$341$	−445.656	+	771.898i	−0.0707731	+	0.122583i
$342$	5208.76			0.823560
$343$		0			0
$344$	−15765.6			−2.47099
$345$	−624.638	+	1081.91i	−0.0974765	+	0.168834i
$346$	568.723	+	985.057i	0.0883663	+	0.153055i
$347$	1668.22	+	2889.45i	0.258083	+	0.447013i	0.965728	−	0.259555i	$-0.0835758\pi$
$347$	1668.22	+	2889.45i	0.258083	+	0.447013i	−0.707645	+	0.706568i	$0.750242\pi$
$348$	2190.09	−	3793.34i	0.337359	−	0.584323i
$349$	2424.54			0.371870			0.185935	−	0.982562i	$-0.440469\pi$
$349$	2424.54			0.371870			0.185935	+	0.982562i	$0.440469\pi$
$350$		0			0
$351$	−1044.14			−0.158781
$352$	3114.06	−	5393.71i	0.471534	−	0.816721i
$353$	−6201.56	−	10741.4i	−0.935059	−	1.61957i	−0.774528	−	0.632540i	$-0.782013\pi$
$353$	−6201.56	−	10741.4i	−0.935059	−	1.61957i	−0.160531	−	0.987031i	$-0.551321\pi$
$354$	4180.69	+	7241.17i	0.627687	+	1.08719i
$355$	2184.05	−	3782.88i	0.326528	−	0.565562i
$356$	−31993.1			−4.76300
$357$		0			0
$358$	−12937.5			−1.90997
$359$	−676.921	+	1172.46i	−0.0995168	+	0.172368i	−0.911485	−	0.411334i	$-0.865063\pi$
$359$	−676.921	+	1172.46i	−0.0995168	+	0.172368i	0.811968	+	0.583702i	$0.198396\pi$
$360$	1617.81	+	2802.13i	0.236850	+	0.410236i
$361$	−2514.03	−	4354.42i	−0.366529	−	0.634848i
$362$	−659.903	+	1142.99i	−0.0958114	+	0.165950i
$363$	−3411.92			−0.493332
$364$		0			0
$365$	−1841.61			−0.264093
$366$	−3053.08	+	5288.10i	−0.436031	+	0.755227i
$367$	−689.031	−	1193.44i	−0.0980031	−	0.169746i	0.812855	−	0.582466i	$-0.197912\pi$
$367$	−689.031	−	1193.44i	−0.0980031	−	0.169746i	−0.910858	+	0.412720i	$0.864579\pi$
$368$	6803.67	+	11784.3i	0.963766	+	1.66929i
$369$	−111.565	+	193.237i	−0.0157395	+	0.0272615i
$370$	−5571.52			−0.782837
$371$		0			0
$372$	−3876.78			−0.540327
$373$	−2728.46	+	4725.83i	−0.378752	+	0.656017i	−0.990881	−	0.134741i	$-0.956980\pi$
$373$	−2728.46	+	4725.83i	−0.378752	+	0.656017i	0.612129	+	0.790758i	$0.290313\pi$
$374$	−1606.05	−	2781.76i	−0.222051	−	0.384603i
$375$	−1827.51	−	3165.34i	−0.251659	−	0.435887i
$376$	−20057.5	+	34740.6i	−2.75103	+	4.76492i
$377$	2798.25			0.382273
$378$		0			0
$379$	554.675			0.0751761			0.0375881	−	0.999293i	$-0.488033\pi$
$379$	554.675			0.0751761			0.0375881	+	0.999293i	$0.488033\pi$
$380$	6117.43	−	10595.7i	0.825836	−	1.43039i
$381$	−263.723	−	456.781i	−0.0354618	−	0.0614216i
$382$	11447.5	+	19827.7i	1.53327	+	2.65569i
$383$	2930.33	−	5075.48i	0.390948	−	0.677141i	−0.601627	−	0.798777i	$-0.705481\pi$
$383$	2930.33	−	5075.48i	0.390948	−	0.677141i	0.992575	+	0.121636i	$0.0388140\pi$
$384$	3937.50			0.523267
$385$		0			0
$386$	10939.6			1.44252
$387$	1097.47	−	1900.87i	0.144153	−	0.249681i
$388$	799.809	+	1385.31i	0.104650	+	0.181259i
$389$	−3889.43	−	6736.69i	−0.506946	−	0.878056i	−0.999968	−	0.00803932i	$-0.997441\pi$
$389$	−3889.43	−	6736.69i	−0.506946	−	0.878056i	0.493022	−	0.870017i	$-0.335892\pi$
$390$	−1712.48	+	2966.10i	−0.222345	+	0.385113i
$391$	3255.60			0.421081
$392$		0			0
$393$	−3377.79			−0.433555
$394$	4422.04	−	7659.20i	0.565429	−	0.979352i
$395$	1216.96	+	2107.84i	0.155018	+	0.268499i
$396$	1263.71	+	2188.81i	0.160363	+	0.277757i
$397$	4013.94	−	6952.35i	0.507440	−	0.878912i	−0.492523	−	0.870300i	$-0.663925\pi$
$397$	4013.94	−	6952.35i	0.507440	−	0.878912i	0.999963	−	0.00861270i	$-0.00274154\pi$
$398$	5772.95			0.727065
$399$		0			0
$400$	−17095.2			−2.13690
$401$	−389.990	+	675.482i	−0.0485665	+	0.0841196i	−0.889287	−	0.457350i	$-0.848799\pi$
$401$	−389.990	+	675.482i	−0.0485665	+	0.0841196i	0.840720	+	0.541470i	$0.182132\pi$
$402$	−1577.49	−	2732.30i	−0.195717	−	0.338991i
$403$	−1238.33	−	2144.85i	−0.153066	−	0.265118i
$404$	11652.5	−	20182.8i	1.43499	−	2.48547i
$405$	−450.473			−0.0552696
$406$		0			0
$407$	−2626.59			−0.319890
$408$	4215.99	−	7302.30i	0.511574	−	0.886073i
$409$	7346.25	+	12724.1i	0.888139	+	1.53830i	0.842073	+	0.539363i	$0.181335\pi$
$409$	7346.25	+	12724.1i	0.888139	+	1.53830i	0.0460654	+	0.998938i	$0.485332\pi$
$410$	365.953	+	633.850i	0.0440809	+	0.0763503i
$411$	−2803.05	+	4855.02i	−0.336409	+	0.582678i
$412$	29154.4			3.48624
$413$		0			0
$414$	−3577.26			−0.424669
$415$	−670.820	+	1161.89i	−0.0793476	+	0.137434i
$416$	8652.95	+	14987.3i	1.01982	+	1.76638i
$417$	−4225.79	−	7319.28i	−0.496254	−	0.859537i
$418$	4027.35	−	6975.57i	0.471254	−	0.816236i
$419$	−3370.31			−0.392960			−0.196480	−	0.980508i	$-0.562951\pi$
$419$	−3370.31			−0.392960			−0.196480	+	0.980508i	$0.562951\pi$
$420$		0			0
$421$	15651.0			1.81184			0.905919	−	0.423450i	$-0.139181\pi$
$421$	15651.0			1.81184			0.905919	+	0.423450i	$0.139181\pi$
$422$	12412.0	−	21498.3i	1.43178	−	2.47991i
$423$	−2792.47	−	4836.70i	−0.320980	−	0.555953i
$424$	9303.58	+	16114.3i	1.06562	+	1.84570i
$425$	−2045.04	+	3542.12i	−0.233410	+	0.404277i
$426$	12507.9			1.42256
$427$		0			0
$428$	19995.6			2.25823
$429$	−807.314	+	1398.31i	−0.0908567	+	0.157368i
$430$	−3599.88	−	6235.17i	−0.403724	−	0.699271i
$431$	−2444.06	−	4233.24i	−0.273147	−	0.473104i	0.696519	−	0.717538i	$-0.254731\pi$
$431$	−2444.06	−	4233.24i	−0.273147	−	0.473104i	−0.969666	+	0.244434i	$0.921398\pi$
$432$	−2453.32	+	4249.27i	−0.273230	+	0.473248i
$433$	5255.73			0.583313			0.291656	−	0.956523i	$-0.405794\pi$
$433$	5255.73			0.583313			0.291656	+	0.956523i	$0.405794\pi$
$434$		0			0
$435$	1207.25			0.133065
$436$	−19705.5	+	34131.0i	−2.16450	+	3.74903i
$437$	4081.88	+	7070.03i	0.446826	+	0.773925i
$438$	−2636.69	−	4566.88i	−0.287639	−	0.498205i
$439$	−412.488	+	714.451i	−0.0448451	+	0.0776740i	−0.887577	−	0.460660i	$-0.847613\pi$
$439$	−412.488	+	714.451i	−0.0448451	+	0.0776740i	0.842732	+	0.538334i	$0.180946\pi$
$440$	5003.48			0.542117
$441$		0			0
$442$	8925.37			0.960490
$443$	−6513.64	+	11281.9i	−0.698583	+	1.20998i	0.270375	+	0.962755i	$0.412852\pi$
$443$	−6513.64	+	11281.9i	−0.698583	+	1.20998i	−0.968958	+	0.247226i	$0.920481\pi$
$444$	−5712.21	−	9893.83i	−0.610561	−	1.05752i
$445$	−4408.92	−	7636.47i	−0.469669	−	0.813491i
$446$	8615.44	−	14922.4i	0.914693	−	1.58429i
$447$	5400.98			0.571493
$448$		0			0
$449$	16526.1			1.73700			0.868500	−	0.495689i	$-0.165084\pi$
$449$	16526.1			1.73700			0.868500	+	0.495689i	$0.165084\pi$
$450$	2247.10	−	3892.09i	0.235399	−	0.407722i
$451$	172.522	+	298.817i	0.0180127	+	0.0311989i
$452$	−6788.71	−	11758.4i	−0.706447	−	1.22360i
$453$	679.476	−	1176.89i	0.0704737	−	0.122064i
$454$	−27274.9			−2.81954
$455$		0			0
$456$	21144.1			2.17141
$457$	1855.41	−	3213.67i	0.189918	−	0.328947i	−0.755305	−	0.655374i	$-0.772511\pi$
$457$	1855.41	−	3213.67i	0.189918	−	0.328947i	0.945223	+	0.326426i	$0.105844\pi$
$458$	1631.79	+	2826.34i	0.166481	+	0.288354i
$459$	586.963	+	1016.65i	0.0596887	+	0.103384i
$460$	−4201.31	+	7276.89i	−0.425842	+	0.737580i
$461$	9714.00			0.981401			0.490701	−	0.871328i	$-0.336741\pi$
$461$	9714.00			0.981401			0.490701	+	0.871328i	$0.336741\pi$
$462$		0			0
$463$	−43.2780			−0.00434406			−0.00217203	−	0.999998i	$-0.500691\pi$
$463$	−43.2780			−0.00434406			−0.00217203	+	0.999998i	$0.500691\pi$
$464$	6574.79	−	11387.9i	0.657817	−	1.13937i
$465$	−534.254	−	925.355i	−0.0532805	−	0.0922845i
$466$	−7504.38	−	12998.0i	−0.745995	−	1.29210i
$467$	−766.618	+	1327.82i	−0.0759633	+	0.131572i	−0.901505	−	0.432769i	$-0.857537\pi$
$467$	−766.618	+	1327.82i	−0.0759633	+	0.131572i	0.825541	+	0.564341i	$0.190870\pi$
$468$	−7022.87			−0.693659
$469$		0			0
$470$	−18319.6			−1.79791
$471$	−2795.49	+	4841.93i	−0.273480	+	0.473682i
$472$	16970.8	+	29394.3i	1.65497	+	2.86649i
$473$	−1697.09	−	2939.45i	−0.164974	−	0.285743i
$474$	−3484.74	+	6035.74i	−0.337678	+	0.584875i
$475$	−10256.3			−0.990722
$476$		0			0
$477$	−2590.55			−0.248665
$478$	9110.23	−	15779.4i	0.871741	−	1.50990i
$479$	−3517.69	−	6092.81i	−0.335547	−	0.581185i	0.648042	−	0.761604i	$-0.275588\pi$
$479$	−3517.69	−	6092.81i	−0.335547	−	0.581185i	−0.983590	+	0.180419i	$0.942255\pi$
$480$	3733.15	+	6466.00i	0.354988	+	0.614857i
$481$	3649.21	−	6320.62i	0.345924	−	0.599159i
$482$	13993.3			1.32236
$483$		0			0
$484$	−22948.6			−2.15520
$485$	−220.441	+	381.815i	−0.0206386	+	0.0357471i
$486$	−644.958	−	1117.10i	−0.0601973	−	0.104265i
$487$	7685.64	+	13311.9i	0.715132	+	1.23865i	0.962908	+	0.269828i	$0.0869669\pi$
$487$	7685.64	+	13311.9i	0.715132	+	1.23865i	−0.247776	+	0.968817i	$0.579700\pi$
$488$	−12393.5	+	21466.1i	−1.14964	+	1.99124i
$489$	6963.41			0.643960
$490$		0			0
$491$	−2393.35			−0.219980			−0.109990	−	0.993933i	$-0.535082\pi$
$491$	−2393.35			−0.219980			−0.109990	+	0.993933i	$0.535082\pi$
$492$	−750.388	+	1299.71i	−0.0687604	+	0.119096i
$493$	−1573.04	−	2724.58i	−0.143704	−	0.248903i
$494$	11190.7	+	19382.8i	1.01921	+	1.76533i
$495$	−348.300	+	603.274i	−0.0316261	+	0.0547781i
$496$	−11638.4			−1.05359
$497$		0			0
$498$	−3841.74			−0.345688
$499$	−346.760	+	600.606i	−0.0311084	+	0.0538814i	−0.881160	−	0.472817i	$-0.843237\pi$
$499$	−346.760	+	600.606i	−0.0311084	+	0.0538814i	0.850052	+	0.526699i	$0.176570\pi$
$500$	−12291.8	−	21290.1i	−1.09941	−	1.90424i
$501$	4817.43	+	8344.03i	0.429594	+	0.744079i
$502$	5461.10	−	9458.91i	0.485540	−	0.840979i
$503$	8646.95			0.766498			0.383249	−	0.923645i	$-0.374805\pi$
$503$	8646.95			0.766498			0.383249	+	0.923645i	$0.374805\pi$
$504$		0			0
$505$	6423.27			0.566003
$506$	−2765.89	+	4790.67i	−0.243002	+	0.420892i
$507$	1052.24	+	1822.53i	0.0921729	+	0.159648i
$508$	−1773.80	−	3072.31i	−0.154920	−	0.268330i
$509$	−7750.44	+	13424.1i	−0.674916	+	1.16899i	0.301578	+	0.953441i	$0.402487\pi$
$509$	−7750.44	+	13424.1i	−0.674916	+	1.16899i	−0.976494	+	0.215546i	$0.930847\pi$
$510$	3850.68			0.334335
$511$		0			0
$512$	−12656.9			−1.09250
$513$	−1471.87	+	2549.36i	−0.126676	+	0.219409i
$514$	5706.96	+	9884.75i	0.489734	+	0.848245i
$515$	4017.72	+	6958.89i	0.343771	+	0.595428i
$516$	7381.55	−	12785.2i	0.629757	−	1.09077i
$517$	−8636.41			−0.734678
$518$		0			0
$519$	−642.831			−0.0543683
$520$	−6951.50	+	12040.4i	−0.586238	+	1.01539i
$521$	432.354	+	748.858i	0.0363565	+	0.0629714i	0.883631	−	0.468184i	$-0.155091\pi$
$521$	432.354	+	748.858i	0.0363565	+	0.0629714i	−0.847275	+	0.531155i	$0.821758\pi$
$522$	1728.46	+	2993.78i	0.144928	+	0.251023i
$523$	−3127.81	+	5417.52i	−0.261509	+	0.452947i	−0.966643	−	0.256127i	$-0.917554\pi$
$523$	−3127.81	+	5417.52i	−0.261509	+	0.452947i	0.705134	+	0.709074i	$0.250887\pi$
$524$	−22719.0			−1.89406
$525$		0			0
$526$	−24365.9			−2.01978
$527$	−1392.26	+	2411.46i	−0.115081	+	0.199326i
$528$	3793.75	+	6570.97i	0.312693	+	0.541600i
$529$	3280.15	+	5681.39i	0.269594	+	0.466951i
$530$	−4248.72	+	7359.01i	−0.348213	+	0.603122i
$531$	−4725.46			−0.386191
$532$		0			0
$533$	−958.762			−0.0779148
$534$	12624.8	−	21866.8i	1.02309	−	1.77204i
$535$	2755.56	+	4772.78i	0.222679	+	0.385692i
$536$	−6403.56	−	11091.3i	−0.516029	−	0.893789i
$537$	3655.83	−	6332.09i	0.293782	−	0.508845i
$538$	2013.85			0.161381
$539$		0			0
$540$	−3029.88			−0.241454
$541$	−71.9353	+	124.596i	−0.00571671	+	0.00990164i	−0.868870	−	0.495041i	$-0.835153\pi$
$541$	−71.9353	+	124.596i	−0.00571671	+	0.00990164i	0.863153	+	0.504943i	$0.168486\pi$
$542$	−14249.7	−	24681.2i	−1.12929	−	1.95599i
$543$	−372.946	−	645.962i	−0.0294745	−	0.0510514i
$544$	9728.53	−	16850.3i	0.766741	−	1.32804i
$545$	−10862.4			−0.853747
$546$		0			0
$547$	5455.65			0.426448			0.213224	−	0.977003i	$-0.431604\pi$
$547$	5455.65			0.426448			0.213224	+	0.977003i	$0.431604\pi$
$548$	−18853.3	+	32654.9i	−1.46966	+	2.54552i
$549$	−1725.46	−	2988.58i	−0.134136	−	0.232331i
$550$	−3474.86	−	6018.63i	−0.269397	−	0.466610i
$551$	3944.56	−	6832.18i	0.304980	−	0.528241i
$552$	−14521.3			−1.11969
$553$		0			0
$554$	−25382.2			−1.94654
$555$	1574.38	−	2726.91i	0.120412	−	0.208560i
$556$	−28422.7	−	49229.5i	−2.16797	−	3.75503i
$557$	−12404.9	−	21486.0i	−0.943652	−	1.63445i	−0.758428	−	0.651756i	$-0.774032\pi$
$557$	−12404.9	−	21486.0i	−0.943652	−	1.63445i	−0.185223	−	0.982696i	$-0.559301\pi$
$558$	1529.82	−	2649.72i	0.116062	−	0.201025i
$559$	9431.33			0.713600
$560$		0			0
$561$	1815.33			0.136619
$562$	5511.51	−	9546.22i	0.413682	−	0.716517i
$563$	8184.91	+	14176.7i	0.612705	+	1.06124i	0.990782	+	0.135462i	$0.0432520\pi$
$563$	8184.91	+	14176.7i	0.612705	+	1.06124i	−0.378077	+	0.925774i	$0.623415\pi$
$564$	−18782.1	−	32531.6i	−1.40225	−	2.42877i
$565$	1871.08	−	3240.81i	0.139322	−	0.241313i
$566$	−13576.6			−1.00824
$567$		0			0
$568$	50773.7			3.75074
$569$	9225.29	−	15978.7i	0.679691	−	1.17726i	−0.295383	−	0.955379i	$-0.595447\pi$
$569$	9225.29	−	15978.7i	0.679691	−	1.17726i	0.975074	−	0.221881i	$-0.0712195\pi$
$570$	4828.00	+	8362.34i	0.354777	+	0.614491i
$571$	3554.34	+	6156.30i	0.260499	+	0.451197i	0.966374	−	0.257139i	$-0.0827797\pi$
$571$	3554.34	+	6156.30i	0.260499	+	0.451197i	−0.705876	+	0.708335i	$0.749446\pi$
$572$	−5429.99	+	9405.02i	−0.396922	+	0.687489i
$573$	−12939.2			−0.943358
$574$		0			0
$575$	7043.82			0.510865
$576$	−4147.57	+	7183.80i	−0.300026	+	0.519661i
$577$	3797.09	+	6576.75i	0.273960	+	0.474512i	0.969872	−	0.243615i	$-0.0783332\pi$
$577$	3797.09	+	6576.75i	0.273960	+	0.474512i	−0.695912	+	0.718127i	$0.745000\pi$
$578$	8022.42	+	13895.2i	0.577316	+	0.999940i
$579$	−3091.28	+	5354.25i	−0.221881	+	0.384309i
$580$	8119.96			0.581315
$581$		0			0
$582$	−1262.45			−0.0899146
$583$	−2002.98	+	3469.26i	−0.142290	+	0.246453i
$584$	−10703.2	−	18538.5i	−0.758392	−	1.31357i
$585$	−967.811	−	1676.30i	−0.0684001	−	0.118472i
$586$	1486.45	−	2574.61i	0.104786	−	0.181495i
$587$	1763.34			0.123988			0.0619939	−	0.998077i	$-0.480254\pi$
$587$	1763.34			0.123988			0.0619939	+	0.998077i	$0.480254\pi$
$588$		0			0
$589$	−6982.47			−0.488468
$590$	−7750.16	+	13423.7i	−0.540795	+	0.936684i
$591$	2499.13	+	4328.62i	0.173943	+	0.301279i
$592$	−17148.4	−	29702.0i	−1.19054	−	2.06207i
$593$	−6158.07	+	10666.1i	−0.426445	+	0.738624i	−0.996554	−	0.0829448i	$-0.973567\pi$
$593$	−6158.07	+	10666.1i	−0.426445	+	0.738624i	0.570109	+	0.821569i	$0.306901\pi$
$594$	−1994.69			−0.137783
$595$		0			0
$596$	36327.0			2.49666
$597$	−1631.30	+	2825.49i	−0.111834	+	0.193702i
$598$	−7685.50	−	13311.7i	−0.525558	−	0.910293i
$599$	4451.70	+	7710.57i	0.303659	+	0.525952i	0.976962	−	0.213414i	$-0.0684584\pi$
$599$	4451.70	+	7710.57i	0.303659	+	0.525952i	−0.673303	+	0.739367i	$0.735125\pi$
$600$	9121.72	−	15799.3i	0.620655	−	1.07501i
$601$	19157.1			1.30022			0.650112	−	0.759838i	$-0.274722\pi$
$601$	19157.1			1.30022			0.650112	+	0.759838i	$0.274722\pi$
$602$		0			0
$603$	1783.05			0.120417
$604$	4570.15	−	7915.74i	0.307876	−	0.533256i
$605$	−3162.51	−	5477.62i	−0.212519	−	0.368094i
$606$	9196.41	+	15928.6i	0.616466	+	1.06775i
$607$	−3784.96	+	6555.75i	−0.253092	+	0.438369i	−0.964376	−	0.264537i	$-0.914781\pi$
$607$	−3784.96	+	6555.75i	−0.253092	+	0.438369i	0.711283	+	0.702905i	$0.248114\pi$
$608$	48790.7			3.25448
$609$		0			0
$610$	−11319.6			−0.751340
$611$	11998.9	−	20782.6i	0.794471	−	1.37606i
$612$	3947.91	+	6837.99i	0.260760	+	0.451649i
$613$	−1453.56	−	2517.65i	−0.0957730	−	0.165884i	0.814158	−	0.580643i	$-0.197199\pi$
$613$	−1453.56	−	2517.65i	−0.0957730	−	0.165884i	−0.909931	+	0.414760i	$0.863866\pi$
$614$	9695.65	−	16793.4i	0.637272	−	1.10379i
$615$	−413.640			−0.0271212
$616$		0			0
$617$	−12510.9			−0.816320			−0.408160	−	0.912910i	$-0.633829\pi$
$617$	−12510.9			−0.816320			−0.408160	+	0.912910i	$0.633829\pi$
$618$	−11504.6	+	19926.6i	−0.748840	+	1.29703i
$619$	5032.78	+	8717.03i	0.326792	+	0.566021i	0.981873	−	0.189538i	$-0.0606989\pi$
$619$	5032.78	+	8717.03i	0.326792	+	0.566021i	−0.655081	+	0.755558i	$0.727366\pi$
$620$	−3593.39	−	6223.93i	−0.232764	−	0.403160i
$621$	1010.85	−	1750.84i	0.0653205	−	0.113138i
$622$	−18538.0			−1.19503
$623$		0			0
$624$	−21083.2			−1.35257
$625$	−2491.59	+	4315.56i	−0.159462	+	0.276196i
$626$	23123.2	+	40050.5i	1.47634	+	2.55709i
$627$	2276.07	+	3942.27i	0.144972	+	0.251099i
$628$	−18802.4	+	32566.8i	−1.19474	+	2.06936i
$629$	−8205.63			−0.520159
$630$		0			0
$631$	−25146.6			−1.58648			−0.793242	−	0.608907i	$-0.791608\pi$
$631$	−25146.6			−1.58648			−0.793242	+	0.608907i	$0.791608\pi$
$632$	−14145.7	+	24501.1i	−0.890325	+	1.54209i
$633$	7014.71	+	12149.8i	0.440458	+	0.762895i
$634$	−5149.92	−	8919.92i	−0.322602	−	0.558762i
$635$	488.889	−	846.781i	0.0305527	−	0.0529189i
$636$	−17424.0			−1.08633
$637$		0			0
$638$	5345.70			0.331721
$639$	−3534.44	+	6121.83i	−0.218811	+	0.378992i
$640$	3649.66	+	6321.41i	0.225415	+	0.390430i
$641$	14479.5	+	25079.1i	0.892206	+	1.54535i	0.837225	+	0.546859i	$0.184176\pi$
$641$	14479.5	+	25079.1i	0.892206	+	1.54535i	0.0549809	+	0.998487i	$0.482490\pi$
$642$	−7890.46	+	13666.7i	−0.485065	+	0.840157i
$643$	−7341.90			−0.450290			−0.225145	−	0.974325i	$-0.572286\pi$
$643$	−7341.90			−0.450290			−0.225145	+	0.974325i	$0.572286\pi$
$644$		0			0
$645$	4068.97			0.248396
$646$	12581.7	−	21792.1i	0.766285	−	1.32725i
$647$	3035.99	+	5258.49i	0.184478	+	0.319525i	0.943400	−	0.331656i	$-0.107607\pi$
$647$	3035.99	+	5258.49i	0.184478	+	0.319525i	−0.758923	+	0.651181i	$0.774274\pi$
$648$	−2618.10	−	4534.67i	−0.158717	−	0.274906i
$649$	−3653.67	+	6328.34i	−0.220985	+	0.382756i
$650$	19311.0			1.16529
$651$		0			0
$652$	46835.9			2.81324
$653$	−13131.1	+	22743.7i	−0.786920	+	1.36298i	0.140926	+	0.990020i	$0.454992\pi$
$653$	−13131.1	+	22743.7i	−0.786920	+	1.36298i	−0.927846	+	0.372965i	$0.878341\pi$
$654$	−15552.0	−	26936.9i	−0.929864	−	1.61057i
$655$	−3130.88	−	5422.84i	−0.186769	−	0.323493i
$656$	−2252.72	+	3901.82i	−0.134076	+	0.232226i
$657$	2980.27			0.176973
$658$		0			0
$659$	26130.1			1.54459			0.772296	−	0.635263i	$-0.219108\pi$
$659$	26130.1			1.54459			0.772296	+	0.635263i	$0.219108\pi$
$660$	−2342.67	+	4057.62i	−0.138164	+	0.239307i
$661$	−5962.75	−	10327.8i	−0.350868	−	0.607722i	0.635533	−	0.772073i	$-0.280780\pi$
$661$	−5962.75	−	10327.8i	−0.350868	−	0.607722i	−0.986402	+	0.164351i	$0.947447\pi$
$662$	15212.3	+	26348.4i	0.893114	+	1.54692i
$663$	−2522.10	+	4368.41i	−0.147738	+	0.255890i
$664$	−15594.9			−0.911444
$665$		0			0
$666$	9016.38			0.524591
$667$	−2709.04	+	4692.19i	−0.157263	+	0.272387i
$668$	32402.0	+	56121.9i	1.87675	+	3.25063i
$669$	4869.04	+	8433.43i	0.281387	+	0.487377i
$670$	2924.35	−	5065.13i	0.168623	−	0.292064i
$671$	−5336.42			−0.307019
$672$		0			0
$673$	−6359.85			−0.364271			−0.182135	−	0.983273i	$-0.558301\pi$
$673$	−6359.85			−0.364271			−0.182135	+	0.983273i	$0.558301\pi$
$674$	−6379.89	+	11050.3i	−0.364606	+	0.631516i
$675$	1269.96	+	2199.63i	0.0724158	+	0.125428i
$676$	7077.36	+	12258.4i	0.402672	+	0.697449i
$677$	4280.81	−	7414.57i	0.243020	−	0.420924i	−0.718553	−	0.695472i	$-0.755195\pi$
$677$	4280.81	−	7414.57i	0.243020	−	0.420924i	0.961573	+	0.274549i	$0.0885285\pi$
$678$	10715.6			0.606975
$679$		0			0
$680$	15631.2			0.881513
$681$	7707.24	−	13349.3i	0.433689	−	0.751171i
$682$	−2365.67	−	4097.46i	−0.132824	−	0.230059i
$683$	3352.94	+	5807.47i	0.187843	+	0.325354i	0.944531	−	0.328423i	$-0.106517\pi$
$683$	3352.94	+	5807.47i	0.187843	+	0.325354i	−0.756688	+	0.653776i	$0.773184\pi$
$684$	−9899.82	+	17147.0i	−0.553405	+	0.958526i
$685$	−10392.6			−0.579679
$686$		0			0
$687$	−1844.42			−0.102429
$688$	22160.0	−	38382.2i	1.22797	−	2.12690i
$689$	−5565.62	−	9639.94i	−0.307741	−	0.533022i
$690$	−3315.76	−	5743.07i	−0.182941	−	0.316862i
$691$	−12665.3	+	21937.0i	−0.697267	+	1.20770i	0.272143	+	0.962257i	$0.412268\pi$
$691$	−12665.3	+	21937.0i	−0.697267	+	1.20770i	−0.969410	+	0.245445i	$0.921066\pi$
$692$	−4323.68			−0.237517
$693$		0			0
$694$	−17710.8			−0.968723
$695$	7833.77	−	13568.5i	0.427557	−	0.740550i
$696$	7016.39	+	12152.7i	0.382120	+	0.661851i
$697$	538.969	+	933.522i	0.0292897	+	0.0507312i
$698$	−6435.08	+	11145.9i	−0.348956	+	0.604410i
$699$	8482.25			0.458981
$700$		0			0
$701$	−27184.1			−1.46467			−0.732333	−	0.680947i	$-0.761568\pi$
$701$	−27184.1			−1.46467			−0.732333	+	0.680947i	$0.761568\pi$
$702$	2771.30	−	4800.03i	0.148997	−	0.258070i
$703$	−10288.3	−	17819.8i	−0.551961	−	0.956025i
$704$	6413.69	+	11108.8i	0.343360	+	0.594716i
$705$	5176.68	−	8966.27i	0.276546	−	0.478992i
$706$	65839.5			3.50977
$707$		0			0
$708$	−31783.4			−1.68714
$709$	−8072.75	+	13982.4i	−0.427614	+	0.740649i	−0.996661	−	0.0816561i	$-0.973979\pi$
$709$	−8072.75	+	13982.4i	−0.427614	+	0.740649i	0.569047	+	0.822305i	$0.307312\pi$
$710$	11593.6	+	20080.7i	0.612816	+	1.06143i
$711$	−1969.41	−	3411.12i	−0.103880	−	0.179925i
$712$	51248.2	−	88764.5i	2.69748	−	4.67218i
$713$	4795.41			0.251879
$714$		0			0
$715$	−2993.20			−0.156558
$716$	24589.1	−	42589.6i	1.28343	−	2.22297i
$717$	5148.68	+	8917.77i	0.268174	+	0.464491i
$718$	−3593.30	−	6223.77i	−0.186770	−	0.323494i
$719$	8648.74	−	14980.0i	0.448600	−	0.776998i	−0.549695	−	0.835365i	$-0.685256\pi$
$719$	8648.74	−	14980.0i	0.448600	−	0.776998i	0.998295	+	0.0583673i	$0.0185895\pi$
$720$	−9095.92			−0.470812
$721$		0			0
$722$	26690.4			1.37578
$723$	−3954.17	+	6848.82i	−0.203398	+	0.352296i
$724$	−2508.44	−	4344.74i	−0.128764	−	0.223026i
$725$	−3403.43	−	5894.91i	−0.174345	−	0.301975i
$726$	9055.74	−	15685.0i	0.462934	−	0.801825i
$727$	−3514.71			−0.179303			−0.0896516	−	0.995973i	$-0.528575\pi$
$727$	−3514.71			−0.179303			−0.0896516	+	0.995973i	$0.528575\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	4887.89	−	8466.08i	0.247821	−	0.429238i
$731$	−5301.83	−	9183.04i	−0.268256	−	0.464633i
$732$	−11605.4	−	20101.2i	−0.585996	−	1.01498i
$733$	−13755.6	+	23825.4i	−0.693144	+	1.20056i	0.277658	+	0.960680i	$0.410442\pi$
$733$	−13755.6	+	23825.4i	−0.693144	+	1.20056i	−0.970802	+	0.239881i	$0.922892\pi$
$734$	7315.16			0.367858
$735$		0			0
$736$	−33508.4			−1.67817
$737$	1378.63	−	2387.86i	0.0689044	−	0.119346i
$738$	−592.222	−	1025.76i	−0.0295393	−	0.0511635i
$739$	−8050.80	−	13944.4i	−0.400749	−	0.694117i	0.593068	−	0.805153i	$-0.297917\pi$
$739$	−8050.80	−	13944.4i	−0.400749	−	0.694117i	−0.993816	+	0.111035i	$0.964583\pi$
$740$	10589.3	−	18341.2i	0.526040	−	0.911129i
$741$	−12648.9			−0.627083
$742$		0			0
$743$	14682.4			0.724961			0.362480	−	0.931991i	$-0.381930\pi$
$743$	14682.4			0.724961			0.362480	+	0.931991i	$0.381930\pi$
$744$	6210.03	−	10756.1i	0.306009	−	0.530024i
$745$	5006.17	+	8670.93i	0.246190	+	0.426414i
$746$	−14483.5	−	25086.1i	−0.710828	−	1.23119i
$747$	1085.59	−	1880.29i	0.0531720	−	0.0920967i
$748$	12209.9			0.596843
$749$		0			0
$750$	19401.9			0.944611
$751$	3636.53	−	6298.66i	0.176696	−	0.306047i	−0.764051	−	0.645156i	$-0.776792\pi$
$751$	3636.53	−	6298.66i	0.176696	−	0.306047i	0.940747	+	0.339109i	$0.110126\pi$
$752$	−56385.3	−	97662.2i	−2.73426	−	4.73587i
$753$	3086.36	+	5345.73i	0.149367	+	0.258711i
$754$	−7426.96	+	12863.9i	−0.358719	+	0.621319i
$755$	2519.23			0.121436
$756$		0			0
$757$	8505.93			0.408393			0.204196	−	0.978930i	$-0.434542\pi$
$757$	8505.93			0.408393			0.204196	+	0.978930i	$0.434542\pi$
$758$	−1472.19	+	2549.91i	−0.0705440	+	0.122186i
$759$	−1563.15	−	2707.46i	−0.0747548	−	0.129479i
$760$	19598.4	+	33945.5i	0.935408	+	1.62017i
$761$	7108.86	−	12312.9i	0.338628	−	0.586521i	−0.645547	−	0.763721i	$-0.723370\pi$
$761$	7108.86	−	12312.9i	0.338628	−	0.586521i	0.984175	+	0.177200i	$0.0567038\pi$
$762$	2799.84			0.133107
$763$		0			0
$764$	−87029.3			−4.12121
$765$	−1088.11	+	1884.67i	−0.0514259	+	0.0890722i
$766$	15555.1	+	26942.2i	0.733717	+	1.27084i
$767$	−10152.3	−	17584.4i	−0.477939	−	0.827815i
$768$	609.482	−	1055.65i	0.0286364	−	0.0495998i
$769$	−16379.1			−0.768068			−0.384034	−	0.923319i	$-0.625466\pi$
$769$	−16379.1			−0.768068			−0.384034	+	0.923319i	$0.625466\pi$
$770$		0			0
$771$	−6450.62			−0.301314
$772$	−20791.9	+	36012.6i	−0.969323	+	1.67892i
$773$	−19948.3	−	34551.6i	−0.928192	−	1.60768i	−0.786346	−	0.617787i	$-0.788030\pi$
$773$	−19948.3	−	34551.6i	−0.928192	−	1.60768i	−0.141846	−	0.989889i	$-0.545304\pi$
$774$	5825.67	+	10090.4i	0.270542	+	0.468593i
$775$	−3012.29	+	5217.45i	−0.139619	+	0.241827i
$776$	−5124.70			−0.237070
$777$		0			0
$778$	41292.5			1.90284
$779$	−1351.52	+	2340.91i	−0.0621609	+	0.107666i
$780$	−6509.50	−	11274.8i	−0.298817	−	0.517566i
$781$	5465.57	+	9466.65i	0.250414	+	0.433730i
$782$	−8640.83	+	14966.4i	−0.395135	+	0.684394i
$783$	−1953.69			−0.0891688
$784$		0			0
$785$	−10364.5			−0.471244
$786$	8965.16	−	15528.1i	0.406840	−	0.704668i
$787$	−16564.3	−	28690.2i	−0.750257	−	1.29948i	−0.947698	−	0.319169i	$-0.896596\pi$
$787$	−16564.3	−	28690.2i	−0.750257	−	1.29948i	0.197440	−	0.980315i	$-0.436737\pi$
$788$	16809.1	+	29114.3i	0.759899	+	1.31618i
$789$	6885.23	−	11925.6i	0.310672	−	0.538100i
$790$	−12920.0			−0.581865
$791$		0			0
$792$	−8097.12			−0.363281
$793$	7414.07	−	12841.5i	0.332007	−	0.575052i
$794$	21307.2	+	36905.1i	0.952346	+	1.64951i
$795$	−2401.18	−	4158.97i	−0.107121	−	0.185539i
$796$	−10972.1	+	19004.3i	−0.488563	+	0.846216i
$797$	17851.5			0.793390			0.396695	−	0.917951i	$-0.370157\pi$
$797$	17851.5			0.793390			0.396695	+	0.917951i	$0.370157\pi$
$798$		0			0
$799$	−26980.7			−1.19463
$800$	21048.7	−	36457.4i	0.930229	−	1.61120i
$801$	7134.94	+	12358.1i	0.314733	+	0.545133i
$802$	−2070.18	−	3585.66i	−0.0911479	−	0.157873i
$803$	2304.30	−	3991.17i	0.101267	−	0.175399i
$804$	11992.8			0.526061
$805$		0			0
$806$	13146.8			0.574538
$807$	−569.066	+	985.652i	−0.0248229	+	0.0429945i
$808$	37331.2	+	64659.6i	1.62538	+	2.81524i
$809$	2528.52	+	4379.52i	0.109886	+	0.190328i	0.915724	−	0.401808i	$-0.131618\pi$
$809$	2528.52	+	4379.52i	0.109886	+	0.190328i	−0.805838	+	0.592136i	$0.798285\pi$
$810$	1195.62	−	2070.88i	0.0518641	−	0.0898312i
$811$	17535.4			0.759251			0.379626	−	0.925140i	$-0.376053\pi$
$811$	17535.4			0.759251			0.379626	+	0.925140i	$0.376053\pi$
$812$		0			0
$813$	16106.5			0.694810
$814$	6971.35	−	12074.7i	0.300179	−	0.519925i
$815$	6454.39	+	11179.3i	0.277408	+	0.480484i
$816$	11851.9	+	20528.1i	0.508456	+	0.880672i
$817$	13294.9	−	23027.5i	0.569315	−	0.986083i
$818$	−77992.1			−3.33366
$819$		0			0
$820$	−2782.14			−0.118484
$821$	9350.39	−	16195.3i	0.397480	−	0.688455i	−0.595935	−	0.803033i	$-0.703218\pi$
$821$	9350.39	−	16195.3i	0.397480	−	0.688455i	0.993414	+	0.114578i	$0.0365516\pi$
$822$	−14879.4	−	25771.9i	−0.631361	−	1.09355i
$823$	−11111.3	−	19245.4i	−0.470615	−	0.815129i	0.528820	−	0.848734i	$-0.322635\pi$
$823$	−11111.3	−	19245.4i	−0.470615	−	0.815129i	−0.999435	+	0.0336046i	$0.989301\pi$
$824$	−46701.0	+	80888.5i	−1.97440	+	3.41976i
$825$	3927.66			0.165750
$826$		0			0
$827$	25178.9			1.05872			0.529358	−	0.848399i	$-0.322433\pi$
$827$	25178.9			1.05872			0.529358	+	0.848399i	$0.322433\pi$
$828$	6798.98	−	11776.2i	0.285363	−	0.494264i
$829$	6139.45	+	10633.8i	0.257216	+	0.445511i	0.965495	−	0.260421i	$-0.0838615\pi$
$829$	6139.45	+	10633.8i	0.257216	+	0.445511i	−0.708279	+	0.705933i	$0.750528\pi$
$830$	−3560.91	−	6167.67i	−0.148917	−	0.257931i
$831$	7172.41	−	12423.0i	0.299408	−	0.518590i
$832$	−35643.1			−1.48522
$833$		0			0
$834$	44863.5			1.86270
$835$	−8930.54	+	15468.2i	−0.370125	+	0.641075i
$836$	15308.8	+	26515.7i	0.633334	+	1.09697i
$837$	864.582	+	1497.50i	0.0357041	+	0.0618413i
$838$	8945.30	−	15493.7i	0.368747	−	0.638689i
$839$	25765.0			1.06020			0.530098	−	0.847936i	$-0.322155\pi$
$839$	25765.0			1.06020			0.530098	+	0.847936i	$0.322155\pi$
$840$		0			0
$841$	−19153.2			−0.785321
$842$	−41540.1	+	71949.6i	−1.70020	+	2.94483i
$843$	3114.85	+	5395.08i	0.127261	+	0.220423i
$844$	47180.9	+	81719.7i	1.92421	+	3.33283i
$845$	−1950.64	+	3378.61i	−0.0794132	+	0.137548i
$846$	29646.5			1.20481
$847$		0			0
$848$	−52308.2			−2.11824
$849$	3836.42	−	6644.88i	0.155083	−	0.268612i
$850$	−10855.7	−	18802.6i	−0.438055	−	0.758734i
$851$	7065.75	+	12238.2i	0.284619	+	0.492974i
$852$	−23772.6	+	41175.4i	−0.955912	+	1.65569i
$853$	−37864.5			−1.51988			−0.759939	−	0.649995i	$-0.774771\pi$
$853$	−37864.5			−1.51988			−0.759939	+	0.649995i	$0.774771\pi$
$854$		0			0
$855$	−5457.12			−0.218280
$856$	−32030.0	+	55477.6i	−1.27893	+	2.21517i
$857$	−14604.4	−	25295.5i	−0.582118	−	1.00826i	−0.995228	−	0.0975771i	$-0.968891\pi$
$857$	−14604.4	−	25295.5i	−0.582118	−	1.00826i	0.413110	−	0.910681i	$-0.364443\pi$
$858$	−4285.46	−	7422.64i	−0.170517	−	0.295343i
$859$	17451.5	−	30226.8i	0.693173	−	1.20061i	−0.277619	−	0.960691i	$-0.589545\pi$
$859$	17451.5	−	30226.8i	0.693173	−	1.20061i	0.970793	−	0.239920i	$-0.0771213\pi$
$860$	27367.8			1.08516
$861$		0			0
$862$	25947.6			1.02527
$863$	6794.67	−	11768.7i	0.268011	−	0.464208i	−0.700337	−	0.713812i	$-0.746967\pi$
$863$	6794.67	−	11768.7i	0.268011	−	0.464208i	0.968348	+	0.249604i	$0.0803004\pi$
$864$	−6041.35	−	10463.9i	−0.237883	−	0.412025i
$865$	−595.840	−	1032.03i	−0.0234210	−	0.0405664i
$866$	−13949.5	+	24161.2i	−0.547371	+	0.948074i
$867$	−9067.79			−0.355200
$868$		0			0
$869$	−6090.89			−0.237767
$870$	−3204.22	+	5549.87i	−0.124866	+	0.216274i
$871$	3830.76	+	6635.07i	0.149025	+	0.258118i
$872$	−63130.7	−	109346.i	−2.45169	−	4.24645i
$873$	356.739	−	617.890i	0.0138302	−	0.0239547i
$874$	−43335.7			−1.67717
$875$		0			0
$876$	20045.3			0.773135
$877$	1189.87	−	2060.92i	0.0458144	−	0.0793528i	−0.842209	−	0.539151i	$-0.818745\pi$
$877$	1189.87	−	2060.92i	0.0458144	−	0.0793528i	0.888023	+	0.459799i	$0.152078\pi$
$878$	−2189.61	−	3792.51i	−0.0841637	−	0.145776i
$879$	840.074	+	1455.05i	0.0322355	+	0.0558335i
$880$	−7032.85	+	12181.3i	−0.269406	+	0.466625i
$881$	24235.5			0.926803			0.463401	−	0.886148i	$-0.346629\pi$
$881$	24235.5			0.926803			0.463401	+	0.886148i	$0.346629\pi$
$882$		0			0
$883$	−9844.13			−0.375177			−0.187589	−	0.982248i	$-0.560067\pi$
$883$	−9844.13			−0.375177			−0.187589	+	0.982248i	$0.560067\pi$
$884$	−16963.6	+	29381.9i	−0.645418	+	1.11790i
$885$	−4380.03	−	7586.43i	−0.166365	−	0.288153i
$886$	−34576.3	−	59887.9i	−1.31108	−	2.27085i
$887$	14304.9	−	24776.9i	0.541502	−	0.937910i	−0.457316	−	0.889304i	$-0.651189\pi$
$887$	14304.9	−	24776.9i	0.541502	−	0.937910i	0.998818	−	0.0486051i	$-0.0154776\pi$
$888$	36600.5			1.38314
$889$		0			0
$890$	46807.7			1.76292
$891$	563.654	−	976.277i	0.0211932	−	0.0367076i
$892$	32749.2	+	56723.2i	1.22929	+	2.12919i
$893$	−33828.5	−	58592.7i	−1.26767	−	2.19567i
$894$	−14335.0	+	24828.9i	−0.536279	+	0.928863i
$895$	13554.4			0.506226
$896$		0			0
$897$	8686.98			0.323355
$898$	−43862.6	+	75972.2i	−1.62997	+	2.82319i
$899$	−2317.04	−	4013.24i	−0.0859596	−	0.148886i
$900$	8541.72	+	14794.7i	0.316360	+	0.547952i
$901$	−6257.44	+	10838.2i	−0.231371	+	0.400747i
$902$	−1831.59			−0.0676113
$903$		0			0
$904$	43498.0			1.60036
$905$	691.368	−	1197.48i	0.0253943	−	0.0439842i
$906$	3606.86	+	6247.26i	0.132263	+	0.229086i
$907$	−22289.2	−	38606.0i	−0.815986	−	1.41333i	−0.908618	−	0.417629i	$-0.862861\pi$
$907$	−22289.2	−	38606.0i	−0.815986	−	1.41333i	0.0926313	−	0.995700i	$-0.470472\pi$
$908$	51838.8	−	89787.5i	1.89464	−	3.28161i
$909$	−10394.8			−0.379288
$910$		0			0
$911$	45870.6			1.66823			0.834116	−	0.551589i	$-0.185978\pi$
$911$	45870.6			1.66823			0.834116	+	0.551589i	$0.185978\pi$
$912$	−29720.0	+	51476.5i	−1.07909	+	1.86903i
$913$	−1678.72	−	2907.63i	−0.0608517	−	0.105398i
$914$	9849.07	+	17059.1i	0.356431	+	0.617357i
$915$	3198.66	−	5540.24i	0.115568	−	0.200169i
$916$	−12405.6			−0.447479
$917$		0			0
$918$	−6231.55			−0.224043
$919$	−15544.1	+	26923.3i	−0.557948	+	0.966394i	0.439720	+	0.898135i	$0.355078\pi$
$919$	−15544.1	+	26923.3i	−0.557948	+	0.966394i	−0.997668	+	0.0682590i	$0.978256\pi$
$920$	−13459.8	−	23313.0i	−0.482343	−	0.835443i
$921$	5479.53	+	9490.83i	0.196044	+	0.339558i
$922$	−25782.4	+	44656.4i	−0.920930	+	1.59510i
$923$	−30374.0			−1.08318
$924$		0			0
$925$	−17753.7			−0.631069
$926$	114.866	−	198.954i	0.00407639	−	0.00706052i
$927$	−6501.87	−	11261.6i	−0.230366	−	0.399006i
$928$	16190.6	+	28042.9i	0.572717	+	0.991975i
$929$	−21047.3	+	36454.9i	−0.743313	+	1.28746i	0.207665	+	0.978200i	$0.433414\pi$
$929$	−21047.3	+	36454.9i	−0.743313	+	1.28746i	−0.950979	+	0.309257i	$0.899920\pi$
$930$	5671.95			0.199990
$931$		0			0
$932$	57051.5			2.00513
$933$	5238.40	−	9073.18i	0.183813	−	0.318374i
$934$	−4069.43	−	7048.47i	−0.142565	−	0.246930i
$935$	1682.63	+	2914.40i	0.0588534	+	0.101937i
$936$	11249.6	−	19484.9i	0.392847	−	0.680431i
$937$	44385.1			1.54749			0.773745	−	0.633497i	$-0.218381\pi$
$937$	44385.1			1.54749			0.773745	+	0.633497i	$0.218381\pi$
$938$		0			0
$939$	−26136.3			−0.908334
$940$	34818.3	−	60307.1i	1.20814	−	2.09255i
$941$	20495.8	+	35499.8i	0.710036	+	1.22982i	0.964843	+	0.262827i	$0.0846547\pi$
$941$	20495.8	+	35499.8i	0.710036	+	1.22982i	−0.254807	+	0.966992i	$0.582012\pi$
$942$	−14839.3	−	25702.4i	−0.513259	−	0.888990i
$943$	928.197	−	1607.68i	0.0320533	−	0.0555179i
$944$	−95416.1			−3.28976
$945$		0			0
$946$	18017.4			0.619233
$947$	26311.2	−	45572.4i	0.902851	−	1.56378i	0.0790737	−	0.996869i	$-0.474804\pi$
$947$	26311.2	−	45572.4i	0.902851	−	1.56378i	0.823777	−	0.566914i	$-0.191863\pi$
$948$	−13246.2	−	22943.2i	−0.453816	−	0.786033i
$949$	6402.90	+	11090.1i	0.219017	+	0.379348i
$950$	27221.8	−	47149.6i	0.929676	−	1.61025i
$951$	5820.99			0.198484
$952$		0			0
$953$	−10798.1			−0.367035			−0.183517	−	0.983016i	$-0.558748\pi$
$953$	−10798.1			−0.367035			−0.183517	+	0.983016i	$0.558748\pi$
$954$	6875.70	−	11909.1i	0.233343	−	0.404162i
$955$	−11993.4	−	20773.1i	−0.406384	−	0.703877i
$956$	34630.0	+	59980.9i	1.17156	+	2.02921i
$957$	−1510.57	+	2616.38i	−0.0510238	+	0.0883758i
$958$	37345.8			1.25949
$959$		0			0
$960$	−15377.5			−0.516987
$961$	12844.7	−	22247.7i	0.431162	−	0.746794i
$962$	19371.1	+	33551.7i	0.649219	+	1.12448i
$963$	−4459.32	−	7723.77i	−0.149221	−	0.258458i
$964$	−26595.7	+	46065.1i	−0.888579	+	1.53906i
$965$	−11461.2			−0.382331
$966$		0			0
$967$	15648.9			0.520408			0.260204	−	0.965554i	$-0.416210\pi$
$967$	15648.9			0.520408			0.260204	+	0.965554i	$0.416210\pi$
$968$	36760.2	−	63670.6i	1.22058	−	2.11410i
$969$	7110.59	+	12315.9i	0.235733	+	0.408301i
$970$	−1170.17	−	2026.79i	−0.0387338	−	0.0670889i
$971$	23629.9	−	40928.2i	0.780968	−	1.35268i	−0.150411	−	0.988624i	$-0.548060\pi$
$971$	23629.9	−	40928.2i	0.780968	−	1.35268i	0.931379	−	0.364052i	$-0.118607\pi$
$972$	4903.25			0.161802
$973$		0			0
$974$	−81595.2			−2.68427
$975$	−5456.83	+	9451.51i	−0.179239	+	0.310452i
$976$	−34840.4	−	60345.3i	−1.14264	−	1.97910i
$977$	24483.2	+	42406.2i	0.801728	+	1.38863i	0.918478	+	0.395473i	$0.129419\pi$
$977$	24483.2	+	42406.2i	0.801728	+	1.38863i	−0.116749	+	0.993161i	$0.537247\pi$
$978$	−18481.9	+	32011.6i	−0.604281	+	1.04665i
$979$	22066.6			0.720380
$980$		0			0
$981$	17578.5			0.572109
$982$	6352.29	−	11002.5i	0.206426	−	0.357540i
$983$	−9555.64	−	16550.9i	−0.310049	−	0.537020i	0.668324	−	0.743870i	$-0.267012\pi$
$983$	−9555.64	−	16550.9i	−0.310049	−	0.537020i	−0.978373	+	0.206850i	$0.933679\pi$
$984$	−2404.02	−	4163.89i	−0.0778836	−	0.134898i
$985$	−4632.89	+	8024.39i	−0.149864	+	0.259572i
$986$	16700.3			0.539397
$987$		0			0
$988$	−85076.4			−2.73951
$989$	−9130.65	+	15814.8i	−0.293567	+	0.508473i
$990$	−1848.88	−	3202.36i	−0.0593548	−	0.102806i
$991$	27051.3	+	46854.1i	0.867115	+	1.50189i	0.864931	+	0.501890i	$0.167362\pi$
$991$	27051.3	+	46854.1i	0.867115	+	1.50189i	0.00218424	+	0.999998i	$0.499305\pi$
$992$	14329.9	−	24820.1i	0.458643	−	0.794393i
$993$	−17194.5			−0.549498
$994$		0			0
$995$	−6048.21			−0.192705
$996$	7301.65	−	12646.8i	0.232291	−	0.402339i
$997$	4596.40	+	7961.20i	0.146008	+	0.252892i	0.929748	−	0.368196i	$-0.120024\pi$
$997$	4596.40	+	7961.20i	0.146008	+	0.252892i	−0.783741	+	0.621088i	$0.786691\pi$
$998$	−1840.70	−	3188.19i	−0.0583832	−	0.101123i
$999$	−2547.82	+	4412.95i	−0.0806901	+	0.139759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.n.79.1		6
3.2	odd	2		441.4.e.w.226.3		6
7.2	even	3		147.4.a.m.1.3		3
7.3	odd	6		21.4.e.b.4.1	✓	6
7.4	even	3	inner	147.4.e.n.67.1		6
7.5	odd	6		147.4.a.l.1.3		3
7.6	odd	2		21.4.e.b.16.1	yes	6
21.2	odd	6		441.4.a.t.1.1		3
21.5	even	6		441.4.a.s.1.1		3
21.11	odd	6		441.4.e.w.361.3		6
21.17	even	6		63.4.e.c.46.3		6
21.20	even	2		63.4.e.c.37.3		6
28.3	even	6		336.4.q.k.193.2		6
28.19	even	6		2352.4.a.ci.1.2		3
28.23	odd	6		2352.4.a.cg.1.2		3
28.27	even	2		336.4.q.k.289.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.1	✓	6	7.3	odd	6
21.4.e.b.16.1	yes	6	7.6	odd	2
63.4.e.c.37.3		6	21.20	even	2
63.4.e.c.46.3		6	21.17	even	6
147.4.a.l.1.3		3	7.5	odd	6
147.4.a.m.1.3		3	7.2	even	3
147.4.e.n.67.1		6	7.4	even	3	inner
147.4.e.n.79.1		6	1.1	even	1	trivial
336.4.q.k.193.2		6	28.3	even	6
336.4.q.k.289.2		6	28.27	even	2
441.4.a.s.1.1		3	21.5	even	6
441.4.a.t.1.1		3	21.2	odd	6
441.4.e.w.226.3		6	3.2	odd	2
441.4.e.w.361.3		6	21.11	odd	6
2352.4.a.cg.1.2		3	28.23	odd	6
2352.4.a.ci.1.2		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)

\(f(q)\)	\(=\)	\(q+(-2.65415 + 4.59712i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-10.0890 - 17.4746i) q^{4} +(2.78070 - 4.81631i) q^{5} +15.9249 q^{6} +64.6443 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.65415 + 4.59712i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-10.0890 - 17.4746i) q^{4} +(2.78070 - 4.81631i) q^{5} +15.9249 q^{6} +64.6443 q^{8} +(-4.50000 + 7.79423i) q^{9} +(14.7608 + 25.5664i) q^{10} +(6.95869 + 12.0528i) q^{11} +(-30.2670 + 52.4239i) q^{12} -38.6718 q^{13} -16.6842 q^{15} +(-90.8636 + 157.380i) q^{16} +(21.7394 + 37.6537i) q^{17} +(-23.8873 - 41.3741i) q^{18} +(-54.5139 + 94.4208i) q^{19} -112.218 q^{20} -73.8775 q^{22} +(37.4389 - 64.8461i) q^{23} +(-96.9665 - 167.951i) q^{24} +(47.0354 + 81.4677i) q^{25} +(102.641 - 177.779i) q^{26} +27.0000 q^{27} -72.3589 q^{29} +(44.2823 - 76.6992i) q^{30} +(32.0215 + 55.4629i) q^{31} +(-223.754 - 387.553i) q^{32} +(20.8761 - 36.1584i) q^{33} -230.798 q^{34} +181.602 q^{36} +(-94.3636 + 163.443i) q^{37} +(-289.376 - 501.213i) q^{38} +(58.0077 + 100.472i) q^{39} +(179.756 - 311.347i) q^{40} +24.7923 q^{41} -243.881 q^{43} +(140.412 - 243.201i) q^{44} +(25.0263 + 43.3468i) q^{45} +(198.737 + 344.222i) q^{46} +(-310.274 + 537.411i) q^{47} +545.182 q^{48} -499.356 q^{50} +(65.2182 - 112.961i) q^{51} +(390.159 + 675.776i) q^{52} +(143.919 + 249.276i) q^{53} +(-71.6620 + 124.122i) q^{54} +77.4001 q^{55} +327.083 q^{57} +(192.051 - 332.642i) q^{58} +(262.526 + 454.708i) q^{59} +(168.327 + 291.551i) q^{60} +(-191.718 + 332.065i) q^{61} -339.960 q^{62} +921.681 q^{64} +(-107.535 + 186.255i) q^{65} +(110.816 + 191.939i) q^{66} +(-99.0583 - 171.574i) q^{67} +(438.657 - 759.776i) q^{68} -224.634 q^{69} +785.432 q^{71} +(-290.900 + 503.853i) q^{72} +(-165.570 - 286.776i) q^{73} +(-500.910 - 867.602i) q^{74} +(141.106 - 244.403i) q^{75} +2199.96 q^{76} -615.844 q^{78} +(-218.823 + 379.013i) q^{79} +(505.329 + 875.255i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-65.8024 + 113.973i) q^{82} -241.241 q^{83} +241.803 q^{85} +(647.297 - 1121.15i) q^{86} +(108.538 + 187.994i) q^{87} +(449.840 + 779.145i) q^{88} +(792.772 - 1373.12i) q^{89} -265.694 q^{90} -1510.88 q^{92} +(96.0646 - 166.389i) q^{93} +(-1647.03 - 2852.73i) q^{94} +(303.173 + 525.112i) q^{95} +(-671.261 + 1162.66i) q^{96} -79.2754 q^{97} -125.256 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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