LMFDB - Embedded newform 147.4.e.n.79.3

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			79.3
Root			$-2.27818 + 3.94593i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.n.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27818 - 3.94593i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} -13.6691 q^{6} -21.6905 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(2.27818 - 3.94593i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} -13.6691 q^{6} -21.6905 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-40.7184 - 70.5264i) q^{10} +(5.69708 + 9.86762i) q^{11} +(-19.1407 + 33.1527i) q^{12} +13.0987 q^{13} -53.6196 q^{15} +(1.62706 - 2.81815i) q^{16} +(26.6337 + 46.1309i) q^{17} +(20.5036 + 35.5134i) q^{18} +(-21.2111 + 36.7388i) q^{19} -228.071 q^{20} +51.9159 q^{22} +(-76.0427 + 131.710i) q^{23} +(32.5357 + 56.3535i) q^{24} +(-97.2257 - 168.400i) q^{25} +(29.8412 - 51.6864i) q^{26} +27.0000 q^{27} +186.493 q^{29} +(-122.155 + 211.579i) q^{30} +(-78.9369 - 136.723i) q^{31} +(-94.1753 - 163.116i) q^{32} +(17.0912 - 29.6029i) q^{33} +242.706 q^{34} +114.844 q^{36} +(-1.87294 + 3.24403i) q^{37} +(96.6457 + 167.395i) q^{38} +(-19.6480 - 34.0313i) q^{39} +(-193.839 + 335.739i) q^{40} +39.3230 q^{41} +429.439 q^{43} +(72.6974 - 125.916i) q^{44} +(80.4294 + 139.308i) q^{45} +(346.478 + 600.118i) q^{46} +(10.5934 - 18.3484i) q^{47} -9.76236 q^{48} -885.992 q^{50} +(79.9010 - 138.393i) q^{51} +(-83.5726 - 144.752i) q^{52} +(-182.952 - 316.882i) q^{53} +(61.5109 - 106.540i) q^{54} +203.650 q^{55} +127.267 q^{57} +(424.866 - 735.889i) q^{58} +(-113.289 - 196.222i) q^{59} +(342.106 + 592.545i) q^{60} +(325.987 - 564.626i) q^{61} -719.331 q^{62} -832.161 q^{64} +(117.058 - 202.750i) q^{65} +(-77.8739 - 134.882i) q^{66} +(-72.7166 - 125.949i) q^{67} +(339.858 - 588.652i) q^{68} +456.256 q^{69} -368.962 q^{71} +(97.6071 - 169.060i) q^{72} +(304.453 + 527.328i) q^{73} +(8.53380 + 14.7810i) q^{74} +(-291.677 + 505.200i) q^{75} +541.328 q^{76} -179.047 q^{78} +(-455.119 + 788.289i) q^{79} +(-29.0808 - 50.3694i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(89.5850 - 155.166i) q^{82} +327.929 q^{83} +952.058 q^{85} +(978.340 - 1694.53i) q^{86} +(-279.740 - 484.524i) q^{87} +(-123.572 - 214.033i) q^{88} +(-18.8059 + 32.5728i) q^{89} +732.932 q^{90} +1940.68 q^{92} +(-236.811 + 410.168i) q^{93} +(-48.2676 - 83.6019i) q^{94} +(379.111 + 656.640i) q^{95} +(-282.526 + 489.349i) q^{96} -722.013 q^{97} -102.547 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 $

$2$	2.27818	−	3.94593i	0.805459	−	1.39510i	−0.110521	−	0.993874i	$-0.535252\pi$
$2$	2.27818	−	3.94593i	0.805459	−	1.39510i	0.915981	−	0.401223i	$-0.131415\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−6.38024	−	11.0509i	−0.797530	−	1.38136i
$5$	8.93660	−	15.4786i	0.799314	−	1.38445i	−0.120749	−	0.992683i	$-0.538530\pi$
$5$	8.93660	−	15.4786i	0.799314	−	1.38445i	0.920063	−	0.391769i	$-0.128137\pi$
$6$	−13.6691			−0.930064
$7$		0			0
$7$		0			0
$8$	−21.6905			−0.958592
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−40.7184	−	70.5264i	−1.28763	−	2.23024i
$11$	5.69708	+	9.86762i	0.156158	+	0.270473i	0.933480	−	0.358630i	$-0.116756\pi$
$11$	5.69708	+	9.86762i	0.156158	+	0.270473i	−0.777322	+	0.629102i	$0.783423\pi$
$12$	−19.1407	+	33.1527i	−0.460454	+	0.797530i
$13$	13.0987			0.279455			0.139728	−	0.990190i	$-0.455377\pi$
$13$	13.0987			0.279455			0.139728	+	0.990190i	$0.455377\pi$
$14$		0			0
$15$	−53.6196			−0.922968
$16$	1.62706	−	2.81815i	0.0254228	−	0.0440336i
$17$	26.6337	+	46.1309i	0.379977	+	0.658140i	0.991059	−	0.133428i	$-0.0425984\pi$
$17$	26.6337	+	46.1309i	0.379977	+	0.658140i	−0.611081	+	0.791568i	$0.709265\pi$
$18$	20.5036	+	35.5134i	0.268486	+	0.465032i
$19$	−21.2111	+	36.7388i	−0.256114	+	0.443603i	−0.965198	−	0.261522i	$-0.915776\pi$
$19$	−21.2111	+	36.7388i	−0.256114	+	0.443603i	0.709083	+	0.705125i	$0.249109\pi$
$20$	−228.071			−2.54991
$21$		0			0
$22$	51.9159			0.503114
$23$	−76.0427	+	131.710i	−0.689391	+	1.19406i	0.282644	+	0.959225i	$0.408789\pi$
$23$	−76.0427	+	131.710i	−0.689391	+	1.19406i	−0.972035	+	0.234836i	$0.924545\pi$
$24$	32.5357	+	56.3535i	0.276722	+	0.479296i
$25$	−97.2257	−	168.400i	−0.777806	−	1.34720i
$26$	29.8412	−	51.6864i	0.225090	−	0.389867i
$27$	27.0000			0.192450
$28$		0			0
$29$	186.493			1.19417			0.597085	−	0.802178i	$-0.296325\pi$
$29$	186.493			1.19417			0.597085	+	0.802178i	$0.296325\pi$
$30$	−122.155	+	211.579i	−0.743413	+	1.28763i
$31$	−78.9369	−	136.723i	−0.457338	−	0.792133i	0.541481	−	0.840713i	$-0.317864\pi$
$31$	−78.9369	−	136.723i	−0.457338	−	0.792133i	−0.998819	+	0.0485801i	$0.984530\pi$
$32$	−94.1753	−	163.116i	−0.520250	−	0.901099i
$33$	17.0912	−	29.6029i	0.0901576	−	0.156158i
$34$	242.706			1.22423
$35$		0			0
$36$	114.844			0.531686
$37$	−1.87294	+	3.24403i	−0.00832188	+	0.0144139i	−0.870156	−	0.492776i	$-0.835982\pi$
$37$	−1.87294	+	3.24403i	−0.00832188	+	0.0144139i	0.861834	+	0.507190i	$0.169316\pi$
$38$	96.6457	+	167.395i	0.412579	+	0.714608i
$39$	−19.6480	−	34.0313i	−0.0806718	−	0.139728i
$40$	−193.839	+	335.739i	−0.766216	+	1.32712i
$41$	39.3230			0.149786			0.0748930	−	0.997192i	$-0.476138\pi$
$41$	39.3230			0.149786			0.0748930	+	0.997192i	$0.476138\pi$
$42$		0			0
$43$	429.439			1.52300			0.761498	−	0.648168i	$-0.224464\pi$
$43$	429.439			1.52300			0.761498	+	0.648168i	$0.224464\pi$
$44$	72.6974	−	125.916i	0.249080	−	0.431420i
$45$	80.4294	+	139.308i	0.266438	+	0.461484i
$46$	346.478	+	600.118i	1.11055	+	1.92354i
$47$	10.5934	−	18.3484i	0.0328768	−	0.0569444i	−0.849119	−	0.528202i	$-0.822866\pi$
$47$	10.5934	−	18.3484i	0.0328768	−	0.0569444i	0.881996	+	0.471258i	$0.156200\pi$
$48$	−9.76236			−0.0293557
$49$		0			0
$50$	−885.992			−2.50596
$51$	79.9010	−	138.393i	0.219380	−	0.379977i
$52$	−83.5726	−	144.752i	−0.222874	−	0.386029i
$53$	−182.952	−	316.882i	−0.474158	−	0.821266i	0.525404	−	0.850853i	$-0.323914\pi$
$53$	−182.952	−	316.882i	−0.474158	−	0.821266i	−0.999562	+	0.0295866i	$0.990581\pi$
$54$	61.5109	−	106.540i	0.155011	−	0.268486i
$55$	203.650			0.499276
$56$		0			0
$57$	127.267			0.295735
$58$	424.866	−	735.889i	0.961856	−	1.66598i
$59$	−113.289	−	196.222i	−0.249982	−	0.432982i	0.713538	−	0.700616i	$-0.247091\pi$
$59$	−113.289	−	196.222i	−0.249982	−	0.432982i	−0.963521	+	0.267634i	$0.913758\pi$
$60$	342.106	+	592.545i	0.736095	+	1.27495i
$61$	325.987	−	564.626i	0.684235	−	1.18513i	−0.289442	−	0.957196i	$-0.593470\pi$
$61$	325.987	−	564.626i	0.684235	−	1.18513i	0.973677	−	0.227934i	$-0.0731970\pi$
$62$	−719.331			−1.47347
$63$		0			0
$64$	−832.161			−1.62532
$65$	117.058	−	202.750i	0.223372	−	0.386892i
$66$	−77.8739	−	134.882i	−0.145237	−	0.251557i
$67$	−72.7166	−	125.949i	−0.132593	−	0.229658i	0.792082	−	0.610414i	$-0.208997\pi$
$67$	−72.7166	−	125.949i	−0.132593	−	0.229658i	−0.924675	+	0.380756i	$0.875664\pi$
$68$	339.858	−	588.652i	0.606086	−	1.04977i
$69$	456.256			0.796041
$70$		0			0
$71$	−368.962			−0.616728			−0.308364	−	0.951268i	$-0.599782\pi$
$71$	−368.962			−0.616728			−0.308364	+	0.951268i	$0.599782\pi$
$72$	97.6071	−	169.060i	0.159765	−	0.276722i
$73$	304.453	+	527.328i	0.488130	+	0.845466i	0.999907	−	0.0136522i	$-0.00434576\pi$
$73$	304.453	+	527.328i	0.488130	+	0.845466i	−0.511777	+	0.859119i	$0.671012\pi$
$74$	8.53380	+	14.7810i	0.0134059	+	0.0232197i
$75$	−291.677	+	505.200i	−0.449066	+	0.777806i
$76$	541.328			0.817034
$77$		0			0
$78$	−179.047			−0.259911
$79$	−455.119	+	788.289i	−0.648163	+	1.12265i	0.335399	+	0.942076i	$0.391129\pi$
$79$	−455.119	+	788.289i	−0.648163	+	1.12265i	−0.983561	+	0.180574i	$0.942204\pi$
$80$	−29.0808	−	50.3694i	−0.0406416	−	0.0703933i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	89.5850	−	155.166i	0.120646	−	0.208966i
$83$	327.929			0.433674			0.216837	−	0.976208i	$-0.430426\pi$
$83$	327.929			0.433674			0.216837	+	0.976208i	$0.430426\pi$
$84$		0			0
$85$	952.058			1.21489
$86$	978.340	−	1694.53i	1.22671	−	2.12473i
$87$	−279.740	−	484.524i	−0.344727	−	0.597085i
$88$	−123.572	−	214.033i	−0.149691	−	0.259273i
$89$	−18.8059	+	32.5728i	−0.0223980	+	0.0387945i	−0.877007	−	0.480477i	$-0.840463\pi$
$89$	−18.8059	+	32.5728i	−0.0223980	+	0.0387945i	0.854609	+	0.519272i	$0.173797\pi$
$90$	732.932			0.858420
$91$		0			0
$92$	1940.68			2.19924
$93$	−236.811	+	410.168i	−0.264044	+	0.457338i
$94$	−48.2676	−	83.6019i	−0.0529619	−	0.0917327i
$95$	379.111	+	656.640i	0.409431	+	0.709156i
$96$	−282.526	+	489.349i	−0.300366	+	0.520250i
$97$	−722.013			−0.755766			−0.377883	−	0.925853i	$-0.623348\pi$
$97$	−722.013			−0.755766			−0.377883	+	0.925853i	$0.623348\pi$
$98$		0			0
$99$	−102.547			−0.104105
$100$	−1240.65	+	2148.86i	−1.24065	+	2.14886i
$101$	759.336	+	1315.21i	0.748087	+	1.29572i	0.948739	+	0.316062i	$0.102361\pi$
$101$	759.336	+	1315.21i	0.748087	+	1.29572i	−0.200652	+	0.979663i	$0.564306\pi$
$102$	−364.058	−	630.568i	−0.353403	−	0.612113i
$103$	−525.942	+	910.957i	−0.503132	+	0.871450i	0.496862	+	0.867830i	$0.334486\pi$
$103$	−525.942	+	910.957i	−0.503132	+	0.871450i	−0.999993	+	0.00361990i	$0.998848\pi$
$104$	−284.116			−0.267883
$105$		0			0
$106$	−1667.19			−1.52766
$107$	−383.260	+	663.826i	−0.346273	+	0.599762i	−0.985584	−	0.169186i	$-0.945886\pi$
$107$	−383.260	+	663.826i	−0.346273	+	0.599762i	0.639312	+	0.768948i	$0.279219\pi$
$108$	−172.266	−	298.374i	−0.153485	−	0.265843i
$109$	713.524	+	1235.86i	0.627002	+	1.08600i	0.988150	+	0.153491i	$0.0490516\pi$
$109$	713.524	+	1235.86i	0.627002	+	1.08600i	−0.361148	+	0.932509i	$0.617615\pi$
$110$	463.952	−	803.588i	0.402146	−	0.696538i
$111$	11.2376			0.00960928
$112$		0			0
$113$	362.564			0.301833			0.150917	−	0.988546i	$-0.451778\pi$
$113$	362.564			0.301833			0.150917	+	0.988546i	$0.451778\pi$
$114$	289.937	−	502.186i	0.238203	−	0.412579i
$115$	1359.13	+	2354.08i	1.10208	+	1.90886i
$116$	−1189.87	−	2060.92i	−0.952386	−	1.64958i
$117$	−58.9440	+	102.094i	−0.0465759	+	0.0806718i
$118$	−1032.37			−0.805402
$119$		0			0
$120$	1163.03			0.884750
$121$	600.587	−	1040.25i	0.451230	−	0.781553i
$122$	−1485.31	−	2572.64i	−1.10225	−	1.90915i
$123$	−58.9845	−	102.164i	−0.0432395	−	0.0748930i
$124$	−1007.27	+	1744.65i	−0.729481	+	1.26350i
$125$	−1241.32			−0.888216
$126$		0			0
$127$	974.777			0.681082			0.340541	−	0.940230i	$-0.389390\pi$
$127$	974.777			0.681082			0.340541	+	0.940230i	$0.389390\pi$
$128$	−1142.41	+	1978.72i	−0.788875	+	1.36637i
$129$	−644.158	−	1115.71i	−0.439651	−	0.761498i
$130$	−533.357	−	923.802i	−0.359835	−	0.623252i
$131$	−896.351	+	1552.53i	−0.597821	+	1.03546i	0.395321	+	0.918543i	$0.370633\pi$
$131$	−896.351	+	1552.53i	−0.597821	+	1.03546i	−0.993142	+	0.116914i	$0.962700\pi$
$132$	−436.184			−0.287613
$133$		0			0
$134$	−662.647			−0.427194
$135$	241.288	−	417.924i	0.153828	−	0.266438i
$136$	−577.697	−	1000.60i	−0.364243	−	0.630888i
$137$	−842.208	−	1458.75i	−0.525217	−	0.909702i	−0.999569	−	0.0293665i	$-0.990651\pi$
$137$	−842.208	−	1458.75i	−0.525217	−	0.909702i	0.474352	−	0.880335i	$-0.342682\pi$
$138$	1039.44	−	1800.35i	0.641178	−	1.11055i
$139$	−315.089			−0.192270			−0.0961350	−	0.995368i	$-0.530648\pi$
$139$	−315.089			−0.192270			−0.0961350	+	0.995368i	$0.530648\pi$
$140$		0			0
$141$	−63.5606			−0.0379629
$142$	−840.563	+	1455.90i	−0.496750	+	0.860396i
$143$	74.6241	+	129.253i	0.0436390	+	0.0755850i
$144$	14.6435	+	25.3633i	0.00847427	+	0.0146779i
$145$	1666.62	−	2886.67i	0.954517	−	1.65327i
$146$	2774.40			1.57268
$147$		0			0
$148$	47.7992			0.0265478
$149$	−946.887	+	1640.06i	−0.520617	+	0.901736i	0.479095	+	0.877763i	$0.340965\pi$
$149$	−946.887	+	1640.06i	−0.520617	+	0.901736i	−0.999713	+	0.0239729i	$0.992368\pi$
$150$	1328.99	+	2301.87i	0.723409	+	1.25298i
$151$	1005.92	+	1742.31i	0.542124	+	0.938986i	0.998782	+	0.0493434i	$0.0157129\pi$
$151$	1005.92	+	1742.31i	0.542124	+	0.938986i	−0.456658	+	0.889642i	$0.650954\pi$
$152$	460.079	−	796.881i	0.245509	−	0.425234i
$153$	−479.406			−0.253318
$154$		0			0
$155$	−2821.71			−1.46223
$156$	−250.718	+	434.256i	−0.128676	+	0.222874i
$157$	−1914.25	−	3315.58i	−0.973082	−	1.68543i	−0.686125	−	0.727483i	$-0.740690\pi$
$157$	−1914.25	−	3315.58i	−0.973082	−	1.68543i	−0.286956	−	0.957944i	$-0.592643\pi$
$158$	2073.69	+	3591.73i	1.04414	+	1.80850i
$159$	−548.856	+	950.647i	−0.273755	+	0.474158i
$160$	−3366.43			−1.66337
$161$		0			0
$162$	−369.066			−0.178991
$163$	1754.63	−	3039.11i	0.843148	−	1.46038i	−0.0440718	−	0.999028i	$-0.514033\pi$
$163$	1754.63	−	3039.11i	0.843148	−	1.46038i	0.887220	−	0.461347i	$-0.152634\pi$
$164$	−250.890	−	434.554i	−0.119459	−	0.206909i
$165$	−305.475	−	529.098i	−0.144128	−	0.249638i
$166$	747.083	−	1293.99i	0.349307	−	0.605017i
$167$	343.008			0.158939			0.0794694	−	0.996837i	$-0.474677\pi$
$167$	343.008			0.158939			0.0794694	+	0.996837i	$0.474677\pi$
$168$		0			0
$169$	−2025.42			−0.921905
$170$	2168.96	−	3756.75i	0.978541	−	1.69488i
$171$	−190.900	−	330.649i	−0.0853714	−	0.147868i
$172$	−2739.92	−	4745.68i	−1.21463	−	2.10381i
$173$	−2093.61	+	3626.23i	−0.920081	+	1.59363i	−0.120793	+	0.992678i	$0.538544\pi$
$173$	−2093.61	+	3626.23i	−0.920081	+	1.59363i	−0.799288	+	0.600949i	$0.794790\pi$
$174$	−2549.20			−1.11066
$175$		0			0
$176$	37.0779			0.0158798
$177$	−339.866	+	588.666i	−0.144327	+	0.249982i
$178$	85.6866	+	148.413i	0.0360813	+	0.0624947i
$179$	985.143	+	1706.32i	0.411358	+	0.712493i	0.995039	−	0.0994906i	$-0.0317213\pi$
$179$	985.143	+	1706.32i	0.411358	+	0.712493i	−0.583681	+	0.811983i	$0.698388\pi$
$180$	1026.32	−	1777.63i	0.424984	−	0.736095i
$181$	3613.10			1.48376			0.741878	−	0.670535i	$-0.233935\pi$
$181$	3613.10			1.48376			0.741878	+	0.670535i	$0.233935\pi$
$182$		0			0
$183$	−1955.92			−0.790086
$184$	1649.40	−	2856.85i	0.660845	−	1.14462i
$185$	33.4755	+	57.9812i	0.0133036	+	0.0230425i
$186$	1079.00	+	1868.88i	0.425354	+	0.736734i
$187$	−303.468	+	525.622i	−0.118673	+	0.205547i
$188$	−270.355			−0.104881
$189$		0			0
$190$	3454.74			1.31912
$191$	−953.884	+	1652.18i	−0.361365	+	0.625902i	−0.988186	−	0.153261i	$-0.951022\pi$
$191$	−953.884	+	1652.18i	−0.361365	+	0.625902i	0.626821	+	0.779163i	$0.284356\pi$
$192$	1248.24	+	2162.02i	0.469188	+	0.812658i
$193$	−1199.96	−	2078.40i	−0.447540	−	0.775162i	0.550685	−	0.834713i	$-0.314366\pi$
$193$	−1199.96	−	2078.40i	−0.447540	−	0.775162i	−0.998225	+	0.0595509i	$0.981033\pi$
$194$	−1644.88	+	2849.01i	−0.608738	+	1.05437i
$195$	−702.346			−0.257928
$196$		0			0
$197$	1514.32			0.547668			0.273834	−	0.961777i	$-0.411708\pi$
$197$	1514.32			0.547668			0.273834	+	0.961777i	$0.411708\pi$
$198$	−233.622	+	404.645i	−0.0838524	+	0.145237i
$199$	683.889	+	1184.53i	0.243616	+	0.421955i	0.961742	−	0.273958i	$-0.0883330\pi$
$199$	683.889	+	1184.53i	0.243616	+	0.421955i	−0.718126	+	0.695914i	$0.755000\pi$
$200$	2108.87	+	3652.67i	0.745598	+	1.29141i
$201$	−218.150	+	377.847i	−0.0765527	+	0.132593i
$202$	6919.63			2.41021
$203$		0			0
$204$	−2039.15			−0.699848
$205$	351.414	−	608.667i	0.119726	−	0.207371i
$206$	2396.38	+	4150.66i	0.810504	+	1.40383i
$207$	−684.384	−	1185.39i	−0.229797	−	0.398020i
$208$	21.3123	−	36.9140i	0.00710453	−	0.0123054i
$209$	−483.366			−0.159977
$210$		0			0
$211$	4302.52			1.40378			0.701891	−	0.712285i	$-0.252339\pi$
$211$	4302.52			1.40378			0.701891	+	0.712285i	$0.252339\pi$
$212$	−2334.55	+	4043.57i	−0.756311	+	1.30997i
$213$	553.443	+	958.591i	0.178034	+	0.308364i
$214$	1746.27	+	3024.64i	0.557817	+	0.966167i
$215$	3837.72	−	6647.13i	1.21735	−	2.10851i
$216$	−585.642			−0.184481
$217$		0			0
$218$	6502.16			2.02010
$219$	913.359	−	1581.98i	0.281822	−	0.488130i
$220$	−1299.34	−	2250.51i	−0.398187	−	0.689680i
$221$	348.866	+	604.253i	0.106187	+	0.183921i
$222$	25.6014	−	44.3429i	0.00773988	−	0.0134059i
$223$	1497.19			0.449592			0.224796	−	0.974406i	$-0.427828\pi$
$223$	1497.19			0.449592			0.224796	+	0.974406i	$0.427828\pi$
$224$		0			0
$225$	1750.06			0.518537
$226$	825.987	−	1430.65i	0.243114	−	0.421086i
$227$	801.662	+	1388.52i	0.234397	+	0.405988i	0.959097	−	0.283076i	$-0.0913550\pi$
$227$	801.662	+	1388.52i	0.234397	+	0.405988i	−0.724700	+	0.689065i	$0.758022\pi$
$228$	−811.992	−	1406.41i	−0.235858	−	0.408517i
$229$	505.261	−	875.137i	0.145802	−	0.252536i	−0.783870	−	0.620925i	$-0.786757\pi$
$229$	505.261	−	875.137i	0.145802	−	0.252536i	0.929672	+	0.368389i	$0.120091\pi$
$230$	12385.4			3.55072
$231$		0			0
$232$	−4045.13			−1.14472
$233$	−99.1084	+	171.661i	−0.0278661	+	0.0482656i	−0.879622	−	0.475673i	$-0.842205\pi$
$233$	−99.1084	+	171.661i	−0.0278661	+	0.0482656i	0.851756	+	0.523939i	$0.175538\pi$
$234$	268.571	+	465.178i	0.0750299	+	0.129956i
$235$	−189.339	−	327.944i	−0.0525578	−	0.0910329i
$236$	−1445.62	+	2503.88i	−0.398736	+	0.690631i
$237$	2730.71			0.748434
$238$		0			0
$239$	−1201.19			−0.325098			−0.162549	−	0.986700i	$-0.551972\pi$
$239$	−1201.19			−0.325098			−0.162549	+	0.986700i	$0.551972\pi$
$240$	−87.2423	+	151.108i	−0.0234644	+	0.0406416i
$241$	−1366.35	−	2366.58i	−0.365204	−	0.632551i	0.623605	−	0.781739i	$-0.285667\pi$
$241$	−1366.35	−	2366.58i	−0.365204	−	0.632551i	−0.988809	+	0.149188i	$0.952334\pi$
$242$	−2736.49	−	4739.74i	−0.726894	−	1.25902i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−8319.49			−2.18279
$245$		0			0
$246$	−537.510			−0.139311
$247$	−277.838	+	481.229i	−0.0715724	+	0.123967i
$248$	1712.18	+	2965.58i	0.438401	+	0.759332i
$249$	−491.894	−	851.985i	−0.125191	−	0.216837i
$250$	−2827.95	+	4898.16i	−0.715422	+	1.23915i
$251$	−7565.82			−1.90259			−0.951295	−	0.308281i	$-0.900246\pi$
$251$	−7565.82			−1.90259			−0.951295	+	0.308281i	$0.900246\pi$
$252$		0			0
$253$	−1732.88			−0.430615
$254$	2220.72	−	3846.40i	0.548584	−	0.950175i
$255$	−1428.09	−	2473.52i	−0.350707	−	0.607443i
$256$	1876.61	+	3250.38i	0.458156	+	0.793550i
$257$	2504.34	−	4337.64i	0.607846	−	1.05282i	−0.383749	−	0.923437i	$-0.625367\pi$
$257$	2504.34	−	4337.64i	0.607846	−	1.05282i	0.991595	−	0.129382i	$-0.0412994\pi$
$258$	−5870.04			−1.41648
$259$		0			0
$260$	−2987.42			−0.712584
$261$	−839.220	+	1453.57i	−0.199028	+	0.344727i
$262$	4084.10	+	7073.88i	0.963041	+	1.66804i
$263$	3124.40	+	5411.63i	0.732544	+	1.26880i	0.955793	+	0.294042i	$0.0950004\pi$
$263$	3124.40	+	5411.63i	0.732544	+	1.26880i	−0.223249	+	0.974761i	$0.571666\pi$
$264$	−370.716	+	642.100i	−0.0864243	+	0.149691i
$265$	−6539.88			−1.51601
$266$		0			0
$267$	112.835			0.0258630
$268$	−927.898	+	1607.17i	−0.211494	+	0.366318i
$269$	−1794.22	−	3107.69i	−0.406676	−	0.704383i	0.587839	−	0.808978i	$-0.299979\pi$
$269$	−1794.22	−	3107.69i	−0.406676	−	0.704383i	−0.994515	+	0.104595i	$0.966645\pi$
$270$	−1099.40	−	1904.21i	−0.247804	−	0.429210i
$271$	−991.571	+	1717.45i	−0.222264	+	0.384973i	−0.955495	−	0.295007i	$-0.904678\pi$
$271$	−991.571	+	1717.45i	−0.222264	+	0.384973i	0.733231	+	0.679980i	$0.238012\pi$
$272$	173.338			0.0386404
$273$		0			0
$274$	−7674.81			−1.69216
$275$	1107.80	−	1918.77i	0.242920	−	0.420751i
$276$	−2911.02	−	5042.04i	−0.634866	−	1.09962i
$277$	−3681.96	−	6377.33i	−0.798654	−	1.38331i	−0.920493	−	0.390760i	$-0.872212\pi$
$277$	−3681.96	−	6377.33i	−0.798654	−	1.38331i	0.121838	−	0.992550i	$-0.461121\pi$
$278$	−717.831	+	1243.32i	−0.154866	+	0.268235i
$279$	1420.86			0.304892
$280$		0			0
$281$	−5312.05			−1.12772			−0.563861	−	0.825869i	$-0.690685\pi$
$281$	−5312.05			−1.12772			−0.563861	+	0.825869i	$0.690685\pi$
$282$	−144.803	+	250.806i	−0.0305776	+	0.0529619i
$283$	−545.882	−	945.495i	−0.114662	−	0.198600i	0.802983	−	0.596002i	$-0.203245\pi$
$283$	−545.882	−	945.495i	−0.114662	−	0.198600i	−0.917645	+	0.397402i	$0.869912\pi$
$284$	2354.06	+	4077.36i	0.491859	+	0.851925i
$285$	1137.33	−	1969.92i	0.236385	−	0.409431i
$286$	680.030			0.140598
$287$		0			0
$288$	1695.16			0.346833
$289$	1037.79	−	1797.51i	0.211234	−	0.365869i
$290$	−7593.72	−	13152.7i	−1.53765	−	2.66329i
$291$	1083.02	+	1875.84i	0.218171	+	0.377883i
$292$	3884.96	−	6728.95i	0.778597	−	1.34857i
$293$	7191.86			1.43397			0.716985	−	0.697089i	$-0.245522\pi$
$293$	7191.86			1.43397			0.716985	+	0.697089i	$0.245522\pi$
$294$		0			0
$295$	−4049.67			−0.799257
$296$	40.6249	−	70.3645i	0.00797729	−	0.0138171i
$297$	153.821	+	266.426i	0.0300525	+	0.0520525i
$298$	4314.36	+	7472.70i	0.838672	+	1.45262i
$299$	−996.058	+	1725.22i	−0.192654	+	0.333687i
$300$	7443.88			1.43257
$301$		0			0
$302$	9166.69			1.74663
$303$	2278.01	−	3945.63i	0.431908	−	0.748087i
$304$	69.0236	+	119.552i	0.0130223	+	0.0225552i
$305$	−5826.43	−	10091.7i	−1.09384	−	1.89458i
$306$	−1092.18	+	1891.70i	−0.204038	+	0.353403i
$307$	−541.355			−0.100641			−0.0503204	−	0.998733i	$-0.516024\pi$
$307$	−541.355			−0.100641			−0.0503204	+	0.998733i	$0.516024\pi$
$308$		0			0
$309$	3155.65			0.580966
$310$	−6428.37	+	11134.3i	−1.17776	+	2.03995i
$311$	27.0084	+	46.7799i	0.00492446	+	0.00852941i	0.868477	−	0.495729i	$-0.165099\pi$
$311$	27.0084	+	46.7799i	0.00492446	+	0.00852941i	−0.863553	+	0.504259i	$0.831766\pi$
$312$	426.174	+	738.155i	0.0773313	+	0.133942i
$313$	1886.47	−	3267.46i	0.340670	−	0.590058i	−0.643887	−	0.765120i	$-0.722679\pi$
$313$	1886.47	−	3267.46i	0.340670	−	0.590058i	0.984557	+	0.175063i	$0.0560128\pi$
$314$	−17444.1			−3.13511
$315$		0			0
$316$	11615.1			2.06772
$317$	−859.618	+	1488.90i	−0.152306	+	0.263802i	−0.932075	−	0.362266i	$-0.882003\pi$
$317$	−859.618	+	1488.90i	−0.152306	+	0.263802i	0.779769	+	0.626068i	$0.215337\pi$
$318$	2500.79	+	4331.49i	0.440998	+	0.763831i
$319$	1062.47	+	1840.25i	0.186479	+	0.322991i
$320$	−7436.70	+	12880.7i	−1.29914	+	2.25017i
$321$	2299.56			0.399841
$322$		0			0
$323$	−2259.72			−0.389270
$324$	−516.799	+	895.122i	−0.0886144	+	0.153485i
$325$	−1273.53	−	2205.81i	−0.217362	−	0.376482i
$326$	−7994.73	−	13847.3i	−1.35824	−	2.35255i
$327$	2140.57	−	3707.58i	0.362000	−	0.627002i
$328$	−852.934			−0.143584
$329$		0			0
$330$	−2783.71			−0.464358
$331$	−4204.11	+	7281.73i	−0.698123	+	1.20918i	0.270994	+	0.962581i	$0.412648\pi$
$331$	−4204.11	+	7281.73i	−0.698123	+	1.20918i	−0.969117	+	0.246603i	$0.920686\pi$
$332$	−2092.27	−	3623.91i	−0.345868	−	0.599060i
$333$	−16.8565	−	29.1963i	−0.00277396	−	0.00480464i
$334$	781.436	−	1353.49i	0.128019	−	0.221735i
$335$	−2599.36			−0.423935
$336$		0			0
$337$	2789.46			0.450894			0.225447	−	0.974255i	$-0.427616\pi$
$337$	2789.46			0.450894			0.225447	+	0.974255i	$0.427616\pi$
$338$	−4614.29	+	7992.18i	−0.742557	+	1.28615i
$339$	−543.846	−	941.969i	−0.0871317	−	0.150917i
$340$	−6074.36	−	10521.1i	−0.968907	−	1.67820i
$341$	899.419	−	1557.84i	0.142834	−	0.247395i
$342$	−1739.62			−0.275053
$343$		0			0
$344$	−9314.72			−1.45993
$345$	4077.38	−	7062.23i	0.636286	−	1.10208i
$346$	9539.24	+	16522.4i	1.48217	+	2.56720i
$347$	1735.98	+	3006.81i	0.268566	+	0.465170i	0.968492	−	0.249046i	$-0.0801170\pi$
$347$	1735.98	+	3006.81i	0.268566	+	0.465170i	−0.699926	+	0.714216i	$0.746784\pi$
$348$	−3569.61	+	6182.75i	−0.549860	+	0.952386i
$349$	6626.12			1.01630			0.508149	−	0.861269i	$-0.330330\pi$
$349$	6626.12			1.01630			0.508149	+	0.861269i	$0.330330\pi$
$350$		0			0
$351$	353.664			0.0537812
$352$	1073.05	−	1858.57i	0.162482	−	0.281427i
$353$	4734.20	+	8199.87i	0.713813	+	1.23636i	0.963416	+	0.268012i	$0.0863666\pi$
$353$	4734.20	+	8199.87i	0.713813	+	1.23636i	−0.249603	+	0.968348i	$0.580300\pi$
$354$	1548.56	+	2682.18i	0.232499	+	0.402701i
$355$	−3297.27	+	5711.03i	−0.492960	+	0.853831i
$356$	479.944			0.0714522
$357$		0			0
$358$	8977.35			1.32533
$359$	3139.78	−	5438.25i	0.461591	−	0.799499i	−0.537450	−	0.843296i	$-0.680612\pi$
$359$	3139.78	−	5438.25i	0.461591	−	0.799499i	0.999040	+	0.0437971i	$0.0139455\pi$
$360$	−1744.55	−	3021.65i	−0.255405	−	0.442375i
$361$	2529.68	+	4381.53i	0.368811	+	0.638800i
$362$	8231.31	−	14257.0i	1.19510	−	2.06998i
$363$	−3603.52			−0.521035
$364$		0			0
$365$	10883.1			1.56068
$366$	−4455.94	+	7717.92i	−0.636382	+	1.10225i
$367$	−5413.91	−	9377.17i	−0.770038	−	1.33374i	−0.937542	−	0.347873i	$-0.886904\pi$
$367$	−5413.91	−	9377.17i	−0.770038	−	1.33374i	0.167504	−	0.985871i	$-0.446429\pi$
$368$	247.452	+	428.599i	0.0350525	+	0.0607127i
$369$	−176.954	+	306.493i	−0.0249643	+	0.0432395i
$370$	305.053			0.0428620
$371$		0			0
$372$	6043.63			0.842332
$373$	−2619.61	+	4537.30i	−0.363642	+	0.629846i	−0.988557	−	0.150846i	$-0.951800\pi$
$373$	−2619.61	+	4537.30i	−0.363642	+	0.629846i	0.624915	+	0.780693i	$0.285134\pi$
$374$	1382.71	+	2394.93i	0.191172	+	0.331120i
$375$	1861.98	+	3225.04i	0.256406	+	0.444108i
$376$	−229.777	+	397.985i	−0.0315155	+	0.0545864i
$377$	2442.81			0.333717
$378$		0			0
$379$	−11050.4			−1.49768			−0.748839	−	0.662751i	$-0.769389\pi$
$379$	−11050.4			−1.49768			−0.748839	+	0.662751i	$0.769389\pi$
$380$	4837.64	−	8379.03i	0.653067	−	1.13115i
$381$	−1462.16	−	2532.54i	−0.196611	−	0.340541i
$382$	4346.25	+	7527.92i	0.582129	+	1.00828i
$383$	−5234.02	+	9065.59i	−0.698292	+	1.20948i	0.270766	+	0.962645i	$0.412723\pi$
$383$	−5234.02	+	9065.59i	−0.698292	+	1.20948i	−0.969058	+	0.246832i	$0.920610\pi$
$384$	6854.48			0.910915
$385$		0			0
$386$	−10934.9			−1.44190
$387$	−1932.47	+	3347.14i	−0.253833	+	0.439651i
$388$	4606.61	+	7978.88i	0.602745	+	1.04399i
$389$	5807.02	+	10058.1i	0.756884	+	1.31096i	0.944432	+	0.328705i	$0.106612\pi$
$389$	5807.02	+	10058.1i	0.756884	+	1.31096i	−0.187549	+	0.982255i	$0.560054\pi$
$390$	−1600.07	+	2771.41i	−0.207751	+	0.359835i
$391$	−8101.19			−1.04781
$392$		0			0
$393$	5378.11			0.690304
$394$	3449.89	−	5975.38i	0.441124	−	0.764049i
$395$	8134.43	+	14089.2i	1.03617	+	1.79470i
$396$	654.276	+	1133.24i	0.0830268	+	0.143807i
$397$	−3353.65	+	5808.69i	−0.423967	+	0.734332i	−0.996323	−	0.0856726i	$-0.972696\pi$
$397$	−3353.65	+	5808.69i	−0.423967	+	0.734332i	0.572356	+	0.820005i	$0.306029\pi$
$398$	6232.10			0.784892
$399$		0			0
$400$	−632.768			−0.0790960
$401$	−2763.19	+	4785.98i	−0.344107	+	0.596011i	−0.985191	−	0.171459i	$-0.945152\pi$
$401$	−2763.19	+	4785.98i	−0.344107	+	0.596011i	0.641084	+	0.767471i	$0.278485\pi$
$402$	993.970	+	1721.61i	0.123320	+	0.213597i
$403$	−1033.97	−	1790.89i	−0.127805	−	0.221366i
$404$	9689.49	−	16782.7i	1.19324	−	2.06676i
$405$	−1447.73			−0.177625
$406$		0			0
$407$	−42.6811			−0.00519810
$408$	−1733.09	+	3001.80i	−0.210296	+	0.364243i
$409$	−659.453	−	1142.21i	−0.0797258	−	0.138089i	0.823406	−	0.567453i	$-0.192071\pi$
$409$	−659.453	−	1142.21i	−0.0797258	−	0.138089i	−0.903132	+	0.429364i	$0.858738\pi$
$410$	−1601.17	−	2773.31i	−0.192869	−	0.334059i
$411$	−2526.62	+	4376.24i	−0.303234	+	0.525217i
$412$	13422.5			1.60505
$413$		0			0
$414$	−6236.61			−0.740369
$415$	2930.57	−	5075.90i	0.346641	−	0.600401i
$416$	−1233.57	−	2136.61i	−0.145387	−	0.251817i
$417$	472.634	+	818.626i	0.0555036	+	0.0961350i
$418$	−1101.20	+	1907.33i	−0.128855	+	0.223183i
$419$	−3656.13			−0.426286			−0.213143	−	0.977021i	$-0.568370\pi$
$419$	−3656.13			−0.426286			−0.213143	+	0.977021i	$0.568370\pi$
$420$		0			0
$421$	−135.389			−0.0156733			−0.00783663	−	0.999969i	$-0.502495\pi$
$421$	−135.389			−0.0156733			−0.00783663	+	0.999969i	$0.502495\pi$
$422$	9801.93	−	16977.4i	1.13069	−	1.95841i
$423$	95.3409	+	165.135i	0.0109589	+	0.0189815i
$424$	3968.31	+	6873.32i	0.454524	+	0.787259i
$425$	5178.96	−	8970.22i	0.591097	−	1.02381i
$426$	5043.38			0.573597
$427$		0			0
$428$	9781.16			1.10465
$429$	223.872	−	387.758i	0.0251950	−	0.0436390i
$430$	−17486.1	−	30286.8i	−1.96105	−	3.39665i
$431$	−4194.58	−	7265.23i	−0.468784	−	0.811958i	0.530579	−	0.847635i	$-0.321974\pi$
$431$	−4194.58	−	7265.23i	−0.468784	−	0.811958i	−0.999363	+	0.0356776i	$0.988641\pi$
$432$	43.9306	−	76.0900i	0.00489262	−	0.00847427i
$433$	8243.02			0.914859			0.457430	−	0.889246i	$-0.348770\pi$
$433$	8243.02			0.914859			0.457430	+	0.889246i	$0.348770\pi$
$434$		0			0
$435$	−9999.70			−1.10218
$436$	9104.91	−	15770.2i	1.00011	−	1.73223i
$437$	−3225.91	−	5587.43i	−0.353126	−	0.611632i
$438$	−4161.60	−	7208.10i	−0.453993	−	0.786338i
$439$	−9141.59	+	15833.7i	−0.993859	+	1.72142i	−0.401104	+	0.916032i	$0.631374\pi$
$439$	−9141.59	+	15833.7i	−0.993859	+	1.72142i	−0.592755	+	0.805383i	$0.701960\pi$
$440$	−4417.26			−0.478602
$441$		0			0
$442$	3179.12			0.342116
$443$	−605.218	+	1048.27i	−0.0649092	+	0.112426i	−0.896654	−	0.442733i	$-0.854009\pi$
$443$	−605.218	+	1048.27i	−0.0649092	+	0.112426i	0.831745	+	0.555159i	$0.187342\pi$
$444$	−71.6988	−	124.186i	−0.00766368	−	0.0132739i
$445$	336.122	+	582.180i	0.0358061	+	0.0620179i
$446$	3410.86	−	5907.79i	0.362128	−	0.627224i
$447$	5681.32			0.601157
$448$		0			0
$449$	−8301.16			−0.872508			−0.436254	−	0.899824i	$-0.643695\pi$
$449$	−8301.16			−0.872508			−0.436254	+	0.899824i	$0.643695\pi$
$450$	3986.96	−	6905.62i	0.417661	−	0.723409i
$451$	224.026	+	388.025i	0.0233902	+	0.0405130i
$452$	−2313.24	−	4006.66i	−0.240721	−	0.416941i
$453$	3017.76	−	5226.92i	0.312995	−	0.542124i
$454$	7305.34			0.755190
$455$		0			0
$456$	−2760.48			−0.283489
$457$	6146.88	−	10646.7i	0.629188	−	1.08979i	−0.358527	−	0.933519i	$-0.616721\pi$
$457$	6146.88	−	10646.7i	0.629188	−	1.08979i	0.987715	−	0.156266i	$-0.0499458\pi$
$458$	−2302.15	−	3987.45i	−0.234875	−	0.406815i
$459$	719.109	+	1245.53i	0.0731267	+	0.126659i
$460$	17343.1	−	30039.1i	1.75788	−	3.04474i
$461$	−19434.2			−1.96343			−0.981717	−	0.190346i	$-0.939039\pi$
$461$	−19434.2			−1.96343			−0.981717	+	0.190346i	$0.939039\pi$
$462$		0			0
$463$	−12491.1			−1.25380			−0.626902	−	0.779098i	$-0.715678\pi$
$463$	−12491.1			−1.25380			−0.626902	+	0.779098i	$0.715678\pi$
$464$	303.436	−	525.566i	0.0303592	−	0.0525836i
$465$	4232.56	+	7331.02i	0.422109	+	0.731113i
$466$	451.574	+	782.150i	0.0448901	+	0.0777519i
$467$	1692.59	−	2931.65i	0.167716	−	0.290493i	−0.769900	−	0.638164i	$-0.779694\pi$
$467$	1692.59	−	2931.65i	0.167716	−	0.290493i	0.937617	+	0.347671i	$0.113027\pi$
$468$	1504.31			0.148583
$469$		0			0
$470$	−1725.39			−0.169333
$471$	−5742.75	+	9946.74i	−0.561809	+	0.973082i
$472$	2457.29	+	4256.14i	0.239631	+	0.415053i
$473$	2446.54	+	4237.54i	0.237827	+	0.411929i
$474$	6221.06	−	10775.2i	0.602833	−	1.04414i
$475$	8249.07			0.796828
$476$		0			0
$477$	3293.14			0.316106
$478$	−2736.53	+	4739.80i	−0.261853	+	0.453543i
$479$	2989.71	+	5178.32i	0.285184	+	0.493953i	0.972654	−	0.232260i	$-0.0746120\pi$
$479$	2989.71	+	5178.32i	0.285184	+	0.493953i	−0.687470	+	0.726213i	$0.741279\pi$
$480$	5049.64	+	8746.24i	0.480174	+	0.831686i
$481$	−24.5330	+	42.4925i	−0.00232559	+	0.00402804i
$482$	−12451.1			−1.17663
$483$		0			0
$484$	−15327.5			−1.43948
$485$	−6452.34	+	11175.8i	−0.604094	+	1.04632i
$486$	553.598	+	958.861i	0.0516702	+	0.0894955i
$487$	557.481	+	965.586i	0.0518725	+	0.0898457i	0.890796	−	0.454404i	$-0.150148\pi$
$487$	557.481	+	965.586i	0.0518725	+	0.0898457i	−0.838923	+	0.544250i	$0.816814\pi$
$488$	−7070.80	+	12247.0i	−0.655902	+	1.13606i
$489$	−10527.8			−0.973583
$490$		0			0
$491$	1086.23			0.0998387			0.0499194	−	0.998753i	$-0.484104\pi$
$491$	1086.23			0.0998387			0.0499194	+	0.998753i	$0.484104\pi$
$492$	−752.670	+	1303.66i	−0.0689695	+	0.119459i
$493$	4967.00	+	8603.10i	0.453758	+	0.785932i
$494$	1265.93	+	2192.66i	0.115297	+	0.199701i
$495$	−916.425	+	1587.29i	−0.0832126	+	0.144128i
$496$	−513.740			−0.0465073
$497$		0			0
$498$	−4482.50			−0.403344
$499$	1106.75	−	1916.95i	0.0992884	−	0.171973i	−0.812102	−	0.583516i	$-0.801677\pi$
$499$	1106.75	−	1916.95i	0.0992884	−	0.171973i	0.911390	+	0.411543i	$0.135010\pi$
$500$	7919.92	+	13717.7i	0.708379	+	1.22695i
$501$	−514.512	−	891.162i	−0.0458817	−	0.0794694i
$502$	−17236.3	+	29854.2i	−1.53246	+	2.65430i
$503$	2643.32			0.234314			0.117157	−	0.993113i	$-0.462622\pi$
$503$	2643.32			0.234314			0.117157	+	0.993113i	$0.462622\pi$
$504$		0			0
$505$	27143.5			2.39183
$506$	−3947.83	+	6837.84i	−0.346843	+	0.600749i
$507$	3038.14	+	5262.21i	0.266131	+	0.460952i
$508$	−6219.31	−	10772.2i	−0.543183	−	0.940821i
$509$	−332.584	+	576.053i	−0.0289618	+	0.0501633i	−0.880143	−	0.474709i	$-0.842553\pi$
$509$	−332.584	+	576.053i	−0.0289618	+	0.0501633i	0.851181	+	0.524872i	$0.175887\pi$
$510$	−13013.8			−1.12992
$511$		0			0
$512$	−1177.58			−0.101645
$513$	−572.701	+	991.947i	−0.0492892	+	0.0853714i
$514$	−11410.7	−	19763.9i	−0.979190	−	1.69601i
$515$	9400.26	+	16281.7i	0.804320	+	1.39312i
$516$	−8219.76	+	14237.0i	−0.701269	+	1.21463i
$517$	241.406			0.0205359
$518$		0			0
$519$	12561.6			1.06242
$520$	−2539.03	+	4397.73i	−0.214123	+	0.370872i
$521$	−5880.99	−	10186.2i	−0.494531	−	0.856554i	0.505449	−	0.862857i	$-0.331327\pi$
$521$	−5880.99	−	10186.2i	−0.494531	−	0.856554i	−0.999980	+	0.00630307i	$0.997994\pi$
$522$	3823.79	+	6623.01i	0.320619	+	0.555328i
$523$	5061.30	−	8766.43i	0.423165	−	0.732943i	−0.573082	−	0.819498i	$-0.694252\pi$
$523$	5061.30	−	8766.43i	0.423165	−	0.732943i	0.996247	+	0.0865547i	$0.0275857\pi$
$524$	22875.7			1.90712
$525$		0			0
$526$	28471.9			2.36014
$527$	4204.76	−	7282.85i	0.347556	−	0.601985i
$528$	−55.6169	−	96.3312i	−0.00458412	−	0.00793992i
$529$	−5481.49	−	9494.22i	−0.450521	−	0.780325i
$530$	−14899.0	+	25805.9i	−1.22108	+	2.11497i
$531$	2039.20			0.166655
$532$		0			0
$533$	515.079			0.0418585
$534$	257.060	−	445.240i	0.0208316	−	0.0360813i
$535$	6850.09	+	11864.7i	0.553561	+	0.958796i
$536$	1577.26	+	2731.89i	0.127103	+	0.220148i
$537$	2955.43	−	5118.95i	0.237498	−	0.411358i
$538$	−16350.3			−1.31024
$539$		0			0
$540$	−6157.90			−0.490730
$541$	−8058.98	+	13958.6i	−0.640449	+	1.10929i	0.344884	+	0.938645i	$0.387918\pi$
$541$	−8058.98	+	13958.6i	−0.640449	+	1.10929i	−0.985333	+	0.170644i	$0.945415\pi$
$542$	4517.96	+	7825.34i	0.358050	+	0.620161i
$543$	−5419.65	−	9387.11i	−0.428323	−	0.741878i
$544$	5016.47	−	8688.78i	0.395366	−	0.684795i
$545$	25505.9			2.00469
$546$		0			0
$547$	−626.100			−0.0489399			−0.0244699	−	0.999701i	$-0.507790\pi$
$547$	−626.100			−0.0489399			−0.0244699	+	0.999701i	$0.507790\pi$
$548$	−10747.0	+	18614.3i	−0.837751	+	1.45103i
$549$	2933.88	+	5081.63i	0.228078	+	0.395043i
$550$	−5047.56	−	8742.64i	−0.391325	−	0.677795i
$551$	−3955.74	+	6851.54i	−0.305844	+	0.529737i
$552$	−9896.41			−0.763078
$553$		0			0
$554$	−33552.7			−2.57313
$555$	100.426	−	173.944i	0.00768083	−	0.0133036i
$556$	2010.34	+	3482.02i	0.153341	+	0.265594i
$557$	−10385.6	−	17988.4i	−0.790039	−	1.36839i	−0.925942	−	0.377665i	$-0.876727\pi$
$557$	−10385.6	−	17988.4i	−0.790039	−	1.36839i	0.135903	−	0.990722i	$-0.456606\pi$
$558$	3236.99	−	5606.63i	0.245578	−	0.425354i
$559$	5625.08			0.425609
$560$		0			0
$561$	1820.81			0.137031
$562$	−12101.8	+	20961.0i	−0.908335	+	1.57328i
$563$	−2760.86	−	4781.95i	−0.206672	−	0.357966i	0.743992	−	0.668188i	$-0.232930\pi$
$563$	−2760.86	−	4781.95i	−0.206672	−	0.357966i	−0.950664	+	0.310222i	$0.899597\pi$
$564$	405.532	+	702.402i	0.0302765	+	0.0524405i
$565$	3240.09	−	5612.00i	0.241260	−	0.417874i
$566$	−4974.48			−0.369422
$567$		0			0
$568$	8002.95			0.591191
$569$	−3787.40	+	6559.97i	−0.279044	+	0.483319i	−0.971147	−	0.238480i	$-0.923351\pi$
$569$	−3787.40	+	6559.97i	−0.279044	+	0.483319i	0.692103	+	0.721799i	$0.256684\pi$
$570$	−5182.11	−	8975.67i	−0.380797	−	0.659560i
$571$	165.624	+	286.869i	0.0121386	+	0.0210247i	0.872031	−	0.489451i	$-0.162803\pi$
$571$	165.624	+	286.869i	0.0121386	+	0.0210247i	−0.859892	+	0.510476i	$0.829469\pi$
$572$	952.239	−	1649.33i	0.0696068	−	0.120563i
$573$	5723.31			0.417268
$574$		0			0
$575$	29573.2			2.14485
$576$	3744.73	−	6486.06i	0.270886	−	0.469188i
$577$	1019.06	+	1765.06i	0.0735248	+	0.127349i	0.900444	−	0.434972i	$-0.143242\pi$
$577$	1019.06	+	1765.06i	0.0735248	+	0.127349i	−0.826919	+	0.562321i	$0.809909\pi$
$578$	−4728.57	−	8190.13i	−0.340281	−	0.589385i
$579$	−3599.89	+	6235.19i	−0.258387	+	0.447540i
$580$	−42533.6			−3.04502
$581$		0			0
$582$	9869.26			0.702911
$583$	2084.58	−	3610.60i	0.148087	−	0.256494i
$584$	−6603.72	−	11438.0i	−0.467918	−	0.810457i
$585$	1053.52	+	1824.75i	0.0744575	+	0.128964i
$586$	16384.4	−	28378.6i	1.15500	−	2.00053i
$587$	−5232.90			−0.367947			−0.183973	−	0.982931i	$-0.558896\pi$
$587$	−5232.90			−0.367947			−0.183973	+	0.982931i	$0.558896\pi$
$588$		0			0
$589$	6697.36			0.468523
$590$	−9225.88	+	15979.7i	−0.643769	+	1.11504i
$591$	−2271.47	−	3934.31i	−0.158098	−	0.273834i
$592$	6.09477	+	10.5565i	0.000423131	+	0.000732884i
$593$	−2860.12	+	4953.87i	−0.198062	+	0.343054i	−0.947900	−	0.318568i	$-0.896798\pi$
$593$	−2860.12	+	4953.87i	−0.198062	+	0.343054i	0.749838	+	0.661622i	$0.230132\pi$
$594$	1401.73			0.0968244
$595$		0			0
$596$	24165.5			1.66083
$597$	2051.67	−	3553.59i	0.140652	−	0.243616i
$598$	4538.41	+	7860.75i	0.310350	+	0.537542i
$599$	−9044.21	−	15665.0i	−0.616922	−	1.06854i	−0.990044	−	0.140758i	$-0.955046\pi$
$599$	−9044.21	−	15665.0i	−0.616922	−	1.06854i	0.373122	−	0.927782i	$-0.378287\pi$
$600$	6326.61	−	10958.0i	0.430471	−	0.745598i
$601$	1821.43			0.123623			0.0618117	−	0.998088i	$-0.480312\pi$
$601$	1821.43			0.123623			0.0618117	+	0.998088i	$0.480312\pi$
$602$		0			0
$603$	1308.90			0.0883955
$604$	12836.0	−	22232.6i	0.864719	−	1.49774i
$605$	−10734.4	−	18592.5i	−0.721348	−	1.24941i
$606$	−10379.4	−	17977.7i	−0.695769	−	1.20511i
$607$	1186.10	−	2054.39i	0.0793120	−	0.137372i	−0.823641	−	0.567111i	$-0.808061\pi$
$607$	1186.10	−	2054.39i	0.0793120	−	0.137372i	0.902953	+	0.429739i	$0.141394\pi$
$608$	7990.26			0.532974
$609$		0			0
$610$	−53094.7			−3.52416
$611$	138.760	−	240.339i	0.00918760	−	0.0159134i
$612$	3058.72	+	5297.87i	0.202029	+	0.349924i
$613$	−4862.54	−	8422.16i	−0.320385	−	0.554923i	0.660182	−	0.751105i	$-0.270479\pi$
$613$	−4862.54	−	8422.16i	−0.320385	−	0.554923i	−0.980567	+	0.196182i	$0.937146\pi$
$614$	−1233.30	+	2136.15i	−0.0810621	+	0.140404i
$615$	−2108.48			−0.138248
$616$		0			0
$617$	−5329.51			−0.347744			−0.173872	−	0.984768i	$-0.555628\pi$
$617$	−5329.51			−0.347744			−0.173872	+	0.984768i	$0.555628\pi$
$618$	7189.15	−	12452.0i	0.467945	−	0.810504i
$619$	−7988.29	−	13836.1i	−0.518702	−	0.898418i	−0.999764	−	0.0217314i	$-0.993082\pi$
$619$	−7988.29	−	13836.1i	−0.518702	−	0.898418i	0.481062	−	0.876687i	$-0.340251\pi$
$620$	18003.2	+	31182.4i	1.16617	+	2.01986i
$621$	−2053.15	+	3556.17i	−0.132673	+	0.229797i
$622$	246.120			0.0158658
$623$		0			0
$624$	−127.874			−0.00820361
$625$	1060.03	−	1836.03i	0.0678420	−	0.117506i
$626$	−8595.45	−	14887.8i	−0.548791	−	0.950535i
$627$	725.049	+	1255.82i	0.0461813	+	0.0799883i
$628$	−24426.7	+	42308.4i	−1.55212	+	2.68836i
$629$	−199.533			−0.0126485
$630$		0			0
$631$	−4199.98			−0.264974			−0.132487	−	0.991185i	$-0.542296\pi$
$631$	−4199.98			−0.264974			−0.132487	+	0.991185i	$0.542296\pi$
$632$	9871.73	−	17098.3i	0.621324	−	1.07616i
$633$	−6453.78	−	11178.3i	−0.405237	−	0.701891i
$634$	3916.74	+	6783.99i	0.245352	+	0.424963i
$635$	8711.19	−	15088.2i	0.544399	−	0.942926i
$636$	14007.3			0.873312
$637$		0			0
$638$	9681.97			0.600804
$639$	1660.33	−	2875.77i	0.102788	−	0.178034i
$640$	20418.6	+	35366.0i	1.26112	+	2.18432i
$641$	−1324.25	−	2293.67i	−0.0815988	−	0.141333i	0.822338	−	0.568999i	$-0.192669\pi$
$641$	−1324.25	−	2293.67i	−0.0815988	−	0.141333i	−0.903937	+	0.427666i	$0.859336\pi$
$642$	5238.82	−	9073.91i	0.322056	−	0.557817i
$643$	−13.4305			−0.000823715			−0.000411857	−	1.00000i	$-0.500131\pi$
$643$	−13.4305			−0.000823715			−0.000411857		1.00000i	$0.500131\pi$
$644$		0			0
$645$	−23026.3			−1.40568
$646$	−5148.06	+	8916.70i	−0.313541	+	0.543070i
$647$	5812.07	+	10066.8i	0.353162	+	0.611695i	0.986802	−	0.161934i	$-0.0517730\pi$
$647$	5812.07	+	10066.8i	0.353162	+	0.611695i	−0.633639	+	0.773628i	$0.718440\pi$
$648$	878.463	+	1521.54i	0.0532551	+	0.0922405i
$649$	1290.83	−	2235.78i	0.0780732	−	0.135227i
$650$	−11605.3			−0.700305
$651$		0			0
$652$	−44779.8			−2.68974
$653$	14258.3	−	24696.1i	0.854471	−	1.47999i	−0.0226638	−	0.999743i	$-0.507215\pi$
$653$	14258.3	−	24696.1i	0.854471	−	1.47999i	0.877135	−	0.480244i	$-0.159452\pi$
$654$	−9753.23	−	16893.1i	−0.583152	−	1.01005i
$655$	16020.7	+	27748.6i	0.955694	+	1.65531i
$656$	63.9809	−	110.818i	0.00380798	−	0.00659561i
$657$	−5480.15			−0.325420
$658$		0			0
$659$	18048.6			1.06688			0.533440	−	0.845838i	$-0.320899\pi$
$659$	18048.6			1.06688			0.533440	+	0.845838i	$0.320899\pi$
$660$	−3898.01	+	6751.54i	−0.229893	+	0.398187i
$661$	8920.72	+	15451.1i	0.524926	+	0.909198i	0.999579	+	0.0290250i	$0.00924023\pi$
$661$	8920.72	+	15451.1i	0.524926	+	0.909198i	−0.474653	+	0.880173i	$0.657426\pi$
$662$	19155.5	+	33178.2i	1.12462	+	1.94790i
$663$	1046.60	−	1812.76i	0.0613069	−	0.106187i
$664$	−7112.94			−0.415716
$665$		0			0
$666$	−153.608			−0.00893725
$667$	−14181.5	+	24563.0i	−0.823251	+	1.42591i
$668$	−2188.47	−	3790.55i	−0.126758	−	0.219552i
$669$	−2245.78	−	3889.80i	−0.129786	−	0.224796i
$670$	−5921.81	+	10256.9i	−0.341462	+	0.591430i
$671$	7428.68			0.427394
$672$		0			0
$673$	−6826.13			−0.390978			−0.195489	−	0.980706i	$-0.562629\pi$
$673$	−6826.13			−0.390978			−0.195489	+	0.980706i	$0.562629\pi$
$674$	6354.89	−	11007.0i	0.363177	−	0.629041i
$675$	−2625.09	−	4546.80i	−0.149689	−	0.259269i
$676$	12922.7	+	22382.8i	0.735246	+	1.27348i
$677$	−10643.4	+	18435.0i	−0.604225	+	1.04655i	0.387949	+	0.921681i	$0.373184\pi$
$677$	−10643.4	+	18435.0i	−0.604225	+	1.04655i	−0.992173	+	0.124867i	$0.960150\pi$
$678$	−4955.92			−0.280724
$679$		0			0
$680$	−20650.6			−1.16458
$681$	2404.99	−	4165.56i	0.135329	−	0.234397i
$682$	−4098.08	−	7098.08i	−0.230093	−	0.398533i
$683$	10348.4	+	17924.0i	0.579753	+	1.00416i	0.995507	+	0.0946842i	$0.0301841\pi$
$683$	10348.4	+	17924.0i	0.579753	+	1.00416i	−0.415755	+	0.909477i	$0.636483\pi$
$684$	−2435.98	+	4219.24i	−0.136172	+	0.235858i
$685$	−30105.9			−1.67925
$686$		0			0
$687$	−3031.56			−0.168357
$688$	698.722	−	1210.22i	0.0387188	−	0.0670629i
$689$	−2396.43	−	4150.74i	−0.132506	−	0.229507i
$690$	−18578.0	−	32178.1i	−1.02501	−	1.77536i
$691$	15671.0	−	27142.9i	0.862738	−	1.49431i	−0.00653825	−	0.999979i	$-0.502081\pi$
$691$	15671.0	−	27142.9i	0.862738	−	1.49431i	0.869276	−	0.494327i	$-0.164585\pi$
$692$	53430.8			2.93517
$693$		0			0
$694$	15819.5			0.865276
$695$	−2815.83	+	4877.16i	−0.153684	+	0.266189i
$696$	6067.69	+	10509.5i	0.330453	+	0.572361i
$697$	1047.32	+	1814.01i	0.0569153	+	0.0985801i
$698$	15095.5	−	26146.2i	0.818587	−	1.41783i
$699$	594.651			0.0321770
$700$		0			0
$701$	−9213.32			−0.496408			−0.248204	−	0.968708i	$-0.579840\pi$
$701$	−9213.32			−0.496408			−0.248204	+	0.968708i	$0.579840\pi$
$702$	805.712	−	1395.53i	0.0433185	−	0.0750299i
$703$	−79.4544	−	137.619i	−0.00426270	−	0.00738322i
$704$	−4740.89	−	8211.46i	−0.253805	−	0.439604i
$705$	−568.016	+	983.833i	−0.0303443	+	0.0525578i
$706$	43141.5			2.29979
$707$		0			0
$708$	8673.71			0.460421
$709$	−7258.27	+	12571.7i	−0.384471	+	0.665923i	−0.991696	−	0.128607i	$-0.958949\pi$
$709$	−7258.27	+	12571.7i	−0.384471	+	0.665923i	0.607225	+	0.794530i	$0.292283\pi$
$710$	15023.5	+	26021.6i	0.794118	+	1.37545i
$711$	−4096.07	−	7094.60i	−0.216054	−	0.374217i
$712$	407.908	−	706.518i	0.0214705	−	0.0371880i
$713$	24010.3			1.26114
$714$		0			0
$715$	2667.54			0.139525
$716$	12570.9	−	21773.4i	0.656140	−	1.13647i
$717$	1801.78	+	3120.78i	0.0938477	+	0.162549i
$718$	−14306.0	−	24778.7i	−0.743585	−	1.28793i
$719$	12941.2	−	22414.8i	0.671246	−	1.16263i	−0.306306	−	0.951933i	$-0.599093\pi$
$719$	12941.2	−	22414.8i	0.671246	−	1.16263i	0.977551	−	0.210698i	$-0.0675737\pi$
$720$	523.454			0.0270944
$721$		0			0
$722$	23052.3			1.18825
$723$	−4099.04	+	7099.74i	−0.210850	+	0.365204i
$724$	−23052.4	−	39928.0i	−1.18334	−	2.04960i
$725$	−18132.0	−	31405.5i	−0.928833	−	1.60879i
$726$	−8209.48	+	14219.2i	−0.419673	+	0.726894i
$727$	−32181.2			−1.64172			−0.820862	−	0.571127i	$-0.806506\pi$
$727$	−32181.2			−1.64172			−0.820862	+	0.571127i	$0.806506\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	24793.7	−	42943.9i	1.25706	−	2.17730i
$731$	11437.5	+	19810.4i	0.578704	+	1.00234i
$732$	12479.2	+	21614.7i	0.630117	+	1.09139i
$733$	10418.1	−	18044.6i	0.524966	−	0.909268i	−0.474611	−	0.880195i	$-0.657411\pi$
$733$	10418.1	−	18044.6i	0.524966	−	0.909268i	0.999577	−	0.0290722i	$-0.00925528\pi$
$734$	−49335.5			−2.48094
$735$		0			0
$736$	28645.4			1.43462
$737$	828.544	−	1435.08i	0.0414109	−	0.0717257i
$738$	806.265	+	1396.49i	0.0402155	+	0.0696553i
$739$	−13217.4	−	22893.3i	−0.657931	−	1.13957i	−0.981150	−	0.193246i	$-0.938098\pi$
$739$	−13217.4	−	22893.3i	−0.657931	−	1.13957i	0.323219	−	0.946324i	$-0.395235\pi$
$740$	427.163	−	739.867i	0.0212200	−	0.0367541i
$741$	1667.03			0.0826447
$742$		0			0
$743$	9954.69			0.491524			0.245762	−	0.969330i	$-0.420962\pi$
$743$	9954.69			0.491524			0.245762	+	0.969330i	$0.420962\pi$
$744$	5136.53	−	8896.73i	0.253111	−	0.438401i
$745$	16923.9	+	29313.1i	0.832274	+	1.44154i
$746$	11935.9	+	20673.6i	0.585798	+	1.01463i
$747$	−1475.68	+	2555.96i	−0.0722790	+	0.125191i
$748$	7744.79			0.378580
$749$		0			0
$750$	16967.7			0.826098
$751$	16602.3	−	28756.0i	0.806692	−	1.39723i	−0.108451	−	0.994102i	$-0.534589\pi$
$751$	16602.3	−	28756.0i	0.806692	−	1.39723i	0.915143	−	0.403129i	$-0.132077\pi$
$752$	−34.4723	−	59.7078i	−0.00167164	−	0.00289537i
$753$	11348.7	+	19656.6i	0.549231	+	0.951295i
$754$	5565.18	−	9639.17i	0.268796	−	0.465568i
$755$	35958.1			1.73331
$756$		0			0
$757$	1964.06			0.0942998			0.0471499	−	0.998888i	$-0.484986\pi$
$757$	1964.06			0.0942998			0.0471499	+	0.998888i	$0.484986\pi$
$758$	−25174.8	+	43604.0i	−1.20632	+	2.08941i
$759$	2599.33	+	4502.17i	0.124308	+	0.215307i
$760$	−8223.09	−	14242.8i	−0.392477	−	0.679791i
$761$	−19276.9	+	33388.6i	−0.918248	+	1.59045i	−0.116174	+	0.993229i	$0.537063\pi$
$761$	−19276.9	+	33388.6i	−0.918248	+	1.59045i	−0.802075	+	0.597224i	$0.796270\pi$
$762$	−13324.3			−0.633450
$763$		0			0
$764$	24344.0			1.15280
$765$	−4284.26	+	7420.56i	−0.202481	+	0.350707i
$766$	23848.1	+	41306.1i	1.12489	+	1.94837i
$767$	−1483.93	−	2570.25i	−0.0698588	−	0.120999i
$768$	5629.83	−	9751.15i	0.264517	−	0.458156i
$769$	19715.0			0.924501			0.462251	−	0.886749i	$-0.347042\pi$
$769$	19715.0			0.924501			0.462251	+	0.886749i	$0.347042\pi$
$770$		0			0
$771$	−15026.0			−0.701880
$772$	−15312.1	+	26521.3i	−0.713853	+	1.23643i
$773$	−7350.34	−	12731.2i	−0.342010	−	0.592378i	0.642796	−	0.766037i	$-0.277774\pi$
$773$	−7350.34	−	12731.2i	−0.342010	−	0.592378i	−0.984806	+	0.173659i	$0.944441\pi$
$774$	8805.06	+	15250.8i	0.408904	+	0.708242i
$775$	−15349.4	+	26585.9i	−0.711440	+	1.23225i
$776$	15660.8			0.724471
$777$		0			0
$778$	52917.8			2.43856
$779$	−834.086	+	1444.68i	−0.0383623	+	0.0664454i
$780$	4481.13	+	7761.55i	0.205705	+	0.356292i
$781$	−2102.00	−	3640.78i	−0.0963068	−	0.166808i
$782$	−18456.0	+	31966.7i	−0.843970	+	1.46180i
$783$	5035.32			0.229818
$784$		0			0
$785$	−68427.6			−3.11119
$786$	12252.3	−	21221.6i	0.556012	−	0.963041i
$787$	−11959.3	−	20714.1i	−0.541681	−	0.938218i	−0.998808	−	0.0488169i	$-0.984455\pi$
$787$	−11959.3	−	20714.1i	−0.541681	−	0.938218i	0.457127	−	0.889401i	$-0.348878\pi$
$788$	−9661.69	−	16734.5i	−0.436781	−	0.756527i
$789$	9373.21	−	16234.9i	0.422934	−	0.732544i
$790$	74126.9			3.33837
$791$		0			0
$792$	2224.30			0.0997942
$793$	4269.99	−	7395.84i	0.191213	−	0.331191i
$794$	15280.5	+	26466.5i	0.682976	+	1.18295i
$795$	9809.82	+	16991.1i	0.437633	+	0.758003i
$796$	8726.75	−	15115.2i	0.388582	−	0.673044i
$797$	−38252.7			−1.70010			−0.850051	−	0.526700i	$-0.823429\pi$
$797$	−38252.7			−1.70010			−0.850051	+	0.526700i	$0.823429\pi$
$798$		0			0
$799$	1128.57			0.0499698
$800$	−18312.5	+	31718.2i	−0.809307	+	1.40176i
$801$	−169.253	−	293.155i	−0.00746600	−	0.0129315i
$802$	12590.1	+	21806.7i	0.554329	+	0.960126i
$803$	−3468.98	+	6008.45i	−0.152450	+	0.264052i
$804$	5567.39			0.244212
$805$		0			0
$806$	−9422.27			−0.411769
$807$	−5382.67	+	9323.06i	−0.234794	+	0.406676i
$808$	−16470.3	−	28527.5i	−0.717110	−	1.24207i
$809$	15717.8	+	27224.0i	0.683075	+	1.18312i	0.974038	+	0.226386i	$0.0726912\pi$
$809$	15717.8	+	27224.0i	0.683075	+	1.18312i	−0.290962	+	0.956734i	$0.593975\pi$
$810$	−3298.19	+	5712.64i	−0.143070	+	0.247804i
$811$	−11467.0			−0.496501			−0.248250	−	0.968696i	$-0.579856\pi$
$811$	−11467.0			−0.496501			−0.248250	+	0.968696i	$0.579856\pi$
$812$		0			0
$813$	5949.43			0.256649
$814$	−97.2354	+	168.417i	−0.00418686	+	0.00725185i
$815$	−31360.8	−	54318.6i	−1.34788	−	2.33460i
$816$	−260.007	−	450.346i	−0.0111545	−	0.0193202i
$817$	−9108.88	+	15777.1i	−0.390061	+	0.675605i
$818$	−6009.42			−0.256864
$819$		0			0
$820$	−8968.42			−0.381940
$821$	2515.29	−	4356.60i	0.106923	−	0.185197i	−0.807599	−	0.589732i	$-0.799233\pi$
$821$	2515.29	−	4356.60i	0.106923	−	0.185197i	0.914522	+	0.404535i	$0.132567\pi$
$822$	11512.2	+	19939.8i	0.488485	+	0.846081i
$823$	6992.59	+	12111.5i	0.296168	+	0.512978i	0.975256	−	0.221079i	$-0.0709578\pi$
$823$	6992.59	+	12111.5i	0.296168	+	0.512978i	−0.679088	+	0.734057i	$0.737625\pi$
$824$	11407.9	−	19759.1i	0.482298	−	0.835364i
$825$	−6646.83			−0.280500
$826$		0			0
$827$	−13939.5			−0.586125			−0.293063	−	0.956093i	$-0.594674\pi$
$827$	−13939.5			−0.586125			−0.293063	+	0.956093i	$0.594674\pi$
$828$	−8733.07	+	15126.1i	−0.366540	+	0.634866i
$829$	−10052.2	−	17410.9i	−0.421143	−	0.729441i	0.574909	−	0.818218i	$-0.305038\pi$
$829$	−10052.2	−	17410.9i	−0.421143	−	0.729441i	−0.996052	+	0.0887769i	$0.971704\pi$
$830$	−13352.8	−	23127.7i	−0.558411	−	0.967197i
$831$	−11045.9	+	19132.0i	−0.461103	+	0.798654i
$832$	−10900.2			−0.454203
$833$		0			0
$834$	4306.99			0.178823
$835$	3065.33	−	5309.31i	0.127042	−	0.220043i
$836$	3083.99	+	5341.62i	0.127586	+	0.220986i
$837$	−2131.30	−	3691.51i	−0.0880148	−	0.152446i
$838$	−8329.33	+	14426.8i	−0.343356	+	0.594710i
$839$	−15949.5			−0.656302			−0.328151	−	0.944625i	$-0.606425\pi$
$839$	−15949.5			−0.656302			−0.328151	+	0.944625i	$0.606425\pi$
$840$		0			0
$841$	10390.8			0.426043
$842$	−308.440	+	534.235i	−0.0126242	+	0.0218657i
$843$	7968.07	+	13801.1i	0.325546	+	0.563861i
$844$	−27451.1	−	47546.7i	−1.11956	−	1.93913i
$845$	−18100.4	+	31350.8i	−0.736891	+	1.27633i
$846$	868.817			0.0353080
$847$		0			0
$848$	−1190.70			−0.0482177
$849$	−1637.65	+	2836.49i	−0.0662001	+	0.114662i
$850$	−23597.2	−	40871.6i	−0.952210	−	1.64928i
$851$	−284.847	−	493.369i	−0.0114741	−	0.0198737i
$852$	7062.19	−	12232.1i	0.283975	−	0.491859i
$853$	−11802.0			−0.473730			−0.236865	−	0.971543i	$-0.576120\pi$
$853$	−11802.0			−0.473730			−0.236865	+	0.971543i	$0.576120\pi$
$854$		0			0
$855$	−6824.00			−0.272954
$856$	8313.09	−	14398.7i	0.331934	−	0.574927i
$857$	4797.64	+	8309.76i	0.191230	+	0.331220i	0.945658	−	0.325162i	$-0.105419\pi$
$857$	4797.64	+	8309.76i	0.191230	+	0.331220i	−0.754428	+	0.656383i	$0.772086\pi$
$858$	−1020.04	−	1766.77i	−0.0405871	−	0.0702989i
$859$	10920.4	−	18914.7i	0.433760	−	0.751295i	−0.563433	−	0.826162i	$-0.690520\pi$
$859$	10920.4	−	18914.7i	0.433760	−	0.751295i	0.997194	+	0.0748666i	$0.0238531\pi$
$860$	−97942.3			−3.88350
$861$		0			0
$862$	−38224.1			−1.51035
$863$	13265.8	−	22977.1i	0.523260	−	0.906313i	−0.476374	−	0.879243i	$-0.658049\pi$
$863$	13265.8	−	22977.1i	0.523260	−	0.906313i	0.999634	−	0.0270699i	$-0.00861768\pi$
$864$	−2542.73	−	4404.14i	−0.100122	−	0.173417i
$865$	37419.5	+	64812.4i	1.47087	+	2.54762i
$866$	18779.1	−	32526.4i	0.736882	−	1.27632i
$867$	−6226.77			−0.243912
$868$		0			0
$869$	−10371.4			−0.404862
$870$	−22781.2	+	39458.1i	−0.887762	+	1.53765i
$871$	−952.491	−	1649.76i	−0.0370539	−	0.0641792i
$872$	−15476.7	−	26806.4i	−0.601039	−	1.04103i
$873$	3249.06	−	5627.53i	0.125961	−	0.218171i
$874$	−29396.8			−1.13771
$875$		0			0
$876$	−23309.8			−0.899046
$877$	3416.23	−	5917.09i	0.131537	−	0.227829i	−0.792732	−	0.609570i	$-0.791342\pi$
$877$	3416.23	−	5917.09i	0.131537	−	0.227829i	0.924269	+	0.381741i	$0.124675\pi$
$878$	41652.4	+	72144.1i	1.60103	+	2.77306i
$879$	−10787.8	−	18685.0i	−0.413951	−	0.716985i
$880$	331.351	−	573.916i	0.0126930	−	0.0219849i
$881$	3994.77			0.152766			0.0763832	−	0.997079i	$-0.475663\pi$
$881$	3994.77			0.152766			0.0763832	+	0.997079i	$0.475663\pi$
$882$		0			0
$883$	13727.0			0.523161			0.261580	−	0.965182i	$-0.415756\pi$
$883$	13727.0			0.523161			0.261580	+	0.965182i	$0.415756\pi$
$884$	4451.69	−	7710.56i	0.169374	−	0.293364i
$885$	6074.50	+	10521.3i	0.230726	+	0.399628i
$886$	2757.59	+	4776.29i	0.104563	+	0.181109i
$887$	22059.7	−	38208.5i	0.835054	−	1.44636i	−0.0589333	−	0.998262i	$-0.518770\pi$
$887$	22059.7	−	38208.5i	0.835054	−	1.44636i	0.893987	−	0.448093i	$-0.147897\pi$
$888$	−243.750			−0.00921138
$889$		0			0
$890$	3062.99			0.115361
$891$	461.463	−	799.278i	0.0173508	−	0.0300525i
$892$	−9552.40	−	16545.2i	−0.358563	−	0.621049i
$893$	449.398	+	778.380i	0.0168405	+	0.0291685i
$894$	12943.1	−	22418.1i	0.484208	−	0.838672i
$895$	35215.3			1.31522
$896$		0			0
$897$	5976.35			0.222458
$898$	−18911.6	+	32755.8i	−0.702769	+	1.21723i
$899$	−14721.2	−	25497.9i	−0.546140	−	0.945942i
$900$	−11165.8	−	19339.8i	−0.413549	−	0.716287i
$901$	9745.37	−	16879.5i	0.360339	−	0.624125i
$902$	2041.49			0.0753594
$903$		0			0
$904$	−7864.18			−0.289335
$905$	32288.9	−	55925.9i	1.18599	−	2.05419i
$906$	−13750.0	−	23815.7i	−0.504210	−	0.873317i
$907$	−18452.9	−	31961.4i	−0.675545	−	1.17008i	−0.976309	−	0.216380i	$-0.930575\pi$
$907$	−18452.9	−	31961.4i	−0.675545	−	1.17008i	0.300764	−	0.953698i	$-0.402758\pi$
$908$	10229.6	−	17718.2i	0.373878	−	0.647575i
$909$	−13668.1			−0.498725
$910$		0			0
$911$	−3169.56			−0.115271			−0.0576356	−	0.998338i	$-0.518356\pi$
$911$	−3169.56			−0.115271			−0.0576356	+	0.998338i	$0.518356\pi$
$912$	207.071	−	358.657i	0.00751842	−	0.0130223i
$913$	1868.24	+	3235.88i	0.0677214	+	0.117297i
$914$	−28007.4	−	48510.3i	−1.01357	−	1.75556i
$915$	−17479.3	+	30275.0i	−0.631527	+	1.09384i
$916$	−12894.7			−0.465124
$917$		0			0
$918$	6553.05			0.235602
$919$	−4363.50	+	7557.80i	−0.156625	+	0.271283i	−0.933650	−	0.358188i	$-0.883395\pi$
$919$	−4363.50	+	7557.80i	−0.156625	+	0.271283i	0.777024	+	0.629470i	$0.216728\pi$
$920$	−29480.1	−	51061.0i	−1.05645	−	1.82982i
$921$	812.032	+	1406.48i	0.0290525	+	0.0503204i
$922$	−44274.8	+	76686.2i	−1.58147	+	2.73918i
$923$	−4832.91			−0.172348
$924$		0			0
$925$	728.392			0.0258912
$926$	−28457.1	+	49289.1i	−1.00989	+	1.74918i
$927$	−4733.47	−	8198.62i	−0.167711	−	0.290483i
$928$	−17563.1	−	30420.1i	−0.621267	−	1.07607i
$929$	9702.54	−	16805.3i	0.342659	−	0.593502i	−0.642267	−	0.766481i	$-0.722006\pi$
$929$	9702.54	−	16805.3i	0.342659	−	0.593502i	0.984926	+	0.172979i	$0.0553392\pi$
$930$	38570.2			1.35997
$931$		0			0
$932$	2529.34			0.0888963
$933$	81.0252	−	140.340i	0.00284314	−	0.00492446i
$934$	−7712.04	−	13357.6i	−0.270177	−	0.467961i
$935$	5423.95	+	9394.55i	0.189713	+	0.328593i
$936$	1278.52	−	2214.47i	0.0446472	−	0.0773313i
$937$	615.692			0.0214662			0.0107331	−	0.999942i	$-0.496583\pi$
$937$	615.692			0.0214662			0.0107331	+	0.999942i	$0.496583\pi$
$938$		0			0
$939$	−11318.8			−0.393372
$940$	−2416.05	+	4184.72i	−0.0838329	+	0.145203i
$941$	−14801.0	−	25636.1i	−0.512751	−	0.888111i	−0.999891	−	0.0147865i	$-0.995293\pi$
$941$	−14801.0	−	25636.1i	−0.512751	−	0.888111i	0.487140	−	0.873324i	$-0.338040\pi$
$942$	26166.1	+	45321.0i	0.905029	+	1.56756i
$943$	−2990.23	+	5179.23i	−0.103261	+	0.178854i
$944$	−737.310			−0.0254210
$945$		0			0
$946$	22294.7			0.766240
$947$	−6768.71	+	11723.8i	−0.232264	+	0.402292i	−0.958474	−	0.285180i	$-0.907947\pi$
$947$	−6768.71	+	11723.8i	−0.232264	+	0.402292i	0.726210	+	0.687473i	$0.241280\pi$
$948$	−17422.6	−	30176.8i	−0.596898	−	1.03386i
$949$	3987.93	+	6907.29i	0.136411	+	0.236270i
$950$	18792.9	−	32550.3i	0.641813	−	1.11165i
$951$	5157.71			0.175868
$952$		0			0
$953$	33468.5			1.13762			0.568810	−	0.822469i	$-0.307404\pi$
$953$	33468.5			1.13762			0.568810	+	0.822469i	$0.307404\pi$
$954$	7502.37	−	12994.5i	0.254610	−	0.440998i
$955$	17049.0	+	29529.7i	0.577688	+	1.00058i
$956$	7663.86	+	13274.2i	0.259275	+	0.449078i
$957$	3187.40	−	5520.74i	0.107664	−	0.186479i
$958$	27244.4			0.918817
$959$		0			0
$960$	44620.2			1.50011
$961$	2433.44	−	4214.85i	0.0816838	−	0.141480i
$962$	111.781	+	193.611i	0.00374634	+	0.00648885i
$963$	−3449.34	−	5974.44i	−0.115424	−	0.199921i
$964$	−17435.2	+	30198.7i	−0.582521	+	1.00896i
$965$	−42894.4			−1.43090
$966$		0			0
$967$	−55733.5			−1.85343			−0.926715	−	0.375764i	$-0.877380\pi$
$967$	−55733.5			−1.85343			−0.926715	+	0.375764i	$0.877380\pi$
$968$	−13027.0	+	22563.4i	−0.432545	+	0.749190i
$969$	3389.58	+	5870.93i	0.112373	+	0.194635i
$970$	29399.2	+	50920.9i	0.973146	+	1.68554i
$971$	−9745.65	+	16880.0i	−0.322094	+	0.557882i	−0.980920	−	0.194413i	$-0.937720\pi$
$971$	−9745.65	+	16880.0i	−0.322094	+	0.557882i	0.658826	+	0.752295i	$0.271053\pi$
$972$	3100.79			0.102323
$973$		0			0
$974$	5080.18			0.167125
$975$	−3820.58	+	6617.44i	−0.125494	+	0.217362i
$976$	−1060.80	−	1837.36i	−0.0347903	−	0.0602586i
$977$	3120.78	+	5405.35i	0.102193	+	0.177004i	0.912588	−	0.408881i	$-0.134081\pi$
$977$	3120.78	+	5405.35i	0.102193	+	0.177004i	−0.810395	+	0.585884i	$0.800747\pi$
$978$	−23984.2	+	41541.8i	−0.784182	+	1.35824i
$979$	−428.554			−0.0139905
$980$		0			0
$981$	−12843.4			−0.418001
$982$	2474.63	−	4286.18i	0.0804160	−	0.139285i
$983$	29847.3	+	51697.0i	0.968444	+	1.67739i	0.700062	+	0.714082i	$0.253155\pi$
$983$	29847.3	+	51697.0i	0.968444	+	1.67739i	0.268382	+	0.963313i	$0.413511\pi$
$984$	1279.40	+	2215.99i	0.0414490	+	0.0717918i
$985$	13532.8	−	23439.6i	0.437758	−	0.758220i
$986$	45263.0			1.46193
$987$		0			0
$988$	7090.68			0.228324
$989$	−32655.7	+	56561.3i	−1.04994	+	1.81855i
$990$	4175.57	+	7232.30i	0.134049	+	0.232179i
$991$	−7780.82	−	13476.8i	−0.249411	−	0.431992i	0.713952	−	0.700195i	$-0.246904\pi$
$991$	−7780.82	−	13476.8i	−0.249411	−	0.431992i	−0.963362	+	0.268203i	$0.913570\pi$
$992$	−14867.8	+	25751.8i	−0.475860	+	0.824214i
$993$	25224.6			0.806123
$994$		0			0
$995$	24446.6			0.778903
$996$	−6276.80	+	10871.7i	−0.199687	+	0.345868i
$997$	9942.47	+	17220.9i	0.315829	+	0.547031i	0.979613	−	0.200892i	$-0.0643842\pi$
$997$	9942.47	+	17220.9i	0.315829	+	0.547031i	−0.663785	+	0.747924i	$0.731051\pi$
$998$	−5042.76	−	8734.31i	−0.159946	−	0.277034i
$999$	−50.5694	+	87.5888i	−0.00160155	+	0.00277396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.n.79.3		6
3.2	odd	2		441.4.e.w.226.1		6
7.2	even	3		147.4.a.m.1.1		3
7.3	odd	6		21.4.e.b.4.3	✓	6
7.4	even	3	inner	147.4.e.n.67.3		6
7.5	odd	6		147.4.a.l.1.1		3
7.6	odd	2		21.4.e.b.16.3	yes	6
21.2	odd	6		441.4.a.t.1.3		3
21.5	even	6		441.4.a.s.1.3		3
21.11	odd	6		441.4.e.w.361.1		6
21.17	even	6		63.4.e.c.46.1		6
21.20	even	2		63.4.e.c.37.1		6
28.3	even	6		336.4.q.k.193.1		6
28.19	even	6		2352.4.a.ci.1.3		3
28.23	odd	6		2352.4.a.cg.1.1		3
28.27	even	2		336.4.q.k.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.3	✓	6	7.3	odd	6
21.4.e.b.16.3	yes	6	7.6	odd	2
63.4.e.c.37.1		6	21.20	even	2
63.4.e.c.46.1		6	21.17	even	6
147.4.a.l.1.1		3	7.5	odd	6
147.4.a.m.1.1		3	7.2	even	3
147.4.e.n.67.3		6	7.4	even	3	inner
147.4.e.n.79.3		6	1.1	even	1	trivial
336.4.q.k.193.1		6	28.3	even	6
336.4.q.k.289.1		6	28.27	even	2
441.4.a.s.1.3		3	21.5	even	6
441.4.a.t.1.3		3	21.2	odd	6
441.4.e.w.226.1		6	3.2	odd	2
441.4.e.w.361.1		6	21.11	odd	6
2352.4.a.cg.1.1		3	28.23	odd	6
2352.4.a.ci.1.3		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)

\(f(q)\)	\(=\)	\(q+(2.27818 - 3.94593i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} -13.6691 q^{6} -21.6905 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(2.27818 - 3.94593i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} -13.6691 q^{6} -21.6905 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-40.7184 - 70.5264i) q^{10} +(5.69708 + 9.86762i) q^{11} +(-19.1407 + 33.1527i) q^{12} +13.0987 q^{13} -53.6196 q^{15} +(1.62706 - 2.81815i) q^{16} +(26.6337 + 46.1309i) q^{17} +(20.5036 + 35.5134i) q^{18} +(-21.2111 + 36.7388i) q^{19} -228.071 q^{20} +51.9159 q^{22} +(-76.0427 + 131.710i) q^{23} +(32.5357 + 56.3535i) q^{24} +(-97.2257 - 168.400i) q^{25} +(29.8412 - 51.6864i) q^{26} +27.0000 q^{27} +186.493 q^{29} +(-122.155 + 211.579i) q^{30} +(-78.9369 - 136.723i) q^{31} +(-94.1753 - 163.116i) q^{32} +(17.0912 - 29.6029i) q^{33} +242.706 q^{34} +114.844 q^{36} +(-1.87294 + 3.24403i) q^{37} +(96.6457 + 167.395i) q^{38} +(-19.6480 - 34.0313i) q^{39} +(-193.839 + 335.739i) q^{40} +39.3230 q^{41} +429.439 q^{43} +(72.6974 - 125.916i) q^{44} +(80.4294 + 139.308i) q^{45} +(346.478 + 600.118i) q^{46} +(10.5934 - 18.3484i) q^{47} -9.76236 q^{48} -885.992 q^{50} +(79.9010 - 138.393i) q^{51} +(-83.5726 - 144.752i) q^{52} +(-182.952 - 316.882i) q^{53} +(61.5109 - 106.540i) q^{54} +203.650 q^{55} +127.267 q^{57} +(424.866 - 735.889i) q^{58} +(-113.289 - 196.222i) q^{59} +(342.106 + 592.545i) q^{60} +(325.987 - 564.626i) q^{61} -719.331 q^{62} -832.161 q^{64} +(117.058 - 202.750i) q^{65} +(-77.8739 - 134.882i) q^{66} +(-72.7166 - 125.949i) q^{67} +(339.858 - 588.652i) q^{68} +456.256 q^{69} -368.962 q^{71} +(97.6071 - 169.060i) q^{72} +(304.453 + 527.328i) q^{73} +(8.53380 + 14.7810i) q^{74} +(-291.677 + 505.200i) q^{75} +541.328 q^{76} -179.047 q^{78} +(-455.119 + 788.289i) q^{79} +(-29.0808 - 50.3694i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(89.5850 - 155.166i) q^{82} +327.929 q^{83} +952.058 q^{85} +(978.340 - 1694.53i) q^{86} +(-279.740 - 484.524i) q^{87} +(-123.572 - 214.033i) q^{88} +(-18.8059 + 32.5728i) q^{89} +732.932 q^{90} +1940.68 q^{92} +(-236.811 + 410.168i) q^{93} +(-48.2676 - 83.6019i) q^{94} +(379.111 + 656.640i) q^{95} +(-282.526 + 489.349i) q^{96} -722.013 q^{97} -102.547 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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