LMFDB - Embedded newform 147.4.e.c.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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.c.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} -12.0000 q^{6} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-2.00000 + 3.46410i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} -12.0000 q^{6} +(-4.50000 + 7.79423i) q^{9} +(8.00000 + 13.8564i) q^{10} +(-31.0000 - 53.6936i) q^{11} +(12.0000 - 20.7846i) q^{12} -62.0000 q^{13} +12.0000 q^{15} +(32.0000 - 55.4256i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(-18.0000 - 31.1769i) q^{18} +(-50.0000 + 86.6025i) q^{19} -32.0000 q^{20} +248.000 q^{22} +(21.0000 - 36.3731i) q^{23} +(54.5000 + 94.3968i) q^{25} +(124.000 - 214.774i) q^{26} -27.0000 q^{27} -10.0000 q^{29} +(-24.0000 + 41.5692i) q^{30} +(24.0000 + 41.5692i) q^{31} +(128.000 + 221.703i) q^{32} +(93.0000 - 161.081i) q^{33} +336.000 q^{34} +72.0000 q^{36} +(123.000 - 213.042i) q^{37} +(-200.000 - 346.410i) q^{38} +(-93.0000 - 161.081i) q^{39} -248.000 q^{41} +68.0000 q^{43} +(-248.000 + 429.549i) q^{44} +(18.0000 + 31.1769i) q^{45} +(84.0000 + 145.492i) q^{46} +(-162.000 + 280.592i) q^{47} +192.000 q^{48} -436.000 q^{50} +(126.000 - 218.238i) q^{51} +(248.000 + 429.549i) q^{52} +(-129.000 - 223.435i) q^{53} +(54.0000 - 93.5307i) q^{54} -248.000 q^{55} -300.000 q^{57} +(20.0000 - 34.6410i) q^{58} +(-60.0000 - 103.923i) q^{59} +(-48.0000 - 83.1384i) q^{60} +(-311.000 + 538.668i) q^{61} -192.000 q^{62} -512.000 q^{64} +(-124.000 + 214.774i) q^{65} +(372.000 + 644.323i) q^{66} +(-452.000 - 782.887i) q^{67} +(-336.000 + 581.969i) q^{68} +126.000 q^{69} -678.000 q^{71} +(321.000 + 555.988i) q^{73} +(492.000 + 852.169i) q^{74} +(-163.500 + 283.190i) q^{75} +800.000 q^{76} +744.000 q^{78} +(-370.000 + 640.859i) q^{79} +(-128.000 - 221.703i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(496.000 - 859.097i) q^{82} +468.000 q^{83} -336.000 q^{85} +(-136.000 + 235.559i) q^{86} +(-15.0000 - 25.9808i) q^{87} +(-100.000 + 173.205i) q^{89} -144.000 q^{90} -336.000 q^{92} +(-72.0000 + 124.708i) q^{93} +(-648.000 - 1122.37i) q^{94} +(200.000 + 346.410i) q^{95} +(-384.000 + 665.108i) q^{96} -1266.00 q^{97} +558.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 3 q^{3} - 8 q^{4} + 4 q^{5} - 24 q^{6} - 9 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 + 3 * q^3 - 8 * q^4 + 4 * q^5 - 24 * q^6 - 9 * q^9	$ 2 q - 4 q^{2} + 3 q^{3} - 8 q^{4} + 4 q^{5} - 24 q^{6} - 9 q^{9} + 16 q^{10} - 62 q^{11} + 24 q^{12} - 124 q^{13} + 24 q^{15} + 64 q^{16} - 84 q^{17} - 36 q^{18} - 100 q^{19} - 64 q^{20} + 496 q^{22} + 42 q^{23} + 109 q^{25} + 248 q^{26} - 54 q^{27} - 20 q^{29} - 48 q^{30} + 48 q^{31} + 256 q^{32} + 186 q^{33} + 672 q^{34} + 144 q^{36} + 246 q^{37} - 400 q^{38} - 186 q^{39} - 496 q^{41} + 136 q^{43} - 496 q^{44} + 36 q^{45} + 168 q^{46} - 324 q^{47} + 384 q^{48} - 872 q^{50} + 252 q^{51} + 496 q^{52} - 258 q^{53} + 108 q^{54} - 496 q^{55} - 600 q^{57} + 40 q^{58} - 120 q^{59} - 96 q^{60} - 622 q^{61} - 384 q^{62} - 1024 q^{64} - 248 q^{65} + 744 q^{66} - 904 q^{67} - 672 q^{68} + 252 q^{69} - 1356 q^{71} + 642 q^{73} + 984 q^{74} - 327 q^{75} + 1600 q^{76} + 1488 q^{78} - 740 q^{79} - 256 q^{80} - 81 q^{81} + 992 q^{82} + 936 q^{83} - 672 q^{85} - 272 q^{86} - 30 q^{87} - 200 q^{89} - 288 q^{90} - 672 q^{92} - 144 q^{93} - 1296 q^{94} + 400 q^{95} - 768 q^{96} - 2532 q^{97} + 1116 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 + 3 * q^3 - 8 * q^4 + 4 * q^5 - 24 * q^6 - 9 * q^9 + 16 * q^10 - 62 * q^11 + 24 * q^12 - 124 * q^13 + 24 * q^15 + 64 * q^16 - 84 * q^17 - 36 * q^18 - 100 * q^19 - 64 * q^20 + 496 * q^22 + 42 * q^23 + 109 * q^25 + 248 * q^26 - 54 * q^27 - 20 * q^29 - 48 * q^30 + 48 * q^31 + 256 * q^32 + 186 * q^33 + 672 * q^34 + 144 * q^36 + 246 * q^37 - 400 * q^38 - 186 * q^39 - 496 * q^41 + 136 * q^43 - 496 * q^44 + 36 * q^45 + 168 * q^46 - 324 * q^47 + 384 * q^48 - 872 * q^50 + 252 * q^51 + 496 * q^52 - 258 * q^53 + 108 * q^54 - 496 * q^55 - 600 * q^57 + 40 * q^58 - 120 * q^59 - 96 * q^60 - 622 * q^61 - 384 * q^62 - 1024 * q^64 - 248 * q^65 + 744 * q^66 - 904 * q^67 - 672 * q^68 + 252 * q^69 - 1356 * q^71 + 642 * q^73 + 984 * q^74 - 327 * q^75 + 1600 * q^76 + 1488 * q^78 - 740 * q^79 - 256 * q^80 - 81 * q^81 + 992 * q^82 + 936 * q^83 - 672 * q^85 - 272 * q^86 - 30 * q^87 - 200 * q^89 - 288 * q^90 - 672 * q^92 - 144 * q^93 - 1296 * q^94 + 400 * q^95 - 768 * q^96 - 2532 * q^97 + 1116 * 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 $

$2$	−2.00000	+	3.46410i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$2$	−2.00000	+	3.46410i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−4.00000	−	6.92820i	−0.500000	−	0.866025i
$5$	2.00000	−	3.46410i	0.178885	−	0.309839i	−0.762614	−	0.646854i	$-0.776084\pi$
$5$	2.00000	−	3.46410i	0.178885	−	0.309839i	0.941499	+	0.337016i	$0.109418\pi$
$6$	−12.0000			−0.816497
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	8.00000	+	13.8564i	0.252982	+	0.438178i
$11$	−31.0000	−	53.6936i	−0.849714	−	1.47175i	−0.881464	−	0.472252i	$-0.843441\pi$
$11$	−31.0000	−	53.6936i	−0.849714	−	1.47175i	0.0317500	−	0.999496i	$-0.489892\pi$
$12$	12.0000	−	20.7846i	0.288675	−	0.500000i
$13$	−62.0000			−1.32275			−0.661373	−	0.750057i	$-0.730026\pi$
$13$	−62.0000			−1.32275			−0.661373	+	0.750057i	$0.730026\pi$
$14$		0			0
$15$	12.0000			0.206559
$16$	32.0000	−	55.4256i	0.500000	−	0.866025i
$17$	−42.0000	−	72.7461i	−0.599206	−	1.03785i	−0.992939	−	0.118630i	$-0.962150\pi$
$17$	−42.0000	−	72.7461i	−0.599206	−	1.03785i	0.393733	−	0.919225i	$-0.371183\pi$
$18$	−18.0000	−	31.1769i	−0.235702	−	0.408248i
$19$	−50.0000	+	86.6025i	−0.603726	+	1.04568i	0.388526	+	0.921438i	$0.372984\pi$
$19$	−50.0000	+	86.6025i	−0.603726	+	1.04568i	−0.992251	+	0.124246i	$0.960349\pi$
$20$	−32.0000			−0.357771
$21$		0			0
$22$	248.000			2.40335
$23$	21.0000	−	36.3731i	0.190383	−	0.329753i	−0.754994	−	0.655731i	$-0.772360\pi$
$23$	21.0000	−	36.3731i	0.190383	−	0.329753i	0.945377	+	0.325979i	$0.105694\pi$
$24$		0			0
$25$	54.5000	+	94.3968i	0.436000	+	0.755174i
$26$	124.000	−	214.774i	0.935323	−	1.62003i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−10.0000			−0.0640329			−0.0320164	−	0.999487i	$-0.510193\pi$
$29$	−10.0000			−0.0640329			−0.0320164	+	0.999487i	$0.510193\pi$
$30$	−24.0000	+	41.5692i	−0.146059	+	0.252982i
$31$	24.0000	+	41.5692i	0.139049	+	0.240840i	0.927137	−	0.374723i	$-0.122262\pi$
$31$	24.0000	+	41.5692i	0.139049	+	0.240840i	−0.788088	+	0.615563i	$0.788929\pi$
$32$	128.000	+	221.703i	0.707107	+	1.22474i
$33$	93.0000	−	161.081i	0.490582	−	0.849714i
$34$	336.000			1.69481
$35$		0			0
$36$	72.0000			0.333333
$37$	123.000	−	213.042i	0.546516	−	0.946593i	−0.451994	−	0.892021i	$-0.649287\pi$
$37$	123.000	−	213.042i	0.546516	−	0.946593i	0.998510	−	0.0545719i	$-0.0173794\pi$
$38$	−200.000	−	346.410i	−0.853797	−	1.47882i
$39$	−93.0000	−	161.081i	−0.381844	−	0.661373i
$40$		0			0
$41$	−248.000			−0.944661			−0.472330	−	0.881422i	$-0.656587\pi$
$41$	−248.000			−0.944661			−0.472330	+	0.881422i	$0.656587\pi$
$42$		0			0
$43$	68.0000			0.241161			0.120580	−	0.992704i	$-0.461524\pi$
$43$	68.0000			0.241161			0.120580	+	0.992704i	$0.461524\pi$
$44$	−248.000	+	429.549i	−0.849714	+	1.47175i
$45$	18.0000	+	31.1769i	0.0596285	+	0.103280i
$46$	84.0000	+	145.492i	0.269242	+	0.466341i
$47$	−162.000	+	280.592i	−0.502769	+	0.870821i	0.497226	+	0.867621i	$0.334352\pi$
$47$	−162.000	+	280.592i	−0.502769	+	0.870821i	−0.999995	+	0.00319997i	$0.998981\pi$
$48$	192.000			0.577350
$49$		0			0
$50$	−436.000			−1.23319
$51$	126.000	−	218.238i	0.345952	−	0.599206i
$52$	248.000	+	429.549i	0.661373	+	1.14553i
$53$	−129.000	−	223.435i	−0.334330	−	0.579077i	0.649026	−	0.760767i	$-0.275177\pi$
$53$	−129.000	−	223.435i	−0.334330	−	0.579077i	−0.983356	+	0.181689i	$0.941843\pi$
$54$	54.0000	−	93.5307i	0.136083	−	0.235702i
$55$	−248.000			−0.608006
$56$		0			0
$57$	−300.000			−0.697122
$58$	20.0000	−	34.6410i	0.0452781	−	0.0784239i
$59$	−60.0000	−	103.923i	−0.132396	−	0.229316i	0.792204	−	0.610256i	$-0.208934\pi$
$59$	−60.0000	−	103.923i	−0.132396	−	0.229316i	−0.924600	+	0.380941i	$0.875600\pi$
$60$	−48.0000	−	83.1384i	−0.103280	−	0.178885i
$61$	−311.000	+	538.668i	−0.652778	+	1.13064i	0.329668	+	0.944097i	$0.393063\pi$
$61$	−311.000	+	538.668i	−0.652778	+	1.13064i	−0.982446	+	0.186548i	$0.940270\pi$
$62$	−192.000			−0.393291
$63$		0			0
$64$	−512.000			−1.00000
$65$	−124.000	+	214.774i	−0.236620	+	0.409838i
$66$	372.000	+	644.323i	0.693788	+	1.20168i
$67$	−452.000	−	782.887i	−0.824188	−	1.42754i	−0.902538	−	0.430609i	$-0.858299\pi$
$67$	−452.000	−	782.887i	−0.824188	−	1.42754i	0.0783505	−	0.996926i	$-0.475035\pi$
$68$	−336.000	+	581.969i	−0.599206	+	1.03785i
$69$	126.000			0.219835
$70$		0			0
$71$	−678.000			−1.13329			−0.566646	−	0.823961i	$-0.691759\pi$
$71$	−678.000			−1.13329			−0.566646	+	0.823961i	$0.691759\pi$
$72$		0			0
$73$	321.000	+	555.988i	0.514660	+	0.891418i	0.999855	+	0.0170119i	$0.00541532\pi$
$73$	321.000	+	555.988i	0.514660	+	0.891418i	−0.485195	+	0.874406i	$0.661251\pi$
$74$	492.000	+	852.169i	0.772890	+	1.33868i
$75$	−163.500	+	283.190i	−0.251725	+	0.436000i
$76$	800.000			1.20745
$77$		0			0
$78$	744.000			1.08002
$79$	−370.000	+	640.859i	−0.526940	+	0.912687i	0.472567	+	0.881295i	$0.343327\pi$
$79$	−370.000	+	640.859i	−0.526940	+	0.912687i	−0.999507	+	0.0313921i	$0.990006\pi$
$80$	−128.000	−	221.703i	−0.178885	−	0.309839i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	496.000	−	859.097i	0.667976	−	1.15697i
$83$	468.000			0.618912			0.309456	−	0.950914i	$-0.399853\pi$
$83$	468.000			0.618912			0.309456	+	0.950914i	$0.399853\pi$
$84$		0			0
$85$	−336.000			−0.428757
$86$	−136.000	+	235.559i	−0.170526	+	0.295360i
$87$	−15.0000	−	25.9808i	−0.0184847	−	0.0320164i
$88$		0			0
$89$	−100.000	+	173.205i	−0.119101	+	0.206289i	−0.919412	−	0.393297i	$-0.871335\pi$
$89$	−100.000	+	173.205i	−0.119101	+	0.206289i	0.800311	+	0.599585i	$0.204668\pi$
$90$	−144.000			−0.168655
$91$		0			0
$92$	−336.000			−0.380765
$93$	−72.0000	+	124.708i	−0.0802801	+	0.139049i
$94$	−648.000	−	1122.37i	−0.711022	−	1.23153i
$95$	200.000	+	346.410i	0.215995	+	0.374115i
$96$	−384.000	+	665.108i	−0.408248	+	0.707107i
$97$	−1266.00			−1.32518			−0.662592	−	0.748981i	$-0.730544\pi$
$97$	−1266.00			−1.32518			−0.662592	+	0.748981i	$0.730544\pi$
$98$		0			0
$99$	558.000			0.566476
$100$	436.000	−	755.174i	0.436000	−	0.755174i
$101$	−116.000	−	200.918i	−0.114281	−	0.197941i	0.803211	−	0.595695i	$-0.203123\pi$
$101$	−116.000	−	200.918i	−0.114281	−	0.197941i	−0.917492	+	0.397754i	$0.869790\pi$
$102$	504.000	+	872.954i	0.489249	+	0.847405i
$103$	896.000	−	1551.92i	0.857141	−	1.48461i	−0.0175038	−	0.999847i	$-0.505572\pi$
$103$	896.000	−	1551.92i	0.857141	−	1.48461i	0.874645	−	0.484765i	$-0.161095\pi$
$104$		0			0
$105$		0			0
$106$	1032.00			0.945629
$107$	953.000	−	1650.64i	0.861028	−	1.49134i	−0.00990992	−	0.999951i	$-0.503154\pi$
$107$	953.000	−	1650.64i	0.861028	−	1.49134i	0.870938	−	0.491393i	$-0.163512\pi$
$108$	108.000	+	187.061i	0.0962250	+	0.166667i
$109$	45.0000	+	77.9423i	0.0395433	+	0.0684910i	0.885120	−	0.465363i	$-0.154076\pi$
$109$	45.0000	+	77.9423i	0.0395433	+	0.0684910i	−0.845576	+	0.533854i	$0.820743\pi$
$110$	496.000	−	859.097i	0.429925	−	0.744652i
$111$	738.000			0.631062
$112$		0			0
$113$	458.000			0.381283			0.190642	−	0.981660i	$-0.438943\pi$
$113$	458.000			0.381283			0.190642	+	0.981660i	$0.438943\pi$
$114$	600.000	−	1039.23i	0.492940	−	0.853797i
$115$	−84.0000	−	145.492i	−0.0681134	−	0.117976i
$116$	40.0000	+	69.2820i	0.0320164	+	0.0554541i
$117$	279.000	−	483.242i	0.220458	−	0.381844i
$118$	480.000			0.374471
$119$		0			0
$120$		0			0
$121$	−1256.50	+	2176.32i	−0.944027	+	1.63510i
$122$	−1244.00	−	2154.67i	−0.923168	−	1.59897i
$123$	−372.000	−	644.323i	−0.272700	−	0.472330i
$124$	192.000	−	332.554i	0.139049	−	0.240840i
$125$	936.000			0.669747
$126$		0			0
$127$	804.000			0.561760			0.280880	−	0.959743i	$-0.409374\pi$
$127$	804.000			0.561760			0.280880	+	0.959743i	$0.409374\pi$
$128$		0			0
$129$	102.000	+	176.669i	0.0696170	+	0.120580i
$130$	−496.000	−	859.097i	−0.334631	−	0.579599i
$131$	−406.000	+	703.213i	−0.270782	+	0.469007i	−0.969062	−	0.246817i	$-0.920615\pi$
$131$	−406.000	+	703.213i	−0.270782	+	0.469007i	0.698281	+	0.715824i	$0.253949\pi$
$132$	−1488.00			−0.981165
$133$		0			0
$134$	3616.00			2.33116
$135$	−54.0000	+	93.5307i	−0.0344265	+	0.0596285i
$136$		0			0
$137$	−207.000	−	358.535i	−0.129089	−	0.223589i	0.794235	−	0.607611i	$-0.207872\pi$
$137$	−207.000	−	358.535i	−0.129089	−	0.223589i	−0.923324	+	0.384022i	$0.874539\pi$
$138$	−252.000	+	436.477i	−0.155447	+	0.269242i
$139$	−1620.00			−0.988537			−0.494268	−	0.869309i	$-0.664564\pi$
$139$	−1620.00			−0.988537			−0.494268	+	0.869309i	$0.664564\pi$
$140$		0			0
$141$	−972.000			−0.580547
$142$	1356.00	−	2348.66i	0.801359	−	1.38799i
$143$	1922.00	+	3329.00i	1.12396	+	1.94675i
$144$	288.000	+	498.831i	0.166667	+	0.288675i
$145$	−20.0000	+	34.6410i	−0.0114545	+	0.0198399i
$146$	−2568.00			−1.45568
$147$		0			0
$148$	−1968.00			−1.09303
$149$	−1185.00	+	2052.48i	−0.651537	+	1.12849i	0.331213	+	0.943556i	$0.392542\pi$
$149$	−1185.00	+	2052.48i	−0.651537	+	1.12849i	−0.982750	+	0.184939i	$0.940791\pi$
$150$	−654.000	−	1132.76i	−0.355993	−	0.616597i
$151$	284.000	+	491.902i	0.153057	+	0.265102i	0.932350	−	0.361558i	$-0.117755\pi$
$151$	284.000	+	491.902i	0.153057	+	0.265102i	−0.779293	+	0.626660i	$0.784422\pi$
$152$		0			0
$153$	756.000			0.399470
$154$		0			0
$155$	192.000			0.0994956
$156$	−744.000	+	1288.65i	−0.381844	+	0.661373i
$157$	133.000	+	230.363i	0.0676086	+	0.117102i	0.897848	−	0.440305i	$-0.145130\pi$
$157$	133.000	+	230.363i	0.0676086	+	0.117102i	−0.830240	+	0.557407i	$0.811796\pi$
$158$	−1480.00	−	2563.44i	−0.745206	−	1.29073i
$159$	387.000	−	670.304i	0.193026	−	0.334330i
$160$	1024.00			0.505964
$161$		0			0
$162$	324.000			0.157135
$163$	136.000	−	235.559i	0.0653518	−	0.113193i	−0.831498	−	0.555527i	$-0.812516\pi$
$163$	136.000	−	235.559i	0.0653518	−	0.113193i	0.896850	+	0.442335i	$0.145850\pi$
$164$	992.000	+	1718.19i	0.472330	+	0.818100i
$165$	−372.000	−	644.323i	−0.175516	−	0.304003i
$166$	−936.000	+	1621.20i	−0.437637	+	0.758009i
$167$	−1876.00			−0.869277			−0.434638	−	0.900605i	$-0.643124\pi$
$167$	−1876.00			−0.869277			−0.434638	+	0.900605i	$0.643124\pi$
$168$		0			0
$169$	1647.00			0.749659
$170$	672.000	−	1163.94i	0.303177	−	0.525118i
$171$	−450.000	−	779.423i	−0.201242	−	0.348561i
$172$	−272.000	−	471.118i	−0.120580	−	0.208851i
$173$	76.0000	−	131.636i	0.0333998	−	0.0578502i	−0.848842	−	0.528646i	$-0.822700\pi$
$173$	76.0000	−	131.636i	0.0333998	−	0.0578502i	0.882242	+	0.470796i	$0.156033\pi$
$174$	120.000			0.0522826
$175$		0			0
$176$	−3968.00			−1.69943
$177$	180.000	−	311.769i	0.0764386	−	0.132396i
$178$	−400.000	−	692.820i	−0.168434	−	0.291736i
$179$	−305.000	−	528.275i	−0.127356	−	0.220588i	0.795295	−	0.606222i	$-0.207316\pi$
$179$	−305.000	−	528.275i	−0.127356	−	0.220588i	−0.922652	+	0.385635i	$0.873982\pi$
$180$	144.000	−	249.415i	0.0596285	−	0.103280i
$181$	1042.00			0.427907			0.213954	−	0.976844i	$-0.431366\pi$
$181$	1042.00			0.427907			0.213954	+	0.976844i	$0.431366\pi$
$182$		0			0
$183$	−1866.00			−0.753763
$184$		0			0
$185$	−492.000	−	852.169i	−0.195527	−	0.338663i
$186$	−288.000	−	498.831i	−0.113533	−	0.196645i
$187$	−2604.00	+	4510.26i	−1.01831	+	1.76376i
$188$	2592.00			1.00554
$189$		0			0
$190$	−1600.00			−0.610927
$191$	1019.00	−	1764.96i	0.386033	−	0.668628i	−0.605879	−	0.795557i	$-0.707179\pi$
$191$	1019.00	−	1764.96i	0.386033	−	0.668628i	0.991912	+	0.126928i	$0.0405118\pi$
$192$	−768.000	−	1330.22i	−0.288675	−	0.500000i
$193$	1301.00	+	2253.40i	0.485223	+	0.840431i	0.999856	−	0.0169798i	$-0.00540511\pi$
$193$	1301.00	+	2253.40i	0.485223	+	0.840431i	−0.514633	+	0.857411i	$0.672072\pi$
$194$	2532.00	−	4385.55i	0.937046	−	1.62301i
$195$	−744.000			−0.273225
$196$		0			0
$197$	2354.00			0.851348			0.425674	−	0.904877i	$-0.360037\pi$
$197$	2354.00			0.851348			0.425674	+	0.904877i	$0.360037\pi$
$198$	−1116.00	+	1932.97i	−0.400559	+	0.693788i
$199$	−840.000	−	1454.92i	−0.299226	−	0.518275i	0.676733	−	0.736229i	$-0.263395\pi$
$199$	−840.000	−	1454.92i	−0.299226	−	0.518275i	−0.975959	+	0.217954i	$0.930062\pi$
$200$		0			0
$201$	1356.00	−	2348.66i	0.475845	−	0.824188i
$202$	928.000			0.323237
$203$		0			0
$204$	−2016.00			−0.691903
$205$	−496.000	+	859.097i	−0.168986	+	0.292692i
$206$	3584.00	+	6207.67i	1.21218	+	2.09956i
$207$	189.000	+	327.358i	0.0634609	+	0.109918i
$208$	−1984.00	+	3436.39i	−0.661373	+	1.14553i
$209$	6200.00			2.05198
$210$		0			0
$211$	−668.000			−0.217948			−0.108974	−	0.994045i	$-0.534757\pi$
$211$	−668.000			−0.217948			−0.108974	+	0.994045i	$0.534757\pi$
$212$	−1032.00	+	1787.48i	−0.334330	+	0.579077i
$213$	−1017.00	−	1761.50i	−0.327153	−	0.566646i
$214$	3812.00	+	6602.58i	1.21768	+	2.10908i
$215$	136.000	−	235.559i	0.0431401	−	0.0747209i
$216$		0			0
$217$		0			0
$218$	−360.000			−0.111845
$219$	−963.000	+	1667.96i	−0.297139	+	0.514660i
$220$	992.000	+	1718.19i	0.304003	+	0.526548i
$221$	2604.00	+	4510.26i	0.792597	+	1.37282i
$222$	−1476.00	+	2556.51i	−0.446228	+	0.772890i
$223$	−1832.00			−0.550134			−0.275067	−	0.961425i	$-0.588700\pi$
$223$	−1832.00			−0.550134			−0.275067	+	0.961425i	$0.588700\pi$
$224$		0			0
$225$	−981.000			−0.290667
$226$	−916.000	+	1586.56i	−0.269608	+	0.466975i
$227$	−2472.00	−	4281.63i	−0.722786	−	1.25190i	−0.959879	−	0.280415i	$-0.909528\pi$
$227$	−2472.00	−	4281.63i	−0.722786	−	1.25190i	0.237093	−	0.971487i	$-0.423805\pi$
$228$	1200.00	+	2078.46i	0.348561	+	0.603726i
$229$	2735.00	−	4737.16i	0.789231	−	1.36699i	−0.137208	−	0.990542i	$-0.543813\pi$
$229$	2735.00	−	4737.16i	0.789231	−	1.36699i	0.926439	−	0.376446i	$-0.122854\pi$
$230$	672.000			0.192654
$231$		0			0
$232$		0			0
$233$	1401.00	−	2426.60i	0.393917	−	0.682284i	−0.599046	−	0.800715i	$-0.704453\pi$
$233$	1401.00	−	2426.60i	0.393917	−	0.682284i	0.992962	+	0.118431i	$0.0377866\pi$
$234$	1116.00	+	1932.97i	0.311774	+	0.540009i
$235$	648.000	+	1122.37i	0.179876	+	0.311554i
$236$	−480.000	+	831.384i	−0.132396	+	0.229316i
$237$	−2220.00			−0.608458
$238$		0			0
$239$	−1170.00			−0.316657			−0.158328	−	0.987386i	$-0.550610\pi$
$239$	−1170.00			−0.316657			−0.158328	+	0.987386i	$0.550610\pi$
$240$	384.000	−	665.108i	0.103280	−	0.178885i
$241$	1169.00	+	2024.77i	0.312456	+	0.541190i	0.978893	−	0.204371i	$-0.0655150\pi$
$241$	1169.00	+	2024.77i	0.312456	+	0.541190i	−0.666437	+	0.745561i	$0.732182\pi$
$242$	−5026.00	−	8705.29i	−1.33506	−	2.31238i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	4976.00			1.30556
$245$		0			0
$246$	2976.00			0.771312
$247$	3100.00	−	5369.36i	0.798576	−	1.38317i
$248$		0			0
$249$	702.000	+	1215.90i	0.178664	+	0.309456i
$250$	−1872.00	+	3242.40i	−0.473583	+	0.820269i
$251$	2792.00			0.702109			0.351055	−	0.936355i	$-0.385823\pi$
$251$	2792.00			0.702109			0.351055	+	0.936355i	$0.385823\pi$
$252$		0			0
$253$	−2604.00			−0.647083
$254$	−1608.00	+	2785.14i	−0.397224	+	0.688012i
$255$	−504.000	−	872.954i	−0.123771	−	0.214378i
$256$	−2048.00	−	3547.24i	−0.500000	−	0.866025i
$257$	−3512.00	+	6082.96i	−0.852422	+	1.47644i	0.0265936	+	0.999646i	$0.491534\pi$
$257$	−3512.00	+	6082.96i	−0.852422	+	1.47644i	−0.879016	+	0.476792i	$0.841799\pi$
$258$	−816.000			−0.196907
$259$		0			0
$260$	1984.00			0.473240
$261$	45.0000	−	77.9423i	0.0106721	−	0.0184847i
$262$	−1624.00	−	2812.85i	−0.382943	−	0.663277i
$263$	−1219.00	−	2111.37i	−0.285805	−	0.495029i	0.686999	−	0.726658i	$-0.258928\pi$
$263$	−1219.00	−	2111.37i	−0.285805	−	0.495029i	−0.972804	+	0.231629i	$0.925594\pi$
$264$		0			0
$265$	−1032.00			−0.239227
$266$		0			0
$267$	−600.000			−0.137526
$268$	−3616.00	+	6263.10i	−0.824188	+	1.42754i
$269$	3390.00	+	5871.65i	0.768372	+	1.33086i	0.938446	+	0.345427i	$0.112266\pi$
$269$	3390.00	+	5871.65i	0.768372	+	1.33086i	−0.170074	+	0.985431i	$0.554401\pi$
$270$	−216.000	−	374.123i	−0.0486864	−	0.0843274i
$271$	964.000	−	1669.70i	0.216084	−	0.374269i	−0.737523	−	0.675322i	$-0.764005\pi$
$271$	964.000	−	1669.70i	0.216084	−	0.374269i	0.953607	+	0.301053i	$0.0973381\pi$
$272$	−5376.00			−1.19841
$273$		0			0
$274$	1656.00			0.365119
$275$	3379.00	−	5852.60i	0.740950	−	1.28336i
$276$	−504.000	−	872.954i	−0.109918	−	0.190383i
$277$	−2777.00	−	4809.91i	−0.602360	−	1.04332i	−0.992463	−	0.122547i	$-0.960894\pi$
$277$	−2777.00	−	4809.91i	−0.602360	−	1.04332i	0.390103	−	0.920771i	$-0.372440\pi$
$278$	3240.00	−	5611.84i	0.699001	−	1.21071i
$279$	−432.000			−0.0926995
$280$		0			0
$281$	1942.00			0.412278			0.206139	−	0.978523i	$-0.433910\pi$
$281$	1942.00			0.412278			0.206139	+	0.978523i	$0.433910\pi$
$282$	1944.00	−	3367.11i	0.410509	−	0.711022i
$283$	−2414.00	−	4181.17i	−0.507058	−	0.878250i	−0.999967	−	0.00816911i	$-0.997400\pi$
$283$	−2414.00	−	4181.17i	−0.507058	−	0.878250i	0.492909	−	0.870081i	$-0.335934\pi$
$284$	2712.00	+	4697.32i	0.566646	+	0.981460i
$285$	−600.000	+	1039.23i	−0.124705	+	0.215995i
$286$	−15376.0			−3.17903
$287$		0			0
$288$	−2304.00			−0.471405
$289$	−1071.50	+	1855.89i	−0.218095	+	0.377751i
$290$	−80.0000	−	138.564i	−0.0161992	−	0.0280578i
$291$	−1899.00	−	3289.16i	−0.382548	−	0.662592i
$292$	2568.00	−	4447.91i	0.514660	−	0.891418i
$293$	−6152.00			−1.22663			−0.613317	−	0.789837i	$-0.710165\pi$
$293$	−6152.00			−1.22663			−0.613317	+	0.789837i	$0.710165\pi$
$294$		0			0
$295$	−480.000			−0.0947345
$296$		0			0
$297$	837.000	+	1449.73i	0.163527	+	0.283238i
$298$	−4740.00	−	8209.92i	−0.921412	−	1.59593i
$299$	−1302.00	+	2255.13i	−0.251828	+	0.436179i
$300$	2616.00			0.503449
$301$		0			0
$302$	−2272.00			−0.432910
$303$	348.000	−	602.754i	0.0659805	−	0.114281i
$304$	3200.00	+	5542.56i	0.603726	+	1.04568i
$305$	1244.00	+	2154.67i	0.233545	+	0.404512i
$306$	−1512.00	+	2618.86i	−0.282468	+	0.489249i
$307$	5884.00			1.09387			0.546934	−	0.837176i	$-0.315795\pi$
$307$	5884.00			1.09387			0.546934	+	0.837176i	$0.315795\pi$
$308$		0			0
$309$	5376.00			0.989741
$310$	−384.000	+	665.108i	−0.0703540	+	0.121857i
$311$	−4566.00	−	7908.54i	−0.832521	−	1.44197i	−0.896033	−	0.443988i	$-0.853563\pi$
$311$	−4566.00	−	7908.54i	−0.832521	−	1.44197i	0.0635115	−	0.997981i	$-0.479770\pi$
$312$		0			0
$313$	4691.00	−	8125.05i	0.847128	−	1.46727i	−0.0366327	−	0.999329i	$-0.511663\pi$
$313$	4691.00	−	8125.05i	0.847128	−	1.46727i	0.883760	−	0.467940i	$-0.155004\pi$
$314$	−1064.00			−0.191226
$315$		0			0
$316$	5920.00			1.05388
$317$	−1557.00	+	2696.80i	−0.275867	+	0.477816i	−0.970353	−	0.241690i	$-0.922298\pi$
$317$	−1557.00	+	2696.80i	−0.275867	+	0.477816i	0.694487	+	0.719506i	$0.255632\pi$
$318$	1548.00	+	2681.21i	0.272980	+	0.472815i
$319$	310.000	+	536.936i	0.0544096	+	0.0942402i
$320$	−1024.00	+	1773.62i	−0.178885	+	0.309839i
$321$	5718.00			0.994229
$322$		0			0
$323$	8400.00			1.44702
$324$	−324.000	+	561.184i	−0.0555556	+	0.0962250i
$325$	−3379.00	−	5852.60i	−0.576718	−	0.998904i
$326$	544.000	+	942.236i	0.0924214	+	0.160079i
$327$	−135.000	+	233.827i	−0.0228303	+	0.0395433i
$328$		0			0
$329$		0			0
$330$	2976.00			0.496435
$331$	−766.000	+	1326.75i	−0.127200	+	0.220317i	−0.922591	−	0.385780i	$-0.873932\pi$
$331$	−766.000	+	1326.75i	−0.127200	+	0.220317i	0.795391	+	0.606097i	$0.207266\pi$
$332$	−1872.00	−	3242.40i	−0.309456	−	0.535993i
$333$	1107.00	+	1917.38i	0.182172	+	0.315531i
$334$	3752.00	−	6498.65i	0.614672	−	1.06464i
$335$	−3616.00			−0.589741
$336$		0			0
$337$	−4166.00			−0.673402			−0.336701	−	0.941612i	$-0.609311\pi$
$337$	−4166.00			−0.673402			−0.336701	+	0.941612i	$0.609311\pi$
$338$	−3294.00	+	5705.38i	−0.530089	+	0.918141i
$339$	687.000	+	1189.92i	0.110067	+	0.190642i
$340$	1344.00	+	2327.88i	0.214378	+	0.371314i
$341$	1488.00	−	2577.29i	0.236304	−	0.409291i
$342$	3600.00			0.569198
$343$		0			0
$344$		0			0
$345$	252.000	−	436.477i	0.0393253	−	0.0681134i
$346$	304.000	+	526.543i	0.0472345	+	0.0818126i
$347$	5683.00	+	9843.24i	0.879191	+	1.52280i	0.852230	+	0.523168i	$0.175250\pi$
$347$	5683.00	+	9843.24i	0.879191	+	1.52280i	0.0269617	+	0.999636i	$0.491417\pi$
$348$	−120.000	+	207.846i	−0.0184847	+	0.0320164i
$349$	9310.00			1.42795			0.713973	−	0.700174i	$-0.246894\pi$
$349$	9310.00			1.42795			0.713973	+	0.700174i	$0.246894\pi$
$350$		0			0
$351$	1674.00			0.254563
$352$	7936.00	−	13745.6i	1.20168	−	2.08137i
$353$	4286.00	+	7423.57i	0.646234	+	1.11931i	0.984015	+	0.178086i	$0.0569905\pi$
$353$	4286.00	+	7423.57i	0.646234	+	1.11931i	−0.337780	+	0.941225i	$0.609676\pi$
$354$	720.000	+	1247.08i	0.108100	+	0.187236i
$355$	−1356.00	+	2348.66i	−0.202730	+	0.351138i
$356$	1600.00			0.238202
$357$		0			0
$358$	2440.00			0.360218
$359$	2395.00	−	4148.26i	0.352098	−	0.609852i	−0.634519	−	0.772908i	$-0.718802\pi$
$359$	2395.00	−	4148.26i	0.352098	−	0.609852i	0.986617	+	0.163056i	$0.0521350\pi$
$360$		0			0
$361$	−1570.50	−	2720.19i	−0.228969	−	0.396586i
$362$	−2084.00	+	3609.59i	−0.302576	+	0.524077i
$363$	−7539.00			−1.09007
$364$		0			0
$365$	2568.00			0.368261
$366$	3732.00	−	6464.01i	0.532991	−	0.923168i
$367$	−2712.00	−	4697.32i	−0.385736	−	0.668115i	0.606135	−	0.795362i	$-0.292719\pi$
$367$	−2712.00	−	4697.32i	−0.385736	−	0.668115i	−0.991871	+	0.127247i	$0.959386\pi$
$368$	−1344.00	−	2327.88i	−0.190383	−	0.329753i
$369$	1116.00	−	1932.97i	0.157443	−	0.272700i
$370$	3936.00			0.553035
$371$		0			0
$372$	1152.00			0.160560
$373$	−919.000	+	1591.75i	−0.127571	+	0.220960i	−0.922735	−	0.385435i	$-0.874051\pi$
$373$	−919.000	+	1591.75i	−0.127571	+	0.220960i	0.795164	+	0.606395i	$0.207385\pi$
$374$	−10416.0	−	18041.0i	−1.44010	−	2.49433i
$375$	1404.00	+	2431.80i	0.193339	+	0.334874i
$376$		0			0
$377$	620.000			0.0846993
$378$		0			0
$379$	−4260.00			−0.577365			−0.288683	−	0.957425i	$-0.593217\pi$
$379$	−4260.00			−0.577365			−0.288683	+	0.957425i	$0.593217\pi$
$380$	1600.00	−	2771.28i	0.215995	−	0.374115i
$381$	1206.00	+	2088.85i	0.162166	+	0.280880i
$382$	4076.00	+	7059.84i	0.545933	+	0.945583i
$383$	−4524.00	+	7835.80i	−0.603566	+	1.04541i	0.388711	+	0.921360i	$0.372920\pi$
$383$	−4524.00	+	7835.80i	−0.603566	+	1.04541i	−0.992276	+	0.124046i	$0.960413\pi$
$384$		0			0
$385$		0			0
$386$	−10408.0			−1.37242
$387$	−306.000	+	530.008i	−0.0401934	+	0.0696170i
$388$	5064.00	+	8771.11i	0.662592	+	1.14764i
$389$	5745.00	+	9950.63i	0.748800	+	1.29696i	0.948398	+	0.317081i	$0.102703\pi$
$389$	5745.00	+	9950.63i	0.748800	+	1.29696i	−0.199599	+	0.979878i	$0.563964\pi$
$390$	1488.00	−	2577.29i	0.193200	−	0.334631i
$391$	−3528.00			−0.456314
$392$		0			0
$393$	−2436.00			−0.312672
$394$	−4708.00	+	8154.50i	−0.601994	+	1.04268i
$395$	1480.00	+	2563.44i	0.188524	+	0.326533i
$396$	−2232.00	−	3865.94i	−0.283238	−	0.490582i
$397$	933.000	−	1616.00i	0.117949	−	0.204294i	−0.801005	−	0.598657i	$-0.795701\pi$
$397$	933.000	−	1616.00i	0.117949	−	0.204294i	0.918955	+	0.394363i	$0.129035\pi$
$398$	6720.00			0.846340
$399$		0			0
$400$	6976.00			0.872000
$401$	−6831.00	+	11831.6i	−0.850683	+	1.47343i	0.0299100	+	0.999553i	$0.490478\pi$
$401$	−6831.00	+	11831.6i	−0.850683	+	1.47343i	−0.880593	+	0.473873i	$0.842855\pi$
$402$	5424.00	+	9394.64i	0.672947	+	1.16558i
$403$	−1488.00	−	2577.29i	−0.183927	−	0.318571i
$404$	−928.000	+	1607.34i	−0.114281	+	0.197941i
$405$	−324.000			−0.0397523
$406$		0			0
$407$	−15252.0			−1.85753
$408$		0			0
$409$	6605.00	+	11440.2i	0.798524	+	1.38308i	0.920577	+	0.390560i	$0.127719\pi$
$409$	6605.00	+	11440.2i	0.798524	+	1.38308i	−0.122054	+	0.992524i	$0.538948\pi$
$410$	−1984.00	−	3436.39i	−0.238982	−	0.413930i
$411$	621.000	−	1075.60i	0.0745296	−	0.129089i
$412$	−14336.0			−1.71428
$413$		0			0
$414$	−1512.00			−0.179495
$415$	936.000	−	1621.20i	0.110714	−	0.191763i
$416$	−7936.00	−	13745.6i	−0.935323	−	1.62003i
$417$	−2430.00	−	4208.88i	−0.285366	−	0.494268i
$418$	−12400.0	+	21477.4i	−1.45097	+	2.51315i
$419$	6960.00			0.811499			0.405750	−	0.913984i	$-0.367010\pi$
$419$	6960.00			0.811499			0.405750	+	0.913984i	$0.367010\pi$
$420$		0			0
$421$	8162.00			0.944873			0.472437	−	0.881365i	$-0.343375\pi$
$421$	8162.00			0.944873			0.472437	+	0.881365i	$0.343375\pi$
$422$	1336.00	−	2314.02i	0.154112	−	0.266931i
$423$	−1458.00	−	2525.33i	−0.167590	−	0.290274i
$424$		0			0
$425$	4578.00	−	7929.33i	0.522507	−	0.905009i
$426$	8136.00			0.925330
$427$		0			0
$428$	−15248.0			−1.72206
$429$	−5766.00	+	9987.00i	−0.648916	+	1.12396i
$430$	544.000	+	942.236i	0.0610093	+	0.105671i
$431$	−8301.00	−	14377.8i	−0.927715	−	1.60685i	−0.787136	−	0.616780i	$-0.788437\pi$
$431$	−8301.00	−	14377.8i	−0.927715	−	1.60685i	−0.140579	−	0.990069i	$-0.544896\pi$
$432$	−864.000	+	1496.49i	−0.0962250	+	0.166667i
$433$	7738.00			0.858810			0.429405	−	0.903112i	$-0.358723\pi$
$433$	7738.00			0.858810			0.429405	+	0.903112i	$0.358723\pi$
$434$		0			0
$435$	−120.000			−0.0132266
$436$	360.000	−	623.538i	0.0395433	−	0.0684910i
$437$	2100.00	+	3637.31i	0.229878	+	0.398160i
$438$	−3852.00	−	6671.86i	−0.420218	−	0.727840i
$439$	420.000	−	727.461i	0.0456617	−	0.0790885i	−0.842291	−	0.539023i	$-0.818794\pi$
$439$	420.000	−	727.461i	0.0456617	−	0.0790885i	0.887953	+	0.459934i	$0.152127\pi$
$440$		0			0
$441$		0			0
$442$	−20832.0			−2.24180
$443$	−3309.00	+	5731.36i	−0.354888	+	0.614684i	−0.987099	−	0.160113i	$-0.948814\pi$
$443$	−3309.00	+	5731.36i	−0.354888	+	0.614684i	0.632211	+	0.774796i	$0.282148\pi$
$444$	−2952.00	−	5113.01i	−0.315531	−	0.546516i
$445$	400.000	+	692.820i	0.0426108	+	0.0738041i
$446$	3664.00	−	6346.23i	0.389003	−	0.673773i
$447$	−7110.00			−0.752330
$448$		0			0
$449$	3090.00			0.324780			0.162390	−	0.986727i	$-0.448080\pi$
$449$	3090.00			0.324780			0.162390	+	0.986727i	$0.448080\pi$
$450$	1962.00	−	3398.28i	0.205532	−	0.355993i
$451$	7688.00	+	13316.0i	0.802691	+	1.39030i
$452$	−1832.00	−	3173.12i	−0.190642	−	0.330201i
$453$	−852.000	+	1475.71i	−0.0883674	+	0.153057i
$454$	19776.0			2.04435
$455$		0			0
$456$		0			0
$457$	−2957.00	+	5121.67i	−0.302675	+	0.524249i	−0.976741	−	0.214422i	$-0.931213\pi$
$457$	−2957.00	+	5121.67i	−0.302675	+	0.524249i	0.674066	+	0.738671i	$0.264546\pi$
$458$	10940.0	+	18948.6i	1.11614	+	1.93321i
$459$	1134.00	+	1964.15i	0.115317	+	0.199735i
$460$	−672.000	+	1163.94i	−0.0681134	+	0.117976i
$461$	−15968.0			−1.61324			−0.806620	−	0.591070i	$-0.798706\pi$
$461$	−15968.0			−1.61324			−0.806620	+	0.591070i	$0.798706\pi$
$462$		0			0
$463$	−1172.00			−0.117640			−0.0588202	−	0.998269i	$-0.518734\pi$
$463$	−1172.00			−0.117640			−0.0588202	+	0.998269i	$0.518734\pi$
$464$	−320.000	+	554.256i	−0.0320164	+	0.0554541i
$465$	288.000	+	498.831i	0.0287219	+	0.0497478i
$466$	5604.00	+	9706.41i	0.557082	+	0.964895i
$467$	−2652.00	+	4593.40i	−0.262784	+	0.455154i	−0.966981	−	0.254850i	$-0.917974\pi$
$467$	−2652.00	+	4593.40i	−0.262784	+	0.455154i	0.704197	+	0.710005i	$0.251307\pi$
$468$	−4464.00			−0.440916
$469$		0			0
$470$	−5184.00			−0.508766
$471$	−399.000	+	691.088i	−0.0390339	+	0.0676086i
$472$		0			0
$473$	−2108.00	−	3651.16i	−0.204917	−	0.354927i
$474$	4440.00	−	7690.31i	0.430245	−	0.745206i
$475$	−10900.0			−1.05290
$476$		0			0
$477$	2322.00			0.222887
$478$	2340.00	−	4053.00i	0.223910	−	0.387824i
$479$	−2870.00	−	4970.99i	−0.273765	−	0.474176i	0.696057	−	0.717986i	$-0.254936\pi$
$479$	−2870.00	−	4970.99i	−0.273765	−	0.474176i	−0.969823	+	0.243810i	$0.921603\pi$
$480$	1536.00	+	2660.43i	0.146059	+	0.252982i
$481$	−7626.00	+	13208.6i	−0.722902	+	1.25210i
$482$	−9352.00			−0.883759
$483$		0			0
$484$	20104.0			1.88805
$485$	−2532.00	+	4385.55i	−0.237056	+	0.410593i
$486$	486.000	+	841.777i	0.0453609	+	0.0785674i
$487$	−4472.00	−	7745.73i	−0.416110	−	0.720724i	0.579434	−	0.815019i	$-0.303274\pi$
$487$	−4472.00	−	7745.73i	−0.416110	−	0.720724i	−0.995544	+	0.0942951i	$0.969940\pi$
$488$		0			0
$489$	816.000			0.0754617
$490$		0			0
$491$	−5558.00			−0.510853			−0.255427	−	0.966828i	$-0.582216\pi$
$491$	−5558.00			−0.510853			−0.255427	+	0.966828i	$0.582216\pi$
$492$	−2976.00	+	5154.58i	−0.272700	+	0.472330i
$493$	420.000	+	727.461i	0.0383689	+	0.0664568i
$494$	12400.0	+	21477.4i	1.12936	+	1.95610i
$495$	1116.00	−	1932.97i	0.101334	−	0.175516i
$496$	3072.00			0.278099
$497$		0			0
$498$	−5616.00			−0.505339
$499$	9910.00	−	17164.6i	0.889043	−	1.53987i	0.0480349	−	0.998846i	$-0.484704\pi$
$499$	9910.00	−	17164.6i	0.889043	−	1.53987i	0.841008	−	0.541022i	$-0.181963\pi$
$500$	−3744.00	−	6484.80i	−0.334874	−	0.580018i
$501$	−2814.00	−	4873.99i	−0.250939	−	0.434638i
$502$	−5584.00	+	9671.77i	−0.496466	+	0.859905i
$503$	1848.00			0.163814			0.0819068	−	0.996640i	$-0.473899\pi$
$503$	1848.00			0.163814			0.0819068	+	0.996640i	$0.473899\pi$
$504$		0			0
$505$	−928.000			−0.0817732
$506$	5208.00	−	9020.52i	0.457557	−	0.792512i
$507$	2470.50	+	4279.03i	0.216408	+	0.374829i
$508$	−3216.00	−	5570.28i	−0.280880	−	0.486498i
$509$	−170.000	+	294.449i	−0.0148038	+	0.0256409i	−0.873332	−	0.487125i	$-0.838046\pi$
$509$	−170.000	+	294.449i	−0.0148038	+	0.0256409i	0.858529	+	0.512766i	$0.171379\pi$
$510$	4032.00			0.350078
$511$		0			0
$512$	16384.0			1.41421
$513$	1350.00	−	2338.27i	0.116187	−	0.201242i
$514$	−14048.0	−	24331.8i	−1.20551	−	2.08800i
$515$	−3584.00	−	6207.67i	−0.306660	−	0.531151i
$516$	816.000	−	1413.35i	0.0696170	−	0.120580i
$517$	20088.0			1.70884
$518$		0			0
$519$	456.000			0.0385668
$520$		0			0
$521$	−5106.00	−	8843.85i	−0.429363	−	0.743678i	0.567454	−	0.823405i	$-0.307928\pi$
$521$	−5106.00	−	8843.85i	−0.429363	−	0.743678i	−0.996817	+	0.0797272i	$0.974595\pi$
$522$	180.000	+	311.769i	0.0150927	+	0.0261413i
$523$	4666.00	−	8081.75i	0.390115	−	0.675698i	−0.602350	−	0.798232i	$-0.705769\pi$
$523$	4666.00	−	8081.75i	0.390115	−	0.675698i	0.992464	+	0.122534i	$0.0391021\pi$
$524$	6496.00			0.541563
$525$		0			0
$526$	9752.00			0.808379
$527$	2016.00	−	3491.81i	0.166638	−	0.288626i
$528$	−5952.00	−	10309.2i	−0.490582	−	0.849714i
$529$	5201.50	+	9009.26i	0.427509	+	0.740467i
$530$	2064.00	−	3574.95i	0.169159	−	0.292993i
$531$	1080.00			0.0882637
$532$		0			0
$533$	15376.0			1.24955
$534$	1200.00	−	2078.46i	0.0972455	−	0.168434i
$535$	−3812.00	−	6602.58i	−0.308051	−	0.533559i
$536$		0			0
$537$	915.000	−	1584.83i	0.0735292	−	0.127356i
$538$	−27120.0			−2.17328
$539$		0			0
$540$	864.000			0.0688530
$541$	4499.00	−	7792.50i	0.357536	−	0.619271i	−0.630012	−	0.776585i	$-0.716950\pi$
$541$	4499.00	−	7792.50i	0.357536	−	0.619271i	0.987549	+	0.157314i	$0.0502835\pi$
$542$	3856.00	+	6678.79i	0.305589	+	0.529296i
$543$	1563.00	+	2707.20i	0.123526	+	0.213954i
$544$	10752.0	−	18623.0i	0.847405	−	1.46775i
$545$	360.000			0.0282949
$546$		0			0
$547$	−3416.00			−0.267016			−0.133508	−	0.991048i	$-0.542624\pi$
$547$	−3416.00			−0.267016			−0.133508	+	0.991048i	$0.542624\pi$
$548$	−1656.00	+	2868.28i	−0.129089	+	0.223589i
$549$	−2799.00	−	4848.01i	−0.217593	−	0.376882i
$550$	13516.0	+	23410.4i	1.04786	+	1.81495i
$551$	500.000	−	866.025i	0.0386583	−	0.0669581i
$552$		0			0
$553$		0			0
$554$	22216.0			1.70373
$555$	1476.00	−	2556.51i	0.112888	−	0.195527i
$556$	6480.00	+	11223.7i	0.494268	+	0.856098i
$557$	263.000	+	455.529i	0.0200066	+	0.0346524i	0.875855	−	0.482574i	$-0.160298\pi$
$557$	263.000	+	455.529i	0.0200066	+	0.0346524i	−0.855849	+	0.517226i	$0.826965\pi$
$558$	864.000	−	1496.49i	0.0655485	−	0.113533i
$559$	−4216.00			−0.318994
$560$		0			0
$561$	−15624.0			−1.17584
$562$	−3884.00	+	6727.29i	−0.291524	+	0.504935i
$563$	3356.00	+	5812.76i	0.251223	+	0.435131i	0.963863	−	0.266399i	$-0.0858339\pi$
$563$	3356.00	+	5812.76i	0.251223	+	0.435131i	−0.712640	+	0.701530i	$0.752501\pi$
$564$	3888.00	+	6734.21i	0.290274	+	0.502769i
$565$	916.000	−	1586.56i	0.0682060	−	0.118136i
$566$	19312.0			1.43418
$567$		0			0
$568$		0			0
$569$	−2095.00	+	3628.65i	−0.154353	+	0.267348i	−0.932823	−	0.360334i	$-0.882663\pi$
$569$	−2095.00	+	3628.65i	−0.154353	+	0.267348i	0.778470	+	0.627682i	$0.215996\pi$
$570$	−2400.00	−	4156.92i	−0.176360	−	0.305464i
$571$	−1516.00	−	2625.79i	−0.111108	−	0.192445i	0.805109	−	0.593126i	$-0.202107\pi$
$571$	−1516.00	−	2625.79i	−0.111108	−	0.192445i	−0.916217	+	0.400682i	$0.868773\pi$
$572$	15376.0	−	26632.0i	1.12396	−	1.94675i
$573$	6114.00			0.445752
$574$		0			0
$575$	4578.00			0.332027
$576$	2304.00	−	3990.65i	0.166667	−	0.288675i
$577$	−2717.00	−	4705.98i	−0.196032	−	0.339537i	0.751207	−	0.660067i	$-0.229472\pi$
$577$	−2717.00	−	4705.98i	−0.196032	−	0.339537i	−0.947238	+	0.320531i	$0.896139\pi$
$578$	−4286.00	−	7423.57i	−0.308433	−	0.534221i
$579$	−3903.00	+	6760.19i	−0.280144	+	0.485223i
$580$	320.000			0.0229091
$581$		0			0
$582$	15192.0			1.08201
$583$	−7998.00	+	13852.9i	−0.568170	+	0.984100i
$584$		0			0
$585$	−1116.00	−	1932.97i	−0.0788734	−	0.136613i
$586$	12304.0	−	21311.2i	0.867361	−	1.50231i
$587$	464.000			0.0326258			0.0163129	−	0.999867i	$-0.494807\pi$
$587$	464.000			0.0326258			0.0163129	+	0.999867i	$0.494807\pi$
$588$		0			0
$589$	−4800.00			−0.335790
$590$	960.000	−	1662.77i	0.0669874	−	0.116026i
$591$	3531.00	+	6115.87i	0.245763	+	0.425674i
$592$	−7872.00	−	13634.7i	−0.546516	−	0.946593i
$593$	−5874.00	+	10174.1i	−0.406773	+	0.704551i	−0.994526	−	0.104489i	$-0.966679\pi$
$593$	−5874.00	+	10174.1i	−0.406773	+	0.704551i	0.587753	+	0.809040i	$0.300013\pi$
$594$	−6696.00			−0.462526
$595$		0			0
$596$	18960.0			1.30307
$597$	2520.00	−	4364.77i	0.172758	−	0.299226i
$598$	−5208.00	−	9020.52i	−0.356139	−	0.616850i
$599$	−3825.00	−	6625.09i	−0.260910	−	0.451910i	0.705574	−	0.708636i	$-0.250689\pi$
$599$	−3825.00	−	6625.09i	−0.260910	−	0.451910i	−0.966484	+	0.256727i	$0.917356\pi$
$600$		0			0
$601$	−22878.0			−1.55277			−0.776384	−	0.630261i	$-0.782948\pi$
$601$	−22878.0			−1.55277			−0.776384	+	0.630261i	$0.782948\pi$
$602$		0			0
$603$	8136.00			0.549459
$604$	2272.00	−	3935.22i	0.153057	−	0.265102i
$605$	5026.00	+	8705.29i	0.337745	+	0.584992i
$606$	1392.00	+	2411.01i	0.0933105	+	0.161618i
$607$	−352.000	+	609.682i	−0.0235375	+	0.0407681i	−0.877554	−	0.479477i	$-0.840826\pi$
$607$	−352.000	+	609.682i	−0.0235375	+	0.0407681i	0.854017	+	0.520246i	$0.174160\pi$
$608$	−25600.0			−1.70759
$609$		0			0
$610$	−9952.00			−0.660565
$611$	10044.0	−	17396.7i	0.665036	−	1.15188i
$612$	−3024.00	−	5237.72i	−0.199735	−	0.345952i
$613$	−12479.0	−	21614.3i	−0.822222	−	1.42413i	−0.904024	−	0.427482i	$-0.859401\pi$
$613$	−12479.0	−	21614.3i	−0.822222	−	1.42413i	0.0818021	−	0.996649i	$-0.473932\pi$
$614$	−11768.0	+	20382.8i	−0.773482	+	1.33971i
$615$	−2976.00			−0.195128
$616$		0			0
$617$	−8826.00			−0.575886			−0.287943	−	0.957648i	$-0.592971\pi$
$617$	−8826.00			−0.575886			−0.287943	+	0.957648i	$0.592971\pi$
$618$	−10752.0	+	18623.0i	−0.699853	+	1.21218i
$619$	−10610.0	−	18377.1i	−0.688937	−	1.19327i	−0.972182	−	0.234226i	$-0.924744\pi$
$619$	−10610.0	−	18377.1i	−0.688937	−	1.19327i	0.283245	−	0.959047i	$-0.408589\pi$
$620$	−768.000	−	1330.22i	−0.0497478	−	0.0861657i
$621$	−567.000	+	982.073i	−0.0366392	+	0.0634609i
$622$	36528.0			2.35473
$623$		0			0
$624$	−11904.0			−0.763688
$625$	−4940.50	+	8557.20i	−0.316192	+	0.547661i
$626$	18764.0	+	32500.2i	1.19802	+	2.07503i
$627$	9300.00	+	16108.1i	0.592354	+	1.02599i
$628$	1064.00	−	1842.90i	0.0676086	−	0.117102i
$629$	−20664.0			−1.30990
$630$		0			0
$631$	−3268.00			−0.206176			−0.103088	−	0.994672i	$-0.532872\pi$
$631$	−3268.00			−0.206176			−0.103088	+	0.994672i	$0.532872\pi$
$632$		0			0
$633$	−1002.00	−	1735.51i	−0.0629162	−	0.108974i
$634$	−6228.00	−	10787.2i	−0.390135	−	0.675733i
$635$	1608.00	−	2785.14i	0.100491	−	0.174055i
$636$	−6192.00			−0.386052
$637$		0			0
$638$	−2480.00			−0.153894
$639$	3051.00	−	5284.49i	0.188882	−	0.327153i
$640$		0			0
$641$	−6531.00	−	11312.0i	−0.402432	−	0.697033i	0.591587	−	0.806241i	$-0.298502\pi$
$641$	−6531.00	−	11312.0i	−0.402432	−	0.697033i	−0.994019	+	0.109208i	$0.965168\pi$
$642$	−11436.0	+	19807.7i	−0.703026	+	1.21768i
$643$	−28012.0			−1.71802			−0.859009	−	0.511961i	$-0.828919\pi$
$643$	−28012.0			−1.71802			−0.859009	+	0.511961i	$0.828919\pi$
$644$		0			0
$645$	816.000			0.0498139
$646$	−16800.0	+	29098.5i	−1.02320	+	1.77223i
$647$	−1922.00	−	3329.00i	−0.116788	−	0.202282i	0.801705	−	0.597720i	$-0.203926\pi$
$647$	−1922.00	−	3329.00i	−0.116788	−	0.202282i	−0.918493	+	0.395437i	$0.870593\pi$
$648$		0			0
$649$	−3720.00	+	6443.23i	−0.224997	+	0.389705i
$650$	27032.0			1.63120
$651$		0			0
$652$	−2176.00			−0.130704
$653$	14241.0	−	24666.1i	0.853436	−	1.47819i	−0.0246533	−	0.999696i	$-0.507848\pi$
$653$	14241.0	−	24666.1i	0.853436	−	1.47819i	0.878089	−	0.478498i	$-0.158818\pi$
$654$	−540.000	−	935.307i	−0.0322870	−	0.0559227i
$655$	1624.00	+	2812.85i	0.0968778	+	0.167797i
$656$	−7936.00	+	13745.6i	−0.472330	+	0.818100i
$657$	−5778.00			−0.343107
$658$		0			0
$659$	−9330.00			−0.551510			−0.275755	−	0.961228i	$-0.588928\pi$
$659$	−9330.00			−0.551510			−0.275755	+	0.961228i	$0.588928\pi$
$660$	−2976.00	+	5154.58i	−0.175516	+	0.304003i
$661$	−4391.00	−	7605.44i	−0.258381	−	0.447530i	0.707427	−	0.706786i	$-0.249856\pi$
$661$	−4391.00	−	7605.44i	−0.258381	−	0.447530i	−0.965808	+	0.259257i	$0.916522\pi$
$662$	−3064.00	−	5307.00i	−0.179888	−	0.311575i
$663$	−7812.00	+	13530.8i	−0.457606	+	0.792597i
$664$		0			0
$665$		0			0
$666$	−8856.00			−0.515260
$667$	−210.000	+	363.731i	−0.0121908	+	0.0211150i
$668$	7504.00	+	12997.3i	0.434638	+	0.752816i
$669$	−2748.00	−	4759.68i	−0.158810	−	0.275067i
$670$	7232.00	−	12526.2i	0.417010	−	0.722282i
$671$	38564.0			2.21870
$672$		0			0
$673$	−10562.0			−0.604956			−0.302478	−	0.953156i	$-0.597814\pi$
$673$	−10562.0			−0.604956			−0.302478	+	0.953156i	$0.597814\pi$
$674$	8332.00	−	14431.4i	0.476167	−	0.824746i
$675$	−1471.50	−	2548.71i	−0.0839082	−	0.145333i
$676$	−6588.00	−	11410.8i	−0.374829	−	0.649223i
$677$	13008.0	−	22530.5i	0.738461	−	1.27905i	−0.214727	−	0.976674i	$-0.568886\pi$
$677$	13008.0	−	22530.5i	0.738461	−	1.27905i	0.953188	−	0.302378i	$-0.0977804\pi$
$678$	−5496.00			−0.311317
$679$		0			0
$680$		0			0
$681$	7416.00	−	12844.9i	0.417301	−	0.722786i
$682$	5952.00	+	10309.2i	0.334185	+	0.578825i
$683$	−4449.00	−	7705.89i	−0.249248	−	0.431710i	0.714070	−	0.700075i	$-0.246850\pi$
$683$	−4449.00	−	7705.89i	−0.249248	−	0.431710i	−0.963317	+	0.268365i	$0.913517\pi$
$684$	−3600.00	+	6235.38i	−0.201242	+	0.348561i
$685$	−1656.00			−0.0923686
$686$		0			0
$687$	16410.0			0.911325
$688$	2176.00	−	3768.94i	0.120580	−	0.208851i
$689$	7998.00	+	13852.9i	0.442234	+	0.765973i
$690$	1008.00	+	1745.91i	0.0556144	+	0.0963269i
$691$	−15286.0	+	26476.1i	−0.841544	+	1.45760i	0.0470452	+	0.998893i	$0.485020\pi$
$691$	−15286.0	+	26476.1i	−0.841544	+	1.45760i	−0.888589	+	0.458704i	$0.848314\pi$
$692$	−1216.00			−0.0667997
$693$		0			0
$694$	−45464.0			−2.48673
$695$	−3240.00	+	5611.84i	−0.176835	+	0.306287i
$696$		0			0
$697$	10416.0	+	18041.0i	0.566046	+	0.980421i
$698$	−18620.0	+	32250.8i	−1.00971	+	1.74887i
$699$	8406.00			0.454856
$700$		0			0
$701$	−30618.0			−1.64968			−0.824840	−	0.565366i	$-0.808735\pi$
$701$	−30618.0			−1.64968			−0.824840	+	0.565366i	$0.808735\pi$
$702$	−3348.00	+	5798.91i	−0.180003	+	0.311774i
$703$	12300.0	+	21304.2i	0.659891	+	1.14296i
$704$	15872.0	+	27491.1i	0.849714	+	1.47175i
$705$	−1944.00	+	3367.11i	−0.103851	+	0.179876i
$706$	−34288.0			−1.82783
$707$		0			0
$708$	−2880.00			−0.152877
$709$	4065.00	−	7040.79i	0.215323	−	0.372951i	−0.738049	−	0.674747i	$-0.764253\pi$
$709$	4065.00	−	7040.79i	0.215323	−	0.372951i	0.953373	+	0.301796i	$0.0975861\pi$
$710$	−5424.00	−	9394.64i	−0.286703	−	0.496584i
$711$	−3330.00	−	5767.73i	−0.175647	−	0.304229i
$712$		0			0
$713$	2016.00			0.105890
$714$		0			0
$715$	15376.0			0.804237
$716$	−2440.00	+	4226.20i	−0.127356	+	0.220588i
$717$	−1755.00	−	3039.75i	−0.0914110	−	0.158328i
$718$	9580.00	+	16593.0i	0.497942	+	0.862461i
$719$	13920.0	−	24110.1i	0.722014	−	1.25057i	−0.238177	−	0.971222i	$-0.576550\pi$
$719$	13920.0	−	24110.1i	0.722014	−	1.25057i	0.960191	−	0.279344i	$-0.0901169\pi$
$720$	2304.00			0.119257
$721$		0			0
$722$	12564.0			0.647623
$723$	−3507.00	+	6074.30i	−0.180397	+	0.312456i
$724$	−4168.00	−	7219.19i	−0.213954	−	0.370579i
$725$	−545.000	−	943.968i	−0.0279183	−	0.0483560i
$726$	15078.0	−	26115.9i	0.770795	−	1.33506i
$727$	14624.0			0.746044			0.373022	−	0.927822i	$-0.378322\pi$
$727$	14624.0			0.746044			0.373022	+	0.927822i	$0.378322\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−5136.00	+	8895.81i	−0.260400	+	0.451026i
$731$	−2856.00	−	4946.74i	−0.144505	−	0.250290i
$732$	7464.00	+	12928.0i	0.376882	+	0.652778i
$733$	10431.0	−	18067.0i	0.525618	−	0.910397i	−0.473937	−	0.880559i	$-0.657168\pi$
$733$	10431.0	−	18067.0i	0.525618	−	0.910397i	0.999555	−	0.0298378i	$-0.00949909\pi$
$734$	21696.0			1.09103
$735$		0			0
$736$	10752.0			0.538484
$737$	−28024.0	+	48539.0i	−1.40065	+	2.42599i
$738$	4464.00	+	7731.87i	0.222659	+	0.385656i
$739$	6960.00	+	12055.1i	0.346452	+	0.600072i	0.985616	−	0.168998i	$-0.0540532\pi$
$739$	6960.00	+	12055.1i	0.346452	+	0.600072i	−0.639165	+	0.769070i	$0.720720\pi$
$740$	−3936.00	+	6817.35i	−0.195527	+	0.338663i
$741$	18600.0			0.922116
$742$		0			0
$743$	25578.0			1.26294			0.631471	−	0.775400i	$-0.282452\pi$
$743$	25578.0			1.26294			0.631471	+	0.775400i	$0.282452\pi$
$744$		0			0
$745$	4740.00	+	8209.92i	0.233101	+	0.403743i
$746$	−3676.00	−	6367.02i	−0.180413	−	0.312484i
$747$	−2106.00	+	3647.70i	−0.103152	+	0.178664i
$748$	41664.0			2.03661
$749$		0			0
$750$	−11232.0			−0.546846
$751$	−16736.0	+	28987.6i	−0.813189	+	1.40849i	0.0974312	+	0.995242i	$0.468937\pi$
$751$	−16736.0	+	28987.6i	−0.813189	+	1.40849i	−0.910621	+	0.413243i	$0.864396\pi$
$752$	10368.0	+	17957.9i	0.502769	+	0.870821i
$753$	4188.00	+	7253.83i	0.202682	+	0.351055i
$754$	−1240.00	+	2147.74i	−0.0598914	+	0.103735i
$755$	2272.00			0.109519
$756$		0			0
$757$	25934.0			1.24516			0.622581	−	0.782556i	$-0.286084\pi$
$757$	25934.0			1.24516			0.622581	+	0.782556i	$0.286084\pi$
$758$	8520.00	−	14757.1i	0.408259	−	0.707125i
$759$	−3906.00	−	6765.39i	−0.186797	−	0.323542i
$760$		0			0
$761$	−13476.0	+	23341.1i	−0.641925	+	1.11185i	0.343078	+	0.939307i	$0.388530\pi$
$761$	−13476.0	+	23341.1i	−0.641925	+	1.11185i	−0.985003	+	0.172539i	$0.944803\pi$
$762$	−9648.00			−0.458675
$763$		0			0
$764$	−16304.0			−0.772065
$765$	1512.00	−	2618.86i	0.0714594	−	0.123771i
$766$	−18096.0	−	31343.2i	−0.853571	−	1.47843i
$767$	3720.00	+	6443.23i	0.175126	+	0.303327i
$768$	6144.00	−	10641.7i	0.288675	−	0.500000i
$769$	23450.0			1.09965			0.549824	−	0.835281i	$-0.314695\pi$
$769$	23450.0			1.09965			0.549824	+	0.835281i	$0.314695\pi$
$770$		0			0
$771$	−21072.0			−0.984293
$772$	10408.0	−	18027.2i	0.485223	−	0.840431i
$773$	−19784.0	−	34266.9i	−0.920545	−	1.59443i	−0.798574	−	0.601896i	$-0.794412\pi$
$773$	−19784.0	−	34266.9i	−0.920545	−	1.59443i	−0.121970	−	0.992534i	$-0.538921\pi$
$774$	−1224.00	−	2120.03i	−0.0568421	−	0.0984534i
$775$	−2616.00	+	4531.04i	−0.121251	+	0.210013i
$776$		0			0
$777$		0			0
$778$	−45960.0			−2.11793
$779$	12400.0	−	21477.4i	0.570316	−	0.987816i
$780$	2976.00	+	5154.58i	0.136613	+	0.236620i
$781$	21018.0	+	36404.2i	0.962975	+	1.66792i
$782$	7056.00	−	12221.4i	0.322662	−	0.558868i
$783$	270.000			0.0123231
$784$		0			0
$785$	1064.00			0.0483768
$786$	4872.00	−	8438.55i	0.221092	−	0.382943i
$787$	6178.00	+	10700.6i	0.279825	+	0.484670i	0.971341	−	0.237690i	$-0.0763904\pi$
$787$	6178.00	+	10700.6i	0.279825	+	0.484670i	−0.691516	+	0.722361i	$0.743057\pi$
$788$	−9416.00	−	16309.0i	−0.425674	−	0.737289i
$789$	3657.00	−	6334.11i	0.165010	−	0.285805i
$790$	−11840.0			−0.533226
$791$		0			0
$792$		0			0
$793$	19282.0	−	33397.4i	0.863460	−	1.49556i
$794$	3732.00	+	6464.01i	0.166806	+	0.288916i
$795$	−1548.00	−	2681.21i	−0.0690590	−	0.119614i
$796$	−6720.00	+	11639.4i	−0.299226	+	0.518275i
$797$	−21736.0			−0.966033			−0.483017	−	0.875611i	$-0.660459\pi$
$797$	−21736.0			−0.966033			−0.483017	+	0.875611i	$0.660459\pi$
$798$		0			0
$799$	27216.0			1.20505
$800$	−13952.0	+	24165.6i	−0.616597	+	1.06798i
$801$	−900.000	−	1558.85i	−0.0397003	−	0.0687629i
$802$	−27324.0	−	47326.6i	−1.20305	−	2.08374i
$803$	19902.0	−	34471.3i	0.874628	−	1.51490i
$804$	−21696.0			−0.951690
$805$		0			0
$806$	11904.0			0.520224
$807$	−10170.0	+	17615.0i	−0.443620	+	0.768372i
$808$		0			0
$809$	19155.0	+	33177.4i	0.832452	+	1.44185i	0.896088	+	0.443877i	$0.146397\pi$
$809$	19155.0	+	33177.4i	0.832452	+	1.44185i	−0.0636356	+	0.997973i	$0.520270\pi$
$810$	648.000	−	1122.37i	0.0281091	−	0.0486864i
$811$	2132.00			0.0923115			0.0461558	−	0.998934i	$-0.485303\pi$
$811$	2132.00			0.0923115			0.0461558	+	0.998934i	$0.485303\pi$
$812$		0			0
$813$	5784.00			0.249513
$814$	30504.0	−	52834.5i	1.31347	−	2.27500i
$815$	−544.000	−	942.236i	−0.0233810	−	0.0404970i
$816$	−8064.00	−	13967.3i	−0.345952	−	0.599206i
$817$	−3400.00	+	5888.97i	−0.145595	+	0.252178i
$818$	−52840.0			−2.25857
$819$		0			0
$820$	7936.00			0.337972
$821$	−2501.00	+	4331.86i	−0.106316	+	0.184145i	−0.914275	−	0.405094i	$-0.867239\pi$
$821$	−2501.00	+	4331.86i	−0.106316	+	0.184145i	0.807959	+	0.589239i	$0.200572\pi$
$822$	2484.00	+	4302.41i	0.105401	+	0.182560i
$823$	1806.00	+	3128.08i	0.0764923	+	0.132489i	0.901734	−	0.432291i	$-0.142295\pi$
$823$	1806.00	+	3128.08i	0.0764923	+	0.132489i	−0.825242	+	0.564779i	$0.808961\pi$
$824$		0			0
$825$	20274.0			0.855576
$826$		0			0
$827$	−27666.0			−1.16329			−0.581645	−	0.813443i	$-0.697591\pi$
$827$	−27666.0			−1.16329			−0.581645	+	0.813443i	$0.697591\pi$
$828$	1512.00	−	2618.86i	0.0634609	−	0.109918i
$829$	−6445.00	−	11163.1i	−0.270017	−	0.467683i	0.698849	−	0.715269i	$-0.253696\pi$
$829$	−6445.00	−	11163.1i	−0.270017	−	0.467683i	−0.968866	+	0.247586i	$0.920363\pi$
$830$	3744.00	+	6484.80i	0.156574	+	0.271194i
$831$	8331.00	−	14429.7i	0.347773	−	0.602360i
$832$	31744.0			1.32275
$833$		0			0
$834$	19440.0			0.807137
$835$	−3752.00	+	6498.65i	−0.155501	+	0.269336i
$836$	−24800.0	−	42954.9i	−1.02599	−	1.77706i
$837$	−648.000	−	1122.37i	−0.0267600	−	0.0463498i
$838$	−13920.0	+	24110.1i	−0.573817	+	0.993880i
$839$	−9340.00			−0.384330			−0.192165	−	0.981363i	$-0.561551\pi$
$839$	−9340.00			−0.384330			−0.192165	+	0.981363i	$0.561551\pi$
$840$		0			0
$841$	−24289.0			−0.995900
$842$	−16324.0	+	28274.0i	−0.668126	+	1.15723i
$843$	2913.00	+	5045.46i	0.119014	+	0.206139i
$844$	2672.00	+	4628.04i	0.108974	+	0.188748i
$845$	3294.00	−	5705.38i	0.134103	−	0.232273i
$846$	11664.0			0.474015
$847$		0			0
$848$	−16512.0			−0.668661
$849$	7242.00	−	12543.5i	0.292750	−	0.507058i
$850$	18312.0	+	31717.3i	0.738937	+	1.27988i
$851$	−5166.00	−	8947.77i	−0.208094	−	0.360430i
$852$	−8136.00	+	14092.0i	−0.327153	+	0.566646i
$853$	−33082.0			−1.32791			−0.663954	−	0.747773i	$-0.731123\pi$
$853$	−33082.0			−1.32791			−0.663954	+	0.747773i	$0.731123\pi$
$854$		0			0
$855$	−3600.00			−0.143997
$856$		0			0
$857$	−3772.00	−	6533.30i	−0.150349	−	0.260412i	0.781007	−	0.624523i	$-0.214706\pi$
$857$	−3772.00	−	6533.30i	−0.150349	−	0.260412i	−0.931356	+	0.364110i	$0.881373\pi$
$858$	−23064.0	−	39948.0i	−0.917706	−	1.58951i
$859$	−4090.00	+	7084.09i	−0.162455	+	0.281381i	−0.935749	−	0.352668i	$-0.885275\pi$
$859$	−4090.00	+	7084.09i	−0.162455	+	0.281381i	0.773293	+	0.634048i	$0.218608\pi$
$860$	−2176.00			−0.0862802
$861$		0			0
$862$	66408.0			2.62397
$863$	−5259.00	+	9108.86i	−0.207437	+	0.359292i	−0.950907	−	0.309478i	$-0.899846\pi$
$863$	−5259.00	+	9108.86i	−0.207437	+	0.359292i	0.743469	+	0.668770i	$0.233179\pi$
$864$	−3456.00	−	5985.97i	−0.136083	−	0.235702i
$865$	−304.000	−	526.543i	−0.0119495	−	0.0206971i
$866$	−15476.0	+	26805.2i	−0.607270	+	1.05182i
$867$	−6429.00			−0.251834
$868$		0			0
$869$	45880.0			1.79099
$870$	240.000	−	415.692i	0.00935260	−	0.0161992i
$871$	28024.0	+	48539.0i	1.09019	+	1.88827i
$872$		0			0
$873$	5697.00	−	9867.49i	0.220864	−	0.382548i
$874$	−16800.0			−0.650193
$875$		0			0
$876$	15408.0			0.594279
$877$	−7067.00	+	12240.4i	−0.272104	+	0.471299i	−0.969401	−	0.245484i	$-0.921053\pi$
$877$	−7067.00	+	12240.4i	−0.272104	+	0.471299i	0.697296	+	0.716783i	$0.254386\pi$
$878$	1680.00	+	2909.85i	0.0645755	+	0.111848i
$879$	−9228.00	−	15983.4i	−0.354099	−	0.613317i
$880$	−7936.00	+	13745.6i	−0.304003	+	0.526548i
$881$	6492.00			0.248265			0.124132	−	0.992266i	$-0.460385\pi$
$881$	6492.00			0.248265			0.124132	+	0.992266i	$0.460385\pi$
$882$		0			0
$883$	38228.0			1.45694			0.728468	−	0.685080i	$-0.240233\pi$
$883$	38228.0			1.45694			0.728468	+	0.685080i	$0.240233\pi$
$884$	20832.0	−	36082.1i	0.792597	−	1.37282i
$885$	−720.000	−	1247.08i	−0.0273475	−	0.0473673i
$886$	−13236.0	−	22925.4i	−0.501887	−	0.869294i
$887$	21538.0	−	37304.9i	0.815305	−	1.41215i	−0.0938042	−	0.995591i	$-0.529903\pi$
$887$	21538.0	−	37304.9i	0.815305	−	1.41215i	0.909109	−	0.416558i	$-0.136764\pi$
$888$		0			0
$889$		0			0
$890$	−3200.00			−0.120522
$891$	−2511.00	+	4349.18i	−0.0944126	+	0.163527i
$892$	7328.00	+	12692.5i	0.275067	+	0.476430i
$893$	−16200.0	−	28059.2i	−0.607069	−	1.05147i
$894$	14220.0	−	24629.8i	0.531978	−	0.921412i
$895$	−2440.00			−0.0911287
$896$		0			0
$897$	−7812.00			−0.290786
$898$	−6180.00	+	10704.1i	−0.229654	+	0.397772i
$899$	−240.000	−	415.692i	−0.00890372	−	0.0154217i
$900$	3924.00	+	6796.57i	0.145333	+	0.251725i
$901$	−10836.0	+	18768.5i	−0.400665	+	0.693973i
$902$	−61504.0			−2.27035
$903$		0			0
$904$		0			0
$905$	2084.00	−	3609.59i	0.0765464	−	0.132582i
$906$	−3408.00	−	5902.83i	−0.124970	−	0.216455i
$907$	16118.0	+	27917.2i	0.590065	+	1.02202i	0.994223	+	0.107334i	$0.0342314\pi$
$907$	16118.0	+	27917.2i	0.590065	+	1.02202i	−0.404158	+	0.914689i	$0.632435\pi$
$908$	−19776.0	+	34253.0i	−0.722786	+	1.25190i
$909$	2088.00			0.0761877
$910$		0			0
$911$	−46518.0			−1.69178			−0.845889	−	0.533359i	$-0.820930\pi$
$911$	−46518.0			−1.69178			−0.845889	+	0.533359i	$0.820930\pi$
$912$	−9600.00	+	16627.7i	−0.348561	+	0.603726i
$913$	−14508.0	−	25128.6i	−0.525898	−	0.910882i
$914$	−11828.0	−	20486.7i	−0.428048	−	0.741400i
$915$	−3732.00	+	6464.01i	−0.134837	+	0.233545i
$916$	−43760.0			−1.57846
$917$		0			0
$918$	−9072.00			−0.326166
$919$	−8920.00	+	15449.9i	−0.320178	+	0.554565i	−0.980525	−	0.196396i	$-0.937076\pi$
$919$	−8920.00	+	15449.9i	−0.320178	+	0.554565i	0.660347	+	0.750961i	$0.270409\pi$
$920$		0			0
$921$	8826.00	+	15287.1i	0.315773	+	0.546934i
$922$	31936.0	−	55314.8i	1.14073	−	1.97581i
$923$	42036.0			1.49906
$924$		0			0
$925$	26814.0			0.953123
$926$	2344.00	−	4059.93i	0.0831843	−	0.144079i
$927$	8064.00	+	13967.3i	0.285714	+	0.494870i
$928$	−1280.00	−	2217.03i	−0.0452781	−	0.0784239i
$929$	−3500.00	+	6062.18i	−0.123607	+	0.214094i	−0.921188	−	0.389118i	$-0.872780\pi$
$929$	−3500.00	+	6062.18i	−0.123607	+	0.214094i	0.797580	+	0.603213i	$0.206113\pi$
$930$	−2304.00			−0.0812378
$931$		0			0
$932$	−22416.0			−0.787833
$933$	13698.0	−	23725.6i	0.480656	−	0.832521i
$934$	−10608.0	−	18373.6i	−0.371632	−	0.643686i
$935$	10416.0	+	18041.0i	0.364320	+	0.631022i
$936$		0			0
$937$	36114.0			1.25912			0.629559	−	0.776953i	$-0.283236\pi$
$937$	36114.0			1.25912			0.629559	+	0.776953i	$0.283236\pi$
$938$		0			0
$939$	28146.0			0.978179
$940$	5184.00	−	8978.95i	0.179876	−	0.311554i
$941$	2374.00	+	4111.89i	0.0822425	+	0.142448i	0.904213	−	0.427082i	$-0.140458\pi$
$941$	2374.00	+	4111.89i	0.0822425	+	0.142448i	−0.821970	+	0.569530i	$0.807125\pi$
$942$	−1596.00	−	2764.35i	−0.0552022	−	0.0956130i
$943$	−5208.00	+	9020.52i	−0.179847	+	0.311504i
$944$	−7680.00			−0.264791
$945$		0			0
$946$	16864.0			0.579594
$947$	−21347.0	+	36974.1i	−0.732507	+	1.26874i	0.223301	+	0.974749i	$0.428317\pi$
$947$	−21347.0	+	36974.1i	−0.732507	+	1.26874i	−0.955808	+	0.293990i	$0.905017\pi$
$948$	8880.00	+	15380.6i	0.304229	+	0.526940i
$949$	−19902.0	−	34471.3i	−0.680765	−	1.17912i
$950$	21800.0	−	37758.7i	0.744511	−	1.28953i
$951$	−9342.00			−0.318544
$952$		0			0
$953$	−16742.0			−0.569073			−0.284537	−	0.958665i	$-0.591840\pi$
$953$	−16742.0			−0.569073			−0.284537	+	0.958665i	$0.591840\pi$
$954$	−4644.00	+	8043.64i	−0.157605	+	0.272980i
$955$	−4076.00	−	7059.84i	−0.138111	−	0.239216i
$956$	4680.00	+	8106.00i	0.158328	+	0.274233i
$957$	−930.000	+	1610.81i	−0.0314134	+	0.0544096i
$958$	22960.0			0.774326
$959$		0			0
$960$	−6144.00			−0.206559
$961$	13743.5	−	23804.4i	0.461331	−	0.799048i
$962$	−30504.0	−	52834.5i	−1.02234	−	1.77074i
$963$	8577.00	+	14855.8i	0.287009	+	0.497115i
$964$	9352.00	−	16198.1i	0.312456	−	0.541190i
$965$	10408.0			0.347197
$966$		0			0
$967$	−9956.00			−0.331089			−0.165545	−	0.986202i	$-0.552938\pi$
$967$	−9956.00			−0.331089			−0.165545	+	0.986202i	$0.552938\pi$
$968$		0			0
$969$	12600.0	+	21823.8i	0.417720	+	0.723512i
$970$	−10128.0	−	17542.2i	−0.335248	−	0.580666i
$971$	13194.0	−	22852.7i	0.436061	−	0.755280i	−0.561320	−	0.827599i	$-0.689706\pi$
$971$	13194.0	−	22852.7i	0.436061	−	0.755280i	0.997382	+	0.0723182i	$0.0230397\pi$
$972$	−1944.00			−0.0641500
$973$		0			0
$974$	35776.0			1.17694
$975$	10137.0	−	17557.8i	0.332968	−	0.576718i
$976$	19904.0	+	34474.7i	0.652778	+	1.13064i
$977$	393.000	+	680.696i	0.0128692	+	0.0222901i	0.872388	−	0.488814i	$-0.162570\pi$
$977$	393.000	+	680.696i	0.0128692	+	0.0222901i	−0.859519	+	0.511104i	$0.829237\pi$
$978$	−1632.00	+	2826.71i	−0.0533595	+	0.0924214i
$979$	12400.0			0.404807
$980$		0			0
$981$	−810.000			−0.0263622
$982$	11116.0	−	19253.5i	0.361228	−	0.625665i
$983$	−25944.0	−	44936.3i	−0.841796	−	1.45803i	−0.888375	−	0.459118i	$-0.848165\pi$
$983$	−25944.0	−	44936.3i	−0.841796	−	1.45803i	0.0465796	−	0.998915i	$-0.485168\pi$
$984$		0			0
$985$	4708.00	−	8154.50i	0.152294	−	0.263781i
$986$	−3360.00			−0.108524
$987$		0			0
$988$	−49600.0			−1.59715
$989$	1428.00	−	2473.37i	0.0459128	−	0.0795233i
$990$	4464.00	+	7731.87i	0.143308	+	0.248217i
$991$	25964.0	+	44971.0i	0.832264	+	1.44152i	0.896239	+	0.443572i	$0.146289\pi$
$991$	25964.0	+	44971.0i	0.832264	+	1.44152i	−0.0639747	+	0.997952i	$0.520378\pi$
$992$	−6144.00	+	10641.7i	−0.196645	+	0.340600i
$993$	−4596.00			−0.146878
$994$		0			0
$995$	−6720.00			−0.214109
$996$	5616.00	−	9727.20i	0.178664	−	0.309456i
$997$	193.000	+	334.286i	0.00613076	+	0.0106188i	0.869075	−	0.494681i	$-0.164715\pi$
$997$	193.000	+	334.286i	0.00613076	+	0.0106188i	−0.862944	+	0.505300i	$0.831382\pi$
$998$	39640.0	+	68658.5i	1.25730	+	2.17770i
$999$	−3321.00	+	5752.14i	−0.105177	+	0.182172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.c.79.1		2
3.2	odd	2		441.4.e.m.226.1		2
7.2	even	3		21.4.a.b.1.1	✓	1
7.3	odd	6		147.4.e.b.67.1		2
7.4	even	3	inner	147.4.e.c.67.1		2
7.5	odd	6		147.4.a.g.1.1		1
7.6	odd	2		147.4.e.b.79.1		2
21.2	odd	6		63.4.a.a.1.1		1
21.5	even	6		441.4.a.b.1.1		1
21.11	odd	6		441.4.e.m.361.1		2
21.17	even	6		441.4.e.n.361.1		2
21.20	even	2		441.4.e.n.226.1		2
28.19	even	6		2352.4.a.l.1.1		1
28.23	odd	6		336.4.a.h.1.1		1
35.2	odd	12		525.4.d.b.274.2		2
35.9	even	6		525.4.a.b.1.1		1
35.23	odd	12		525.4.d.b.274.1		2
56.37	even	6		1344.4.a.w.1.1		1
56.51	odd	6		1344.4.a.i.1.1		1
84.23	even	6		1008.4.a.m.1.1		1
105.44	odd	6		1575.4.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.b.1.1	✓	1	7.2	even	3
63.4.a.a.1.1		1	21.2	odd	6
147.4.a.g.1.1		1	7.5	odd	6
147.4.e.b.67.1		2	7.3	odd	6
147.4.e.b.79.1		2	7.6	odd	2
147.4.e.c.67.1		2	7.4	even	3	inner
147.4.e.c.79.1		2	1.1	even	1	trivial
336.4.a.h.1.1		1	28.23	odd	6
441.4.a.b.1.1		1	21.5	even	6
441.4.e.m.226.1		2	3.2	odd	2
441.4.e.m.361.1		2	21.11	odd	6
441.4.e.n.226.1		2	21.20	even	2
441.4.e.n.361.1		2	21.17	even	6
525.4.a.b.1.1		1	35.9	even	6
525.4.d.b.274.1		2	35.23	odd	12
525.4.d.b.274.2		2	35.2	odd	12
1008.4.a.m.1.1		1	84.23	even	6
1344.4.a.i.1.1		1	56.51	odd	6
1344.4.a.w.1.1		1	56.37	even	6
1575.4.a.k.1.1		1	105.44	odd	6
2352.4.a.l.1.1		1	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)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} -12.0000 q^{6} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} -12.0000 q^{6} +(-4.50000 + 7.79423i) q^{9} +(8.00000 + 13.8564i) q^{10} +(-31.0000 - 53.6936i) q^{11} +(12.0000 - 20.7846i) q^{12} -62.0000 q^{13} +12.0000 q^{15} +(32.0000 - 55.4256i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(-18.0000 - 31.1769i) q^{18} +(-50.0000 + 86.6025i) q^{19} -32.0000 q^{20} +248.000 q^{22} +(21.0000 - 36.3731i) q^{23} +(54.5000 + 94.3968i) q^{25} +(124.000 - 214.774i) q^{26} -27.0000 q^{27} -10.0000 q^{29} +(-24.0000 + 41.5692i) q^{30} +(24.0000 + 41.5692i) q^{31} +(128.000 + 221.703i) q^{32} +(93.0000 - 161.081i) q^{33} +336.000 q^{34} +72.0000 q^{36} +(123.000 - 213.042i) q^{37} +(-200.000 - 346.410i) q^{38} +(-93.0000 - 161.081i) q^{39} -248.000 q^{41} +68.0000 q^{43} +(-248.000 + 429.549i) q^{44} +(18.0000 + 31.1769i) q^{45} +(84.0000 + 145.492i) q^{46} +(-162.000 + 280.592i) q^{47} +192.000 q^{48} -436.000 q^{50} +(126.000 - 218.238i) q^{51} +(248.000 + 429.549i) q^{52} +(-129.000 - 223.435i) q^{53} +(54.0000 - 93.5307i) q^{54} -248.000 q^{55} -300.000 q^{57} +(20.0000 - 34.6410i) q^{58} +(-60.0000 - 103.923i) q^{59} +(-48.0000 - 83.1384i) q^{60} +(-311.000 + 538.668i) q^{61} -192.000 q^{62} -512.000 q^{64} +(-124.000 + 214.774i) q^{65} +(372.000 + 644.323i) q^{66} +(-452.000 - 782.887i) q^{67} +(-336.000 + 581.969i) q^{68} +126.000 q^{69} -678.000 q^{71} +(321.000 + 555.988i) q^{73} +(492.000 + 852.169i) q^{74} +(-163.500 + 283.190i) q^{75} +800.000 q^{76} +744.000 q^{78} +(-370.000 + 640.859i) q^{79} +(-128.000 - 221.703i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(496.000 - 859.097i) q^{82} +468.000 q^{83} -336.000 q^{85} +(-136.000 + 235.559i) q^{86} +(-15.0000 - 25.9808i) q^{87} +(-100.000 + 173.205i) q^{89} -144.000 q^{90} -336.000 q^{92} +(-72.0000 + 124.708i) q^{93} +(-648.000 - 1122.37i) q^{94} +(200.000 + 346.410i) q^{95} +(-384.000 + 665.108i) q^{96} -1266.00 q^{97} +558.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 3 q^{3} - 8 q^{4} + 4 q^{5} - 24 q^{6} - 9 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 + 3 * q^3 - 8 * q^4 + 4 * q^5 - 24 * q^6 - 9 * q^9	\( 2 q - 4 q^{2} + 3 q^{3} - 8 q^{4} + 4 q^{5} - 24 q^{6} - 9 q^{9} + 16 q^{10} - 62 q^{11} + 24 q^{12} - 124 q^{13} + 24 q^{15} + 64 q^{16} - 84 q^{17} - 36 q^{18} - 100 q^{19} - 64 q^{20} + 496 q^{22} + 42 q^{23} + 109 q^{25} + 248 q^{26} - 54 q^{27} - 20 q^{29} - 48 q^{30} + 48 q^{31} + 256 q^{32} + 186 q^{33} + 672 q^{34} + 144 q^{36} + 246 q^{37} - 400 q^{38} - 186 q^{39} - 496 q^{41} + 136 q^{43} - 496 q^{44} + 36 q^{45} + 168 q^{46} - 324 q^{47} + 384 q^{48} - 872 q^{50} + 252 q^{51} + 496 q^{52} - 258 q^{53} + 108 q^{54} - 496 q^{55} - 600 q^{57} + 40 q^{58} - 120 q^{59} - 96 q^{60} - 622 q^{61} - 384 q^{62} - 1024 q^{64} - 248 q^{65} + 744 q^{66} - 904 q^{67} - 672 q^{68} + 252 q^{69} - 1356 q^{71} + 642 q^{73} + 984 q^{74} - 327 q^{75} + 1600 q^{76} + 1488 q^{78} - 740 q^{79} - 256 q^{80} - 81 q^{81} + 992 q^{82} + 936 q^{83} - 672 q^{85} - 272 q^{86} - 30 q^{87} - 200 q^{89} - 288 q^{90} - 672 q^{92} - 144 q^{93} - 1296 q^{94} + 400 q^{95} - 768 q^{96} - 2532 q^{97} + 1116 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 3 * q^3 - 8 * q^4 + 4 * q^5 - 24 * q^6 - 9 * q^9 + 16 * q^10 - 62 * q^11 + 24 * q^12 - 124 * q^13 + 24 * q^15 + 64 * q^16 - 84 * q^17 - 36 * q^18 - 100 * q^19 - 64 * q^20 + 496 * q^22 + 42 * q^23 + 109 * q^25 + 248 * q^26 - 54 * q^27 - 20 * q^29 - 48 * q^30 + 48 * q^31 + 256 * q^32 + 186 * q^33 + 672 * q^34 + 144 * q^36 + 246 * q^37 - 400 * q^38 - 186 * q^39 - 496 * q^41 + 136 * q^43 - 496 * q^44 + 36 * q^45 + 168 * q^46 - 324 * q^47 + 384 * q^48 - 872 * q^50 + 252 * q^51 + 496 * q^52 - 258 * q^53 + 108 * q^54 - 496 * q^55 - 600 * q^57 + 40 * q^58 - 120 * q^59 - 96 * q^60 - 622 * q^61 - 384 * q^62 - 1024 * q^64 - 248 * q^65 + 744 * q^66 - 904 * q^67 - 672 * q^68 + 252 * q^69 - 1356 * q^71 + 642 * q^73 + 984 * q^74 - 327 * q^75 + 1600 * q^76 + 1488 * q^78 - 740 * q^79 - 256 * q^80 - 81 * q^81 + 992 * q^82 + 936 * q^83 - 672 * q^85 - 272 * q^86 - 30 * q^87 - 200 * q^89 - 288 * q^90 - 672 * q^92 - 144 * q^93 - 1296 * q^94 + 400 * q^95 - 768 * q^96 - 2532 * q^97 + 1116 * q^99

Introduction

L-functions

Modular forms

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