LMFDB - Embedded newform 225.3.j.b.101.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,3,Mod(101,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.101"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Root			$3.73655i$ of defining polynomial
Character	$\chi$	$=$	225.101
Dual form			225.3.j.b.176.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23594 + 1.86827i) q^{2} +(-2.62117 - 1.45927i) q^{3} +(4.98088 + 8.62715i) q^{4} +(-5.75562 - 9.61919i) q^{6} +(-3.63061 + 6.28840i) q^{7} +22.2764i q^{8} +(4.74103 + 7.65001i) q^{9} +(6.50668 + 3.75663i) q^{11} +(-0.466354 - 29.8817i) q^{12} +(1.46668 + 2.54036i) q^{13} +(-23.4969 + 13.5659i) q^{14} +(-21.6949 + 37.5766i) q^{16} -1.90107i q^{17} +(1.04942 + 33.6125i) q^{18} -7.38378 q^{19} +(18.6929 - 11.1849i) q^{21} +(14.0368 + 24.3125i) q^{22} +(30.6549 - 17.6986i) q^{23} +(32.5074 - 58.3902i) q^{24} +10.9606i q^{26} +(-1.26358 - 26.9704i) q^{27} -72.3346 q^{28} +(-14.2015 - 8.19922i) q^{29} +(-13.3206 - 23.0720i) q^{31} +(-63.2391 + 36.5111i) q^{32} +(-11.5731 - 19.3418i) q^{33} +(3.55172 - 6.15176i) q^{34} +(-42.3832 + 79.0054i) q^{36} +44.6613 q^{37} +(-23.8935 - 13.7949i) q^{38} +(-0.137323 - 8.79899i) q^{39} +(14.8634 - 8.58140i) q^{41} +(81.3857 - 1.27016i) q^{42} +(20.5554 - 35.6031i) q^{43} +74.8454i q^{44} +132.263 q^{46} +(-36.4950 - 21.0704i) q^{47} +(111.701 - 66.8359i) q^{48} +(-1.86263 - 3.22616i) q^{49} +(-2.77419 + 4.98303i) q^{51} +(-14.6107 + 25.3065i) q^{52} +100.474i q^{53} +(46.2992 - 89.6354i) q^{54} +(-140.083 - 80.8770i) q^{56} +(19.3541 + 10.7750i) q^{57} +(-30.6367 - 53.0644i) q^{58} +(-4.12003 + 2.37870i) q^{59} +(38.4629 - 66.6197i) q^{61} -99.5461i q^{62} +(-65.3191 + 2.03933i) q^{63} -99.2915 q^{64} +(-1.31425 - 84.2107i) q^{66} +(-41.9225 - 72.6119i) q^{67} +(16.4008 - 9.46903i) q^{68} +(-106.179 + 1.65710i) q^{69} +23.1134i q^{71} +(-170.415 + 105.613i) q^{72} +103.753 q^{73} +(144.521 + 83.4395i) q^{74} +(-36.7778 - 63.7010i) q^{76} +(-47.2464 + 27.2777i) q^{77} +(15.9945 - 28.7296i) q^{78} +(-40.2610 + 69.7340i) q^{79} +(-36.0452 + 72.5379i) q^{81} +64.1296 q^{82} +(17.1034 + 9.87463i) q^{83} +(189.601 + 105.556i) q^{84} +(133.032 - 76.8063i) q^{86} +(25.2595 + 42.2153i) q^{87} +(-83.6843 + 144.945i) q^{88} -29.0566i q^{89} -21.2997 q^{91} +(305.377 + 176.310i) q^{92} +(1.24719 + 79.9139i) q^{93} +(-78.7306 - 136.365i) q^{94} +(219.040 - 3.41849i) q^{96} +(-47.7972 + 82.7872i) q^{97} -13.9196i q^{98} +(2.11011 + 67.5864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} + 16 q^{4} - 22 q^{6} - 2 q^{7} + 8 q^{9} - 18 q^{11} + 22 q^{12} + 10 q^{13} - 54 q^{14} - 32 q^{16} + 8 q^{18} - 52 q^{19} + 72 q^{21} + 24 q^{22} + 54 q^{23} + 108 q^{24} - 34 q^{27} - 32 q^{28}+ \cdots - 824 q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 + 16 * q^4 - 22 * q^6 - 2 * q^7 + 8 * q^9 - 18 * q^11 + 22 * q^12 + 10 * q^13 - 54 * q^14 - 32 * q^16 + 8 * q^18 - 52 * q^19 + 72 * q^21 + 24 * q^22 + 54 * q^23 + 108 * q^24 - 34 * q^27 - 32 * q^28 - 54 * q^29 + 32 * q^31 - 216 * q^32 - 62 * q^33 + 54 * q^34 - 86 * q^36 - 44 * q^37 - 252 * q^38 + 160 * q^39 + 144 * q^41 + 270 * q^42 + 124 * q^43 - 108 * q^46 + 216 * q^47 + 172 * q^48 - 54 * q^49 - 106 * q^51 - 62 * q^52 - 316 * q^54 - 18 * q^56 + 236 * q^57 - 90 * q^58 - 486 * q^59 + 62 * q^61 + 132 * q^63 + 256 * q^64 + 208 * q^66 - 14 * q^67 + 288 * q^68 + 90 * q^69 - 804 * q^72 + 268 * q^73 + 540 * q^74 - 106 * q^76 - 702 * q^77 - 290 * q^78 - 40 * q^79 - 112 * q^81 + 204 * q^82 - 522 * q^83 + 714 * q^84 + 54 * q^86 - 106 * q^87 - 144 * q^88 + 136 * q^91 + 1332 * q^92 - 90 * q^93 - 150 * q^94 + 166 * q^96 + 142 * q^97 - 824 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	3.23594	+	1.86827i	1.61797	+	0.934136i	0.987444	+	0.157969i	$0.0504947\pi$
$2$	3.23594	+	1.86827i	1.61797	+	0.934136i	0.630528	+	0.776167i	$0.282839\pi$
$3$	−2.62117	−	1.45927i	−0.873722	−	0.486425i
$3$	−2.62117	−	1.45927i	−0.873722	−	0.486425i
$4$	4.98088	+	8.62715i	1.24522	+	2.15679i
$5$		0			0
$5$		0			0
$6$	−5.75562	−	9.61919i	−0.959271	−	1.60320i
$7$	−3.63061	+	6.28840i	−0.518658	+	0.898342i	0.481107	+	0.876662i	$0.340235\pi$
$7$	−3.63061	+	6.28840i	−0.518658	+	0.898342i	−0.999765	+	0.0216804i	$0.993098\pi$
$8$			22.2764i			2.78455i
$9$	4.74103	+	7.65001i	0.526781	+	0.850001i
$10$		0			0
$11$	6.50668	+	3.75663i	0.591516	+	0.341512i	0.765697	−	0.643202i	$-0.222394\pi$
$11$	6.50668	+	3.75663i	0.591516	+	0.341512i	−0.174181	+	0.984714i	$0.555728\pi$
$12$	−0.466354	−	29.8817i	−0.0388628	−	2.49014i
$13$	1.46668	+	2.54036i	0.112821	+	0.195412i	0.916907	−	0.399102i	$-0.130678\pi$
$13$	1.46668	+	2.54036i	0.112821	+	0.195412i	−0.804085	+	0.594514i	$0.797345\pi$
$14$	−23.4969	+	13.5659i	−1.67835	+	0.968995i
$15$		0			0
$16$	−21.6949	+	37.5766i	−1.35593	+	2.34854i
$17$		−	1.90107i		−	0.111828i	−0.998436	−	0.0559139i	$-0.982193\pi$
$17$		−	1.90107i		−	0.111828i	0.998436	−	0.0559139i	$-0.0178072\pi$
$18$	1.04942	+	33.6125i	0.0583009	+	1.86736i
$19$	−7.38378			−0.388620			−0.194310	−	0.980940i	$-0.562247\pi$
$19$	−7.38378			−0.388620			−0.194310	+	0.980940i	$0.562247\pi$
$20$		0			0
$21$	18.6929	−	11.1849i	0.890140	−	0.532614i
$22$	14.0368	+	24.3125i	0.638037	+	1.10511i
$23$	30.6549	−	17.6986i	1.33282	−	0.769506i	0.347091	−	0.937831i	$-0.387169\pi$
$23$	30.6549	−	17.6986i	1.33282	−	0.769506i	0.985731	+	0.168326i	$0.0538360\pi$
$24$	32.5074	−	58.3902i	1.35448	−	2.43293i
$25$		0			0
$26$			10.9606i			0.421562i
$27$	−1.26358	−	26.9704i	−0.0467992	−	0.998904i
$28$	−72.3346			−2.58338
$29$	−14.2015	−	8.19922i	−0.489705	−	0.282732i	0.234747	−	0.972057i	$-0.424574\pi$
$29$	−14.2015	−	8.19922i	−0.489705	−	0.282732i	−0.724452	+	0.689325i	$0.757907\pi$
$30$		0			0
$31$	−13.3206	−	23.0720i	−0.429697	−	0.744257i	0.567149	−	0.823615i	$-0.308046\pi$
$31$	−13.3206	−	23.0720i	−0.429697	−	0.744257i	−0.996846	+	0.0793581i	$0.974713\pi$
$32$	−63.2391	+	36.5111i	−1.97622	+	1.14097i
$33$	−11.5731	−	19.3418i	−0.350701	−	0.586115i
$34$	3.55172	−	6.15176i	0.104462	−	0.180934i
$35$		0			0
$36$	−42.3832	+	79.0054i	−1.17731	+	2.19459i
$37$	44.6613			1.20706			0.603531	−	0.797340i	$-0.293760\pi$
$37$	44.6613			1.20706			0.603531	+	0.797340i	$0.293760\pi$
$38$	−23.8935	−	13.7949i	−0.628776	−	0.363024i
$39$	−0.137323	−	8.79899i	−0.00352110	−	0.225615i
$40$		0			0
$41$	14.8634	−	8.58140i	0.362522	−	0.209302i	−0.307664	−	0.951495i	$-0.599547\pi$
$41$	14.8634	−	8.58140i	0.362522	−	0.209302i	0.670187	+	0.742193i	$0.266214\pi$
$42$	81.3857	−	1.27016i	1.93775	−	0.0302419i
$43$	20.5554	−	35.6031i	0.478033	−	0.827978i	−0.521650	−	0.853160i	$-0.674683\pi$
$43$	20.5554	−	35.6031i	0.478033	−	0.827978i	0.999683	+	0.0251818i	$0.00801646\pi$
$44$			74.8454i			1.70103i
$45$		0			0
$46$	132.263			2.87529
$47$	−36.4950	−	21.0704i	−0.776490	−	0.448307i	0.0586949	−	0.998276i	$-0.481306\pi$
$47$	−36.4950	−	21.0704i	−0.776490	−	0.448307i	−0.835185	+	0.549969i	$0.814639\pi$
$48$	111.701	−	66.8359i	2.32710	−	1.39241i
$49$	−1.86263	−	3.22616i	−0.0380128	−	0.0658401i
$50$		0			0
$51$	−2.77419	+	4.98303i	−0.0543959	+	0.0977065i
$52$	−14.6107	+	25.3065i	−0.280975	+	0.486663i
$53$			100.474i			1.89573i	0.318671	+	0.947865i	$0.396764\pi$
$53$			100.474i			1.89573i	−0.318671	+	0.947865i	$0.603236\pi$
$54$	46.2992	−	89.6354i	0.857393	−	1.65992i
$55$		0			0
$56$	−140.083	−	80.8770i	−2.50148	−	1.44423i
$57$	19.3541	+	10.7750i	0.339546	+	0.189035i
$58$	−30.6367	−	53.0644i	−0.528220	−	0.914903i
$59$	−4.12003	+	2.37870i	−0.0698310	+	0.0403169i	−0.534509	−	0.845163i	$-0.679503\pi$
$59$	−4.12003	+	2.37870i	−0.0698310	+	0.0403169i	0.464678	+	0.885480i	$0.346170\pi$
$60$		0			0
$61$	38.4629	−	66.6197i	0.630539	−	1.09213i	−0.356902	−	0.934142i	$-0.616167\pi$
$61$	38.4629	−	66.6197i	0.630539	−	1.09213i	0.987442	−	0.157985i	$-0.0504996\pi$
$62$		−	99.5461i		−	1.60558i
$63$	−65.3191	+	2.03933i	−1.03681	+	0.0323703i
$64$	−99.2915			−1.55143
$65$		0			0
$66$	−1.31425	−	84.2107i	−0.0199129	−	1.27592i
$67$	−41.9225	−	72.6119i	−0.625709	−	1.08376i	−0.988403	−	0.151852i	$-0.951476\pi$
$67$	−41.9225	−	72.6119i	−0.625709	−	1.08376i	0.362694	−	0.931908i	$-0.381857\pi$
$68$	16.4008	−	9.46903i	0.241189	−	0.139250i
$69$	−106.179	+	1.65710i	−1.53882	+	0.0240159i
$70$		0			0
$71$			23.1134i			0.325540i	0.986664	+	0.162770i	$0.0520429\pi$
$71$			23.1134i			0.325540i	−0.986664	+	0.162770i	$0.947957\pi$
$72$	−170.415	+	105.613i	−2.36687	+	1.46685i
$73$	103.753			1.42127			0.710637	−	0.703559i	$-0.248407\pi$
$73$	103.753			1.42127			0.710637	+	0.703559i	$0.248407\pi$
$74$	144.521	+	83.4395i	1.95299	+	1.12756i
$75$		0			0
$76$	−36.7778	−	63.7010i	−0.483918	−	0.838171i
$77$	−47.2464	+	27.2777i	−0.613589	+	0.354256i
$78$	15.9945	−	28.7296i	0.205058	−	0.368328i
$79$	−40.2610	+	69.7340i	−0.509633	+	0.882709i	0.490305	+	0.871551i	$0.336885\pi$
$79$	−40.2610	+	69.7340i	−0.509633	+	0.882709i	−0.999938	+	0.0111586i	$0.996448\pi$
$80$		0			0
$81$	−36.0452	+	72.5379i	−0.445003	+	0.895529i
$82$	64.1296			0.782068
$83$	17.1034	+	9.87463i	0.206065	+	0.118971i	0.599481	−	0.800389i	$-0.295374\pi$
$83$	17.1034	+	9.87463i	0.206065	+	0.118971i	−0.393417	+	0.919360i	$0.628707\pi$
$84$	189.601	+	105.556i	2.25715	+	1.25662i
$85$		0			0
$86$	133.032	−	76.8063i	1.54689	−	0.893097i
$87$	25.2595	+	42.2153i	0.290339	+	0.485234i
$88$	−83.6843	+	144.945i	−0.950958	+	1.64711i
$89$		−	29.0566i		−	0.326478i	−0.986587	−	0.163239i	$-0.947806\pi$
$89$		−	29.0566i		−	0.326478i	0.986587	−	0.163239i	$-0.0521942\pi$
$90$		0			0
$91$	−21.2997			−0.234063
$92$	305.377	+	176.310i	3.31932	+	1.91641i
$93$	1.24719	+	79.9139i	0.0134107	+	0.859289i
$94$	−78.7306	−	136.365i	−0.837559	−	1.45070i
$95$		0			0
$96$	219.040	−	3.41849i	2.28167	−	0.0356092i
$97$	−47.7972	+	82.7872i	−0.492755	+	0.853476i	−0.999965	−	0.00834602i	$-0.997343\pi$
$97$	−47.7972	+	82.7872i	−0.492755	+	0.853476i	0.507210	+	0.861822i	$0.330677\pi$
$98$		−	13.9196i		−	0.142036i
$99$	2.11011	+	67.5864i	0.0213143	+	0.682691i
$100$		0			0
$101$	117.817	+	68.0219i	1.16651	+	0.673484i	0.952855	−	0.303426i	$-0.0981305\pi$
$101$	117.817	+	68.0219i	1.16651	+	0.673484i	0.213653	+	0.976910i	$0.431464\pi$
$102$	−18.2868	+	10.9419i	−0.179282	+	0.107273i
$103$	−85.9401	−	148.853i	−0.834370	−	1.44517i	−0.894542	−	0.446983i	$-0.852498\pi$
$103$	−85.9401	−	148.853i	−0.834370	−	1.44517i	0.0601721	−	0.998188i	$-0.480835\pi$
$104$	−56.5901	+	32.6723i	−0.544135	+	0.314157i
$105$		0			0
$106$	−187.712	+	325.127i	−1.77087	+	3.06724i
$107$			98.6056i			0.921548i	0.887518	+	0.460774i	$0.152428\pi$
$107$			98.6056i			0.921548i	−0.887518	+	0.460774i	$0.847572\pi$
$108$	226.384	−	145.238i	2.09615	−	1.34479i
$109$	2.62651			0.0240965			0.0120482	−	0.999927i	$-0.496165\pi$
$109$	2.62651			0.0240965			0.0120482	+	0.999927i	$0.496165\pi$
$110$		0			0
$111$	−117.065	−	65.1731i	−1.05464	−	0.587145i
$112$	−157.531	−	272.852i	−1.40653	−	2.43618i
$113$	−2.36782	+	1.36706i	−0.0209542	+	0.0120979i	−0.510440	−	0.859913i	$-0.670518\pi$
$113$	−2.36782	+	1.36706i	−0.0209542	+	0.0120979i	0.489486	+	0.872011i	$0.337184\pi$
$114$	42.4983	+	71.0260i	0.372792	+	0.623035i
$115$		0			0
$116$		−	163.357i		−	1.40825i
$117$	−12.4802	+	23.2640i	−0.106668	+	0.198838i
$118$	−17.7762			−0.150646
$119$	11.9547	+	6.90205i	0.100460	+	0.0580004i
$120$		0			0
$121$	−32.2754	−	55.9027i	−0.266739	−	0.462006i
$122$	248.928	−	143.718i	2.04039	−	1.17802i
$123$	−51.4821	+	0.803465i	−0.418554	+	0.00653224i
$124$	132.697	−	229.838i	1.07014	−	1.85353i
$125$		0			0
$126$	−215.179	−	115.435i	−1.70777	−	0.916149i
$127$	−193.060			−1.52015			−0.760077	−	0.649833i	$-0.774839\pi$
$127$	−193.060			−1.52015			−0.760077	+	0.649833i	$0.774839\pi$
$128$	−68.3455	−	39.4593i	−0.533950	−	0.308276i
$129$	−105.834	+	63.3255i	−0.820418	+	0.490896i
$130$		0			0
$131$	−201.259	+	116.197i	−1.53633	+	0.886999i	−0.537278	+	0.843405i	$0.680547\pi$
$131$	−201.259	+	116.197i	−1.53633	+	0.886999i	−0.999049	+	0.0435937i	$0.986119\pi$
$132$	109.220	−	196.182i	0.827424	−	1.48623i
$133$	26.8076	−	46.4322i	0.201561	−	0.349114i
$134$		−	313.291i		−	2.33799i
$135$		0			0
$136$	42.3491			0.311390
$137$	−154.172	−	89.0111i	−1.12534	−	0.649716i	−0.182582	−	0.983191i	$-0.558445\pi$
$137$	−154.172	−	89.0111i	−1.12534	−	0.649716i	−0.942759	+	0.333475i	$0.891779\pi$
$138$	−346.685	−	193.009i	−2.51221	−	1.39861i
$139$	−16.0343	−	27.7722i	−0.115355	−	0.199800i	0.802567	−	0.596562i	$-0.203467\pi$
$139$	−16.0343	−	27.7722i	−0.115355	−	0.199800i	−0.917922	+	0.396762i	$0.870134\pi$
$140$		0			0
$141$	64.9120	+	108.485i	0.460369	+	0.769400i
$142$	−43.1820	+	74.7935i	−0.304099	+	0.526715i
$143$			22.0390i			0.154119i
$144$	−390.318	+	12.1861i	−2.71054	+	0.0846257i
$145$		0			0
$146$	335.739	+	193.839i	2.29958	+	1.32766i
$147$	0.174395	+	11.1744i	0.00118636	+	0.0760163i
$148$	222.453	+	385.299i	1.50306	+	2.60337i
$149$	80.4653	−	46.4567i	0.540036	−	0.311790i	−0.205058	−	0.978750i	$-0.565738\pi$
$149$	80.4653	−	46.4567i	0.540036	−	0.311790i	0.745093	+	0.666960i	$0.232405\pi$
$150$		0			0
$151$	113.614	−	196.785i	0.752408	−	1.30321i	−0.194245	−	0.980953i	$-0.562226\pi$
$151$	113.614	−	196.785i	0.752408	−	1.30321i	0.946653	−	0.322256i	$-0.104441\pi$
$152$		−	164.484i		−	1.08213i
$153$	14.5432	−	9.01305i	0.0950537	−	0.0589088i
$154$	−203.849			−1.32369
$155$		0			0
$156$	75.2261	−	45.0114i	0.482219	−	0.288535i
$157$	−0.792406	−	1.37249i	−0.00504717	−	0.00874196i	0.863491	−	0.504365i	$-0.168273\pi$
$157$	−0.792406	−	1.37249i	−0.00504717	−	0.00874196i	−0.868538	+	0.495623i	$0.834940\pi$
$158$	−260.564	+	150.437i	−1.64914	+	0.952133i
$159$	146.619	−	263.358i	0.922131	−	1.65634i
$160$		0			0
$161$			257.027i			1.59644i
$162$	−252.161	+	167.386i	−1.55655	+	1.03325i
$163$	41.6801			0.255706			0.127853	−	0.991793i	$-0.459191\pi$
$163$	41.6801			0.255706			0.127853	+	0.991793i	$0.459191\pi$
$164$	148.066	+	85.4859i	0.902841	+	0.521256i
$165$		0			0
$166$	36.8970	+	63.9075i	0.222271	+	0.384985i
$167$	−8.01405	+	4.62692i	−0.0479884	+	0.0277061i	−0.523802	−	0.851840i	$-0.675487\pi$
$167$	−8.01405	+	4.62692i	−0.0479884	+	0.0277061i	0.475814	+	0.879546i	$0.342154\pi$
$168$	249.159	+	416.412i	1.48309	+	2.47864i
$169$	80.1977	−	138.907i	0.474543	−	0.821932i
$170$		0			0
$171$	−35.0068	−	56.4860i	−0.204718	−	0.330327i
$172$	409.537			2.38103
$173$	127.637	+	73.6913i	0.737787	+	0.425962i	0.821264	−	0.570548i	$-0.193269\pi$
$173$	127.637	+	73.6913i	0.737787	+	0.425962i	−0.0834771	+	0.996510i	$0.526603\pi$
$174$	2.86848	+	183.798i	0.0164855	+	1.05631i
$175$		0			0
$176$	−282.323	+	162.999i	−1.60411	+	0.926133i
$177$	14.2705	−	0.222714i	0.0806240	−	0.00125827i
$178$	54.2856	−	94.0254i	0.304975	−	0.528233i
$179$			160.022i			0.893977i	0.894540	+	0.446988i	$0.147504\pi$
$179$			160.022i			0.893977i	−0.894540	+	0.446988i	$0.852496\pi$
$180$		0			0
$181$	−30.3346			−0.167595			−0.0837973	−	0.996483i	$-0.526705\pi$
$181$	−30.3346			−0.167595			−0.0837973	+	0.996483i	$0.526705\pi$
$182$	−68.9246	−	39.7937i	−0.378707	−	0.218646i
$183$	−198.034	+	118.493i	−1.08215	+	0.647505i
$184$	394.262	+	682.882i	2.14273	+	3.71132i
$185$		0			0
$186$	−145.265	+	260.927i	−0.780995	+	1.40283i
$187$	7.14163	−	12.3697i	0.0381905	−	0.0661480i
$188$		−	419.797i		−	2.23296i
$189$	174.188	+	89.9731i	0.921631	+	0.476048i
$190$		0			0
$191$	−249.938	−	144.302i	−1.30857	−	0.755506i	−0.326716	−	0.945122i	$-0.605942\pi$
$191$	−249.938	−	144.302i	−1.30857	−	0.755506i	−0.981858	+	0.189617i	$0.939275\pi$
$192$	260.260	+	144.894i	1.35552	+	0.754654i
$193$	−47.3339	−	81.9847i	−0.245253	−	0.424791i	0.716949	−	0.697125i	$-0.245538\pi$
$193$	−47.3339	−	81.9847i	−0.245253	−	0.424791i	−0.962203	+	0.272334i	$0.912205\pi$
$194$	−309.338	+	178.596i	−1.59453	+	0.920600i
$195$		0			0
$196$	18.5551	−	32.1383i	0.0946686	−	0.163971i
$197$		−	129.755i		−	0.658657i	−0.944215	−	0.329329i	$-0.893178\pi$
$197$		−	129.755i		−	0.658657i	0.944215	−	0.329329i	$-0.106822\pi$
$198$	−119.442	+	222.648i	−0.603241	+	1.12449i
$199$	136.428			0.685570			0.342785	−	0.939414i	$-0.388630\pi$
$199$	136.428			0.685570			0.342785	+	0.939414i	$0.388630\pi$
$200$		0			0
$201$	3.92515	+	251.504i	0.0195281	+	1.25127i
$202$	254.167	+	440.230i	1.25825	+	2.17936i
$203$	103.120	−	59.5363i	0.507980	−	0.293282i
$204$	−56.8072	+	0.886573i	−0.278467	+	0.00434594i
$205$		0			0
$206$		−	642.238i		−	3.11766i
$207$	280.731	+	150.601i	1.35619	+	0.727539i
$208$	−127.278			−0.611911
$209$	−48.0439	−	27.7382i	−0.229875	−	0.132718i
$210$		0			0
$211$	−79.1144	−	137.030i	−0.374950	−	0.649432i	0.615370	−	0.788239i	$-0.289007\pi$
$211$	−79.1144	−	137.030i	−0.374950	−	0.649432i	−0.990320	+	0.138806i	$0.955673\pi$
$212$	−866.802	+	500.448i	−4.08869	+	2.36060i
$213$	33.7287	−	60.5840i	0.158351	−	0.284432i
$214$	−184.222	+	319.082i	−0.860851	+	1.49104i
$215$		0			0
$216$	600.804	−	28.1480i	2.78150	−	0.130315i
$217$	193.448			0.891463
$218$	8.49925	+	4.90704i	0.0389874	+	0.0225094i
$219$	−271.954	−	151.404i	−1.24180	−	0.691343i
$220$		0			0
$221$	4.82941	−	2.78826i	0.0218525	−	0.0126166i
$222$	−257.054	−	429.605i	−1.15790	−	1.93516i
$223$	−103.124	+	178.616i	−0.462440	+	0.800969i	−0.999082	−	0.0428406i	$-0.986359\pi$
$223$	−103.124	+	178.616i	−0.462440	+	0.800969i	0.536642	+	0.843810i	$0.319693\pi$
$224$		−	530.230i		−	2.36710i
$225$		0			0
$226$	−10.2162			−0.0452044
$227$	127.562	+	73.6481i	0.561948	+	0.324441i	0.753927	−	0.656958i	$-0.228157\pi$
$227$	127.562	+	73.6481i	0.561948	+	0.324441i	−0.191979	+	0.981399i	$0.561490\pi$
$228$	3.44346	+	220.640i	0.0151029	+	0.967718i
$229$	13.5751	+	23.5127i	0.0592798	+	0.102676i	0.894142	−	0.447783i	$-0.147786\pi$
$229$	13.5751	+	23.5127i	0.0592798	+	0.102676i	−0.834863	+	0.550458i	$0.814453\pi$
$230$		0			0
$231$	163.646	−	2.55398i	0.708426	−	0.0110562i
$232$	182.649	−	316.358i	0.787281	−	1.36361i
$233$			39.6011i			0.169962i	0.996383	+	0.0849808i	$0.0270829\pi$
$233$			39.6011i			0.169962i	−0.996383	+	0.0849808i	$0.972917\pi$
$234$	−83.8487	+	51.9646i	−0.358328	+	0.222071i
$235$		0			0
$236$	−41.0428	−	23.6960i	−0.173910	−	0.100407i
$237$	207.292	−	124.033i	0.874649	−	0.523345i
$238$	25.7898	+	44.6693i	0.108361	+	0.187686i
$239$	54.9394	−	31.7193i	0.229872	−	0.132717i	−0.380641	−	0.924723i	$-0.624297\pi$
$239$	54.9394	−	31.7193i	0.229872	−	0.132717i	0.610513	+	0.792006i	$0.290963\pi$
$240$		0			0
$241$	69.1161	−	119.713i	0.286789	−	0.496733i	−0.686253	−	0.727363i	$-0.740746\pi$
$241$	69.1161	−	119.713i	0.286789	−	0.496733i	0.973041	+	0.230630i	$0.0740789\pi$
$242$		−	241.197i		−	0.996683i
$243$	200.333	−	137.534i	0.824416	−	0.565984i
$244$	766.317			3.14064
$245$		0			0
$246$	−168.094	−	93.5827i	−0.683310	−	0.380417i
$247$	−10.8296	−	18.7575i	−0.0438446	−	0.0759411i
$248$	513.961	−	296.735i	2.07242	−	1.19651i
$249$	−30.4210	−	50.8415i	−0.122173	−	0.204183i
$250$		0			0
$251$			186.477i			0.742936i	0.928446	+	0.371468i	$0.121145\pi$
$251$			186.477i			0.742936i	−0.928446	+	0.371468i	$0.878855\pi$
$252$	−342.941	−	553.360i	−1.36088	−	2.19587i
$253$	265.949			1.05118
$254$	−624.730	−	360.688i	−2.45957	−	1.42003i
$255$		0			0
$256$	51.1416	+	88.5798i	0.199772	+	0.346015i
$257$	−201.713	+	116.459i	−0.784877	+	0.453149i	−0.838156	−	0.545431i	$-0.816366\pi$
$257$	−201.713	+	116.459i	−0.784877	+	0.453149i	0.0532790	+	0.998580i	$0.483033\pi$
$258$	−460.782	+	7.19128i	−1.78598	+	0.0278732i
$259$	−162.148	+	280.848i	−0.626053	+	1.08435i
$260$		0			0
$261$	−4.60553	−	147.514i	−0.0176457	−	0.565188i
$262$	−868.350			−3.31431
$263$	9.34728	+	5.39665i	0.0355410	+	0.0205196i	0.517665	−	0.855583i	$-0.326801\pi$
$263$	9.34728	+	5.39665i	0.0355410	+	0.0205196i	−0.482124	+	0.876103i	$0.660135\pi$
$264$	430.866	−	257.808i	1.63207	−	0.976545i
$265$		0			0
$266$	173.496	−	100.168i	0.652240	−	0.376571i
$267$	−42.4015	+	76.1622i	−0.158807	+	0.285252i
$268$	417.622	−	723.343i	1.55829	−	2.69904i
$269$			58.4601i			0.217324i	0.994079	+	0.108662i	$0.0346566\pi$
$269$			58.4601i			0.217324i	−0.994079	+	0.108662i	$0.965343\pi$
$270$		0			0
$271$	−65.5995			−0.242065			−0.121032	−	0.992649i	$-0.538620\pi$
$271$	−65.5995			−0.242065			−0.121032	+	0.992649i	$0.538620\pi$
$272$	71.4360	+	41.2436i	0.262632	+	0.151631i
$273$	55.8301	+	31.0821i	0.204506	+	0.113854i
$274$	−332.594	−	576.069i	−1.21385	−	2.10244i
$275$		0			0
$276$	−543.161	−	907.767i	−1.96797	−	3.28901i
$277$	134.128	−	232.317i	0.484218	−	0.838690i	−0.515618	−	0.856819i	$-0.672438\pi$
$277$	134.128	−	232.317i	0.484218	−	0.838690i	0.999836	+	0.0181286i	$0.00577084\pi$
$278$		−	119.826i		−	0.431028i
$279$	113.347	−	211.288i	0.406263	−	0.757303i
$280$		0			0
$281$	159.428	+	92.0461i	0.567361	+	0.327566i	0.756095	−	0.654462i	$-0.227105\pi$
$281$	159.428	+	92.0461i	0.567361	+	0.327566i	−0.188734	+	0.982028i	$0.560438\pi$
$282$	7.37144	+	472.326i	0.0261399	+	1.67491i
$283$	−231.303	−	400.628i	−0.817324	−	1.41565i	−0.907647	−	0.419734i	$-0.862123\pi$
$283$	−231.303	−	400.628i	−0.817324	−	1.41565i	0.0903234	−	0.995912i	$-0.471210\pi$
$284$	−199.402	+	115.125i	−0.702121	+	0.405370i
$285$		0			0
$286$	−41.1750	+	71.3171i	−0.143968	+	0.249361i
$287$			124.623i			0.434226i
$288$	−579.129	−	310.679i	−2.01086	−	1.07875i
$289$	285.386			0.987495
$290$		0			0
$291$	246.094	−	147.250i	0.845683	−	0.506013i
$292$	516.782	+	895.093i	1.76980	+	3.06539i
$293$	−248.349	+	143.384i	−0.847608	+	0.489367i	−0.859843	−	0.510559i	$-0.829439\pi$
$293$	−248.349	+	143.384i	−0.847608	+	0.489367i	0.0122351	+	0.999925i	$0.496105\pi$
$294$	−20.3125	+	36.4855i	−0.0690901	+	0.124100i
$295$		0			0
$296$			994.894i			3.36113i
$297$	93.0962	−	180.235i	0.313455	−	0.606850i
$298$	347.175			1.16502
$299$	89.9217	+	51.9163i	0.300741	+	0.173633i
$300$		0			0
$301$	149.257	+	258.521i	0.495872	+	0.858875i
$302$	735.294	−	424.522i	2.43475	−	1.40570i
$303$	−209.556	−	350.225i	−0.691605	−	1.15586i
$304$	160.190	−	277.458i	0.526942	−	0.912690i
$305$		0			0
$306$	63.8999	−	1.99502i	0.208823	−	0.00651966i
$307$	236.738			0.771133			0.385567	−	0.922680i	$-0.374006\pi$
$307$	236.738			0.771133			0.385567	+	0.922680i	$0.374006\pi$
$308$	−470.658	−	271.734i	−1.52811	−	0.882254i
$309$	8.04646	+	515.578i	0.0260403	+	1.66854i
$310$		0			0
$311$	448.597	−	258.997i	1.44243	−	0.832789i	0.444421	−	0.895818i	$-0.353409\pi$
$311$	448.597	−	258.997i	1.44243	−	0.832789i	0.998012	+	0.0630292i	$0.0200761\pi$
$312$	196.010	−	3.05907i	0.628237	−	0.00980470i
$313$	−247.615	+	428.882i	−0.791102	+	1.37023i	0.134183	+	0.990957i	$0.457159\pi$
$313$	−247.615	+	428.882i	−0.791102	+	1.37023i	−0.925285	+	0.379272i	$0.876174\pi$
$314$		−	5.92172i		−	0.0188590i
$315$		0			0
$316$	−802.141			−2.53842
$317$	189.840	+	109.604i	0.598864	+	0.345754i	0.768595	−	0.639736i	$-0.220956\pi$
$317$	189.840	+	109.604i	0.598864	+	0.345754i	−0.169731	+	0.985491i	$0.554290\pi$
$318$	966.475	−	578.289i	3.03923	−	1.81852i
$319$	−61.6029	−	106.699i	−0.193112	−	0.334481i
$320$		0			0
$321$	143.893	−	258.462i	0.448264	−	0.805177i
$322$	−480.197	+	831.725i	−1.49129	+	2.58300i
$323$			14.0371i			0.0434586i
$324$	−805.332	+	50.3356i	−2.48559	+	0.155357i
$325$		0			0
$326$	134.874	+	77.8697i	0.413725	+	0.238864i
$327$	−6.88453	−	3.83281i	−0.0210536	−	0.0117211i
$328$	191.163	+	331.104i	0.582813	+	1.00946i
$329$	264.998	−	152.997i	0.805466	−	0.465036i
$330$		0			0
$331$	47.4838	−	82.2443i	0.143455	−	0.248472i	−0.785340	−	0.619064i	$-0.787512\pi$
$331$	47.4838	−	82.2443i	0.143455	−	0.248472i	0.928796	+	0.370592i	$0.120845\pi$
$332$			196.738i			0.592583i
$333$	211.741	+	341.659i	0.635858	+	1.02600i
$334$	−34.5774			−0.103525
$335$		0			0
$336$	14.7494	+	945.072i	0.0438972	+	2.81272i
$337$	−257.989	−	446.850i	−0.765547	−	1.32597i	−0.939957	−	0.341293i	$-0.889135\pi$
$337$	−257.989	−	446.850i	−0.765547	−	1.32597i	0.174411	−	0.984673i	$-0.444198\pi$
$338$	519.031	−	299.662i	1.53559	−	0.886575i
$339$	8.20138	−	0.127996i	0.0241929	−	0.000377570i
$340$		0			0
$341$		−	200.162i		−	0.586986i
$342$	−7.74866	−	248.188i	−0.0226569	−	0.725695i
$343$	−328.750			−0.958454
$344$	793.109	+	457.902i	2.30555	+	1.33111i
$345$		0			0
$346$	275.351	+	476.922i	0.795812	+	1.37839i
$347$	96.4994	−	55.7140i	0.278096	−	0.160559i	−0.354465	−	0.935069i	$-0.615337\pi$
$347$	96.4994	−	55.7140i	0.278096	−	0.160559i	0.632561	+	0.774510i	$0.282004\pi$
$348$	−238.383	+	428.187i	−0.685010	+	1.23042i
$349$	−310.131	+	537.162i	−0.888627	+	1.53915i	−0.0471279	+	0.998889i	$0.515007\pi$
$349$	−310.131	+	537.162i	−0.888627	+	1.53915i	−0.841499	+	0.540258i	$0.818327\pi$
$350$		0			0
$351$	66.6613	−	42.7668i	0.189918	−	0.121843i
$352$	−548.635			−1.55862
$353$	−488.067	−	281.786i	−1.38263	−	0.798260i	−0.390157	−	0.920748i	$-0.627579\pi$
$353$	−488.067	−	281.786i	−1.38263	−	0.798260i	−0.992470	+	0.122488i	$0.960913\pi$
$354$	46.5945	+	25.9404i	0.131623	+	0.0732780i
$355$		0			0
$356$	250.675	−	144.727i	0.704144	−	0.406538i
$357$	−21.2633	−	35.5366i	−0.0595610	−	0.0995424i
$358$	−298.964	+	517.822i	−0.835096	+	1.44643i
$359$		−	415.128i		−	1.15635i	−0.815915	−	0.578173i	$-0.803766\pi$
$359$		−	415.128i		−	1.15635i	0.815915	−	0.578173i	$-0.196234\pi$
$360$		0			0
$361$	−306.480			−0.848974
$362$	−98.1611	−	56.6733i	−0.271163	−	0.156556i
$363$	3.02191	+	193.629i	0.00832482	+	0.533413i
$364$	−106.091	−	183.756i	−0.291460	−	0.504823i
$365$		0			0
$366$	−862.205	+	13.4562i	−2.35575	+	0.0367655i
$367$	313.940	−	543.761i	0.855423	−	1.48164i	−0.0208286	−	0.999783i	$-0.506630\pi$
$367$	313.940	−	543.761i	0.855423	−	1.48164i	0.876252	−	0.481853i	$-0.160036\pi$
$368$			1535.88i			4.17358i
$369$	136.116	+	73.0205i	0.368877	+	0.197888i
$370$		0			0
$371$	−631.819	−	364.781i	−1.70302	−	0.983237i
$372$	−683.217	+	408.802i	−1.83660	+	1.09893i
$373$	195.467	+	338.559i	0.524040	+	0.907665i	0.999608	+	0.0279857i	$0.00890929\pi$
$373$	195.467	+	338.559i	0.524040	+	0.907665i	−0.475568	+	0.879679i	$0.657757\pi$
$374$	46.2198	−	26.6850i	0.123582	−	0.0713503i
$375$		0			0
$376$	469.373	−	812.979i	1.24833	−	2.16218i
$377$		−	48.1024i		−	0.127593i
$378$	395.569	+	616.579i	1.04648	+	1.63116i
$379$	52.4430			0.138372			0.0691860	−	0.997604i	$-0.477960\pi$
$379$	52.4430			0.138372			0.0691860	+	0.997604i	$0.477960\pi$
$380$		0			0
$381$	506.042	+	281.727i	1.32819	+	0.739441i
$382$	−539.189	−	933.904i	−1.41149	−	2.44477i
$383$	96.0614	−	55.4610i	0.250813	−	0.144807i	−0.369324	−	0.929301i	$-0.620411\pi$
$383$	96.0614	−	55.4610i	0.250813	−	0.144807i	0.620136	+	0.784494i	$0.287077\pi$
$384$	121.563	+	203.164i	0.316571	+	0.529074i
$385$		0			0
$386$		−	353.731i		−	0.916400i
$387$	369.818	−	11.5461i	0.955601	−	0.0298348i
$388$	−952.290			−2.45435
$389$	−91.6114	−	52.8918i	−0.235505	−	0.135969i	0.377604	−	0.925967i	$-0.376748\pi$
$389$	−91.6114	−	52.8918i	−0.235505	−	0.135969i	−0.613109	+	0.789998i	$0.710081\pi$
$390$		0			0
$391$	−33.6464	−	58.2773i	−0.0860521	−	0.149047i
$392$	71.8674	−	41.4926i	0.183335	−	0.105849i
$393$	697.096	−	10.8794i	1.77378	−	0.0276829i
$394$	242.419	−	419.881i	0.615276	−	1.06569i
$395$		0			0
$396$	−572.568	+	354.844i	−1.44588	+	0.896072i
$397$	−99.8892			−0.251610			−0.125805	−	0.992055i	$-0.540151\pi$
$397$	−99.8892			−0.251610			−0.125805	+	0.992055i	$0.540151\pi$
$398$	441.475	+	254.885i	1.10923	+	0.640416i
$399$	−138.025	+	82.5868i	−0.345926	+	0.206984i
$400$		0			0
$401$	−136.080	+	78.5658i	−0.339352	+	0.195925i	−0.659985	−	0.751279i	$-0.729437\pi$
$401$	−136.080	+	78.5658i	−0.339352	+	0.195925i	0.320634	+	0.947203i	$0.396104\pi$
$402$	−457.177	+	821.187i	−1.13726	+	2.04275i
$403$	39.0740	−	67.6782i	0.0969579	−	0.167936i
$404$			1355.24i			3.35455i
$405$		0			0
$406$	444.920			1.09586
$407$	290.597	+	167.776i	0.713996	+	0.412226i
$408$	−111.004	−	61.7990i	−0.272069	−	0.151468i
$409$	−342.619	−	593.434i	−0.837700	−	1.45094i	−0.891813	−	0.452404i	$-0.850567\pi$
$409$	−342.619	−	593.434i	−0.837700	−	1.45094i	0.0541134	−	0.998535i	$-0.482767\pi$
$410$		0			0
$411$	274.218	+	458.292i	0.667197	+	1.11506i
$412$	856.116	−	1482.84i	2.07795	−	3.59912i
$413$		−	34.5445i		−	0.0836428i
$414$	627.065	+	1011.82i	1.51465	+	2.44400i
$415$		0			0
$416$	−185.502	−	107.100i	−0.445919	−	0.257452i
$417$	1.50127	+	96.1942i	0.00360017	+	0.230681i
$418$	−103.645	−	179.518i	−0.247954	−	0.429469i
$419$	−44.6836	+	25.7981i	−0.106643	+	0.0615706i	−0.552373	−	0.833597i	$-0.686278\pi$
$419$	−44.6836	+	25.7981i	−0.106643	+	0.0615706i	0.445730	+	0.895168i	$0.352944\pi$
$420$		0			0
$421$	−7.37620	+	12.7760i	−0.0175207	+	0.0303467i	−0.874653	−	0.484750i	$-0.838911\pi$
$421$	−7.37620	+	12.7760i	−0.0175207	+	0.0303467i	0.857132	+	0.515097i	$0.172244\pi$
$422$		−	591.229i		−	1.40102i
$423$	−11.8353	−	379.083i	−0.0279795	−	0.896177i
$424$	−2238.20			−5.27876
$425$		0			0
$426$	222.332	−	133.032i	0.521905	−	0.312281i
$427$	279.287	+	483.740i	0.654069	+	1.13288i
$428$	−850.685	+	491.143i	−1.98758	+	1.14753i
$429$	32.1610	−	57.7680i	0.0749674	−	0.134657i
$430$		0			0
$431$		−	38.6810i		−	0.0897472i	−0.998993	−	0.0448736i	$-0.985711\pi$
$431$		−	38.6810i		−	0.0897472i	0.998993	−	0.0448736i	$-0.0142885\pi$
$432$	1040.87	+	537.639i	2.40942	+	1.24454i
$433$	544.647			1.25784			0.628922	−	0.777468i	$-0.283496\pi$
$433$	544.647			1.25784			0.628922	+	0.777468i	$0.283496\pi$
$434$	625.985	+	361.413i	1.44236	+	0.832748i
$435$		0			0
$436$	13.0824	+	22.6593i	0.0300054	+	0.0519709i
$437$	−226.349	+	130.683i	−0.517962	+	0.299045i
$438$	−597.163	−	998.020i	−1.36339	−	2.27858i
$439$	−125.709	+	217.735i	−0.286353	+	0.495978i	−0.972936	−	0.231073i	$-0.925776\pi$
$439$	−125.709	+	217.735i	−0.286353	+	0.495978i	0.686583	+	0.727051i	$0.259110\pi$
$440$		0			0
$441$	15.8494	−	29.5444i	0.0359397	−	0.0669942i
$442$	20.8369			0.0471423
$443$	−632.952	−	365.435i	−1.42878	−	0.824909i	−0.431760	−	0.901989i	$-0.642107\pi$
$443$	−632.952	−	365.435i	−1.42878	−	0.824909i	−0.997025	+	0.0770796i	$0.975440\pi$
$444$	−20.8280	−	1334.55i	−0.0469098	−	3.00575i
$445$		0			0
$446$	−667.407	+	385.328i	−1.49643	+	0.863964i
$447$	−278.706	+	4.34968i	−0.623504	+	0.00973083i
$448$	360.489	−	624.385i	0.804662	−	1.39372i
$449$		−	94.7211i		−	0.210960i	−0.994421	−	0.105480i	$-0.966362\pi$
$449$		−	94.7211i		−	0.210960i	0.994421	−	0.105480i	$-0.0336379\pi$
$450$		0			0
$451$	128.949			0.285917
$452$	−23.5877	−	13.6184i	−0.0521852	−	0.0301291i
$453$	−584.963	+	350.012i	−1.29131	+	0.772653i
$454$	275.190	+	476.642i	0.606144	+	1.04987i
$455$		0			0
$456$	−240.028	+	431.141i	−0.526377	+	0.945484i
$457$	−204.206	+	353.695i	−0.446840	+	0.773949i	−0.998178	−	0.0603323i	$-0.980784\pi$
$457$	−204.206	+	353.695i	−0.446840	+	0.773949i	0.551339	+	0.834282i	$0.314117\pi$
$458$			101.448i			0.221502i
$459$	−51.2727	+	2.40215i	−0.111705	+	0.00523345i
$460$		0			0
$461$	−511.735	−	295.450i	−1.11005	−	0.640890i	−0.171211	−	0.985234i	$-0.554768\pi$
$461$	−511.735	−	295.450i	−1.11005	−	0.640890i	−0.938843	+	0.344344i	$0.888101\pi$
$462$	534.322	+	297.471i	1.15654	+	0.643878i
$463$	400.967	+	694.496i	0.866020	+	1.49999i	0.866031	+	0.499991i	$0.166663\pi$
$463$	400.967	+	694.496i	0.866020	+	1.49999i	−1.04649e−5		1.00000i	$0.500003\pi$
$464$	616.198	−	355.762i	1.32801	−	0.766729i
$465$		0			0
$466$	−73.9856	+	128.147i	−0.158767	+	0.274993i
$467$			20.6432i			0.0442039i	0.999756	+	0.0221019i	$0.00703584\pi$
$467$			20.6432i			0.0442039i	−0.999756	+	0.0221019i	$0.992964\pi$
$468$	−262.864	+	8.20688i	−0.561676	+	0.0175361i
$469$	608.817			1.29812
$470$		0			0
$471$	0.0741920	+	4.75386i	0.000157520	+	0.0100931i
$472$	−52.9889	−	91.7795i	−0.112265	−	0.194448i
$473$	267.495	−	154.438i	0.565529	−	0.326508i
$474$	902.512	−	14.0852i	1.90403	−	0.0297156i
$475$		0			0
$476$			137.513i			0.288893i
$477$	−768.625	+	476.349i	−1.61137	+	0.998636i
$478$	237.041			0.495902
$479$	435.378	+	251.366i	0.908931	+	0.524771i	0.880087	−	0.474812i	$-0.157484\pi$
$479$	435.378	+	251.366i	0.908931	+	0.524771i	0.0288439	+	0.999584i	$0.490817\pi$
$480$		0			0
$481$	65.5037	+	113.456i	0.136182	+	0.235875i
$482$	447.312	−	258.255i	0.928032	−	0.535800i
$483$	375.073	−	673.711i	0.776549	−	1.39485i
$484$	321.521	−	556.890i	0.664299	−	1.15060i
$485$		0			0
$486$	905.218	−	70.7752i	1.86259	−	0.145628i
$487$	−80.4336			−0.165161			−0.0825807	−	0.996584i	$-0.526316\pi$
$487$	−80.4336			−0.165161			−0.0825807	+	0.996584i	$0.526316\pi$
$488$	1484.05	+	856.816i	3.04108	+	1.75577i
$489$	−109.250	−	60.8227i	−0.223416	−	0.124382i
$490$		0			0
$491$	−417.972	+	241.316i	−0.851267	+	0.491479i	−0.861078	−	0.508473i	$-0.830210\pi$
$491$	−417.972	+	241.316i	−0.851267	+	0.491479i	0.00981129	+	0.999952i	$0.496877\pi$
$492$	−263.358	−	440.142i	−0.535281	−	0.894597i
$493$	−15.5873	+	26.9980i	−0.0316173	+	0.0547627i
$494$		−	80.9307i		−	0.163827i
$495$		0			0
$496$	1155.96			2.33056
$497$	−145.346	−	83.9155i	−0.292447	−	0.168844i
$498$	−3.45462	−	221.355i	−0.00693698	−	0.444488i
$499$	17.5059	+	30.3212i	0.0350820	+	0.0607638i	0.883033	−	0.469310i	$-0.155497\pi$
$499$	17.5059	+	30.3212i	0.0350820	+	0.0607638i	−0.847951	+	0.530074i	$0.822164\pi$
$500$		0			0
$501$	27.7581	−	0.433212i	0.0554054	−	0.000864695i
$502$	−348.390	+	603.429i	−0.694004	+	1.20205i
$503$		−	211.016i		−	0.419514i	−0.977754	−	0.209757i	$-0.932733\pi$
$503$		−	211.016i		−	0.419514i	0.977754	−	0.209757i	$-0.0672673\pi$
$504$	−45.4289	−	1455.08i	−0.0901367	−	2.88706i
$505$		0			0
$506$	860.595	+	496.865i	1.70078	+	0.981947i
$507$	−412.914	+	247.067i	−0.814427	+	0.487311i
$508$	−961.608	−	1665.55i	−1.89293	−	3.27865i
$509$	−732.292	+	422.789i	−1.43869	+	0.830627i	−0.997759	−	0.0669144i	$-0.978685\pi$
$509$	−732.292	+	422.789i	−1.43869	+	0.830627i	−0.440930	+	0.897542i	$0.645351\pi$
$510$		0			0
$511$	−376.687	+	652.440i	−0.737156	+	1.27679i
$512$			697.860i			1.36301i
$513$	9.32998	+	199.144i	0.0181871	+	0.388194i
$514$	−870.311			−1.69321
$515$		0			0
$516$	−1073.46	−	597.627i	−2.08036	−	1.15819i
$517$	−158.308	−	274.197i	−0.306204	−	0.530361i
$518$	−1049.40	+	605.872i	−2.02587	+	1.16964i
$519$	−227.022	−	379.415i	−0.437423	−	0.731050i
$520$		0			0
$521$			260.960i			0.500883i	0.968132	+	0.250442i	$0.0805758\pi$
$521$			260.960i			0.500883i	−0.968132	+	0.250442i	$0.919424\pi$
$522$	260.693	−	485.951i	0.499412	−	0.930941i
$523$	−553.330			−1.05799			−0.528996	−	0.848624i	$-0.677431\pi$
$523$	−553.330			−1.05799			−0.528996	+	0.848624i	$0.677431\pi$
$524$	−2004.89	−	1157.53i	−3.82613	−	2.20902i
$525$		0			0
$526$	20.1648	+	34.9265i	0.0383362	+	0.0664003i
$527$	−43.8615	+	25.3234i	−0.0832286	+	0.0480521i
$528$	977.877	−	15.2614i	1.85204	−	0.0289042i
$529$	361.983	−	626.973i	0.684278	−	1.18520i
$530$		0			0
$531$	−37.7302	−	20.2407i	−0.0710551	−	0.0381182i
$532$	534.103			1.00395
$533$	43.5996	+	25.1723i	0.0818005	+	0.0472275i
$534$	−279.501	+	167.239i	−0.523409	+	0.313181i
$535$		0			0
$536$	1617.53	−	933.884i	3.01779	−	1.74232i
$537$	233.516	−	419.444i	0.434853	−	0.781088i
$538$	−109.219	+	189.174i	−0.203010	+	0.351624i
$539$		−	27.9888i		−	0.0519273i
$540$		0			0
$541$	−795.168			−1.46981			−0.734906	−	0.678169i	$-0.762774\pi$
$541$	−795.168			−1.46981			−0.734906	+	0.678169i	$0.762774\pi$
$542$	−212.276	−	122.558i	−0.391654	−	0.226121i
$543$	79.5121	+	44.2665i	0.146431	+	0.0815222i
$544$	69.4102	+	120.222i	0.127592	+	0.220996i
$545$		0			0
$546$	122.593	+	204.886i	0.224529	+	0.375249i
$547$	−303.604	+	525.858i	−0.555035	+	0.961348i	0.442866	+	0.896588i	$0.353962\pi$
$547$	−303.604	+	525.858i	−0.555035	+	0.961348i	−0.997901	+	0.0647606i	$0.979372\pi$
$548$		−	1773.42i		−	3.23616i
$549$	691.995	−	21.6048i	1.26046	−	0.0393529i
$550$		0			0
$551$	104.861	+	60.5412i	0.190309	+	0.109875i
$552$	−36.9143	−	2365.28i	−0.0668736	−	4.28494i
$553$	−292.344	−	506.354i	−0.528650	−	0.915649i
$554$	868.064	−	501.177i	1.56690	−	0.904651i
$555$		0			0
$556$	159.730	−	276.661i	0.287284	−	0.497591i
$557$			686.808i			1.23305i	0.787336	+	0.616524i	$0.211460\pi$
$557$			686.808i			1.23305i	−0.787336	+	0.616524i	$0.788540\pi$
$558$	761.528	−	471.951i	1.36475	−	0.845791i
$559$	120.593			0.215729
$560$		0			0
$561$	−36.7702	+	22.0014i	−0.0655439	+	0.0392181i
$562$	343.934	+	595.712i	0.611983	+	1.05999i
$563$	208.976	−	120.652i	0.371182	−	0.214302i	−0.302792	−	0.953057i	$-0.597919\pi$
$563$	208.976	−	120.652i	0.371182	−	0.214302i	0.673975	+	0.738754i	$0.264586\pi$
$564$	−612.600	+	1100.36i	−1.08617	+	1.95099i
$565$		0			0
$566$		−	1728.55i		−	3.05397i
$567$	−325.281	−	490.023i	−0.573688	−	0.864238i
$568$	−514.883			−0.906484
$569$	−666.084	−	384.564i	−1.17062	−	0.675859i	−0.216796	−	0.976217i	$-0.569561\pi$
$569$	−666.084	−	384.564i	−1.17062	−	0.675859i	−0.953827	+	0.300358i	$0.902894\pi$
$570$		0			0
$571$	−48.7253	−	84.3947i	−0.0853333	−	0.147802i	0.820200	−	0.572077i	$-0.193862\pi$
$571$	−48.7253	−	84.3947i	−0.0853333	−	0.147802i	−0.905533	+	0.424275i	$0.860529\pi$
$572$	−190.134	+	109.774i	−0.332402	+	0.191913i
$573$	444.553	+	742.966i	0.775834	+	1.29663i
$574$	−232.829	+	403.272i	−0.405626	+	0.702565i
$575$		0			0
$576$	−470.745	−	759.581i	−0.817265	−	1.31872i
$577$	−277.283			−0.480560			−0.240280	−	0.970704i	$-0.577239\pi$
$577$	−277.283			−0.480560			−0.240280	+	0.970704i	$0.577239\pi$
$578$	923.493	+	533.179i	1.59774	+	0.922454i
$579$	4.43181	+	283.969i	0.00765425	+	0.490447i
$580$		0			0
$581$	−124.191	+	71.7018i	−0.213754	+	0.123411i
$582$	1071.45	−	16.7218i	1.84098	−	0.0287315i
$583$	−377.443	+	653.750i	−0.647415	+	1.12136i
$584$			2311.25i			3.95761i
$585$		0			0
$586$	−1071.52			−1.82854
$587$	−405.017	−	233.836i	−0.689977	−	0.398358i	0.113626	−	0.993524i	$-0.463753\pi$
$587$	−405.017	−	233.836i	−0.689977	−	0.398358i	−0.803603	+	0.595165i	$0.797087\pi$
$588$	−95.5345	+	57.1629i	−0.162474	+	0.0972158i
$589$	98.3565	+	170.358i	0.166989	+	0.289233i
$590$		0			0
$591$	−189.349	+	340.111i	−0.320387	+	0.575483i
$592$	−968.922	+	1678.22i	−1.63669	+	2.83483i
$593$		−	254.411i		−	0.429023i	−0.976721	−	0.214512i	$-0.931184\pi$
$593$		−	254.411i		−	0.429023i	0.976721	−	0.214512i	$-0.0688160\pi$
$594$	637.981	−	409.300i	1.07404	−	0.689057i
$595$		0			0
$596$	801.577	+	462.791i	1.34493	+	0.776495i
$597$	−357.602	−	199.087i	−0.598998	−	0.333478i
$598$	193.988	+	335.997i	0.324394	+	0.561867i
$599$	352.081	−	203.274i	0.587780	−	0.339355i	−0.176439	−	0.984312i	$-0.556458\pi$
$599$	352.081	−	203.274i	0.587780	−	0.339355i	0.764219	+	0.644956i	$0.223124\pi$
$600$		0			0
$601$	−249.967	+	432.956i	−0.415919	+	0.720393i	−0.995524	−	0.0945042i	$-0.969873\pi$
$601$	−249.967	+	432.956i	−0.415919	+	0.720393i	0.579605	+	0.814897i	$0.303207\pi$
$602$			1115.41i			1.85285i
$603$	356.726	−	664.963i	0.591585	−	1.10276i
$604$	2263.59			3.74766
$605$		0			0
$606$	−23.7973	−	1524.81i	−0.0392695	−	2.51620i
$607$	29.9627	+	51.8970i	0.0493620	+	0.0854975i	0.889651	−	0.456642i	$-0.150948\pi$
$607$	29.9627	+	51.8970i	0.0493620	+	0.0854975i	−0.840289	+	0.542139i	$0.817615\pi$
$608$	466.944	−	269.590i	0.767999	−	0.443405i
$609$	−357.174	+	5.57430i	−0.586493	+	0.00915321i
$610$		0			0
$611$		−	123.614i		−	0.202314i
$612$	150.195	+	80.5735i	0.245417	+	0.131656i
$613$	373.866			0.609896			0.304948	−	0.952369i	$-0.401361\pi$
$613$	373.866			0.609896			0.304948	+	0.952369i	$0.401361\pi$
$614$	766.071	+	442.291i	1.24767	+	0.720344i
$615$		0			0
$616$	−607.650	−	1052.48i	−0.986444	−	1.70857i
$617$	320.088	−	184.803i	0.518782	−	0.299519i	−0.217654	−	0.976026i	$-0.569841\pi$
$617$	320.088	−	184.803i	0.518782	−	0.299519i	0.736436	+	0.676507i	$0.236507\pi$
$618$	−937.202	+	1683.41i	−1.51651	+	2.72397i
$619$	−598.225	+	1036.16i	−0.966438	+	1.67392i	−0.260738	+	0.965410i	$0.583966\pi$
$619$	−598.225	+	1036.16i	−0.966438	+	1.67392i	−0.705701	+	0.708510i	$0.749368\pi$
$620$		0			0
$621$	−516.074	−	804.413i	−0.831037	−	1.29535i
$622$	1935.51			3.11175
$623$	182.719	+	105.493i	0.293289	+	0.169331i
$624$	333.616	+	185.733i	0.534640	+	0.297649i
$625$		0			0
$626$	−1602.54	+	925.224i	−2.55996	+	1.47799i
$627$	85.4535	+	142.816i	0.136289	+	0.227776i
$628$	7.89377	−	13.6724i	0.0125697	−	0.0217713i
$629$		−	84.9044i		−	0.134983i
$630$		0			0
$631$	628.525			0.996078			0.498039	−	0.867155i	$-0.334054\pi$
$631$	628.525			0.996078			0.498039	+	0.867155i	$0.334054\pi$
$632$	−1553.43	−	896.870i	−2.45795	−	1.41910i
$633$	7.40738	+	474.629i	0.0117020	+	0.749808i
$634$	409.541	+	709.345i	0.645963	+	1.11884i
$635$		0			0
$636$	3002.32	−	46.8563i	4.72063	−	0.0736734i
$637$	5.46374	−	9.46347i	0.00857730	−	0.0148563i
$638$		−	460.364i		−	0.721573i
$639$	−176.817	+	109.581i	−0.276709	+	0.171489i
$640$		0			0
$641$	824.417	+	475.977i	1.28614	+	0.742554i	0.977964	−	0.208774i	$-0.0669474\pi$
$641$	824.417	+	475.977i	1.28614	+	0.742554i	0.308178	+	0.951329i	$0.400281\pi$
$642$	948.506	−	567.537i	1.47742	−	0.884014i
$643$	−35.7759	−	61.9656i	−0.0556390	−	0.0963696i	0.836864	−	0.547410i	$-0.184386\pi$
$643$	−35.7759	−	61.9656i	−0.0556390	−	0.0963696i	−0.892503	+	0.451041i	$0.851053\pi$
$644$	−2217.41	+	1280.22i	−3.44318	+	1.98792i
$645$		0			0
$646$	−26.2252	+	45.4233i	−0.0405962	+	0.0703147i
$647$		−	900.292i		−	1.39149i	−0.718290	−	0.695744i	$-0.755075\pi$
$647$		−	900.292i		−	1.39149i	0.718290	−	0.695744i	$-0.244925\pi$
$648$	−1615.88	−	802.958i	−2.49365	−	1.23913i
$649$	−35.7436			−0.0550748
$650$		0			0
$651$	−507.058	−	282.293i	−0.778892	−	0.433630i
$652$	207.604	+	359.580i	0.318410	+	0.551503i
$653$	222.825	−	128.648i	0.341233	−	0.197011i	−0.319584	−	0.947558i	$-0.603543\pi$
$653$	222.825	−	128.648i	0.341233	−	0.197011i	0.660817	+	0.750547i	$0.270210\pi$
$654$	−15.1172	−	25.2649i	−0.0231150	−	0.0386314i
$655$		0			0
$656$			744.690i			1.13520i
$657$	491.897	+	793.711i	0.748701	+	1.20808i
$658$	1143.36			1.73763
$659$	477.967	+	275.954i	0.725291	+	0.418747i	0.816697	−	0.577067i	$-0.195803\pi$
$659$	477.967	+	275.954i	0.725291	+	0.418747i	−0.0914057	+	0.995814i	$0.529136\pi$
$660$		0			0
$661$	523.413	+	906.578i	0.791851	+	1.37153i	0.924820	+	0.380405i	$0.124216\pi$
$661$	523.413	+	906.578i	0.791851	+	1.37153i	−0.132969	+	0.991120i	$0.542451\pi$
$662$	307.309	−	177.425i	0.464214	−	0.268014i
$663$	−16.7275	+	0.261061i	−0.0252300	+	0.000393757i
$664$	−219.971	+	381.002i	−0.331282	+	0.573798i
$665$		0			0
$666$	46.8683	+	1501.18i	0.0703728	+	2.25402i
$667$	−580.460			−0.870254
$668$	−79.8342	−	46.0923i	−0.119512	−	0.0690004i
$669$	530.956	−	317.696i	0.793656	−	0.474883i
$670$		0			0
$671$	500.531	−	288.982i	0.745948	−	0.430673i
$672$	−773.751	+	1389.82i	−1.15142	+	2.06819i
$673$	118.875	−	205.898i	0.176635	−	0.305940i	−0.764091	−	0.645108i	$-0.776812\pi$
$673$	118.875	−	205.898i	0.176635	−	0.305940i	0.940726	+	0.339168i	$0.110146\pi$
$674$		−	1927.98i		−	2.86050i
$675$		0			0
$676$	1597.82			2.36364
$677$	145.591	+	84.0570i	0.215053	+	0.124161i	0.603658	−	0.797244i	$-0.293709\pi$
$677$	145.591	+	84.0570i	0.215053	+	0.124161i	−0.388605	+	0.921405i	$0.627043\pi$
$678$	26.7783	+	14.9082i	0.0394961	+	0.0219885i
$679$	−347.066	−	601.136i	−0.511143	−	0.885325i
$680$		0			0
$681$	−226.889	−	379.192i	−0.333171	−	0.556817i
$682$	373.958	−	647.714i	0.548325	−	0.949727i
$683$			995.446i			1.45746i	0.684800	+	0.728731i	$0.259889\pi$
$683$			995.446i			1.45746i	−0.684800	+	0.728731i	$0.740111\pi$
$684$	312.948	−	583.359i	0.457527	−	0.852864i
$685$		0			0
$686$	−1063.82	−	614.194i	−1.55075	−	0.895327i
$687$	−1.27102	−	81.4405i	−0.00185010	−	0.118545i
$688$	891.896	+	1544.81i	1.29636	+	2.24536i
$689$	−255.239	+	147.362i	−0.370449	+	0.213879i
$690$		0			0
$691$	298.570	−	517.138i	0.432084	−	0.748391i	−0.564969	−	0.825112i	$-0.691112\pi$
$691$	298.570	−	517.138i	0.432084	−	0.748391i	0.997053	+	0.0767211i	$0.0244451\pi$
$692$			1468.19i			2.12167i
$693$	−432.671	−	232.111i	−0.624345	−	0.334936i
$694$	416.355			0.599936
$695$		0			0
$696$	−940.407	+	562.691i	−1.35116	+	0.808464i
$697$	−16.3139	−	28.2564i	−0.0234058	−	0.0405401i
$698$	−2007.13	+	1158.82i	−2.87555	+	1.66020i
$699$	57.7888	−	103.801i	0.0826736	−	0.148499i
$700$		0			0
$701$		−	413.729i		−	0.590199i	−0.955467	−	0.295099i	$-0.904647\pi$
$701$		−	413.729i		−	0.590199i	0.955467	−	0.295099i	$-0.0953528\pi$
$702$	295.612	−	13.8496i	0.421100	−	0.0197287i
$703$	−329.769			−0.469089
$704$	−646.058	−	373.002i	−0.917696	−	0.529832i
$705$		0			0
$706$	−1052.91	−	1823.69i	−1.49137	−	2.58312i
$707$	−855.497	+	493.921i	−1.21004	+	0.698616i
$708$	73.0009	+	122.004i	0.103109	+	0.172322i
$709$	328.568	−	569.096i	0.463424	−	0.802674i	−0.535705	−	0.844405i	$-0.679954\pi$
$709$	328.568	−	569.096i	0.463424	−	0.802674i	0.999129	+	0.0417311i	$0.0132873\pi$
$710$		0			0
$711$	−724.345	+	22.6147i	−1.01877	+	0.0318070i
$712$	647.277			0.909096
$713$	−816.684	−	471.513i	−1.14542	−	0.661308i
$714$	−2.41467	−	154.720i	−0.00338189	−	0.216695i
$715$		0			0
$716$	−1380.53	+	797.051i	−1.92812	+	1.11320i
$717$	−190.293	+	2.96984i	−0.265401	+	0.00414203i
$718$	775.572	−	1343.33i	1.08018	−	1.87093i
$719$			217.226i			0.302122i	0.988524	+	0.151061i	$0.0482690\pi$
$719$			217.226i			0.302122i	−0.988524	+	0.151061i	$0.951731\pi$
$720$		0			0
$721$	1248.06			1.73101
$722$	−991.751	−	572.588i	−1.37362	−	0.793058i
$723$	−355.858	+	212.927i	−0.492197	+	0.294505i
$724$	−151.093	−	261.701i	−0.208692	−	0.361466i
$725$		0			0
$726$	−351.973	+	632.218i	−0.484812	+	0.870824i
$727$	304.437	−	527.300i	0.418757	−	0.725309i	−0.577057	−	0.816704i	$-0.695799\pi$
$727$	304.437	−	527.300i	0.418757	−	0.725309i	0.995815	+	0.0913946i	$0.0291325\pi$
$728$		−	474.481i		−	0.651760i
$729$	−725.807	+	68.1584i	−0.995620	+	0.0934958i
$730$		0			0
$731$	−67.6840	−	39.0774i	−0.0925910	−	0.0534574i
$732$	−2008.65	−	1118.27i	−2.74405	−	1.52769i
$733$	−440.351	−	762.709i	−0.600751	−	1.04053i	−0.992708	−	0.120548i	$-0.961535\pi$
$733$	−440.351	−	762.709i	−0.600751	−	1.04053i	0.391957	−	0.919984i	$-0.371798\pi$
$734$	2031.79	−	1173.05i	2.76810	−	1.59816i
$735$		0			0
$736$	−1292.39	+	2238.49i	−1.75597	+	3.04143i
$737$		−	629.950i		−	0.854749i
$738$	304.040	+	490.592i	0.411979	+	0.664758i
$739$	−917.157			−1.24108			−0.620540	−	0.784175i	$-0.713086\pi$
$739$	−917.157			−1.24108			−0.620540	+	0.784175i	$0.713086\pi$
$740$		0			0
$741$	1.01396	+	64.9698i	0.00136837	+	0.0876786i
$742$	−1363.02	−	2360.82i	−1.83695	−	3.18170i
$743$	956.492	−	552.231i	1.28734	−	0.743245i	0.309159	−	0.951010i	$-0.399952\pi$
$743$	956.492	−	552.231i	1.28734	−	0.743245i	0.978179	+	0.207765i	$0.0666191\pi$
$744$	−1780.20	+	27.7830i	−2.39274	+	0.0373427i
$745$		0			0
$746$			1460.74i			1.95810i
$747$	5.54662	+	177.657i	0.00742519	+	0.237827i
$748$	142.287			0.190223
$749$	−620.071	−	357.998i	−0.827866	−	0.477968i
$750$		0			0
$751$	−330.239	−	571.990i	−0.439732	−	0.761638i	0.557936	−	0.829884i	$-0.311593\pi$
$751$	−330.239	−	571.990i	−0.439732	−	0.761638i	−0.997669	+	0.0682453i	$0.978260\pi$
$752$	1583.51	−	914.241i	2.10573	−	1.21575i
$753$	272.121	−	488.787i	0.361383	−	0.649120i
$754$	89.8684	−	155.657i	0.119189	−	0.206441i
$755$		0			0
$756$	91.4003	+	1950.89i	0.120900	+	2.58055i
$757$	353.728			0.467276			0.233638	−	0.972324i	$-0.424937\pi$
$757$	353.728			0.467276			0.233638	+	0.972324i	$0.424937\pi$
$758$	169.702	+	97.9778i	0.223882	+	0.129258i
$759$	−697.096	−	388.093i	−0.918441	−	0.511321i
$760$		0			0
$761$	708.380	−	408.983i	0.930854	−	0.537429i	0.0437722	−	0.999042i	$-0.486062\pi$
$761$	708.380	−	408.983i	0.930854	−	0.537429i	0.887081	+	0.461613i	$0.152729\pi$
$762$	1111.18	+	1857.08i	1.45824	+	2.43711i
$763$	−9.53584	+	16.5166i	−0.0124978	+	0.0216469i
$764$		−	2875.00i		−	3.76309i
$765$		0			0
$766$	414.465			0.541078
$767$	−12.0855	−	6.97756i	−0.0157568	−	0.00909721i
$768$	−4.78832	−	306.812i	−0.00623479	−	0.399495i
$769$	500.408	+	866.732i	0.650725	+	1.12709i	0.982947	+	0.183888i	$0.0588684\pi$
$769$	500.408	+	866.732i	0.650725	+	1.12709i	−0.332222	+	0.943201i	$0.607798\pi$
$770$		0			0
$771$	698.670	−	10.9039i	0.906187	−	0.0141426i
$772$	471.530	−	816.713i	0.610790	−	1.05792i
$773$			860.440i			1.11312i	0.830808	+	0.556559i	$0.187879\pi$
$773$			860.440i			1.11312i	−0.830808	+	0.556559i	$0.812121\pi$
$774$	1218.28	+	653.558i	1.57401	+	0.844390i
$775$		0			0
$776$	−1844.20	−	1064.75i	−2.37655	−	1.37210i
$777$	834.850	−	499.531i	1.07445	−	0.642898i
$778$	−197.633	−	342.310i	−0.254027	−	0.439987i
$779$	−109.748	+	63.3632i	−0.140884	+	0.0813391i
$780$		0			0
$781$	−86.8283	+	150.391i	−0.111176	+	0.192562i
$782$		−	251.442i		−	0.321538i
$783$	−203.192	+	393.380i	−0.259504	+	0.502401i
$784$	161.638			0.206171
$785$		0			0
$786$	2276.09	+	1267.16i	2.89579	+	1.61216i
$787$	463.491	+	802.789i	0.588933	+	1.02006i	0.994372	+	0.105940i	$0.0337853\pi$
$787$	463.491	+	802.789i	0.588933	+	1.02006i	−0.405439	+	0.914122i	$0.632881\pi$
$788$	1119.42	−	646.297i	1.42058	−	0.820174i
$789$	−16.6256	−	27.7858i	−0.0210717	−	0.0352165i
$790$		0			0
$791$		−	19.8531i		−	0.0250987i
$792$	−1505.58	+	47.0058i	−1.90099	+	0.0593507i
$793$	225.651			0.284553
$794$	−323.236	−	186.620i	−0.407098	−	0.235038i
$795$		0			0
$796$	679.534	+	1176.99i	0.853686	+	1.47863i
$797$	825.230	−	476.447i	1.03542	−	0.597800i	0.116888	−	0.993145i	$-0.462708\pi$
$797$	825.230	−	476.447i	1.03542	−	0.597800i	0.918533	+	0.395345i	$0.129375\pi$
$798$	−600.934	+	9.37859i	−0.753050	+	0.0117526i
$799$	−40.0564	+	69.3797i	−0.0501332	+	0.0868332i
$800$		0			0
$801$	222.283	−	137.758i	0.277507	−	0.171983i
$802$	−587.129			−0.732082
$803$	675.087	+	389.762i	0.840707	+	0.485382i
$804$	−2150.21	+	1286.58i	−2.67440	+	1.60022i
$805$		0			0
$806$	252.883	−	146.002i	0.313750	−	0.181144i
$807$	85.3094	−	153.234i	0.105712	−	0.189881i
$808$	−1515.28	+	2624.55i	−1.87535	+	3.24820i
$809$			1425.22i			1.76171i	0.473387	+	0.880855i	$0.343031\pi$
$809$			1425.22i			1.76171i	−0.473387	+	0.880855i	$0.656969\pi$
$810$		0			0
$811$	−473.774			−0.584185			−0.292093	−	0.956390i	$-0.594352\pi$
$811$	−473.774			−0.584185			−0.292093	+	0.956390i	$0.594352\pi$
$812$	1027.26	+	593.087i	1.26509	+	0.730402i
$813$	171.947	+	95.7277i	0.211497	+	0.117746i
$814$	626.903	+	1085.83i	0.770151	+	1.33394i
$815$		0			0
$816$	−127.060	−	212.351i	−0.155711	−	0.260234i
$817$	−151.777	+	262.885i	−0.185773	+	0.321769i
$818$		−	2560.42i		−	3.13010i
$819$	−100.983	−	162.943i	−0.123300	−	0.198953i
$820$		0			0
$821$	−63.4905	−	36.6562i	−0.0773331	−	0.0446483i	0.460835	−	0.887486i	$-0.347550\pi$
$821$	−63.4905	−	36.6562i	−0.0773331	−	0.0446483i	−0.538168	+	0.842838i	$0.680883\pi$
$822$	31.1403	+	1995.32i	0.0378836	+	2.42740i
$823$	316.027	+	547.374i	0.383994	+	0.665096i	0.991629	−	0.129120i	$-0.0412151\pi$
$823$	316.027	+	547.374i	0.383994	+	0.665096i	−0.607635	+	0.794216i	$0.707882\pi$
$824$	3315.90	−	1914.44i	4.02416	−	2.32335i
$825$		0			0
$826$	64.5385	−	111.784i	0.0781338	−	0.135332i
$827$			226.153i			0.273462i	0.990608	+	0.136731i	$0.0436597\pi$
$827$			226.153i			0.273462i	−0.990608	+	0.136731i	$0.956340\pi$
$828$	99.0338	+	3172.03i	0.119606	+	3.83095i
$829$	−522.396			−0.630152			−0.315076	−	0.949067i	$-0.602030\pi$
$829$	−522.396			−0.630152			−0.315076	+	0.949067i	$0.602030\pi$
$830$		0			0
$831$	−690.588	+	413.212i	−0.831032	+	0.497247i
$832$	−145.629	−	252.236i	−0.175034	−	0.303168i
$833$	−6.13317	+	3.54099i	−0.00736275	+	0.00425089i
$834$	−174.859	+	314.084i	−0.209663	+	0.376599i
$835$		0			0
$836$		−	552.642i		−	0.661055i
$837$	−605.429	+	388.415i	−0.723332	+	0.464057i
$838$	−192.792			−0.230061
$839$	511.329	+	295.216i	0.609450	+	0.351866i	0.772750	−	0.634710i	$-0.218881\pi$
$839$	511.329	+	295.216i	0.609450	+	0.351866i	−0.163300	+	0.986576i	$0.552214\pi$
$840$		0			0
$841$	−286.046	−	495.446i	−0.340126	−	0.589115i
$842$	−47.7379	+	27.5615i	−0.0566959	+	0.0327334i
$843$	−283.568	−	473.918i	−0.336380	−	0.562180i
$844$	788.120	−	1365.06i	0.933791	−	1.61737i
$845$		0			0
$846$	669.931	−	1248.80i	0.791881	−	1.47613i
$847$	468.718			0.553386
$848$	−3775.47	−	2179.77i	−4.45220	−	2.57048i
$849$	21.6566	+	1387.65i	0.0255083	+	1.63445i
$850$		0			0
$851$	1369.09	−	790.444i	1.60880	−	0.928841i
$852$	690.666	−	10.7790i	0.810640	−	0.0126514i
$853$	693.749	−	1201.61i	0.813305	−	1.40869i	−0.0972332	−	0.995262i	$-0.530999\pi$
$853$	693.749	−	1201.61i	0.813305	−	1.40869i	0.910538	−	0.413424i	$-0.135667\pi$
$854$			2087.14i			2.44396i
$855$		0			0
$856$	−2196.58			−2.56610
$857$	683.058	+	394.363i	0.797033	+	0.460167i	0.842433	−	0.538801i	$-0.181123\pi$
$857$	683.058	+	394.363i	0.797033	+	0.460167i	−0.0453994	+	0.998969i	$0.514456\pi$
$858$	211.998	−	126.848i	0.247084	−	0.147842i
$859$	−413.601	−	716.378i	−0.481491	−	0.833968i	0.518283	−	0.855209i	$-0.326571\pi$
$859$	−413.601	−	716.378i	−0.481491	−	0.833968i	−0.999774	+	0.0212416i	$0.993238\pi$
$860$		0			0
$861$	181.859	−	326.657i	0.211218	−	0.379393i
$862$	72.2667	−	125.170i	0.0838361	−	0.145208i
$863$			1089.70i			1.26268i	0.775504	+	0.631342i	$0.217496\pi$
$863$			1089.70i			1.26268i	−0.775504	+	0.631342i	$0.782504\pi$
$864$	1064.63	+	1659.45i	1.23221	+	1.92066i
$865$		0			0
$866$	1762.45	+	1017.55i	2.03516	+	1.17500i
$867$	−748.044	−	416.457i	−0.862796	−	0.480342i
$868$	963.540	+	1668.90i	1.11007	+	1.92270i
$869$	−523.930	+	302.491i	−0.602912	+	0.348091i
$870$		0			0
$871$	122.974	−	212.996i	0.141187	−	0.244542i
$872$			58.5093i			0.0670979i
$873$	−859.931	+	26.8479i	−0.985029	+	0.0307536i
$874$	−976.605			−1.11740
$875$		0			0
$876$	−48.3856	−	3100.31i	−0.0552347	−	3.53917i
$877$	213.875	+	370.443i	0.243872	+	0.422398i	0.961814	−	0.273705i	$-0.0882491\pi$
$877$	213.875	+	370.443i	0.243872	+	0.422398i	−0.717942	+	0.696103i	$0.754916\pi$
$878$	−813.575	+	469.718i	−0.926623	+	0.534986i
$879$	860.202	−	13.4249i	0.978614	−	0.0152729i
$880$		0			0
$881$			1113.87i			1.26432i	0.774837	+	0.632161i	$0.217832\pi$
$881$			1113.87i			1.26432i	−0.774837	+	0.632161i	$0.782168\pi$
$882$	106.485	−	65.9932i	0.120731	−	0.0748222i
$883$	408.581			0.462719			0.231359	−	0.972868i	$-0.425683\pi$
$883$	408.581			0.462719			0.231359	+	0.972868i	$0.425683\pi$
$884$	48.1094	+	27.7760i	0.0544224	+	0.0314208i
$885$		0			0
$886$	−1365.46	−	2365.05i	−1.54116	−	2.66936i
$887$	755.098	−	435.956i	0.851294	−	0.491495i	−0.00979311	−	0.999952i	$-0.503117\pi$
$887$	755.098	−	435.956i	0.851294	−	0.491495i	0.861087	+	0.508457i	$0.169784\pi$
$888$	1451.82	−	2607.78i	1.63494	−	2.93669i
$889$	700.924	−	1214.04i	0.788441	−	1.36562i
$890$		0			0
$891$	−507.033	+	336.572i	−0.569060	+	0.377746i
$892$	−2054.60			−2.30336
$893$	269.471	+	155.579i	0.301760	+	0.174221i
$894$	−910.004	−	506.624i	−1.01790	−	0.566693i
$895$		0			0
$896$	496.272	−	286.523i	0.553875	−	0.319780i
$897$	−159.940	−	267.302i	−0.178305	−	0.297995i
$898$	176.965	−	306.512i	0.197066	−	0.341328i
$899$			436.874i			0.485956i
$900$		0			0
$901$	191.008			0.211995
$902$	417.270	+	240.911i	0.462606	+	0.267085i
$903$	−13.9748	−	895.436i	−0.0154759	−	0.991623i
$904$	−30.4533	−	52.7466i	−0.0336872	−	0.0583480i
$905$		0			0
$906$	−2546.82	+	39.7475i	−2.81106	+	0.0438714i
$907$	−843.097	+	1460.29i	−0.929544	+	1.61002i	−0.145459	+	0.989364i	$0.546466\pi$
$907$	−843.097	+	1460.29i	−0.929544	+	1.61002i	−0.784085	+	0.620653i	$0.786867\pi$
$908$			1467.33i			1.61600i
$909$	38.2081	+	1223.80i	0.0420332	+	1.34631i
$910$		0			0
$911$	−383.084	−	221.173i	−0.420509	−	0.242781i	0.274786	−	0.961505i	$-0.411393\pi$
$911$	−383.084	−	221.173i	−0.420509	−	0.242781i	−0.695295	+	0.718724i	$0.744726\pi$
$912$	−824.773	+	493.502i	−0.904356	+	0.541120i
$913$	74.1907	+	128.502i	0.0812603	+	0.140747i
$914$	−1321.60	+	763.024i	−1.44595	+	0.834819i
$915$		0			0
$916$	−135.232	+	234.228i	−0.147633	+	0.255708i
$917$		−	1687.46i		−	1.84020i
$918$	−170.404	−	88.0182i	−0.185625	−	0.0958804i
$919$	−182.236			−0.198298			−0.0991489	−	0.995073i	$-0.531612\pi$
$919$	−182.236			−0.198298			−0.0991489	+	0.995073i	$0.531612\pi$
$920$		0			0
$921$	−620.530	−	345.466i	−0.673757	−	0.375099i
$922$	−1103.96	−	1912.12i	−1.19736	−	2.07388i
$923$	−58.7162	+	33.8998i	−0.0636145	+	0.0367279i
$924$	837.137	+	1399.08i	0.905992	+	1.51416i
$925$		0			0
$926$			2996.47i			3.23592i
$927$	731.279	−	1363.16i	0.788866	−	1.47050i
$928$	1197.45			1.29035
$929$	−1150.27	−	664.111i	−1.23819	−	0.714867i	−0.269463	−	0.963011i	$-0.586846\pi$
$929$	−1150.27	−	664.111i	−1.23819	−	0.714867i	−0.968723	+	0.248144i	$0.920179\pi$
$930$		0			0
$931$	13.7532	+	23.8213i	0.0147725	+	0.0255868i
$932$	−341.644	+	197.248i	−0.366571	+	0.211640i
$933$	−1553.79	+	24.2496i	−1.66537	+	0.0259910i
$934$	−38.5671	+	66.8003i	−0.0412924	+	0.0715206i
$935$		0			0
$936$	−518.239	−	278.014i	−0.553674	−	0.297024i
$937$	276.582			0.295178			0.147589	−	0.989049i	$-0.452849\pi$
$937$	276.582			0.295178			0.147589	+	0.989049i	$0.452849\pi$
$938$	1970.10	+	1137.44i	2.10032	+	1.21262i
$939$	1274.90	−	762.832i	1.35772	−	0.812388i
$940$		0			0
$941$	1083.50	−	625.557i	1.15143	−	0.664779i	0.202196	−	0.979345i	$-0.435192\pi$
$941$	1083.50	−	625.557i	1.15143	−	0.664779i	0.949236	+	0.314566i	$0.101859\pi$
$942$	−8.64142	+	15.5218i	−0.00917348	+	0.0164775i
$943$	303.758	−	526.124i	0.322119	−	0.557926i
$944$		−	206.422i		−	0.218668i
$945$		0			0
$946$	1154.13			1.22001
$947$	935.323	+	540.009i	0.987670	+	0.570232i	0.904577	−	0.426310i	$-0.140187\pi$
$947$	935.323	+	540.009i	0.987670	+	0.570232i	0.0830930	+	0.996542i	$0.473520\pi$
$948$	2102.55	+	1170.54i	2.21788	+	1.23475i
$949$	152.172	+	263.570i	0.160350	+	0.277734i
$950$		0			0
$951$	−337.660	−	564.319i	−0.355057	−	0.593396i
$952$	−153.753	+	266.308i	−0.161505	+	0.279735i
$953$		−	328.534i		−	0.344737i	−0.985033	−	0.172369i	$-0.944858\pi$
$953$		−	328.534i		−	0.344737i	0.985033	−	0.172369i	$-0.0551420\pi$
$954$	−3377.18	+	105.439i	−3.54002	+	0.110523i
$955$		0			0
$956$	547.294	+	315.980i	0.572483	+	0.330523i
$957$	5.76780	+	369.572i	0.00602696	+	0.386178i
$958$	939.239	+	1626.81i	0.980416	+	1.69813i
$959$	1119.47	−	646.328i	1.16733	−	0.673961i
$960$		0			0
$961$	125.623	−	217.585i	0.130721	−	0.226416i
$962$			489.515i			0.508851i
$963$	−754.334	+	467.493i	−0.783316	+	0.485454i
$964$	1377.04			1.42846
$965$		0			0
$966$	2472.39	−	1479.35i	2.55941	−	1.53142i
$967$	−298.854	−	517.631i	−0.309053	−	0.535296i	0.669102	−	0.743170i	$-0.266679\pi$
$967$	−298.854	−	517.631i	−0.309053	−	0.535296i	−0.978155	+	0.207875i	$0.933345\pi$
$968$	1245.31	−	718.981i	1.28648	−	0.742749i
$969$	20.4840	−	36.7936i	0.0211393	−	0.0379707i
$970$		0			0
$971$			711.597i			0.732850i	0.930448	+	0.366425i	$0.119418\pi$
$971$			711.597i			0.732850i	−0.930448	+	0.366425i	$0.880582\pi$
$972$	2184.36	+	1043.26i	2.24729	+	1.07332i
$973$	232.857			0.239319
$974$	−260.279	−	150.272i	−0.267226	−	0.154283i
$975$		0			0
$976$	1668.90	+	2890.61i	1.70994	+	2.96169i
$977$	−292.262	+	168.738i	−0.299142	+	0.172710i	−0.642058	−	0.766656i	$-0.721919\pi$
$977$	−292.262	+	168.738i	−0.299142	+	0.172710i	0.342915	+	0.939366i	$0.388586\pi$
$978$	−239.895	−	400.928i	−0.245291	−	0.409947i
$979$	109.155	−	189.062i	0.111496	−	0.193117i
$980$		0			0
$981$	12.4524	+	20.0928i	0.0126936	+	0.0204820i
$982$	−1803.38			−1.83643
$983$	274.504	+	158.485i	0.279252	+	0.161226i	0.633085	−	0.774083i	$-0.281789\pi$
$983$	274.504	+	158.485i	0.279252	+	0.161226i	−0.353833	+	0.935309i	$0.615122\pi$
$984$	−17.8983	−	1146.84i	−0.0181894	−	1.16549i
$985$		0			0
$986$	−100.879	+	58.2427i	−0.102312	+	0.0590697i
$987$	−917.869	+	14.3249i	−0.929959	+	0.0145136i
$988$	107.882	−	186.857i	0.109193	−	0.189127i
$989$		−	1455.21i		−	1.47140i
$990$		0			0
$991$	685.922			0.692152			0.346076	−	0.938207i	$-0.387514\pi$
$991$	685.922			0.692152			0.346076	+	0.938207i	$0.387514\pi$
$992$	1684.76	+	972.700i	1.69835	+	0.980544i
$993$	−244.480	+	146.284i	−0.246203	+	0.147315i
$994$	−313.554	−	543.092i	−0.315447	−	0.546370i
$995$		0			0
$996$	287.094	−	515.682i	0.288247	−	0.517753i
$997$	293.035	−	507.551i	0.293917	−	0.509078i	−0.680816	−	0.732455i	$-0.738375\pi$
$997$	293.035	−	507.551i	0.293917	−	0.509078i	0.974732	+	0.223376i	$0.0717079\pi$
$998$			130.823i			0.131086i
$999$	−56.4330	−	1204.53i	−0.0564895	−	1.20574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.j.b.101.8		16
3.2	odd	2		675.3.j.b.251.1		16
5.2	odd	4		225.3.i.b.74.1		32
5.3	odd	4		225.3.i.b.74.16		32
5.4	even	2		45.3.i.a.11.1	✓	16
9.4	even	3		675.3.j.b.476.1		16
9.5	odd	6	inner	225.3.j.b.176.8		16
15.2	even	4		675.3.i.c.224.16		32
15.8	even	4		675.3.i.c.224.1		32
15.14	odd	2		135.3.i.a.116.8		16
20.19	odd	2		720.3.bs.c.641.2		16
45.4	even	6		135.3.i.a.71.8		16
45.13	odd	12		675.3.i.c.449.16		32
45.14	odd	6		45.3.i.a.41.1	yes	16
45.22	odd	12		675.3.i.c.449.1		32
45.23	even	12		225.3.i.b.149.1		32
45.29	odd	6		405.3.c.a.161.1		16
45.32	even	12		225.3.i.b.149.16		32
45.34	even	6		405.3.c.a.161.16		16
60.59	even	2		2160.3.bs.c.1601.1		16
180.59	even	6		720.3.bs.c.401.2		16
180.139	odd	6		2160.3.bs.c.881.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.1	✓	16	5.4	even	2
45.3.i.a.41.1	yes	16	45.14	odd	6
135.3.i.a.71.8		16	45.4	even	6
135.3.i.a.116.8		16	15.14	odd	2
225.3.i.b.74.1		32	5.2	odd	4
225.3.i.b.74.16		32	5.3	odd	4
225.3.i.b.149.1		32	45.23	even	12
225.3.i.b.149.16		32	45.32	even	12
225.3.j.b.101.8		16	1.1	even	1	trivial
225.3.j.b.176.8		16	9.5	odd	6	inner
405.3.c.a.161.1		16	45.29	odd	6
405.3.c.a.161.16		16	45.34	even	6
675.3.i.c.224.1		32	15.8	even	4
675.3.i.c.224.16		32	15.2	even	4
675.3.i.c.449.1		32	45.22	odd	12
675.3.i.c.449.16		32	45.13	odd	12
675.3.j.b.251.1		16	3.2	odd	2
675.3.j.b.476.1		16	9.4	even	3
720.3.bs.c.401.2		16	180.59	even	6
720.3.bs.c.641.2		16	20.19	odd	2
2160.3.bs.c.881.1		16	180.139	odd	6
2160.3.bs.c.1601.1		16	60.59	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23594 + 1.86827i) q^{2} +(-2.62117 - 1.45927i) q^{3} +(4.98088 + 8.62715i) q^{4} +(-5.75562 - 9.61919i) q^{6} +(-3.63061 + 6.28840i) q^{7} +22.2764i q^{8} +(4.74103 + 7.65001i) q^{9} +(6.50668 + 3.75663i) q^{11} +(-0.466354 - 29.8817i) q^{12} +(1.46668 + 2.54036i) q^{13} +(-23.4969 + 13.5659i) q^{14} +(-21.6949 + 37.5766i) q^{16} -1.90107i q^{17} +(1.04942 + 33.6125i) q^{18} -7.38378 q^{19} +(18.6929 - 11.1849i) q^{21} +(14.0368 + 24.3125i) q^{22} +(30.6549 - 17.6986i) q^{23} +(32.5074 - 58.3902i) q^{24} +10.9606i q^{26} +(-1.26358 - 26.9704i) q^{27} -72.3346 q^{28} +(-14.2015 - 8.19922i) q^{29} +(-13.3206 - 23.0720i) q^{31} +(-63.2391 + 36.5111i) q^{32} +(-11.5731 - 19.3418i) q^{33} +(3.55172 - 6.15176i) q^{34} +(-42.3832 + 79.0054i) q^{36} +44.6613 q^{37} +(-23.8935 - 13.7949i) q^{38} +(-0.137323 - 8.79899i) q^{39} +(14.8634 - 8.58140i) q^{41} +(81.3857 - 1.27016i) q^{42} +(20.5554 - 35.6031i) q^{43} +74.8454i q^{44} +132.263 q^{46} +(-36.4950 - 21.0704i) q^{47} +(111.701 - 66.8359i) q^{48} +(-1.86263 - 3.22616i) q^{49} +(-2.77419 + 4.98303i) q^{51} +(-14.6107 + 25.3065i) q^{52} +100.474i q^{53} +(46.2992 - 89.6354i) q^{54} +(-140.083 - 80.8770i) q^{56} +(19.3541 + 10.7750i) q^{57} +(-30.6367 - 53.0644i) q^{58} +(-4.12003 + 2.37870i) q^{59} +(38.4629 - 66.6197i) q^{61} -99.5461i q^{62} +(-65.3191 + 2.03933i) q^{63} -99.2915 q^{64} +(-1.31425 - 84.2107i) q^{66} +(-41.9225 - 72.6119i) q^{67} +(16.4008 - 9.46903i) q^{68} +(-106.179 + 1.65710i) q^{69} +23.1134i q^{71} +(-170.415 + 105.613i) q^{72} +103.753 q^{73} +(144.521 + 83.4395i) q^{74} +(-36.7778 - 63.7010i) q^{76} +(-47.2464 + 27.2777i) q^{77} +(15.9945 - 28.7296i) q^{78} +(-40.2610 + 69.7340i) q^{79} +(-36.0452 + 72.5379i) q^{81} +64.1296 q^{82} +(17.1034 + 9.87463i) q^{83} +(189.601 + 105.556i) q^{84} +(133.032 - 76.8063i) q^{86} +(25.2595 + 42.2153i) q^{87} +(-83.6843 + 144.945i) q^{88} -29.0566i q^{89} -21.2997 q^{91} +(305.377 + 176.310i) q^{92} +(1.24719 + 79.9139i) q^{93} +(-78.7306 - 136.365i) q^{94} +(219.040 - 3.41849i) q^{96} +(-47.7972 + 82.7872i) q^{97} -13.9196i q^{98} +(2.11011 + 67.5864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} + 16 q^{4} - 22 q^{6} - 2 q^{7} + 8 q^{9} - 18 q^{11} + 22 q^{12} + 10 q^{13} - 54 q^{14} - 32 q^{16} + 8 q^{18} - 52 q^{19} + 72 q^{21} + 24 q^{22} + 54 q^{23} + 108 q^{24} - 34 q^{27} - 32 q^{28}+ \cdots - 824 q^{99}+O(q^{100}) \) 16 * q - 4 * q^3 + 16 * q^4 - 22 * q^6 - 2 * q^7 + 8 * q^9 - 18 * q^11 + 22 * q^12 + 10 * q^13 - 54 * q^14 - 32 * q^16 + 8 * q^18 - 52 * q^19 + 72 * q^21 + 24 * q^22 + 54 * q^23 + 108 * q^24 - 34 * q^27 - 32 * q^28 - 54 * q^29 + 32 * q^31 - 216 * q^32 - 62 * q^33 + 54 * q^34 - 86 * q^36 - 44 * q^37 - 252 * q^38 + 160 * q^39 + 144 * q^41 + 270 * q^42 + 124 * q^43 - 108 * q^46 + 216 * q^47 + 172 * q^48 - 54 * q^49 - 106 * q^51 - 62 * q^52 - 316 * q^54 - 18 * q^56 + 236 * q^57 - 90 * q^58 - 486 * q^59 + 62 * q^61 + 132 * q^63 + 256 * q^64 + 208 * q^66 - 14 * q^67 + 288 * q^68 + 90 * q^69 - 804 * q^72 + 268 * q^73 + 540 * q^74 - 106 * q^76 - 702 * q^77 - 290 * q^78 - 40 * q^79 - 112 * q^81 + 204 * q^82 - 522 * q^83 + 714 * q^84 + 54 * q^86 - 106 * q^87 - 144 * q^88 + 136 * q^91 + 1332 * q^92 - 90 * q^93 - 150 * q^94 + 166 * q^96 + 142 * q^97 - 824 * q^99

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