LMFDB - Embedded newform 350.4.j.e.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(149,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, 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:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.4.j.e.249.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(-16.4545 - 8.50000i) q^{7} -8.00000i q^{8} +(-13.0000 + 22.5167i) q^{9} +O(q^{10})$	\(q+(-1.73205 - 1.00000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(-16.4545 - 8.50000i) q^{7} -8.00000i q^{8} +(-13.0000 + 22.5167i) q^{9} +(1.00000 + 1.73205i) q^{11} +(-3.46410 - 2.00000i) q^{12} -8.00000i q^{13} +(20.0000 + 31.1769i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(45.0333 - 26.0000i) q^{17} +(45.0333 - 26.0000i) q^{18} +(13.0000 - 22.5167i) q^{19} +(18.5000 - 0.866025i) q^{21} -4.00000i q^{22} +(-58.0237 - 33.5000i) q^{23} +(4.00000 + 6.92820i) q^{24} +(-8.00000 + 13.8564i) q^{26} -53.0000i q^{27} +(-3.46410 - 74.0000i) q^{28} -69.0000 q^{29} +(166.000 + 287.520i) q^{31} +(27.7128 - 16.0000i) q^{32} +(-1.73205 - 1.00000i) q^{33} -104.000 q^{34} -104.000 q^{36} +(169.741 + 98.0000i) q^{37} +(-45.0333 + 26.0000i) q^{38} +(4.00000 + 6.92820i) q^{39} +353.000 q^{41} +(-32.9090 - 17.0000i) q^{42} -369.000i q^{43} +(-4.00000 + 6.92820i) q^{44} +(67.0000 + 116.047i) q^{46} +(76.2102 + 44.0000i) q^{47} -16.0000i q^{48} +(198.500 + 279.726i) q^{49} +(-26.0000 + 45.0333i) q^{51} +(27.7128 - 16.0000i) q^{52} +(504.027 - 291.000i) q^{53} +(-53.0000 + 91.7987i) q^{54} +(-68.0000 + 131.636i) q^{56} +26.0000i q^{57} +(119.512 + 69.0000i) q^{58} +(-175.000 - 303.109i) q^{59} +(233.500 - 404.434i) q^{61} -664.000i q^{62} +(405.300 - 260.000i) q^{63} -64.0000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-252.013 + 145.500i) q^{67} +(180.133 + 104.000i) q^{68} +67.0000 q^{69} +770.000 q^{71} +(180.133 + 104.000i) q^{72} +(543.864 - 314.000i) q^{73} +(-196.000 - 339.482i) q^{74} +104.000 q^{76} +(-1.73205 - 37.0000i) q^{77} -16.0000i q^{78} +(585.000 - 1013.25i) q^{79} +(-324.500 - 562.050i) q^{81} +(-611.414 - 353.000i) q^{82} +525.000i q^{83} +(40.0000 + 62.3538i) q^{84} +(-369.000 + 639.127i) q^{86} +(59.7558 - 34.5000i) q^{87} +(13.8564 - 8.00000i) q^{88} +(44.5000 - 77.0763i) q^{89} +(-68.0000 + 131.636i) q^{91} -268.000i q^{92} +(-287.520 - 166.000i) q^{93} +(-88.0000 - 152.420i) q^{94} +(-16.0000 + 27.7128i) q^{96} +290.000i q^{97} +(-64.0859 - 683.000i) q^{98} -52.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9	$ 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9} + 4 q^{11} + 80 q^{14} - 32 q^{16} + 52 q^{19} + 74 q^{21} + 16 q^{24} - 32 q^{26} - 276 q^{29} + 664 q^{31} - 416 q^{34} - 416 q^{36} + 16 q^{39} + 1412 q^{41} - 16 q^{44} + 268 q^{46} + 794 q^{49} - 104 q^{51} - 212 q^{54} - 272 q^{56} - 700 q^{59} + 934 q^{61} - 256 q^{64} + 8 q^{66} + 268 q^{69} + 3080 q^{71} - 784 q^{74} + 416 q^{76} + 2340 q^{79} - 1298 q^{81} + 160 q^{84} - 1476 q^{86} + 178 q^{89} - 272 q^{91} - 352 q^{94} - 64 q^{96} - 208 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9 + 4 * q^11 + 80 * q^14 - 32 * q^16 + 52 * q^19 + 74 * q^21 + 16 * q^24 - 32 * q^26 - 276 * q^29 + 664 * q^31 - 416 * q^34 - 416 * q^36 + 16 * q^39 + 1412 * q^41 - 16 * q^44 + 268 * q^46 + 794 * q^49 - 104 * q^51 - 212 * q^54 - 272 * q^56 - 700 * q^59 + 934 * q^61 - 256 * q^64 + 8 * q^66 + 268 * q^69 + 3080 * q^71 - 784 * q^74 + 416 * q^76 + 2340 * q^79 - 1298 * q^81 + 160 * q^84 - 1476 * q^86 + 178 * q^89 - 272 * q^91 - 352 * q^94 - 64 * q^96 - 208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i	−0.581013	−	0.813894i	$-0.697344\pi$
$3$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i	0.414346	+	0.910119i	$0.364010\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	2.00000			0.136083
$7$	−16.4545	−	8.50000i	−0.888459	−	0.458957i
$7$	−16.4545	−	8.50000i	−0.888459	−	0.458957i
$8$		−	8.00000i		−	0.353553i
$9$	−13.0000	+	22.5167i	−0.481481	+	0.833950i
$10$		0			0
$11$	1.00000	+	1.73205i	0.0274101	+	0.0474757i	0.879405	−	0.476074i	$-0.157941\pi$
$11$	1.00000	+	1.73205i	0.0274101	+	0.0474757i	−0.851995	+	0.523550i	$0.824607\pi$
$12$	−3.46410	−	2.00000i	−0.0833333	−	0.0481125i
$13$		−	8.00000i		−	0.170677i	−0.996352	−	0.0853385i	$-0.972803\pi$
$13$		−	8.00000i		−	0.170677i	0.996352	−	0.0853385i	$-0.0271972\pi$
$14$	20.0000	+	31.1769i	0.381802	+	0.595170i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	45.0333	−	26.0000i	0.642481	−	0.370937i	−0.143088	−	0.989710i	$-0.545703\pi$
$17$	45.0333	−	26.0000i	0.642481	−	0.370937i	0.785570	+	0.618773i	$0.212370\pi$
$18$	45.0333	−	26.0000i	0.589692	−	0.340459i
$19$	13.0000	−	22.5167i	0.156969	−	0.271878i	−0.776805	−	0.629741i	$-0.783161\pi$
$19$	13.0000	−	22.5167i	0.156969	−	0.271878i	0.933774	+	0.357863i	$0.116495\pi$
$20$		0			0
$21$	18.5000	−	0.866025i	0.192240	−	0.00899915i
$22$		−	4.00000i		−	0.0387638i
$23$	−58.0237	−	33.5000i	−0.526034	−	0.303706i	0.213366	−	0.976972i	$-0.431557\pi$
$23$	−58.0237	−	33.5000i	−0.526034	−	0.303706i	−0.739400	+	0.673267i	$0.764891\pi$
$24$	4.00000	+	6.92820i	0.0340207	+	0.0589256i
$25$		0			0
$26$	−8.00000	+	13.8564i	−0.0603434	+	0.104518i
$27$		−	53.0000i		−	0.377772i
$28$	−3.46410	−	74.0000i	−0.0233805	−	0.499453i
$29$	−69.0000			−0.441827			−0.220913	−	0.975293i	$-0.570904\pi$
$29$	−69.0000			−0.441827			−0.220913	+	0.975293i	$0.570904\pi$
$30$		0			0
$31$	166.000	+	287.520i	0.961757	+	1.66581i	0.718085	+	0.695955i	$0.245019\pi$
$31$	166.000	+	287.520i	0.961757	+	1.66581i	0.243672	+	0.969858i	$0.421648\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	−1.73205	−	1.00000i	−0.00913671	−	0.00527508i
$34$	−104.000			−0.524584
$35$		0			0
$36$	−104.000			−0.481481
$37$	169.741	+	98.0000i	0.754196	+	0.435435i	0.827208	−	0.561896i	$-0.189928\pi$
$37$	169.741	+	98.0000i	0.754196	+	0.435435i	−0.0730121	+	0.997331i	$0.523261\pi$
$38$	−45.0333	+	26.0000i	−0.192247	+	0.110994i
$39$	4.00000	+	6.92820i	0.0164234	+	0.0284462i
$40$		0			0
$41$	353.000			1.34462			0.672309	−	0.740271i	$-0.265303\pi$
$41$	353.000			1.34462			0.672309	+	0.740271i	$0.265303\pi$
$42$	−32.9090	−	17.0000i	−0.120904	−	0.0624561i
$43$		−	369.000i		−	1.30865i	−0.756213	−	0.654325i	$-0.772953\pi$
$43$		−	369.000i		−	1.30865i	0.756213	−	0.654325i	$-0.227047\pi$
$44$	−4.00000	+	6.92820i	−0.0137051	+	0.0237379i
$45$		0			0
$46$	67.0000	+	116.047i	0.214752	+	0.371962i
$47$	76.2102	+	44.0000i	0.236519	+	0.136554i	0.613576	−	0.789636i	$-0.289730\pi$
$47$	76.2102	+	44.0000i	0.236519	+	0.136554i	−0.377057	+	0.926190i	$0.623064\pi$
$48$		−	16.0000i		−	0.0481125i
$49$	198.500	+	279.726i	0.578717	+	0.815528i
$50$		0			0
$51$	−26.0000	+	45.0333i	−0.0713868	+	0.123646i
$52$	27.7128	−	16.0000i	0.0739053	−	0.0426692i
$53$	504.027	−	291.000i	1.30629	−	0.754187i	0.324816	−	0.945777i	$-0.394698\pi$
$53$	504.027	−	291.000i	1.30629	−	0.754187i	0.981475	+	0.191590i	$0.0613644\pi$
$54$	−53.0000	+	91.7987i	−0.133563	+	0.231337i
$55$		0			0
$56$	−68.0000	+	131.636i	−0.162266	+	0.314118i
$57$			26.0000i			0.0604173i
$58$	119.512	+	69.0000i	0.270563	+	0.156209i
$59$	−175.000	−	303.109i	−0.386154	−	0.668838i	0.605775	−	0.795636i	$-0.292863\pi$
$59$	−175.000	−	303.109i	−0.386154	−	0.668838i	−0.991928	+	0.126798i	$0.959530\pi$
$60$		0			0
$61$	233.500	−	404.434i	0.490108	−	0.848893i	−0.509827	−	0.860277i	$-0.670291\pi$
$61$	233.500	−	404.434i	0.490108	−	0.848893i	0.999935	+	0.0113844i	$0.00362386\pi$
$62$		−	664.000i		−	1.36013i
$63$	405.300	−	260.000i	0.810524	−	0.519951i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	2.00000	+	3.46410i	0.00373005	+	0.00646063i
$67$	−252.013	+	145.500i	−0.459527	+	0.265308i	−0.711846	−	0.702336i	$-0.752140\pi$
$67$	−252.013	+	145.500i	−0.459527	+	0.265308i	0.252318	+	0.967644i	$0.418807\pi$
$68$	180.133	+	104.000i	0.321241	+	0.185468i
$69$	67.0000			0.116896
$70$		0			0
$71$	770.000			1.28707			0.643537	−	0.765415i	$-0.277466\pi$
$71$	770.000			1.28707			0.643537	+	0.765415i	$0.277466\pi$
$72$	180.133	+	104.000i	0.294846	+	0.170229i
$73$	543.864	−	314.000i	0.871979	−	0.503437i	0.00397357	−	0.999992i	$-0.498735\pi$
$73$	543.864	−	314.000i	0.871979	−	0.503437i	0.868005	+	0.496555i	$0.165402\pi$
$74$	−196.000	−	339.482i	−0.307899	−	0.533297i
$75$		0			0
$76$	104.000			0.156969
$77$	−1.73205	−	37.0000i	−0.00256345	−	0.0547603i
$78$		−	16.0000i		−	0.0232262i
$79$	585.000	−	1013.25i	0.833135	−	1.44303i	−0.0624054	−	0.998051i	$-0.519877\pi$
$79$	585.000	−	1013.25i	0.833135	−	1.44303i	0.895540	−	0.444981i	$-0.146789\pi$
$80$		0			0
$81$	−324.500	−	562.050i	−0.445130	−	0.770988i
$82$	−611.414	−	353.000i	−0.823407	−	0.475394i
$83$			525.000i			0.694292i	0.937811	+	0.347146i	$0.112849\pi$
$83$			525.000i			0.694292i	−0.937811	+	0.347146i	$0.887151\pi$
$84$	40.0000	+	62.3538i	0.0519566	+	0.0809924i
$85$		0			0
$86$	−369.000	+	639.127i	−0.462678	+	0.801382i
$87$	59.7558	−	34.5000i	0.0736378	−	0.0425148i
$88$	13.8564	−	8.00000i	0.0167852	−	0.00969094i
$89$	44.5000	−	77.0763i	0.0529999	−	0.0917985i	−0.838308	−	0.545197i	$-0.816455\pi$
$89$	44.5000	−	77.0763i	0.0529999	−	0.0917985i	0.891308	+	0.453398i	$0.149788\pi$
$90$		0			0
$91$	−68.0000	+	131.636i	−0.0783334	+	0.151639i
$92$		−	268.000i		−	0.303706i
$93$	−287.520	−	166.000i	−0.320586	−	0.185090i
$94$	−88.0000	−	152.420i	−0.0965586	−	0.167244i
$95$		0			0
$96$	−16.0000	+	27.7128i	−0.0170103	+	0.0294628i
$97$			290.000i			0.303557i	0.988415	+	0.151779i	$0.0485001\pi$
$97$			290.000i			0.303557i	−0.988415	+	0.151779i	$0.951500\pi$
$98$	−64.0859	−	683.000i	−0.0660577	−	0.704014i
$99$	−52.0000			−0.0527899
$100$		0			0
$101$	616.500	+	1067.81i	0.607367	+	1.05199i	0.991673	+	0.128784i	$0.0411075\pi$
$101$	616.500	+	1067.81i	0.607367	+	1.05199i	−0.384306	+	0.923206i	$0.625559\pi$
$102$	90.0666	−	52.0000i	0.0874307	−	0.0504781i
$103$	−1344.94	−	776.500i	−1.28661	−	0.742823i	−0.308560	−	0.951205i	$-0.599847\pi$
$103$	−1344.94	−	776.500i	−1.28661	−	0.742823i	−0.978048	+	0.208381i	$0.933181\pi$
$104$	−64.0000			−0.0603434
$105$		0			0
$106$	−1164.00			−1.06658
$107$	1585.69	+	915.500i	1.43266	+	0.827147i	0.997323	−	0.0731204i	$-0.0232957\pi$
$107$	1585.69	+	915.500i	1.43266	+	0.827147i	0.435337	+	0.900267i	$0.356629\pi$
$108$	183.597	−	106.000i	0.163580	−	0.0944431i
$109$	405.500	+	702.347i	0.356329	+	0.617180i	0.987344	−	0.158590i	$-0.0506949\pi$
$109$	405.500	+	702.347i	0.356329	+	0.617180i	−0.631016	+	0.775770i	$0.717362\pi$
$110$		0			0
$111$	−196.000			−0.167599
$112$	249.415	−	160.000i	0.210424	−	0.134987i
$113$			2170.00i			1.80652i	0.429097	+	0.903259i	$0.358832\pi$
$113$			2170.00i			1.80652i	−0.429097	+	0.903259i	$0.641168\pi$
$114$	26.0000	−	45.0333i	0.0213607	−	0.0369979i
$115$		0			0
$116$	−138.000	−	239.023i	−0.110457	−	0.191317i
$117$	180.133	+	104.000i	0.142336	+	0.0821778i
$118$			700.000i			0.546104i
$119$	−962.000	+	45.0333i	−0.741062	+	0.0346907i
$120$		0			0
$121$	663.500	−	1149.22i	0.498497	−	0.863423i
$122$	−808.868	+	467.000i	−0.600258	+	0.346559i
$123$	−305.707	+	176.500i	−0.224103	+	0.129386i
$124$	−664.000	+	1150.08i	−0.480879	+	0.832906i
$125$		0			0
$126$	−962.000	+	45.0333i	−0.680173	+	0.0318404i
$127$		−	48.0000i		−	0.0335379i	−0.999859	−	0.0167689i	$-0.994662\pi$
$127$		−	48.0000i		−	0.0335379i	0.999859	−	0.0167689i	$-0.00533797\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	184.500	+	319.563i	0.125925	+	0.218108i
$130$		0			0
$131$	396.000	−	685.892i	0.264112	−	0.457456i	−0.703219	−	0.710974i	$-0.748254\pi$
$131$	396.000	−	685.892i	0.264112	−	0.457456i	0.967331	+	0.253518i	$0.0815878\pi$
$132$		−	8.00000i		−	0.00527508i
$133$	−405.300	+	260.000i	−0.264240	+	0.169510i
$134$	582.000			0.375203
$135$		0			0
$136$	−208.000	−	360.267i	−0.131146	−	0.227151i
$137$	−938.772	+	542.000i	−0.585436	+	0.338001i	−0.763291	−	0.646055i	$-0.776418\pi$
$137$	−938.772	+	542.000i	−0.585436	+	0.338001i	0.177855	+	0.984057i	$0.443084\pi$
$138$	−116.047	−	67.0000i	−0.0715841	−	0.0413291i
$139$	46.0000			0.0280696			0.0140348	−	0.999902i	$-0.495532\pi$
$139$	46.0000			0.0280696			0.0140348	+	0.999902i	$0.495532\pi$
$140$		0			0
$141$	−88.0000			−0.0525598
$142$	−1333.68	−	770.000i	−0.788168	−	0.455049i
$143$	13.8564	−	8.00000i	0.00810301	−	0.00467828i
$144$	−208.000	−	360.267i	−0.120370	−	0.208488i
$145$		0			0
$146$	−1256.00			−0.711968
$147$	−311.769	−	143.000i	−0.174927	−	0.0802343i
$148$			784.000i			0.435435i
$149$	−184.500	+	319.563i	−0.101442	+	0.175702i	−0.912279	−	0.409570i	$-0.865679\pi$
$149$	−184.500	+	319.563i	−0.101442	+	0.175702i	0.810837	+	0.585272i	$0.199012\pi$
$150$		0			0
$151$	−1240.00	−	2147.74i	−0.668277	−	1.15749i	−0.978386	−	0.206788i	$-0.933699\pi$
$151$	−1240.00	−	2147.74i	−0.668277	−	1.15749i	0.310109	−	0.950701i	$-0.399634\pi$
$152$	−180.133	−	104.000i	−0.0961233	−	0.0554968i
$153$			1352.00i			0.714397i
$154$	−34.0000	+	65.8179i	−0.0177909	+	0.0344400i
$155$		0			0
$156$	−16.0000	+	27.7128i	−0.00821170	+	0.0142231i
$157$	−1061.75	+	613.000i	−0.539724	+	0.311610i	−0.744967	−	0.667101i	$-0.767535\pi$
$157$	−1061.75	+	613.000i	−0.539724	+	0.311610i	0.205243	+	0.978711i	$0.434201\pi$
$158$	−2026.50	+	1170.00i	−1.02038	+	0.589115i
$159$	−291.000	+	504.027i	−0.145143	+	0.251396i
$160$		0			0
$161$	670.000	+	1044.43i	0.327971	+	0.511257i
$162$			1298.00i			0.629509i
$163$	571.577	+	330.000i	0.274659	+	0.158574i	0.631003	−	0.775781i	$-0.282644\pi$
$163$	571.577	+	330.000i	0.274659	+	0.158574i	−0.356344	+	0.934355i	$0.615977\pi$
$164$	706.000	+	1222.83i	0.336154	+	0.582237i
$165$		0			0
$166$	525.000	−	909.327i	0.245469	−	0.425165i
$167$			949.000i			0.439735i	0.975530	+	0.219868i	$0.0705626\pi$
$167$			949.000i			0.439735i	−0.975530	+	0.219868i	$0.929437\pi$
$168$	−6.92820	−	148.000i	−0.00318168	−	0.0679670i
$169$	2133.00			0.970869
$170$		0			0
$171$	338.000	+	585.433i	0.151155	+	0.261808i
$172$	1278.25	−	738.000i	0.566662	−	0.327163i
$173$	−2937.56	−	1696.00i	−1.29097	−	0.745344i	−0.312147	−	0.950034i	$-0.601048\pi$
$173$	−2937.56	−	1696.00i	−1.29097	−	0.745344i	−0.978827	+	0.204690i	$0.934381\pi$
$174$	−138.000			−0.0601250
$175$		0			0
$176$	−32.0000			−0.0137051
$177$	303.109	+	175.000i	0.128718	+	0.0743153i
$178$	−154.153	+	89.0000i	−0.0649113	+	0.0374766i
$179$	134.000	+	232.095i	0.0559532	+	0.0969139i	0.892645	−	0.450760i	$-0.148847\pi$
$179$	134.000	+	232.095i	0.0559532	+	0.0969139i	−0.836692	+	0.547674i	$0.815514\pi$
$180$		0			0
$181$	−4093.00			−1.68083			−0.840415	−	0.541943i	$-0.817689\pi$
$181$	−4093.00			−1.68083			−0.840415	+	0.541943i	$0.817689\pi$
$182$	249.415	−	160.000i	0.101582	−	0.0651648i
$183$			467.000i			0.188643i
$184$	−268.000	+	464.190i	−0.107376	+	0.185981i
$185$		0			0
$186$	332.000	+	575.041i	0.130879	+	0.226688i
$187$	90.0666	+	52.0000i	0.0352210	+	0.0203348i
$188$			352.000i			0.136554i
$189$	−450.500	+	872.088i	−0.173381	+	0.335635i
$190$		0			0
$191$	989.000	−	1713.00i	0.374668	−	0.648943i	−0.615610	−	0.788051i	$-0.711090\pi$
$191$	989.000	−	1713.00i	0.374668	−	0.648943i	0.990277	+	0.139108i	$0.0444235\pi$
$192$	55.4256	−	32.0000i	0.0208333	−	0.0120281i
$193$	−3462.37	+	1999.00i	−1.29133	+	0.745550i	−0.978890	−	0.204387i	$-0.934480\pi$
$193$	−3462.37	+	1999.00i	−1.29133	+	0.745550i	−0.312441	+	0.949937i	$0.601146\pi$
$194$	290.000	−	502.295i	0.107324	−	0.185890i
$195$		0			0
$196$	−572.000	+	1247.08i	−0.208455	+	0.454474i
$197$			3030.00i			1.09583i	0.836534	+	0.547915i	$0.184578\pi$
$197$			3030.00i			1.09583i	−0.836534	+	0.547915i	$0.815422\pi$
$198$	90.0666	+	52.0000i	0.0323271	+	0.0186640i
$199$	178.000	+	308.305i	0.0634075	+	0.109825i	0.895986	−	0.444081i	$-0.146470\pi$
$199$	178.000	+	308.305i	0.0634075	+	0.109825i	−0.832579	+	0.553906i	$0.813137\pi$
$200$		0			0
$201$	145.500	−	252.013i	0.0510586	−	0.0884361i
$202$		−	2466.00i		−	0.858946i
$203$	1135.36	+	586.500i	0.392545	+	0.202779i
$204$	−208.000			−0.0713868
$205$		0			0
$206$	1553.00	+	2689.87i	0.525256	+	0.909769i
$207$	1508.62	−	871.000i	0.506551	−	0.292457i
$208$	110.851	+	64.0000i	0.0369527	+	0.0213346i
$209$	52.0000			0.0172101
$210$		0			0
$211$	−2602.00			−0.848953			−0.424476	−	0.905439i	$-0.639542\pi$
$211$	−2602.00			−0.848953			−0.424476	+	0.905439i	$0.639542\pi$
$212$	2016.11	+	1164.00i	0.653145	+	0.377094i
$213$	−666.840	+	385.000i	−0.214512	+	0.123849i
$214$	−1831.00	−	3171.39i	−0.584881	−	1.01304i
$215$		0			0
$216$	−424.000			−0.133563
$217$	−287.520	−	6142.00i	−0.0899454	−	1.92141i
$218$		−	1622.00i		−	0.503925i
$219$	−314.000	+	543.864i	−0.0968865	+	0.167812i
$220$		0			0
$221$	−208.000	−	360.267i	−0.0633104	−	0.109657i
$222$	339.482	+	196.000i	0.102633	+	0.0592552i
$223$		−	3156.00i		−	0.947719i	−0.880600	−	0.473860i	$-0.842860\pi$
$223$		−	3156.00i		−	0.947719i	0.880600	−	0.473860i	$-0.157140\pi$
$224$	−592.000	+	27.7128i	−0.176583	+	0.00826625i
$225$		0			0
$226$	2170.00	−	3758.55i	0.638700	−	1.10626i
$227$	−3668.48	+	2118.00i	−1.07262	+	0.619280i	−0.928897	−	0.370337i	$-0.879242\pi$
$227$	−3668.48	+	2118.00i	−1.07262	+	0.619280i	−0.143727	+	0.989617i	$0.545909\pi$
$228$	−90.0666	+	52.0000i	−0.0261614	+	0.0151043i
$229$	3167.00	−	5485.40i	0.913892	−	1.58291i	0.105376	−	0.994432i	$-0.466395\pi$
$229$	3167.00	−	5485.40i	0.913892	−	1.58291i	0.808516	−	0.588475i	$-0.200271\pi$
$230$		0			0
$231$	20.0000	+	31.1769i	0.00569655	+	0.00888004i
$232$			552.000i			0.156209i
$233$	4059.93	+	2344.00i	1.14152	+	0.659058i	0.946807	−	0.321802i	$-0.104288\pi$
$233$	4059.93	+	2344.00i	1.14152	+	0.659058i	0.194715	+	0.980860i	$0.437622\pi$
$234$	−208.000	−	360.267i	−0.0581085	−	0.100647i
$235$		0			0
$236$	700.000	−	1212.44i	0.193077	−	0.334419i
$237$			1170.00i			0.320674i
$238$	1711.27	+	884.000i	0.466071	+	0.240761i
$239$	−1856.00			−0.502321			−0.251160	−	0.967945i	$-0.580812\pi$
$239$	−1856.00			−0.502321			−0.251160	+	0.967945i	$0.580812\pi$
$240$		0			0
$241$	2403.00	+	4162.12i	0.642286	+	1.11247i	0.984921	+	0.173003i	$0.0553470\pi$
$241$	2403.00	+	4162.12i	0.642286	+	1.11247i	−0.342636	+	0.939468i	$0.611320\pi$
$242$	−2298.43	+	1327.00i	−0.610532	+	0.352491i
$243$	1801.33	+	1040.00i	0.475537	+	0.274552i
$244$	1868.00			0.490108
$245$		0			0
$246$	706.000			0.182979
$247$	−180.133	−	104.000i	−0.0464033	−	0.0267909i
$248$	2300.16	−	1328.00i	0.588954	−	0.340033i
$249$	−262.500	−	454.663i	−0.0668083	−	0.115715i
$250$		0			0
$251$	−3200.00			−0.804710			−0.402355	−	0.915484i	$-0.631808\pi$
$251$	−3200.00			−0.804710			−0.402355	+	0.915484i	$0.631808\pi$
$252$	1711.27	+	884.000i	0.427776	+	0.220979i
$253$		−	134.000i		−	0.0332984i
$254$	−48.0000	+	83.1384i	−0.0118574	+	0.0205377i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−969.948	−	560.000i	−0.235423	−	0.135922i	0.377648	−	0.925949i	$-0.376733\pi$
$257$	−969.948	−	560.000i	−0.235423	−	0.135922i	−0.613071	+	0.790028i	$0.710066\pi$
$258$		−	738.000i		−	0.178085i
$259$	−1960.00	−	3055.34i	−0.470226	−	0.733009i
$260$		0			0
$261$	897.000	−	1553.65i	0.212731	−	0.368462i
$262$	−1371.78	+	792.000i	−0.323470	+	0.186755i
$263$	5546.89	−	3202.50i	1.30052	−	0.750854i	0.320025	−	0.947409i	$-0.396309\pi$
$263$	5546.89	−	3202.50i	1.30052	−	0.750854i	0.980493	+	0.196555i	$0.0629755\pi$
$264$	−8.00000	+	13.8564i	−0.00186502	+	0.00323031i
$265$		0			0
$266$	962.000	−	45.0333i	0.221744	−	0.0103803i
$267$			89.0000i			0.0203997i
$268$	−1008.05	−	582.000i	−0.229764	−	0.132654i
$269$	2467.50	+	4273.84i	0.559279	+	0.968700i	0.997557	+	0.0698604i	$0.0222554\pi$
$269$	2467.50	+	4273.84i	0.559279	+	0.968700i	−0.438277	+	0.898840i	$0.644411\pi$
$270$		0			0
$271$	723.000	−	1252.27i	0.162063	−	0.280702i	−0.773545	−	0.633741i	$-0.781518\pi$
$271$	723.000	−	1252.27i	0.162063	−	0.280702i	0.935608	+	0.353039i	$0.114852\pi$
$272$			832.000i			0.185468i
$273$	−6.92820	−	148.000i	−0.00153595	−	0.0328109i
$274$	2168.00			0.478006
$275$		0			0
$276$	134.000	+	232.095i	0.0292241	+	0.0506176i
$277$	6945.52	−	4010.00i	1.50656	−	0.869811i	0.506585	−	0.862190i	$-0.330908\pi$
$277$	6945.52	−	4010.00i	1.50656	−	0.869811i	0.999971	−	0.00762078i	$-0.00242579\pi$
$278$	−79.6743	−	46.0000i	−0.0171890	−	0.00992409i
$279$	−8632.00			−1.85227
$280$		0			0
$281$	4978.00			1.05681			0.528403	−	0.848994i	$-0.322791\pi$
$281$	4978.00			1.05681			0.528403	+	0.848994i	$0.322791\pi$
$282$	152.420	+	88.0000i	0.0321862	+	0.0185827i
$283$	5067.98	−	2926.00i	1.06452	−	0.614603i	0.137844	−	0.990454i	$-0.455983\pi$
$283$	5067.98	−	2926.00i	1.06452	−	0.614603i	0.926680	+	0.375851i	$0.122650\pi$
$284$	1540.00	+	2667.36i	0.321768	+	0.557319i
$285$		0			0
$286$	−32.0000			−0.00661608
$287$	−5808.43	−	3000.50i	−1.19464	−	0.617122i
$288$			832.000i			0.170229i
$289$	−1104.50	+	1913.05i	−0.224812	+	0.389385i
$290$		0			0
$291$	−145.000	−	251.147i	−0.0292098	−	0.0505929i
$292$	2175.46	+	1256.00i	0.435989	+	0.251719i
$293$		−	3012.00i		−	0.600556i	−0.953852	−	0.300278i	$-0.902921\pi$
$293$		−	3012.00i		−	0.600556i	0.953852	−	0.300278i	$-0.0970795\pi$
$294$	397.000	+	559.452i	0.0787534	+	0.110979i
$295$		0			0
$296$	784.000	−	1357.93i	0.153950	−	0.266648i
$297$	91.7987	−	53.0000i	0.0179350	−	0.0103548i
$298$	639.127	−	369.000i	0.124240	−	0.0717302i
$299$	−268.000	+	464.190i	−0.0518356	+	0.0897819i
$300$		0			0
$301$	−3136.50	+	6071.70i	−0.600614	+	1.16268i
$302$			4960.00i			0.945086i
$303$	−1067.81	−	616.500i	−0.202456	−	0.116888i
$304$	208.000	+	360.267i	0.0392422	+	0.0679694i
$305$		0			0
$306$	1352.00	−	2341.73i	0.252577	−	0.437477i
$307$		−	9443.00i		−	1.75551i	−0.479113	−	0.877753i	$-0.659042\pi$
$307$		−	9443.00i		−	1.75551i	0.479113	−	0.877753i	$-0.340958\pi$
$308$	124.708	−	80.0000i	0.0230710	−	0.0148001i
$309$	1553.00			0.285913
$310$		0			0
$311$	4997.00	+	8655.06i	0.911106	+	1.57808i	0.812505	+	0.582954i	$0.198103\pi$
$311$	4997.00	+	8655.06i	0.911106	+	1.57808i	0.0986008	+	0.995127i	$0.468563\pi$
$312$	55.4256	−	32.0000i	0.0100572	−	0.00580655i
$313$	−1260.93	−	728.000i	−0.227707	−	0.131466i	0.381807	−	0.924242i	$-0.375302\pi$
$313$	−1260.93	−	728.000i	−0.227707	−	0.131466i	−0.609514	+	0.792776i	$0.708635\pi$
$314$	2452.00			0.440683
$315$		0			0
$316$	4680.00			0.833135
$317$	5951.33	+	3436.00i	1.05445	+	0.608785i	0.923891	−	0.382655i	$-0.124990\pi$
$317$	5951.33	+	3436.00i	1.05445	+	0.608785i	0.130556	+	0.991441i	$0.458324\pi$
$318$	1008.05	−	582.000i	0.177764	−	0.102632i
$319$	−69.0000	−	119.512i	−0.0121105	−	0.0209760i
$320$		0			0
$321$	−1831.00			−0.318369
$322$	−116.047	−	2479.00i	−0.0200841	−	0.429035i
$323$		−	1352.00i		−	0.232902i
$324$	1298.00	−	2248.20i	0.222565	−	0.385494i
$325$		0			0
$326$	−660.000	−	1143.15i	−0.112129	−	0.194213i
$327$	−702.347	−	405.500i	−0.118776	−	0.0685755i
$328$		−	2824.00i		−	0.475394i
$329$	−880.000	−	1371.78i	−0.147465	−	0.229875i
$330$		0			0
$331$	196.000	−	339.482i	0.0325472	−	0.0563735i	−0.849293	−	0.527922i	$-0.822971\pi$
$331$	196.000	−	339.482i	0.0325472	−	0.0563735i	0.881840	+	0.471548i	$0.156305\pi$
$332$	−1818.65	+	1050.00i	−0.300637	+	0.173573i
$333$	−4413.27	+	2548.00i	−0.726263	+	0.419308i
$334$	949.000	−	1643.72i	0.155470	−	0.269282i
$335$		0			0
$336$	−136.000	+	263.272i	−0.0220816	+	0.0427460i
$337$		−	3926.00i		−	0.634608i	−0.948324	−	0.317304i	$-0.897222\pi$
$337$		−	3926.00i		−	0.634608i	0.948324	−	0.317304i	$-0.102778\pi$
$338$	−3694.46	−	2133.00i	−0.594534	−	0.343254i
$339$	−1085.00	−	1879.28i	−0.173832	−	0.301086i
$340$		0			0
$341$	−332.000	+	575.041i	−0.0527238	+	0.0913203i
$342$		−	1352.00i		−	0.213765i
$343$	−888.542	−	6290.00i	−0.139874	−	0.990169i
$344$	−2952.00			−0.462678
$345$		0			0
$346$	3392.00	+	5875.12i	0.527038	+	0.912856i
$347$	1545.86	−	892.500i	0.239152	−	0.138075i	−0.375635	−	0.926768i	$-0.622575\pi$
$347$	1545.86	−	892.500i	0.239152	−	0.138075i	0.614787	+	0.788693i	$0.289242\pi$
$348$	239.023	+	138.000i	0.0368189	+	0.0212574i
$349$	1591.00			0.244024			0.122012	−	0.992529i	$-0.461065\pi$
$349$	1591.00			0.244024			0.122012	+	0.992529i	$0.461065\pi$
$350$		0			0
$351$	−424.000			−0.0644771
$352$	55.4256	+	32.0000i	0.00839260	+	0.00484547i
$353$	1460.12	−	843.000i	0.220154	−	0.127106i	−0.385868	−	0.922554i	$-0.626098\pi$
$353$	1460.12	−	843.000i	0.220154	−	0.127106i	0.606021	+	0.795448i	$0.292765\pi$
$354$	−350.000	−	606.218i	−0.0525488	−	0.0910173i
$355$		0			0
$356$	356.000			0.0529999
$357$	810.600	−	520.000i	0.120172	−	0.0770905i
$358$		−	536.000i		−	0.0791298i
$359$	3686.00	−	6384.34i	0.541893	−	0.938586i	−0.456902	−	0.889517i	$-0.651041\pi$
$359$	3686.00	−	6384.34i	0.541893	−	0.938586i	0.998795	−	0.0490695i	$-0.0156256\pi$
$360$		0			0
$361$	3091.50	+	5354.64i	0.450722	+	0.780673i
$362$	7089.28	+	4093.00i	1.02929	+	0.594263i
$363$			1327.00i			0.191872i
$364$	−592.000	+	27.7128i	−0.0852451	+	0.00399051i
$365$		0			0
$366$	467.000	−	808.868i	0.0666953	−	0.115520i
$367$	−5747.81	+	3318.50i	−0.817529	+	0.472001i	−0.849564	−	0.527486i	$-0.823135\pi$
$367$	−5747.81	+	3318.50i	−0.817529	+	0.472001i	0.0320344	+	0.999487i	$0.489801\pi$
$368$	928.379	−	536.000i	0.131508	−	0.0759264i
$369$	−4589.00	+	7948.38i	−0.647409	+	1.12134i
$370$		0			0
$371$	−10767.0	+	504.027i	−1.50672	+	0.0705331i
$372$		−	1328.00i		−	0.185090i
$373$	−3010.30	−	1738.00i	−0.417876	−	0.241261i	0.276292	−	0.961074i	$-0.410894\pi$
$373$	−3010.30	−	1738.00i	−0.417876	−	0.241261i	−0.694168	+	0.719813i	$0.744228\pi$
$374$	−104.000	−	180.133i	−0.0143789	−	0.0249050i
$375$		0			0
$376$	352.000	−	609.682i	0.0482793	−	0.0836222i
$377$			552.000i			0.0754097i
$378$	1652.38	−	1060.00i	0.224839	−	0.144234i
$379$	2378.00			0.322295			0.161147	−	0.986930i	$-0.448481\pi$
$379$	2378.00			0.322295			0.161147	+	0.986930i	$0.448481\pi$
$380$		0			0
$381$	24.0000	+	41.5692i	0.00322718	+	0.00558965i
$382$	−3426.00	+	1978.00i	−0.458872	+	0.264930i
$383$	2127.82	+	1228.50i	0.283882	+	0.163899i	0.635179	−	0.772365i	$-0.280926\pi$
$383$	2127.82	+	1228.50i	0.283882	+	0.163899i	−0.351298	+	0.936264i	$0.614259\pi$
$384$	−128.000			−0.0170103
$385$		0			0
$386$	7996.00			1.05437
$387$	8308.65	+	4797.00i	1.09135	+	0.630091i
$388$	−1004.59	+	580.000i	−0.131444	+	0.0758893i
$389$	4281.00	+	7414.91i	0.557983	+	0.966455i	0.997665	+	0.0683010i	$0.0217578\pi$
$389$	4281.00	+	7414.91i	0.557983	+	0.966455i	−0.439682	+	0.898154i	$0.644909\pi$
$390$		0			0
$391$	−3484.00			−0.450623
$392$	2237.81	−	1588.00i	0.288333	−	0.204607i
$393$			792.000i			0.101657i
$394$	3030.00	−	5248.11i	0.387435	−	0.671056i
$395$		0			0
$396$	−104.000	−	180.133i	−0.0131975	−	0.0228587i
$397$	−8523.42	−	4921.00i	−1.07753	−	0.622111i	−0.147299	−	0.989092i	$-0.547058\pi$
$397$	−8523.42	−	4921.00i	−1.07753	−	0.622111i	−0.930228	+	0.366981i	$0.880391\pi$
$398$		−	712.000i		−	0.0896717i
$399$	221.000	−	427.817i	0.0277289	−	0.0536782i
$400$		0			0
$401$	4048.50	−	7012.21i	0.504171	−	0.873249i	−0.495818	−	0.868427i	$-0.665132\pi$
$401$	4048.50	−	7012.21i	0.504171	−	0.873249i	0.999988	−	0.00482260i	$-0.00153509\pi$
$402$	−504.027	+	291.000i	−0.0625338	+	0.0361039i
$403$	2300.16	−	1328.00i	0.284316	−	0.164150i
$404$	−2466.00	+	4271.24i	−0.303683	+	0.525995i
$405$		0			0
$406$	−1380.00	−	2151.21i	−0.168690	−	0.262962i
$407$			392.000i			0.0477413i
$408$	360.267	+	208.000i	0.0437153	+	0.0252391i
$409$	7629.50	+	13214.7i	0.922383	+	1.59761i	0.795717	+	0.605668i	$0.207094\pi$
$409$	7629.50	+	13214.7i	0.922383	+	1.59761i	0.126665	+	0.991946i	$0.459573\pi$
$410$		0			0
$411$	542.000	−	938.772i	0.0650484	−	0.112667i
$412$		−	6212.00i		−	0.742823i
$413$	303.109	+	6475.00i	0.0361138	+	0.771462i
$414$	−3484.00			−0.413597
$415$		0			0
$416$	−128.000	−	221.703i	−0.0150859	−	0.0261295i
$417$	−39.8372	+	23.0000i	−0.00467826	+	0.00270099i
$418$	−90.0666	−	52.0000i	−0.0105390	−	0.00608470i
$419$	−16224.0			−1.89163			−0.945817	−	0.324701i	$-0.894736\pi$
$419$	−16224.0			−1.89163			−0.945817	+	0.324701i	$0.894736\pi$
$420$		0			0
$421$	2977.00			0.344632			0.172316	−	0.985042i	$-0.444875\pi$
$421$	2977.00			0.344632			0.172316	+	0.985042i	$0.444875\pi$
$422$	4506.80	+	2602.00i	0.519875	+	0.300150i
$423$	−1981.47	+	1144.00i	−0.227759	+	0.131497i
$424$	−2328.00	−	4032.21i	−0.266645	−	0.461843i
$425$		0			0
$426$	1540.00			0.175148
$427$	−7279.81	+	4670.00i	−0.825046	+	0.529267i
$428$			7324.00i			0.827147i
$429$	−8.00000	+	13.8564i	−0.000900335	+	0.00155943i
$430$		0			0
$431$	−7101.00	−	12299.3i	−0.793604	−	1.37456i	−0.923722	−	0.383063i	$-0.874869\pi$
$431$	−7101.00	−	12299.3i	−0.793604	−	1.37456i	0.130119	−	0.991498i	$-0.458464\pi$
$432$	734.390	+	424.000i	0.0817901	+	0.0472215i
$433$			14310.0i			1.58821i	0.607781	+	0.794105i	$0.292060\pi$
$433$			14310.0i			1.58821i	−0.607781	+	0.794105i	$0.707940\pi$
$434$	−5644.00	+	10925.8i	−0.624241	+	1.20842i
$435$		0			0
$436$	−1622.00	+	2809.39i	−0.178164	+	0.308590i
$437$	−1508.62	+	871.000i	−0.165142	+	0.0953446i
$438$	1087.73	−	628.000i	0.118661	−	0.0685091i
$439$	−1178.00	+	2040.36i	−0.128070	+	0.221824i	−0.922929	−	0.384970i	$-0.874212\pi$
$439$	−1178.00	+	2040.36i	−0.128070	+	0.221824i	0.794859	+	0.606795i	$0.207545\pi$
$440$		0			0
$441$	−8879.00	+	833.116i	−0.958752	+	0.0899597i
$442$			832.000i			0.0895344i
$443$	−7180.22	−	4145.50i	−0.770073	−	0.444602i	0.0628276	−	0.998024i	$-0.479988\pi$
$443$	−7180.22	−	4145.50i	−0.770073	−	0.444602i	−0.832901	+	0.553422i	$0.813322\pi$
$444$	−392.000	−	678.964i	−0.0418998	−	0.0725725i
$445$		0			0
$446$	−3156.00	+	5466.35i	−0.335069	+	0.580357i
$447$		−	369.000i		−	0.0390450i
$448$	1053.09	+	544.000i	0.111057	+	0.0573696i
$449$	3521.00			0.370081			0.185040	−	0.982731i	$-0.440758\pi$
$449$	3521.00			0.370081			0.185040	+	0.982731i	$0.440758\pi$
$450$		0			0
$451$	353.000	+	611.414i	0.0368561	+	0.0638367i
$452$	−7517.10	+	4340.00i	−0.782245	+	0.451629i
$453$	2147.74	+	1240.00i	0.222759	+	0.128610i
$454$	8472.00			0.875794
$455$		0			0
$456$	208.000			0.0213607
$457$	−4704.25	−	2716.00i	−0.481522	−	0.278007i	0.239529	−	0.970889i	$-0.423007\pi$
$457$	−4704.25	−	2716.00i	−0.481522	−	0.278007i	−0.721051	+	0.692882i	$0.756340\pi$
$458$	−10970.8	+	6334.00i	−1.11928	+	0.646219i
$459$	−1378.00	−	2386.77i	−0.140130	−	0.242712i
$460$		0			0
$461$	−5350.00			−0.540508			−0.270254	−	0.962789i	$-0.587108\pi$
$461$	−5350.00			−0.540508			−0.270254	+	0.962789i	$0.587108\pi$
$462$	−3.46410	−	74.0000i	−0.000348841	−	0.00745193i
$463$		−	10123.0i		−	1.01610i	−0.861327	−	0.508052i	$-0.830366\pi$
$463$		−	10123.0i		−	1.01610i	0.861327	−	0.508052i	$-0.169634\pi$
$464$	552.000	−	956.092i	0.0552284	−	0.0956583i
$465$		0			0
$466$	−4688.00	−	8119.85i	−0.466024	−	0.807178i
$467$	5597.12	+	3231.50i	0.554612	+	0.320206i	0.750980	−	0.660325i	$-0.229581\pi$
$467$	5597.12	+	3231.50i	0.554612	+	0.320206i	−0.196368	+	0.980530i	$0.562915\pi$
$468$			832.000i			0.0821778i
$469$	5383.50	−	252.013i	0.530036	−	0.0248121i
$470$		0			0
$471$	613.000	−	1061.75i	0.0599693	−	0.103870i
$472$	−2424.87	+	1400.00i	−0.236470	+	0.136526i
$473$	639.127	−	369.000i	0.0621291	−	0.0358703i
$474$	1170.00	−	2026.50i	0.113375	−	0.196372i
$475$		0			0
$476$	−2080.00	−	3242.40i	−0.200287	−	0.312217i
$477$			15132.0i			1.45251i
$478$	3214.69	+	1856.00i	0.307607	+	0.177597i
$479$	−8820.00	−	15276.7i	−0.841328	−	1.45722i	−0.888772	−	0.458349i	$-0.848441\pi$
$479$	−8820.00	−	15276.7i	−0.841328	−	1.45722i	0.0474444	−	0.998874i	$-0.484892\pi$
$480$		0			0
$481$	784.000	−	1357.93i	0.0743188	−	0.128724i
$482$		−	9612.00i		−	0.908329i
$483$	−1102.45	−	569.500i	−0.103858	−	0.0536504i
$484$	5308.00			0.498497
$485$		0			0
$486$	−2080.00	−	3602.67i	−0.194137	−	0.336256i
$487$	8687.97	−	5016.00i	0.808397	−	0.466728i	−0.0380019	−	0.999278i	$-0.512099\pi$
$487$	8687.97	−	5016.00i	0.808397	−	0.466728i	0.846399	+	0.532549i	$0.178766\pi$
$488$	−3235.47	−	1868.00i	−0.300129	−	0.173279i
$489$	−660.000			−0.0610352
$490$		0			0
$491$	5916.00			0.543758			0.271879	−	0.962331i	$-0.412355\pi$
$491$	5916.00			0.543758			0.271879	+	0.962331i	$0.412355\pi$
$492$	−1222.83	−	706.000i	−0.112051	−	0.0646930i
$493$	−3107.30	+	1794.00i	−0.283866	+	0.163890i
$494$	208.000	+	360.267i	0.0189441	+	0.0328121i
$495$		0			0
$496$	−5312.00			−0.480879
$497$	−12670.0	−	6545.00i	−1.14351	−	0.590711i
$498$			1050.00i			0.0944812i
$499$	6947.00	−	12032.6i	0.623227	−	1.07946i	−0.365653	−	0.930751i	$-0.619154\pi$
$499$	6947.00	−	12032.6i	0.623227	−	1.07946i	0.988881	−	0.148710i	$-0.0475122\pi$
$500$		0			0
$501$	−474.500	−	821.858i	−0.0423136	−	0.0732892i
$502$	5542.56	+	3200.00i	0.492782	+	0.284508i
$503$			18427.0i			1.63344i	0.577036	+	0.816719i	$0.304209\pi$
$503$			18427.0i			1.63344i	−0.577036	+	0.816719i	$0.695791\pi$
$504$	−2080.00	−	3242.40i	−0.183830	−	0.286563i
$505$		0			0
$506$	−134.000	+	232.095i	−0.0117728	+	0.0203911i
$507$	−1847.23	+	1066.50i	−0.161812	+	0.0934219i
$508$	166.277	−	96.0000i	0.0145223	−	0.00838447i
$509$	9278.50	−	16070.8i	0.807981	−	1.39946i	−0.106279	−	0.994336i	$-0.533894\pi$
$509$	9278.50	−	16070.8i	0.807981	−	1.39946i	0.914260	−	0.405128i	$-0.132773\pi$
$510$		0			0
$511$	−11618.0	+	543.864i	−1.00577	+	0.0470824i
$512$			512.000i			0.0441942i
$513$	−1193.38	−	689.000i	−0.102708	−	0.0592984i
$514$	1120.00	+	1939.90i	0.0961111	+	0.166469i
$515$		0			0
$516$	−738.000	+	1278.25i	−0.0629625	+	0.109054i
$517$			176.000i			0.0149719i
$518$	339.482	+	7252.00i	0.0287953	+	0.615125i
$519$	3392.00			0.286883
$520$		0			0
$521$	4965.00	+	8599.63i	0.417506	+	0.723142i	0.995688	−	0.0927663i	$-0.0295710\pi$
$521$	4965.00	+	8599.63i	0.417506	+	0.723142i	−0.578182	+	0.815908i	$0.696238\pi$
$522$	−3107.30	+	1794.00i	−0.260542	+	0.150424i
$523$	6862.39	+	3962.00i	0.573750	+	0.331255i	0.758646	−	0.651504i	$-0.225861\pi$
$523$	6862.39	+	3962.00i	0.573750	+	0.331255i	−0.184896	+	0.982758i	$0.559195\pi$
$524$	3168.00			0.264112
$525$		0			0
$526$	−12810.0			−1.06187
$527$	14951.1	+	8632.00i	1.23582	+	0.713503i
$528$	27.7128	−	16.0000i	0.00228418	−	0.00131877i
$529$	−3839.00	−	6649.34i	−0.315526	−	0.546506i
$530$		0			0
$531$	9100.00			0.743703
$532$	−1711.27	−	884.000i	−0.139460	−	0.0720418i
$533$		−	2824.00i		−	0.229495i
$534$	89.0000	−	154.153i	0.00721237	−	0.0124922i
$535$		0			0
$536$	1164.00	+	2016.11i	0.0938006	+	0.162467i
$537$	−232.095	−	134.000i	−0.0186511	−	0.0107682i
$538$		−	9870.00i		−	0.790940i
$539$	−286.000	+	623.538i	−0.0228551	+	0.0498287i
$540$		0			0
$541$	11748.5	−	20349.0i	0.933655	−	1.61714i	0.156641	−	0.987656i	$-0.449934\pi$
$541$	11748.5	−	20349.0i	0.933655	−	1.61714i	0.777015	−	0.629483i	$-0.216733\pi$
$542$	−2504.55	+	1446.00i	−0.198486	+	0.114596i
$543$	3544.64	−	2046.50i	0.280138	−	0.161738i
$544$	832.000	−	1441.07i	0.0655730	−	0.113576i
$545$		0			0
$546$	−136.000	+	263.272i	−0.0106598	+	0.0206355i
$547$		−	11131.0i		−	0.870068i	−0.900414	−	0.435034i	$-0.856736\pi$
$547$		−	11131.0i		−	0.870068i	0.900414	−	0.435034i	$-0.143264\pi$
$548$	−3755.09	−	2168.00i	−0.292718	−	0.169001i
$549$	6071.00	+	10515.3i	0.471956	+	0.817452i
$550$		0			0
$551$	−897.000	+	1553.65i	−0.0693530	+	0.120123i
$552$		−	536.000i		−	0.0413291i
$553$	−18238.5	+	11700.0i	−1.40249	+	0.899701i
$554$	−16040.0			−1.23010
$555$		0			0
$556$	92.0000	+	159.349i	0.00701739	+	0.0121545i
$557$	10373.3	−	5989.00i	0.789100	−	0.455587i	−0.0505455	−	0.998722i	$-0.516096\pi$
$557$	10373.3	−	5989.00i	0.789100	−	0.455587i	0.839646	+	0.543135i	$0.182763\pi$
$558$	14951.1	+	8632.00i	1.13428	+	0.654878i
$559$	−2952.00			−0.223357
$560$		0			0
$561$	−104.000			−0.00782689
$562$	−8622.15	−	4978.00i	−0.647159	−	0.373637i
$563$	−8711.35	+	5029.50i	−0.652113	+	0.376498i	−0.789265	−	0.614052i	$-0.789538\pi$
$563$	−8711.35	+	5029.50i	−0.652113	+	0.376498i	0.137152	+	0.990550i	$0.456205\pi$
$564$	−176.000	−	304.841i	−0.0131400	−	0.0227591i
$565$		0			0
$566$	−11704.0			−0.869180
$567$	562.050	+	12006.5i	0.0416295	+	0.889287i
$568$		−	6160.00i		−	0.455049i
$569$	−7833.00	+	13567.2i	−0.577111	+	0.999586i	0.418697	+	0.908126i	$0.362487\pi$
$569$	−7833.00	+	13567.2i	−0.577111	+	0.999586i	−0.995809	+	0.0914605i	$0.970846\pi$
$570$		0			0
$571$	−1265.00	−	2191.04i	−0.0927121	−	0.160582i	0.815939	−	0.578138i	$-0.196220\pi$
$571$	−1265.00	−	2191.04i	−0.0927121	−	0.160582i	−0.908651	+	0.417555i	$0.862887\pi$
$572$	55.4256	+	32.0000i	0.00405151	+	0.00233914i
$573$			1978.00i			0.144210i
$574$	7060.00	+	11005.5i	0.513378	+	0.800276i
$575$		0			0
$576$	832.000	−	1441.07i	0.0601852	−	0.104244i
$577$	−11100.7	+	6409.00i	−0.800916	+	0.462409i	−0.843791	−	0.536671i	$-0.819682\pi$
$577$	−11100.7	+	6409.00i	−0.800916	+	0.462409i	0.0428751	+	0.999080i	$0.486348\pi$
$578$	3826.10	−	2209.00i	0.275337	−	0.158966i
$579$	1999.00	−	3462.37i	0.143481	−	0.248517i
$580$		0			0
$581$	4462.50	−	8638.60i	0.318650	−	0.616850i
$582$			580.000i			0.0413089i
$583$	1008.05	+	582.000i	0.0716112	+	0.0413447i
$584$	−2512.00	−	4350.91i	−0.177992	−	0.308291i
$585$		0			0
$586$	−3012.00	+	5216.94i	−0.212329	+	0.367764i
$587$			15228.0i			1.07074i	0.844616	+	0.535372i	$0.179829\pi$
$587$			15228.0i			1.07074i	−0.844616	+	0.535372i	$0.820171\pi$
$588$	−128.172	−	1366.00i	−0.00898931	−	0.0958042i
$589$	8632.00			0.603863
$590$		0			0
$591$	−1515.00	−	2624.06i	−0.105446	−	0.182638i
$592$	−2715.86	+	1568.00i	−0.188549	+	0.108859i
$593$	2249.93	+	1299.00i	0.155807	+	0.0899554i	0.575877	−	0.817537i	$-0.304661\pi$
$593$	2249.93	+	1299.00i	0.155807	+	0.0899554i	−0.420069	+	0.907492i	$0.637994\pi$
$594$	−212.000			−0.0146439
$595$		0			0
$596$	−1476.00			−0.101442
$597$	−308.305	−	178.000i	−0.0211358	−	0.0122028i
$598$	928.379	−	536.000i	0.0634854	−	0.0366533i
$599$	−1274.00	−	2206.63i	−0.0869019	−	0.150518i	0.819298	−	0.573368i	$-0.194363\pi$
$599$	−1274.00	−	2206.63i	−0.0869019	−	0.150518i	−0.906200	+	0.422849i	$0.861030\pi$
$600$		0			0
$601$	1706.00			0.115789			0.0578945	−	0.998323i	$-0.481561\pi$
$601$	1706.00			0.115789			0.0578945	+	0.998323i	$0.481561\pi$
$602$	11504.3	−	7380.00i	0.778870	−	0.499645i
$603$		−	7566.00i		−	0.510964i
$604$	4960.00	−	8590.97i	0.334138	−	0.578745i
$605$		0			0
$606$	1233.00	+	2135.62i	0.0826521	+	0.143158i
$607$	−10883.3	−	6283.50i	−0.727745	−	0.420164i	0.0898517	−	0.995955i	$-0.471361\pi$
$607$	−10883.3	−	6283.50i	−0.727745	−	0.420164i	−0.817597	+	0.575791i	$0.804694\pi$
$608$		−	832.000i		−	0.0554968i
$609$	−1276.50	+	59.7558i	−0.0849366	+	0.00397607i
$610$		0			0
$611$	352.000	−	609.682i	0.0233067	−	0.0403684i
$612$	−4683.47	+	2704.00i	−0.309343	+	0.178599i
$613$	−8338.09	+	4814.00i	−0.549384	+	0.317187i	−0.748874	−	0.662713i	$-0.769405\pi$
$613$	−8338.09	+	4814.00i	−0.549384	+	0.317187i	0.199490	+	0.979900i	$0.436072\pi$
$614$	−9443.00	+	16355.8i	−0.620665	+	1.07502i
$615$		0			0
$616$	−296.000	+	13.8564i	−0.0193607	+	0.000906316i
$617$			4316.00i			0.281614i	0.990037	+	0.140807i	$0.0449696\pi$
$617$			4316.00i			0.281614i	−0.990037	+	0.140807i	$0.955030\pi$
$618$	−2689.87	−	1553.00i	−0.175085	−	0.101085i
$619$	8201.00	+	14204.5i	0.532514	+	0.922341i	0.999279	+	0.0379598i	$0.0120859\pi$
$619$	8201.00	+	14204.5i	0.532514	+	0.922341i	−0.466766	+	0.884381i	$0.654581\pi$
$620$		0			0
$621$	−1775.50	+	3075.26i	−0.114732	+	0.198721i
$622$		−	19988.0i		−	1.28850i
$623$	−1387.37	+	890.000i	−0.0892198	+	0.0572345i
$624$	−128.000			−0.00821170
$625$		0			0
$626$	1456.00	+	2521.87i	0.0929608	+	0.161013i
$627$	−45.0333	+	26.0000i	−0.00286835	+	0.00165604i
$628$	−4246.99	−	2452.00i	−0.269862	−	0.155805i
$629$	10192.0			0.646076
$630$		0			0
$631$	8490.00			0.535628			0.267814	−	0.963471i	$-0.413699\pi$
$631$	8490.00			0.535628			0.267814	+	0.963471i	$0.413699\pi$
$632$	−8106.00	−	4680.00i	−0.510189	−	0.294558i
$633$	2253.40	−	1301.00i	0.141492	−	0.0816905i
$634$	−6872.00	−	11902.7i	−0.430476	−	0.745607i
$635$		0			0
$636$	−2328.00			−0.145143
$637$	2237.81	−	1588.00i	0.139192	−	0.0987737i
$638$			276.000i			0.0171269i
$639$	−10010.0	+	17337.8i	−0.619702	+	1.07336i
$640$		0			0
$641$	61.5000	+	106.521i	0.00378955	+	0.00656370i	0.867914	−	0.496715i	$-0.165460\pi$
$641$	61.5000	+	106.521i	0.00378955	+	0.00656370i	−0.864124	+	0.503278i	$0.832127\pi$
$642$	3171.39	+	1831.00i	0.194960	+	0.112560i
$643$		−	23924.0i		−	1.46729i	−0.679530	−	0.733647i	$-0.737816\pi$
$643$		−	23924.0i		−	1.46729i	0.679530	−	0.733647i	$-0.262184\pi$
$644$	−2278.00	+	4409.80i	−0.139388	+	0.269830i
$645$		0			0
$646$	−1352.00	+	2341.73i	−0.0823432	+	0.142623i
$647$	−156.751	+	90.5000i	−0.00952473	+	0.00549911i	−0.504755	−	0.863263i	$-0.668417\pi$
$647$	−156.751	+	90.5000i	−0.00952473	+	0.00549911i	0.495230	+	0.868762i	$0.335084\pi$
$648$	−4496.40	+	2596.00i	−0.272586	+	0.157377i
$649$	350.000	−	606.218i	0.0211690	−	0.0366658i
$650$		0			0
$651$	3320.00	+	5175.37i	0.199879	+	0.311580i
$652$			2640.00i			0.158574i
$653$	15425.6	+	8906.00i	0.924429	+	0.533719i	0.885045	−	0.465505i	$-0.154127\pi$
$653$	15425.6	+	8906.00i	0.924429	+	0.533719i	0.0393836	+	0.999224i	$0.487461\pi$
$654$	811.000	+	1404.69i	0.0484902	+	0.0839875i
$655$		0			0
$656$	−2824.00	+	4891.31i	−0.168077	+	0.291118i
$657$			16328.0i			0.969583i
$658$	152.420	+	3256.00i	0.00903035	+	0.192906i
$659$	−15334.0			−0.906416			−0.453208	−	0.891405i	$-0.649720\pi$
$659$	−15334.0			−0.906416			−0.453208	+	0.891405i	$0.649720\pi$
$660$		0			0
$661$	−668.500	−	1157.88i	−0.0393368	−	0.0681334i	0.845687	−	0.533680i	$-0.179191\pi$
$661$	−668.500	−	1157.88i	−0.0393368	−	0.0681334i	−0.885024	+	0.465546i	$0.845858\pi$
$662$	−678.964	+	392.000i	−0.0398621	+	0.0230144i
$663$	360.267	+	208.000i	0.0211035	+	0.0121841i
$664$	4200.00			0.245469
$665$		0			0
$666$	10192.0			0.592991
$667$	4003.64	+	2311.50i	0.232416	+	0.134185i
$668$	−3287.43	+	1898.00i	−0.190411	+	0.109934i
$669$	1578.00	+	2733.18i	0.0911943	+	0.157953i
$670$		0			0
$671$	934.000			0.0537357
$672$	498.831	−	320.000i	0.0286351	−	0.0183694i
$673$		−	15112.0i		−	0.865564i	−0.901499	−	0.432782i	$-0.857532\pi$
$673$		−	15112.0i		−	0.865564i	0.901499	−	0.432782i	$-0.142468\pi$
$674$	−3926.00	+	6800.03i	−0.224368	+	0.388616i
$675$		0			0
$676$	4266.00	+	7388.93i	0.242717	+	0.420399i
$677$	21990.1	+	12696.0i	1.24837	+	0.720749i	0.970785	−	0.239951i	$-0.0771315\pi$
$677$	21990.1	+	12696.0i	1.24837	+	0.720749i	0.277589	+	0.960700i	$0.410465\pi$
$678$			4340.00i			0.245836i
$679$	2465.00	−	4771.80i	0.139320	−	0.269698i
$680$		0			0
$681$	2118.00	−	3668.48i	0.119181	−	0.206427i
$682$	1150.08	−	664.000i	0.0645732	−	0.0372813i
$683$	25314.8	−	14615.5i	1.41822	−	0.818809i	0.422076	−	0.906560i	$-0.361301\pi$
$683$	25314.8	−	14615.5i	1.41822	−	0.818809i	0.996142	+	0.0877512i	$0.0279681\pi$
$684$	−1352.00	+	2341.73i	−0.0755775	+	0.130904i
$685$		0			0
$686$	−4751.00	+	11783.1i	−0.264423	+	0.655805i
$687$			6334.00i			0.351757i
$688$	5113.01	+	2952.00i	0.283331	+	0.163581i
$689$	−2328.00	−	4032.21i	−0.128722	−	0.222954i
$690$		0			0
$691$	3769.00	−	6528.10i	0.207496	−	0.359393i	−0.743429	−	0.668814i	$-0.766802\pi$
$691$	3769.00	−	6528.10i	0.207496	−	0.359393i	0.950925	+	0.309421i	$0.100135\pi$
$692$		−	13568.0i		−	0.745344i
$693$	855.633	+	442.000i	0.0469016	+	0.0242283i
$694$	−3570.00			−0.195267
$695$		0			0
$696$	−276.000	−	478.046i	−0.0150313	−	0.0260349i
$697$	15896.8	−	9178.00i	0.863892	−	0.498768i
$698$	−2755.69	−	1591.00i	−0.149433	−	0.0862754i
$699$	−4688.00			−0.253672
$700$		0			0
$701$	22125.0			1.19208			0.596041	−	0.802954i	$-0.296739\pi$
$701$	22125.0			1.19208			0.596041	+	0.802954i	$0.296739\pi$
$702$	734.390	+	424.000i	0.0394840	+	0.0227961i
$703$	4413.27	−	2548.00i	0.236770	−	0.136699i
$704$	−64.0000	−	110.851i	−0.00342627	−	0.00593447i
$705$		0			0
$706$	−3372.00			−0.179755
$707$	−1067.81	−	22810.5i	−0.0568021	−	1.21340i
$708$			1400.00i			0.0743153i
$709$	−2219.50	+	3844.29i	−0.117567	+	0.203632i	−0.918803	−	0.394716i	$-0.870843\pi$
$709$	−2219.50	+	3844.29i	−0.117567	+	0.203632i	0.801236	+	0.598349i	$0.204176\pi$
$710$		0			0
$711$	15210.0	+	26344.5i	0.802278	+	1.38959i
$712$	−616.610	−	356.000i	−0.0324557	−	0.0187383i
$713$		−	22244.0i		−	1.16837i
$714$	−1924.00	+	90.0666i	−0.100846	+	0.00472081i
$715$		0			0
$716$	−536.000	+	928.379i	−0.0279766	+	0.0484569i
$717$	1607.34	−	928.000i	0.0837201	−	0.0483358i
$718$	−12768.7	+	7372.00i	−0.663681	+	0.383176i
$719$	6825.00	−	11821.2i	0.354005	−	0.613155i	−0.632942	−	0.774199i	$-0.718153\pi$
$719$	6825.00	−	11821.2i	0.354005	−	0.613155i	0.986947	+	0.161045i	$0.0514863\pi$
$720$		0			0
$721$	15530.0	+	24208.9i	0.802174	+	1.25047i
$722$		−	12366.0i		−	0.637417i
$723$	−4162.12	−	2403.00i	−0.214095	−	0.123608i
$724$	−8186.00	−	14178.6i	−0.420208	−	0.727821i
$725$		0			0
$726$	1327.00	−	2298.43i	0.0678369	−	0.117497i
$727$			11397.0i			0.581419i	0.956811	+	0.290709i	$0.0938913\pi$
$727$			11397.0i			0.581419i	−0.956811	+	0.290709i	$0.906109\pi$
$728$	1053.09	+	544.000i	0.0536126	+	0.0276950i
$729$	15443.0			0.784586
$730$		0			0
$731$	−9594.00	−	16617.3i	−0.485427	−	0.840784i
$732$	−1617.74	+	934.000i	−0.0816847	+	0.0471607i
$733$	−14450.5	−	8343.00i	−0.728160	−	0.420403i	0.0895886	−	0.995979i	$-0.471445\pi$
$733$	−14450.5	−	8343.00i	−0.728160	−	0.420403i	−0.817749	+	0.575575i	$0.804778\pi$
$734$	13274.0			0.667510
$735$		0			0
$736$	−2144.00			−0.107376
$737$	−504.027	−	291.000i	−0.0251914	−	0.0145443i
$738$	15896.8	−	9178.00i	0.792910	−	0.457787i
$739$	11235.0	+	19459.6i	0.559251	+	0.968650i	0.997559	+	0.0698258i	$0.0222444\pi$
$739$	11235.0	+	19459.6i	0.559251	+	0.968650i	−0.438309	+	0.898825i	$0.644422\pi$
$740$		0			0
$741$	208.000			0.0103118
$742$	19153.0	+	9894.00i	0.947614	+	0.489515i
$743$			5625.00i			0.277741i	0.990311	+	0.138870i	$0.0443471\pi$
$743$			5625.00i			0.277741i	−0.990311	+	0.138870i	$0.955653\pi$
$744$	−1328.00	+	2300.16i	−0.0654393	+	0.113344i
$745$		0			0
$746$	3476.00	+	6020.61i	0.170597	+	0.295483i
$747$	−11821.2	−	6825.00i	−0.579005	−	0.334289i
$748$			416.000i			0.0203348i
$749$	−18310.0	−	28542.5i	−0.893235	−	1.39242i
$750$		0			0
$751$	−8810.00	+	15259.4i	−0.428071	+	0.741441i	−0.996702	−	0.0811520i	$-0.974140\pi$
$751$	−8810.00	+	15259.4i	−0.428071	+	0.741441i	0.568631	+	0.822593i	$0.307473\pi$
$752$	−1219.36	+	704.000i	−0.0591298	+	0.0341386i
$753$	2771.28	−	1600.00i	0.134118	−	0.0774333i
$754$	552.000	−	956.092i	0.0266613	−	0.0461788i
$755$		0			0
$756$	−3922.00	+	183.597i	−0.188680	+	0.00883250i
$757$		−	39056.0i		−	1.87518i	−0.347737	−	0.937592i	$-0.613050\pi$
$757$		−	39056.0i		−	1.87518i	0.347737	−	0.937592i	$-0.386950\pi$
$758$	−4118.82	−	2378.00i	−0.197364	−	0.113948i
$759$	67.0000	+	116.047i	0.00320414	+	0.00554974i
$760$		0			0
$761$	−14869.0	+	25753.9i	−0.708280	+	1.22678i	0.257215	+	0.966354i	$0.417195\pi$
$761$	−14869.0	+	25753.9i	−0.708280	+	1.22678i	−0.965495	+	0.260422i	$0.916138\pi$
$762$		−	96.0000i		−	0.00456393i
$763$	−702.347	−	15003.5i	−0.0333246	−	0.711878i
$764$	7912.00			0.374668
$765$		0			0
$766$	−2457.00	−	4255.65i	−0.115894	−	0.200735i
$767$	−2424.87	+	1400.00i	−0.114155	+	0.0659075i
$768$	221.703	+	128.000i	0.0104167	+	0.00601407i
$769$	1118.00			0.0524267			0.0262133	−	0.999656i	$-0.491655\pi$
$769$	1118.00			0.0524267			0.0262133	+	0.999656i	$0.491655\pi$
$770$		0			0
$771$	1120.00			0.0523162
$772$	−13849.5	−	7996.00i	−0.645665	−	0.372775i
$773$	11632.5	−	6716.00i	0.541255	−	0.312494i	−0.204332	−	0.978902i	$-0.565502\pi$
$773$	11632.5	−	6716.00i	0.541255	−	0.312494i	0.745587	+	0.666408i	$0.232169\pi$
$774$	−9594.00	−	16617.3i	−0.445542	−	0.771701i
$775$		0			0
$776$	2320.00			0.107324
$777$	3225.08	+	1666.00i	0.148905	+	0.0769207i
$778$		−	17124.0i		−	0.789107i
$779$	4589.00	−	7948.38i	0.211063	−	0.365572i
$780$		0			0
$781$	770.000	+	1333.68i	0.0352788	+	0.0611047i
$782$	6034.47	+	3484.00i	0.275949	+	0.159319i
$783$			3657.00i			0.166910i
$784$	−5464.00	+	512.687i	−0.248907	+	0.0233549i
$785$		0			0
$786$	792.000	−	1371.78i	0.0359411	−	0.0622518i
$787$	8096.47	−	4674.50i	0.366719	−	0.211725i	−0.305305	−	0.952255i	$-0.598758\pi$
$787$	8096.47	−	4674.50i	0.366719	−	0.211725i	0.672024	+	0.740529i	$0.265425\pi$
$788$	−10496.2	+	6060.00i	−0.474508	+	0.273958i
$789$	−3202.50	+	5546.89i	−0.144502	+	0.250285i
$790$		0			0
$791$	18445.0	−	35706.2i	0.829113	−	1.60502i
$792$			416.000i			0.0186640i
$793$	−3235.47	−	1868.00i	−0.144886	−	0.0836502i
$794$	9842.00	+	17046.8i	0.439899	+	0.761927i
$795$		0			0
$796$	−712.000	+	1233.22i	−0.0317037	+	0.0549125i
$797$			28008.0i			1.24479i	0.782705	+	0.622393i	$0.213839\pi$
$797$			28008.0i			1.24479i	−0.782705	+	0.622393i	$0.786161\pi$
$798$	−810.600	+	520.000i	−0.0359585	+	0.0230674i
$799$	4576.00			0.202612
$800$		0			0
$801$	1157.00	+	2003.98i	0.0510369	+	0.0883986i
$802$	−14024.4	+	8097.00i	−0.617480	+	0.356503i
$803$	1087.73	+	628.000i	0.0478021	+	0.0275986i
$804$	1164.00			0.0510586
$805$		0			0
$806$	−5312.00			−0.232143
$807$	−4273.84	−	2467.50i	−0.186426	−	0.107633i
$808$	8542.47	−	4932.00i	0.371935	−	0.214737i
$809$	9834.50	+	17033.9i	0.427395	+	0.740270i	0.996641	−	0.0818975i	$-0.0260980\pi$
$809$	9834.50	+	17033.9i	0.427395	+	0.740270i	−0.569246	+	0.822167i	$0.692765\pi$
$810$		0			0
$811$	31860.0			1.37948			0.689739	−	0.724059i	$-0.257725\pi$
$811$	31860.0			1.37948			0.689739	+	0.724059i	$0.257725\pi$
$812$	239.023	+	5106.00i	0.0103301	+	0.220672i
$813$			1446.00i			0.0623781i
$814$	392.000	−	678.964i	0.0168791	−	0.0292355i
$815$		0			0
$816$	−416.000	−	720.533i	−0.0178467	−	0.0309114i
$817$	−8308.65	−	4797.00i	−0.355793	−	0.205417i
$818$		−	30518.0i		−	1.30445i
$819$	−2080.00	−	3242.40i	−0.0887437	−	0.138338i
$820$		0			0
$821$	−1115.00	+	1931.24i	−0.0473980	+	0.0820958i	−0.888751	−	0.458390i	$-0.848426\pi$
$821$	−1115.00	+	1931.24i	−0.0473980	+	0.0820958i	0.841353	+	0.540486i	$0.181760\pi$
$822$	−1877.54	+	1084.00i	−0.0796677	+	0.0459962i
$823$	12819.8	−	7401.50i	0.542976	−	0.313487i	−0.203308	−	0.979115i	$-0.565169\pi$
$823$	12819.8	−	7401.50i	0.542976	−	0.313487i	0.746284	+	0.665627i	$0.231836\pi$
$824$	−6212.00	+	10759.5i	−0.262628	+	0.454885i
$825$		0			0
$826$	5950.00	−	11518.1i	0.250638	−	0.485190i
$827$		−	13257.0i		−	0.557426i	−0.960374	−	0.278713i	$-0.910092\pi$
$827$		−	13257.0i		−	0.557426i	0.960374	−	0.278713i	$-0.0899078\pi$
$828$	6034.47	+	3484.00i	0.253276	+	0.146229i
$829$	−10787.0	−	18683.6i	−0.451928	−	0.782762i	0.546578	−	0.837408i	$-0.315930\pi$
$829$	−10787.0	−	18683.6i	−0.451928	−	0.782762i	−0.998506	+	0.0546465i	$0.982597\pi$
$830$		0			0
$831$	−4010.00	+	6945.52i	−0.167395	+	0.289937i
$832$			512.000i			0.0213346i
$833$	16212.0	+	7436.00i	0.674325	+	0.309294i
$834$	92.0000			0.00381978
$835$		0			0
$836$	104.000	+	180.133i	0.00430253	+	0.00745220i
$837$	15238.6	−	8798.00i	0.629298	−	0.363325i
$838$	28100.8	+	16224.0i	1.15838	+	0.668793i
$839$	−12990.0			−0.534523			−0.267261	−	0.963624i	$-0.586119\pi$
$839$	−12990.0			−0.534523			−0.267261	+	0.963624i	$0.586119\pi$
$840$		0			0
$841$	−19628.0			−0.804789
$842$	−5156.32	−	2977.00i	−0.211043	−	0.121846i
$843$	−4311.07	+	2489.00i	−0.176134	+	0.101691i
$844$	−5204.00	−	9013.59i	−0.212238	−	0.367607i
$845$		0			0
$846$	4576.00			0.185965
$847$	−20685.9	+	13270.0i	−0.839168	+	0.538327i
$848$			9312.00i			0.377094i
$849$	−2926.00	+	5067.98i	−0.118280	+	0.204868i
$850$		0			0
$851$	−6566.00	−	11372.6i	−0.264488	−	0.458107i
$852$	−2667.36	−	1540.00i	−0.107256	−	0.0619243i
$853$			24838.0i			0.996995i	0.866891	+	0.498498i	$0.166115\pi$
$853$			24838.0i			0.996995i	−0.866891	+	0.498498i	$0.833885\pi$
$854$	17279.0	−	808.868i	0.692360	−	0.0324109i
$855$		0			0
$856$	7324.00	−	12685.5i	0.292441	−	0.506522i
$857$	14744.9	−	8513.00i	0.587722	−	0.339322i	−0.176474	−	0.984305i	$-0.556469\pi$
$857$	14744.9	−	8513.00i	0.587722	−	0.339322i	0.764196	+	0.644984i	$0.223136\pi$
$858$	27.7128	−	16.0000i	0.00110268	−	0.000636633i
$859$	3364.00	−	5826.62i	0.133618	−	0.231434i	−0.791450	−	0.611233i	$-0.790674\pi$
$859$	3364.00	−	5826.62i	0.133618	−	0.231434i	0.925069	+	0.379800i	$0.124007\pi$
$860$		0			0
$861$	6530.50	−	305.707i	0.258489	−	0.0121004i
$862$			28404.0i			1.12232i
$863$	26066.5	+	15049.5i	1.02817	+	0.593616i	0.916461	−	0.400124i	$-0.131033\pi$
$863$	26066.5	+	15049.5i	1.02817	+	0.593616i	0.111713	+	0.993741i	$0.464366\pi$
$864$	−848.000	−	1468.78i	−0.0333907	−	0.0578344i
$865$		0			0
$866$	14310.0	−	24785.6i	0.561517	−	0.972576i
$867$		−	2209.00i		−	0.0865301i
$868$	20701.5	−	13280.0i	0.809509	−	0.519300i
$869$	2340.00			0.0913453
$870$		0			0
$871$	1164.00	+	2016.11i	0.0452820	+	0.0784308i
$872$	5618.77	−	3244.00i	0.218206	−	0.125981i
$873$	−6529.83	−	3770.00i	−0.253152	−	0.146157i
$874$	3484.00			0.134838
$875$		0			0
$876$	−2512.00			−0.0968865
$877$	−4872.26	−	2813.00i	−0.187599	−	0.108310i	0.403259	−	0.915086i	$-0.367877\pi$
$877$	−4872.26	−	2813.00i	−0.187599	−	0.108310i	−0.590858	+	0.806775i	$0.701211\pi$
$878$	4080.71	−	2356.00i	0.156853	−	0.0905594i
$879$	1506.00	+	2608.47i	0.0577885	+	0.100093i
$880$		0			0
$881$	−15927.0			−0.609074			−0.304537	−	0.952500i	$-0.598502\pi$
$881$	−15927.0			−0.609074			−0.304537	+	0.952500i	$0.598502\pi$
$882$	16212.0	+	7436.00i	0.618919	+	0.283881i
$883$			39124.0i			1.49108i	0.666458	+	0.745542i	$0.267809\pi$
$883$			39124.0i			1.49108i	−0.666458	+	0.745542i	$0.732191\pi$
$884$	832.000	−	1441.07i	0.0316552	−	0.0548284i
$885$		0			0
$886$	8291.00	+	14360.4i	0.314381	+	0.544524i
$887$	−21937.3	−	12665.5i	−0.830419	−	0.479443i	0.0235768	−	0.999722i	$-0.492495\pi$
$887$	−21937.3	−	12665.5i	−0.830419	−	0.479443i	−0.853996	+	0.520279i	$0.825828\pi$
$888$			1568.00i			0.0592552i
$889$	−408.000	+	789.815i	−0.0153924	+	0.0297970i
$890$		0			0
$891$	649.000	−	1124.10i	0.0244022	−	0.0422658i
$892$	10932.7	−	6312.00i	0.410374	−	0.236930i
$893$	1981.47	−	1144.00i	0.0742522	−	0.0428695i
$894$	−369.000	+	639.127i	−0.0138045	+	0.0239101i
$895$		0			0
$896$	−1280.00	−	1995.32i	−0.0477252	−	0.0743963i
$897$		−	536.000i		−	0.0199515i
$898$	−6098.55	−	3521.00i	−0.226627	−	0.130843i
$899$	−11454.0	−	19838.9i	−0.424930	−	0.736001i
$900$		0			0
$901$	15132.0	−	26209.4i	0.559512	−	0.969103i
$902$		−	1412.00i		−	0.0521225i
$903$	−319.563	−	6826.50i	−0.0117767	−	0.251574i
$904$	17360.0			0.638700
$905$		0			0
$906$	−2480.00	−	4295.49i	−0.0909409	−	0.157514i
$907$	−22850.1	+	13192.5i	−0.836521	+	0.482966i	−0.856080	−	0.516843i	$-0.827107\pi$
$907$	−22850.1	+	13192.5i	−0.836521	+	0.482966i	0.0195592	+	0.999809i	$0.493774\pi$
$908$	−14673.9	−	8472.00i	−0.536312	−	0.309640i
$909$	−32058.0			−1.16974
$910$		0			0
$911$	−40770.0			−1.48273			−0.741367	−	0.671100i	$-0.765822\pi$
$911$	−40770.0			−1.48273			−0.741367	+	0.671100i	$0.765822\pi$
$912$	−360.267	−	208.000i	−0.0130807	−	0.00755216i
$913$	−909.327	+	525.000i	−0.0329620	+	0.0190306i
$914$	5432.00	+	9408.50i	0.196581	+	0.340487i
$915$		0			0
$916$	25336.0			0.913892
$917$	−12346.1	+	7920.00i	−0.444605	+	0.285214i
$918$			5512.00i			0.198173i
$919$	−7309.00	+	12659.6i	−0.262352	+	0.454407i	−0.966867	−	0.255282i	$-0.917832\pi$
$919$	−7309.00	+	12659.6i	−0.262352	+	0.454407i	0.704514	+	0.709690i	$0.251165\pi$
$920$		0			0
$921$	4721.50	+	8177.88i	0.168924	+	0.292584i
$922$	9266.47	+	5350.00i	0.330992	+	0.191099i
$923$		−	6160.00i		−	0.219674i
$924$	−68.0000	+	131.636i	−0.00242103	+	0.00468669i
$925$		0			0
$926$	−10123.0	+	17533.6i	−0.359247	+	0.622233i
$927$	34968.4	−	20189.0i	1.23896	−	0.715311i
$928$	−1912.18	+	1104.00i	−0.0676406	+	0.0390523i
$929$	20661.5	−	35786.8i	0.729690	−	1.26386i	−0.227324	−	0.973819i	$-0.572998\pi$
$929$	20661.5	−	35786.8i	0.729690	−	1.26386i	0.957014	−	0.290041i	$-0.0936689\pi$
$930$		0			0
$931$	8879.00	−	833.116i	0.312564	−	0.0293279i
$932$			18752.0i			0.659058i
$933$	−8655.06	−	4997.00i	−0.303702	−	0.175342i
$934$	−6463.00	−	11194.2i	−0.226420	−	0.392170i
$935$		0			0
$936$	832.000	−	1441.07i	0.0290542	−	0.0503234i
$937$			22620.0i			0.788648i	0.918971	+	0.394324i	$0.129021\pi$
$937$			22620.0i			0.788648i	−0.918971	+	0.394324i	$0.870979\pi$
$938$	−9576.51	−	4947.00i	−0.333352	−	0.172202i
$939$	1456.00			0.0506015
$940$		0			0
$941$	−25989.0	−	45014.3i	−0.900337	−	1.55943i	−0.827057	−	0.562118i	$-0.809987\pi$
$941$	−25989.0	−	45014.3i	−0.900337	−	1.55943i	−0.0732801	−	0.997311i	$-0.523347\pi$
$942$	−2123.49	+	1226.00i	−0.0734471	+	0.0424047i
$943$	−20482.4	−	11825.5i	−0.707315	−	0.408368i
$944$	5600.00			0.193077
$945$		0			0
$946$	−1476.00			−0.0507282
$947$	8649.00	+	4993.50i	0.296784	+	0.171348i	0.640997	−	0.767543i	$-0.278521\pi$
$947$	8649.00	+	4993.50i	0.296784	+	0.171348i	−0.344213	+	0.938892i	$0.611854\pi$
$948$	−4053.00	+	2340.00i	−0.138856	+	0.0801684i
$949$	−2512.00	−	4350.91i	−0.0859252	−	0.148827i
$950$		0			0
$951$	−6872.00			−0.234322
$952$	360.267	+	7696.00i	0.0122650	+	0.262005i
$953$			6588.00i			0.223931i	0.993712	+	0.111966i	$0.0357146\pi$
$953$			6588.00i			0.223931i	−0.993712	+	0.111966i	$0.964285\pi$
$954$	15132.0	−	26209.4i	0.513539	−	0.889476i
$955$		0			0
$956$	−3712.00	−	6429.37i	−0.125580	−	0.217511i
$957$	119.512	+	69.0000i	0.00403684	+	0.00233067i
$958$			35280.0i			1.18982i
$959$	20054.0	−	938.772i	0.675263	−	0.0316105i
$960$		0			0
$961$	−40216.5	+	69657.0i	−1.34995	+	2.33819i
$962$	−2715.86	+	1568.00i	−0.0910215	+	0.0525513i
$963$	−41228.0	+	23803.0i	−1.37960	+	0.796512i
$964$	−9612.00	+	16648.5i	−0.321143	+	0.556236i
$965$		0			0
$966$	1340.00	+	2088.85i	0.0446313	+	0.0695732i
$967$			4091.00i			0.136047i	0.997684	+	0.0680236i	$0.0216693\pi$
$967$			4091.00i			0.136047i	−0.997684	+	0.0680236i	$0.978331\pi$
$968$	−9193.73	−	5308.00i	−0.305266	−	0.176245i
$969$	676.000	+	1170.87i	0.0224110	+	0.0388170i
$970$		0			0
$971$	−11820.0	+	20472.8i	−0.390651	+	0.676627i	−0.992536	−	0.121956i	$-0.961083\pi$
$971$	−11820.0	+	20472.8i	−0.390651	+	0.676627i	0.601885	+	0.798583i	$0.294417\pi$
$972$			8320.00i			0.274552i
$973$	−756.906	−	391.000i	−0.0249386	−	0.0128827i
$974$	−20064.0			−0.660053
$975$		0			0
$976$	3736.00	+	6470.94i	0.122527	+	0.212223i
$977$	−31753.7	+	18333.0i	−1.03981	+	0.600332i	−0.919778	−	0.392438i	$-0.871632\pi$
$977$	−31753.7	+	18333.0i	−1.03981	+	0.600332i	−0.120028	+	0.992771i	$0.538298\pi$
$978$	1143.15	+	660.000i	0.0373763	+	0.0215792i
$979$	178.000			0.00581093
$980$		0			0
$981$	−21086.0			−0.686263
$982$	−10246.8	−	5916.00i	−0.332983	−	0.192248i
$983$	−35568.5	+	20535.5i	−1.15408	+	0.666308i	−0.949878	−	0.312621i	$-0.898793\pi$
$983$	−35568.5	+	20535.5i	−1.15408	+	0.666308i	−0.204201	+	0.978929i	$0.565460\pi$
$984$	1412.00	+	2445.66i	0.0457448	+	0.0792324i
$985$		0			0
$986$	7176.00			0.231775
$987$	1447.99	+	748.000i	0.0466972	+	0.0241227i
$988$		−	832.000i		−	0.0267909i
$989$	−12361.5	+	21410.7i	−0.397445	+	0.688394i
$990$		0			0
$991$	−15992.0	−	27699.0i	−0.512616	−	0.887877i	−0.999893	−	0.0146297i	$-0.995343\pi$
$991$	−15992.0	−	27699.0i	−0.512616	−	0.887877i	0.487277	−	0.873248i	$-0.337990\pi$
$992$	9200.65	+	5312.00i	0.294477	+	0.170016i
$993$			392.000i			0.0125274i
$994$	15400.0	+	24006.2i	0.491407	+	0.766027i
$995$		0			0
$996$	1050.00	−	1818.65i	0.0334041	−	0.0578577i
$997$	38013.3	−	21947.0i	1.20752	−	0.697160i	0.245300	−	0.969447i	$-0.421113\pi$
$997$	38013.3	−	21947.0i	1.20752	−	0.697160i	0.962216	+	0.272287i	$0.0877801\pi$
$998$	−24065.1	+	13894.0i	−0.763294	+	0.440688i
$999$	5194.00	−	8996.27i	0.164495	−	0.284914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.e.149.1		4
5.2	odd	4		70.4.e.c.51.1	yes	2
5.3	odd	4		350.4.e.a.51.1		2
5.4	even	2	inner	350.4.j.e.149.2		4
7.4	even	3	inner	350.4.j.e.249.2		4
15.2	even	4		630.4.k.b.541.1		2
20.7	even	4		560.4.q.d.401.1		2
35.2	odd	12		490.4.a.c.1.1		1
35.4	even	6	inner	350.4.j.e.249.1		4
35.12	even	12		490.4.a.e.1.1		1
35.17	even	12		490.4.e.m.361.1		2
35.18	odd	12		350.4.e.a.151.1		2
35.23	odd	12		2450.4.a.bg.1.1		1
35.27	even	4		490.4.e.m.471.1		2
35.32	odd	12		70.4.e.c.11.1	✓	2
35.33	even	12		2450.4.a.be.1.1		1
105.32	even	12		630.4.k.b.361.1		2
140.67	even	12		560.4.q.d.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.c.11.1	✓	2	35.32	odd	12
70.4.e.c.51.1	yes	2	5.2	odd	4
350.4.e.a.51.1		2	5.3	odd	4
350.4.e.a.151.1		2	35.18	odd	12
350.4.j.e.149.1		4	1.1	even	1	trivial
350.4.j.e.149.2		4	5.4	even	2	inner
350.4.j.e.249.1		4	35.4	even	6	inner
350.4.j.e.249.2		4	7.4	even	3	inner
490.4.a.c.1.1		1	35.2	odd	12
490.4.a.e.1.1		1	35.12	even	12
490.4.e.m.361.1		2	35.17	even	12
490.4.e.m.471.1		2	35.27	even	4
560.4.q.d.81.1		2	140.67	even	12
560.4.q.d.401.1		2	20.7	even	4
630.4.k.b.361.1		2	105.32	even	12
630.4.k.b.541.1		2	15.2	even	4
2450.4.a.be.1.1		1	35.33	even	12
2450.4.a.bg.1.1		1	35.23	odd	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(-16.4545 - 8.50000i) q^{7} -8.00000i q^{8} +(-13.0000 + 22.5167i) q^{9} +O(q^{10})\)	\(q+(-1.73205 - 1.00000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(-16.4545 - 8.50000i) q^{7} -8.00000i q^{8} +(-13.0000 + 22.5167i) q^{9} +(1.00000 + 1.73205i) q^{11} +(-3.46410 - 2.00000i) q^{12} -8.00000i q^{13} +(20.0000 + 31.1769i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(45.0333 - 26.0000i) q^{17} +(45.0333 - 26.0000i) q^{18} +(13.0000 - 22.5167i) q^{19} +(18.5000 - 0.866025i) q^{21} -4.00000i q^{22} +(-58.0237 - 33.5000i) q^{23} +(4.00000 + 6.92820i) q^{24} +(-8.00000 + 13.8564i) q^{26} -53.0000i q^{27} +(-3.46410 - 74.0000i) q^{28} -69.0000 q^{29} +(166.000 + 287.520i) q^{31} +(27.7128 - 16.0000i) q^{32} +(-1.73205 - 1.00000i) q^{33} -104.000 q^{34} -104.000 q^{36} +(169.741 + 98.0000i) q^{37} +(-45.0333 + 26.0000i) q^{38} +(4.00000 + 6.92820i) q^{39} +353.000 q^{41} +(-32.9090 - 17.0000i) q^{42} -369.000i q^{43} +(-4.00000 + 6.92820i) q^{44} +(67.0000 + 116.047i) q^{46} +(76.2102 + 44.0000i) q^{47} -16.0000i q^{48} +(198.500 + 279.726i) q^{49} +(-26.0000 + 45.0333i) q^{51} +(27.7128 - 16.0000i) q^{52} +(504.027 - 291.000i) q^{53} +(-53.0000 + 91.7987i) q^{54} +(-68.0000 + 131.636i) q^{56} +26.0000i q^{57} +(119.512 + 69.0000i) q^{58} +(-175.000 - 303.109i) q^{59} +(233.500 - 404.434i) q^{61} -664.000i q^{62} +(405.300 - 260.000i) q^{63} -64.0000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-252.013 + 145.500i) q^{67} +(180.133 + 104.000i) q^{68} +67.0000 q^{69} +770.000 q^{71} +(180.133 + 104.000i) q^{72} +(543.864 - 314.000i) q^{73} +(-196.000 - 339.482i) q^{74} +104.000 q^{76} +(-1.73205 - 37.0000i) q^{77} -16.0000i q^{78} +(585.000 - 1013.25i) q^{79} +(-324.500 - 562.050i) q^{81} +(-611.414 - 353.000i) q^{82} +525.000i q^{83} +(40.0000 + 62.3538i) q^{84} +(-369.000 + 639.127i) q^{86} +(59.7558 - 34.5000i) q^{87} +(13.8564 - 8.00000i) q^{88} +(44.5000 - 77.0763i) q^{89} +(-68.0000 + 131.636i) q^{91} -268.000i q^{92} +(-287.520 - 166.000i) q^{93} +(-88.0000 - 152.420i) q^{94} +(-16.0000 + 27.7128i) q^{96} +290.000i q^{97} +(-64.0859 - 683.000i) q^{98} -52.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9	\( 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9} + 4 q^{11} + 80 q^{14} - 32 q^{16} + 52 q^{19} + 74 q^{21} + 16 q^{24} - 32 q^{26} - 276 q^{29} + 664 q^{31} - 416 q^{34} - 416 q^{36} + 16 q^{39} + 1412 q^{41} - 16 q^{44} + 268 q^{46} + 794 q^{49} - 104 q^{51} - 212 q^{54} - 272 q^{56} - 700 q^{59} + 934 q^{61} - 256 q^{64} + 8 q^{66} + 268 q^{69} + 3080 q^{71} - 784 q^{74} + 416 q^{76} + 2340 q^{79} - 1298 q^{81} + 160 q^{84} - 1476 q^{86} + 178 q^{89} - 272 q^{91} - 352 q^{94} - 64 q^{96} - 208 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9 + 4 * q^11 + 80 * q^14 - 32 * q^16 + 52 * q^19 + 74 * q^21 + 16 * q^24 - 32 * q^26 - 276 * q^29 + 664 * q^31 - 416 * q^34 - 416 * q^36 + 16 * q^39 + 1412 * q^41 - 16 * q^44 + 268 * q^46 + 794 * q^49 - 104 * q^51 - 212 * q^54 - 272 * q^56 - 700 * q^59 + 934 * q^61 - 256 * q^64 + 8 * q^66 + 268 * q^69 + 3080 * q^71 - 784 * q^74 + 416 * q^76 + 2340 * q^79 - 1298 * q^81 + 160 * q^84 - 1476 * q^86 + 178 * q^89 - 272 * q^91 - 352 * q^94 - 64 * q^96 - 208 * q^99

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