LMFDB - Embedded newform 490.3.f.o.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,3,Mod(197,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("490.197");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	490.f (of order $4$, degree $2$, 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:	$13.3515329537$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 2x^{5} + 730x^{4} - 1570x^{3} + 1682x^{2} + 4930x + 7225 $ x^8 - 2x^7 + 2x^6 + 2x^5 + 730x^4 - 1570x^3 + 1682x^2 + 4930*x + 7225
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Root			$3.59340 - 3.59340i$ of defining polynomial
Character	$\chi$	$=$	490.197
Dual form			490.3.f.o.393.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-3.59340 + 3.59340i) q^{3} +2.00000i q^{4} +(-4.98137 - 0.431169i) q^{5} -7.18681 q^{6} +(-2.00000 + 2.00000i) q^{8} -16.8251i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-3.59340 + 3.59340i) q^{3} +2.00000i q^{4} +(-4.98137 - 0.431169i) q^{5} -7.18681 q^{6} +(-2.00000 + 2.00000i) q^{8} -16.8251i q^{9} +(-4.55021 - 5.41254i) q^{10} -0.948733 q^{11} +(-7.18681 - 7.18681i) q^{12} +(0.862338 - 0.862338i) q^{13} +(19.4495 - 16.3507i) q^{15} -4.00000 q^{16} +(-21.5130 - 21.5130i) q^{17} +(16.8251 - 16.8251i) q^{18} +24.1474i q^{19} +(0.862338 - 9.96275i) q^{20} +(-0.948733 - 0.948733i) q^{22} +(4.00763 - 4.00763i) q^{23} -14.3736i q^{24} +(24.6282 + 4.29563i) q^{25} +1.72468 q^{26} +(28.1187 + 28.1187i) q^{27} -7.33636i q^{29} +(35.8002 + 3.09873i) q^{30} +47.0632 q^{31} +(-4.00000 - 4.00000i) q^{32} +(3.40918 - 3.40918i) q^{33} -43.0259i q^{34} +33.6502 q^{36} +(-5.82128 - 5.82128i) q^{37} +(-24.1474 + 24.1474i) q^{38} +6.19746i q^{39} +(10.8251 - 9.10041i) q^{40} +53.3601 q^{41} +(-33.0776 + 33.0776i) q^{43} -1.89747i q^{44} +(-7.25446 + 83.8121i) q^{45} +8.01526 q^{46} +(-21.5130 - 21.5130i) q^{47} +(14.3736 - 14.3736i) q^{48} +(20.3326 + 28.9238i) q^{50} +154.609 q^{51} +(1.72468 + 1.72468i) q^{52} +(9.51508 - 9.51508i) q^{53} +56.2374i q^{54} +(4.72600 + 0.409064i) q^{55} +(-86.7715 - 86.7715i) q^{57} +(7.33636 - 7.33636i) q^{58} -50.2432i q^{59} +(32.7014 + 38.8989i) q^{60} -45.4957 q^{61} +(47.0632 + 47.0632i) q^{62} -8.00000i q^{64} +(-4.66744 + 3.92382i) q^{65} +6.81836 q^{66} +(-48.3153 - 48.3153i) q^{67} +(43.0259 - 43.0259i) q^{68} +28.8020i q^{69} -11.9203 q^{71} +(33.6502 + 33.6502i) q^{72} +(-38.9464 + 38.9464i) q^{73} -11.6426i q^{74} +(-103.935 + 73.0631i) q^{75} -48.2949 q^{76} +(-6.19746 + 6.19746i) q^{78} -70.8989i q^{79} +(19.9255 + 1.72468i) q^{80} -50.6578 q^{81} +(53.3601 + 53.3601i) q^{82} +(85.7452 - 85.7452i) q^{83} +(97.8884 + 116.440i) q^{85} -66.1553 q^{86} +(26.3625 + 26.3625i) q^{87} +(1.89747 - 1.89747i) q^{88} -156.750i q^{89} +(-91.0665 + 76.5576i) q^{90} +(8.01526 + 8.01526i) q^{92} +(-169.117 + 169.117i) q^{93} -43.0259i q^{94} +(10.4116 - 120.287i) q^{95} +28.7472 q^{96} +(-87.1790 - 87.1790i) q^{97} +15.9625i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 2 q^{3} + 2 q^{5} - 4 q^{6} - 16 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 - 2 * q^3 + 2 * q^5 - 4 * q^6 - 16 * q^8	$ 8 q + 8 q^{2} - 2 q^{3} + 2 q^{5} - 4 q^{6} - 16 q^{8} + 6 q^{10} - 40 q^{11} - 4 q^{12} + 8 q^{13} - 10 q^{15} - 32 q^{16} - 46 q^{17} + 52 q^{18} + 8 q^{20} - 40 q^{22} - 54 q^{23} + 26 q^{25} + 16 q^{26} - 26 q^{27} + 22 q^{30} + 208 q^{31} - 32 q^{32} + 22 q^{33} + 104 q^{36} + 38 q^{37} - 36 q^{38} + 4 q^{40} - 36 q^{41} + 72 q^{43} - 254 q^{45} - 108 q^{46} - 46 q^{47} + 8 q^{48} - 30 q^{50} + 136 q^{51} + 16 q^{52} - 30 q^{53} - 96 q^{55} - 246 q^{57} - 132 q^{58} + 64 q^{60} + 120 q^{61} + 208 q^{62} - 230 q^{65} + 44 q^{66} + 74 q^{67} + 92 q^{68} + 8 q^{71} + 104 q^{72} + 54 q^{73} - 300 q^{75} - 72 q^{76} + 84 q^{78} - 8 q^{80} - 244 q^{81} - 36 q^{82} + 32 q^{83} + 272 q^{85} + 144 q^{86} + 236 q^{87} + 80 q^{88} - 524 q^{90} - 108 q^{92} - 142 q^{93} + 396 q^{95} + 16 q^{96} + 68 q^{97}+O(q^{100}) $ 8 * q + 8 * q^2 - 2 * q^3 + 2 * q^5 - 4 * q^6 - 16 * q^8 + 6 * q^10 - 40 * q^11 - 4 * q^12 + 8 * q^13 - 10 * q^15 - 32 * q^16 - 46 * q^17 + 52 * q^18 + 8 * q^20 - 40 * q^22 - 54 * q^23 + 26 * q^25 + 16 * q^26 - 26 * q^27 + 22 * q^30 + 208 * q^31 - 32 * q^32 + 22 * q^33 + 104 * q^36 + 38 * q^37 - 36 * q^38 + 4 * q^40 - 36 * q^41 + 72 * q^43 - 254 * q^45 - 108 * q^46 - 46 * q^47 + 8 * q^48 - 30 * q^50 + 136 * q^51 + 16 * q^52 - 30 * q^53 - 96 * q^55 - 246 * q^57 - 132 * q^58 + 64 * q^60 + 120 * q^61 + 208 * q^62 - 230 * q^65 + 44 * q^66 + 74 * q^67 + 92 * q^68 + 8 * q^71 + 104 * q^72 + 54 * q^73 - 300 * q^75 - 72 * q^76 + 84 * q^78 - 8 * q^80 - 244 * q^81 - 36 * q^82 + 32 * q^83 + 272 * q^85 + 144 * q^86 + 236 * q^87 + 80 * q^88 - 524 * q^90 - 108 * q^92 - 142 * q^93 + 396 * q^95 + 16 * q^96 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−3.59340	+	3.59340i	−1.19780	+	1.19780i	−0.222977	+	0.974824i	$0.571578\pi$
$3$	−3.59340	+	3.59340i	−1.19780	+	1.19780i	−0.974824	+	0.222977i	$0.928422\pi$
$4$			2.00000i			0.500000i
$5$	−4.98137	−	0.431169i	−0.996275	−	0.0862338i
$5$	−4.98137	−	0.431169i	−0.996275	−	0.0862338i
$6$	−7.18681			−1.19780
$7$		0			0
$7$		0			0
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	16.8251i		−	1.86945i
$10$	−4.55021	−	5.41254i	−0.455021	−	0.541254i
$11$	−0.948733			−0.0862485			−0.0431242	−	0.999070i	$-0.513731\pi$
$11$	−0.948733			−0.0862485			−0.0431242	+	0.999070i	$0.513731\pi$
$12$	−7.18681	−	7.18681i	−0.598900	−	0.598900i
$13$	0.862338	−	0.862338i	0.0663337	−	0.0663337i	−0.673162	−	0.739495i	$-0.735064\pi$
$13$	0.862338	−	0.862338i	0.0663337	−	0.0663337i	0.739495	+	0.673162i	$0.235064\pi$
$14$		0			0
$15$	19.4495	−	16.3507i	1.29663	−	1.09005i
$16$	−4.00000			−0.250000
$17$	−21.5130	−	21.5130i	−1.26547	−	1.26547i	−0.948404	−	0.317064i	$-0.897303\pi$
$17$	−21.5130	−	21.5130i	−1.26547	−	1.26547i	−0.317064	−	0.948404i	$-0.602697\pi$
$18$	16.8251	−	16.8251i	0.934727	−	0.934727i
$19$			24.1474i			1.27092i	0.772135	+	0.635459i	$0.219189\pi$
$19$			24.1474i			1.27092i	−0.772135	+	0.635459i	$0.780811\pi$
$20$	0.862338	−	9.96275i	0.0431169	−	0.498137i
$21$		0			0
$22$	−0.948733	−	0.948733i	−0.0431242	−	0.0431242i
$23$	4.00763	−	4.00763i	0.174245	−	0.174245i	−0.614597	−	0.788841i	$-0.710681\pi$
$23$	4.00763	−	4.00763i	0.174245	−	0.174245i	0.788841	+	0.614597i	$0.210681\pi$
$24$		−	14.3736i		−	0.598900i
$25$	24.6282	+	4.29563i	0.985127	+	0.171825i
$26$	1.72468			0.0663337
$27$	28.1187	+	28.1187i	1.04143	+	1.04143i
$28$		0			0
$29$		−	7.33636i		−	0.252978i	−0.991968	−	0.126489i	$-0.959629\pi$
$29$		−	7.33636i		−	0.252978i	0.991968	−	0.126489i	$-0.0403708\pi$
$30$	35.8002	+	3.09873i	1.19334	+	0.103291i
$31$	47.0632			1.51817			0.759083	−	0.650994i	$-0.225648\pi$
$31$	47.0632			1.51817			0.759083	+	0.650994i	$0.225648\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	3.40918	−	3.40918i	0.103308	−	0.103308i
$34$		−	43.0259i		−	1.26547i
$35$		0			0
$36$	33.6502			0.934727
$37$	−5.82128	−	5.82128i	−0.157332	−	0.157332i	0.624051	−	0.781383i	$-0.285486\pi$
$37$	−5.82128	−	5.82128i	−0.157332	−	0.157332i	−0.781383	+	0.624051i	$0.785486\pi$
$38$	−24.1474	+	24.1474i	−0.635459	+	0.635459i
$39$			6.19746i			0.158909i
$40$	10.8251	−	9.10041i	0.270627	−	0.227510i
$41$	53.3601			1.30147			0.650733	−	0.759306i	$-0.274462\pi$
$41$	53.3601			1.30147			0.650733	+	0.759306i	$0.274462\pi$
$42$		0			0
$43$	−33.0776	+	33.0776i	−0.769247	+	0.769247i	−0.977974	−	0.208727i	$-0.933068\pi$
$43$	−33.0776	+	33.0776i	−0.769247	+	0.769247i	0.208727	+	0.977974i	$0.433068\pi$
$44$		−	1.89747i		−	0.0431242i
$45$	−7.25446	+	83.8121i	−0.161210	+	1.86249i
$46$	8.01526			0.174245
$47$	−21.5130	−	21.5130i	−0.457722	−	0.457722i	0.440185	−	0.897907i	$-0.354913\pi$
$47$	−21.5130	−	21.5130i	−0.457722	−	0.457722i	−0.897907	+	0.440185i	$0.854913\pi$
$48$	14.3736	−	14.3736i	0.299450	−	0.299450i
$49$		0			0
$50$	20.3326	+	28.9238i	0.406651	+	0.578476i
$51$	154.609			3.03156
$52$	1.72468	+	1.72468i	0.0331669	+	0.0331669i
$53$	9.51508	−	9.51508i	0.179530	−	0.179530i	−0.611621	−	0.791151i	$-0.709482\pi$
$53$	9.51508	−	9.51508i	0.179530	−	0.179530i	0.791151	+	0.611621i	$0.209482\pi$
$54$			56.2374i			1.04143i
$55$	4.72600	+	0.409064i	0.0859272	+	0.00743754i
$56$		0			0
$57$	−86.7715	−	86.7715i	−1.52231	−	1.52231i
$58$	7.33636	−	7.33636i	0.126489	−	0.126489i
$59$		−	50.2432i		−	0.851580i	−0.904822	−	0.425790i	$-0.859996\pi$
$59$		−	50.2432i		−	0.851580i	0.904822	−	0.425790i	$-0.140004\pi$
$60$	32.7014	+	38.8989i	0.545024	+	0.648315i
$61$	−45.4957			−0.745831			−0.372915	−	0.927865i	$-0.621642\pi$
$61$	−45.4957			−0.745831			−0.372915	+	0.927865i	$0.621642\pi$
$62$	47.0632	+	47.0632i	0.759083	+	0.759083i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−4.66744	+	3.92382i	−0.0718068	+	0.0603664i
$66$	6.81836			0.103308
$67$	−48.3153	−	48.3153i	−0.721123	−	0.721123i	0.247711	−	0.968834i	$-0.420322\pi$
$67$	−48.3153	−	48.3153i	−0.721123	−	0.721123i	−0.968834	+	0.247711i	$0.920322\pi$
$68$	43.0259	−	43.0259i	0.632734	−	0.632734i
$69$			28.8020i			0.417421i
$70$		0			0
$71$	−11.9203			−0.167892			−0.0839460	−	0.996470i	$-0.526752\pi$
$71$	−11.9203			−0.167892			−0.0839460	+	0.996470i	$0.526752\pi$
$72$	33.6502	+	33.6502i	0.467364	+	0.467364i
$73$	−38.9464	+	38.9464i	−0.533512	+	0.533512i	−0.921616	−	0.388104i	$-0.873130\pi$
$73$	−38.9464	+	38.9464i	−0.533512	+	0.533512i	0.388104	+	0.921616i	$0.373130\pi$
$74$		−	11.6426i		−	0.157332i
$75$	−103.935	+	73.0631i	−1.38580	+	0.974174i
$76$	−48.2949			−0.635459
$77$		0			0
$78$	−6.19746	+	6.19746i	−0.0794546	+	0.0794546i
$79$		−	70.8989i		−	0.897454i	−0.893669	−	0.448727i	$-0.851877\pi$
$79$		−	70.8989i		−	0.897454i	0.893669	−	0.448727i	$-0.148123\pi$
$80$	19.9255	+	1.72468i	0.249069	+	0.0215585i
$81$	−50.6578			−0.625405
$82$	53.3601	+	53.3601i	0.650733	+	0.650733i
$83$	85.7452	−	85.7452i	1.03307	−	1.03307i	0.0336406	−	0.999434i	$-0.489290\pi$
$83$	85.7452	−	85.7452i	1.03307	−	1.03307i	0.999434	−	0.0336406i	$-0.0107102\pi$
$84$		0			0
$85$	97.8884	+	116.440i	1.15163	+	1.36988i
$86$	−66.1553			−0.769247
$87$	26.3625	+	26.3625i	0.303017	+	0.303017i
$88$	1.89747	−	1.89747i	0.0215621	−	0.0215621i
$89$		−	156.750i		−	1.76124i	−0.473822	−	0.880621i	$-0.657126\pi$
$89$		−	156.750i		−	1.76124i	0.473822	−	0.880621i	$-0.342874\pi$
$90$	−91.0665	+	76.5576i	−1.01185	+	0.850640i
$91$		0			0
$92$	8.01526	+	8.01526i	0.0871224	+	0.0871224i
$93$	−169.117	+	169.117i	−1.81846	+	1.81846i
$94$		−	43.0259i		−	0.457722i
$95$	10.4116	−	120.287i	0.109596	−	1.26618i
$96$	28.7472			0.299450
$97$	−87.1790	−	87.1790i	−0.898753	−	0.898753i	0.0965731	−	0.995326i	$-0.469212\pi$
$97$	−87.1790	−	87.1790i	−0.898753	−	0.898753i	−0.995326	+	0.0965731i	$0.969212\pi$
$98$		0			0
$99$			15.9625i			0.161238i
$100$	−8.59126	+	49.2564i	−0.0859126	+	0.492564i
$101$	−50.4522			−0.499527			−0.249763	−	0.968307i	$-0.580353\pi$
$101$	−50.4522			−0.499527			−0.249763	+	0.968307i	$0.580353\pi$
$102$	154.609	+	154.609i	1.51578	+	1.51578i
$103$	102.220	−	102.220i	0.992431	−	0.992431i	−0.00754105	−	0.999972i	$-0.502400\pi$
$103$	102.220	−	102.220i	0.992431	−	0.992431i	0.999972	+	0.00754105i	$0.00240041\pi$
$104$			3.44935i			0.0331669i
$105$		0			0
$106$	19.0302			0.179530
$107$	−4.90653	−	4.90653i	−0.0458554	−	0.0458554i	0.683807	−	0.729663i	$-0.260323\pi$
$107$	−4.90653	−	4.90653i	−0.0458554	−	0.0458554i	−0.729663	+	0.683807i	$0.760323\pi$
$108$	−56.2374	+	56.2374i	−0.520717	+	0.520717i
$109$		−	48.8774i		−	0.448417i	−0.974541	−	0.224208i	$-0.928020\pi$
$109$		−	48.8774i		−	0.448417i	0.974541	−	0.224208i	$-0.0719796\pi$
$110$	4.31693	+	5.13506i	0.0392448	+	0.0466824i
$111$	41.8364			0.376905
$112$		0			0
$113$	−8.29274	+	8.29274i	−0.0733871	+	0.0733871i	−0.742848	−	0.669461i	$-0.766525\pi$
$113$	−8.29274	+	8.29274i	−0.0733871	+	0.0733871i	0.669461	+	0.742848i	$0.266525\pi$
$114$		−	173.543i		−	1.52231i
$115$	−21.6915	+	18.2355i	−0.188621	+	0.158570i
$116$	14.6727			0.126489
$117$	−14.5089	−	14.5089i	−0.124008	−	0.124008i
$118$	50.2432	−	50.2432i	0.425790	−	0.425790i
$119$		0			0
$120$	−6.19746	+	71.6003i	−0.0516455	+	0.596670i
$121$	−120.100			−0.992561
$122$	−45.4957	−	45.4957i	−0.372915	−	0.372915i
$123$	−191.745	+	191.745i	−1.55890	+	1.55890i
$124$			94.1263i			0.759083i
$125$	−120.830	−	32.0171i	−0.966641	−	0.256136i
$126$		0			0
$127$	−80.3440	−	80.3440i	−0.632630	−	0.632630i	0.316097	−	0.948727i	$-0.397627\pi$
$127$	−80.3440	−	80.3440i	−0.632630	−	0.632630i	−0.948727	+	0.316097i	$0.897627\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	237.723i		−	1.84281i
$130$	−8.59126	−	0.743627i	−0.0660866	−	0.00572021i
$131$	25.0858			0.191495			0.0957475	−	0.995406i	$-0.469476\pi$
$131$	25.0858			0.191495			0.0957475	+	0.995406i	$0.469476\pi$
$132$	6.81836	+	6.81836i	0.0516542	+	0.0516542i
$133$		0			0
$134$		−	96.6305i		−	0.721123i
$135$	−127.946	−	152.194i	−0.947747	−	1.12736i
$136$	86.0518			0.632734
$137$	−48.3627	−	48.3627i	−0.353012	−	0.353012i	0.508217	−	0.861229i	$-0.330305\pi$
$137$	−48.3627	−	48.3627i	−0.353012	−	0.353012i	−0.861229	+	0.508217i	$0.830305\pi$
$138$	−28.8020	+	28.8020i	−0.208710	+	0.208710i
$139$		−	67.3054i		−	0.484212i	−0.970250	−	0.242106i	$-0.922162\pi$
$139$		−	67.3054i		−	0.484212i	0.970250	−	0.242106i	$-0.0778381\pi$
$140$		0			0
$141$	154.609			1.09652
$142$	−11.9203	−	11.9203i	−0.0839460	−	0.0839460i
$143$	−0.818129	+	0.818129i	−0.00572118	+	0.00572118i
$144$			67.3004i			0.467364i
$145$	−3.16321	+	36.5452i	−0.0218153	+	0.252036i
$146$	−77.8927			−0.533512
$147$		0			0
$148$	11.6426	−	11.6426i	0.0786660	−	0.0786660i
$149$			60.0185i			0.402809i	0.979508	+	0.201404i	$0.0645505\pi$
$149$			60.0185i			0.402809i	−0.979508	+	0.201404i	$0.935449\pi$
$150$	−176.998	−	30.8719i	−1.17999	−	0.205812i
$151$	47.8037			0.316581			0.158290	−	0.987393i	$-0.449402\pi$
$151$	47.8037			0.316581			0.158290	+	0.987393i	$0.449402\pi$
$152$	−48.2949	−	48.2949i	−0.317729	−	0.317729i
$153$	−361.957	+	361.957i	−2.36573	+	2.36573i
$154$		0			0
$155$	−234.439	−	20.2922i	−1.51251	−	0.130917i
$156$	−12.3949			−0.0794546
$157$	73.9549	+	73.9549i	0.471050	+	0.471050i	0.902254	−	0.431204i	$-0.141911\pi$
$157$	73.9549	+	73.9549i	0.471050	+	0.471050i	−0.431204	+	0.902254i	$0.641911\pi$
$158$	70.8989	−	70.8989i	0.448727	−	0.448727i
$159$			68.3830i			0.430082i
$160$	18.2008	+	21.6502i	0.113755	+	0.135314i
$161$		0			0
$162$	−50.6578	−	50.6578i	−0.312702	−	0.312702i
$163$	−29.0689	+	29.0689i	−0.178337	+	0.178337i	−0.790631	−	0.612294i	$-0.790247\pi$
$163$	−29.0689	+	29.0689i	−0.178337	+	0.178337i	0.612294	+	0.790631i	$0.290247\pi$
$164$			106.720i			0.650733i
$165$	−18.4523	+	15.5125i	−0.111832	+	0.0940150i
$166$	171.490			1.03307
$167$	26.4354	+	26.4354i	0.158296	+	0.158296i	0.781811	−	0.623515i	$-0.214296\pi$
$167$	26.4354	+	26.4354i	0.158296	+	0.158296i	−0.623515	+	0.781811i	$0.714296\pi$
$168$		0			0
$169$			167.513i			0.991200i
$170$	−18.5514	+	214.328i	−0.109126	+	1.26075i
$171$	406.283			2.37592
$172$	−66.1553	−	66.1553i	−0.384624	−	0.384624i
$173$	−177.508	+	177.508i	−1.02606	+	1.02606i	−0.0264055	+	0.999651i	$0.508406\pi$
$173$	−177.508	+	177.508i	−1.02606	+	1.02606i	−0.999651	+	0.0264055i	$0.991594\pi$
$174$			52.7250i			0.303017i
$175$		0			0
$176$	3.79493			0.0215621
$177$	180.544	+	180.544i	1.02002	+	1.02002i
$178$	156.750	−	156.750i	0.880621	−	0.880621i
$179$		−	54.0621i		−	0.302023i	−0.988532	−	0.151012i	$-0.951747\pi$
$179$		−	54.0621i		−	0.302023i	0.988532	−	0.151012i	$-0.0482531\pi$
$180$	−167.624	−	14.5089i	−0.931245	−	0.0806051i
$181$	201.453			1.11300			0.556501	−	0.830847i	$-0.312143\pi$
$181$	201.453			1.11300			0.556501	+	0.830847i	$0.312143\pi$
$182$		0			0
$183$	163.484	−	163.484i	0.893357	−	0.893357i
$184$			16.0305i			0.0871224i
$185$	26.4880	+	31.5079i	0.143179	+	0.170313i
$186$	−338.234			−1.81846
$187$	20.4101	+	20.4101i	0.109145	+	0.109145i
$188$	43.0259	−	43.0259i	0.228861	−	0.228861i
$189$		0			0
$190$	130.699	−	109.876i	0.687890	−	0.578294i
$191$	175.741			0.920112			0.460056	−	0.887890i	$-0.347829\pi$
$191$	175.741			0.920112			0.460056	+	0.887890i	$0.347829\pi$
$192$	28.7472	+	28.7472i	0.149725	+	0.149725i
$193$	−36.9027	+	36.9027i	−0.191206	+	0.191206i	−0.796217	−	0.605011i	$-0.793169\pi$
$193$	−36.9027	+	36.9027i	−0.191206	+	0.191206i	0.605011	+	0.796217i	$0.293169\pi$
$194$		−	174.358i		−	0.898753i
$195$	2.67215	−	30.8719i	0.0137033	−	0.158317i
$196$		0			0
$197$	−62.8178	−	62.8178i	−0.318872	−	0.318872i	0.529462	−	0.848334i	$-0.322394\pi$
$197$	−62.8178	−	62.8178i	−0.318872	−	0.318872i	−0.848334	+	0.529462i	$0.822394\pi$
$198$	−15.9625	+	15.9625i	−0.0806188	+	0.0806188i
$199$		−	25.9383i		−	0.130343i	−0.997874	−	0.0651717i	$-0.979241\pi$
$199$		−	25.9383i		−	0.130343i	0.997874	−	0.0651717i	$-0.0207595\pi$
$200$	−57.8476	+	40.6651i	−0.289238	+	0.203326i
$201$	347.232			1.72752
$202$	−50.4522	−	50.4522i	−0.249763	−	0.249763i
$203$		0			0
$204$			309.219i			1.51578i
$205$	−265.807	−	23.0073i	−1.29662	−	0.112230i
$206$	204.441			0.992431
$207$	−67.4287	−	67.4287i	−0.325743	−	0.325743i
$208$	−3.44935	+	3.44935i	−0.0165834	+	0.0165834i
$209$		−	22.9095i		−	0.109615i
$210$		0			0
$211$	−223.675			−1.06007			−0.530036	−	0.847975i	$-0.677822\pi$
$211$	−223.675			−1.06007			−0.530036	+	0.847975i	$0.677822\pi$
$212$	19.0302	+	19.0302i	0.0897649	+	0.0897649i
$213$	42.8346	−	42.8346i	0.201101	−	0.201101i
$214$		−	9.81306i		−	0.0458554i
$215$	179.034	−	150.510i	0.832717	−	0.700047i
$216$	−112.475			−0.520717
$217$		0			0
$218$	48.8774	−	48.8774i	0.224208	−	0.224208i
$219$		−	279.900i		−	1.27808i
$220$	−0.818129	+	9.45199i	−0.00371877	+	0.0429636i
$221$	−37.1029			−0.167886
$222$	41.8364	+	41.8364i	0.188452	+	0.188452i
$223$	−131.856	+	131.856i	−0.591282	+	0.591282i	−0.937978	−	0.346696i	$-0.887304\pi$
$223$	−131.856	+	131.856i	−0.591282	+	0.591282i	0.346696	+	0.937978i	$0.387304\pi$
$224$		0			0
$225$	72.2744	−	414.371i	0.321219	−	1.84165i
$226$	−16.5855			−0.0733871
$227$	268.065	+	268.065i	1.18090	+	1.18090i	0.979511	+	0.201393i	$0.0645467\pi$
$227$	268.065	+	268.065i	1.18090	+	1.18090i	0.201393	+	0.979511i	$0.435453\pi$
$228$	173.543	−	173.543i	0.761153	−	0.761153i
$229$			46.0098i			0.200916i	0.994941	+	0.100458i	$0.0320308\pi$
$229$			46.0098i			0.200916i	−0.994941	+	0.100458i	$0.967969\pi$
$230$	−39.9270	−	3.45593i	−0.173596	−	0.0150258i
$231$		0			0
$232$	14.6727	+	14.6727i	0.0632445	+	0.0632445i
$233$	73.8301	−	73.8301i	0.316867	−	0.316867i	−0.530695	−	0.847563i	$-0.678069\pi$
$233$	73.8301	−	73.8301i	0.316867	−	0.316867i	0.847563	+	0.530695i	$0.178069\pi$
$234$		−	29.0178i		−	0.124008i
$235$	97.8884	+	116.440i	0.416546	+	0.495489i
$236$	100.486			0.425790
$237$	254.768	+	254.768i	1.07497	+	1.07497i
$238$		0			0
$239$		−	4.00351i		−	0.0167511i	−0.999965	−	0.00837554i	$-0.997334\pi$
$239$		−	4.00351i		−	0.0167511i	0.999965	−	0.00837554i	$-0.00266605\pi$
$240$	−77.7978	+	65.4029i	−0.324158	+	0.272512i
$241$	−297.798			−1.23568			−0.617839	−	0.786305i	$-0.711992\pi$
$241$	−297.798			−1.23568			−0.617839	+	0.786305i	$0.711992\pi$
$242$	−120.100	−	120.100i	−0.496281	−	0.496281i
$243$	−71.0344	+	71.0344i	−0.292323	+	0.292323i
$244$		−	90.9914i		−	0.372915i
$245$		0			0
$246$	−383.489			−1.55890
$247$	20.8233	+	20.8233i	0.0843047	+	0.0843047i
$248$	−94.1263	+	94.1263i	−0.379542	+	0.379542i
$249$			616.234i			2.47484i
$250$	−88.8130	−	152.847i	−0.355252	−	0.611389i
$251$	300.624			1.19770			0.598852	−	0.800860i	$-0.295624\pi$
$251$	300.624			1.19770			0.598852	+	0.800860i	$0.295624\pi$
$252$		0			0
$253$	−3.80217	+	3.80217i	−0.0150283	+	0.0150283i
$254$		−	160.688i		−	0.632630i
$255$	−770.167	−	66.6628i	−3.02026	−	0.261423i
$256$	16.0000			0.0625000
$257$	−233.671	−	233.671i	−0.909226	−	0.909226i	0.0869836	−	0.996210i	$-0.472277\pi$
$257$	−233.671	−	233.671i	−0.909226	−	0.909226i	−0.996210	+	0.0869836i	$0.972277\pi$
$258$	237.723	−	237.723i	0.921405	−	0.921405i
$259$		0			0
$260$	−7.84763	−	9.33489i	−0.0301832	−	0.0359034i
$261$	−123.435			−0.472931
$262$	25.0858	+	25.0858i	0.0957475	+	0.0957475i
$263$	267.673	−	267.673i	1.01777	−	1.01777i	0.0179289	−	0.999839i	$-0.494293\pi$
$263$	267.673	−	267.673i	1.01777	−	1.01777i	0.999839	−	0.0179289i	$-0.00570724\pi$
$264$			13.6367i			0.0516542i
$265$	−51.5008	+	43.2956i	−0.194343	+	0.163379i
$266$		0			0
$267$	563.268	+	563.268i	2.10962	+	2.10962i
$268$	96.6305	−	96.6305i	0.360562	−	0.360562i
$269$		−	144.898i		−	0.538654i	−0.963049	−	0.269327i	$-0.913199\pi$
$269$		−	144.898i		−	0.538654i	0.963049	−	0.269327i	$-0.0868012\pi$
$270$	24.2478	−	280.139i	0.0898068	−	1.03755i
$271$	−330.621			−1.22000			−0.610002	−	0.792400i	$-0.708831\pi$
$271$	−330.621			−1.22000			−0.610002	+	0.792400i	$0.708831\pi$
$272$	86.0518	+	86.0518i	0.316367	+	0.316367i
$273$		0			0
$274$		−	96.7254i		−	0.353012i
$275$	−23.3656	−	4.07541i	−0.0849657	−	0.0148197i
$276$	−57.6041			−0.208710
$277$	55.5765	+	55.5765i	0.200637	+	0.200637i	0.800273	−	0.599636i	$-0.204688\pi$
$277$	55.5765	+	55.5765i	0.200637	+	0.200637i	−0.599636	+	0.800273i	$0.704688\pi$
$278$	67.3054	−	67.3054i	0.242106	−	0.242106i
$279$		−	791.842i		−	2.83814i
$280$		0			0
$281$	−342.866			−1.22016			−0.610081	−	0.792339i	$-0.708863\pi$
$281$	−342.866			−1.22016			−0.610081	+	0.792339i	$0.708863\pi$
$282$	154.609	+	154.609i	0.548260	+	0.548260i
$283$	−65.6744	+	65.6744i	−0.232065	+	0.232065i	−0.813554	−	0.581489i	$-0.802470\pi$
$283$	−65.6744	+	65.6744i	−0.232065	+	0.232065i	0.581489	+	0.813554i	$0.302470\pi$
$284$		−	23.8407i		−	0.0839460i
$285$	394.828	+	469.654i	1.38536	+	1.64791i
$286$	−1.63626			−0.00572118
$287$		0			0
$288$	−67.3004	+	67.3004i	−0.233682	+	0.233682i
$289$			636.614i			2.20282i
$290$	−39.7084	+	33.3819i	−0.136925	+	0.115110i
$291$	626.539			2.15305
$292$	−77.8927	−	77.8927i	−0.266756	−	0.266756i
$293$	−345.276	+	345.276i	−1.17842	+	1.17842i	−0.198270	+	0.980147i	$0.563532\pi$
$293$	−345.276	+	345.276i	−1.17842	+	1.17842i	−0.980147	+	0.198270i	$0.936468\pi$
$294$		0			0
$295$	−21.6633	+	250.280i	−0.0734350	+	0.848408i
$296$	23.2851			0.0786660
$297$	−26.6771	−	26.6771i	−0.0898220	−	0.0898220i
$298$	−60.0185	+	60.0185i	−0.201404	+	0.201404i
$299$		−	6.91186i		−	0.0231166i
$300$	−146.126	−	207.870i	−0.487087	−	0.692899i
$301$		0			0
$302$	47.8037	+	47.8037i	0.158290	+	0.158290i
$303$	181.295	−	181.295i	0.598334	−	0.598334i
$304$		−	96.5897i		−	0.317729i
$305$	226.631	+	19.6163i	0.743053	+	0.0643159i
$306$	−723.915			−2.36573
$307$	−344.100	−	344.100i	−1.12085	−	1.12085i	−0.991614	−	0.129233i	$-0.958748\pi$
$307$	−344.100	−	344.100i	−1.12085	−	1.12085i	−0.129233	−	0.991614i	$-0.541252\pi$
$308$		0			0
$309$			734.638i			2.37747i
$310$	−214.147	−	254.731i	−0.690797	−	0.821714i
$311$	−330.319			−1.06212			−0.531059	−	0.847335i	$-0.678206\pi$
$311$	−330.319			−1.06212			−0.531059	+	0.847335i	$0.678206\pi$
$312$	−12.3949	−	12.3949i	−0.0397273	−	0.0397273i
$313$	60.5472	−	60.5472i	0.193442	−	0.193442i	−0.603740	−	0.797181i	$-0.706323\pi$
$313$	60.5472	−	60.5472i	0.193442	−	0.193442i	0.797181	+	0.603740i	$0.206323\pi$
$314$			147.910i			0.471050i
$315$		0			0
$316$	141.798			0.448727
$317$	−124.597	−	124.597i	−0.393049	−	0.393049i	0.482724	−	0.875773i	$-0.339648\pi$
$317$	−124.597	−	124.597i	−0.393049	−	0.393049i	−0.875773	+	0.482724i	$0.839648\pi$
$318$	−68.3830	+	68.3830i	−0.215041	+	0.215041i
$319$			6.96025i			0.0218190i
$320$	−3.44935	+	39.8510i	−0.0107792	+	0.124534i
$321$	35.2623			0.109851
$322$		0			0
$323$	519.483	−	519.483i	1.60831	−	1.60831i
$324$		−	101.316i		−	0.312702i
$325$	24.9421	−	17.5335i	0.0767450	−	0.0539494i
$326$	−58.1379			−0.178337
$327$	175.636	+	175.636i	0.537114	+	0.537114i
$328$	−106.720	+	106.720i	−0.325367	+	0.325367i
$329$		0			0
$330$	−33.9648	−	2.93987i	−0.102924	−	0.00890869i
$331$	321.473			0.971217			0.485608	−	0.874177i	$-0.338598\pi$
$331$	321.473			0.971217			0.485608	+	0.874177i	$0.338598\pi$
$332$	171.490	+	171.490i	0.516537	+	0.516537i
$333$	−97.9436	+	97.9436i	−0.294125	+	0.294125i
$334$			52.8708i			0.158296i
$335$	219.844	+	261.509i	0.656252	+	0.780622i
$336$		0			0
$337$	−77.9872	−	77.9872i	−0.231416	−	0.231416i	0.581868	−	0.813284i	$-0.302322\pi$
$337$	−77.9872	−	77.9872i	−0.231416	−	0.231416i	−0.813284	+	0.581868i	$0.802322\pi$
$338$	−167.513	+	167.513i	−0.495600	+	0.495600i
$339$		−	59.5983i		−	0.175806i
$340$	−232.880	+	195.777i	−0.684940	+	0.575814i
$341$	−44.6504			−0.130940
$342$	406.283	+	406.283i	1.18796	+	1.18796i
$343$		0			0
$344$		−	132.311i		−	0.384624i
$345$	12.4186	−	143.474i	0.0359958	−	0.415866i
$346$	−355.016			−1.02606
$347$	−238.374	−	238.374i	−0.686955	−	0.686955i	0.274602	−	0.961558i	$-0.411454\pi$
$347$	−238.374	−	238.374i	−0.686955	−	0.686955i	−0.961558	+	0.274602i	$0.911454\pi$
$348$	−52.7250	+	52.7250i	−0.151509	+	0.151509i
$349$		−	287.505i		−	0.823797i	−0.911230	−	0.411899i	$-0.864866\pi$
$349$		−	287.505i		−	0.823797i	0.911230	−	0.411899i	$-0.135134\pi$
$350$		0			0
$351$	48.4957			0.138164
$352$	3.79493	+	3.79493i	0.0107811	+	0.0107811i
$353$	117.277	−	117.277i	0.332229	−	0.332229i	−0.521203	−	0.853433i	$-0.674517\pi$
$353$	117.277	−	117.277i	0.332229	−	0.332229i	0.853433	+	0.521203i	$0.174517\pi$
$354$			361.088i			1.02002i
$355$	59.3796	+	5.13968i	0.167267	+	0.0144780i
$356$	313.501			0.880621
$357$		0			0
$358$	54.0621	−	54.0621i	0.151012	−	0.151012i
$359$		−	374.507i		−	1.04319i	−0.853192	−	0.521597i	$-0.825337\pi$
$359$		−	374.507i		−	1.04319i	0.853192	−	0.521597i	$-0.174663\pi$
$360$	−153.115	−	182.133i	−0.425320	−	0.505925i
$361$	−222.098			−0.615231
$362$	201.453	+	201.453i	0.556501	+	0.556501i
$363$	431.567	−	431.567i	1.18889	−	1.18889i
$364$		0			0
$365$	210.799	−	177.214i	0.577531	−	0.485518i
$366$	326.969			0.893357
$367$	23.0861	+	23.0861i	0.0629048	+	0.0629048i	0.737859	−	0.674955i	$-0.235837\pi$
$367$	23.0861	+	23.0861i	0.0629048	+	0.0629048i	−0.674955	+	0.737859i	$0.735837\pi$
$368$	−16.0305	+	16.0305i	−0.0435612	+	0.0435612i
$369$		−	897.789i		−	2.43303i
$370$	−5.01992	+	57.9960i	−0.0135673	+	0.156746i
$371$		0			0
$372$	−338.234	−	338.234i	−0.909231	−	0.909231i
$373$	521.014	−	521.014i	1.39682	−	1.39682i	0.587855	−	0.808967i	$-0.299973\pi$
$373$	521.014	−	521.014i	1.39682	−	1.39682i	0.808967	−	0.587855i	$-0.200027\pi$
$374$			40.8201i			0.109145i
$375$	549.241	−	319.141i	1.46464	−	0.851043i
$376$	86.0518			0.228861
$377$	−6.32643	−	6.32643i	−0.0167810	−	0.0167810i
$378$		0			0
$379$		−	287.166i		−	0.757693i	−0.925460	−	0.378846i	$-0.876321\pi$
$379$		−	287.166i		−	0.757693i	0.925460	−	0.378846i	$-0.123679\pi$
$380$	240.575	+	20.8233i	0.633092	+	0.0547980i
$381$	577.416			1.51553
$382$	175.741	+	175.741i	0.460056	+	0.460056i
$383$	−323.016	+	323.016i	−0.843383	+	0.843383i	−0.989297	−	0.145915i	$-0.953388\pi$
$383$	−323.016	+	323.016i	−0.843383	+	0.843383i	0.145915	+	0.989297i	$0.453388\pi$
$384$			57.4944i			0.149725i
$385$		0			0
$386$	−73.8055			−0.191206
$387$	556.534	+	556.534i	1.43807	+	1.43807i
$388$	174.358	−	174.358i	0.449376	−	0.449376i
$389$		−	543.189i		−	1.39637i	−0.715915	−	0.698187i	$-0.753990\pi$
$389$		−	543.189i		−	1.39637i	0.715915	−	0.698187i	$-0.246010\pi$
$390$	33.5440	−	28.1997i	0.0860103	−	0.0723069i
$391$	−172.432			−0.441002
$392$		0			0
$393$	−90.1435	+	90.1435i	−0.229373	+	0.229373i
$394$		−	125.636i		−	0.318872i
$395$	−30.5694	+	353.174i	−0.0773909	+	0.894111i
$396$	−31.9250			−0.0806188
$397$	451.793	+	451.793i	1.13802	+	1.13802i	0.988805	+	0.149211i	$0.0476734\pi$
$397$	451.793	+	451.793i	1.13802	+	1.13802i	0.149211	+	0.988805i	$0.452327\pi$
$398$	25.9383	−	25.9383i	0.0651717	−	0.0651717i
$399$		0			0
$400$	−98.5127	−	17.1825i	−0.246282	−	0.0429563i
$401$	447.272			1.11539			0.557696	−	0.830045i	$-0.311685\pi$
$401$	447.272			1.11539			0.557696	+	0.830045i	$0.311685\pi$
$402$	347.232	+	347.232i	0.863762	+	0.863762i
$403$	40.5844	−	40.5844i	0.100706	−	0.100706i
$404$		−	100.904i		−	0.249763i
$405$	252.345	+	21.8421i	0.623075	+	0.0539311i
$406$		0			0
$407$	5.52284	+	5.52284i	0.0135696	+	0.0135696i
$408$	−309.219	+	309.219i	−0.757889	+	0.757889i
$409$			23.0666i			0.0563975i	0.999602	+	0.0281988i	$0.00897713\pi$
$409$			23.0666i			0.0563975i	−0.999602	+	0.0281988i	$0.991023\pi$
$410$	−242.800	−	288.814i	−0.592194	−	0.704425i
$411$	347.573			0.845677
$412$	204.441	+	204.441i	0.496215	+	0.496215i
$413$		0			0
$414$		−	134.857i		−	0.325743i
$415$	−464.100	+	390.158i	−1.11831	+	0.940140i
$416$	−6.89871			−0.0165834
$417$	241.856	+	241.856i	0.579989	+	0.579989i
$418$	22.9095	−	22.9095i	0.0548073	−	0.0548073i
$419$			502.792i			1.19998i	0.800007	+	0.599990i	$0.204829\pi$
$419$			502.792i			1.19998i	−0.800007	+	0.599990i	$0.795171\pi$
$420$		0			0
$421$	48.4897			0.115177			0.0575887	−	0.998340i	$-0.481659\pi$
$421$	48.4897			0.115177			0.0575887	+	0.998340i	$0.481659\pi$
$422$	−223.675	−	223.675i	−0.530036	−	0.530036i
$423$	−361.957	+	361.957i	−0.855691	+	0.855691i
$424$			38.0603i			0.0897649i
$425$	−437.413	−	622.237i	−1.02921	−	1.46409i
$426$	85.6691			0.201101
$427$		0			0
$428$	9.81306	−	9.81306i	0.0229277	−	0.0229277i
$429$		−	5.87973i		−	0.0137057i
$430$	329.544	+	28.5241i	0.766382	+	0.0663352i
$431$	−371.451			−0.861836			−0.430918	−	0.902391i	$-0.641810\pi$
$431$	−371.451			−0.861836			−0.430918	+	0.902391i	$0.641810\pi$
$432$	−112.475	−	112.475i	−0.260358	−	0.260358i
$433$	449.707	−	449.707i	1.03858	−	1.03858i	0.0393595	−	0.999225i	$-0.487468\pi$
$433$	449.707	−	449.707i	1.03858	−	1.03858i	0.999225	−	0.0393595i	$-0.0125318\pi$
$434$		0			0
$435$	−119.955	−	142.688i	−0.275758	−	0.328019i
$436$	97.7549			0.224208
$437$	96.7739	+	96.7739i	0.221451	+	0.221451i
$438$	279.900	−	279.900i	0.639041	−	0.639041i
$439$			587.500i			1.33827i	0.743141	+	0.669134i	$0.233335\pi$
$439$			587.500i			1.33827i	−0.743141	+	0.669134i	$0.766665\pi$
$440$	−10.2701	+	8.63386i	−0.0233412	+	0.0196224i
$441$		0			0
$442$	−37.1029	−	37.1029i	−0.0839432	−	0.0839432i
$443$	3.35781	−	3.35781i	0.00757971	−	0.00757971i	−0.703307	−	0.710886i	$-0.748294\pi$
$443$	3.35781	−	3.35781i	0.00757971	−	0.00757971i	0.710886	+	0.703307i	$0.248294\pi$
$444$			83.6729i			0.188452i
$445$	−67.5860	+	780.833i	−0.151879	+	1.75468i
$446$	−263.712			−0.591282
$447$	−215.671	−	215.671i	−0.482485	−	0.482485i
$448$		0			0
$449$		−	40.6375i		−	0.0905067i	−0.998976	−	0.0452533i	$-0.985590\pi$
$449$		−	40.6375i		−	0.0905067i	0.998976	−	0.0452533i	$-0.0144095\pi$
$450$	486.646	−	342.097i	1.08144	−	0.760216i
$451$	−50.6245			−0.112250
$452$	−16.5855	−	16.5855i	−0.0366935	−	0.0366935i
$453$	−171.778	+	171.778i	−0.379200	+	0.379200i
$454$			536.130i			1.18090i
$455$		0			0
$456$	347.086			0.761153
$457$	232.446	+	232.446i	0.508634	+	0.508634i	0.914107	−	0.405473i	$-0.132893\pi$
$457$	232.446	+	232.446i	0.508634	+	0.508634i	−0.405473	+	0.914107i	$0.632893\pi$
$458$	−46.0098	+	46.0098i	−0.100458	+	0.100458i
$459$		−	1209.83i		−	2.63580i
$460$	−36.4711	−	43.3829i	−0.0792849	−	0.0943107i
$461$	64.7559			0.140468			0.0702341	−	0.997531i	$-0.477625\pi$
$461$	64.7559			0.140468			0.0702341	+	0.997531i	$0.477625\pi$
$462$		0			0
$463$	−604.400	+	604.400i	−1.30540	+	1.30540i	−0.380701	+	0.924698i	$0.624317\pi$
$463$	−604.400	+	604.400i	−1.30540	+	1.30540i	−0.924698	+	0.380701i	$0.875683\pi$
$464$			29.3454i			0.0632445i
$465$	915.353	−	769.517i	1.96850	−	1.65487i
$466$	147.660			0.316867
$467$	−252.713	−	252.713i	−0.541142	−	0.541142i	0.382722	−	0.923864i	$-0.374987\pi$
$467$	−252.713	−	252.713i	−0.541142	−	0.541142i	−0.923864	+	0.382722i	$0.874987\pi$
$468$	29.0178	−	29.0178i	0.0620039	−	0.0620039i
$469$		0			0
$470$	−18.5514	+	214.328i	−0.0394712	+	0.456017i
$471$	−531.499			−1.12845
$472$	100.486	+	100.486i	0.212895	+	0.212895i
$473$	31.3818	−	31.3818i	0.0663464	−	0.0663464i
$474$			509.537i			1.07497i
$475$	−103.728	+	594.707i	−0.218376	+	1.25202i
$476$		0			0
$477$	−160.092	−	160.092i	−0.335623	−	0.335623i
$478$	4.00351	−	4.00351i	0.00837554	−	0.00837554i
$479$		−	587.359i		−	1.22622i	−0.789998	−	0.613109i	$-0.789919\pi$
$479$		−	587.359i		−	1.22622i	0.789998	−	0.613109i	$-0.210081\pi$
$480$	−143.201	−	12.3949i	−0.298335	−	0.0258227i
$481$	−10.0398			−0.0208728
$482$	−297.798	−	297.798i	−0.617839	−	0.617839i
$483$		0			0
$484$		−	240.200i		−	0.496281i
$485$	396.682	+	471.860i	0.817902	+	0.972908i
$486$	−142.069			−0.292323
$487$	402.218	+	402.218i	0.825909	+	0.825909i	0.986948	−	0.161039i	$-0.0514845\pi$
$487$	402.218	+	402.218i	0.825909	+	0.825909i	−0.161039	+	0.986948i	$0.551485\pi$
$488$	90.9914	−	90.9914i	0.186458	−	0.186458i
$489$		−	208.913i		−	0.427224i
$490$		0			0
$491$	485.037			0.987856			0.493928	−	0.869503i	$-0.335561\pi$
$491$	485.037			0.987856			0.493928	+	0.869503i	$0.335561\pi$
$492$	−383.489	−	383.489i	−0.779449	−	0.779449i
$493$	−157.827	+	157.827i	−0.320135	+	0.320135i
$494$			41.6465i			0.0843047i
$495$	6.88255	−	79.5153i	0.0139041	−	0.160637i
$496$	−188.253			−0.379542
$497$		0			0
$498$	−616.234	+	616.234i	−1.23742	+	1.23742i
$499$		−	577.617i		−	1.15755i	−0.815488	−	0.578774i	$-0.803531\pi$
$499$		−	577.617i		−	1.15755i	0.815488	−	0.578774i	$-0.196469\pi$
$500$	64.0341	−	241.660i	0.128068	−	0.483320i
$501$	−189.986			−0.379214
$502$	300.624	+	300.624i	0.598852	+	0.598852i
$503$	−417.802	+	417.802i	−0.830620	+	0.830620i	−0.987602	−	0.156981i	$-0.949824\pi$
$503$	−417.802	+	417.802i	−0.830620	+	0.830620i	0.156981	+	0.987602i	$0.449824\pi$
$504$		0			0
$505$	251.321	+	21.7534i	0.497666	+	0.0430761i
$506$	−7.60434			−0.0150283
$507$	−601.941	−	601.941i	−1.18726	−	1.18726i
$508$	160.688	−	160.688i	0.316315	−	0.316315i
$509$		−	158.084i		−	0.310578i	−0.987869	−	0.155289i	$-0.950369\pi$
$509$		−	158.084i		−	0.310578i	0.987869	−	0.155289i	$-0.0496308\pi$
$510$	−703.505	−	836.830i	−1.37942	−	1.64084i
$511$		0			0
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−678.994	+	678.994i	−1.32358	+	1.32358i
$514$		−	467.342i		−	0.909226i
$515$	−553.272	+	465.124i	−1.07431	+	0.903153i
$516$	475.445			0.921405
$517$	20.4101	+	20.4101i	0.0394779	+	0.0394779i
$518$		0			0
$519$		−	1275.71i		−	2.45802i
$520$	1.48725	−	17.1825i	0.00286011	−	0.0330433i
$521$	−116.499			−0.223606			−0.111803	−	0.993730i	$-0.535663\pi$
$521$	−116.499			−0.223606			−0.111803	+	0.993730i	$0.535663\pi$
$522$	−123.435	−	123.435i	−0.236465	−	0.236465i
$523$	−178.911	+	178.911i	−0.342085	+	0.342085i	−0.857151	−	0.515066i	$-0.827768\pi$
$523$	−178.911	+	178.911i	−0.342085	+	0.342085i	0.515066	+	0.857151i	$0.327768\pi$
$524$			50.1717i			0.0957475i
$525$		0			0
$526$	535.346			1.01777
$527$	−1012.47	−	1012.47i	−1.92119	−	1.92119i
$528$	−13.6367	+	13.6367i	−0.0258271	+	0.0258271i
$529$			496.878i			0.939278i
$530$	−94.7963	−	8.20522i	−0.178861	−	0.0154815i
$531$	−845.347			−1.59199
$532$		0			0
$533$	46.0145	−	46.0145i	0.0863311	−	0.0863311i
$534$			1126.54i			2.10962i
$535$	22.3257	+	26.5568i	0.0417303	+	0.0496389i
$536$	193.261			0.360562
$537$	194.267	+	194.267i	0.361764	+	0.361764i
$538$	144.898	−	144.898i	0.269327	−	0.269327i
$539$		0			0
$540$	304.387	−	255.892i	0.563680	−	0.473873i
$541$	−841.136			−1.55478			−0.777390	−	0.629019i	$-0.783457\pi$
$541$	−841.136			−1.55478			−0.777390	+	0.629019i	$0.783457\pi$
$542$	−330.621	−	330.621i	−0.610002	−	0.610002i
$543$	−723.903	+	723.903i	−1.33316	+	1.33316i
$544$			172.104i			0.316367i
$545$	−21.0744	+	243.477i	−0.0386687	+	0.446746i
$546$		0			0
$547$	228.297	+	228.297i	0.417362	+	0.417362i	0.884294	−	0.466931i	$-0.154640\pi$
$547$	228.297	+	228.297i	0.417362	+	0.417362i	−0.466931	+	0.884294i	$0.654640\pi$
$548$	96.7254	−	96.7254i	0.176506	−	0.176506i
$549$			765.469i			1.39430i
$550$	−19.2902	−	27.4410i	−0.0350730	−	0.0498927i
$551$	177.154			0.321514
$552$	−57.6041	−	57.6041i	−0.104355	−	0.104355i
$553$		0			0
$554$			111.153i			0.200637i
$555$	−208.403	−	18.0386i	−0.375501	−	0.0325019i
$556$	134.611			0.242106
$557$	−677.740	−	677.740i	−1.21677	−	1.21677i	−0.968757	−	0.248010i	$-0.920223\pi$
$557$	−677.740	−	677.740i	−1.21677	−	1.21677i	−0.248010	−	0.968757i	$-0.579777\pi$
$558$	791.842	−	791.842i	1.41907	−	1.41907i
$559$			57.0482i			0.102054i
$560$		0			0
$561$	−146.683			−0.261467
$562$	−342.866	−	342.866i	−0.610081	−	0.610081i
$563$	−655.737	+	655.737i	−1.16472	+	1.16472i	−0.181290	+	0.983430i	$0.558027\pi$
$563$	−655.737	+	655.737i	−1.16472	+	1.16472i	−0.983430	+	0.181290i	$0.941973\pi$
$564$			309.219i			0.548260i
$565$	44.8848	−	37.7337i	0.0794422	−	0.0667853i
$566$	−131.349			−0.232065
$567$		0			0
$568$	23.8407	−	23.8407i	0.0419730	−	0.0419730i
$569$		−	452.093i		−	0.794539i	−0.917702	−	0.397270i	$-0.869958\pi$
$569$		−	452.093i		−	0.794539i	0.917702	−	0.397270i	$-0.130042\pi$
$570$	−74.8264	+	864.482i	−0.131274	+	1.51664i
$571$	390.743			0.684313			0.342157	−	0.939643i	$-0.388843\pi$
$571$	390.743			0.684313			0.342157	+	0.939643i	$0.388843\pi$
$572$	−1.63626	−	1.63626i	−0.00286059	−	0.00286059i
$573$	−631.510	+	631.510i	−1.10211	+	1.10211i
$574$		0			0
$575$	115.916	−	81.4853i	0.201593	−	0.141714i
$576$	−134.601			−0.233682
$577$	−320.736	−	320.736i	−0.555868	−	0.555868i	0.372260	−	0.928128i	$-0.378583\pi$
$577$	−320.736	−	320.736i	−0.555868	−	0.555868i	−0.928128	+	0.372260i	$0.878583\pi$
$578$	−636.614	+	636.614i	−1.10141	+	1.10141i
$579$		−	265.213i		−	0.458053i
$580$	−73.0903	−	6.32643i	−0.126018	−	0.0109076i
$581$		0			0
$582$	626.539	+	626.539i	1.07653	+	1.07653i
$583$	−9.02727	+	9.02727i	−0.0154842	+	0.0154842i
$584$		−	155.785i		−	0.266756i
$585$	66.0186	+	78.5302i	0.112852	+	0.134240i
$586$	−690.553			−1.17842
$587$	−132.759	−	132.759i	−0.226165	−	0.226165i	0.584924	−	0.811088i	$-0.301124\pi$
$587$	−132.759	−	132.759i	−0.226165	−	0.226165i	−0.811088	+	0.584924i	$0.801124\pi$
$588$		0			0
$589$			1136.45i			1.92946i
$590$	−271.944	+	228.617i	−0.460922	+	0.387487i
$591$	451.460			0.763891
$592$	23.2851	+	23.2851i	0.0393330	+	0.0393330i
$593$	96.8819	−	96.8819i	0.163376	−	0.163376i	−0.620685	−	0.784060i	$-0.713145\pi$
$593$	96.8819	−	96.8819i	0.163376	−	0.163376i	0.784060	+	0.620685i	$0.213145\pi$
$594$		−	53.3543i		−	0.0898220i
$595$		0			0
$596$	−120.037			−0.201404
$597$	93.2068	+	93.2068i	0.156125	+	0.156125i
$598$	6.91186	−	6.91186i	0.0115583	−	0.0115583i
$599$			616.168i			1.02866i	0.857592	+	0.514331i	$0.171960\pi$
$599$			616.168i			1.02866i	−0.857592	+	0.514331i	$0.828040\pi$
$600$	61.7437	−	353.996i	0.102906	−	0.589993i
$601$	−660.812			−1.09952			−0.549760	−	0.835322i	$-0.685281\pi$
$601$	−660.812			−1.09952			−0.549760	+	0.835322i	$0.685281\pi$
$602$		0			0
$603$	−812.909	+	812.909i	−1.34811	+	1.34811i
$604$			95.6073i			0.158290i
$605$	598.263	+	51.7834i	0.988864	+	0.0855924i
$606$	362.590			0.598334
$607$	−273.346	−	273.346i	−0.450324	−	0.450324i	0.445138	−	0.895462i	$-0.353155\pi$
$607$	−273.346	−	273.346i	−0.450324	−	0.450324i	−0.895462	+	0.445138i	$0.853155\pi$
$608$	96.5897	−	96.5897i	0.158865	−	0.158865i
$609$		0			0
$610$	207.015	+	246.247i	0.339368	+	0.403684i
$611$	−37.1029			−0.0607249
$612$	−723.915	−	723.915i	−1.18287	−	1.18287i
$613$	−36.5778	+	36.5778i	−0.0596701	+	0.0596701i	−0.736312	−	0.676642i	$-0.763434\pi$
$613$	−36.5778	+	36.5778i	−0.0596701	+	0.0596701i	0.676642	+	0.736312i	$0.263434\pi$
$614$		−	688.200i		−	1.12085i
$615$	1037.83	−	872.477i	1.68752	−	1.41866i
$616$		0			0
$617$	−616.887	−	616.887i	−0.999816	−	0.999816i	0.000183933	−	1.00000i	$-0.499941\pi$
$617$	−616.887	−	616.887i	−0.999816	−	0.999816i	−1.00000		0.000183933i	$0.999941\pi$
$618$	−734.638	+	734.638i	−1.18873	+	1.18873i
$619$			519.411i			0.839113i	0.907729	+	0.419556i	$0.137814\pi$
$619$			519.411i			0.839113i	−0.907729	+	0.419556i	$0.862186\pi$
$620$	40.5844	−	468.878i	0.0654587	−	0.756256i
$621$	225.379			0.362928
$622$	−330.319	−	330.319i	−0.531059	−	0.531059i
$623$		0			0
$624$		−	24.7898i		−	0.0397273i
$625$	588.095	+	211.587i	0.940952	+	0.338539i
$626$	121.094			0.193442
$627$	82.3229	+	82.3229i	0.131297	+	0.131297i
$628$	−147.910	+	147.910i	−0.235525	+	0.235525i
$629$			250.466i			0.398197i
$630$		0			0
$631$	−427.140			−0.676925			−0.338463	−	0.940980i	$-0.609907\pi$
$631$	−427.140			−0.676925			−0.338463	+	0.940980i	$0.609907\pi$
$632$	141.798	+	141.798i	0.224364	+	0.224364i
$633$	803.755	−	803.755i	1.26976	−	1.26976i
$634$		−	249.193i		−	0.393049i
$635$	365.582	+	434.865i	0.575719	+	0.684827i
$636$	−136.766			−0.215041
$637$		0			0
$638$	−6.96025	+	6.96025i	−0.0109095	+	0.0109095i
$639$			200.561i			0.313866i
$640$	−43.3004	+	36.4016i	−0.0676568	+	0.0568776i
$641$	270.127			0.421415			0.210707	−	0.977549i	$-0.432423\pi$
$641$	270.127			0.421415			0.210707	+	0.977549i	$0.432423\pi$
$642$	35.2623	+	35.2623i	0.0549257	+	0.0549257i
$643$	192.668	−	192.668i	0.299639	−	0.299639i	−0.541234	−	0.840872i	$-0.682043\pi$
$643$	192.668	−	192.668i	0.299639	−	0.299639i	0.840872	+	0.541234i	$0.182043\pi$
$644$		0			0
$645$	−102.499	+	1184.19i	−0.158913	+	1.83595i
$646$	1038.97			1.60831
$647$	173.589	+	173.589i	0.268299	+	0.268299i	0.828415	−	0.560116i	$-0.189243\pi$
$647$	173.589	+	173.589i	0.268299	+	0.268299i	−0.560116	+	0.828415i	$0.689243\pi$
$648$	101.316	−	101.316i	0.156351	−	0.156351i
$649$			47.6674i			0.0734475i
$650$	42.4757	+	7.40857i	0.0653472	+	0.0113978i
$651$		0			0
$652$	−58.1379	−	58.1379i	−0.0891685	−	0.0891685i
$653$	−322.471	+	322.471i	−0.493831	+	0.493831i	−0.909511	−	0.415680i	$-0.863544\pi$
$653$	−322.471	+	322.471i	−0.493831	+	0.493831i	0.415680	+	0.909511i	$0.363544\pi$
$654$			351.273i			0.537114i
$655$	−124.962	−	10.8162i	−0.190782	−	0.0165133i
$656$	−213.441			−0.325367
$657$	655.276	+	655.276i	0.997376	+	0.997376i
$658$		0			0
$659$		−	973.026i		−	1.47652i	−0.674517	−	0.738259i	$-0.735648\pi$
$659$		−	973.026i		−	1.47652i	0.674517	−	0.738259i	$-0.264352\pi$
$660$	−31.0249	−	36.9047i	−0.0470075	−	0.0559162i
$661$	−305.100			−0.461573			−0.230787	−	0.973004i	$-0.574130\pi$
$661$	−305.100			−0.461573			−0.230787	+	0.973004i	$0.574130\pi$
$662$	321.473	+	321.473i	0.485608	+	0.485608i
$663$	133.326	−	133.326i	0.201094	−	0.201094i
$664$			342.981i			0.516537i
$665$		0			0
$666$	−195.887			−0.294125
$667$	−29.4014	−	29.4014i	−0.0440801	−	0.0440801i
$668$	−52.8708	+	52.8708i	−0.0791479	+	0.0791479i
$669$		−	947.623i		−	1.41648i
$670$	−41.6641	+	481.353i	−0.0621852	+	0.718437i
$671$	43.1633			0.0643268
$672$		0			0
$673$	567.081	−	567.081i	0.842616	−	0.842616i	−0.146582	−	0.989198i	$-0.546827\pi$
$673$	567.081	−	567.081i	0.842616	−	0.842616i	0.989198	+	0.146582i	$0.0468273\pi$
$674$		−	155.974i		−	0.231416i
$675$	571.725	+	813.300i	0.847000	+	1.20489i
$676$	−335.025			−0.495600
$677$	282.504	+	282.504i	0.417289	+	0.417289i	0.884268	−	0.466980i	$-0.154658\pi$
$677$	282.504	+	282.504i	0.417289	+	0.417289i	−0.466980	+	0.884268i	$0.654658\pi$
$678$	59.5983	−	59.5983i	0.0879031	−	0.0879031i
$679$		0			0
$680$	−428.656	−	37.1029i	−0.630377	−	0.0545631i
$681$	−1926.53			−2.82897
$682$	−44.6504	−	44.6504i	−0.0654698	−	0.0654698i
$683$	673.378	−	673.378i	0.985912	−	0.985912i	−0.0139906	−	0.999902i	$-0.504453\pi$
$683$	673.378	−	673.378i	0.985912	−	0.985912i	0.999902	+	0.0139906i	$0.00445349\pi$
$684$			812.565i			1.18796i
$685$	220.060	+	261.765i	0.321256	+	0.382139i
$686$		0			0
$687$	−165.332	−	165.332i	−0.240657	−	0.240657i
$688$	132.311	−	132.311i	0.192312	−	0.192312i
$689$		−	16.4104i		−	0.0238178i
$690$	155.892	−	131.055i	0.225931	−	0.189935i
$691$	−470.834			−0.681380			−0.340690	−	0.940176i	$-0.610661\pi$
$691$	−470.834			−0.681380			−0.340690	+	0.940176i	$0.610661\pi$
$692$	−355.016	−	355.016i	−0.513028	−	0.513028i
$693$		0			0
$694$		−	476.747i		−	0.686955i
$695$	−29.0200	+	335.274i	−0.0417554	+	0.482408i
$696$	−105.450			−0.151509
$697$	−1147.93	−	1147.93i	−1.64696	−	1.64696i
$698$	287.505	−	287.505i	0.411899	−	0.411899i
$699$			530.602i			0.759088i
$700$		0			0
$701$	−1335.50			−1.90514			−0.952569	−	0.304322i	$-0.901570\pi$
$701$	−1335.50			−1.90514			−0.952569	+	0.304322i	$0.901570\pi$
$702$	48.4957	+	48.4957i	0.0690821	+	0.0690821i
$703$	140.569	−	140.569i	0.199956	−	0.199956i
$704$			7.58986i			0.0107811i
$705$	−770.167	−	66.6628i	−1.09244	−	0.0945572i
$706$	234.554			0.332229
$707$		0			0
$708$	−361.088	+	361.088i	−0.510012	+	0.510012i
$709$			1327.97i			1.87302i	0.350640	+	0.936510i	$0.385964\pi$
$709$			1327.97i			1.87302i	−0.350640	+	0.936510i	$0.614036\pi$
$710$	54.2400	+	64.5193i	0.0763943	+	0.0908723i
$711$	−1192.88			−1.67775
$712$	313.501	+	313.501i	0.440310	+	0.440310i
$713$	188.612	−	188.612i	0.264532	−	0.264532i
$714$		0			0
$715$	4.42816	−	3.72265i	0.00619323	−	0.00520651i
$716$	108.124			0.151012
$717$	14.3862	+	14.3862i	0.0200645	+	0.0200645i
$718$	374.507	−	374.507i	0.521597	−	0.521597i
$719$			281.916i			0.392095i	0.980594	+	0.196048i	$0.0628107\pi$
$719$			281.916i			0.392095i	−0.980594	+	0.196048i	$0.937189\pi$
$720$	29.0178	−	335.248i	0.0403026	−	0.465623i
$721$		0			0
$722$	−222.098	−	222.098i	−0.307616	−	0.307616i
$723$	1070.11	−	1070.11i	1.48010	−	1.48010i
$724$			402.907i			0.556501i
$725$	31.5143	−	180.681i	0.0434680	−	0.249216i
$726$	863.135			1.18889
$727$	830.098	+	830.098i	1.14181	+	1.14181i	0.988118	+	0.153694i	$0.0491171\pi$
$727$	830.098	+	830.098i	1.14181	+	1.14181i	0.153694	+	0.988118i	$0.450883\pi$
$728$		0			0
$729$		−	966.430i		−	1.32569i
$730$	388.013	+	33.5849i	0.531524	+	0.0460068i
$731$	1423.20			1.94692
$732$	326.969	+	326.969i	0.446678	+	0.446678i
$733$	843.583	−	843.583i	1.15086	−	1.15086i	0.164484	−	0.986380i	$-0.447404\pi$
$733$	843.583	−	843.583i	1.15086	−	1.15086i	0.986380	−	0.164484i	$-0.0525959\pi$
$734$			46.1721i			0.0629048i
$735$		0			0
$736$	−32.0610			−0.0435612
$737$	45.8383	+	45.8383i	0.0621958	+	0.0621958i
$738$	897.789	−	897.789i	1.21652	−	1.21652i
$739$			567.194i			0.767516i	0.923434	+	0.383758i	$0.125370\pi$
$739$			567.194i			0.767516i	−0.923434	+	0.383758i	$0.874630\pi$
$740$	−63.0159	+	52.9761i	−0.0851566	+	0.0715893i
$741$	−149.653			−0.201960
$742$		0			0
$743$	−121.240	+	121.240i	−0.163176	+	0.163176i	−0.783972	−	0.620796i	$-0.786810\pi$
$743$	−121.240	+	121.240i	−0.163176	+	0.163176i	0.620796	+	0.783972i	$0.286810\pi$
$744$		−	676.468i		−	0.909231i
$745$	25.8781	−	298.975i	0.0347358	−	0.401308i
$746$	1042.03			1.39682
$747$	−1442.67	−	1442.67i	−1.93129	−	1.93129i
$748$	−40.8201	+	40.8201i	−0.0545723	+	0.0545723i
$749$		0			0
$750$	868.382	+	230.100i	1.15784	+	0.306801i
$751$	999.032			1.33027			0.665135	−	0.746723i	$-0.268374\pi$
$751$	999.032			1.33027			0.665135	+	0.746723i	$0.268374\pi$
$752$	86.0518	+	86.0518i	0.114431	+	0.114431i
$753$	−1080.26	+	1080.26i	−1.43461	+	1.43461i
$754$		−	12.6529i		−	0.0167810i
$755$	−238.128	−	20.6115i	−0.315401	−	0.0273000i
$756$		0			0
$757$	290.904	+	290.904i	0.384285	+	0.384285i	0.872643	−	0.488358i	$-0.162404\pi$
$757$	290.904	+	290.904i	0.384285	+	0.384285i	−0.488358	+	0.872643i	$0.662404\pi$
$758$	287.166	−	287.166i	0.378846	−	0.378846i
$759$		−	27.3255i		−	0.0360019i
$760$	219.752	+	261.398i	0.289147	+	0.343945i
$761$	−370.356			−0.486670			−0.243335	−	0.969942i	$-0.578241\pi$
$761$	−370.356			−0.486670			−0.243335	+	0.969942i	$0.578241\pi$
$762$	577.416	+	577.416i	0.757764	+	0.757764i
$763$		0			0
$764$			351.483i			0.460056i
$765$	1959.11	−	1646.98i	2.56093	−	2.15292i
$766$	−646.031			−0.843383
$767$	−43.3267	−	43.3267i	−0.0564885	−	0.0564885i
$768$	−57.4944	+	57.4944i	−0.0748626	+	0.0748626i
$769$		−	615.359i		−	0.800207i	−0.916470	−	0.400103i	$-0.868974\pi$
$769$		−	615.359i		−	0.800207i	0.916470	−	0.400103i	$-0.131026\pi$
$770$		0			0
$771$	1679.35			2.17814
$772$	−73.8055	−	73.8055i	−0.0956030	−	0.0956030i
$773$	−596.400	+	596.400i	−0.771540	+	0.771540i	−0.978376	−	0.206836i	$-0.933683\pi$
$773$	−596.400	+	596.400i	−0.771540	+	0.771540i	0.206836	+	0.978376i	$0.433683\pi$
$774$			1113.07i			1.43807i
$775$	1159.08	+	202.166i	1.49559	+	0.260859i
$776$	348.716			0.449376
$777$		0			0
$778$	543.189	−	543.189i	0.698187	−	0.698187i
$779$			1288.51i			1.65406i
$780$	61.7437	+	5.34431i	0.0791586	+	0.00685167i
$781$	11.3092			0.0144804
$782$	−172.432	−	172.432i	−0.220501	−	0.220501i
$783$	206.289	−	206.289i	0.263460	−	0.263460i
$784$		0			0
$785$	−336.510	−	400.284i	−0.428675	−	0.509916i
$786$	−180.287			−0.229373
$787$	322.202	+	322.202i	0.409406	+	0.409406i	0.881531	−	0.472125i	$-0.156513\pi$
$787$	322.202	+	322.202i	0.409406	+	0.409406i	−0.472125	+	0.881531i	$0.656513\pi$
$788$	125.636	−	125.636i	0.159436	−	0.159436i
$789$			1923.71i			2.43817i
$790$	−383.743	+	322.605i	−0.485751	+	0.408360i
$791$		0			0
$792$	−31.9250	−	31.9250i	−0.0403094	−	0.0403094i
$793$	−39.2327	+	39.2327i	−0.0494737	+	0.0494737i
$794$			903.585i			1.13802i
$795$	29.4846	−	340.641i	0.0370876	−	0.428480i
$796$	51.8766			0.0651717
$797$	−1040.82	−	1040.82i	−1.30592	−	1.30592i	−0.924331	−	0.381592i	$-0.875376\pi$
$797$	−1040.82	−	1040.82i	−1.30592	−	1.30592i	−0.381592	−	0.924331i	$-0.624624\pi$
$798$		0			0
$799$			925.614i			1.15847i
$800$	−81.3302	−	115.695i	−0.101663	−	0.144619i
$801$	−2637.34			−3.29256
$802$	447.272	+	447.272i	0.557696	+	0.557696i
$803$	36.9497	−	36.9497i	0.0460146	−	0.0460146i
$804$			694.465i			0.863762i
$805$		0			0
$806$	81.1687			0.100706
$807$	520.676	+	520.676i	0.645200	+	0.645200i
$808$	100.904	−	100.904i	0.124882	−	0.124882i
$809$		−	222.024i		−	0.274443i	−0.990540	−	0.137221i	$-0.956183\pi$
$809$		−	222.024i		−	0.274443i	0.990540	−	0.137221i	$-0.0438172\pi$
$810$	230.503	+	274.187i	0.284572	+	0.338503i
$811$	1418.65			1.74926			0.874632	−	0.484788i	$-0.161103\pi$
$811$	1418.65			1.74926			0.874632	+	0.484788i	$0.161103\pi$
$812$		0			0
$813$	1188.06	−	1188.06i	1.46132	−	1.46132i
$814$			11.0457i			0.0135696i
$815$	157.337	−	132.270i	0.193051	−	0.162294i
$816$	−618.438			−0.757889
$817$	−798.740	−	798.740i	−0.977650	−	0.977650i
$818$	−23.0666	+	23.0666i	−0.0281988	+	0.0281988i
$819$		0			0
$820$	46.0145	−	531.614i	0.0561152	−	0.648309i
$821$	−384.554			−0.468397			−0.234198	−	0.972189i	$-0.575247\pi$
$821$	−384.554			−0.468397			−0.234198	+	0.972189i	$0.575247\pi$
$822$	347.573	+	347.573i	0.422839	+	0.422839i
$823$	47.2089	−	47.2089i	0.0573619	−	0.0573619i	−0.677844	−	0.735206i	$-0.737085\pi$
$823$	47.2089	−	47.2089i	0.0573619	−	0.0573619i	0.735206	+	0.677844i	$0.237085\pi$
$824$			408.881i			0.496215i
$825$	98.6065	−	69.3173i	0.119523	−	0.0840210i
$826$		0			0
$827$	595.969	+	595.969i	0.720639	+	0.720639i	0.968735	−	0.248096i	$-0.0798048\pi$
$827$	595.969	+	595.969i	0.720639	+	0.720639i	−0.248096	+	0.968735i	$0.579805\pi$
$828$	134.857	−	134.857i	0.162871	−	0.162871i
$829$			703.538i			0.848659i	0.905508	+	0.424329i	$0.139490\pi$
$829$			703.538i			0.848659i	−0.905508	+	0.424329i	$0.860510\pi$
$830$	−854.258	−	73.9414i	−1.02923	−	0.0890860i
$831$	−399.417			−0.480646
$832$	−6.89871	−	6.89871i	−0.00829172	−	0.00829172i
$833$		0			0
$834$			483.711i			0.579989i
$835$	−120.286	−	143.083i	−0.144056	−	0.171357i
$836$	45.8189			0.0548073
$837$	1323.35	+	1323.35i	1.58107	+	1.58107i
$838$	−502.792	+	502.792i	−0.599990	+	0.599990i
$839$			3.00042i			0.00357618i	0.999998	+	0.00178809i	$0.000569167\pi$
$839$			3.00042i			0.00357618i	−0.999998	+	0.00178809i	$0.999431\pi$
$840$		0			0
$841$	787.178			0.936002
$842$	48.4897	+	48.4897i	0.0575887	+	0.0575887i
$843$	1232.05	−	1232.05i	1.46151	−	1.46151i
$844$		−	447.351i		−	0.530036i
$845$	72.2263	−	834.444i	0.0854750	−	0.987507i
$846$	−723.915			−0.855691
$847$		0			0
$848$	−38.0603	+	38.0603i	−0.0448824	+	0.0448824i
$849$		−	471.989i		−	0.555936i
$850$	184.823	−	1059.65i	0.217439	−	1.24665i
$851$	−46.6591			−0.0548285
$852$	85.6691	+	85.6691i	0.100551	+	0.100551i
$853$	657.357	−	657.357i	0.770641	−	0.770641i	−0.207577	−	0.978219i	$-0.566558\pi$
$853$	657.357	−	657.357i	0.770641	−	0.770641i	0.978219	+	0.207577i	$0.0665579\pi$
$854$		0			0
$855$	−2023.85	−	175.177i	−2.36707	−	0.204885i
$856$	19.6261			0.0229277
$857$	−748.481	−	748.481i	−0.873374	−	0.873374i	0.119465	−	0.992838i	$-0.461882\pi$
$857$	−748.481	−	748.481i	−0.873374	−	0.873374i	−0.992838	+	0.119465i	$0.961882\pi$
$858$	5.87973	−	5.87973i	0.00685284	−	0.00685284i
$859$		−	863.004i		−	1.00466i	−0.864676	−	0.502331i	$-0.832476\pi$
$859$		−	863.004i		−	1.00466i	0.864676	−	0.502331i	$-0.167524\pi$
$860$	301.020	+	358.068i	0.350023	+	0.416359i
$861$		0			0
$862$	−371.451	−	371.451i	−0.430918	−	0.430918i
$863$	861.246	−	861.246i	0.997968	−	0.997968i	−0.00203002	−	0.999998i	$-0.500646\pi$
$863$	861.246	−	861.246i	0.997968	−	0.997968i	0.999998	+	0.00203002i	$0.000646176\pi$
$864$		−	224.950i		−	0.260358i
$865$	960.769	−	807.697i	1.11072	−	0.933754i
$866$	899.414			1.03858
$867$	−2287.61	−	2287.61i	−2.63854	−	2.63854i
$868$		0			0
$869$			67.2641i			0.0774041i
$870$	22.7334	−	262.643i	0.0261303	−	0.301888i
$871$	−83.3282			−0.0956696
$872$	97.7549	+	97.7549i	0.112104	+	0.112104i
$873$	−1466.79	+	1466.79i	−1.68018	+	1.68018i
$874$			193.548i			0.221451i
$875$		0			0
$876$	559.800			0.639041
$877$	−958.274	−	958.274i	−1.09267	−	1.09267i	−0.995242	−	0.0974307i	$-0.968938\pi$
$877$	−958.274	−	958.274i	−1.09267	−	1.09267i	−0.0974307	−	0.995242i	$-0.531062\pi$
$878$	−587.500	+	587.500i	−0.669134	+	0.669134i
$879$		−	2481.43i		−	2.82302i
$880$	−18.9040	−	1.63626i	−0.0214818	−	0.00185938i
$881$	906.106			1.02850			0.514248	−	0.857641i	$-0.328071\pi$
$881$	906.106			1.02850			0.514248	+	0.857641i	$0.328071\pi$
$882$		0			0
$883$	−479.615	+	479.615i	−0.543166	+	0.543166i	−0.924455	−	0.381290i	$-0.875480\pi$
$883$	−479.615	+	479.615i	−0.543166	+	0.543166i	0.381290	+	0.924455i	$0.375480\pi$
$884$		−	74.2058i		−	0.0839432i
$885$	−821.513	−	977.203i	−0.928263	−	1.10418i
$886$	6.71562			0.00757971
$887$	272.371	+	272.371i	0.307070	+	0.307070i	0.843772	−	0.536702i	$-0.180330\pi$
$887$	272.371	+	272.371i	0.307070	+	0.307070i	−0.536702	+	0.843772i	$0.680330\pi$
$888$	−83.6729	+	83.6729i	−0.0942262	+	0.0942262i
$889$		0			0
$890$	−848.419	+	713.247i	−0.953279	+	0.801401i
$891$	48.0607			0.0539402
$892$	−263.712	−	263.712i	−0.295641	−	0.295641i
$893$	519.483	−	519.483i	0.581727	−	0.581727i
$894$		−	431.341i		−	0.482485i
$895$	−23.3099	+	269.304i	−0.0260446	+	0.300898i
$896$		0			0
$897$	24.8371	+	24.8371i	0.0276891	+	0.0276891i
$898$	40.6375	−	40.6375i	0.0452533	−	0.0452533i
$899$		−	345.272i		−	0.384063i
$900$	828.743	+	144.549i	0.920825	+	0.160610i
$901$	−409.395			−0.454378
$902$	−50.6245	−	50.6245i	−0.0561248	−	0.0561248i
$903$		0			0
$904$		−	33.1710i		−	0.0366935i
$905$	−1003.52	−	86.8605i	−1.10886	−	0.0959785i
$906$	−343.556			−0.379200
$907$	578.476	+	578.476i	0.637791	+	0.637791i	0.950010	−	0.312219i	$-0.101072\pi$
$907$	578.476	+	578.476i	0.637791	+	0.637791i	−0.312219	+	0.950010i	$0.601072\pi$
$908$	−536.130	+	536.130i	−0.590452	+	0.590452i
$909$			848.863i			0.933843i
$910$		0			0
$911$	719.634			0.789939			0.394969	−	0.918694i	$-0.370755\pi$
$911$	719.634			0.789939			0.394969	+	0.918694i	$0.370755\pi$
$912$	347.086	+	347.086i	0.380577	+	0.380577i
$913$	−81.3493	+	81.3493i	−0.0891011	+	0.0891011i
$914$			464.891i			0.508634i
$915$	−884.866	+	743.887i	−0.967067	+	0.812992i
$916$	−92.0195			−0.100458
$917$		0			0
$918$	1209.83	−	1209.83i	1.31790	−	1.31790i
$919$			456.469i			0.496702i	0.968670	+	0.248351i	$0.0798886\pi$
$919$			456.469i			0.496702i	−0.968670	+	0.248351i	$0.920111\pi$
$920$	6.91186	−	79.8540i	0.00751290	−	0.0867978i
$921$	2472.98			2.68510
$922$	64.7559	+	64.7559i	0.0702341	+	0.0702341i
$923$	−10.2794	+	10.2794i	−0.0111369	+	0.0111369i
$924$		0			0
$925$	−118.362	−	168.374i	−0.127958	−	0.182026i
$926$	−1208.80			−1.30540
$927$	−1719.87	−	1719.87i	−1.85530	−	1.85530i
$928$	−29.3454	+	29.3454i	−0.0316222	+	0.0316222i
$929$		−	301.111i		−	0.324124i	−0.986781	−	0.162062i	$-0.948186\pi$
$929$		−	301.111i		−	0.324124i	0.986781	−	0.162062i	$-0.0518145\pi$
$930$	1684.87	+	145.836i	1.81169	+	0.156813i
$931$		0			0
$932$	147.660	+	147.660i	0.158434	+	0.158434i
$933$	1186.97	−	1186.97i	1.27221	−	1.27221i
$934$		−	505.427i		−	0.541142i
$935$	−92.8699	−	110.470i	−0.0993261	−	0.118150i
$936$	58.0357			0.0620039
$937$	201.407	+	201.407i	0.214949	+	0.214949i	0.806366	−	0.591417i	$-0.201431\pi$
$937$	201.407	+	201.407i	0.214949	+	0.214949i	−0.591417	+	0.806366i	$0.701431\pi$
$938$		0			0
$939$			435.141i			0.463409i
$940$	−232.880	+	195.777i	−0.247744	+	0.208273i
$941$	−470.543			−0.500046			−0.250023	−	0.968240i	$-0.580438\pi$
$941$	−470.543			−0.500046			−0.250023	+	0.968240i	$0.580438\pi$
$942$	−531.499	−	531.499i	−0.564224	−	0.564224i
$943$	213.848	−	213.848i	0.226774	−	0.226774i
$944$			200.973i			0.212895i
$945$		0			0
$946$	62.7637			0.0663464
$947$	200.546	+	200.546i	0.211770	+	0.211770i	0.805019	−	0.593249i	$-0.202155\pi$
$947$	200.546	+	200.546i	0.211770	+	0.211770i	−0.593249	+	0.805019i	$0.702155\pi$
$948$	−509.537	+	509.537i	−0.537486	+	0.537486i
$949$			67.1699i			0.0707796i
$950$	−698.436	+	490.979i	−0.735196	+	0.516820i
$951$	895.451			0.941589
$952$		0			0
$953$	627.876	−	627.876i	0.658842	−	0.658842i	−0.296264	−	0.955106i	$-0.595741\pi$
$953$	627.876	−	627.876i	0.658842	−	0.658842i	0.955106	+	0.296264i	$0.0957409\pi$
$954$		−	320.184i		−	0.335623i
$955$	−875.434	−	75.7743i	−0.916685	−	0.0793448i
$956$	8.00702			0.00837554
$957$	−25.0110	−	25.0110i	−0.0261348	−	0.0261348i
$958$	587.359	−	587.359i	0.613109	−	0.613109i
$959$		0			0
$960$	−130.806	−	155.596i	−0.136256	−	0.162079i
$961$	1253.94			1.30483
$962$	−10.0398	−	10.0398i	−0.0104364	−	0.0104364i
$963$	−82.5528	+	82.5528i	−0.0857246	+	0.0857246i
$964$		−	595.597i		−	0.617839i
$965$	199.738	−	167.915i	0.206982	−	0.174005i
$966$		0			0
$967$	−929.872	−	929.872i	−0.961604	−	0.961604i	0.0376852	−	0.999290i	$-0.488002\pi$
$967$	−929.872	−	929.872i	−0.961604	−	0.961604i	−0.999290	+	0.0376852i	$0.988002\pi$
$968$	240.200	−	240.200i	0.248140	−	0.248140i
$969$			3733.42i			3.85286i
$970$	−75.1778	+	868.543i	−0.0775029	+	0.895405i
$971$	1257.96			1.29553			0.647767	−	0.761839i	$-0.275703\pi$
$971$	1257.96			1.29553			0.647767	+	0.761839i	$0.275703\pi$
$972$	−142.069	−	142.069i	−0.146161	−	0.146161i
$973$		0			0
$974$			804.435i			0.825909i
$975$	−26.6220	+	152.632i	−0.0273046	+	0.156546i
$976$	181.983			0.186458
$977$	133.818	+	133.818i	0.136968	+	0.136968i	0.772267	−	0.635298i	$-0.219123\pi$
$977$	133.818	+	133.818i	0.136968	+	0.136968i	−0.635298	+	0.772267i	$0.719123\pi$
$978$	208.913	−	208.913i	0.213612	−	0.213612i
$979$			148.714i			0.151904i
$980$		0			0
$981$	−822.367			−0.838295
$982$	485.037	+	485.037i	0.493928	+	0.493928i
$983$	992.555	−	992.555i	1.00972	−	1.00972i	0.00976842	−	0.999952i	$-0.496891\pi$
$983$	992.555	−	992.555i	1.00972	−	1.00972i	0.999952	−	0.00976842i	$-0.00310943\pi$
$984$		−	766.978i		−	0.779449i
$985$	285.834	+	340.004i	0.290187	+	0.345182i
$986$	−315.654			−0.320135
$987$		0			0
$988$	−41.6465	+	41.6465i	−0.0421523	+	0.0421523i
$989$			265.126i			0.268075i
$990$	86.3978	−	72.6327i	0.0872705	−	0.0733664i
$991$	−516.141			−0.520829			−0.260414	−	0.965497i	$-0.583859\pi$
$991$	−516.141			−0.520829			−0.260414	+	0.965497i	$0.583859\pi$
$992$	−188.253	−	188.253i	−0.189771	−	0.189771i
$993$	−1155.18	+	1155.18i	−1.16332	+	1.16332i
$994$		0			0
$995$	−11.1838	+	129.208i	−0.0112400	+	0.129858i
$996$	−1232.47			−1.23742
$997$	934.225	+	934.225i	0.937036	+	0.937036i	0.998132	−	0.0610958i	$-0.0194595\pi$
$997$	934.225	+	934.225i	0.937036	+	0.937036i	−0.0610958	+	0.998132i	$0.519460\pi$
$998$	577.617	−	577.617i	0.578774	−	0.578774i
$999$		−	327.374i		−	0.327701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.3.f.o.197.1		8
5.3	odd	4	inner	490.3.f.o.393.1		8
7.2	even	3		70.3.l.c.67.1	yes	16
7.4	even	3		70.3.l.c.37.4	yes	16
7.6	odd	2		490.3.f.p.197.4		8
35.2	odd	12		350.3.p.e.193.1		16
35.4	even	6		350.3.p.e.107.1		16
35.9	even	6		350.3.p.e.207.4		16
35.13	even	4		490.3.f.p.393.4		8
35.18	odd	12		70.3.l.c.23.1	✓	16
35.23	odd	12		70.3.l.c.53.4	yes	16
35.32	odd	12		350.3.p.e.93.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.1	✓	16	35.18	odd	12
70.3.l.c.37.4	yes	16	7.4	even	3
70.3.l.c.53.4	yes	16	35.23	odd	12
70.3.l.c.67.1	yes	16	7.2	even	3
350.3.p.e.93.4		16	35.32	odd	12
350.3.p.e.107.1		16	35.4	even	6
350.3.p.e.193.1		16	35.2	odd	12
350.3.p.e.207.4		16	35.9	even	6
490.3.f.o.197.1		8	1.1	even	1	trivial
490.3.f.o.393.1		8	5.3	odd	4	inner
490.3.f.p.197.4		8	7.6	odd	2
490.3.f.p.393.4		8	35.13	even	4

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	490.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-3.59340 + 3.59340i) q^{3} +2.00000i q^{4} +(-4.98137 - 0.431169i) q^{5} -7.18681 q^{6} +(-2.00000 + 2.00000i) q^{8} -16.8251i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-3.59340 + 3.59340i) q^{3} +2.00000i q^{4} +(-4.98137 - 0.431169i) q^{5} -7.18681 q^{6} +(-2.00000 + 2.00000i) q^{8} -16.8251i q^{9} +(-4.55021 - 5.41254i) q^{10} -0.948733 q^{11} +(-7.18681 - 7.18681i) q^{12} +(0.862338 - 0.862338i) q^{13} +(19.4495 - 16.3507i) q^{15} -4.00000 q^{16} +(-21.5130 - 21.5130i) q^{17} +(16.8251 - 16.8251i) q^{18} +24.1474i q^{19} +(0.862338 - 9.96275i) q^{20} +(-0.948733 - 0.948733i) q^{22} +(4.00763 - 4.00763i) q^{23} -14.3736i q^{24} +(24.6282 + 4.29563i) q^{25} +1.72468 q^{26} +(28.1187 + 28.1187i) q^{27} -7.33636i q^{29} +(35.8002 + 3.09873i) q^{30} +47.0632 q^{31} +(-4.00000 - 4.00000i) q^{32} +(3.40918 - 3.40918i) q^{33} -43.0259i q^{34} +33.6502 q^{36} +(-5.82128 - 5.82128i) q^{37} +(-24.1474 + 24.1474i) q^{38} +6.19746i q^{39} +(10.8251 - 9.10041i) q^{40} +53.3601 q^{41} +(-33.0776 + 33.0776i) q^{43} -1.89747i q^{44} +(-7.25446 + 83.8121i) q^{45} +8.01526 q^{46} +(-21.5130 - 21.5130i) q^{47} +(14.3736 - 14.3736i) q^{48} +(20.3326 + 28.9238i) q^{50} +154.609 q^{51} +(1.72468 + 1.72468i) q^{52} +(9.51508 - 9.51508i) q^{53} +56.2374i q^{54} +(4.72600 + 0.409064i) q^{55} +(-86.7715 - 86.7715i) q^{57} +(7.33636 - 7.33636i) q^{58} -50.2432i q^{59} +(32.7014 + 38.8989i) q^{60} -45.4957 q^{61} +(47.0632 + 47.0632i) q^{62} -8.00000i q^{64} +(-4.66744 + 3.92382i) q^{65} +6.81836 q^{66} +(-48.3153 - 48.3153i) q^{67} +(43.0259 - 43.0259i) q^{68} +28.8020i q^{69} -11.9203 q^{71} +(33.6502 + 33.6502i) q^{72} +(-38.9464 + 38.9464i) q^{73} -11.6426i q^{74} +(-103.935 + 73.0631i) q^{75} -48.2949 q^{76} +(-6.19746 + 6.19746i) q^{78} -70.8989i q^{79} +(19.9255 + 1.72468i) q^{80} -50.6578 q^{81} +(53.3601 + 53.3601i) q^{82} +(85.7452 - 85.7452i) q^{83} +(97.8884 + 116.440i) q^{85} -66.1553 q^{86} +(26.3625 + 26.3625i) q^{87} +(1.89747 - 1.89747i) q^{88} -156.750i q^{89} +(-91.0665 + 76.5576i) q^{90} +(8.01526 + 8.01526i) q^{92} +(-169.117 + 169.117i) q^{93} -43.0259i q^{94} +(10.4116 - 120.287i) q^{95} +28.7472 q^{96} +(-87.1790 - 87.1790i) q^{97} +15.9625i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 2 q^{3} + 2 q^{5} - 4 q^{6} - 16 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 - 2 * q^3 + 2 * q^5 - 4 * q^6 - 16 * q^8	\( 8 q + 8 q^{2} - 2 q^{3} + 2 q^{5} - 4 q^{6} - 16 q^{8} + 6 q^{10} - 40 q^{11} - 4 q^{12} + 8 q^{13} - 10 q^{15} - 32 q^{16} - 46 q^{17} + 52 q^{18} + 8 q^{20} - 40 q^{22} - 54 q^{23} + 26 q^{25} + 16 q^{26} - 26 q^{27} + 22 q^{30} + 208 q^{31} - 32 q^{32} + 22 q^{33} + 104 q^{36} + 38 q^{37} - 36 q^{38} + 4 q^{40} - 36 q^{41} + 72 q^{43} - 254 q^{45} - 108 q^{46} - 46 q^{47} + 8 q^{48} - 30 q^{50} + 136 q^{51} + 16 q^{52} - 30 q^{53} - 96 q^{55} - 246 q^{57} - 132 q^{58} + 64 q^{60} + 120 q^{61} + 208 q^{62} - 230 q^{65} + 44 q^{66} + 74 q^{67} + 92 q^{68} + 8 q^{71} + 104 q^{72} + 54 q^{73} - 300 q^{75} - 72 q^{76} + 84 q^{78} - 8 q^{80} - 244 q^{81} - 36 q^{82} + 32 q^{83} + 272 q^{85} + 144 q^{86} + 236 q^{87} + 80 q^{88} - 524 q^{90} - 108 q^{92} - 142 q^{93} + 396 q^{95} + 16 q^{96} + 68 q^{97}+O(q^{100}) \) 8 * q + 8 * q^2 - 2 * q^3 + 2 * q^5 - 4 * q^6 - 16 * q^8 + 6 * q^10 - 40 * q^11 - 4 * q^12 + 8 * q^13 - 10 * q^15 - 32 * q^16 - 46 * q^17 + 52 * q^18 + 8 * q^20 - 40 * q^22 - 54 * q^23 + 26 * q^25 + 16 * q^26 - 26 * q^27 + 22 * q^30 + 208 * q^31 - 32 * q^32 + 22 * q^33 + 104 * q^36 + 38 * q^37 - 36 * q^38 + 4 * q^40 - 36 * q^41 + 72 * q^43 - 254 * q^45 - 108 * q^46 - 46 * q^47 + 8 * q^48 - 30 * q^50 + 136 * q^51 + 16 * q^52 - 30 * q^53 - 96 * q^55 - 246 * q^57 - 132 * q^58 + 64 * q^60 + 120 * q^61 + 208 * q^62 - 230 * q^65 + 44 * q^66 + 74 * q^67 + 92 * q^68 + 8 * q^71 + 104 * q^72 + 54 * q^73 - 300 * q^75 - 72 * q^76 + 84 * q^78 - 8 * q^80 - 244 * q^81 - 36 * q^82 + 32 * q^83 + 272 * q^85 + 144 * q^86 + 236 * q^87 + 80 * q^88 - 524 * q^90 - 108 * q^92 - 142 * q^93 + 396 * q^95 + 16 * q^96 + 68 * q^97

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