LMFDB - Embedded newform 490.3.f.p.393.3

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			393.3
Root			$1.93183 - 1.93183i$ of defining polynomial
Character	$\chi$	$=$	490.393
Dual form			490.3.f.p.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.93183 + 1.93183i) q^{3} -2.00000i q^{4} +(-4.87575 - 1.10773i) q^{5} +3.86367 q^{6} +(-2.00000 - 2.00000i) q^{8} -1.53604i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.93183 + 1.93183i) q^{3} -2.00000i q^{4} +(-4.87575 - 1.10773i) q^{5} +3.86367 q^{6} +(-2.00000 - 2.00000i) q^{8} -1.53604i q^{9} +(-5.98348 + 3.76802i) q^{10} -20.0461 q^{11} +(3.86367 - 3.86367i) q^{12} +(-2.21546 - 2.21546i) q^{13} +(-7.27919 - 11.5591i) q^{15} -4.00000 q^{16} +(-8.73498 + 8.73498i) q^{17} +(-1.53604 - 1.53604i) q^{18} +18.2374i q^{19} +(-2.21546 + 9.75150i) q^{20} +(-20.0461 + 20.0461i) q^{22} +(-29.0830 - 29.0830i) q^{23} -7.72733i q^{24} +(22.5459 + 10.8020i) q^{25} -4.43092 q^{26} +(20.3539 - 20.3539i) q^{27} -19.0242i q^{29} +(-18.8383 - 4.27990i) q^{30} -6.28154 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-38.7257 - 38.7257i) q^{33} +17.4700i q^{34} -3.07208 q^{36} +(-26.8360 + 26.8360i) q^{37} +(18.2374 + 18.2374i) q^{38} -8.55979i q^{39} +(7.53604 + 11.9670i) q^{40} +16.3689 q^{41} +(-4.26669 - 4.26669i) q^{43} +40.0922i q^{44} +(-1.70152 + 7.48935i) q^{45} -58.1661 q^{46} +(-8.73498 + 8.73498i) q^{47} +(-7.72733 - 7.72733i) q^{48} +(33.3479 - 11.7439i) q^{50} -33.7490 q^{51} +(-4.43092 + 4.43092i) q^{52} +(-37.8602 - 37.8602i) q^{53} -40.7077i q^{54} +(97.7397 + 22.2056i) q^{55} +(-35.2316 + 35.2316i) q^{57} +(-19.0242 - 19.0242i) q^{58} -95.1326i q^{59} +(-23.1182 + 14.5584i) q^{60} -8.45917 q^{61} +(-6.28154 + 6.28154i) q^{62} +8.00000i q^{64} +(8.34789 + 13.2561i) q^{65} -77.4514 q^{66} +(8.03738 - 8.03738i) q^{67} +(17.4700 + 17.4700i) q^{68} -112.367i q^{69} +94.8180 q^{71} +(-3.07208 + 3.07208i) q^{72} +(5.76760 + 5.76760i) q^{73} +53.6720i q^{74} +(22.6872 + 64.4226i) q^{75} +36.4747 q^{76} +(-8.55979 - 8.55979i) q^{78} +17.4416i q^{79} +(19.5030 + 4.43092i) q^{80} +64.8162 q^{81} +(16.3689 - 16.3689i) q^{82} +(63.0967 + 63.0967i) q^{83} +(52.2656 - 32.9136i) q^{85} -8.53337 q^{86} +(36.7515 - 36.7515i) q^{87} +(40.0922 + 40.0922i) q^{88} +77.4582i q^{89} +(5.78784 + 9.19087i) q^{90} +(-58.1661 + 58.1661i) q^{92} +(-12.1349 - 12.1349i) q^{93} +17.4700i q^{94} +(20.2021 - 88.9209i) q^{95} -15.4547 q^{96} +(-105.134 + 105.134i) q^{97} +30.7916i 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 $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.93183	+	1.93183i	0.643944	+	0.643944i	0.951523	−	0.307578i	$-0.0995186\pi$
$3$	1.93183	+	1.93183i	0.643944	+	0.643944i	−0.307578	+	0.951523i	$0.599519\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−4.87575	−	1.10773i	−0.975150	−	0.221546i
$5$	−4.87575	−	1.10773i	−0.975150	−	0.221546i
$6$	3.86367			0.643944
$7$		0			0
$7$		0			0
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		−	1.53604i		−	0.170671i
$10$	−5.98348	+	3.76802i	−0.598348	+	0.376802i
$11$	−20.0461			−1.82237			−0.911186	−	0.411996i	$-0.864832\pi$
$11$	−20.0461			−1.82237			−0.911186	+	0.411996i	$0.864832\pi$
$12$	3.86367	−	3.86367i	0.321972	−	0.321972i
$13$	−2.21546	−	2.21546i	−0.170420	−	0.170420i	0.616744	−	0.787164i	$-0.288451\pi$
$13$	−2.21546	−	2.21546i	−0.170420	−	0.170420i	−0.787164	+	0.616744i	$0.788451\pi$
$14$		0			0
$15$	−7.27919	−	11.5591i	−0.485279	−	0.770606i
$16$	−4.00000			−0.250000
$17$	−8.73498	+	8.73498i	−0.513822	+	0.513822i	−0.915695	−	0.401873i	$-0.868359\pi$
$17$	−8.73498	+	8.73498i	−0.513822	+	0.513822i	0.401873	+	0.915695i	$0.368359\pi$
$18$	−1.53604	−	1.53604i	−0.0853356	−	0.0853356i
$19$			18.2374i			0.959862i	0.877306	+	0.479931i	$0.159338\pi$
$19$			18.2374i			0.959862i	−0.877306	+	0.479931i	$0.840662\pi$
$20$	−2.21546	+	9.75150i	−0.110773	+	0.487575i
$21$		0			0
$22$	−20.0461	+	20.0461i	−0.911186	+	0.911186i
$23$	−29.0830	−	29.0830i	−1.26448	−	1.26448i	−0.948898	−	0.315582i	$-0.897800\pi$
$23$	−29.0830	−	29.0830i	−1.26448	−	1.26448i	−0.315582	−	0.948898i	$-0.602200\pi$
$24$		−	7.72733i		−	0.321972i
$25$	22.5459	+	10.8020i	0.901835	+	0.432081i
$26$	−4.43092			−0.170420
$27$	20.3539	−	20.3539i	0.753847	−	0.753847i
$28$		0			0
$29$		−	19.0242i		−	0.656006i	−0.944677	−	0.328003i	$-0.893624\pi$
$29$		−	19.0242i		−	0.656006i	0.944677	−	0.328003i	$-0.106376\pi$
$30$	−18.8383	−	4.27990i	−0.627942	−	0.142663i
$31$	−6.28154			−0.202630			−0.101315	−	0.994854i	$-0.532305\pi$
$31$	−6.28154			−0.202630			−0.101315	+	0.994854i	$0.532305\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−38.7257	−	38.7257i	−1.17351	−	1.17351i
$34$			17.4700i			0.513822i
$35$		0			0
$36$	−3.07208			−0.0853356
$37$	−26.8360	+	26.8360i	−0.725298	+	0.725298i	−0.969679	−	0.244381i	$-0.921415\pi$
$37$	−26.8360	+	26.8360i	−0.725298	+	0.725298i	0.244381	+	0.969679i	$0.421415\pi$
$38$	18.2374	+	18.2374i	0.479931	+	0.479931i
$39$		−	8.55979i		−	0.219482i
$40$	7.53604	+	11.9670i	0.188401	+	0.299174i
$41$	16.3689			0.399242			0.199621	−	0.979873i	$-0.436029\pi$
$41$	16.3689			0.399242			0.199621	+	0.979873i	$0.436029\pi$
$42$		0			0
$43$	−4.26669	−	4.26669i	−0.0992252	−	0.0992252i	0.655752	−	0.754977i	$-0.272352\pi$
$43$	−4.26669	−	4.26669i	−0.0992252	−	0.0992252i	−0.754977	+	0.655752i	$0.772352\pi$
$44$			40.0922i			0.911186i
$45$	−1.70152	+	7.48935i	−0.0378115	+	0.166430i
$46$	−58.1661			−1.26448
$47$	−8.73498	+	8.73498i	−0.185851	+	0.185851i	−0.793900	−	0.608049i	$-0.791952\pi$
$47$	−8.73498	+	8.73498i	−0.185851	+	0.185851i	0.608049	+	0.793900i	$0.291952\pi$
$48$	−7.72733	−	7.72733i	−0.160986	−	0.160986i
$49$		0			0
$50$	33.3479	−	11.7439i	0.666958	−	0.234877i
$51$	−33.7490			−0.661746
$52$	−4.43092	+	4.43092i	−0.0852099	+	0.0852099i
$53$	−37.8602	−	37.8602i	−0.714343	−	0.714343i	0.253098	−	0.967441i	$-0.418551\pi$
$53$	−37.8602	−	37.8602i	−0.714343	−	0.714343i	−0.967441	+	0.253098i	$0.918551\pi$
$54$		−	40.7077i		−	0.753847i
$55$	97.7397	+	22.2056i	1.77709	+	0.403739i
$56$		0			0
$57$	−35.2316	+	35.2316i	−0.618098	+	0.618098i
$58$	−19.0242	−	19.0242i	−0.328003	−	0.328003i
$59$		−	95.1326i		−	1.61242i	−0.591631	−	0.806209i	$-0.701516\pi$
$59$		−	95.1326i		−	1.61242i	0.591631	−	0.806209i	$-0.298484\pi$
$60$	−23.1182	+	14.5584i	−0.385303	+	0.242640i
$61$	−8.45917			−0.138675			−0.0693375	−	0.997593i	$-0.522089\pi$
$61$	−8.45917			−0.138675			−0.0693375	+	0.997593i	$0.522089\pi$
$62$	−6.28154	+	6.28154i	−0.101315	+	0.101315i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	8.34789	+	13.2561i	0.128429	+	0.203941i
$66$	−77.4514			−1.17351
$67$	8.03738	−	8.03738i	0.119961	−	0.119961i	−0.644578	−	0.764539i	$-0.722967\pi$
$67$	8.03738	−	8.03738i	0.119961	−	0.119961i	0.764539	+	0.644578i	$0.222967\pi$
$68$	17.4700	+	17.4700i	0.256911	+	0.256911i
$69$		−	112.367i		−	1.62851i
$70$		0			0
$71$	94.8180			1.33547			0.667733	−	0.744401i	$-0.267265\pi$
$71$	94.8180			1.33547			0.667733	+	0.744401i	$0.267265\pi$
$72$	−3.07208	+	3.07208i	−0.0426678	+	0.0426678i
$73$	5.76760	+	5.76760i	0.0790083	+	0.0790083i	0.745507	−	0.666498i	$-0.232208\pi$
$73$	5.76760	+	5.76760i	0.0790083	+	0.0790083i	−0.666498	+	0.745507i	$0.732208\pi$
$74$			53.6720i			0.725298i
$75$	22.6872	+	64.4226i	0.302496	+	0.858967i
$76$	36.4747			0.479931
$77$		0			0
$78$	−8.55979	−	8.55979i	−0.109741	−	0.109741i
$79$			17.4416i			0.220780i	0.993888	+	0.110390i	$0.0352100\pi$
$79$			17.4416i			0.220780i	−0.993888	+	0.110390i	$0.964790\pi$
$80$	19.5030	+	4.43092i	0.243787	+	0.0553865i
$81$	64.8162			0.800200
$82$	16.3689	−	16.3689i	0.199621	−	0.199621i
$83$	63.0967	+	63.0967i	0.760201	+	0.760201i	0.976359	−	0.216157i	$-0.0693525\pi$
$83$	63.0967	+	63.0967i	0.760201	+	0.760201i	−0.216157	+	0.976359i	$0.569352\pi$
$84$		0			0
$85$	52.2656	−	32.9136i	0.614889	−	0.387219i
$86$	−8.53337			−0.0992252
$87$	36.7515	−	36.7515i	0.422431	−	0.422431i
$88$	40.0922	+	40.0922i	0.455593	+	0.455593i
$89$			77.4582i			0.870317i	0.900354	+	0.435158i	$0.143308\pi$
$89$			77.4582i			0.870317i	−0.900354	+	0.435158i	$0.856692\pi$
$90$	5.78784	+	9.19087i	0.0643093	+	0.102121i
$91$		0			0
$92$	−58.1661	+	58.1661i	−0.632240	+	0.632240i
$93$	−12.1349	−	12.1349i	−0.130483	−	0.130483i
$94$			17.4700i			0.185851i
$95$	20.2021	−	88.9209i	0.212653	−	0.936009i
$96$	−15.4547			−0.160986
$97$	−105.134	+	105.134i	−1.08385	+	1.08385i	−0.0877043	+	0.996147i	$0.527953\pi$
$97$	−105.134	+	105.134i	−1.08385	+	1.08385i	−0.996147	+	0.0877043i	$0.972047\pi$
$98$		0			0
$99$			30.7916i			0.311026i
$100$	21.6040	−	45.0917i	0.216040	−	0.450917i
$101$	−127.439			−1.26177			−0.630887	−	0.775874i	$-0.717309\pi$
$101$	−127.439			−1.26177			−0.630887	+	0.775874i	$0.717309\pi$
$102$	−33.7490	+	33.7490i	−0.330873	+	0.330873i
$103$	−5.31067	−	5.31067i	−0.0515599	−	0.0515599i	0.680857	−	0.732417i	$-0.261608\pi$
$103$	−5.31067	−	5.31067i	−0.0515599	−	0.0515599i	−0.732417	+	0.680857i	$0.761608\pi$
$104$			8.86183i			0.0852099i
$105$		0			0
$106$	−75.7204			−0.714343
$107$	81.6414	−	81.6414i	0.763004	−	0.763004i	−0.213860	−	0.976864i	$-0.568604\pi$
$107$	81.6414	−	81.6414i	0.763004	−	0.763004i	0.976864	+	0.213860i	$0.0686038\pi$
$108$	−40.7077	−	40.7077i	−0.376924	−	0.376924i
$109$		−	42.6209i		−	0.391017i	−0.980702	−	0.195509i	$-0.937364\pi$
$109$		−	42.6209i		−	0.391017i	0.980702	−	0.195509i	$-0.0626357\pi$
$110$	119.945	−	75.5341i	1.09041	−	0.686673i
$111$	−103.685			−0.934103
$112$		0			0
$113$	−13.6000	−	13.6000i	−0.120354	−	0.120354i	0.644365	−	0.764718i	$-0.277122\pi$
$113$	−13.6000	−	13.6000i	−0.120354	−	0.120354i	−0.764718	+	0.644365i	$0.777122\pi$
$114$			70.4631i			0.618098i
$115$	109.586	+	174.018i	0.952917	+	1.51320i
$116$	−38.0483			−0.328003
$117$	−3.40304	+	3.40304i	−0.0290858	+	0.0290858i
$118$	−95.1326	−	95.1326i	−0.806209	−	0.806209i
$119$		0			0
$120$	−8.55979	+	37.6765i	−0.0713316	+	0.313971i
$121$	280.845			2.32104
$122$	−8.45917	+	8.45917i	−0.0693375	+	0.0693375i
$123$	31.6220	+	31.6220i	0.257090	+	0.257090i
$124$			12.5631i			0.101315i
$125$	−97.9623	−	77.6427i	−0.783699	−	0.621141i
$126$		0			0
$127$	24.7683	−	24.7683i	0.195026	−	0.195026i	−0.602838	−	0.797864i	$-0.705963\pi$
$127$	24.7683	−	24.7683i	0.195026	−	0.195026i	0.797864	+	0.602838i	$0.205963\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	16.4850i		−	0.127791i
$130$	21.6040	+	4.90825i	0.166185	+	0.0377558i
$131$	−144.724			−1.10477			−0.552383	−	0.833590i	$-0.686282\pi$
$131$	−144.724			−1.10477			−0.552383	+	0.833590i	$0.686282\pi$
$132$	−77.4514	+	77.4514i	−0.586753	+	0.586753i
$133$		0			0
$134$		−	16.0748i		−	0.119961i
$135$	−121.787	+	76.6938i	−0.902126	+	0.568102i
$136$	34.9399			0.256911
$137$	33.3725	−	33.3725i	0.243595	−	0.243595i	−0.574741	−	0.818336i	$-0.694897\pi$
$137$	33.3725	−	33.3725i	0.243595	−	0.243595i	0.818336	+	0.574741i	$0.194897\pi$
$138$	−112.367	−	112.367i	−0.814255	−	0.814255i
$139$			121.473i			0.873910i	0.899483	+	0.436955i	$0.143943\pi$
$139$			121.473i			0.873910i	−0.899483	+	0.436955i	$0.856057\pi$
$140$		0			0
$141$	−33.7490			−0.239355
$142$	94.8180	−	94.8180i	0.667733	−	0.667733i
$143$	44.4113	+	44.4113i	0.310568	+	0.310568i
$144$			6.14417i			0.0426678i
$145$	−21.0736	+	92.7571i	−0.145335	+	0.639704i
$146$	11.5352			0.0790083
$147$		0			0
$148$	53.6720	+	53.6720i	0.362649	+	0.362649i
$149$			135.757i			0.911119i	0.890205	+	0.455560i	$0.150561\pi$
$149$			135.757i			0.911119i	−0.890205	+	0.455560i	$0.849439\pi$
$150$	87.1097	+	41.7354i	0.580732	+	0.278236i
$151$	82.7236			0.547839			0.273919	−	0.961753i	$-0.411680\pi$
$151$	82.7236			0.547839			0.273919	+	0.961753i	$0.411680\pi$
$152$	36.4747	−	36.4747i	0.239965	−	0.239965i
$153$	13.4173	+	13.4173i	0.0876947	+	0.0876947i
$154$		0			0
$155$	30.6272	+	6.95825i	0.197595	+	0.0448919i
$156$	−17.1196			−0.109741
$157$	27.7332	−	27.7332i	0.176645	−	0.176645i	−0.613247	−	0.789891i	$-0.710137\pi$
$157$	27.7332	−	27.7332i	0.176645	−	0.176645i	0.789891	+	0.613247i	$0.210137\pi$
$158$	17.4416	+	17.4416i	0.110390	+	0.110390i
$159$		−	146.279i		−	0.919994i
$160$	23.9339	−	15.0721i	0.149587	−	0.0942005i
$161$		0			0
$162$	64.8162	−	64.8162i	0.400100	−	0.400100i
$163$	−87.3885	−	87.3885i	−0.536126	−	0.536126i	0.386263	−	0.922389i	$-0.373766\pi$
$163$	−87.3885	−	87.3885i	−0.536126	−	0.536126i	−0.922389	+	0.386263i	$0.873766\pi$
$164$		−	32.7378i		−	0.199621i
$165$	145.919	+	231.714i	0.884359	+	1.40433i
$166$	126.193			0.760201
$167$	173.339	−	173.339i	1.03796	−	1.03796i	0.0387094	−	0.999251i	$-0.487675\pi$
$167$	173.339	−	173.339i	1.03796	−	1.03796i	0.999251	−	0.0387094i	$-0.0123247\pi$
$168$		0			0
$169$		−	159.183i		−	0.941914i
$170$	19.3520	−	85.1791i	0.113835	−	0.501054i
$171$	28.0134			0.163821
$172$	−8.53337	+	8.53337i	−0.0496126	+	0.0496126i
$173$	171.272	+	171.272i	0.990012	+	0.990012i	0.999951	−	0.00993824i	$-0.00316349\pi$
$173$	171.272	+	171.272i	0.990012	+	0.990012i	−0.00993824	+	0.999951i	$0.503163\pi$
$174$		−	73.5030i		−	0.422431i
$175$		0			0
$176$	80.1843			0.455593
$177$	183.780	−	183.780i	1.03831	−	1.03831i
$178$	77.4582	+	77.4582i	0.435158	+	0.435158i
$179$		−	173.381i		−	0.968608i	−0.874900	−	0.484304i	$-0.839073\pi$
$179$		−	173.381i		−	0.968608i	0.874900	−	0.484304i	$-0.160927\pi$
$180$	14.9787	+	3.40304i	0.0832151	+	0.0189058i
$181$	−237.263			−1.31085			−0.655424	−	0.755262i	$-0.727510\pi$
$181$	−237.263			−1.31085			−0.655424	+	0.755262i	$0.727510\pi$
$182$		0			0
$183$	−16.3417	−	16.3417i	−0.0892989	−	0.0892989i
$184$			116.332i			0.632240i
$185$	160.573	−	101.119i	0.867961	−	0.546587i
$186$	−24.2698			−0.130483
$187$	175.102	−	175.102i	0.936375	−	0.936375i
$188$	17.4700	+	17.4700i	0.0929253	+	0.0929253i
$189$		0			0
$190$	−68.7188	−	109.123i	−0.361678	−	0.574331i
$191$	20.9842			0.109865			0.0549324	−	0.998490i	$-0.482506\pi$
$191$	20.9842			0.109865			0.0549324	+	0.998490i	$0.482506\pi$
$192$	−15.4547	+	15.4547i	−0.0804930	+	0.0804930i
$193$	−35.3917	−	35.3917i	−0.183377	−	0.183377i	0.609449	−	0.792826i	$-0.291391\pi$
$193$	−35.3917	−	35.3917i	−0.183377	−	0.183377i	−0.792826	+	0.609449i	$0.791391\pi$
$194$			210.267i			1.08385i
$195$	−9.48193	+	41.7354i	−0.0486253	+	0.214028i
$196$		0			0
$197$	−85.5963	+	85.5963i	−0.434499	+	0.434499i	−0.890156	−	0.455657i	$-0.849404\pi$
$197$	−85.5963	+	85.5963i	−0.434499	+	0.434499i	0.455657	+	0.890156i	$0.349404\pi$
$198$	30.7916	+	30.7916i	0.155513	+	0.155513i
$199$		−	307.461i		−	1.54503i	−0.634996	−	0.772515i	$-0.718998\pi$
$199$		−	307.461i		−	1.54503i	0.634996	−	0.772515i	$-0.281002\pi$
$200$	−23.4877	−	66.6958i	−0.117439	−	0.333479i
$201$	31.0537			0.154496
$202$	−127.439	+	127.439i	−0.630887	+	0.630887i
$203$		0			0
$204$			67.4981i			0.330873i
$205$	−79.8107	−	18.1323i	−0.389321	−	0.0884504i
$206$	−10.6213			−0.0515599
$207$	−44.6728	+	44.6728i	−0.215810	+	0.215810i
$208$	8.86183	+	8.86183i	0.0426050	+	0.0426050i
$209$		−	365.588i		−	1.74922i
$210$		0			0
$211$	−116.585			−0.552533			−0.276267	−	0.961081i	$-0.589097\pi$
$211$	−116.585			−0.552533			−0.276267	+	0.961081i	$0.589097\pi$
$212$	−75.7204	+	75.7204i	−0.357172	+	0.357172i
$213$	183.173	+	183.173i	0.859965	+	0.859965i
$214$		−	163.283i		−	0.763004i
$215$	16.0770	+	25.5296i	0.0747766	+	0.118742i
$216$	−81.4155			−0.376924
$217$		0			0
$218$	−42.6209	−	42.6209i	−0.195509	−	0.195509i
$219$			22.2841i			0.101754i
$220$	44.4113	−	195.479i	0.201869	−	0.888543i
$221$	38.7040			0.175131
$222$	−103.685	+	103.685i	−0.467051	+	0.467051i
$223$	93.2689	+	93.2689i	0.418246	+	0.418246i	0.884599	−	0.466353i	$-0.154432\pi$
$223$	93.2689	+	93.2689i	0.418246	+	0.418246i	−0.466353	+	0.884599i	$0.654432\pi$
$224$		0			0
$225$	16.5924	−	34.6314i	0.0737438	−	0.153917i
$226$	−27.1999			−0.120354
$227$	−238.300	+	238.300i	−1.04978	+	1.04978i	−0.0510852	+	0.998694i	$0.516268\pi$
$227$	−238.300	+	238.300i	−1.04978	+	1.04978i	−0.998694	+	0.0510852i	$0.983732\pi$
$228$	70.4631	+	70.4631i	0.309049	+	0.309049i
$229$		−	381.893i		−	1.66765i	−0.552026	−	0.833827i	$-0.686145\pi$
$229$		−	381.893i		−	1.66765i	0.552026	−	0.833827i	$-0.313855\pi$
$230$	283.603	+	64.4323i	1.23306	+	0.280140i
$231$		0			0
$232$	−38.0483	+	38.0483i	−0.164001	+	0.164001i
$233$	236.020	+	236.020i	1.01296	+	1.01296i	0.999915	+	0.0130448i	$0.00415242\pi$
$233$	236.020	+	236.020i	1.01296	+	1.01296i	0.0130448	+	0.999915i	$0.495848\pi$
$234$			6.80607i			0.0290858i
$235$	52.2656	−	32.9136i	0.222407	−	0.140058i
$236$	−190.265			−0.806209
$237$	−33.6943	+	33.6943i	−0.142170	+	0.142170i
$238$		0			0
$239$		−	437.169i		−	1.82916i	−0.404406	−	0.914579i	$-0.632522\pi$
$239$		−	437.169i		−	1.82916i	0.404406	−	0.914579i	$-0.367478\pi$
$240$	29.1167	+	46.2363i	0.121320	+	0.192651i
$241$	3.89241			0.0161511			0.00807554	−	0.999967i	$-0.497429\pi$
$241$	3.89241			0.0161511			0.00807554	+	0.999967i	$0.497429\pi$
$242$	280.845	−	280.845i	1.16052	−	1.16052i
$243$	−57.9708	−	57.9708i	−0.238563	−	0.238563i
$244$			16.9183i			0.0693375i
$245$		0			0
$246$	63.2440			0.257090
$247$	40.4041	−	40.4041i	0.163579	−	0.163579i
$248$	12.5631	+	12.5631i	0.0506576	+	0.0506576i
$249$			243.785i			0.979054i
$250$	−175.605	+	20.3197i	−0.702420	+	0.0812787i
$251$	−368.235			−1.46707			−0.733535	−	0.679651i	$-0.762131\pi$
$251$	−368.235			−1.46707			−0.733535	+	0.679651i	$0.762131\pi$
$252$		0			0
$253$	583.001	+	583.001i	2.30435	+	2.30435i
$254$		−	49.5366i		−	0.195026i
$255$	164.552	+	37.3848i	0.645302	+	0.146607i
$256$	16.0000			0.0625000
$257$	−187.252	+	187.252i	−0.728605	+	0.728605i	−0.970342	−	0.241736i	$-0.922283\pi$
$257$	−187.252	+	187.252i	−0.728605	+	0.728605i	0.241736	+	0.970342i	$0.422283\pi$
$258$	−16.4850	−	16.4850i	−0.0638955	−	0.0638955i
$259$		0			0
$260$	26.5123	−	16.6958i	0.101970	−	0.0642146i
$261$	−29.2219			−0.111961
$262$	−144.724	+	144.724i	−0.552383	+	0.552383i
$263$	−194.119	−	194.119i	−0.738097	−	0.738097i	0.234113	−	0.972209i	$-0.424781\pi$
$263$	−194.119	−	194.119i	−0.738097	−	0.738097i	−0.972209	+	0.234113i	$0.924781\pi$
$264$			154.903i			0.586753i
$265$	142.658	+	226.536i	0.538332	+	0.854851i
$266$		0			0
$267$	−149.636	+	149.636i	−0.560436	+	0.560436i
$268$	−16.0748	−	16.0748i	−0.0599804	−	0.0599804i
$269$		−	139.255i		−	0.517677i	−0.965921	−	0.258839i	$-0.916660\pi$
$269$		−	139.255i		−	0.517677i	0.965921	−	0.258839i	$-0.0833398\pi$
$270$	−45.0932	+	198.481i	−0.167012	+	0.735114i
$271$	−62.0657			−0.229025			−0.114512	−	0.993422i	$-0.536531\pi$
$271$	−62.0657			−0.229025			−0.114512	+	0.993422i	$0.536531\pi$
$272$	34.9399	−	34.9399i	0.128456	−	0.128456i
$273$		0			0
$274$		−	66.7450i		−	0.243595i
$275$	−451.956	−	216.538i	−1.64348	−	0.787412i
$276$	−224.734			−0.814255
$277$	−294.136	+	294.136i	−1.06186	+	1.06186i	−0.0639081	+	0.997956i	$0.520356\pi$
$277$	−294.136	+	294.136i	−1.06186	+	1.06186i	−0.997956	+	0.0639081i	$0.979644\pi$
$278$	121.473	+	121.473i	0.436955	+	0.436955i
$279$			9.64871i			0.0345832i
$280$		0			0
$281$	−370.599			−1.31886			−0.659428	−	0.751767i	$-0.729202\pi$
$281$	−370.599			−1.31886			−0.659428	+	0.751767i	$0.729202\pi$
$282$	−33.7490	+	33.7490i	−0.119677	+	0.119677i
$283$	−341.319	−	341.319i	−1.20607	−	1.20607i	−0.972289	−	0.233784i	$-0.924889\pi$
$283$	−341.319	−	341.319i	−1.20607	−	1.20607i	−0.233784	−	0.972289i	$-0.575111\pi$
$284$		−	189.636i		−	0.667733i
$285$	210.807	−	132.753i	0.739675	−	0.465801i
$286$	88.8225			0.310568
$287$		0			0
$288$	6.14417	+	6.14417i	0.0213339	+	0.0213339i
$289$			136.400i			0.471973i
$290$	71.6835	+	113.831i	0.247184	+	0.392520i
$291$	−406.201			−1.39588
$292$	11.5352	−	11.5352i	0.0395041	−	0.0395041i
$293$	203.433	+	203.433i	0.694312	+	0.694312i	0.963178	−	0.268866i	$-0.0866489\pi$
$293$	203.433	+	203.433i	0.694312	+	0.694312i	−0.268866	+	0.963178i	$0.586649\pi$
$294$		0			0
$295$	−105.381	+	463.843i	−0.357224	+	1.57235i
$296$	107.344			0.362649
$297$	−408.015	+	408.015i	−1.37379	+	1.37379i
$298$	135.757	+	135.757i	0.455560	+	0.455560i
$299$			128.865i			0.430985i
$300$	128.845	−	45.3743i	0.429484	−	0.151248i
$301$		0			0
$302$	82.7236	−	82.7236i	0.273919	−	0.273919i
$303$	−246.191	−	246.191i	−0.812513	−	0.812513i
$304$		−	72.9495i		−	0.239965i
$305$	41.2448	+	9.37047i	0.135229	+	0.0307228i
$306$	26.8346			0.0876947
$307$	−0.207402	+	0.207402i	−0.000675578	+	0.000675578i	−0.707444	−	0.706769i	$-0.750152\pi$
$307$	−0.207402	+	0.207402i	−0.000675578	+	0.000675578i	0.706769	+	0.707444i	$0.250152\pi$
$308$		0			0
$309$		−	20.5187i		−	0.0664034i
$310$	37.5855	−	23.6690i	0.121243	−	0.0763516i
$311$	−356.021			−1.14476			−0.572382	−	0.819987i	$-0.693980\pi$
$311$	−356.021			−1.14476			−0.572382	+	0.819987i	$0.693980\pi$
$312$	−17.1196	+	17.1196i	−0.0548705	+	0.0548705i
$313$	184.173	+	184.173i	0.588411	+	0.588411i	0.937201	−	0.348790i	$-0.113407\pi$
$313$	184.173	+	184.173i	0.588411	+	0.588411i	−0.348790	+	0.937201i	$0.613407\pi$
$314$		−	55.4664i		−	0.176645i
$315$		0			0
$316$	34.8833			0.110390
$317$	−54.6955	+	54.6955i	−0.172541	+	0.172541i	−0.788095	−	0.615554i	$-0.788932\pi$
$317$	−54.6955	+	54.6955i	−0.172541	+	0.172541i	0.615554	+	0.788095i	$0.288932\pi$
$318$	−146.279	−	146.279i	−0.459997	−	0.459997i
$319$			381.360i			1.19549i
$320$	8.86183	−	39.0060i	0.0276932	−	0.121894i
$321$	315.435			0.982664
$322$		0			0
$323$	−159.303	−	159.303i	−0.493198	−	0.493198i
$324$		−	129.632i		−	0.400100i
$325$	−26.0180	−	73.8809i	−0.0800554	−	0.227326i
$326$	−174.777			−0.536126
$327$	82.3364	−	82.3364i	0.251793	−	0.251793i
$328$	−32.7378	−	32.7378i	−0.0998105	−	0.0998105i
$329$		0			0
$330$	377.634	+	85.7951i	1.14434	+	0.259985i
$331$	86.2829			0.260674			0.130337	−	0.991470i	$-0.458394\pi$
$331$	86.2829			0.260674			0.130337	+	0.991470i	$0.458394\pi$
$332$	126.193	−	126.193i	0.380101	−	0.380101i
$333$	41.2212	+	41.2212i	0.123788	+	0.123788i
$334$		−	346.679i		−	1.03796i
$335$	−48.0915	+	30.2850i	−0.143557	+	0.0904030i
$336$		0			0
$337$	92.8454	−	92.8454i	0.275506	−	0.275506i	−0.555806	−	0.831312i	$-0.687590\pi$
$337$	92.8454	−	92.8454i	0.275506	−	0.275506i	0.831312	+	0.555806i	$0.187590\pi$
$338$	−159.183	−	159.183i	−0.470957	−	0.470957i
$339$		−	52.5457i		−	0.155002i
$340$	−65.8272	−	104.531i	−0.193609	−	0.307444i
$341$	125.920			0.369268
$342$	28.0134	−	28.0134i	0.0819104	−	0.0819104i
$343$		0			0
$344$			17.0667i			0.0496126i
$345$	−124.472	+	547.874i	−0.360789	+	1.58804i
$346$	342.544			0.990012
$347$	−283.244	+	283.244i	−0.816264	+	0.816264i	−0.985565	−	0.169300i	$-0.945849\pi$
$347$	−283.244	+	283.244i	−0.816264	+	0.816264i	0.169300	+	0.985565i	$0.445849\pi$
$348$	−73.5030	−	73.5030i	−0.211216	−	0.211216i
$349$		−	202.323i		−	0.579723i	−0.957069	−	0.289862i	$-0.906391\pi$
$349$		−	202.323i		−	0.579723i	0.957069	−	0.289862i	$-0.0936093\pi$
$350$		0			0
$351$	−90.1863			−0.256941
$352$	80.1843	−	80.1843i	0.227796	−	0.227796i
$353$	233.476	+	233.476i	0.661405	+	0.661405i	0.955711	−	0.294306i	$-0.0950885\pi$
$353$	233.476	+	233.476i	0.661405	+	0.661405i	−0.294306	+	0.955711i	$0.595089\pi$
$354$		−	367.561i		−	1.03831i
$355$	−462.309	−	105.033i	−1.30228	−	0.295867i
$356$	154.916			0.435158
$357$		0			0
$358$	−173.381	−	173.381i	−0.484304	−	0.484304i
$359$		−	31.3178i		−	0.0872361i	−0.999048	−	0.0436181i	$-0.986112\pi$
$359$		−	31.3178i		−	0.0872361i	0.999048	−	0.0436181i	$-0.0138885\pi$
$360$	18.3817	−	11.5757i	0.0510604	−	0.0321546i
$361$	28.3982			0.0786655
$362$	−237.263	+	237.263i	−0.655424	+	0.655424i
$363$	542.546	+	542.546i	1.49462	+	1.49462i
$364$		0			0
$365$	−21.7324	−	34.5103i	−0.0595409	−	0.0945488i
$366$	−32.6834			−0.0892989
$367$	−124.103	+	124.103i	−0.338157	+	0.338157i	−0.855673	−	0.517517i	$-0.826857\pi$
$367$	−124.103	+	124.103i	−0.338157	+	0.338157i	0.517517	+	0.855673i	$0.326857\pi$
$368$	116.332	+	116.332i	0.316120	+	0.316120i
$369$		−	25.1433i		−	0.0681391i
$370$	59.4541	−	261.691i	0.160687	−	0.707274i
$371$		0			0
$372$	−24.2698	+	24.2698i	−0.0652414	+	0.0652414i
$373$	76.4288	+	76.4288i	0.204903	+	0.204903i	0.802097	−	0.597194i	$-0.203718\pi$
$373$	76.4288	+	76.4288i	0.204903	+	0.204903i	−0.597194	+	0.802097i	$0.703718\pi$
$374$		−	350.204i		−	0.936375i
$375$	−39.2542	−	339.240i	−0.104678	−	0.904639i
$376$	34.9399			0.0929253
$377$	−42.1472	+	42.1472i	−0.111796	+	0.111796i
$378$		0			0
$379$			370.389i			0.977279i	0.872486	+	0.488639i	$0.162507\pi$
$379$			370.389i			0.977279i	−0.872486	+	0.488639i	$0.837493\pi$
$380$	−177.842	−	40.4041i	−0.468005	−	0.106327i
$381$	95.6964			0.251172
$382$	20.9842	−	20.9842i	0.0549324	−	0.0549324i
$383$	−2.48825	−	2.48825i	−0.00649673	−	0.00649673i	0.703851	−	0.710348i	$-0.251462\pi$
$383$	−2.48825	−	2.48825i	−0.00649673	−	0.00649673i	−0.710348	+	0.703851i	$0.751462\pi$
$384$			30.9093i			0.0804930i
$385$		0			0
$386$	−70.7834			−0.183377
$387$	−6.55381	+	6.55381i	−0.0169349	+	0.0169349i
$388$	210.267	+	210.267i	0.541925	+	0.541925i
$389$		−	725.344i		−	1.86464i	−0.361637	−	0.932319i	$-0.617782\pi$
$389$		−	725.344i		−	1.86464i	0.361637	−	0.932319i	$-0.382218\pi$
$390$	32.2535	+	51.2173i	0.0827012	+	0.131326i
$391$	508.079			1.29944
$392$		0			0
$393$	−279.583	−	279.583i	−0.711408	−	0.711408i
$394$			171.193i			0.434499i
$395$	19.3206	−	85.0410i	0.0489129	−	0.215294i
$396$	61.5832			0.155513
$397$	90.5936	−	90.5936i	0.228195	−	0.228195i	−0.583743	−	0.811938i	$-0.698412\pi$
$397$	90.5936	−	90.5936i	0.228195	−	0.228195i	0.811938	+	0.583743i	$0.198412\pi$
$398$	−307.461	−	307.461i	−0.772515	−	0.772515i
$399$		0			0
$400$	−90.1835	−	43.2081i	−0.225459	−	0.108020i
$401$	−700.963			−1.74804			−0.874019	−	0.485892i	$-0.838495\pi$
$401$	−700.963			−1.74804			−0.874019	+	0.485892i	$0.838495\pi$
$402$	31.0537	−	31.0537i	0.0772481	−	0.0772481i
$403$	13.9165	+	13.9165i	0.0345322	+	0.0345322i
$404$			254.878i			0.630887i
$405$	−316.028	−	71.7988i	−0.780315	−	0.177281i
$406$		0			0
$407$	537.957	−	537.957i	1.32176	−	1.32176i
$408$	67.4981	+	67.4981i	0.165436	+	0.165436i
$409$			452.456i			1.10625i	0.833099	+	0.553124i	$0.186564\pi$
$409$			452.456i			1.10625i	−0.833099	+	0.553124i	$0.813436\pi$
$410$	−97.9431	+	61.6784i	−0.238886	+	0.150435i
$411$	128.940			0.313723
$412$	−10.6213	+	10.6213i	−0.0257799	+	0.0257799i
$413$		0			0
$414$			89.3455i			0.215810i
$415$	−237.750	−	377.538i	−0.572891	−	0.909729i
$416$	17.7237			0.0426050
$417$	−234.666	+	234.666i	−0.562749	+	0.562749i
$418$	−365.588	−	365.588i	−0.874612	−	0.874612i
$419$		−	248.174i		−	0.592302i	−0.955141	−	0.296151i	$-0.904297\pi$
$419$		−	248.174i		−	0.592302i	0.955141	−	0.296151i	$-0.0957031\pi$
$420$		0			0
$421$	−238.992			−0.567676			−0.283838	−	0.958872i	$-0.591608\pi$
$421$	−238.992			−0.567676			−0.283838	+	0.958872i	$0.591608\pi$
$422$	−116.585	+	116.585i	−0.276267	+	0.276267i
$423$	13.4173	+	13.4173i	0.0317194	+	0.0317194i
$424$			151.441i			0.357172i
$425$	−291.293	+	102.582i	−0.685396	+	0.241370i
$426$	366.345			0.859965
$427$		0			0
$428$	−163.283	−	163.283i	−0.381502	−	0.381502i
$429$			171.590i			0.399977i
$430$	41.6066	+	9.45266i	0.0967595	+	0.0219829i
$431$	−130.746			−0.303355			−0.151677	−	0.988430i	$-0.548468\pi$
$431$	−130.746			−0.303355			−0.151677	+	0.988430i	$0.548468\pi$
$432$	−81.4155	+	81.4155i	−0.188462	+	0.188462i
$433$	−456.850	−	456.850i	−1.05508	−	1.05508i	−0.998392	−	0.0566898i	$-0.981945\pi$
$433$	−456.850	−	456.850i	−1.05508	−	1.05508i	−0.0566898	−	0.998392i	$-0.518055\pi$
$434$		0			0
$435$	−219.902	+	138.480i	−0.505522	+	0.318346i
$436$	−85.2417			−0.195509
$437$	530.398	−	530.398i	1.21373	−	1.21373i
$438$	22.2841	+	22.2841i	0.0508769	+	0.0508769i
$439$		−	216.958i		−	0.494209i	−0.968989	−	0.247105i	$-0.920521\pi$
$439$		−	216.958i		−	0.494209i	0.968989	−	0.247105i	$-0.0794792\pi$
$440$	−151.068	−	239.891i	−0.343337	−	0.545206i
$441$		0			0
$442$	38.7040	−	38.7040i	0.0875655	−	0.0875655i
$443$	−30.6228	−	30.6228i	−0.0691258	−	0.0691258i	0.671699	−	0.740824i	$-0.265565\pi$
$443$	−30.6228	−	30.6228i	−0.0691258	−	0.0691258i	−0.740824	+	0.671699i	$0.765565\pi$
$444$			207.371i			0.467051i
$445$	85.8027	−	377.667i	0.192815	−	0.848690i
$446$	186.538			0.418246
$447$	−262.259	+	262.259i	−0.586710	+	0.586710i
$448$		0			0
$449$			48.2524i			0.107466i	0.998555	+	0.0537332i	$0.0171120\pi$
$449$			48.2524i			0.107466i	−0.998555	+	0.0537332i	$0.982888\pi$
$450$	−18.0390	−	51.2237i	−0.0400868	−	0.113831i
$451$	−328.133			−0.727567
$452$	−27.1999	+	27.1999i	−0.0601768	+	0.0601768i
$453$	159.808	+	159.808i	0.352778	+	0.352778i
$454$			476.600i			1.04978i
$455$		0			0
$456$	140.926			0.309049
$457$	−204.908	+	204.908i	−0.448377	+	0.448377i	−0.894815	−	0.446438i	$-0.852692\pi$
$457$	−204.908	+	204.908i	−0.448377	+	0.448377i	0.446438	+	0.894815i	$0.352692\pi$
$458$	−381.893	−	381.893i	−0.833827	−	0.833827i
$459$			355.581i			0.774687i
$460$	348.036	−	219.171i	0.756599	−	0.476459i
$461$	−348.242			−0.755407			−0.377703	−	0.925927i	$-0.623286\pi$
$461$	−348.242			−0.755407			−0.377703	+	0.925927i	$0.623286\pi$
$462$		0			0
$463$	−268.097	−	268.097i	−0.579044	−	0.579044i	0.355596	−	0.934640i	$-0.384278\pi$
$463$	−268.097	−	268.097i	−0.579044	−	0.579044i	−0.934640	+	0.355596i	$0.884278\pi$
$464$			76.0967i			0.164001i
$465$	45.7245	+	72.6089i	0.0983323	+	0.156148i
$466$	472.039			1.01296
$467$	−352.594	+	352.594i	−0.755019	+	0.755019i	−0.975411	−	0.220392i	$-0.929266\pi$
$467$	−352.594	+	352.594i	−0.755019	+	0.755019i	0.220392	+	0.975411i	$0.429266\pi$
$468$	6.80607	+	6.80607i	0.0145429	+	0.0145429i
$469$		0			0
$470$	19.3520	−	85.1791i	0.0411744	−	0.181232i
$471$	107.152			0.227499
$472$	−190.265	+	190.265i	−0.403104	+	0.403104i
$473$	85.5303	+	85.5303i	0.180825	+	0.180825i
$474$			67.3886i			0.142170i
$475$	−197.000	+	411.177i	−0.414738	+	0.865637i
$476$		0			0
$477$	−58.1548	+	58.1548i	−0.121918	+	0.121918i
$478$	−437.169	−	437.169i	−0.914579	−	0.914579i
$479$		−	374.806i		−	0.782475i	−0.920290	−	0.391238i	$-0.872047\pi$
$479$		−	374.806i		−	0.782475i	0.920290	−	0.391238i	$-0.127953\pi$
$480$	75.3531	+	17.1196i	0.156986	+	0.0356658i
$481$	118.908			0.247210
$482$	3.89241	−	3.89241i	0.00807554	−	0.00807554i
$483$		0			0
$484$		−	561.691i		−	1.16052i
$485$	629.064	−	396.145i	1.29704	−	0.816795i
$486$	−115.942			−0.238563
$487$	277.508	−	277.508i	0.569832	−	0.569832i	−0.362249	−	0.932081i	$-0.617991\pi$
$487$	277.508	−	277.508i	0.569832	−	0.569832i	0.932081	+	0.362249i	$0.117991\pi$
$488$	16.9183	+	16.9183i	0.0346687	+	0.0346687i
$489$		−	337.640i		−	0.690470i
$490$		0			0
$491$	100.451			0.204585			0.102293	−	0.994754i	$-0.467382\pi$
$491$	100.451			0.204585			0.102293	+	0.994754i	$0.467382\pi$
$492$	63.2440	−	63.2440i	0.128545	−	0.128545i
$493$	166.176	+	166.176i	0.337070	+	0.337070i
$494$		−	80.8083i		−	0.163579i
$495$	34.1088	−	150.132i	0.0689066	−	0.303297i
$496$	25.1262			0.0506576
$497$		0			0
$498$	243.785	+	243.785i	0.489527	+	0.489527i
$499$		−	394.800i		−	0.791182i	−0.918427	−	0.395591i	$-0.870540\pi$
$499$		−	394.800i		−	0.791182i	0.918427	−	0.395591i	$-0.129460\pi$
$500$	−155.285	+	195.925i	−0.310571	+	0.391849i
$501$	669.725			1.33678
$502$	−368.235	+	368.235i	−0.733535	+	0.733535i
$503$	38.4894	+	38.4894i	0.0765197	+	0.0765197i	0.744331	−	0.667811i	$-0.232769\pi$
$503$	38.4894	+	38.4894i	0.0765197	+	0.0765197i	−0.667811	+	0.744331i	$0.732769\pi$
$504$		0			0
$505$	621.362	+	141.168i	1.23042	+	0.279541i
$506$	1166.00			2.30435
$507$	307.516	−	307.516i	0.606540	−	0.606540i
$508$	−49.5366	−	49.5366i	−0.0975129	−	0.0975129i
$509$		−	510.759i		−	1.00346i	−0.865025	−	0.501728i	$-0.832698\pi$
$509$		−	510.759i		−	1.00346i	0.865025	−	0.501728i	$-0.167302\pi$
$510$	201.937	−	127.167i	0.395954	−	0.249347i
$511$		0			0
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	371.201	+	371.201i	0.723589	+	0.723589i
$514$			374.503i			0.728605i
$515$	20.0107	+	31.7763i	0.0388557	+	0.0617015i
$516$	−32.9701			−0.0638955
$517$	175.102	−	175.102i	0.338689	−	0.338689i
$518$		0			0
$519$			661.738i			1.27503i
$520$	9.81651	−	43.2081i	0.0188779	−	0.0830925i
$521$	785.097			1.50690			0.753452	−	0.657503i	$-0.228387\pi$
$521$	785.097			1.50690			0.753452	+	0.657503i	$0.228387\pi$
$522$	−29.2219	+	29.2219i	−0.0559807	+	0.0559807i
$523$	216.640	+	216.640i	0.414226	+	0.414226i	0.883208	−	0.468982i	$-0.155379\pi$
$523$	216.640	+	216.640i	0.414226	+	0.414226i	−0.468982	+	0.883208i	$0.655379\pi$
$524$			289.449i			0.552383i
$525$		0			0
$526$	−388.239			−0.738097
$527$	54.8691	−	54.8691i	0.104116	−	0.104116i
$528$	154.903	+	154.903i	0.293376	+	0.293376i
$529$			1162.65i			2.19782i
$530$	369.194	+	83.8777i	0.696592	+	0.158260i
$531$	−146.128			−0.275193
$532$		0			0
$533$	−36.2647	−	36.2647i	−0.0680387	−	0.0680387i
$534$			299.273i			0.560436i
$535$	−488.500	+	307.627i	−0.913084	+	0.575003i
$536$	−32.1495			−0.0599804
$537$	334.943	−	334.943i	0.623730	−	0.623730i
$538$	−139.255	−	139.255i	−0.258839	−	0.258839i
$539$		0			0
$540$	153.388	+	243.574i	0.284051	+	0.451063i
$541$	529.610			0.978947			0.489474	−	0.872018i	$-0.337189\pi$
$541$	529.610			0.978947			0.489474	+	0.872018i	$0.337189\pi$
$542$	−62.0657	+	62.0657i	−0.114512	+	0.114512i
$543$	−458.353	−	458.353i	−0.844113	−	0.844113i
$544$		−	69.8798i		−	0.128456i
$545$	−47.2124	+	207.809i	−0.0866282	+	0.381300i
$546$		0			0
$547$	−343.777	+	343.777i	−0.628477	+	0.628477i	−0.947685	−	0.319207i	$-0.896583\pi$
$547$	−343.777	+	343.777i	−0.628477	+	0.628477i	0.319207	+	0.947685i	$0.396583\pi$
$548$	−66.7450	−	66.7450i	−0.121797	−	0.121797i
$549$			12.9936i			0.0236678i
$550$	−668.495	+	235.418i	−1.21544	+	0.428033i
$551$	346.951			0.629675
$552$	−224.734	+	224.734i	−0.407127	+	0.407127i
$553$		0			0
$554$			588.273i			1.06186i
$555$	505.544	+	114.855i	0.910890	+	0.206947i
$556$	242.947			0.436955
$557$	263.079	−	263.079i	0.472315	−	0.472315i	−0.430348	−	0.902663i	$-0.641609\pi$
$557$	263.079	−	263.079i	0.472315	−	0.472315i	0.902663	+	0.430348i	$0.141609\pi$
$558$	9.64871	+	9.64871i	0.0172916	+	0.0172916i
$559$			18.9053i			0.0338199i
$560$		0			0
$561$	676.536			1.20595
$562$	−370.599	+	370.599i	−0.659428	+	0.659428i
$563$	678.813	+	678.813i	1.20571	+	1.20571i	0.972404	+	0.233302i	$0.0749532\pi$
$563$	678.813	+	678.813i	1.20571	+	1.20571i	0.233302	+	0.972404i	$0.425047\pi$
$564$			67.4981i			0.119677i
$565$	51.2449	+	81.3750i	0.0906989	+	0.144027i
$566$	−682.637			−1.20607
$567$		0			0
$568$	−189.636	−	189.636i	−0.333866	−	0.333866i
$569$		−	668.937i		−	1.17564i	−0.808993	−	0.587818i	$-0.799987\pi$
$569$		−	668.937i		−	1.17564i	0.808993	−	0.587818i	$-0.200013\pi$
$570$	78.0540	−	343.561i	0.136937	−	0.602738i
$571$	−272.787			−0.477735			−0.238868	−	0.971052i	$-0.576776\pi$
$571$	−272.787			−0.477735			−0.238868	+	0.971052i	$0.576776\pi$
$572$	88.8225	−	88.8225i	0.155284	−	0.155284i
$573$	40.5379	+	40.5379i	0.0707468	+	0.0707468i
$574$		0			0
$575$	−341.547	−	969.858i	−0.593995	−	1.68671i
$576$	12.2883			0.0213339
$577$	−153.009	+	153.009i	−0.265180	+	0.265180i	−0.827155	−	0.561974i	$-0.810042\pi$
$577$	−153.009	+	153.009i	−0.265180	+	0.265180i	0.561974	+	0.827155i	$0.310042\pi$
$578$	136.400	+	136.400i	0.235987	+	0.235987i
$579$		−	136.742i		−	0.236169i
$580$	185.514	+	42.1472i	0.319852	+	0.0726677i
$581$		0			0
$582$	−406.201	+	406.201i	−0.697940	+	0.697940i
$583$	758.948	+	758.948i	1.30180	+	1.30180i
$584$		−	23.0704i		−	0.0395041i
$585$	20.3620	−	12.8227i	0.0348068	−	0.0219192i
$586$	406.867			0.694312
$587$	193.451	−	193.451i	0.329559	−	0.329559i	−0.522860	−	0.852419i	$-0.675135\pi$
$587$	193.451	−	193.451i	0.329559	−	0.329559i	0.852419	+	0.522860i	$0.175135\pi$
$588$		0			0
$589$		−	114.559i		−	0.194497i
$590$	358.462	+	569.224i	0.607562	+	0.964786i
$591$	−330.715			−0.559586
$592$	107.344	−	107.344i	0.181324	−	0.181324i
$593$	102.991	+	102.991i	0.173679	+	0.173679i	0.788593	−	0.614915i	$-0.210810\pi$
$593$	102.991	+	102.991i	0.173679	+	0.173679i	−0.614915	+	0.788593i	$0.710810\pi$
$594$			816.031i			1.37379i
$595$		0			0
$596$	271.514			0.455560
$597$	593.964	−	593.964i	0.994914	−	0.994914i
$598$	128.865	+	128.865i	0.215492	+	0.215492i
$599$		−	457.291i		−	0.763424i	−0.924281	−	0.381712i	$-0.875335\pi$
$599$		−	457.291i		−	0.763424i	0.924281	−	0.381712i	$-0.124665\pi$
$600$	83.4708	−	174.219i	0.139118	−	0.290366i
$601$	−369.587			−0.614953			−0.307477	−	0.951556i	$-0.599485\pi$
$601$	−369.587			−0.614953			−0.307477	+	0.951556i	$0.599485\pi$
$602$		0			0
$603$	−12.3457	−	12.3457i	−0.0204739	−	0.0204739i
$604$		−	165.447i		−	0.273919i
$605$	−1369.33	−	311.101i	−2.26336	−	0.514216i
$606$	−492.383			−0.812513
$607$	165.381	−	165.381i	0.272456	−	0.272456i	−0.557632	−	0.830088i	$-0.688290\pi$
$607$	165.381	−	165.381i	0.272456	−	0.272456i	0.830088	+	0.557632i	$0.188290\pi$
$608$	−72.9495	−	72.9495i	−0.119983	−	0.119983i
$609$		0			0
$610$	50.6153	−	31.8743i	0.0829758	−	0.0522530i
$611$	38.7040			0.0633453
$612$	26.8346	−	26.8346i	0.0438474	−	0.0438474i
$613$	678.753	+	678.753i	1.10726	+	1.10726i	0.993509	+	0.113756i	$0.0362882\pi$
$613$	678.753	+	678.753i	1.10726	+	1.10726i	0.113756	+	0.993509i	$0.463712\pi$
$614$			0.414805i			0.000675578i
$615$	−119.152	−	189.210i	−0.193744	−	0.307658i
$616$		0			0
$617$	22.6455	−	22.6455i	0.0367026	−	0.0367026i	−0.688517	−	0.725220i	$-0.741738\pi$
$617$	22.6455	−	22.6455i	0.0367026	−	0.0367026i	0.725220	+	0.688517i	$0.241738\pi$
$618$	−20.5187	−	20.5187i	−0.0332017	−	0.0332017i
$619$		−	497.226i		−	0.803274i	−0.915799	−	0.401637i	$-0.868441\pi$
$619$		−	497.226i		−	0.803274i	0.915799	−	0.401637i	$-0.131559\pi$
$620$	13.9165	−	61.2545i	0.0224460	−	0.0987975i
$621$	−1183.91			−1.90645
$622$	−356.021	+	356.021i	−0.572382	+	0.572382i
$623$		0			0
$624$			34.2392i			0.0548705i
$625$	391.633	+	487.082i	0.626612	+	0.779331i
$626$	368.345			0.588411
$627$	706.255	−	706.255i	1.12640	−	1.12640i
$628$	−55.4664	−	55.4664i	−0.0883224	−	0.0883224i
$629$		−	468.824i		−	0.745348i
$630$		0			0
$631$	965.780			1.53056			0.765278	−	0.643700i	$-0.222602\pi$
$631$	965.780			1.53056			0.765278	+	0.643700i	$0.222602\pi$
$632$	34.8833	−	34.8833i	0.0551950	−	0.0551950i
$633$	−225.222	−	225.222i	−0.355801	−	0.355801i
$634$			109.391i			0.172541i
$635$	−148.201	+	93.3274i	−0.233387	+	0.146972i
$636$	−292.558			−0.459997
$637$		0			0
$638$	381.360	+	381.360i	0.597743	+	0.597743i
$639$		−	145.644i		−	0.227926i
$640$	−30.1442	−	47.8678i	−0.0471003	−	0.0747935i
$641$	1199.96			1.87202			0.936008	−	0.351978i	$-0.114491\pi$
$641$	1199.96			1.87202			0.936008	+	0.351978i	$0.114491\pi$
$642$	315.435	−	315.435i	0.491332	−	0.491332i
$643$	−405.030	−	405.030i	−0.629906	−	0.629906i	0.318138	−	0.948044i	$-0.396942\pi$
$643$	−405.030	−	405.030i	−0.629906	−	0.629906i	−0.948044	+	0.318138i	$0.896942\pi$
$644$		0			0
$645$	−18.2610	+	80.3770i	−0.0283116	+	0.124615i
$646$	−318.606			−0.493198
$647$	59.6805	−	59.6805i	0.0922418	−	0.0922418i	−0.659480	−	0.751722i	$-0.729224\pi$
$647$	59.6805	−	59.6805i	0.0922418	−	0.0922418i	0.751722	+	0.659480i	$0.229224\pi$
$648$	−129.632	−	129.632i	−0.200050	−	0.200050i
$649$			1907.04i			2.93842i
$650$	−99.8989	−	47.8628i	−0.153691	−	0.0736351i
$651$		0			0
$652$	−174.777	+	174.777i	−0.268063	+	0.268063i
$653$	−339.289	−	339.289i	−0.519586	−	0.519586i	0.397860	−	0.917446i	$-0.369753\pi$
$653$	−339.289	−	339.289i	−0.519586	−	0.519586i	−0.917446	+	0.397860i	$0.869753\pi$
$654$		−	164.673i		−	0.251793i
$655$	705.640	+	160.315i	1.07731	+	0.244756i
$656$	−65.4757			−0.0998105
$657$	8.85928	−	8.85928i	0.0134844	−	0.0134844i
$658$		0			0
$659$			168.872i			0.256255i	0.991758	+	0.128127i	$0.0408966\pi$
$659$			168.872i			0.256255i	−0.991758	+	0.128127i	$0.959103\pi$
$660$	463.429	−	291.838i	0.702165	−	0.442179i
$661$	503.549			0.761799			0.380900	−	0.924616i	$-0.375614\pi$
$661$	503.549			0.761799			0.380900	+	0.924616i	$0.375614\pi$
$662$	86.2829	−	86.2829i	0.130337	−	0.130337i
$663$	74.7696	+	74.7696i	0.112775	+	0.112775i
$664$		−	252.387i		−	0.380101i
$665$		0			0
$666$	82.4425			0.123788
$667$	−553.281	+	553.281i	−0.829506	+	0.829506i
$668$	−346.679	−	346.679i	−0.518980	−	0.518980i
$669$			360.360i			0.538655i
$670$	−17.8065	+	78.3765i	−0.0265768	+	0.116980i
$671$	169.573			0.252717
$672$		0			0
$673$	143.862	+	143.862i	0.213763	+	0.213763i	0.805864	−	0.592101i	$-0.201701\pi$
$673$	143.862	+	143.862i	0.213763	+	0.213763i	−0.592101	+	0.805864i	$0.701701\pi$
$674$		−	185.691i		−	0.275506i
$675$	678.759	−	239.033i	1.00557	−	0.354123i
$676$	−318.367			−0.470957
$677$	−85.9199	+	85.9199i	−0.126913	+	0.126913i	−0.767710	−	0.640797i	$-0.778604\pi$
$677$	−85.9199	+	85.9199i	−0.126913	+	0.126913i	0.640797	+	0.767710i	$0.278604\pi$
$678$	−52.5457	−	52.5457i	−0.0775010	−	0.0775010i
$679$		0			0
$680$	−170.358	−	38.7040i	−0.250527	−	0.0569176i
$681$	−920.711			−1.35200
$682$	125.920	−	125.920i	0.184634	−	0.184634i
$683$	−573.593	−	573.593i	−0.839814	−	0.839814i	0.149020	−	0.988834i	$-0.452388\pi$
$683$	−573.593	−	573.593i	−0.839814	−	0.839814i	−0.988834	+	0.149020i	$0.952388\pi$
$684$		−	56.0267i		−	0.0819104i
$685$	−199.684	+	125.748i	−0.291509	+	0.183574i
$686$		0			0
$687$	737.753	−	737.753i	1.07388	−	1.07388i
$688$	17.0667	+	17.0667i	0.0248063	+	0.0248063i
$689$			167.755i			0.243476i
$690$	423.402	+	672.347i	0.613626	+	0.974415i
$691$	32.6336			0.0472266			0.0236133	−	0.999721i	$-0.492483\pi$
$691$	32.6336			0.0472266			0.0236133	+	0.999721i	$0.492483\pi$
$692$	342.544	−	342.544i	0.495006	−	0.495006i
$693$		0			0
$694$			566.487i			0.816264i
$695$	134.560	−	592.274i	0.193611	−	0.852193i
$696$	−147.006			−0.211216
$697$	−142.982	+	142.982i	−0.205139	+	0.205139i
$698$	−202.323	−	202.323i	−0.289862	−	0.289862i
$699$			911.901i			1.30458i
$700$		0			0
$701$	−311.596			−0.444503			−0.222251	−	0.974989i	$-0.571341\pi$
$701$	−311.596			−0.444503			−0.222251	+	0.974989i	$0.571341\pi$
$702$	−90.1863	+	90.1863i	−0.128471	+	0.128471i
$703$	−489.418	−	489.418i	−0.696186	−	0.696186i
$704$		−	160.369i		−	0.227796i
$705$	164.552	+	37.3848i	0.233407	+	0.0530281i
$706$	466.952			0.661405
$707$		0			0
$708$	−367.561	−	367.561i	−0.519154	−	0.519154i
$709$			719.127i			1.01428i	0.861863	+	0.507142i	$0.169298\pi$
$709$			719.127i			1.01428i	−0.861863	+	0.507142i	$0.830702\pi$
$710$	−567.342	+	357.276i	−0.799073	+	0.503206i
$711$	26.7911			0.0376808
$712$	154.916	−	154.916i	0.217579	−	0.217579i
$713$	182.686	+	182.686i	0.256222	+	0.256222i
$714$		0			0
$715$	−167.343	−	265.734i	−0.234045	−	0.371656i
$716$	−346.762			−0.484304
$717$	844.538	−	844.538i	1.17788	−	1.17788i
$718$	−31.3178	−	31.3178i	−0.0436181	−	0.0436181i
$719$			321.939i			0.447760i	0.974617	+	0.223880i	$0.0718724\pi$
$719$			321.939i			0.447760i	−0.974617	+	0.223880i	$0.928128\pi$
$720$	6.80607	−	29.9574i	0.00945288	−	0.0416075i
$721$		0			0
$722$	28.3982	−	28.3982i	0.0393327	−	0.0393327i
$723$	7.51949	+	7.51949i	0.0104004	+	0.0104004i
$724$			474.527i			0.655424i
$725$	205.499	−	428.916i	0.283447	−	0.591609i
$726$	1085.09			1.49462
$727$	905.157	−	905.157i	1.24506	−	1.24506i	0.287182	−	0.957876i	$-0.407282\pi$
$727$	905.157	−	905.157i	1.24506	−	1.24506i	0.957876	−	0.287182i	$-0.0927184\pi$
$728$		0			0
$729$		−	807.326i		−	1.10744i
$730$	−56.2428	−	12.7779i	−0.0770449	−	0.0175039i
$731$	74.5388			0.101968
$732$	−32.6834	+	32.6834i	−0.0446495	+	0.0446495i
$733$	−652.173	−	652.173i	−0.889731	−	0.889731i	0.104766	−	0.994497i	$-0.466591\pi$
$733$	−652.173	−	652.173i	−0.889731	−	0.889731i	−0.994497	+	0.104766i	$0.966591\pi$
$734$			248.207i			0.338157i
$735$		0			0
$736$	232.664			0.316120
$737$	−161.118	+	161.118i	−0.218613	+	0.218613i
$738$	−25.1433	−	25.1433i	−0.0340696	−	0.0340696i
$739$		−	452.333i		−	0.612088i	−0.952017	−	0.306044i	$-0.900995\pi$
$739$		−	452.333i		−	0.612088i	0.952017	−	0.306044i	$-0.0990055\pi$
$740$	−202.237	−	321.145i	−0.273294	−	0.433980i
$741$	156.108			0.210672
$742$		0			0
$743$	664.894	+	664.894i	0.894877	+	0.894877i	0.994977	−	0.100100i	$-0.0319164\pi$
$743$	664.894	+	664.894i	0.894877	+	0.894877i	−0.100100	+	0.994977i	$0.531916\pi$
$744$			48.5396i			0.0652414i
$745$	150.382	−	661.916i	0.201855	−	0.888478i
$746$	152.858			0.204903
$747$	96.9191	−	96.9191i	0.129744	−	0.129744i
$748$	−350.204	−	350.204i	−0.468187	−	0.468187i
$749$		0			0
$750$	−378.494	−	299.985i	−0.504658	−	0.399980i
$751$	−225.769			−0.300625			−0.150312	−	0.988639i	$-0.548028\pi$
$751$	−225.769			−0.300625			−0.150312	+	0.988639i	$0.548028\pi$
$752$	34.9399	−	34.9399i	0.0464627	−	0.0464627i
$753$	−711.368	−	711.368i	−0.944712	−	0.944712i
$754$			84.2945i			0.111796i
$755$	−403.340	−	91.6354i	−0.534225	−	0.121371i
$756$		0			0
$757$	−445.497	+	445.497i	−0.588503	+	0.588503i	−0.937226	−	0.348723i	$-0.886615\pi$
$757$	−445.497	+	445.497i	−0.588503	+	0.588503i	0.348723	+	0.937226i	$0.386615\pi$
$758$	370.389	+	370.389i	0.488639	+	0.488639i
$759$			2252.52i			2.96775i
$760$	−218.246	+	137.438i	−0.287166	+	0.180839i
$761$	359.782			0.472775			0.236388	−	0.971659i	$-0.424036\pi$
$761$	359.782			0.472775			0.236388	+	0.971659i	$0.424036\pi$
$762$	95.6964	−	95.6964i	0.125586	−	0.125586i
$763$		0			0
$764$		−	41.9683i		−	0.0549324i
$765$	−50.5566	−	80.2821i	−0.0660871	−	0.104944i
$766$	−4.97649			−0.00649673
$767$	−210.762	+	210.762i	−0.274788	+	0.274788i
$768$	30.9093	+	30.9093i	0.0402465	+	0.0402465i
$769$			1100.57i			1.43117i	0.698527	+	0.715584i	$0.253839\pi$
$769$			1100.57i			1.43117i	−0.698527	+	0.715584i	$0.746161\pi$
$770$		0			0
$771$	−723.478			−0.938363
$772$	−70.7834	+	70.7834i	−0.0916884	+	0.0916884i
$773$	9.13968	+	9.13968i	0.0118236	+	0.0118236i	0.712994	−	0.701170i	$-0.247339\pi$
$773$	9.13968	+	9.13968i	0.0118236	+	0.0118236i	−0.701170	+	0.712994i	$0.747339\pi$
$774$			13.1076i			0.0169349i
$775$	−141.623	−	67.8533i	−0.182739	−	0.0875527i
$776$	420.534			0.541925
$777$		0			0
$778$	−725.344	−	725.344i	−0.932319	−	0.932319i
$779$			298.526i			0.383217i
$780$	83.4708	+	18.9639i	0.107014	+	0.0243126i
$781$	−1900.73			−2.43371
$782$	508.079	−	508.079i	0.649718	−	0.649718i
$783$	−387.216	−	387.216i	−0.494528	−	0.494528i
$784$		0			0
$785$	−165.941	+	104.499i	−0.211390	+	0.133120i
$786$	−559.167			−0.711408
$787$	878.847	−	878.847i	1.11671	−	1.11671i	0.124484	−	0.992222i	$-0.460273\pi$
$787$	878.847	−	878.847i	1.11671	−	1.11671i	0.992222	−	0.124484i	$-0.0397274\pi$
$788$	171.193	+	171.193i	0.217249	+	0.217249i
$789$		−	750.013i		−	0.950586i
$790$	−65.7204	−	104.362i	−0.0831904	−	0.132103i
$791$		0			0
$792$	61.5832	−	61.5832i	0.0777566	−	0.0777566i
$793$	18.7409	+	18.7409i	0.0236330	+	0.0236330i
$794$		−	181.187i		−	0.228195i
$795$	−162.038	+	713.220i	−0.203821	+	0.897133i
$796$	−614.922			−0.772515
$797$	658.639	−	658.639i	0.826398	−	0.826398i	−0.160618	−	0.987017i	$-0.551349\pi$
$797$	658.639	−	658.639i	0.826398	−	0.826398i	0.987017	+	0.160618i	$0.0513489\pi$
$798$		0			0
$799$		−	152.600i		−	0.190988i
$800$	−133.392	+	46.9754i	−0.166739	+	0.0587193i
$801$	118.979			0.148538
$802$	−700.963	+	700.963i	−0.874019	+	0.874019i
$803$	−115.618	−	115.618i	−0.143982	−	0.143982i
$804$		−	62.1075i		−	0.0772481i
$805$		0			0
$806$	27.8330			0.0345322
$807$	269.018	−	269.018i	0.333355	−	0.333355i
$808$	254.878	+	254.878i	0.315444	+	0.315444i
$809$		−	823.241i		−	1.01760i	−0.860884	−	0.508802i	$-0.830089\pi$
$809$		−	823.241i		−	1.01760i	0.860884	−	0.508802i	$-0.169911\pi$
$810$	−387.826	+	244.229i	−0.478798	+	0.301517i
$811$	1415.46			1.74533			0.872666	−	0.488318i	$-0.162390\pi$
$811$	1415.46			1.74533			0.872666	+	0.488318i	$0.162390\pi$
$812$		0			0
$813$	−119.901	−	119.901i	−0.147479	−	0.147479i
$814$		−	1075.91i		−	1.32176i
$815$	329.282	+	522.887i	0.404026	+	0.641579i
$816$	134.996			0.165436
$817$	77.8131	−	77.8131i	0.0952425	−	0.0952425i
$818$	452.456	+	452.456i	0.553124	+	0.553124i
$819$		0			0
$820$	−36.2647	+	159.621i	−0.0442252	+	0.194660i
$821$	57.6843			0.0702610			0.0351305	−	0.999383i	$-0.488815\pi$
$821$	57.6843			0.0702610			0.0351305	+	0.999383i	$0.488815\pi$
$822$	128.940	−	128.940i	0.156861	−	0.156861i
$823$	273.359	+	273.359i	0.332150	+	0.332150i	0.853403	−	0.521252i	$-0.174535\pi$
$823$	273.359	+	273.359i	0.332150	+	0.332150i	−0.521252	+	0.853403i	$0.674535\pi$
$824$			21.2427i			0.0257799i
$825$	−454.789	−	1291.42i	−0.551259	−	1.56536i
$826$		0			0
$827$	84.0099	−	84.0099i	0.101584	−	0.101584i	−0.654488	−	0.756072i	$-0.727116\pi$
$827$	84.0099	−	84.0099i	0.101584	−	0.101584i	0.756072	+	0.654488i	$0.227116\pi$
$828$	89.3455	+	89.3455i	0.107905	+	0.107905i
$829$			1016.80i			1.22654i	0.789875	+	0.613268i	$0.210146\pi$
$829$			1016.80i			1.22654i	−0.789875	+	0.613268i	$0.789854\pi$
$830$	−615.287	−	139.788i	−0.741310	−	0.168419i
$831$	−1136.44			−1.36756
$832$	17.7237	−	17.7237i	0.0213025	−	0.0213025i
$833$		0			0
$834$			469.333i			0.562749i
$835$	−1037.17	+	653.146i	−1.24212	+	0.782211i
$836$	−731.176			−0.874612
$837$	−127.854	+	127.854i	−0.152752	+	0.152752i
$838$	−248.174	−	248.174i	−0.296151	−	0.296151i
$839$			538.853i			0.642256i	0.947036	+	0.321128i	$0.104062\pi$
$839$			538.853i			0.642256i	−0.947036	+	0.321128i	$0.895938\pi$
$840$		0			0
$841$	479.081			0.569656
$842$	−238.992	+	238.992i	−0.283838	+	0.283838i
$843$	−715.935	−	715.935i	−0.849271	−	0.849271i
$844$			233.169i			0.276267i
$845$	−176.332	+	776.139i	−0.208677	+	0.918508i
$846$	26.8346			0.0317194
$847$		0			0
$848$	151.441	+	151.441i	0.178586	+	0.178586i
$849$		−	1318.74i		−	1.55329i
$850$	−188.711	+	393.875i	−0.222013	+	0.463383i
$851$	1560.95			1.83425
$852$	366.345	−	366.345i	0.429983	−	0.429983i
$853$	1067.08	+	1067.08i	1.25098	+	1.25098i	0.955283	+	0.295694i	$0.0955510\pi$
$853$	1067.08	+	1067.08i	1.25098	+	1.25098i	0.295694	+	0.955283i	$0.404449\pi$
$854$		0			0
$855$	−136.586	−	31.0312i	−0.159750	−	0.0362938i
$856$	−326.566			−0.381502
$857$	−717.100	+	717.100i	−0.836756	+	0.836756i	−0.988431	−	0.151674i	$-0.951534\pi$
$857$	−717.100	+	717.100i	−0.836756	+	0.836756i	0.151674	+	0.988431i	$0.451534\pi$
$858$	171.590	+	171.590i	0.199989	+	0.199989i
$859$			227.147i			0.264432i	0.991221	+	0.132216i	$0.0422092\pi$
$859$			227.147i			0.264432i	−0.991221	+	0.132216i	$0.957791\pi$
$860$	51.0592	−	32.1539i	0.0593712	−	0.0373883i
$861$		0			0
$862$	−130.746	+	130.746i	−0.151677	+	0.151677i
$863$	−344.431	−	344.431i	−0.399109	−	0.399109i	0.478810	−	0.877919i	$-0.341068\pi$
$863$	−344.431	−	344.431i	−0.399109	−	0.399109i	−0.877919	+	0.478810i	$0.841068\pi$
$864$			162.831i			0.188462i
$865$	−645.357	−	1024.80i	−0.746077	−	1.18474i
$866$	−913.701			−1.05508
$867$	−263.503	+	263.503i	−0.303925	+	0.303925i
$868$		0			0
$869$		−	349.636i		−	0.402343i
$870$	−81.4214	+	358.382i	−0.0935879	+	0.411934i
$871$	−35.6129			−0.0408874
$872$	−85.2417	+	85.2417i	−0.0977543	+	0.0977543i
$873$	161.489	+	161.489i	0.184982	+	0.184982i
$874$		−	1060.80i		−	1.21373i
$875$		0			0
$876$	44.5682			0.0508769
$877$	−100.877	+	100.877i	−0.115025	+	0.115025i	−0.762277	−	0.647251i	$-0.775918\pi$
$877$	−100.877	+	100.877i	−0.115025	+	0.115025i	0.647251	+	0.762277i	$0.275918\pi$
$878$	−216.958	−	216.958i	−0.247105	−	0.247105i
$879$			785.998i			0.894196i
$880$	−390.959	−	88.8225i	−0.444271	−	0.100935i
$881$	−21.6989			−0.0246299			−0.0123149	−	0.999924i	$-0.503920\pi$
$881$	−21.6989			−0.0246299			−0.0123149	+	0.999924i	$0.503920\pi$
$882$		0			0
$883$	−100.328	−	100.328i	−0.113622	−	0.113622i	0.648010	−	0.761632i	$-0.275602\pi$
$883$	−100.328	−	100.328i	−0.113622	−	0.113622i	−0.761632	+	0.648010i	$0.775602\pi$
$884$		−	77.4079i		−	0.0875655i
$885$	−1099.65	+	692.488i	−1.24254	+	0.782473i
$886$	−61.2455			−0.0691258
$887$	344.638	−	344.638i	0.388543	−	0.388543i	−0.485625	−	0.874167i	$-0.661408\pi$
$887$	344.638	−	344.638i	0.388543	−	0.388543i	0.874167	+	0.485625i	$0.161408\pi$
$888$	207.371	+	207.371i	0.233526	+	0.233526i
$889$		0			0
$890$	−291.864	−	463.470i	−0.327937	−	0.520752i
$891$	−1299.31			−1.45826
$892$	186.538	−	186.538i	0.209123	−	0.209123i
$893$	−159.303	−	159.303i	−0.178391	−	0.178391i
$894$			524.519i			0.586710i
$895$	−192.059	+	845.362i	−0.214591	+	0.944539i
$896$		0			0
$897$	−248.945	+	248.945i	−0.277530	+	0.277530i
$898$	48.2524	+	48.2524i	0.0537332	+	0.0537332i
$899$			119.501i			0.132927i
$900$	−69.2628	−	33.1847i	−0.0769587	−	0.0368719i
$901$	661.416			0.734091
$902$	−328.133	+	328.133i	−0.363783	+	0.363783i
$903$		0			0
$904$			54.3998i			0.0601768i
$905$	1156.84	+	262.823i	1.27827	+	0.290413i
$906$	319.616			0.352778
$907$	6.57168	−	6.57168i	0.00724552	−	0.00724552i	−0.703475	−	0.710720i	$-0.748369\pi$
$907$	6.57168	−	6.57168i	0.00724552	−	0.00724552i	0.710720	+	0.703475i	$0.248369\pi$
$908$	476.600	+	476.600i	0.524890	+	0.524890i
$909$			195.752i			0.215349i
$910$		0			0
$911$	−1071.38			−1.17605			−0.588027	−	0.808841i	$-0.700095\pi$
$911$	−1071.38			−1.17605			−0.588027	+	0.808841i	$0.700095\pi$
$912$	140.926	−	140.926i	0.154524	−	0.154524i
$913$	−1264.84	−	1264.84i	−1.38537	−	1.38537i
$914$			409.817i			0.448377i
$915$	61.5759	+	97.7802i	0.0672960	+	0.106864i
$916$	−763.785			−0.833827
$917$		0			0
$918$	355.581	+	355.581i	0.387343	+	0.387343i
$919$		−	1369.97i		−	1.49071i	−0.666666	−	0.745357i	$-0.732279\pi$
$919$		−	1369.97i		−	1.49071i	0.666666	−	0.745357i	$-0.267721\pi$
$920$	128.865	−	567.207i	0.140070	−	0.616529i
$921$	−0.801333			−0.000870069
$922$	−348.242	+	348.242i	−0.377703	+	0.377703i
$923$	−210.065	−	210.065i	−0.227590	−	0.227590i
$924$		0			0
$925$	−894.925	+	315.158i	−0.967486	+	0.340712i
$926$	−536.194			−0.579044
$927$	−8.15741	+	8.15741i	−0.00879979	+	0.00879979i
$928$	76.0967	+	76.0967i	0.0820007	+	0.0820007i
$929$		−	944.660i		−	1.01686i	−0.861104	−	0.508429i	$-0.830227\pi$
$929$		−	944.660i		−	1.01686i	0.861104	−	0.508429i	$-0.169773\pi$
$930$	118.333	+	26.8843i	0.127240	+	0.0289079i
$931$		0			0
$932$	472.039	−	472.039i	0.506480	−	0.506480i
$933$	−687.774	−	687.774i	−0.737164	−	0.737164i
$934$			705.188i			0.755019i
$935$	−1047.72	+	659.788i	−1.12056	+	0.705656i
$936$	13.6121			0.0145429
$937$	−649.423	+	649.423i	−0.693087	+	0.693087i	−0.962910	−	0.269823i	$-0.913035\pi$
$937$	−649.423	+	649.423i	−0.693087	+	0.693087i	0.269823	+	0.962910i	$0.413035\pi$
$938$		0			0
$939$			711.582i			0.757808i
$940$	−65.8272	−	104.531i	−0.0700289	−	0.111203i
$941$	36.1795			0.0384479			0.0192240	−	0.999815i	$-0.493880\pi$
$941$	36.1795			0.0384479			0.0192240	+	0.999815i	$0.493880\pi$
$942$	107.152	−	107.152i	0.113749	−	0.113749i
$943$	−476.058	−	476.058i	−0.504833	−	0.504833i
$944$			380.530i			0.403104i
$945$		0			0
$946$	171.061			0.180825
$947$	−1069.11	+	1069.11i	−1.12895	+	1.12895i	−0.138599	+	0.990349i	$0.544260\pi$
$947$	−1069.11	+	1069.11i	−1.12895	+	1.12895i	−0.990349	+	0.138599i	$0.955740\pi$
$948$	67.3886	+	67.3886i	0.0710850	+	0.0710850i
$949$		−	25.5558i		−	0.0269291i
$950$	214.177	+	608.178i	0.225450	+	0.640187i
$951$	−211.325			−0.222214
$952$		0			0
$953$	−152.501	−	152.501i	−0.160022	−	0.160022i	0.622555	−	0.782576i	$-0.286095\pi$
$953$	−152.501	−	152.501i	−0.160022	−	0.160022i	−0.782576	+	0.622555i	$0.786095\pi$
$954$			116.310i			0.121918i
$955$	−102.314	−	23.2448i	−0.107135	−	0.0243401i
$956$	−874.338			−0.914579
$957$	−736.724	+	736.724i	−0.769826	+	0.769826i
$958$	−374.806	−	374.806i	−0.391238	−	0.391238i
$959$		0			0
$960$	92.4727	−	58.2335i	0.0963257	−	0.0606599i
$961$	−921.542			−0.958941
$962$	118.908	−	118.908i	0.123605	−	0.123605i
$963$	−125.405	−	125.405i	−0.130223	−	0.130223i
$964$		−	7.78482i		−	0.00807554i
$965$	133.357	+	211.766i	0.138194	+	0.219446i
$966$		0			0
$967$	440.127	−	440.127i	0.455147	−	0.455147i	−0.441911	−	0.897059i	$-0.645699\pi$
$967$	440.127	−	440.127i	0.455147	−	0.455147i	0.897059	+	0.441911i	$0.145699\pi$
$968$	−561.691	−	561.691i	−0.580259	−	0.580259i
$969$		−	615.494i		−	0.635185i
$970$	232.919	−	1025.21i	0.240123	−	1.05692i
$971$	−620.316			−0.638843			−0.319421	−	0.947613i	$-0.603489\pi$
$971$	−620.316			−0.638843			−0.319421	+	0.947613i	$0.603489\pi$
$972$	−115.942	+	115.942i	−0.119281	+	0.119281i
$973$		0			0
$974$		−	555.017i		−	0.569832i
$975$	92.4630	−	192.988i	0.0948339	−	0.197936i
$976$	33.8367			0.0346687
$977$	75.5113	−	75.5113i	0.0772890	−	0.0772890i	−0.667406	−	0.744694i	$-0.732595\pi$
$977$	75.5113	−	75.5113i	0.0772890	−	0.0772890i	0.744694	+	0.667406i	$0.232595\pi$
$978$	−337.640	−	337.640i	−0.345235	−	0.345235i
$979$		−	1552.73i		−	1.58604i
$980$		0			0
$981$	−65.4674			−0.0667354
$982$	100.451	−	100.451i	0.102293	−	0.102293i
$983$	34.3933	+	34.3933i	0.0349881	+	0.0349881i	0.724384	−	0.689396i	$-0.242124\pi$
$983$	34.3933	+	34.3933i	0.0349881	+	0.0349881i	−0.689396	+	0.724384i	$0.742124\pi$
$984$		−	126.488i		−	0.128545i
$985$	512.164	−	322.529i	0.519963	−	0.327440i
$986$	332.351			0.337070
$987$		0			0
$988$	−80.8083	−	80.8083i	−0.0817897	−	0.0817897i
$989$			248.176i			0.250937i
$990$	−116.023	−	184.241i	−0.117195	−	0.186102i
$991$	726.700			0.733300			0.366650	−	0.930359i	$-0.380505\pi$
$991$	726.700			0.733300			0.366650	+	0.930359i	$0.380505\pi$
$992$	25.1262	−	25.1262i	0.0253288	−	0.0253288i
$993$	166.684	+	166.684i	0.167859	+	0.167859i
$994$		0			0
$995$	−340.584	+	1499.10i	−0.342295	+	1.50664i
$996$	487.569			0.489527
$997$	−964.210	+	964.210i	−0.967112	+	0.967112i	−0.999476	−	0.0323644i	$-0.989696\pi$
$997$	−964.210	+	964.210i	−0.967112	+	0.967112i	0.0323644	+	0.999476i	$0.489696\pi$
$998$	−394.800	−	394.800i	−0.395591	−	0.395591i
$999$			1092.43i			1.09353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.3.f.p.393.3		8
5.2	odd	4	inner	490.3.f.p.197.3		8
7.3	odd	6		70.3.l.c.23.2	✓	16
7.5	odd	6		70.3.l.c.53.3	yes	16
7.6	odd	2		490.3.f.o.393.2		8
35.3	even	12		350.3.p.e.107.2		16
35.12	even	12		70.3.l.c.67.2	yes	16
35.17	even	12		70.3.l.c.37.3	yes	16
35.19	odd	6		350.3.p.e.193.2		16
35.24	odd	6		350.3.p.e.93.3		16
35.27	even	4		490.3.f.o.197.2		8
35.33	even	12		350.3.p.e.207.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.2	✓	16	7.3	odd	6
70.3.l.c.37.3	yes	16	35.17	even	12
70.3.l.c.53.3	yes	16	7.5	odd	6
70.3.l.c.67.2	yes	16	35.12	even	12
350.3.p.e.93.3		16	35.24	odd	6
350.3.p.e.107.2		16	35.3	even	12
350.3.p.e.193.2		16	35.19	odd	6
350.3.p.e.207.3		16	35.33	even	12
490.3.f.o.197.2		8	35.27	even	4
490.3.f.o.393.2		8	7.6	odd	2
490.3.f.p.197.3		8	5.2	odd	4	inner
490.3.f.p.393.3		8	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.93183 + 1.93183i) q^{3} -2.00000i q^{4} +(-4.87575 - 1.10773i) q^{5} +3.86367 q^{6} +(-2.00000 - 2.00000i) q^{8} -1.53604i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.93183 + 1.93183i) q^{3} -2.00000i q^{4} +(-4.87575 - 1.10773i) q^{5} +3.86367 q^{6} +(-2.00000 - 2.00000i) q^{8} -1.53604i q^{9} +(-5.98348 + 3.76802i) q^{10} -20.0461 q^{11} +(3.86367 - 3.86367i) q^{12} +(-2.21546 - 2.21546i) q^{13} +(-7.27919 - 11.5591i) q^{15} -4.00000 q^{16} +(-8.73498 + 8.73498i) q^{17} +(-1.53604 - 1.53604i) q^{18} +18.2374i q^{19} +(-2.21546 + 9.75150i) q^{20} +(-20.0461 + 20.0461i) q^{22} +(-29.0830 - 29.0830i) q^{23} -7.72733i q^{24} +(22.5459 + 10.8020i) q^{25} -4.43092 q^{26} +(20.3539 - 20.3539i) q^{27} -19.0242i q^{29} +(-18.8383 - 4.27990i) q^{30} -6.28154 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-38.7257 - 38.7257i) q^{33} +17.4700i q^{34} -3.07208 q^{36} +(-26.8360 + 26.8360i) q^{37} +(18.2374 + 18.2374i) q^{38} -8.55979i q^{39} +(7.53604 + 11.9670i) q^{40} +16.3689 q^{41} +(-4.26669 - 4.26669i) q^{43} +40.0922i q^{44} +(-1.70152 + 7.48935i) q^{45} -58.1661 q^{46} +(-8.73498 + 8.73498i) q^{47} +(-7.72733 - 7.72733i) q^{48} +(33.3479 - 11.7439i) q^{50} -33.7490 q^{51} +(-4.43092 + 4.43092i) q^{52} +(-37.8602 - 37.8602i) q^{53} -40.7077i q^{54} +(97.7397 + 22.2056i) q^{55} +(-35.2316 + 35.2316i) q^{57} +(-19.0242 - 19.0242i) q^{58} -95.1326i q^{59} +(-23.1182 + 14.5584i) q^{60} -8.45917 q^{61} +(-6.28154 + 6.28154i) q^{62} +8.00000i q^{64} +(8.34789 + 13.2561i) q^{65} -77.4514 q^{66} +(8.03738 - 8.03738i) q^{67} +(17.4700 + 17.4700i) q^{68} -112.367i q^{69} +94.8180 q^{71} +(-3.07208 + 3.07208i) q^{72} +(5.76760 + 5.76760i) q^{73} +53.6720i q^{74} +(22.6872 + 64.4226i) q^{75} +36.4747 q^{76} +(-8.55979 - 8.55979i) q^{78} +17.4416i q^{79} +(19.5030 + 4.43092i) q^{80} +64.8162 q^{81} +(16.3689 - 16.3689i) q^{82} +(63.0967 + 63.0967i) q^{83} +(52.2656 - 32.9136i) q^{85} -8.53337 q^{86} +(36.7515 - 36.7515i) q^{87} +(40.0922 + 40.0922i) q^{88} +77.4582i q^{89} +(5.78784 + 9.19087i) q^{90} +(-58.1661 + 58.1661i) q^{92} +(-12.1349 - 12.1349i) q^{93} +17.4700i q^{94} +(20.2021 - 88.9209i) q^{95} -15.4547 q^{96} +(-105.134 + 105.134i) q^{97} +30.7916i 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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