LMFDB - Embedded newform 490.4.e.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.361
Dual form			490.4.e.c.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.50000 + 4.33013i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +10.0000 q^{6} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.50000 + 4.33013i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +10.0000 q^{6} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-10.0000 - 17.3205i) q^{12} +7.00000 q^{13} +25.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(25.5000 - 44.1673i) q^{17} +(2.00000 - 3.46410i) q^{18} +(-15.0000 - 25.9808i) q^{19} +20.0000 q^{20} -2.00000 q^{22} +(25.0000 + 43.3013i) q^{23} +(-20.0000 + 34.6410i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-7.00000 - 12.1244i) q^{26} -145.000 q^{27} +79.0000 q^{29} +(-25.0000 - 43.3013i) q^{30} +(106.000 - 183.597i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(2.50000 + 4.33013i) q^{33} -102.000 q^{34} -8.00000 q^{36} +(95.0000 + 164.545i) q^{37} +(-30.0000 + 51.9615i) q^{38} +(-17.5000 + 30.3109i) q^{39} +(-20.0000 - 34.6410i) q^{40} -308.000 q^{41} +422.000 q^{43} +(2.00000 + 3.46410i) q^{44} +(5.00000 - 8.66025i) q^{45} +(50.0000 - 86.6025i) q^{46} +(-60.5000 - 104.789i) q^{47} +80.0000 q^{48} +50.0000 q^{50} +(127.500 + 220.836i) q^{51} +(-14.0000 + 24.2487i) q^{52} +(-332.000 + 575.041i) q^{53} +(145.000 + 251.147i) q^{54} -5.00000 q^{55} +150.000 q^{57} +(-79.0000 - 136.832i) q^{58} +(-314.000 + 543.864i) q^{59} +(-50.0000 + 86.6025i) q^{60} +(342.000 + 592.361i) q^{61} -424.000 q^{62} +64.0000 q^{64} +(-17.5000 - 30.3109i) q^{65} +(5.00000 - 8.66025i) q^{66} +(-528.000 + 914.523i) q^{67} +(102.000 + 176.669i) q^{68} -250.000 q^{69} +744.000 q^{71} +(8.00000 + 13.8564i) q^{72} +(-363.000 + 628.734i) q^{73} +(190.000 - 329.090i) q^{74} +(-62.5000 - 108.253i) q^{75} +120.000 q^{76} +70.0000 q^{78} +(203.500 + 352.472i) q^{79} +(-40.0000 + 69.2820i) q^{80} +(335.500 - 581.103i) q^{81} +(308.000 + 533.472i) q^{82} +644.000 q^{83} -255.000 q^{85} +(-422.000 - 730.925i) q^{86} +(-197.500 + 342.080i) q^{87} +(4.00000 - 6.92820i) q^{88} +(440.000 + 762.102i) q^{89} -20.0000 q^{90} -200.000 q^{92} +(530.000 + 917.987i) q^{93} +(-121.000 + 209.578i) q^{94} +(-75.0000 + 129.904i) q^{95} +(-80.0000 - 138.564i) q^{96} -1351.00 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 5 q^{3} - 4 q^{4} - 5 q^{5} + 20 q^{6} + 16 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 5 * q^3 - 4 * q^4 - 5 * q^5 + 20 * q^6 + 16 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 5 q^{3} - 4 q^{4} - 5 q^{5} + 20 q^{6} + 16 q^{8} + 2 q^{9} - 10 q^{10} + q^{11} - 20 q^{12} + 14 q^{13} + 50 q^{15} - 16 q^{16} + 51 q^{17} + 4 q^{18} - 30 q^{19} + 40 q^{20} - 4 q^{22} + 50 q^{23} - 40 q^{24} - 25 q^{25} - 14 q^{26} - 290 q^{27} + 158 q^{29} - 50 q^{30} + 212 q^{31} - 32 q^{32} + 5 q^{33} - 204 q^{34} - 16 q^{36} + 190 q^{37} - 60 q^{38} - 35 q^{39} - 40 q^{40} - 616 q^{41} + 844 q^{43} + 4 q^{44} + 10 q^{45} + 100 q^{46} - 121 q^{47} + 160 q^{48} + 100 q^{50} + 255 q^{51} - 28 q^{52} - 664 q^{53} + 290 q^{54} - 10 q^{55} + 300 q^{57} - 158 q^{58} - 628 q^{59} - 100 q^{60} + 684 q^{61} - 848 q^{62} + 128 q^{64} - 35 q^{65} + 10 q^{66} - 1056 q^{67} + 204 q^{68} - 500 q^{69} + 1488 q^{71} + 16 q^{72} - 726 q^{73} + 380 q^{74} - 125 q^{75} + 240 q^{76} + 140 q^{78} + 407 q^{79} - 80 q^{80} + 671 q^{81} + 616 q^{82} + 1288 q^{83} - 510 q^{85} - 844 q^{86} - 395 q^{87} + 8 q^{88} + 880 q^{89} - 40 q^{90} - 400 q^{92} + 1060 q^{93} - 242 q^{94} - 150 q^{95} - 160 q^{96} - 2702 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 5 * q^3 - 4 * q^4 - 5 * q^5 + 20 * q^6 + 16 * q^8 + 2 * q^9 - 10 * q^10 + q^11 - 20 * q^12 + 14 * q^13 + 50 * q^15 - 16 * q^16 + 51 * q^17 + 4 * q^18 - 30 * q^19 + 40 * q^20 - 4 * q^22 + 50 * q^23 - 40 * q^24 - 25 * q^25 - 14 * q^26 - 290 * q^27 + 158 * q^29 - 50 * q^30 + 212 * q^31 - 32 * q^32 + 5 * q^33 - 204 * q^34 - 16 * q^36 + 190 * q^37 - 60 * q^38 - 35 * q^39 - 40 * q^40 - 616 * q^41 + 844 * q^43 + 4 * q^44 + 10 * q^45 + 100 * q^46 - 121 * q^47 + 160 * q^48 + 100 * q^50 + 255 * q^51 - 28 * q^52 - 664 * q^53 + 290 * q^54 - 10 * q^55 + 300 * q^57 - 158 * q^58 - 628 * q^59 - 100 * q^60 + 684 * q^61 - 848 * q^62 + 128 * q^64 - 35 * q^65 + 10 * q^66 - 1056 * q^67 + 204 * q^68 - 500 * q^69 + 1488 * q^71 + 16 * q^72 - 726 * q^73 + 380 * q^74 - 125 * q^75 + 240 * q^76 + 140 * q^78 + 407 * q^79 - 80 * q^80 + 671 * q^81 + 616 * q^82 + 1288 * q^83 - 510 * q^85 - 844 * q^86 - 395 * q^87 + 8 * q^88 + 880 * q^89 - 40 * q^90 - 400 * q^92 + 1060 * q^93 - 242 * q^94 - 150 * q^95 - 160 * q^96 - 2702 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	−2.50000	+	4.33013i	−0.481125	+	0.833333i	−0.999765	−	0.0216593i	$-0.993105\pi$
$3$	−2.50000	+	4.33013i	−0.481125	+	0.833333i	0.518640	+	0.854993i	$0.326438\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	10.0000			0.680414
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	1.00000	+	1.73205i	0.0370370	+	0.0641500i
$10$	−5.00000	+	8.66025i	−0.158114	+	0.273861i
$11$	0.500000	−	0.866025i	0.0137051	−	0.0237379i	−0.859092	−	0.511822i	$-0.828971\pi$
$11$	0.500000	−	0.866025i	0.0137051	−	0.0237379i	0.872797	+	0.488084i	$0.162304\pi$
$12$	−10.0000	−	17.3205i	−0.240563	−	0.416667i
$13$	7.00000			0.149342			0.0746712	−	0.997208i	$-0.476209\pi$
$13$	7.00000			0.149342			0.0746712	+	0.997208i	$0.476209\pi$
$14$		0			0
$15$	25.0000			0.430331
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	25.5000	−	44.1673i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	25.5000	−	44.1673i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	2.00000	−	3.46410i	0.0261891	−	0.0453609i
$19$	−15.0000	−	25.9808i	−0.181118	−	0.313705i	0.761144	−	0.648583i	$-0.224638\pi$
$19$	−15.0000	−	25.9808i	−0.181118	−	0.313705i	−0.942261	+	0.334878i	$0.891305\pi$
$20$	20.0000			0.223607
$21$		0			0
$22$	−2.00000			−0.0193819
$23$	25.0000	+	43.3013i	0.226646	+	0.392563i	0.956812	−	0.290707i	$-0.0938906\pi$
$23$	25.0000	+	43.3013i	0.226646	+	0.392563i	−0.730166	+	0.683270i	$0.760557\pi$
$24$	−20.0000	+	34.6410i	−0.170103	+	0.294628i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−7.00000	−	12.1244i	−0.0528005	−	0.0914531i
$27$	−145.000			−1.03353
$28$		0			0
$29$	79.0000			0.505860			0.252930	−	0.967485i	$-0.418606\pi$
$29$	79.0000			0.505860			0.252930	+	0.967485i	$0.418606\pi$
$30$	−25.0000	−	43.3013i	−0.152145	−	0.263523i
$31$	106.000	−	183.597i	0.614134	−	1.06371i	−0.376401	−	0.926457i	$-0.622839\pi$
$31$	106.000	−	183.597i	0.614134	−	1.06371i	0.990536	−	0.137255i	$-0.0438280\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	2.50000	+	4.33013i	0.0131877	+	0.0228418i
$34$	−102.000			−0.514496
$35$		0			0
$36$	−8.00000			−0.0370370
$37$	95.0000	+	164.545i	0.422106	+	0.731108i	0.996145	−	0.0877193i	$-0.0279578\pi$
$37$	95.0000	+	164.545i	0.422106	+	0.731108i	−0.574040	+	0.818827i	$0.694625\pi$
$38$	−30.0000	+	51.9615i	−0.128070	+	0.221823i
$39$	−17.5000	+	30.3109i	−0.0718524	+	0.124452i
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	−308.000			−1.17321			−0.586604	−	0.809874i	$-0.699535\pi$
$41$	−308.000			−1.17321			−0.586604	+	0.809874i	$0.699535\pi$
$42$		0			0
$43$	422.000			1.49661			0.748307	−	0.663353i	$-0.230867\pi$
$43$	422.000			1.49661			0.748307	+	0.663353i	$0.230867\pi$
$44$	2.00000	+	3.46410i	0.00685253	+	0.0118689i
$45$	5.00000	−	8.66025i	0.0165635	−	0.0286888i
$46$	50.0000	−	86.6025i	0.160263	−	0.277584i
$47$	−60.5000	−	104.789i	−0.187762	−	0.325214i	0.756742	−	0.653714i	$-0.226790\pi$
$47$	−60.5000	−	104.789i	−0.187762	−	0.325214i	−0.944504	+	0.328500i	$0.893457\pi$
$48$	80.0000			0.240563
$49$		0			0
$50$	50.0000			0.141421
$51$	127.500	+	220.836i	0.350070	+	0.606339i
$52$	−14.0000	+	24.2487i	−0.0373356	+	0.0646671i
$53$	−332.000	+	575.041i	−0.860447	+	1.49034i	0.0110504	+	0.999939i	$0.496482\pi$
$53$	−332.000	+	575.041i	−0.860447	+	1.49034i	−0.871498	+	0.490400i	$0.836851\pi$
$54$	145.000	+	251.147i	0.365407	+	0.632904i
$55$	−5.00000			−0.0122582
$56$		0			0
$57$	150.000			0.348561
$58$	−79.0000	−	136.832i	−0.178848	−	0.309775i
$59$	−314.000	+	543.864i	−0.692870	+	1.20009i	0.278024	+	0.960574i	$0.410321\pi$
$59$	−314.000	+	543.864i	−0.692870	+	1.20009i	−0.970894	+	0.239511i	$0.923013\pi$
$60$	−50.0000	+	86.6025i	−0.107583	+	0.186339i
$61$	342.000	+	592.361i	0.717846	+	1.24335i	0.961852	+	0.273572i	$0.0882052\pi$
$61$	342.000	+	592.361i	0.717846	+	1.24335i	−0.244005	+	0.969774i	$0.578461\pi$
$62$	−424.000			−0.868517
$63$		0			0
$64$	64.0000			0.125000
$65$	−17.5000	−	30.3109i	−0.0333940	−	0.0578400i
$66$	5.00000	−	8.66025i	0.00932511	−	0.0161516i
$67$	−528.000	+	914.523i	−0.962768	+	1.66756i	−0.247273	+	0.968946i	$0.579534\pi$
$67$	−528.000	+	914.523i	−0.962768	+	1.66756i	−0.715495	+	0.698617i	$0.753799\pi$
$68$	102.000	+	176.669i	0.181902	+	0.315063i
$69$	−250.000			−0.436181
$70$		0			0
$71$	744.000			1.24361			0.621807	−	0.783171i	$-0.286399\pi$
$71$	744.000			1.24361			0.621807	+	0.783171i	$0.286399\pi$
$72$	8.00000	+	13.8564i	0.0130946	+	0.0226805i
$73$	−363.000	+	628.734i	−0.581999	+	1.00805i	0.413243	+	0.910621i	$0.364396\pi$
$73$	−363.000	+	628.734i	−0.581999	+	1.00805i	−0.995242	+	0.0974313i	$0.968937\pi$
$74$	190.000	−	329.090i	0.298474	−	0.516972i
$75$	−62.5000	−	108.253i	−0.0962250	−	0.166667i
$76$	120.000			0.181118
$77$		0			0
$78$	70.0000			0.101615
$79$	203.500	+	352.472i	0.289817	+	0.501978i	0.973766	−	0.227552i	$-0.0730722\pi$
$79$	203.500	+	352.472i	0.289817	+	0.501978i	−0.683949	+	0.729530i	$0.739739\pi$
$80$	−40.0000	+	69.2820i	−0.0559017	+	0.0968246i
$81$	335.500	−	581.103i	0.460219	−	0.797124i
$82$	308.000	+	533.472i	0.414792	+	0.718440i
$83$	644.000			0.851665			0.425832	−	0.904802i	$-0.359981\pi$
$83$	644.000			0.851665			0.425832	+	0.904802i	$0.359981\pi$
$84$		0			0
$85$	−255.000			−0.325396
$86$	−422.000	−	730.925i	−0.529133	−	0.916485i
$87$	−197.500	+	342.080i	−0.243382	+	0.421550i
$88$	4.00000	−	6.92820i	0.00484547	−	0.00839260i
$89$	440.000	+	762.102i	0.524044	+	0.907671i	0.999608	+	0.0279897i	$0.00891056\pi$
$89$	440.000	+	762.102i	0.524044	+	0.907671i	−0.475564	+	0.879681i	$0.657756\pi$
$90$	−20.0000			−0.0234243
$91$		0			0
$92$	−200.000			−0.226646
$93$	530.000	+	917.987i	0.590951	+	1.02356i
$94$	−121.000	+	209.578i	−0.132768	+	0.229961i
$95$	−75.0000	+	129.904i	−0.0809983	+	0.140293i
$96$	−80.0000	−	138.564i	−0.0850517	−	0.147314i
$97$	−1351.00			−1.41416			−0.707079	−	0.707135i	$-0.749987\pi$
$97$	−1351.00			−1.41416			−0.707079	+	0.707135i	$0.749987\pi$
$98$		0			0
$99$	2.00000			0.00203038
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	−27.0000	+	46.7654i	−0.0266000	+	0.0460726i	−0.879019	−	0.476787i	$-0.841801\pi$
$101$	−27.0000	+	46.7654i	−0.0266000	+	0.0460726i	0.852419	+	0.522859i	$0.175135\pi$
$102$	255.000	−	441.673i	0.247537	−	0.428746i
$103$	513.500	+	889.408i	0.491230	+	0.850835i	0.999949	−	0.0100976i	$-0.00321423\pi$
$103$	513.500	+	889.408i	0.491230	+	0.850835i	−0.508719	+	0.860932i	$0.669881\pi$
$104$	56.0000			0.0528005
$105$		0			0
$106$	1328.00			1.21686
$107$	−157.000	−	271.932i	−0.141848	−	0.245688i	0.786344	−	0.617788i	$-0.211971\pi$
$107$	−157.000	−	271.932i	−0.141848	−	0.245688i	−0.928193	+	0.372100i	$0.878638\pi$
$108$	290.000	−	502.295i	0.258382	−	0.447531i
$109$	805.500	−	1395.17i	0.707825	−	1.22599i	−0.257838	−	0.966188i	$-0.583010\pi$
$109$	805.500	−	1395.17i	0.707825	−	1.22599i	0.965662	−	0.259800i	$-0.0836567\pi$
$110$	5.00000	+	8.66025i	0.00433392	+	0.00750657i
$111$	−950.000			−0.812342
$112$		0			0
$113$	366.000			0.304694			0.152347	−	0.988327i	$-0.451317\pi$
$113$	366.000			0.304694			0.152347	+	0.988327i	$0.451317\pi$
$114$	−150.000	−	259.808i	−0.123235	−	0.213449i
$115$	125.000	−	216.506i	0.101359	−	0.175559i
$116$	−158.000	+	273.664i	−0.126465	+	0.219044i
$117$	7.00000	+	12.1244i	0.00553120	+	0.00958032i
$118$	1256.00			0.979866
$119$		0			0
$120$	200.000			0.152145
$121$	665.000	+	1151.81i	0.499624	+	0.865375i
$122$	684.000	−	1184.72i	0.507594	−	0.879178i
$123$	770.000	−	1333.68i	0.564460	−	0.977673i
$124$	424.000	+	734.390i	0.307067	+	0.531856i
$125$	125.000			0.0894427
$126$		0			0
$127$	604.000			0.422018			0.211009	−	0.977484i	$-0.432325\pi$
$127$	604.000			0.422018			0.211009	+	0.977484i	$0.432325\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−1055.00	+	1827.31i	−0.720059	+	1.24718i
$130$	−35.0000	+	60.6218i	−0.0236131	+	0.0408991i
$131$	−1457.00	−	2523.60i	−0.971746	−	1.68311i	−0.690281	−	0.723541i	$-0.742513\pi$
$131$	−1457.00	−	2523.60i	−0.971746	−	1.68311i	−0.281464	−	0.959572i	$-0.590820\pi$
$132$	−20.0000			−0.0131877
$133$		0			0
$134$	2112.00			1.36156
$135$	362.500	+	627.868i	0.231104	+	0.400284i
$136$	204.000	−	353.338i	0.128624	−	0.222783i
$137$	−1284.00	+	2223.95i	−0.800726	+	1.38690i	0.118412	+	0.992965i	$0.462220\pi$
$137$	−1284.00	+	2223.95i	−0.800726	+	1.38690i	−0.919139	+	0.393934i	$0.871114\pi$
$138$	250.000	+	433.013i	0.154213	+	0.267105i
$139$	1274.00			0.777405			0.388702	−	0.921363i	$-0.372923\pi$
$139$	1274.00			0.777405			0.388702	+	0.921363i	$0.372923\pi$
$140$		0			0
$141$	605.000			0.361349
$142$	−744.000	−	1288.65i	−0.439684	−	0.761555i
$143$	3.50000	−	6.06218i	0.00204675	−	0.00354507i
$144$	16.0000	−	27.7128i	0.00925926	−	0.0160375i
$145$	−197.500	−	342.080i	−0.113114	−	0.195919i
$146$	1452.00			0.823071
$147$		0			0
$148$	−760.000			−0.422106
$149$	−297.000	−	514.419i	−0.163297	−	0.282838i	0.772752	−	0.634707i	$-0.218879\pi$
$149$	−297.000	−	514.419i	−0.163297	−	0.282838i	−0.936049	+	0.351870i	$0.885546\pi$
$150$	−125.000	+	216.506i	−0.0680414	+	0.117851i
$151$	763.500	−	1322.42i	0.411475	−	0.712696i	−0.583576	−	0.812058i	$-0.698347\pi$
$151$	763.500	−	1322.42i	0.411475	−	0.712696i	0.995051	+	0.0993625i	$0.0316804\pi$
$152$	−120.000	−	207.846i	−0.0640348	−	0.110911i
$153$	102.000			0.0538968
$154$		0			0
$155$	−1060.00			−0.549298
$156$	−70.0000	−	121.244i	−0.0359262	−	0.0622260i
$157$	−265.000	+	458.993i	−0.134709	+	0.233323i	−0.925486	−	0.378781i	$-0.876343\pi$
$157$	−265.000	+	458.993i	−0.134709	+	0.233323i	0.790777	+	0.612104i	$0.209677\pi$
$158$	407.000	−	704.945i	0.204932	−	0.354952i
$159$	−1660.00	−	2875.20i	−0.827966	−	1.43408i
$160$	160.000			0.0790569
$161$		0			0
$162$	−1342.00			−0.650849
$163$	1831.00	+	3171.39i	0.879847	+	1.52394i	0.851509	+	0.524341i	$0.175688\pi$
$163$	1831.00	+	3171.39i	0.879847	+	1.52394i	0.0283379	+	0.999598i	$0.490979\pi$
$164$	616.000	−	1066.94i	0.293302	−	0.508014i
$165$	12.5000	−	21.6506i	0.00589772	−	0.0102151i
$166$	−644.000	−	1115.44i	−0.301109	−	0.521536i
$167$	−315.000			−0.145961			−0.0729803	−	0.997333i	$-0.523251\pi$
$167$	−315.000			−0.145961			−0.0729803	+	0.997333i	$0.523251\pi$
$168$		0			0
$169$	−2148.00			−0.977697
$170$	255.000	+	441.673i	0.115045	+	0.199263i
$171$	30.0000	−	51.9615i	0.0134161	−	0.0232374i
$172$	−844.000	+	1461.85i	−0.374153	+	0.648053i
$173$	625.500	+	1083.40i	0.274890	+	0.476123i	0.970107	−	0.242677i	$-0.0780254\pi$
$173$	625.500	+	1083.40i	0.274890	+	0.476123i	−0.695218	+	0.718799i	$0.744692\pi$
$174$	790.000			0.344194
$175$		0			0
$176$	−16.0000			−0.00685253
$177$	−1570.00	−	2719.32i	−0.666714	−	1.15478i
$178$	880.000	−	1524.20i	0.370555	−	0.641820i
$179$	74.0000	−	128.172i	0.0308996	−	0.0535196i	−0.850162	−	0.526521i	$-0.823496\pi$
$179$	74.0000	−	128.172i	0.0308996	−	0.0535196i	0.881062	+	0.473001i	$0.156829\pi$
$180$	20.0000	+	34.6410i	0.00828173	+	0.0143444i
$181$	−1344.00			−0.551927			−0.275963	−	0.961168i	$-0.588997\pi$
$181$	−1344.00			−0.551927			−0.275963	+	0.961168i	$0.588997\pi$
$182$		0			0
$183$	−3420.00			−1.38150
$184$	200.000	+	346.410i	0.0801315	+	0.138792i
$185$	475.000	−	822.724i	0.188771	−	0.326962i
$186$	1060.00	−	1835.97i	0.417865	−	0.723764i
$187$	−25.5000	−	44.1673i	−0.00997190	−	0.0172718i
$188$	484.000			0.187762
$189$		0			0
$190$	300.000			0.114549
$191$	280.500	+	485.840i	0.106263	+	0.184053i	0.914254	−	0.405142i	$-0.132778\pi$
$191$	280.500	+	485.840i	0.106263	+	0.184053i	−0.807990	+	0.589196i	$0.799445\pi$
$192$	−160.000	+	277.128i	−0.0601407	+	0.104167i
$193$	−1508.00	+	2611.93i	−0.562426	+	0.974150i	0.434858	+	0.900499i	$0.356799\pi$
$193$	−1508.00	+	2611.93i	−0.562426	+	0.974150i	−0.997284	+	0.0736514i	$0.976535\pi$
$194$	1351.00	+	2340.00i	0.499980	+	0.865991i
$195$	175.000			0.0642667
$196$		0			0
$197$	−3232.00			−1.16889			−0.584443	−	0.811435i	$-0.698687\pi$
$197$	−3232.00			−1.16889			−0.584443	+	0.811435i	$0.698687\pi$
$198$	−2.00000	−	3.46410i	−0.000717848	−	0.00124335i
$199$	582.000	−	1008.05i	0.207321	−	0.359091i	−0.743549	−	0.668682i	$-0.766859\pi$
$199$	582.000	−	1008.05i	0.207321	−	0.359091i	0.950870	+	0.309591i	$0.100192\pi$
$200$	−100.000	+	173.205i	−0.0353553	+	0.0612372i
$201$	−2640.00	−	4572.61i	−0.926424	−	1.60461i
$202$	108.000			0.0376181
$203$		0			0
$204$	−1020.00			−0.350070
$205$	770.000	+	1333.68i	0.262337	+	0.454381i
$206$	1027.00	−	1778.82i	0.347352	−	0.601631i
$207$	−50.0000	+	86.6025i	−0.0167886	+	0.0290787i
$208$	−56.0000	−	96.9948i	−0.0186678	−	0.0323336i
$209$	−30.0000			−0.00992892
$210$		0			0
$211$	569.000			0.185647			0.0928236	−	0.995683i	$-0.470411\pi$
$211$	569.000			0.185647			0.0928236	+	0.995683i	$0.470411\pi$
$212$	−1328.00	−	2300.16i	−0.430224	−	0.745169i
$213$	−1860.00	+	3221.61i	−0.598334	+	1.03634i
$214$	−314.000	+	543.864i	−0.100302	+	0.173728i
$215$	−1055.00	−	1827.31i	−0.334653	−	0.579636i
$216$	−1160.00			−0.365407
$217$		0			0
$218$	−3222.00			−1.00102
$219$	−1815.00	−	3143.67i	−0.560029	−	0.969999i
$220$	10.0000	−	17.3205i	0.00306454	−	0.00530795i
$221$	178.500	−	309.171i	0.0543313	−	0.0941045i
$222$	950.000	+	1645.45i	0.287206	+	0.497456i
$223$	693.000			0.208102			0.104051	−	0.994572i	$-0.466820\pi$
$223$	693.000			0.208102			0.104051	+	0.994572i	$0.466820\pi$
$224$		0			0
$225$	−50.0000			−0.0148148
$226$	−366.000	−	633.931i	−0.107725	−	0.186586i
$227$	2139.50	−	3705.72i	0.625567	−	1.08351i	−0.362864	−	0.931842i	$-0.618201\pi$
$227$	2139.50	−	3705.72i	0.625567	−	1.08351i	0.988431	−	0.151671i	$-0.0484655\pi$
$228$	−300.000	+	519.615i	−0.0871403	+	0.150931i
$229$	1658.00	+	2871.74i	0.478444	+	0.828690i	0.999695	−	0.0247141i	$-0.00786756\pi$
$229$	1658.00	+	2871.74i	0.478444	+	0.828690i	−0.521250	+	0.853404i	$0.674534\pi$
$230$	−500.000			−0.143344
$231$		0			0
$232$	632.000			0.178848
$233$	−1956.00	−	3387.89i	−0.549965	−	0.952567i	−0.998276	−	0.0586897i	$-0.981308\pi$
$233$	−1956.00	−	3387.89i	−0.549965	−	0.952567i	0.448311	−	0.893877i	$-0.352026\pi$
$234$	14.0000	−	24.2487i	0.00391115	−	0.00677431i
$235$	−302.500	+	523.945i	−0.0839699	+	0.145440i
$236$	−1256.00	−	2175.46i	−0.346435	−	0.600043i
$237$	−2035.00			−0.557753
$238$		0			0
$239$	−5451.00			−1.47530			−0.737648	−	0.675185i	$-0.764064\pi$
$239$	−5451.00			−1.47530			−0.737648	+	0.675185i	$0.764064\pi$
$240$	−200.000	−	346.410i	−0.0537914	−	0.0931695i
$241$	−125.000	+	216.506i	−0.0334106	+	0.0578689i	−0.882247	−	0.470786i	$-0.843970\pi$
$241$	−125.000	+	216.506i	−0.0334106	+	0.0578689i	0.848837	+	0.528655i	$0.177304\pi$
$242$	1330.00	−	2303.63i	0.353288	−	0.611912i
$243$	−280.000	−	484.974i	−0.0739177	−	0.128029i
$244$	−2736.00			−0.717846
$245$		0			0
$246$	−3080.00			−0.798267
$247$	−105.000	−	181.865i	−0.0270485	−	0.0468494i
$248$	848.000	−	1468.78i	0.217129	−	0.376079i
$249$	−1610.00	+	2788.60i	−0.409757	+	0.709721i
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	910.000			0.228839			0.114420	−	0.993432i	$-0.463499\pi$
$251$	910.000			0.228839			0.114420	+	0.993432i	$0.463499\pi$
$252$		0			0
$253$	50.0000			0.0124248
$254$	−604.000	−	1046.16i	−0.149206	−	0.258432i
$255$	637.500	−	1104.18i	0.156556	−	0.271163i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	3247.00	+	5623.97i	0.788102	+	1.36503i	0.927128	+	0.374744i	$0.122270\pi$
$257$	3247.00	+	5623.97i	0.788102	+	1.36503i	−0.139026	+	0.990289i	$0.544397\pi$
$258$	4220.00			1.01832
$259$		0			0
$260$	140.000			0.0333940
$261$	79.0000	+	136.832i	0.0187355	+	0.0324509i
$262$	−2914.00	+	5047.20i	−0.687128	+	1.19014i
$263$	−717.000	+	1241.88i	−0.168107	+	0.291170i	−0.937754	−	0.347300i	$-0.887099\pi$
$263$	−717.000	+	1241.88i	−0.168107	+	0.291170i	0.769647	+	0.638469i	$0.220432\pi$
$264$	20.0000	+	34.6410i	0.00466256	+	0.00807578i
$265$	3320.00			0.769607
$266$		0			0
$267$	−4400.00			−1.00852
$268$	−2112.00	−	3658.09i	−0.481384	−	0.833782i
$269$	2507.00	−	4342.25i	0.568232	−	0.984207i	−0.428509	−	0.903538i	$-0.640961\pi$
$269$	2507.00	−	4342.25i	0.568232	−	0.984207i	0.996741	−	0.0806695i	$-0.0257058\pi$
$270$	725.000	−	1255.74i	0.163415	−	0.283043i
$271$	−2710.00	−	4693.86i	−0.607457	−	1.05215i	−0.991658	−	0.128897i	$-0.958856\pi$
$271$	−2710.00	−	4693.86i	−0.607457	−	1.05215i	0.384201	−	0.923249i	$-0.374477\pi$
$272$	−816.000			−0.181902
$273$		0			0
$274$	5136.00			1.13240
$275$	12.5000	+	21.6506i	0.00274101	+	0.00474757i
$276$	500.000	−	866.025i	0.109045	−	0.188872i
$277$	−1837.00	+	3181.78i	−0.398464	+	0.690161i	−0.993537	−	0.113512i	$-0.963790\pi$
$277$	−1837.00	+	3181.78i	−0.398464	+	0.690161i	0.595072	+	0.803672i	$0.297123\pi$
$278$	−1274.00	−	2206.63i	−0.274854	−	0.476061i
$279$	424.000			0.0909829
$280$		0			0
$281$	7331.00			1.55634			0.778169	−	0.628055i	$-0.216149\pi$
$281$	7331.00			1.55634			0.778169	+	0.628055i	$0.216149\pi$
$282$	−605.000	−	1047.89i	−0.127756	−	0.221280i
$283$	−135.500	+	234.693i	−0.0284616	+	0.0492970i	−0.879905	−	0.475149i	$-0.842394\pi$
$283$	−135.500	+	234.693i	−0.0284616	+	0.0492970i	0.851444	+	0.524446i	$0.175728\pi$
$284$	−1488.00	+	2577.29i	−0.310903	+	0.538500i
$285$	−375.000	−	649.519i	−0.0779406	−	0.134997i
$286$	−14.0000			−0.00289454
$287$		0			0
$288$	−64.0000			−0.0130946
$289$	1156.00	+	2002.25i	0.235294	+	0.407541i
$290$	−395.000	+	684.160i	−0.0799834	+	0.138535i
$291$	3377.50	−	5850.00i	0.680387	−	1.17846i
$292$	−1452.00	−	2514.94i	−0.291000	−	0.504026i
$293$	4305.00			0.858364			0.429182	−	0.903218i	$-0.358802\pi$
$293$	4305.00			0.858364			0.429182	+	0.903218i	$0.358802\pi$
$294$		0			0
$295$	3140.00			0.619722
$296$	760.000	+	1316.36i	0.149237	+	0.258486i
$297$	−72.5000	+	125.574i	−0.0141646	+	0.0245338i
$298$	−594.000	+	1028.84i	−0.115468	+	0.199997i
$299$	175.000	+	303.109i	0.0338479	+	0.0586262i
$300$	500.000			0.0962250
$301$		0			0
$302$	−3054.00			−0.581914
$303$	−135.000	−	233.827i	−0.0255959	−	0.0443333i
$304$	−240.000	+	415.692i	−0.0452794	+	0.0784263i
$305$	1710.00	−	2961.81i	0.321031	−	0.556041i
$306$	−102.000	−	176.669i	−0.0190554	−	0.0330049i
$307$	2639.00			0.490605			0.245302	−	0.969447i	$-0.421113\pi$
$307$	2639.00			0.490605			0.245302	+	0.969447i	$0.421113\pi$
$308$		0			0
$309$	−5135.00			−0.945372
$310$	1060.00	+	1835.97i	0.194206	+	0.336375i
$311$	4257.00	−	7373.34i	0.776181	−	1.34439i	−0.157947	−	0.987448i	$-0.550488\pi$
$311$	4257.00	−	7373.34i	0.776181	−	1.34439i	0.934128	−	0.356938i	$-0.116179\pi$
$312$	−140.000	+	242.487i	−0.0254037	+	0.0440004i
$313$	−109.500	−	189.660i	−0.0197741	−	0.0342498i	0.855969	−	0.517027i	$-0.172961\pi$
$313$	−109.500	−	189.660i	−0.0197741	−	0.0342498i	−0.875743	+	0.482777i	$0.839628\pi$
$314$	1060.00			0.190507
$315$		0			0
$316$	−1628.00			−0.289817
$317$	2013.00	+	3486.62i	0.356660	+	0.617754i	0.987401	−	0.158240i	$-0.0505820\pi$
$317$	2013.00	+	3486.62i	0.356660	+	0.617754i	−0.630740	+	0.775994i	$0.717249\pi$
$318$	−3320.00	+	5750.41i	−0.585460	+	1.01405i
$319$	39.5000	−	68.4160i	0.00693284	−	0.0120080i
$320$	−160.000	−	277.128i	−0.0279508	−	0.0484123i
$321$	1570.00			0.272987
$322$		0			0
$323$	−1530.00			−0.263565
$324$	1342.00	+	2324.41i	0.230110	+	0.398562i
$325$	−87.5000	+	151.554i	−0.0149342	+	0.0258669i
$326$	3662.00	−	6342.77i	0.622145	−	1.07759i
$327$	4027.50	+	6975.83i	0.681105	+	1.17971i
$328$	−2464.00			−0.414792
$329$		0			0
$330$	−50.0000			−0.00834063
$331$	3518.00	+	6093.35i	0.584190	+	1.01185i	0.994976	+	0.100114i	$0.0319209\pi$
$331$	3518.00	+	6093.35i	0.584190	+	1.01185i	−0.410786	+	0.911732i	$0.634746\pi$
$332$	−1288.00	+	2230.88i	−0.212916	+	0.368782i
$333$	−190.000	+	329.090i	−0.0312671	+	0.0541562i
$334$	315.000	+	545.596i	0.0516049	+	0.0893823i
$335$	5280.00			0.861126
$336$		0			0
$337$	10362.0			1.67494			0.837469	−	0.546485i	$-0.184034\pi$
$337$	10362.0			1.67494			0.837469	+	0.546485i	$0.184034\pi$
$338$	2148.00	+	3720.45i	0.345668	+	0.598715i
$339$	−915.000	+	1584.83i	−0.146596	+	0.253911i
$340$	510.000	−	883.346i	0.0813489	−	0.140900i
$341$	−106.000	−	183.597i	−0.0168335	−	0.0291565i
$342$	−120.000			−0.0189733
$343$		0			0
$344$	3376.00			0.529133
$345$	625.000	+	1082.53i	0.0975330	+	0.168932i
$346$	1251.00	−	2166.80i	0.194376	−	0.336670i
$347$	4211.00	−	7293.67i	0.651465	−	1.12837i	−0.331303	−	0.943525i	$-0.607488\pi$
$347$	4211.00	−	7293.67i	0.651465	−	1.12837i	0.982768	−	0.184846i	$-0.0591786\pi$
$348$	−790.000	−	1368.32i	−0.121691	−	0.210775i
$349$	−7350.00			−1.12733			−0.563663	−	0.826005i	$-0.690608\pi$
$349$	−7350.00			−1.12733			−0.563663	+	0.826005i	$0.690608\pi$
$350$		0			0
$351$	−1015.00			−0.154350
$352$	16.0000	+	27.7128i	0.00242274	+	0.00419630i
$353$	−1528.50	+	2647.44i	−0.230464	+	0.399176i	−0.957945	−	0.286953i	$-0.907358\pi$
$353$	−1528.50	+	2647.44i	−0.230464	+	0.399176i	0.727481	+	0.686128i	$0.240691\pi$
$354$	−3140.00	+	5438.64i	−0.471438	+	0.816555i
$355$	−1860.00	−	3221.61i	−0.278080	−	0.481649i
$356$	−3520.00			−0.524044
$357$		0			0
$358$	−296.000			−0.0436986
$359$	−4196.00	−	7267.69i	−0.616870	−	1.06845i	−0.990053	−	0.140693i	$-0.955067\pi$
$359$	−4196.00	−	7267.69i	−0.616870	−	1.06845i	0.373183	−	0.927758i	$-0.378266\pi$
$360$	40.0000	−	69.2820i	0.00585607	−	0.0101430i
$361$	2979.50	−	5160.65i	0.434393	−	0.752390i
$362$	1344.00	+	2327.88i	0.195136	+	0.337985i
$363$	−6650.00			−0.961527
$364$		0			0
$365$	3630.00			0.520556
$366$	3420.00	+	5923.61i	0.488432	+	0.845990i
$367$	−4188.50	+	7254.69i	−0.595744	+	1.03186i	0.397698	+	0.917516i	$0.369809\pi$
$367$	−4188.50	+	7254.69i	−0.595744	+	1.03186i	−0.993441	+	0.114342i	$0.963524\pi$
$368$	400.000	−	692.820i	0.0566615	−	0.0981406i
$369$	−308.000	−	533.472i	−0.0434521	−	0.0752613i
$370$	−1900.00			−0.266963
$371$		0			0
$372$	−4240.00			−0.590951
$373$	984.000	+	1704.34i	0.136594	+	0.236588i	0.926205	−	0.377020i	$-0.123051\pi$
$373$	984.000	+	1704.34i	0.136594	+	0.236588i	−0.789611	+	0.613607i	$0.789718\pi$
$374$	−51.0000	+	88.3346i	−0.00705120	+	0.0122130i
$375$	−312.500	+	541.266i	−0.0430331	+	0.0745356i
$376$	−484.000	−	838.313i	−0.0663840	−	0.114981i
$377$	553.000			0.0755463
$378$		0			0
$379$	1052.00			0.142579			0.0712897	−	0.997456i	$-0.477289\pi$
$379$	1052.00			0.142579			0.0712897	+	0.997456i	$0.477289\pi$
$380$	−300.000	−	519.615i	−0.0404991	−	0.0701466i
$381$	−1510.00	+	2615.40i	−0.203044	+	0.351682i
$382$	561.000	−	971.681i	0.0751394	−	0.130145i
$383$	1154.00	+	1998.79i	0.153960	+	0.266666i	0.932680	−	0.360705i	$-0.117464\pi$
$383$	1154.00	+	1998.79i	0.153960	+	0.266666i	−0.778720	+	0.627372i	$0.784131\pi$
$384$	640.000			0.0850517
$385$		0			0
$386$	6032.00			0.795390
$387$	422.000	+	730.925i	0.0554301	+	0.0960078i
$388$	2702.00	−	4680.00i	0.353539	−	0.612348i
$389$	−1140.50	+	1975.40i	−0.148652	+	0.257473i	−0.930730	−	0.365708i	$-0.880827\pi$
$389$	−1140.50	+	1975.40i	−0.148652	+	0.257473i	0.782077	+	0.623181i	$0.214160\pi$
$390$	−175.000	−	303.109i	−0.0227217	−	0.0393552i
$391$	2550.00			0.329819
$392$		0			0
$393$	14570.0			1.87013
$394$	3232.00	+	5597.99i	0.413263	+	0.715793i
$395$	1017.50	−	1762.36i	0.129610	−	0.224491i
$396$	−4.00000	+	6.92820i	−0.000507595	+	0.000879180i
$397$	7317.50	+	12674.3i	0.925075	+	1.60228i	0.791440	+	0.611246i	$0.209332\pi$
$397$	7317.50	+	12674.3i	0.925075	+	1.60228i	0.133635	+	0.991031i	$0.457335\pi$
$398$	−2328.00			−0.293196
$399$		0			0
$400$	400.000			0.0500000
$401$	−2820.50	−	4885.25i	−0.351245	−	0.608373i	0.635223	−	0.772329i	$-0.280908\pi$
$401$	−2820.50	−	4885.25i	−0.351245	−	0.608373i	−0.986468	+	0.163955i	$0.947575\pi$
$402$	−5280.00	+	9145.23i	−0.655081	+	1.13463i
$403$	742.000	−	1285.18i	0.0917163	−	0.158857i
$404$	−108.000	−	187.061i	−0.0133000	−	0.0230363i
$405$	−3355.00			−0.411633
$406$		0			0
$407$	190.000			0.0231399
$408$	1020.00	+	1766.69i	0.123768	+	0.214373i
$409$	−3205.00	+	5551.22i	−0.387474	+	0.671125i	−0.992109	−	0.125378i	$-0.959986\pi$
$409$	−3205.00	+	5551.22i	−0.387474	+	0.671125i	0.604635	+	0.796503i	$0.293319\pi$
$410$	1540.00	−	2667.36i	0.185500	−	0.321296i
$411$	−6420.00	−	11119.8i	−0.770499	−	1.33454i
$412$	−4108.00			−0.491230
$413$		0			0
$414$	200.000			0.0237427
$415$	−1610.00	−	2788.60i	−0.190438	−	0.329848i
$416$	−112.000	+	193.990i	−0.0132001	+	0.0228633i
$417$	−3185.00	+	5516.58i	−0.374029	+	0.647837i
$418$	30.0000	+	51.9615i	0.00351040	+	0.00608019i
$419$	4816.00			0.561520			0.280760	−	0.959778i	$-0.409413\pi$
$419$	4816.00			0.561520			0.280760	+	0.959778i	$0.409413\pi$
$420$		0			0
$421$	15325.0			1.77410			0.887048	−	0.461676i	$-0.152752\pi$
$421$	15325.0			1.77410			0.887048	+	0.461676i	$0.152752\pi$
$422$	−569.000	−	985.537i	−0.0656362	−	0.113685i
$423$	121.000	−	209.578i	0.0139083	−	0.0240899i
$424$	−2656.00	+	4600.33i	−0.304214	+	0.526914i
$425$	637.500	+	1104.18i	0.0727607	+	0.126025i
$426$	7440.00			0.846172
$427$		0			0
$428$	1256.00			0.141848
$429$	17.5000	+	30.3109i	0.00196948	+	0.00341124i
$430$	−2110.00	+	3654.63i	−0.236635	+	0.409865i
$431$	−937.500	+	1623.80i	−0.104774	+	0.181475i	−0.913646	−	0.406511i	$-0.866745\pi$
$431$	−937.500	+	1623.80i	−0.104774	+	0.181475i	0.808872	+	0.587985i	$0.200079\pi$
$432$	1160.00	+	2009.18i	0.129191	+	0.223765i
$433$	−13874.0			−1.53982			−0.769910	−	0.638153i	$-0.779699\pi$
$433$	−13874.0			−1.53982			−0.769910	+	0.638153i	$0.779699\pi$
$434$		0			0
$435$	1975.00			0.217687
$436$	3222.00	+	5580.67i	0.353912	+	0.612994i
$437$	750.000	−	1299.04i	0.0820992	−	0.142200i
$438$	−3630.00	+	6287.34i	−0.396000	+	0.685893i
$439$	1721.00	+	2980.86i	0.187104	+	0.324074i	0.944284	−	0.329133i	$-0.106756\pi$
$439$	1721.00	+	2980.86i	0.187104	+	0.324074i	−0.757179	+	0.653207i	$0.773423\pi$
$440$	−40.0000			−0.00433392
$441$		0			0
$442$	−714.000			−0.0768360
$443$	−8375.00	−	14505.9i	−0.898213	−	1.55575i	−0.829777	−	0.558095i	$-0.811533\pi$
$443$	−8375.00	−	14505.9i	−0.898213	−	1.55575i	−0.0684355	−	0.997656i	$-0.521801\pi$
$444$	1900.00	−	3290.90i	0.203086	−	0.351755i
$445$	2200.00	−	3810.51i	0.234360	−	0.405923i
$446$	−693.000	−	1200.31i	−0.0735751	−	0.127436i
$447$	2970.00			0.314264
$448$		0			0
$449$	695.000			0.0730492			0.0365246	−	0.999333i	$-0.488371\pi$
$449$	695.000			0.0730492			0.0365246	+	0.999333i	$0.488371\pi$
$450$	50.0000	+	86.6025i	0.00523783	+	0.00907218i
$451$	−154.000	+	266.736i	−0.0160789	+	0.0278494i
$452$	−732.000	+	1267.86i	−0.0761734	+	0.131936i
$453$	3817.50	+	6612.10i	0.395942	+	0.685792i
$454$	−8558.00			−0.884685
$455$		0			0
$456$	1200.00			0.123235
$457$	−2880.00	−	4988.31i	−0.294794	−	0.510598i	0.680143	−	0.733079i	$-0.261918\pi$
$457$	−2880.00	−	4988.31i	−0.294794	−	0.510598i	−0.974937	+	0.222482i	$0.928584\pi$
$458$	3316.00	−	5743.48i	0.338311	−	0.585972i
$459$	−3697.50	+	6404.26i	−0.376001	+	0.651253i
$460$	500.000	+	866.025i	0.0506796	+	0.0877797i
$461$	13440.0			1.35784			0.678919	−	0.734213i	$-0.262449\pi$
$461$	13440.0			1.35784			0.678919	+	0.734213i	$0.262449\pi$
$462$		0			0
$463$	−7348.00			−0.737561			−0.368780	−	0.929517i	$-0.620225\pi$
$463$	−7348.00			−0.737561			−0.368780	+	0.929517i	$0.620225\pi$
$464$	−632.000	−	1094.66i	−0.0632325	−	0.109522i
$465$	2650.00	−	4589.93i	0.264281	−	0.457749i
$466$	−3912.00	+	6775.78i	−0.388884	+	0.673567i
$467$	8962.50	+	15523.5i	0.888084	+	1.53821i	0.842138	+	0.539262i	$0.181297\pi$
$467$	8962.50	+	15523.5i	0.888084	+	1.53821i	0.0459455	+	0.998944i	$0.485370\pi$
$468$	−56.0000			−0.00553120
$469$		0			0
$470$	1210.00			0.118751
$471$	−1325.00	−	2294.97i	−0.129624	−	0.224515i
$472$	−2512.00	+	4350.91i	−0.244966	+	0.424294i
$473$	211.000	−	365.463i	0.0205112	−	0.0355264i
$474$	2035.00	+	3524.72i	0.197195	+	0.341553i
$475$	750.000			0.0724471
$476$		0			0
$477$	−1328.00			−0.127474
$478$	5451.00	+	9441.41i	0.521596	+	0.903431i
$479$	−6173.00	+	10691.9i	−0.588834	+	1.01989i	0.405551	+	0.914072i	$0.367080\pi$
$479$	−6173.00	+	10691.9i	−0.588834	+	1.01989i	−0.994385	+	0.105818i	$0.966254\pi$
$480$	−400.000	+	692.820i	−0.0380363	+	0.0658808i
$481$	665.000	+	1151.81i	0.0630382	+	0.109185i
$482$	500.000			0.0472497
$483$		0			0
$484$	−5320.00			−0.499624
$485$	3377.50	+	5850.00i	0.316215	+	0.547701i
$486$	−560.000	+	969.948i	−0.0522677	+	0.0905304i
$487$	−7507.00	+	13002.5i	−0.698511	+	1.20986i	0.270472	+	0.962728i	$0.412820\pi$
$487$	−7507.00	+	13002.5i	−0.698511	+	1.20986i	−0.968983	+	0.247128i	$0.920513\pi$
$488$	2736.00	+	4738.89i	0.253797	+	0.439589i
$489$	−18310.0			−1.69327
$490$		0			0
$491$	−4723.00			−0.434106			−0.217053	−	0.976160i	$-0.569644\pi$
$491$	−4723.00			−0.434106			−0.217053	+	0.976160i	$0.569644\pi$
$492$	3080.00	+	5334.72i	0.282230	+	0.488837i
$493$	2014.50	−	3489.22i	0.184034	−	0.318755i
$494$	−210.000	+	363.731i	−0.0191262	+	0.0331276i
$495$	−5.00000	−	8.66025i	−0.000454007	−	0.000786363i
$496$	−3392.00			−0.307067
$497$		0			0
$498$	6440.00			0.579485
$499$	−5613.50	−	9722.87i	−0.503597	−	0.872255i	−0.999991	−	0.00415815i	$-0.998676\pi$
$499$	−5613.50	−	9722.87i	−0.503597	−	0.872255i	0.496395	−	0.868097i	$-0.334657\pi$
$500$	−250.000	+	433.013i	−0.0223607	+	0.0387298i
$501$	787.500	−	1363.99i	0.0702254	−	0.121634i
$502$	−910.000	−	1576.17i	−0.0809069	−	0.140135i
$503$	−4557.00			−0.403949			−0.201975	−	0.979391i	$-0.564736\pi$
$503$	−4557.00			−0.403949			−0.201975	+	0.979391i	$0.564736\pi$
$504$		0			0
$505$	270.000			0.0237918
$506$	−50.0000	−	86.6025i	−0.00439283	−	0.00760860i
$507$	5370.00	−	9301.11i	0.470395	−	0.814747i
$508$	−1208.00	+	2092.32i	−0.105505	+	0.182739i
$509$	7055.00	+	12219.6i	0.614356	+	1.06410i	0.990497	+	0.137534i	$0.0439176\pi$
$509$	7055.00	+	12219.6i	0.614356	+	1.06410i	−0.376141	+	0.926563i	$0.622749\pi$
$510$	−2550.00			−0.221404
$511$		0			0
$512$	512.000			0.0441942
$513$	2175.00	+	3767.21i	0.187190	+	0.324223i
$514$	6494.00	−	11247.9i	0.557272	−	0.965224i
$515$	2567.50	−	4447.04i	0.219685	−	0.380505i
$516$	−4220.00	−	7309.25i	−0.360029	−	0.623589i
$517$	−121.000			−0.0102932
$518$		0			0
$519$	−6255.00			−0.529025
$520$	−140.000	−	242.487i	−0.0118066	−	0.0204495i
$521$	−951.000	+	1647.18i	−0.0799694	+	0.138511i	−0.903237	−	0.429143i	$-0.858816\pi$
$521$	−951.000	+	1647.18i	−0.0799694	+	0.138511i	0.823267	+	0.567654i	$0.192149\pi$
$522$	158.000	−	273.664i	0.0132480	−	0.0229463i
$523$	986.000	+	1707.80i	0.0824374	+	0.142786i	0.904296	−	0.426905i	$-0.140396\pi$
$523$	986.000	+	1707.80i	0.0824374	+	0.142786i	−0.821859	+	0.569691i	$0.807063\pi$
$524$	11656.0			0.971746
$525$		0			0
$526$	2868.00			0.237739
$527$	−5406.00	−	9363.47i	−0.446848	−	0.773964i
$528$	40.0000	−	69.2820i	0.00329693	−	0.00571044i
$529$	4833.50	−	8371.87i	0.397263	−	0.688080i
$530$	−3320.00	−	5750.41i	−0.272097	−	0.471286i
$531$	−1256.00			−0.102647
$532$		0			0
$533$	−2156.00			−0.175210
$534$	4400.00	+	7621.02i	0.356567	+	0.617592i
$535$	−785.000	+	1359.66i	−0.0634365	+	0.109875i
$536$	−4224.00	+	7316.18i	−0.340390	+	0.589573i
$537$	370.000	+	640.859i	0.0297331	+	0.0514993i
$538$	−10028.0			−0.803602
$539$		0			0
$540$	−2900.00			−0.231104
$541$	12516.5	+	21679.2i	0.994688	+	1.72285i	0.586487	+	0.809959i	$0.300511\pi$
$541$	12516.5	+	21679.2i	0.994688	+	1.72285i	0.408202	+	0.912892i	$0.366156\pi$
$542$	−5420.00	+	9387.72i	−0.429537	+	0.743980i
$543$	3360.00	−	5819.69i	0.265546	−	0.459939i
$544$	816.000	+	1413.35i	0.0643120	+	0.111392i
$545$	−8055.00			−0.633098
$546$		0			0
$547$	−236.000			−0.0184472			−0.00922361	−	0.999957i	$-0.502936\pi$
$547$	−236.000			−0.0184472			−0.00922361	+	0.999957i	$0.502936\pi$
$548$	−5136.00	−	8895.81i	−0.400363	−	0.693449i
$549$	−684.000	+	1184.72i	−0.0531738	+	0.0920997i
$550$	25.0000	−	43.3013i	0.00193819	−	0.00335704i
$551$	−1185.00	−	2052.48i	−0.0916201	−	0.158691i
$552$	−2000.00			−0.154213
$553$		0			0
$554$	7348.00			0.563514
$555$	2375.00	+	4113.62i	0.181645	+	0.314619i
$556$	−2548.00	+	4413.27i	−0.194351	+	0.336626i
$557$	−7752.00	+	13426.9i	−0.589700	+	1.02139i	0.404572	+	0.914506i	$0.367421\pi$
$557$	−7752.00	+	13426.9i	−0.589700	+	1.02139i	−0.994272	+	0.106884i	$0.965913\pi$
$558$	−424.000	−	734.390i	−0.0321673	−	0.0557154i
$559$	2954.00			0.223508
$560$		0			0
$561$	255.000			0.0191909
$562$	−7331.00	−	12697.7i	−0.550248	−	0.953058i
$563$	4474.00	−	7749.20i	0.334914	−	0.580088i	−0.648554	−	0.761168i	$-0.724626\pi$
$563$	4474.00	−	7749.20i	0.334914	−	0.580088i	0.983468	+	0.181080i	$0.0579594\pi$
$564$	−1210.00	+	2095.78i	−0.0903372	+	0.156469i
$565$	−915.000	−	1584.83i	−0.0681316	−	0.118007i
$566$	542.000			0.0402508
$567$		0			0
$568$	5952.00			0.439684
$569$	−6933.00	−	12008.3i	−0.510802	−	0.884735i	−0.999922	−	0.0125186i	$-0.996015\pi$
$569$	−6933.00	−	12008.3i	−0.510802	−	0.884735i	0.489119	−	0.872217i	$-0.337318\pi$
$570$	−750.000	+	1299.04i	−0.0551124	+	0.0954574i
$571$	−4994.00	+	8649.86i	−0.366011	+	0.633950i	−0.988938	−	0.148330i	$-0.952610\pi$
$571$	−4994.00	+	8649.86i	−0.366011	+	0.633950i	0.622927	+	0.782280i	$0.285943\pi$
$572$	14.0000	+	24.2487i	0.00102337	+	0.00177253i
$573$	−2805.00			−0.204504
$574$		0			0
$575$	−1250.00			−0.0906584
$576$	64.0000	+	110.851i	0.00462963	+	0.00801875i
$577$	1292.50	−	2238.68i	0.0932539	−	0.161520i	−0.815625	−	0.578581i	$-0.803607\pi$
$577$	1292.50	−	2238.68i	0.0932539	−	0.161520i	0.908879	+	0.417061i	$0.136940\pi$
$578$	2312.00	−	4004.50i	0.166378	−	0.288175i
$579$	−7540.00	−	13059.7i	−0.541195	−	0.937377i
$580$	1580.00			0.113114
$581$		0			0
$582$	−13510.0			−0.962212
$583$	332.000	+	575.041i	0.0235850	+	0.0408504i
$584$	−2904.00	+	5029.88i	−0.205768	+	0.356400i
$585$	35.0000	−	60.6218i	0.00247363	−	0.00428445i
$586$	−4305.00	−	7456.48i	−0.303478	−	0.525639i
$587$	19656.0			1.38210			0.691048	−	0.722809i	$-0.257149\pi$
$587$	19656.0			1.38210			0.691048	+	0.722809i	$0.257149\pi$
$588$		0			0
$589$	−6360.00			−0.444922
$590$	−3140.00	−	5438.64i	−0.219105	−	0.379500i
$591$	8080.00	−	13995.0i	0.562380	−	0.974071i
$592$	1520.00	−	2632.72i	0.105526	−	0.182777i
$593$	−10623.5	−	18400.4i	−0.735674	−	1.27423i	−0.954427	−	0.298445i	$-0.903532\pi$
$593$	−10623.5	−	18400.4i	−0.735674	−	1.27423i	0.218753	−	0.975780i	$-0.429801\pi$
$594$	290.000			0.0200317
$595$		0			0
$596$	2376.00			0.163297
$597$	2910.00	+	5040.27i	0.199495	+	0.345535i
$598$	350.000	−	606.218i	0.0239341	−	0.0414550i
$599$	4662.50	−	8075.69i	0.318038	−	0.550857i	−0.662041	−	0.749468i	$-0.730309\pi$
$599$	4662.50	−	8075.69i	0.318038	−	0.550857i	0.980079	+	0.198610i	$0.0636428\pi$
$600$	−500.000	−	866.025i	−0.0340207	−	0.0589256i
$601$	5362.00			0.363928			0.181964	−	0.983305i	$-0.441755\pi$
$601$	5362.00			0.363928			0.181964	+	0.983305i	$0.441755\pi$
$602$		0			0
$603$	−2112.00			−0.142632
$604$	3054.00	+	5289.68i	0.205738	+	0.356348i
$605$	3325.00	−	5759.07i	0.223439	−	0.387007i
$606$	−270.000	+	467.654i	−0.0180990	+	0.0313484i
$607$	−7865.50	−	13623.4i	−0.525949	−	0.910970i	−0.999543	−	0.0302267i	$-0.990377\pi$
$607$	−7865.50	−	13623.4i	−0.525949	−	0.910970i	0.473594	−	0.880743i	$-0.342956\pi$
$608$	960.000			0.0640348
$609$		0			0
$610$	−6840.00			−0.454006
$611$	−423.500	−	733.524i	−0.0280409	−	0.0485682i
$612$	−204.000	+	353.338i	−0.0134742	+	0.0233380i
$613$	6871.00	−	11900.9i	0.452720	−	0.784133i	−0.545834	−	0.837893i	$-0.683787\pi$
$613$	6871.00	−	11900.9i	0.452720	−	0.784133i	0.998554	+	0.0537599i	$0.0171206\pi$
$614$	−2639.00	−	4570.88i	−0.173455	−	0.300433i
$615$	−7700.00			−0.504868
$616$		0			0
$617$	18286.0			1.19314			0.596569	−	0.802561i	$-0.296530\pi$
$617$	18286.0			1.19314			0.596569	+	0.802561i	$0.296530\pi$
$618$	5135.00	+	8894.08i	0.334239	+	0.578920i
$619$	−12361.0	+	21409.9i	−0.802634	+	1.39020i	0.115243	+	0.993337i	$0.463235\pi$
$619$	−12361.0	+	21409.9i	−0.802634	+	1.39020i	−0.917877	+	0.396866i	$0.870098\pi$
$620$	2120.00	−	3671.95i	0.137325	−	0.237853i
$621$	−3625.00	−	6278.68i	−0.234245	−	0.405725i
$622$	−17028.0			−1.09769
$623$		0			0
$624$	560.000			0.0359262
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−219.000	+	379.319i	−0.0139824	+	0.0242183i
$627$	75.0000	−	129.904i	0.00477705	−	0.00827410i
$628$	−1060.00	−	1835.97i	−0.0673545	−	0.116661i
$629$	9690.00			0.614254
$630$		0			0
$631$	−22181.0			−1.39938			−0.699692	−	0.714444i	$-0.746680\pi$
$631$	−22181.0			−1.39938			−0.699692	+	0.714444i	$0.746680\pi$
$632$	1628.00	+	2819.78i	0.102466	+	0.177476i
$633$	−1422.50	+	2463.84i	−0.0893196	+	0.154706i
$634$	4026.00	−	6973.24i	0.252197	−	0.436818i
$635$	−1510.00	−	2615.40i	−0.0943662	−	0.163447i
$636$	13280.0			0.827966
$637$		0			0
$638$	−158.000			−0.00980451
$639$	744.000	+	1288.65i	0.0460598	+	0.0797778i
$640$	−320.000	+	554.256i	−0.0197642	+	0.0342327i
$641$	11799.0	−	20436.5i	0.727040	−	1.25927i	−0.231089	−	0.972933i	$-0.574229\pi$
$641$	11799.0	−	20436.5i	0.727040	−	1.25927i	0.958129	−	0.286337i	$-0.0924378\pi$
$642$	−1570.00	−	2719.32i	−0.0965155	−	0.167170i
$643$	13349.0			0.818714			0.409357	−	0.912374i	$-0.365753\pi$
$643$	13349.0			0.818714			0.409357	+	0.912374i	$0.365753\pi$
$644$		0			0
$645$	10550.0			0.644040
$646$	1530.00	+	2650.04i	0.0931843	+	0.161400i
$647$	12244.0	−	21207.2i	0.743990	−	1.28863i	−0.206676	−	0.978410i	$-0.566264\pi$
$647$	12244.0	−	21207.2i	0.743990	−	1.28863i	0.950665	−	0.310218i	$-0.100402\pi$
$648$	2684.00	−	4648.82i	0.162712	−	0.281826i
$649$	314.000	+	543.864i	0.0189916	+	0.0328945i
$650$	350.000			0.0211202
$651$		0			0
$652$	−14648.0			−0.879847
$653$	−10811.0	−	18725.2i	−0.647882	−	1.12217i	−0.983628	−	0.180212i	$-0.942322\pi$
$653$	−10811.0	−	18725.2i	−0.647882	−	1.12217i	0.335745	−	0.941953i	$-0.391012\pi$
$654$	8055.00	−	13951.7i	0.481614	−	0.834180i
$655$	−7285.00	+	12618.0i	−0.434578	+	0.752711i
$656$	2464.00	+	4267.77i	0.146651	+	0.254007i
$657$	−1452.00			−0.0862221
$658$		0			0
$659$	−2973.00			−0.175738			−0.0878692	−	0.996132i	$-0.528006\pi$
$659$	−2973.00			−0.175738			−0.0878692	+	0.996132i	$0.528006\pi$
$660$	50.0000	+	86.6025i	0.00294886	+	0.00510757i
$661$	−9456.00	+	16378.3i	−0.556423	+	0.963753i	0.441368	+	0.897326i	$0.354493\pi$
$661$	−9456.00	+	16378.3i	−0.556423	+	0.963753i	−0.997791	+	0.0664272i	$0.978840\pi$
$662$	7036.00	−	12186.7i	0.413084	−	0.715483i
$663$	892.500	+	1545.86i	0.0522803	+	0.0905521i
$664$	5152.00			0.301109
$665$		0			0
$666$	760.000			0.0442183
$667$	1975.00	+	3420.80i	0.114651	+	0.198582i
$668$	630.000	−	1091.19i	0.0364902	−	0.0632028i
$669$	−1732.50	+	3000.78i	−0.100123	+	0.173418i
$670$	−5280.00	−	9145.23i	−0.304454	−	0.527330i
$671$	684.000			0.0393525
$672$		0			0
$673$	688.000			0.0394063			0.0197032	−	0.999806i	$-0.493728\pi$
$673$	688.000			0.0394063			0.0197032	+	0.999806i	$0.493728\pi$
$674$	−10362.0	−	17947.5i	−0.592180	−	1.02569i
$675$	1812.50	−	3139.34i	0.103353	−	0.179012i
$676$	4296.00	−	7440.89i	0.244424	−	0.423355i
$677$	−6395.50	−	11077.3i	−0.363071	−	0.628857i	0.625394	−	0.780309i	$-0.284938\pi$
$677$	−6395.50	−	11077.3i	−0.363071	−	0.628857i	−0.988465	+	0.151452i	$0.951605\pi$
$678$	3660.00			0.207318
$679$		0			0
$680$	−2040.00			−0.115045
$681$	10697.5	+	18528.6i	0.601952	+	1.04261i
$682$	−212.000	+	367.195i	−0.0119031	+	0.0206167i
$683$	3826.00	−	6626.83i	0.214345	−	0.371257i	−0.738725	−	0.674007i	$-0.764572\pi$
$683$	3826.00	−	6626.83i	0.214345	−	0.371257i	0.953070	+	0.302751i	$0.0979049\pi$
$684$	120.000	+	207.846i	0.00670806	+	0.0116187i
$685$	12840.0			0.716192
$686$		0			0
$687$	−16580.0			−0.920766
$688$	−3376.00	−	5847.40i	−0.187077	−	0.324026i
$689$	−2324.00	+	4025.29i	−0.128501	+	0.222571i
$690$	1250.00	−	2165.06i	0.0689662	−	0.119453i
$691$	1266.00	+	2192.78i	0.0696974	+	0.120719i	0.898768	−	0.438424i	$-0.144463\pi$
$691$	1266.00	+	2192.78i	0.0696974	+	0.120719i	−0.829071	+	0.559144i	$0.811130\pi$
$692$	−5004.00			−0.274890
$693$		0			0
$694$	−16844.0			−0.921311
$695$	−3185.00	−	5516.58i	−0.173833	−	0.301088i
$696$	−1580.00	+	2736.64i	−0.0860485	+	0.149040i
$697$	−7854.00	+	13603.5i	−0.426817	+	0.739269i
$698$	7350.00	+	12730.6i	0.398570	+	0.690343i
$699$	19560.0			1.05841
$700$		0			0
$701$	−2133.00			−0.114925			−0.0574624	−	0.998348i	$-0.518301\pi$
$701$	−2133.00			−0.114925			−0.0574624	+	0.998348i	$0.518301\pi$
$702$	1015.00	+	1758.03i	0.0545708	+	0.0945194i
$703$	2850.00	−	4936.34i	0.152902	−	0.264833i
$704$	32.0000	−	55.4256i	0.00171313	−	0.00296723i
$705$	−1512.50	−	2619.73i	−0.0808001	−	0.139950i
$706$	6114.00			0.325926
$707$		0			0
$708$	12560.0			0.666714
$709$	9576.50	+	16587.0i	0.507268	+	0.878614i	0.999965	+	0.00841279i	$0.00267790\pi$
$709$	9576.50	+	16587.0i	0.507268	+	0.878614i	−0.492697	+	0.870201i	$0.663989\pi$
$710$	−3720.00	+	6443.23i	−0.196633	+	0.340578i
$711$	−407.000	+	704.945i	−0.0214679	+	0.0371835i
$712$	3520.00	+	6096.82i	0.185277	+	0.320910i
$713$	10600.0			0.556765
$714$		0			0
$715$	−35.0000			−0.00183067
$716$	296.000	+	512.687i	0.0154498	+	0.0267598i
$717$	13627.5	−	23603.5i	0.709802	−	1.22941i
$718$	−8392.00	+	14535.4i	−0.436193	+	0.755509i
$719$	10667.0	+	18475.8i	0.553285	+	0.958318i	0.998035	+	0.0626630i	$0.0199593\pi$
$719$	10667.0	+	18475.8i	0.553285	+	0.958318i	−0.444750	+	0.895655i	$0.646707\pi$
$720$	−160.000			−0.00828173
$721$		0			0
$722$	−11918.0			−0.614324
$723$	−625.000	−	1082.53i	−0.0321494	−	0.0556844i
$724$	2688.00	−	4655.75i	0.137982	−	0.238991i
$725$	−987.500	+	1710.40i	−0.0505860	+	0.0876175i
$726$	6650.00	+	11518.1i	0.339951	+	0.588813i
$727$	11480.0			0.585653			0.292826	−	0.956166i	$-0.405404\pi$
$727$	11480.0			0.585653			0.292826	+	0.956166i	$0.405404\pi$
$728$		0			0
$729$	20917.0			1.06269
$730$	−3630.00	−	6287.34i	−0.184044	−	0.318774i
$731$	10761.0	−	18638.6i	0.544473	−	0.943055i
$732$	6840.00	−	11847.2i	0.345374	−	0.598205i
$733$	−9881.50	−	17115.3i	−0.497928	−	0.862437i	0.502069	−	0.864828i	$-0.332572\pi$
$733$	−9881.50	−	17115.3i	−0.497928	−	0.862437i	−0.999997	+	0.00239041i	$0.999239\pi$
$734$	16754.0			0.842509
$735$		0			0
$736$	−1600.00			−0.0801315
$737$	528.000	+	914.523i	0.0263896	+	0.0457081i
$738$	−616.000	+	1066.94i	−0.0307253	+	0.0532178i
$739$	20076.5	−	34773.5i	0.999359	−	1.73094i	0.468666	−	0.883375i	$-0.344735\pi$
$739$	20076.5	−	34773.5i	0.999359	−	1.73094i	0.530693	−	0.847564i	$-0.321932\pi$
$740$	1900.00	+	3290.90i	0.0943857	+	0.163481i
$741$	1050.00			0.0520549
$742$		0			0
$743$	−30896.0			−1.52552			−0.762762	−	0.646679i	$-0.776157\pi$
$743$	−30896.0			−1.52552			−0.762762	+	0.646679i	$0.776157\pi$
$744$	4240.00	+	7343.90i	0.208933	+	0.361882i
$745$	−1485.00	+	2572.10i	−0.0730284	+	0.126489i
$746$	1968.00	−	3408.68i	0.0965866	−	0.167293i
$747$	644.000	+	1115.44i	0.0315431	+	0.0546343i
$748$	204.000			0.00997190
$749$		0			0
$750$	1250.00			0.0608581
$751$	−5984.50	−	10365.5i	−0.290782	−	0.503650i	0.683213	−	0.730219i	$-0.260582\pi$
$751$	−5984.50	−	10365.5i	−0.290782	−	0.503650i	−0.973995	+	0.226570i	$0.927249\pi$
$752$	−968.000	+	1676.63i	−0.0469406	+	0.0813035i
$753$	−2275.00	+	3940.42i	−0.110100	+	0.190700i
$754$	−553.000	−	957.824i	−0.0267096	−	0.0462625i
$755$	−7635.00			−0.368035
$756$		0			0
$757$	−10456.0			−0.502021			−0.251010	−	0.967984i	$-0.580763\pi$
$757$	−10456.0			−0.502021			−0.251010	+	0.967984i	$0.580763\pi$
$758$	−1052.00	−	1822.12i	−0.0504094	−	0.0873117i
$759$	−125.000	+	216.506i	−0.00597788	+	0.0103540i
$760$	−600.000	+	1039.23i	−0.0286372	+	0.0496011i
$761$	14391.0	+	24925.9i	0.685510	+	1.18734i	0.973276	+	0.229638i	$0.0737542\pi$
$761$	14391.0	+	24925.9i	0.685510	+	1.18734i	−0.287766	+	0.957701i	$0.592912\pi$
$762$	6040.00			0.287147
$763$		0			0
$764$	−2244.00			−0.106263
$765$	−255.000	−	441.673i	−0.0120517	−	0.0208741i
$766$	2308.00	−	3997.57i	0.108866	−	0.188562i
$767$	−2198.00	+	3807.05i	−0.103475	+	0.179224i
$768$	−640.000	−	1108.51i	−0.0300703	−	0.0520833i
$769$	−14630.0			−0.686048			−0.343024	−	0.939327i	$-0.611451\pi$
$769$	−14630.0			−0.686048			−0.343024	+	0.939327i	$0.611451\pi$
$770$		0			0
$771$	−32470.0			−1.51670
$772$	−6032.00	−	10447.7i	−0.281213	−	0.487075i
$773$	−12175.5	+	21088.6i	−0.566523	+	0.981247i	0.430383	+	0.902646i	$0.358378\pi$
$773$	−12175.5	+	21088.6i	−0.566523	+	0.981247i	−0.996906	+	0.0786004i	$0.974955\pi$
$774$	844.000	−	1461.85i	0.0391950	−	0.0678878i
$775$	2650.00	+	4589.93i	0.122827	+	0.212742i
$776$	−10808.0			−0.499980
$777$		0			0
$778$	4562.00			0.210226
$779$	4620.00	+	8002.07i	0.212489	+	0.368041i
$780$	−350.000	+	606.218i	−0.0160667	+	0.0278283i
$781$	372.000	−	644.323i	0.0170438	−	0.0295207i
$782$	−2550.00	−	4416.73i	−0.116608	−	0.201972i
$783$	−11455.0			−0.522820
$784$		0			0
$785$	2650.00			0.120487
$786$	−14570.0	−	25236.0i	−0.661189	−	1.14521i
$787$	−1164.50	+	2016.97i	−0.0527445	+	0.0913562i	−0.891192	−	0.453626i	$-0.850130\pi$
$787$	−1164.50	+	2016.97i	−0.0527445	+	0.0913562i	0.838448	+	0.544982i	$0.183464\pi$
$788$	6464.00	−	11196.0i	0.292221	−	0.506142i
$789$	−3585.00	−	6209.40i	−0.161761	−	0.280178i
$790$	−4070.00			−0.183296
$791$		0			0
$792$	16.0000			0.000717848
$793$	2394.00	+	4146.53i	0.107205	+	0.185684i
$794$	14635.0	−	25348.6i	0.654127	−	1.13298i
$795$	−8300.00	+	14376.0i	−0.370278	+	0.641340i
$796$	2328.00	+	4032.21i	0.103661	+	0.179545i
$797$	−11067.0			−0.491861			−0.245931	−	0.969287i	$-0.579094\pi$
$797$	−11067.0			−0.491861			−0.245931	+	0.969287i	$0.579094\pi$
$798$		0			0
$799$	−6171.00			−0.273234
$800$	−400.000	−	692.820i	−0.0176777	−	0.0306186i
$801$	−880.000	+	1524.20i	−0.0388181	+	0.0672349i
$802$	−5641.00	+	9770.50i	−0.248367	+	0.430185i
$803$	363.000	+	628.734i	0.0159527	+	0.0276308i
$804$	21120.0			0.926424
$805$		0			0
$806$	−2968.00			−0.129706
$807$	12535.0	+	21711.3i	0.546782	+	0.947054i
$808$	−216.000	+	374.123i	−0.00940452	+	0.0162891i
$809$	1939.50	−	3359.31i	0.0842882	−	0.145992i	−0.820799	−	0.571216i	$-0.806472\pi$
$809$	1939.50	−	3359.31i	0.0842882	−	0.145992i	0.905088	+	0.425225i	$0.139805\pi$
$810$	3355.00	+	5811.03i	0.145534	+	0.252073i
$811$	7518.00			0.325515			0.162758	−	0.986666i	$-0.447961\pi$
$811$	7518.00			0.325515			0.162758	+	0.986666i	$0.447961\pi$
$812$		0			0
$813$	27100.0			1.16905
$814$	−190.000	−	329.090i	−0.00818120	−	0.0141703i
$815$	9155.00	−	15856.9i	0.393479	−	0.681526i
$816$	2040.00	−	3533.38i	0.0875175	−	0.151585i
$817$	−6330.00	−	10963.9i	−0.271063	−	0.469495i
$818$	12820.0			0.547972
$819$		0			0
$820$	−6160.00			−0.262337
$821$	−19900.5	−	34468.7i	−0.845959	−	1.46524i	−0.884786	−	0.465998i	$-0.845695\pi$
$821$	−19900.5	−	34468.7i	−0.845959	−	1.46524i	0.0388270	−	0.999246i	$-0.487638\pi$
$822$	−12840.0	+	22239.5i	−0.544825	+	0.943665i
$823$	1782.00	−	3086.51i	0.0754758	−	0.130728i	−0.825817	−	0.563938i	$-0.809286\pi$
$823$	1782.00	−	3086.51i	0.0754758	−	0.130728i	0.901293	+	0.433210i	$0.142619\pi$
$824$	4108.00	+	7115.26i	0.173676	+	0.300816i
$825$	−125.000			−0.00527508
$826$		0			0
$827$	10838.0			0.455712			0.227856	−	0.973695i	$-0.426828\pi$
$827$	10838.0			0.455712			0.227856	+	0.973695i	$0.426828\pi$
$828$	−200.000	−	346.410i	−0.00839430	−	0.0145394i
$829$	−20978.0	+	36335.0i	−0.878885	+	1.52227i	−0.0263202	+	0.999654i	$0.508379\pi$
$829$	−20978.0	+	36335.0i	−0.878885	+	1.52227i	−0.852565	+	0.522621i	$0.824954\pi$
$830$	−3220.00	+	5577.20i	−0.134660	+	0.233238i
$831$	−9185.00	−	15908.9i	−0.383423	−	0.664107i
$832$	448.000			0.0186678
$833$		0			0
$834$	12740.0			0.528957
$835$	787.500	+	1363.99i	0.0326378	+	0.0565303i
$836$	60.0000	−	103.923i	0.00248223	−	0.00429935i
$837$	−15370.0	+	26621.6i	−0.634725	+	1.09938i
$838$	−4816.00	−	8341.56i	−0.198527	−	0.343860i
$839$	−28714.0			−1.18155			−0.590773	−	0.806838i	$-0.701177\pi$
$839$	−28714.0			−1.18155			−0.590773	+	0.806838i	$0.701177\pi$
$840$		0			0
$841$	−18148.0			−0.744106
$842$	−15325.0	−	26543.7i	−0.627238	−	1.08641i
$843$	−18327.5	+	31744.2i	−0.748793	+	1.29695i
$844$	−1138.00	+	1971.07i	−0.0464118	+	0.0803876i
$845$	5370.00	+	9301.11i	0.218620	+	0.378660i
$846$	−484.000			−0.0196693
$847$		0			0
$848$	10624.0			0.430224
$849$	−677.500	−	1173.46i	−0.0273872	−	0.0474360i
$850$	1275.00	−	2208.36i	0.0514496	−	0.0891133i
$851$	−4750.00	+	8227.24i	−0.191337	+	0.331406i
$852$	−7440.00	−	12886.5i	−0.299167	−	0.518172i
$853$	15442.0			0.619841			0.309920	−	0.950763i	$-0.399698\pi$
$853$	15442.0			0.619841			0.309920	+	0.950763i	$0.399698\pi$
$854$		0			0
$855$	−300.000			−0.0119997
$856$	−1256.00	−	2175.46i	−0.0501509	−	0.0868640i
$857$	8989.00	−	15569.4i	0.358295	−	0.620584i	−0.629382	−	0.777096i	$-0.716692\pi$
$857$	8989.00	−	15569.4i	0.358295	−	0.620584i	0.987676	+	0.156512i	$0.0500250\pi$
$858$	35.0000	−	60.6218i	0.00139263	−	0.00241211i
$859$	−9654.00	−	16721.2i	−0.383458	−	0.664168i	0.608096	−	0.793863i	$-0.291934\pi$
$859$	−9654.00	−	16721.2i	−0.383458	−	0.664168i	−0.991554	+	0.129695i	$0.958600\pi$
$860$	8440.00			0.334653
$861$		0			0
$862$	3750.00			0.148173
$863$	−8732.00	−	15124.3i	−0.344427	−	0.596566i	0.640822	−	0.767689i	$-0.278594\pi$
$863$	−8732.00	−	15124.3i	−0.344427	−	0.596566i	−0.985250	+	0.171124i	$0.945260\pi$
$864$	2320.00	−	4018.36i	0.0913519	−	0.158226i
$865$	3127.50	−	5416.99i	0.122934	−	0.212928i
$866$	13874.0	+	24030.5i	0.544408	+	0.942943i
$867$	−11560.0			−0.452824
$868$		0			0
$869$	407.000			0.0158878
$870$	−1975.00	−	3420.80i	−0.0769641	−	0.133306i
$871$	−3696.00	+	6401.66i	−0.143782	+	0.249038i
$872$	6444.00	−	11161.3i	0.250254	−	0.433452i
$873$	−1351.00	−	2340.00i	−0.0523762	−	0.0907182i
$874$	−3000.00			−0.116106
$875$		0			0
$876$	14520.0			0.560029
$877$	11981.0	+	20751.7i	0.461311	+	0.799014i	0.999027	−	0.0441124i	$-0.0140460\pi$
$877$	11981.0	+	20751.7i	0.461311	+	0.799014i	−0.537716	+	0.843126i	$0.680713\pi$
$878$	3442.00	−	5961.72i	0.132303	−	0.229155i
$879$	−10762.5	+	18641.2i	−0.412981	+	0.715304i
$880$	40.0000	+	69.2820i	0.00153227	+	0.00265397i
$881$	−35168.0			−1.34488			−0.672440	−	0.740151i	$-0.734754\pi$
$881$	−35168.0			−1.34488			−0.672440	+	0.740151i	$0.734754\pi$
$882$		0			0
$883$	−37896.0			−1.44428			−0.722142	−	0.691745i	$-0.756842\pi$
$883$	−37896.0			−1.44428			−0.722142	+	0.691745i	$0.756842\pi$
$884$	714.000	+	1236.68i	0.0271656	+	0.0470523i
$885$	−7850.00	+	13596.6i	−0.298164	+	0.516435i
$886$	−16750.0	+	29011.9i	−0.635132	+	1.10008i
$887$	−15184.0	−	26299.5i	−0.574779	−	0.995546i	−0.996066	−	0.0886187i	$-0.971755\pi$
$887$	−15184.0	−	26299.5i	−0.574779	−	0.995546i	0.421287	−	0.906927i	$-0.361579\pi$
$888$	−7600.00			−0.287206
$889$		0			0
$890$	−8800.00			−0.331434
$891$	−335.500	−	581.103i	−0.0126147	−	0.0218493i
$892$	−1386.00	+	2400.62i	−0.0520255	+	0.0901107i
$893$	−1815.00	+	3143.67i	−0.0680142	+	0.117804i
$894$	−2970.00	−	5144.19i	−0.111109	−	0.192447i
$895$	−740.000			−0.0276374
$896$		0			0
$897$	−1750.00			−0.0651402
$898$	−695.000	−	1203.78i	−0.0258268	−	0.0447333i
$899$	8374.00	−	14504.2i	0.310666	−	0.538089i
$900$	100.000	−	173.205i	0.00370370	−	0.00641500i
$901$	16932.0	+	29327.1i	0.626067	+	1.08438i
$902$	616.000			0.0227390
$903$		0			0
$904$	2928.00			0.107725
$905$	3360.00	+	5819.69i	0.123415	+	0.213760i
$906$	7635.00	−	13224.2i	0.279973	−	0.484928i
$907$	16937.0	−	29335.7i	0.620048	−	1.07396i	−0.369428	−	0.929259i	$-0.620446\pi$
$907$	16937.0	−	29335.7i	0.620048	−	1.07396i	0.989476	−	0.144696i	$-0.0462204\pi$
$908$	8558.00	+	14822.9i	0.312783	+	0.541757i
$909$	−108.000			−0.00394074
$910$		0			0
$911$	24880.0			0.904842			0.452421	−	0.891804i	$-0.350560\pi$
$911$	24880.0			0.904842			0.452421	+	0.891804i	$0.350560\pi$
$912$	−1200.00	−	2078.46i	−0.0435701	−	0.0754657i
$913$	322.000	−	557.720i	0.0116721	−	0.0202167i
$914$	−5760.00	+	9976.61i	−0.208451	+	0.361047i
$915$	8550.00	+	14809.0i	0.308912	+	0.535051i
$916$	−13264.0			−0.478444
$917$		0			0
$918$	14790.0			0.531746
$919$	12649.5	+	21909.6i	0.454046	+	0.786431i	0.998633	−	0.0522735i	$-0.0166468\pi$
$919$	12649.5	+	21909.6i	0.454046	+	0.786431i	−0.544587	+	0.838705i	$0.683313\pi$
$920$	1000.00	−	1732.05i	0.0358359	−	0.0620696i
$921$	−6597.50	+	11427.2i	−0.236042	+	0.408837i
$922$	−13440.0	−	23278.8i	−0.480068	−	0.831502i
$923$	5208.00			0.185724
$924$		0			0
$925$	−4750.00			−0.168842
$926$	7348.00	+	12727.1i	0.260767	+	0.451662i
$927$	−1027.00	+	1778.82i	−0.0363874	+	0.0630248i
$928$	−1264.00	+	2189.31i	−0.0447121	+	0.0774436i
$929$	−3396.00	−	5882.04i	−0.119934	−	0.207733i	0.799807	−	0.600257i	$-0.204935\pi$
$929$	−3396.00	−	5882.04i	−0.119934	−	0.207733i	−0.919742	+	0.392525i	$0.871602\pi$
$930$	−10600.0			−0.373750
$931$		0			0
$932$	15648.0			0.549965
$933$	21285.0	+	36866.7i	0.746881	+	1.29364i
$934$	17925.0	−	31047.0i	0.627970	−	1.08768i
$935$	−127.500	+	220.836i	−0.00445957	+	0.00772420i
$936$	56.0000	+	96.9948i	0.00195557	+	0.00338715i
$937$	−43575.0			−1.51925			−0.759623	−	0.650364i	$-0.774616\pi$
$937$	−43575.0			−1.51925			−0.759623	+	0.650364i	$0.774616\pi$
$938$		0			0
$939$	1095.00			0.0380554
$940$	−1210.00	−	2095.78i	−0.0419849	−	0.0727201i
$941$	−22686.0	+	39293.3i	−0.785911	+	1.36124i	0.142542	+	0.989789i	$0.454472\pi$
$941$	−22686.0	+	39293.3i	−0.785911	+	1.36124i	−0.928453	+	0.371449i	$0.878861\pi$
$942$	−2650.00	+	4589.93i	−0.0916578	+	0.158756i
$943$	−7700.00	−	13336.8i	−0.265903	−	0.460557i
$944$	10048.0			0.346435
$945$		0			0
$946$	−844.000			−0.0290072
$947$	19576.0	+	33906.6i	0.671737	+	1.16348i	0.977411	+	0.211346i	$0.0677846\pi$
$947$	19576.0	+	33906.6i	0.671737	+	1.16348i	−0.305675	+	0.952136i	$0.598882\pi$
$948$	4070.00	−	7049.45i	0.139438	−	0.241514i
$949$	−2541.00	+	4401.14i	−0.0869171	+	0.150545i
$950$	−750.000	−	1299.04i	−0.0256139	−	0.0443646i
$951$	−20130.0			−0.686393
$952$		0			0
$953$	−18632.0			−0.633316			−0.316658	−	0.948540i	$-0.602561\pi$
$953$	−18632.0			−0.633316			−0.316658	+	0.948540i	$0.602561\pi$
$954$	1328.00	+	2300.16i	0.0450688	+	0.0780614i
$955$	1402.50	−	2429.20i	0.0475223	−	0.0823111i
$956$	10902.0	−	18882.8i	0.368824	−	0.638822i
$957$	197.500	+	342.080i	0.00667113	+	0.0115547i
$958$	24692.0			0.832737
$959$		0			0
$960$	1600.00			0.0537914
$961$	−7576.50	−	13122.9i	−0.254322	−	0.440498i
$962$	1330.00	−	2303.63i	0.0445748	−	0.0772058i
$963$	314.000	−	543.864i	0.0105073	−	0.0181991i
$964$	−500.000	−	866.025i	−0.0167053	−	0.0289344i
$965$	15080.0			0.503049
$966$		0			0
$967$	48862.0			1.62492			0.812459	−	0.583018i	$-0.198128\pi$
$967$	48862.0			1.62492			0.812459	+	0.583018i	$0.198128\pi$
$968$	5320.00	+	9214.51i	0.176644	+	0.305956i
$969$	3825.00	−	6625.09i	0.126808	−	0.219637i
$970$	6755.00	−	11700.0i	0.223598	−	0.387283i
$971$	−9948.00	−	17230.4i	−0.328781	−	0.569466i	0.653489	−	0.756936i	$-0.273305\pi$
$971$	−9948.00	−	17230.4i	−0.328781	−	0.569466i	−0.982270	+	0.187470i	$0.939971\pi$
$972$	2240.00			0.0739177
$973$		0			0
$974$	30028.0			0.987843
$975$	−437.500	−	757.772i	−0.0143705	−	0.0248904i
$976$	5472.00	−	9477.78i	0.179462	−	0.310836i
$977$	−2565.00	+	4442.71i	−0.0839935	+	0.145481i	−0.904962	−	0.425493i	$-0.860101\pi$
$977$	−2565.00	+	4442.71i	−0.0839935	+	0.145481i	0.820968	+	0.570974i	$0.193434\pi$
$978$	18310.0	+	31713.9i	0.598660	+	1.03691i
$979$	880.000			0.0287282
$980$		0			0
$981$	3222.00			0.104863
$982$	4723.00	+	8180.48i	0.153480	+	0.265834i
$983$	5786.50	−	10022.5i	0.187752	−	0.325197i	−0.756748	−	0.653707i	$-0.773213\pi$
$983$	5786.50	−	10022.5i	0.187752	−	0.325197i	0.944501	+	0.328510i	$0.106546\pi$
$984$	6160.00	−	10669.4i	0.199567	−	0.345660i
$985$	8080.00	+	13995.0i	0.261371	+	0.452707i
$986$	−8058.00			−0.260263
$987$		0			0
$988$	840.000			0.0270485
$989$	10550.0	+	18273.1i	0.339202	+	0.587515i
$990$	−10.0000	+	17.3205i	−0.000321031	+	0.000556042i
$991$	−17300.0	+	29964.5i	−0.554544	+	0.960498i	0.443395	+	0.896326i	$0.353774\pi$
$991$	−17300.0	+	29964.5i	−0.554544	+	0.960498i	−0.997939	+	0.0641714i	$0.979560\pi$
$992$	3392.00	+	5875.12i	0.108565	+	0.188039i
$993$	−35180.0			−1.12427
$994$		0			0
$995$	−5820.00			−0.185434
$996$	−6440.00	−	11154.4i	−0.204879	−	0.354860i
$997$	7599.50	−	13162.7i	0.241403	−	0.418122i	−0.719711	−	0.694273i	$-0.755726\pi$
$997$	7599.50	−	13162.7i	0.241403	−	0.418122i	0.961114	+	0.276152i	$0.0890592\pi$
$998$	−11227.0	+	19445.7i	−0.356097	+	0.616778i
$999$	−13775.0	−	23859.0i	−0.436258	−	0.755621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.e.c.361.1		2
7.2	even	3	inner	490.4.e.c.471.1		2
7.3	odd	6		490.4.a.j.1.1		1
7.4	even	3		70.4.a.e.1.1	✓	1
7.5	odd	6		490.4.e.g.471.1		2
7.6	odd	2		490.4.e.g.361.1		2
21.11	odd	6		630.4.a.b.1.1		1
28.11	odd	6		560.4.a.f.1.1		1
35.4	even	6		350.4.a.c.1.1		1
35.18	odd	12		350.4.c.k.99.1		2
35.24	odd	6		2450.4.a.r.1.1		1
35.32	odd	12		350.4.c.k.99.2		2
56.11	odd	6		2240.4.a.bc.1.1		1
56.53	even	6		2240.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.e.1.1	✓	1	7.4	even	3
350.4.a.c.1.1		1	35.4	even	6
350.4.c.k.99.1		2	35.18	odd	12
350.4.c.k.99.2		2	35.32	odd	12
490.4.a.j.1.1		1	7.3	odd	6
490.4.e.c.361.1		2	1.1	even	1	trivial
490.4.e.c.471.1		2	7.2	even	3	inner
490.4.e.g.361.1		2	7.6	odd	2
490.4.e.g.471.1		2	7.5	odd	6
560.4.a.f.1.1		1	28.11	odd	6
630.4.a.b.1.1		1	21.11	odd	6
2240.4.a.h.1.1		1	56.53	even	6
2240.4.a.bc.1.1		1	56.11	odd	6
2450.4.a.r.1.1		1	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.50000 + 4.33013i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +10.0000 q^{6} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.50000 + 4.33013i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +10.0000 q^{6} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-10.0000 - 17.3205i) q^{12} +7.00000 q^{13} +25.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(25.5000 - 44.1673i) q^{17} +(2.00000 - 3.46410i) q^{18} +(-15.0000 - 25.9808i) q^{19} +20.0000 q^{20} -2.00000 q^{22} +(25.0000 + 43.3013i) q^{23} +(-20.0000 + 34.6410i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-7.00000 - 12.1244i) q^{26} -145.000 q^{27} +79.0000 q^{29} +(-25.0000 - 43.3013i) q^{30} +(106.000 - 183.597i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(2.50000 + 4.33013i) q^{33} -102.000 q^{34} -8.00000 q^{36} +(95.0000 + 164.545i) q^{37} +(-30.0000 + 51.9615i) q^{38} +(-17.5000 + 30.3109i) q^{39} +(-20.0000 - 34.6410i) q^{40} -308.000 q^{41} +422.000 q^{43} +(2.00000 + 3.46410i) q^{44} +(5.00000 - 8.66025i) q^{45} +(50.0000 - 86.6025i) q^{46} +(-60.5000 - 104.789i) q^{47} +80.0000 q^{48} +50.0000 q^{50} +(127.500 + 220.836i) q^{51} +(-14.0000 + 24.2487i) q^{52} +(-332.000 + 575.041i) q^{53} +(145.000 + 251.147i) q^{54} -5.00000 q^{55} +150.000 q^{57} +(-79.0000 - 136.832i) q^{58} +(-314.000 + 543.864i) q^{59} +(-50.0000 + 86.6025i) q^{60} +(342.000 + 592.361i) q^{61} -424.000 q^{62} +64.0000 q^{64} +(-17.5000 - 30.3109i) q^{65} +(5.00000 - 8.66025i) q^{66} +(-528.000 + 914.523i) q^{67} +(102.000 + 176.669i) q^{68} -250.000 q^{69} +744.000 q^{71} +(8.00000 + 13.8564i) q^{72} +(-363.000 + 628.734i) q^{73} +(190.000 - 329.090i) q^{74} +(-62.5000 - 108.253i) q^{75} +120.000 q^{76} +70.0000 q^{78} +(203.500 + 352.472i) q^{79} +(-40.0000 + 69.2820i) q^{80} +(335.500 - 581.103i) q^{81} +(308.000 + 533.472i) q^{82} +644.000 q^{83} -255.000 q^{85} +(-422.000 - 730.925i) q^{86} +(-197.500 + 342.080i) q^{87} +(4.00000 - 6.92820i) q^{88} +(440.000 + 762.102i) q^{89} -20.0000 q^{90} -200.000 q^{92} +(530.000 + 917.987i) q^{93} +(-121.000 + 209.578i) q^{94} +(-75.0000 + 129.904i) q^{95} +(-80.0000 - 138.564i) q^{96} -1351.00 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 5 q^{3} - 4 q^{4} - 5 q^{5} + 20 q^{6} + 16 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 5 * q^3 - 4 * q^4 - 5 * q^5 + 20 * q^6 + 16 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 5 q^{3} - 4 q^{4} - 5 q^{5} + 20 q^{6} + 16 q^{8} + 2 q^{9} - 10 q^{10} + q^{11} - 20 q^{12} + 14 q^{13} + 50 q^{15} - 16 q^{16} + 51 q^{17} + 4 q^{18} - 30 q^{19} + 40 q^{20} - 4 q^{22} + 50 q^{23} - 40 q^{24} - 25 q^{25} - 14 q^{26} - 290 q^{27} + 158 q^{29} - 50 q^{30} + 212 q^{31} - 32 q^{32} + 5 q^{33} - 204 q^{34} - 16 q^{36} + 190 q^{37} - 60 q^{38} - 35 q^{39} - 40 q^{40} - 616 q^{41} + 844 q^{43} + 4 q^{44} + 10 q^{45} + 100 q^{46} - 121 q^{47} + 160 q^{48} + 100 q^{50} + 255 q^{51} - 28 q^{52} - 664 q^{53} + 290 q^{54} - 10 q^{55} + 300 q^{57} - 158 q^{58} - 628 q^{59} - 100 q^{60} + 684 q^{61} - 848 q^{62} + 128 q^{64} - 35 q^{65} + 10 q^{66} - 1056 q^{67} + 204 q^{68} - 500 q^{69} + 1488 q^{71} + 16 q^{72} - 726 q^{73} + 380 q^{74} - 125 q^{75} + 240 q^{76} + 140 q^{78} + 407 q^{79} - 80 q^{80} + 671 q^{81} + 616 q^{82} + 1288 q^{83} - 510 q^{85} - 844 q^{86} - 395 q^{87} + 8 q^{88} + 880 q^{89} - 40 q^{90} - 400 q^{92} + 1060 q^{93} - 242 q^{94} - 150 q^{95} - 160 q^{96} - 2702 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 5 * q^3 - 4 * q^4 - 5 * q^5 + 20 * q^6 + 16 * q^8 + 2 * q^9 - 10 * q^10 + q^11 - 20 * q^12 + 14 * q^13 + 50 * q^15 - 16 * q^16 + 51 * q^17 + 4 * q^18 - 30 * q^19 + 40 * q^20 - 4 * q^22 + 50 * q^23 - 40 * q^24 - 25 * q^25 - 14 * q^26 - 290 * q^27 + 158 * q^29 - 50 * q^30 + 212 * q^31 - 32 * q^32 + 5 * q^33 - 204 * q^34 - 16 * q^36 + 190 * q^37 - 60 * q^38 - 35 * q^39 - 40 * q^40 - 616 * q^41 + 844 * q^43 + 4 * q^44 + 10 * q^45 + 100 * q^46 - 121 * q^47 + 160 * q^48 + 100 * q^50 + 255 * q^51 - 28 * q^52 - 664 * q^53 + 290 * q^54 - 10 * q^55 + 300 * q^57 - 158 * q^58 - 628 * q^59 - 100 * q^60 + 684 * q^61 - 848 * q^62 + 128 * q^64 - 35 * q^65 + 10 * q^66 - 1056 * q^67 + 204 * q^68 - 500 * q^69 + 1488 * q^71 + 16 * q^72 - 726 * q^73 + 380 * q^74 - 125 * q^75 + 240 * q^76 + 140 * q^78 + 407 * q^79 - 80 * q^80 + 671 * q^81 + 616 * q^82 + 1288 * q^83 - 510 * q^85 - 844 * q^86 - 395 * q^87 + 8 * q^88 + 880 * q^89 - 40 * q^90 - 400 * q^92 + 1060 * q^93 - 242 * q^94 - 150 * q^95 - 160 * q^96 - 2702 * q^97 + 4 * q^99

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