LMFDB - Embedded newform 196.3.g.g.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,3,Mod(67,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("196.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	196.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.34061318146$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.1
Root			$-1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	196.67
Dual form			196.3.g.g.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-3.87298 - 2.23607i) q^{3} +4.00000 q^{4} +(3.87298 + 6.70820i) q^{5} +(-7.74597 - 4.47214i) q^{6} +8.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-3.87298 - 2.23607i) q^{3} +4.00000 q^{4} +(3.87298 + 6.70820i) q^{5} +(-7.74597 - 4.47214i) q^{6} +8.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +(7.74597 + 13.4164i) q^{10} +(6.00000 + 3.46410i) q^{11} +(-15.4919 - 8.94427i) q^{12} +7.74597 q^{13} -34.6410i q^{15} +16.0000 q^{16} +(7.74597 - 13.4164i) q^{17} +(11.0000 + 19.0526i) q^{18} +(11.6190 - 6.70820i) q^{19} +(15.4919 + 26.8328i) q^{20} +(12.0000 + 6.92820i) q^{22} +(-18.0000 + 10.3923i) q^{23} +(-30.9839 - 17.8885i) q^{24} +(-17.5000 + 30.3109i) q^{25} +15.4919 q^{26} -8.94427i q^{27} -26.0000 q^{29} -69.2820i q^{30} +(23.2379 + 13.4164i) q^{31} +32.0000 q^{32} +(-15.4919 - 26.8328i) q^{33} +(15.4919 - 26.8328i) q^{34} +(22.0000 + 38.1051i) q^{36} +(1.00000 + 1.73205i) q^{37} +(23.2379 - 13.4164i) q^{38} +(-30.0000 - 17.3205i) q^{39} +(30.9839 + 53.6656i) q^{40} -46.4758 q^{41} -48.4974i q^{43} +(24.0000 + 13.8564i) q^{44} +(-42.6028 + 73.7902i) q^{45} +(-36.0000 + 20.7846i) q^{46} +(-69.7137 + 40.2492i) q^{47} +(-61.9677 - 35.7771i) q^{48} +(-35.0000 + 60.6218i) q^{50} +(-60.0000 + 34.6410i) q^{51} +30.9839 q^{52} +(23.0000 - 39.8372i) q^{53} -17.8885i q^{54} +53.6656i q^{55} -60.0000 q^{57} -52.0000 q^{58} +(-58.0948 - 33.5410i) q^{59} -138.564i q^{60} +(3.87298 + 6.70820i) q^{61} +(46.4758 + 26.8328i) q^{62} +64.0000 q^{64} +(30.0000 + 51.9615i) q^{65} +(-30.9839 - 53.6656i) q^{66} +(-78.0000 - 45.0333i) q^{67} +(30.9839 - 53.6656i) q^{68} +92.9516 q^{69} +96.9948i q^{71} +(44.0000 + 76.2102i) q^{72} +(61.9677 - 107.331i) q^{73} +(2.00000 + 3.46410i) q^{74} +(135.554 - 78.2624i) q^{75} +(46.4758 - 26.8328i) q^{76} +(-60.0000 - 34.6410i) q^{78} +(24.0000 - 13.8564i) q^{79} +(61.9677 + 107.331i) q^{80} +(29.5000 - 51.0955i) q^{81} -92.9516 q^{82} -93.9149i q^{83} +120.000 q^{85} -96.9948i q^{86} +(100.698 + 58.1378i) q^{87} +(48.0000 + 27.7128i) q^{88} +(30.9839 + 53.6656i) q^{89} +(-85.2056 + 147.580i) q^{90} +(-72.0000 + 41.5692i) q^{92} +(-60.0000 - 103.923i) q^{93} +(-139.427 + 80.4984i) q^{94} +(90.0000 + 51.9615i) q^{95} +(-123.935 - 71.5542i) q^{96} -46.4758 q^{97} +76.2102i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 16 q^{4} + 32 q^{8} + 22 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 16 * q^4 + 32 * q^8 + 22 * q^9	$ 4 q + 8 q^{2} + 16 q^{4} + 32 q^{8} + 22 q^{9} + 24 q^{11} + 64 q^{16} + 44 q^{18} + 48 q^{22} - 72 q^{23} - 70 q^{25} - 104 q^{29} + 128 q^{32} + 88 q^{36} + 4 q^{37} - 120 q^{39} + 96 q^{44} - 144 q^{46} - 140 q^{50} - 240 q^{51} + 92 q^{53} - 240 q^{57} - 208 q^{58} + 256 q^{64} + 120 q^{65} - 312 q^{67} + 176 q^{72} + 8 q^{74} - 240 q^{78} + 96 q^{79} + 118 q^{81} + 480 q^{85} + 192 q^{88} - 288 q^{92} - 240 q^{93} + 360 q^{95}+O(q^{100}) $ 4 * q + 8 * q^2 + 16 * q^4 + 32 * q^8 + 22 * q^9 + 24 * q^11 + 64 * q^16 + 44 * q^18 + 48 * q^22 - 72 * q^23 - 70 * q^25 - 104 * q^29 + 128 * q^32 + 88 * q^36 + 4 * q^37 - 120 * q^39 + 96 * q^44 - 144 * q^46 - 140 * q^50 - 240 * q^51 + 92 * q^53 - 240 * q^57 - 208 * q^58 + 256 * q^64 + 120 * q^65 - 312 * q^67 + 176 * q^72 + 8 * q^74 - 240 * q^78 + 96 * q^79 + 118 * q^81 + 480 * q^85 + 192 * q^88 - 288 * q^92 - 240 * q^93 + 360 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000			1.00000
$2$	2.00000			1.00000
$3$	−3.87298	−	2.23607i	−1.29099	−	0.745356i	−0.312164	−	0.950028i	$-0.601054\pi$
$3$	−3.87298	−	2.23607i	−1.29099	−	0.745356i	−0.978831	+	0.204672i	$0.934387\pi$
$4$	4.00000			1.00000
$5$	3.87298	+	6.70820i	0.774597	+	1.34164i	0.935021	+	0.354593i	$0.115380\pi$
$5$	3.87298	+	6.70820i	0.774597	+	1.34164i	−0.160424	+	0.987048i	$0.551286\pi$
$6$	−7.74597	−	4.47214i	−1.29099	−	0.745356i
$7$		0			0
$7$		0			0
$8$	8.00000			1.00000
$9$	5.50000	+	9.52628i	0.611111	+	1.05848i
$10$	7.74597	+	13.4164i	0.774597	+	1.34164i
$11$	6.00000	+	3.46410i	0.545455	+	0.314918i	0.747287	−	0.664502i	$-0.231356\pi$
$11$	6.00000	+	3.46410i	0.545455	+	0.314918i	−0.201832	+	0.979420i	$0.564690\pi$
$12$	−15.4919	−	8.94427i	−1.29099	−	0.745356i
$13$	7.74597			0.595844			0.297922	−	0.954590i	$-0.403707\pi$
$13$	7.74597			0.595844			0.297922	+	0.954590i	$0.403707\pi$
$14$		0			0
$15$		−	34.6410i		−	2.30940i
$16$	16.0000			1.00000
$17$	7.74597	−	13.4164i	0.455645	−	0.789200i	−0.543080	−	0.839681i	$-0.682742\pi$
$17$	7.74597	−	13.4164i	0.455645	−	0.789200i	0.998725	+	0.0504805i	$0.0160753\pi$
$18$	11.0000	+	19.0526i	0.611111	+	1.05848i
$19$	11.6190	−	6.70820i	0.611524	−	0.353063i	−0.162038	−	0.986785i	$-0.551807\pi$
$19$	11.6190	−	6.70820i	0.611524	−	0.353063i	0.773562	+	0.633721i	$0.218473\pi$
$20$	15.4919	+	26.8328i	0.774597	+	1.34164i
$21$		0			0
$22$	12.0000	+	6.92820i	0.545455	+	0.314918i
$23$	−18.0000	+	10.3923i	−0.782609	+	0.451839i	−0.837354	−	0.546661i	$-0.815899\pi$
$23$	−18.0000	+	10.3923i	−0.782609	+	0.451839i	0.0547453	+	0.998500i	$0.482565\pi$
$24$	−30.9839	−	17.8885i	−1.29099	−	0.745356i
$25$	−17.5000	+	30.3109i	−0.700000	+	1.21244i
$26$	15.4919			0.595844
$27$		−	8.94427i		−	0.331269i
$28$		0			0
$29$	−26.0000			−0.896552			−0.448276	−	0.893895i	$-0.647962\pi$
$29$	−26.0000			−0.896552			−0.448276	+	0.893895i	$0.647962\pi$
$30$		−	69.2820i		−	2.30940i
$31$	23.2379	+	13.4164i	0.749610	+	0.432787i	0.825553	−	0.564325i	$-0.190863\pi$
$31$	23.2379	+	13.4164i	0.749610	+	0.432787i	−0.0759432	+	0.997112i	$0.524197\pi$
$32$	32.0000			1.00000
$33$	−15.4919	−	26.8328i	−0.469453	−	0.813116i
$34$	15.4919	−	26.8328i	0.455645	−	0.789200i
$35$		0			0
$36$	22.0000	+	38.1051i	0.611111	+	1.05848i
$37$	1.00000	+	1.73205i	0.0270270	+	0.0468122i	0.879223	−	0.476411i	$-0.158063\pi$
$37$	1.00000	+	1.73205i	0.0270270	+	0.0468122i	−0.852196	+	0.523223i	$0.824729\pi$
$38$	23.2379	−	13.4164i	0.611524	−	0.353063i
$39$	−30.0000	−	17.3205i	−0.769231	−	0.444116i
$40$	30.9839	+	53.6656i	0.774597	+	1.34164i
$41$	−46.4758			−1.13356			−0.566778	−	0.823871i	$-0.691810\pi$
$41$	−46.4758			−1.13356			−0.566778	+	0.823871i	$0.691810\pi$
$42$		0			0
$43$		−	48.4974i		−	1.12785i	−0.825827	−	0.563924i	$-0.809291\pi$
$43$		−	48.4974i		−	1.12785i	0.825827	−	0.563924i	$-0.190709\pi$
$44$	24.0000	+	13.8564i	0.545455	+	0.314918i
$45$	−42.6028	+	73.7902i	−0.946729	+	1.63978i
$46$	−36.0000	+	20.7846i	−0.782609	+	0.451839i
$47$	−69.7137	+	40.2492i	−1.48327	+	0.856366i	−0.999819	−	0.0190051i	$-0.993950\pi$
$47$	−69.7137	+	40.2492i	−1.48327	+	0.856366i	−0.483451	+	0.875372i	$0.660617\pi$
$48$	−61.9677	−	35.7771i	−1.29099	−	0.745356i
$49$		0			0
$50$	−35.0000	+	60.6218i	−0.700000	+	1.21244i
$51$	−60.0000	+	34.6410i	−1.17647	+	0.679236i
$52$	30.9839			0.595844
$53$	23.0000	−	39.8372i	0.433962	−	0.751645i	−0.563248	−	0.826288i	$-0.690448\pi$
$53$	23.0000	−	39.8372i	0.433962	−	0.751645i	0.997210	+	0.0746432i	$0.0237818\pi$
$54$		−	17.8885i		−	0.331269i
$55$			53.6656i			0.975739i
$56$		0			0
$57$	−60.0000			−1.05263
$58$	−52.0000			−0.896552
$59$	−58.0948	−	33.5410i	−0.984657	−	0.568492i	−0.0809839	−	0.996715i	$-0.525806\pi$
$59$	−58.0948	−	33.5410i	−0.984657	−	0.568492i	−0.903673	+	0.428224i	$0.859140\pi$
$60$		−	138.564i		−	2.30940i
$61$	3.87298	+	6.70820i	0.0634915	+	0.109971i	0.896024	−	0.444006i	$-0.146443\pi$
$61$	3.87298	+	6.70820i	0.0634915	+	0.109971i	−0.832532	+	0.553976i	$0.813110\pi$
$62$	46.4758	+	26.8328i	0.749610	+	0.432787i
$63$		0			0
$64$	64.0000			1.00000
$65$	30.0000	+	51.9615i	0.461538	+	0.799408i
$66$	−30.9839	−	53.6656i	−0.469453	−	0.813116i
$67$	−78.0000	−	45.0333i	−1.16418	−	0.672139i	−0.211877	−	0.977296i	$-0.567958\pi$
$67$	−78.0000	−	45.0333i	−1.16418	−	0.672139i	−0.952302	+	0.305157i	$0.901291\pi$
$68$	30.9839	−	53.6656i	0.455645	−	0.789200i
$69$	92.9516			1.34712
$70$		0			0
$71$			96.9948i			1.36612i	0.730360	+	0.683062i	$0.239352\pi$
$71$			96.9948i			1.36612i	−0.730360	+	0.683062i	$0.760648\pi$
$72$	44.0000	+	76.2102i	0.611111	+	1.05848i
$73$	61.9677	−	107.331i	0.848873	−	1.47029i	−0.0333417	−	0.999444i	$-0.510615\pi$
$73$	61.9677	−	107.331i	0.848873	−	1.47029i	0.882215	−	0.470847i	$-0.156052\pi$
$74$	2.00000	+	3.46410i	0.0270270	+	0.0468122i
$75$	135.554	−	78.2624i	1.80739	−	1.04350i
$76$	46.4758	−	26.8328i	0.611524	−	0.353063i
$77$		0			0
$78$	−60.0000	−	34.6410i	−0.769231	−	0.444116i
$79$	24.0000	−	13.8564i	0.303797	−	0.175398i	−0.340350	−	0.940299i	$-0.610546\pi$
$79$	24.0000	−	13.8564i	0.303797	−	0.175398i	0.644148	+	0.764901i	$0.277212\pi$
$80$	61.9677	+	107.331i	0.774597	+	1.34164i
$81$	29.5000	−	51.0955i	0.364198	−	0.630809i
$82$	−92.9516			−1.13356
$83$		−	93.9149i		−	1.13150i	−0.824575	−	0.565752i	$-0.808586\pi$
$83$		−	93.9149i		−	1.13150i	0.824575	−	0.565752i	$-0.191414\pi$
$84$		0			0
$85$	120.000			1.41176
$86$		−	96.9948i		−	1.12785i
$87$	100.698	+	58.1378i	1.15744	+	0.668250i
$88$	48.0000	+	27.7128i	0.545455	+	0.314918i
$89$	30.9839	+	53.6656i	0.348133	+	0.602985i	0.985918	−	0.167230i	$-0.0534823\pi$
$89$	30.9839	+	53.6656i	0.348133	+	0.602985i	−0.637785	+	0.770215i	$0.720149\pi$
$90$	−85.2056	+	147.580i	−0.946729	+	1.63978i
$91$		0			0
$92$	−72.0000	+	41.5692i	−0.782609	+	0.451839i
$93$	−60.0000	−	103.923i	−0.645161	−	1.11745i
$94$	−139.427	+	80.4984i	−1.48327	+	0.856366i
$95$	90.0000	+	51.9615i	0.947368	+	0.546963i
$96$	−123.935	−	71.5542i	−1.29099	−	0.745356i
$97$	−46.4758			−0.479132			−0.239566	−	0.970880i	$-0.577005\pi$
$97$	−46.4758			−0.479132			−0.239566	+	0.970880i	$0.577005\pi$
$98$		0			0
$99$			76.2102i			0.769800i
$100$	−70.0000	+	121.244i	−0.700000	+	1.21244i
$101$	34.8569	−	60.3738i	0.345117	−	0.597761i	−0.640258	−	0.768160i	$-0.721172\pi$
$101$	34.8569	−	60.3738i	0.345117	−	0.597761i	0.985375	+	0.170399i	$0.0545058\pi$
$102$	−120.000	+	69.2820i	−1.17647	+	0.679236i
$103$	−69.7137	+	40.2492i	−0.676832	+	0.390769i	−0.798660	−	0.601782i	$-0.794458\pi$
$103$	−69.7137	+	40.2492i	−0.676832	+	0.390769i	0.121828	+	0.992551i	$0.461124\pi$
$104$	61.9677			0.595844
$105$		0			0
$106$	46.0000	−	79.6743i	0.433962	−	0.751645i
$107$	150.000	−	86.6025i	1.40187	−	0.809370i	0.407285	−	0.913301i	$-0.366476\pi$
$107$	150.000	−	86.6025i	1.40187	−	0.809370i	0.994584	+	0.103932i	$0.0331423\pi$
$108$		−	35.7771i		−	0.331269i
$109$	−47.0000	+	81.4064i	−0.431193	+	0.746848i	−0.996976	−	0.0777061i	$-0.975240\pi$
$109$	−47.0000	+	81.4064i	−0.431193	+	0.746848i	0.565784	+	0.824554i	$0.308574\pi$
$110$			107.331i			0.975739i
$111$		−	8.94427i		−	0.0805790i
$112$		0			0
$113$	−82.0000			−0.725664			−0.362832	−	0.931855i	$-0.618190\pi$
$113$	−82.0000			−0.725664			−0.362832	+	0.931855i	$0.618190\pi$
$114$	−120.000			−1.05263
$115$	−139.427	−	80.4984i	−1.21241	−	0.699986i
$116$	−104.000			−0.896552
$117$	42.6028	+	73.7902i	0.364127	+	0.630686i
$118$	−116.190	−	67.0820i	−0.984657	−	0.568492i
$119$		0			0
$120$		−	277.128i		−	2.30940i
$121$	−36.5000	−	63.2199i	−0.301653	−	0.522478i
$122$	7.74597	+	13.4164i	0.0634915	+	0.109971i
$123$	180.000	+	103.923i	1.46341	+	0.844903i
$124$	92.9516	+	53.6656i	0.749610	+	0.432787i
$125$	−77.4597			−0.619677
$126$		0			0
$127$		−	48.4974i		−	0.381869i	−0.981603	−	0.190935i	$-0.938848\pi$
$127$		−	48.4974i		−	0.381869i	0.981603	−	0.190935i	$-0.0611519\pi$
$128$	128.000			1.00000
$129$	−108.444	+	187.830i	−0.840648	+	1.45604i
$130$	60.0000	+	103.923i	0.461538	+	0.799408i
$131$	11.6190	−	6.70820i	0.0886943	−	0.0512077i	−0.454997	−	0.890493i	$-0.650360\pi$
$131$	11.6190	−	6.70820i	0.0886943	−	0.0512077i	0.543691	+	0.839285i	$0.317026\pi$
$132$	−61.9677	−	107.331i	−0.469453	−	0.813116i
$133$		0			0
$134$	−156.000	−	90.0666i	−1.16418	−	0.672139i
$135$	60.0000	−	34.6410i	0.444444	−	0.256600i
$136$	61.9677	−	107.331i	0.455645	−	0.789200i
$137$	−47.0000	+	81.4064i	−0.343066	+	0.594207i	−0.985000	−	0.172552i	$-0.944799\pi$
$137$	−47.0000	+	81.4064i	−0.343066	+	0.594207i	0.641935	+	0.766759i	$0.278132\pi$
$138$	185.903			1.34712
$139$			93.9149i			0.675646i	0.941210	+	0.337823i	$0.109691\pi$
$139$			93.9149i			0.675646i	−0.941210	+	0.337823i	$0.890309\pi$
$140$		0			0
$141$	360.000			2.55319
$142$			193.990i			1.36612i
$143$	46.4758	+	26.8328i	0.325006	+	0.187642i
$144$	88.0000	+	152.420i	0.611111	+	1.05848i
$145$	−100.698	−	174.413i	−0.694466	−	1.20285i
$146$	123.935	−	214.663i	0.848873	−	1.47029i
$147$		0			0
$148$	4.00000	+	6.92820i	0.0270270	+	0.0468122i
$149$	−13.0000	−	22.5167i	−0.0872483	−	0.151119i	0.819099	−	0.573653i	$-0.194474\pi$
$149$	−13.0000	−	22.5167i	−0.0872483	−	0.151119i	−0.906347	+	0.422534i	$0.861141\pi$
$150$	271.109	−	156.525i	1.80739	−	1.04350i
$151$	6.00000	+	3.46410i	0.0397351	+	0.0229411i	0.519736	−	0.854327i	$-0.326030\pi$
$151$	6.00000	+	3.46410i	0.0397351	+	0.0229411i	−0.480001	+	0.877268i	$0.659364\pi$
$152$	92.9516	−	53.6656i	0.611524	−	0.353063i
$153$	170.411			1.11380
$154$		0			0
$155$			207.846i			1.34094i
$156$	−120.000	−	69.2820i	−0.769231	−	0.444116i
$157$	−19.3649	+	33.5410i	−0.123343	+	0.213637i	−0.921084	−	0.389363i	$-0.872695\pi$
$157$	−19.3649	+	33.5410i	−0.123343	+	0.213637i	0.797741	+	0.603001i	$0.206028\pi$
$158$	48.0000	−	27.7128i	0.303797	−	0.175398i
$159$	−178.157	+	102.859i	−1.12049	+	0.646913i
$160$	123.935	+	214.663i	0.774597	+	1.34164i
$161$		0			0
$162$	59.0000	−	102.191i	0.364198	−	0.630809i
$163$	150.000	−	86.6025i	0.920245	−	0.531304i	0.0365321	−	0.999332i	$-0.488369\pi$
$163$	150.000	−	86.6025i	0.920245	−	0.531304i	0.883713	+	0.468029i	$0.155036\pi$
$164$	−185.903			−1.13356
$165$	120.000	−	207.846i	0.727273	−	1.25967i
$166$		−	187.830i		−	1.13150i
$167$			187.830i			1.12473i	0.826890	+	0.562364i	$0.190108\pi$
$167$			187.830i			1.12473i	−0.826890	+	0.562364i	$0.809892\pi$
$168$		0			0
$169$	−109.000			−0.644970
$170$	240.000			1.41176
$171$	127.808	+	73.7902i	0.747418	+	0.431522i
$172$		−	193.990i		−	1.12785i
$173$	−158.792	−	275.036i	−0.917875	−	1.58981i	−0.802637	−	0.596468i	$-0.796570\pi$
$173$	−158.792	−	275.036i	−0.917875	−	1.58981i	−0.115238	−	0.993338i	$-0.536763\pi$
$174$	201.395	+	116.276i	1.15744	+	0.668250i
$175$		0			0
$176$	96.0000	+	55.4256i	0.545455	+	0.314918i
$177$	150.000	+	259.808i	0.847458	+	1.46784i
$178$	61.9677	+	107.331i	0.348133	+	0.602985i
$179$	90.0000	+	51.9615i	0.502793	+	0.290288i	0.729866	−	0.683590i	$-0.239582\pi$
$179$	90.0000	+	51.9615i	0.502793	+	0.290288i	−0.227073	+	0.973878i	$0.572916\pi$
$180$	−170.411	+	295.161i	−0.946729	+	1.63978i
$181$	−209.141			−1.15548			−0.577738	−	0.816222i	$-0.696064\pi$
$181$	−209.141			−1.15548			−0.577738	+	0.816222i	$0.696064\pi$
$182$		0			0
$183$		−	34.6410i		−	0.189295i
$184$	−144.000	+	83.1384i	−0.782609	+	0.451839i
$185$	−7.74597	+	13.4164i	−0.0418701	+	0.0725211i
$186$	−120.000	−	207.846i	−0.645161	−	1.11745i
$187$	92.9516	−	53.6656i	0.497067	−	0.286982i
$188$	−278.855	+	160.997i	−1.48327	+	0.856366i
$189$		0			0
$190$	180.000	+	103.923i	0.947368	+	0.546963i
$191$	−60.0000	+	34.6410i	−0.314136	+	0.181367i	−0.648776	−	0.760980i	$-0.724719\pi$
$191$	−60.0000	+	34.6410i	−0.314136	+	0.181367i	0.334640	+	0.942346i	$0.391385\pi$
$192$	−247.871	−	143.108i	−1.29099	−	0.745356i
$193$	−19.0000	+	32.9090i	−0.0984456	+	0.170513i	−0.911041	−	0.412315i	$-0.864720\pi$
$193$	−19.0000	+	32.9090i	−0.0984456	+	0.170513i	0.812596	+	0.582828i	$0.198054\pi$
$194$	−92.9516			−0.479132
$195$		−	268.328i		−	1.37604i
$196$		0			0
$197$	2.00000			0.0101523			0.00507614	−	0.999987i	$-0.498384\pi$
$197$	2.00000			0.0101523			0.00507614	+	0.999987i	$0.498384\pi$
$198$			152.420i			0.769800i
$199$	23.2379	+	13.4164i	0.116773	+	0.0674191i	0.557249	−	0.830345i	$-0.311857\pi$
$199$	23.2379	+	13.4164i	0.116773	+	0.0674191i	−0.440476	+	0.897765i	$0.645190\pi$
$200$	−140.000	+	242.487i	−0.700000	+	1.21244i
$201$	201.395	+	348.827i	1.00197	+	1.73546i
$202$	69.7137	−	120.748i	0.345117	−	0.597761i
$203$		0			0
$204$	−240.000	+	138.564i	−1.17647	+	0.679236i
$205$	−180.000	−	311.769i	−0.878049	−	1.52083i
$206$	−139.427	+	80.4984i	−0.676832	+	0.390769i
$207$	−198.000	−	114.315i	−0.956522	−	0.552248i
$208$	123.935			0.595844
$209$	92.9516			0.444744
$210$		0			0
$211$		−	242.487i		−	1.14923i	−0.818425	−	0.574614i	$-0.805152\pi$
$211$		−	242.487i		−	1.14923i	0.818425	−	0.574614i	$-0.194848\pi$
$212$	92.0000	−	159.349i	0.433962	−	0.751645i
$213$	216.887	−	375.659i	1.01825	−	1.76366i
$214$	300.000	−	173.205i	1.40187	−	0.809370i
$215$	325.331	−	187.830i	1.51317	−	0.873627i
$216$		−	71.5542i		−	0.331269i
$217$		0			0
$218$	−94.0000	+	162.813i	−0.431193	+	0.746848i
$219$	−480.000	+	277.128i	−2.19178	+	1.26543i
$220$			214.663i			0.975739i
$221$	60.0000	−	103.923i	0.271493	−	0.470240i
$222$		−	17.8885i		−	0.0805790i
$223$		−	375.659i		−	1.68457i	−0.539031	−	0.842286i	$-0.681210\pi$
$223$		−	375.659i		−	1.68457i	0.539031	−	0.842286i	$-0.318790\pi$
$224$		0			0
$225$	−385.000			−1.71111
$226$	−164.000			−0.725664
$227$	−58.0948	−	33.5410i	−0.255924	−	0.147758i	0.366550	−	0.930398i	$-0.380539\pi$
$227$	−58.0948	−	33.5410i	−0.255924	−	0.147758i	−0.622474	+	0.782641i	$0.713872\pi$
$228$	−240.000			−1.05263
$229$	166.538	+	288.453i	0.727241	+	1.25962i	0.958045	+	0.286619i	$0.0925313\pi$
$229$	166.538	+	288.453i	0.727241	+	1.25962i	−0.230803	+	0.973000i	$0.574135\pi$
$230$	−278.855	−	160.997i	−1.21241	−	0.699986i
$231$		0			0
$232$	−208.000			−0.896552
$233$	169.000	+	292.717i	0.725322	+	1.25629i	0.958841	+	0.283942i	$0.0916424\pi$
$233$	169.000	+	292.717i	0.725322	+	1.25629i	−0.233519	+	0.972352i	$0.575024\pi$
$234$	85.2056	+	147.580i	0.364127	+	0.630686i
$235$	−540.000	−	311.769i	−2.29787	−	1.32668i
$236$	−232.379	−	134.164i	−0.984657	−	0.568492i
$237$	−123.935			−0.522934
$238$		0			0
$239$			242.487i			1.01459i	0.861772	+	0.507295i	$0.169355\pi$
$239$			242.487i			1.01459i	−0.861772	+	0.507295i	$0.830645\pi$
$240$		−	554.256i		−	2.30940i
$241$	−100.698	+	174.413i	−0.417832	+	0.723707i	−0.995721	−	0.0924088i	$-0.970543\pi$
$241$	−100.698	+	174.413i	−0.417832	+	0.723707i	0.577889	+	0.816115i	$0.303877\pi$
$242$	−73.0000	−	126.440i	−0.301653	−	0.522478i
$243$	−298.220	+	172.177i	−1.22724	+	0.708548i
$244$	15.4919	+	26.8328i	0.0634915	+	0.109971i
$245$		0			0
$246$	360.000	+	207.846i	1.46341	+	0.844903i
$247$	90.0000	−	51.9615i	0.364372	−	0.210371i
$248$	185.903	+	107.331i	0.749610	+	0.432787i
$249$	−210.000	+	363.731i	−0.843373	+	1.46077i
$250$	−154.919			−0.619677
$251$			469.574i			1.87081i	0.353573	+	0.935407i	$0.384967\pi$
$251$			469.574i			1.87081i	−0.353573	+	0.935407i	$0.615033\pi$
$252$		0			0
$253$	−144.000			−0.569170
$254$		−	96.9948i		−	0.381869i
$255$	−464.758	−	268.328i	−1.82258	−	1.05227i
$256$	256.000			1.00000
$257$	30.9839	+	53.6656i	0.120560	+	0.208816i	0.919989	−	0.391945i	$-0.128198\pi$
$257$	30.9839	+	53.6656i	0.120560	+	0.208816i	−0.799429	+	0.600761i	$0.794864\pi$
$258$	−216.887	+	375.659i	−0.840648	+	1.45604i
$259$		0			0
$260$	120.000	+	207.846i	0.461538	+	0.799408i
$261$	−143.000	−	247.683i	−0.547893	−	0.948978i
$262$	23.2379	−	13.4164i	0.0886943	−	0.0512077i
$263$	132.000	+	76.2102i	0.501901	+	0.289773i	0.729498	−	0.683983i	$-0.239754\pi$
$263$	132.000	+	76.2102i	0.501901	+	0.289773i	−0.227597	+	0.973755i	$0.573087\pi$
$264$	−123.935	−	214.663i	−0.469453	−	0.813116i
$265$	356.314			1.34458
$266$		0			0
$267$		−	277.128i		−	1.03793i
$268$	−312.000	−	180.133i	−1.16418	−	0.672139i
$269$	−19.3649	+	33.5410i	−0.0719885	+	0.124688i	−0.899773	−	0.436359i	$-0.856268\pi$
$269$	−19.3649	+	33.5410i	−0.0719885	+	0.124688i	0.827784	+	0.561047i	$0.189601\pi$
$270$	120.000	−	69.2820i	0.444444	−	0.256600i
$271$	92.9516	−	53.6656i	0.342995	−	0.198028i	−0.318601	−	0.947889i	$-0.603213\pi$
$271$	92.9516	−	53.6656i	0.342995	−	0.198028i	0.661596	+	0.749861i	$0.269880\pi$
$272$	123.935	−	214.663i	0.455645	−	0.789200i
$273$		0			0
$274$	−94.0000	+	162.813i	−0.343066	+	0.594207i
$275$	−210.000	+	121.244i	−0.763636	+	0.440886i
$276$	371.806			1.34712
$277$	107.000	−	185.329i	0.386282	−	0.669059i	−0.605665	−	0.795720i	$-0.707093\pi$
$277$	107.000	−	185.329i	0.386282	−	0.669059i	0.991946	+	0.126661i	$0.0404260\pi$
$278$			187.830i			0.675646i
$279$			295.161i			1.05792i
$280$		0			0
$281$	−194.000			−0.690391			−0.345196	−	0.938531i	$-0.612187\pi$
$281$	−194.000			−0.690391			−0.345196	+	0.938531i	$0.612187\pi$
$282$	720.000			2.55319
$283$	267.236	+	154.289i	0.944296	+	0.545190i	0.891304	−	0.453405i	$-0.149791\pi$
$283$	267.236	+	154.289i	0.944296	+	0.545190i	0.0529918	+	0.998595i	$0.483124\pi$
$284$			387.979i			1.36612i
$285$	−232.379	−	402.492i	−0.815365	−	1.41225i
$286$	92.9516	+	53.6656i	0.325006	+	0.187642i
$287$		0			0
$288$	176.000	+	304.841i	0.611111	+	1.05848i
$289$	24.5000	+	42.4352i	0.0847751	+	0.146835i
$290$	−201.395	−	348.827i	−0.694466	−	1.20285i
$291$	180.000	+	103.923i	0.618557	+	0.357124i
$292$	247.871	−	429.325i	0.848873	−	1.47029i
$293$	333.077			1.13678			0.568390	−	0.822759i	$-0.307566\pi$
$293$	333.077			1.13678			0.568390	+	0.822759i	$0.307566\pi$
$294$		0			0
$295$		−	519.615i		−	1.76141i
$296$	8.00000	+	13.8564i	0.0270270	+	0.0468122i
$297$	30.9839	−	53.6656i	0.104323	−	0.180692i
$298$	−26.0000	−	45.0333i	−0.0872483	−	0.151119i
$299$	−139.427	+	80.4984i	−0.466312	+	0.269226i
$300$	542.218	−	313.050i	1.80739	−	1.04350i
$301$		0			0
$302$	12.0000	+	6.92820i	0.0397351	+	0.0229411i
$303$	−270.000	+	155.885i	−0.891089	+	0.514471i
$304$	185.903	−	107.331i	0.611524	−	0.353063i
$305$	−30.0000	+	51.9615i	−0.0983607	+	0.170366i
$306$	340.823			1.11380
$307$		−	93.9149i		−	0.305912i	−0.988233	−	0.152956i	$-0.951121\pi$
$307$		−	93.9149i		−	0.305912i	0.988233	−	0.152956i	$-0.0488792\pi$
$308$		0			0
$309$	360.000			1.16505
$310$			415.692i			1.34094i
$311$	185.903	+	107.331i	0.597759	+	0.345117i	0.768160	−	0.640258i	$-0.221173\pi$
$311$	185.903	+	107.331i	0.597759	+	0.345117i	−0.170400	+	0.985375i	$0.554506\pi$
$312$	−240.000	−	138.564i	−0.769231	−	0.444116i
$313$	−131.681	−	228.079i	−0.420707	−	0.728687i	0.575301	−	0.817942i	$-0.304885\pi$
$313$	−131.681	−	228.079i	−0.420707	−	0.728687i	−0.996009	+	0.0892548i	$0.971551\pi$
$314$	−38.7298	+	67.0820i	−0.123343	+	0.213637i
$315$		0			0
$316$	96.0000	−	55.4256i	0.303797	−	0.175398i
$317$	239.000	+	413.960i	0.753943	+	1.30587i	0.945898	+	0.324464i	$0.105184\pi$
$317$	239.000	+	413.960i	0.753943	+	1.30587i	−0.191955	+	0.981404i	$0.561483\pi$
$318$	−356.314	+	205.718i	−1.12049	+	0.646913i
$319$	−156.000	−	90.0666i	−0.489028	−	0.282341i
$320$	247.871	+	429.325i	0.774597	+	1.34164i
$321$	−774.597			−2.41307
$322$		0			0
$323$		−	207.846i		−	0.643486i
$324$	118.000	−	204.382i	0.364198	−	0.630809i
$325$	−135.554	+	234.787i	−0.417091	+	0.722422i
$326$	300.000	−	173.205i	0.920245	−	0.531304i
$327$	364.060	−	210.190i	1.11333	−	0.642784i
$328$	−371.806			−1.13356
$329$		0			0
$330$	240.000	−	415.692i	0.727273	−	1.25967i
$331$	486.000	−	280.592i	1.46828	−	0.847711i	0.468910	−	0.883246i	$-0.344647\pi$
$331$	486.000	−	280.592i	1.46828	−	0.847711i	0.999368	+	0.0355355i	$0.0113137\pi$
$332$		−	375.659i		−	1.13150i
$333$	−11.0000	+	19.0526i	−0.0330330	+	0.0572149i
$334$			375.659i			1.12473i
$335$		−	697.653i		−	2.08255i
$336$		0			0
$337$	−446.000			−1.32344			−0.661721	−	0.749750i	$-0.730174\pi$
$337$	−446.000			−1.32344			−0.661721	+	0.749750i	$0.730174\pi$
$338$	−218.000			−0.644970
$339$	317.585	+	183.358i	0.936828	+	0.540878i
$340$	480.000			1.41176
$341$	92.9516	+	160.997i	0.272585	+	0.472132i
$342$	255.617	+	147.580i	0.747418	+	0.431522i
$343$		0			0
$344$		−	387.979i		−	1.12785i
$345$	360.000	+	623.538i	1.04348	+	1.80736i
$346$	−317.585	−	550.073i	−0.917875	−	1.58981i
$347$	258.000	+	148.956i	0.743516	+	0.429269i	0.823346	−	0.567539i	$-0.192105\pi$
$347$	258.000	+	148.956i	0.743516	+	0.429269i	−0.0798304	+	0.996808i	$0.525438\pi$
$348$	402.790	+	232.551i	1.15744	+	0.668250i
$349$	−209.141			−0.599258			−0.299629	−	0.954056i	$-0.596863\pi$
$349$	−209.141			−0.599258			−0.299629	+	0.954056i	$0.596863\pi$
$350$		0			0
$351$		−	69.2820i		−	0.197385i
$352$	192.000	+	110.851i	0.545455	+	0.314918i
$353$	−46.4758	+	80.4984i	−0.131659	+	0.228041i	−0.924316	−	0.381627i	$-0.875364\pi$
$353$	−46.4758	+	80.4984i	−0.131659	+	0.228041i	0.792657	+	0.609668i	$0.208697\pi$
$354$	300.000	+	519.615i	0.847458	+	1.46784i
$355$	−650.661	+	375.659i	−1.83285	+	1.05820i
$356$	123.935	+	214.663i	0.348133	+	0.602985i
$357$		0			0
$358$	180.000	+	103.923i	0.502793	+	0.290288i
$359$	−354.000	+	204.382i	−0.986072	+	0.569309i	−0.904098	−	0.427325i	$-0.859456\pi$
$359$	−354.000	+	204.382i	−0.986072	+	0.569309i	−0.0819745	+	0.996634i	$0.526123\pi$
$360$	−340.823	+	590.322i	−0.946729	+	1.63978i
$361$	−90.5000	+	156.751i	−0.250693	+	0.434212i
$362$	−418.282			−1.15548
$363$			326.466i			0.899355i
$364$		0			0
$365$	960.000			2.63014
$366$		−	69.2820i		−	0.189295i
$367$	−139.427	−	80.4984i	−0.379911	−	0.219342i	0.297868	−	0.954607i	$-0.403724\pi$
$367$	−139.427	−	80.4984i	−0.379911	−	0.219342i	−0.677780	+	0.735265i	$0.737058\pi$
$368$	−288.000	+	166.277i	−0.782609	+	0.451839i
$369$	−255.617	−	442.741i	−0.692729	−	1.19984i
$370$	−15.4919	+	26.8328i	−0.0418701	+	0.0725211i
$371$		0			0
$372$	−240.000	−	415.692i	−0.645161	−	1.11745i
$373$	−349.000	−	604.486i	−0.935657	−	1.62061i	−0.773458	−	0.633847i	$-0.781475\pi$
$373$	−349.000	−	604.486i	−0.935657	−	1.62061i	−0.162198	−	0.986758i	$-0.551858\pi$
$374$	185.903	−	107.331i	0.497067	−	0.286982i
$375$	300.000	+	173.205i	0.800000	+	0.461880i
$376$	−557.710	+	321.994i	−1.48327	+	0.856366i
$377$	−201.395			−0.534205
$378$		0			0
$379$			339.482i			0.895731i	0.894101	+	0.447865i	$0.147816\pi$
$379$			339.482i			0.895731i	−0.894101	+	0.447865i	$0.852184\pi$
$380$	360.000	+	207.846i	0.947368	+	0.546963i
$381$	−108.444	+	187.830i	−0.284629	+	0.492991i
$382$	−120.000	+	69.2820i	−0.314136	+	0.181367i
$383$	−69.7137	+	40.2492i	−0.182020	+	0.105089i	−0.588241	−	0.808685i	$-0.700180\pi$
$383$	−69.7137	+	40.2492i	−0.182020	+	0.105089i	0.406221	+	0.913775i	$0.366846\pi$
$384$	−495.742	−	286.217i	−1.29099	−	0.745356i
$385$		0			0
$386$	−38.0000	+	65.8179i	−0.0984456	+	0.170513i
$387$	462.000	−	266.736i	1.19380	−	0.689240i
$388$	−185.903			−0.479132
$389$	−47.0000	+	81.4064i	−0.120823	+	0.209271i	−0.920092	−	0.391702i	$-0.871887\pi$
$389$	−47.0000	+	81.4064i	−0.120823	+	0.209271i	0.799270	+	0.600973i	$0.205220\pi$
$390$		−	536.656i		−	1.37604i
$391$			321.994i			0.823514i
$392$		0			0
$393$	−60.0000			−0.152672
$394$	4.00000			0.0101523
$395$	185.903	+	107.331i	0.470641	+	0.271725i
$396$			304.841i			0.769800i
$397$	274.982	+	476.282i	0.692649	+	1.19970i	0.970967	+	0.239215i	$0.0768900\pi$
$397$	274.982	+	476.282i	0.692649	+	1.19970i	−0.278317	+	0.960489i	$0.589777\pi$
$398$	46.4758	+	26.8328i	0.116773	+	0.0674191i
$399$		0			0
$400$	−280.000	+	484.974i	−0.700000	+	1.21244i
$401$	−293.000	−	507.491i	−0.730673	−	1.26556i	−0.956596	−	0.291418i	$-0.905873\pi$
$401$	−293.000	−	507.491i	−0.730673	−	1.26556i	0.225922	−	0.974145i	$-0.427460\pi$
$402$	402.790	+	697.653i	1.00197	+	1.73546i
$403$	180.000	+	103.923i	0.446650	+	0.257874i
$404$	139.427	−	241.495i	0.345117	−	0.597761i
$405$	457.012			1.12842
$406$		0			0
$407$			13.8564i			0.0340452i
$408$	−480.000	+	277.128i	−1.17647	+	0.679236i
$409$	333.077	−	576.906i	0.814368	−	1.41053i	−0.0954126	−	0.995438i	$-0.530417\pi$
$409$	333.077	−	576.906i	0.814368	−	1.41053i	0.909781	−	0.415089i	$-0.136250\pi$
$410$	−360.000	−	623.538i	−0.878049	−	1.52083i
$411$	364.060	−	210.190i	0.885792	−	0.511412i
$412$	−278.855	+	160.997i	−0.676832	+	0.390769i
$413$		0			0
$414$	−396.000	−	228.631i	−0.956522	−	0.552248i
$415$	630.000	−	363.731i	1.51807	−	0.876459i
$416$	247.871			0.595844
$417$	210.000	−	363.731i	0.503597	−	0.872256i
$418$	185.903			0.444744
$419$		−	281.745i		−	0.672421i	−0.941787	−	0.336211i	$-0.890855\pi$
$419$		−	281.745i		−	0.672421i	0.941787	−	0.336211i	$-0.109145\pi$
$420$		0			0
$421$	−166.000			−0.394299			−0.197150	−	0.980373i	$-0.563168\pi$
$421$	−166.000			−0.394299			−0.197150	+	0.980373i	$0.563168\pi$
$422$		−	484.974i		−	1.14923i
$423$	−766.851	−	442.741i	−1.81289	−	1.04667i
$424$	184.000	−	318.697i	0.433962	−	0.751645i
$425$	271.109	+	469.574i	0.637903	+	1.10488i
$426$	433.774	−	751.319i	1.01825	−	1.76366i
$427$		0			0
$428$	600.000	−	346.410i	1.40187	−	0.809370i
$429$	−120.000	−	207.846i	−0.279720	−	0.484490i
$430$	650.661	−	375.659i	1.51317	−	0.873627i
$431$	90.0000	+	51.9615i	0.208817	+	0.120560i	0.600761	−	0.799428i	$-0.294864\pi$
$431$	90.0000	+	51.9615i	0.208817	+	0.120560i	−0.391945	+	0.919989i	$0.628198\pi$
$432$		−	143.108i		−	0.331269i
$433$	821.072			1.89624			0.948121	−	0.317911i	$-0.102981\pi$
$433$	821.072			1.89624			0.948121	+	0.317911i	$0.102981\pi$
$434$		0			0
$435$			900.666i			2.07050i
$436$	−188.000	+	325.626i	−0.431193	+	0.746848i
$437$	−139.427	+	241.495i	−0.319056	+	0.552621i
$438$	−960.000	+	554.256i	−2.19178	+	1.26543i
$439$	743.613	−	429.325i	1.69388	−	0.977961i	0.742547	−	0.669795i	$-0.233618\pi$
$439$	743.613	−	429.325i	1.69388	−	0.977961i	0.951332	−	0.308167i	$-0.0997155\pi$
$440$			429.325i			0.975739i
$441$		0			0
$442$	120.000	−	207.846i	0.271493	−	0.470240i
$443$	−270.000	+	155.885i	−0.609481	+	0.351884i	−0.772762	−	0.634696i	$-0.781125\pi$
$443$	−270.000	+	155.885i	−0.609481	+	0.351884i	0.163281	+	0.986580i	$0.447792\pi$
$444$		−	35.7771i		−	0.0805790i
$445$	−240.000	+	415.692i	−0.539326	+	0.934140i
$446$		−	751.319i		−	1.68457i
$447$			116.276i			0.260124i
$448$		0			0
$449$	−334.000			−0.743875			−0.371938	−	0.928258i	$-0.621306\pi$
$449$	−334.000			−0.743875			−0.371938	+	0.928258i	$0.621306\pi$
$450$	−770.000			−1.71111
$451$	−278.855	−	160.997i	−0.618303	−	0.356978i
$452$	−328.000			−0.725664
$453$	−15.4919	−	26.8328i	−0.0341985	−	0.0592336i
$454$	−116.190	−	67.0820i	−0.255924	−	0.147758i
$455$		0			0
$456$	−480.000			−1.05263
$457$	29.0000	+	50.2295i	0.0634573	+	0.109911i	0.896009	−	0.444037i	$-0.146454\pi$
$457$	29.0000	+	50.2295i	0.0634573	+	0.109911i	−0.832551	+	0.553948i	$0.813121\pi$
$458$	333.077	+	576.906i	0.727241	+	1.25962i
$459$	−120.000	−	69.2820i	−0.261438	−	0.150941i
$460$	−557.710	−	321.994i	−1.21241	−	0.699986i
$461$	441.520			0.957744			0.478872	−	0.877885i	$-0.341046\pi$
$461$	441.520			0.957744			0.478872	+	0.877885i	$0.341046\pi$
$462$		0			0
$463$			484.974i			1.04746i	0.851884	+	0.523730i	$0.175460\pi$
$463$			484.974i			1.04746i	−0.851884	+	0.523730i	$0.824540\pi$
$464$	−416.000			−0.896552
$465$	464.758	−	804.984i	0.999480	−	1.73115i
$466$	338.000	+	585.433i	0.725322	+	1.25629i
$467$	−313.712	+	181.122i	−0.671759	+	0.387840i	−0.796743	−	0.604318i	$-0.793446\pi$
$467$	−313.712	+	181.122i	−0.671759	+	0.387840i	0.124984	+	0.992159i	$0.460112\pi$
$468$	170.411	+	295.161i	0.364127	+	0.630686i
$469$		0			0
$470$	−1080.00	−	623.538i	−2.29787	−	1.32668i
$471$	150.000	−	86.6025i	0.318471	−	0.183870i
$472$	−464.758	−	268.328i	−0.984657	−	0.568492i
$473$	168.000	−	290.985i	0.355180	−	0.615189i
$474$	−247.871			−0.522934
$475$			469.574i			0.988577i
$476$		0			0
$477$	506.000			1.06080
$478$			484.974i			1.01459i
$479$	23.2379	+	13.4164i	0.0485134	+	0.0280092i	0.524061	−	0.851681i	$-0.324417\pi$
$479$	23.2379	+	13.4164i	0.0485134	+	0.0280092i	−0.475547	+	0.879690i	$0.657750\pi$
$480$		−	1108.51i		−	2.30940i
$481$	7.74597	+	13.4164i	0.0161039	+	0.0278927i
$482$	−201.395	+	348.827i	−0.417832	+	0.723707i
$483$		0			0
$484$	−146.000	−	252.879i	−0.301653	−	0.522478i
$485$	−180.000	−	311.769i	−0.371134	−	0.642823i
$486$	−596.439	+	344.354i	−1.22724	+	0.708548i
$487$	−582.000	−	336.018i	−1.19507	−	0.689975i	−0.235619	−	0.971845i	$-0.575712\pi$
$487$	−582.000	−	336.018i	−1.19507	−	0.689975i	−0.959453	+	0.281870i	$0.909045\pi$
$488$	30.9839	+	53.6656i	0.0634915	+	0.109971i
$489$	−774.597			−1.58404
$490$		0			0
$491$		−	145.492i		−	0.296318i	−0.988964	−	0.148159i	$-0.952665\pi$
$491$		−	145.492i		−	0.296318i	0.988964	−	0.148159i	$-0.0473348\pi$
$492$	720.000	+	415.692i	1.46341	+	0.844903i
$493$	−201.395	+	348.827i	−0.408509	+	0.707559i
$494$	180.000	−	103.923i	0.364372	−	0.210371i
$495$	−511.234	+	295.161i	−1.03280	+	0.596285i
$496$	371.806	+	214.663i	0.749610	+	0.432787i
$497$		0			0
$498$	−420.000	+	727.461i	−0.843373	+	1.46077i
$499$	−270.000	+	155.885i	−0.541082	+	0.312394i	−0.745517	−	0.666486i	$-0.767798\pi$
$499$	−270.000	+	155.885i	−0.541082	+	0.312394i	0.204435	+	0.978880i	$0.434464\pi$
$500$	−309.839			−0.619677
$501$	420.000	−	727.461i	0.838323	−	1.45202i
$502$			939.149i			1.87081i
$503$		−	375.659i		−	0.746838i	−0.927663	−	0.373419i	$-0.878185\pi$
$503$		−	375.659i		−	0.746838i	0.927663	−	0.373419i	$-0.121815\pi$
$504$		0			0
$505$	540.000			1.06931
$506$	−288.000			−0.569170
$507$	422.155	+	243.731i	0.832653	+	0.480733i
$508$		−	193.990i		−	0.381869i
$509$	58.0948	+	100.623i	0.114135	+	0.197688i	0.917434	−	0.397889i	$-0.130257\pi$
$509$	58.0948	+	100.623i	0.114135	+	0.197688i	−0.803299	+	0.595576i	$0.796924\pi$
$510$	−929.516	−	536.656i	−1.82258	−	1.05227i
$511$		0			0
$512$	512.000			1.00000
$513$	−60.0000	−	103.923i	−0.116959	−	0.202579i
$514$	61.9677	+	107.331i	0.120560	+	0.208816i
$515$	−540.000	−	311.769i	−1.04854	−	0.605377i
$516$	−433.774	+	751.319i	−0.840648	+	1.45604i
$517$	−557.710			−1.07874
$518$		0			0
$519$			1420.28i			2.73657i
$520$	240.000	+	415.692i	0.461538	+	0.799408i
$521$	−209.141	+	362.243i	−0.401422	+	0.695284i	−0.993898	−	0.110304i	$-0.964817\pi$
$521$	−209.141	+	362.243i	−0.401422	+	0.695284i	0.592475	+	0.805589i	$0.298151\pi$
$522$	−286.000	−	495.367i	−0.547893	−	0.948978i
$523$	336.950	−	194.538i	0.644263	−	0.371965i	−0.141992	−	0.989868i	$-0.545351\pi$
$523$	336.950	−	194.538i	0.644263	−	0.371965i	0.786255	+	0.617902i	$0.212017\pi$
$524$	46.4758	−	26.8328i	0.0886943	−	0.0512077i
$525$		0			0
$526$	264.000	+	152.420i	0.501901	+	0.289773i
$527$	360.000	−	207.846i	0.683112	−	0.394395i
$528$	−247.871	−	429.325i	−0.469453	−	0.813116i
$529$	−48.5000	+	84.0045i	−0.0916824	+	0.158799i
$530$	712.629			1.34458
$531$		−	737.902i		−	1.38965i
$532$		0			0
$533$	−360.000			−0.675422
$534$		−	554.256i		−	1.03793i
$535$	1161.90	+	670.820i	2.17177	+	1.25387i
$536$	−624.000	−	360.267i	−1.16418	−	0.672139i
$537$	−232.379	−	402.492i	−0.432736	−	0.749520i
$538$	−38.7298	+	67.0820i	−0.0719885	+	0.124688i
$539$		0			0
$540$	240.000	−	138.564i	0.444444	−	0.256600i
$541$	323.000	+	559.452i	0.597043	+	1.03411i	0.993255	+	0.115949i	$0.0369910\pi$
$541$	323.000	+	559.452i	0.597043	+	1.03411i	−0.396213	+	0.918159i	$0.629676\pi$
$542$	185.903	−	107.331i	0.342995	−	0.198028i
$543$	810.000	+	467.654i	1.49171	+	0.861241i
$544$	247.871	−	429.325i	0.455645	−	0.789200i
$545$	−728.121			−1.33600
$546$		0			0
$547$		−	48.4974i		−	0.0886607i	−0.999017	−	0.0443304i	$-0.985885\pi$
$547$		−	48.4974i		−	0.0886607i	0.999017	−	0.0443304i	$-0.0141154\pi$
$548$	−188.000	+	325.626i	−0.343066	+	0.594207i
$549$	−42.6028	+	73.7902i	−0.0776008	+	0.134408i
$550$	−420.000	+	242.487i	−0.763636	+	0.440886i
$551$	−302.093	+	174.413i	−0.548263	+	0.316540i
$552$	743.613			1.34712
$553$		0			0
$554$	214.000	−	370.659i	0.386282	−	0.669059i
$555$	60.0000	−	34.6410i	0.108108	−	0.0624162i
$556$			375.659i			0.675646i
$557$	359.000	−	621.806i	0.644524	−	1.11635i	−0.339887	−	0.940466i	$-0.610389\pi$
$557$	359.000	−	621.806i	0.644524	−	1.11635i	0.984411	−	0.175882i	$-0.0562779\pi$
$558$			590.322i			1.05792i
$559$		−	375.659i		−	0.672020i
$560$		0			0
$561$	−480.000			−0.855615
$562$	−388.000			−0.690391
$563$	−546.091	−	315.286i	−0.969966	−	0.560010i	−0.0707399	−	0.997495i	$-0.522536\pi$
$563$	−546.091	−	315.286i	−0.969966	−	0.560010i	−0.899226	+	0.437485i	$0.855869\pi$
$564$	1440.00			2.55319
$565$	−317.585	−	550.073i	−0.562097	−	0.973580i
$566$	534.472	+	308.577i	0.944296	+	0.545190i
$567$		0			0
$568$			775.959i			1.36612i
$569$	43.0000	+	74.4782i	0.0755712	+	0.130893i	0.901335	−	0.433124i	$-0.142589\pi$
$569$	43.0000	+	74.4782i	0.0755712	+	0.130893i	−0.825763	+	0.564017i	$0.809255\pi$
$570$	−464.758	−	804.984i	−0.815365	−	1.41225i
$571$	594.000	+	342.946i	1.04028	+	0.600606i	0.919913	−	0.392123i	$-0.128259\pi$
$571$	594.000	+	342.946i	1.04028	+	0.600606i	0.120368	+	0.992729i	$0.461593\pi$
$572$	185.903	+	107.331i	0.325006	+	0.187642i
$573$	309.839			0.540731
$574$		0			0
$575$		−	727.461i		−	1.26515i
$576$	352.000	+	609.682i	0.611111	+	1.05848i
$577$	−263.363	+	456.158i	−0.456435	+	0.790568i	−0.998769	−	0.0495943i	$-0.984207\pi$
$577$	−263.363	+	456.158i	−0.456435	+	0.790568i	0.542335	+	0.840163i	$0.317540\pi$
$578$	49.0000	+	84.8705i	0.0847751	+	0.146835i
$579$	147.173	−	84.9706i	0.254185	−	0.146754i
$580$	−402.790	−	697.653i	−0.694466	−	1.20285i
$581$		0			0
$582$	360.000	+	207.846i	0.618557	+	0.357124i
$583$	276.000	−	159.349i	0.473413	−	0.273325i
$584$	495.742	−	858.650i	0.848873	−	1.47029i
$585$	−330.000	+	571.577i	−0.564103	+	0.977054i
$586$	666.153			1.13678
$587$			469.574i			0.799956i	0.916525	+	0.399978i	$0.130982\pi$
$587$			469.574i			0.799956i	−0.916525	+	0.399978i	$0.869018\pi$
$588$		0			0
$589$	360.000			0.611205
$590$		−	1039.23i		−	1.76141i
$591$	−7.74597	−	4.47214i	−0.0131065	−	0.00756707i
$592$	16.0000	+	27.7128i	0.0270270	+	0.0468122i
$593$	−77.4597	−	134.164i	−0.130623	−	0.226246i	0.793294	−	0.608839i	$-0.208365\pi$
$593$	−77.4597	−	134.164i	−0.130623	−	0.226246i	−0.923917	+	0.382593i	$0.875031\pi$
$594$	61.9677	−	107.331i	0.104323	−	0.180692i
$595$		0			0
$596$	−52.0000	−	90.0666i	−0.0872483	−	0.151119i
$597$	−60.0000	−	103.923i	−0.100503	−	0.174075i
$598$	−278.855	+	160.997i	−0.466312	+	0.269226i
$599$	−624.000	−	360.267i	−1.04174	−	0.601447i	−0.121412	−	0.992602i	$-0.538742\pi$
$599$	−624.000	−	360.267i	−1.04174	−	0.601447i	−0.920325	+	0.391156i	$0.872075\pi$
$600$	1084.44	−	626.099i	1.80739	−	1.04350i
$601$	495.742			0.824862			0.412431	−	0.910989i	$-0.364680\pi$
$601$	495.742			0.824862			0.412431	+	0.910989i	$0.364680\pi$
$602$		0			0
$603$		−	990.733i		−	1.64301i
$604$	24.0000	+	13.8564i	0.0397351	+	0.0229411i
$605$	282.728	−	489.699i	0.467319	−	0.809420i
$606$	−540.000	+	311.769i	−0.891089	+	0.514471i
$607$	−557.710	+	321.994i	−0.918797	+	0.530468i	−0.883251	−	0.468901i	$-0.844650\pi$
$607$	−557.710	+	321.994i	−0.918797	+	0.530468i	−0.0355457	+	0.999368i	$0.511317\pi$
$608$	371.806	−	214.663i	0.611524	−	0.353063i
$609$		0			0
$610$	−60.0000	+	103.923i	−0.0983607	+	0.170366i
$611$	−540.000	+	311.769i	−0.883797	+	0.510260i
$612$	681.645			1.11380
$613$	−131.000	+	226.899i	−0.213703	+	0.370145i	−0.952871	−	0.303377i	$-0.901886\pi$
$613$	−131.000	+	226.899i	−0.213703	+	0.370145i	0.739168	+	0.673522i	$0.235219\pi$
$614$		−	187.830i		−	0.305912i
$615$			1609.97i			2.61784i
$616$		0			0
$617$	898.000			1.45543			0.727715	−	0.685880i	$-0.240582\pi$
$617$	898.000			1.45543			0.727715	+	0.685880i	$0.240582\pi$
$618$	720.000			1.16505
$619$	−708.756	−	409.200i	−1.14500	−	0.661067i	−0.197337	−	0.980336i	$-0.563229\pi$
$619$	−708.756	−	409.200i	−1.14500	−	0.661067i	−0.947664	+	0.319269i	$0.896563\pi$
$620$			831.384i			1.34094i
$621$	92.9516	+	160.997i	0.149681	+	0.259254i
$622$	371.806	+	214.663i	0.597759	+	0.345117i
$623$		0			0
$624$	−480.000	−	277.128i	−0.769231	−	0.444116i
$625$	137.500	+	238.157i	0.220000	+	0.381051i
$626$	−263.363	−	456.158i	−0.420707	−	0.728687i
$627$	−360.000	−	207.846i	−0.574163	−	0.331493i
$628$	−77.4597	+	134.164i	−0.123343	+	0.213637i
$629$	30.9839			0.0492589
$630$		0			0
$631$		−	581.969i		−	0.922296i	−0.887323	−	0.461148i	$-0.847438\pi$
$631$		−	581.969i		−	0.922296i	0.887323	−	0.461148i	$-0.152562\pi$
$632$	192.000	−	110.851i	0.303797	−	0.175398i
$633$	−542.218	+	939.149i	−0.856584	+	1.48365i
$634$	478.000	+	827.920i	0.753943	+	1.30587i
$635$	325.331	−	187.830i	0.512332	−	0.295795i
$636$	−712.629	+	411.437i	−1.12049	+	0.646913i
$637$		0			0
$638$	−312.000	−	180.133i	−0.489028	−	0.282341i
$639$	−924.000	+	533.472i	−1.44601	+	0.834854i
$640$	495.742	+	858.650i	0.774597	+	1.34164i
$641$	−173.000	+	299.645i	−0.269891	+	0.467465i	−0.968833	−	0.247713i	$-0.920321\pi$
$641$	−173.000	+	299.645i	−0.269891	+	0.467465i	0.698943	+	0.715178i	$0.253654\pi$
$642$	−1549.19			−2.41307
$643$			93.9149i			0.146057i	0.997330	+	0.0730287i	$0.0232665\pi$
$643$			93.9149i			0.146057i	−0.997330	+	0.0730287i	$0.976734\pi$
$644$		0			0
$645$	−1680.00			−2.60465
$646$		−	415.692i		−	0.643486i
$647$	23.2379	+	13.4164i	0.0359164	+	0.0207363i	0.517851	−	0.855471i	$-0.326732\pi$
$647$	23.2379	+	13.4164i	0.0359164	+	0.0207363i	−0.481934	+	0.876207i	$0.660066\pi$
$648$	236.000	−	408.764i	0.364198	−	0.630809i
$649$	−232.379	−	402.492i	−0.358057	−	0.620173i
$650$	−271.109	+	469.574i	−0.417091	+	0.722422i
$651$		0			0
$652$	600.000	−	346.410i	0.920245	−	0.531304i
$653$	−83.0000	−	143.760i	−0.127106	−	0.220153i	0.795448	−	0.606021i	$-0.207235\pi$
$653$	−83.0000	−	143.760i	−0.127106	−	0.220153i	−0.922554	+	0.385868i	$0.873902\pi$
$654$	728.121	−	420.381i	1.11333	−	0.642784i
$655$	90.0000	+	51.9615i	0.137405	+	0.0793306i
$656$	−743.613			−1.13356
$657$	1363.29			2.07502
$658$		0			0
$659$		−	242.487i		−	0.367962i	−0.982930	−	0.183981i	$-0.941101\pi$
$659$		−	242.487i		−	0.367962i	0.982930	−	0.183981i	$-0.0588985\pi$
$660$	480.000	−	831.384i	0.727273	−	1.25967i
$661$	251.744	−	436.033i	0.380853	−	0.659657i	−0.610331	−	0.792146i	$-0.708964\pi$
$661$	251.744	−	436.033i	0.380853	−	0.659657i	0.991184	+	0.132489i	$0.0422970\pi$
$662$	972.000	−	561.184i	1.46828	−	0.847711i
$663$	−464.758	+	268.328i	−0.700992	+	0.404718i
$664$		−	751.319i		−	1.13150i
$665$		0			0
$666$	−22.0000	+	38.1051i	−0.0330330	+	0.0572149i
$667$	468.000	−	270.200i	0.701649	−	0.405097i
$668$			751.319i			1.12473i
$669$	−840.000	+	1454.92i	−1.25561	+	2.17477i
$670$		−	1395.31i		−	2.08255i
$671$			53.6656i			0.0799786i
$672$		0			0
$673$	−194.000			−0.288262			−0.144131	−	0.989559i	$-0.546039\pi$
$673$	−194.000			−0.288262			−0.144131	+	0.989559i	$0.546039\pi$
$674$	−892.000			−1.32344
$675$	271.109	+	156.525i	0.401643	+	0.231889i
$676$	−436.000			−0.644970
$677$	−267.236	−	462.866i	−0.394735	−	0.683702i	0.598332	−	0.801248i	$-0.295830\pi$
$677$	−267.236	−	462.866i	−0.394735	−	0.683702i	−0.993067	+	0.117547i	$0.962497\pi$
$678$	635.169	+	366.715i	0.936828	+	0.540878i
$679$		0			0
$680$	960.000			1.41176
$681$	150.000	+	259.808i	0.220264	+	0.381509i
$682$	185.903	+	321.994i	0.272585	+	0.472132i
$683$	762.000	+	439.941i	1.11567	+	0.644130i	0.940291	−	0.340372i	$-0.110553\pi$
$683$	762.000	+	439.941i	1.11567	+	0.644130i	0.175375	+	0.984502i	$0.443886\pi$
$684$	511.234	+	295.161i	0.747418	+	0.431522i
$685$	−728.121			−1.06295
$686$		0			0
$687$		−	1489.56i		−	2.16821i
$688$		−	775.959i		−	1.12785i
$689$	178.157	−	308.577i	0.258574	−	0.447863i
$690$	720.000	+	1247.08i	1.04348	+	1.80736i
$691$	662.280	−	382.368i	0.958437	−	0.553354i	0.0627455	−	0.998030i	$-0.480014\pi$
$691$	662.280	−	382.368i	0.958437	−	0.553354i	0.895692	+	0.444676i	$0.146681\pi$
$692$	−635.169	−	1100.15i	−0.917875	−	1.58981i
$693$		0			0
$694$	516.000	+	297.913i	0.743516	+	0.429269i
$695$	−630.000	+	363.731i	−0.906475	+	0.523353i
$696$	805.581	+	465.102i	1.15744	+	0.668250i
$697$	−360.000	+	623.538i	−0.516499	+	0.894603i
$698$	−418.282			−0.599258
$699$		−	1511.58i		−	2.16249i
$700$		0			0
$701$	−362.000			−0.516405			−0.258203	−	0.966091i	$-0.583130\pi$
$701$	−362.000			−0.516405			−0.258203	+	0.966091i	$0.583130\pi$
$702$		−	138.564i		−	0.197385i
$703$	23.2379	+	13.4164i	0.0330553	+	0.0190845i
$704$	384.000	+	221.703i	0.545455	+	0.314918i
$705$	1394.27	+	2414.95i	1.97769	+	3.42547i
$706$	−92.9516	+	160.997i	−0.131659	+	0.228041i
$707$		0			0
$708$	600.000	+	1039.23i	0.847458	+	1.46784i
$709$	169.000	+	292.717i	0.238364	+	0.412858i	0.960245	−	0.279159i	$-0.0900556\pi$
$709$	169.000	+	292.717i	0.238364	+	0.412858i	−0.721881	+	0.692017i	$0.756722\pi$
$710$	−1301.32	+	751.319i	−1.83285	+	1.05820i
$711$	264.000	+	152.420i	0.371308	+	0.214375i
$712$	247.871	+	429.325i	0.348133	+	0.602985i
$713$	−557.710			−0.782201
$714$		0			0
$715$			415.692i			0.581388i
$716$	360.000	+	207.846i	0.502793	+	0.290288i
$717$	542.218	−	939.149i	0.756231	−	1.30983i
$718$	−708.000	+	408.764i	−0.986072	+	0.569309i
$719$	255.617	−	147.580i	0.355517	−	0.205258i	−0.311595	−	0.950215i	$-0.600863\pi$
$719$	255.617	−	147.580i	0.355517	−	0.205258i	0.667113	+	0.744957i	$0.267530\pi$
$720$	−681.645	+	1180.64i	−0.946729	+	1.63978i
$721$		0			0
$722$	−181.000	+	313.501i	−0.250693	+	0.434212i
$723$	780.000	−	450.333i	1.07884	−	0.622868i
$724$	−836.564			−1.15548
$725$	455.000	−	788.083i	0.627586	−	1.08701i
$726$			652.932i			0.899355i
$727$		−	939.149i		−	1.29181i	−0.763416	−	0.645907i	$-0.776479\pi$
$727$		−	939.149i		−	1.29181i	0.763416	−	0.645907i	$-0.223521\pi$
$728$		0			0
$729$	1009.00			1.38409
$730$	1920.00			2.63014
$731$	−650.661	−	375.659i	−0.890097	−	0.513898i
$732$		−	138.564i		−	0.189295i
$733$	546.091	+	945.857i	0.745008	+	1.29039i	0.950191	+	0.311668i	$0.100888\pi$
$733$	546.091	+	945.857i	0.745008	+	1.29039i	−0.205183	+	0.978724i	$0.565779\pi$
$734$	−278.855	−	160.997i	−0.379911	−	0.219342i
$735$		0			0
$736$	−576.000	+	332.554i	−0.782609	+	0.451839i
$737$	−312.000	−	540.400i	−0.423338	−	0.733243i
$738$	−511.234	−	885.483i	−0.692729	−	1.19984i
$739$	−246.000	−	142.028i	−0.332882	−	0.192190i	0.324238	−	0.945976i	$-0.394892\pi$
$739$	−246.000	−	142.028i	−0.332882	−	0.192190i	−0.657120	+	0.753786i	$0.728226\pi$
$740$	−30.9839	+	53.6656i	−0.0418701	+	0.0725211i
$741$	−464.758			−0.627204
$742$		0			0
$743$		−	1212.44i		−	1.63181i	−0.578185	−	0.815905i	$-0.696239\pi$
$743$		−	1212.44i		−	1.63181i	0.578185	−	0.815905i	$-0.303761\pi$
$744$	−480.000	−	831.384i	−0.645161	−	1.11745i
$745$	100.698	−	174.413i	0.135165	−	0.234112i
$746$	−698.000	−	1208.97i	−0.935657	−	1.62061i
$747$	894.659	−	516.532i	1.19767	−	0.691475i
$748$	371.806	−	214.663i	0.497067	−	0.286982i
$749$		0			0
$750$	600.000	+	346.410i	0.800000	+	0.461880i
$751$	−690.000	+	398.372i	−0.918775	+	0.530455i	−0.883244	−	0.468914i	$-0.844646\pi$
$751$	−690.000	+	398.372i	−0.918775	+	0.530455i	−0.0355309	+	0.999369i	$0.511312\pi$
$752$	−1115.42	+	643.988i	−1.48327	+	0.856366i
$753$	1050.00	−	1818.65i	1.39442	−	2.41521i
$754$	−402.790			−0.534205
$755$			53.6656i			0.0710803i
$756$		0			0
$757$	−362.000			−0.478203			−0.239102	−	0.970995i	$-0.576853\pi$
$757$	−362.000			−0.478203			−0.239102	+	0.970995i	$0.576853\pi$
$758$			678.964i			0.895731i
$759$	557.710	+	321.994i	0.734795	+	0.424234i
$760$	720.000	+	415.692i	0.947368	+	0.546963i
$761$	−457.012	−	791.568i	−0.600541	−	1.04017i	−0.992739	−	0.120287i	$-0.961618\pi$
$761$	−457.012	−	791.568i	−0.600541	−	1.04017i	0.392198	−	0.919881i	$-0.371715\pi$
$762$	−216.887	+	375.659i	−0.284629	+	0.492991i
$763$		0			0
$764$	−240.000	+	138.564i	−0.314136	+	0.181367i
$765$	660.000	+	1143.15i	0.862745	+	1.49432i
$766$	−139.427	+	80.4984i	−0.182020	+	0.105089i
$767$	−450.000	−	259.808i	−0.586701	−	0.338732i
$768$	−991.484	−	572.433i	−1.29099	−	0.745356i
$769$	170.411			0.221601			0.110801	−	0.993843i	$-0.464659\pi$
$769$	170.411			0.221601			0.110801	+	0.993843i	$0.464659\pi$
$770$		0			0
$771$		−	277.128i		−	0.359440i
$772$	−76.0000	+	131.636i	−0.0984456	+	0.170513i
$773$	143.300	−	248.204i	0.185382	−	0.321091i	−0.758323	−	0.651879i	$-0.773981\pi$
$773$	143.300	−	248.204i	0.185382	−	0.321091i	0.943705	+	0.330788i	$0.107314\pi$
$774$	924.000	−	533.472i	1.19380	−	0.689240i
$775$	−813.327	+	469.574i	−1.04945	+	0.605902i
$776$	−371.806			−0.479132
$777$		0			0
$778$	−94.0000	+	162.813i	−0.120823	+	0.209271i
$779$	−540.000	+	311.769i	−0.693196	+	0.400217i
$780$		−	1073.31i		−	1.37604i
$781$	−336.000	+	581.969i	−0.430218	+	0.745159i
$782$			643.988i			0.823514i
$783$			232.551i			0.297000i
$784$		0			0
$785$	−300.000			−0.382166
$786$	−120.000			−0.152672
$787$	−708.756	−	409.200i	−0.900579	−	0.519950i	−0.0231912	−	0.999731i	$-0.507383\pi$
$787$	−708.756	−	409.200i	−0.900579	−	0.519950i	−0.877388	+	0.479781i	$0.840716\pi$
$788$	8.00000			0.0101523
$789$	−340.823	−	590.322i	−0.431968	−	0.748190i
$790$	371.806	+	214.663i	0.470641	+	0.271725i
$791$		0			0
$792$			609.682i			0.769800i
$793$	30.0000	+	51.9615i	0.0378310	+	0.0655253i
$794$	549.964	+	952.565i	0.692649	+	1.19970i
$795$	−1380.00	−	796.743i	−1.73585	−	1.00219i
$796$	92.9516	+	53.6656i	0.116773	+	0.0674191i
$797$	224.633			0.281848			0.140924	−	0.990020i	$-0.454993\pi$
$797$	224.633			0.281848			0.140924	+	0.990020i	$0.454993\pi$
$798$		0			0
$799$			1247.08i			1.56080i
$800$	−560.000	+	969.948i	−0.700000	+	1.21244i
$801$	−340.823	+	590.322i	−0.425496	+	0.736981i
$802$	−586.000	−	1014.98i	−0.730673	−	1.26556i
$803$	743.613	−	429.325i	0.926043	−	0.534651i
$804$	805.581	+	1395.31i	1.00197	+	1.73546i
$805$		0			0
$806$	360.000	+	207.846i	0.446650	+	0.257874i
$807$	150.000	−	86.6025i	0.185874	−	0.107314i
$808$	278.855	−	482.991i	0.345117	−	0.597761i
$809$	−523.000	+	905.863i	−0.646477	+	1.11973i	0.337481	+	0.941332i	$0.390425\pi$
$809$	−523.000	+	905.863i	−0.646477	+	1.11973i	−0.983958	+	0.178399i	$0.942908\pi$
$810$	914.024			1.12842
$811$			281.745i			0.347404i	0.984798	+	0.173702i	$0.0555729\pi$
$811$			281.745i			0.347404i	−0.984798	+	0.173702i	$0.944427\pi$
$812$		0			0
$813$	−480.000			−0.590406
$814$			27.7128i			0.0340452i
$815$	1161.90	+	670.820i	1.42564	+	0.823093i
$816$	−960.000	+	554.256i	−1.17647	+	0.679236i
$817$	−325.331	−	563.489i	−0.398201	−	0.689705i
$818$	666.153	−	1153.81i	0.814368	−	1.41053i
$819$		0			0
$820$	−720.000	−	1247.08i	−0.878049	−	1.52083i
$821$	659.000	+	1141.42i	0.802680	+	1.39028i	0.917846	+	0.396936i	$0.129926\pi$
$821$	659.000	+	1141.42i	0.802680	+	1.39028i	−0.115167	+	0.993346i	$0.536740\pi$
$822$	728.121	−	420.381i	0.885792	−	0.511412i
$823$	468.000	+	270.200i	0.568651	+	0.328311i	0.756610	−	0.653866i	$-0.226854\pi$
$823$	468.000	+	270.200i	0.568651	+	0.328311i	−0.187959	+	0.982177i	$0.560187\pi$
$824$	−557.710	+	321.994i	−0.676832	+	0.390769i
$825$	1084.44			1.31447
$826$		0			0
$827$			533.472i			0.645068i	0.946558	+	0.322534i	$0.104535\pi$
$827$			533.472i			0.645068i	−0.946558	+	0.322534i	$0.895465\pi$
$828$	−792.000	−	457.261i	−0.956522	−	0.552248i
$829$	34.8569	−	60.3738i	0.0420469	−	0.0728273i	−0.844236	−	0.535971i	$-0.819945\pi$
$829$	34.8569	−	60.3738i	0.0420469	−	0.0728273i	0.886283	+	0.463144i	$0.153279\pi$
$830$	1260.00	−	727.461i	1.51807	−	0.876459i
$831$	−828.818	+	478.519i	−0.997375	+	0.575835i
$832$	495.742			0.595844
$833$		0			0
$834$	420.000	−	727.461i	0.503597	−	0.872256i
$835$	−1260.00	+	727.461i	−1.50898	+	0.871211i
$836$	371.806			0.444744
$837$	120.000	−	207.846i	0.143369	−	0.248323i
$838$		−	563.489i		−	0.672421i
$839$			1314.81i			1.56711i	0.621320	+	0.783557i	$0.286597\pi$
$839$			1314.81i			1.56711i	−0.621320	+	0.783557i	$0.713403\pi$
$840$		0			0
$841$	−165.000			−0.196195
$842$	−332.000			−0.394299
$843$	751.359	+	433.797i	0.891292	+	0.514587i
$844$		−	969.948i		−	1.14923i
$845$	−422.155	−	731.194i	−0.499592	−	0.865319i
$846$	−1533.70	−	885.483i	−1.81289	−	1.04667i
$847$		0			0
$848$	368.000	−	637.395i	0.433962	−	0.751645i
$849$	−690.000	−	1195.12i	−0.812721	−	1.40767i
$850$	542.218	+	939.149i	0.637903	+	1.10488i
$851$	−36.0000	−	20.7846i	−0.0423032	−	0.0244237i
$852$	867.548	−	1502.64i	1.01825	−	1.76366i
$853$	−1510.46			−1.77077			−0.885383	−	0.464862i	$-0.846104\pi$
$853$	−1510.46			−1.77077			−0.885383	+	0.464862i	$0.846104\pi$
$854$		0			0
$855$			1143.15i			1.33702i
$856$	1200.00	−	692.820i	1.40187	−	0.809370i
$857$	−317.585	+	550.073i	−0.370577	+	0.641858i	−0.989654	−	0.143472i	$-0.954173\pi$
$857$	−317.585	+	550.073i	−0.370577	+	0.641858i	0.619077	+	0.785330i	$0.287507\pi$
$858$	−240.000	−	415.692i	−0.279720	−	0.484490i
$859$	−1127.04	+	650.696i	−1.31204	+	0.757504i	−0.982433	−	0.186616i	$-0.940248\pi$
$859$	−1127.04	+	650.696i	−1.31204	+	0.757504i	−0.329602	+	0.944120i	$0.606915\pi$
$860$	1301.32	−	751.319i	1.51317	−	0.873627i
$861$		0			0
$862$	180.000	+	103.923i	0.208817	+	0.120560i
$863$	948.000	−	547.328i	1.09849	−	0.634216i	0.162669	−	0.986681i	$-0.447990\pi$
$863$	948.000	−	547.328i	1.09849	−	0.634216i	0.935825	+	0.352465i	$0.114656\pi$
$864$		−	286.217i		−	0.331269i
$865$	1230.00	−	2130.42i	1.42197	−	2.46292i
$866$	1642.14			1.89624
$867$		−	219.135i		−	0.252750i
$868$		0			0
$869$	192.000			0.220944
$870$			1801.33i			2.07050i
$871$	−604.185	−	348.827i	−0.693669	−	0.400490i
$872$	−376.000	+	651.251i	−0.431193	+	0.746848i
$873$	−255.617	−	442.741i	−0.292803	−	0.507149i
$874$	−278.855	+	482.991i	−0.319056	+	0.552621i
$875$		0			0
$876$	−1920.00	+	1108.51i	−2.19178	+	1.26543i
$877$	−167.000	−	289.252i	−0.190422	−	0.329820i	0.754968	−	0.655761i	$-0.227652\pi$
$877$	−167.000	−	289.252i	−0.190422	−	0.329820i	−0.945390	+	0.325941i	$0.894319\pi$
$878$	1487.23	−	858.650i	1.69388	−	0.977961i
$879$	−1290.00	−	744.782i	−1.46758	−	0.847306i
$880$			858.650i			0.975739i
$881$	929.516			1.05507			0.527535	−	0.849534i	$-0.323117\pi$
$881$	929.516			1.05507			0.527535	+	0.849534i	$0.323117\pi$
$882$		0			0
$883$		−	921.451i		−	1.04355i	−0.853084	−	0.521773i	$-0.825271\pi$
$883$		−	921.451i		−	1.04355i	0.853084	−	0.521773i	$-0.174729\pi$
$884$	240.000	−	415.692i	0.271493	−	0.470240i
$885$	−1161.90	+	2012.46i	−1.31288	+	2.27397i
$886$	−540.000	+	311.769i	−0.609481	+	0.351884i
$887$	−69.7137	+	40.2492i	−0.0785949	+	0.0453768i	−0.538782	−	0.842445i	$-0.681116\pi$
$887$	−69.7137	+	40.2492i	−0.0785949	+	0.0453768i	0.460188	+	0.887822i	$0.347782\pi$
$888$		−	71.5542i		−	0.0805790i
$889$		0			0
$890$	−480.000	+	831.384i	−0.539326	+	0.934140i
$891$	354.000	−	204.382i	0.397306	−	0.229385i
$892$		−	1502.64i		−	1.68457i
$893$	−540.000	+	935.307i	−0.604703	+	1.04738i
$894$			232.551i			0.260124i
$895$			804.984i			0.899424i
$896$		0			0
$897$	720.000			0.802676
$898$	−668.000			−0.743875
$899$	−604.185	−	348.827i	−0.672064	−	0.388016i
$900$	−1540.00			−1.71111
$901$	−356.314	−	617.155i	−0.395466	−	0.684966i
$902$	−557.710	−	321.994i	−0.618303	−	0.356978i
$903$		0			0
$904$	−656.000			−0.725664
$905$	−810.000	−	1402.96i	−0.895028	−	1.55023i
$906$	−30.9839	−	53.6656i	−0.0341985	−	0.0592336i
$907$	510.000	+	294.449i	0.562293	+	0.324640i	0.754065	−	0.656799i	$-0.228090\pi$
$907$	510.000	+	294.449i	0.562293	+	0.324640i	−0.191772	+	0.981439i	$0.561423\pi$
$908$	−232.379	−	134.164i	−0.255924	−	0.147758i
$909$	766.851			0.843620
$910$		0			0
$911$			1600.41i			1.75677i	0.477956	+	0.878384i	$0.341378\pi$
$911$			1600.41i			1.75677i	−0.477956	+	0.878384i	$0.658622\pi$
$912$	−960.000			−1.05263
$913$	325.331	−	563.489i	0.356331	−	0.617184i
$914$	58.0000	+	100.459i	0.0634573	+	0.109911i
$915$	232.379	−	134.164i	0.253966	−	0.146627i
$916$	666.153	+	1153.81i	0.727241	+	1.25962i
$917$		0			0
$918$	−240.000	−	138.564i	−0.261438	−	0.150941i
$919$	444.000	−	256.344i	0.483134	−	0.278937i	−0.238588	−	0.971121i	$-0.576684\pi$
$919$	444.000	−	256.344i	0.483134	−	0.278937i	0.721722	+	0.692183i	$0.243351\pi$
$920$	−1115.42	−	643.988i	−1.21241	−	0.699986i
$921$	−210.000	+	363.731i	−0.228013	+	0.394930i
$922$	883.040			0.957744
$923$			751.319i			0.813997i
$924$		0			0
$925$	−70.0000			−0.0756757
$926$			969.948i			1.04746i
$927$	−766.851	−	442.741i	−0.827239	−	0.477607i
$928$	−832.000			−0.896552
$929$	410.536	+	711.070i	0.441912	+	0.765414i	0.997831	−	0.0658222i	$-0.0209670\pi$
$929$	410.536	+	711.070i	0.441912	+	0.765414i	−0.555919	+	0.831236i	$0.687634\pi$
$930$	929.516	−	1609.97i	0.999480	−	1.73115i
$931$		0			0
$932$	676.000	+	1170.87i	0.725322	+	1.25629i
$933$	−480.000	−	831.384i	−0.514469	−	0.891087i
$934$	−627.423	+	362.243i	−0.671759	+	0.387840i
$935$	720.000	+	415.692i	0.770053	+	0.444591i
$936$	340.823	+	590.322i	0.364127	+	0.630686i
$937$	−1239.35			−1.32268			−0.661342	−	0.750085i	$-0.730013\pi$
$937$	−1239.35			−1.32268			−0.661342	+	0.750085i	$0.730013\pi$
$938$		0			0
$939$			1177.79i			1.25431i
$940$	−2160.00	−	1247.08i	−2.29787	−	1.32668i
$941$	577.075	−	999.522i	0.613257	−	1.06219i	−0.377431	−	0.926038i	$-0.623192\pi$
$941$	577.075	−	999.522i	0.613257	−	1.06219i	0.990688	−	0.136154i	$-0.0434742\pi$
$942$	300.000	−	173.205i	0.318471	−	0.183870i
$943$	836.564	−	482.991i	0.887131	−	0.512185i
$944$	−929.516	−	536.656i	−0.984657	−	0.568492i
$945$		0			0
$946$	336.000	−	581.969i	0.355180	−	0.615189i
$947$	990.000	−	571.577i	1.04541	−	0.603566i	0.124047	−	0.992276i	$-0.460413\pi$
$947$	990.000	−	571.577i	1.04541	−	0.603566i	0.921360	+	0.388711i	$0.127079\pi$
$948$	−495.742			−0.522934
$949$	480.000	−	831.384i	0.505796	−	0.876064i
$950$			939.149i			0.988577i
$951$		−	2137.68i		−	2.24782i
$952$		0			0
$953$	338.000			0.354669			0.177335	−	0.984151i	$-0.443252\pi$
$953$	338.000			0.354669			0.177335	+	0.984151i	$0.443252\pi$
$954$	1012.00			1.06080
$955$	−464.758	−	268.328i	−0.486658	−	0.280972i
$956$			969.948i			1.01459i
$957$	402.790	+	697.653i	0.420888	+	0.729000i
$958$	46.4758	+	26.8328i	0.0485134	+	0.0280092i
$959$		0			0
$960$		−	2217.03i		−	2.30940i
$961$	−120.500	−	208.712i	−0.125390	−	0.217182i
$962$	15.4919	+	26.8328i	0.0161039	+	0.0278927i
$963$	1650.00	+	952.628i	1.71340	+	0.989229i
$964$	−402.790	+	697.653i	−0.417832	+	0.723707i
$965$	−294.347			−0.305023
$966$		0			0
$967$			727.461i			0.752287i	0.926561	+	0.376143i	$0.122750\pi$
$967$			727.461i			0.752287i	−0.926561	+	0.376143i	$0.877250\pi$
$968$	−292.000	−	505.759i	−0.301653	−	0.522478i
$969$	−464.758	+	804.984i	−0.479626	+	0.830737i
$970$	−360.000	−	623.538i	−0.371134	−	0.642823i
$971$	−964.373	+	556.781i	−0.993175	+	0.573410i	−0.906222	−	0.422803i	$-0.861046\pi$
$971$	−964.373	+	556.781i	−0.993175	+	0.573410i	−0.0869531	+	0.996212i	$0.527713\pi$
$972$	−1192.88	+	688.709i	−1.22724	+	0.708548i
$973$		0			0
$974$	−1164.00	−	672.036i	−1.19507	−	0.689975i
$975$	1050.00	−	606.218i	1.07692	−	0.621762i
$976$	61.9677	+	107.331i	0.0634915	+	0.109971i
$977$	121.000	−	209.578i	0.123849	−	0.214512i	−0.797434	−	0.603407i	$-0.793810\pi$
$977$	121.000	−	209.578i	0.123849	−	0.214512i	0.921282	+	0.388895i	$0.127143\pi$
$978$	−1549.19			−1.58404
$979$			429.325i			0.438534i
$980$		0			0
$981$	−1034.00			−1.05403
$982$		−	290.985i		−	0.296318i
$983$	999.230	+	576.906i	1.01651	+	0.586883i	0.913091	−	0.407755i	$-0.133688\pi$
$983$	999.230	+	576.906i	1.01651	+	0.586883i	0.103419	+	0.994638i	$0.467022\pi$
$984$	1440.00	+	831.384i	1.46341	+	0.844903i
$985$	7.74597	+	13.4164i	0.00786393	+	0.0136207i
$986$	−402.790	+	697.653i	−0.408509	+	0.707559i
$987$		0			0
$988$	360.000	−	207.846i	0.364372	−	0.210371i
$989$	504.000	+	872.954i	0.509606	+	0.882663i
$990$	−1022.47	+	590.322i	−1.03280	+	0.596285i
$991$	384.000	+	221.703i	0.387487	+	0.223716i	0.681071	−	0.732217i	$-0.261515\pi$
$991$	384.000	+	221.703i	0.387487	+	0.223716i	−0.293584	+	0.955933i	$0.594848\pi$
$992$	743.613	+	429.325i	0.749610	+	0.432787i
$993$	−2509.69			−2.52738
$994$		0			0
$995$			207.846i			0.208891i
$996$	−840.000	+	1454.92i	−0.843373	+	1.46077i
$997$	143.300	−	248.204i	0.143732	−	0.248950i	−0.785167	−	0.619284i	$-0.787423\pi$
$997$	143.300	−	248.204i	0.143732	−	0.248950i	0.928899	+	0.370333i	$0.120756\pi$
$998$	−540.000	+	311.769i	−0.541082	+	0.312394i
$999$	15.4919	−	8.94427i	0.0155074	−	0.00895323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.g.g.67.1		4
4.3	odd	2		196.3.g.c.67.2		4
7.2	even	3		196.3.g.c.79.2		4
7.3	odd	6		196.3.c.d.99.3	yes	4
7.4	even	3		196.3.c.d.99.4	yes	4
7.5	odd	6		196.3.g.c.79.1		4
7.6	odd	2	inner	196.3.g.g.67.2		4
28.3	even	6		196.3.c.d.99.2	yes	4
28.11	odd	6		196.3.c.d.99.1	✓	4
28.19	even	6	inner	196.3.g.g.79.2		4
28.23	odd	6	inner	196.3.g.g.79.1		4
28.27	even	2		196.3.g.c.67.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.3.c.d.99.1	✓	4	28.11	odd	6
196.3.c.d.99.2	yes	4	28.3	even	6
196.3.c.d.99.3	yes	4	7.3	odd	6
196.3.c.d.99.4	yes	4	7.4	even	3
196.3.g.c.67.1		4	28.27	even	2
196.3.g.c.67.2		4	4.3	odd	2
196.3.g.c.79.1		4	7.5	odd	6
196.3.g.c.79.2		4	7.2	even	3
196.3.g.g.67.1		4	1.1	even	1	trivial
196.3.g.g.67.2		4	7.6	odd	2	inner
196.3.g.g.79.1		4	28.23	odd	6	inner
196.3.g.g.79.2		4	28.19	even	6	inner

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	196.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-3.87298 - 2.23607i) q^{3} +4.00000 q^{4} +(3.87298 + 6.70820i) q^{5} +(-7.74597 - 4.47214i) q^{6} +8.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-3.87298 - 2.23607i) q^{3} +4.00000 q^{4} +(3.87298 + 6.70820i) q^{5} +(-7.74597 - 4.47214i) q^{6} +8.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +(7.74597 + 13.4164i) q^{10} +(6.00000 + 3.46410i) q^{11} +(-15.4919 - 8.94427i) q^{12} +7.74597 q^{13} -34.6410i q^{15} +16.0000 q^{16} +(7.74597 - 13.4164i) q^{17} +(11.0000 + 19.0526i) q^{18} +(11.6190 - 6.70820i) q^{19} +(15.4919 + 26.8328i) q^{20} +(12.0000 + 6.92820i) q^{22} +(-18.0000 + 10.3923i) q^{23} +(-30.9839 - 17.8885i) q^{24} +(-17.5000 + 30.3109i) q^{25} +15.4919 q^{26} -8.94427i q^{27} -26.0000 q^{29} -69.2820i q^{30} +(23.2379 + 13.4164i) q^{31} +32.0000 q^{32} +(-15.4919 - 26.8328i) q^{33} +(15.4919 - 26.8328i) q^{34} +(22.0000 + 38.1051i) q^{36} +(1.00000 + 1.73205i) q^{37} +(23.2379 - 13.4164i) q^{38} +(-30.0000 - 17.3205i) q^{39} +(30.9839 + 53.6656i) q^{40} -46.4758 q^{41} -48.4974i q^{43} +(24.0000 + 13.8564i) q^{44} +(-42.6028 + 73.7902i) q^{45} +(-36.0000 + 20.7846i) q^{46} +(-69.7137 + 40.2492i) q^{47} +(-61.9677 - 35.7771i) q^{48} +(-35.0000 + 60.6218i) q^{50} +(-60.0000 + 34.6410i) q^{51} +30.9839 q^{52} +(23.0000 - 39.8372i) q^{53} -17.8885i q^{54} +53.6656i q^{55} -60.0000 q^{57} -52.0000 q^{58} +(-58.0948 - 33.5410i) q^{59} -138.564i q^{60} +(3.87298 + 6.70820i) q^{61} +(46.4758 + 26.8328i) q^{62} +64.0000 q^{64} +(30.0000 + 51.9615i) q^{65} +(-30.9839 - 53.6656i) q^{66} +(-78.0000 - 45.0333i) q^{67} +(30.9839 - 53.6656i) q^{68} +92.9516 q^{69} +96.9948i q^{71} +(44.0000 + 76.2102i) q^{72} +(61.9677 - 107.331i) q^{73} +(2.00000 + 3.46410i) q^{74} +(135.554 - 78.2624i) q^{75} +(46.4758 - 26.8328i) q^{76} +(-60.0000 - 34.6410i) q^{78} +(24.0000 - 13.8564i) q^{79} +(61.9677 + 107.331i) q^{80} +(29.5000 - 51.0955i) q^{81} -92.9516 q^{82} -93.9149i q^{83} +120.000 q^{85} -96.9948i q^{86} +(100.698 + 58.1378i) q^{87} +(48.0000 + 27.7128i) q^{88} +(30.9839 + 53.6656i) q^{89} +(-85.2056 + 147.580i) q^{90} +(-72.0000 + 41.5692i) q^{92} +(-60.0000 - 103.923i) q^{93} +(-139.427 + 80.4984i) q^{94} +(90.0000 + 51.9615i) q^{95} +(-123.935 - 71.5542i) q^{96} -46.4758 q^{97} +76.2102i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 16 q^{4} + 32 q^{8} + 22 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 16 * q^4 + 32 * q^8 + 22 * q^9	\( 4 q + 8 q^{2} + 16 q^{4} + 32 q^{8} + 22 q^{9} + 24 q^{11} + 64 q^{16} + 44 q^{18} + 48 q^{22} - 72 q^{23} - 70 q^{25} - 104 q^{29} + 128 q^{32} + 88 q^{36} + 4 q^{37} - 120 q^{39} + 96 q^{44} - 144 q^{46} - 140 q^{50} - 240 q^{51} + 92 q^{53} - 240 q^{57} - 208 q^{58} + 256 q^{64} + 120 q^{65} - 312 q^{67} + 176 q^{72} + 8 q^{74} - 240 q^{78} + 96 q^{79} + 118 q^{81} + 480 q^{85} + 192 q^{88} - 288 q^{92} - 240 q^{93} + 360 q^{95}+O(q^{100}) \) 4 * q + 8 * q^2 + 16 * q^4 + 32 * q^8 + 22 * q^9 + 24 * q^11 + 64 * q^16 + 44 * q^18 + 48 * q^22 - 72 * q^23 - 70 * q^25 - 104 * q^29 + 128 * q^32 + 88 * q^36 + 4 * q^37 - 120 * q^39 + 96 * q^44 - 144 * q^46 - 140 * q^50 - 240 * q^51 + 92 * q^53 - 240 * q^57 - 208 * q^58 + 256 * q^64 + 120 * q^65 - 312 * q^67 + 176 * q^72 + 8 * q^74 - 240 * q^78 + 96 * q^79 + 118 * q^81 + 480 * q^85 + 192 * q^88 - 288 * q^92 - 240 * q^93 + 360 * q^95

Introduction

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