LMFDB - Embedded newform 1050.3.h.c.349.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(349,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.349");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.h (of order $2$, degree $1$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.12
Character	$\chi$	$=$	1050.349
Dual form			1050.3.h.c.349.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(-1.07086 + 6.91761i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(-1.07086 + 6.91761i) q^{7} -2.82843i q^{8} +3.00000 q^{9} -9.92899 q^{11} +3.46410 q^{12} -20.2629 q^{13} +(-9.78297 - 1.51442i) q^{14} +4.00000 q^{16} +18.9405 q^{17} +4.24264i q^{18} -4.68861i q^{19} +(1.85478 - 11.9816i) q^{21} -14.0417i q^{22} +25.4738i q^{23} +4.89898i q^{24} -28.6560i q^{26} -5.19615 q^{27} +(2.14171 - 13.8352i) q^{28} -15.9850 q^{29} -20.9499i q^{31} +5.65685i q^{32} +17.1975 q^{33} +26.7859i q^{34} -6.00000 q^{36} +30.1846i q^{37} +6.63069 q^{38} +35.0963 q^{39} -42.2896i q^{41} +(16.9446 + 2.62305i) q^{42} -49.7705i q^{43} +19.8580 q^{44} -36.0253 q^{46} -2.91549 q^{47} -6.92820 q^{48} +(-46.7065 - 14.8155i) q^{49} -32.8059 q^{51} +40.5258 q^{52} -11.1921i q^{53} -7.34847i q^{54} +(19.5659 + 3.02884i) q^{56} +8.12091i q^{57} -22.6062i q^{58} +63.6910i q^{59} -89.2830i q^{61} +29.6277 q^{62} +(-3.21257 + 20.7528i) q^{63} -8.00000 q^{64} +24.3210i q^{66} +13.5923i q^{67} -37.8810 q^{68} -44.1218i q^{69} -50.9899 q^{71} -8.48528i q^{72} +78.9059 q^{73} -42.6875 q^{74} +9.37722i q^{76} +(10.6325 - 68.6848i) q^{77} +49.6337i q^{78} +69.8667 q^{79} +9.00000 q^{81} +59.8066 q^{82} +68.8876 q^{83} +(-3.70956 + 23.9633i) q^{84} +70.3860 q^{86} +27.6868 q^{87} +28.0834i q^{88} -156.083i q^{89} +(21.6987 - 140.171i) q^{91} -50.9475i q^{92} +36.2863i q^{93} -4.12313i q^{94} -9.79796i q^{96} +154.698 q^{97} +(20.9523 - 66.0530i) q^{98} -29.7870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 72 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 + 72 * q^9	$ 24 q - 48 q^{4} + 72 q^{9} - 32 q^{11} - 16 q^{14} + 96 q^{16} - 12 q^{21} - 96 q^{29} - 144 q^{36} + 24 q^{39} + 64 q^{44} + 160 q^{46} - 236 q^{49} + 144 q^{51} + 32 q^{56} - 192 q^{64} + 496 q^{71} + 128 q^{74} + 416 q^{79} + 216 q^{81} + 24 q^{84} + 256 q^{86} - 316 q^{91} - 96 q^{99}+O(q^{100}) $ 24 * q - 48 * q^4 + 72 * q^9 - 32 * q^11 - 16 * q^14 + 96 * q^16 - 12 * q^21 - 96 * q^29 - 144 * q^36 + 24 * q^39 + 64 * q^44 + 160 * q^46 - 236 * q^49 + 144 * q^51 + 32 * q^56 - 192 * q^64 + 496 * q^71 + 128 * q^74 + 416 * q^79 + 216 * q^81 + 24 * q^84 + 256 * q^86 - 316 * q^91 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	−1.07086	+	6.91761i	−0.152980	+	0.988229i
$7$	−1.07086	+	6.91761i	−0.152980	+	0.988229i
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$		0			0
$11$	−9.92899			−0.902635			−0.451318	−	0.892363i	$-0.649046\pi$
$11$	−9.92899			−0.902635			−0.451318	+	0.892363i	$0.649046\pi$
$12$	3.46410			0.288675
$13$	−20.2629			−1.55868			−0.779342	−	0.626599i	$-0.784446\pi$
$13$	−20.2629			−1.55868			−0.779342	+	0.626599i	$0.784446\pi$
$14$	−9.78297	−	1.51442i	−0.698784	−	0.108173i
$15$		0			0
$16$	4.00000			0.250000
$17$	18.9405			1.11415			0.557073	−	0.830463i	$-0.311924\pi$
$17$	18.9405			1.11415			0.557073	+	0.830463i	$0.311924\pi$
$18$			4.24264i			0.235702i
$19$		−	4.68861i		−	0.246769i	−0.992359	−	0.123384i	$-0.960625\pi$
$19$		−	4.68861i		−	0.246769i	0.992359	−	0.123384i	$-0.0393748\pi$
$20$		0			0
$21$	1.85478	−	11.9816i	0.0883228	−	0.570554i
$22$		−	14.0417i		−	0.638259i
$23$			25.4738i			1.10755i	0.832665	+	0.553777i	$0.186814\pi$
$23$			25.4738i			1.10755i	−0.832665	+	0.553777i	$0.813186\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$		−	28.6560i		−	1.10216i
$27$	−5.19615			−0.192450
$28$	2.14171	−	13.8352i	0.0764898	−	0.494115i
$29$	−15.9850			−0.551207			−0.275604	−	0.961271i	$-0.588878\pi$
$29$	−15.9850			−0.551207			−0.275604	+	0.961271i	$0.588878\pi$
$30$		0			0
$31$		−	20.9499i		−	0.675804i	−0.941181	−	0.337902i	$-0.890283\pi$
$31$		−	20.9499i		−	0.675804i	0.941181	−	0.337902i	$-0.109717\pi$
$32$			5.65685i			0.176777i
$33$	17.1975			0.521137
$34$			26.7859i			0.787821i
$35$		0			0
$36$	−6.00000			−0.166667
$37$			30.1846i			0.815800i	0.913027	+	0.407900i	$0.133739\pi$
$37$			30.1846i			0.815800i	−0.913027	+	0.407900i	$0.866261\pi$
$38$	6.63069			0.174492
$39$	35.0963			0.899906
$40$		0			0
$41$		−	42.2896i		−	1.03145i	−0.856753	−	0.515727i	$-0.827522\pi$
$41$		−	42.2896i		−	1.03145i	0.856753	−	0.515727i	$-0.172478\pi$
$42$	16.9446	+	2.62305i	0.403443	+	0.0624537i
$43$		−	49.7705i		−	1.15745i	−0.815522	−	0.578726i	$-0.803550\pi$
$43$		−	49.7705i		−	1.15745i	0.815522	−	0.578726i	$-0.196450\pi$
$44$	19.8580			0.451318
$45$		0			0
$46$	−36.0253			−0.783159
$47$	−2.91549			−0.0620318			−0.0310159	−	0.999519i	$-0.509874\pi$
$47$	−2.91549			−0.0620318			−0.0310159	+	0.999519i	$0.509874\pi$
$48$	−6.92820			−0.144338
$49$	−46.7065	−	14.8155i	−0.953194	−	0.302358i
$50$		0			0
$51$	−32.8059			−0.643253
$52$	40.5258			0.779342
$53$		−	11.1921i		−	0.211171i	−0.994410	−	0.105586i	$-0.966328\pi$
$53$		−	11.1921i		−	0.211171i	0.994410	−	0.105586i	$-0.0336717\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	19.5659	+	3.02884i	0.349392	+	0.0540865i
$57$			8.12091i			0.142472i
$58$		−	22.6062i		−	0.389762i
$59$			63.6910i			1.07951i	0.841823	+	0.539754i	$0.181483\pi$
$59$			63.6910i			1.07951i	−0.841823	+	0.539754i	$0.818517\pi$
$60$		0			0
$61$		−	89.2830i		−	1.46365i	−0.681490	−	0.731827i	$-0.738668\pi$
$61$		−	89.2830i		−	1.46365i	0.681490	−	0.731827i	$-0.261332\pi$
$62$	29.6277			0.477865
$63$	−3.21257	+	20.7528i	−0.0509932	+	0.329410i
$64$	−8.00000			−0.125000
$65$		0			0
$66$			24.3210i			0.368499i
$67$			13.5923i			0.202871i	0.994842	+	0.101435i	$0.0323435\pi$
$67$			13.5923i			0.202871i	−0.994842	+	0.101435i	$0.967656\pi$
$68$	−37.8810			−0.557073
$69$		−	44.1218i		−	0.639447i
$70$		0			0
$71$	−50.9899			−0.718168			−0.359084	−	0.933305i	$-0.616911\pi$
$71$	−50.9899			−0.718168			−0.359084	+	0.933305i	$0.616911\pi$
$72$		−	8.48528i		−	0.117851i
$73$	78.9059			1.08090			0.540451	−	0.841375i	$-0.318254\pi$
$73$	78.9059			1.08090			0.540451	+	0.841375i	$0.318254\pi$
$74$	−42.6875			−0.576858
$75$		0			0
$76$			9.37722i			0.123384i
$77$	10.6325	−	68.6848i	0.138085	−	0.892011i
$78$			49.6337i			0.636330i
$79$	69.8667			0.884388			0.442194	−	0.896919i	$-0.354200\pi$
$79$	69.8667			0.884388			0.442194	+	0.896919i	$0.354200\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	59.8066			0.729348
$83$	68.8876			0.829971			0.414985	−	0.909828i	$-0.363787\pi$
$83$	68.8876			0.829971			0.414985	+	0.909828i	$0.363787\pi$
$84$	−3.70956	+	23.9633i	−0.0441614	+	0.285277i
$85$		0			0
$86$	70.3860			0.818442
$87$	27.6868			0.318240
$88$			28.0834i			0.319130i
$89$		−	156.083i		−	1.75374i	−0.480726	−	0.876871i	$-0.659627\pi$
$89$		−	156.083i		−	1.75374i	0.480726	−	0.876871i	$-0.340373\pi$
$90$		0			0
$91$	21.6987	−	140.171i	0.238447	−	1.54034i
$92$		−	50.9475i		−	0.553777i
$93$			36.2863i			0.390175i
$94$		−	4.12313i		−	0.0438631i
$95$		0			0
$96$		−	9.79796i		−	0.102062i
$97$	154.698			1.59482			0.797410	−	0.603437i	$-0.206203\pi$
$97$	154.698			1.59482			0.797410	+	0.603437i	$0.206203\pi$
$98$	20.9523	−	66.0530i	0.213799	−	0.674010i
$99$	−29.7870			−0.300878
$100$		0			0
$101$		−	133.558i		−	1.32236i	−0.750228	−	0.661179i	$-0.770057\pi$
$101$		−	133.558i		−	1.32236i	0.750228	−	0.661179i	$-0.229943\pi$
$102$		−	46.3946i		−	0.454849i
$103$	81.7942			0.794118			0.397059	−	0.917793i	$-0.370031\pi$
$103$	81.7942			0.794118			0.397059	+	0.917793i	$0.370031\pi$
$104$			57.3121i			0.551078i
$105$		0			0
$106$	15.8280			0.149321
$107$		−	160.090i		−	1.49617i	−0.663604	−	0.748084i	$-0.730974\pi$
$107$		−	160.090i		−	1.49617i	0.663604	−	0.748084i	$-0.269026\pi$
$108$	10.3923			0.0962250
$109$	183.616			1.68455			0.842276	−	0.539047i	$-0.181215\pi$
$109$	183.616			1.68455			0.842276	+	0.539047i	$0.181215\pi$
$110$		0			0
$111$		−	52.2812i		−	0.471002i
$112$	−4.28343	+	27.6704i	−0.0382449	+	0.247057i
$113$		−	14.6971i		−	0.130063i	−0.997883	−	0.0650314i	$-0.979285\pi$
$113$		−	14.6971i		−	0.130063i	0.997883	−	0.0650314i	$-0.0207147\pi$
$114$	−11.4847			−0.100743
$115$		0			0
$116$	31.9700			0.275604
$117$	−60.7887			−0.519561
$118$	−90.0727			−0.763328
$119$	−20.2826	+	131.023i	−0.170442	+	1.10103i
$120$		0			0
$121$	−22.4152			−0.185250
$122$	126.265			1.03496
$123$			73.2478i			0.595511i
$124$			41.8998i			0.337902i
$125$		0			0
$126$	−29.3489	−	4.54326i	−0.232928	−	0.0360576i
$127$			193.465i			1.52335i	0.647962	+	0.761673i	$0.275622\pi$
$127$			193.465i			1.52335i	−0.647962	+	0.761673i	$0.724378\pi$
$128$		−	11.3137i		−	0.0883883i
$129$			86.2050i			0.668255i
$130$		0			0
$131$		−	98.8368i		−	0.754480i	−0.926116	−	0.377240i	$-0.876873\pi$
$131$		−	98.8368i		−	0.754480i	0.926116	−	0.377240i	$-0.123127\pi$
$132$	−34.3950			−0.260568
$133$	32.4339	+	5.02083i	0.243864	+	0.0377506i
$134$	−19.2225			−0.143451
$135$		0			0
$136$		−	53.5718i		−	0.393910i
$137$			40.3738i			0.294699i	0.989084	+	0.147350i	$0.0470742\pi$
$137$			40.3738i			0.294699i	−0.989084	+	0.147350i	$0.952926\pi$
$138$	62.3977			0.452157
$139$			35.3525i			0.254334i	0.991881	+	0.127167i	$0.0405885\pi$
$139$			35.3525i			0.254334i	−0.991881	+	0.127167i	$0.959412\pi$
$140$		0			0
$141$	5.04978			0.0358141
$142$		−	72.1106i		−	0.507821i
$143$	201.190			1.40692
$144$	12.0000			0.0833333
$145$		0			0
$146$			111.590i			0.764313i
$147$	80.8981	+	25.6613i	0.550327	+	0.174566i
$148$		−	60.3692i		−	0.407900i
$149$	−274.171			−1.84007			−0.920035	−	0.391836i	$-0.871840\pi$
$149$	−274.171			−1.84007			−0.920035	+	0.391836i	$0.871840\pi$
$150$		0			0
$151$	160.545			1.06322			0.531608	−	0.846991i	$-0.321588\pi$
$151$	160.545			1.06322			0.531608	+	0.846991i	$0.321588\pi$
$152$	−13.2614			−0.0872460
$153$	56.8215			0.371382
$154$	97.1350	+	15.0367i	0.630747	+	0.0976407i
$155$		0			0
$156$	−70.1927			−0.449953
$157$	−266.232			−1.69574			−0.847871	−	0.530202i	$-0.822116\pi$
$157$	−266.232			−1.69574			−0.847871	+	0.530202i	$0.822116\pi$
$158$			98.8064i			0.625357i
$159$			19.3852i			0.121920i
$160$		0			0
$161$	−176.217	−	27.2788i	−1.09452	−	0.169433i
$162$			12.7279i			0.0785674i
$163$		−	187.398i		−	1.14968i	−0.818265	−	0.574842i	$-0.805064\pi$
$163$		−	187.398i		−	1.14968i	0.818265	−	0.574842i	$-0.194936\pi$
$164$			84.5793i			0.515727i
$165$		0			0
$166$			97.4217i			0.586878i
$167$	−262.937			−1.57447			−0.787237	−	0.616650i	$-0.788489\pi$
$167$	−262.937			−1.57447			−0.787237	+	0.616650i	$0.788489\pi$
$168$	−33.8892	−	5.24611i	−0.201721	−	0.0312268i
$169$	241.584			1.42949
$170$		0			0
$171$		−	14.0658i		−	0.0822563i
$172$			99.5409i			0.578726i
$173$	0.130787			0.000755997			0.000377998	−	1.00000i	$-0.499880\pi$
$173$	0.130787			0.000755997			0.000377998		1.00000i	$0.499880\pi$
$174$			39.1551i			0.225029i
$175$		0			0
$176$	−39.7159			−0.225659
$177$		−	110.316i		−	0.623255i
$178$	220.735			1.24008
$179$	−143.431			−0.801293			−0.400646	−	0.916233i	$-0.631214\pi$
$179$	−143.431			−0.801293			−0.400646	+	0.916233i	$0.631214\pi$
$180$		0			0
$181$			264.455i			1.46108i	0.682871	+	0.730539i	$0.260731\pi$
$181$			264.455i			1.46108i	−0.682871	+	0.730539i	$0.739269\pi$
$182$	198.231	+	30.6865i	1.08918	+	0.168607i
$183$			154.643i			0.845042i
$184$	72.0507			0.391580
$185$		0			0
$186$	−51.3166			−0.275896
$187$	−188.060			−1.00567
$188$	5.83099			0.0310159
$189$	5.56434	−	35.9449i	0.0294409	−	0.190185i
$190$		0			0
$191$	218.722			1.14514			0.572571	−	0.819855i	$-0.305946\pi$
$191$	218.722			1.14514			0.572571	+	0.819855i	$0.305946\pi$
$192$	13.8564			0.0721688
$193$		−	162.709i		−	0.843052i	−0.906816	−	0.421526i	$-0.861495\pi$
$193$		−	162.709i		−	0.843052i	0.906816	−	0.421526i	$-0.138505\pi$
$194$			218.775i			1.12771i
$195$		0			0
$196$	93.4131	+	29.6311i	0.476597	+	0.151179i
$197$		−	175.537i		−	0.891052i	−0.895269	−	0.445526i	$-0.853017\pi$
$197$		−	175.537i		−	0.891052i	0.895269	−	0.445526i	$-0.146983\pi$
$198$		−	42.1251i		−	0.212753i
$199$		−	61.4878i		−	0.308984i	−0.987994	−	0.154492i	$-0.950626\pi$
$199$		−	61.4878i		−	0.308984i	0.987994	−	0.154492i	$-0.0493741\pi$
$200$		0			0
$201$		−	23.5426i		−	0.117127i
$202$	188.880			0.935048
$203$	17.1177	−	110.578i	0.0843235	−	0.544719i
$204$	65.6118			0.321627
$205$		0			0
$206$			115.674i			0.561527i
$207$			76.4213i			0.369185i
$208$	−81.0515			−0.389671
$209$			46.5531i			0.222742i
$210$		0			0
$211$	126.033			0.597314			0.298657	−	0.954361i	$-0.403461\pi$
$211$	126.033			0.597314			0.298657	+	0.954361i	$0.403461\pi$
$212$			22.3842i			0.105586i
$213$	88.3171			0.414634
$214$	226.401			1.05795
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	144.923	+	22.4344i	0.667849	+	0.103384i
$218$			259.672i			1.19116i
$219$	−136.669			−0.624059
$220$		0			0
$221$	−383.789			−1.73660
$222$	73.9368			0.333049
$223$	−62.6219			−0.280816			−0.140408	−	0.990094i	$-0.544841\pi$
$223$	−62.6219			−0.280816			−0.140408	+	0.990094i	$0.544841\pi$
$224$	−39.1319	−	6.05768i	−0.174696	−	0.0270432i
$225$		0			0
$226$	20.7848			0.0919683
$227$	−220.557			−0.971619			−0.485809	−	0.874065i	$-0.661475\pi$
$227$	−220.557			−0.971619			−0.485809	+	0.874065i	$0.661475\pi$
$228$		−	16.2418i		−	0.0712360i
$229$		−	206.797i		−	0.903043i	−0.892260	−	0.451521i	$-0.850881\pi$
$229$		−	206.797i		−	0.903043i	0.892260	−	0.451521i	$-0.149119\pi$
$230$		0			0
$231$	−18.4161	+	118.966i	−0.0797233	+	0.515003i
$232$			45.2124i			0.194881i
$233$		−	167.313i		−	0.718082i	−0.933322	−	0.359041i	$-0.883104\pi$
$233$		−	167.313i		−	0.718082i	0.933322	−	0.359041i	$-0.116896\pi$
$234$		−	85.9681i		−	0.367385i
$235$		0			0
$236$		−	127.382i		−	0.539754i
$237$	−121.013			−0.510602
$238$	−185.294	−	28.6839i	−0.778548	−	0.120521i
$239$	14.5321			0.0608036			0.0304018	−	0.999538i	$-0.490321\pi$
$239$	14.5321			0.0608036			0.0304018	+	0.999538i	$0.490321\pi$
$240$		0			0
$241$		−	337.752i		−	1.40146i	−0.713427	−	0.700730i	$-0.752858\pi$
$241$		−	337.752i		−	1.40146i	0.713427	−	0.700730i	$-0.247142\pi$
$242$		−	31.6999i		−	0.130991i
$243$	−15.5885			−0.0641500
$244$			178.566i			0.731827i
$245$		0			0
$246$	−103.588			−0.421090
$247$			95.0047i			0.384635i
$248$	−59.2553			−0.238933
$249$	−119.317			−0.479184
$250$		0			0
$251$			391.239i			1.55872i	0.626576	+	0.779360i	$0.284456\pi$
$251$			391.239i			1.55872i	−0.626576	+	0.779360i	$0.715544\pi$
$252$	6.42514	−	41.5056i	0.0254966	−	0.164705i
$253$		−	252.929i		−	0.999718i
$254$	−273.601			−1.07717
$255$		0			0
$256$	16.0000			0.0625000
$257$	−275.467			−1.07186			−0.535928	−	0.844264i	$-0.680038\pi$
$257$	−275.467			−1.07186			−0.535928	+	0.844264i	$0.680038\pi$
$258$	−121.912			−0.472528
$259$	−208.805	−	32.3234i	−0.806197	−	0.124801i
$260$		0			0
$261$	−47.9550			−0.183736
$262$	139.776			0.533498
$263$			352.033i			1.33853i	0.743025	+	0.669264i	$0.233390\pi$
$263$			352.033i			1.33853i	−0.743025	+	0.669264i	$0.766610\pi$
$264$		−	48.6419i		−	0.184250i
$265$		0			0
$266$	−7.10053	+	45.8685i	−0.0266937	+	0.172438i
$267$			270.344i			1.01252i
$268$		−	27.1847i		−	0.101435i
$269$		−	90.5828i		−	0.336739i	−0.985724	−	0.168370i	$-0.946150\pi$
$269$		−	90.5828i		−	0.336739i	0.985724	−	0.168370i	$-0.0538502\pi$
$270$		0			0
$271$		−	56.5234i		−	0.208573i	−0.994547	−	0.104287i	$-0.966744\pi$
$271$		−	56.5234i		−	0.208573i	0.994547	−	0.104287i	$-0.0332559\pi$
$272$	75.7620			0.278537
$273$	−37.5832	+	242.783i	−0.137667	+	0.889314i
$274$	−57.0971			−0.208384
$275$		0			0
$276$			88.2437i			0.319723i
$277$			158.702i			0.572931i	0.958091	+	0.286466i	$0.0924804\pi$
$277$			158.702i			0.572931i	−0.958091	+	0.286466i	$0.907520\pi$
$278$	−49.9960			−0.179842
$279$		−	62.8497i		−	0.225268i
$280$		0			0
$281$	−50.2344			−0.178770			−0.0893850	−	0.995997i	$-0.528490\pi$
$281$	−50.2344			−0.178770			−0.0893850	+	0.995997i	$0.528490\pi$
$282$			7.14147i			0.0253244i
$283$	−104.925			−0.370760			−0.185380	−	0.982667i	$-0.559352\pi$
$283$	−104.925			−0.370760			−0.185380	+	0.982667i	$0.559352\pi$
$284$	101.980			0.359084
$285$		0			0
$286$			284.525i			0.994844i
$287$	292.543	+	45.2862i	1.01931	+	0.157792i
$288$			16.9706i			0.0589256i
$289$	69.7425			0.241323
$290$		0			0
$291$	−267.944			−0.920770
$292$	−157.812			−0.540451
$293$	−506.046			−1.72712			−0.863560	−	0.504247i	$-0.831770\pi$
$293$	−506.046			−1.72712			−0.863560	+	0.504247i	$0.831770\pi$
$294$	−36.2905	+	114.407i	−0.123437	+	0.389140i
$295$		0			0
$296$	85.3749			0.288429
$297$	51.5925			0.173712
$298$		−	387.736i		−	1.30113i
$299$		−	516.172i		−	1.72633i
$300$		0			0
$301$	344.292	+	53.2971i	1.14383	+	0.177067i
$302$			227.046i			0.751807i
$303$			231.329i			0.763463i
$304$		−	18.7544i		−	0.0616922i
$305$		0			0
$306$			80.3577i			0.262607i
$307$	−221.769			−0.722376			−0.361188	−	0.932493i	$-0.617629\pi$
$307$	−221.769			−0.722376			−0.361188	+	0.932493i	$0.617629\pi$
$308$	−21.2651	+	137.370i	−0.0690424	+	0.446005i
$309$	−141.672			−0.458485
$310$		0			0
$311$			80.8561i			0.259988i	0.991515	+	0.129994i	$0.0414957\pi$
$311$			80.8561i			0.259988i	−0.991515	+	0.129994i	$0.958504\pi$
$312$		−	99.2675i		−	0.318165i
$313$	−340.104			−1.08659			−0.543297	−	0.839541i	$-0.682824\pi$
$313$	−340.104			−1.08659			−0.543297	+	0.839541i	$0.682824\pi$
$314$		−	376.508i		−	1.19907i
$315$		0			0
$316$	−139.733			−0.442194
$317$			304.527i			0.960654i	0.877090	+	0.480327i	$0.159482\pi$
$317$			304.527i			0.960654i	−0.877090	+	0.480327i	$0.840518\pi$
$318$	−27.4149			−0.0862103
$319$	158.715			0.497539
$320$		0			0
$321$			277.284i			0.863813i
$322$	38.5780	−	249.209i	0.119807	−	0.773941i
$323$		−	88.8046i		−	0.274937i
$324$	−18.0000			−0.0555556
$325$		0			0
$326$	265.021			0.812949
$327$	−318.032			−0.972576
$328$	−119.613			−0.364674
$329$	3.12208	−	20.1682i	0.00948960	−	0.0613016i
$330$		0			0
$331$	323.175			0.976361			0.488180	−	0.872743i	$-0.337661\pi$
$331$	323.175			0.976361			0.488180	+	0.872743i	$0.337661\pi$
$332$	−137.775			−0.414985
$333$			90.5538i			0.271933i
$334$		−	371.849i		−	1.11332i
$335$		0			0
$336$	7.41912	−	47.9266i	0.0220807	−	0.142639i
$337$		−	333.282i		−	0.988966i	−0.869187	−	0.494483i	$-0.835357\pi$
$337$		−	333.282i		−	0.988966i	0.869187	−	0.494483i	$-0.164643\pi$
$338$			341.652i			1.01080i
$339$			25.4561i			0.0750918i
$340$		0			0
$341$			208.011i			0.610004i
$342$	19.8921			0.0581640
$343$	152.504	−	307.232i	0.444618	−	0.895720i
$344$	−140.772			−0.409221
$345$		0			0
$346$			0.184961i			0.000534571i
$347$		−	257.512i		−	0.742110i	−0.928611	−	0.371055i	$-0.878996\pi$
$347$		−	257.512i		−	0.742110i	0.928611	−	0.371055i	$-0.121004\pi$
$348$	−55.3737			−0.159120
$349$		−	306.979i		−	0.879596i	−0.898097	−	0.439798i	$-0.855050\pi$
$349$		−	306.979i		−	0.879596i	0.898097	−	0.439798i	$-0.144950\pi$
$350$		0			0
$351$	105.289			0.299969
$352$		−	56.1668i		−	0.159565i
$353$	−248.442			−0.703802			−0.351901	−	0.936037i	$-0.614465\pi$
$353$	−248.442			−0.703802			−0.351901	+	0.936037i	$0.614465\pi$
$354$	156.010			0.440708
$355$		0			0
$356$			312.166i			0.876871i
$357$	35.1304	−	226.938i	0.0984046	−	0.635682i
$358$		−	202.843i		−	0.566600i
$359$	348.412			0.970507			0.485253	−	0.874374i	$-0.338727\pi$
$359$	348.412			0.970507			0.485253	+	0.874374i	$0.338727\pi$
$360$		0			0
$361$	339.017			0.939105
$362$	−373.996			−1.03314
$363$	38.8243			0.106954
$364$	−43.3973	+	280.341i	−0.119223	+	0.770168i
$365$		0			0
$366$	−218.698			−0.597535
$367$	−73.9213			−0.201420			−0.100710	−	0.994916i	$-0.532112\pi$
$367$	−73.9213			−0.201420			−0.100710	+	0.994916i	$0.532112\pi$
$368$			101.895i			0.276889i
$369$		−	126.869i		−	0.343818i
$370$		0			0
$371$	77.4224	+	11.9851i	0.208686	+	0.0323049i
$372$		−	72.5726i		−	0.195088i
$373$		−	52.9503i		−	0.141958i	−0.997478	−	0.0709789i	$-0.977388\pi$
$373$		−	52.9503i		−	0.141958i	0.997478	−	0.0709789i	$-0.0226123\pi$
$374$		−	265.957i		−	0.711115i
$375$		0			0
$376$			8.24626i			0.0219315i
$377$	323.902			0.859157
$378$	50.8338	+	7.86916i	0.134481	+	0.0208179i
$379$	−112.721			−0.297417			−0.148709	−	0.988881i	$-0.547512\pi$
$379$	−112.721			−0.297417			−0.148709	+	0.988881i	$0.547512\pi$
$380$		0			0
$381$		−	335.091i		−	0.879504i
$382$			309.320i			0.809737i
$383$	524.061			1.36830			0.684152	−	0.729339i	$-0.260172\pi$
$383$	524.061			1.36830			0.684152	+	0.729339i	$0.260172\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	230.105			0.596128
$387$		−	149.311i		−	0.385817i
$388$	−309.395			−0.797410
$389$	114.232			0.293655			0.146827	−	0.989162i	$-0.453094\pi$
$389$	114.232			0.293655			0.146827	+	0.989162i	$0.453094\pi$
$390$		0			0
$391$			482.486i			1.23398i
$392$	−41.9047	+	132.106i	−0.106900	+	0.337005i
$393$			171.190i			0.435599i
$394$	248.247			0.630069
$395$		0			0
$396$	59.5739			0.150439
$397$	−657.463			−1.65608			−0.828039	−	0.560670i	$-0.810544\pi$
$397$	−657.463			−1.65608			−0.828039	+	0.560670i	$0.810544\pi$
$398$	86.9569			0.218485
$399$	−56.1772	−	8.69634i	−0.140795	−	0.0217953i
$400$		0			0
$401$	−614.317			−1.53196			−0.765981	−	0.642863i	$-0.777747\pi$
$401$	−614.317			−1.53196			−0.765981	+	0.642863i	$0.777747\pi$
$402$	33.2943			0.0828216
$403$			424.506i			1.05336i
$404$			267.116i			0.661179i
$405$		0			0
$406$	156.381	+	24.2080i	0.385175	+	0.0596257i
$407$		−	299.702i		−	0.736369i
$408$			92.7891i			0.227424i
$409$			195.617i			0.478282i	0.970985	+	0.239141i	$0.0768658\pi$
$409$			195.617i			0.478282i	−0.970985	+	0.239141i	$0.923134\pi$
$410$		0			0
$411$		−	69.9294i		−	0.170145i
$412$	−163.588			−0.397059
$413$	−440.589	−	68.2040i	−1.06680	−	0.165143i
$414$	−108.076			−0.261053
$415$		0			0
$416$		−	114.624i		−	0.275539i
$417$		−	61.2323i		−	0.146840i
$418$	−65.8361			−0.157503
$419$			320.586i			0.765121i	0.923930	+	0.382561i	$0.124958\pi$
$419$			320.586i			0.765121i	−0.923930	+	0.382561i	$0.875042\pi$
$420$		0			0
$421$	394.568			0.937217			0.468609	−	0.883406i	$-0.344755\pi$
$421$	394.568			0.937217			0.468609	+	0.883406i	$0.344755\pi$
$422$			178.238i			0.422365i
$423$	−8.74648			−0.0206773
$424$	−31.6560			−0.0746603
$425$		0			0
$426$			124.899i			0.293191i
$427$	617.624	+	95.6093i	1.44643	+	0.223909i
$428$			320.180i			0.748084i
$429$	−348.471			−0.812287
$430$		0			0
$431$	−687.598			−1.59535			−0.797677	−	0.603084i	$-0.793938\pi$
$431$	−687.598			−1.59535			−0.797677	+	0.603084i	$0.793938\pi$
$432$	−20.7846			−0.0481125
$433$	−738.775			−1.70618			−0.853089	−	0.521766i	$-0.825273\pi$
$433$	−738.775			−1.70618			−0.853089	+	0.521766i	$0.825273\pi$
$434$	−31.7270	+	204.952i	−0.0731037	+	0.472241i
$435$		0			0
$436$	−367.232			−0.842276
$437$	119.436			0.273310
$438$		−	193.279i		−	0.441277i
$439$		−	323.601i		−	0.737133i	−0.929601	−	0.368567i	$-0.879849\pi$
$439$		−	323.601i		−	0.737133i	0.929601	−	0.368567i	$-0.120151\pi$
$440$		0			0
$441$	−140.120	−	44.4466i	−0.317731	−	0.100786i
$442$		−	542.760i		−	1.22796i
$443$		−	246.877i		−	0.557285i	−0.960395	−	0.278642i	$-0.910116\pi$
$443$		−	246.877i		−	0.557285i	0.960395	−	0.278642i	$-0.0898844\pi$
$444$			104.562i			0.235501i
$445$		0			0
$446$		−	88.5608i		−	0.198567i
$447$	474.877			1.06237
$448$	8.56686	−	55.3408i	0.0191225	−	0.123529i
$449$	472.482			1.05230			0.526150	−	0.850392i	$-0.323635\pi$
$449$	472.482			1.05230			0.526150	+	0.850392i	$0.323635\pi$
$450$		0			0
$451$			419.893i			0.931027i
$452$			29.3942i			0.0650314i
$453$	−278.073			−0.613848
$454$		−	311.915i		−	0.687038i
$455$		0			0
$456$	22.9694			0.0503715
$457$			601.310i			1.31578i	0.753115	+	0.657889i	$0.228550\pi$
$457$			601.310i			1.31578i	−0.753115	+	0.657889i	$0.771450\pi$
$458$	292.455			0.638548
$459$	−98.4177			−0.214418
$460$		0			0
$461$			270.297i			0.586328i	0.956062	+	0.293164i	$0.0947081\pi$
$461$			270.297i			0.586328i	−0.956062	+	0.293164i	$0.905292\pi$
$462$	−168.243	−	26.0443i	−0.364162	−	0.0563729i
$463$		−	579.731i		−	1.25212i	−0.779775	−	0.626060i	$-0.784667\pi$
$463$		−	579.731i		−	1.25212i	0.779775	−	0.626060i	$-0.215333\pi$
$464$	−63.9400			−0.137802
$465$		0			0
$466$	236.616			0.507761
$467$	−895.295			−1.91712			−0.958560	−	0.284891i	$-0.908043\pi$
$467$	−895.295			−1.91712			−0.958560	+	0.284891i	$0.908043\pi$
$468$	121.577			0.259781
$469$	−94.0264	−	14.5555i	−0.200483	−	0.0310351i
$470$		0			0
$471$	461.127			0.979037
$472$	180.145			0.381664
$473$			494.170i			1.04476i
$474$		−	171.138i		−	0.361050i
$475$		0			0
$476$	40.5651	−	262.046i	0.0852209	−	0.550516i
$477$		−	33.5762i		−	0.0703904i
$478$			20.5515i			0.0429947i
$479$			252.755i			0.527673i	0.964567	+	0.263836i	$0.0849879\pi$
$479$			252.755i			0.527673i	−0.964567	+	0.263836i	$0.915012\pi$
$480$		0			0
$481$		−	611.627i		−	1.27157i
$482$	477.653			0.990981
$483$	305.217	+	47.2482i	0.631920	+	0.0978224i
$484$	44.8305			0.0926249
$485$		0			0
$486$		−	22.0454i		−	0.0453609i
$487$			421.873i			0.866269i	0.901329	+	0.433135i	$0.142593\pi$
$487$			421.873i			0.866269i	−0.901329	+	0.433135i	$0.857407\pi$
$488$	−252.530			−0.517480
$489$			324.584i			0.663770i
$490$		0			0
$491$	−232.477			−0.473476			−0.236738	−	0.971574i	$-0.576078\pi$
$491$	−232.477			−0.473476			−0.236738	+	0.971574i	$0.576078\pi$
$492$		−	146.496i		−	0.297755i
$493$	−302.764			−0.614126
$494$	−134.357			−0.271978
$495$		0			0
$496$		−	83.7997i		−	0.168951i
$497$	54.6029	−	352.728i	0.109865	−	0.709714i
$498$		−	168.739i		−	0.338834i
$499$	528.736			1.05959			0.529796	−	0.848125i	$-0.322269\pi$
$499$	528.736			1.05959			0.529796	+	0.848125i	$0.322269\pi$
$500$		0			0
$501$	455.421			0.909023
$502$	−553.295			−1.10218
$503$	−865.962			−1.72160			−0.860798	−	0.508948i	$-0.830035\pi$
$503$	−865.962			−1.72160			−0.860798	+	0.508948i	$0.830035\pi$
$504$	58.6978	+	9.08653i	0.116464	+	0.0180288i
$505$		0			0
$506$	357.695			0.706907
$507$	−418.437			−0.825319
$508$		−	386.930i		−	0.761673i
$509$		−	614.157i		−	1.20659i	−0.797516	−	0.603297i	$-0.793853\pi$
$509$		−	614.157i		−	1.20659i	0.797516	−	0.603297i	$-0.206147\pi$
$510$		0			0
$511$	−84.4970	+	545.840i	−0.165356	+	1.06818i
$512$			22.6274i			0.0441942i
$513$			24.3627i			0.0474907i
$514$		−	389.569i		−	0.757917i
$515$		0			0
$516$		−	172.410i		−	0.334128i
$517$	28.9479			0.0559921
$518$	45.7122	−	295.295i	0.0882475	−	0.570068i
$519$	−0.226531			−0.000436475
$520$		0			0
$521$		−	428.487i		−	0.822432i	−0.911538	−	0.411216i	$-0.865104\pi$
$521$		−	428.487i		−	0.822432i	0.911538	−	0.411216i	$-0.134896\pi$
$522$		−	67.8186i		−	0.129921i
$523$	1029.66			1.96876			0.984379	−	0.176060i	$-0.0563353\pi$
$523$	1029.66			1.96876			0.984379	+	0.176060i	$0.0563353\pi$
$524$			197.674i			0.377240i
$525$		0			0
$526$	−497.850			−0.946482
$527$		−	396.802i		−	0.752945i
$528$	68.7900			0.130284
$529$	−119.912			−0.226677
$530$		0			0
$531$			191.073i			0.359836i
$532$	−64.8679	−	10.0417i	−0.121932	−	0.0188753i
$533$			856.910i			1.60771i
$534$	−382.324			−0.715962
$535$		0			0
$536$	38.4449			0.0717256
$537$	248.431			0.462627
$538$	128.103			0.238111
$539$	463.748	+	147.103i	0.860387	+	0.272919i
$540$		0			0
$541$	−533.849			−0.986782			−0.493391	−	0.869808i	$-0.664243\pi$
$541$	−533.849			−0.986782			−0.493391	+	0.869808i	$0.664243\pi$
$542$	79.9361			0.147484
$543$		−	458.050i		−	0.843554i
$544$			107.144i			0.196955i
$545$		0			0
$546$	−343.347	−	53.1506i	−0.628840	−	0.0973455i
$547$			349.653i			0.639220i	0.947549	+	0.319610i	$0.103552\pi$
$547$			349.653i			0.639220i	−0.947549	+	0.319610i	$0.896448\pi$
$548$		−	80.7476i		−	0.147350i
$549$		−	267.849i		−	0.487885i
$550$		0			0
$551$			74.9474i			0.136021i
$552$	−124.795			−0.226079
$553$	−74.8172	+	483.310i	−0.135293	+	0.873978i
$554$	−224.438			−0.405124
$555$		0			0
$556$		−	70.7050i		−	0.127167i
$557$		−	193.971i		−	0.348243i	−0.984724	−	0.174122i	$-0.944291\pi$
$557$		−	193.971i		−	0.348243i	0.984724	−	0.174122i	$-0.0557086\pi$
$558$	88.8830			0.159288
$559$			1008.49i			1.80410i
$560$		0			0
$561$	325.729			0.580623
$562$		−	71.0421i		−	0.126410i
$563$	388.914			0.690788			0.345394	−	0.938458i	$-0.387745\pi$
$563$	388.914			0.690788			0.345394	+	0.938458i	$0.387745\pi$
$564$	−10.0996			−0.0179070
$565$		0			0
$566$		−	148.386i		−	0.262167i
$567$	−9.63772	+	62.2584i	−0.0169977	+	0.109803i
$568$			144.221i			0.253911i
$569$	470.383			0.826683			0.413342	−	0.910576i	$-0.364362\pi$
$569$	470.383			0.826683			0.413342	+	0.910576i	$0.364362\pi$
$570$		0			0
$571$	887.703			1.55465			0.777323	−	0.629101i	$-0.216577\pi$
$571$	887.703			1.55465			0.777323	+	0.629101i	$0.216577\pi$
$572$	−402.380			−0.703461
$573$	−378.838			−0.661148
$574$	−64.0443	+	413.718i	−0.111575	+	0.720764i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	927.661			1.60773			0.803866	−	0.594811i	$-0.202773\pi$
$577$	927.661			1.60773			0.803866	+	0.594811i	$0.202773\pi$
$578$			98.6307i			0.170641i
$579$			281.820i			0.486736i
$580$		0			0
$581$	−73.7688	+	476.537i	−0.126969	+	0.820201i
$582$		−	378.930i		−	0.651083i
$583$			111.126i			0.190611i
$584$		−	223.180i		−	0.382157i
$585$		0			0
$586$		−	715.657i		−	1.22126i
$587$	504.818			0.859996			0.429998	−	0.902830i	$-0.358514\pi$
$587$	504.818			0.859996			0.429998	+	0.902830i	$0.358514\pi$
$588$	−161.796	−	51.3225i	−0.275164	−	0.0872832i
$589$	−98.2260			−0.166767
$590$		0			0
$591$			304.039i			0.514449i
$592$			120.738i			0.203950i
$593$	931.909			1.57152			0.785758	−	0.618534i	$-0.212273\pi$
$593$	931.909			1.57152			0.785758	+	0.618534i	$0.212273\pi$
$594$			72.9629i			0.122833i
$595$		0			0
$596$	548.341			0.920035
$597$			106.500i			0.178392i
$598$	729.977			1.22070
$599$	−841.411			−1.40469			−0.702347	−	0.711835i	$-0.747864\pi$
$599$	−841.411			−1.40469			−0.702347	+	0.711835i	$0.747864\pi$
$600$		0			0
$601$		−	116.550i		−	0.193926i	−0.995288	−	0.0969632i	$-0.969087\pi$
$601$		−	116.550i		−	0.193926i	0.995288	−	0.0969632i	$-0.0309129\pi$
$602$	−75.3734	+	486.903i	−0.125205	+	0.808809i
$603$			40.7770i			0.0676236i
$604$	−321.091			−0.531608
$605$		0			0
$606$	−327.149			−0.539850
$607$	6.57481			0.0108316			0.00541582	−	0.999985i	$-0.498276\pi$
$607$	6.57481			0.0108316			0.00541582	+	0.999985i	$0.498276\pi$
$608$	26.5228			0.0436230
$609$	−29.6487	+	191.527i	−0.0486842	+	0.314494i
$610$		0			0
$611$	59.0763			0.0966879
$612$	−113.643			−0.185691
$613$		−	51.9420i		−	0.0847340i	−0.999102	−	0.0423670i	$-0.986510\pi$
$613$		−	51.9420i		−	0.0847340i	0.999102	−	0.0423670i	$-0.0134899\pi$
$614$		−	313.629i		−	0.510797i
$615$		0			0
$616$	−194.270	−	30.0733i	−0.315373	−	0.0488203i
$617$			1064.09i			1.72462i	0.506383	+	0.862309i	$0.330982\pi$
$617$			1064.09i			1.72462i	−0.506383	+	0.862309i	$0.669018\pi$
$618$		−	200.354i		−	0.324198i
$619$			585.402i			0.945722i	0.881137	+	0.472861i	$0.156779\pi$
$619$			585.402i			0.945722i	−0.881137	+	0.472861i	$0.843221\pi$
$620$		0			0
$621$		−	132.366i		−	0.213149i
$622$	−114.348			−0.183839
$623$	1079.72	+	167.143i	1.73310	+	0.268287i
$624$	140.385			0.224977
$625$		0			0
$626$		−	480.980i		−	0.768338i
$627$		−	80.6324i		−	0.128600i
$628$	532.463			0.847871
$629$			571.711i			0.908921i
$630$		0			0
$631$	−827.999			−1.31220			−0.656101	−	0.754673i	$-0.727795\pi$
$631$	−827.999			−1.31220			−0.656101	+	0.754673i	$0.727795\pi$
$632$		−	197.613i		−	0.312678i
$633$	−218.296			−0.344859
$634$	−430.667			−0.679285
$635$		0			0
$636$		−	38.7705i		−	0.0609599i
$637$	946.409	+	300.206i	1.48573	+	0.471280i
$638$			224.457i			0.351813i
$639$	−152.970			−0.239389
$640$		0			0
$641$	−806.971			−1.25893			−0.629463	−	0.777031i	$-0.716725\pi$
$641$	−806.971			−1.25893			−0.629463	+	0.777031i	$0.716725\pi$
$642$	−392.139			−0.610808
$643$	588.657			0.915485			0.457743	−	0.889085i	$-0.348658\pi$
$643$	588.657			0.915485			0.457743	+	0.889085i	$0.348658\pi$
$644$	352.435	+	54.5575i	0.547259	+	0.0847167i
$645$		0			0
$646$	125.589			0.194410
$647$	−51.4386			−0.0795032			−0.0397516	−	0.999210i	$-0.512657\pi$
$647$	−51.4386			−0.0795032			−0.0397516	+	0.999210i	$0.512657\pi$
$648$		−	25.4558i		−	0.0392837i
$649$		−	632.387i		−	0.974403i
$650$		0			0
$651$	−251.014	−	38.8575i	−0.385583	−	0.0596889i
$652$			374.797i			0.574842i
$653$		−	843.699i		−	1.29204i	−0.763322	−	0.646018i	$-0.776433\pi$
$653$		−	843.699i		−	1.29204i	0.763322	−	0.646018i	$-0.223567\pi$
$654$		−	449.766i		−	0.687715i
$655$		0			0
$656$		−	169.159i		−	0.257864i
$657$	236.718			0.360301
$658$	28.5222	+	4.41529i	0.0433468	+	0.00671016i
$659$	203.437			0.308705			0.154352	−	0.988016i	$-0.450671\pi$
$659$	203.437			0.308705			0.154352	+	0.988016i	$0.450671\pi$
$660$		0			0
$661$		−	1141.47i		−	1.72688i	−0.504454	−	0.863439i	$-0.668306\pi$
$661$		−	1141.47i		−	1.72688i	0.504454	−	0.863439i	$-0.331694\pi$
$662$			457.039i			0.690391i
$663$	664.742			1.00263
$664$		−	194.843i		−	0.293439i
$665$		0			0
$666$	−128.062			−0.192286
$667$		−	407.198i		−	0.610492i
$668$	525.874			0.787237
$669$	108.464			0.162129
$670$		0			0
$671$			886.489i			1.32115i
$672$	67.7784	+	10.4922i	0.100861	+	0.0156134i
$673$		−	1259.69i		−	1.87175i	−0.352327	−	0.935877i	$-0.614609\pi$
$673$		−	1259.69i		−	1.87175i	0.352327	−	0.935877i	$-0.385391\pi$
$674$	471.331			0.699305
$675$		0			0
$676$	−483.169			−0.714747
$677$	563.250			0.831979			0.415989	−	0.909369i	$-0.363435\pi$
$677$	563.250			0.831979			0.415989	+	0.909369i	$0.363435\pi$
$678$	−36.0004			−0.0530979
$679$	−165.659	+	1070.14i	−0.243975	+	1.57605i
$680$		0			0
$681$	382.017			0.560964
$682$	−294.173			−0.431338
$683$		−	881.725i		−	1.29096i	−0.763778	−	0.645480i	$-0.776658\pi$
$683$		−	881.725i		−	1.29096i	0.763778	−	0.645480i	$-0.223342\pi$
$684$			28.1317i			0.0411281i
$685$		0			0
$686$	434.492	+	215.673i	0.633370	+	0.314393i
$687$			358.183i			0.521372i
$688$		−	199.082i		−	0.289363i
$689$			226.784i			0.329149i
$690$		0			0
$691$			33.6567i			0.0487072i	0.999703	+	0.0243536i	$0.00775276\pi$
$691$			33.6567i			0.0487072i	−0.999703	+	0.0243536i	$0.992247\pi$
$692$	−0.261575			−0.000377998
$693$	31.8976	−	206.054i	0.0460283	−	0.297337i
$694$	364.177			0.524751
$695$		0			0
$696$		−	78.3102i		−	0.112515i
$697$		−	800.987i		−	1.14919i
$698$	434.134			0.621968
$699$			289.795i			0.414585i
$700$		0			0
$701$	123.366			0.175986			0.0879928	−	0.996121i	$-0.471955\pi$
$701$	123.366			0.175986			0.0879928	+	0.996121i	$0.471955\pi$
$702$			148.901i			0.212110i
$703$	141.524			0.201314
$704$	79.4319			0.112829
$705$		0			0
$706$		−	351.350i		−	0.497663i
$707$	923.902	+	143.022i	1.30679	+	0.202294i
$708$			220.632i			0.311627i
$709$	−1271.96			−1.79401			−0.897007	−	0.442016i	$-0.854264\pi$
$709$	−1271.96			−1.79401			−0.897007	+	0.442016i	$0.854264\pi$
$710$		0			0
$711$	209.600			0.294796
$712$	−441.469			−0.620041
$713$	533.673			0.748489
$714$	320.939	+	49.6820i	0.449495	+	0.0695826i
$715$		0			0
$716$	286.863			0.400646
$717$	−25.1703			−0.0351050
$718$			492.729i			0.686252i
$719$			482.510i			0.671085i	0.942025	+	0.335542i	$0.108920\pi$
$719$			482.510i			0.671085i	−0.942025	+	0.335542i	$0.891080\pi$
$720$		0			0
$721$	−87.5899	+	565.820i	−0.121484	+	0.784771i
$722$			479.442i			0.664048i
$723$			585.003i			0.809133i
$724$		−	528.910i		−	0.730539i
$725$		0			0
$726$			54.9059i			0.0756279i
$727$	1033.97			1.42224			0.711119	−	0.703071i	$-0.248189\pi$
$727$	1033.97			1.42224			0.711119	+	0.703071i	$0.248189\pi$
$728$	−396.462	−	61.3731i	−0.544591	−	0.0843037i
$729$	27.0000			0.0370370
$730$		0			0
$731$		−	942.677i		−	1.28957i
$732$		−	309.285i		−	0.422521i
$733$	199.138			0.271676			0.135838	−	0.990731i	$-0.456627\pi$
$733$	199.138			0.271676			0.135838	+	0.990731i	$0.456627\pi$
$734$		−	104.541i		−	0.142426i
$735$		0			0
$736$	−144.101			−0.195790
$737$		−	134.958i		−	0.183118i
$738$	179.420			0.243116
$739$	102.937			0.139292			0.0696460	−	0.997572i	$-0.477813\pi$
$739$	102.937			0.139292			0.0696460	+	0.997572i	$0.477813\pi$
$740$		0			0
$741$		−	164.553i		−	0.222069i
$742$	−16.9495	+	109.492i	−0.0228430	+	0.147563i
$743$		−	366.082i		−	0.492707i	−0.969180	−	0.246354i	$-0.920768\pi$
$743$		−	366.082i		−	0.492707i	0.969180	−	0.246354i	$-0.0792325\pi$
$744$	102.633			0.137948
$745$		0			0
$746$	74.8830			0.100379
$747$	206.663			0.276657
$748$	376.120			0.502834
$749$	1107.44	+	171.434i	1.47856	+	0.228883i
$750$		0			0
$751$	−230.728			−0.307227			−0.153614	−	0.988131i	$-0.549091\pi$
$751$	−230.728			−0.307227			−0.153614	+	0.988131i	$0.549091\pi$
$752$	−11.6620			−0.0155079
$753$		−	677.646i		−	0.899928i
$754$			458.067i			0.607516i
$755$		0			0
$756$	−11.1287	+	71.8899i	−0.0147205	+	0.0950924i
$757$		−	1340.08i		−	1.77026i	−0.465348	−	0.885128i	$-0.654071\pi$
$757$		−	1340.08i		−	1.77026i	0.465348	−	0.885128i	$-0.345929\pi$
$758$		−	159.412i		−	0.210306i
$759$			438.085i			0.577187i
$760$		0			0
$761$		−	1256.80i		−	1.65151i	−0.564027	−	0.825756i	$-0.690749\pi$
$761$		−	1256.80i		−	1.65151i	0.564027	−	0.825756i	$-0.309251\pi$
$762$	473.890			0.621903
$763$	−196.627	+	1270.18i	−0.257702	+	1.66472i
$764$	−437.444			−0.572571
$765$		0			0
$766$			741.134i			0.967537i
$767$		−	1290.56i		−	1.68261i
$768$	−27.7128			−0.0360844
$769$		−	361.861i		−	0.470560i	−0.971928	−	0.235280i	$-0.924399\pi$
$769$		−	361.861i		−	0.470560i	0.971928	−	0.235280i	$-0.0756007\pi$
$770$		0			0
$771$	477.123			0.618836
$772$			325.418i			0.421526i
$773$	−746.551			−0.965783			−0.482892	−	0.875680i	$-0.660414\pi$
$773$	−746.551			−0.965783			−0.482892	+	0.875680i	$0.660414\pi$
$774$	211.158			0.272814
$775$		0			0
$776$		−	437.551i		−	0.563854i
$777$	361.661	+	55.9858i	0.465458	+	0.0720537i
$778$			161.548i			0.207645i
$779$	−198.280			−0.254531
$780$		0			0
$781$	506.278			0.648243
$782$	−682.338			−0.872555
$783$	83.0605			0.106080
$784$	−186.826	−	59.2622i	−0.238299	−	0.0755895i
$785$		0			0
$786$	−242.100			−0.308015
$787$	−1121.67			−1.42524			−0.712622	−	0.701548i	$-0.752493\pi$
$787$	−1121.67			−1.42524			−0.712622	+	0.701548i	$0.752493\pi$
$788$			351.074i			0.445526i
$789$		−	609.739i		−	0.772799i
$790$		0			0
$791$	101.669	+	15.7385i	0.128532	+	0.0198970i
$792$			84.2502i			0.106377i
$793$			1809.13i			2.28137i
$794$		−	929.793i		−	1.17102i
$795$		0			0
$796$			122.976i			0.154492i
$797$	1458.38			1.82983			0.914916	−	0.403644i	$-0.132257\pi$
$797$	1458.38			1.82983			0.914916	+	0.403644i	$0.132257\pi$
$798$	12.2985	−	79.4466i	0.0154116	−	0.0995572i
$799$	−55.2209			−0.0691125
$800$		0			0
$801$		−	468.249i		−	0.584580i
$802$		−	868.775i		−	1.08326i
$803$	−783.455			−0.975661
$804$			47.0852i			0.0585637i
$805$		0			0
$806$	−600.342			−0.744841
$807$			156.894i			0.194416i
$808$	−377.759			−0.467524
$809$	384.044			0.474714			0.237357	−	0.971422i	$-0.423719\pi$
$809$	384.044			0.474714			0.237357	+	0.971422i	$0.423719\pi$
$810$		0			0
$811$		−	723.519i		−	0.892132i	−0.895000	−	0.446066i	$-0.852825\pi$
$811$		−	723.519i		−	0.892132i	0.895000	−	0.446066i	$-0.147175\pi$
$812$	−34.2353	+	221.156i	−0.0421617	+	0.272360i
$813$			97.9013i			0.120420i
$814$	423.843			0.520692
$815$		0			0
$816$	−131.224			−0.160813
$817$	−233.354			−0.285623
$818$	−276.645			−0.338196
$819$	65.0960	−	420.512i	0.0794823	−	0.513446i
$820$		0			0
$821$	77.1102			0.0939223			0.0469611	−	0.998897i	$-0.485046\pi$
$821$	77.1102			0.0939223			0.0469611	+	0.998897i	$0.485046\pi$
$822$	98.8952			0.120310
$823$		−	234.896i		−	0.285414i	−0.989765	−	0.142707i	$-0.954419\pi$
$823$		−	234.896i		−	0.285414i	0.989765	−	0.142707i	$-0.0455807\pi$
$824$		−	231.349i		−	0.280763i
$825$		0			0
$826$	96.4550	−	623.087i	0.116774	−	0.754343i
$827$			173.944i			0.210331i	0.994455	+	0.105166i	$0.0335373\pi$
$827$			173.944i			0.210331i	−0.994455	+	0.105166i	$0.966463\pi$
$828$		−	152.843i		−	0.184592i
$829$			800.748i			0.965920i	0.875642	+	0.482960i	$0.160438\pi$
$829$			800.748i			0.965920i	−0.875642	+	0.482960i	$0.839562\pi$
$830$		0			0
$831$		−	274.880i		−	0.330782i
$832$	162.103			0.194835
$833$	−884.645	−	280.614i	−1.06200	−	0.336871i
$834$	86.5955			0.103832
$835$		0			0
$836$		−	93.1063i		−	0.111371i
$837$			108.859i			0.130058i
$838$	−453.377			−0.541022
$839$			943.082i			1.12406i	0.827118	+	0.562028i	$0.189979\pi$
$839$			943.082i			1.12406i	−0.827118	+	0.562028i	$0.810021\pi$
$840$		0			0
$841$	−585.480			−0.696171
$842$			558.004i			0.662713i
$843$	87.0085			0.103213
$844$	−252.067			−0.298657
$845$		0			0
$846$		−	12.3694i		−	0.0146210i
$847$	24.0035	−	155.060i	0.0283395	−	0.183069i
$848$		−	44.7683i		−	0.0527928i
$849$	181.735			0.214058
$850$		0			0
$851$	−768.915			−0.903543
$852$	−176.634			−0.207317
$853$	−225.297			−0.264124			−0.132062	−	0.991241i	$-0.542160\pi$
$853$	−225.297			−0.264124			−0.132062	+	0.991241i	$0.542160\pi$
$854$	−135.212	+	873.453i	−0.158328	+	1.02278i
$855$		0			0
$856$	−452.803			−0.528975
$857$	−899.165			−1.04920			−0.524600	−	0.851349i	$-0.675785\pi$
$857$	−899.165			−1.04920			−0.524600	+	0.851349i	$0.675785\pi$
$858$		−	492.813i		−	0.574374i
$859$		−	785.611i		−	0.914564i	−0.889322	−	0.457282i	$-0.848823\pi$
$859$		−	785.611i		−	0.914564i	0.889322	−	0.457282i	$-0.151177\pi$
$860$		0			0
$861$	−506.699	−	78.4379i	−0.588501	−	0.0911010i
$862$		−	972.410i		−	1.12809i
$863$		−	694.379i		−	0.804610i	−0.915506	−	0.402305i	$-0.868209\pi$
$863$		−	694.379i		−	0.804610i	0.915506	−	0.402305i	$-0.131791\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$		−	1044.79i		−	1.20645i
$867$	−120.797			−0.139328
$868$	−289.846	−	44.8687i	−0.333925	−	0.0516921i
$869$	−693.705			−0.798280
$870$		0			0
$871$		−	275.420i		−	0.316211i
$872$		−	519.345i		−	0.595579i
$873$	464.093			0.531607
$874$			168.909i			0.193259i
$875$		0			0
$876$	273.338			0.312030
$877$		−	699.811i		−	0.797960i	−0.916960	−	0.398980i	$-0.869364\pi$
$877$		−	699.811i		−	0.797960i	0.916960	−	0.398980i	$-0.130636\pi$
$878$	457.642			0.521232
$879$	876.497			0.997153
$880$		0			0
$881$		−	1112.73i		−	1.26303i	−0.775362	−	0.631517i	$-0.782433\pi$
$881$		−	1112.73i		−	1.26303i	0.775362	−	0.631517i	$-0.217567\pi$
$882$	62.8570	−	198.159i	0.0712664	−	0.224670i
$883$			522.489i			0.591720i	0.955231	+	0.295860i	$0.0956062\pi$
$883$			522.489i			0.591720i	−0.955231	+	0.295860i	$0.904394\pi$
$884$	767.578			0.868301
$885$		0			0
$886$	349.137			0.394060
$887$	149.877			0.168971			0.0844853	−	0.996425i	$-0.473075\pi$
$887$	149.877			0.168971			0.0844853	+	0.996425i	$0.473075\pi$
$888$	−147.874			−0.166524
$889$	−1338.31	−	207.173i	−1.50541	−	0.233041i
$890$		0			0
$891$	−89.3609			−0.100293
$892$	125.244			0.140408
$893$			13.6696i			0.0153075i
$894$			671.578i			0.751206i
$895$		0			0
$896$	78.2638	+	12.1154i	0.0873480	+	0.0135216i
$897$			894.036i			0.996695i
$898$			668.191i			0.744088i
$899$			334.885i			0.372508i
$900$		0			0
$901$		−	211.983i		−	0.235276i
$902$	−593.819			−0.658336
$903$	−596.332	−	92.3132i	−0.660390	−	0.102229i
$904$	−41.5697			−0.0459841
$905$		0			0
$906$		−	393.254i		−	0.434056i
$907$			1544.51i			1.70288i	0.524452	+	0.851440i	$0.324270\pi$
$907$			1544.51i			1.70288i	−0.524452	+	0.851440i	$0.675730\pi$
$908$	441.115			0.485809
$909$		−	400.674i		−	0.440786i
$910$		0			0
$911$	1324.82			1.45425			0.727126	−	0.686504i	$-0.240856\pi$
$911$	1324.82			1.45425			0.727126	+	0.686504i	$0.240856\pi$
$912$			32.4836i			0.0356180i
$913$	−683.984			−0.749161
$914$	−850.381			−0.930395
$915$		0			0
$916$			413.594i			0.451521i
$917$	683.714	+	105.840i	0.745599	+	0.115420i
$918$		−	139.184i		−	0.151616i
$919$	1469.75			1.59930			0.799648	−	0.600470i	$-0.205020\pi$
$919$	1469.75			1.59930			0.799648	+	0.600470i	$0.205020\pi$
$920$		0			0
$921$	384.116			0.417064
$922$	−382.258			−0.414596
$923$	1033.20			1.11940
$924$	36.8322	−	237.931i	0.0398616	−	0.257501i
$925$		0			0
$926$	819.864			0.885382
$927$	245.383			0.264706
$928$		−	90.4249i		−	0.0974406i
$929$		−	1613.82i		−	1.73715i	−0.495554	−	0.868577i	$-0.665035\pi$
$929$		−	1613.82i		−	1.73715i	0.495554	−	0.868577i	$-0.334965\pi$
$930$		0			0
$931$	−69.4643	+	218.989i	−0.0746125	+	0.235219i
$932$			334.626i			0.359041i
$933$		−	140.047i		−	0.150104i
$934$		−	1266.14i		−	1.35561i
$935$		0			0
$936$			171.936i			0.183693i
$937$	1422.24			1.51787			0.758934	−	0.651167i	$-0.225720\pi$
$937$	1422.24			1.51787			0.758934	+	0.651167i	$0.225720\pi$
$938$	20.5845	−	132.973i	0.0219451	−	0.141763i
$939$	589.077			0.627345
$940$		0			0
$941$			904.869i			0.961603i	0.876829	+	0.480802i	$0.159654\pi$
$941$			904.869i			0.961603i	−0.876829	+	0.480802i	$0.840346\pi$
$942$			652.131i			0.692284i
$943$	1077.28			1.14239
$944$			254.764i			0.269877i
$945$		0			0
$946$	−698.862			−0.738755
$947$			414.868i			0.438087i	0.975715	+	0.219043i	$0.0702936\pi$
$947$			414.868i			0.438087i	−0.975715	+	0.219043i	$0.929706\pi$
$948$	242.025			0.255301
$949$	−1598.86			−1.68478
$950$		0			0
$951$		−	527.457i		−	0.554634i
$952$	370.589	+	57.3678i	0.389274	+	0.0602603i
$953$			30.9413i			0.0324672i	0.999868	+	0.0162336i	$0.00516755\pi$
$953$			30.9413i			0.0324672i	−0.999868	+	0.0162336i	$0.994832\pi$
$954$	47.4840			0.0497735
$955$		0			0
$956$	−29.0641			−0.0304018
$957$	−274.902			−0.287254
$958$	−357.450			−0.373121
$959$	−279.290	−	43.2346i	−0.291230	−	0.0450830i
$960$		0			0
$961$	522.101			0.543289
$962$	864.971			0.899138
$963$		−	480.270i		−	0.498723i
$964$			675.503i			0.700730i
$965$		0			0
$966$	−66.8190	+	431.643i	−0.0691709	+	0.446835i
$967$		−	1662.25i		−	1.71897i	−0.511159	−	0.859486i	$-0.670784\pi$
$967$		−	1662.25i		−	1.71897i	0.511159	−	0.859486i	$-0.329216\pi$
$968$			63.3998i			0.0654957i
$969$			153.814i			0.158735i
$970$		0			0
$971$		−	5.10561i		−	0.00525810i	−0.999997	−	0.00262905i	$-0.999163\pi$
$971$		−	5.10561i		−	0.00525810i	0.999997	−	0.00262905i	$-0.000836853\pi$
$972$	31.1769			0.0320750
$973$	−244.555	−	37.8575i	−0.251341	−	0.0389080i
$974$	−596.619			−0.612545
$975$		0			0
$976$		−	357.132i		−	0.365914i
$977$		−	531.274i		−	0.543781i	−0.962328	−	0.271891i	$-0.912351\pi$
$977$		−	531.274i		−	0.543781i	0.962328	−	0.271891i	$-0.0876489\pi$
$978$	−459.031			−0.469356
$979$			1549.75i			1.58299i
$980$		0			0
$981$	550.848			0.561517
$982$		−	328.772i		−	0.334798i
$983$	−1746.75			−1.77696			−0.888481	−	0.458913i	$-0.848239\pi$
$983$	−1746.75			−1.77696			−0.888481	+	0.458913i	$0.848239\pi$
$984$	207.176			0.210545
$985$		0			0
$986$		−	428.173i		−	0.434252i
$987$	−5.40760	+	34.9324i	−0.00547882	+	0.0353925i
$988$		−	190.009i		−	0.192317i
$989$	1267.84			1.28194
$990$		0			0
$991$	301.944			0.304687			0.152343	−	0.988328i	$-0.451318\pi$
$991$	301.944			0.304687			0.152343	+	0.988328i	$0.451318\pi$
$992$	118.511			0.119466
$993$	−559.756			−0.563702
$994$	498.833	+	77.2202i	0.501844	+	0.0776863i
$995$		0			0
$996$	238.633			0.239592
$997$	−521.642			−0.523212			−0.261606	−	0.965175i	$-0.584252\pi$
$997$	−521.642			−0.523212			−0.261606	+	0.965175i	$0.584252\pi$
$998$			747.746i			0.749244i
$999$		−	156.844i		−	0.157001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.h.c.349.12		24
5.2	odd	4		1050.3.f.c.601.4	yes	12
5.3	odd	4		1050.3.f.d.601.9	yes	12
5.4	even	2	inner	1050.3.h.c.349.13		24
7.6	odd	2	inner	1050.3.h.c.349.14		24
35.13	even	4		1050.3.f.d.601.12	yes	12
35.27	even	4		1050.3.f.c.601.1	✓	12
35.34	odd	2	inner	1050.3.h.c.349.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.f.c.601.1	✓	12	35.27	even	4
1050.3.f.c.601.4	yes	12	5.2	odd	4
1050.3.f.d.601.9	yes	12	5.3	odd	4
1050.3.f.d.601.12	yes	12	35.13	even	4
1050.3.h.c.349.11		24	35.34	odd	2	inner
1050.3.h.c.349.12		24	1.1	even	1	trivial
1050.3.h.c.349.13		24	5.4	even	2	inner
1050.3.h.c.349.14		24	7.6	odd	2	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(-1.07086 + 6.91761i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(-1.07086 + 6.91761i) q^{7} -2.82843i q^{8} +3.00000 q^{9} -9.92899 q^{11} +3.46410 q^{12} -20.2629 q^{13} +(-9.78297 - 1.51442i) q^{14} +4.00000 q^{16} +18.9405 q^{17} +4.24264i q^{18} -4.68861i q^{19} +(1.85478 - 11.9816i) q^{21} -14.0417i q^{22} +25.4738i q^{23} +4.89898i q^{24} -28.6560i q^{26} -5.19615 q^{27} +(2.14171 - 13.8352i) q^{28} -15.9850 q^{29} -20.9499i q^{31} +5.65685i q^{32} +17.1975 q^{33} +26.7859i q^{34} -6.00000 q^{36} +30.1846i q^{37} +6.63069 q^{38} +35.0963 q^{39} -42.2896i q^{41} +(16.9446 + 2.62305i) q^{42} -49.7705i q^{43} +19.8580 q^{44} -36.0253 q^{46} -2.91549 q^{47} -6.92820 q^{48} +(-46.7065 - 14.8155i) q^{49} -32.8059 q^{51} +40.5258 q^{52} -11.1921i q^{53} -7.34847i q^{54} +(19.5659 + 3.02884i) q^{56} +8.12091i q^{57} -22.6062i q^{58} +63.6910i q^{59} -89.2830i q^{61} +29.6277 q^{62} +(-3.21257 + 20.7528i) q^{63} -8.00000 q^{64} +24.3210i q^{66} +13.5923i q^{67} -37.8810 q^{68} -44.1218i q^{69} -50.9899 q^{71} -8.48528i q^{72} +78.9059 q^{73} -42.6875 q^{74} +9.37722i q^{76} +(10.6325 - 68.6848i) q^{77} +49.6337i q^{78} +69.8667 q^{79} +9.00000 q^{81} +59.8066 q^{82} +68.8876 q^{83} +(-3.70956 + 23.9633i) q^{84} +70.3860 q^{86} +27.6868 q^{87} +28.0834i q^{88} -156.083i q^{89} +(21.6987 - 140.171i) q^{91} -50.9475i q^{92} +36.2863i q^{93} -4.12313i q^{94} -9.79796i q^{96} +154.698 q^{97} +(20.9523 - 66.0530i) q^{98} -29.7870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 72 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 + 72 * q^9	\( 24 q - 48 q^{4} + 72 q^{9} - 32 q^{11} - 16 q^{14} + 96 q^{16} - 12 q^{21} - 96 q^{29} - 144 q^{36} + 24 q^{39} + 64 q^{44} + 160 q^{46} - 236 q^{49} + 144 q^{51} + 32 q^{56} - 192 q^{64} + 496 q^{71} + 128 q^{74} + 416 q^{79} + 216 q^{81} + 24 q^{84} + 256 q^{86} - 316 q^{91} - 96 q^{99}+O(q^{100}) \) 24 * q - 48 * q^4 + 72 * q^9 - 32 * q^11 - 16 * q^14 + 96 * q^16 - 12 * q^21 - 96 * q^29 - 144 * q^36 + 24 * q^39 + 64 * q^44 + 160 * q^46 - 236 * q^49 + 144 * q^51 + 32 * q^56 - 192 * q^64 + 496 * q^71 + 128 * q^74 + 416 * q^79 + 216 * q^81 + 24 * q^84 + 256 * q^86 - 316 * q^91 - 96 * q^99

Introduction

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