LMFDB - Embedded newform 1050.3.f.c.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(601,1050)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1050.601");

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.f (of order $2$, degree $1$, 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 103 x^{10} + 14 x^{9} + 7600 x^{8} + 1474 x^{7} + 229961 x^{6} + 442438 x^{5} + \cdots + 69739201 $ x^12 - 2x^11 + 103x^10 + 14x^9 + 7600x^8 + 1474x^7 + 229961x^6 + 442438x^5 + 4765612x^4 + 4021754x^3 + 21002899x^2 - 8701742*x + 69739201
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			601.1
Root			$3.24795 - 5.62562i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.c.601.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.91761 + 1.07086i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.91761 + 1.07086i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -9.92899 q^{11} -3.46410i q^{12} -20.2629i q^{13} +(9.78297 - 1.51442i) q^{14} +4.00000 q^{16} -18.9405i q^{17} +4.24264 q^{18} -4.68861i q^{19} +(1.85478 + 11.9816i) q^{21} +14.0417 q^{22} +25.4738 q^{23} +4.89898i q^{24} +28.6560i q^{26} +5.19615i q^{27} +(-13.8352 + 2.14171i) q^{28} +15.9850 q^{29} +20.9499i q^{31} -5.65685 q^{32} +17.1975i q^{33} +26.7859i q^{34} -6.00000 q^{36} -30.1846 q^{37} +6.63069i q^{38} -35.0963 q^{39} +42.2896i q^{41} +(-2.62305 - 16.9446i) q^{42} -49.7705 q^{43} -19.8580 q^{44} -36.0253 q^{46} +2.91549i q^{47} -6.92820i q^{48} +(46.7065 - 14.8155i) q^{49} -32.8059 q^{51} -40.5258i q^{52} -11.1921 q^{53} -7.34847i q^{54} +(19.5659 - 3.02884i) q^{56} -8.12091 q^{57} -22.6062 q^{58} +63.6910i q^{59} +89.2830i q^{61} -29.6277i q^{62} +(20.7528 - 3.21257i) q^{63} +8.00000 q^{64} -24.3210i q^{66} -13.5923 q^{67} -37.8810i q^{68} -44.1218i q^{69} -50.9899 q^{71} +8.48528 q^{72} +78.9059i q^{73} +42.6875 q^{74} -9.37722i q^{76} +(68.6848 - 10.6325i) q^{77} +49.6337 q^{78} -69.8667 q^{79} +9.00000 q^{81} -59.8066i q^{82} +68.8876i q^{83} +(3.70956 + 23.9633i) q^{84} +70.3860 q^{86} -27.6868i q^{87} +28.0834 q^{88} -156.083i q^{89} +(21.6987 + 140.171i) q^{91} +50.9475 q^{92} +36.2863 q^{93} -4.12313i q^{94} +9.79796i q^{96} -154.698i q^{97} +(-66.0530 + 20.9523i) q^{98} +29.7870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{4} - 10 q^{7} - 36 q^{9}+O(q^{10}) $ 12 * q + 24 * q^4 - 10 * q^7 - 36 * q^9	$ 12 q + 24 q^{4} - 10 q^{7} - 36 q^{9} - 16 q^{11} + 8 q^{14} + 48 q^{16} - 6 q^{21} - 48 q^{22} - 20 q^{28} + 48 q^{29} - 72 q^{36} + 64 q^{37} - 12 q^{39} + 24 q^{42} - 108 q^{43} - 32 q^{44} + 80 q^{46} + 118 q^{49} + 72 q^{51} + 176 q^{53} + 16 q^{56} - 132 q^{57} + 128 q^{58} + 30 q^{63} + 96 q^{64} - 4 q^{67} + 248 q^{71} - 64 q^{74} - 396 q^{77} + 48 q^{78} - 208 q^{79} + 108 q^{81} - 12 q^{84} + 128 q^{86} - 96 q^{88} - 158 q^{91} + 252 q^{93} - 240 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q + 24 * q^4 - 10 * q^7 - 36 * q^9 - 16 * q^11 + 8 * q^14 + 48 * q^16 - 6 * q^21 - 48 * q^22 - 20 * q^28 + 48 * q^29 - 72 * q^36 + 64 * q^37 - 12 * q^39 + 24 * q^42 - 108 * q^43 - 32 * q^44 + 80 * q^46 + 118 * q^49 + 72 * q^51 + 176 * q^53 + 16 * q^56 - 132 * q^57 + 128 * q^58 + 30 * q^63 + 96 * q^64 - 4 * q^67 + 248 * q^71 - 64 * q^74 - 396 * q^77 + 48 * q^78 - 208 * q^79 + 108 * q^81 - 12 * q^84 + 128 * q^86 - 96 * q^88 - 158 * q^91 + 252 * q^93 - 240 * q^98 + 48 * 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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−6.91761	+	1.07086i	−0.988229	+	0.152980i
$7$	−6.91761	+	1.07086i	−0.988229	+	0.152980i
$8$	−2.82843			−0.353553
$9$	−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	$0.649046\pi$
$12$		−	3.46410i		−	0.288675i
$13$		−	20.2629i		−	1.55868i	−0.626599	−	0.779342i	$-0.715554\pi$
$13$		−	20.2629i		−	1.55868i	0.626599	−	0.779342i	$-0.284446\pi$
$14$	9.78297	−	1.51442i	0.698784	−	0.108173i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	18.9405i		−	1.11415i	−0.830463	−	0.557073i	$-0.811924\pi$
$17$		−	18.9405i		−	1.11415i	0.830463	−	0.557073i	$-0.188076\pi$
$18$	4.24264			0.235702
$19$		−	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
$22$	14.0417			0.638259
$23$	25.4738			1.10755			0.553777	−	0.832665i	$-0.313186\pi$
$23$	25.4738			1.10755			0.553777	+	0.832665i	$0.313186\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$			28.6560i			1.10216i
$27$			5.19615i			0.192450i
$28$	−13.8352	+	2.14171i	−0.494115	+	0.0764898i
$29$	15.9850			0.551207			0.275604	−	0.961271i	$-0.411122\pi$
$29$	15.9850			0.551207			0.275604	+	0.961271i	$0.411122\pi$
$30$		0			0
$31$			20.9499i			0.675804i	0.941181	+	0.337902i	$0.109717\pi$
$31$			20.9499i			0.675804i	−0.941181	+	0.337902i	$0.890283\pi$
$32$	−5.65685			−0.176777
$33$			17.1975i			0.521137i
$34$			26.7859i			0.787821i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−30.1846			−0.815800			−0.407900	−	0.913027i	$-0.633739\pi$
$37$	−30.1846			−0.815800			−0.407900	+	0.913027i	$0.633739\pi$
$38$			6.63069i			0.174492i
$39$	−35.0963			−0.899906
$40$		0			0
$41$			42.2896i			1.03145i	0.856753	+	0.515727i	$0.172478\pi$
$41$			42.2896i			1.03145i	−0.856753	+	0.515727i	$0.827522\pi$
$42$	−2.62305	−	16.9446i	−0.0624537	−	0.403443i
$43$	−49.7705			−1.15745			−0.578726	−	0.815522i	$-0.696450\pi$
$43$	−49.7705			−1.15745			−0.578726	+	0.815522i	$0.696450\pi$
$44$	−19.8580			−0.451318
$45$		0			0
$46$	−36.0253			−0.783159
$47$			2.91549i			0.0620318i	0.999519	+	0.0310159i	$0.00987425\pi$
$47$			2.91549i			0.0620318i	−0.999519	+	0.0310159i	$0.990126\pi$
$48$		−	6.92820i		−	0.144338i
$49$	46.7065	−	14.8155i	0.953194	−	0.302358i
$50$		0			0
$51$	−32.8059			−0.643253
$52$		−	40.5258i		−	0.779342i
$53$	−11.1921			−0.211171			−0.105586	−	0.994410i	$-0.533672\pi$
$53$	−11.1921			−0.211171			−0.105586	+	0.994410i	$0.533672\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	19.5659	−	3.02884i	0.349392	−	0.0540865i
$57$	−8.12091			−0.142472
$58$	−22.6062			−0.389762
$59$			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	$0.261332\pi$
$61$			89.2830i			1.46365i	−0.681490	+	0.731827i	$0.738668\pi$
$62$		−	29.6277i		−	0.477865i
$63$	20.7528	−	3.21257i	0.329410	−	0.0509932i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	24.3210i		−	0.368499i
$67$	−13.5923			−0.202871			−0.101435	−	0.994842i	$-0.532344\pi$
$67$	−13.5923			−0.202871			−0.101435	+	0.994842i	$0.532344\pi$
$68$		−	37.8810i		−	0.557073i
$69$		−	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	$0.616911\pi$
$72$	8.48528			0.117851
$73$			78.9059i			1.08090i	0.841375	+	0.540451i	$0.181746\pi$
$73$			78.9059i			1.08090i	−0.841375	+	0.540451i	$0.818254\pi$
$74$	42.6875			0.576858
$75$		0			0
$76$		−	9.37722i		−	0.123384i
$77$	68.6848	−	10.6325i	0.892011	−	0.138085i
$78$	49.6337			0.636330
$79$	−69.8667			−0.884388			−0.442194	−	0.896919i	$-0.645800\pi$
$79$	−69.8667			−0.884388			−0.442194	+	0.896919i	$0.645800\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	59.8066i		−	0.729348i
$83$			68.8876i			0.829971i	0.909828	+	0.414985i	$0.136213\pi$
$83$			68.8876i			0.829971i	−0.909828	+	0.414985i	$0.863787\pi$
$84$	3.70956	+	23.9633i	0.0441614	+	0.285277i
$85$		0			0
$86$	70.3860			0.818442
$87$		−	27.6868i		−	0.318240i
$88$	28.0834			0.319130
$89$		−	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
$92$	50.9475			0.553777
$93$	36.2863			0.390175
$94$		−	4.12313i		−	0.0438631i
$95$		0			0
$96$			9.79796i			0.102062i
$97$		−	154.698i		−	1.59482i	−0.603437	−	0.797410i	$-0.706203\pi$
$97$		−	154.698i		−	1.59482i	0.603437	−	0.797410i	$-0.293797\pi$
$98$	−66.0530	+	20.9523i	−0.674010	+	0.213799i
$99$	29.7870			0.300878
$100$		0			0
$101$			133.558i			1.32236i	0.750228	+	0.661179i	$0.229943\pi$
$101$			133.558i			1.32236i	−0.750228	+	0.661179i	$0.770057\pi$
$102$	46.3946			0.454849
$103$			81.7942i			0.794118i	0.917793	+	0.397059i	$0.129969\pi$
$103$			81.7942i			0.794118i	−0.917793	+	0.397059i	$0.870031\pi$
$104$			57.3121i			0.551078i
$105$		0			0
$106$	15.8280			0.149321
$107$	160.090			1.49617			0.748084	−	0.663604i	$-0.230974\pi$
$107$	160.090			1.49617			0.748084	+	0.663604i	$0.230974\pi$
$108$			10.3923i			0.0962250i
$109$	−183.616			−1.68455			−0.842276	−	0.539047i	$-0.818785\pi$
$109$	−183.616			−1.68455			−0.842276	+	0.539047i	$0.818785\pi$
$110$		0			0
$111$			52.2812i			0.471002i
$112$	−27.6704	+	4.28343i	−0.247057	+	0.0382449i
$113$	−14.6971			−0.130063			−0.0650314	−	0.997883i	$-0.520715\pi$
$113$	−14.6971			−0.130063			−0.0650314	+	0.997883i	$0.520715\pi$
$114$	11.4847			0.100743
$115$		0			0
$116$	31.9700			0.275604
$117$			60.7887i			0.519561i
$118$		−	90.0727i		−	0.763328i
$119$	20.2826	+	131.023i	0.170442	+	1.10103i
$120$		0			0
$121$	−22.4152			−0.185250
$122$		−	126.265i		−	1.03496i
$123$	73.2478			0.595511
$124$			41.8998i			0.337902i
$125$		0			0
$126$	−29.3489	+	4.54326i	−0.232928	+	0.0360576i
$127$	−193.465			−1.52335			−0.761673	−	0.647962i	$-0.775622\pi$
$127$	−193.465			−1.52335			−0.761673	+	0.647962i	$0.775622\pi$
$128$	−11.3137			−0.0883883
$129$			86.2050i			0.668255i
$130$		0			0
$131$			98.8368i			0.754480i	0.926116	+	0.377240i	$0.123127\pi$
$131$			98.8368i			0.754480i	−0.926116	+	0.377240i	$0.876873\pi$
$132$			34.3950i			0.260568i
$133$	5.02083	+	32.4339i	0.0377506	+	0.243864i
$134$	19.2225			0.143451
$135$		0			0
$136$			53.5718i			0.393910i
$137$	−40.3738			−0.294699			−0.147350	−	0.989084i	$-0.547074\pi$
$137$	−40.3738			−0.294699			−0.147350	+	0.989084i	$0.547074\pi$
$138$			62.3977i			0.452157i
$139$			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
$142$	72.1106			0.507821
$143$			201.190i			1.40692i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$		−	111.590i		−	0.764313i
$147$	−25.6613	−	80.8981i	−0.174566	−	0.550327i
$148$	−60.3692			−0.407900
$149$	274.171			1.84007			0.920035	−	0.391836i	$-0.128160\pi$
$149$	274.171			1.84007			0.920035	+	0.391836i	$0.128160\pi$
$150$		0			0
$151$	160.545			1.06322			0.531608	−	0.846991i	$-0.321588\pi$
$151$	160.545			1.06322			0.531608	+	0.846991i	$0.321588\pi$
$152$			13.2614i			0.0872460i
$153$			56.8215i			0.371382i
$154$	−97.1350	+	15.0367i	−0.630747	+	0.0976407i
$155$		0			0
$156$	−70.1927			−0.449953
$157$			266.232i			1.69574i	0.530202	+	0.847871i	$0.322116\pi$
$157$			266.232i			1.69574i	−0.530202	+	0.847871i	$0.677884\pi$
$158$	98.8064			0.625357
$159$			19.3852i			0.121920i
$160$		0			0
$161$	−176.217	+	27.2788i	−1.09452	+	0.169433i
$162$	−12.7279			−0.0785674
$163$	−187.398			−1.14968			−0.574842	−	0.818265i	$-0.694936\pi$
$163$	−187.398			−1.14968			−0.574842	+	0.818265i	$0.694936\pi$
$164$			84.5793i			0.515727i
$165$		0			0
$166$		−	97.4217i		−	0.586878i
$167$			262.937i			1.57447i	0.616650	+	0.787237i	$0.288489\pi$
$167$			262.937i			1.57447i	−0.616650	+	0.787237i	$0.711511\pi$
$168$	−5.24611	−	33.8892i	−0.0312268	−	0.201721i
$169$	−241.584			−1.42949
$170$		0			0
$171$			14.0658i			0.0822563i
$172$	−99.5409			−0.578726
$173$			0.130787i			0.000755997i	1.00000		0.000377998i	$0.000120321\pi$
$173$			0.130787i			0.000755997i	−1.00000		0.000377998i	$0.999880\pi$
$174$			39.1551i			0.225029i
$175$		0			0
$176$	−39.7159			−0.225659
$177$	110.316			0.623255
$178$			220.735i			1.24008i
$179$	143.431			0.801293			0.400646	−	0.916233i	$-0.368786\pi$
$179$	143.431			0.801293			0.400646	+	0.916233i	$0.368786\pi$
$180$		0			0
$181$		−	264.455i		−	1.46108i	−0.682871	−	0.730539i	$-0.739269\pi$
$181$		−	264.455i		−	1.46108i	0.682871	−	0.730539i	$-0.260731\pi$
$182$	−30.6865	−	198.231i	−0.168607	−	1.08918i
$183$	154.643			0.845042
$184$	−72.0507			−0.391580
$185$		0			0
$186$	−51.3166			−0.275896
$187$			188.060i			1.00567i
$188$			5.83099i			0.0310159i
$189$	−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	$0.305946\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	−162.709			−0.843052			−0.421526	−	0.906816i	$-0.638505\pi$
$193$	−162.709			−0.843052			−0.421526	+	0.906816i	$0.638505\pi$
$194$			218.775i			1.12771i
$195$		0			0
$196$	93.4131	−	29.6311i	0.476597	−	0.151179i
$197$	175.537			0.891052			0.445526	−	0.895269i	$-0.353017\pi$
$197$	175.537			0.891052			0.445526	+	0.895269i	$0.353017\pi$
$198$	−42.1251			−0.212753
$199$		−	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
$202$		−	188.880i		−	0.935048i
$203$	−110.578	+	17.1177i	−0.544719	+	0.0843235i
$204$	−65.6118			−0.321627
$205$		0			0
$206$		−	115.674i		−	0.561527i
$207$	−76.4213			−0.369185
$208$		−	81.0515i		−	0.389671i
$209$			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	$0.403461\pi$
$212$	−22.3842			−0.105586
$213$			88.3171i			0.414634i
$214$	−226.401			−1.05795
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−22.4344	−	144.923i	−0.103384	−	0.667849i
$218$	259.672			1.19116
$219$	136.669			0.624059
$220$		0			0
$221$	−383.789			−1.73660
$222$		−	73.9368i		−	0.333049i
$223$		−	62.6219i		−	0.280816i	−0.990094	−	0.140408i	$-0.955159\pi$
$223$		−	62.6219i		−	0.280816i	0.990094	−	0.140408i	$-0.0448414\pi$
$224$	39.1319	−	6.05768i	0.174696	−	0.0270432i
$225$		0			0
$226$	20.7848			0.0919683
$227$			220.557i			0.971619i	0.874065	+	0.485809i	$0.161475\pi$
$227$			220.557i			0.971619i	−0.874065	+	0.485809i	$0.838525\pi$
$228$	−16.2418			−0.0712360
$229$		−	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
$232$	−45.2124			−0.194881
$233$	−167.313			−0.718082			−0.359041	−	0.933322i	$-0.616896\pi$
$233$	−167.313			−0.718082			−0.359041	+	0.933322i	$0.616896\pi$
$234$		−	85.9681i		−	0.367385i
$235$		0			0
$236$			127.382i			0.539754i
$237$			121.013i			0.510602i
$238$	−28.6839	−	185.294i	−0.120521	−	0.778548i
$239$	−14.5321			−0.0608036			−0.0304018	−	0.999538i	$-0.509679\pi$
$239$	−14.5321			−0.0608036			−0.0304018	+	0.999538i	$0.509679\pi$
$240$		0			0
$241$			337.752i			1.40146i	0.713427	+	0.700730i	$0.247142\pi$
$241$			337.752i			1.40146i	−0.713427	+	0.700730i	$0.752858\pi$
$242$	31.6999			0.130991
$243$		−	15.5885i		−	0.0641500i
$244$			178.566i			0.731827i
$245$		0			0
$246$	−103.588			−0.421090
$247$	−95.0047			−0.384635
$248$		−	59.2553i		−	0.238933i
$249$	119.317			0.479184
$250$		0			0
$251$		−	391.239i		−	1.55872i	−0.626576	−	0.779360i	$-0.715544\pi$
$251$		−	391.239i		−	1.55872i	0.626576	−	0.779360i	$-0.284456\pi$
$252$	41.5056	−	6.42514i	0.164705	−	0.0254966i
$253$	−252.929			−0.999718
$254$	273.601			1.07717
$255$		0			0
$256$	16.0000			0.0625000
$257$			275.467i			1.07186i	0.844264	+	0.535928i	$0.180038\pi$
$257$			275.467i			1.07186i	−0.844264	+	0.535928i	$0.819962\pi$
$258$		−	121.912i		−	0.472528i
$259$	208.805	−	32.3234i	0.806197	−	0.124801i
$260$		0			0
$261$	−47.9550			−0.183736
$262$		−	139.776i		−	0.533498i
$263$	352.033			1.33853			0.669264	−	0.743025i	$-0.266610\pi$
$263$	352.033			1.33853			0.669264	+	0.743025i	$0.266610\pi$
$264$		−	48.6419i		−	0.184250i
$265$		0			0
$266$	−7.10053	−	45.8685i	−0.0266937	−	0.172438i
$267$	−270.344			−1.01252
$268$	−27.1847			−0.101435
$269$		−	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	$0.0332559\pi$
$271$			56.5234i			0.208573i	−0.994547	+	0.104287i	$0.966744\pi$
$272$		−	75.7620i		−	0.278537i
$273$	242.783	−	37.5832i	0.889314	−	0.137667i
$274$	57.0971			0.208384
$275$		0			0
$276$		−	88.2437i		−	0.319723i
$277$	−158.702			−0.572931			−0.286466	−	0.958091i	$-0.592480\pi$
$277$	−158.702			−0.572931			−0.286466	+	0.958091i	$0.592480\pi$
$278$		−	49.9960i		−	0.179842i
$279$		−	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	$0.528490\pi$
$282$	−7.14147			−0.0253244
$283$		−	104.925i		−	0.370760i	−0.982667	−	0.185380i	$-0.940648\pi$
$283$		−	104.925i		−	0.370760i	0.982667	−	0.185380i	$-0.0593516\pi$
$284$	−101.980			−0.359084
$285$		0			0
$286$		−	284.525i		−	0.994844i
$287$	−45.2862	−	292.543i	−0.157792	−	1.01931i
$288$	16.9706			0.0589256
$289$	−69.7425			−0.241323
$290$		0			0
$291$	−267.944			−0.920770
$292$			157.812i			0.540451i
$293$		−	506.046i		−	1.72712i	−0.504247	−	0.863560i	$-0.668230\pi$
$293$		−	506.046i		−	1.72712i	0.504247	−	0.863560i	$-0.331770\pi$
$294$	36.2905	+	114.407i	0.123437	+	0.389140i
$295$		0			0
$296$	85.3749			0.288429
$297$		−	51.5925i		−	0.173712i
$298$	−387.736			−1.30113
$299$		−	516.172i		−	1.72633i
$300$		0			0
$301$	344.292	−	53.2971i	1.14383	−	0.177067i
$302$	−227.046			−0.751807
$303$	231.329			0.763463
$304$		−	18.7544i		−	0.0616922i
$305$		0			0
$306$		−	80.3577i		−	0.262607i
$307$			221.769i			0.722376i	0.932493	+	0.361188i	$0.117629\pi$
$307$			221.769i			0.722376i	−0.932493	+	0.361188i	$0.882371\pi$
$308$	137.370	−	21.2651i	0.446005	−	0.0690424i
$309$	141.672			0.458485
$310$		0			0
$311$		−	80.8561i		−	0.259988i	−0.991515	−	0.129994i	$-0.958504\pi$
$311$		−	80.8561i		−	0.259988i	0.991515	−	0.129994i	$-0.0414957\pi$
$312$	99.2675			0.318165
$313$		−	340.104i		−	1.08659i	−0.839541	−	0.543297i	$-0.817176\pi$
$313$		−	340.104i		−	1.08659i	0.839541	−	0.543297i	$-0.182824\pi$
$314$		−	376.508i		−	1.19907i
$315$		0			0
$316$	−139.733			−0.442194
$317$	−304.527			−0.960654			−0.480327	−	0.877090i	$-0.659482\pi$
$317$	−304.527			−0.960654			−0.480327	+	0.877090i	$0.659482\pi$
$318$		−	27.4149i		−	0.0862103i
$319$	−158.715			−0.497539
$320$		0			0
$321$		−	277.284i		−	0.863813i
$322$	249.209	−	38.5780i	0.773941	−	0.119807i
$323$	−88.8046			−0.274937
$324$	18.0000			0.0555556
$325$		0			0
$326$	265.021			0.812949
$327$			318.032i			0.972576i
$328$		−	119.613i		−	0.364674i
$329$	−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	$0.337661\pi$
$332$			137.775i			0.414985i
$333$	90.5538			0.271933
$334$		−	371.849i		−	1.11332i
$335$		0			0
$336$	7.41912	+	47.9266i	0.0220807	+	0.142639i
$337$	333.282			0.988966			0.494483	−	0.869187i	$-0.335357\pi$
$337$	333.282			0.988966			0.494483	+	0.869187i	$0.335357\pi$
$338$	341.652			1.01080
$339$			25.4561i			0.0750918i
$340$		0			0
$341$		−	208.011i		−	0.610004i
$342$		−	19.8921i		−	0.0581640i
$343$	−307.232	+	152.504i	−0.895720	+	0.444618i
$344$	140.772			0.409221
$345$		0			0
$346$		−	0.184961i		−	0.000534571i
$347$	257.512			0.742110			0.371055	−	0.928611i	$-0.378996\pi$
$347$	257.512			0.742110			0.371055	+	0.928611i	$0.378996\pi$
$348$		−	55.3737i		−	0.159120i
$349$		−	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
$352$	56.1668			0.159565
$353$		−	248.442i		−	0.703802i	−0.936037	−	0.351901i	$-0.885535\pi$
$353$		−	248.442i		−	0.703802i	0.936037	−	0.351901i	$-0.114465\pi$
$354$	−156.010			−0.440708
$355$		0			0
$356$		−	312.166i		−	0.876871i
$357$	226.938	−	35.1304i	0.635682	−	0.0984046i
$358$	−202.843			−0.566600
$359$	−348.412			−0.970507			−0.485253	−	0.874374i	$-0.661273\pi$
$359$	−348.412			−0.970507			−0.485253	+	0.874374i	$0.661273\pi$
$360$		0			0
$361$	339.017			0.939105
$362$			373.996i			1.03314i
$363$			38.8243i			0.106954i
$364$	43.3973	+	280.341i	0.119223	+	0.770168i
$365$		0			0
$366$	−218.698			−0.597535
$367$			73.9213i			0.201420i	0.994916	+	0.100710i	$0.0321115\pi$
$367$			73.9213i			0.201420i	−0.994916	+	0.100710i	$0.967888\pi$
$368$	101.895			0.276889
$369$		−	126.869i		−	0.343818i
$370$		0			0
$371$	77.4224	−	11.9851i	0.208686	−	0.0323049i
$372$	72.5726			0.195088
$373$	−52.9503			−0.141958			−0.0709789	−	0.997478i	$-0.522612\pi$
$373$	−52.9503			−0.141958			−0.0709789	+	0.997478i	$0.522612\pi$
$374$		−	265.957i		−	0.711115i
$375$		0			0
$376$		−	8.24626i		−	0.0219315i
$377$		−	323.902i		−	0.859157i
$378$	7.86916	+	50.8338i	0.0208179	+	0.134481i
$379$	112.721			0.297417			0.148709	−	0.988881i	$-0.452488\pi$
$379$	112.721			0.297417			0.148709	+	0.988881i	$0.452488\pi$
$380$		0			0
$381$			335.091i			0.879504i
$382$	−309.320			−0.809737
$383$			524.061i			1.36830i	0.729339	+	0.684152i	$0.239828\pi$
$383$			524.061i			1.36830i	−0.729339	+	0.684152i	$0.760172\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	230.105			0.596128
$387$	149.311			0.385817
$388$		−	309.395i		−	0.797410i
$389$	−114.232			−0.293655			−0.146827	−	0.989162i	$-0.546906\pi$
$389$	−114.232			−0.293655			−0.146827	+	0.989162i	$0.546906\pi$
$390$		0			0
$391$		−	482.486i		−	1.23398i
$392$	−132.106	+	41.9047i	−0.337005	+	0.106900i
$393$	171.190			0.435599
$394$	−248.247			−0.630069
$395$		0			0
$396$	59.5739			0.150439
$397$			657.463i			1.65608i	0.560670	+	0.828039i	$0.310544\pi$
$397$			657.463i			1.65608i	−0.560670	+	0.828039i	$0.689456\pi$
$398$			86.9569i			0.218485i
$399$	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	$0.777747\pi$
$402$		−	33.2943i		−	0.0828216i
$403$	424.506			1.05336
$404$			267.116i			0.661179i
$405$		0			0
$406$	156.381	−	24.2080i	0.385175	−	0.0596257i
$407$	299.702			0.736369
$408$	92.7891			0.227424
$409$			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
$412$			163.588i			0.397059i
$413$	−68.2040	−	440.589i	−0.165143	−	1.06680i
$414$	108.076			0.261053
$415$		0			0
$416$			114.624i			0.275539i
$417$	61.2323			0.146840
$418$		−	65.8361i		−	0.157503i
$419$			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	$0.344755\pi$
$422$	−178.238			−0.422365
$423$		−	8.74648i		−	0.0206773i
$424$	31.6560			0.0746603
$425$		0			0
$426$		−	124.899i		−	0.293191i
$427$	−95.6093	−	617.624i	−0.223909	−	1.44643i
$428$	320.180			0.748084
$429$	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	$0.793938\pi$
$432$			20.7846i			0.0481125i
$433$		−	738.775i		−	1.70618i	−0.521766	−	0.853089i	$-0.674727\pi$
$433$		−	738.775i		−	1.70618i	0.521766	−	0.853089i	$-0.325273\pi$
$434$	31.7270	+	204.952i	0.0731037	+	0.472241i
$435$		0			0
$436$	−367.232			−0.842276
$437$		−	119.436i		−	0.273310i
$438$	−193.279			−0.441277
$439$		−	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
$442$	542.760			1.22796
$443$	−246.877			−0.557285			−0.278642	−	0.960395i	$-0.589884\pi$
$443$	−246.877			−0.557285			−0.278642	+	0.960395i	$0.589884\pi$
$444$			104.562i			0.235501i
$445$		0			0
$446$			88.5608i			0.198567i
$447$		−	474.877i		−	1.06237i
$448$	−55.3408	+	8.56686i	−0.123529	+	0.0191225i
$449$	−472.482			−1.05230			−0.526150	−	0.850392i	$-0.676365\pi$
$449$	−472.482			−1.05230			−0.526150	+	0.850392i	$0.676365\pi$
$450$		0			0
$451$		−	419.893i		−	0.931027i
$452$	−29.3942			−0.0650314
$453$		−	278.073i		−	0.613848i
$454$		−	311.915i		−	0.687038i
$455$		0			0
$456$	22.9694			0.0503715
$457$	−601.310			−1.31578			−0.657889	−	0.753115i	$-0.728550\pi$
$457$	−601.310			−1.31578			−0.657889	+	0.753115i	$0.728550\pi$
$458$			292.455i			0.638548i
$459$	98.4177			0.214418
$460$		0			0
$461$		−	270.297i		−	0.586328i	−0.956062	−	0.293164i	$-0.905292\pi$
$461$		−	270.297i		−	0.586328i	0.956062	−	0.293164i	$-0.0947081\pi$
$462$	26.0443	+	168.243i	0.0563729	+	0.364162i
$463$	−579.731			−1.25212			−0.626060	−	0.779775i	$-0.715333\pi$
$463$	−579.731			−1.25212			−0.626060	+	0.779775i	$0.715333\pi$
$464$	63.9400			0.137802
$465$		0			0
$466$	236.616			0.507761
$467$			895.295i			1.91712i	0.284891	+	0.958560i	$0.408043\pi$
$467$			895.295i			1.91712i	−0.284891	+	0.958560i	$0.591957\pi$
$468$			121.577i			0.259781i
$469$	94.0264	−	14.5555i	0.200483	−	0.0310351i
$470$		0			0
$471$	461.127			0.979037
$472$		−	180.145i		−	0.381664i
$473$	494.170			1.04476
$474$		−	171.138i		−	0.361050i
$475$		0			0
$476$	40.5651	+	262.046i	0.0852209	+	0.550516i
$477$	33.5762			0.0703904
$478$	20.5515			0.0429947
$479$			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
$482$		−	477.653i		−	0.990981i
$483$	47.2482	+	305.217i	0.0978224	+	0.631920i
$484$	−44.8305			−0.0926249
$485$		0			0
$486$			22.0454i			0.0453609i
$487$	−421.873			−0.866269			−0.433135	−	0.901329i	$-0.642593\pi$
$487$	−421.873			−0.866269			−0.433135	+	0.901329i	$0.642593\pi$
$488$		−	252.530i		−	0.517480i
$489$			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	$0.576078\pi$
$492$	146.496			0.297755
$493$		−	302.764i		−	0.614126i
$494$	134.357			0.271978
$495$		0			0
$496$			83.7997i			0.168951i
$497$	352.728	−	54.6029i	0.709714	−	0.109865i
$498$	−168.739			−0.338834
$499$	−528.736			−1.05959			−0.529796	−	0.848125i	$-0.677731\pi$
$499$	−528.736			−1.05959			−0.529796	+	0.848125i	$0.677731\pi$
$500$		0			0
$501$	455.421			0.909023
$502$			553.295i			1.10218i
$503$		−	865.962i		−	1.72160i	−0.508948	−	0.860798i	$-0.669965\pi$
$503$		−	865.962i		−	1.72160i	0.508948	−	0.860798i	$-0.330035\pi$
$504$	−58.6978	+	9.08653i	−0.116464	+	0.0180288i
$505$		0			0
$506$	357.695			0.706907
$507$			418.437i			0.825319i
$508$	−386.930			−0.761673
$509$		−	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
$512$	−22.6274			−0.0441942
$513$	24.3627			0.0474907
$514$		−	389.569i		−	0.757917i
$515$		0			0
$516$			172.410i			0.334128i
$517$		−	28.9479i		−	0.0559921i
$518$	−295.295	+	45.7122i	−0.570068	+	0.0882475i
$519$	0.226531			0.000436475
$520$		0			0
$521$			428.487i			0.822432i	0.911538	+	0.411216i	$0.134896\pi$
$521$			428.487i			0.822432i	−0.911538	+	0.411216i	$0.865104\pi$
$522$	67.8186			0.129921
$523$			1029.66i			1.96876i	0.176060	+	0.984379i	$0.443665\pi$
$523$			1029.66i			1.96876i	−0.176060	+	0.984379i	$0.556335\pi$
$524$			197.674i			0.377240i
$525$		0			0
$526$	−497.850			−0.946482
$527$	396.802			0.752945
$528$			68.7900i			0.130284i
$529$	119.912			0.226677
$530$		0			0
$531$		−	191.073i		−	0.359836i
$532$	10.0417	+	64.8679i	0.0188753	+	0.121932i
$533$	856.910			1.60771
$534$	382.324			0.715962
$535$		0			0
$536$	38.4449			0.0717256
$537$		−	248.431i		−	0.462627i
$538$			128.103i			0.238111i
$539$	−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	$0.664243\pi$
$542$		−	79.9361i		−	0.147484i
$543$	−458.050			−0.843554
$544$			107.144i			0.196955i
$545$		0			0
$546$	−343.347	+	53.1506i	−0.628840	+	0.0973455i
$547$	−349.653			−0.639220			−0.319610	−	0.947549i	$-0.603552\pi$
$547$	−349.653			−0.639220			−0.319610	+	0.947549i	$0.603552\pi$
$548$	−80.7476			−0.147350
$549$		−	267.849i		−	0.487885i
$550$		0			0
$551$		−	74.9474i		−	0.136021i
$552$			124.795i			0.226079i
$553$	483.310	−	74.8172i	0.873978	−	0.135293i
$554$	224.438			0.405124
$555$		0			0
$556$			70.7050i			0.127167i
$557$	193.971			0.348243			0.174122	−	0.984724i	$-0.444291\pi$
$557$	193.971			0.348243			0.174122	+	0.984724i	$0.444291\pi$
$558$			88.8830i			0.159288i
$559$			1008.49i			1.80410i
$560$		0			0
$561$	325.729			0.580623
$562$	71.0421			0.126410
$563$			388.914i			0.690788i	0.938458	+	0.345394i	$0.112255\pi$
$563$			388.914i			0.690788i	−0.938458	+	0.345394i	$0.887745\pi$
$564$	10.0996			0.0179070
$565$		0			0
$566$			148.386i			0.262167i
$567$	−62.2584	+	9.63772i	−0.109803	+	0.0169977i
$568$	144.221			0.253911
$569$	−470.383			−0.826683			−0.413342	−	0.910576i	$-0.635638\pi$
$569$	−470.383			−0.826683			−0.413342	+	0.910576i	$0.635638\pi$
$570$		0			0
$571$	887.703			1.55465			0.777323	−	0.629101i	$-0.216577\pi$
$571$	887.703			1.55465			0.777323	+	0.629101i	$0.216577\pi$
$572$			402.380i			0.703461i
$573$		−	378.838i		−	0.661148i
$574$	64.0443	+	413.718i	0.111575	+	0.720764i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$		−	927.661i		−	1.60773i	−0.594811	−	0.803866i	$-0.702773\pi$
$577$		−	927.661i		−	1.60773i	0.594811	−	0.803866i	$-0.297227\pi$
$578$	98.6307			0.170641
$579$			281.820i			0.486736i
$580$		0			0
$581$	−73.7688	−	476.537i	−0.126969	−	0.820201i
$582$	378.930			0.651083
$583$	111.126			0.190611
$584$		−	223.180i		−	0.382157i
$585$		0			0
$586$			715.657i			1.22126i
$587$		−	504.818i		−	0.859996i	−0.902830	−	0.429998i	$-0.858514\pi$
$587$		−	504.818i		−	0.859996i	0.902830	−	0.429998i	$-0.141486\pi$
$588$	−51.3225	−	161.796i	−0.0872832	−	0.275164i
$589$	98.2260			0.166767
$590$		0			0
$591$		−	304.039i		−	0.514449i
$592$	−120.738			−0.203950
$593$			931.909i			1.57152i	0.618534	+	0.785758i	$0.287727\pi$
$593$			931.909i			1.57152i	−0.618534	+	0.785758i	$0.712273\pi$
$594$			72.9629i			0.122833i
$595$		0			0
$596$	548.341			0.920035
$597$	−106.500			−0.178392
$598$			729.977i			1.22070i
$599$	841.411			1.40469			0.702347	−	0.711835i	$-0.252136\pi$
$599$	841.411			1.40469			0.702347	+	0.711835i	$0.252136\pi$
$600$		0			0
$601$			116.550i			0.193926i	0.995288	+	0.0969632i	$0.0309129\pi$
$601$			116.550i			0.193926i	−0.995288	+	0.0969632i	$0.969087\pi$
$602$	−486.903	+	75.3734i	−0.808809	+	0.125205i
$603$	40.7770			0.0676236
$604$	321.091			0.531608
$605$		0			0
$606$	−327.149			−0.539850
$607$		−	6.57481i		−	0.0108316i	−0.999985	−	0.00541582i	$-0.998276\pi$
$607$		−	6.57481i		−	0.0108316i	0.999985	−	0.00541582i	$-0.00172392\pi$
$608$			26.5228i			0.0436230i
$609$	29.6487	+	191.527i	0.0486842	+	0.314494i
$610$		0			0
$611$	59.0763			0.0966879
$612$			113.643i			0.185691i
$613$	−51.9420			−0.0847340			−0.0423670	−	0.999102i	$-0.513490\pi$
$613$	−51.9420			−0.0847340			−0.0423670	+	0.999102i	$0.513490\pi$
$614$		−	313.629i		−	0.510797i
$615$		0			0
$616$	−194.270	+	30.0733i	−0.315373	+	0.0488203i
$617$	−1064.09			−1.72462			−0.862309	−	0.506383i	$-0.830982\pi$
$617$	−1064.09			−1.72462			−0.862309	+	0.506383i	$0.830982\pi$
$618$	−200.354			−0.324198
$619$			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
$622$			114.348i			0.183839i
$623$	167.143	+	1079.72i	0.268287	+	1.73310i
$624$	−140.385			−0.224977
$625$		0			0
$626$			480.980i			0.768338i
$627$	80.6324			0.128600
$628$			532.463i			0.847871i
$629$			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	$0.727795\pi$
$632$	197.613			0.312678
$633$		−	218.296i		−	0.344859i
$634$	430.667			0.679285
$635$		0			0
$636$			38.7705i			0.0609599i
$637$	−300.206	−	946.409i	−0.471280	−	1.48573i
$638$	224.457			0.351813
$639$	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	$0.716725\pi$
$642$			392.139i			0.610808i
$643$			588.657i			0.915485i	0.889085	+	0.457743i	$0.151342\pi$
$643$			588.657i			0.915485i	−0.889085	+	0.457743i	$0.848658\pi$
$644$	−352.435	+	54.5575i	−0.547259	+	0.0847167i
$645$		0			0
$646$	125.589			0.194410
$647$			51.4386i			0.0795032i	0.999210	+	0.0397516i	$0.0126567\pi$
$647$			51.4386i			0.0795032i	−0.999210	+	0.0397516i	$0.987343\pi$
$648$	−25.4558			−0.0392837
$649$		−	632.387i		−	0.974403i
$650$		0			0
$651$	−251.014	+	38.8575i	−0.385583	+	0.0596889i
$652$	−374.797			−0.574842
$653$	−843.699			−1.29204			−0.646018	−	0.763322i	$-0.723567\pi$
$653$	−843.699			−1.29204			−0.646018	+	0.763322i	$0.723567\pi$
$654$		−	449.766i		−	0.687715i
$655$		0			0
$656$			169.159i			0.257864i
$657$		−	236.718i		−	0.360301i
$658$	4.41529	+	28.5222i	0.00671016	+	0.0433468i
$659$	−203.437			−0.308705			−0.154352	−	0.988016i	$-0.549329\pi$
$659$	−203.437			−0.308705			−0.154352	+	0.988016i	$0.549329\pi$
$660$		0			0
$661$			1141.47i			1.72688i	0.504454	+	0.863439i	$0.331694\pi$
$661$			1141.47i			1.72688i	−0.504454	+	0.863439i	$0.668306\pi$
$662$	−457.039			−0.690391
$663$			664.742i			1.00263i
$664$		−	194.843i		−	0.293439i
$665$		0			0
$666$	−128.062			−0.192286
$667$	407.198			0.610492
$668$			525.874i			0.787237i
$669$	−108.464			−0.162129
$670$		0			0
$671$		−	886.489i		−	1.32115i
$672$	−10.4922	−	67.7784i	−0.0156134	−	0.100861i
$673$	−1259.69			−1.87175			−0.935877	−	0.352327i	$-0.885391\pi$
$673$	−1259.69			−1.87175			−0.935877	+	0.352327i	$0.885391\pi$
$674$	−471.331			−0.699305
$675$		0			0
$676$	−483.169			−0.714747
$677$		−	563.250i		−	0.831979i	−0.909369	−	0.415989i	$-0.863435\pi$
$677$		−	563.250i		−	0.831979i	0.909369	−	0.415989i	$-0.136565\pi$
$678$		−	36.0004i		−	0.0530979i
$679$	165.659	+	1070.14i	0.243975	+	1.57605i
$680$		0			0
$681$	382.017			0.560964
$682$			294.173i			0.431338i
$683$	−881.725			−1.29096			−0.645480	−	0.763778i	$-0.723342\pi$
$683$	−881.725			−1.29096			−0.645480	+	0.763778i	$0.723342\pi$
$684$			28.1317i			0.0411281i
$685$		0			0
$686$	434.492	−	215.673i	0.633370	−	0.314393i
$687$	−358.183			−0.521372
$688$	−199.082			−0.289363
$689$			226.784i			0.329149i
$690$		0			0
$691$		−	33.6567i		−	0.0487072i	−0.999703	−	0.0243536i	$-0.992247\pi$
$691$		−	33.6567i		−	0.0487072i	0.999703	−	0.0243536i	$-0.00775276\pi$
$692$			0.261575i			0.000377998i
$693$	−206.054	+	31.8976i	−0.297337	+	0.0460283i
$694$	−364.177			−0.524751
$695$		0			0
$696$			78.3102i			0.112515i
$697$	800.987			1.14919
$698$			434.134i			0.621968i
$699$			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	$0.471955\pi$
$702$	−148.901			−0.212110
$703$			141.524i			0.201314i
$704$	−79.4319			−0.112829
$705$		0			0
$706$			351.350i			0.497663i
$707$	−143.022	−	923.902i	−0.202294	−	1.30679i
$708$	220.632			0.311627
$709$	1271.96			1.79401			0.897007	−	0.442016i	$-0.145736\pi$
$709$	1271.96			1.79401			0.897007	+	0.442016i	$0.145736\pi$
$710$		0			0
$711$	209.600			0.294796
$712$			441.469i			0.620041i
$713$			533.673i			0.748489i
$714$	−320.939	+	49.6820i	−0.449495	+	0.0695826i
$715$		0			0
$716$	286.863			0.400646
$717$			25.1703i			0.0351050i
$718$	492.729			0.686252
$719$			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
$722$	−479.442			−0.664048
$723$	585.003			0.809133
$724$		−	528.910i		−	0.730539i
$725$		0			0
$726$		−	54.9059i		−	0.0756279i
$727$		−	1033.97i		−	1.42224i	−0.703071	−	0.711119i	$-0.748189\pi$
$727$		−	1033.97i		−	1.42224i	0.703071	−	0.711119i	$-0.251811\pi$
$728$	−61.3731	−	396.462i	−0.0843037	−	0.544591i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			942.677i			1.28957i
$732$	309.285			0.422521
$733$			199.138i			0.271676i	0.990731	+	0.135838i	$0.0433726\pi$
$733$			199.138i			0.271676i	−0.990731	+	0.135838i	$0.956627\pi$
$734$		−	104.541i		−	0.142426i
$735$		0			0
$736$	−144.101			−0.195790
$737$	134.958			0.183118
$738$			179.420i			0.243116i
$739$	−102.937			−0.139292			−0.0696460	−	0.997572i	$-0.522187\pi$
$739$	−102.937			−0.139292			−0.0696460	+	0.997572i	$0.522187\pi$
$740$		0			0
$741$			164.553i			0.222069i
$742$	−109.492	+	16.9495i	−0.147563	+	0.0228430i
$743$	−366.082			−0.492707			−0.246354	−	0.969180i	$-0.579232\pi$
$743$	−366.082			−0.492707			−0.246354	+	0.969180i	$0.579232\pi$
$744$	−102.633			−0.137948
$745$		0			0
$746$	74.8830			0.100379
$747$		−	206.663i		−	0.276657i
$748$			376.120i			0.502834i
$749$	−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	$0.549091\pi$
$752$			11.6620i			0.0155079i
$753$	−677.646			−0.899928
$754$			458.067i			0.607516i
$755$		0			0
$756$	−11.1287	−	71.8899i	−0.0147205	−	0.0950924i
$757$	1340.08			1.77026			0.885128	−	0.465348i	$-0.154071\pi$
$757$	1340.08			1.77026			0.885128	+	0.465348i	$0.154071\pi$
$758$	−159.412			−0.210306
$759$			438.085i			0.577187i
$760$		0			0
$761$			1256.80i			1.65151i	0.564027	+	0.825756i	$0.309251\pi$
$761$			1256.80i			1.65151i	−0.564027	+	0.825756i	$0.690749\pi$
$762$		−	473.890i		−	0.621903i
$763$	1270.18	−	196.627i	1.66472	−	0.257702i
$764$	437.444			0.572571
$765$		0			0
$766$		−	741.134i		−	0.967537i
$767$	1290.56			1.68261
$768$		−	27.7128i		−	0.0360844i
$769$		−	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
$772$	−325.418			−0.421526
$773$		−	746.551i		−	0.965783i	−0.875680	−	0.482892i	$-0.839586\pi$
$773$		−	746.551i		−	0.965783i	0.875680	−	0.482892i	$-0.160414\pi$
$774$	−211.158			−0.272814
$775$		0			0
$776$			437.551i			0.563854i
$777$	−55.9858	−	361.661i	−0.0720537	−	0.465458i
$778$	161.548			0.207645
$779$	198.280			0.254531
$780$		0			0
$781$	506.278			0.648243
$782$			682.338i			0.872555i
$783$			83.0605i			0.106080i
$784$	186.826	−	59.2622i	0.238299	−	0.0755895i
$785$		0			0
$786$	−242.100			−0.308015
$787$			1121.67i			1.42524i	0.701548	+	0.712622i	$0.252493\pi$
$787$			1121.67i			1.42524i	−0.701548	+	0.712622i	$0.747507\pi$
$788$	351.074			0.445526
$789$		−	609.739i		−	0.772799i
$790$		0			0
$791$	101.669	−	15.7385i	0.128532	−	0.0198970i
$792$	−84.2502			−0.106377
$793$	1809.13			2.28137
$794$		−	929.793i		−	1.17102i
$795$		0			0
$796$		−	122.976i		−	0.154492i
$797$		−	1458.38i		−	1.82983i	−0.403644	−	0.914916i	$-0.632257\pi$
$797$		−	1458.38i		−	1.82983i	0.403644	−	0.914916i	$-0.367743\pi$
$798$	−79.4466	+	12.2985i	−0.0995572	+	0.0154116i
$799$	55.2209			0.0691125
$800$		0			0
$801$			468.249i			0.584580i
$802$	868.775			1.08326
$803$		−	783.455i		−	0.975661i
$804$			47.0852i			0.0585637i
$805$		0			0
$806$	−600.342			−0.744841
$807$	−156.894			−0.194416
$808$		−	377.759i		−	0.467524i
$809$	−384.044			−0.474714			−0.237357	−	0.971422i	$-0.576281\pi$
$809$	−384.044			−0.474714			−0.237357	+	0.971422i	$0.576281\pi$
$810$		0			0
$811$			723.519i			0.892132i	0.895000	+	0.446066i	$0.147175\pi$
$811$			723.519i			0.892132i	−0.895000	+	0.446066i	$0.852825\pi$
$812$	−221.156	+	34.2353i	−0.272360	+	0.0421617i
$813$	97.9013			0.120420
$814$	−423.843			−0.520692
$815$		0			0
$816$	−131.224			−0.160813
$817$			233.354i			0.285623i
$818$		−	276.645i		−	0.338196i
$819$	−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	$0.485046\pi$
$822$		−	98.8952i		−	0.120310i
$823$	−234.896			−0.285414			−0.142707	−	0.989765i	$-0.545581\pi$
$823$	−234.896			−0.285414			−0.142707	+	0.989765i	$0.545581\pi$
$824$		−	231.349i		−	0.280763i
$825$		0			0
$826$	96.4550	+	623.087i	0.116774	+	0.754343i
$827$	−173.944			−0.210331			−0.105166	−	0.994455i	$-0.533537\pi$
$827$	−173.944			−0.210331			−0.105166	+	0.994455i	$0.533537\pi$
$828$	−152.843			−0.184592
$829$			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
$832$		−	162.103i		−	0.194835i
$833$	−280.614	−	884.645i	−0.336871	−	1.06200i
$834$	−86.5955			−0.103832
$835$		0			0
$836$			93.1063i			0.111371i
$837$	−108.859			−0.130058
$838$		−	453.377i		−	0.541022i
$839$			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
$842$	−558.004			−0.662713
$843$			87.0085i			0.103213i
$844$	252.067			0.298657
$845$		0			0
$846$			12.3694i			0.0146210i
$847$	155.060	−	24.0035i	0.183069	−	0.0283395i
$848$	−44.7683			−0.0527928
$849$	−181.735			−0.214058
$850$		0			0
$851$	−768.915			−0.903543
$852$			176.634i			0.207317i
$853$		−	225.297i		−	0.264124i	−0.991241	−	0.132062i	$-0.957840\pi$
$853$		−	225.297i		−	0.264124i	0.991241	−	0.132062i	$-0.0421597\pi$
$854$	135.212	+	873.453i	0.158328	+	1.02278i
$855$		0			0
$856$	−452.803			−0.528975
$857$			899.165i			1.04920i	0.851349	+	0.524600i	$0.175785\pi$
$857$			899.165i			1.04920i	−0.851349	+	0.524600i	$0.824215\pi$
$858$	−492.813			−0.574374
$859$		−	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
$862$	972.410			1.12809
$863$	−694.379			−0.804610			−0.402305	−	0.915506i	$-0.631791\pi$
$863$	−694.379			−0.804610			−0.402305	+	0.915506i	$0.631791\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$			1044.79i			1.20645i
$867$			120.797i			0.139328i
$868$	−44.8687	−	289.846i	−0.0516921	−	0.333925i
$869$	693.705			0.798280
$870$		0			0
$871$			275.420i			0.316211i
$872$	519.345			0.595579
$873$			464.093i			0.531607i
$874$			168.909i			0.193259i
$875$		0			0
$876$	273.338			0.312030
$877$	699.811			0.797960			0.398980	−	0.916960i	$-0.369364\pi$
$877$	699.811			0.797960			0.398980	+	0.916960i	$0.369364\pi$
$878$			457.642i			0.521232i
$879$	−876.497			−0.997153
$880$		0			0
$881$			1112.73i			1.26303i	0.775362	+	0.631517i	$0.217567\pi$
$881$			1112.73i			1.26303i	−0.775362	+	0.631517i	$0.782433\pi$
$882$	198.159	−	62.8570i	0.224670	−	0.0712664i
$883$	522.489			0.591720			0.295860	−	0.955231i	$-0.404394\pi$
$883$	522.489			0.591720			0.295860	+	0.955231i	$0.404394\pi$
$884$	−767.578			−0.868301
$885$		0			0
$886$	349.137			0.394060
$887$		−	149.877i		−	0.168971i	−0.996425	−	0.0844853i	$-0.973075\pi$
$887$		−	149.877i		−	0.168971i	0.996425	−	0.0844853i	$-0.0269246\pi$
$888$		−	147.874i		−	0.166524i
$889$	1338.31	−	207.173i	1.50541	−	0.233041i
$890$		0			0
$891$	−89.3609			−0.100293
$892$		−	125.244i		−	0.140408i
$893$	13.6696			0.0153075
$894$			671.578i			0.751206i
$895$		0			0
$896$	78.2638	−	12.1154i	0.0873480	−	0.0135216i
$897$	−894.036			−0.996695
$898$	668.191			0.744088
$899$			334.885i			0.372508i
$900$		0			0
$901$			211.983i			0.235276i
$902$			593.819i			0.658336i
$903$	−92.3132	−	596.332i	−0.102229	−	0.660390i
$904$	41.5697			0.0459841
$905$		0			0
$906$			393.254i			0.434056i
$907$	−1544.51			−1.70288			−0.851440	−	0.524452i	$-0.824270\pi$
$907$	−1544.51			−1.70288			−0.851440	+	0.524452i	$0.824270\pi$
$908$			441.115i			0.485809i
$909$		−	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	$0.240856\pi$
$912$	−32.4836			−0.0356180
$913$		−	683.984i		−	0.749161i
$914$	850.381			0.930395
$915$		0			0
$916$		−	413.594i		−	0.451521i
$917$	−105.840	−	683.714i	−0.115420	−	0.745599i
$918$	−139.184			−0.151616
$919$	−1469.75			−1.59930			−0.799648	−	0.600470i	$-0.794980\pi$
$919$	−1469.75			−1.59930			−0.799648	+	0.600470i	$0.794980\pi$
$920$		0			0
$921$	384.116			0.417064
$922$			382.258i			0.414596i
$923$			1033.20i			1.11940i
$924$	−36.8322	−	237.931i	−0.0398616	−	0.257501i
$925$		0			0
$926$	819.864			0.885382
$927$		−	245.383i		−	0.264706i
$928$	−90.4249			−0.0974406
$929$		−	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
$932$	−334.626			−0.359041
$933$	−140.047			−0.150104
$934$		−	1266.14i		−	1.35561i
$935$		0			0
$936$		−	171.936i		−	0.183693i
$937$		−	1422.24i		−	1.51787i	−0.651167	−	0.758934i	$-0.725720\pi$
$937$		−	1422.24i		−	1.51787i	0.651167	−	0.758934i	$-0.274280\pi$
$938$	−132.973	+	20.5845i	−0.141763	+	0.0219451i
$939$	−589.077			−0.627345
$940$		0			0
$941$		−	904.869i		−	0.961603i	−0.876829	−	0.480802i	$-0.840346\pi$
$941$		−	904.869i		−	0.961603i	0.876829	−	0.480802i	$-0.159654\pi$
$942$	−652.131			−0.692284
$943$			1077.28i			1.14239i
$944$			254.764i			0.269877i
$945$		0			0
$946$	−698.862			−0.738755
$947$	−414.868			−0.438087			−0.219043	−	0.975715i	$-0.570294\pi$
$947$	−414.868			−0.438087			−0.219043	+	0.975715i	$0.570294\pi$
$948$			242.025i			0.255301i
$949$	1598.86			1.68478
$950$		0			0
$951$			527.457i			0.554634i
$952$	−57.3678	−	370.589i	−0.0602603	−	0.389274i
$953$	30.9413			0.0324672			0.0162336	−	0.999868i	$-0.494832\pi$
$953$	30.9413			0.0324672			0.0162336	+	0.999868i	$0.494832\pi$
$954$	−47.4840			−0.0497735
$955$		0			0
$956$	−29.0641			−0.0304018
$957$			274.902i			0.287254i
$958$		−	357.450i		−	0.373121i
$959$	279.290	−	43.2346i	0.291230	−	0.0450830i
$960$		0			0
$961$	522.101			0.543289
$962$		−	864.971i		−	0.899138i
$963$	−480.270			−0.498723
$964$			675.503i			0.700730i
$965$		0			0
$966$	−66.8190	−	431.643i	−0.0691709	−	0.446835i
$967$	1662.25			1.71897			0.859486	−	0.511159i	$-0.170784\pi$
$967$	1662.25			1.71897			0.859486	+	0.511159i	$0.170784\pi$
$968$	63.3998			0.0654957
$969$			153.814i			0.158735i
$970$		0			0
$971$			5.10561i			0.00525810i	0.999997	+	0.00262905i	$0.000836853\pi$
$971$			5.10561i			0.00525810i	−0.999997	+	0.00262905i	$0.999163\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−37.8575	−	244.555i	−0.0389080	−	0.251341i
$974$	596.619			0.612545
$975$		0			0
$976$			357.132i			0.365914i
$977$	531.274			0.543781			0.271891	−	0.962328i	$-0.412351\pi$
$977$	531.274			0.543781			0.271891	+	0.962328i	$0.412351\pi$
$978$		−	459.031i		−	0.469356i
$979$			1549.75i			1.58299i
$980$		0			0
$981$	550.848			0.561517
$982$	328.772			0.334798
$983$		−	1746.75i		−	1.77696i	−0.458913	−	0.888481i	$-0.651761\pi$
$983$		−	1746.75i		−	1.77696i	0.458913	−	0.888481i	$-0.348239\pi$
$984$	−207.176			−0.210545
$985$		0			0
$986$			428.173i			0.434252i
$987$	−34.9324	+	5.40760i	−0.0353925	+	0.00547882i
$988$	−190.009			−0.192317
$989$	−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	$0.451318\pi$
$992$		−	118.511i		−	0.119466i
$993$		−	559.756i		−	0.563702i
$994$	−498.833	+	77.2202i	−0.501844	+	0.0776863i
$995$		0			0
$996$	238.633			0.239592
$997$			521.642i			0.523212i	0.965175	+	0.261606i	$0.0842521\pi$
$997$			521.642i			0.523212i	−0.965175	+	0.261606i	$0.915748\pi$
$998$	747.746			0.749244
$999$		−	156.844i		−	0.157001i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.91761 + 1.07086i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-6.91761 + 1.07086i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -9.92899 q^{11} -3.46410i q^{12} -20.2629i q^{13} +(9.78297 - 1.51442i) q^{14} +4.00000 q^{16} -18.9405i q^{17} +4.24264 q^{18} -4.68861i q^{19} +(1.85478 + 11.9816i) q^{21} +14.0417 q^{22} +25.4738 q^{23} +4.89898i q^{24} +28.6560i q^{26} +5.19615i q^{27} +(-13.8352 + 2.14171i) q^{28} +15.9850 q^{29} +20.9499i q^{31} -5.65685 q^{32} +17.1975i q^{33} +26.7859i q^{34} -6.00000 q^{36} -30.1846 q^{37} +6.63069i q^{38} -35.0963 q^{39} +42.2896i q^{41} +(-2.62305 - 16.9446i) q^{42} -49.7705 q^{43} -19.8580 q^{44} -36.0253 q^{46} +2.91549i q^{47} -6.92820i q^{48} +(46.7065 - 14.8155i) q^{49} -32.8059 q^{51} -40.5258i q^{52} -11.1921 q^{53} -7.34847i q^{54} +(19.5659 - 3.02884i) q^{56} -8.12091 q^{57} -22.6062 q^{58} +63.6910i q^{59} +89.2830i q^{61} -29.6277i q^{62} +(20.7528 - 3.21257i) q^{63} +8.00000 q^{64} -24.3210i q^{66} -13.5923 q^{67} -37.8810i q^{68} -44.1218i q^{69} -50.9899 q^{71} +8.48528 q^{72} +78.9059i q^{73} +42.6875 q^{74} -9.37722i q^{76} +(68.6848 - 10.6325i) q^{77} +49.6337 q^{78} -69.8667 q^{79} +9.00000 q^{81} -59.8066i q^{82} +68.8876i q^{83} +(3.70956 + 23.9633i) q^{84} +70.3860 q^{86} -27.6868i q^{87} +28.0834 q^{88} -156.083i q^{89} +(21.6987 + 140.171i) q^{91} +50.9475 q^{92} +36.2863 q^{93} -4.12313i q^{94} +9.79796i q^{96} -154.698i q^{97} +(-66.0530 + 20.9523i) q^{98} +29.7870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{4} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) 12 * q + 24 * q^4 - 10 * q^7 - 36 * q^9	\( 12 q + 24 q^{4} - 10 q^{7} - 36 q^{9} - 16 q^{11} + 8 q^{14} + 48 q^{16} - 6 q^{21} - 48 q^{22} - 20 q^{28} + 48 q^{29} - 72 q^{36} + 64 q^{37} - 12 q^{39} + 24 q^{42} - 108 q^{43} - 32 q^{44} + 80 q^{46} + 118 q^{49} + 72 q^{51} + 176 q^{53} + 16 q^{56} - 132 q^{57} + 128 q^{58} + 30 q^{63} + 96 q^{64} - 4 q^{67} + 248 q^{71} - 64 q^{74} - 396 q^{77} + 48 q^{78} - 208 q^{79} + 108 q^{81} - 12 q^{84} + 128 q^{86} - 96 q^{88} - 158 q^{91} + 252 q^{93} - 240 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 24 * q^4 - 10 * q^7 - 36 * q^9 - 16 * q^11 + 8 * q^14 + 48 * q^16 - 6 * q^21 - 48 * q^22 - 20 * q^28 + 48 * q^29 - 72 * q^36 + 64 * q^37 - 12 * q^39 + 24 * q^42 - 108 * q^43 - 32 * q^44 + 80 * q^46 + 118 * q^49 + 72 * q^51 + 176 * q^53 + 16 * q^56 - 132 * q^57 + 128 * q^58 + 30 * q^63 + 96 * q^64 - 4 * q^67 + 248 * q^71 - 64 * q^74 - 396 * q^77 + 48 * q^78 - 208 * q^79 + 108 * q^81 - 12 * q^84 + 128 * q^86 - 96 * q^88 - 158 * q^91 + 252 * q^93 - 240 * q^98 + 48 * q^99

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