LMFDB - Embedded newform 1911.2.c.g.883.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(883,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1911.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.c (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:	$15.2594118263$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1531626496.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 12x^{4} + 37x^{2} + 16 $ x^6 + 12x^4 + 37x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			883.2
Root			$-2.09002i$ of defining polynomial
Character	$\chi$	$=$	1911.883
Dual form			1911.2.c.g.883.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09002i q^{2} -1.00000 q^{3} -2.36817 q^{4} +3.58670i q^{5} +2.09002i q^{6} +0.769489i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.09002i q^{2} -1.00000 q^{3} -2.36817 q^{4} +3.58670i q^{5} +2.09002i q^{6} +0.769489i q^{8} +1.00000 q^{9} +7.49628 q^{10} +5.50056i q^{11} +2.36817 q^{12} +(0.368173 + 3.58670i) q^{13} -3.58670i q^{15} -3.12810 q^{16} +4.00000 q^{17} -2.09002i q^{18} -5.25955i q^{19} -8.49394i q^{20} +11.4963 q^{22} -6.12810 q^{23} -0.769489i q^{24} -7.86445 q^{25} +(7.49628 - 0.769489i) q^{26} -1.00000 q^{27} -4.86445 q^{29} -7.49628 q^{30} +6.44621i q^{31} +8.07676i q^{32} -5.50056i q^{33} -8.36007i q^{34} -2.36817 q^{36} -11.7058i q^{37} -10.9926 q^{38} +(-0.368173 - 3.58670i) q^{39} -2.75993 q^{40} -1.67284i q^{41} -6.86445 q^{43} -13.0263i q^{44} +3.58670i q^{45} +12.8078i q^{46} -3.23439i q^{47} +3.12810 q^{48} +16.4368i q^{50} -4.00000 q^{51} +(-0.871898 - 8.49394i) q^{52} -4.86445 q^{53} +2.09002i q^{54} -19.7289 q^{55} +5.25955i q^{57} +10.1668i q^{58} -1.32053i q^{59} +8.49394i q^{60} -8.73635 q^{61} +13.4727 q^{62} +10.6244 q^{64} +(-12.8644 + 1.32053i) q^{65} -11.4963 q^{66} -11.0011i q^{67} -9.47269 q^{68} +6.12810 q^{69} -2.85951i q^{71} +0.769489i q^{72} +11.7283i q^{73} -24.4652 q^{74} +7.86445 q^{75} +12.4555i q^{76} +(-7.49628 + 0.769489i) q^{78} +7.60080 q^{79} -11.2196i q^{80} +1.00000 q^{81} -3.49628 q^{82} +1.29796i q^{83} +14.3468i q^{85} +14.3468i q^{86} +4.86445 q^{87} -4.23262 q^{88} +11.9468i q^{89} +7.49628 q^{90} +14.5124 q^{92} -6.44621i q^{93} -6.75993 q^{94} +18.8644 q^{95} -8.07676i q^{96} +4.55492i q^{97} +5.50056i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} - 12 q^{4} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^3 - 12 * q^4 + 6 * q^9	$ 6 q - 6 q^{3} - 12 q^{4} + 6 q^{9} + 4 q^{10} + 12 q^{12} + 20 q^{16} + 24 q^{17} + 28 q^{22} + 2 q^{23} - 4 q^{25} + 4 q^{26} - 6 q^{27} + 14 q^{29} - 4 q^{30} - 12 q^{36} + 16 q^{38} + 20 q^{40} + 2 q^{43} - 20 q^{48} - 24 q^{51} - 44 q^{52} + 14 q^{53} - 32 q^{55} - 48 q^{61} + 72 q^{62} - 16 q^{64} - 34 q^{65} - 28 q^{66} - 48 q^{68} - 2 q^{69} - 56 q^{74} + 4 q^{75} - 4 q^{78} - 2 q^{79} + 6 q^{81} + 20 q^{82} - 14 q^{87} + 20 q^{88} + 4 q^{90} - 68 q^{92} - 4 q^{94} + 70 q^{95}+O(q^{100}) $ 6 * q - 6 * q^3 - 12 * q^4 + 6 * q^9 + 4 * q^10 + 12 * q^12 + 20 * q^16 + 24 * q^17 + 28 * q^22 + 2 * q^23 - 4 * q^25 + 4 * q^26 - 6 * q^27 + 14 * q^29 - 4 * q^30 - 12 * q^36 + 16 * q^38 + 20 * q^40 + 2 * q^43 - 20 * q^48 - 24 * q^51 - 44 * q^52 + 14 * q^53 - 32 * q^55 - 48 * q^61 + 72 * q^62 - 16 * q^64 - 34 * q^65 - 28 * q^66 - 48 * q^68 - 2 * q^69 - 56 * q^74 + 4 * q^75 - 4 * q^78 - 2 * q^79 + 6 * q^81 + 20 * q^82 - 14 * q^87 + 20 * q^88 + 4 * q^90 - 68 * q^92 - 4 * q^94 + 70 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times$.

$n$	$638$	$1471$	$1522$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	2.09002i		−	1.47787i	−0.673779	−	0.738933i	$-0.735330\pi$
$2$		−	2.09002i		−	1.47787i	0.673779	−	0.738933i	$-0.264670\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−2.36817			−1.18409
$5$			3.58670i			1.60402i	0.597309	+	0.802011i	$0.296237\pi$
$5$			3.58670i			1.60402i	−0.597309	+	0.802011i	$0.703763\pi$
$6$			2.09002i			0.853246i
$7$		0			0
$7$		0			0
$8$			0.769489i			0.272055i
$9$	1.00000			0.333333
$10$	7.49628			2.37053
$11$			5.50056i			1.65848i	0.558891	+	0.829241i	$0.311227\pi$
$11$			5.50056i			1.65848i	−0.558891	+	0.829241i	$0.688773\pi$
$12$	2.36817			0.683633
$13$	0.368173	+	3.58670i	0.102113	+	0.994773i
$13$	0.368173	+	3.58670i	0.102113	+	0.994773i
$14$		0			0
$15$		−	3.58670i		−	0.926083i
$16$	−3.12810			−0.782025
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		−	2.09002i		−	0.492622i
$19$		−	5.25955i		−	1.20662i	−0.797505	−	0.603312i	$-0.793848\pi$
$19$		−	5.25955i		−	1.20662i	0.797505	−	0.603312i	$-0.206152\pi$
$20$		−	8.49394i		−	1.89930i
$21$		0			0
$22$	11.4963			2.45101
$23$	−6.12810			−1.27780			−0.638899	−	0.769291i	$-0.720610\pi$
$23$	−6.12810			−1.27780			−0.638899	+	0.769291i	$0.720610\pi$
$24$		−	0.769489i		−	0.157071i
$25$	−7.86445			−1.57289
$26$	7.49628	−	0.769489i	1.47014	−	0.150909i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−4.86445			−0.903305			−0.451653	−	0.892194i	$-0.649165\pi$
$29$	−4.86445			−0.903305			−0.451653	+	0.892194i	$0.649165\pi$
$30$	−7.49628			−1.36863
$31$			6.44621i			1.15777i	0.815408	+	0.578887i	$0.196513\pi$
$31$			6.44621i			1.15777i	−0.815408	+	0.578887i	$0.803487\pi$
$32$			8.07676i			1.42778i
$33$		−	5.50056i		−	0.957525i
$34$		−	8.36007i		−	1.43374i
$35$		0			0
$36$	−2.36817			−0.394696
$37$		−	11.7058i		−	1.92442i	−0.272317	−	0.962208i	$-0.587790\pi$
$37$		−	11.7058i		−	1.92442i	0.272317	−	0.962208i	$-0.412210\pi$
$38$	−10.9926			−1.78323
$39$	−0.368173	−	3.58670i	−0.0589549	−	0.574332i
$40$	−2.75993			−0.436383
$41$		−	1.67284i		−	0.261254i	−0.991432	−	0.130627i	$-0.958301\pi$
$41$		−	1.67284i		−	0.261254i	0.991432	−	0.130627i	$-0.0416991\pi$
$42$		0			0
$43$	−6.86445			−1.04682			−0.523409	−	0.852081i	$-0.675340\pi$
$43$	−6.86445			−1.04682			−0.523409	+	0.852081i	$0.675340\pi$
$44$		−	13.0263i		−	1.96379i
$45$			3.58670i			0.534674i
$46$			12.8078i			1.88841i
$47$		−	3.23439i		−	0.471784i	−0.971779	−	0.235892i	$-0.924199\pi$
$47$		−	3.23439i		−	0.471784i	0.971779	−	0.235892i	$-0.0758012\pi$
$48$	3.12810			0.451503
$49$		0			0
$50$			16.4368i			2.32452i
$51$	−4.00000			−0.560112
$52$	−0.871898	−	8.49394i	−0.120911	−	1.17790i
$53$	−4.86445			−0.668183			−0.334092	−	0.942541i	$-0.608430\pi$
$53$	−4.86445			−0.668183			−0.334092	+	0.942541i	$0.608430\pi$
$54$			2.09002i			0.284415i
$55$	−19.7289			−2.66024
$56$		0			0
$57$			5.25955i			0.696644i
$58$			10.1668i			1.33496i
$59$		−	1.32053i		−	0.171918i	−0.996299	−	0.0859591i	$-0.972605\pi$
$59$		−	1.32053i		−	0.171918i	0.996299	−	0.0859591i	$-0.0273954\pi$
$60$			8.49394i			1.09656i
$61$	−8.73635			−1.11857			−0.559287	−	0.828974i	$-0.688925\pi$
$61$	−8.73635			−1.11857			−0.559287	+	0.828974i	$0.688925\pi$
$62$	13.4727			1.71103
$63$		0			0
$64$	10.6244			1.32805
$65$	−12.8644	+	1.32053i	−1.59564	+	0.163791i
$66$	−11.4963			−1.41509
$67$		−	11.0011i		−	1.34400i	−0.740550	−	0.672001i	$-0.765435\pi$
$67$		−	11.0011i		−	1.34400i	0.740550	−	0.672001i	$-0.234565\pi$
$68$	−9.47269			−1.14873
$69$	6.12810			0.737737
$70$		0			0
$71$		−	2.85951i		−	0.339361i	−0.985499	−	0.169680i	$-0.945726\pi$
$71$		−	2.85951i		−	0.339361i	0.985499	−	0.169680i	$-0.0542736\pi$
$72$			0.769489i			0.0906851i
$73$			11.7283i			1.37270i	0.727273	+	0.686348i	$0.240787\pi$
$73$			11.7283i			1.37270i	−0.727273	+	0.686348i	$0.759213\pi$
$74$	−24.4652			−2.84403
$75$	7.86445			0.908108
$76$			12.4555i			1.42875i
$77$		0			0
$78$	−7.49628	+	0.769489i	−0.848786	+	0.0871274i
$79$	7.60080			0.855156			0.427578	−	0.903978i	$-0.359367\pi$
$79$	7.60080			0.855156			0.427578	+	0.903978i	$0.359367\pi$
$80$		−	11.2196i		−	1.25439i
$81$	1.00000			0.111111
$82$	−3.49628			−0.386099
$83$			1.29796i			0.142470i	0.997460	+	0.0712350i	$0.0226940\pi$
$83$			1.29796i			0.142470i	−0.997460	+	0.0712350i	$0.977306\pi$
$84$		0			0
$85$			14.3468i			1.55613i
$86$			14.3468i			1.54706i
$87$	4.86445			0.521524
$88$	−4.23262			−0.451199
$89$			11.9468i			1.26636i	0.774006	+	0.633178i	$0.218250\pi$
$89$			11.9468i			1.26636i	−0.774006	+	0.633178i	$0.781750\pi$
$90$	7.49628			0.790177
$91$		0			0
$92$	14.5124			1.51302
$93$		−	6.44621i		−	0.668441i
$94$	−6.75993			−0.697233
$95$	18.8644			1.93545
$96$		−	8.07676i		−	0.824331i
$97$			4.55492i			0.462482i	0.972897	+	0.231241i	$0.0742785\pi$
$97$			4.55492i			0.462482i	−0.972897	+	0.231241i	$0.925721\pi$
$98$		0			0
$99$			5.50056i			0.552827i
$100$	18.6244			1.86244
$101$	2.52731			0.251476			0.125738	−	0.992063i	$-0.459870\pi$
$101$	2.52731			0.251476			0.125738	+	0.992063i	$0.459870\pi$
$102$			8.36007i			0.827770i
$103$	−14.2562			−1.40471			−0.702353	−	0.711829i	$-0.747867\pi$
$103$	−14.2562			−1.40471			−0.702353	+	0.711829i	$0.747867\pi$
$104$	−2.75993	+	0.283305i	−0.270633	+	0.0277804i
$105$		0			0
$106$			10.1668i			0.987485i
$107$	0.736347			0.0711853			0.0355927	−	0.999366i	$-0.488668\pi$
$107$	0.736347			0.0711853			0.0355927	+	0.999366i	$0.488668\pi$
$108$	2.36817			0.227878
$109$			5.01438i			0.480291i	0.970737	+	0.240145i	$0.0771951\pi$
$109$			5.01438i			0.480291i	−0.970737	+	0.240145i	$0.922805\pi$
$110$			41.2337i			3.93148i
$111$			11.7058i			1.11106i
$112$		0			0
$113$	11.3918			1.07165			0.535823	−	0.844330i	$-0.320001\pi$
$113$	11.3918			1.07165			0.535823	+	0.844330i	$0.320001\pi$
$114$	10.9926			1.02955
$115$		−	21.9797i		−	2.04962i
$116$	11.5199			1.06959
$117$	0.368173	+	3.58670i	0.0340376	+	0.331591i
$118$	−2.75993			−0.254072
$119$		0			0
$120$	2.75993			0.251946
$121$	−19.2562			−1.75056
$122$			18.2591i			1.65310i
$123$			1.67284i			0.150835i
$124$		−	15.2657i		−	1.37090i
$125$		−	10.2739i		−	0.918928i
$126$		0			0
$127$	−4.73635			−0.420283			−0.210141	−	0.977671i	$-0.567392\pi$
$127$	−4.73635			−0.420283			−0.210141	+	0.977671i	$0.567392\pi$
$128$		−	6.05160i		−	0.534891i
$129$	6.86445			0.604381
$130$	2.75993	+	26.8869i	0.242062	+	2.35814i
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$			13.0263i			1.13379i
$133$		0			0
$134$	−22.9926			−1.98625
$135$		−	3.58670i		−	0.308694i
$136$			3.07795i			0.263932i
$137$		−	3.96159i		−	0.338461i	−0.985576	−	0.169231i	$-0.945872\pi$
$137$		−	3.96159i		−	0.338461i	0.985576	−	0.169231i	$-0.0541283\pi$
$138$		−	12.8078i		−	1.09028i
$139$	−21.2016			−1.79830			−0.899148	−	0.437645i	$-0.855813\pi$
$139$	−21.2016			−1.79830			−0.899148	+	0.437645i	$0.855813\pi$
$140$		0			0
$141$			3.23439i			0.272385i
$142$	−5.97642			−0.501530
$143$	−19.7289	+	2.02516i	−1.64981	+	0.169352i
$144$	−3.12810			−0.260675
$145$		−	17.4473i		−	1.44892i
$146$	24.5124			2.02866
$147$		0			0
$148$			27.7213i			2.27867i
$149$			7.03954i			0.576702i	0.957525	+	0.288351i	$0.0931069\pi$
$149$			7.03954i			0.576702i	−0.957525	+	0.288351i	$0.906893\pi$
$150$		−	16.4368i		−	1.34206i
$151$			9.06470i			0.737675i	0.929494	+	0.368838i	$0.120244\pi$
$151$			9.06470i			0.737675i	−0.929494	+	0.368838i	$0.879756\pi$
$152$	4.04716			0.328268
$153$	4.00000			0.323381
$154$		0			0
$155$	−23.1207			−1.85710
$156$	0.871898	+	8.49394i	0.0698077	+	0.680059i
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$		−	15.8858i		−	1.26381i
$159$	4.86445			0.385776
$160$	−28.9690			−2.29020
$161$		0			0
$162$		−	2.09002i		−	0.164207i
$163$		−	5.71901i		−	0.447948i	−0.974595	−	0.223974i	$-0.928097\pi$
$163$		−	5.71901i		−	0.447948i	0.974595	−	0.223974i	$-0.0719030\pi$
$164$			3.96159i			0.309348i
$165$	19.7289			1.53589
$166$	2.71276			0.210551
$167$		−	11.1124i		−	0.859906i	−0.902851	−	0.429953i	$-0.858530\pi$
$167$		−	11.1124i		−	0.859906i	0.902851	−	0.429953i	$-0.141470\pi$
$168$		0			0
$169$	−12.7289	+	2.64106i	−0.979146	+	0.203158i
$170$	29.9851			2.29975
$171$		−	5.25955i		−	0.402208i
$172$	16.2562			1.23952
$173$	2.52731			0.192148			0.0960738	−	0.995374i	$-0.469372\pi$
$173$	2.52731			0.192148			0.0960738	+	0.995374i	$0.469372\pi$
$174$		−	10.1668i		−	0.770742i
$175$		0			0
$176$		−	17.2063i		−	1.29698i
$177$			1.32053i			0.0992570i
$178$	24.9690			1.87150
$179$	15.8570			1.18521			0.592604	−	0.805494i	$-0.298100\pi$
$179$	15.8570			1.18521			0.592604	+	0.805494i	$0.298100\pi$
$180$		−	8.49394i		−	0.633101i
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$		0			0
$183$	8.73635			0.645809
$184$		−	4.71550i		−	0.347632i
$185$	41.9851			3.08681
$186$	−13.4727			−0.987866
$187$			22.0023i			1.60896i
$188$			7.65959i			0.558633i
$189$		0			0
$190$		−	39.4270i		−	2.86034i
$191$	4.73635			0.342710			0.171355	−	0.985209i	$-0.445185\pi$
$191$	4.73635			0.342710			0.171355	+	0.985209i	$0.445185\pi$
$192$	−10.6244			−0.766748
$193$		−	19.3612i		−	1.39365i	−0.717241	−	0.696825i	$-0.754596\pi$
$193$		−	19.3612i		−	1.39365i	0.717241	−	0.696825i	$-0.245404\pi$
$194$	9.51986			0.683486
$195$	12.8644	−	1.32053i	0.921242	−	0.0945650i
$196$		0			0
$197$			4.66622i			0.332454i	0.986087	+	0.166227i	$0.0531585\pi$
$197$			4.66622i			0.332454i	−0.986087	+	0.166227i	$0.946842\pi$
$198$	11.4963			0.817005
$199$	−10.5273			−0.746261			−0.373130	−	0.927779i	$-0.621716\pi$
$199$	−10.5273			−0.746261			−0.373130	+	0.927779i	$0.621716\pi$
$200$		−	6.05160i		−	0.427913i
$201$			11.0011i			0.775960i
$202$		−	5.28212i		−	0.371648i
$203$		0			0
$204$	9.47269			0.663221
$205$	6.00000			0.419058
$206$			29.7957i			2.07597i
$207$	−6.12810			−0.425933
$208$	−1.15168	−	11.2196i	−0.0798549	−	0.777938i
$209$	28.9305			2.00116
$210$		0			0
$211$	−27.8570			−1.91775			−0.958877	−	0.283820i	$-0.908398\pi$
$211$	−27.8570			−1.91775			−0.958877	+	0.283820i	$0.908398\pi$
$212$	11.5199			0.791187
$213$			2.85951i			0.195930i
$214$		−	1.53898i		−	0.105202i
$215$		−	24.6207i		−	1.67912i
$216$		−	0.769489i		−	0.0523571i
$217$		0			0
$218$	10.4801			0.709805
$219$		−	11.7283i		−	0.792527i
$220$	46.7214			3.14996
$221$	1.47269	+	14.3468i	0.0990641	+	0.965071i
$222$	24.4652			1.64200
$223$		−	3.80515i		−	0.254812i	−0.991851	−	0.127406i	$-0.959335\pi$
$223$		−	3.80515i		−	0.254812i	0.991851	−	0.127406i	$-0.0406651\pi$
$224$		0			0
$225$	−7.86445			−0.524297
$226$		−	23.8090i		−	1.58375i
$227$			20.6817i			1.37269i	0.727274	+	0.686347i	$0.240787\pi$
$227$			20.6817i			1.37269i	−0.727274	+	0.686347i	$0.759213\pi$
$228$		−	12.4555i		−	0.824887i
$229$			18.1745i			1.20101i	0.799622	+	0.600504i	$0.205033\pi$
$229$			18.1745i			1.20101i	−0.799622	+	0.600504i	$0.794967\pi$
$230$	−45.9379			−3.02906
$231$		0			0
$232$		−	3.74314i		−	0.245749i
$233$	14.3371			0.939257			0.469629	−	0.882864i	$-0.344388\pi$
$233$	14.3371			0.939257			0.469629	+	0.882864i	$0.344388\pi$
$234$	7.49628	−	0.769489i	0.490047	−	0.0503030i
$235$	11.6008			0.756752
$236$			3.12724i			0.203566i
$237$	−7.60080			−0.493725
$238$		0			0
$239$			0.486183i			0.0314486i	0.999876	+	0.0157243i	$0.00500541\pi$
$239$			0.486183i			0.0314486i	−0.999876	+	0.0157243i	$0.994995\pi$
$240$			11.2196i			0.724221i
$241$		−	10.2739i		−	0.661802i	−0.943665	−	0.330901i	$-0.892647\pi$
$241$		−	10.2739i		−	0.661802i	0.943665	−	0.330901i	$-0.107353\pi$
$242$			40.2458i			2.58710i
$243$	−1.00000			−0.0641500
$244$	20.6892			1.32449
$245$		0			0
$246$	3.49628			0.222914
$247$	18.8644	−	1.93643i	1.20032	−	0.123212i
$248$	−4.96029			−0.314978
$249$		−	1.29796i		−	0.0822550i
$250$	−21.4727			−1.35805
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		−	33.7080i		−	2.11920i
$254$			9.89905i			0.621121i
$255$		−	14.3468i		−	0.898433i
$256$	8.60080			0.537550
$257$	13.4727			0.840404			0.420202	−	0.907431i	$-0.361959\pi$
$257$	13.4727			0.840404			0.420202	+	0.907431i	$0.361959\pi$
$258$		−	14.3468i		−	0.893194i
$259$		0			0
$260$	30.4652	−	3.12724i	1.88937	−	0.193943i
$261$	−4.86445			−0.301102
$262$		−	16.7201i		−	1.03297i
$263$	−4.65541			−0.287065			−0.143532	−	0.989646i	$-0.545846\pi$
$263$	−4.65541			−0.287065			−0.143532	+	0.989646i	$0.545846\pi$
$264$	4.23262			0.260500
$265$		−	17.4473i		−	1.07178i
$266$		0			0
$267$		−	11.9468i		−	0.731131i
$268$			26.0526i			1.59141i
$269$	−29.9851			−1.82822			−0.914112	−	0.405462i	$-0.867111\pi$
$269$	−29.9851			−1.82822			−0.914112	+	0.405462i	$0.867111\pi$
$270$	−7.49628			−0.456209
$271$		−	2.64106i		−	0.160433i	−0.996777	−	0.0802164i	$-0.974439\pi$
$271$		−	2.64106i		−	0.160433i	0.996777	−	0.0802164i	$-0.0255611\pi$
$272$	−12.5124			−0.758676
$273$		0			0
$274$	−8.27979			−0.500200
$275$		−	43.2589i		−	2.60861i
$276$	−14.5124			−0.873544
$277$	13.1207			0.788344			0.394172	−	0.919037i	$-0.371031\pi$
$277$	13.1207			0.788344			0.394172	+	0.919037i	$0.371031\pi$
$278$			44.3117i			2.65764i
$279$			6.44621i			0.385925i
$280$		0			0
$281$			23.3228i			1.39132i	0.718371	+	0.695660i	$0.244888\pi$
$281$			23.3228i			1.39132i	−0.718371	+	0.695660i	$0.755112\pi$
$282$	6.75993			0.402548
$283$	−23.4578			−1.39442			−0.697211	−	0.716866i	$-0.745576\pi$
$283$	−23.4578			−1.39442			−0.697211	+	0.716866i	$0.745576\pi$
$284$			6.77181i			0.401833i
$285$	−18.8644			−1.11743
$286$	4.23262	+	41.2337i	0.250280	+	2.43820i
$287$		0			0
$288$			8.07676i			0.475928i
$289$	−1.00000			−0.0588235
$290$	−36.4652			−2.14131
$291$		−	4.55492i		−	0.267014i
$292$		−	27.7747i		−	1.62539i
$293$			20.7889i			1.21450i	0.794511	+	0.607249i	$0.207727\pi$
$293$			20.7889i			1.21450i	−0.794511	+	0.607249i	$0.792273\pi$
$294$		0			0
$295$	4.73635			0.275761
$296$	9.00745			0.523547
$297$		−	5.50056i		−	0.319175i
$298$	14.7128			0.852288
$299$	−2.25620	−	21.9797i	−0.130480	−	1.27112i
$300$	−18.6244			−1.07528
$301$		0			0
$302$	18.9454			1.09018
$303$	−2.52731			−0.145190
$304$			16.4524i			0.943610i
$305$		−	31.3347i		−	1.79422i
$306$		−	8.36007i		−	0.477913i
$307$		−	2.61849i		−	0.149445i	−0.997204	−	0.0747226i	$-0.976193\pi$
$307$		−	2.61849i		−	0.149445i	0.997204	−	0.0747226i	$-0.0238071\pi$
$308$		0			0
$309$	14.2562			0.811007
$310$			48.3226i			2.74454i
$311$	−6.94539			−0.393837			−0.196918	−	0.980420i	$-0.563093\pi$
$311$	−6.94539			−0.393837			−0.196918	+	0.980420i	$0.563093\pi$
$312$	2.75993	−	0.283305i	0.156250	−	0.0160390i
$313$	26.7214			1.51039			0.755193	−	0.655503i	$-0.227543\pi$
$313$	26.7214			1.51039			0.755193	+	0.655503i	$0.227543\pi$
$314$			8.36007i			0.471786i
$315$		0			0
$316$	−18.0000			−1.01258
$317$			4.66622i			0.262081i	0.991377	+	0.131040i	$0.0418318\pi$
$317$			4.66622i			0.262081i	−0.991377	+	0.131040i	$0.958168\pi$
$318$		−	10.1668i		−	0.570125i
$319$		−	26.7572i		−	1.49812i
$320$			38.1065i			2.13022i
$321$	−0.736347			−0.0410989
$322$		0			0
$323$		−	21.0382i		−	1.17060i
$324$	−2.36817			−0.131565
$325$	−2.89548	−	28.2075i	−0.160612	−	1.56467i
$326$	−11.9528			−0.662006
$327$		−	5.01438i		−	0.277296i
$328$	1.28724			0.0710757
$329$		0			0
$330$		−	41.2337i		−	2.26984i
$331$		−	23.4115i		−	1.28681i	−0.765524	−	0.643407i	$-0.777520\pi$
$331$		−	23.4115i		−	1.28681i	0.765524	−	0.643407i	$-0.222480\pi$
$332$		−	3.07380i		−	0.168697i
$333$		−	11.7058i		−	0.641472i
$334$	−23.2252			−1.27082
$335$	39.4578			2.15581
$336$		0			0
$337$	−9.13555			−0.497645			−0.248823	−	0.968549i	$-0.580044\pi$
$337$	−9.13555			−0.497645			−0.248823	+	0.968549i	$0.580044\pi$
$338$	5.51986	+	26.6036i	0.300241	+	1.44705i
$339$	−11.3918			−0.618715
$340$		−	33.9758i		−	1.84259i
$341$	−35.4578			−1.92015
$342$	−10.9926			−0.594409
$343$		0			0
$344$		−	5.28212i		−	0.284793i
$345$			21.9797i			1.18335i
$346$		−	5.28212i		−	0.283968i
$347$	−8.73635			−0.468992			−0.234496	−	0.972117i	$-0.575344\pi$
$347$	−8.73635			−0.468992			−0.234496	+	0.972117i	$0.575344\pi$
$348$	−11.5199			−0.617529
$349$			27.4844i			1.47121i	0.677413	+	0.735603i	$0.263101\pi$
$349$			27.4844i			1.47121i	−0.677413	+	0.735603i	$0.736899\pi$
$350$		0			0
$351$	−0.368173	−	3.58670i	−0.0196516	−	0.191444i
$352$	−44.4268			−2.36795
$353$			30.3665i			1.61624i	0.589015	+	0.808122i	$0.299516\pi$
$353$			30.3665i			1.61624i	−0.589015	+	0.808122i	$0.700484\pi$
$354$	2.75993			0.146689
$355$	10.2562			0.544343
$356$		−	28.2920i		−	1.49947i
$357$		0			0
$358$		−	33.1414i		−	1.75158i
$359$		−	2.85951i		−	0.150919i	−0.997149	−	0.0754595i	$-0.975958\pi$
$359$		−	2.85951i		−	0.150919i	0.997149	−	0.0754595i	$-0.0240424\pi$
$360$	−2.75993			−0.145461
$361$	−8.66286			−0.455940
$362$		−	25.0802i		−	1.31819i
$363$	19.2562			1.01069
$364$		0			0
$365$	−42.0660			−2.20184
$366$		−	18.2591i		−	0.954419i
$367$	−2.25620			−0.117773			−0.0588864	−	0.998265i	$-0.518755\pi$
$367$	−2.25620			−0.117773			−0.0588864	+	0.998265i	$0.518755\pi$
$368$	19.1693			0.999270
$369$		−	1.67284i		−	0.0870848i
$370$		−	87.7496i		−	4.56188i
$371$		0			0
$372$			15.2657i			0.791492i
$373$	−21.7289			−1.12508			−0.562540	−	0.826770i	$-0.690176\pi$
$373$	−21.7289			−1.12508			−0.562540	+	0.826770i	$0.690176\pi$
$374$	45.9851			2.37783
$375$			10.2739i			0.530543i
$376$	2.48883			0.128351
$377$	−1.79096	−	17.4473i	−0.0922391	−	0.898584i
$378$		0			0
$379$			7.65544i			0.393233i	0.980480	+	0.196617i	$0.0629955\pi$
$379$			7.65544i			0.393233i	−0.980480	+	0.196617i	$0.937005\pi$
$380$	−44.6743			−2.29174
$381$	4.73635			0.242650
$382$		−	9.89905i		−	0.506479i
$383$			21.3864i			1.09279i	0.837527	+	0.546396i	$0.184001\pi$
$383$			21.3864i			1.09279i	−0.837527	+	0.546396i	$0.815999\pi$
$384$			6.05160i			0.308820i
$385$		0			0
$386$	−40.4652			−2.05963
$387$	−6.86445			−0.348940
$388$		−	10.7868i		−	0.547618i
$389$	−8.52731			−0.432352			−0.216176	−	0.976354i	$-0.569358\pi$
$389$	−8.52731			−0.432352			−0.216176	+	0.976354i	$0.569358\pi$
$390$	−2.75993	−	26.8869i	−0.139754	−	1.36147i
$391$	−24.5124			−1.23965
$392$		0			0
$393$	−8.00000			−0.403547
$394$	9.75248			0.491323
$395$			27.2618i			1.37169i
$396$		−	13.0263i		−	0.654596i
$397$		−	18.9017i		−	0.948651i	−0.880350	−	0.474325i	$-0.842692\pi$
$397$		−	18.9017i		−	0.948651i	0.880350	−	0.474325i	$-0.157308\pi$
$398$			22.0023i			1.10287i
$399$		0			0
$400$	24.6008			1.23004
$401$		−	29.7464i		−	1.48547i	−0.669588	−	0.742733i	$-0.733529\pi$
$401$		−	29.7464i		−	1.48547i	0.669588	−	0.742733i	$-0.266471\pi$
$402$	22.9926			1.14676
$403$	−23.1207	+	2.37332i	−1.15172	+	0.118224i
$404$	−5.98510			−0.297770
$405$			3.58670i			0.178225i
$406$		0			0
$407$	64.3883			3.19161
$408$		−	3.07795i		−	0.152381i
$409$			26.5572i			1.31317i	0.754253	+	0.656584i	$0.227999\pi$
$409$			26.5572i			1.31317i	−0.754253	+	0.656584i	$0.772001\pi$
$410$		−	12.5401i		−	0.619312i
$411$			3.96159i			0.195411i
$412$	33.7612			1.66329
$413$		0			0
$414$			12.8078i			0.629471i
$415$	−4.65541			−0.228525
$416$	−28.9690	+	2.97365i	−1.42032	+	0.145795i
$417$	21.2016			1.03825
$418$		−	60.4652i		−	2.95745i
$419$	−4.00000			−0.195413			−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000			−0.195413			−0.0977064	+	0.995215i	$0.531151\pi$
$420$		0			0
$421$			36.3491i			1.77155i	0.464119	+	0.885773i	$0.346371\pi$
$421$			36.3491i			1.77155i	−0.464119	+	0.885773i	$0.653629\pi$
$422$			58.2216i			2.83418i
$423$		−	3.23439i		−	0.157261i
$424$		−	3.74314i		−	0.181783i
$425$	−31.4578			−1.52593
$426$	5.97642			0.289558
$427$		0			0
$428$	−1.74380			−0.0842896
$429$	19.7289	−	2.02516i	0.952520	−	0.0977757i
$430$	−51.4578			−2.48152
$431$		−	6.20520i		−	0.298894i	−0.988770	−	0.149447i	$-0.952251\pi$
$431$		−	6.20520i		−	0.298894i	0.988770	−	0.149447i	$-0.0477493\pi$
$432$	3.12810			0.150501
$433$	0.736347			0.0353866			0.0176933	−	0.999843i	$-0.494368\pi$
$433$	0.736347			0.0353866			0.0176933	+	0.999843i	$0.494368\pi$
$434$		0			0
$435$			17.4473i			0.836536i
$436$		−	11.8749i		−	0.568706i
$437$			32.2311i			1.54182i
$438$	−24.5124			−1.17125
$439$	9.20159			0.439168			0.219584	−	0.975594i	$-0.429530\pi$
$439$	9.20159			0.439168			0.219584	+	0.975594i	$0.429530\pi$
$440$		−	15.1812i		−	0.723734i
$441$		0			0
$442$	29.9851	−	3.07795i	1.42625	−	0.146403i
$443$	−30.3843			−1.44360			−0.721801	−	0.692101i	$-0.756685\pi$
$443$	−30.3843			−1.44360			−0.721801	+	0.692101i	$0.756685\pi$
$444$		−	27.7213i		−	1.31559i
$445$	−42.8495			−2.03126
$446$	−7.95284			−0.376578
$447$		−	7.03954i		−	0.332959i
$448$		0			0
$449$			22.3587i			1.05517i	0.849501	+	0.527587i	$0.176903\pi$
$449$			22.3587i			1.05517i	−0.849501	+	0.527587i	$0.823097\pi$
$450$			16.4368i			0.774840i
$451$	9.20159			0.433286
$452$	−26.9777			−1.26892
$453$		−	9.06470i		−	0.425897i
$454$	43.2252			2.02866
$455$		0			0
$456$	−4.04716			−0.189526
$457$			28.4259i			1.32971i	0.746974	+	0.664854i	$0.231506\pi$
$457$			28.4259i			1.32971i	−0.746974	+	0.664854i	$0.768494\pi$
$458$	37.9851			1.77493
$459$	−4.00000			−0.186704
$460$			52.0517i			2.42692i
$461$		−	15.3150i		−	0.713292i	−0.934240	−	0.356646i	$-0.883920\pi$
$461$		−	15.3150i		−	0.713292i	0.934240	−	0.356646i	$-0.116080\pi$
$462$		0			0
$463$		−	18.6566i		−	0.867044i	−0.901143	−	0.433522i	$-0.857271\pi$
$463$		−	18.6566i		−	0.867044i	0.901143	−	0.433522i	$-0.142729\pi$
$464$	15.2165			0.706408
$465$	23.1207			1.07219
$466$		−	29.9649i		−	1.38810i
$467$	27.4578			1.27060			0.635298	−	0.772267i	$-0.280877\pi$
$467$	27.4578			1.27060			0.635298	+	0.772267i	$0.280877\pi$
$468$	−0.871898	−	8.49394i	−0.0403035	−	0.392632i
$469$		0			0
$470$		−	24.2459i		−	1.11838i
$471$	4.00000			0.184310
$472$	1.01613			0.0467713
$473$		−	37.7583i		−	1.73613i
$474$			15.8858i			0.729659i
$475$			41.3635i			1.89789i
$476$		0			0
$477$	−4.86445			−0.222728
$478$	1.01613			0.0464768
$479$		−	38.3968i		−	1.75439i	−0.480130	−	0.877197i	$-0.659411\pi$
$479$		−	38.3968i		−	1.75439i	0.480130	−	0.877197i	$-0.340589\pi$
$480$	28.9690			1.32225
$481$	41.9851	−	4.30975i	1.91436	−	0.196508i
$482$	−21.4727			−0.978054
$483$		0			0
$484$	45.6020			2.07282
$485$	−16.3371			−0.741831
$486$			2.09002i			0.0948051i
$487$			33.9758i			1.53959i	0.638292	+	0.769794i	$0.279641\pi$
$487$			33.9758i			1.53959i	−0.638292	+	0.769794i	$0.720359\pi$
$488$		−	6.72252i		−	0.304314i
$489$			5.71901i			0.258623i
$490$		0			0
$491$	−15.2637			−0.688839			−0.344420	−	0.938816i	$-0.611924\pi$
$491$	−15.2637			−0.688839			−0.344420	+	0.938816i	$0.611924\pi$
$492$		−	3.96159i		−	0.178602i
$493$	−19.4578			−0.876335
$494$	−4.04716	−	39.4270i	−0.182091	−	1.77391i
$495$	−19.7289			−0.886748
$496$		−	20.1644i		−	0.905408i
$497$		0			0
$498$	−2.71276			−0.121562
$499$			24.3756i			1.09120i	0.838045	+	0.545600i	$0.183698\pi$
$499$			24.3756i			1.09120i	−0.838045	+	0.545600i	$0.816302\pi$
$500$			24.3304i			1.08809i
$501$			11.1124i			0.496467i
$502$			25.0802i			1.11938i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$			9.06470i			0.403374i
$506$	−70.4503			−3.13190
$507$	12.7289	−	2.64106i	0.565310	−	0.117293i
$508$	11.2165			0.497651
$509$		−	18.4156i		−	0.816255i	−0.912925	−	0.408127i	$-0.866182\pi$
$509$		−	18.4156i		−	0.816255i	0.912925	−	0.408127i	$-0.133818\pi$
$510$	−29.9851			−1.32776
$511$		0			0
$512$		−	30.0790i		−	1.32932i
$513$			5.25955i			0.232215i
$514$		−	28.1582i		−	1.24200i
$515$		−	51.1328i		−	2.25318i
$516$	−16.2562			−0.715639
$517$	17.7910			0.782446
$518$		0			0
$519$	−2.52731			−0.110936
$520$	−1.01613	−	9.89905i	−0.0445603	−	0.434102i
$521$	15.4578			0.677218			0.338609	−	0.940927i	$-0.390044\pi$
$521$	15.4578			0.677218			0.338609	+	0.940927i	$0.390044\pi$
$522$			10.1668i			0.444988i
$523$	30.2562			1.32301			0.661506	−	0.749940i	$-0.269918\pi$
$523$	30.2562			1.32301			0.661506	+	0.749940i	$0.269918\pi$
$524$	−18.9454			−0.827633
$525$		0			0
$526$			9.72989i			0.424243i
$527$			25.7848i			1.12321i
$528$			17.2063i			0.748809i
$529$	14.5536			0.632767
$530$	−36.4652			−1.58395
$531$		−	1.32053i		−	0.0573061i
$532$		0			0
$533$	6.00000	−	0.615897i	0.259889	−	0.0266775i
$534$	−24.9690			−1.08051
$535$			2.64106i			0.114183i
$536$	8.46524			0.365643
$537$	−15.8570			−0.684280
$538$			62.6694i			2.70187i
$539$		0			0
$540$			8.49394i			0.365521i
$541$		−	7.65544i		−	0.329133i	−0.986366	−	0.164566i	$-0.947377\pi$
$541$		−	7.65544i		−	0.329133i	0.986366	−	0.164566i	$-0.0526225\pi$
$542$	−5.51986			−0.237098
$543$	−12.0000			−0.514969
$544$			32.3071i			1.38515i
$545$	−17.9851			−0.770397
$546$		0			0
$547$	22.0660			0.943476			0.471738	−	0.881739i	$-0.343627\pi$
$547$	22.0660			0.943476			0.471738	+	0.881739i	$0.343627\pi$
$548$			9.38172i			0.400767i
$549$	−8.73635			−0.372858
$550$	−90.4119			−3.85517
$551$			25.5848i			1.08995i
$552$			4.71550i			0.200705i
$553$		0			0
$554$		−	27.4224i		−	1.16507i
$555$	−41.9851			−1.78217
$556$	50.2090			2.12934
$557$			7.30728i			0.309619i	0.987944	+	0.154810i	$0.0494764\pi$
$557$			7.30728i			0.309619i	−0.987944	+	0.154810i	$0.950524\pi$
$558$	13.4727			0.570345
$559$	−2.52731	−	24.6207i	−0.106894	−	1.04135i
$560$		0			0
$561$		−	22.0023i		−	0.928936i
$562$	48.7450			2.05618
$563$	39.4578			1.66295			0.831474	−	0.555564i	$-0.187498\pi$
$563$	39.4578			1.66295			0.831474	+	0.555564i	$0.187498\pi$
$564$		−	7.65959i		−	0.322527i
$565$			40.8589i			1.71895i
$566$			49.0272i			2.06077i
$567$		0			0
$568$	2.20036			0.0923250
$569$	15.3918			0.645256			0.322628	−	0.946526i	$-0.395434\pi$
$569$	15.3918			0.645256			0.322628	+	0.946526i	$0.395434\pi$
$570$			39.4270i			1.65142i
$571$	19.8570			0.830990			0.415495	−	0.909596i	$-0.363608\pi$
$571$	19.8570			0.830990			0.415495	+	0.909596i	$0.363608\pi$
$572$	46.7214	−	4.79593i	1.95352	−	0.200528i
$573$	−4.73635			−0.197864
$574$		0			0
$575$	48.1941			2.00983
$576$	10.6244			0.442682
$577$		−	25.3028i		−	1.05337i	−0.850061	−	0.526685i	$-0.823435\pi$
$577$		−	25.3028i		−	1.05337i	0.850061	−	0.526685i	$-0.176565\pi$
$578$			2.09002i			0.0869333i
$579$			19.3612i			0.804624i
$580$			41.3183i			1.71565i
$581$		0			0
$582$	−9.51986			−0.394611
$583$		−	26.7572i		−	1.10817i
$584$	−9.02481			−0.373449
$585$	−12.8644	+	1.32053i	−0.531879	+	0.0545971i
$586$	43.4491			1.79487
$587$			32.6327i			1.34689i	0.739236	+	0.673447i	$0.235187\pi$
$587$			32.6327i			1.34689i	−0.739236	+	0.673447i	$0.764813\pi$
$588$		0			0
$589$	33.9042			1.39700
$590$		−	9.89905i		−	0.407537i
$591$		−	4.66622i		−	0.191943i
$592$			36.6168i			1.50494i
$593$			11.9919i			0.492449i	0.969213	+	0.246224i	$0.0791900\pi$
$593$			11.9919i			0.492449i	−0.969213	+	0.246224i	$0.920810\pi$
$594$	−11.4963			−0.471698
$595$		0			0
$596$		−	16.6709i		−	0.682865i
$597$	10.5273			0.430854
$598$	−45.9379	+	4.71550i	−1.87854	+	0.192831i
$599$	−46.8024			−1.91229			−0.956147	−	0.292888i	$-0.905384\pi$
$599$	−46.8024			−1.91229			−0.956147	+	0.292888i	$0.905384\pi$
$600$			6.05160i			0.247056i
$601$	−18.2090			−0.742762			−0.371381	−	0.928481i	$-0.621116\pi$
$601$	−18.2090			−0.742762			−0.371381	+	0.928481i	$0.621116\pi$
$602$		0			0
$603$		−	11.0011i		−	0.448001i
$604$		−	21.4668i		−	0.873471i
$605$		−	69.0663i		−	2.80794i
$606$			5.28212i			0.214571i
$607$	2.25620			0.0915765			0.0457882	−	0.998951i	$-0.485420\pi$
$607$	2.25620			0.0915765			0.0457882	+	0.998951i	$0.485420\pi$
$608$	42.4801			1.72280
$609$		0			0
$610$	−65.4901			−2.65161
$611$	11.6008	−	1.19082i	0.469318	−	0.0481752i
$612$	−9.47269			−0.382911
$613$		−	27.2844i		−	1.10201i	−0.834503	−	0.551003i	$-0.814245\pi$
$613$		−	27.2844i		−	1.10201i	0.834503	−	0.551003i	$-0.185755\pi$
$614$	−5.47269			−0.220860
$615$	−6.00000			−0.241943
$616$		0			0
$617$		−	2.99753i		−	0.120676i	−0.998178	−	0.0603380i	$-0.980782\pi$
$617$		−	2.99753i		−	0.120676i	0.998178	−	0.0603380i	$-0.0192178\pi$
$618$		−	29.7957i		−	1.19856i
$619$		−	16.9879i		−	0.682800i	−0.939918	−	0.341400i	$-0.889099\pi$
$619$		−	16.9879i		−	0.682800i	0.939918	−	0.341400i	$-0.110901\pi$
$620$	54.7537			2.19896
$621$	6.12810			0.245912
$622$			14.5160i			0.582038i
$623$		0			0
$624$	1.15168	+	11.2196i	0.0461042	+	0.449143i
$625$	−2.47269			−0.0989077
$626$		−	55.8483i		−	2.23215i
$627$	−28.9305			−1.15537
$628$	9.47269			0.378002
$629$		−	46.8230i		−	1.86696i
$630$		0			0
$631$			27.7213i			1.10357i	0.833988	+	0.551783i	$0.186052\pi$
$631$			27.7213i			1.10357i	−0.833988	+	0.551783i	$0.813948\pi$
$632$			5.84873i			0.232650i
$633$	27.8570			1.10722
$634$	9.75248			0.387320
$635$		−	16.9879i		−	0.674143i
$636$	−11.5199			−0.456792
$637$		0			0
$638$	−55.9230			−2.21401
$639$		−	2.85951i		−	0.113120i
$640$	21.7053			0.857978
$641$	32.0660			1.26653			0.633266	−	0.773934i	$-0.281714\pi$
$641$	32.0660			1.26653			0.633266	+	0.773934i	$0.281714\pi$
$642$			1.53898i			0.0607386i
$643$		−	7.65544i		−	0.301901i	−0.988541	−	0.150951i	$-0.951767\pi$
$643$		−	7.65544i		−	0.301901i	0.988541	−	0.150951i	$-0.0482334\pi$
$644$		0			0
$645$			24.6207i			0.969441i
$646$	−43.9702			−1.72998
$647$	17.0546			0.670486			0.335243	−	0.942132i	$-0.391182\pi$
$647$	17.0546			0.670486			0.335243	+	0.942132i	$0.391182\pi$
$648$			0.769489i			0.0302284i
$649$	7.26365			0.285123
$650$	−58.9541	+	6.05160i	−2.31237	+	0.237363i
$651$		0			0
$652$			13.5436i			0.530409i
$653$	11.9851			0.469013			0.234507	−	0.972115i	$-0.424653\pi$
$653$	11.9851			0.469013			0.234507	+	0.972115i	$0.424653\pi$
$654$	−10.4801			−0.409806
$655$			28.6936i			1.12115i
$656$			5.23283i			0.204308i
$657$			11.7283i			0.457566i
$658$		0			0
$659$	2.92651			0.114001			0.0570004	−	0.998374i	$-0.481846\pi$
$659$	2.92651			0.114001			0.0570004	+	0.998374i	$0.481846\pi$
$660$	−46.7214			−1.81863
$661$			41.8312i			1.62705i	0.581533	+	0.813523i	$0.302453\pi$
$661$			41.8312i			1.62705i	−0.581533	+	0.813523i	$0.697547\pi$
$662$	−48.9305			−1.90174
$663$	−1.47269	−	14.3468i	−0.0571947	−	0.557184i
$664$	−0.998768			−0.0387597
$665$		0			0
$666$	−24.4652			−0.948009
$667$	29.8098			1.15424
$668$			26.3162i			1.01820i
$669$			3.80515i			0.147116i
$670$		−	82.4675i		−	3.18600i
$671$		−	48.0548i		−	1.85514i
$672$		0			0
$673$	33.1207			1.27671			0.638354	−	0.769743i	$-0.279616\pi$
$673$	33.1207			1.27671			0.638354	+	0.769743i	$0.279616\pi$
$674$			19.0935i			0.735453i
$675$	7.86445			0.302703
$676$	30.1442	−	6.25448i	1.15939	−	0.240557i
$677$	−20.0000			−0.768662			−0.384331	−	0.923195i	$-0.625568\pi$
$677$	−20.0000			−0.768662			−0.384331	+	0.923195i	$0.625568\pi$
$678$			23.8090i			0.914378i
$679$		0			0
$680$	−11.0397			−0.423354
$681$		−	20.6817i		−	0.792525i
$682$			74.1074i			2.83772i
$683$			25.5664i			0.978271i	0.872208	+	0.489135i	$0.162688\pi$
$683$			25.5664i			0.978271i	−0.872208	+	0.489135i	$0.837312\pi$
$684$			12.4555i			0.476249i
$685$	14.2090			0.542900
$686$		0			0
$687$		−	18.1745i		−	0.693402i
$688$	21.4727			0.818639
$689$	−1.79096	−	17.4473i	−0.0682301	−	0.664691i
$690$	45.9379			1.74883
$691$		−	19.1160i		−	0.727208i	−0.931554	−	0.363604i	$-0.881546\pi$
$691$		−	19.1160i		−	0.727208i	0.931554	−	0.363604i	$-0.118454\pi$
$692$	−5.98510			−0.227519
$693$		0			0
$694$			18.2591i			0.693107i
$695$		−	76.0438i		−	2.88451i
$696$			3.74314i			0.141883i
$697$		−	6.69138i		−	0.253454i
$698$	57.4429			2.17425
$699$	−14.3371			−0.542281
$700$		0			0
$701$	−11.8098			−0.446051			−0.223026	−	0.974813i	$-0.571593\pi$
$701$	−11.8098			−0.446051			−0.223026	+	0.974813i	$0.571593\pi$
$702$	−7.49628	+	0.769489i	−0.282929	+	0.0290425i
$703$	−61.5670			−2.32204
$704$			58.4401i			2.20254i
$705$	−11.6008			−0.436911
$706$	63.4665			2.38859
$707$		0			0
$708$		−	3.12724i		−	0.117529i
$709$		−	10.2965i		−	0.386693i	−0.981131	−	0.193347i	$-0.938066\pi$
$709$		−	10.2965i		−	0.386693i	0.981131	−	0.193347i	$-0.0619342\pi$
$710$		−	21.4356i		−	0.804465i
$711$	7.60080			0.285052
$712$	−9.19291			−0.344519
$713$		−	39.5030i		−	1.47940i
$714$		0			0
$715$	−7.26365	−	70.7617i	−0.271645	−	2.64634i
$716$	−37.5521			−1.40339
$717$		−	0.486183i		−	0.0181569i
$718$	−5.97642			−0.223038
$719$	30.9454			1.15407			0.577034	−	0.816720i	$-0.304210\pi$
$719$	30.9454			1.15407			0.577034	+	0.816720i	$0.304210\pi$
$720$		−	11.2196i		−	0.418129i
$721$		0			0
$722$			18.1055i			0.673818i
$723$			10.2739i			0.382092i
$724$	−28.4181			−1.05615
$725$	38.2562			1.42080
$726$		−	40.2458i		−	1.49366i
$727$	19.0397			0.706144			0.353072	−	0.935596i	$-0.385137\pi$
$727$	19.0397			0.706144			0.353072	+	0.935596i	$0.385137\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$			87.9188i			3.25402i
$731$	−27.4578			−1.01556
$732$	−20.6892			−0.764694
$733$			42.7502i			1.57901i	0.613742	+	0.789506i	$0.289663\pi$
$733$			42.7502i			1.57901i	−0.613742	+	0.789506i	$0.710337\pi$
$734$			4.71550i			0.174052i
$735$		0			0
$736$		−	49.4952i		−	1.82442i
$737$	60.5124			2.22900
$738$	−3.49628			−0.128700
$739$		−	36.7860i		−	1.35319i	−0.736354	−	0.676597i	$-0.763454\pi$
$739$		−	36.7860i		−	1.35319i	0.736354	−	0.676597i	$-0.236546\pi$
$740$	−99.4280			−3.65505
$741$	−18.8644	+	1.93643i	−0.693003	+	0.0711364i
$742$		0			0
$743$		−	16.7694i		−	0.615211i	−0.951514	−	0.307605i	$-0.900472\pi$
$743$		−	16.7694i		−	0.615211i	0.951514	−	0.307605i	$-0.0995276\pi$
$744$	4.96029			0.181853
$745$	−25.2488			−0.925043
$746$			45.4138i			1.66272i
$747$			1.29796i			0.0474900i
$748$		−	52.1052i		−	1.90515i
$749$		0			0
$750$	21.4727			0.784072
$751$	−7.91906			−0.288971			−0.144485	−	0.989507i	$-0.546153\pi$
$751$	−7.91906			−0.288971			−0.144485	+	0.989507i	$0.546153\pi$
$752$			10.1175i			0.368947i
$753$	12.0000			0.437304
$754$	−36.4652	+	3.74314i	−1.32799	+	0.136317i
$755$	−32.5124			−1.18325
$756$		0			0
$757$	15.6629			0.569276			0.284638	−	0.958635i	$-0.408127\pi$
$757$	15.6629			0.569276			0.284638	+	0.958635i	$0.408127\pi$
$758$	16.0000			0.581146
$759$			33.7080i			1.22352i
$760$			14.5160i			0.526550i
$761$			9.52832i			0.345401i	0.984974	+	0.172701i	$0.0552493\pi$
$761$			9.52832i			0.345401i	−0.984974	+	0.172701i	$0.944751\pi$
$762$		−	9.89905i		−	0.358605i
$763$		0			0
$764$	−11.2165			−0.405798
$765$			14.3468i			0.518710i
$766$	44.6979			1.61500
$767$	4.73635	−	0.486183i	0.171020	−	0.0175551i
$768$	−8.60080			−0.310354
$769$		−	19.3386i		−	0.697369i	−0.937240	−	0.348684i	$-0.886628\pi$
$769$		−	19.3386i		−	0.697369i	0.937240	−	0.348684i	$-0.113372\pi$
$770$		0			0
$771$	−13.4727			−0.485207
$772$			45.8507i			1.65020i
$773$			3.34154i			0.120187i	0.998193	+	0.0600933i	$0.0191398\pi$
$773$			3.34154i			0.120187i	−0.998193	+	0.0600933i	$0.980860\pi$
$774$			14.3468i			0.515686i
$775$		−	50.6959i		−	1.82105i
$776$	−3.50496			−0.125821
$777$		0			0
$778$			17.8222i			0.638958i
$779$	−8.79841			−0.315236
$780$	−30.4652	+	3.12724i	−1.09083	+	0.111973i
$781$	15.7289			0.562824
$782$			51.2314i			1.83203i
$783$	4.86445			0.173841
$784$		0			0
$785$		−	14.3468i		−	0.512060i
$786$			16.7201i			0.596388i
$787$		−	42.5275i		−	1.51594i	−0.652287	−	0.757972i	$-0.726190\pi$
$787$		−	42.5275i		−	1.51594i	0.652287	−	0.757972i	$-0.273810\pi$
$788$		−	11.0504i		−	0.393655i
$789$	4.65541			0.165737
$790$	56.9777			2.02717
$791$		0			0
$792$	−4.23262			−0.150400
$793$	−3.21649	−	31.3347i	−0.114221	−	1.11273i
$794$	−39.5050			−1.40198
$795$			17.4473i			0.618793i
$796$	24.9305			0.883638
$797$	−33.5670			−1.18900			−0.594502	−	0.804094i	$-0.702651\pi$
$797$	−33.5670			−1.18900			−0.594502	+	0.804094i	$0.702651\pi$
$798$		0			0
$799$		−	12.9376i		−	0.457698i
$800$		−	63.5193i		−	2.24575i
$801$			11.9468i			0.422119i
$802$	−62.1706			−2.19532
$803$	−64.5124			−2.27659
$804$		−	26.0526i		−	0.918804i
$805$		0			0
$806$	4.96029	+	48.3226i	0.174719	+	1.70209i
$807$	29.9851			1.05553
$808$			1.94473i			0.0684155i
$809$	21.2825			0.748254			0.374127	−	0.927378i	$-0.377942\pi$
$809$	21.2825			0.748254			0.374127	+	0.927378i	$0.377942\pi$
$810$	7.49628			0.263392
$811$		−	24.3756i		−	0.855942i	−0.903792	−	0.427971i	$-0.859228\pi$
$811$		−	24.3756i		−	0.855942i	0.903792	−	0.427971i	$-0.140772\pi$
$812$		0			0
$813$			2.64106i			0.0926259i
$814$		−	134.573i		−	4.71677i
$815$	20.5124			0.718518
$816$	12.5124			0.438022
$817$			36.1039i			1.26312i
$818$	55.5050			1.94069
$819$		0			0
$820$	−14.2090			−0.496201
$821$			28.0777i			0.979920i	0.871745	+	0.489960i	$0.162989\pi$
$821$			28.0777i			0.979920i	−0.871745	+	0.489960i	$0.837011\pi$
$822$	8.27979			0.288791
$823$	48.5124			1.69104			0.845518	−	0.533947i	$-0.179292\pi$
$823$	48.5124			1.69104			0.845518	+	0.533947i	$0.179292\pi$
$824$		−	10.9700i		−	0.382158i
$825$			43.2589i			1.50608i
$826$		0			0
$827$			32.2578i			1.12171i	0.827913	+	0.560856i	$0.189528\pi$
$827$			32.2578i			1.12171i	−0.827913	+	0.560856i	$0.810472\pi$
$828$	14.5124			0.504341
$829$	23.7761			0.825777			0.412888	−	0.910782i	$-0.364520\pi$
$829$	23.7761			0.825777			0.412888	+	0.910782i	$0.364520\pi$
$830$			9.72989i			0.337729i
$831$	−13.1207			−0.455150
$832$	3.91161	+	38.1065i	0.135611	+	1.32111i
$833$		0			0
$834$		−	44.3117i		−	1.53439i
$835$	39.8570			1.37931
$836$	−68.5124			−2.36955
$837$		−	6.44621i		−	0.222814i
$838$			8.36007i			0.288794i
$839$		−	12.5894i		−	0.434634i	−0.976101	−	0.217317i	$-0.930269\pi$
$839$		−	12.5894i		−	0.434634i	0.976101	−	0.217317i	$-0.0697305\pi$
$840$		0			0
$841$	−5.33714			−0.184039
$842$	75.9702			2.61811
$843$		−	23.3228i		−	0.803279i
$844$	65.9702			2.27079
$845$	−9.47269	−	45.6548i	−0.325871	−	1.57057i
$846$	−6.75993			−0.232411
$847$		0			0
$848$	15.2165			0.522536
$849$	23.4578			0.805069
$850$			65.7473i			2.25512i
$851$			71.7341i			2.45901i
$852$		−	6.77181i		−	0.231998i
$853$			17.9377i			0.614174i	0.951681	+	0.307087i	$0.0993543\pi$
$853$			17.9377i			0.614174i	−0.951681	+	0.307087i	$0.900646\pi$
$854$		0			0
$855$	18.8644			0.645151
$856$			0.566610i			0.0193663i
$857$	53.9851			1.84410			0.922048	−	0.387076i	$-0.126515\pi$
$857$	53.9851			1.84410			0.922048	+	0.387076i	$0.126515\pi$
$858$	−4.23262	−	41.2337i	−0.144499	−	1.40770i
$859$	−42.4032			−1.44678			−0.723389	−	0.690441i	$-0.757417\pi$
$859$	−42.4032			−1.44678			−0.723389	+	0.690441i	$0.757417\pi$
$860$			58.3062i			1.98822i
$861$		0			0
$862$	−12.9690			−0.441725
$863$		−	5.76830i		−	0.196355i	−0.995169	−	0.0981776i	$-0.968699\pi$
$863$		−	5.76830i		−	0.196355i	0.995169	−	0.0981776i	$-0.0313013\pi$
$864$		−	8.07676i		−	0.274777i
$865$			9.06470i			0.308209i
$866$		−	1.53898i		−	0.0522966i
$867$	1.00000			0.0339618
$868$		0			0
$869$			41.8087i			1.41826i
$870$	36.4652			1.23629
$871$	39.4578	−	4.05032i	1.33698	−	0.137240i
$872$	−3.85851			−0.130666
$873$			4.55492i			0.154161i
$874$	67.3635			2.27860
$875$		0			0
$876$			27.7747i			0.938420i
$877$			9.06470i			0.306093i	0.988219	+	0.153047i	$0.0489085\pi$
$877$			9.06470i			0.306093i	−0.988219	+	0.153047i	$0.951092\pi$
$878$		−	19.2315i		−	0.649031i
$879$		−	20.7889i		−	0.701191i
$880$	61.7140			2.08038
$881$	−24.9305			−0.839929			−0.419965	−	0.907540i	$-0.637958\pi$
$881$	−24.9305			−0.839929			−0.419965	+	0.907540i	$0.637958\pi$
$882$		0			0
$883$	40.1941			1.35264			0.676320	−	0.736608i	$-0.263574\pi$
$883$	40.1941			1.35264			0.676320	+	0.736608i	$0.263574\pi$
$884$	−3.48759	−	33.9758i	−0.117300	−	1.14273i
$885$	−4.73635			−0.159211
$886$			63.5037i			2.13345i
$887$	26.4032			0.886532			0.443266	−	0.896390i	$-0.353820\pi$
$887$	26.4032			0.886532			0.443266	+	0.896390i	$0.353820\pi$
$888$	−9.00745			−0.302270
$889$		0			0
$890$			89.5563i			3.00193i
$891$			5.50056i			0.184276i
$892$			9.01126i			0.301719i
$893$	−17.0114			−0.569266
$894$	−14.7128			−0.492068
$895$			56.8744i			1.90110i
$896$		0			0
$897$	2.25620	+	21.9797i	0.0753324	+	0.733880i
$898$	46.7301			1.55940
$899$		−	31.3573i		−	1.04582i
$900$	18.6244			0.620813
$901$	−19.4578			−0.648233
$902$		−	19.2315i		−	0.640338i
$903$		0			0
$904$			8.76583i			0.291547i
$905$			43.0405i			1.43071i
$906$	−18.9454			−0.629418
$907$	−33.5859			−1.11520			−0.557601	−	0.830109i	$-0.688278\pi$
$907$	−33.5859			−1.11520			−0.557601	+	0.830109i	$0.688278\pi$
$908$		−	48.9779i		−	1.62539i
$909$	2.52731			0.0838255
$910$		0			0
$911$	−49.5859			−1.64285			−0.821427	−	0.570314i	$-0.806822\pi$
$911$	−49.5859			−1.64285			−0.821427	+	0.570314i	$0.806822\pi$
$912$		−	16.4524i		−	0.544794i
$913$	−7.13953			−0.236284
$914$	59.4106			1.96513
$915$			31.3347i			1.03589i
$916$		−	43.0405i		−	1.42210i
$917$		0			0
$918$			8.36007i			0.275923i
$919$	34.1792			1.12747			0.563735	−	0.825956i	$-0.309364\pi$
$919$	34.1792			1.12747			0.563735	+	0.825956i	$0.309364\pi$
$920$	16.9131			0.557609
$921$			2.61849i			0.0862822i
$922$	−32.0087			−1.05415
$923$	10.2562	−	1.05279i	0.337587	−	0.0346531i
$924$		0			0
$925$			92.0593i			3.02689i
$926$	−38.9926			−1.28137
$927$	−14.2562			−0.468235
$928$		−	39.2890i		−	1.28972i
$929$		−	18.1561i		−	0.595683i	−0.954615	−	0.297842i	$-0.903733\pi$
$929$		−	18.1561i		−	0.595683i	0.954615	−	0.297842i	$-0.0962667\pi$
$930$		−	48.3226i		−	1.58456i
$931$		0			0
$932$	−33.9528			−1.11216
$933$	6.94539			0.227382
$934$		−	57.3873i		−	1.87777i
$935$	−78.9156			−2.58082
$936$	−2.75993	+	0.283305i	−0.0902111	+	0.00926012i
$937$	−5.27855			−0.172443			−0.0862214	−	0.996276i	$-0.527479\pi$
$937$	−5.27855			−0.172443			−0.0862214	+	0.996276i	$0.527479\pi$
$938$		0			0
$939$	−26.7214			−0.872021
$940$	−27.4727			−0.896060
$941$			8.82369i			0.287644i	0.989604	+	0.143822i	$0.0459393\pi$
$941$			8.82369i			0.287644i	−0.989604	+	0.143822i	$0.954061\pi$
$942$		−	8.36007i		−	0.272386i
$943$			10.2514i			0.333830i
$944$			4.13075i			0.134444i
$945$		0			0
$946$	−78.9156			−2.56577
$947$			15.9745i			0.519102i	0.965729	+	0.259551i	$0.0835746\pi$
$947$			15.9745i			0.519102i	−0.965729	+	0.259551i	$0.916425\pi$
$948$	18.0000			0.584613
$949$	−42.0660	+	4.31806i	−1.36552	+	0.140170i
$950$	86.4503			2.80482
$951$		−	4.66622i		−	0.151313i
$952$		0			0
$953$	20.6082			0.667567			0.333783	−	0.942650i	$-0.391675\pi$
$953$	20.6082			0.667567			0.333783	+	0.942650i	$0.391675\pi$
$954$			10.1668i			0.329162i
$955$			16.9879i			0.549715i
$956$		−	1.15137i		−	0.0372379i
$957$			26.7572i			0.864938i
$958$	−80.2500			−2.59276
$959$		0			0
$960$		−	38.1065i		−	1.22988i
$961$	−10.5536			−0.340440
$962$	−9.00745	−	87.7496i	−0.290412	−	2.82916i
$963$	0.736347			0.0237284
$964$			24.3304i			0.783631i
$965$	69.4429			2.23545
$966$		0			0
$967$		−	8.62781i		−	0.277452i	−0.990331	−	0.138726i	$-0.955699\pi$
$967$		−	8.62781i		−	0.277452i	0.990331	−	0.138726i	$-0.0443007\pi$
$968$		−	14.8174i		−	0.476250i
$969$			21.0382i			0.675844i
$970$			34.1449i			1.09633i
$971$	−33.5670			−1.07722			−0.538608	−	0.842556i	$-0.681050\pi$
$971$	−33.5670			−1.07722			−0.538608	+	0.842556i	$0.681050\pi$
$972$	2.36817			0.0759592
$973$		0			0
$974$	71.0099			2.27530
$975$	2.89548	+	28.2075i	0.0927296	+	0.903361i
$976$	27.3282			0.874754
$977$			44.0932i			1.41067i	0.708875	+	0.705334i	$0.249203\pi$
$977$			44.0932i			1.41067i	−0.708875	+	0.705334i	$0.750797\pi$
$978$	11.9528			0.382210
$979$	−65.7140			−2.10023
$980$		0			0
$981$			5.01438i			0.160097i
$982$			31.9013i			1.01801i
$983$			43.9015i			1.40024i	0.714025	+	0.700120i	$0.246870\pi$
$983$			43.9015i			1.40024i	−0.714025	+	0.700120i	$0.753130\pi$
$984$	−1.28724			−0.0410356
$985$	−16.7363			−0.533264
$986$			40.6671i			1.29511i
$987$		0			0
$988$	−44.6743	+	4.58579i	−1.42128	+	0.145893i
$989$	42.0660			1.33762
$990$			41.2337i			1.31049i
$991$	55.0397			1.74839			0.874197	−	0.485571i	$-0.161388\pi$
$991$	55.0397			1.74839			0.874197	+	0.485571i	$0.161388\pi$
$992$	−52.0645			−1.65305
$993$			23.4115i			0.742942i
$994$		0			0
$995$		−	37.7583i		−	1.19702i
$996$			3.07380i			0.0973971i
$997$	−55.4578			−1.75637			−0.878183	−	0.478325i	$-0.841244\pi$
$997$	−55.4578			−1.75637			−0.878183	+	0.478325i	$0.841244\pi$
$998$	50.9454			1.61265
$999$			11.7058i			0.370354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.c.g.883.2	✓	6
7.6	odd	2		1911.2.c.i.883.2	yes	6
13.12	even	2	inner	1911.2.c.g.883.5	yes	6
91.90	odd	2		1911.2.c.i.883.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.c.g.883.2	✓	6	1.1	even	1	trivial
1911.2.c.g.883.5	yes	6	13.12	even	2	inner
1911.2.c.i.883.2	yes	6	7.6	odd	2
1911.2.c.i.883.5	yes	6	91.90	odd	2

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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.09002i q^{2} -1.00000 q^{3} -2.36817 q^{4} +3.58670i q^{5} +2.09002i q^{6} +0.769489i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.09002i q^{2} -1.00000 q^{3} -2.36817 q^{4} +3.58670i q^{5} +2.09002i q^{6} +0.769489i q^{8} +1.00000 q^{9} +7.49628 q^{10} +5.50056i q^{11} +2.36817 q^{12} +(0.368173 + 3.58670i) q^{13} -3.58670i q^{15} -3.12810 q^{16} +4.00000 q^{17} -2.09002i q^{18} -5.25955i q^{19} -8.49394i q^{20} +11.4963 q^{22} -6.12810 q^{23} -0.769489i q^{24} -7.86445 q^{25} +(7.49628 - 0.769489i) q^{26} -1.00000 q^{27} -4.86445 q^{29} -7.49628 q^{30} +6.44621i q^{31} +8.07676i q^{32} -5.50056i q^{33} -8.36007i q^{34} -2.36817 q^{36} -11.7058i q^{37} -10.9926 q^{38} +(-0.368173 - 3.58670i) q^{39} -2.75993 q^{40} -1.67284i q^{41} -6.86445 q^{43} -13.0263i q^{44} +3.58670i q^{45} +12.8078i q^{46} -3.23439i q^{47} +3.12810 q^{48} +16.4368i q^{50} -4.00000 q^{51} +(-0.871898 - 8.49394i) q^{52} -4.86445 q^{53} +2.09002i q^{54} -19.7289 q^{55} +5.25955i q^{57} +10.1668i q^{58} -1.32053i q^{59} +8.49394i q^{60} -8.73635 q^{61} +13.4727 q^{62} +10.6244 q^{64} +(-12.8644 + 1.32053i) q^{65} -11.4963 q^{66} -11.0011i q^{67} -9.47269 q^{68} +6.12810 q^{69} -2.85951i q^{71} +0.769489i q^{72} +11.7283i q^{73} -24.4652 q^{74} +7.86445 q^{75} +12.4555i q^{76} +(-7.49628 + 0.769489i) q^{78} +7.60080 q^{79} -11.2196i q^{80} +1.00000 q^{81} -3.49628 q^{82} +1.29796i q^{83} +14.3468i q^{85} +14.3468i q^{86} +4.86445 q^{87} -4.23262 q^{88} +11.9468i q^{89} +7.49628 q^{90} +14.5124 q^{92} -6.44621i q^{93} -6.75993 q^{94} +18.8644 q^{95} -8.07676i q^{96} +4.55492i q^{97} +5.50056i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} - 12 q^{4} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^3 - 12 * q^4 + 6 * q^9	\( 6 q - 6 q^{3} - 12 q^{4} + 6 q^{9} + 4 q^{10} + 12 q^{12} + 20 q^{16} + 24 q^{17} + 28 q^{22} + 2 q^{23} - 4 q^{25} + 4 q^{26} - 6 q^{27} + 14 q^{29} - 4 q^{30} - 12 q^{36} + 16 q^{38} + 20 q^{40} + 2 q^{43} - 20 q^{48} - 24 q^{51} - 44 q^{52} + 14 q^{53} - 32 q^{55} - 48 q^{61} + 72 q^{62} - 16 q^{64} - 34 q^{65} - 28 q^{66} - 48 q^{68} - 2 q^{69} - 56 q^{74} + 4 q^{75} - 4 q^{78} - 2 q^{79} + 6 q^{81} + 20 q^{82} - 14 q^{87} + 20 q^{88} + 4 q^{90} - 68 q^{92} - 4 q^{94} + 70 q^{95}+O(q^{100}) \) 6 * q - 6 * q^3 - 12 * q^4 + 6 * q^9 + 4 * q^10 + 12 * q^12 + 20 * q^16 + 24 * q^17 + 28 * q^22 + 2 * q^23 - 4 * q^25 + 4 * q^26 - 6 * q^27 + 14 * q^29 - 4 * q^30 - 12 * q^36 + 16 * q^38 + 20 * q^40 + 2 * q^43 - 20 * q^48 - 24 * q^51 - 44 * q^52 + 14 * q^53 - 32 * q^55 - 48 * q^61 + 72 * q^62 - 16 * q^64 - 34 * q^65 - 28 * q^66 - 48 * q^68 - 2 * q^69 - 56 * q^74 + 4 * q^75 - 4 * q^78 - 2 * q^79 + 6 * q^81 + 20 * q^82 - 14 * q^87 + 20 * q^88 + 4 * q^90 - 68 * q^92 - 4 * q^94 + 70 * q^95

Introduction

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