LMFDB - Embedded newform 3234.2.e.a.2155.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.16
Root			$0.500000 - 3.43554i$ of defining polynomial
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.a.2155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +4.30156i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +4.30156i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} -4.30156 q^{10} +(2.11424 + 2.55539i) q^{11} -1.00000i q^{12} +1.00074 q^{13} -4.30156 q^{15} +1.00000 q^{16} +3.33708 q^{17} -1.00000i q^{18} -3.23111 q^{19} -4.30156i q^{20} +(-2.55539 + 2.11424i) q^{22} -5.72998 q^{23} +1.00000 q^{24} -13.5035 q^{25} +1.00074i q^{26} -1.00000i q^{27} -7.74872i q^{29} -4.30156i q^{30} +3.20322i q^{31} +1.00000i q^{32} +(-2.55539 + 2.11424i) q^{33} +3.33708i q^{34} +1.00000 q^{36} -2.52944 q^{37} -3.23111i q^{38} +1.00074i q^{39} +4.30156 q^{40} +1.45111 q^{41} +4.14572i q^{43} +(-2.11424 - 2.55539i) q^{44} -4.30156i q^{45} -5.72998i q^{46} +3.20101i q^{47} +1.00000i q^{48} -13.5035i q^{50} +3.33708i q^{51} -1.00074 q^{52} -11.3155 q^{53} +1.00000 q^{54} +(-10.9922 + 9.09452i) q^{55} -3.23111i q^{57} +7.74872 q^{58} -3.44231i q^{59} +4.30156 q^{60} -14.8504 q^{61} -3.20322 q^{62} -1.00000 q^{64} +4.30476i q^{65} +(-2.11424 - 2.55539i) q^{66} -0.330392 q^{67} -3.33708 q^{68} -5.72998i q^{69} +2.84974 q^{71} +1.00000i q^{72} +14.8958 q^{73} -2.52944i q^{74} -13.5035i q^{75} +3.23111 q^{76} -1.00074 q^{78} +16.0923i q^{79} +4.30156i q^{80} +1.00000 q^{81} +1.45111i q^{82} +1.75062 q^{83} +14.3547i q^{85} -4.14572 q^{86} +7.74872 q^{87} +(2.55539 - 2.11424i) q^{88} -2.78460i q^{89} +4.30156 q^{90} +5.72998 q^{92} -3.20322 q^{93} -3.20101 q^{94} -13.8988i q^{95} -1.00000 q^{96} +12.3347i q^{97} +(-2.11424 - 2.55539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 16 * q^6 - 16 * q^9	$ 16 q - 16 q^{4} - 16 q^{6} - 16 q^{9} - 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} + 20 q^{19} + 2 q^{22} + 8 q^{23} + 16 q^{24} - 20 q^{25} + 2 q^{33} + 16 q^{36} - 28 q^{37} + 4 q^{40} + 32 q^{41} - 8 q^{44} + 16 q^{54} - 14 q^{55} + 4 q^{60} - 56 q^{61} - 8 q^{62} - 16 q^{64} - 8 q^{66} + 32 q^{67} - 56 q^{71} + 88 q^{73} - 20 q^{76} + 16 q^{81} + 8 q^{83} + 24 q^{86} - 2 q^{88} + 4 q^{90} - 8 q^{92} - 8 q^{93} - 28 q^{94} - 16 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 16 * q^6 - 16 * q^9 - 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 + 20 * q^19 + 2 * q^22 + 8 * q^23 + 16 * q^24 - 20 * q^25 + 2 * q^33 + 16 * q^36 - 28 * q^37 + 4 * q^40 + 32 * q^41 - 8 * q^44 + 16 * q^54 - 14 * q^55 + 4 * q^60 - 56 * q^61 - 8 * q^62 - 16 * q^64 - 8 * q^66 + 32 * q^67 - 56 * q^71 + 88 * q^73 - 20 * q^76 + 16 * q^81 + 8 * q^83 + 24 * q^86 - 2 * q^88 + 4 * q^90 - 8 * q^92 - 8 * q^93 - 28 * q^94 - 16 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$			4.30156i			1.92372i	0.273546	+	0.961859i	$0.411803\pi$
$5$			4.30156i			1.92372i	−0.273546	+	0.961859i	$0.588197\pi$
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−4.30156			−1.36027
$11$	2.11424	+	2.55539i	0.637466	+	0.770478i
$11$	2.11424	+	2.55539i	0.637466	+	0.770478i
$12$		−	1.00000i		−	0.288675i
$13$	1.00074			0.277556			0.138778	−	0.990324i	$-0.455683\pi$
$13$	1.00074			0.277556			0.138778	+	0.990324i	$0.455683\pi$
$14$		0			0
$15$	−4.30156			−1.11066
$16$	1.00000			0.250000
$17$	3.33708			0.809361			0.404681	−	0.914458i	$-0.367383\pi$
$17$	3.33708			0.809361			0.404681	+	0.914458i	$0.367383\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−3.23111			−0.741266			−0.370633	−	0.928779i	$-0.620859\pi$
$19$	−3.23111			−0.741266			−0.370633	+	0.928779i	$0.620859\pi$
$20$		−	4.30156i		−	0.961859i
$21$		0			0
$22$	−2.55539	+	2.11424i	−0.544810	+	0.450757i
$23$	−5.72998			−1.19478			−0.597392	−	0.801950i	$-0.703796\pi$
$23$	−5.72998			−1.19478			−0.597392	+	0.801950i	$0.703796\pi$
$24$	1.00000			0.204124
$25$	−13.5035			−2.70069
$26$			1.00074i			0.196262i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	7.74872i		−	1.43890i	−0.694544	−	0.719450i	$-0.744394\pi$
$29$		−	7.74872i		−	1.43890i	0.694544	−	0.719450i	$-0.255606\pi$
$30$		−	4.30156i		−	0.785355i
$31$			3.20322i			0.575315i	0.957733	+	0.287657i	$0.0928764\pi$
$31$			3.20322i			0.575315i	−0.957733	+	0.287657i	$0.907124\pi$
$32$			1.00000i			0.176777i
$33$	−2.55539	+	2.11424i	−0.444836	+	0.368041i
$34$			3.33708i			0.572305i
$35$		0			0
$36$	1.00000			0.166667
$37$	−2.52944			−0.415837			−0.207918	−	0.978146i	$-0.566669\pi$
$37$	−2.52944			−0.415837			−0.207918	+	0.978146i	$0.566669\pi$
$38$		−	3.23111i		−	0.524154i
$39$			1.00074i			0.160247i
$40$	4.30156			0.680137
$41$	1.45111			0.226625			0.113313	−	0.993559i	$-0.463854\pi$
$41$	1.45111			0.226625			0.113313	+	0.993559i	$0.463854\pi$
$42$		0			0
$43$			4.14572i			0.632216i	0.948723	+	0.316108i	$0.102376\pi$
$43$			4.14572i			0.632216i	−0.948723	+	0.316108i	$0.897624\pi$
$44$	−2.11424	−	2.55539i	−0.318733	−	0.385239i
$45$		−	4.30156i		−	0.641239i
$46$		−	5.72998i		−	0.844840i
$47$			3.20101i			0.466915i	0.972367	+	0.233458i	$0.0750040\pi$
$47$			3.20101i			0.466915i	−0.972367	+	0.233458i	$0.924996\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$		−	13.5035i		−	1.90968i
$51$			3.33708i			0.467285i
$52$	−1.00074			−0.138778
$53$	−11.3155			−1.55430			−0.777150	−	0.629315i	$-0.783336\pi$
$53$	−11.3155			−1.55430			−0.777150	+	0.629315i	$0.783336\pi$
$54$	1.00000			0.136083
$55$	−10.9922	+	9.09452i	−1.48218	+	1.22631i
$56$		0			0
$57$		−	3.23111i		−	0.427970i
$58$	7.74872			1.01746
$59$		−	3.44231i		−	0.448151i	−0.974572	−	0.224075i	$-0.928064\pi$
$59$		−	3.44231i		−	0.448151i	0.974572	−	0.224075i	$-0.0719362\pi$
$60$	4.30156			0.555330
$61$	−14.8504			−1.90140			−0.950702	−	0.310106i	$-0.899635\pi$
$61$	−14.8504			−1.90140			−0.950702	+	0.310106i	$0.899635\pi$
$62$	−3.20322			−0.406809
$63$		0			0
$64$	−1.00000			−0.125000
$65$			4.30476i			0.533940i
$66$	−2.11424	−	2.55539i	−0.260245	−	0.314546i
$67$	−0.330392			−0.0403638			−0.0201819	−	0.999796i	$-0.506425\pi$
$67$	−0.330392			−0.0403638			−0.0201819	+	0.999796i	$0.506425\pi$
$68$	−3.33708			−0.404681
$69$		−	5.72998i		−	0.689809i
$70$		0			0
$71$	2.84974			0.338201			0.169101	−	0.985599i	$-0.445914\pi$
$71$	2.84974			0.338201			0.169101	+	0.985599i	$0.445914\pi$
$72$			1.00000i			0.117851i
$73$	14.8958			1.74342			0.871710	−	0.490022i	$-0.163011\pi$
$73$	14.8958			1.74342			0.871710	+	0.490022i	$0.163011\pi$
$74$		−	2.52944i		−	0.294041i
$75$		−	13.5035i		−	1.55924i
$76$	3.23111			0.370633
$77$		0			0
$78$	−1.00074			−0.113312
$79$			16.0923i			1.81052i	0.424855	+	0.905261i	$0.360325\pi$
$79$			16.0923i			1.81052i	−0.424855	+	0.905261i	$0.639675\pi$
$80$			4.30156i			0.480929i
$81$	1.00000			0.111111
$82$			1.45111i			0.160248i
$83$	1.75062			0.192155			0.0960777	−	0.995374i	$-0.469370\pi$
$83$	1.75062			0.192155			0.0960777	+	0.995374i	$0.469370\pi$
$84$		0			0
$85$			14.3547i			1.55698i
$86$	−4.14572			−0.447044
$87$	7.74872			0.830750
$88$	2.55539	−	2.11424i	0.272405	−	0.225378i
$89$		−	2.78460i		−	0.295167i	−0.989050	−	0.147583i	$-0.952851\pi$
$89$		−	2.78460i		−	0.295167i	0.989050	−	0.147583i	$-0.0471494\pi$
$90$	4.30156			0.453425
$91$		0			0
$92$	5.72998			0.597392
$93$	−3.20322			−0.332158
$94$	−3.20101			−0.330159
$95$		−	13.8988i		−	1.42599i
$96$	−1.00000			−0.102062
$97$			12.3347i			1.25240i	0.779661	+	0.626201i	$0.215391\pi$
$97$			12.3347i			1.25240i	−0.779661	+	0.626201i	$0.784609\pi$
$98$		0			0
$99$	−2.11424	−	2.55539i	−0.212489	−	0.256826i
$100$	13.5035			1.35035
$101$	−0.0562448			−0.00559657			−0.00279828	−	0.999996i	$-0.500891\pi$
$101$	−0.0562448			−0.00559657			−0.00279828	+	0.999996i	$0.500891\pi$
$102$	−3.33708			−0.330420
$103$		−	14.7949i		−	1.45779i	−0.684627	−	0.728893i	$-0.740035\pi$
$103$		−	14.7949i		−	1.45779i	0.684627	−	0.728893i	$-0.259965\pi$
$104$		−	1.00074i		−	0.0981309i
$105$		0			0
$106$		−	11.3155i		−	1.09906i
$107$		−	10.6139i		−	1.02608i	−0.858364	−	0.513042i	$-0.828519\pi$
$107$		−	10.6139i		−	1.02608i	0.858364	−	0.513042i	$-0.171481\pi$
$108$			1.00000i			0.0962250i
$109$		−	0.348204i		−	0.0333519i	−0.999861	−	0.0166759i	$-0.994692\pi$
$109$		−	0.348204i		−	0.0333519i	0.999861	−	0.0166759i	$-0.00530836\pi$
$110$	−9.09452	−	10.9922i	−0.867129	−	1.04806i
$111$		−	2.52944i		−	0.240084i
$112$		0			0
$113$	−18.9549			−1.78313			−0.891564	−	0.452895i	$-0.850391\pi$
$113$	−18.9549			−1.78313			−0.891564	+	0.452895i	$0.850391\pi$
$114$	3.23111			0.302621
$115$		−	24.6479i		−	2.29843i
$116$			7.74872i			0.719450i
$117$	−1.00074			−0.0925187
$118$	3.44231			0.316890
$119$		0			0
$120$			4.30156i			0.392677i
$121$	−2.06001	+	10.8054i	−0.187273	+	0.982308i
$122$		−	14.8504i		−	1.34450i
$123$			1.45111i			0.130842i
$124$		−	3.20322i		−	0.287657i
$125$		−	36.5781i		−	3.27165i
$126$		0			0
$127$		−	5.90909i		−	0.524347i	−0.965021	−	0.262173i	$-0.915561\pi$
$127$		−	5.90909i		−	0.524347i	0.965021	−	0.262173i	$-0.0844392\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.14572			−0.365010
$130$	−4.30476			−0.377552
$131$	12.1043			1.05756			0.528778	−	0.848760i	$-0.322651\pi$
$131$	12.1043			1.05756			0.528778	+	0.848760i	$0.322651\pi$
$132$	2.55539	−	2.11424i	0.222418	−	0.184021i
$133$		0			0
$134$		−	0.330392i		−	0.0285415i
$135$	4.30156			0.370220
$136$		−	3.33708i		−	0.286152i
$137$	9.89121			0.845063			0.422532	−	0.906348i	$-0.361142\pi$
$137$	9.89121			0.845063			0.422532	+	0.906348i	$0.361142\pi$
$138$	5.72998			0.487768
$139$	−1.58746			−0.134647			−0.0673235	−	0.997731i	$-0.521446\pi$
$139$	−1.58746			−0.134647			−0.0673235	+	0.997731i	$0.521446\pi$
$140$		0			0
$141$	−3.20101			−0.269574
$142$			2.84974i			0.239145i
$143$	2.11581	+	2.55729i	0.176933	+	0.213851i
$144$	−1.00000			−0.0833333
$145$	33.3316			2.76804
$146$			14.8958i			1.23278i
$147$		0			0
$148$	2.52944			0.207918
$149$			17.0794i			1.39920i	0.714535	+	0.699599i	$0.246638\pi$
$149$			17.0794i			1.39920i	−0.714535	+	0.699599i	$0.753362\pi$
$150$	13.5035			1.10255
$151$		−	8.31552i		−	0.676707i	−0.941019	−	0.338354i	$-0.890130\pi$
$151$		−	8.31552i		−	0.676707i	0.941019	−	0.338354i	$-0.109870\pi$
$152$			3.23111i			0.262077i
$153$	−3.33708			−0.269787
$154$		0			0
$155$	−13.7788			−1.10674
$156$		−	1.00074i		−	0.0801236i
$157$			1.25113i			0.0998510i	0.998753	+	0.0499255i	$0.0158984\pi$
$157$			1.25113i			0.0998510i	−0.998753	+	0.0499255i	$0.984102\pi$
$158$	−16.0923			−1.28023
$159$		−	11.3155i		−	0.897376i
$160$	−4.30156			−0.340068
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	7.21571			0.565178			0.282589	−	0.959241i	$-0.408807\pi$
$163$	7.21571			0.565178			0.282589	+	0.959241i	$0.408807\pi$
$164$	−1.45111			−0.113313
$165$	−9.09452	−	10.9922i	−0.708008	−	0.855739i
$166$			1.75062i			0.135874i
$167$	15.4393			1.19473			0.597364	−	0.801970i	$-0.296215\pi$
$167$	15.4393			1.19473			0.597364	+	0.801970i	$0.296215\pi$
$168$		0			0
$169$	−11.9985			−0.922963
$170$	−14.3547			−1.10095
$171$	3.23111			0.247089
$172$		−	4.14572i		−	0.316108i
$173$	6.22042			0.472930			0.236465	−	0.971640i	$-0.424011\pi$
$173$	6.22042			0.472930			0.236465	+	0.971640i	$0.424011\pi$
$174$			7.74872i			0.587429i
$175$		0			0
$176$	2.11424	+	2.55539i	0.159367	+	0.192620i
$177$	3.44231			0.258740
$178$	2.78460			0.208714
$179$	3.07893			0.230130			0.115065	−	0.993358i	$-0.463292\pi$
$179$	3.07893			0.230130			0.115065	+	0.993358i	$0.463292\pi$
$180$			4.30156i			0.320620i
$181$			18.3243i			1.36203i	0.732268	+	0.681016i	$0.238462\pi$
$181$			18.3243i			1.36203i	−0.732268	+	0.681016i	$0.761538\pi$
$182$		0			0
$183$		−	14.8504i		−	1.09778i
$184$			5.72998i			0.422420i
$185$		−	10.8805i		−	0.799953i
$186$		−	3.20322i		−	0.234871i
$187$	7.05538	+	8.52753i	0.515940	+	0.623595i
$188$		−	3.20101i		−	0.233458i
$189$		0			0
$190$	13.8988			1.00833
$191$	20.8202			1.50650			0.753248	−	0.657736i	$-0.228486\pi$
$191$	20.8202			1.50650			0.753248	+	0.657736i	$0.228486\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			4.51641i			0.325099i	0.986700	+	0.162549i	$0.0519716\pi$
$193$			4.51641i			0.325099i	−0.986700	+	0.162549i	$0.948028\pi$
$194$	−12.3347			−0.885583
$195$	−4.30476			−0.308270
$196$		0			0
$197$			17.3563i			1.23659i	0.785947	+	0.618293i	$0.212176\pi$
$197$			17.3563i			1.23659i	−0.785947	+	0.618293i	$0.787824\pi$
$198$	2.55539	−	2.11424i	0.181603	−	0.150252i
$199$		−	7.81660i		−	0.554104i	−0.960855	−	0.277052i	$-0.910643\pi$
$199$		−	7.81660i		−	0.554104i	0.960855	−	0.277052i	$-0.0893575\pi$
$200$			13.5035i			0.954838i
$201$		−	0.330392i		−	0.0233040i
$202$		−	0.0562448i		−	0.00395737i
$203$		0			0
$204$		−	3.33708i		−	0.233642i
$205$			6.24205i			0.435963i
$206$	14.7949			1.03081
$207$	5.72998			0.398261
$208$	1.00074			0.0693890
$209$	−6.83132	−	8.25673i	−0.472532	−	0.571130i
$210$		0			0
$211$			21.9923i			1.51401i	0.653406	+	0.757007i	$0.273339\pi$
$211$			21.9923i			1.51401i	−0.653406	+	0.757007i	$0.726661\pi$
$212$	11.3155			0.777150
$213$			2.84974i			0.195261i
$214$	10.6139			0.725550
$215$	−17.8331			−1.21620
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	0.348204			0.0235833
$219$			14.8958i			1.00656i
$220$	10.9922	−	9.09452i	0.741091	−	0.613153i
$221$	3.33956			0.224643
$222$	2.52944			0.169765
$223$		−	8.30245i		−	0.555973i	−0.960585	−	0.277987i	$-0.910333\pi$
$223$		−	8.30245i		−	0.555973i	0.960585	−	0.277987i	$-0.0896671\pi$
$224$		0			0
$225$	13.5035			0.900230
$226$		−	18.9549i		−	1.26086i
$227$	−7.91253			−0.525173			−0.262587	−	0.964908i	$-0.584576\pi$
$227$	−7.91253			−0.525173			−0.262587	+	0.964908i	$0.584576\pi$
$228$			3.23111i			0.213985i
$229$		−	10.7093i		−	0.707688i	−0.935304	−	0.353844i	$-0.884874\pi$
$229$		−	10.7093i		−	0.707688i	0.935304	−	0.353844i	$-0.115126\pi$
$230$	24.6479			1.62523
$231$		0			0
$232$	−7.74872			−0.508728
$233$		−	17.7106i		−	1.16026i	−0.814525	−	0.580129i	$-0.803002\pi$
$233$		−	17.7106i		−	1.16026i	0.814525	−	0.580129i	$-0.196998\pi$
$234$		−	1.00074i		−	0.0654206i
$235$	−13.7693			−0.898213
$236$			3.44231i			0.224075i
$237$	−16.0923			−1.04531
$238$		0			0
$239$		−	26.6356i		−	1.72291i	−0.507832	−	0.861456i	$-0.669553\pi$
$239$		−	26.6356i		−	1.72291i	0.507832	−	0.861456i	$-0.330447\pi$
$240$	−4.30156			−0.277665
$241$	−3.71041			−0.239009			−0.119504	−	0.992834i	$-0.538131\pi$
$241$	−3.71041			−0.239009			−0.119504	+	0.992834i	$0.538131\pi$
$242$	−10.8054	−	2.06001i	−0.694597	−	0.132422i
$243$			1.00000i			0.0641500i
$244$	14.8504			0.950702
$245$		0			0
$246$	−1.45111			−0.0925195
$247$	−3.23351			−0.205743
$248$	3.20322			0.203404
$249$			1.75062i			0.110941i
$250$	36.5781			2.31341
$251$			10.6948i			0.675051i	0.941316	+	0.337526i	$0.109590\pi$
$251$			10.6948i			0.675051i	−0.941316	+	0.337526i	$0.890410\pi$
$252$		0			0
$253$	−12.1145	−	14.6423i	−0.761634	−	0.920555i
$254$	5.90909			0.370769
$255$	−14.3547			−0.898924
$256$	1.00000			0.0625000
$257$			23.8220i			1.48597i	0.669305	+	0.742987i	$0.266592\pi$
$257$			23.8220i			1.48597i	−0.669305	+	0.742987i	$0.733408\pi$
$258$		−	4.14572i		−	0.258101i
$259$		0			0
$260$		−	4.30476i		−	0.266970i
$261$			7.74872i			0.479633i
$262$			12.1043i			0.747804i
$263$			17.0516i			1.05145i	0.850655	+	0.525725i	$0.176206\pi$
$263$			17.0516i			1.05145i	−0.850655	+	0.525725i	$0.823794\pi$
$264$	2.11424	+	2.55539i	0.130122	+	0.157273i
$265$		−	48.6743i		−	2.99004i
$266$		0			0
$267$	2.78460			0.170414
$268$	0.330392			0.0201819
$269$		−	9.61064i		−	0.585971i	−0.956117	−	0.292986i	$-0.905351\pi$
$269$		−	9.61064i		−	0.585971i	0.956117	−	0.292986i	$-0.0946488\pi$
$270$			4.30156i			0.261785i
$271$	−5.11228			−0.310549			−0.155274	−	0.987871i	$-0.549626\pi$
$271$	−5.11228			−0.310549			−0.155274	+	0.987871i	$0.549626\pi$
$272$	3.33708			0.202340
$273$		0			0
$274$			9.89121i			0.597550i
$275$	−28.5495	−	34.5066i	−1.72160	−	2.08082i
$276$			5.72998i			0.344904i
$277$			26.3274i			1.58186i	0.611906	+	0.790931i	$0.290403\pi$
$277$			26.3274i			1.58186i	−0.611906	+	0.790931i	$0.709597\pi$
$278$		−	1.58746i		−	0.0952098i
$279$		−	3.20322i		−	0.191772i
$280$		0			0
$281$		−	10.5684i		−	0.630459i	−0.949015	−	0.315230i	$-0.897918\pi$
$281$		−	10.5684i		−	0.630459i	0.949015	−	0.315230i	$-0.102082\pi$
$282$		−	3.20101i		−	0.190617i
$283$	10.4076			0.618667			0.309333	−	0.950954i	$-0.399894\pi$
$283$	10.4076			0.618667			0.309333	+	0.950954i	$0.399894\pi$
$284$	−2.84974			−0.169101
$285$	13.8988			0.823294
$286$	−2.55729	+	2.11581i	−0.151215	+	0.125110i
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−5.86389			−0.344935
$290$			33.3316i			1.95730i
$291$	−12.3347			−0.723075
$292$	−14.8958			−0.871710
$293$	−31.4600			−1.83792			−0.918958	−	0.394356i	$-0.870968\pi$
$293$	−31.4600			−1.83792			−0.918958	+	0.394356i	$0.870968\pi$
$294$		0			0
$295$	14.8073			0.862116
$296$			2.52944i			0.147021i
$297$	2.55539	−	2.11424i	0.148279	−	0.122680i
$298$	−17.0794			−0.989383
$299$	−5.73424			−0.331620
$300$			13.5035i			0.779622i
$301$		0			0
$302$	8.31552			0.478504
$303$		−	0.0562448i		−	0.00323118i
$304$	−3.23111			−0.185317
$305$		−	63.8801i		−	3.65776i
$306$		−	3.33708i		−	0.190768i
$307$	18.4994			1.05582			0.527910	−	0.849301i	$-0.322976\pi$
$307$	18.4994			1.05582			0.527910	+	0.849301i	$0.322976\pi$
$308$		0			0
$309$	14.7949			0.841653
$310$		−	13.7788i		−	0.782585i
$311$			30.9979i			1.75773i	0.477073	+	0.878864i	$0.341698\pi$
$311$			30.9979i			1.75773i	−0.477073	+	0.878864i	$0.658302\pi$
$312$	1.00074			0.0566559
$313$			9.60149i			0.542708i	0.962480	+	0.271354i	$0.0874714\pi$
$313$			9.60149i			0.542708i	−0.962480	+	0.271354i	$0.912529\pi$
$314$	−1.25113			−0.0706053
$315$		0			0
$316$		−	16.0923i		−	0.905261i
$317$	−11.9425			−0.670759			−0.335379	−	0.942083i	$-0.608864\pi$
$317$	−11.9425			−0.670759			−0.335379	+	0.942083i	$0.608864\pi$
$318$	11.3155			0.634541
$319$	19.8010	−	16.3826i	1.10864	−	0.917251i
$320$		−	4.30156i		−	0.240465i
$321$	10.6139			0.592409
$322$		0			0
$323$	−10.7825			−0.599952
$324$	−1.00000			−0.0555556
$325$	−13.5135			−0.749593
$326$			7.21571i			0.399641i
$327$	0.348204			0.0192557
$328$		−	1.45111i		−	0.0801242i
$329$		0			0
$330$	10.9922	−	9.09452i	0.605099	−	0.500637i
$331$	6.49162			0.356812			0.178406	−	0.983957i	$-0.442906\pi$
$331$	6.49162			0.356812			0.178406	+	0.983957i	$0.442906\pi$
$332$	−1.75062			−0.0960777
$333$	2.52944			0.138612
$334$			15.4393i			0.844800i
$335$		−	1.42120i		−	0.0776485i
$336$		0			0
$337$		−	5.74869i		−	0.313151i	−0.987666	−	0.156576i	$-0.949955\pi$
$337$		−	5.74869i		−	0.313151i	0.987666	−	0.156576i	$-0.0500455\pi$
$338$		−	11.9985i		−	0.652633i
$339$		−	18.9549i		−	1.02949i
$340$		−	14.3547i		−	0.778491i
$341$	−8.18546	+	6.77236i	−0.443267	+	0.366744i
$342$			3.23111i			0.174718i
$343$		0			0
$344$	4.14572			0.223522
$345$	24.6479			1.32700
$346$			6.22042i			0.334412i
$347$		−	14.6253i		−	0.785125i	−0.919725	−	0.392563i	$-0.871589\pi$
$347$		−	14.6253i		−	0.785125i	0.919725	−	0.392563i	$-0.128411\pi$
$348$	−7.74872			−0.415375
$349$	15.2458			0.816091			0.408046	−	0.912962i	$-0.366210\pi$
$349$	15.2458			0.816091			0.408046	+	0.912962i	$0.366210\pi$
$350$		0			0
$351$		−	1.00074i		−	0.0534157i
$352$	−2.55539	+	2.11424i	−0.136203	+	0.112689i
$353$			27.4483i			1.46093i	0.682952	+	0.730463i	$0.260696\pi$
$353$			27.4483i			1.46093i	−0.682952	+	0.730463i	$0.739304\pi$
$354$			3.44231i			0.182957i
$355$			12.2583i			0.650604i
$356$			2.78460i			0.147583i
$357$		0			0
$358$			3.07893i			0.162726i
$359$		−	16.2962i		−	0.860078i	−0.902810	−	0.430039i	$-0.858500\pi$
$359$		−	16.2962i		−	0.860078i	0.902810	−	0.430039i	$-0.141500\pi$
$360$	−4.30156			−0.226712
$361$	−8.55996			−0.450524
$362$	−18.3243			−0.963102
$363$	−10.8054	−	2.06001i	−0.567136	−	0.108122i
$364$		0			0
$365$			64.0752i			3.35385i
$366$	14.8504			0.776245
$367$			3.39392i			0.177161i	0.996069	+	0.0885807i	$0.0282331\pi$
$367$			3.39392i			0.177161i	−0.996069	+	0.0885807i	$0.971767\pi$
$368$	−5.72998			−0.298696
$369$	−1.45111			−0.0755418
$370$	10.8805			0.565652
$371$		0			0
$372$	3.20322			0.166079
$373$		−	6.51584i		−	0.337378i	−0.985669	−	0.168689i	$-0.946047\pi$
$373$		−	6.51584i		−	0.337378i	0.985669	−	0.168689i	$-0.0539533\pi$
$374$	−8.52753	+	7.05538i	−0.440948	+	0.364825i
$375$	36.5781			1.88889
$376$	3.20101			0.165079
$377$		−	7.75447i		−	0.399376i
$378$		0			0
$379$	−27.4324			−1.40911			−0.704555	−	0.709650i	$-0.748853\pi$
$379$	−27.4324			−1.40911			−0.704555	+	0.709650i	$0.748853\pi$
$380$			13.8988i			0.712994i
$381$	5.90909			0.302732
$382$			20.8202i			1.06525i
$383$		−	8.83690i		−	0.451545i	−0.974180	−	0.225772i	$-0.927509\pi$
$383$		−	8.83690i		−	0.451545i	0.974180	−	0.225772i	$-0.0724906\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−4.51641			−0.229879
$387$		−	4.14572i		−	0.210739i
$388$		−	12.3347i		−	0.626201i
$389$	8.92306			0.452417			0.226209	−	0.974079i	$-0.427367\pi$
$389$	8.92306			0.452417			0.226209	+	0.974079i	$0.427367\pi$
$390$		−	4.30476i		−	0.217980i
$391$	−19.1214			−0.967011
$392$		0			0
$393$			12.1043i			0.610580i
$394$	−17.3563			−0.874399
$395$	−69.2220			−3.48293
$396$	2.11424	+	2.55539i	0.106244	+	0.128413i
$397$		−	4.77555i		−	0.239678i	−0.992793	−	0.119839i	$-0.961762\pi$
$397$		−	4.77555i		−	0.239678i	0.992793	−	0.119839i	$-0.0382379\pi$
$398$	7.81660			0.391811
$399$		0			0
$400$	−13.5035			−0.675173
$401$	2.53972			0.126827			0.0634137	−	0.997987i	$-0.479801\pi$
$401$	2.53972			0.126827			0.0634137	+	0.997987i	$0.479801\pi$
$402$	0.330392			0.0164784
$403$			3.20560i			0.159682i
$404$	0.0562448			0.00279828
$405$			4.30156i			0.213746i
$406$		0			0
$407$	−5.34783	−	6.46369i	−0.265082	−	0.320393i
$408$	3.33708			0.165210
$409$	0.0642013			0.00317455			0.00158728	−	0.999999i	$-0.499495\pi$
$409$	0.0642013			0.00317455			0.00158728	+	0.999999i	$0.499495\pi$
$410$	−6.24205			−0.308273
$411$			9.89121i			0.487897i
$412$			14.7949i			0.728893i
$413$		0			0
$414$			5.72998i			0.281613i
$415$			7.53040i			0.369653i
$416$			1.00074i			0.0490655i
$417$		−	1.58746i		−	0.0777385i
$418$	8.25673	−	6.83132i	0.403850	−	0.334131i
$419$			23.7720i			1.16134i	0.814140	+	0.580669i	$0.197209\pi$
$419$			23.7720i			1.16134i	−0.814140	+	0.580669i	$0.802791\pi$
$420$		0			0
$421$	−1.11501			−0.0543422			−0.0271711	−	0.999631i	$-0.508650\pi$
$421$	−1.11501			−0.0543422			−0.0271711	+	0.999631i	$0.508650\pi$
$422$	−21.9923			−1.07057
$423$		−	3.20101i		−	0.155638i
$424$			11.3155i			0.549528i
$425$	−45.0621			−2.18583
$426$	−2.84974			−0.138070
$427$		0			0
$428$			10.6139i			0.513042i
$429$	−2.55729	+	2.11581i	−0.123467	+	0.102152i
$430$		−	17.8331i		−	0.859987i
$431$		−	29.3790i		−	1.41514i	−0.706644	−	0.707569i	$-0.749792\pi$
$431$		−	29.3790i		−	1.41514i	0.706644	−	0.707569i	$-0.250208\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			13.1705i			0.632934i	0.948604	+	0.316467i	$0.102497\pi$
$433$			13.1705i			0.632934i	−0.948604	+	0.316467i	$0.897503\pi$
$434$		0			0
$435$			33.3316i			1.59813i
$436$			0.348204i			0.0166759i
$437$	18.5142			0.885653
$438$	−14.8958			−0.711748
$439$	10.2133			0.487454			0.243727	−	0.969844i	$-0.421630\pi$
$439$	10.2133			0.487454			0.243727	+	0.969844i	$0.421630\pi$
$440$	9.09452	+	10.9922i	0.433564	+	0.524031i
$441$		0			0
$442$			3.33956i			0.158847i
$443$	27.3723			1.30050			0.650250	−	0.759721i	$-0.274664\pi$
$443$	27.3723			1.30050			0.650250	+	0.759721i	$0.274664\pi$
$444$			2.52944i			0.120042i
$445$	11.9781			0.567817
$446$	8.30245			0.393133
$447$	−17.0794			−0.807828
$448$		0			0
$449$	1.35953			0.0641602			0.0320801	−	0.999485i	$-0.489787\pi$
$449$	1.35953			0.0641602			0.0320801	+	0.999485i	$0.489787\pi$
$450$			13.5035i			0.636559i
$451$	3.06799	+	3.70815i	0.144466	+	0.174610i
$452$	18.9549			0.891564
$453$	8.31552			0.390697
$454$		−	7.91253i		−	0.371354i
$455$		0			0
$456$	−3.23111			−0.151310
$457$			21.8981i			1.02435i	0.858880	+	0.512176i	$0.171160\pi$
$457$			21.8981i			1.02435i	−0.858880	+	0.512176i	$0.828840\pi$
$458$	10.7093			0.500411
$459$		−	3.33708i		−	0.155762i
$460$			24.6479i			1.14921i
$461$	−13.4227			−0.625159			−0.312579	−	0.949892i	$-0.601193\pi$
$461$	−13.4227			−0.625159			−0.312579	+	0.949892i	$0.601193\pi$
$462$		0			0
$463$	−21.1422			−0.982562			−0.491281	−	0.871001i	$-0.663471\pi$
$463$	−21.1422			−0.982562			−0.491281	+	0.871001i	$0.663471\pi$
$464$		−	7.74872i		−	0.359725i
$465$		−	13.7788i		−	0.638978i
$466$	17.7106			0.820426
$467$			2.87475i			0.133027i	0.997786	+	0.0665137i	$0.0211876\pi$
$467$			2.87475i			0.133027i	−0.997786	+	0.0665137i	$0.978812\pi$
$468$	1.00074			0.0462594
$469$		0			0
$470$		−	13.7693i		−	0.635133i
$471$	−1.25113			−0.0576490
$472$	−3.44231			−0.158445
$473$	−10.5939	+	8.76502i	−0.487108	+	0.403016i
$474$		−	16.0923i		−	0.739143i
$475$	43.6311			2.00193
$476$		0			0
$477$	11.3155			0.518100
$478$	26.6356			1.21828
$479$	3.83882			0.175400			0.0877000	−	0.996147i	$-0.472048\pi$
$479$	3.83882			0.175400			0.0877000	+	0.996147i	$0.472048\pi$
$480$		−	4.30156i		−	0.196339i
$481$	−2.53132			−0.115418
$482$		−	3.71041i		−	0.169005i
$483$		0			0
$484$	2.06001	−	10.8054i	0.0936367	−	0.491154i
$485$	−53.0587			−2.40927
$486$	−1.00000			−0.0453609
$487$	−9.68084			−0.438681			−0.219340	−	0.975648i	$-0.570391\pi$
$487$	−9.68084			−0.438681			−0.219340	+	0.975648i	$0.570391\pi$
$488$			14.8504i			0.672248i
$489$			7.21571i			0.326306i
$490$		0			0
$491$		−	15.8886i		−	0.717041i	−0.933522	−	0.358520i	$-0.883281\pi$
$491$		−	15.8886i		−	0.717041i	0.933522	−	0.358520i	$-0.116719\pi$
$492$		−	1.45111i		−	0.0654211i
$493$		−	25.8581i		−	1.16459i
$494$		−	3.23351i		−	0.145482i
$495$	10.9922	−	9.09452i	0.494061	−	0.408768i
$496$			3.20322i			0.143829i
$497$		0			0
$498$	−1.75062			−0.0784471
$499$	−30.0440			−1.34495			−0.672477	−	0.740118i	$-0.734769\pi$
$499$	−30.0440			−1.34495			−0.672477	+	0.740118i	$0.734769\pi$
$500$			36.5781i			1.63582i
$501$			15.4393i			0.689776i
$502$	−10.6948			−0.477333
$503$	4.66798			0.208135			0.104067	−	0.994570i	$-0.466814\pi$
$503$	4.66798			0.208135			0.104067	+	0.994570i	$0.466814\pi$
$504$		0			0
$505$		−	0.241941i		−	0.0107662i
$506$	14.6423	−	12.1145i	0.650931	−	0.538557i
$507$		−	11.9985i		−	0.532873i
$508$			5.90909i			0.262173i
$509$			30.9460i			1.37166i	0.727763	+	0.685829i	$0.240560\pi$
$509$			30.9460i			1.37166i	−0.727763	+	0.685829i	$0.759440\pi$
$510$		−	14.3547i		−	0.635635i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			3.23111i			0.142657i
$514$	−23.8220			−1.05074
$515$	63.6413			2.80437
$516$	4.14572			0.182505
$517$	−8.17982	+	6.76769i	−0.359748	+	0.297643i
$518$		0			0
$519$			6.22042i			0.273046i
$520$	4.30476			0.188776
$521$		−	11.0536i		−	0.484267i	−0.970243	−	0.242134i	$-0.922153\pi$
$521$		−	11.0536i		−	0.484267i	0.970243	−	0.242134i	$-0.0778473\pi$
$522$	−7.74872			−0.339152
$523$	−4.13481			−0.180803			−0.0904013	−	0.995905i	$-0.528815\pi$
$523$	−4.13481			−0.180803			−0.0904013	+	0.995905i	$0.528815\pi$
$524$	−12.1043			−0.528778
$525$		0			0
$526$	−17.0516			−0.743487
$527$			10.6894i			0.465637i
$528$	−2.55539	+	2.11424i	−0.111209	+	0.0920103i
$529$	9.83268			0.427508
$530$	48.6743			2.11427
$531$			3.44231i			0.149384i
$532$		0			0
$533$	1.45219			0.0629013
$534$			2.78460i			0.120501i
$535$	45.6563			1.97389
$536$			0.330392i			0.0142707i
$537$			3.07893i			0.132866i
$538$	9.61064			0.414344
$539$		0			0
$540$	−4.30156			−0.185110
$541$		−	39.8272i		−	1.71231i	−0.516723	−	0.856153i	$-0.672848\pi$
$541$		−	39.8272i		−	1.71231i	0.516723	−	0.856153i	$-0.327152\pi$
$542$		−	5.11228i		−	0.219591i
$543$	−18.3243			−0.786370
$544$			3.33708i			0.143076i
$545$	1.49782			0.0641596
$546$		0			0
$547$			37.7080i			1.61228i	0.591728	+	0.806138i	$0.298446\pi$
$547$			37.7080i			1.61228i	−0.591728	+	0.806138i	$0.701554\pi$
$548$	−9.89121			−0.422532
$549$	14.8504			0.633801
$550$	34.5066	−	28.5495i	1.47136	−	1.21735i
$551$			25.0369i			1.06661i
$552$	−5.72998			−0.243884
$553$		0			0
$554$	−26.3274			−1.11854
$555$	10.8805			0.461853
$556$	1.58746			0.0673235
$557$			31.5451i			1.33661i	0.743888	+	0.668304i	$0.232979\pi$
$557$			31.5451i			1.33661i	−0.743888	+	0.668304i	$0.767021\pi$
$558$	3.20322			0.135603
$559$			4.14880i			0.175475i
$560$		0			0
$561$	−8.52753	+	7.05538i	−0.360033	+	0.297878i
$562$	10.5684			0.445802
$563$	37.7986			1.59302			0.796511	−	0.604625i	$-0.206677\pi$
$563$	37.7986			1.59302			0.796511	+	0.604625i	$0.206677\pi$
$564$	3.20101			0.134787
$565$		−	81.5357i		−	3.43023i
$566$			10.4076i			0.437463i
$567$		0			0
$568$		−	2.84974i		−	0.119572i
$569$			18.4881i			0.775061i	0.921857	+	0.387530i	$0.126672\pi$
$569$			18.4881i			0.775061i	−0.921857	+	0.387530i	$0.873328\pi$
$570$			13.8988i			0.582157i
$571$			15.2403i			0.637785i	0.947791	+	0.318892i	$0.103311\pi$
$571$			15.2403i			0.637785i	−0.947791	+	0.318892i	$0.896689\pi$
$572$	−2.11581	−	2.55729i	−0.0884664	−	0.106926i
$573$			20.8202i			0.869776i
$574$		0			0
$575$	77.3745			3.22674
$576$	1.00000			0.0416667
$577$			27.3882i			1.14018i	0.821581	+	0.570092i	$0.193092\pi$
$577$			27.3882i			1.14018i	−0.821581	+	0.570092i	$0.806908\pi$
$578$		−	5.86389i		−	0.243906i
$579$	−4.51641			−0.187696
$580$	−33.3316			−1.38402
$581$		0			0
$582$		−	12.3347i		−	0.511291i
$583$	−23.9236	−	28.9154i	−0.990814	−	1.19755i
$584$		−	14.8958i		−	0.616392i
$585$		−	4.30476i		−	0.177980i
$586$		−	31.4600i		−	1.29960i
$587$			17.1517i			0.707927i	0.935259	+	0.353964i	$0.115166\pi$
$587$			17.1517i			0.707927i	−0.935259	+	0.353964i	$0.884834\pi$
$588$		0			0
$589$		−	10.3499i		−	0.426461i
$590$			14.8073i			0.609608i
$591$	−17.3563			−0.713944
$592$	−2.52944			−0.103959
$593$	5.26141			0.216060			0.108030	−	0.994148i	$-0.465546\pi$
$593$	5.26141			0.216060			0.108030	+	0.994148i	$0.465546\pi$
$594$	2.11424	+	2.55539i	0.0867482	+	0.104849i
$595$		0			0
$596$		−	17.0794i		−	0.699599i
$597$	7.81660			0.319912
$598$		−	5.73424i		−	0.234490i
$599$	−35.6885			−1.45819			−0.729096	−	0.684411i	$-0.760059\pi$
$599$	−35.6885			−1.45819			−0.729096	+	0.684411i	$0.760059\pi$
$600$	−13.5035			−0.551276
$601$	−9.98679			−0.407370			−0.203685	−	0.979036i	$-0.565292\pi$
$601$	−9.98679			−0.407370			−0.203685	+	0.979036i	$0.565292\pi$
$602$		0			0
$603$	0.330392			0.0134546
$604$			8.31552i			0.338354i
$605$	−46.4801	−	8.86125i	−1.88968	−	0.360261i
$606$	0.0562448			0.00228479
$607$	−23.6993			−0.961924			−0.480962	−	0.876742i	$-0.659712\pi$
$607$	−23.6993			−0.961924			−0.480962	+	0.876742i	$0.659712\pi$
$608$		−	3.23111i		−	0.131039i
$609$		0			0
$610$	63.8801			2.58643
$611$			3.20339i			0.129595i
$612$	3.33708			0.134894
$613$			25.8159i			1.04269i	0.853345	+	0.521347i	$0.174570\pi$
$613$			25.8159i			1.04269i	−0.853345	+	0.521347i	$0.825430\pi$
$614$			18.4994i			0.746577i
$615$	−6.24205			−0.251704
$616$		0			0
$617$	4.44499			0.178949			0.0894743	−	0.995989i	$-0.471481\pi$
$617$	4.44499			0.178949			0.0894743	+	0.995989i	$0.471481\pi$
$618$			14.7949i			0.595139i
$619$			34.6603i			1.39311i	0.717501	+	0.696557i	$0.245286\pi$
$619$			34.6603i			1.39311i	−0.717501	+	0.696557i	$0.754714\pi$
$620$	13.7788			0.553371
$621$			5.72998i			0.229936i
$622$	−30.9979			−1.24290
$623$		0			0
$624$			1.00074i			0.0400618i
$625$	89.8260			3.59304
$626$	−9.60149			−0.383753
$627$	8.25673	−	6.83132i	0.329742	−	0.272817i
$628$		−	1.25113i		−	0.0499255i
$629$	−8.44094			−0.336562
$630$		0			0
$631$	32.7549			1.30395			0.651975	−	0.758240i	$-0.273941\pi$
$631$	32.7549			1.30395			0.651975	+	0.758240i	$0.273941\pi$
$632$	16.0923			0.640116
$633$	−21.9923			−0.874117
$634$		−	11.9425i		−	0.474298i
$635$	25.4183			1.00870
$636$			11.3155i			0.448688i
$637$		0			0
$638$	16.3826	+	19.8010i	0.648594	+	0.783928i
$639$	−2.84974			−0.112734
$640$	4.30156			0.170034
$641$	−35.0833			−1.38571			−0.692854	−	0.721078i	$-0.743647\pi$
$641$	−35.0833			−1.38571			−0.692854	+	0.721078i	$0.743647\pi$
$642$			10.6139i			0.418897i
$643$			4.02224i			0.158622i	0.996850	+	0.0793109i	$0.0252720\pi$
$643$			4.02224i			0.158622i	−0.996850	+	0.0793109i	$0.974728\pi$
$644$		0			0
$645$		−	17.8331i		−	0.702176i
$646$		−	10.7825i		−	0.424230i
$647$			5.70997i			0.224482i	0.993681	+	0.112241i	$0.0358028\pi$
$647$			5.70997i			0.224482i	−0.993681	+	0.112241i	$0.964197\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	8.79644	−	7.27786i	0.345290	−	0.285681i
$650$		−	13.5135i		−	0.530043i
$651$		0			0
$652$	−7.21571			−0.282589
$653$	−14.3938			−0.563272			−0.281636	−	0.959521i	$-0.590877\pi$
$653$	−14.3938			−0.563272			−0.281636	+	0.959521i	$0.590877\pi$
$654$			0.348204i			0.0136158i
$655$			52.0673i			2.03444i
$656$	1.45111			0.0566564
$657$	−14.8958			−0.581140
$658$		0			0
$659$			1.73466i			0.0675728i	0.999429	+	0.0337864i	$0.0107566\pi$
$659$			1.73466i			0.0675728i	−0.999429	+	0.0337864i	$0.989243\pi$
$660$	9.09452	+	10.9922i	0.354004	+	0.427869i
$661$			28.0265i			1.09010i	0.838402	+	0.545052i	$0.183490\pi$
$661$			28.0265i			1.09010i	−0.838402	+	0.545052i	$0.816510\pi$
$662$			6.49162i			0.252304i
$663$			3.33956i			0.129698i
$664$		−	1.75062i		−	0.0679372i
$665$		0			0
$666$			2.52944i			0.0980137i
$667$			44.4000i			1.71917i
$668$	−15.4393			−0.597364
$669$	8.30245			0.320991
$670$	1.42120			0.0549058
$671$	−31.3973	−	37.9486i	−1.21208	−	1.46499i
$672$		0			0
$673$		−	11.9436i		−	0.460394i	−0.973144	−	0.230197i	$-0.926063\pi$
$673$		−	11.9436i		−	0.460394i	0.973144	−	0.230197i	$-0.0739370\pi$
$674$	5.74869			0.221431
$675$			13.5035i			0.519748i
$676$	11.9985			0.461481
$677$	−40.4669			−1.55527			−0.777634	−	0.628717i	$-0.783580\pi$
$677$	−40.4669			−1.55527			−0.777634	+	0.628717i	$0.783580\pi$
$678$	18.9549			0.727959
$679$		0			0
$680$	14.3547			0.550476
$681$		−	7.91253i		−	0.303209i
$682$	−6.77236	−	8.18546i	−0.259327	−	0.313437i
$683$	−18.3199			−0.700990			−0.350495	−	0.936565i	$-0.613987\pi$
$683$	−18.3199			−0.700990			−0.350495	+	0.936565i	$0.613987\pi$
$684$	−3.23111			−0.123544
$685$			42.5477i			1.62566i
$686$		0			0
$687$	10.7093			0.408584
$688$			4.14572i			0.158054i
$689$	−11.3239			−0.431406
$690$			24.6479i			0.938329i
$691$			44.6823i			1.69980i	0.526947	+	0.849898i	$0.323337\pi$
$691$			44.6823i			1.69980i	−0.526947	+	0.849898i	$0.676663\pi$
$692$	−6.22042			−0.236465
$693$		0			0
$694$	14.6253			0.555167
$695$		−	6.82858i		−	0.259023i
$696$		−	7.74872i		−	0.293714i
$697$	4.84248			0.183422
$698$			15.2458i			0.577064i
$699$	17.7106			0.669875
$700$		0			0
$701$		−	18.6437i		−	0.704161i	−0.935970	−	0.352081i	$-0.885474\pi$
$701$		−	18.6437i		−	0.704161i	0.935970	−	0.352081i	$-0.114526\pi$
$702$	1.00074			0.0377706
$703$	8.17288			0.308246
$704$	−2.11424	−	2.55539i	−0.0796833	−	0.0963098i
$705$		−	13.7693i		−	0.518584i
$706$	−27.4483			−1.03303
$707$		0			0
$708$	−3.44231			−0.129370
$709$	−4.90134			−0.184074			−0.0920368	−	0.995756i	$-0.529338\pi$
$709$	−4.90134			−0.184074			−0.0920368	+	0.995756i	$0.529338\pi$
$710$	−12.2583			−0.460047
$711$		−	16.0923i		−	0.603508i
$712$	−2.78460			−0.104357
$713$		−	18.3544i		−	0.687376i
$714$		0			0
$715$	−11.0003	+	9.10128i	−0.411389	+	0.340369i
$716$	−3.07893			−0.115065
$717$	26.6356			0.994724
$718$	16.2962			0.608167
$719$		−	22.2470i		−	0.829674i	−0.909896	−	0.414837i	$-0.863839\pi$
$719$		−	22.2470i		−	0.829674i	0.909896	−	0.414837i	$-0.136161\pi$
$720$		−	4.30156i		−	0.160310i
$721$		0			0
$722$		−	8.55996i		−	0.318569i
$723$		−	3.71041i		−	0.137992i
$724$		−	18.3243i		−	0.681016i
$725$			104.634i			3.88603i
$726$	2.06001	−	10.8054i	0.0764541	−	0.401025i
$727$		−	27.5807i		−	1.02291i	−0.859310	−	0.511456i	$-0.829106\pi$
$727$		−	27.5807i		−	1.02291i	0.859310	−	0.511456i	$-0.170894\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−64.0752			−2.37153
$731$			13.8346i			0.511691i
$732$			14.8504i			0.548888i
$733$	17.9014			0.661203			0.330602	−	0.943770i	$-0.392748\pi$
$733$	17.9014			0.661203			0.330602	+	0.943770i	$0.392748\pi$
$734$	−3.39392			−0.125272
$735$		0			0
$736$		−	5.72998i		−	0.211210i
$737$	−0.698526	−	0.844279i	−0.0257305	−	0.0310994i
$738$		−	1.45111i		−	0.0534161i
$739$		−	28.8613i		−	1.06168i	−0.847471	−	0.530841i	$-0.821876\pi$
$739$		−	28.8613i		−	1.06168i	0.847471	−	0.530841i	$-0.178124\pi$
$740$			10.8805i			0.399976i
$741$		−	3.23351i		−	0.118786i
$742$		0			0
$743$		−	34.0656i		−	1.24975i	−0.780726	−	0.624873i	$-0.785151\pi$
$743$		−	34.0656i		−	1.24975i	0.780726	−	0.624873i	$-0.214849\pi$
$744$			3.20322i			0.117436i
$745$	−73.4681			−2.69166
$746$	6.51584			0.238562
$747$	−1.75062			−0.0640518
$748$	−7.05538	−	8.52753i	−0.257970	−	0.311798i
$749$		0			0
$750$			36.5781i			1.33565i
$751$	−12.5636			−0.458452			−0.229226	−	0.973373i	$-0.573619\pi$
$751$	−12.5636			−0.458452			−0.229226	+	0.973373i	$0.573619\pi$
$752$			3.20101i			0.116729i
$753$	−10.6948			−0.389741
$754$	7.75447			0.282401
$755$	35.7697			1.30179
$756$		0			0
$757$	7.03843			0.255816			0.127908	−	0.991786i	$-0.459174\pi$
$757$	7.03843			0.255816			0.127908	+	0.991786i	$0.459174\pi$
$758$		−	27.4324i		−	0.996391i
$759$	14.6423	−	12.1145i	0.531483	−	0.439730i
$760$	−13.8988			−0.504163
$761$	−1.64145			−0.0595025			−0.0297512	−	0.999557i	$-0.509472\pi$
$761$	−1.64145			−0.0595025			−0.0297512	+	0.999557i	$0.509472\pi$
$762$			5.90909i			0.214064i
$763$		0			0
$764$	−20.8202			−0.753248
$765$		−	14.3547i		−	0.518994i
$766$	8.83690			0.319290
$767$		−	3.44487i		−	0.124387i
$768$			1.00000i			0.0360844i
$769$	5.29585			0.190973			0.0954867	−	0.995431i	$-0.469559\pi$
$769$	5.29585			0.190973			0.0954867	+	0.995431i	$0.469559\pi$
$770$		0			0
$771$	−23.8220			−0.857928
$772$		−	4.51641i		−	0.162549i
$773$			19.7087i			0.708874i	0.935080	+	0.354437i	$0.115327\pi$
$773$			19.7087i			0.708874i	−0.935080	+	0.354437i	$0.884673\pi$
$774$	4.14572			0.149015
$775$		−	43.2545i		−	1.55375i
$776$	12.3347			0.442791
$777$		0			0
$778$			8.92306i			0.319907i
$779$	−4.68869			−0.167990
$780$	4.30476			0.154135
$781$	6.02502	+	7.28218i	0.215592	+	0.260577i
$782$		−	19.1214i		−	0.683780i
$783$	−7.74872			−0.276917
$784$		0			0
$785$	−5.38181			−0.192085
$786$	−12.1043			−0.431745
$787$	52.0997			1.85715			0.928576	−	0.371141i	$-0.121033\pi$
$787$	52.0997			1.85715			0.928576	+	0.371141i	$0.121033\pi$
$788$		−	17.3563i		−	0.618293i
$789$	−17.0516			−0.607055
$790$		−	69.2220i		−	2.46281i
$791$		0			0
$792$	−2.55539	+	2.11424i	−0.0908017	+	0.0751261i
$793$	−14.8615			−0.527746
$794$	4.77555			0.169478
$795$	48.6743			1.72630
$796$			7.81660i			0.277052i
$797$			39.4609i			1.39778i	0.715230	+	0.698889i	$0.246322\pi$
$797$			39.4609i			1.39778i	−0.715230	+	0.698889i	$0.753678\pi$
$798$		0			0
$799$			10.6820i			0.377903i
$800$		−	13.5035i		−	0.477419i
$801$			2.78460i			0.0983888i
$802$			2.53972i			0.0896805i
$803$	31.4932	+	38.0645i	1.11137	+	1.34327i
$804$			0.330392i			0.0116520i
$805$		0			0
$806$	−3.20560			−0.112912
$807$	9.61064			0.338311
$808$			0.0562448i			0.00197868i
$809$			1.64396i			0.0577984i	0.999582	+	0.0288992i	$0.00920019\pi$
$809$			1.64396i			0.0577984i	−0.999582	+	0.0288992i	$0.990800\pi$
$810$	−4.30156			−0.151142
$811$	18.9381			0.665006			0.332503	−	0.943102i	$-0.392107\pi$
$811$	18.9381			0.665006			0.332503	+	0.943102i	$0.392107\pi$
$812$		0			0
$813$		−	5.11228i		−	0.179295i
$814$	6.46369	−	5.34783i	0.226552	−	0.187441i
$815$			31.0389i			1.08724i
$816$			3.33708i			0.116821i
$817$		−	13.3952i		−	0.468640i
$818$			0.0642013i			0.00224475i
$819$		0			0
$820$		−	6.24205i		−	0.217982i
$821$		−	16.1682i		−	0.564274i	−0.959374	−	0.282137i	$-0.908957\pi$
$821$		−	16.1682i		−	0.564274i	0.959374	−	0.282137i	$-0.0910433\pi$
$822$	−9.89121			−0.344996
$823$	3.87280			0.134997			0.0674986	−	0.997719i	$-0.478498\pi$
$823$	3.87280			0.134997			0.0674986	+	0.997719i	$0.478498\pi$
$824$	−14.7949			−0.515405
$825$	34.5066	−	28.5495i	1.20136	−	0.993966i
$826$		0			0
$827$		−	17.5641i		−	0.610762i	−0.952230	−	0.305381i	$-0.901216\pi$
$827$		−	17.5641i		−	0.610762i	0.952230	−	0.305381i	$-0.0987838\pi$
$828$	−5.72998			−0.199131
$829$		−	31.8636i		−	1.10667i	−0.832959	−	0.553335i	$-0.813355\pi$
$829$		−	31.8636i		−	1.10667i	0.832959	−	0.553335i	$-0.186645\pi$
$830$	−7.53040			−0.261384
$831$	−26.3274			−0.913288
$832$	−1.00074			−0.0346945
$833$		0			0
$834$	1.58746			0.0549694
$835$			66.4131i			2.29832i
$836$	6.83132	+	8.25673i	0.236266	+	0.285565i
$837$	3.20322			0.110719
$838$	−23.7720			−0.821190
$839$			13.8360i			0.477670i	0.971060	+	0.238835i	$0.0767656\pi$
$839$			13.8360i			0.477670i	−0.971060	+	0.238835i	$0.923234\pi$
$840$		0			0
$841$	−31.0426			−1.07043
$842$		−	1.11501i		−	0.0384258i
$843$	10.5684			0.363996
$844$		−	21.9923i		−	0.757007i
$845$		−	51.6124i		−	1.77552i
$846$	3.20101			0.110053
$847$		0			0
$848$	−11.3155			−0.388575
$849$			10.4076i			0.357187i
$850$		−	45.0621i		−	1.54562i
$851$	14.4936			0.496835
$852$		−	2.84974i		−	0.0976304i
$853$	−9.77894			−0.334825			−0.167412	−	0.985887i	$-0.553541\pi$
$853$	−9.77894			−0.334825			−0.167412	+	0.985887i	$0.553541\pi$
$854$		0			0
$855$			13.8988i			0.475329i
$856$	−10.6139			−0.362775
$857$	−43.7118			−1.49317			−0.746583	−	0.665293i	$-0.768307\pi$
$857$	−43.7118			−1.49317			−0.746583	+	0.665293i	$0.768307\pi$
$858$	−2.11581	−	2.55729i	−0.0722325	−	0.0873043i
$859$			46.2851i			1.57923i	0.613604	+	0.789614i	$0.289719\pi$
$859$			46.2851i			1.57923i	−0.613604	+	0.789614i	$0.710281\pi$
$860$	17.8331			0.608102
$861$		0			0
$862$	29.3790			1.00065
$863$	−28.6154			−0.974081			−0.487041	−	0.873379i	$-0.661924\pi$
$863$	−28.6154			−0.974081			−0.487041	+	0.873379i	$0.661924\pi$
$864$	1.00000			0.0340207
$865$			26.7576i			0.909784i
$866$	−13.1705			−0.447552
$867$		−	5.86389i		−	0.199148i
$868$		0			0
$869$	−41.1220	+	34.0229i	−1.39497	+	1.15415i
$870$	−33.3316			−1.13005
$871$	−0.330637			−0.0112032
$872$	−0.348204			−0.0117917
$873$		−	12.3347i		−	0.417468i
$874$			18.5142i			0.626251i
$875$		0			0
$876$		−	14.8958i		−	0.503282i
$877$		−	55.6056i		−	1.87767i	−0.344370	−	0.938834i	$-0.611907\pi$
$877$		−	55.6056i		−	1.87767i	0.344370	−	0.938834i	$-0.388093\pi$
$878$			10.2133i			0.344682i
$879$		−	31.4600i		−	1.06112i
$880$	−10.9922	+	9.09452i	−0.370546	+	0.306576i
$881$		−	31.8585i		−	1.07334i	−0.843792	−	0.536671i	$-0.819682\pi$
$881$		−	31.8585i		−	1.07334i	0.843792	−	0.536671i	$-0.180318\pi$
$882$		0			0
$883$	55.9427			1.88262			0.941311	−	0.337539i	$-0.109595\pi$
$883$	55.9427			1.88262			0.941311	+	0.337539i	$0.109595\pi$
$884$	−3.33956			−0.112322
$885$			14.8073i			0.497743i
$886$			27.3723i			0.919592i
$887$	−10.9802			−0.368678			−0.184339	−	0.982863i	$-0.559014\pi$
$887$	−10.9802			−0.368678			−0.184339	+	0.982863i	$0.559014\pi$
$888$	−2.52944			−0.0848823
$889$		0			0
$890$			11.9781i			0.401507i
$891$	2.11424	+	2.55539i	0.0708296	+	0.0856087i
$892$			8.30245i			0.277987i
$893$		−	10.3428i		−	0.346109i
$894$		−	17.0794i		−	0.571220i
$895$			13.2442i			0.442705i
$896$		0			0
$897$		−	5.73424i		−	0.191461i
$898$			1.35953i			0.0453681i
$899$	24.8208			0.827820
$900$	−13.5035			−0.450115
$901$	−37.7607			−1.25799
$902$	−3.70815	+	3.06799i	−0.123468	+	0.102153i
$903$		0			0
$904$			18.9549i			0.630431i
$905$	−78.8230			−2.62017
$906$			8.31552i			0.276265i
$907$	2.11933			0.0703712			0.0351856	−	0.999381i	$-0.488798\pi$
$907$	2.11933			0.0703712			0.0351856	+	0.999381i	$0.488798\pi$
$908$	7.91253			0.262587
$909$	0.0562448			0.00186552
$910$		0			0
$911$	1.06472			0.0352757			0.0176379	−	0.999844i	$-0.494385\pi$
$911$	1.06472			0.0352757			0.0176379	+	0.999844i	$0.494385\pi$
$912$		−	3.23111i		−	0.106993i
$913$	3.70122	+	4.47351i	0.122493	+	0.148052i
$914$	−21.8981			−0.724326
$915$	63.8801			2.11181
$916$			10.7093i			0.353844i
$917$		0			0
$918$	3.33708			0.110140
$919$			41.2735i			1.36149i	0.732522	+	0.680744i	$0.238343\pi$
$919$			41.2735i			1.36149i	−0.732522	+	0.680744i	$0.761657\pi$
$920$	−24.6479			−0.812617
$921$			18.4994i			0.609577i
$922$		−	13.4227i		−	0.442054i
$923$	2.85185			0.0938699
$924$		0			0
$925$	34.1561			1.12305
$926$		−	21.1422i		−	0.694776i
$927$			14.7949i			0.485929i
$928$	7.74872			0.254364
$929$			20.3459i			0.667528i	0.942657	+	0.333764i	$0.108319\pi$
$929$			20.3459i			0.667528i	−0.942657	+	0.333764i	$0.891681\pi$
$930$	13.7788			0.451826
$931$		0			0
$932$			17.7106i			0.580129i
$933$	−30.9979			−1.01482
$934$	−2.87475			−0.0940646
$935$	−36.6817	+	30.3492i	−1.19962	+	0.992524i
$936$			1.00074i			0.0327103i
$937$	−21.9119			−0.715831			−0.357916	−	0.933754i	$-0.616512\pi$
$937$	−21.9119			−0.715831			−0.357916	+	0.933754i	$0.616512\pi$
$938$		0			0
$939$	−9.60149			−0.313333
$940$	13.7693			0.449107
$941$	−52.6097			−1.71503			−0.857514	−	0.514460i	$-0.827992\pi$
$941$	−52.6097			−1.71503			−0.857514	+	0.514460i	$0.827992\pi$
$942$		−	1.25113i		−	0.0407640i
$943$	−8.31484			−0.270768
$944$		−	3.44231i		−	0.112038i
$945$		0			0
$946$	−8.76502	−	10.5939i	−0.284976	−	0.344438i
$947$	−25.0357			−0.813550			−0.406775	−	0.913528i	$-0.633347\pi$
$947$	−25.0357			−0.813550			−0.406775	+	0.913528i	$0.633347\pi$
$948$	16.0923			0.522653
$949$	14.9069			0.483897
$950$			43.6311i			1.41558i
$951$		−	11.9425i		−	0.387263i
$952$		0			0
$953$			27.4386i			0.888823i	0.895823	+	0.444411i	$0.146587\pi$
$953$			27.4386i			0.888823i	−0.895823	+	0.444411i	$0.853413\pi$
$954$			11.3155i			0.366352i
$955$			89.5594i			2.89807i
$956$			26.6356i			0.861456i
$957$	16.3826	+	19.8010i	0.529575	+	0.640074i
$958$			3.83882i			0.124027i
$959$		0			0
$960$	4.30156			0.138832
$961$	20.7394			0.669013
$962$		−	2.53132i		−	0.0816129i
$963$			10.6139i			0.342028i
$964$	3.71041			0.119504
$965$	−19.4276			−0.625398
$966$		0			0
$967$		−	44.4870i		−	1.43061i	−0.698815	−	0.715303i	$-0.746289\pi$
$967$		−	44.4870i		−	1.43061i	0.698815	−	0.715303i	$-0.253711\pi$
$968$	10.8054	+	2.06001i	0.347298	+	0.0662112i
$969$		−	10.7825i		−	0.346383i
$970$		−	53.0587i		−	1.70361i
$971$		−	8.27547i		−	0.265573i	−0.991145	−	0.132786i	$-0.957608\pi$
$971$		−	8.27547i		−	0.265573i	0.991145	−	0.132786i	$-0.0423924\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$		−	9.68084i		−	0.310194i
$975$		−	13.5135i		−	0.432778i
$976$	−14.8504			−0.475351
$977$	28.8701			0.923637			0.461818	−	0.886975i	$-0.347197\pi$
$977$	28.8701			0.923637			0.461818	+	0.886975i	$0.347197\pi$
$978$	−7.21571			−0.230733
$979$	7.11572	−	5.88729i	0.227419	−	0.188159i
$980$		0			0
$981$			0.348204i			0.0111173i
$982$	15.8886			0.507025
$983$		−	44.6135i		−	1.42295i	−0.702711	−	0.711476i	$-0.748027\pi$
$983$		−	44.6135i		−	1.42295i	0.702711	−	0.711476i	$-0.251973\pi$
$984$	1.45111			0.0462597
$985$	−74.6593			−2.37884
$986$	25.8581			0.823490
$987$		0			0
$988$	3.23351			0.102872
$989$		−	23.7549i		−	0.755361i
$990$	9.09452	+	10.9922i	0.289043	+	0.349354i
$991$	−37.0562			−1.17713			−0.588565	−	0.808450i	$-0.700307\pi$
$991$	−37.0562			−1.17713			−0.588565	+	0.808450i	$0.700307\pi$
$992$	−3.20322			−0.101702
$993$			6.49162i			0.206005i
$994$		0			0
$995$	33.6236			1.06594
$996$		−	1.75062i		−	0.0554705i
$997$	−34.4937			−1.09243			−0.546213	−	0.837647i	$-0.683931\pi$
$997$	−34.4937			−1.09243			−0.546213	+	0.837647i	$0.683931\pi$
$998$		−	30.0440i		−	0.951025i
$999$			2.52944i			0.0800278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.a.2155.16		16
7.2	even	3		462.2.p.a.241.8	✓	16
7.3	odd	6		462.2.p.b.439.4	yes	16
7.6	odd	2		3234.2.e.b.2155.9		16
11.10	odd	2		3234.2.e.b.2155.8		16
21.2	odd	6		1386.2.bk.a.703.1		16
21.17	even	6		1386.2.bk.b.901.5		16
77.10	even	6		462.2.p.a.439.8	yes	16
77.65	odd	6		462.2.p.b.241.4	yes	16
77.76	even	2	inner	3234.2.e.a.2155.1		16
231.65	even	6		1386.2.bk.b.703.5		16
231.164	odd	6		1386.2.bk.a.901.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.8	✓	16	7.2	even	3
462.2.p.a.439.8	yes	16	77.10	even	6
462.2.p.b.241.4	yes	16	77.65	odd	6
462.2.p.b.439.4	yes	16	7.3	odd	6
1386.2.bk.a.703.1		16	21.2	odd	6
1386.2.bk.a.901.1		16	231.164	odd	6
1386.2.bk.b.703.5		16	231.65	even	6
1386.2.bk.b.901.5		16	21.17	even	6
3234.2.e.a.2155.1		16	77.76	even	2	inner
3234.2.e.a.2155.16		16	1.1	even	1	trivial
3234.2.e.b.2155.8		16	11.10	odd	2
3234.2.e.b.2155.9		16	7.6	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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +4.30156i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +4.30156i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} -4.30156 q^{10} +(2.11424 + 2.55539i) q^{11} -1.00000i q^{12} +1.00074 q^{13} -4.30156 q^{15} +1.00000 q^{16} +3.33708 q^{17} -1.00000i q^{18} -3.23111 q^{19} -4.30156i q^{20} +(-2.55539 + 2.11424i) q^{22} -5.72998 q^{23} +1.00000 q^{24} -13.5035 q^{25} +1.00074i q^{26} -1.00000i q^{27} -7.74872i q^{29} -4.30156i q^{30} +3.20322i q^{31} +1.00000i q^{32} +(-2.55539 + 2.11424i) q^{33} +3.33708i q^{34} +1.00000 q^{36} -2.52944 q^{37} -3.23111i q^{38} +1.00074i q^{39} +4.30156 q^{40} +1.45111 q^{41} +4.14572i q^{43} +(-2.11424 - 2.55539i) q^{44} -4.30156i q^{45} -5.72998i q^{46} +3.20101i q^{47} +1.00000i q^{48} -13.5035i q^{50} +3.33708i q^{51} -1.00074 q^{52} -11.3155 q^{53} +1.00000 q^{54} +(-10.9922 + 9.09452i) q^{55} -3.23111i q^{57} +7.74872 q^{58} -3.44231i q^{59} +4.30156 q^{60} -14.8504 q^{61} -3.20322 q^{62} -1.00000 q^{64} +4.30476i q^{65} +(-2.11424 - 2.55539i) q^{66} -0.330392 q^{67} -3.33708 q^{68} -5.72998i q^{69} +2.84974 q^{71} +1.00000i q^{72} +14.8958 q^{73} -2.52944i q^{74} -13.5035i q^{75} +3.23111 q^{76} -1.00074 q^{78} +16.0923i q^{79} +4.30156i q^{80} +1.00000 q^{81} +1.45111i q^{82} +1.75062 q^{83} +14.3547i q^{85} -4.14572 q^{86} +7.74872 q^{87} +(2.55539 - 2.11424i) q^{88} -2.78460i q^{89} +4.30156 q^{90} +5.72998 q^{92} -3.20322 q^{93} -3.20101 q^{94} -13.8988i q^{95} -1.00000 q^{96} +12.3347i q^{97} +(-2.11424 - 2.55539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 16 * q^6 - 16 * q^9	\( 16 q - 16 q^{4} - 16 q^{6} - 16 q^{9} - 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} + 20 q^{19} + 2 q^{22} + 8 q^{23} + 16 q^{24} - 20 q^{25} + 2 q^{33} + 16 q^{36} - 28 q^{37} + 4 q^{40} + 32 q^{41} - 8 q^{44} + 16 q^{54} - 14 q^{55} + 4 q^{60} - 56 q^{61} - 8 q^{62} - 16 q^{64} - 8 q^{66} + 32 q^{67} - 56 q^{71} + 88 q^{73} - 20 q^{76} + 16 q^{81} + 8 q^{83} + 24 q^{86} - 2 q^{88} + 4 q^{90} - 8 q^{92} - 8 q^{93} - 28 q^{94} - 16 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 16 * q^6 - 16 * q^9 - 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 + 20 * q^19 + 2 * q^22 + 8 * q^23 + 16 * q^24 - 20 * q^25 + 2 * q^33 + 16 * q^36 - 28 * q^37 + 4 * q^40 + 32 * q^41 - 8 * q^44 + 16 * q^54 - 14 * q^55 + 4 * q^60 - 56 * q^61 - 8 * q^62 - 16 * q^64 - 8 * q^66 + 32 * q^67 - 56 * q^71 + 88 * q^73 - 20 * q^76 + 16 * q^81 + 8 * q^83 + 24 * q^86 - 2 * q^88 + 4 * q^90 - 8 * q^92 - 8 * q^93 - 28 * q^94 - 16 * q^96 - 8 * q^99

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