LMFDB - Embedded newform 1764.2.b.l.1567.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(1567,1764)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1764.1567"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-4,0,-4,0,0,0,-4,0,0,0,0,0,0,0,-4,0,0,0,-24,0,0,0,0,-12,24, 0,0,-32,0,-16,-4,0,-32,0,0,32,-24,0,32,0,0,0,24,0,24,0,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(50)] == traces)

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.15911316233388032.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 35 x^{8} - 56 x^{7} + 84 x^{6} - 112 x^{5} + 140 x^{4} + \cdots + 64 $ x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 588)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.3
Root			$1.22594 + 0.705031i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.l.1567.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22594 - 0.705031i) q^{2} +(1.00586 + 1.72865i) q^{4} +3.64758i q^{5} +(-0.0143727 - 2.82839i) q^{8} +(2.57166 - 4.47172i) q^{10} +6.07019i q^{11} +0.483253i q^{13} +(-1.97648 + 3.47757i) q^{16} +2.55250i q^{17} +1.21909 q^{19} +(-6.30540 + 3.66896i) q^{20} +(4.27968 - 7.44170i) q^{22} +3.46720i q^{23} -8.30483 q^{25} +(0.340708 - 0.592439i) q^{26} -8.21857 q^{29} +6.31249 q^{31} +(4.87485 - 2.86982i) q^{32} +(1.79959 - 3.12921i) q^{34} +1.19016 q^{37} +(-1.49454 - 0.859498i) q^{38} +(10.3168 - 0.0524254i) q^{40} -6.59422i q^{41} +3.51184i q^{43} +(-10.4933 + 6.10578i) q^{44} +(2.44449 - 4.25059i) q^{46} +11.6622 q^{47} +(10.1812 + 5.85517i) q^{50} +(-0.835376 + 0.486085i) q^{52} -2.62782 q^{53} -22.1415 q^{55} +(10.0755 + 5.79435i) q^{58} +1.16160 q^{59} +0.208458i q^{61} +(-7.73874 - 4.45050i) q^{62} +(-7.99959 + 0.0813030i) q^{64} -1.76270 q^{65} -1.77617i q^{67} +(-4.41238 + 2.56746i) q^{68} -9.13166i q^{71} +6.04928i q^{73} +(-1.45907 - 0.839100i) q^{74} +(1.22624 + 2.10739i) q^{76} -3.17938i q^{79} +(-12.6847 - 7.20938i) q^{80} +(-4.64913 + 8.08412i) q^{82} -7.49842 q^{83} -9.31044 q^{85} +(2.47595 - 4.30530i) q^{86} +(17.1689 - 0.0872448i) q^{88} -12.2872i q^{89} +(-5.99359 + 3.48753i) q^{92} +(-14.2972 - 8.22221i) q^{94} +4.44674i q^{95} -11.8376i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} - 24 q^{20} - 12 q^{25} + 24 q^{26} - 32 q^{29} - 16 q^{31} - 4 q^{32} - 32 q^{34} + 32 q^{37} - 24 q^{38} + 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} - 32 q^{52}+ \cdots + 24 q^{88}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 - 24 * q^20 - 12 * q^25 + 24 * q^26 - 32 * q^29 - 16 * q^31 - 4 * q^32 - 32 * q^34 + 32 * q^37 - 24 * q^38 + 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 - 32 * q^52 + 32 * q^53 - 16 * q^55 + 16 * q^58 - 16 * q^59 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 32 * q^74 + 32 * q^76 - 16 * q^80 - 32 * q^82 - 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.22594	−	0.705031i	−0.866871	−	0.498532i
$2$	−1.22594	−	0.705031i	−0.866871	−	0.498532i
$3$		0			0
$3$		0			0
$4$	1.00586	+	1.72865i	0.502931	+	0.864327i
$5$			3.64758i			1.63125i	0.578583	+	0.815624i	$0.303606\pi$
$5$			3.64758i			1.63125i	−0.578583	+	0.815624i	$0.696394\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−0.0143727	−	2.82839i	−0.00508150	−	0.999987i
$9$		0			0
$10$	2.57166	−	4.47172i	0.813229	−	1.41408i
$11$			6.07019i			1.83023i	0.403190	+	0.915116i	$0.367901\pi$
$11$			6.07019i			1.83023i	−0.403190	+	0.915116i	$0.632099\pi$
$12$		0			0
$13$			0.483253i			0.134030i	0.997752	+	0.0670151i	$0.0213476\pi$
$13$			0.483253i			0.134030i	−0.997752	+	0.0670151i	$0.978652\pi$
$14$		0			0
$15$		0			0
$16$	−1.97648	+	3.47757i	−0.494121	+	0.869393i
$17$			2.55250i			0.619072i	0.950888	+	0.309536i	$0.100174\pi$
$17$			2.55250i			0.619072i	−0.950888	+	0.309536i	$0.899826\pi$
$18$		0			0
$19$	1.21909			0.279679			0.139840	−	0.990174i	$-0.455341\pi$
$19$	1.21909			0.279679			0.139840	+	0.990174i	$0.455341\pi$
$20$	−6.30540	+	3.66896i	−1.40993	+	0.820405i
$21$		0			0
$22$	4.27968	−	7.44170i	0.912430	−	1.58658i
$23$			3.46720i			0.722962i	0.932379	+	0.361481i	$0.117729\pi$
$23$			3.46720i			0.722962i	−0.932379	+	0.361481i	$0.882271\pi$
$24$		0			0
$25$	−8.30483			−1.66097
$26$	0.340708	−	0.592439i	0.0668184	−	0.116187i
$27$		0			0
$28$		0			0
$29$	−8.21857			−1.52615			−0.763075	−	0.646310i	$-0.776311\pi$
$29$	−8.21857			−1.52615			−0.763075	+	0.646310i	$0.776311\pi$
$30$		0			0
$31$	6.31249			1.13376			0.566878	−	0.823801i	$-0.308151\pi$
$31$	6.31249			1.13376			0.566878	+	0.823801i	$0.308151\pi$
$32$	4.87485	−	2.86982i	0.861760	−	0.507317i
$33$		0			0
$34$	1.79959	−	3.12921i	0.308627	−	0.536655i
$35$		0			0
$36$		0			0
$37$	1.19016			0.195661			0.0978305	−	0.995203i	$-0.468810\pi$
$37$	1.19016			0.195661			0.0978305	+	0.995203i	$0.468810\pi$
$38$	−1.49454	−	0.859498i	−0.242446	−	0.139429i
$39$		0			0
$40$	10.3168	−	0.0524254i	1.63123	−	0.00828918i
$41$		−	6.59422i		−	1.02984i	−0.857237	−	0.514922i	$-0.827821\pi$
$41$		−	6.59422i		−	1.02984i	0.857237	−	0.514922i	$-0.172179\pi$
$42$		0			0
$43$			3.51184i			0.535550i	0.963481	+	0.267775i	$0.0862884\pi$
$43$			3.51184i			0.535550i	−0.963481	+	0.267775i	$0.913712\pi$
$44$	−10.4933	+	6.10578i	−1.58192	+	0.920480i
$45$		0			0
$46$	2.44449	−	4.25059i	0.360420	−	0.626715i
$47$	11.6622			1.70111			0.850553	−	0.525889i	$-0.176267\pi$
$47$	11.6622			1.70111			0.850553	+	0.525889i	$0.176267\pi$
$48$		0			0
$49$		0			0
$50$	10.1812	+	5.85517i	1.43984	+	0.828046i
$51$		0			0
$52$	−0.835376	+	0.486085i	−0.115846	+	0.0674079i
$53$	−2.62782			−0.360959			−0.180479	−	0.983579i	$-0.557765\pi$
$53$	−2.62782			−0.360959			−0.180479	+	0.983579i	$0.557765\pi$
$54$		0			0
$55$	−22.1415			−2.98556
$56$		0			0
$57$		0			0
$58$	10.0755	+	5.79435i	1.32298	+	0.760835i
$59$	1.16160			0.151228			0.0756138	−	0.997137i	$-0.475908\pi$
$59$	1.16160			0.151228			0.0756138	+	0.997137i	$0.475908\pi$
$60$		0			0
$61$			0.208458i			0.0266903i	0.999911	+	0.0133451i	$0.00424802\pi$
$61$			0.208458i			0.0266903i	−0.999911	+	0.0133451i	$0.995752\pi$
$62$	−7.73874	−	4.45050i	−0.982821	−	0.565215i
$63$		0			0
$64$	−7.99959	+	0.0813030i	−0.999948	+	0.0101629i
$65$	−1.76270			−0.218636
$66$		0			0
$67$		−	1.77617i		−	0.216993i	−0.994097	−	0.108497i	$-0.965396\pi$
$67$		−	1.77617i		−	0.216993i	0.994097	−	0.108497i	$-0.0346037\pi$
$68$	−4.41238	+	2.56746i	−0.535080	+	0.311350i
$69$		0			0
$70$		0			0
$71$		−	9.13166i		−	1.08373i	−0.840466	−	0.541864i	$-0.817719\pi$
$71$		−	9.13166i		−	1.08373i	0.840466	−	0.541864i	$-0.182281\pi$
$72$		0			0
$73$			6.04928i			0.708015i	0.935243	+	0.354007i	$0.115181\pi$
$73$			6.04928i			0.708015i	−0.935243	+	0.354007i	$0.884819\pi$
$74$	−1.45907	−	0.839100i	−0.169613	−	0.0975433i
$75$		0			0
$76$	1.22624	+	2.10739i	0.140659	+	0.241734i
$77$		0			0
$78$		0			0
$79$		−	3.17938i		−	0.357708i	−0.983876	−	0.178854i	$-0.942761\pi$
$79$		−	3.17938i		−	0.357708i	0.983876	−	0.178854i	$-0.0572390\pi$
$80$	−12.6847	−	7.20938i	−1.41820	−	0.806033i
$81$		0			0
$82$	−4.64913	+	8.08412i	−0.513410	+	0.892742i
$83$	−7.49842			−0.823059			−0.411529	−	0.911396i	$-0.635005\pi$
$83$	−7.49842			−0.823059			−0.411529	+	0.911396i	$0.635005\pi$
$84$		0			0
$85$	−9.31044			−1.00986
$86$	2.47595	−	4.30530i	0.266989	−	0.464253i
$87$		0			0
$88$	17.1689	−	0.0872448i	1.83021	−	0.00930033i
$89$		−	12.2872i		−	1.30244i	−0.758887	−	0.651222i	$-0.774257\pi$
$89$		−	12.2872i		−	1.30244i	0.758887	−	0.651222i	$-0.225743\pi$
$90$		0			0
$91$		0			0
$92$	−5.99359	+	3.48753i	−0.624875	+	0.363600i
$93$		0			0
$94$	−14.2972	−	8.22221i	−1.47464	−	0.848057i
$95$			4.44674i			0.456226i
$96$		0			0
$97$		−	11.8376i		−	1.20192i	−0.799277	−	0.600962i	$-0.794784\pi$
$97$		−	11.8376i		−	1.20192i	0.799277	−	0.600962i	$-0.205216\pi$
$98$		0			0
$99$		0			0
$100$	−8.35352	−	14.3562i	−0.835352	−	1.43562i
$101$		−	5.72662i		−	0.569820i	−0.958554	−	0.284910i	$-0.908036\pi$
$101$		−	5.72662i		−	0.569820i	0.958554	−	0.284910i	$-0.0919637\pi$
$102$		0			0
$103$	−4.95307			−0.488041			−0.244020	−	0.969770i	$-0.578466\pi$
$103$	−4.95307			−0.488041			−0.244020	+	0.969770i	$0.578466\pi$
$104$	1.36683	−	0.00694562i	0.134028	−	0.000681074i
$105$		0			0
$106$	3.22155	+	1.85270i	0.312905	+	0.179950i
$107$			13.7280i			1.32713i	0.748118	+	0.663566i	$0.230958\pi$
$107$			13.7280i			1.32713i	−0.748118	+	0.663566i	$0.769042\pi$
$108$		0			0
$109$	−13.6507			−1.30750			−0.653752	−	0.756709i	$-0.726806\pi$
$109$	−13.6507			−1.30750			−0.653752	+	0.756709i	$0.726806\pi$
$110$	27.1442	+	15.6105i	2.58810	+	1.48840i
$111$		0			0
$112$		0			0
$113$	7.11968			0.669764			0.334882	−	0.942260i	$-0.391304\pi$
$113$	7.11968			0.669764			0.334882	+	0.942260i	$0.391304\pi$
$114$		0			0
$115$	−12.6469			−1.17933
$116$	−8.26674	−	14.2071i	−0.767548	−	1.31909i
$117$		0			0
$118$	−1.42406	−	0.818966i	−0.131095	−	0.0753919i
$119$		0			0
$120$		0			0
$121$	−25.8472			−2.34975
$122$	0.146969	−	0.255557i	0.0133060	−	0.0231370i
$123$		0			0
$124$	6.34949	+	10.9121i	0.570201	+	0.979936i
$125$		−	12.0546i		−	1.07820i
$126$		0			0
$127$			3.03609i			0.269409i	0.990886	+	0.134705i	$0.0430086\pi$
$127$			3.03609i			0.269409i	−0.990886	+	0.134705i	$0.956991\pi$
$128$	9.86434	+	5.54029i	0.871893	+	0.489697i
$129$		0			0
$130$	2.16097	+	1.24276i	0.189530	+	0.108997i
$131$	−14.4666			−1.26395			−0.631974	−	0.774989i	$-0.717755\pi$
$131$	−14.4666			−1.26395			−0.631974	+	0.774989i	$0.717755\pi$
$132$		0			0
$133$		0			0
$134$	−1.25225	+	2.17747i	−0.108178	+	0.188105i
$135$		0			0
$136$	7.21946	−	0.0366862i	0.619064	−	0.00314581i
$137$	−11.5627			−0.987866			−0.493933	−	0.869500i	$-0.664441\pi$
$137$	−11.5627			−0.987866			−0.493933	+	0.869500i	$0.664441\pi$
$138$		0			0
$139$	17.6203			1.49453			0.747266	−	0.664525i	$-0.231366\pi$
$139$	17.6203			1.49453			0.747266	+	0.664525i	$0.231366\pi$
$140$		0			0
$141$		0			0
$142$	−6.43811	+	11.1949i	−0.540274	+	0.939453i
$143$	−2.93344			−0.245306
$144$		0			0
$145$		−	29.9779i		−	2.48953i
$146$	4.26493	−	7.41606i	0.352968	−	0.613757i
$147$		0			0
$148$	1.19714	+	2.05737i	0.0984040	+	0.169115i
$149$	−6.11467			−0.500934			−0.250467	−	0.968125i	$-0.580584\pi$
$149$	−6.11467			−0.500934			−0.250467	+	0.968125i	$0.580584\pi$
$150$		0			0
$151$			14.2427i			1.15906i	0.814952	+	0.579529i	$0.196763\pi$
$151$			14.2427i			1.15906i	−0.814952	+	0.579529i	$0.803237\pi$
$152$	−0.0175216	−	3.44807i	−0.00142119	−	0.279675i
$153$		0			0
$154$		0			0
$155$			23.0253i			1.84944i
$156$		0			0
$157$			21.0971i			1.68373i	0.539689	+	0.841865i	$0.318542\pi$
$157$			21.0971i			1.68373i	−0.539689	+	0.841865i	$0.681458\pi$
$158$	−2.24156	+	3.89773i	−0.178329	+	0.310087i
$159$		0			0
$160$	10.4679	+	17.7814i	0.827559	+	1.40574i
$161$		0			0
$162$		0			0
$163$			19.1370i			1.49893i	0.662046	+	0.749464i	$0.269689\pi$
$163$			19.1370i			1.49893i	−0.662046	+	0.749464i	$0.730311\pi$
$164$	11.3991	−	6.63287i	0.890121	−	0.517940i
$165$		0			0
$166$	9.19262	+	5.28662i	0.713486	+	0.410322i
$167$	7.69624			0.595553			0.297776	−	0.954636i	$-0.403755\pi$
$167$	7.69624			0.595553			0.297776	+	0.954636i	$0.403755\pi$
$168$		0			0
$169$	12.7665			0.982036
$170$	11.4140	+	6.56415i	0.875417	+	0.503447i
$171$		0			0
$172$	−6.07075	+	3.53242i	−0.462890	+	0.269345i
$173$			0.823365i			0.0625993i	0.999510	+	0.0312996i	$0.00996461\pi$
$173$			0.823365i			0.0625993i	−0.999510	+	0.0312996i	$0.990035\pi$
$174$		0			0
$175$		0			0
$176$	−21.1095	−	11.9976i	−1.59119	−	0.904356i
$177$		0			0
$178$	−8.66288	+	15.0634i	−0.649311	+	1.12905i
$179$		−	9.47297i		−	0.708043i	−0.935237	−	0.354022i	$-0.884814\pi$
$179$		−	9.47297i		−	0.708043i	0.935237	−	0.354022i	$-0.115186\pi$
$180$		0			0
$181$		−	2.06119i		−	0.153207i	−0.997062	−	0.0766034i	$-0.975592\pi$
$181$		−	2.06119i		−	0.153207i	0.997062	−	0.0766034i	$-0.0244075\pi$
$182$		0			0
$183$		0			0
$184$	9.80661	−	0.0498329i	0.722953	−	0.00367373i
$185$			4.34120i			0.319171i
$186$		0			0
$187$	−15.4942			−1.13304
$188$	11.7306	+	20.1599i	0.855539	+	1.47031i
$189$		0			0
$190$	3.13509	−	5.45144i	0.227443	−	0.395489i
$191$			10.8564i			0.785541i	0.919637	+	0.392770i	$0.128483\pi$
$191$			10.8564i			0.785541i	−0.919637	+	0.392770i	$0.871517\pi$
$192$		0			0
$193$	9.71346			0.699190			0.349595	−	0.936901i	$-0.386319\pi$
$193$	9.71346			0.699190			0.349595	+	0.936901i	$0.386319\pi$
$194$	−8.34587	+	14.5122i	−0.599198	+	1.04191i
$195$		0			0
$196$		0			0
$197$	15.9300			1.13496			0.567481	−	0.823386i	$-0.307918\pi$
$197$	15.9300			1.13496			0.567481	+	0.823386i	$0.307918\pi$
$198$		0			0
$199$	10.0572			0.712935			0.356467	−	0.934308i	$-0.383981\pi$
$199$	10.0572			0.712935			0.356467	+	0.934308i	$0.383981\pi$
$200$	0.119363	+	23.4893i	0.00844020	+	1.66095i
$201$		0			0
$202$	−4.03745	+	7.02050i	−0.284074	+	0.493961i
$203$		0			0
$204$		0			0
$205$	24.0529			1.67993
$206$	6.07217	+	3.49207i	0.423068	+	0.243304i
$207$		0			0
$208$	−1.68055	−	0.955141i	−0.116525	−	0.0662271i
$209$			7.40013i			0.511878i
$210$		0			0
$211$		−	1.03227i		−	0.0710647i	−0.999369	−	0.0355324i	$-0.988687\pi$
$211$		−	1.03227i		−	0.0710647i	0.999369	−	0.0355324i	$-0.0113127\pi$
$212$	−2.64322	−	4.54259i	−0.181537	−	0.311986i
$213$		0			0
$214$	9.67863	−	16.8297i	0.661618	−	1.15045i
$215$	−12.8097			−0.873614
$216$		0			0
$217$		0			0
$218$	16.7350	+	9.62420i	1.13344	+	0.651833i
$219$		0			0
$220$	−22.2713	−	38.2750i	−1.50153	−	2.58050i
$221$	−1.23350			−0.0829743
$222$		0			0
$223$	9.57250			0.641022			0.320511	−	0.947245i	$-0.396145\pi$
$223$	9.57250			0.641022			0.320511	+	0.947245i	$0.396145\pi$
$224$		0			0
$225$		0			0
$226$	−8.72831	−	5.01960i	−0.580599	−	0.333899i
$227$	−11.1538			−0.740307			−0.370153	−	0.928971i	$-0.620695\pi$
$227$	−11.1538			−0.740307			−0.370153	+	0.928971i	$0.620695\pi$
$228$		0			0
$229$			10.1285i			0.669308i	0.942341	+	0.334654i	$0.108619\pi$
$229$			10.1285i			0.669308i	−0.942341	+	0.334654i	$0.891381\pi$
$230$	15.5043	+	8.91646i	1.02233	+	0.587934i
$231$		0			0
$232$	0.118123	+	23.2453i	0.00775513	+	1.52613i
$233$	−12.6414			−0.828168			−0.414084	−	0.910239i	$-0.635898\pi$
$233$	−12.6414			−0.828168			−0.414084	+	0.910239i	$0.635898\pi$
$234$		0			0
$235$			42.5388i			2.77492i
$236$	1.16841	+	2.00801i	0.0760571	+	0.130710i
$237$		0			0
$238$		0			0
$239$		−	5.46050i		−	0.353211i	−0.984282	−	0.176605i	$-0.943488\pi$
$239$		−	5.46050i		−	0.353211i	0.984282	−	0.176605i	$-0.0565116\pi$
$240$		0			0
$241$		−	13.6377i		−	0.878484i	−0.898369	−	0.439242i	$-0.855247\pi$
$241$		−	13.6377i		−	0.878484i	0.898369	−	0.439242i	$-0.144753\pi$
$242$	31.6872	+	18.2231i	2.03693	+	1.17143i
$243$		0			0
$244$	−0.360351	+	0.209680i	−0.0230691	+	0.0134234i
$245$		0			0
$246$		0			0
$247$			0.589130i			0.0374854i
$248$	−0.0907272	−	17.8542i	−0.00576119	−	1.13374i
$249$		0			0
$250$	−8.49890	+	14.7783i	−0.537518	+	0.934661i
$251$	−28.2425			−1.78265			−0.891324	−	0.453367i	$-0.850223\pi$
$251$	−28.2425			−1.78265			−0.891324	+	0.453367i	$0.850223\pi$
$252$		0			0
$253$	−21.0466			−1.32319
$254$	2.14054	−	3.72206i	0.134309	−	0.233543i
$255$		0			0
$256$	−8.18702	−	13.7467i	−0.511689	−	0.859171i
$257$		−	20.1625i		−	1.25770i	−0.777525	−	0.628852i	$-0.783525\pi$
$257$		−	20.1625i		−	1.25770i	0.777525	−	0.628852i	$-0.216475\pi$
$258$		0			0
$259$		0			0
$260$	−1.77304	−	3.04710i	−0.109959	−	0.188973i
$261$		0			0
$262$	17.7351	+	10.1994i	1.09568	+	0.630119i
$263$			12.5084i			0.771300i	0.922645	+	0.385650i	$0.126023\pi$
$263$			12.5084i			0.771300i	−0.922645	+	0.385650i	$0.873977\pi$
$264$		0			0
$265$		−	9.58518i		−	0.588813i
$266$		0			0
$267$		0			0
$268$	3.07037	−	1.78658i	0.187553	−	0.109133i
$269$			13.0548i			0.795962i	0.917394	+	0.397981i	$0.130289\pi$
$269$			13.0548i			0.795962i	−0.917394	+	0.397981i	$0.869711\pi$
$270$		0			0
$271$	−10.2934			−0.625282			−0.312641	−	0.949871i	$-0.601214\pi$
$271$	−10.2934			−0.625282			−0.312641	+	0.949871i	$0.601214\pi$
$272$	−8.87650	−	5.04497i	−0.538217	−	0.305896i
$273$		0			0
$274$	14.1752	+	8.15205i	0.856352	+	0.492483i
$275$		−	50.4119i		−	3.03995i
$276$		0			0
$277$	−18.9622			−1.13933			−0.569665	−	0.821877i	$-0.692927\pi$
$277$	−18.9622			−1.13933			−0.569665	+	0.821877i	$0.692927\pi$
$278$	−21.6014	−	12.4228i	−1.29557	−	0.745073i
$279$		0			0
$280$		0			0
$281$	−17.5144			−1.04482			−0.522412	−	0.852693i	$-0.674968\pi$
$281$	−17.5144			−1.04482			−0.522412	+	0.852693i	$0.674968\pi$
$282$		0			0
$283$	18.9419			1.12598			0.562990	−	0.826464i	$-0.309651\pi$
$283$	18.9419			1.12598			0.562990	+	0.826464i	$0.309651\pi$
$284$	15.7855	−	9.18519i	0.936696	−	0.545041i
$285$		0			0
$286$	3.59622	+	2.06816i	0.212649	+	0.122293i
$287$		0			0
$288$		0			0
$289$	10.4848			0.616750
$290$	−21.1353	+	36.7511i	−1.24111	+	2.15810i
$291$		0			0
$292$	−10.4571	+	6.08474i	−0.611956	+	0.356082i
$293$			25.2760i			1.47664i	0.674451	+	0.738320i	$0.264380\pi$
$293$			25.2760i			1.47664i	−0.674451	+	0.738320i	$0.735620\pi$
$294$		0			0
$295$			4.23703i			0.246690i
$296$	−0.0171057	−	3.36624i	−0.000994251	−	0.195658i
$297$		0			0
$298$	7.49623	+	4.31104i	0.434245	+	0.249732i
$299$	−1.67554			−0.0968987
$300$		0			0
$301$		0			0
$302$	10.0416	−	17.4608i	0.577828	−	1.00475i
$303$		0			0
$304$	−2.40952	+	4.23948i	−0.138195	+	0.243151i
$305$	−0.760366			−0.0435385
$306$		0			0
$307$	10.2457			0.584750			0.292375	−	0.956304i	$-0.405554\pi$
$307$	10.2457			0.584750			0.292375	+	0.956304i	$0.405554\pi$
$308$		0			0
$309$		0			0
$310$	16.2336	−	28.2277i	0.922005	−	1.60322i
$311$	30.3837			1.72290			0.861451	−	0.507840i	$-0.169556\pi$
$311$	30.3837			1.72290			0.861451	+	0.507840i	$0.169556\pi$
$312$		0			0
$313$		−	17.1215i		−	0.967764i	−0.875133	−	0.483882i	$-0.839226\pi$
$313$		−	17.1215i		−	0.967764i	0.875133	−	0.483882i	$-0.160774\pi$
$314$	14.8741	−	25.8638i	0.839394	−	1.45958i
$315$		0			0
$316$	5.49605	−	3.19802i	0.309177	−	0.179903i
$317$	12.3657			0.694527			0.347264	−	0.937768i	$-0.387111\pi$
$317$	12.3657			0.694527			0.347264	+	0.937768i	$0.387111\pi$
$318$		0			0
$319$		−	49.8883i		−	2.79321i
$320$	−0.296559	−	29.1791i	−0.0165782	−	1.63116i
$321$		0			0
$322$		0			0
$323$			3.11173i			0.173141i
$324$		0			0
$325$		−	4.01333i		−	0.222620i
$326$	13.4922	−	23.4609i	0.747264	−	1.29938i
$327$		0			0
$328$	−18.6510	+	0.0947764i	−1.02983	+	0.00523315i
$329$		0			0
$330$		0			0
$331$		−	7.68197i		−	0.422239i	−0.977460	−	0.211120i	$-0.932289\pi$
$331$		−	7.68197i		−	0.422239i	0.977460	−	0.211120i	$-0.0677109\pi$
$332$	−7.54238	−	12.9622i	−0.413942	−	0.711392i
$333$		0			0
$334$	−9.43514	−	5.42609i	−0.516268	−	0.296902i
$335$	6.47871			0.353969
$336$		0			0
$337$	−13.3863			−0.729201			−0.364600	−	0.931164i	$-0.618794\pi$
$337$	−13.3863			−0.729201			−0.364600	+	0.931164i	$0.618794\pi$
$338$	−15.6509	−	9.00076i	−0.851299	−	0.489577i
$339$		0			0
$340$	−9.36501	−	16.0945i	−0.507889	−	0.872848i
$341$			38.3180i			2.07504i
$342$		0			0
$343$		0			0
$344$	9.93284	−	0.0504744i	0.535543	−	0.00272140i
$345$		0			0
$346$	0.580498	−	1.00940i	0.0312078	−	0.0542655i
$347$		−	31.8786i		−	1.71133i	−0.517529	−	0.855666i	$-0.673148\pi$
$347$		−	31.8786i		−	1.71133i	0.517529	−	0.855666i	$-0.326852\pi$
$348$		0			0
$349$		−	9.51634i		−	0.509398i	−0.967020	−	0.254699i	$-0.918024\pi$
$349$		−	9.51634i		−	0.509398i	0.967020	−	0.254699i	$-0.0819764\pi$
$350$		0			0
$351$		0			0
$352$	17.4203	+	29.5913i	0.928507	+	1.57722i
$353$			14.1326i			0.752201i	0.926579	+	0.376100i	$0.122735\pi$
$353$			14.1326i			0.752201i	−0.926579	+	0.376100i	$0.877265\pi$
$354$		0			0
$355$	33.3085			1.76783
$356$	21.2404	−	12.3593i	1.12574	−	0.655040i
$357$		0			0
$358$	−6.67874	+	11.6133i	−0.352982	+	0.613782i
$359$		−	22.4656i		−	1.18569i	−0.805318	−	0.592843i	$-0.798005\pi$
$359$		−	22.4656i		−	1.18569i	0.805318	−	0.592843i	$-0.201995\pi$
$360$		0			0
$361$	−17.5138			−0.921780
$362$	−1.45320	+	2.52689i	−0.0763785	+	0.132811i
$363$		0			0
$364$		0			0
$365$	−22.0652			−1.15495
$366$		0			0
$367$	−11.9991			−0.626349			−0.313174	−	0.949696i	$-0.601392\pi$
$367$	−11.9991			−0.626349			−0.313174	+	0.949696i	$0.601392\pi$
$368$	−12.0575	−	6.85287i	−0.628538	−	0.357231i
$369$		0			0
$370$	3.06068	−	5.32206i	0.159117	−	0.276680i
$371$		0			0
$372$		0			0
$373$	5.62760			0.291386			0.145693	−	0.989330i	$-0.453459\pi$
$373$	5.62760			0.291386			0.145693	+	0.989330i	$0.453459\pi$
$374$	18.9949	+	10.9239i	0.982204	+	0.564859i
$375$		0			0
$376$	−0.167617	−	32.9852i	−0.00864417	−	1.70108i
$377$		−	3.97165i		−	0.204550i
$378$		0			0
$379$		−	21.3356i		−	1.09594i	−0.836500	−	0.547968i	$-0.815402\pi$
$379$		−	21.3356i		−	1.09594i	0.836500	−	0.547968i	$-0.184598\pi$
$380$	−7.68687	+	4.47280i	−0.394328	+	0.229450i
$381$		0			0
$382$	7.65410	−	13.3093i	0.391618	−	0.680963i
$383$	−7.55189			−0.385884			−0.192942	−	0.981210i	$-0.561803\pi$
$383$	−7.55189			−0.385884			−0.192942	+	0.981210i	$0.561803\pi$
$384$		0			0
$385$		0			0
$386$	−11.9081	−	6.84829i	−0.606108	−	0.348569i
$387$		0			0
$388$	20.4631	−	11.9070i	1.03886	−	0.604485i
$389$	2.65061			0.134391			0.0671957	−	0.997740i	$-0.478595\pi$
$389$	2.65061			0.134391			0.0671957	+	0.997740i	$0.478595\pi$
$390$		0			0
$391$	−8.85003			−0.447565
$392$		0			0
$393$		0			0
$394$	−19.5292	−	11.2311i	−0.983866	−	0.565816i
$395$	11.5970			0.583511
$396$		0			0
$397$			18.6502i			0.936025i	0.883722	+	0.468012i	$0.155030\pi$
$397$			18.6502i			0.936025i	−0.883722	+	0.468012i	$0.844970\pi$
$398$	−12.3295	−	7.09063i	−0.618023	−	0.355421i
$399$		0			0
$400$	16.4144	−	28.8807i	0.820718	−	1.44403i
$401$	23.8483			1.19093			0.595464	−	0.803382i	$-0.296968\pi$
$401$	23.8483			1.19093			0.595464	+	0.803382i	$0.296968\pi$
$402$		0			0
$403$			3.05053i			0.151958i
$404$	9.89934	−	5.76019i	0.492511	−	0.286580i
$405$		0			0
$406$		0			0
$407$			7.22450i			0.358105i
$408$		0			0
$409$			17.4269i			0.861706i	0.902422	+	0.430853i	$0.141787\pi$
$409$			17.4269i			0.861706i	−0.902422	+	0.430853i	$0.858213\pi$
$410$	−29.4875	−	16.9581i	−1.45628	−	0.837499i
$411$		0			0
$412$	−4.98211	−	8.56215i	−0.245451	−	0.421827i
$413$		0			0
$414$		0			0
$415$		−	27.3511i		−	1.34261i
$416$	1.38685	+	2.35578i	0.0679957	+	0.115502i
$417$		0			0
$418$	5.21732	−	9.07212i	0.255188	−	0.443732i
$419$	26.6148			1.30022			0.650109	−	0.759841i	$-0.274723\pi$
$419$	26.6148			1.30022			0.650109	+	0.759841i	$0.274723\pi$
$420$		0			0
$421$	17.2196			0.839234			0.419617	−	0.907701i	$-0.362164\pi$
$421$	17.2196			0.839234			0.419617	+	0.907701i	$0.362164\pi$
$422$	−0.727786	+	1.26551i	−0.0354281	+	0.0616040i
$423$		0			0
$424$	0.0377688	+	7.43250i	0.00183421	+	0.360954i
$425$		−	21.1981i		−	1.02826i
$426$		0			0
$427$		0			0
$428$	−23.7309	+	13.8084i	−1.14707	+	0.667455i
$429$		0			0
$430$	15.7039	+	9.03124i	0.757311	+	0.435525i
$431$			19.6830i			0.948095i	0.880499	+	0.474047i	$0.157207\pi$
$431$			19.6830i			0.948095i	−0.880499	+	0.474047i	$0.842793\pi$
$432$		0			0
$433$		−	6.43311i		−	0.309156i	−0.987981	−	0.154578i	$-0.950598\pi$
$433$		−	6.43311i		−	0.309156i	0.987981	−	0.154578i	$-0.0494017\pi$
$434$		0			0
$435$		0			0
$436$	−13.7308	−	23.5974i	−0.657584	−	1.13011i
$437$			4.22684i			0.202197i
$438$		0			0
$439$	6.95350			0.331872			0.165936	−	0.986137i	$-0.446935\pi$
$439$	6.95350			0.331872			0.165936	+	0.986137i	$0.446935\pi$
$440$	0.318232	+	62.6248i	0.0151711	+	2.98552i
$441$		0			0
$442$	1.51220	+	0.869657i	0.0719280	+	0.0413654i
$443$			7.78413i			0.369835i	0.982754	+	0.184918i	$0.0592018\pi$
$443$			7.78413i			0.369835i	−0.982754	+	0.184918i	$0.940798\pi$
$444$		0			0
$445$	44.8187			2.12461
$446$	−11.7353	−	6.74891i	−0.555684	−	0.319570i
$447$		0			0
$448$		0			0
$449$	13.4404			0.634290			0.317145	−	0.948377i	$-0.397276\pi$
$449$	13.4404			0.634290			0.317145	+	0.948377i	$0.397276\pi$
$450$		0			0
$451$	40.0282			1.88485
$452$	7.16142	+	12.3075i	0.336845	+	0.578894i
$453$		0			0
$454$	13.6740	+	7.86381i	0.641750	+	0.369067i
$455$		0			0
$456$		0			0
$457$	−1.16365			−0.0544333			−0.0272166	−	0.999630i	$-0.508664\pi$
$457$	−1.16365			−0.0544333			−0.0272166	+	0.999630i	$0.508664\pi$
$458$	7.14088	−	12.4169i	0.333672	−	0.580203i
$459$		0			0
$460$	−12.7210	−	21.8621i	−0.593121	−	1.01933i
$461$			21.4211i			0.997678i	0.866695	+	0.498839i	$0.166240\pi$
$461$			21.4211i			0.997678i	−0.866695	+	0.498839i	$0.833760\pi$
$462$		0			0
$463$			14.4408i			0.671119i	0.942019	+	0.335560i	$0.108925\pi$
$463$			14.4408i			0.671119i	−0.942019	+	0.335560i	$0.891075\pi$
$464$	16.2439	−	28.5807i	0.754103	−	1.32682i
$465$		0			0
$466$	15.4977	+	8.91261i	0.717915	+	0.412869i
$467$	29.7659			1.37740			0.688701	−	0.725045i	$-0.258181\pi$
$467$	29.7659			1.37740			0.688701	+	0.725045i	$0.258181\pi$
$468$		0			0
$469$		0			0
$470$	29.9912	−	52.1500i	1.38339	−	2.40550i
$471$		0			0
$472$	−0.0166953	−	3.28546i	−0.000768464	−	0.151226i
$473$	−21.3175			−0.980181
$474$		0			0
$475$	−10.1244			−0.464538
$476$		0			0
$477$		0			0
$478$	−3.84983	+	6.69426i	−0.176087	+	0.306188i
$479$	−28.3552			−1.29558			−0.647790	−	0.761819i	$-0.724307\pi$
$479$	−28.3552			−1.29558			−0.647790	+	0.761819i	$0.724307\pi$
$480$		0			0
$481$			0.575148i			0.0262245i
$482$	−9.61504	+	16.7191i	−0.437953	+	0.761533i
$483$		0			0
$484$	−25.9988	−	44.6809i	−1.18176	−	2.03095i
$485$	43.1785			1.96064
$486$		0			0
$487$			9.56787i			0.433561i	0.976220	+	0.216781i	$0.0695557\pi$
$487$			9.56787i			0.433561i	−0.976220	+	0.216781i	$0.930444\pi$
$488$	0.589600	−	0.00299609i	0.0266899	−	0.000135627i
$489$		0			0
$490$		0			0
$491$		−	17.7521i		−	0.801141i	−0.916266	−	0.400571i	$-0.868812\pi$
$491$		−	17.7521i		−	0.801141i	0.916266	−	0.400571i	$-0.131188\pi$
$492$		0			0
$493$		−	20.9779i		−	0.944796i
$494$	0.415355	−	0.722238i	0.0186877	−	0.0324950i
$495$		0			0
$496$	−12.4765	+	21.9521i	−0.560213	+	0.985681i
$497$		0			0
$498$		0			0
$499$			9.40111i			0.420852i	0.977610	+	0.210426i	$0.0674850\pi$
$499$			9.40111i			0.420852i	−0.977610	+	0.210426i	$0.932515\pi$
$500$	20.8383	−	12.1253i	0.931917	−	0.542260i
$501$		0			0
$502$	34.6236	+	19.9118i	1.54533	+	0.888708i
$503$	40.9278			1.82488			0.912440	−	0.409211i	$-0.134196\pi$
$503$	40.9278			1.82488			0.912440	+	0.409211i	$0.134196\pi$
$504$		0			0
$505$	20.8883			0.929517
$506$	25.8019	+	14.8385i	1.14703	+	0.659652i
$507$		0			0
$508$	−5.24834	+	3.05389i	−0.232858	+	0.135494i
$509$			14.4104i			0.638729i	0.947632	+	0.319365i	$0.103470\pi$
$509$			14.4104i			0.638729i	−0.947632	+	0.319365i	$0.896530\pi$
$510$		0			0
$511$		0			0
$512$	0.344932	+	22.6248i	0.0152440	+	0.999884i
$513$		0			0
$514$	−14.2152	+	24.7181i	−0.627007	+	1.09027i
$515$		−	18.0667i		−	0.796115i
$516$		0			0
$517$			70.7918i			3.11342i
$518$		0			0
$519$		0			0
$520$	0.0253347	+	4.98561i	0.00111100	+	0.218634i
$521$			10.6100i			0.464834i	0.972616	+	0.232417i	$0.0746634\pi$
$521$			10.6100i			0.464834i	−0.972616	+	0.232417i	$0.925337\pi$
$522$		0			0
$523$	−36.2715			−1.58604			−0.793022	−	0.609193i	$-0.791493\pi$
$523$	−36.2715			−1.58604			−0.793022	+	0.609193i	$0.791493\pi$
$524$	−14.5514	−	25.0077i	−0.635679	−	1.09246i
$525$		0			0
$526$	8.81880	−	15.3345i	0.384518	−	0.668618i
$527$			16.1126i			0.701877i
$528$		0			0
$529$	10.9785			0.477326
$530$	−6.75785	+	11.7509i	−0.293542	+	0.510425i
$531$		0			0
$532$		0			0
$533$	3.18667			0.138030
$534$		0			0
$535$	−50.0738			−2.16488
$536$	−5.02369	+	0.0255282i	−0.216990	+	0.00110265i
$537$		0			0
$538$	9.20401	−	16.0044i	0.396813	−	0.689997i
$539$		0			0
$540$		0			0
$541$	−23.6346			−1.01613			−0.508065	−	0.861319i	$-0.669639\pi$
$541$	−23.6346			−1.01613			−0.508065	+	0.861319i	$0.669639\pi$
$542$	12.6191	+	7.25719i	0.542038	+	0.311723i
$543$		0			0
$544$	7.32520	+	12.4430i	0.314065	+	0.533491i
$545$		−	49.7922i		−	2.13286i
$546$		0			0
$547$		−	40.9096i		−	1.74917i	−0.484875	−	0.874583i	$-0.661135\pi$
$547$		−	40.9096i		−	1.74917i	0.484875	−	0.874583i	$-0.338865\pi$
$548$	−11.6305	−	19.9879i	−0.496828	−	0.853839i
$549$		0			0
$550$	−35.5420	+	61.8021i	−1.51552	+	2.63525i
$551$	−10.0192			−0.426832
$552$		0			0
$553$		0			0
$554$	23.2466	+	13.3690i	0.987652	+	0.567993i
$555$		0			0
$556$	17.7236	+	30.4594i	0.751647	+	1.29176i
$557$	38.2781			1.62190			0.810948	−	0.585119i	$-0.198952\pi$
$557$	38.2781			1.62190			0.810948	+	0.585119i	$0.198952\pi$
$558$		0			0
$559$	−1.69710			−0.0717799
$560$		0			0
$561$		0			0
$562$	21.4717	+	12.3482i	0.905727	+	0.520878i
$563$	4.56016			0.192188			0.0960939	−	0.995372i	$-0.469365\pi$
$563$	4.56016			0.192188			0.0960939	+	0.995372i	$0.469365\pi$
$564$		0			0
$565$			25.9696i			1.09255i
$566$	−23.2216	−	13.3546i	−0.976079	−	0.561337i
$567$		0			0
$568$	−25.8279	+	0.131246i	−1.08371	+	0.00550697i
$569$	−43.8157			−1.83685			−0.918425	−	0.395596i	$-0.870538\pi$
$569$	−43.8157			−1.83685			−0.918425	+	0.395596i	$0.870538\pi$
$570$		0			0
$571$		−	8.45294i		−	0.353745i	−0.984234	−	0.176872i	$-0.943402\pi$
$571$		−	8.45294i		−	0.353745i	0.984234	−	0.176872i	$-0.0565980\pi$
$572$	−2.95063	−	5.07090i	−0.123372	−	0.212025i
$573$		0			0
$574$		0			0
$575$		−	28.7945i		−	1.20082i
$576$		0			0
$577$			25.2153i			1.04973i	0.851187	+	0.524863i	$0.175883\pi$
$577$			25.2153i			1.04973i	−0.851187	+	0.524863i	$0.824117\pi$
$578$	−12.8537	−	7.39208i	−0.534643	−	0.307470i
$579$		0			0
$580$	51.8214	−	30.1536i	2.15176	−	1.25206i
$581$		0			0
$582$		0			0
$583$		−	15.9514i		−	0.660639i
$584$	17.1097	−	0.0869442i	0.708005	−	0.00359778i
$585$		0			0
$586$	17.8204	−	30.9869i	0.736152	−	1.28006i
$587$	−3.61615			−0.149254			−0.0746272	−	0.997212i	$-0.523777\pi$
$587$	−3.61615			−0.149254			−0.0746272	+	0.997212i	$0.523777\pi$
$588$		0			0
$589$	7.69551			0.317088
$590$	2.98724	−	5.19435i	0.122983	−	0.213848i
$591$		0			0
$592$	−2.35233	+	4.13887i	−0.0966802	+	0.170106i
$593$		−	8.49515i		−	0.348854i	−0.984670	−	0.174427i	$-0.944193\pi$
$593$		−	8.49515i		−	0.348854i	0.984670	−	0.174427i	$-0.0558073\pi$
$594$		0			0
$595$		0			0
$596$	−6.15052	−	10.5702i	−0.251935	−	0.432970i
$597$		0			0
$598$	2.05411	+	1.18130i	0.0839987	+	0.0483071i
$599$			18.4899i			0.755479i	0.925912	+	0.377739i	$0.123298\pi$
$599$			18.4899i			0.755479i	−0.925912	+	0.377739i	$0.876702\pi$
$600$		0			0
$601$			31.5493i			1.28692i	0.765479	+	0.643461i	$0.222502\pi$
$601$			31.5493i			1.28692i	−0.765479	+	0.643461i	$0.777498\pi$
$602$		0			0
$603$		0			0
$604$	−24.6208	+	14.3262i	−1.00180	+	0.582926i
$605$		−	94.2799i		−	3.83302i
$606$		0			0
$607$	15.5209			0.629974			0.314987	−	0.949096i	$-0.398000\pi$
$607$	15.5209			0.629974			0.314987	+	0.949096i	$0.398000\pi$
$608$	5.94289	−	3.49857i	0.241016	−	0.141886i
$609$		0			0
$610$	0.932164	+	0.536082i	0.0377422	+	0.0217053i
$611$			5.63579i			0.228000i
$612$		0			0
$613$	−5.54811			−0.224086			−0.112043	−	0.993703i	$-0.535739\pi$
$613$	−5.54811			−0.224086			−0.112043	+	0.993703i	$0.535739\pi$
$614$	−12.5606	−	7.22351i	−0.506903	−	0.291517i
$615$		0			0
$616$		0			0
$617$	32.3633			1.30290			0.651448	−	0.758693i	$-0.274162\pi$
$617$	32.3633			1.30290			0.651448	+	0.758693i	$0.274162\pi$
$618$		0			0
$619$	−2.08906			−0.0839665			−0.0419832	−	0.999118i	$-0.513368\pi$
$619$	−2.08906			−0.0839665			−0.0419832	+	0.999118i	$0.513368\pi$
$620$	−39.8028	+	23.1603i	−1.59852	+	0.930139i
$621$		0			0
$622$	−37.2486	−	21.4215i	−1.49353	−	0.858923i
$623$		0			0
$624$		0			0
$625$	2.44610			0.0978440
$626$	−12.0712	+	20.9899i	−0.482462	+	0.838927i
$627$		0			0
$628$	−36.4695	+	21.2207i	−1.45529	+	0.846800i
$629$			3.03788i			0.121128i
$630$		0			0
$631$			37.2258i			1.48194i	0.671541	+	0.740968i	$0.265633\pi$
$631$			37.2258i			1.48194i	−0.671541	+	0.740968i	$0.734367\pi$
$632$	−8.99253	+	0.0456961i	−0.357704	+	0.00181769i
$633$		0			0
$634$	−15.1596	−	8.71821i	−0.602066	−	0.346244i
$635$	−11.0744			−0.439473
$636$		0			0
$637$		0			0
$638$	−35.1728	+	61.1601i	−1.39250	+	2.42135i
$639$		0			0
$640$	−20.2086	+	35.9810i	−0.798816	+	1.42227i
$641$	11.5614			0.456649			0.228324	−	0.973585i	$-0.426675\pi$
$641$	11.5614			0.456649			0.228324	+	0.973585i	$0.426675\pi$
$642$		0			0
$643$	5.82948			0.229892			0.114946	−	0.993372i	$-0.463330\pi$
$643$	5.82948			0.229892			0.114946	+	0.993372i	$0.463330\pi$
$644$		0			0
$645$		0			0
$646$	2.19387	−	3.81480i	0.0863165	−	0.150091i
$647$	46.2772			1.81934			0.909671	−	0.415329i	$-0.136333\pi$
$647$	46.2772			1.81934			0.909671	+	0.415329i	$0.136333\pi$
$648$		0			0
$649$			7.05115i			0.276782i
$650$	−2.82953	+	4.92011i	−0.110983	+	0.192983i
$651$		0			0
$652$	−33.0813	+	19.2492i	−1.29556	+	0.753857i
$653$	−23.5761			−0.922605			−0.461303	−	0.887243i	$-0.652618\pi$
$653$	−23.5761			−0.922605			−0.461303	+	0.887243i	$0.652618\pi$
$654$		0			0
$655$		−	52.7679i		−	2.06181i
$656$	22.9319	+	13.0334i	0.895339	+	0.508867i
$657$		0			0
$658$		0			0
$659$		−	20.7935i		−	0.810001i	−0.914316	−	0.405001i	$-0.867271\pi$
$659$		−	20.7935i		−	0.810001i	0.914316	−	0.405001i	$-0.132729\pi$
$660$		0			0
$661$		−	33.2815i		−	1.29450i	−0.762278	−	0.647249i	$-0.775919\pi$
$661$		−	33.2815i		−	1.29450i	0.762278	−	0.647249i	$-0.224081\pi$
$662$	−5.41603	+	9.41764i	−0.210500	+	0.366027i
$663$		0			0
$664$	0.107772	+	21.2085i	0.00418237	+	0.823048i
$665$		0			0
$666$		0			0
$667$		−	28.4954i		−	1.10335i
$668$	7.74136	+	13.3041i	0.299522	+	0.514752i
$669$		0			0
$670$	−7.94251	−	4.56769i	−0.306846	−	0.176465i
$671$	−1.26538			−0.0488494
$672$		0			0
$673$	−13.1796			−0.508037			−0.254019	−	0.967199i	$-0.581752\pi$
$673$	−13.1796			−0.508037			−0.254019	+	0.967199i	$0.581752\pi$
$674$	16.4109	+	9.43779i	0.632123	+	0.363530i
$675$		0			0
$676$	12.8413	+	22.0688i	0.493896	+	0.848800i
$677$		−	43.9651i		−	1.68972i	−0.534991	−	0.844858i	$-0.679685\pi$
$677$		−	43.9651i		−	1.68972i	0.534991	−	0.844858i	$-0.320315\pi$
$678$		0			0
$679$		0			0
$680$	0.133816	+	26.3336i	0.00513160	+	1.00985i
$681$		0			0
$682$	27.0154	−	46.9757i	1.03447	−	1.79879i
$683$			11.9327i			0.456594i	0.973592	+	0.228297i	$0.0733156\pi$
$683$			11.9327i			0.456594i	−0.973592	+	0.228297i	$0.926684\pi$
$684$		0			0
$685$		−	42.1758i		−	1.61145i
$686$		0			0
$687$		0			0
$688$	−12.2127	−	6.94109i	−0.465603	−	0.264626i
$689$		−	1.26990i		−	0.0483794i
$690$		0			0
$691$	37.2750			1.41801			0.709003	−	0.705205i	$-0.249145\pi$
$691$	37.2750			1.41801			0.709003	+	0.705205i	$0.249145\pi$
$692$	−1.42331	+	0.828191i	−0.0541062	+	0.0314831i
$693$		0			0
$694$	−22.4754	+	39.0812i	−0.853154	+	1.48350i
$695$			64.2714i			2.43795i
$696$		0			0
$697$	16.8317			0.637547
$698$	−6.70932	+	11.6665i	−0.253951	+	0.441582i
$699$		0			0
$700$		0			0
$701$	30.9151			1.16765			0.583823	−	0.811881i	$-0.301556\pi$
$701$	30.9151			1.16765			0.583823	+	0.811881i	$0.301556\pi$
$702$		0			0
$703$	1.45091			0.0547223
$704$	−0.493525	−	48.5590i	−0.0186004	−	1.83014i
$705$		0			0
$706$	9.96390	−	17.3257i	0.374996	−	0.652061i
$707$		0			0
$708$		0			0
$709$	−8.65551			−0.325065			−0.162532	−	0.986703i	$-0.551966\pi$
$709$	−8.65551			−0.325065			−0.162532	+	0.986703i	$0.551966\pi$
$710$	−40.8342	−	23.4835i	−1.53248	−	0.881320i
$711$		0			0
$712$	−34.7531	+	0.176600i	−1.30243	+	0.00661837i
$713$			21.8867i			0.819663i
$714$		0			0
$715$		−	10.6999i		−	0.400155i
$716$	16.3755	−	9.52850i	0.611980	−	0.356097i
$717$		0			0
$718$	−15.8389	+	27.5414i	−0.591103	+	1.02784i
$719$	27.6536			1.03131			0.515653	−	0.856798i	$-0.327549\pi$
$719$	27.6536			1.03131			0.515653	+	0.856798i	$0.327549\pi$
$720$		0			0
$721$		0			0
$722$	21.4709	+	12.3478i	0.799064	+	0.459537i
$723$		0			0
$724$	3.56308	−	2.07327i	0.132421	−	0.0770524i
$725$	68.2539			2.53488
$726$		0			0
$727$	−31.3975			−1.16447			−0.582235	−	0.813021i	$-0.697822\pi$
$727$	−31.3975			−1.16447			−0.582235	+	0.813021i	$0.697822\pi$
$728$		0			0
$729$		0			0
$730$	27.0507	+	15.5567i	1.00119	+	0.575778i
$731$	−8.96395			−0.331544
$732$		0			0
$733$			19.4953i			0.720074i	0.932938	+	0.360037i	$0.117236\pi$
$733$			19.4953i			0.720074i	−0.932938	+	0.360037i	$0.882764\pi$
$734$	14.7102	+	8.45975i	0.542964	+	0.312255i
$735$		0			0
$736$	9.95023	+	16.9021i	0.366771	+	0.623019i
$737$	10.7817			0.397148
$738$		0			0
$739$		−	39.5099i		−	1.45340i	−0.686957	−	0.726698i	$-0.741054\pi$
$739$		−	39.5099i		−	1.45340i	0.686957	−	0.726698i	$-0.258946\pi$
$740$	−7.50443	+	4.36665i	−0.275868	+	0.160521i
$741$		0			0
$742$		0			0
$743$			10.9193i			0.400590i	0.979736	+	0.200295i	$0.0641901\pi$
$743$			10.9193i			0.400590i	−0.979736	+	0.200295i	$0.935810\pi$
$744$		0			0
$745$		−	22.3038i		−	0.817147i
$746$	−6.89911	−	3.96764i	−0.252594	−	0.145265i
$747$		0			0
$748$	−15.5850	−	26.7840i	−0.569843	−	0.979321i
$749$		0			0
$750$		0			0
$751$			30.3164i			1.10626i	0.833095	+	0.553130i	$0.186567\pi$
$751$			30.3164i			1.10626i	−0.833095	+	0.553130i	$0.813433\pi$
$752$	−23.0501	+	40.5561i	−0.840552	+	1.47893i
$753$		0			0
$754$	−2.80013	+	4.86900i	−0.101975	+	0.177319i
$755$	−51.9515			−1.89071
$756$		0			0
$757$	18.4211			0.669526			0.334763	−	0.942302i	$-0.391344\pi$
$757$	18.4211			0.669526			0.334763	+	0.942302i	$0.391344\pi$
$758$	−15.0423	+	26.1562i	−0.546359	+	0.950035i
$759$		0			0
$760$	12.5771	−	0.0639114i	0.456220	−	0.00231831i
$761$			33.6013i			1.21805i	0.793152	+	0.609023i	$0.208438\pi$
$761$			33.6013i			1.21805i	−0.793152	+	0.609023i	$0.791562\pi$
$762$		0			0
$763$		0			0
$764$	−18.7669	+	10.9200i	−0.678964	+	0.395073i
$765$		0			0
$766$	9.25817	+	5.32432i	0.334511	+	0.192375i
$767$			0.561347i			0.0202691i
$768$		0			0
$769$		−	0.776682i		−	0.0280079i	−0.999902	−	0.0140039i	$-0.995542\pi$
$769$		−	0.776682i		−	0.0280079i	0.999902	−	0.0140039i	$-0.00445774\pi$
$770$		0			0
$771$		0			0
$772$	9.77040	+	16.7912i	0.351644	+	0.604329i
$773$			20.3612i			0.732340i	0.930548	+	0.366170i	$0.119331\pi$
$773$			20.3612i			0.732340i	−0.930548	+	0.366170i	$0.880669\pi$
$774$		0			0
$775$	−52.4242			−1.88313
$776$	−33.4813	+	0.170138i	−1.20191	+	0.00610758i
$777$		0			0
$778$	−3.24949	−	1.86876i	−0.116500	−	0.0669984i
$779$		−	8.03896i		−	0.288026i
$780$		0			0
$781$	55.4309			1.98348
$782$	10.8496	+	6.23955i	0.387981	+	0.223126i
$783$		0			0
$784$		0			0
$785$	−76.9532			−2.74658
$786$		0			0
$787$	−48.7815			−1.73887			−0.869437	−	0.494043i	$-0.835518\pi$
$787$	−48.7815			−1.73887			−0.869437	+	0.494043i	$0.835518\pi$
$788$	16.0233	+	27.5374i	0.570808	+	0.980978i
$789$		0			0
$790$	−14.2173	−	8.17628i	−0.505828	−	0.290899i
$791$		0			0
$792$		0			0
$793$	−0.100738			−0.00357730
$794$	13.1489	−	22.8640i	0.466639	−	0.811413i
$795$		0			0
$796$	10.1161	+	17.3854i	0.358557	+	0.616209i
$797$			5.84706i			0.207113i	0.994624	+	0.103557i	$0.0330223\pi$
$797$			5.84706i			0.207113i	−0.994624	+	0.103557i	$0.966978\pi$
$798$		0			0
$799$			29.7677i			1.05311i
$800$	−40.4848	+	23.8333i	−1.43135	+	0.842636i
$801$		0			0
$802$	−29.2366	−	16.8138i	−1.03238	−	0.593716i
$803$	−36.7203			−1.29583
$804$		0			0
$805$		0			0
$806$	2.15072	−	3.73977i	0.0757558	−	0.131728i
$807$		0			0
$808$	−16.1971	+	0.0823067i	−0.569813	+	0.00289554i
$809$	−25.1875			−0.885544			−0.442772	−	0.896634i	$-0.646005\pi$
$809$	−25.1875			−0.885544			−0.442772	+	0.896634i	$0.646005\pi$
$810$		0			0
$811$	−12.4012			−0.435465			−0.217733	−	0.976008i	$-0.569866\pi$
$811$	−12.4012			−0.435465			−0.217733	+	0.976008i	$0.569866\pi$
$812$		0			0
$813$		0			0
$814$	5.09350	−	8.85681i	0.178527	−	0.310431i
$815$	−69.8038			−2.44512
$816$		0			0
$817$			4.28125i			0.149782i
$818$	12.2865	−	21.3644i	0.429588	−	0.746988i
$819$		0			0
$820$	24.1939	+	41.5792i	0.844889	+	1.45201i
$821$	−14.2786			−0.498328			−0.249164	−	0.968461i	$-0.580156\pi$
$821$	−14.2786			−0.498328			−0.249164	+	0.968461i	$0.580156\pi$
$822$		0			0
$823$			14.1742i			0.494081i	0.969005	+	0.247040i	$0.0794581\pi$
$823$			14.1742i			0.494081i	−0.969005	+	0.247040i	$0.920542\pi$
$824$	0.0711888	+	14.0092i	0.00247998	+	0.488034i
$825$		0			0
$826$		0			0
$827$			25.5816i			0.889559i	0.895640	+	0.444779i	$0.146718\pi$
$827$			25.5816i			0.889559i	−0.895640	+	0.444779i	$0.853282\pi$
$828$		0			0
$829$		−	40.6638i		−	1.41231i	−0.708056	−	0.706156i	$-0.750428\pi$
$829$		−	40.6638i		−	1.41231i	0.708056	−	0.706156i	$-0.249572\pi$
$830$	−19.2834	+	33.5308i	−0.669336	+	1.16387i
$831$		0			0
$832$	−0.0392899	−	3.86582i	−0.00136213	−	0.134023i
$833$		0			0
$834$		0			0
$835$			28.0726i			0.971494i
$836$	−12.7923	+	7.44351i	−0.442429	+	0.257439i
$837$		0			0
$838$	−32.6282	−	18.7643i	−1.12712	−	0.648201i
$839$	24.4293			0.843394			0.421697	−	0.906737i	$-0.361435\pi$
$839$	24.4293			0.843394			0.421697	+	0.906737i	$0.361435\pi$
$840$		0			0
$841$	38.5449			1.32913
$842$	−21.1103	−	12.1404i	−0.727508	−	0.418385i
$843$		0			0
$844$	1.78445	−	1.03833i	0.0614231	−	0.0357406i
$845$			46.5667i			1.60194i
$846$		0			0
$847$		0			0
$848$	5.19384	−	9.13844i	0.178357	−	0.313815i
$849$		0			0
$850$	−14.9453	+	25.9876i	−0.512620	+	0.891367i
$851$			4.12652i			0.141455i
$852$		0			0
$853$			21.6039i			0.739705i	0.929091	+	0.369852i	$0.120592\pi$
$853$			21.6039i			0.739705i	−0.929091	+	0.369852i	$0.879408\pi$
$854$		0			0
$855$		0			0
$856$	38.8280	−	0.197307i	1.32711	−	0.00674382i
$857$		−	2.37802i		−	0.0812317i	−0.999175	−	0.0406159i	$-0.987068\pi$
$857$		−	2.37802i		−	0.0812317i	0.999175	−	0.0406159i	$-0.0129320\pi$
$858$		0			0
$859$	41.8671			1.42849			0.714244	−	0.699897i	$-0.246771\pi$
$859$	41.8671			1.42849			0.714244	+	0.699897i	$0.246771\pi$
$860$	−12.8848	−	22.1435i	−0.439368	−	0.755088i
$861$		0			0
$862$	13.8771	−	24.1301i	0.472656	−	0.821876i
$863$		−	39.7743i		−	1.35393i	−0.736014	−	0.676967i	$-0.763294\pi$
$863$		−	39.7743i		−	1.35393i	0.736014	−	0.676967i	$-0.236706\pi$
$864$		0			0
$865$	−3.00329			−0.102115
$866$	−4.53554	+	7.88661i	−0.154124	+	0.267998i
$867$		0			0
$868$		0			0
$869$	19.2995			0.654689
$870$		0			0
$871$	0.858337			0.0290836
$872$	0.196197	+	38.6096i	0.00664408	+	1.30749i
$873$		0			0
$874$	2.98006	−	5.18186i	0.100802	−	0.175279i
$875$		0			0
$876$		0			0
$877$	26.7180			0.902203			0.451102	−	0.892473i	$-0.351031\pi$
$877$	26.7180			0.902203			0.451102	+	0.892473i	$0.351031\pi$
$878$	−8.52458	−	4.90243i	−0.287690	−	0.165449i
$879$		0			0
$880$	43.7623	−	76.9987i	1.47523	−	2.59563i
$881$		−	39.2357i		−	1.32188i	−0.750437	−	0.660942i	$-0.770157\pi$
$881$		−	39.2357i		−	1.32188i	0.750437	−	0.660942i	$-0.229843\pi$
$882$		0			0
$883$			57.7837i			1.94458i	0.233783	+	0.972289i	$0.424889\pi$
$883$			57.7837i			1.94458i	−0.233783	+	0.972289i	$0.575111\pi$
$884$	−1.24073	−	2.13230i	−0.0417303	−	0.0717169i
$885$		0			0
$886$	5.48806	−	9.54288i	0.184375	−	0.320599i
$887$	49.9754			1.67801			0.839005	−	0.544124i	$-0.183138\pi$
$887$	49.9754			1.67801			0.839005	+	0.544124i	$0.183138\pi$
$888$		0			0
$889$		0			0
$890$	−54.9450	−	31.5986i	−1.84176	−	1.05919i
$891$		0			0
$892$	9.62861	+	16.5475i	0.322390	+	0.554052i
$893$	14.2173			0.475764
$894$		0			0
$895$	34.5534			1.15499
$896$		0			0
$897$		0			0
$898$	−16.4771	−	9.47587i	−0.549847	−	0.316214i
$899$	−51.8796			−1.73028
$900$		0			0
$901$		−	6.70750i		−	0.223459i
$902$	−49.0722	−	28.2211i	−1.63392	−	0.939660i
$903$		0			0
$904$	−0.102329	−	20.1372i	−0.00340340	−	0.669755i
$905$	7.51834			0.249918
$906$		0			0
$907$			15.4793i			0.513982i	0.966414	+	0.256991i	$0.0827310\pi$
$907$			15.4793i			0.513982i	−0.966414	+	0.256991i	$0.917269\pi$
$908$	−11.2192	−	19.2811i	−0.372323	−	0.639867i
$909$		0			0
$910$		0			0
$911$			2.22992i			0.0738807i	0.999317	+	0.0369403i	$0.0117612\pi$
$911$			2.22992i			0.0738807i	−0.999317	+	0.0369403i	$0.988239\pi$
$912$		0			0
$913$		−	45.5169i		−	1.50639i
$914$	1.42657	+	0.820410i	0.0471866	+	0.0271368i
$915$		0			0
$916$	−17.5086	+	10.1878i	−0.578500	+	0.336616i
$917$		0			0
$918$		0			0
$919$			30.2165i			0.996750i	0.866962	+	0.498375i	$0.166070\pi$
$919$			30.2165i			0.996750i	−0.866962	+	0.498375i	$0.833930\pi$
$920$	0.181769	+	35.7704i	0.00599276	+	1.17931i
$921$		0			0
$922$	15.1025	−	26.2610i	0.497375	−	0.864859i
$923$	4.41290			0.145252
$924$		0			0
$925$	−9.88408			−0.324986
$926$	10.1812	−	17.7035i	0.334575	−	0.581774i
$927$		0			0
$928$	−40.0643	+	23.5858i	−1.31517	+	0.774241i
$929$		−	2.79127i		−	0.0915787i	−0.998951	−	0.0457894i	$-0.985420\pi$
$929$		−	2.79127i		−	0.0915787i	0.998951	−	0.0457894i	$-0.0145803\pi$
$930$		0			0
$931$		0			0
$932$	−12.7155	−	21.8527i	−0.416511	−	0.715808i
$933$		0			0
$934$	−36.4912	−	20.9859i	−1.19403	−	0.686680i
$935$		−	56.5161i		−	1.84828i
$936$		0			0
$937$			13.5645i			0.443133i	0.975145	+	0.221566i	$0.0711169\pi$
$937$			13.5645i			0.443133i	−0.975145	+	0.221566i	$0.928883\pi$
$938$		0			0
$939$		0			0
$940$	−73.5348	+	42.7881i	−2.39844	+	1.39560i
$941$			26.2750i			0.856541i	0.903650	+	0.428271i	$0.140877\pi$
$941$			26.2750i			0.856541i	−0.903650	+	0.428271i	$0.859123\pi$
$942$		0			0
$943$	22.8635			0.744538
$944$	−2.29589	+	4.03956i	−0.0747248	+	0.131476i
$945$		0			0
$946$	26.1340	+	15.0295i	0.849690	+	0.488652i
$947$			9.01711i			0.293017i	0.989209	+	0.146508i	$0.0468035\pi$
$947$			9.01711i			0.293017i	−0.989209	+	0.146508i	$0.953196\pi$
$948$		0			0
$949$	−2.92333			−0.0948953
$950$	12.4119	+	7.13799i	0.402694	+	0.231587i
$951$		0			0
$952$		0			0
$953$	−5.49448			−0.177984			−0.0889918	−	0.996032i	$-0.528364\pi$
$953$	−5.49448			−0.177984			−0.0889918	+	0.996032i	$0.528364\pi$
$954$		0			0
$955$	−39.5995			−1.28141
$956$	9.43932	−	5.49251i	0.305289	−	0.177641i
$957$		0			0
$958$	34.7618	+	19.9913i	1.12310	+	0.645889i
$959$		0			0
$960$		0			0
$961$	8.84755			0.285405
$962$	0.405497	−	0.705097i	0.0130738	−	0.0227332i
$963$		0			0
$964$	23.5749	−	13.7177i	0.759297	−	0.441817i
$965$			35.4306i			1.14055i
$966$		0			0
$967$		−	45.1993i		−	1.45351i	−0.686896	−	0.726756i	$-0.741027\pi$
$967$		−	45.1993i		−	1.45351i	0.686896	−	0.726756i	$-0.258973\pi$
$968$	0.371494	+	73.1061i	0.0119403	+	2.34972i
$969$		0			0
$970$	−52.9343	−	30.4422i	−1.69962	−	0.977441i
$971$	41.0558			1.31754			0.658772	−	0.752342i	$-0.271076\pi$
$971$	41.0558			1.31754			0.658772	+	0.752342i	$0.271076\pi$
$972$		0			0
$973$		0			0
$974$	6.74564	−	11.7296i	0.216144	−	0.375842i
$975$		0			0
$976$	−0.724927	−	0.412013i	−0.0232044	−	0.0131882i
$977$	−57.2191			−1.83060			−0.915301	−	0.402770i	$-0.868048\pi$
$977$	−57.2191			−1.83060			−0.915301	+	0.402770i	$0.868048\pi$
$978$		0			0
$979$	74.5859			2.38378
$980$		0			0
$981$		0			0
$982$	−12.5158	+	21.7630i	−0.399395	+	0.694486i
$983$	−52.3743			−1.67048			−0.835241	−	0.549884i	$-0.814672\pi$
$983$	−52.3743			−1.67048			−0.835241	+	0.549884i	$0.814672\pi$
$984$		0			0
$985$			58.1058i			1.85140i
$986$	−14.7901	+	25.7176i	−0.471011	+	0.819016i
$987$		0			0
$988$	−1.01840	+	0.592583i	−0.0323997	+	0.0188526i
$989$	−12.1762			−0.387182
$990$		0			0
$991$			59.5704i			1.89232i	0.323704	+	0.946158i	$0.395072\pi$
$991$			59.5704i			1.89232i	−0.323704	+	0.946158i	$0.604928\pi$
$992$	30.7724	−	18.1157i	0.977026	−	0.575174i
$993$		0			0
$994$		0			0
$995$			36.6844i			1.16297i
$996$		0			0
$997$			32.3500i			1.02454i	0.858826	+	0.512268i	$0.171194\pi$
$997$			32.3500i			1.02454i	−0.858826	+	0.512268i	$0.828806\pi$
$998$	6.62808	−	11.5252i	0.209808	−	0.364824i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.l.1567.3		12
3.2	odd	2		588.2.b.c.391.10	yes	12
4.3	odd	2		1764.2.b.m.1567.4		12
7.6	odd	2		1764.2.b.m.1567.3		12
12.11	even	2		588.2.b.d.391.9	yes	12
21.2	odd	6		588.2.o.f.31.8		24
21.5	even	6		588.2.o.e.31.8		24
21.11	odd	6		588.2.o.f.19.3		24
21.17	even	6		588.2.o.e.19.3		24
21.20	even	2		588.2.b.d.391.10	yes	12
28.27	even	2	inner	1764.2.b.l.1567.4		12
84.11	even	6		588.2.o.e.19.8		24
84.23	even	6		588.2.o.e.31.3		24
84.47	odd	6		588.2.o.f.31.3		24
84.59	odd	6		588.2.o.f.19.8		24
84.83	odd	2		588.2.b.c.391.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.9	✓	12	84.83	odd	2
588.2.b.c.391.10	yes	12	3.2	odd	2
588.2.b.d.391.9	yes	12	12.11	even	2
588.2.b.d.391.10	yes	12	21.20	even	2
588.2.o.e.19.3		24	21.17	even	6
588.2.o.e.19.8		24	84.11	even	6
588.2.o.e.31.3		24	84.23	even	6
588.2.o.e.31.8		24	21.5	even	6
588.2.o.f.19.3		24	21.11	odd	6
588.2.o.f.19.8		24	84.59	odd	6
588.2.o.f.31.3		24	84.47	odd	6
588.2.o.f.31.8		24	21.2	odd	6
1764.2.b.l.1567.3		12	1.1	even	1	trivial
1764.2.b.l.1567.4		12	28.27	even	2	inner
1764.2.b.m.1567.3		12	7.6	odd	2
1764.2.b.m.1567.4		12	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22594 - 0.705031i) q^{2} +(1.00586 + 1.72865i) q^{4} +3.64758i q^{5} +(-0.0143727 - 2.82839i) q^{8} +(2.57166 - 4.47172i) q^{10} +6.07019i q^{11} +0.483253i q^{13} +(-1.97648 + 3.47757i) q^{16} +2.55250i q^{17} +1.21909 q^{19} +(-6.30540 + 3.66896i) q^{20} +(4.27968 - 7.44170i) q^{22} +3.46720i q^{23} -8.30483 q^{25} +(0.340708 - 0.592439i) q^{26} -8.21857 q^{29} +6.31249 q^{31} +(4.87485 - 2.86982i) q^{32} +(1.79959 - 3.12921i) q^{34} +1.19016 q^{37} +(-1.49454 - 0.859498i) q^{38} +(10.3168 - 0.0524254i) q^{40} -6.59422i q^{41} +3.51184i q^{43} +(-10.4933 + 6.10578i) q^{44} +(2.44449 - 4.25059i) q^{46} +11.6622 q^{47} +(10.1812 + 5.85517i) q^{50} +(-0.835376 + 0.486085i) q^{52} -2.62782 q^{53} -22.1415 q^{55} +(10.0755 + 5.79435i) q^{58} +1.16160 q^{59} +0.208458i q^{61} +(-7.73874 - 4.45050i) q^{62} +(-7.99959 + 0.0813030i) q^{64} -1.76270 q^{65} -1.77617i q^{67} +(-4.41238 + 2.56746i) q^{68} -9.13166i q^{71} +6.04928i q^{73} +(-1.45907 - 0.839100i) q^{74} +(1.22624 + 2.10739i) q^{76} -3.17938i q^{79} +(-12.6847 - 7.20938i) q^{80} +(-4.64913 + 8.08412i) q^{82} -7.49842 q^{83} -9.31044 q^{85} +(2.47595 - 4.30530i) q^{86} +(17.1689 - 0.0872448i) q^{88} -12.2872i q^{89} +(-5.99359 + 3.48753i) q^{92} +(-14.2972 - 8.22221i) q^{94} +4.44674i q^{95} -11.8376i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} - 24 q^{20} - 12 q^{25} + 24 q^{26} - 32 q^{29} - 16 q^{31} - 4 q^{32} - 32 q^{34} + 32 q^{37} - 24 q^{38} + 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} - 32 q^{52}+ \cdots + 24 q^{88}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 - 24 * q^20 - 12 * q^25 + 24 * q^26 - 32 * q^29 - 16 * q^31 - 4 * q^32 - 32 * q^34 + 32 * q^37 - 24 * q^38 + 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 - 32 * q^52 + 32 * q^53 - 16 * q^55 + 16 * q^58 - 16 * q^59 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 32 * q^74 + 32 * q^76 - 16 * q^80 - 32 * q^82 - 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

Introduction

L-functions

Modular forms

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Representations

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Database

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