LMFDB - Embedded newform 588.2.b.d.391.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(391,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, 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("588.391"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,4,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.10
Root			$1.22594 + 0.705031i$ of defining polynomial
Character	$\chi$	$=$	588.391
Dual form			588.2.b.d.391.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22594 + 0.705031i) q^{2} +1.00000 q^{3} +(1.00586 + 1.72865i) q^{4} +3.64758i q^{5} +(1.22594 + 0.705031i) q^{6} +(0.0143727 + 2.82839i) q^{8} +1.00000 q^{9} +(-2.57166 + 4.47172i) q^{10} -6.07019i q^{11} +(1.00586 + 1.72865i) q^{12} -0.483253i q^{13} +3.64758i q^{15} +(-1.97648 + 3.47757i) q^{16} +2.55250i q^{17} +(1.22594 + 0.705031i) q^{18} -1.21909 q^{19} +(-6.30540 + 3.66896i) q^{20} +(4.27968 - 7.44170i) q^{22} -3.46720i q^{23} +(0.0143727 + 2.82839i) q^{24} -8.30483 q^{25} +(0.340708 - 0.592439i) q^{26} +1.00000 q^{27} +8.21857 q^{29} +(-2.57166 + 4.47172i) q^{30} -6.31249 q^{31} +(-4.87485 + 2.86982i) q^{32} -6.07019i q^{33} +(-1.79959 + 3.12921i) q^{34} +(1.00586 + 1.72865i) q^{36} +1.19016 q^{37} +(-1.49454 - 0.859498i) q^{38} -0.483253i q^{39} +(-10.3168 + 0.0524254i) q^{40} -6.59422i q^{41} +3.51184i q^{43} +(10.4933 - 6.10578i) q^{44} +3.64758i q^{45} +(2.44449 - 4.25059i) q^{46} +11.6622 q^{47} +(-1.97648 + 3.47757i) q^{48} +(-10.1812 - 5.85517i) q^{50} +2.55250i q^{51} +(0.835376 - 0.486085i) q^{52} +2.62782 q^{53} +(1.22594 + 0.705031i) q^{54} +22.1415 q^{55} -1.21909 q^{57} +(10.0755 + 5.79435i) q^{58} +1.16160 q^{59} +(-6.30540 + 3.66896i) q^{60} -0.208458i q^{61} +(-7.73874 - 4.45050i) q^{62} +(-7.99959 + 0.0813030i) q^{64} +1.76270 q^{65} +(4.27968 - 7.44170i) q^{66} -1.77617i q^{67} +(-4.41238 + 2.56746i) q^{68} -3.46720i q^{69} +9.13166i q^{71} +(0.0143727 + 2.82839i) q^{72} -6.04928i q^{73} +(1.45907 + 0.839100i) q^{74} -8.30483 q^{75} +(-1.22624 - 2.10739i) q^{76} +(0.340708 - 0.592439i) q^{78} -3.17938i q^{79} +(-12.6847 - 7.20938i) q^{80} +1.00000 q^{81} +(4.64913 - 8.08412i) q^{82} -7.49842 q^{83} -9.31044 q^{85} +(-2.47595 + 4.30530i) q^{86} +8.21857 q^{87} +(17.1689 - 0.0872448i) q^{88} -12.2872i q^{89} +(-2.57166 + 4.47172i) q^{90} +(5.99359 - 3.48753i) q^{92} -6.31249 q^{93} +(14.2972 + 8.22221i) q^{94} -4.44674i q^{95} +(-4.87485 + 2.86982i) q^{96} +11.8376i q^{97} -6.07019i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 12 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{8} + 12 q^{9} - 4 q^{12} - 4 q^{16} + 4 q^{18} - 24 q^{20} + 4 q^{24} - 12 q^{25} + 24 q^{26} + 12 q^{27} + 32 q^{29} + 16 q^{31} + 4 q^{32} + 32 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) $ 12 * q + 4 * q^2 + 12 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^8 + 12 * q^9 - 4 * q^12 - 4 * q^16 + 4 * q^18 - 24 * q^20 + 4 * q^24 - 12 * q^25 + 24 * q^26 + 12 * q^27 + 32 * q^29 + 16 * q^31 + 4 * q^32 + 32 * q^34 - 4 * q^36 + 32 * q^37 - 24 * q^38 - 32 * q^40 - 24 * q^44 + 24 * q^46 - 4 * q^48 - 28 * q^50 + 32 * q^52 - 32 * q^53 + 4 * q^54 + 16 * q^55 + 16 * q^58 - 16 * q^59 - 24 * q^60 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 4 * q^72 - 32 * q^74 - 12 * q^75 - 32 * q^76 + 24 * q^78 - 16 * q^80 + 12 * q^81 + 32 * q^82 - 16 * q^83 + 16 * q^85 - 24 * q^86 + 32 * q^87 + 24 * q^88 + 16 * q^93 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	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	$0.696394\pi$
$6$	1.22594	+	0.705031i	0.500488	+	0.287828i
$7$		0			0
$7$		0			0
$8$	0.0143727	+	2.82839i	0.00508150	+	0.999987i
$9$	1.00000			0.333333
$10$	−2.57166	+	4.47172i	−0.813229	+	1.41408i
$11$		−	6.07019i		−	1.83023i	−0.403190	−	0.915116i	$-0.632099\pi$
$11$		−	6.07019i		−	1.83023i	0.403190	−	0.915116i	$-0.367901\pi$
$12$	1.00586	+	1.72865i	0.290367	+	0.499019i
$13$		−	0.483253i		−	0.134030i	−0.997752	−	0.0670151i	$-0.978652\pi$
$13$		−	0.483253i		−	0.134030i	0.997752	−	0.0670151i	$-0.0213476\pi$
$14$		0			0
$15$			3.64758i			0.941801i
$16$	−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	$0.899826\pi$
$18$	1.22594	+	0.705031i	0.288957	+	0.166177i
$19$	−1.21909			−0.279679			−0.139840	−	0.990174i	$-0.544659\pi$
$19$	−1.21909			−0.279679			−0.139840	+	0.990174i	$0.544659\pi$
$20$	−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	$-0.882271\pi$
$23$		−	3.46720i		−	0.722962i	0.932379	−	0.361481i	$-0.117729\pi$
$24$	0.0143727	+	2.82839i	0.00293381	+	0.577343i
$25$	−8.30483			−1.66097
$26$	0.340708	−	0.592439i	0.0668184	−	0.116187i
$27$	1.00000			0.192450
$28$		0			0
$29$	8.21857			1.52615			0.763075	−	0.646310i	$-0.223689\pi$
$29$	8.21857			1.52615			0.763075	+	0.646310i	$0.223689\pi$
$30$	−2.57166	+	4.47172i	−0.469518	+	0.816420i
$31$	−6.31249			−1.13376			−0.566878	−	0.823801i	$-0.691849\pi$
$31$	−6.31249			−1.13376			−0.566878	+	0.823801i	$0.691849\pi$
$32$	−4.87485	+	2.86982i	−0.861760	+	0.507317i
$33$		−	6.07019i		−	1.05669i
$34$	−1.79959	+	3.12921i	−0.308627	+	0.536655i
$35$		0			0
$36$	1.00586	+	1.72865i	0.167644	+	0.288109i
$37$	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
$39$		−	0.483253i		−	0.0773824i
$40$	−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
$45$			3.64758i			0.543749i
$46$	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	$0.176267\pi$
$48$	−1.97648	+	3.47757i	−0.285281	+	0.501944i
$49$		0			0
$50$	−10.1812	−	5.85517i	−1.43984	−	0.828046i
$51$			2.55250i			0.357421i
$52$	0.835376	−	0.486085i	0.115846	−	0.0674079i
$53$	2.62782			0.360959			0.180479	−	0.983579i	$-0.442235\pi$
$53$	2.62782			0.360959			0.180479	+	0.983579i	$0.442235\pi$
$54$	1.22594	+	0.705031i	0.166829	+	0.0959426i
$55$	22.1415			2.98556
$56$		0			0
$57$	−1.21909			−0.161473
$58$	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	$0.475908\pi$
$60$	−6.30540	+	3.66896i	−0.814024	+	0.473661i
$61$		−	0.208458i		−	0.0266903i	−0.999911	−	0.0133451i	$-0.995752\pi$
$61$		−	0.208458i		−	0.0266903i	0.999911	−	0.0133451i	$-0.00424802\pi$
$62$	−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
$66$	4.27968	−	7.44170i	0.526792	−	0.916010i
$67$		−	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
$69$		−	3.46720i		−	0.417402i
$70$		0			0
$71$			9.13166i			1.08373i	0.840466	+	0.541864i	$0.182281\pi$
$71$			9.13166i			1.08373i	−0.840466	+	0.541864i	$0.817719\pi$
$72$	0.0143727	+	2.82839i	0.00169383	+	0.333329i
$73$		−	6.04928i		−	0.708015i	−0.935243	−	0.354007i	$-0.884819\pi$
$73$		−	6.04928i		−	0.708015i	0.935243	−	0.354007i	$-0.115181\pi$
$74$	1.45907	+	0.839100i	0.169613	+	0.0975433i
$75$	−8.30483			−0.958960
$76$	−1.22624	−	2.10739i	−0.140659	−	0.241734i
$77$		0			0
$78$	0.340708	−	0.592439i	0.0385776	−	0.0670805i
$79$		−	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
$81$	1.00000			0.111111
$82$	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
$87$	8.21857			0.881123
$88$	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	$-0.225743\pi$
$90$	−2.57166	+	4.47172i	−0.271076	+	0.471360i
$91$		0			0
$92$	5.99359	−	3.48753i	0.624875	−	0.363600i
$93$	−6.31249			−0.654575
$94$	14.2972	+	8.22221i	1.47464	+	0.848057i
$95$		−	4.44674i		−	0.456226i
$96$	−4.87485	+	2.86982i	−0.497537	+	0.292899i
$97$			11.8376i			1.20192i	0.799277	+	0.600962i	$0.205216\pi$
$97$			11.8376i			1.20192i	−0.799277	+	0.600962i	$0.794784\pi$
$98$		0			0
$99$		−	6.07019i		−	0.610077i
$100$	−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	$-0.0919637\pi$
$102$	−1.79959	+	3.12921i	−0.178186	+	0.309838i
$103$	4.95307			0.488041			0.244020	−	0.969770i	$-0.421534\pi$
$103$	4.95307			0.488041			0.244020	+	0.969770i	$0.421534\pi$
$104$	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	$-0.769042\pi$
$107$		−	13.7280i		−	1.32713i	0.748118	−	0.663566i	$-0.230958\pi$
$108$	1.00586	+	1.72865i	0.0967891	+	0.166340i
$109$	−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
$111$	1.19016			0.112965
$112$		0			0
$113$	−7.11968			−0.669764			−0.334882	−	0.942260i	$-0.608696\pi$
$113$	−7.11968			−0.669764			−0.334882	+	0.942260i	$0.608696\pi$
$114$	−1.49454	−	0.859498i	−0.139976	−	0.0804994i
$115$	12.6469			1.17933
$116$	8.26674	+	14.2071i	0.767548	+	1.31909i
$117$		−	0.483253i		−	0.0446767i
$118$	1.42406	+	0.818966i	0.131095	+	0.0753919i
$119$		0			0
$120$	−10.3168	+	0.0524254i	−0.941789	+	0.00478576i
$121$	−25.8472			−2.34975
$122$	0.146969	−	0.255557i	0.0133060	−	0.0231370i
$123$		−	6.59422i		−	0.594581i
$124$	−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
$129$			3.51184i			0.309200i
$130$	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	$0.717755\pi$
$132$	10.4933	−	6.10578i	0.913321	−	0.531440i
$133$		0			0
$134$	1.25225	−	2.17747i	0.108178	−	0.188105i
$135$			3.64758i			0.313934i
$136$	−7.21946	+	0.0366862i	−0.619064	+	0.00314581i
$137$	11.5627			0.987866			0.493933	−	0.869500i	$-0.335559\pi$
$137$	11.5627			0.987866			0.493933	+	0.869500i	$0.335559\pi$
$138$	2.44449	−	4.25059i	0.208089	−	0.361834i
$139$	−17.6203			−1.49453			−0.747266	−	0.664525i	$-0.768634\pi$
$139$	−17.6203			−1.49453			−0.747266	+	0.664525i	$0.768634\pi$
$140$		0			0
$141$	11.6622			0.982134
$142$	−6.43811	+	11.1949i	−0.540274	+	0.939453i
$143$	−2.93344			−0.245306
$144$	−1.97648	+	3.47757i	−0.164707	+	0.289798i
$145$			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	$-0.419416\pi$
$149$	6.11467			0.500934			0.250467	+	0.968125i	$0.419416\pi$
$150$	−10.1812	−	5.85517i	−0.831294	−	0.478072i
$151$			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
$153$			2.55250i			0.206357i
$154$		0			0
$155$		−	23.0253i		−	1.84944i
$156$	0.835376	−	0.486085i	0.0668836	−	0.0389180i
$157$		−	21.0971i		−	1.68373i	−0.539689	−	0.841865i	$-0.681458\pi$
$157$		−	21.0971i		−	1.68373i	0.539689	−	0.841865i	$-0.318542\pi$
$158$	2.24156	−	3.89773i	0.178329	−	0.310087i
$159$	2.62782			0.208400
$160$	−10.4679	−	17.7814i	−0.827559	−	1.40574i
$161$		0			0
$162$	1.22594	+	0.705031i	0.0963190	+	0.0553925i
$163$			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
$165$	22.1415			1.72371
$166$	−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
$171$	−1.21909			−0.0932263
$172$	−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	$0.990035\pi$
$174$	10.0755	+	5.79435i	0.763820	+	0.439268i
$175$		0			0
$176$	21.1095	+	11.9976i	1.59119	+	0.904356i
$177$	1.16160			0.0873113
$178$	8.66288	−	15.0634i	0.649311	−	1.12905i
$179$			9.47297i			0.708043i	0.935237	+	0.354022i	$0.115186\pi$
$179$			9.47297i			0.708043i	−0.935237	+	0.354022i	$0.884814\pi$
$180$	−6.30540	+	3.66896i	−0.469977	+	0.273468i
$181$			2.06119i			0.153207i	0.997062	+	0.0766034i	$0.0244075\pi$
$181$			2.06119i			0.153207i	−0.997062	+	0.0766034i	$0.975592\pi$
$182$		0			0
$183$		−	0.208458i		−	0.0154096i
$184$	9.80661	−	0.0498329i	0.722953	−	0.00367373i
$185$			4.34120i			0.319171i
$186$	−7.73874	−	4.45050i	−0.567432	−	0.326327i
$187$	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	$-0.871517\pi$
$191$		−	10.8564i		−	0.785541i	0.919637	−	0.392770i	$-0.128483\pi$
$192$	−7.99959	+	0.0813030i	−0.577320	+	0.00586754i
$193$	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
$195$	1.76270			0.126230
$196$		0			0
$197$	−15.9300			−1.13496			−0.567481	−	0.823386i	$-0.692082\pi$
$197$	−15.9300			−1.13496			−0.567481	+	0.823386i	$0.692082\pi$
$198$	4.27968	−	7.44170i	0.304143	−	0.528858i
$199$	−10.0572			−0.712935			−0.356467	−	0.934308i	$-0.616019\pi$
$199$	−10.0572			−0.712935			−0.356467	+	0.934308i	$0.616019\pi$
$200$	−0.119363	−	23.4893i	−0.00844020	−	1.66095i
$201$		−	1.77617i		−	0.125281i
$202$	4.03745	−	7.02050i	0.284074	−	0.493961i
$203$		0			0
$204$	−4.41238	+	2.56746i	−0.308929	+	0.179758i
$205$	24.0529			1.67993
$206$	6.07217	+	3.49207i	0.423068	+	0.243304i
$207$		−	3.46720i		−	0.240987i
$208$	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
$213$			9.13166i			0.625691i
$214$	9.67863	−	16.8297i	0.661618	−	1.15045i
$215$	−12.8097			−0.873614
$216$	0.0143727	+	2.82839i	0.000977935	+	0.192448i
$217$		0			0
$218$	−16.7350	−	9.62420i	−1.13344	−	0.651833i
$219$		−	6.04928i		−	0.408772i
$220$	22.2713	+	38.2750i	1.50153	+	2.58050i
$221$	1.23350			0.0829743
$222$	1.45907	+	0.839100i	0.0979260	+	0.0563167i
$223$	−9.57250			−0.641022			−0.320511	−	0.947245i	$-0.603855\pi$
$223$	−9.57250			−0.641022			−0.320511	+	0.947245i	$0.603855\pi$
$224$		0			0
$225$	−8.30483			−0.553656
$226$	−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	$0.620695\pi$
$228$	−1.22624	−	2.10739i	−0.0812096	−	0.139565i
$229$		−	10.1285i		−	0.669308i	−0.942341	−	0.334654i	$-0.891381\pi$
$229$		−	10.1285i		−	0.669308i	0.942341	−	0.334654i	$-0.108619\pi$
$230$	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	$-0.364102\pi$
$233$	12.6414			0.828168			0.414084	+	0.910239i	$0.364102\pi$
$234$	0.340708	−	0.592439i	0.0222728	−	0.0387290i
$235$			42.5388i			2.77492i
$236$	1.16841	+	2.00801i	0.0760571	+	0.130710i
$237$		−	3.17938i		−	0.206523i
$238$		0			0
$239$			5.46050i			0.353211i	0.984282	+	0.176605i	$0.0565116\pi$
$239$			5.46050i			0.353211i	−0.984282	+	0.176605i	$0.943488\pi$
$240$	−12.6847	−	7.20938i	−0.818795	−	0.465364i
$241$			13.6377i			0.878484i	0.898369	+	0.439242i	$0.144753\pi$
$241$			13.6377i			0.878484i	−0.898369	+	0.439242i	$0.855247\pi$
$242$	−31.6872	−	18.2231i	−2.03693	−	1.17143i
$243$	1.00000			0.0641500
$244$	0.360351	−	0.209680i	0.0230691	−	0.0134234i
$245$		0			0
$246$	4.64913	−	8.08412i	0.296418	−	0.515425i
$247$			0.589130i			0.0374854i
$248$	−0.0907272	−	17.8542i	−0.00576119	−	1.13374i
$249$	−7.49842			−0.475193
$250$	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
$255$	−9.31044			−0.583042
$256$	−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	$-0.216475\pi$
$258$	−2.47595	+	4.30530i	−0.154146	+	0.268036i
$259$		0			0
$260$	1.77304	+	3.04710i	0.109959	+	0.188973i
$261$	8.21857			0.508717
$262$	−17.7351	−	10.1994i	−1.09568	−	0.630119i
$263$		−	12.5084i		−	0.771300i	−0.922645	−	0.385650i	$-0.873977\pi$
$263$		−	12.5084i		−	0.771300i	0.922645	−	0.385650i	$-0.126023\pi$
$264$	17.1689	−	0.0872448i	1.05667	−	0.00536955i
$265$			9.58518i			0.588813i
$266$		0			0
$267$		−	12.2872i		−	0.751967i
$268$	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	$0.869711\pi$
$270$	−2.57166	+	4.47172i	−0.156506	+	0.272140i
$271$	10.2934			0.625282			0.312641	−	0.949871i	$-0.398786\pi$
$271$	10.2934			0.625282			0.312641	+	0.949871i	$0.398786\pi$
$272$	−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
$276$	5.99359	−	3.48753i	0.360772	−	0.209925i
$277$	−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
$279$	−6.31249			−0.377919
$280$		0			0
$281$	17.5144			1.04482			0.522412	−	0.852693i	$-0.325032\pi$
$281$	17.5144			1.04482			0.522412	+	0.852693i	$0.325032\pi$
$282$	14.2972	+	8.22221i	0.851384	+	0.489626i
$283$	−18.9419			−1.12598			−0.562990	−	0.826464i	$-0.690349\pi$
$283$	−18.9419			−1.12598			−0.562990	+	0.826464i	$0.690349\pi$
$284$	−15.7855	+	9.18519i	−0.936696	+	0.545041i
$285$		−	4.44674i		−	0.263402i
$286$	−3.59622	−	2.06816i	−0.212649	−	0.122293i
$287$		0			0
$288$	−4.87485	+	2.86982i	−0.287253	+	0.169106i
$289$	10.4848			0.616750
$290$	−21.1353	+	36.7511i	−1.24111	+	2.15810i
$291$			11.8376i			0.693932i
$292$	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
$297$		−	6.07019i		−	0.352228i
$298$	7.49623	+	4.31104i	0.434245	+	0.249732i
$299$	−1.67554			−0.0968987
$300$	−8.35352	−	14.3562i	−0.482290	−	0.828854i
$301$		0			0
$302$	−10.0416	+	17.4608i	−0.577828	+	1.00475i
$303$		−	5.72662i		−	0.328986i
$304$	2.40952	−	4.23948i	0.138195	−	0.243151i
$305$	0.760366			0.0435385
$306$	−1.79959	+	3.12921i	−0.102876	+	0.178885i
$307$	−10.2457			−0.584750			−0.292375	−	0.956304i	$-0.594446\pi$
$307$	−10.2457			−0.584750			−0.292375	+	0.956304i	$0.594446\pi$
$308$		0			0
$309$	4.95307			0.281770
$310$	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	$0.169556\pi$
$312$	1.36683	−	0.00694562i	0.0773814	−	0.000393219i
$313$			17.1215i			0.967764i	0.875133	+	0.483882i	$0.160774\pi$
$313$			17.1215i			0.967764i	−0.875133	+	0.483882i	$0.839226\pi$
$314$	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	$-0.612889\pi$
$317$	−12.3657			−0.694527			−0.347264	+	0.937768i	$0.612889\pi$
$318$	3.22155	+	1.85270i	0.180656	+	0.103894i
$319$		−	49.8883i		−	2.79321i
$320$	−0.296559	−	29.1791i	−0.0165782	−	1.63116i
$321$		−	13.7280i		−	0.766220i
$322$		0			0
$323$		−	3.11173i		−	0.173141i
$324$	1.00586	+	1.72865i	0.0558812	+	0.0960363i
$325$			4.01333i			0.222620i
$326$	−13.4922	+	23.4609i	−0.747264	+	1.29938i
$327$	−13.6507			−0.754888
$328$	18.6510	−	0.0947764i	1.02983	−	0.00523315i
$329$		0			0
$330$	27.1442	+	15.6105i	1.49424	+	0.859327i
$331$		−	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
$333$	1.19016			0.0652203
$334$	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
$339$	−7.11968			−0.386688
$340$	−9.36501	−	16.0945i	−0.507889	−	0.872848i
$341$			38.3180i			2.07504i
$342$	−1.49454	−	0.859498i	−0.0808152	−	0.0464763i
$343$		0			0
$344$	−9.93284	+	0.0504744i	−0.535543	+	0.00272140i
$345$	12.6469			0.680886
$346$	−0.580498	+	1.00940i	−0.0312078	+	0.0542655i
$347$			31.8786i			1.71133i	0.517529	+	0.855666i	$0.326852\pi$
$347$			31.8786i			1.71133i	−0.517529	+	0.855666i	$0.673148\pi$
$348$	8.26674	+	14.2071i	0.443144	+	0.761578i
$349$			9.51634i			0.509398i	0.967020	+	0.254699i	$0.0819764\pi$
$349$			9.51634i			0.509398i	−0.967020	+	0.254699i	$0.918024\pi$
$350$		0			0
$351$		−	0.483253i		−	0.0257941i
$352$	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	$0.877265\pi$
$354$	1.42406	+	0.818966i	0.0756877	+	0.0435275i
$355$	−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	$0.201995\pi$
$359$			22.4656i			1.18569i	−0.805318	+	0.592843i	$0.798005\pi$
$360$	−10.3168	+	0.0524254i	−0.543742	+	0.00276306i
$361$	−17.5138			−0.921780
$362$	−1.45320	+	2.52689i	−0.0763785	+	0.132811i
$363$	−25.8472			−1.35663
$364$		0			0
$365$	22.0652			1.15495
$366$	0.146969	−	0.255557i	0.00768221	−	0.0133582i
$367$	11.9991			0.626349			0.313174	−	0.949696i	$-0.398608\pi$
$367$	11.9991			0.626349			0.313174	+	0.949696i	$0.398608\pi$
$368$	12.0575	+	6.85287i	0.628538	+	0.357231i
$369$		−	6.59422i		−	0.343281i
$370$	−3.06068	+	5.32206i	−0.159117	+	0.276680i
$371$		0			0
$372$	−6.34949	−	10.9121i	−0.329206	−	0.565766i
$373$	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
$375$		−	12.0546i		−	0.622499i
$376$	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
$381$			3.03609i			0.155544i
$382$	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	$0.561803\pi$
$384$	−9.86434	−	5.54029i	−0.503388	−	0.282727i
$385$		0			0
$386$	11.9081	+	6.84829i	0.606108	+	0.348569i
$387$			3.51184i			0.178517i
$388$	−20.4631	+	11.9070i	−1.03886	+	0.604485i
$389$	−2.65061			−0.134391			−0.0671957	−	0.997740i	$-0.521405\pi$
$389$	−2.65061			−0.134391			−0.0671957	+	0.997740i	$0.521405\pi$
$390$	2.16097	+	1.24276i	0.109425	+	0.0629296i
$391$	8.85003			0.447565
$392$		0			0
$393$	−14.4666			−0.729741
$394$	−19.5292	−	11.2311i	−0.983866	−	0.565816i
$395$	11.5970			0.583511
$396$	10.4933	−	6.10578i	0.527306	−	0.306827i
$397$		−	18.6502i		−	0.936025i	−0.883722	−	0.468012i	$-0.844970\pi$
$397$		−	18.6502i		−	0.936025i	0.883722	−	0.468012i	$-0.155030\pi$
$398$	−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	$-0.703032\pi$
$401$	−23.8483			−1.19093			−0.595464	+	0.803382i	$0.703032\pi$
$402$	1.25225	−	2.17747i	0.0624567	−	0.108603i
$403$			3.05053i			0.151958i
$404$	9.89934	−	5.76019i	0.492511	−	0.286580i
$405$			3.64758i			0.181250i
$406$		0			0
$407$		−	7.22450i		−	0.358105i
$408$	−7.21946	+	0.0366862i	−0.357417	+	0.00181624i
$409$		−	17.4269i		−	0.861706i	−0.902422	−	0.430853i	$-0.858213\pi$
$409$		−	17.4269i		−	0.861706i	0.902422	−	0.430853i	$-0.141787\pi$
$410$	29.4875	+	16.9581i	1.45628	+	0.837499i
$411$	11.5627			0.570345
$412$	4.98211	+	8.56215i	0.245451	+	0.421827i
$413$		0			0
$414$	2.44449	−	4.25059i	0.120140	−	0.208905i
$415$		−	27.3511i		−	1.34261i
$416$	1.38685	+	2.35578i	0.0679957	+	0.115502i
$417$	−17.6203			−0.862869
$418$	−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
$423$	11.6622			0.567035
$424$	0.0377688	+	7.43250i	0.00183421	+	0.360954i
$425$		−	21.1981i		−	1.02826i
$426$	−6.43811	+	11.1949i	−0.311927	+	0.542394i
$427$		0			0
$428$	23.7309	−	13.8084i	1.14707	−	0.667455i
$429$	−2.93344			−0.141628
$430$	−15.7039	−	9.03124i	−0.757311	−	0.435525i
$431$		−	19.6830i		−	0.948095i	−0.880499	−	0.474047i	$-0.842793\pi$
$431$		−	19.6830i		−	0.948095i	0.880499	−	0.474047i	$-0.157207\pi$
$432$	−1.97648	+	3.47757i	−0.0950936	+	0.167315i
$433$			6.43311i			0.309156i	0.987981	+	0.154578i	$0.0494017\pi$
$433$			6.43311i			0.309156i	−0.987981	+	0.154578i	$0.950598\pi$
$434$		0			0
$435$			29.9779i			1.43733i
$436$	−13.7308	−	23.5974i	−0.657584	−	1.13011i
$437$			4.22684i			0.202197i
$438$	4.26493	−	7.41606i	0.203786	−	0.354353i
$439$	−6.95350			−0.331872			−0.165936	−	0.986137i	$-0.553065\pi$
$439$	−6.95350			−0.331872			−0.165936	+	0.986137i	$0.553065\pi$
$440$	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	$-0.940798\pi$
$443$		−	7.78413i		−	0.369835i	0.982754	−	0.184918i	$-0.0592018\pi$
$444$	1.19714	+	2.05737i	0.0568136	+	0.0976386i
$445$	44.8187			2.12461
$446$	−11.7353	−	6.74891i	−0.555684	−	0.319570i
$447$	6.11467			0.289214
$448$		0			0
$449$	−13.4404			−0.634290			−0.317145	−	0.948377i	$-0.602724\pi$
$449$	−13.4404			−0.634290			−0.317145	+	0.948377i	$0.602724\pi$
$450$	−10.1812	−	5.85517i	−0.479948	−	0.276015i
$451$	−40.0282			−1.88485
$452$	−7.16142	−	12.3075i	−0.336845	−	0.578894i
$453$			14.2427i			0.669183i
$454$	−13.6740	−	7.86381i	−0.641750	−	0.369067i
$455$		0			0
$456$	−0.0175216	−	3.44807i	−0.000820524	−	0.161471i
$457$	−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
$459$			2.55250i			0.119140i
$460$	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
$465$		−	23.0253i		−	1.06777i
$466$	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	$0.258181\pi$
$468$	0.835376	−	0.486085i	0.0386153	−	0.0224693i
$469$		0			0
$470$	−29.9912	+	52.1500i	−1.38339	+	2.40550i
$471$		−	21.0971i		−	0.972102i
$472$	0.0166953	+	3.28546i	0.000768464	+	0.151226i
$473$	21.3175			0.980181
$474$	2.24156	−	3.89773i	0.102958	−	0.179029i
$475$	10.1244			0.464538
$476$		0			0
$477$	2.62782			0.120320
$478$	−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	$0.724307\pi$
$480$	−10.4679	−	17.7814i	−0.477791	−	0.811606i
$481$		−	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
$486$	1.22594	+	0.705031i	0.0556098	+	0.0319809i
$487$			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
$489$			19.1370i			0.865406i
$490$		0			0
$491$			17.7521i			0.801141i	0.916266	+	0.400571i	$0.131188\pi$
$491$			17.7521i			0.801141i	−0.916266	+	0.400571i	$0.868812\pi$
$492$	11.3991	−	6.63287i	0.513912	−	0.299033i
$493$			20.9779i			0.944796i
$494$	−0.415355	+	0.722238i	−0.0186877	+	0.0324950i
$495$	22.1415			0.995187
$496$	12.4765	−	21.9521i	0.560213	−	0.985681i
$497$		0			0
$498$	−9.19262	−	5.28662i	−0.411931	−	0.236899i
$499$			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
$501$	7.69624			0.343843
$502$	−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
$507$	12.7665			0.566979
$508$	−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	$0.896530\pi$
$510$	−11.4140	−	6.56415i	−0.505422	−	0.290665i
$511$		0			0
$512$	−0.344932	−	22.6248i	−0.0152440	−	0.999884i
$513$	−1.21909			−0.0538242
$514$	14.2152	−	24.7181i	0.627007	−	1.09027i
$515$			18.0667i			0.796115i
$516$	−6.07075	+	3.53242i	−0.267250	+	0.155506i
$517$		−	70.7918i		−	3.11342i
$518$		0			0
$519$			0.823365i			0.0361417i
$520$	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	$0.925337\pi$
$522$	10.0755	+	5.79435i	0.440992	+	0.253612i
$523$	36.2715			1.58604			0.793022	−	0.609193i	$-0.208507\pi$
$523$	36.2715			1.58604			0.793022	+	0.609193i	$0.208507\pi$
$524$	−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
$528$	21.1095	+	11.9976i	0.918675	+	0.522130i
$529$	10.9785			0.477326
$530$	−6.75785	+	11.7509i	−0.293542	+	0.510425i
$531$	1.16160			0.0504092
$532$		0			0
$533$	−3.18667			−0.138030
$534$	8.66288	−	15.0634i	0.374880	−	0.651858i
$535$	50.0738			2.16488
$536$	5.02369	−	0.0255282i	0.216990	−	0.00110265i
$537$			9.47297i			0.408789i
$538$	−9.20401	+	16.0044i	−0.396813	+	0.689997i
$539$		0			0
$540$	−6.30540	+	3.66896i	−0.271341	+	0.157887i
$541$	−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
$543$			2.06119i			0.0884540i
$544$	−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
$549$		−	0.208458i		−	0.00889676i
$550$	−35.5420	+	61.8021i	−1.51552	+	2.63525i
$551$	−10.0192			−0.426832
$552$	9.80661	−	0.0498329i	0.417397	−	0.00212103i
$553$		0			0
$554$	−23.2466	−	13.3690i	−0.987652	−	0.567993i
$555$			4.34120i			0.184274i
$556$	−17.7236	−	30.4594i	−0.751647	−	1.29176i
$557$	−38.2781			−1.62190			−0.810948	−	0.585119i	$-0.801048\pi$
$557$	−38.2781			−1.62190			−0.810948	+	0.585119i	$0.801048\pi$
$558$	−7.73874	−	4.45050i	−0.327607	−	0.188405i
$559$	1.69710			0.0717799
$560$		0			0
$561$	15.4942			0.654164
$562$	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	$0.469365\pi$
$564$	11.7306	+	20.1599i	0.493946	+	0.848885i
$565$		−	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	$-0.129462\pi$
$569$	43.8157			1.83685			0.918425	+	0.395596i	$0.129462\pi$
$570$	3.13509	−	5.45144i	0.131314	−	0.228336i
$571$		−	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
$573$		−	10.8564i		−	0.453532i
$574$		0			0
$575$			28.7945i			1.20082i
$576$	−7.99959	+	0.0813030i	−0.333316	+	0.00338762i
$577$		−	25.2153i		−	1.04973i	−0.851187	−	0.524863i	$-0.824117\pi$
$577$		−	25.2153i		−	1.04973i	0.851187	−	0.524863i	$-0.175883\pi$
$578$	12.8537	+	7.39208i	0.534643	+	0.307470i
$579$	9.71346			0.403678
$580$	−51.8214	+	30.1536i	−2.15176	+	1.25206i
$581$		0			0
$582$	−8.34587	+	14.5122i	−0.345947	+	0.601549i
$583$		−	15.9514i		−	0.660639i
$584$	17.1097	−	0.0869442i	0.708005	−	0.00359778i
$585$	1.76270			0.0728788
$586$	−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
$591$	−15.9300			−0.655271
$592$	−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	$-0.0558073\pi$
$594$	4.27968	−	7.44170i	0.175597	−	0.305337i
$595$		0			0
$596$	6.15052	+	10.5702i	0.251935	+	0.432970i
$597$	−10.0572			−0.411613
$598$	−2.05411	−	1.18130i	−0.0839987	−	0.0483071i
$599$		−	18.4899i		−	0.755479i	−0.925912	−	0.377739i	$-0.876702\pi$
$599$		−	18.4899i		−	0.755479i	0.925912	−	0.377739i	$-0.123298\pi$
$600$	−0.119363	−	23.4893i	−0.00487295	−	0.958947i
$601$		−	31.5493i		−	1.28692i	−0.765479	−	0.643461i	$-0.777498\pi$
$601$		−	31.5493i		−	1.28692i	0.765479	−	0.643461i	$-0.222502\pi$
$602$		0			0
$603$		−	1.77617i		−	0.0723311i
$604$	−24.6208	+	14.3262i	−1.00180	+	0.582926i
$605$		−	94.2799i		−	3.83302i
$606$	4.03745	−	7.02050i	0.164010	−	0.285188i
$607$	−15.5209			−0.629974			−0.314987	−	0.949096i	$-0.602000\pi$
$607$	−15.5209			−0.629974			−0.314987	+	0.949096i	$0.602000\pi$
$608$	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
$612$	−4.41238	+	2.56746i	−0.178360	+	0.103783i
$613$	−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
$615$	24.0529			0.969908
$616$		0			0
$617$	−32.3633			−1.30290			−0.651448	−	0.758693i	$-0.725838\pi$
$617$	−32.3633			−1.30290			−0.651448	+	0.758693i	$0.725838\pi$
$618$	6.07217	+	3.49207i	0.244259	+	0.140472i
$619$	2.08906			0.0839665			0.0419832	−	0.999118i	$-0.486632\pi$
$619$	2.08906			0.0839665			0.0419832	+	0.999118i	$0.486632\pi$
$620$	39.8028	−	23.1603i	1.59852	−	0.930139i
$621$		−	3.46720i		−	0.139134i
$622$	37.2486	+	21.4215i	1.49353	+	0.858923i
$623$		0			0
$624$	1.68055	+	0.955141i	0.0672757	+	0.0382362i
$625$	2.44610			0.0978440
$626$	−12.0712	+	20.9899i	−0.482462	+	0.838927i
$627$			7.40013i			0.295533i
$628$	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
$633$		−	1.03227i		−	0.0410292i
$634$	−15.1596	−	8.71821i	−0.602066	−	0.346244i
$635$	−11.0744			−0.439473
$636$	2.64322	+	4.54259i	0.104811	+	0.180125i
$637$		0			0
$638$	35.1728	−	61.1601i	1.39250	−	2.42135i
$639$			9.13166i			0.361243i
$640$	20.2086	−	35.9810i	0.798816	−	1.42227i
$641$	−11.5614			−0.456649			−0.228324	−	0.973585i	$-0.573325\pi$
$641$	−11.5614			−0.456649			−0.228324	+	0.973585i	$0.573325\pi$
$642$	9.67863	−	16.8297i	0.381985	−	0.664214i
$643$	−5.82948			−0.229892			−0.114946	−	0.993372i	$-0.536670\pi$
$643$	−5.82948			−0.229892			−0.114946	+	0.993372i	$0.536670\pi$
$644$		0			0
$645$	−12.8097			−0.504381
$646$	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	$0.136333\pi$
$648$	0.0143727	+	2.82839i	0.000564611	+	0.111110i
$649$		−	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	$-0.347382\pi$
$653$	23.5761			0.922605			0.461303	+	0.887243i	$0.347382\pi$
$654$	−16.7350	−	9.62420i	−0.654390	−	0.376336i
$655$		−	52.7679i		−	2.06181i
$656$	22.9319	+	13.0334i	0.895339	+	0.508867i
$657$		−	6.04928i		−	0.236005i
$658$		0			0
$659$			20.7935i			0.810001i	0.914316	+	0.405001i	$0.132729\pi$
$659$			20.7935i			0.810001i	−0.914316	+	0.405001i	$0.867271\pi$
$660$	22.2713	+	38.2750i	0.866909	+	1.48985i
$661$			33.2815i			1.29450i	0.762278	+	0.647249i	$0.224081\pi$
$661$			33.2815i			1.29450i	−0.762278	+	0.647249i	$0.775919\pi$
$662$	5.41603	−	9.41764i	0.210500	−	0.366027i
$663$	1.23350			0.0479052
$664$	−0.107772	−	21.2085i	−0.00418237	−	0.823048i
$665$		0			0
$666$	1.45907	+	0.839100i	0.0565376	+	0.0325144i
$667$		−	28.4954i		−	1.10335i
$668$	7.74136	+	13.3041i	0.299522	+	0.514752i
$669$	−9.57250			−0.370094
$670$	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
$675$	−8.30483			−0.319653
$676$	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	$-0.320315\pi$
$678$	−8.72831	−	5.01960i	−0.335209	−	0.192777i
$679$		0			0
$680$	−0.133816	−	26.3336i	−0.00513160	−	1.00985i
$681$	−11.1538			−0.427416
$682$	−27.0154	+	46.9757i	−1.03447	+	1.79879i
$683$		−	11.9327i		−	0.456594i	−0.973592	−	0.228297i	$-0.926684\pi$
$683$		−	11.9327i		−	0.456594i	0.973592	−	0.228297i	$-0.0733156\pi$
$684$	−1.22624	−	2.10739i	−0.0468864	−	0.0805780i
$685$			42.1758i			1.61145i
$686$		0			0
$687$		−	10.1285i		−	0.386425i
$688$	−12.2127	−	6.94109i	−0.465603	−	0.264626i
$689$		−	1.26990i		−	0.0483794i
$690$	15.5043	+	8.91646i	0.590241	+	0.339444i
$691$	−37.2750			−1.41801			−0.709003	−	0.705205i	$-0.750855\pi$
$691$	−37.2750			−1.41801			−0.709003	+	0.705205i	$0.750855\pi$
$692$	−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
$696$	0.118123	+	23.2453i	0.00447743	+	0.881112i
$697$	16.8317			0.637547
$698$	−6.70932	+	11.6665i	−0.253951	+	0.441582i
$699$	12.6414			0.478143
$700$		0			0
$701$	−30.9151			−1.16765			−0.583823	−	0.811881i	$-0.698444\pi$
$701$	−30.9151			−1.16765			−0.583823	+	0.811881i	$0.698444\pi$
$702$	0.340708	−	0.592439i	0.0128592	−	0.0223602i
$703$	−1.45091			−0.0547223
$704$	0.493525	+	48.5590i	0.0186004	+	1.83014i
$705$			42.5388i			1.60210i
$706$	−9.96390	+	17.3257i	−0.374996	+	0.652061i
$707$		0			0
$708$	1.16841	+	2.00801i	0.0439116	+	0.0754655i
$709$	−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
$711$		−	3.17938i		−	0.119236i
$712$	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
$717$			5.46050i			0.203926i
$718$	−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	$0.327549\pi$
$720$	−12.6847	−	7.20938i	−0.472732	−	0.268678i
$721$		0			0
$722$	−21.4709	−	12.3478i	−0.799064	−	0.459537i
$723$			13.6377i			0.507193i
$724$	−3.56308	+	2.07327i	−0.132421	+	0.0770524i
$725$	−68.2539			−2.53488
$726$	−31.6872	−	18.2231i	−1.17602	−	0.676323i
$727$	31.3975			1.16447			0.582235	−	0.813021i	$-0.302178\pi$
$727$	31.3975			1.16447			0.582235	+	0.813021i	$0.302178\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	27.0507	+	15.5567i	1.00119	+	0.575778i
$731$	−8.96395			−0.331544
$732$	0.360351	−	0.209680i	0.0133190	−	0.00774999i
$733$		−	19.4953i		−	0.720074i	−0.932938	−	0.360037i	$-0.882764\pi$
$733$		−	19.4953i		−	0.720074i	0.932938	−	0.360037i	$-0.117236\pi$
$734$	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
$738$	4.64913	−	8.08412i	0.171137	−	0.297581i
$739$		−	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
$741$			0.589130i			0.0216422i
$742$		0			0
$743$		−	10.9193i		−	0.400590i	−0.979736	−	0.200295i	$-0.935810\pi$
$743$		−	10.9193i		−	0.400590i	0.979736	−	0.200295i	$-0.0641901\pi$
$744$	−0.0907272	−	17.8542i	−0.00332622	−	0.654566i
$745$			22.3038i			0.817147i
$746$	6.89911	+	3.96764i	0.252594	+	0.145265i
$747$	−7.49842			−0.274353
$748$	15.5850	+	26.7840i	0.569843	+	0.979321i
$749$		0			0
$750$	8.49890	−	14.7783i	0.310336	−	0.539627i
$751$			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
$753$	−28.2425			−1.02921
$754$	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
$759$	−21.0466			−0.763943
$760$	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	$0.791562\pi$
$762$	−2.14054	+	3.72206i	−0.0775435	+	0.134836i
$763$		0			0
$764$	18.7669	−	10.9200i	0.678964	−	0.395073i
$765$	−9.31044			−0.336620
$766$	−9.25817	−	5.32432i	−0.334511	−	0.192375i
$767$		−	0.561347i		−	0.0202691i
$768$	−8.18702	−	13.7467i	−0.295424	−	0.496042i
$769$			0.776682i			0.0280079i	0.999902	+	0.0140039i	$0.00445774\pi$
$769$			0.776682i			0.0280079i	−0.999902	+	0.0140039i	$0.995542\pi$
$770$		0			0
$771$		−	20.1625i		−	0.726136i
$772$	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	$0.880669\pi$
$774$	−2.47595	+	4.30530i	−0.0889963	+	0.154751i
$775$	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
$780$	1.77304	+	3.04710i	0.0634848	+	0.109104i
$781$	55.4309			1.98348
$782$	10.8496	+	6.23955i	0.387981	+	0.223126i
$783$	8.21857			0.293708
$784$		0			0
$785$	76.9532			2.74658
$786$	−17.7351	−	10.1994i	−0.632591	−	0.363800i
$787$	48.7815			1.73887			0.869437	−	0.494043i	$-0.164482\pi$
$787$	48.7815			1.73887			0.869437	+	0.494043i	$0.164482\pi$
$788$	−16.0233	−	27.5374i	−0.570808	−	0.980978i
$789$		−	12.5084i		−	0.445310i
$790$	14.2173	+	8.17628i	0.505828	+	0.290899i
$791$		0			0
$792$	17.1689	−	0.0872448i	0.610070	−	0.00310011i
$793$	−0.100738			−0.00357730
$794$	13.1489	−	22.8640i	0.466639	−	0.811413i
$795$			9.58518i			0.339951i
$796$	−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
$801$		−	12.2872i		−	0.434148i
$802$	−29.2366	−	16.8138i	−1.03238	−	0.593716i
$803$	−36.7203			−1.29583
$804$	3.07037	−	1.78658i	0.108284	−	0.0630077i
$805$		0			0
$806$	−2.15072	+	3.73977i	−0.0757558	+	0.131728i
$807$			13.0548i			0.459549i
$808$	16.1971	−	0.0823067i	0.569813	−	0.00289554i
$809$	25.1875			0.885544			0.442772	−	0.896634i	$-0.353995\pi$
$809$	25.1875			0.885544			0.442772	+	0.896634i	$0.353995\pi$
$810$	−2.57166	+	4.47172i	−0.0903588	+	0.157120i
$811$	12.4012			0.435465			0.217733	−	0.976008i	$-0.430134\pi$
$811$	12.4012			0.435465			0.217733	+	0.976008i	$0.430134\pi$
$812$		0			0
$813$	10.2934			0.361006
$814$	5.09350	−	8.85681i	0.178527	−	0.310431i
$815$	−69.8038			−2.44512
$816$	−8.87650	−	5.04497i	−0.310739	−	0.176609i
$817$		−	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	$-0.419844\pi$
$821$	14.2786			0.498328			0.249164	+	0.968461i	$0.419844\pi$
$822$	14.1752	+	8.15205i	0.494415	+	0.284335i
$823$			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
$825$			50.4119i			1.75512i
$826$		0			0
$827$		−	25.5816i		−	0.889559i	−0.895640	−	0.444779i	$-0.853282\pi$
$827$		−	25.5816i		−	0.889559i	0.895640	−	0.444779i	$-0.146718\pi$
$828$	5.99359	−	3.48753i	0.208292	−	0.121200i
$829$			40.6638i			1.41231i	0.708056	+	0.706156i	$0.249572\pi$
$829$			40.6638i			1.41231i	−0.708056	+	0.706156i	$0.750428\pi$
$830$	19.2834	−	33.5308i	0.669336	−	1.16387i
$831$	−18.9622			−0.657792
$832$	0.0392899	+	3.86582i	0.00136213	+	0.134023i
$833$		0			0
$834$	−21.6014	−	12.4228i	−0.747996	−	0.430168i
$835$			28.0726i			0.971494i
$836$	−12.7923	+	7.44351i	−0.442429	+	0.257439i
$837$	−6.31249			−0.218192
$838$	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
$843$	17.5144			0.603229
$844$	1.78445	−	1.03833i	0.0614231	−	0.0357406i
$845$			46.5667i			1.60194i
$846$	14.2972	+	8.22221i	0.491547	+	0.282686i
$847$		0			0
$848$	−5.19384	+	9.13844i	−0.178357	+	0.313815i
$849$	−18.9419			−0.650084
$850$	14.9453	−	25.9876i	0.512620	−	0.891367i
$851$		−	4.12652i		−	0.141455i
$852$	−15.7855	+	9.18519i	−0.540801	+	0.314679i
$853$		−	21.6039i		−	0.739705i	−0.929091	−	0.369852i	$-0.879408\pi$
$853$		−	21.6039i		−	0.739705i	0.929091	−	0.369852i	$-0.120592\pi$
$854$		0			0
$855$		−	4.44674i		−	0.152075i
$856$	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	$-0.0129320\pi$
$858$	−3.59622	−	2.06816i	−0.122773	−	0.0706060i
$859$	−41.8671			−1.42849			−0.714244	−	0.699897i	$-0.753229\pi$
$859$	−41.8671			−1.42849			−0.714244	+	0.699897i	$0.753229\pi$
$860$	−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	$0.236706\pi$
$863$			39.7743i			1.35393i	−0.736014	+	0.676967i	$0.763294\pi$
$864$	−4.87485	+	2.86982i	−0.165846	+	0.0976331i
$865$	−3.00329			−0.102115
$866$	−4.53554	+	7.88661i	−0.154124	+	0.267998i
$867$	10.4848			0.356081
$868$		0			0
$869$	−19.2995			−0.654689
$870$	−21.1353	+	36.7511i	−0.716555	+	1.24598i
$871$	−0.858337			−0.0290836
$872$	−0.196197	−	38.6096i	−0.00664408	−	1.30749i
$873$			11.8376i			0.400642i
$874$	−2.98006	+	5.18186i	−0.100802	+	0.175279i
$875$		0			0
$876$	10.4571	−	6.08474i	0.353313	−	0.205584i
$877$	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
$879$			25.2760i			0.852538i
$880$	−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
$885$			4.23703i			0.142426i
$886$	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	$0.183138\pi$
$888$	0.0171057	+	3.36624i	0.000574031	+	0.112963i
$889$		0			0
$890$	54.9450	+	31.5986i	1.84176	+	1.05919i
$891$		−	6.07019i		−	0.203359i
$892$	−9.62861	−	16.5475i	−0.322390	−	0.554052i
$893$	−14.2173			−0.475764
$894$	7.49623	+	4.31104i	0.250711	+	0.144183i
$895$	−34.5534			−1.15499
$896$		0			0
$897$	−1.67554			−0.0559445
$898$	−16.4771	−	9.47587i	−0.549847	−	0.316214i
$899$	−51.8796			−1.73028
$900$	−8.35352	−	14.3562i	−0.278451	−	0.478539i
$901$			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
$906$	−10.0416	+	17.4608i	−0.333609	+	0.580095i
$907$			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
$909$		−	5.72662i		−	0.189940i
$910$		0			0
$911$		−	2.22992i		−	0.0738807i	−0.999317	−	0.0369403i	$-0.988239\pi$
$911$		−	2.22992i		−	0.0738807i	0.999317	−	0.0369403i	$-0.0117612\pi$
$912$	2.40952	−	4.23948i	0.0797871	−	0.140383i
$913$			45.5169i			1.50639i
$914$	−1.42657	−	0.820410i	−0.0471866	−	0.0271368i
$915$	0.760366			0.0251369
$916$	17.5086	−	10.1878i	0.578500	−	0.336616i
$917$		0			0
$918$	−1.79959	+	3.12921i	−0.0593953	+	0.103279i
$919$			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
$921$	−10.2457			−0.337606
$922$	−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
$927$	4.95307			0.162680
$928$	−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	$-0.0145803\pi$
$930$	16.2336	−	28.2277i	0.532320	−	0.925622i
$931$		0			0
$932$	12.7155	+	21.8527i	0.416511	+	0.715808i
$933$	30.3837			0.994718
$934$	36.4912	+	20.9859i	1.19403	+	0.686680i
$935$			56.5161i			1.84828i
$936$	1.36683	−	0.00694562i	0.0446762	−	0.000227025i
$937$		−	13.5645i		−	0.443133i	−0.975145	−	0.221566i	$-0.928883\pi$
$937$		−	13.5645i		−	0.443133i	0.975145	−	0.221566i	$-0.0711169\pi$
$938$		0			0
$939$			17.1215i			0.558739i
$940$	−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	$0.859123\pi$
$942$	14.8741	−	25.8638i	0.484624	−	0.842687i
$943$	−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	$-0.953196\pi$
$947$		−	9.01711i		−	0.293017i	0.989209	−	0.146508i	$-0.0468035\pi$
$948$	5.49605	−	3.19802i	0.178503	−	0.103867i
$949$	−2.92333			−0.0948953
$950$	12.4119	+	7.13799i	0.402694	+	0.231587i
$951$	−12.3657			−0.400986
$952$		0			0
$953$	5.49448			0.177984			0.0889918	−	0.996032i	$-0.471636\pi$
$953$	5.49448			0.177984			0.0889918	+	0.996032i	$0.471636\pi$
$954$	3.22155	+	1.85270i	0.104302	+	0.0599832i
$955$	39.5995			1.28141
$956$	−9.43932	+	5.49251i	−0.305289	+	0.177641i
$957$		−	49.8883i		−	1.61266i
$958$	−34.7618	−	19.9913i	−1.12310	−	0.645889i
$959$		0			0
$960$	−0.296559	−	29.1791i	−0.00957140	−	0.941752i
$961$	8.84755			0.285405
$962$	0.405497	−	0.705097i	0.0130738	−	0.0227332i
$963$		−	13.7280i		−	0.442377i
$964$	−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
$969$		−	3.11173i		−	0.0999632i
$970$	−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	$0.271076\pi$
$972$	1.00586	+	1.72865i	0.0322630	+	0.0554466i
$973$		0			0
$974$	−6.74564	+	11.7296i	−0.216144	+	0.375842i
$975$			4.01333i			0.128530i
$976$	0.724927	+	0.412013i	0.0232044	+	0.0131882i
$977$	57.2191			1.83060			0.915301	−	0.402770i	$-0.131952\pi$
$977$	57.2191			1.83060			0.915301	+	0.402770i	$0.131952\pi$
$978$	−13.4922	+	23.4609i	−0.431433	+	0.750195i
$979$	−74.5859			−2.38378
$980$		0			0
$981$	−13.6507			−0.435835
$982$	−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	$0.814672\pi$
$984$	18.6510	−	0.0947764i	0.594573	−	0.00302136i
$985$		−	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
$990$	27.1442	+	15.6105i	0.862699	+	0.496133i
$991$			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
$993$		−	7.68197i		−	0.243780i
$994$		0			0
$995$		−	36.6844i		−	1.16297i
$996$	−7.54238	−	12.9622i	−0.238989	−	0.410722i
$997$		−	32.3500i		−	1.02454i	−0.858826	−	0.512268i	$-0.828806\pi$
$997$		−	32.3500i		−	1.02454i	0.858826	−	0.512268i	$-0.171194\pi$
$998$	−6.62808	+	11.5252i	−0.209808	+	0.364824i
$999$	1.19016			0.0376550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.b.d.391.10	yes	12
3.2	odd	2		1764.2.b.m.1567.3		12
4.3	odd	2		588.2.b.c.391.9	✓	12
7.2	even	3		588.2.o.e.31.8		24
7.3	odd	6		588.2.o.f.19.3		24
7.4	even	3		588.2.o.e.19.3		24
7.5	odd	6		588.2.o.f.31.8		24
7.6	odd	2		588.2.b.c.391.10	yes	12
12.11	even	2		1764.2.b.l.1567.4		12
21.20	even	2		1764.2.b.l.1567.3		12
28.3	even	6		588.2.o.e.19.8		24
28.11	odd	6		588.2.o.f.19.8		24
28.19	even	6		588.2.o.e.31.3		24
28.23	odd	6		588.2.o.f.31.3		24
28.27	even	2	inner	588.2.b.d.391.9	yes	12
84.83	odd	2		1764.2.b.m.1567.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.9	✓	12	4.3	odd	2
588.2.b.c.391.10	yes	12	7.6	odd	2
588.2.b.d.391.9	yes	12	28.27	even	2	inner
588.2.b.d.391.10	yes	12	1.1	even	1	trivial
588.2.o.e.19.3		24	7.4	even	3
588.2.o.e.19.8		24	28.3	even	6
588.2.o.e.31.3		24	28.19	even	6
588.2.o.e.31.8		24	7.2	even	3
588.2.o.f.19.3		24	7.3	odd	6
588.2.o.f.19.8		24	28.11	odd	6
588.2.o.f.31.3		24	28.23	odd	6
588.2.o.f.31.8		24	7.5	odd	6
1764.2.b.l.1567.3		12	21.20	even	2
1764.2.b.l.1567.4		12	12.11	even	2
1764.2.b.m.1567.3		12	3.2	odd	2
1764.2.b.m.1567.4		12	84.83	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22594 + 0.705031i) q^{2} +1.00000 q^{3} +(1.00586 + 1.72865i) q^{4} +3.64758i q^{5} +(1.22594 + 0.705031i) q^{6} +(0.0143727 + 2.82839i) q^{8} +1.00000 q^{9} +(-2.57166 + 4.47172i) q^{10} -6.07019i q^{11} +(1.00586 + 1.72865i) q^{12} -0.483253i q^{13} +3.64758i q^{15} +(-1.97648 + 3.47757i) q^{16} +2.55250i q^{17} +(1.22594 + 0.705031i) q^{18} -1.21909 q^{19} +(-6.30540 + 3.66896i) q^{20} +(4.27968 - 7.44170i) q^{22} -3.46720i q^{23} +(0.0143727 + 2.82839i) q^{24} -8.30483 q^{25} +(0.340708 - 0.592439i) q^{26} +1.00000 q^{27} +8.21857 q^{29} +(-2.57166 + 4.47172i) q^{30} -6.31249 q^{31} +(-4.87485 + 2.86982i) q^{32} -6.07019i q^{33} +(-1.79959 + 3.12921i) q^{34} +(1.00586 + 1.72865i) q^{36} +1.19016 q^{37} +(-1.49454 - 0.859498i) q^{38} -0.483253i q^{39} +(-10.3168 + 0.0524254i) q^{40} -6.59422i q^{41} +3.51184i q^{43} +(10.4933 - 6.10578i) q^{44} +3.64758i q^{45} +(2.44449 - 4.25059i) q^{46} +11.6622 q^{47} +(-1.97648 + 3.47757i) q^{48} +(-10.1812 - 5.85517i) q^{50} +2.55250i q^{51} +(0.835376 - 0.486085i) q^{52} +2.62782 q^{53} +(1.22594 + 0.705031i) q^{54} +22.1415 q^{55} -1.21909 q^{57} +(10.0755 + 5.79435i) q^{58} +1.16160 q^{59} +(-6.30540 + 3.66896i) q^{60} -0.208458i q^{61} +(-7.73874 - 4.45050i) q^{62} +(-7.99959 + 0.0813030i) q^{64} +1.76270 q^{65} +(4.27968 - 7.44170i) q^{66} -1.77617i q^{67} +(-4.41238 + 2.56746i) q^{68} -3.46720i q^{69} +9.13166i q^{71} +(0.0143727 + 2.82839i) q^{72} -6.04928i q^{73} +(1.45907 + 0.839100i) q^{74} -8.30483 q^{75} +(-1.22624 - 2.10739i) q^{76} +(0.340708 - 0.592439i) q^{78} -3.17938i q^{79} +(-12.6847 - 7.20938i) q^{80} +1.00000 q^{81} +(4.64913 - 8.08412i) q^{82} -7.49842 q^{83} -9.31044 q^{85} +(-2.47595 + 4.30530i) q^{86} +8.21857 q^{87} +(17.1689 - 0.0872448i) q^{88} -12.2872i q^{89} +(-2.57166 + 4.47172i) q^{90} +(5.99359 - 3.48753i) q^{92} -6.31249 q^{93} +(14.2972 + 8.22221i) q^{94} -4.44674i q^{95} +(-4.87485 + 2.86982i) q^{96} +11.8376i q^{97} -6.07019i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 12 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{8} + 12 q^{9} - 4 q^{12} - 4 q^{16} + 4 q^{18} - 24 q^{20} + 4 q^{24} - 12 q^{25} + 24 q^{26} + 12 q^{27} + 32 q^{29} + 16 q^{31} + 4 q^{32} + 32 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) \) 12 * q + 4 * q^2 + 12 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^8 + 12 * q^9 - 4 * q^12 - 4 * q^16 + 4 * q^18 - 24 * q^20 + 4 * q^24 - 12 * q^25 + 24 * q^26 + 12 * q^27 + 32 * q^29 + 16 * q^31 + 4 * q^32 + 32 * q^34 - 4 * q^36 + 32 * q^37 - 24 * q^38 - 32 * q^40 - 24 * q^44 + 24 * q^46 - 4 * q^48 - 28 * q^50 + 32 * q^52 - 32 * q^53 + 4 * q^54 + 16 * q^55 + 16 * q^58 - 16 * q^59 - 24 * q^60 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 4 * q^72 - 32 * q^74 - 12 * q^75 - 32 * q^76 + 24 * q^78 - 16 * q^80 + 12 * q^81 + 32 * q^82 - 16 * q^83 + 16 * q^85 - 24 * q^86 + 32 * q^87 + 24 * q^88 + 16 * q^93 + 4 * q^96

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