LMFDB - Embedded newform 605.2.b.g.364.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(364,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("605.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1480160000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 27x^{4} + 31x^{2} + 11 $ x^8 + 9x^6 + 27x^4 + 31*x^2 + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.3
Root			$-1.23399i$ of defining polynomial
Character	$\chi$	$=$	605.364
Dual form			605.2.b.g.364.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.23399i q^{2} -0.363982i q^{3} +0.477260 q^{4} +(1.29496 - 1.82293i) q^{5} -0.449152 q^{6} -2.58558i q^{7} -3.05692i q^{8} +2.86752 q^{9} +(-2.24948 - 1.59798i) q^{10} -0.173714i q^{12} +2.75929i q^{13} -3.19059 q^{14} +(-0.663514 - 0.471344i) q^{15} -2.81770 q^{16} +3.85124i q^{17} -3.53850i q^{18} +0.277591 q^{19} +(0.618034 - 0.870011i) q^{20} -0.941105 q^{21} +8.40180i q^{23} -1.11267 q^{24} +(-1.64614 - 4.72125i) q^{25} +3.40495 q^{26} -2.13567i q^{27} -1.23399i q^{28} -3.32307 q^{29} +(-0.581635 + 0.818772i) q^{30} +0.564263 q^{31} -2.63682i q^{32} +4.75241 q^{34} +(-4.71333 - 3.34823i) q^{35} +1.36855 q^{36} -0.522583i q^{37} -0.342546i q^{38} +1.00433 q^{39} +(-5.57255 - 3.95860i) q^{40} -5.11188 q^{41} +1.16132i q^{42} -2.54457i q^{43} +(3.71333 - 5.22728i) q^{45} +10.3678 q^{46} -4.92477i q^{47} +1.02559i q^{48} +0.314780 q^{49} +(-5.82599 + 2.03133i) q^{50} +1.40178 q^{51} +1.31690i q^{52} +8.72086i q^{53} -2.63541 q^{54} -7.90392 q^{56} -0.101038i q^{57} +4.10065i q^{58} -7.50726 q^{59} +(-0.316669 - 0.224953i) q^{60} +14.1791 q^{61} -0.696297i q^{62} -7.41419i q^{63} -8.88922 q^{64} +(5.03000 + 3.57318i) q^{65} +3.20618i q^{67} +1.83804i q^{68} +3.05810 q^{69} +(-4.13169 + 5.81622i) q^{70} -8.40099 q^{71} -8.76578i q^{72} +13.0353i q^{73} -0.644864 q^{74} +(-1.71845 + 0.599167i) q^{75} +0.132483 q^{76} -1.23934i q^{78} -9.70425 q^{79} +(-3.64882 + 5.13647i) q^{80} +7.82520 q^{81} +6.30802i q^{82} -3.29699i q^{83} -0.449152 q^{84} +(7.02054 + 4.98721i) q^{85} -3.13998 q^{86} +1.20954i q^{87} -2.48823 q^{89} +(-6.45043 - 4.58222i) q^{90} +7.13437 q^{91} +4.00984i q^{92} -0.205382i q^{93} -6.07713 q^{94} +(0.359470 - 0.506029i) q^{95} -0.959755 q^{96} -10.9014i q^{97} -0.388437i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 4 q^{5} + 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 2 q^{24} - 8 q^{25} + 10 q^{26} - 24 q^{29} - 22 q^{30} + 14 q^{31} - 8 q^{34} - 14 q^{35}+ \cdots - 8 q^{96}+O(q^{100}) $ 8 * q - 2 * q^4 + 4 * q^5 + 6 * q^6 - 4 * q^9 + 4 * q^14 - 8 * q^15 - 22 * q^16 - 12 * q^19 - 4 * q^20 + 4 * q^21 - 2 * q^24 - 8 * q^25 + 10 * q^26 - 24 * q^29 - 22 * q^30 + 14 * q^31 - 8 * q^34 - 14 * q^35 + 20 * q^36 - 30 * q^39 - 24 * q^40 + 34 * q^41 + 6 * q^45 + 24 * q^46 + 30 * q^49 - 16 * q^50 + 54 * q^51 - 20 * q^54 - 10 * q^56 + 6 * q^59 + 34 * q^60 + 20 * q^61 - 14 * q^64 - 20 * q^65 - 32 * q^69 + 8 * q^70 - 42 * q^71 + 4 * q^74 - 20 * q^75 + 28 * q^76 - 16 * q^79 - 28 * q^80 - 36 * q^81 + 6 * q^84 + 4 * q^85 + 46 * q^86 + 12 * q^89 - 46 * q^90 + 20 * q^91 + 42 * q^94 - 26 * q^95 - 8 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.23399i		−	0.872565i	−0.899810	−	0.436283i	$-0.856295\pi$
$2$		−	1.23399i		−	0.872565i	0.899810	−	0.436283i	$-0.143705\pi$
$3$		−	0.363982i		−	0.210145i	−0.994465	−	0.105073i	$-0.966492\pi$
$3$		−	0.363982i		−	0.210145i	0.994465	−	0.105073i	$-0.0335075\pi$
$4$	0.477260			0.238630
$5$	1.29496	−	1.82293i	0.579125	−	0.815239i
$5$	1.29496	−	1.82293i	0.579125	−	0.815239i
$6$	−0.449152			−0.183365
$7$		−	2.58558i		−	0.977257i	−0.872492	−	0.488629i	$-0.837497\pi$
$7$		−	2.58558i		−	0.977257i	0.872492	−	0.488629i	$-0.162503\pi$
$8$		−	3.05692i		−	1.08079i
$9$	2.86752			0.955839
$10$	−2.24948	−	1.59798i	−0.711349	−	0.505324i
$11$		0			0
$11$		0			0
$12$		−	0.173714i		−	0.0501470i
$13$			2.75929i			0.765290i	0.923895	+	0.382645i	$0.124987\pi$
$13$			2.75929i			0.765290i	−0.923895	+	0.382645i	$0.875013\pi$
$14$	−3.19059			−0.852721
$15$	−0.663514	−	0.471344i	−0.171319	−	0.121700i
$16$	−2.81770			−0.704426
$17$			3.85124i			0.934063i	0.884241	+	0.467031i	$0.154677\pi$
$17$			3.85124i			0.934063i	−0.884241	+	0.467031i	$0.845323\pi$
$18$		−	3.53850i		−	0.834032i
$19$	0.277591			0.0636838			0.0318419	−	0.999493i	$-0.489863\pi$
$19$	0.277591			0.0636838			0.0318419	+	0.999493i	$0.489863\pi$
$20$	0.618034	−	0.870011i	0.138197	−	0.194540i
$21$	−0.941105			−0.205366
$22$		0			0
$23$			8.40180i			1.75190i	0.482406	+	0.875948i	$0.339763\pi$
$23$			8.40180i			1.75190i	−0.482406	+	0.875948i	$0.660237\pi$
$24$	−1.11267			−0.227122
$25$	−1.64614	−	4.72125i	−0.329228	−	0.944250i
$26$	3.40495			0.667766
$27$		−	2.13567i		−	0.411010i
$28$		−	1.23399i		−	0.233203i
$29$	−3.32307			−0.617079			−0.308539	−	0.951212i	$-0.599840\pi$
$29$	−3.32307			−0.617079			−0.308539	+	0.951212i	$0.599840\pi$
$30$	−0.581635	+	0.818772i	−0.106192	+	0.149487i
$31$	0.564263			0.101345			0.0506723	−	0.998715i	$-0.483864\pi$
$31$	0.564263			0.101345			0.0506723	+	0.998715i	$0.483864\pi$
$32$		−	2.63682i		−	0.466128i
$33$		0			0
$34$	4.75241			0.815031
$35$	−4.71333	−	3.34823i	−0.796698	−	0.565954i
$36$	1.36855			0.228092
$37$		−	0.522583i		−	0.0859121i	−0.999077	−	0.0429560i	$-0.986322\pi$
$37$		−	0.522583i		−	0.0859121i	0.999077	−	0.0429560i	$-0.0136775\pi$
$38$		−	0.342546i		−	0.0555682i
$39$	1.00433			0.160822
$40$	−5.57255	−	3.95860i	−0.881098	−	0.625910i
$41$	−5.11188			−0.798341			−0.399170	−	0.916877i	$-0.630702\pi$
$41$	−5.11188			−0.798341			−0.399170	+	0.916877i	$0.630702\pi$
$42$			1.16132i			0.179195i
$43$		−	2.54457i		−	0.388043i	−0.980997	−	0.194022i	$-0.937847\pi$
$43$		−	2.54457i		−	0.388043i	0.980997	−	0.194022i	$-0.0621532\pi$
$44$		0			0
$45$	3.71333	−	5.22728i	0.553550	−	0.779237i
$46$	10.3678			1.52864
$47$		−	4.92477i		−	0.718351i	−0.933270	−	0.359176i	$-0.883058\pi$
$47$		−	4.92477i		−	0.718351i	0.933270	−	0.359176i	$-0.116942\pi$
$48$			1.02559i			0.148032i
$49$	0.314780			0.0449686
$50$	−5.82599	+	2.03133i	−0.823920	+	0.287273i
$51$	1.40178			0.196289
$52$			1.31690i			0.182621i
$53$			8.72086i			1.19790i	0.800786	+	0.598951i	$0.204416\pi$
$53$			8.72086i			1.19790i	−0.800786	+	0.598951i	$0.795584\pi$
$54$	−2.63541			−0.358633
$55$		0			0
$56$	−7.90392			−1.05621
$57$		−	0.101038i		−	0.0133828i
$58$			4.10065i			0.538441i
$59$	−7.50726			−0.977362			−0.488681	−	0.872463i	$-0.662522\pi$
$59$	−7.50726			−0.977362			−0.488681	+	0.872463i	$0.662522\pi$
$60$	−0.316669	−	0.224953i	−0.0408818	−	0.0290414i
$61$	14.1791			1.81544			0.907721	−	0.419573i	$-0.137820\pi$
$61$	14.1791			1.81544			0.907721	+	0.419573i	$0.137820\pi$
$62$		−	0.696297i		−	0.0884298i
$63$		−	7.41419i		−	0.934100i
$64$	−8.88922			−1.11115
$65$	5.03000	+	3.57318i	0.623894	+	0.443199i
$66$		0			0
$67$			3.20618i			0.391698i	0.980634	+	0.195849i	$0.0627462\pi$
$67$			3.20618i			0.391698i	−0.980634	+	0.195849i	$0.937254\pi$
$68$			1.83804i			0.222895i
$69$	3.05810			0.368153
$70$	−4.13169	+	5.81622i	−0.493832	+	0.695171i
$71$	−8.40099			−0.997014			−0.498507	−	0.866886i	$-0.666118\pi$
$71$	−8.40099			−0.997014			−0.498507	+	0.866886i	$0.666118\pi$
$72$		−	8.76578i		−	1.03306i
$73$			13.0353i			1.52566i	0.646598	+	0.762831i	$0.276191\pi$
$73$			13.0353i			1.52566i	−0.646598	+	0.762831i	$0.723809\pi$
$74$	−0.644864			−0.0749639
$75$	−1.71845	+	0.599167i	−0.198430	+	0.0691858i
$76$	0.132483			0.0151969
$77$		0			0
$78$		−	1.23934i		−	0.140328i
$79$	−9.70425			−1.09181			−0.545907	−	0.837846i	$-0.683815\pi$
$79$	−9.70425			−1.09181			−0.545907	+	0.837846i	$0.683815\pi$
$80$	−3.64882	+	5.13647i	−0.407951	+	0.574275i
$81$	7.82520			0.869467
$82$			6.30802i			0.696604i
$83$		−	3.29699i		−	0.361892i	−0.983493	−	0.180946i	$-0.942084\pi$
$83$		−	3.29699i		−	0.361892i	0.983493	−	0.180946i	$-0.0579159\pi$
$84$	−0.449152			−0.0490065
$85$	7.02054	+	4.98721i	0.761484	+	0.540939i
$86$	−3.13998			−0.338593
$87$			1.20954i			0.129676i
$88$		0			0
$89$	−2.48823			−0.263752			−0.131876	−	0.991266i	$-0.542100\pi$
$89$	−2.48823			−0.263752			−0.131876	+	0.991266i	$0.542100\pi$
$90$	−6.45043	−	4.58222i	−0.679935	−	0.483009i
$91$	7.13437			0.747885
$92$			4.00984i			0.418055i
$93$		−	0.205382i		−	0.0212971i
$94$	−6.07713			−0.626808
$95$	0.359470	−	0.506029i	0.0368809	−	0.0519175i
$96$	−0.959755			−0.0979546
$97$		−	10.9014i		−	1.10687i	−0.832891	−	0.553437i	$-0.813316\pi$
$97$		−	10.9014i		−	1.10687i	0.832891	−	0.553437i	$-0.186684\pi$
$98$		−	0.388437i		−	0.0392380i
$99$		0			0
$100$	−0.785638	−	2.25326i	−0.0785638	−	0.225326i
$101$	13.8382			1.37696			0.688478	−	0.725257i	$-0.258279\pi$
$101$	13.8382			1.37696			0.688478	+	0.725257i	$0.258279\pi$
$102$		−	1.72979i		−	0.171275i
$103$		−	13.3899i		−	1.31935i	−0.751553	−	0.659673i	$-0.770695\pi$
$103$		−	13.3899i		−	1.31935i	0.751553	−	0.659673i	$-0.229305\pi$
$104$	8.43495			0.827115
$105$	−1.21870	+	1.71557i	−0.118933	+	0.167422i
$106$	10.7615			1.04525
$107$			10.2594i			0.991815i	0.868375	+	0.495907i	$0.165164\pi$
$107$			10.2594i			0.991815i	−0.868375	+	0.495907i	$0.834836\pi$
$108$		−	1.01927i		−	0.0980794i
$109$	4.94262			0.473417			0.236708	−	0.971581i	$-0.423931\pi$
$109$	4.94262			0.473417			0.236708	+	0.971581i	$0.423931\pi$
$110$		0			0
$111$	−0.190211			−0.0180540
$112$			7.28539i			0.688405i
$113$			9.92408i			0.933579i	0.884369	+	0.466789i	$0.154589\pi$
$113$			9.92408i			0.933579i	−0.884369	+	0.466789i	$0.845411\pi$
$114$	−0.124681			−0.0116774
$115$	15.3159	+	10.8800i	1.42821	+	1.01457i
$116$	−1.58597			−0.147254
$117$			7.91232i			0.731494i
$118$			9.26391i			0.852812i
$119$	9.95769			0.912820
$120$	−1.44086	+	2.02831i	−0.131532	+	0.185159i
$121$		0			0
$122$		−	17.4969i		−	1.58409i
$123$			1.86063i			0.167768i
$124$	0.269300			0.0241839
$125$	−10.7382	−	3.11304i	−0.960454	−	0.278439i
$126$	−9.14906			−0.815063
$127$			11.1357i			0.988138i	0.869423	+	0.494069i	$0.164491\pi$
$127$			11.1357i			0.988138i	−0.869423	+	0.494069i	$0.835509\pi$
$128$			5.69561i			0.503425i
$129$	−0.926179			−0.0815455
$130$	4.40928	−	6.20698i	0.386720	−	0.544388i
$131$	10.1649			0.888114			0.444057	−	0.895999i	$-0.353539\pi$
$131$	10.1649			0.888114			0.444057	+	0.895999i	$0.353539\pi$
$132$		0			0
$133$		−	0.717734i		−	0.0622354i
$134$	3.95641			0.341782
$135$	−3.89318	−	2.76562i	−0.335072	−	0.238026i
$136$	11.7729			1.00952
$137$		−	4.34606i		−	0.371309i	−0.982615	−	0.185655i	$-0.940559\pi$
$137$		−	4.34606i		−	0.371309i	0.982615	−	0.185655i	$-0.0594406\pi$
$138$		−	3.77368i		−	0.321237i
$139$	8.30246			0.704206			0.352103	−	0.935961i	$-0.385467\pi$
$139$	8.30246			0.704206			0.352103	+	0.935961i	$0.385467\pi$
$140$	−2.24948	−	1.59798i	−0.190116	−	0.135054i
$141$	−1.79253			−0.150958
$142$			10.3668i			0.869960i
$143$		0			0
$144$	−8.07981			−0.673318
$145$	−4.30325	+	6.05772i	−0.357366	+	0.503067i
$146$	16.0854			1.33124
$147$		−	0.114574i		−	0.00944994i
$148$		−	0.249408i		−	0.0205012i
$149$	−8.46690			−0.693636			−0.346818	−	0.937933i	$-0.612738\pi$
$149$	−8.46690			−0.693636			−0.346818	+	0.937933i	$0.612738\pi$
$150$	0.739368	+	2.12056i	0.0603691	+	0.173143i
$151$	11.1023			0.903493			0.451746	−	0.892146i	$-0.350801\pi$
$151$	11.1023			0.903493			0.451746	+	0.892146i	$0.350801\pi$
$152$		−	0.848575i		−	0.0688285i
$153$			11.0435i			0.892814i
$154$		0			0
$155$	0.730700	−	1.02861i	0.0586912	−	0.0826201i
$156$	0.479328			0.0383770
$157$			13.7662i			1.09867i	0.835604	+	0.549333i	$0.185118\pi$
$157$			13.7662i			1.09867i	−0.835604	+	0.549333i	$0.814882\pi$
$158$			11.9750i			0.952678i
$159$	3.17424			0.251734
$160$	−4.80673	−	3.41458i	−0.380006	−	0.269946i
$161$	21.7235			1.71205
$162$		−	9.65625i		−	0.758667i
$163$		−	8.94093i		−	0.700308i	−0.936692	−	0.350154i	$-0.886129\pi$
$163$		−	8.94093i		−	0.700308i	0.936692	−	0.350154i	$-0.113871\pi$
$164$	−2.43969			−0.190508
$165$		0			0
$166$	−4.06846			−0.315774
$167$		−	16.9182i		−	1.30917i	−0.755990	−	0.654583i	$-0.772844\pi$
$167$		−	16.9182i		−	1.30917i	0.755990	−	0.654583i	$-0.227156\pi$
$168$			2.87689i			0.221957i
$169$	5.38630			0.414331
$170$	6.15419	−	8.66330i	0.472005	−	0.664445i
$171$	0.795997			0.0608714
$172$		−	1.21442i		−	0.0925988i
$173$		−	3.37990i		−	0.256969i	−0.991712	−	0.128484i	$-0.958989\pi$
$173$		−	3.37990i		−	0.256969i	0.991712	−	0.128484i	$-0.0410112\pi$
$174$	1.49256			0.113151
$175$	−12.2072	+	4.25623i	−0.922775	+	0.321741i
$176$		0			0
$177$			2.73251i			0.205388i
$178$			3.07046i			0.230141i
$179$	−13.8239			−1.03325			−0.516624	−	0.856212i	$-0.672812\pi$
$179$	−13.8239			−1.03325			−0.516624	+	0.856212i	$0.672812\pi$
$180$	1.77222	−	2.49477i	0.132094	−	0.185949i
$181$	−2.59901			−0.193183			−0.0965913	−	0.995324i	$-0.530794\pi$
$181$	−2.59901			−0.193183			−0.0965913	+	0.995324i	$0.530794\pi$
$182$		−	8.80377i		−	0.652579i
$183$		−	5.16093i		−	0.381507i
$184$	25.6836			1.89342
$185$	−0.952632	−	0.676725i	−0.0700389	−	0.0497538i
$186$	−0.253440			−0.0185831
$187$		0			0
$188$		−	2.35039i		−	0.171420i
$189$	−5.52195			−0.401663
$190$	−0.624436	−	0.443584i	−0.0453014	−	0.0321810i
$191$	2.21832			0.160512			0.0802560	−	0.996774i	$-0.474426\pi$
$191$	2.21832			0.160512			0.0802560	+	0.996774i	$0.474426\pi$
$192$			3.23552i			0.233504i
$193$			10.4765i			0.754112i	0.926190	+	0.377056i	$0.123064\pi$
$193$			10.4765i			0.754112i	−0.926190	+	0.377056i	$0.876936\pi$
$194$	−13.4523			−0.965820
$195$	1.30058	−	1.83083i	0.0931361	−	0.131108i
$196$	0.150232			0.0107309
$197$		−	1.32667i		−	0.0945210i	−0.998883	−	0.0472605i	$-0.984951\pi$
$197$		−	1.32667i		−	0.0945210i	0.998883	−	0.0472605i	$-0.0150491\pi$
$198$		0			0
$199$	5.20321			0.368846			0.184423	−	0.982847i	$-0.440958\pi$
$199$	5.20321			0.368846			0.184423	+	0.982847i	$0.440958\pi$
$200$	−14.4325	+	5.03213i	−1.02053	+	0.355825i
$201$	1.16699			0.0823134
$202$		−	17.0763i		−	1.20148i
$203$			8.59206i			0.603045i
$204$	0.669015			0.0468404
$205$	−6.61969	+	9.31859i	−0.462339	+	0.650838i
$206$	−16.5230			−1.15122
$207$			24.0923i			1.67453i
$208$		−	7.77487i		−	0.539090i
$209$		0			0
$210$	2.11700	+	1.50386i	0.146087	+	0.103776i
$211$	18.9165			1.30227			0.651134	−	0.758963i	$-0.274294\pi$
$211$	18.9165			1.30227			0.651134	+	0.758963i	$0.274294\pi$
$212$			4.16212i			0.285855i
$213$			3.05781i			0.209518i
$214$	12.6600			0.865423
$215$	−4.63857	−	3.29512i	−0.316348	−	0.224726i
$216$	−6.52859			−0.444214
$217$		−	1.45895i		−	0.0990398i
$218$		−	6.09916i		−	0.413087i
$219$	4.74460			0.320611
$220$		0			0
$221$	−10.6267			−0.714829
$222$			0.234719i			0.0157533i
$223$		−	21.8723i		−	1.46468i	−0.680942	−	0.732338i	$-0.738429\pi$
$223$		−	21.8723i		−	1.46468i	0.680942	−	0.732338i	$-0.261571\pi$
$224$	−6.81770			−0.455527
$225$	−4.72034	−	13.5383i	−0.314689	−	0.902551i
$226$	12.2462			0.814608
$227$		−	2.43865i		−	0.161859i	−0.996720	−	0.0809294i	$-0.974211\pi$
$227$		−	2.43865i		−	0.161859i	0.996720	−	0.0809294i	$-0.0257888\pi$
$228$		−	0.0482215i		−	0.00319355i
$229$	−7.30119			−0.482476			−0.241238	−	0.970466i	$-0.577553\pi$
$229$	−7.30119			−0.482476			−0.241238	+	0.970466i	$0.577553\pi$
$230$	13.4259	−	18.8997i	0.885275	−	1.24621i
$231$		0			0
$232$			10.1584i			0.666930i
$233$		−	4.45831i		−	0.292073i	−0.989279	−	0.146037i	$-0.953348\pi$
$233$		−	4.45831i		−	0.292073i	0.989279	−	0.146037i	$-0.0466518\pi$
$234$	9.76375			0.638276
$235$	−8.97750	−	6.37739i	−0.585628	−	0.416015i
$236$	−3.58291			−0.233228
$237$			3.53217i			0.229439i
$238$		−	12.2877i		−	0.796495i
$239$	−24.1747			−1.56373			−0.781867	−	0.623446i	$-0.785732\pi$
$239$	−24.1747			−1.56373			−0.781867	+	0.623446i	$0.785732\pi$
$240$	1.86959	+	1.32811i	0.120681	+	0.0857289i
$241$	−12.0393			−0.775522			−0.387761	−	0.921760i	$-0.626751\pi$
$241$	−12.0393			−0.775522			−0.387761	+	0.921760i	$0.626751\pi$
$242$		0			0
$243$		−	9.25525i		−	0.593725i
$244$	6.76710			0.433219
$245$	0.407629	−	0.573822i	0.0260424	−	0.0366601i
$246$	2.29601			0.146388
$247$			0.765955i			0.0487366i
$248$		−	1.72491i		−	0.109532i
$249$	−1.20005			−0.0760498
$250$	−3.84148	+	13.2509i	−0.242956	+	0.838059i
$251$	−0.536388			−0.0338565			−0.0169283	−	0.999857i	$-0.505389\pi$
$251$	−0.536388			−0.0338565			−0.0169283	+	0.999857i	$0.505389\pi$
$252$		−	3.53850i		−	0.222904i
$253$		0			0
$254$	13.7414			0.862214
$255$	1.81526	−	2.55535i	0.113676	−	0.160022i
$256$	−10.7501			−0.671882
$257$			23.7199i			1.47961i	0.672822	+	0.739805i	$0.265082\pi$
$257$			23.7199i			1.47961i	−0.672822	+	0.739805i	$0.734918\pi$
$258$			1.14290i			0.0711538i
$259$	−1.35118			−0.0839582
$260$	2.40062	+	1.70534i	0.148880	+	0.105761i
$261$	−9.52896			−0.589828
$262$		−	12.5435i		−	0.774937i
$263$			4.97643i			0.306860i	0.988160	+	0.153430i	$0.0490320\pi$
$263$			4.97643i			0.306860i	−0.988160	+	0.153430i	$0.950968\pi$
$264$		0			0
$265$	15.8975	+	11.2932i	0.976576	+	0.693735i
$266$	−0.885679			−0.0543044
$267$			0.905671i			0.0554262i
$268$			1.53018i			0.0934708i
$269$	−28.8046			−1.75625			−0.878124	−	0.478434i	$-0.841205\pi$
$269$	−28.8046			−1.75625			−0.878124	+	0.478434i	$0.841205\pi$
$270$	−3.41275	+	4.80416i	−0.207694	+	0.292372i
$271$	−16.0762			−0.976559			−0.488280	−	0.872687i	$-0.662375\pi$
$271$	−16.0762			−0.976559			−0.488280	+	0.872687i	$0.662375\pi$
$272$		−	10.8517i		−	0.657978i
$273$		−	2.59679i		−	0.157165i
$274$	−5.36301			−0.323992
$275$		0			0
$276$	1.45951			0.0878522
$277$			18.0038i			1.08174i	0.841105	+	0.540871i	$0.181905\pi$
$277$			18.0038i			1.08174i	−0.841105	+	0.540871i	$0.818095\pi$
$278$		−	10.2452i		−	0.614465i
$279$	1.61803			0.0968692
$280$	−10.2353	+	14.4083i	−0.611675	+	0.861059i
$281$	13.7150			0.818167			0.409084	−	0.912497i	$-0.365848\pi$
$281$	13.7150			0.818167			0.409084	+	0.912497i	$0.365848\pi$
$282$			2.21197i			0.131721i
$283$			20.5044i			1.21886i	0.792839	+	0.609431i	$0.208602\pi$
$283$			20.5044i			1.21886i	−0.792839	+	0.609431i	$0.791398\pi$
$284$	−4.00946			−0.237918
$285$	−0.184186	−	0.130841i	−0.0109102	−	0.00775034i
$286$		0			0
$287$			13.2172i			0.780184i
$288$		−	7.56112i		−	0.445543i
$289$	2.16795			0.127526
$290$	7.47519	+	5.31019i	0.438958	+	0.311825i
$291$	−3.96793			−0.232604
$292$			6.22121i			0.364069i
$293$		−	22.4133i		−	1.30940i	−0.755890	−	0.654699i	$-0.772796\pi$
$293$		−	22.4133i		−	1.30940i	0.755890	−	0.654699i	$-0.227204\pi$
$294$	−0.141384			−0.00824569
$295$	−9.72162	+	13.6852i	−0.566015	+	0.796783i
$296$	−1.59750			−0.0928525
$297$		0			0
$298$			10.4481i			0.605242i
$299$	−23.1830			−1.34071
$300$	−0.820148	+	0.285958i	−0.0473513	+	0.0165098i
$301$	−6.57919			−0.379218
$302$		−	13.7002i		−	0.788356i
$303$		−	5.03688i		−	0.289361i
$304$	−0.782169			−0.0448605
$305$	18.3614	−	25.8474i	1.05137	−	1.48002i
$306$	13.6276			0.779038
$307$		−	20.3044i		−	1.15883i	−0.815032	−	0.579416i	$-0.803281\pi$
$307$		−	20.3044i		−	1.15883i	0.815032	−	0.579416i	$-0.196719\pi$
$308$		0			0
$309$	−4.87369			−0.277254
$310$	−1.26930	−	0.901679i	−0.0720914	−	0.0512119i
$311$	−8.75881			−0.496666			−0.248333	−	0.968675i	$-0.579883\pi$
$311$	−8.75881			−0.496666			−0.248333	+	0.968675i	$0.579883\pi$
$312$		−	3.07017i		−	0.173814i
$313$		−	1.73123i		−	0.0978550i	−0.998802	−	0.0489275i	$-0.984420\pi$
$313$		−	1.73123i		−	0.0978550i	0.998802	−	0.0489275i	$-0.0155803\pi$
$314$	16.9875			0.958657
$315$	−13.5155	−	9.60110i	−0.761515	−	0.540961i
$316$	−4.63145			−0.260539
$317$			17.4764i			0.981573i	0.871280	+	0.490786i	$0.163290\pi$
$317$			17.4764i			0.981573i	−0.871280	+	0.490786i	$0.836710\pi$
$318$		−	3.91699i		−	0.219654i
$319$		0			0
$320$	−11.5112	+	16.2044i	−0.643496	+	0.905855i
$321$	3.73424			0.208425
$322$		−	26.8067i		−	1.49388i
$323$			1.06907i			0.0594846i
$324$	3.73466			0.207481
$325$	13.0273	−	4.54219i	0.722626	−	0.251955i
$326$	−11.0331			−0.611064
$327$		−	1.79902i		−	0.0994863i
$328$			15.6266i			0.862835i
$329$	−12.7334			−0.702014
$330$		0			0
$331$	12.6193			0.693620			0.346810	−	0.937935i	$-0.387265\pi$
$331$	12.6193			0.693620			0.346810	+	0.937935i	$0.387265\pi$
$332$		−	1.57352i		−	0.0863582i
$333$		−	1.49852i		−	0.0821181i
$334$	−20.8769			−1.14233
$335$	5.84464	+	4.15189i	0.319327	+	0.226842i
$336$	2.65175			0.144665
$337$		−	11.8599i		−	0.646047i	−0.946391	−	0.323024i	$-0.895301\pi$
$337$		−	11.8599i		−	0.646047i	0.946391	−	0.323024i	$-0.104699\pi$
$338$		−	6.64666i		−	0.361531i
$339$	3.61219			0.196187
$340$	3.35062	+	2.38020i	0.181713	+	0.129084i
$341$		0			0
$342$		−	0.982255i		−	0.0531143i
$343$		−	18.9129i		−	1.02120i
$344$	−7.77856			−0.419392
$345$	3.96013	−	5.57471i	0.213206	−	0.300132i
$346$	−4.17077			−0.224222
$347$		−	22.3040i		−	1.19734i	−0.800994	−	0.598672i	$-0.795695\pi$
$347$		−	22.3040i		−	1.19734i	0.800994	−	0.598672i	$-0.204305\pi$
$348$			0.577265i			0.0309446i
$349$	−15.9679			−0.854740			−0.427370	−	0.904077i	$-0.640560\pi$
$349$	−15.9679			−0.854740			−0.427370	+	0.904077i	$0.640560\pi$
$350$	5.25216	+	15.0636i	0.280740	+	0.805182i
$351$	5.89295			0.314542
$352$		0			0
$353$		−	24.1406i		−	1.28488i	−0.766337	−	0.642439i	$-0.777923\pi$
$353$		−	24.1406i		−	1.28488i	0.766337	−	0.642439i	$-0.222077\pi$
$354$	3.37190			0.179214
$355$	−10.8790	+	15.3144i	−0.577396	+	0.812805i
$356$	−1.18753			−0.0629391
$357$		−	3.62442i		−	0.191825i
$358$			17.0586i			0.901577i
$359$	−20.3784			−1.07553			−0.537764	−	0.843095i	$-0.680731\pi$
$359$	−20.3784			−1.07553			−0.537764	+	0.843095i	$0.680731\pi$
$360$	−15.9794	−	11.3514i	−0.842188	−	0.598269i
$361$	−18.9229			−0.995944
$362$			3.20716i			0.168564i
$363$		0			0
$364$	3.40495			0.178468
$365$	23.7624	+	16.8802i	1.24378	+	0.883549i
$366$	−6.36855			−0.332889
$367$		−	5.40430i		−	0.282102i	−0.990002	−	0.141051i	$-0.954952\pi$
$367$		−	5.40430i		−	0.282102i	0.990002	−	0.141051i	$-0.0450482\pi$
$368$		−	23.6738i		−	1.23408i
$369$	−14.6584			−0.763085
$370$	−0.835075	+	1.17554i	−0.0434135	+	0.0611135i
$371$	22.5485			1.17066
$372$		−	0.0980205i		−	0.00508213i
$373$		−	17.0982i		−	0.885311i	−0.896692	−	0.442656i	$-0.854036\pi$
$373$		−	17.0982i		−	0.885311i	0.896692	−	0.442656i	$-0.145964\pi$
$374$		0			0
$375$	−1.13309	+	3.90852i	−0.0585127	+	0.201835i
$376$	−15.0546			−0.776384
$377$		−	9.16933i		−	0.472244i
$378$			6.81405i			0.350477i
$379$	8.59196			0.441339			0.220670	−	0.975349i	$-0.429176\pi$
$379$	8.59196			0.441339			0.220670	+	0.975349i	$0.429176\pi$
$380$	0.171561	−	0.241507i	0.00880088	−	0.0123891i
$381$	4.05321			0.207652
$382$		−	2.73739i		−	0.140057i
$383$		−	9.66958i		−	0.494093i	−0.969004	−	0.247046i	$-0.920540\pi$
$383$		−	9.66958i		−	0.494093i	0.969004	−	0.247046i	$-0.0794600\pi$
$384$	2.07310			0.105792
$385$		0			0
$386$	12.9279			0.658012
$387$		−	7.29660i		−	0.370907i
$388$		−	5.20283i		−	0.264133i
$389$	27.3693			1.38768			0.693841	−	0.720129i	$-0.255917\pi$
$389$	27.3693			1.38768			0.693841	+	0.720129i	$0.255917\pi$
$390$	−2.25923	−	1.60490i	−0.114401	−	0.0812673i
$391$	−32.3573			−1.63638
$392$		−	0.962259i		−	0.0486014i
$393$		−	3.69985i		−	0.186633i
$394$	−1.63710			−0.0824758
$395$	−12.5666	+	17.6902i	−0.632296	+	0.890088i
$396$		0			0
$397$			10.6518i			0.534596i	0.963614	+	0.267298i	$0.0861308\pi$
$397$			10.6518i			0.534596i	−0.963614	+	0.267298i	$0.913869\pi$
$398$		−	6.42073i		−	0.321842i
$399$	−0.261242			−0.0130785
$400$	4.63834	+	13.3031i	0.231917	+	0.665154i
$401$	13.7146			0.684875			0.342437	−	0.939541i	$-0.388748\pi$
$401$	13.7146			0.684875			0.342437	+	0.939541i	$0.388748\pi$
$402$		−	1.44006i		−	0.0718238i
$403$			1.55697i			0.0775581i
$404$	6.60444			0.328583
$405$	10.1333	−	14.2648i	0.503530	−	0.708823i
$406$	10.6026			0.526196
$407$		0			0
$408$		−	4.28514i		−	0.212146i
$409$	22.3083			1.10308			0.551538	−	0.834150i	$-0.314041\pi$
$409$	22.3083			1.10308			0.551538	+	0.834150i	$0.314041\pi$
$410$	11.4991	+	8.16865i	0.567899	+	0.403421i
$411$	−1.58189			−0.0780289
$412$		−	6.39046i		−	0.314836i
$413$			19.4106i			0.955134i
$414$	29.7297			1.46114
$415$	−6.01018	−	4.26948i	−0.295028	−	0.209581i
$416$	7.27576			0.356723
$417$		−	3.02195i		−	0.147986i
$418$		0			0
$419$	0.510725			0.0249506			0.0124753	−	0.999922i	$-0.496029\pi$
$419$	0.510725			0.0249506			0.0124753	+	0.999922i	$0.496029\pi$
$420$	−0.581635	+	0.818772i	−0.0283809	+	0.0399520i
$421$	13.2150			0.644058			0.322029	−	0.946730i	$-0.395635\pi$
$421$	13.2150			0.644058			0.322029	+	0.946730i	$0.395635\pi$
$422$		−	23.3429i		−	1.13631i
$423$		−	14.1219i		−	0.686628i
$424$	26.6590			1.29468
$425$	18.1827	−	6.33969i	0.881989	−	0.307520i
$426$	3.77332			0.182818
$427$		−	36.6611i		−	1.77415i
$428$			4.89641i			0.236677i
$429$		0			0
$430$	−4.06616	+	5.72397i	−0.196088	+	0.276034i
$431$	−29.4064			−1.41645			−0.708227	−	0.705985i	$-0.750505\pi$
$431$	−29.4064			−1.41645			−0.708227	+	0.705985i	$0.750505\pi$
$432$			6.01769i			0.289526i
$433$			10.2165i			0.490975i	0.969400	+	0.245488i	$0.0789481\pi$
$433$			10.2165i			0.490975i	−0.969400	+	0.245488i	$0.921052\pi$
$434$	−1.80033			−0.0864187
$435$	2.20490	+	1.56631i	0.105717	+	0.0750987i
$436$	2.35891			0.112971
$437$			2.33226i			0.111567i
$438$		−	5.85481i		−	0.279754i
$439$	1.53306			0.0731691			0.0365846	−	0.999331i	$-0.488352\pi$
$439$	1.53306			0.0731691			0.0365846	+	0.999331i	$0.488352\pi$
$440$		0			0
$441$	0.902638			0.0429827
$442$			13.1133i			0.623735i
$443$		−	3.39254i		−	0.161185i	−0.996747	−	0.0805923i	$-0.974319\pi$
$443$		−	3.39254i		−	0.161185i	0.996747	−	0.0805923i	$-0.0256812\pi$
$444$	−0.0907801			−0.00430823
$445$	−3.22216	+	4.53587i	−0.152745	+	0.215021i
$446$	−26.9902			−1.27802
$447$			3.08180i			0.145764i
$448$			22.9838i			1.08588i
$449$	32.3501			1.52669			0.763347	−	0.645989i	$-0.223555\pi$
$449$	32.3501			1.52669			0.763347	+	0.645989i	$0.223555\pi$
$450$	−16.7061	+	5.82487i	−0.787535	+	0.274587i
$451$		0			0
$452$			4.73637i			0.222780i
$453$		−	4.04104i		−	0.189865i
$454$	−3.00928			−0.141232
$455$	9.23875	−	13.0055i	0.433119	−	0.609705i
$456$	−0.308866			−0.0144640
$457$			12.1730i			0.569427i	0.958613	+	0.284714i	$0.0918985\pi$
$457$			12.1730i			0.569427i	−0.958613	+	0.284714i	$0.908101\pi$
$458$			9.00962i			0.420992i
$459$	8.22499			0.383910
$460$	7.30966	+	5.19260i	0.340814	+	0.242106i
$461$	−16.5699			−0.771739			−0.385869	−	0.922553i	$-0.626098\pi$
$461$	−16.5699			−0.771739			−0.385869	+	0.922553i	$0.626098\pi$
$462$		0			0
$463$		−	14.6302i		−	0.679924i	−0.940439	−	0.339962i	$-0.889586\pi$
$463$		−	14.6302i		−	0.679924i	0.940439	−	0.339962i	$-0.110414\pi$
$464$	9.36343			0.434686
$465$	−0.374396	−	0.265962i	−0.0173622	−	0.0123337i
$466$	−5.50152			−0.254853
$467$			30.4853i			1.41069i	0.708862	+	0.705347i	$0.249209\pi$
$467$			30.4853i			1.41069i	−0.708862	+	0.705347i	$0.750791\pi$
$468$			3.77623i			0.174556i
$469$	8.28984			0.382789
$470$	−7.86966	+	11.0782i	−0.363000	+	0.510998i
$471$	5.01067			0.230879
$472$			22.9491i			1.05632i
$473$		0			0
$474$	4.35868			0.200201
$475$	−0.456954	−	1.31058i	−0.0209665	−	0.0601334i
$476$	4.75241			0.217826
$477$			25.0072i			1.14500i
$478$			29.8315i			1.36446i
$479$	−13.9993			−0.639643			−0.319822	−	0.947478i	$-0.603623\pi$
$479$	−13.9993			−0.639643			−0.319822	+	0.947478i	$0.603623\pi$
$480$	−1.24285	+	1.74957i	−0.0567280	+	0.0798564i
$481$	1.44196			0.0657477
$482$			14.8565i			0.676693i
$483$		−	7.90697i		−	0.359780i
$484$		0			0
$485$	−19.8726	−	14.1170i	−0.902367	−	0.641019i
$486$	−11.4209			−0.518064
$487$			34.1311i			1.54663i	0.634024	+	0.773313i	$0.281402\pi$
$487$			34.1311i			1.54663i	−0.634024	+	0.773313i	$0.718598\pi$
$488$		−	43.3443i		−	1.96210i
$489$	−3.25434			−0.147166
$490$	−0.708093	−	0.503011i	−0.0319884	−	0.0227237i
$491$	−3.19431			−0.144157			−0.0720786	−	0.997399i	$-0.522963\pi$
$491$	−3.19431			−0.144157			−0.0720786	+	0.997399i	$0.522963\pi$
$492$			0.888005i			0.0400344i
$493$		−	12.7979i		−	0.576390i
$494$	0.945184			0.0425258
$495$		0			0
$496$	−1.58993			−0.0713898
$497$			21.7214i			0.974339i
$498$			1.48085i			0.0663584i
$499$	−6.52850			−0.292256			−0.146128	−	0.989266i	$-0.546681\pi$
$499$	−6.52850			−0.292256			−0.146128	+	0.989266i	$0.546681\pi$
$500$	−5.12491	−	1.48573i	−0.229193	−	0.0664439i
$501$	−6.15791			−0.275115
$502$			0.661899i			0.0295420i
$503$		−	1.00387i		−	0.0447603i	−0.999750	−	0.0223802i	$-0.992876\pi$
$503$		−	1.00387i		−	0.0447603i	0.999750	−	0.0223802i	$-0.00712442\pi$
$504$	−22.6646			−1.00956
$505$	17.9200	−	25.2261i	0.797430	−	1.12255i
$506$		0			0
$507$		−	1.96052i		−	0.0870697i
$508$			5.31465i			0.235799i
$509$	4.27401			0.189442			0.0947211	−	0.995504i	$-0.469804\pi$
$509$	4.27401			0.189442			0.0947211	+	0.995504i	$0.469804\pi$
$510$	−3.15329	−	2.24002i	−0.139630	−	0.0991896i
$511$	33.7037			1.49096
$512$			24.6568i			1.08969i
$513$		−	0.592844i		−	0.0261747i
$514$	29.2703			1.29106
$515$	−24.4088	−	17.3394i	−1.07558	−	0.764066i
$516$	−0.442028			−0.0194592
$517$		0			0
$518$			1.66735i			0.0732590i
$519$	−1.23022			−0.0540008
$520$	10.9229	−	15.3763i	0.479003	−	0.674296i
$521$	−9.88817			−0.433208			−0.216604	−	0.976259i	$-0.569498\pi$
$521$	−9.88817			−0.433208			−0.216604	+	0.976259i	$0.569498\pi$
$522$			11.7587i			0.514663i
$523$		−	44.1670i		−	1.93129i	−0.259870	−	0.965644i	$-0.583680\pi$
$523$		−	44.1670i		−	1.93129i	0.259870	−	0.965644i	$-0.416320\pi$
$524$	4.85131			0.211931
$525$	1.54919	+	4.44319i	0.0676123	+	0.193917i
$526$	6.14089			0.267755
$527$			2.17311i			0.0946623i
$528$		0			0
$529$	−47.5902			−2.06914
$530$	13.9357	−	19.6174i	0.605329	−	0.852127i
$531$	−21.5272			−0.934200
$532$		−	0.342546i		−	0.0148512i
$533$		−	14.1052i		−	0.610963i
$534$	1.11759			0.0483630
$535$	18.7022	+	13.2856i	0.808566	+	0.574385i
$536$	9.80105			0.423341
$537$			5.03166i			0.217132i
$538$			35.5447i			1.53244i
$539$		0			0
$540$	−1.85806	−	1.31992i	−0.0799581	−	0.0568002i
$541$	−21.2695			−0.914449			−0.457224	−	0.889351i	$-0.651156\pi$
$541$	−21.2695			−0.914449			−0.457224	+	0.889351i	$0.651156\pi$
$542$			19.8379i			0.852112i
$543$			0.945992i			0.0405964i
$544$	10.1550			0.435393
$545$	6.40050	−	9.01004i	0.274168	−	0.385948i
$546$	−3.20442			−0.137136
$547$			4.13393i			0.176754i	0.996087	+	0.0883771i	$0.0281681\pi$
$547$			4.13393i			0.176754i	−0.996087	+	0.0883771i	$0.971832\pi$
$548$		−	2.07420i		−	0.0886055i
$549$	40.6587			1.73527
$550$		0			0
$551$	−0.922455			−0.0392979
$552$		−	9.34839i		−	0.397894i
$553$			25.0911i			1.06698i
$554$	22.2166			0.943891
$555$	−0.246316	+	0.346741i	−0.0104555	+	0.0147183i
$556$	3.96243			0.168045
$557$			31.6671i			1.34178i	0.741557	+	0.670890i	$0.234088\pi$
$557$			31.6671i			1.34178i	−0.741557	+	0.670890i	$0.765912\pi$
$558$		−	1.99664i		−	0.0845247i
$559$	7.02122			0.296966
$560$	13.2808	+	9.43431i	0.561214	+	0.398673i
$561$		0			0
$562$		−	16.9242i		−	0.713904i
$563$			12.7467i			0.537210i	0.963250	+	0.268605i	$0.0865626\pi$
$563$			12.7467i			0.537210i	−0.963250	+	0.268605i	$0.913437\pi$
$564$	−0.855502			−0.0360231
$565$	18.0909	+	12.8513i	0.761090	+	0.540659i
$566$	25.3023			1.06354
$567$		−	20.2327i		−	0.849693i
$568$			25.6812i			1.07756i
$569$	−15.6352			−0.655461			−0.327730	−	0.944771i	$-0.606284\pi$
$569$	−15.6352			−0.655461			−0.327730	+	0.944771i	$0.606284\pi$
$570$	−0.161457	+	0.227284i	−0.00676268	+	0.00951987i
$571$	−3.61999			−0.151492			−0.0757460	−	0.997127i	$-0.524134\pi$
$571$	−3.61999			−0.151492			−0.0757460	+	0.997127i	$0.524134\pi$
$572$		0			0
$573$		−	0.807429i		−	0.0337308i
$574$	16.3099			0.680762
$575$	39.6670	−	13.8305i	1.65423	−	0.576774i
$576$	−25.4900			−1.06208
$577$		−	23.8352i		−	0.992273i	−0.868245	−	0.496136i	$-0.834752\pi$
$577$		−	23.8352i		−	0.992273i	0.868245	−	0.496136i	$-0.165248\pi$
$578$		−	2.67523i		−	0.111275i
$579$	3.81325			0.158473
$580$	−2.05377	+	2.89111i	−0.0852782	+	0.120047i
$581$	−8.52463			−0.353661
$582$			4.89641i			0.202963i
$583$		0			0
$584$	39.8478			1.64891
$585$	14.4236	+	10.2462i	0.596342	+	0.423627i
$586$	−27.6578			−1.14253
$587$		−	1.24698i		−	0.0514684i	−0.999669	−	0.0257342i	$-0.991808\pi$
$587$		−	1.24698i		−	0.0514684i	0.999669	−	0.0257342i	$-0.00819235\pi$
$588$		−	0.0546818i		−	0.00225504i
$589$	0.156634			0.00645401
$590$	16.8874	+	11.9964i	0.695245	+	0.493885i
$591$	−0.482883			−0.0198631
$592$			1.47248i			0.0605187i
$593$			18.5288i			0.760886i	0.924804	+	0.380443i	$0.124228\pi$
$593$			18.5288i			0.760886i	−0.924804	+	0.380443i	$0.875772\pi$
$594$		0			0
$595$	12.8948	−	18.1522i	0.528637	−	0.744166i
$596$	−4.04091			−0.165522
$597$		−	1.89388i		−	0.0775112i
$598$			28.6077i			1.16986i
$599$	−33.8359			−1.38250			−0.691248	−	0.722617i	$-0.742939\pi$
$599$	−33.8359			−1.38250			−0.691248	+	0.722617i	$0.742939\pi$
$600$	1.83161	+	5.25318i	0.0747750	+	0.214460i
$601$	−21.3026			−0.868951			−0.434475	−	0.900684i	$-0.643066\pi$
$601$	−21.3026			−0.868951			−0.434475	+	0.900684i	$0.643066\pi$
$602$			8.11868i			0.330893i
$603$			9.19378i			0.374400i
$604$	5.29869			0.215601
$605$		0			0
$606$	−6.21547			−0.252486
$607$		−	37.4601i		−	1.52046i	−0.649654	−	0.760230i	$-0.725086\pi$
$607$		−	37.4601i		−	1.52046i	0.649654	−	0.760230i	$-0.274914\pi$
$608$		−	0.731957i		−	0.0296848i
$609$	3.12736			0.126727
$610$	−31.8956	−	22.6578i	−1.29141	−	0.917387i
$611$	13.5889			0.549747
$612$			5.27062i			0.213052i
$613$		−	20.0047i		−	0.807983i	−0.914763	−	0.403991i	$-0.867623\pi$
$613$		−	20.0047i		−	0.807983i	0.914763	−	0.403991i	$-0.132377\pi$
$614$	−25.0555			−1.01116
$615$	3.39180	+	2.40945i	0.136771	+	0.0971584i
$616$		0			0
$617$		−	34.7932i		−	1.40072i	−0.713790	−	0.700360i	$-0.753023\pi$
$617$		−	34.7932i		−	1.40072i	0.713790	−	0.700360i	$-0.246977\pi$
$618$			6.01410i			0.241922i
$619$	46.0840			1.85227			0.926136	−	0.377189i	$-0.123109\pi$
$619$	46.0840			1.85227			0.926136	+	0.377189i	$0.123109\pi$
$620$	0.348734	−	0.490915i	0.0140055	−	0.0197156i
$621$	17.9435			0.720047
$622$			10.8083i			0.433374i
$623$			6.43351i			0.257753i
$624$	−2.82991			−0.113287
$625$	−19.5804	+	15.5437i	−0.783217	+	0.621748i
$626$	−2.13633			−0.0853849
$627$		0			0
$628$			6.57008i			0.262175i
$629$	2.01259			0.0802473
$630$	−11.8477	+	16.6781i	−0.472024	+	0.664471i
$631$	−20.5380			−0.817604			−0.408802	−	0.912623i	$-0.634053\pi$
$631$	−20.5380			−0.817604			−0.408802	+	0.912623i	$0.634053\pi$
$632$			29.6651i			1.18002i
$633$		−	6.88529i		−	0.273666i
$634$	21.5658			0.856486
$635$	20.2997	+	14.4204i	0.805568	+	0.572255i
$636$	1.51494			0.0600712
$637$			0.868571i			0.0344140i
$638$		0			0
$639$	−24.0900			−0.952985
$640$	10.3827	+	7.37560i	0.410412	+	0.291546i
$641$	15.9095			0.628389			0.314194	−	0.949359i	$-0.398266\pi$
$641$	15.9095			0.628389			0.314194	+	0.949359i	$0.398266\pi$
$642$		−	4.60803i		−	0.181865i
$643$			42.3039i			1.66830i	0.551536	+	0.834151i	$0.314042\pi$
$643$			42.3039i			1.66830i	−0.551536	+	0.834151i	$0.685958\pi$
$644$	10.3678			0.408547
$645$	−1.19937	+	1.68836i	−0.0472250	+	0.0664790i
$646$	1.31923			0.0519042
$647$			7.48891i			0.294419i	0.989105	+	0.147210i	$0.0470292\pi$
$647$			7.48891i			0.294419i	−0.989105	+	0.147210i	$0.952971\pi$
$648$		−	23.9210i		−	0.939707i
$649$		0			0
$650$	−5.60503	−	16.0756i	−0.219847	−	0.630538i
$651$	−0.531031			−0.0208127
$652$		−	4.26715i		−	0.167114i
$653$			16.4702i			0.644531i	0.946649	+	0.322265i	$0.104444\pi$
$653$			16.4702i			0.644531i	−0.946649	+	0.322265i	$0.895556\pi$
$654$	−2.21999			−0.0868083
$655$	13.1632	−	18.5299i	0.514329	−	0.724025i
$656$	14.4037			0.562372
$657$			37.3788i			1.45829i
$658$			15.7129i			0.612553i
$659$	−23.7359			−0.924619			−0.462310	−	0.886719i	$-0.652979\pi$
$659$	−23.7359			−0.924619			−0.462310	+	0.886719i	$0.652979\pi$
$660$		0			0
$661$	13.4183			0.521911			0.260956	−	0.965351i	$-0.415962\pi$
$661$	13.4183			0.521911			0.260956	+	0.965351i	$0.415962\pi$
$662$		−	15.5721i		−	0.605229i
$663$			3.86793i			0.150218i
$664$	−10.0786			−0.391127
$665$	−1.30838	−	0.929439i	−0.0507367	−	0.0360421i
$666$	−1.84916			−0.0716534
$667$		−	27.9198i		−	1.08106i
$668$		−	8.07436i		−	0.312407i
$669$	−7.96112			−0.307795
$670$	5.12340	−	7.21225i	0.197934	−	0.278634i
$671$		0			0
$672$			2.48152i			0.0957268i
$673$			48.2870i			1.86133i	0.365875	+	0.930664i	$0.380770\pi$
$673$			48.2870i			1.86133i	−0.365875	+	0.930664i	$0.619230\pi$
$674$	−14.6350			−0.563718
$675$	−10.0830	+	3.51562i	−0.388097	+	0.135316i
$676$	2.57067			0.0988718
$677$		−	24.3637i		−	0.936374i	−0.883629	−	0.468187i	$-0.844907\pi$
$677$		−	24.3637i		−	0.936374i	0.883629	−	0.468187i	$-0.155093\pi$
$678$		−	4.45742i		−	0.171186i
$679$	−28.1866			−1.08170
$680$	15.2455	−	21.4612i	0.584639	−	0.823001i
$681$	−0.887625			−0.0340139
$682$		0			0
$683$			38.9856i			1.49174i	0.666090	+	0.745871i	$0.267966\pi$
$683$			38.9856i			1.49174i	−0.666090	+	0.745871i	$0.732034\pi$
$684$	0.379898			0.0145257
$685$	−7.92257	−	5.62799i	−0.302706	−	0.215034i
$686$	−23.3384			−0.891066
$687$			2.65750i			0.101390i
$688$			7.16984i			0.273348i
$689$	−24.0634			−0.916743
$690$	−6.87915	−	4.88678i	−0.261885	−	0.186036i
$691$	5.91854			0.225152			0.112576	−	0.993643i	$-0.464090\pi$
$691$	5.91854			0.225152			0.112576	+	0.993643i	$0.464090\pi$
$692$		−	1.61309i		−	0.0613205i
$693$		0			0
$694$	−27.5230			−1.04476
$695$	10.7514	−	15.1348i	0.407823	−	0.574096i
$696$	3.69747			0.140152
$697$		−	19.6871i		−	0.745701i
$698$			19.7042i			0.745817i
$699$	−1.62275			−0.0613779
$700$	−5.82599	+	2.03133i	−0.220202	+	0.0767770i
$701$	11.9672			0.451996			0.225998	−	0.974128i	$-0.427436\pi$
$701$	11.9672			0.451996			0.225998	+	0.974128i	$0.427436\pi$
$702$		−	7.27186i		−	0.274459i
$703$		−	0.145064i		−	0.00547120i
$704$		0			0
$705$	−2.32126	+	3.26765i	−0.0874236	+	0.123067i
$706$	−29.7894			−1.12114
$707$		−	35.7799i		−	1.34564i
$708$			1.30412i			0.0490117i
$709$	−6.80850			−0.255699			−0.127849	−	0.991794i	$-0.540807\pi$
$709$	−6.80850			−0.255699			−0.127849	+	0.991794i	$0.540807\pi$
$710$	18.8979	+	13.4246i	0.709225	+	0.503816i
$711$	−27.8271			−1.04360
$712$			7.60633i			0.285059i
$713$			4.74082i			0.177545i
$714$	−4.47251			−0.167380
$715$		0			0
$716$	−6.59761			−0.246564
$717$			8.79917i			0.328611i
$718$			25.1468i			0.938469i
$719$	9.26411			0.345493			0.172746	−	0.984966i	$-0.444736\pi$
$719$	9.26411			0.345493			0.172746	+	0.984966i	$0.444736\pi$
$720$	−10.4631	+	14.7289i	−0.389935	+	0.548915i
$721$	−34.6206			−1.28934
$722$			23.3508i			0.869026i
$723$			4.38210i			0.162972i
$724$	−1.24040			−0.0460992
$725$	5.47025	+	15.6891i	0.203160	+	0.582677i
$726$		0			0
$727$		−	19.4121i		−	0.719956i	−0.932961	−	0.359978i	$-0.882784\pi$
$727$		−	19.4121i		−	0.719956i	0.932961	−	0.359978i	$-0.117216\pi$
$728$		−	21.8092i		−	0.808304i
$729$	20.1069			0.744699
$730$	20.8300	−	29.3226i	0.770954	−	1.08528i
$731$	9.79975			0.362457
$732$		−	2.46310i		−	0.0910390i
$733$			11.5620i			0.427054i	0.976937	+	0.213527i	$0.0684951\pi$
$733$			11.5620i			0.427054i	−0.976937	+	0.213527i	$0.931505\pi$
$734$	−6.66887			−0.246153
$735$	−0.208861	−	0.148370i	−0.00770396	−	0.00547270i
$736$	22.1540			0.816608
$737$		0			0
$738$			18.0884i			0.665842i
$739$	−9.10736			−0.335020			−0.167510	−	0.985870i	$-0.553573\pi$
$739$	−9.10736			−0.335020			−0.167510	+	0.985870i	$0.553573\pi$
$740$	−0.454653	−	0.322974i	−0.0167134	−	0.0118728i
$741$	0.278794			0.0102418
$742$		−	27.8247i		−	1.02148i
$743$			0.0731008i			0.00268181i	0.999999	+	0.00134090i	$0.000426823\pi$
$743$			0.0731008i			0.00268181i	−0.999999	+	0.00134090i	$0.999573\pi$
$744$	−0.627836			−0.0230176
$745$	−10.9643	+	15.4346i	−0.401702	+	0.565479i
$746$	−21.0991			−0.772492
$747$		−	9.45417i		−	0.345910i
$748$		0			0
$749$	26.5265			0.969258
$750$	4.82308	+	1.39823i	0.176114	+	0.0510561i
$751$	−38.5239			−1.40576			−0.702878	−	0.711310i	$-0.748102\pi$
$751$	−38.5239			−1.40576			−0.702878	+	0.711310i	$0.748102\pi$
$752$			13.8765i			0.506025i
$753$			0.195236i			0.00711479i
$754$	−11.3149			−0.412064
$755$	14.3771	−	20.2387i	0.523235	−	0.736562i
$756$	−2.63541			−0.0958488
$757$		−	28.1617i		−	1.02355i	−0.859118	−	0.511777i	$-0.828987\pi$
$757$		−	28.1617i		−	1.02355i	0.859118	−	0.511777i	$-0.171013\pi$
$758$		−	10.6024i		−	0.385097i
$759$		0			0
$760$	−1.54689	−	1.09887i	−0.0561116	−	0.0398603i
$761$	−29.4894			−1.06899			−0.534496	−	0.845171i	$-0.679498\pi$
$761$	−29.4894			−1.06899			−0.534496	+	0.845171i	$0.679498\pi$
$762$		−	5.00164i		−	0.181190i
$763$		−	12.7795i		−	0.462650i
$764$	1.05871			0.0383030
$765$	20.1315	+	14.3009i	0.727856	+	0.517051i
$766$	−11.9322			−0.431128
$767$		−	20.7147i		−	0.747965i
$768$			3.91285i			0.141193i
$769$	−8.42410			−0.303781			−0.151890	−	0.988397i	$-0.548536\pi$
$769$	−8.42410			−0.303781			−0.151890	+	0.988397i	$0.548536\pi$
$770$		0			0
$771$	8.63364			0.310933
$772$			5.00000i			0.179954i
$773$			0.897483i			0.0322802i	0.999870	+	0.0161401i	$0.00513778\pi$
$773$			0.897483i			0.0322802i	−0.999870	+	0.0161401i	$0.994862\pi$
$774$	−9.00396			−0.323641
$775$	−0.928857	−	2.66403i	−0.0333655	−	0.0956947i
$776$	−33.3249			−1.19629
$777$			0.491805i			0.0176434i
$778$		−	33.7736i		−	1.21084i
$779$	−1.41901			−0.0508413
$780$	0.620713	−	0.873782i	0.0222251	−	0.0312864i
$781$		0			0
$782$			39.9287i			1.42785i
$783$			7.09699i			0.253626i
$784$	−0.886957			−0.0316770
$785$	25.0949	+	17.8268i	0.895675	+	0.636265i
$786$	−4.56559			−0.162849
$787$			37.8007i			1.34745i	0.738983	+	0.673724i	$0.235306\pi$
$787$			37.8007i			1.34745i	−0.738983	+	0.673724i	$0.764694\pi$
$788$		−	0.633165i		−	0.0225556i
$789$	1.81133			0.0644852
$790$	21.8295	+	15.5072i	0.776660	+	0.551720i
$791$	25.6595			0.912346
$792$		0			0
$793$			39.1242i			1.38934i
$794$	13.1442			0.466470
$795$	4.11052	−	5.78641i	0.145785	−	0.205223i
$796$	2.48329			0.0880177
$797$		−	15.1906i		−	0.538078i	−0.963129	−	0.269039i	$-0.913294\pi$
$797$		−	15.1906i		−	0.538078i	0.963129	−	0.269039i	$-0.0867061\pi$
$798$			0.322371i			0.0114118i
$799$	18.9665			0.670985
$800$	−12.4491	+	4.34058i	−0.440142	+	0.153463i
$801$	−7.13504			−0.252104
$802$		−	16.9237i		−	0.597598i
$803$		0			0
$804$	0.556959			0.0196424
$805$	28.1311	−	39.6004i	0.991492	−	1.39573i
$806$	1.92129			0.0676745
$807$			10.4844i			0.369067i
$808$		−	42.3024i		−	1.48819i
$809$	39.7109			1.39616			0.698080	−	0.716020i	$-0.254038\pi$
$809$	39.7109			1.39616			0.698080	+	0.716020i	$0.254038\pi$
$810$	−17.6027	−	12.5045i	−0.618494	−	0.439363i
$811$	8.81679			0.309599			0.154800	−	0.987946i	$-0.450527\pi$
$811$	8.81679			0.309599			0.154800	+	0.987946i	$0.450527\pi$
$812$			4.10065i			0.143905i
$813$			5.85145i			0.205219i
$814$		0			0
$815$	−16.2987	−	11.5782i	−0.570918	−	0.405566i
$816$	−3.94981			−0.138271
$817$		−	0.706350i		−	0.0247121i
$818$		−	27.5283i		−	0.962506i
$819$	20.4579			0.714858
$820$	−3.15931	+	4.44739i	−0.110328	+	0.155310i
$821$	−8.42070			−0.293884			−0.146942	−	0.989145i	$-0.546943\pi$
$821$	−8.42070			−0.293884			−0.146942	+	0.989145i	$0.546943\pi$
$822$			1.95204i			0.0680853i
$823$			23.9040i			0.833241i	0.909080	+	0.416621i	$0.136786\pi$
$823$			23.9040i			0.833241i	−0.909080	+	0.416621i	$0.863214\pi$
$824$	−40.9319			−1.42593
$825$		0			0
$826$	23.9526			0.833416
$827$			47.5118i			1.65215i	0.563561	+	0.826074i	$0.309431\pi$
$827$			47.5118i			1.65215i	−0.563561	+	0.826074i	$0.690569\pi$
$828$			11.4983i			0.399593i
$829$	28.2003			0.979437			0.489718	−	0.871881i	$-0.337100\pi$
$829$	28.2003			0.979437			0.489718	+	0.871881i	$0.337100\pi$
$830$	−5.26851	+	7.41652i	−0.182873	+	0.257431i
$831$	6.55306			0.227323
$832$		−	24.5280i		−	0.850354i
$833$			1.21229i			0.0420035i
$834$	−3.72907			−0.129127
$835$	−30.8406	−	21.9084i	−1.06728	−	0.758171i
$836$		0			0
$837$		−	1.20508i		−	0.0416537i
$838$		−	0.630232i		−	0.0217710i
$839$	−22.3406			−0.771284			−0.385642	−	0.922648i	$-0.626020\pi$
$839$	−22.3406			−0.771284			−0.385642	+	0.922648i	$0.626020\pi$
$840$	5.24436	+	3.72546i	0.180948	+	0.128541i
$841$	−17.9572			−0.619214
$842$		−	16.3072i		−	0.561983i
$843$		−	4.99201i		−	0.171934i
$844$	9.02811			0.310760
$845$	6.97506	−	9.81884i	0.239949	−	0.337778i
$846$	−17.4263			−0.599128
$847$		0			0
$848$		−	24.5728i		−	0.843833i
$849$	7.46325			0.256138
$850$	−7.82314	−	22.4373i	−0.268331	−	0.769593i
$851$	4.39063			0.150509
$852$			1.45937i			0.0499973i
$853$		−	8.15265i		−	0.279141i	−0.990212	−	0.139571i	$-0.955428\pi$
$853$		−	8.15265i		−	0.279141i	0.990212	−	0.139571i	$-0.0445723\pi$
$854$	−45.2395			−1.54807
$855$	1.03079	−	1.45105i	0.0352522	−	0.0496247i
$856$	31.3622			1.07194
$857$		−	4.42433i		−	0.151132i	−0.997141	−	0.0755662i	$-0.975924\pi$
$857$		−	4.42433i		−	0.151132i	0.997141	−	0.0755662i	$-0.0240764\pi$
$858$		0			0
$859$	−2.90501			−0.0991176			−0.0495588	−	0.998771i	$-0.515782\pi$
$859$	−2.90501			−0.0991176			−0.0495588	+	0.998771i	$0.515782\pi$
$860$	−2.21381	−	1.57263i	−0.0754901	−	0.0536263i
$861$	4.81081			0.163952
$862$			36.2873i			1.23595i
$863$		−	17.7101i		−	0.602858i	−0.953489	−	0.301429i	$-0.902536\pi$
$863$		−	17.7101i		−	0.602858i	0.953489	−	0.301429i	$-0.0974636\pi$
$864$	−5.63138			−0.191583
$865$	−6.16131	−	4.37684i	−0.209491	−	0.148817i
$866$	12.6071			0.428408
$867$		−	0.789095i		−	0.0267991i
$868$		−	0.696297i		−	0.0236339i
$869$		0			0
$870$	1.93281	−	2.72084i	0.0655285	−	0.0922450i
$871$	−8.84680			−0.299762
$872$		−	15.1092i		−	0.511662i
$873$		−	31.2601i		−	1.05799i
$874$	2.87800			0.0973497
$875$	−8.04902	+	27.7645i	−0.272107	+	0.938610i
$876$	2.26441			0.0765073
$877$		−	51.3798i		−	1.73497i	−0.497461	−	0.867487i	$-0.665734\pi$
$877$		−	51.3798i		−	1.73497i	0.497461	−	0.867487i	$-0.334266\pi$
$878$		−	1.89179i		−	0.0638448i
$879$	−8.15803			−0.275164
$880$		0			0
$881$	33.6727			1.13446			0.567231	−	0.823559i	$-0.308015\pi$
$881$	33.6727			1.13446			0.567231	+	0.823559i	$0.308015\pi$
$882$		−	1.11385i		−	0.0375052i
$883$		−	13.9106i		−	0.468128i	−0.972221	−	0.234064i	$-0.924797\pi$
$883$		−	13.9106i		−	0.468128i	0.972221	−	0.234064i	$-0.0752026\pi$
$884$	−5.07170			−0.170580
$885$	4.98117	+	3.53850i	0.167440	+	0.118945i
$886$	−4.18638			−0.140644
$887$		−	44.7006i		−	1.50090i	−0.660927	−	0.750450i	$-0.729837\pi$
$887$		−	44.7006i		−	1.50090i	0.660927	−	0.750450i	$-0.270163\pi$
$888$			0.581460i			0.0195125i
$889$	28.7923			0.965664
$890$	5.59723	+	3.97613i	0.187620	+	0.133280i
$891$		0			0
$892$		−	10.4388i		−	0.349516i
$893$		−	1.36707i		−	0.0457473i
$894$	3.80292			0.127189
$895$	−17.9015	+	25.2000i	−0.598380	+	0.842344i
$896$	14.7264			0.491976
$897$			8.43821i			0.281744i
$898$		−	39.9198i		−	1.33214i
$899$	−1.87509			−0.0625376
$900$	−2.25283	−	6.46127i	−0.0750943	−	0.215376i
$901$	−33.5861			−1.11892
$902$		0			0
$903$			2.39471i			0.0796909i
$904$	30.3371			1.00900
$905$	−3.36562	+	4.73781i	−0.111877	+	0.157490i
$906$	−4.98662			−0.165669
$907$		−	22.7980i		−	0.756994i	−0.925602	−	0.378497i	$-0.876441\pi$
$907$		−	22.7980i		−	0.756994i	0.925602	−	0.378497i	$-0.123559\pi$
$908$		−	1.16387i		−	0.0386244i
$909$	39.6814			1.31615
$910$	−16.0486	−	11.4006i	−0.532007	−	0.377925i
$911$	37.5625			1.24450			0.622250	−	0.782819i	$-0.286219\pi$
$911$	37.5625			1.24450			0.622250	+	0.782819i	$0.286219\pi$
$912$			0.284696i			0.00942722i
$913$		0			0
$914$	15.0214			0.496863
$915$	−9.40801	−	6.68321i	−0.311019	−	0.220940i
$916$	−3.48456			−0.115133
$917$		−	26.2822i		−	0.867915i
$918$		−	10.1496i		−	0.334986i
$919$	−39.7124			−1.30999			−0.654996	−	0.755632i	$-0.727330\pi$
$919$	−39.7124			−1.30999			−0.654996	+	0.755632i	$0.727330\pi$
$920$	33.2594	−	46.8195i	1.09653	−	1.54359i
$921$	−7.39044			−0.243523
$922$			20.4472i			0.673392i
$923$		−	23.1808i		−	0.763005i
$924$		0			0
$925$	−2.46724	+	0.860246i	−0.0811225	+	0.0282847i
$926$	−18.0536			−0.593278
$927$		−	38.3958i		−	1.26108i
$928$			8.76234i			0.287638i
$929$	−20.7298			−0.680123			−0.340061	−	0.940403i	$-0.610448\pi$
$929$	−20.7298			−0.680123			−0.340061	+	0.940403i	$0.610448\pi$
$930$	−0.328195	+	0.462003i	−0.0107619	+	0.0151497i
$931$	0.0873802			0.00286377
$932$		−	2.12777i		−	0.0696975i
$933$			3.18805i			0.104372i
$934$	37.6187			1.23092
$935$		0			0
$936$	24.1874			0.790588
$937$		−	55.8506i		−	1.82456i	−0.409568	−	0.912280i	$-0.634320\pi$
$937$		−	55.8506i		−	1.82456i	0.409568	−	0.912280i	$-0.365680\pi$
$938$		−	10.2296i		−	0.334009i
$939$	−0.630138			−0.0205638
$940$	−4.28460	−	3.04367i	−0.139748	−	0.0992737i
$941$	−13.3644			−0.435667			−0.217834	−	0.975986i	$-0.569899\pi$
$941$	−13.3644			−0.435667			−0.217834	+	0.975986i	$0.569899\pi$
$942$		−	6.18313i		−	0.201457i
$943$		−	42.9489i		−	1.39861i
$944$	21.1532			0.688479
$945$	−7.15072	+	10.0661i	−0.232613	+	0.327451i
$946$		0			0
$947$			42.2245i			1.37211i	0.727550	+	0.686055i	$0.240659\pi$
$947$			42.2245i			1.37211i	−0.727550	+	0.686055i	$0.759341\pi$
$948$			1.68577i			0.0547511i
$949$	−35.9681			−1.16757
$950$	−1.61724	+	0.563879i	−0.0524703	+	0.0182946i
$951$	6.36110			0.206273
$952$		−	30.4399i		−	0.986562i
$953$			14.7188i			0.476790i	0.971168	+	0.238395i	$0.0766213\pi$
$953$			14.7188i			0.476790i	−0.971168	+	0.238395i	$0.923379\pi$
$954$	30.8587			0.999089
$955$	2.87264	−	4.04384i	0.0929565	−	0.130856i
$956$	−11.5376			−0.373154
$957$		0			0
$958$			17.2750i			0.558131i
$959$	−11.2371			−0.362865
$960$	5.89812	+	4.18988i	0.190361	+	0.135228i
$961$	−30.6816			−0.989729
$962$		−	1.77937i		−	0.0573691i
$963$			29.4190i			0.948015i
$964$	−5.74589			−0.185063
$965$	19.0979	+	13.5666i	0.614782	+	0.436725i
$966$	−9.75715			−0.313931
$967$			32.2786i			1.03801i	0.854771	+	0.519005i	$0.173697\pi$
$967$			32.2786i			1.03801i	−0.854771	+	0.519005i	$0.826303\pi$
$968$		0			0
$969$	0.389123			0.0125004
$970$	−17.4203	+	24.5226i	−0.559331	+	0.787374i
$971$	−42.8008			−1.37354			−0.686771	−	0.726874i	$-0.740973\pi$
$971$	−42.8008			−1.37354			−0.686771	+	0.726874i	$0.740973\pi$
$972$		−	4.41716i		−	0.141681i
$973$		−	21.4667i		−	0.688190i
$974$	42.1175			1.34953
$975$	−1.65328	−	4.74171i	−0.0529472	−	0.151856i
$976$	−39.9524			−1.27884
$977$		−	12.1972i		−	0.390222i	−0.980781	−	0.195111i	$-0.937493\pi$
$977$		−	12.1972i		−	0.390222i	0.980781	−	0.195111i	$-0.0625067\pi$
$978$			4.01584i			0.128412i
$979$		0			0
$980$	0.194545	−	0.273862i	0.00621451	−	0.00874821i
$981$	14.1730			0.452510
$982$			3.94176i			0.125787i
$983$			14.0671i			0.448670i	0.974512	+	0.224335i	$0.0720211\pi$
$983$			14.0671i			0.448670i	−0.974512	+	0.224335i	$0.927979\pi$
$984$	5.68781			0.181321
$985$	−2.41842	−	1.71798i	−0.0770572	−	0.0547395i
$986$	−15.7926			−0.502938
$987$			4.63472i			0.147525i
$988$			0.365560i			0.0116300i
$989$	21.3790			0.679811
$990$		0			0
$991$	−22.9455			−0.728887			−0.364444	−	0.931225i	$-0.618741\pi$
$991$	−22.9455			−0.728887			−0.364444	+	0.931225i	$0.618741\pi$
$992$		−	1.48786i		−	0.0472396i
$993$		−	4.59321i		−	0.145761i
$994$	26.8041			0.850175
$995$	6.73797	−	9.48509i	0.213608	−	0.300698i
$996$	−0.572734			−0.0181478
$997$		−	3.63447i		−	0.115105i	−0.998342	−	0.0575525i	$-0.981670\pi$
$997$		−	3.63447i		−	0.115105i	0.998342	−	0.0575525i	$-0.0183297\pi$
$998$			8.05612i			0.255012i
$999$	−1.11607			−0.0353108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.b.g.364.3		8
5.2	odd	4		3025.2.a.bl.1.6		8
5.3	odd	4		3025.2.a.bl.1.3		8
5.4	even	2	inner	605.2.b.g.364.6		8
11.2	odd	10		605.2.j.d.444.3		16
11.3	even	5		605.2.j.h.9.2		16
11.4	even	5		605.2.j.h.269.3		16
11.5	even	5		55.2.j.a.14.3	yes	16
11.6	odd	10		605.2.j.d.124.2		16
11.7	odd	10		605.2.j.g.269.2		16
11.8	odd	10		605.2.j.g.9.3		16
11.9	even	5		55.2.j.a.4.2	✓	16
11.10	odd	2		605.2.b.f.364.6		8
33.5	odd	10		495.2.ba.a.289.2		16
33.20	odd	10		495.2.ba.a.334.3		16
44.27	odd	10		880.2.cd.c.289.2		16
44.31	odd	10		880.2.cd.c.609.3		16
55.4	even	10		605.2.j.h.269.2		16
55.9	even	10		55.2.j.a.4.3	yes	16
55.14	even	10		605.2.j.h.9.3		16
55.19	odd	10		605.2.j.g.9.2		16
55.24	odd	10		605.2.j.d.444.2		16
55.27	odd	20		275.2.h.d.201.2		16
55.29	odd	10		605.2.j.g.269.3		16
55.32	even	4		3025.2.a.bk.1.3		8
55.38	odd	20		275.2.h.d.201.3		16
55.39	odd	10		605.2.j.d.124.3		16
55.42	odd	20		275.2.h.d.26.2		16
55.43	even	4		3025.2.a.bk.1.6		8
55.49	even	10		55.2.j.a.14.2	yes	16
55.53	odd	20		275.2.h.d.26.3		16
55.54	odd	2		605.2.b.f.364.3		8
165.104	odd	10		495.2.ba.a.289.3		16
165.119	odd	10		495.2.ba.a.334.2		16
220.119	odd	10		880.2.cd.c.609.2		16
220.159	odd	10		880.2.cd.c.289.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.2	✓	16	11.9	even	5
55.2.j.a.4.3	yes	16	55.9	even	10
55.2.j.a.14.2	yes	16	55.49	even	10
55.2.j.a.14.3	yes	16	11.5	even	5
275.2.h.d.26.2		16	55.42	odd	20
275.2.h.d.26.3		16	55.53	odd	20
275.2.h.d.201.2		16	55.27	odd	20
275.2.h.d.201.3		16	55.38	odd	20
495.2.ba.a.289.2		16	33.5	odd	10
495.2.ba.a.289.3		16	165.104	odd	10
495.2.ba.a.334.2		16	165.119	odd	10
495.2.ba.a.334.3		16	33.20	odd	10
605.2.b.f.364.3		8	55.54	odd	2
605.2.b.f.364.6		8	11.10	odd	2
605.2.b.g.364.3		8	1.1	even	1	trivial
605.2.b.g.364.6		8	5.4	even	2	inner
605.2.j.d.124.2		16	11.6	odd	10
605.2.j.d.124.3		16	55.39	odd	10
605.2.j.d.444.2		16	55.24	odd	10
605.2.j.d.444.3		16	11.2	odd	10
605.2.j.g.9.2		16	55.19	odd	10
605.2.j.g.9.3		16	11.8	odd	10
605.2.j.g.269.2		16	11.7	odd	10
605.2.j.g.269.3		16	55.29	odd	10
605.2.j.h.9.2		16	11.3	even	5
605.2.j.h.9.3		16	55.14	even	10
605.2.j.h.269.2		16	55.4	even	10
605.2.j.h.269.3		16	11.4	even	5
880.2.cd.c.289.2		16	44.27	odd	10
880.2.cd.c.289.3		16	220.159	odd	10
880.2.cd.c.609.2		16	220.119	odd	10
880.2.cd.c.609.3		16	44.31	odd	10
3025.2.a.bk.1.3		8	55.32	even	4
3025.2.a.bk.1.6		8	55.43	even	4
3025.2.a.bl.1.3		8	5.3	odd	4
3025.2.a.bl.1.6		8	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.23399i q^{2} -0.363982i q^{3} +0.477260 q^{4} +(1.29496 - 1.82293i) q^{5} -0.449152 q^{6} -2.58558i q^{7} -3.05692i q^{8} +2.86752 q^{9} +(-2.24948 - 1.59798i) q^{10} -0.173714i q^{12} +2.75929i q^{13} -3.19059 q^{14} +(-0.663514 - 0.471344i) q^{15} -2.81770 q^{16} +3.85124i q^{17} -3.53850i q^{18} +0.277591 q^{19} +(0.618034 - 0.870011i) q^{20} -0.941105 q^{21} +8.40180i q^{23} -1.11267 q^{24} +(-1.64614 - 4.72125i) q^{25} +3.40495 q^{26} -2.13567i q^{27} -1.23399i q^{28} -3.32307 q^{29} +(-0.581635 + 0.818772i) q^{30} +0.564263 q^{31} -2.63682i q^{32} +4.75241 q^{34} +(-4.71333 - 3.34823i) q^{35} +1.36855 q^{36} -0.522583i q^{37} -0.342546i q^{38} +1.00433 q^{39} +(-5.57255 - 3.95860i) q^{40} -5.11188 q^{41} +1.16132i q^{42} -2.54457i q^{43} +(3.71333 - 5.22728i) q^{45} +10.3678 q^{46} -4.92477i q^{47} +1.02559i q^{48} +0.314780 q^{49} +(-5.82599 + 2.03133i) q^{50} +1.40178 q^{51} +1.31690i q^{52} +8.72086i q^{53} -2.63541 q^{54} -7.90392 q^{56} -0.101038i q^{57} +4.10065i q^{58} -7.50726 q^{59} +(-0.316669 - 0.224953i) q^{60} +14.1791 q^{61} -0.696297i q^{62} -7.41419i q^{63} -8.88922 q^{64} +(5.03000 + 3.57318i) q^{65} +3.20618i q^{67} +1.83804i q^{68} +3.05810 q^{69} +(-4.13169 + 5.81622i) q^{70} -8.40099 q^{71} -8.76578i q^{72} +13.0353i q^{73} -0.644864 q^{74} +(-1.71845 + 0.599167i) q^{75} +0.132483 q^{76} -1.23934i q^{78} -9.70425 q^{79} +(-3.64882 + 5.13647i) q^{80} +7.82520 q^{81} +6.30802i q^{82} -3.29699i q^{83} -0.449152 q^{84} +(7.02054 + 4.98721i) q^{85} -3.13998 q^{86} +1.20954i q^{87} -2.48823 q^{89} +(-6.45043 - 4.58222i) q^{90} +7.13437 q^{91} +4.00984i q^{92} -0.205382i q^{93} -6.07713 q^{94} +(0.359470 - 0.506029i) q^{95} -0.959755 q^{96} -10.9014i q^{97} -0.388437i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{5} + 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 2 q^{24} - 8 q^{25} + 10 q^{26} - 24 q^{29} - 22 q^{30} + 14 q^{31} - 8 q^{34} - 14 q^{35}+ \cdots - 8 q^{96}+O(q^{100}) \) 8 * q - 2 * q^4 + 4 * q^5 + 6 * q^6 - 4 * q^9 + 4 * q^14 - 8 * q^15 - 22 * q^16 - 12 * q^19 - 4 * q^20 + 4 * q^21 - 2 * q^24 - 8 * q^25 + 10 * q^26 - 24 * q^29 - 22 * q^30 + 14 * q^31 - 8 * q^34 - 14 * q^35 + 20 * q^36 - 30 * q^39 - 24 * q^40 + 34 * q^41 + 6 * q^45 + 24 * q^46 + 30 * q^49 - 16 * q^50 + 54 * q^51 - 20 * q^54 - 10 * q^56 + 6 * q^59 + 34 * q^60 + 20 * q^61 - 14 * q^64 - 20 * q^65 - 32 * q^69 + 8 * q^70 - 42 * q^71 + 4 * q^74 - 20 * q^75 + 28 * q^76 - 16 * q^79 - 28 * q^80 - 36 * q^81 + 6 * q^84 + 4 * q^85 + 46 * q^86 + 12 * q^89 - 46 * q^90 + 20 * q^91 + 42 * q^94 - 26 * q^95 - 8 * q^96

Introduction

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