LMFDB - Embedded newform 360.2.q.d.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(121,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("360.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.q (of order $3$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			241.1
Root			$1.71903 - 0.211943i$ of defining polynomial
Character	$\chi$	$=$	360.241
Dual form			360.2.q.d.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71903 + 0.211943i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.719035 + 1.24540i) q^{7} +(2.91016 - 0.728674i) q^{9} +O(q^{10})$	\(q+(-1.71903 + 0.211943i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.719035 + 1.24540i) q^{7} +(2.91016 - 0.728674i) q^{9} +(0.675970 - 1.17081i) q^{11} +(2.76210 + 4.78410i) q^{13} +(1.04307 + 1.38276i) q^{15} +4.82032 q^{17} -0.648061 q^{19} +(0.972091 - 2.29329i) q^{21} +(4.45323 + 7.71321i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.84823 + 1.86940i) q^{27} +(3.58613 - 6.21136i) q^{29} +(2.32403 + 4.02534i) q^{31} +(-0.913870 + 2.15594i) q^{33} +1.43807 q^{35} +1.35194 q^{37} +(-5.76210 - 7.63862i) q^{39} +(-0.175970 - 0.304788i) q^{41} +(-2.41016 + 4.17452i) q^{43} +(-2.08613 - 2.15594i) q^{45} +(4.74694 - 8.22195i) q^{47} +(2.46598 + 4.27120i) q^{49} +(-8.28630 + 1.02163i) q^{51} -8.17226 q^{53} -1.35194 q^{55} +(1.11404 - 0.137352i) q^{57} +(-0.734191 - 1.27166i) q^{59} +(-3.34823 + 5.79930i) q^{61} +(-1.18501 + 4.14827i) q^{63} +(2.76210 - 4.78410i) q^{65} +(-6.21533 - 10.7653i) q^{67} +(-9.29001 - 12.3155i) q^{69} +2.22808 q^{71} -4.34452 q^{73} +(0.675970 - 1.59470i) q^{75} +(0.972091 + 1.68371i) q^{77} +(6.52420 - 11.3002i) q^{79} +(7.93807 - 4.24111i) q^{81} +(2.63290 - 4.56032i) q^{83} +(-2.41016 - 4.17452i) q^{85} +(-4.84823 + 11.4376i) q^{87} -11.0000 q^{89} -7.94418 q^{91} +(-4.84823 - 6.42714i) q^{93} +(0.324030 + 0.561237i) q^{95} +(-8.79001 + 15.2247i) q^{97} +(1.11404 - 3.89982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9}+O(q^{10}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9} + 2 q^{11} - q^{15} + 4 q^{17} - 8 q^{19} + 12 q^{21} + 7 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 16 q^{31} - 20 q^{33} - 10 q^{35} + 4 q^{37} - 18 q^{39} + q^{41} - 2 q^{43} + 2 q^{45} + 13 q^{47} - 10 q^{49} - 20 q^{53} - 4 q^{55} - 14 q^{57} + 6 q^{59} + 11 q^{61} + 27 q^{63} - q^{67} - 33 q^{69} - 28 q^{71} + 32 q^{73} + 2 q^{75} + 12 q^{77} + 6 q^{79} + 29 q^{81} + 21 q^{83} - 2 q^{85} + 2 q^{87} - 66 q^{89} - 60 q^{91} + 2 q^{93} + 4 q^{95} - 30 q^{97} - 14 q^{99}+O(q^{100}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9 + 2 * q^11 - q^15 + 4 * q^17 - 8 * q^19 + 12 * q^21 + 7 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 16 * q^31 - 20 * q^33 - 10 * q^35 + 4 * q^37 - 18 * q^39 + q^41 - 2 * q^43 + 2 * q^45 + 13 * q^47 - 10 * q^49 - 20 * q^53 - 4 * q^55 - 14 * q^57 + 6 * q^59 + 11 * q^61 + 27 * q^63 - q^67 - 33 * q^69 - 28 * q^71 + 32 * q^73 + 2 * q^75 + 12 * q^77 + 6 * q^79 + 29 * q^81 + 21 * q^83 - 2 * q^85 + 2 * q^87 - 66 * q^89 - 60 * q^91 + 2 * q^93 + 4 * q^95 - 30 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.71903	+	0.211943i	−0.992485	+	0.122365i
$3$	−1.71903	+	0.211943i	−0.992485	+	0.122365i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.719035	+	1.24540i	−0.271770	+	0.470719i	−0.969315	−	0.245822i	$-0.920942\pi$
$7$	−0.719035	+	1.24540i	−0.271770	+	0.470719i	0.697545	+	0.716541i	$0.254276\pi$
$8$		0			0
$9$	2.91016	−	0.728674i	0.970054	−	0.242891i
$10$		0			0
$11$	0.675970	−	1.17081i	0.203813	−	0.353014i	−0.745941	−	0.666012i	$-0.768000\pi$
$11$	0.675970	−	1.17081i	0.203813	−	0.353014i	0.949754	+	0.312998i	$0.101333\pi$
$12$		0			0
$13$	2.76210	+	4.78410i	0.766069	+	1.32687i	0.939680	+	0.342056i	$0.111123\pi$
$13$	2.76210	+	4.78410i	0.766069	+	1.32687i	−0.173611	+	0.984814i	$0.555544\pi$
$14$		0			0
$15$	1.04307	+	1.38276i	0.269318	+	0.357026i
$16$		0			0
$17$	4.82032			1.16910			0.584550	−	0.811358i	$-0.301271\pi$
$17$	4.82032			1.16910			0.584550	+	0.811358i	$0.301271\pi$
$18$		0			0
$19$	−0.648061			−0.148675			−0.0743377	−	0.997233i	$-0.523684\pi$
$19$	−0.648061			−0.148675			−0.0743377	+	0.997233i	$0.523684\pi$
$20$		0			0
$21$	0.972091	−	2.29329i	0.212128	−	0.500436i
$22$		0			0
$23$	4.45323	+	7.71321i	0.928562	+	1.60832i	0.785730	+	0.618569i	$0.212287\pi$
$23$	4.45323	+	7.71321i	0.928562	+	1.60832i	0.142831	+	0.989747i	$0.454379\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.84823	+	1.86940i	−0.933042	+	0.359767i
$28$		0			0
$29$	3.58613	−	6.21136i	0.665928	−	1.15342i	−0.313105	−	0.949718i	$-0.601369\pi$
$29$	3.58613	−	6.21136i	0.665928	−	1.15342i	0.979033	−	0.203702i	$-0.0652974\pi$
$30$		0			0
$31$	2.32403	+	4.02534i	0.417408	+	0.722972i	0.995678	−	0.0928735i	$-0.0296052\pi$
$31$	2.32403	+	4.02534i	0.417408	+	0.722972i	−0.578270	+	0.815846i	$0.696272\pi$
$32$		0			0
$33$	−0.913870	+	2.15594i	−0.159084	+	0.375300i
$34$		0			0
$35$	1.43807			0.243078
$36$		0			0
$37$	1.35194			0.222257			0.111129	−	0.993806i	$-0.464553\pi$
$37$	1.35194			0.222257			0.111129	+	0.993806i	$0.464553\pi$
$38$		0			0
$39$	−5.76210	−	7.63862i	−0.922674	−	1.22316i
$40$		0			0
$41$	−0.175970	−	0.304788i	−0.0274818	−	0.0475999i	0.851957	−	0.523611i	$-0.175416\pi$
$41$	−0.175970	−	0.304788i	−0.0274818	−	0.0475999i	−0.879439	+	0.476011i	$0.842082\pi$
$42$		0			0
$43$	−2.41016	+	4.17452i	−0.367546	+	0.636608i	−0.989181	−	0.146698i	$-0.953135\pi$
$43$	−2.41016	+	4.17452i	−0.367546	+	0.636608i	0.621635	+	0.783307i	$0.286469\pi$
$44$		0			0
$45$	−2.08613	−	2.15594i	−0.310982	−	0.321388i
$46$		0			0
$47$	4.74694	−	8.22195i	0.692413	−	1.19929i	−0.278632	−	0.960398i	$-0.589881\pi$
$47$	4.74694	−	8.22195i	0.692413	−	1.19929i	0.971045	−	0.238896i	$-0.0767856\pi$
$48$		0			0
$49$	2.46598	+	4.27120i	0.352283	+	0.610171i
$50$		0			0
$51$	−8.28630	+	1.02163i	−1.16031	+	0.143057i
$52$		0			0
$53$	−8.17226			−1.12255			−0.561273	−	0.827631i	$-0.689688\pi$
$53$	−8.17226			−1.12255			−0.561273	+	0.827631i	$0.689688\pi$
$54$		0			0
$55$	−1.35194			−0.182295
$56$		0			0
$57$	1.11404	−	0.137352i	0.147558	−	0.0181927i
$58$		0			0
$59$	−0.734191	−	1.27166i	−0.0955835	−	0.165556i	0.814268	−	0.580488i	$-0.197138\pi$
$59$	−0.734191	−	1.27166i	−0.0955835	−	0.165556i	−0.909852	+	0.414933i	$0.863805\pi$
$60$		0			0
$61$	−3.34823	+	5.79930i	−0.428697	+	0.742525i	−0.996758	−	0.0804618i	$-0.974361\pi$
$61$	−3.34823	+	5.79930i	−0.428697	+	0.742525i	0.568061	+	0.822987i	$0.307694\pi$
$62$		0			0
$63$	−1.18501	+	4.14827i	−0.149298	+	0.522633i
$64$		0			0
$65$	2.76210	−	4.78410i	0.342596	−	0.593394i
$66$		0			0
$67$	−6.21533	−	10.7653i	−0.759323	−	1.31519i	−0.943196	−	0.332236i	$-0.892197\pi$
$67$	−6.21533	−	10.7653i	−0.759323	−	1.31519i	0.183873	−	0.982950i	$-0.441136\pi$
$68$		0			0
$69$	−9.29001	−	12.3155i	−1.11839	−	1.48261i
$70$		0			0
$71$	2.22808			0.264424			0.132212	−	0.991221i	$-0.457792\pi$
$71$	2.22808			0.264424			0.132212	+	0.991221i	$0.457792\pi$
$72$		0			0
$73$	−4.34452			−0.508488			−0.254244	−	0.967140i	$-0.581827\pi$
$73$	−4.34452			−0.508488			−0.254244	+	0.967140i	$0.581827\pi$
$74$		0			0
$75$	0.675970	−	1.59470i	0.0780542	−	0.184140i
$76$		0			0
$77$	0.972091	+	1.68371i	0.110780	+	0.191877i
$78$		0			0
$79$	6.52420	−	11.3002i	0.734030	−	1.27138i	−0.221118	−	0.975247i	$-0.570971\pi$
$79$	6.52420	−	11.3002i	0.734030	−	1.27138i	0.955148	−	0.296130i	$-0.0956961\pi$
$80$		0			0
$81$	7.93807	−	4.24111i	0.882008	−	0.471235i
$82$		0			0
$83$	2.63290	−	4.56032i	0.288999	−	0.500561i	−0.684572	−	0.728945i	$-0.740011\pi$
$83$	2.63290	−	4.56032i	0.288999	−	0.500561i	0.973571	+	0.228384i	$0.0733443\pi$
$84$		0			0
$85$	−2.41016	−	4.17452i	−0.261419	−	0.452790i
$86$		0			0
$87$	−4.84823	+	11.4376i	−0.519785	+	1.22624i
$88$		0			0
$89$	−11.0000			−1.16600			−0.582999	−	0.812473i	$-0.698121\pi$
$89$	−11.0000			−1.16600			−0.582999	+	0.812473i	$0.698121\pi$
$90$		0			0
$91$	−7.94418			−0.832777
$92$		0			0
$93$	−4.84823	−	6.42714i	−0.502738	−	0.666463i
$94$		0			0
$95$	0.324030	+	0.561237i	0.0332448	+	0.0575817i
$96$		0			0
$97$	−8.79001	+	15.2247i	−0.892490	+	1.54584i	−0.0556097	+	0.998453i	$0.517710\pi$
$97$	−8.79001	+	15.2247i	−0.892490	+	1.54584i	−0.836880	+	0.547386i	$0.815623\pi$
$98$		0			0
$99$	1.11404	−	3.89982i	0.111965	−	0.391946i
$100$		0			0
$101$	−1.43807	+	2.49081i	−0.143093	+	0.247845i	−0.928660	−	0.370932i	$-0.879038\pi$
$101$	−1.43807	+	2.49081i	−0.143093	+	0.247845i	0.785567	+	0.618777i	$0.212372\pi$
$102$		0			0
$103$	7.93436	+	13.7427i	0.781796	+	1.35411i	0.930895	+	0.365288i	$0.119029\pi$
$103$	7.93436	+	13.7427i	0.781796	+	1.35411i	−0.149099	+	0.988822i	$0.547637\pi$
$104$		0			0
$105$	−2.47209	+	0.304788i	−0.241251	+	0.0297443i
$106$		0			0
$107$	0.314208			0.0303757			0.0151878	−	0.999885i	$-0.495165\pi$
$107$	0.314208			0.0303757			0.0151878	+	0.999885i	$0.495165\pi$
$108$		0			0
$109$	15.9320			1.52600			0.763002	−	0.646396i	$-0.223724\pi$
$109$	15.9320			1.52600			0.763002	+	0.646396i	$0.223724\pi$
$110$		0			0
$111$	−2.32403	+	0.286534i	−0.220587	+	0.0271966i
$112$		0			0
$113$	−3.25839	−	5.64370i	−0.306524	−	0.530914i	0.671076	−	0.741389i	$-0.265833\pi$
$113$	−3.25839	−	5.64370i	−0.306524	−	0.530914i	−0.977599	+	0.210474i	$0.932499\pi$
$114$		0			0
$115$	4.45323	−	7.71321i	0.415265	−	0.719261i
$116$		0			0
$117$	11.5242	+	11.9098i	1.06541	+	1.10106i
$118$		0			0
$119$	−3.46598	+	6.00325i	−0.317726	+	0.550317i
$120$		0			0
$121$	4.58613	+	7.94341i	0.416921	+	0.722128i
$122$		0			0
$123$	0.367095	+	0.486646i	0.0330999	+	0.0438794i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−8.19777			−0.727434			−0.363717	−	0.931509i	$-0.618492\pi$
$127$	−8.19777			−0.727434			−0.363717	+	0.931509i	$0.618492\pi$
$128$		0			0
$129$	3.25839	−	7.68696i	0.286885	−	0.676799i
$130$		0			0
$131$	3.64806	+	6.31863i	0.318733	+	0.552061i	0.980224	−	0.197892i	$-0.0634095\pi$
$131$	3.64806	+	6.31863i	0.318733	+	0.552061i	−0.661491	+	0.749953i	$0.730076\pi$
$132$		0			0
$133$	0.465978	−	0.807098i	0.0404054	−	0.0699843i
$134$		0			0
$135$	4.04307	+	3.26399i	0.347972	+	0.280919i
$136$		0			0
$137$	6.43807	−	11.1511i	0.550041	−	0.952700i	−0.448230	−	0.893919i	$-0.647945\pi$
$137$	6.43807	−	11.1511i	0.550041	−	0.952700i	0.998271	−	0.0587811i	$-0.0187214\pi$
$138$		0			0
$139$	−2.70388	−	4.68325i	−0.229340	−	0.397228i	0.728273	−	0.685287i	$-0.240323\pi$
$139$	−2.70388	−	4.68325i	−0.229340	−	0.397228i	−0.957613	+	0.288059i	$0.906990\pi$
$140$		0			0
$141$	−6.41758	+	15.1399i	−0.540458	+	1.27501i
$142$		0			0
$143$	7.46838			0.624537
$144$		0			0
$145$	−7.17226			−0.595624
$146$		0			0
$147$	−5.14435	−	6.81969i	−0.424299	−	0.562479i
$148$		0			0
$149$	1.44178	+	2.49723i	0.118115	+	0.204581i	0.919021	−	0.394209i	$-0.128981\pi$
$149$	1.44178	+	2.49723i	0.118115	+	0.204581i	−0.800906	+	0.598791i	$0.795648\pi$
$150$		0			0
$151$	5.32403	−	9.22149i	0.433263	−	0.750434i	−0.563889	−	0.825851i	$-0.690695\pi$
$151$	5.32403	−	9.22149i	0.433263	−	0.750434i	0.997152	+	0.0754165i	$0.0240286\pi$
$152$		0			0
$153$	14.0279	−	3.51244i	1.13409	−	0.283964i
$154$		0			0
$155$	2.32403	−	4.02534i	0.186671	−	0.323323i
$156$		0			0
$157$	−8.14195	−	14.1023i	−0.649798	−	1.12548i	−0.983171	−	0.182688i	$-0.941520\pi$
$157$	−8.14195	−	14.1023i	−0.649798	−	1.12548i	0.333373	−	0.942795i	$-0.391813\pi$
$158$		0			0
$159$	14.0484	−	1.73205i	1.11411	−	0.137361i
$160$		0			0
$161$	−12.8081			−1.00942
$162$		0			0
$163$	14.1164			1.10569			0.552843	−	0.833286i	$-0.313543\pi$
$163$	14.1164			1.10569			0.552843	+	0.833286i	$0.313543\pi$
$164$		0			0
$165$	2.32403	−	0.286534i	0.180926	−	0.0223066i
$166$		0			0
$167$	9.30146	+	16.1106i	0.719768	+	1.24668i	0.961091	+	0.276230i	$0.0890853\pi$
$167$	9.30146	+	16.1106i	0.719768	+	1.24668i	−0.241323	+	0.970445i	$0.577581\pi$
$168$		0			0
$169$	−8.75839	+	15.1700i	−0.673722	+	1.16692i
$170$		0			0
$171$	−1.88596	+	0.472225i	−0.144223	+	0.0361119i
$172$		0			0
$173$	−12.4003	+	21.4780i	−0.942780	+	1.63294i	−0.182645	+	0.983179i	$0.558466\pi$
$173$	−12.4003	+	21.4780i	−0.942780	+	1.63294i	−0.760136	+	0.649764i	$0.774868\pi$
$174$		0			0
$175$	−0.719035	−	1.24540i	−0.0543539	−	0.0941437i
$176$		0			0
$177$	1.53162	+	2.03041i	0.115123	+	0.152615i
$178$		0			0
$179$	−15.8687			−1.18608			−0.593042	−	0.805172i	$-0.702073\pi$
$179$	−15.8687			−1.18608			−0.593042	+	0.805172i	$0.702073\pi$
$180$		0			0
$181$	11.5168			0.856036			0.428018	−	0.903770i	$-0.359212\pi$
$181$	11.5168			0.856036			0.428018	+	0.903770i	$0.359212\pi$
$182$		0			0
$183$	4.52660	−	10.6788i	0.334616	−	0.789402i
$184$		0			0
$185$	−0.675970	−	1.17081i	−0.0496983	−	0.0860799i
$186$		0			0
$187$	3.25839	−	5.64370i	0.238277	−	0.412708i
$188$		0			0
$189$	1.15788	−	7.38217i	0.0842236	−	0.536974i
$190$		0			0
$191$	−0.114039	+	0.197521i	−0.00825157	+	0.0142921i	−0.870122	−	0.492837i	$-0.835960\pi$
$191$	−0.114039	+	0.197521i	−0.00825157	+	0.0142921i	0.861870	+	0.507129i	$0.169293\pi$
$192$		0			0
$193$	−12.9344	−	22.4030i	−0.931036	−	1.61260i	−0.781555	−	0.623836i	$-0.785573\pi$
$193$	−12.9344	−	22.4030i	−0.931036	−	1.61260i	−0.149481	−	0.988765i	$-0.547760\pi$
$194$		0			0
$195$	−3.73419	+	8.80944i	−0.267411	+	0.630857i
$196$		0			0
$197$	−0.419983			−0.0299225			−0.0149613	−	0.999888i	$-0.504762\pi$
$197$	−0.419983			−0.0299225			−0.0149613	+	0.999888i	$0.504762\pi$
$198$		0			0
$199$	12.0410			0.853562			0.426781	−	0.904355i	$-0.359647\pi$
$199$	12.0410			0.853562			0.426781	+	0.904355i	$0.359647\pi$
$200$		0			0
$201$	12.9660	+	17.1886i	0.914550	+	1.21239i
$202$		0			0
$203$	5.15710	+	8.93237i	0.361958	+	0.626929i
$204$		0			0
$205$	−0.175970	+	0.304788i	−0.0122903	+	0.0212873i
$206$		0			0
$207$	18.5800	+	19.2017i	1.29140	+	1.33461i
$208$		0			0
$209$	−0.438069	+	0.758758i	−0.0303019	+	0.0524844i
$210$		0			0
$211$	−3.49629	−	6.05575i	−0.240695	−	0.416895i	0.720218	−	0.693748i	$-0.244042\pi$
$211$	−3.49629	−	6.05575i	−0.240695	−	0.416895i	−0.960912	+	0.276853i	$0.910709\pi$
$212$		0			0
$213$	−3.83014	+	0.472225i	−0.262437	+	0.0323563i
$214$		0			0
$215$	4.82032			0.328743
$216$		0			0
$217$	−6.68423			−0.453755
$218$		0			0
$219$	7.46838	−	0.920789i	0.504666	−	0.0622212i
$220$		0			0
$221$	13.3142	+	23.0609i	0.895611	+	1.55124i
$222$		0			0
$223$	7.04307	−	12.1989i	0.471639	−	0.816902i	−0.527835	−	0.849347i	$-0.676996\pi$
$223$	7.04307	−	12.1989i	0.471639	−	0.816902i	0.999474	+	0.0324450i	$0.0103294\pi$
$224$		0			0
$225$	−0.824030	+	2.88461i	−0.0549354	+	0.192307i
$226$		0			0
$227$	11.7244	−	20.3072i	0.778174	−	1.34784i	−0.154820	−	0.987943i	$-0.549480\pi$
$227$	11.7244	−	20.3072i	0.778174	−	1.34784i	0.932993	−	0.359894i	$-0.117187\pi$
$228$		0			0
$229$	6.40645	+	11.0963i	0.423350	+	0.733264i	0.996265	−	0.0863510i	$-0.0275207\pi$
$229$	6.40645	+	11.0963i	0.423350	+	0.733264i	−0.572915	+	0.819615i	$0.694187\pi$
$230$		0			0
$231$	−2.02791	−	2.68833i	−0.133427	−	0.176879i
$232$		0			0
$233$	−28.7449			−1.88314			−0.941569	−	0.336820i	$-0.890649\pi$
$233$	−28.7449			−1.88314			−0.941569	+	0.336820i	$0.890649\pi$
$234$		0			0
$235$	−9.49389			−0.619313
$236$		0			0
$237$	−8.82032	+	20.8083i	−0.572941	+	1.35164i
$238$		0			0
$239$	0.321627	+	0.557074i	0.0208043	+	0.0360341i	0.876240	−	0.481875i	$-0.160044\pi$
$239$	0.321627	+	0.557074i	0.0208043	+	0.0360341i	−0.855436	+	0.517909i	$0.826711\pi$
$240$		0			0
$241$	10.4344	−	18.0728i	0.672136	−	1.16417i	−0.305161	−	0.952301i	$-0.598710\pi$
$241$	10.4344	−	18.0728i	0.672136	−	1.16417i	0.977297	−	0.211873i	$-0.0679564\pi$
$242$		0			0
$243$	−12.7469	+	8.97304i	−0.817717	+	0.575621i
$244$		0			0
$245$	2.46598	−	4.27120i	0.157546	−	0.272877i
$246$		0			0
$247$	−1.79001	−	3.10039i	−0.113896	−	0.197273i
$248$		0			0
$249$	−3.55953	+	8.39738i	−0.225576	+	0.532162i
$250$		0			0
$251$	−17.8687			−1.12786			−0.563932	−	0.825821i	$-0.690712\pi$
$251$	−17.8687			−1.12786			−0.563932	+	0.825821i	$0.690712\pi$
$252$		0			0
$253$	12.0410			0.757010
$254$		0			0
$255$	5.02791	+	6.66533i	0.314860	+	0.417399i
$256$		0			0
$257$	−5.70388	−	9.87941i	−0.355798	−	0.616260i	0.631456	−	0.775412i	$-0.282458\pi$
$257$	−5.70388	−	9.87941i	−0.355798	−	0.616260i	−0.987254	+	0.159151i	$0.949124\pi$
$258$		0			0
$259$	−0.972091	+	1.68371i	−0.0604028	+	0.104621i
$260$		0			0
$261$	5.91016	−	20.6892i	0.365830	−	1.28063i
$262$		0			0
$263$	−0.237900	+	0.412055i	−0.0146696	+	0.0254084i	−0.873267	−	0.487242i	$-0.838003\pi$
$263$	−0.237900	+	0.412055i	−0.0146696	+	0.0254084i	0.858597	+	0.512650i	$0.171336\pi$
$264$		0			0
$265$	4.08613	+	7.07739i	0.251009	+	0.434760i
$266$		0			0
$267$	18.9094	−	2.33137i	1.15724	−	0.142677i
$268$		0			0
$269$	−7.57260			−0.461709			−0.230855	−	0.972988i	$-0.574152\pi$
$269$	−7.57260			−0.461709			−0.230855	+	0.972988i	$0.574152\pi$
$270$		0			0
$271$	−19.6965			−1.19647			−0.598237	−	0.801319i	$-0.704132\pi$
$271$	−19.6965			−1.19647			−0.598237	+	0.801319i	$0.704132\pi$
$272$		0			0
$273$	13.6563	−	1.68371i	0.826518	−	0.101903i
$274$		0			0
$275$	0.675970	+	1.17081i	0.0407625	+	0.0706027i
$276$		0			0
$277$	10.7547	−	18.6277i	0.646186	−	1.11923i	−0.337840	−	0.941204i	$-0.609696\pi$
$277$	10.7547	−	18.6277i	0.646186	−	1.11923i	0.984026	−	0.178024i	$-0.0569704\pi$
$278$		0			0
$279$	9.69646	+	10.0209i	0.580512	+	0.599937i
$280$		0			0
$281$	5.08242	−	8.80301i	0.303192	−	0.525144i	−0.673665	−	0.739037i	$-0.735281\pi$
$281$	5.08242	−	8.80301i	0.303192	−	0.525144i	0.976857	+	0.213893i	$0.0686144\pi$
$282$		0			0
$283$	11.2432	+	19.4739i	0.668341	+	1.15760i	0.978368	+	0.206873i	$0.0663286\pi$
$283$	11.2432	+	19.4739i	0.668341	+	1.15760i	−0.310027	+	0.950728i	$0.600338\pi$
$284$		0			0
$285$	−0.675970	−	0.896110i	−0.0400410	−	0.0530810i
$286$		0			0
$287$	0.506113			0.0298749
$288$		0			0
$289$	6.23550			0.366794
$290$		0			0
$291$	11.8836	−	28.0348i	0.696626	−	1.64343i
$292$		0			0
$293$	2.99760	+	5.19199i	0.175121	+	0.303319i	0.940203	−	0.340614i	$-0.110635\pi$
$293$	2.99760	+	5.19199i	0.175121	+	0.303319i	−0.765082	+	0.643933i	$0.777302\pi$
$294$		0			0
$295$	−0.734191	+	1.27166i	−0.0427463	+	0.0740387i
$296$		0			0
$297$	−1.08853	+	6.94003i	−0.0631631	+	0.402702i
$298$		0			0
$299$	−24.6005	+	42.6093i	−1.42268	+	2.46416i
$300$		0			0
$301$	−3.46598	−	6.00325i	−0.199776	−	0.346022i
$302$		0			0
$303$	1.94418	−	4.58658i	0.111690	−	0.263492i
$304$		0			0
$305$	6.69646			0.383438
$306$		0			0
$307$	−23.9549			−1.36718			−0.683588	−	0.729868i	$-0.739581\pi$
$307$	−23.9549			−1.36718			−0.683588	+	0.729868i	$0.739581\pi$
$308$		0			0
$309$	−16.5521	−	21.9426i	−0.941617	−	1.24827i
$310$		0			0
$311$	−13.7547	−	23.8238i	−0.779956	−	1.35092i	−0.931966	−	0.362545i	$-0.881908\pi$
$311$	−13.7547	−	23.8238i	−0.779956	−	1.35092i	0.152010	−	0.988379i	$-0.451425\pi$
$312$		0			0
$313$	−1.50371	+	2.60450i	−0.0849947	+	0.147215i	−0.905389	−	0.424583i	$-0.860421\pi$
$313$	−1.50371	+	2.60450i	−0.0849947	+	0.147215i	0.820394	+	0.571798i	$0.193754\pi$
$314$		0			0
$315$	4.18501	−	1.04788i	0.235799	−	0.0590415i
$316$		0			0
$317$	−5.20017	+	9.00696i	−0.292071	+	0.505881i	−0.974299	−	0.225258i	$-0.927678\pi$
$317$	−5.20017	+	9.00696i	−0.292071	+	0.505881i	0.682229	+	0.731139i	$0.261011\pi$
$318$		0			0
$319$	−4.84823	−	8.39738i	−0.271449	−	0.470163i
$320$		0			0
$321$	−0.540135	+	0.0665941i	−0.0301474	+	0.00371692i
$322$		0			0
$323$	−3.12386			−0.173816
$324$		0			0
$325$	−5.52420			−0.306427
$326$		0			0
$327$	−27.3876	+	3.37666i	−1.51454	+	0.186730i
$328$		0			0
$329$	6.82643	+	11.8237i	0.376353	+	0.651863i
$330$		0			0
$331$	4.61775	−	7.99817i	0.253814	−	0.439619i	−0.710758	−	0.703436i	$-0.751648\pi$
$331$	4.61775	−	7.99817i	0.253814	−	0.439619i	0.964573	+	0.263817i	$0.0849814\pi$
$332$		0			0
$333$	3.93436	−	0.985122i	0.215602	−	0.0539844i
$334$		0			0
$335$	−6.21533	+	10.7653i	−0.339580	+	0.588169i
$336$		0			0
$337$	−17.3748	−	30.0941i	−0.946467	−	1.63933i	−0.752786	−	0.658265i	$-0.771291\pi$
$337$	−17.3748	−	30.0941i	−0.946467	−	1.63933i	−0.193681	−	0.981064i	$-0.562043\pi$
$338$		0			0
$339$	6.79743	+	9.01112i	0.369186	+	0.489417i
$340$		0			0
$341$	6.28390			0.340292
$342$		0			0
$343$	−17.1590			−0.926498
$344$		0			0
$345$	−6.02049	+	14.2031i	−0.324132	+	0.764670i
$346$		0			0
$347$	−10.8105	−	18.7243i	−0.580338	−	1.00517i	−0.995439	−	0.0953996i	$-0.969587\pi$
$347$	−10.8105	−	18.7243i	−0.580338	−	1.00517i	0.415101	−	0.909775i	$-0.363746\pi$
$348$		0			0
$349$	−3.61644	+	6.26386i	−0.193584	+	0.335297i	−0.946435	−	0.322893i	$-0.895344\pi$
$349$	−3.61644	+	6.26386i	−0.193584	+	0.335297i	0.752852	+	0.658190i	$0.228678\pi$
$350$		0			0
$351$	−22.3347	−	18.0309i	−1.19214	−	0.962420i
$352$		0			0
$353$	11.6406	−	20.1622i	0.619569	−	1.07312i	−0.369996	−	0.929034i	$-0.620641\pi$
$353$	11.6406	−	20.1622i	0.619569	−	1.07312i	0.989564	−	0.144091i	$-0.0460259\pi$
$354$		0			0
$355$	−1.11404	−	1.92957i	−0.0591271	−	0.102411i
$356$		0			0
$357$	4.68579	−	11.0544i	0.247998	−	0.585060i
$358$		0			0
$359$	−31.9655			−1.68708			−0.843538	−	0.537070i	$-0.819531\pi$
$359$	−31.9655			−1.68708			−0.843538	+	0.537070i	$0.819531\pi$
$360$		0			0
$361$	−18.5800			−0.977896
$362$		0			0
$363$	−9.56726	−	12.6830i	−0.502151	−	0.665685i
$364$		0			0
$365$	2.17226	+	3.76247i	0.113701	+	0.196936i
$366$		0			0
$367$	−7.76210	+	13.4444i	−0.405178	+	0.701789i	−0.994342	−	0.106224i	$-0.966124\pi$
$367$	−7.76210	+	13.4444i	−0.405178	+	0.701789i	0.589164	+	0.808014i	$0.299457\pi$
$368$		0			0
$369$	−0.734191	−	0.758758i	−0.0382205	−	0.0394994i
$370$		0			0
$371$	5.87614	−	10.1778i	0.305074	−	0.528404i
$372$		0			0
$373$	−15.6661	−	27.1346i	−0.811162	−	1.40497i	−0.912051	−	0.410077i	$-0.865502\pi$
$373$	−15.6661	−	27.1346i	−0.811162	−	1.40497i	0.100889	−	0.994898i	$-0.467831\pi$
$374$		0			0
$375$	−1.71903	+	0.211943i	−0.0887706	+	0.0109447i
$376$		0			0
$377$	39.6210			2.04059
$378$		0			0
$379$	22.0000			1.13006			0.565032	−	0.825069i	$-0.308864\pi$
$379$	22.0000			1.13006			0.565032	+	0.825069i	$0.308864\pi$
$380$		0			0
$381$	14.0922	−	1.73746i	0.721967	−	0.0890126i
$382$		0			0
$383$	−14.6382	−	25.3542i	−0.747979	−	1.29554i	−0.948790	−	0.315908i	$-0.897691\pi$
$383$	−14.6382	−	25.3542i	−0.747979	−	1.29554i	0.200811	−	0.979630i	$-0.435642\pi$
$384$		0			0
$385$	0.972091	−	1.68371i	0.0495424	−	0.0858099i
$386$		0			0
$387$	−3.97209	+	13.9047i	−0.201913	+	0.706818i
$388$		0			0
$389$	1.00371	−	1.73848i	0.0508901	−	0.0881442i	−0.839458	−	0.543424i	$-0.817128\pi$
$389$	1.00371	−	1.73848i	0.0508901	−	0.0881442i	0.890348	+	0.455280i	$0.150461\pi$
$390$		0			0
$391$	21.4660	+	37.1802i	1.08558	+	1.88028i
$392$		0			0
$393$	−7.61033	−	10.0888i	−0.383890	−	0.508911i
$394$		0			0
$395$	−13.0484			−0.656536
$396$		0			0
$397$	16.9368			0.850032			0.425016	−	0.905186i	$-0.360268\pi$
$397$	16.9368			0.850032			0.425016	+	0.905186i	$0.360268\pi$
$398$		0			0
$399$	−0.629974	+	1.48619i	−0.0315382	+	0.0744026i
$400$		0			0
$401$	−10.9065	−	18.8905i	−0.544642	−	0.943348i	−0.998629	−	0.0523397i	$-0.983332\pi$
$401$	−10.9065	−	18.8905i	−0.544642	−	0.943348i	0.453987	−	0.891008i	$-0.350001\pi$
$402$		0			0
$403$	−12.8384	+	22.2368i	−0.639527	+	1.10769i
$404$		0			0
$405$	−7.64195	−	4.75401i	−0.379731	−	0.236229i
$406$		0			0
$407$	0.913870	−	1.58287i	0.0452988	−	0.0784599i
$408$		0			0
$409$	7.40034	+	12.8178i	0.365923	+	0.633798i	0.988924	−	0.148424i	$-0.0474200\pi$
$409$	7.40034	+	12.8178i	0.365923	+	0.633798i	−0.623001	+	0.782221i	$0.714087\pi$
$410$		0			0
$411$	−8.70388	+	20.5336i	−0.429331	+	1.01285i
$412$		0			0
$413$	2.11164			0.103907
$414$		0			0
$415$	−5.26581			−0.258488
$416$		0			0
$417$	5.64064	+	7.47761i	0.276223	+	0.366180i
$418$		0			0
$419$	6.14435	+	10.6423i	0.300171	+	0.519912i	0.976175	−	0.216987i	$-0.0696228\pi$
$419$	6.14435	+	10.6423i	0.300171	+	0.519912i	−0.676003	+	0.736899i	$0.736290\pi$
$420$		0			0
$421$	6.69646	−	11.5986i	0.326365	−	0.565282i	−0.655422	−	0.755263i	$-0.727509\pi$
$421$	6.69646	−	11.5986i	0.326365	−	0.565282i	0.981788	+	0.189981i	$0.0608426\pi$
$422$		0			0
$423$	7.82325	−	27.3862i	0.380380	−	1.33156i
$424$		0			0
$425$	−2.41016	+	4.17452i	−0.116910	+	0.202494i
$426$		0			0
$427$	−4.81499	−	8.33980i	−0.233014	−	0.403591i
$428$		0			0
$429$	−12.8384	+	1.58287i	−0.619844	+	0.0764216i
$430$		0			0
$431$	12.0968			0.582682			0.291341	−	0.956619i	$-0.405899\pi$
$431$	12.0968			0.582682			0.291341	+	0.956619i	$0.405899\pi$
$432$		0			0
$433$	21.1648			1.01712			0.508559	−	0.861027i	$-0.330178\pi$
$433$	21.1648			1.01712			0.508559	+	0.861027i	$0.330178\pi$
$434$		0			0
$435$	12.3294	−	1.52011i	0.591148	−	0.0728836i
$436$		0			0
$437$	−2.88596	−	4.99863i	−0.138054	−	0.239117i
$438$		0			0
$439$	0.741609	−	1.28451i	0.0353951	−	0.0613061i	−0.847785	−	0.530340i	$-0.822064\pi$
$439$	0.741609	−	1.28451i	0.0353951	−	0.0613061i	0.883180	+	0.469034i	$0.155398\pi$
$440$		0			0
$441$	10.2887	+	10.6330i	0.489938	+	0.506333i
$442$		0			0
$443$	1.77726	−	3.07830i	0.0844400	−	0.146254i	−0.820712	−	0.571341i	$-0.806423\pi$
$443$	1.77726	−	3.07830i	0.0844400	−	0.146254i	0.905152	+	0.425087i	$0.139757\pi$
$444$		0			0
$445$	5.50000	+	9.52628i	0.260725	+	0.451589i
$446$		0			0
$447$	−3.00774	−	3.98726i	−0.142261	−	0.188591i
$448$		0			0
$449$	40.3659			1.90498			0.952491	−	0.304566i	$-0.0985114\pi$
$449$	40.3659			1.90498			0.952491	+	0.304566i	$0.0985114\pi$
$450$		0			0
$451$	−0.475800			−0.0224046
$452$		0			0
$453$	−7.19777	+	16.9805i	−0.338181	+	0.797811i
$454$		0			0
$455$	3.97209	+	6.87986i	0.186215	+	0.322533i
$456$		0			0
$457$	−14.2002	+	24.5954i	−0.664256	+	1.15052i	0.315231	+	0.949015i	$0.397918\pi$
$457$	−14.2002	+	24.5954i	−0.664256	+	1.15052i	−0.979486	+	0.201510i	$0.935415\pi$
$458$		0			0
$459$	−23.3700	+	9.01112i	−1.09082	+	0.420603i
$460$		0			0
$461$	−9.87483	+	17.1037i	−0.459917	+	0.796599i	−0.998956	−	0.0456813i	$-0.985454\pi$
$461$	−9.87483	+	17.1037i	−0.459917	+	0.796599i	0.539039	+	0.842281i	$0.318787\pi$
$462$		0			0
$463$	−0.0885340	−	0.153345i	−0.00411452	−	0.00712656i	0.863961	−	0.503559i	$-0.167976\pi$
$463$	−0.0885340	−	0.153345i	−0.00411452	−	0.00712656i	−0.868075	+	0.496432i	$0.834643\pi$
$464$		0			0
$465$	−3.14195	+	7.41226i	−0.145704	+	0.343735i
$466$		0			0
$467$	21.5094			0.995335			0.497667	−	0.867368i	$-0.334190\pi$
$467$	21.5094			0.995335			0.497667	+	0.867368i	$0.334190\pi$
$468$		0			0
$469$	17.8761			0.825443
$470$		0			0
$471$	16.9852	+	22.5167i	0.782635	+	1.03751i
$472$		0			0
$473$	3.25839	+	5.64370i	0.149821	+	0.259498i
$474$		0			0
$475$	0.324030	−	0.561237i	0.0148675	−	0.0257513i
$476$		0			0
$477$	−23.7826	+	5.95491i	−1.08893	+	0.272657i
$478$		0			0
$479$	−0.655479	+	1.13532i	−0.0299496	+	0.0518742i	−0.880612	−	0.473839i	$-0.842868\pi$
$479$	−0.655479	+	1.13532i	−0.0299496	+	0.0518742i	0.850662	+	0.525713i	$0.176201\pi$
$480$		0			0
$481$	3.73419	+	6.46781i	0.170264	+	0.294907i
$482$		0			0
$483$	22.0176	−	2.71458i	1.00183	−	0.123518i
$484$		0			0
$485$	17.5800			0.798267
$486$		0			0
$487$	10.4152			0.471957			0.235978	−	0.971758i	$-0.424171\pi$
$487$	10.4152			0.471957			0.235978	+	0.971758i	$0.424171\pi$
$488$		0			0
$489$	−24.2667	+	2.99188i	−1.09738	+	0.135297i
$490$		0			0
$491$	−0.0935486	−	0.162031i	−0.00422179	−	0.00731235i	0.863907	−	0.503652i	$-0.168011\pi$
$491$	−0.0935486	−	0.162031i	−0.00422179	−	0.00731235i	−0.868129	+	0.496339i	$0.834677\pi$
$492$		0			0
$493$	17.2863	−	29.9407i	0.778536	−	1.34846i
$494$		0			0
$495$	−3.93436	+	0.985122i	−0.176836	+	0.0442780i
$496$		0			0
$497$	−1.60207	+	2.77486i	−0.0718625	+	0.124469i
$498$		0			0
$499$	16.8990	+	29.2700i	0.756505	+	1.31030i	0.944623	+	0.328158i	$0.106428\pi$
$499$	16.8990	+	29.2700i	0.756505	+	1.31030i	−0.188118	+	0.982146i	$0.560239\pi$
$500$		0			0
$501$	−19.4040	−	25.7233i	−0.866909	−	1.14923i
$502$		0			0
$503$	20.9623			0.934661			0.467331	−	0.884083i	$-0.345216\pi$
$503$	20.9623			0.934661			0.467331	+	0.884083i	$0.345216\pi$
$504$		0			0
$505$	2.87614			0.127986
$506$		0			0
$507$	11.8408	−	27.9340i	0.525869	−	1.24059i
$508$		0			0
$509$	12.3687	+	21.4233i	0.548234	+	0.949569i	0.998396	+	0.0566220i	$0.0180330\pi$
$509$	12.3687	+	21.4233i	0.548234	+	0.949569i	−0.450162	+	0.892947i	$0.648634\pi$
$510$		0			0
$511$	3.12386	−	5.41069i	0.138191	−	0.239355i
$512$		0			0
$513$	3.14195	−	1.21149i	0.138720	−	0.0534884i
$514$		0			0
$515$	7.93436	−	13.7427i	0.349630	−	0.605576i
$516$		0			0
$517$	−6.41758	−	11.1156i	−0.282245	−	0.488862i
$518$		0			0
$519$	16.7645	−	39.5496i	0.735880	−	1.73604i
$520$		0			0
$521$	−7.28390			−0.319113			−0.159557	−	0.987189i	$-0.551006\pi$
$521$	−7.28390			−0.319113			−0.159557	+	0.987189i	$0.551006\pi$
$522$		0			0
$523$	12.0255			0.525839			0.262919	−	0.964818i	$-0.415315\pi$
$523$	12.0255			0.525839			0.262919	+	0.964818i	$0.415315\pi$
$524$		0			0
$525$	1.50000	+	1.98850i	0.0654654	+	0.0867852i
$526$		0			0
$527$	11.2026	+	19.4034i	0.487992	+	0.845226i
$528$		0			0
$529$	−28.1624	+	48.7788i	−1.22445	+	2.12082i
$530$		0			0
$531$	−3.06324	−	3.16574i	−0.132933	−	0.137381i
$532$		0			0
$533$	0.972091	−	1.68371i	0.0421059	−	0.0729296i
$534$		0			0
$535$	−0.157104	−	0.272112i	−0.00679220	−	0.0117644i
$536$		0			0
$537$	27.2789	−	3.36326i	1.17717	−	0.145135i
$538$		0			0
$539$	6.66771			0.287198
$540$		0			0
$541$	−23.6890			−1.01847			−0.509236	−	0.860627i	$-0.670072\pi$
$541$	−23.6890			−1.01847			−0.509236	+	0.860627i	$0.670072\pi$
$542$		0			0
$543$	−19.7977	+	2.44090i	−0.849603	+	0.104749i
$544$		0			0
$545$	−7.96598	−	13.7975i	−0.341225	−	0.591019i
$546$		0			0
$547$	−7.77485	+	13.4664i	−0.332429	+	0.575783i	−0.982987	−	0.183673i	$-0.941201\pi$
$547$	−7.77485	+	13.4664i	−0.332429	+	0.575783i	0.650559	+	0.759456i	$0.274535\pi$
$548$		0			0
$549$	−5.51809	+	19.3167i	−0.235506	+	0.824416i
$550$		0			0
$551$	−2.32403	+	4.02534i	−0.0990070	+	0.171485i
$552$		0			0
$553$	9.38225	+	16.2505i	0.398974	+	0.691043i
$554$		0			0
$555$	1.41016	+	1.86940i	0.0598580	+	0.0793517i
$556$		0			0
$557$	12.2477			0.518953			0.259476	−	0.965749i	$-0.416450\pi$
$557$	12.2477			0.518953			0.259476	+	0.965749i	$0.416450\pi$
$558$		0			0
$559$	−26.6284			−1.12626
$560$		0			0
$561$	−4.40515	+	10.3923i	−0.185985	+	0.438763i
$562$		0			0
$563$	−11.0989	−	19.2238i	−0.467762	−	0.810188i	0.531559	−	0.847021i	$-0.321606\pi$
$563$	−11.0989	−	19.2238i	−0.467762	−	0.810188i	−0.999321	+	0.0368333i	$0.988273\pi$
$564$		0			0
$565$	−3.25839	+	5.64370i	−0.137082	+	0.237432i
$566$		0			0
$567$	−0.425843	+	12.9356i	−0.0178837	+	0.543245i
$568$		0			0
$569$	10.4078	−	18.0268i	0.436316	−	0.755721i	−0.561086	−	0.827757i	$-0.689616\pi$
$569$	10.4078	−	18.0268i	0.436316	−	0.755721i	0.997402	+	0.0720362i	$0.0229497\pi$
$570$		0			0
$571$	22.8007	+	39.4919i	0.954179	+	1.65269i	0.736237	+	0.676724i	$0.236601\pi$
$571$	22.8007	+	39.4919i	0.954179	+	1.65269i	0.217942	+	0.975962i	$0.430066\pi$
$572$		0			0
$573$	0.154174	−	0.363716i	0.00644070	−	0.0151944i
$574$		0			0
$575$	−8.90645			−0.371425
$576$		0			0
$577$	−0.172260			−0.00717129			−0.00358565	−	0.999994i	$-0.501141\pi$
$577$	−0.172260			−0.00717129			−0.00358565	+	0.999994i	$0.501141\pi$
$578$		0			0
$579$	26.9828	+	35.7701i	1.12137	+	1.48656i
$580$		0			0
$581$	3.78630	+	6.55806i	0.157082	+	0.272074i
$582$		0			0
$583$	−5.52420	+	9.56819i	−0.228789	+	0.396274i
$584$		0			0
$585$	4.55211	−	15.9352i	0.188207	−	0.658838i
$586$		0			0
$587$	6.22515	−	10.7823i	0.256939	−	0.445032i	−0.708481	−	0.705730i	$-0.750619\pi$
$587$	6.22515	−	10.7823i	0.256939	−	0.445032i	0.965420	+	0.260698i	$0.0839526\pi$
$588$		0			0
$589$	−1.50611	−	2.60866i	−0.0620583	−	0.107488i
$590$		0			0
$591$	0.721965	−	0.0890123i	0.0296977	−	0.00366148i
$592$		0			0
$593$	13.2403			0.543714			0.271857	−	0.962338i	$-0.412362\pi$
$593$	13.2403			0.543714			0.271857	+	0.962338i	$0.412362\pi$
$594$		0			0
$595$	6.93196			0.284183
$596$		0			0
$597$	−20.6989	+	2.55200i	−0.847148	+	0.104446i
$598$		0			0
$599$	−22.6406	−	39.2147i	−0.925072	−	1.60227i	−0.791446	−	0.611239i	$-0.790671\pi$
$599$	−22.6406	−	39.2147i	−0.925072	−	1.60227i	−0.133626	−	0.991032i	$-0.542662\pi$
$600$		0			0
$601$	15.0558	−	26.0774i	0.614140	−	1.06372i	−0.376395	−	0.926459i	$-0.622837\pi$
$601$	15.0558	−	26.0774i	0.614140	−	1.06372i	0.990535	−	0.137262i	$-0.0438302\pi$
$602$		0			0
$603$	−25.9320	−	26.7997i	−1.05603	−	1.09137i
$604$		0			0
$605$	4.58613	−	7.94341i	0.186453	−	0.322946i
$606$		0			0
$607$	14.2153	+	24.6217i	0.576982	+	0.999363i	0.995823	+	0.0913030i	$0.0291032\pi$
$607$	14.2153	+	24.6217i	0.576982	+	0.999363i	−0.418841	+	0.908060i	$0.637564\pi$
$608$		0			0
$609$	−10.7584	−	14.2620i	−0.435952	−	0.577927i
$610$		0			0
$611$	52.4461			2.12174
$612$		0			0
$613$	3.06804			0.123917			0.0619586	−	0.998079i	$-0.480265\pi$
$613$	3.06804			0.123917			0.0619586	+	0.998079i	$0.480265\pi$
$614$		0			0
$615$	0.237900	−	0.561237i	0.00959306	−	0.0226313i
$616$		0			0
$617$	−0.741609	−	1.28451i	−0.0298561	−	0.0517122i	0.850711	−	0.525633i	$-0.176172\pi$
$617$	−0.741609	−	1.28451i	−0.0298561	−	0.0517122i	−0.880567	+	0.473921i	$0.842838\pi$
$618$		0			0
$619$	0.552108	−	0.956280i	0.0221911	−	0.0384361i	−0.854717	−	0.519095i	$-0.826269\pi$
$619$	0.552108	−	0.956280i	0.0221911	−	0.0384361i	0.876908	+	0.480659i	$0.159602\pi$
$620$		0			0
$621$	−36.0094	−	29.0706i	−1.44501	−	1.16656i
$622$		0			0
$623$	7.90938	−	13.6995i	0.316883	−	0.548857i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	0.592243	−	1.39718i	0.0236519	−	0.0557979i
$628$		0			0
$629$	6.51678			0.259841
$630$		0			0
$631$	−8.07546			−0.321479			−0.160740	−	0.986997i	$-0.551388\pi$
$631$	−8.07546			−0.321479			−0.160740	+	0.986997i	$0.551388\pi$
$632$		0			0
$633$	7.29372	+	9.66904i	0.289899	+	0.384310i
$634$		0			0
$635$	4.09888	+	7.09947i	0.162659	+	0.281734i
$636$		0			0
$637$	−13.6226	+	23.5950i	−0.539745	+	0.934866i
$638$		0			0
$639$	6.48406	−	1.62354i	0.256506	−	0.0642263i
$640$		0			0
$641$	−0.269518	+	0.466819i	−0.0106453	+	0.0184383i	−0.871299	−	0.490753i	$-0.836722\pi$
$641$	−0.269518	+	0.466819i	−0.0106453	+	0.0184383i	0.860654	+	0.509191i	$0.170055\pi$
$642$		0			0
$643$	−8.51145	−	14.7423i	−0.335659	−	0.581378i	0.647952	−	0.761681i	$-0.275626\pi$
$643$	−8.51145	−	14.7423i	−0.335659	−	0.581378i	−0.983611	+	0.180303i	$0.942292\pi$
$644$		0			0
$645$	−8.28630	+	1.02163i	−0.326273	+	0.0402267i
$646$		0			0
$647$	−45.1952			−1.77680			−0.888402	−	0.459065i	$-0.848184\pi$
$647$	−45.1952			−1.77680			−0.888402	+	0.459065i	$0.848184\pi$
$648$		0			0
$649$	−1.98516			−0.0779245
$650$		0			0
$651$	11.4904	−	1.41667i	0.450345	−	0.0555239i
$652$		0			0
$653$	8.62015	+	14.9305i	0.337333	+	0.584277i	0.983930	−	0.178554i	$-0.0571420\pi$
$653$	8.62015	+	14.9305i	0.337333	+	0.584277i	−0.646597	+	0.762831i	$0.723809\pi$
$654$		0			0
$655$	3.64806	−	6.31863i	0.142542	−	0.246889i
$656$		0			0
$657$	−12.6433	+	3.16574i	−0.493260	+	0.123507i
$658$		0			0
$659$	−5.25839	+	9.10780i	−0.204838	+	0.354790i	−0.950081	−	0.312003i	$-0.899000\pi$
$659$	−5.25839	+	9.10780i	−0.204838	+	0.354790i	0.745243	+	0.666793i	$0.232333\pi$
$660$		0			0
$661$	2.23550	+	3.87199i	0.0869507	+	0.150603i	0.906221	−	0.422805i	$-0.138954\pi$
$661$	2.23550	+	3.87199i	0.0869507	+	0.150603i	−0.819270	+	0.573408i	$0.805621\pi$
$662$		0			0
$663$	−27.7752	−	36.8206i	−1.07870	−	1.42999i
$664$		0			0
$665$	−0.931956			−0.0361397
$666$		0			0
$667$	63.8794			2.47342
$668$		0			0
$669$	−9.52180	+	22.4631i	−0.368134	+	0.868475i
$670$		0			0
$671$	4.52660	+	7.84031i	0.174748	+	0.302672i
$672$		0			0
$673$	−2.43567	+	4.21870i	−0.0938880	+	0.162619i	−0.909144	−	0.416482i	$-0.863263\pi$
$673$	−2.43567	+	4.21870i	−0.0938880	+	0.162619i	0.815256	+	0.579101i	$0.196596\pi$
$674$		0			0
$675$	0.805165	−	5.13339i	0.0309908	−	0.197584i
$676$		0			0
$677$	−6.85565	+	11.8743i	−0.263484	+	0.456368i	−0.967165	−	0.254148i	$-0.918205\pi$
$677$	−6.85565	+	11.8743i	−0.263484	+	0.456368i	0.703681	+	0.710516i	$0.251538\pi$
$678$		0			0
$679$	−12.6406	−	21.8942i	−0.485103	−	0.840224i
$680$		0			0
$681$	−15.8506	+	37.3937i	−0.607398	+	1.43293i
$682$		0			0
$683$	31.8687			1.21942			0.609711	−	0.792624i	$-0.291285\pi$
$683$	31.8687			1.21942			0.609711	+	0.792624i	$0.291285\pi$
$684$		0			0
$685$	−12.8761			−0.491972
$686$		0			0
$687$	−13.3647	−	17.7171i	−0.509895	−	0.675950i
$688$		0			0
$689$	−22.5726	−	39.0969i	−0.859948	−	1.48947i
$690$		0			0
$691$	−16.0484	+	27.7966i	−0.610510	+	1.05743i	0.380645	+	0.924721i	$0.375702\pi$
$691$	−16.0484	+	27.7966i	−0.610510	+	1.05743i	−0.991155	+	0.132713i	$0.957631\pi$
$692$		0			0
$693$	4.05582	+	4.19153i	0.154068	+	0.159223i
$694$		0			0
$695$	−2.70388	+	4.68325i	−0.102564	+	0.177646i
$696$		0			0
$697$	−0.848230	−	1.46918i	−0.0321290	−	0.0556491i
$698$		0			0
$699$	49.4134	−	6.09226i	1.86899	−	0.230431i
$700$		0			0
$701$	11.5268			0.435362			0.217681	−	0.976020i	$-0.430151\pi$
$701$	11.5268			0.435362			0.217681	+	0.976020i	$0.430151\pi$
$702$		0			0
$703$	−0.876139			−0.0330442
$704$		0			0
$705$	16.3203	−	2.01216i	0.614659	−	0.0757823i
$706$		0			0
$707$	−2.06804	−	3.58196i	−0.0777768	−	0.134713i
$708$		0			0
$709$	12.6345	−	21.8836i	0.474500	−	0.821858i	−0.525074	−	0.851057i	$-0.675962\pi$
$709$	12.6345	−	21.8836i	0.474500	−	0.821858i	0.999574	+	0.0291990i	$0.00929566\pi$
$710$		0			0
$711$	10.7523	−	37.6395i	0.403242	−	1.41159i
$712$		0			0
$713$	−20.6989	+	35.8515i	−0.775179	+	1.34265i
$714$		0			0
$715$	−3.73419	−	6.46781i	−0.139651	−	0.241882i
$716$		0			0
$717$	−0.670955	−	0.889462i	−0.0250573	−	0.0332176i
$718$		0			0
$719$	20.6284			0.769310			0.384655	−	0.923060i	$-0.374320\pi$
$719$	20.6284			0.769310			0.384655	+	0.923060i	$0.374320\pi$
$720$		0			0
$721$	−22.8203			−0.849873
$722$		0			0
$723$	−14.1066	+	33.2793i	−0.524631	+	1.23767i
$724$		0			0
$725$	3.58613	+	6.21136i	0.133186	+	0.230684i
$726$		0			0
$727$	−11.9979	+	20.7810i	−0.444978	+	0.770725i	−0.998051	−	0.0624084i	$-0.980122\pi$
$727$	−11.9979	+	20.7810i	−0.444978	+	0.770725i	0.553073	+	0.833133i	$0.313455\pi$
$728$		0			0
$729$	20.0107	−	18.1266i	0.741136	−	0.671355i
$730$		0			0
$731$	−11.6177	+	20.1225i	−0.429698	+	0.744259i
$732$		0			0
$733$	4.64064	+	8.03783i	0.171406	+	0.296884i	0.938912	−	0.344158i	$-0.111836\pi$
$733$	4.64064	+	8.03783i	0.171406	+	0.296884i	−0.767506	+	0.641042i	$0.778502\pi$
$734$		0			0
$735$	−3.33385	+	7.86499i	−0.122971	+	0.290104i
$736$		0			0
$737$	−16.8055			−0.619038
$738$		0			0
$739$	−31.3323			−1.15258			−0.576289	−	0.817246i	$-0.695500\pi$
$739$	−31.3323			−1.15258			−0.576289	+	0.817246i	$0.695500\pi$
$740$		0			0
$741$	3.73419	+	4.95029i	0.137179	+	0.181854i
$742$		0			0
$743$	−12.9216	−	22.3809i	−0.474048	−	0.821075i	0.525511	−	0.850787i	$-0.323874\pi$
$743$	−12.9216	−	22.3809i	−0.474048	−	0.821075i	−0.999558	+	0.0297121i	$0.990541\pi$
$744$		0			0
$745$	1.44178	−	2.49723i	0.0528227	−	0.0914916i
$746$		0			0
$747$	4.33919	−	15.1898i	0.158763	−	0.555766i
$748$		0			0
$749$	−0.225927	+	0.391316i	−0.00825518	+	0.0142984i
$750$		0			0
$751$	−1.58984	−	2.75368i	−0.0580141	−	0.100483i	0.835560	−	0.549400i	$-0.185143\pi$
$751$	−1.58984	−	2.75368i	−0.0580141	−	0.100483i	−0.893574	+	0.448916i	$0.851810\pi$
$752$		0			0
$753$	30.7170	−	3.78714i	1.11939	−	0.138011i
$754$		0			0
$755$	−10.6481			−0.387523
$756$		0			0
$757$	45.0288			1.63660			0.818299	−	0.574793i	$-0.194917\pi$
$757$	45.0288			1.63660			0.818299	+	0.574793i	$0.194917\pi$
$758$		0			0
$759$	−20.6989	+	2.55200i	−0.751321	+	0.0926317i
$760$		0			0
$761$	−14.5107	−	25.1332i	−0.526011	−	0.911078i	−0.999541	−	0.0303004i	$-0.990354\pi$
$761$	−14.5107	−	25.1332i	−0.526011	−	0.911078i	0.473530	−	0.880778i	$-0.342980\pi$
$762$		0			0
$763$	−11.4556	+	19.8417i	−0.414722	+	0.718319i
$764$		0			0
$765$	−10.0558	−	10.3923i	−0.363569	−	0.375735i
$766$		0			0
$767$	4.05582	−	7.02488i	0.146447	−	0.253654i
$768$		0			0
$769$	−6.80679	−	11.7897i	−0.245459	−	0.425148i	0.716801	−	0.697277i	$-0.245605\pi$
$769$	−6.80679	−	11.7897i	−0.245459	−	0.425148i	−0.962261	+	0.272130i	$0.912272\pi$
$770$		0			0
$771$	11.8990	+	15.7741i	0.428533	+	0.568092i
$772$		0			0
$773$	−17.7523			−0.638505			−0.319253	−	0.947670i	$-0.603432\pi$
$773$	−17.7523			−0.638505			−0.319253	+	0.947670i	$0.603432\pi$
$774$		0			0
$775$	−4.64806			−0.166963
$776$		0			0
$777$	1.31421	−	3.10039i	0.0471470	−	0.111226i
$778$		0			0
$779$	0.114039	+	0.197521i	0.00408587	+	0.00707694i
$780$		0			0
$781$	1.50611	−	2.60866i	0.0538930	−	0.0933453i
$782$		0			0
$783$	−5.77485	+	36.8180i	−0.206376	+	1.31577i
$784$		0			0
$785$	−8.14195	+	14.1023i	−0.290599	+	0.503332i
$786$		0			0
$787$	−27.9344	−	48.3837i	−0.995752	−	1.72469i	−0.577612	−	0.816311i	$-0.696015\pi$
$787$	−27.9344	−	48.3837i	−0.995752	−	1.72469i	−0.418140	−	0.908383i	$-0.637318\pi$
$788$		0			0
$789$	0.321627	−	0.758758i	0.0114502	−	0.0270125i
$790$		0			0
$791$	9.37158			0.333215
$792$		0			0
$793$	−36.9926			−1.31365
$794$		0			0
$795$	−8.52420	−	11.3002i	−0.302322	−	0.400778i
$796$		0			0
$797$	−20.7850	−	36.0007i	−0.736242	−	1.27521i	−0.954176	−	0.299245i	$-0.903265\pi$
$797$	−20.7850	−	36.0007i	−0.736242	−	1.27521i	0.217934	−	0.975964i	$-0.430068\pi$
$798$		0			0
$799$	22.8818	−	39.6324i	0.809500	−	1.40209i
$800$		0			0
$801$	−32.0118	+	8.01541i	−1.13108	+	0.283211i
$802$		0			0
$803$	−2.93676	+	5.08662i	−0.103636	+	0.179503i
$804$		0			0
$805$	6.40405	+	11.0921i	0.225713	+	0.390946i
$806$		0			0
$807$	13.0176	−	1.60496i	0.458240	−	0.0564972i
$808$		0			0
$809$	17.6917			0.622005			0.311003	−	0.950409i	$-0.399335\pi$
$809$	17.6917			0.622005			0.311003	+	0.950409i	$0.399335\pi$
$810$		0			0
$811$	13.5438			0.475589			0.237794	−	0.971316i	$-0.423576\pi$
$811$	13.5438			0.475589			0.237794	+	0.971316i	$0.423576\pi$
$812$		0			0
$813$	33.8589	−	4.17452i	1.18748	−	0.146407i
$814$		0			0
$815$	−7.05822	−	12.2252i	−0.247239	−	0.428230i
$816$		0			0
$817$	1.56193	−	2.70534i	0.0546450	−	0.0946480i
$818$		0			0
$819$	−23.1188	+	5.78872i	−0.807838	+	0.202274i
$820$		0			0
$821$	0.768213	−	1.33058i	0.0268108	−	0.0464377i	−0.852309	−	0.523039i	$-0.824798\pi$
$821$	0.768213	−	1.33058i	0.0268108	−	0.0464377i	0.879119	+	0.476601i	$0.158131\pi$
$822$		0			0
$823$	4.43274	+	7.67772i	0.154515	+	0.267629i	0.932882	−	0.360181i	$-0.117285\pi$
$823$	4.43274	+	7.67772i	0.154515	+	0.267629i	−0.778367	+	0.627809i	$0.783952\pi$
$824$		0			0
$825$	−1.41016	−	1.86940i	−0.0490955	−	0.0650842i
$826$		0			0
$827$	−14.4307			−0.501803			−0.250901	−	0.968013i	$-0.580727\pi$
$827$	−14.4307			−0.501803			−0.250901	+	0.968013i	$0.580727\pi$
$828$		0			0
$829$	−3.30354			−0.114737			−0.0573683	−	0.998353i	$-0.518271\pi$
$829$	−3.30354			−0.114737			−0.0573683	+	0.998353i	$0.518271\pi$
$830$		0			0
$831$	−14.5397	+	34.3010i	−0.504376	+	1.18989i
$832$		0			0
$833$	11.8868	+	20.5886i	0.411853	+	0.713351i
$834$		0			0
$835$	9.30146	−	16.1106i	0.321890	−	0.557530i
$836$		0			0
$837$	−18.7924	−	15.1712i	−0.649561	−	0.524394i
$838$		0			0
$839$	−0.0353272	+	0.0611885i	−0.00121963	+	0.00211246i	−0.866635	−	0.498943i	$-0.833722\pi$
$839$	−0.0353272	+	0.0611885i	−0.00121963	+	0.00211246i	0.865415	+	0.501056i	$0.167055\pi$
$840$		0			0
$841$	−11.2207	−	19.4348i	−0.386919	−	0.670164i
$842$		0			0
$843$	−6.87112	+	16.2099i	−0.236654	+	0.558297i
$844$		0			0
$845$	17.5168			0.602596
$846$		0			0
$847$	−13.1903			−0.453226
$848$		0			0
$849$	−23.4549	−	31.0933i	−0.804968	−	1.06712i
$850$		0			0
$851$	6.02049	+	10.4278i	0.206380	+	0.357460i
$852$		0			0
$853$	−7.62015	+	13.1985i	−0.260909	+	0.451908i	−0.966484	−	0.256728i	$-0.917356\pi$
$853$	−7.62015	+	13.1985i	−0.260909	+	0.451908i	0.705575	+	0.708636i	$0.250689\pi$
$854$		0			0
$855$	1.35194	+	1.39718i	0.0462353	+	0.0477825i
$856$		0			0
$857$	−22.5702	+	39.0927i	−0.770983	+	1.33538i	0.166041	+	0.986119i	$0.446901\pi$
$857$	−22.5702	+	39.0927i	−0.770983	+	1.33538i	−0.937025	+	0.349263i	$0.886432\pi$
$858$		0			0
$859$	−25.5144	−	44.1922i	−0.870539	−	1.50782i	−0.861440	−	0.507860i	$-0.830437\pi$
$859$	−25.5144	−	44.1922i	−0.870539	−	1.50782i	−0.00909955	−	0.999959i	$-0.502897\pi$
$860$		0			0
$861$	−0.870026	+	0.107267i	−0.0296504	+	0.00365565i
$862$		0			0
$863$	−12.6784			−0.431577			−0.215788	−	0.976440i	$-0.569232\pi$
$863$	−12.6784			−0.431577			−0.215788	+	0.976440i	$0.569232\pi$
$864$		0			0
$865$	24.8007			0.843248
$866$		0			0
$867$	−10.7190	+	1.32157i	−0.364038	+	0.0448828i
$868$		0			0
$869$	−8.82032	−	15.2772i	−0.299209	−	0.518245i
$870$		0			0
$871$	34.3347	−	59.4694i	1.16339	−	2.01505i
$872$		0			0
$873$	−14.4865	+	50.7115i	−0.490293	+	1.71632i
$874$		0			0
$875$	−0.719035	+	1.24540i	−0.0243078	+	0.0421024i
$876$		0			0
$877$	16.1747	+	28.0153i	0.546180	+	0.946011i	0.998532	+	0.0541714i	$0.0172517\pi$
$877$	16.1747	+	28.0153i	0.546180	+	0.946011i	−0.452352	+	0.891839i	$0.649415\pi$
$878$		0			0
$879$	−6.25338	−	8.28989i	−0.210921	−	0.279611i
$880$		0			0
$881$	−40.6816			−1.37060			−0.685299	−	0.728261i	$-0.740329\pi$
$881$	−40.6816			−1.37060			−0.685299	+	0.728261i	$0.740329\pi$
$882$		0			0
$883$	−10.3700			−0.348979			−0.174490	−	0.984659i	$-0.555828\pi$
$883$	−10.3700			−0.348979			−0.174490	+	0.984659i	$0.555828\pi$
$884$		0			0
$885$	0.992582	−	2.34163i	0.0333653	−	0.0787129i
$886$		0			0
$887$	5.24532	+	9.08516i	0.176121	+	0.305050i	0.940548	−	0.339659i	$-0.110312\pi$
$887$	5.24532	+	9.08516i	0.176121	+	0.305050i	−0.764428	+	0.644709i	$0.776978\pi$
$888$		0			0
$889$	5.89448	−	10.2095i	0.197694	−	0.342417i
$890$		0			0
$891$	0.400338	−	12.1609i	0.0134118	−	0.407404i
$892$		0			0
$893$	−3.07631	+	5.32832i	−0.102945	+	0.178305i
$894$		0			0
$895$	7.93436	+	13.7427i	0.265216	+	0.459368i
$896$		0			0
$897$	33.2584	−	78.4608i	1.11047	−	2.61973i
$898$		0			0
$899$	33.3371			1.11185
$900$		0			0
$901$	−39.3929			−1.31237
$902$		0			0
$903$	7.23048	+	9.58521i	0.240615	+	0.318976i
$904$		0			0
$905$	−5.75839	−	9.97383i	−0.191415	−	0.331541i
$906$		0			0
$907$	−0.556597	+	0.964053i	−0.0184815	+	0.0320109i	−0.875118	−	0.483909i	$-0.839217\pi$
$907$	−0.556597	+	0.964053i	−0.0184815	+	0.0320109i	0.856637	+	0.515920i	$0.172550\pi$
$908$		0			0
$909$	−2.37003	+	8.29654i	−0.0786088	+	0.275179i
$910$		0			0
$911$	8.61775	−	14.9264i	0.285519	−	0.494533i	−0.687216	−	0.726453i	$-0.741167\pi$
$911$	8.61775	−	14.9264i	0.285519	−	0.494533i	0.972735	+	0.231920i	$0.0745008\pi$
$912$		0			0
$913$	−3.55953	−	6.16528i	−0.117803	−	0.204041i
$914$		0			0
$915$	−11.5114	+	1.41927i	−0.380557	+	0.0469195i
$916$		0			0
$917$	−10.4923			−0.346487
$918$		0			0
$919$	28.4413			0.938193			0.469096	−	0.883147i	$-0.344580\pi$
$919$	28.4413			0.938193			0.469096	+	0.883147i	$0.344580\pi$
$920$		0			0
$921$	41.1792	−	5.07706i	1.35690	−	0.167295i
$922$		0			0
$923$	6.15417	+	10.6593i	0.202567	+	0.350857i
$924$		0			0
$925$	−0.675970	+	1.17081i	−0.0222257	+	0.0384961i
$926$		0			0
$927$	33.1042	+	34.2119i	1.08729	+	1.12367i
$928$		0			0
$929$	29.4610	−	51.0279i	0.966583	−	1.67417i	0.261282	−	0.965263i	$-0.415855\pi$
$929$	29.4610	−	51.0279i	0.966583	−	1.67417i	0.705301	−	0.708908i	$-0.250812\pi$
$930$		0			0
$931$	−1.59810	−	2.76800i	−0.0523757	−	0.0907174i
$932$		0			0
$933$	28.6941	+	38.0387i	0.939401	+	1.24533i
$934$		0			0
$935$	−6.51678			−0.213122
$936$		0			0
$937$	−32.0458			−1.04689			−0.523445	−	0.852059i	$-0.675353\pi$
$937$	−32.0458			−1.04689			−0.523445	+	0.852059i	$0.675353\pi$
$938$		0			0
$939$	2.03292	−	4.79593i	0.0663419	−	0.156509i
$940$		0			0
$941$	−11.1661	−	19.3403i	−0.364006	−	0.630477i	0.624610	−	0.780937i	$-0.285258\pi$
$941$	−11.1661	−	19.3403i	−0.364006	−	0.630477i	−0.988616	+	0.150460i	$0.951925\pi$
$942$		0			0
$943$	1.56726	−	2.71458i	0.0510372	−	0.0883990i
$944$		0			0
$945$	−6.97209	+	2.68833i	−0.226802	+	0.0874514i
$946$		0			0
$947$	−19.0915	+	33.0674i	−0.620389	+	1.07455i	0.369024	+	0.929420i	$0.379692\pi$
$947$	−19.0915	+	33.0674i	−0.620389	+	1.07455i	−0.989413	+	0.145126i	$0.953641\pi$
$948$		0			0
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$		0			0
$951$	7.03031	−	16.5854i	0.227974	−	0.537819i
$952$		0			0
$953$	14.1771			0.459240			0.229620	−	0.973280i	$-0.426252\pi$
$953$	14.1771			0.459240			0.229620	+	0.973280i	$0.426252\pi$
$954$		0			0
$955$	0.228078			0.00738043
$956$		0			0
$957$	10.1140	+	13.4078i	0.326940	+	0.433414i
$958$		0			0
$959$	9.25839	+	16.0360i	0.298969	+	0.517830i
$960$		0			0
$961$	4.69777	−	8.13677i	0.151541	−	0.262476i
$962$		0			0
$963$	0.914396	−	0.228955i	0.0294660	−	0.00737798i
$964$		0			0
$965$	−12.9344	+	22.4030i	−0.416372	+	0.721177i
$966$		0			0
$967$	11.7042	+	20.2723i	0.376382	+	0.651912i	0.990533	−	0.137276i	$-0.0438348\pi$
$967$	11.7042	+	20.2723i	0.376382	+	0.651912i	−0.614151	+	0.789188i	$0.710501\pi$
$968$		0			0
$969$	5.37003	−	0.662080i	0.172510	−	0.0212691i
$970$		0			0
$971$	−32.7300			−1.05036			−0.525178	−	0.850992i	$-0.676001\pi$
$971$	−32.7300			−1.05036			−0.525178	+	0.850992i	$0.676001\pi$
$972$		0			0
$973$	7.77673			0.249311
$974$		0			0
$975$	9.49629	−	1.17081i	0.304125	−	0.0374960i
$976$		0			0
$977$	14.7802	+	25.6000i	0.472860	+	0.819018i	0.999518	−	0.0310599i	$-0.00988828\pi$
$977$	14.7802	+	25.6000i	0.472860	+	0.819018i	−0.526657	+	0.850078i	$0.676555\pi$
$978$		0			0
$979$	−7.43567	+	12.8790i	−0.237645	+	0.411613i
$980$		0			0
$981$	46.3646	−	11.6092i	1.48031	−	0.370653i
$982$		0			0
$983$	−22.8233	+	39.5310i	−0.727949	+	1.26084i	0.229800	+	0.973238i	$0.426193\pi$
$983$	−22.8233	+	39.5310i	−0.727949	+	1.26084i	−0.957749	+	0.287606i	$0.907141\pi$
$984$		0			0
$985$	0.209991	+	0.363716i	0.00669088	+	0.0115889i
$986$		0			0
$987$	−14.2408	−	18.8786i	−0.453291	−	0.600912i
$988$		0			0
$989$	−42.9320			−1.36516
$990$		0			0
$991$	−45.9245			−1.45884			−0.729421	−	0.684066i	$-0.760210\pi$
$991$	−45.9245			−1.45884			−0.729421	+	0.684066i	$0.760210\pi$
$992$		0			0
$993$	−6.24291	+	14.7278i	−0.198113	+	0.467374i
$994$		0			0
$995$	−6.02049	−	10.4278i	−0.190862	−	0.330583i
$996$		0			0
$997$	14.3700	−	24.8896i	0.455103	−	0.788262i	−0.543591	−	0.839350i	$-0.682936\pi$
$997$	14.3700	−	24.8896i	0.455103	−	0.788262i	0.998694	+	0.0510883i	$0.0162690\pi$
$998$		0			0
$999$	−6.55451	+	2.52732i	−0.207376	+	0.0799608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.q.d.241.1	yes	6
3.2	odd	2		1080.2.q.d.721.1		6
4.3	odd	2		720.2.q.j.241.3		6
9.2	odd	6		3240.2.a.q.1.3		3
9.4	even	3	inner	360.2.q.d.121.1	✓	6
9.5	odd	6		1080.2.q.d.361.1		6
9.7	even	3		3240.2.a.r.1.3		3
12.11	even	2		2160.2.q.j.721.3		6
36.7	odd	6		6480.2.a.bx.1.1		3
36.11	even	6		6480.2.a.bu.1.1		3
36.23	even	6		2160.2.q.j.1441.3		6
36.31	odd	6		720.2.q.j.481.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.d.121.1	✓	6	9.4	even	3	inner
360.2.q.d.241.1	yes	6	1.1	even	1	trivial
720.2.q.j.241.3		6	4.3	odd	2
720.2.q.j.481.3		6	36.31	odd	6
1080.2.q.d.361.1		6	9.5	odd	6
1080.2.q.d.721.1		6	3.2	odd	2
2160.2.q.j.721.3		6	12.11	even	2
2160.2.q.j.1441.3		6	36.23	even	6
3240.2.a.q.1.3		3	9.2	odd	6
3240.2.a.r.1.3		3	9.7	even	3
6480.2.a.bu.1.1		3	36.11	even	6
6480.2.a.bx.1.1		3	36.7	odd	6

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71903 + 0.211943i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.719035 + 1.24540i) q^{7} +(2.91016 - 0.728674i) q^{9} +O(q^{10})\)	\(q+(-1.71903 + 0.211943i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.719035 + 1.24540i) q^{7} +(2.91016 - 0.728674i) q^{9} +(0.675970 - 1.17081i) q^{11} +(2.76210 + 4.78410i) q^{13} +(1.04307 + 1.38276i) q^{15} +4.82032 q^{17} -0.648061 q^{19} +(0.972091 - 2.29329i) q^{21} +(4.45323 + 7.71321i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.84823 + 1.86940i) q^{27} +(3.58613 - 6.21136i) q^{29} +(2.32403 + 4.02534i) q^{31} +(-0.913870 + 2.15594i) q^{33} +1.43807 q^{35} +1.35194 q^{37} +(-5.76210 - 7.63862i) q^{39} +(-0.175970 - 0.304788i) q^{41} +(-2.41016 + 4.17452i) q^{43} +(-2.08613 - 2.15594i) q^{45} +(4.74694 - 8.22195i) q^{47} +(2.46598 + 4.27120i) q^{49} +(-8.28630 + 1.02163i) q^{51} -8.17226 q^{53} -1.35194 q^{55} +(1.11404 - 0.137352i) q^{57} +(-0.734191 - 1.27166i) q^{59} +(-3.34823 + 5.79930i) q^{61} +(-1.18501 + 4.14827i) q^{63} +(2.76210 - 4.78410i) q^{65} +(-6.21533 - 10.7653i) q^{67} +(-9.29001 - 12.3155i) q^{69} +2.22808 q^{71} -4.34452 q^{73} +(0.675970 - 1.59470i) q^{75} +(0.972091 + 1.68371i) q^{77} +(6.52420 - 11.3002i) q^{79} +(7.93807 - 4.24111i) q^{81} +(2.63290 - 4.56032i) q^{83} +(-2.41016 - 4.17452i) q^{85} +(-4.84823 + 11.4376i) q^{87} -11.0000 q^{89} -7.94418 q^{91} +(-4.84823 - 6.42714i) q^{93} +(0.324030 + 0.561237i) q^{95} +(-8.79001 + 15.2247i) q^{97} +(1.11404 - 3.89982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9}+O(q^{10}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9} + 2 q^{11} - q^{15} + 4 q^{17} - 8 q^{19} + 12 q^{21} + 7 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 16 q^{31} - 20 q^{33} - 10 q^{35} + 4 q^{37} - 18 q^{39} + q^{41} - 2 q^{43} + 2 q^{45} + 13 q^{47} - 10 q^{49} - 20 q^{53} - 4 q^{55} - 14 q^{57} + 6 q^{59} + 11 q^{61} + 27 q^{63} - q^{67} - 33 q^{69} - 28 q^{71} + 32 q^{73} + 2 q^{75} + 12 q^{77} + 6 q^{79} + 29 q^{81} + 21 q^{83} - 2 q^{85} + 2 q^{87} - 66 q^{89} - 60 q^{91} + 2 q^{93} + 4 q^{95} - 30 q^{97} - 14 q^{99}+O(q^{100}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9 + 2 * q^11 - q^15 + 4 * q^17 - 8 * q^19 + 12 * q^21 + 7 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 16 * q^31 - 20 * q^33 - 10 * q^35 + 4 * q^37 - 18 * q^39 + q^41 - 2 * q^43 + 2 * q^45 + 13 * q^47 - 10 * q^49 - 20 * q^53 - 4 * q^55 - 14 * q^57 + 6 * q^59 + 11 * q^61 + 27 * q^63 - q^67 - 33 * q^69 - 28 * q^71 + 32 * q^73 + 2 * q^75 + 12 * q^77 + 6 * q^79 + 29 * q^81 + 21 * q^83 - 2 * q^85 + 2 * q^87 - 66 * q^89 - 60 * q^91 + 2 * q^93 + 4 * q^95 - 30 * q^97 - 14 * q^99

Introduction

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