LMFDB - Embedded newform 592.2.i.f.433.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(417,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("592.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.i (of order $3$, degree $2$, not 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.27870912.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} + 2x^{3} + 38x^{2} - 12x + 4 $ x^6 - x^5 + 7x^4 + 2x^3 + 38x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 148)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.3
Root			$1.42789 + 2.47317i$ of defining polynomial
Character	$\chi$	$=$	592.433
Dual form			592.2.i.f.417.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42789 - 2.47317i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.07772 - 3.59871i) q^{7} +(-2.57772 - 4.46474i) q^{9} +1.29966 q^{11} +(-1.77805 + 3.07968i) q^{13} +(-1.42789 - 2.47317i) q^{15} +(1.79966 + 3.11711i) q^{17} +(-2.42789 + 4.20522i) q^{19} +(-5.93349 - 10.2771i) q^{21} -5.01121 q^{23} +(2.00000 + 3.46410i) q^{25} -6.15544 q^{27} +8.86698 q^{29} -1.29966 q^{31} +(1.85577 - 3.21429i) q^{33} +(-2.07772 - 3.59871i) q^{35} +(1.27805 - 5.94698i) q^{37} +(5.07772 + 8.79487i) q^{39} +(-5.35577 + 9.27647i) q^{41} +10.3109 q^{43} -5.15544 q^{45} -8.72275 q^{47} +(-5.13383 - 8.89205i) q^{49} +10.2789 q^{51} +(-5.07772 - 8.79487i) q^{53} +(0.649832 - 1.12554i) q^{55} +(6.93349 + 12.0092i) q^{57} +(-4.63383 - 8.02602i) q^{59} +(-1.35577 + 2.34827i) q^{61} -21.4231 q^{63} +(1.77805 + 3.07968i) q^{65} +(3.98399 - 6.90048i) q^{67} +(-7.15544 + 12.3936i) q^{69} +(-5.63383 + 9.75807i) q^{71} +2.28845 q^{73} +11.4231 q^{75} +(2.70034 - 4.67712i) q^{77} +(1.28366 - 2.22336i) q^{79} +(-1.05611 + 1.82923i) q^{81} +(4.98399 + 8.63253i) q^{83} +3.59933 q^{85} +(12.6610 - 21.9296i) q^{87} +(2.21155 + 3.83051i) q^{89} +(7.38859 + 12.7974i) q^{91} +(-1.85577 + 3.21429i) q^{93} +(2.42789 + 4.20522i) q^{95} +9.97920 q^{97} +(-3.35017 - 5.80266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 3 q^{5} + q^{7} - 4 q^{9} - 7 q^{13} - q^{15} + 3 q^{17} - 7 q^{19} - 9 q^{21} + 8 q^{23} + 12 q^{25} - 14 q^{27} - 4 q^{33} - q^{35} + 4 q^{37} + 19 q^{39} - 17 q^{41} + 16 q^{43} - 8 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 6 * q + q^3 + 3 * q^5 + q^7 - 4 * q^9 - 7 * q^13 - q^15 + 3 * q^17 - 7 * q^19 - 9 * q^21 + 8 * q^23 + 12 * q^25 - 14 * q^27 - 4 * q^33 - q^35 + 4 * q^37 + 19 * q^39 - 17 * q^41 + 16 * q^43 - 8 * q^45 + 16 * q^47 - 12 * q^49 - 14 * q^51 - 19 * q^53 + 15 * q^57 - 9 * q^59 + 7 * q^61 - 68 * q^63 + 7 * q^65 + 9 * q^67 - 20 * q^69 - 15 * q^71 + 44 * q^73 + 8 * q^75 + 24 * q^77 - 15 * q^79 + q^81 + 15 * q^83 + 6 * q^85 + 34 * q^87 - 17 * q^89 - 13 * q^91 + 4 * q^93 + 7 * q^95 - 8 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.42789	−	2.47317i	0.824391	−	1.42789i	−0.0779937	−	0.996954i	$-0.524851\pi$
$3$	1.42789	−	2.47317i	0.824391	−	1.42789i	0.902384	−	0.430932i	$-0.141815\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	2.07772	−	3.59871i	0.785304	−	1.36019i	−0.143514	−	0.989648i	$-0.545840\pi$
$7$	2.07772	−	3.59871i	0.785304	−	1.36019i	0.928817	−	0.370538i	$-0.120827\pi$
$8$		0			0
$9$	−2.57772	−	4.46474i	−0.859239	−	1.48825i
$10$		0			0
$11$	1.29966			0.391863			0.195932	−	0.980618i	$-0.437227\pi$
$11$	1.29966			0.391863			0.195932	+	0.980618i	$0.437227\pi$
$12$		0			0
$13$	−1.77805	+	3.07968i	−0.493144	+	0.854150i	−0.999969	−	0.00789918i	$-0.997486\pi$
$13$	−1.77805	+	3.07968i	−0.493144	+	0.854150i	0.506825	+	0.862049i	$0.330819\pi$
$14$		0			0
$15$	−1.42789	−	2.47317i	−0.368679	−	0.638570i
$16$		0			0
$17$	1.79966	+	3.11711i	0.436483	+	0.756010i	0.997415	−	0.0718513i	$-0.0228907\pi$
$17$	1.79966	+	3.11711i	0.436483	+	0.756010i	−0.560933	+	0.827861i	$0.689557\pi$
$18$		0			0
$19$	−2.42789	+	4.20522i	−0.556995	+	0.964744i	0.440750	+	0.897630i	$0.354713\pi$
$19$	−2.42789	+	4.20522i	−0.556995	+	0.964744i	−0.997745	+	0.0671143i	$0.978621\pi$
$20$		0			0
$21$	−5.93349	−	10.2771i	−1.29479	−	2.24265i
$22$		0			0
$23$	−5.01121			−1.04491			−0.522455	−	0.852667i	$-0.674984\pi$
$23$	−5.01121			−1.04491			−0.522455	+	0.852667i	$0.674984\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	−6.15544			−1.18461
$28$		0			0
$29$	8.86698			1.64656			0.823279	−	0.567638i	$-0.192142\pi$
$29$	8.86698			1.64656			0.823279	+	0.567638i	$0.192142\pi$
$30$		0			0
$31$	−1.29966			−0.233427			−0.116713	−	0.993166i	$-0.537236\pi$
$31$	−1.29966			−0.233427			−0.116713	+	0.993166i	$0.537236\pi$
$32$		0			0
$33$	1.85577	−	3.21429i	0.323049	−	0.559536i
$34$		0			0
$35$	−2.07772	−	3.59871i	−0.351198	−	0.608294i
$36$		0			0
$37$	1.27805	−	5.94698i	0.210111	−	0.977678i
$37$	1.27805	−	5.94698i	0.210111	−	0.977678i
$38$		0			0
$39$	5.07772	+	8.79487i	0.813086	+	1.40831i
$40$		0			0
$41$	−5.35577	+	9.27647i	−0.836431	+	1.44874i	0.0564287	+	0.998407i	$0.482029\pi$
$41$	−5.35577	+	9.27647i	−0.836431	+	1.44874i	−0.892860	+	0.450335i	$0.851305\pi$
$42$		0			0
$43$	10.3109			1.57239			0.786197	−	0.617976i	$-0.212047\pi$
$43$	10.3109			1.57239			0.786197	+	0.617976i	$0.212047\pi$
$44$		0			0
$45$	−5.15544			−0.768527
$46$		0			0
$47$	−8.72275			−1.27234			−0.636172	−	0.771547i	$-0.719483\pi$
$47$	−8.72275			−1.27234			−0.636172	+	0.771547i	$0.719483\pi$
$48$		0			0
$49$	−5.13383	−	8.89205i	−0.733404	−	1.27029i
$50$		0			0
$51$	10.2789			1.43933
$52$		0			0
$53$	−5.07772	−	8.79487i	−0.697478	−	1.20807i	−0.969338	−	0.245731i	$-0.920972\pi$
$53$	−5.07772	−	8.79487i	−0.697478	−	1.20807i	0.271860	−	0.962337i	$-0.412361\pi$
$54$		0			0
$55$	0.649832	−	1.12554i	0.0876233	−	0.151768i
$56$		0			0
$57$	6.93349	+	12.0092i	0.918363	+	1.59065i
$58$		0			0
$59$	−4.63383	−	8.02602i	−0.603273	−	1.04490i	−0.992322	−	0.123682i	$-0.960530\pi$
$59$	−4.63383	−	8.02602i	−0.603273	−	1.04490i	0.389049	−	0.921217i	$-0.372804\pi$
$60$		0			0
$61$	−1.35577	+	2.34827i	−0.173589	+	0.300665i	−0.939672	−	0.342077i	$-0.888870\pi$
$61$	−1.35577	+	2.34827i	−0.173589	+	0.300665i	0.766083	+	0.642741i	$0.222203\pi$
$62$		0			0
$63$	−21.4231			−2.69906
$64$		0			0
$65$	1.77805	+	3.07968i	0.220540	+	0.381987i
$66$		0			0
$67$	3.98399	−	6.90048i	0.486722	−	0.843028i	−0.513161	−	0.858292i	$-0.671526\pi$
$67$	3.98399	−	6.90048i	0.486722	−	0.843028i	0.999883	+	0.0152644i	$0.00485899\pi$
$68$		0			0
$69$	−7.15544	+	12.3936i	−0.861413	+	1.49201i
$70$		0			0
$71$	−5.63383	+	9.75807i	−0.668612	+	1.15807i	0.309680	+	0.950841i	$0.399778\pi$
$71$	−5.63383	+	9.75807i	−0.668612	+	1.15807i	−0.978292	+	0.207230i	$0.933555\pi$
$72$		0			0
$73$	2.28845			0.267843			0.133922	−	0.990992i	$-0.457243\pi$
$73$	2.28845			0.267843			0.133922	+	0.990992i	$0.457243\pi$
$74$		0			0
$75$	11.4231			1.31902
$76$		0			0
$77$	2.70034	−	4.67712i	0.307732	−	0.533007i
$78$		0			0
$79$	1.28366	−	2.22336i	0.144423	−	0.250148i	−0.784735	−	0.619832i	$-0.787201\pi$
$79$	1.28366	−	2.22336i	0.144423	−	0.250148i	0.929157	+	0.369684i	$0.120534\pi$
$80$		0			0
$81$	−1.05611	+	1.82923i	−0.117345	+	0.203248i
$82$		0			0
$83$	4.98399	+	8.63253i	0.547064	+	0.947543i	0.998474	+	0.0552265i	$0.0175881\pi$
$83$	4.98399	+	8.63253i	0.547064	+	0.947543i	−0.451409	+	0.892317i	$0.649079\pi$
$84$		0			0
$85$	3.59933			0.390402
$86$		0			0
$87$	12.6610	−	21.9296i	1.35741	−	2.35110i
$88$		0			0
$89$	2.21155	+	3.83051i	0.234423	+	0.406033i	0.959105	−	0.283051i	$-0.0913465\pi$
$89$	2.21155	+	3.83051i	0.234423	+	0.406033i	−0.724682	+	0.689084i	$0.758013\pi$
$90$		0			0
$91$	7.38859	+	12.7974i	0.774535	+	1.34153i
$92$		0			0
$93$	−1.85577	+	3.21429i	−0.192435	+	0.333307i
$94$		0			0
$95$	2.42789	+	4.20522i	0.249096	+	0.431447i
$96$		0			0
$97$	9.97920			1.01323			0.506617	−	0.862171i	$-0.330896\pi$
$97$	9.97920			1.01323			0.506617	+	0.862171i	$0.330896\pi$
$98$		0			0
$99$	−3.35017	−	5.80266i	−0.336705	−	0.583189i
$100$		0			0
$101$	2.84456			0.283045			0.141522	−	0.989935i	$-0.454800\pi$
$101$	2.84456			0.283045			0.141522	+	0.989935i	$0.454800\pi$
$102$		0			0
$103$	6.88778			0.678673			0.339337	−	0.940665i	$-0.389797\pi$
$103$	6.88778			0.678673			0.339337	+	0.940665i	$0.389797\pi$
$104$		0			0
$105$	−11.8670			−1.15810
$106$		0			0
$107$	−1.63383	+	2.82987i	−0.157948	+	0.273574i	−0.934129	−	0.356937i	$-0.883821\pi$
$107$	−1.63383	+	2.82987i	−0.157948	+	0.273574i	0.776181	+	0.630511i	$0.217155\pi$
$108$		0			0
$109$	−6.65544	−	11.5276i	−0.637475	−	1.10414i	−0.985985	−	0.166834i	$-0.946646\pi$
$109$	−6.65544	−	11.5276i	−0.637475	−	1.10414i	0.348510	−	0.937305i	$-0.386688\pi$
$110$		0			0
$111$	−12.8830	−	11.6525i	−1.22280	−	1.10600i
$112$		0			0
$113$	1.93349	+	3.34890i	0.181888	+	0.315038i	0.942523	−	0.334140i	$-0.108446\pi$
$113$	1.93349	+	3.34890i	0.181888	+	0.315038i	−0.760636	+	0.649179i	$0.775113\pi$
$114$		0			0
$115$	−2.50560	+	4.33983i	−0.233649	+	0.404692i
$116$		0			0
$117$	18.3333			1.69491
$118$		0			0
$119$	14.9568			1.37109
$120$		0			0
$121$	−9.31087			−0.846443
$122$		0			0
$123$	15.2949	+	26.4915i	1.37909	+	2.38866i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−2.02721	−	3.51124i	−0.179886	−	0.311572i	0.761955	−	0.647630i	$-0.224240\pi$
$127$	−2.02721	−	3.51124i	−0.179886	−	0.311572i	−0.941841	+	0.336058i	$0.890906\pi$
$128$		0			0
$129$	14.7228	−	25.5006i	1.29627	−	2.24520i
$130$		0			0
$131$	5.58332	+	9.67060i	0.487817	+	0.844924i	0.999902	−	0.0140108i	$-0.00445993\pi$
$131$	5.58332	+	9.67060i	0.487817	+	0.844924i	−0.512085	+	0.858935i	$0.671127\pi$
$132$		0			0
$133$	10.0889	+	17.4745i	0.874821	+	1.51523i
$134$		0			0
$135$	−3.07772	+	5.33076i	−0.264888	+	0.458799i
$136$		0			0
$137$	−1.15544			−0.0987156			−0.0493578	−	0.998781i	$-0.515717\pi$
$137$	−1.15544			−0.0987156			−0.0493578	+	0.998781i	$0.515717\pi$
$138$		0			0
$139$	−8.72755	−	15.1166i	−0.740261	−	1.28217i	−0.952376	−	0.304925i	$-0.901369\pi$
$139$	−8.72755	−	15.1166i	−0.740261	−	1.28217i	0.212115	−	0.977245i	$-0.431965\pi$
$140$		0			0
$141$	−12.4551	+	21.5729i	−1.04891	+	1.81676i
$142$		0			0
$143$	−2.31087	+	4.00255i	−0.193245	+	0.334710i
$144$		0			0
$145$	4.43349	−	7.67903i	0.368181	−	0.637709i
$146$		0			0
$147$	−29.3221			−2.41844
$148$		0			0
$149$	1.15544			0.0946571			0.0473285	−	0.998879i	$-0.484929\pi$
$149$	1.15544			0.0946571			0.0473285	+	0.998879i	$0.484929\pi$
$150$		0			0
$151$	−3.17144	+	5.49310i	−0.258088	+	0.447022i	−0.965730	−	0.259550i	$-0.916426\pi$
$151$	−3.17144	+	5.49310i	−0.258088	+	0.447022i	0.707641	+	0.706572i	$0.249759\pi$
$152$		0			0
$153$	9.27805	−	16.0701i	0.750086	−	1.29919i
$154$		0			0
$155$	−0.649832	+	1.12554i	−0.0521958	+	0.0904057i
$156$		0			0
$157$	0.355773	+	0.616216i	0.0283937	+	0.0491794i	0.879873	−	0.475209i	$-0.157627\pi$
$157$	0.355773	+	0.616216i	0.0283937	+	0.0491794i	−0.851479	+	0.524388i	$0.824294\pi$
$158$		0			0
$159$	−29.0016			−2.29998
$160$		0			0
$161$	−10.4119	+	18.0339i	−0.820571	+	1.42127i
$162$		0			0
$163$	1.63383	+	2.82987i	0.127971	+	0.221653i	0.922890	−	0.385063i	$-0.125820\pi$
$163$	1.63383	+	2.82987i	0.127971	+	0.221653i	−0.794919	+	0.606715i	$0.792487\pi$
$164$		0			0
$165$	−1.85577	−	3.21429i	−0.144472	−	0.250232i
$166$		0			0
$167$	−10.7893	+	18.6876i	−0.834898	+	1.44609i	0.0592150	+	0.998245i	$0.481140\pi$
$167$	−10.7893	+	18.6876i	−0.834898	+	1.44609i	−0.894113	+	0.447841i	$0.852193\pi$
$168$		0			0
$169$	0.177047	+	0.306654i	0.0136190	+	0.0235887i
$170$		0			0
$171$	25.0336			1.91437
$172$		0			0
$173$	5.79966	+	10.0453i	0.440940	+	0.763731i	0.997760	−	0.0669027i	$-0.0213117\pi$
$173$	5.79966	+	10.0453i	0.440940	+	0.763731i	−0.556819	+	0.830634i	$0.687978\pi$
$174$		0			0
$175$	16.6217			1.25649
$176$		0			0
$177$	−26.4663			−1.98933
$178$		0			0
$179$	1.19866			0.0895918			0.0447959	−	0.998996i	$-0.485736\pi$
$179$	1.19866			0.0895918			0.0447959	+	0.998996i	$0.485736\pi$
$180$		0			0
$181$	1.65544	−	2.86730i	0.123048	−	0.213125i	−0.797920	−	0.602763i	$-0.794067\pi$
$181$	1.65544	−	2.86730i	0.123048	−	0.213125i	0.920968	+	0.389638i	$0.127400\pi$
$182$		0			0
$183$	3.87178	+	6.70612i	0.286210	+	0.495730i
$184$		0			0
$185$	−4.51121	−	4.08032i	−0.331671	−	0.299991i
$186$		0			0
$187$	2.33896	+	4.05120i	0.171042	+	0.296253i
$188$		0			0
$189$	−12.7893	+	22.1517i	−0.930282	+	1.61130i
$190$		0			0
$191$	−5.58812			−0.404342			−0.202171	−	0.979350i	$-0.564800\pi$
$191$	−5.58812			−0.404342			−0.202171	+	0.979350i	$0.564800\pi$
$192$		0			0
$193$	2.55611			0.183993			0.0919964	−	0.995759i	$-0.470675\pi$
$193$	2.55611			0.183993			0.0919964	+	0.995759i	$0.470675\pi$
$194$		0			0
$195$	10.1554			0.727246
$196$		0			0
$197$	6.76765	+	11.7219i	0.482175	+	0.835152i	0.999791	−	0.0204613i	$-0.00651348\pi$
$197$	6.76765	+	11.7219i	0.482175	+	0.835152i	−0.517615	+	0.855613i	$0.673180\pi$
$198$		0			0
$199$	−1.68913			−0.119739			−0.0598695	−	0.998206i	$-0.519068\pi$
$199$	−1.68913			−0.119739			−0.0598695	+	0.998206i	$0.519068\pi$
$200$		0			0
$201$	−11.3774	−	19.7062i	−0.802499	−	1.38997i
$202$		0			0
$203$	18.4231	−	31.9097i	1.29305	−	2.23962i
$204$		0			0
$205$	5.35577	+	9.27647i	0.374063	+	0.647897i
$206$		0			0
$207$	12.9175	+	22.3737i	0.897827	+	1.55508i
$208$		0			0
$209$	−3.15544	+	5.46538i	−0.218266	+	0.378048i
$210$		0			0
$211$	−10.8878			−0.749546			−0.374773	−	0.927117i	$-0.622279\pi$
$211$	−10.8878			−0.749546			−0.374773	+	0.927117i	$0.622279\pi$
$212$		0			0
$213$	16.0889	+	27.8668i	1.10240	+	1.90940i
$214$		0			0
$215$	5.15544	−	8.92948i	0.351598	−	0.608985i
$216$		0			0
$217$	−2.70034	+	4.67712i	−0.183311	+	0.317504i
$218$		0			0
$219$	3.26765	−	5.65974i	0.220808	−	0.382450i
$220$		0			0
$221$	−12.7996			−0.860994
$222$		0			0
$223$	0.187447			0.0125524			0.00627620	−	0.999980i	$-0.498002\pi$
$223$	0.187447			0.0125524			0.00627620	+	0.999980i	$0.498002\pi$
$224$		0			0
$225$	10.3109	−	17.8590i	0.687392	−	1.19060i
$226$		0			0
$227$	−9.72755	+	16.8486i	−0.645640	+	1.11828i	0.338513	+	0.940962i	$0.390076\pi$
$227$	−9.72755	+	16.8486i	−0.645640	+	1.11828i	−0.984153	+	0.177320i	$0.943257\pi$
$228$		0			0
$229$	8.62343	−	14.9362i	0.569852	−	0.987013i	−0.426728	−	0.904380i	$-0.640334\pi$
$229$	8.62343	−	14.9362i	0.569852	−	0.987013i	0.996580	−	0.0826327i	$-0.0263328\pi$
$230$		0			0
$231$	−7.71155	−	13.3568i	−0.507382	−	0.878812i
$232$		0			0
$233$	−18.6009			−1.21859			−0.609294	−	0.792944i	$-0.708547\pi$
$233$	−18.6009			−1.21859			−0.609294	+	0.792944i	$0.708547\pi$
$234$		0			0
$235$	−4.36138	+	7.55413i	−0.284505	+	0.492777i
$236$		0			0
$237$	−3.66584	−	6.34942i	−0.238122	−	0.412439i
$238$		0			0
$239$	−6.67705	−	11.5650i	−0.431902	−	0.748077i	0.565135	−	0.824999i	$-0.308824\pi$
$239$	−6.67705	−	11.5650i	−0.431902	−	0.748077i	−0.997037	+	0.0769219i	$0.975491\pi$
$240$		0			0
$241$	−8.08893	+	14.0104i	−0.521054	+	0.902491i	0.478647	+	0.878008i	$0.341128\pi$
$241$	−8.08893	+	14.0104i	−0.521054	+	0.902491i	−0.999700	+	0.0244837i	$0.992206\pi$
$242$		0			0
$243$	−6.21715	−	10.7684i	−0.398830	−	0.690794i
$244$		0			0
$245$	−10.2677			−0.655976
$246$		0			0
$247$	−8.63383	−	14.9542i	−0.549357	−	0.951515i
$248$		0			0
$249$	28.4663			1.80398
$250$		0			0
$251$	−11.5095			−0.726475			−0.363238	−	0.931697i	$-0.618329\pi$
$251$	−11.5095			−0.726475			−0.363238	+	0.931697i	$0.618329\pi$
$252$		0			0
$253$	−6.51289			−0.409462
$254$		0			0
$255$	5.13943	−	8.90176i	0.321844	−	0.557450i
$256$		0			0
$257$	−0.756444	−	1.31020i	−0.0471857	−	0.0817280i	0.841468	−	0.540307i	$-0.181692\pi$
$257$	−0.756444	−	1.31020i	−0.0471857	−	0.0817280i	−0.888654	+	0.458579i	$0.848359\pi$
$258$		0			0
$259$	−18.7460	−	16.9555i	−1.16482	−	1.05356i
$260$		0			0
$261$	−22.8566	−	39.5888i	−1.41479	−	2.45048i
$262$		0			0
$263$	7.52161	−	13.0278i	0.463802	−	0.803329i	−0.535344	−	0.844634i	$-0.679818\pi$
$263$	7.52161	−	13.0278i	0.463802	−	0.803329i	0.999147	+	0.0413047i	$0.0131515\pi$
$264$		0			0
$265$	−10.1554			−0.623844
$266$		0			0
$267$	12.6313			0.773025
$268$		0			0
$269$	0.887783			0.0541291			0.0270645	−	0.999634i	$-0.491384\pi$
$269$	0.887783			0.0541291			0.0270645	+	0.999634i	$0.491384\pi$
$270$		0			0
$271$	−9.59453	−	16.6182i	−0.582826	−	1.00948i	−0.995143	−	0.0984440i	$-0.968613\pi$
$271$	−9.59453	−	16.6182i	−0.582826	−	1.00948i	0.412316	−	0.911041i	$-0.364720\pi$
$272$		0			0
$273$	42.2003			2.55408
$274$		0			0
$275$	2.59933	+	4.50217i	0.156745	+	0.271491i
$276$		0			0
$277$	1.79966	−	3.11711i	0.108131	−	0.187289i	−0.806882	−	0.590713i	$-0.798847\pi$
$277$	1.79966	−	3.11711i	0.108131	−	0.187289i	0.915013	+	0.403424i	$0.132180\pi$
$278$		0			0
$279$	3.35017	+	5.80266i	0.200569	+	0.347396i
$280$		0			0
$281$	−14.2660	−	24.7094i	−0.851037	−	1.47404i	−0.880274	−	0.474466i	$-0.842641\pi$
$281$	−14.2660	−	24.7094i	−0.851037	−	1.47404i	0.0292371	−	0.999573i	$-0.490692\pi$
$282$		0			0
$283$	4.07772	−	7.06282i	0.242395	−	0.419841i	−0.719001	−	0.695009i	$-0.755400\pi$
$283$	4.07772	−	7.06282i	0.242395	−	0.419841i	0.961396	+	0.275168i	$0.0887336\pi$
$284$		0			0
$285$	13.8670			0.821409
$286$		0			0
$287$	22.2556	+	38.5478i	1.31370	+	2.27540i
$288$		0			0
$289$	2.02242	−	3.50293i	0.118966	−	0.206055i
$290$		0			0
$291$	14.2492	−	24.6803i	0.835301	−	1.44678i
$292$		0			0
$293$	3.65544	−	6.33140i	0.213553	−	0.369884i	−0.739271	−	0.673408i	$-0.764830\pi$
$293$	3.65544	−	6.33140i	0.213553	−	0.369884i	0.952824	+	0.303524i	$0.0981631\pi$
$294$		0			0
$295$	−9.26765			−0.539584
$296$		0			0
$297$	−8.00000			−0.464207
$298$		0			0
$299$	8.91020	−	15.4329i	0.515290	−	0.892509i
$300$		0			0
$301$	21.4231	−	37.1059i	1.23481	−	2.13875i
$302$		0			0
$303$	4.06171	−	7.03509i	0.233339	−	0.404156i
$304$		0			0
$305$	1.35577	+	2.34827i	0.0776313	+	0.134461i
$306$		0			0
$307$	17.1122			0.976646			0.488323	−	0.872663i	$-0.337609\pi$
$307$	17.1122			0.976646			0.488323	+	0.872663i	$0.337609\pi$
$308$		0			0
$309$	9.83497	−	17.0347i	0.559492	−	0.969068i
$310$		0			0
$311$	15.0569	+	26.0793i	0.853799	+	1.47882i	0.877754	+	0.479111i	$0.159041\pi$
$311$	15.0569	+	26.0793i	0.853799	+	1.47882i	−0.0239549	+	0.999713i	$0.507626\pi$
$312$		0			0
$313$	15.7789	+	27.3298i	0.891874	+	1.54477i	0.837626	+	0.546244i	$0.183943\pi$
$313$	15.7789	+	27.3298i	0.891874	+	1.54477i	0.0542477	+	0.998528i	$0.482724\pi$
$314$		0			0
$315$	−10.7115	+	18.5529i	−0.603527	+	1.04534i
$316$		0			0
$317$	−15.1105	−	26.1722i	−0.848692	−	1.46998i	−0.882376	−	0.470546i	$-0.844057\pi$
$317$	−15.1105	−	26.1722i	−0.848692	−	1.46998i	0.0336833	−	0.999433i	$-0.489276\pi$
$318$		0			0
$319$	11.5241			0.645226
$320$		0			0
$321$	4.66584	+	8.08147i	0.260422	+	0.451064i
$322$		0			0
$323$	−17.4775			−0.972475
$324$		0			0
$325$	−14.2244			−0.789030
$326$		0			0
$327$	−38.0128			−2.10211
$328$		0			0
$329$	−18.1234	+	31.3907i	−0.999177	+	1.73063i
$330$		0			0
$331$	−1.23315	−	2.13589i	−0.0677803	−	0.117399i	0.830144	−	0.557550i	$-0.188258\pi$
$331$	−1.23315	−	2.13589i	−0.0677803	−	0.117399i	−0.897924	+	0.440151i	$0.854925\pi$
$332$		0			0
$333$	−29.8462	+	9.62346i	−1.63556	+	0.527362i
$334$		0			0
$335$	−3.98399	−	6.90048i	−0.217669	−	0.377014i
$336$		0			0
$337$	11.2228	−	19.4384i	0.611342	−	1.05888i	−0.379672	−	0.925121i	$-0.623963\pi$
$337$	11.2228	−	19.4384i	0.611342	−	1.05888i	0.991014	−	0.133755i	$-0.0427035\pi$
$338$		0			0
$339$	11.0432			0.599785
$340$		0			0
$341$	−1.68913			−0.0914713
$342$		0			0
$343$	−13.5785			−0.733172
$344$		0			0
$345$	7.15544	+	12.3936i	0.385236	+	0.667248i
$346$		0			0
$347$	−32.4343			−1.74116			−0.870582	−	0.492023i	$-0.836258\pi$
$347$	−32.4343			−1.74116			−0.870582	+	0.492023i	$0.836258\pi$
$348$		0			0
$349$	5.36698	+	9.29588i	0.287288	+	0.497597i	0.973161	−	0.230123i	$-0.0739130\pi$
$349$	5.36698	+	9.29588i	0.287288	+	0.497597i	−0.685873	+	0.727721i	$0.740580\pi$
$350$		0			0
$351$	10.9447	−	18.9568i	0.584185	−	1.01184i
$352$		0			0
$353$	−12.0785	−	20.9206i	−0.642875	−	1.11349i	−0.984788	−	0.173761i	$-0.944408\pi$
$353$	−12.0785	−	20.9206i	−0.642875	−	1.11349i	0.341913	−	0.939732i	$-0.388925\pi$
$354$		0			0
$355$	5.63383	+	9.75807i	0.299012	+	0.517905i
$356$		0			0
$357$	21.3566	−	36.9907i	1.13031	−	1.95775i
$358$		0			0
$359$	2.84618			0.150216			0.0751078	−	0.997175i	$-0.476070\pi$
$359$	2.84618			0.150216			0.0751078	+	0.997175i	$0.476070\pi$
$360$		0			0
$361$	−2.28926	−	3.96512i	−0.120488	−	0.208691i
$362$		0			0
$363$	−13.2949	+	23.0274i	−0.697800	+	1.20862i
$364$		0			0
$365$	1.14423	−	1.98186i	0.0598916	−	0.103735i
$366$		0			0
$367$	1.23315	−	2.13589i	0.0643702	−	0.111492i	−0.832044	−	0.554709i	$-0.812829\pi$
$367$	1.23315	−	2.13589i	0.0643702	−	0.111492i	0.896414	+	0.443217i	$0.146163\pi$
$368$		0			0
$369$	55.2227			2.87478
$370$		0			0
$371$	−42.2003			−2.19093
$372$		0			0
$373$	7.61222	−	13.1847i	0.394146	−	0.682680i	−0.598846	−	0.800864i	$-0.704374\pi$
$373$	7.61222	−	13.1847i	0.394146	−	0.682680i	0.992992	+	0.118184i	$0.0377072\pi$
$374$		0			0
$375$	12.8510	−	22.2585i	0.663622	−	1.14943i
$376$		0			0
$377$	−15.7660	+	27.3075i	−0.811989	+	1.40641i
$378$		0			0
$379$	15.9447	+	27.6170i	0.819024	+	1.41859i	0.906402	+	0.422416i	$0.138818\pi$
$379$	15.9447	+	27.6170i	0.819024	+	1.41859i	−0.0873777	+	0.996175i	$0.527849\pi$
$380$		0			0
$381$	−11.5785			−0.593186
$382$		0			0
$383$	−3.94470	+	6.83242i	−0.201565	+	0.349120i	−0.949033	−	0.315177i	$-0.897936\pi$
$383$	−3.94470	+	6.83242i	−0.201565	+	0.349120i	0.747468	+	0.664298i	$0.231269\pi$
$384$		0			0
$385$	−2.70034	−	4.67712i	−0.137622	−	0.238368i
$386$		0			0
$387$	−26.5785	−	46.0354i	−1.35106	−	2.34011i
$388$		0			0
$389$	−18.1795	+	31.4879i	−0.921739	+	1.59650i	−0.125015	+	0.992155i	$0.539898\pi$
$389$	−18.1795	+	31.4879i	−0.921739	+	1.59650i	−0.796724	+	0.604344i	$0.793435\pi$
$390$		0			0
$391$	−9.01849	−	15.6205i	−0.456085	−	0.789962i
$392$		0			0
$393$	31.8894			1.60861
$394$		0			0
$395$	−1.28366	−	2.22336i	−0.0645879	−	0.111869i
$396$		0			0
$397$	5.73235			0.287698			0.143849	−	0.989600i	$-0.454052\pi$
$397$	5.73235			0.287698			0.143849	+	0.989600i	$0.454052\pi$
$398$		0			0
$399$	57.6234			2.88478
$400$		0			0
$401$	−13.7115			−0.684722			−0.342361	−	0.939569i	$-0.611227\pi$
$401$	−13.7115			−0.684722			−0.342361	+	0.939569i	$0.611227\pi$
$402$		0			0
$403$	2.31087	−	4.00255i	0.115113	−	0.199381i
$404$		0			0
$405$	1.05611	+	1.82923i	0.0524784	+	0.0908953i
$406$		0			0
$407$	1.66104	−	7.72908i	0.0823348	−	0.383116i
$408$		0			0
$409$	3.46799	+	6.00673i	0.171481	+	0.297014i	0.938938	−	0.344087i	$-0.111811\pi$
$409$	3.46799	+	6.00673i	0.171481	+	0.297014i	−0.767457	+	0.641101i	$0.778478\pi$
$410$		0			0
$411$	−1.64983	+	2.85759i	−0.0813802	+	0.140955i
$412$		0			0
$413$	−38.5111			−1.89501
$414$		0			0
$415$	9.96799			0.489309
$416$		0			0
$417$	−49.8478			−2.44106
$418$		0			0
$419$	6.21074	+	10.7573i	0.303414	+	0.525529i	0.976907	−	0.213665i	$-0.0685400\pi$
$419$	6.21074	+	10.7573i	0.303414	+	0.525529i	−0.673493	+	0.739194i	$0.735207\pi$
$420$		0			0
$421$	−1.81879			−0.0886422			−0.0443211	−	0.999017i	$-0.514112\pi$
$421$	−1.81879			−0.0886422			−0.0443211	+	0.999017i	$0.514112\pi$
$422$		0			0
$423$	22.4848	+	38.9448i	1.09325	+	1.89356i
$424$		0			0
$425$	−7.19866	+	12.4684i	−0.349186	+	0.604808i
$426$		0			0
$427$	5.63383	+	9.75807i	0.272640	+	0.472226i
$428$		0			0
$429$	6.59933	+	11.4304i	0.318619	+	0.551864i
$430$		0			0
$431$	−5.02721	+	8.70739i	−0.242152	+	0.419420i	−0.961327	−	0.275409i	$-0.911187\pi$
$431$	−5.02721	+	8.70739i	−0.242152	+	0.419420i	0.719175	+	0.694829i	$0.244520\pi$
$432$		0			0
$433$	−39.7996			−1.91265			−0.956323	−	0.292311i	$-0.905576\pi$
$433$	−39.7996			−1.91265			−0.956323	+	0.292311i	$0.905576\pi$
$434$		0			0
$435$	−12.6610	−	21.9296i	−0.607050	−	1.05144i
$436$		0			0
$437$	12.1666	−	21.0732i	0.582010	−	1.00807i
$438$		0			0
$439$	12.9447	−	22.4209i	0.617817	−	1.07009i	−0.372066	−	0.928206i	$-0.621351\pi$
$439$	12.9447	−	22.4209i	0.617817	−	1.07009i	0.989883	−	0.141884i	$-0.0453160\pi$
$440$		0			0
$441$	−26.4671	+	45.8424i	−1.26034	+	2.18297i
$442$		0			0
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$		0			0
$445$	4.42309			0.209675
$446$		0			0
$447$	1.64983	−	2.85759i	0.0780344	−	0.135160i
$448$		0			0
$449$	15.6450	−	27.0980i	0.738335	−	1.27883i	−0.214910	−	0.976634i	$-0.568946\pi$
$449$	15.6450	−	27.0980i	0.738335	−	1.27883i	0.953245	−	0.302200i	$-0.0977209\pi$
$450$		0			0
$451$	−6.96071	+	12.0563i	−0.327767	+	0.567709i
$452$		0			0
$453$	9.05692	+	15.6870i	0.425531	+	0.737041i
$454$		0			0
$455$	14.7772			0.692765
$456$		0			0
$457$	−7.66665	+	13.2790i	−0.358631	+	0.621166i	−0.987732	−	0.156157i	$-0.950090\pi$
$457$	−7.66665	+	13.2790i	−0.358631	+	0.621166i	0.629102	+	0.777323i	$0.283423\pi$
$458$		0			0
$459$	−11.0777	−	19.1872i	−0.517064	−	0.895580i
$460$		0			0
$461$	3.04571	+	5.27532i	0.141853	+	0.245696i	0.928194	−	0.372096i	$-0.121361\pi$
$461$	3.04571	+	5.27532i	0.141853	+	0.245696i	−0.786342	+	0.617792i	$0.788027\pi$
$462$		0			0
$463$	−16.2332	+	28.1166i	−0.754419	+	1.30669i	0.191244	+	0.981543i	$0.438748\pi$
$463$	−16.2332	+	28.1166i	−0.754419	+	1.30669i	−0.945663	+	0.325149i	$0.894586\pi$
$464$		0			0
$465$	1.85577	+	3.21429i	0.0860594	+	0.149059i
$466$		0			0
$467$	27.4231			1.26899			0.634495	−	0.772927i	$-0.281208\pi$
$467$	27.4231			1.26899			0.634495	+	0.772927i	$0.281208\pi$
$468$		0			0
$469$	−16.5552	−	28.6745i	−0.764450	−	1.32407i
$470$		0			0
$471$	2.03201			0.0936301
$472$		0			0
$473$	13.4007			0.616164
$474$		0			0
$475$	−19.4231			−0.891192
$476$		0			0
$477$	−26.1779	+	45.3414i	−1.19860	+	2.07604i
$478$		0			0
$479$	−2.32295	−	4.02347i	−0.106138	−	0.183837i	0.808064	−	0.589094i	$-0.200515\pi$
$479$	−2.32295	−	4.02347i	−0.106138	−	0.183837i	−0.914203	+	0.405257i	$0.867182\pi$
$480$		0			0
$481$	16.0423	+	14.5101i	0.731468	+	0.661601i
$482$		0			0
$483$	29.7340	+	51.5007i	1.35294	+	2.34336i
$484$		0			0
$485$	4.98960	−	8.64224i	0.226566	−	0.392424i
$486$		0			0
$487$	−13.3861			−0.606582			−0.303291	−	0.952898i	$-0.598085\pi$
$487$	−13.3861			−0.606582			−0.303291	+	0.952898i	$0.598085\pi$
$488$		0			0
$489$	9.33167			0.421993
$490$		0			0
$491$	−17.3445			−0.782746			−0.391373	−	0.920232i	$-0.628000\pi$
$491$	−17.3445			−0.782746			−0.391373	+	0.920232i	$0.628000\pi$
$492$		0			0
$493$	15.9576	+	27.6394i	0.718694	+	1.24481i
$494$		0			0
$495$	−6.70034			−0.301158
$496$		0			0
$497$	23.4110	+	40.5491i	1.05013	+	1.81887i
$498$		0			0
$499$	−14.7388	+	25.5283i	−0.659797	+	1.14280i	0.320870	+	0.947123i	$0.396025\pi$
$499$	−14.7388	+	25.5283i	−0.659797	+	1.14280i	−0.980668	+	0.195680i	$0.937309\pi$
$500$		0			0
$501$	30.8117	+	53.3674i	1.37656	+	2.38428i
$502$		0			0
$503$	−0.459897	−	0.796565i	−0.0205058	−	0.0355171i	0.855590	−	0.517653i	$-0.173194\pi$
$503$	−0.459897	−	0.796565i	−0.0205058	−	0.0355171i	−0.876096	+	0.482136i	$0.839861\pi$
$504$		0			0
$505$	1.42228	−	2.46346i	0.0632907	−	0.109623i
$506$		0			0
$507$	1.01121			0.0449094
$508$		0			0
$509$	−2.48879	−	4.31071i	−0.110314	−	0.191069i	0.805583	−	0.592483i	$-0.201852\pi$
$509$	−2.48879	−	4.31071i	−0.110314	−	0.191069i	−0.915897	+	0.401414i	$0.868519\pi$
$510$		0			0
$511$	4.75476	−	8.23549i	0.210338	−	0.364317i
$512$		0			0
$513$	14.9447	−	25.8850i	0.659825	−	1.14285i
$514$		0			0
$515$	3.44389	−	5.96500i	0.151756	−	0.262849i
$516$		0			0
$517$	−11.3367			−0.498585
$518$		0			0
$519$	33.1250			1.45403
$520$		0			0
$521$	19.1321	−	33.1379i	0.838195	−	1.45180i	−0.0532081	−	0.998583i	$-0.516945\pi$
$521$	19.1321	−	33.1379i	0.838195	−	1.45180i	0.891403	−	0.453212i	$-0.149722\pi$
$522$		0			0
$523$	19.3269	−	33.4751i	0.845105	−	1.46377i	−0.0404243	−	0.999183i	$-0.512871\pi$
$523$	19.3269	−	33.4751i	0.845105	−	1.46377i	0.885530	−	0.464583i	$-0.153796\pi$
$524$		0			0
$525$	23.7340	−	41.1084i	1.03584	−	1.79412i
$526$		0			0
$527$	−2.33896	−	4.05120i	−0.101887	−	0.176473i
$528$		0			0
$529$	2.11222			0.0918355
$530$		0			0
$531$	−23.8894	+	41.3777i	−1.03671	+	1.79564i
$532$		0			0
$533$	−19.0457	−	32.9881i	−0.824961	−	1.42887i
$534$		0			0
$535$	1.63383	+	2.82987i	0.0706365	+	0.122346i
$536$		0			0
$537$	1.71155	−	2.96448i	0.0738586	−	0.127927i
$538$		0			0
$539$	−6.67225	−	11.5567i	−0.287394	−	0.497781i
$540$		0			0
$541$	−34.3125			−1.47521			−0.737605	−	0.675233i	$-0.764043\pi$
$541$	−34.3125			−1.47521			−0.737605	+	0.675233i	$0.764043\pi$
$542$		0			0
$543$	−4.72755	−	8.18836i	−0.202879	−	0.351396i
$544$		0			0
$545$	−13.3109			−0.570175
$546$		0			0
$547$	31.3221			1.33924			0.669618	−	0.742706i	$-0.266458\pi$
$547$	31.3221			1.33924			0.669618	+	0.742706i	$0.266458\pi$
$548$		0			0
$549$	13.9792			0.596618
$550$		0			0
$551$	−21.5280	+	37.2876i	−0.917125	+	1.58851i
$552$		0			0
$553$	−5.33416	−	9.23904i	−0.226832	−	0.392884i
$554$		0			0
$555$	−16.5328	+	5.33076i	−0.701779	+	0.226278i
$556$		0			0
$557$	10.3990	+	18.0116i	0.440619	+	0.763175i	0.997736	−	0.0672594i	$-0.0214255\pi$
$557$	10.3990	+	18.0116i	0.440619	+	0.763175i	−0.557116	+	0.830435i	$0.688092\pi$
$558$		0			0
$559$	−18.3333	+	31.7542i	−0.775416	+	1.34306i
$560$		0			0
$561$	13.3591			0.564020
$562$		0			0
$563$	16.1874			0.682220			0.341110	−	0.940023i	$-0.389197\pi$
$563$	16.1874			0.682220			0.341110	+	0.940023i	$0.389197\pi$
$564$		0			0
$565$	3.86698			0.162685
$566$		0			0
$567$	4.38859	+	7.60126i	0.184304	+	0.319223i
$568$		0			0
$569$	−1.73235			−0.0726237			−0.0363119	−	0.999341i	$-0.511561\pi$
$569$	−1.73235			−0.0726237			−0.0363119	+	0.999341i	$0.511561\pi$
$570$		0			0
$571$	−8.82856	−	15.2915i	−0.369464	−	0.639930i	0.620018	−	0.784588i	$-0.287125\pi$
$571$	−8.82856	−	15.2915i	−0.369464	−	0.639930i	−0.989482	+	0.144658i	$0.953792\pi$
$572$		0			0
$573$	−7.97920	+	13.8204i	−0.333336	+	0.577355i
$574$		0			0
$575$	−10.0224	−	17.3593i	−0.417964	−	0.723934i
$576$		0			0
$577$	6.63383	+	11.4901i	0.276170	+	0.478340i	0.970430	−	0.241384i	$-0.0776014\pi$
$577$	6.63383	+	11.4901i	0.276170	+	0.478340i	−0.694260	+	0.719725i	$0.744268\pi$
$578$		0			0
$579$	3.64983	−	6.32169i	0.151682	−	0.262721i
$580$		0			0
$581$	41.4213			1.71845
$582$		0			0
$583$	−6.59933	−	11.4304i	−0.273316	−	0.473398i
$584$		0			0
$585$	9.16665	−	15.8771i	0.378994	−	0.656437i
$586$		0			0
$587$	9.42789	−	16.3296i	0.389131	−	0.673994i	−0.603202	−	0.797588i	$-0.706109\pi$
$587$	9.42789	−	16.3296i	0.389131	−	0.673994i	0.992333	+	0.123594i	$0.0394422\pi$
$588$		0			0
$589$	3.15544	−	5.46538i	0.130018	−	0.225197i
$590$		0			0
$591$	38.6538			1.59000
$592$		0			0
$593$	13.8928			0.570507			0.285254	−	0.958452i	$-0.407922\pi$
$593$	13.8928			0.570507			0.285254	+	0.958452i	$0.407922\pi$
$594$		0			0
$595$	7.47839	−	12.9530i	0.306584	−	0.531019i
$596$		0			0
$597$	−2.41188	+	4.17750i	−0.0987117	+	0.170974i
$598$		0			0
$599$	−16.5513	+	28.6677i	−0.676268	+	1.17133i	0.299828	+	0.953993i	$0.403071\pi$
$599$	−16.5513	+	28.6677i	−0.676268	+	1.17133i	−0.976096	+	0.217338i	$0.930263\pi$
$600$		0			0
$601$	−5.60101	−	9.70123i	−0.228470	−	0.395721i	0.728885	−	0.684636i	$-0.240039\pi$
$601$	−5.60101	−	9.70123i	−0.228470	−	0.395721i	−0.957355	+	0.288915i	$0.906706\pi$
$602$		0			0
$603$	−41.0785			−1.67284
$604$		0			0
$605$	−4.65544	+	8.06345i	−0.189270	+	0.327826i
$606$		0			0
$607$	13.0496	+	22.6026i	0.529668	+	0.917412i	0.999401	+	0.0346037i	$0.0110169\pi$
$607$	13.0496	+	22.6026i	0.529668	+	0.917412i	−0.469733	+	0.882809i	$0.655650\pi$
$608$		0			0
$609$	−52.6122	−	91.1269i	−2.13195	−	3.69265i
$610$		0			0
$611$	15.5095	−	26.8633i	0.627448	−	1.08677i
$612$		0			0
$613$	−4.46799	−	7.73878i	−0.180460	−	0.312567i	0.761577	−	0.648074i	$-0.224425\pi$
$613$	−4.46799	−	7.73878i	−0.180460	−	0.312567i	−0.942037	+	0.335508i	$0.891092\pi$
$614$		0			0
$615$	30.5897			1.23350
$616$		0			0
$617$	4.63383	+	8.02602i	0.186551	+	0.323116i	0.944098	−	0.329665i	$-0.106936\pi$
$617$	4.63383	+	8.02602i	0.186551	+	0.323116i	−0.757547	+	0.652780i	$0.773602\pi$
$618$		0			0
$619$	−2.88778			−0.116070			−0.0580349	−	0.998315i	$-0.518483\pi$
$619$	−2.88778			−0.116070			−0.0580349	+	0.998315i	$0.518483\pi$
$620$		0			0
$621$	30.8462			1.23781
$622$		0			0
$623$	18.3799			0.736374
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$	9.01121	+	15.6079i	0.359873	+	0.623318i
$628$		0			0
$629$	20.8375	−	6.71873i	0.830844	−	0.267893i
$630$		0			0
$631$	−9.73876	−	16.8680i	−0.387694	−	0.671506i	0.604445	−	0.796647i	$-0.293395\pi$
$631$	−9.73876	−	16.8680i	−0.387694	−	0.671506i	−0.992139	+	0.125141i	$0.960062\pi$
$632$		0			0
$633$	−15.5465	+	26.9274i	−0.617919	+	1.07027i
$634$		0			0
$635$	−4.05443			−0.160895
$636$		0			0
$637$	36.5129			1.44669
$638$		0			0
$639$	58.0897			2.29799
$640$		0			0
$641$	3.69866	+	6.40626i	0.146088	+	0.253032i	0.929778	−	0.368120i	$-0.119998\pi$
$641$	3.69866	+	6.40626i	0.146088	+	0.253032i	−0.783690	+	0.621152i	$0.786665\pi$
$642$		0			0
$643$	10.9024			0.429947			0.214973	−	0.976620i	$-0.431034\pi$
$643$	10.9024			0.429947			0.214973	+	0.976620i	$0.431034\pi$
$644$		0			0
$645$	−14.7228	−	25.5006i	−0.579708	−	1.00408i
$646$		0			0
$647$	−6.54403	+	11.3346i	−0.257272	+	0.445609i	−0.965510	−	0.260365i	$-0.916157\pi$
$647$	−6.54403	+	11.3346i	−0.257272	+	0.445609i	0.708238	+	0.705974i	$0.249490\pi$
$648$		0			0
$649$	−6.02242	−	10.4311i	−0.236401	−	0.409458i
$650$		0			0
$651$	7.71155	+	13.3568i	0.302239	+	0.523494i
$652$		0			0
$653$	−19.6234	+	33.9888i	−0.767924	+	1.33008i	0.170763	+	0.985312i	$0.445377\pi$
$653$	−19.6234	+	33.9888i	−0.767924	+	1.33008i	−0.938687	+	0.344771i	$0.887957\pi$
$654$		0			0
$655$	11.1666			0.436317
$656$		0			0
$657$	−5.89899	−	10.2174i	−0.230142	−	0.398617i
$658$		0			0
$659$	2.65624	−	4.60075i	0.103473	−	0.179220i	−0.809641	−	0.586926i	$-0.800338\pi$
$659$	2.65624	−	4.60075i	0.103473	−	0.179220i	0.913113	+	0.407706i	$0.133671\pi$
$660$		0			0
$661$	−3.81087	+	6.60063i	−0.148226	+	0.256735i	−0.930572	−	0.366109i	$-0.880690\pi$
$661$	−3.81087	+	6.60063i	−0.148226	+	0.256735i	0.782346	+	0.622844i	$0.214023\pi$
$662$		0			0
$663$	−18.2764	+	31.6556i	−0.709796	+	1.22940i
$664$		0			0
$665$	20.1779			0.782464
$666$		0			0
$667$	−44.4343			−1.72050
$668$		0			0
$669$	0.267653	−	0.463589i	0.0103481	−	0.0179234i
$670$		0			0
$671$	−1.76205	+	3.05196i	−0.0680231	+	0.117820i
$672$		0			0
$673$	−6.00249	+	10.3966i	−0.231379	+	0.400760i	−0.958214	−	0.286052i	$-0.907657\pi$
$673$	−6.00249	+	10.3966i	−0.231379	+	0.400760i	0.726835	+	0.686812i	$0.240990\pi$
$674$		0			0
$675$	−12.3109	−	21.3231i	−0.473846	−	0.820725i
$676$		0			0
$677$	35.5527			1.36640			0.683202	−	0.730230i	$-0.260587\pi$
$677$	35.5527			1.36640			0.683202	+	0.730230i	$0.260587\pi$
$678$		0			0
$679$	20.7340	−	35.9123i	0.795696	−	1.37819i
$680$		0			0
$681$	27.7797	+	48.1158i	1.06452	+	1.84380i
$682$		0			0
$683$	−15.7893	−	27.3478i	−0.604159	−	1.04643i	−0.992184	−	0.124786i	$-0.960176\pi$
$683$	−15.7893	−	27.3478i	−0.604159	−	1.04643i	0.388024	−	0.921649i	$-0.373158\pi$
$684$		0			0
$685$	−0.577718	+	1.00064i	−0.0220735	+	0.0382324i
$686$		0			0
$687$	−24.6265	−	42.6544i	−0.939561	−	1.62737i
$688$		0			0
$689$	36.1138			1.37583
$690$		0			0
$691$	−5.59453	−	9.69001i	−0.212826	−	0.368625i	0.739772	−	0.672858i	$-0.234933\pi$
$691$	−5.59453	−	9.69001i	−0.212826	−	0.368625i	−0.952598	+	0.304232i	$0.901600\pi$
$692$		0			0
$693$	−27.8428			−1.05766
$694$		0			0
$695$	−17.4551			−0.662110
$696$		0			0
$697$	−38.5544			−1.46035
$698$		0			0
$699$	−26.5600	+	46.0033i	−1.00459	+	1.74001i
$700$		0			0
$701$	13.7893	+	23.8837i	0.520813	+	0.902075i	0.999707	+	0.0242022i	$0.00770456\pi$
$701$	13.7893	+	23.8837i	0.520813	+	0.902075i	−0.478894	+	0.877873i	$0.658962\pi$
$702$		0			0
$703$	21.9054	+	19.8131i	0.826178	+	0.747265i
$704$		0			0
$705$	12.4551	+	21.5729i	0.469086	+	0.812481i
$706$		0			0
$707$	5.91020	−	10.2368i	0.222276	−	0.384993i
$708$		0			0
$709$	9.50953			0.357138			0.178569	−	0.983927i	$-0.442853\pi$
$709$	9.50953			0.357138			0.178569	+	0.983927i	$0.442853\pi$
$710$		0			0
$711$	−13.2356			−0.496375
$712$		0			0
$713$	6.51289			0.243910
$714$		0			0
$715$	2.31087	+	4.00255i	0.0864218	+	0.149687i
$716$		0			0
$717$	−38.1363			−1.42422
$718$		0			0
$719$	−9.94077	−	17.2179i	−0.370728	−	0.642120i	0.618949	−	0.785431i	$-0.287559\pi$
$719$	−9.94077	−	17.2179i	−0.370728	−	0.642120i	−0.989678	+	0.143311i	$0.954225\pi$
$720$		0			0
$721$	14.3109	−	24.7872i	0.532965	−	0.923122i
$722$		0			0
$723$	23.1001	+	40.0106i	0.859103	+	1.48801i
$724$		0			0
$725$	17.7340	+	30.7161i	0.658623	+	1.14077i
$726$		0			0
$727$	1.23315	−	2.13589i	0.0457352	−	0.0792157i	−0.842252	−	0.539085i	$-0.818770\pi$
$727$	1.23315	−	2.13589i	0.0457352	−	0.0792157i	0.887987	+	0.459869i	$0.152104\pi$
$728$		0			0
$729$	−41.8462			−1.54986
$730$		0			0
$731$	18.5561	+	32.1401i	0.686322	+	1.18875i
$732$		0			0
$733$	−22.3998	+	38.7976i	−0.827356	+	1.43302i	0.0727502	+	0.997350i	$0.476822\pi$
$733$	−22.3998	+	38.7976i	−0.827356	+	1.43302i	−0.900106	+	0.435672i	$0.856511\pi$
$734$		0			0
$735$	−14.6610	+	25.3937i	−0.540781	+	0.936660i
$736$		0			0
$737$	5.17785	−	8.96831i	0.190729	−	0.330352i
$738$		0			0
$739$	27.4085			1.00824			0.504119	−	0.863634i	$-0.331817\pi$
$739$	27.4085			1.00824			0.504119	+	0.863634i	$0.331817\pi$
$740$		0			0
$741$	−49.3125			−1.81154
$742$		0			0
$743$	5.69554	−	9.86496i	0.208949	−	0.361910i	−0.742435	−	0.669918i	$-0.766329\pi$
$743$	5.69554	−	9.86496i	0.208949	−	0.361910i	0.951384	+	0.308008i	$0.0996624\pi$
$744$		0			0
$745$	0.577718	−	1.00064i	0.0211660	−	0.0366605i
$746$		0			0
$747$	25.6947	−	44.5045i	0.940119	−	1.62833i
$748$		0			0
$749$	6.78926	+	11.7593i	0.248074	+	0.429677i
$750$		0			0
$751$	33.7340			1.23097			0.615485	−	0.788149i	$-0.288960\pi$
$751$	33.7340			1.23097			0.615485	+	0.788149i	$0.288960\pi$
$752$		0			0
$753$	−16.4343	+	28.4650i	−0.598899	+	1.03732i
$754$		0			0
$755$	3.17144	+	5.49310i	0.115421	+	0.199914i
$756$		0			0
$757$	−16.1795	−	28.0238i	−0.588055	−	1.01854i	−0.994487	−	0.104860i	$-0.966560\pi$
$757$	−16.1795	−	28.0238i	−0.588055	−	1.01854i	0.406432	−	0.913681i	$-0.366773\pi$
$758$		0			0
$759$	−9.29966	+	16.1075i	−0.337556	+	0.584665i
$760$		0			0
$761$	−6.05611	−	10.4895i	−0.219534	−	0.380244i	0.735132	−	0.677924i	$-0.237120\pi$
$761$	−6.05611	−	10.4895i	−0.219534	−	0.380244i	−0.954666	+	0.297681i	$0.903787\pi$
$762$		0			0
$763$	−55.3125			−2.00245
$764$		0			0
$765$	−9.27805	−	16.0701i	−0.335449	−	0.581014i
$766$		0			0
$767$	32.9568			1.19000
$768$		0			0
$769$	−12.5577			−0.452843			−0.226422	−	0.974029i	$-0.572703\pi$
$769$	−12.5577			−0.452843			−0.226422	+	0.974029i	$0.572703\pi$
$770$		0			0
$771$	−4.32047			−0.155598
$772$		0			0
$773$	−10.3878	+	17.9922i	−0.373623	+	0.647133i	−0.990120	−	0.140224i	$-0.955218\pi$
$773$	−10.3878	+	17.9922i	−0.373623	+	0.647133i	0.616497	+	0.787357i	$0.288551\pi$
$774$		0			0
$775$	−2.59933	−	4.50217i	−0.0933706	−	0.161723i
$776$		0			0
$777$	−68.7011	+	22.1517i	−2.46464	+	0.794686i
$778$		0			0
$779$	−26.0064	−	45.0444i	−0.931776	−	1.61388i
$780$		0			0
$781$	−7.32208	+	12.6822i	−0.262005	+	0.453805i
$782$		0			0
$783$	−54.5801			−1.95054
$784$		0			0
$785$	0.711545			0.0253961
$786$		0			0
$787$	−5.02578			−0.179150			−0.0895748	−	0.995980i	$-0.528551\pi$
$787$	−5.02578			−0.179150			−0.0895748	+	0.995980i	$0.528551\pi$
$788$		0			0
$789$	−21.4800	−	37.2045i	−0.764708	−	1.32451i
$790$		0			0
$791$	16.0690			0.571348
$792$		0			0
$793$	−4.82127	−	8.35069i	−0.171208	−	0.296542i
$794$		0			0
$795$	−14.5008	+	25.1161i	−0.514291	+	0.890778i
$796$		0			0
$797$	−13.1434	−	22.7650i	−0.465562	−	0.806376i	0.533665	−	0.845696i	$-0.320814\pi$
$797$	−13.1434	−	22.7650i	−0.465562	−	0.806376i	−0.999227	+	0.0393196i	$0.987481\pi$
$798$		0			0
$799$	−15.6980	−	27.1898i	−0.555356	−	0.961905i
$800$		0			0
$801$	11.4015	−	19.7479i	0.402851	−	0.697759i
$802$		0			0
$803$	2.97422			0.104958
$804$		0			0
$805$	10.4119	+	18.0339i	0.366971	+	0.635612i
$806$		0			0
$807$	1.26765	−	2.19564i	0.0446235	−	0.0772902i
$808$		0			0
$809$	20.6770	−	35.8137i	0.726966	−	1.25914i	−0.231193	−	0.972908i	$-0.574263\pi$
$809$	20.6770	−	35.8137i	0.726966	−	1.25914i	0.958160	−	0.286235i	$-0.0924037\pi$
$810$		0			0
$811$	−23.9239	+	41.4374i	−0.840082	+	1.45506i	0.0497432	+	0.998762i	$0.484160\pi$
$811$	−23.9239	+	41.4374i	−0.840082	+	1.45506i	−0.889825	+	0.456302i	$0.849174\pi$
$812$		0			0
$813$	−54.7996			−1.92191
$814$		0			0
$815$	3.26765			0.114461
$816$		0			0
$817$	−25.0336	+	43.3595i	−0.875816	+	1.51696i
$818$		0			0
$819$	38.0914	−	65.9763i	1.33102	−	2.30540i
$820$		0			0
$821$	−6.76685	+	11.7205i	−0.236165	+	0.409049i	−0.959610	−	0.281332i	$-0.909224\pi$
$821$	−6.76685	+	11.7205i	−0.236165	+	0.409049i	0.723446	+	0.690381i	$0.242557\pi$
$822$		0			0
$823$	−3.30446	−	5.72349i	−0.115186	−	0.199508i	0.802668	−	0.596426i	$-0.203413\pi$
$823$	−3.30446	−	5.72349i	−0.115186	−	0.199508i	−0.917854	+	0.396918i	$0.870080\pi$
$824$		0			0
$825$	14.8462			0.516878
$826$		0			0
$827$	−1.34376	+	2.32745i	−0.0467269	+	0.0809334i	−0.888443	−	0.458987i	$-0.848212\pi$
$827$	−1.34376	+	2.32745i	−0.0467269	+	0.0809334i	0.841716	+	0.539921i	$0.181546\pi$
$828$		0			0
$829$	4.51040	+	7.81224i	0.156653	+	0.271330i	0.933660	−	0.358162i	$-0.116596\pi$
$829$	4.51040	+	7.81224i	0.156653	+	0.271330i	−0.777007	+	0.629492i	$0.783263\pi$
$830$		0			0
$831$	−5.13943	−	8.90176i	−0.178285	−	0.308798i
$832$		0			0
$833$	18.4783	−	32.0054i	0.640236	−	1.10892i
$834$		0			0
$835$	10.7893	+	18.6876i	0.373378	+	0.646709i
$836$		0			0
$837$	8.00000			0.276520
$838$		0			0
$839$	−10.3381	−	17.9061i	−0.356910	−	0.618187i	0.630533	−	0.776163i	$-0.282837\pi$
$839$	−10.3381	−	17.9061i	−0.356910	−	0.618187i	−0.987443	+	0.157976i	$0.949503\pi$
$840$		0			0
$841$	49.6234			1.71115
$842$		0			0
$843$	−81.4808			−2.80635
$844$		0			0
$845$	0.354093			0.0121812
$846$		0			0
$847$	−19.3454	+	33.5072i	−0.664715	+	1.15132i
$848$		0			0
$849$	−11.6450	−	20.1698i	−0.399657	−	0.692226i
$850$		0			0
$851$	−6.40460	+	29.8016i	−0.219547	+	1.02158i
$852$		0			0
$853$	−1.81087	−	3.13652i	−0.0620031	−	0.107393i	0.833358	−	0.552734i	$-0.186416\pi$
$853$	−1.81087	−	3.13652i	−0.0620031	−	0.107393i	−0.895361	+	0.445342i	$0.853082\pi$
$854$		0			0
$855$	12.5168	−	21.6798i	0.428066	−	0.741432i
$856$		0			0
$857$	12.6201			0.431095			0.215548	−	0.976493i	$-0.430846\pi$
$857$	12.6201			0.431095			0.215548	+	0.976493i	$0.430846\pi$
$858$		0			0
$859$	45.6059			1.55605			0.778027	−	0.628231i	$-0.216221\pi$
$859$	45.6059			1.55605			0.778027	+	0.628231i	$0.216221\pi$
$860$		0			0
$861$	127.114			4.33202
$862$		0			0
$863$	25.9015	+	44.8627i	0.881697	+	1.52714i	0.849454	+	0.527663i	$0.176932\pi$
$863$	25.9015	+	44.8627i	0.881697	+	1.52714i	0.0322430	+	0.999480i	$0.489735\pi$
$864$		0			0
$865$	11.5993			0.394389
$866$		0			0
$867$	−5.77557	−	10.0036i	−0.196149	−	0.339739i
$868$		0			0
$869$	1.66833	−	2.88962i	0.0565941	−	0.0980238i
$870$		0			0
$871$	14.1675	+	24.5389i	0.480048	+	0.831468i
$872$		0			0
$873$	−25.7236	−	44.5545i	−0.870611	−	1.50794i
$874$		0			0
$875$	18.6995	−	32.3884i	0.632157	−	1.09493i
$876$		0			0
$877$	17.7356			0.598888			0.299444	−	0.954114i	$-0.403199\pi$
$877$	17.7356			0.598888			0.299444	+	0.954114i	$0.403199\pi$
$878$		0			0
$879$	−10.4391	−	18.0810i	−0.352102	−	0.609858i
$880$		0			0
$881$	−4.36698	+	7.56383i	−0.147127	+	0.254832i	−0.930165	−	0.367143i	$-0.880336\pi$
$881$	−4.36698	+	7.56383i	−0.147127	+	0.254832i	0.783037	+	0.621975i	$0.213669\pi$
$882$		0			0
$883$	−26.6170	+	46.1019i	−0.895732	+	1.55145i	−0.0628353	+	0.998024i	$0.520014\pi$
$883$	−26.6170	+	46.1019i	−0.895732	+	1.55145i	−0.832896	+	0.553429i	$0.813319\pi$
$884$		0			0
$885$	−13.2332	+	22.9205i	−0.444828	+	0.770464i
$886$		0			0
$887$	20.6363			0.692900			0.346450	−	0.938069i	$-0.387387\pi$
$887$	20.6363			0.692900			0.346450	+	0.938069i	$0.387387\pi$
$888$		0			0
$889$	−16.8479			−0.565061
$890$		0			0
$891$	−1.37259	+	2.37739i	−0.0459834	+	0.0796455i
$892$		0			0
$893$	21.1779	−	36.6811i	0.708690	−	1.22749i
$894$		0			0
$895$	0.599328	−	1.03807i	0.0200333	−	0.0346987i
$896$		0			0
$897$	−25.4455	−	44.0729i	−0.849601	−	1.47155i
$898$		0			0
$899$	−11.5241			−0.384350
$900$		0			0
$901$	18.2764	−	31.6556i	0.608874	−	1.05460i
$902$		0			0
$903$	−61.1795	−	105.966i	−2.03593	−	3.52633i
$904$		0			0
$905$	−1.65544	−	2.86730i	−0.0550286	−	0.0953123i
$906$		0			0
$907$	15.0962	−	26.1474i	0.501261	−	0.868210i	−0.498737	−	0.866753i	$-0.666203\pi$
$907$	15.0962	−	26.1474i	0.501261	−	0.868210i	0.999999	−	0.00145724i	$-0.000463853\pi$
$908$		0			0
$909$	−7.33248	−	12.7002i	−0.243203	−	0.421240i
$910$		0			0
$911$	5.76100			0.190870			0.0954352	−	0.995436i	$-0.469576\pi$
$911$	5.76100			0.190870			0.0954352	+	0.995436i	$0.469576\pi$
$912$		0			0
$913$	6.47752	+	11.2194i	0.214375	+	0.371308i
$914$		0			0
$915$	7.74356			0.255994
$916$		0			0
$917$	46.4023			1.53234
$918$		0			0
$919$	19.6105			0.646892			0.323446	−	0.946247i	$-0.395159\pi$
$919$	19.6105			0.646892			0.323446	+	0.946247i	$0.395159\pi$
$920$		0			0
$921$	24.4343	−	42.3214i	0.805138	−	1.39454i
$922$		0			0
$923$	−20.0345	−	34.7008i	−0.659444	−	1.14219i
$924$		0			0
$925$	23.1571	−	7.46665i	0.761399	−	0.245502i
$926$		0			0
$927$	−17.7548	−	30.7522i	−0.583143	−	1.01003i
$928$		0			0
$929$	26.5016	−	45.9021i	0.869490	−	1.50600i	0.00697095	−	0.999976i	$-0.497781\pi$
$929$	26.5016	−	45.9021i	0.869490	−	1.50600i	0.862519	−	0.506025i	$-0.168886\pi$
$930$		0			0
$931$	49.8574			1.63401
$932$		0			0
$933$	85.9983			2.81546
$934$		0			0
$935$	4.67792			0.152984
$936$		0			0
$937$	−6.38940	−	11.0668i	−0.208733	−	0.361535i	0.742583	−	0.669754i	$-0.233600\pi$
$937$	−6.38940	−	11.0668i	−0.208733	−	0.361535i	−0.951316	+	0.308219i	$0.900267\pi$
$938$		0			0
$939$	90.1217			2.94101
$940$		0			0
$941$	−11.4360	−	19.8077i	−0.372802	−	0.645712i	0.617193	−	0.786812i	$-0.288270\pi$
$941$	−11.4360	−	19.8077i	−0.372802	−	0.645712i	−0.989995	+	0.141099i	$0.954936\pi$
$942$		0			0
$943$	26.8389	−	46.4863i	0.873995	−	1.51380i
$944$		0			0
$945$	12.7893	+	22.1517i	0.416035	+	0.720593i
$946$		0			0
$947$	−4.34537	−	7.52640i	−0.141206	−	0.244575i	0.786745	−	0.617278i	$-0.211765\pi$
$947$	−4.34537	−	7.52640i	−0.141206	−	0.244575i	−0.927951	+	0.372703i	$0.878431\pi$
$948$		0			0
$949$	−4.06900	+	7.04771i	−0.132085	+	0.228778i
$950$		0			0
$951$	−86.3045			−2.79862
$952$		0			0
$953$	−20.7460	−	35.9332i	−0.672030	−	1.16399i	−0.977327	−	0.211733i	$-0.932089\pi$
$953$	−20.7460	−	35.9332i	−0.672030	−	1.16399i	0.305297	−	0.952257i	$-0.401244\pi$
$954$		0			0
$955$	−2.79406	+	4.83945i	−0.0904136	+	0.156601i
$956$		0			0
$957$	16.4551	−	28.5011i	0.531918	−	0.921309i
$958$		0			0
$959$	−2.40067	+	4.15809i	−0.0775217	+	0.134272i
$960$		0			0
$961$	−29.3109			−0.945512
$962$		0			0
$963$	16.8462			0.542861
$964$		0			0
$965$	1.27805	−	2.21365i	0.0411420	−	0.0712601i
$966$		0			0
$967$	−12.8117	+	22.1905i	−0.411996	+	0.713598i	−0.995108	−	0.0987939i	$-0.968502\pi$
$967$	−12.8117	+	22.1905i	−0.411996	+	0.713598i	0.583112	+	0.812392i	$0.301835\pi$
$968$		0			0
$969$	−24.9559	+	43.2249i	−0.801699	+	1.38858i
$970$		0			0
$971$	5.48232	+	9.49565i	0.175936	+	0.304730i	0.940485	−	0.339836i	$-0.110372\pi$
$971$	5.48232	+	9.49565i	0.175936	+	0.304730i	−0.764549	+	0.644566i	$0.777038\pi$
$972$		0			0
$973$	−72.5336			−2.32532
$974$		0			0
$975$	−20.3109	+	35.1795i	−0.650469	+	1.12664i
$976$		0			0
$977$	−11.4672	−	19.8617i	−0.366868	−	0.635433i	0.622206	−	0.782853i	$-0.286236\pi$
$977$	−11.4672	−	19.8617i	−0.366868	−	0.635433i	−0.989074	+	0.147420i	$0.952903\pi$
$978$		0			0
$979$	2.87427	+	4.97837i	0.0918619	+	0.159110i
$980$		0			0
$981$	−34.3117	+	59.4296i	−1.09549	+	1.89744i
$982$		0			0
$983$	17.1731	+	29.7446i	0.547736	+	0.948706i	0.998429	+	0.0560271i	$0.0178433\pi$
$983$	17.1731	+	29.7446i	0.547736	+	0.948706i	−0.450694	+	0.892679i	$0.648823\pi$
$984$		0			0
$985$	13.5353			0.431271
$986$		0			0
$987$	51.7564	+	89.6447i	1.64742	+	2.85342i
$988$		0			0
$989$	−51.6699			−1.64301
$990$		0			0
$991$	−59.4263			−1.88774			−0.943870	−	0.330318i	$-0.892844\pi$
$991$	−59.4263			−1.88774			−0.943870	+	0.330318i	$0.892844\pi$
$992$		0			0
$993$	−7.04322			−0.223510
$994$		0			0
$995$	−0.844563	+	1.46283i	−0.0267745	+	0.0463747i
$996$		0			0
$997$	−7.86449	−	13.6217i	−0.249071	−	0.431404i	0.714197	−	0.699944i	$-0.246792\pi$
$997$	−7.86449	−	13.6217i	−0.249071	−	0.431404i	−0.963268	+	0.268541i	$0.913459\pi$
$998$		0			0
$999$	−7.86698	+	36.6063i	−0.248900	+	1.15817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.i.f.433.3		6
4.3	odd	2		148.2.e.a.137.1	yes	6
12.11	even	2		1332.2.j.e.433.1		6
37.10	even	3	inner	592.2.i.f.417.3		6
148.11	odd	6		5476.2.a.g.1.3		3
148.47	odd	6		148.2.e.a.121.1	✓	6
148.63	odd	6		5476.2.a.f.1.3		3
444.47	even	6		1332.2.j.e.1009.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
148.2.e.a.121.1	✓	6	148.47	odd	6
148.2.e.a.137.1	yes	6	4.3	odd	2
592.2.i.f.417.3		6	37.10	even	3	inner
592.2.i.f.433.3		6	1.1	even	1	trivial
1332.2.j.e.433.1		6	12.11	even	2
1332.2.j.e.1009.1		6	444.47	even	6
5476.2.a.f.1.3		3	148.63	odd	6
5476.2.a.g.1.3		3	148.11	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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.42789 - 2.47317i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.07772 - 3.59871i) q^{7} +(-2.57772 - 4.46474i) q^{9} +1.29966 q^{11} +(-1.77805 + 3.07968i) q^{13} +(-1.42789 - 2.47317i) q^{15} +(1.79966 + 3.11711i) q^{17} +(-2.42789 + 4.20522i) q^{19} +(-5.93349 - 10.2771i) q^{21} -5.01121 q^{23} +(2.00000 + 3.46410i) q^{25} -6.15544 q^{27} +8.86698 q^{29} -1.29966 q^{31} +(1.85577 - 3.21429i) q^{33} +(-2.07772 - 3.59871i) q^{35} +(1.27805 - 5.94698i) q^{37} +(5.07772 + 8.79487i) q^{39} +(-5.35577 + 9.27647i) q^{41} +10.3109 q^{43} -5.15544 q^{45} -8.72275 q^{47} +(-5.13383 - 8.89205i) q^{49} +10.2789 q^{51} +(-5.07772 - 8.79487i) q^{53} +(0.649832 - 1.12554i) q^{55} +(6.93349 + 12.0092i) q^{57} +(-4.63383 - 8.02602i) q^{59} +(-1.35577 + 2.34827i) q^{61} -21.4231 q^{63} +(1.77805 + 3.07968i) q^{65} +(3.98399 - 6.90048i) q^{67} +(-7.15544 + 12.3936i) q^{69} +(-5.63383 + 9.75807i) q^{71} +2.28845 q^{73} +11.4231 q^{75} +(2.70034 - 4.67712i) q^{77} +(1.28366 - 2.22336i) q^{79} +(-1.05611 + 1.82923i) q^{81} +(4.98399 + 8.63253i) q^{83} +3.59933 q^{85} +(12.6610 - 21.9296i) q^{87} +(2.21155 + 3.83051i) q^{89} +(7.38859 + 12.7974i) q^{91} +(-1.85577 + 3.21429i) q^{93} +(2.42789 + 4.20522i) q^{95} +9.97920 q^{97} +(-3.35017 - 5.80266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 3 q^{5} + q^{7} - 4 q^{9} - 7 q^{13} - q^{15} + 3 q^{17} - 7 q^{19} - 9 q^{21} + 8 q^{23} + 12 q^{25} - 14 q^{27} - 4 q^{33} - q^{35} + 4 q^{37} + 19 q^{39} - 17 q^{41} + 16 q^{43} - 8 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 6 * q + q^3 + 3 * q^5 + q^7 - 4 * q^9 - 7 * q^13 - q^15 + 3 * q^17 - 7 * q^19 - 9 * q^21 + 8 * q^23 + 12 * q^25 - 14 * q^27 - 4 * q^33 - q^35 + 4 * q^37 + 19 * q^39 - 17 * q^41 + 16 * q^43 - 8 * q^45 + 16 * q^47 - 12 * q^49 - 14 * q^51 - 19 * q^53 + 15 * q^57 - 9 * q^59 + 7 * q^61 - 68 * q^63 + 7 * q^65 + 9 * q^67 - 20 * q^69 - 15 * q^71 + 44 * q^73 + 8 * q^75 + 24 * q^77 - 15 * q^79 + q^81 + 15 * q^83 + 6 * q^85 + 34 * q^87 - 17 * q^89 - 13 * q^91 + 4 * q^93 + 7 * q^95 - 8 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

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